⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡅⠀⢈⠿⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⣴⡶⠾⠿⣷⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⢧⡖⡉⠉⠀⣀⠱⠕⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣀
⠀⡿⠀⠀⠀⠀⠈⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢫⢥⡅⡴⠋⠁⠀⠠⠀⠫⢦⢄⣀⠀⠀⠀⠀⠀⠀⢀⠤⣔⠴⠶⢶⣤⡀⠀⠀⠀⡸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⣾⡯⡠⠄⠂⠀⠀⠀⣠⠆⠀⢹⠛⣧⠀⢀⡴⠞⠁⠀⡈⠀⠀⠀⢀⣯⣍⢲⣛⠛⣶⢄⡀⠀⠈
⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣄⣏⣀⣤⣤⠴⠚⠁⠀⢀⡊⠀⢨⣿⠣⠀⢀⡴⠖⠋⠉⠉⠉⠙⠁⠀⠙⠥⣀⡈⠙⢓⣳⠟⠉⠉
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡌⠼⣤⣤⣤⡤⠔⠛⠀⢀⡾⠋⢣⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⣰⡆⠀⠀⠘⣿⠍⣫⢉⠀⠀⠀⢀⣠⡾⠃⢀⠌⡇
⠀⠀⠀⠠⣍⡐⢄⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢮⣔⡀⠐⠈⠿⠋⠀⣠⠎⠐⢥⡀
⠀⠀⠀⠀⠈⠑⣤⣦⣶⣦⣀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⢸⣖⡇⢹⡐⢀⣄⣤⠔⠨⠁⠀⣀⠞⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢿⣦⣽⣣⡀⠀⠀⢠⣆⣲⡾⠽⣆⣾⡨⣎⣁⣀⣀⡤⢄⠆⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⢸⡇⣁⣀⡀⠀⠀⠙⣦⣽⣬⡄⠉⠀⠀⠀⠀⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡅⠀⡏⣼⠉⠀⠻⣦⠀⠀⠀⠻⣿⡆⠀⠀⠀⢀⠤⠚⡿⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⢸⠀⣏⡐⣿⡆⣿⡆⠀⠀⠀⡌⠻⡂⣀⣬⢴⠬⣤⢧⡺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣇⣸⡀⡸⣦⠈⠁⣿⡇⠀⠀⣴⣯⣵⡋⠰⢹⣼⡸⢚⡧⠻⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⡛⡤⢹⡍⠙⠉⠹⣿⢾⡿⢾⡟⠁⠠⢮⣪⠿⡽⢱⠦⢕⠢⢭⢭⠓⢻⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠰⣈⠗⠨⠠⠀⠼⠉⠉⡓⣤⢄⣀⡼⢇⣢⡸⣔⠌⠡⣽⣿⣷⡏⣾⣀⡀⡙⠒⡊⠤⠀⠇⢽⣖⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠠⡜⠛⠶⣴⣽⣋⣿⣿⣾⡗⡠⠄⠈⠉⠁⠀⠀⡀⡄⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣖⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣉⢣⠐⣟⠲⣺⣸⠎⡈⠁⠐⠒⠒⠒⠀⢐⠝⠝⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⡫⠟⠛⠋⠩⠉⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⣮⣼⣁⣹⡇⡇⡿⠆⠱⢀⠀⠀⠀⡀⠀⡌⢀⡛⠀⠀⠀⠠⢐⣰⡴⣃⣙⣫⡄⠤⣂⣠⣤⣶⣿⣟⠅
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠉⠺⢞⣳⣵⣭⢁⠀⠉⣠⠺⢿⠎⡶⣋⣹⡋⠹⠝⣶⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠟⠯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢀⢸⣻⣩⢻⢵⣦⣀⡯⢟⡉⡀⣧⡣⠀⠹⣧⠸⣫⠿⢻⠛⢉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠀⠀⠀⢠⣺⠧⡏⡄⠀⣅⡈⣿⠼⠿⠽⠋⣠⣤⣌⣻⡟⣧⡐⣾⣲⠎⡍⠒⢦⠰⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⠀⢠⣫⣣⡆⡏⢢⢫⣲⣼⡟⣥⠀⢠⡞⢁⣴⢿⡋⡏⠀⠙⠀⠈⠻⠤⢤⢿⣸⣍⣉⡹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡆⣾⡏⢮⣧⢓⣞⠑⠂⣿⢣⢱⢄⣽⣷⡿⠟⣸⢧⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢍⣥⣺⢓⠈⣝⡚⢿⠦⡤⢘⣷⣷⢿⡋⣿⣾⡿⣿⣯⢃⣀⡀
⠀⠀⠀⠀⠀⠤⠠⠤⠆⡀⠠⠤⠭⠍⠉⠉⠂⢂⡠⣶⣾⣿⣿⣿⣾⣦⣩⣰⣤⡤⢿⡛⠉⠻⠴⠭⢟⣿⣾⣿⣶⣶⣆⣄⣐⣒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠩⠘⠛⠫⢽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦⣄⣤⣴⣿⣿⣿⣛⣛⣿⣿⣟⣛⣛⣷⣶⣶⣶⠶⠶⠶⣶⣶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⢉⣍⣉⣉⣉⣉⠭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠛⠿⠛⠿⠟⠿⠉⠉⠍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠁⠛⠛⠛⠉⠉⠉⠉⠉⠁