Cute letters Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠿⠿⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠐⢧⡀⠀⢘⣋⣉⡀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠀⢠⣤⠶⠆⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠀⢀⣤⣤⣷⣄⠈⣭⡭⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠈⠁
⠀⠀⢀⠀⡀⠄⠀⠀⠀⠙⣆⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⣤⣤⠤⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠠⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⠀⠀⣼⠇
⠀⠀⠐⠀⠀⠀⠀⢻⡆⠰⠖⠶⠿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠄⠀⠀⠀⠀⠀⢠⣤⣤⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡿
⠀⠀⠐⠀⠀⠀⠀⣸⡇⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠛⠋⠉⣿⠀⠀⢸⠀⠀⠀⠀⠀⢤⣤⣴⣶⣶⡶⠶⠆⠀⠈⠻⢦⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠈⣄⠀⠀⢀⣴⡆⠀⠈⠀⢸⡆⢀⣿⠁
⠀⠀⠀⠂⠀⠀⠀⠀⣿⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠙⢷⣶⠟⢹⡇⠀⠀⠀⢹⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠿⠿⠶⠒⠓⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠠⠘⠛⠛⠛⠛⠛⠋⠘⠀⠐⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡀⡂⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠿⠿⠿⡿⡿⠿⠿⠿⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠡⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠈⠻⣷⣄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡄⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠧⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⢀⣈⣁⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⡀⠀⠀⢠⡶⠀⠀⢤⡀⠀⠀⠀⢀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⣼⠏⠀⠀⠔⠀⠀⠀⠀⠀⢸⡇⠈⢠⠀⠀⡿⠁⠀⠀⠈⢿⡄⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢴⡆⠀⠶⠶⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠏⠀⠀⠀⠔⠀⢀⣠⣄⠀⢸⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠟⠀⠀⠀⠀⠄⠀⠿⠋⠙⢷⣼⡇⠀⢠⡿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠛⠛⠛⠁⠉⠁⠀⠈⠉⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣃⣀⣻⣁⣀⣐⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣿⡟⣻⣿⣿⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣻⣿⢿⣿⣿⢿⡿⠛⠿⢿⣿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣻⣿⣿⣸⡿⢿⣿⡿⣿⢼⢿⣿⣿⣧⣻⢛⣿⣿⣿⣿⡿⢿⠇⣧⠿⣿⣿⡟⢻⣿⢿⣿⣿⣿⡇⣿⣿⢡⣾⢻⡟⣼⡿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣃⣻⣽⣿⣿⣟⣚⣇⣶⣿⣴⣿⣿⣿⣿⣿⡸⣿⣿⣿⣟⣿⣌⣸⣿⣼⣾⣿⣇⣾⣧⣴⣾⣿⣿⣿⣿⣿⣌⣛⣼⣧⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⢀⠀⢤⣄⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣣⠀⠀⠀⠀⠀⠀⠠⠊⠛⠒⠀⠭⠓⠢
⠀⠈⠻⢾⣿⡆⠀⠀⠀⠛⠈⢢⣠⣴⣾⣿⣧⠤⢤⡀⣰⣾⣆⠁⠀⢠⠜⠁⠅⠀⠈⠢⡀⡰⠿⠃⢄⣀⠠⣿⠄
⠀⠸⣳⠞⠛⠛⢢⠘⠉⣑⠄⢀⣹⡟⠋⡀⠉⢺⣟⠁⠉⢻⠉⠱⣄⠟⣀⣤⢰⣤⠂⡶⣀⣧⣤⡀⠀⠀⠀⠀⡌
⠀⠀⡇⠀⠀⠀⡀⠉⡜⢀⠴⡯⠴⠠⠀⠀⠀⢘⠉⠀⢀⠜⠁⠐⢼⣞⢇⠀⠑⠈⠠⠐⢸⡷⠈⠁⠀⠐⠠⣤⣄
⢠⠂⠴⠀⠲⠟⠉⠀⠧⢘⡀⢄⡠⠧⢤⣆⣈⠉⠙⢶⠁⠤⠔⠀⡸⢇⣮⡈⢸⠉⣱⣲⡁⠂⣘⠻⣤⣀⠀⢠⣿
⠈⠃⢁⠉⡢⢀⠴⠚⣯⠉⡰⠁⠀⣰⣁⠄⠀⢷⡀⠀⡧⢠⠴⠚⠂⠚⠛⠛⠻⠾⣼⣷⣿⣶⣿⣶⡉⠀⠀⠸⠁⠀⣀
⠀⠀⠣⣁⣠⠀⡼⠉⠉⢹⠁⠀⢰⠋⠙⠂⠀⠀⡸⢟⣩⣄⠀⠀⠔⠢⣀⠴⡴⠊⢠⡠⠛⠛⠃⠠⣀⠀⠀⣶⣤⣼⠏
⠀⠀⠀⠀⠐⣡⠃⠀⡦⣼⡀⠀⠀⢀⠀⡀⠀⠀⡁⠀⠀⠀⡅⣉⠩⣻⠝⠀⠀⢈⣻⡇⠀⢀⠀⠀⠈⡗⠼⠻⣿⡟⠃
⠀⠀⣀⢸⡟⠈⣄⡀⠈⠀⢣⠀⠸⡀⣢⣀⠠⠄⠇⠄⠀⢀⠐⢀⠀⣿⡈⠀⡀⠀⣹⠀⣦⣤⣀⣀⣀⡅⠀⠰⠿⠏
⠀⠀⢻⣿⠇⢸⣿⠃⠉⣩⢈⠆⢠⡋⣀⡼⢉⠀⡬⠦⢄⠘⠓⠤⣌⠙⠃⠐⠁⠁⢀⠀⠂⠛⢿⡷⡟⢀⣠⡄⠐
⠀⠀⠸⣿⡿⠾⠏⢲⣤⢸⣅⡀⠌⠈⠛⣁⠠⣾⠐⠲⡤⢉⣒⡒⠋⠀⠀⣀⢤⡾⣥⡀⣠⠄⠊⠉⣁⠀⠀⢃
⠀⠀⠀⢨⠀⣰⣿⣄⣀⡀⠀⢀⣅⠘⢷⣾⠿⠋⠃⠀⢻⣹⢿⡧⣿⢾⣿⣏⣾⡿⢝⣿⣶⠀⠀⠫⠬⠀⠀⠈
⠀⠀⢎⠁⠸⣋⠙⠛⠉⡉⠻⣿⣿⡄⠈⠃⠤⠐⠁⢀⢜⡿⠞⠓⠻⢷⣿⣿⣿⡷⠿⠛⠛⠧⣀⠀⠀⢀⠀⠀⠠
⠀⢠⠒⠀⢰⡄⠈⠈⠀⠀⢠⣿⡿⢯⠶⠤⣤⣤⣖⣹⠋⢀⠀⠀⣄⠀⢻⡿⠉⢀⡴⠃⢸⡄⠈⡖⠁⠂⠐⠊⢰
⠀⠀⠂⠐⡈⢿⣶⣤⣴⣾⠟⠁⠪⠠⢀⠞⢳⡿⡇⢇⠀⢫⢤⣶⣾⡁⢸⠁⠀⢩⣴⣤⣶⡍⠀⡇⠀⠀⠀⠀⡠
⠀⠀⠀⠀⣅⠜⣿⠿⣿⡏⢀⠀⠀⠀⠀⠁⠁⢹⣿⣼⠀⣿⡿⡿⣿⡇⠀⠆⠀⠈⣿⣙⣻⣅⡜⠑⠀⠒⡀⠉⡀
⠀⠀⠀⢀⣁⣀⣿⡶⠒⠁⠤⢄⡀⠀⠀⠠⠄⡸⠈⠿⣄⠘⠿⡾⠯⢃⡀⣮⠀⡤⠭⠭⢥⣸⠀⠀⠀⠀⠠⠀⢰
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠊⠄⠀⡀⠘⡀⢞⠛⠉⠹⠕⠁⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠎⠁⠘⠚

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⡛⠀⠀⠀⠀⢰⠃⠀⠑⠀⠀⠀⠘⠀⠀⠈⣢⠀⠀⣠⠖⠂
⠀⠀⠀⠀⠀⠤⠀⢸⣄⠀⠀⢀⠀⢀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⣠⠄⠀⢀⡴⠋⠀⠀⠀⠀⠠⠀⠀⢀⡈⠀⠀⠀⢐⠂⠀⠀⠤⠀⣰⠁⠀⠐⠠⠎⠠⠄
⠀⠀⠀⠀⠀⡯⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠬⠀⠀⠀⠀⢀⡏⠀⠀⠀⢘
⠀⠀⠀⠈⠰⠃⠀⠀⠘⢧⡄⠀⠀⠀⠀⠃⠀⠠⠂⠀⠈⠁⠠⠋⠀⠀⠀⢁⠼⠃⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⢘⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡆⠀⠉⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⢞
⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⠄⠀⠀⠀⡅⠀⠀⠀⡀⢰⣗⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⢀⢠⠃⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠄⢠⠂⠀⠀⠀⠀⣴⡋⡀⠀⠀⠀⠀⡀⢠⠆⠀⠀⢠
⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠘⢉⡀⠀⠀⠀⠀⠐⢀⠍⠀⠀⠀⠀⠀⠁⠀⠟⠀⠀⠐⠂⠰⠃⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠂⠈⠵⠀⠀⠀⠀⠀⠁⠠⢳⠀⠀⠀⠆⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⣀⠀⠀⠭⠀⠀⠀⠀⠀⡀⢸⡖⠀⠀⠀⢀⣼⠝
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠋⠀⠀⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣾⣿⠿⠿⠿⠿⠿⢿⣷⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠟⠛⠛⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⣀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⡀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠈⢿⣧
⠀⠀⣼⣿⠃⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠸⣿
⠀⣸⣿⠃⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿
⢠⣿⡏⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⢠⣿
⢸⣿⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⣼⣿
⣿⡟⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠛⠛⠉⠉⠉⠉⠉⠙⠛⠻⠿⣷⣦⣄⣀⣀⣀⣀⣠⣶⡿⠟⠁⠀⠀⠀⠀⣰⣿⠃
⣿⡇⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣴⣿⠋
⢿⣧⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⢸⣿⡀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠁
⠈⣿⣇⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⠋⠉
⠀⠸⣿⣆⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⣼⡿⠃⠀⠀⠀⠀⢀⣤⣾⡿⠿⠟⠛⠻⠿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⢻⣿⡄
⠀⣸⣿⠃⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⢿⣷
⠀⣿⡏⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠈⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠸⣿⡇
⢰⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⣿⣧
⠘⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢻⣿
⠀⣿⣇⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿
⠀⢻⣿⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⣿⣿
⠀⠸⣿⡇⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⣿⡇
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⢰⣿⠏
⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣶⣶⣶⣦⣤⣴⣶⣶⣶⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣴⣶⣾⡿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠿⠿⠿⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡿⠋⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠻⠷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠉⠁⠀⠀⠀⢀⣴⡿⠋⠉⠀⠈⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢷⣦⣄⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⣀⣴⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠹⣷⡀
⠀⠀⣼⠟⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠘⣿⡀
⠀⢸⡟⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠸⣷
⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⡇
⠀⢻⡇⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⣧
⠀⠸⣿⡀⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡏
⠀⠀⠹⣷⡄⠀⠀⠀⠈⠛⠿⠿⠶⠿⠛⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣾⡇
⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠰⣿⡄
⠀⠀⠀⠀⠀⠈⣿⡗⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸
⠀⠀⠀⠀⢀⣠⣿⡧⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⢸
⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣭⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸
⠀⣠⡿⠋⠀⠀⠀⢀⣠⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⣼
⢠⣿⠁⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⣰⡿
⣾⡇⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⣰⡿⠁
⣿⡇⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠀⠀⠀⢀⣾⠟
⢻⣇⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⣠⣴⠟⠁
⠘⣿⡄⠀⠀⠀⠙⢿⣦⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠾⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠛⠁
⠀⠈⢿⣦⡀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣄⣀⣤⣴⡾⠋⠀⠀⠀⢀⣤⣶⡶⠾⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠶⠶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋

⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⣴⣶⢦⡀⠀⠀⠀⢀⣴⣾⣿⣷⡦⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⣴⣶⣶⡆⠀⠀⣴⣶⣶⡆⠀⠀⠀⣠⣴⣶⣶⡤
⠀⠀⠀⠀⠀⠀⢰⠟⢻⣇⠀⠀⠀⣼⣇⣸⠇⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⢰⣿⡟⢻⣿⣧⠀⠀⢻⣟⣀⠀⠀⠀⣿⡏⠁⠀⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⠀⠀⠀⣿⡟⠛⢶⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⣠⣿⡟⠀⠀⣸⡿⠿⠀⠀⠀⣿⣿⡿⠀⠀⠀⣿⡇⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⢸⣿⠇⢹⣿⡆⠀⠀⣿⣇⣀⡼⠃⠀⠀⠹⣿⣦⣤⣤⣤⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⣿⣷⣦⠄⠀⠀⣿⡇⠀⠀⠀⠀⠙⢿⣦⣤⣤⡿⠋
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣠⣾⠏⠀⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⣿⣆⠀⣼⣿⣿⠀⠀⢸⣿⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣤⣼⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡿⣿⣴⣿⢿⣿⠀⠀⢸⣿⣿⣧⣸⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠛⢻⣿⠀⠀⠈⣿⠀⠀⠀⠀⢠⣿⡇⠀⠀⣿⡿⢿⣷⡀⠀⠀⠀⣽⣿⠀⠀⠀⠀⢸⣿⡇⠹⣿⠃⢼⣿⠀⠀⢸⣿⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠏⠀⠸⠿⠀⠀⠐⣿⠀⠀⠘⠿⠿⠿⠁⠀⠀⠿⠗⠈⠻⠷⠀⠀⠀⠺⠿⠿⠿⠄⠀⠸⠿⠁⠀⠀⠀⠹⠿⠀⠀⠸⠿⠀⠈⠻⠿


⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⣄⠀⠀⠀⣴⣶⠶⢶⣄⠀⠀⠀⢀⣴⣶⣿⣷⣦⡄⠀⠀⠀⣶⡶⠶⢦⡄⠀⠀⠀⣠⣶⣶⡦⠀⠀⢰⣶⣶⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠀⣾⡿⠉⠀⠈⠙⣿⡆⠀⠀⣿⣿⣀⣸⣿⠀⠀⢠⣿⠟⠁⠀⠈⠹⣿⡆⠀⠀⣿⣇⣀⣼⡿⠀⠀⠀⢻⣯⡀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢀⣿⡇⠀⠀⣿⡿⠛⠋⠁⠀⠀⢸⣿⡄⠀⠀⣀⢠⣿⠇⠀⠀⣿⣿⣿⡉⠀⠀⠀⠀⠀⠉⢻⣷⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣴⣾⡟⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠻⣿⣦⣬⣿⣿⣏⠀⠀⠀⣿⡏⠿⠉⠀⠀⠀⠀⣶⣦⣾⣿⠁⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁⠀⠀⠀⠉⠁⠀⠙⠛⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⢠⣄⠀⠀⠀⢀⣀⠀⠀⢀⣀⡀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣄⡀⠀⠀⣠⣄⠀⠀⢀⣄⡀⠀⢀⣀⠀⠀⢀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⢸⣿⡆⠀⠀⣾⣿⠀⠀⠸⣿⡇⢸⣿⠇⠀⠀⢸⣿⡀⠀⣠⣄⠀⠀⣼⡿⠀⠀⠀⢸⣿⡄⣰⣿⠃⠀⠀⠀⢿⣷⣠⣿⡏⠀⠀⠀⠋⠛⢻⣿⡿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⣾⣿⠀⠀⠀⠈⣿⡇⣰⣿⣿⡄⢰⣿⠇⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠘⣿⣧⠀⢠⣿⡏⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⠇⢹⣿⣿⡟⠀⠀⠀⠀⢰⣿⠏⢻⣿⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⠀⠈⠻⠋⠀⠀⠻⠟⠀⠀⠀⠀⠠⠬⠏⠀⠈⠿⠧⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⡆⠀⠀⠀⣸⢷⡆⠀⠀⠀⠀⣴⣾⣿⣷⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣷⠀⠀⠀⣿⢸⣇⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⢸⣿⠛⣿⡇⠀⠀⣿⣿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⣿⡀⠀⠀⣿⠀⢹⣷⡀⠀⢸⣿⣿⠃⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠹⠇⠀⠀⣿⢤⡾⠟⠀⠀⠈⠻⣿⣷⠿⠀⠀⠀⠿⠿⠛⠋⠀⠀⠀⠀⢿⣧⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠶⠀⠀⢀⣴⣶⣶⡆⠀⠀⠀⣠⣶⡄⢠⣾⣷⠀⠀⠀⠐⠛⣀⠀⠀⠀⠀⠤⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠆⠀⠀⢸⣿⡟⠉⠁⠀⠀⢀⣿⣿⣧⣾⣿⣿⠀⠀⠛⢻⣿⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡆⢀⣤⡄⠀⢸⣿⣿⡇⢼⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⣀⡀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠘⢿⣿⣿⠿⠃⠀⠀⢿⡿⠀⢻⣿⠇⠀⠀⠀⢸⣿⣿⠀⠀⢻⣿⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⣠⣤⣤⠀⠠⣤⣤⡄⠀⠀⠀⢠⣤⡄⠀⢠⣤⣤⠀⢠⣤⣤⡄⢠⡀⠀⠀⣤⣴⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣄⣿⣿⣿⠀⢸⣿⣿⡟⣾⡇⠀⣾⣿⡇⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⢸⣿⠀⢀⣀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⡇⠀⢿⣿⣿⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠏⠙⠿⠶⠀⠀⠈⠿⠶⠿⠏⠀⠀⠿⠿⠛⠛⠿⠿⠀⠸⠿⠿⠇⠸⠇⠀⠀⠙⠻⢶⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⣠⣶⣶⣦⣄⠀⠀⢠⣤⣤⣤⣤⡀⠀⢀⣤⠤⠠⣤⠀⠀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣁⣽⡇⠀⣸⣿⠟⠛⢻⣿⡇⠀⢸⣿⣿⡟⣿⣿⠀⠸⣿⣧⣀⠀⠀⠀⠉⢹⣿⡏⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠋⠀⠀⣿⣿⡀⠀⣸⣿⠃⠀⢸⣿⣿⣿⣿⡁⠀⢀⠘⢿⣿⣷⡀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠻⣿⣿⣿⡿⣿⡷⠀⠸⣿⣿⠇⠿⠧⠀⢸⠧⣄⣿⠿⠀⠀⠀⠸⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⢀⣀⡀⠀⠀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⣀⡀⠀⢀⡀⠀⣠⠀⢀⡤⢀⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠈⣿⡏⠀⠈⣿⠋⠀⠉⢿⣿⡀⣼⡿⠉⠀⢹⣿⣿⡇⠀⠀⢠⡏⠀⠹⣿⣴⣿⠃⠀⣿⣿⣿⡇⠈⠉⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⠀⠀⠀⠘⣿⣷⣿⠃⠀⠀⠀⣿⣿⣿⣾⣦⣿⠁⠀⢠⣿⣿⣿⡄⠀⠈⠉⢹⡇⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠘⠿⢶⡾⠿⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠘⠿⠿⠋⠻⠃⠀⠀⢾⠟⠉⠿⠗⠀⣀⣀⣾⠃⠠⠾⠿⠏⠠⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⢿⠿⢿⡿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠹⠿⠿⠿⠀⠀⠀⣿⣿⣿⣿⣾⡟⠀⠀⣾⣿⠛⠇⠘⠛⠀⠀⠛⠃⢀⣿⣿⣿⡿⢀⣤⠶
⢶⣄⠀⠙⠿⠿⠛⠷⠂⠀⠀⠀⣀⡀⠀⠀⠀⢿⡟⢸⣿⡏⠀⠀⠀⠈⠛⠀⠀⠀⢀⣤⡴⠶⣤⠈⠙⠛⠉⠀⠙⣿⣾
⣾⠏⠀⠀⠀⠀⣠⡴⢦⡀⠀⠀⢻⡇⣼⠟⠀⠀⠀⠀⠉⠀⠀⢀⣶⡄⠀⠀⠀⢰⣿⣿⣧⣤⣿⡧⠀⠀⠀⡀⠀⠈⢿
⠁⢠⣤⡄⠀⠘⢿⣷⣾⡷⠀⠀⢸⣿⠋⠀⠀⢰⣿⠿⣷⡄⢀⣾⣿⣧⣼⣿⠇⠈⢿⣿⣿⠿⠛⠁⠀⠀⠹⣿⣆⠀⠈
⢠⣿⣻⣷⠀⠀⠈⢻⣯⡀⠀⠀⠸⠟⠀⢰⣶⣄⣻⡄⠈⠀⣾⡟⣿⡿⣻⣿⠀⠀⠘⠃⠀⠀⣀⣠⣴⡄⠀⠘⣿⣆
⣾⡿⠿⣿⣇⠀⠀⠀⠙⠁⠠⣴⡆⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠉⠀⠿⠿⠀⠀⠀⠀⠀⢻⠟⢿⣏⠀⠀⠶⠿⠋
⠛⠁⠀⠛⠋⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⢠⣶⡄⠀⣤⣤⡀⢰⣶⠀⠀⠀⢠⣦⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⡀
⣦⡀⠀⠀⠀⠀⣴⡿⠃⣀⠀⠀⢻⣷⡀⠀⢀⣴⣿⠟⠁⠀⢹⣿⢿⣜⣿⡀⠀⠀⣾⡟⣠⣾⡦⠀⠘⠋⠀⠀⣰⣿⠗
⣽⣿⠀⠀⣠⣾⠿⣷⣾⡿⠃⠀⠀⠁⠀⠐⢿⣿⣁⠀⠀⠀⢸⣿⡆⢻⣿⡇⠀⣸⣿⣿⠟⠉⠀⣀⣤⠶⣤⠀⢻⣿⣄
⠟⠁⠀⠀⠙⠁⣴⡿⠋⠀⠀⢀⣤⣀⡀⠀⠀⠙⠋⠀⠀⠀⠈⠛⠁⠀⠉⠁⠀⠈⠛⠁⠀⠀⠀⠹⣿⣶⣿⠇⠀⠙⠻
⠀⢠⣤⠀⠀⠀⠈⠀⠀⠀⢀⣾⣟⠛⠃⠀⣀⣀⣄⡀⠀⠀⢠⣾⡧⠀⠀⠀⠀⢠⣶⣦⣄⠀⠀⠀⢻⣿⡉
⣷⣌⣿⡆⠀⢀⣤⡀⠀⠀⣾⣟⡉⠀⠀⣼⣿⣀⣼⣿⠆⠀⢸⣿⡄⠀⢸⣷⠀⠈⢿⣯⣿⣿⣶⡄⠀⠛⠃⠀⣤⡀⢹
⡏⠻⣿⣷⠀⠈⢻⣷⡀⠀⠉⠙⠛⠀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠙⠿⣿⡿⠋⠀⠀⠘⣿⣇⠈⠋⠀⠀⠠⣶⣄⣿⡇⠈
⠿⠀⠘⠛⠀⠀⢀⣿⣿⠀⠀⢀⣀⠀⠀⠈⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠘⠋⠀⢰⣶⠒⣦⠈⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠘⣿⣿⣷⣶⣤⠀⠀⢰⣿⣡⣶⠆⠀⢠⣿⡿⠛⠻⣿⠆⠀⠀⣾⣿⣿⣟⠀⠀⠈⠛⠃
⠂⠀⠀⠀⠐⢿⣦⡀⠀⠠⣶⣶⣾⣿⣷⡍⠉⠀⠀⣾⣿⣿⡁⠀⠀⠸⣿⣦⣼⡶⠀⠀⠀⢠⣿⣯⣤⡟⠀⠀⢀⣤⣾
⣄⠀⠺⣿⣄⠀⠹⣷⡀⠀⠈⠙⠿⣷⣭⠁⠀⠀⠠⢿⠃⢻⣧⠀⠀⠀⠈⠙⠋⠀⣠⣶⡦⡄⠀⠈⠁⢀⣤⠀⠹⠋⠻
⣿⠆⠀⠙⢿⣶⣶⡿⠁⢀⣤⡀⠀⠈⠁⠀⠀⣶⡄⠀⠀⠀⠈⣀⣀⣀⣠⠀⠀⣴⣿⣿⣦⠏⠀⢠⣦⡈⣿⣷⡀
⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠻⠂⠀⠀⢰⣶⣼⣿⣶⣤⣄⠀⠙⠋⣽⡟⠀⠺⠏⣸⡇⠀⠀⠀⠀⠹⣿⣟⠙⣿⡆
⡟⢀⣤⡀⠀⠀⠠⣾⠟⠙⠃⠀⠀⠀⠀⠀⠀⠈⠻⣷⡉⠁⠀⢀⣼⡟⣀⡀⠀⠀⠉⠁⣤⡄⠀⠀⠀⠘⢿⠆⠈⠀⢀
⣾⡿⠋⢁⣠⣤⣀⠀⠀⠀⣠⣾⠿⢿⠂⠀⠀⠀⠀⠙⠁⠀⠀⠸⠿⠟⠛⠃⠀⠀⠀⠀⢿⣧⠀⠀⢠⣦⣤⡀⠀⢀⣾
⠉⠀⢠⡏⠈⣿⣿⡆⠀⠀⣿⡏⠀⢀⠀⠀⠀⣿⡇⣠⣤⢀⣄⡀⠀⠀⢀⣠⣴⣾⡄⠀⠸⣿⡄⠀⣼⣿⡀⣽⠄⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡜⢳⡆
⠀⠀⠀⢠⠆⠠⣤⣤⡄⢀⡴⠖⠓⠲⣶⣤⠐⠀⠀⠀⠀⠀⠀⠀⢰⣒⣦⠤⣥⣬⣡⣤⣥⠀⢀⣒⣶⠀⠀⠀⠀⢀⠘⢀⣈⣳⣿⡞⣉⢀⣀⠀⣀⡉⠇⢰
⠀⠀⠀⠈⠁⠀⠈⣿⣦⡟⠁⠀⡀⠀⢸⣿⡍⠀⠘⠀⠀⠀⠀⠀⢸⠋⣀⣀⢈⣿⣿⣻⠉⠀⠀⠈⣿⠀⠀⠀⠀⠚⠢⠞⣿⣿⡏⣿⠋⠉⠉⠉⢙⡣⢐⡩⠄
⠀⠀⠀⠀⠇⠀⠀⣻⡿⠀⠆⠀⣀⣀⣸⡿⠁⠀⢀⡀⠀⠀⠀⠀⠈⠀⠨⠿⢁⣽⣿⣿⠀⢶⡄⠀⠈⠀⠀⠀⠀⠂⠀⠀⣿⣟⣣⡘⢦⣤⣶⣿⠿⠟⣁
⠀⠀⠀⠀⠀⣰⠆⣾⡇⡀⢰⡉⠀⣩⠟⢿⣷⣥⡀⠈⠀⠀⠀⠀⠀⣀⣠⠀⠈⢿⣽⣷⠀⠈⠁⡶⠃⠀⠀⠀⠀⠘⢳⣅⣿⣿⣤⣽⡄⢹⠿⡿⣧⠾⣯⣤⡄
⠀⠀⠀⠀⠈⠁⠀⣿⡇⠀⠀⠉⠁⢀⣁⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠓⠺⡀⠃⡀⣿⣶⡠⢀⣾⠟⠁⠀⠀⠀⠀⣀⠀⢀⣿⡏⠀⣴⣴⡶⠲⣄⠈⢀⣷⣻⡆
⠀⠀⠀⠀⠄⠀⢰⣿⣿⡀⠁⠀⠀⠀⣻⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⡦⠶⣿⡏⢨⣿⣟⠰⡀⠈⠠⣨⣋⣿⠇
⠀⠀⢀⠄⠀⠀⣸⣿⠿⣷⡀⠀⢠⡴⠿⠋⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⣄⣿⣿⣦⣬⣿⣧⣴⣶⣬⣾⠹⠁
⠀⠀⠘⠦⠄⠒⠻⠿⠇⠀⠙⠶⠤⠤⠤⠖⠋⡡⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢦⣿⣽⣦⣄⠀⠀⠀⠀⠀⠀⠀⠓⠛⡄⠰⠴⠄⣠⡮⠶⠖⠶⠖⠋⣡⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⢀⠀⢤⣄⡀⠀⡀⠀⠀⢄⠀⣀⡤⠶⠤⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣀⠀⣠⠄⣀
⠀⠀⠀⠀⠐⣚⣿⣿⢁⣾⣇⣀⠀⠈⣾⠇⢸⡟⢁⠀⠀⠀⠀⠼⣠⣤⣤⠐⢃⡟⣿⣧⢦⣉⢋⢀⡠⠀⠄⠀⠀⠀⠀⢈⣬⡄⢀⣠⣥⣧⣄⣼⣀⣀⡖
⠀⠀⠀⠀⡌⡁⠼⢿⡎⠻⢿⡇⠠⡼⣏⢀⡞⠐⠋⡄⠀⠀⠀⣼⣿⡉⢉⡁⣼⢁⠸⣟⣛⢁⠠⠌⡅⠃⠀⠀⠀⠀⢰⠃⣦⡽⣽⣿⠉⠀⠹⣄⡉⢻⡇⢤⡀
⠀⠀⠀⠀⠡⠁⠂⠹⣿⡌⢾⡇⠀⣳⢭⡞⠐⠒⢦⡀⠀⠀⠀⠁⣁⢛⠣⢱⠇⢼⠇⢹⣿⢂⠠⠐⠀⠈⠁⠀⠀⢀⠈⢃⡀⠈⠿⠿⣷⣄⠀⠸⠰⡼⡧⣉
⠀⠀⠀⠀⠀⣼⣶⡦⠹⣿⡌⢻⣤⢦⡞⠀⡀⠘⠐⡇⠀⠀⠀⠆⢿⡆⢄⡟⠀⠋⣠⠄⢻⣶⡀⠲⠂⠌⠀⠀⠀⠀⣷⣦⠈⠉⠉⡜⠹⠿⣿⣻⢦⣄⠉⢁⡀
⠀⠀⠀⠀⢀⡴⠟⢿⣦⡹⣿⡌⢣⡞⠀⣧⠘⠒⠲⠁⠀⠀⠀⣤⣌⠃⣼⠷⠒⠀⢠⡐⠺⣿⣷⠈⢁⠋⠀⠀⠀⠀⠉⣹⠔⠒⠲⡾⠒⢡⡾⠉⠻⣿⣷⡄
⠀⠀⠀⠀⢾⠃⢰⡖⡟⢻⣿⣿⡞⢀⠑⣾⠀⠠⣥⡀⠀⠀⠀⣸⡟⣸⠇⡐⢄⢰⡏⣄⡀⠸⣿⣧⠀⣿⠀⠀⠀⠀⡜⠀⠀⢹⠀⡏⠀⡜⠀⡀⢑⣼⣿⠃
⠀⠀⠀⠀⢨⠃⠤⣀⡠⠴⣷⢟⣀⠁⣾⣿⣶⠀⠈⠇⠀⠀⠀⠘⢡⡟⠀⢧⠈⡌⢃⣨⣴⠧⢹⣿⣆⠘⠀⠀⠀⠀⢇⠀⠀⢸⡿⠟⢛⡷⠶⣾⡿⠟⠃⠘⠁
⠀⠀⠀⠀⠈⠑⠒⠋⠀⠘⠁⠉⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠢⠘⠁⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣦⢞⡟⡭⣉⠙⣿⣷⣼⣿⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⠿⠋⣩⠃⠀⠀⡈⢿⣿⡀⠄⣙⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠹⡔⢰⠺⢦⠰⣄⣩⡾⢿⣽⣷⣟⡏⡇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣛⡀⡔⠻⣟⣦⣽⣿⣀⣀⠀⢀⠈⠉⢏⣿⡷⠾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣥⡥⢦⡽⡋⢽⠟⣷⡦⡏⢉⡦⠤⢴⡞⢻⠂⠀⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠋⠉⠂⢳⠁⠂⠂⣼⢷⢯⣻⣽⣢⣼⡧⣤⣀⡔⠋⠛⣧⣄
⠀⠀⠀⠀⠀⠀⠠⣤⢷⡔⠀⣁⠈⣦⣷⣤⣰⠉⠈⠈⢻⣿⠉⣹⠃⢋⠛⠛⣁⠀⠀⠛⣦
⠀⠀⠀⠀⠀⠀⢠⣿⡷⠼⡦⡝⢰⣅⢀⡂⡉⣆⡀⣀⣼⣣⣶⠯⢤⠉⣙⣋⠅⠄⠄⠐⣯⡀
⠀⠀⠀⠀⠀⢠⡟⢅⠠⢀⣢⣾⣿⡀⠙⠑⢒⣛⣹⡏⠿⣿⣿⣤⡂⡀⢤⣿⠀⡀⢀⣾⢿⡇
⠀⠀⠀⠀⢠⡟⠒⠞⢽⣶⣽⣷⣭⡗⢤⠊⠉⢿⡏⠀⠀⠈⢻⣿⣝⣦⣾⣍⠟⠛⠿⢿⠛⢷⣆
⠀⠀⠀⠀⡾⠃⠠⢟⡿⠋⠓⠿⣾⣳⡀⠀⢀⡴⢛⣶⣤⣠⣾⠓⢄⢻⣘⣇⣱⣿⣦⣸⠋⢸⣿
⠀⠀⠀⢰⡏⠀⢠⡾⣧⡈⠈⢀⡿⢛⣯⣶⣤⣽⣣⢠⣿⡬⠋⠉⢺⣿⡏⠉⠙⢉⢘⣏⠚⠛⣿
⠀⠀⠀⢰⣟⣳⢾⢻⣷⣻⡿⠿⢽⢾⠋⣥⡅⣹⣿⠂⢌⢇⠘⢀⡼⠛⠓⠢⢴⠀⢺⣁⠀⠉⣟⣷
⠀⠀⠀⣼⠋⠘⠛⣞⡵⠢⣣⠀⠙⣾⠛⣯⠟⠻⠾⠿⠒⠛⠻⣭⠀⠂⠀⠀⢸⡦⢧⣉⠠⢸⠭⣽⡂
⠀⠀⠀⢻⣄⠱⡰⠛⠛⠶⢶⢧⡀⠹⠿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣞⣱⡗⢠⣿⠗⣤⣼⡇
⠀⠀⠀⠀⠉⠛⠳⣄⣀⣀⡸⢫⣅⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣠⣿⣟⣠⣭⣂⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀
⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⡄
⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣠⣶⣿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⢰⣿⠇⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⣿⡿⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⢐⣿⡇⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⢻⣿⡄
⠀⢸⣿⡇⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢻⣿⡄
⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠈⣿⣧
⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⢻⣿
⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠉⠉⠉⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⣿⣶⣶⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿
⠀⣼⣿⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢸⣿
⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⣾⣿
⠀⣿⣿⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⢰⣿⡏
⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⢀⣾⡿
⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⢀⣾⡿⠁
⠀⣿⡿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁
⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⢰⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⡋
⢸⣿⡇⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠈⢻⣿⣄
⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠻⣿⣆
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠹⣿⡆
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⢿⣿
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⢸⣿
⣼⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⢀⣿⡿
⣿⣿⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣄⣀⣀⣤⣴⣾⡿⠟⠀⠀⠀⠀⠀⢀⣾⡿⠃
⣿⣿⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⢸⣿⡄⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠈⢿⣷⡀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⠃⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠋⠁
⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠉⠙⠻⢿⣿⣶⣶⣶⣶⣶⣾⣿⠿⠛⠋⠁
⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⠿⠋⠁

⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡀⠀⠀⠀⢠⢀⣠⠤⠤⠤⣀⣠⡄⠀⠀⠀⣀⠀⠠⢤⣄⡀⠀⠀⠀⢠⣤⠄⠀⠠⠄⠀⠀⠀⠀⠀⣠⢤⣤⡀
⠀⠀⡏⠉⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⢹⡷⣆⡀⡿⠀⠀⠀⣰⡟⠀⠀⠀⠀⠺⠛⠀⠀⠀⠸⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢘⡿⠀⠀⠘⠋
⠀⠘⣧⣄⣀⠈⣿⣧⠀⠀⠀⠀⠀⠀⢸⡇⣽⡿⣅⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⡷⠒⠒⢸⠇⠀⠀⠀⢈⣿⣀⡀
⠀⠀⠹⡾⠁⢐⡿⣿⣇⠀⠀⠀⠀⠀⢸⡟⠁⠀⣹⠆⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣾⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠙⠋
⠀⠀⠀⠀⠀⣼⠓⢹⣿⡄⠀⠀⠀⠀⠘⠃⠀⠐⠋⠀⠀⠀⠐⠉⠳⠦⠤⠔⠊⠀⠃⠀⠀⠸⠛⠃⠤⠒⠋⠁⠀⠀⠀⠀⠋⠀⠀⠴⠒⠀⠀⠀⠘⠻
⠀⠀⠀⠀⢰⡏⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⣾⣠⣄⣀⣈⣿⣇⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⢻⡇⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢝⠀⠀⠀⣻⠀⠀⠀⠌⠀⠀⠀⠸⣿
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⣿⠀⠀⠀⢠⡄⠀⠀⠀⣇⡀⣠⡄⣸⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⠀⠠⡀⠀⠀⠀⠀⠀⠋⠀⠀⡄
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠙⠣⢄⡀⠰⡇⠀⠀⢸⣇⠀⠃⠀⢹⡇⠀⠀⠀⠀⠃⠀⠀⠀⣀⠀⣠⠏⠀⠀⠀⣿⠀⠀⠸⣄⠀⠀⠀⠀⡇⠀⠀⢶⡀
⠀⢠⡿⣇⠀⠀⠀⠀⠀⠀⢸⣉⣿⣄⠀⠀⠰⠞⠃⠀⠁⠀⠀⠸⠿⠄⠀⠀⠘⠑⠀⠀⠀⠀⠾⠄⠀⠀⠹⠍⠀⠀⠀⠀⠐⠟⠂⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⢠⠤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⡤⣶⡆⠀⠀⠀⠀⠀⣠⠔⠀⠀⠒⢦⣄⠢⠀⠀⠀⢲⣲⡆⠘⠳⣦⠀⠀⠀⣠⡶⠋⠉⠉⠉⠲⣤⡀
⠀⢠⣼⠆⠀⠀⠀⠀⠀⢼⢳⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⢸⣿⣀⠀⠀⣽⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣇⠀⠀⠀⠀⠀⢸⣿⢻⣆⠀⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣽⠏⠙⠛⠁⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⢠⠀⠀⠀⣀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠸⣿⠀⠙⢧⣿⡇⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢸⢿⠀⠀⠀⣤⠄⠀⠈⠛⢆⠀⠀⠀⢀⣀⡾⠋
⠀⠀⠦⠾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠙⠁⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠈⠀⠀⠀⠀⠀⠘⠛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⡀
⠀⠀⢻⣽⠋⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⢚⣷⠶⠓⠂⠀⠀⠀⠀⠀⠉⢉⡿⠂⠀⠀⠀⢹⡏⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⡟⠁
⠀⠀⢸⣿⠀⠀⠀⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⢚⠄⡀⠀⠀⠀⠀⠀⠀⢀⣶⠏⠁⠀⣴⡀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣧⠀⠀⠀⡸
⠀⠀⢸⣿⠤⢴⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣣⡀⠀⠀⠀⠀⣾⣿⠀⠀⣟⡷⠧⢤⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠈⣿⣇⠀⡰⠁
⠀⠀⢸⣿⠀⠀⠙⢗⢀⠀⠀⣠⠄⠀⠀⠀⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢹⣿⡀⠀⠈⠊⠈⢀⡇⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠸⣿⡤⠁
⠀⠀⣼⡽⠇⠀⠀⠈⠛⠷⣤⣽⠆⠀⠀⠸⠳⢦⣤⠠⠞⠁⠀⠀⠀⠀⠀⠙⠻⠦⠤⢤⠤⠊⠀⠀⠀⠀⠈⠻⠷⢦⡴⠖⠀⠼⠿⠆⠀⠀⠀⠀⠀⠹⠇

⠀⠀⣠⢶⣤⡤⡤⣶⠶⣦⣠⣤⠄⠀⠰⣦⢀⡆⠀⠀⠲⣖⣲⡆⠀⠀⠀⠠⣶⠶⠒⠀⠀⠀⢐⡒⢶⣤⠀⠀⠀⠀⠐⣖⢰⠂⠀⠐⠦⠀⠐⠲⠶⠦⠤⢶⣖⡶⠁
⠀⠀⠉⠀⢠⡶⠀⠀⠀⠀⣴⠆⠀⠀⠀⣿⣸⡁⠀⠀⠀⠈⢿⣷⣄⠀⢀⣀⠁⠀⠀⠀⠀⠀⣾⠆⠘⣿⣧⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣾⡟
⠀⠀⠀⢀⣼⡇⠀⠀⠀⣰⡏⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠻⣿⢦⡸⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣻⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡟
⠀⠀⠀⣸⣿⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⢈⣿⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢢⡍
⠀⠀⠀⠸⣻⣇⠀⠀⠈⣟⣵⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢠⡞⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⡴⠞⢹⣿⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠛⢾⣶⣤⣀⣼⠻⣷⣤⣤⡤⣾⣿⡇⠀⠀⠒⡟⣂⣍⡤⠀⠀⠙⣿⠷⣄⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠀⠀⠠⣿⢃⣀⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠓⠁⠀⠀⠀⠛⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⠓⠛⠉⠉⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠁⡀⢀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠠⠤⠆⡜⠀⠀⠀⡯⠛⠛⡿⡀⠙⢯⣶⣻⡇
⠀⠀⠀⠄⠀⢐⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠎⣸⢁⠀⠀⠀⣧⣮⣻⢱⢹⡄⢻⣾⣾⡇
⠀⠀⠀⠀⠀⠀⠂⠒⠂⠐⠂⠀⠀⠀⠀⢠⠋⠀⢀⠂⠀⠒⢢⡍⠉⠀⠀⠀⡷⣸⠇⢿⣾⡷⠈⢿⣛⡇
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢐⡠⠀⠀⠀⠇⠀⠀⠀⢀⠎⠀⣾⠀⠀⠀⠀⠀⡇⡜⡼⣿⣧⣛⢧⠈⣏⡿
⠀⠀⠀⠒⠀⠀⠂⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠊⠀⠀⠀⠀⠿⠥⠿⠿⠿⠷⠾⠦⠼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⡀⠳⠄⣠⣭⣤⡀⠀⡁⠀⠀⠀⠸⢿⡛⢉⠉⣿⣭⣛⢻⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠂⠑⠶⠿⢛⠉⡙⢿⣆⠘⠀⠀⠀⢀⡎⠀⣾⣷⣿⣶⣿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣤⣿⡜⢣⠀⢻⠀⠀⠀⠀⣸⡅⠰⡟⡽⠀⠬⠟⣿⣻⠀⠀⠀⡐⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⣀⣘⣸⡃⠃⠀⡾⠀⠀⠀⠀⢻⡇⠀⢧⣑⠠⣰⡿⢱⠻⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠢⠉⠛⠷⠶⠊⠰⠀⠀⠀⠀⠸⠎⠈⠲⠯⠭⠥⠶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⢀⣀⠄⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠆⠀⠠⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⡀⠀⡜⠂⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⣠⠐⣰
⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡀⡦⠐⢴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠀⠀⢁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣶⠌⡆⡄⣩⣁⡄⠰⢖⣴⠄⣠⠶⢰⠀⠰⣠⢈⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣋⣴⣯⣐⣯⠙⠁⡘⠛⣣⡶⠐⣂⡘⢢⣐⠻⡿⢃⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠉⠀⠀⠙⠛⠋⠀⠙⠋⠙⠛⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⡿⣷⣶⣦⠀⠀⠀⢺⣿⣿⣿⡶⠀⠀⣀⣴⣶⣶⣶⣦⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣹⣿⡿⠀⠀⠀⢸⣿⣿⣿⡇⠀⣴⣿⣿⣿⠏⠀⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣶⡀⠀⣾⣿⣿⣿⠇⢰⣿⣿⣿⣿⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⡷⠀⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⠈⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣿⠿⠛⠁⢰⣿⣿⣿⣿⡀⠀⠈⠻⣿⣿⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣈⣁⣉⣉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠁⡀⠀⠀⡈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⣀⣠⠴⠁⡀⢀⠳⢤⣄⣀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠨⣭⠤⠶⠎⣇⡞⠳⠲⠶⡶⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢧⡀⠀⢀⠏⢇⠀⠀⣠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠉⠉⠀⠈⠙⠛⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⠖⠶⢦⡤⣄⠀⣏⡇⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⡇⣀⠀⡌⠛⠁⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⢯⣅⣀⣀⡤⠴⠚⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠂⠀⣀⠀⠀⠀⢠⣢⡘⠋⢈⠷⣣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸
⠀⠀⠀⠀⠀⢤⣈⠂⠀⠀⠎⠁⣏⠹⢗⣋⢁⠙⠧⢔⡄⠀⠀⠠⠺⠇⢀⠀⠀⠀⠀⠈⠁⣠⣞⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠙⠁⠛⢣⣄⣓⢬⠄⣬⡒⠇⠀⠠⠀⠀⡀⠀⢉⠖⠀⠀⠾⢿⡟⠉⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢶⢄⣤⣼⢀⠁⠾⠧⠕⡀⡄⠀⠀⡀⣠⢴⠛⢋⠠⢂⠀⠤⣀⡄⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠐⠂⢌⠉⠰⠆⠁⠀⠈⠉⢿⡁⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠈⠑⠂⠤⡀⠀⠀⠁⠈⠼⠀⠀⠀⠈⠙⠷⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠢⣄⠉⠒⠄⣐⠂⠀⣆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠄⡠⠀⠀⠤⠀⠀⠀⠠⢠⠐
⠀⠀⠀⠀⠉⠀⣠⣿⡟⠓⠚⢷⣾⡚⠛⠋⠙⠲⠀⠀⠀⠠⡀⣠⡆⠀⠈⢹⣦⡇⣀⠀⠂⠠⠠
⠀⠀⠠⠊⢀⠾⠛⣿⠷⠒⠂⠀⠀⠘⠯⠶⠲⢾⠆⠀⠐⣎⠂⠀⠀⠀⠀⠈⠨⠛⡧⢶⣠⣇⣰
⠀⠀⠀⠈⠁⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⢀
⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠖⠦⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢡⣶⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣦⠀⠉⠀⣐⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⢠⣶⣶⣤⠀⠀⣀⣤⣤⣤⠀⢰⣶⡦⣄⠀⠀⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⢘⣿⣿⣿⡇⢰⣿⡟⠁⠀⠀⢸⡟⠰⠿⣇⠀⣿⣯⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠛⢻⣿⡀⢸⣿⣿⣿⣿⠸⣿⣧⠀⠀⠀⢸⡿⣠⣶⡇⠀⣿⣿⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠈⠛⠃⠘⠿⠿⠛⠁⠀⠙⠻⠛⠓⠀⠸⠾⠿⠋⠀⠀⠿⠟⠿⠻⠂

⠀⠀⠀⠀⠀⠀⣾⣿⠿⠇⠀⣤⣾⡿⠛⠀⠀⣿⣿⣀⣸⣿⠀⠸⢿⣿⡿⠀⠀⠀⠀⢿⣿⡿⢰⣿⣢⣾⡶
⠀⠀⠀⠀⠀⠀⣿⣿⣶⡆⠀⣿⣟⢀⣀⠀⠀⣿⣿⠿⢿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡃⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⠻⣿⣎⣿⣆⠀⣿⣿⠀⢸⣿⠀⢠⣼⣿⣤⠀⣦⣤⣴⣿⡿⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠀⠈⠉⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠈⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⣧⡀⠀⣴⣿⡇⠀⠀⣿⣟⣦⠀⣾⣿⢀⣾⣿⣿⣿⣷⡀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣸⡿⠻⣧⣾⡟⢻⣷⠀⠀⣿⣿⣟⣧⣽⣿⢸⣿⣿⣏⣹⣿⡇⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⠀⠀⣿⡇⠀⠘⠟⠀⠸⣿⡄⠀⣿⣿⠈⢻⣟⣿⠈⢿⣿⣿⣿⡿⠁⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠉⠉⠀⠀⠉⠉⠉⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣾⣻⣿⣽⣦⠀⠀⣻⣿⣿⣦⠀⣠⣾⠿⠛⠃⠸⠯⢿⣯⣿⠧⠇⢸⡇⠀⠀⠀⣬⡄⢻⣧⠀⢰⣿⠁
⠀⠀⠀⠀⢸⣟⣿⣯⣿⣿⡇⠀⢺⣿⡟⠃⠀⢻⣧⣀⠀⠀⠀⠀⢸⣟⡇⠀⠀⢸⣳⣄⠀⣰⣿⠆⠘⣿⡀⣼⡿
⠀⠀⠀⠀⠘⣿⢿⣿⣿⣽⣇⠀⣽⣿⢿⣦⡀⠀⢈⡙⣻⣷⣦⠀⢘⡿⡇⠀⠀⠈⢿⣽⣿⣿⠟⠀⠀⢻⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠋⠀⠈⠉⠀⠉⠉⠀⠈⠉⠉⠉⠁⠀⠈⠙⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⣀⠀⠀⣰⡗⠠⣾⣦⣀⣴⣿⡦⠀⢶⣷⣄⣠⣾⡦⠀⣶⣆⣶⣶⣖⣳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣰⣯⣤⠀⣿⠇⠀⠘⣿⣿⣿⡏⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⠀⢀⡼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡻⠃⢹⡷⣿⠀⢀⣴⣿⠿⣿⣷⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⢿⣟⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠙⠋⠀⠀⠙⠃⠀⠈⠛⠁⠀⠀⠀⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠓⠛⠃
⠀⠁

⠀⠀⠀⢧⠀⠀⣸⠘⡇⠀⢼⠀⠀⠀⢸⠀⡆⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⢠⠀⠀⢸⠀⡇⠀⢸⡇⠀⠈⡇⠀⢸⢶⡀⠀⢸⡇⠀⠀⠘⡆⣿⠀⠀⠳⣄
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢴⠀⢰⠀⠀⡇⠰⠀⢠⡇⠀⡆⠀⢸⢀⡆⠀⠘⢄⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⢳⣹⡀⠀⠀⠹⡄⠀⠀⢹⡄⠀⠀⣰⠃
⠀⠀⠀⠀⠈⠀⠉⠀⠀⠁⠀⠀⠀⠁⠘⠃⠀⠈⠀⠁⠀⠀⠈⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠐⡆⠀⠀⢸⡀⡇⠀⢠⡆⠀⠀⣶⠀⣆⠀⠀⡇⠀⠀⠈⡇⠀⠀⢰⠁⠀⠀⠀⢸⠀⡇⠀⢰⡇⠀⠀⠀⡇⠀⠀⡇⡄⠀⠀⢸⠀⠀⢹⡀⢺⠀⠀⠱⣄
⠀⠀⠙⠀⠀⠘⠀⠟⠀⠀⠃⠀⠀⠉⠀⠏⠀⠀⠧⣄⠀⠀⠃⠀⠀⠘⠂⠘⠀⠀⠘⠀⠃⠀⠘⠃⠀⠀⠀⠇⠀⠀⠃⠹⠄⠀⠺⢄⡀⠀⠃⠘⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⢠⡆⠀⢰⠀⠀⢲⢰⡆⠀⣰⠀⠀⡆⠀⠀⡆⣲⠀⠀⢦⡀⠀⠀⢈⢹⠉⠀⢸⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⢧⢣⠀⠀⠀⠘⣆⠀⠀⠈⢦⠀⠀⠀⢠⠇
⠀⠈⠇⠀⠜⠀⠀⠼⠈⠀⠀⠙⠀⢤⠃⠀⠀⠏⠣⡀⠀⠀⠙⠀⠀⠀⠸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠊⠃⠀⠀⠀⠘⠆⠀⠀⠸⠀⠀⠠⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠘⠀⠈⠀⠙⠀⠀⠀⠐⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢰⡀⢰⡄⠀⠀⡆⠀⠠⣆⠀⠀⢰⠀⠀⠐⢒⠀⢠⠀⡀⠀⠒⠂⠀⢤⡀⠀⢴⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠁⠸⠇⠀⠬⠄⠀⠀⠜⠀⠀⠸⠀⠀⠀⠘⠀⠘⠀⠃⠀⠞⠀⠀⠀⠙⠀⠈⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⡀⠄⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠊⣡⣴⣾⣿⢿⡇⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠠⠃⣠⣾⣿⠿⠛⢉⠏⠀⣼⣿⢀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⠀⣸⣆⠈⢱⡄
⠀⠀⠀⠀⠀⢇⠀⣿⣟⣏⣦⡠⠁⢀⡼⢋⠀⠀⣷⡄⢀⠀⠀⢀⢀⣾⣷⠀⠀⣴⣿⠃⢀⣼⣿
⠀⠀⠀⠀⠀⠈⠳⣶⣶⣿⠏⠀⡠⢋⡴⠃⢠⡾⠋⠀⢠⣷⠈⢲⡝⣿⠃⠀⣼⡿⠃⢀⣾⡿⠁⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢱⠃⠀⢀⣴⠟⠀⡴⢋⡖⠀⣰⣿⠃⢀⣾⡿⠁⢀⣾⡿⠁⠠⠟⣋⣠⣴⡿⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣠⣿⠏⠀⢊⣴⡿⠀⣼⣿⠃⢠⡿⢫⠀⢀⡾⡋⠀⣰⣆⠹⣿⡿⢫⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣿⠟⠢⣴⣿⡟⢇⠀⣿⡏⠣⣬⣾⣿⠧⣤⣶⣿⣤⣿⡏⠢⣭⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠋⠀⠀⠢⡘⢇⡀⢈⠏⣹⡄⠈⠛⠋⠀⠙⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠄⠐⢶⣶⠂⠀⢲⣦⡀⠀⠀⢀⣴⠖⠈⠉⠐⠀⠀⠀⡠⠂⠐⣿⡟⠉⠉⠑⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣷⡀⠀⠀⠁⠀⠀⢸⣿⠀⠀⢠⣿⠇⠀⢰⣿⠁⠀⠀⠀⠺⠗⠀⠐⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⣧⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⢷⣄⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⣿⣇⠀⠀⠄⠀⣼⣿⠀⠀⠀⣸⣿⠀⠈⢿⣦⡀⠀⠀⠀⢀⠔⠀⠑⠠⠀⣿⡗⠀⠀⠀⣰⡿⠃
⠀⢴⡦⠀⠀⢠⠞⠀⠀⠀⠀⠐⠛⠛⠓⠀⠀⠐⠛⠛⠓⠒⠚⠛⠁⠀⠀⠀⠉⠙⠓⠒⠊⠁⠀⠀⠀⠀⠚⠛⠛⠓⠒⠛⠉
⠀⠢⠀⠠⠐⠁⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠠⢤⡄⠀⠀⢀⡤⠖⠒⠒⠠⠀⠀⠀⠀⠠⣤⣤⡄⠀⠀⠠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡸⠟⠀⠀⠀⠁⠀⣿⡇⠀⢀⠀⠙⠀⣴⡟⠀⠀⠀⠀⢴⡶⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠺⡇⠀⠀⠀⢠⠀⠀⣿⡇⠀⢿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢤⣤⣤⠀⠀⠀⢸⣿⠀⠒⠀⠂⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡤⠀⠀⠑⠠⣿⡇⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠴⠿⠷⠤⠤⠴⠿⠃⠀⠀⠀⠴⠿⠷⠄⠀⠀⠀⠀⠀⠙⠻⠶⠤⠤⠚⠛⠃⠀⠀⠀⢸⡏⠀⠀⠀⠠⠿⠿⠄
⠀⠀⠀⠀⠀⠀⢤⣤⣤⠄⠀⠀⠀⠀⠀⢤⣤⣤⠄⠀⠀⠀⠠⣤⣤⡤⠀⠀⠀⢀⠤⢄⠀⢀⣄⠀⠀⠀⣾⠃⢤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠄⠀⠘⠛⠁⠈⠉⠀⣀⠼⠃⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡀⢾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣤⣤⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠈⠁⢠⡿⠃⢀⠄⣀⣄⠀⣸⡟⠀⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠋⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⠛⠋⣠⠟⠁⠀⢄⡀
⠀⠀⠀⠀⠐⢶⣶⡀⠀⠀⠀⢰⣶⡖⠀⠀⠐⢶⣦⡈⠁⠉⠁⠀⠀⠁⠘⠃⠀⢀⣤⠖⠀⠐⠶⣄⠀⠀⠀⠀⡀⢤⣶⠖⠐⠲⣦
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⢀⠈⣿⡇⠀⠀⠀⢈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢹⣷⠀⠀⡔⠀⢸⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠌⠀⢿⣧⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢨⣿⠇⠀⠄⠀⢸⣿⠀⠀⠛⠉
⣠⣄⠀⠀⠀⠂⠀⠀⢻⡟⠀⠀⢸⣿⠀⠀⠀⣠⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠻⣧⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢼⣿⠄
⠏⡉⢀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠘⠛⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋⠁⠀⠀⠀⠀⠐⠛⠛⠓
⠀⠀⠀⠀⠀⣠⡶⠋⠉⠉⠳⣦⡀⠀⠀⠀⠀⣴⣶⠋⠉⠳⣶⡄⠀⠀⠀⠀⢠⡎⠁⠉⠹⡆⠀⠀⠀⡴⠒⠐⢶⣶⠂⠐⢶⡆
⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⢸⣿⠀⠀⢀⣿⠟⠀⠀⠀⠀⠸⣷⣤⣀⡀⠀⠀⠀⠐⢀⡀⠀⢸⣿⠀⠀⠀⠁
⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⡀⢸⡟⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⢬⡍⠛⢿⣷⡀⠀⠀⠙⠃⠀⢸⣿
⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢻⣿⠀⠀⠀⢻⣷⡄⠀⠀⠀⢀⠈⠁⠀⠀⣿⠃⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠉⡳⢶⣖⡉⠀⠀⠀⡀⠀⠐⠛⠛⠂⠀⠀⠀⠉⠛⠦⠀⠀⠀⠐⠀⠐⠚⠁⠀⠀⠀⠀⠀⠐⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠞⠁
⠀⠀⠐⠀⢲⣶⠆⠀⠀⠀⠳⠖⠀⠀⢳⣿⡎⠀⠀⠀⢢⠀⠲⣶⡆⠀⠀⠀⣰⡄⠀⠀⠀⠠⠊⠉⣁⠂⠀⠀⠰⣶⣶⠂⠀⢲⠶
⢠⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡺⠗⠀⠌⠀⠀⢹⣿⡀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠈⢿⣧⡀⠁
⠀⢦⡀⠀⢸⣿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠐⠀⠀⠀⠀⢻⣷⠀⠂⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⡄
⠀⠀⠀⠁⠘⢿⣆⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⢿⡷⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠾⢂⠔⠁⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠉⠛⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠰⠶⠀⠀⠀⠀⠀⣠⡤⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⠤⣴⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠖⠛⠛⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣶⣿⡆⢰⣇⣠⣄⡀⠀⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⠇⠀⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠋⢠⣾⡇⠀⠀⠀⢀⣀⡀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠐⢿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠁⠀⡄⣿⢿⣄⡛⢻⡟⢉⡉⠙⢦⠈⠹⢿⡿⠟⣻⡿⠿⠷⣦⡙⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⣧⡟⢨⡻⣧⡘⠧⠼⠏⢠⣸⠀⣰⢏⣀⢈⡋⣲⣄⣄⠈⠻⣦⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢠⢹⡄⠀⠙⠲⢤⣤⣤⣴⣿⣯⠀⡿⢤⣽⣯⣽⣿⡿⣦⡀⠀⢹⡆⠀⠹⣿⣿⡆⠀⠀⢀⡴⠋
⠀⠀⠀⠈⢩⡟⣩⡛⣦⢠⣿⣿⣿⣿⣿⣿⠀⠀⠈⣆⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠟⢿⣅⣼⣻⣟⠙⠃⣸⠃⠀⠀⠈⠻⣿⣠⠖⣋⣀⣀
⠀⠀⠀⠀⠈⠳⠞⠁⢸⠐⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⡌⠻⢿⣷⠶⠾⣇⣀⠀⠀⠀⠀⠙⠒⡋⠙⠉⢛⡈⠁⡰⠃⠀⢀⣠⡤⠖⠋⠰⠿⠿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⠀⠈⠪⣽⣻⡿⣿⣿⣶⡤⠀⣀⣾⣏⣴⠿⣋⣴⣋⣤⣶⣊⣉⡀⠀⠀⠈⠛⠿⠿⠟⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠭⠽⠷⠦⠈⠉⠙⠳⠄⠠⣄⡀
⠀⠀⢀⣀⠀⠀⢀⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠉⠉⠛⠓⠲⢦⡈⠉⠀⠀⠀⠉⠉⠉⠀⠉⠉⠲⣢⣏
⠀⠀⣁⣤⡈⠢⢸⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠙⢢⠀⣴⠆⢡⠀⠀⣦⡴⣦⣠⣌⠀⢳⡀
⠀⠀⠈⠉⠀⠀⠸⢀⡴⠚⣩⣉⡒⢤⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣈⠉⠁⠀⠀⢨⠘⣯⣿⡷⢀⡜⠹
⠀⠀⠀⠀⠀⠀⢶⡞⠀⣻⣿⣭⣿⢈⡇⠀⠀⠉⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠑⠰⠨⠖⠋⠀⠐⠀⠀⢰⡶⠄
⠀⠀⠀⠀⠀⠀⠀⢧⡀⣈⠋⠙⠧⠻⡧⠀⠀⠋⢰⣿⠀⢦⡉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⡆⠑⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠯⢤⣀⡀⠀⠀⠀⠀⠈⠂⠀⠀⠄⠙⣦⣀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠠⣄⠀⠉⠉⢩⣉⣉⣉⣉⣀⣒⣢⣭⣝⣳⣶⣤⣄⣀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⡇
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠙⠳⠶⠶⣶⣷⠶⣶⡾⢟⣛⣿⣿⣿⣿⠿⠶⠿⣝⣲⣤⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣸⠁
⠈⠻⣶⣿⣿⣿⣟⣛⠛⠆⠀⢀⣀⡤⠤⠒⠂⢀⡴⠋⣡⠶⠿⠋⣴⡿⠉⠀⠘⠛⢿⣿⣿⣾⣭⣓⢦⡀⠀⠀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⢿⠀⣠⠶⣄
⠀⠀⠈⠛⠻⠿⠿⢟⣫⠴⠚⠉⠁⠀⠀⠀⣴⠋⠀⣤⣰⣆⣰⣆⣤⠤⣄⠀⠀⠀⠀⠈⠛⣫⣤⣭⣝⣮⣂⠀⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠘⢧⣝⣣⣿⣤
⠀⠀⠀⠀⠀⣠⠖⠋⢹⣦⡀⠀⠀⠀⠀⢸⡇⠐⣤⣼⣿⣽⠋⢹⣧⡴⠘⣧⠀⠀⠀⠀⠀⠉⠁⠀⠈⠛⢿⣧⢹⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⠞⠁⠀⠀⠈⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⠛⣿⣿⣿⣛⣾⠛⠣⣿⠘⠷⣶⣶⡶⢶⣤⣄⠀⠀⠀⢻⡆⡇⠀⠀⣿⣿⣿⣿⣿⣿⡏
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠈⢿⣄⠈⠛⠛⢿⢉⡏⠙⠓⣰⠏⢠⡞⡟⢀⣠⣀⠀⢬⣙⢦⠀⢀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⠀⢸⣥⣴⣦⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⣄⠙⢷⣶⣦⣶⣟⣃⣤⣾⣥⠀⢸⡇⠀⠺⠗⠈⡧⠀⣽⣷⢣⡏⣽⠀⠀⣸⣿⣿⣿⣿⣿⠃
⠀⢹⣿⣿⣿⡇⠀⠀⣀⣀⡀⢿⣿⣿⣿⣿⣿⣷⣦⣈⠉⠙⠛⠋⠉⠙⠛⠶⣄⠙⠶⢤⣤⣾⠷⠶⠄⢹⣿⡇⠋⢀⣼⣿⣿⣿⣿⡿⠁
⠀⠈⢿⣿⣿⡇⠀⠘⢿⣿⢿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣶⣿⣿⣿⣿⡿⠋
⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⣸⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠉⠛⠓⠒⠋⠁⠀⠀⠹⠿⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⣿⣿⡿⠿⠿⠿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣁⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⢬⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⡋⠀⠈⠑⠓⠄⠀⠀⠀⠀⠰
⠈⠋⠉⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡔⠀⡄⠀⠀⠀⠣⠄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠳⠀⠀⠐⡄⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠐⣆⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡁⠠⠤⠄⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⡀⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣵⣤⢄⠐⠂
⠀⠀⠁⠀⠀⢐⣀⣠⡀⠐⠲⠶⣶⡶⠀⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠋⠁⢠⠆⠀⠀⠀⢘⠀⠀⠀⢠⣤⣴
⠀⠐⠁⠀⠀⠀⠉⠁⣀⠀⠀⡄⠁⢐⡆⠀⠀⠀⠀⠀⠐⠈⠆⠶⣄⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠉⠑⠦⠀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⠀⣴⢀⠀⢰⠁
⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠧⠠⠀⠃⠀⠀⠠⢄⡂⠐⢦⠘⠱⡀⢧⠇⢀⡠⠤
⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡓⠦⢙⣦⣁⣆⢀⡡⠀⡨
⠀⠀⠈⢀⠀⠠⡄⠁⠈⠀⠀⠀⠀⠀⡘⠖⠉⣠⡼⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠛⠙⠻⢿⣿⣿⡶⠒⠛⠁
⠀⠀⠀⠈⠷⠢⣤⠀⡀⠀⠀⠀⢀⠐⢁⣦⠟⡉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⢰⣥⠴⡺⠋⢁⠞⡿⢹⢟⢣⣀⠀⠁⠁⠀⠐
⠀⠀⠀⠀⠤⠒⠄⠁⠀⠀⠀⠀⠀⣴⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠤⠂⠁⠐⠀⣰⠈⣥⠜⢆⠉⠁
⢄⠀⡄⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠀⠀⢠⡄
⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢐⡀⠀⠀⠀⠴⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠃⠀⠈⠸⠀⣴⡃⡀⠄⡠⠀⠀⠀⠀⠐⣡⠾⠀⠀⠀⠀⠐⠀⠂⡨⠿⢧⡀
⠠⠄⠀⠀⡀⠀⡐⠀⠀⠃⠀⠈⠁⠀⠊⠀⠀⠀⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢸⠀⠀⠁⠈⠁⠀⠀⡠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⢀
⠅⠊⡀⠌⠀⠀⠠⠄⢀⠠⣈⣉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠁⣀⣒⠒⠂⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣈⠄⡤⠈⠓⠒⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⠊⠉⠄⠘⠉⠉⠐⡄⠀⠀⠀⠤⢀⡐⠠⠀⠠⣄⠉⣠
⠀⠀⠒⠀⠂⠉⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠰⢄⡙⣳⣄⡀⠁⠘⠛⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠱⣤⠉⠛⠶⣶⣸⠀⠋⠃⡀
⣉⣯⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠐⢒⡀⠙⢛⢃⣀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⣄⠀⠀⠀⡠⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⠀⣀⠈⢧⠀⠐⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣞⠀⠀⠀⠀⠀⠱⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠍⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡍⠠⠇⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⠀⠀⠐⠉⠀⠀⢀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⢘⠂⡢⠀⠀⠀⣇⣸⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠈⠱⠀⠀⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠀⠀⢠⣀⠀⠁⠀⡀⠀⠀⠀⢀⣀⠀⠀⠄⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠚⠋⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠠⠀⢠⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠈⠀⠀⠎⢀⡀⢀⠀⠆⠀⣀⣀⠇⠀⠀⠄⠂⠀⠒⠐⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⢀⠔⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠶⠒⠒⠚⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠀⠀⠀⠀⢠⣠⠄⠀⠀⠀⠀⠀⢀⡴⠞⣡⡀⠀⠀⠀⠀⢀⠀⠉⠉⢞⠆⡀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢘⠛⠀⠀⠀⠀⠀⢀⣏⠉⠀⠈⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⣪⣖⠀⠀⢀⣔⠞⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢘⡆⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⡇⠀⠀⠟⢊
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠹⠇⠀⠀⠔⠃⠀⠛⠀⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠯⠋⠀⠀⠀⠘⠾⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⢠⠦⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢐⡁⠀⠀⠀⠀⢀⢛⠂⠀⠀⠀⣴⠀⠀⣾⠃⠀⠀⠘⠀⠶⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠉⣟⡂⠀⠀⢸⣷⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⢈⣙⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠠⠆⢠⣍⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢙⡁⠀⠀⠰⠀⠀⢮⡌⠀⠀⠀⠀⠤⠀⣾⡇⠀⠀⢀⠀⠘⠃
⠀⠀⠀⠀⠀⠴⠛⠀⠀⠀⠀⠈⠛⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠉⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠰⠆⠰⢷⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⠂⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠏
⠀⠀⠀⠀⠀⠀⠀⣘⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠢⠆
⠀⠀⠀⠀⠀⠀⠠⣭⠃⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⡶⠀⠀⠀⠐⠰⠆⠘⣿⡇⠀⠀⠀⠀⠐⢿⠇⠀⠀⠀⠀⠀⠀⠀⡤⠰⡍
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⡁⠀⠀⠀⠀⠀⠀⢸⣷⡘⠂⠀⠀⠀⠀⠀⠘⠆⣼⠏⠀⠀⠀⠀⠃⠀⠀⡔
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡁⠀⠀⠀⠀⠀⠀⡀⠙⢿⣦⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠙⣉⣀⠀⢀⠀⠀⠀⠀⠠⠆⠠⡭⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⡿⠀⠀⠀⠀⠓⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⡀⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠲⣦⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡤⡶⠂⠀⠀⠀⡀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠘⢃⠏⠀⠀⠀⠀⠀⠀⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠲⢛⠀⠀⠀⠀⠀⠀⠀⠀⠰⢎⠆⠀⠀⠀⠀⠋⠀⢀⢾
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣩⠀⠀⠀⠀⠀⠀⢀⡀⢰⣷⠃⠀⠀⠀⠀⠀⡰⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠑⠤⠂⠀⠀⠀⠈⢱⠆⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⢾⡄⠀⠀⠀⠀⠀⠉⣠⠾⠋⠀⠀⠀⠀⣠⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠑⠦⡤⠋⠈⢱⣆⡤⠒⠚⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢵⠀⢠⣀⢀⣶⣌⣁⡴⢀⣾⠟⠉⢀⣀⢄⣀
⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⣦⣸⠀⠀⣸⡆⠘⠿⣛⣟⡈⠹⣡⣿⠋⣠⠞⠁⠀⣀⡄⠙⣦
⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⣿⠇⠀⢠⣿⡿⠶⣿⠁⡀⠉⣶⠽⢯⡰⠁⠀⢀⣾⣿⠇⠀⣼⣇
⠀⠀⠀⡜⠀⠀⣴⠀⠀⡼⠋⢀⣴⠿⠇⠀⢰⣿⣾⠃⠀⣠⠀⣸⠁⠀⢠⣿⣏⠘⢦⣤⣾⠟⠁⡰⠋⣷⡄
⠀⠀⢸⠁⠀⣼⡏⠀⠀⠁⢀⣠⠄⠀⢀⡀⠘⢛⡅⠀⣰⣿⡀⠋⠀⠀⡀⠀⣬⡍⠙⣧⣁⡤⠊⠀⣼⡿
⠀⠀⠈⡇⣸⡿⡇⠀⠀⣾⣿⠏⠀⠀⢞⡻⠿⠛⠛⠒⠛⠓⠛⠂⠀⠀⣿⣦⣌⠀⢀⣉⣀⣀⣴⣾⠟
⠀⠀⠀⠘⠿⠃⢣⠀⠀⠸⣿⣀⣀⣴⠏⠀⠀⣀⣠⣤⣴⣶⣶⣶⡀⠀⣿⠿⠁⠀⣼⡟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢹⡍⠛⢧⣶⣾⣟⣋⣵⣾⠿⠛⠉⠀⠑⢤⣀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢣⠀⠀⢀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠸⠀⢈⠀⡔⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠈⢢⠀⠀⣀⡄⠻⡲⣕⣾⡰⠧⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢸⢠⠋⠀⠀⠀⠈⡩⠯⡖⠉⠁⠉⠑⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠐⠒⢤⠙⣤⣀⠴⢁⡤⠊⣀⠠⠬⢕⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠠⠷⣜⠀⡰⠻⠛⠭⡑⠄⠀⢀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠐⠳⠀⣸⠊⠀⠸⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⣆⠀⢀⡐⢤⣴⠗⠉⢉⠇⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⠢⣗⡔⠁⡄⡸⠋⢰⣌⢡⠊⠉⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⢄⣀⣱⠾⣧⡀⠃⠃⢠⣜⢼⡶⠤⡴⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣍⣿⡟⠰⠀⡇⠘⣄⡥⢎⠀⢀⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠉⡟⠲⡄⠡⣀⡿⢀⠄⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⢒⡩⠤⣀⢱⠀⣹⡗⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣀⡀⠴⣋⠻⡀⠈⠉⡩⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠆⠙⢄⠀⡁⢘⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠉⠑⠪⣢⡄⣴⣭⣛⣺⣾⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣒⣂⣉⠤⣏⠁⠀⡠⠤⠤⢬⠖⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠁⠰⠁⠱⠀⣇⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠊⠀⠀⠈⢢⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡇⢰⡤
⠀⠀⢀⣤⣀⡀⠀⠈⣿⣿⡀⢀⠀⠀⠀⣠⡄⢀⣀⠀⠀⢀⣿⠁⡀⠀⠀⢀⣴⠀⣀⠀⠀⢹⣿⣇⠀⡀⠀⣠⡄⢀
⠀⠀⠿⣿⡏⢀⠀⠀⢿⣿⡇⢸⡄⠀⢸⣿⡇⠘⠋⠀⠀⣿⣿⡀⢹⠀⠀⣿⣿⡄⢀⠀⠀⠸⣿⣿⠀⠀⢸⣿⣇⠈⡇
⠀⠀⢼⣿⣧⣄⡀⠀⢸⣿⣷⣄⡀⠀⢸⣿⣿⣄⡀⠀⠀⢿⣿⣧⣄⠀⠀⢻⣿⣷⣄⡀⠀⠀⣿⣿⣇⡀⢸⣿⣿⣄⠁
⠀⠀⠈⠛⠟⠋⠀⠀⠀⠛⠛⠋⠀⠀⠀⠙⠿⠋⠁⠀⠀⠈⠛⠛⠉⠀⠀⠈⠛⠟⠋⠀⠀⠀⠙⠛⠁⠀⠀⢻⣿⣏⠙
⠀⠀⢠⣾⡇⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣄⠀⠀⢠⣾⡇⠀⠀⠀⢠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟
⠀⠀⢸⣿⣿⠀⢀⠀⠀⢿⣿⡇⠀⠸⣿⣿⠁⠀⢸⣿⣷⠀⣆⠀⠈⣿⣿⡀⠀⠀⢀⣤⠀⡀⠀⠀⠀⠀⢀⣤⠀⡀
⠀⠀⠀⣿⣿⡄⢸⠀⠀⢹⣿⣇⠀⠀⣿⣿⡄⠀⠈⣿⣿⡄⢀⠀⠀⢿⣿⡇⠀⠀⣿⣿⠀⣧⠈⡇⠀⠠⣿⣿⠀⣧
⠀⠀⠀⢻⣿⣇⣘⣇⡀⠸⣿⣿⣀⠀⢻⣿⡇⠀⠀⢿⣿⣇⣸⣆⡀⢸⣿⣷⣀⠀⣿⣿⣆⣸⣀⣳⣀⠀⣿⣿⣆⣸⣀
⠀⠀⠀⠘⠿⠻⠿⠋⠀⠀⠿⠟⠁⢀⣸⡏⠛⠀⠀⠘⠿⠻⠟⠋⠀⠈⠿⠟⠁⠀⠹⠿⠿⠿⠿⠟⠁⠀⠹⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣧
⠀⠀⢀⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡀⠀⡀⠀⢈⣿⣿⠀⢠⠀⠀⣀⣴⠀⣦
⠀⢰⣿⣇⠈⡇⠀⢰⣿⣧⠀⡇⠀⠀⣾⣿⡀⢹⠀⠀⢰⣿⣷⠀⠟⠁⢠⣿⣿⣄⡉⠁⠀⢿⣿⡇⠀⠀⠀⣿⣿⡄⢸
⠀⠸⣿⣿⣄⠁⠀⠘⣿⣿⠀⠉⠀⠀⢿⣿⣧⡈⠀⠀⠈⣿⣿⣀⡀⠀⠀⣻⣿⣇⡉⠀⠀⢸⣿⣷⣄⡀⠀⢹⣿⣧⡈
⠀⠀⠻⠿⠟⠉⠀⠀⣿⣿⡇⠈⠀⠀⠘⠿⣿⣿⡇⠀⠀⠿⠿⠋⠀⠀⠀⠙⠿⠿⠋⠀⠀⠈⠻⠿⠟⠁⠀⠈⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠂⠀⠀⠀⠀⢸⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⣀⡄⢠⡄⠀⠀⠀⣠⠀⣤⠀⡄⠀⠀⠀⣠⡄⢠⠀⠀⠀⢀⡄⢠⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⡇⠀⠀⣿⣿⡆⢸⠀⢳⠀⠀⢺⣿⣧⠈⠁⠀⢸⣿⣧⠀⡇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⢹⣿⣷⡀⠀⠈⠀⠀⠘⣿⣿⠀⣧⠀⠘⣿⣿⡀⠛⠀⠀⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠀⠀⠈⠻⣿⢿⣿⠟⠁⠀⠀⣿⡿⣿⡿⠋⠀⠻⣿⡿⠷⠄⠀⠘⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣤⡀
⠀⠀⢠⡆⠀⢠⡶⠀⠀⠀⣦⡄⠀⢀⣀⠀⠀⠸⡄⡏⡄⠀⠀⠀⠿⣿⣤⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠘⢷⡀⣼⠟
⠀⢀⠘⡇⡴⢋⡀⠀⣀⡀⠹⠿⣾⡿⠟⠀⢀⠳⣜⢊⡴⢀⠀⢀⣠⡛⠁⠀⠀⠀⣴⣿⣷⣦⡄⠀⠀⠀⠀⠈⠳⢁⣴
⠀⠘⣧⡈⢠⠾⠁⡄⠻⣷⣄⠀⣠⣴⡦⠀⣬⢷⡈⡡⠴⢋⡄⠘⠿⣿⣿⠀⢠⣷⣹⣯⣿⣾⣽⣷⡄⠀⠀⣈⢣⡿⠋
⠀⠀⢨⠛⠆⣠⡾⠃⠀⣨⡍⡀⠛⢋⠀⢀⡙⢇⢹⣠⠶⢟⠀⠀⢀⠀⡀⠀⣼⡛⣿⣿⣿⣿⣿⣻⣥⠀⠈⣿⢿⠁
⠀⠀⠸⣦⡀⠋⠀⠀⠀⠘⠿⣧⣾⡿⠃⠀⡳⡌⣯⣶⠞⠁⠀⢾⡿⣿⣿⠀⣻⠿⣯⣿⣿⣿⣿⢿⣿⢃⣀⠈⢿⢋⣤⡄
⠀⠀⠀⠈⠳⣠⡄⠀⠀⢿⣦⣏⣴⣶⠀⠀⠳⣘⣡⠆⠀⠀⠀⢀⣀⠀⣀⠀⢿⣋⣿⡟⢻⣏⣹⣿⣦⠈⠿⡀⡸⠚⡋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠟⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢿⠿⠿⠂⠀⠉⠉⠀⠀⠻⠿⠿⠃⠀⠀⠰⢡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⣶⣄⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣆⢀⣤⣤⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⢸⣧⠀⠀⡀
⠀⠀⠀⢻⣿⠆⠃⣀⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⣈⠛⠋⠀⠀⠀⠺⣦⡀⢹⡿⠃⠀⠀⠙⠀⣾⠇
⠀⠀⠀⠀⠉⣥⣾⣿⠇⠀⠀⠀⠘⢿⡇⣠⣴⣶⠀⣤⡄⠸⡟⢷⡶⠀⢀⣤⣤⡬⢥⡄⣀⣀⣄⠻⣶⡤⡄⠀⣰⣿⠂
⠀⠀⣀⣤⣀⠘⠋⠀⣀⣀⠀⢀⣄⠀⡀⣿⡿⠃⠀⢙⣥⡄⠀⢰⣶⡆⠈⠛⣡⡀⠀⠱⠀⢉⡋⠀⠀⠀⠬⣀⠛⢁
⠀⠀⠻⣿⡿⠿⡇⣾⣿⡿⠂⠸⣿⣷⠸⡇⢀⣴⡆⠈⠻⠓⢤⠘⠛⡁⠀⠘⢿⣧⠀⢆⣾⡿⠃⠀⢀⣤⣀⢸⠐⠁
⠀⠀⠀⠀⠀⣀⣸⠈⠉⠀⠀⠀⠉⠻⡄⣶⣿⣿⠟⠀⠀⠐⣄⢀⠞⠀⠀⠀⠀⠉⢠⠋⠁⠀⠀⠀⠀⠙⢻⠘
⠀⠀⠀⠰⣾⣿⡿⣠⣴⣆⢸⣿⣷⡄⢸⠛⠋⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡄⡞
⠀⠀⠀⠀⠈⠁⠀⠟⠛⠁⠀⠙⠛⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠏⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡾⠶⠦⠴⢦⣦⢀⣄⠀⠀⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣸⠅⢴⣶⡶⠈⡷⠈⣻⡇⠈⠀⠈⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠘⢋⠐⢿⢠⣾⣿⣿⡿⠠⣦⣄⣀⠈⠁⠉⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣼⡇⠺⠻⣷⠀⠈⠛⣷⡀⢰⠀⠘⣿⣿⡟⠀⠁⠀⠉⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠠⠀⠀⠀⠀⠸⣷⡿⣃⠀⣠⣷⣄⠛⠁⠀⠀⠀⡿⠻⢿⡿⠃⠀⣠⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣄⠀⠀⣀⣠⠼⠋⠛⠟⠙⠷⣤⣵⣤⠄⠀⠀⠀⡀⣀⣤⡀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠛⠁⢰⣿⣷⣀⣸⡀⢰⣿⠉⢀⡀⠀⠉⢘⣿⡿⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠀⠀⢰⡀⠸⣏⣉⠉⠉⡇⠀⢶⣦⡈⢠⣶⡀⢙⣿⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣒⡶⠀⠀⢀⠇⠀⠀⠈⣷⡀⠈⠁⢀⡤⠇⠀⠠⢻⡇⠀⠙⡧⡈⠉⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠛⢳⡄⢀⢰⠂⠒⠀⢠⣿⠟⠓⠒⢿⠀⠀⠀⣶⡿⠀⠀⠀⢡⡤⠞⣳⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⢀⠀⠈⠀⣀⣠⣾⡏⠀⢀⣤⠆⢀⣴⣴⠁⠀⠀⠀⣶⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢡⣾⡀⠀⣴⣿⣿⢻⠗⢰⣿⡁⠀⢾⢠⡇⠀⠀⠀⠐⠰⣤⣀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣿⠃⠀⠈⣿⣅⠁⠠⠚⠋⠻⠀⠈⣀⠳⢀⡄⢀⢀⣤⣿⡟⠀⣀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢲⡄⠙⠛⠴⢰⠀⠀⠘⢿⣿⣶⡄⠀⠀⠰⠟⠀⠶⣾⣿⡿⢋⣉⠀⢀⣽⡿⠿⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠼⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⣠⣶⣦⠘⣿⡄⠹⠿⢃⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡼⠀⠈⠢⠸⠗⢄⠀⠀⠘⣿⣥⠔⠀⠠⡞⢁⠙⠃⠀⠀⠀⣀⠙⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠠⠬⠅⢀⠤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠳⠾⠀⠈⠀⣠⣾⣿⡁⠀⣭⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣹⢤⡠⡄⡀⢀⣀⣰⣷⠀⠀⠉⠀⠄⢴⡖⠀⠀⠀⣹⠏⢻⡄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠙⢯⡐⠂⠉⠀⣄⠀⠀⡀⠀⠺⢏⠀⢠⣆⠀⠻⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠐⠢⠀⠀⡟⠠⣿⣿⠀⣴⠿⡠⣯⡀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⠀⠀⠈⠅⢠⡋⠾⡇⢀⣀⡼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠀⠐⠂⠀⠀⠻⠃⣀⠀⠐⡄⠈⣼⠿⣋⣴⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⡏⣷⣤⠀⠀⣧⣤⣩⡍⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢻⠀⠀⠿⠀⠠⡎⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡇⠀⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠸⡄⢸⠇⡃⢰⠀⠁⣸⠀⡆⢸⠌⠀⣯⡌⢰⠁⢈⠀⠀⠀⠀⡆⡀⠀⠄⡀⡆⢀⠄⢰⠁
⠀⠀⠀⠀⠉⠈⠉⠁⠈⠀⠁⠉⠈⠀⠈⠈⠁⠉⠀⠀⠀⠉⠀⠀⠉⠀⠁⠀⠈⠀⠀⠁⠈⠁⠈⠀⠲
⠀⠀⠀⡄⢠⠀⡀⠀⢠⠀⣄⠀⠀⡄⠀⠠⣄⠠⡆⠠⢄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⢀⡀⡀⠀⢀
⠀⠀⠀⠇⠸⠀⠧⠀⠟⠀⠏⠱⠄⠃⠰⠠⠈⠁⠧⠀⠈⠇⠀⠀⠀⠀⠀⣰⠸⠡⠀⠇⠠⠰⠰⠀⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⢀
⠀⠀⠘⠀⠸⠀⡆⠃⠀⠀⡰⠀⠀⡇⢈⢠⠀⢀⠀⠀⡀⡀⠀⠀⢀⠀⡂⡆⠀⡀⢐⠂⠐⡆⢉⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠐⣀⠂⠀⢆⠶⡀⠀⢠⠀⠀⢂⡐⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⢀⢠⡀⢀⡄⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠁⠐⠀⠐⠀⠘⠂⠀⠃⠐⠀⠀⠀⠀⠀⠘⠀⠈⠀⠁⠀⠀⢠⠃⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡇⠀⢀⡆⠀⠐⡄⠀⡆⡄⠀⢠⠁⠀⠰⡅⠀⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠁⠀⠀⠀⠁⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠁⠁⠀⠁
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⠀⠇⠠⣤⠄⢀⡀⠀⢶⡡⠀⡀⡀⡄⡀⠘⣯⠀⠸⠂⢂⡀⠀⠿⠀⢱
⠀⠀⠀⠘⠄⠈⠀⠃⠈⠁⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠀⠀⠋⠀⠀⠁⠈⠁⠀⠀⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠙⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⣠⣴⣿⣿⣷⣶⣶⣷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠂⠀⠹⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⣀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣏⣻⣿⣿⣛⣻⣛⣛⣭⣽⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⠈⠂⣠⠄⠄⠀⠀⢀⡀⠀⠒⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠠⡀⠀⠈⠀⠀⠀⠸⡀⠀⡀⠀⠀⠃⠀⠀⡀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠈⠖⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠘⢄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡄⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠩⠒⠤⠤⠤⠔⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⣀⡀⠠⠄⠒⠁

⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⢀⢀⣿⣞⠀⡤⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣀⡀⢰⡆⣀⢠⣄⡀⣼⠇⡀
⠀⠀⠀⢰⢉⡆⠀⢹⠟⢩⣿⠞⡁⠀⠀⣼⢋⡇⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠐⠂⢀⣤⠍⢈⣿⢾⠷⡇⣾⣡⡞⢿⡼⢓⣶⠆
⠀⠀⠀⠸⠛⣶⠆⢿⣤⠏⣈⠖⠁⢟⢳⡏⡼⠀⠰⠀⣴⢶⠞⣋⣁⢀⣸⠇⠀⠀⢀⡀⢀⠸⣯⣴⠟⠋⢀⠚⠁⣿⠛⠁⠀⢰⡟⢡⠂
⠀⠀⠀⠀⣼⠏⢀⡴⣲⡆⣦⢠⣦⢋⢾⡿⣤⡜⢷⡖⡀⠀⡏⠀⠈⠉⠁⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⢐⠘⠏⠀⠈⠀⠸⢷⡏⠘⠁
⠀⠀⠀⠀⢿⣄⡼⣷⠻⠟⣿⡼⢇⡟⣸⡇⡽⠷⠿⠷⣇⡰⠃⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠀⠖
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⢸⢠⡏⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣷
⠀⠀⠀⠀⢀⡄⠀⢰⠏⢠⣿⠀⠀⠀⣠⣤⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⡆⠀⠀⠠⡀⢀⡀
⠀⠀⠀⢠⡏⠀⠀⣞⣠⡿⠁⠀⠀⣰⣏⡟⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠓⢤⠀⢾⣩⠞⠁
⠀⠀⠀⠈⠳⣤⣶⠟⠋⠀⠀⠀⢠⡿⣼⢱⡏⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⢀⣸⡀⠀⢸⠧⠜⢇⡠⠿⡹⠀⠘⠀⠜⠁
⠀⠀⠀⠀⠀⠀⡸⢰⣿⡆⣾⠇⣸⣷⠃⣿⢡⠃⡠⢶⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡸⠓⢲⡋⠀⠒⡀⠄⠀⡇⢀⠛⢋⡄⠉
⠀⠀⠀⠀⠀⠀⣷⠇⣿⢱⡟⠀⣿⠃⠀⣿⠋⢠⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡠⡟⠁⠀⠀⠀⡀⣀⠀⣘⠋⠛⠀⠈⠂
⠀⠀⠀⠀⠀⠀⣿⠀⢻⠞⢷⠴⢻⡦⣴⠻⣴⠋⡷⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⣇⣥⠚⠆⣤⢰⡟⢩⡇⢿⣀⣁⢠⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣠⠇⠁⠀⠃⣹⢍⡁⢸⠃⡐⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠠⠀⠠⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠐⠉⠁⠒⠛⠶⣅⣈⠛⢀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⣠⡴⢄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢰⣿⠀⢸⡦⠀⠀⣄⢀⣄⢸⡿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢸⡇⢀⣄⠐⠂⠀⠀⠈⡠⣺⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠸⣧⠀⣾⣡⡿⢀⢣⡾⠁⢸⡇⢠⠎⠀⠟⠀⠙⡆⠀⠀⠀⠀⠀⠀⡀⣀⣾⠋⠋⡜⢸⡧⡿⢐⣦⠴⠁⡀⠢⠀⠀⠈⠂⠄⠐⡂
⠀⠀⠀⠀⠀⠙⣫⡿⠘⠧⠂⢺⣀⠔⠀⠉⢉⣰⡇⠘⢣⠖⠐⠀⠀⠀⠀⠀⠈⠀⠁⢽⠁⠀⡹⠿⢠⣧⣾⠉⠠⠤⠇⢀⡴⠚⠁⠠⠀⠀⠉⡄
⠀⠀⠀⠀⠀⣴⢻⡇⣶⠖⣲⣤⠴⢴⣦⠀⣌⣻⠓⢱⡋⠀⠃⠀⠀⠀⠀⠀⠰⠆⠐⠂⠀⠎⠀⠀⠀⢹⠀⠹⠁⠴⠀⠀⠁⠒⢂⡄⠰
⠀⠀⠀⠀⢰⡏⣸⠁⢻⡾⠟⢿⡄⠀⠹⣦⠿⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣼⠀⠒⠀⠀⠰
⠀⠀⠀⠀⠀⠛⠁⠀⠘⣇⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠑⠠⠄⠀⠀⠀⠐⠒⠑⠂⠀⠀⠀⠈⠒⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣛⣜⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣽⣿⣿⣿⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠱⢃⡴⠖⠶⢤⣀⠀⠀⠀⠀⠀⢠⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⢌⠳⢄⡀⠀⢀⣼⣜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠏⠉⠉⣩⠍⣓⠳⢤⣵⡒⣮⠻⠟⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣆⣀⣈⡴⠲⢤⣵⢤⠤⠃⣼⡷⠖⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⡙⠷⣤⡗⣿⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⡷⡟⢸⠀⠀⠀⠀⠀⠀⣴⣋⠭⠖⠒⠂⠈⠁⠀⠉⠀⡨⢿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠟⠀⠛⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣤⣄⣁⣀⣀⣀⣀⣀⣀⣸⣇⠀⠠⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡉⠙⠯⠍⠉⠙⠛⠛⠛⠉⠉⠩⠽⣶⣬⢹⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡓⠆⠀⠀⠀⠀⣀⠤⠤⠶⠤⣄⣀⡀⠀⠸⣧⠿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣠⠞⠁⢀⣠⣤⡀⠀⠙⣦⠀⠀⢰⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢭⣿⣧⠀⢿⣿⣿⣿⣷⣿⠁⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⡢⠔⠛⣦⣬⠉⠛⠿⠋⠡⣪⠟⢩⠤⢌⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣗⡀⠀⠀⠙⠳⠶⠶⠖⠛⠁⠀⠠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠩⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⣀⣀⣤⣤⣄⣀⣀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⣤⣌⡒⠦⣄⡀⠀⠀⠀⠀⠀⠸⣯⣀⣉⣛⠙⠛⠛⠛⠉⢙⣻⣿⠇⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⠬⠙⠓⠶⣭⣓⠦⢄⡀⠀⠀⠀⠈⠉⠙⢛⣛⠛⢛⣛⣋⣉⣁⠀⠀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢙⡻⢶⣮⣀⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠢⡈⠙⠽⠳⢶⣄⡀⠀⠀⠈⠑⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⢦⣄⣐⣐⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣄⣭⣤⡁⢂⣡⡼⣁⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⠛⠋⠥⠤⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⢀⠤⠐⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠂⠂⠀⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢜⠀⠀⠀⠠⠶⢦⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⣄⠀⣀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠇⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠁⠀⠀⠒⠒⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠳⠆⠀⢠⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢀⠿⠇⠀⠀⠀⠀⠀⢀⠐⠒⠲⣉⠀⣠⣿⣤⠄⠀⢀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠻⢓⠀⠀⠀⠀⠀⠀⢈⠈⠤⠘⠂⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⣠⣽⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠰⢠⠟⠀⠀⠰⠞⠁
⠀⠀⠀⠀⢀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⣀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⡄⢠⡄⡀⢀⠀⠀⠀⢀⣀
⠀⢠⠊⠉⠋⠀⠀⠿⠀⠟⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣿⠶⢾⠇⠀⠀⠀⡀⠀⡏⠀⡇⠀⣀⡀⠀⠀⢠⠀⢳⣞⠁⠀⢸⠉⠁⢸⠆⠀⠀⢸⣿
⠀⢾⠒⠒⠛⡆⠀⡟⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⣾⠙⢁⡀⠀⠇⠀⡇⠙⢷⡄⢘⢀⡀⢸⡀
⠀⠈⢷⣤⡴⠃⠀⠽⠶⣜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⡃⠈⠓⠛⠁⠀⠀⠘⠃⠀⠀⠁⠚⠀⠓⠐⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣄⣄⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⢿⣠⠇⠀⠐⢀⠈⠁⠀⠀⢀⡴⠚⠓⣦⠀⠀⠉⠉⡆⠀⡉⠁⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠁⢹⠁⡇⠀⠸⠈⢰⡆⡁⠀⠀⠀⢀⠘⡇⢠⠃⡶⢲⡄⠀⠤⡇⠀⠐⠖⠀⢾⠀⠀⠀⢸⡆⢀⡟⠉⠀⠀⡙⠒⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⡀⣼⡀⣇⡲⠨⠀⠸⠀⠁⢀⠊⣡⠊⠀⣧⠇⠀⠁⠀⠁⠀⠀⠰⠤⠆⡀⠀⠘⣆⣀⣀⣼⠃⢰⡇⠀⠀⠀⡄⢰⡆
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣈⠠⢬⣄⡉⠀⠈⢀⣤⣴⣧⣤⡉⠁⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠀⠀⡠⠀⢄⠀⠀⠁⢸⡗
⠀⣴⠟⠉⠷⡍⠢⠀⠀⡌⠁⠖⠒⠈⢿⣆⢀⣿⣿⡟⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢛⠀⠐⠀⢤⡀⠀⠀⢀⣀⠀⠀⠀⠀⠡⣕⠃⠀⠀⠀⠘⠁
⢰⡟⠀⠀⠀⡇⠀⠀⢸⠁⠈⠀⠀⠀⣼⣿⢸⣿⣿⠀⢸⣿⣿⡇⢀⠀⠐⠀⠀⠀⠀⠸⠀⡌⠀⠀⠈⠳⠄⠀⠀⠉⠒⠄⢠⣖⠆⡇⠀⠀⠰⣏⣉
⠘⢿⣄⠀⠞⣧⠘⠶⠀⢧⡀⠰⢖⠙⡿⣿⠈⠻⣿⣶⣿⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠕⠁⠀⠀⠰⠦⠟
⠀⣠⣭⣭⣭⣭⣥⡀⡀⠀⠉⠉⠉⠁⠈⠁⠀⠀⠈⠀⠀⠘⠉⠀⠀⢀⠀⠀⣀⠀⢠⠀⢀⡄⠠⡤⢠⡤⠀⣤⠤⢤⣤⠀⢀⣀⣀⣀⡀⠀⠀⡀
⠀⠉⠛⢻⣿⠛⠛⢁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢀⡴⣿⠟⠀⠀⠀⠀⠉⠀⠀⢁⡽⠃
⠀⠀⠀⢀⣻⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣒⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢳⡼⠀⠀⣠⠀⠀⢰⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠹⠆⠀⠐⠤⠆⠀⠀⠀⠀⠀⠛⠷⠾⠟⠖⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛⠀⡈⠛⠁⣀⠈⠉⠉⢉⡉⠀⠛⠉⣉⣉⣀⣁⣈⣁⣈
⠀⠐⡄⠀⣰⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢾⡿⠈⠿⠏⠻⡟⠃⠀⠀⠀⠁⣴⠟⣿⠄⠁⠈⡆⠀⣿⠀⠀⠀⢸⣿⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⢈⡞⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡀⡀⢰⣀⠮⢷⡼⠀⠀⡄⢀⠀⠃⠀⣰⠋⠀⠀⢠⠁⢰⡇⠀⢀⠀⢸⡇
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⠁⢀⣿⡄⢰⣧⠀⠀⠁⠤⠌⠀⠀⢨⠀⠀⠀⠈⡀⠨⠅⠀⠸⠄⠸⠀⠀⠆⠘⠀⠨⠭⠭⠀⠸⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢿⣏⣠⡤⠶⢿⣿⣟⣒⠒⠶⣶⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠀⠀⠀⠄⠈⠙⠺⠧⠀⠀⠈
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡼⣿⣥⣤⡀⠈⠻⣿⣿⣷⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⢐⠀⠀⠀⢹⡀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠘⢿⣆⢀⡎⠀⠈⠻⣿⣿⡄⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠵⢀⠀⠀⠀⠀⠂
⠀⠀⠀⢶⣤⣄⠀⠙⡿⠀⠀⣀⣤⣤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠥⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢻⣿⣇⠀⢡⢠⡼⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠐⢛⡁⠀⠀⠀⠀⢁⠄
⠀⠀⠀⠀⠀⠉⠉⠙⠻⡏⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠀⠀⠀⠘⠡⠂
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡘⢄⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⡀⢢⠸⡅⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣻⠀⠀⠀⠀⠀⠀⠐⠪⠅⠳⡗⡨⠊⡁⠀⠀⠀⠀⠀⠹⣦⡄⠸⡇⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣦⠀⠀⡼⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢅⠀⠶⡗⢐⠄⠄⠀⠀⠀⠀⠀⠀⠘⢿⡄⣇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡆⢀⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠑⢤⡷⠥⡐⢥⠀⠀⠀⠀⠀⢀⠀⠀⠻⣿⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡇⡼⠋⢀⣀⣀⣀⡀⠀⠀⠀⠀⢈⢢⡀⢐⣠⡧⠊⠀⢐⡀⠀⠀⠀⠀⠘⣿⡆⠀⢹⡇⠀⣠⣴
⠀⠀⠀⠀⠀⠀⡾⢆⠀⠀⠹⣾⣞⡥⠚⠉⠀⣠⠜⠁⠀⠀⠀⠀⠈⠂⠀⠠⣄⣧⣐⠈⠄⠊⠀⠀⠀⠀⠀⠈⠻⣄⢸⡇⢠⡿⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠳⡄⢠⠟⠛⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣬⣧⠐⠀⠈⠩⠀⠀⠀⠀⠀⡀⠀⠘⢾⣇⡞⠁
⠀⠀⠀⠀⠀⠀⢧⡀⠀⣷⠏⣀⡠⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠐⠠⣀⡇⠄⠀⠀⠰⠀⠀⠀⠀⠀⣿⣦⠀⢸⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⣚⣁⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠊⠉⠠⣁⠈⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⣦⢸⠃⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠙⡟⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣾⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⡟⠃⠠⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⡀⣀⢀⣀⣀⠀⢀⢀⢀⡀⡀⡀⡀⣀⢀⣀⡀⢀⡀⠀⡀⣀⢀⢀⣀⢀⡀⡀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠊⠘⠋⠿⠻⠻⠸⠀⠟⠺⠜⠃⠟⠓⠓⠻⠻⠇⠃⠸⠷⠀⠛⠛⠟⠛⠛⠸⠛⠇⠛⠸⠂

⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠀⢰⣶⣶⠀⢠⣶⡆⠀⠀⣶⣶⠀⠀⠀⠀⣠⣶⣶⣦⠀⣴⣶⣶⣤⢰⣶⠀⠀⠀⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣾⣿⣿⡇⠸⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⣿⣏⠘⠿⢻⣿⡇⢸⣿⣾⣿⠀⠀⠀⣿⣿⣿⡇⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⣿⣧⠀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠘⢿⣷⣄⢸⣿⡇⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣧⣿⣿⠀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⣤⡄⢹⣿⣾⣿⡇⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⡿⠉⠹⣿⡦⣿⣷⣶⣶⣿⣿⣶⣶⠄⠀⠻⣿⣾⠿⠉⠿⣷⣿⠟⢸⣿⣷⣶⡶⣿⡿⣿⣷⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣇⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠉⠉⠁⣿⣿⣿⠋⠉⢻⣿⣿⡇⣿⣿⣿⣿⣿⡀⢸⣿⣿⡇⠉⠉⠉⣿⣿⣿⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣧⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣀⣀⡀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠉⠁⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⣿⡇⢹⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣾⣿⣿⠇⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⣿⣿⣿⠇⠀⠀⢿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⠀⡄⢠⢠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣠⣤⣠⡀⠀⣠⣠⣤⣤⣠⡀⠀⣠⣤⣄⣤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⢰⠀⣘⡐⡇⠈⠀⠃⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⡇⠀⣿⣽⣿⣻⣿⡿⠀⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠁

⠄⢣⣶⢶⡄⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⠻⠆⢣⣾⠻⣆⠀⠀⣰⡿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠈⠻⡾⠃⠀⠀⠙⣻⠟⠀⠀⠀⠀⠀⠀⣾⣿⣧⣛⣚⠃⠀⠀⠈⣛⠛⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠟⠉⠀⣀⣀⢾⡁⢰⠄⠀⠀⠀⠀⠀⠙⠛⠃⠛⠁⠂⣤⣄⢺⣁⢰⠆⣀⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠺⣉⣹⠆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠃⠉⠁⢺⣏⢹⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡄⣄⣼⣗⠶⠖⠒⠒⠒⠒⠒⢦⠒⠒⠚⠓⠖
⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⡆⠈⠁⠀⠀⠈⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢷⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⡠⢄⡀⣤⣶
⠀⠀⠀⠀⠀⢿⠶⡄⠀⢘⡃⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠉⠀⠈⠛⣀⡄⠀⠀⠀⠀⠲⣿⡵⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠾⡇⠀⢀⠀⠀⠠⠐⠊⠁
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⣄⠀⠀⠸⣿⡂⠀⣀⠀⠀⠀⢰⣾⠚⢗⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣷⣰
⠀⠀⠀⠀⡅⠀⠀⠀⠘⠻⠃⢻⠀⠀⠈⠉⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠰⣤⢧⠆⠀⠀⠀⡉⢟⣿⣻⢏⠛
⠀⠀⠀⠀⠛⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠛⠞⠀⠀⠀⠀⠀⣼⠈⢑⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠒⠒⠂⠀⠐⠒⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠀⠰⡆⠀⠀⢀⣀⢉⢲⣄⣄⢀⣀⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⠇⠨⠧⠦⠆⠦⠽⠶⠤⠤⠰⠒⢳⣳⣋⡭⠶⠷⢿⠛⠿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜
⠀⠀⠀⠀⢰⣅⡰⢀⢠⣀⠴⢬⣀⢀⣠⢀⡴⠖⠉⠈⣃⠀⡀⡄⠈⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠱⠚⠓⠊⠉⠓⢳⢹⣔⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠶⢦⣀⡋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡴⠛⠂⠉⠒⠀⠤⡀⠈⠑⢆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡅⠤⣠⣤⡀⠀⠀⠀⠐⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠉⠙⠢⣀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠑⠒⠂⢤⡀⠀⠀⠹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠶⠴⠶⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣀⠀⠀⠀⠈⠒⢴⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠉⠒⠤⡂⠄⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠠⠄⣀⣤⣈⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠳⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠂⠁⠠⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢑⠆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢦⠀⠀⡀⠀⠈⢀⠀⠰⡆⠁⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠤⠚⠃⠀⠀⠁⠀⡃⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⢀⣀⣀⣐⡂⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⡤⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠆⣠⣾⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣀⠛⠀⠤⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢿⣿⠿⢛⣥⣾⣿⣿⣿⣿⡙⠿⡧⠴⠾⠿⠟⠉⠉⠟⠛⠛⠉⠉⠀⠀⠀⠀⠩⠿⣏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠉⢿⣿⢿⣿⣿⠀⢺⣧⣿⣿⣿⡟⠉⠀⢀⠤⠤⠀⣀⡀⠀⠀⠀⢠⣶⣿⣿⣆⣠⣶⡀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⣠⣴⣶⣦⣄⢻⣄⠈⠻⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⣶⣾⣿⣿⠀⠹⣿⡦⠀⢐⣶⣴⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠉⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆⠀⠸⣿⠿⠛⠁⠀⢴⠿⢃⣠⠘⡛⢹⣿⣿⣻⣿⣿⣺⣿⣿⣿⠃⠀⠀⠀⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⣿⠀⣀⠀⢀⣠⣾⣿⣏⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⢸⣿⢦⣿⣿⣿⠂⠈⣘⣀⣼⣿⣿⠿⡿⠿⠸⣿⣿⠇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣯⠀⠙⢿⣾⣿⡿⠟⠛⡛⢛⠻⣟⠛⠻⠶⣶⣿⣧⣄⡀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠋⢠⡄⠈⣿⡟⡀⢀⢑⡀⠈⠉⠈⠀⠀⢀⡠⠙⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⣧⠀⢿⣠⣾⠟⠀⡄⠀⠈⠛⠀⢂⠁⠄⠀⠀⢰⠃⢼⣦⣉⠉⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢿⠂⣲⠛⡃⠀⠠⠉⠠⠀⠀⠠⠌⠀⠀⠀⠀⡀⠀⡈⢁⡜⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⣗⣶⠊⠏⠐⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠲⠆⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⡆⠀⢾⣶⣆⠀⠀⠀⠁⠀⣀⣀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠐⠆⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠠⣿⡇⠀⢸⣿⡿⠑⢄⠀⠀⠐⠈⠛⠷⢦⣤⣤⠄⠲⣾⣿⢶⡀⠀⠀⠙⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⡇⠀⢸⣿⣧⢰⣄⢁⡀⠆⠀⠀⠀⠀⠀⠄⢠⣤⣼⣿⡘⠳⠀⢠⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣏⡀⠁⣸⣿⣟⣁⣙⣾⣷⡿⠟⢢⣀⣀⠀⣀⣨⡟⠛⣿⡇⡀⢠⠃⣜⢸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡯⣿⢾⢿⣿⣿⣿⣿⣿⣿⠷⠄⠬⠿⠟⢻⣿⣿⣿⣾⣿⣿⡇⢠⡈⣿⢠⠶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⠿⣥⣿⣾⣌⣿⣿⠿⣿⣿⣿⣿⣿⡷⠶⠶⣮⣭⣝⣿⣿⣿⣥⣇⠀⢖⡋⣨⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠉⠙⠉⠁⠀⠈⡿⠧⠿⡿⠤⠀⠃⢀⣾⣿⣝⣿⣿⣿⢹⣿⠀⡐⠀⢒⡉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⠀⢹⣟⣛⣿⠂⢰⣇⢠⣙⠦⠒⠀⣀⣀⠀⠀⠀⠈⠉⠉⠀⠿⢀⡱⣤⣤⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⠉⠉⠉⡠⠋⠙⠃⠉⠉⠀⠀⠉⠉⢹⡆⠀⠀⠈⠀⠀⠀⣩⡇⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣶⣶⡖⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣺⣶⣤⣠⣤⣤⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠐⠼⢿⣽⣿⠿⠿⡿⢏⡁⠀⢀⡀⠀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣴⢯⣉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠛⣦⡼⠟⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠳⠶⢿⠁⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠳⠦⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣴⠎⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣱⣾⡄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢿⣯⡼⠛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠘⣃⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡿⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡾⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠈⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣿⣾⠟⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠷⠟⠈⢇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠴⠖⠛⣛⣛⣛⣋⣉⣉⣉⣉⣍⠩⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠴⠶⠶⠶⠶⠶⢶⣟⣛⡳⢶⣤⡀
⢠⡞⢻⡷⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠉⠙⡆
⢻⡄⠈⠳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠞⠋⠁⠀⠀⠀⢹
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⣄⠀⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⡇⠀⠀⠀⠀⣠⠛⢳⡀⠀⣸⠀⠀⢧⣀⣠⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡄⠀⠀⠀⢰⠋⠉⢻
⢸⡇⠀⠀⠀⠀⣿⠆⠈⠳⠞⠃⠀⠀⠈⠉⠁⠀⠀⠀⢨⡇⠀⠀⠀⣠⠞⠋⠛⠳⣄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⢀⡄⢀⡼
⣾⠀⠀⠀⠀⢸⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢠⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣹⣦⣤⡴⠾⠛⢻
⡿⠀⠀⠀⠀⣿⠿⠦⠤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠂⣾⠀⠀⠀⠘⡷⠒⠒⠲⠖⠛⠷⢶⡄⠀⠀⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠱⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣤⠴⡇
⠀⢹⠶⣮⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⠤⠤⠤⠤⢾⡀⠀⠀⠀⣸⠓⠚⠛⠛⠉⠉⠁⠀⠀⢸
⢀⡟⣁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⣈⡉⠉⠉⡁⠀⢠⡀⢀⣀⡀⢀⡀⠛⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣿⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡆⠀⡟⠉⢹⠀⠘⡛⠳⣼⣇⢸⡦⠀⠀⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁
⠀⠈⢳⣾⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠛⠀⠙⠶⠞⠀⠀⠁⠀⠈⠋⠈⢉⣉⣀⡀⣥⣤⣤⣤⣤⠤⠄⠶⠶⠒⠉⠉⠀⠀⡇
⠀⠀⡿⠂⠀⠈⠉⠉⠉⠛⠋⠙⠛⠛⠒⠋⠘⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⣟⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠈⠙⣿⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠛⠋⠉⠹⡆
⠀⠀⠀⠸⣧⠀⠈⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠸⣧⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠃
⠀⠀⠀⠀⠀⠈⢹⡷⢦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠊⠉⠉⠸⠁
⠀⠀⠀⠀⠀⠀⠘⣶⡠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠚⠛⠛⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡟⣩⣉⣐⣀⡜⣁⠀⣠⣀⡜⣠⠆⣠⠆⣤⣤⣼⣷⠷⠏

⣿⣿⣿⣿⡏⣿⣎⠻⣧⣹⣷⣌⢷⣌⠛⠿⣶⣦⣤⣽⣿⣿⣿⣿⣿⣿⠏⣠⣾⣿⣷⠟⣋⣵⣿⣴⣾⣿⠟⣀⣾⣫⡾⠋⢀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠘⢿⣦⠀⠙⣿⣿⣷⣿⣷⣦⣄⠈⠉⠻⣿⣏⠛⣿⣿⣿⣸⣿⣿⣫⣶⠟⣋⣭⣿⣿⣿⣷⣿⣿⣿⠋⣀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠘⢿⣷⡀⢸⣿⡏⠉⠛⠻⢿⣿⣦⡄⢹⣿⢀⣿⣿⣿⣿⣿⣿⡟⣡⣿⣿⣿⠿⠛⠛⠉⢻⣿⣣⣾⣿⠿⢋⣾⡟⣸⡿⣿⣿
⣿⣿⣿⣿⢿⣿⣆⠈⢿⣧⣸⣿⢰⠟⠓⢶⣄⠈⠛⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣠⠶⢛⢻⡜⣿⣿⡿⠁⣠⣾⠟⢠⣿⢣⣿⣿
⣿⣿⣿⣿⣯⠻⣿⣦⠘⣿⣿⡇⣾⢹⢿⠴⣬⠳⡄⠀⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⣠⠏⢥⣾⢆⠙⡇⣿⡿⣠⣾⡟⠉⢀⣾⣣⣾⣿⣿
⣿⣿⡜⣿⡙⣷⣝⢿⣷⣹⣿⡇⣿⢸⣌⠽⠎⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⠽⣯⡯⡄⡇⣼⣿⡿⠋⢀⣴⣿⣿⡿⣿⣿⣿
⣿⣿⣷⡸⣷⡈⠻⣿⣿⣿⣿⣷⢻⡸⣫⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣚⣟⢡⣧⣿⣿⣤⣾⣿⣿⠟⣫⣼⣿⣿⣿
⣿⣷⣽⣷⣿⣿⣤⡈⠻⣿⡿⢿⠿⠳⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⢿⠿⢿⣿⣿⣯⣵⣿⣿⢟⣵⣿⣿
⣿⣯⡙⠛⠿⣿⣿⣟⠛⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠛⣿⣿⣿⣶⣿⣿⣿⣿
⣿⡤⠶⠶⠶⣶⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡾⠛⠛⣷⢦⡀⠀⠀⠀⠀⠀⢀⡴⣾⠛⠛⣦⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣶⣦⣼
⣿⣶⣾⣿⣿⣿⣷⣶⠶⠭⠙⠂⠀⠀⠀⠀⠘⡇⠀⢸⣿⠀⢳⠀⠀⠀⠀⢠⠏⠀⣿⡀⠀⣸⠀⠀⠀⠀⠀⠀⠩⠽⠿⣿⣿⣿⣿⣿⣿⣶⣿
⣿⡿⢛⣽⣿⣯⣥⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢸⡿⠀⣸⠀⠀⠀⠀⠸⣆⠀⣿⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣭⣿⣷⡦⣍⣛⣿
⣿⣴⠿⣫⣿⣿⠋⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠁⠀⠠⡤⢄⠀⠈⠑⠛⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠻⣿⣿⣿⣶⣍⣻
⣿⣵⣾⣿⣿⢃⡴⠞⣩⣵⠿⠛⠋⣻⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣟⠉⠛⠿⣯⡛⠳⣤⡹⣿⣿⢿⣿⣿
⣿⣵⣿⣿⣿⡟⠁⣴⠟⠁⠀⢀⣴⠟⡟⠀⠈⠙⠳⢦⣄⣀⣀⣀⣴⣿⣄⣀⣀⣀⣤⠶⠟⠋⠁⠀⣟⠻⣆⠀⠀⠈⠻⣆⠈⣷⣿⣿⣾⣿⢿
⣿⡿⣿⠉⣿⡇⢸⠏⠀⠀⠀⠋⠀⣴⣷⠀⠀⠀⠀⠀⠀⠈⠉⠓⡞⡟⣶⠋⠉⠁⠀⠀⠀⠀⠀⠀⡿⡄⠈⠑⠀⠀⠀⠈⠀⢸⣿⣿⣾⢃⣾
⣿⣷⣿⠀⢻⣧⠈⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⡾⢀⣧⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⢿⡏⣿⣿⣿
⣿⣿⣿⣧⠈⢻⡆⢸⣄⠀⠤⠴⠞⢫⣿⡇⠀⠀⠀⠀⠀⠀⡼⢁⡾⡟⢧⠙⣆⠀⠀⠀⠀⠀⡀⣿⣯⡙⠓⠦⠀⠀⣰⡇⣸⠏⠚⢀⣿⣿⣿
⣿⣿⣿⣿⣷⣀⠙⠘⣿⠳⠶⢴⣶⡿⠋⣷⡇⠀⠀⠀⠀⡼⢁⡞⠀⡇⠈⢧⡘⣆⠀⠀⢀⠀⣷⡿⠹⢿⣶⠤⠶⢚⡿⠐⠋⠀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣷⣶⣾⣿⣾⣿⣥⣤⡀⠸⣧⡜⠀⠀⣸⣡⠏⠀⠀⡇⢀⠈⠳⡼⡆⠀⠀⣧⣿⠃⣀⣤⣽⣿⣿⣿⣶⣶⣶⣿⢿⣿⣿⣿⣿
⣿⣮⡛⣿⣧⠀⢈⣽⣿⣿⣿⣷⣦⡈⢻⣆⢹⣇⠀⠀⣿⣿⠀⠀⠠⡷⠀⠁⢠⣿⡇⠀⠀⣼⠃⣴⠏⣡⣴⣾⣿⣿⣿⣭⠁⠀⣾⡿⢋⣾⣿
⣿⣿⣷⠈⢿⣦⣾⣿⡏⣿⣏⢻⣿⣿⣆⣿⢸⡟⢦⡀⢸⣿⡆⠄⠄⡄⠈⡀⢸⣿⠃⣠⠞⣿⣰⣏⣼⣿⣿⡏⣾⡟⢹⣿⣧⣼⡟⢠⣿⣿⣿
⣿⣿⣿⡇⠈⣿⣿⢿⣷⣽⣿⣾⡿⠘⣿⣿⣿⠇⠀⠹⣄⣿⣧⠀⠐⠙⢀⠀⣿⡟⣴⠃⠀⢹⣿⣿⣿⡉⣿⣷⣿⣧⣾⠿⣿⡟⠀⣸⣿⣿⣿
⣿⣿⣿⣷⠀⢸⣿⡘⢹⣿⡏⢻⣿⣾⣿⣿⡟⠀⠀⠀⠹⣿⣿⠀⠉⠀⠑⢠⣿⣿⠃⠀⠀⡈⢿⣿⣿⣶⡿⡯⢻⣿⡇⣹⣿⠇⢀⣿⣿⡟⢸
⣿⡘⢿⣿⣆⠈⢿⣿⣿⣫⣄⣱⣦⣾⣿⣿⡇⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢸⣿⣿⣷⣮⣐⣮⣹⣿⣿⠟⢀⣼⣿⡿⢁⣼
⣿⣿⣾⣿⣿⣷⣦⣭⣝⣛⡻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⣛⣋⣭⣤⣴⣿⣿⣿⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣤⣤⣤⣔⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡞⣩⣶⡶⠦⢍⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢸⣿⠁⠀⠀⠀⠑⡹⣷⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⡻⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣌⠂⠄⢀⠀⠀⠀⠀⠀⠀⠋⠾⠟⠁⠀⠀⠈⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣿⣷⣦⣬⡁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⣇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⢿⣿⣿⣧⠘⣷⣦⣤⡄⠀⠀⠀⠀⣸⣸⣿⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣧⠙⣿⣿⣇⠀⠀⠀⢀⢣⣿⡇⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠛⠿⢷⠘⢿⣿⣆⠀⠀⠌⠘⠟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢻⣿⣦⡜⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⢹⡟⠁⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⣴⣿⣿⠋
⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢀⣤⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⢀⠀⠀⠤⠀⠤⠀⠀⠀⠀⣀⣀⣤⡶⠾⠛⠉⠁
⠀⠀⠀⠀⠈⠁⠀⠒⠐⠒⠚⠛⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⢠⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢂⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣤⣤⣤⠋⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣹⡷⠴⣠⣄⠱⣿⣶⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣚⠋⠶⣦⣝⣿⣷⠘⣿⠇⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⠉⠐⢿⣦⣈⣿⣷⣻⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠏⡀⠀⠐⠄⠙⡿⣮⣿⠛⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠦⡀⣊⣢⠟⡫⠃⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⠭⠁⠜⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠤⠄⠠⡇⠀⣤⠀⠤⠤⠤⠤⠤⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣂⣉⣀⣲⡤⢶⠤⠃⢀⠰⣶⠦⠴⠄⠀⣀⣀⡀⠀⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠴⢏⣙⣇⣸⡠⡧⠼⣦⠀⠈⠐⢦⣤⠤⠤⠤⢤⣄⠀⠙⠢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣶⢮⣉⣉⠭⠄⣀⠀⠠⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢑⣤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣽⣂⠈⣉⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⡄⠐⣁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣝⡻⣟⠀⣴⡂⠀⠀⠀⢠⣶⡄⢰⡯⢦⡀⢂⡀⣇⢈⣀⡥⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢈⢀⡇⠁⠈⠋⢮⡇⠀⠀⠂⢨⠟⡻⢿⠺⠾⠟⠛⠋⠙⠁⠃⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠀⠀⠀⠀⢀⠀⠀⢀⠓⢸⡃⢌⢂⢃⠀⡀⠠⠠⠀⠀⡘⢰⠀⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⣠⣆⠀⠤⠅⣼⡷⠶⠶⢄⠀⠀⠁⠆⡀⠀⠃⡈⠀⠁⢈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⣠⡾⠃⠈⠳⠶⠞⣦⣀⠀⡀⢋⣆⠀⠀⠠⠀⡘⢀⠃⠃⠠⢸⢠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⠀⣔⠝⢁⡀⠠⠠⠤⠤⣴⣿⣤⡟⢀⠄⠘⣧⡀⠀⠈⠁⠸⢰⡖⠓⠮⡈⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉⠠⢄⠀⣠⣶⣯⢁⣿⠃⠀⠀⣀⠘⢟⡄⠀⠀⠃⣼⠀⠀⠀⠡⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠆⠀⠨⡥⣀⡠⢶⣦⣙⡿⣿⠀⢀⡄⠀⠀⡜⡌⠀⠀⢀⠻⠀⣄⠀⠀⠀⠠⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣁⠀⠔⢸⠷⣶⣝⣿⢷⠻⡃⠈⣠⠂⡘⡘⠀⠀⢨⡘⢀⠶⣈⡁⠾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠴⠐⠀⠀⠀⠀⠰⠘⢆⠶⠻⠷⠼⢋⢾⡈⠤⠁⠐⠁⣲⠌⠀⠀⠀⠀⠃⡈⡀⢁⠁⠆⠀⢠⡸⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠱⠈⠖⢎⢦⡀⠋⠀⠀⠀⠖⢠⡳⠁⠀⠠⢀⠂⠈⠰⢡⠁⠄⡘⠰⠀⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠚⠭⠴⠶⠖⣂⣀⣀⣰⠏⠀⠀⢀⠂⠌⡀⢀⢃⢃⠆⡠⢁⢃⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠐⡐⡀⢀⠎⠎⡰⢁⠎⣀⠎
⠀⠀⠀⠀⠀⠀⠐⠢⠀⠂⠀⠊⠑⣠⣉⠂⠑⢊⠔⡠⠂⠂⠐⠀⠁⡠⢁⠌⠔⠜⠀⠀⠎⠈⠀⣤⠞⣣⠀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢂⠠⠀⠄⢉⡰⠛⡰⠦⣤⢀⣀⣀⢀⢀⡀⣀⡀⢀⡤⠀⠄⣐⢞⠕⢁⠈⡡⢊⠐⢁⠔⡡⢂⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠡⠒⢁⠔⢉⠔⢊⠤⠂⠠⠀⠀⠀⡁⠀⡠⠂⠔⠠⠂⡠⢁⠄⡡⠊⡄⠁⠔⢁⠘⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠊⠐⠀⠐⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⢀⡄⠀⠀⣠⣀⠀⠀⠀⢀⣀⠀⠀⣠⣀⡀⠀⠀⣠⣤⣤⡀⠀⢀⣄⣤⡄⠀⠀⠀⣀⣄⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⡏⡄⠀⠀⡇⠀⠀⠀⢰⡏⠀⠀⠀⣿⠀⡄⠀⠀⣸⠀⣀⠀⠀⢸⡇⢀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡇⢀⡿
⠀⠀⠀⢠⠃⢀⠀⠀⡇⢠⠁⠀⠸⡇⢢⡄⠀⣿⠀⠏⠀⠀⢿⠀⣠⡀⠀⢸⡇⠀⠀⠀⠀⢿⠐⠏⠃⠀⠀⡇⠀⡄
⠀⠀⠀⠈⠀⠈⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠁
⠀⠀⠀⣤⣤⣤⡄⠀⢠⡤⠤⠤⠀⠀⣤⠄⣠⠤⠀⢀⡤⠄⠀⠀⠀⢠⠤⢠⡤⠄⠀⠀⢠⣤⡀⣠⠄⠀⠀⢀⣤⠄
⠀⠀⠀⠉⣆⠀⠀⠀⠈⢰⠀⠀⠀⠀⡇⠘⠁⠀⠀⢸⡇⠀⠀⠀⠀⣼⠀⠀⡀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⣿⠁⢰⡆
⠀⠀⠀⣠⠿⠀⠄⠀⣴⠺⠀⠀⠀⠀⣿⠀⡄⠀⠀⢸⡇⠐⠶⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠀⠘⣆⠀⠀⠀⢿⡀⠘⠃
⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠉
⠀⠀⠀⢠⠤⠄⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⡴⠢⠀⠀⠀⠀⣴⠖⠂⠀⠀⡶⠶⠒⠶⠀⠀⡶⠆⣶⠆⠀⠠⡶⢦⡶⠶
⠀⠀⠀⢸⠀⠐⠂⠀⠀⣾⠀⢰⠂⠀⠀⠀⣿⠘⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣇⠠⡟⠀⠀⠀⣧⠘⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣆⠀⠀⠂⠀⠀⣿⢠⡀⠀⠀⠀⢼⠗⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⢻

⠀⠀⢰⠶⠀⠀⢰⠖⠆⠰⡖⠖⢠⠖⠆⠀⣶⠒⢴⠶⠆⠀⢰⠒⠒⠒⠀⠀⡶⠄⠀⡤⠂⠄
⠀⠀⢸⡆⠰⠋⠺⠀⠀⠀⢹⡄⠈⠀⠀⠀⠘⣦⠈⠀⠀⠀⠀⣠⠃⠀⠀⠀⡇⠀⠀⢠⠟
⠀⠀⠀⣧⠀⢰⡀⠀⠀⠀⡜⠀⠰⡀⠀⠀⠀⡞⠀⠀⠀⠀⢰⠃⠐⠂⠀⠀⡴⠄⠀⢨⠶⠀⢠⡶⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⡀⣠⡀⢀⣤⣤⡀⠀⢀⣀⣀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢰⡏⠐⣦⠀⢰⣉⠀⠀⠀⢿⣤⠀⠀⠈⢁⡄⠀⠀⠀⣿⠀⠇⠀⢸⠀⠀⠀⠀⣟⠀⠀⠀⠀⠁⢰
⠀⠀⠀⠸⣇⠀⠟⡀⢀⣸⠀⠀⢀⡞⡡⠀⠀⢀⡀⠱⠀⠀⠀⠀⠀⡇⠀⢈⣡⠆⠀⠀⢻⠀⣤⠀⠀⠀⡞
⠀⠀⠀⠀⠉⠁⠈⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠂⠀⠀⠈⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⡀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⣏⠐⠀⠀⠏⠠⠄⠆⠀⠘⠉⡾⠉⠁⠀⢀⣸⠉⠁⠀⠀⢀⣀⣠⣤⠀⠀⢹⡉⠋⠉⠀⢠⠤⠤⠴⠄
⠀⠀⠀⠰⡏⢀⡆⠀⢀⣀⡆⠀⠀⠀⣸⠁⢀⡀⠀⠙⢠⠄⠀⠀⠀⠙⠀⠀⠀⠀⠀⣰⠃⡀⠀⠀⠀⠖⠒⠛⠃
⠀⠀⠀⠀⠙⠂⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠋⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠙

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠤⠀⢠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢤⡄⡀⠒⠀⠀⠀⠀⠀⠀⡢⠀⠀⠐⡀⠠⠂⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⠁⠀⢀⠀⠀⠀⠠⠐⠐⠀⢀
⠀⠀⠐⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠒⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡔⡀
⡎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠘⡀⠀⠀⠀⠄⡐⠀⠀⠀⠀⠀⡀⡐⠀⡀⠀⠀⡀⠈⡀⠀⠀⠂⠀⠀⠀⠠⠂⠔⠡⠠⠀⠀⡄
⠁⠠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠄⡖⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡐⠐⠀⣁⡀⠀⠌⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡐⠀⠀⠀⠁⠲⡀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⡀⡘⠁⠐⠊⠄⠀⠐⡘⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐
⠀⠀⠀⠀⠀⠘⠀⠀⠆⠀⠀⠰⠐⠀⠀⠀⠀⠹⠀⠄⠀⠀⠀⠀⠀⠀⡊⠀⠀⢰⠁⢰⠠⠀⢰⠀⠀⠀⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠰⢱⠀⠁⠀⠀⠀⠀⠀⡀⢸⠌⠀⠀⠀⠀⠀⠀⠈⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠧⠀⠀⠻⠁⠀⠀⠉⠀⠘⠀⠀⠀⠇⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠈⠔⠒⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⡀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡠⠀⡃⠀⠀⠀⠰⠁⠀⡠⠃⠀⠀⠁⠠⢪⠂⠐⠠⠀⡎⠠⠀⠀⢠⠄⠀⢈⠀⠀⠀⣠⠇⡘⠐⠀⢀⠀⠈⠁
⠀⠀⠀⠀⠑⠀⠳⠈⠀⠀⠁⠀⠒⠢⠀⠐⠔⠀⠀⠂⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠣⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠒⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡤⠀⢀⠀⡀⠀⠀⡀⠀⡀⡀⠠⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⢀⠈⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠊⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡆⢸⣀⠄⠀⠀⠀⠀⠐⠂⠐⣆⠀⢠⠂⡟⠀⠀⡰⠂⠀⡗⠀⠀⠀⠀⠀⢸⠀⠈⢦⠀⠀⠀⡇⠀⠀⠀⣰⠂⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡁⢸⠃⠀⠀⠀⠀⠀⠀⣃⠰⢇⡀⢸⡀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⡇⠀⠀⢀⠷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡴⠀⡀⠀⠀⠀⡇⠀⢠⡇⢸⠀⠆⠀⢸⡄⠀⠀⣄⡄⠀⠀⢠⡄⢸⡄⠀⢀⣇⠀⢀⡇⠀⢰⡇⠀⠀⣤⡖
⠀⠀⠀⠀⣠⠀⢸⠀⠘⠀⠃⠘⠛⠀⠀⠰⠧⠐⠋⠀⠈⠀⠁⠀⠀⠛⠂⠘⠁⠙⠐⠃⠀⠛⠾⠇⠔⠋⠈⠃⠈⢷⠀⠈⠛⠀⠀⠁⠙
⠀⠀⠀⠀⠛⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠁⢘⡇⠀⢠⡇⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⡀⠀⠀⡟⠀⢸⠀⢸⡇⠁⠀⠀⠀⡟⠀⠀⢹⡄⠀⠀⠀⡠⠂⢸⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣼⡠⠀⠀⡇⠀⠀⣸⠇⠀⠀⠀⢸⠆⠀⡗⠀⢸⠋⢸⡇⢄⠀⠀⠀⢿⡀⠀⣸⠁⡄⠀⣼⠁⠀⢸⡀⠠⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢸⠀⠈⢷⡀⠀⣿⢀⡂⣤⡠⠃⠀⠀⡇⠀⢸⠀⢸⡇⣼⠀⠀⠀⠀⠙⣰⠏⢰⡇⠀⠿⠄⢃⣾⠁⢸⡀⠐⠁
⠀⠀⠀⠀⣴⠂⢀⡼⠁⠀⣧⡸⠀⠀⠀⢠⣼⡏⠀⡕⡏⠀⠀⠀⠀⠁⠀⠸⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣴⢁⡏⢠⢺⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠰⡶⢀⠄⡂⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⠀⠀⠀⢀⠄⡄⠀⡀⠀⠀⠀⠀⠀⠀⣦⠀⣄⠀⠀⠀⠀⠀⡀⠀⢠⣤
⠀⠀⠀⠀⠀⣷⡜⠀⠀⣾⠀⡀⠀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠀⠀⢼⠀⡇⢸⢹⡆⠀⠀⠀⠀⠀⣟⠀⢸⡀⠀⠀⠀⢰⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⡟⠁⡆⠀⣿⢦⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⢸⠀⣇⡘⢸⠁⣤⢰⣀⠀⠀⣿⠀⢸⡇⢀⠀⡄⢻⠀⠀⠀⠀⡟⠀⢀
⠀⠀⠀⠀⠀⡏⠀⡇⠀⢿⢸⡇⠀⢺⡀⠘⠓⠤⡀⠸⡀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠿⠸⠀⡇⠀⡿⠀⢸⡇⠰⠀⡇⠈⠷⣀⠀⠐⠉⠄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠾⠀⠀⠀⠘⠃⠀⠀⠀⡇⠀⠀⠀⠘⠇⠀⠀⠧

⠀⠀⠀⠀⠀⢘⡃⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⠀⠘⢦⠀⠀⢰⡇⠀⠀⣴⠃⠈⠁⠀⠀⠀⠀⠀⠐⠂⢰⠀⠂⢰⡆
⠀⠀⠀⠀⢀⣸⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠰⠀⠀⡼⢰⡂⢾⠀⠀⠀⠛⠂⠂⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⠃⠈
⠀⠀⠀⠀⠀⢹⠖⠐⠋⢴⠀⢠⠀⠀⡀⢀⡀⢀⠇⢀⠀⡀⠀⠈⢹⠂⠙⡆⠀⠀⢸⠀⢠⠂⠀⠀⠀⣼⠁⠤⠄⠀⠀⠀⠀⢸⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⠂⠀⠀⢸⠶⠛⠀⠀⠓⠆⠙⠛⠀⠘⠢⣷⠀⠀⠘⠀⠀⡇⠀⠀⢸⠀⠈⠓⠄⠀⠘⠁⠀⠀⠀⣳⠀⡀⠀⢸⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠓⠀⠐⠋⠈⠓⠀⠘⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠁⣸⠁⠘⢦⠀⠀⠀⠀⠀⠴⠀⡟⠀⠀⡀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⠀⢀⡏⠀⠀⠘⡇⠀⠀⡄⠶⠀⠀⡇⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⣇⠀⣸⡇⠀⢀⡄⠀⠀⢧⡀⠀⢠⠇⢰⠀⣻⠀⠀⠘⣇⠀⠀⣿⠀⢀⡞⠠⡇⢰⡆⣿⠀⠀⠀⠀⢠⠿⡆⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠁⠓⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠉⠀⠉⠉⠀⠀⠉⠈⠉⠁⠀⣰⠐⢠⠟⠀⠙⠀⠠⠐⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠆⢰⠀⢠⡄⠀⠀⠀⢠⡀⠀⠈⠀⣸⠀⠀⠀⠐⠲⣄
⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠁⣸⠇⠀⣀⣶⠞⠀⠀⠰⢋⣿⠀⠀⣠⡏⠜⠁
⠀⠀⠀⠀⠀⠀⢠⣎⡽⠀⢰⡉⡇⠀⠀⠀⢠⣿⠏⠀⢰⣉⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⢿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⢲⣤⣤⣤⣤⠠⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢠⣀⣄⡀⠀⠀⠐⡶⣶⣶⡶⠶⣶⣶⣤
⠀⢹⣧⡉⠙⠷⣷⣷⡘⡦⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⠩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⡟⠛⡄⠀⠀⢘⣶⢮⡱⣞⢀⠓⠀⠁⢂
⠀⠀⠍⠿⢗⣀⠀⠈⠉⠃⠁⣿⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠴⢒⠓⠲⠸⠄⠀⠀⢿⣿⢿⣦⣈⢣⠀⠀⣼
⠀⠀⠘⢿⣭⡽⠞⣣⡄⡀⠀⠙⠃⠀⠀⢀⣔⠀⢸⡁⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⢀⠀⠀⠂⡄⠀⠀⠨⠿⣷⣎⡈⠁
⠀⠀⠀⠀⠑⠂⠁⠀⠈⠺⠷⠦⣀⠠⠀⠀⠙⠛⠎⠓⠚⠓⠲⠇⠀⠀⠀⠀⠀⠉⠀⣤⣀⢻⣄⣄⣬⡿⣿⣷⠿⠆⠀⠀⠀⠻⠯⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣅⢹⣶⣽⣟⣿⠿⠛⠀⢀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠰⠀⠀⠀⡄⡏⠉⠠⠀⠢⡀
⠀⡀⠀⠖⠀⠀⠀⠀⠀⠨⢻⣤⠀⠀⠀⠀⠀⡐⢿⠇⢰⢃⠀⠀⢀⢠⢤⡄⢀⢀⠀⣤⡤⢀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢩⠀⠸⠀⠀⠰⠆
⢸⣷⠋⢰⠆⠀⠰⡄⠀⠀⠂⢽⡇⠀⠀⠀⠀⡝⣿⠀⢨⡟⠀⣰⢻⠿⣼⢣⡤⠾⠋⣁⢴⠖⠀⠀⠀⠀⠀⠀⠈⣑⠦⠀⠠⡀⠀⠀⠀⠀⠀⠀⣆
⣸⣿⡿⠁⠀⠀⣤⠘⣆⠈⣻⣲⡇⠀⠈⡐⢀⣤⡌⠀⣼⡧⣠⣿⠂⠴⠋⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⣀⠐⠀⠀⠀⠀⠀⠀⠀⣸
⢹⣛⡄⠂⠄⠀⠀⢀⠀⢠⣜⡟⠀⠀⠀⠁⠀⠙⠁⠀⠻⠁⠛⠁⠀⠠⠤⣼⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡤⡄
⠀⢿⠡⢎⡄⠀⠀⣄⢁⡰⡎⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡐⠷⠶⢶⣔⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⣬⣌⡀
⠀⠘⢷⣎⠄⠀⢦⢰⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠿⠳⠦⢤⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⢻⡆⢼⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢛⠑⠀⠀⠀⢀⡀⡐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⣧⣄⣀
⠀⠀⠀⠀⠁⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳⠘⡅⠘⢧⢉⠀⠙⠟⠟⠈⠉⠀⠀⠀⠀⠀⢫⣄⢀⠀⠘⠀⠀⠸⣯⠿⡿⣷⣶⡆⢠⣄
⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣀⣤⣤⡶⣾⣾⣷⣦⣄⠀⠀⠙⢿⡄⡀⠀⢠⣶⣿⣄⠸⠇⢸⡟⢿⡿⣠
⠀⠀⠀⠀⠈⠳⣯⣟⣷⢮⡙⠆⠀⢀⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⠋⠻⣮⠻⣿⠝⣻⠆⠀⠀⠀⠙⠁⠀⢘⡻⢿⡖⠂⠀⠘⠀⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠟⠂⢤⣄⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣽⡷⠖⣚⣶⣦⡆⠁⠉⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⣙⡀⠀⠈⠐⠋
⠀⠀⣴⣶⡶⠶⢷⠖⠂⠀⠀⠘⠳⣶⣿⣛⠲⡄⠀⠀⠀⢀⠴⢿⣿⢯⣭⠄⠀⠈⠙⠉⠄⠀⢀⠀⠀⠀⠀⠁⠀⠈⠻⢿⣿⣽⣥⡄⠀⠰⡀
⠀⠀⢈⣙⣛⣛⣛⡛⠃⠀⢤⡙⢷⣤⡀⠉⠙⠉⠀⠀⣠⣾⡛⣛⣫⣤⠴⢀⣀⣴⣤⡾⠂⣀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⣾⣿⣿⣯⣿⣯⡅⢀⡐⢦⡙⠳⣽⣻⣆⠀⠀⠀⠀⠉⠛⠟⠿⣿⣿⣿⠟⣻⣿⡏⡅⣴⣟⣰⣿⠇⠀⠀⠀⠀⠀⠀⢦⣶⡆⠀⠀⣠⡄
⠀⣈⣭⣭⣽⡶⠄⠠⣌⣳⣦⡛⢷⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⢳⣿⣿⠿⠏⠀⠀⠀⠀⠀⢰⠤⢹⣙⣤⡞⣽⢟⡏
⢼⣯⣿⣿⡿⠟⠀⠸⣿⡿⣿⣟⠿⠿⠀⠀⠀⢀⣠⣤⠤⢦⠀⠠⣤⣤⣀⠀⠈⠉⠁⠁⠁⠀⠀⠀⠀⢠⣶⠀⢀⡶⣢⣾⡿⠋⣻⣿⣆⣋⡜⢳⡀
⠀⣤⡶⠟⢛⡯⢠⣷⣬⡻⢿⣿⡆⠀⢀⣤⡾⠿⡛⠣⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢸⣤⡌⠀⠛⠙⠳⢚⢉⣭⡸⣟⣿⡯
⠘⠻⠟⠛⣩⣧⡌⢻⣿⢿⡄⠀⠀⢠⡾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠁⠀⠀⠀⠀⣀⠄⠤⠚⠀⠉⢀⡈⢠⣥⣈⡘⠻⣷⣾⣥⣿⣧
⠀⠀⠀⢸⣿⣿⡇⠀⠙⠻⠃⠀⣠⣏⠀⠀⠀⠀⠀⠀⢠⢂⢂⣾⣶⡾⠁⠀⠀⠀⠀⠀⠊⠁⣀⣠⠴⢤⣯⠉⠙⠿⣿⣿⡛⢦⣬⣽⣣⡌⠉
⠀⠀⠀⠘⢿⠟⠁⠀⠀⠀⠀⠈⠉⠉⠙⠓⠀⢠⣤⣤⣷⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⣀⣀⢠⣤⣄⣒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠾⣟⣋⣉⠉⠉⠁⠀⠀⠈⣀⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠨⣗⡲⠦⢭⣍⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣊⢻⣿⣿⣶⡖⠒⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠶⠋⠀⣤⡀⠉⢿⣿⣍⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⠰⠶⠶⣾⡋⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⡉⠁⠀⡄⠀⠀⠝⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⢤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⢀⡀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⡛⠻⠿⠿⠿⠯⠷⠢⢒⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⠽⠛⠓⠒⠶⠖⠚⠛⠉⠁⠀⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⡜⢆⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⢧⢹⣾⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡿⠿⠿⠃


⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡄⢠⣶⡄⠀⠀⠀⣠⠀⢠⣶⡄⠀⠀⠀⣠⠀⢠⣦⣀⡀⠀⣼⣷⠀⢰⣦⠀⠀⠀⠀⣴⠀⢰⣶⠂⠀⠀⣴⠀⢰⣶⠆⠀⣤⠀⢰⣦⣀⡀
⠀⢰⣿⣇⠀⢉⣁⠀⠀⢰⣿⡇⠀⢉⡀⠀⠀⣼⣿⡇⠘⣿⠟⠀⠀⣿⣿⡆⠘⣿⡇⠀⠀⣾⣿⡄⠈⣁⠀⠀⣼⣿⡆⠈⣁⠀⣾⣿⡄⠸⣏⡉
⠀⠸⣿⣿⠀⢸⣿⡄⠀⢸⣿⣿⡀⠙⠿⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⢹⣿⣧⠀⠻⠟⠀⠀⢻⣿⣧⠀⠋⠀⠀⢹⣿⣧⠀⠛⠀⢹⣿⣧⠀⠻⠟
⠀⠀⢿⣿⣧⣴⣿⣷⡶⠀⢿⣿⣿⣶⣶⠖⠀⠀⣿⣿⣿⣶⣶⠆⠀⠈⣿⣿⣦⣴⣶⠂⠀⠘⣿⣿⣿⣶⣶⡖⠘⣿⣿⣦⠆⠀⠘⣿⣿⣿⣶⣶⠂
⠀⠀⠸⠿⠋⠈⠿⠛⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠻⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠻⠿⠃⠀⠀⠀⠈⠛⠿⠛⠁
⠀⠀⣠⠀⠀⢠⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠀⠀⢠⡄⠀⠀⠀⣠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⡄
⠀⣴⣿⡆⠐⣿⡇⠀⠀⣼⣿⡀⠀⠀⠀⠀⢰⣿⣧⠀⠀⣴⣿⡆⠀⣿⡇⠀⠀⣼⣿⡄⠀⠀⢠⣿⣧⠀⢿⣷⠀⠀⢠⣾⣇⠀⢶⣶⠀⢸⣿⡀
⠀⢸⣿⣷⠀⢠⣤⠀⠀⢻⣿⣇⠀⠀⠀⠀⠘⣿⣿⡀⠀⢸⣿⣷⠀⢠⣄⠀⠀⢻⣿⣧⠀⠀⠘⣿⣿⡀⢸⣿⡆⠀⠘⣿⣿⡀⢸⣿⡆⠘⣿⡇
⠀⠈⣿⣿⡄⠸⣿⡇⠀⠸⣿⣿⠀⠀⠀⣰⣦⡈⠛⠁⠀⠀⣿⣿⡆⠘⣿⡇⠀⠘⣿⣿⡀⠀⠀⢿⣿⣇⠀⣿⣷⠀⠀⢻⣿⣇⠀⣿⣧⠀⢻⣿
⠀⠀⢹⣿⣷⢶⣿⣿⠟⠀⢿⣿⣷⠃⠸⣿⣿⣿⣿⠟⠀⠀⢹⣿⣷⠶⣿⣿⡟⠀⢻⣿⣷⣾⠃⠸⣿⣿⡶⣿⣿⡿⠃⠸⣿⣿⡶⣿⣿⡷⢿⣿⡿⠃
⠀⠀⠈⠛⠋⠀⠛⠋⠀⠀⠘⠛⠁⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠛⠋⠀⠙⠋⠀⠀⠈⠛⠛⠁⠀⠀⠛⠛⠀⠙⠋⠀⠀⠀⠛⠛⠁⠙⠛⠁⠘⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡀⠀⠀⡀⠀⢀⣄⠀⢀⣶
⠀⢀⣾⡀⢸⣿⡆⠀⠀⢠⣾⠀⠸⠿⠀⠀⠀⣰⣧⠀⢿⣷⠀⠀⠀⢠⣾⡀⠸⠿⠀⠀⠀⢠⣾⡀⠘⠿⠶⠂⢾⣿⣿⡇⠈⠁⠀⣿⣿⡀⢸⣿⡆
⠀⢺⣿⣇⠀⢿⣷⠀⠀⢿⣿⡇⠀⣴⠖⠀⠀⣿⣿⡄⠸⣿⡆⠀⠀⢻⣿⣇⠀⣤⣤⠀⠀⢿⣿⣿⠶⣦⣄⠀⠈⠹⣿⣿⠀⠀⠀⢿⣿⣇⠀⣿⣧
⠀⠘⣿⣿⣦⣈⣁⡀⠀⢸⣿⣿⡀⠉⠀⠀⠀⢻⣿⣷⣄⣉⣁⣀⠀⠸⣿⣿⡀⢸⣿⣄⡀⠈⣻⣿⣄⣈⢁⡀⠀⠀⣿⣿⣇⣀⠀⠸⣿⣿⣦⣈⣁⣀⡀
⠀⠀⠻⣿⣿⣿⡟⠁⠀⠀⣿⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⣿⣿⡿⢻⣿⡿⠁⠀⠻⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⠋⠀⠀⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⣠⡆⠀⠀⠀⣠⡄⠀⣠⡆⠀⣠⣆⠀⠀⠀⣠⡆⠀⣠⣆⠀⠀⠀⣠⡆⠀⣠⣆⠀⠀⠀⣰⣆⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢿⣿⠀⠀⢰⣿⣧⠀⢿⣷⠀⢹⣿⡀⠀⢰⣿⣿⡀⠙⠟⠀⠀⢰⣿⣷⡀⠻⠟⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠸⣿⡆⠀⠘⣿⣿⡄⢸⣿⡆⠘⣿⡇⠀⠀⣿⣿⡇⠀⣴⣄⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⣈⣀⠀⠀⢻⣿⣷⣄⡉⢀⣠⣈⣀⡀⠀⢨⣿⣷⡀⣻⣿⣀⡀⠈⠛⣿⣿⣆⣀⠀⠀⠀⣼⣟⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠋⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⠟⢿⣿⠟⠁⠀⠀⢹⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠁

⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣤⠶⢶⣦⡀⠀⠀⠀⣤⠶⢦⣄⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⢠⡤⢤⣤⡄
⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠁⠠⢀⣿⠇⠀⠀⠀⢤⣄⣠⠟⠀⠀⠀⠀⠀⡼⡁⣿⡇⠀⠀⠀⠀⣿⣄⣀⣀⡀
⠀⠀⠠⠀⣿⡀⠀⠀⠀⢀⣄⣠⠴⠛⢉⠘⣦⠀⠀⠀⠉⠉⡿⠆⠀⠀⠀⣼⣡⣆⣿⣇⡿⠀⠀⠀⠀⠀⠀⢹⢷⠜
⠀⠀⠀⢠⣿⡄⠁⠀⠀⠚⠿⣿⣦⣤⣴⡇⠀⠀⠸⠧⣀⡡⠿⢹⠁⠀⠀⠿⠿⢭⣿⣧⠄⠀⠀⠰⠿⣄⣀⡾⠏

⠀⠀⠀⠀⡀
⠀⢀⣾⡯⠉⢻⡀⠀⠀⠀⠘⠉⠉⢻⠏⠀⠀⠀⠀⣾⡁⢙⣷⠀⠀⠀⢀⣾⠋⠉⢳⣄⠀⠀⠀⡀⣴⡏⠈⢻⣦
⠀⢸⣿⣟⠙⢻⣆⠀⠀⠀⠀⡀⣰⣏⡀⠀⠀⠀⢻⣿⠿⣿⣯⡀⠀⠲⠺⣿⡀⠀⣰⣟⠀⠀⠀⢸⣿⢀⣄⣸⣿
⢀⣼⣿⡩⡍⢸⣿⠀⠀⠀⠬⢽⣿⢋⡀⠀⠀⠀⣿⡇⠃⠈⣿⣗⡀⠀⠁⢈⠙⠛⣽⡿⡶⠆⠀⠘⣿⡄⣍⢻⡿⡖⠤
⠀⠯⠉⠓⠒⠛⠶⠀⠀⠀⠀⠘⠛⠊⠀⠀⠀⠸⠉⠙⠓⠚⠋⠉⠀⠀⠀⠘⠓⠚⠛⠋⠀⠀⠀⠀⠈⠙⠒⠉

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣁⠈⠙⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠷⣶⣤⣈⣉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣦⣄⡉⠙⠳⠦⡤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⠀⢀⡞⢉⡼⠛⣫⣷⠆⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣀⡟⢁⡞⢁⡴⠋⣺⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣾⡄⣼⡁⣼⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡴⢆⢀⣀⠀⠀⠀⠀⠀⠀⠉⡛⠿⣿⣷⡿⡿⢃⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠢⣼⡈⣻⡇⣸⠃⣸⠤⠄⣀⡴⠖⣋⣩⣥⡷⢤⡉⠧⠆⡼⠀⣉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠚⠢⣼⣿⣿⣿⣿⣿⡇⢠⠞⣡⣶⣟⣭⠵⠶⣒⣚⣗⣛⣒⡇⠀⠀⠀⠀⠀⣄⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣁⠒⣿⣿⣿⣾⣧⣿⢧⡏⣼⣿⣿⣽⢶⣛⣋⣭⡭⣯⠭⢽⠃⠀⠀⠀⢈⡲⢤⡙⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⡬⣝⠛⡿⢿⢿⣻⢸⡇⡜⢿⣿⣿⣻⣭⡷⠶⠖⡟⠲⢺⣷⣶⣤⣄⣲⣽⣶⡝⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⣞⣾⠉⢻⣧⡼⣾⡟⣼⣷⣜⠦⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⢛⣩⣾⣿⣿⣆
⠀⠀⠀⠀⢠⠖⠦⣄⣇⠀⠘⣇⠀⣸⡏⠀⠸⣼⣿⣿⣿⡷⣤⣉⠀⠀⠀⠉⢉⣉⣉⣩⣭⣥⣴⣶⣾⣿⣿⣿⣿⡿⢿⡆⠀⠀⢀⡀⠀⡀
⠀⠀⠀⣀⣈⣣⣀⠀⢽⣾⣶⣿⣾⣿⣾⣤⢶⣿⣟⠷⣬⡛⠲⢭⣙⠛⠶⠶⠶⠶⠶⠶⠶⠶⢛⣛⣯⣿⣿⣿⣿⡿⣻⣿⠐⢦⡏⠱⡾⢹⣤⢤⡀
⠀⠀⠸⣅⠀⠈⢽⣿⣿⣿⡿⣛⣛⣻⣿⣯⢸⣿⣝⠷⣄⠉⠓⠂⠀⠈⠀⠀⠀⠀⠐⠒⠛⢛⣋⣩⣥⡾⣿⣿⣿⡿⣫⣿⠰⣴⣿⣶⣿⣟⣅⡼⠶⣄
⠀⠀⡴⠚⠛⠓⠺⣿⣿⣯⣾⣿⣿⣿⣿⣿⡞⣿⣟⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣩⣥⣶⡾⣿⣿⣿⣿⣫⡿⢬⣿⣿⣽⣯⣿⣿⠦⠶⣅
⠀⠀⢙⡶⠖⠶⠚⢿⣿⣿⣿⣿⣿⣿⣿⣉⠳⢻⣿⣿⢶⣍⡑⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣥⣤⠶⢾⣿⣿⣿⣿⣿⣃⡤⠾⣿⣿⣿⣿⣿⠣⣴⠚
⠀⠀⠘⠲⣦⠶⠒⠚⢛⡿⠋⢹⡏⠙⡄⠈⣳⣿⣿⣿⣷⣦⣍⣙⠒⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⢶⣿⣿⣿⣿⢿⣿⣿⣯⣤⡞⠁⡾⢻⡟⢱⡦⠼⠃
⠀⠀⠀⠀⠿⠶⠴⣖⣉⠀⣠⣿⣇⣠⣿⣶⣿⣿⣿⣿⣿⣿⣦⣭⣙⡓⠒⠶⠤⠤⠤⢤⡶⠶⠶⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣷⣾⣧⣸⣓⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣯⣝⣛⠳⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠯⠭⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠚⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⡤⠤⠤⠤⠤⠤⠤

⠁⠀⠀⠀⡀
⡄⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠁⠀⠀⠀⠀⢀⡤⠀⠀⡠⠀⢤⡀⠀⠀⠀⡠⡀⠀⣠⢤⠄
⠀⠀⠀⠀⠀⠈⠁⠁⠈⠁⠀⠁⠁⠀⠀⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠤⣄⡄⠠⠢⡀⠀⢠⠄⡄⠀⠠⠄⠀⠠⡤⣤

⠀⠀⠀⠀⠀⠀⠀⠲⡂⠐⠀⠖⠴⡖⠐⠠⠔⠲⠀⠤⠦⠶⠂⠀⠀⠀⢸⠀⡂⠢⢠⠠
⠄⠀⠀⠀⢀⢤⠤⠄⠠⡤⡄⢠⠀⠄⠠⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠛⠁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠴⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠁⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⣀⡀⠀⢀⢀⠀⢀⢀⠀⢀⣀⠈⣁⡀⠀⠠⣀⡀⠀⡀⠀⢀⢀⢀⠀⣀⡀⠀⢀⡀
⠀⠀⡀⡉⠁⠁⢈⠉⠉⠁⡀⠉⠁⠀⢉⠉⢀⢈⣈⢀⠈⠀⠈⡁⠈⠁⡀⠀⡀⠀⢁⣀⠈⠈⠉⠈⡁⡁⠀⠈⠁⡀
⠀⠀⠉⢃⠈⠁⠀⠁⠀⠈⠉⠁⠈⠀⠈⠀⠙⠈⠈⠉⠃⠀⠉⠉⠉⠈⠉⠉⠁⠀⠊⠈⠁⠀⠈⠙⠈⠃⠁⠀⠁
⠀⠀⠀⠀⠁⠐⠙⠙⠃⠙⠂⠀⠂⠙⠛⠀⠋⠛⠀⠑⠀⠑⠀⠘⠛⠀⠐⠚⠃⠁⠉⠛⠃⠀⠋⠓⠚⠓⠚⠉⠁
⠀⠀⠃⠲⠰⠳⠃⠂⠚⠑⠀⠛⠑⠀⠇⠀⠀⠃⠀⠒⠀⠃⠐⠃⠚⠘⠀⠐⠑⠓⠃⠈⠓⠛⠆⠓⠂⠀⠒⠐⠓⠃

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠄⠀⠘⠱⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠀⠀⠀⠓⠛⢁
⠀⠀⠀⠀⠁⠓⡀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⡚⢠
⠀⠠⠀⠈⠀⢠⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⡉⡸⠀⡀
⠀⠀⠀⠀⠀⡤⠀⢤⠀⡻⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠐⠲⠤⡀⢀⠜
⠀⠂⠀⠀⠈⠀⠠⣀⠆⡴⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠆⠄⢀⠀⠠⠒⠁
⠀⠀⠀⠀⠨⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠈⢥⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⡀⠀⠀⢨⠟⢃⠀⠂⠤⠄⠀⠊⠐⡀⠀⠀⡤⢄⠀⠀⠀⠀⠀⡄
⠀⠀⠸⡁⠀⠀⠀⠀⣴⠂⠀⠀⠀⣉⣁⠤⠀⠀⠀⠀⠘⢅⢁⠂⢀⠄⢄⠀⣤⠘⠂⠀⠀⠀⠀⠀⢀⠢⠤
⠀⠀⢘⡇⠀⠀⠀⡶⢗⠀⠀⠀⣀⣀⠀⠀⠄⠀⠀⠀⠖⠂⠠⢤⠞⠀⢀⠈⠁⠀⣀⠄⠀⠀⠀⢤⠀⠑
⠀⠀⢸⠁⠀⠀⠢⣭⠵⠀⡀⠀⠀⠀⠁⠀⢀⠄⠀⠀⠀⠐⢃⣬⣄⠛⢆⠲⠷⠢⠀⠀⠀⠀⠠⠀⠀⢈⣤⡀
⠀⠀⡎⠀⠀⠙⠦⠶⠍⡉⠀⠀⠲⠄⢀⠠⠡⠀⠀⠀⠀⠀⠘⠀⠀⠫⠀⠆⠠⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠉⠲⢶⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁
⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠛⠘⠛⠃⠤⠀⠸⠷⠀⠤⠞⠃⠿⠛⠀⠠⠄⠛⠦⠄⠐⠿⠘⠻⠇⠤⠤⠸⠷⠄⠤⠾⠷⠿⠿⢀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠠⠤⠄⣀⠀⢀⣠⠤⣤⡤⠄⠀⣀⠠⢄⡀⠀⣤⡤⢤⣤⢀⣀⡀⣤⣀⢀⣠⣤⣤⣤⡄⠀⠀⠨⠅
⠀⠀⠀⠀⠀⠀⠒⢀⠀⣓⣀⠐⠂⠀⢛⠀⠘⠛⡀⢛⣃⡀⠚⠉⢐⡊⠁⢚⣉⠐⠚⠉⢘⠋⠁⠛⣉⠘⣋⡁⠛⠋⠁⡀⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣩⠀⠉⣭⠐⢦⡄⠻⣤⠐⢾⣍⠛⢯⡅⠀⣶⠈⢱⡆⠉⢿⡗⠲⣶⠘⢷⡆⠲⣿⠘⢻⡿⣠⣤⡈⣭⣤⢠⣬
⠀⠀⠀⠀⠀⠀⠲⠶⠂⣄⠀⢰⡆⠀⣠⡶⢰⣶⠖⠀⢠⡀⠶⣤⠀⢰⡆⠲⣶⣆⣤⣄⢰⣦⡄⣤⣶⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠉⠁⣉⣉⠈⣉⡁⠉⣉⡉⠉⣉⠙⣉⡁⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠈⠉⠁⠉⠉⢈⣀⡀⣙⡀⢈⣁⠀⢈⠙
⠀⠀⠀⠀⠀⠀⠷⠀⠀⠿⠿⠸⠿⠇⠾⠿⠧⠾⠿⠰⠿⠇⠶⠾⠀⠀⠄⠀⠤⠄⠀⠴⠠⠴⠇⠀⠼⠸⠿⠗⠿⠿⠿⠿⠷⠸⠿
⠀⠀⠀⠀⠀⠀⣿⣦⠀⣤⣀⢸⣿⡇⢿⣿⡞⢿⣿⠘⢿⡇⢻⣿⠈⠀⠀⠉⠁⠸⠃⠀⠸⠋⠀⡟⠀⠸⠟⠃⣿⣿⢶⣿⡿⢸⣿
⠀⠀⠀⠀⠀⠀⣭⣭⠄⣭⡭⠀⠈⠅⠀⠤⠄⠈⢥⠠⢤⡄⠀⢭⢠⣤⡄⠠⣤⣤⡀⣠⢠⣤⠄⣤⣤⢠⡀⠀⠨⡥⠀⠀⣠⠈⠁
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠐⠛⠛⠛⠛⠘⠓⠀⠋⠙⠘⠁⠀⠀⠀⠀⠀⠙⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡀⠇⠀⠀⠀⠸⢀⣀
⠀⠀⠀⠀⠀⠀⠐⠒⠀⣖⣂⠐⠒⠂⠶⠶⢰⣶⣶⣴⣶⡆⣶⣶⠀⠀⣦⠀⢰⡆⢰⣶⠀⣶⡆⣶⣶⠠⡆⠀⠀⢰⠀⠶⠦
⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⢀⣀⡀⠀⠀⠀⣀⣀⢀⣀⠀⣉⢉⠀⠀⠉⢀⣈⠁⣈⡋⢀⣙⠁⡙⢛⠈⣁⠀⢀⣈⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠻⠿⠀⠿⠟⠸⠿⠇⠀⠀⠀⠿⠿⠘⠕⠅⠕⠕⠨⠭⠅⠸⠿⠀⠿⠇⠠⠷⠀⠟⠙⠘⠁⠀⠀⠙⠂⠰⠇⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⠀⢀⡄⠀⠀⢠⣤⣤⢀⣀⠀⢀⡀⠀⣠⠀⢀⣄⠀⡠⢄⢀⡀⠀⣀⢀⠀⠀⠄⣠⣤⣠⣤⣤⢠⣄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠛⠀⠐⠁⠀⠀⠘⡛⡛⠈⠋⠀⠉⠃⠀⠙⠁⠈⠃⠀⠃⠂⠐⠚⠃⠀⠈⠀⠈⠂⠙⠺⠙⠛⠗⠐⠛
⠀⠀⠀⠀⠀⠀⠨⠹⠀⢯⠀⠀⠸⠁⠀⠉⢸⣿⣿⠀⠗⠀⠸⠃⠀⠾⠀⠀⠇⠀⢸⠆⠀⠈


⠀⠀⠀⠈
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠠⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡀⠀⢠⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⣰⣞⣋⣙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⡄⠀⠀⠀⠀⣠⡤⠶⠴⠢⢤⣤⠤⠤⠬⢧⣤⡉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠶⠶⠖⠒⠒⠛⠻⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠢⣹⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠒⠒⠒⠀⠀⠀⠘⠒⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡍⠳⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠁⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣐⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡤⠤⠀⠹⣇
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡄⠀⡤⠀⢠⠲⡀⠀⠁⠈⠁⠘⠒⠄⠀⠀⢿⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠃⡅⡌⠉⢠⠋⠀⢱⠸⠙⢦⡃⢰⠖⠑⡞⢀⡱⠞⡔⠢⣀⠔⡆⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠐⠃⠀⠈⠈⠙⢸⡗⢠⣄⠑⢪⡄⠀⡇⠡⢄⠀⠘⢆⢠⠊⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡀⠔⡆⢠⢰⠈⠂⠘⠃⠀⡀⠑⡄⠀⠀⠇⠏⠁⡀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠳⠤⠡⢠⠀⠢⠤⠌⠘⠒⠀⠀⠘⠢⠃⠣⠤⠤⠇⠀⢧⠃⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⠾⠁

⠀⢀⡀⠀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⣀⠀⢀⡀⢀⡀
⠀⠈⡇⠀⢻⡀⢸⠀⢰⡄⠙⣶⠀⠆⠀⣠⠏⡖⠈⣿⠀⠹⡆⠀⠀⠈⣳⠀⠒⠀⡴⠋⢤⡀⣽⠀⠈⣷⠈⠓⢰⠐⠂
⠀⠀⢷⡀⠸⠇⢽⡀⢀⠀⢀⣿⠀⡶⣰⠏⠰⡆⠀⣿⢸⡄⠀⠀⠀⠈⣷⠀⠀⠈⢧⠀⠞⠁⢾⠀⣧⠀⠀⠀⣿
⠀⠀⠀⠈⠂⠀⠈⠃⠈⠓⠈⠃⠀⠀⠛⠀⠉⠃⠀⠋⠀⠙⠀⠂⠀⠐⠟⠀⠀⠀⠈⠓⠀⠀⠈⠐⠘⠂⠀⠀⠓

⠀⠀⠀⠀⢠⠄⠀⢠⠀⠀⢀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡀⠀⠀⠀⣤⠀⣤⠀⠀⡐⠯⠐
⠀⠀⠀⢠⠏⠖⠀⠈⣷⠘⠃⠀⢸⠁⠲⠀⠊⢹⠀⠰⡀⢨⡗⠀⡛⠀⣸⠇⠉⠁⢸⠁⣶⠀⠂⡿⠀⠟⠀⠄⢳
⠀⠀⢠⠏⢨⡇⠐⢠⡿⠘⠃⠀⠺⠀⠚⠀⠀⠸⣆⠚⠁⢠⠟⠀⠔⠀⣸⠁⠈⠀⢾⡀⠓⠀⠀⢸⠀⣿⠀⠀⢸⠀⠠
⠀⠀⠀⣀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠉⠀⠀⠈
⠀⠀⡄⠙⠂⠠⢦⡀⢰⡆⠀⠰⡆⠀⠀⠀⣴⠀⣰⠃⠀⢰⡆⠰⣇⠀⢐⡇⡀⠀⢧⡀⢀⡀⠀⠀⡶⠀⠀⢧⡀⢀
⠀⢀⡼⢺⡇⠀⢸⠀⣌⠁⠀⠀⡇⠠⡀⠀⡟⢰⡍⣇⠀⢸⡇⣆⠁⠰⣏⠀⡽⠀⠸⡇⠈⠃⠀⢾⠀⡽⠂⢸⡇⠘⠁
⠀⠈⠑⠦⠀⠀⠈⠳⠘⠆⠀⠰⠇⠈⠁⠈⠃⠀⠺⠁⠀⠘⠃⠙⠆⠀⠘⠆⠀⠀⠀⠧⠀⠀⠀⠀⠣⠐⠆⠈⠇⠙⠆⠠
⠀⠀⠀⡤⠀⠀⠀⢤⠀⠀⠀⠀⢠⠄⠠⡄⠀⠀⡤⠀⣠⠀⠄⢀⡤⠀⣤⠀⠀⢀⡤⢠⡄⠠⢠⠀⢠⠄⠀⣤⠀⣀⠠
⠀⠀⠸⣁⡘⠀⠁⠈⢱⠆⠋⠀⢸⡇⠘⡧⠀⠀⣷⠀⢻⠀⠀⢸⡇⠴⢸⡇⠀⠀⢳⡈⠁⠀⠸⠇⡛⠀⠀⢈⡽⠋⡀
⠀⠀⠐⣆⠙⠃⠀⠀⣸⠀⠀⠀⠀⠳⣄⠛⠀⠀⠙⢄⠈⠀⠀⠀⣇⠀⢳⡁⡀⢠⡎⢰⡄⠀⠀⣆⠋⠀⢀⡼⠁⠾

⠀⠀⢦⠀⠲⡀⠀⢀⡇⠀⠀⠐⠃⣠⠜⠁⠀⠀⠀⡀⠀⠈⠀⠀⠀⢆⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠅⠘⢎⠀⠉⠓⡞⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⡍⠀⠀⠀⠀⠀⠀⠳⡀⠀⢠⠇
⢀⠀⠀⠰⡄⠀⣠⡇⣀⠀⠀⢐⠁⠀⠀⠀⠐⣲⠀⠈⢆⠀⠀⠈⠰⠀⠘⢄⠀⣀⣀⠸⡄⠀⠈⠓⡞
⢪⠀⠀⠀⡧⠀⠆⠐⢆⠀⢒⡟⠀⠀⠀⠀⠀⠁⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠇⠀⣀⣸⡇⣀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⣎⠀⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⡄⠐⠌⠁⠀⢣⠀⠘⡇⠁
⠀⢀⠀⡀⠸⡆⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢷⣠⠏⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⡀
⠠⠀⠈⠈⠙⢇⠀⠠⠀⠀⠀⠀⠙⣄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠆⠀⠀⢸⠁⠉⠁
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠠⠀⠀⠈⢷⡋⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠘⢦⡀⠀⣠⠀⠀⠀⡈
⠀⠠⡀⠀⠀⢸⡄⠀⠀⠀⠀⠆⠂⡶⠀⠳⡄⠀⠀⠀⠀⠆⠀⠈⠲⡀⠀⠀⠹⣶⠅⡀⠀⢠⠃
⠀⠀⡸⠓⠂⠘⡇⠀⠄⢦⡀⢀⠎⢀⠀⠀⠹⣄⠀⠀⠀⠰⡤⠂⠀⠀⢄⠀⠀⡈⠀⠈⠂⡌⠀⠀⠀⢀⢀
⢄⡖⠀⠑⠀⠒⡇⠁⠀⠀⢰⠃⠀⠀⠢⠐⠈⠙⣆⠀⢀⣤⡄⠀⠀⠀⠀⠱⡀⠀⠀⠀⣸⠂⠀⠀⣀⠀⠈
⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡸⠞⠉⠀⠀⢤⠀⠀⠀⠀⠘⢦⡀⣰⠏⠉⠋⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠁⠀⢀⡴⠃⠤⠄⠀⢠⠀⠀⢣⡀⠀⠀⠀⠘⣦⠛⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⠋⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⡀⠀⠉⠉⠉⠉⠙⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠈⠙⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣧⣄⡀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠉⠉⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⡙⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠸⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣴⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠁⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⣠⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠋
⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠘⣿⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⢿⣿⠟
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣉⣹⣏⣙⣉⣽⣉⣷⣈⣉⣙⣙⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣤⣵⣮⣴⣿⣦⣼⣿⣧⣯⣥⣭⣭⣧⣬⣭⣭⣥⣬⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠀⠀⠀⠀⢠⣠⠄⠀⠀⠀⠀⠀⢀⡐⠚⢡⡀⠀⠀⠀⠀⢀⠀⠉⠉⢞⠆⡀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⢀⡌⠁⠀⠈⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⢊⣖⠀⠀⢀⣔⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢐⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡇⠀⠀⠞⢊
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠹⠇⠀⠀⠐⠃⠀⠚⠀⠀⠀⠀⠈⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠪⠊⠀⠀⠀⠈⠺⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⢠⠦⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⣤⠀⠀⣾⠁⠀⠀⠐⠀⠶⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠉⣟⠂⠀⠀⢰⣧⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⢈⣉⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠠⠆⢠⣍⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢈⡁⠀⠀⠰⠀⠀⢤⡌⠀⠀⠀⠀⠤⠀⣸⡅⠀⠀⢀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⠀⠉⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⠆⠰⢦⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⠂⠀⠀⣠⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠍
⠀⠀⠀⠀⠀⠀⠀⣘⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣝⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠠⠄
⠀⠀⠀⠀⠀⠀⠠⣭⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡦⠀⠀⠀⠀⠠⠀⠀⣽⡇⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡍
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠀⠀⠀⠀⠀⠀⣀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠼⠀⠀⠀⠀⠀⠀⠀⢸⣷⡘⠂⠀⠀⠀⠀⠀⠐⠂⣼⠇⠀⠀⠀⠀⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⡀⠉⢻⣦⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣉⡀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠌⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠟⠀⠀⠀⠀⠒⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡤⠒⠂⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⠆⠀⠀⠀⠀⠃⠀⢀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣩⠀⠀⠀⠀⠀⠀⢀⡀⢘⢷⠂⠀⠀⠀⠀⠀⡰⣫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⢡⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⢲⡄⠀⠀⠀⠀⠀⠈⣠⠞⠋⠀⠀⠀⠀⡠⠮⠗⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠢⢀⠀⡁⠀⡀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣻⣿⢷⡤⣀⠀⠀⠀⠀⠀⠐⢄⡀⢠⣹⣥⣔⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡶⣦⢳⣱⣿⠿⠿⢯⡀⠀⠀⠀⠀⠀⠁⠀⠀⠏⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣿⣮⡷⠉⠁⠐⢆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡃⣿⢿⣿⡿⣃⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢀⡜⠀⡄⠐⢇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⣤⡄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣠⣄⠀⣭⡈⠀⣰⡈⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠛⠃
⠀⠀⠀⢀⣀⠀⢈⣀⠁⢉⡀⠉⣁⡉⢉⣩⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠉⠁
⠀⠀⢠⡋⠉⠁⠁⢉⡀⠉⣹⠚⠉⢓⠋⢉⡋⠁⠀⠀⠀⣠⣼⠾⣏⠙⣧⠈⣧⢈⣠⠤⠔⠚⠉⠉
⠀⠀⠈⠇⠙⠈⡃⠉⠛⠐⠊⠑⠘⠛⠃⢘⠋⠀⠀⠀⠀⡏⢹⡆⢹⣆⢽⣶⣾⡿⠃
⠀⠀⠀⠘⠃⡈⠛⠆⠛⠛⠀⠞⠛⢆⠘⠀⠶⠀⠀⠀⠀⠸⣿⣿⣷⣿⣾⣿⠛⠁
⠀⠀⠀⠈⠳⠶⡄⠜⠶⠤⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⠨⡝⠃⠀⣚⠠⠌⢹⡻⠦⣥⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡀⠈⢘⠷⢤⣀⣈⣵⡒⠜⢃⡴⠋⣛⣻⣿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡉⠀⠀⠈⠐⠯⢁⠵⠔⣩⡿⠙⠈⠉⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢶⣴⠀⢳⢉⣶⢻⡇⢠⡴⠖⠚⠩
⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⣀⠀⠀⠐⢀⣺⣖⢂⣸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣦⡙⠛⠟⠀⢸⡏⠀⠀⣠⢤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢉⠛⠳⠛⠛⢻⡯⡹⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡤⡼⠧⠤⠞⠛⠉⡇
⠀⠀⠀⠀⠀⠤⠀⠐⣷⠀⠁⠀⠒⢄⢚⡄⣿⡝⠯⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⣄⠠⢀⡀⠀⠀⠀⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠝⠻⣦⡵⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡛⠊⠿⢶⣥⠴⡧⠤⠆⠂⠈⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠓⠀⠀⡠⠀⠳⡟⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠅⠀⠀⠈⣀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣦⡇⢀⢓⣶⣾⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⡤⠀⡶⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡴⠋⠉⡿⠀⠀⠀⠀⠀⡴⠊⣉⡿⠀⠀⠀⢠⡞⢩⡉⠉⠑⣦⠀⠀⠀⠀⠀⣟⠉⠱
⠀⠀⠀⣀⣀⡀⢠⢿⢀⡀⠀⠀⠈⠃⠀⠾⠒⢶⡀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠈⠃⣘⠀⠀⠀⣼⠀⠀⠀⢀⡴⠚⠃
⠀⠀⠀⠀⠀⡰⠋⢻⠉⠀⠀⠀⠀⢸⠄⠀⣀⡾⠃⠀⠀⢧⡀⠀⠀⢐⡦⠀⠀⠀⢠⣇⣠⠴⠞⠁⠀⠀⢀⡏⠀⠀⠀⡤
⠀⠰⣤⡴⠞⠁⠀⠘⠦⠄⠀⠀⠀⠲⠒⠛⠉⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⢼⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠔⠒⡒⠒⡻⠃⠀⠀⣠⠖⠋⠉⠟⠀⠀⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⡽⠀⠀⠀⠀⠴⠊⡧⠉⠀⠀⠀⠈⣿⢀⡴⠓
⠀⠀⢀⡼⠴⠀⠀⠀⠀⡜⠁⠀⣤⠦⠀⠀⠀⡰⢲⡷⠤⡿⠎⠀⠀⠀⢰⠇⠀⠀⠀⠀⡀⢰⠗⠆⠀⠀⠀⠀⣿⠋
⠀⠀⢩⠇⠀⠀⠀⠀⠸⣄⠀⡾⢁⡼⠀⠀⠀⠁⣸⠃⢀⣇⣀⠀⠀⠀⢼⠀⠀⠀⢠⡋⣠⠞⠀⠀⠀⠀⠀⣰⠋⠱⣀⡔
⠀⠠⠿⠀⠀⠀⠀⠀⠀⠙⢿⣟⠋⠀⠀⠀⢀⡴⠃⠀⠈⠋⠁⠀⠀⠀⠘⠋⠀⠀⠈⠛⠋⠀⠀⠀⠀⢀⡴⠃⠀⠀⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠁⠀⠀⠀⢀⡀
⠀⠀⠀⡜⢹⠇⠀⠀⠀⣼⠉⣷⠀⠀⣠⡔⠈⠁⠀⠞⢋⠓⡄⠀⠀⢀⠴⠋⠀⠀⡴⡯⠁⠈⡆⠀⠀⠀⢀⡴⠊⠁⠈⢷
⠀⠀⣸⠴⠋⠀⠀⠀⠀⠈⠸⠈⣆⡾⢁⡇⠀⠀⠀⠀⣼⠀⠘⡄⢠⠂⠀⠀⠀⢀⡞⠀⠀⡼⠀⠀⠀⠀⣾⠀⡔⠀⣠⠟
⠀⠈⢹⠀⠀⢀⠆⠀⠀⠀⡇⠀⠛⠀⠘⣧⠄⠀⠀⢠⣇⠀⠀⠘⡏⠀⠀⠀⠀⢸⣀⣠⠞⠁⠀⠀⠀⠀⠀⣰⠥⠞⠁
⠀⠀⢸⣤⠴⠋⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣇⡀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡉⠁
⠀⠀⢠⠞⠉⠈⢷⢴⠀⠀⠀⣠⠖⠋⠉⢙⡟⠀⠀⠀⢠⠖⠋⠉⠙⠁⠀⠀⣴⠟⠉⢉⠉⠉⠋⠁⠀⠀⡹⠃⠀⢠⣿
⠀⢠⡏⣀⣀⡀⡸⡘⠀⠀⠈⠃⣰⠀⣀⠞⠀⠀⠀⠀⠘⠓⠶⠦⢤⣄⠀⠀⠉⠀⠀⡖⠀⠀⠀⠀⠀⢰⠃⠀⠀⣸⠇
⠀⠘⣟⡳⠤⢘⣷⣁⢀⡀⠀⢠⡇⠲⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢺⣀⣀⡴⢻⣄⡴
⠀⠀⠈⠉⠉⠁⠀⠉⠉⠀⠀⠘⠧⠄⠀⠙⠶⠶⠃⠀⠀⠻⠒⠋⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠠⠚⡇⠀⠀⠀⡠⠊⠀⠀⢹⠀⠀⠀⠀⠈⣻⠀⠘⠉⠉⣷⠀⠀⡴⠋⠁⠀⠈⡏⠀⠀⡏⠀⠀⠀⠚⠉⠉⠉⣩⠟
⠀⠀⠀⣥⠀⢠⡞⠁⠀⠀⠀⡄⠀⡔⡦⠀⢀⠏⠀⠀⠀⠀⠸⣄⠞⠀⠀⠀⠀⠐⡇⠀⣸⠃⠀⠀⠀⠀⠈⣩⠟⠙⠁
⠀⠀⠀⢸⣰⡟⠀⠀⠀⠀⢰⠀⢸⡴⠃⢀⠎⠀⠀⡀⠀⢀⡴⢻⡄⠀⠀⠀⠀⠀⠛⠚⣻⠤⠤⠀⠀⢀⣜⣁⣀⣀⢉⡹
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠘⠗⠋⠻⠞⠁⠀⠀⠀⠈⠛⠋⠀⠀⠙⠶⠖⠀⠀⠀⣠⠋⡙⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⣰⣃⠸⠇⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠘⠁⠀⠀⠀⢰⠀⣟⢉⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠹⣤⠀⠴⠿⠅
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠃⠀⠀⠀⢸⡈⢷⡁⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠂⠉⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⡤⠀⠀⠀⠈⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠆
⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⡄⠀⠀⡠⠂⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⡑⣐⠎⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆⠖⠀⠀⠀⠀⣠⣿⡃⠀⠀⠀⠀⠘⣦⠁⣀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠄⠙⢋⠀⠀⢠⡆⠛⠀⠀⠀⠀⠙⡿⠟⠁⠀⠀⠀⠐⣆⡍⠉⠀⠀⠀⠀⠀⠀⠧⡀⠂⠁
⠀⠀⠀⢀⠀⠀⠀⢀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠸⡇⢴⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢼⣖⡤⠶⡟⠁⠀⠀⠈⠈⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⣀⠀⠀⠀⢀⠔
⠐⢤⣤⣄⡀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠢⡧⠃
⠀⠀⠙⠂⠀⢈⡢⡄⠀⠈⠀⣾⢓⡄⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠉⠻⣄⠑⢀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢬⡙⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠠

⠀⠀⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢃⠀⢠⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⣠⠖⠂⢉⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠦⠄⠀⣴
⠀⠀⠈⡄⠀⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⡀⡎⠀⠀⠠⢴⠋⠀⣀⠴⠟⠀⠀⠀⢀⡀⠱⠶⠄⠀⣒⡲⠔⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠴⠀⡀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡇⠀⠶⢅⡀⠀⣱⠛⠁⠀⢰⠃⠀⠈⠠⠀⠈⠀⢀⠂⠁⠀⠈⠀⠀⢀⠂
⠀⠀⠀⠀⢱⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠄⠐⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠀⠀⠀⠀⠀⠈⠀⠀⠡
⠀⠀⠀⠀⢀⠷⠊⠉⠭⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠄⠀⢠⡶⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢦⠂⢀⠤⠒⠒⠚⢆⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠸⠎⢀⠄⠐⠀⠉⠙⡄⠀⠀⠀⢀⠀⠀⠘⠀⡄⠀⠀⢠⠀⠀⢸⠀⠀⠆⠀⢀⡇⠀⡤⠀⠀⠀⡓⠀⢼⣷⡆⠀⠀⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠻⠁⡠⠒⠊⠉⠁⣇⠀⠀⠀⢸⠀⠀⡇⠀⣇⠀⠀⢸⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠂
⠀⠀⠀⠀⠀⠀⠙⢤⢀⠀⡠⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢀⡀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠠⢄⡀⠐⠋⠁
⠀⠀⢀⠀⣀⠙⠀⠀⡇⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠤⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⢈⢺⡇⠀⠀⠀⠄⠂⠀⠀⡀⠀⠠⣌⠀⢉⢢⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠜⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⣄⣉⣉⠉⠉⠉⣩⡝⢛⢛⠉⠋⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡐⠐⠉⠀⠈⠀⠘⠀⢄⠉⠀⢌⠀⠈⠁⠀⠀⣁
⠀⠀⠀⢀⠀⠀⠐⠒⠀⠀⠀⠜⠀⠀⠀⠠⠜⠉⠉⠀⠉⢷⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢁⠈⠠⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⠆⠀⠀⡀
⠀⣁⠰⠀⣅⠀⠀⡁⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠙⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡁⠂⠠⠌⠙⠁⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢤⠀⢄⠀⠀⡀⢠⠄⠁⠀⠀⠲⠀⢠⠀⠀⠀⠀⢦⣈⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠂⠀⠀⠐⠔⠀⠈⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠑⠈⠒⠘⠂⠀⠀⠠⠀⠠⠈⠀⠈⠀⠀⠀⠀⠀⠛⠥⣴⣀⣀⣀⡩⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠋⢉⣉⣉⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠈⠉⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢀⡴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⠃⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠳⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠚⠛⠉⠁⢀⣀⣠⣴⠾⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⡶⠶⠾⠛⠛⠉⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠾⠛⠋⠉⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠀⢹⡀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⡴⠛⠛⠳⡄⠀⠀⠀⠀⠘⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣀⣤⣤⣀⠀⣼⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠠⣴⡏⠀⢀⣿⣿⡿⠓⠦⣾⡃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣤⣼⣿⣿⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⣫⠟⠻⣧⣀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠠⡇⠀⠀⢀⡿⠙⣿⠋⠉⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠙⠶⠶⠋⠀⣴⠛⠛⠲⢤⠀⠀⠀⠀⢀⣼⠃⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⣿⠀⠀⢨⡿⠶⣤⣀⣠⠞⠁⠀⠀⠀⢸⡇⣀⣤⠾⠋⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⣿⠀⢠⡟⠀⠀⠀⠈⣿⠀⠀⣀⣤⡴⠾⠛⠉⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⣿⠀⢹⠀⠀⠀⣀⣤⡿⠶⠛⠉⠁⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠂⠴⠞⠁⠀⠀⡇⠀⠀⢿⣤⣼⠶⠞⠛⠉⠀⢀⣠⣤⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⣿⣿⣶⣶⣶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠄⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠐⠤⠐⠓⠒⡉⠁⠐⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠁
⠀⠀⢘⠃⢀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋
⠀⠀⡬⠂⠁⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠤⠔⠛⠁⠀⠀⠀⠠
⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡐⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢀⡷⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠠⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠁⢠⡄
⠀⠀⠀⠀⠀⠀⣀⠀⢔⠀⠀⠁⠀⠀⠀⠀⡴⠀⠰⠀⠀⢁⡀⢠⡄⠰⠦⡚⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠂⠀⠀⠀⢠
⠀⠀⠀⠤⠈⠓⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣀⠜⠂⢈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⣠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⣀⠵⠿⠁⡁⠉⠐⠂⠈⠁⡄⠀⠀⠀⠀⠀⠁⠆⢡⢘⣁⠁⠰⢀⡀⠰⠆⠸⠇⠀⠀⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠁⠁⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠁⠈⢣⠀⠃⠀⠀⠁⠀⠀⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⡂⠐⠈
⠀⠀⠀⠈⠀⠀⠀⠂⣀⠠⢌⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠢⠂⠐⠢⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠐⠀⠁⠀⠀⠀⠀⠤⠀⠀⠠⡀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠢⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐⠀⠓⠈⠂⠈⠀⡀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠈⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⡠⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠃⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⡠
⠀⢶⣟⣛⡧⡄
⠀⢐⣏⣭⣯⠃⠀⠀⠀⠀⠀⠀⢀⡽⣿⣍⣀⠀⣀⡀
⠀⠠⢯⡧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⣻⣯⣟⢥⣿⡄
⠀⠈⠫⠯⠇⠀⠀⠀⢿⠂⠀⠀⠀⠀⠀⣻⣿⣟⢯⠀⠀⣦⣄⣴⠆⠠⢵⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡲⠀⠀⠀⠠⠂⠹⣿⢹⣛⡢⣀⠀⠉⠀⠀⠀⠠⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡡⠀⠀⠀⠀⠀⠀⠀⠩⣫⣹⣟⠆
⠀⠀⠀⠀⡀⠀⠀⠀⠘⣅⣀⠀⠀⠄⡀⢄⣀⢀⢙⠻⢟⣿⣠⣄⡀
⠀⠀⠀⢠⣁⢀⡀⠀⠀⢼⣿⣻⣮⣧⡤⣤⠀⡀⢞⠰⠳⠟⠙⠽⣣⡤⠄
⠀⣄⣠⣔⡶⣶⢆⠀⠀⠘⢿⣾⢯⡿⢗⣾⡷⣄⠄⠤⢀⠀⢀⡀⠀⠀⠀⠁
⣸⡯⢑⣺⣛⣽⣿⡄⠀⠀⠈⢛⠛⠚⢟⣛⣿⣷⣛⣶⠁⣁⣀⠁
⣵⡿⠾⣿⣯⣻⣙⣗⡀⠀⠀⠈⢹⣮⡉⠻⢿⡿⠟⠳⣯⣖⣧⣽⣤⣀⡀
⣿⣯⢯⣾⣾⣿⣭⣿⣿⣦⣦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣯⣿⣵⣵⣷⡀⠀⠀⠀⠀⠀⠀⠚⢦⡄
⣿⣿⣿⡢⠍⠽⡮⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉
⣿⣿⣿⡾⢓⣆⡀⠉⠉
⣿⣏⠽⠀⠀⡿⠃
⣿⡯⣿⣷⡖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⡿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠉⠙⠉⠉⠁⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠀⠐⣿⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣯⣤⣠⣿⡆⠀⠀⢠⢀⠄⢀⣰⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢫⠏⡙⠉⠉⢋⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢿⣶⣶⣶⣶⣶⢾⣾⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⣸⣡⣇⣸⣠⣆⣰⣸⣃⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠿⡟⢛⡻⣿⣻⣛⡟⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡿⣾⣷⣿⢿⣷⢷⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣇⣣⣇⣾⣸⣸⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣟⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣟⣛⣻⣛⣛⣛⣛⣛⣛⣛⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣟⣛⣛⣿⣟⣛⣛⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡿⢃⠀⠀⣿⣉⡇⠀⣴⡟⠉⠁⠀⣿⡏⠑⡀⢸⣿⠀⠀⢸⣿⠀⠀⣰⡟⠉⠁⠀⣼⡇⢀⠀⠀⣾⡇
⠀⠀⣾⡗⠺⡀⠀⣿⣁⡱⠀⢻⣇⣀⡀⠀⣿⣇⡠⠃⢸⣿⠉⠀⢸⣿⠉⠀⠻⣧⣀⡹⠀⣿⡏⠉⠄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣦⠀⢰⣆⡠⠀⠀⣴⡄⠀⠀⣶⣄⠀⣠⠀⢠⣶⡀⢠⠀⢠⡴⠢⡄⠀⣴⡒⢆⠀⣤⠖⠢⡀⢰⡖⠢
⠀⠀⠀⣿⠀⢸⡿⢄⠀⠀⣿⡇⠀⠀⣿⠀⠛⢠⠀⢸⣿⠱⣼⠀⣿⡇⠀⡸⠀⣿⡗⠊⠀⣿⠀⠀⡇⢸⡷⡎
⠀⠀⠙⠋⠀⠘⠋⠀⠁⠀⠛⠓⠂⠀⠛⠀⠀⠈⠀⠘⠋⠀⠈⠀⠈⠛⠊⠁⠀⠛⠁⠀⠀⠉⠓⠛⠀⠘⠃⠈
⠀⠀⠀⠀⣠⢄⠀⠀⢤⡤⠀⠀⣄⠀⠀⢀⡀⠀⢀⠀⣄⠀⢠⡄⠀⠀⢀⡀⢀⠀⢠⡀⠀⡀⠀⠠⣤⡀
⠀⠀⠀⠀⢿⣤⠀⠀⢸⡇⠀⠈⣿⠀⡄⠈⢿⣄⠆⠀⢹⣆⠜⣷⡌⠀⠈⣷⡃⠀⠈⢿⡜⠀⠀⣰⡟
⠀⠀⠀⠀⠤⠽⠁⠀⠸⠇⠀⠀⠻⠤⠃⠀⠈⠟⠀⠀⠀⠻⠀⠹⠀⠀⠜⠉⠿⠄⠀⠸⠇⠀⠰⠿⠤

⠀⠀⢸⡇⠀⠀⠈⣿⠄⠀⢈⣷⠀⠀⣠⣾⠀⠀⣿⣉⠀⠀⡜⡁⠀⠀⢉⣿⠃⠀⣿⣽⠀⢐⠁⣷⠀⢰⡏⢣
⠀⠀⢸⡇⠀⢀⣼⡏⠀⠀⣈⣿⠄⠐⠓⣿⠂⠀⢁⢈⡇⠀⣿⣉⡇⠀⣼⠏⠀⠰⡉⣿⠄⠀⣽⠏⠀⢸⣇⡸
⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠉⠁
⠀⠀⠀⢀⣤⠀⠠⣄⠀⢀⠀⣠⡄⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣢⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢸⣇⠀⠀⣿⠀⠈⣼⠏⡀⠀⠲⣿⡗⠀⠲⠾⠷⠀⠈⠉⠁⠀⣼⠏⡀⠀⢹⣧⠀⠀⢣⠀⠀⡜
⠀⠀⠀⠀⠛⠀⠘⠋⠀⠈⠋⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠙⠋⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡤⣄⠀⠀⡄⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡟⠀⢠⣷⡟⣟⠀⠀⢰⠏⠀⠀⡇⠀⢠⡿⠁⠀⢠⡧⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠁⠀⠀⠛⠻⠋⠀⠀⠸⠀⠀⠀⠇⠀⠀⠳⠀⠰⠟⠁⠀⠉⠀⠉