⠀⠀⠀⠀⠰⣶⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠙⠷⣄⡀⣠⠀⠀⠀⠀⡀⠀⣠⠞⠉⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣝⠙⠋⠀⠀⠀⠀⠙⠛⣥⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠻⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⠿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡿⣣⢏⡳⡝⣮⢳⡟⣿⣻⢿⣿⣿⣿⣿⡿⣟⡿⣽⣛⢮⡳⣙⠧⣏⠿⣿⣿⡇⠀⠀⠀⠀⢸⡷⢡⢎⡱⣙⢦⡛⣼⢣⡟⣯⢷⣟⡿⣾⡽⣏⡟⣶⠹⣎⠵⣉⠞⣬⠻⣵⣻⡇⠀⠀⠀⠀⢸⠣⡅⢢⠑⣎⠲⣙⢦⢫⡜⢧⣛⢮⡟⣶⡹⢮⡝⢦⢛⠤⡓⠬⡘⢤⠛⣶⣹⣿⠀⠀⠀⠀⢸⢣⠘⣀⠣⢌⢣⡑⢎⡱⢊⢧⡙⢮⠵⣪⢕⡣⢞⡡⢚⠤⠑⠢⠑⡌⡙⢦⣻⡷⠀⠀⠀⠀⠘⣧⢊⠄⢂⠌⠢⠜⡠⢃⢍⢢⡙⣌⠣⡕⢪⡑⠎⡔⠣⠌⣈⠁⠒⡠⣙⢮⣳⡏⠀⠀⠀⠀⠀⢷⣉⠆⠠⢈⠁⠎⡐⢁⠊⠔⡰⢈⡱⢌⠱⣈⠱⣈⠱⠐⠀⡀⠁⡰⠱⢮⣽⠂⠀⠀⠀⠀⠀⠘⣷⣊⠅⡀⠈⠄⠐⠠⢈⠰⢀⠣⡐⠌⡒⢄⠣⡐⠂⠁⡀⠀⠤⣑⢫⣽⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⡴⣁⢂⠀⠠⠀⠀⠂⠄⡁⢊⠐⡈⢐⠠⠁⢂⠠⡑⢦⣹⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣖⡍⢦⡐⡄⣠⠀⡄⣀⠂⡁⢄⡰⡐⣆⢧⡽⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠶⢥⡿⣴⢣⣻⡼⠷⠾⠓⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣶⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠋⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠙⠷⣄⡀⣠⠀⠀⠀⠀⡀⠀⣠⠞⠉⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣝⠙⠋⠀⠀⠀⠀⠙⠛⣥⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋
⠀⠀⠻⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡟⠁⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⣼⣿⠿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⢀⡿⣣⢏⡳⡝⣮⢳⡟⣿⣻⢿⣿⣿⣿⣿⡿⣟⡿⣽⣛⢮⡳⣙⠧⣏⠿⣿⣿⡇⠀⠀
⠀⠀⢸⡷⢡⢎⡱⣙⢦⡛⣼⢣⡟⣯⢷⣟⡿⣾⡽⣏⡟⣶⠹⣎⠵⣉⠞⣬⠻⣵⣻⡇⠀⠀
⠀⠀⢸⠣⡅⢢⠑⣎⠲⣙⢦⢫⡜⢧⣛⢮⡟⣶⡹⢮⡝⢦⢛⠤⡓⠬⡘⢤⠛⣶⣹⣿⠀⠀
⠀⠀⢸⢣⠘⣀⠣⢌⢣⡑⢎⡱⢊⢧⡙⢮⠵⣪⢕⡣⢞⡡⢚⠤⠑⠢⠑⡌⡙⢦⣻⡷⠀⠀
⠀⠀⠘⣧⢊⠄⢂⠌⠢⠜⡠⢃⢍⢢⡙⣌⠣⡕⢪⡑⠎⡔⠣⠌⣈⠁⠒⡠⣙⢮⣳⡏⠀⠀
⠀⠀⠀⢷⣉⠆⠠⢈⠁⠎⡐⢁⠊⠔⡰⢈⡱⢌⠱⣈⠱⣈⠱⠐⠀⡀⠁⡰⠱⢮⣽⠂⠀⠀
⠀⠀⠀⠘⣷⣊⠅⡀⠈⠄⠐⠠⢈⠰⢀⠣⡐⠌⡒⢄⠣⡐⠂⠁⡀⠀⠤⣑⢫⣽⠏⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣏⡴⣁⢂⠀⠠⠀⠀⠂⠄⡁⢊⠐⡈⢐⠠⠁⢂⠠⡑⢦⣹⡾⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⢭⣖⡍⢦⡐⡄⣠⠀⡄⣀⠂⡁⢄⡰⡐⣆⢧⡽⠞⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠶⢥⡿⣴⢣⣻⡼⠷⠾⠓⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀