⣚⢴⢫⣞⡭⣏⡝⣮⡝⣭⢫⡝⣭⢏⣝⣫⢽⣙⢯⣙⣏⣻⣹⣋⣟⣹⣫⣝⣫⢻⣭⣛⣭⢻⡹⣭⢯⡽⣭⣛⣭⡻⣝⢯⡻⣝⣯⢻⣝⣯⣻⣝⣻⣝⣯⣻⣝⣯⣻⣝⣯⢻⣝⣯⣻⡝⣯⣻⣝⣯⣻⣝⣯⣻⣝⣻⣏⣟⣻⣛⣟⣻⣛⣟⣻⣛⣟⣻⣻⣽ ⡜⢮⢳⣎⠷⢮⡝⣶⡹⣎⢷⡹⣞⠾⣜⢧⡻⣜⢧⡻⣜⢶⣣⢽⡎⣷⢺⡜⣧⣛⢶⡹⣎⢷⡻⣜⢧⣛⡶⣽⢲⡟⣮⢷⡻⡼⢮⠷⣞⣶⣳⠾⣵⣞⣶⣳⣞⣶⡻⣼⣞⣻⢮⣳⣳⣛⡷⣳⣞⣶⣛⡾⢶⣛⣾⢳⡾⡽⣶⣻⣞⡷⣻⣞⣷⡻⣞⣷⣳⢾ ⠼⣹⢲⡭⢞⢧⢻⠴⣳⡹⢎⡳⣭⢻⡜⣧⢻⡜⣧⠻⣜⢧⣛⡮⣝⢶⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣻⡜⣧⣛⢮⡳⣽⡹⣏⣟⣳⡽⣚⢿⣳⣞⣧⠿⡼⠳⠟⠧⠯⢽⢯⣗⣯⣽⡳⣟⣞⣞⢷⣻⣽⣹⢞⣯⡽⣳⣏⡷⣞⣽⣳⡽⢶⣻⡽⢶⣏⣿ ⡹⣜⢣⡞⡝⣮⢫⡝⣶⡙⡯⡵⣭⠳⣞⠵⣫⢞⡵⢻⡜⣧⢻⡼⣹⢞⡼⣫⢞⡵⣫⢞⡵⣫⢞⣵⢫⡞⣵⢛⡶⣹⢎⣷⢣⣟⠾⠜⠓⠙⡉⢉⠀⡀⠀⠄⡐⠠⢀⠂⠄⡀⠀⠀⠀⠉⠙⠙⠾⢮⣟⡵⡾⣝⣯⢶⣻⡵⣫⢟⡾⣵⣳⢯⡟⣵⢯⣻⢞⣼ ⡱⢎⢧⣝⠺⣥⢳⡝⢦⣛⡵⣛⡴⣻⢜⣫⢧⠻⣜⢧⡻⣜⡳⣞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⢧⡻⢼⡹⣜⢧⣛⡮⠛⠈⡀⠆⡑⢂⠐⡀⢂⠡⠈⠐⠀⢂⠠⠐⢀⠠⠈⠐⠈⠀⠄⡀⠀⠀⠀⠙⠛⠾⣭⠷⣯⢷⣯⢿⣜⣧⡟⣯⣞⣯⢷⣛⣾⣹ ⡱⢫⠞⣬⣛⣬⢳⡚⡧⣝⡲⣝⡲⡝⣎⡳⢎⡿⣜⣣⢟⡲⣝⠶⣹⠵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡱⣏⢾⡹⠞⢁⡀⠆⠡⠐⠠⠐⡀⠂⠐⡀⢀⠂⠁⡈⢀⠠⠀⠂⠀⠄⠁⡈⠄⠐⠀⡈⠄⠂⠀⠄⠀⠈⠙⠸⢯⣞⣟⡾⣞⣽⣣⢿⡼⣫⢿⣼⢫ ⡱⢫⢞⡱⢎⡖⢧⡛⣖⣣⣝⢲⣍⡳⢭⡹⢮⠵⢮⡵⣎⢷⣩⢏⣗⡫⣗⢫⡞⣵⢫⡞⡵⣋⢶⡹⢎⣷⡹⠎⣁⠒⠄⠂⠌⠠⠁⢂⠁⠠⠈⠄⠐⡀⢀⠂⠠⢀⠀⠂⢁⠈⢀⠂⢀⠐⠈⡀⠄⢀⠂⠁⠠⠈⡀⠄⠠⠀⠈⠑⠿⡽⣞⡽⣞⣳⢯⡷⣞⢿ ⡱⢫⡜⣭⣓⠾⣡⠟⣴⢣⢎⠷⡬⣝⢣⢯⡹⣚⠧⡞⣭⠶⣹⣚⢦⡻⡜⣧⢻⣬⢳⢭⡳⣝⣎⢷⡻⠜⣁⠒⠤⠉⠄⠡⠈⠄⠡⠀⠌⡀⠡⠐⠠⠐⢀⠠⠁⡀⠂⢁⠀⢂⠠⠐⢀⠀⢂⠀⠄⠂⠀⠌⠀⡁⠠⠐⠠⢁⠘⠤⣀⠙⠫⣽⢯⣯⢷⣛⣾⣹ ⡱⢫⡜⢶⡩⢞⡥⣛⠦⣏⢞⡹⣜⢎⢧⡳⢭⣣⢏⡳⢎⡽⡱⣎⢧⡳⢽⢬⣓⢮⡝⡶⣙⠶⣎⠷⠁⠨⠄⡉⠄⠡⠈⠄⠡⠈⠄⠡⠐⢀⠂⢁⠐⡀⠂⠄⡐⠀⡐⠀⡈⢀⠠⠐⢀⠈⡀⠄⠂⠄⡁⠂⢁⠀⠂⠌⡐⠠⢊⠔⡡⢆⡂⠨⡓⢟⡾⣽⢞⣽ ⡱⢳⡘⣧⣙⢮⡱⢭⠞⡜⢮⠵⣚⢮⢣⡝⡞⡴⢫⡵⣋⡞⡵⣩⢶⡹⢭⠞⣜⣣⢞⡵⣋⡟⠈⢀⡴⠁⠠⠐⡈⠄⠡⠈⠄⠡⢈⠐⢈⠀⠂⠄⢂⠐⡈⠄⠐⡀⠄⠁⡐⠠⠀⠌⡀⠐⡀⠐⡈⠠⠐⠈⠀⠌⡐⡀⠆⡑⠨⣌⠁⡪⣙⢆⠍⢦⡙⢞⡻⣞ ⡱⢣⡝⣲⢍⠶⣙⢮⡹⣙⡎⢷⡩⣎⢳⢎⡵⣋⢧⡳⣍⢞⣱⠳⣎⡵⢫⢞⡵⣙⢮⢞⢍⠄⠀⡼⠁⠰⠀⡡⠔⠈⠠⠁⠌⡐⠠⠈⠄⡈⠐⡈⠄⢂⠐⡈⠐⠠⢀⠡⠀⢂⠁⠂⠄⠡⢀⠡⢀⠡⢈⠀⠈⡐⡐⠈⠔⠡⢃⡔⢃⠜⣎⠮⣅⠂⢹⣦⡹⣟ ⡱⢫⡜⡵⢪⡝⣣⠮⣕⢣⡝⡲⡵⣩⡓⢮⣱⢹⣒⢳⡬⢏⡖⡻⢴⣩⢳⢫⡼⣙⠮⣡⠎⠀⠐⠀⢀⠠⢁⠐⠀⠠⠁⠌⠠⢀⠡⠐⡐⢀⠃⡐⠬⠀⢂⣀⡑⣂⠄⣂⠈⠄⠨⠌⢠⠁⢂⠐⡀⠂⢄⠂⠀⢀⠱⡘⡌⢷⠐⡌⢒⠌⡤⢁⢊⡘⠥⠘⣷⡘ ⡱⢳⡸⣱⢫⡜⣥⢛⡬⣓⠮⣕⢣⠧⣝⢣⣎⢳⡜⣣⠞⡭⢞⣹⠲⣍⢧⢳⣚⡍⣰⠃⠀⠀⠁⠀⡀⠆⡐⠀⠀⢂⠡⠐⠀⠂⠄⡁⠄⠂⡐⠠⢀⠡⠀⡀⠀⠄⠠⠈⠁⠈⠁⡉⠄⡉⠄⠡⢀⠁⠂⡌⠀⠀⠂⠤⠘⠠⡐⢌⠢⡘⠄⢣⠘⡄⠘⣆⠘⣿ ⡱⢣⠳⣥⢓⡞⣬⠳⡜⣥⢛⡬⢇⡻⣌⡳⢬⠳⣜⢣⡛⡼⢣⣇⠻⡜⣎⢧⠍⡴⠃⠀⠀⠀⠀⡐⢀⠂⠀⠀⠐⡀⢂⠀⠈⡐⠠⠐⠠⠀⠠⠁⡀⠂⡁⠀⠡⠈⡀⠁⠌⠀⠀⢀⠂⠄⠈⡐⠠⢈⠡⢀⠑⠀⠈⠐⡀⠡⠐⠌⡐⠠⠌⡀⠣⠄⠀⠎⣆⢹ ⠸⣍⠳⣬⠳⡜⢦⡛⣜⠲⣍⢞⡱⢳⣌⠳⣍⡳⢎⠧⡽⣘⠧⣎⡝⡳⣜⠎⣰⠋⠀⠀⠀⠀⠐⡀⢂⠀⣈⠀⠀⢀⠂⠀⠀⢀⠂⠄⠁⠄⠀⠁⠐⠀⡐⠀⠀⠐⠀⠂⠀⠁⡀⠀⠠⠈⢀⠀⠐⡀⠂⠄⠊⠄⠀⠐⠀⠀⡁⢂⠤⢁⠂⠄⡑⠂⠀⠘⡰⠂ ⠹⣌⠳⣥⢛⡜⣣⠽⣌⠻⡜⢮⡱⢳⣌⠻⡴⣙⢎⡳⡱⣍⠾⣰⡹⡱⢎⢡⠇⠀⠀⠀⠀⠠⢁⠰⠀⢀⡇⠀⠈⠀⠠⠁⠀⠀⠐⡀⠈⠀⠀⠈⠀⠀⠄⠂⡀⠈⠐⠈⢀⠀⠀⠀⠀⠐⢀⠀⠐⢀⠡⢈⠐⡈⠀⠀⠠⠀⠐⡀⠂⡄⢈⠐⠠⠁⠀⠀⠡⡁ ⠳⣜⠳⣌⡳⡜⣥⢓⣎⢳⡙⢦⡝⣣⢎⡳⡱⣍⢮⡱⢳⣌⠳⣥⢳⣙⠎⡘⠀⠀⠀⠀⢀⠡⢂⠂⠠⣼⣿⡀⠀⠀⠡⠀⢀⠀⠐⠠⠀⡀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠠⠀⠐⠀⠀⠀⠀⢀⠂⠀⠀⡐⢀⠂⡐⠀⠀⠀⠀⠀⠄⢃⠐⡈⠄⡑⠀⠀⠀⢁⠐ ⠱⢎⡵⢪⠵⣙⢦⢫⡌⢧⣙⢦⡙⢦⣋⠶⡹⡜⢦⡙⢧⢎⡳⣬⢓⢮⠅⠀⠀⠀⠀⢀⠂⠆⠂⢀⢳⣿⣿⣧⠀⠀⠐⠀⢨⣆⠀⠐⠀⠠⠐⠀⠀⠀⠀⠈⠀⢁⠀⠀⢀⠀⠡⠀⠀⠀⠀⠐⠀⠀⢀⠂⡐⠠⢁⠀⠀⠀⠀⢈⠰⢀⢂⠐⡈⠄⠀⠀⠀⠌ ⡙⢮⡘⢧⡛⡜⢮⡱⢎⡳⡜⢦⢛⢦⡙⢮⡱⣙⠶⣙⡎⢮⡕⣮⣙⢎⠀⠀⠀⠀⠀⢂⠈⠤⠁⡌⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣦⡀⠀⠀⠂⢡⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠐⠀⠀⠀⠈⢀⠀⠀⡐⠠⢁⠂⠀⠀⠀⠀⢀⠂⠆⡐⣈⠐⠀⠀⠀⠀⠂ ⢸⢱⢊⢧⡹⣜⢣⡝⢮⡱⣙⢮⡙⢦⣋⢧⠳⣍⢞⡱⢎⡳⢎⡵⢊⡌⠀⠀⠀⠀⢌⠀⠌⠄⢠⢹⣿⣿⣿⣿⣿⣧⢠⠀⠈⢿⣿⣷⡄⠀⠀⠈⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠁⣂⠘⡀⠀⠀⠀⠀⡘⠄⡰⠀⠀⠀⠀⠀⠀⠂ ⡘⢮⢩⢖⡱⢎⡳⢜⡣⢵⡩⢖⡹⢦⡙⣎⢳⡜⢮⡕⣫⢞⣣⡝⡸⠀⠀⠀⠀⢀⠂⠀⠎⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣮⡢⡈⣛⠿⢿⢰⣄⢀⠈⢷⣅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠄⠒⡀⠀⠀⠀⠀⠰⠈⠄⠀⠀⠀⠀⠀⠀⠐ ⢸⢸⡘⢮⡱⢫⡜⣣⠝⣦⡙⢮⡱⢣⠽⣌⡳⣜⡣⢞⣱⢎⡗⡆⠁⠀⠀⡆⠀⠤⠀⡘⠀⢠⢹⣿⣿⣯⣝⠛⠿⠿⠟⠛⣋⣿⣾⣿⣿⣸⢿⣸⣷⣄⢝⣳⣔⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⠠⣁⠀⠀⠀⠀⠡⠊⠀⠀⠀⠀⠀⠀⠀⠐ ⡘⢦⡙⢦⡙⣇⢞⣡⢛⡴⣩⢧⡙⢧⡛⡴⣓⢮⡹⢎⡷⣫⠞⠀⣸⠀⡄⠃⣀⠂⠀⠄⠂⡘⡞⢀⣈⡉⠻⢷⠦⢤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣍⠉⠛⠛⠿⠿⠿⠮⢝⡶⣤⡈⢒⠄⠀⡀⠀⠀⠀⠀⠀⠠⠡⡁⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⢘⠦⣙⢦⡹⢜⣊⠶⣩⢖⡱⣎⡝⢶⣙⢮⢵⣫⢞⡽⣺⣽⣻⣧⢹⢠⠘⠀⠄⠀⠈⡠⠁⢇⡀⣾⣿⣿⣤⠀⠙⢤⡊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣍⢦⡀⠀⠀⠀⠀⠡⡐⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡸⢤⢣⡝⢎⡜⣣⢓⢮⡱⢞⡜⢧⠞⠞⣮⠵⠯⠞⠷⢞⣯⡿⣇⢺⠀⠈⠄⠀⢠⠑⠀⢸⡂⣿⣿⣿⣿⢠⡀⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣭⣤⠭⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⡝⠅⠀⠀⠀⠡⠐⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⡱⢊⡵⢌⡳⡜⣥⠫⢂⣍⠉⢊⣴⣚⠜⣀⣴⣿⡿⠋⣠⣥⣶⣶⠦⠀⡉⠀⠀⠄⡋⠀⢸⡷⠸⣿⣿⣿⣷⣥⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⡉⢁⠀⠀⢰⣶⣦⣤⣤⣈⠙⠻⠿⠿⣻⣿⠀⠀⠀⠀⢠⠉⡌⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠒⣍⠲⣍⢲⠙⢂⡴⢃⡰⣢⣾⣿⣿⣾⣿⣿⡟⣡⣮⢟⣿⣿⣿⡇⠐⡀⠀⢈⠰⡁⠀⢸⠻⢿⣨⡻⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡴⣨⣇⢠⣀⢴⣼⣿⣿⣿⣷⣽⣳⡀⢸⣿⣿⡧⠀⠀⠀⠠⢀⠊⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⡙⢦⢹⠰⣡⠞⢙⣴⣧⣶⣿⣿⣿⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⠇⡐⠀⠀⡈⢆⠁⠄⠈⡳⠄⡌⢫⢶⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⣘⣻⣿⠇⠀⠀⠀⠐⠀⠣⠀⡅⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀ ⢣⠀⠀⣡⣞⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠿⠿⠿⢛⡭⢡⣴⠀⡐⠀⠀⡐⠌⠀⡂⠁⢳⣌⣐⣨⢇⢯⡙⢯⢟⡿⠋⣼⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⣿⣿⣏⠃⠀⠀⠀⡘⠄⡇⠀⠄⠀⠀⡀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢫⢟⠶⢉⡀⠄⠀⠀⡐⣈⠀⠅⣂⠈⢶⣏⣶⣋⠶⣙⢎⢮⠁⢠⡹⢏⢿⡻⢿⡿⣿⣮⣟⣻⠿⠿⠿⠿⠿⠿⣛⣵⣿⣿⣿⡳⠃⠖⠀⠀⢀⠘⡄⠁⠀⠂⡴⠃⢀⠴⢋⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣁⣴⣾⣏⡇⠀⠀⠀⡐⠠⠀⡃⡄⢆⡈⢾⣿⣯⣷⣭⢞⡼⣀⠣⡝⣎⠶⣩⠧⡹⢜⡭⣛⠶⣛⢯⢹⡟⠿⠧⠼⣿⢟⡟⡇⠁⠀⠀⠀⠀⠠⠌⡀⠁⠠⠁⣀⠴⣋⡴⠁⠀⠀⣀⠄⠀⣠⠞⡵ ⠀⡀⠐⠀⠈⢎⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⢇⠀⠀⠀⠠⢁⠀⠄⡝⢦⡱⡀⢻⣿⣿⣿⣿⣾⣿⣾⣵⣎⡳⣥⢚⡵⣩⢲⠱⡎⠵⢊⢄⡒⡄⠢⡐⢨⠚⠜⢀⠐⡀⠀⠀⠀⣁⠢⠁⠀⠐⠀⣡⠞⠈⣀⡠⣴⢺⣁⣤⠺⣜⣫⢅ ⠀⢀⡀⠀⠀⠀⠉⠪⡻⣿⢿⠿⠿⠻⠛⠉⢡⣴⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠐⡈⠀⢸⢘⣣⠳⡵⣄⠘⢿⣿⠟⠛⠙⠛⠿⣿⣿⣾⣟⣶⣧⣏⡷⣼⣩⣇⡶⢤⠬⣔⠢⠃⢁⡐⠂⡌⠀⠀⠀⠠⢀⠂⠁⠀⡁⡄⢡⣄⣚⣑⣋⡒⠏⠶⣎⠟⣴⢃⡞ ⣶⡏⣍⠆⠀⠀⠀⠀⠀⠀⠤⡒⢦⠩⡝⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠆⠀⠀⠀⠐⡀⠰⢈⠲⣛⡴⢣⠆⡄⠻⢂⠤⣉⠒⡊⠘⠛⠿⣿⣿⣿⣿⣿⣷⣿⣯⡻⠭⠚⠀⡐⡐⠢⠄⣊⠀⠀⠀⢀⠁⢂⠁⠀⠀⢰⣁⣿⣿⣿⣿⡿⠻⢷⡄⠙⡺⢁⢮⡜ ⣿⠋⠀⠀⠀⠀⠀⢠⠀⠀⣇⠙⢀⡙⠘⡄⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢠⠀⠀⠀⠀⡀⠀⡇⣿⣄⠈⠛⡄⣉⠃⣈⡜⡈⠁⢀⠃⡀⠀⢻⣿⣿⣿⣿⣿⠋⠁⠁⣀⠀⣄⢡⢁⠋⡀⠀⠀⠀⠀⠀⡈⢀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣇⠛⢈⣿⡇⠀⣉⣤⢹ ⠀⠀⠀⢀⠔⡩⢘⠤⡙⢬⡐⢣⠎⡔⢫⠄⢿⣿⣿⣿⣿⣿⣿⡗⣹⣿⢰⡀⠀⠀⠀⠀⠀⢣⢹⣿⣦⠘⡜⣱⢂⡍⣷⠧⠈⡎⡜⠱⡀⣼⡿⠟⢋⢡⠀⡴⣨⠳⡜⣎⢖⡣⢞⢠⠁⠀⠀⠀⡈⠐⡀⠂⠀⠀⣼⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⢬⢳ ⠀⢠⠘⡄⢎⠰⢡⠊⠴⠡⡌⠥⠚⣌⢃⢎⢸⣿⣿⣿⣿⣿⣿⢣⣿⣿⣸⣷⠀⠀⠀⠀⠀⠸⡇⣿⣿⣷⡙⣶⢘⢸⡷⠇⢱⠜⢁⠃⡀⡖⣤⣹⠘⣠⣻⡴⣯⠽⠟⠾⢚⣉⡃⠀⠀⠀⠀⡐⠠⢁⠀⠀⠀⡀⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⢮⢳ ⡈⢆⠱⡈⢆⡡⢃⡜⢡⠃⡜⣨⠑⣢⢉⢆⠂⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⣿⡆⠀⣧⠀⠀⠀⢻⡸⣿⡿⣻⠄⣈⠀⣝⡥⡆⠢⠃⢤⣽⢾⣵⠏⣰⣭⣵⣶⣶⣶⣿⣿⡿⡫⠀⠀⠀⠀⡐⠀⠡⠀⠀⠀⣼⡧⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣏⢞ ⠰⡈⢆⠑⠢⠰⢡⠘⢄⣣⣔⣦⡁⢆⠪⣘⠢⠸⠿⢿⠿⠿⢋⣸⣿⣿⣿⣜⣷⣣⢸⣷⡀⠀⠈⣧⠟⠌⡱⣜⣢⢀⡅⣠⠸⡅⢊⠿⠜⣋⣥⣾⡿⣿⣿⣿⣿⣿⡿⣫⠞⠁⠀⠀⠀⠀⠄⡈⠀⠀⢀⣾⣟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡝⢮ ⠂⠥⢰⣿⣿⣿⣷⣶⣮⣝⣻⠿⣿⣶⡁⢆⡙⠄⢛⣡⣶⣾⣿⣿⣿⣿⣿⣿⣮⣟⣓⣿⡇⢦⡄⠈⡃⠨⣗⣯⢿⠣⣶⢱⢢⢹⠘⣶⣿⣿⣿⣷⣾⣿⣿⣿⢟⢕⡾⠉⠀⠀⠀⠀⠀⠌⠀⠀⠀⣴⡿⣫⡞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡝⢮ ⠘⡐⣼⣿⣿⣿⣿⣿⣿⣿⢫⣤⡐⠭⢑⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⡻⡤⢁⠢⢓⢮⢻⠷⣖⢫⠒⠄⠀⣿⣿⣿⣿⣿⡿⢟⡯⣪⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣾⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣏⢳ ⣡⣾⣿⣿⣿⣮⣝⣛⡻⠵⢿⠟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⢣⡆⡌⣌⢣⢋⡜⢢⠉⡜⠀⠿⠿⣿⣿⣿⣾⣭⣮⠕⠁⠀⠀⠀⢀⣀⠤⠀⠀⣠⣾⣷⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⣌⢳ ⢻⣿⣿⣿⣿⣿⣿⣿⡏⠟⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣃⠀⠙⡖⣌⠖⠡⠜⠢⢁⡀⢶⣩⢳⣎⣶⣳⢾⣽⣤⣤⣴⣶⣶⠿⡻⢁⡤⣠⣾⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣚⢬⢣ ⣿⣯⣛⣻⡿⠿⢿⡿⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡀⠐⠈⠰⠈⢁⣠⣶⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣾⣶⡿⣼⣿⣿⣿⣿⣿⣿⣫⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡓⢎⡵ ⣿⣿⣿⣿⣿⣿⡷⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⠁⡌⠈⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠲⣉⠶⣘ ⢸⣿⠿⢿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢉⠀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⢓⡌⢲⢡ ⠸⣿⣿⣿⣶⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⢳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡚⠔⣌⠣⢎ ⢀⢿⠟⠿⣿⢟⢸⣿⣿⣿⣿⣿⣿⢻⣝⡿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⡌⡞⣥⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⢑⢊⠤⠓⡬ ⠀⠆⡉⠓⡐⢂⡘⣿⣿⣿⣿⡟⣼⠛⠊⡓⢯⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⢃⡱⢩⠶⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠣⢌⠒⡍⠴ ⠈⠤⢁⢃⠰⣁⠂⢿⣿⣿⡷⣙⠖⢀⠩⢭⡢⠛⡮⢿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠢⠈⢿⣷⣶⣧⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⠱⡈⡜⢌⠲ ⠀⠂⠌⠠⠒⠠⣁⠘⡿⣿⡰⢍⡞⣄⠂⠄⠓⢀⡏⢯⡽⡳⢯⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣄⣾⣿⣾⣝⡛⢏⠆⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢢⠑⡰⡘⠬⣑ ⠀⠡⠈⠄⠡⠁⠄⠂⠘⣿⣧⢈⠲⡡⢏⡚⢭⠳⣜⢣⠳⣭⢻⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡹⠁⣠⣔⣸⢿⣿⣿⣿⣿⣶⣄⠹⣿⣿⣿⣿⣿⣿⣿⠃⢌⠢⡑⢢⡑⢣⠜ ⠀⠠⠁⠈⠄⠡⠈⡐⠀⠙⢿⣷⣐⠑⡊⠜⡡⢓⡌⢎⣵⣻⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣷⣮⣟⠿⣿⣿⣿⣷⠈⢿⡿⢃⣬⠙⣃⣀⣊⡐⠡⢃⡜⡡⢞ ⠀⠀⠀⠁⣀⣤⣴⣲⣞⣥⡈⠻⢿⣷⣬⣔⣑⣮⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣘⠿⣿⣿⣿⣿⣿⣿⣮⣭⢛⡥⠃⣨⢁⡌⣈⠄⢱⢋⠟⠇⡟⠶⡬⢑⠊ ⢀⠤⣲⣿⣿⣾⣽⣷⣿⣿⢋⠤⣉⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠄⣻⣽⣿⣿⣿⣿⣿⣿⡿⣏⣿⣻⢿⣿⣿⣿⡿⣟⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣮⡻⢿⣿⣿⣟⠿⡟⣼⠚⣰⡇⠠⢎⠥⣫⠀⠌⡌⠐⠌⡳⠌⣁⡰ ⢎⡳⡛⠿⣿⡿⠟⡻⠋⣑⠬⠅⣠⣬⣤⣌⣙⡛⠻⠿⠿⡿⢿⠿⠿⠛⠂⠁⠀⢸⣻⣿⣿⣿⣿⣿⡿⡱⢎⠷⣭⢟⡾⠽⠾⢝⡳⢮⡱⢏⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣷⣝⣛⡿⣛⡼⡭⢡⠿⠁⢞⣘⡒⡁⠠⠣⠜⠩⠒⡄⢐⣂⣑ ⣫⣶⣍⡛⠰⢊⣥⡒⡽⡜⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣂⠄⠠⠀⠀⠀⠈⠷⣿⣿⣿⣿⣿⢧⡙⢮⡹⠜⢢⡞⠭⣹⡆⢫⢣⠝⡎⣎⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣍⡻⢿⣿⣿⣿⣿⣿⢱⡯⠟⡀⣶⠏⣸⣿⣿⣿⣦⠸⢡⢋⠕⢂⣴⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⢟⡼⣱⠧⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⠀⠀⠀⠘⢽⣿⣿⣿⣿⣧⡘⢥⢚⡱⠈⡃⠄⣀⠉⣠⢣⡙⠴⣡⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣿⠿⣛⠵⠃⣫⣴⣷⣮⢡⣿⣿⣿⣿⣿⠧⠀⢁⣴⣿⣿⣿⣿⣿ ⣍⢻⢻⣍⡓⣎⠏⠈⠤⠰⠭⠖⣖⡶⢤⣍⡛⠿⣿⣿⣿⣿⣿⣿⢟⡡⠞⣰⣾⣦⡄⠈⠻⣿⣿⣿⣿⣄⠊⢆⠱⢃⡌⠤⣀⠖⠤⢃⡌⢃⣼⣿⣿⣿⣿⣿⣿⡿⠃⣤⠘⢻⣿⣿⣿⣿⠃⢎⣡⣵⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿ ⣎⣋⡤⢈⣴⣶⣿⣿⣿⣿⣿⡿⣷⣾⣍⡲⣝⡜⢤⡉⣙⠩⣕⠲⠍⡀⣾⣿⣿⣿⣿⣧⣄⠘⠻⣿⣿⣿⣷⣬⣐⠡⠘⡤⢁⠎⢘⣢⣴⣿⣿⣿⣿⣿⢿⣫⠗⣡⢻⡴⢳⡀⠈⢍⠉⢥⣶⣿⣿⣿⢟⣫⣭⣭⡍⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗ ⠳⣽⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠦⣓⢌⡒⡀⢀⢊⡱⠿⣿⣿⣿⣿⣿⣿⣷⣶⣌⡙⠻⣿⣻⣿⣿⣿⣶⣾⣿⣿⣿⣿⢿⢿⢻⡝⠎⣃⠴⣎⡵⣻⢼⣳⣣⠀⡈⠒⡄⡙⠛⠿⠧⠘⠿⠿⠿⠄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃ ⣿⣦⡃⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡑⠂⢠⠒⠭⠢⠍⠳⠔⢦⢭⣉⠛⢿⣿⣿⣿⣿⣷⣦⣉⠘⠓⠋⠿⠹⠞⠓⠛⢈⣋⣬⣥⣶⣿⣿⡌⣳⡽⣯⡿⣶⣯⡇⢥⠀⢂⠱⡈⠔⡠⠘⢠⠒⠰⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡜ ⣿⣿⣷⣌⠑⠝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣬⣶⣾⣿⣿⣿⣿⣿⣶⣮⣅⡻⢌⠙⣿⣿⣿⣿⣿⣿⣷⣄⠡⢆⡑⣂⠢⢀⠠⡄⣿⣿⣿⣿⣿⣿⠨⣿⣷⣿⣻⣷⡏⢸⡆⠈⡐⠌⢂⠡⣉⣤⣬⣥⠤⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣱ ⣿⣿⣿⣿⣷⣄⠁⠈⢙⠻⠿⣿⣿⠿⠿⡛⠅⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⡇⣣⡘⠴⣊⢿⣷⣶⣎⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠁⣾⡑⡀⠐⠌⢂⠡⢈⠻⠿⠯⠲⠁⢨⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣵ ⣿⣿⣿⣿⣿⣿⣮⢢⠀⠁⢣⠒⡤⢃⠖⢡⢚⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⢿⣿⣿⡿⡱⠇⣥⡹⡜⡎⢿⡿⣿⣷⣸⣿⣿⣿⣿⠃⢿⣿⣿⣿⠏⡀⣷⠡⠂⠁⠌⣀⠒⡀⢂⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠙⡤⣀⠉⠒⡍⠐⡎⠘⠑⠈⠙⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠣⠜⡭⢶⣹⢸⣟⢷⡜⡽⠸⠇⣿⣿⣿⣿⣿⣿⡿⠐⣼⣿⣿⠟⡰⢐⠏⠴⠁⠂⡐⢀⠂⠄⠡⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿ ⣿⣿⣿⣿⣿⣿⣿⡿⡘⡰⠁⣀⠤⡐⢦⠰⡩⢖⡒⢦⠰⣉⠄⣊⠙⠏⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠰⢬⡔⠣⢝⢺⣿⣿⣿⢸⣃⢸⣿⣿⣿⣿⣿⣿⢃⡇⣿⣿⠏⡜⡄⢎⡜⡡⠀⠐⡀⠂⠌⠠⠁⠌⠀⠀⢀⠀⡀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢟⡫⢐⡡⠆⠵⣊⣶⡙⢦⢫⡕⢮⡜⢦⣋⢦⡹⢄⡏⡜⢢⠤⣀⠩⢛⠿⠿⠿⢟⡵⡃⣠⢳⣝⢫⢶⡸⣿⣿⣿⡇⢣⠘⣿⣿⣿⣿⣿⡏⢚⢦⡛⠫⢈⠖⡸⢄⢚⠀⠀⡁⠠⠁⡈⠄⠡⠈⠀⠀⠀⢀⣀⣀⣀⣂⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⠟⠋⣀⣠⣵⣶⣿⣿⣿⣿⣿⣿⣷⣾⣷⣼⡣⢞⡴⢣⢫⠴⣙⢆⠳⣌⠱⢢⢌⡑⠊⢳⢚⣡⢷⢸⣿⣷⣌⢓⠹⣿⣿⠇⣘⠆⢻⣿⣿⡿⠟⢠⣏⠶⠹⠁⡌⢢⡱⢈⠂⠀⠐⠀⡁⠐⠀⠌⠔⠀⠀⠠⢠⡿⢟⡻⣿⡟⠀⠀⠄⠁⠐⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠡⠈⠠⠉⣀⠀⠀⣁⡘⣶⣳⢯⡭⡌⠑⠀⠉⠓⠻⠀⠀⠀⠀⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠁⠠⠈⠀⠄⠁⠂⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢂⠀⠁⢀⡬⢤⣤⣤⢮⣥⣟⣧⡟⠙⢆⣀⣀⣰⠶⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠈⠀⠄⠐⠀⠠⠁⠌⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⠐⢢⣤⢟⣿⡺⣝⢶⡽⠸⢨⣟⡳⣏⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠐⠀⡀⠂⠈⠠⠈⠄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⡀⢸⣻⣻⢼⣫⢶⣻⣝⢮⡷⣼⣻⣜⣳⢯⣞⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠄⠀⠀⠄⠁⠌⡀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠈⢷⢯⣳⣭⠷⣤⢭⡝⡾⣵⣩⡜⣧⡟⡞⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠈⠀⠄⠂⠀⠄⡈⠄⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠙⠷⣺⣻⢭⡟⣾⣹⡳⢯⡽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠡⠀⠌⠀⠄⠂⠁⠀⠀⠀⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠙⠺⠝⣞⡷⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠄⠁⠀⠂⠠⠀⠂⠈⡀⠡⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣤⣶⣦⢰⣦⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠌⠀⠠⠁⡀⠐⠠⢁⠠⠐⢀⠂ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠄⠀⠰⣿⡟⠿⣿⣿⣵⡻⢀⠁⠸⠁⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⠁⡀⠄⡁⠂⠄⠂⠌⠠⢀ ⢥⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⠀⠀⠀⢈⣁⣭⣤⠤⣤⠤⠴⠠⢀⠀⠀⠀⠈⠀⠀⠀⠠⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠁⡀⠀⠄⠠⠁⠌⡐⢈⠐⠠ ⢦⡑⢆⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣦⣤⠀⠀⠀⠀⢀⣠⡠⠘⠋⠉⢤⣔⠒⣰⠒⢦⡐⠀⠦⠥⢤⣤⣀⡄⠈⠐⠀⠄⠂⠌⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠐⠈⢀⠁⢂⠐⠠⢈⠐ ⢢⠝⣲⠰⣀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣻⡷⣿⣿⠯⣰⢡⣿⠶⠢⠔⣋⣡⠤⢖⣚⣻⣽⡿⡿⣽⢿⡿⣾⣿⣷⣾⡶⢦⢦⠤⠄⢀⠈⢀⡐⠂⢀⠉⠆⢠⢶⣳⠀⠆⠀⠀⠀⠀⠀⠄⠀⡐⠀⡁⠂⠄⢈⠀⠄⡁⠂⠄ ⢌⡳⢌⡳⣅⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣽⣿⠾⣽⣻⡽⢋⣼⠿⠋⣁⠤⣒⣯⣭⣶⣾⣿⣿⣿⣷⣿⢿⢽⣾⣽⣯⡽⢯⡽⠽⢫⢭⡛⠟⡦⣌⠄⢢⠡⠀⠈⠀⠘⢋⣠⡴⣆⡰⠇⠀⠀⠀⠈⠀⠀⡀⠄⠐⡈⠄⡈⠰⣀⠣⢈ ⠸⣔⠫⡔⣎⠣⢖⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣷⣯⠯⡰⢯⡁⢊⠡⠔⠩⠚⣟⠿⢿⡛⢷⣟⡿⠿⠯⠞⠛⠚⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⢐⣂⣀⣀⡀⠀⠀⠈⠀⠀⠀⡾⠃⠉⢤⢤⠌⠄⠀⠀⠀⠐⠀⠠⢈⠐⡁⠢⠌⡑⢄⠃⠆ ⢱⡊⡵⣩⠖⣹⢊⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣳⣟⢾⣟⠚⠛⣠⣉⣤⣤⠄⠀⠂⠘⠁⢶⠾⠛⢉⣁⣤⣤⣠⣀⣄⣀⡀⢀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠻⠆⠈⢁⠈⠀⠀⠀⠀⠀⠀⠐⠠⠁⠤⢁⠂⠔⡈⠌⠠ ⢢⠝⣔⠣⡞⣡⠳⣘⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢗⣾⣿⣿⢦⠉⡵⢛⣈⡉⠀⠂⠀⠀⢀⣠⣴⣾⣿⣿⢿⣻⣿⢿⣯⣿⢿⣿⡷⣦⠀⠉⠙⢿⣟⣯⣿⣿⣿⣽⣯⣿⢿⣿⣿⣿⣿⣷⣄⠀⠙⠂⠀⠐⣶⠤⡀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣌⢫⡜⣣⢕⡣⡝⢬⠂⠄⡀⢠⠀⠀⠀⠀⠀⠀⠀⢾⣷⡿⠟⢋⠥⢢⣷⣞⠻⣞⡽⠋⠀⠀⣠⣿⣿⡿⣟⡯⠟⢯⠹⣙⠻⣽⢯⣟⣷⣻⡟⡿⣄⠀⠀⠈⢻⡿⣟⣿⡿⣿⢯⣿⣷⣯⣷⢿⡿⣿⡳⠄⠀⠀⠂⠌⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⠦⢎⡱⢎⡲⢍⡎⡅⠠⢐⠂⢡⠂⠀⠀⠀⣀⣴⢿⣿⣷⠈⠜⢈⠡⡔⣼⢲⢶⣺⠁⠀⢠⣿⣿⣿⡽⢣⠜⣉⠆⠓⢈⠳⣌⣻⣿⣾⡳⣝⠳⡥⠂⠀⠀⠀⠙⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣽⣿⡑⢫⠄⠀⢈⠐⡀⠣⠉⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡙⢎⡳⣩⠖⣍⠲⡄⢁⠢⢁⠂⠌⠠⠀⢘⣫⣍⣁⣀⡌⠐⠀⠂⠀⠉⡏⣴⢢⣜⠆⠀⣿⣿⣻⣾⢧⢃⠞⡠⠀⡀⢌⡒⢬⢻⣿⣿⠳⣍⠳⢌⠡⠀⠀⠀⠀⠘⣯⡿⣿⣿⣽⣿⣿⢯⣷⣻⢾⡱⠠⢌⠀⡀⠎⡐⢁⠀⠄⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⠝⡪⡕⢦⡹⢌⡳⠄⠂⠌⡄⠘⢀⣥⣾⠟⢉⣩⢴⣲⠶⡖⢜⡡⣄⠀⠹⣌⠉⠈⠀⢐⣿⣻⣿⣞⡿⣌⠲⣡⠓⣌⡑⡎⣖⡻⣞⢥⡛⠤⠋⠄⠂⠀⠀⠀⠀⠀⢹⡿⣽⣿⣯⣿⣾⢿⣳⢯⢿⡹⢣⠌⠀⠄⡃⠜⡀⢂⠈⡀⠞⡀⠀⠀⠀⠀⠀⠀⠀ ⢌⡳⢱⡩⢖⡡⢏⡴⠃⠈⡔⢀⠲⡿⢋⢄⣴⣿⣿⣻⠔⣮⢍⡴⠷⡧⢈⣇⠀⠈⠀⠀⢸⣿⣟⣷⣟⡿⣯⢷⣦⣛⣤⡻⡼⢎⡳⢍⠦⡉⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣻⢾⡽⣻⡜⣏⢎⡑⠃⠌⠀⡐⠐⢂⠡⡀⠆⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡔⣣⢓⠎⡵⢪⢔⠃⡐⠄⢂⠈⢢⢣⣾⣿⣿⢿⣽⣻⡜⣼⣿⠓⡙⠠⠙⠠⠁⠀⠀⠀⢿⣻⡾⣽⡽⣏⡿⣼⡹⢎⡳⡙⢎⡑⠊⠔⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠻⣭⢓⠣⠜⠠⠂⠀⠁⠀⠐⠠⢁⠂⠤⢁⠌⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⠕⣫⢜⠲⢥⡚⡜⡄⠡⠐⡈⢤⡞⣼⣿⣿⣟⡾⣟⣿⡇⣿⢯⡰⢅⡆⢀⠂⠀⠀⠀⠀⠘⢯⡷⢯⡳⣝⣣⢭⠳⣘⠣⠓⡌⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠜⠀⠐⠀⠀⠀⠀⠀⠂⠄⢈⠐⠠⠈⠀⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⢎⡱⢪⡙⢦⡱⢚⠄⠠⠁⢠⡟⠆⣻⣟⡾⣽⣻⣟⣿⡟⣼⢊⡗⠊⠜⠣⢀⠠⢀⠀⠀⠀⠀⠙⠢⡙⢆⠱⢊⠱⢀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠂⠀⠄⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡡⣍⠧⣙⠦⡱⢋⡄⠂⠁⠀⣥⣆⠷⣮⡿⣿⣽⣿⣿⣽⣜⠎⣈⠂⡈⠄⡠⠘⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⠵⡸⢜⡡⢞⡡⢏⠄⠠⠁⠀⢹⣿⣌⢿⣻⣽⢯⣻⠣⢏⡋⠂⢄⡐⠌⡐⢁⠢⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⠲⣉⠮⣑⢎⡱⢎⠀⠂⢁⠠⠀⠿⣿⣿⣯⣟⣷⣯⠟⠠⢁⢁⠢⡐⠌⡐⡈⠀⠀⠀⠀⢀⠀⠀⠘⣧⢳⡽⣻⡿⣿⢶⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢌⡣⡍⠶⣉⢎⢖⡩⠀⢈⠀⠄⠂⠈⠻⢿⡙⠋⠌⣀⢐⠢⢃⠆⠒⡀⠎⠐⠀⠀⠀⢂⠀⠀⢂⠀⠀⢣⢧⣙⠧⣝⡳⣏⠾⣙⠦⡐⡀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡔⣩⠳⣉⢎⠦⡓⠀⢀⠂⠐⠈⠀⠀⠀⠄⢒⠨⠄⠊⡔⠁⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠺⣌⠳⣎⠵⣭⡛⣜⠲⣱⣴⣟⡶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠕⣣⠣⣍⠎⣖⡁⠠⠀⠄⠡⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧⣿⣼⣛⡶⣹⢌⢷⣻⢞⡼⡹⢧⡍⢣⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⢜⢢⡓⢬⢚⢤⠃⠀⠐⠀⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢯⣟⡷⣯⣟⡵⣏⠞⣬⢓⡯⡞⣝⠲⡘⠄⠡⢂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡱⢊⡵⣘⢣⢚⠬⢁⠀⠂⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣽⣳⢯⣻⢼⡙⣦⢻⠼⡱⢎⡵⡈⠌⠀⠶⣐⠠⠀⠀⠂⠀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣱⣭⣶⣵⣮⣬⣬⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⡀⢄⢀⣀⡀⡀⢀⡴⣿⣾⣿⣿⣿⣿⣿⢯⣻⢧⣛⢾⣱⢏⣳⡙⢮⡔⡩⠀⡤⢛⠤⡁⠀⠀⠌⡀⢃⠩⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣾⣳⢮⠗⣠⡿⣿⢯⣿⢿⣛⡷⣯⣟⣯⢯⢷⣫⢏⡷⢫⢖⡹⢆⡜⡡⢰⡙⡌⢢⠁⠀⠀⠠⠀⠀⠀⠈⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣬⣥⣾⣓⡫⠟⢋⡼⣯⢿⣿⢿⣯⣟⣯⡟⣷⣛⠾⣹⠞⣥⢏⡜⣣⢏⠶⣉⠖⣱⠣⠜⡠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠈⡔⠠⢃⠜⡐⢢⠐⣀⠀⡀⢀⠠⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⣫⢿⡽⣯⣟⡿⣞⡽⣶⢻⠶⣙⠮⣱⢋⠶⣉⢞⡱⢎⡳⣉⠮⣡⢃⠱⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢣⢎⡘⣄⠡⠄⡡⠐⡀⢂⠡⠐⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣜⡯⢿⣽⣳⢯⡽⣏⡿⣭⢏⡳⣉⠖⡡⢎⠣⡝⡸⣌⠧⢣⡑⢎⠰⡈⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡒⣎⠱⡌⢥⠃⡌⠱⣀⠂⢄⠣⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡴⣫⢞⡽⢯⣶⡻⣯⢟⡽⣳⡝⢮⠱⡌⢢⠑⡊⠱⡜⡱⠜⣌⠣⠜⡠⢃⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡱⣌⡱⢌⢢⡑⡌⡱⢀⠎⡄⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠽⢲⣏⣓⢯⠾⡵⣏⢶⣏⢾⣝⡯⢃⠾⣵⣏⣾⣹⢧⣷⡻⣽⢺⡝⡱⢎⢇⡓⢌⠢⠁⠄⠐⡩⠜⡱⢈⠆⡱⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠑⢢⢁⠊⠄⡰⠀⠅⢊⠰⡈⢆⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠽⡬⣍⡯⣝⢮⡿⣱⢏⡷⣺⡝⡞⣠⢯⣟⣷⣛⣶⢻⣟⣷⣿⣲⢯⡜⡱⡉⢆⡘⠠⢂⢁⠊⠤⠑⡌⠰⡁⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⢈⡐⠢⢌⠒⡠⢡⠘⣄⠣⡘⣄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢿⢿⡻⢟⢯⡟⣭⢿⡹⣝⢮⡝⣾⣹⡞⣥⣏⢾⣱⡛⣰⢳⣟⣾⣳⣻⣞⡿⣽⣿⣿⣟⡿⣶⢦⣁⠢⠐⢡⠂⠄⡈⠄⠡⢈⠁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⡄⢊⡕⢪⠔⡱⢊⡵⡈⢖⡱⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡘⢎⠶⣙⢎⡳⡜⢧⣏⢷⡹⢮⣽⢳⢧⡿⣱⣞⣷⡛⡰⣵⣻⣞⡷⣯⢷⣹⣻⣳⣿⣿⣽⣳⢯⡷⣎⠳⣄⠡⠈⠔⠠⢈⠐⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⡌⢡⢊⠱⣃⠖⡩⢆⠣⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⡙⡬⢚⡱⢎⡵⣫⠳⣞⡬⢏⡳⡝⢮⡹⢳⡟⣼⣳⠡⢿⣼⣳⢯⡿⣽⢯⡷⣯⣿⢿⣻⣞⢷⣻⠼⣌⠳⣌⠒⡡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣄⠊⡵⡘⠰⣁⢎⡱⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⠱⡜⣣⢝⡺⣜⠵⣋⠶⣙⢮⡱⢎⢧⡙⢧⣻⢼⡃⢺⣟⡾⣭⣟⡾⣝⡿⣞⣷⣻⣿⣳⢯⡟⣧⢛⡌⢳⣀⠣⠄⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠀⠀⠀⠀⠀⠁⢢⠩⡔⡡⢃⠔⢢⠑⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⢦⢱⢫⡜⢧⡙⢦⡛⣔⢫⡜⣱⢚⡬⣓⢼⣫⢞⠡⣾⢽⣳⢯⣟⣷⡻⣷⢯⣟⣽⣯⣟⣾⢳⡝⡎⠵⡊⢍⠂⠤⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡹⢌⠂⠄⠀⠀⠀⠀⠀⢈⠦⣑⠃⡌⠰⡈⢆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣆⢫⢎⡝⠶⣙⢦⡹⢤⠳⣜⡱⢎⠶⣩⢎⡧⠏⢐⣯⡟⣽⣻⢞⣷⣻⣽⣛⡾⣽⣞⣷⢫⠷⣸⠩⢖⡉⢆⠩⠄⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⢯⣳⠹⣌⠜⡀⢂⠀⠀⠀⠀⠀⡚⢤⠃⡌⠱⡈⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⣘⢎⡞⡜⢣⡙⢦⠓⣬⠳⣌⠞⣩⠖⣥⠻⣜⠣⣞⡳⣟⡷⣯⣟⣾⣳⢯⡿⣽⣳⣟⣮⢏⡷⣡⠛⡤⡉⢆⠱⠈⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣻⡳⣭⠳⡜⢢⠑⡄⠀⠀⠀⠀⠀⢉⠦⡉⠔⣡⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⣍⢺⢰⡉⢧⡙⢎⡹⢤⢳⡘⢮⡱⢚⡴⣛⡬⢳⢨⢟⡮⣟⣵⣻⣞⡽⣯⣟⣷⣻⢾⣝⢾⡰⢣⡙⡔⢡⠊⡔⠡⠐⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣟⡷⣭⢳⣍⢳⠩⢆⠣⢄⠡⠀⠀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡘⢆⣣⠚⣥⠚⡥⢓⡜⡢⢝⢢⠓⣍⠲⡕⣎⢳⠈⣞⡳⡽⢮⣳⢾⡽⣳⣟⡾⣽⢯⡞⣧⢹⡱⡘⣌⠢⡑⠄⢃⠂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢫⡶⢻⣝⠾⣱⢫⡜⢪⡑⢎⠰⣈⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⡑⢎⠴⣉⠦⡛⣌⢣⠜⣡⢋⠼⣉⠖⣩⠞⣌⠧⡀⢣⢟⣹⡳⣝⢾⣹⠷⡽⣾⢽⣳⡟⣬⢓⠦⣑⠢⡑⢌⡘⢀⠆⠐⠈⠀⠀⠀⠀⠀⠀⠀⢰⣫⢷⡹⣏⢾⡹⢥⡓⡬⢣⠜⣈⠒⡄⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡘⡌⠲⢡⢓⡱⢌⠦⡙⢦⢩⢒⠥⡚⢥⠚⡌⢞⡁⠸⡭⢶⡹⣎⢷⣫⠿⣽⢞⡭⢷⣛⢬⡓⢎⡔⢣⠘⡄⠢⢁⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⣟⡼⣣⢟⡼⢣⡝⢦⢣⡑⢣⠜⡠⢃⠌⡡⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢑⡈⡑⢂⠧⡘⣌⠲⣉⢆⡃⢎⡒⡍⢦⡙⠌⠦⡉⠄⣛⠶⣙⢮⡳⣭⢻⡜⣯⡝⣣⡝⢦⡙⠦⡘⢢⠑⢌⢂⡁⠂⠄⠈⠀⠀⠀⠀⠀⠀⣸⢣⣟⡱⢯⡜⣣⠞⣢⠣⡜⢡⢊⠔⡡⢊⠔⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠃⠤⠑⡈⠤⠑⠠⠃⠐⠂⠉⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⡞⣭⠲⣝⠼⣣⢛⠶⣩⠳⣌⠧⡘⠥⡑⢢⠉⡄⢢⠠⠁⠌⠀⠐⠀⠀⠀⠀⠠⣞⡳⢮⡝⣣⠞⣡⠞⡤⠓⡬⢡⠊⡔⢡⠊⡔⡉⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢊⠷⣌⠳⣍⢞⡣⢇⡛⣤⢣⠙⡤⢑⠢⢡⠘⡀⠆⢁⠂⠁⠀⠀⠀⠀⠀⢰⡫⢗⠯⣜⡱⢎⡱⢊⠴⣉⠦⡑⡸⢀⠣⡘⠤⢘⠠⢁⠂⠀⢀⠀⡀⢄⢠⠂⡔⡠⢂⠔⡠⢃⠜⡠⢃⠒⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠲⣌⠳⡜⢢⡙⢬⡑⠦⡑⢊⠔⡡⠂⢅⢂⠡⠈⠄⡀⠂⠁⠀⠀⠀⠀⢭⣓⢯⠳⣜⠲⣉⠖⣩⠒⣅⠲⢡⠑⡌⢢⠑⡌⢢⢁⠂⠀⠰⣈⠒⡉⢆⢢⢉⡔⠡⢎⠢⡑⢌⠢⡑⠌⡆⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡤⠤⠤⢤⣒⡫⠭⣀⣤⣤⠤⠽⣿⡒⠶⢤⣭⠽⣖⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡩⢗⣾⠟⣹⠞⢻⠉⠛⠀⢶⢭⡁⠀⠀⠈⠙⠀⠈⠩⣛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠔⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣠⡴⢿⡇⢤⣻⣃⠈⢇⠀⠀⠀⠱⡿⣦⠀⠙⣶⡄⠢⡀⠈⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢷⣄⣠⡾⠓⢠⡀⠀⠀⠀⠀⠀⠀⡾⠃⡴⣿⡿⣠⠾⡇⣬⣿⢿⡄⣼⣆⠘⡄⠀⠹⡜⣆⠀⠘⣿⣆⠘⢦⡀⠀⠙⢿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠙⠶⣁⠀⢀⣵⠀⠀⠀⠀⠀⣜⢴⠏⣰⣿⠟⠁⢀⣿⠻⣇⢸⣿⡟⣯⣙⣻⢰⠶⠿⣽⢦⣀⣾⠿⣷⡀⢷⡄⠀⠠⣿⡏⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠤⢤⡀⠙⢣⡎⠀⠀⠀⢀⡠⠞⢡⠊⣧⡿⠃⣀⣤⠆⠹⠎⡿⣿⣿⣹⣇⠀⣿⣟⠛⢢⣿⣬⠛⢻⡆⢿⡟⠺⣿⣄⠀⣿⣿⠀⠈⢻⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡴⠃⠀⠀⣠⠖⠉⢀⡴⠃⢸⡞⢠⠾⠿⢏⡀⠀⠀⠓⠻⣿⣇⡘⣦⣿⣿⣆⠀⣿⣿⡗⢾⣿⠸⣷⠒⣇⠹⠤⣸⢹⡇⡀⠀⢿⣿⣌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⣀⣤⡾⠋⠀⢠⣿⠀⡎⢀⡀⠀⢳⡀⠀⠈⢦⠈⠉⠛⡿⠇⡏⢿⣦⣼⣿⡇⢘⣿⠀⣿⡀⢹⡆⠀⢸⠀⢧⡀⠀⠸⣿⣿⣦⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣣⣾⣟⡽⠁⡠⣠⣿⣿⣶⡿⣿⣾⣽⡊⠁⠀⠀⢀⣓⣺⣍⣀⠀⠀⠘⣿⣿⣿⠁⢸⢹⠀⢹⣷⠘⣿⠀⢾⡄⣸⡇⠀⠀⢿⣸⣿⣷⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡄⡷⡀⠀⠀⠀⢰⣿⡟⣿⣹⠋⡠⠚⣱⣿⠉⣿⠽⠦⠶⠿⢿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⠙⣾⡏⠀⢸⣼⢸⠸⣿⣇⣿⣧⣾⡇⣿⡇⠀⠀⢸⣏⣿⣧⢣⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠁⠃⠀⠀⠀⠀⢻⡤⠜⡡⣚⠔⢚⣿⡏⣸⠇⠀⣠⣤⠖⣻⠆⠀⠀⠀⠀⠑⠻⠿⢿⣟⠙⢻⣿⣽⡁⠀⡆⡏⢸⡇⣿⣿⣿⣿⣿⢷⣿⠇⠀⠀⣾⣿⣿⣿⣆⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠀⠀⣀⠴⠚⣉⡴⠞⠉⢀⣴⣿⣿⢣⡿⠀⡞⠁⠸⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢉⡏⠁⢸⢷⠃⢸⠇⣿⡿⣿⣿⣿⣿⣿⠀⠀⢸⢻⣿⣿⣿⣿⣆⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣔⡭⠄⣶⠟⠁⢀⣠⣴⣿⣿⣿⣿⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⢀⣏⡎⠀⣿⠀⣿⠀⣿⣿⣿⣿⡇⠐⢃⡟⢸⢹⢻⡇⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡏⠀⣠⢊⣴⣤⣾⣽⣿⣿⣿⣿⣿⣿⣿⡿⡌⠀⠀⠀⢲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡇⠀⣜⡜⠀⢸⡏⠀⣿⣰⣿⣿⣿⡿⣤⠀⣼⣡⣿⣾⢸⣷⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣿⠳⣿⣜⣵⣿⣿⣿⣿⢿⣿⠟⣽⣿⡿⣿⣿⡇⡙⢆⠀⠀⠐⠶⠈⠀⠀⠀⠀⠀⠀⠒⠀⡴⠁⣾⠇⢀⡽⠁⢀⣿⠀⣸⣿⣿⣿⣿⣿⠃⠉⢰⣧⢻⢿⣿⢸⣿⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠄⠀⠀⣿⡀⢰⠉⢻⣿⣟⡟⠀⠈⢀⣼⠿⢏⠀⣿⢃⢷⣧⣌⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣼⣿⣴⡟⠀⢀⣾⣷⢠⣿⣿⣿⣿⣿⡿⠷⢠⠟⠁⣼⣽⣿⣼⣷⣼⣸⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡟⢠⡟⠀⠈⠻⢺⠀⢰⡇⣿⡇⢀⣴⡟⡟⠀⠈⢻⡇⠀⢇⠙⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⠏⠀⢀⣾⣿⠇⣾⢻⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⡟⣠⠯⣄⠀⠀⠀⠈⣆⢸⣧⣿⣿⠟⢹⣿⡏⠑⠢⢄⡀⠀⠈⠳⣿⢤⣻⣿⣷⣶⡖⠊⠉⡉⠁⢀⣤⣾⣻⠟⠁⠀⣠⣿⣿⣏⢲⣿⣼⣿⣿⠞⠁⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠃⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⢠⡟⢀⣿⠀⠘⠓⠶⢍⡉⠁⠀⠀⠈⠉⠉⠺⡛⠧⠀⣀⣀⠈⠉⠩⠅⠒⢢⣬⣙⣋⣿⡇⢿⣾⣭⡾⠛⡿⠋⠀⠀⣠⣾⢿⣿⣿⣯⣿⣿⣿⢻⣿⠶⣶⣾⡿⠿⣿⣿⣿⣿⢟⡿⠋⢀⠐⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⡇⠚⢡⣮⢋⡔⠉⠀⠀⠀⠹⢀⠀⠀⠀⠀⠀⠀⠈⠂⠑⢄⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣳⠤⠷⢧⣤⣞⣁⣠⠤⠖⢋⡴⠋⠋⣿⣿⣿⡿⣿⣿⠥⣾⠟⢻⢇⣴⣿⣸⠟⠋⠉⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢠⣿⠀⢠⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢌⣙⠲⢤⣈⣀⣴⣚⠛⠻⠋⠉⠀⠀⠀⠃⠀⠘⠋⠀⠉⠀⢀⡠⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡺⡇⣰⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠴⣈⡳⣌⠉⢉⡒⢖⣒⣉⠉⠉⠑⠲⢄⠀⠀⠀⡟⠙⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠃⡇⠀⠀⠠⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣄⢯⣏⡿⡑⣄⠈⢢⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣰⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠤⢄⣉⣰⣠⣻⠁⡜⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠋⠒⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠉⠑⡄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣢⣀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠐⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠛⠳⣧⣼⡁⠀⡽⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⢍⠒⠢⢄⡀⠀⠀⠀⠀⣠⠞⠁⢀⠄⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡄⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⢠⣧⠀⢨⠓⠷⣄⡈⠛⠢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣵⡄⠀⠈⠓⢤⡤⠞⡥⠚⠔⠁⠀⠀⠀⡰⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡓⢤⡀⠀⠀⠀⠘⢦⡀⠀⠀⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⢙⠏⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣾⠃⢠⢣⠃⠀⡠⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠒⠒⠲⠬⠿⣄⠴⠞⠉⠀⡀⠐⣀⠄⠀⢀⠴⠊⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⠀⠀⠀⠀⠀⠨⣀⡀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⣜⠏⢀⢎⠇⢠⢲⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⡄⠀⢀⠾⠬⠒⠒⣲⣛⣉⠤⡴⠅⠒⠊⠀⡰⠁⠀⠀⠀⠀⣸⠏⢀⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠐⢤⣀⠀⠘⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣸⡏⠀⡞⡎⢠⢧⠃⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀ ⢈⣶⣿⠴⢚⡿⠋⠢⠤⠔⠊⠀⠀⣀⡴⠊⠁⠀⠀⠔⣊⣥⡈⠀⠈⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⣠⣚⠁⠀⠀⠀⠒⢉⠤⠀⠀⠀⠀⠀⠀⠈⠣⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢠⡻⠀⡸⡜⢀⣮⠇⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⡄⠀ ⠼⠋⠀⢀⡜⠁⠀⢀⣤⠤⠒⠶⣾⠃⠀⢂⣀⣤⣾⣿⣿⡟⠀⢄⣠⡇⠀⠉⠛⠿⣿⣟⠋⠛⠒⠶⢾⣓⠢⠤⣤⣤⠤⠥⡤⣤⣶⣶⣶⣿⣿⣭⣽⣽⣄⡀⠀⢠⠖⠈⢉⡇⠀⠀⢀⣠⠥⠶⣖⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣼⠆⢀⢿⠁⢰⡿⠀⣜⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⢹⡇⠀ ⠀⠀⢀⡞⠀⢀⡴⠋⠀⠀⠀⠀⣸⠀⠀⢸⡿⠋⠀⠀⠉⠳⣄⠀⢿⣧⡀⠚⠀⠀⠘⢯⠉⠓⣦⣄⠀⠈⠽⠶⠼⣿⣇⣘⡛⣠⢬⣙⣛⣛⣿⣿⣿⣿⣟⣉⣭⢦⡤⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠇⠀⣜⠃⢠⢷⠁⡼⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠇⣸⣿⠀ ⠀⢀⠏⢠⣤⠎⠀⠀⠀⠀⠀⠀⡟⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠓⠦⠼⠿⠀⠀⠀⠀⠘⠆⠀⠉⠻⢯⣷⣤⣀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠾⣿⣟⡏⠙⠻⠿⣿⣿⣿⣶⢾⣿⣉⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⡤⠋⠀⡸⡎⠀⠎⠁⡰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡎⡰⢻⡇⠆ ⠀⠘⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣦⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣭⡀⠀⡉⠻⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡎⠀⡾⠀⠀⢠⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡘⢠⠇⣾⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣤⡰⢤⡀⠀⠀⠈⢳⡍⠢⡘⠆⠀⢻⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⡇⢸⠃⠀⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⢁⡿⢰⠇⡜⠀

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⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⡠⠆⣠⠊⠀⠀⢀⡴⠋⢀⣤⡴⠚⠙⡟⡄⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀ ⠀⠀⠀⣠⡞⠋⠀⡴⠀⣠⠊⠀⡴⠃⠀⠀⣠⠊⠀⣴⡿⠋⠀⠀⠀⢳⣇⢠⡄⠀⣧⠀⢹⣇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣆ ⠀⢀⡴⠋⢀⣤⠎⢀⡔⠁⢠⡞⠁⠀⢀⣾⠋⣠⣾⠋⠀⠀⠀⠀⠀⠈⢧⠸⣧⠀⢻⡄⠈⣿⠀⠸⣇⠀⠀⣇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⣠⠟⠀⣠⣺⠋⢠⠊⠀⣰⡟⠀⠀⢠⠞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠣⣻⣦⠈⡿⡄⢻⢣⡀⢹⣧⠀⠸⡆⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠋⠀⡰⣱⠃⡰⠁⠀⣰⡟⠀⠀⣠⠋⣰⡟⠁⠀⠀⣄⡀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠑⠿⡈⢮⡄⠑⢌⢿⡄⠀⢣⠀⡄⠀⠀⠀⠸⡀⠀⠀ ⠀⡰⣱⠃⡼⠁⠀⢰⡟⠀⠀⡴⢁⡾⠋⠀⠀⠀⠀⠘⢯⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡄⠘⡄⢱⠀⠀⠀⠀⢡⠀⠀ ⣰⢣⠃⡜⠀⠀⢠⡿⠁⠀⡸⢁⡞⠁⠀⣀⣠⣤⣶⣶⣾⣯⣦⣌⡳⣄⡀⠀⠀⠀⠀⢠⣤⡤⠄⠤⢤⡴⠖⠙⢄⢹⡜⡄⠀⠀⠀⠈⠀⠀ ⢣⠏⡜⠀⠀⢀⣿⠃⠀⣰⡇⡞⠀⢀⣠⡿⠋⠁⠀⠀⣀⣤⣙⠻⣯⠉⠁⠀⠀⠀⠀⠀⠈⣽⣒⣚⣁⡀⠀⠀⠈⢪⣿⡇⠀⠀⠀⠀⠀⠀ ⡞⣸⠁⠀⠀⡼⡟⠀⢠⣿⣿⡇⠀⢠⡟⠀⠀⠀⠀⡼⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⢴⡾⠟⠛⠋⠙⠛⢿⣦⡀⠀⠉⣷⠀⠀⠀⠀⠀⠄ ⢡⠃⠀⠀⢰⢁⠃⠀⣿⢻⣿⡇⠀⠸⡇⠀⠀⠀⠀⣇⡛⢿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠹⣿⠂⠀⣿⠀⠀⠀⠀⠀⠰ ⡎⠀⠀⠀⡎⡼⠀⢸⡇⢸⣿⡇⠀⠀⠙⠦⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣿⡿⠟⠀⠀⠀⣿⠗⠀⢼⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡇⠀⣿⣿⠈⢻⣧⠀⠀⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢀⡟⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⢀⣿⣿⣇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠋⠀⠀⣰⣿⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣷⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡸⣹⠛⣧⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠽⠃⢀⣾⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⣀⣴⣿⣿⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⢧⠀⠙⢿⣆⠉⠻⢿⣏⣛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡀⠸⠀⠀⠀ ⠀⠀⠀⢰⢸⠀⢸⠀⠀⠀⢈⡠⠴⣒⣋⣉⣽⣿⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠿⠟⠛⢩⣿⣿⣿⡇⠀⡄⠀⠀ ⠀⡆⠀⠈⡟⡀⢸⠀⠀⠀⡇⠀⠈⠙⠿⣿⣿⣿⠀⠈⢻⣶⣤⣀⠀⠀⠀⢀⣀⣠⣴⡶⠟⢻⣿⣿⣿⣷⣦⡀⠐⠋⠝⠋⡝⡇⠀⡇⠀⠀ ⠀⣿⠀⠀⢻⣃⠘⡆⠀⠀⢣⠀⠑⣦⣄⣀⠉⠛⠢⢄⡀⠙⢿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⣸⣿⣿⡿⠟⠛⢿⠆⠀⠀⣸⣵⡇⠀⡇⠀⠀ ⡀⡿⣇⠀⠈⣿⡀⣇⠀⠀⠈⢧⠀⢿⣿⣿⣷⣶⣤⡀⠙⢦⠀⠹⣿⠿⠛⠉⢀⡤⠤⠶⠒⠛⠉⣁⣠⠄⢀⠟⠀⠀⣰⣿⡯⡇⢰⠀⠀⠀ ⠁⣷⠘⢆⠀⠘⣷⣸⡀⠀⠀⢸⡇⠸⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠘⠀⠀⠀⡼⠀⢀⣤⣶⣶⣿⣿⡷⢀⡎⠀⠀⠘⠋⠉⠀⡇⠈⠀⠀⠀ ⠤⠬⣤⣌⣳⣀⠈⠁⢣⣠⠴⣾⡇⠀⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⢠⡇⠀⣾⣿⣿⣿⣿⣿⢣⡞⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⡄⢀ ⠀⠀⠀⠀⠀⢩⠟⠢⢷⣧⣸⣿⣇⠀⢹⣿⣿⣿⣿⣿⠀⡟⠀⠀⠀⠀⠀⢸⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠒⠲⢄⡀⠀⡌⢀⣴⠋⢠⠎ ⣶⣶⣶⣶⣶⡞⠀⠀⠀⠀⢻⢻⣿⣦⡘⢿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⡸⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⢻⠗⠉⣀⣔⣁⣤

⠀⠔⠂⠈⠁⠀⠀⢀⢔⠕⠁⡠⠂⢑⡤⡂⠀⠆⢠⠀⢂⢄⠉⠐⠠⡀⠀⠀⠀ ⠊⠀⠀⣀⠄⢊⡕⡑⠁⣠⠎⢀⡾⠋⠀⠠⠀⢫⠄⠣⡀⠈⠢⡀⠙⡙⠂⠀⠀ ⣀⣠⠊⠁⣊⡜⡐⠀⡐⢃⠖⠋⠀⠀⣀⠀⢙⡢⠽⡦⡻⡳⡰⡈⠄⠸⣄⠀⠀ ⠀⠑⠲⣮⡟⢠⠁⠰⡐⠁⣀⣤⣤⣠⣀⠀⠉⠀⠀⠀⠺⡨⣺⣵⡇⢒⢞⠗⠂ ⣲⡴⠁⠠⡃⡀⢀⡇⠃⢰⠋⠁⣴⠾⡟⠇⠀⠀⠀⢀⢀⢀⠀⠈⣷⠘⠈⠇⠀ ⣿⡇⠀⠀⠈⠳⡚⢇⡀⢣⠀⠀⢏⣪⠅⠀⠀⠀⠀⡽⣿⠉⠳⣆⡿⢰⠀⠀⠀ ⠻⠢⡀⠀⠀⠀⠈⠐⢓⣄⠁⠐⠂⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⣏⡧⠂⠀⠀⠀ ⡀⠀⠈⠂⢄⠀⢠⠊⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢊⡜⠃⠀⠀⠀⠀ ⣿⣄⠀⠀⠀⠈⢁⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡸⠀⠀⠀⠀ ⢿⡁⣿⣷⡶⢦⣬⣆⣠⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡘⠀⠀⠀⠀⠀ ⠀⠀⠻⡏⡅⢸⢀⠀⠀⢁⠈⠲⣄⣀⠀⠀⠀⢀⢠⣴⠿⠿⡗⠀⠀⠀⠀⠀⠀ ⠁⠒⠠⣤⣓⣾⠀⠀⠀⢂⢷⡤⣈⠙⠛⠟⢭⡀⢸⡁⡀⠀⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣄⠁⠀⠈⣦⣦⠉⠀⠛⠀⠌⠄⠈⢧⠡⡀⠀⢒⡤⡀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣄⢄⠀⠈⢩⣱⣶⡠⡤⣀⣆⡀⠈⠳⣴⡀⢈⠅⠈⡆⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠒⠦⠟⡭⠇⠤⢿⣿⣆⠀⠉⣸⠠⣊⣎⣀⠃⠀⠀

⢸⣿⠁⡄⠀⠀⡽⠂⣠⣾⡇⠀⢀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⣈⠱⣌⠢⡀⠀⠀⠀⠀⠉⠉⢻⣍⠐⠒⠀ ⠀⡿⠀⠱⠀⢸⠀⣾⠋⠀⢠⣴⠟⠁⡀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡳⡌⠢⣀⣤⡤⠶⣶⡟⠈⢩⣷⣿ ⠀⡄⠀⠀⢃⡜⠀⠧⣠⡼⠟⠀⡠⠊⠁⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⢰⣾⣄⠀⠀⠈⢣⠀⠀⠀⠀⠀⡝⢾⣦⡙⢿⡀⢰⡟⢱⠀⣾⣿⣿ ⣦⡁⠀⠀⠀⡇⢠⡾⠋⠀⢀⠞⠁⠀⠀⠀⠀⢠⣾⠃⠹⣷⡀⠸⣿⣼⣿⠹⣄⣤⡀⠸⡇⠀⠀⢦⡄⠘⣾⣷⣙⣦⠈⠺⡇⢀⣷⠉⠟⣛ ⣜⡿⡟⢖⠂⣷⠟⠀⠀⢠⠋⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠙⣿⢦⣻⣿⢿⡄⠈⠻⣷⣤⣿⡀⠀⠘⣿⡄⢸⣿⢿⡄⠑⢄⠈⠻⣞⡶⠃⠀ ⠈⣧⢐⢨⡿⠃⠀⠀⣰⠇⠀⠀⠀⠀⣠⣾⠏⠀⡠⢔⣒⣶⡬⠀⠉⠉⠃⠁⠰⠶⢍⣙⣻⣵⣄⡀⠸⡇⠘⣿⣇⠹⣄⣘⣗⣀⣈⣁⣀⣀ ⠉⠉⢹⡟⠁⠀⠀⢠⠏⠀⠀⠀⢠⣿⡟⠁⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣄⣿⣼⣼⠸⡄⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⢀⡞⡰⠀⠀⠀⡾⠋⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠙⢿⣿⣿⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⣾⢁⠃⠀⢠⠂⡇⠀⣤⣤⡶⠶⠿⠶⢾⣽⡂⠀⠀⠀⠀⠀⢠⡿⠿⠛⠛⠳⢶⣤⣀⡈⢿⣿⡆⢸⡀⠀⢻⡄⣀⣀⣀⣀ ⡟⠀⠀⠀⠀⣼⡏⠈⠀⠀⢸⢰⣧⣾⠟⠁⠀⠀⢠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⠀⠈⢿⡤⢼⣿⡇⠸⡇⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠈⢸⣿⠇⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠃⠀⠀⠀⠘⡇⢸⡟⠀⠀⣿⠀⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⢸⠹⣆⠀⠀⠀⠀⠳⣍⡿⠇⠀⠀⠀⠀⠀⠀⠀⠳⠽⠿⠁⠀⠀⠀⣰⠇⣼⡇⠀⠀⠸⡄⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⠀⣼⣿⠀⢸⠀⠀⠀⢸⡀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠁⠀⣿⡇⠀⠀⠀⢧⠀⠀⠀⠈⢧⠀ ⠀⠀⠀⠀⣿⣿⠀⠈⡆⠀⢠⠈⡇⣀⣤⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⢲⢿⣿⠀⠀⠀⠸⡄⠀⠀⠀⠈⢣ ⢀⠀⠀⠀⢿⣿⠀⠀⡇⠀⢸⠀⢃⠙⠛⠋⠀⠀⠀⠀⣠⣶⣒⣒⣉⣉⣉⣙⣶⡆⠀⠀⠀⠀⠀⠈⢀⣞⣼⣿⡆⠀⠀⠀⢳⡀⠀⠀⢰⣦ ⡏⠀⠀⡀⠸⣿⡀⠀⢸⠀⠀⢇⠘⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⢶⡄⠀⠀⣠⣾⠻⣫⠏⣷⠀⠀⠀⠀⢳⡀⠀⡀⢿ ⣇⠀⢠⣿⡆⢻⡇⠀⠀⢇⠀⠘⡄⢹⣷⣤⡀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠋⢀⣠⣼⠬⢹⣠⣶⡿⢃⣴⣷⣾⣿⣇⠀⠀⠀⠀⠳⣠⠛⡼ ⠹⣆⠸⣿⡟⢦⣿⠀⠀⠘⡄⠀⠘⡄⢿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⣠⣴⡾⠋⠀⡏⠀⢸⠉⠙⠳⢿⠿⢻⡿⢻⣽⡀⠀⠀⠀⠀⠹⡀⠁ ⠀⠙⣆⠹⣷⠀⠉⢧⡀⠀⠱⡀⠀⠘⢎⣯⠛⢿⣿⠀⠙⠻⣷⣶⠞⠟⠁⢀⡴⢾⠁⠀⣼⠙⠲⢴⣈⡇⠈⠠⠿⠛⡇⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠙⠺⣧⡀⠈⢷⡀⠀⠙⢄⠀⠀⠻⣷⡞⠀⠑⠢⢤⣀⡿⠀⠀⠒⠁⢠⠇⠀⢠⣿⣄⣀⠀⢸⠙⠒⢦⠀⠀⢸⠀⠀⠀⠀⡀⢸⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⢈⣻⣦⡀⠸⣷⣀⠀⠈⠻⣆⡀⠀⠀⠀⢇⣀⠀⠀⠠⠊⠀⠀⣼⣷⣽⣿⣦⢸⣤⠤⣼⣀⡀⢸⠀⠀⡀⣿⢡⡿⠀ ⠀⠀⠀⠀⢀⣠⣶⡾⠿⠛⠋⠙⢶⡼⠿⠷⣦⣄⣀⣉⣳⠦⠀⣸⣿⡀⢠⠀⠀⠀⠀⣿⣿⣿⣿⣹⣯⠀⠀⡟⠉⢿⡾⠀⣰⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⡞⠛⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠙⣄⠀⠈⢆⠀⢠⣿⣷⣽⡞⠀⠀⠀⠀⠘⠉⠻⣿⡿⠏⠁⢸⠁⠀⢸⢇⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡈⢳⣤⣼⣧⡜⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⣸⠀⠀⢾⠟⠉⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠙⠈⣿⡟⢋⣧⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢱⣠⠇⠀⠀⣸⠀⠀⠀⠀⠙⣄⠀⠀

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⢸⠁⡀⠐⣣⠞⢀⡠⠖⠉⠀⠀⠀⠀⠀⢀⠀⠀⠉⠑⠢⢕⣕⢄⠀⢀⣉⡽⠅⣀ ⢨⠀⠠⠇⢁⡴⠋⡠⠊⠀⠀⡰⣇⠀⣀⢰⣆⠀⠐⡀⠀⠀⢝⡦⡙⢇⣼⢃⣼⣿ ⣳⡤⡄⡴⠋⢀⠎⠀⠀⢀⡼⠁⠘⡧⣹⡾⡌⠺⣄⣧⠀⢳⡌⣿⢞⠢⡙⢼⠬⠑ ⠼⢤⡞⠁⢀⠎⠀⢀⣤⠟⡠⠦⠐⠂⠈⠉⠀⠚⠋⠹⠧⡄⣇⡝⠋⢦⠙⠀⠁⠀ ⢀⡞⠀⠀⡜⠂⠀⡜⠁⠀⠀⡀⣀⠀⠀⠀⠀⢀⣠⣄⠀⠈⢻⣿⠸⠈⢆⠀⠀⠀ ⡞⠀⠀⣼⠙⠀⠀⣇⡴⠋⠉⣉⣙⠃⠀⠀⠀⢋⣭⡀⠉⠳⣄⡟⠀⡇⠈⢖⠒⠒ ⠀⠀⢠⡿⢠⠀⡇⣿⠀⠀⠰⡻⣿⠀⠀⠀⠀⢘⣿⡅⠀⠀⡇⡟⠀⢡⠀⠈⣆⠀ ⠀⠀⢸⡇⢸⠀⡇⡌⠣⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠊⢀⣷⠀⠘⡄⠀⠘⡄ ⠀⠀⢸⡇⠈⠀⠁⢇⠶⠇⠀⠀⣠⣤⣄⣀⣠⡄⠀⠀⠘⠛⣙⣿⡀⠀⠱⠀⠀⣌ ⡇⢠⡌⣧⠀⠃⠘⡘⣄⠀⠀⠀⠹⢿⣿⣿⡿⠁⡞⢆⢀⡴⢛⣏⣧⠀⠀⠡⢀⢼ ⢳⠸⡟⢜⡄⠘⡀⠑⡹⣿⣶⡤⣀⡀⢈⢡⠖⢉⠇⢸⡙⠲⡟⡿⣫⡄⠀⠀⠩⠊ ⠀⠑⠽⣄⠹⡄⠐⠄⠘⢧⡝⠃⠌⣙⠏⠡⠐⡙⠀⣬⣈⠑⠧⢤⠉⢁⠀⠀⡀⡇ ⠀⠀⠀⢀⣠⣼⡦⣘⣦⣄⠙⠠⢀⠀⣤⠀⠐⠁⢰⣷⣿⢦⠒⢺⢤⡘⠀⣼⡳⠃ ⠀⠀⠘⠋⠁⠀⠀⠈⠂⡈⢍⠉⢅⠰⣿⣧⡂⠀⠈⠛⠿⡟⠁⡆⠀⣧⡾⠋⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠲⢻⡿⣇⠘⣿⣷⡄⠀⠀⠀⠐⣠⠃⠈⠃⠀⠑⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣯⠵⠚⠉⠀⣠⠖⠉⠀⠀⣿⠁⣈⣷⠞⢛⣥⣶⢟⣭⣶⣿⢿⡇⠀⢀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⢉⣙⠓⠲⣤⣀⠀⠀⠀⠀⠘⠀⠠ ⠀⠀⠀⠀⢀⣠⡴⠶⠾⠛⠛⠉⠀⠀⠀⢀⡞⠁⠀⠀⢠⣾⡷⠟⣋⣤⠾⣿⣿⠷⠛⠓⠚⠉⠉⠁⢠⠞⠁⠀⠀⠀⠀⠀⣀⡤⠖⣮⠟⠊⠉⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀ ⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⢻⣶⡶⢞⣫⣵⢶⣫⣿⠞⠉⠁⠀⠀⢀⡔⠀⠀⠀⠀⠉⢄⡤⠴⠶⠖⠊⠉⠀⠐⠶⣤⡤⢖⣦⣌⠉⠉⠉⠉⠉⠒⠶⢭⣻⣷⡀⠀⠀ ⠛⠁⠀⠀⠀⠀⣀⠀⠤⠀⢀⣀⣶⠾⠶⠛⠛⠛⠛⠉⢁⣀⡠⠞⢁⡠⠄⠀⠀⡠⠋⠀⠀⢧⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠘⢯⣫⣄⣙⡛⢤⡀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀ ⠀⠀⠸⢤⡀⠙⠛⠛⠞⠚⠋⠉⠀⠀⢀⣀⡤⠴⣾⣿⠟⠋⢀⣴⡿⠃⠠⢶⠞⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⠀⠀⠀⠈⠳⣝⢏⠀⠀⠙⣆⠀⠀⠀⠀⠀⠈⠲⣌⢷ ⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⡤⠖⠚⠉⠁⢀⣼⣿⠃⠀⣤⣟⡭⠀⢀⣴⠏⠀⠀⠀⢠⠀⠀⠙⣦⡀⠀⠀⠀⠤⢤⣀⣀⣈⣉⣒⣢⡄⠀⠘⣎⢧⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠉⠀⠀⠀⠀⠀⢋⣾⡏⣠⣾⠟⢉⣠⠖⠋⡇⠀⠀⠀⠀⠈⣇⠀⠀⢸⣏⠓⠒⠒⠒⠋⠉⠁⣆⠀⠀⠀⠀⠀⠀⢸⡄⢇⠀⠀⢹⡆⠀⠀⠀⠀⠀⣠⠏ ⠀⠀⠀⠀⠀⢀⡴⠪⠀⠀⠀⠀⠀⠀⠀⢀⣿⢏⣴⣟⡵⠞⠉⠀⠀⠀⢧⡀⠀⠀⠀⣰⠿⡄⠀⠈⡏⢧⠀⠀⠀⠀⠀⠀⠈⠙⢶⡶⠤⠄⠀⠀⣷⠈⠀⠀⠀⢷⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⡠⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⢰⢻⡀⠙⠀⠀⢧⠈⠳⣄⡀⠀⠀⠲⣆⠀⠀⠙⠲⢤⡀⠀⢻⠀⠀⠀⠀⠘⡇⠀⢠⠞⠀⠀⠀ ⣲⣶⡦⢴⣶⣤⣤⣶⣮⡍⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣀⣤⡒⠒⠢⣄⠹⣜⣿⣆⠛⢦⣀⢦⣘⡄⠀⠈⠙⠳⡶⢦⠭⢷⣖⠦⠤⠖⠚⠓⠺⡆⠀⠀⠀⠀⢻⣤⠏⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢬⣳⡈⠙⠉⠀⠀⠈⠙⠛⠻⠆⠀⠀⠀⡇⠘⡆⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⡇⠀⠀⢸⠛⠢⣄⠀⠀⢠ ⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣼⢶⣭⢻⣟⠀⠸⣦⣀⡀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢹⠀⢹⡄⠀⠀⢠⠀⡘⡾⡄⡇⠀⡇⠀⠀⢸⠀⠀⠈⠹⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢀⣿⣿⣾⠿⠿⠿⠿⣾⣟⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠦⣌⣓⢄⣧⠀⣻⡀⠀⢸⡇⢿⢹⢿⠃⠀⡇⠀⢠⠞⠀⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⠤⢾⣿⠟⠁⠀⠀⠀⠀⠈⠙⠿⣾⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠮⢧⡇⠙⢦⡀⢇⣾⢸⡿⠀⢰⠁⡰⠋⠀⠀⠀⠀⢠⢇⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣠⢿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣦⣽⣷⡃⠀⠀⠀⠀⠀⢀⣠⡤⠴⠢⠤⢤⣀⠀⠀⠘⣧⠀⠀⠙⢾⣿⡟⠓⠦⣼⡞⠁⠀⠀⠀⠀⣠⠎⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣰⣟⡈⢿⡀⠀⠀⠀⠀⣼⢿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠠⢾⣶⣿⠿⠿⢿⣶⣦⣄⠀⠀⠈⠳⣼⢸⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣼⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⡇⢻⣎⢳⡄⠀⠀⠀⢿⣸⢿⣍⠃⠀⠀⠀⠀⠀⠀⠀⠾⢁⣀⣤⣀⠀⠀⠉⠻⣷⣤⣀⡀⢹⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢡⣾⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⡇⠈⣿⡄⠁⠐⠒⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣼⡄⠀⠀⠀⢻⣿⣄⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣰⣿⢿⣷⣄⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⢸⡟⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣛⠿⠀⠀⠀⠀⠈⣿⢁⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⣼⣿⣧⣰⣯⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠘⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣰⣿⣿⣤⣬⠽⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⣤⡤⠖⢫⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣾⣟⣛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢟⡽⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣽⠋⣀⣀⠤⠶⠖⠒⠒⢠⡞⣁⣾⣟⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⢛⡿⢸⠇⠀⠀⠀⠀⠀⠀⠻⣎⢷⡄⠀⠀⠀⠀⢾⣿⣦⣄⣉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢴⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⡻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠴⠛⠉⠉⠉⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠙⣦⡀⠀⠀⠈⠻⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣠⠾⠫⣀⡉⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠ ⠀⠀⠀⠀⠀⠀⣇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠙⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⡞⠙⢧⣀⡀⢀⣀⣤⠴⠚⣻⢱⣿⣿⡭⠆⡀⠀⠉⣙⠲⠶⠤⠤⠤⠒⠋⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠦⣙⠿⣶⣶⣶⣤⣴⣶⣶⣶⡾⠟⠻⢦⣟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⣿⣸⣹⣿⠖⣉⣵⣞⣋⣉⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠛⠾⠿⠿⣿⡿⠿⠻⡁⠀⢀⣰⣿⣿⣷⣶⠶⠶⠶⠦⠤⣤⣀⡀⠿⠙⠙⢻⡏⠅⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠘⠳⣄⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⡈⢣⡀⠀⠀⠀⣄⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣦⣤⣤⣤⣴⠶⠚⠉⠁⠈⠉⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡸⢻⠀⠀⠀⣾⢰⠛⢤⡀⢀⣀⣀⣤⣤⠤⠤⠒⢢⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣸⠘⣿⣷⣤⣈⣥⣴⣶⣶⣶⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠹⣧⣾⠀⠀⣸⣷⢿⣀⠰⡿⠋⠁⠀⠀⠀⣀⣀⣤⢾⣿⣿⣿⣿⣿⣿⡇⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⣀⡶⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠘⣿⢀⣴⣿⠃⠀⠉⠛⠛⢿⣿⣿⣿⡿⠟⠁⠀⠀⢿⣿⣿⡿⠏⠀⣇⡾⠃⠀⠀⠀⠀⠀⠀⠀⣼⣹⣠⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠴⠛⠒⠚⠉⠹⢣⡀⠀⠀⢀⣼⡁⠀⠀⢠⣿⠛⠋⢹⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠘⣿⠟⠀⠀⠀⡏⠀⠁⠀⠀⠀⠀⠀⠀⡰⣻⣣⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠤⠒⠂⠉⠉⠀⠀⠀⠀⠀⢀⠔⣫⠖⠉⠀⢀⠤⠒⢉⠀⣀⢾⠀⠀⢳⠀⢀⠀⠐⠢⢄⠈⠉⠁⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡔⢁⠎⠀⠀⣠⡴⠁⢀⣴⣿⠟⠁⢸⠀⠀⢀⢇⠈⢧⠀⠈⠲⢵⣄⠀⠀⠠⣀⣉⠢⡀⠀⠀⠀⠀ ⠊⠀⠀⠀⠀⠀⣀⡤⠖⢉⣤⠋⡰⠃⠀⢀⣴⠟⠀⢐⣟⠟⠁⠀⠀⠘⡄⠀⠈⣎⢆⠈⢣⡀⠀⠀⠙⢧⡀⠀⠈⢢⡉⠻⠄⠀⠀⠀ ⠀⠀⠀⣀⡴⠚⠁⡠⠖⣹⠃⡜⠁⠀⢠⡾⠃⣀⣴⠟⠁⠀⠀⠀⠀⠀⠘⢦⡀⠈⢶⣦⡀⢻⣮⣧⡠⣄⠙⢦⠀⠀⠱⡀⠀⠀⠀⠀ ⢄⣀⣾⠏⠀⠀⢈⣠⣴⠃⠰⠁⠀⢠⠛⢁⡨⠛⠁⠀⠀⠀⠀⢤⢤⠠⠤⢀⣉⠑⠺⠿⠻⣌⡟⢌⠳⡈⢦⢠⡃⠀⠘⢿⡄⠀⠀⠀ ⠀⠈⠳⢤⣤⣶⣛⣽⠃⠀⠇⠀⢀⠇⡔⠁⠀⠀⢀⠀⢀⣀⡀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⢠⡥⣀⡑⢿⣌⢲⣿⠀⢤⣤⠽⣶⠦⡀ ⠀⠀⠀⣀⡽⠿⢿⡇⠀⡘⠀⠀⡎⢸⠀⠀⠀⣤⣼⠿⠿⠷⣾⣭⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠬⠦⠽⣿⣿⠀⠸⡌⢧⣹⠀⠀ ⢹⣦⣤⠃⠀⠀⣸⠀⢀⡇⠀⢰⡇⡜⠀⢠⡿⠋⠀⠀⣠⣾⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢻⡇⠀⡇⠈⠿⠀⠀ ⣿⣿⡏⠀⠀⠀⠈⠢⣸⠀⣀⣿⡆⡇⠀⢸⠃⠀⠀⠀⡿⣯⣠⢿⠇⠀⠀⠀⠀⠀⠀⠠⣿⣷⡾⠶⣯⣄⡀⠀⢸⡇⠀⡇⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⢄⠈⠣⣧⠀⠸⣆⠀⠀⠀⠳⠤⠽⠞⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⣿⡆⠀⠙⣿⣭⣿⠇⢀⠃⠀⠀⠀⠀ ⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣽⣄⠀⠈⠓⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢻⡭⠀⠀⠀⢸⣏⡿⢠⠏⠀⠀⠀⠀⠀ ⠀⢹⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡼⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠑⠦⡀⠀⠀⠀⡴⠋⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠴⠛⢄⡟⢱⠀⠀⠀⠀⠀⠀⠀ ⣷⣾⠀⠀⠀⠀⠀⠈⠑⠢⢴⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⢹⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡏⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⠋⢸⣿⣷⣶⣤⣤⣀⡀⠱⡀⠀⢠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣿⠅⡻⠁⠀⠀⠀⠀⠀⠀⠀ ⠙⠿⠀⣿⣿⣿⣿⡟⠉⢻⢿⠛⠓⠚⠛⣧⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡏⠀⠇⠀⡇⠸⠀⠀⠀⠀⠸⡀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⢿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢄⣀⡀⠀⠈⠸⢄⡀⣣⠀⠁⠀⠀⠐⡄⢳⣄⡀⠀⠙⠿⣿⣶⣦⣤⡤⠔⠒⠉⠩⣿⠋⡇⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⣯⣭⣽⣿⠀⠠⠀⠀⠀⠸⡄⢻⠿⣦⠤⢀⡀⠉⢩⠏⠉⠓⣦⠀⠀⣿⠀⢧⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡻⢿⣿⡄⠀⠃⠀⠀⠀⢻⣆⡳⣌⠉⠓⠒⠨⠍⣀⡀⠀⣇⠀⠀⢻⣆⠈⣆⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢿⣿⣟⣃⠀⠀⠀⠀⠀⠈⠉⠚⡆⠀⠈⢿⣦⡈⢆⠀⠀⠀⢰⣏⠑⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡐⢤⡀⠀⠀⠀⠳⡄⢙⣿⣷⡒⢦⣤⣀⣀⣸⡁⠀⠀⠀⠙⢿⣦⣦⠀⠀⢸⣾⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣷⣤⣀⢀⡀⠘⣽⡟⠻⢿⠀⠈⢸⣿⣿⣿⡓⠒⠒⠂⠤⢽⣿⠀⠀⣾⣼⠄⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠙⠓⠳⢉⡶⠾⠤⠐⠚⣿⣿⣿⣿⡄⠀⠀⠀⣠⡯⠴⢮⣴⣏⣀⣤⠎⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠒⠂⠠⠤⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡚⠉⢀⣆⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⢊⣠⣴⠋⠹⡤⢠⠘⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⠀⠀⠠⣆⠀⢠⠊⣴⢀⣖⣽⠡⢤⡀⠙⠌⣧⣣⣂⢀⠀⡀⢀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⡠⠀⣰⠁⣜⠆⡞⠁⠀⠀⡀⠀⠀⠀⠀⠈⠉⠻⣄⢁⢸⠘⡀⢡⠈ ⠀⠀⠀⠀⠀⠀⣰⡏⠰⡜⢸⣭⠋⠉⣉⡪⠀⠀⠀⠖⠛⠑⠲⡬⢿⠀⡇⠃⠈⠀ ⠀⠀⠀⠀⠀⡰⡟⢀⢳⠇⡇⡇⠀⠸⣿⠇⠀⠀⠀⠀⣿⠗⠀⢹⢼⢀⡇⢰⠀⠇ ⠀⠀⠀⠀⢠⢡⠁⡾⢸⢠⡇⠘⠠⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠜⢸⢸⠁⢸⣦⡆ ⠀⠀⠀⠀⡎⣸⢸⡇⡿⢸⡇⠀⠀⣀⡀⣀⣀⣀⡀⠀⡀⠠⠀⠀⡈⡘⠀⢺⣿⠇ ⠀⠀⠀⠀⠃⠇⣿⡇⢱⠸⡿⠦⠄⡿⢷⣶⣦⣤⣤⡶⠎⠀⠀⣠⢣⠃⠸⢸⣿⠀ ⢉⡓⠤⠀⠘⣰⠘⡆⡀⠊⢀⢴⡾⠥⢤⡀⠀⠀⢀⡀⠄⠀⣿⠏⠎⢀⠇⡞⡏⣼ ⠨⡩⢯⡻⢦⡹⠀⡛⠀⡰⠋⠁⣠⠴⠾⡟⠗⢋⣁⣠⣤⣴⢏⠊⢀⠆⡰⢰⣼⡗ ⠀⠀⠑⢌⢳⠹⣴⠃⠐⠁⠀⠞⠁⢀⣴⠁⢀⣾⣿⣿⠟⡱⠁⠠⠂⡠⢁⣽⡫⠔ ⠀⠀⠀⠈⠂⣨⠟⠀⠀⠀⠀⠓⠊⢁⡉⠀⣸⣿⣿⣛⣉⡀⣔⣁⣴⣷⣦⢄⠀⠀ ⠀⠀⠀⠀⠰⣷⣇⠀⠀⠀⠀⠀⣠⣾⣷⣾⣿⣿⠟⢠⣿⣿⡿⠡⠒⠒⠈⠩⣧⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⡁⠀⠀⠈⠻⣦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠃⠻⣿⣄⠐⢦⡄⣜⡻⣦⡀⠉⠺⢷⡦⣒⠦⣄⠀⠀⠀⠀⠠⡄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⣰⢀⠟⢿⣦⣄⡻⣾⣟⠺⢍⡉⠻⣦⠽⣿⣿⡾⢷⣄⠀⠀⠀⠈⢢⡀⠀⠀⠘⢆⠀⠀⢳⣄⠀⠀⠀⠀⢙⠲⢄⠀ ⠀⠀⠀⠀⣰⠃⠀⢀⣿⢸⠀⠀⠉⠺⢿⣿⡛⠳⠀⠈⣉⠿⢳⠆⠈⠉⠓⠾⣦⠀⠀⠀⠀⠙⢦⡀⠀⠈⢣⠀⠀⠙⢷⡄⠨⣷⣾⠛⣮⡳ ⠀⠀⠀⢰⠇⠀⠀⣼⡏⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⡜⠁⡠⠋⠀⠀⠀⠀⣀⠈⢧⠀⠀⠀⠀⠀⠱⣄⠀⠀⢇⠀⠀⠱⣿⣧⡸⣮⡉⠺⠣ ⠀⠀⠀⡏⠀⠀⠀⣿⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣤⣦⠶⠒⠛⠳⢶⣾⣣⠀⠀⠀⠀⠀⠘⢦⠀⠘⡆⠀⠀⠘⢿⣷⣌⠁⠀⠀ ⠀⠀⢸⠃⠀⠀⢀⣿⠃⠀⣠⠔⠋⠉⣲⠄⠀⠀⠀⠀⠀⣾⠟⠀⢀⣴⣤⡀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠈⢳⡶⢿⡀⠀⠀⠈⠛⠮⠆⠀⠀ ⠀⠀⡏⠀⢀⡄⢸⡇⠀⠀⠉⠈⠉⢉⣀⣀⣀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣇⠀⠀⠈⡿⢧⠀⡄⠀⠀⠀⠀⢻⠓⠟⣆⠀⠀⢰⡀⠀⠀⠀ ⠀⢰⠃⠄⡼⠀⢸⡁⠀⠀⠀⣀⡤⠗⠚⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⢀⠇⠈⢧⠘⣶⠀⠀⠀⠀⢣⣠⢸⡄⠀⠀⢣⠀⠀⠀ ⠀⡼⢼⣰⠇⠀⣼⡇⠀⢀⣼⠋⠀⠀⠀⢴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣯⣿⣧⣿⡆⠀⠀⠀⠀⢧⡸⠁⠀⠀⠘⣷⠀⠀ ⢠⠇⠞⢻⢀⣦⣿⠘⡄⢠⣿⠀⠀⠀⠀⠘⢿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢻⠀⠀ ⡞⠀⠀⢸⡞⢸⣿⠀⠹⡌⢿⡄⠀⠀⠀⠀⠀⠉⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⣿⣿⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀ ⠁⠀⠀⢸⡇⢼⡇⠀⠀⣿⡄⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣼⣿⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣾⠀⠀ ⠀⠀⠀⢸⠀⢹⠇⠀⢠⣿⣿⣆⠀⣨⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿⠀⠀⠀⠀⠀⢸⠀⡰⢿⠟⡏⠀⠔ ⠀⠀⠀⠸⡀⢸⠀⠀⣸⣿⣿⣿⡶⠿⠟⠁⠀⠀⠀⠀⠀⠰⠧⠶⠛⠁⠀⠀⠀⠀⠀⠀⣴⠟⠀⢸⡿⠀⠀⠀⠀⠀⣼⣾⠷⠋⠐⠃⠀⠐ ⠀⠀⠀⠀⢇⢸⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⢸⡇⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣾⡀⣿⢹⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠀⠀⢀⣾⠀⡾⠀⠀⢀⡞⠀⠀⠀⠀⢀⡠⠄⠒ ⠀⠀⠀⠀⠀⠘⣷⣧⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣶⣶⣾⣿⡿⠿⠿⠁⢀⡴⢻⣇⣼⠃⠀⢠⡾⠷⠔⣶⠖⠋⠁⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠘⣿⡟⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⡄⠀⠀⣠⠖⠁⢠⡾⡿⠃⣀⠴⣟⣁⠔⣩⠏⠀⠀⠀⠀⠀⠀ ⠢⡘⣦⡀⠀⠀⠀⠈⢣⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠘⡍⠙⢲⡼⣷⡄⠒⢉⠼⠥⠊⢁⡜⠁⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⡿⠓⢤⣀⣀⣀⣈⡷⠆⠀⠀⠉⠙⠛⠛⠿⠿⠿⠛⠀⠀⠀⢠⡇⢀⠾⠀⠈⡏⠢⡀⠀⠀⢠⠎⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠢⣈⣳⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡇⡎⠀⡇⠀⢣⢀⡙⢦⣠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢠⡟⠀⣀⣧⣴⡾⠛⠁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⠁⠀⢟⠁⣸⡤⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⣠⣼⢾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣤⠤⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⠶⠊⠁⠀⠀⣠⠴⠊⢉⠄⠀⣠⡞⠀⠀⠘⡆⠀⠀⠀⠀⠐⢦⣄⠈⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⠁⠀⠀⢀⣴⠚⠁⠀⡴⣫⢶⠞⠁⡇⠀⠀⠀⢱⡀⠘⣧⠀⠀⠠⣌⡓⢄⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀ ⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢩⡿⠁⡴⠃⠀⠀⠀⣴⡿⠁⠀⡠⣮⢞⡵⠋⠀⠀⣇⠀⠀⠀⣆⢳⠀⠘⣧⠀⠀⠀⠉⠺⣷⡄⠀⠀⠈⠲⡶⠦⣝⣦⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⣀⣴⠏⢀⡞⠀⠀⠀⣠⣿⠟⠀⠀⣨⢞⠕⠉⠀⠀⠀⠀⠸⡄⠀⠀⠸⣆⢷⡀⠈⢳⡄⢀⡀⠀⠈⠙⣄⠀⠀⠀⠙⢦⠀⠙⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡴⠛⠁⢀⡴⠞⣽⠏⢀⠎⠀⠀⠀⣴⡻⠁⢀⣠⣾⠗⠉⠀⠀⠀⠀⠀⠀⠀⠙⢴⣄⠀⠘⣦⡱⣄⠀⢻⣦⡹⣔⠢⡀⠈⠳⣄⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣴⡿⠋⠀⠀⠐⠋⢀⣴⠃⠀⡞⠀⠀⠀⡼⡽⠃⢀⣮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣌⣿⡺⣧⡈⡿⣍⠺⢧⠙⢦⠀⠘⢆⠀⠀⢦⣷⡀⠀⠀⠀⠀ ⠙⠲⣼⡟⠁⠀⠀⢀⣴⣾⣿⠇⠀⡸⠀⠀⠀⡼⠁⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢍⣉⣉⣲⡶⠀⠀⠉⠉⠈⠻⣽⠈⠳⣌⢧⡈⣧⠹⣮⠀⠀⠀⠙⣿⣄⠀⠀⠀ ⠀⠀⠀⠙⢶⣴⣿⢟⣚⣴⠏⠀⢠⠇⠀⠀⣰⠁⡼⠁⠀⠀⠀⠠⣀⠀⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠦⣀⡈⠳⣷⡈⣾⢿⠃⠘⡶⢶⡶⢾⡿⠷⠄ ⠀⠀⠀⠀⢀⣈⣻⡾⣿⡟⠀⠀⡿⠀⠀⢠⡏⢸⠇⠀⠀⠠⣤⣤⣼⡿⠿⠿⣶⣦⣭⣛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠬⣳⣜⢿⣾⣟⡆⠀⢹⡄⢳⣄⡇⠀⠀ ⠲⣄⠀⢀⡏⠁⠀⠀⢰⡇⠀⢰⠁⠀⠀⣼⠁⡸⠀⠀⢐⣾⡿⠉⠁⠀⠀⣠⣶⣾⣭⡟⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠸⡇⠀⢻⡇⠀⠀ ⣸⣿⣿⡾⠁⠀⠀⠀⢾⡀⠐⢸⠀⠀⢀⣿⠀⡇⠀⠀⣼⠟⠀⠀⠀⠀⣾⣿⡟⠛⣷⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣒⣒⠢⢤⠀⠀⠀⠀⢸⢀⠀⠀⡇⠀⠈⠁⠀⠀ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⠙⢦⣞⣀⣀⣼⣽⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⡿⠿⣤⡞⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣛⡛⠿⢿⣶⣄⣀⠀⢸⣾⠀⢠⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⠙⢦⢧⠀⠀⢻⡄⠀⠀⠀⠀⠹⢦⣀⣹⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠻⣿⣿⠀⠀⠉⢿⣯⣉⣼⡇⠀⢸⠇⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣈⢻⣄⠀⠀⠛⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣛⡏⠀⠀⠀⠀⣿⠂⣿⠇⢠⠏⠀⠀⠀⠀⠀⠀ ⠙⢻⡏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⢦⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠴⠛⠁⠀⠀⠀⠀⣿⢰⣿⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⣦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢄⡀⠀⠀⠀⠀⣼⠋⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠛⢡⣰⠏⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣼⡇⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠛⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣴⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⡴⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⢰⣿⣿⣿⣶⣶⣤⣤⣀⡀⠈⢧⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢧⠊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣇⠀⣾⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⠾⠷⠶⠿⢿⡇⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⢿⣿⣿⡿⠋⡹⠀⠀⡏⠉⡇⠀⠀⠀⠀⠈⢇⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣟⡏⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣇⢠⡇⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⢻⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡟⠿⠛⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⣤⣤⣀⠀⠀⠀⠈⠸⢧⣀⠀⣇⠀⠉⠀⠀⠀⠀⢣⡀⢻⢦⡀⠀⠀⠉⠻⣿⣿⣿⣶⣶⣦⠴⠖⠒⠋⠉⠀⣿⣿⠉⡇⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠻⣖⣶⡞⢛⣋⣭⣿⠀⠀⡄⠀⠀⠀⠈⢣⠀⢷⢯⡳⢤⣀⠀⠀⠉⠉⠉⣹⠋⠙⠷⢶⡄⠀⠀⣿⣇⠀⣧⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⢿⣿⣿⣿⠀⠀⠸⡄⠀⠀⠀⠸⣷⡈⢧⡈⢳⠮⢍⣑⡒⠶⠶⠟⠀⠀⠀⢸⠃⠀⠀⢸⣿⠀⠹⡄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣝⡿⣿⣇⠀⠀⠁⠀⠀⠀⠀⠸⣷⣤⣙⣦⡄⠀⠀⠀⠉⠓⠒⠤⠤⣀⡘⣆⠀⠀⠈⣿⣇⠀⢳⡄⠀⠀⠀⠀⠙⠳⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣽⣕⡄⠀⠀⠀⠀⠀⠀⢻⡻⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡆⠀⠀⠈⢿⣷⣄⠙⣄⠀⠀⠀⠀⢻⣷⠈⠓⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣎⠢⣤⠀⠀⠀⠀⠀⠻⢤⡉⠩⣽⣶⡶⠦⣤⣄⡀⠀⠀⠀⡞⠁⠀⠀⠀⠈⠳⣝⢷⡌⣇⠀⠀⠀⢸⣌⡇⠀⠈⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡈⢳⡀⠀⠀⠀⠀⠈⢳⢸⣿⣿⣿⣷⠬⠑⠊⣿⣿⣾⡿⣶⢤⣄⣀⣀⣀⡈⠳⣷⢹⡄⠀⠀⣼⠘⡆⠀⠀⢘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⠦⣄⣦⣄⡀⣟⢯⡀⠈⢩⠇⠀⠀⢸⣿⣿⡿⣿⣦⠀⠀⠀⠀⠉⠛⠺⢿⠀⢀⡼⠻⣇⠇⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠉⠉⡻⢆⣨⡽⠓⠒⠒⠛⠋⣻⣶⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⡯⠖⠻⣤⡼⢭⠤⢤⡴⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡡⠖⠁⠀⢀⣴⡟⢿⡄⠆⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⠜⠁⡄⣴⣵⡿⠋⠀⠘⢿⡘⡄⣆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⢀⡔⠁⢠⠎⢀⣾⡾⣻⣏⣀⣀⠀⠀⠈⠻⡀⢹⣦⠸⣆⢣⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⢠⠏⠀⣰⢫⠁⣼⣿⠞⠓⠒⠉⠓⠛⠆⠀⠀⠈⠺⠿⠷⢿⣦⣧⠸⡀⠀⠇⠀⠘⡀⡆⠀⠀⡄⠀⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠏⠀⣰⢣⠇⣸⠟⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣷⡀⢸⠀⠀⡇⠸⡀⠀⢰⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⣰⣯⠃⢰⢣⡟⢀⡟⢠⣶⡶⠖⠲⢮⣝⠢⡀⠀⠀⠀⠀⣠⣤⣶⣦⣄⡀⠈⢷⣬⡇⠀⣷⠀⢧⠀⠀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⢀⡏⣾⠁⣼⣷⡞⠁⠀⠀⣠⣤⡌⠃⠀⠀⠀⠀⠰⠟⠉⢀⡀⠈⠙⢷⡞⢻⡇⠀⣿⠀⢸⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⡸⢸⡏⢀⡿⢸⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠈⣿⡀⡇⠀⣿⠀⠈⡄⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡿⠀⣰⡇⣼⠃⢸⣇⠸⣆⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⣸⠉⡇⠀⣿⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠇⢰⢻⠀⡿⠀⣼⣷⠀⠋⠢⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡇⢰⡏⠀⠀⣷⣶⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⣾⠀⡾⡎⢠⡇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⠇⢸⠃⠀⡀⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏⢸⡇⡇⢸⡇⠀⣿⣇⠀⠀⠀⢠⣤⣤⠤⣀⣀⣀⣀⣠⠤⠤⠤⢤⡀⠀⠊⠀⠀⠀⣸⠀⡾⠀⢠⠀⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⢸⡇⣘⣿⡇⠘⡇⠀⣿⣿⣦⠀⣀⣸⣿⣿⣶⣤⣤⣤⣀⣀⣀⣀⣤⣴⠇⠀⠀⠀⠀⢀⡇⢰⠃⠀⡘⠀⣿⣿⡇⠀ ⣤⣄⡀⠀⠀⠀⠀⢱⠘⣇⣿⣿⠁⠀⠧⢀⡽⠛⠉⠉⠱⣤⠏⠉⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⢀⣠⣶⡿⢀⡏⠀⢀⠇⢠⣿⣿⠀⢀ ⣀⠉⠻⢶⡄⠀⠀⠈⡆⣿⡇⢻⡇⢀⠴⠋⠀⠀⣠⣶⣾⣿⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢁⣿⣿⠃⡜⠀⠀⡸⠀⡼⠛⡏⢠⣟ ⠘⠿⠓⢶⠦⣴⣦⡀⠘⣿⠇⠀⣧⠏⠀⠀⣴⣻⠗⠋⠁⠀⠀⣀⢽⣷⣤⣤⣤⡤⠖⠋⠁⠀⠀⠀⣸⣽⠃⡜⠀⠀⣰⠁⢠⠇⡸⢠⣿⢯ ⠙⠲⢄⠺⣷⣌⠛⢿⣦⣹⠇⠀⡟⠀⠀⣸⠟⠁⠀⢀⣤⡶⠿⠟⠻⣯⠙⠋⠁⣀⣤⣤⣶⣶⣶⣶⡿⢡⠎⠀⠀⡰⠁⢀⡏⢰⣷⣿⡿⠃ ⠀⠀⠀⠙⠢⡈⠙⢦⠈⢻⣦⣾⠇⠀⠠⠃⠀⠀⣠⡟⠉⠀⠀⢀⣴⠟⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⡴⠁⠀⠀⡜⠀⠀⡜⠀⢋⣽⠟⣀⡴ ⠀⠀⠀⠀⠀⠈⡆⠈⡇⢹⣯⡟⠀⠀⠀⠀⠀⠐⢉⠀⠀⣠⠴⢿⡟⠀⠀⢠⣿⣿⣿⣿⣿⢛⣡⠜⠁⠀⣠⠎⠀⢀⡞⠀⠰⠿⠵⠚⠉⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⡇⣬⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠻⠁⠀⢀⡇⠀⠀⣼⣿⣿⣿⣛⠛⠉⠀⠀⣠⠞⠁⣀⣴⣿⣿⣷⡲⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣀⣀⣴⣿⣿⣿⣿⡿⠛⢻⣿⣿⣶⣿⡿⠛⠛⠛⠛⠛⠻⠦⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰⣿⣿⣿⣿⡟⠀⠎⠁⠀⠀⠀⠈⠁⢺⣿⡀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⣞⡯⠖⠋⢀⡴⠊⠁⢀⣟⣠⡽⢛⣩⣶⣿⡵⣿⣿⠇⢀⡴⠋⠁⠀⠀⠀⠀⢀⣠⢖⣉⠉⠉⠒⠦⢄⡀⠀⠀⠀⠐ ⠀⠀⣠⠴⠚⠉⠉⠁⠀⠀⠀⢀⢮⣀⣀⡴⣟⣫⣵⣾⠿⠛⠋⠁⡀⠀⠀⠀⠎⠀⣀⣀⡠⠔⠒⣉⡛⢁⣀⡠⠄⠤⠤⠤⣀⣨⢷⣄⠀⠀ ⠖⠉⠀⠀⠀⠀⠀⠀⠀⣤⣬⡵⠶⠿⠓⠛⠉⣩⠟⢁⠀⠀⢀⠎⠀⢠⠀⠀⠈⠛⢄⡀⠀⠀⠀⠀⠹⣷⣏⠛⠦⣀⠀⠀⠀⠈⠙⠻⣄⠀ ⠀⠀⠢⣄⣙⣛⡓⠊⠉⠀⣀⡠⠤⢶⣾⠟⠉⣠⡾⠃⠐⡾⠁⠀⠀⠀⢆⠀⠀⠀⠀⠈⠒⠤⢄⡀⠀⠈⢻⣯⠀⠈⢣⠀⠀⠀⠀⠈⠮⣳ ⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⢠⣾⡏⢀⣾⠟⢂⡠⡞⠀⠀⠀⢰⠀⠈⢷⢤⣀⣀⡐⠶⠖⠒⠚⠛⠂⠀⢹⢣⠀⠀⢧⠀⠀⠀⠀⠀⡹ ⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⣰⡟⣴⣯⠴⠊⠁⠀⣇⠀⠀⠀⡼⣆⠀⢸⢧⠀⠀⠀⠀⠀⠑⢦⡤⠀⠀⠀⡇⠃⠀⠘⡆⠀⠀⢀⠜⠀ ⠀⠀⠠⠔⠃⠀⠀⠀⠀⠀⠀⠀⣿⡾⠋⠀⠀⠀⠀⠀⠈⢦⢀⣸⢧⡘⠀⠸⡄⠳⣄⡀⠀⠰⣄⠀⠙⠢⢄⡀⢳⠀⠀⠀⢹⡀⢠⠊⠀⠀ ⣿⣿⣾⣿⣶⣿⣿⣦⡀⠀⠀⠀⣸⠁⠀⠀⠀⠐⠦⠍⣑⢢⡙⠿⠆⠙⠲⢷⣷⡀⠀⠈⡏⢳⠛⠛⠃⠈⠉⡉⢹⠀⠀⠀⠈⣷⣃⠀⠀⠀ ⠿⠿⠿⠟⠛⠋⠉⠉⠉⣹⣟⡿⣿⠀⢠⡀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⠀⢇⠀⠀⢀⠀⢷⢸⠀⢸⠀⠀⡇⠈⠑⢤⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠿⠃⣽⣷⡾⠛⠛⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠚⠛⠩⢕⣦⣧⢈⣆⠀⢸⠘⢻⣿⠀⡌⠀⡰⠃⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢟⠒⠒⢺⣿⠋⠀⠀⠀⠀⠀⡙⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⢿⠈⠳⣌⣿⣿⣇⠀⣇⠜⠀⠀⠀⢀⢎⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡏⢿⡀⠀⠀⠀⣰⣿⣿⡿⠟⠀⠀⠀⠀⣴⣾⣯⣭⣭⣥⣀⠀⠈⠦⣠⢈⢹⠏⠀⠉⠁⠀⠀⠀⢠⢊⣾⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⣿⠙⣮⢳⡀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠘⢉⣤⣄⠀⠉⠻⣷⣄⣀⣹⣸⠃⠀⠀⠀⠀⠀⠀⡰⢡⣾⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⢹⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠆⠀⠀⢹⡷⢦⡟⠁⠀⠀⠀⠀⠀⢀⠞⣴⡿⢻⣷⣌ ⠀⠀⠀⠀⠀⠀⠀⣠⠏⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠊⠀⠀⠀⣸⣷⠏⠀⠀⠀⠀⠀⠀⡰⢣⣾⣟⣛⣻⠿⠛ ⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⢲⠟⠁⠀⠀⠀⠀⠀⡠⢊⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡟⡟⠀⠀⠀⠀⢻⡷⡄⠀⠀⠀⠀⣤⡒⠢⢄⠀⠀⠀⠀⠀⠀⠀⢰⠋⣰⣋⠤⠐⠒⠈⠉⠀⣎⣴⣿⠟⠃⠀⠀⠀⠀⠀⠀ ⣀⡠⠖⠋⢸⠁⡇⠀⠀⠀⠀⠀⠳⡝⢦⡀⠀⠀⠻⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀⠈⣹⠋⠀⠀⠀⠀⠀⢀⡼⠛⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢸⡀⢇⠀⠀⠀⠀⠀⠀⠙⡌⢿⣦⡀⠀⠀⠉⠁⠀⠀⠀⠀⣀⡤⣶⠛⢇⣀⣀⣀⡤⠴⣚⣹⣶⡿⢄⠀⠉⡓⠦⠤⠤⠤⠒⠁ ⠀⠀⠀⠀⠀⢧⠘⢆⠀⠀⠀⠀⠀⠀⠘⢆⠓⢽⣻⣶⣶⣶⣶⣶⠿⠋⠙⣾⣏⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣥⠶⠯⠅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣬⡀⠠⣄⠀⠀⠀⠀⠈⢆⠀⠈⠉⠉⠛⠉⠀⠀⠀⣼⣿⣿⣿⡉⠉⠉⠉⠓⠲⢥⡀⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠱⡄⠀⠀⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⢳⣶⣤⣤⣄⣠⣤⠶⠚⠉⠙⢒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣧⢹⠀⠀⣼⡸⠑⣤⡤⠤⠤⠤⠒⠂⢒⣿⣿⣿⣿⣿⠀⢀⡄⠀⠀⠀⠀⠀⣿⠹⣿⣶⣤⣶⣶⣿⣿⣿⣿ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⡏⠀⠙⣿⠀⣰⡟⠙⠦⠿⣥⣤⣤⣤⡴⠒⠋⢿⣿⣿⡿⢻⢠⡞⠀⠀⠀⠀⠀⠀⣿⢠⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠴⠚⠻⠛⢶⡄⠀⠀⢠⡇⠀⠀⣼⠛⠛⣇⠀⠀⠀⠈⠉⢉⣉⣀⠀⠀⠘⡿⠋⠀⢘⡏⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣰⢊⣄⢀⡙⢦⡀⠄⡀⡀⣀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠙⠢⢄⠀⠀⠀ ⠀⠀⠀⡜⠁⡄⠺⢦⣝⣽⡻⢄⣲⡹⢷⣷⢄⠀⠈⠢⡀⠈⢂⠀⢢⡀⢀⠉⡢⣄ ⠀⠀⡜⠀⢸⠻⠀⠀⠉⠓⠉⠠⢊⠝⠀⠀⢉⢂⠀⠀⠘⢄⠀⢃⠀⢹⣦⢻⡉⠯ ⠀⢠⠁⠀⣼⠃⢀⠠⢀⡀⠀⠈⢁⡴⠒⣉⠑⠺⣧⠀⠀⠀⠣⣀⡆⠀⠙⢗⡁⠀ ⠀⡌⢀⠀⡏⠀⠑⢂⢈⡀⠀⠀⠈⠁⠸⣿⡇⠀⢹⢣⢀⠀⠀⠱⡫⢆⠀⢂⠀⠀ ⢀⢳⡌⢀⡇⢀⡴⠋⠁⣤⣦⠀⠀⠀⠀⠀⠁⠀⢬⣤⣦⣥⠀⠀⠱⡸⠀⠀⣄⠀ ⡘⠈⣧⢾⠛⡠⡇⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⡀⠘⣾⠀⠀⠀⠃⠀⠀⢸⠀ ⠁⠀⡇⣾⠀⢰⡝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⠀⠀⠀⢸⠀⣀⡼⠀ ⠀⠀⡇⡌⠀⣿⣿⣤⡾⠀⠀⠀⠀⠄⠤⠂⠀⠀⠀⣠⠎⢸⠀⠀⠀⣸⡮⠍⠇⠨ ⠀⠀⠠⡇⣰⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⡞⢀⠀⢀⠋⠀⠀⠀⢀ ⠀⠀⠀⠻⣯⡿⢿⣿⣿⣿⣷⣶⣦⣤⣤⣶⠾⠟⠏⡠⢲⣣⠇⢀⠞⢀⡖⠂⠁⠀ ⢄⢄⠀⠀⠙⡁⠈⢿⣿⣿⣿⣿⣿⣿⠛⢛⠣⣤⣎⠠⣪⠣⢂⠍⢊⠊⠀⠀⠀⠀ ⠀⠙⢇⢢⣤⠈⠓⠀⠈⠉⠉⠛⠋⠀⢀⢼⠰⠃⢸⠑⢄⢠⠊⠰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⢀⠜⠁⢸⠁⡰⠴⠛⣨⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣀⣦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠤⠶⠙⠈⡠⠊⣀⡯⣞⣭⠾⠿⠟⠃⠔⠁⠀⣀⢠⠴⠉⠉⡁⠂⠄⡀⠀ ⠀⠉⢀⣀⢀⡠⠦⠟⢛⣛⠩⣋⠀⡠⠂⠀⠀⠐⠍⡁⠀⠉⢾⣓⠦⡀⠈⠁⠳⣄ ⠀⠈⠒⠒⡀⠄⠒⢨⡿⢡⠾⣁⡜⠀⢠⠈⢄⣀⣀⡬⠤⠦⠄⠹⠄⠐⡀⠀⠀⢸ ⠀⠀⡠⠊⠀⠀⠀⣼⡵⠕⠈⠀⢂⠀⣰⠆⢸⢂⠀⠀⡈⠲⣂⠀⡎⠀⢱⠀⡠⠁ ⣶⣶⣶⣶⣤⣀⣀⣹⠀⠀⠐⠦⢂⡛⠏⠒⠦⠆⠉⠒⠞⠒⠒⢅⠁⠀⠀⡖⡀⢀ ⠉⠉⠁⠀⠀⣼⡿⣻⡼⠶⢤⣤⡀⠀⠀⠀⠀⠴⢂⣜⡐⡀⢠⠼⡄⠀⢀⠃⠈⢻ ⠀⠀⠀⠀⠀⡅⢠⣿⠀⠀⢀⣬⣿⠄⠀⠀⣠⣤⡤⠈⠸⡈⡪⡷⠣⠗⠁⠀⡠⡍ ⠀⠀⠀⠀⠀⢣⣟⢞⠆⠀⠻⡿⠃⠀⠀⠈⣫⣭⠉⠳⡤⢈⡼⠁⠀⠀⠀⢔⣞⠿ ⠀⠀⠀⠀⢀⠚⣗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⣿⠍⠀⠀⠀⡠⣪⡿⣼⠷ ⠀⠀⠀⣰⠃⠀⢻⣆⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠶⡾⢁⡀⠀⢀⢀⣾⠏⠁⠀⠀ ⡠⠔⢹⢸⠀⠀⠀⠹⡢⡀⠈⠷⣶⠆⠀⠀⠀⢈⡞⠉⠀⠀⣠⢞⠫⣀⠀⠀⠀⠀ ⠀⠀⠈⡌⢄⠀⠀⠀⠑⡹⢲⢤⣤⣤⡤⠔⣾⡃⠑⠒⠊⢹⣾⣿⡠⠆⢉⠉⠁⠀ ⠀⠀⠀⠈⠪⣄⠠⠀⠀⠘⡀⠈⠉⠁⠀⢰⣿⣿⡍⠉⠉⠘⠤⣈⡁⠀⢀⣀⠤⢀ ⠀⠀⠀⠀⠀⢸⢷⣱⠀⣌⠓⡤⠤⠄⠀⣺⣿⣿⡇⢀⠀⠀⠀⢩⢹⣯⣽⣶⣶⣾ ⠠⠤⠦⡀⠀⡘⠀⣹⠼⡇⠉⠑⠛⣛⠁⠈⡿⠋⢰⠃⠀⠀⢀⣾⢼⣿⣿⣿⣿⣿

⠀⠀⢀⠔⢉⠀⡠⢂⠊⠀⡠⢊⣰⠔⠉⣷⢀⠀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄ ⢀⡔⢁⡔⢡⠊⡰⠁⢀⡞⣠⠞⠁⠀⠀⠘⡸⡄⢧⠘⡇⢳⡀⢠⠀⠀⠈⠄⠀⠈ ⠎⠠⡝⡐⠁⡼⠁⢠⢋⡞⠁⢀⠀⠀⣄⠀⠈⠛⠸⡡⡋⢄⢷⠈⡆⡄⠀⠘⡀⠀ ⠠⡝⡜⠀⣸⠁⡰⡱⠋⠀⢀⣈⣪⣒⢄⠀⠀⠀⠀⠀⠀⠀⣈⠣⠰⢠⠀⠀⢡⠀ ⡳⡜⠀⢰⠇⢠⣧⠁⢠⠟⠉⠉⣩⣝⢷⠉⠀⠀⠀⢉⣖⣂⣁⡀⠑⣿⠀⠀⠀⠀ ⠳⠀⢀⠹⠀⡿⣿⠀⢏⠀⠀⢈⠿⡿⠀⠀⠀⠀⠈⢋⣵⣦⠈⠹⡦⠈⡇⠀⠀⠀ ⠃⠀⠈⠇⢸⡰⣿⠀⢈⡂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⡟⠀⡇⡀⠀⠀ ⠀⠀⢀⠀⣿⣧⠘⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣸⣿⠁⠀⠀ ⠀⠀⠘⢀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡑⠎⣸⢰⠀⠀ ⠀⠀⠀⢸⠹⣿⠻⢿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⣾⣿⠀⡀⠀ ⠀⠀⣼⠀⠀⠀⡡⢄⣛⣽⡗⢄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⢛⣿⣿⡄⡅⠀ ⢸⡀⢨⡄⡇⠀⡆⠠⣈⠛⠣⢀⠙⢷⣦⣤⣶⠞⠛⠉⣿⣿⠿⢦⠀⠉⣜⡇⡇⠀ ⢼⢣⠀⢧⢀⠀⠘⡄⣿⣿⣶⣦⠙⡀⠻⠋⠁⡔⢒⣈⣩⣤⠂⠌⠀⠼⠟⡇⠁⠀ ⠬⠦⠥⣈⢋⠤⢴⡇⢸⣿⣿⣿⢀⠁⠀⠀⢰⠀⣾⣿⣿⣟⣌⡀⠀⠀⢀⠁⣠⢀ ⣤⣤⣤⠎⠈⠙⡾⣧⡘⣿⣿⣿⢸⠀⠀⠀⠘⢠⣿⣿⣿⣿⡇⠀⠉⠒⡮⠚⣡⣃

⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⣠⠄⢀⡔⠁⠀⠀⠀⢀⡴⠋⠁⢀⣄⣰⠾⠉⣿⢻⠀⠀⠀⠀⠀⠀⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⡀⠀⠀⣰⠚⠀⢠⠏⠀⠀⠀⠀⡴⠋⠀⢀⡴⣻⠞⠁⠀⠀⠹⡞⡄⢀⠀⠀⠘⣆⠀⠀⣿⡄⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⢀⣴⠟⠀⠀⢠⠞⠀⢠⠞⠁⢀⣰⠋⠀⠀⠀⢠⣾⠁⠀⣰⣯⠞⠁⠀⠀⠀⠀⠀⢷⠳⢸⣿⠀⠀⣽⡀⠀⢸⣷⠀⠘⣧⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠷ ⠀⠀⣠⠿⠁⠀⡰⣳⠋⠀⣴⠋⠀⢠⣿⠃⠀⠀⠀⣴⡿⠁⣠⣞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢿⡆⠀⢹⣷⠀⠘⣿⡃⠀⢹⣧⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠰ ⢀⣾⠋⠀⢀⡾⡽⠁⢠⡞⠁⠀⣰⡿⠁⠀⠀⢀⣾⠋⢀⣴⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣿⣆⠀⢯⢷⡀⢿⢳⡄⠀⢻⣿⡀⠀⢯⡇⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀ ⡟⠁⠀⢠⢏⡾⠁⣠⠋⠀⠀⣰⡿⠁⠀⠀⢀⡾⠁⣴⣯⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠈⠚⠋⠲⣼⡄⢳⡜⡆⠙⣄⠘⣿⡇⠀⠸⢿⠀⢠⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⢠⢋⡾⠁⡰⠃⠀⠀⣰⣷⠁⠀⠀⢠⠟⢀⣾⠟⠁⠀⠀⠀⠘⢿⣦⣄⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠉⠷⠀⠈⠳⣜⡿⡄⠀⠸⡄⠘⡄⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⣰⢇⡾⠁⣼⠁⠀⠀⢠⣿⠃⠀⠀⣰⠃⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⢳⣌⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⢧⠀⣧⠀⠀⠀⠀⠀⠸⡄⠀⠀ ⢠⠇⡼⠁⡼⠁⠀⠀⢠⣯⠇⠀⠀⣰⠋⢰⠟⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣬⣷⣦⣈⡛⢦⣀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⣀⣀⠤⠤⣤⡴⠃⠙⣆⠸⣧⢸⡄⠀⠀⠀⠀⠀⢃⠀⠀ ⠏⣼⠃⡾⠁⠀⠀⢀⡞⡞⠀⠀⢠⡏⢀⠏⠀⠀⠀⣩⣿⠿⠛⠉⠉⠉⠉⠉⠛⠿⣿⣿⠒⠛⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣤⣒⠚⠁⠀⠀⠀⠈⢦⢻⡞⡇⠀⠀⠀⠀⠀⠈⠄⠀ ⢰⠃⣸⠁⠀⠀⠀⣼⣹⠃⠀⢠⣿⡇⣾⠀⠀⠐⣾⡿⠁⠀⠀⠀⠀⢀⣴⣾⣿⢦⡈⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣭⣿⣶⣶⣶⣶⣤⣀⠀⠀⠈⠻⣽⣷⠀⠀⠀⠀⠀⠀⢠⠀ ⡟⢸⡇⠀⠀⠀⢰⠇⡇⠀⠀⣾⣙⣿⣿⠀⠀⢰⣿⠀⠀⠀⠀⠀⢰⠿⢿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⠋⣉⣁⡀⠀⠉⠙⢿⣷⡄⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠆ ⢀⡏⠀⠀⠀⠀⡇⢸⠁⠀⣸⡟⢻⣼⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⠸⣄⠻⠿⣛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠀⠀⢹⣿⡛⠋⠀⣿⡀⠀⠀⠀⠀⠀⠀⢰ ⡼⠀⠀⠀⠀⣸⠃⡞⠀⠀⣿⠃⣸⣿⣿⠀⠀⠀⢘⣦⣀⠀⠀⠀⠀⠙⠿⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠹⣿⣿⣿⡿⠀⠀⠀⠀⣿⣧⣄⠀⡿⡇⠀⠀⠀⠀⠀⠀⠈ ⠇⠀⠀⠀⠀⡿⢸⡇⠀⢸⣿⡇⣇⣇⣿⠀⠀⠀⠀⠀⢉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣭⣿⣭⠁⠀⠀⠀⠀⣿⡇⠀⠀⣯⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣸⠀⠀⣼⣿⣷⠀⢸⢿⡆⠀⠐⣪⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⢰⣿⣧⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⣿⣿⣆⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠛⠇⠀⠀⠀⣾⢟⣿⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣦⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡂⢀⡾⣵⢿⢹⡀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⣼⣥⠏⠘⢸⡇⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⠏⠀⣠⣾⡇⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣿⣿⣟⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠦⠤⠤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣀⢀⣠⣾⣿⣿⡇⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠙⢿⣿⡆⠉⠻⣿⣿⡟⠿⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⡆⠀⢹⠀⠀⠀⠉⠻⠆⠀⢀⣉⡿⠶⠲⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⠀⠘⠀⠀⠀⠀ ⠀⢠⠀⠀⠸⡄⡇⠀⢸⠀⠀⠀⢀⣠⠴⠚⢉⣥⣤⣴⣶⣾⣿⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣷⣟⡛⠛⠋⠉⠁⣠⣾⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀ ⠀⣾⠀⠀⠀⣧⢧⠀⢸⡇⠀⠀⠈⡇⠀⠀⠈⠉⠻⢿⣿⣿⣿⠀⠀⠈⠻⣷⣦⣤⣀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡿⠛⢋⣿⣿⣿⣿⣿⣶⣄⠀⠒⠋⠡⠚⠉⣸⢻⠀⠀⡇⠀⠀⠀ ⠀⣿⡇⠀⠀⢻⣸⡄⠸⡇⠀⠀⠀⢷⠀⠈⠷⣤⣀⠀⠈⠙⠻⠦⣄⡀⠀⠈⢻⣿⣿⣿⣿⣾⣿⣿⣿⡿⠛⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⣷⡄⠀⠀⠀⢠⢇⣼⠄⠀⡇⠀⠀⠀ ⠀⣿⢷⠀⠀⠀⢇⢇⠀⢻⠀⠀⠀⠘⣧⠀⠐⣮⣻⢿⣶⣤⣀⠀⠀⠙⢳⣄⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣀⣀⣿⠿⠿⠛⠉⠀⠀⠀⡿⠁⠀⠀⢠⣯⣾⢿⠇⢰⠃⠀⠀⠀ ⣆⢹⠘⣧⠀⠀⠸⣞⡄⢸⠀⠀⠀⠀⠘⣇⠀⢻⣿⣿⣿⣿⣿⣿⣶⣤⠀⠘⡇⠀⠈⢻⡛⠋⠁⠀⠀⣴⠟⠋⠉⠉⠀⠀⣀⣠⣴⡾⠋⢀⡼⠁⠀⠀⢠⣿⣿⠵⢻⠀⢸⠀⠀⠀⠀ ⠈⢾⡇⠈⢧⠀⠀⠘⡽⡌⡇⠀⠀⠀⠀⣾⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⡇⠀⠀⠀⠁⠌⠀⠀⢠⡇⠀⠀⣴⣶⣾⣿⣿⣿⣷⡿⠀⣼⠁⠀⠀⠐⠋⠉⠀⠀⢸⠀⠈⠀⠀⡀⠀ ⣤⣄⣓⣀⠈⠳⡄⠀⠙⠞⠹⡄⢀⣠⣴⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⢃⡀⠀ ⠀⠈⠉⠉⠉⠛⠛⢷⢤⣄⢦⣹⠉⠀⣟⣿⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣼⡧⣤⣤⣀⣀⡀⠀⠀⠀⢠⡇⠀⣠⡟⡎⠀⡴ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠉⠻⠷⣼⣟⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⠦⣤⣄⡼⢀⡴⡻⠀⣠⠞⠓ ⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⠉⣿⣿⣧⣄⠻⣿⣿⣿⣿⣿⣿⠀⣾⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠀⠀⠀⠀⠀⠀⠀⣹⡟⠋⢀⣠⣞⣡⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠃⠀⠀⠀⠉⢳⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡥⣼⣷⡄⠀⢰⢀⠀⠙⢮⣦⡀⠈⠑⠦⣔⠦⣄⠠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢰⠘⣏⠿⣆⠀⠻⣷⡘⣷⣝⢮⡶⢄⣤⣌⡙⢮⣝⡦⣌⡻⢶⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠙⢦⠀⠀⠀⠰⣄⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⢸⢀⡏⠳⣝⡳⢤⣌⠻⣮⣯⡙⠦⢄⣀⠛⢿⡒⠬⢿⣳⡿⠗⠿⣧⡀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢳⡄⠀⠀⠙⣷⣄⠀⠀⢠⡀⠀⢨⣙⠳⣄⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⡜⡇⣼⠀⠀⠀⠙⠦⣝⣿⣟⠿⠿⠤⠀⠉⠙⣻⠿⢶⡆⠈⠉⠛⠶⢬⣷⡀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠹⡄⠀⠀⠈⢫⣳⡄⠀⣝⢾⡾⡋⢦⡘⠷ ⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⣷⠇⡟⠀⠀⠀⠀⠀⠈⠉⠛⠓⠂⠀⠀⣴⠋⠁⣠⠟⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠀⠀⠀⠈⠹⣄⠀⠀⠀⢻⡄⠀⠀⠐⣝⢿⢦⠈⣳⣕⠌⢮⡻⡄ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡜⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣠⠞⠁⠀⠀⠀⠀⣀⣠⡾⠃⠀⣹⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢳⠀⠀⠀⠈⢧⡫⡷⡜⢮⡶⠀⠉⠈ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⣼⢧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⠞⠋⠉⠉⠙⠻⢿⣯⣹⡄⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⣧⠀⠀⠀⠀⠳⡽⡝⣆⠁⠀⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⡟⡞⠀⠀⢀⡤⠚⠉⠉⠓⣦⡄⠀⠀⠀⠀⠀⠀⠸⣿⠏⠀⠀⣠⡤⢤⡀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⠤⣽⡄⠀⠀⠀⠀⠙⠛⣞⠇⠀⠀⠀ ⠀⠀⢀⡿⠀⠀⢀⠀⢸⡿⠁⠀⠀⠛⠤⠖⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⣶⢦⡽⣦⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⡞⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠤⢒⣒⡒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣺⡆⠀⠀⠀⢸⠀⢳⡀⢱⡄⡀⠀⠀⠀⠀⠘⣄⠙⠈⣧⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⢀⡿⠀⡆⣼⠁⠀⢸⡇⠀⠀⠀⠀⣠⣴⠾⠋⠉⠉⠉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠿⠀⠀⢷⡀⢳⢳⠀⠀⠀⠀⠀⠹⣆⠆⢸⡆⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⢸⡇⡿⢠⡟⠀⠀⣾⣧⠀⠀⢀⣼⡿⠁⠀⠀⠀⢠⣾⣿⣝⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⢍⣿⣷⢌⡿⡇⠀⠀⠀⠀⠀⢹⡄⡾⠁⠀⠀⠀⠘⣿⡆⠀⠀ ⠀⡾⢀⣼⢞⠇⢠⢠⣿⠛⡆⠀⢉⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⡾⣹⣳⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀ ⢰⠃⠈⠃⢸⢠⠎⣮⢿⠀⢹⡄⠺⣿⡀⠀⠀⠀⠀⠀⠀⠙⠪⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢻⡿⣿⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⡾⠀⠀⠀⢸⣿⠆⣼⣸⠀⠀⢻⡄⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣾⣽⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠃⠀⠀⠀⢸⣿⠠⣟⡇⠀⠀⢸⣿⣆⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⡟⣿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣠⣼⡇⠀⠀ ⠀⠀⠀⠀⢸⠃⢸⢻⠃⠀⠀⢸⣹⣼⣦⠀⠀⠈⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⢻⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣰⡿⡿⣿⠀⠀⣠ ⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⠀⡼⡟⣿⣻⣇⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⣨⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⡟⣠⣾⣨⠞⢁⣏⠀⢈⣀ ⠀⠀⠀⠀⠈⡇⠀⡿⠀⠀⢰⣿⣼⣿⣿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠀⡇⠀⠀⣿⣷⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢿⠀⡼⡎⢻⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⢠⣿⠁⣠⡆⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴ ⠀⠀⠀⠀⠀⠀⠘⣿⡄⣽⢣⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⣀⡀⠀⠀⣀⣀⣀⣠⣴⣿⣿⣿⣿⡟⠀⠀⢀⣠⣾⡇⢠⣿⠀⠀⠀⣠⣯⡀⣀⣀⣀⣠⠤⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠁⢀⡴⠟⢡⡿⣴⣿⠃⠀⠀⣴⡿⠋⠉⣩⣽⡏⠀⠀⠀⠀⠀⠀⠠ ⠀⢀⡀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣆⠀⠀⠀⣠⡴⠋⠁⢀⣾⢟⡿⠃⢀⡴⢚⡟⣀⡴⠋⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡈⢷⣄⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠉⢹⠉⠛⠶⣤⣼⣧⣀⠠⠴⠋⣠⣞⡠⠖⠉⢀⠞⠈⠉⢠⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣻⣷⣤⡀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠉⠀⠀⢸⠀⠀⢀⡟⠉⠙⡟⢦⡀⠈⠉⠀⠀⠀⣠⠏⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢯⡁⠙⢷⡦⢤⣤⠤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀⣾⡄⢠⡞⢸⡀⠀⢳⠀⠙⣦⡀⠀⠀⡰⠃⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢦⣈⡻⣏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢸⠀⡞⠀⢸⡇⠀⠸⡆⢀⣬⠳⣄⡼⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢸⣾⠁⠀⠀⡇⣠⣴⡿⠛⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢸⠃⠒⢚⡿⠋⢉⡇⠀⣀⡤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣀⣼⣟⣫⢵⣻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣻⣟⣫⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⠁⠄⠀⠀⡟⣿⡻⢟⡿⢠⠠⠀⠀⠔⠌⠀⠐⡁⠀⠐⠀⠂⢈⡱⢢⡌⠁⠹⠶⣏⢠⠟⡿⣿⣿⢻⠆⣘⠇⣿⣿⠹⢓⣌⣷⣿⢸⢷⣡⢚⢳⠊⡑⢌⢢⠱⣌⠳⢆⣙⠴⢫⢣⡴⢞⡣⣼⣷⣾⣷⣿⣿⣿⣿⣿⣿⣶⣵⣠⣀⠋⠟⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⣂⣀⣀⣀⢀⠀⠀⠀⠈⠡⠄⡈⠁⠠⡁⠀⠀⢚⢄⡸⠖⢈⠫⡛⢦⢚⡏⣿⣿⣿⣿⣿⠘⢣⡇⣿⣿⣿⡸⢶⢫⣝⢳⣠⡃⡵⢟⠿⠿⠿⢛⠩⣀⠤⢢⡜⡏⢄⡹⢦⣋⢦⡜⢮⡕⢫⢦⡙⣶⣊⠵⠆⡡⢐⡫⢟⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⡀⠀⢀⠀⠀⠌⠁⠠⠌⠂⡀⠐⠀⡡⡜⢎⡄⡜⠏⣿⣿⡇⢃⣿⣿⣿⣿⣿⣿⢸⣃⢸⣿⣿⣿⢺⢝⠣⡔⢬⠰⢳⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠙⣊⠄⣉⠰⢦⡒⢖⡩⠰⢦⡐⠤⣀⠁⡰⡘⡿⣿⣿⣿⣿⣿⣿⣿ ⢿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠡⠄⠂⢀⡐⠂⠁⠴⠏⢐⡰⠟⣿⣿⣼⠐⡿⣿⣿⣿⣿⣿⣿⠇⠸⡽⡜⢷⣟⢸⣹⢶⡭⠜⠣⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡛⠙⠈⠑⠘⡎⠐⡍⠒⠉⣀⡤⠙⣧⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⢂⡀⠒⣀⠌⠁⠂⠡⣷⡀⠏⣿⣿⣿⢿⠃⣿⣿⣿⣿⣸⣷⣿⡿⢿⡎⡜⡹⣥⠇⡱⡿⣿⣿⢿⠻⡈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢚⢡⠖⢃⡤⠒⢣⠁⠀⢢⣮⣿⣿⣿⣿⣿⣿ ⣵⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢨⠁⠲⠯⠿⠻⢈⠡⢂⠌⠐⡀⡑⣾⠁⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠘⣎⣶⣷⢿⣊⠴⡘⣣⡇⣿⣿⣿⣿⣿⢿⠈⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡀⠅⡛⠿⠿⣿⣿⠿⠻⢙⠈⠁⣄⣷⣿⣿⣿⣿ ⣱⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡈⠤⣥⣬⣤⣉⠡⢂⠌⡐⠈⡆⢸⡏⣷⣻⣿⣷⣿⠨⣿⣿⣿⣿⣿⣿⡄⠠⢀⠢⣂⡑⢆⠡⣄⣷⣿⣿⣿⣿⣿⣿⠙⢌⡻⣅⣮⣶⣿⣿⣿⣿⣿⣾⣶⣬⢀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠝⠑⣌⣷⣿⣿ ⡜⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡀⠰⠒⢠⠘⡠⠔⡈⠱⢂⠀⢥⡇⣯⣶⡿⣯⡽⣳⡌⣿⣿⣶⣥⣬⣋⢈⠛⠓⠞⠹⠿⠋⠓⠘⣉⣦⣷⣿⣿⣿⣿⢿⠛⣉⢭⢦⠔⠳⠍⠢⠭⠒⢠⠂⡑⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⡃⣦⣿ ⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠄⠿⠿⠿⠘⠧⠿⠛⡙⡄⠒⡈⠀⣣⣳⢼⣻⡵⣎⠴⣃⠎⡝⢻⢿⢿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣻⣿⠻⡙⣌⣶⣷⣿⣿⣿⣿⣿⣿⠿⡱⢊⢀⡀⡒⢌⣓⠦⣝⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣽⠳ ⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡍⣭⣭⣫⢟⣿⣿⣿⣶⢥⠉⢍⠈⡀⢳⡴⢻⣡⠗⣫⢿⣿⣿⣿⣿⣿⣴⣢⢘⠎⢁⡤⠘⠡⣐⣬⣷⣿⣿⣿⠻⠘⣄⣧⣿⣿⣿⣿⣾⡀⠍⠲⣕⠩⣙⡉⢤⡜⣝⡲⣍⣾⣷⡿⣿⣿⣿⣿⣿⣶⣴⢈⡤⣋⣎ ⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣵⣡⢎⠃⣿⣿⣿⣿⢻⠘⣤⠃⡿⣿⣿⣿⣿⣿⣿⣼⢃⡌⢃⠤⠖⣀⠤⡌⢃⠱⢆⠊⣄⣿⣿⣿⣿⠻⠈⡄⣦⣾⣰⠞⡡⢟⣿⣿⣿⣿⣿⣿⠿⡛⣍⢤⡶⣖⠖⠭⠰⠤⠈⠏⣎⡓⣍⢻⢻⣍ ⣿⣿⣿⣿⣿⣴⢁⠀⠧⣿⣿⣿⣿⣿⢡⣮⣷⣴⣫⠃⠵⣛⠿⣿⣿⣷⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣡⠴⡙⢣⣠⠉⣀⠄⡃⠈⡱⢚⢥⡘⣧⣿⣿⣿⣿⢽⠘⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠻⠧⣱⡼⢟⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣴⢂⠕⢋⢡⠸⣦⣿⣿⣿⣸⠏⣶⡀⠟⡯⢱⣿⣿⣿⣿⣿⢿⡻⣍⣤⢡⡿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡎⠝⢣⢫⡆⣹⠭⡞⢢⠜⡹⢮⡙⢧⣿⣿⣿⣿⣿⠷⠈⠀⠀⠀⠠⠄⣂⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⢣⡜⡽⡒⣥⢊⠰⡛⣍⣶⣫ ⣑⣂⢐⡄⠒⠩⠜⠣⠠⡁⡒⣘⢞⠁⠿⢡⡭⡼⣛⡿⣛⣝⣷⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⢏⡱⢮⡳⢝⠾⠽⡾⢟⣭⠷⢎⡱⡿⣿⣿⣿⣿⣿⣻⢸⠀⠁⠂⠛⠿⠿⢿⡿⠿⠿⠻⡛⣙⣌⣤⣬⣠⠅⠬⣑⠋⡻⠟⡿⣿⠿⡛⡳⢎ ⡰⣁⠌⡳⠌⠐⡌⠌⠀⣫⠥⢎⠠⡇⣰⠚⣼⡟⠿⣟⣿⣿⢿⡻⣮⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣟⡿⣿⣿⣿⢿⣻⣿⣏⡿⣿⣿⣿⣿⣿⣿⣽⣻⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠻⣉⠤⢋⣿⣿⣷⣽⣾⣿⣿⣲⠤⢀ ⠊⢑⡬⠶⡟⠇⠟⢋⢱⠄⣈⡌⢁⣨⠃⡥⢛⣭⣮⣿⣿⣿⣿⣿⣿⠿⣘⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣮⣑⣔⣬⣷⢿⠻⡈⣥⣞⣲⣴⣤⣀⠁⠀⠀⠀ ⢞⡡⡜⢃⠡⡐⣊⣀⣃⠙⣬⢃⡿⢿⠈⣷⣿⣿⣿⠿⣟⣮⣷⣿⣿⣿⣾⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣻⣵⢎⡌⢓⡡⠜⡊⠑⣐⣷⢿⠙⠀⡐⠈⠡⠄⠈⠁⠠⠀ ⠜⢣⡑⢢⡑⠢⢌⠃⣿⣿⣿⣿⣿⣿⣿⠹⣄⣶⣿⣿⣿⣿⢿⣸⣔⣠⠁⡹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⢻⣭⠳⢣⣜⠳⢭⡚⢏⡡⠲⢈⣧⣿⠘⠂⠄⠁⠡⠄⠈⠡⠀ ⣑⠬⡘⡰⠑⢢⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢏⡛⣝⣾⣿⣾⣄⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⢯⡳⡽⢯⡏⢀⠓⠄⠂⣄⡞⢍⡰⣿⡿⠘⣁⠠⠒⠠⠌⠂⠀ ⠲⢌⡜⡈⠱⢈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡝⣧⣶⣷⢿⠈⠢⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢿⡮⠛⡢⢭⠩⢀⠖⣙⡷⣿⣿⢿⠂⣁⠰⢃⢁⠤⠈ ⠴⡍⠒⢌⠣⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠶⢩⡱⢃⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⢯⡓⠊⠛⣼⡟⣿⣿⣿⣿⡘⢂⡐⠓⡉⠆⠀ ⡬⠓⠤⢊⢑⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣥⡞⡌⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣞⡿⣝⢻⣿⣿⣿⣿⣿⣿⢸⢟⣿⠿⠟⢿⢀ ⢎⠣⣌⠔⡚⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢳⣄⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣠⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣆⣶⣿⣿⣿⠸ ⢡⢲⡌⢓⠤⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢊⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⢉⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⢿⠿⣿⢸ ⣘⠶⣉⠲⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡿⣿⣵⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⠈⡌⠁⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⡷⣿⣿⣿⣿⣿⣿ ⡵⢎⡓⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣫⣿⣿⣿⣿⣿⣿⣼⡿⣶⣾⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣠⢁⠈⠰⠈⠐⡀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢩⡿⢿⠿⡿⣻⣛⣯⣿ ⢣⢬⣚⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⣿⣿⣿⣿⣿⣾⣠⡤⢁⡻⠿⣶⣶⣴⣤⣤⣽⢾⣳⣶⣎⢳⣩⢶⡀⢁⠢⠜⠡⠖⣌⡖⠙⠀⣃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣰⠟⡏⣿⣿⣿⣿⣿⣿⣿⢻ ⢳⣌⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣷⣾⣠⠀⠀⠤⣀⢀⠀⠀⠀⠁⠕⣮⣭⣾⣿⣿⣿⠿⠿⠀⡜⠉⢢⡜⢋⢣⣌⡌⡆⢣⠁⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣩⠟⢿⠵⡻⣛⣝⣮⣿⣿⣿⣾⣡ ⢳⣏⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣾⣫⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣵⣪⡯⢟⡿⣿⣿⣿⣿⣿⠀⠄⠒⢫⣖⠷⢻⢮⢓⠢⢁⡤⡻⣹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⢑⠭⡐⣤⢫⣿⣿⣿⣿⣿⣿⣿⣼⡐⠘ ⢮⡝⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡞⣫⡿⣴⠀⠀⠀⠌⠀⠀⠀⠀⠀⠉⡾⢕⢟⣿⣿⣿⣾⣷⣿⣿⣿⣶⠘⢹⢢⢱⣶⠣⢿⣯⣗⠨⡃⠈⡄⢦⡇⣿⣓⣟⣮⣿⣿⣿⣿⣿⣿⣾⣶⣡⢛⠄⡙⢆⡁⣶⣿⠿⣻⣝⣮⣶⣷⣿⣿⣿⢰⠥⠂ ⢮⡝⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣟⣾⢀⠀⠀⡈⠄⠀⠀⠀⠀⠁⠞⣫⡿⣿⣿⣿⣿⣿⡿⣾⣥⣋⠜⠿⢊⡅⠸⣠⡅⢀⣢⣜⡱⠌⠟⣧⠈⠀⡀⣷⢸⣣⣷⣜⣿⣿⣿⣸⢋⠿⠿⢿⠿⠸⠢⣘⠪⢆⡁⣦⣔⣣⢄⠘⢡⠰⠢⠑⢆⡈⠰ ⢞⣏⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡧⣼⠀⠀⠀⠡⠀⡐⠀⠀⠀⠀⡫⡿⣿⣿⣶⣶⣶⣵⣭⣰⠏⣵⢾⣽⢤⠃⠢⡆⡥⣝⠀⣈⠄⣻⡿⣿⡸⢻⠀⠀⠀⣧⠀⡆⣿⡏⣿⣿⢸⣿⣿⣿⣿⣿⣿⠂⢆⢉⣢⠑⣨⡜⠃⢡⡜⢃⡡⢆⡈⠱⢆⡈ ⢳⢮⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⡀⠀⠀⠀⢁⠠⡐⠀⠀⠀⠀⡃⣉⢚⠾⠟⠽⣯⡴⣻⣠⠘⣹⣤⡖⡀⠃⢁⠜⢱⠇⡷⢸⢘⣶⡙⣷⣿⣿⡇⠸⠀⠀⠀⠀⠀⣷⣸⣿⣿⢣⣿⣿⣿⣿⣿⣿⢸⢎⢃⣌⠚⠥⡌⠡⠴⠊⢡⠰⢎⡄⠘⢠⠀ ⢳⢬⢳⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣼⠀⠀⠂⡀⠐⡈⠀⠀⠀⠁⢠⢞⡣⢖⣎⡜⠳⣨⡴⠀⢡⢋⠟⡿⣼⡀⠱⡜⡎⠈⠧⣷⡍⢂⣱⡜⠘⣦⣿⢹⢣⠀⠀⠀⠀⠀⡀⢰⣿⣹⡗⣿⣿⣿⣿⣿⣿⢿⠄⢫⡔⠎⢣⡐⢬⡙⠤⢘⡩⠔⢀⠀⠀⠀ ⢹⣤⣉⠀⡇⣿⢈⠛⣇⣿⣿⣿⣿⢸⣿⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⡀⠋⢁⢡⣄⠀⣀⠁⠁⠋⣿⣿⣿⣿⣿⢻⠀⡀⠃⢀⠁⡈⡜⣈⠃⣉⡄⠛⠈⣄⣿⡇⠀⡀⠀⠀⠀⠀⢠⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡄⠘⡙⢀⠙⣇⠀⠀⢠⠀⠀⠀⠀⠀⠋⣿ ⡜⢮⢁⡺⠙⡄⢷⠻⡿⣿⣿⣿⣿⣁⢰⠀⠀⠁⢂⠁⢀⠀⠀⠀⣊⠄⠢⡐⡐⠀⠚⠭⡻⣯⣿⣷⣿⣿⣿⣿⣿⠿⠛⠘⡊⠒⣉⠤⢂⠻⡄⠆⢣⡴⣛⠲⢈⠰⡀⠐⠀⠀⠀⠆⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡝⠩⢦⡒⠤⠀⠀⠀⠀⠀⠀⠆⣍⡏⣶ ⡞⢃⣴⠟⣎⠶⠏⡒⣋⣑⣚⣄⢡⡄⡁⠀⠁⠂⢀⠠⠀⠀⠀⡌⠂⡐⢁⠃⠢⣔⠬⢤⡶⣇⣩⣼⡷⣏⣧⣶⣟⣾⣿⣿⠿⠛⠙⠛⠟⣿⢿⠘⣄⡵⠳⣣⢘⢸⠀⡈⠐⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣴⢡⠉⠛⠻⠿⠿⢿⣿⡻⠪⠉⠀⠀⠀⡀⢀⠀ ⢅⣫⣜⠺⣤⣁⢺⣴⡠⣀⠈⠞⣡⠀⠐⠀⠁⠢⣁⠀⠀⠀⡀⠐⢀⠜⠚⢨⡐⠢⡄⡒⢄⢊⠵⡎⠱⢲⣩⡵⢚⣥⡳⣎⣵⣾⣿⣾⣿⣿⣿⣿⢻⡀⡱⢦⡝⠄⠀⢁⠠⠀⠀⠀⢇⣿⣿⣿⣿⣾⣫⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢎⠈⠀⠐⡀⠀ ⡵⠞⣠⠀⠄⣀⠀⠀⠁⡴⣋⠴⣀⠁⠠⠁⡀⠌⠠⠀⠀⠀⠀⠁⡇⡟⢟⣿⠼⠧⠿⡟⢹⢯⣛⠶⣛⡭⢜⡹⠧⣩⠶⣎⡝⠣⣀⡼⢞⣭⣷⣯⣿⢾⡈⢆⡄⡃⠀⠠⡐⠀⠀⠀⡇⣏⣾⣴⣁⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀ ⣰⠀⠀⠀⠀⠀⠀⠀⢋⠴⢀⠃⡴⠂⠀⠁⡄⠘⢀⠀⠀⠖⠃⡳⣿⣿⣿⣵⣛⠿⠿⠿⠿⠿⠿⣻⣟⣮⣿⡿⢿⡻⢿⢏⡹⢠⠁⢮⢎⣙⠶⣋⣶⣏⢶⠈⣂⠅⠀⣈⡐⠀⠀⠄⡀⢉⠶⢟⢫⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡴⢀⠀⡀⠀⠀⠄⠀⡇⠄⡘⠀⠀⠀⠃⣏⣿⣿⣼⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣼⠋⡿⢟⢯⡙⢯⢇⣨⣐⣌⢳⠁⡂⠀⠌⡐⠀⠀⡐⠀⣴⢡⡭⢛⠿⠿⠿⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣞⣡⠀⠀⢣ ⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⡅⠀⠣⠀⠐⠀⠀⠀⠇⣿⣻⣘⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣭⣭⢶⢫⡌⠄⡳⠈⠄⠁⢆⡈⠀⠀⡐⠇⣿⣿⣿⣿⣿⣿⣴⡟⣿⣿⣿⣿⣿⣿⣶⣧⣴⢙⠞⣡⠰⢹⢦⡙⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡔⠊⢀⠠⠀⠀⠀⡧⣿⣿⢸⡀⣳⣽⣷⣿⣿⣿⣼⢴⣀⢠⣇⣨⡴⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡻⣨⢿⠻⢸⠀⡁⠰⢈⠀⡀⠐⡇⣿⣿⣿⢟⣮⣡⡟⣿⣿⣾⣿⣿⣾⣢⡰⢃⡴⢂⠙⢲⣍⠲⣍⠒⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡌⠉⢠⠀⠀⠀⠀⣿⣻⠿⠿⠻⠙⣈⣤⣤⣦⣶⢰⠀⠀⢁⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣸⣄⣿⣥⣷⣿⣿⣿⠸⡷⢸⠀⡋⠄⠀⠀⡉⠀⠦⣶⣶⣥⣠⠋⡿⣿⣴⣀⠜⣚⣴⢊⠉⣍⢂⠫⣥⡜⡳⢌⡵⢊⡱⢘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠐⠡⠀⠀⠀⠅⡝⣶⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠭⣤⣭⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⡀⡀⢠⣿⣿⣿⣿⡂⢸⠀⠑⢠⠀⠄⠈⠀⢺⣇⡿⣯⢞⠷⠞⠯⠵⣮⠞⠞⢧⡜⢞⡱⢮⢓⣣⡜⢎⡝⢣⢤⡸⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⡐⠡⠀⠀⠀⠀⡀⢦⣍⣷⣿⣿⣿⣿⣿⣿⣾⣴⣤⣤⢤⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡊⢤⠙⠀⣤⣿⣿⣾⡀⢇⠁⡠⠈⠀⠄⠀⠘⢠⢹⣧⣻⣽⣺⡽⢞⣫⢵⢮⣙⢶⡝⣎⡱⢖⣩⠶⣊⢜⡹⢦⣙⠦⢘ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⡁⠡⠠⠀⠀⠀⠀⠀⡀⠀⠄⢒⡈⣤⡶⢝⠮⠿⠿⠿⠛⠛⠉⣍⣷⣿⣿⣿⣿⣿⣿⣿⣶⢤⠦⢷⠻⡉⣈⢀⡞⡘⠂⠄⠀⠂⣀⠃⡄⠀⣸⠀⠞⣫⡷⢎⡹⢮⣓⡴⡛⢧⡙⢧⣩⡴⢛⣡⢞⣇⡙⢦⡙⢦⡘ ⠐⠀⠀⠀⠀⠀⠀⠀⠊⠡⠀⠀⠀⠀⣁⠠⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠢⣔⣳⢝⣄⣷⣸⢿⣸⣿⣿⣾⣿⣋⠛⠟⠿⠿⠛⣝⣯⣿⣿⢹⢠⠀⡘⠀⠤⠀⡆⠀⠀⠁⡆⡗⢎⣱⢞⡣⣜⡳⣌⠽⢣⡱⢮⡙⣦⠝⣣⡜⢫⡱⢮⡘⢸⢸ ⠐⠀⠀⠀⠀⠀⠀⠄⠈⠰⠀⠀⠀⠀⡀⠒⠄⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⢷⠈⢀⣄⢰⢿⠿⣛⡈⡢⣮⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠎⠀⠂⢀⠀⠀⠀⠀⡸⡝⣣⢞⣫⡕⢮⡜⢳⣎⡙⢦⡹⢖⡩⢵⡣⢜⡳⢎⡱⢖⢩⢮⡘ ⠂⠀⠀⠀⠀⠀⠀⡰⠄⡘⠀⠀⠀⠀⡀⠘⣂⠁⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣦⠈⠀⠀⡄⣷⣿⢿⠈⠀⢠⣧⣿⣿⣿⣿⣿⢹⢠⠄⠌⠀⢌⠀⠀⠀⠀⡌⢊⡵⢎⡳⢎⡱⢞⣍⠳⢧⣋⢦⡙⢮⣙⡱⢮⡝⢣⣜⡹⢧⢊⢱⢸ ⠂⠀⠀⠀⠀⠐⣈⡐⠆⠂⢀⠀⠀⠀⠀⠂⢁⠠⡐⠀⠀⢀⠈⠀⠀⠀⠐⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⢡⠂⠀⠀⡀⣦⣿⢸⠀⠀⠀⣇⣿⣿⣿⣿⡌⠁⠤⠈⢂⠀⠀⠀⠀⠀⢎⣙⣮⡕⢮⡎⣙⠶⣙⡱⢮⡙⢦⢛⢦⡜⡳⢎⡱⢮⡜⡛⢧⡘⢮⡙ ⠌⠀⠀⠀⠄⡈⠐⢂⢀⠰⢈⠀⠀⠀⠀⢁⠠⡐⠂⢀⠀⠀⠐⠀⠀⠀⠀⠡⠀⢀⠀⠀⢁⠀⠈⠀⠀⠀⠀⠐⠠⠀⠐⠀⣆⢨⠀⠐⠀⠀⣧⣿⣿⢳⢀⠂⠆⠂⢀⠀⠀⠀⠀⠅⢮⢓⣬⡳⢎⢧⡙⢦⡜⡹⠶⣋⢦⡙⢦⣙⢧⡌⢫⢦⣙⠵⢪⡵⢎⠱ ⠐⢁⠀⠀⠀⡑⠄⡈⠐⢃⠄⠀⠀⠀⠀⠀⡐⠂⢀⡐⠀⠀⠂⢀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠄⠀⠐⠀⠀⠀⠀⡀⠀⠠⠐⠀⢀⠀⠡⠀⠀⡀⣿⣼⠠⠂⢂⠡⢀⠀⠀⠀⠀⡘⠎⣙⢳⣥⠳⣌⢳⡱⢮⣍⡱⡳⢎⣣⡝⢦⡙⢳⣎⢓⣥⡜⡳⣌⠳⣜⠳ ⡁⠡⠀⠀⠁⠠⠐⢈⡄⠂⡀⠐⠀⠠⠀⠀⡈⠐⢈⠡⢀⠐⠀⢀⠐⠀⠀⠀⠀⢀⠈⠐⠈⡀⠂⠄⠀⠀⠈⠀⠀⠈⡀⠐⠀⠀⠁⠠⠀⠈⠀⡇⢀⠀⠰⢁⠠⠀⠀⠀⠀⠇⢡⢎⡱⡹⣰⠾⣍⡱⡳⢎⣙⡴⠻⣌⢳⡱⢮⡜⠻⣌⠽⣣⡜⢛⣥⠳⣌⠹ ⠂⡰⠘⠀⠂⡑⠄⠂⢁⠤⢂⡁⠀⠀⠐⠀⠄⠊⠄⠂⡀⠐⠀⢀⠈⠠⠀⡀⠁⠀⠂⠀⠐⠀⠀⡐⠀⠐⠁⠀⠄⠁⠄⠂⢀⠀⠀⠂⢀⠀⠀⣈⠀⢂⡀⠐⠀⠀⠀⠀⠋⣰⠎⣜⡳⡝⣎⠧⣘⡽⠧⢎⡳⣍⠳⣌⢳⡱⢞⣍⠲⣜⡛⢦⡜⠳⣬⠳⣍⠸ ⢹⣆⠎⠀⠄⠣⡀⠌⠠⡐⠌⠐⠡⡀⠐⠈⠀⠑⢀⠡⢈⠠⡐⠈⠄⠂⢀⠀⠀⠌⠁⡀⠈⠡⠀⡁⠂⡀⠁⠠⠀⠠⠐⠠⡐⠈⠀⢂⡀⠐⠀⠀⠂⢀⡐⠀⠀⠀⠀⠃⡴⠍⢧⣎⡜⠻⣇⢣⡼⡛⢣⣜⠳⢬⡳⣌⡻⢇⡬⢛⣥⡜⠳⣬⡞⢓⣥⠳⢣⡱ ⣿⠘⣆⠘⡄⠘⢣⠄⡘⠢⢌⡐⠠⠘⠤⠂⠀⠀⡌⠂⠁⢀⠡⠄⡉⠄⡉⠁⠈⠁⠈⠠⠄⠀⡀⠀⠡⢀⠠⡐⠂⠄⡁⠄⠂⠀⠐⠡⢂⠀⠀⡐⠆⡀⠀⠁⠀⠀⠃⣰⡍⣚⢳⢧⣍⠲⣹⢞⡭⠞⣣⡜⢳⣎⢣⣝⠧⢣⣕⠮⣓⡬⢛⣥⡜⢫⣱⡸⢳⡱ ⡘⣷⠘⠥⡘⢊⢁⡤⠌⢒⡌⠐⢷⡌⡘⠱⢀⠀⠂⢄⠂⡀⠐⢂⠁⢠⠌⠨⠄⠈⣂⠄⣂⡑⣀⢂⠀⠬⡐⠃⢀⡐⠐⠡⢀⠠⠌⠁⠠⠀⠐⢁⠠⢀⠀⠐⠀⠎⣡⠮⣙⡼⢫⢳⣩⢴⡻⡖⢏⡬⢳⣒⢹⣱⢮⡓⣩⡵⡲⡝⢣⣕⠮⣣⡝⢪⡵⡜⢫⡱ ⣟⡹⣦⢹⠂⣅⠮⣎⠜⢃⡔⢃⠡⠔⠈⡐⡐⠈⠀⢈⠡⢀⠡⢀⠡⠄⠂⠁⢂⠀⠡⢀⠠⠐⡈⠐⢂⠄⡈⠐⡈⠄⠈⠠⡐⠌⠁⠠⠈⠔⡡⠀⠰⠁⡼⠀⠄⢍⢞⢮⣙⡵⢞⢫⡵⣎⠳⣱⢞⣍⡳⢧⣋⡵⢎⢳⣎⡩⢷⡎⣙⡹⢮⣙⠶⢍⣲⡝⢣⡱ ⣞⡻⢞⡙⢦⠍⢆⣙⡪⠁⣌⠨⡑⠆⡀⡐⠌⠀⠈⠐⠠⡈⠐⡀⠐⡀⠌⠀⠠⡐⠁⠄⡀⠐⠄⡈⠐⢂⠄⠂⠀⢈⠐⢈⠡⠄⠈⠡⠄⡈⠐⠠⠁⡴⢀⠈⡟⣋⡵⢞⣣⣜⠞⢭⡹⢶⣩⡵⡞⣋⡵⢫⡴⡞⡝⢣⢮⣚⠵⢮⡜⠞⢭⡱⢮⣙⣧⡘⢳⡱ ⣽⢞⣽⡾⢟⡓⠨⡂⢆⡡⠔⢊⠠⡐⠌⠂⠀⢁⠂⡁⠄⠂⠄⡀⠈⢀⠐⠠⢀⡈⠀⡐⠀⡐⠄⠂⡀⠐⢁⠂⢀⠐⠡⠄⠈⠡⠄⠈⠡⠄⡉⠄⠨⠁⠷⣎⠶⣙⡶⡝⢮⣓⢬⢽⡳⢧⣎⡱⡽⢎⡳⢏⣣⢭⡳⢧⢎⣜⡹⢞⣏⠦⣛⡥⢞⡩⢶⡜⢫⡱ ⣹⣾⣛⢷⣯⢯⣽⠫⠙⣀⠤⠘⢁⠠⠐⠠⡁⠀⠌⠀⠂⠄⠀⢂⠀⢀⠐⠠⢂⠀⢁⠂⡀⠁⠠⢀⠐⠠⠐⠡⡀⠌⠀⠡⠄⠈⠡⠄⠉⠤⠒⣁⠜⡻⢷⣎⣝⡳⢭⢳⣬⢻⣧⡜⡻⢦⣚⣹⠶⣭⡞⠧⣚⡹⢯⢣⣝⡬⠷⢎⢣⣴⠟⣡⠾⣓⣭⡜⢫⡱ ⢿⣞⡷⢯⣳⣞⡽⣞⡽⠿⠑⠈⠀⠠⠄⡀⠈⠠⠁⠂⢀⠄⡀⠈⠐⢀⠂⢀⠈⢁⠂⠀⢀⠠⠂⢀⡀⠐⠄⠈⠠⠁⢂⠁⠠⠌⠂⠄⠒⣁⠎⡹⣷⢎⡹⢶⣋⡵⡞⢫⣵⡞⢫⣗⡫⣗⢏⣩⢷⣎⡵⢮⠵⢮⡹⢭⡳⣍⢲⣝⣣⣖⡛⢧⡖⢎⡱⢞⢫⡱ ⢫⣼⢿⣫⡼⢿⣣⣽⣞⡾⣟⣞⢯⠸⠙⠈⠀⠄⠀⠂⠄⡈⠀⠐⠄⡈⠁⠄⠀⠂⠀⠠⢀⡈⠁⠂⢀⡀⠐⠂⡀⠐⠠⠐⠡⠆⡀⢁⠞⡹⢾⣏⡱⢞⣫⡵⢞⣫⡵⢞⣫⡵⢞⣫⠵⣹⠶⣝⡲⢟⣣⣜⡿⢎⡳⣎⡝⡲⣝⡲⣝⡧⡚⢳⣬⣛⣬⠞⢫⡱ ⣹⣾⣛⢷⣯⣞⣯⡟⣧⣜⢿⣯⢷⣯⠷⣭⠾⠛⠙⠀⠀⠀⡀⠄⠀⠈⠐⠈⠠⢀⠐⠠⢂⠀⠐⠈⠡⢂⡀⠐⢂⡑⠆⡀⠈⠛⡮⣛⢧⣜⡹⢼⡻⢧⢞⣫⡵⢞⣫⡵⢞⣫⡵⢞⣫⡵⣞⡳⣜⡻⢧⣜⠻⢧⣫⢜⣻⡴⣛⡵⣛⢦⡝⢳⣥⠺⣝⢧⢎⡱ ⣼⢞⣻⢯⣵⡟⢯⣳⣵⡾⢟⣫⡵⣻⢶⣯⣝⡾⡵⣟⢮⠾⠙⠙⠉⠀⠀⠀⡀⠄⠂⢀⠠⡐⠄⠀⡀⠀⢉⡉⠙⠓⠜⠾⣟⢣⣷⢎⣹⡶⢛⣵⡞⢫⣵⢞⣫⡵⢞⣫⡵⢞⣫⡼⢞⣹⡼⢻⣧⡜⢻⡵⢞⣫⠵⣞⠳⣭⡵⡯⡙⣶⡝⢫⣮⡝⡞⢣⣜⡹ ⣿⣏⢶⡽⣻⢶⡽⣳⣽⣞⡷⣏⣳⡽⣯⢞⣹⣽⣻⢷⣞⣞⣟⡳⣽⣯⣗⢯⢽⠯⠧⠟⠳⡼⠿⣧⣞⣳⢿⣚⡽⣳⣟⣏⡹⣽⡳⢮⣛⣧⡜⣻⡵⢞⣫⡵⢞⣫⡵⢞⣫⡵⢞⣫⢶⣝⡮⣛⢧⣜⠻⣧⡜⢻⣧⡜⢻⣭⡳⢎⡹⣳⠴⢻⢧⢞⡭⢲⣹⠼ ⢾⣳⣷⣞⡻⣷⣞⣻⡷⣞⣻⣶⡽⡾⢳⣾⣛⢶⡾⣛⣶⣞⣳⡷⣛⣳⣳⢮⣻⣞⣼⡻⣶⣞⣳⣶⣞⣵⠾⣳⣶⣞⠷⢮⡼⡻⢷⣮⡟⢲⣽⡶⣛⢧⣜⡻⢷⣎⡹⢶⣛⣧⡜⢺⣷⡎⢽⣣⢶⣜⡻⢧⣜⡻⢧⣜⠾⣞⡹⢷⣎⡹⣶⡝⢮⠷⣎⢳⢮⡜ ⣽⣻⣻⣟⣛⣻⣟⣛⣻⣟⣛⣻⣟⣏⣻⣝⣻⣯⣝⣻⣯⣝⣻⣯⡝⣻⣯⣝⢻⣯⣝⣻⣯⣝⣻⣯⣝⣻⣝⣻⣯⣝⢻⣯⣝⡻⢯⣝⡻⣭⣛⣭⡽⢯⣭⡹⢻⣭⣛⣭⢻⣫⣝⣫⣹⣟⣋⣹⣻⣏⣙⢯⣙⢽⣫⣝⢏⣭⡝⢫⣭⡝⣮⡝⣏⡭⣞⢫⢴⣚

⠱⡆⠌⡑⠢⢌⡑⠢⢎⠡⡔⢉⢢⢆⡉⠒⣈⠰⠀⠂⢁⢢⡌⠑⢢⡌⠑⢡⠲⣅⠒⣩⠖⣉⠲⣜⠳⢯⣓⢭⠀⠀⠀⠀⠁⠂⡀⠄⠈⠡⢂⢅⠂⡡⠔⢊⡑⠦⡑⢬⡙⢢⡜⠳⣌⠲⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠒⢃⡠⠜⢃⡠⠔⢂⡠⡔⠂⢠⢄⡀⠀⢀⠀⠂⢁⠠⢘⠤⡘⠣⢀⡸⡑⠦⣉⠴⢊⡱⢎⡱⣜⠯⢗⡫⢰⠀⠀⠀⠀⠀⠁⠂⢁⠆⡀⠘⢡⠢⢑⡤⠙⢣⣤⡛⢇⡣⢞⣍⠳⣌⠷⢊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡉⡔⠊⢡⡔⠊⢡⡬⠓⡤⠞⣡⠞⣣⡝⢮⡳⣞⠠⠀⠀⠀⠀⠐⠀⠌⠁⠠⢢⡄⠉⢢⡑⠥⡘⠧⣌⠳⣩⠶⢛⣣⠼⣝⠲⣭⡞⠈⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠂⠐⠃⠠⠑⠤⡈⠑⠤⠃⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⠔⢊⡡⠔⢊⢡⡜⠣⣢⠞⣣⡜⢯⡱⣟⢣⣸⠀⠀⠀⠀⠀⠀⠈⠄⠂⡁⢂⢌⠑⢢⡘⠦⡙⢦⡝⣣⡝⣯⡜⢻⣭⡳⢮⣙⠶⣛⠄⡉⠦⠌⡙⢦⡍⡒⢎⡃⢆⣉⠲⣌⡘⠧⢂⡑⡈⢑⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⡡⠌⢃⡠⠜⢣⡑⢣⢦⡝⢣⡼⢟⣣⡼⣟⠀⠀⠀⠀⠀⠀⠀⠀⡐⠌⢁⠢⡄⠘⢣⡔⢎⡓⢬⣛⢷⡭⢞⣽⠿⣫⢷⣎⡹⢶⡭⠸⡁⢞⡌⠚⢥⡚⠥⢒⢩⢦⡙⠦⢌⡱⢓⢡⠲⡌⡘⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠒⣈⠜⢣⡬⡓⢥⡹⢾⣏⡹⢷⣫⢰⠀⠀⠀⠀⠀⠀⠀⠈⠐⠆⢀⡘⢌⡑⠢⣑⠦⢓⣬⡟⣳⢽⣾⡽⠷⣹⢾⣝⡳⣹⢟⢣⡀⠧⣌⠞⣩⠖⣉⠼⢋⣡⠜⢣⣌⡛⠦⣉⠴⢎⡑⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣈⠰⢎⡑⢪⡜⢫⣱⠾⣝⢻⡶⢫⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⢃⠄⡑⠢⣌⡘⡱⢹⣧⡞⢯⣽⡾⣟⣳⡽⢾⣳⢮⡽⡳⣞⠈⢳⣎⡕⠲⣍⠓⢢⢝⡢⡜⢓⡥⠚⣥⠚⣣⢆⡘⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠡⢄⠣⢆⠩⢳⣍⢳⣭⡷⣟⡿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠐⠡⡔⠊⢡⡔⡙⢣⡰⢾⣝⢾⣻⣷⣟⣯⡽⣞⣻⣵⣟⡮⢟⢨⢳⡬⣛⡴⢚⡱⢮⡘⢳⢤⡹⢎⡙⢧⡉⢰⢺⣍⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠘⣡⠔⡉⠦⢉⠀⠀⠀⠀⠀⡄⠑⢢⡜⠳⣭⡳⣻⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠈⠱⢆⡉⡤⠛⣡⡷⢏⣮⣟⣳⣽⡿⢯⣳⣾⣟⣯⡷⣟⡳⣞⠣⣜⠻⣥⠖⣩⠞⣌⠳⣬⠓⢦⡙⢣⡜⡞⢎⣘⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⡈⠱⡌⠃⢤⡚⠀⠀⠀⠀⠀⢂⡀⠜⣌⠹⣳⢯⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠩⢆⡉⢖⠩⣸⠷⢫⣷⣞⣽⡾⣛⣽⣻⣷⢞⣻⣽⡟⣯⢐⠏⡧⢎⣩⠶⢎⡱⣜⠳⢤⡹⢦⣙⠶⡝⢎⢫⣆⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢆⡈⠰⡌⠃⣑⠦⢈⠀⠀⠀⠀⠀⠄⠂⢌⡹⢶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠤⠂⢍⡊⠵⡎⡝⢳⣾⣟⣯⣽⣟⢯⣷⡻⣷⣟⢯⣳⢽⣾⠡⢞⣫⢼⣓⡬⢚⣱⡜⢫⣔⡛⢦⡙⢧⡜⢫⢱⢦⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⢢⠔⢃⡡⡔⠩⢢⠁⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠄⠣⣀⢳⡌⢛⣧⡟⢯⣳⣿⣻⣷⣞⡿⣝⡾⣟⣭⡾⣟⢺⡃⢼⣻⢧⡙⢧⢎⡱⢮⣙⠶⣋⠵⣜⡺⢝⣣⡜⠱⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⢎⣁⠰⡘⡵⠊⣄⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠒⣌⠳⣌⠼⣻⢷⣞⣻⢿⣿⣯⡷⢯⣽⡿⢯⣳⣼⢿⠡⣳⣼⡟⢳⡹⢮⡝⡳⢏⡬⣞⠳⣫⡵⢎⡱⢚⡬⡙⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠣⢆⡩⠖⣃⠱⢊⢡⡌⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⢈⠠⠔⠈⠡⣄⠳⣎⡷⢯⣳⣽⣿⣿⣳⣻⣹⢷⣯⡷⣞⣻⣵⡰⡛⣷⣞⣱⡿⢧⢳⣽⢮⡹⢷⣏⢧⡜⡳⢎⣙⠶⢎⡘⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡱⢖⡈⡵⢊⡱⠔⢪⡕⢊⡄⢶⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠁⢈⠡⠄⡈⠄⠂⢡⠐⠢⣁⢦⣶⡿⣟⣿⣿⣽⡿⣞⣻⣳⣾⣟⢳⣰⡛⣱⢾⣏⣥⡞⣹⣾⡝⢮⣝⡹⢿⣭⡟⢯⢟⡻⢿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⡘⠣⣄⠘⢡⡠⠒⢌⠢⡐⢈⡼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠌⡁⠰⡌⠑⠤⠊⢁⢂⠠⡘⢆⡉⡱⡜⢯⣲⣿⣷⣟⢻⣶⣛⣷⣟⢯⣠⡞⡝⣺⡷⢏⣱⡿⢮⣝⡯⣍⡬⠽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢆⡈⠰⢊⠅⠀⡰⠄⠊⢁⢢⠑⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡱⠆⢈⡱⠜⡩⠐⠄⠁⠢⢌⡓⢇⢎⡱⡝⢺⣽⡻⣷⢧⣹⣾⣏⣵⠾⢃⡯⣝⢾⣏⢶⣏⡵⠾⢯⣓⣏⢲⠽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⠎⢀⡱⡌⡑⢢⢌⡱⣌⡱⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢃⡠⠜⠣⣌⠜⡱⡜⠱⡊⠑⢢⡌⠱⢮⡝⣳⡽⢟⣯⡻⣶⢯⡽⢞⣫⡴⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠣⢄⠂⣀⠱⡌⠃⢥⡌⠱⣎⡒⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡈⠰⢎⡑⢣⠧⣌⡸⡝⠣⢎⡡⠖⣉⡳⢏⣭⡿⣏⡽⢯⣳⣽⢿⡯⣜⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⡡⠐⠡⢂⡀⠐⡡⠄⠡⣄⡘⢎⢣⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠱⢃⣡⠮⣉⡳⢎⡱⢞⣉⠶⢋⣱⠮⣙⠶⢻⣶⡽⣞⡿⣟⣯⡽⢿⣫⡵⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠠⢀⡀⠀⣀⠐⢢⡐⠜⢃⠠⡔⠈⠀⠀⠀⠀⠀⠀⠀⠂⢁⡠⠜⠣⣱⠖⣉⠶⢏⣣⡜⢏⣥⠞⣹⠾⣛⣷⡟⣯⣟⣯⢿⣿⢿⣯⡼⢋⠟⡫⣓⣾⣥⣬⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣆⠈⠀⠀⠀⠠⠀⠀⠁⢢⡌⡙⢰⡡⡜⢆⡹⢖⢫⡷⢏⣫⢷⢯⣯⣟⣯⡷⣛⢿⣿⢯⣿⡿⣠⠗⢮⣳⣾⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠩⢃⡀⠌⠀⠀⡁⠤⢛⡤⠀⡩⡔⢮⡙⣳⢏⣱⢾⣛⢧⣻⢯⣿⣿⣿⣿⣿⣾⣿⡴⢀⡀⡀⣀⢀⢄⡀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣬⣬⣮⣵⣶⣭⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠀⠂⠀⠀⠠⣐⠶⠀⠌⡈⡵⢎⡱⠼⢻⣦⡙⢼⣻⢯⣳⣽⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠂⠀⢁⠬⢚⢣⣘⡵⢊⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢂⠡⠄⡘⠲⣝⡞⡯⢓⣬⠞⣏⡵⣟⣯⡷⣟⢯⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⠐⠀⠃⢤⢚⢬⡓⢢⢜⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⡍⢧⡹⡼⢞⣻⢷⢌⣹⡶⣛⣼⣿⢧⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠠⡁⣖⠎⣍⠣⣣⠕⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⡶⣟⣴⣱⠲⣜⡛⣭⠵⣎⠳⣌⠺⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢂⠁⡔⠊⠄⠨⢒⠄⠀⠀⠀⠈⠐⠂⢀⠀⡓⠦⢎⣉⠳⣩⡔⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⡐⠦⣙⠾⣏⡳⣝⠧⣙⢧⢣⠀⠀⢂⠀⠀⢂⠀⠀⠀⠐⠎⡀⠒⠆⢃⠢⢐⣀⠌⠋⡙⢿⠻⠈⠂⠄⠀⢈⠀⡩⢖⢎⣉⠶⡍⡣⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⣄⢶⣿⡿⣻⡽⢳⣧⠘⠀⠀⢀⠀⠀⠀⠀⡈⡐⠌⡐⠢⢁⢁⠠⠟⣯⣷⣟⣯⣿⣿⠿⠀⠠⢁⠂⠀⢎⡱⢎⣑⠮⣉⠲⣘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣠⠀⠀⠀⠀⠀⠀⠁⠢⢁⡐⠌⡐⢄⠂⡋⢏⠣⣻⢯⣽⣻⢿⣌⣿⢹⠀⠁⠠⠄⢏⡡⢞⡡⢜⡸⠵⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠘⡠⠄⡈⠂⣈⠎⣜⣽⣿⣿⣽⣿⡿⣮⠷⣆⣥⠀⠁⠂⡄⢋⡱⠦⣙⠧⣍⡡⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠄⠀⠂⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢀⠱⢊⠱⢆⡙⠢⠙⠀⠀⠀⠀⢀⠠⢀⠣⠜⠊⡗⢊⣼⡟⣿⣟⣻⣽⡾⣟⣻⠆⡟⢠⠁⠠⠄⢚⡱⢦⡙⢪⡱⢎⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠈⠠⠐⢈⠄⠂⠀⠀⠀⠀⠀⠐⠀⠜⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⡌⠓⠣⣘⠳⢭⣣⣝⡳⢯⡷⢯⠘⠀⠀⠀⠀⠂⢀⡆⢅⡰⢯⣿⡇⣿⣟⡾⣟⣿⣿⣼⡞⢤⡈⠐⠡⡄⡜⡚⢥⠲⢜⣫⠕⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠌⢁⠤⠂⢁⠠⠐⠀⠁⠀⠂⠠⠜⠣⢓⣭⠻⢯⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠔⠊⡑⢎⡙⡳⢎⡹⣼⡿⣏⡽⣽⡾⣻⢿⠀⠀⠀⠁⠠⠙⠠⡙⠓⣿⣼⡜⣻⣽⢿⣿⣿⣾⢣⢢⠈⢂⠄⡐⠃⢔⢪⡵⠎⢓⣣⡔⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠆⡀⠡⢂⠐⡐⠀⠌⠃⡑⢎⣏⡜⣻⡽⢾⣻⣷⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⡉⠦⢍⡳⢎⡼⡻⣤⣛⣦⢷⣯⡿⣟⣷⣟⣿⢸⠀⠀⠈⠀⣇⢈⡧⠷⡴⢍⣮⠔⣻⣿⣿⣴⢄⢋⡿⠲⢀⡔⠈⠃⡴⢏⡡⢖⡩⢱⡳⢌ ⠀⠀⠀⠀⠀⠀⠀⡀⠞⡀⠈⢂⡀⠜⡃⠄⠀⠌⢣⡹⢿⢯⣳⢿⣾⣿⣯⣿⣽⡿⢹⠀⠀⠀⠀⠀⠂⠄⠋⠤⡛⢥⣞⡻⣖⡎⡑⣌⠓⣡⠲⣌⡿⣞⣿⣻⣿⢐⠀⠈⠉⣌⠹⠀⣄⡡⢜⡖⠶⣲⢴⣩⢉⠟⣾⣥⢀⠘⡄⠌⠂⠄⡳⢌⡹⢦⡕⡪⠝⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⢆⠉⠄⠀⢁⡐⠎⡀⠀⢌⠠⡱⢾⣻⣷⢯⣿⣿⣽⣿⣿⡿⣯⠘⠀⠀⠀⠀⠡⢌⠳⣍⠳⣿⣿⢻⢬⡒⢌⡀⠀⡠⠞⢃⢧⣾⣻⣿⣿⠀⠆⣜⢢⣴⡏⠉⠀⠂⠀⠐⡌⣀⣁⣍⣫⢘⠀⠠⠌⠂⢁⠢⢁⡄⠲⣍⠖⣩⡳⢎⡙⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡳⠉⠣⡀⠐⢈⠀⠄⢫⡑⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⠙⠀⠀⠀⠂⡥⠳⣝⡳⣾⣿⣻⣌⠳⢈⠓⠆⣉⠜⢣⡽⣿⣿⣿⢠⠀⠁⣺⢶⢲⣼⡔⠡⢈⠜⠈⣷⣿⢿⣴⣀⠀⠀⠀⠂⢡⠂⢐⠠⡅⡎⢍⡲⢎⡱⢎⠦⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣤⠌⠂⠀⠀⠄⡳⣿⡿⢿⣷⣯⣷⣿⢯⣿⡿⣿⣟⡿⢻⠈⠀⠀⣄⡿⡟⣻⣷⣟⢯⣽⠻⣙⠹⢯⠟⡯⣟⡿⣿⣿⣠⠀⠀⠋⡽⣞⠻⣞⣷⢢⠥⢋⠟⡿⣷⢾⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠂⢬⡝⡣⢕⣣⡜⢫⣌ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⡀⠤⣶⠐⠀⠂⠙⠀⣄⣷⣿⣿⣿⣿⢿⣿⣯⣽⣿⣿⣿⣯⣟⢿⠙⠉⠀⣦⡷⣿⢿⣿⣯⢿⣿⣻⢿⣿⣿⣾⣴⣠⢀⠀⠀⠂⠀⡉⣈⢛⡵⠉⢦⣿⣿⣾⢗⣯⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⣘⠳⣡⡞⠣⣔⠝⢢ ⠠⠌⡈⠔⠂⢁⠤⠁⠠⠐⠀⠀⠀⠀⠀⠀⠈⢁⠈⠆⠻⠀⣀⣄⣦⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣤⢀⠀⠀⠀⢀⡀⣀⣄⣀⣠⣤⣤⣁⢉⠛⠾⢶⠁⠘⠂⠀⠄⣤⣤⣉⣠⠛⠚⣟⢾⣟⣳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡖⢊⣹⠖⣩⡵⡊⢱ ⠆⠃⢄⡑⠌⠢⡁⠐⢈⠠⠀⠐⠀⠀⠀⠄⠌⢤⢤⠉⠃⡾⠀⠀⠀⠈⠀⠀⡀⣀⣀⣂⢐⠀⠀⠀⠀⠀⠁⠈⠁⠉⠋⠚⠛⠞⠯⠿⡿⣟⢷⡛⢿⠿⣟⠚⠩⠔⠡⢊⡁⢯⡰⠯⣯⣷⣟⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢖⠣⣎⡔⠫⣔⠸ ⢈⠣⣀⠰⡈⠄⡈⠐⠄⡀⠀⠀⠈⠀⠀⠀⠇⡰⣆⡴⣠⢋⠘⠀⠈⠀⠡⢢⠄⣌⡦⠟⡛⢭⢫⠽⡽⢯⡽⣯⣽⣾⢽⢿⣿⣷⣿⣿⣿⣾⣶⣭⣯⣒⠤⣁⠋⠿⣼⢋⡽⣻⣽⠾⣿⣽⣿⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒⣅⡳⢌⡳⢌ ⠄⠂⡁⠄⠀⢈⠄⠂⡁⠀⡐⠀⠄⠀⠀⠀⠀⠀⠆⠀⣳⢶⢠⠆⠉⢀⠂⡐⢀⠈⢀⠄⠤⢦⢦⡶⣾⣷⣿⣾⡿⢿⣽⡿⡿⣽⣻⣚⢖⠤⣡⣋⠔⠢⠶⣿⢡⣰⠯⣿⣿⡷⣻⣿⣿⣿⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣀⠰⣲⠝⢢ ⠐⢈⠠⠐⢂⠁⢀⠈⠐⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⠌⠂⠄⠀⠐⠈⡄⣀⣤⢤⠥⠦⠀⡐⢦⠒⣰⠒⣔⢤⠉⠋⠘⡠⣠⢀⠀⠀⠀⠀⣤⣦⣷⣿⣿⣿⣾⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢆⡑⢦ ⠠⠐⢈⡐⠌⠁⠠⠄⠀⡀⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠠⠀⠀⠀⠈⠀⠀⠀⢀⠠⠴⠤⣤⠤⣤⣭⣁⢈⠀⠀⠀⠀⠀⠈⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢥ ⢀⠠⠌⠂⠄⠂⡁⠄⡀⠁⠠⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠁⠸⠁⢀⡻⣵⣿⣿⠿⡟⣿⠰⠀⠄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠂⢀⠐⠠⢁⠠⠐⡀⠁⠠⠀⠌⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣄⣦⢰⣦⣶⣤⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠡⡀⠈⠂⠀⠠⠂⠀⠁⠄⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⡷⣞⠝⠺⠙⡀⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠠⠀⠀⠀⠁⠂⠄⠀⠌⠀⠡⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡽⢯⡳⣹⣾⡟⢭⣻⣺⠷⠙⠈⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠄⡈⠄⠀⠂⠄⠀⠈⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⡞⡟⣧⡜⣩⣵⡾⡝⢭⣤⠷⣭⣳⢯⢷⠈⠀⠀⡀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⡀⠌⠁⠄⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣞⢯⣳⣜⣻⣼⡷⢮⣝⣻⢶⣫⢼⣻⣻⢸⡀⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠄⠈⠠⠈⠂⡀⠀⠐⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢉⣏⡳⣟⢨⠸⡽⢶⣝⡺⣿⢟⣤⢢⠐⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠌⠁⠠⠀⠐⠄⠀⠈⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠶⣰⣀⣀⢆⠙⡟⣧⣟⣥⢮⣤⣤⢤⡬⢀⠁⠀⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠂⠁⠄⠀⠈⠠⠁⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⠀⠀⠻⠓⠉⠀⠑⡌⡭⢯⣳⣶⡘⣁⠀⠀⣀⠉⠠⠈⠡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢂⠂⣂⠂⡂⢀⠰⡤⡀⡐⠀⡦⠂⡄⠂⡒⠀⡂⡆⡆⠀⠀⠠⠰⠤⢢⡄⠂⡄⠀⠆⢂⡀⠂⠀⠢⠀⡖⠄⠠⠢⢰

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⠀⡜⠇⢰⡿⢁⠱⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠃⢸⡇⢰⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣿⣿⣿⣿⣿⢻⠀⠆⡘⠢⡍⢳⠈⠀⠀⡀⢤⡰⣤⢶⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣚⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣿⣾⠇⢠⡘⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡿⢠⠀⠀⡾⠀⡎⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⢿⠻⡉⠀⡀⣭⣿⠻⠙⠈⠀⠀⠀⠀⠀⣀⣤⣦⣶⠿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇⣦⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠘⠀ ⠆⡇⢻⡰⡎⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡰⠁⠎⠀⡎⡸⠀⠋⡤⠀⠁⢸⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠙⣉⣿⢾⣶⣿⣿⣿⠿⠻⠙⡏⣟⣿⠾⠻⠛⠙⠉⠉⠈⠀⠀⠀⣀⣤⣷⢯⠻⠉⠀⠆⠘⠀⠀⠀⠀⠿⠼⠦⠓⠈⠀⠀⠀⠀⠀⠁⡜⠀⠀⡟⠀⠀⠀⠀⠀⠀⠎⣤⢠⠏⢀⠀ ⠀⣿⣸⠇⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡼⠁⢷⢠⠃⣜⠀⠇⢠⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⣀⣀⡤⢦⣭⣉⣟⣿⣿⣿⣿⣛⣛⣙⢬⣠⡛⣘⣇⣿⠼⠶⠽⠈⠀⣄⣦⠓⠉⢯⠘⠀⠀⠚⡀⣧⢿⠀⣄⠳⠉⠀⠀⠋⡿⢸⠀⠀⣸⠀⠀⠀⠀⠋⡴⢀⠀⡞⢀⠀⠀ ⠀⡇⢹⢣⢠⠀⠀⠀⠀⠀⠀⠀⠀⡎⣜⠀⡿⢰⠁⢿⢀⠆⣼⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡢⣖⠶⠥⣠⢀⠀⠀⡇⢉⠈⠖⢠⠀⡀⣄⣽⣽⣭⣿⣿⣶⣶⣶⣤⡤⠥⠤⣤⣤⠤⠢⣓⢾⠶⠒⠛⠋⣟⣿⠿⠛⠉⠀⡇⣠⢄⠀⡟⣿⣿⣾⣤⣀⢂⠀⠃⣾⠶⠒⠤⣤⢀⠀⠁⡜⢀⠀⠋⠼ ⠀⡄⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠇⣮⢀⡜⡸⠀⡻⢠⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠣⠈⠀⠀⠀⠀⠀⠀⠤⢉⠒⠀⠀⠀⠁⣚⣠⠀⠀⠀⠀⣀⣄⣦⣷⣿⣿⣿⠈⠀⡈⣥⣊⠔⠀⠀⠁⠊⡴⣀⠀⠀⠊⠔⠤⠢⠋⡿⢚⠴⣿⣶⢈ ⠀⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠃⢧⢠⡎⡞⠀⡏⣸⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⠘⠀⣀⢤⠐⠀⠀⠀⠀⡜⢀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣧⢀⠏⣸⠀⠀⠀⠀⠁⡰⠀⠊⠒⠅⡴⠤⣉⣛⣲⠒⠒⠬⠾⢀⠀⡄ ⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠁⢲⢠⠇⢎⢀⠏⣜⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡔⢀⠀⠀⠀⠀⠀⠀⠀⠁⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⣀⠨⠀⠀⠀⠀⠀⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠊⠴⢀⠀⠄⣀⠐⡀⠀⠉⠞⠴⣄⠿⠬⠲⠒⠒⣴⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⢻⠀⣆⣿⣿⣿⣾⠀⠀⠇⣿⢷⣿⣿⣿⣿⣿⡇⢸⡏⡆⠀⡁⣽⣿⢻⠙⣟⢿⠿⠻⠑⠀⠀⠀⠀⠆⣻⠖⣤⣠⠀⠇⣸⡏⣿⢚⠔⣚⡡⠜⡤⢻⠀⠀⠀⠀⠃⠁⡝⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠘⢣⣧⣿⣏⢸⠀⠀⡇⣿⡇⣾⣧⣿⣇⣿⠸⢸⣼⢸⠀⡏⣾⠙⣦⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠃⢿⠿⠶⠦⠽⣿⠉⣿⣱⠚⡠⠋⣹⣿⡟⣿⢰⠀⠀⠀⡀⡷⡄⡷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢆⡘⣷⣿⣸⢿⠀⠀⡇⣸⡄⢾⠀⣿⠘⣷⢹⠀⢹⢸⠁⣿⣿⣿⠘⠀⠀⣀⣍⣺⣓⢀⠀⠀⠁⡊⣽⣾⣿⡿⣶⣿⣿⣠⡠⠁⡽⣟⣾⣣⣿⣰⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣦⣿⣿⠸⠀⡀⢧⠀⢸⠀⡆⢹⡀⣿⠀⣿⢘⡇⣿⣼⣦⢿⡏⠇⡿⠛⠉⠈⢦⠈⠀⡀⢳⠀⡀⢀⡎⠀⣿⢠⠀⠋⡾⣤⣀⠊⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⣌⣿⢿⠀⡀⡇⢹⣸⠤⠹⣇⠒⣷⠸⣿⢾⡗⣿⣿⠀⣆⣿⣿⣦⡘⣇⣿⠻⠓⠀⠀⡀⢏⠿⠾⢠⡞⢸⠃⡴⢀⠉⠖⣠⠀⠀⠃⡴⠹⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⣮⢻⠈⠀⣿⣿⠀⣄⣿⠺⡟⢿⡆⢻⠛⣬⣿⢢⠛⣟⣿⠀⣇⣹⣿⣿⡿⠎⠹⠆⣤⣀⠃⡿⣧⠊⢡⠞⡠⢀⠀⠀⠀⡎⢣⠙⡀⢤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠻⡏⣿⠠⠀⡄⢷⡀⣷⠿⣾⣀⢦⣽⠿⠶⢰⣻⣙⣯⡟⣿⢸⣇⠻⣿⢀⠁⠟⣿⣰⠏⢴⣜⠀⠀⠀⠀⠀⣵⢀⠀⣁⠶⠙⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⣿⣿⢿⠙⠀⡀⢦⠘⣆⣿⠘⠀⣆⡜⠹⠀⡄⠘⣆⣼⡄⢿⣿⣬⡇⠾⣠⡿⣿⡴⠃⡾⠀⠀⠀⠀⠀⠀⡀⢠⠓⡾⣠⣄⢷⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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