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