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