⠀⠀⠀⠀⠀⠀⠀TYB⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠾⠛⠛⢛⡛⠛⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣋⡁⠀⠖⠀⠀⠉⠙⢓⣶⣴⣾⣿⣤⣤⣤⣤⣤⣭⣚⣀⡀⠀⢰⣍⠓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⣚⡛⠛⠛⢛⣛⡛⠛⠒⣈⣤⣶⣿⣟⣋⣩⣍⣉⣉⡉⠉⠉⠉⠈⠩⠍⠛⠷⣦⣍⢁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⣚⣟⣭⣍⣭⣽⣟⣛⣛⡲⢶⣭⣵⣾⣻⡭⠭⠉⠉⠋⠬⠭⠭⢭⣟⣛⠳⢾⣬⣞⡤⠞⡛⠁⠉⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠁⢀⣠⣄⣀⠀⠀⠀⠈⠉⠙⢲⣿⠟⠁⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠈⠉⠓⠶⢭⣝⣃⡀⠀⠀⠀⠀⠀⠀⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣼⣿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⠂⠁⠀⠀⠀⠀⠀⡸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠸⣧⣄⣼⣿⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣧⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⣠⡴⢻⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⠀⠀⠈⠉⠉⠉⠀⢀⣀⣠⠴⢚⣻⣦⡀⠀⠀⠀⠙⠛⠻⠟⠋⠀⠀⠀⣀⣠⠞⣋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣟⣛⣛⣛⣻⣿⣭⠿⠖⢚⣷⡿⣫⡝⢿⣖⡦⠤⢤⣤⡤⢤⠤⠶⣖⣛⣭⡶⠛⠉⠐⢚⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⣿⣷⣶⣤⣷⣾⡟⣃⠀⠁⠐⠒⡍⠛⠷⣶⣶⣶⣲⣚⣛⣋⣙⣒⣯⣤⣶⠾⠛⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢄⠀⠀⠀⠐⢂⡿⠋⠀⠉⠀⠀⠀⠀⠈⠁⠀⠴⠌⠉⠻⠿⡛⢛⡋⠉⠉⠒⠒⠀⠀⠀⣂⣈⣤⣄⡀⣶⣄⠀⠀⠀⠀⠀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⣍⡒⠄⠀⢀⡀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⣀⣀⣬⣤⣶⣶⣛⣿⣽⣿⣭⣿⡆⢙⠷⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣷⣶⣾⣭⣤⣶⣂⣐⣂⣀⣈⣀⣀⣀⣀⣀⣨⣤⣭⣼⣶⣶⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⡿⣻⡇⠡⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠙⣷⣿⣿⣿⣿⣶⣿⣿⣭⣽⣿⣿⣭⣽⣿⣿⡿⣿⣿⣿⣛⣛⣿⣽⣿⣷⣿⣿⣿⣟⣿⣿⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⢊⠜⠁⠀⡤⣾⣟⡿⠛⠁⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⡿⣿⡿⠋⠀⠂⠀⠀⠀⠀⠀⠀⢀⠠⣠⠇
⠀⠀⠀⠀⠀⢠⠊⢠⠃⠀⠀⣾⢿⣷⣏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⢀⣀⣤⢾⣿⣿⡾⣿⡵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⠙⢮⡻⣯⣿⣶⢦⣤⣤⣀⣀⣈⣛⣿⣷⣿⣿⣿⣯⣤⡤⣴⣶⣿⣿⣿⣽⣟⣯⡷⢛⣩⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣈⠴⠋
⠀⠀⠀⠀⡌⠀⠀⠘⠤⠀⢀⣀⣀⣿⣿⣶⣾⣿⣿⣿⣤⣾⣧⣿⣿⣿⣶⠿⣿⣿⣿⣿⣟⣻⣿⣿⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⢊⣡⠔⠋⠁
⠀⠀⡠⠊⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⡟⢛⠛⠋⠩⠓⠠⢄⡀⠀⠀⡀⢀⣀⠠⠢⣀⣬⠴⠚⠉
⢠⠎⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠻⣦⣤⣤⣠⣤⣤⣄⣤⣬⠥⠥⠤⠒⠚⠉⠁
⠂⠀⠀⠀⠀⢸⡿⠂⠀⢠⣋⡧⠀⢀⣶⣿⠆⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠧⠄⠀⠀⠙⠲⠂⠀⠀⠙⠀⠀⠠⣾⠃⠀⠀⠀⠀⠀⢸⡇
⣆⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⣀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠃
⠈⠢⡀⠀⠀⠀⠀⢸⠀⢘⡀⠀⡎⠈⣷⠀⣮⣀⣨⠇⢀⡖⠙⢿⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠘⢦⠀⠀⠀⠀⠉⠉⡇⠀⠉⠉⠀⠀⠈⠁⠀⠀⠈⠓⠒⠛⠂⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⢸⠀⠀⠀⠰⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠈⡇⠀⠀⠀⠈⠁⠀⠀⢰⠖⢦⣤⠶⢦⠀⠀⠐⢉⣱⡄⠀⢻⡟⠁⢦⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠘⠀⠈⠟⠀⠀⡆⠀⠰⢥⡼⠇⠀⠸⠀⠀⠸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠈⠁