⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣴⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⢰⣄⠀⠁⣰⡿⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⢀⠻⢧⢰⠋⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⠠⣸⣸⡆⡈⠇⢀⡄⢿⡸⠄⠲⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣄⢰⣿⠇⠀⠀⠀⢾⠖⠀⠀⠲⡀⠂⢠⢀⡀⠀⢀⠀⢄⣀⡙⢇⡟⠀⢸⢇⠿⠟⠋⠀⠀⠀⠀⡄⡆⠀⡇⠜⠀⠀⠠⣿⠄⠀⠀⠘⣿⡇⢠⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣼⢃⠴⠗⠀⠀⠀⠀⠀⠘⠓⣚⠣⡘⡜⠀⠀⠘⠳⣀⠈⢉⣑⢧⡀⣸⣥⡤⢀⡤⠛⠀⢀⠀⢸⢃⠴⢛⠊⠃⠀⠀⠘⠀⠀⠘⠓⣌⢣⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⡿⢁⣤⠀⣀⠀⠀⠀⠀⠀⠠⠝⢒⠾⠵⣀⠃⠀⡤⠾⠓⠒⡛⢝⡷⢩⠔⠈⠁⠓⠂⠀⠈⣇⠾⠷⢔⠛⠄⠀⠀⠀⠀⠀⣀⠀⢤⣌⢻⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣷⠀⣧⠿⠋⡠⠋⣡⡄⠀⠸⠂⠀⠀⠃⠀⠀⠘⡆⠀⠀⠒⠀⠀⠻⢦⠱⣽⠟⠁⠀⠘⠀⠀⢠⠏⠀⠀⠈⠃⠀⠀⠗⠀⠀⣤⡉⢦⠈⠻⢿⡇⣾⡇⠀⠀⠀
⠀⠀⣄⠀⠠⣤⣽⡀⡏⠀⡰⠓⠉⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠳⠁⠀⠀⠀⢀⠀⠀⠘⠀⠀⠒⠀⠀⣀⣀⠀⠀⠀⠀⠈⠑⢷⠀⢸⣇⢋⣴⠆⠀⣠⠀
⠀⠀⢻⣧⣦⢀⡉⠹⡇⢰⠁⢀⣆⠀⠀⠀⣾⣿⣟⣋⠁⠒⢤⡀⠀⠀⠈⣿⠁⠀⠀⠀⢠⠀⠀⠀⠀⢹⠃⠀⠀⢀⣠⠒⠈⡙⣹⣿⣿⠆⠀⠀⢰⡀⠀⡇⢸⠟⠉⡀⢴⢰
⠀⢀⣀⠙⢶⢸⣷⠀⢹⣼⠀⣾⡿⠀⡀⠀⠹⣿⠓⡁⢄⡉⠑⠻⡶⣄⠀⠀⠀⢠⡄⠀⠀⠀⠀⡄⠀⠀⠀⣠⢾⠟⠋⣁⡠⠄⠼⣿⡏⠀⠀⠀⢸⣿⠀⢸⡌⠀⢼⡇⡨⢊
⠀⠀⠙⠿⠾⢯⣃⠰⠆⢻⠀⡿⢡⣶⡇⠀⠀⢹⢫⠥⠆⠂⠡⢒⢤⣺⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣃⡤⡒⠍⢀⠴⠬⠓⡟⠀⠀⠀⣷⣄⢻⠀⡼⠱⡆⢸⡵⠕⠻
⠀⠀⠀⠀⠀⢀⠈⣲⢧⠈⢣⢣⡿⠋⠀⠀⠀⠈⢆⠀⠙⠉⢉⣻⣿⣿⣿⠛⢳⣄⠀⢄⠀⡐⠀⣠⡾⠋⣻⣿⣿⣯⣭⣀⣈⠠⣬⠁⠀⠀⠀⠙⢿⢸⡴⠁⣸⣔⣁⣀⠀⠀
⠀⠀⠸⠃⠀⠙⣥⠊⠉⠙⠢⢿⡁⢀⣄⢠⣦⠀⠹⠉⠒⠓⠀⢈⣙⣻⣿⣾⣮⡽⢳⣠⣿⣄⣖⠯⡴⢾⡿⢯⣉⡉⠉⠘⠋⠍⡟⠀⢸⡆⢠⡀⢀⡿⠔⠋⠉⠙⣦⠉
⠀⢠⣄⠀⠀⠀⠀⠀⢤⣤⣤⣀⠉⢢⡉⠪⡟⠀⠀⠙⢷⣀⡁⣁⡠⠠⠬⢷⣞⣉⣽⣿⣟⣿⣯⣁⡙⡗⠫⠴⠤⣠⣉⣁⡰⠋⠀⠀⢸⡷⠉⡴⠋⣠⣤⣤⡤⠀⠀⠀⠀⠀
⠀⠸⣿⣷⡀⠀⢢⣄⠀⠈⠉⢉⡁⠦⠽⣤⢳⠀⠀⣠⡀⠈⢉⡽⢟⢛⠻⠟⡻⠋⣾⣿⢿⣿⣿⠌⢫⡻⠿⣛⢛⠿⢍⠁⠀⣤⠀⠀⣘⣤⠯⠔⢊⣍⠉⠁⠀⢀⣴⠀⠀
⠀⠀⠙⠻⢇⠀⠸⣿⣦⠀⠀⢈⠀⠀⠀⠈⠙⢧⡀⠉⠀⢀⣏⠔⠃⡁⣡⣞⠄⡼⣹⣿⡿⣿⢿⢷⡤⣽⣦⣐⠹⡃⣝⡄⠀⠉⠀⡴⠋⠁⠀⠀⠀⣀⠀⠀⣰⣿⠏⠀⡸⠟
⠰⠾⠿⠿⠷⠛⠢⠌⢻⣇⠀⠈⢿⣦⠀⠀⠀⠀⠑⣄⠀⠀⢿⣔⣬⣜⣿⣿⣮⣧⡏⠻⢿⠟⠈⣜⣷⣿⣿⣳⢔⣵⡽⠁⠀⢠⠎⠀⠀⠀⠀⣴⣿⠃⠀⣠⡟⠡⠔⠚⠻
⠀⠀⠀⠀⠀⠲⢿⣿⣶⢬⡭⠶⠦⠽⣆⠀⠀⠠⠄⠈⣧⠀⠀⠙⣇⣼⠻⠿⣏⡿⠀⠀⠀⠀⠀⢾⣽⡻⡏⢑⣴⠋⠀⠀⡰⠃⠀⠄⠀⠀⣠⠯⠔⠾⠭⣤⢶⣿⠿⠗⠂⠀
⠀⠀⠀⢠⣴⣾⣷⠶⠈⠁⣤⣶⡶⠂⠈⠑⠦⡀⠀⠀⠈⢇⠀⠀⠈⢳⣿⢦⣷⠃⠀⠀⢺⠂⠀⠈⢿⡧⢷⡞⠁⠀⠀⢰⠃⠀⠀⢀⡔⠊⠁⠀⠺⣶⣦⡀⠁⠲⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠆⠀⠀⠀⡿⢸⠃⠀⠀⠀⢀⠀⠀⠀⠈⠇⣼⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠘⠃⠀⠀⠀⠀⡀⠀⠀⢰⣛⠎⢠⡄⠀⠀⢸⠀⠀⢠⡄⠸⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠄⠀⠈⠇⠀⢀⣤⡿⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠹⣼⡄⠀⠘⠗⠀⠀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠰⣄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⣤⡾⠊⠀⠀⢀⣤⣶⢊⢾⡎⠢⣤⣄⡀⠀⠙⠿⣦⢄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣠⡞⠀⠀⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣉⠴⠦⠭⠷⠤⢤⠴⡎⠀⠀⠀⣴⠾⠕⠉⠀⠀⠀⠀⠉⢉⡴⠃⢸⠘⣄⠈⠛⠓⠀⠀⠀⠈⠑⠿⣦⠀⠀⠀⢸⡲⣤⠤⠶⠭⠴⠦⠍⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢦⣤⣀⠀⢀⣠⠶⢁⢜⡄⠀⠀⠀⠃⠀⠀⠀⣀⣤⠔⢒⡼⢁⣼⠀⢸⠀⢸⠢⣀⠀⠀⠀⣀⣀⡀⠀⠘⠃⠀⠀⢠⡗⣀⢓⢦⣀⠀⣀⣤⡶⠂⠀⢀⡀⠀
⠀⠀⡀⠀⠚⠢⠤⢤⣤⠍⠋⡱⢁⠃⠉⢸⠇⠀⠠⠀⠀⠀⠀⣴⠟⢋⡔⢱⠁⠘⣿⠁⢸⠀⣸⠀⠈⠻⣏⠡⠬⣙⠛⠂⠀⠀⠤⠀⠸⡏⠈⠈⡏⢪⡑⠢⢤⣤⠤⠐⠒
⠀⠀⠟⠃⢀⠜⠉⣡⠡⠾⢻⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⣷⠀⠀⠁⢀⠿⡄⢿⠃⠀⠀⣋⠣⡀⠈⠻⣷⡄⠀⠀⠀⠀⠁⠀⢠⡇⠀⣏⠻⠆⢢⡈⠛⣄⠈⠓
⠀⠀⠀⠀⠃⠀⠼⠋⠀⢀⣼⡀⠘⠇⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⣎⠀⠘⣿⠇⠀⣤⠃⢠⢰⣌⠀⠀⢠⣿⠀⢰⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠇⠀⣼⡄⠀⠈⠿⠀⠈⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⣿⡟⠀⠀⠙⠀⢸⡿⠀⢠⠀⢿⣧⠀⠸⠟⠀⢸⣿⣆⠀⠀⠀⢺⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠙⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀