⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣛⣻⣿⣿⣭⣭⣽⣿⣿⣿⣛⡳⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣿⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣽⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣞⠻⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣍⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⡧⠒⡌⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⣰⣿⣿⣿⡿⢇⠱⣘⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⢰⡟⣾⣿⣿⡇⡜⢢⡑⢦⡐⠂⡌⡐⢄⢂⠰⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⢸⡇⣿⣿⡿⠶⣈⢱⠸⣆⡈⢱⣀⠱⡈⢆⣁⠉⠶⡈⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⡾⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⣿⣧⣿⣿⡏⠱⣠⣣⣷⣼⣾⣥⣆⡳⣉⠶⣌⡛⢶⡉⢆⣲⣠⣥⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠙⢾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⢀⣿⣦⣿⣿⢃⣿⡿⠟⡉⠉⠈⠙⠛⠿⣷⣷⣢⡙⢦⡙⢆⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠡⣌⢳⣄⠀⠀⠀⠀⠀⠀⠀
⠀ ⢠⣿⣿⢿⣿⣿⣿⠋⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⡢⢍⠚⣿⣿⣿⣿⣿⣿⢳⠐⡄⠡⣀⠂⢄⣿⠁⠀⠀⠀⠀⠈⠉⠙⢧⡀⠀⠀⠀⠀⠀
⣰⢻⡗⡛⠛⢋⣉⡀⠁⠚⠶⣥⣆⡀⠀⠀⠀⠀⠀⠀⠹⣷⡌⠒⡈⠛⡿⠿⡟⡡⢆⡹⢄⡓⢄⠊⣼⡏⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣆⠀⠀⠀⠀
⣿⢸⣟⣷⣫⣿⡿⠿⣷⣤⣀⠈⠙⠻⠇⠄⠀⠀⠀⠀⢀⠹⣿⡤⢁⠣⡘⠱⢨⠑⢎⡔⠣⠌⣀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣇⠀⠀⠀
⠹⣿⣏⣹⣯⠿⣡⡴⣭⣛⠿⣿⣦⣄⢀⣮⣐⠤⣘⠼⣌⣳⣽⣿⣦⡁⠌⡑⠢⢉⠆⡌⠑⣠⣺⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⣧⡀⠀
⠀⠘⠿⣿⣭⣼⣱⣮⣵⣭⣟⣼⣫⠿⣿⣿⣿⣿⣩⢟⡻⣏⢯⣟⣿⡿⠂⠄⠡⢈⠐⡈⣖⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⣷⡀
⠀⠀ ⠀⣨⣿⣿⣿⡻⠍⠀⠉⠉⠛⠻⢷⣾⣽⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣁⣮⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇
⠀ ⠀⢸⣏⣾⡏⡹⢃⠌⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⢶⣶⣶⠾⠷⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⢀⣿⣹⣟⣠⠱⣁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡏
⠀⢸⣇⡿⢈⡖⢡⠢⣍⠢⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣾⠇
⠀⣿⢸⡇⢘⡜⡄⠳⣄⠳⣄⢁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢻⡟⠀
⠀⣿⢸⡗⢘⠣⡜⠳⣌⠳⡌⢆⡡⢐⠠⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣿⠁⠀
⠀⣿⢸⣟⠠⠓⢌⠳⣌⠳⣍⢲⡑⢎⡰⢈⡔⡁⢆⠰⢠⠁⡌⡐⢠⠐⢠⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣹⠇⠀⠀
⠀ ⣿⢸⡏⠀⠸⠀⠷⡈⢇⠸⢆⠹⡸⢶⢇⡸⢱⠎⣱⢈⢱⢰⢁⡆⢉⡀⢇⠸⢀⡀⠆⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢱⡏⠀⠀⠀
⠀⢻⣼⣯⠀⠀⢁⠒⡩⢘⡌⢪⠱⣉⠖⣪⠱⣉⠞⣡⢋⠖⡍⠶⣘⠧⡜⢦⠓⢦⠑⡌⠄⠁⠂⠁⠀⠀⢀⠠⠐⡈⠤⡁⠈⣴⣿⣷⠟⠁⠀⠀⠀
⠀ ⠀⢻⣿⢷⡀⠀⠂⠁⠒⡌⢡⠚⡄⢋⠔⠣⢌⠳⢰⡉⢎⡙⢲⡉⢎⡙⢎⡹⢄⠣⠐⠈⠀⢀⠠⠐⣀⢂⠦⡑⣌⠒⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀ ⠀⠹⢮⣿⣦⡀⠀⠁⠈⠢⢑⡘⠌⡌⠱⡈⢆⠡⡘⠤⠙⡠⠓⡌⠱⢊⠔⡈⠄⢁⠐⡠⢂⠦⡑⠦⣉⠖⡱⠈⡴⢟⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠙⢧⣜⡛⢦⣀⠀⠀⠐⠈⠰⠁⠒⡈⠒⠤⠑⠌⡑⠢⢌⠱⡈⠆⡐⢨⠰⠌⠒⠡⢊⠑⠢⠐⠈⢰⣼⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀ ⠈⠙⠶⣬⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢁⠊⠄⠑⠠⠑⠀⠂⠈⠄⠁⣂⣨⣤⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢭⣝⣛⠳⠶⢶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⡶⣛⣭⣵⡿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀ ⠉⢛⡛⠷⠶⢶⣦⣭⣭⣝⡻⠟⠷⠛⢫⣭⡷⠟⢛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀