Muscles Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⠿⠿⠷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡾⠀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠙⡁⠀⠈⠉⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣤⣄⣀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠈⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠁⠀⠀⠀⠈⠀⠂⠱⣸⠃⠻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠢⠀⠽⡀⠀⠀⠿⠢⣄⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠳⣄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⠀⢢⣤⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠈⣦⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠈⠓⠄⠉⠉⢹⣧⡀⠠⠄⠀⠀⠀⢀⣰⠿⢍⣀⡀⠀⢠⣼⡏⢻⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⠻⢿⣿⣿⠿⠛⢋⠉⠀⢠⡤⠈⣉⣿⣿⣿⡇⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠎⠀⠀⠀⠁⢀⣾⣧⡀⢶⣽⣄⡀⠈⢀⡀⠀⢀⡄⢀⣨⢿⡿⣿⣇⠀⠀⢂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢶⡶⠟⠈⠛⢿⣿⣿⠉⠛⣦⠀⡉⠉⠁⠀⠉⠋⢺⠇⠈⠻⣷⣶⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠹⡄⠀⠠⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⡁⠛⠒⠐⠃⠚⡑⢿⠀⠀⠀⢸⣇⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢐⡆⠀⠀⠀⠀⠀⡿⢦⡀⠀⢇⠀⠀⠠⠀⠀⡇⢸⠀⠀⠀⢸⡇⠦⠀⢀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠳⡀⢰⠎⡀⠀⠀⠀⠀⢸⡟⠀⠿⡅⠀⠁⠀⠀⠀⣰⣃⠨⡆⠀⠀⠸⣇⠀⠁⡜⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠑⣌⢰⠃⠀⠀⠀⢀⣾⠖⠀⠀⠄⣶⠄⠀⠀⠀⢩⣱⡆⠵⡀⠀⠀⠙⣇⠀⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⠀⠀⠀⠀⠀⢸⣿⠁⠀⠉⣚⠈⣷⡀⠀⠀⠟⠁⡈⢔⣇⠀⠀⠀⠈⢃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⣼⣯⡂⠀⠀⠉⢀⢏⠳⣄⠀⠀⣠⠁⠀⣸⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠤⠢⢷⡘⣠⠞⠋⠀⠀⠻⡇⠀⢀⠠⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠬⢿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠴⠒⠀⠀⠀⣧⠀⠀⣤⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⠖⠀⠘⠀⠀⠀⠀⠀⠀⠰⠻⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⠀⠀⠀⠀⢠⡾⡟⠛⣻⣿⣿⣴⣶⡄⠀⠀⠀⠀⠀⡈⠉⢙⡲⠠⣄
⠀⠀⠀⠀⠀⠀⢠⣿⢺⣸⠿⡇⠀⠀⠀⢸⠀⡇⢐⣿⡿⠆⢚⡿⠃⠀⠠⠊⠀⠉⠀⠐⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣺⠃⠀⠀⠀⠈⡇⢻⠛⣿⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⠇⡀⣿⠓⡀
⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⠿⠀⠀⠀⠀⠀⠹⣬⣾⡿⡏⡇⠀⠀⠀⠀⠀⠀⠀⢈⢩⣀⡿⠂⡗⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠠⠙⣿⠻⠀⠀⠀⠀⠀⠀⠀⢹⠙⣿⣿⣆⠀⠀⠀⠀⠀⠒⠀⣣⠘⣿⡏⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣷⡇⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣇⣿⠀⠀⠀⠀⠀⠠⣾⣿⠇⢹⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⡆⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⠋⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣦⣸⠇
⠀⠀⠀⠀⠀⢀⢢⣦⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡸⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠘⢻⣘⡍⠇⠀⠀⠀⠀⠀⠀⠀⠈⣆⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣍⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠶⣿⠀⣸⠷⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣿⢿⣝⣃⠈⣴⡿⢿⣿⡏⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠃⣸⡆⢸⡆⠛⢻⣏⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣽⡿⣿⣴⣮⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣶⣶⣇⣷⣾⣿⣶⣾⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣿⣿⡹⠟⢳⠛⢿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣿⡟⢻⡇⣸⠛⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢸⠏⣿⣿⠀⢹⠂⢺⣿⠋⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⠃⣿⣿⠞⠙⠙⢾⣿⡇⢻⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⡼⠀⣿⢽⡉⠸⠁⣙⢽⠀⢰⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠀⣿⣿⠀⠀⠀⢸⣿⡇⠘⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠃⠀⣿⡿⡁⠉⠀⠁⢿⡇⠀⢻⣍⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⠀⣻⣧⣄⠀⢀⣠⣽⡇⠀⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠁⠀⢸⣿⣄⢳⣴⣶⢀⣾⣇⠀⠀⠻⠧⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⢠⣿⡟⠻⣷⡿⠛⢿⣧⠀⠀⠹⡿
⠀⠀⠀⠀⠀⠀⡦⣦⡄⠀⠀⣾⠋⢻⣿⠉⣻⡿⠋⢿⡀⠀⠀⡄⠐⠆⠀⠀⠀⣴⢆⡄⠀⠀⢈⣿⣄⣠⣿⣷⣀⣼⡏⠀⠀⠀⣦⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⡄⢻⡇⣿⢁⢠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢾⣼⣿⣿⡏⣿⣿⣯⣸⡇⠀⠀⠀⠚⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣸⠃⣿⣾⣄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡟⣿⣿⡇⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠹⠀⢸⢸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⡇⠀⢸⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠸⠃⠀⠀⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠄⠀⠀⠸⣿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡄⠀⠀⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⡄⠀⠀⣠⣿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢹⡇⠀⠀⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⡇⠀⠀⣷⡿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠁⠀⠀⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢈⠃⠀⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠶⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇
⠀⠀⠀⠀⣾⣿⣧⡉⣱⣿⣿⡄⠀⠀⢠⣾⣿⣹⠀⣏⣿⣷⡄⠀⠀⠀⠀⢀⣀⢼⡿⢀⣀⠀⠀⠀⠀⢀⣀⣼⠙⣄⣀
⠀⠀⠀⠀⣿⣿⠿⠇⠿⣿⣿⡇⠀⠀⢨⣷⣿⣿⠀⣿⣿⡿⡇⠀⠀⠀⠀⣿⠉⠁⡄⠉⢻⡆⠀⠀⠀⣾⣿⣿⠸⣾⣿⡇
⠀⠀⠀⠀⣿⢻⣄⡀⣄⡸⢻⡇⠀⠀⢰⡘⢿⡟⠀⢻⡿⢃⡄⠀⠀⠀⠀⣿⢰⣤⣷⣴⢸⡇⠀⠀⠀⠛⢹⣤⠀⣴⠈⠃
⠀⠀⠀⢸⡇⢸⣿⣷⣿⣿⠘⣧⠀⠀⢸⡇⡸⠁⠀⠀⢧⢸⡇⠀⠀⠀⢠⡟⣸⣿⣿⣯⠸⡇⠀⠀⠀⡷⢸⠏⠀⠻⡄⣾
⠀⠀⠀⢸⡁⣿⣿⣿⣿⣿⡇⣽⠀⠀⢘⠀⣵⣦⣀⣴⣾⠀⠋⠀⠀⠀⢸⢳⣿⣿⣿⣿⡆⢿⠀⠀⢸⡇⣾⣶⣤⣶⣇⢹
⠀⠀⠀⠘⠀⡿⣿⡍⣿⡟⠃⠈⠀⠀⠸⠠⢿⣿⠿⣿⡿⠆⠙⠀⠀⠀⠴⢸⣻⣯⢹⣿⡇⠰⠀⠀⢰⠀⢿⣿⢻⣿⠟⠠⡄
⠀⠀⠀⠀⠀⣧⣿⠃⣿⣷⠆⠀⠀⠀⠀⠀⣾⣿⠀⣿⣷⠀⠀⠀⠀⠀⠀⠐⣿⡿⢸⣿⡇⠀⠀⠀⠀⠀⣾⣿⠘⣿⣷
⠀⠀⠀⠀⠀⠈⢻⠀⢹⠋⠀⠀⠀⠀⠀⠀⡿⣿⠀⢿⢿⠀⠀⠀⠀⠀⠀⠀⠉⡃⢨⠛⠁⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⣧⡟⠀⢸⣼⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⣆⡇⠈⣇⡆⠀⠀⠀⠀⠀⣼⡟⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⡿⡇⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠿⡇
⠀⠀⠀⠀⠀⢘⠃⠀⠀⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠻⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⡄
⠀⠀⠀⠀⠐⠋⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠂⠀⠀⠀⠀⠀⠊⠀⠀⠀⠃
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣀⠀⢠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣿⣿⣷⠀⢸⣿⣿⠙⢟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣽⠀⢸⣿⠃⠀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠁⠀⢸⣿⣄⠀⢙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠈⠀⠀⢸⣿⣿⣦⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⢸⣏⠿⣿⣿⣿⢡
⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠉⢿⣿⡆⢠⡀
⠀⢶⠿⣛⣻⣟⣻⡛⠛⠉⠐⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣹⣷⣮⣿⣳⣄⢷⣤⣤⣤⣤⣄⢀⣠⣴⣶⠾⠃⠉⢠⢤⡀
⠀⢾⠿⠛⣹⣿⣫⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⣽⣿⡎⠻⣷⡿⣦⡯⡭⠽⢚⣽⣿⡿⠛⠁⠀⣠⠲⠀⢼⣷
⠀⢺⣶⢿⣿⣏⠉⠙⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣝⣿⠇⢀⢼⣿⣿⣷⢲⣾⣿⠿⠋⣀⠀⡠⠊⠁⠀⠀⢾⣿
⠀⠀⠀⠈⢻⣯⣤⠀⠀⠹⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⡆⢈⣿⣿⢇⣿⠛⢋⣡⣶⣾⣿⣿⣏⠀⠀⠀⢌⣿⣿
⠀⠀⣤⣤⣾⣿⡏⢀⣀⣀⣀⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠙⣧⣿⣿⣷⣤⣝⣿⣶⣿⣧⣸⣿⢿⠟⣿⠟⠻⣶⣄⡲⣷⣿⣿
⠀⠀⠈⠉⠉⠀⠀⠈⢿⣿⡿⠻⢿⠿⣧⡈⠙⠋⠉⠉⠉⠉⠙⠟⠛⠀⠘⣽⣿⣿⡿⣿⣿⣿⡇⣿⣿⣿⣟⣦⡾⠋⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡑⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣷⢯⣿⣿⡇⢿⣿⣋⣿⠁⠀⣠⡶⣻⣿⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⣿⣿⡌⣼⡿⢸⣧⣿⣿⣿⣷⣴⣾⣩⣾⣿⠛⠀⠁⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣠⣄⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⢸⣿⣱⣿⠇⠘⣿⣿⡿⣿⡧⠹⣿⣿⡿⠃⠀⠀⢠⣿⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠚⡇⣼⡏⣧⣿⠀⣄⢀⣿⣿⣟⠻⣾⠇⠘⣷⠀⣤⣿⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⢶⠘⢛⢿⡻⣷⡀⠀⠀⠀⠀⠀⠖⣿⣿⣾⣧⣿⠀⠛⣻⣿⣿⠿⢟⣿⠀⠀⢻⣿⡟⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢳⡀⠢⠙⣝⢿⡄⠀⠀⠀⠠⠾⣿⠿⠋⠁⢀⡴⠛⢫⣽⡿⣿⢻⡇⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠣⠀⠙⢌⠃⠙⣦⠀⠀⠘⠇⢸⡆⠀⠀⣀⣴⣾⣿⣿⡷⢻⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠈⠂⠀⢨⣧⡀⠐⠆⢸⠄⠀⠀⣻⣽⣿⣿⡖⣿⠹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠆⠀⠀⠀⠀⠀⠀⡀⢻⣇⠘⠇⢸⡀⠀⠈⣩⣿⣿⡿⡇⢸⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢙⡧⢸⣀⣴⡾⠛⠏⣏⢰⣧⢻⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠃⡿⢿⡋⠀⠀⢠⡿⢸⣿⡟⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣧⡄⢼⡄⠀⠀⠀⠀⠀⠰⠀⡷⠘⢧⢠⣿⢸⡇⢸⣿⣧⢿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡇⠐⠈⠳⣿⣿⠇⠘⣻⣿⣜⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣯⣿⣯⣥⣌⠀⠀⠀⠀⠀⠀⠀⠈⢢⣽⣤⣼⣿⣂⣲⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⣿⡿⠟⣻⣻⡄⠀⠀⠀⠀⠒⠀⠀⠀⣭⠛⣿⡿⣯⣍⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣠⡾⠋⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⡜⢡⡾⠛⠝⠶⠉⠻⣦⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠘⣻⣦⣆⠀⠀⠀⣰⣿⣦⡔⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡇⢆⣰⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⡄⣵⣺⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⡄⠀⠀⠀⠀⠀⠀⢠⢫⣿⣿⣽⣿⣿⣿⣿⣆⡠⡀⠀⢠⣄⣶⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⣰⡌⠀⠀⡴⣡⢿⡿⣯⣿⢣⣿⣿⣿⣿⣿⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣾⣿⣴⣿⢿⡽⣻⣴⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢾⡿⢿⡿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⢻⠛⢻⡟⠙⡿⠻⣟⠿⢻⣻⠟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣾⣿⣾⣷⣶⣿⣶⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⡣⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣹⠋⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣐⠋⠐⢿⠀⠐⢉⠭⠓⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡐⢞⣻⣿⣠⣀⠈⠀⡄⠊⣶⣄⡀⠠⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣣⣼⣿⠞⢻⠁⠀⢰⠀⣹⣿⣿⡦⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⠃⠀⡿⠋⠀⠀⣿⠀⣴⠇⣠⣽⣿⡟⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠏⠀⠘⣿⡧⠀⠀⣧⣼⡏⢴⠤⣾⣿⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⠏⠀⠀⠀⣧⣇⢀⣴⣿⠁⢀⣤⣴⣿⡟⠀⠀⠀⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣤⣴⠏⠀⠀⠀⢠⣸⠟⠋⢹⡿⠀⣸⠉⣽⡿⠀⠀⠀⠀⢱⡀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⡇⢸⣿⡇⠀⠀⠀⠀⠈⣿⣷⠿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⡿⠃⠀⠀⠀⠀⠀⠀⢸⠇⠀⡸⢠⡟⠀⠘⣿⡇⠀⠀⠀⠀⠀⠘⣿⡠⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠊⡱⠋⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⠀⣧⠊⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⢷⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠐⣿⣤⣉⣻⡷⠍⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇
⠀⠀⠀⠀⠐⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠁⠈⢻⣿⣿⡇⠀⣄⣀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⢿⣿⠀⠀⠀⢻⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⢸⡏⠀⠀⠀⠘⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⠀⠀⠀⠀⠸⣿⣷⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⣿⠀⠀⠀⠀⠀⢟⢹⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢩⡇⠀⠀⠀⠀⠀⠘⢶⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣾⣇⠀⠀⠀⠀⠀⠀⠸⡆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⣿⡇⠀⠀⠀⠀⠀⠹⡿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠚⠛⠛⠉⠁⠀⠀⠀⠀⠈⠋⠛⠒⠶⠦⠄⠶⠖⠒⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠁⠉
⠀⢈⣵⣷⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣹⢗⡠⠐⣾⣆⢀⡄
⠀⠀⠘⢿⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣧⣼⣛⣻⣿⣛⡿⠁
⠀⠀⠀⠀⠻⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣵⣄⡀⢀⣀⣀⣤⣄⣀⣠⣾⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣟⠹⣿⣿⡏⢻⣷⠝⣉⣭⣭⣭⠯⣥⣶⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣼⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣙⡟⢁⣴⣉⣉⡷⢤⢀⣿⣟⣀⠛⠛⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣽⣿⣧⡿⠀⣾⢧⣨⣿⣷⣿⣿⠛⣿⣿⣿⣧⣿⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠛⠦⠰⣿⣽⣿⡟⠻⣾⣻⣿⡿⣟⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢟⣠⣿⡷⣶⣶⣾⣿⣴⣿⣿⣿⣿⣷⠈⢻⣏⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣸⠍⣯⠙⠞⠟⣛⣻⣾⣿⣿⣿⡿⠋⣆⢸⣿⣿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣷⡘⣛⣉⡩⣿⡿⣿⡟⠁⠀⠘⢿⣿⡿⢻⣞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⢻⣿⣧⡬⢭⣿⡿⠿⠋⠀⠀⠀⠀⠈⠹⣷⠸⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⠀⢨⣹⣿⣿⣿⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⠀⠸⣅⣿⣿⣿⡷⢺⡅⠀⠀⠀⠀⠀⠀⠀⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡆⠛⠀⢷⣿⡿⢛⠉⢀⠛⢸⡀⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠒⠚⣫⡉⣾⡇⠠⡔⠿⣿⡴⢿⣶⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⣷⣿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣡⣴⣶⣿⣿⡿⠃⡴⠓⠄⠐⢙⡇⢘⣿⢿⠠⠿⣿⡇⠀⠀⠀⠀⠀⣿⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠛⠉⣯⣿⠟⠀⠀⠀⠀⠀⠀⠘⠀⡈⢣⡌⠀⠀⣿⡇⠀⠀⠀⠀⠀⠿⠆⠙
⠀⠀⠀⠀⠀⢀⣴⣻⣿⣿⣿⣿⣿⣷⣧⣾⠿⣷⠿⣷⣶⡟⠲⣶⡆⠀⢦⢱⣿⠀⠀⢻⡟⠀⠀⠀⠀⠀⠘⢀⡀⣤⢂
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣋⠿⣿⣿⣧⠈⠓⠉⠀⠀⠀⣿⠁⣠⡿⠉⠉⠠⢠⡟⠀⠀⠀⠀⠀⠀⠰⠋⠻⠾⢻
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣥⡾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠰⣿⢰⣿⠀⠀⠰⣧⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠘⠻⢟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡿⢠⠀⢠⣿⡩
⠀⠀⠀⠀⠀⢹⡟⣿⣿⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡟⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠘⣇⢹⣿⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢻⡘⣿⣧⣆⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⡿⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠟⣸⡧⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠘⢹⢿⣷⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣠⡿⢳⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢻⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⠶⢎⣿⣭⣾⡟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⣠⠖⣚⣻⣿⣾⣿⣿⣿⣿⣍⣾⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟
⣷⣾⠻⠛⠛⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣭⠁
⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣸⣇⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⣈⣣⣤⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⢋⣾⣧⠾⠛⠛⠷⠶⠶⠖⠒⠒⠒⠶⢶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠀⠈⠁
⣶⣷⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣾⣶⣾⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⡇⠐⢸⠻⣿⣿⡙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⢻⡇⠀⢸⠄⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠃⠹⣿⣾⣇⠀⠀⠀⠀⠘⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢠⣿⡿⣿⠀⠀⡆⠀⠀⢿⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠚⠉⣿⣼⡄⢀⡛⠔⢂⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⡼⠋⠻⠇⠘⠁⠀⠈⠀⠀⢫⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⠀⠀⠀⠀⠀⠀⣀⢠⡄⢠⡬⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣏⠀⠀⠀⠀⣠⡴⠞⣅⠀⡃⢘⠃⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣝⠀⡀⠀⡾⠁⣇⠠⢏⠘⠇⢸⣷⠘⢿⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⡳⠉⣸⠇⢸⢾⡄⠸⠃⠀⠸⢻⡄⣷⣝⢿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠔⣠⣾⡏⠀⣾⢸⠀⠀⡄⠀⠠⠋⠁⣿⠉⠀⠀⠩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠁⠈⢠⡿⠟⠀⠀⣿⢸⢰⡇⢰⡖⣧⠀⣾⣿⡇⠀⠀⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⠁⠀⣸⣿⠟⠀⠀⢰⡿⠀⢾⣇⠀⣷⡿⠀⣿⣿⣇⣈⣶⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢀⣴⣿⣷⠀⠀⠀⢸⡏⠀⢸⣿⡄⢹⣷⠀⣹⣿⣿⣿⣿⠀⠀⡈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⢠⣿⣿⡿⠃⠀⠀⠀⢸⡇⠀⣸⣿⡇⠈⡷⠀⢿⣿⣿⣿⣿⠃⠀⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠌⠀⠈⢈⣋⠀⠀⢀⣶⣆⢸⡇⠀⣿⣿⣧⠀⢁⠀⢸⣿⣿⠏⠙⢦⠀⠀⡸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⢻⠀⠀⠀⠈⣿⡿⠀⠇⡆⢹⣿⣿⡆⠘⣦⠼⣿⣿⠀⠀⠀⢁⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣀⢈⣤⠁⠀⠀⣾⠀⡍⠀⠀⠀⡇⢸⣿⠇⠀⠀⣧⠀⢻⡟⠀⠀⠀⠀⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⣰⠀⣼⡇⠀⠀⠀⡟⠀⡿⠁⠀⠀⠘⠀⣾⠃⠀⠀⠀⠀⡀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢰⠀⢠⣿⡞⠁⣠⣠⠀⢰⡇⢠⣧⡀⠀⠀⠂⢠⡟⠀⠀⠀⠀⠀⠰⠄⠠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡈⠀⢸⡿⠀⠀⣿⠡⠀⢸⣿⠏⠀⢻⠀⠀⠹⣾⠁⠀⠀⠀⠀⠀⠀⢠⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⡀⠁⠀⣸⠃⠀⠀⠉⠀⠀⣿⡏⠀⠀⠸⡆⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠘⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠏⠀⠀⠠⠇⠀⠀⢿⠀⠀⠀⡀⠀⠀⣿⠇⠀⠀⠈⠁⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⡞⠀⠀⠠⠶⠀⢀⡿⡄⠀⠀⠸⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⡟⠀⠀⠀⣧⠀⠀⠀⣱⠂⠀⠀⢠⡀⠀⠀⡼
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇⠀⠀⠀⠘⠇⠀⢠⡟⠀⠀⠀⠈⠧⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠌⠀⠀⠀⠀⣼⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⣧⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⠄⣼⠃⠀⠀⠀⠀⠀⠈⢀⡇
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢸⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣄⠀⢀⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣹⣿⣿⡂⢸⣿⣿⣽⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⠃⠈⣿⠃⠛⢯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠸⣿⣇⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⣿⠹⣿⣿⣿⡸
⠀⠀⢀⣀⣤⣄⣠⣀⣀⣀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣦⡈⢻⣿⡇⠠⡄
⠀⢺⣻⣿⣿⣿⣿⣛⠋⠉⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣌⣿⢶⣿⣾⣄⠳⣦⣤⣴⣶⡆⢠⣴⣶⡿⠛⠁⢀⡴⢦
⠀⢿⠛⣋⣽⣯⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⢾⣿⡇⠙⢿⣿⣷⡷⠴⢖⣩⣿⣿⠟⠋⠀⣠⡔⠂⠀⣾⣧
⠀⠾⠿⣿⣯⡅⠀⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣮⣿⡓⢠⣰⣿⣿⣿⣳⣿⡿⠛⢁⣄⣀⣔⠈⠀⠀⠐⣿⣿
⠀⠀⠀⠀⢹⣿⡶⠀⠀⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⢸⣿⡇⠠⣿⣿⠃⣿⡉⢁⣴⣾⣿⣿⣿⣿⡀⠀⠀⣿⣿⡟
⠀⠐⢶⣶⡿⠿⠦⣤⣤⣤⣤⣿⣿⣄⠀⣀⣀⣀⠀⢀⣀⣠⣀⣀⠀⢈⣽⣾⣿⣿⣶⣦⣿⠿⣿⣷⣿⣿⢿⣻⣿⠟⢹⣷⣤⡛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠙⠏⢻⣦⠀⠉⠁⠀⠀⠈⠈⠉⠉⠀⢀⣿⣿⣿⡟⣿⣿⣿⡆⣿⣿⣿⣿⡿⠟⠁⢀⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⢻⢫⣿⣿⡇⣽⣿⣿⣟⠀⢀⡼⣫⣾⣿⠿⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢈⣼⡿⣟⡏⣼⡟⢸⣿⣾⣿⣿⡿⢾⣯⣾⣿⠏⠀⠀⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣈⣿⢡⡟⡜⣿⡇⠈⢟⠿⢻⣿⣇⢹⡿⣿⡇⠀⢀⣀⣼⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢬⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡉⢼⣾⣷⡽⣿⠃⣤⣠⣾⣿⣧⣹⣿⠁⠸⣧⣰⣿⠿⠟⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢣⡈⢯⠻⡻⣷⡀⠀⠀⠀⠀⣉⣹⣿⣿⠿⠛⠉⣀⣽⣿⣿⣝⣿⡟⠀⠀⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢱⠈⠣⡜⣎⠳⡀⠀⠀⠀⡉⠻⡋⠁⠀⠀⠛⣩⣴⣿⣟⣿⣹⡇⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠐⠈⠂⠙⣆⠀⠀⣉⠘⡇⠀⠀⣤⣿⣿⣿⡛⣿⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡉⠀⡇⠀⢀⡼⣿⣿⣿⡇⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠳⡈⠻⢄⣧⠀⡇⠀⣠⣶⣿⣿⣿⣷⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠄⠀⠁⠀⢈⡗⢰⣷⡿⠋⠀⡟⣿⢸⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⢠⡄⠀⠈⠀⠀⠀⢀⠁⠊⠹⡇⠀⣷⢡⡿⢸⣿⡟⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣧⣦⣷⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⢶⣿⣸⡇⠸⣿⣧⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⠰⣿⡿⠛⠄⠀⠀⠀⠀⠀⠀⠸⣄⠢⡈⢻⣿⡅⢠⣾⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⡿⡄⠀⠀⠀⠀⢠⠀⠀⠀⢿⡿⣿⣿⣶⠓⠒⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢁⣼⠟⠉⠙⠸⣿⣆⠀⠀⠀⠀⠀⠀⢠⠎⣠⣾⢿⣟⠳⣤⣀⡨⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⠁⠀⠀⠀⠀⠙⢻⣄⡀⠀⠀⠀⢀⣾⣜⡉⠀⠈⠀⠁⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⣀⢀⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠐⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣯⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠐⣹⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⡀⣤⣦⣻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡼⠀⠀⡠⠀⠀⢀⡔⣱⣿⣿⣾⡟⣿⣿⣿⣿⣷⣷⣦⣪⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣰⣾⣷⣤⣴⡞⣴⣻⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠀⣶⡷⢦⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣠⣶⣿⢫⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣰⣿⣔⠂⠛⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣭⣾⣿⣿⣆⣬⡩⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣈⣡⡬⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣽⢘⡧⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣹⡟⢁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢀⠠⠉⢂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠿⣿⣿⡿⢫⠟⢳⣿⣿⣿⣗⣠⣿⣼⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀⣴⠎⣁⡤⠛⠀⠈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣀⣀⣀⣈⣁⣀⣀⠀⠉⠀⣿⣿⣿⣿⣿⣿⡹⢉⣏⣉⡉⠈⠙⣿⣾⣿⠿⣶⡟⢀⣤
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣋⣽⣿⡄⠀⠀⣿⡃⢹⡿⣿⣷⣶⣾⣿⠶⠾⠿⠷⠤⠬⣾⠿⣶⣾⠋
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢼⣿⣿⠁⠿⠛⠿⢿⡯⠛⣷⣶⣤⠀⠄⠠⠴⠛
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⣿⣇⢠⣧
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⣹⣿⣿⣿⣿⣿⣹⣿⣿⣿⢻⣟⡟⠃⠀⢻⠿⢿⡏
⠀⠀⠀⠀⢀⡾⣯⠀⣿⠁⣠⣿⣿⣼⣿⣿⣿⣿⣿⣿⣾⡿⠁⠀⠀⠀⢠⡀⠈⡇
⠀⠀⠀⠀⣼⣷⣿⣠⣿⣶⠟⠀⢿⣿⣿⣿⣿⣿⣿⣻⠿⢇⠀⠀⢀⠀⠀⠹⠆⡇
⠀⠀⠀⣰⣿⢿⡿⣿⣿⠋⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢷⣦⠀⠀⠀⠐⠂⣼⠂⠁
⠀⠀⢀⣿⣿⣾⣸⡏⠀⠀⠀⠀⠀⠀⠙⣿⣍⣯⣙⠿⣯⡙⠀⠀⡆⠀⠀⠘⣿
⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣼⣿⠀⠀⢿⠆⠀⡀⣻
⠀⠀⣾⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢈⡉⡁⠈⠀⠀⠐⠀⠀⠀⢹⡄
⠀⠀⣿⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⡟⠻⣶⣤⣿⣤⠀⠀⠀⣧⠀⠀⢸⠁
⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣰⡏⠻⣦⣌⡙⠻⣿⣆⣠⣤⣿⣷⣴⣏⣀
⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⡏⢉⣀⠀⠍⢻⣧⠹⣿⣿⣿⣿⣿⣿⣿⡌⠛⠂
⠀⠀⠀⢿⣿⠻⠿⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣷⣦⣼⡿⢠⢻⣿⣙⣿⣟⠀⠙⢿⣆⣲⡀
⠀⠀⢀⣿⣿⠖⠷⠀⠀⠀⠀⠀⠸⣿⠀⣾⡿⣤⢉⣿⡇⠘⣿⣿⣿⣿⣈⠃⣀⡻⠻⣿⣧⠀⠐⢦⣄⠀⠀⠀⣀
⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣆⣸⣷⠟⢿⣿⠀⠀⠀⢻⣿⣿⣿⣷⣜⠛⢧⡉⠙⢷⡀⠀⠹⣿⡷⢦⣤⣤⣄
⠀⢸⣿⣿⢿⡟⠻⡗⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠈⢳⣆⡼⠀⠈⣿⡟⠉⠺⣿⣷⣦⣉⠓⢾⣿⣇⠀⢸⣿⣶⣈⣿⣿⣷⡀
⠀⠘⠿⠅⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⢀⠀⠀⣿⠁⣠⠀⢻⡇⠀⠀⠀⠙⠻⢿⣷⣦⣭⣻⣿⣦⣿⣿⣿⣍⡙⠛⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⠀⠋⠀⠹⣀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡇⠀⡄⠀⠈⡟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣽⠿⠈⠁⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠇⠀⣿⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⠀⣿⠰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⡎⢰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⢿⠂⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡘⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢷⠀⠃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣷⡞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⡇⠸⠂⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡞⢁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣸⠇⣼⡄⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢀⣿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠿⠿⠛⠷⠾⣷⣶⣤⣌⡁⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠿⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣤⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣼⣿⣿⣿⡿⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⢴⣾⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠫⠙⠉⠉⠀⠀⠀⠈⠀⠀⠀⠈⠙⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⠛⠳⠁⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣶⣃⣀⠀⠀⣀⣠⣎⠀⠀⠀⠀⡱⠄⠀⠤⡀⠀⠠⡀⠀⠉⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠟⠈⢛⠟⠣⡴⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠒⠂⡐⢀⣘⠈⠙⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣻⠀⢀⡎⠀⠀⢸⡇⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⡮⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⣉⣄⠘⣇⡀⠰⣾⣿⣦⣀⣳⣄⢈⣿⣆⡀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠅⠀⢈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⣶⣶⣅⣄⣀⣀⡀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⡻⣿⡿⠻⣯⣽⣟⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⣛⣿⣿⣿⣿⣯⣭⣭⣿⡿⣛⣴⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠁⠹⣿⣿⣿⣮⣹⣿⠿⢿⣿⣿⣿⡖⢤⠴⠒⠢⣼⡟⣻⣿⠿⢿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠀⠀⠀⠀⠋⠙⡿⢿⣿⣿⣆⠀⠹⠉⣿⡇⠀⠀⠀⢠⠉⢠⡿⠁⣠⣾⣿⡿⣋⣵⠟⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⢷⣝⠳⡈⠻⣦⠀⢀⣿⡇⠀⠀⠀⢸⡀⠘⠁⣴⣿⠟⣡⠞⡛⠛⠀⠀⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⠿⣷⣬⡑⠮⡂⠈⠷⢸⣿⡇⠀⠀⠀⠈⡇⢀⡼⠋⠠⣪⠥⠬⣡⣤⣤⣤⣤⣤⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠁⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢹⡄⠀⠀⠈⠁⢀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣾⣭⣭⣁⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⣉⣩⣭⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠀⠀⡀⢰⣿⣿⣿⣿⣄⠋⠁⡤⠄⠊⠃⠄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠠⣀⣀⡀⠀⠻⠟⠉⠉⠙⢿⣷⣿⣤⣄⢀⣀⣄⣡⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢾⣥⣤⣤⣤⣤⣤⡽⠿⠿⠧⣤⣤⣤⡄⠈⠉⠀⠉⡙⢻⣿⣤⣬⣭⣽⣿⣶⣶⣶⣾⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣟⣹⢛⣟⢋⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡎⠀⣠⣦⠈⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⢀⣦⡀⠈⣲⣤⡀
⠀⠀⠀⠀⢀⢄⣠⡼⠟⢁⡴⢫⣿⠛⠹⣧⣄⣀⣀⡀⠀⠀⠀⠀⠀⡿⠿⠧⠤⠤⠿⠿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣤⡼⠙⠻⣿⡳⣄⠙⠻⣤⣀⢀
⠀⠀⠀⣔⡵⠋⠉⠀⢀⣾⣴⣿⠁⠀⠀⠀⠉⠛⠟⠁⠀⠀⠀⠀⠀⡄⠙⠛⠗⠿⠛⠁⣼⠀⠀⠀⠀⠀⠙⠻⠋⠁⠀⠀⠀⠹⣷⣜⣇⠀⠈⠉⠱⣄⡄
⠀⠀⢸⣿⠁⠀⠀⠀⠨⢾⣿⡥⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡏⠇⣬⠕⠬⡄⠏⣃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⣽⣿⠮⠃⠀⠀⠀⢸⣿
⠀⠀⡘⠿⣧⡀⠒⠢⢶⡟⠋⠀⠀⠠⣘⣶⠀⠀⠀⠈⢲⣄⠀⠀⢸⢿⣆⢀⣉⣉⢀⣾⢿⡀⠀⢀⣴⠊⠁⠀⠀⢰⣶⡠⠀⠀⠈⠛⣿⠦⠒⠂⣠⣾⠟⡂
⠀⠀⠙⠻⣄⠀⠀⠐⢺⣗⠤⠀⠀⠀⠈⣿⣿⣧⣀⠀⠈⠉⠛⠛⠾⢠⣝⣿⣿⣿⣛⣥⠸⠞⠛⠊⠉⠀⢀⣠⣿⣿⡟⠀⠀⠀⠀⠴⣿⠓⠂⠀⢀⡼⠟⠁
⠀⠀⠀⠀⠈⢻⣷⠮⠍⠻⣷⣦⣄⣀⣠⣿⣿⣟⣶⠨⠀⠀⠀⠀⠀⠀⢙⣿⡿⣿⣟⡁⠀⠀⠀⠀⠀⠨⢴⣞⣿⣿⣧⣀⣀⣤⣶⡿⠋⠭⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠛⣿⣿⣿⣷⡦⠼⡿⣷⣤⡀⠀⠀⠀⠀⠈⣿⣟⣿⣏⠄⠀⠀⠀⠀⣀⣴⡿⣿⠥⣶⣾⣿⣿⡟⠋⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢶⣿⠿⠿⡿⠁⣰⠀⠹⣿⣿⣾⣷⣶⣶⣶⣶⣿⣸⣸⣷⣶⣶⣶⣶⣿⣶⣿⣿⠁⢰⡄⠙⡿⠿⠿⣷⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⣿⠀⢀⣾⣻⣿⣿⣿⡿⠿⠿⠯⣽⡭⠿⠿⠿⣿⣿⣿⣿⢻⣇⠀⢸⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣾⣁⡟⠁⣻⠋⢀⣀⣀⣀⣿⣇⣀⣀⣀⡀⢻⡇⠙⣧⣘⣦⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠉⣽⠁⢰⣿⠟⠋⠉⠉⠻⣧⡿⠋⠉⠉⠛⠻⣷⠀⢸⡏⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣿⠀⠸⣇⠀⠀⣀⣀⣠⡟⣷⣀⣀⡀⠀⠀⣿⠀⢸⣟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠄⠲⣿⡿⠟⠛⠉⠻⣾⣿⠋⠙⠛⠿⣿⡷⠆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⢸⠁⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⢹⠁⢠⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠂⠸⣧⣀⣀⣀⣼⣷⣿⣤⣀⣀⣠⣿⠂⠚⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⢿⠉⠉⠀⠀⠹⠁⠀⠀⠉⢹⠇⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣤⣤⣴⣤⣤⣴⡾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⡿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⢻⣿⣿⣿⣸⣿⢿⣿⢣⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣥⣶⣾⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠈⢿⡿⠿⠇⡿⠋⠉⠙⠻⣿⣿⡿⠟⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⣛⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠈⣿⣶⣿⠿⠿⢛⣛⣭⣭⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠶⢦⡿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⠀⠀⠀⠀⢹⣆⣀⣀⣤⣄⣀⣴⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣴⣦⣤⣤⣽⣿⣿⣶⣤⣤⣴⣿⣿⡿⠿⠛⣿⡟⠛⢉⣠⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣽⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣦⣤⣾⣿⢹⠉⢹⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⡁⠀⠀⠀⠀⠀⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⠃⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣟⣉⡉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣭⡿⠀⠀⠀⠀⢸⡇⣿⣿⣯⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡆⢸⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⣀⣤⣄⣀⡀
⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⢿⣿⡟⠋⠙⠛⠇⠀⠀⠀⠀⢀⡄
⠀⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⡁⢀⣶⡟⠑⠾⠋⠿⢇⣰⣄⣤⣴⣿⠇
⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣻⠠⣀⣈⢀⣙⠛⢛⡋⠉⠉
⠀⢿⣿⣿⣿⣿⣿⣆⢠⠀⠀⠀⠀⠀⠀⠀⣠⡜⠟⢉⠴⠖⠀⠁⢻⡧⠀⠉⠛⠻⠀⠀⠀⠀⠠⠶
⠀⠘⣿⣿⣿⣿⣿⣿⡄⣆⠀⢀⣄⡀⢠⣿⣿⢸⣞⣿⡈⠀⠀⠀⣻⡇⠀⠀⠀⢠⣰⡶⠶⠶⣷⣦⠀⡀
⠀⠀⠹⣿⣿⣿⣿⣿⡇⣿⣷⣾⣿⣿⣿⣿⣟⣄⣽⣿⣷⣀⡀⣠⢿⣤⠀⠀⠀⢠⡇⣀⡀⣀⡉⠛⢀⡀
⠀⠀⠀⠙⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠉⠋⠉⠉⣿⢉⡿⠤⣦⠉⠛⢷⣿⣿⡿⠟⠟⠉⠀⢀⣼⢿⡤
⠀⠀⠀⠀⠈⠻⢿⡿⠣⣿⣿⡿⠛⠋⠀⠀⠀⠀⢀⣤⣿⣺⠿⠰⣟⡓⣚⠹⠃⠁⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣏⣧⠀⠆⠀⠈⢁⣴⡢⠞⠁⠠⠞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠛⠛⠿⣿⣿⣶⣶⣶⣶⡿⠯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡏⠀⠀⠀⠙⣿⣿⣿⡋⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢹⡇⠀⠀⠀⠀⢸⢿⣿⣿⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⡶⠀⠀⢷⠟⠸⡏⠻⣧⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣿⡇⠀⠀⣸⡄⠀⣇⠀⠙⣧⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠹⠿⡦⢶⠟⠀⠀⠹⣧⡀⠈⣿⡀⢀⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢢⣄⣤⠄⢦⡀⠀⠀⠀⠈⠻⠾⢿⡟⠋⠀⠁⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡿⣷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⣶⡆⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⢸⣿⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⡈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠀⠀⣀⣀⣤⣍⣙⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⢀⣴⠿⠛⠛⠛⠛⠛⠛⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠖⢁⣉⣘⠂⢰⣯⣤⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠙⣿⡀⠀⠀⠀⠈⠉⠀⠈⢁⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⠳⠄⠀⠀⠀⠀⠀⣀⠜⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⢹⡿⠿⢶⣶⣶⡶⢾⣿⣿⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠑⠀⠀⠀⠈⠁⠘⣿⣿⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣦⣽⣿⣷⡶⠶⣦⣤⣤⣽⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣈⡿⠿⠿⡦⢠⣷⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠋⢁⣤⠾⠋⠁⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣄⠀⠀⠀⢀⡿⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡰⣿⡇⢃⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠋⣼⣿⣿⠷⠦⠤⠚⠁⠀⠀⠀⠿⠁⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⣿⡈⠀⠀⠀⣀⣠⡄⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣇
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⣿⣷⣠⡴⠛⢉⣠⠶⠛⠉⠛⠿⢶⣦⣤⣤⣴⣶⣶⣿⣿⡿⠋⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⣿
⠀⠀⠀⠀⢠⠏⠀⠀⣴⠀⠀⠀⠀⠘⣿⣿⣶⣾⠛⠁⠀⢠⡇⠀⠀⠀⠀⠈⠉⠻⣿⣿⠉⠉⠀⠀⠀⢿⣿⣆⠀⠀⠀⢀⡄⠀⠀⢿⣷⣀⣿
⠀⠀⠀⠀⡞⠀⠀⠀⣿⡀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠄⠀⢸⡦⠶⠖⠒⠛⠂⠀⠀⠘⣿⣇⣠⡴⠂⠀⠈⢿⣿⣷⣄⠀⠀⣷⠀⠀⠘⣿⣿⣿⣷
⠀⠀⠀⢨⠃⠀⠀⠀⢹⣷⡀⠀⣰⣿⠏⢹⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿⣇⣀⡴⠀⠀⠀⣻⣿⠛⢷⣾⣿⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⠀⣾⠀⠀⠀⠠⣬⣿⣿⣿⡿⠁⠀⢸⣿⣧⠀⠀⠀⢸⠗⠊⠉⠉⠉⠀⠀⠃⡇⠀⣿⣿⡉⣠⠀⠀⠀⣿⡇⢀⡴⠛⠛⠳⠀⠀⠀⠀⢻⣿⡇
⠀⠀⢀⡇⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⠀⣿⡇⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⢀⣧⡇⠀⢸⣿⡟⠁⠀⠀⢰⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣿⣷⡠⠤⠀⠀⣶⠒⠀⠀⠀⠀⠿⣼⠁⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⢸⡇⠀⢸⣿⡇⠀⠀⣠⡟⠙⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⣷⠀⠈⠲⣄⡀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢽⢸⡇⠀⢸⣿⣇⣀⡴⠋⠀⠀⠀⠀⣀⣤⠾⠋⣱⣿⠿⠃
⠀⠀⠀⢸⡄⠀⠀⠈⠛⢿⣿⠃⠀⠀⠀⠀⣿⣿⣶⠶⠶⣾⣿⣤⣤⣤⣤⣤⣧⣿⣤⣤⣼⣿⡿⠋⠀⠀⠀⡤⠶⠛⠉⠀⣠⡾⠟⠁
⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⠒⠀⠀⠀⢀⣐⣶⣶⣶⡿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠘⣆⠀⠀⠀⣨⣧⠴⢤⣀⠀⢠⣿⣿⠟⠓⠀⠀⠀⠀⣻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢻
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣀⢉⣻⣿⣿⣿⠀⠀⠀⠀⢠⡾⢅⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣇⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠉⢀⣸⣿⡿⠀⠀⠀⠀⠸⣇⣀⣀⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⢻⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣶⡀⠀⠀⣀⣤⡶⠿⢿⣿⣿⣿⣆⠈⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠟⠛⠉⠀⠀⠀⠀⠉⠻⢿⣆⣸⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⣿⣿⣿⣿⣥⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠻⠿⠿⠟⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡴⠶⠆⠀⠀⠰⠶⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠀⢰⡀⠀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⢀⣀⣠⠖⠀⠙⠻⣾⡁⠀⣀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⠀⢈⣷⠟⠋⠀⠒⣄⣀⡀
⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠙⢟⠛⠛⠛⠻⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⠛⠛⡻⠋⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠉⢻⣿⣿⡟⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡀⠀⠀⠀⠀⠀⠐⣿⡿⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢠⣿⣦⠀⠀⣀⠀⣰⣦⠀⠀⠉⠉⢻⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡟⠉⠉⠀⠀⣴⡆⠀⣀⠀⢀⣴⣿
⡏⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣰⣦⣄⣀⣠⣴⣾⣿⣿⣷⣦⣄⣀⣠⣴⣆⡀⠀⢀
⠸⣄⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⣿⣿⣿⠟⠛⠟⠿⣿⣿⠿⠻⠛⠻⣿⣿⣿⠟⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠈⠉⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⢀⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡀
⠀⠈⠻⣾⣿⣿⣿⣿⣿⣦⣴⣤⣶⠶⠾⢷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⡾⠷⠶⣶⣤⣦⣶⣿⣿⣿⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠙⠛⠿⠿⢛⡿⠿⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⢿⠛⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠘⠉⠙⠻⣶⣤⡀⠀⠀⢀⣤⣶⠟⠋⠉⠃⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠟⠉⠉⠻⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣾⣦⣀⣀⡴⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⢦⣀⣀⣴⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⣯⠀⠈⠉⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠉⠁⠀⣽⠿⣄
⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠙⢦⣤⠞⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠳⣤⡴⠋⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⢲⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡆⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⢀⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⡀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠠⣅⠀⠀⠀⣀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣀⠀⠀⠀⣨⠄
⣤⣤⣤⣤⣤⣤⣤⣽⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣯⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠁⠀⠀⠸⠇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⢦⣄⠀⠀⣼⠀⠀⠀⠈⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢤⣠⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣿⣵⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢂⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣀⠀⠀⠀⢀⠐⠢⣄⠀⠠⠈⠠⣄⠀⠀⠀⠊⠁⣾⡏⠀⠀⠀⠀⢠⡄⢀⣀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣈⡀⠀⠈⠙⠀⠀⠀⠙⠃⡀⠀⠀⣸⡿⠂⠀⠴⠃⠀⠹⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠂⠂⠉⠉⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠠⠶⣎⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣼⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢀⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠉⠉⠁⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠶⢶⣯⡴⠇⠀⠀⠤⠤⣿⣟⣠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠒⢄⡈⠳⣌⢀⠠⣼⠓⠀⢀⣿⠃⠀⠀⠀⠘⣧⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⢳⡄⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠈⠓⠀⠀⢹⣿⡟⠛⠛⠛⠓⠒⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣿⡀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣷⣿⠿⠆⠀⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣿⡟⠁⠀⠈⡄⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⣾⣿⠇⠀⠀⠀⠹⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⣿⠿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣟⣻⣟⣿⣿⣿⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡃⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⠐⠃⡀
⠀⢀⣀⠀⠐⣬⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠐⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⣠⠏⠀⠀⠀⢀⠴⠀⠀⣁⠈⠀⠀⠀⢀⠀⠀⡴⠋
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⢀⣀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⢀⡈⢉⠀⠀⠉⡠⠆⠀⠃
⠀⠀⠀⣀⠀⠀⠀⠋⠀⠈⠛⠂⠴⠓⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠀⠀⡄
⠀⠀⠂⠌⠀⠀⣀⢀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠛⡒⠤⠀⠀⢸⠀⠀⠀⠀⠂⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⡀⢀⡠⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠄⠄⠀⠀⠀⠀⡀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⠀⢀⠌⠀⠠⠒⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠱⠄⠀⠣⡀⠐⠁⠿⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⠀⣀⠀⡀⠀⠀⠀⠀⠋⠒⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⡴⠒⠀⠀⠀⠀⠀⠐⡌⠓⠀⠃⠀⠀⠀⠀⠀⠁⠂⠀⠀⠐⢢⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⡄⠐⠀⣠⠞
⠀⠀⠤⠀⠀⠓⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣴⢟⣉⡁⢀⠀⡀⠀⠀⠀⠀⣉⡡⠤⠔⠋
⠀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠷⠀⠀⠀⢀⡤⠀⡆⠀⠔⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠒⠋⠁⠐⢀⣡⣌⠢⣀⡤⠟
⠀⠉⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠋⠉⠉⠈⠉⠈⡧⣈⠂
⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⣠⡄⠀⠹⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⡰⠃⠀⠀⠀⠄⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⡀⠀⠈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠢⢌⠙⢤⠀⠀⠀⠀⠀⠁⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⢇⠀⠀⠀⠀⢤⣀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠒⠒⠀⠀⠀⠀⠀⠐⢄⠀⠈⠀⠀⠀⠀⠀⢀⠀⡸⠁⠀⠀⠀⠀⠈⠗⢠⡎⠀⠀⠀⡀⠀⠀⠀⠀⠈⡦⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡤⠒⢀⠀⠄⢀⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢀⠤⠀⠀⠀⠀⠃⠀⠀⠠⠀⠸
⠀⠀⠀⠀⠁⠊⠀⠀⠀⠈⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠐⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠉⠛⢳⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠭⠀⠘⠿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠉⠁⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠈⠉⠉⠀⠘⠦⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠋⠀⣀⣀⠀⠁⠀⣀⠀⢀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠂⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣆⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣿⡟⠷⠤⠤⠖⠋⠈⠓⠲⠶⠶⠾⠏⢡⣧⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡏⢹⡀⠀⠒⠒⢀⠀⠛⠛⠉⠀⠀⢀⡞⠙⢦⡀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠂⢀⡼⠁⢸⡀⠀⠒⠀⠈⠠⠤⠤⠖⠀⠠⡟⠀⠀⠀⢁⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠃⢠⠀⠀⠉⠀⠀⠀⢰⠀⢀⡇⠀⠀⠀⠸⡇⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⡼⠀⠀⣼⣀⢸⡆⠀⢸⠀⠀⢀⡟⣀⣸⣇⠀⠀⠀⠀⠹⣆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡼⠁⠀⣼⠓⠍⡛⠛⠓⣾⣟⣛⠛⣛⠉⠡⢿⡄⠀⠀⠀⠀⠹⡆⠀⢿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⠁⠀⠀⠁⠒⠚⠁⠀⠈⢿⠉⠁⠀⠘⠓⠒⠘⡇⠀⠀⠀⠀⠀⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠰⡄⠘⣇⠧⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡗⢠⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣿⣆⣸⣿⣤⣾⣇⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⣿⣷⣿⡟⣿⣿⣿⣿⣿⢿⣷⣴⡿⠁⠀⠀⠀⢀⠀⢠⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣹⣿⣿⣿⠟⢣⢻⣉⣩⣽⣧⣿⣿⣿⣿⣾⡟⠰⣦⣼⣷⣾⣷⣿⣶⣿⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣛⠿⣅⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣉⠉⢻⡟⠁⠈⢻⣿⣧⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣾⣿⡿⠟⠛⠉⠹⡍⠉⠉⠛⠻⣿⣿⣿⣯⣷⣾⣿⣦⣤⣾⠿⣿⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣰⣄⣶⣲⢽⣿⣫⣿⣿⠟⠉⢦⣀⣠⠤⢶⣷⠶⠦⣤⣞⠀⠈⠛⢿⣿⣾⣿⣿⡿⠀⠀⠈⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠃⠀⣠⠞⠻⣀⠀⠠⡿⠄⠠⣯⠟⠓⣤⢀⣨⢿⣿⣿⣻⡾⢿⡟⢻⣜⠛⠂
⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠲⣴⣇⢀⡀⠋⠀⣀⣅⣄⠴⠉⠢⡀⠘⢻⡀⠀⢻⣿⣿⣷⣾⢷⡞⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⡇⠀⢰⡏⠈⠛⠀⢠⣿⣿⡿⣇⣾⣦⠀⠀⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣙⣿⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⢼⣗⣲⡆⠀⣿⣿⣿⣅⣿⣿⣿⠆⠀⠓⠂⣿⠉⠉⣿⣿⣿⡿⡜⡟⠛⠒⡾⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⡇⠀⣠⡀⠘⢿⣿⣾⣿⣿⠟⠀⣰⢦⣀⡟⠀⢀⠿⣿⡋⡠⢟⣙⣤⣘⡳⣇⠑⢄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⡔⠋⠻⢭⣻⣿⣿⣿⡄⠀⣹⣾⠟⠓⢀⡀⠈⠉⠉⠀⣠⡄⠀⢉⡟⠓⠦⣼⣿⠒⠽⣱⡟⠉⠉⠉⢻⣎⢶⡩⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣧⡀⢀⣸⣿⣿⣽⣿⣿⣎⠁⠈⠳⣤⣼⠋⠀⠘⠇⠀⠈⣭⡶⠋⠀⠀⣜⢫⣏⣀⡇⢿⡀⠀⠿⠀⢠⡿⢘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⠛⠉⢻⣿⣿⣿⣿⣿⣿⢿⣿⣷⣄⠀⡰⠉⠛⠒⠒⡗⠚⠉⠁⠘⢠⣬⡷⠿⢿⣭⣵⠛⢌⠻⣦⣤⣴⠟⡡⠯⣝⡳⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣄⣀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣦⣤⣄⣀⣧⣤⣤⣶⠔⣶⣿⣇⣀⣸⣧⣈⣣⣴⢫⠖⠒⢶⢻⣠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣹⣿⣿⠏⠀⠉⣿⣿⣾⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⢛⣿⡿⢧⢿⣿⠟⠻⣎⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⠿⣷⣤⣴⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⢸⣿⣿⣿⣷⡒⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣛⣿⣾⠂⠉⠉⠙⣿⣿⣿⠉⢹⣿⣿⡇⠈⠉⠒⢦⣄⡀⠀⠀⣰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣄⠀⢀⣰⣿⣿⣿⣷⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣷⣦⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⢿⣿⣿⣿⡟⠋⠉⠻⣿⣿⠏⠁⠈⠙⣿⣿⣿⣿⣌⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⡀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣿⣿⣿⠉⠙⠁⠙⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⡿⠿⣿⣦⣴⣾⣿⣿⣿⣷⣾⣿⣿⡉⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡿⠉⣿⡿⠻⣿⡟⢻⣿⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠻⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⢰⣿⠀⠈⣁⣾⡆
⠀⠀⠀⠀⣤⠛⣿⡇⠈⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⡇⠀⢹⣿⡇
⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠃⠘⣆⠀⠀⠀⠀⣾⠏⠹⠟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠘⣆⠀⠀⢸⠉⠠⠄⣀⡀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣁⠀⡄⠉⠙⢦⠈⢀⣤⣤⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⢿⡇⠀⠀⠈⢿⣦⠈⢈⣡⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡏⠀⠀⠀⠀⠻⣿⣿⣿⣉⠣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⣧⠀⠀⠀⠀⢀⠉⠈⠀⠀⠀⠈⠉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⣿⣦⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠙⠉⢛⣶⠋⣴⣄⡀⠀⠀⢐⣶⣆⠀⠘⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠈⠉⢀⠈⠻⣿⣿⢿⣿⣿⡏⢷⣄⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠒⠏⠙⢷⣦⣤⣬⣿⣿⡟⠀⠀⠙⠻⢶⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⢘⣽⣿⣯⠟⠀⠀⠀⠀⠀⠀⠻⠶⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠀⠀⠰⢯⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠖⠊⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⢠⣄⣀⣄⣠⡄⢶⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢺⣿⣿⣿⣡⡜⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣄⣿⣿⣿⣾⣿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠻⣿⣿⣯⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠉⣿⣿⡏⠀⠀⠀⠀⠀⠘⠻⠆⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⢉⠉⠙⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠶⠚⢧⠀⠈⠂⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⢠⠞⢃⡀⠈⠛⢦⡜⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠊⠀⠨⣍⣲⠀⢀⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⡀⠲⡄⠀⢀⢰⡏⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢱⡀⠁⠀⢤⡟⣠⢾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⠙⣆⠀⠙⠲⠤⣤⡴⠃⠀⠀⠉⠛⠲⣦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠏⠁⢤⣼⣀⣬⠶⠶⠖⠶⠶⠶⠶⢦⣄⠀⠀⠀⠙⠋⠀⠈⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢠⡎⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⡆⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⠀⢀⡀⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢿⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡋⠉⠉⠉⠉⠙⣷⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢤⡿⠃⠐⢂⣛⢉⡑⠲⠶⠶⠶⠶⠶⠶⠶⠞⠋⠁⠀⢷⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡌⢻⠀⣰⠋⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠾⠳⣤⡀⠀⠀⢠⠇⠀⠀⠀⢿
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⣀⡼⠁⠈⢧⡈⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢉⣿⠇⠀⠀⣴⠂⠀⢸
⠀⢀⣀⣿⠸⣄⠀⠀⠀⣠⠞⠉⠀⠈⠉⠉⠀⠀⠀⣀⡽⢦⠀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣤⠞⠁⢻⣀⣰⡇⠀⠀⠘
⣰⠯⠉⣹⠆⠈⢷⡤⠞⠁⠀⢀⣀⣠⠤⠀⠀⢀⡴⠋⠀⠈⣾⣧⠀⠀⠀⠀⠸⠓⢤⡀⠀⠀⢀⣠⣤⠖⠛⠁⠀⠀⠀⢹⣧⡗
⢳⡶⠒⣿⠀⠀⠀⠀⠀⠀⠀⠬⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⢸⠇⠀⠀⣴⠃⠀⠀⠀⠀⠀⢈⣠⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣰
⠀⠙⢇⣼⣇⡰⠾⠶⠖⠒⠒⠶⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⡞⠁⠀⠀⢀⡀⢀⡴⠛⠁⠀⠀⠀⠀⠀⣀⣀⣤⠟⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⣤⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⠞⡉⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠐⠿⢊⡿⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣆⠀⠀⠀⣠⠖⣫⣖⣤⣀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠛⠊⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣹⠟⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⣤⠴⠞⠉⠀⣠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡴⠋⠀⠀⠀⣠⠞⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡏⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢷⣄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢷⡄⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⢦⡀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣿⣦⠀⠀⠉⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡏⠘⣆⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢸⡇⠀⢹⡆⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠈⣧⠀⠈⢿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠛⠁⣀⣠⣤⣀⣀⡿⠀⢠⡟⢀⣠⡿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣯⣤⣦⣤⣤⣶⣶⣾⣿⣿⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠁⠙⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠉⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢣⡀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠁⠀⠑⠄⣀⠐⠘⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢞⣫⠭⢍⡁⠀⢀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠠⢤⣝⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠏⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⢳⡄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⣿⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠠⠴⣾⡿⠿⠻⠷⢶⣤⣤⠶⠾⠛⠋⠀⠙⠲⠤⣶⠏⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠠⡶⠚⠉⠉⠉⠙⡏⠀⠈⡿⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢀⡟⠀⢀⠀⢸⡟⠛⠛⠙⢿⣇⠀⠀⠀⠀⣠⡇⠀⠲⢤⣄⣠⣿⠤⢾⠷⢴⠞⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢸⢇⠀⠀⣷⠀⣇⠀⠀⠀⠈⠻⣧⡀⠀⠀⠙⣦⠀⢀⣀⣀⣴⣏⣠⡏⠀⢸⡇⠠⡆⠀⢿⡄
⠀⠀⠀⠀⠀⢸⡆⠀⠀⡟⢠⡏⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⡇⠀⠀⠀⠀⢸⠇⢸⡇⠀⢸⡄⠀⢳⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠹⡆⠀⠇⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡈⠀⠀⠀⠀⠈⠀⣸⠃⠀⠀⠻⣄⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⠉⠓⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠈⠃⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠚⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣻⣿⠵⡇⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡾⠇⠀⣀⡼⢿⣿⣿⣭⣩⡿⢤⣤⡀⢀⣀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠉⠁⠀⡴⠋⠉⠀⠀⠈⠉⣋⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⠉⠘⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⡄⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠉⠉⣿⣉⠉⠀⠀⠀⠀⠤⣤⣴⣷⠆⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢿⣾⡇⠟⠙⠁⠻⣟⠁⠀⠀⠀⠀⠈⠛⣿⡅⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡶⠉⠃⠀⠀⠀⠀⢻⣷⣦⣤⣤⣤⣴⠞⠿⠳⣶⣤⣤⣤⣤⣴⡇⠀⠀⠀⠀⢷⡀⢦⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠆⣤⣼⡄⠘⠀⠀⣠⣾⣿⠟⠛⠃⠈⠁⠀⣶⡄⠼⠀⣙⠁⠸⣿⣿⣄⠀⠀⠀⣹⡇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⢹⣿⣶⡶⠛⠁⠈⠙⣇⠀⠘⠃⣄⣀⣴⣄⢠⡜⠉⠀⡖⠉⠀⠀⠙⢳⠶⠋⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⢤⠀⣏⠁⠀⠀⠈⠀⢹⣧⣤⢤⣤⣀⣸⣇⡀⠈⠁⠀⢸⡇⢀⡄⠀⢺⡇⠀⠀⠀⠀⠸⣄⠀⠁⠀⠀⠑
⠀⠀⠀⠀⠀⣠⣌⣉⣧⣾⣴⣿⣾⡄⠋⠠⠀⠠⢦⣴⡿⢋⣶⣾⣧⣼⣿⣍⢡⣤⣷⡀⢠⣄⠸⠇⠀⣀⠙⣦⠀⠀⠀⠈⠳⣿⡶⠀⠀⢀
⠀⠀⠀⠀⢤⣠⣸⣿⣿⣿⣿⣿⣿⣿⠀⡆⠀⠀⣸⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣜⣍⡿⣉⣼⠷⠠⠀⣉⠣⠘⣧⡀⠀⠀⠀⠀⣷⣴⣇⣨
⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⢀⠀⠀⢉⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠠⡆⡆⠹⡄⠀⠈⢳⡄⠀⠀⠀⠀⣻⠿⣿
⠀⢘⣃⡀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⣥⢰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣹⣏⣸⡄⢳⡀⣷⠀⡀⠀⢷⠀⠄⠀⠘⠁⣤⣿
⢰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠹⣇⣼⠁⠀⢾⠀⠀⠀⠠⠀⠐⠋
⠀⠀⠁⠀⠀⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢷⣼⠁⠻⣿⠀⠀⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠽⠛⣿⣿⣿⣿⠿⠆⠀⠀⠀⠰⠿⣿⣿⡿⣿⡿⣿⠛⠈⢁⡞⠁⠀⠀⠈⠀⠀⢠⡿⢻⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⢓⡀⣜⠛⠿⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠨⠉⠁⠘⢣⠀⠀⠀⠀⠀⠀⠚⢧⣀⣴⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⡇⢸⡀⢈⡇⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠘⢡⠈⢃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠈⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠚⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⣙⢻⡋⣉⠛⢛⣟⠋⣿⡿⣻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡔⣍⣁⣀⣀⣈⣹⡵⣄⣤⣤⣤⣤⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠓⢸⣿⣿⣿⡟⣳⣾⣤⣠⡈⢀⠀⠀⣀⣱⣧⣼⢻⣿⣿⣿⡆⠈⠘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⢠⡟⠀⣹⢟⣣⣹⣏⣘⣿⣯⡉⢹⡄⣿⣿⣿⣧⠀⠀⠀⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡀⢤⣿⣿⣿⣿⡶⣟⣽⣿⡿⠟⢛⡛⠿⢿⣿⣿⣿⣇⣿⣿⣿⣿⡄⠠⢀⣯⣉⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢸⣿⣿⣿⡇⢠⣿⡟⠁⠐⠀⢸⠃⠀⠂⠉⢿⣷⡌⢸⣿⣿⣿⡇⠀⠀⠀⠸⡗⢻⣿⣷⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢸⣿⣿⣿⡇⣿⡟⠀⠛⠀⠀⢸⡀⠀⠀⠚⠈⢿⣷⢸⣿⣿⣿⡇⠀⠀⠀⢀⠟⣫⡿⠿⢿⡃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠱⢤⠤⢼⣿⣿⣿⡿⣿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣾⣿⣿⣿⡷⢤⡤⣤⣼⡼⡿⠁⠰⣟⣙⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇⢻⣿⡄⠿⠀⡀⠀⠀⢀⡀⠚⣰⣿⠇⣿⣿⣿⣿⠀⠀⠀⢸⣩⠼⠃⠠⣖⠻⣏⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⣿⣿⣿⡄⠻⣿⣶⣄⣁⠐⠂⣀⣥⣾⣿⠋⣸⣿⣿⣿⠇⠀⠀⠀⡘⠁⠀⣴⠲⣎⠛⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠹⠅⠛⠻⢿⡿⠿⠿⣛⡫⣹⠙⠛⠛⠛⠛⠉⠉⢉⡉⠁⣴⠶⡜⠓⢾⡗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣾⣽⢷⡞⣷⢠⡶⣦⢠⢶⡄⣿⢹⡆⠹⢦⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠼⣿⡁⢸⣧⠟⠸⣠⡇⢙⣿⣇⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠋⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣆⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣿⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⢀⣿⡇⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⡤⠞⠁⠀⠀⢀⣴⡿⠟⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⣿⠁⢀⠜⠀⢀⣤⣤⣾⡟⠉⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣶⡾⠟⠋⠁⠀⢸⡟⠀⠁⠀⠚⠁⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣧⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣀⣀⡀
⠀⠀⢰⠟⠀⠀⠀⣠⡟⠁⠀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⢠⣾⣿⡟⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠈⠁⠈⢳
⠀⠀⡻⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⡤⡼⣷⣴⣶⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⢻⣷⣴⣶⣶⠶⠶⠶⣦⣀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠃
⡠⠞⠁⠀⠀⠀⢻⠀⠀⠀⢀⠞⠁⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠘⠀⠀⠎⠀⠀⢀⣀⣠⣤⡶⠶⠟⣿⡟⠋⠉⠙⣿⣿⣆⠀⠀⠀⠀⠙⠷⠶⣤⡀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠏⠀⠀⢠⣿⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠘⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣤⣤⠤⠤⢄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⣿⣇⠈⠉⠛⠿⢿⣧⣄⠀⠀⠓⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⣰⠚⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣇⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⠿⢶⣶⣤⣤⣤⣄⣀⣤⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠉⢠⡞⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⢻⣆⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⣫⣿⣿⠟⠀⠀⣿⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠋⠁⣠⣾⣿⣿⠁⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣾⣿⠟⠁⢻⣇⠀⠀⠀⠈⠻⣆⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⣴⣿⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠉⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣸⣿⠇⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣆⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠙⠦⣀⠀⠀⠀⠀⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠞⢻⣿⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠷⠴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃

⠀⠀⠀⠀⠀⠀⡀⠀⣈⢠⡀
⠀⠀⠀⠀⠀⣸⣏⠀⢁⣼⡷
⠀⠀⠀⠀⣮⢉⣿⠀⠸⣿⣧
⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⣿
⠀⠀⠀⠀⠻⣿⣿⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⢳⡄⣀⠻⣄⠀⠀⠀⠀⢀⣴⣦⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠘⡆⠀⠀⢀⡿⠃⠈⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠹⠦⣄⠀⠇⠈⠁⠒⠂⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⢦⣾⠀⠀⠘⣦⡄⠻⠛⢆⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⣿⠀⠀⠀⠘⢿⣦⣴⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠈⠛⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⣧⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠙⠟⠳⣦⡼⢣⣀⠀⠀⠀⠠⣤⡀⠀⠸⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠛⠃⠘⠻⣿⣶⣶⣿⣿⡟⣦⡀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠐⠞⠻⢷⣤⣈⣙⣿⣿⡟⠀⠈⠛⢶⣤⡀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢘⣿⣿⣯⠟⠀⠀⠀⠀⠀⠘⠷⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠠⠄⠀⠠⢯⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠒⠊⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡴⣤⣤⣤⣤⣄⢶⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠸⣿⣿⣿⣥⡌⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣿⣿⠇⠀⠀⠀⠘⢿⣿⡳⠻⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠸⠿⠏⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣾⣿⡶
⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠈⠉⠉⣿⡿⠃⠀⠀⠀⠀⠘⠛⣿⣿⠟⠀⠀⠀⠀⠀⠸⢿⣿⠋
⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣀⡀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⢀⣾⣿⣇⣀⣀
⠀⠀⠀⠀⠛⢿⣿⣷⣦⠀⠀⠀⠀⠘⣻⣿⣿⣟⡀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠘⢻⣿⣿⠟⠁⠀⠀⠀⠈⢹⡟⠁⠀⠀⠀⠉⠁⣸⣿⡟⠁
⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠉⠙⠳⡤⠶⠠⠀⡀⠀⠀⢀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⣼⣿⣓⠦⣄⡀⠀⢀⣀⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠳⣄⠉⠉⠀⠀⠉⠻⠋⠉⠩⠋⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠴⣚⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⠷⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣥⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⡀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠳⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠁⠀⠀⠀⠀⠁⢐⡟⠀⠀⢀⣀⣠⡴⠖⠋⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠈⠛⠻⢯⣍⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⣻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⢾⡛⠉⠋⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠃⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⢰⣴⣮⡀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡼⠃⢿⠹⣿⡏⠇⠙⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣠⢤⡖⠒⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⠁⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣆⠀⡤⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠲⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡏⢸⡄⠀⠀⠀⠀⢀⣄⠀⠀⠀⢘⡆⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠀⠀⠙⠶⣤⣤⠶⠋⠹⣄⣀⣠⡾⠁⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀⠀⢀⣴⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠈⠻⠛⠁⠹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⡀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣷⣦⣤⣤⣄⠀⣠⣿⣿⣿⣿⣯⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠘⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣯⣭⣧⣬⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⣿⣷⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⡶⠒⠛⠛⠙⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠏
⠀⠀⠀⢠⡇⡰⣊⠩⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⡟
⠀⠀⠀⢸⡇⠁⠁⠀⠙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠘⠒⠒⠲⢦⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⠛⠉⠉⣹⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣹⠇⠀⠀⠀⡜⠀⣀⣀⡀⠀⠀⠀⣴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⢉⡟⠀⠀⠀⠀⣼⠃⠀⠀⢀⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣯⣤⣄⠀⠀⠀⢲⡏⠀⠀⠀⠀⠉⠉⢉⡽⠃⢀⢀⡼⠁
⠀⠀⠀⣿⣀⣠⣤⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⣏⣴⡶⠟⢋⡏⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣢⡟
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⣁⣀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠟⢛⡿
⠀⠀⠀⠀⠀⠰⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢠⠏⠀⠀⠀⠀⠿⠛⠒⡖⠀⢠⡟
⠀⠀⠀⠀⠀⢸⡧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡤⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠟
⠀⠀⠀⠀⠀⢸⡇⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋
⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠠⡇⢷⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡴⠶⠖⠒⡒⣲⠆
⠀⠀⠀⠀⠀⢰⣶⠛⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢀⡇⠈⢣⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⡶⠛⠁⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⢠⡶⠞⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡞⠉⠀⠀⢀⢂⡴⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣰⢏⠀⠀⠀⠀⢠⣿⣃⣀⣀⡀
⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⣭⠇⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠐⠉⠉⠉⣩⠞⠁
⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧⣤⡄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠠⣞⠃⠀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠓⢲⠀⠀⠀⠀⠀⣸⠀⢀⡀⠀⢠⠞⠀⠀⠀⢰⡯⠶⠖⠚⣿⠀⠀⠁⣴⠋
⠀⠀⠀⠀⠹⣆⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡜⡀⢸⠀⠀⠀⠀⠀⠙⠋⢹⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡄⠀⠀⠀⠀⠀⢀⡟⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠹⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡇⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢨⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠙⠙⠂⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠋⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠀⠐⣂⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡖⠀⠀⠀⠀⠀⣼⡆⠀⠀⠰⡀⠁⠋⠀⢹⡵⠋⠀⠰⢀⠀⢀⡁⢀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡭⠁⠀⠃⠀⠈⠓⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠊⠰⠄⠀⠀⠀⠀⠊⣭⢤⡼⢃⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠸⣦⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠒⠒⢿⡣⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢴⡾⠛⠓⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡄⢸⣷⠀⣿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⣀⡏⠉⠁⠐⠘⠀⠀⠀⣤⠠⠞⠃⠰⠆⢠⣤⣌⡶⡚⠀⡆⠀⢩⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣼⠃⠁⠀⢰⠆⡴⠃⠰⠦⠐⠤⠄⠀⠃⠀⣀⣀⣤⢅⡆⠇⢴⡀⢈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣾⠗⠀⢠⡖⠐⠺⢦⡀⡦⠤⢿⣷⣶⣶⣦⣭⣥⣴⣾⣿⣷⣆⣀⠘⣿⣯⡴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠻⣦⣒⠲⣽⣮⣻⣯⣙⣭⢙⠉⢻⣭⣿⣤⣯⣛⣛⡛⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠛⠉⠀⣯⣽⠙⣈⣁⢉⡞⠂⠨⣻⣿⡃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢊⠉⠹⠻⡇⠳⢷⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠉⡛⣻⡆⢀⠤⡆⢄⢟⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⢸⠀⣘⡇⠸⡀⣴⣿⣨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⣼⣿⡏⠗⢀⣀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠃⠿⠿⠁⠶⠌⠁⠀⠙⠋⢹⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠰⠀⣀⠀⠀⠉⠙⠃⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⣲⣿⣠⣄⢲⣴⣤⣤⣦⣬⣿⣟⡾⣠⣤⣀⣰⣽⣿⣵⣆⣀⠀⠠⠤⠶⡤⣦⣤⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠠⠤⠤⠬⠿⠿⠶⠌⠐⠂⠒⠚⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣠⠀⣠⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⣠⣻⠂⠀⢈⠁⠰⠦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠺⠐⠩⠙⠀⠈⢦⣤⣅⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡀⠀⠀⣀⡀⠀⠉⡿⠡⣤⡒⡆⠀⢀⠀⠄⠐
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠩⡐⠐⠲⣋⡦⠴⡤⡒⠐⠀⠙⣦⠀⠀⠠⠐⠈
⠀⠀⠐⢋⣠⣀⠀⠁⠀⠀⢐⣶⠦⠄⠠⡄⠀⠠⠀⡀⡿⠀⠀⠈⠉⡔⠸⡁⠦⠔⠆⢱⡖⠀⠄⠀⠐
⠀⠀⠀⠉⠩⠙⠛⢡⡾⠋⣡⠦⢄⠀⠀⠈⠁⠀⠀⠈⢷⠄⠀⠠⠦⣤⠓⠉⣀⡙⠉⠉⠂⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⢀⣬⣾⣝⡛⠛⠦⠄⠀⠀⡀⠀⠀⠀⢈⣀⠏⠙⠋⠃⠀⠀⠀⣀⠀⡀⣌⡉⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣼⣿⠋⢻⣿⣿⣶⣤⡨⢒⡠⠑⠶⡶⠦⠴⠮⣿⡾⢍⡿⠋⢷⢿⣦⡀⠉
⠀⠀⠀⠀⢠⡾⢈⠁⡤⣋⡽⣿⣿⣿⣿⣿⣟⡿⣤⣥⢈⡵⢀⠀⠈⠳⣦⡀⠨⠑⢭⣟⠛⠂⡀
⠀⠀⠀⠀⣸⠀⡈⢼⡁⠯⠀⣼⣟⠛⢿⣿⣿⣿⣿⣿⣿⡙⢧⡑⢄⠀⠈⠻⣷⣦⠀⢿⠳⢄⠈
⠀⠀⠀⢀⣿⣧⠈⣆⢱⡀⠘⣿⢻⡄⠀⠹⣿⡏⠃⣿⡻⠿⣶⠁⢄⠀⠢⠄⠀⢻⣷⣀⢀⠀⣽⣆⣦
⠀⠀⠀⠀⠡⢾⡇⣘⣷⣟⡷⣬⣍⣷⣤⣀⢿⣿⠈⣼⣷⡆⢸⣧⡀⢀⠀⠈⢶⠀⠜⢏⠘⡇⠈⠋⢧
⠀⠀⠀⠀⢸⠔⢳⣼⠣⣽⡭⢚⠙⠛⠻⠿⣿⣬⠜⣽⠙⠃⠀⠀⠉⢦⠐⠨⡎⢶⢀⣿⣤⢹⣦⠀⢸⡆
⠀⠀⠀⠀⠈⣤⡀⣿⣷⣿⣝⡾⢿⣭⣿⣽⣿⣷⣾⡝⣡⡄⠀⠀⠀⠈⣁⠀⣽⡌⢠⡝⣾⣬⣽⣧⡿⠃
⠀⠀⠀⠀⡀⢽⣦⢻⣿⣧⢿⣷⣿⣿⢴⣷⣶⣾⣿⡟⠉⠀⠀⠀⠀⢠⠉⠁⣈⣿⣶⣙⢿⣿⣿⠟
⠀⠀⠀⠒⢀⡿⣿⠾⠿⣿⡏⠀⠀⠉⠙⠿⢽⣿⣿⣿⣤⣄⠀⠀⣠⣾⡷⢤⣛⣻⣿⣿⠻⣿⠏
⠀⠀⢠⣾⣿⣾⠟⣿⣦⣝⣷⡀⠀⠀⠀⠀⠀⠙⢻⣷⣬⣙⠷⣸⣿⠏⠀⠀⢸⣿⣷⣿⣷⠇
⠀⠀⠾⠿⠿⣧⣄⠹⠿⣯⠻⠷⡄⠀⠀⠀⢀⡴⠞⣹⢿⠟⣵⡟⣾⠀⠀⠆⢺⣹⣿⡿⠋
⠀⠀⠀⢀⡤⠀⠈⠙⠳⠈⢮⠀⠀⠀⠀⠈⠜⠡⠚⢉⣳⣿⠫⡼⡃⠁⠀⠈⣩⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⢈⠟⠧⣾⢽⠃⡄⢀⣣⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠘⣶⢻⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠈

⠀⠀⠀⠀⠀⠀⣀⠄⢊⡔⠊⠁⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠉⠐⣀⠃⢤⡀
⠀⠀⠀⣠⡤⠟⢡⢖⡿⠋⠧⣤⣤⡀⠀⠀⠀⠾⣿⣶⣾⡿⠆⠀⠀⠀⢠⣤⡤⠏⠻⣟⢢⠙⠷⣤⡀
⠀⢀⣾⠁⠀⠀⣿⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⡣⣄⠩⢉⠤⡇⠀⠀⠀⠀⠁⠀⠀⠀⣸⣿⡧⠀⠀⢹⣦
⠀⢘⡻⠄⠐⢶⡟⠋⠀⠀⣶⡀⠀⠁⣦⣀⣀⢷⣄⣠⣀⣴⢧⣀⢠⡖⠁⠀⣰⡆⠀⠈⠙⣷⠖⠂⠼⣟
⠀⠀⠙⢦⣄⡩⢿⣄⠀⠀⣹⣿⣶⠀⠀⠈⠉⠐⢾⣿⣿⠖⠈⠉⠀⠀⢠⣾⣿⡁⠀⢀⣼⠯⣁⣤⠜⠁
⠀⠀⠀⠀⠻⣄⠀⠙⣿⣿⣿⠭⢿⣦⣀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣠⣾⠯⢭⣿⣿⡟⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⢁⡆⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⠀⣆⢹⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⣣⠋⣿⢋⣀⣀⣽⣇⣀⣈⢻⡏⢳⣱⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣿⢰⡟⠉⠉⠉⣿⡏⠉⠉⠙⣷⢘⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠠⣷⡶⠖⠺⣿⡿⠒⠶⣶⡧⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⠀⠀⠀⣿⡇⠀⠀⢸⡁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⡗⠒⠚⠻⠛⠒⠒⡿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣧⡀⠀⠀⠀⠀⢀⣧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠓⠚⠋⠁

⠀⠀⢀⠐⡢⠙⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠀⡒⢀
⠀⠀⡈⠀⣧⠀⢀⣬⣦⣴⡈⢩⢳⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠻⠌⡱⠤⣤⣬⣄⢀⢃⡇⠈⡀
⠀⠰⢿⣄⠁⡐⠈⠈⡆⠀⠀⢢⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠞⠀⠀⠀⡌⠀⠀⣀⢁⣼⠧
⠀⠀⠀⠣⠷⠼⠇⠴⠃⠀⠀⠈⡀⠘⣄⠀⠀⠀⠀⢠⡶⣶⣦⡀⠀⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠳⠄⠾⠵⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⢲⡀⠀⠀⢸⠠⠀⢄⡇⠀⠀⢠⡎⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠠⠈⠀⠩⣂⠀⣅⠀⣬⢀⣴⠋⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠁⠄⠀⡀⠀⠬⠅⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⠀⣄⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢿⠶⢚⣭⣒⢶⡟⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠸⠃⡦⠘⡉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠉⣯⠁⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢣⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠋⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⢂⠶⠖⠛⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣂⠀⠀⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡒⣄⠀⣸⣹⡆⠀⠀⢠⠊⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢷⡜⣧⢻⡄⣷⢺⡇⠀⠀⠠⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠙⣇⠀⠀⠀⠀⠀⢀⣤⣤⣝⣦⡹⠞⠊⠉⠉⠉⣽⢳⠀⣂⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⠠⢈⢽⡀⠀⠀⠀⣾⠞⢁⡽⠉⢀⠀⡄⣸⠤⡷⣿⢸⠇⠨⠂⠐⠂⠔⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠲⢶⡀⠀⠀⠀⠙⠲⣄⣀⣈⣳⡞⠀⠀⣄⢷⣼⡶⣛⣿⠿⠿⠶⡄⢧⣀⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⣌⡂⠄⠉⠈⣩⠋⠹⡀⢤⣝⣿⡋⠘⠻⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢉⡦⠍⠢⠀⠀⠀⠈⡉⠐⢻⣔⠗⠁⠀⠀⢠⣤⡥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠉⠀⠀⣎⡠⣀⣄⣀⣦⠐⢾⣎⣉⡟⠀⠀⠀⠀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡞⢁⠴⠐⠦⡉⢳⡟⣫⡅⠠⠞⠀⡀⡤⣼⠙⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⣼⠀⠡⠁⠀⠁⢸⠀⣽⣿⡷⢀⠀⠀⠭⠁⠛⠀⠐⣿⣲⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⢀⠼⣆⠢⢅⣀⡠⠎⣰⣾⢛⡀⠨⣿⠛⠓⠲⣦⠠⢤⠋⠉⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣢⠏⠀⢌⢷⣦⢤⣴⣶⡿⠃⢄⠐⠀⠈⠣⡀⡐⠉⢛⠨⡆⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢫⣷⠃⢀⣡⣴⠎⠉⡛⠉⠁⠀⠀⣠⣷⣄⠂⢰⠌⠿⠷⢊⣼⠉⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣏⡟⠀⠠⢬⡿⠖⠦⢤⣤⠶⠓⠊⠉⠉⠀⢱⣬⠾⣚⣿⠉⠀⠒⡖⢌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣇⣀⣀⡸⠂⢀⡋⠒⠠⠷⣶⡴⣤⠆⢚⣛⣦⠰⣿⡿⠃⢀⢠⣉⢦⢚⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣻⠉⠉⠉⣗⣠⣁⣰⣼⣷⣦⡀⢿⡤⡆⠄⣼⢀⣠⠇⠐⡠⢄⠓⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⣷⠇⠀⢀⡔⠉⠉⠉⠁⡉⠱⣏⣀⣙⠛⢛⣁⣈⡇⠀⠠⢀⡟⠑⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⣴⠛⢦⣇⠈⠟⠀⠀⠀⠀⡰⠀⠁⠘⠒⠚⠈⠉⠳⡀⠒⣄⠑⣄⡧⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡼⠛⢄⠀⠂⢝⡴⠱⠆⠀⠀⠀⠀⠀⢀⠛⡘⡞⠥⡇⢸⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣝⢦⣴⠋⠓⠦⣆⡈⠃⠀⠀⠉⠁⠀⠀⠠⠄⡡⠛⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡼⠓⠃⠀⠀⠀⠀⠙⠳⠦⢴⣤⣤⣤⡤⠶⠛⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠐⠫⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠆⠀⠀⠀⠀⣰⣿⣿⡶⠛⠀⠀⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠼⢿⣿⡿⠋⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢈⡽⠟⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢀⠐⡁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠁⠌⠁⠀⠀⠀⠀⠀⠐⠁⢠⢌⠁⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⢃⠔⠃
⠀⠀⠀⠀⢀⢀⡘⠂⡰⠀⠀⠀⠀⠈⠀⡪⠐⠁⠀⠀⠀⠀⠈⣱⠃⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⢀⠔⠁⠈⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢴⡩⠇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠠⣸⣁⣀⡀⠀⠀⠀⡠⠋⢠⣎⠁⠀⠀⠀⣠⠊⢘⡂⠖⠀⠀⠀⠀⢠⠎⣠⠄
⠀⠀⠀⠀⠰⢓⢖⡴⠋⠀⠀⠀⠈⣩⡿⠒⠁⠀⠀⠀⠀⣩⠏⠋⠀⠀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠰⠎
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣎⠁
⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀
⠀⠀⠀⠀⠐⠛⠛⠋⠉⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⡶⠾⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣀⣀⣀⡄⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠉⠉⢀⡇⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿
⠀⡀⠀⣠⡶⢻⡄⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠙⣦⠄⠀⠀⠀⠀⠀⠘⣿⠙⠛⠳⠿
⠀⠱⠞⠁⠀⠈⢷⣀⣴⠟⠉⣷⠀⠀⣠⠔⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⢠⣤⣄⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠘⣧⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡇
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⠔⠂⠀⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢀⠀⣀⠀⠀⠇⠀⠀⠀⠯⡀⠀⠀⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠂⡀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠔⠋⠈⠲⠖⠂⠀⢰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢰⡄⠀⠀⢀⠡⢀⡆⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠎⠀⠀⢀⠄⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠰⠋⠈⠑⠂⠂⠀⢸⡇⠀⠀⠀⠤⠀⢂⡃⠀⠀⠀⡀⠀⠊⠁⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⠤⢄⡀⠀⠄⠀⢠⠞⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⢰⠇⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠔⠀⢀⡼⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠤⠦⢄⡀⠀⠀⠀⠀⠀⠈⣦⠀⢀⡴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣁⣒⠀⢀⣀⠠⠄⠀⠀⠀⠈⠠⠄⠈⠀⠠⠞⠁⠰⡅⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠀⠀⠀⢄⠀⠀⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠇⠀⢡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠲⠶⠤⣄⠀⠀⢘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠠⠐⠚⠛⠺⣟⠂⠼⢻⠃⠁⠉⠉⠉⠉⠉⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⡿⠶⠖⠚⠀⢀⣈⣩⣭⠥⠤⠤⠤⠀⠀⠀⢑⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⣸⠁⠀⠀⢀⡥⠞⠉⠀⠀⠀⣀⣀⠤⢔⣢⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠠⠃⠀⢀⡜⢰⠇⠀⠀⣀⣀⠤⢀⣠⡤⠀⠩⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢰⠇⢀⠆⠀⢠⠏⢠⠟⡀⠀⠀⢡⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡉⠲⣤⣤⠀⠀⠒⠚⠉⠁⠀⠉⠁⠀⣸⣠⠏⢀⡴⠃⣠⠏⠀⠈⢢⠀⢸⠇
⠀⡀⠀⢀⠤⠚⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠞⢀⡴⠃⠀⠀⠀⠀⢣⠀⠀⢀
⠀⠀⠠⠯⠤⠤⠤⠤⠄⠒⠒⠒⠀⠈⠉⠉⠉⠛⠒⠲⠶⠶⠤⠤⠭⠭⠬⠿⠋⠀⠀⠀⠀⠀⠀⠤⠷⠶⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣏⣴⣶⣿⣿⣶⣄⣀⣠⣤⣄⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣠⣤⣄⣀⣠⣶⣿⣿⣶⣦⣹⣿⣿⣿⣿⣡⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⡿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣷⣌⡛⠻⠿⠿⢥⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⣬⠿⠿⠟⢋⣡⣾⠿⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣴⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣉⡻⣿⣿⣿⣿⣋⣙⣿⣿⣿⣿⢟⣉⣴⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠋⣿⣿⣯⡙⣿⣿⡿⠿⠿⢿⣿⣿⢋⣽⣿⣿⡘⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⣿⣿⣿⡿⣿⣿⣿⣶⣶⣿⣿⣿⢿⣿⣿⣿⠇⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣸⣿⣟⡋⢙⣻⣿⣇⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢻⣿⠀⣿⣿⣧⣼⣿⣿⠀⣿⡟⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠆⠿⣧⣿⣿⣿⣿⣿⣿⣼⠿⠰⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⣳⣤⠄⢀⣠⣴⡾⠛⠚⠛⢶⣶⣤⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢕⢶⣿⡿⠟⢻⠿⠒⠣⠀⠀⠀⢉⠙⢿⣤⡄⠲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⠋⠀⠃⠁⠀⠀⣀⣄⡀⠀⠀⠽⣿⠿⣾⣷⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡿⠖⠀⠀⠀⠔⠉⠀⠀⠈⠁⠀⠀⠈⠀⠈⢻⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⡿⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣇⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⡢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣫⣷⡁⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡿⠉⠛⠦⣌⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢫⡻⢿⣿⣷⡷⣄⠙⠚⠳⢤⣤⠒⠅⠀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠛⠚⠛⠛⠋⠙⠿⠿⠿⠿⠛⠓⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⠒⠒⠊⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠀⠂⢀⠀⠁⠀⠀⣀
⠀⠀⠀⠈⠀⠀⡀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠉
⠀⠠⠈⠀⢀⡀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠦⠁
⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠰⠁⢉⠄⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠒⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠈⠱⣫⠆⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⡄⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠂⠀⠀⢀⡀
⡔⠐⠂⠀⠀⠀⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⢀⠁⠀⢀⠀⠀⡀
⣑⣐⣁⣀⣠⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣘⣰⣄⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠈⠉⠙⠓⢂⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠉⠀⠀⠉⠁⠀⠀⠙⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⢤⡀⠀⠀⠤⠄⢘⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠁⠁⠠⠈⠁⠁⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⠒⠚⠀⢀⠄⠰⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠔⠉⢹⠦⣄⡠⠞⠉⠀⠀⢀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠉⠉⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣁⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣠⠖⠋⠀⠀⠀⠑⠀⠀⠠⠴⠖⠲⠶⠶⠶⠚⡛⠉⠉⠁⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡸⠁⠀⠤⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡄⠀⠀⠉⠁⡼⠀⠀⣀⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⡇⠀⠀⠀⠉⠉⠂⠀⠀⠀⠉⣻⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠠⣀⠀⠙⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠓⣄⠊⠗⠒⠦⠤⠤⠤⠄⠤⠤⠶⠚⠉⠀⢹⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡀⠀⠀⠹⢄⣀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠐⠒⠢⢄⠀⠈⠉⠉⠀⠀⠀⢀⠴⠊⣠⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡐⢤⣀⡀⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⢊⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣉⠉⠒⠄⠀⠀⠀⠀⠈⠉⠙⠢⡔⠉⠀⠀⠀⣀⠄⠀⠀⡠⠊⣠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⠰⠂⠀⠀⢄⠠⠠⡀⢀⢸⠀⠀⠐⠋⠀⠀⣀⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⣄⣱⠬⠋⠐⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣂⣀⢠⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡙⠛⠈⠙⢩⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠠⣿⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣭⣿⣵⣧⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠉⢷⣿⣿⣿⣿⠋⠀⠀⠐⠛⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠔⠚⠉⠉⢿⠿⠁⠀⠀⠀⠀⢄⠀⠀⠈⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⣦⣵⣤⠆⡜⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣷⣿⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡠⢞⣽⣿⣿⣿⡷⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠋⢹⣷⣄⣀⣀⣬⠵⠛⠶⣦⣤⣥⣾⣿⣿⣿⠀⠇⡇⠀⢣⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⡿⣿⡿⠿⠙⠀⠀⣤⣈⣽⠟⣿⣿⣿⣿⡄⠀⠁⠀⢠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣄⣀⣼⡇⢸⣧⣀⠀⠀⠀⠀⠈⠀⡚⠱⣫⣿⢿⣧⣀⡶⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⣿⡟⠀⢸⠸⠉⠉⠉⠴⠒⠚⢛⣿⢿⣿⢿⠈⠀⢻⠁⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⡇⠀⡜⠀⣇⠀⠐⠲⠤⣤⣾⠇⣹⠋⣾⠀⠀⢸⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⢠⡇⠇⠀⢳⡄⢉⠀⠀⠀⡠⢞⡟⢀⣵⣾⣧⡇⠀⠂⠀⠊⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⣧⠀⢀⣾⣷⣤⣷⣦⣤⣤⣾⣦⣿⣿⣿⣿⡇⠀⡀⠀⠴⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⢛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠃⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⣄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡡⢊⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣮⣇⠀⠙⠻⢿⣿⣿⣿⣿⡟⠉⠀⠀⢼⣦⣾⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣼⡇⠛⠀⠀⠀⠀⠈⠛⠿⠛⠀⠀⠀⠀⠋⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⡿⢿⠇⠀⠀⠀⠀⠀⠀⠙⣙⡛⠋⠛⢀⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣿⣿⣷⣤⣶⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢷⡙⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣧⠈⠙⠛⠋⠀⠀⠀⣠⣶⣾⣛⣓⠂⢠⣾⣿⣿⣿⣿⣷⣬⣙⣛⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣛⣘⣿⠷⠀⢰⣧⠀⢀⡀⢻⣿⣿⣿⣿⡷⢰⣾⣿⡿⢟⣭⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣶⣍⠰⣿⣿⣾⣿⣿⣿⣿⢃⣍⢩⣴⣾⣿⣿⣿⣿⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⡙⢣⣾⣿⠈⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣻⣿⠿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡼⣿⣿⣿⡇⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⣵⣾⣿⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⢀⣜⣿⠿⠏⣼⣿⠏
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⡴⢠⣾⣿⡿⣻⣿⣿⣿⣿⣿⣿⡻⠋
⠀⠀⠀⠀⠴⣿⣿⣿⣷⣮⡙⠋⠁⠀⠀⠀⣰⣿⡟⠋⣴⣿⣿⢏⣸⣿⣿⣿⣿⣏⣿⣿⡇
⠀⠀⠀⢀⣶⣮⣿⣿⣿⣿⣟⡂⣀⠀⠀⢴⣿⣿⣧⠘⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⢸⣿⡗
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣮⣓⠦⣀⠈⣿⣿⡄⢿⣿⣿⣿⣿⡗⠈⣩⣭⣥⣌⣭⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣶⣥⡘⠻⠇⢸⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣮⣟⢿⣿⣷⡈⣉⣉⣉⣘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⢾⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠟⠁⠀⠉⠉⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠁

⠐⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠋
⡄⠀⠀⠀⠀⠀⠀⠐⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠂⠄⠀⠀⠀⠀⠰⣍⡀⢀⠠⣈⠩⠍
⡗⠀⠀⠀⠀⠀⠀⠀⠢⠀⠑⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉
⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣦⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠿⢯⣼⠏⢹⣮⣤⣤⡄
⣷⣤⣤⣦⡄⠀⠀⠒⠀⠀⠀⡀⢀⡀⠀⠀⠻⣝⢶⣤⣦⡴⠞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠋⠉⠛⠧
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣿⣿⣷⣾⣧⠀⠀⢀⡀⣈⣈⡈⠐⣽⠉⣀⣋⣁⣹
⣿⣿⡿⠟⠒⠒⠂⠀⠃⠐⠃⠀⠊⠋⠀⠠⠌⠁⠀⠉⠀⠐⠀⠃⠀⠀⠤⠄⠆⠤⠀⠤⠥⠰⠦⢠⠤⠈
⣿⣿⠇⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠩⠠⠭⠅⠄⠭⠭⠽
⣿⣿⠃⠄⠀⠀⠀⠨⠉⠋⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⢀⣥⠀⠀⠀⢀⣸⣄⠀⠀⠀⠀⠀⠉⠀⠀⠃
⣿⡿⠀⠀⠀⠀⠀⣀⡄⣺⣶⠿⢛⣻⣿⣿⣿⣿⣿⣯⣽⣿⣿⣶⣶⣶⣿⣿⣿⡇
⠋⠁⠀⠀⠀⠀⠼⣽⡿⠛⠓⣶⣾⣿⣿⣿⣿⠟⢻⣿⣿⡿⠿⠿⢻⣿⣿⣯⠟⠁
⣿⠂⠀⠀⠀⠐⢤⡯⠤⡤⠤⣤⣬⣥⣤⣤⣤⣭⣬⣥⣤⣤⣴⣶⣼⠿⢿⢸⡆
⣟⣀⠀⠀⠀⠀⠋⠀⠀⢀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉
⡏⠁⠀⠀⠀⠀⠀⠀⠓⠉⠙⠁⠘⠐⠃⠊⠀⠀⠂⠂⠀⠒⠒⠀⠁
⣯⣤⣤⣤⣤⣤⣽⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢈⡏⠁⣠⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⠁⠃⣨⠙⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠶⠀⠸⠇⢀⡾⢡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣱⠄⠀⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⡱⣦⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠧⠀⠀⠋⠠⠋⠔⠁⠀⠀⠀⠀⠀⠀⢀⡀⡠⠀⠃⠀⠀⠀⢠⣄⣂⣀⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⡄⠇⠀⠀⠁⠀⠀⠀⠉⠙⠛⠻⠷⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠒⠶⠲⢀⣤⠄⣠⠴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠟⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠰⠀⠐⠂⠘⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠙⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠆⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠞⠢⠄⠀⠤⠊⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⡀⣀⡀⠠⢀⠐⠃
⠀⠀⠀⠀⠀⠀⡬⢀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣷⡾⠷⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣈⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠠⢛⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⡄⠐⠃⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⢤⡀⢤⠈⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟
⠀⣠⠀⠀⠀⠀⠈⠀⣀⠒⣀⠀⠂⡐⢂⣤⡄⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡀⣀⠀⡀⣀⡠⠆
⠘⢋⡙⠉⠉⠁⡀⠀⠻⠿⣃⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠚⠃⠰⠂⠉⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠼⢇⡨⠍⠀⠀⢀⠄⠀⠛⠀⠀⠠⠀⠐⢢⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡃⠐⢀⠀⠀⡁⢠⡤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠛⠂⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡼⠃⠀⠚⠃⠀⠀⠀⠁⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤
⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠁⠀⠀⢠⡀⢃⡰⠐⠶⠀⠑⠲⢄⣠⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡰⠚⠎⠀⣠⣀⠀⠀⠀⠀⣀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀
⠀⠀⠐⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠉⠀⠀⡰⠀⠀⠀⠀⠠⠤⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀
⣀⣀⣀⣀⣈⣉⣉⣁⣀⣘⣢⣄⣀⣀⣐⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡶⣻⣽⣏⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⢰⣿⣶⡆
⠀⠀⠀⠀⠀⠀⣼⣿⡟⢁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣾⣿⠟
⠀⠀⠀⠀⠀⣼⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣼⣏⣀⡀⠀⠀⠀⢰⣿⣯⣤⡄
⠀⠀⠀⠀⠰⢫⣿⣿⢏⣠⠄⠀⠀⠀⠀⢰⡿⢀⣠⡄⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠐⠛⣻⡟⠀⠀⠀⠀⠞⢻⣿⡿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⢛⣿⣿⠃⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠚⢁⣿⣿⠃⠀⠀⠀⠀⠀⠟⠋⣽⡟⠀⠀⠀⠀⠀⣸⣿⣿⡶⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣸⣿⣃⡀
⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠟⣿⡿⠁⠀⠀⠀⠼⠿⣿⠁⠀⠀⠀⢀⣿⣿⡟⠁
⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣹⡟
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣶⣶⣶⡶
⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⣼⣿⣿⣿⣶⡦
⠀⠀⠀⠀⣰⣿⡟⠀⠀⣀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣀⠀⠀⠘⠛⢻⣿⣿⣿⠁
⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣤⡄⠀⠀⢀⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠛⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣷⣶⠂
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠾⢿⣿⡿⠁⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⣿⡶⠀⠀⠀⠀⠉⢹⣿⣿⠃
⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢉⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠰⣿⣇⡀⠀⠀⠑⡀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡀⣀⣿⡷⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠤⡶⠋⠉⠛⠿⠷⠦⠂⠀⠀⠀⢰⡏⠙⢛⠃⠛⠃⠀⡐⠀⠀⠀⠀⠢⠶⠿⠟⠋⠉⠳⡦⠄⠀⠀⠁⠢
⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣘⣒⡀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠈⠢
⠀⠀⠀⣰⣟⠀⠀⠀⢀⣠⣾⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡿⠚⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣦⣀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⣟⢷⣤⠀⠀⢉⡭⠁⠀⠀⠀⠐⢶⡀⠀⠀⠀⢤⣴⡞⠙⠀⠘⣟⠒⠒⠉⠀⠀⠃⠀⣤⠄⠀⠀⠀⣱⠖⠀⠀⠀⠀⠹⡍⠀⠀⢀⣴⢟⡇
⠀⠀⠀⠈⢷⣭⣀⡀⠙⠘⢦⠀⣀⣀⠀⠈⢻⣏⠀⠀⠀⠀⠉⠁⠠⢀⣈⠦⢔⣁⠀⠀⠈⠁⠀⠀⠀⠀⡀⠁⠀⣀⣀⡀⢠⠞⠀⠀⣀⣨⣵⠏
⠀⠀⠀⠀⠀⠻⣷⣬⡀⠀⠈⠑⠚⢛⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠿⢛⣛⠛⠒⠉⠀⠀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣶⣶⣾⣿⣿⣿⡿⠋⠻⣷⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠈⠉⠙⣿⣿⣶⣶⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⣿⠁⠀⠀⢸⣿⣷⣶⡶⠴⡶⠖⠋⠓⠶⠶⢴⣶⡶⠿⣻⠀⠀⠀⠀⢠⡏⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢀⢾⣥⡜⠀⣴⠋⢀⡀⢸⣧⣄⠀⠀⠀⠀⠀⣽⣆⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⢈⡷⡜⠀⢠⡿⠛⠉⠀⢠⡍⠉⠳⢦⠀⠀⠀⡴⣏⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⣴⡏⠀⠀⣷⣄⡀⠀⢸⣧⣀⠀⠀⡀⠀⠈⣷⣥⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠘⣟⠉⠉⠀⠀⡏⠉⠀⠀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⣿⡶⣤⡀⢘⣧⣤⡤⢤⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢧⠀⠡⠀⠀⠀⠀⠀⢀⠀⢠⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣼⠁⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣴⡟⠀⢱⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣤⠔⠀⠀⠠⠴⣛⠁⠀⠈⠷⣿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣿⣆⠀⠀⠀⠀⢻⣿⠀⠀⠀⢠⠘⣧⡜⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣈⣓⠀⠤⣀⠙⠿⣾⡶⠂⣻⣿⣄⠀⠀⢈⣷⠙⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⣦⣈⢷⡀⠙⢻⣿⣯⣽⣿⡆⢠⣠⠁⠑⣦⠀⣰⠖⢬⡥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢿⣿⣿⠿⠿⠻⢄⣶⣿⠇⣼⣿⠄⠘⣻⣇⠀⠈⠷⣏⠀⠀⣼⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠙⣆⠀⠀⠈⣿⠁⢠⣿⠿⠀⡈⠀⠘⢷⣀⢳⢳⡀⠘⢃⣞⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣜⣦⢀⣸⣿⣷⡿⠇⢹⠀⠁⠀⠀⠀⠙⠻⢮⡃⢐⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣬⣿⠿⠈⢃⠀⡌⠀⠀⠀⠀⠀⡀⠀⠀⠉⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⢀⣿⡗⠀⠀⠀⣀⡤⣂⡉⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠀⠀⠀⣺⣿⡷⠀⠀⠀⡡⢖⣉⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⡐⢿⠟⠀⠀⠀⢠⠶⢿⣤⣀⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⣽⣿⡇⠀⠀⠐⠀⠀⠔⠋⠡⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⡏⠀⠀⠀⢈⠀⠀⠀⠀⠀⠘⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣹⣿⣿⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢰⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠉⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠠⠃⡠⠀⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠐⠀⠀⠀⠁⡜⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢰⣶⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠄⠿⣿⣻⣯⣿⣿⣷⣦⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠿⠃⠙⣿⡿⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣏⠀⠀⠀⣽⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢚⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠻⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡀⠀⠀⠀⠀⠠⠀⡰⠀⠀⢀⠀⠚⣿⣿⣿⣿⣯⣾⣿⠀⠀⠀⠀⠀⢻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣿⠀⠀⠀⠀⠀⡇⠈⠀⠁⢀⠈⠻⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠂⠀⠀⠀⣷⠀⠀⠀⠘⠇⠀⠸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⢴⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠚⢷⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⠀⠀⠀⠀⢸⣿⡟⣿⣯⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠐⠀⠀⠀⠈⠿⣿⣾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⠿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠈⠭⢻⠘⠛⠏⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠼⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⣒⡂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢻⠀⠠⢀⣤⡤⠔⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⢀⠁⠀⠐⣄⠀⣠⠀⠀⠙⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠃⠀⠀⠈⠉⠁⠀⠙⠛⠒⠺⠷⠷⠚⠛⠃⠉⠉⠘⠓⠂⠢⡄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⣀⠀⠀⠀⠀⠶⣿⠒⠂⠀⠀⠀⠲⢼⡤⠤⠀⠀⠀⠠⣴⠀⠀⠀⠠⢴⡃
⠀⠀⠀⠀⠀⠀⠀⠈⡛⠉⠀⠀⠀⠀⠀⢢⡈⢣⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠶⠷⠾⠿⠶⢶⣤⣤⣼⣧⡤⠄⠀⠰⢾⣇⠀⡀⠀⠀⠀⠁⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣦⣭⠗⠋⠁⠀⠀⠀⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠒⠚⠋⠀⠀⠀⣀⣤⠴⠶⢛⣭⡶⠛⠛⠉⠀⠀⠤⢤⣤⣴⠾⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠰⠴⢊⡀⣀⣀⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⣀⣀⣤⠴⠒⣀⣤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⣶⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⣿⣷⣤⣤⣶⣿⠶⢦⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢸⣿⡏⠀⠈⢻⠀⠀⠀⣼⠁⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⠀⢻⣿⠀⠀⠀⠀⠀⢀⡇⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⢾⠦⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠉⢾⣳⣿⣷⡖⠈⠁⠀⢰⠓⡄⢰⢠⢴⣶⣴⢂⣿⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠙⢷⣍⠀⠜⡰⠀⣼⣶⣥⡾⠿⠼⢿⣟⢯⣽⡂⠙⢦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡤⣄⠘⣛⡙⢆⠉⣦⣿⣿⡟⣿⣟⣿⣿⣯⣿⢟⣷⣴⣶⣿⢾⡗⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣦⢹⡿⣮⢻⣧⣿⢫⣉⣭⠑⢙⢿⣿⣿⣿⣿⣿⣿⣏⣈⡄⢀⣀⠤⠒⠺⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡈⠻⠇⢀⣜⣿⣿⣿⣿⣯⡳⠌⣡⣭⡉⢻⡿⢻⣿⣮⣼⣦⣻⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣼⡛⠏⣨⡿⣿⠿⣿⣻⣿⣏⡁⢸⢱⣿⣿⣾⡗⣿⣿⣃⡝⣧⣽⢯⣜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⡇⠘⢿⡻⣶⣝⣿⢿⣧⣙⠃⠘⡎⢿⣿⡿⢡⣿⣿⣿⣿⣻⠟⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡒⠒⣚⣻⡄⠺⣿⣿⣿⠻⡷⣽⠇⣠⣛⣿⣦⡿⣶⣿⣿⣿⣿⣾⢻⠃⠀⠑⢲⠫⢭⣓⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣹⣷⠶⣾⢯⣭⣄⢹⣿⢟⣷⠅⣉⣉⡙⢿⣿⣿⢂⣼⣿⣷⣍⣡⠄⠉⠀⣀⠈⢦⣻⣥⣍⣁⠢⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⡟⠚⣾⡷⠜⣫⣿⣁⣼⣟⠙⢿⠀⣛⢁⣾⣿⣿⣿⣩⡇⠸⣄⠰⠐⠠⠚⠉⢠⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡐⢉⣰⢎⣼⣿⣿⣿⣿⣤⠟⠠⠿⢸⣿⣿⣿⣿⣻⠃⠀⠛⣷⡌⠄⠠⣤⡐⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡸⠟⠋⢜⣿⣿⢟⣿⣿⣻⡟⢽⣷⣾⣷⣷⢾⣿⣿⣽⠁⢂⢰⡀⠈⠙⢦⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡤⠠⣯⠟⢃⡈⢉⣃⠘⣄⡈⢙⢷⡟⠻⣦⠙⠻⠈⣳⣧⡀⠑⠀⠀⠀⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠄⠠⠔⠉⠁⢻⡉⠂⠿⡞⣻⢶⣟⢰⣻⣦⠀⠀⠙⢾⡓⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⢂⡀⠀⠈⠇⠄⢸⡿⠏⠻⠇⠀⠀⠸⠖⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠃⠐⠃⠀⠀⠴⣫⠄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠐⠁⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠭⢻⠘⠛⠍⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠼⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠐⣒⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄⢻⠀⠠⠄⣤⠤⠔⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⣀⡁⠀⠐⣄⠀⡠⠀⠀⠙⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠙⠃⠀⠀⠈⠁⠀⠁⠉⠛⠒⠺⠷⠗⠚⠋⠉⠀⠉⠙⠓⠐⠢⠤⢀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⣀⠀⠀⠀⠀⠺⣿⠒⠒⠀⠀⠀⠀⢬⡤⠔⠀⠀⠀⠠⣼⡀⠀⠀⠠⢴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠉⠀⠀⠠⠀⠈⠲⡀⢣⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠢⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠐⠒⠳⠾⠿⠷⠶⢦⣤⣼⣧⠤⠆⠐⠲⢾⣇⠀⡀⠀⠀⠀⠑⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⠀⠀⠀⠀⢀⡀⢀⣴⣶⡬⠗⠋⠁⠀⠀⠀⡄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣄⠀⠀⠒⠚⠋⠀⠀⠀⣠⡤⠶⠖⢋⣽⠞⠛⠉⠁⠀⠀⠰⠶⠶⠶⠾⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠐⠶⢊⣀⣀⣠⣀⣤⣶⡿⠛⠁⠀⠀⠀⣀⣀⣀⣤⠴⢂⣀⣴⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣾⣿⣿⣿⣿⣿⠟⠛⠛⡛⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣷⣶⣶⣶⣿⠶⠶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢸⣿⡏⠀⠀⢱⠀⠀⠀⣼⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢄⠀⢻⣿⠀⠀⠀⠀⠀⢀⠇⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠙

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡛⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣧⣬⠇⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⣟⢺⣿⣿⣿⡀⢿⠇⠀⠀⠀⢀⣾⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⠟⠀⠀⠀⠀⠀⢠⣿⠸⣿⣿⣿⣷⡞⠀⠀⠀⠀⠈⠻⣿⠿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡆⣿⣿⢟⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣧⡀
⠀⠀⠀⠀⠀⣠⣿⡟⢸⠃⠀⣠⣶⣿⣿⣿⣷⠾⠿⠿⠿⠼⣿⣿⣿⡾⠯⠿⠿⢿⣷⣾⣿⣿⣿⣶⣄⠀⠘⠊⣿⣿⣄
⠀⠀⠀⠀⣴⣿⣿⠁⢸⣆⣀⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠈⣇⣴⣶⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣀⣠⢸⡼⣿⣿⣆
⠀⠀⠀⢰⣿⣿⣿⠀⢸⡿⠋⠁⠀⢨⣿⣿⠻⣿⣷⣤⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⢛⣿⣿⣿⣿⣼⣧⣿⣿⣿⡄
⠀⠀⠀⠸⣿⣿⣿⠀⣸⣇⣤⣤⡾⣻⣿⣿⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣡⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢀⣿⠿⣿⣴⠿⠿⠿⢗⣿⠏⢹⣿⣟⢿⣿⡟⠛⠋⣉⣤⡄⣈⣭⣙⣋⣿⣿⢿⣿⡇⠹⣿⣶⣿⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠘⠿⢷⠶⠶⠀⠀⠚⠋⠁⠀⠀⢻⣿⢿⡿⢽⣶⠾⢋⣭⡏⣉⣛⣿⣿⡩⣿⣿⡿⠁⠀⠈⠙⠛⠓⠚⠿⠿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡙⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣹⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣖⡩⠔⠊⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣿⡯⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣒⣒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣤⣤⣤⣤⣤⣐⣀⡠⢄⡀⣓⠘⡧⠼⣆⢢⠈⠿⣿⣿⢿⣷⠧⣭⡉⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠈⠩⢥⣿⣿⣿⣯⣵⣊⣝⠉⠩⡤⢼⣶⡷⣞⢿⣯⡑⠦⠉⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠈⡿⠐⠩⠞⣡⣿⢿⣿⣶⠀⢧⣀⠟⠈⠈⢣⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠁⠁⠈⡘⢿⢿⡳⠂⣠⠁⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠴⠀⠀⣩⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠛⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢐⡆⢄⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠛⠒⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡤⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⣀⡀⣠⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⢀⡀⠄⠀⠀⠀⠁⠀⠀⠐⢦⡤⠾⠋⠀⠘⣁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡄⠀⠂⠀⠀⣼⠫⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⣠⠌⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠶⠤⠀⢄⣴⠋⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠈⢡⡄⠀⠀⠀⠀⠛⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⠀⠀⠄⣼⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠿⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠐⠀⠈⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠲⣌⠁⡰⠛⠋⠉⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣦⣀⠀⠈⠀⠀⣼⠀⢄⡀⠀⠀⣀⠀⠐⢦⣶⡾⠋⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣾⣧⡧⢾⣦⣼⣶⠿⠷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡆⢾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⢺⣿⠓⢶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠂⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸⣿⠏⠁⣤⠆⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⣛⣿⡿⠀⠀⣾⠠⣤⠀⠀⠀⠀⠀⡄
⠀⠀⢀⣤⣀⠀⠒⠀⠀⠔⠀⠀⠀⠳⠒⠶⠟⠷⢄⡀⣹⠀⠉⠀⠰⠄⠀⢀⣀⠀⠀⠀⠀⠀⠃
⠀⠀⣽⣽⣿⣷⣿⣤⣽⣤⣴⣀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠇⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠁⠙⠛⠖⠺⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠒⡀⠐⠒⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣌⡙⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠉⠉⠉⠉⠁
⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣶⣶⣶⣦⣾⣦⣾⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣄⠀⠀⣤⣤⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⣿⠏⠁⢏⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠰⣿⣇⡀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠑⠀⠀⠀⣿⣿⣧⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⡇⠆
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠈⢹⣿⣷⠠⡀
⠀⢰⠶⣿⣻⣟⣿⡿⠿⠛⠃⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡙⣷⣤⣿⣏⣄⠱⣄⣀⣀⣀⣀⣀⢀⣠⣤⣴⠶⠂⠀⣠⡀
⠀⣼⠿⠟⢛⣿⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣼⣶⡏⠻⣿⣽⣦⣽⣉⣩⠽⢓⣷⣿⡿⠟⠀⠀⡠⠀⢀⣽⣆
⠀⣴⣦⣾⣿⡛⠉⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣹⣿⣧⡀⠈⣿⣿⣿⠤⣤⣾⣻⠟⠁⠀⠀⠀⠟⠀⠀⣠⣿⣿
⠀⠈⠀⠙⢟⣿⣀⡀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⣿⡆⠈⣻⣾⡟⣹⡗⠟⢋⣡⣴⣾⣷⣞⡶⠀⠀⠀⣼⣿⣿
⠀⢀⣀⣀⣼⣿⣟⠁⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣸⣿⣷⣄⡙⢻⣧⣽⣷⣰⣿⣿⣿⣿⣿⡿⣿⣄⠠⣴⣽⣿⡇
⠀⠀⠙⠛⠋⠉⠉⠙⢿⣿⣿⡿⣿⣿⣆⠘⠲⠶⠆⠀⠒⠒⠲⠶⠶⠀⠐⣿⣿⣿⣿⢿⣿⣿⡇⢹⣿⣿⣿⣯⣿⡿⠋⠀⣸⣿⣿⣮⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠡⠀⠈⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣯⡿⣿⣿⡇⢸⣿⣿⣿⡟⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢪⣿⣿⡸⢱⣿⠟⣿⣸⣿⣿⣿⣄⣠⡾⣫⣾⡿⠋⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⣀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠏⣧⠃⢺⡿⠀⣿⣿⣿⣿⣿⢹⣿⣾⣿⡟⠁⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢤⢸⢸⣏⢦⣿⡇⠀⠁⢨⣍⣿⠿⣄⣿⠛⢿⠀⢀⣠⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣆⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⢸⣿⣏⣞⣿⡇⠾⠴⣿⣿⣿⣶⣿⡇⠀⢹⣶⣼⠿⠋⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢧⠈⢎⠱⣝⣷⡄⠀⠀⠀⠀⣤⢼⣿⡿⠛⠉⣡⣤⠼⢿⣿⣷⡼⣾⠁⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⢣⠈⠳⡜⢎⠻⣄⠀⠀⠀⣤⠘⡅⠀⠀⠀⢉⣠⣶⣿⣯⣽⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠁⠄⠀⠘⣦⠀⠀⣤⠀⡇⠀⠀⢰⣽⣿⣿⣏⢹⡆⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⡄⠀⡇⠀⠀⠴⣿⣿⣿⣯⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠱⡈⠻⢀⡷⠀⡗⠀⣠⣾⣿⣿⡇⣿⢾⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡗⢸⣷⡿⠋⠀⣕⣿⠅⣿⣟⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⠀⢠⡀⠀⠘⠀⠀⠀⢈⠀⡈⠙⣇⠀⣷⡏⣿⠀⣿⣯⢹⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢿⣼⣼⣷⠀⠀⠀⠀⠀⠘⠀⠃⠐⠈⢆⣿⢸⡏⠀⣿⣿⡈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡇⢼⡿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⡌⠻⣿⣇⠀⣴⣿⣷⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⠀⠀⠈⠿⣿⣷⣿⣶⠷⠶⠾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⣈⣽⠟⠉⠎⣵⣷⡀⠀⠀⠀⠈⠀⠀⠀⡜⢡⣼⡿⣟⠳⣦⡀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠟⠁⠀⠀⠀⠈⠛⢿⡀⡀⠀⠈⠀⠀⣾⣰⡟⠉⠀⠋⠀⠂⠝⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⠀⠀⣼⣷⣟⡷⠀⠀⠀⠀⠀⠀⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣼⣾⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⢿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⢢⠸⣯⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡆⠀⠀⠀⠀⠀⠀⡴⢹⣿⡿⣽⣿⢿⣿⣿⣿⣦⣦⡀⢀⢣⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣤⣾⣄⣄⣠⡜⢠⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠿⠛⠻⠿⠛⠟⠻⠿⠿⠛⠻⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⡠⠊⠀⣨⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠠⠔⠂⠒⠀⠀⠀⠄⠉⠑⠄⠀⠀⠈⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠊⠰⠦⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣸⢆⡀⠀⠁⢀⠀⠄⠀⠀⠀⢠⠊⠁⠘⠀⢀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠁⠀⠀⠀⠀⡸⠀⢀⠀⠛⠠⠆⠀⠀⣤⢀⣀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⢠⢋⠄⠀⡴⠁⠈⠀⠄⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⢈⠀⠂⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠈⣢⠀⣠⠄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠠⠐⠀⠀⠀⠀⠐⠀⠀⠚⠁⠰⠄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⢀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢒⣒⣄⡀⢸⣦⢀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠔⠈⠀⠀⠉⡇⠈⠹⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢸⠷⠖⠚⠀⣀⣭⠭⠥⠤⠄⠀⠀⢑⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢀⢀⡏⠀⠀⠤⠚⠁⠀⠤⠤⠔⣒⡦⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠀⢠⠎⡼⠁⠀⠖⣲⠶⠛⠁⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡠⠖⠒⣄⣀⠀⠀⠴⠒⠋⠓⠒⠀⣏⡴⠁⡴⢃⡜⠀⠢⡀⢸⠇
⠀⠀⢀⠔⠊⠉⠀⠀⠀⡄⠀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠀⣞⣠⠎⠀⠀⠀⠑⡀⠠
⠀⠀⠓⠒⠒⠒⠂⠉⠉⠁⠀⠀⠈⠉⠉⠉⠙⠛⠛⠓⠒⠛⠁⠀⠀⠀⠀⠀⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠟⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⣤⡀⠀⣀⣸⠇⠀⡀⠰⠶⢶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠛⢛⡏⠀⠀⢀⠀⠀⠄⢀⡈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⡌⠀⠀⠀⠀⠴⠄⠀⠀⠰⠀⠈⢹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢠⢦⣤⠸⣷⣤⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠺⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠴⠢⠿⠟⠛⢿⣿⣿⣧⣀⣠⣆⡐⠒⠒⢦⣤⠶⢦⣬⢻⡆⠀⠈⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⣠⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁⠀⠀⠀⠀⠈⠁⠀⢀⣘⣿⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⣤⣞⣿⣳⣷⣾⣦⣤⠄⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⣀⡀⠀⠀⢿⣿⠷⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠿⢿⣿⣍⣀⣀⣀⢀⣀⣿⣿⣦⠀⠀⣀⠞⣉⡵⠤⠄⠀⠠⣀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⠛⠟⠀⠀⠀⢿⣾⢿⡿⠛⠛⠛⠋⠀⠉⢻⡿⠙⢧⣤⠄⠀⠀⠀⠀⢀⡹⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣶⣿⠀⡆⠀⠃⢸⣦⠀⠀⣠⡤⠀⣴⢤⣴⠆⠀⠀⠀⠙⠀⠺⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣧⠈⢻⣿⠇⢸⡟⢛⡁⣼⣿⣷⣾⡿⠐⠀⠳⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢇⣿⠀⠈⢾⣷⡈⠋⠉⣅⠀⠀⠲⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⢰⡈⠘⠷⣄⠀⠹⣿⣧⣀⣿⣦⡄⢀⣀⣾⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡛⢾⡔⢫⢧⡀⢠⡤⠍⠉⡉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢳⡘⣧⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠷⡤⣙⣿⣿⡌⠣⠀⠀⢶⣢⠴⣋⠄⣠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⣿⣟⢷⡀⠀⠀⠈⣵⢞⡡⠾⠛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⢿⣆⢁⢠⠀⢀⠀⠀⠀⢀⡤⠉⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣅⣀⣀⣀⣀⡀⢠⣾⡛⠻⣟⠈⠨⢀⡘⣥⡆⢠⣾⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣻⣿⠛⠛⠓⣠⢀⣽⡉⡁⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⠙⣯⡗⠉⠃⠀⠀⠁⠈⠉⢹⣿⡟⣿⡗⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣷⡦⡄⠀⢠⡤⠀⠀⠙⢿⡟⠘⠻⠿⣿⣿⣶⣶⣿⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⢻⡿⠋⠀⠀⠀⠀⣠⡤⠄⢀⠀⠀⠀⠉⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣠⡛⣿⡷⠁⠐⠁⠀⠀⠰⠏⠀⠀⠈⣧⠹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠘⢃⣿⡄⠀⠀⠀⠀⠀⠐⣧⣀⣤⣾⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡄⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⣿⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⣿⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣧⠀⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠛⠛⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠻⠿⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣷⣤⣨⣭⠖⢀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠓⠒⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣛⠛⠃⢰⣾⣿⠧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠁⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣀⡀⣀⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢉⡤⠍⠛⠒⠤⢄⣀⣀⠤⠤⠐⠒⠒⠠⠤⢄⣉⠉⠛⠭⣕⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⢔⠢⡜⢱⠀⠙⠢⡀⠀⠙⢢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢠⣚⢎⠈⡧⡭⣃⠀⠈⢦⠀⠀⢱⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡤⠤⠏⠣⠛⣦⣟⣁⠣⢢⠀⢇⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⡠⢊⡥⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢖⢊⠔⠉⠉⠑⡄⠮⡄⣱⠸⡄⢸⠀⢠⠃⢸
⠀⠀⠀⠀⠀⣠⠊⠀⢏⣵⡜⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠎⠀⣎⡸⡀⠀⠀⠀⡼⠰⣛⣁⡏⠁⢸⠋⠁⢀⠎
⠀⠀⠀⢀⡾⠤⢃⡐⠠⠤⠤⠀⠀⠈⠑⠒⠒⠒⠒⠉⠀⠀⠀⠰⠥⡌⢒⠒⣊⣐⡏⠁⠈⠀⠀⡼⠤⠒⠁
⠀⠀⠀⢸⣀⣀⣀⣈⣉⣒⣀⣀⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣑⣃⡀⣀⢀⣀⣀⠜⠁
⠀⠀⠀⠀⠓⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣯⠉⠉⠉⠻⠉⠉⠉⢋⣻⣿⣿⣿⣿⣿⡘⠉⠉⠉⠟⠁⠈⠉⣹⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣀⣀⣀⣀⡀⠀⠀⣾⠟⠉⠉⠉⠉⠻⣷⠀⠀⢀⣀⣀⣀⣀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠋⣅⠀⠉⠁⢨⠀⠀⣿⠆⣦⡄⢠⣴⠰⣿⠀⠀⡅⠈⠉⠀⣨⠙⠢⣸
⠀⠀⠀⠀⠀⠀⡠⠖⠁⣠⠞⠉⠹⡇⠤⠚⠀⠠⠘⡦⣀⠄⠠⣀⢴⠃⠄⠀⠓⠤⢰⠏⠉⠳⣄⠈⠳⢄
⠀⠀⠀⠀⢠⣿⠆⠀⣼⢳⣇⣀⠀⢀⡀⠤⠖⣠⠷⠗⡌⠠⠄⢡⠺⠮⣄⠒⠤⢀⡀⠀⡀⣸⡞⣧⠀⠰⣿⡄
⠀⠀⠀⠀⣿⡟⠀⠀⣡⠏⠁⠶⢿⣯⣤⡀⠨⠷⢦⣀⣻⣿⣿⣟⣀⡴⠾⠅⢀⣤⣽⡿⠶⠈⠹⣌⠀⠀⢛⣿
⠀⠀⠀⠀⡾⢛⢰⠋⠁⠀⠀⣀⣼⡟⠃⠀⠀⠀⠀⠈⠉⢻⡟⠉⠁⠀⠀⠀⠀⠸⢻⣧⣀⠀⠀⠈⠙⡆⡚⢷
⠀⠀⠀⠀⠘⠲⠿⢧⣔⠶⣿⣿⣇⠹⣦⣠⣤⣄⣀⠀⠀⠘⡃⠀⠀⣀⣠⣤⣄⣴⠏⣸⣿⣿⠶⣢⡼⠿⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠿⢿⣿⣷⣿⡟⠿⣿⣿⣷⡖⣴⣧⢠⣾⣿⣿⡿⢻⣿⣿⣿⡿⠿⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⡀⠙⢦⣝⡻⠿⠛⠿⠿⠛⠿⢟⣫⡴⠋⢀⡟⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠳⢴⣤⡴⣤⣶⡀⢀⡀⢀⣶⣤⢦⣤⡦⠞⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠘⢆⠀⠀⠀⠊⣇⢡⡏⢹⠁⣀⣁⠘⡏⢹⡌⣸⠑⠀⠀⠀⡰⠃⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠳⡀⠀⠀⢿⣾⠁⢹⡟⠛⠛⢻⡏⠀⣷⡿⠀⠀⢀⠄⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠈⠢⢄⣸⣯⠀⠈⠣⣤⣤⠌⠁⠀⣽⣇⣠⠔⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠙⠻⣧⣄⣲⣌⣡⣖⣠⣼⠟⠋⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠉⠛⠻⠟⠛⠩⠀⢀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⠀⠤⠐⠈


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠑⠀⠈⢠⡀⣧⠛⠾⡓⠀⠀⠀⠀⠀⠀⢀⠸⡃⠀⢀⠀⡀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠐⣠⠄⠀⣠⠊
⢀⣶⣕⠌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠁⠀⠐⠁⠘⢆
⡉⠀⠁⢠⠶⠈⠀⠀⠀⡀⠆⠘⠖⠒⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠈
⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠓⠀⠀⠀⢀⠐⠑⠆⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠐⠂⠁⢀⠀⣀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠁⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠋
⠀⢀⡄⠀⠂⢘⠀⠀⠀⠀⠏⠈⠀⠀⠢⠀⠀⠀⠁⠐⠀⠀⠀⠸⠂⢈⠄⠋⠈⠁⡆⠓⡀⠀⢄⠀⠀⠀⠐
⡈⠀⠀⠀⠀⠠⠛⠈⠁⢐⠀⠊⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠥⠀⠀⠰
⠉⠁⠀⠀⢀⠤⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠂⠠⡄⠀⠀⢨⠥
⠓⠠⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰


⣉⣉⣀⠤
⣉⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⣉⣤⡴⠖⡊
⠉⣥⠶⢃⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⢿⣶
⣈⣴⣮⣅⣤⣴⣎⣠⣠⣄⣤⣄⣠⣇⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣀⣤⣤⣈⣤⣌⣵⣦⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣠⣼⣿⣿⣧⣄⣀⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣠⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⣿⣿⡿⢛⣩⣵⣶⣶⣾⣿⣶⣶⣮⣭⣛⠿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⣡⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣮⡙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣿⡿⣡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣮⠻⣿⣿⣦⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣱⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢹⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⣿⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣷⡹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢻⡿⠟⢿⣿⣷⡝⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡙⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡿⣿⣿⣷⣬⣙⡻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠙⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⠏⠉⠙⢻⣿⣿⡟⠋⠉⠙⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠉⠁

⠬⠒⠃⠀⠀⠀⠈⠀⠄⠀⠀⠂⠀⠀⢀⠀⠘⠦⠀⠀⡀⠀⠅⠀⠁⢧⡀⢹⠋⢻⣬⢺⣣⣼⣼⡿⠉⡽⠁⡨⢋⠁⠃⠼⢁⠞⠹⠃⢈⡼⠋
⣅⡀⠀⠀⠀⠀⠀⠈⠀⠈⢢⣠⣤⣄⣤⣀⡀⠀⠠⠀⠀⠀⠀⣠⠖⠾⣇⡀⢱⢋⡷⠻⠋⠀⠈⣷⡼⢁⣀⠀⡈⠀⠀⢀⡀⠀⣀⠐⠁⠀⠈⠀⠀⢀⡴
⢤⢉⠁⠤⣀⠀⠀⠀⠀⠀⣾⠉⠀⡀⢀⣉⣻⡖⡦⠥⡀⣀⣴⠧⠁⠀⠙⠉⢨⠮⣤⡀⠀⠀⠰⠟⠗⠛⠉⠙⠉⣹⠋⠁⠹⠏⢉⠷⡄⠀⡀⠔⠊⠉⠉
⣓⠀⠀⡀⠀⠐⠀⠀⠀⠀⢻⡍⠀⠈⠯⡉⠁⠀⠁⠀⠀⠉⠉⠗⠲⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠉⠀⠀⠸⠀⠀⣈⡗⠂⠁⠀⠀⠠⠐
⠦⣠⠀⠁⠉⠒⠀⠀⠀⠀⠻⣆⡄⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⣲⢤⠤⢤⠀⠀⠀⠀⢲⡋⠀⠀⠀⠀⠠⣄⠼
⠂⠀⠅⠀⠂⠀⠀⡀⠀⠀⠀⠈⣟⠁⠀⠀⠀⠀⢀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⡀⠀⠠⠆⠀⠈⠹⠀⢀⣸⠃⠀⠀⣀⣠⠇⠀⠀⠀⠀⠀⠀⢀
⠙⠃⠀⠀⠀⠀⢀⢀⣠⣔⡓⢺⡋⣷⠒⠀⠀⠀⠀⠀⠀⠈⠁⠉⠠⠄⠀⠀⠱⠀⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡰⠞⠁⣴⣃⣠⡀⠀⠀⠀⠀⠄
⠚⠛⠓⠲⠆⠀⢰⣏⡀⠉⠀⠀⠃⠈⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠹⠻⡟⢲⡄⣀
⣛⠖⠃⠀⠀⢀⣿⠉⠀⣀⠴⠚⠁⠀⠙⠂⠀⠀⠀⠒⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠀⠀⠀⠁⠀⠀⢀⡼⢋⣑
⠻⠍⣠⣶⠋⠙⠇⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶
⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⣀⠀⠀⠀⢠⣤⣄
⠤⠼⢿⣓⣤⣰⠯⠀⠸⣧⣀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠂⢠⠀⢀⡀⠀⠀⠀⠀⠁⠀⠉⠉
⠃⠉⠀⠀⠀⠉⢳⣀⠀⠀⠈⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠘⠆⠀⠀⠁⠢⠄⠀⠀⠀⠀⠀⠀⠀⠈⣠⣸⠇⠀⣠⡼⠟⠂⠒⠠⠤
⣴⡖⠊⠀⠀⠀⠀⠈⠛⠷⠖⢡⡀⠀⠀⠀⠀⠺⢤⠴⠦⠄⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠠⠀⠀⠠⠨⠆⠀⢀⠀⠀⠀⣹⡝⠀⢙⠀⠀⢄⣀⠀⠘⠑
⡩⠀⠀⠀⠀⠀⣀⠄⠈⠁⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⢆⣀⡔⠀⠀⠰⣤⠤⡀⠙⠆⠀⠀⢀⣄⠀⠀⡀⠘⠒⠋⢹⣷⣛⠁⢠⣴⡏⠀⠀⠀⠀⠉⠀⠈
⠂⠀⢀⡀⠄⠊⠀⠀⣀⡤⡾⠊⠳⠴⠤⠴⠻⣄⣀⣰⣯⠉⣅⡀⡐⢀⣽⡆⠁⠘⠲⢤⢶⡞⠉⠓⠚⠻⣤⣤⡽⠛⠀⠉⠙⠋⠁⠀⠀⠀⠀⠑⠢⢈⡐
⣪⠕⠉⠀⠀⣀⠔⠛⡉⠈⠁⠀⠀⠀⠀⢀⠀⠀⠁⡰⠃⢠⠻⣤⠶⣞⠈⡻⣆⠀⡀⣀⡾⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠁⠀⢂⡠⠋⣡⡴⡋⢀⣄⣠⠊⡰⢂⠔⣉⡴⠀⣰⠃⣰⣦⣢⠘⣶⡔⣾⣧⣨⣃⢹⡉⡀⠀⡀⠀⠪⠀⠰⣄⠀⠐⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠐⢀⣀