Deli Emojis & Symbols

⠀⠀⠀⠀⠀⣠⠔⠐⢉⣷⠂⠀⠀⠀⠀⠀⠠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠠⠊⠀⠀⢀⢨⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⢲⢀
⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡡⠤⠂⠀⠘⠾⡧⡇
⠀⠀⠤⠤⠄⠉⠀⠒⡂⠄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠀⠀⠐⠦⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠾⠡⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢠⠃⠑⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⣠⠬⠂⠂⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠠⠃⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡃⢰⠁⠀⠀⠈⢳⠪⠥⠀⡖⠂⠤⠖⠀⠀⢀⡴⠛⠁⠈⠉⢲⢄⡔⠁⠠⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠒⠁⢀⡀⣠⡤⠂⢠⠂⢠⠃⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⡪⠟⢣
⠀⠀⠀⠀⠀⠀⠀⠎⠀⣴⡍⠉⠉⠀⢀⡰⠀⠁⠀⠀⠀⠀⠀⠰⢬⣳⣶⣦⠤⠊⣡⠜⠁
⠀⠀⠀⠀⠀⠀⢸⡄⢸⠁⠀⠀⠀⠀⠉⢿
⠀⠀⠀⠀⠀⠘⠻⠃⠈⢦⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣴⣾⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠤⢤⡀⠒⠲⢄⡒⠢⢀
⠄⠉⡉⠛⠢⢄⡀⠈⠑⠀⢀⠙⠲⣤⠀⠀⠙⠳⠦⠄⠉⠲⢄⠀⠆⠀⠀⠀⠀⠀⢈⠀⠀⠀⡈
⠭⢂⠀⡐⠀⠀⠈⠢⣄⠀⠈⠂⣤⠀⠙⠺⣆⠀⠀⠀⠢⠠⢤⡷⠐⠀⠀⠀⠀⠀⠀⠒⠄⠀⠘
⢚⠊⡁⡄⢰⠑⠀⠀⢈⠀⠀⠀⠀⡅⠀⠀⢸⠀⠀⠀⠑⠀⠀⡆⢀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠌⢀⡁⠀⠀⡨⠀⠀⣀⡠⠁⠀⠠⠷⠀⠀⠈⠒⠀⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢐⠠⢼⣁⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡀⣀⡤⠑⠒⠪⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡁⠠⡆⢐⢀⣜⢒⡪⠟⠈⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠈⠐⠆⠀⢀⠀⣰⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⣠⢠⣜⣢⠤⠝⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢐⢦⡀⢀⡄⠀⠀⠀⠈⣷⡽⠁⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠘⠦⡎⠀⢀⡜
⠀⠀⠀⠀⠲⠛⠋⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠈⠢⣌⡟⠶⠦⠤⠴⣪⡿⠁⠀⠀⠀⠀⠈⠀⠀⠚⠀⠀⠀⠀⣠⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⡐⠦⣀⠈⠙⠛⠛⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠈⠉⠀⠀⠀⠀⠀⣼⣮⡓⠢⠤⠬⠁⣀⣂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢱⡆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡒⠻⠿⠿⠷⠶⠶⠬⡝⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠢⠇⠀⠀⡄⠀⠛⠑⠀⠇⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠀⢀⢀⣀⠀⠔⠓⠈⠉
⠀⠀⠀⠀⠀⢤⠀⠀⠀⠙⠀⢂⠀⠀⠈⠀⢀⠀⠧⠄⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢇⠀⠀⠀⠀⠙⠒⠒⠒⠋⠉
⠀⠀⠐⢀⠀⢤⣉⣀⠀⠀⠀⠀⠉⠉⠀⠀⠰⠊⠀⠀⢂⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠀⠀⠉⠂⠄⡀⠉⠻⢖⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⠀⠀⡀⢀⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⠀⠀⠐⡂⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⠀⡀⠠⠀⢠⠚⠔⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⡇⠀⠀⣀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠓⠚⠋⠒⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠁⡀⠀⠈⢶⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⣄⠑⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢆⡀⣀⠈⠑⠒⠛⠓⠒⠻⠤⠤⠖⠋
⠀⠀⠸⢀⡀⠀⠀⢀⣀⣠⣬⡷⠦⠤⠀⠀⠀⠌⠀⠐⠚⠿⠏⠀⢠⠤⠄⠐⠊⠳⣄⠀⠀⠈⠑⠛⠋⠉⠁⠈⠂⠛⠋
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⢀⠈⠀⠀⣤⡐⠀⠀⠀⢀⡀⠄⠂⠀⠀⢀⣠⠖⠁
⠀⠀⠀⢀⠴⠿⠒⠠⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⣡⠎⠀⠀⠀⠛⣭⡤⠶⣞⡉⠀⠀⣀⡴⠚⠉⠀⠀⠀⡀⠀⢀⣀⡀⠀⣀
⠀⠀⠀⠈⢥⡢⣠⣀⡀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠈⠉⠒⠂⠚⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠽⠖⠋⠁⠠⢤⡀⠐⢧⠀⠙⠂⠀⠡⠀⠰⡎⡀
⠀⠀⠀⠀⠀⢐⠊⠁⡀⠈⠑⡀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡄⠀⠸⠀⠀⢁⡰⠃⠃
⠀⠀⠀⠀⡤⠤⠤⠀⠀⠀⠠⠤⠤⠀⠀⡀⠀⠀⠀⣤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣆⠀⣠⡷⠖⠋⠁
⠀⠀⠀⠀⢢⡠⢀⡤⠤⠒⢂⣍⣉⣱⣶⠌⠀⠀⠀⠑⠙⢟⠰⣦⢤⡀⠀⠀⠀⠀⢦⡀⠈⠁⠀⠀⠀⠀⠀⣲⠀⠀⣀⣀⡰⠷⠞⠛⠉⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠁⠀⠀⠀⠀⠁⠀⠀⠈⠓⠒⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⢾⣉⡇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣤⣄⠀⠀⠀⠉⠀⠀⠀⠀⠈⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠘⢧⠿⠁⠀⠐⣿⣿⠀⠀⠀⠀⠀⠙⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡟⠀⠀⠀⠉⠙⠛⠿⣶⣦⣤⣀⠀⠀⠀⠀⠙⠛⢠⣤⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⣴⡾⠛⠛⢷⣦⠀⠀⠀⠈⠉⠛⠻⢷⣶⣤⣄⡀⠀⠀⠀⠀⡶⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣧⠀⠀⠀⣿⡄⠀⠀⣀⣀⡀⠀⠀⠀⠉⠛⠻⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠙⢷⣄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⡀⠘⠿⠾⠟⠛⠛⠛⣷⡄⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣤⣄⣀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⡀⠀⠀⠀⠘⣿⡀⢀⣤⡶⠿⠛⢷⡄⠀⠀⠀⠈⠙⠛⠿⢷⣶⣬⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⡀⠈⠛⠛⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠉⠛⠻⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⡀⠀⠀⠀⢿⣄⣠⣴⠿⠛⠉⠉⢳⣄⠀⠀⠀⠀⢻⡏⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⣌⣛⠋⠁⠀⠀⠀⠀⠀⠙⢦⣀⠀⢀⣾⡧⠤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⣤⣄⣀⠀⠀⠀⠉⠛⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢶⣦⣄⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣾⠇





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢿⠛⡿⢻⡿⢻⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠛⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠿⠟⣿⣿⣿⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢉⣁⣴⡂⠀⠀⢰⡀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣻⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠇⣾⣿⣦⢰⣶⣶⡄⢰⣾⣿⣷⠄⣾⣷⠸⡄⠀⠀⠀⠀⣿⣿⣿⣿⡿⣼⠋⠉⢹⡟⠉⠙⢻⣿⣭⣯⣻⣿⡋⠉⣧⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣷⠏⠉⠁⠉⠉⠉⠉⠋⠿⠻⠟⠿⠿⠻⠿⠻⣾⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣄⡀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢤⢆⡀⢀⡤⢼⡦⣄⠰⢀⡀⠀⠠⠎⠀⠀⠈⢁⠀⠀⠠⠶⠀⠝⠂⢀⠀⠀⠀⠸⣧⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠐⠀⡷⠊
⠀⠀⠀⠦⠄⠸⢅⡀⢄⠠⠠⠾⠀⠀⠀⠘⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣼⠗⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡄⢄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣼⠟⠁
⠀⠀⠀⢀⣀⣄⣄⣀⠆⡰⠀⠀⠀⠀⠈⠁⠀⡀⣄⠀⠈⢠⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠰⣄⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⢪⡭⠖⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠗⠘⠗⢸⠀⠀⠀⠘⠂⠂⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠄⢘⠉⠩⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠁⢀⡀⠤⡀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣄⠀⣨⡅⠀⠀⠀⠀⠀⠀⡀⠠⠀⢄⠀⠀⠀⠀⢀⠒⠖⠲⢦⣷⡼
⠀⠀⠀⠀⠀⠀⠒⣲⠀⠀⠀⠈⠀⠀⠀⠀⠈⠓⢬⣦⣀⠀⠀⠀⠀⠁⠐⠬⠅⠤⠟⠀⠀⠀⠀⢀⣠⠚⠱⠀⠖⢈⣤⠀⠀⠀⠀⡀⠀⠛⠉⠁
⠀⠀⠀⡀⠤⠴⠦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣌⣻⣾⣛⣧⠙⣩⣿⠟⠀⠀⠐⠦⠾⣦⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠐⠀⡂⠀⠀⠀⢀⡀⠀⣤⠀⠰⢶⡲⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠃⠚⠃⠀⠀⠀⠈⠁⢠⣴⣷⣦⣼⣿⣿⠃⠀⠀⠰⢗⢦⣤⣀⡀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⠽⠛⠁⠀⠀⠀⠀⠘⠷⣕⣬⡙⠲⢦⣄⠀⠀⠛⢆⣈⠁⣄⡀
⠀⠀⠀⢤⣀⣐⡒⠀⣴⢁⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣌⡓⠠⣌⣓⠀⠀⠀⠙⡀⠘⠋⠑⠦⣀⡀
⠀⠀⠀⠈⠚⠫⠭⠆⠐⠃⠘⠉⠁⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠐⠦⠤⠶⠤⠴⠶⠤⠶⠀⠀⠀⠀⠀⠉⠓⠦⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⡸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠀⠂⡀⠀⠁⠀⠀⠉⠐⠒⠁⠈⠁⢀⠀⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⠐⠀⠀⣀⣄⣠
⠀⠀⠀⠀⠀⠀⠦⣭⣕⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⡈⠀⣀⣠⣶⣻⡣
⠀⠀⠀⠀⠈⠂⡀⠂⣼⠉⢠⡴⡒⣦⡤⣄⠀⢀⣀⣀⣀⣀⡀⣡⣠⣶⢦⡒⠛⣷⠌⠚⡽⣷⡄
⠀⠀⠀⠀⠀⠀⣥⣄⣘⠷⠾⣿⣿⣿⡶⠀⠐⠀⢒⣽⡾⠩⠀⠁⡉⠉⣼⢷⡒⠶⠂⡁⡠⠜⠉
⠀⠀⠀⠀⠀⠑⠂⠘⢝⠛⠑⠲⠆⠴⠭⠭⠨⣩⣉⡉⠉⢀⣨⠿⠗⠆⡒⠝⠂⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠒⠒⠒⠒⠒⠒⠛⠁⠛⠀⠈⠁





⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣛⣉⠀⠈⢉⣉⣉⠙⠛⠛⠒⠲⠶⠶⠤⢤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠋⠉⠀⠀⠻⠞⠃⠀⢯⣥⣭⠗⠀⠀⠀⢿⡽⠆⠀⢀⣠⡴⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠗⠶⠶⠤⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢰⣖⣦⠀⣀⡤⠖⠋⣁⣠⣾
⠀⠀⠀⠀⠀⠀⠀⢸⡦⢤⣤⣀⣀⡀⠀⠈⠉⠉⠉⠛⠛⠒⠲⠶⠶⠶⠛⣉⡤⠖⠋⠉⢀⣘⣇
⠀⠀⠀⠀⠀⠀⠀⡾⠀⡀⠀⣠⣍⠉⠙⠛⠒⠲⠶⠤⢤⣤⣤⣄⣠⡴⠚⠉⠀⢀⣸⡟⠉⣹⠉
⠀⠀⠀⠀⠀⠀⠀⢹⣋⡙⠚⠁⠸⣇⣠⡴⢦⣀⣤⣀⣠⠀⠀⢀⠀⢀⣀⡟⢳⣾⣴⠖⠋⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⠛⢲⡾⠧⢤⣤⣉⣀⣉⡈⠳⠖⠋⠙⣛⣥⣞⠋⣱⣃⡤⠖⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠛⠓⠶⠶⠤⣷⡀⢀⣀⣤⠬⠟⠛⠉⠙⠛⠛⠉⣀⡼⠟⠋⢡⣦⠴⢶⠷
⠀⠀⠀⠀⠀⠀⠀⢷⡴⢦⣤⠞⢳⡄⠉⢉⡉⠉⠛⠛⠒⠒⠶⠶⠶⠚⠁⣴⣄⣴⠚⠃⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⠀⠈⠳⠚⠋⠙⠶⠛⠒⠻⣄⣠⡴⢦⣴⠖⠃⣈⣥⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠶⠤⣤⣤⣀⣀⣀⣀⠀⢀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⢤⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡚⣮⠧⠐⠳⣍⠇⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣹⣶⣾⣶⣈⣶⣳⡆
⠀⠀⠐⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⢲⣤⡦⢼⣤⣴⣶⣦⡞⢳⠀⣿⡿⣟⠛⣟⣻⣿⣏⠘⠛⠉⠉⢻
⠀⠴⠶⠆⠒⠒⢠⠀⠤⣐⣢⣤⣤⣴⣆⡀⠀⢀⣀⣀⣀⣧⣾⣗⣶⣺⣿⣏⣥⣌⣵⡞⢰⣿⣇⣿⣶⣿⣿⣿⣿⢀⠀⠀⠀⠀⣧
⠀⢠⠤⢀⡠⢚⣿⡿⠛⡻⠋⠳⡹⢿⣟⣫⣙⣉⣩⣙⢻⣿⡟⣛⣛⣿⣿⣛⣉⣻⣿⣿⣼⣿⣟⣿⣿⣿⣿⣿⣿⣼⣄⣀⣠⣶⣼⣆⡀
⠀⠐⠛⠒⠓⠛⠛⠓⠚⠒⠒⠒⠛⠉⠙⠋⠉⠉⠉⠉⠋⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠙⣿⣿⡛⠛⠛⢿⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⡿⠛⠛⠻⢿⡟⠀⠀⠀⠩⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋
⠀⠀⠀⣿⣿⡇⠀⠀⠀⢹⣿⣷⠀⣠⣤⡄⠀⣿⣿⣗⣀⣀⣤⡄⠀⣠⣤⡀⠀⣿⣿⡇⠀⠀⠀⣤⣤⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠙⠿⠃⠀⣿⣿⡏⠉⠉⠙⠁⠀⠻⠿⠃⠀⣿⣿⡇⠀⠀⠀⠻⡟⠁⠀⠀⢸⣿⣿
⠀⠀⢀⣿⣿⣃⣀⣀⣤⣿⡿⠃⠀⠀⠀⠀⢀⣿⣿⡇⣀⣀⣀⣤⣦⠀⠀⠀⢀⣿⣿⣇⣀⣀⣠⣤⣶⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠙⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠋⠉⠉⠉⠙⠛⠛⠋⠁⠀⠘⠛⠛⠛⠛
⠀⠀⠀⣠⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⢠⣭⣽⣿⡅⠀⢀⣠⣤⡀⠈⠁⠀⠀⠀⡄⢠⠄⠀⢀⡤⢤⡀⠀⠀⠀⠀⢠⡭⣾⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠐⢿⡟⠛⠃⠀⣿⠃⠀⢻⣀⣀⠠⠀⠀⠁⠀⢀⡄⠘⢠⠀⡄⠀⠠⠀⠔⠀⠀⠀⠹⣿⠀⠀⣶⠒⢶⡄⠀⠀⠀⠈⠁
⠀⠀⠐⠴⣌⣛⣽⠀⣿⡄⠀⠀⡈⠁⠀⠀⢀⠀⢌⠉⠈⠀⡰⢶⠁⢀⠁⠀⠀⠀⠀⠀⠀⠋⢈⠀⣿⠀⢸⡇⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⡀⠀⠀⠑⠮⢶⠬⠽⠖⠀⠀⠈⠳⢤⣄⣀⣀⣀⣤⠴⠞⣀⠭⣄⠘⠁
⠀⠠⡇⠁⠀⠀⠀⠀⠀⡀⠀⠐⣀⠀⠐⠎⠑⢠⣤⠒⢂⡔⡤⠄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠺⠁⠉⡉⠆
⠀⠀⠀⠀⠀⠀⢠⡀⡈⠰⠄⣠⠤⠤⢿⣿⠟⠛⠛⠘⠠⠜⠀⠀⠀⠘⡀⠀⠀⠀⡀⢤⢴⠞⢿⡍⠀⠀⢀⠉⠚
⠀⠀⠀⡀⠀⣀⣉⠭⡿⣴⡲⣥⡴⠚⠉⠀⠁⠁⠀⠛⠛⠿⠿⢿⣿⢟⣿⡔⢀⠔⠉⠣⣀⡡⠖⡇⠀⠀⢀⣂⣑⣀⣀⣀⢠
⠀⠀⣙⣛⣿⡉⢉⣀⢓⠿⣯⢻⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠣⣏⠐⡖⠈⡉⠙⢶⠁⠸⠉⠙⠛⠿⣿⣿⣯⠈
⠀⠀⠉⡡⠀⠉⣠⣽⣍⢈⣤⠿⠒⠉⠁⠀⠀⠀⠀⠀⢰⡄⠀⠀⢸⠸⣿⠀⠻⠌⣳⣜⣤⠖⠚⠓⠒⢄⠀⠀⠀⢿⣿⡗
⠀⠀⡄⡁⣀⣴⡮⠃⠉⣿⠋⠀⠀⠈⠓⠦⠤⠠⠴⠟⠉⠉⠓⠲⠾⠞⠋⠀⠀⠀⠙⠛⠹⠀⠀⠀⠀⠈⠀⠐⠠⠾⠛⠁
⠀⠀⠀⠈⠹⣿⠏⣠⠞⠁⢀⠴⢂⠀⢀⠈⠬⠡⠔⠀⠒⠢⠀⠀⠀⠒⠀⠀⡆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⠀⠀⠈⠀⠀⢀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⢰⡡⢀⢄⣀⠄⡁⡠⡀⠀⠀⠀⠀⠙⠂
⠀⣠⢠⠤⠄⠀⠀⠀⠀⠄⢸⡢⢹⠓⢀⣀⣤⠠⠮⠤⢢⡀⠀⠀⠀⡀⠀⠀⠈⠀⠄⠉⢡⣤⢀⡆⢔
⠨⠥⠁⠀⠀⢀⡀⠰⠂⠈⠑⠁⠈⠉⠌⣾⠁⠀⠀⠔⠁⠀⠀⠐⠀⠁⠀⢀⠀⠖⠘⠐⠣⡤⠦⠙⠈⠀⠀⠀⠀⠀⣀⣠⠸
⠀⡷⣤⣰⠂⠀⠀⠀⡀⠀⠎⠀⠀⠀⠀⠰⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⡀⣄⠀⢀⢠⠂⠀⠀⠀⠀⢀⣀⣤⣤⠶⠟⢫⣡⠆
⠀⠁⠀⠴⠛⢃⣀⡤⠖⠚⠉⢄⡀⣐⠁⠀⠀⠀⠀⢘⡤⠤⠤⠤⠴⢆⠀⠀⠀⠀⣾⣿⠷⠒⠓⠾⠿⠉⣒⣀⡤⠴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⢀⢼⠀⣠⡄⠀⠛⢁⡄⠀⠓⠄⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⡀⣤⢀⠀⠀⢣⡆⠀⠀⣼⡷⣀⢠⠙⠑⠄⢀⠄⠉⠙⢷⡖⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠡⢀⣀⣱⠁⠹⠘⡿⢁⡴⠛⡭⠁⠓⣿⣿⣿⣦⡔⠀⢦⡁⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⠀⠀⠐⠃⡀⠰⠶⡀⠀⡀⣴⡆⠀⠈⢻⠀⢀⠴⠒⠺⣴⡔⡄⢁⡀⠟⠛⣅⣰⣶⣦⣶⣴⠀⠀⢀⣴⠁
⠀⠀⠀⠀⠀⠀⣴⡃⢰⡆⠈⣿⠀⠃⢰⠀⠉⢀⢤⣎⠀⠀⠀⢈⣿⠳⣾⣀⠀⠀⠍⣙⡵⢄⡴⣿⠇⡄⢸⣿⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⣠⠀⠈⠀⡰⠠⠄⠛⠀⠉⠹⣧⠶⣇⣤⣻⠄⠂⠀⢸⠿⡄⢻⣿⠛⠂⠀⢹⣷⣾⣣⣿⠎⠉⢘⣿⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢰⣿⠀⠀⠀⣋⡇⠀⠀⠀⠀⢚⣼⣦⣤⡴⢞⣿⠿⡉⣩⣟⢂⡬⠛⠂⢈⣠⢾⣛⡭⠾⡏⠰⣦⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠛⠛⠀⠠⠼⢿⣇⠀⠀⠀⢀⣾⣿⡿⠁⠀⠉⢻⣦⣤⣴⣟⡙⢿⠊⠀⠐⠦⠘⠋⢀⠀⣀⢠⣿⡇⠀⣠⡏⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠘⠁⣿⢠⣷⡖⠿⣷⡈⠛⣦⢹⣮⠤⠂⠐⠀⠸⠁⢠⠐⠒⣫⣾⣿⡇⠁⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿
⠀⠀⣤⠀⠀⠠⠁⠀⠀⠀⢀⡀⣀⣀⠀⢿⣆⢻⣿⡀⢹⡇⠀⢹⠇⡊⠶⠈⣤⣗⢠⣀⡀⠖⠋⠁⢀⠁⠁⠀⡠⢤⣀⣀⠀⢀⠀⠀⣻⣃
⠀⠀⢹⡄⣁⣤⡤⠤⠄⢀⣀⡀⠀⠀⢀⡀⠈⠻⢾⣥⠬⣓⣀⣐⡚⠛⠚⠛⠉⣁⣴⡏⠁⠀⠀⠀⠹⡅⠀⠀⠈⣤⢀⣭⣉⠁⠀⣐⣿⡏
⠀⠀⠰⣿⡉⠉⠀⠀⠀⠀⡈⠀⠤⣤⢨⣿⠤⠀⢠⣽⠁⢰⣦⣤⣤⡴⢶⣾⡿⢿⠛⠃⡊⠁⠙⣎⡀⢙⢓⡀⢋⣀⣤⣤⣤⡵⠀⣺⠟
⠀⠀⠀⢠⣿⣦⠄⠴⠄⠈⠇⠀⠈⠁⠈⠁⠀⠀⠈⠁⠀⠈⠉⠻⠇⠀⣿⡏⢠⣧⠀⠀⠙⢌⣀⡈⣛⣃⠘⠃⠅⠀⠀⠀⠉⠀⡠⠉
⠀⠀⠀⠀⠉⠙⢷⣄⡚⣤⠀⠈⢻⠀⠀⠂⠵⠆⠀⠀⠀⠀⠠⠄⠀⢀⡏⢷⣄⠙⠳⢦⡄⠀⠹⣄⠈⠛⠦⢤⣠⠄⠉⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣄⠀⢤⠐⠓⠔⠲⡤⠀⢀⣀⡠⠤⠀⡀⠈⠄⢠⣇⠀⠀⠈⠻⢦⣄⡈⠁⠤⠄⠀⣀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢿⣯⣤⣀⡂⠀⠀⠈⠙⠋⠀⠀⠀⠋⠀⠈⠙⠻⠶⠤⠄⠈⠀⣀⣠⣤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠿⣿⣷⣾⣶⣦⣤⣄⣀⣦⣤⣤⣤⣶⣶⣶⣾⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠟⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠨⣉⣩⡓⠻⡤⠶⠶⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡄⠀⠀⠀⠀⠀⠒⢒⣁⣀⣠⣤⣦⠤⠴⠒⠚⠛⠛⠛⠛⠛⠛⠓⡖⢲
⠀⠀⠀⠀⠀⠀⠛⠒⠶⣷⣤⡀⠀⠚⡧⠭⢤⡖⢠⣤⣶⣾⠿⣲⣯⡇⠀⠀⠀⣠⠶⠛⠋⡹⠟⠋⠁⢀⣀⠄⣤⣀⣰⣤⣦⣤⣤⣶⣾⣯⡾
⠀⠀⠀⠀⠀⠀⢴⡀⠄⠈⠉⠛⠛⠠⢤⣖⡄⠀⠀⣟⠻⣾⣫⠟⢋⡼⠀⠀⠀⠁⣠⣴⣿⢀⣤⣠⡤⠵⢾⡿⠟⠉⠀⠀⣀⣴⡿⠟⠋⠉⠙⣆⣤
⠀⠀⠀⠀⠀⢀⠀⠉⠛⠂⠀⠐⣄⠀⠀⠀⠀⠉⠁⣹⣀⠉⣤⣖⣿⣾⡄⠀⠀⠙⠛⠏⠀⣉⢻⣡⣤⠶⠋⠀⢀⢶⡿⠟⠛⠛⠒⠒⠒⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠑⠛⠦⢵⣶⣤⣴⠂⢿⣿⣧⣸⠟⠛⠁⡠⠀⠀⠀⠀⠐⠿⠟⠛⠙⠁⠀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠈⠉⢈⠃⠀⣀⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠟⠋⠀⠀⠀⢀⣀⠀⠤⠀⣄⢀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠉⠁⠒⠂⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠙⠈⠁⢀
⠀⠀⢀⣀⢀⠋⠁⢨⠟⠉⠉⠐⢂⣄⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⢀⣀⣴⣄⡀⠀⠀⠀⠀⠡
⠀⠀⠰⣬⡇⠀⣴⠃⠀⠀⢀⠞⠁⠀⠀⠀⣉⢶⠒⠉⠁⠬⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⣀⣰⣾⣾⡿⠿⠿⠿⣷⡀⠀⠀⠀⠀⢀
⠀⠐⠀⢹⣇⡠⠟⠀⠀⢠⡏⠀⠀⠀⢀⡜⠀⠈⠠⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣀⣦⡾⠟⠉⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⢴
⠀⠀⠀⢸⣿⣽⣦⣀⣀⣼⠁⠀⠀⠀⣸⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⣇⡀⣀⠰⣶⡿⠋⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⣄⣸⡼
⠀⠀⠀⠀⠻⣿⣿⣯⣿⣻⣶⣶⣤⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⠁⠉⠙⠛⠂⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣦⣴⣿⡃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣤⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣷⣦⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠁⠀⠻⣷⡂⣀⡄⣀⣠⣄⣤⣤⣶⣴⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠤⠤⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠠⠀⠀⠀⠀⠈⠙⠓⠋⠘⠘⠐⠐⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⣀⣤⣤⣀⢲⡄⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠷⠶⠿⠿⠿⠿⠿⠿⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠄⢤⢄⡀
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢖⣛⣋⠭⣤⠀⣿⠀⠀⣤⣄⠀⠀⠀⠀⡶⠦⢤⣄⣀⠀⠀⠀⠀⠁⠀⠒⠂
⠀⠀⠀⠀⠀⢠⢶⡴⣶⠚⠀⠀⡔⠒⠚⠉⠉⠀⠀⠀⣿⠀⣿⠀⠀⣿⣟⠀⠀⠀⢰⡇⡀⠀⠀⠈⠉⠙⡆⠀⠸⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢸⠬⠁⠒⠐⠀⠀⣧⣤⠀⢤⠤⢤⣤⡤⣿⠀⣿⠀⠀⠹⢿⡇⠀⠀⠸⣧⣟⣛⣋⣀⣀⣀⡇⠀⢰⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢼⢀⣀⣀⡀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠒⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠄⠀⠀⠀⠃
⠀⣀⣀⣀⠀⢻⣿⣿⣿⣿⠛⣻⢿⡷⢶⢶⣶⣦⣤⣤⣄⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣿⣿⣿⠁⢸⠄⢛⡻⠽⠟⠛⠻⠷⠿⣾⣿⣿⣧⣵⣯⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡆
⠀⣿⣿⣿⣀⣘⠲⠥⣶⣬⡉⠀⠘⠚⢒⠴⠀⡤⣬⣍⣉⠀⣤⠀⠀⠀⠈⠀⠀⠀⠀⠁⠐⠀⠀⠠⡇⣨⠀⠁
⠀⢿⣿⣿⣿⣿⣿⣿⣶⣦⣍⠙⠓⠒⠮⢬⣄⣒⠂⠀⠁⠀⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣌⠉⠙⡒⠆⠿⠀⠀⡀⠈⠀⠈⠀⠀⠀⠀⡀⠀⠀⠈⡉⠀⣤⣴⣤⡤⢤
⠀⡾⢟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠐⢀⠀⠀⣠⣶⡇
⠀⣾⣿⣿⡮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣻⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣬⣿⣿⡇
⠀⠿⠛⠽⠾⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠿⠽⠿⠦⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠘⢛⢃⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠒⢒⠓⠓⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⢉⢁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠂⠀⠐⠚⠘⠘⣤⡀⠀⠀⠄⢀⣀⠀⠀⠀⠀⢰⠶⢀⣠⡴⠄⠁⠀⠀⣍⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⡤⠆⠲⡄⠀⣌⡓⠀⠤⠔⠒⠒⠉⠉⠉⠀⠈⠉⠉⢉⠙⢒⠤⢤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⡀⠀⢀⠀⣀⣀⣷⠀⠁⠀⠀⠀⠀⠀⢀⡀⠄⠤⠶⢶⡟⠛⠁⢀⣠⣧⡬⢄⣀⠈⠁⠒⠆⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠨⠁⢀⡾⠀⠀⠀⠀⢀⠀⣈⣒⡤⢓⣂⠄⢐⡀⠄⢈⡀⠠⠥⠀⠠⢉⡉⠥⠄⠌⠐⣀⡠⠽⠧
⠀⠀⠀⠀⠀⡍⠀⠀⠐⠊⣳⢸⠀⠈⡀⠈⠀⠀⢈⢉⠉⢰⠒⣶⣌⣘⠳⡖⡭⠐⠚⠭⠤⣍⡉⠚⢯⠥⢞⡩⠤⣀⠈⠠⣄⣲⣤⠶⠍⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡀⠀⠀⢀⣈⣁⣸⣄⣌⠂⠤⠤⠤⠤⠤⠆⠹⠒⠀⠀⢆⠻⡇⢈⠁⠀⠈⠁⠀⠈⠑⠒⠠⠔⠠⠀⠐⠀⠈⠁⠤⣐⠤⣐⡢⢀⣀⣵⠠⠔
⠀⠀⠀⠀⠈⠁⠒⠒⢺⠙⠉⠐⠒⢜⠂⠀⠀⠀⠀⢀⠁⢾⣣⠄⠀⠰⣒⡟⢛⠾⠛⠴⠖⠢⠾⢷⣶⣦⣴⣄⡀⠇⠴⠖⢒⣉⡁⠥⠔⠒⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠥⠬⠼⠦⠤⣀⣀⣀⣠⡴⠋⠉⠉⠋⠉⣕⠖⠅⠿⠁⠀⠀⢀⠀⠀⠈⠈⠉⠓⠑⠠⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠉⠀⠀⠈⡍⠁⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⣿⡿⢿⡟⢿⡟⢿⡿⠻⣿⡿⢻⣿⠟⣿⡿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⣠⡶⣿⡟⠻⡆⠹⡆⠹⡇⠘⠃⠸⠇⠸⠁⠀⠟⠀⡼⠁⢰⠏⢀⣿⠟⢉⣿⠿⣿⣿⣦⣄
⠀⠀⠀⠉⠳⡈⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⡄⠀⠀⠀⠀⠘⠁⠀⠊⠀⠘⠁⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡙⣿⡝⢧⡘⣷⡀
⠀⠀⠀⢠⠐⣆⠹⣏⠉⢷⣄⠀⠀⠀⠈⠛⢷⣌⣻⣮⡳⣼⡻⣶⢄
⠀⠀⠀⣨⣷⡈⠣⣌⢑⣦⡙⢷⡒⢦⣄⠀⠀⠈⠻⣿⣧⢻⣇⢹⡌⢄⡀⠀⣀⠤⣴⠤⣤⣤⣶⣆
⠀⠀⠀⠀⠉⠛⠶⣿⣿⣯⣻⣆⠳⣌⠻⣦⣀⣀⣀⣈⣻⣦⣍⠓⢯⠱⡄⢹⡵⠚⢉⡭⠯⠭⠤⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣏⣽⣾⣿⡿⣍⠻⣝⢮⣧⡬⠿⣷⡈⢧⡙⠦⢰⣞⢩⡴⢋⣩⣻⣋⣩⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣉⡽⠿⣿⣿⡷⡜⢷⡙⠷⠾⠿⠷⢶⡭⣻⣆⠹⣆⢳⡾⠿⠿⠛⠉
⠀⠀⠀⢰⡿⢛⣩⠽⠿⠭⠤⠞⢉⣠⠞⠋⠙⣷⡘⠦⠭⠭⠭⢍⡙⢦⡙⢮⣻⣦⡙⢮⣷⢄⣀
⠀⠀⠀⠰⢿⣿⣴⠞⠋⡉⣉⡓⠛⢁⣄⣼⡿⠿⠟⠻⢿⣿⣷⣦⣝⢦⡙⢦⣈⣽⡟⠲⣌⠓⢮⣍⣝⠖
⠀⠀⠀⠀⠀⠈⠻⣮⣿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣥⡿⠿⠛⠛⢾⣆⣸⡿⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⢔⡲⠈⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⣥⣾⡷⠛⠁⠀⠀⠀⠀⣠⣭⡒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠙⠲⢿⡛⠻⢥⡀⠀⠀⠀⢀⣤⣮⡥⢋⡴⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢐⣠⣭⣿⣶⣤⣀⠀⠀⠀⠈⠙⠲⢽⣦⣴⣾⠿⣛⣥⣺⢵⣚⣭⣶⡆
⠀⠀⠀⠀⠀⠀⣀⣠⢤⢲⣻⠿⠟⠋⠉⠘⢦⡉⠛⢦⣄⡀⠀⠀⠀⠈⣉⢲⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠐⠠⢉⡛⠋⠁⠀⠀⠀⠀⢀⣠⣤⣿⣷⡶⣞⣻⣷⡆⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢄⡀⠀⠀⣊⠕⡢⢄⡠⢶⣯⡥⢞⣛⣭⣶⣿⣿⣿⣽⡇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⢷⣶⣍⡂⠀⠉⠓⢶⣾⣿⣿⣿⣿⣿⡿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠑⢤⡀⠨⡛⢿⣷⣤⣀⢸⣿⡿⢿⣻⣭⣷⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠈⢹⣾⣭⣶⣿⣿⠿⣛⣭⣷⣿⡿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠢⣀⠈⡳⢦⣸⡿⢟⣛⣭⢶⣻⣿⣿⣿⡿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡂⠙⠿⣟⣭⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⢸⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠉⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⢀⡠⠤⠖⠓⢒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⣀⠴⠊⠁⣀⡠⠴⠚⠋⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⣪⣴⣂⠔⠋⠁⠀⠀⠀⢀⣠⠞⡛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⢄⡴⢞⠵⠋⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⡴⡥⣫⠔⠁⢀⣠⠴⠚⢁⣠⡃⣜⡧⠟⠶⠄⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠊⠀⠀⠠⠊⢀⠞⠁⣠⠔⢋⢰⣬⢰⡸⢸⠷⠏⣁⡠⠴⠒⠛⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠐⢁⡴⠁⡠⠞⠡⣰⣯⣧⣿⠻⢃⡤⠖⠉⢀⣀⣤⠤⠴⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⢠⠎⢠⠞⣥⡛⢖⠓⠉⢀⡠⠚⠁⢀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠠⠃⡰⠃⠀⠁⢀⠈⢁⡴⠋⢀⣴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠦⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠈⠀⡠⠁⡼⠁⢀⣤⡤⠀⡠⠊⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡩⣴⣶⡿⠿⠿⢓⣮⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡰⠁⢰⡧⠞⣻⡟⠁⠜⠁⢀⡔⠁⠀⠀⠀⠀⠀⠀⣠⢖⣩⣴⠌⠑⣊⠥⠒⢊⢉⣭⡉⠙⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡜⠀⠀⠉⠀⡰⠋⢠⠊⠀⡰⠊⠀⠀⠀⠀⠀⢀⣴⣫⡶⠟⠋⣠⠔⣋⡤⡀⢿⣿⣿⣷⠠⢀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣠⠞⠁⡰⠁⢀⠞⠁⠀⠀⠀⠀⣠⣶⠏⡡⠊⢀⡤⢮⣥⣝⠿⠿⠿⠷⣏⣙⣛⠀⠀⠓⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠄⣀⣠⠖⠁⠀⠀⠀⠴⠋⠀⠔⠀⣠⠋⠀⠀⠀⠀⣠⡾⢿⡿⠋⣀⠔⣣⡝⠮⢟⣩⠵⠒⠊⠉⠉⣀⣈⣉⠉⢲⠎
⠀⠀⠀⣀⠀⣀⠀⡀⠈⠀⠀⠠⠀⠀⣼⠓⡽⠁⠀⠀⠀⢀⡰⠦⠊⢀⡔⠁⠀⠀⢀⢴⣿⣯⠔⠂⡠⠚⣁⠶⠈⡠⠖⠉⠀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠋
⠀⠀⠸⣄⢀⡉⠈⡀⠀⠐⣠⣶⣿⠛⠁⠚⠀⠀⠀⢀⡴⠏⠔⠀⢀⠌⠀⠀⡀⢂⢕⡛⠚⣁⡤⠊⠀⠀⣈⠔⠈⠀⢀⡤⠚⠁
⠀⠀⠀⠁⠀⠀⠀⢚⠽⢷⣿⡉⠡⠔⠀⠀⠀⠀⣔⢂⠐⠁⠀⠔⠁⠀⠠⣪⠞⠕⠊⠠⠚⠁⠀⢀⠀⠊⡠⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠈⢦⣀⣀⠊⣹⠁⢸⡀⠀⢤⠶⡓⠂⠀⢀⠔⠀⠀⢀⡡⠊⠉⠀⠀⠀⠀⠀⠀⠔⠁⠤⣊⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠎⠀⡆⢀⢨⡙⠷⣯⣥⣴⣇⣾⣡⡀⠄⠚⠉⢀⠀⠀⠀⢀⡠⠔⠊⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⢸⣷⢼⣤⣤⡠⠄⢀⣀⡀⠤⠔⠒⠈⠁⠀⠀⢛⡥⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣦⣾⣿⣶⣦⣤⣐⣤⡲⠖⠛⠂⡀⠤⠚⠁⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠟⠿⠋⠉⠉⠈⠀⠀⣈⣡⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢍⣃⣀⠠⠤⠒⠉⠁



⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠑⠒⠒⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡚⠛⠉⠉⠉⠉⠒⠤⣔⣲⠶⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⣉⣉⣽⡶⠆
⠀⠀⠀⠀⠙⠛⠿⣯⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣽⣗⡢⢄⣀⠀⠠⢀⡀⠈⠉⠓⡓⠤⢤⣀⣴⣾⣯⣷⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⣿⠒⠦⣌⡙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠈⢙⣛⣛⣈⣉⣲⣤⣤⠝⠒⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⢸⡷⠦⣄⡉⠙⠲⢤⣉⡛⢒⣛⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⡀⣻⡿⠿⠿⠿⠿⠯⠅⠀⠐⠒
⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣟⡒⠤⣀⠀⠀⠀⠀⣹⣟⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⢍⡓⠦⢍⣀⠒⠠⠄⠙⣩⠵⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠈⠁⠀⠉⠓⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣍⣙⠒⠒⠖⠋⣱⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠐⠒⠛⢣⣄⡀⠀⠈⠐⠛⠷⠆⠀⠀⠀⣀⣠⣤⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⢟⠂⠤⣀⠀⠀⠀⠀⠀⠈⠙⢋⣉⣐⢤⡶⠒⠋⠀⣻⣿⣿⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣤⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠉⠒⠲⠶⣾⣿⣿⣿⣿⣿⣽⡇⢀⣀⣤⣿⣿⣯⣴⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⣉⡒⠾⣿⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠤⣀⠀⠈⢿⣿⣿⣿⠿⠟⢛⣳⣯⠛⠉⢁⣼⣿⣯⡽
⠀⠀⠀⠀⠀⢈⡀⠠⢤⣴⣿⠢⠬⣭⣿⣿⣿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠿⢤⣀⡈⠀⠒⠛⠉⢀⣴⣾⣿⣿⡿⠒⠚⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠬⢭⣛⣿⣊⣁⡒⠺⣿⡿⣿⡀⠤⢤⣴⣿⡆⠀⠀⠀⠀⢸⡏⠑⠒⠤⢍⣀⡐⠀⠀⢼⣻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢀⣑⠒⠶⣿⡟⠢⢬⣽⣿⣿⣿⠌⣙⣻⣿⣛⣧⠄⠀⠀⠀⠈⠣⠄⣀⠀⠀⠀⠉⠉⣒⣭⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠬⢉⣛⣿⣛⡁⠒⠲⢿⣯⣿⡓⠲⢾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠒⠶⠚⠁
⠀⠀⠀⠀⠀⠐⠓⠶⢾⣿⣧⠬⢐⣒⣶⣿⣿⡅⠙⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⢾⣿⣿⠿






⡿⢿⡿⠿⣿⡿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣟⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣦⢲⠆⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠙⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⢄⣀⣓⣠⢂⣘⣀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠘⢧⡀⠀⠰⠄⠀⠀⠀⢥⠁⡔⠊⢀⠄⠀⠀⠀⠘⣣⡔⠀⠀⣀⢄⡟⠂⣄⠀⠈⠁⠀⢹⡋⠀⠀⡈⠉⠁⠀⢙⡇
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠖⢀⠞⠁⢀⡄⠊⠀⠀⠀⠀⠀⠠⣡⠜⢧⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣼⠁⣀
⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⢀⠌⠈⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠠⣔⣄⣶⠨⠍⡠⠖⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠐⢤⡆⠀⢧⠀⠂⠀⠀⠄⠀⡅⢤⣥⠔⠚⢀⡠⠆⠀⠀⠀⠙⠠⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⢤⠀⠀⣀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢗⣸⢩⡍⢮⡛⠀⠀⣄⢶⠆⠀⠀⣀⠀⠀⢦⣆⡄⠈
⠀⠀⠀⠀⡶⠚⠁⢃⣀⣀⠀⣀⠀⠀⠘⢡⠾⣼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠷⡉⠀⠀⠀⠀⠁⠀⠀⠀⢊⢱⡆
⠀⠀⠀⠀⠀⠀⡞⠋⢀⡠⠴⠬⢤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡄⢐⢰⠀⡄⢀⠇⠀⠂⢰⠀⠰⣀⠂⡦⢀⠀⠀⠀⠀⠀⠘⢼⣁⠄⡓⣧⢂
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠳⠁⠬⠸⠄⠇⠨⠤⠀⠀⠇⠱⠐⠻⠀⠗⠀⠇⠁⠀⢲⡦⡄⢩⢽⣶⠲⠨⠇⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠠⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠹⢾⣤⡜⠿⢭⠘⣧
⠀⠀⠀⠀⣠⠀⠀⠢⡇⡀⣀⠀⣠⠅⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠎⠃⠀⠀⣄⠀⠀⠀⠀⠘⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠠⠎⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⢠⡄
⠀⠀⠀⢠⠀⡈⠀⠀⠀⢠⡀⢠⠔⠀⠀⠀⢄⠀⠀⠁⠀⠀⠁⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⠲⠀⠀⠀⠀⠘⠀⣴⡀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠻⡿⢤⠂⠀⢠⣿⣿⠃⢠
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠎⠁⡀⠀⠰⠄⠀⢡⣹⠓⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⣟⠁⠀⠀⠂⠀⡜⠀⠀⠀⠀⠾⠋⠐⠀⡀
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠙⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡘⠁⠁⣀⠤⠥⠖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠁⠀⢰⠁⠀⣀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣋⠥⠚⢀⡤⠤⠊⣼⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⣪⠅⠒⠊⡡⠤⠴⠊⠀⣀⡤⣣⠀⣠⠤⣤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⢉⡁⠴⠒⢉⢔⠶⠆⠉⠛⠋⠈⢠⠒⢁⠊⠁⠀⣀⠭⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⠞⢠⠃⠠⡦⠶⠛⠁⠀⠀⠀⠀⠀⠀⡄⢀⠞⠀⠀⡎⠀⠀⡰⡟
⠀⠀⠀⠀⢀⡠⠖⠒⠤⠤⠤⠠⠖⠁⣠⠎⢰⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠖⣊⠤⠃⢀⡠⠔⠡⡶⠛⠊
⠀⢀⠔⠁⠈⢀⣀⣀⠤⠤⠠⠔⠊⣩⠔⠒⠁⠀⢠⣾⠇⢀⠀⠄⠒⡩⠭⠔⢊⡀⠠⠔⠁⠀⣠⡔⡇
⠀⠸⠀⠀⡜⠉⢠⠔⠒⣒⠒⣒⡉⠀⢀⣾⠍⠭⠛⠁⢀⠇⢠⠒⢉⡠⠔⠒⡡⡦⠶⠦⠉⠙⠓⠉
⠀⠸⠤⠼⠥⠴⣁⣀⣯⠖⠭⠕⠒⠛⠒⠁⠀⠀⠀⡔⠉⡠⠃⡜⠁⣔⠤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠠⠤⢀⢄⣀⡤⠎⠀⡼⢡⡜⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠉⢀⣀⣀⢤⣀⡠⠖⢊⡩⠔⠊⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠊⠁⡠⠄⠠⠐⠒⡒⠉⠀⣰⡢⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠰⠇⡠⠮⠤⡞⠀⣸⡭⠭⠭⠒⠁⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢴⡶⢫⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣭⡍⢩⡍⡉⠉⡿⠉⡍⢩⣷⣿⣿⣿⠿⡟⢸⣿⠟⣥⣯⣭⣭⣿⣿⣿⣿⣿⣿⣶⠸⣧⠻⠴⠛⠚⢻⢀⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⠾⠛⠓⠈⠁⢀⠈⠉⠁⠈⠉⣉⠝⣡⡖⢁⡇⡟⣵⠋⠀⢋⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠓⠀⢸⢸⢿⡵⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠁⠀⠀⢀⣤⠠⢄⠀⠀⠀⠀⡜⣠⣾⣿⢃⡼⢱⡿⣿⠀⠀⢸⠀⠀⠀⠀⣄⣠⣤⣠⢤⠀⠈⠀⠀⠀⠀⡜⡜⣼⣏⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢎⡴⠁⠠⠄⠀⠀⠸⣌⣉⠴⠀⠀⠀⢸⣵⣿⣟⣡⢃⡆⣼⣼⣿⡄⠀⡼⠀⠀⠀⣸⢻⣿⠿⢯⠏⠀⠀⠀⠀⠀⡰⢱⠡⣽⣾⣏⡝
⠀⠀⠀⠀⠀⠀⡠⢣⠎⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠘⡻⣿⡿⢁⢾⡇⣿⣾⡿⠁⡴⠁⠀⠀⣆⠀⢀⠄⣀⡀⣤⣤⣤⣴⡖⣰⢣⢣⡜⣽⣿⡿⠁
⠀⠀⠀⠀⠀⡔⣱⣿⣶⣶⣶⡖⠰⡆⣴⣠⣞⣪⠉⡥⣤⣤⣤⣿⡟⢠⢋⣾⡇⣿⣧⣶⡧⢤⣤⢤⣤⢀⣤⣤⠄⠤⢤⡥⣭⠵⠒⠺⢃⣯⢻⣰⣿⡿⠁
⠀⠀⠀⠀⢾⢤⠴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⣤⣤⣭⣉⣉⣉⣹⣡⣏⣤⣼⣄⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⣭⡴⠶⠒⣒⣛⡿⣱⣷⣿⡿⠁
⠀⠀⠀⠀⢘⡿⣿⡿⢗⣒⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⠤⢤⣬⣿⣿⣋⠈⠀⡐⠒⠲⠶⠶⠶⢴⣶⣿⣽⣿⠃
⠀⠀⠀⠀⠸⣯⣭⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣽⢿⣯⠿⠿⠿⠿⠿⠿⠦⠶⠶⠿⢿⣾⣿⣿⣿⣿⣿⢿⣻⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢚⡔⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠖⢤⠏⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠾⣤⠎⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠐⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⢄⡔⢲⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢃⠾⣡⠎⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⣠⢐⡖⠁⡀⢡⠴⠾⡧⠖⠓⠀⠀⠘⠉⠉⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠈⢁⣨⠤⠁⢢
⠀⠀⠀⠀⡸⡱⠊⡀⠊⠀⠈⠂⠀⠠⠤⠠⠒⢶⠲⠚⠙⣻⣻⡯⠉⠫⣭⠫⠼⢏⠙⠿⣯⠜⢛⡷⠮
⠀⠀⠀⠐⢻⢠⠊⠀⠀⠀⠐⠀⠁⠊⡁⠀⠀⠀⢳⣤⡴⠏⠁⠛⠻⡹⠊⠁⠠⠼⠷⠈⠤⢿⣛⣽⠤
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣲⠶⠤⢤⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠉⠉⠀⠀⠰⡅⢃⠴⣣⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠲⠭⠙⠛⠫⠷⢦⣄⠀⠀⣠⣾⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⡿⠥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡐⠌⠊⠁⠀⠣⡠⠀⠐⢉⠝⣓⡶⢤⢠⠐⣸⣿⣿⠿⠏⣆⣴⣾⡆
⠀⠀⠀⠀⠀⣠⠐⢊⣥⠞⠁⠛⠀⠀⠀⠀⠀⠈⠉⠉⢉⢥⡪⣾⣿⡀⣳⣯⣿⢍⣡⣾⣿⣿⢏⡇
⠀⠀⠀⠀⠀⣾⢛⠒⠤⣼⣒⠤⣁⠀⡀⠤⣤⠄⢤⣲⣵⣿⣿⣿⡿⢐⣿⡛⠈⠀⡉⣿⡾⣻⢏⡀
⠀⠀⠀⠀⠀⡷⠈⠹⠷⣒⠭⠹⣶⣯⣠⣚⣭⣶⣽⣾⣿⣿⣿⡿⢟⣋⣀⡀⢠⢴⡃⣿⣿⠿⣤⠉⠹⡖⠤⢄⡀
⠀⠀⠀⠀⠀⠑⠢⠤⣐⡢⠭⣝⡂⠝⡓⠮⣿⣯⣷⣿⠿⠋⢉⣁⡠⢴⢻⣻⢮⠷⢻⡿⠖⠚⠹⣧⢤⡐⢋⣵⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣗⡲⢬⣙⡒⢧⣿⣿⡋⠭⠃⠀⠀⠀⡔⣵⣿⣿⠲⣱⡋⠀⢀⠔⠀⠀⠁⢚⠻⠿⡿⢿⡀
⠀⠀⠀⠀⠀⠀⣤⠒⠩⠍⠁⣂⡐⠀⢍⡛⠑⠁⠀⣀⢀⣀⡠⣪⣾⣿⣿⣿⣼⠁⠀⠒⠁⠀⠀⠀⠤⠀⠀⠀⠃⠰⣨⠉⣲⡄
⠀⠀⠀⠀⠀⠠⣗⠂⠈⠩⠥⠐⣂⡈⠓⠲⠤⢔⣉⣐⣊⢔⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⢕⡤⢖⡫⢔⣷
⠀⠀⠀⠀⠀⠀⢿⣊⡠⠬⠍⠁⠐⠒⢒⣀⣤⣬⢐⣶⣂⣭⣾⣿⣿⣧⣤⡠⠤⣤⠄⣀⠀⢀⡀⠠⣐⡮⢝⣪⣵⣾⣿⣾⢿⡃
⠀⠀⠀⠀⠀⠀⠉⣶⢖⠶⡮⢭⠥⡤⡥⣤⢶⢖⡶⡶⣲⢻⣿⡫⡃⠀⠙⠻⣖⠬⣙⣠⣭⣶⣦⣟⣾⣿⣿⡿⣟⣊⣥⣒⣿
⠀⠀⠀⠀⠀⠀⠈⡯⠁⠑⠊⠂⢄⣈⡘⠐⠑⠠⠊⠄⠔⠔⡠⣻⣮⡀⠀⠀⠉⠯⢃⣬⣭⣍⣬⣿⣻⢿⣷⣾⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠈⢻⢦⡉⠭⠽⢓⣾⡿⣿⣿⣿⢿⠶⠄⡀⠀⠰⣷⡶⣶⡷⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⢯⢍⠑⢾⣻⣷⣿⣿⠟⠋⠁⠀⠀⠀⠑⠒⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⠃⠐⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠢⠰⢀⠄⡠⡀⢀⠀⠀⢐⠅⡨⢀⠀⡠⠀⠔⠁⠀⢀⠔⠡⠊⠀⢀⢀⠑⡡⠂⢀⠔⡁⡠⢀⢔⢕⡔⡰⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠡⠪⠀⠅⠨⠀⠕⡨⢂⠔⠀⡨⠀⠀⡠⠪⢀⢀⠔⡡⠂⠂⠐⠁⠊⠌⠐⠁⠃⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣰⡷⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣁⡴⠛⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣤⡦⢂⣥⡞⣻⡍⠀⢺⠟⠄⠀⢠⣤⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣀⣤⣠⣀⠀⢀⠒⠚⠉⢨⡥⠶⠟⠋⣀⡴⠋⣰⢟⢴⠒⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⠀⠠⠤⣤⣤⠄⠠⢀⡀⢀⢀⠐⢛⠁⠴⠚⢁⣾⡇⡀
⠀⠀⠀⠀⠀⢀⣤⠤⠀⠿⠛⠙⠛⠷⠶⠶⠂⠄⣊⣭⡾⢛⣥⢞⡩⢄⠀⣀⡤⠟⠈⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢸⣟⡙⠛⠓⠒⠒⠀⠂⠀⠀⠀⠉⠉⠤⠶⢛⠕⣹⠯⠗⠋⠀⠀⠀⠠⠤⠚⠁⠀⠀⣨⠞⣻⣦
⠀⠀⠀⠀⠀⢸⣿⠿⢯⣤⣀⣉⣉⣉⣀⡩⢹⣡⣬⠵⠖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠁⢸⡟⠛⢳
⠀⠀⠀⠀⠀⠸⠑⠀⠀⠀⠉⠙⠛⠋⢉⡀⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠴⣊⣤⠟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢠⠠⢤⣀⣀⡄⠤⠄⠴⠶⠶⣚⠉⢀⠔⠁⠺⠛⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠶⠦⠴⠂⠈⠉⣿⠛⠋⡡⡬⠞⠛⠁⠒⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⣀⠀⢀⡔⠈⣰⠃
⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠘⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⠏⠉⢹⣿⣯⠉⠙⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⣰⣶⡖⠀⠐⣶⣶⡀⠀⢿⣿⣿⣿
⠀⠀⠀⣾⣿⠟⠀⠀⢸⣿⡿⠀⠀⠸⣿⣿⠄⠀⠀⢸⣿⣿⣿⡃⠀⣠⣿⣿⣇⠀⢀⣿⣿⣧⡀⠀⣻⣿⣿
⠀⠀⠀⠀⣶⣿⣶⣾⣷⣶⣾⣷⣶⣾⣷⡆⠀⠀⠀⢸⣿⣿⣿⣿⠉⠁⠉⠉⠈⠉⠉⠈⠉⠁⠉⢹⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⢾⣿⡇⢸⣿⣿⠀⣿⣿⡆⢸⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣶⣿⡇⠀⠀⣿⣷⣶⣿⣇⠀⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⢸⣿⣿⠀⠉⠉⠁⢸⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠈⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣴⠶⠿⠿⠿⢿⣤⡀⠀⠀⡀⠀⠀⠀⠀⣉⣉⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⢿⡿⢋⠀⠰⠄⠀⠀⠒⣈⣉⣤⣤⣴⣶⠶⠿⠟⠛⠋⢿⣇
⠀⠀⠀⠀⠀⠀⣈⣤⣴⣶⠿⠛⠋⠁⠀⢀⣉⣉⣥⣤⣶⡶⠾⠛⠛⠿⢿⣭⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⠉⣡⣤⣤⣶⡶⠿⠿⠛⠛⠉⣹⡟⡁⠀⢐⣦⣀⠀⠀⠈⢻⣆⠀⠀⡀⢀⣀⡀⡀⣿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣩⣥⣤⣤⣤⣤⣤⣬⣭⣬⣤⣤⣭⣭⣬⣥⣤⣤⣥⣭⣤⣤⣥⣭⣭⣥⣥⣭⣭⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣿⣟⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿⠛⠉⠉⡉⠉⠙⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠀⠀⢀⡀⠀⠀⠀⣼⠋⠀⠀⣠⠾⡗⣦⠀⠀⠈⢿⡄⠀⠀⠀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⣿⡟⠀⢠⣶⣦⠀⠀⢸⡏⠀⠀⠀⠻⣶⣇⡉⠀⠀⠀⠘⣷⠀⠀⢠⣶⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⣷⠀⠈⠛⠋⠀⠀⢸⣧⠀⠀⠀⣤⡌⡟⢻⡆⠀⠀⢠⡿⠀⠀⠈⠛⠋⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠙⠲⡷⠛⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣠⣀⣀⣀⣀⣀⣀⣀⣹⣷⣦⣄⣀⣁⣀⣤⣾⣟⣡⣄⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢉⣉⣉⣉⣉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠖⠉⠈⣠⢀⣠⠨⠝⠑⢢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⢾⠀⠘⠢⠄⠀⠀⠀⠀⠀⠠⠤⠊⠀⢸⠶⠦⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⢲⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚⠒⠛⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠉⠉⠉⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠂⣉⣠⡀⠀⠤⠖⡒⣀⠌⠉⠿⠛⢋⣰⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠁⠀⠀⢠⠤⠦⠤⠤⠀⠀⠀⠒⠋⠁⠀⠀⢀⠀⠀⠀⢀⡤⢀⣴⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⠄⠀⠐⠛⠀⠀⠊⠀⠀⠀⣀⣤⣾⠁⠀⠙⠛⠷⣶⣿⣧⣭⣉⣟⣿⠟⠁
⠀⠀⠀⠀⠀⠊⢀⣰⡴⠚⠋⠁⣀⣤⣶⣶⡦⢰⣿⡿⠿⣿⣿⣿⣿⣿⠇⠀⠊⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢁⣴⣶⣾⠿⠿⣛⣥⣤⣶⣶⣶⣿⠶⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡻⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠿⠅⠀⠠⠀⠀⠀⢀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣂⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠄⡀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⣔⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⡄⠀⠀⠀⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡠⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⣶⠏
⠀⠀⠀⡁⠤⡀⠀⠀⠉⠒⠠⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠤⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠓⢄⠀⠑⠂⠄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠈⠂⠤⣀⠈⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠠⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⡀⠈⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⢀⣀⡤⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠄⣀⢀⠀⢀⣀⣀⣀⣠⠤⠦⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠓⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠒⢉⡁⢰⣶⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠋⣉⡠⠤⠖⠒⠋⠉⠈⢇⠀⠿⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠚⣉⣁⠤⠤⠶⢊⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠘⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠂⣉⣉⡤⠤⠔⢂⠟⠋⠁⢀⣤⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧
⠀⠀⠀⠀⠀⡔⠒⢈⠉⢠⡤⠤⠒⠊⠉⠁⠀⠀⠀⡔⠁⠀⠀⣴⣾⣿⡿⣷⡆⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀
⠀⠀⠀⠀⠀⢱⠀⠘⣢⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⣿⡁⢹⣷⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠘⡆⢀⠥⠔⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠻⣿⣾⣿⣦⣤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹
⠀⠀⠀⠀⠀⠀⢡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⢻⣷⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠀⠏⡇
⠀⠀⠀⠀⠀⠀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢠⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠰⡇⠀⢧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠐⠿⣷⣶⣿⣿⡿⠋⠀⠀⣠⠋⠀⠀⠀⠀⣀⣠⠤⠄⠓⠀⣉⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠛⠁⢀⣠⣞⠥⠤⠒⠒⢉⣁⠤⠤⠖⠒⠈⠉⠀⣳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡲⠶⠶⠒⠊⣉⣁⠤⠔⠒⢺⠋⠁⠀⠀⠀⠀⠀⢀⠞⢁⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢴⠀⠙⡆⠀⣀⣀⠤⠄⠒⠚⢉⣁⠠⠤⠶⣶⣿⣿⠟⠁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⢸⡄⠈⡳⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⠇⠀⢉⣉⡁⠤⠔⠒⠋⠉⠓⢤⣀⠀⠀⠀⠈⠉⢀⣀⣴⣋⡠⠤⠤⠒⠒⠂⢋⣉⣉⡡⠤⠤⠰⡖⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠧⢲⠊⠙⡍⠀⠀⠀⠀⠀⣀⣀⣀⠠⠬⠽⠛⠒⠊⢉⣉⣁⡠⠤⠤⢲⠖⠂⠉⠉⠉⠀⠀⠀⠀⣀⣀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡷⠀⠻⠒⠒⠊⣉⣁⣤⠤⠤⢤⠒⠒⠊⠉⠻⠟⠉⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠦⠤⠖⠲⠶⠬⠭⠥⠤⠤⠤⠤⠤⠤⠭⠶⠦⠤⠤⠤⠤⠶⠮⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠨⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⣶⣶⣷⣗⣠⢄⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⢿⣿⠮⠿⡜⠀⠀⠊⣄⣁⣀⠀⠢⠀⠁⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⣀⠀⠘⣄⠈⠡⠀⠀⠀⠀⠈⠈⠀⠀⠉⠁⠉⠁⠀⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠻⠀⢷⠄⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠘⢁⣀⣤⣤⣤⣶⣶⣶⣄⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣷⡆⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁
⠀⠀⠐⠀⠀⢀⠀⠀⠒⠄⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⢿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⠔⠁⢀⠀⢃⠴⠂⠐⣻⣿⣿⣿⣿⣿⣿⡇⣿⣿⡹⣿⣼⡾⣷⣟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⠲⠒⠁⠚⠁⠀⠈⠀⢙⣛⣿⣿⡿⣿⣿⢿⡿⣿⣿⢿⣿⣿⡿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠐⠀⠀⠀⢏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣿⣯⡛⣿⣽⣿⣟⡗⣾⣾⣿⢻⣿⣸⢻⣷⣾⢸⣧⣿⠛⠁⠀⠀⢠⣂⣤⠃⠀⠀⠠⠐⢉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⡀⠀⠈⢿⣿⣯⣿⣿⣾⣿⣾⣷⣿⣾⣿⣷⣿⣿⡾⠿⠿⠾⠿⠟⠀⠀⠐⠀⢘⣳⡿⡖⢴⠶⠀⠳⣤⠇
⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠛⠈⠃⢀
⠀⠀⠤⠐⠀⠐⠀⠀⠀⡀⠀⠈⠄⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⢠⠀⠀⠐⠀⠀⠈
⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⠂⠑⠀⠀⠀⠀⠀⣀⠀⢀⠅⠀⠀⢀⣀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠰⢀⠆⡦⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⣐⡳⠂⠀⠀⠀⠡⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⣦⣠⡐⠂⠀⠀⠀⠀⠀⠀⠸⠀⢁⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⣿⣿⡶⠀⠘⣧⣴⣶⣦⠀⢀⠀⠰⣦⡦⢄⣸⡧⠂⠲
⠀⠀⠀⠀⠀⢠⡄⠀⡄⡐⣦⠐⡀⢢⢠⠀⢠⠀⡀⠀⠀⢸⣼⣿⣿⣿⣿⣟⠀⣰⣿⣿⣿⡟⠀⢀⣦⣴⣾⡀⠀⠻⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠲⠛⠛⢛⣀⣉⡙⠉⠙⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢈⠷⣿⣿⣿⠆⠀⣿⣿⣿⣿⡇⢠⣀⣇⡀⣤⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢻⢿⣿⣿⣿⣭⣿⢻⣿⢻⣿⢰⠀⠸⠇⠹⠂⠠⠀⡾⣁⢙⣯⢾⣇⣾⣀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣼⣿⣿⣿⣶⠛⢠⣿⣦⣿⣶⣄⣈⠐⠊⠂⣪⡆⢾⠑⠊⣷⣾⣷⣿⣿⡟
⠀⠀⡉⠙⠃⠀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⡀⣤⣀⣤⣤⠀⣿⣿⣿⣿⡇⠀⡈⣍⣍⡩⠭⣿⣿⣿⣿⣿⣿⣷⢋⡀⠀⢻⠟⠻⣿⡿⡇
⠀⠀⢻⣿⣳⡀⠀⠟⢀⠀⡖⠺⠆⠸⣿⢹⠧⣿⠿⢿⣿⣿⠀⣿⣿⣿⠿⠇⠀⠂⠀⣰⡇⠀⠤⠶⢴⡦⠄⠶⠀⢸⣿⣄⠀⠀⠀⠘⡇⠆⢀
⠀⠀⠀⠙⠃⠁⣾⢠⢠⣤⢨⣗⣶⣴⡾⠇⠀⢹⣾⡌⣿⣿⠀⣿⣟⣉⠀⠀⡆⢀⣷⣿⡧⠖⠆⠖⢷⡖⠲⠿⠖⣻⣛⠗⠚⠀⠀⠘⢿⣶
⠀⠀⠀⠀⠀⠀⠐⠀⠋⣍⢻⠁⢹⢸⡇⡇⠀⣼⣟⣿⣿⣿⢸⣿⡇⠀⠐⢂⡌⠀⣃⣿⡇⠀⠛⠃⠚⠛⠃⠁⠀⣯⣤⣥⣾⡇⠀⠀⠂⠁
⠀⠀⠀⡆⢴⠀⣀⠀⢳⠈⠘⠀⠀⠘⡇⡅⢀⡏⠋⠿⣿⠟⢀⠙⠋⠉⠉⠉⠓⠚⠛⠛⠛⠛⠛⠋⠉⠋⠙⠛⠛⠋⠛⠙⠉⠃
⠀⠀⢀⠘⠘⠀⠋⠀⠀⡀⠃⠀⠀⠢⣿⣇⣼⠁⠀⠘⣿⣿⣿⡿⠿⠗⠛⠒⠒⠻⠿⠟⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⣟⡛⢛⠛⠛⠙⠉⠉⠉⠉
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠋⠹⠏⠀⠀⢸⣟⣿⡆⠀⣀⢰⡶⠶⢶⡶⠶⣷⣾⢿⣶⡀⠀⣶⣶⠿⠿⢞⠲⠶⠖⠒⡆⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⢠⠀⠀⠀⠀⣿⢛⠇⠁⠿⢸⡀⢀⡾⠃⡀⠀⢉⡴⣿⠷⠀⣿⣀⡈⠁⠀⠀⠀⠀⠀⠃⠀⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢛⡄⠀⠀⠀⠈⠱⠿⠓⠒⠀⠈⠉⠁⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣤⡄⠀⢀⠈⣢⠠⣦⣤⣀⣀⠀⠤⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠶⠶⠂
⠀⠀⠀⠀⠀⣤⣤⣄⣠⣤⣤⣤⣀⣀⠀⠤⠀⠀⣠⢋⣼⣿⣿⠀⣸⠗⠀⠲⡌⠉⠿⠿⠾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠉⠉⠉⠉⣡⠴⠫⠛⣸⣿⣿⣿⡀⠠⣀⠀⠀⡿⠀⠒⠒⠒⠴⠒⠠⣿⣴⠒⠀⠢⠀⢄⠒⠒⠒⠒⠀⠚⠒⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠁⠀⠀⠀⠘⢿⣿⣿⣵⣶⡯⠾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠈⣾⡦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣴⣶⡄⠀⠀⠈⢩⡒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣼⣿⡇⠀⣰⣄
⠀⢀⣤⠀⠀⢀⠀⠤⢠⣾⣿⣿⣿⣿⣿⢿⡿⠃⠀⠈⣒⠉⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠹⠛⣵⣾⣿⣿⡆
⠀⠉⢛⣯⣄⠈⠉⠉⣽⣿⣿⣿⣻⡿⢿⣏⢰⠀⠀⠰⡍⣨⣿⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣡⢄⣀⠄⠿⣿⣷⣿⣄
⠀⠀⢀⣿⣯⣽⣛⣺⣿⣿⣿⣿⣿⣿⣿⣿⣧⠒⠈⠀⢿⣿⣿⣇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣶⣤⣭⣤⣄⠹⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠺⠟⣟⠑⢂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢠⡀⢱⣬⣻⣿⡍⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣁⢈⣽⣿⣿⣿⣿⣿⣿⣶⡦
⠀⠀⠀⠀⠀⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢉⠿⢙⠃⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠉⠛⠛⠟⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠿⣿⣿⡟⠻⠿⠦⠁⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠂

⠀⠀⠀⠀⠀⠔⠁⠐⠈
⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣦⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣶⣶⣦⢰⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣏⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡇⣷⣦
⠀⠀⠀⠀⠈⠂⡑⢄⡀⠀⠀⠰⠴⠶⢛⠻⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⢸⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠐⠂⠥⠒⢒⣠⣤⣭⣭⡽⠿⠿⠵⠿⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⢿⣿⣿⢇⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠾⠾⠿⠟⣿⠛⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢘⡻⠿⣿⡿⢟⣵⣿⣿⢟⣼⣿⣿⡿⠿⣛⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠸⠀⠡⣽⠀⠐⢿⠁⠉⠻⡛⠋⠁⣋⡛⢻⣶⢖⣽⡛⣫⣵⡿⢟⣫⣵⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢸⠢⠄⢸⠑⠂⠀⠈⢁⡾⢫⠗⣨⡥⢛⣯⣶⣍⣵⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠣⡀⠈⢆⠀⠀⠀⡊⣴⢃⢾⣽⡿⣍⣫⣷⣻⣿⣿⣿⣿⣯⣟⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣼⠃⠲⣟⣥⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠳⠾⠿⠷⣶⣶⣶⣶⣦⣷⡴⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠾⣭⣵⣟⡹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⠿⠿⠿⠛⠛⠉⠁







⣿⠛⠛⣿⠶⠷⢶⠿⠾⣷⡾⣿⠷⠾⢶⠾⠷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡶⠾⢿⠶⠶⣶⡿⠿⠿⠷⠿⠿⠿⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⡇⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠈⠙⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠀⠀⣸⠀⠀⠀⠀⠟⠀⠀⠳⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠖⢻⡟
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⠛⠉⠉⠁⠀⠀⢀⡎⣠⠏
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⢀⡄⠀⠀⢰⠂⣀⣺⡴⠃
⠀⠀⠀⢀⡾⠃⠀⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⣁⣠⡤⠶⠚⠋⠉⠉⠓⣦⣄
⠀⠀⢠⣏⠰⠂⠀⢀⡤⠀⠀⠈⠁⠀⢀⣀⣀⣤⡤⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠾⢏⡉⠀⠀⢀⡴⠖⢺⡏⠉⠉⠁
⠀⠀⢸⡏⠓⠲⠶⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢴⡶⣿⣭⣭⣤⡤⠤⠤⠴⠶⠖⠚⠋⠑⠀⣠⠷⣤
⠀⠀⠈⡇⣇⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠒⠛⢛⡟⠛⠿⠶⠴⠶⠋⠀⠈⡆⠀⠀⠀⠀⠀⠀⠄⢀⣀⡤⠶⠛⣡⣾⠁
⠀⠀⠀⠳⢦⣤⣬⣁⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠖⠛⠉⠉⣇⠀⠈⠆⠀⢀⡼⠁⠀⠀⡆⠀⠰⠀⠀⠀⠁⠀⠂⣀⣤⡤⠶⠚⠉⣁⣠⠴⠚⠁⠘⣇
⠀⠀⠀⠀⠸⣇⠰⠁⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠶⠶⠾⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠛⣉⣁⣤⡤⠶⠚⠋⠉⠀⠀⢰⠀⠀⣿
⠀⠀⠀⠀⣰⠟⠳⢤⣥⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠴⠶⠶⠒⣒⣚⣛⣋⣭⣭⠥⠴⠖⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⠄⠀⠈⣠⡼⠃
⠀⠀⠀⠀⠷⣤⣤⠤⠶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣤⠶⠛⠁
⠀⠀⠀⠀⠀⡟⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠘⣇⠸⠀⢰⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠈⠛⠒⠶⠷⠶⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠲⢤⡀
⠀⠀⠀⡌⡀⠝⠲⢍⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣄⣡
⠀⠀⠀⢣⠄⠈⡠⢘⠇⠀⠀⠐⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠤⠜⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠛⠙⠟⠋⠛⠂⡀
⠀⠀⢰⠊⢾⡤⠤⢾⡶⠤⠤⠤⠾⠙⢷⡀⠀⠀⠀⠀⠀⢢⣠⡠⣆⣎⠐⢲⡀⣶⡟⠀⠀⠀⠀⠀⠀⠀⢢⠄⣀⣠⠀⠀⠂⠀⡶⠓
⠀⠀⢣⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⡰⠛⠛⠣⢛⠀⠀⠉⠃⠻⠦⠀⠀⠀⠀⠀⠀⠠⢈⠀⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠞⠚⠒⠴⠧⠶⠤⠐⠲⠒⠚⠊⠀⠀⠀⠀⠀⠀⣱⡖⡐⣀⠀⠀⠀⠲⢶⣤⣖⠀⠀⠀⠀⠀⠀⠾⠯⠀⠀⠀⠀⠀⠀⢀⣀⡰⠶
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠐⠻⡝⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢨⠁⠈⠁⠀⠀⠀⠈⠉⠀⢹⠃⠀⠀⠀⠀⠳⠤⠤⢦⣀⡄⠠⡤⢀⠄⠰⠴⠆⠀⠀⠀⠀⠓⠤⡤⠒⠀⠢⡄⠀⠈⠀⠀⠖⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢣⠀⠄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠐⠴⠄⡆⠀⡀⠀⠠⠼⠃⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠰⢅⠀⠀⢠⠀⢀⠀⠅
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠘⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⣄
⠀⠀⠀⠀⢀⡽⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⣠⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢈⡀⣀⠐⠓⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⣆⣻⡀⠀⢶⢾⣏⣛⡈⠈⠢⠀⠀⠀⠀⠀⠀⠊⠉⠁⠠⢶⠖⠚⠉⠉⠱
⠀⠀⠀⢀⢌⡩⠁⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣀⡀⠀⣀⢀⣀⣀⣴⡄
⠀⠀⢀⡁⠂⠂⢠⡀⠀⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⠆⠀⢠⠀⡄⢀⠀⠄⠀⠀⡀⠀⠒⠀⠀⠀⠀⠈⠑⠄⠈⠀⠉⠋⠙⠻⠉⢄⠀⠘⡀
⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⣄⣄⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠂⠀⠀⠈⣠⠀⡀
⠀⠀⢸⠷⠄⠚⠣⠀⠂⠠⠒⠀⠒⠰⠶⠀⠀⠀⠀⠃⠀⠁⠉⠂⠰⠶⠒⠂⠘⠋⠉⡝⠁⠀⠀⠀⠸⠖⠠⠷⠤⠀⡠⢦⡄⠀⢠⠷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⠶⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠈⠀⠠⠤⡤⠦⠤⠦⠶⠢⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⢀⡀⣀⣀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⢠⡈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠛⠉⠈⠁⠁⡀⠀⠀⠀⢀⣏⠉⠛⠑⠛⠒⠖⠒⠛⠛⠓⠐⢛⣇
⠀⠀⠷⠒⠦⢀⠀⢀⣀⣀⡠⡄⠀⠤⠊⡁⠀⠀⠀⠀⣤⣀⣤⠤⠄⠀⠀⠤⠤⣴⠞⡀⠀⠀⠀⠀⣟⣛⠛⠛⢓⠒⠒⡒⠲⢚⣛⣫⣛⡇
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠘⠁⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠈⠉⠋⠙⠀⠉⠉⢘⠅
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠊⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠛⠋⠙⠛⠉⠉⠉⠉⠉⠙⠛⠉⠛⠋⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⠀⠀⢀⣐⣋⡉⠀⠀⠐⠿⠇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠎⠀⠀⠉⢢⢀⠄⠂⠠⡀⠀⠈⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡎⠀⠀⠀⣀⠀⡏⢀⠀⠀⢱⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⢱⡀⠀⠀⠀⣰⢇⠀⠀⠀⣸⠀⠈⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⡀⠀⠙⠶⠤⠚⠁⠈⠳⠤⠖⠁⠀⣠⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠉⠀⠒⠒⠒⠂⠈⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣇⣀⣀⡀
⠀⠀⠀⠀⠀⣠⠖⠋⢁⣀⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⠉⠓⢦⡀
⠀⠀⠀⠀⡜⠁⢠⠞⠉⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⢆⠀⠱⡄
⠀⢀⡤⠞⠁⠀⢮⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢨⠆⠀⠙⠦⣄
⣰⠋⢀⣤⡄⠀⢼⡀⠀⠀⠀⣼⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣸⠄⢀⣤⡀⠈⢣
⢧⣠⡞⡸⠘⠦⣤⠇⠀⠀⠀⡟⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡇⠀⠀⠘⢧⡤⠞⠸⡘⣦⣠
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠦⠤⠤⠦⣤⢤⣤⣤⢤⡤⠦⠤⠤⠦⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⡇⡇⢸⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠉⠙⠓⠿⠀⡇⡇⠸⠖⠛⠉⠉⠉⠉⠉⠓⢤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣗⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣃⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠒⠊⠁⠠⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢲⠁⣘⠀⠀⣀⣀⣠⡇⢉⣭⡄⠸⡄
⠀⢀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠜⠀⠀⢀⠀⠀⣀⢈⣤⡖⡦⢖⡞⠀⠇⠀⣾⠙⢯⠏⣿⣯⠽⠁⢠⣷
⠀⠈⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⡐⠁⠀⡰⠁⢰⠏⣽⠀⣽⣛⣿⢈⠃⠘⠀⠀⣧⣤⣄⣈⣀⣀⣠⠴⠫⠃
⠀⠀⠀⠀⠈⠐⠀⠂⠠⠂⠄⠀⠠⠂⠒⠀⠀⠀⢰⠁⣰⣏⡓⠯⠿⢼⡿⠐⠁⢠⠂⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⣷⣂⡃⠴⠔⠋⢀⡠⠒⠁
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⡝⠓⠢⢀⠀⠀⠀⡜⠀⠜⠉⢁⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠠⡤⠆⠀⠀⠠
⠀⡠⠊⠁⠀⠀⠀⠀⠀⢰⡃⠀⠀⠈⠀⢌⢠⠇⡐⠂⠉⠁⠀⠀⠀⠀⠀⠀⡀⢠⣀⡆⠀⠀⠹⠅⠀⠀⠉⠀⠀⠁
⢰⣁⠀⣀⠀⠀⠀⠀⢈⡸⢻⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⠀⠀⠑⠀⠀⠀⠀⡀⠠⠄⠂
⠙⠀⠀⠀⣱⠤⠔⠊⠁⠀⢊⠀⠐⠁⠀⠀⠀⠀⢀⠄⠒⢖⡃⠀⠀⠀⠈⠀⠀⣀
⠰⡄⠀⠀⠉⠉⠁⠲⠀⠀⠀⠀⠀⡀⣀⠆⠀⠙⠽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠁⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠⢐⣦⡴⠊⠀⡈⣯⠝⠉⠀⢈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢸⠟⠁⠀⢸⠟⠁⠀⠀⢠⣟⠭⠛⠳
⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⢀⠀⠀⠀⢀⠠⠀⢒⣀⢀⡐⠒⠀⠄⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀
⠀⠀⡠⠔⢁⣄⣈⣉⠙⠻⠦⣹⠀⡔⠁⢰⢚⣋⣸⣁⠋⣛⣻⢦⠈⠂⠈⡓⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠒⡏
⣠⡊⣐⡶⠦⢤⣌⠉⣳⠔⠋⠁⠀⠀⠀⠀⠀⠿⠠⣤⡤⠭⠓⠁⠀⠀⠀⢠⡁⠀⠀⠩⠉⠉⠉⠉⠉⠁⠄⠀⢀⡼
⢇⠶⠶⢶⡏⢢⡴⠊⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠊⣀⠔⠁⠀⠀⠳⢮⣀⣀⠀⠀⠀⠀⠐⠀⣐⣨⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⣿⡏⠉⢻⣿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠑⠀⠀⣰⣿⡇⢀⣾⣋⣾⡏⢈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣰⣟⡿⠀⣾⢣⣏⣿⠃⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢀⣼⣿⡟⠁⣼⣏⣾⣿⣿⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡀⠀⢀⣾⣿⠏⠀⣰⣿⣿⣻⣿⠇⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠰⠀⢀⣞⣿⠃⢀⣼⣿⡻⣫⣿⠋⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣿⣼⠇⣴⡏⡵⢨⣿⡟⠁⠀⣰⡿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢸⣿⡟⢸⣿⣝⡆⣺⡟⠀⢀⣾⢟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢠⣿⣿⠁⣾⣿⣿⣷⣿⠁⣰⡟⣡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⣴⢿⡿⠃⣰⣿⢿⣿⣿⠏⣴⣫⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⣴⢟⣡⡟⠁⣰⡿⣿⡟⣹⠏⣰⡟⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⢀⡴⠟⣡⡾⢋⣤⢾⡿⣿⢋⡽⠋⣠⣿⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢀⣴⣯⣾⡾⠋⣴⣟⣽⣋⠀⣡⠟⠁⠐⣱⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣾⣿⣿⠫⠀⣼⢿⡟⡾⢃⣾⠋⢀⣴⠟⣱⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣸⣿⣿⠃⠀⢰⡟⣿⡟⢀⡾⠁⢀⣾⠃⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠀⢠⣿⣿⠏⠀⢀⣾⣿⣿⠖⣼⠇⠀⣼⠇⣾⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⣴⣿⣿⠏⠀⢠⣾⢿⣿⡷⣻⡟⠀⢸⡿⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⣰⣿⡿⠋⠀⢀⡴⢛⠏⡂⣿⣿⠟⠀⠀⣼⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣼⣿⠏⠀⠀⣴⠏⡀⠤⢊⣾⠟⠁⠀⢀⡼⣳⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠰⢢⣾⣿⠋⠀⠀⣼⣿⣬⣻⣿⡟⠁⠀⠀⣴⢟⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠛⠑⢁⣠⣿⡿⠁⠀⣠⣾⡟⣿⣿⡿⠿⢂⢀⣢⣞⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⣠⣶⣿⡿⠋⣁⣴⣿⣿⣿⣿⣿⣥⡤⠶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡀⣠⣾⢻⡾⠋⢀⣴⠟⢰⢿⣿⡿⢿⣿⣷⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢀⣴⣿⣿⠟⠁⣠⣾⣫⣴⣽⣿⣭⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣏⣀⣤⣾⡿⣯⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡔⠒⠒⢤⠄⣠⡤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⢰⠀⠀⠀⠀⡿⠐⠉⣡⠀⠀⠀⠁⠀⠀⠀⠀⠉⠒⠀⠀⠀⢆⠀⠀⠀⢄⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⣠⠚⠁
⠀⠀⡀⢸⡄⠀⢸⠰⡟⠂⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠸⠀⠀⠀⠀⢀⠀⠂⠀⠐⢢⠄⠀⠀⠀⠀⠠⠴⠈⢀⡰⠋
⠀⠀⠀⠉⠋⠐⠚⠓⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠘⣿⣦⠀⠁⠀⠀⠀⠀⠈⢤⠄⠀⠐⠺⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠤⡴⠷⠾⠆⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠘⠖⠒⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠊⠀⠀⠈⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠉
⠀⠀⠀⣶⠆⠤⠆⢀⠁⠘⠉⠅⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⢾⡄⣀⣠⠀⠀⡄⠀⠀⢰⡖⠀⠀⠀⠀⠀⢸⣲⣦⠴⡂⠉
⠀⠀⠀⠀⠒⠃⠀⠈⠁⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠋⠉⠿⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠉⠉⠙⠓⠶⣦⣄⠀⠀⣹⡶⠶⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠁⣠⣿⣏⢩⣅⡤⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠂⢙⠻⢿⣯⠀⠀⠀⢁⠖⠀⠀⠀⠀⡉⠁⠘⣤⠴⢦⠀⠀⠀⠁⠀⠒⠛⠉⠉
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠟
⠀⠀⠀⠺⡄⠀⠀⠀⠀⡸⢀⠆⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⡩⠤⠃⢐⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⣀⡔⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⠯⠤⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢣⡴⠠⢄⡜⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠦⠊⠀⠠⠚⢛⠶⠓⡤
⠀⠀⠀⠀⠀⠀⠐⠒⠒⢲⣤⡄⡤⠂⠘⡇⠐⠀⠀⠀⠀⠀⣀⣠⠤⠂⠀⠀⠠⠄⠀⣀⣠⠜⠁⠀⠀⠀⠀⠀⠎⠀⠀⠉⠁⠈
⠀⠀⠛⢲⠶⠶⣦⠺⠫⠉⣿⠁⠀⠤⠴⠇⠀⠀⠀⠀⠀⠺⢬⡃⢀⣀⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠡⡏⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠉⢢⡀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠎⠁⠀⠀⡀⠋⠒⢤⡀⢳⠀⠀⣧⣀⡼⠗⠀⠀⠀⠀⡀⠀⠀⣤⠠
⠀⠀⠀⠀⠀⢠⠂⠤⠀⠀⠠⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⡄⠀⠀⠄⣷⣼⡷⠞⠋⠁⠀⠀⠀⠀⠀⢀⣠⠔⠶⠛⠲⠶⠀⡤⠃
⠀⠀⠤⠤⠊⠁⠦⠄⠀⣀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠐⠂⠤⠰⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠘⠐⠒⠂⠀⠘⠁
⠀⠀⠐⠀⠠⠤⠔⠈⠉⠀⠀⠀⠀⠀⠀⠠⣀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣀⡤⠴⠃⠀⠀⠀⠀⠀⠀⠁

⣿⠿⠿⠿⣿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣧⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⣄⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠉⠙⠓⠒⠒⠒⡶⢯⣤⣔⣙⣉⠑⣂⠀⠀⠀⠠⢀⡠⣤⣾⣿⠟⠉⢃⣸⣶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⠊⣷⣕⡒⠋⠀⢠⡶⠒⠋⡡⠞⠉⠀⢀⣀⠽⠟⠛⠛⣶⡶⠶⠗⠓⣿⡹⠄⠊⢀⣾⠏⣿⣧⠁⠘⢿⣒
⠀⠀⠀⠀⢀⣴⣿⣶⣿⣟⣿⣷⠀⢸⣷⣚⣛⣀⠀⠤⠒⠅⡉⢓⢒⡟⢋⣙⠉⢙⣙⣋⣡⣤⣴⣶⣿⣯⣴⣿⣿⡄⠀⠼⠁⣰⣄⢒⡛⠂⣤⢄⡀
⠀⠀⠀⠀⡽⣿⣿⣿⡉⠛⠷⣀⠀⠈⠉⠛⠚⠿⢷⣦⣤⣤⣌⣭⣵⣾⣿⡟⠃⠸⣿⡿⣭⣽⣿⡟⠓⠞⢩⣠⠄⠁⠀⠀⡌⠋⢸⠆⢀⠀⠀⠀⠀⢢⡄
⠀⠠⣄⣀⠀⣬⣿⡇⠙⠓⠲⡦⠀⠐⢀⡀⠀⠀⠀⠈⠉⠛⠛⠋⢉⣠⠟⠀⠀⠀⠀⡠⠋⣤⠈⠹⠃⠀⠈⠀⠀⢀⣴⠋⠀⢠⠓⠠⠞⠉⡀⢀⣴⡿
⠀⠀⠀⠈⠉⠙⣿⣿⠀⠀⠀⠀⠈⠙⣉⠛⠢⠄⠀⣀⠀⠀⠈⠉⠀⣀⣀⠀⢒⣐⣿⡺⣿⣿⣃⡀⠈⠀⢀⣠⠚⠁⡇⠀⠐⠇⣄⢀⠀⡼⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⠒⢛⣋⣉⣥⣽⣿⣷⢶⣿⣿⡏⠉⠀⣠⣴⠎⠋⠀⣰⠷⠃⠀⣷⢐⡴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⡿⠿⣿⣿⠿⡿⠟⠛⠂⢰⡃⠛⣿⡀⠉⠱⠍⣀⣀⣴⠋⠀⠐⠄⠈⢃⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠛⠲⢬⡝⠛⠤⠀⠀⠿⠅⠀⠈⢷⡀⠐⠈⡋⠙⢿⣾⣿⠷⢆⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣛⠓⠂⢤⣄⡀⠀⠀⠙⢦⡀⣼⣶⣴⡿⠓⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠐⠢⠄⠙⠉⠉⠁⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠂⠀⡀⠀⠠⠀⠀⢠⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⠂⠀⠆⠠⠀⠀⢸⣧⣴⣻⠟⣻⣿⠷⣷⠞⠀⠀⠀⠀⠢⠄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⣋⡹⠿⣿⣯⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠓⠀⠀⢠⡄⠀⠈
⠀⠀⠀⠄⠖⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠛⠉⠉⠀⠈⠙⢿⣿⡄⠀⠀⠀⠀⣴⣶⡆⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⢀⣴⠿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⣾⡿⣿⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠽⠟⠀⠀⠀⠀⠿⠀⠀⠀⣠⣾⠟⠁⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⢸⣿⢹⠇⠀⣸⡿⠀⠀⢀⣴⡶⠖⢷⣆⠀⠀⠀⡄
⠀⠀⠀⠀⠂⠄⠤⢀⠀⠀⠀⠀⠀⡅⠀⢀⣴⠟⠁⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⡟⣠⣤⡀⣼⣏⡟⠀⢰⣿⠇⠀⠀⣼⣿⠇⠀⠀⢹⡆⠀⠀⡃⣠⠆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣠⡟⣼⡟⣽⠃⣿⣿⠁⢀⣿⣿⠀⠀⠀⢿⣿⠀⠀⠀⠀⠟⠛⠒⠁
⠀⠀⠀⠀⠀⢂⠐⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⠟⠠⣿⣰⠏⠀⣿⠃⠀⣾⢻⡇⠀⠀⠀⠸⠿⠆⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⡀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⡼⠋⠀⢀⣿⠋⣠⡾⢻⣇⣼⠃⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⣠⡴⠟⠙⠛⠋⠀⠀⠛⠁⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⡟⢿⣿⣧⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠋⠁⠀⠀⢀⠀⠄⢤⣄⠀⠐⠀⣉⣛⡧⠄⠀⠀⠀⣰⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠗⠀⠌⠻⠇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣂⠐⠀⠀⠊⠀⠀⠀⠤⠀⠀⠈⢻⠓⠈⠛⠿⠶⠊⠈⠁⣀⣤⣤⡶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⢠⠥⠤⠰⢲⠄⡀⠀⠀⠃⢀⡀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠙⢿⡷⠶⠞⠓⠀⠀⠀⠀⠀⠀⠀⠩⠗⠂⠙⠶⣄⡐⠐⠋⠉⠀⣤⡼⣶⣤
⠀⠀⠀⠀⠀⠀⠳⣄⣂⣀⣀⣈⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡴⠆⠀⠀⠀⠀⠀⠀⠤⠒⠋⠀⠀⠀⠐⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⢀⠀⠈⠙⠛⠋⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢤⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⣴⣶⣿⡤⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠁⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⢤⡅⠁⠀⠈⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⢿⣖⣶⠤⠄⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠰⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⢀⠀⠒⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠘⠆⠠⠤⠠⠤⠀⠀⠄⠤⡠⠤⢤⡀⠀⡀
⠀⠈⠛⠶⠦⠤⠤⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⢠⡇⠀⠀⠀⠀⢠⠇⠀⠀⠰⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣀⣀⣀⣀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠊⠙⣀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⠁
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣀⠀⠀⠚⠚⠻⠆⠀⠀⠀⠸⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⢠⣤⠖⠹⡇⠀⠀⠈
⠀⠀⣬⠉⠀⠈⠁⠀⠀⢠⠀⣿⡇⠀⣿⠄⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣶⢄⡀⠶⣽⠁⠠⠶⣶⣶⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⠆
⠀⠸⠿⠀⠀⠀⠀⠀⠀⠜⠀⠻⠇⠀⡿⠄⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⡐⠀⠘⢬⣴⣥⠜⠂⢄⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠋⠁⠀⠀⠈⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢿⡿⣿⣿⣶⣶⣦⣤⣤⡄⢠⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣘⣿⣯⣲⣦⠀⠀⠀⠀⢀⠄⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠈⣧⠀⠀⢠⣿⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⢿⣿⣿⣆⣿⡇⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣽⣿⣿⣿⣿⣿⠷⠚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⣩⣿⣿⣿⣾⣶⡶⢲⣾⡑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⣾⣿⣿⣿⣿⠟⣸⠃⠈⠻⡿⣄⠁⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⡀⠋⢠⡄⣤⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⢀⣴⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣽⣯⠀⠀⣿⣿⡟⡇⣿⠿⠛⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⠀⢿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠛⢹⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠀⢠⣤⣿⢸⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢈⣹⣻⣿⣿⣷⡶⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⢀⠠⠀⠀⠀⢀⣿⣿⣼⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣤⣮⣿⣿⣿⣿⣿⣿⣷⣂⣀⡤⠖⣾⣿⣏⢻⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⢷
⠀⠀⠀⠀⢶⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣽⣿⠿⢛⣁⣀⣀⣿⣿⣷⡬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠛⠛⣿⣯⣍⣉⣉⣉⡙⠛⠛⠻⠿⡯⠔⠚⠋⠉⠉⣙⡻⣿⣿⣧⢀⡀⢰⣁⠀⠀⠀⡆⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠐⠿⠿⠿⣿⣿⣿⣻⣻⣶⣶⣦⣤⣄⣀⡀⠐⠉⠁⣀⣿⣿⣿⣧⡬⠙⠿⠿⡿⠀⣂⣠⡤⠞⠋⠁
⠀⠀⠀⠀⢸⣶⣦⣤⣀⣀⡀⠊⠉⠉⠛⠛⠻⠿⣿⣯⡤⠴⣚⣉⣽⡿⠿⣿⣿⣿⣿⣿⣻⣟⠁⡿⠟
⠀⠀⠀⠀⠙⠿⠷⠾⣯⣿⣿⣿⣶⣶⣦⣤⣀⣤⠼⠗⠊⢉⣉⡠⠼⠁⠀⠀⣌⠁⠀⠀⢠⡿⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣧⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⡼⢽⡧⠀⠼⣏⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣻⡗⢀⡚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠷⢦⣯⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⡤⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣒⣒⣢⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠄⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢍⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⣀⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠤⠀⠀⢀⣀⣀⠠⠔⠋⢀⡼⠋⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣋⣀⠀⠀⠉⠉⠙⠛⠒⠲⠶⠦⢤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡎⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⠤⠔⠋⣇⣀⣠⣄⠀⠀⠀⣀⣀⡀⠀⠉⠉⡉⠛⠛⠛⠛⠋⠀⠀⣴⣾⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠦⢤⣤⣄⣈⣉⣀⣈⣳⣶⡚⠁⠀⠙⠦⡴⠋⠉⠳⣄⣀⡞⠛⠢⣤⣿⢜⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠈⠲⢤⣀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠒⠲⠦⢬⣅⣀⣤⣾⢟⡿⠋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⣒⡲⢤⣶⣺⠿⠳⣶⣶⠶⠶⠤⠤⣤⣴⣶⣶⡒⠋⠁⣀⣼⡿⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠛⠒⠦⠤⢄⡤⠌⠽⠿⣿⣟⡛⠋⠁⠀⠉⠛⠋⢛⠛⠛⢙⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠤⠤⢄⣀⣀⣀⡀⠀⠀⠈⠉⠉⠉⠛⠒⠚⠉⠉⣉⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡵⠋⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡺⠛⠛⠓⠶⣤⠀⠀⢸⡟⠲⠦⠤⠤⠴⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⠀⠀⠀⠀⣀⣼⡇⠀⣿⣝⠷⠶⠤⠤⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⣉⡙⠛⠛⢋⣹⡿⠃⠀⢻⣍⡙⠛⠛⠛⠋⣿⡟⠀⠀⠀⣀⣤⠴⠚⣋⣥⣙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣥⣍⣉⣛⣫⣽⣿⠀⠀⠀⠀⠈⠙⠛⢛⣛⣫⣥⣤⠶⠚⠋⠉⠀⠀⠉⠁⠀⠉⠓⠌⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣀⣀⣤⠾⠛⢀⣀⣀⣤⡤⠶⠒⠛⠻⣿⣿⣿⣷⣄⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⣷⠈⠻⣿⣿⣿⣷⣄⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠈⠻⣿⣿⣿⣿⣦⡛⠀⠀⠀⢀⣠⡴⢚⣩⡴⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡛⢦⡀⠈⠳⣄⡀⢄⡀⠀⠀⠀⠉⠻⠷⣦⣬⠙⢿⣿⣿⣿⣦⡴⢞⣫⡵⣞⣫⠵⢶⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡛⢦⡙⢦⣄⠈⠛⢦⡙⠶⣤⣤⠤⠤⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠿⢛⣋⡭⠶⣚⣻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢦⡙⢦⡙⠷⣄⠀⠙⠶⠶⠶⣒⣛⣯⠽⣷⣿⡿⢿⣿⣿⣿⠶⣛⣭⠵⠖⠋⢩⡴⣞⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢦⣙⢦⣈⠳⠶⠖⢛⣋⣭⠵⠖⣛⣭⠴⢖⣻⣿⣿⠟⠋⠁⠀⠀⠀⠀⣿⣜⣃⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢦⣝⠷⠶⢚⣋⣥⠴⢞⣫⡭⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⢻⣤⣉⠙⠛⢋⣉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⣚⣫⡥⠖⠛⠉⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⣿⠦⣤⣍⣉⣩⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠒⠁⠀⠀⠈⠙⣆⠀⠙⠶⣤⣤⣤⣤⡤⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⢤⣤⠤⠶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⡤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠤⢢⠤⢀⣄⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠃⠀⠰⠏⣠⣀⣸⣷⣎⣉⣀⡿⣷⣼⣟⠋⣼⣿⡿⣿⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠉⠉⠉⢉⣉⡁⣤⡤⢾⣛⣿⡟⠀⡹⠃⢀⣤⣞⣯⣴⢅⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠿⣧⠀⣠⣴⣾⣿⣿⣿⣷⣿⣿⣽⣿⡿⢿⣶⢁⣾⣿⣿⣏⣿⣁⡀⠘
⠀⠀⠀⠀⠶⣤⣤⣤⣿⡛⠋⠉⣉⣽⣛⣛⣺⡿⠋⢡⣶⣾⣿⣾⣿⣿⢧⣿⣏⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⢛⣩⠙⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⣟⣿⣿⡏⣾⡏⢙⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⡿⣹⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠘⠃⠐⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡷⣿⣿⣿⣿⣿⣷⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣙⣏⣿⣿⣾⡿⣻⣿⣯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⡝⠠⣿⢻⣿⣿⡏⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠋⠀⠘⠚⠯⡼⢻⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡉⠑⠒⠶⠤⠤⣠⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠂⠀⠰⠟⡉
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠉⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠋⠁⠀⠀⢀⣠⠴⢎⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠈⢄⠀⠀⠉⣿⡩⢙⠶⠦⣤⣀⡀⠀⠀⠀⠀⠉⠐⠂⠠⠄⠀⠀⠀⠀⠐⠂⠁⠈⠿⠀⠀⠴⣶⡉⣀⣀⣀⣡⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⣲⣾⣷⣌⣀⠀⠀⠎⠉⠛⠶⢤⣄⣀⠀⠀⡀⠀⠀⠀⣶⠀⠀⠀⣀⣤⣶⠁⠀⣀⣀⢙⠉⢉⣽⡃⠀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢀⡈⠙⠻⢯⣶⣖⣶⣶⣾⠿⣿⣿⡟⠶⠦⣤⣀⣀⣈⡤⠶⠻⠁⢠⡷⠺⠫⢉⡍⣾⡾⠟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠲⣄⠀⠀⢀⣀⠀⠀⠀⢉⣉⣻⣶⡀⠺⠀⠉⠡⢀⡀⠄⣠⣏⡠⠤⠚⠋⠰⠁⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢄⡀⠀⠈⠑⠢⠤⠀⡀⠉⠁⠀⠚⠂⠙⠻⣷⣤⣤⣤⡤⢶⡮⠭⠤⢤⣤⣤⠄⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣁⡀⠈⠐⠠⢄⡀⠀⠀⠀⠙⠢⣄⠀⠀⢀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣯⣿⣿⢷⣜⣿⠞⠛⠳⣤⣀⠀⠀⠈⠷⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡍⠛⠿⣏⣿⣴⠶⠤⣄⣀⠉⠲⢦⣄⡀⠀⠀⠀⣀⠀⠀⣀⣤⡀⠀⠀⠈⠀⢀⡰⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠉⠻⠦⢀⣄⠉⠓⢦⣄⠈⠛⠓⠒⠶⠾⣶⠿⠮⣙⣿⠷⠶⠶⠚⢋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠓⠄⠄⣈⠳⣤⡀⠀⠀⠀⠀⢀⠠⠀⠛⠛⠃⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠀⠀⠀⠀⠉⠘⠛⠂⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠒⠦⢤⣀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⠿⢿⣿⠟⣣⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⣵⣶⣶⣶⠞⣢⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣡⣾⣿⠿⣋⣵⣾⣿⠟⣋⡛⠿⠿⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣋⣼⡿⢋⣵⣾⣿⠟⣋⣴⣿⣿⣿⣿⣿⣷⡌⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢛⣥⣾⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢟⣡⣾⣿⣿⣿⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢟⣩⣶⣿⡿⢛⣥⣿⣿⠃⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢠⣾⠟⣫⣴⣿⡿⢟⣡⣶⣿⣿⣿⣿⣄⠙⠛⢉⣉⠙⢿⣿⣿⣿⣿⣿⠿⣋⣴⣿⡿⠟⠉
⠀⠀⠀⢀⣴⡿⢱⣿⣿⣿⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⠿⣋⣵⣾⣿⠟⠉
⠀⠀⠀⣾⣿⣿⡘⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⡀⢺⣿⣿⣾⣿⠟⠋
⠀⠀⠀⠻⣿⣿⣿⣌⢿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⠿⠋
⠀⠀⠀⠀⠈⠙⢿⣿⣦⡹⣿⣷⡜⢿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡜⢿⣿⣮⣥⣤⣭⡛⣩⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢀⣠⣿⡿⠓⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠓⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⣾⡿⠟⣉⡤⠞⣠⠟⠉⠛⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣀⣤⣾⡿⠋⣸⠛⡶⢤⣀⡀⠀⠀⠀⡟⠀⢀⣿⡏⢀⡞⣡⠖⠋⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⡿⠋⣡⠴⣚⣥⠞⠁⠀⠈⣹⠀⠀⡴⠃⠀⣸⣿⠁⣼⢰⡏⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⣿⠃⣰⢃⡞⠉⠀⠀⠀⣠⠖⠃⡤⠚⠁⢀⣴⣿⠋⢠⠇⣼⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⣾⡟⢀⡏⣼⠁⠀⠀⠀⣰⠃⢀⠞⠁⢀⣴⡿⠋⢁⡴⢃⡼⠃⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⢀⣴⣿⠟⢀⡜⢡⠏⠀⠀⠀⠀⡇⠀⡟⠀⢀⣾⡟⠁⡴⢁⡴⠋⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⣰⣿⠏⢀⡔⢋⡴⠋⠀⠀⠀⢀⡼⠃⣰⠃⠀⣸⣿⠀⡼⢡⡟⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⣿⠃⣠⠋⡴⠋⠀⠀⠀⣠⠞⢋⡥⠞⠁⢀⣴⣿⠃⢠⠇⣾⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⣾⡟⢀⡇⣼⠁⠀⠀⠀⡼⠁⢠⠏⠀⢀⣾⡿⠛⢁⡴⢋⡼⠃⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣴⠚⠁⢀⣴⣿⠟⢀⡜⢠⠇⠀⠀⠀⢸⡇⠀⡞⠀⢀⣿⡟⢀⡜⢡⡶⠋⠀⠀⠀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⣼⠁⠀⣴⣿⠋⢡⠔⣋⡴⠋⠀⠀⠀⢀⡞⠀⡼⠁⠀⣼⣿⠁⡼⢠⡏⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⢰⠇⠀⢰⣿⠃⣰⢃⡼⠉⠀⠀⠀⣠⠞⠉⡴⠋⠀⣠⣼⣿⠃⣰⠃⡾⠀⠀⠀⢀⡏
⠀⠀⠀⢀⣠⠏⠀⢀⣿⡟⢠⡇⣼⠁⠀⠀⠀⡞⠁⠀⠀⠓⠦⣾⣿⠋⣡⠖⣃⡼⠁⠀⠀⠀⡼⠁
⠀⠀⢰⣏⡀⣠⣶⡿⠟⢀⠞⣰⠇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣅⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠙⠻⠿⣤⡞⣡⠖⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠴⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠁⠀⠊⠀⠀⠤⠀⠀⠀⠀⠐⠀⠾⡀
⠀⠀⠀⠀⣱⠢⠄⠀⠀⠀⠤⡄⠀⠀⠀⠀⠊⠀⠂⠠⠀⠠⠀⠂⠐⡠⠀⠀⣅⡀⠀⢀⡰⠂
⠀⠀⠀⢠⡏⣈⣀⣀⣀⣀⣐⣋⠑⠀⠀⠀⡻⠔⠀⠀⠀⠀⣒⡢⠽⠁⠀⠀⠸⣵⣈⣷⣄⢤⣠⢤⡅
⠀⠀⠀⠑⠛⠠⠤⠀⠐⠊⠉⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⡀⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⢹⣭⣭⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠠⣀⣀⠀⠀⠀⠈⠉⣀⢢⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢸⠂⠀⠀⠀⢀⠠⠊⠀⠙⢈⠖⠂⠠
⠀⢀⠀⢤⣀⣀⣉⠉⠁⢀⣀⣠⡴⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⢠⠎⠀⠀⡠⠀⠁⠀⠐⠀⠂⢀⠌⠁⠂
⠀⠀⢀⠀⡩⠉⠉⠉⠉⠉⣉⠔⠁⢀⠀⠀⠘⠙⢦⠀⢀⡠⠚⠁⠀⠀⠑⠑⠀⠀⠀⢀⠀⡰
⠀⠀⠀⠉⣤⠒⠀⡄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⣐⠔
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠘⢧⠜⡀⠀⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⢩⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢷⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡶⠛⠉⠀⠀⠁⣱⣄⣀⠀⠀⠀⠀⢸⠀⠀⣈⡻⢃⢸
⠀⠀⢄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣝⠆⠀⠀⠀⠃⢠⠐⠘⡋⣋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠄⠤⠤⠀⠠⠀⠄⠀⠀⠐⡀⢠⠀⠀⠀⠀⠀⠀⣀⣈⣀⣠⡄⣤⠤⢔⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⣤
⠀⠀⠀⠘⠲⠶⠶⠶⠶⠶⠶⠶⠶⠦⠀⠁⠀⠀⠀⠀⠀⠀⠐⢶⣾⣶⣷⣾⣿⣯⡿⡿⠇⠀⠀⠀⠀⠀⠈⠙⣛⡛⣛⡛⣛⣓⣛⣛⣛⡓⠉
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠛⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣤⣦⣶⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠄⠠⠀⠠⠄⠀⠂⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⢤⡄
⠀⠀⠀⠀⠳⣤⣈⣄⣩⣤⣄⣑⣂⣻⣿⣿⠇⠀⠀⠀⠀⠀⠈⠦⣄⢠⣀⣀⣀⣀⣀⣠⡤⠂⠀⠀⠀⠀⠸⣡⠀⣽⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⡤⢤⡤⣤⣤⠬⡥⣤⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣬⣭⡍⣭⣥⣤⡄⠀⠀⠀⠀⠀⠀⠈⡙⡛⢛⢛⢒⣒⡛⡛⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠰⠶⠰⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠴⠴⠴⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠙⠛⠘⠃⠃⠃⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⢢⣶⡔⣦⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢐⣤⣤⡈⢸⣯⣶⣿⣆
⠀⠀⠀⠀⣾⣫⣽⣁⠧⠒⠒⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠄⢴⣟⣛⣛⣛⣛⣋⣥⠹⣿⢟⡽
⠀⠀⠀⠀⠈⠉⣛⢛⣛⡛⣛⢋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⢛⡛⣛⢛⢛⡉⠁
⠀⠀⠀⠀⠀⠀⠓⠙⠛⠋⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢓⣐⣐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠿⠿⠟⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠖⠲⠤⠤⠤⢴⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⣼⣿⡧
⠀⠀⠀⠠⡁⠀⠀⠀⣿⣿⡆⠀⠀⠀⢀⡵⠀⠀⠀⠀⠀⠀⠛⣀⠀⡈⠉⠈⠉⠀⠀⠂⡹⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠁⢳⣄⢻⣯⣻
⠀⠀⠀⠀⠈⠐⠦⠤⠽⠿⠧⠤⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣠⣨⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠘⠻⢧⣼⣮⣴⡿⣶⣏⠿⠃
⠀⠀⠀⠀⠰⠶⠶⠶⠒⠶⠶⠶⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣦⣶⣤⣄⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠦⡦⣦⠤⡤⠴⠰⢴⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠈⠉⠀⠰⠀⢀⠂⠀⢶⡔⠡⠐⡄⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠁⣀⠐⣄⠈⠲⣦⠀⠀⠆⠀⠀⠀⢀⠈⠀⡐⠀⠈⠂⠀⠀⠄⢮⣱
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠘⠂⠀⠈⠁⢀⣀⠀⠀⠄⠡⠀⠀⠀⠁⠀⠐⠀⠀⢀⠈⠱⡃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⠑⢐⣀⣀⠠⠀⢠⠁⠁⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠱⡄⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⣀⣁⣤⣼⡶⠂⠀⠀⠀⠈⢐⡄⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠀⡀⡀⠀⠈⠀⠀⠀⠀⠄⠀⠈⠉⠘⠿⠋⠊⣀⠀⠘⠀⣄⠀⠁⠀⠀⡀⠀⠀⠀⢠⠐⠀⠤⠀⠀⠀⠀⢐⠀⠀⢀
⠀⠀⠀⠀⢐⠀⠀⠀⡄⠀⠀⠀⠀⠒⠃⠉⠀⠀⠀⠁⠐⠡⠀⠀⠀⠀⠂⠀⠈⠘⡤⢔⡊⠁⠘⠠⠀⠀⠀⠂⠀⠀⠈⠠⡀⠘
⠠⠀⠌⠴⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠁⢈⣦⠞⠡⠀⠉⢦⡀⠀⠈⠁⠀⠀⠠⠑⠂
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢈⣠⠄⠀⠀⠀⢠⠈⣂⠀⠀⠀⠀⠀⠀⠀⣴⡟⠣⠀⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠒⠂⣤⣀⣀⣀⠀⠀⠀⠠⠀⠀⠐⠂⠀⠂⠀⠀⠁⠀⢀⣴⣾⡏⠁⠀⠀⠀⠀⠀⠉⠉⠙⢦⠀⠀⢀⠀⡄⠀⠤⢀⠠
⠀⠀⠀⠀⠈⠙⠛⣿⣿⡆⠀⠀⠀⠀⠐⠠⠄⠂⠀⠐⠒⠠⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣰⣶⠶⣶⣶⣦⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⠉⠛⠓

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢈⣉⣄⠙⢁⣩⠏⠉⠞⠁⡀⠖⠠⠦⣤⡤⢶⡦⡀⠀⠀⠀⠀⠀⣿⣿⣒⣂⣒⡂⢀⣐⡒⣂⣀⢀⠀⠀⠂⡀⡀⠨
⠀⠀⠀⢠⠈⠁⠙⠉⢁⣈⡤⠶⣾⣗⣡⣤⣬⣽⠿⡟⠇⠁⠀⠀⠀⢀⣸⣧⣿⠿⠛⠟⠛⢩⣿⣿⣽⣿⣿⣷⣶⣺⣿⠿⣶⣶⡀
⠀⠀⠀⢘⣛⣛⣻⢯⢉⣴⣾⣭⣥⣤⣄⢠⣤⣴⣶⣮⡁⠀⠀⠀⢠⣿⣿⠭⠟⣶⣤⣲⢶⢻⠛⠻⠽⠿⠿⣿⣿⣇⣶⣶⢿⠛⠂
⠀⠀⠀⠈⠛⠻⠭⠛⠋⠀⠀⠀⠀⠀⠉⠁⠀⠠⠞⠛⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤
⠀⠀⠀⠀⠀⣠⣶⡿⠟⠊⠃⠉⠉⠛⠉⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠘⣦⣀⣀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠻⠿⣿⢦
⠀⠀⠀⢈⢿⣿⣿⣛⣛⣛⣙⣛⢛⣋⣉⣉⣭⣭⣝⢩⣿⡿⠀⠀⠀⠀⠘⣾⣻⢁⢷⠧⢀⡀⠤⠄⠒⣀⣀⣀⢀⣀⣀⠀⠐⠰
⠀⠀⠀⠈⢿⠶⠆⠀⡿⣿⢽⣧⢹⡯⠿⠽⠿⠿⠗⣚⡁⠀⠀⠀⠀⠀⠀⢼⣽⢶⣮⣵⢒⡛⣿⡇⢀⠛⢛⣶⣞⣛⣛⣓⣚⣃⡀
⠀⠀⠀⠀⢸⣶⣶⣦⣤⠤⠦⠴⠶⠶⠒⠒⢒⣸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠿⣾⡋⠟⡹⢻⢇⣨⡄⣢⣘⣋⣹⣯⣥⣼⢿⣅⢨⡷
⠀⠀⠀⠈⡉⠙⣻⣷⣶⣤⣤⣄⣠⠴⠶⢺⣿⣽⣽⣶⡍⠀⠀⠀⠀⠀⠓⢶⣿⣿⢟⠹⣼⣾⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠸⠏⠁⠁⠀⠀⠘⠻⢧⣠⡿⢟⣛⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣾⠷⠿⠿⠿⠉⠋⠉⠉⠓⠊⠉⠁⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠
⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀
⠀⠀⠀⢀⡴⠻⢛⡳⢤⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⠃⠐
⠀⠀⠜⢡⣤⠶⠦⠁⠨⣿⡇⠀⠹⡆⠀⠀⣀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⡙⡄⢀
⠀⠀⠀⠀⠀⢠⣤⣠⣄⣀⠉⠉⠙⢿⡟⠛⠛⠦⣍⠙⠓⠒⠀⠀⠀⢐⣶⠂⠀⠉⠉⠉⢛⣓⠺⠛⠉⠝⠓⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣰⡀⠰⠻⡍⠻⣍⠑⠦⠷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⣀⣀⣐⣚⡋⠂⠀⠀⠀⠀⠠⠄⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠻⣷⡶⠂⠈⠲⣤⣌⣑⡖⣶⣄⠀⠀⠀⠀⠀⠀⢀⠴⠺⠿⢿⣯⣭⠬⣬⣟⠛⣛⡶
⠀⠀⠀⠀⠀⠀⠙⢅⡾⣷⠆⠠⠞⠋⠭⠉⠛⠳⣄⠀⠀⢀⣴⠧⠀⠀⢴⡀⠀⢀⡀⠀⡀⠀⠀⣀⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠁⠀⠈⠁⠀⠈⠂⠰⠧⠀⠀⠀⠀⠀⠈⠧⠀⠀⠠⠷⠗⠂⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡁⠀⠀⠀⠀⠀⠀⢀⣴⣴⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⢦⣤⠀⢰⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⣿⣷⣜⣧⣾⣵⠀⢠⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣤⣶⣾⣿⣿⢿⠟⠛⠷⣤⣿⣶⣦⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢉⣾⢻⢏⡇⠞⠈⡠⡀⠀⠆⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠸⣿⠛⠘⠀⣴⠀⠀⡀⣤⣾⣤⣤⣤⣤⡔
⠀⠀⠀⠀⠀⢀⣤⣲⣖⣂⡖⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠈⠀⠀⢿⡷⠖⠋⠉⠅
⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⢠⣶⡀⢀⡀⢰⣿⣀⣤⣤⣤⡾⠁
⠀⠀⢸⣿⡿⢿⣿⣿⣿⡇⡇⠈⣄⣀⡀⠀⠀⠀⠀⣠⣼⠏⠀⠀⢀⣴⣿⣿⢿⠿⠟⡩⣥⠀⠀⠀⠀⠘⡄
⠀⠀⢘⠛⠀⠈⠈⢠⢸⡇⡇⠀⢻⣀⣀⡀⢠⣴⣿⣿⠋⠀⠀⠀⠸⣿⣅⣿⢰⣄⡀⣠⣿⣤⣤⣤⣴⣶⡇
⠀⠀⣼⣀⣧⣧⣼⣾⣿⣇⢳⠀⠸⣿⣛⣿⣭⣽⣿⠇⠀⠀⠀⠀⠀⠙⢿⣿⣼⣟⠙⠉⠉⠉⠉⠉⠉⠉⢱
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⢻⣿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⢧⠀⠘⡇⠀⠀⢸⡃⠀⠀⠀⠀⠀⢠⣶⡄⣿⠀⣿⢘⣿⡄⠀⠀⠀⠀⢤
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡸⣄⠀⠙⠀⠀⢺⣵⣄⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠀⠀⠀⠀⣄⣿⣿⣿⣶⡄⠀⠀⠀⠀⠻⠉⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠆
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣦⣤⣤⣤⣄⡀⣀⣀⠀⢀⣀⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁


⣾⣷⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿

⠀⠀⠀⢠⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⣦⣄
⠀⠀⠀⣿⠀⡉⠙⠛⠛⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢠⠞⢡⠊⠳⣄
⠀⠀⠀⣿⠢⢄⠀⠉⠉⠀⠒⠒⠚⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⢶⣦⠾⢋⠔⠁⡰⠁⢀⠔⠉⠳⢤⡀
⠀⢀⡴⢏⡀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠒⠫⢍⠋⠭⠹⢛⡛⢲⣦⠖⠋⠁⠀⢀⡴⠋⠄⠈⡠⠔⠊⠀⡠⠃⠀⣠⠴⠖⠛
⠀⠛⠷⢶⡈⠉⠒⣂⣨⠥⠤⢤⣀⡈⠑⠂⠤⣀⡈⢐⣒⣤⠶⠋⡁⠄⠤⠤⢠⣾⠕⠁⢀⡎⠀⢠⠔⠊⠀⡴⠋⠁
⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠉⠓⠲⣶⣤⠾⠋⠁⠀⠐⠁⠀⠀⣀⣠⡿⠃⠀⢀⡜⠀⢠⠃⣀⣴⠾⢅
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⢉⣉⣛⣛⣉⠭⠤⠀⠂⣀⡀⠤⠔⢒⣭⡿⠋⣠⠔⢒⡉⠤⠔⠁⡼⢥⣀⣠⠏
⠀⠀⠀⠀⢀⡴⠋⢀⡠⠒⠉⢁⣀⠀⠠⠤⠐⠒⠈⢁⣀⠠⠤⣲⡯⠊⠀⢠⠁⢰⠁⣀⣤⣴⠞⢧⣀⣰⠃
⠀⣀⣠⠴⠋⢀⠴⢋⠄⠊⠉⠀⠀⠀⡠⠒⢁⡤⠤⠤⠤⣤⠖⡫⠤⠒⠂⠁⠀⢤⠞⠁⠀⠈⠻⢦⣼⠏
⢻⡉⢀⡠⠊⢁⡔⢁⠄⠀⠀⠀⠀⣉⣤⣴⠏⢀⠤⠒⢉⡤⢊⠀⠐⠒⢀⣀⡠⠏
⠀⠻⣤⡤⠔⠉⡐⠁⣰⠞⠛⠛⠋⠁⣰⢋⠞⡠⠔⠈⠁⠀⠀⠀⡴⠋⠉
⠀⠀⠘⢷⣤⠞⢀⡾⠁⠀⠀⠀⣠⠞⢁⠎⡜⠀⠠⠂⢀⣀⣠⡼⠁
⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠚⠥⣤⣋⡐⠀⠀⡄⠀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣴⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⣭⣭⠿⠀⠀⠀⢠⠈⠡⠤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠠⢜⠀⠀⠶⠖⣿⠍⠡⠤⠤⢵⠀⢚⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣉⣿⣉⠘⣛⣛⣽⡇⠀⢒⣚⡿⠀⠥⠵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢤⣷⠀⢈⣁⣀⢽⡇⠈⣉⣭⣿⡀⢒⣲⡧⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⡤⢄⡐⢒⡲⠒⠚⠓⠒⠛⠂⠀⠂⠤⢾⡃⠀⠶⣺⣯⠄⣉⡥⣿⢉⣽⡇
⠀⠀⠀⠀⠘⠙⠓⠻⢶⠀⠈⠀⠀⠀⠀⣀⣠⠴⠖⠒⠈⢉⠉⠈⢻⣽⡻⡤⠤⣶⣷⢴⣿⣧⡆⢀⣤⣤
⠀⠀⠀⠀⢀⡀⠀⢈⢹⠀⠀⠀⠀⠀⠀⡿⠿⠷⢤⣬⣦⡶⣰⣭⣿⣶⣒⣖⣒⣲⣾⣽⠿⠿⣯⣽⣿⣿⠷⠂
⠀⠀⠀⠀⠈⠙⠊⠛⠻⢦⣀⠀⠀⠀⠀⣏⠂⠀⠀⠀⠀⡏⠁⠉⠈⠉⠩⣏⠉⠉⠾⣁⣐⣐⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠤⠹⠷⢶⣦⣄⣀⣇⣠⣤⣶⣾⠽⠏⠂⠐⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀
⠀⠀⠀⢀⠔⠈⠹⣁⣀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠔⠀⢈⠚⠁⠀⠀⡢⢄
⠀⠀⠘⠁⠤⣀⣀⡀⠀⣈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠃⠀⠀⡌⠀⠀⠀⠐⠀⠀⠀⢄⠀⢠⠋⠉⡆
⠀⠀⡸⢄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢀⠃
⠀⢰⠒⢘⠁⠹⠉⠉⢃⠀⢹⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠁⠀⡎⣛⣟⢓
⠀⠀⢆⠈⡀⠀⡄⠀⠸⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠉⠉⡁
⠀⠀⠈⠢⣐⡀⠰⡀⢰⢀⣃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠦⠀⣀⣀⣈⠑⣶⣻⠤⠔⠀⣉⣁⣀⠀⠈⠑⢢⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐⠀⠀⠈⠐⠀⠠⡀⠀⠀⠀⠀⠀⠓⠋⠣⡐⠢⠄⣀⠀⠀⠀⠉⠰⢆⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⢀⢀⡠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠈⢁⠰⠃⠁⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⡂⠀⠈⠺⢤⠔⠊⠀⠀⠑⢄⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⠇
⠀⠀⠘⣉⠀⠚⠾⠀⠀⡀⠄⠒⠈⠑⢄⠀⠀⠀⠢⠀⠄⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠶⠷⠆
⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⣱⢲⡀⠀⠀⠀⠲⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⡟⠂⣈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⣷⠏⣈⡰⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⡰⠆⠛⠈⢩⠉⢶⠠⡄⠀⠀⠀⠀⠀⠀⠣⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⢓⡈⣅⠠⣆⡒⠃⠁⢠⡴⠂⢄
⠀⠀⡤⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠢⡀⠀⠀⠀⠀⠀⠀⢰⠂⠏⠙⣀⢠⡔⠁⠈⠛⠋⠀⡡⠱⠣⣽⢁
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢠⢄⢀⣀⠀⠘⡆⠀⠀⠀⠀⠀⠰⣇⢙⡁⣡⡌⢀⢤⡔⢲⠎⣉⠝⠃⢜⢘⠀⠆
⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠵⠯⠴⠮⠬⠭⠄⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⡴⠇⡨⠓⢤⡌⢱⠎⣠⠋⢃⠸
⠀⠙⠒⠲⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⢲⠖⢲⠶⠶⠒⠒⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣉⡰⢆⣨⢓⣤⠩⠵⠞⠢⠃
⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⣸⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⡀⠤⠀⠠⠄⡀
⠀⠀⠀⢰⠀⢠⠀⡇⠀⢰⡖⢒⣒⣒⣛⣛⣓⣚⣒⣒⣒⣦⠀⢰⣲⣒⣒⣒⣒⣒⣒⣒⣲⣒⣀⣀⢀⠈⡇⠀⡰⢁⠀⠂⠀⠀⠠⠀⠑⠄
⠀⠀⠀⣸⠀⢸⠀⢇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠈⠓⠲⡀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠸⠀⠄⢠⠂⠉⠁⠢⠀⠀⠈⡀
⠀⠀⢠⠃⠀⢸⠀⠘⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢣⠀⠀⠑⠎⠙⢄⠌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠇
⠀⣴⠣⠤⠤⠼⠤⠤⠽⠤⠤⠤⠭⠶⠤⠤⠤⠴⠮⠥⠤⠤⡄⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠄⠈⠈⡐⠀⢒⠤⣀⠎⡘
⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠔⠁⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠑⠎⠀⠁⠁⠀⠄⠊
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢰⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠓⣆⠀⠻⣿⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠆⠀⢸⣿⡇⠀⠀⠸⡆⠀⢻⡆⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣷⠀⢸⣿⠁⠀⠀⠀⠀⢿⣧⠀⠀⢀⡇⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣧⠸⣿⡇⠀⠀⠀⠀⠈⠻⣦⣠⡾⠁⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠋⣸⣄
⠀⠀⠀⠀⠀⣤⣴⠞⢷⡆⠀⠀⠀⠀⠀⠀⠀⢿⣧⡴⢿⡆⠹⣿⣄⠀⢀⣤⠀⠀⠈⠁⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⠛⢁⣤⣾⠛⠉⡆
⠀⠀⠀⠀⠀⢻⣇⠀⣸⣇⣠⣤⣄⣀⡀⠀⠀⢸⣯⠀⢸⣿⡀⠈⠛⠻⠟⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⣁⠤⠤⠴⢞⣹⠁⠀⣀⡇
⠀⠀⠀⠀⠀⠈⣿⡾⠛⠉⠉⠉⠉⠻⣿⣷⡀⢸⣿⠀⠀⢿⡧⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣛⡽⠋⣠⠾⣗⡼⠤⠵⠋⢀⣠⣾⡿⢷
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⢹⣿⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⠫⢿⠟⠛⠛⠋⢀⡼⣧⠤⠞⠀⢀⣠⣶⣿⠿⠃⣠⡟
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣠⠿⠋⠀⠈⠀⠀⣀⣤⣶⡶⡾⣟⢣⣼⣮⠟⠁⠀⣠⡄⣴⣿⡽⠃⣀⣴⣿⣿⠟⠋⠀⡠⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡴⠖⠋⠁⠀⠀⣀⣀⣴⣾⣿⠿⠛⠛⠛⠋⠉⠉⢀⣀⣀⣼⣿⠷⠋⣡⣶⣾⣷⡷⠛⠁⢀⠔⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣀⣤⣴⡶⣿⣿⣿⣿⣿⠿⠁⠀⠀⢀⠔⠢⠤⢲⣻⠿⠛⢁⣠⣴⣿⣿⠟⠋⠁⢀⣤⡶⠕⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣻⠻⣷⣼⠿⠃⠛⠋⠀⣀⡠⠔⢾⣩⣄⡤⠚⢉⣤⠤⢶⣿⡶⠟⠚⠋⣀⡴⠞⠉⠁
⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣭⠜⠋⠀⠀⠀⣤⢶⢁⠁⣠⠴⠋⢀⣠⣴⣾⣿⡿⠿⠋⠁⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⣤⡖⣤⡉⠁⣤⡶⠍⢡⣥⠴⠛⠟⢛⢉⣠⣶⣿⣿⣿⠟⠋⠀⣀⣤⡶⠟⠊⠁
⠀⠀⠀⠀⠀⣿⣿⣜⣩⠿⡿⠖⠋⠉⢀⣠⢴⣾⣏⢾⡿⠓⠾⠋⣀⣤⡶⠞⠋
⠀⠀⠀⠀⠀⡄⡇⠀⢀⣀⣠⣤⣶⡞⣛⣳⠾⠷⠛⠋⢀⣠⡴⠞⠊⠁
⠀⠀⠀⠀⣼⣿⠋⢩⣿⣿⣿⠿⠋⠉⠉⠀⢀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⢯⡏⠉⠉⠀⠀⠀⠀⠀⡀⠄⣂⠕⠊
⠀⠀⠀⠀⠘⡴⡤⠄⠠⢄⣐⠠⠁⠒⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⡤⠴⠶⠦⠤⢤⣖⠢⣤⣀⡀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣾⣶⣾⣾⣷⡀⠀⠀⠀⠀⠀⣠⠴⠶⡿⠷⠦⣄⡀
⠀⠀⠐⠦⠀⠀⠀⠈⢳⣀⣈⣉⢀⠞⠀⠀⠀⣀⠴⠚⠁⠀⠈⠉⠉⠉⠉⠀⠙⠢⣄⠀⠀⠀⠈⢦⣀⣀⣀⣀⡜⠁⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠼⢿⠿⢿⠿⣄⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠿⢿⡿⠿⠿⢷⡀
⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢀⡤⠶⠧⢤⠀⠀⠀⠀⠀⠀⠈⢷⠁⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⡴⠁⠀⠀⠀⣠⠤⣄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣠⠦⡄⠀⠀⠀⠈⢢⡀
⠀⠀⢸⠁⠀⠀⠀⠀⢧⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣅⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⣇⢀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⡏
⠀⠀⠘⡄⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠛⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠩⢞⡦⢄⣀⣀⣀⣀⣀⣀⣀⣠⣼⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⡯⣀⡀⠀⠀⠀⠀⢀⣠⡔⣋⣀⣀
⠀⠀⠀⠀⠀⠞⠁⠼⠋⡽⢋⠜⢋⠔⢁⠔⢁⠞⣩⢟⡿⢛⡿⠋⣹⠟⣹⠋⡹⢋⡽⠁⠎⠰⠋⠞⠙⢫⠟⡽⠁⠞⠙⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠈⠀⠀⠁⠀⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⣶⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠶⢦⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣹⡟
⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣽⣟⣛⣲⡄
⠀⠀⠀⠀⠀⠀⢸⡿⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⢀⣼⠟⠈⢙⣻⡄
⠀⠀⠀⠀⣠⠶⠛⢷⣄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⢤⣤⣀⣀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⢀⣴⣿⡟⠛⣻⠟⠉
⠀⠀⠀⠀⠛⢶⡶⠂⠉⠛⠒⠲⠶⠦⠤⣤⣤⣄⣀⣀⣀⠀⠀⣸⣿⣤⣤⡴⠞⠋⠁⠀⣀⣤⠞⢋⣠⡤⣿⢿⣇
⠀⠀⠀⠀⠀⠘⢿⣅⣠⣤⣶⣆⣤⡀⢐⣀⣀⣀⡈⠉⠉⠉⠛⢻⡏⠉⠁⠀⣀⣠⡴⠞⠋⠑⠀⠈⢛⣺⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠉⠛⠒⠿⢿⡏⠉⠉⠻⣥⣶⠿⣟⣂⡹⠿⠟⠛⠻⢥⣄⣰⣏⠭⠛⠛⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣈⡁⠀⠸⣇⣀⣠⠶⠋⠉⠛⠻⠷⠶⠶⠖⠚⠛⠛⠉⠉⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠾⢿⣤⣤⣤⣄⣀⣀⣀⣦⡀⠀⠀⣂⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠖⠋⠉⠁⠀⣏⣉⣙⣛⠳⣶⣴⡏⠁⢤⡁⠛⢲⣤⠖⠋⢉⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⡇⣼⠁⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⢛⡎⣇⠁⣢⣀⣧⣾⣄⠁⠈⠀⢸⡇⠒⠤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⢠⣼⣿⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣭⣍⡑⣛⣹⣷⣿⡟⢦⣀⠀⣸⣧⠀⠠⠼⢏⠦⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⣷⣋⣉⢻⡿⣟⣳⢄⣀⠀⠀⠠⢤⣴⣫⣾⡟⡏⢯⠹⡇⢹⠈⡇⡟⠀⠈⠉⠛⠁⠀⠀⠵⢤⡼⠗⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣼⣟⣴⢻⡿⠿⠟⠀⠸⠽⢿⣍⠓⢯⣽⣋⣟⢻⣿⡻⣿⣷⣱⠸⡀⢦⠀⡄⠀⢻⡶⠒⢢⡄⠀⣤⠤⣤⣤⠤⢦⣄⣀⣈⣿⣛⡷
⠀⠀⠀⠀⠀⢀⠟⠛⣹⣧⠟⣹⣿⣽⣝⣓⣒⢦⣹⣷⠻⠿⣠⠮⠽⢿⣮⣽⣿⢦⢳⠸⡀⠇⢸⢸⣧⡄⠤⠷⣈⡷⠀⢤⣤⠤⠄⣤⡤⠍⣿⣶⠧⡀
⠀⠀⠀⠀⠠⠋⡰⢾⡟⣡⡞⠉⠀⠀⠈⠉⡻⠉⠉⣿⣛⣿⣿⠾⣟⡟⢋⡿⠿⠷⣷⣧⣇⣠⣸⠞⠻⣦⠤⠎⢵⡷⠴⠋⣌⣷⣾⣄⣵⣮⣼⣗⣶⡿⠷
⠀⠀⠀⣤⣾⣋⡹⠯⢾⣉⡩⣶⣄⠀⠀⣠⢶⡀⢸⡿⠿⠷⠶⠤⠚⠛⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠹⣦⣤⣤⠖⢶⣤⣯⣭⡀⡟⠀⠀⠉⠉⠛⠲⠾⢄⡀
⠀⠠⠞⠉⠛⠓⠒⠛⠻⠋⠉⠛⢙⡇⢠⣏⣾⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠾⡗⠛⠛⡇⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⢷⠒⠲⠶⠶⠶⠶⠖⠚⠚⢿⡇⠀⠈⠁⡞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠂⢀⡤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⣦⢿⣷⠀⠀⠀⣰⠀⠀⢀⡞⠁⣤⡀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡸⠁⠀⢀⣴⠖⠙⠋⠂⠀⠀⠀⣼⠃⠀⡾⢁⠂⢀⡀⠀⠀⣀⠀⠀⠀⠀⠈⡄⠹⡎⣿⡀⢀⡔⠋⠓⠒⠶⣷⣚⠅⡇
⠀⠀⢈⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣷⣤⡤⠃⠀⣰⡟⠁⠀⠀⠀⠀⠀⣀⢰⣯⠀⣸⡗⠂⢰⠏⠀⠀⡾⠁⠀⠀⠀⠀⠀⠹⠨⠡⣹⠟⠀⠕⠒⠀⠂⠀⠚⠻⣏
⠀⠀⢸⡋⠉⠉⠉⠉⡉⠩⢿⡀⡟⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣴⠏⠉⢹⢁⠀⣿⠀⠀⠹⠀⠀⠸⡇⠀⠔⠁⠀⠀⠀⠀⣇⣴⡗⠀⠂⢀⠈⠀⠈⠀⠀⣶⣿
⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣼⣯⣵⡏⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠛⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⣀⣀⡴⢦⡾⠻⣦⡿⠘⡇
⠀⠀⠘⣷⠖⠛⠉⣋⠀⠀⠈⠀⠈⠉⠓⠦⡄⠀⠀⠀⠀⠀⢀⣶⢹⡄⠀⠀⠁⠀⠁⢀⡾⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣍⡩⣴⣞⡶⣤⣪⠔⠠⣿
⠀⢠⡞⠀⢀⣀⣨⠤⠴⠒⠲⠒⠢⣤⡄⠀⠈⡄⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⠀⢀⣾⠁⢀⡴⠁⠃⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢉⠟⠛⣆⡸⢝⣡⡷⠞⠁
⠀⢾⠀⠐⠀⠙⡛⠒⢚⣛⡛⠛⠉⠁⠀⢀⠴⡇⠀⠀⠀⡠⠼⣿⢀⡤⠀⠀⠀⠀⣼⠇⢀⡿⠀⠀⢸⡑⣿⠀⠀⠀⠀⠀⠀⣠⡆⣀⣀⣬⠁⠀⢼⡿⠋⣡⠖⢛⣷
⠀⠀⢷⠒⠉⠒⠦⠚⠉⠀⠉⠢⠐⠉⠑⢎⣼⡀⠀⠀⡞⠁⢀⣿⡞⠁⠀⠀⠀⢠⡟⠀⠈⠿⠄⠀⠀⠀⢧⠀⠀⠀⠀⢠⠯⢿⡏⠁⠒⠛⠓⠛⡿⢁⣜⣻⣦⠴⠃
⠀⣠⣼⢷⡤⣄⣠⣤⣶⣶⣶⣲⣶⣶⣖⣋⢏⡽⡀⠀⠁⠀⠉⠻⠃⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⣾⣦⣤⣄⣀⣀⣸⣧⣾⣾⠥⠴⣶⡆
⠀⠙⠈⠙⢿⠿⠿⠿⠟⠛⠛⠁⠈⣃⢨⡿⠛⠙⢯⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢰⣄⠀⠀⠀⠀⠀⠀⡀⣠⣟⣇⢠⡟⢭⠉⣿⠟⡾⣏⠑⣶⠋⠁
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢰⣿⣾⣴⠓⢒⣿⢑⣾⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠟⠞⠣⣈⡲⢿⠛⠃⡔⠑⠓⠶⠿⢿⡿⢦⣾⡿⣸⢣⡌⢟⡅
⠀⠀⠀⠀⠀⣨⢶⡄⢀⣀⣠⡴⢚⣙⣥⡿⠉⠭⠉⠉⠻⡖⣰⡆⣶⡍⠲⡄⢠⡦⠵⣿⠓⢺⠒⢺⠃⠹⠃⢸⠄⡸⠁⠀⠦⠀⢀⣼⡧⠈⡼⢁⣿⡿⠖⠉
⠀⠀⠀⠀⠀⠳⠌⠠⠤⢻⣷⠞⠛⢉⣸⠃⠀⠀⠀⠀⠀⢷⢌⣀⣘⢰⠀⢙⣼⠻⡇⠈⡆⠘⠀⠀⠆⠀⡄⢸⡔⠀⢀⣄⠀⠀⡘⣹⠟⠊⠛⠛⢯
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠛⠉⢈⣄⣦⠀⠀⠀⣠⠖⠉⣹⠀⣌⣽⠶⠛⠛⠛⠻⢦⡸⢤⣧⣀⣤⣤⣷⣿⣁⡀⠀⠀⠀⡄⠀⡿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⠷⠛⠉⡟⠀⢹⠰⡟⠰⠂⠀⢉⡰⠿⠁⠀⠀⠀⠀⠠⠶⠷⣾⣯⢩⠁⣤⠰⡟⢣⣤⡙⢛⣚⣯⠺⠁⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⣼⡀⣀⠷⠊⢀⡇⠑⡶⠂⣹⡿⢁⡗⠀⠀⠀⡠⠀⠀⠀⠀⠈⡇⠀⠀⢰⠀⢸⡀⠿⢠⡏⠝⢩⡗⠠⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣁⣀⣀⠾⠢⠤⠌⠒⣸⢏⠘⣀⣃⠀⠀⣰⠁⣀⣤⡴⠒⠛⣧⠈⠀⠘⡀⠀⣡⠈⠀⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠈⠣⡀⡟⣿⣻⠟⢶⡛⠛⠋⠉⠛⠣⣀⡼⠟⠓⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⠁⠀⠀⠐⠒⠒⠉
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠒⠊⠉⠉⠉⡉⣉⢉⠉⡉⠉⢒⠒⠒⠠⠤⢄⣀⡀
⢀⢶⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠕⠘⠚⠻⠲⠀⠀⡹⡆
⢸⠏⠑⠫⢔⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡧
⣿⠀⠀⠀⠀⠈⣑⠊⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⢟⡸⣧
⢻⡄⢀⡀⠀⢸⡹⡷⡀⠀⠉⠑⠫⠖⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⡠⣻⡿⡆⣡⣿
⠀⡇⠘⠗⠀⠈⠧⣀⡅⠀⠀⠀⠀⣠⡀⠉⠑⠛⠵⣖⡤⣀⡀⡰⣵⣝⣷⡛⣿⣿
⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠁⠀⣠⢲⡶⣄⠈⠙⠺⣻⡇⢹⡿⢁⡿⣿
⢸⡆⠀⣠⣤⡀⠀⠀⣾⣹⠼⠟⡆⠀⠀⢸⣷⠅⠀⢈⠀⠀⠀⣿⣼⡎⠟⢛⢳⣿⡶⢶⣖⠒⠂⠠⠤⠤
⢸⡇⢸⣿⡟⠚⡆⠀⠙⢇⣀⠰⠁⠀⠀⠀⠙⠤⠴⠊⠀⣠⠶⡿⠙⡕⡀⣸⠛⣿⡛⢉⣉⠉⣉⣉⣈⡁⠉
⢸⡧⡀⠙⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠠⣷⣵⠂⢸⣷⡟⣏⣿⡿⠔⠀⠤⠦⠤⠔⠂
⠀⠙⠪⣕⡤⣀⠀⠀⠀⣴⢦⠀⠀⠀⣾⣶⡵⠛⠆⠀⠀⠉⠓⣔⣳⣿⣷⣿⣿⣃⣉⣉⣉⣭⡭
⠀⠀⠀⠀⠙⠳⢽⣦⣀⠈⠊⠀⠀⠀⠙⢏⡀⣀⠇⠀⠀⠀⠀⣿⠄⠦⢶⡿⠷⠺⠿⠖⢳⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⢿⡏⣿⠍⠉⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣒⣄⡀⠀⠀⢠⡶⡄⠰⣷⢁⣼⣽⡯⠍⠉⠉⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣗⣤⡀⠉⠀⠀⠈⡿⣿⣟⣓⣒⣐⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⣦⢄⡀⠀⣧⡯⠌⠥⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣶⣿⣿⠛⠛⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢻⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣷⣌⡻⣆⠀⣀⠠⠄⣀
⠀⠀⢄⠀⠀⡠⠄⢸⣿⣷⣏⢷⣽⣿⣮⡇⠀⠀⠀⠈⣷⠞⠉⠑⠢⣄⠀⢀⡀
⠀⠀⠀⠑⠄⣈⠀⣸⣿⡟⣟⣸⢿⠇⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣼⠋⠁⠉⠑⣄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣶⡿⠄⠛⠠⠤⠄⣀⠼⠄⣄⡀⠀⠀⡏⠀⠀⠀⠀⣸⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠛⠙⠛⡟⠀⠀⠀⠀⠀⠸⠁⠀⠀⠠⠁⠀⢸⠁⠀⠀⠀⢠⡏⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⠀⠲⡀⠀⠀⠀⠀⠰⠧⣀⣴⢇⡜⠀⡟⠀⠀⠀⢀⡞⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠀⠲⣤⣀⣀⣀⣤⣴⠋⠀⢸⡇⠀⠀⢠⡞⠀⠀⠀⣴⣷⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⣿⡿⡟⠹⡿⢶⢶⣿⣷⣴⢶⣯⣀⣀⣠⣾⣽⣏⢻⣾⣿⡿⠋⣡⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠞⠁⠃⠀⠀⠈⡇⠛⢿⡀⠀⠉⢍⣍⠙⢿⣯⣻⣫⣾⡿⠀⣮⡈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢻⢢⠈⠻⣿⣿⣿⡇⢸⣿⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⡄⠀⠀⠀⢡⡀⠙⠹⣿⠀⠘⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⣀⡀⠀⢀⣀⣼⣣⠀⠈⠀⠀⣀⠀⣟⠦⣀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠙⠛⠛⠛⠋⠥⢤⣤⣤⣤⡼⠋⠦⠖⠚⠙⠓⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⢿⣦⣄⡀⠀⠉⠙⠻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣠⣾⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠿⠿⢷⣶⣶⣶⢶⣶⣶⡾⠿⠿⠟⠋⠁⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⣿⡇⠐⠿⠀⠈⠉⢀⣀⠀⢴⡆⠀⠈⠉⠀⠀⠀⢠⣿⠃
⣤⣤⣤⣤⣤⣤⣾⡟⠛⣿⣦⣤⡄⠀⣿⠇⢀⣤⠀⠀⠀⠘⠛⠀⠀⠀⣠⡄⠀⠸⠿⠀⢸⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤
⣿⣏⣉⣉⡉⠉⣿⡇⠀⣿⠉⠉⠀⢸⣿⣤⣀⣉⣀⣀⣠⣤⣤⣤⣄⣀⣈⣁⣀⣤⣄⣀⣸⣿⠀⢈⣉⣉⣉⣉⣉⣉⣿
⣿⡟⠛⠛⠛⠀⣿⡇⠀⣿⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠀⠉⠙⠛⠛⠛⠋⠉⠉⠛⠋⠁⠀⠘⠛⠛⠛⠛⠛⠛⣿
⢿⣷⡶⣶⣶⣶⣿⣇⣀⣿⡷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣿
⢸⣿⣤⣤⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿
⢸⣿⠉⠉⠀⢰⣶⣶⣶⣶⣶⡆⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠈⠉⢹⣿
⢸⣿⠀⠀⠀⢸⣯⣤⣤⣤⣿⡇⠀⠀⠀⣼⡏⠉⠉⠉⠉⠉⠉⠉⢿⣇⠀⠀⢠⣿⠋⠉⠉⠉⠉⠉⠉⠹⣿⡀⠀⢸⣿
⢸⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⢰⣿⠁⣤⡀⢀⣤⡀⣠⣄⢸⣿⡀⠀⣼⡟⢠⣤⠀⣠⣄⠀⣤⡄⢻⣧⠀⢸⣿
⢘⣿⠀⠀⣿⡿⠿⠿⠿⠿⠿⢿⣿⠀⠻⣿⡿⠿⠿⢿⣿⠟⠿⠿⢿⣿⠇⠐⢿⣿⠛⠛⠛⢿⡿⠿⠿⠿⣿⡿⠀⢸⣿
⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⢸⣿
⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⢸⣿
⢸⣿⠀⠀⣿⡿⣷⡀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⢸⣿
⣸⣿⣀⣀⣿⡇⠙⠁⠀⠀⠀⢸⣿⣀⣀⣿⣇⣀⣀⣸⣿⣀⣀⣀⣸⣿⣀⣀⣸⣿⣀⣀⣀⣼⣧⣀⣀⣀⣿⣇⣀⣸⣿
⣿⡟⠛⠛⣿⡇⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣤⣤⣀⠀⠈⠉⠑⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢸⣵⣿⣿⣿⢇⠀⢰⢰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⣤⣤⡀⠀⠉⠹⠿⠗⠃⠀⠘⣞⢷⣝⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⢴⣶⣤⡀⠈⠉⠁⢀⣤⠶⠶⠶⢦⣄⠀⠈⠙⠚⠭⠉⠉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠘⠻⣿⡿⠏⠀⠀⢰⣿⣶⣿⣿⣿⣿⣿⣷⠒⠒⢒⣛⡉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⣠⠔⣋⣀⣀⣀⣤⠤⠤⠴⠖⠒⠒⠋⠉⠉⠻⢿⣿⣿⣿⣿⠿⣫⠂⠀⢿⣿⣷⡄⠀⢸
⠀⠀⠀⠀⠀⣾⠉⠉⣽⣂⡀⠀⠀⣠⢖⣒⣒⡂⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠀⠀⠀⠈⠙⠋⣀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠸⠿⠇⠀⠘⣱⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢔⣂⡀⠀⠀⢀⡴⣫⢷⣶⣿
⠀⠀⠀⠀⠀⣿⣀⣀⡠⢄⡀⠀⠀⢿⣿⣿⣿⢿⡟⠀⢀⡤⢤⠤⠀⠀⠀⣿⣿⣿⡆⠀⡞⡾⣱⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢶⣝⢦⠀⠀⠙⠛⠚⠋⠀⠀⠋⣾⣿⣿⣷⡀⠀⠙⠒⠋⠀⠀⡜⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢻⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣛⡿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⢀⣀⣀⣀⡤⠬⠥⠤⠶⠒⠒⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢿⣿⡿⠿⠿⠿⠓⠒⠒⠛⠉⠉⠉⠁