⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣇⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣰⣿⣾⠇⣝⢳⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣔⣿⣿⢾⣃⡺⠷⢶⡿⢷⣝⠫⣩⣵⠳⠀⠀⠀⠀⠀
⠀⠀⢀⣬⣟⣙⠃⠀⠀⡉⠢⡀⠙⢄⠹⣷⢿⠛⠅⠀⠀⠀⠀⠀
⠀⢀⢒⣿⡈⣿⢠⠀⠠⠈⠒⣜⣄⢀⠣⡘⠀⡗⢊⠂⠀⠀⠀⠀
⠀⡘⣾⢷⢱⣯⣼⠆⡆⣧⡐⠪⢺⡀⢆⢷⡰⢸⣼⠀⠀⠀⠀⠀
⠀⣶⣿⢸⡆⣿⢿⢎⡙⣿⠙⣢⢕⣇⢈⢹⣷⡘⠏⠀⠀⠀⠀⠀
⠀⠩⣿⢾⢧⣿⡩⡮⣯⣹⠰⣖⡾⢿⢸⡬⢻⡋⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢯⣿⣿⡿⠿⠈⠈⠁⠀⠀⢸⡞⣇⡗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣞⢄⡀⠀⠀⠀⢠⣵⣷⠻⢁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⢿⣿⣏⠑⡶⡾⠁⡼⠃⠀⠀⠁⠂⠠⠤⡀⠀⠀
⠀⠀⠀⠀⣴⠗⠉⠫⠈⣾⡿⢷⠉⠀⠀⠀⠀⡀⠄⢎⠐⢰⠀⠀
⠀⠀⠀⠀⡌⣄⢀⡠⠐⠉⣈⣸⠀⡀⢤⡖⢊⣵⠞⡩⡩⠙⠀⠀
⠀⠀⠀⢸⠗⣼⣆⡀⣠⠞⠈⠁⡞⠲⠋⠷⠋⠁⢸⡨⠔⠠⠀⠀
⠀⠀⠀⣾⡀⠈⠗⠶⠋⠀⠠⢼⠀⠀⡘⢅⢂⡠⡌⠀⠀⠀⠀⠀
⠀⠀⢀⡆⢣⠀⢰⣢⠠⠀⠀⣸⠀⠀⢇⠀⠁⠌⠇⠀⠀⠀⡆⠀
⠀⠀⢸⢣⠀⠱⣸⢸⡀⠄⠈⠋⠀⠀⠈⣁⠽⢀⡀⠀⠄⠀⡇⠀
⠀⠀⢠⡞⡀⠀⡍⡜⠀⠀⠀⣄⡠⠖⠉⠀⠀⢸⡇⠀⠀⡆⡇⠀
⠀⠀⣿⠀⠁⡸⡇⠁⢀⠠⠒⠹⠀⠀⠀⠀⠀⠂⡇⠀⢠⠀⡇⠀
⠀⢐⡇⠀⣰⠳⠓⢉⣀⠠⠅⢻⠂⠈⠉⠀⠀⠀⢚⣀⡆⠀⡇⠀
⠀⢘⠡⣞⢽⣿⢷⠦⣤⣀⡰⡂⠀⢀⣀⣀⡤⠶⢺⣧⠃⠀⡇⠀
⠀⣸⠞⣀⣼⣿⣿⣿⣼⣌⣙⣿⣟⣿⣿⣿⣾⣿⡟⡿⠀⡀⡇⠀
⢰⡟⠛⢩⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣼⣱⠐⠀⣥⠀
⢸⣿⣶⣼⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠕⠁⡇
⠀⢿⡇⢸⣻⠿⢿⣿⣿⣿⣿⡿⢉⣿⣿⣿⣿⣿⡿⠿⣎⣢⡴⠇
⠀⠸⣡⣿⣿⠀⠀⠀⠀⠀⠈⡇⢈⡇⠀⠀⠀⠀⠀⠀⣩⢁⢽⠀
⠀⠀⠘⠷⣟⡄⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀⢰⡷⠞⠁⠀
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠡⡇⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣥⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠠⡇⢸⢠⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡗⣤⣲⡃⠃⠀⡯⣦⣴⠃⣝⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣯⠁⠀⠀⠀⠀⠀⢳⠉⠁⠀⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣂⡀⠀⠀⡄⠀⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⡇⠀⡃⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⠀⡇⠈⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⢣⠀⡇⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⢆⢵⢸⢣⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠈⣾⣬⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠇⢄⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣢⣤⡄⡄⠀⣀⣀⣴⡅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠫⣴⠼⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀