⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⣿⣿⣻⣇⣶⣰⣦⢦⣙⢦⣻⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢏⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⢠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢂⠀⠀⠀⠀⠀⠐⣠⠺⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢨⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠄⣃⠲⠉⠈⠒⠀⠀⠀⠄⠠⠐⠠⢂⡑⡦⠜⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⣖⣼⢫⣾⣬⡠⠈⠑⢠⢌⣢⠍⠞⠃⠉⠴⠳⠸⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡂⠊⣼⠿⠀⡼⣷⡁⠀⠀⠀⠀⢀⠠⠁⣦⣴⢆⣴⠸⡤⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠀⡟⠸⠠⣻⡿⡏⠀⠀⠀⢀⢀⣶⠿⣻⢿⣿⣶⡓⢹⣆⢆⡐⢀⠠⢈⠐⡀⢀⠀⠀⠀⢀⢀⠌⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠃⡆⡁⠀⠈⠈⠀⠀⠀⡀⠀⠀⣼⠁⢰⣿⣿⣿⣻⡏⡅⡾⠇⡪⣆⠢⢄⡑⡘⢤⢃⣜⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠚⠑⠒⡑⠣⣠⡽⠇⠀⡐⡬⢿⣦⡲⣌⠢⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢱⠃⣦⠀⠀⠀⠀⠁⠉⠂⠀⠀⠀⠀⢀⡐⠌⡰⣫⡶⠛⠀⠀⣴⠏⣰⡛⡑⠦⢑⠂⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣇⢿⡄⠀⠠⢤⣶⣗⡄⠀⠀⢀⠂⢂⠔⣸⣱⡟⠁⠀⣀⠞⣊⡴⢡⠑⡈⠔⡈⠄⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡘⠉⠄⠀⠈⠞⠯⠟⢁⠐⡠⢘⠤⣪⣕⣡⡐⢄⣶⣿⡿⣿⡺⣄⢢⢁⠢⠐⡈⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠰⣢⡀⠀⠀⢌⢠⢊⡴⣩⣖⣧⠟⣡⣰⣿⣿⣿⣶⣳⣟⣦⢳⡌⢢⠡⡐⢈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⡑⢤⣛⣶⣼⡜⢚⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣝⡮⢷⡭⢇⡳⣌⢆⡌⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠔⡢⢽⣿⢯⣷⣾⢿⣿⣿⢿⡻⡝⢯⢞⡼⢭⢳⢯⣟⣾⡹⢧⡻⣍⡗⢮⡲⢬⡑⢦⡉⡔⠠⡀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠣⠀⠀⠈⡜⣡⠟⠚⠛⠛⣟⢯⠟⡵⢇⣳⡙⠈⠚⢜⡣⢏⡞⡼⡳⣯⡳⣝⠶⣩⢧⡹⢲⡙⢦⡓⢬⠓⡔⢢⠔⡠⠀
⠀⠀⠀⠀⠀⠀⠀⢠⢐⣴⣅⠀⠀⠀⠀⠀⠌⠀⠀⠀⠑⠃⡐⠨⢄⡙⡞⡼⣰⠹⣌⢷⣭⢋⡗⢮⡱⢣⡙⢦⡙⡎⡝⣌⢣⠚⡤⢃
⠀⠀⠀⠀⠀⠠⠂⢂⠭⣻⠃⠀⠀⠀⠀⡴⠀⠀⠠⠐⡄⢣⢌⡱⣊⢴⡙⢶⣡⢛⡬⣒⠧⣏⡜⣣⢍⠧⣙⢆⡣⠝⡴⣉⢦⢋⡔⢣
⠀⠀⠀⠀⠠⠡⡘⠢⡰⠁⠀⠀⢀⡰⣉⢶⡁⢎⡡⢓⡌⢧⢎⡵⣩⠶⣙⢦⢧⢫⠶⣭⢻⢦⡹⣐⠎⡜⡌⢦⡙⡜⡰⣉⠦⡓⣌⠣
⠀⠀⠀⠀⡗⠂⣠⡾⠁⠀⠀⡐⢦⡱⢭⢞⣏⢶⣩⢳⢺⣍⢾⡸⣕⣫⡝⣞⢮⣏⢿⣜⡻⠶⡱⣍⢺⡘⡜⢦⠱⣌⡱⢌⠲⡱⢌⠳
⠀⠀⠀⠀⠈⠛⠏⠁⢀⡰⣌⢳⢣⡝⣮⢫⣞⣧⣏⢷⣫⢞⣧⢻⡜⣧⣻⢼⡳⢮⣿⡞⡱⢋⡕⢪⠱⡘⡜⣌⠳⡰⢱⡊⢧⡑⢎⡱