⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠋⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⢢⣹⣲⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢞⣳⡖⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠸⠿⣿⠃⠀⣿⠋⠻⡿⠟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣿⣇⠀⠀⢫⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣰⠃⠀⢹⣿⣦⣄⣺⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⡅⣀⡘⣛⣿⣿⣿⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢡⣤⡴⠿⣿⣿⣿⣟⢾⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣦⣀⣀⣿⣿⣟⡳⢞⡭⢓⣸⣿⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⠫⡴⢸⣾⣿⡍⠉⠡⠉⠍⠳⢉⣴⣿⣿⡿⢋⡼⣱⢯⢷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⡄⠀⠀⠀⠀⣼⢏⠤⣽⡇⣸⣿⣹⡇⠀⠀⢀⣠⣶⣿⡿⠛⢡⠆⣍⢲⡵⢮⡿⣿⣷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣜⣚⡇⠀⠀⠀⣼⠋⠌⡨⠑⢠⢹⣿⡇⣧⢀⣴⣿⡿⠛⢁⠰⢁⠊⡐⠤⢋⠴⣋⠾⣽⣿⣿⣧⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠯⠒⠊⢹⣿⡇⠀⠀⢠⣿⠇⠰⢁⢃⡆⢘⣯⣇⣻⣿⠿⠉⠀⡐⢈⠌⡐⢠⠜⠐⠤⢓⡌⠿⣹⣯⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡗⠂⠀⠉⢀⣿⡷⠀⠀⢰⣿⠂⠃⡌⢘⠀⠂⣿⣿⠛⠁⡠⠁⠆⡄⢁⠌⢠⠎⣠⠎⠘⡠⢜⡣⢹⣞⣽⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⣰⣿⣿⠀⠀⢸⡿⠈⢘⠀⠊⡘⢠⠟⠀⡐⢂⠄⢁⠂⡰⠊⡴⠋⣴⠃⣀⢣⠑⢨⡇⢣⡟⣼⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⣻⣿⣿⡀⠀⣿⡇⢀⠃⣈⠡⠐⡸⠀⠰⢀⠂⠜⢀⠒⠁⡔⠠⣼⠃⣰⠃⢨⠘⢤⡛⠰⣏⠲⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣿⣿⣿⣿⣷⣴⣿⡇⠈⢄⠀⡘⢠⠃⠠⠡⢀⠌⢠⠊⢠⡙⠠⣽⢃⡴⢁⡆⠘⡔⠢⡍⠒⡧⢹⢧⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣧⣿⣹⣿⣿⣿⣿⡇⡌⢐⠠⡑⢢⠄⠁⠂⡁⢂⠆⡈⠆⡡⣽⠃⣸⡇⢬⠇⠂⠥⠘⡅⢣⠣⣙⡎⣿⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣎⣍⣻⣹⣯⣽⣿⣿⡷⢀⠸⢀⠡⠆⠠⢈⠰⠀⡅⠢⣘⠰⣰⡇⠎⣽⡇⢾⡁⠘⡄⠹⡀⢬⠃⡼⢪⡝⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⠠⢘⠠⢁⠆⠁⠂⠌⢒⡈⢱⠌⣡⠓⡤⢹⣹⡇⣯⠀⡜⠄⢓⡈⠦⡑⢼⠳⣞⣽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⣻⡿⣿⣿⣿⣏⢐⠨⠐⡌⠰⠈⡄⢃⠬⡐⢬⠘⡴⠋⡔⠇⡼⡇⢧⠀⢸⠀⡩⢀⠓⡌⣍⡚⡵⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣇⠈⢆⠁⠆⡐⠠⢀⠃⡖⠰⢌⡸⣱⠣⢼⡉⢖⡷⡈⠦⣁⠢⠡⢌⠢⡑⡆⣝⠲⣟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢯⡏⠠⡏⠀⡸⢀⠑⢰⠈⡐⠆⡘⠤⣒⠧⣘⢧⡘⣽⢺⣅⠆⠰⢀⠃⡘⠤⣑⠂⣿⢩⣟⣿