⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣷⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣼⣟⠀⠀⢀⣾⣣
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣖⣾⡏⠀⠀⢾⣏⣤
⠀⠀⠱⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣿⣿⣿⠀⠀⣼⡿⣆⠇
⠀⠀⠀⠈⢖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⢻⡿⢿⣶⣾⣿⣿⡱
⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⢫⡼⢳⣿⣿⣻⣵⡃
⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⣿⢹⡟⢿⣿⡟⠃
⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣾⣧⣝⣦⡽⠟
⠀⠀⠀⠀⠀⡜⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡤⢠⣄⣵⣤⣿⣤⡄⣀
⠀⠀⠀⠀⢀⢇⡇⠀⠀⠀⠀⠀⠀⣀⡶⠷⣿⣿⣿⠷⣎⡸⠷⣾⣷⣾⢶⣏⡶
⠀⠀⠀⠀⡜⡼⠀⠀⠀⠀⠀⠀⠘⣩⢏⣿⣶⣭⣂⢿⣿⡿⢋⣶⣶⠖⢾⣿⣝⡃
⠀⠀⠀⡰⣱⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⣻⢷⣮⣕⡙⠿⠿⠿⠶⠟⣛⣵
⠀⠀⡰⣱⢿⣵⣶⣦⠀⠀⠀⠀⠀⠘⣿⣿⣛⢣⣇⠿⣿⣿⡿⢻⣿⣿⣿⣿⣻⠟
⠀⡰⡱⣟⣞⣩⢿⣟⡀⠀⠀⠀⠀⣜⣿⣿⢯⠀⠈⠙⠼⣋⠴⣣⣿⣿⣿⣧⣿⢏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡖
⢠⡱⡙⠈⠸⣺⣵⣻⢿⣢⣄⣀⣶⢹⣿⣏⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡶⠄⣀⠀⣠⠶⣿⢿⣣⡧
⡰⣱⠃⠀⠀⠈⠀⠃⠉⠂⠀⠒⠂⠚⠀⠉⠀⠀⠀⠀⢨⣿⣿⣿⢿⣿⣿⣿⣿⣛⠛⠷⠎⠉⠉⠁⠙⠚⠃⠁
⡷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⢾⣿⡎⣿⣿⣿⣿⣷⣡
⡗⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣞⣽⣻⣿⣿⢸⣿⣿⣿⣿⡇⣆
⠛⡴⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⢿⣹⠾⣽⣿⣿⡐⣿⣿⣿⣿⣿⢹
⠈⣕⢣⡓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣿⣿⡽⣻⣿⣿⣿⡇⣿⣿⣿⣿⣿⡼⣇
⠀⠈⠢⡝⣢⢓⡤⢠⠤⡀⣀⢠⣤⣤⣶⣿⣿⢸⣿⣷⢻⣽⣿⣿⣿⡇⢻⣿⣿⣿⣿⡇⣳
⠀⠀⠀⠀⠁⠓⠼⠣⢝⣲⡱⠎⠶⠍⢛⣽⡎⣼⣿⣞⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣵⢯⠗⣿⣿⢾⣿⣿⣿⣿⢿⣿⢸⣿⣿⠃⠙⢿⡎⣿⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣾⢯⣿⢰⣿⣿⣿⣿⣿⡿⣯⡿⢹⠘⣿⣧⣄⡀⠀⣿⣌⢯⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣹⣾⡝⣾⡽⣿⣿⣿⢯⢿⢕⡖⢋⢧⠹⣿⣿⣿⣾⣿⣿⣷⣝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⣷⣳⣿⣿⣽⡳⣟⣿⣿⣯⢟⣷⠧⠂⢠⠹⣷⣌⠻⣿⣿⣿⠀⠉⠙⢳⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⣿⠱⣯⣿⣿⣞⡽⣽⣿⣿⣿⣟⠯⠈⠀⠀⢧⡙⣾⢷⣤⣙⠿⣷⣶⣤⣠⣿⣿⣶⣔
⠀⠀⠀⠀⠀⢀⢠⣞⡏⣿⣿⢸⢷⣿⣿⢾⣽⣿⣿⣿⡳⣫⡃⠀⠀⠀⠐⡻⣮⣟⣾⢻⣷⣮⣙⢿⣿⣿⡇⡩⠛⠿⢦⣂
⠀⠀⠀⠀⠀⠖⣸⣯⢱⣿⣿⣎⣿⣿⣿⣿⣿⣿⣻⢎⣵⡟⠁⠀⠀⠀⠀⢰⡝⢟⡾⣯⣿⣿⡿⣷⣜⠻⣷⣥⣍⣢⠅⣿⣧⠂
⠀⠀⠀⠀⠀⠘⢼⡏⠼⣿⣿⣿⣿⣿⣿⣿⣻⢗⣵⣿⠿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠭⢩⣾⢷⡻⢓⢋⣵⣌⠻⢿⣿⣿⣿⣿⠸
⠀⠀⠀⠀⠀⣏⡰⡈⠶⣿⣿⣿⡿⣿⣹⡾⣱⣿⣷⠿⠆⠀⠀⠀⠀⠀⠀⢸⠉⢷⢈⠹⢏⡁⠆⣷⣿⡿⡿⠹⠰⠆⡉⠿⣿⠁
⠀⠀⠀⠀⠀⢹⣿⣷⣷⣾⣿⣿⣿⣷⣿⡿⣟⡿⠞⠳⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢊⡑⠢⢬⠿⠿⢝⡳⠉⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⢿⣻⣞⠶⢋⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⢱⡷⣾⣿⣻
⠀⠀⠀⠀⠀⠀⠀⢯⣛⠿⠿⡶⠈⠈⠁⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⠆
⠀⠀⠀⠀⠀⠀⢠⣾⣿⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣤
⠀⠀⠀⠀⠀⣼⣿⣿⢯⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⡿⠄
⠀⠀⠀⠀⣠⡻⣿⣧⢿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣶⣇
⠀⠀⢀⣼⣿⣿⡶⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠟⡿⣿⣷⣧
⠀⠀⣾⣿⣿⣯⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠟⡿⡷⡄
⠀⢸⣿⡿⣗⠍⠁
⠀⠈⠯⠓⠁