Boos Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⢲⡄⠀⠀⠀⠉⠉⠉⠙⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄
⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⢸⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡆
⠀⠀⠀⠀⡿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢳
⠀⠀⠀⣸⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⠆
⠀⠀⢰⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⡇⠀⣿⣧⠤⠤⠤⢴⡶⠶⠶⠶⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⣶⡶⠦⠤⠤⣬⣿
⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⠤⠤⠤⠴⠶⠒⠒⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠐⢄⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⠉
⠀⠀⠀⠀⠀⠐⢄⠈⠳⣄⠀⠀⠀⠀⠙⠲⣄⣀⣤⠴⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖
⠀⠀⠀⠀⠀⠈⠢⡑⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣀⠤⢂⣠⠴⠊⠁⢸⣀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢦⡙⢦⡀⠀⠀⠀⠀⠀⢀⡤⢚⣩⠔⣊⣤⠖⠋⠁⠀⠀⠙⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢽⣦⡙⢦⡀⣀⡤⢚⡥⢖⣭⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢝⣿⣦⣙⣵⣾⣵⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠓⢐⠜⠀⠐⡜⠀⠂⠖⠂⠂⡆⠐⡆⠰⠒⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡏⠙⠂⠀⠉⠀⠀⠈⠀⠀⠈⠒⠂⠀⠑⠂⠁⠀⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⢀⣠⡼⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⢀⣤⡾⠟⣩⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⡶⠚⠛⣉⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣾⠟⣉⣠⣴⠋
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢄⢧⠀⣠⠟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣴⡿⠛⣉⢵⠋
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠚⢿⣿⣼⣵⣮⣉⣀⡠⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⣁⡴⠚⢁⣨⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠒⠒⠒⠓⠲⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣰⡾⠟⠁⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠌⠷⠞⠫⠤⠶⠶⠶⠦
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠰⠶⡄⠀⠲⠦⣴⣏⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠺⠀⠀⠀⠀⠀⠈⠛⠛⠳⢄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⢠⣠⠂⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠃⠂⠉⠃⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠩⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠐⣀⣿⣼⡏⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⡘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣤⣀⣀⣀⣠⣬⣿⣿⡿⠋⡡⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠉⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠛⠛⢙⡋⠉⠉⣥⡔⠋
⠀⠀⠨⢒⣤⣴⣖⣶⣒⣦⣵⣷⢠⢞⡡⠤⠤⠄⠀⠀⠀⠀⠀⢀⣴⠟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢧⠀⠐⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠿⠖⢀⣔⣢⣐⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠸⣷⣤⣤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠉⠉⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⡶⠶⠶⣶⣶⣶⡶⣶⢶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠒⠒⠀⠀⠀⠀⠀⠀⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠢⢭⣙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠒⠦⣌⡉⠒⠦⣍⡛⠷⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡐⠤⢍⣓⠦⢌⡙⠲⠤⣀⡀⠀⠀⠙⠻⣦⣄⠠⠐⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠒⠬⣙⡲⠬⣉⡒⠬⢌⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣙⣳⣦⣍⡓⠂⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠉⠉⠉⠉⠛⠷⢶⣤⣀⣀⠀⠀⢀⣀⣾⠇⢀⣀⣠⣤⣴⠶⠾⠛⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡟⢧⡹⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠸⠀⠈⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⢀⣀⣈⢻⣿⣤⣶⣶⣶⣶⠶⠶⠶⠾⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣀⣤⣤⠶⠞⠛⠋⢹⣿⣴⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⠶⠶⠶⠶⠶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣆
⠀⢀⣴⠿⠋⠉⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢛⣛⣒⣒⣒⣒⣒⡒⠲⠶⠶⠤⠤⠤⠭⠭⠭⠍⠉⠉⠉⠉⢉⣿⡉⠉
⢠⡿⠁⠀⠀⠤⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣂⣀⣀⡀⠀⠀⠀⠀⠨⠭⠭⠭⢭⣭⣭⣭⣅⣀⡀⠀⠀⠀⠀⣾⠀⠉⠓⢦⣄⡀
⣿⠁⠀⠀⠀⠀⠀⠈⠉⠂⠀⠘⣿⡀⠀⠀⠀⠀⠒⠒⠂⠤⠤⠤⠤⠤⢤⣤⣭⣍⣉⣉⣉⣙⣒⣒⡒⠒⠶⠶⠦⠤⠤⠤⠄⠀⠀⠀⣧⠀⠀⠀⠀⠈⠙⠷⣦⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣐⡒⠲⠶⠶⠶⠦⣤⣤⣤⠀⢠⠀⡐⢒⡒⠒⠚⠉⠉⠉⠉⠉⠠⠤⣤⣤⣤⣒⣂⣀⠀⢿⣄⣠⣤⣤⣶⢶⣿⠿⠛
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠻⠶⠶⠾⠷⣬⣤⢦⣥⣥⣬⣥⣤⣿⣿⣿⣿⣷⣦⣄⣀⣐⣒⣲⣶⣖⣂⣈⣹⣯⠉⠀⠀⢰⡇
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⢀⣀⣤⠠⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⣿⠁
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠠⠖⠒⠒⠉⠀⠀⠀⣿
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠒⠂⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡠⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠶⠚⣛⣋⣉⣥⣤⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣌⣛⣬⣑⠒⠀⠀⠀⠀⠒⠊⢉⣉⣉⣩⣭⣤⡴⠶⠶⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⠐⠀⠀⠀⠉⠀⠀⠒⠒⠂⠤⡤⠤⣀⣀⣀
⠀⠀⠀⠖⠚⠁⠤⠄⣀⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢒⣲⣦⠄
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠦⠤⢤⣀⣀⡀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠉⠁⠀⡇
⠀⠀⢀⣑⣤⡤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡖⠉⠁⠀⠀⠀⠀⢀⣀⣤⠷⠂⠤⣄⣀
⠀⠀⠈⣟⠓⠢⠤⣀⡈⠉⠉⠒⠒⠦⠤⣤⣀⣀⠀⠀⠀⠀⢸⡄⠈⠻⣶⣤⠴⠞⠛⠛⠂⠉⠉⠁⠀⠘
⠀⠀⠀⡏⠀⠀⠀⠀⠉⠑⠲⠤⣄⣀⣀⣠⡤⠬⠝⠛⠒⠲⠶⠷⠞⠛⠙⠃
⠀⠀⣲⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⣾⣤
⣼⠟⠛⠶⢬⣽⣳⣶⣤⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⢒⣒⣪⣭⠭⠷⠖⠚⠛⣻⠁
⣿⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣶⣤⣎⣠⡤⠤⢶⣒⣚⣫⣭⠭⠶⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠘⠷⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠒⠛
⠀⠀⠀⠀⠉⠛⠳⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣴⣷⣤⣤⠶⠶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠀⠈⠉⠐⠄⠀⠀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡠⠄⠊⠋⠁⠀⡀
⠀⠀⠀⠀⠀⠀⡃⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢱⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠢⡀⣁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢤⡄⠀⠀⢀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠇⠈⠀⠄⣀⣀⣨⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢈
⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠜⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⠀⠀⠂⠠⠦⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡤⠴⡊⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠆⠀⠀⠀⡌⢀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⢉⠁
⠀⠀⠀⠀⢰⠀⠀⠀⣇⠀⠣⡀⠀⡀⠔⠁⠀⠈⡜⠛⠀⠛⠐⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠛⠃⠀⢀⡨⠖
⠀⠀⠀⠀⠈⢦⡀⠀⠠⠀⠀⠀⠀⠉⠒⠀⠄⠀⡀⠀⠀⣁⠀⣀⠤⠀⠀⠀⠀⠀⢀⣀⢀⡀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠉⢲⠁⠀⠈⠉⠐⠒⠒⢒⠂⠉⠀⠁⠒⠂⠊⠁
⠀⠀⠀⢀⡴⠒⣆⠘⢄⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⢀⡞⠀⡐⠉⠑⠂⠙⠂⢄⡀⠀⠀⠀⠀⠀⠙⢆
⠀⢀⡞⠀⣴⡁⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠑⡄
⢀⡾⢀⣮⡞⠉⠐⠀⠠⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠈⠦⣴⣲⠼⠁⢀⠇
⣼⠃⣢⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠐⠋⠉⢁⡠⠄⠀⠁
⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠠⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠒⠒⠒⠒⠒⠚⠓⠓⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠒⠒⠒⠒⠶⠶⠼⠦⠄⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣄⣀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠛⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣠⣤⠀⠀⠀⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠝⠿⠿⠿⠁⠀⠰⠃⠀⠀⠀⠀⠈⡏⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⢒⣶⡶⣰⠖⠒⠖⠒⠒⠚⠒⢶⠷⢶⠶⠖⠶⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣉⣿⣁⣀⣭⠀⣭⠀⢀⣩⠅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢏⡙⣻⣿⣿⣿⣿⣿⣓⣿⣿⣿⣾⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠿⠿⣏⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⡤⢤⣶⣶⣦⣤⠴⠶⠾⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠘⠉⠉⠉⠁⠀⠀⢀⣾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⢀⣠⣤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⢠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠶⠶⠶⡶⠛⢡⠄⠂⠀⠀⠀⠀⠀⠀⣀⣼⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠲⠦⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⢀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠲⠤⠤⡰⠂⠊⠁

⠀⠀⢀⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠄⣀⠠⠄⠠⢄⡀⠀⠀⠀⠀⢀⢀⡄⡠⠀⢠⠀⢀⢠⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡏⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⡟⣷⠀⠀⠀⣿⣷⣶⣤⣴⣷⣷⣥⣶⣾
⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⡇⢇⣀⡀⣀⠀⠀⢀⣀⣀⣀⡇⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⣷⣥⠶⠶⠦⣍⣏⡥⠶⠶⢮⣷⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⡏⠛⠻⢿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉
⠀⠉⠙⠀⠀⠀⠀⠈

⠀⣿⣿⠿⠿⠿⠿⢿⡗⣶⠀⠀⠀⠀⠀⣀⠠⣤⣤⣤⣤⣤⣤⣤⣤⢤⣄⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⣀⢀⣿⣯⣿⣿⣿⣿⣿⣇⣀⣿⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⡉⠙⣿⡿⣿⣿⣿⣿⣿⡟⠛⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠓⢤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠁⢀⣿⣯⣿⣿⣿⣿⣿⣇⣀⣿⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠓⠒⠒⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠚

⠀⣀⣀⡀⠀⠀⠀⢀⣠⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣤⣤⣤⣀⣠⣶⣦⣀⣠⣤⣤⣤⠀⠀⠀⠀⢠⣀⣀⡜⠉⣰⠋⢀⣜
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⠉⠙⠛⠉⠙⠋⠛⠛⠉⠉⣿⠀⠀⠀⠀⣼⣭⣷⣟⣻⣿⣟⣻⣿⣛
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠚⠿⣿⠏⣿⣿⣿⣿⣿⣿⣿
⠸⠿⠿⠿⠿⠿⠿⠿⠷⠇⠀⠀⠀⠀⠈⠉⠂⢄⡀⣠⡴⠄⣀⣀⠠⠐⠉⠀⠀⠘⠷⠖⠋⠀⣧⣤⢿⣤⣼⢷⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣷⣶⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡔⠁⠀⠈⠄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⣿⠿⠃⠀⠀⠀⠀⠀⢁⢰⠆⢀⠾⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠁⠐⢢⡄⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⠀⠀⠉⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⢻⣦⣈⠀⠀⠀⢠⠄⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢢⡀⠀⠀⠀⠙⠿⡿⠶⢄⠈⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠑⢦⣄⣀⡀⠀⠀⠀⠈⢁⣠⠴⠊⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠘⡄⠀⢸⠁⠀⠀⠀⠀⠉⢹⠁⠒⣶⡀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡙
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⠑⠂⢄⠈⠑⠒⠢⠤⣴⡾⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⢀⠔⠀⠀⠐⠤⡈⠢⠀⠀⠈⠉⠉⢋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠙⠁⠀⠀⢀⡤⠞⣋⡿
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠱⠀⠃⠀⢃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⢀⣠⠖⣋⠔⠊⠀⡂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠰⡄⡄⠀⠀⠉⡩⠛⠩⠭⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠒⠲⠶⠶⠟⠿⠶⠖⠾⠯⠤⠊⠀⠈⠀⢀⣻⢶⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡆⠀⢀⣠⠔⡫⠂⡉
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣼⠀⠈⣦⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠃⠀⣤⣷⡎⠉⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣴⡴⡫⠕⠁⠀⠀⢢⣤
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢹⠀⠔⠊⡱⢤⣀⣠⡴⠊⠁⠀⠈⠐⠀⢼⠉⠘⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠈⠁⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢀⡤⠒⠊⠁⠀⠀⠀⠉⠑⠢⠤⢄⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡜⠉⠑⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⡤⠤⠞⠓⠤⣀⡈⠉⢓⣲⠞⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣠⡶⠒⢦⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡐
⠀⠀⠀⠀⠀⣼⠏⠀⢀⡼⠦⣄⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢀⣾⠏⠀⢠⡎⠀⠀⠀⠈⠁⠀⠉⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⢀⣾⠃⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⣺⡇⠀⣰⣏⡿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣀⣀⠀⢤⠄⠄⢤⡀
⠀⣼⡟⢀⣼⢳⡞⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢀⠾⢖⣃⣭⠷⠔⠋⠀⠀⡪⠃
⣸⡽⠀⢸⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡠⠶⠛⠋⠉⠁⠀⣀⢀⡨⠔⠉
⣿⡇⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⢀⣠⠴⠖⠊⠁
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠤⠤⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠀⠠⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠶⠦⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠒⠦⠤⢍⣁⣀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠬⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠁⠀⢰⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠲⠤⢤⣤⣠⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀
⠀⠀⠀⠀⢀⡀⠨⠶⠒⠶⠶⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠉⠀⠀⠠⠤⢀
⠀⠀⠀⠀⠀⢻⠓⠒⠤⢤⣀⡀⠀⠀⠈⠉⠙⠓⠲⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⠀⠈⠉⠻⣿⣆⣠⣤⣶⡾⠿⠿⠓⠒⠊⠉⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠻⠶⢤⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠶⣤⣤⣀⣀⡀⠹⡆⣀⣤⣴⢾⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣤⣤⣤⠴⠶⠒⠚⠋⠉⠉⠀⠀⠉⠉⠛⠛⠛⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⢶⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣮⣄⣀
⠀⢠⣶⣖⣋⣭⣉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠐⠒⠊⢉⣁⣠⣬⡵⣿⡞⠉
⢀⣿⠏⠀⠉⠉⠛⠻⠶⣤⣍⣛⡳⢦⣤⣀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠖⠒⠚⣉⣉⣡⣤⠤⠴⠖⠒⠋⠉⠉⠉⠁⠀⠀⣾⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⣀⡜⢁⣆⣠⣤⣤⣶⠶⠾⠛⢛⣋⣉⣭⣥⣶⡶⠶⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣯⣥⣶⣶⠾⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣐⣈⣧⣤
⠀⠀⠙⠛⠿⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠾⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠾⢷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⡾⠶⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⢶⣤⣀⣀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣀⣠⣴⡶⠶⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣮⣤⡶⠶⠟⠛⠋⠉⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠀⠄⠀⠀⠀⠠⠀⠄⠄⠀⠀⠀⠀⠀⠐⠠⠂⠀⠆⠄⠀⠀⠰

⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡠⠚⢁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⢸⡇⠀⠐⠿⣟⣳⣤⡀⠀⣀⠄⠊⠀⠀⠀⡠⠐⠁⠀⠀⣾⠆
⠀⠀⢀⣯⣄⣀⣀⠀⠀⠀⠸⠀⠀⢀⣀⣠⠤⠸⣇⠀⠀⠀⠀⠈⠙⡻⢾⣿⡾⠯⣍⡉⠉⠀⠀⢀⡴⠊
⠀⠀⢸⣿⣶⣶⣮⣭⣵⣶⣤⣶⣾⣿⣿⣷⣿⣷⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠓⠦⢬⣧⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⡓⢄⡀⠀⠀⠀⠀⠀⠀⠋⡲⢄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠛⢦⣌⠲⢄⡀⡀⢀⡠⠔⢊⡥⢀⣀
⠀⠀⠀⢞⠓⢄⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⢠⣾⢖⡢⠀⠀⠈⠛⢦⣽⣫⡥⠐⠊⢁⡴⠂⠀⠀⠀⠉⠉⢀⡄
⠀⠀⢠⡌⠢⡀⠑⠄⠀⠀⠈⠙⢦⣄⠀⣰⣿⣿⣭⣿⡧⠀⠀⠀⠀⠉⠀⠑⢀⡴⠋⠀⠀⠀⠀⠀⠀⡴⣫⠇
⠀⠀⠀⠙⣄⠈⠢⡀⡈⣉⣅⣤⣤⣽⣶⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠤⣀⣀⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠀⠀⠈⠳⣄⢈⣉⣭⠭⠛⠋⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠒⠠⠤⣈⣉⢙⡵⠃
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠤⠶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠐⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠤⣙⠲⠬⣙⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠒⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣒⠤⢍⡒⠦⣍⡀⠀⠉⠙⠳⣦⡀⠀⠠⠴⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠬⣔⡢⢍⣒⠪⠅⡂⠈⠁⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣉⣳⣦⣍⡒⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣛⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⣀⣠⣼⣃⣀⣤⡤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡀⡀⠀⢀⣀⢀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢛⣿⣻⣿⡛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣩⣽⣿⡿⠿⠟⠛⠋⠉⠉⠉⠉⢙⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠸⠈⢷⡈⣿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⢻⣿⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⢀⣠⣤⠶⠖⠛⠋⣿⣥⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣈⣷⡄
⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢭⣭⣓⣒⣒⣒⣒⣒⣒⣒⣀⠈⠩⠍⠉⠉⠉⢩⣿⣉⠁
⣸⠋⠀⠀⠐⠢⢄⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠤⠤⣀⣀⣀⣀⣀⣒⡒⠒⠲⠶⠶⠍⠁⠀⠀⠀⣾⠀⠈⠙⠲⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⢀⣀⣈⣉⣉⣉⠉⠉⠉⠒⠒⠒⠒⡒⠒⠤⠭⠍⠉⠉⠉⠁⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣀⣉⣿⡦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⣬⣭⣭⣭⣽⣿⣿⣿⣶⣶⣶⣶⣶⣦⡤⠄⠠⠀⠀⠀⠀⠀⢀⣀⠀⠈⢲⡞⠛⠋⠉⡟⠁
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢄⡀⠀⠀⠀⠉⠉⠉⣉⣉⣭⡭⠿⠿⠛⠛⠛⠛⠛⠛⠒⠒⠛⠛⠃⠀⠀⢸⠇
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠁⢀⡀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣩⣤⣤⠤⠴⠒⣒⣀⣠⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣘⠫⣓⠂⠀⠀⠀⠀⠐⠒⠚⣛⣛⣩⣭⣥⠴⠶⠶⠚⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠴⠖⠒⠒⠶⠶⠤⠤⠤⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠒⠒⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⠉⠒⠒⠒⠒⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢖⣽⠿⠶⠶⠮⢸⣉⣩⣤⣄⣒⣒⠒⠒⠠⠤⠤⠄⢀⣀⣀⡀⣀⣀⣠⡤⡤⡴⣖⣒⣮⡭⣽⣷⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡇⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠉⠉⠛⠛⠛⠛⠒⠒⠶⣶⠿⠟⠟⢛⡫⡫⢛⠕⠩⠪⠂⢙⡇
⠀⠀⠀⠀⠀⠀⠀⢱⣻⣀⣀⣀⠀⠀⠀⠐⠒⠒⠀⠐⠺⠯⠥⠄⠀⠤⠀⠀⢰⡫⣂⢕⠜⡠⣪⢔⠕⡡⣺⣶⣳⣷⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠘⣯⡙⠛⠛⠛⠻⠶⠶⢶⡤⣤⣤⣄⣀⠀⠠⠤⠤⢀⣀⠘⢯⣔⣵⣭⣾⣴⣳⣾⣯⣯⢿⡛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡢⡀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠉⠉⠉⠋⠚⠒⠛⣿⣿⢿⣭⡭⣯⣥⣵⣖⣦⣭⣭⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢴⠁⠈⣾⣆⣁⣀⣀⢠⣤⣤⣤⣤⣰⣖⣶⢾⠴⡿⡻⢻⢗⢗⢞⡝⡩⢋⢏⠜⡑⡱⡡⠩⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡱⡀⢹⡝⠻⣝⠛⡛⡫⠫⢋⠜⠕⡱⡣⢊⢎⠜⡵⡳⡫⢣⢊⠜⡑⡡⢣⢎⠜⡔⡱⡡⡑⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡜⡄⠙⠀⢩⢊⢜⠔⡡⡡⢊⢎⠔⡑⡡⢢⢎⢌⠜⡔⡡⣪⢊⠜⡔⣡⢊⢊⣜⣔⣼⡾⣿⡏⣥⣶⡆
⠀⠀⠀⠀⠀⡠⢔⠊⠁⠀⠙⢾⣄⣠⣷⣡⡣⣮⣼⣴⣥⢧⣾⣾⣶⣷⣷⣾⣾⣾⣿⣷⡿⠾⣽⣿⠽⠿⠿⡻⠿⢟⣷⣶⡿⠋
⠀⠀⢀⣴⣛⣀⣩⣖⣀⣠⠤⡤⠝⣛⣛⠛⠛⠳⠍⠩⠭⠩⢉⣉⡭⠤⠤⣭⡡⠖⢀⠀⠅⠴⠒⠀⠨⠡⢒⣲⣿⡽⠫⠛⡇
⠀⠀⣾⣟⠉⠁⠈⣉⠉⠛⠋⠉⠓⠒⠧⠬⣭⣱⣶⣶⣖⡢⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢞⠃⢀⢃⢠⣻⣦⡀
⠀⠀⣿⣟⠀⠀⢰⣅⡼⠁⠀⠀⠀⠀⠒⠂⠀⠤⠌⠉⠉⠙⠛⠓⠒⠶⢦⣬⣭⡴⣒⣂⠤⣤⣤⡾⡟⡙⡘⠌⠌⣎⢼⣾⠿⠇⠉⠁⠒⠢⣄
⠀⠀⠈⠊⠳⠦⠦⢼⣗⣤⡄⣉⣉⡀⠒⠂⠠⠭⠥⢒⣒⡠⠤⠤⠤⠀⠀⠀⠀⠉⠉⠉⡿⣻⠇⢷⠁⠡⢱⢸⣺⡟⠛⠶⠄⠈⠁⣀⣴⣾⠟
⠀⠀⠀⠀⠀⢀⣴⣞⣿⣿⡟⠛⠖⠯⠿⣶⡶⢤⣄⣠⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡌⡄⠇⣌⣷⡿⠞⠁⠢⠤⣀⢤⣶⡿⡫⣹⡇
⠀⠀⠀⠀⢰⣱⠯⠛⠛⠓⠾⣭⣖⡂⠤⢄⣀⠉⠁⠉⠙⠛⠻⠻⠟⡶⠶⣤⣄⣠⠄⣈⣷⣰⣸⣾⢛⣛⠒⣂⣲⣶⠾⡞⠟⡔⡐⠙⣼⣄⡀
⠀⠀⠀⠀⢨⣿⡀⠀⠀⠀⠀⠀⢈⡙⠻⠶⣤⣍⣒⠢⠄⣀⠀⠀⠀⠀⠈⠀⠘⠉⠛⠛⠞⠟⠛⣶⢶⣚⣿⠗⢟⠍⠔⡍⡜⡔⡔⠜⣜⣷⣒⣒⠀⠤⠄
⠀⠀⠀⠀⠘⣿⣄⡀⠀⠀⢀⠀⠀⠈⠑⢦⣠⣈⠙⠛⠶⢢⠭⣒⠢⠤⣀⠀⠄⡠⢀⣀⣤⣲⡿⢾⢚⡫⠂⢎⢎⢌⠞⠜⣜⢼⢾⡿⠿⠥⠀⠤⠄⠐⠂
⠀⠀⠀⠠⠌⢘⠓⢾⡤⢀⠀⠉⠐⢂⠤⢀⡀⠉⠒⠠⢄⡀⠈⠙⠛⠷⠶⣬⣱⣾⠟⡞⡝⡐⡡⡣⢣⢃⢎⢎⣊⡮⢞⣯⠽⠚⢓⣒⣒⣀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠓⠿⣲⡤⠄⣈⠁⠣⢤⣤⣀⡀⠀⠀⠀⠀⠀⢀⡋⢀⢂⢊⠎⠔⡰⡡⡱⣡⡥⢾⣮⣵⠿⠭⠉⠉⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠨⠔⣀⡤⠍⣈⠃⠄⠄⠀⠀⢸⡷⠡⢃⢊⠎⣔⣵⢴⣯⡧⠟⠋⠡⠈⠍⠩⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠒⠬⣕⡒⠤⢄⡀⢷⣡⣡⡧⣾⣽⠟⠛⠓⠀⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠲⠬⠉⡿⠷⠻⠩⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠡⠱⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠤⠄⠀⠒⠢⠤⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣶⣒⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠤⠤⢄⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣑⣲⣶⣤⣤
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠿⠟⠛⠛⠛⠛⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠟⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢶⣤⣶⣿⣿⠟⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠉⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⢸⣿⡋⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡴⠶⢶⣒⣶⡚⠋
⠀⠀⠀⠀⠀⠀⢀⢼⣓⠢⢄⡀⠀⠀⠀⠉⠛⠲⢤⣄⡀⠀⣿⣧⣀⣀⣀⣀⣀⣤⡤⠶⠖⣚⣋⣭⣭⣶⡾⠶⠶⠟⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⠂⠉⠓⠦⣄⡀⠀⠀⠀⠈⠙⠓⠺⢿⣿⣿⣿⣵⠶⠶⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠐⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠒⠤⣄⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⣖⣛⣻⡟
⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡉⠓⠤⣀⠀⢸⣿⡤⠀⠀⠀⢀⣀⣠⣤⠴⣖⣾⣿⣭⣷⠶⠿⠛⠛⠋⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠛⠿⠿⣛⣛⣯⣿⡿⠿⠾⠛⠛⠉⠉⠁⠀⠀⡀⠠⠄⠐⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣶⣿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⢸⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⣿⣿⡅⣀⣀⣤⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⡾⠿⠟⠛⠉⠉⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠿⠿⠛⠛⠉⢁⣀⣤⣤⢠⣾⠟⠛⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⡾⠿⠟⠛⠋⠉⢀⣠⠀⣶⡶⢿⣶⠘⣿⣭⣤⡈⠛⠿⢿⣷⠀⣿⡇
⠀⠀⢠⣶⣶⠿⠿⠛⠛⠉⣁⠀⣠⡄⢰⣾⠿⣿⡆⢿⡇⢹⣷⣾⣿⡄⢻⣯⣥⣴⠼⠿⠿⠋⠀⢸⣿⡀
⠀⠀⠈⣿⡇⠠⣴⡶⠿⠊⠻⣷⣿⠃⠈⣿⣶⠿⠃⠸⣿⡈⣿⠆⠘⠛⠈⠉⠉⣀⣀⣤⣤⣶⣾⠿⠟⠃
⠀⠀⠀⢸⣿⠀⢿⣷⠾⠆⠀⣼⡿⢷⣤⠹⠷⠀⠀⠀⠉⢀⣀⣠⣤⣴⣶⡿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⣿⡇⠸⣿⠶⠿⠓⠛⠀⠀⣀⣀⣤⣤⣶⣶⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠸⣿⣀⣀⣠⣤⣴⣶⡾⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠻⠿⠛⠋⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⡉⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠉⠉⠉⠁⠀⠂⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠾⠿⠿⠟⠉⠩⠏⠁⠀⠀⠐⡟⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡶⢶⣶⣶⠶⢲⣶⢢⡖⠒⠒⠒⠒⠒⢶⠶⡶⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣥⣿⣤⣴⣦⣼⣄⢠⡷⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠛⠛⠿⠿⢿⣿⣿⣿⢿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⢀⣠⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢾⠟⠛⠉⠉⠉⠉⡥⠖⠒⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠄⠠⣀⣀⣀⣀⡀⠀⢀⡤⠖⢒⠉⠀⠀⠀⠀⠀⣼⣷⡤
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠀⡏⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠑⠒⠒⠢⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠢⠤⠄⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠏⡏⢿⣄⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⢀⡀⠀⠀⣠⡴⠚⠁⠾⢿⡇⣴⡷⡁⢫⣅⡿⠀⢀⡀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠠⠆⣼⠁⢰⡄⠠⠿⠼⠥⠼⠿⢿⠟⠛⣡⣤⣤⠻⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠖⠁⠀⣀⣀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⠀⠐⠶⠤⢀⡀⠸⣧⣾⣾⣄⠉⠙⠛⣿⣽⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢀⡄⢠⣿⡟⠃⠂
⠀⠀⠀⠀⠀⠀⠀⢘⡀⢙⣻⣕⠂⠀⠀⠙⢷⣦⣦⡤⠈⢑⣀⡀⢙⠋⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣿⣿⠮⠛⣿⡀⡇
⠀⠀⠀⠀⠀⠈⣴⡀⣙⢻⣻⡟⠀⣽⣾⣿⣤⠟⢋⣠⣞⣻⢿⡟⢩⡐⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡤⠀⠈⠀⠹⠂⢡⡏⣙⡃
⠀⠀⠀⠀⣯⡵⢛⠖⣛⠻⠟⣿⠿⢿⠻⣶⡆⠀⠃⢉⣽⠛⠦⡀⣀⠙⣢⣿⠀⣠⣠⡄⠠⠄⠀⠀⠀⠀⠂⡀⠀⣠⣤⠶⠀⠈⠀⣸⡇
⠀⠀⠀⠀⣿⣦⡄⣼⢋⠀⣈⠋⠉⡡⠀⠘⠓⠁⠊⠟⠃⢠⠤⠄⠈⠊⠁⢀⠀⣿⣋⠀⠀⠀⠀⠀⢀⠀⠀⠐⠊⠁⢈⠀⠀⢀⡠⢱⡇
⠀⠀⠀⠀⠿⠋⠉⠀⠀⠀⢉⠃⠀⠀⠀⠠⠄⠀⢀⣄⣀⣀⣠⣄⣤⣀⡀⢚⠀⡉⠉⠙⠃⠀⠀⠀⠈⢳⡖⠐⠃⠘⣡⣴⣦⠞⠀⠈⠃
⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⡷⠏⠻⣿⠋⠉⠉⠉⠻⠷⠿⠃⠀⢠⡄⠀⠀⠒⠠⣴⣄⡀⢀⣼⠿⣿⣿⣭⣄⣀⡃
⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣤⣤⣤⣤⡤⠀⠀⠀⢠⠦⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠨⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠉⠀⠈⠁⠀⠉⠁⠁⠀⠀⠀⠀⠀⠒⠀⠀⠉⠙⠛⠃
⠀⠀⠀⠀⣾⣿⣿⠤⣾⡿⣟⣻⣿⣿⢋⣤⣶⣛⢶⣤⠙⣷⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣩⣶⣦⣤⡀⠒⠂
⠀⠀⠀⠀⣻⣿⡶⠀⠺⢛⣩⣽⣿⠇⣾⣿⠋⠛⠿⢺⣷⡟⠀⠀⣚⣛⠁⠀⠀⠀⠀⢀⡀⢲⣶⠿⠆⠀⠀⢠⣾⢭⣯⣉⡍⠛⠓
⠀⠀⠀⠀⣿⣿⣿⣃⣬⣩⣩⣿⠋⠙⠛⢋⣀⢀⡀⠘⣿⡇⠀⠀⠛⠉⠀⠀⠀⣠⠄⠀⣤⠚⠛⢀⣀⣀⠀⠺⢴⣶⠬⠁⠄⠙⠁⠺⠆
⠀⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣙⡃⠀⠀⠈⠛⢺⠃⠀⣸⡇⠀⠀⠀⠀⠀⢠⣼⣯⡄⢠⠀⠈⠀⠈⠛⠿⠃⠀⠚⡀⠀⠀⢸⡎⡞⢠⡄
⠀⠀⠀⠀⣐⣛⣛⣤⡼⠿⢿⣿⣧⡆⠀⠀⠀⠀⢶⡖⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣜⣿⠃⠀⠀⠐⠀⠀⠐⠀⣿⣆⠈⡿⢃⣶⡿⠃
⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣠⣰⠄⣹⣎⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⢴⣾⣿⣿⡟⠃⠄⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠁⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣛⣿⣟⣀⠀⠀⠀⡠⠀⠉⣩⣿⣭⣹⡀⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠊⢁⣀⡠⠄⢀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣶⣞⠀⣠⠊⠠⡉⠛⠻⣾⡄⠢
⠀⠀⠀⠠⠔⣺⡗⠈⠉⠁⠀⠀⢀⣮⡀⠈⡙⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡟⠘⠔⡀⠀⠀⠐⢆⠁⠀⣴⣦⠄
⠀⠀⠀⠐⠿⠿⠇⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠁⠀⠀⠀⠀⠲⠴⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢛⠀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣋⣴⡶⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⣮⣥⠭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡏⠀⠄⣷⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣄⠉⣤⠦⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠸⡄⠀⠀⠀⢀⡀⠀⠀⠀⢀⣤⣀⣃⡀⣴⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢾⠿⣷⣄⡀⠘⢁⣲⠄⠀⠀⠀⠀⠀⠀⣴⠿⠛⢀⠤⠀⠀⠠⠄⠀⠀⠀⡈⠁⣀⠀⠀⣿⣁⡹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⡄⠒⠻⣯⡈⠙⠿⠛⠛⠻⠒⠳⠒⢂⡀⣴⡎⣁⠴⠚⠁⠐⠈⠀⠐⣀⠀⠀⠁⠀⠀⠀⣱⣾⣿⣿⣁⣾⣇⠀⠄
⠀⠀⠀⠀⢀⠀⠀⢉⣁⣀⡀⣀⣠⣤⣆⣠⡤⠖⠊⣉⣀⣼⢷⡄⠀⠠⠀⠀⠀⠈⠀⠁⠀⠀⠀⠐⠆⠶⢿⣿⣿⣿⡿⡃⠋
⠀⠀⠀⠀⢸⣦⠀⠉⠉⠉⠙⣛⣛⠿⢋⣡⣤⣴⢟⣽⠟⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠘⠉⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠈⢾⣇⣀⡘⠛⠛⠛⠛⢲⣿⣿⠟⠁⠀⢀⣴⣁⡄⠀⠀⠀⢠⠀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢻⣏⡠⠿⠟⠻⢷⣦⣿⣧⣤⢶⣾⣭⣿⠉⡁⠀⠀⢤⣈⡀⠉⠉⠙⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⢶⠀⣿⣿⡁⣿⠀⠀⠀⠀⢸⣇⠄⣠⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡉⠀⠿⣿⣿⣿⣷⣻⡟⠛⢳⡇⠚⡴⢿⣝⠂⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠁⠀⠀⠈⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣧⣤⣴⣶⣶⠶⣿⣿⣶⢰⣶⣶⣶⣶⣤⣤⣤⣄⠈⣿⡆
⠀⠀⠀⢰⣾⣿⡏⣽⡿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⣤⣬⣤⠀⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠉⣡⣝⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷
⠀⠀⠀⠿⣦⣧⠀⠀⠀⠀⠈⠩⣗⣀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⢦⣘⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿
⠀⠀⠀⣾⠿⣟⣄⠀⠀⠑⢀⡼⢯⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠤⡮⣸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣽⣿⡇⢸⣿
⠀⠀⠀⣿⠀⡋⣏⠀⠁⠠⡽⡷⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿
⠀⠀⢰⠈⠀⠀⠸⡇⢂⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣴⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣤⣬⣭⣅⠸⣿
⠀⠀⢸⣇⠀⠀⠀⣿⡀⢶⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢦⣿⣼⣿⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⡼⠿⣦⠀⠘⣿⣷⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⣷⠘⠿⠠⠊⢉⣥⣤⣤⣦⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿
⠀⠀⣿⣤⣶⠤⠄⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹
⠀⢰⣟⣉⣐⣶⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠧⣼⣿⡛⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠇⡿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⢀⢰⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⢱⢀
⠀⠀⠀⠀⢀⣤⢸⢸⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢸⢸⢰⢄
⠀⠀⠀⣠⢺⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⢳⡀
⠀⢰⣿⠙⢸⢸⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢸⠈⣼⣿⣷
⠀⢸⡏⠀⡜⠸⡌⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⡇⠛⣿
⠀⢸⡇⠀⡇⡀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⡇⠀⣿⡀
⠀⣿⠁⠀⡇⡇⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⡇⠁⠀⢹⡇
⠀⣿⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⢸⡿⠀⠀⠀⠀⢀⣀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠘⣿
⢸⡇⠀⠀⠀⠀⠀⠀⣉⡒⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⣊⡁⠤⠄⠐⠀⠀⠀⣿
⢸⡇⠀⠂⠀⠀⠀⠐⠒⢊⡽⠒⣽⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣻⣵⠺⣭⡐⠂⠀⠀⠀⠀⠀⠀⣿
⣼⡇⢀⡀⠤⢄⣒⠬⠥⣒⠢⠭⣒⠩⢙⠻⣷⣄⠀⠀⠀⢀⣴⡿⢟⠩⢑⣊⠭⢒⡢⠭⢐⣂⡤⠤⣀⠀⣿
⠻⠿⣶⣦⣭⣑⡒⠩⠕⠒⠨⠕⡂⠍⠒⠍⠢⠙⢧⡀⣠⠟⠡⠊⠕⠊⠅⠒⠩⢔⠒⠯⠙⣒⣩⣥⣶⡾⠿
⠀⠀⠀⠀⠉⠙⠛⠻⠷⢶⣤⣄⣀⡀⠀⠀⠀⠀⣠⣽⣥⣀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢦⡾⠿⠻⠿⠿⣶⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠠⠀⢤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣴⣿⠀⣴⠃⣠⣾⣿⣿⣿⡿⣿⣿⣿⣿⣧⣤⣤⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣳⡄⢸⡟⢦⣟⡛⠋⢁⡠⠷⣮⣯⠘⣛⣿⣷⡼⠃⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣷⡌⣿⣷⣮⣙⡷⣎⠀⠀⠀⠹⣶⣬⠟⠻⢿⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⣿⣿⣿⣿⣿⣷⣾⣷⠀⠀⠀⣹⣿⣶⣴⡷⣿⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠿⣿⣿⣿⡟⣿⣿⣧⣤⣾⡿⢟⢮⣶⢠⡿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⣿⣿⣿⡟⢿⣘⣿⢶⣯⣽⣤⡶⠁⣡⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡞⢿⣿⡜⣷⣌⣹⣛⣿⠿⣿⠿⠾⣛⣯⣾⣏⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣳⡏⠀⠀⢙⣳⣿⣮⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⣠⣿⣿⣿⡿⢿⣦⣿⡟⠉⠉⣿⣿⣧⣾⣿⣫⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⠿⣿⣿⣿⣿⣽⣥⡾⢻⣿⣦⣴⣾⡋⣿⣿⣷⣦⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⢱⢫⣿⡿⣯⣻⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⣼⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣶⣷⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣭⣄⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣍⣿⣿⣿⣿⠿⢦⣿⣿⠻⠿⣿⣿⣿⣿⡿⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡏⠱⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠻⣿⣿⣿⡟⠀⢘⠋⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠶⢷⡉⠉⠀⠈⠛⠿⠿⠿⠟⠀⠉⠉⠉⠀⢠⠿⠟⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠭⣿⠉⡏⠍⣽⠉⢩⣴⡄⠹⠉⡧⢠⣤⡄⠨⠠⢤⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠂⠖⡂⢆⡐⠰⠲⠰⠄⠐⠶⠀⠐⢒⠲⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠉⠉⠉⠁⠁⠀⠉⠁⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢤⠴⠞⠶⠾⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣉⣥⣤⣶⠶⠾⠓⠒⠒⠒⠚⠳⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣩⠴⢚⡩⣖⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠴⠋⣠⠞⣩⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢡⠞⠁⣠⠞⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⣰⠋⠀⣴⠃⠀⠀⠈⠧⣄⡀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⠋⠀⠀⣀⡤⠴⠻⣆
⠀⠀⠀⠀⠀⠀⡼⠁⣰⠃⠀⡼⢻⡀⠀⠀⠀⠀⠈⠙⠋⢠⡖⠃⠀⠀⠀⠀⠀⠀⡴⠋⠙⠶⠟⠀⣰⠛⠁⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢰⠃⢰⠃⠀⣸⠁⢸⠃⠀⠀⠀⠀⢀⡶⠳⣄⠙⠋⠙⢦⣄⠀⠀⢸⠁⠀⠀⠀⠀⠀⣿⠀⡀⠀⣠⢶⡄⢻
⠀⠀⠀⠀⠀⣸⠀⡟⠀⠀⡟⠀⠘⣆⣀⡀⠀⠀⠘⡇⠀⣼⠀⠀⠀⠀⠸⣆⡀⢸⡀⠀⠀⠀⠀⠀⠙⠉⠹⣄⣉⡉⠀⢸⡆
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⠉⠉⣷⠰⡟⠁⠀⣸⠀⠀⠀⠀⠀⠀⠙⢦⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⡏⢸⡇
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⣇⠀⠀⠀⠀⢸⠁⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⡼
⠀⠀⠀⠀⠀⣇⠀⣧⠀⠀⢹⡀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠁⠀⠙⢲⡀⠀⠀⠀⠀⠀⣠⠇⠀⣸⠃
⠀⠀⠀⠀⠀⠸⡄⠸⡀⠀⠈⣧⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠿⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠳⡄⢱⡀⠀⠘⣆⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⢆⠀⠈⢧⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⡴⠋⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⢦⣀⠙⢮⣳⡄⠀⠀⠀⠀⠀⠀⠀⢸⠆⣰⠞⠛⠉⠉⠁⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⡓⠦⣌⡓⢦⣄⣀⠀⢀⣀⣀⡾⠰⣇⠀⠀⢀⣀⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠬⣭⣉⣛⣛⣛⣻⡟⠒⠒⠛⠛⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠛⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡏⠀⢸⣄⣀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠉⢹⠃⠀⠀⣯⠉⠉⠉⠙⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣙⠒⠦⠤⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠶⣚⡭⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⣤⣬⣉⣉⣉⣉⣉⣩⣥⣤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣄⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠼⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠛⠛⠛⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⡀⠀⠂⠀⠀⠠⠶⣤⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠤⡄⠉⠻⣿⣷⣾⣀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠶⢴⠞⠁⢰⠾⡇⠀⠀⢤⡄⠀⠤⢼⠟⠛⠛⠓⠀⢀⡀⠀⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠃⢻⣤⣾⣧⠆⠈⠁⠀⡀⣠⣴⡆⠈⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⡀⠐⠀⢿⣶⡦⡤⠀⠖⠀⣶⢀⡄⠈⣿⠿⠋⠷⠖⠀⠀⡙⠛⠛⠀⠀⠐⠳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠉⠁⠚⠁⢄⡀⠀⢀⣤⣼⣿⡿⡘⢀⢠⣀⣶⣤⠀⣤⠉⠀⠀⢠⠤⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⡀⠀⠀⠀⠀⡀⠉⠩⠉⠓⢷⣿⣦⣿⣟⣛⣿⣿⣾⣆⡄⠐⠀⠐⠀⠠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠖⠀⠋⠉⠂⠠⣄⢀⣼⠟⠉⠁⠉⢻⣿⣿⣿⡿⣓⠂⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠸⣿⡇⠀⠀⠀⠀⠘⡿⢉⣿⣿⡋⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⢦⠄⠀⠞⠋⡀⠚⠟⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣴⢶⠖⠚⠾⣿⡿⣿⣿⣤⣄⣀⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠉⠛⠉⠉⠚⠣⡤⢤⡷⠟⣿⡯⣀⠉⠻⣽⣷⡆⠁⠢⡄
⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣣⠐⠀⣛⢖⢳⠀⠠⠑⠀⢄⡀
⠀⠀⠀⠀⡠⠎⡤⠶⡄⠀⠀⡀⠀⠡⠀⠀⠀⠀⢰⡥⢈⠵⣰⠉⠙⣶⣟⣟⣽⡆⠀⣀⣶⢚⣛⢄
⠀⠀⠀⢰⠈⡖⠁⠀⣻⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠛⠀⠀⠁⠸⡿⢟⣬⢕⠋⠩⠀⠁⠃⠠⡀
⠀⠀⠀⠀⠈⠙⠦⢄⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⢀⣀⣀⣈⠋⠀⠀⠄⠂⠅⠀⠁⢠⡄⡀
⠀⠄⠐⠀⠂⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠌⠀⠃⠐⡀⠄⢂⠀⠀⠀⠀⢦⠄
⠐⠀⠀⠁⠐⠀⠀⠙⡂⠀⠀⠀⠁⠂⠄⠂⠀⠀⠀⠁⠀⠀⡄⠂⠈⠀⡀⠁⢂⠁⠀⡈⢄⠢⠁⠀⠀⠼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⠡⠐⠈⠀⠀⠁⠈⠠⢐⠈⠀⠀⢆⣌
⡃⠀⠈⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠈⠀⠈⠀⠀⠈⢀⠨⠀⠀⠀⠀⠅
⠂⠀⠀⠄⠀⠈⠀⠂⠠⠈⠻⠣⠀⠀⠼⠀⢀⡀⣈⠂⢀⠄⠀⠠⠀⠀⠀⡂⠄⠀⠨⠀⠂⠁⠀⠂⠈
⠀⠀⠀⠀⡀⠁⡀⢐⠀⡂⠀⠀⠢⢀⡈⠒⠁⣫⣄⠉⡲⡗⢡⠄⠀⢐⠉⠀⠈⢀⠂⠀⡀⠀⠀⢀⠀⢠⠴
⠈⠀⠀⠁⠂⠄⢂⠅⠈⠔⡡⢀⠄⡀⠀⠀⠐⢆⢀⡈⡈⠔⠥⠈⠤⡐⠁⢔⠀⠀⠢⠅⠀⠀⠀⡀⠠⣀⠄
⠀⠀⠀⠀⠀⠂⠀⠊⠐⡁⠂⠠⢊⠄⢀⠀⢀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠁⠀⠈⠀⢂⠀⢊⠔⡀⠐⡁⠔⠁⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠐⢀⠀⠀⠀⣀⠂⠄
⠀⠀⠀⠡⡀⠀⠠⢀⠠⢊⠄⠊⠔⠀⢀⠄⠀⠔⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠠⠀⠡⠂
⠀⠀⠀⠀⠈⠢⠀⠀⠈⠄⡈⢐⠁⡊⢔⠀⠀⠀⠀⠐⠁⠢⡀⠀⠀⠠⡀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠈⠐⠁⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣷⣶⣶⣤⣤⣯⡾⡀⢀⠀⢀⣀⡀⠀⠀⡆⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⡉⠋⠀⢋⡿⢶⣜⠋⠙⠁⠉⠉⠉⣹⡇⠀⠀⠀⠀⢶⡗⠀⢻⠁⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣟⣷⣌⠃⠀⠀⠀⠀⠀⠀⢾⡅⠀⠀⢀⠀⢠⣶⡄⢸⡆⠀⠚⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣿⣼⡟⠋⠁⣀⠀⢀⠀⠀⠀⠚⠁⠉⠑⠋⣶⠚⠛⠁⡺⠖
⠀⠀⠀⠀⠀⠀⠀⡀⢴⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⣹⢤⣏⠀⠀⠘⠻⠀⡈⠀⠀⢀⣷⡾⣶⢄⡰⡃⠀⠀⠀⠁⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠲⠖⢠⠀⠀⠄⠀⠀⠀⠀⠀⢰⡏⠀⠉⢀⠀⢐⣼⡟⠃⣠⠾⣹⣿⠶⢿⣾⣿⠉⠉⠀⠈⢀⠄⠀⠃⡀
⠀⠀⠀⠀⠀⠰⢆⣸⣀⢀⣠⢘⠇⠀⠀⠂⠀⠀⠀⠀⠠⣿⣄⠀⠀⠠⢤⣾⡟⠀⡀⢴⡆⢩⠀⢰⠿⣿⣿⡀⠀⠀⠀⠘⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠘⣿⠧⣤⠀⠀⠶⠀⡄⠀⠀⠀⠀⠁⠀⢋⠈⠙⠀⢀⠸⠿⠁⠘⠻⣶⠖⢻⣧⡅⠀⡻⢛⡃⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠂⣠⠆⡁⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⢰⣆⡀⢷⡆⠠⠋⢹⣆⣶⣿⣧⠀⣿⡟⠉⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⢤⡄⠀⣀⠀⠙⣾⠃⠀⠀⠀⠀⠀⠀⠐⣯⣀⣠⡌⣀⢣⣾⣃⡀⠀⠀⠉⠉⣿⢻⡆⠹⠇⠀⢀⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢩⠠⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⣀⢰⡏⠘⠉⠋⠀⠀⠰⠄⡟⠈⠃⢀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠹⠀⠁⠀⠓⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠇⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢺⢀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⣦⣀
⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠸⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠉⠛⢦⡂⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢷⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠈⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡋⠤⠤⠄⠁⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣅⡀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠃⠘⠁⠀⠀⠀⠀⠀⠦⢀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⣴⣷⣶⣿⠛⣶⡄⠀⠀⠀⠀⠀⢢⠀⠀⠀⠘⠉⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⣾⣿⣿⠫⠇⠀⠉⠁⠀⠀⠀⣸⠷⣿⡄⠴⠆⢦⡀⢀⡿⠇⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⣰⠏⢀⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣇⣾⣿⣿⣅⠀⠀⠀⠀⡤⠀⠀⠀⣿⡀⠀⣛⡇⢰⡆⠈⠀⣼⢇⡄⠀⠀⠀⠀⠀⠴⠀⠄⡄⠀⠀⠀⠐⠋⠀⣼⣿⡇
⠀⠀⠀⠀⠀⢾⣿⡿⠿⠟⠉⢿⡷⢄⠀⣀⣀⠀⢀⢀⡉⠁⣀⣽⡷⡄⢰⠀⠀⢠⡟⠁⠀⠀⠀⠰⠆⠀⡀⠀⠀⢠⣤⣿⣼⡆⣸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣮⡀⠀⢦⣤⡀⠁⠈⠻⢿⣿⣴⣿⠉⢁⣴⣿⣿⠟⠋⠀⠰⣤⠆⠘⠂⠀⠀⠀⠀⠀⠀⠀⣆⣠⣼⡿⢸⡿⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠚⣿⣿⣀⣴⡎⠁⢀⠀⠀⠙⢡⣷⠀⢣⠀⡀⣿⡟⢠⠀⡀⢠⠏⢲⣄⠀⠀⠀⠀⣠⢠⢰⣿⣾⣿⣿⣷⣿⠃⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠆⠀⠀⠀⢿⠇⠀⠀⠀⠿⠀⠘⣹⠀⠀⠀⠛⠀⠀⠀⠻⣿⣿⣿⢿⠏⢼⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠈⠉⠉⠙⠛⠻⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠙⠛⠛⠛⠃⠲⠆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⢠⣤⡀⠀⠀⠀⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡇⢺⣶⣶⡦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⢾⠁⠼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⡙⠁⠀⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⡠⠇⢠⡄⡀⣠⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⣿⠆⠀⠇⠀⣼⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⡿⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⢿⣶⣿⣷⠀⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢿⡀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠐⠀⠘⠛⠿⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠰⠼⠧⠀⢿⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠛⠟⠆⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⢾⣶⣄⠀⡈⣧⣀⡾⣿⣿⢹⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⠚⠒⡾⢣⣿⣿⣿⣿⣿⣿⣿⡾⠟⢼⣿⣌⣿⣿⡀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⡙⠛⢿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⢿⣿⣷⠀⠀⠀⠀⢠⠜⠁⠴⠆⢁⣴⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠤⢀⠰⣤⣤⣤⡀⣸⣿⣧⣿⠁⠤⠀⡤⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣿⣿⣿⣿⣿⣿⣿⣏⡈⣧⢰⣿⢿⣿⣿⣿⣧⣹⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣶⢀⠀⠀⢹⣿⡇⣿⣿⣿⡏⠀⠀⡀⣰⣿⣅⠀⠒⠀⠀⠀⠀⠠⠾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣸⣿⠘⠿⣿⣿⣏⠁⢹⣿⣿⣿
⣿⣟⡅⠙⠈⠘⠻⣿⣿⣿⣦⣂⡼⠛⢿⠛⢿⣿⠑⠀⠀⠀⠀⠙⠀⠀⡀⢀⠀⠀⠀⠀⢀⠉⢿⣿⡏⢿⣦⣝⣿⣿⣿⣿⣿⣿⣿⡆⠿⣿⣿⣷⡄⣿⣿⣿⣿
⣿⣿⡂⠀⠀⠀⠀⠿⠿⣿⣿⡏⡄⠁⡌⠀⡘⠃⠀⠀⠁⠀⠀⠀⠀⠀⠱⡘⠆⠀⠀⠐⠉⠀⣨⡟⠃⠘⠛⠉⣿⣿⣿⡟⣷⣿⣿⣷⣶⣿⣿⡿⠿⣿⣿⣿⣿
⣿⣿⣷⠀⠀⠀⠀⣰⣧⣼⣿⣷⣤⡄⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⣿⣇⢠⡤⠀⣰⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⠉⢰⣿⣿⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠈⠉⠛⠿⢭⡙⠃⠀⢀⠇⠀⠀⠀⢃⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠂⠀⡀⢸⣆⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⢀⣵⣟⣛⣷⣄⠀⠀⠀⠀⣤⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⠀⠄⠀⠂⢺⡀⣁⣰⣿⣿⣿⣿⣿⣿⣷⡄⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢰⠀⣄⢾⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⡙⠛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⡷⠀⠛⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢡⣄⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠾⠿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠘⠟⢃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⡶⠶⠶⢦⣄⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⠛⠛⠿⠿⠿⠶⠿⠿⢶⣤⣘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣿⠿⣿⣿⣿⣿⣿⣿⣿⠏⢹⡿⢿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⠲⠆⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⢿⣿⣿⣿⣿⣿⡇⢠⣿⠁⠀⠙⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣝⡻⠉⠛⠀⠒⢶⣶⣿⣾⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢸⣿⣿⣿⣿⣿⣧⣾⣇⣠⠀⠈⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢯⡶⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⡝⠁⠀⢀⣀⣀⡀⠀⠤⠄⠠⠴⢶⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣯⠶⣄⢂⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠄⠒⠒⢒⠒⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⢀⡠⢁⠀⠀⠰⠂⠁⢸⣿⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣷⣗⠀⠀⠀⠀⠀⢀⢘⠚⡉⠉⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⡘⠠⡤⠫⠚⠛⠘⣃⣠⡇⠀⣿⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡯⣿⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡂⢠⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⡀⠸⠀⠀⠀⠈⣿⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠇
⠀⠀⠀⠀⢠⡥⣤⣤⣤⣿⣿⠀⠀⠀⠀⠈⠶⠶⠻⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢐⢘⠂⠀⠀⢀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⢵⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⣍⢹⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠘⠘⠀⠀⠃⡞⠀⠀⠀⠀⠀⢀⠀⠛⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⢸⡍⢹⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⠠⠜
⠀⠀⠀⠀⢸⡓⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⣴⠀⠀⣀⣀⣘⣉⣀⣘⣻
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡆⠀⠀⠀⡇⡇⠀⠀⠀⠈⠀⠂⠈⡄⢀⡀⠀⠀⠀⠀⠻⠉⠓⠒⠺⠿⠒⠛⠻⠃
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢲⡀⠔⡜⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⢸⢰⡆⠀⠀⠀⡤⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡇⠇⠈⢆⠀⠣⠀⠀⠀⠀⠀⠞⣰⠃⡨⢄
⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⡇⢾
⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠑⠀⠐⠀⠀⠀⠀⠤⠎⠀⠀⠀⡈
⠀⠀⠀⠀⢸⠾⢻⠀⠀⠀⠀⢸⠤⠄⠀⠀⠀⠘⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⣿⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢟⣛⠛⠉⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠂⠄⠙⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤⣤⣤⣤⣤⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏

⠀⠀⠀⣾⢇⣿⢰⣿⣿⣿⣾⡟⠻⣄⣈⣁⣤⢹⣦⢹⣦⡿⠗⢸⣿⣿⣿⣇⠀⣴⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⡄
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⠀⣰⣿⡇⢸⣿⣟⣿⢸⣿⡇⠀⣿⣿⣿⡿⢿⠀⣿⣿⣿⣍⣿⣿⣦⡈⢙⣿⣿⣷⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⣿⣿⠏⢩⢸⣿⡇⢰⣿⣿⣳⣶⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⡌⣻⣿⣿⠇
⠀⠀⠠⣿⣿⣿⣿⡏⢿⣿⡇⢰⣿⣿⡧⣿⣿⠀⣾⣸⣿⡇⢸⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡃⣾⣿⡇⢸⣿⣿⣿⣿⣿⠂⣿⠿⣿⡇⢸⣿⣿⣿⣿⢸⣿⡟⠐⣿⣿⠈⣿⣿⣿⡇⣾⣿⡿
⠀⠀⠀⣿⣿⣿⣿⠆⣿⣿⡇⢸⣿⣿⡏⢻⡟⠀⣿⡼⣿⡇⢸⣿⣿⣿⣿⢸⣿⡷⠀⣿⣿⠀⣿⣿⣿⡇⣿⣿⣇
⠀⠀⠀⢿⣿⣿⡿⠀⣿⣿⠆⣿⣿⣿⡇⢹⡇⢰⣿⠉⢻⡇⢸⡿⣿⣿⣿⣸⣿⣧⠰⣿⣿⠀⢿⣿⣿⡗⢿⣿⣿
⠀⠀⠀⢸⣿⣿⡗⠀⣿⣿⠀⣿⣿⣿⠄⢸⡇⢸⣿⡄⢸⡇⢸⡗⠛⠋⠙⠙⠫⡟⠀⣿⣿⠀⣸⣿⣿⡁⣼⣿⣿
⠀⠀⠀⢸⣿⣿⡗⢀⣿⣿⡇⣿⣿⣿⠀⣼⡃⢸⣿⡇⢨⣇⠘⡟⠁⠈⢀⣴⠠⢷⢰⣿⣿⠀⣿⣿⣿⠀⢿⣿⣿⡀
⠀⠀⠀⢾⣿⣿⡇⠨⣿⣿⡇⣿⣿⣿⠀⣿⡇⣼⣿⠃⠰⡯⠀⠓⠀⠀⠈⠁⠀⣽⢸⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⡆
⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇⠋⠡⢿⠀⠿⠃⢿⢿⠂⠀⡇⠀⠀⠀⠀⠀⠀⠐⠻⣼⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⡇⢸⡿⠛⠇⠀⠀⠈⠀⠀⠀⠘⢸⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢤⡻⣿⠀⣿⣿⣿⠀⣽⣿⣿⡇
⠀⠀⠀⢺⣿⣿⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢸⣿⣿⣿⠀⣿⣿⣿⡆
⠀⠀⠀⢾⣿⣿⡇⢰⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇
⠀⠀⠀⣼⢻⣿⡇⠀⣿⠃⠀⠀⠀⠀⢀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠸⣿⣿⡟⠀⣿⣿⣿⡄
⠀⠀⢠⣿⡇⣿⡇⠀⣿⠀⠀⠀⠀⠀⠈⣤⠀⢙⣁⡁⠀⣴⠐⡂⠘⡀⠀⠀⠀⠀⢸⡿⠇⠈⣿⣿⠁⠀⣿⣿⣿⡃
⠀⠀⢸⣿⡇⢹⡇⠀⣿⢰⠀⠀⡀⠀⠀⠙⠛⣿⠁⢹⣷⠜⠃⠁⠔⠃⠀⠀⢠⠀⠸⠁⢀⡀⢹⡏⠀⠀⡹⣿⣿⡇
⠀⠀⣼⣿⢷⣨⣇⣠⡟⡸⠀⠀⢿⣶⣤⣠⣀⣿⣄⣩⣯⡼⠧⡀⠐⠀⢋⠨⠄⠀⠀⢆⡀⠙⠏⢀⡀⠀⣧⣿⣿⠓
⠀⠀⣿⣿⠸⡿⡟⣩⡾⠃⠀⠀⢾⠛⠛⠛⠛⢻⣿⣿⣿⠘⣶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠁⠹⠂
⠀⠀⢿⠟⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣿⣼⠵
⠀⠀⢐⣂⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠘⠿⠒⣀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠉⠐⠛⠘⠉⠉⠈⠁⠀⠀⠀⢀⠀⡤⠀⠸⣄⠀⠀⠐⠒⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣻⣿⣛⡛⠛⠲⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢾⠛⠛⠛⠛⠛⣶⡶⣯⣄⠀⠀⠈⣯⠉⠙⠛⠻⠶⣦⣄⣈⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣩⠟⠀⠈⢧⠀⣠⡴⠞⠉⠀⠀⠉⢛⣶⣶⡿⠇⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⡀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⢀⡾⠁⣀⣠⡴⠞⢿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣴⠏⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠷⢶⠶⢶⠟⠛⠋⠉⠀⠀⠀⠈⣧⡴⣤⡀⢀⡴⠞⠋⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⣠⡴⠟⠙⢷⣄⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣠⡶⠟⠉⠀⠀⠀⠀⠙⢷⣄⠀⠙⢿⣄
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⢠⡟⠀⠀⢰⡟⢶⡄⠀⠀⠀⠀⣼⣿⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠈⢿⣧
⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⠂⠀⣷⠀⠀⠀⢰⡇⠘⣷⡀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠻⣦⣠⣄⡀⠀⠀⠀⢀⣤⣦⡘⣷⡀⠀⢿⣷⡀
⠀⠀⣸⣏⠀⠀⠀⠀⢀⣠⣴⡷⢦⣄⠀⠻⣦⣶⠟⠀⠀⠀⠀⢿⣄⢹⣷⣤⡶⠞⠛⣫⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⡉⠛⠿⠾⠿⠛⠁⠈⠻⣾⣷⣀⣨⣿⣷
⠀⣰⡏⠹⣆⠀⠀⢠⡞⠁⣼⠃⠀⠹⣧⠀⠀⠀⢀⣀⣠⣤⠴⠾⠛⠻⠿⣷⡶⠶⠟⠋⠘⢷⣄⠀⠀⠀⠀⣠⣴⢟⣠⣿⣶⠶⠶⣤⣄⡀⠀⠀⠈⠙⣿⣁⣼⣿⣇
⢀⣿⠁⠀⣿⣀⣀⣿⣁⣠⣿⣤⣤⡶⣿⡶⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⢫⡵⠋⠁⠀⠹⣆⠀⠀⠉⠛⢷⣄⣠⡴⠻⣏⠀⣿⣿
⢸⡟⠛⠋⣿⠛⢉⣯⠉⢁⣧⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⡤⠤⢤⣴⠟⠀⠀⠀⠀⠀⠹⣧⠀⢀⣠⡴⠛⢻⣄⠀⢻⡀⣿⣿
⣿⠇⠀⠀⠈⠛⠛⠁⠀⢸⣿⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠛⠁⠀⠀⠀⢻⣆⠘⡇⢻⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠹⣧⠀⠀⠀⠀⠈⣿⡄⣿⣼⣿
⣿⡄⠀⠀⠀⠀⠀⠀⣤⡾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣠⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⣻⡇⢸⣿⣿
⢻⡇⠀⠀⠀⠀⠀⠀⣿⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⢿⡄⠀⠀⠀⣿⠇⢸⣿⣿
⠸⣷⠀⠀⠀⠀⣠⠀⣿⡇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠛⠙⣿⢦⣄⣀⠀⠀⢀⣀⣤⡶⠟⠁⢿⡄⠀⠀⠘⣧⠀⠀⣰⡟⠀⢸⣿⣿
⠀⣿⡄⠀⠀⣰⡿⣶⠟⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠹⣆⠉⠉⠛⠛⠛⠋⠉⠀⢀⣀⣈⣿⣤⣤⣤⣿⣶⣾⣿⣶⣦⣾⣿⡏
⠀⠸⣷⠀⣰⡟⠀⠀⠀⠀⠀⠈⣿⣀⣀⣤⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣀⣤⣤⠶⠞⠛⠋⠉⠉⠁⠉⠉⠛⠙⣿⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠹⣿⣋⣤⣤⣤⣶⠶⠖⠛⠛⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⡏
⠀⠀⠀⢻⣇⠈⢀⣠⣤⣤⣄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠉⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⣾⣿⡟
⠀⠀⠀⠈⢿⣷⡞⠁⠀⠀⠈⢻⣄⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⡿⠁
⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⢻⡄⠀⠈⢻⣄⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠘⣿⠀⠀⠀⠙⢷⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⢻⡇⠀⢀⣴⡾⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡶⠖⣛⠋⠉⠉⠁⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣧⡴⠛⠁⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⣠⡶⠛⠉⣙⣿⢶⣟⣉⡼⣿⠉⢉⣙⣷⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣤⣄⣀⠀⠀⠀⠈⠙⠳⢦⣄⣼⠃⣠⡴⠛⠉⢀⣀⣨⣥⣴⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠙⠉⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠚⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠄⣀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⣉⡠⠒⠕⠂⠱⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⠀⠀⠀⠘⠀⠀⠤⠤⠤⢀
⠀⠀⠀⠆⢀⡤⠄⠁⠁⠠⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠻⠿⠛⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰
⠀⠈⠇⠤⠀⠀⠀⢰⠄⠀⠀⢱⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⢸⠀⠀⠉⠀⠀⡡⠅⠈⢸
⡂⢀⡜⠀⠈⡰⠦⠜⠀⠈⡃⠤⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⢰⡀⢐⢸⠉⣃⣀⠈⠉⡑⡀⢀⠀⡀
⣇⣎⠃⠀⡰⠀⠀⠀⠀⡴⣁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠘⠀⠉⠁⠀⠭⠤⠤⠬⠭⠠⠈⠀⠀⠃
⠨⡹⠀⠊⠈⠁⠀⠀⠀⢤⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣀⠠⠇
⠀⠘⢦⡘⠀⢠⣀⡰⠌⣀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠉
⠀⢀⠐⠀⠉⠙⠃⠙⠉⠁⠂⠁
⠀⠀⠀⠀⠒⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⣂⠠⠤⢀⣄⣂⠀⠀⠉⠐⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⢌⠐⠒⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⠀⢌⢆⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠹⡄⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠦⠀⠈⠇⠀⠐⡀⠀⠀⠀⡃⠀⠀⠀⠀⡠⢈⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠐⠈⠲⡄⠀⠀⠑⠀⠂⠈⠀⠀⠀⠀⢀⣀⡀⠀⠄⠀⡀⡜⠀⠂⠐⠀⠀⠀⠀⡇⢀⢀⠀⡀⠀⢀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠄⠀⠀⢀⠌⠀⠀⠀⡄⠈⠀⠄⠀⠀⠀⠀⠨⡭⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠀⠂⠠⠐⠒⠀⠂⠂
⠀⠀⠀⠀⠀⠀⢠⢎⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠃⠐⢄⠀⠀⢀⠄⠀⠀⠀⠠⠤⠠⢄⠀⠀⢃⠄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠁⠁⠠⠀⠀⠁⠅
⠀⠀⠀⠀⢀⡴⠃⠀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠄⠈⠄⠀⠀⠀⠒⠐⠂⠀⠁⠀⠀⠀⠀⠑⠃⠂
⠀⠀⠀⣠⠊⠑⠄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠌⠁⠁
⠀⢀⠾⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠤⠤⠤⠄⠐⠊⠁
⠀⠈⠢⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⡅⢢⡔⠀⠀⠀⠀⠀⠀⠀⠆⠈⠢⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⢀⠔⣡⠞⢉⠔⠉⡀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠄⢀⠊⠀⠀⡐
⠀⠀⠀⢀⠔⢁⠔⢁⡼⠋⡠⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⡠⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣠⢁⠀⢀⠐
⠀⢀⡐⢡⣔⣁⣴⠋⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠘⢑⠞⠓⠅⠀⠀⡀
⢀⠘⠁⠀⠀⠀⠁⠜⡇⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⡐⠁⠀⠠⢈⠀⠀⠢⠐
⠉⠀⠀⠀⠀⠀⠃⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⠉⠀⠀⠀⠀⠀⢕⠄⠀⢁
⠐⠒⠒⠒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁

⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⠄⠀⠐⠒⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠶⠞⠻⠛⠛⠛⡏
⠀⠀⠀⠀⠀⠈⠓⠲⣤⣀⠀⠀⠀⠀⠀⠀⠘⠲⣶⣿⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠲⠦⣄⡀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⣶⣶⣒⣺⣿⣯⣽⠇
⠀⠀⠀⠀⠀⠈⠁⠢⠑⠢⢄⡀⠀⠀⠉⠙⠲⠤⣿⣿⣶⣶⣖⣺⣭⡭⠷⠶⠚⠛⠋⠉⠉⠉⠀⠀⠠⡀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⣑⠢⢄⡀⠀⠀⠀⠈⣿⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⡴⣖⣿⠂
⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠈⠑⠢⣌⠑⠢⢀⠀⣿⣄⠀⢀⣀⣀⣤⣴⣶⣺⣿⣽⠷⠾⠛⠛⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠉⠒⢤⠈⣙⣻⣭⡽⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠐⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⢠⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠀⠀⢸⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢸⣷⣆⣀⣠⣤⡤⠴⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⡄⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠐⠃⠀⢀⡠⠔⠋⠁⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠲⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡻⠶⠚⠉⠀⠀⠀⠐⠒⠁⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⢀⣀⣴⣗⣢⡀⠀⠀⢸⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠙⢿⣿⣿⣿⠀⡅⠂⣄⣾⣿⣿⣿⣿⡞⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣸⣿⣿⣿⠀⠇⢸⣿⣿⣿⣿⣿⣿⣶⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢀⣿⣿⣿⣿⢿⣿⣿⠿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⣮⣿⣿⡿⢿⣿⣿⣿⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡿⠿⠃⠘⠛⠋⠈⡁⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢨⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⡿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠉⠹⣿⣿⣿⣿⣿⣿⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠄⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣸⠀⢰⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣠⣉⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⢺
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿⣿⡿⠛⠋⠁⢀⣠⠔⠛⠉⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣄⠀⠀⣿⣿⣿⣏⡁⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣿⣿⠉⠉⢷⣤⠀⠀⠀⠀⠂⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣿⣿⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡄⠀⠀⣿⣯⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠰⣴⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣨⣇⠀⠀⣿⣿⠀⠀⠀⢀⠀⠁⠀⠀⠀⢰⡶⠚⠙⠀⣿⣿⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡠⢼⠨⠩⣟⠀⠀⣿⣿⠀⢀⠀⠀⠀⠀⠀⣀⠞⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⢀⣙⢠⣴⣿⣟⡒⠀⠀⠀⠀⣤⠜⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⢿⡋⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠈⠛⠉⠉⣉⣍⠙⠓⣦⣤⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⣀⠀⠀⢀⠈⠁⠀⠉⠻⢛⣷⠦⠤⣀⠀⠈⠉⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⡈⠀⠀⠉⠁⠁⠀⠀⠘⠉⠀⠀⠀⠈⠀⠀⠑⡂⠉⠁⠀⠀⠀⠈⠐⠀⠠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠄⢀⣀⣀⣀⡤⠤⠒⠀⠀⠂⠐⠂

⠀⠀⠀⠀⠀⢠⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⢸⠉⠉⠹⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⡂⡀⠀⠀⠈⠁⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⡟⢻⣿
⠀⢸⠀⠀⢨⣿⡏⠀⠀⢀⣀⣀⡀⠀⠀⡀⢀⡈⠘⠂⡁⠀⣀⠀⠀⡀⢀⢀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢠⣀⠀⢸⣿
⠀⢸⠀⠀⢸⣿⣇⠀⠀⢺⡇⢈⡷⢸⡧⠅⣾⠀⢸⠇⢻⡄⠏⢸⡧⠁⣼⢠⡟⢠⠹⣇⢈⠳⡌⢰⡏⠉⢸⣧⠉⠀⢸⣿
⠀⢸⠀⠀⢸⣿⣿⡀⠀⡿⠓⠞⠁⠋⠉⠁⠋⠉⠛⠁⠈⠉⠀⠚⠉⠁⠛⠀⠉⠉⠁⠋⠈⠁⠋⠈⠛⠃⢸⠧⠶⠀⢻⣿
⠀⢸⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⠩⠄⠀⠆⠀⠉⠆⢲⠀⠀⠀⡎⠓⠀⠀⠑⠆⠰⠊⠡⠴⠀⠀⠀⠀⠀⠀⢻⣿
⠀⢸⠀⠀⢸⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⢸⠀⠀⢸⣿⣿⠦⢀⣷⣤⠀⠀⠀⠀⠀⡀⠀⢀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢸⠀⠀⢸⣿⣿⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⢸⠄⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠸⢣⠾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⢸⡄⠀⢸⣗⢏⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠿⠄⢠⣧⣶⢗⡾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠄
⠀⢸⠀⠀⢸⣿⣱⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⣀⡼⠛⣯⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿
⠀⢸⠀⠀⢸⡟⠃⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⡘⣧⣠⣾⣏⣫⣹⣿⠀⠀⢀⠀⡂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣁⣿⡾⣻⣷⡜⡿⡿⠄⠀⠀⠄⣃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡄⠀⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢻⣿⣷⣿⣿⣷⣏⡸⡄⣞⡀⠹⣯⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡄⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⢁⢱⡗⣟⣉⣩⣴⢿⣷⣿⣯⣧⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⢸⡇⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⢞⣽⢨⣧⢻⣿⣇⢹⣾⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿
⠀⢸⡇⠀⢸⣿⣿⣶⠀⠀⣰⢾⣧⣄⢀⣠⣧⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣽⠀⠀⠀⠀⠀⠀⠰⣧⣄⡰⣿⣿
⠀⢸⡧⠶⢸⣿⣿⣀⠀⠖⣮⣿⣿⣿⣮⣿⣿⣿⣿⣿⣇⢻⣷⣿⣷⣿⣿⣿⣿⣏⢷⣿⣇⠀⠰⣄⠀⠀⠀⠀⠁⢀⣹⣿
⠀⠘⠷⠶⠾⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠶⠿⠷⠾⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⣇⡶⣼⣠⣴⢴⠢⣶⡖⢲⠂⠀⢴⢲⡦⠶⢰


⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡤⠀⠀⢤⡄⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠮⡀⣠⠇⠀⠀⠈⣰⣆⠀⠀⠀⠀⠀⡐⢂⡀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠂⡠⠁⠈⠢⡄⠀⠀⢀⠞⢻⠏
⠀⠀⠀⢠⡄⠀⠠⠋⠀⠀⠀⣌⠆⠡⣱⠀⠀⡠⠎⣰⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠰⠀⠀⠚⡩⠀⠀⢏⡠⠂
⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠑⠒⠒⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠈

⠀⠀⠀⢰⠀⠀⠐⠒⡆⠀⠀⠀⢀⠦⡄⠀⢠⠦⠖⠴⠤⠆⠀⠀⡔⠒⠒⠒⠂⠀⠀⠀⣴⣦⠀⠀⢀⠀⠤⢀⡒⠀⢀
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡒⠇⢴⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢱⢈⠈⠠⡁⠀⠀⠰⠩⠭⠆⠀⠀⠑⠠⠤⠄⠒⠉⡄
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣮⠃⠈⠀⠀⢘⠀⠀⠉⣠⠇⠀⠀⡇⠈⠁⡀⠁⠀⠀⡱⠀⠀⢊⡀⠀⠸⡀⠀⠀⢐⠒⠗
⠀⠀⠀⠈⠓⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢠⡶⠒⢦⡀⠀⢠⠢⠴⢦⡒⡄⠀⠀⠀⢀⠄⠂⠀⠀⠰⠀⡆⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠀⡀⠰⣒⢤
⠀⠀⠀⠀⢸⣄⠀⣠⠇⠀⢸⠨⠉⠩⠁⡇⠀⠀⢠⠃⡠⠃⠀⡠⠊⠀⠉⢢⠀⠀⢰⠋⠉⢉⠒⠀⠀⢸⠰⡸⢀⢎⠆
⠀⠀⠀⢀⢎⡟⠉⠁⠀⠀⢸⢀⠀⠈⢀⠃⠀⠊⠉⠒⠁⠀⠀⢏⠀⠑⡈⢩⠃⠀⢸⠐⠈⠐⢸⠀⠀⣨⠳⠤⠢⣟⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠈⠑⠒⠒⠁⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⡠⠄⠒⠀⠀⠈⠁⠀⠀⣠⣔⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠖⠉⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⠜⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡴⠃⣰⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣉⣀⢀⠀⠀⡀⡀⠐⠨⡢⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣼⠇⢰⠃
⠀⠀⠀⠀⠀⠀⢠⡲⢿⣿⣿⣿⣟⠳⢖⣒⡚⠵⡲⣦⣄⢱⡀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⣿⠏⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠿⢿⣶⡾⢿⡟⠛⠛⠂⠉⠫⣷⣿⣆⣠⢊⣠⣴⠶⠛⠉⠀⠀⠀⠀⠠⠤⢀⣠⠞⠁⢀⣼⣿⠏⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠒⢁⡴⠊⠙⠒⠦⢄⣒⠤⣄⣈⣿⣿⣿⣿⣭⣤⣤⣤⣀⣀⠀⠀⠠⠄⠠⢤⣀⣀⢠⣾⣿⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢀⡙⢿⣿⣿⡿⣿⣿⣯⣭⣭⡭⠭⠍⠉⠒⠂⠒⠈⠉⠹⣿⣿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠋⠉⠙⠛⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠤⠀⠀⢽⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡇⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢰⡇⡄
⠀⠀⠀⠀⠀⠀⣠⢼⢸⢸⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⡇⡇⡧⣄
⠀⠀⠀⠀⢀⣼⡇⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢸⣧⡀
⠀⠀⠀⣾⣿⣿⡇⡸⡘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢣⢇⢸⣿⣿⣷
⠀⠀⠀⣿⣿⣥⡇⡇⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⢸⢸⢩⣿⣿
⠀⠀⢠⣿⠅⡇⠃⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠘⢸⠈⣿⡄
⠀⠀⢸⣿⠀⢰⠀⡇⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢸⠀⡆⠀⣿⡇
⠀⠀⢸⡇⠀⢸⠀⠃⢂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠘⠀⡇⠀⢸⡇
⠀⠀⣾⡇⠀⠈⢸⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡆⠁⠀⢸⣷
⠀⠀⣿⠇⠀⠀⢸⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⡇⠀⠀⠸⣿
⠀⠀⣿⠀⠀⠀⠈⠀⠂⠤⣐⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⣂⠤⠀⠀⠁⠀⠀⠀⣿
⠀⢰⣿⠀⠀⠀⠀⠐⠒⠤⠤⣍⣓⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣚⣩⠤⠤⠒⠂⠀⠀⠀⠀⣿⡆
⠀⢸⡿⠀⠀⠀⠀⠀⣀⠀⠉⠔⣊⡽⠶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣯⠶⢯⣑⠢⠉⠀⣀⠀⠀⠀⠀⠀⢿⡇
⠀⢸⡧⠄⣀⡀⠬⢄⣒⠠⠭⣑⡒⠬⢍⡒⠭⣛⠿⣷⣄⠀⠀⠀⠀⣠⣾⠿⣛⠭⢒⡩⠥⢒⣊⠭⠔⣒⡨⠥⢀⣀⠠⢼⡇
⠀⠺⠿⣷⣶⣬⣍⣒⠒⠭⢕⡒⠨⠍⠒⠨⠑⠂⠉⠢⠙⢷⡀⢀⡼⠋⠕⠉⠔⠊⠅⢒⠩⠅⢒⡨⠭⠒⣒⣩⣭⣶⣾⠿⠗
⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣦⣬⣀⣀⠀⠀⠀⠀⠀⠀⣀⣹⣏⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⣶⣤⣤⣾⣿⣿⣿⣿⣷⣤⣤⣶⠾⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣀
⠀⢰⠋⠀⠀⠀⠀⠀⠈⡏⢐⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠘⠄⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠤⠤⠄⠀⠰⠈⡆⠀⠀⠀⠁⢉⣉⣉⢀⠀⣠⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡆⠀⠀⠸⣷⣖⠶⠶⠶⢶⣾⠇⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀
⠀⠀⡇⠀⠁⠀⣀⣀⣀⣸⣀⣧⣠⡤⠀⠀⢀⡇⠀⠀⢰⣧⠭⠬⠽⠍⠍⠙⠿⡄⠀⠀⠀⠀⣀⣴⣾⠖⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⡀
⠀⠀⢇⠠⠝⠛⠛⠙⠛⠧⠟⠛⠐⠚⠓⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠉
⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⢀⠉⡀⢠⠅⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠔⢋⠥⠊
⠀⠀⠀⠂⠈⣁⣀⡿⢠⠏⠀⠀⠀⠿⠻⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠉⠈⠀⠐⡀⠀⠀⠀⠀⠊⠁⠀⢀
⠀⠀⠀⠈⢳⡘⣇⣿⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢆⠁
⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⣨⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠉⢢⠀⠀⠀⡆⠉⢲⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠻⣿⢻⠁⠀⠀⠀⠰⠙⠻⠆⠀⠀⡠⠒⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠀⠀⠀⠁⠀⢚⣀⣍⣹⡀
⠀⠀⠀⠀⠠⠖⠀⠪⠀⠠⡀⠀⠀⠀⠀⠰⠛⠺⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠈⠋⠀⠀⠀⠁⠀⠠⣧⡽⢿⡀
⠀⠀⠀⠀⡰⠶⣀⠀⠀⠐⢀⡶⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⢠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣒⣂⡤⠀⠀⠀⠃⠀⠀⠏⠍⠉⡇
⠀⠀⢀⣼⣗⢲⣌⡻⢆⣄⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠁⣆⣀⡀⠅
⠀⠷⣙⠣⣝⡣⡍⢘⢲⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⠁⢀⡀⠀⣀⣀⠀⣀⣀⠀⣀⡀⠀⡃⠀⡇
⠀⠀⠀⠙⠢⣉⠁⣺⠋⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠘⣶⡢⡠⢄⠤⡠⡤⢤⡴⠃⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣌⡠⠐⣩⡮⡨⠺⠃⠀⠀⣇⢀⠇
⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢴⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⠔⣨⠪⢃⠂⠀⠀⠀⠉⠉⠀⠀⢀
⠀⠀⢀⡹⠖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡳⣢⣞⡵
⠀⠀⠀⠈⠂⠔⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣼⡭⡇⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⢒⣤⣶⡦⠦⠠⠀⠃⠀⢰⣿⠋⣻⡆⠈⢡⠀⠀⠀⠀⠘⠻⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣦⠀⣀⣠⣤⡤⠄⠀⠉⠀⠀⠀⠀⠀⠠⠐⡧⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡁⠀⢀⠀⠀⠀⠀⠀⠠⠖⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⣀⢀⣀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⢑⡤⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀⠤⠤⠐⠂⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠑⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡈⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠠⠄⠀⠄
⠀⠀⠀⠐⠀⠀⠀⢀⠀⠁⠈⠀⣄⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡁
⠀⠐⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⠟⢀⣀⣠
⠀⠀⡇⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠹⣄⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢌⠉⠀⣶⠁⠀⠄⠄
⠀⠈⠂⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⡀⠀⡂⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡌⡄⠀⢹⣧⣔⡢⠂⠑⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⣃⣉⣀⣵⣘⡦⠀⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢻⣷⣿⠀⠈⣿⣷⡀⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣻⠁⠀⠩⠃⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⡆⠌⠙⢠⠦⠤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⡇⠂⠀⠀⠀⠙⠀⠀⠰⢤⡴⠋⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⣄⠀⠀⡰⡀⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢠⡆⠀⠀⠀⠀⠀⠀⠇⠈⢀⠀⠙⠷⠄⠂⡅
⠀⠀⠀⠀⠂⠀⠘⠋⠘⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣼⠴⠛⠉
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠒⠋⠀⠐⠦
⠀⠀⠄⡴⠁⠀⢀⣘⠀⠀⠀⡰⠃⠀⡇⠀⠀⠀⠀⠀⠀⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⣠⣴⡾⠛⠉⢁⣀⣀⣤⡤⣐⡴⡀
⠀⠀⠀⠓⠂⠀⠰⠰⠀⢴⡾⠥⠤⠴⠇⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⡀⠀⠁⠀⠁⠀⠀⠀⠚⠒⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠖⠒⠒⠂⠀⠀⠀⠀⠀⠐⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⣉⠒⠬⢍⡛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠤⢍⡒⠦⢌⣑⠂⠈⠙⠛⠶⣤⡀⠀⢀⣀⡤⠴⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣐⠨⢍⡒⠬⢍⡂⠌⠉⠒⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠈⠙⠳⢮⣝⠒⠤⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⠙⠛⠛⠛⠷⢦⣤⣀⡀⠀⠀⠀⣀⡾⠁⠀⣀⣠⣤⡴⠶⠞⠛⠛⠉⠋⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠓⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢶⣶⣤⣤⣤⣤⣤⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⡶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡸⠱⣎⠻⣶⠤⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣀⡤⠴⢶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠁⠀⠹⣦⡿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢶⡿⢀⣠⣤⣤⣤⣽⣿⣿⣿⣿⣿⣛⣛⣉⣉⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⣀⣴⠶⠛⠋⠉⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠭⢭⣭⣍⣉⣉⣙⣛⣛⣛⣛⠛⠓⠶⠶⠶⠶⠶⠶⠶⣶⠿⠇
⢀⡾⠋⠀⢀⡀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠁⠐⠒⠓⠒⠒⢒⡒⠒⡒⠶⠶⠿⠯⠭⠭⠅⠀⠀⠀⢰⠛⠲⢤⣀
⣾⠁⠀⠀⠀⠈⠙⠒⠄⠀⢸⡇⠀⠀⠀⠀⠤⠤⠄⢀⣀⣀⣈⣉⣛⣒⣒⣒⠒⠒⠢⠤⠤⠭⠭⠭⠍⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠶⣤⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣂⠤⠤⠤⠤⣤⣤⣤⣤⣄⣀⣀⣀⣈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣀⣀⣀⣤⣤⣴⡾⠟
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠾⠿⠿⠿⠿⢿⣿⣿⣯⣥⣤⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⡏⠁⠀⠀⡾
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢠⡇
⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⡀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣩⣤⣤⠤⠴⠶⠒⣒⣀⣤⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣈⡻⣝⡒⠀⠀⠀⠀⠀⠒⠚⢛⣋⣉⣩⣭⡤⠶⠶⠖⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠖⠒⠒⠛⠛⠛⠛⠛⠒⠶⠶⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠙⠦⡄⠀⠀⠀⢰⠉⠙⠶⣄⠀⠀⡖⠛⣋⡽⠀⠈⠉⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⣆⣰⢦⡼⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡆⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⠁⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡜⠁⢠⠴⡆⣞⠻⣦⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣦⣀⡀⠀⠙⢶⣟⣀⣸⣀⢿⡿⠀⠈⠻⣦
⠀⠀⠀⠀⣴⢟⣥⡄⣰⡟⠀⠀⠀⢀⣤⠞⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢀⡼⠛⠀⡼⠋⠉⠉⠻⠶⠞⠁⠀⠀⠀⠈⢷⡀
⠀⠀⢀⣾⣿⠏⡿⠀⣿⠁⢀⡴⠛⠉⠀⣠⠖⠚⢉⡿⠀⠀⠀⠀⠀⢀⡴⠋⠀⣾⡟⠀⠈⠛⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⢀⣼⣿⠃⢀⡽⠀⣿⢀⡾⠁⠀⠀⠀⠘⠒⠖⠋⠀⠀⠀⠀⠀⡾⢉⣀⡀⢿⡉⢧⣴⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣼⠯⣷⠚⠉⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡆⠘⠷⢟⣹⣇⡾⣡⡽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⢠⡟⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⢦⠳⡄⠀⣿⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⣾⠇⠀⠀⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⣿⣟⣴⣇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠞⣷⡀⠀⣠⠊⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⠀⢀⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠚⠃⢠⡞⠋⢷⣀⣻⣷⡀⠀⢀⣾⠀⠀⠀⠈⣙⡧⠈⠊⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⡴⠛⠀⢀⣀⠉⣿⣼⢷⣄⣻⡅⢰⣏⡋⠉⠉⠀⠀⢧⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠥⠶⠖⠛⠋⠉⣷⠈⠁⠀⣨⣍⡀⠀⠈⢙⡧⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠙⠶⢦⣼⠇⠈⠙⠛⠛⢋⣀⣀⠀⠀⢸⣏⠙⠳⠶⠖⠛⣷⠀⠀⠀⣿
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⢹⡄⠀⠀⠉⠛⢻⡇⠀⠀⣿⠀⠀⣸⣿
⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠘⢧⡀⢹⡆⠀⣠⡴⠋⠀⠀⠀⣿⠀⠀⣿⠇
⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⣛⣋⣁⡀⠀⠀⠀⠀⠈⠓⣾⡟
⠀⠀⠈⢿⡙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡿⠃⠀⠀⠀⠀⠀⢰⠟
⠀⠀⠀⠀⠻⣄⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⢹⣇⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡴⣻⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠞⠁⣇⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢬⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠖⠋⢀⣯⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣈⣇⣀⣤⣴⠿⠖⠛⠉⠁

⠀⢀
⠀⠀⠀⠀⠄⢀⠀⠀⠄⢀⢀⡀⠀⠀⣀⠀⠀⢀⡀⡀⡀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣀⢀⣀⣀⡀⣀⠀⠀⠀⡀⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠀⠀⠀⠤⠄⠀⠀⠀⠠⠤⠄⠠⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣀
⠀⠀⠐⠀⠂⠀⠐⠂⠂⠀⠀⠀⠀⠀⠄⠀⠀⠦⠠⠄⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⡈⠀⠓⠀⠀⠁⠀⠁⠒⠂⠈⠀⠀⠀⠘⠀⠀⠀⠀⣠⠀⢈⡅⢠⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⡀⡀⠀⠀⢀⠀⠀⠈⠀⠉⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣀⠙⠐⠀⠀⠰⠆⢂⢀⠖⡀⠀⡆⠀⢰⠀⠀⠀⠀⠉⠀⠈⡇⢸⠂⠀⠀⠁⢠⠀⠀⠀⣀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣯⠀⠈⠈⠀⠀⠀⠀⢋⡀⠁⠀⠄⠀⡈⠀⢀⡀⠀⠠⠐⠒⠛⠺⡢⠀⠀⠀⠘⠀⠠⢔⠋⠉⣭⠼⢩⠁⠲⠀⣀⣦⡶⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢐⡏⡀⠀⠀⠀⠀⠀⠀⣈⠓⠈⠉⠉⠉⠉⠉⠛⠀⢰⣀⣂⣀⠀⠀⠈⠀⠀⠄⠄⠰⡳⠚⠚⠊⠀⠂⠄⠌⢳⠿⡴⠄⠀⠀⠀⠀⠀⠀⠳⠒⠛⠒⠀⠈
⠀⠘⡄⠧⠤⠀⠀⠤⠄⠁⢰⠀⠁⠁⠀⠀⠀⢀⡐⣀⢸⠁⠆⠀⠐⡀⠈⠀⠀⠀⣀⢁⠁⣀⣀⠀⠀⠀⡀⠀⣛⢁⠀⡂⡯⠂⠀⠒⠀⠀⠂⢙⣀⠀⢀
⠀⠀⠃⢰⠀⢀⠀⠀⠈⠀⡀⠀⠁⠀⠈⠀⠀⠀⣙⠹⢸⠐⠆⠀⠰⠐⠀⠀⠀⠒⠚⢸⠀⠉⠉⠀⠀⠈⠈⠀⠸⢚⠈⠃⠁⠀⠀⠀⠄⠂⠐⢠⠀⠰⣿⠀⠀⡁
⠀⠰⠛⢿⠛⠦⠴⢺⠶⠦⢽⣥⡀⡒⠒⠲⠶⠀⠘⠂⠀⡄⢀⢀⡀⠀⢀⠀⠀⣲⠀⢸⠀⢰⣆⠀⠀⣠⡆⠀⠓⠼⡇⣠⠀⢡⡄⠀⡴⠒⠀⣽⠂⡦⠃⠀⠀⠁
⠀⠀⡅⠀⢰⣦⣦⡠⢀⠀⢀⠉⢫⡅⠘⠀⠀⠀⣀⣶⠶⠃⢻⣦⣤⠀⠸⠀⠀⣦⡷⠏⠀⠘⠇⠀⠀⠘⠃⠀⠁⠠⡁⢀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠜⠀⠁
⠀⢰⡇⠀⠀⣿⠀⠀⢈⣄⡀⠐⠂⠀⠀⠀⠀⠀⣼⢣⠀⠋⠃⣶⡝⠀⠀⠀⠐⡁⠙⢆⠀⢰⡄⣀⢀⠀⠀⠀⢈⠆⣿⡬⠁⠐⠁⠀⠸⠔⢈⡀⠀⠀⠐
⠀⠀⠰⠀⢰⣿⡆⠀⣸⠳⠆⠀⡀⠀⣰⠀⠄⠀⢸⣿⡆⡳⡆⡉⢷⢄⠈⠇⠀⠀⢈⡊⠰⠬⠉⢉⠢⢘⡖⠶⠟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠷⢶⡄
⠀⢀⠐⠀⠺⡟⠃⢶⠛⠀⠙⠀⠋⠀⠁⢐⠓⠐⢺⠃⠄⡛⠀⡀⠈⠀⢈⡃⠀⣀⠌⠀⠀⠀⢀⣶⣀⣨⠑⠈⡆⠦⠚⡂⠐⡀⢀⠀⣆⢠⠀⠘⠛⠿⡟⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠄
⠀⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠉⠀⠁⠀⠀⠀⠉⠈⠁⠁⠀⠀⠄⠀⠀⠀⠌⣰⡎⠁⠀⡄
⠀⠀⠀⠀⠀⠁⠁⠀⢃⠀⠈⠀⠀⡃⠀⠀⠀⠀⠀⠐⠂⠂⠒⠐⠂⠒⠰⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⢀⠘⠀⠈⠁⠀⠁⠀⠀⠀⠐⠀⠂⠐⠋⡡⣄⠴⣠⠁⡀
⠀⠘⠂⠈⠀⠀⠁⡀⠀⡈⠈⢁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠐⠒⠒⠀⠐⠄⠀⣀⠀⠀⠦⠀⠀⠀⠀⠀⠀⢰⢃⡀⢙⢻⣄⡇
⠀⠀⠂⠀⠀⠀⡀⢠⡼⠁⠀⢸⡿⠋⠁⠀⠐⠓⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠠⡀⠘⡈⠥⣻⡴⠯⢙
⠀⠠⠄⠀⠀⠀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠘⠐⠂⠲⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⢃⡀⠠⠄⠀⠂
⠀⠀⠶⠀⠐⠶⣷⣒⢹⡍⠝⣑⣆⠀⠀⠈⣁⢀⢈⡈⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢈⣀⠀⠀⢀
⠀⠠⣄⠀⢀⡄⠹⢋⣈⠁⣠⣙⢻⣿⣜⠓⢶⣤⣤⡈⠁⠈⠈⠀⠀⠁⠀⠀⠀⢸⠀⡇⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠙⠟⠃⠘⠿⠄
⠀⠀⠈⠛⠩⠿⣥⣹⠉⠐⡸⢻⡛⠒⠉⠁⠀⠪⠭⠀⠀⠠⠄⠀⠄⣀⣀⣰⠀⢸⡍⣭⡿⡆⠀⣦⠀⠀⣔⡁⠀⠀⡀⠋⠀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⢿⡿⠀⡃⠰⠆⠿⡿⡏⢸⡙⡇⢨⡘⣛⠂⠃⢀⠀⠂⠀⠒⠀⠐⠀⠸⠀⠈⠀⠉⠙⠇⠀⣿⣷⠀⢸⠐⠗⣶⡯⢀⣤⣤⢻⠶⡤⠿⠷⠇⠸⣷⣶⡄
⠀⠀⢸⡇⠀⠄⠀⢀⠀⢱⣖⣠⣧⣧⠰⠦⠤⠅⠀⢌⣁⢀⣈⢉⠀⠀⠀⠸⠀⠀⠤⠄⡐⠀⢀⣿⣖⣀⠜⠀⣄⡘⠀⠻⣿⠿⣏⠀⠀⡀⠀⣄⠱⠐⠓⣤⠀⢠
⠀⠀⣼⣧⠀⢠⠂⢸⠄⢸⣿⠹⢻⡜⡔⢒⠒⠀⠂⠀⠀⠀⠬⠀⢠⠀⣀⠀⠀⠈⠀⠘⢓⣲⡿⣿⡟⢻⡽⢿⡿⢹⡆⠀⠉⠀⠘⠃⠈⠁⠀⠉⣠⡀⠀⠅⠀⣰
⠀⠀⢻⣿⠀⠞⠀⢸⠀⠈⣿⡎⢹⡿⡳⠤⠅⣄⡈⠐⠚⠁⠀⠀⠀⠀⣀⠔⠀⠀⣀⣤⠌⢿⡇⠛⢶⣤⣇⣉⣿⣾⠷⠶⠄⠂⢰⠶⣄⠈⠁⠀⣿⣆⠀⠀⠀⠈
⠀⢀⢸⡇⠀⠀⠀⢸⠇⠀⣿⣶⠀⣧⣂⣀⣠⣿⣿⣶⡴⠈⣛⠟⠳⣞⠉⢁⠀⡐⣻⢻⠦⢸⣿⡄⠀⠖⠉⣺⡇⠖⣌⠹⣶⣀⠘⢟⠛⢀⠀⠀⠧⠻⠷⠄⢀⣤
⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣴⣶⣶⣶⡶⠄⠀⠂⢠⣤⠀⠀⠀⠀⠀⠀⠀⡜⠠⠄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣿⡿⠋⠀⠀⠀⠀⠀⠀⠸⠿⠋⠉⠉⠀⠀⠀⣎⠀⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠁⠀⣀⣀⡀⠀⠠⠀⠠⢶⣄⠀⠀⠀⠀⠠⠻⠃⣄⡀⣜⠁⢀⡀⠇
⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠁⠀⢀⡉⠀⢠⣄⠀⠀⠀⠀⣟⢢⠆⠀⢀⣴⣰⠀⠀⢠⡋⢰⡍⢆
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣠⣶⣿⠁⢘⠻⣿⣃⣀⠀⠼⡏⢼⣶⣿⣿⠟⠙⠀⠀⠈⠁⠶⣤⣀⡇
⠀⠀⠀⠀⢽⣷⠀⠂⣄⠀⢼⠹⡿⢃⠀⣻⠀⣌⢛⠻⢺⠻⣿⡈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠃⠙⡇
⠀⠀⠀⠀⠻⣿⣷⠋⣛⠙⣧⡟⠁⣴⡇⣿⠀⣿⣯⣀⠀⢹⡿⠀⠀⣸⡟⠀⠀⠀⠀⣶⣠⢃⡀⢀⡇
⠀⠀⠀⠀⠀⣠⠟⠀⠉⠐⢈⣷⣾⣿⣇⣿⣠⣿⣿⣿⣿⠻⠃⢀⣼⣿⠃⠀⣀⡀⠘⢏⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠈⠁⠁⠉⢀⣀⣈⣉⣉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢤⡤⠄⠰⠀⣰⠈⣦⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡉⢁⠀⠀⢀⠰⠈⠿⠇⠘⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣷⣾⣆⠀⠀⠀⠀⠀⣤⠀⠤⠤⠒⠂⠨⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢻⡟⣿⡇⠠⠤⠀⠀⠄⢠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠧⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⣿⠿⠏
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠶⠶⢶⣦⣶⡏⠻⠿⠃⠀⢀⠀⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢽⡷⣷⠋⠙⠻⠷⠶⠶⠶⠦⠀⠀⠀⠀⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⣠⠤⠀⣀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⢀⡀⠀⠈⠀⢀⡠⢡⠄⠶⠾⠿⠖⠛⠛⠛⠻⠿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣡⡔⣆⠀⣠⢙⣧⠀⠀⠀⣿⢧⡜⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⠠⠋⣹⣿⡆⠐⠶⠃⠀⠀⠀⢸⣇⠀⢀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠊⠹⠇⠰⠈⠀⠀⠲⢄⡄⠀⠈⠻⣻⡭⣈⣿⣽⡿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠄⢀⣬⣤⠾⢋⣹⣿⣷⡞⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠁⠴⢿⠛⢻⣿⣇⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢙⡛⠛⠀⠀⠙⠓⠈⠉⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠦⠤⠤⢤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠶⠦⠤⠤⠤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡋
⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡡⠂⢹⡀
⠀⠀⣰⠋⠙⠛⠛⠛⠓⠲⠶⠶⠦⠤⠤⣤⣤⣄⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⠄⠈⠀⣠⠞⣷
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠒⠾⠶⠶⠶⢶⡶⠋⡡⠀⠁⠀⣠⠞⢡⠎⢸⡄
⠀⠀⢹⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠊⠀⠀⣠⠞⠁⡴⠁⢠⠎
⠀⠀⢰⠃⠉⠉⠉⠙⠛⠒⠒⠲⠦⠤⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠁⣠⠎⠀⡰⠣⢄⡀
⠀⠀⠀⢣⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠒⠲⠤⠤⠤⣤⣸⣦⣞⣁⢀⡴⠁⢀⡜⠁⠀⡠⢾
⠀⠀⠀⠈⠲⢄⡀⠀⠀⠉⠛⠿⣶⣒⠒⠠⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢠⠎⣀⠴⠋⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠦⠤⠤⢀⣀⣀⠀⠀⠀⣿⣰⡡⠚⢁⠀⠊⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⠟⠁⡠⠀⠁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠄⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡠⠚⠁⠠⠂⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⡏⠀⠐⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⢇⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠞⠁

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






⡿⠿⠿⠿⠿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠉⠲⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⡿⠋⢄⡈⠑⠤⣀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⡴⡫⢈⠔⠁⠀⠀⠀⠀⠉⠒⠄⡀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡫⠊⠋⠀⠤⡁⠀⢰⠀⠀⠀⠀⡀⠀⠀⢈⠑⠢⣄⠈⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⣠⡶⠶⣬⡑⠢⢄⠀⠠⠀⠀⠀⠄⠀⠈⡀⠀⠁⠀⢄⡀⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⡒⣾⠛⠀⠀⠀⠍⠓⢦⣉⠢⢄⠐⠂⠀⠀⠊⠀⢀⠔⠠⠀⠈⠒⠤⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⣠⡾⠋⠀⠀⠈⠑⢢⠀⠐⠤⠤⠌⠛⠦⣍⠀⢀⡐⠠⡴⡡⠊⠤⠀⠀⠐⠀⠈⣁⠀⡨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠋⠉⢀⣾⠏⠀⠀⠀⠰⣶⣤⠀⠀⠀⠠⠈⠁⠀⠀⠈⠑⠦⣉⠒⢄⡀⠀⠀⠀⠁⠠⢀⠞⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣪⠆⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⠀⠀⠀⠈⠓⠦⡈⠑⠤⡀⢂⠔⢁⣼⡿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⠞⠁⣰⠟⡅⡆⠀⠠⠂⢀⡆⠐⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢈⣴⡿⣫⢞⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣠⠾⣱⠐⠿⢀⠸⣄⠒⠺⣵⣮⠀⠾⠂⡨⠀⢄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣴⡿⢋⢜⣵⣿⠿⣷⡿⠂
⠀⠀⠀⠀⠀⢀⠞⣹⠞⠁⣠⠞⠁⠀⠛⠃⢠⣦⠠⡌⠁⡠⢄⢀⠅⣠⠘⡀⡠⠶⢆⣀⡘⠀⢠⠀⣀⢀⣤⠞⢁⣴⡯⢋⢔⣵⣿⣯⣜⣷⣾⠁
⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠈⠻⢦⣀⠠⢶⡂⠷⠖⢘⡏⢁⡤⠠⢤⢠⡶⡎⠀⠀⠘⠁⠈⠁⢻⢔⣵⠟⢁⡴⡯⢋⢔⣵⣿⡻⢝⢷⣽⡿⣻⡀
⠀⠀⠀⠀⠀⠈⣿⢨⡙⠳⣦⣄⠢⢝⠳⣤⡀⠘⠉⢻⡁⢞⣻⠁⠄⢿⡉⣳⠈⠑⠠⡄⢌⡴⣵⠟⢁⣴⠏⢀⢔⣵⣿⠻⢷⣌⣳⣿⠏⢈⣼⣿⠆
⠀⠀⠀⠀⠀⠀⣿⡀⢌⡑⢤⡙⠻⣦⣍⠪⢕⠒⠘⠟⠙⣼⡧⢂⠄⡼⢄⠢⠁⠐⠈⠀⣡⠞⢁⣴⢟⡵⠀⣰⣿⠿⣗⢍⣢⣽⣿⢇⢔⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣶⣌⡓⢌⡒⢄⡙⠳⣦⣉⠲⢄⡐⠋⡣⠉⠋⠃⢌⡗⠀⠀⢠⡞⠁⣰⣿⡿⠋⣠⣾⣿⣭⣿⢾⣿⣿⠟⠕⣱⣿⠏
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣌⡓⢬⡂⢌⠉⠙⠲⣍⡢⠀⠺⢦⣀⠀⠀⠀⡴⠋⣠⡾⠿⠉⣰⡾⠟⡧⣊⢝⣷⣿⡟⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣥⣬⣙⠻⣿⣿⣿⣿⣦⠈⠃⠉⣀⠈⠒⠝⣢⣌⠓⢍⡳⠆⠈⣠⡾⣫⠄⣠⣾⣟⡒⢕⡪⣠⣾⡻⢋⢤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⢸⣏⣉⠻⢶⣽⣢⣭⣻⢿⣦⣄⡈⡑⠢⣐⠬⡙⠻⣦⣌⣠⡾⣫⠞⣡⣾⠟⢓⠬⡻⣵⣾⢿⢟⢔⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠸⣏⠠⣉⠢⢌⡙⠿⣯⣻⢮⣝⠻⣿⣗⠤⡉⠢⢕⠀⡽⢋⠜⣡⣾⡟⢁⠪⣑⢉⣾⠟⠕⡱⣫⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣍⠢⢍⡢⢌⠙⠳⣮⣟⡒⠿⢿⣮⣕⠢⠀⡷⣡⣾⠟⡁⢌⡒⠙⣢⣿⠋⠀⣪⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣍⠒⢭⡒⢄⡁⠉⠻⢷⣮⢝⠿⣶⣾⠟⢛⣶⣮⣕⣭⣾⡿⠋⢜⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡈⠑⠉⢀⠀⠑⠪⢿⣿⣦⢤⡲⣿⣿⣿⣿⣿⠏⡰⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⢉⠒⢤⡒⢬⡙⠿⣯⣄⣠⣿⠟⡡⣪⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⡢⣌⡑⠪⣕⠄⣽⠿⠃⢔⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣭⡓⠤⡁⡇⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⣠⠴⢂⣀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⢋⣠⠖⠙⠁⠀⠂⠀⠠⣠⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠔⢁⠔⠁⠐⠂⢀⠠⠢⢡⠒⠀⠁⠉⠀⠀⠀⠀⠀⡡⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠂⡔⠁⠀⣀⡔⢠⡗⠢⠜⠉⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⠃⠌⠀⠀⠀⠜⠃⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡈⠀⠀⣼⡯⠒⠛⣖⣢⣀⣈⠉⠑⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡘⠀⠰⢀⠁⠀⡠⠋⠒⠐⠂⠈⠘⠙⠶⠶⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⡄⠁⠀⠀⠀⠈⠀⠁⠂⠀⣐⡀⠀⠀⠐⠢⠤⠤⠴⠢⣄⡀⠀⠀⠀⠈⠣⠤⠐
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⣤⠀⠀⠁⠀⢰⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⡌⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢳⣄⣀⠔⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠉⡖
⠀⠀⠀⠀⠀⠀⠈⡆⠀⢂⠰⡈⢯⣤⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢂⠱⡀⡀⠈⢹⣀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠢⡙⢌⠢⡀⠻⣤⡀⠀⠀⢀⠟⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠓⢮⡀⢹⡝⠀⠀⠈⠀⠆⠁⡄⠀⠂⠀⠀⠀⠀⠀⢈⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈⠀⠉⠳⠭⣷⣆⣀⣀⣰⠁⠀⠱⠀⠀⢀⣠⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⠀⠀⠂⠨⠉⠉⠛⠒⠒⠀⠀⠩⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢀⣀⣀⡀⠀⣀⣀⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠠⢼⣇⠀⠠⠀⠀⠀⠀⠈⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉

⠀⠀⠀⣠⡀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⣀⠀⠀⣠⠴⠲⠦⣄⠀⠀⣀⣀⡀⠀⢠⠶⣄⠀⠄⠀⢀⣰⠤⢤⣀
⠀⠀⠀⠙⠁⣴⢋⡧⠼⠶⠬⣙⠷⡤⠶⡄⠛⠃⠀⡇⠀⠈⠃⢸⡜⠿⣿⣯⡿⠷⣯⣷⡃⣠⠶⣯⣭⡉⠙⢲⡌⢳⡀
⠀⠀⠀⠄⢸⠅⡎⠀⠀⢁⡤⠞⢁⣀⡦⣗⡴⠻⣄⢳⡀⠀⠈⣸⠁⠀⠀⣀⢰⣦⡻⠾⢱⣃⣀⣀⣀⡧⠠⡞⠹⡄⣷
⠀⠀⢠⣶⡜⣖⢳⡴⠚⢉⣤⠼⠋⢡⣤⢨⡷⢶⡏⠀⠙⠶⣶⡇⢠⣷⣼⣟⣾⢷⡿⡄⠸⣧⠖⣲⣄⣄⠐⠧⣾⠇⡟
⠀⠀⠀⠄⣴⢋⣀⡦⠞⣋⣤⢀⡤⠴⢤⡤⠶⠒⡛⠉⢳⠶⡌⣷⠸⡷⡟⣏⣏⣇⢷⠹⡀⠱⣄⣳⠘⠋⢠⡾⢏⡼⠁
⠀⠀⠰⣷⠌⠶⠋⣠⣞⣩⡇⣏⣴⡼⠷⣽⣾⣉⡽⠆⠈⣇⢷⠸⣄⢳⡹⡼⡼⡜⣎⢇⢳⡀⢀⣉⣿⠯⠽⣒⣉⢀⡄
⠀⠀⠀⠀⠐⠀⢰⣣⠞⢟⣁⡿⢭⣠⠴⠃⣈⡤⠶⠂⠀⢹⡘⡆⢸⠀⢧⢳⣹⣿⣽⡾⠛⢳⠸⢬⣉⡽⠈⡗⣿⠐⠂
⠀⠀⠀⠻⢃⣀⡋⢀⡴⠋⣠⠃⠀⢳⠈⡀⢀⡤⠶⠒⠀⠀⢧⠹⡌⢳⠈⣿⠋⣿⣤⣿⠾⠽⡀⢀⣴⡶⢠⠇⢻⡈⠁
⠀⠀⠀⣞⣩⣼⠇⠙⠶⠚⠁⣤⡀⠘⡇⠠⠀⠠⠖⠛⢁⠀⠸⡆⢳⠈⠇⠘⠿⠟⢉⡥⢤⠘⣛⡈⠋⣱⡷⣶⡶⠿⣄
⠀⠀⠀⠀⡇⠸⣄⡀⠀⠂⢰⣇⢳⡀⢹⡀⠀⠀⠴⠚⢉⣀⣤⣿⣈⡇⣀⡤⢶⠆⠛⠓⠋⣰⣧⡇⢼⣭⣭⣥⡤⠤⠼⠂
⠀⠀⠀⡼⢁⣀⣠⢿⡆⠀⣼⡁⠈⢧⠈⢧⣤⠴⢒⣋⡭⠖⢚⡉⠁⣰⡋⣹⠏⢀⡟⢛⣾⣗⠒⠛⠲⢦⠀⡴⢲⡒⢲⡀
⠀⠀⠀⢻⡋⠈⠙⣫⠇⢀⣯⠀⣤⠈⢧⠀⠈⠛⣉⣄⠐⠾⠛⣡⠞⣩⠏⣡⠖⢸⣧⠾⠛⠻⣧⠦⣄⣸⠀⡇⢸⣴⣼⡇
⠀⠀⠀⠄⢉⡛⢋⡁⠀⣸⠃⢸⠋⣇⠘⣧⠐⣿⡿⣿⠃⣠⠞⢳⡞⢁⣤⠜⠀⣸⠤⠤⠤⣤⣬⣀⣈⡟⠀⡇⢹⠄⢸⡇
⠀⠀⠀⠀⡟⠷⣿⠁⢀⡟⠀⣞⠀⢸⡄⠘⣆⠈⠛⢁⡼⣁⡴⣫⣤⢾⡼⠀⠀⣏⣠⠴⠚⠁⣹⠀⢠⡇⠀⡇⢹⡄⢸⠃
⠀⠀⠀⠀⣇⠀⣇⠀⣼⣉⣀⡉⠉⠉⠁⠀⢹⡄⠀⠾⠞⠁⡴⣣⠦⣽⠃⡖⠒⠿⠤⠤⠤⢼⣥⣀⣸⣁⠀⣧⠿⠤⣼
⠀⠀⠀⢠⠼⠷⠾⠦⢤⡉⠉⠉⠉⣉⣛⠓⠒⠃⠀⡄⢠⢾⣀⠙⣶⠃⣠⡙⢛⡖⢲⠖⠶⢤⠤⣤⣄⣹⠃⠌⠛⠒⠋
⠀⠀⠀⢸⠐⢒⣛⠒⠦⠍⡶⣫⡭⠭⣭⣍⠑⡦⢰⡷⣌⠓⢬⣙⣿⠆⠙⢡⡞⣰⠋⠐⢀⢸⠀⡇⢠⣶⣶⣶⣒⣲⢲⡄
⠀⠀⠀⣸⠀⣉⣉⣉⠓⢰⠧⡧⠤⠤⣤⡞⢰⠃⠀⠳⠼⠀⣶⡆⡶⢶⣄⣞⣰⠃⢠⣦⣤⢸⠀⡇⢸⡿⣕⣧⣤⡼⢻⡇
⠀⠀⠀⣿⠀⣁⠀⠈⠁⣼⠐⠚⠛⠓⠆⢠⠏⠠⢸⣭⣭⣷⠀⣀⡏⠉⡀⢉⡥⠤⣼⣍⠁⠸⠦⠇⠸⡇⠂⡂⣂⣶⣸
⠀⠀⠀⠉⢯⠭⠭⠽⣦⣷⣶⣛⡓⢲⣤⡞⠀⡴⣾⢀⡤⡿⠸⠽⠃⡞⡇⢺⠀⡀⠀⢨⢇⡙⣗⢦⡀⡇⠅⠄⠾⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠈⠷⠃⠈⠙⠓⠚⠁⠘⠛⠈⠋⠀⠙⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⣀⠤⠔⠂⢈⣁⠨⣧⣀⢠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⢔⡠⠖⠉⠑⠠⢀
⢀⢴⡚⠉⣁⡤⣔⣲⠭⠕⠒⢉⣀⡄⠀⠀⠀⠀⢀⠄⢀⣀⣀⠤⠤⠒⠊⠁⠀⠑⢅⠀⠀⠀⠀⠀⠉⠒⢄⡀
⡇⠃⢹⡩⠾⣍⢁⡠⠴⠒⠋⠉⢚⢤⠀⠀⡀⠐⠁⡞⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀
⡇⠀⣼⠃⠀⢸⠀⠀⠀⢀⠔⣋⣑⣤⣤⠎⠀⠀⠀⠳⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢈⡵⠂
⡇⠀⣿⡄⠀⣾⠀⠀⢐⣤⠚⣀⢨⣯⣕⠐⠢⠁⠀⠱⡘⢆⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⣠⠴⠊⡡⢧⡄
⣇⣆⡇⡇⠀⡇⠀⢶⡉⠙⠈⠀⠀⠉⠉⠙⠲⢄⡢⢹⡀⢈⣳⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣶⠉⣀⢔⡪⠚⠉⠓⢦⣀
⠀⠈⠷⣇⣀⣧⠶⣟⢍⡓⠦⣄⡀⠀⠀⠀⠀⢀⡹⢦⠿⣉⠀⠘⢄⠀⠳⣄⣀⣠⠤⠴⠖⠒⢋⣉⢿⣔⡪⠖⠉⠀⠀⠀⣠⢴⡟
⠀⠀⠀⠁⠸⣿⣗⠦⣕⡪⡂⢄⠉⠒⢄⡠⠖⠉⣠⣜⣄⡈⠓⢤⡈⠳⣠⣏⡂⢀⠤⢄⣒⠭⠕⠚⠉⢈⣱⠆⣀⡤⠖⠋⣁⠜⣳
⠀⠀⠀⠀⠀⠈⠪⢑⢄⡉⠛⢷⣬⣀⢠⣧⠴⣫⡞⠣⣀⠉⠢⣀⠉⠲⣌⠓⠒⠒⠉⠁⠀⠀⣀⡤⠞⣉⢿⣞⠉⢀⠴⣊⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⣐⠀⢈⣯⣀⠴⠊⠀⠣⣀⠈⠳⢄⡈⠑⢤⡀⠙⠢⣄⢀⡠⠖⠋⢁⠤⣪⢕⣩⡽⢚⡵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋⠁⠀⠀⠀⠀⠈⠑⢤⡀⠙⠲⣄⡈⠳⣄⣠⣏⠂⠀⣊⣵⡯⠖⢋⡨⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠙⠢⣄⠉⢓⣲⠿⠋⠁⣠⢔⡩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⣹⠫⠒⣀⠔⣪⠔⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣻⣆⣤⣖⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠲⣯⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⣤⠀⠀⠀⠀⠀⠀⠀⠈⢦⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⡶⣾⠉⠀⢀⡠⠒⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢿⣯⣿⣠⢳⠁⠀⠀⠀⠀⡤⠀⠐⠈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⣾⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣿⣥⠀⠉⢹⣛⣁⡠⠀⢠⣷⣲⣚⣛⣩⡐⠂⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣫⣶⠀⠀⣾⡈⠁⠀⠐⠋⠉⠉⠉⢉⠉⢁⡀⢀⡀⡠⠟⠀⠀⠀⠈⢰⡆⠀⠀⠀⠀⠀⠈⠋⠙⡛⠉⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⡿⠷⠠⠤⠤⠤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢧⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⣰⠋⠑⠢⣄
⠀⠀⠀⠀⡔⢋⣉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡆⠀⠀⠀⡏⠀⠸⠀⠀⡴⠃⠀⠀⠀⡜
⠀⠀⠀⠀⡄⠸⡀⠱⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⢄⡀⠀⡆⠀⠸⡀⠀⣸⠀⠀⡇⠀⡼⠁⠀⠀⢀⠞⠀⣠⠔⢾
⠀⠀⠀⠀⠘⢄⠑⢄⢱⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢶⢫⡱⡀⠹⣤⠶⡇⠀⣷⠦⣤⢁⡞⠀⠀⠀⢀⠎⢀⡜⡝⡳⡼
⠀⠀⠀⠀⠀⠈⠳⣄⠙⢧⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠳⡱⡘⣄⢹⡀⢻⢀⡏⢠⣇⠞⠀⠀⠀⢠⠋⢀⢎⠜⡜⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢴⠉⠙⡦⣤⠤⢤⡀⢀⣀⣀⣀⣀⣳⣱⣜⣌⣆⣷⣀⣿⣁⣼⣏⣀⣀⣀⣠⠇⠠⠯⠮⠾⠼⢤⣐⣒⠢⠭⢽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠊⠁⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠧⠝⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠚⠀⠀⠀⠀⠀⢴⣰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⣔⢲⠀⠀⠀⠀⠓⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣄⠀⠑⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠚⠀⠀⠀⠀⠀⠀⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠂⠀⠀⠀⢯⡹⠀⠀⠀⠀⠰⠽⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠦⣤⣀⣀⣤⠤⠦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⡏⠉⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠈⠉⢹⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⣀⣀⣤⣤⣀⢸⣇⣀⣤⣤⣀⣀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⠛⠉⠁⠀⠀⠉⠛⠛⠉⠀⠀⠈⠉⠛⠛⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣾⠟⢦⣄⠀⠀⣺⡇⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢸⣧⠀⠀⣠⡶⢻⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠷⣤⣿⠅⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠨⣿⣴⠾⠋⠀⠀⣿
⠀⠀⠀⠀⣀⠀⢿⡀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣠⡾⠛⠁⠀⠀⠀⢀⡿⠀⣀
⠀⢀⣠⣾⠿⢷⣾⣇⣀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⣀⣼⣿⡾⠿⣷⣄
⣠⣿⣟⡁⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠙⢷⣄⡈⢷⣄⠀⠀⠀⠀⠀⠀⣠⡾⢁⣠⡾⠋⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⢈⣻⣿
⣿⡟⠛⠿⣷⣶⣤⣀⡀⠀⠈⠙⠻⢿⣶⣤⣄⡀⠀⠈⠻⢦⣙⣦⡀⠀⠀⢀⣼⣋⡴⠟⠁⠀⢀⣠⣤⣶⡿⠟⠋⠁⠀⢀⣀⣤⣶⣾⠿⠛⢻
⣿⡇⠀⠀⠀⠈⠙⠛⠿⣷⣶⣤⣀⡀⠈⠙⠻⢿⣷⣦⣄⡀⠙⢿⣿⣆⣰⣿⡿⠋⢀⣠⣴⣾⡿⠟⠋⠁⢀⣠⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣤⣄⣀⠉⠛⠿⢿⣶⣾⣿⣿⣷⣶⡿⠿⠛⠉⣀⣠⣤⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣶⣤⣤⣬⣭⣭⣥⣤⣤⣶⣾⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠉⠉⠉⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿
⠀⠀⠈⠉⠛⠿⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣶⣶⣦⣼⣿⣇⣀⣀⣸⣿⣦⣴⣶⣶⣿⠿⠿⠛⠋⠉

⣏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣙⣆⠋⠌⠛⠉⠀⠀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⣰⠟⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠋⣠⠶⠞⠀⠀⠀⢰⠟⠉⠁
⣷⠀⠀⠀⠀⠀⠀⠀⣀⣰⣤⣶⠶⠛⠿⠟⠉⠋⠁⣤⠟⣼⡟⠛⠛⠛⢻⠋⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣿⣿⣶⣿⣶⠀⠀⠀⠖⠀⠀⠀⠀⠠⡀
⣿⠀⠀⠀⠀⠀⠁⢸⣿⠿⣿⠏⠂⠀⡀⠀⠀⢀⣴⣫⣿⣿⡇⠀⠀⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠸⠀⠟⠈⢿⡟⠃⠀⠀⠞⠀⠈⠀⣄⠀⠀⠈
⡏⠀⠀⠀⠀⠀⢀⣿⡟⢳⠄⠄⠀⠀⠳⣤⣤⣈⣛⣿⡿⠿⡇⠀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠇⠀⣴⡿
⡟⠀⠀⠀⠀⠀⣸⣿⠏⠈⢤⡄⠀⠂⠀⢀⡍⠉⠉⢻⣤⣔⡃⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣖⣤⣤⣽⣷⡆
⡇⠀⢠⣦⡀⢀⣿⣿⠀⣴⣾⣇⠀⠁⢸⡛⠀⠀⠀⠀⣿⣿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⠀⡂⠀⠤⠄⠀⠂⠀⢀⠀⡽⢿⣿⡟⠉⠁
⡷⠰⣾⣿⡁⣸⡏⠀⡘⢃⣙⠛⣄⣀⡈⠻⡄⠀⠀⠀⣽⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⣠⡄⠀⠀⠀⢸⣿⣶⡿⠟⡇
⡟⢸⣿⣿⣷⣿⡟⣿⣿⣾⣿⣤⣿⣿⣿⣶⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡷⣿⠃⠀⠀⢠⣾⡿⠋⠀⢿⢱⡆
⣿⠈⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣿⣦⡀⠀⣸⡇⡆⠀⢰⣧⡄⢿⡶⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⡷⡞⠀⠘⣶⣿⠋⠀⠀⢀⡼
⣿⢠⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⢾⣿⣷⣿⣟⢲⣿⠁⡀⠀⠘⣿⣿⣦⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢹⡗⢿⣿⣷⠠⠤⠖⣿⠁
⡿⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⡶⢂⠀⠈⠻⣿⣿⣶⣿⠀⠀⠀⠀⠙⣿⣿⣧⣀⡐⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⢘⣿⢻⡟⠁⠀⠀⢸⣯
⣿⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣀⣀⡘⠂⣀⣘⠿⠃⠉⠀⠀⠀⠀⠀⢻⣿⡸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡏⠸⠇⠀⠀⠀⠈⠛⢀⣀
⣿⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⡎⠀⢀⣀⡀⠀⠀⣠⠆⣨⠀⣤⣿⠟⠀⠀⠀⠀⠀⠘⠃
⣿⠀⣿⣿⣿⣿⣋⣰⡟⠋⠉⠁⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⠂⠀⠀⠀⣿⣿⣿⣷⣾⣭⡆⠀⣂⣤⣄⠐⣻⠀⡟⣁⠀⠀⠀⠉⣀⢀⣀⡀⢀⣀⣀⣀⣀⣀
⣏⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠈⠀⠉⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣐⣶⣤⠀⠀⠀⢀⠀⠀⣀⣠⡀⠉⠉⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⡇⣠⣀⣤⡄⢠⣴⣾⣿⣧⡴⠷⣶⣿⣾⣦⡿⠿⣿⣷⣖⠘⠿⠛⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠻⠗⠴⠶⠀⠀⠀⠘⠛⠀⠀⠀⣀⣀⣀⠛⠙⠛⠛⠛⠛⠛⠀⠀⠀⠀⠐⠿⠿⠟⠋⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠾⠶⠿⠿⠿
⣿⠀⠠⠶⠶⠶⠤⡤⠦⠤⠤⠤⠤⠤⠶⠠⠤⠄⠤⠤⠤⠤⠄⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠠⠤⠤⠤⠄⠠⠤⠤⠤⠤⢤⣤⡤⠄⠤⠤⢤⡤⠤⠤⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠉⠙⠻⠿⣿⣿⣿⣿⣿⡟
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⡿⠀⠀⠀⠀⡾⠓⠀⡀⠀⠼⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⡄
⣿⠀⠀⠀⠀⢀⣽⠀⢀⣅⢠⠀⠀⢸⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣽⠿⠿⠟⠿⢿⠇
⣿⠀⠀⠀⠀⠘⠿⠀⠀⠉⠀⣴⡆⣾⣾⣿⣉⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤
⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⣍⣉⣓⣭⡁⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀
⡟⠀⠀⠀⠀⠀⠀⠂⣀⠀⠈⠻⠟⠉⠉⠁⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⡀⠀⢀⣸
⣿⠀⣀⣠⣤⣤⣀⣄⣀⣄⣀⣀⣠⣤⣤⣄⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠿⣿⡀⣀⣀⢀⣀⡤⣀⡀⣀⡀⣀⡀⠀⣀⠀⠴⠾⠿⠀⠴⠿⠿⠿⠿⣿
⣿⠀⠈⣿⣿⣭⠛⠋⠈⠁⠉⠈⠻⠆⠈⠀⠁⠁⢸⣶⠶⠉⠐⢈⡀⠘⡇⠀⠈⠆⠀⠀⠀⠐⠛⡁⠒⠈⠉⠘⠃⠀⠀⠈⠃⠒⠂⠈⠉⠙⠛⠋⠉⠐⠋⠉
⣿⠀⣶⣶⣿⣿⢿⣷⢿⡆⣠⡄⠀⠀⠀⠀⠀⠀⢸⣿⠾⠁⠀⠉⠁⠘⠃⢀⠀⠀⢀⣴⣿⣿⣿⣇⣀⣤⣄
⡿⢀⣿⣿⣛⣉⡀⢟⠀⠁⠉⣿⡇⠀⢀⣤⡠⠀⠈⣿⡀⠀⠃⠀⠔⣲⡀⠛⡀⢀⣾⡟⠃⠀⠉⠈⣿⡟⢉⡀⠒⠀⠀⠀⠀⠀⠀⠐⠠⠅⠈⡀⠀⡂
⣿⠈⣿⣿⣿⢿⣿⠞⠃⠠⠀⠈⢻⢠⣿⠛⠿⡇⠀⠉⠀⠠⣄⡀⠀⠀⠀⠀⠁⠘⡋⠹⣤⡀⠀⠀⠀⠀⠈⣿⡆⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⣧⠀⣿⣿⣧⡄⢂⣀⣈⣙⠒⢀⠀⠈⢻⠷⣶⠁⠀⠆⠀⠀⠻⢿⣿⡆⠀⠀⠀⠀⠻⣷⠉⠀⠀⠶⡆⠐⠀⠈⠁⠀⣿⠀⠀⢀⣤⠘⠀⠀⠀⠀⠘⠁
⣿⠀⢻⣿⡁⠀⡜⠙⠉⠛⣷⡀⠀⠀⠀⠀⢈⣤⣿⣾⣇⣠⠖⠚⠿⠀⠀⠀⠀⠀⠀⠀⠛⠠⠛⠀⠁⠀⠘⢳⠄⠀⠴⣾⣿⠿⣿⠆
⣟⠀⠺⣷⠇⠀⠁⠀⠀⠀⣿⡇⠐⠀⠀⣠⣯⠎⠙⠉⠛⠃⠀⠀⣠⣔⣴⣾⠀⣰⡆⠀⣀⠀⠀⠈⠀⠀⠁⠀⠀⠄⣰⡟⠀⣴⣿⠀⠀⠀⠀⠠⣤⣤
⣿⠀⣲⣟⣀⣀⡀⠀⠀⠈⠉⠀⠈⠃⢰⣿⡿⠀⠀⢠⣶⣿⣿⣾⣿⣿⣿⣿⡾⣟⣤⢢⣿⣆⠀⠀⠀⠀⠀⢠⡀⣸⣏⠁⣿⣿⡏⠀⠀⠉⣧⣤⣤⣤⣶⣀
⣿⠀⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣽⣿⣿⣿⣿⠛⢋⣾⣿⣿⣿⡀⠹⠟⠀⢠⢤⣤⣬⣭⣭⣭⣽⣿
⡿⠀⠹⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠿⠟⠀⠸⠿⠿⠿⠿⠿⠿⠷⠸⡿⢿⣿⡿⠋⠈⠉⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠷⠀⠀⠛⠃⠠⠈⠛⠛⠛⠻⠟⠋
⣯⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⡿⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⡿⠿⠛⢋⣉⣤⣶⠿⠛⣻⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠛⠉⣉⣠⣴⡶⠿⠛⢋⣡⣤⣶⣿⠿⠿⠛⢛⣻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠟⠛⠉⢁⣀⣤⣴⡾⠟⠛⢉⣁⣤⣶⠾⠟⠛⠉⣁⣠⣤⣶⣿⣿⡿⠿⠟⢻⣿
⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠟⠛⠉⠁⢀⣀⣤⣶⡾⠟⠛⢉⣀⣤⡶⠾⠛⠋⢁⣀⣤⣴⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⢸⣿
⠀⠀⣠⣶⠿⠛⠉⠁⠀⣀⣠⣴⣶⡿⠟⠛⣉⣠⣤⡶⠿⠛⢉⣁⣤⣴⣶⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⣤⣤⣶⣾⡿⠟⢛⣉⣥⣴⡾⢟⣛⣩⣤⣶⣾⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢰⣿⡏⠙⠻⠿⣿⣶⣿⣿⣿⡿⠿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⣿⡿⠈⠙⠻⠿⠿⠿⠿⠿⠿⠛⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⡿⢿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠁
⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⡿⠟⠛⠉
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠋⠉
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠋⠉
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣤⣴⣶⣿⠿⠟⠋⠉
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⣶⣾⣿⡿⠟⠛⠉
⠈⠻⣷⣤⣀⡀⠀⢀⣀⣠⣤⣴⣿⡿⠟⠛⠉
⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⢀⣀⠀⠀⣀⣀⣀⠀⠀⢰⢴⠾⢿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠁⢢⠄⠀⠀⠀⠈⡿⢉⣻⠁⠤⠀⠒⢒⣦⡤⠟⠀⠀⠀⠢⣄⣀⢀⡀⣀⣀⣂⣀⢀⣀⡀⠄⠀⠀⠂⠈⢳⡄
⠀⠀⠀⠀⠀⠀⡶⠲⠤⠜⣉⡐⠶⢶⣯⣤⢴⣶⣶⠖⠉⢉⠠⠀⠀⠀⠀⣀⠎⠈⠋⠉⠩⠥⠄⠀⣙⣟⠁⠒⢂⣠⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠉⠉⠑⠚⠳⡞⠉⠤⡧⢂⣠⠴⠓⠀⠀⠀⠙⠛⠓⠒⠒⠒⠒⠒⠚⠁⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⢄⣀⡀⠀⠀⠀⡏⣀⡤⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠁⠀⠀⠀⠀⠀⠀⠀⣴⠶⡂⠀⠐⠌⠉⠁⠈⠉⠏⠓⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⡾⠷⠒⠚⠛⠿⠿⡶⠦⣄⣈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⢣⣤⣤⣤⣤⣤⣴⣧⣄⣀⠈⠙⠲⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠭⠁⠀⠰⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⠀⠠⠶⠖⠶⠶⠶⠶⠶⢿⡿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⡀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣧⡴⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠛⠛⠛⠛⠙⡿⣟⡛⠛⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⣶⣇⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⣄⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⢀⣠⠆⠀⡁⠀⢀⣤⡼⠔⡈⠀⠺⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⣦⣤⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠊⡍⠁⡀⠀⡿⣚⢉⡀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠑⠠⢀⠀⠀⠀⠈⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢆⠀⠀⠀⡇⠀⢇⠀⠃⠀⠸⡇⠀⡁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠢⢄⣠⣶⣿⣷⡀⠐⡀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⡇⠀⢻⠀⠁⠒⠒⠁⠀⡷⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⢸⠇⣹⠿⠋⢁⠰⢅⢀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⢀⠀⢸⠀⠀⠄⠤⣆⠀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠠⠈⠱⣄⣴⠾⠋⠀⠀⠀⠀⠀⣦⣼⠀⢸⠀⣍⠀⠀⣿⠁⡄⠀⣠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉⠉⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣤⡴⠟⠋⠀⠰⠁⠀⠀⠀⣀⡴⠚⠉⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠀⠀⠀⠠⠄⣀⣘⣦⡶⠟⠛⢡⡶⠂⠀⡆⢀⠀⣠⡴⠛⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣴⠾⠛⢰⣿⡀⢠⠇⡎⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡀⢀⡀⠀⠤⠒⠂⠀⠀⣀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠁⠐⠒⠒⠒⠒⠀⢠⠿⠞⠋⢁⣴⣾⣞⡇⢿⢸⢠⣱⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⡷⠛⠃⠉⠀⠀⠀⠀⠀⢀⣀⣀⠟
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣇⢀⣴⣾⢿⠋⢘⠈⠁⠛⠛⠘⢻⡶⠛⠛⠉⠁⠀⢠⠀⠀⢀⣇⣤⣤⡤⠤⠶⠶⠟⠛⠋⠁⠒⠒⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠚⡿⠋⢁⣼⣿⣿⠀⠀⠀⠀⠀⣾⣧⣄⣠⣤⣤⠶⠃⠀⠀⣼⣿⣿⢂⣀⣀⣀⣀⣀⣘⣂⣀⣀⣐⣐⣺⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠄⠠⠄⠀⠀⣀⠀⠀⢧⣴⠿⠋⣠⠴⠀⠀⠀⠀⠀⣿⠀⠉⠉⠁⠀⠀⠀⣠⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣬⡆⠀⠀⠀⢀⣿⠤⠤⠀⠠⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⢀⣼⠿⠋⠁⠀⠀⠀⠾⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⣦⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⢸⡄⢸⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠂⣀
⠀⠀⠀⠀⠀⠀⠀⢷⡈⠉⠀⣀⡀⠀⠀⢠⠀⣀⡀⠀⢿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⠉⠻⠟⠻⣿⡏⠁⠀⣸⣿⡿⠛⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣏⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠈⠁⢀⠺⠛⠉⢀⠂⠈⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣿⡿⠷⠀⠀⢀⡀⠀⣠⡾⠂⠀⠈⠉⠀⠘⠀⠘⣦⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢠⡛⣉⢰⠆⣈⣹⢿⣦⠈⠉⣀⣠⠀⠐⣼⣧⣄⡀⣠⣿⠈⢿⣶⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠠⣤⣝⠛⠿⠀⠀⢹⣆⢻⡭⣭⡚⠁⠀⠘⣿⣷⣴⠂⠈⢡⣝⠁⠙⠛⠂⠤⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢀⣿⠀⡈⠀⢀⣠⣾⡿⢇⠱⡌⠧⠀⠠⣿⡏⠙⣫⣧⠀⣨⣯⣀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣾⢿⣿⣿⡾⢊⣣⠱⢠⣄⣠⣿⠿⠟⣿⠛⣿⣄⠈⠁⠙⢦⠀⠀⠀⠀⠛⠀⣶⠀⠀⠀⣠⣿⣿⣷⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⢋⡿⣫⠴⠛⠙⢧⢛⣿⡟⠛⠒⠲⠉⠛⠛⠛⢣⣴⣦⡄⠀⠉⠀⠚⠁⠘⠛⠀⠀⠰⣿⣿⢏⣹⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡈⠻⠿⢳⣏⢲⣍⠀⠀⠀⡻⣿⡅⠗⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⠋⠀⠛⠀⠀⣧⡀⠀⠀⠈⠛⠻⣼⣿⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠙⢷⡙⢦⡀⣾⣯⣉⣀⠀⠙⠶⠀⠀⠈⢀⡀⠲⣀⡐⠉⠀⠁⠀⠈⡈⠿⠇⠀⠀⠀⠀⠀⠀⠉⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠂⣀⢻⡄⠀⠀⠙⠛⢿⡓⣬⠛⠉⠙⠓⣶⠀⣶⡀⣀⣀⠉⢸⢛⡟⠀⠤⣴⠁⠀⠙⠢⢤⡀⠀⠀⣤⣴⣾⣿⠀⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠚⢿⡄⡹⣆⠀⠀⠀⠲⢿⠏⣰⠂⠀⠀⠀⠀⠛⠛⠉⠉⠛⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠰⢻⡌⢧⡀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠰⣴⠟⠀⣀⠀⠀⢀⠀⠀⠀⠀⣤⣴⠛⢿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⡷⠀⠀⡿⢋⢿⡄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢘⡷⠊⠙⠃⢤⣶⠧⠀⠻⣆⠀⠠⣿⣿⡟⣹⠀⢰⣷⢰⡇
⠀⠀⠀⠀⠀⠀⠐⢦⠠⡌⢁⠹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠂⠀⣼⡿⠂⠀⠀⠽⣿⢄⣿⣥⣿⣿⠀⢸⣿⢸⡧
⠀⠀⠀⠀⠀⠀⠰⢦⡙⢴⡛⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠈⠀⠰⠋⠀⠀⠀⠀⠀⠠⡌⣿⣿⣿⣿⠀⢸⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢮⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠈⡆⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠙⠋⢠⣶⣿⠀⠘⠋⠈⠋
⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠙⠷⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⢠⡎⠀⠀⠀⡸⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣀⣠⠄⠀⣠⡤⠀⠀⠀⠀⠀⠀⣀⢴⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠂⠀⠰⠶⠶⣶⠄⠀⠀⠀⠀⠀⠍⠸⠛⠻⢿⣦⡻⡿⠀⣤⣤⣀⣰⣶⠀⠉⣿⡟⠉⣀⣤
⠀⠀⠀⠀⠀⠀⢾⣿⡇⢀⡰⣶⡀⠇⠈⠁⠀⠀⠘⠳⣦⠀⡀⣠⡎⠐⠁⠀⠀⠀⠉⠉⢀⣹⣿⡿⠿⠿⠛⠀⠀⠻⠋⠙⠟⠛⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣧⢙⠁⣏⠉⣠⠀⠀⠀⠀⠀⣴⣄⣼⣟⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⡄⠀⠄⠀⠀⠀⣴⣶⡦
⠀⠀⠀⠀⠀⠀⠸⠇⠙⣰⠀⣿⠻⣻⠿⠃⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠋⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢨⣿⡟⠛⠀⠀⠀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⡸⠿⠿⠃⠀⠀⢼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠶
⠀⠀⠀⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣴⣶⣶⣶⣶⣤⣤⣴⣶⣶⣦⣤⣤⣤⣴⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⣀⣐⣶⣦⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣉⣉⣉⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋⠉⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠉⠑⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣁⠀⠄⠐⠒⠂⠀⠀⠀⢐⡢⢀⡠⠒⠢⢄⡀
⠀⠀⣀⡤⠴⠒⠛⠉⣀⣠⠤⢖⣚⡭⠭⠛⠈⡩⠉⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⢀⣀⡤⠔⠚⢯⣱⠏⠀⠀⠀⠀⠈⠑⠦⣀
⡰⠛⣳⣀⡤⢴⣒⡭⠵⠒⠋⠉⣀⣠⠤⡶⠊⠀⠀⠀⠀⢀⠔⠋⣠⠤⠴⠖⠒⠋⠉⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀
⡇⠀⠀⣇⠞⡛⢦⣀⡤⠴⠚⠋⠁⠀⢈⡩⠦⠀⠀⢀⠔⠉⠀⣾⠁⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⡇⡄⢀⣿⠀⠀⢸⡇⠀⠀⠀⢀⡤⢚⣁⡰⣄⣠⣴⠡⠄⢀⡐⠸⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡷
⡇⡇⢸⢿⢸⠀⢸⠁⠀⠀⠠⣏⠰⠋⠀⠉⣟⡩⠒⠦⡁⠂⢈⠳⡬⢣⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢀⣠⠴⠛⣹⣄
⡇⡇⢸⢸⢸⠀⣸⠀⢀⡤⠖⢻⡥⠒⠉⠉⠚⠛⠲⢤⣈⠐⠄⠰⣎⠡⠹⣄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠞⠉⢀⡤⣊⠵⠺⣄⡀
⠗⠳⣿⢸⢸⠀⡟⠀⣈⣷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡂⢷⣪⠴⠚⢧⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢴⠞⢃⡠⢚⡥⠚⠁⠀⠀⠀⠙⢳
⠀⠀⠙⢹⣸⣅⣷⣊⠹⢍⡢⣈⠙⠲⢤⣀⠀⠀⠀⠀⠀⣠⠔⠛⡞⠱⣄⠀⠀⠹⣄⠀⠙⣆⣤⠤⠶⠒⠛⠉⠉⣁⣠⠤⣻⣶⣥⠞⠉⠀⠀⠀⠀⣠⡴⠚⡏
⠀⠀⠀⠀⠀⠈⣷⣏⠓⠦⣝⡢⣕⠢⣀⠉⠓⠦⣀⠴⠋⠀⣠⢔⣳⣄⠀⠙⢦⣀⠈⢧⣰⣣⡒⠀⡀⠤⢒⣚⡭⠴⠒⠋⠁⠀⣈⡿⠂⣀⣤⠶⠋⠁⣠⠔⣻
⠀⠀⠀⠀⠀⠀⠉⠲⣝⠢⣀⠙⠲⢽⣮⣑⠠⠩⣺⣀⠴⢋⡵⠫⡀⠀⠑⢤⡀⠈⠳⢤⡙⠣⠤⠖⠒⠋⠉⠀⠀⠀⢀⣠⠶⠋⣹⢷⡞⠉⠀⣀⠴⢊⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣑⠤⡀⠨⣝⣟⠓⢋⣡⠞⠉⢇⠀⠈⠳⣄⡀⠈⠲⣄⠀⠉⠲⣄⡀⠀⠀⠀⣠⡴⠚⠉⢀⠴⣊⠵⢛⣧⡤⢚⡡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣐⡿⠔⠋⠀⠀⠀⠀⠑⢦⡀⠀⠙⠦⣄⠀⠙⢦⣀⠀⠙⢢⠔⡫⠁⢀⡤⢚⡥⣚⣥⠖⢻⣥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⠛⢦⣀⠈⠳⢤⣺⡹⠀⣊⣥⣾⡵⠚⠉⢀⡵⣊⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠓⢦⡀⠈⢉⡭⠟⠋⠁⢀⡤⢚⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⢈⣟⠭⠒⢀⡠⢖⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢼⣧⠆⢒⣩⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠛⠛⠛⠛⠛⠷⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⡏⠻⢤⣤⣤⠴⠶⠶⣄⠀⠀⠀⠀⠈⠉⠛⢷⣤⣀
⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⢳⡄⢀⡾⠛⠛⠳⢦⣌⡽⢷⣄⡀
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⣷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠽⣷⡀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⢿⡄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⣷⡀
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠘⣧
⣾⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢿
⣿⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠈⠙⠛⠛⠓⢦⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⣿⣀⣤⢤⡀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠶⠶⣤⡀⣸⠃⠀⠀⠀⠀⠀⣸
⢹⡏⠀⣠⠽⠂⠀⠀⠀⢸⠇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣿
⠘⣷⠀⢧⠀⠀⠀⣠⡴⠋⠀⠀⠀⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⢹⣷⠊⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠻⣦⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡤⠶⢦⡀⠹⣆⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠙⣧⡀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⣻⢰⡏⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⢷⣀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⣧⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣉⠙⠓⠲⠦⣌⠳⣤⡤⢤⣄⣀⣀⣀⣀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⠶⠶⣾⣦⣤⣤⣤⣬⡿⠷⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⡟


⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⡏


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⡆⡄
⠀⠀⠀⠀⠀⠀⠀⡀⣤⣻⢸⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⡇⣟⣤⢀
⠀⠀⠀⠀⠀⢀⣴⠇⡇⡟⣸⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣇⢻⢸⠸⣧⡀
⠀⠀⠀⢠⣤⣾⣿⠀⡇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⠀⣿⣷⣤⡄
⠀⠀⠀⢸⣿⡿⢿⠀⡇⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⢸⠀⡿⢿⣿⡇
⠀⠀⠀⣿⡇⢧⢸⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⡇⡾⢹⣿
⠀⠀⠀⣿⡇⢸⠘⢸⢡⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡌⡇⠃⡇⠸⣿
⠀⠀⢠⣿⠀⠀⡇⢸⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⡇⢸⠀⠀⣿⡄
⠀⠀⢸⣿⠀⠀⡇⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢸⠀⠀⣿⡇
⠀⠀⢸⡏⠀⠀⠃⡌⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢡⠘⠀⠀⢹⡇
⠀⠀⣾⡇⠀⠀⠀⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⢸⣷
⠀⠀⣿⡇⠀⠀⠀⠃⠀⠌⣐⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⣂⠠⠀⠸⠀⠀⠀⢸⣿
⠀⠀⣿⠁⠀⠀⠀⠂⠠⠤⣀⣉⠓⠺⣵⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣮⠕⢚⣉⣀⠠⠤⠀⠀⠀⠀⠘⣿
⠀⢀⣿⠀⠀⠔⠀⠀⠒⠒⠀⠤⠭⠕⣲⣭⣛⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣭⣖⠫⠭⠤⡀⠐⠒⠀⠀⠢⠀⠀⣿
⠀⢸⣿⠀⠂⢀⡀⠤⠄⣀⣒⠢⠬⣍⡒⠮⢭⣛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣛⡭⠕⣒⣩⠥⠔⣒⣀⠤⠄⢀⡀⠐⠀⣿⡆
⠀⢸⣿⣍⣐⡒⠤⢭⣑⡒⠤⢍⣓⠒⠬⣙⡒⠬⣙⠢⢝⠻⣷⡀⠀⠀⢠⣾⠟⡩⠔⣋⠥⢒⣋⠥⠖⣚⡭⠴⢒⣊⡭⠤⢒⣒⣨⣿⡇
⠀⠈⠉⠛⠻⠿⢿⣶⣦⣭⣉⣒⠂⠍⠑⠂⠈⠁⠀⠉⠀⠁⠀⠙⢆⡴⠋⠀⠈⠀⠉⠀⠈⠉⠐⠊⠩⠐⣒⣉⣭⣴⣶⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣤⣤⣀⡀⠀⠀⠀⣀⣴⣾⣷⣦⣀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⡿⠿⠿⠟⠿⢿⣶⡶⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢄⠀⠀⠀⠀⠀⠀⢀⠴⢤⣀⠀⠀⠠⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠂⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠀⠀⢀⠠⠋⠀⠀⠀⠠⣄⣀⣁⣀⡔
⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠁⠐⠀⠤⠠⠁⠄⡀⠁⠀⠀⢌⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠡⠀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠊⠠⠀⡀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⢀⡀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠙⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠐⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣧⣤⣤⣤⣬⣵⣌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢀⠂⠀⠀⠀⠘⢺⣖⣀⡐⠀⣒⣀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠗⠀⠀⠀⠀⠀⠀⠠⡍⠛⠛⠛⠛⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠁⠠⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢶⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠮⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠶⠿⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑
⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡑⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠄⠃⡀⢄
⠀⢀⠂⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣦⡃⢸⠀⠀⠀⠀⠀⡃⠀⠀⠇⠐⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⠀⠀⠀⠠⠁⢀⢸⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠⢤⠠⠀⡀⣰⠀⠁⠀⠀⠀⠀⠀⠼⡿⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⡉⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠓⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⡌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⢁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡠⢘⠀⡁
⠀⠀⢀⣤⠖⠂⠠⠀⡠⠑⠦⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠆⠀⠀⠘⢀⡑⠀⠠⣴⡆⠀⠀⠈⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠈⠀⠂
⠀⢀⠘⠷⡄⠀⠀⠈⠀⢰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢁⣁⡀⣝⠃⠀⠀⠀⠈⠐⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⣒⢐⣀⣀⡀⠤⠠⠤⢄⣤⣀⣢⣤⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠉⠁⠊⠈⠉⠁

⣿⣿⣿⡿⢿⡍⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠹⠷⠄⠀⠀⠤⠾⠿⠝⠛⠁⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⡏⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⢿⡿⢿⡏⠙⢿
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣩⣍⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣤⣤⠤⣤⣄⠀⢤⣀⣤⣤⠀⣤⡄⠀⢀⣀⣠⣄⠀⣠⣤⠀⣄⡀⣤⡀⢠⣄⠠⣤⣄⠀⣀⣀⠀⢀⣤⣄⠀⢤⡀⠀⣀⣀⡀⣄⣀⠸⣤⡄⠀⠀⣻
⣿⣇⠀⠀⠀⠀⣿⡇⠀⠀⣿⠇⢸⣿⢤⠄⢠⣿⠀⠀⢸⡧⠀⢻⣆⢠⠎⠀⣿⡥⠄⠀⢸⡇⣠⡜⠋⢀⡄⢻⣧⠀⢀⠙⣧⡀⠃⣿⠁⠈⠃⢀⣿⣀⡀⠁⠀⠄⣻
⣿⣿⠀⠀⠀⠠⣿⣏⣀⣴⠟⠀⡼⠷⠶⠆⢸⡿⠦⢶⡽⠧⠀⠈⠿⠇⠀⢀⡿⠶⠶⠆⣿⢧⠈⡿⠆⠼⠶⠈⡿⡆⠸⠦⠈⡷⠀⢿⣧⣤⠄⢸⣿⠉⠀⣀⠀⢤⣿
⣿⣿⣆⠀⠀⠸⠉⠉⠙⠁⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠙⠛⠋⠀⠈⣽
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣀⢘⢨⢃⡄⠀⠰⠌⠀⠀⡏⢸⢀⢾⡐⠠⢁⠀⠀⡜⠈⠶⠅⠀⠠⠉⠲⡆⠁⡰⠇⡝⢠⣁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿
⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠀⠀⠉⠃⠀⠀⠀⠈⠈⠈⠃⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⡟⣧⢸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⣿⣤⣀⠀⢂⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠉⠡⠾⣿⣟⣃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡔⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠄⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⣾⠁⣠⣜⠆
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣆⠀⠀⠀⡞⠀⠛⡘⠋⢉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢃⢶⠀⠀⣰⣇⡴⠿⢟⠐⠿⠿⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⡇⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⡗⢸⣿⣐⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⢰⣶⣿
⣇⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣴⠁⠀⠻⣾⣾⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢈⠞⣿⡀⠀⡴⣿⡏⠓⠉⢙⣿⣿⠀⠀⠀⠀⡀⠀⠒⠰⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⣹⡧⢻⣿⣿⣝⠻⢻⣿⣿⣿⠀⠀⠀⠀⠛⠀⣀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⣼⢚⡛⢯⣻⠟⣷⡈⣛⠻⡟⢳⠀⡀⠀⠘⠃⣁⡂⢀⡄
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠸⣿⣛⣽⣦⣾⡟⣼⣷⣸⡿⢀⢿⡄⠃⣿⠀⠀⠂⣯⢉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠿⡍⢲⣿⡿⢷⡿⠛⠛⣧⣼⡀⣧⡸⡏⣶⡀⠀⠙⢛⠛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡈⠸⣟⠹⣉⣄⠀⢠⣄⣌⢿⣿⣿⡾⣿⣇⢹⡄⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠀⠀⢀⣴⢊⡅⡆⣿⠀⣿⣿⣾⡄⠛⣿⡠⣿⣿⣿⣾⣿⣾⣷⣹⡿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⢡⡾⢃⡇⣿⡇⢸⣿⣿⣿⣄⢹⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⣿⣿⣶⣇⠀⠀⠀⠀⣶⢴⣿⣀⣀⠀⠀⠀⣾⣦⣿⣿⣿⣿⣷⠈⢻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠋⠀⠇⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣄⠠⠀⠐⢿⣿
⣿⣿⠀⠈⠀⢀⣄⡁⢠⣼⣿⣿⡆⢀⠛⣸⣿⣼⣿⣿⣿⣿⣿⡅⢸⣿⣯⣹⣿⣯⢠⣿⣿⣿⣿⣿⣿⡀⣶⢀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠰⣿
⣿⣿⣧⣄⣀⡀⣉⣳⢺⣿⣿⣷⣿⣾⣧⣿⣿⣿⣿⣏⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⣿⣆⡀⠀⠚⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣿⣿⣶⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⣶⠖⠠⡀⠀⠀⢠⠔⠒⣴⣆⠀⠀⠀⣠⠶⠀⣶⣤⠀⠀⠀⢀⣴⣶⠂⢀
⠀⠀⠀⠀⠀⠀⠛⢁⣄⠀⢷⠀⠀⣿⣴⡾⠿⣿⡁⠀⠀⠃⠀⠀⠘⠋⡄⠀⢠⣾⣿⣿⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠂⠀⠀⠹⢿⣧⣴⡿⠁⠀⠀⠐⠂⠀⠀⠘⠁⠀⠀⠫⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣆⠀⠀⣴⡿⠭⠁⠀⠀⠀⠀⡴⠋⠁⣾⣷⡄⠀⠀⣠⣿⣿⠭
⠀⠀⠀⠀⠀⢦⠘⢻⣿⠃⠉⠀⠀⢻⣧⡄⢠⣾⡆⠀⠀⢰⣦⠀⠛⡿⠁⠀⠸⡏⢙⣿⡦⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠠⠄⠀⣀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⣼⡿⢿⢿⠃⠀⠀⠀⠐⢠⣄⣀⣿⣇⠀⠀⠈⠉⢀⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠹⠇⠀⠀⠵⠀⠀⠀⢢⣿⣿⣿⣻⠇⠀⠀⠀⠈⠛⠃⠀⠀⠀⠘⢿⣷⣦⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡴⠖
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠸⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠛⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠁⠀⠀⢀⡀⢀⣠⡔⠿⠟⠉
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠰⠆⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠠⠊⠠⠙⠉⣁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣀⡀⠀⠀⣀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠁
⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡻⣿⣿⣿⣿⠟⣹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀
⢀⣀⣱⣀⡀⠀⠤⠂⡠⠁⠠⢀⡠⠀⠐⣿⡟⢿⣿⣿⣿⣿⣿⠟⣿⣿⣧⠠⣠⢿⡃⢠⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢰⠋
⠸⠿⠛⠛⠛⠟⠛⠛⠁⢀⡴⠋⠀⠀⢀⣿⡁⠠⠙⠻⠿⠛⠀⠀⢹⣿⡟⠐⣡⠋⠀⠈⢻⣷⡦⠀⠀⠀⠀⢉⣭⣭⣤⡸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣶⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⡿⢁⣾⠗⣀⣀⠀⠈⡁⠠⠌⠳⡀⠙⠛⠉⠩⠿⠁⠘
⠀⠀⠀⠀⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣟⣴⣿⣿⣿⣿⠟⠉⠁⠀⡄⠀⠀⠸⣆
⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⠁⠀⢀⠀⢀⣀⠠⠠⠄⠙⢆⠀⠀⠀⠛
⢰⡄⠀⠀⠀⠰⠿⠓⠹⣿⣿⣿⣿⣿⡿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣯⡗⠉⢸⠏⠀⣄⡥⠂⠁⠀⠀⠀⠀⠁⡀⠇
⢸⣿⣦⠀⠀⠀⠀⠀⠀⢈⣿⠟⢛⣥⠞⢩⡾⠉⠉⠀⠘⠿⠿⠟⠉⠳⠀⢺⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾
⢸⣿⣿⣷⣤⠤⠄⠒⠊⢁⡤⠞⢉⡤⣪⣿⣦⣤⣤⡀⢀⣄⡀⠀⠀⠀⠀⢸⣆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠈⠉⠀⠀⠀⠀⠀⠴⠚⠉⣠⠔⢉⣴⣿⣿⣿⡿⠻⢷⣿⣿⣿⣿⠿⠇⡀⢠⡻⣿⠹⠇⢠⣀⢀⡀⠀⠀⠀⠃⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⢁⣴⣿⣿⣿⣿⡟⠀⢀⣼⣿⣿⣿⣿⣦⣄⣀⣀⣹⣿⠀⠀⠈⠉⠁
⢀⠠⠀⠀⠀⠀⣤⠾⢀⣴⣿⣿⣿⣿⣿⠟⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⡠
⠀⠀⣠⡶⡣⠛⣡⡴⠻⢿⣿⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⠿⠛⠻⣿⡃⣿⢠⡄⡀⣃⢤⠔⠁⠀⠀⠐⠠⡾⠁
⠰⣛⠝⣈⡴⠞⠁⠀⠀⠈⠁⠉⢻⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠘⣷⠀⢿⣷⣬⣗⢂⡨⠔⠃⠀⣌⠃⠀⠘⠁
⠨⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠙⡻⠿⣿⣿⣿⢿⡇⠀⢿⡀⠘⣿⡿⠤⠛⠁⠀⠀⠀⠈⢷⣄⣄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⣿⢧⠀⠀⠀⠀⠠⠀⠀⢸⡇⠀⢸⡇⠀⠋⠁⠈⠀⠀⠀⠐⠂⠀⠀⠹⢋⠳⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⠏⣸⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠁⠙⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠾⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⢶⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠠⣉⡐⢬⣳⣄⠀⠀⣴⣫⣴⣾⡟⠍⠉⢉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠉⠛⠿⣷⣌⢻⣆⣼⣿⣟⠫⠭⠭⠻⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠄⠘⠁⠀⠀⠀⠀⠀⠉⠛⢿⠿⠿⡋⠄⠀⠀⠀⠄⠈⠉⠛⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡤⠤⠄⠀⠒⠂⠁⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠧⣀⡀⠴⠂⠒⠒⠒⠒⠒⠒⠒⠚⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠲⠒⢲⠖⢉⣰⣄
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠸⠒⢇⣠⡤⠵⠶⠒⠛⠉⠁
⠀⠀⠀⣼⣇⣀⣀⣀⠀⣀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⢈⣧⠀⠀⠈⢦⡀⠀⠀⠀⠀⣀⠔⠉⣀⡴⠗⠒⠋
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠾⠿⠡⠹⠛⠛⠶⠚⠛⠿⠿⠾⠿⠿⠿⠭⠀⠀⠀⠀⠱⡄⢤⣴⡾⠵⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠉⠀⠐⠂⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡔⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡂⢟⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡀⠳⠄⠀⠀⠀⠈⠁⠒⠀⢤⠄⢒⢍⣢⡷⠖⠛⡁⠐⡖⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠉⠙⠛⠒⠂⠠⠼⠶⠿⠋⣁⠄⠂⣁⣤⠖⣇⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⡜⠙⠆⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⣠⡽⣾⠚⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢃⡀⠀⠀⠀⠈⠉⠁⠂⠤⢈⡉⠀⠀⡀⠶⠂⠛⡋⡕⣈⡴⠄⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠠⠴⠒⠲⠤⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠈⠁⠒⠐⠠⠄⣀⠀⠀⠀⠀⠙⡁⠀⣀⣶⠷⠟⠋⠁⠀⠀⠀⠀⠀⠸⠥⠾⠤⠶⠶⠶⠶⠈⣉⣉⣑⡖⠀⠈⢢⣄⣀⣀⣠⣤⣀⣀⣈⣁⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠴⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠶⠿⠷⠶⢶⣶⣤⣄⣀⣀⣠⣤⣴⣶⠶⠶⠶⠶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠉⣀⣀⣠⣤⠤⠤⣤⣄⣀⠈⠉⢻⡟⠉⠁⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣉⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠉⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠁⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠒⠲⢤⠀⠀⣿⠀⠀⣀⡠⠤⠴⠒⠒⠒⠚⠛⠓⠒⠒⠆⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣼⠃⠀⣀⣠⠤⠖⠒⠛⠉⠉⠉⠉⠙⠒⠦⡀⠀⣸⠃⠀⢀⣀⡤⠴⠒⠒⠚⠛⠉⠙⠛⠒⠲⠄⠀⠀⣷⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣧⡟⠀⠈⠁⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿
⠀⠀⠀⠀⠀⠀⣿⡿⣼⠁⢀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠲⠀⢰⡇⠀⠀⣠⠤⠖⠒⠋⠉⠉⠉⠉⠉⠉⠓⠒⠦⠄⠀⢹⣼⣿⡀
⠀⠀⠀⠀⠀⣸⣿⢣⡏⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⢤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⢀⣿⡟⣼⠁⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠠⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠀⠀⣿⣿⣧
⠀⠀⠀⠀⣸⣿⢣⡏⠀⠀⠀⠀⣀⣠⡤⠤⠖⠒⠒⠒⠒⠤⢤⣨⠄⠀⡿⠀⠀⠀⢀⣀⣀⣠⡤⠤⠤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⣿⣿⣼⠁⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⢸⣿⢿⡇
⠀⠀⠀⢰⣿⣯⡟⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣒⣒⣶⠶⠦⣤⣀⠀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⡓⠂⢸⣿⢸⣷
⠀⠀⠀⣸⣿⣿⠃⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣠⣶⣿⣿⣿⣿⣾⡯⠽⠿⠿⠿⠭⠭⣽⣿⣿⣿⣿⣿⣷⣦⣿⡏⣿
⠀⠀⠀⣿⣿⣿⣾⣿⠿⢛⣋⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋
⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣡⡤⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠄⠀⢀⣀
⠀⠀⠀⠠⠤⣤⠄⠂⠊⠝⢢⠀⠀⠀⠀⠀⠀⠀⢰⣻⡾⠯⠐⠒⠊⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠒⡒⠒⠒⠒⠒⠒⠒⠂⠂
⠀⠀⠈⣃⠄⠀⠀⢱⠀⣀⠸⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠻⡁⡀⠁⠀⣹⠃⠘
⠀⠈⢠⠆⠀⠘⠛⠃⠀⠉⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⢐⠸⠤⠛⠤⠗⠂⠤⠜⠧⠜⢀
⠀⠸⢶⠤⠐⠆⠀⠀⢈⡑⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠙⣄⠂⢀⡀⠤⢊⣁⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠀⠉
⠀⠀⠠⠂⠈⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠⠂⠂⠂⠦⠄⢄⠀⠐⢄⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠨⠤⠤⠭⠬⠁⠈⠑⠀⠀⠀⠀⠀⡜⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⡆⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠜⠀⠀⡀⠀⠀⠀⠀⢠⠀⠸⠄⠸⡀⠀⠀⠀⠀⠒⠀⠀⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠑⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⣀⠀⣀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠑⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠰⠈
⠀⠀⠀⠀⠀⢀⡔⠁⠄⠀⡠⠊⠀⠀⠀⠀⢂⠐⡆⠀⠐⠀⠀⠈⠉⠁⠀⠄⠀⠒⠀⠀⠀⠀⠀⡀⡤⠀⠤⠀⠀⠐⠀⢀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠀⢃⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠜
⠀⠀⠀⠎⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠒⠈
⠀⠀⠈⠢⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠄⣠⣤⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠑⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄
⠀⠀⠀⠀⢀⠔⣡⢚⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠠⠁
⠀⠀⢀⡐⣡⣎⣱⠋⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠓⠊
⠀⢀⠈⠀⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠔⠀⠀⢀⡀⠀⠀⠂
⠀⢀⢀⡀⢀⡀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣐⢉⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠡⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢠⡄⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⢄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣄⠀⢀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢰⣾⡀⢸⣆⡀⠀⠀⠀⡀⠀⡤
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠠⠤⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⡙⣦⣤⣤⢞
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠉⠁
⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠁⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠒⠀⠛⠒⠛⠃⠛⠛⠓⠚⠓⠁⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠠⠀⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠔⠁⠠⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⠤⠀⠀⠀⠀⢄⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠒⠒⠂
⠠⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠧⠀⠀⠀⠀⠀⢀⠰⠄⠀⠀⠂⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠁⠿⠛⠉⠀⠀⠀⠀⠀⣨⡀⠈⠀⠀⠀⡀⠀⠰⣔⠒⠼⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠩⣝⠢⣄⡀⡲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠠⠚⡃⠀⠀⠀⠀⠦⠀⠰⣘⢫⡟⢨⡓⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣑⣱⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣖⣤⠆⠀⢠
⣀⣤⣆⣼⣴⣄⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡁⠀⠀⢸⡀⠀⣀
⠉⠙⠊⠉⠀⠈⠉⠀⠈⠀⠀⠀⣠⠔⠛⠁⠀⠐⠃⠀⠀⠀⠀⠀⠘⠉⣉⠉⠉⠉⢉⡛⠀⠠⠈⠀⠄⠀⠀⠀⠏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠤⠀⠀⠤⠀⢢⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⡈⠨⣮⡏⣹⠋⠀⠀⠀⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠄⢜⠲⢏⠅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀
⣷⢮⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡇⠀⠀⡎⠉⡖⠉⠉⣧⠀⠀⠈⠈⠉⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣦⣥⣽⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⡷⣟⣾⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠁⠀⠀⠠⡦⠀⠀⡀
⠔⠀⠀⠀⠀⠀⢼⡤⢀⡀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂⠓⡀⢠⠂⢀⠀⢠⢺⠿⠟⠛
⡾⠇⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣇⣀⡾⢠⠏⠀⠸⢶⣶⠶⠶
⠐⠛⠄⠀⠀⠀⠀⡇⠀⡇⠀⠀⢠⣤⡄⠀⠀⠐⠋⠀⠀⠀⢰⣿⠛⣧⠀⢢⠀⠀⠈⣧⠘⣆⣷⠃⠀⠀⢸⠷⠁⠚⠛
⠀⠀⠀⠀⠀⠀⠀⣇⣠⠁⠀⠀⠈⡈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠈⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂
⢐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤
⠘⠀⠀⠀⠀⡀⢀⣀⡀⠀⢠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠸⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢚⠥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⠻⢿⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⡑⠸⠿⠛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡆⠀⠀⠀⠰⣿⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⡀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠞⠀⠀⠀⢀⣀⠀⠀⣰⡄⠀⠘⡁⠀⠃⠀⠀⠀⢈⣁⣵⡦⠀⠀⠀⠀⡜⢁⡉⠊⣉⣼
⠀⠀⠀⣴⡷⢶⣄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢳⡼⢷⠀⢘⡧⢚⠛⠛⠉⣿⣧⣴⣶⡛⠃
⠀⢠⠼⠋⠑⠶⠇⣠⡾⠑⠀⠀⠄⠀⠀⠀⠀⠀⢀⡸⠀⡻⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⡀⠘⢿⣿⣷⣀⣴⣿⣿⣿⡿⣿⠆
⠀⠈⠀⣰⡄⢣⣾⡟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠼⠷⠂⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣻⣿⣯⣉⠁⣤⣾⣿⣽⡛⣹⣿⣿⠋⢠⣿
⠀⢀⡶⠋⣵⠟⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⠀⠀⠀⠀⣠⡶⢿⣿⣿⡟⠿⢿⣿⣿⠀⣿⣿⣿⠏⠙⠿⢿⣿⣄⣸⠇
⠀⢋⣴⣿⣣⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠋⠀⠀⠀⠀⠀⡍⡉⠘⣿⣿⠉⢷⣌⠛⢿⡀⣿⡟⠉⣀⠀⠂⣸⡯⠽⢟⣦
⠀⢼⣿⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠠⠀⠀⠀⠀⠀⣧⢀⣶⣷⣿⣿⣄⡀⠇⠀⣿⣿⣁⣴⣧⣿⣶⣾⣿⣷⣶⣾⣿⡆
⠀⢸⣿⡏⠠⠁⠀⠀⠰⣶⣶⣶⣶⣶⣦⢤⣤⣾⣧⣦⣤⣴⣦⣤⣤⣤⣿⣿⣿⣿⣿⣤⣥⣤⣀⡿⠿⢿⠿⠿⣿⠿⠛⠛⠉⣽⣿⣿⡁
⠀⢸⡿⣄⠁⠀⠀⠀⠀⠦⠼⣿⣾⣛⠓⠚⢛⣋⣉⡀⢀⡐⠀⠈⠰⠉⢱⣶⣉⣉⣙⠋⠀⣄⠀⠀⠄⠀⠋⠉⢻⣷⠀⢀⣼⣻⣿⣿⡇
⠀⠈⠃⣴⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠶⣶⡶⣀⣴⣼⣧⣤⡆⠀⣄⣼⣿⠿⢿⡇⠀⠀⠁⠀⠀⠁⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡿⡀
⠀⠀⠠⡟⠀⠀⠀⠀⠀⠄⠀⡿⠋⠁⠀⣤⣤⡞⠉⠁⠙⣿⡿⣧⡴⣾⡏⢁⣻⠆⠀⢠⠴⣆⣀⠀⠃⢈⠀⠀⢸⡗⠀⣿⣿⣿⡿⠋
⠀⠀⢠⡇⠀⠀⠀⠀⢀⡃⠀⡂⢀⠀⠀⠀⠀⠁⠀⠀⢀⣸⡶⠧⠶⢾⣶⣿⣿⠂⣶⠴⠤⠾⠉⠠⠄⠘⠓⠏⣠⢡⢄⢻⡿⠋⠁
⠀⠀⣼⠁⠀⠀⠀⠀⠰⠇⠀⠁⠸⠀⠀⠀⠀⠀⣠⣴⣿⠟⠃⠀⠂⠈⣻⣟⠉⠀⣿⠉⠃⢉⣉⣷⠀⠀⣿⠇⡼⠁⣼⠈
⠀⢰⣇⠀⢀⣀⣀⠀⠀⢀⣴⣶⡎⠀⠀⠀⠀⠈⠻⣿⣏⣀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠉⣁⣾⣿⡿⠚⠋⠀⠀⠐⢆
⠀⠻⣿⣷⡘⠿⠛⡛⢽⣿⣿⠿⠅⠀⠀⠀⠀⠘⠿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣦⣄⠂⣠⠞⠋⠁
⠀⣿⣾⣯⣟⠀⢨⣤⣿⠟⢀⣦⠴⠀⠀⣀⣠⣤⣤⣠⣤⣻⣇⣀⠀⠀⢠⡀⣤⢦⣽⠻⢿⣛⣁⠀⠀⠀⣠⠤⠄
⠠⣿⣿⣿⡟⣴⡿⠏⣵⣿⣿⣃⡠⢈⣶⣿⠋⠉⠀⢀⣾⠟⢩⠇⠀⠀⠀⠻⠛⠺⡟⠀⠈⠉⣉⣌⢷⣤⣤⣴⡖⠂⠚⠂⠚⠛⠓
⠀⢿⣿⣿⣾⠋⠀⢀⣺⡿⢿⣉⢀⣿⠇⣷⠀⠀⠶⢚⣡⣾⣤⣄⠀⠀⢀⣠⣤⣶⣼⣶⣔⠋⠉⢹⣮⢿⣿⣿⣇⣀
⠀⢸⣿⣿⣿⣿⣞⣫⣾⣆⣈⣻⣿⡟⢰⣿⡁⣴⣿⡿⢻⣿⣿⣏⢠⡄⠀⠈⢿⢿⡿⠛⠁⣴⣆⠈⢹⣧⣍⣻⣿⣿⣿⣦⣀⡐⠛⠆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣿⠋⠀⠀⢇⠘⣿⣿⣿⣿⠇⢀⣴⣶⣿⣧⠀⡆⣿⣿⠀⠈⠉⠉⢻⡛⢿⣿⣿⠛⠋⠐⡞⠃
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⠀⠀⠀⠁⢸⣿⣿⠟⣁⣴⣿⣷⣿⣿⡿⢦⣀⣾⣥⡀⠀⠋⠀⠊⢙⣼⣿⣉⣲⠶⢶⣠⠁
⠀⣼⣿⣿⣿⣿⢿⣿⣿⠿⢿⣿⣿⣿⣾⣽⡷⠖⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠻⢻⣿⢋⡀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣦⣽⡇
⠀⢹⣿⣿⡿⢦⣄⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣀⣾⡅⠀⣀⡶⠿⠋⠉⢙⣿⣿⣿⣿⡇
⠀⣿⣿⣿⠀⢨⣉⣺⣿⣤⣤⣴⣾⠿⠋⠐⠋⠀⠀⣖⣻⣿⣿⣿⣿⣿⠿⠛⠉⠀⢀⠀⠀⠀⠈⣻⣷⣿⠁⠀⠚⠀⣠⢾⣿⣿⣿⣿⣇
⠀⣿⣿⣿⣷⣡⠟⢹⠋⢻⣿⡤⠀⠀⠀⢀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⣀⠀⢀⡴⣿⣷⠀⠀⠀⣿⣿⣿⠆⠀⠀⠛⣩⣿⣿⣿⣿⣿⡿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠛⠛⠛⠛⡻⠛⠓⠛⢿⣿⣿⣿⠛⠛⠃
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠈⠉⠛⠿⣿⡇⠈⣀⣀⡀⣠⡿⠿⢷⠀⠀⢹⠋⢻⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠈⢿⡇⢾⣋⣿⡃⠉⠛⠷⠿⠀⠀⠈⢀⡘⣣
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⡿⢶⠄⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠐⠋⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠰⠇⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡
⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣯⣿⣾⣿⣧⠰⠖⠀⣠⡄⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢷⡶⠖⠀⠀⠀⢀⡴⠀⡀
⠀⠘⠛⠛⠛⠋⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠉⠛⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠁

⠀⣶⠶⢶⡶⠶⢶⣶⢶
⠀⣿⣏⢩⡅⢸⠛⢝⣿⢠⠄⠀⠀⠀⠀⡀⣤⠀⠀⢠⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡤⠀⠀⠀⢠⡄
⠐⡦⣟⡃⠎⠘⣿⠋⠻⠸⣽⠻⠟⠻⠀⠇⢯⡷⡇⢸⣧⠜⢋⠢⠶⠩⠾⠰⠅⣿⠐⠷⠀⡇⢾⠸⠿⠦⠞⢸⠸⢷⠀⡇⢾⠸⡮⡽⣗
⢰⠓⠀⡱⣆⠨⠉⡶⢽⠀⡄⡀⢀⣀⠀⣠⡀⡀⠀⠬⠁⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠈⠋⠀⠈⠛⠉⠋⠀⠋⠀⠁⠀⠋⠉⠃⠈⠋⠃⠘⠃⠘⠃⠋⠈⠘⠀⠋⠃⠘⠘⠉⠋⠁⠛⠃⠘⠉⠀⠚⠁⠘⠐⠃⠃⠃⠛⠍⠃⠛

⠀⠉⠛⣶⢌⣿⠟⡶⢬⣍⠙⢿⣯⠋⡏⠀⣻⠉⣤⡹⣿⣏⣩⣽⣿⣍⣉⣹⣿⡿⠿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠁
⠀⠀⠀⡈⠋⠉⣉⣻⣶⣿⢟⢳⣋⢂⣦⣯⡀⠙⠉⣁⠂⠉⠛⢻⣅⡉⠉⠀⠉⠁⠒⠇⠐⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠱⠀⠀⠀⠄
⠀⠢⠋⠉⠀⠀⠀⠁⠹⠿⣷⣮⣝⣿⠙⠛⢿⡀⡄⠀⡄⠀⠀⠀⠸⠀⠀⠉⠉⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠀⠀⠀⠀⠀⠐⠟⠿⣷⣽⡟⠋⠡⣤⠀⢻⣧⠁⢀⡃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡠⠀⣐⣶⣿⣿⣿⣿⣿⡿⢿⣯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⠻⢬⠎⠃⣙⣻⢌⣛⠀⠀⠙⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⠛⢋⣭⣍⡉⠉⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠘⢀⠸⠁⠀⠐⠀⠀⢀⣭⡿⣘⣯⠸⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⡍⢻⡄⠀⠀⠀⠀⡃
⠰⠄⢀⠀⠀⠠⡤⠄⠐⣦⠢⣤⠀⠀⣹⣧⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⠁
⠀⠠⠁⢀⠀⣀⣀⠀⢀⡁⠀⠀⠀⠀⠻⢿⡆⠀⠀⠀⣠
⢀⠠⠀⠁⡜⠋⠉⠗⢀⠁⠀⠀⣰⣿⣟⣀⠀⠐⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠸⠀⠄⠀⠷⠀⠀⡸⠳⠂⠀⢠⡟⢻⣿⣿⣷⠂⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡟⢧⣄⢀
⢠⠀⠀⠀⠀⠠⠾⠃⠌⠀⠀⠈⠀⠸⣿⣿⣿⣦⡀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠛⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠦
⢘⢲⡀⠀⠸⣦⣄⣾⠁⡆⠘⣦⡀⠀⠻⣿⣿⣿⣿⠓⢄⠀⠀⠀⠶⠞⣁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣾⡿⣳⣦⢀
⢘⡨⠁⣀⣀⣈⣛⣛⢀⡇⠀⣿⣷⣄⠠⠙⠯⠒⠉⠃⢰⠀⠀⠈⠐⠆⣹⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠸⣇⠻⣷⠾⠃⠀⠀⡀⠀⢀
⠸⠧⡆⢈⠿⠻⠃⣿⣌⠀⠀⣿⣿⣿⡿⢦⣴⣤⣴⡄⠾⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⣿⣶⣶⣷⣽⣿⣿⣻⣿⡃
⢘⠻⠇⡈⢒⡀⠒⢿⡇⠀⢸⣧⣹⡁⠀⠀⠙⠉⠈⠁⠀⢠⡦⢀⠀⢀⠸⠀⠀⠀⠀⡇⠄⠀⠀⠀⠀⠀⠈⠉⠛⠙⠛⠉⠙⠛⠉⠉⠁
⢘⣻⣛⡙⠻⣧⣗⠺⠇⠀⢸⣿⣿⣧⠀⠀⠘⠀⠀⠀⣆⠀⣇⠟⠀⣴⠃⠀⠀⠀⠈⢟⠃
⠘⠁⢿⣏⣵⣿⣾⣾⠃⠀⣸⣿⣿⣽⠀⠀⠀⠂⠀⠀⣿⡀⠘⠀⠘⠏⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠠⠞⣿⣿⣿⠀⠠⡿⢻⣿⣿⡆⠀⠀⠒⠀⠀⣿⣿⠷⠒⢴⡄⠀⠀⠀⠀⢰⣆
⠀⠀⠸⢃⣬⡿⣿⡏⠀⢸⡇⣾⣏⣽⡟⠀⠀⠀⠀⠀⣿⣿⣇⣐⣈⠉⠉⠀⠀⠀⠈⠙⠓⠓⠒⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠐⠲
⠀⠀⠀⢴⠁⠡⡭⠀⣠⣺⠇⣿⡏⠉⡇⠀⠀⠀⣶⣿⣿⣇⢿⠋⠻⣟⡀⢀⣀
⡀⠀⠀⢸⣴⣶⠇⢰⡟⣿⠀⢸⣧⠀⠃⣄⠀⠀⢫⣤⣿⡟⠀⠀⠀⠈⠁
⠄⠀⠦⠿⠿⠋⣠⠟⠀⢽⠀⠈⠻⠚⢺⣿⣷⣾⢛⡿⠉⢇⠀⠀⣠⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠂⠄⠄⠀⠀⠀⡠⠄⠘⠉⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⣶⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⣀⣀⣀⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⣀⣤⣄⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠚⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⡆⠀⠀⠀⠀⢀⡴⠖⠒⠾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢒⡒⠶⣇⠀⠀⠀⢠⢿⣀⣀⣄⣀⣸⠀⠀⠀⠀⠀⢘⠀⢸⠋⠉⠉⠉⠉⡏⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⢒⣒⣋⣿⠀⠀⠀⢸⡌⣿⠀⠀⠈⡏⠀⠀⠀⠀⠀⢘⠀⢸⠀⠀⠀⠀⠀⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠈⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⢸⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡗⠀⢸⠀⠀⠀⠀⠀⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠸⡞⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠱⠅⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠁⠈⠹⡆⠀⢻⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣹⠀⠀⠀⠀⠀⡧⠀⢸⡀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⣴⠃⠈⠲⢄⡀⢀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢉⡞⠁⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠋⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢸⡆⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⣾⠀⠀⠙⠢⢄⡴⠋⠀⠀⠀⠀⢸⣇⡤⠤⢼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠹⣦⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡗⠀⠀⡇⢀⣀⣀⣀⣇⣀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡇⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡰⢶⡲⡖⠂⠒⠂⢠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢉⠟⣻⡼⢘⢭⣇⠀⢀⠼⡠⢔⠭⡰⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢳⡔⠉⢹⣟⣵⠿⡴⣗⠝⡊⢕⠽⣊⣵⡋⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣨⠧⡪⣑⠕⡪⢕⠭⢚⣡⢶⠁⠐⠧⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡄⠀⠀⠀⠀⠀⣸⣗⢕⡪⢐⠥⢊⠥⡺⣿⣯⠏⣓⡽⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣷⠀⠀⣤⣴⠶⣽⢗⠥⣊⠕⡪⢑⣩⠞⣫⡖⠝⢀⡀⡤⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⣊⢗⣆⠙⢗⡨⢚⠅⣊⣴⣬⠔⡫⣔⠝⣻⣄⣬⢈⠗⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢔⡡⢊⣵⠌⠉⠁⠚⢞⣋⢔⡫⡊⢕⠞⡩⡞⠉⠁⠊⠀⢀⠀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⢚⠥⣺⣄⠀⠀⠀⠀⠉⡗⡨⢐⠅⡨⣺⡇⠀⠀⠀⠀⠈⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡵⣊⠔⡩⢓⠦⡀⠀⢰⡫⢐⢕⡮⡪⣊⠝⡩⢷⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡡⢂⠵⡊⠗⢸⡩⢖⢕⡡⡪⠊⡡⢊⠔⡉⢦⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢴⣩⢺⢖⠵⡫⢊⡴⢊⠔⡡⢊⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠒⠋⠒⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠠⠂⠔⠠⠢⠆⠔⠴⠢⠂⠔⠠⠂⠔⠀⠖⠐⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠛⣲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⢍⣒⣠⣤⣀⣀⠀⠐⠉⠙⠛⠷⢦⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠙⠛⠳⠶⣶⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠀⠀⠀⢻⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡉⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⣇⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠑⡦⢄⡈⠒⠦⠬⣉⣉⡑⠒⢒⡼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠴⢇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠢⢄⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣀⠀⠀⠠⠄⠀⠒⠒⠂⠈⠙⡄
⠀⠀⠀⠀⡐⠀⠜⠀⠀⠀⠀⠀⠀⠉⠲⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⠑⠢⠤⣈⡀⠀⢀⠨⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⡤⠐⡂⠍⠉⠑⠒⠢⢴⠁⣀⣀⣀⡀⢀⣀⡀⠠⠄⠤⠄⠒⠲⠶⢀⣉⠉
⠀⠀⠀⠀⠀⠀⣆⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠒⠢⢤⡀
⠀⠀⠀⠀⢀⣀⠧⠌⣐⠒⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠒⠉⡁
⠀⠀⠀⠀⠣⣈⠐⠢⠄⣉⡑⠒⠤⢀⣈⠉⠁⠒⠒⠠⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡠⢒⡡⠔⠂⠁
⠀⠀⠀⠀⠀⠀⢙⠒⠢⠤⣈⣉⠒⠤⠼⠈⢉⣐⠶⠦⠤⣀⣀⠈⠉⠐⠢⢤⠔⢊⡡⠚⢧
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠀⠉⠒⡖⠈⠁⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠴⠒⠁⠀⠀⢸
⠀⠀⠀⠀⠀⡀⢰⠁⠀⠀⠀⠀⠅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠊
⠀⠀⠀⠀⠀⠁⠒⠡⠄⣒⢤⠤⠤⠔⠁⢀⢀⣀⠠⠤⠤⠤⠐⠂⠈⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣒⣒⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄⠀⠂⠀⠀⠀⠀⣠⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⢀⠔⠋⠀⡔⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠊⣠⠋⡼
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣄⣀⣠⡤⣀⠈⠢⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣼⠏⡸⠁
⠀⠀⠀⠀⠀⠘⠺⠿⣿⣯⣟⣤⣶⣶⠮⠕⠻⢳⣼⣦⠀⠠⠊⣀⣠⡤⠖⠂⠀⠀⡀⠀⠀⢀⠞⠁⣠⣿⠏⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⣉⠝⠲⢥⣀⡠⢀⡀⠹⣿⣷⣷⣟⣉⣁⡀⠀⠀⠀⠀⠀⣈⡑⠁⠀⣴⣿⠏⣰⠃
⠀⠀⠀⠀⠀⠀⠈⢉⡥⠚⠁⠀⠀⠀⠀⠈⠁⢈⠹⣿⣿⣿⣿⣯⣭⣭⣭⣽⠒⠓⠒⠀⠉⠉⠺⣿⣿⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠛⠛⠷⠤⣄⣀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢶⠒⠒⠛⠛⠛⠛⠛⠛⠛⢓⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣋⣁⡠⠤⣄⠉⠙⢦⠀⠀⠀⢀⡤⠖⠻⠭⠼⠃⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⠤⢬⡧⡀⠀⠀⢈⡇⠀⠈⠳⣄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠠⢤⡐⢽⢦⡀
⠀⠀⠀⠀⢀⣴⠟⠉⠚⠁⢀⣠⠼⠃⡼⠿⠿⠯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠃⠙⢦⡀
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠈⠳⣤⡴⠃⠀⠀⠀⠀⠀⠑⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⣀⣤⣀⡹⣆
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⡇⠈⠿⠉⠚⣧
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠲⠚⠑⢄⡤⢼⡆
⢠⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⣿
⣾⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠙⠺⣄⠀⠀⠀⡤⠊⠉⠲⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⣠⣄⡀⠀⢸
⣿⠀⠀⠀⠀⠀⠘⡇⠀⠀⢧⣀⣠⢶⠠⣦⣀⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡊⠁⠈⠳⡄⢸
⣿⡀⠀⠀⠀⠀⠀⠙⠓⠦⣄⣀⣀⠈⠃⢢⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⠀⠣⣼
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠮⣖⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⢰⣿
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠈⠙⠒⠒⠛⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠹⣧⡀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠘⢷⡄⠀⠀⠸⠼⠀⠀⠀⠀⠀⠀⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣤⣀⠀⠀⠀⠀⠀⠙⣷⠀⠀⢀⣤⠶⠋⣠⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⢤⣤⣼⣤⣤⣿⣴⡾⠿⠛⠉⠁