⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣂⣶⣄⡀⠀⠀⠉⠉⠐⢒⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣰⠟⠉⠋⠆⠻⢅⠈⠻⣾⢕⠲⡞⢷⡨⣢⡀⠀⠀⠀⠀⠐⠂⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡡⡎⣰⠏⠀⠀⢸⢸⡄⠀⠙⠀⠘⢆⢃⠈⢢⠙⠢⡑⢦⡀⡠⣐⣯⣰⡢⢀⠑⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠓⢸⠀⡹⠏⠀⠀⠈⠐⡹⠀⠀⠀⠀⠈⡂⠀⠀⠱⡀⠹⣆⠉⠎⠣⣗⣭⡹⡆⠣⠘⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠠⠀⠀⠀⣀⣠⢶⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⢳⡆⠀⠀⠀⠀⡁⢀⠀⠀⠁⠀⢩⢃⠘⣄⠹⡞⣯⣛⠀⢡⣷⡀⠀⠀⠀⠀
⠀⠀⣰⠥⡖⠰⣉⡭⣨⡿⠸⠀⠀⠀⡀⢀⠀⠀⠀⢰⠀⠈⠀⠀⠀⢠⢀⢇⢸⣢⡈⢆⠀⠀⠏⡜⡜⣆⠹⣶⢻⠇⠀⢧⢃⠀⠀⠀⠀
⠀⢰⠁⠀⢸⠊⡰⣁⣤⠇⠀⠀⠀⠀⠖⡜⣄⠀⡀⡸⣇⠀⠀⠀⠀⡌⣜⣸⣌⣀⡑⢌⡆⠀⠀⠁⠀⠘⣇⠉⡜⠀⠀⢸⡿⠀⠀⠀⠀
⠀⡇⠀⢠⠃⢀⢝⠗⢹⠀⠀⠀⠀⠀⠃⠈⠘⡷⣶⣃⠘⢦⡇⢀⣴⡟⠡⠛⠀⠀⠈⠙⣷⠀⠀⠀⠀⠀⣭⡇⠁⠀⠀⠀⢳⡆⠀⠀⠀
⠀⠁⠀⠀⠀⠈⠈⠀⠈⠀⠀⡄⠀⢀⢰⢀⣾⡿⠃⠀⠀⡰⣠⡷⠓⣻⣮⣿⣖⣻⣿⣷⢾⡀⡸⠀⢠⠀⣧⠙⠀⠀⠀⠀⠀⡁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠐⢝⡄⣨⣯⣪⣿⣕⣶⣮⣽⠚⠉⠀⠀⠙⠻⠬⠋⠤⠇⢋⡶⣱⣻⡡⢋⡌⢸⡄⠇⠀⠀⠀⠀⠇⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⢰⢯⣧⠀⠘⡺⣽⣠⡿⢻⡿⠿⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⢌⣠⡋⠔⢹⢫⠈⠉⢃⡜⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⡆⣿⡇⠳⣄⠘⠶⣽⠿⠒⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠿⠠⠸⠁⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⢣⠀⠀⠀⠀⡜⡇⠿⠣⣠⣇⡩⡖⠒⢿⡚⡑⡠⠀⠀⠀⠀⠀⣀⡀⠤⢤⠀⠀⡄⢀⡼⠁⣰⣴⠇⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⠀⠀⠀⢇⠃⠐⠁⢸⣿⡈⠳⣦⡸⣻⣟⠃⠀⠀⠀⠒⠽⠦⠭⠔⠁⠀⠀⠉⣻⢶⢊⣯⡟⣹⠁⢸⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀
⠀⢸⠈⠀⠀⠀⠘⡀⢸⡆⠘⣿⡹⡛⢛⠿⢿⢉⠗⣪⡧⠝⠋⠀⠀⠀⠀⠀⠀⣠⢾⠑⢚⡿⢿⣣⣚⣧⡬⡧⠄⠀⠸⠀⠀⠀⢣⠀⠀
⠀⢸⡀⢃⣆⠀⠀⢳⢸⠇⠀⢯⢳⡌⡋⠀⣻⡺⢉⣙⢒⣒⣶⣤⣀⡀⠀⡠⠚⠁⠈⢀⢞⠤⢄⢻⣻⣂⡺⠻⠀⠀⣤⠀⠀⠀⢸⠀⠀
⠀⢨⠀⣿⣼⡄⠀⠀⢾⠀⠀⠈⠎⢸⠃⢸⠟⠀⠸⠞⠾⠖⠛⠛⠷⢄⠀⠀⠀⠀⣠⣫⢎⣆⠈⢳⡒⠿⣾⡗⢦⢰⠘⠀⠀⠀⠈⠀⠀
⠀⠀⢠⠃⢿⢜⡄⠀⠈⢆⠐⠂⠵⣲⣄⠈⠢⡀⠒⠄⡀⠀⠀⠀⠀⢏⡆⠀⠠⠊⠉⢳⡓⢧⣠⠀⠙⢶⣿⠀⠀⡎⠀⡀⠀⠀⠀⡇⠀
⠀⢠⠈⢸⠈⡏⢞⡄⠀⠀⢫⠁⣮⣶⣮⢩⠀⢒⠠⢄⡀⠉⠀⠀⠀⣸⠸⢀⠃⠀⢀⢾⢻⠚⠁⢀⡴⢻⣸⠀⢠⣽⢰⠤⣀⡄⠀⠃⠀
⠀⢸⠀⠘⢇⠇⠘⡬⣦⡀⠢⡳⡟⠹⡿⡾⠆⠀⠈⠁⠇⠁⠀⠀⠀⣿⠀⡿⠀⣠⠁⢸⢨⡀⣰⣿⡟⢊⣿⠀⡌⣯⡈⠙⠪⣣⡀⢠⠀
⠀⢸⠀⠀⢸⠘⡀⢻⡙⢷⢄⢑⠵⡀⡇⣷⠀⠀⠀⢰⠀⠈⠀⠀⢰⡏⠀⡇⢰⠙⠀⢠⠀⡯⠃⣿⡴⣿⠆⠰⢱⢸⡇⡇⠀⠑⢷⡼⠀
⠀⢸⠀⡄⡀⠀⠱⡀⢷⡀⠣⡳⢧⣡⣸⢸⠀⠀⢀⠇⠀⠀⠀⠀⣼⡇⠀⢡⠈⢣⠀⢸⡀⠀⢰⡟⡿⠁⢠⢣⠃⣿⢸⢀⠀⠀⣸⢡⡆
⠀⡇⢸⡇⡏⡆⠀⠙⢌⢿⣆⠑⢌⣾⣿⣼⠀⠀⡞⠀⠀⠀⠀⢰⡛⠃⠀⣼⠀⢸⡀⢸⡇⣄⡜⣧⠁⢠⣣⡷⢰⠇⠈⢸⠀⣠⢿⠈⣥
⢀⠁⣤⢰⣁⠇⠀⠀⠀⠑⠻⢷⡈⠺⡾⣿⣀⡜⠀⠀⠀⠀⠀⡄⡇⢀⢀⢻⠀⠀⢿⣯⡇⣿⣿⡏⢠⠟⠊⠀⡞⠀⠀⢸⠰⡞⣸⠀⠁
⠘⠀⠟⠘⠞⢠⠀⠀⠀⠀⠀⠀⠩⣦⣱⣻⣟⠀⠀⠀⠀⠀⠀⣷⣷⠈⣼⣿⠀⠀⠈⣎⣧⣿⣿⢠⠉⠀⠀⡸⠁⠀⢰⢘⡼⠁⡏⠀