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