Krisha Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠖⠒⢻⣦⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠁⠀⠀⢻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣩⣤⣤⣿⣷⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⣶⡆⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠀⣠⠖⠀⣀⣈⡉⢤⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⢇⣾⢁⡞⠓⠒⠤⠴⢶⣶⣮⣝⣷⣌⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣴⣿⣼⡇⡞⠀⠀⠀⠀⠀⠀⢀⠍⠻⣝⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⣿⣿⠟⠳⠁⠀⠀⠐⠀⢀⠔⠋⢠⠂⠘⡏⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⣿⣷⣉⢅⠈⠒⠢⡄⠈⠀⠴⠃⠀⡆⣱⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠝⠟⣉⠉⠑⠈⡄⠀⠀⠀⠀⠈⣥⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⡀⠀⢉⣀⢤⡀⢀⡐⠸⠉⠁⢀⡤⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⣇⣠⡬⠶⢞⠚⠋⠉⠙⠀⢆⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡤⠬⠶⢖⠊⠉⠉⠏⡡⠤⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢶⡖⠚⠉⠉⠈⠑⠲⡄⠀⠈⠣⠀⠀⡩⠊⠀⠀⠐⢤⡤⡠⠔⠁⠀⠀⠀⡎⠀⠀⢀⠈
⠀⢀⣾⡤⠤⠒⠚⠉⠻⣄⠀⠀⢠⠀⠑⠄⠀⠀⠀⠀⠀⠱⢄⠀⣠⢵⣤⡌⠉⠀⠀⠈⠒⠒⠂⠀⠀⠀⢀⡾⠶⠶⡶⣄⢣
⠀⢀⢜⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⢉⣦⠀⠀⠀⠀⠀⠐⠡⡯⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⣯⠎
⠀⠁⠈⠢⢀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠨⢤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⣀⠀⠀⠔⠁
⣠⠄⢄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠉⠊⠚⠀⢠⣠⠑⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠼⠟⠀⠀⠀⢀⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⣧⡀⢸⣿⡿⢿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣠⠀⢡⢤⣶⣟⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠳⣁⠴⠿⠀⢸⣬⣾⠿⣿⣿⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣺⢿⣦⣠⣤⣾⠿⠃⠐⠿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣷⣦⣾⡿⠛⠋⠀⠀⠀⠀⢀⡠⠬⠙⢿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⢿⣦⠐⣿⣿⣿⡀⠀⠀⠀⠀⡀⢰⠟⠀⠀⠀⠀⣇⠀⣿⣄⢀⠀⣀⣤⣴⣶⣤⣄⡐⣶⢀⡰⠿⢿⢷⣄⣀
⠀⠀⠀⠀⠀⠀⢼⡆⣿⣿⣾⣿⡿⢃⣠⠴⠶⠈⠀⠀⠀⠀⠾⠃⠀⠉⢠⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣧⡐⠀⢌⠹⠿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⡁⠻⣿⣿⣿⡁⠊⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣿⡿⣋⣷⣿⣿⣿⣿⣷⣶⣜⠛⣿⣿⣷⣦⡘⠻⠻⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⣿⣿⣧⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣤⡓⣽⡏
⠀⠀⠀⠀⠀⠀⡿⠁⠀⠙⣿⣄⡈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠙⠛⠛⠻⣿⡏⠈⣿⠋⠹⠯⠱
⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⢿⣿⣧⣘⣶⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠛⠀⠀⢀⡴⠚⠉⠉⠀⠀⠈⢷⠀⢻⣾⣷⣾⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⣀⣀⡀⠀⠈⠀⣤⣬⠁⠀⠀⠀⠈⠀⣸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣷⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠿⣄⣀⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⢻⠯⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠑⣰⠁⣬⡁⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⠀⠹⠟⢿⣿⣿⣿⡿⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⡃⣆⡀⠀⠀⠠⠄⠄⠀⢀⢀⠁⡀⠐⠞⣽⣿⣷⣄⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⣈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠆⠀⢀⠀⡀⠈⢷⠱⡞⠃⠈⠀⠠⠀⠀⠸⣷⡄⠀⠊⢲⠊⣻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠃⣽⠳⢿⠇
⠀⠀⣸⠀⠩⠸⡁⠀⠀⠙⠃⠉⠘⠿⠀⠈⠀⠷⠰⠆⠶⠀⠰⣆⠘⠇⠀⠄⠀⢠⣾⠿⠿⢿⣿⡷⠾⢿⣷⡖⠁⠀⠀⠀⠀⡤⠚⠉⠁⣀⠀⠀⠈⠛⣤
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠃⠀⣀⡀⢠⡤⢤⠄⣦⣤⣭⠤⠄⠀⣉⠁⠀⠀⠿⣇⠘⠃⠘⠀⡽⠁⠀⠀⢀⣤⠺
⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⠀⠿⠋⠀⠀⣠⢮⣇⠀⠀⠀⠠⡭⠁⠀⣐⠂⢀⡠⠴⠂⠀⢀⡵
⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⠼⢇⣤⡤⡀⢆⠓⠃⠀⠆⢠⠀⠈⡀⠤⠖⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⢰⠦⡀⠀⠀⣀⠀⠀⢨⠁⠐⣦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠟⠘⠁⠀⠹⠿⠀⡁⠰⠀⠀⠀⢰⢁⠆
⠀⠀⠀⠤⠀⠀⠀⢠⡄⠀⣨⡟⠛⠙⠀⠀⠐⣛⠀⠈⠀⠀⠀⠀⠀⠂⣾⣆⠀⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠉⠚
⠠⠀⠀⠀⢱⠔⠃⠀⠀⠀⠙⠻⠂⠀⠀⠀⠀⠽⡄⠀⠀⠀⠀⠰⠈⢸⣿⡟⠀⠀⠀⠀⡿⢣⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⢸⢋⠟
⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡐⠀⡈⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⢈⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⢀⠔⠀⠀⠀⠀⠠⣶⠀⠀⠀⠐⢠⢿⣒⣀⣀⠀⠀⠀⠀⠀⡠⠛
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠉⠛⣶⣀⠀⡀⠀⢰⡠
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠂⡈⢿⠖⠀⠀⠛⠁
⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣦⣽⣦⣧⣴⣿⣬⣾⣯⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣤⣤⣼⣽⠀⠀⠀⠀⠀⠀⠀⢀⡤⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡶⠟⢛⡋⢻⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⣧⣀⡀⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠈⠉⠁⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⢀⣀⣶⣤⣶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⣻⠛⠁⣼⡟⠋⢛⣿⠿⢿⡅⠀⠠⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠨⠀⠀⢿⡀⠀⠺⠃⠀⠀⢺⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⣀⠀⠀⠀⠘⠙⠛⡀⠀⠀⠀⢻⡿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⡜⠛⠃⠄⠀⠈⠀⢀⠀⠠⡟⣀⣙⣽⠃⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠞⠀⠀⢀⡄⠀⠀⡀⠀⠀⠀⠀⣿⡉⢳⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠘⡉⣈⠀⠀⠀⣸⣿⣖⣠⡇⠠⠀⠀⠀⢼⡇⠾⣆⠀⠀⠐⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠈⢏⣩⠀⠀⢀⣿⡁⣹⣿⡁⠄⠀⢀⡀⢙⣇⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣤⠀⠀⡸⣽⣿⣿⠋⠀⠀⢠⠊⣀⣼⡟⣼⣿⡁⠠⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡀⠀⠀⢤⣼⡁⣸⠀⠂⡼⡁⣀⡤⢈⣩⣘⣻⣿⣷⣿⣷⠈⠂⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠰⢋⡤⠒⠁⠀⠀⠀⠁⠀⠀⠐⠋⣻⣧⠀⢿⣭⣭⣉⣿⣿⣇⠹⠟⠰⡷⠀⠿⠇⣉⠁⠀⠀⠀⢠⠄
⠀⠀⢰⡎⡀⢀⣤⠀⠀⠠⠄⡁⠀⠠⠀⠈⠠⠆⠀⠁⠀⢻⡛⣿⡟⢡⠆⠰⡀⠀⢢⠖⠀⠃
⠀⠀⠀⠁⣸⣿⡋⠀⠈⠁⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢿⣷⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠡⣾⠁⠀⢼⠁⠀⡀⠀⠀⠀⠀⠢⣼⡶⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢻⣄⣼⠇⠀⣧⢀⣤⣴⣿⠷⣾⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠾⣿⣿⠿⠟⠋⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠘⠛⢻⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢨⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠘⢿⠈⠙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠈⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣤⠀⠀⠀⠘⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡓⢤⣄⢼⣤⣴⣶⡟⣢⣤⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠾⣤⡙⢃⢉⣥⣿⣿⠃⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⡛⢷⣾⣿⡉⢀⡤⠀⠠⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣇⣹⣿⠓⢲⡶⢻⡆⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠁⠀⠒⠛⠀⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠛⠉⠁⠀⠀⠀⠀⠁⠈⢀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⣰⠶⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣻⣿⡟⠿⠿⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠏⣡⠶⠒⢿⣦⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠸⣄⡈⢁⣲⢰⠿⢿⣿⣿⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡹⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⡀⣀⠂⣷⡈⠉⠤⣷⣼⡏⣣⣼⠃⢸⡿⠀⠀⠀⠀⠀⠀⠀⢣⣺⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠦⠀⠀⠀⠀⠈⠟⠉⢀⠸⣿⡾⠧⠽⢟⣷⣤⡟⠳⢿⣷⣦⡀⠀⠀⠀⠀⠀⠈⢹⠃
⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠶⣄⣀⠀⠀⢀⡴⠛⢩⣾⡯⢳⣦⣶⡿⢛⢀⣿⣧⣀⡌⠉⣉⠆⠀⠀⠀⢀⣶⢸
⠀⠀⠀⠀⠀⠀⣼⡿⠀⠘⣤⠜⠻⣿⣄⢀⡘⣤⣾⣧⣿⡈⣷⡽⢿⡇⣸⢹⣿⣿⣿⠃⠘⣧⡄⢀⠀⣸⡏⠨⡆
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠈⣆⠀⣿⢸⣿⡟⠟⠉⢻⡁⢙⠸⡀⢀⣇⣿⣄⣿⠏⠻⠗⣼⠋⠃⠀⣴⠟⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣆⠀⣸⡇⢀⢀⡀⠈⠈⣿⣿⡏⠀⠀⠔⠀⣼⣷⣾⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢀⣿⣿⠃⠀⣿⣿⡿⠿⣿⣿⡿⢸⣧⣴⡆⣿⡟⢀⣶⡀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⣸⡿⠋⢀⠠⠋⠁⠀⠀⠹⣿⣗⠜⠧⡀⣹⣿⣧⣾⣿⣿⡄⠀⠀⠘⢀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠂⣿⣇⠈⠰⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⣤⠉⠿⣷⣿⣿⣿⣿⣿⣯⣿⡇⠀⠀⠀⠸⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⢀⢹⣿⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣇⠀⢤⣿⣯⣉⣉⠉⠙⠿⣇⠀⠀⠀⠀⠀⢸⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠘⢸⣿⠀⠀⢆⠀⠀⠄⣀⡀⠀⢀⣴⣿⣿⡿⠿⢿⣿⣟⠛⠉⠁⠀⠀⠙⠷⠀⠀⠀⠀⠀⠙⢿⣟⠂
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠳⣤⣀⣀⠀⠠⠞⠛⡿⡏⠈⠁⠈⣷⣍⣃⡀⠀⠐⠀⠀⠴⢷⠀⠀⠀⠀⠀⠀⠉⢤
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠞⡓⣠⣤⠠⣀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡄⡀⠊⠀⠀⣿⡟⢰⣿⣷⣤⣤⣠⣤⣤⣤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠐⠢⢴⡅⣿⡟⣁⡩⠥⠊⡉⠈
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠘⣧⣿⣆⣤⣤⣖⣉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⣠⡶⠿⠃⠀⣀⣉⣻⣯⣍⠉⠍⣙⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠿⢦⣢⣾⠋⠀⠀⠀⠀⡉⠛⠉⠈⠋⠁⢋⣉⣀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠀⠀⢦⢀⠀⠁⣀⣠⣴⣶⡿⠟⠋⠉⠁⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠶⠶⠾⠿⠛⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢠⣤⠀⠀⠀⠀⣠⣌⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀
⢰⣿⣷⣄⡀⣈⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡘⣷⣄⢈⡿⠧⠀⢛⡀⠀⠈⠁⣼⣯⠈⣀⣈⡠⠞⠀⠂⠀⠖⠀⠀⠀⠈⠛⠁⠀⠀⣴⣿⣿⣿⡇
⠈⣻⣿⣿⡛⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣝⠻⢮⣿⡾⠿⣤⠆⠈⠉⢻⡿⠂⢁⡌⠀⢹⡏⠁⠀⠈⠓⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡥
⠀⣿⣿⠏⠁⣿⡟⢛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢿⣯⠉⣹⣿⣶⣜⠛⠀⣤⠤⠈⠀⠊⠁⢰⢈⣅⢆⢉⡄⢀⡀⠘⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⣹⣿⣇⣹⣿⠃⣤⣿⡏⠱⣮⣿⣷⡀⠀⣠⣶⣿⣮⣥⣤⣿⠛⠈⠻⠷⠈⠉⠄⠻⣷⣿⣿⠟⢯⡽⠋⣿⣿⣏⠛⠄⠀⠀⠡⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠸⠿⠿⠟⠻⠿⣿⣿⣿⣇⣠⣿⡿⢉⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⠄⠀⠀⠀⠐⢦⡀⠠⣿⣧⣦⣼⠷⣴⡎⢻⠋⠀⠐⣀⡀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⣴⡆⠓⣀⠹⣿⣦⡹⣦⠀⣿⣿⠀⡀⢈⣿⠆⣰⢆⣴⣿⠃⠀⢁⡀
⠀⣴⠟⢗⡀⣤⡀⠀⠈⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠺⣷⣾⣷⡦⢀⡄⢻⣿⡗⢠⠆⠈⠻⣾⣷⣿⠁⠀⡏⢸⣿⣯⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒
⠀⢿⣶⢛⣩⡙⠶⢰⡦⠈⣹⡿⠟⢠⣾⣿⣿⣿⣿⣿⣄⢀⣁⡹⣿⣧⠀⠀⢉⠛⢋⡠⠦⣈⠖⠋⠀⠑⠠⢀⡀⢂⡉⠁⠀⠀⣼⣿⣷⣶⡄
⠀⠘⢿⣟⠙⣁⠴⣿⠄⢶⣏⠠⣾⣿⡟⣉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣴⣿⣄⠀⠁⣠⣶⣶⣦⠀⠠⣴⣛⠽⠓⣶⣾⣿⣿⣿⣿⣿
⠀⣠⣿⣯⣵⡏⢠⣶⣤⣶⣭⣴⣿⢀⡿⠛⠿⠿⢿⣿⠿⠿⠟⠻⠟⢛⠛⠋⣠⡴⠟⠃⠸⠀⠹⣿⣿⠟⠀⡀⠈⠉⠚⠷⣭⣡⡙⠛⢿⣿⣿⡆
⠘⣿⣀⣰⣮⣡⣾⣿⠋⠙⢛⣿⣿⣋⡁⣀⢠⣴⣾⠷⠶⠶⠖⠛⠛⠛⠛⠋⣠⣤⣶⣾⣿⣤⣶⢠⣄⣶⠎⣷⣶⣿⣿⣶⡆⢀⠉⠛⢦⣈⠻⡿
⢠⡿⢛⣣⠈⠙⣻⣿⡌⢿⣿⣽⣿⣿⡿⣿⠟⢉⣠⣦⠀⣶⣾⣿⣷⡼⠿⣧⣿⣿⡿⢻⣿⣿⠇⠀⠈⠛⢿⣿⣿⣿⣿⣿⣴⠛⣹⣿⣦⠈
⠀⣧⣽⣿⠋⢻⣿⣿⢿⣶⣿⡿⠟⠿⣿⣿⣾⣿⣯⣤⣤⣿⣿⣿⣿⠿⡶⠋⠀⠀⠀⠈⠱⡆⠀⠀⣀⠀⠀⡼⠃⠙⠿⣿⣿⣿⣯⠻⢿⣧⡀
⠰⡷⠀⣿⣿⣉⠁⢴⣾⡻⢿⣇⠰⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⠄⠘⡇⠀⠀⠀⠈⠙⢿⡁⣶⠘⡿⠁⠀⠀⠀⠀⡀
⢠⣴⢺⣿⡏⠉⢀⣤⣿⣿⣿⣿⣷⣾⣻⡟⠉⠸⢿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣷⡄⢀⡅⠀⠀⠀⠀⠀⠀⠑⢲⣦⡀⠀⠀⢿⡄
⠀⠀⠚⣻⣿⣦⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠺⠷⣸⣿⡷⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀⠀⠀⢿⡀⢻⠃⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠂⠀⢀
⠀⠘⢶⣿⠿⢿⣿⣶⣿⣿⣿⣿⠁⢻⣿⣿⣷⣾⣿⡟⠃⠀⠰⠾⠟⠛⠛⠛⠛⠻⢿⣿⣿⣶⣄⠛⢋⣛⠃⢀⣤⣶⣾⣿⣿⣿⣷⣦⢸⣿⣿⢿⣦
⠀⠀⠀⠹⢷⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣼⣿⣿⣿⠀⠻⠟⢠⣿⣿⣿⣯⣤⣤⣤⣈⠻⣿⣿⣿⣿⡏⠀⠻⠇
⠂⠀⣀⣴⣮⡻⢿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⠷
⡆⠀⢡⣼⣿⣿⣿⣿⣿⣿⠿⡃⠀⠀⣿⣿⣿⣿⠇⠀⠀⠈⠙⠛⢣⣼⣿⣿⣿⠃⢀⡿⠻⠟⠁⠀⠀⠀⢹⣿⢹⣿⣿⣿⠇⣹⣿⣿⣿⣿⣿⣿⡿
⡀⠀⣾⣿⣿⣿⣿⣿⣿⣽⣿⡛⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠻⢿⠿⠾⠿⠿⢻⣿⣿⣿⣋
⠃⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⣿⠆
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶
⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇
⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⣀⣀⣤⣤⣤⣄⣤⣶⣾⣶⣆⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⣆⣀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠻⣿⣿⣿⣿⣿⡿⠻⠟⠃⠀⠀⢀⣼⣯⣴⣿⣿⣿⣿⣿⣿⣿⣦
⢰⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣿⣿⡏⠀⠀⠀⠀⡀⣠⣿⣿⠤⣨⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣁⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣶⠇⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡟⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣧⣄⣤⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣀⡀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣀⣤⣀⣀⣀⣤⣶⣾⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠿⠟⠛⠻⠿⠷⠄⡀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠈⣿⣿⣿⣿⣿⣏⠙⠿⠂⢤⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⠁⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢴⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢹⣿⠁⠉⣿⠟⠙⠃⠀⠀⠀⠈⢻⡟⠛⣻⣿
⠘⢿⣿⣍⠙⢀⣿⣧⡀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⢱⣌⢻⡟⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣾⡿⠀⣹⣟⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⠙⠛
⠀⠀⢈⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠱⣦⣸⣿⣶⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣽⠿⠇⠀⠹⣿⠀⠐⠷⠾⣿⠿⠂⠀⣹⣻⣿⠚
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⢠⡤⡀⠐⠆⠀⠀⢀⠀⢨⡀⠀⠀⢢⣙⠷⠀⣀⣤⣤⣤⡀⠾⣿⡿⠛⢀
⠀⠀⣿⡏⠀⢸⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠌⠛⠛⠀⠀⣀⠀⢀⡀⠀⠀⢸⡇⠀⡀⠀⠀⠛⣿⣄⡠⠿⣿⣬⣿⠟⢀⣼⡿⣶⠋
⠀⠀⢿⡇⠀⢸⣿⣮⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣤⡀⠀⣾⣿⣶⠿⠶⣦⡀⠂⠀⠈⠀⢈⠁⠀⢀⡼⠃⢠⣄⠀⠀⣰⣿⣿⣿⢾⡶⠿⣷⣤⣼⣿⣦⣉⡀
⠀⠀⣸⡇⠀⠘⣿⡇⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⢠⣿⣿⠃⢀⡀⠘⣷⠄⡄⠀⢰⣦⡀⠈⠉⠀⠀⠁⠄⠀⠀⣿⡟⠀⠁⠀⠀⣀⣀⡛⢻⣿⠿⠿⠃
⠀⠀⣿⡇⠀⠈⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣿⡟⢷⣤⣥⡼⠃⣠⡧⠀⠛⢌⣁⠀⠀⢀⡐⠋⠀⠀⢰⣏⢱⣦⡀⣀⡈⠻⠿⠧⢺⣿⣀
⠀⣸⡿⠁⠀⠀⣿⠀⠁⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⡕⠒⠠⠆⠀⢢⠈⠀⠈⢀⡀⠻⠏⠉⢸⠋⠁⠀⠀⣸⣿⡾⣿⡿⢿⣿⣶⣤⠀⢸⣿⡿
⢠⣿⡧⠀⠀⠀⣿⣄⠀⠀⣼⣷⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢠⠀⢀⠀⢀⠀⠀⠼⣳⣦⡤⠀⣿⠇⠆⠀⢰⣿⠋⠀⠈⠀⠀⠸⠿⠿⠿⣿⣿⠇
⠘⣿⣷⠀⠀⠀⣉⠉⠀⠚⢩⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠘⡷⢸⡇⣼⠀⠀⠀⣍⠙⠁⢸⣿⡆⠀⣠⣾⡏⠀⠀⢲⣤⡜⠀⠀⢰⣾⡿⠉
⠀⢸⣿⡄⠀⠰⡏⠀⢀⣠⡄⢿⠟⠻⢧⠀⠀⠀⣴⠞⠁⠀⠀⢠⡀⠰⠀⠲⠆⠛⠃⢾⣄⠀⣰⠇⠀⠀⢸⣿⠀⢠⡿⢿⠏⣡⡆⠀⠀⢀⠀⣸⣿⣿⠇
⠀⠙⠛⠁⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠈⠁⢠⠘⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⢀⡰⠀⠀⢻⣿⣿⣶⣤⠀⣾⣿⠁⣬⣿⣷⣶⣿⣿⣿⠻⣟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⣤⣶⡀⠀⠈⠃⠀⢀⠈⠙⠙⠿⠟⢢⣿⡟⢐⣿⣿⣿⣿⣿⣿⣿⣶⡿⣉⣿⡏
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠁⠙⠋⠁⢀⠀⠂⢴⣄⠀⣀⡀⠛⠀⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠚⠁⠷⠿⠶⠟⠷⠋⠻⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣄⣀⠀⢀⠀⠁⢪⣥⡜⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠈⠛⢿⣿⣤⣄⠈⠉⠻⣿⣿⣿⣿⣿⣿⣷⡚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡇⠀⠀⣀⣤⣿⠀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⢿⣿⣿⣶⣤⣼⣿⡛⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡂⠀⠈⣉⣿⣆⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣤⣀⠉⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠘⠿⠟⠛⠛⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠿⠗⠘⠛⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢩⡉⢙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⢙⡀⠘⠯⠤⠄⢀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠀⠀⠀⢆⠁⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠁⠀⠑⠠⡖⢀⡀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠠⠖⠶⠢⠀⠀⠁⠀⠀⠈⠃⠀⠈⠐⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⡆⡘⠀⠀⠀⠃⠀⠐⠉⠛⠱⠀⡎⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡂⠀⠄⢀⠩⢄⠀⠠⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠒⠀⢀⣐⠦⠀⠀⢀⠠⠔⠁⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢰⡇⠃⠀⠁⠀⠀⠂⠀⢠⠌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠄⠐⡄⠀⠠⠀⠘⠒⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡄⠀⠀⢀⠀⠈⠻⢇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⠒⣄⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠘⠂⠀⠀⠳⣄⡀⠀⠂⠰⠘⢃⡀⠀⠀⠀⣨⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠁⠂⢀⠀⠈⠉⠙⠓⠂⠭⠕⠚⠑⡠⠔⠂⠀⠀⠀⠙⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠐⠉⠀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠈⡣⢄⡀⠀⠀⠀⠀⠈⠂⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡖⠁⡠⠀⠈⠑⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠑⠀⢻⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠠⠒⠅⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠔⢠⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠇⢨⠄⣉⣀⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠐⠒⢲⠊⠁⠑⣄⡈⠀⠀⠀⠀⠀⠀⠀⠔⠧⣀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠔⠋⠀⠈⠑⠦⡀⢀⠔⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠰⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡎⠀⠀⠀⢀⠀⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣠⢌⢳⡕⠂⣉⠀⠤⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠬⠤⢾⣷⠎⠈⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠀⠀⠀⠀⡀⢠⠂⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⣀⣨⣏⠛⠉⠁⠀⠀⠀⢠⢆⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣤⠀⠀⠀⠀⠀⠀⠈⢯⠁⣿⡷⢄⣀⠐⢈⡡⠋⠀⠁⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠄⠀⠀⠀⠀⣀⡴⠆⠐⠚⠚⠛⠁⠠⠉⠉⠁⠀⠀⠀⠰⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⣆⠠⠤⠤⠔⠖⠒⠫⠦⡀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢣⠀⠑⢤⠀⠀⠉⠁⠙⠀⡀⢀⣽⢄⠀⠀⠀⠊⠀⠀⣴⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠵⢲⠃⠠⣀⠀⠀⠀⠀⢱⠀⠈⢨⡱⡤⣀⣀⠤⣪⠃⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠙⡄⠀⠉⠉⠓⣦⠀⠀⢣⣀⣀⡵⣽⣄⡀⣀⣷⡀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⡦⣄⡀⠀⠀⠀⠀⠀⢫⢹⡀⠈⠺⣝⣛⡼⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣠⢾⣅⠀⢸⠖⢳⣄⣀⣠⡜⠀⢣⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠙⢷⣼⠀⢸⠀⠀⢧⢹⠀⠈⢣⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣀⢸⡄⠀⠸⡄⢧⠀⠀⠱⣄⠀⠀⣾⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡝⣇⠀⠀⠱⡈⠣⡀⠀⠀⠑⠺⢷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠇⠘⢆⡀⠀⡱⣄⠈⠢⣄⣀⡠⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢙⠗⠢⡈⠑⣦⠴⠋⠀⡀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢁⡀⠈⠂⡄⠈⠋⠉⠄⠀⠌⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠇⡀⠢⠤⠄

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢐⠶⣄⡄⠀⠀⡴
⠀⠀⠀⡈⣿⢋⣬⠬⢾⡀⢞⣯⡄
⠀⠀⠀⠈⣇⠘⠁⣠⣤⠁⠈⡵
⠀⠀⠀⠀⠙⠿⣄⠛⠟⠀⢔⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢉⡌⢡⡀⠈⠌⠻⠟⠿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠢⠤⣀⣀⣾⡼⠒⣁⡐⣶⣿⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣧⡸⠟⠶⠚⠁⠀⠈⠑⠺⣿⡿⣦
⠀⠀⠀⠀⠀⢸⣯⡍⡆⠀⠀⠀⠀⠀⠀⡴⠚⢀⡈⢧⣿⣧⣄⠀⣀⣠⣂⣄⣀⣀⡀⠴⢦⡀
⠀⠀⠀⠀⠀⠸⣹⣷⣿⠀⢀⡤⠶⠂⠀⠀⠀⠉⠀⠈⠿⣷⣿⣿⢿⣟⣛⣛⣿⡿⣿⣦⡀⠙⢻⣄
⠀⠀⠀⠀⠀⠀⠉⢻⣿⣤⠈⠀⠒⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣼⣿⣖⢰⠽⣇
⠀⠀⠀⠀⠀⠐⠂⠘⢿⣿⣧⠀⠀⠀⠀⠀⣀⠔⠀⠀⢼⣿⣿⣿⡉⠀⠀⠈⠛⠿⢿⣿⠈⢻⢣⡺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣿⠑⣦⡀⠀⠀⠀⠁⠀⠀⠸⣿⡃⠈⠂⠀⠴⠋⡀⠀⠀⠈⠣⠉⠀⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣾⡏⠀⠀⠀⠀⠀⠀⠀⠉⣳⡂⢒⠄⠀⠈⠁⠀⠀⠀⠀⣤⣾⣧⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢠⠾⡋⠉⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡿⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡨⢿⡽⣿⢣⡄⡀⠀⡴⠁⠦⠚⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠮⡽⠃
⠀⠀⡁⠀⢀⡀⠀⠀⢠⠀⣰⡁⠤⣌⡃⡀⢡⣦⠑⢱⡿⠀⠀⠀⠀⠀⠐⠿⠀⠀⣀⠀⠀⠀⢀⢠⠀⠀⠀⠀⡄
⠀⠀⡟⠀⠀⠁⠉⠉⠉⠉⠈⠉⠉⠉⠁⠙⠁⠃⠈⠁⠀⠀⠠⠀⠄⠀⠀⠀⠀⢁⠄⠀⠀⠀⠀⣉⠀⠀⠀⠀⠈⠒⠄
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠴⠎⠁
⠀⠀⡷⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠁⠈⢶⢴⠆⠀⠀⠀⠀⢐⠀⠀⠐⡃⣀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠓⠁
⠀⠀⠀⠀⠘⠀⠘⠁⠸⡦⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⣿⠄⠀⠀⠜⢣⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢒⠀⠀⠜⠀⠀⢸⠇⠀⠀⠀⡀⠀⠅⠀⡀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣘⠧⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⠺⣿⠷⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢠⣀⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠛⠀⠇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠀⠈⢻⠄⣑⠶⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠿⠉⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠏⠛⠀⠀⣀⠀⠀⢀⠁⢀⡄⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡉⠙⡆⠀⠀⠁⢀⣠⣿⣇⠀⠀⠀⠀⠀⠙⠈⢠⠏⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⠁⠀⠀⠀⠀⠀⠺⠟⠻⠛⠁⠀⠀⠀⠀⣠⡏⠀⣆⡀⠀⠆⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢁⡴⠂⠈⠛⠀⣯⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⣄⡐⢂⣩⠃⠀⠐⠀⠀⢌⠷⣄⠀⠀⠀⠁⢳⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠁⠀⠀⠘⠐⠏⠀⠀⠀⠀⠀⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠖⠀⠀⣴⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⣤⡎⠀⠀⠀⠘⡆⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠠⡀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⡈⠁⠈⢻⠀⠀⠀⠀⢡⠀⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣤⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⢠⠄⠀⠀⠀⠈⠉⠀⠀⠀⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠒⠤⠤⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠰⡤⡎⣁⠀⢠⣶⠶⢇⠀⠀⠀⠿⢻⡿⠂⠠⠀⠀⠀⡆⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⡆⠀⠀⠂⡑⠋⠀⠠⣷⠴⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢉⣇⠀⠀⡄⠠⡤⠀⢰⣿⡴⣩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⣷⢾⡿⠀⠀⣞⠂⡜⠀⠘⣿⠛⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂
⠀⠀⠀⠨⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠉⠐⠂⠀⠀⡐⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠁
⠰⣎⠃⣴⣬⡿⠐⠀⠀⠀⠀⠀⠀⡀⣸⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣰⡷⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⢀⡇
⠀⢧⠾⠿⣿⡇⣙⠶⢀⠀⠀⠀⢸⢯⡿⠀⠘⡛⠀⠀⠀⠀⠀⢹⡆⠋⠁⡀⠶⠁⠀⠀⠀⠀⣸⡅⡀
⠀⠀⠀⠀⢸⣾⡟⣳⣾⣷⡀⠀⣼⣧⣾⠀⠀⠋⠀⠀⠀⠀⠀⢸⣟⣷⠐⣿⢢⠀⠀⠀⠀⢂⣾⡧⢩⣴⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢻⣿⢟⣹⡿⠇⠀⠀⠉⢿⣷⠿⠀⠀⠀⠀⠀⠀⠸⢁⣹⡆⣿⣠⡆⠀⠀⠠⣟⣿⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠛⣽⡷⣀⠀⠀⢀⣾⣽⢇⣀⠄⠀⠀⠀⠀⠀⠿⠋⠀⠉⢙⠁⠀⠀⠀⠉⠿⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠾⣧⣹⣄⠀⠀⠁⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⣿⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⠁⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣽⣿⢤⡀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣝⣠⠂⠀⠀⠀⢰⠃⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢘⡆⠀⠈⠳⡀⠀⣴⠀⠀⠀⢀⡀⠀⠀⢀⠀⣠⠀⠃⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣧⠀⠠⠀⡹⢷⣟⡀⠀⠀⢊⠀⠀⠀⠈⠈⠀⠀⢀⣠⠞⠇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣼⢁⣴⠀⡤⢀⣈⣷⣠⣴⠟⠁⠀⢹⣧⠐⠀⠘⠀⠀⡀⠀⢀⡄⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡟⣿⣿⣿⣷⣼⠋⠉⠉⠉⢠⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠿⠉⠛⠛⠠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠐⠒⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⢤⠒⠰⠀⠂⠀⠀⢠⠋⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⢀⠡⡦⠀⢘⠐⠀⠠⠔⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠠⠠⠐⠒⠚⠓⠐⠃⠝⣁⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢀⠄⠀⢐⡀⠠⠤⠀⠀⠀⠀⠀⠐⢀⡄⡥⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⣀⠔⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣀⠀⠀⠀⠠⠄⠀⠂⠁⠀⠀⠀⠀⠀⠀⣦⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠐⠦⡤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠄⡄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⢳⡈⠾⠃⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠲⢄⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠂⠶⣄⡙⠢⠤⠤⠤⠊⠱⠄⠀⠐⠒⠀⠀⠂⠀⠀⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⢭⣁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠒
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠋⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠁⠐⠂⠐⠶⢄⡈⣀⠠⡤⠐⠃⠀⠀⠂⠀⠀⠠⠀⠀⢀⡤⠎⢁⡁⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡸⡀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢀⠱⣄⠀⠀⠈⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠑⠦⡀⠀⠀⠀⠠⠂⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡵⡬⣷⣷⣕⣴⣀⣊⢄⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠻⣿⡵⠃⠘⣛⣿⢿⡎⡆⠀⡀⠬⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣎⢷⢙⠀⡆⢀⣤⡙⣦⣇⡇⠀⠒⠒⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣵⡍⡠⢰⣸⡿⠃⢋⣷⠁⠀⠀⠨⠅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠨⢍⣐⣂⣓⣤⣴⣯⡿⠠⠀⠐⠒⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠀⠤⠤⠤⠄⣐⡂⠀⡀⠀⢀⠉⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠭⣭⡤⠴⢚⣃⣬⠀⠀⠉⡒⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣤⢴⣾⡿⠋⢀⣀⣤⣀⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡫⢋⢝⣵⡿⠋⠐⠊⢉⣁⣠⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱⣡⢫⢊⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢱⢃⠇⠎⡎⢫⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣷⡷⠟⢯⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡇⡘⢸⠀⠁⠀⠑⠀⣀⣤⣄⡈⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⣦⡀⠠⠘⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠁⡇⠇⠀⢰⠋⠉⢳⣸⠁⠀⠈⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⠸⠧⠬⠋⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠆⠑⡐⠀⠘⣦⡀⡼⠉⣓⣮⠞⢣⣶⣾⠻⣿⣼⡁⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⢀⣀⡬⠟⣧⠶⠿⠇⠀⠘⢮⣿⠛⠛⢦⡙⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣼⠁⠀⠀⡠⠤⣄⠻⡄⢀⣠⠴⡗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢳⡰⣋⠤⠴⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠚⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡴⡄⢸⣇⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣍⡀⠛⠛⣠⡞⡛⠑⠩⠘⢦⢙⡿⢿⣂⡀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠀⡈⠑⠘⢛⠛⠤⡀⠛⡛⠛⢶⣾⢥⠽⠿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠈⢉⡀⠨⠤⡄⠢⡤⠀⣄⡂⢅⠠⢄⠲⠬⣦⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣠⡚⣰⣜⣛⣣⣶⣤⡻⣏⣹⣻⢑⣏⣓⣠⣸⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣽⡽⠋⠉⠉⠺⡀⠀⠀⠈⠉⠉⠻⢿⣍⢛⣁⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢸⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠻⣯⡐⠟⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢸⡄⠐⢊⣉⡓⠂⠀⠀⠐⢚⣉⣍⡙⠂⠀⢻⣷⡶⢖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣹⡇⠰⠏⢿⣏⠃⠀⠀⠘⠋⢻⣯⠿⠃⠀⠈⣿⡄⢸⢏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣬⣷⠀⠀⠀⠀⠀⠤⠠⠦⠀⠀⠀⠀⠀⠀⢠⣠⡿⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⣧⠀⠀⠀⠀⠖⠒⠳⠊⠀⠀⠀⠀⢠⡾⡈⢧⡘⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣁⢛⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠱⠥⠾⡟⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⣿⡿⢶⢤⣤⠤⠴⠒⠉⠁⠀⠀⠀⠀⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⠟⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⠀⢀⠋⠈⠁⠐⢀⡴⢠⡄⢿⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠉⠙⠋⢀⠀⠡⠒⠀⠀⢀⠉⠀⠉⠙⠀⢀⠀⠀⡀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣈⡌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠠⠀⠀⠀⡐⠂⠀⠀⠈⠠⡄⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⣱⠂⡀⠛⠀⢠⠀⠀⠀⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠶⠶⣮⠀⠁⠀⠈⣰⠗⠲⡆⠀⣆⠷⠀⠀⠀⠀⠀⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡀⠠⠀⢀⣹⣄⣠⡇⡀⠘⠤⠀⠀⠀⠁⠀⠄⠀⢀⡀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠰⠆⠆⠤⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢤⠈⠀⠑⠆⡘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠒⠠⣾⡀⢀⡀⠀⠙⡆⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠶⢪⢷⠈⠀⠀⠀⠀⠀⡑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠉⣧⠄⠈⢰⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⢁⠁⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠤⢠⡴⢇⢤⡀⠾⢦⡤⠟⠀⠟⢲⠀⠒⠐⠚⠛⠉⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠈⠀⡀⣇⠀⠀⠰⠀⠐⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⣄⠐⣲⣤⡄⣆⠀⡄⢀⡀⢀⣤⡠⠁
⠀⠀⠀⠀⠀⢀⣼⠀⡤⣀⢸⣿⣙⠫⣥⠏⠀⢱⠃⠛⣿⣨⡽⠛⡿⣿⣶⡀⠁
⠀⠀⠀⠀⠘⢛⡈⣻⠟⣿⡏⠘⠋⠠⡈⠀⢀⠈⠀⠀⠀⡸⠁⡠⢃⢻⣿⣤⢀⢀⠄
⠀⠀⠀⠀⠙⠻⢻⣯⡼⠋⠀⠀⠀⠀⢃⢠⣿⡄⠀⠀⠀⡇⢠⠃⢈⠟⡉⣙⣧⣍⣄⣤⣄⢠⣠⡀
⠀⠀⣠⣀⡒⢀⠝⠁⠀⠀⠀⠀⠀⠀⣨⣞⣿⣄⠀⠀⠀⠷⠁⠀⠓⣩⠔⠁⠀⠈⠛⠀⠈⠀⠉
⢰⣼⠿⢯⡽⠋⠀⠀⠀⠀⠀⠀⠀⢠⡏⠝⣿⣿⠇⠀⠀⠀⠀⡰⣉⣀
⠀⠀⠀⠀⣀⣀⣤⣤⣷⣴⣾⢷⠀⢿⠶⠶⠈⣿⣄⠀⠀⠀⢎⣾⠿⡶⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⡆⢈⢦⣸⡇⣠⠞⣻⢿⡀⠀⢰⠇⢹⠃⠀⡼⣗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢳⣧⠈⡏⠙⡷⢵⣯⢸⡇⢀⢾⡠⠚⣷⣌⠿⠉⠻⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⢸⢻⡂⠑⣄⡠⠔⡹⠹⠁⢸⡀⠉⢩⠃⡹⡆⠀⣠⠱⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠳⢙⠘⠇⢄⠇⠃⠆⡇⠁⠀⡎⠔⠻⣧⢜⢆⠱⠎⠉⠑⠪⣻⣷
⠀⠀⠀⠀⠀⠀⠀⢘⣇⣴⠘⠾⣧⢦⣀⣼⠸⣿⠀⢸⡿⠀⠊⣨⠈⡞⠊⡄⠀⠀⠀⠸⡷
⠀⠀⠀⠀⠀⠀⠀⠸⠅⠐⠿⢂⣸⣝⢹⣣⠀⢦⠀⢻⠇⠀⡜⢿⣷⣷⣀⣨⠖⣠⣶⠊⠀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢀⠏⠈⢮⡹⢤⠘⠀⢸⡄⠘⡄⠀⠙⣿⣯⡰⠾⡍⢸⣴⣶⣄⡌⣍⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠇⠀⠳⣌⢛⠀⠀⠣⡅⠁⠀⠀⠈⠻⠋⢸⠀⢸⡦⢘⡋⠚⠚⢢⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⢀⡀⢣⠀⠀⡸⠉⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⡆⡀⠘⡟⠛⠓⠺⡷⠀⣈⣶
⠀⠀⠀⠀⠀⣴⣦⣶⣄⡃⢀⡉⡱⣜⡆⠠⠃⠀⠀⡰⡏⡈⠀⠀⡇⠀⠀⠀⠀⣧⠖⢳⣤⣀⠀⠈⢠⡀⠁
⠀⠀⠀⠀⠰⣿⠁⠀⢙⣷⡀⠹⠷⠞⠁⠀⠀⡠⢺⢎⣜⠃⠀⠆⡇⠀⠀⠀⢰⠘⣊⢯⠀⠉⠛⠛⡿⢀⣣
⠀⠀⠠⠶⠿⢉⣩⣷⣥⣬⢵⢤⠁⠀⠠⢚⠫⣿⣁⠞⡝⠒⢲⢄⣇⡄⣀⠤⠼⡖⢣⣤⣷⣤⣴⡚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣠⢒⣡⡄⣳⣇⡀⣴⡧⢦⡙⡿⢿⣤⣄⣆⣀⡇⢀⡀⣀⣠⣹⡿⠛⠁
⠀⠀⠀⠀⠠⠴⠛⠉⠀⢀⡄⣈⡜⠀⢻⠛⠛⠓⠛⢤⡿⣝⣿⠛⢻⣛⣻⡋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣤⠴⠿⠗⠤⠀⠀⠀⠸⣀⣱⡀⠙⣿⠖⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠢⠴⠦⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠉⠉⠉⠐⠀⠆⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠁⠁⠀⠄⠀⢀⣐⣀⢡⡄⠄⠝⠐⠀⡠⠊⢂⢰⠀⠡⠀⠀⠀⢀⠈⠀⠀⠨⠑⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⣠⢠⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠚⠦⢩⡼⠀⡀⢀⡸⠟⠐⡆⠀⠀⠀⠀⠀⠀⢖⠀⠄⠓⡆
⠀⠀⠀⠀⠀⠀⠀⡘⠈⢂⡜⠁⠀⢀⡤⠐⠒⠒⣒⠒⠒⠀⢄⢀⡈⠀⠉⠴⠈⠄⠚⠀⣴⣶⠀⡄⢠⡀⠀⠀⠀⠀⠘⠋⢠
⠀⠀⠀⠀⠀⠀⢰⠀⠄⡿⠀⠀⡴⠇⣢⢠⠦⠂⠉⠰⢤⠦⠖⡟⣽⠂⠰⠀⠀⠀⠀⠀⠁⣡⠖⣵⢴⡆⠀⠀⠀⠀⠛⠀⠂⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠶⠀⠀⢼⠁⠈⡅⠀⠀⠀⠀⠀⠔⠂⢀⣇⠀⢀⡘⠋⠰⣀⣠⢀⢀⠈⠀⡍⠸⡃⢀⠀⠀⠀⠀⢀⠐⢰
⠀⠀⠀⠀⠀⠀⢸⡐⠠⣷⠀⠸⠀⠠⠇⠀⠀⠁⠀⠀⠀⠀⢿⡾⡀⣈⠉⡴⠁⠙⣋⠆⢈⣲⡬⡷⢆⠻⠎⠀⠀⠀⢀⣙⡀⢰
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⢀⠀⠳⢤⣠⡆⣆⠀⠀⠀⠀⠠⠀⢀⠙⢟⡀⠂⠂⠐⠁⠠⢌⠛⢷⠑⣾⡀⠀⠀⢰⠟⣷⣶⣤⠰
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠋⢢⠠⢈⣏⠷⢀⣀⡠⢶⠤⣔⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠙⠋⠀⠄⠀⠈⠀⣿⠀⡏⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡖⡃⠀⠀⠈⢛⡁⣛⡷⡤⢰⣋⠆⠀⠀⠀⠀⠀⢀⡀⢄⣀⣳⣿⣗⣀⠀⣤⣴⣴⠄⠀⠻⣘⣓⢴⠁⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠁⠀⠀⠀⢠⡼⡦⠁⡈⣁⡀⠠⠠⡄⠂⠀⠉⠈⠠⠅⠠⠲⡿⢆⠳⣮⡌⣵⣼⣦⠐⠷⠫⣏⢳⣁⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⡴⣏⠋⠀⠀⠀⢀⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⣷⣿⣿⡿⠛⣫⡽⠿⣆⡈⢻⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢀⠀⠐⠷⣿⣿⠟⠋⠁⠐⠒⠛⠛⠳⢶⣄⠀⠀⠀⠀⠀⠀⠈⢳⢸⣿⠟⣁⠶⣈⠩⡔⠀⢢⠉⠲⢝⡻⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡅⠹⠀⢹⣿⠀⠀⠒⡤⠀⠀⢠⣤⣀⠹⠇⠐⠂⢤⠶⠖⠂⢠⣟⡥⢊⣵⡾⠏⠀⠀⠚⠡⠀⠀⣈⣙⣉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⢀⣿⠟⠀⠀⠀⠈⠐⠤⠘⠿⠋⠀⠀⠀⠀⠀⣶⣦⣄⣼⣥⣾⡇⠀⠀⠀⠀⠀⣀⠀⢠⡞⠁⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠆⡸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣹⣛⡿⠉⣠⡴⠶⠶⣦⡄⠉⠀⢨⣿⡆⠑⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣽⣾⠛⡋⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠰⡇⠊⢁⣠⣄⠀⢀⠀⠀⠀⠀⠉⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠋⠀⢡⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⠃⠀⠀⠀⠀⣠⣿⣿⣉⣿⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡟
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢃⣶⠐⠀⠱⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠀⢀⠐⠹⣿⣿⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠛⣦
⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠉⠉⠱⠮⠉⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⣤⠾⣿⣿⡇⠘⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋
⠀⠀⠀⠀⢠⣿⣿⠋⠀⢀⠻⠀⢶⣽⡄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⣲⣿⣿⣷⠾⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⡀⢀⠀⣀⣨⠿⠇⢀⣀⠉⠃⠀⠀⠈⠛⠃⠴⠆⣀⠶⠆⢀⠲⠗⠉⡀⠛⢣⣅⣁⣀⣀⣁⣿⣿⢏⣥⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠐
⠃⠘⠀⠈⠁⠐⠒⠀⠿⠖⠀⠀⠀⠀⠀⠙⢦⣾⡭⢀⡀⣈⣁⣀⡄⣐⣿⠾⣿⣿⣿⣿⣿⣿⣿⣄⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡤⢤⡠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠞⠿⠷⠾⠋⠫⢀⣼⠛⠛⠛⠛⠋⠀⠈⠙⠻⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⢤⡛⠸⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡶⠐⣧⠰⡦⣀⠀⠀⠀⢀⣀⣠⣔⠽⢬⡀⠀⠀⠀⡂⠀⠀⠀⠀⠈⠸⡿⠧⣄⡀⠀⠀⠀⠀⠀⣝⠃⠀⠈⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⢷⠬⠋⢿⠽⣙⠊⡑⠈⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⠛⠐⠢⠴⠾⣋⣣⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣛⢉⡕⢂⡰⠄⢂⠁⠐⠉⠉⠛⠛⠟⠀⠁⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢸⡻⣆⣿⠀⠀⡃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠩⠅⠄⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⡷⠏⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠀⠀⣼⣷⣶⣦⣤⠟⠋⠀⠀⠀⠀⠀⠈⠳⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠙⠀⠘⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡛⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⠀⠀⠀⠀⠀⠂⠀⣰⠋⠘⠁
⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣧⣤⣬⣥⣴⣥⣼⣧⣴⣿⣥⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢿⣳⣈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣽⣲⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⡾⡽⢿⣷⣾⣿⡏⣹⢿⡿⣦⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⠃⠀⣈⢃⡛⢺⡧⠆⡥⠄⡿⠒⢡⠀⡀⠙⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢘⣄⠅⡟⢳⠈⠃⡞⢻⡂⠁⣄⠀⠀⠀⢱⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⡀⠀⠀⣴⠃⢃⡾⢁⣤⠙⢋⣽⠯⣿⠀⠈⣡⡀⠀⡄⢙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⢀⣨⣾⣵⢸⣏⠎⣿⠉⠉⡆⢀⣿⠄⠀⣠⣅⡀⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡠⠖⠚⠛⢿⠀⣨⠈⠀⢃⡂⣿⠸⢷⠿⠙⠉⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⣤⡄⠈⢋⠜⠀⡈⢀⡷⣄⡀⣀⣀⡀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡿⢛⣺⣿⣸⠀⢿⡜⠀⣿⡄⣙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠊⠇⢀⣺⣿⠙⠷⣊⠑⠀⢻⡏⠏⢻⡏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢠⣿⠳⡄⠈⠈⠑⠲⡜⣿⡊⠈⢏⠀⠈⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠁⠀⣼⠇⠀⠈⢑⣤⡀⡀⠀⣿⣷⢠⠈⠠⠀⡋⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢄⡜⢀⢀⣼⠟⡠⠖⢊⣿⣿⡏⠙⣦⠇⢻⣆⠃⠀⠙⣰⡅⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠞⠀⡇⢀⡔⠙⠈⢡⠀⢸⠀⠈⢿⣔⠀⠀⠈⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠋⠀⡀⡧⠈⠠⣄⢤⣴⡿⠆⠀⠀⠈⣿⣆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⡁⢉⠂⠅⡊⠐⠢⠤⢤⠼⣎⣩⡐⠠⣁⢘⣿⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡄⣹⠐⡪⢂⠍⠀⠸⡇⢸⠃⠠⣇⠊⢔⡀⡈⠈⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡜⣀⠄⡰⢓⠀⣘⠑⠈⣀⣐⠑⠡⢂⢄⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣥⢄⣤⣤⠄⡤⣤⠀⢠⣄⠤⡤⡼⣦⢤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠓⠒⠚⠓⠒⠚⠚⠒⠓⠓⠒⠚⠒⠒⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢢⢰⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣜⢊⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠙⠗⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢰⣉⠠⠴⣤⡄⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡀⠀⠀⠀⣀⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⣼⣿⠀⠀⣸⣿⠟⠈⠠⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠖⠻⠿⠷⠶⠿⠃⠀⠀⠀⣡⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠀⢠⡄⠀⠀⡀⢀⠀⠄⢀⣴⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠂⡾⢻⡀⠀⠀⠀⠀⡈⡟⢸⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠞⠀⣰⠁⠈⣗⠀⠀⠀⠀⢸⡇⠈⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠚⠁⢀⠴⠁⠀⠀⣿⢀⣀⠠⠄⠚⡇⢠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠤⠞⢁⡠⠒⠁⠀⠀⠀⠀⣏⠁⠐⠒⠐⠂⢹⠸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠠⠘⠁⠀⠀⠀⠀⠀⠀⢠⡏⠄⠑⠀⠀⠀⢹⠀⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⢀⠀⠀⠀⠸⡜⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠁⠀⠀⢀⡗⡦⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠀⠀⣀⣄⡈⠠⠄⣗⠸⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡸⠁⠀⢣⡀⠀⢸⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⠀⡇⠀⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇⠀⠀⠀⢱⠀⠀⢁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡞⠀⠀⠀⠀⠸⡄⠀⢸⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡼⠀⡼⠁⠀⠀⠀⠀⠀⣇⠀⣸⣧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠇⢰⠁⠀⠀⠀⠀⠀⠀⢹⡀⣸⠸⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠃⠀⠀⣀⠔⠊⠀⠀⢎⠀⠀⠀⠀⣀⠤⠒⠁⠀⢸⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠐⠒⠋⠀⠀⠐⠧⠴⠒⠒⠒⠒⠊⠀⠀⠁
⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣟⣻⣿⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢳⣈⣅⣧⣅⣉⣙⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡠⢞⠙⣿⣿⡿⣿⣿⡟⠉⠶⣈⠳⣄⠀⠀⠀⠀⠀⠀⣸⣅⡀
⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⡀⠀⠀⢀⡲⢁⣎⠑⡼⣥⣴⣤⣤⣤⣤⣤⡼⣤⠉⣦⠘⣆⠀⠀⠀⠀⣰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣰⣿⡇⡀⠊⠀⠀⠀⣬⠁⡞⢢⣿⣧⣿⣿⣿⣧⣿⣿⣧⣿⣼⣯⠐⢃⠸⡆⠀⠀⠀⣽⣿⣹⣿⠇
⠀⠀⠀⠀⣰⠿⠻⠇⢰⠀⡀⠀⠀⡇⢨⢁⣸⠿⠟⡟⢻⣿⡍⣹⣿⣛⡟⠿⢿⣓⣹⠀⠓⠀⠀⡿⣿⣻⢿⣹⠃
⠀⠀⠀⠘⠁⠀⠀⣠⣎⣄⠀⢠⠀⠁⠸⢤⣿⣤⡇⢧⣨⡝⣫⣿⣋⣄⡷⣃⣦⢿⢼⠀⠀⡄⠈⠉⣿⠟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢦⡼⢅⠀⠀⠀⣠⠄⣿⠇⣸⡟⠋⠁⠀⢘⠁⠀⠈⠙⢿⡃⢼⡏⢠⡂⠀⠀⠀⠧⠖⠈⠛⠣
⠀⠀⠀⠀⠀⠀⢁⠞⠁⠀⠀⠀⠂⠀⠈⢀⢸⡿⠃⠀⠀⠀⢸⡄⠂⠀⠀⠈⠛⣀⠈⠁
⠀⠀⠀⢀⡀⠀⡯⠀⠀⠀⠀⠀⠀⠀⡄⠈⣿⠀⠰⢆⡉⠀⠈⠀⠈⢤⠖⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙
⠀⠀⠴⠊⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⡄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡠⠀⠀⠀⠀⠀⠀⣿⣾⣳⣾⣷⡤⣣
⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠛⠀⠈
⠀⠀⠀⣸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠰⠧⣶⣾⣿⡇⢀⠀⠀⠀⠄⠀⠀⠂⢠⣿⣷⣶⠄
⠀⠀⠀⢸⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠹⡧⠻⣷⠀⠐⠂⠀⠅⠀⢀⠀⢾⡟⢸⠏
⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢧⡀⢶⣦⡄⠀⠀⠀⣼⠿⢂⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠐⠀⠀⠹⡄⢹⠃⠘⠀⠀⠉⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⣄⣠⣴⡖⣹⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢹⠆
⠀⠀⠀⠀⠀⠀⢠⠟⠀⠐⣦⣞⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣟⣫⡟⠁⠀⠀⠀⠀⠠⣞⣀⡈⣠⣤⠈⢧
⠀⠀⠀⠀⠀⢨⡃⠀⢻⣿⣿⣿⣷⣄⡜⠀⠀⠀⠀⠀⣿⣿⣯⡉⣿⠎⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⢀⢸⠇⠀⠀⢶⡽⢿⣿⣿⣿⠃⠀⡆
⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠈⠋⠀⠸⣼⡆⠀⠀⠀⠠⣄⠉⠉⠀⢀⠐⠁⠀⢺⣦⡀⠀⠀⠀⢠⣤⡶
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠐⠀⣺⠟⠃
⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠘⢣⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠘⠀⠀⠀⠒⠉⣀⣀⣀⣤⠂⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣤⣶⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠠⠾⠿⢿⣿⡁⠀⠀⠀⠈⠓⠄⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡠⠞⠋⠀⣸⣿⡿⠛⠛⠂
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠹⣤⣦⣀⣈⣛⠃⠈⠛⠛⠳⢿⣦⣿⠳⠶⠛⢋⣤⣀⢠⣼⡿⠁
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠓⠖⠚⠀⠈⠃⠀⡀⣀⡀⠈⠀⠈⠳⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⡀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢰⠃
⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠆⢠⣐⡏⠄
⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡀⠁⠀⠉⣀⠳⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠁⠀⣄⣀⡀⠀⠈⠀⠈⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠀⠀⢀⠤⠴⠀⡀⠐⠒⠲⠶⠶⠶⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠴⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⢠⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣿⣽⠼⣾⣬⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡆⢂⢅⡛⢰⡶⣶⠙⣃⢅⡆⢢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡕⢄⣧⡲⠤⣓⠈⢓⡏⢐⡡⢟⣭⣔⠰⣝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢈⠳⣣⡴⠞⠚⠛⢛⡳⠶⣜⠳⢋⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣥⣅⣴⠋⠀⠀⣀⠴⢋⡀⠀⠈⠳⡷⣤⡔⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠛⣿⠁⠠⢔⣃⠀⠰⠀⢀⣑⠤⢀⢹⡛⠩⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡋⡗⠲⠶⠬⣅⢛⢀⡭⠴⠶⢺⡏⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡀⠰⠶⢘⡇⡏⠰⠆⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠓⠒⣋⠀⠈⠒⠒⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⣄⠀⠉⠒⠃⠀⢠⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠹⣄⠈⠛⠛⠛⠛⠛⠉⣀⠜⢀⠀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⢈⠒⠢⠭⢛⣛⣛⣛⣛⠫⠥⠒⠂⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⢲⡄⠓⢤⣀⠀⠀⠀⠀⠀⣀⡤⠚⠁⡴⣐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⣇⠰⡶⠤⠍⣁⣐⣈⡩⠤⢴⠖⢰⠇⡏⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠸⡄⠈⠲⠄⣀⣀⣀⡠⠔⠁⠀⡞⠀⡷⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣗⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡟⠀⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡯⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⣀⣀⡴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢄⣀⣠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣴⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠉⠳⡼⣟⢿⠈⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡚⠁⣠⣄⣀⡤⠬⡟⠳⣄⣹⡈⠩⣿⠗⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠠⠆⠀⠉⣤⡀⠘⠁⣹⠀⠱⣄⡀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢶⣶⡄⠈⠛⣇⠐⠖⠀⢀⣠⢄⠀⢰⠁⢀⡠⠚⠃⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠻⠏⡇⠀⠀⠘⣆⠀⠘⢿⣀⡼⢠⡾⠚⡏⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠶⠿⢧⠀⣀⡴⢾⢓⡶⣶⣲⢶⢋⠿⣄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡋⠁⣀⡤⣼⣿⠿⢳⡿⢯⡠⠜⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⣀⣈⡧⣄⣀⣠⣴⠟⣠⠴⣇⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠛⠛⠻⡖⠚⠁⠀⢨⠿⠟⠋⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣰⠋⠂⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠦⢄⣀⠀⠀⠈⠳⢶⠇⠉⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣼⠟⠒⣶⠦⣄⠙⠲⠤⣄⣀⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣠⠞⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠋⠀⠀⠀⠀⡴⠟⢦⡀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⢳⠀⠀⠈⠁⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠘⣆⣀⣤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡽

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣀⡀
⠀⠀⠀⠀⠀⡀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⢀⡀⠄⣀⠀⣀⠠⣀⡀⠬⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣗⣺⣿⣿⣦⡀
⠀⡀⠀⢘⠠⠤⡀⠤⡀⠤⠄⠃⠀⡀⠀⠀⠀⠀⠀⠨⠭⠁⠀⠀⡇⠀⢼⠀⠈⠈⠭⠄⠀⠀⠀⠀⠀⢀⣴⣿⣥⣟⣟⢯⡽⣿⣻⣧⠿⣦⡀
⠀⠂⠐⢏⠈⠢⢆⣀⠴⠌⠈⡹⠀⠆⠀⠀⠀⠀⠀⣉⣀⠁⠀⠀⠷⠀⠿⠀⠀⠈⣀⣉⠀⠀⠀⠀⠀⢻⣿⣇⣎⢾⣏⣧⣼⣽⢿⣺⣸⣾⣿
⠀⠴⣶⠳⢤⣄⠺⣿⠇⣠⡤⠷⣶⡇⠀⠀⠀⠀⣠⠓⢦⣈⠅⢶⠀⣶⠀⡶⠨⣀⡴⠺⣄⠀⠀⠀⠀⠸⠿⡀⢙⠈⠉⠉⠉⠉⠉⣉⠀⡿⠏
⠀⠘⠿⠧⠀⠨⠄⠋⠰⠄⠀⡟⠟⠁⠀⠀⠀⠀⡏⠀⢠⠷⠂⠉⣳⣀⣞⠁⠐⢾⡄⠀⣹⠀⠀⠀⠀⡟⠙⡇⢢⡤⠤⡀⢀⡤⠦⡔⢸⡋⢹
⠀⢈⡨⢴⡄⠀⠄⣀⠀⠀⣸⡄⣀⠀⠀⠀⠀⠀⠙⢪⣏⠀⣀⢀⢠⠀⡄⡀⡀⠀⣿⡔⠋⠀⠀⠀⠀⠹⢌⢹⡄⠹⡄⠀⠀⢀⠎⢠⡟⢡⠞
⠀⠀⢀⠐⠁⣄⠀⠀⠀⡠⠁⠂⠈⠀⠀⠀⠀⠀⠀⠘⡹⣿⠰⢘⡀⠀⢐⡃⠄⣿⢟⠉⠀⠀⠀⠀⠀⠀⠀⠉⣍⠀⠀⡐⢐⠀⠀⢨⠉
⠀⠘⡂⠙⠚⡘⠏⣽⠝⢐⠓⠋⡘⠁⠀⠀⠀⠀⠀⠈⠹⡅⢀⣭⠤⠀⠤⣭⡀⢨⠏⠁⠀⠀⠀⠀⠀⢀⠐⠀⢋⢢⡀⢨⢅⢀⡴⡛⠂⠂⡀
⠀⠀⢡⠖⠀⠈⠇⠀⠞⠀⠐⢦⡅⠀⠀⠀⠀⠀⠀⡠⠀⡇⢸⣬⠷⣒⢾⣤⡇⢸⠀⣄⠀⠀⠀⠀⠀⠀⢀⠰⠦⠉⠀⠶⠲⠄⠉⠱⡆⡀
⠀⠀⠀⠀⠀⠀⢴⣀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⡑⠚⠮⠀⢋⠀⠵⠓⢋⠃⠘⡆⠀⠀⠀⠀⠀⡣⠄⡰⠠⣾⡏⢙⣷⠄⢆⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠁⠋⠑⠿⢳⡶⠿⠇⠙⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢠⣦⠀⠀⡀⡀
⢀⢀⡰⠄⠀⢀⠀⢸⠆⠁⠀⠀⠱⢀⢀⡀⠀⠀⠀⠀⠀⢠⠚⠃⣤⣲⣿⣦⡄⠛⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⣥
⣴⢨⠓⣀⠀⡀⠋⠘⠋⠋⡀⠀⣁⠫⡐⡇⠀⠀⠀⠀⠀⢆⣿⢐⡒⣰⣴⡂⢒⢸⣏⡆⠀⠀⠀⠀⠀⠀⠀⠾⡆⢹⠼⠀⠒⠸⢧⡃⠰⠂
⣰⠁⠀⠁⠐⠘⠃⠀⠐⠚⠁⠂⠈⡀⠙⡄⠀⠀⠀⠀⠀⢁⠉⠒⢗⢴⣠⢶⠗⠊⠁⡁⠀⠀⠀⠀⠀⠀⠀⣀⠐⠋⠀⠈⠀⠀⠀⠑
⡟⠳⣔⣄⣠⠀⠲⡟⢷⠆⢄⣄⡴⣠⠚⠃⠀⠀⠀⠀⠀⣼⢦⣄⠀⢠⢥⠀⠀⡠⣿⡆⠀⠀⠀⠀⠀⣠⣰⠁⠀⠀⠠⡋⠯⣻⡄⠀⡀⠨⡄
⠀⢂⣿⡮⠁⢠⣨⠀⢠⣣⠄⠉⢿⣗⠀⠀⠀⠀⠀⠀⠰⢳⣅⠈⢷⠈⠊⢠⡟⢀⣼⠻⠀⠀⠀⠀⠀⠀⣅⠃⠤⣄⢀⠉⠖⢁⣀⣠⠅⠀⡁
⠀⡭⠝⣄⠀⠉⠉⠀⠀⠉⠉⠀⡨⠪⠥⠀⠀⠀⠀⠀⠀⢶⣌⣡⠌⡲⠐⡂⢥⣉⣴⠦⠀⠀⠀⠀⠀⢀⠘⣀⢘⡭⠵⠆⠀⠶⠯⢝⠂⡄⢃
⠀⠶⡆⠸⠀⡈⣶⣦⣴⣞⡀⠀⠇⣰⠆⠀⠀⠀⠀⠀⠀⣿⠈⢘⣦⣅⣀⣥⣞⠈⢈⡅⠀⠀⠀⠀⠀⠈⠙⠃⡆⢀⡴⢒⠶⠚⢤⠀⣄⠹⠋
⢰⢷⢹⡢⣌⣴⣖⣚⢓⣰⣌⡤⢞⣧⠾⡆⠀⠀⠀⠀⠀⣼⡅⣹⣯⣙⣖⣫⣽⡁⣼⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠⠘⠓⣷⠚⠣⡤⢀
⠈⠛⠚⠻⢗⣛⢒⣺⡗⡖⣛⡻⠟⠻⠛⠁⠀⠀⠀⠀⠀⢀⣧⣏⠙⠉⠟⠙⠋⣧⢇⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣀⡀⢀⣶⡠⢀⣰⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⢦⣼⣏⢛⣻⢤⡼⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⣠⣤⣤⣤⡸⣷⡀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡟⠁⠀⢹⣷⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣰⡏⢻⣆⠀⢀⣾⠇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠙⠛⠛⠁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢁⣴⠶⢶⣦⠀⠀⠀⠀⠀⠀⢹⠉⣭⠀⠀⣶⠄⣴⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡿⠁⠀⠀⣿⠆⠀⠀⠀⠀⠀⢸⡄⣿⣤⣶⣿⡀⣿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠈⣷⣄⣀⣼⠟⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⣿⠀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⡄⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠘⣿⠀⢠⣄⠀⣼⡇⣠⡾⠛⠻⣦⠀⣟⢀⣀⣼⡟⢰⡇⠀⠀⠀⣿⠀⠀⠹⣿⡄⣾
⠀⠀⠀⠀⠀⠀⢻⣇⣿⣿⣷⣿⢡⡟⠀⠀⠀⣿⠃⣿⣿⣟⠉⠀⢸⣿⠀⠀⠀⣿⠀⠀⣠⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡟⠘⣿⡿⠈⢿⣤⣤⣾⠏⠀⣿⠀⠻⣷⠄⢸⣿⣤⣤⡀⣿⣴⡾⠟⠃⠀⡛



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⡿⣷⠾⡁⠉⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣼⣁⡨⣋⣛⣼⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⣾⣍⢷⣿⣿⣿⣷⣝⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⣴⣿⣱⣿⣦⡿⣤⣤⣌⣿⠹⡢⢽⣿⣶⣿⣦⠀⠀⠀⣤
⠀⠀⠀⠀⠘⢠⠘⢳⠄⡂⠀⢠⣯⣙⣿⡉⣿⡗⠛⠻⣿⠛⠣⢽⡞⠛⣏⠙⡻⠇⠰⢾⡆⢳⡄
⠀⠀⠀⠀⠀⠟⢠⠟⠁⠀⠠⣌⠉⣍⡈⠉⢿⡏⠶⠆⡴⠶⢠⣿⢡⠉⢀⡦⠁⣠⠄⠈⠣⡈⠃
⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠻⠀⠘⡂⣸⡞⠿⡄⢲⡗⢀⡼⠿⣼⡀⢘⡃⢈⠁⠀⠀⠀⠘⡣⢤⣄⣠
⠀⠀⢐⠂⠈⠀⠀⠀⠀⠀⢀⣴⣟⣴⣩⣝⠧⠔⣏⣀⣀⣹⣧⣠⡯⣔⢣⠘⠳⣄⠀⠀⠀⠀⠘⢾⣿⠁
⠢⢼⡀⡄⢀⡀⠀⠀⢀⢴⣯⠋⡜⢲⣿⠏⣀⣼⡄⠩⠍⢀⣿⢳⢰⣿⢄⡁⠑⠈⣃⠀⠀⢀⣈⠀⣙⠒
⠀⢠⠋⡁⢈⣧⠀⠀⠸⣬⠿⢤⣍⣿⡿⣠⡝⣿⡟⠒⠖⠋⣿⢈⠸⣿⡦⡤⠀⢊⡀⠳⠀⡸⠽⢾⡏
⠀⠀⠀⠹⠅⠈⢁⣦⠶⠿⠻⢾⡧⢾⣧⡛⠁⢻⡅⣄⠀⢰⡟⢈⢾⣿⡇⣥⣠⠤⣿⣦⣴⣄⡀⣰⠁
⠀⠀⠀⠀⠀⠀⣾⠂⢀⡴⠷⠾⠟⠊⣧⡆⠰⢊⡕⠈⠀⢸⠁⡜⢸⣿⠂⠷⢲⣿⠿⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠉⠲⠃⠀⠀⠀⠀⣀⢥⢵⢂⢹⡇⢀⠐⡈⠙⢧⢹⠉⠀⠀⠈⠀⠀⠉⢱⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢳⣿⣿⡬⣀⣙⢸⢸⣇⠀⣤⢱⣰⡞⠚⣶⡆⢤⣤⣤⣤⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡼⣿⠹⡗⢻⣼⣿⠀⣽⠀⣿⡐⡏⢃⠀⣿⡧⢴⡁⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣞⢢⡄⣿⠐⣋⣻⣿⡟⠳⣯⡀⡼⠿⢃⠄⠁⣿⣷⠰⡅⢿⣿⡚⡿⡄
⠀⠀⠀⠀⠀⠀⢀⠞⢀⠢⡈⠏⢠⢄⣿⣿⡗⢄⠈⠛⢦⡀⠀⠀⠀⢻⣿⠂⠂⠘⣿⣇⠈⠙⢆
⠀⠀⠀⠀⢀⠤⠋⠠⠠⠁⡐⠀⠴⢸⣿⡟⣮⡀⠀⠀⢀⠉⠘⠦⣴⠸⣿⣗⠚⡀⠹⡟⠂⠀⠀⢹⣦⣄⡀
⠀⢀⡠⢆⠡⠀⠀⠁⠀⢐⠂⢀⢠⣿⡞⠁⠨⠻⢆⡀⠀⠈⠀⠈⢌⠂⣼⣿⣗⣣⠀⠑⡄⠀⠀⢐⠧⣿⠉
⠘⠀⠱⠈⢦⠀⠀⠀⡠⠀⢀⢀⣴⣿⠁⡀⠀⠀⠀⣹⡖⣤⣀⠀⠀⠀⣺⢿⣿⢀⣥⠀⠈⢢⡀⡞⠀⡿
⠀⠁⡀⠙⢄⠳⣤⠍⠀⠀⢁⣼⣿⢿⠐⡀⣤⠶⡁⣼⡟⣿⠉⣹⢦⡄⡿⠘⣿⣦⠤⢆⠀⠀⠙⠋⢠⠏
⠀⠀⠈⠢⡈⠑⠎⠀⠠⢀⡴⣿⠋⢸⡏⠝⠠⠐⣼⣿⡇⡻⢂⠀⢊⢹⡇⠀⢸⣿⡗⠚⡄⠀⠀⠈⠿⠅⡼
⠀⠀⠀⠀⠈⠒⠀⠐⢠⡾⢿⠏⠀⢸⡂⠀⢀⡜⠃⢸⠀⠁⠷⣀⠀⣺⠇⠀⠀⢹⣿⣗⡑⢄⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠈⣰⡺⠟⠃⠀⠀⠸⣋⡠⠋⢀⣀⢀⢀⣀⣠⠵⣂⣿⠀⠀⠀⠀⢷⣿⡦⠘⡀
⠀⠀⠀⠀⠠⢀⣼⢩⡝⢀⡀⠀⣤⠘⣯⡁⠐⠠⠬⠿⣭⡯⢿⠞⣩⣩⡄⠀⠤⢀⠀⢻⣿⣖⣉⢆
⠀⠀⢀⠀⢠⣾⡿⠊⡅⢎⣁⠛⢤⠌⡃⠈⠙⠚⢦⠶⠶⡶⢾⣭⡀⣄⣈⠛⠴⢄⡠⢈⢿⡿⠦⠄⢃
⠀⠀⠂⠄⣸⣿⣁⠂⢽⠀⣥⡚⠠⠌⣙⠉⠉⠀⣾⠀⢸⠿⣀⡀⠹⡇⣡⠛⢰⢌⠁⡼⠀⠛⠟⡓⠋
⠀⠀⠀⠀⠈⣹⠇⡁⣹⠀⡧⠌⡁⠦⣩⠄⠐⠊⣽⡀⢸⡅⠀⠈⢻⠶⢁⡘⠢⢌⠀⢠⠀⠁⢺⡇
⠀⠀⠀⠀⠀⠘⠋⠀⡾⠀⠃⠄⣉⠶⠘⠒⠀⠈⢁⡟⣅⠋⠀⠈⡛⠰⠆⡌⠁⠦⡄⠀⡀⣀⠚
⠀⠀⠀⠀⠀⠀⠀⡹⠃⠚⠃⠀⠈⠀⠈⠁⠀⠘⡆⠘⠁⠀⠈⠈⠉⠀⠐⢦⡙⠂⠈⠘⠄
⠀⠀⠀⠀⠀⠀⠚⢻⠟⡗⠊⡤⠶⣶⠀⢷⣿⢺⠇⢤⠀⢭⡖⣶⢲⣿⢾⣷⠿⠒⠶⡶⢻⠦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢷⢟⣍⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣾⣿⣆⠉⢤⠀⣶⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⡀⠘⣿⣿⣷⠈⣰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡁⢁⡜⠑⠒⠊⡙⢏⠁⠉⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⡟⠁⢀⡀⣖⢁⡀⠐⢴⣿⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠚⡇⠰⠚⠂⠀⠰⠲⠢⢸⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠈⣹⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣆⠀⠐⠒⠒⠀⣠⣎⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡿⠇⠀⠀⠀⠸⠟⠁⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠈⢻⣶⢶⠐⠈⠀⠀⠀⠀⣏⣈⡗⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠙⣄⠠⠄⠀⠀⣔⢶⠴⠅⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⡟⣿⠀⠀⠀⠀⠀⡬⠂⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣶⣌⣥⣧⢳⣸⠀⠀⠀⠀⠐⠈⠂⡠⡄⠀⠖⠀⣀⣠⠤⣴⡾⣀⣤⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣶⣻⣿⢟⠙⠻⢷⣿⡀⠀⠀⠉⠁⠀⠀⠀⠙⣆⠀⠈⣿⣿⡿⣫⣾⣿⡿⢀⡀
⠀⠀⠀⠀⢦⣤⣹⢿⡿⡫⠂⠀⣀⠈⠲⣿⣷⣄⣀⡴⠀⠀⠀⠀⠀⠈⢧⡀⣿⣿⣧⢿⣿⣯⣿⣿⠁
⠀⠀⠀⠀⠸⣿⣿⣷⡵⠁⣰⣦⠃⢙⠀⣯⣿⠟⠋⠀⠀⠀⠀⠀⠀⡴⠀⠓⣿⣿⣿⢾⣿⣿⣿⣯⣤⣤
⠀⠀⠀⠀⣀⣙⣿⣿⢳⠁⠁⠀⠀⡆⡆⠈⠁⠀⠀⠀⠀⠀⢀⡠⢚⣤⣾⢠⣿⢿⣿⡟⣿⠿⣻⣿⠛⠁
⠀⠀⠀⠀⠉⢻⡟⣿⣾⣶⣿⣶⣦⣕⢡⣧⣶⣶⣶⣦⣄⣴⣷⣾⣿⣿⣿⢸⣿⣿⣿⣿⣱⡿⣿⡿⠟⠂
⠀⠀⠀⠰⠿⢿⣿⣮⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⡏⣿⣿⣟⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠾⠿⣿⡿⢿⣟⣻⣻⣿⣗⣙⣻⡿⢟⣛⣛⣫⣭⣭⣛⣷⣿⡏⣷⡉⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⣹⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠃⠸⠿⠣⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠺⠿⠟⠛⠁⠀⠉⠛⠛⠻⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⣼⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⢠⣿⡿⠿⠛⠛⠿⢃⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠈⣿⠿⠟⢋⣉⣤⣤⣶⣾⣿⣷⡀⢺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣿⣿⠇⠹⣿⣿⣿⣿⣿⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣈⣉⣙⢋⣠⣄⡙⠛⠻⠿⠟⠀⠹⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣦⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣧⠀⣉⣉⣉⣙⣛⠁⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⠻⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡛⣛⣛⡛⢛⣻⣿⣿⠿⠿⢿⡿⠿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⢰⡿⣋⡉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠂⢈⡁⠀⠀⠹⠆⠀⣻⣇⠀⣉⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣞⣶⡏⡠⠀⣴⠈⣼⣷⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠙⠻⠛⠦⠀⠜⠛⠰⢟⡤⢱⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣰⠇⢀⡠⠒⠁⠊⠶⠀⢤⣖⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣾⠏⣰⠆⠀⠀⣆⠀⢸⣿⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠃⠀⠉⠛⠁⠀⠛⠛⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⣠⡀⠂⠀⢰⣿⣿⡿⣄⠀⠀⠀⠀⢀⠐⠀⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣠⣠⣤⢀⣶⠸⢶⡤⠛⠳⢾⠁⠀⠰⣶⣛⣉⠛⣿⠋⠀⣄⠀⠛⠀⣁⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⢀⠰⡟⠁⢼⠿⠦⡀⠀⠉⣸⠟⣽⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⢰⡤⠀⢾⠃⠀⠀⢠⠀⠀⠀⢀⡇⠀⠤⠀⠂⠙⣽⡿⠋⣼⣯⠖⠒⢤⣀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⡄⠀⠸⣄⠠⡿⠿⠄⠀⠀⣼⠇⠴⠗⡀⠀⠰⣼⣥⠼⡏⠀⠀⠀⢀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⡶⠀⢀⢰⣄⠀⠀⠋⠰⢆⠀⠀⣠⠿⠙⣧⡀⠀⠀⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡶⠈⠀⠀⠐⣀⠀⠀⠀⠀⠙⠁⠀⠀⠘⣠⠄⠎⠁⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣳⣄⣴⠈⠁⢠⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⣠⡄⠛⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢼⣿⡇⠈⠀⡄⠀⠁⠀⠀⣿⠐⢰⠈⠑⠲⠖⣣⡟⢀⠀⠀⠀⢶⣠⡤⠐⢀⡦⠒⠈⠉⠁⠀⠀⢁⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣀⡿⠀⣦⠀⠃⠈⡆⠁⠀⢻⡀⠘⠀⠀⠸⠋⠙⡇⠈⠀⠀⠀⠘⣿⡗⠀⠀⢰⡆⠀⠀⠀⠀⢀⠀⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠴⢀⡀⠀⠀⡃⠀⠀⢩⠀⠀⢼⢀⠀⠀⠰⠀⠀⢹⡃⢈⡀⠰⢄⡀⠀⡄⠀⠀⢆⠀⠀⢸⡇⠀⡀⢸⡇⠀⠀⠀⠀⠈⠀⠲⡜⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⠀⠀⣴⠰⡄⠀⠀⠀⠀⣾⠆⢸⡇⠋⣈⠀⢀⣉⠒⠈⠁⠱⠀⣈⠀⠀⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣏⠀⠀⣹⠤⡇⠀⠀⠀⠎⠟⢀⣿⣹⣿⣻⠆⣶⡿⢋⠛⠖⠒⠲⡏⡁⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠛⠋⠀⠀⣿⠀⣠⡀⠀⠀⢀⠄⠈⠁⣬⢦⢙⠁⠻⠁⡈⠀⠀⠄⢀⡚⠉⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠀⡛⠀⠁⡀⠘⠀⠀⣦⣟⢀⡀⠀⢸⡀⠀⠁⢄⠀⠈⠃⠀⠀⠀⢀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣌⠀⠀⠀⠀⠸⠆⠀⢛⡏⠈⠏⠀⢰⠀⠃⠀⠀⠙⣦⡔⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⠆⠀⡶⠰⡦⢺⡄⠀⢹⣆⠀⠀⠀⠘⠀⠀⠀⠉⢶⡈⠁⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠸⠂⠀⠀⠀⢠⠁⠀⠀⠂⠀⠀⠀⣋⠀⣠⠆⠀⢄⡈⣆⠀⢻⡟⠀⠇⣠⡟⠲⡄⠀⠀⣀⠿⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⡶⠀⠀⠀⠘⠀⠤⢴⡇⠀⠀⠀⠁⠀⢹⢀⡤⠈⠀⠱⣄⡨⣅⠋⡰⠏⢀⠀⠈⢢⡄⠉⣦⠀⢀⡀⠰⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⢀⣴⠶⠷⠄⣀⣼⠃⠀⡻⠛⠁⠀⠀⠀⣨⡿⠛⢿⠟⢻⣏⠀⠀⠀⠘⡆⠀⠀⠉⢁⡆⠀⠰⠿⠁⢀⡆⠀⠀⠀⠀⠀⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠙⡄⠀⠂⠉⠉⠁⠒⠂⠒⠒⠶⠶⠳⡀⢰⠀⠀⠀⠿⠇⣀⣨⣶⡶⠛⠣⣄⡀⠀⠈⠀⠐⠀⠘⠃⢰⣿⣧⠐⠚⠃⠉⠴⠂⣄⡀⢀⠙⢁⡉
⠀⠀⠀⠀⠀⠀⠐⠈⡄⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠘⢿⡀⠄⠀⠀⠀⠐⣇⠸⠏⠁⠀⠀⠀⠀⠠⠀⣾⣷⣿⡶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣸⡄⠀⠀⠀⠀⠀⠀⢘⠇⡀⠀⠀⠈⠁⠀⠀⠀⠀⠐⢁⠀⢀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠻⣧⡆
⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⡄⠀⡘⠀⠀⣟⡟⠁⢸⠀⢀⠀⠀⠀⠘⠀⢰⡄⠀⡀⠀⠀⠀⠀⢀⡼⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠘⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠁⠈⠀⢦⠀⠘⠁⠀⠙⢀⡸⠀⠀⠀⠀⠀⠸⠖⢦⠁⠀⢠⣴⠛⠁⣀⠀⠈⠂⠁⠀⠀⣼⣿⠗⠀⠀⠋⣠⡀
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠈⠁⣄⠀⠀⠀⠀⠶⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⡀
⠀⠀⠀⠀⢠⠀⢀⡇⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⠙⢀⣠⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠆⠀⠀⡘⠛⠻⠇⠀⢠⡀⢀⣿⡟⠁⠀⠀⠀⠀⢠⡄⠀⠘⠎⠀⠀⢠⠄⠧⠀⠀⠀⠀⠀⠈⠀⣀⡀⠀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡜⠀⠀⣀
⠀⠤⠀⠀⠙⠀⠀⠀⡄⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⢻⣤⠀⠀⡀⠀⠆⠀⠀⠀⢠⣴⠀⢀⠀⢀⠟⠉⣟⡀⢲⡄⠀⢰⡤⠀⠀⠀⠀⢠⡔⠁⠸⠀⠀⡄⠀⠁⠂
⠐⠀⠀⠀⠀⢺⣟⣹⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠈⠀⠀⠐⠀⠠⠆⡉⠀⠀⢸⠖⠋⠀⠈⠙⠛⠻⡿⠒⠁⠀⠀⠀⠀⠀⢠⠉⠀⣤⡄⠀⢳
⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣋⢤⡐⠧⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠉⠀⢀⣦⠠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣠⣤⠰⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢿⡧⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠖⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠀⠀⠀⢀⡴⠒⠲⡄
⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⣤⣀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣿⠀⠀⠀⢻⠀⢠⣾⠂⠀⢠⣿⣧
⠀⠀⠀⣠⠴⠋⣉⣐⣦⣀⢦⡈⠳⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⣹⣦⣀⣀⣸⣀⣸⣿⠀⠀⢸⠘⣿⡄⠀⠀⠀⠀⢀⣤⣄⡀⠀⣰⣶⣄
⠀⠀⠀⠈⠓⠦⣄⣩⡟⠋⣽⣫⠽⠋⠉⠉⠉⠉⠉⢹⣿⡴⢺⣿⠀⠀⠀⡼⠀⠈⣿⠀⠀⡞⠀⣿⣧⠴⠋⠉⠉⠉⠛⠛⠉⠉⢹⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡤⢺⣿⠀⠘⣿⣄⣀⡼⠁⠀⠀⠙⠓⠚⢁⠴⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠞⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢣⡶⠴⠀⠀⠤⢦⡜⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠊⣁⣘⡠⣀⡤⠄⣒⢄⣃⣈⠓⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡼⣛⣭⠥⢴⢰⠁⠀⠀⢘⡎⡤⠬⣽⣻⢧⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡻⡯⢁⢸⣸⠾⡸⣆⠀⢀⣰⢧⠳⣇⡇⡈⢽⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⣿⡤⠿⠒⠻⠮⢟⡯⠵⠛⠒⠯⢤⣿⠞⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣧⠃⢉⣠⠴⠚⠈⠐⠀⠀⠀⠀⠂⠁⠑⠶⣄⡉⢘⣼⣀⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣀⡀⠈⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠉⢀⣀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠩⠈⠪⢳⣸⢁⡤⠶⠶⣶⣦⠀⠀⠀⠀⣴⣶⠶⠶⢤⡈⣇⡞⠕⠑⠉⠢⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⢀⠔⠢⠅⣲⡗⣁⣴⣶⣴⣢⢤⠀⠀⠀⠀⡤⣔⣶⣶⣦⣌⢺⣖⠌⠔⠢⡀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⣀⠤⢸⠗⠟⡛⢿⣭⣍⢿⡇⠀⠀⢸⡿⣹⣯⡽⢛⠻⠺⡇⠤⣀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡆⠀⠙⠶⠶⢟⠞⠁⠀⠀⠀⠳⡻⠶⠶⠋⠀⢰⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⢷⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⢄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⢄⠀⢀⣷⡄⠀⠀⢇⡰⠀⠀⠀⠀⢆⡰⠀⠀⢠⣾⡀⠀⡠⠤⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⡲⡄⠈⠁⠀⠀⠀⠀⠈⠀⠢⢖⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠲⣉⠜⡻⢢⡄⠀⠀⠀⠀⢠⡜⣟⠣⣀⠖⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣍⠛⠥⣧⣴⡀⠀⠀⠀⠀⠙⢬⠛⢩⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣠⣹⣄⠀⠀⠀⠀⠀⠉⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⠤⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣟⢩⣵⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠡⣿⠰⢬⢿⡑⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣶⢠⡌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⣼⣶⣆⠀⠀⢀⡇⠀⠀⢀⣿⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠏⠉⠁⣺⣿⠄⢀⡙⣫⡜⠿⡿⠟⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠍⠀⠀⠀⢻⡇⢠⣎⡹⢯⡻⠷⣚⡷⡀⢰⠿⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢛⡃⣀⡀⠀⣐⣧⣄⠹⣷⢂⠉⣹⣥⠿⢻⣷⣿⢧⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⡧⠈⣯⣵⣾⣤⡌⠻⢾⡿⣃⣴⣌⠻⠋⠈⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⣿⡀⣉⣡⡙⢿⣿⣷⣭⣾⣿⠟⣡⠂⠀⠀⠀⢻⣿⣿⣦⡀⠀⢀⣀⣤⣴⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡽⣿⣿⣷⢏⣹⣿⣗⡬⣙⣻⡏⣴⠾⢟⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⡜⠻⣿⣿⠒⣿⣻⣿⡱⣾⣿⣿⣷⣄⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠙⣿⣿⣏⢻⠌⢿⡟⣺⣧⢻⣷⣮⣟⠻⠿⠿⣃⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠘⢿⣿⡄⠾⠾⢿⣡⡝⢫⡻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠙⠛⢲⠰⡿⠿⣶⡞⣻⣿⣟⡿⠿⠿⠿⢟⡁
⠀⠀⠀⡿⣦⣀⢀⣀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣣⡴⠟⠻⣷⣯⣨⡿⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠱⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⣛⣂⣽⡿⣷⣾⣋⡿⣿⡇
⠀⠀⠀⠀⡇⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣧⡼⠟⣿⣧⣾⠁
⠀⠀⠀⠀⢣⡙⣿⡿⢛⡅⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡏⢸⣾⡟⢻⢷⣿⡍⢳⣧⠄
⠀⠀⠀⠀⠀⠙⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⣿⣧⣧⢸⣖⣯⠻⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⢸⣿⢇⣿⢸⣿⠸⣧⣬⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢙⠻⢋⣿⡟⣼⡿⢸⣿⡇⣿⢸⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⣧⣘⠛⣵⣿⢃⣾⣿⣇⣿⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⣿⣏⣾⣆⡛⢃⣾⣿⡿⣹⡿⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢺⣿⠿⣿⡇⣿⡘⠿⠟⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢋⣫⡄⠀⠘⠛⣿⠁⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠂⠛⠓⠟⠛⠂⠀⣀⣴⣿⡿⠟⠀⢀⣤⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠠⡀⠀⠀⠠⠂⠒⠀⡄⠀⠁⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠁⢰⠒⠂⠒⠀⠀⢂
⠀⠀⠀⠀⠀⠀⢐⠉⠐⠀⠀⠀⠀⠠⠁⠀⡀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠠⠄⣄⠀⠀⠀⠤⠐⠀⠠⠀⠠⠠⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⠀⠃⠀⡐⠁⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠃
⠀⠀⠀⠀⡀⠀⣀⠁⠄⠀⠀⠉⠀⢀⠄⠀⠀⠰⠀⠀⠘⡀⠀⢀⡀⠤⠒⠇⠀⠀⡄⣀⠈⠀⠀⠀⢡⠀⠀⡰⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠂⠀⠀⠀⠀⠑⠀⠂⠁⠀⡄⠀⠀⠀⠑⠂⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠃⠒⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⠀⠠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠀⠀⠀⢀⠀⡄⠒⢤⢀⠀⠀⠀⠀⠀⢐⣰
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠃⠁⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢈⢉⠣⡀⠇
⠀⠐⢄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠐⠤⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⠀⠀⠀⠢⢀⠂⠀⠀⠀⠀⠐⡄⠂⡀⠀⡡⢄⠀⠀⠀⠀⠀⡠⠤⠄⡀
⠀⠀⠀⠈⠀⠐⠁⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠑⠰⢉⡈⠄⠐⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄⠀⢀
⠀⠀⠀⠀⠒⣤⠒⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡎⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠐⠀⠒⠁
⠀⠀⢄⠈⢢⠦⣔⠁⡰⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠠⠄
⠀⠠⠌⣠⠝⠰⢂⣈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⢀⡠⠣⠀⡀
⠀⠀⠀⠠⠄⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⢀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⢢⠀⠀⠀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⠀⠀⢀⠤⠄⡀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⢁⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄
⠀⠀⠀⠐⢄⠀⠁⠀⠀⠀⠀⠢⠀⠀⠠⠊⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠀⡀⠆⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠡⠀⠐⠈⠀⠀⠀⠀⠀⠃⠄⠁
⠀⠀⠀⠀⠐⢠⠉⢒⢀⠆⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠔⠠⠰⣅⠀⠀⠀⠀⡐⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢄⡀⠄
⠀⠀⣀⡀⠁⢠⠄⠐⠢⢀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡡⠊⠀⠀⠀⠀⠀⠈⠁⢀⠀⠒⠀⠀⡐⠀⠀⠀⠀⠀⡠⡅⠙⢠⠁⠀⡃⠜⠠
⠀⠈⠄⠈⠖⠀⠀⠀⠀⠈⢃⡀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡅⠀⢀⠂⠉⠁⠢⠀⠀⠈⠀⠀⠀⠜⠀⠀⠀⠀⠀⡀⠴⠐⠦⡀⠆⠬⠁⣀⠈⠰
⠀⢀⠦⠠⢆⠀⠤⠀⠴⠀⡈⠀⠢⠈⠀⠀⠔⠁⠀⠂⠁⠀⢀⠃⠀⠐⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠆⠠⠤⢄⡀⡀⢅⡀⠈⠱⠄
⠀⠈⠰⠁⢀⠱⠤⢤⡄⠊⢋⠐⡆⠀⠀⠀⠈⠢⠀⣀⡀⠀⠊⠡⡀⠀⠀⠈⠁⠀⠀⢀⠴⣀⡀⢠⠀⠀⠀⠀⠀⠀⠈⠚⢀⡠⠎⠀⣧⠀⠑⡈⠄
⠀⠀⠀⠀⠁⠼⡀⣤⠈⠦⠜⠀⠀⠀⠀⠥⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⢂⡠⠂⡐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⣻⣟⣿⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣽⣯⣿⢷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⢀⣀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣿⣿⡏⢘⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⡿⢿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣾⣿⣿⣿⡆⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠾⡿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⠿⡿⠟⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠒⡗⠂⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⡀⣀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣶⣨⢫⡛⣉⡤⠦⣍⡙⡿⣁⣴⣦⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣿⣿⠛⢋⣴⣠⣟⠛⢿⣿⠗⠛⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠖⠻⠃⠀⢘⣿⣫⡟⠀⠘⠛⠷⢿⢠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣯⠻⡄⠀⠀⣶⣟⢻⣿⡄⠐⠀⣚⣼⣿⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠛⣽⠋⢠⣾⣴⣿⡝⢏⣿⣧⣾⣄⠉⡾⡻⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣠⣴⣉⠾⠟⣻⢿⣻⣿⡻⣿⠋⠼⣃⣶⣁⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣈⡦⠀⠄
⢀⠆⠁⢦⡀⠀⢠⣶⠀⠀⠀⠀⢤⣒⣂⣀⣀⠻⣃⣸⣏⡴⢾⣿⣸⠁⠀⣹⢾⣿⠶⣬⣏⣀⠿⠃⣀⣐⣒⣢⡄⠀⠀⠀⠀⠘⣧⣀⣶⠉⠀⡠⠆
⡇⠀⠁⠀⠙⠂⡻⢿⡀⢸⣳⣠⠟⠉⠁⠹⣟⢳⣿⣿⣿⠻⡄⠻⣮⣳⣶⣩⡾⢁⡾⢛⣿⣿⣶⠻⡿⠀⠉⠙⢦⣀⡀⠀⠀⣀⠀⢻⣿⣦⠂⡀⠂
⠡⠀⡄⠀⠀⢨⣹⡞⠁⠠⣿⡏⠀⠐⠃⢠⣅⢘⢙⣷⣬⢳⡈⢀⠀⢀⡾⠀⡄⠈⣴⣋⣵⡟⢃⢐⣅⠀⠡⠂⠘⣿⣧⠒⠰⣥⢾⠀⠈⠛⠉⠉⠃
⠀⠛⠀⠀⠀⢸⠏⠉⠀⠀⠙⢧⠀⠀⠀⣿⣿⣏⡷⣽⣹⡷⠄⢰⡆⠀⠀⠠⣟⠀⠺⣯⣫⡟⣹⣿⣿⠇⠠⡀⢠⠟⠀⠀⢠⠿⠊⡠⢀⣀
⠀⠀⠀⠀⢠⡀⠌⠀⠀⠀⠀⠘⢦⡀⠀⠈⠛⠋⣰⠈⠁⠀⠀⠉⠁⠀⠀⡀⠉⠀⠀⠀⠁⢴⠉⠛⠋⠀⣠⣡⠇⠀⠀⠀⠀⠀⠘⠑⢚⡇⠂
⠀⠀⠀⡣⢀⣿⡄⠀⠀⠀⠀⠀⠀⢠⡀⠠⠄⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣴⡆⠀⡰⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠹
⠀⠀⠀⢀⠀⡙⠀⠀⢀⠀⠀⠀⠀⢠⡷⠂⠀⠀⠓⣇⠐⠀⢠⠁⠀⠀⠀⠀⠀⠀⣤⠆⢰⡓⠁⢰⣄⠘⠃⠀⠀⠀⠀⡸⠋⠀⠀⠀⣀⠆
⠀⠀⠀⠘⣀⠁⠀⠀⠹⢦⠀⢀⠀⠐⠁⢀⠀⡀⣰⡿⢓⢀⡶⠀⠀⡀⢀⠀⠀⣰⠆⢴⠻⣇⠀⣴⡇⠈⢲⣤⣀⡀⢰⣿⣦⡀⢠⡾⠁⠀⠁
⠀⠀⠀⠀⢃⣴⡀⠀⢠⡾⢦⡘⣶⠀⡀⣣⠀⠄⠋⠠⠄⢼⡇⠀⠀⠀⠀⠀⣴⠋⠐⠋⣀⠉⠛⠁⣟⠀⠘⢿⣿⡆⠀⠙⢋⣽⣟
⠀⠀⠀⢰⣿⡏⢻⣞⠛⢉⠂⠉⠻⡗⠉⠀⠀⠀⢇⠀⠀⢼⡇⠀⠀⠀⠀⣼⠃⡔⠉⢉⠉⠙⢦⠀⢨⡁⡀⠘⠿⣿⡀⠠⠦⠀⠈⢀⡂⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⣦⡀⢀⠀⠀⠀⢀⡠⠎⠰⣇⢾⡇⠀⠀⠀⠀⢿⠀⠀⠀⠈⢦⠀⢸⡇⢸⡇⠀⣠⣼⡏⠁⢶⡀⠞⢠⣄⠐⣈⢱⣶
⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠆⠹⣿⡀⠀⠘⠋⠀⠀⣰⣷⡾⢿⣆⠀⠀⠀⠀⠑⠂⠀⠀⠼⠀⣼⡁⣸⡇⠀⣿⠀⠉⠈⠉⠓⠂⠀⠉⠉⠉⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢳⣿⡀⠀⡀⢀⣤⣾⣿⣌⠳⡈⠛⢦⢀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣻⣿⣴⠂⠀⠁⠀⠀⠁⠀⠀⢠⣄⠀⠁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⠋⠾⠳⡶⢿⠇⠈⢿⣽⣧⡘⣤⡀⠁⠘⠃⠐⠒⠚⢉⡴⢉⣶⣯⡿⠉⠠⣾⣠⡼⢶⠂⠐⠂⠀⠰⠂⠠
⠀⠀⠀⠀⠀⠀⣠⠤⠚⢡⠀⠀⠀⠈⠓⢀⡟⠀⠀⠈⢻⣿⣿⡟⢿⣷⣄⣤⣄⣴⣿⠟⣱⢿⣿⠟⠀⠀⠀⠹⡇⢳⣄⠀⢀⣠⠈
⠀⠀⠀⠀⣰⠋⠈⠀⣘⠂⠠⣤⣀⣀⡤⠊⠀⠀⠀⠀⠀⠹⣿⣷⡤⠻⣿⡏⣩⣿⠻⢴⣽⣿⠁⠀⠀⠀⠀⠀⣇⠀⠙⠛⠟⠃
⠀⠀⠀⡘⣅⠐⠤⠜⠁⠀⠀⠈⠹⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢀⡟⣡⠋⢱⡌⣳⠂⣹⠁⠀⠀⠀⠀⠀⠀⣿⣷⣶⡿
⠀⠀⢠⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⡷⡀⠀⠀⠠⢿⡛⠉⠀⠀⠀⠀⠀⠀⠀⣼⡇⠑⠒⠒⠒⠂⣀⣀
⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠠⢜⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠻⢦⡴⠗⡎⠁⠀⠀⠀⠀⠀⠀⠀⠠⠿⢀⣤⡶⠮⠙⠃⠉⠙⠷⣦⣀
⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢋⠔⠂⠀⠀⠀⠀⠀⠘⡎⢶
⠀⠀⢡⣼⠀⣆⠀⠀⠀⠀⠀⢰⡀⠀⠈⢺⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠁⢀⣠⠔⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣿⠀⢻⡄⡄⠀⠀⢂⠀⠂⠀⠀⠈⢿⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡀⣤⣾⣭⣶⡿⠛⠀⠶⠒⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⣿⡄⠀⠀⠰⡀⠀⠈⢣⡀⠑⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣢⣤⣲⣬⡴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠉⣿⠀⠀⢢⠹⣦⣄⡀⠙⠲⢄⣀⣀⣤⣤⣶⣿⣿⣿⣶⡶⣶⡞⢃⣩⠤⠈⠉⠁⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡴⢎⠳
⠀⠀⠀⡇⢸⣇⠀⠀⠣⡈⠉⠭⣻⣿⢟⡽⢋⠝⣡⡴⣶⣟⠕⣋⣴⢿⡟⢫⠁⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⠐⠢⠤⠤⠤⠤⠄⠒⠎⠋⢀⠌⠁
⠀⠀⠀⠹⣦⣿⣆⠀⢀⡈⠛⠚⠉⠁⢀⡔⢡⣞⠏⡰⠿⠿⢞⢩⡏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠙⣠⠴⠉
⠀⠀⠀⠀⠈⠙⢿⠷⣀⠙⠛⢲⣶⠾⠁⢠⡿⠋⣰⡃⣤⠀⠂⠀⢷⠀⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂⠀⠒⠴⣶⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠢⣄⡘⣋⢉⡁⠤⣸⡿⢿⣾⣇⡟⠉⣡⠀⠀⠈⠶⣌⣧⠀⠑⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣤⣴⣻⡟⢻⡾⢟⠟⣥⠊⠈⠃⠀⠀⡠⠉⠙⠷⠶⠾⠿⠿⠶⢶⣄⠐⠤⢤⡀⣰⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣧⠾⢋⣵⠇⠀⣿⠃⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⡟⣁⣠⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠘⢀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⢠⢤⠹⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠊⠀⣀⠈⠉⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡈⠲⢀⡆⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠒⠦⠀⠀⠀⢀⣈⠋⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⡄⠀⠀⠁⠀⠈⠀⠁⢂⠆⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠐⠘⠂⣀⠀⠐⠂⠀⠠⠪⠀⢤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢠⠲⠊⠀⠀⠀⡈⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⡀⠀⠀⠀⠀⢀⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡥⡈⠑⠂⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠊⡦⠠⢆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠁⠀⢁⠀⠈⠑⠦⢤⣀⣁⠨⢶⣄⠀⢀⠒⠂⠒⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠊⠁⠀⠀⠀⢀⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠒⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡔⢁⠠⠈⠑⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠑⠈⠗⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⣈⠴⡀⠐⠀⠀⠀⠀⠀⠀⠈⡘⠒⠠⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⠼⠒⠤⣀⠀⠀⡀⠐⠀⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢰⢰⡆⡆⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣝⢎⣼⣼⣧⣱⡱⣫⢞⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⠢⢟⣾⣿⠫⡉⣩⢙⠿⣽⡫⠖⠃⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣣⠇⣼⠀⢳⡱⠈⣙⠠⣾⡟⢻⣯⠔⡫⢄⠞⣼⠇⠹⡜⢆⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣝⠦⢱⡈⢮⡰⣝⠧⣀⠹⠷⠾⡃⣠⠝⣫⡮⢉⣇⣙⠸⣮⡛⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠐⢻⣿⢻⣶⢁⡌⢓⣂⣠⣤⣬⣄⣒⠺⢁⡵⣿⡟⣿⡯⣁⠙⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢁⡴⠀⠠⡙⠛⢉⡴⠞⠛⠉⠉⠉⢉⡉⡹⠛⡿⣷⡛⠛⠉⣤⢄⠰⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢧⢉⣐⠖⢜⣼⠛⠉⠀⠀⢀⠠⢒⡱⠊⡀⠀⠀⠉⠹⣶⡰⠉⣊⠱⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡁⣿⣿⡿⣜⠃⠀⣀⠤⢚⣤⣾⡿⣿⣷⣬⡓⠤⣀⠀⡸⢧⣿⣿⣷⡈⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡼⣉⠆⠡⣼⠁⣂⣍⣒⡻⠷⣬⡙⢧⡾⣋⣤⠾⢿⣾⣥⣀⢈⡞⠉⠰⡔⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⡏⠻⣿⣿⣿⡿⢶⣬⣻⣄⣸⣏⣥⣶⣾⣿⣿⣿⠋⢿⡿⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⠈⠉⢀⣴⣶⣤⡙⣯⡿⢁⣴⣶⣤⡈⠉⠀⠀⠄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣷⡀⠀⢿⣏⠀⣹⡇⢸⡄⣿⡁⠈⣿⡇⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣼⣷⣤⣈⡛⠛⡋⣴⣿⣷⣌⡛⠛⢋⣀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡀⣽⡟⣼⣿⣿⣿⡏⠠⣿⣿⢿⣿⣿⣿⣿⡮⣿⡇⣁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⣿⣿⣟⢹⣿⣰⣷⣤⣴⣾⣿⣿⢻⣿⣷⣿⡇⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠘⣿⣿⣿⣦⣈⠉⠉⠁⠉⠉⢉⣠⣾⣿⣿⡿⠁⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣤⣤⡀⢡⠀⠈⠻⣿⣭⣛⣿⣿⣿⣿⣿⣿⣛⣽⡿⠟⠀⢠⠊⣠⣤⣤⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣿⣿⠇⢠⠚⠓⠶⠤⣌⣉⣉⣉⣉⣉⣉⣉⣉⣥⠤⠶⠂⢺⠀⢿⣿⡿⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⡄⢤⣐⠊⠲⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⡴⠋⠑⣤⠄⢤⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢰⡆⢿⡆⠀⠈⠙⠲⢤⣀⣀⡀⠀⠀⣀⣀⡤⠶⠛⠁⠀⠀⣸⡇⣺⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡇⢸⢧⠀⢻⡓⠶⢤⣤⣀⣉⣉⣉⣁⣀⣤⡤⠖⣾⠇⠀⡟⡇⢺⠀⡝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⢸⡇⢸⢸⡄⠀⠙⢦⣀⠀⠀⠈⠉⠉⠁⠀⢀⣠⠞⠁⠀⣸⢃⠀⢹⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⡇⠀⡀⣷⠀⠀⠀⠈⠙⠲⠖⠶⠖⠶⠊⠉⠀⠀⠀⠀⡿⢸⠀⣹⡀⢸⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⠀⢸⡇⠀⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠀⢿⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⠀⢸⡇⠀⢀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡆⠀⣽⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⢸⡇⠀⠘⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠃⠀⣻⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣾⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⡀⠈⠁⠀⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⠀⠈⠀⠀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣤⣤⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠛⣯⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢋⣹⣥⣍⣽⡏⠴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⣾⣶⣦⡍⣉⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣦⣠⠀⠀⠀⠀⡆⠀⠀⠀⣷⣿⣿⣿⣿⣶⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠓⠒⠠⣼⣷⡀⠀⠲⡟⣠⣾⣿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⠟⠀⠀⠀⣿⡏⠀⡹⢷⡞⣿⣬⣭⣴⡄⠀⣠⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠀⠀⠀⠀⢨⡅⡘⢷⣇⡝⠲⠷⡖⣫⣴⣴⣯⣶⡘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣴⣶⡄⠰⡶⢟⣵⠄⠻⢶⣂⣶⡿⢋⡀⢿⣿⠋⠇⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣽⣿⣇⠐⡿⠛⢿⣿⣷⣄⠽⢋⣴⣿⡷⢀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣄⣶⢾⣦⣙⠻⣿⣿⣿⠟⣋⣴⡇⠀⠀⠀⠀⢿⣿⣿⣷⣤⣤⣤⣶⣾⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⣿⣿⣿⢠⣼⣿⣿⢛⣶⢼⣷⠾⢛⣩⣶⣶⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣿⣦⣈⢿⣿⣍⣻⡎⣿⣯⠻⣿⣿⣿⣿⣦⠀⠀⠀⠈⠛⠛⠿⠿⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠘⣿⣿⣧⠙⣁⢻⣯⣽⢻⡜⣿⣿⣶⣭⣙⣛⣯⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠈⠿⣿⣆⠛⠛⣻⣦⠶⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠄⡀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠈⠉⢻⠘⠗⠛⣷⡟⢸⡿⣿⣝⣛⣛⣛⣛⣥
⠀⠀⠀⢿⢲⣦⣀⣠⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣱⡞⠛⣙⠿⣿⣄⡿⠻⣿⣿⣿⣿⡏
⠀⠀⠀⠈⠆⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣙⣃⡸⡽⢿⣿⣟⣬⡻⣿
⠀⠀⠀⠀⣼⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⡟⢙⣿⣾⣏
⠀⠀⠀⠀⠸⡜⢿⡿⢟⡡⠂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⢸⣧⣿⢛⡿⣿⣯⠙⣾⡶
⠀⠀⠀⠀⠀⠈⠳⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⠀⣷⢺⣝⢿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⢷⣿⡏⣿⡆⣿⡏⢿⡤⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠛⠿⠟⣾⣿⢱⣿⠁⣿⣿⢸⡇⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⣧⢘⠟⢣⣿⡟⣰⣿⣿⢸⡇⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣿⣿⣸⣆⠻⠟⣰⣿⣿⠏⣿⡇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣼⣿⡿⣿⣯⣿⡄⣿⡿⢫⣾⣿⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⠟⢿⡃⠀⠀⢿⢿⡟⠁⣰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⠀⠘⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠠⠰⣷⣤⣴⢦⠀⠀⠀⣀⣴⣿⣿⠆⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⣴⣦⣄⡀⠀⠀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠘⣿⣽⢟⠆⢼⡯⠰⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠈⠑⣡⣶⣶⣤⣤⣤⣴⣶⣶⣿⣿⣷⠦⣀
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠙⠿⣽⠋⠹⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⡮⠍⠁⠀⢀⡤⠖⣂⠀⠀⠙⢳⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢰
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡉⠀⣀⣐⠃⠋⠰⠟⠋⠀⠀⠀⠁⣸⡄⠀⠀⠀⠀⠀⠀⠈⠗⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀⢃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠴⢿⢇⠈⠀⠀⠀⠀⠀⣼⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⢀⠀⣰⣀⣀⠎⠀⠀⠀⠀⠀⠀⠀⣀⢎⢀⣷⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡙⠏⣰⠃⠀⠀⠀⠀⠀⢠⡤⠉⢈⠈⠀⠀⠀⠀⠀⣀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠀⠐⠄⠀⠀⢀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢰⡒⠲⠒⢒⡒⠶⠦⣤⣀⠀⠀⢀⠀⠀⠀⠀⠐⠙⠂⠝⠋⠋⠀⠀⠐⠂⠎⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡴⣍⠁⠀⠈⠁⠈⠀⠈⠠⠊⠀⠛⢨⢛⡂⢠⠀⠀⠛⠀⠀⠀⠀⠼⠀⠐⠲⠄⠀⠔⠀⠀⠔⠒⠊⠉
⠀⠀⠀⠀⣠⠋⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠵⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⠀⠁
⡆⠀⠀⢰⠗⠖⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠈⠀⠒⠂⠠⠰⣘⡄⠀⠀⠀⠘⠂⠀⢊⠄
⠇⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠇⠀⠀⠀⠀⠀⠈⢴⠇
⠰⡀⠀⠸⡆⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⢄⠀⠹⣖⠁⡄⠀⠀⠐⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠈⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡀⣀⣀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⣲⣴⣿⣿⡿⠟⠻⠋⣿⣿⠎⠻⠈⠃⠀⠀⠢⣤⡄⣀⡀⢀⣀⡆⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠁⠀⠀⠸⢿⡏⠀⠲⢤⣴⣖⢶⣿⣿⣿⣤⣽⡿⣯⣽⣿⣤⣸⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣩⣹⣦⣤⣤⣄⣸⠶⠶⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡠⣝⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣣⣀⣉⣙⣿⣿⣿⣿⡷⣀⢠⣿⣿⣿⣿⢿⣿⡿⠿⣿⡿⣿⣿⣳⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠙⣵⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣮⣿⠉⠉⢿⡻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠛⢻⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣻⣿⣿⣿⣿⣿⣤⣼⣫⣭⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⡽⢻⣿⡟⠀⠈⢿⣿⣷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⡿⢟⣿⣿⣿⣿⣿⣿⣿⡟⠉⣹⣥⡾⠿⢫⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠚⠿⢿⣧⣾⢿⣤⣼⣿⣿⣿⣿⣷⣾⠿⠟⠀⢀⣼⡿⠟⢣⢸⣿⣿⡿⠿⠿⢿⢿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠛⠃⠀⠈⠀⠈⠉⠁⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣽⣿⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠛⠛⠛⠋⠙⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⢀⡀⠀⠀⠀⠀⠐⠶⠄⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢹⡄⠉⣿⣯⠃⠀⠀⠀⣴⣶⡒⠤⢼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⣄⠀⠀⠐⠦⠶⠀⠀⠀⠀⣀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡿⢷⡦⠄⢀⣀⣀⠠⠴⠚⠻⠆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢶⡾⢷⡆⠀⠀⠀⠀⠈⠹⣆⠀⢸⣇⠀⠀⠀⣸⡇⠀⠀⠀⣸⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠃⠀⠀⠠⢀⣴⠃⠀⠀⠀⠠⡀⣿⣀⠀⠻⢷⣖⣾⠟⢸⠀⠀⡀⢻⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣅⢀⣀⣤⣤⣶⣿⣿⣄⠀⠀⢀⣀⣅⠀⢀⠀⡀⠀⠙⠀⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⢿⣿⡿⠿⠟⠛⠉⠻⣷⣶⠋⠁⠉⠃⠈⡀⠙⠦⣤⡴⠋⠀⠀⠀⠀⠁⠀⢀⣄⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⢀⡀⠀⢡⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣶⡞⠀⠀⠀⣃⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠛⢅⠀⠀⠀⠀⠀⣿⣿⡿⣫⣿⣮⣝⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢹⡏⠀⠀⠀⢹⣇⠀⠁⢆⠀⠀⠸⣫⣵⣾⣿⣿⣿⣿⣿⣦⡙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣼⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⣆⠀⠀⠑⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠃
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣾⣿⡟⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣄⣀⣴⣿⣿⣿⣿⣿⣿⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠛⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠆⠈⠻⠇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡄⠤⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡁⢦⠛⠒⠀⠀⠀⠀⠀⠀⠈⠁⢆⠀⠀⠀⠀⣤⣶⣰⠢
⠀⠀⠀⠀⠠⣷⣈⣺⣧⡐⢋⠒⡰⢢⣶⣓⡒⠂⠈⢢⣤⣶⡿⢉⣂⠈⡞⠂
⠀⠀⠀⠀⡄⠛⢯⣿⣿⣿⣥⣦⣷⠉⠀⠒⢢⠀⠀⠀⠀⠜⣶⣌⣠⡶⠃
⠀⠀⠀⢀⠂⠀⢦⣹⢻⣭⠭⠝⠊⠀⠀⠀⠀⠉⠀⠆⠀⣔⠁⠀⠁
⠀⠀⠀⠈⠀⢰⠋⠙⣴⡷⠇⠀⠀⠀⠠⠤⣄⠀⢀⡇⡀
⠀⠄⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠠⣄⠀⠀⠀⠀⠂⠉⢀⠃⠀⠠⡀
⠀⠀⠁⢠⠴⠀⠾⣱⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠄⠈⠱⣄⠀⠈⠑⠦⡀
⢀⠀⠀⡇⠀⠺⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠠⠀⠐⠓⠙⢢⣤⣤⣴⡽⣦
⠀⠀⡧⠀⠀⡔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⢀⣀⡼⣹⣶⡶⠞⠉⡀
⠠⠀⢠⢀⣠⡜⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⣀⡤⠀⠀⠀⠀⠀⠊⠙⣟⠷⠿⢿⣿⠂
⠀⠰⣸⠘⣧⠉⠢⢀⠀⠀⠀⠀⠀⢢⡇⡀⠑⣦⠀⠀⠀⠀⠀⠀⡸⡟⠀⠀⠀⠛⢿⣦
⠀⠀⠈⠐⣿⠘⠀⠀⠁⠀⠐⠈⠀⢐⡽⠀⢠⠋⠑⠂⠑⠁⠀⡸⠇⢂⠀⠀⠀⠀⡈⢇⣣⡀
⠀⠀⠀⠀⡏⡇⠇⠀⠀⠀⠀⠀⠀⢈⠁⢀⡆⠀⠀⠀⠐⢄⠀⠀⠘⣼⡿⢶⣿⠾⠿⢿⣿⡁
⠀⠀⠀⠀⢰⡇⠐⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠁⣠⠞⡇⢁⡀⠀⠀⠀⢸
⠀⠘⡄⠀⢸⣷⠀⠀⠀⠀⠀⣠⠊⡐⢰⠁⡆⠀⠀⠀⠀⠀⠀⣄⠼⠀⡞⠀⡠⠀⢀⣾⡾⠄
⠀⠀⠸⡀⠈⡆⠆⠀⠀⠀⠈⠠⠞⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⣸⢁⣠⣷⡿⡶⣿⣯
⠀⠀⠀⢣⠀⡇⠈⠀⠀⠀⠊⠀⠀⡼⠀⠀⡇⠀⠀⠀⠀⠀⠀⣗⠀⡟⠀⣽⣿⢀⠀⠙⠉
⠀⠀⠀⠈⡆⢳⠀⠀⣿⠂⠀⢀⠜⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⡏⢸⠇⠀⠀⠘⠈⡀⡄⢀
⠀⠀⠀⠀⡇⠀⠳⡀⠉⢀⡴⠋⠀⠀⠀⣼⠀⣀⣀⣠⡄⠀⢰⡇⣞⢤⠀⠀⢀⠀⠀⡆⠀⠳⡀
⠀⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⢰⢻⡤⠚⣉⠠⠄⠀⢸⡷⠁⢢⡳⣀⣎⠀⠁⢉⠀⡁⠘⢆
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡗⠉⠀⠀⠀⠀⣼⠃⠀⠀⢱⡟⠀⠓⣄⠀⠀⠱⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢹⠀⠀⠀⠀⠀⡿⠀⠀⢀⡾⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠙⣄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⢰⠀⠀⠀⠀⢸⡁⠀⢠⡞⣀⡠⣀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠘⡄
⠀⠘⠛⠻⠟⠻⠿⠷⠶⠶⠚⠋⠉⠱⡄⠀⠆⠀⠀⠀⠀⠛⠮⣵⠯⠽⠓⠚⠉⢢⡀⠀⠀⠀⠙⣆⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⢰⠛⠱⡀⠀⠀⠀⠀⠀⠔⠀⢢
⠀⢀⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡆⠀⢸⠀⠀⢱⠀⠀⠀⠀⡘⠀⠀⢸
⠀⢸⢁⠀⠠⢌⠳⡄⠀⠀⠀⠀⢀⠤⠒⠉⠉⠈⠉⠑⠠⡀⠸⡴⣚⠧⢀⠼⣴⢤⣸⡀⠀⠀⢀⠃⠀⠀⡌
⠀⠈⢮⡈⠁⠀⣹⣼⣆⠀⠀⠰⠃⠀⡀⠀⠀⠀⠈⠀⠀⠈⢆⠹⡀⢀⠀⣀⠈⠓⠺⡇⠀⠀⢸⠀⠀⢸⠁
⠀⠀⠀⠑⣤⠀⣩⡅⠈⢆⠀⡅⠀⡀⠀⣠⠔⠢⣄⠀⠈⠀⠘⡀⠈⢦⠀⠀⠀⠉⢀⡇⠀⠀⡧⠂⠀⡎
⠀⠀⠀⠀⠈⠻⡻⣠⣤⣼⡄⡇⠀⠁⣰⠃⠀⠀⠈⡆⠀⠄⠀⡇⠀⠀⢏⠀⠀⠀⠨⠇⠀⢸⣣⡠⣰⠁
⠀⠀⠀⠀⠀⠀⠙⡟⠿⠟⢃⢸⠀⠀⠜⢦⡀⠀⡰⠁⠂⠆⢠⠁⠀⠀⢸⣤⣤⣍⣸⠀⠀⣇⣈⣍⡏
⢀⡤⡀⠀⠀⠀⠀⢸⡄⢒⢻⠀⢃⠀⠠⠀⠈⠉⠀⠠⠂⢀⠎⠀⠀⠀⠤⠸⠿⠿⠇⠀⠘⠯⠿⡾⠁
⣏⠀⠈⢂⠀⠀⠀⡸⠁⠀⠉⠀⠀⠳⢄⠀⠀⠀⠀⣀⠔⠁⠀⣀⠴⠚⠫⢲⡵⠃⠀⢀⣤⢬⡉
⠱⡀⠀⠀⡱⣲⢾⡅⠀⢠⠁⠀⠀⠀⠀⠉⠉⠈⢉⠔⠒⠊⠉⠀⠀⠀⣠⠞⠀⠀⢰⠁⢿⡄⢸
⠀⠑⠤⢀⡇⢘⠂⢉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠤⠔⠊⠀⠀⠀⠀⠈⠢⠿⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⣴⣶⡟⠉⠹⣿⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢊⣉⣩⡍⠙⠛⠻⣆⠸⣿⣧⣼⣿⣗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢁⡒⠛⠛⠿⢿⣧⢠⣆⣿⡛⣯⡭⠏⠛⠉⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡈⣽⣵⣁⡃⢀⣸⣿⣦⡿⣿⣿⣷⣶⣶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⢿⢺⡇⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣸⣘⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⢁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡟⡕⡻⢻⣿⣿⣿⣿⠙⢿⣍⠢⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⢏⠌⠀⠉⣟⢅⠙⣆⠻⣢⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡎⣀⡀⢀⣬⣺⣶⣌⣷⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⣶⣾⣿⣿⣿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡿⣿⢸⣿⡟⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣷⣿⣽⡿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠹⡇⣿⣿⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⠀⢘⡇⠻⠋⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⡇⠄⢸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⠇⠀⢸⡄⡄⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⢸⠀⠀⠈⡇⡇⠀⣿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣷⡇⠀⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠘⣿⠀⠘⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢹⠀⠀⢸⡼⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣃⣀⣀⣀⣀⣀⣈⣀⣀⣀⣓⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⣴⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢀⠀⠀⠈⢛⠃⠀⠔⣿⣿⡗⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⡀⠸⢿⠿⡿⠃⢀⠀⠀⠀⣠⠂⣸⣿⣇⠀⡀⠀⠀⠀⢘⢹⣿⣧⠀⢺⠀⠀⠀⠹⣦⣤⣶⣶⣿⣶⣦⣤⠞⠀⠀⠀⢻⣀⣿⣧⣠⠇
⠀⠀⠀⠙⠶⣿⣿⣿⡷⠋⠀⠀⠀⢈⣿⠂⠀⠰⣿⣁⠀⠀⠐⢦⢿⣿⣿⣇⣀⠇⠀⠀⢤⣤⡼⣿⣿⣿⣿⣿⣥⣾⠗⠀⠀⢀⡼⠉⢿⣿⠂
⠀⠀⠀⠀⠀⠈⠉⢙⡇⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⡀⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⣀⢀⡃⢰⠠⣾⡄⢠⠀⠀⠀⠀⠀⠀⢠⣶⠄
⠀⠀⠀⡄⣄⣨⣿⣷⡤⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠠⣄⣠⠻⠟⣢⡤⠖⠀⠀⠉⢁⣑⣾⡞⠿⢳⣾⣚⣁⠀⠀⠀⠀⡚⠿⢃
⠀⠀⠀⠀⡨⠛⠻⠿⡅⠀⠀⠀⠀⠃⢸⠿⣿⡝⠳⠆⠀⠀⠀⠀⣨⡿⠖⠉⠛⣧⡤⠀⠀⠀⠀⢀⡼⠣⣤⡜⢦⡀⠀⠀⠀⢀⡼⠁⠀⠙⢦
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⡤⠀⠀⠀⠀⠀⠀⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄


⠀⠀⠀⢀⡴⠀⡀⠆⠀⣤⠀⠀⠀⠀⢰⣶⠀⣄⠠⣷⡄
⠀⠀⠀⢰⠀⠀⣰⡄⠀⢹⡄⠀⠀⢀⡔⠀⣴⣤⡆⠀⣤⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢰⡆⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠈⠧⣤⣿⣿⣤⠞⠀⠀⠀⠀⠹⢤⣟⣛⣫⡴⠃⠀⠀⠀⠀⢲⢾⣿⡇⠀⠀⠀⠀⠀⢳⣾⣿⣷⣤⢾⣷⠀⠀⠀⠀⠀⣙⣜⣁
⠀⠀⠀⠀⠀⠸⣿⣿⢧⣄⡀⠀⠀⠀⠀⠐⢿⣿⡿⣤⣀⠀⠀⠀⠀⠾⢿⣿⣿⡇⠀⠀⠀⣀⡼⠿⣿⡿⢧⣠⣥⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢘⠁⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⡘⠋⠉⠙
⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⣿⠀⠀⠀⠀⠀⢠⣾⠀⣿⢸⡇⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡷⠂⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⣼⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠠⢾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣾⣆⠀⣰⣦⢀⣷⡄⠀⠀⠀⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣼⣡⣿⣼⣯⣝⢿⣦⣽⣆⠀⠀⣏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣼⣫⣿⣿⡳⣿⣧⡂⡝⢿⣿⣷⣄⡂⣣⠀⠀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⡶⣟⣼⡿⣫⣮⡶⣿⣿⣷⣦⣄⠙⢿⣿⣿⣄⠡⢀⣯⡄
⡇⠀⠀⠀⠀⠀⢠⠃⠀⣰⣿⣿⣿⣿⣛⣴⣿⡿⠾⣛⣟⣻⣾⣿⡷⣌⠻⣿⣿⣷⡙⣿⠳⡀
⡇⠀⠀⠀⠀⢀⠞⣑⣖⣾⢻⣿⡿⣶⡟⡽⣞⣫⣵⣾⣾⣷⣾⣯⣓⠻⣣⡙⢿⣿⣻⡆⢞⣧⠀⠀⣾
⡇⠀⠀⠀⠀⡘⣃⡽⣽⠋⣾⡟⣼⣭⠟⣿⣿⣿⢟⣻⣿⣿⣿⢿⣿⣷⡌⣻⣿⣿⣿⣿⡘⣿⡆⢸⣿
⡇⠀⠀⠀⠀⠟⣸⢿⣿⣾⢿⢸⢏⣋⣾⣷⢟⣵⡿⠛⣿⣟⡿⣿⣞⣿⣿⡎⣿⣿⣿⣿⡇⢸⣿⡇⣿
⡇⠀⠀⠀⠀⡦⢹⣿⣧⣿⣷⣻⣿⢼⣷⣿⣸⣿⣷⣾⣿⣿⣴⣿⣿⢸⣿⣿⢹⣿⣿⣿⣇⢸⣿⡇⢿
⡇⠀⠀⠀⠀⣷⢙⣾⣇⣹⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⢇⣼⡿⡿⣼⣿⣿⣿⡇⣽⣻⠇⡞
⡇⠀⠀⠀⠀⠘⣬⣻⣷⡈⣿⣿⣿⢷⣽⣿⣷⣏⣿⣿⣿⣿⣿⣯⣰⣿⣻⢣⣿⣿⣿⡿⣱⣯⡟⣰⠃
⡇⠀⠀⠀⠀⠀⠘⢿⣿⣯⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣹⣿⠿⣱⣿⣿⡴⠃⣴⠎
⡇⠀⠀⢀⣀⠀⠀⠈⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣶⣿⠗⢋⣤⡾⠁⠀⣀
⡇⠀⠀⠀⠙⠳⣤⡀⠰⣽⣿⣿⣷⣼⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⠿⣻⣵⡾⠟⣁⢠⡄⣠⡟
⡇⠀⠀⠀⠀⠀⠈⢿⣦⡈⠻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣵⡿⠛⢉⣴⡞⣱⠏⣰⡿
⡇⠀⠀⠀⠀⠀⣀⣀⠙⢿⣶⣌⠻⣿⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣠⣾⢟⣫⣾⣷⣾⠟⣰⡏
⡇⠀⠀⠀⠀⠀⠉⠙⠻⣷⣿⣿⣷⣦⣝⠛⢿⣿⣭⣹⣿⣿⣿⣿⣿⣿⠋⣰⣿⣯⣷⡻⣿⣿⠟⢁⣴⠟⣤⠀⣤⠀⣀
⡇⠀⠀⠀⠀⠀⣀⣀⣀⠀⠉⠻⣿⣿⡿⣿⣶⣮⣝⣻⣿⣟⢻⣿⣻⠃⣼⣿⣿⣛⣿⣿⠟⢁⣴⡿⠃⣼⡟⢠⡟⢰⡿
⡇⠀⠀⠀⠘⠛⠛⠛⠿⠿⣿⣶⣬⡛⢿⣦⣍⠛⠿⣿⣿⣿⣿⣿⡟⣸⣿⣿⡿⣿⠟⢁⣴⡿⠋⢀⡼⣳⢇⣿⣣⣿⠃
⡇⠀⠀⠀⠀⠀⠀⠲⠶⠶⣶⣭⣽⣿⣷⣝⠻⣿⣷⣦⣽⣛⡻⢿⣇⣿⣿⣗⣿⠃⡴⢿⠞⢀⣴⡿⣱⢯⣾⣫⣿⠏
⡇⠀⠀⠀⠴⠶⣶⣦⣤⣤⣀⡈⠙⠻⣿⣿⣿⣶⣬⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⡼⢷⠏⣠⣟⢵⡴⣻⡿⣷⣿⠏⣀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢷⣦⣄⡙⠻⣿⣽⣿⣟⣿⣽⣿⣿⣿⣿⣿⢰⠷⡏⡼⡟⣫⢟⣼⢟⣿⣿⢯⣾⠃⣸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⡈⠙⠿⣷⣶⣬⣭⣽⣿⣿⣿⡿⠿⠿⣯⠸⣿⣼⠁⢰⢯⣾⢫⣿⡻⢫⣿⠃⢠⣿⣷⣧
⡇⠀⠀⢠⣴⣶⣶⣶⣶⣶⣦⣤⣍⣛⠷⣶⣤⣍⣛⡛⠻⠿⠿⣿⣿⣿⣷⣶⣶⣾⣧⠅⣿⣿⢧⣿⣯⢣⣿⡏⢀⣾⡿⢸⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣶⣽⣛⢽⣿⣟⣲⡖⣶⢶⣶⢶⢶⣤⣽⣗⢸⣿⣿⣾⡿⡆⣾⣿⠃⣸⣿⠇⣸⣿
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠻⢿⣿⣶⣾⣭⣭⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢻⢐⣿⣿⢠⣿⡿⠀⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⡬⣙⡻⠿⢿⣶⣿⣿⣿⣿⠿⠿⠛⠛⠻⠿⣿⡻⢸⣿⡟⢸⣽⡇⢸⣯⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⢿⣿⣶⣦⣤⣤⣶⣶⣾⣿⣟⣯⣽⡯⠿⢷⣸⣿⣇⢸⢿⣇⣿⣻⡿
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣿⣿⣿⣿⣿⣿⣛⣭⣥⢶⡾⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣷
⡇⢤⣤⣀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠁⠈⠉⠉⢛⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣀⣤⡄⣠⣆⣿⣿⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣠⣾⡻⢿⠿⠿⢷⣿⣟⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢰⣟⠀⣁⣚⣸⢃⡾⣠⢙⠆⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⣤⢋⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣧⣴⣾⠋⢻⣿⣿⣿⣯⣾⣿⣾⠇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢲⣿⣟⡛⠧⣸⣦⣤⣿⡿⢏⡀⢾⣿⣿⣿⣿⢏⠙⠁⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠟⠁⠀⣿⣾⣿⣿⡉⣵⣮⣽⣿⡉⠑⠋⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣻⡋⠀⠀⣠⡶⣿⣿⣿⣧⠻⠮⠟⠛⣫⣶⣿⣷⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣍⣡⣶⡼⣿⡏⣡⣴⣄⡿⠾⢒⢉⣼⡟⣡⣶⣮⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣧⣿⣷⣋⣩⣤⡀⣶⠏⣼⠟⢿⣿⣿⣿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣿⣿⡏⣹⣝⣿⣿⣿⣏⣠⣼⣧⣈⠻⢿⠟⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⢿⣿⡟⣿⣳⠿⣿⣿⣿⣿⣿⣿⣿⡷⣠⡀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠸⣿⢇⣶⣿⢰⣟⢿⣿⣿⣿⡿⣿⡾⢟⣡⡀⠀⢿⣿⣿⣦⡀⠀⠀⠀⢀⠀⢳⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢄⣿⣿⠇⠀⢻⣆⠻⢻⢼⣿⢸⣯⣝⢿⣿⣮⡰⣿⣿⣧⡀⠘⣿⣿⣿⣿⣶⣶⣾⣿⣧⠀⢻⡀
⠀⠀⠘⢀⣶⣤⣄⠀⣀⣡⣾⠿⣿⠀⠀⠈⢻⣿⣿⠘⣿⣬⣿⣽⣮⢿⣿⣿⣮⣙⠿⠿⢲⡜⣿⣿⣿⣿⣿⣿⣯⣿⣇⢸⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢫⠀⠀⠀⠀⣹⣮⡇⢿⣇⢻⡿⣿⣦⡹⣿⣿⣿⣿⣿⡇⠈⢬⠻⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠹⠛⢱⡜⢿⠰⡆⣿⣻⣿⣬⡙⠿⣿⣿⡇⠀⠀⠑⠉⠛⠿⢿⣿⡿⠁⣾
⠀⠀⠀⠈⢾⣿⣶⠾⢋⠅⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⢷⡜⠧⢶⣄⣴⡿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣠⣶⣿⣦⣼⣧⡛⢻⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⠛⣍⣻⣿⣿⣿⣛⠿⢦⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣻⡿⢋⡽⣙⢟⣿⡞⣭⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣮⠟⢇⢺⣿⡿⢂⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣿⣿⣟⢻⣿⣧⣿⡯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⣵⣿⣿⣿⢠⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⢿⣾⣿⣸⡟⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡇⡙⢻⣿⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣼⣇⣿⢸⣿⠿⣾⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣵⡿⢸⣿⣘⠏⠰⣩⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣩⣥⣾⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⣤⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠉⠁⠐⠮⣀⠚⠀⣦⠀⠀⠀⠠⠄⠉⠁⠈⠋⠙⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⠀⠀⠈⠳⠀⠉⣆⠐⠁⠀⡀⠐⠀⠀⠀⠢⡀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⠊⠙⠁⡀⢉⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠘⢇⠀⠀⠀⠈⠁⠀⠀⠀⢰⡆⣤⣶⠀⠈⠃⠀⠀⠀⠀⣀⠁⠈⡇⠘⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⢄⠀⠀⠀⠀⢰⠀⢰⠾⠃⠘⠷⢦⡜⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠂⡀⠼⠉⣠⠀⠀⠈⠂⠙⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⡃⠀⠀⠀⠈⠀⠀⢀⡀⣀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣥⡤⠚⠀⣇⠀⠀⠀⠃⢸⡆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠉⠀⠀⠀⠀⠀⠀⢪⠛⠉⠉⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣶⠀⠀⠀⠀⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⢤⡀⠀⠛⠷
⠀⢀⠛⢀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠐⡖⢢⠀⠄
⢀⡎⠀⠀⢣⡀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⠴⠋⠀⠐⠄⢀⣀⠠⠂⢀⠈⠁⠐⠒⣦⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡿⠀⡴⠒⢢
⠈⢃⠀⠀⡘⠀⠀⠀⠀⡝⠀⠀⠀⠀⢀⡴⠁⠀⠀⠈⠂⠀⠈⠉⢀⡠⠌⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠗⠘⢄⡀
⠀⠀⡇⠀⢃⠀⠀⠀⠀⣷⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘⠣⠞⠋⠁⠀⣤⣶⣶⣦⣤⣀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠁⢠
⠀⢀⠀⠀⠈⢂⠀⠀⠀⠸⡄⠀⠀⡟⢠⣶⡿⠿⢿⠄⠀⠀⠐⠂⠀⠀⠀⠛⠋⠉⠉⠉⠙⠛⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⢀⡴⠋
⠀⠀⡄⠀⠀⡾⠀⠀⠀⠀⠹⣆⠸⡖⠋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣶⣦⣀⠀⠀⢨⣀⠄⠒⠚⠃⢤⠀⢩⠛⣀⡲⠟⠉
⠀⠀⢸⣆⠘⣧⠀⠀⠀⠀⠀⠈⠳⣷⣀⡾⠟⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⣿⣿⠈⠙⠇⠀⠀⠉⢀⠄⠀⠄⠀⠻⣮⠛⠉
⡀⠄⢠⡁⠀⠁⠔⠁⢰⠀⠀⠀⠀⠈⠟⣀⠻⣿⣿⡿⠳⠀⠀⠀⠀⠀⠀⠀⣁⣙⣻⣟⣫⡴⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡟⢠⣴
⠃⠠⠄⣀⡄⢠⠄⠉⠁⠀⠀⠀⠀⠀⢸⠀⠙⠋⠉⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠤⠤⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠉⠳⠶⠶⠛⠃⣴⡆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⢋⣥⠀⠀⠀⠀⢦⣀⣀⡠⠎
⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣵⣶⡶⠶⠞⠛⠉⢩⣏⢻⣤⣀⣦⡀⠀⠀⢀⡽⠃
⠀⠀⠀⠀⠀⣠⡄⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⢯⣅⢠⢀⣙⡷⠛⠄⠉⠀⠀⣈⣟⠉⠉⠁
⠀⠀⠀⠀⠈⡿⠤⡀⠀⠈⠳⣦⠴⣄⡀⠀⠀⣀⠴⠋⢡⡉⠀⠄⠀⠀⠀⠀⠀⢠⡈⠀⠀⠀⠀⠈⠛⠶⣄
⠀⠀⠀⠀⠀⢻⠀⢹⡆⠀⡷⠉⢠⠀⠀⠈⠉⠀⠀⠀⡘⣿⣦⠀⠀⠀⠈⣠⡄⢞⡑⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠈⢲⡞⢹⣦⣷⣀⡘⠀⠀⠀⠀⠀⠀⠀⣿⠱⡄⠛⠉⠛⠁⡞⠀⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠈⠉⠙⠲⠒⠦⠤⠤⠒⠶⣹⠀⢻⡁⠒⢃⠎⠁⠀⠒⠀⠀⠀⠀⢢⣄⡀⠀⠀⠀⠀⠀⠀⠈⢶⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠛⠀⠀⠀⠰⡁⠀⠀⠀⠀⣼⢩⠉⠑⠲⣄⠀⠀⠀⠀⠀⣟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡀⠀⠀⠈⠳⣄⣀⠶⠙⠂⢙⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠟⠳⣶⠄⠒⠒⢒⠂⠂⠀⠈⠉⠈⢿⠘⣧⠀⠀⠀⠀⠈⠻⢆⠠⠔⠁⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠚⠗⠀⠀⠀⠀⠈⠉⠉⠅⠁⠀⠀⠀⠀⠀⢇⠘⠡⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⢠⠅
⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡆⡠⢦⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢀⠠⣾⠀⠀⠀⠀⠀⠈⠁⠉⠐⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⢡⡔⠠⣤⠐⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠘⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠐⠓⢤⠒⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠈⢙⣄⠀⠙⢍⠓⠒⠤⢤⠤⠤⢤⡄
⠀⠀⠀⠘⡀⠈⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠰⢮⡁⢁⠀⠈⠁⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠙⣿⠂⠀⠀⠀⠄⢠⠄⠺⣆⠀⠀⠀⠀⠀⠙⠲⠤⢄⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡦⠄⠤⠤⠴⠟⠀⢦⣄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣼⡆⠀⠀⠙⢢⡤⠤⠤⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋⠉⠉⠉⠁⣧⠀⠀⠀⠀⣶⠀⠒⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠈⣠⣀⣀⠠⠴⠶⠋⠀⠀⠀⢸⡇⠀⠀⠀⠠⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣀⢀⢀⣀⠜
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣾⣷⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠃⡉⠹⣏⠀⡟⢉⢙⣏⠛⢨⡿⠏⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢠⣄⠀⢀⣄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⡤⠀⠀⠀⠀⢳⡿⠀⠸⠿⠀⠀⠀⠀⠐⠒⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠉⠁⠤⠄⠉⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⢤⡀⠀⠀⠀⠀⣠⠴⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠙⣆⠀⠀⡾⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠸⣆⢀⡞⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠹⡾⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⢀⣀⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣰⠋⠀⠀⠹⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢻⠀⠀⠀⠀⣿⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⣫⣽⡓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⢲⣾⣟⢙⣿⣖⣊⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⠞⠻⣿⣿⣿⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⣶⣿⣿⣾⣿⣿⣿⣷⣶⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢖⠉⠀⠀⠁⠀⠉⠒⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠆⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⣿⠀⠀⠀⠀⡀⣆⠀⠀⠀⠀⠀⠀⣠⢂⠄
⠀⠀⠀⠀⠀⠀⢺⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠋⠸⡿⠛⠃⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⣐⣦⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠷⣝⡿⠒⠀⠀⠀⠀⠂⢾⣻⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⠀⡄⠈⠁⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠑⠦⠶⠚⠀⠀⠀⠀⠀⠘⠻⠿⠟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣶⣤⣄⣀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠛⠛⠛⠛⠟⢻⣿⣿⣿⠿⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠉⠈⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣛⠛⠲⢤⢤⣦⣤⣤⣤⣤⣤⣶⣶⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣉⡛⠓⠶⠶⠍⠀⢹⣿⣟⣿⣿⣾⣦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣛⡻⠿⠿⠶⠦⠀⢸⣿⡇⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠀⢸⣿⣷⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠈⣿⣿⣎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠄⠀⡀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠁⠐⠒⠒⠈⡉⠁⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡡⠊⡠⠔⠂⠁⢀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⢢⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⢀⠀⠀⠐⠈⡠⠐⢀⠐⠢⡀⠠⡀⠀⠈⠂⠀⠣⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠠⠀⠀⢁⠠⠒⠁⠀⠀⠈⠢⣀⠀⢄⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⠀⠀⠀⠀⠀⠀⢡⠤⢤⠀⠒⠀⠉⢀⡀⠀⠀⠀⠀⠀⢀⡀⠁⠂⠌⠁⣀⣀⣄⠀⠀⠀⠐⠰⠌⠸⠡⢗⠝
⠀⠀⠀⠀⠀⠀⣘⡑⠆⠏⢀⡠⡄⠀⠀⠀⠀⡇⠊⣺⠀⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⣜⠗⠉⠀⠀⠀⡰⢄⠀⠀⠀⢈⠝
⠀⠀⠀⠀⠀⠀⠩⡁⠀⠀⠀⢰⠀⠀⠀⠀⠀⢱⠀⡌⢃⠀⠀⢆⡰⠀⠀⠐⠤⠔⠀⠀⠀⠅⠅⠀⣔⠀⠀⠠⢄⠔⠊⠀⠀⠑⡄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢢⠤⠐⠊⠢⡀⠀⠀⠀⡮⠀⢨⠞⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣀⡙⢆⠀⠈⢆⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠑⠂⠴⠁⢠⠂⢤⠂⡎⠁⠂⢤⠄⣀⠀⠀⡠⠄⡶⠁⠀⢡⠈⠂⠀⠙⡀⠠⢆⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢠⠦⣠⠎⠀⠈⡀⠈⢲⠄⣠⠣⣈⠒⠒⣁⠜⣄⡠⠐⢩⠀⢸⠀⠀⠈⣖⠡⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⡊⠁⠚⠀⠀⠀⡇⠀⢸⠀⠘⢄⠙⡀⢠⠋⡠⠃⠀⠀⠘⠀⢨⡀⠔⠉⠀⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠐⠓⡖⠀⢰⠀⠀⡄⠀⠀⠀⠑⡜⠣⠊⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠰⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⢀⠃⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢣⠎⠤⠀⠀⣀⣀⣀⣀⣇⣁⡀⠀⠀⠤⠤⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡼⢄⣀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⣀⡠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠁⡠⠉⠹⠁⠐⠒⡖⠐⡆⠘⠉⢹⠀⢡⠈⡌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡰⠁⡐⠁⢠⠃⢀⠇⠀⡇⠀⡇⠀⡆⠈⠀⠀⠆⠈⠄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠌⢀⡜⠀⢠⠃⠀⡘⠀⢠⠁⠀⠃⠀⡇⠀⡇⠀⠘⡀⠈⢆⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡠⠁⢠⠊⠀⡰⠁⠀⢠⠁⠀⢸⠀⢰⠀⠀⡇⠀⢠⠀⠀⢃⠀⠈⢣⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⠧⢀⡜⠀⠀⢠⠃⠀⠀⡆⠀⢸⠀⠀⡇⠀⠘⡄⠀⠈⡆⠀⣀⠱⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠈⠁⡲⠃⠤⠀⢠⣁⣀⣈⣀⣀⣇⡀⠀⠧⡄⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡏⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣡⣄⡠⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠁⠂⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⡀⢀⡱

⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣴⣧⣼⣼⣷⣾⣼⣼⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣿⣾⣿⣿⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡏⠄⠀⠀⠀⣀⠀⠠⠤⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡤⢌⢳⣜⠶⠊⠉⣁⡀⡄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠃⢈⣠⣿⣀⡔⠉⠅⠀⠐⠀⠀⠈⠠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣁⢸⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⣀⣀⠀⢠⠠⠏⠁⠀⡜⢆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣋⠛⠃⠈⠁⠀⠀⠀⠀⢀⢇⠘⠄⠰⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⡹⣿⣦⡀⠀⠀⠤⠀⠞⢀⢎⠀⠓⠢⣾⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢘⣇⣰⣯⡟⠈⠑⡶⠤⠤⠖⠁⠀⠀⠀⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠜⠀⠀⠀⠀⠀⠀⣩⠾⠛⠃⠉⢡⡀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡘⠀⠀⢰⣆⣀⡠⠤⠤⠖⠲⠒⠙⠋⠷⢄⡀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⠘⢦⣀⡀⠔⠒⠀⠐⠚⠧⡀⠀⠀⠀⣿⡄⠀⠀⠁⠀⠤⠊⠀⠀⢀⡾⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠣⣄⣀⡜⠁⠀⠀⠀⠀⠀⠀⠈⢶⠀⠚⢿⡸⡦⡀⠀⠀⠀⠀⠀⡠⣻⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠖⢉⢹⠀⠀⢳⣄⣀⡀⠀⠀⠀⠈⣇⠀⠀⠙⣧⢻⡗⠶⠤⠔⠊⡴⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠁⠸⡆⠀⠀⠀⠉⠉⢻⡆⠀⠀⠘⢦⣀⣀⣨⢷⡻⣤⡀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⣦⣄⠀⠀⠀⠀⠁⠀⠀⠀⠈⡏⢻⡄⠀⠙⢮⣛⠿⢟⣼⣇⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⡟⠈⠙⠲⣄⣤⡀⠀⠀⡠⠄⡀⠀⢷⡀⠀⠀⠉⠛⠛⠁⢻⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⠾⠛⢷⣄⠀⢸⡇⠀⣿⠲⠤⣤⠾⡇⠀⠈⢧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⢷⣾⠀⠀⣿⠀⠀⢸⡆⢻⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡀⠀⣿⠀⠀⠀⢷⠈⢧⠀⠀⠀⠳⣄⠀⠀⠀⣸⡇⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠈⠉⠓⣼⡄⠀⠀⠘⣆⠈⢧⡀⠀⠀⠈⠳⢄⣠⣏⡇⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⡇⢧⠀⠀⠀⠘⣆⠀⠳⣄⠀⠀⠀⠀⠈⢩⡇⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⠁⠈⢷⣄⠀⠀⡸⢣⡀⠈⠓⢦⣀⣀⡴⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⣻⠖⢣⠀⠉⠳⢤⣤⠤⠋⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬⠆⡀⠀⠻⡀⠀⠙⠲⠖⠛⠁⠀⠀⡔⠉⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡤⠇⠀⠀⠀⡇⠀⢀⠀⠀⠁⡀⠀⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠬⠗⠒⠒⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣭⣛⣿⣿⣷⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⣇⡂⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣉⣿⣿⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⡿⣆⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣸⣗⡾⠍⠁⠀⠀⠈⣿⣿⣿⡅⢀⡄⡙⢿⣛⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⢾⡿⣿⣄⠙⠉⠁⠈⣥⣿⣿⣿⣿⣶⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠁⣸⣷⣦⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⣿⡛⠿⢿⣷⣿⠁⠀⠻⢿⠿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢁⠀⠀⠀⠀⣀⣀⣠⢷⡶⢾⠛⠋⠠⠂⠀⠀⠊⠻⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣫⣽⣿⣯⣷⣦⣉⠀⠀⣀⢀⣄⢀⡀⠙⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⣾⡟⢸⣿⡿⠟⢛⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣿⣿⣿⡿⠟⠋⢿⣿⣿⣿⡟⣼⣿⡇⠉⣤⣿⣧⠄⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠋⠁⠀⠀⢀⣬⡻⠿⣋⣼⣿⡿⠁⠀⠀⠀⠻⣷⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢳⣄⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠄⠀⠀⣿⣿⣿⣯⣉⡉⢀⡀⠜⡹⡆⠀⠀⠀⠀⠀⠈⠙⠻⢿⣴⣤⣤⣤⠖⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣇⡀⠀⣠⣿⣿⣷⡍⠉⠁⠀⠀⠀⣀⣴⣦⣀⣤⣴⣿⣿⣦⡀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢛⣻⣿⣿⣿⡜⢿⣮⣝⣛⣿⣿⣿⣿⢯⣙⣛⣉⠀⣤⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡀⣠⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣷⣝⣛⣿⣿⣿⣾⡋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣷⣍⡉⣿⡏⠻⢿⠿⢿⣿⡿⠿⠟⣡⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣩⣁⣐⠒⢶⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢷⣍⠻⣷⡄⠘⠿⣶⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣆⣿⣿⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠚⠋⠸⣿⣿⣿⣿⣿⣿⣿⢫⣴⣿⠏⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⣫⣬⣉⣡⣴⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣹⡿⠻⡿⠛⠋⢹⣿⡅⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⡿⣿⢿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠻⣍⣷⣼⣷⣿⣾⣧⣾⣩⡟⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢯⣹⣿⡿⣟⣿⠋⠀⠙⣿⣻⢿⣿⣏⡽⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠛⣾⣿⣻⠽⠾⠃⢰⣭⠆⠘⢷⣯⣞⣿⣷⠟⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣹⡟⠳⠏⠐⠗⣀⠛⠛⠛⢀⠾⠙⠟⠚⠻⣏⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡽⠀⠀⠀⣀⠀⠿⢠⣿⡐⠛⠂⠀⣀⠀⠀⢫⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⠦⡄⠠⠿⢃⡠⣔⣽⠿⣯⣢⢄⡙⠿⠄⢠⢴⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⣷⣸⣷⠿⠶⠟⠊⠁⠀⠈⠙⠫⠶⢿⣷⣅⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⣿⠀⣷⣦⣶⡶⣆⠠⡀⢄⡴⢶⣶⣶⡆⠀⣿⠋⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸⡄⢠⣍⢻⠑⠀⢫⡟⣭⡄⣰⠇⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣿⠘⠀⠙⠶⠷⢟⠀⠀⠈⠻⠾⠞⠁⠀⠂⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢹⡄⠀⠀⣄⠀⠈⠑⣒⠁⠀⠀⣀⠀⠀⢠⡏⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⢲⣄⠀⠻⡄⠀⠛⠷⣶⣿⣿⣷⡶⠾⠋⠀⢠⠟⠀⣠⣴⠒⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠠⣩⡡⠈⡗⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⣌⠣⠀⣉⠀⠊⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠌⢄⢀⡟⠒⠶⢄⣈⡉⠛⠓⠒⠚⠛⠉⢁⣀⡠⠤⠩⡆⡀⠍⢀⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢺⠲⣿⠰⣄⠀⠀⠀⠉⠉⠉⢓⠒⠉⠉⠉⠀⠀⣀⡶⣿⠖⣳⢲⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡄⢸⠀⢹⡆⣬⡙⠶⣤⣀⡀⠀⠰⠀⠀⣀⣠⡤⠞⣉⣠⡟⡀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠇⢸⠁⠌⣷⠈⢯⡓⠦⢬⣉⣉⣛⣛⣉⣉⡤⠔⣺⠟⣸⠃⠀⣿⠀⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⢸⠀⠀⢸⡆⠀⠙⢦⣀⡀⠀⠀⠀⠀⣀⣤⠞⠁⠀⡟⢰⠀⣿⠀⠃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⠀⢸⠃⠘⠀⣧⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⢸⠇⠀⠀⣿⠀⢰⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡀⠀⢸⠄⠀⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⡀⠀⣿⠀⠈⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠃⠀⢸⠁⠀⠚⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⠃⠀⣿⠀⠀⠂⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠀⠀⠀⢀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢤⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠷⣤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠓⠲⢤⡀⠀⠀⠀⢀⡞⠉⠀⠈⠙⢦⠀⠀⠀⠀⣠⠎⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡀⠀⠀⠀⠀⠈⢧⠀⠀⣰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢧⡀⠀⠀⠀⠀⠈⢇⣰⠃⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⠀⠀⠀⢠⣻⡆⠀⣜⣦⠀⠀⠀⠀⢀⣀⠈⣇⠈⠳⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢈⡇⢸⠁⠘⡏⠀⠀⠀⠀⠈⠛⠃⠀⠙⠋⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⢀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢰⠏
⠀⢰⠋⠀⠈⣧⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠸⡆⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⠀⠀⠀⠸⠶⠟⠀⠀⠀⠀⠀⠀⢸⠇⠀⢳⡀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⣰⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠉⠩⠭⠉⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠤⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⡀⠀⠀⣿⣿⠀⠀⢀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⣰⠃⠀⢰⣿⣿⡆⠀⠈⣦⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣼⡇⠀⣠⣿⣿⢿⣿⣆⠀⢸⣷⡀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⢀⣠⣶⠟⠁⢳⡾⠋⠀⢠⣄⠀⠙⢷⣞⠈⠻⣷⣄⡀⠈⠻⣿⣦⣄
⠀⠀⠰⠶⢿⣿⣿⣅⠀⠒⢿⣿⣿⣤⣴⠏⠀⠀⠀⣿⣿⠀⠀⠀⠙⣶⣤⣿⣿⡿⠖⠀⣨⣿⣿⡿⠶⠆
⠀⠀⠀⠀⠀⠈⠉⠛⠷⢦⣴⡟⠻⢿⣷⣀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣼⡿⠟⢻⣦⡴⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⠉⠻⢷⣦⣀⠘⠇⣀⣴⡾⠟⠉⠠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠙⣿⣿⣿⣿⠋⢀⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⢻⡆⠸⣿⣿⠇⢠⡟⠉⠈⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⡇⠀⣿⣿⠀⢸⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⣿⠀⢸⡇⠀⢸⡟⠀⢸⡇⠀⣿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⡇⠀⢸⡇⠀⢸⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣶⣤⣴⣞⡻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡜⠻⣿⡿⠿⠃⢘⠛⣼⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣽⣿⣿⣿⣆⡀⠰⡆⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⠁⠀⢿⣿⣿⣿⣆⠙⢠⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠯⠵⠂⣸⠷⢄⣘⣛⠿⣿⡟⠂⠘⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡖⢀⣼⠁⠀⠀⠠⠀⡆⠈⠣⡀⠀⣸⣯⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⠋⠠⠤⣤⠠⢻⠅⣤⠤⠈⢲⣿⣟⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠖⣿⠀⠴⠺⠷⠄⠀⠠⠶⠷⢦⠀⣿⡏⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣿⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠟⢻⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡏⢁⠀⠀⠀⣈⡀⣈⡀⠀⠀⢠⠔⣿⣷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡃⢈⣦⡀⠀⠈⠉⠉⠁⠀⣠⣦⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣾⣿⠇⠀⠀⠤⠄⠐⣹⠟⠁⠘⠁⠁⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠐⠄⣤⣄⠀⠀⠀⣀⡠⠎⡀⠀⠀⠀⢠⡶⢦⡝⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⡇⠀⠀⠀⠀⢿⣿⢛⠧⠉⠄⡐⠀⠀⠀⠀⢸⣄⣀⡟⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⡇⠀⠀⠀⠀⠀⠹⣆⠀⣀⡄⠀⠀⢀⣐⢤⣥⡼⠥⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⡸⣿⡇⠀⠀⢀⠀⠀⠀⡘⢣⠀⠀⠀⠀⠈⢋⢫⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⢠⡟⣷⢹⣇⢹⡇⠀⠀⠈⠀⠁⠀⠻⡄⠀⠀⠀⠀⠀⡈⡘⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣿⣿⣿⣦⣷⡹⣆⢻⣜⠇⠀⠀⠀⣁⣀⠈⠁⠈⡱⠴⣶⠀⠐⠛⠁⣀⣄⣰⡒⣺⣽⠿⣃⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡻⣿⣿⢟⡙⠻⢿⣷⣻⡄⠀⠀⠀⠘⠍⠁⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⣿⣿⡇⡿⣡⣾⣿⣿⡟
⠀⠀⠀⠀⠀⢀⡀⠀⢹⣿⣿⣿⡟⣨⠅⠈⠀⠘⠲⣽⣿⣿⣄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⢸⣿⣿⣿⢸⣿⣿⡿⢿⢷⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣿⣶⣭⡻⢏⠞⡁⢀⠀⡶⠤⡄⠀⣸⣿⣿⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⢸⣿⣿⣿⣈⣽⣶⣿⣿⣾⡿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡾⡀⢧⡼⠾⠃⠀⢇⠀⢼⣾⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣶⣶⠖
⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⢾⠉⠉⠀⠀⠀⠄⢰⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣁⣴⣿⠄⣾⣿⢿⡏⣿⢸⣿⠿⠿⣵⣿⠟⠉
⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⣟⣩⣤⣴⣦⣤⣄⡘⠼⢃⣗⣀⣀⣤⣤⣀⣀⠀⢀⣲⣭⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢻⡇⢫⣴⣿⣿⣿⣷⡶
⠀⠀⠀⠀⠀⣀⣠⣝⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢹⡼⣿⡞⣿⡹⣾⣝⡛⠉⠁
⠀⠀⠀⠀⠘⠛⠛⠿⠿⣿⣷⣽⠿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⢸⡇⣿⣿⢻⣷⢻⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⡿⢎⣙⢻⣿⠿⠟⠻⠛⢛⣭⣭⣭⣝⢫⡖⣿⣿⢸⣷⡌⠉⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⠘⢿⣿⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠟⠋⠁⣴⣿⣿⣿⡿⠋⠈⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠃

⠀⡀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⢠⣄⠀⠀⢀⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀
⢰⣿⣧⣄⡀⢉⡿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡜⣷⡄⢙⠛⣧⠈⠉⢀⡐⣌⠃⣽⡿⠃⣠⣀⣾⠃⠀⠧⠀⠒⠀⠀⠀⠈⠉⠁⠀⠀⣴⣾⣿⣿⡇
⠈⢛⣿⣿⡛⢻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣝⡻⣿⣿⡿⢿⣷⠄⠡⠈⢳⡿⠃⠘⠃⠈⢻⡏⠀⠁⠀⠾⠦⠐⠁⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡧
⠀⣿⣿⠏⠀⣿⡟⢬⣯⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣿⣏⠉⣿⣿⣶⣟⠻⢄⣠⡄⢠⡴⢊⣁⠐⣿⣁⡖⠈⣀⠒⣀⡀⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⣸⣿⡆⢸⣿⠃⣠⣿⡟⢡⣮⣿⣷⠀⠀⣠⣶⣶⣮⣭⣴⣿⡿⠇⠙⠓⠘⠛⣌⠻⣷⣿⣿⣷⡟⠻⠃⣿⣿⡟⠋⠥⠀⢠⠾⠂
⠸⠿⠿⠿⠛⢿⣶⣿⣿⡗⢠⣿⡿⠋⣷⣾⣿⣿⣿⣿⡿⠏⠀⣠⡄⠀⠈⠉⠡⠌⠁⠀⣿⣧⣠⡼⢶⣾⣩⡿⠊⠁⠠⢀⡀⠀⣀⠀⠶
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⢟⡀⣇⣻⣿⣿⣿⣿⣿⡇⠀⠀⣤⡤⠛⠀⢸⣿⣦⠱⣄⠙⣼⡏⠁⠀⢹⣿⠁⣤⠿⣴⣿⠇⢰⡌
⠀⣴⢊⠷⠲⣦⡀⠀⠘⣿⣷⣿⣿⡿⡿⣿⣿⣿⣿⣿⡃⠸⣷⣾⣶⣀⠓⡀⢻⣿⣷⠈⡁⠈⢷⣶⣶⣿⡁⠈⣹⢾⣿⡟⠒⠀⢸⣿⡆⢀
⠀⠿⣦⣿⣛⣻⡷⣄⡤⠙⢛⣿⠿⢤⣴⣿⣿⣿⣿⣟⡁⢸⣇⢹⣿⣿⠀⠡⠈⢻⣟⡺⢄⡛⠠⠜⠁⠀⠀⡀⠙⠋⣉⡁⠆⠀⣼⣿⣧⣬⡀
⠀⠺⣿⡟⠛⢁⠴⣿⡅⣴⡟⢡⣶⣾⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣐⣀⣤⣬⡗⠾⠋⢠⣦⣴⣦⠀⢹⣿⣿⣭⠿⣦⣾⣿⣿⣿⣿⣷
⠀⢀⣼⣼⣿⡙⢠⣤⣴⣾⣍⢠⡞⢦⣻⡿⠿⣿⣿⣿⣿⠿⣿⠿⢿⠟⠻⢟⣉⣠⠾⠛⢟⡀⠻⣿⣿⡿⠀⣰⠏⠛⠷⣾⣉⣉⡙⠿⣿⣿⣿⡆
⠰⣿⡉⢡⣼⢃⣼⣿⠙⠛⠿⣿⣿⠞⡁⠈⢠⣤⣾⣷⡤⠴⠶⠶⠿⠟⠿⠟⣉⣩⣤⣜⣯⣱⣦⣈⣉⣤⠘⣧⣴⣾⣶⣤⡄⠉⠛⠲⣦⡉⢻⣿
⢠⣿⠟⢇⠘⢻⣿⣿⡄⣿⣿⡙⣿⣿⣻⣿⠿⠛⢡⣤⠀⣶⣶⣶⣆⡰⣶⣼⣿⣿⡿⢿⣿⣿⡏⠉⠙⠲⣿⣿⣿⡿⢿⣿⡵⠾⢶⣶⣄⠙⠀⠁
⠈⣯⣾⣿⡟⠢⣟⣿⣷⣾⣿⣿⠿⢿⣿⣯⣶⣿⣮⣉⣤⣿⣿⣿⣿⣶⣤⠟⠉⠉⠀⠈⠻⣀⠁⠀⠀⠀⠀⣴⠏⠹⢿⣿⣿⣶⡟⢻⣿⣆
⢠⣯⠙⣿⣿⠒⠋⣠⣾⣿⣿⡇⢠⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⢠⣿⡀⢠⡀⠀⠀⠈⠉⠻⣿⠋⣤⣴⣿⠃
⢀⣠⠶⣿⡿⠛⣀⣈⣿⣷⣾⣿⣶⣼⠿⡿⠛⠳⣿⣿⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣽⡅⢸⡇⠀⠀⠀⠀⠀⠀⠲⣤⣄⡁⠀⠀⣾⡄⠸⠃
⠈⠉⠸⢟⣷⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⢶⣶⢸⣿⡏⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢧⠈⢿⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠈⠅
⡀⠐⣦⣿⣿⣿⣿⣥⣿⣿⣿⣿⠋⣿⣿⣷⣦⣴⣿⣿⠇⠀⣀⣶⠾⠿⠿⠿⠿⢿⣿⣷⣶⣤⡘⠳⢾⠶⠚⠀⣀⣤⣶⣶⣶⣶⣦⡄⢸⣿⣿⣦⡄⠀⠈
⠄⠀⠈⢿⣦⣼⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣬⣉⣿⣿⣿⠄⢾⡷⢀⣾⣿⣿⣟⣉⣉⡉⠙⢿⣾⣿⣿⣾⠓⠀⢶⡆
⠆⠀⠀⣀⣼⠿⣿⢿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣧⣦
⡇⠀⢚⣹⣿⣷⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠘⠿⠿⠏⢹⣿⣿⣿⠏⢈⣿⣿⡟⠀⠀⠀⠀⢺⣿⢻⣿⣿⣿⡏⢻⣿⣷⣾⣿⣿⣿⣿
⠁⠀⣾⣻⣿⣿⣿⣿⡿⣫⣾⠇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣶⠎⠉⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣿⣿⣴⣾⣿⢿⣿⣿⣿⡟⠁
⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠉⠁⠀⠀⠀⠰⣿⣿⣿⣷⡄
⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣭⣤
⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⣤⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡷
⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣀⣀⠈⠉⣹⣥⣄⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡁⠁
⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢫⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⡟⣀⣿⣿⣿⣿⣿⣿⣿⡀
⢀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⡟⠃⠀⠀⠀⠀⢀⣴⡿⢛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢉⣄⣠⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⣠⣤⣾⣿⣿⣬⡛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣧⣤
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡏⠋⠁⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣇⡀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⠄⠀⠲⡄⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⡟⠈⠙⠿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠙⣿⣿⣿⣟⣿⣷⡄⢰⣷⣶⣿⣷⣶⣶⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⠷⣤⠀⠙⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⠛⠀⢀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠲⣀⠀⠈⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⢀⠙⣿⠟⠿⣿⡿⢷⡄⠁⠀⠙⠻⣿⣿⣿⣿⣿
⢸⣿⣿⠿⣿⠋⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠸⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⢰⣿⠁⠀⠀⠀⢀⡀⠀⠘⢧⡀⢿⣿
⠀⠎⠻⣶⣤⣾⣿⣿⣦⡀⠀⠀⠈⠶⠀⣀⣤⣆⠀⠀⠀⠈⠷⠉⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣾⣿⡟⠘⢻⣯⠀⠰⣀⢠⣌⣤⡀⠀⢾⣷⣤⣠
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠀⠉⠀⣻⠋⠁⠠⠈⣿⣀⠀⠉⠙⠛⠉⠀⣤⣾⣾⣿⠉
⠀⠀⣿⣿⠟⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⢀⠰⢢⣤⠀⠙⠳⠈⠁⠀⢠⠄⢰⡀⠙⢆⡀⠄⣼⣶⠉⠀⣶⡿⠻⣿⣦⠉⢻⣏⢀⡴
⠀⠀⣿⡇⠀⢸⣿⡽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣀⣄⠀⠀⠀⠲⠄⢠⠴⠇⠀⣾⡇⠀⠄⠀⠀⢨⣿⣶⣎⣩⣟⣿⡟⠁⢶⣿⡟⠿
⠀⠀⣿⡇⠀⢸⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⣾⡄⠀⣸⣿⠟⠉⠙⠻⣆⠐⠂⠀⠀⢀⡀⢀⣤⠋⠀⡻⠂⠁⠀⢻⣿⠛⠟⠉⠋⠉⠛⣿⣿⣿⣷⣶⡆
⠀⠀⣿⡇⠀⠈⣿⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⢀⣿⣿⣄⠰⠶⢀⣟⠀⡆⢀⣼⠿⠁⠀⠀⠀⣼⠻⠀⠀⢀⡿⣇⡀⠀⠀⢠⣶⣶⡄⢸⣿⠉⠉
⠀⢠⣿⠃⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⢸⣿⢮⡟⠻⠟⠛⣁⠜⠋⠨⠉⠠⣤⣤⠤⣤⠉⠆⠀⠀⠘⣧⣸⣷⣤⣶⣤⡉⠉⠋⢸⣿⣶
⠀⣿⡏⠀⠀⢀⣿⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠉⠑⠊⠁⠁⠀⠀⠀⢲⡀⠛⠀⠀⣿⡄⡐⠀⢀⣿⡿⠛⠿⠛⠛⢿⣿⣿⣤⣽⣿⡟
⢰⣿⡗⠀⠀⠈⢿⠷⠀⢠⡾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠛⠄⢀⣁⣤⡀⡄⠠⠀⡰⢿⣿⠏⢀⣿⠁⠀⠀⣸⡿⠁⠀⡀⠀⣀⠈⠛⠛⣩⣿⡿⠃
⠈⢿⣿⠀⠀⢀⣤⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⢀⡘⢋⣼⣿⡸⠃⠀⢀⡆⠀⠀⢸⣿⡇⠀⣴⣿⡧⠀⠀⠘⠻⠋⠀⢀⣼⣿⡟
⠀⣼⣿⠇⠀⠘⠃⠀⢠⠚⠟⠙⠃⠘⠳⣀⠀⢠⡞⠁⠀⠀⣀⠐⠦⠘⠋⠉⡉⠉⠉⡱⣏⣠⣾⢃⠀⠀⢸⣿⡇⢶⣟⣟⢀⣾⣏⣠⣤⣤⣤⣼⣿⡿⠁
⠀⠈⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠁⢰⠆⠀⠀⠀⠀⢤⠁⠀⡀⠐⠀⠹⣀⠿⠀⠸⣿⣿⣿⣶⠀⣿⣯⣧⣾⣿⣿⣿⣿⣿⣯⢹⣦⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣶⣿⡦⠃⠀⠉⠀⠱⠤⠤⠁⣩⠃⣼⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⠀⠀⠉⠠⠀⠁⠈⢿⡄⣠⠤⣄⢉⠀⣬⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠈⠠⠂⢠⠀⠄⣰⡦⠆⠀⠙⠛⠋⠉⠛⠁⠈⣿⠛⢿⣿⣿⣿⠙⠻⢿⣿⣽⣿⣿⣿⣿⣿⣿⠿⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣽⣦⣤⡄⠠⠀⠀⠱⣶⠋⠰⡆⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠀⠈⠻⣿⣶⣦⣀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣤⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄⡀⠀⢶⣴⣷⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠛⢿⣿⣿⣷⣾⣿⠍⠙⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣄⣠⣄⣼⣿⣿⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣤⡀⢹⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠢⠢⣐⡀⠜⣀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠰⢀⠐⠀⠤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢰⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡰⢀⠀⡍⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠊⢀⠈⠊⠡⠘⢄⠀⠠⠀⠀⠔⠃⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⣶⡡⠔⠊⡠⠖⠁⠀⠀⠀⠑⢄⠳⣔⠀⠀⡀⠀⣀⡠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⣖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡑⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠂⠄⠀⠀⠁⠁⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠤⠇⠁⠀⠀⠀⠀⠐⠢⠠⢤⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠉⠀⠘⠒⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣹⣏⣛⣟⣛⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠔⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⣶⡂⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⠀⡠⠂⠀⢀⡈⠠⢔⡂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⡏⣼⢃⡞⠓⠒⠒⠲⠶⢶⡦⣽⣷⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣼⡏⡜⠀⠀⠀⠀⠀⠀⢠⠈⠓⢝⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⡛⠙⡃⠀⠀⠈⠀⢠⠞⠁⡰⠀⠸⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢿⣤⣨⣉⠉⡑⢄⠀⠠⠒⠁⠀⣀⡟⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠛⣤⡉⠈⠈⣂⠀⠀⠀⠀⠘⣖⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢄⠀⠌⢥⣲⣀⣤⠆⡌⠀⢀⡤⠚⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢀⣀⣠⣧⡴⠞⠛⠫⠉⠁⠀⠁⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⢤⠒⠒⠋⠫⡁⠀⠀⣇⢔⠒⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡄
⠀⠀⣀⠀⠀⠀⣀⣀⡠⠤⠔⠒⠛⢻⡉⠀⠀⠀⠀⠉⢧⠀⠀⠈⢄⠀⠰⠁⠤⠀⢈⠐⠖⠐⠉⠀⠀⠀⣰⣁⡀⠀⢄
⠀⠀⢳⠒⠉⠉⠀⠀⠙⢆⠀⠀⠊⠀⠑⣄⣀⠀⠀⠀⠈⠓⠀⡰⣪⢯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠉⠛⢟⠆
⠀⠔⢩⡀⠀⠀⠀⠀⠀⠀⠳⠄⠀⡀⠠⢂⣾⠆⠀⠀⠀⠀⠀⠁⠛⠁⠑⠠⣀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠸⠊
⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⠀⠁
⢖⣂⣠
⠀⠀⠀⠀⠐⠳⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢔⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠵⣌⠳⣕⣄⠀⠀⠀⠀⠀⠀⣶⢚⢳⠒⠖⣶⠄⠀⠀⠀⠀⢀⣴⡵⢋⡴⢗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠳⣬⣳⢮⡳⣕⠀⠀⠀⠀⠀⠛⠁⢎⡑⡈⠛⠀⠀⠀⠀⠐⡱⣫⢿⣫⠴⢋⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢭⣙⠢⢽⡳⢍⠪⣢⠦⡀⠀⠀⠆⠈⢀⠇⠀⠠⠀⠀⣠⠺⡮⣊⠕⣫⡷⣚⡭⢞⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠦⣍⣻⡭⠓⠬⣾⠀⠙⡄⠠⣀⣶⡛⢛⣶⣄⠃⡰⠁⠀⡿⠐⠉⣐⣯⠵⣚⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣝⣒⣾⡍⠒⠤⣶⠀⠀⢘⠘⣟⠛⠋⠘⠛⣻⠇⠁⠀⠀⡿⠒⠉⣵⣗⡩⠭⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣒⣒⠽⢯⣔⡒⠸⡆⠀⠠⣼⣿⣷⣾⣷⣶⣿⣷⠀⠀⣸⢓⠈⢥⣞⢓⣚⣭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠭⠿⡇⠀⣀⣹⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠧⠄⠀⣸⢛⣒⣲⠎
⠀⠀⡀⠈⠵⢌⠑⠢⣄⢀⣤⡀⠐⡲⠖⠒⢿⠿⣽⠛⠋⠙⡯⠍⠟⠋⢻⣿⣿⣿⣿⡟⠙⠉⠈⠉⡏⠙⠋⣽⠷⠦⠒⠶⢖⠂⢠⣤⢀⣠⠔⠊⡤⠮⠁⣀
⠀⠸⣇⠩⢷⠀⠛⣀⠀⢉⣈⣋⣀⣀⣂⣀⣈⣀⣙⠿⡄⡀⢹⡄⢹⡀⢘⣿⣿⣿⣿⡇⠀⠀⠀⢸⣀⢠⢿⣉⣀⣁⣀⣂⣀⣀⣛⣀⠁⠄⣀⠛⠀⡾⠭⣼⠇
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⢉⣡⡿⠋⣹⣧⡄⢧⠸⠿⠿⠟⠻⠇⠀⠀⣠⢾⡙⢿⣯⣉⠈⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⣀⣤⢶⢣⡟⢣⠎⠀⡿⣒⠌⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢶⠳⣹⢳⢦⣀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠴⠞⢛⣚⣼⡞⢠⠇⠀⠀⠁⠘⣄⠚⣧⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⡆⢹⣎⣜⣈⠛⠶⢤⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⡎⠈⠜⣈⡼⠛⠸⡗⡞⠀⠀⠀⢸⠀⠘⢄⠈⢢⣀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠚⡎⠘⠿⣌⡌⠆⠘⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡼⡙⡠⣰⡿⠫⠀⠁⣸⡆⠇⠀⠀⠀⠀⠷⠀⠘⠖⠖⠷⠒⠀⠀⠆⠀⠀⠀⠀⢸⠀⣿⡀⠀⡈⠻⣖⡀⡎⡷⡌⢆
⠀⠀⠀⠀⠀⠀⠀⣎⡾⢁⢡⣳⠋⢡⠀⠠⠡⡍⡷⢲⠀⠀⠀⣠⠋⡖⣻⠞⠒⠒⠀⠀⠀⠙⡄⠀⠀⠀⡸⢲⠉⡥⡀⠀⠰⠙⢳⣳⢠⠱⣞⡄
⠀⠀⠀⠀⠀⠀⠘⢻⣇⠸⡾⡇⠂⠀⢣⢠⡝⠀⠸⡀⣧⠀⢀⡇⠀⡇⢸⠘⠀⠀⠀⢠⣿⣷⢻⠀⠀⣠⢃⡞⠀⠘⡕⢰⠁⢀⠃⠿⡎⡠⡏⣟
⠀⠀⠀⠀⠀⠀⢠⢸⣏⢷⢣⢠⠀⡘⣄⡛⠀⠀⠀⠙⢍⠳⣼⠁⠀⡦⣿⠀⠀⠀⠀⠀⠈⠸⠘⣇⠔⢡⠏⠀⠀⠀⠙⣣⡆⡌⠰⢰⢳⢇⣿⢘
⠀⠀⠀⠀⠀⢀⢸⣸⢹⠈⡘⡄⢇⢱⠏⠀⠀⠀⠀⠀⠈⠳⢎⠓⠼⣅⣻⢐⠀⠀⠀⠀⣀⡠⠖⣹⠖⠁⠀⠀⠀⠀⠀⠈⠿⢠⠃⡏⡄⣈⢹⣸
⠀⠀⠀⠀⠀⠰⡟⢹⢸⡄⣇⢳⣘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠾⢍⣉⣸⣇⣉⡩⠽⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣸⢁⡇⣿⢸⠹⠾
⠀⠀⠀⠀⠀⠇⡇⣾⠘⡇⠻⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢼⠀⡏⢸⡄⡇⡇
⠀⠀⠀⠀⢸⢰⠇⣿⠠⠱⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠁⢸⡇⣇⢰
⠀⠀⠀⠀⡇⣾⢠⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⢡⢸⡈⡄
⠀⠀⠀⠀⠷⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠱⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣴⣯⠭⢭⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⠭⠽⣷⣄
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠈⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣆
⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⡀⠀⠀⠀⠀⠠⠴⣞⠉⠀⠈⢓⣶⠤
⠀⠀⠀⠀⢀⢜⣿⡿⢿⣶⣭⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⣵⣾⠿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠱⡄⣰⠋
⠀⠀⠀⠀⢀⣼⣹⣳⣾⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣾⣧⡿⣿⣶⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢹⠃
⠀⠀⠀⠀⢾⠀⠀⠀⠉⠉⠛⠛⠯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠖⠚⠋⠉⠁⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠶⠒⠛⠉⠁

⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠇⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠙
⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⡀⢀⡤⠶⠋⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠻⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣀⡤⠔⣺⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣍⠙⠓⠒⠒⠲⠶⠶⠶⠶⠒⠒⠚⠋⠉⣠⢴⣾⣿⣿⠋⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠲⠞⠲⠶⣄⣀⣀⣀⣀⡶⠒⠛⠋⠁⠀⠙⡿⠁⠀⠀⠀⣀⣤⠏⢀⡴⠾⠷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡼⢡⠏⢠⠏⣠⠶⠾⠷⠶⢭⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⡥⣏⣰⣋⣰⠃⣀⣀⣠⠶⢬⣷⣷
⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠳⣄⢀⠀⣀⠀⠀⠀⠀⣀⣀⡀⣼⠋⠀⠀⠀⠀⠀⠀⣧⡌⠀⠉⠧⠖⠁⠈⠁⣠⣄⡀⠙⡇
⠀⠠⢶⡋⠈⡷⠆⠀⠀⠀⠀⠀⠀⠈⠻⣍⡉⠛⠙⠛⠛⠉⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⢳⠞
⠀⠀⠀⠹⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⢀⣀⣤⡎⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠋⠁⠀⠉⠛⠲⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣃⣈⣷⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⣫⢼⣾⢼⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⠀⡠⢷⡈⠾⠿⠞⡿⢇⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢒⠟⠀⠘⢸⠘⠂⠀⠚⢩⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠮⡇⠀⢀⡘⢠⣶⠀⢀⣴⣧⢠⡀⠀⢲⠩⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⣠⢖⠉⠐⢘⡿⡀⠘⣻⣏⡎⠑⠀⢈⠆⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠀⢵⠀⠄⢠⠃⡀⠉⠀⡀⢀⣧⢈⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢆⠀⣼⠃⠐⠮⡶⢴⠓⠏⠙⠫⠎⣍⣩⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⡸⣌⠸⣛⠀⠀⠀⠉⠛⠊⠀⢀⣸⡋⢀⡔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠣⠅⠈⢤⡄⠀⠉⠑⢶⣤⣥⣤⣤⡴⠏⠡⠈⠉⢨⠊⢱⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠱⠊⠐⠀⣀⠀⠀⠀⠸⡂⡝⡀⠐⣄⠀⠠⡄⣰⡿⠒⢈⠚⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⡒⠤⠜⠀⠀⠀⠐⢺⡇⠘⢆⣬⠆⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⣕⠖⠂⠀⠰⠀⠀⠀⢿⠀⢨⠁⠀⠀⢈⠟⢃⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⣀⣀⡐⠁⡰⠂⠸⠇⠲⢆⣠⣂⣠⠄⠥⠔⠉⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠝⡒⠣⠔⠢⣭⣓⣈⡠⠟⠐⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠰⢄⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⠂⠀⠀⠀⠀⠀⣠⠏⡐⠶⠃⠀⠀⠀⢀⡐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⢀⣞⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠡⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⡵⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠤⣌⠆⠀⠀⠀⢰⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢥⠊⠀⠀⢔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣤⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⡀⠀⠀⠀⢤⡐⠀⠁⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡀⠀⠈⠢⡤⠀⢄⠀⠀⠀⠀⠀⠀⠠⣎⢂⢈⡰⠂⠁⠀⠀⠀⠀⢈⡤⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠉⢆⠀⠀⢄⡀⣠⠀⠀⠀⠀⡖⢢⠀⣩⠜⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡐⠀⠀⠀⠑⡄⠀⠀⠀⠑⢤⡈⢆⢙⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠒⠣⣰⣁⠁⠑⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⡠⠊⠈⠢⡀⠀⠀⡠⣅⡜⠉⠀⠀⠀⢀⠊⠈⠲⠀⠀⠀⠀⢀⣠⢉⠀⠐⠗⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⢀⠔⠁⠀⠀⢀⠜⠓⢄⠑⠉⠈⢢⠀⠀⠀⠀⠢⠄⠘⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⡰⠃⠀⠀⡠⠖⠁⠀⠀⠀⣁⠦⢀⡀⠡
⠀⠀⠀⠀⠀⠀⡌⠌⠀⡠⠊⠀⢀⠤⠊⠀⠀⢀⠠⠒⠉⠀⣀⠠⠘⠋
⠀⠀⠀⠀⠀⡐⠌⢀⠔⠁⡠⠐⠁⢀⡠⠐⠈⣀⠠⠐⠊⠉
⠀⠀⠀⠀⢰⠏⡠⢃⠴⠊⡀⠄⢂⠡⠔⠒⠉
⠀⠀⠀⢠⣏⣨⢔⣡⠔⠍⠒⠉
⠀⠀⢠⡿⠟⠛⠉


⣿⢿⠿⡿⡿⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠋⣀⠤⠄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠚⡕⠣⠎⠉⡇⠐⠁⠀⠀⠈⡰⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢠⠰⠵⠆⠀⡱⠔⠠⠤⠄⠊⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢤⡀⠄⠉⠀⢊⠥⠜⠒⠒⠒⠒⠺⠌⡑⢇⠒⠒⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡼⠓⢲⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⢀⠔⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠠⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠠⠆⡠⠐⢏⡀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡴⠈⡇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠈⠀⠠⣠⠞⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠐⠂⠀⠈⠁⢀⡀⣀⠐⢡⠆⠉⠀⢀⠀⠀⠀⠈⢀⢠⢖⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢕⠂⣤⣀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠉⠀⠀⡘⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢀⡠⠤⡞⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡂⠀⢳⠈⠂⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣸⣧⠀⠘⣧⠀⢦⡔⠀⠀⠀⠀⣤⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⣧⠀⠀⠈⠑⢌⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠂⠀⠈⠀⠉⠓⠒⠀⣤⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⡀⠂⠀⠒⠀⠀⠚⡁⠀⠀⠀⠀⠈⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⠠⠆⠀⠀⠈⠉⠉⠁⠐⠒⠶⣦⣀⡙⠲⠦⠤⠴⠖⠋⠙⠦⠄⠀⠐⠓⠁⠀⠀⠓⡀⠀⡩⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣈⢈⡉⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⢠⢢⠝⠚⠣⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠰⠘⠂⣄⠀⣀⠀⠀⠀⠀⢀⠀⠐⠁⠀⠀⠀⡰⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠴⠀⠀⡎⠀⠈⠉⠓⢦⠠⠄⠐⠲⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠴⠚⠃⠀⣦⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢃⠀⠀⠀⢀⡼⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁⠀⣷⡀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠒⠀⠐⠒⠉⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠁⠒⠐⠒⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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