⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⡻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡙⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⣿⣿⣨⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣄⣠⣤⣤⣤⣴⣿⠏⠻⢷⣶⣶⠶⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣶⣶⠀⠀⠀⠀
⠀⠀⠀⣤⣶⣶⠶⠿⢿⣿⣿⠿⠿⣿⣿⡏⠉⠁⠀⣿⣷⣀⣤⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⡉⢈⣿⣿⣦⡀⣽⡿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠀⣤⣼⠿⠇⠀⠀⢰⣿⣿⣿⣿⠀⣶⡾⣿⣿⣯⡉⠉⠙⢿⣿⣧⣼⣿⠻⢿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⢸⣿⣿⡶⠟⠛⣀⡀⠀⠀⠈⣻⣿⣿⠹⣶⠘⢿⡟⣿⣿⣷⣄⠀⠀⠹⣿⣿⣥⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⣩⣴⣶⣶⣿⡁⠀⠀⠀⣿⣿⣿⣀⣰⣦⠈⠁⠈⣿⣿⣿⣷⡰⠆⣸⣿⣿⣿⠏⠉⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠋⢙⣿⡿⣿⣧⣄⠙⠿⢿⣿⠿⢫⣄⠀⠀⠀⠙⠛⠙⢻⣾⡿⠋⠙⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⡿⠃⠀⠉⠉⠸⢿⣿⠁⠀⠘⣿⣄⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠉⢿⡀⠰⣿⣿⣿⡄⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠿⣿⡀⠙⠛⠛⠃⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⣤⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠘⣿⣷⡶⣴⣦⣤⣿⣷⣶⡈⠻⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣷⠀⠹⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠻⠿⣿⠟⢿⣿⣿⢻⣿⠿⠏⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠿⣧⣤⡛⠿⠘⠋⠀⠀⢸⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠈⠙⣷⡄⠀⠀⠀⠀⠈⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣆⣆⣆⣆⣆⣆⣆⣆⣆⣆⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡂⢢⠦⡀⠀⡆⠆⢀⡠⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⢒⠶⣰⡢⣂⠆⠀⠀⣠⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⡉⠉⠑⣵⢻⠀⡝⡶⡔⠁⠈⠃⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠉⠛⣫⡞⠇⣶⣯⢃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣇⠀⠀⠈⠀⠀⣗⣿⡇⠀⠀⢦⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⠋⠀⠀⠀⡈⣺⡔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠻⢧⣄⠀⠀⠀⣴⢮⠃⠀⣀⢽⡿⠃⠀⡄⢄⠤⣠⣤⡠⠤⠀⠀⠀⠀⣾⠺⠃⠀⠀⠀⢯⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢾⡲⡤⡀⠐⠘⢢⢼⣼⠽⣧⠀⠀⠘⠁⠢⠂⠦⠯⠼⠄⠀⠀⠀⢻⣻⠅⠀⠀⠀⠐⠽⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⣄⠴⠀⡲⣮⠆⠀⠋⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠲⠅⠀⠀⠀⠀⡈⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⢄⠀⣠⣟⢾⠀⣥⣺⡆⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⠢⠀⠀⠀⠀⠀⡸⣳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⢨⠿⠻⠃⠀⣷⣿⠆⠀⠀⢷⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠠⠆⠀⠀⠀⠀⠀⣷⡔⡇