⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⣹⠉⣷⡞⣿⡛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣉⠤⠒⠙⠯⣄⡀⠘⠀⣈⣽⠙⠒⠌⡛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⡰⠉⠀⠀⠀⠀⢀⣄⣹⢶⣞⣁⣀⠀⠀⠀⠀⠑⢌⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⢠⡶⠳⡾⠃⡐⠁⣀⣤⣴⠶⢿⣿⠾⠿⣾⡿⠷⠿⢷⣲⢤⣀⠀⠈⡇⠀⣟⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠿⢷⣧⣠⠷⠛⠉⣡⠔⠊⠁⠀⠀⠀⠀⠈⠑⢄⠀⠀⠉⠛⠿⣢⣌⡆⢩⢃⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠚⢋⡶⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡀⠢⡀⠀⠈⠛⢷⣞⣋⣉⣉⠻⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⢋⢼⠀⡴⠃⠀⠀⢀⠞⠁⠀⢀⣀⣀⣠⠔⢊⣉⡙⣲⣋⠁⠤⠌⢙⣋⣳⡀⠀⠀⠹⡷⡀⠀⢣⡘⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠇⡜⢸⠟⠀⠀⠀⣀⣿⡼⣄⣜⡃⢀⣼⡤⠛⠃⠀⠘⠻⣄⠀⠀⠀⢀⣿⡀⠸⡀⠀⠀⠸⣿⡀⢸⠣⠘⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡀⢻⡀⣤⠏⠀⠀⠀⢀⣿⡃⣿⣿⣁⡀⣀⡯⠟⠳⠦⠴⠒⠚⠉⠉⠓⢲⣾⠚⠙⠲⢿⡀⠀⠀⠘⢷⣸⠀⢱⠘⣧⠀⠀⠀⠀
⠀⠀⣴⣿⣿⢿⣿⣿⠇⠀⠀⠀⢠⣾⣿⣿⡿⡼⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⢳⡀⠀⠀⠈⣿⠀⡸⢰⠇⣀⣀⠀⠀
⠀⢸⣿⣽⡿⣿⣾⡏⠀⠀⠀⢠⣿⢻⡟⢿⡿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⢆⠀⠀⠘⣧⠀⠀⠀⠸⣷⣧⣿⢿⣟⣿⣷⣀
⠀⣾⣯⣿⣽⡳⣿⠀⠀⠀⠀⡸⠁⢀⡇⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡇⠀⠈⢦⠀⠀⢿⠀⠀⠀⠀⣿⣿⣿⣻⢟⣿⣻⣿
⠀⢹⣿⣿⣷⣿⡇⠀⠀⠀⠀⡅⢀⢎⡇⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡇⠀⠀⠈⣷⡀⢸⡆⠀⠀⠀⢸⣿⡾⣭⣟⣿⣿⣿
⠀⠀⠙⢿⣿⣿⠃⠀⠀⠀⢰⢃⡞⠁⢰⠈⡆⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⢸⢶⡠⣀⠀⠘⣷⡜⡇⠀⠀⠀⠸⣿⣿⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠉⣿⡃⠀⠀⠀⢸⣿⡡⠔⠉⡆⢡⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⡸⠀⠀⡞⠀⠀⠉⠓⢄⢹⡘⡇⠀⠀⠀⢈⡿⣿⣿⠟⠉⠀⠀
⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢸⠏⠀⠀⠀⠼⣄⡃⠀⠀⢻⠸⣆⣀⣀⣀⣀⣀⡃⣀⣰⠖⠠⢄⠀⠀⠀⠈⣯⡇⠀⠀⠀⢨⡗⣿⡁⠀⠀⠀⠀
⠀⠀⠀⠀⣼⢹⡇⠀⠀⠀⢸⡂⣠⣴⣾⣿⣿⣿⡿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣷⣦⣄⠀⢻⠁⠀⠀⠀⢸⠿⡽⣧⠀⠀⠀⠀
⠀⠀⠀⢰⠇⢸⢹⡄⠀⠀⢼⣿⡟⠉⣤⣴⡿⣿⣿⡆⠉⠀⠀⠀⠀⠀⠀⠀⠐⢋⣧⣠⣿⣿⣿⣟⠻⣿⣾⣂⠀⠀⠀⡾⠀⢱⠙⣆⠀⠀⠀
⠀⠀⢠⠏⠀⠘⡆⢷⡀⠀⠀⢟⠆⠐⡿⡿⠿⠿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣟⡻⢿⠀⢸⡏⠁⠀⠀⢰⢳⠀⠈⡇⠹⣆⠀⠀
⠀⢠⡟⠀⡎⠀⠇⠈⣷⡀⠀⠘⣄⠀⠹⣁⣐⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠂⠀⡱⠋⠀⡜⠀⠀⠀⢀⠇⢸⠀⠀⠸⠀⢹⡄⠀
⢀⡞⠀⢸⠀⠀⢸⠀⠘⣟⢦⣄⣈⠦⠤⠉⠀⠀⠀⠀⠀⢀⣀⣀⡐⢀⣀⡀⠀⠀⠀⠀⠈⣕⣀⡠⠊⠀⠀⢀⡠⠋⣠⠇⠀⠀⠀⡇⠀⢿⠀
⣼⠃⠀⡎⠀⠀⢸⡆⠀⢸⠫⣷⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⢤⣏⣽⣿⣤⣿⡄⠀⠀⠀⠀⠈⠒⢤⠤⢖⣺⣿⢥⠞⠁⣰⠀⠀⠀⢹⠀⣼⡃
⢻⡄⠀⢱⠀⠀⠘⣿⡀⠀⢆⠨⢧⡀⠀⠀⠀⠀⠀⣾⡿⣄⣾⠟⠉⣧⡜⣄⢻⡶⣆⠀⠀⠀⠐⠓⣺⡏⢇⡶⠋⢀⡴⡇⠀⠀⠀⣸⣰⣿⠁
⠈⢳⡄⠘⡆⠀⠀⢹⣧⠀⠈⡆⢣⠙⣦⡄⠀⢠⣾⣿⣭⠙⢻⣽⡎⢡⡟⣿⣿⣿⣿⠀⠀⠀⣤⣾⡟⣼⠋⣤⡖⢫⣼⠁⠀⠀⢠⣿⡟⠁⠀
⠀⠈⠳⣄⢻⡄⠀⠀⢿⣇⠀⠀⠘⣶⣽⣿⣷⡿⣟⠳⡄⠑⢄⣹⣿⣉⣿⠧⠒⢻⣿⣴⡶⢿⣿⡿⣶⡶⢻⡏⣜⡺⠃⠀⠀⣠⠾⠋⠀⠀⠀
⠀⠀⠀⠈⠙⠛⠷⣄⡀⢻⣷⡀⠀⠹⣿⣸⣿⢷⡿⡆⠘⣧⣾⣿⣿⣿⢃⡴⠋⣛⣻⣿⣶⡓⠺⠛⠻⢦⣟⣱⠞⢁⣠⡴⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣿⣄⠀⢹⡿⣹⡞⠀⢿⣄⣻⣿⣿⣿⣿⡟⢀⡼⢷⣏⠉⠻⣿⡃⠠⠴⣿⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⡾⡶⢻⠀⠀⢸⢻⣿⣿⣿⣻⣿⣷⡏⠀⠀⣿⠦⡀⠹⣇⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣱⡟⡑⠁⡏⠀⠀⡎⢐⣿⣿⣯⠷⣯⢿⣷⠀⠀⡇⢣⣸⡶⣿⢿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡴⠁⠀⡇⠀⡜⠀⢸⡏⠛⢻⣿⡝⠋⢿⡄⠰⢃⣾⡟⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡅⠀⠀⣃⠜⠀⢀⣾⣢⣴⣿⣶⣿⣦⣺⣇⡀⠘⣷⣿⢿⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠚⠛⠛⠛⠛⠉⠉⠉⠉⠈⠁⠉⠉⠛⠲⠦⠬⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀