Calamari Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠈⠀⠀⠀⠀⣀⣀⡃
⠀⠀⠄⠀⠀⢀⠄⠂⠀⠀⠠⠀⡁⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠚⠀⠀⠀⠀⠐⠚⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣷⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⡀⠉⢀⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠈⠄⠈⠉⠁⠀⠀⠀⠠⠀⠀⠀⡄
⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠈⠀⠀⠀⢐⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢄⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠉⠚⠈⠑⠆⠀⢀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠄⠀⢠⠄⠀⠀⠇⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣦⡐⠀⠀⠀⢁⠄⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠑
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠠⠆⠀⡀⠀⠀⠤⠤⢤⠤⠴⠦⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⣼⡟⠀⠀⣀⡇⣀⣀⡀
⠀⠀⠀⣠⠶⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠛⢷⣾⢿⣤⣴⢟⠛⠋⠉⠐⠀⠌⠁
⠀⠀⠈⠢⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠻⣿⣿⣿⣿⣛⡛⠛
⠀⠀⠀⠀⠀⠉⠉⢉⠑⠒⠒⠀⠀⠤⠤⣤⣤⡄⠀⠀⠀⠀⣿⣿⡷⣶⣄⣭⣙⢿⣿⣽⣛⠓⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠈⢻⣷⠙⡟⠛⠿⣯⣿⡲⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠂⠀⠻⢟⣿⣿⣿⣿⣿⣿⡻⠟⠀⠐⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⡴⠞⠛⢷⣆⠀⢙⣿⣿⣿⣿⣿⣿⡋⠀⣰⡾⠛⠳⢦⣌⠙⢦⡀
⠀⠀⠀⠀⠀⢀⣿⠁⢰⣏⡠⠀⢀⣾⡟⠀⠘⣏⣻⣿⣿⣟⣹⠃⠀⢻⣷⡀⠀⢄⣹⡆⠈⣿⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⢀⣴⣿⠋⣰⠏⠃⢸⣿⣿⣿⣿⡇⠘⠹⣆⠙⣿⣦⠀⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⣾⣿⠁⠀⠹⣧⣄⣼⣿⣿⣿⣿⣧⣠⣼⠏⠀⠈⣿⣷⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠹⣿⣷⣶⣶⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣶⣾⣿⠏⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣄⣉⣉⣭⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣭⣉⣉⣠⣤⣾⠿⠋
⠀⠀⣴⠛⠛⠻⢷⣦⣄⣈⡙⠛⠛⢛⣛⣯⣿⣿⡿⠋⠙⢿⣿⣿⣽⣛⡛⠛⠛⢋⣁⣠⣴⡾⠟⠛⠛⣦
⠀⠀⠈⠉⠁⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⢿⣿⣿⣿⣿⠷⠦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠱⡄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⣠⣼⡿⠟⣋⣭⣶⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣴⡿⢋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣴⣶⡿⠿⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣠⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣶⣶⠶⠟⠋⢀⣼⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠻⣿⣿⣿⡏
⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⠻⠟⠁
⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠘⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣠⠤⠤⠤⠄⣀⣀
⠀⠘⣿⣷⣄⠀⠀⠀⠀⢀⣴⡿⠟⠛⠟⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⡄
⠀⠀⠈⠙⠿⣿⣷⣶⣶⣿⣻⣶⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿
⠀⠀⠀⠀⢀⣴⠿⢻⡿⠉⠉⣉⣹⣿⠻⠵⠛⠉⣡⣿⣿⣿⣿⠱⠗⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿
⠀⠀⠀⢀⡟⠁⢀⡾⣥⠶⠛⣹⣿⠃⠀⠀⠀⣼⣟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢸⠁⢠⠞⡟⠁⠀⣰⡟⠃⠀⠀⠀⠰⣿⣾⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠨⠐⠋⠘⠀⠀⣰⡟⠀⠀⠀⣀⣤⣿⠟⢹⣿⣿⣱⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣀⣤⡿⠟⢩⡟⠀⢘⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡼⠛⠁⠀⣠⠏⣠⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠐⠊⠀⠀⣰⠋⠀⠀⠂⣩⡴⠛⠉⢀⡿⠉⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠜⠁⠀⣀⣤⠞⠁⠀⠀⠛⢿⣷⣦⣤⣤⣤⣤⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠂⠀⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⠒⠀⡒⠠⣉⡛⠳⡀⠀⠀⠀⡼⠉⠀⠈⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠄⠀⠀⡇⠀⠀⠀⣮⠁⠀⠀⠀⠀⠀⠠⠤⠍⠁⠀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠈⠂⠈
⠀⠀⠀⠀⠆⠀⠠⠀⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡃⠀⠀⠀⢀⠮⠉⠀⠀⠀⠀⢠⢼⡄⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠘⠚⣃⣠⣤⠖⠁
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠈⢤⠀⠀⠀⢀⠀⠀⠀⠀⣿⡄⠈⠓⠒⠋⠁⠀⣠⠆⠀⠀⠁⢀⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⢴⣆⡈⠓⠠⠄⣄⣠⠠⠽⠿⠢⣄⣀⣠⠤⠚⠁⠀⢀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣾⡦⢋⣑⣶⣀⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣀⣴⡞⠁⠈
⠀⠀⠀⠀⢀⡔⠊⠑⠀⠀⠀⠼⠁⠀⠀⠀⠈⠁⠱⠴⣦⡴⢴⠎⠀⢀⣴⣫⡟
⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠘⢠⡀⠀⠀⠀⠀⢀⡀⠄⠀⠉⠀⠀⣼⠛⠃⠁⢀
⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠤⠚⠉⢁⡀⢴⡖⠩⠑⠒⢹⡇⠀⠰⣯⣀⡠⠒⠁
⠀⠀⠀⠀⠀⠈⠓⠠⢄⣠⡄⠴⠀⠛⠀⠀⠀⢀⠰⠔⠂⡿⢳⡀⠐⠿⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢰⡇⢸⡷⣄⠀⠉⠐⠂⠰⢂⢶⡖⡀⡀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠘⡇⠰⠆⠃⠀⠀⠀⠀⠀⠀⢠⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠹⣄⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠣⡀⠈⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢰⡄
⠀⠀⣀⣀⣀⡥⠠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⣦⣴⣶⣦⣀⣼⡿⠁⢀⣠⣴⣿⣤⠶⢒⢂⢀⠤⠀⡀
⡠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣀⢸⣟⣛⣻⣿⣟⣯⣀⣀⣠⠀⠀⠁⠂⠂
⠀⠲⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡟⠋⠘⢚⣿⣿⣿⣿⣭⣉⠉⠁
⠀⠀⠀⠀⠈⠉⡉⠉⠐⠒⠀⠀⠀⠠⠤⢤⣤⣤⠀⠀⠀⠀⠀⢻⣿⣿⡷⣶⣤⣨⣭⡛⢿⣿⣭⣙⡛⠁⠀⠀⠀⠀⠀⣴⡤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠉⠈⠀⠹⣿⣇⠹⡟⠻⢿⣿⣣⣿⢀⡀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⡄⠁⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣴⣭⣿⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⡿⠿⠟⡚⠉⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠛⠉⢁⠂⡀⠀⠀⠀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠉⢀⡤⠔⠀⠀⠁⠀⠀⢀⡴⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢧⣢⡶⠃⠏⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⠀⠀⠀⣠⡜⢛⠋⠙⣯⣢⠀⠀⠀⠀⣀⣤⡶⠡⠶⠴⠖⠚⠁
⠀⠀⢀⠀⠀⡠⠔⠋⠁⠀⢐⣀⠀⠄⠐⠁⠳⢤⡠⠈⣿⣧⣤⣶⣾⠿⠛⠁
⠀⠀⠈⠄⢚⣀⣀⡼⠶⠿⠟⠛⣛⡁⠂⠀⠀⠲⠛⡰⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠙⣡⡴⣢⡾⠟⢋⣥⠄⠂⣄⠔⠋⠁
⠀⠀⠀⠰⠴⢚⣥⠞⠡⣠⢭⣤⣶⠞⠋
⠀⠀⠀⠀⢠⠞⠁⠀⠘⣱⠟⡽⠁
⠀⠀⠀⠀⠀⡞⢀⡤⠎⠁⠀⠧⡄⠠⠴⠂⠄⠊⠁
⠀⠀⠀⠀⠈⠀⠁

⠀⠀⢶⣦⣴⣶⣶⣶⣶⡆
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⢠⡞
⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡩⣮⣻⣶⣤⣤⣴⣶⣿⣿⣿⣆⠀⠀⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠹⣿⣧⣸⡉⣣⣿⢀⣤⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⡟⣿⢿⣿⣿⣦⣌⠻⢿⣿⠛⣱⡟⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⢟⣿⣟⠻⣾⣷⣭⣿⢿⣍⡿⣾⣿⡴⠋⠴⢾⡿⠦⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡆⠀⠻⣿⣆⣈⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⢀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣴⣾⣿⣿⣿⣷⣴⣿⣻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⣿⠀⠀⠀⠀⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⠀⠀⠀⢀⣀⡀⠙⠶⢤⣤⣤⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣄⠀⠀⠀⠀⠈⢿⣥⠀⠀⠀⠀⢰⣏⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣤⠽⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀
⠀⠀⠀⠀⣀⣀⡧⠀⠀⠀⠀⠂⠒⠒⠘⠛⠀⠀⠀⠀⠀⣦⣴⣄⣀⣾⠇⢀⣤⣾⡤⠤⢄⠠
⠀⠀⢠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢸⣿⣽⣿⣿⢧⣤⠄⠀⠀⠁
⠀⠀⠀⠉⠓⠒⠂⠤⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣾⣿⣅⡀⢸⠿⣿⣟⠷⠤⠄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠛⠋⠙⠛⠉⣻⣮⢻⡿⣷⣶⣴⣤⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡌⠗⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⠁⠀⠀⠀⠀⢙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠇⠀⠀⠀⠀⠀⠀⠇⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠤⣈⢹⠆⠀⠀⠀⠀⠀⠀⢾⢉⡠⠴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡇⠠⡀⠀⠀⠀⠀⡰⠈⡇⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠈⠀⠀⠀⠈⢀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⠀⠑⠁⢀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠐⠀⠀⠀⠀⢳⠄⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡀⠀⠀⠀⠠⠊⠀⠀⣠⠈⠀⠀⠀⠀⠀⠈⢠⡀⠀⠈⠢⡀⠀⠀⠀⡀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⢀⠀⠀⠀⢀⠀⠁⠀⡎⠀⠀⠀⠘⡆⠀⠁⢀⠀⠀⠈⢀⠀⠈⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠂⠐⠀⠀⠈⠁⠀⠀⡠⠀⢲⠀⢰⠀⠠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⣀⡐⠀⠁⠀⠀⠘⣀⣘⠀⠀⠀⡀⠐⣀⡠⠔⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡈⠉⠁⢀⡠⠞⠉⠀⠈⠙⢦⣀⠀⠈⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠁
⠀⠀⠀⠀⢠⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠂
⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠈⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⣽⣿⣿⣿⣿⣿⣿⡿⣀⣸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠺⣮⣽⣿⣿⣿⣿⣿⠟⠉⠀⣀⣀⠄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣿⣦⣉⠛⠻⢿⣿⠟⠁⢀⡀⢺⣿⣿⣿⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⢠⠏⠠⠀⠘⠀⠀⠙⠟⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⢋⣁⣀⠈⡟⠀⠀⠀⢿⣦⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢿⣿⣟⣿⣣⡇⠀⣀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡛⠃⠉⢠⢧⠐⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⢐⠇⠀⠑⠈⢧⠀⠀⠀⠀⢈⠉⠀⠈⠛⠉⠻⡿⠛⠛⠉⠉⠉⠉⣁⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠐⢴⣸⠀⠉⡹⠛⠒⠒⠤⢄⡀⠀⠀⠁⠈⠙⠻⡏⠉⣀⡙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣽⣦⠎⠀⠀⠀⠀⠀⠘⠁⣲⡄⠀⠀⠀⠘⢤⣿⡿⢟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡤⠚⠉⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠐⠀⠆⠀⡾⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⠔⠉⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡿⠀⢀⠀⠀⣀⢀⠈⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠆⠈⠀⢸⣃⡴⣢⠀⠠⣿⣿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⢀⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢈⡁⠀⠀⣠⣶⣿⠿⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡂⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⡦⣄⣿⣿⣏⠀⠀⠊⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠈⠧⢸⡄⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⣿⡿⠛⠁⠀⠀⡌⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡄⢉⠅⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⢈⠒⠋⠀⠀⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣶⡀⠸⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠒⣩⠉⢢⠁⢐⡏⠀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⢀⣀⡀⡀⢙⠁⠀⠄⣀⡀⠀⠀⠀⢰⡁⣷⠘⢆⠀⠀⠮⠀⠀⠀⠀⠀⣤⣿⣮⡟⠀⠀⠀⠀⢀⣠⣄
⠀⠉⠉⠁⠐⠋⠓⠀⠐⠓⠒⠋⠀⠀⠈⣇⠈⣀⡜⠀⠀⠐⠒⢐⠀⠀⠘⠿⣽⠟⠀⠀⠀⠀⠀⠺⠷⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢞⠉⠀⠀⠀⠀⢀⠀⡠⡄⠀⠀⢀⡰⡖⠃⡄⠀⠘⠚⠿⠟⠃⠀⠀⢀⡁⠀⢤⡀⠀⠰⠷⣾⠿⠄
⠀⠀⠀⢠⠆⠀⠀⢠⠐⠐⢋⠀⠀⠀⢈⠁⠄⠊⠀⠀⠀⠀⠀⠀⣠⠄⠰⠋⣐⣂⠀⠁⠀⠀⠐⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠄⠀⠀⢈⠁⠶⠄⡀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠰⣦⣤⠀⠰⠁⠀⠀⠀⠚⠀⠈⠁⠀⠀⠁⠀⢠⣤⣀⣤⡄⠀⠀⠘⢀⣀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢠⠐⣀⡤⠀⠀⠀⡀⢠⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⡀⡀⣤⡈⠀⠠⠤⠴⠊⠁⠀⠀⠤⠄⢀⡀⠀⠀⠘⠄⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠐⠒⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠈⠀⠀⠈⢀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠲⡀⠀⠀⠀⠐⠀⠀⡀⣂⢢⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠿⠞
⠀⠀⠀⠓⠄⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⡀⠰⡆⠀⠀⠀⠀⣀⠀⠀⣀
⠀⢦⣤⣤⣤⡴⠀⠐⠿⣽⣦⠿⠀⠀⡀⠊⠑⢀⠀⠀⠉⠁⠀⠉⠡⠀⠰⢁⢶⠦⣔⢢⡀⠾⢏⡽⠃
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉
⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠰⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠀⠘⢻⡙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠿⠄⠀⠀⠀⠀⢦⣤⡤⠟⠁
⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠁⣠⡆⠀⠠⠄⠂⠴⠈⠀⠀⣀⣿⣄⡑⠀⠀⠀⢀⠀⢢⠀⠀⠀⠀⠀⠛⠃⠈⠀⢠⡤⡤⢤⡄
⠀⠀⠀⠈⠂⠀⠀⠀⢀⣀⠀⠀⠀⠤⠟⠽⠑⠷⠀⠀⢀⡘⢑⡎⠀⠀⠘⠋⣤⠀⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠂
⠀⠀⠂⣀⡀⠀⠀⠀⠀⠉⡄⠀⠀⢀⣠⡴⠶⠂⠀⠀⠀⠀⡀⠒⠀⠀⠀⠒⠒⠂⠤⠀⠀⠘⠃⠀⢴⢓⡄
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣀⠀⠿⠁⠀⢀⣶⡤⠼⠶⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣷⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⡀⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢿⠋⢴⣮⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⠁⣤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⡅⠀⠀⠀⣠⠞⢡⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡇⠠⣤⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⢋⢟⡁⡀⠢⣄⠀⢀⣴⡖⣶⣶⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⣶⠛⢳⣾⡇⣶⠛⣷⡾⣷⣿⡿⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢷⡀⣀⢉⣹⣯⣿⣯⣿⣿⡟⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠈⢷⡀⠀⠀⢉⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⣿⣷⣯⣄⠙⢶⣄⠀⠉⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⡎⣴⠅⠀⠀⠙⣿⣿⣿⣷⣦⣍⣳⣶⡁
⠀⠀⠀⠀⠀⠀⠀⢧⠙⣄⡀⠀⣤⣼⣿⣿⣿⣿⣿⣿⡈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡻⣷⣬⣿⠟⢙⣿⣿⣿⣿⣿⣆⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣿⣠⠎⠙⣿⣿⣿⣿⣣⣆⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡵⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠅⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡛⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠄⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣠⣈⣡⡘⠋⠀⠀⠀⠀⠀⢀⡀⠄⢀⡀⠴⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠑⠀⠐⠈⠀⠀⠀⠈⣅⣀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡠⠃⠀⠀⢀⠀⠀⠀⠀⠀⠁⡀⠐⠁⠀⡀⢀⠀⠀⠁⠀⠠⠀⠀⠠⠀⠊⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠠⢐⠡⠂⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠋⢉⠡⡉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡆⢠⠋⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢋⠀⠂⠀⠐⠖⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⠀⠀⢀
⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠰⢄⠰⠄⠤⠂⠀⢀⡤⠠⠀⠆⠆⠰⠀⠀⠀⠀⠜⠢⢀⡠⠄⠤⠄⢠⡤⠀⠰⠄⠠⠀⠀⡠⠄⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠰⠂⠸⠀⠀⠀⠀⠀⠀⠠⠤⠥⠀⠐⠀⣈⢐⠂⠀⠀⠃⠠⠄⠆⢀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠙⠂⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠐⠒⠀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠠⠄⠀⠂⠀⠀⠀⠠⢉⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢉⠁⠀⠂
⠇⠀⠈⠀⠑⠦⠠⠄⠀⠈⡄⠀⢀⠤⠆⠀⠈⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠒⠀⠀⠸⡀⠀⡇⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠥⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠒⠈⠀⠄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⡀⠀⢠⡴⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠬⢉⠡⡐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠈⠁⠀⢠⣰⡀⠀⠀⠀⠠⠀⢀⠀⠀⢀
⠀⠀⠀⠂⠐⢊⠢⠀⠀⠀⠀⠀⣈⠀⠤⣴⠁⠀⠀⠀⠀⠁⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠀⠂⠀⠀⠐⠂⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠇⠀⠀⠀⠀⡤⠀⣈⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢛⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣤⣤⣤⣤⡀⠀⠙⠚⠋⢙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡓⠋⠁⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⣿⡆⠀⣠⣶⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢼⣧⣤⣴⡓⠋⠀⠀⠀⣸
⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣠⡶⠛⣲⣶⣿⣿⣿⣶⣿⣿⡅⣀⣤⣶⣶⣶⣦⡀⠰⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣼⡿⠋⠉⣹⣷⠀⠀⠀⠀⣿
⠀⠘⠷⣶⠛⠛⢿⣷⡄⣸⡿⠷⠀⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣻⡿⠛⢻⣿⣿⣶⣶⠟⠀⠀⣀⣠⣶⣶⠤⠀⠀⠀⠀⠀⣴⠋⣴⣿⣟⣀⣴⣾⣿⠿⢀⣀⣔⣶⣿
⠀⠀⠀⠘⣷⣤⣾⣿⣷⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣦⣀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⠀⢿⡀⠀⢷⣼⣿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿
⣶⣾⣶⣴⣿⣿⣿⣿⣼⣿⣇⠈⠛⠚⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⠻⣿⣷⣶⣿⣿⣿⣉⣙⣻⣿⡿⠷⢟⣉⡳⠀⢹⣿⡀⢲⣿⣿⣿⢿⣿⣿⣷⣿⣿⡻
⣿⣈⠙⠛⢛⣿⣿⣿⣿⣿⣿⣷⣤⠀⠙⢛⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣎⣻⡿⣿⣿⣷⣿⣿⣽⡿⡇⢰⡏⣉⣡⣤⣨⣿⣷⣾⣿⣷⣻⣹⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢋⣿⣿⣛⣿⣿⣿⣿⣧⣠⣿⣿⣿⣻⣷⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⢋⣿⣾⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣇⣀⣥⣤⣿⣿⣛⡛⢿⣿⢿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡻⠛⢿⣿⣿⣿⣿⡿⢩⡇⣠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠐⣀⣴⣿⣿⠏⠀⠀⠀⠈⠋⡀⠀⠡⠁⡀⠀⠤⠀⠔⠀⢀⠀⠀⡀⡀⠁⢀⠄⠀⠀⢼⠿⠟⠻⠿⠿⣷⡀
⠀⡀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠟⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠐⠆⠉⠛⠁⠉⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⣜⣠⡖⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⡐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣐⢎⠗⣼⣷⡱⡀
⠀⠀⠉⣠⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡿⢷⣮⠡⠊⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⢯⣠⣴⣾⠫
⠀⠀⠀⡆⢀⠀⠀⠀⢀⡴⠖⣢⡶⢶⡄⠀⠘⠀⠀⠀⠸⢛⠿⠟⠀⠀⢀⠂⣵⠁⠀⡱⢍⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⢰⠀⢠⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⠀⠇⠀⠐⠀⢀⠀⠀⢶⡷⣷⠆
⠀⡄⠰⠔⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢆⣾⠇⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢫⢯⡇⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠋⡼⢰⣾⡞⣃⢉⢹⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣶⣳⣰⢸⡘⡆⡇⣿⡧⣌⢢⣿⡿⡇⢀⢠⢠⠀⠀⠀⠂⠀⠂⠓⠀⠁
⠀⠀⠀⠀⠀⢴⡶⣶⣿⣿⣽⠖⡴⠻⢹⡼⢳⣧⡇⢿⢹⣬⣿⣿⣇⣧⠎⠑⠓⠷⣤⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠑⢮⡻⣿⣿⣷⣶⣾⣾⣶⣯⣾⣾⣿⣿⣿⡟⡜⠀⠀⠀⠀⣽⣿⠀⣈⠻⠉⠁⣶⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⡻⢿⣿⡏⠓⠪⣝⢿⣿⣿⡿⢟⠞⠀⠀⠀⠀⠀⠞⣻⣦⠉⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠑⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠰⠋⠡


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣈⠫⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠨⣥⠀⠙⣃⠀⠐⠀⠀⠀⠀⠐⠈⠁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⢰⣋⠰⠿⠀⠺⠽⡀⠀⡀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡦⠁⣤⠠⢞⡇⠠⡇⠀⡀⠀⠀⠀⠀⢤⢆⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⡇⢸⠅⣐⡋⢈⠧⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠄⠐⠀⠂⠒⠸⢎⣀⡚⣠⢀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⣫⣑⠂⢦⡀⠀⠀⠀⢠⣴⣶⣤⣤⣤⠒⠀⠀⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣙⣤⠤⢤⡃⠀⠐⠿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⡋⢈⡂⡁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡷⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⢄⡀⠀⠹⣿⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠉⠀⠀⣀⣄⠀⢀
⠀⠀⠀⠀⠘⢷⣤⣄⣀⠀⣀⣠⠜⠁⠀⠀⠀⢀⠀⠘⣄⠀⠤⠂⠀⡅⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⠶⠷⠶⠷⠶⠶⠶⠾⢻⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡴⢟⡋⣠⣐⣒⣤⣄⠐⣃⡀⣈⡁⠰⢶⣄⣉⡁⠙⠛⠻⢷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⢀⡄⠈⣴⠏⢉⣉⠀⠴⠀⠉⠁⠋⠉⠰⢶⠀⠀⠁⠖⠸⠳⢦⣀⠬⡉⢿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⢋⡉⡡⢖⡚⠁⣥⡾⢳⡄⢀⠀⠀⣛⡛⠀⠙⢁⡀⢀⡤⠶⠖⢲⡀⠲⠆⣈⠐⠀⣤⠀⡍⢿⣤⡀
⠀⠀⠀⣴⡶⠶⠶⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⣶⡄
⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⠙⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⣀⠤⠔⠒⠊⠙⣏
⠀⠀⠀⠀⠀⠀⠀⢰⡡⠤⠒⠊⠁⢣⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢈⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⣀⣀⠀⣧⣞⡂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣯⣖⡀⢱⠙⠺⡖⠙⡖⠒⠒⠒⠒⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⠭⠔⠃⠠⡄⢼⢽⠁⠀⠈⠛⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡲⠄⠀⠀⠈⠉⠁⡤⢄⡙⠫⣅⠒⠻⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⢾⠁⠀⢠⡀⠀⢸⡀⢱⣄⠈⠳⡢⢽⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡱⠁⡸⢠⢻⢸⢳⠀⢸⠘⢦⡹⡑⢄⠈⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢠⢣⠃⢸⡎⠀⡇⠸⡆⠀⠙⠪⣦⡳⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⠁⠀⠇⡇⠸⡀⠀⠀⠈⠁⢸⠂⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠘⠙⢄⠛⢹⠔⣄⠀⠀⢏⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠩⠗⣦⠈⡖⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡐⠀⠐⢀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠊⣀⣴⠏⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⢤⡀
⢀⠠⠤⠤⢀⣀⠀⠀⡀⠀⠀⠀⠀⠔⠊⠁⡠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⡸⢀⠤⠤⢄⡀⠈⠣⡀
⠀⠀⠀⠀⠀⠈⠻⣁⠈⠢⠀⠐⠁⠀⣰⠝⠀⠀⠀⠀⡠⠤⠤⢄⡀⠀⠀⠰⣇⠀⠀⠀⠙⢦⠀⢱
⡀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣰⠃⠀⢜⡁⠀⠀⠀⠀⡜⠀⡰⢶⡤⠴⠄⡀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠈⠻⡿⢶⣦⡀⠀⠀⠀⠱⣿⠀⠀⣾⡇⣄⠀⠀⢀⠇⢠⠋⠁⠀⢀⡀⠀⠐⠄⣀⠀⣀⡤⠋⢀⡞
⠀⠀⠘⡄⠈⠹⡦⡀⠀⠀⠸⠀⠀⢸⠃⠀⠉⠈⠁⢀⠏⠀⠈⣸⡟⠀⠢⢀⠀⠈⠁⠀⠀⡠⠊
⢢⠀⠀⢷⠀⠀⡀⠈⢦⡀⢸⡇⠀⢰⣿⡤⠤⠴⠚⠉⠀⣤⣰⡿⠁⠀⠀⠀⠉⠙⠒⠈⠁
⣾⡀⠀⠘⣄⠀⠁⠀⠀⠙⠸⣧⠀⠠⣿⣶⠀⠀⠀⢀⣠⡾⡟⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⣀
⢧⣹⡄⠀⠙⢄⣄⠀⠤⢤⣀⡘⠀⢠⢿⡹⠓⠛⠉⠀⢸⠘⣇⣀⣼⠆⢠⠞⣁⡶⠒⠛⠳⣮⠳
⠺⣿⡙⣆⡀⠈⠙⠂⠴⠶⠚⠁⠀⣼⡟⡥⣀⠀⠀⠀⠀⠓⠦⠕⢊⡴⣁⡼⠋⠀⠀⠀⠀⡾⣠⠁
⣤⣦⣽⠽⣭⣦⠠⣄⣀⣤⣀⣔⣾⢛⠯⣄⣠⠀⠁⠐⠢⠤⠔⠚⢁⣴⠟⠁⠀⠀⠈⠃⠛⠒⠁
⣿⠭⠛⠁⠚⠫⠹⠿⢛⠲⠛⠉⠉⠀⠀⠀⠉⠙⠙⠆⠶⠴⠲⠛⠋

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠁⠀⠀⠀⠀⠉⠈⣆⠈⠁⡎⠀⠂⠀⠑⡄⠀⠀⠠⠁⡠⠖⢄⠠⠕⠌⠀⠀⠀⠀⠀⠃⠠⠀⡠⠂⠀⠂⠁⠀⢅⢜⠀⢀⠄⠒⣄⢤
⠀⠀⠀⡀⠀⠤⠀⢐⠊⢮⡀⠀⠳⡀⠈⠆⢄⠀⡆⠀⢇⣀⡠⢀⠔⠀⠀⠀⠠⠀⠀⢀⠀⡀⢀⠊⠀⠀⠈⡰⠁⢠⣤⡉⠀⠓⠒⠂⠌⠉
⠀⠀⠐⡲⠤⠁⠀⡀⢈⠠⠃⠀⠀⠑⠢⣈⠠⡑⠘⠀⡀⢒⢝⣱⠀⠀⠀⢠⢁⣄⡀⡈⠀⠃⠂⠀⠀⢀⠜⢡⠀⠀⠀⠀⠄
⠀⢰⡀⠐⢒⠂⠀⠀⣠⠄⡒⢢⢂⠒⠠⣀⠀⠁⢀⣾⠅⠘⡮⡞⠀⠀⢢⡐⠁⠀⠰⠀⠀⢈⠐⢄⠔⠁⠀⠀⠏⠑⠒⠂⠀⠀⠀⠈⠁⢄
⠀⠀⠁⠀⠘⠀⠠⠊⠄⠄⢀⢁⠂⣬⠤⣂⡗⠀⠈⠁⢀⠀⢹⠃⠀⠈⠙⠥⢀⣀⢾⡢⠄⠈⠀⠁⠠⢁⠂⠀⠑⠒⠊⠀⡄⡘⠂⡄⠀⠈
⠀⠀⡏⠙⡆⠀⢡⠬⢉⠭⠆⠤⠔⠊⣉⡴⠀⢸⠉⠉⠑⢢⠈⠁⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠁⠐⠗⠀⠐⠀⠀⠀⠀⠐⡀⠠
⠀⠀⡷⢀⠘⢄⠀⠐⠒⠒⠒⠒⠋⠉⠀⠀⠀⡌⠀⠀⠀⡷⠀⢀⠠⠀⠠⡊⠘⠀⠀⢠⣾⣿⣻⣟⣙⣷⠀⢠⠀⠀⢠⡀⠀⣰⠃⢀⠋
⠀⠀⢧⠐⠂⡸⠀⠀⠀⢖⠒⠂⠠⠤⠐⠲⠂⠙⠀⠒⠊⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⡀⢀⠿⠁⠀⠀⠀⢃⠐⢀⡀⠐⠀⠀⠈⠉⠁
⠀⠀⠈⠉⠉⢁⠔⣄⡀⣄⠉⠀⠒⠒⠈⠁⠀⠀⣀⢒⣂⠀⠀⡠⢀⡀⠀⠒⡲⢲⠀⢡⠀⠀⠀⡙⠅⠨⠀⢀⡀⢇⠀⠀⣠⠈⠣⠈⠀⡆
⠀⢌⡀⠅⠀⠂⠀⠈⠀⠈⠀⠀⠀⠊⠖⣂⡎⠧⠓⢃⠜⣠⡄⢰⠀⣀⣀⡀⠁⠁⠀⠀⠐⠂⠀⠐⠀⠁⠰⠀⠀⠉⠀⢐⠁⠀⡠⠋⠑⠕
⠀⠀⠀⠀⠌⠀⠀⠄⠠⠀⢸⠆⠈⢉⡀⢁⠀⠄⠂⢁⠬⠐⡁⢀⡮⠞⠁⠀⠀⠀⠈⡄⠀⠋⠀⢠⠦⠄⠰⠢⠄⣤⠀⢇⡀⠼⡀
⠀⠀⠀⡈⠠⢄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠄⠰⠗⠚⠓⠉⠀⣠⠾⠆⠀⠀⠠⡠⠁⠀⠀⠃⠌⠀⠁⠉⠀⠃⠀⠱⠀⠐⠊⢁⠔⠂
⠀⢰⡀⠁⠀⠠⠒⠀⠀⠀⣐⣥⡌⠁⠄⠀⣀⣀⣤⡄⣸⣆⠀⠀⠲⠉⢀⠳⠒⠀⠠⠲⠀⢀⠠⠀⠁⠀⠠⠀⠀⠀⠴⠀⠀⠀⡄⢀
⠀⠀⠉⢀⡄⢢⠞⠁⠀⠀⠀⠘⢄⠁⠀⠜⠉⠀⠀⠠⠀⠚⠛⠂⠠⢒⠁⡀⠀⠀⡀⠀⡀⠸⠂⠀⢀⣀⣀⣀⣀⠤⠶⡀⠀⢀⠁⠀⠘⡆
⠀⢐⠁⠖⠀⠠⠀⢈⠀⣀⢀⣀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠠⠀⠒⠄⠀⠑⠁⠅⡀⠤⠊⠁⠀⢀⢀⠀⠀⠀⠀⠀⠂⠈⠐⢂⠈⢤⣀⠠
⠀⠈⡄⠀⢀⠤⠂⠀⡊⡴⠀⡄⠡⡀⠐⠀⠀⠐⠒⠛⠠⠁⠀⠀⢰⠀⠠⠀⠤⠃⠔⠐⠄⠰⠯⢀⡀⠀⠀⣀⠔⠆⠀⠙⠗⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢱⠈⠈⣀⠀⠄⢰⠁⠂⠒⠀⠐⠀⠀⠀⠄⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠒⠺⡀⡀⢀⠱⠀⠀⠀⠀⡀
⠀⢠⠄⠅⠋⢇⢸⡄⠈⠒⣊⡀⠀⠠⣁⢠⢔⠁⠐⠀⠀⠙⠀⠀⠱⠀⠐⠈⣉⠀⠀⠠⠒⠉⠀⠀⢀⠔⠂⠁⢁⡟⠁⠀⠀⢺⣿⡤⠐
⠀⠀⢀⠀⣂⢀⠠⠄⠀⠈⡤⠌⠂⠀⠀⠈⠈⡄⠀⠢⠁⢀⡠⠴⠁⠀⠀⡀⠀⢠⠂⠣⣀⡀⢐⣢⠄⣀⣀⡠⠎⡐⠇
⠀⠀⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⡀⠔⠀⠀⠀⢀⡠⢤⣄⠀⠠⢀⠀⢀⠊⠐⠠⠑⠂⠀⠀⠀⠑⠊⠈⠁⠒⠉⠀⠰⠅⠀⠀⠈⠀⠰⡀
⠀⠀⠀⠁⠀⠀⠀⠄⠀⡀⢆⠀⠀⠁⠀⢔⠒⡂⢹⠀⠀⡜⠂⠀⠌⠀⢀⠀⠀⢀⠄⠀⠀⢰⢩⠇⠔⢉⠆⠆⠙⠄⠀⠀⠀⢠⡠⡀⡀
⠀⠘⠜⠀⠀⣀⠀⠀⠀⠈⣉⠀⠀⡀⢀⠀⠋⠀⠘⠤⠤⠧⠀⠠⠀⣠⡀⠁⠈⠋⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢰⠉⠀⠒⠀⠀⠐⣺
⠀⠀⡴⡝⠃⣴⠓⠀⡠⡈⢂⠄⠂⠀⠀⡅⠀⢀⠄⠂⣀⣂⡄⠀⠀⢀⠠⠠⠆⠀⠀⠀⠠⠀⠐⢢⠴⣶⣖⠀⠐⠀⠀⢣⠄⣀⣀⣀⡐⠃
⠀⠀⣧⠤⠙⠀⠀⡄⠀⠀⢀⠀⠀⣀⠔⣁⠀⡂⡰⠋⠀⠤⠈⠂⠤⠤⠄⠊⠀⠠⠂⠀⠀⡀⡀⠜⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠃⠀⠀⡀⠀⠀⠀⠤⠤⠤⠤⠔⠶⠿⠆⠀⠀⠀⠀⠀⠀⢠⡄⢀⣀⣀⠀⠀⣼⣿⠃⠀⠀⣀⣠⡇⣀⣀⣀⣀⡀
⠀⢀⣴⠷⠶⠚⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣶⣾⣿⣇⣤⣤⣾⠟⠟⠛⠋⠁⠒⠒⡀⠩⠃⠂
⢖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣆⡄⡿⡿⡶⢿⣿⡿⠾⣧⣤⡤⠂
⠀⠙⠳⢶⢤⣤⣀⣀⡀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⡄⠀⡀⢀⠀⣀⣤⣶⣿⣟⠉⠀⠩⣽⣿⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠁⠀⠀⠈⠉⠈⠉⠀⠓⠂⠶⠲⡶⣶⣴⣤⠆⠀⠀⠘⢀⠃⣿⣿⣿⡿⣻⣶⣤⣶⣬⣟⢿⣿⣿⣍⣉⡉⡁⠀⠀⠀⠀⣀⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠉⠉⠀⠈⢫⣿⡇⠙⡝⠻⢿⣿⣟⣰⣷⢒⡈⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢿⡀⠉⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠇

⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠁⣿⣎⠇⠀⠐⠫⠐⠛⠀⠀⢀⠺⠹⠀⠀⠀⠰⠥⠀⠄⠀⠀⣄⣔⠒⠀⠀⠠⠤⠭⠤⠀⠀⠠⠌⡫⠄⠀⠀⠈⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡔⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⡀
⠀⠒⠒⠂⠂⠀⠀⠸⠿⠃⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠯⠽⠃⠀⠀⠀⠾⠥

⠀⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⢄⠀⠀⣀⡀⢄⡀⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢀⠘⠀⠀⠈⠉⠉⠁⠀⠀⠛⠛⠛⠁⠀⠀⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠄
⠀⠒⠒⠒⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠐⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠈⠁⠁

⠀⠠⠠⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⣀⣈⡁⠀⠀⢀⠰⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠐⠐⠂⠀⠀⣀⣀⣢⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⡀⠄⠒⠀⠈⠉⠙⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⡀
⣴⡏⠀⠀⠀⠀⠀⢀⠀⣀⣀⠤⠼⠖⠂⠀⠤⢀⡀⠀⠀⠀⡠⠊⠁⣔⡧⡱⠎⠄
⣿⣶⡶⣂⣺⣏⣶⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⣰⠃⠀⡾⠁⠀⠸⣽
⣿⠦⠄⠉⠙⠛⠁⠀⠀⠀⢀⡀⠰⡎⢤⣙⡟⡀⢶⠤⠀⠈⠓⠼⣇⣀⣠⠤⠟⢛⡈⣭⢨⣅⣤⣀
⠟⠀⠀⠀⠀⠀⠀⠀⣀⢐⠻⡜⢳⢾⠶⣷⡦⠰⢯⡁⢼⣳⡒⣦⠠⣤⢀⣤⣮⡽⠾⣿⡝⠉⠙⠻⣷⣶⣤⣤⠶⠃
⣗⠀⠀⢀⡠⢤⡴⡘⣣⣍⠞⠟⠛⢿⡀⢓⠀⡀⠀⠑⢤⣇⣉⠿⠗⠋⢉⠟⢙⡁⠀⠈⠻⣗⠀⠀⠀⠈⠁
⣾⢁⣈⣋⣐⡠⠷⠤⣝⣙⣮⣠⠷⠀⠹⣝⠂⢚⠀⡀⠀⠉⠀⠀⣀⠴⠁⠀⠈⢇⠀⠀⠀⠻⣄⠀⠀⠀⠀⡀
⠀⢉⣅⡞⠉⠀⠀⠀⠀⠹⣶⢡⣆⣰⠦⠡⡈⠙⠤⢡⣤⡦⡶⣺⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠒⠒⠊⠁
⣷⢨⠏⠀⠀⠀⠀⠀⠀⠀⠈⠹⡼⠕⣆⠰⠐⠦⠴⠊⠀⠾⢰⠃
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠏⣸⠖⣀⠚⡀⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠉⠉



⣀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⡀⢀⣀
⣿⣿⢛⠿⢛⠛⢿⢟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢲⣾⠁⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣻⢫⢀⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢋⡇⢠⢿⠼⡈⡃⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡶⡍⡄⡇⢿⢰⢸⣸⣀⠣⣝⣾⣿⠄⠀⠄⢀⠀⠀⠀⠄⠀⠄⠣⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣀⢤⣤⣴⣷⣿⡽⣍⡿⡇⣇⡿⣌⢸⠸⡏⢏⣱⣿⣿⢷⢃⠔⢴⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠁⠫⣝⢿⣿⣷⣾⣤⣤⣯⣤⣽⣻⣦⣷⣾⣿⣿⡿⡜⠁⠀⠀⠀⣶⣿⠀⠐⢶⠒⠂⣠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣿⣿⡿⠿⢽⡻⣿⣿⣿⣿⣿⢟⡝⠀⠀⠀⠀⠀⡹⣿⡄⠟⠀⢤⣄⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠛⠋⠀⠀⠈⠒⠽⠛⠫⠕⠊⠀⠀⠀⠀⠀⠀⠀⠛⠉⠐⠀⠀⠀⢤⠄⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⣠⠤⣀⡀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠘⢦⣄⠉⠛⠫⢍⡉⠉⠉⠉⠩⣦
⠀⠀⠀⠀⠀⠸⣷⣷⣄⠀⠀⠀⠀⠀⢀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⣿⣿⡷⣝⢦⡀⠀⠀⠀⠙⠲⣾⡄
⠀⠀⠀⠀⠀⠀⢹⣿⣇⠈⠣⡙⢦⡀⠀⠀⠀⠀⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠘⡏⢿⣄⠀⠙⢦⣝⠳⣄⠀⠀⠀⠀⠀⠉⢷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢭⣑⣦⣀⣿⣷⣝⠳⣄⡀⠀⠀⠀⠀⢹⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⢮⡻⣦⣀⣀⠀⡀⠋⠀⠉⠳⡆⠀⢀⡠⠔⣪⡽⠟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣟⡫⠺⣿⣄⠀⠀⠀⣛⡚⠛⠶⠾⣥⠤⠤⠶⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢥⣸⠷⡍⠛⠯⢽⣿⠮⣳⡛⠋⢉⣳⣌⡢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢿⣿⣷⡶⢬⡳⣽⣗⣲⠗⠛⠻⠍⠒⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣦⡻⣏⠻⡶⣍⡲⢭⡷⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡾⠈⡇⣹⡇⢱⢳⠙⣆⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢼⡀⢰⠇⡇⡇⢫⡏⠀⢹⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⢦⡳⣽⡶⢽⠓⠘⣇⣓⣫⠭⠽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡼⠻⣎⣓⣦⣌⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣻⣻⡟⣿⣿⣟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣧⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣶⣶⣤⣤⣤⢤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⡻⣗⡯⢞⣽⣾⣿⠿⢋⣴⢿⣻⢿⣿⣿⡷⠶⠷⠶⢬⡆
⠀⠀⠀⠀⠀⢾⡀⣹⣿⣯⢞⣵⡧⢞⡿⣻⡟⣴⡟⡱⢛⣵⢉⣀⢀⣀⡀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣯⠟⠴⠟⣥⣿⣾⠋⣼⢡⡞⣯⡀⠿⠟⢈⡗⠀⠀⠀⢤⡀⢣
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⡠⠒⠊⠀⠙⣿⣷⣗⣿⣹⢰⣿⣙⢶⠖⣿⡄⠘⢶⣄⠀⠹⣄⢣
⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠐⠂⠤⢹⣿⣿⣿⣿⡿⠀⣞⣵⢇⣇⢿⣄⠈⠻⣷⣄⠘⣆⡃⣤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠉⠉⠘⠋⡞⣍⢧⢻⢷⣤⣈⠙⠳⣝⠛⢮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⠎⢯⡻⢿⣛⠲⣜⣾⡛⢻⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠦⠙⢷⡀


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠊⠁⠀⠀⠀⠀⠈⠙⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⠉⠉⠀⠀⢨⡙⠦⠀⠀⣄⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣤⠖⡡⠀⠀⣠⣷⣜⣫⠴⠶⠶⠋⠉⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢊⣉⣤⠞⣠⢀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢂⠀⢀⣔⡭⢶⢹⡿⢿⡇⣼⣇⢺⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢠⠋⢋⣴⣷⢸⠁⡼⢣⣿⣿⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣶⠷⠋⠁⣸⣔⣤⢸⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢠⠞⡹⣯⡍⡜⠉⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⡴⢻⣿⣿⡎⠘⣧⣠⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡝⠉⠀⡴⢻⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠀⠐⢼⣃⠜⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣧⠀⠀⢸⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡈⠀⠀⠀⢱⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠈⠁⠀⠀⣠⠏⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣟⡅⣀⣀⣠⡤⠤⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣶⠿⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠂⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣦⣤⡀⠀⠀⠈⣯⡞⠄⠀⡽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⣿⣦⡀⠀⢻⠒⣃⣄⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠸⣿⡧⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢿⣉⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢸⣦⠼⡙⣀⠀⠀⠀⣠⣴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣼⣟⣿⠃⠀⣼⣿⠖⣫⡉⣀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣶⣿⣿⣿⠃⠀⠖⣪⣽⡷⠦⢎⣉⡘⣿⣿⡀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⣿⣧⠚⣚⠤⣾⣿⠨⠤⡈⢁⡙⢿⣿⣶⣿⠋⠉⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠼⢇⣩⣭⡟⠁⢠⣷⠛⢉⢭⢴⡏⢻⡶⠂⣌⠉⢃⢨⣿⣯⣿⡷⣄⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡼⠾⣉⣤⣽⣃⣴⣿⡿⠛⡁⠂⣾⠇⢸⡦⠴⣀⠋⠛⣿⣿⠈⢳⣍⡁⠒⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣸⢿⡷⠾⣹⣭⣿⣿⡽⠻⢗⠪⠠⣥⣿⠀⣸⡤⠥⠋⠓⠚⣿⣿⡄⢈⡧⠄⢊⢃⢸⡇
⠀⠀⠀⠀⠀⠀⣰⡟⢸⠶⠺⣱⢤⢿⡟⠀⡷⠶⢊⢄⣨⣿⠀⣿⣄⣠⠂⠒⠒⣿⣿⣷⣼⠷⠂⢀⣉⠸⣇
⠀⠀⠀⠀⠀⢰⢹⠇⢸⡶⠚⢋⡶⠛⢷⣰⠶⠴⠉⡀⣀⣿⣸⣏⡀⠀⠐⠦⠄⡆⢿⣿⡟⠓⠂⠠⠤⠀⢿⡄
⠀⠀⠀⠀⠀⢨⡈⣇⠈⣿⡶⢋⠊⡭⣉⣿⠤⠤⡢⡀⠀⣿⡟⠁⢀⠀⢆⣀⢠⡅⣿⣟⢉⡈⠀⠀⠶⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⢊⠈⠳⢼⣿⣷⠏⠩⠐⢭⠀⠀⠄⢉⣽⠟⠋⠉⠁⡄⠀⢀⡙⡰⡏⠁⠀⠀⠐⠒⠃⠀⢰⠣⠇

⣶⠿⣍⡙⠳⠶⠖⠒⣒⡶⢤
⢹⡳⣿⣌⠳⢦⣄⡀⠀⢠⡞
⠀⢇⠈⠻⣄⠀⢀⠹⠗⠺⢤⣀
⠀⢸⡄⠀⠘⣧⡸⡷⠀⠀⠀⠈⠙⠢⣄⡀
⠀⠸⡇⠀⣀⠼⢷⡀⠀⠀⠑⠦⡄⠀⠈⠹⠦⣄
⠀⠀⠣⠞⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠠⣄⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣄⡀⠀⠀⠀⠹⠀⡿⠘⣷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢉⣡⢾⣋⠁⠲⠀⠐⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡌⢽⡝⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠠⡄⠀⠙⠲⠤⠀⠙⠚⢿⡦⡷⢶⠌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣤⠀⠈⢮⣑⡢⠄⢐⠢⢄⠁⢈⠪⣫⡳⣥⣌⣒⣢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢳⡓⣄⠂⠙⠿⣆⡀⠉⠲⣄⠢⣄⣈⠊⠍⡉⠙⢆⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⢄⠗⣤⣀⠀⢁⠢⡀⠳⡌⠚⢿⠭⡆⢈⠑⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠑⣎⠹⡟⢦⡀⠈⢤⡈⢀⢬⣁⠀⠛⠓⠄⠉⡒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⣶⢛⡄⢳⣄⠈⢂⠈⠁⠒⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣧⠾⡀⠑⢍⡒⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠛⢽⣎⠀⠉⣲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠓⠀⠈⠀⠻⣦
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⠤⢴⡶⠶⠒⠒⠛⠓⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⢤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠙⠲⠦⣤⣉⣉⠛⠒⠶⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⡆⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠛⠛⠛⣛⣻⣿⠿⠟⠛⢛⣿⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣙⣲⣦⣄⣀⣀⣀⣠⣤⡤⠤⠶⠶⠒⠒⢛⣉⣉⣤⡤⠶⠖⠛⣹⣇⣤⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣠⡄⠙⢯⡉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣉⣁⣠⣤⠴⣒⣋⣽⣟⣩⠿⡟⠁
⠀⠀⠀⠀⠀⣾⣋⠀⠀⠀⠀⠈⠳⠦⠤⠤⠤⠤⢴⣶⣒⣚⣿⣭⣭⣿⣶⣚⣻⠯⠿⠟⠛⠉⠁⠀⣼⠃
⠀⠀⠀⠀⠀⢸⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠛⠻⡶⢦⡀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢃⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⡶⠶⠛⠋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢶⣬⣿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣶⡶⠶⣚⣛⣻⡏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢡⠀⠀⠀⣐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⣒⠂
⠀⠀⠀⠀⠀⢠⡰⠐⠑⠚⠚⠔⡄⡄⠀⠀⠀⠀⠀⠀⣾⠀⠔⡢
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠈⠐⠅⢅⠈⠀⠀⢴⠂⠠⠁⡂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢘⣆⠀⢐⠃⣀⠍⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⡢⠃⠈⠩⠀⠀⢈⡀⠀⠀⠀⢀⡠⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠁⠀⠂⠀⠈⡋⠀⠀⢐⠀⢀⣂⠀⠀⠀⢴⠋
⠀⠀⠀⠀⠀⢀⠀⠀⡸⠀⠀⠀⠀⠀⢐⡒⢐⠂⠔⡀⠐⠀⠀⠀⠂⠄⡐⠁
⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⢐⠀⢨⠀⠁⠆⠀⡂⠀⢈⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠀⠅⠈⠅⠀⠄⠀⠀⠐⠀⠀⠨

⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣖⡀⠢⢗⣦⣀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢠⡀⠀⠀⠀⢀⠀⢀⠀⠀⢠
⠀⠠⢌⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣡⣮⣿⢶⡇⠀⠀⠀⡀⠀⢀⣉⠿⠇⠁⠘⠀⠀⠀⠀⢀⠈⠀⡄
⠀⠀⠘⠀⠂⠀⠰⠔⠁⠀⠀⠀⠀⠀⢠⡆⡆⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠘⠓⡚⢁⣀⠠⠄⢂⠀⠰⠣⡀⠀⠀⠀⡀⠀⣀
⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣉⢸⠗⠤⠔⠂⠁⣰⠳⡀
⠀⠐⡀⠠⠀⠀⠈⠢⠤⠄⣤⣤⡄⠍⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣅⠄⠀⠀⠈⢴⣰⠂⠀⡀⠀⠈
⠀⠃⢀⠰⠦⠀⠀⠀⠀⠀⠁⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠖⠚⠉⠉⠀⠀⠘⠟
⠐⠀⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⠆
⠀⠀⢀⠀⠀⠀⢀⠄⡄⠓⣴⡄⠀⠀⠀⢀⠠⢠⠀⠀⣠⢠⡀⠠⠠⠀⠠⢀⢠⢀⠄⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⡀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⡌⡿⣿⣿⡧⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠀⠈⠁⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⣄⠀⠑⠆⠈⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⣤⣖⡢⠐⠋⠀⠀⢤
⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣴⡽⠟⠿⠑⠺⠫⠈⠂⠀⠠⠒
⠀⠀⠠⡀⠀⠁⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⢀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠐⠀⠉⢉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣩⡭⢎⠉⠿⠀⠀⠠⠒⠀⠀⠀⠸⠣⠀⠀⠀⠀⣀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢒⡯⢉⣶⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⡤⠦⠠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠲⠲⠒⡐⢢⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠉⠘⢼⡋⣾⡏⣿⡖⣦⣤⣀
⠀⠀⠀⢀⡀⠀⢀⠤⠠⢄⡔⠁⠀⠀⠀⠀⠀⠀⣠⣸⠻⢡⣟⠱⢿⠂⡽⢃⣬⣿⢲⣦⢄⡀
⠀⠀⠀⢦⠽⡚⠡⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⢻⠰⣂⠟⣣⣷⠘⣅⣿⣡⣝⠎⡿⢜⡟⣗⣶⡤⣤⣀⣀⡀
⠀⠀⠀⠀⣉⠽⠶⠂⠀⠀⠐⠚⠸⠀⠀⠀⠀⠈⠻⡚⠃⢉⢁⠙⠺⠁⠫⢭⢈⣵⠰⠞⣜⣵⡿⠻⣃⡌⣮⠏⠹
⠀⠀⠠⠾⠓⡖⡰⢚⡲⠖⣠⠶⠂⠀⣀⠤⠒⠀⠒⠛⠿⠯⣮⣧⠐⣤⡝⢟⡋⢁⠠⡄⠐⣯⠤⠤⣙⣃⣈⠕⠁
⠀⠀⠀⠀⠀⡗⢰⠗⣽⣋⠤⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠙⠿⠻⠟
⠀⠀⠀⠀⠀⠁⠀⢸⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡆⠀⠁⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡆⠠⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠃⠀⠠⡀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡀⠀⡄⠀⠀⠠⠀⠀⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠄⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠰⠌⠂⠀⠀⠀⠀⠈⠊⢢⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠊⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⡓⠀⠀⠀⠀⠌⠰⣀⠱⢐⣚⠂⣑⣂⠀⡀⠆⠀⠘⠈⠉⠀⠀⠀⠀⠀⠊⠠⠀⡖⠀⠀⠀⠀⠀⣀⠐⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡀⠀⠀⢀⡐⠹⠉⠀⠀⠈⣀⣄⠂⢈⢣⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠈⠀⠀⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢰⠁⢀⠴⠂⢿⠂⠀⠀⡴⠁⠀⠈⠡⡈⣶⠃⠀⠠⠄⠁⠀⣤⠀⠀⠀⠀⢰⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⣸⠎⡙⠀⠀⢋⠁⠀⠀⣗⢟⣻⠊⠀⠀⡁⢀⠀⠀⠀⣰⠁⢺⠀⠀⠀⠂⢠⢂⠄⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⢀⣅⠔⠈⣀⠁⠀⢾⢥⠀⡄⠀⢸⠀⡄⢠⠀⠠⡃⠂⠀⠀⠠⢓⠄⡠⡀⠀⠀⠀⢸⠈⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠃⠀⠠⠄⠀⡹⠃⢰⣤⠋⠀⠠⢈⠣⢧⠀⠀⢰⠏⠀⡤⠒⠉⠀⠀⠀⠀⢠⠟⠀⡲⠥⠀⡀⣴⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠁⠀⢤⣏⠀⡜⡱⠁⠀⠀⠀⢀⡜⠀⢸⠀⠀⠀⠀⠠⠂⡤⠏⠀⠐⢁⣼⠏⠩⠉⠐⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠈⡀⠀⠐⠀⢸⠀⠀⠐⢯⠀⡁⢁⠀⠀⠀⠰⡏⠀⠀⡘⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⠋⠐⠀⠠⠀⠉⠀⣠⠖⠉
⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⢧⠀⠀⠀⢷⣇⣫⠀⠂⠀⠀⠹⡄⠀⡇⠀⠀⠀⠀⠀⠞⠁⢀⠀⠘⡆⠘⠀⠀⠀⠀⡞⠋⠀⠀⠀⠀⡄⠀⠀⡀
⠀⠁⠀⠀⠀⡇⠀⠀⣀⠀⠈⣧⠀⢌⠢⠙⣾⢰⠀⠂⠀⠀⠈⠳⣧⠀⠀⠐⠀⠄⠘⢷⠂⠠⡜⠀⠰⠑⠀⠀⠀⡇⠀⠀⠀⠂⠀⠁⠀⠀⠐⠄
⠀⠀⠀⠀⢀⠇⢸⠀⠀⠂⠀⢸⠀⠈⠆⠃⠘⣮⡀⠀⠠⡀⠀⠀⢸⡀⠀⠀⠀⠁⠀⠾⠀⠀⣻⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠐⣫⡄⠀⢰⠀⠀⠀⣳⢀⠀⠀⢄⠀⠈⡇⠀⠀⠀⠀⠠⠈⠳⡄⡞⠀⠀⠀⠈⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⡌⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠳⣧⡀⠀⠀⠠⠀⠘⡄⠀⠀⠀⠀⠀⠀⠣⣩⠀⠘⠀⠀⠀⠀⠀⡇⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⣄⣰⠋⣳
⠀⠀⠀⣠⣻⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⡠⠶⣇⣠⣇⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⣀⠴⠒⠲⡄
⢀⡴⣧⠬⣧⠀⠀⠑⠤⣀⡀⠀⡀⠀⠀⢸⣧⢇⣴⣉⣷⢭⡟⢳⠀⠀⠀⠀⠀⢇⠀⠀⣠⠤⠤⣄⠀⢧⡀
⠛⠛⡇⠀⠈⠑⢦⣀⣀⣀⣈⣹⣡⠀⠀⢸⡛⠳⠧⠤⢼⠏⠀⠈⡇⠀⠀⠀⠀⢀⡷⠠⡇⠀⠀⢘⡆⠀⠙⣆
⠀⠀⠙⢦⣀⠀⠀⠈⠉⠙⢳⡴⡆⠀⠀⠀⢧⠀⠉⢠⠏⠈⠀⠀⢹⡀⠀⠀⢰⠋⠀⠀⠑⠦⠤⠊⠀⠀⠀⡼
⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠚⢶⠃⠀⠀⠀⠀⠳⣴⠃⠀⠀⠁⠀⠀⢧⠀⠀⠸⢄⣀⡠⠴⠒⠒⠦⢤⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠒⠀⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡀⠈⢦⡀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⣌⡅⠉⠁⠀⠀⠀⠀⠀⠈⠓⣿⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣆⡄⢴⢉⣆
⠀⠀⠀⣀⣀⣸⣻⣀⣀⣀⡀⠀⠀⠀⠀⢀⣴⣁⣣⣄⠀⢰⡇⡆⠀⠀⢀⣴⠆⠀⢀⣄⣱⡏⣹⡾⣻⡈⢯⠆
⠀⠾⡭⠭⠭⠤⠤⠴⠶⢶⠟⠀⠀⠀⠀⡸⠖⠒⠒⠪⣀⠈⡇⢣⡞⠓⢿⠁⠀⠀⠘⠒⣦⡉⠣⡇⡟⢳⠈⣣⡀
⠀⠀⢧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⡖⠓⢿⡦⠞⠀⠀⠀⠀⠹⡛⠛⠒⠛⠓⠛⠋⣹⠁
⠀⠀⢸⡄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠶⢿⡦⠜⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⢀⡴⠦⣿⣤⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣀⣀⢀⡇
⠀⠀⠀⠸⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⢸⣄⣀⣸⣄⡀⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠶⠤⢄⣀
⠀⠀⣠⠿⢛⠻⠯⣹⠯⣽⣦⣄⡀⠀⠀⠀⠁⠀⣠⠴⠒⠒⣶⠦⣄⡀⠀⠀⠀⠀⠀⣻⠴⣄⣀⡄⠈⠙⠲⣄
⠀⣰⠁⠀⠀⠰⠀⠈⠳⡟⢮⡦⣝⡆⠀⠀⠀⡞⠥⠈⠃⠓⡀⠚⣠⠽⡄⠀⠀⠀⠀⣿⠳⡄⠈⡙⠲⢆⡀⡀⠱
⠀⠘⢄⠀⠠⠀⠀⠀⠠⠜⡌⢻⣷⣽⠀⠀⠀⢹⠲⣶⠶⠾⢷⣶⠶⢶⣟⠀⠀⠀⠀⣿⠵⢃⣴⣚⣿⣶⣝⡦⠴
⠀⠀⠀⠙⠢⣄⡀⠁⢀⠀⢹⣼⢼⠇⠀⠀⠀⢻⣍⣭⠭⢿⣭⡬⠭⠭⣾⠀⠀⠀⠀⡧⣄⢸⣝⠾⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣨⡧⠋⠀⠀⠀⠀⠀⠳⠤⣄⣀⣈⣹⠦⠴⠃⠀⠀⠀⠀⠧⠚⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠒⠾⣄⠀⠉⠱⣄⣀⣀⡤⠤⠶⠒⠒⠚⢋⣭⣭⡉⠉⠉⠉⠛⠒⠒⡶⣦⠤⢤⣀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣹⣦⡀⠀⠈⠛⠙⣄⣇⠈⢧⣀⠀⠀⠀⠀⣠⡿⣽⢿⡟⢿⣿⠶⣤⠀⢰⢃⡷⣴⢳⢠⠏⣼⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠸⣀⠀⠈⣇⠀⠀⢀⠘⢾⠂⠈⠈⢧⠀⠀⢰⡟⢸⣇⣾⣳⣤⣿⠶⣾⡇⡜⣸⢠⢃⣾⢋⡼⢉⠗⡹⠊⠑⠦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠉⠓⠪⣕⢦⡳⢄⣦⡘⢦⡀⢿⣁⡞⢹⣿⡋⠁⢻⣄⣼⣧⣇⢇⡎⣸⢣⢞⡴⡡⢊⣤⣖⣽⠧⢚⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⣒⠶⣭⡳⣌⠳⡵⡄⠉⢙⠲⣍⢿⣿⡀⡸⢘⡏⠲⣤⠏⢠⣿⡸⣸⢱⣣⢫⢎⣾⣿⣿⢟⡫⠗⠋⢁⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢡⣖⡺⠟⢮⣧⠹⡿⣄⠀⠙⢮⣇⣟⠻⣤⣾⣟⣦⣾⣖⣻⣿⣷⣷⡿⡱⣳⢟⢽⣫⡗⢉⡴⢤⢴⠋⠉⢳⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣰⢫⢮⣻⡻⣦⣀⣳⡳⣝⠮⣗⣶⣪⠽⡷⢚⠽⠀⠀⠀⠀⠀⠉⠛⢿⠿⢵⣵⣟⠵⢫⡏⠈⡹⠧⡤⢦⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⢨⣧⣗⣿⡛⠻⣍⠛⡻⠛⠉⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⠀⠀⠉⠲⣍⢠⠚⢁⡴⢦⡞⠀⢸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠺⣿⡏⠳⡉⢳⠈⣿⡁⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠖⠒⠒⠋⠁⠀⠀⠀⠀⠀⢈⡏⠐⡅⢀⡞⢑⡶⠋⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠙⠢⣌⣹⢀⡟⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠗⢲⣋⠭⠛⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠦⣀⠀⠀⠀⠈⠙⠓⠾⠦⣝⣛⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣺⣽⡿⠭⠖⠚⠉⠀⠀⠀⢀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠙⠒⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠒⠉⠁⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠓⠒⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠋⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⣒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣉⠉⠙⠛⠒⠒⠚⠛⠋⠉⢉⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠨⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠁⠈⠑⠂⢄⠀⠀⡄⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⠀⠑⠄⠈⠀⣀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠒⠀⠀⠀⠀⠀⠐⠒⠒⠨⠄⢀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠡⡀⠈⢂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠐⡀⠀⢂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠁⠀⠲⢀⠀⢢⠀⠀⠀⠀⣢⡬⢤⢒⠚⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠂⠱⠤⠠⠶⣷⣿⠞⠈⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠃⡀⠀⠀⠀⠀⢀⠠⠐⠁⠀⡀⠄⠂⠀⠀⠑⠒⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁
⠀⠀⢠⠒⠀⠐⠂⠉⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⠐⠠⢀⣀⣀⠤⠀⠀⠀⠀⢰⡻⠷⣾⣥⠆⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠂⠉
⠀⠀⠀⠑⠂⠀⠀⢂⠠⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠚⠋⠉⠀⠀⠀⣠⠀⠀⢀⠩⠛⠋⠁⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⢀⠔⠁⡀⠠⠀⠒⠒⡰⠒⠁⠀⠀⣀⠀⠀⣤⠄⠒⣩⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠔⠀⠀⡠⠀⠁⠀⠀⡔⠀⢀⠊⢀⠀⠀⢠⠐⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠂⠀⡠⠊⠀⠀⠀⠀⡜⠀⢀⠃⠀⠈⠄⠀⠸⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⢀⠤⠊⠀⠀⠀⠀⢀⠌⠀⢀⠃⠀⠀⠀⠐⠀⠀⠓⠠⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠈⠁⠀⠀⠀⠀⢀⠠⠊⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠈⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠢⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢨⠍⠉⢋⡭⡩⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠪⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠠⡊⡇⠀⠀⠀⡢⠈
⠀⡀⠂⠀⠀⢈⠐⡀⠈
⡆⠀⠀⢀⠰⡧⠊
⡇⢀⣶⣬⠀⣄
⡇⣿⣿⣿⣿⣿⣷⣄
⠃⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣄⣀⡀
⠀⠸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⣤⣄⣀
⠀⠀⠙⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣟⣿⣛⡵⣫⡽⣻⣿⣿⣿⣷⣶⣦⣤⣤⣀⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣾⣿⣞⢥⡾⣫⡴⢛⣽⣿⣿⣿⡿⠛⣿⢿⣿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢋⣔⣧⣾⣫⣶⣻⣿⡿⠁⠈⠛⠎⠹⠚⠋⠹⢏⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢄⣀⠈⠑⠦⣑⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⣭⣽⣾⡎⡧⣵⣠⣶⣼⢿⣿⣖⣾⣿⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣛⢿⠯⠙⡓⠿⠿⠿⠳⠙⠛⠛⠛⠻⣿⣝⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣾⣛⡲⣄
⠀⠀⠀⠀⣰⠞⠩⠍⠩⠉⠭⠙⢦⡀⠀⠀⠀⠀⢀⣴⣒⣚⣓⣒⣦⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⢀⡴⢛⣭⢽⡇⡷⣋⣙⣮⣷
⠀⠀⠀⢸⣧⣬⣥⣬⣤⣬⣤⣥⣤⡷⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣭⡇⠀⠀⠀⠀⠀⣼⠛⠛⢷⠀⠀⠀⠀⢀⡟⣴⣫⣄⢸⡟⣿⠷⣛⡭⡄
⠀⠀⠀⢘⡷⠶⠶⠴⠶⠦⠴⠶⠶⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏⠙⡆⢸⡇⠀⠀⠀⢸⠰⡇⠳⡞⢹⡤⢖⣋⢹⡇⡇
⠀⠀⠀⠀⣿⠛⢿⡛⠉⠉⢛⡿⢻⠇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠛⠁⢸⠀⠀⠀⠀⠘⣇⢳⡸⣿⠆⣂⡛⢛⡼⢡⠇
⠀⠀⠀⠀⠈⠛⠛⠛⢦⡾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡀⠀⠀⠀⠀⠘⠦⣙⠒⠾⠭⠟⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⣤⢦⡞⢳⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡶⣤⡀
⠀⠀⠀⢠⣿⣹⣌⣧⣼⣡⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠨⠇⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠍⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠂⠙⠮⣷
⠀⠀⠀⠘⡇⠈⠉⠉⠉⠉⠁⢸⠇⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿⠶⣄⠀⠀⠀⢺⣥⠤⣅⣤⢥⣨⠤⣬⡇⠀⠀⠀⠀⢰⠇⠈⠀⡁⠈⣰⠋
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣧⠴⠃⠀⠀⠀⠀⢹⡀⢸⠀⠀⡟⢠⡏⠀⠀⠀⠀⢀⡞⢳⣅⣤⠴⠛⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⡒⠚⠛⠒⠒⠒⠚⠓⠒⡶⠀⠀⠀⠀⠀⣧⠘⡇⢸⡇⣼⠁⠀⠀⠀⣟⠋⡶⠋
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠛⠁⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⣠⠟⠓⢶⠚⢧⡀
⠀⠀⠀⠀⠀⡴⠖⠛⠁⠘⢦⡀⠀⠀⠀⠀⣠⠶⠒⢲⡴⠒⠲⡴⠖⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣄⣹⡄⠀⠀⠰⣟⣛⣛⣛⣛⣛⡷
⠀⠀⠀⠀⣾⠛⠛⠛⠋⠛⠛⢳⠀⠀⠀⢠⣏⣀⣀⣈⣁⣀⣀⣁⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⢀⡴⢯⣀⠀⠉⡧⠀⠀⠀⠸⣄⣤⠶⢋⣽
⠀⠀⠀⠀⢿⠉⢻⡏⠙⡟⠉⡿⠀⠀⠀⢸⣿⠯⠼⣿⠬⠖⠦⠴⣿⠽⢛⣿⠂⠀⠀⠀⢀⡤⢿⡄⠀⠈⠓⢶⠃⠀⠀⠀⠀⢿⡤⠖⢻⠇
⠀⠀⠀⠀⠘⡇⢸⡇⢸⡇⢸⠃⠀⠀⠀⠘⢯⣽⣓⣛⣛⣛⣛⣛⣛⣛⣯⠿⠀⠀⢠⡖⠛⣆⠀⠙⢦⡀⣠⠞⠀⠀⠀⠀⠀⠘⡷⠚⡿
⠀⠀⠀⠀⠀⠻⠤⠧⠼⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠓⠞⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⡟⠷⢶⠀⠀⠀⠀⢀⡴⢶⡀⠀⡴⠶⣄⠀⠀⠀⠀⢰⣟⣚⣳⢀⡼⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⢟⡷⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡾⢻⣳⣟⡦⠀⠀⢠⠟⠀⣦⠙⣾⠁⣦⠙⣦⠀⠀⠀⠀⡇⠀⡇⢈⡿⠛⣟⠀⠀⠀⠀⠀⠀⣠⠞⣱⢋⡞⠀⠀⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠟⠚⣧⠟⠀⠀⠀⢸⠀⢰⠏⠀⣿⢠⠏⠀⣸⠀⠀⠀⣠⠇⠀⢷⡏⠁⠀⠈⣷⠀⠀⢀⡴⢚⡵⢾⡵⠋⠀⠀⢀⡞
⠀⠀⠀⢴⠋⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠈⢷⡘⢃⡴⢿⡌⠃⡰⠋⠀⠀⠀⡏⠀⠀⠈⡇⠀⠀⠀⣿⠀⠀⠘⣟⡽⠞⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠳⣤⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠙⠚⠁⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠉⢷⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠒⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣾⣥⡀
⠀⠀⠀⢀⣾⣻⣟⣍⣿⡇
⠀⠀⠀⠸⣧⡈⠈⠉⠉
⠀⠀⠀⠀⠹⣿⣾⣄⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣿⡿⣫⣶⣿⣿⣿⠿⠿⣿⣿⣷⣄⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢰⣫⣾⣿⣿⠋⠁⠀⠀⠀⠈⠻⢿⣾⣐⣀⣶⣼⠆
⠀⠀⠀⢀⣴⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣠⣤⣴⣿⣿⣿⣿⡿⡟
⣿⣿⣿⣿⣽⣿⣿⡇⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⣙⠛⠛⣋⣽⣿⣿⣧⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⣿⣧⡀
⣀⣼⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰
⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⣿
⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣠⣤⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣯⣽⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠐⢋⣠⣶⣿⡿⠁
⠉⠁⠀⠙⠻⣿⣿⣭⣿⣯⡼⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠉⠉⠓⠻⡿⠟⠻⠟⠉⠀⠀⠀⠀⠀⠀⠙⠛⠿⣽⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠐⠒⠒⠈⠉⠉⠁⠒⠒⠒⠀⠀⠒⠒⠢⠤⣀
⠀⠀⠀⢀⡂⠐⠰⠀⠀⣠⠠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠄⠈⠉⠀⠂⢄⣀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⠒⢰⠤⡄⡀⠀⠀⠈⢀
⠀⠈⠦⣌⠋⠀⠶⠴⠶⠂⠘⠟⠀⠀⡁⢀⠈⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⠲⠶⢀⢠⡄⠀⢀⡄
⠀⠀⠑⢝⠢⡀⠠⡀⠀⠠⢁⠂⠒⢠⢂⣊⣩⠁⠀⠀⢀⣠⡄⠀⢐⠀⠐⢰⠲⣍⣈⣀⣀⠀⠀⠈⠀⠀⢠⠇⠀⠊⡇⠀⢙
⠀⠀⠈⠛⢷⣤⣀⣁⡈⢁⢛⣶⠴⡯⠝⠒⠉⠀⠀⠀⡙⠀⢠⢒⠋⠄⢆⣀⢈⣑⡇⠁⠀⣀⠀⠀⠀⢀⠊⣠⠎⢀⡇⠀⢨
⠀⠀⠀⠠⠀⠀⠁⠉⠀⠠⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⡁⢸⡡⢼⠀⠀⠀⠀⡈⠁⠂⠀⢀⡀⠀⣠⡔⢁⡌⠀⣠⠞⠀⠀⠔
⠀⠀⠀⠀⠀⡤⢠⣔⠒⣀⢶⣆⣀⠠⠀⠀⠀⠀⠀⠀⠈⢺⠱⣏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠞⠉⠔⣟⣤⠖⠁⠀⣀⠂
⠀⠀⠀⠀⢤⡀⠀⠀⠉⠛⢷⠞⠐⣊⣄⡀⠀⠁⠀⠘⣀⠸⡔⠋⢁⠐⠒⠒⢒⡈⢩⠏⠋⠥⢈⠄⡤⠁⠴⠖⠋⣨
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡄⠹⡤⢠⣶⠅⠀⠀⠀⠀⠙⠉⣧⡀⠑⠤⠤⠖⠉⠀⣀⡴⣊⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⣧⠈⣶⠈⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠶⡖⢺⡁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⣄⠈⢆⢅⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢨
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠣⠤⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠁⠀⣰⠋⠈⠙⢳⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠸⣄⠀⠀⠀⠀⠀⡴⠛⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠙⣇⣠⣤⠞⠛⠆⢶⡰⠛⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣇
⠀⠀⠀⠀⠀⢸⡧⠤⠤⠰⢤⡤⠟⣤⠼⣏⡉⠒⠋⠁⠀⠹⣇⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠰⢟⣠⠤⢼⢀⡞⠉⠳⣄⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠷⣤⣴⡋⠀⠀⠀⢰⡶⠀⠀⠀⠀⣶⢀⣠⡾⠀⠀⠀⠀⡀
⠀⠀⣶⣤⣄⣀⣀⣘⠉⠛⠛⠛⠾⠿⠿⠿⠿⣿⣻⡛⠋⠉⠀⠀⠤⠶⢚⣋⣀⣀⣤⣤⡶
⠀⠀⠈⠙⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠋⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⠶⣦⣄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⢠⡾⠛⣿⣦⠀⠀⠀⢠⣶⠉⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠙⢀⣿⡿⠀⠀⠀⠈⣿⣧⠀⢀⣴⡾⠟⢁⣤⣶⣶⣦⣤⡀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣴⣿⠁⠀⠀⠀⠀⢠⣴⣿⠋⠀⠀⠀⢀⣼⣿⠏⢠⣿⠋⠀⠀⢸⣿⣿⠁⠀⢻⣿⡆⢸⡅⠙
⠀⠀⢠⣶⣻⣭⣽⣫⠖⢿⣿⠟⠋⠀⠀⠀⠀⠀⡏⣿⣿⣧⣤⣤⣶⣿⡿⠋⠀⢸⣽⣧⡀⠀⠘⣿⣿⣦⣀⣸⣿⣇⣸⣿⠄
⠀⣨⣼⡿⠛⠛⠻⣿⡴⣎⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠛⢿⣿⣯⣳⣮⣛⠿⢿⣿⣿⡿⠿⠋
⠀⣿⣿⣧⣀⣠⣤⣼⣧⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠛⠉⢿⣿⣿⢛⠀⠀⠀⠈⠛⠿⣿⣽⣷⣾⡿⠃
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣬⢯⡛⡱⢖⡠⠤⢤⣤⡀⠀⠈⣿⣿⣦⣴⣿⣿⢇⡞⠀⠀⠀⢀⣴⣾⡿⠿⠛⣯⢳⡄
⠀⠀⠀⠉⠉⠉⠉⠘⣿⣿⣶⣦⣭⣬⣓⣹⡛⢙⣗⠟⢲⣿⣿⢿⣿⣿⣿⠛⠀⠀⠀⠀⣼⣿⠿⠁⢀⣤⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⢿⣿⣿⣷⣞⢻⣿⡿⠟⠹⢾⡛⣿⣦⡀⠀⠀⢻⣿⣿⢹⡟⢹⣿⢏⣽⠇⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣠⣾⣿⣿⣿⠇⣿⣿⣤⣤⣤⣤⣿⣛⣿⣷⠀⠀⠀⠉⢛⣿⣷⣾⣿⣼⣷⠾⠟⠁
⠀⠀⠀⠀⡠⢴⣿⣿⣿⣿⣿⣿⣛⣙⣽⣿⣿⡿⠿⣿⣿⣻⡟⢛⡿⣿⣿⣿⣿⣿⣦⣄⠀⣰⣿⡟⢿⣿⣿⣿⣦
⠀⠀⣠⠾⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⢀⣀⣑⣾⣿⡹⢶⢧⡚⣻⣿⣿⣿⣟⠈⢻⢿⣿⡀⠀⠹⣿⣿⣿⣧
⠀⠈⣕⣰⠀⣿⣿⣿⡿⠛⠉⠁⠀⠀⢀⡴⠚⣿⣿⣿⣿⣿⣿⣿⣿⠽⣾⣿⣿⣿⣿⣀⣸⣦⣿⣿⣶⣶⣿⣿⣿⣿⣀⣀
⠰⡺⢩⡏⢰⣿⣿⡟⠁⠀⠀⠀⠀⣴⣏⣴⣼⣿⣿⣿⠟⠛⠉⠁⠀⢀⣼⣿⣿⣿⣿⣿⡟⢀⣽⣿⣿⣿⣿⣿⣿⣯⣽⠿⣗⡤⡀
⠠⣙⣬⣿⡀⢿⣿⣧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣿⡿⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠏⢠⠋⠀⣿⣿⣿⣿⡿⢿⡿⢿⣿⠾⣶⠣
⠀⠩⡃⠠⡹⣾⣿⣿⣦⣀⠀⠀⣿⣿⣿⣿⡿⡌⣷⢳⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣯⣴⣾⣿⣿⣿⡟⠀⠈⣇⣨⣟⠈⣸⠁
⠀⠑⠴⣷⠖⢻⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣘⢻⣝⢫⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⣸⣿⣿⣿⡟⣿⡍

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⡒⠈⠁⠀⠀⣀⠀⠈⠉
⠀⠀⠀⠀⣀⣴⣁⣠⠤⠴⠶⠤⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠁⠐⠚⡑⠂⠉⠉⠱⠿⢮⣤⠤⠔⠒
⠀⠀⠀⠻⠶⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠤⢀⠀⠀⠀⠒⠒⠶⠒⠂⠀⠀⠐⠶⣆⠠⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠙⠒⠶⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢧⣾⣇⡽⢲⣦⠬⢀⣀⣄⡡⠤⠤⠖⠦⠼⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡈⠛⠒⠦⢀⣒⣀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣄⣀



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

⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠈⠐⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⡆⠱⠀⠀⠀⠀⠀⠀⠀⣀⢰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣾⠏⡸⣴⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡏⠀⣿⠀⣤⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠠⡄⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣇⢸⡟⣰⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠘⠰⢫⠵⠓⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠰⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠃⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠈⢻⡄⠀⠀⠀⢄
⠀⠀⢀⠄⡠⠆⠀⠀⠀⠀⠀⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠳⢄⠀⠀⠈⢙⡒⠶⢤⠄
⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⣦⠏⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢲⡘⣦⣍⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⣾⠟⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣸⡼⣷⡌⠿⣶⣤⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠀⠙⠿⠅⢀⠙⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡇⣿⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣰⠏⢸⡟⠀⢉⢿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⠀⣾⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢰⠋⡴⢟⣥⣀⡀⠀⠀⠀⠀⠀⢀⣀⡈⠨⠛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡜⠀⠀⢈⠕⠉⠀⠀⠙⠀⠀⠀⠀⠀⠨⣝⢿⣦⣐⠺⣿⣆⣠⠞⠉
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡉⢻⣷⡌⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡴⠃⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣈⡛⠶⢬⡓⠌⠉⢂⡀
⡄⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠦⡀⠀⠀⠈
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣏⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣘⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠁⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⢠⣴⡶⢆⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⠀⠀⠀⠱
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠉⠳⡐⡄⠀⠀⠀⠀⠐⡇⡀⠀⠀⠀⣧⠀⠀⠀⠀⡶
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢹⠘⡄⢄⠀⡄⠀⢳⡀⠀⠀⠀⠸⣄⠀⠀⠀⣿⡄
⠀⠀⢸⠃⠀⣶⣶⣶⣶⣶⣶⣶⡇⢱⣾⣶⣷⣶⣶⣇⠰⣶⣶⣶⣿⣷⣶⣶⣿⢱⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⡆⢇⠸⡜⢷⠄⠈⢧⠀⠀⠀⣽⣄⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣼⣄⠀⣿⠀⡀⠀⠀⠀⠀⠀⢹⡌⣄⢣⠀⠳⡔⢮⣧⠀⣀⣾⡏⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢠⣿⡏⢿⠀⣿⠀⠁⣄⣀⣀⡀⠀⠈⢳⡌⢆⠱⡀⢸⣦⡘⢧⣹⣼⢶⠶⢖⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡾⡿⡙⠀⠀⣿⠀⠀⠀⠉⠛⠢⠤⣥⣿⡿⢄⠣⡙⣦⡉⢷⡀⠹⣿⠃⠎⠁⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢱⣧⣇⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠛⠳⠸⣿⣿⣄⠹⣆⢹⡰⡄⠨⠉⢷⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⢡⠖⢰⢾⣷⣶⣌⡙⢻⠣⠈⠀⠁⢁⠀⠀⢨⡇⠀⠑⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠃⢰⡧⠓⠉⠪⢟⣿⣌⣒⣤⡀⠀⠀⢣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠨⠀⠀⠀⠀⠈⢯⣿⡋⢏⠹⣆⠰⣆⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⠟⠀⠀⡀⠀⠀⠀⠀⢸⣿⡿⣸⣦⣿⠹⠀⠙⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⠏⣉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠶⠘⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠀⢦⠀⠀⠀⠀⠀⠈⠉⠈⠓⢠⠛
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠊⠀⠀⠀⠈⢷⡵⡀
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⠞⠁⠀⠀⠀⠀⠀⠀⠙⡐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡀⠀⢶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠆⢄⡀⠀⠀⠀⠀⠀⠉⢛⢀⣞⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⣀⠀⠀⠻⣡⣿⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡙⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣾⣿⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣀⣰
⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⣯⡉⠙⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⣠⣿⣿⣿⣻⣿⠀⢀⢀⣴⣷⣿⣿⣿
⠀⠀⠀⢠⣿⣿⠏⠸⡁⠀⠀⠀⠘⣿⡀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⢀⣴⣿⣿⣿⣿⡿⣁⣴⣿⣿⡿⢿⣯⣭⣿
⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⢟⣿⣿⣥⣾⣿⣬⣾⣿⣾⣾⣿⣿⣿
⠀⠀⠀⠈⢿⣿⣦⣤⣤⣤⣴⣾⠟⠁⠀⠀⣠⣿⣟⣿⣃⣀⣀⣀⣀⣀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠟⢩⣿⣿⣿⣿
⠀⠀⢀⣀⣀⡈⠉⠋⠉⠉⠉⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⠟⣻⣿⡿⡿⠋⠁⢠⣿⣿⣿⣿⣿
⠀⣴⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣿⡿⣟⣸⣿⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿
⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣅⠀⠀⣀⣀⣤⣾⣿⡟⣛⣿⣵⣿⣿⣽⢿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⢿⣿⣻⣿⣧⣾⣿⣿⣟⣟⢾⣟⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠘⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⡿⠟⠁⠀⠘⠿⠿⣿⣿⣿⣿⣿⣟⣻⣿⠍⠊⠀⠉⠻⡿⣿⣿⣟⣻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠿⢿⣿⢿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⣿⡟⠁⠀⠀⢀⣠⡶⠚⠛⠛⡟⠛⠻⠛⠛⠛⠋⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⣤⡶⠟⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⣠⠎⠉⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢆⠀⠶⠚⠉⠉⠉⠳⢆
⠀⠀⠼⠀⠀⠀⢀⣀⣠⡶⠷⠤⠤⢀⢀⣀⠀⠀⠀⠀⡇⠀⠀⣻⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⢲⣄⡀⠀⣾⡛⡟⠀⠀⣀⠀⠀⢻⡀⠀⢘⠉⠻⡛⢷⣾⠿⠇⠀⠸⠿⢷⡄⠀⠀⢧
⠀⠀⠀⠉⠻⢦⠀⠉⠻⣄⢸⣏⣷⠀⠈⡇⠀⢹⡄⠀⢙⠃⠀⢳⡆⠀⠀⠀⠀⢹⠀⠀⠘
⠀⠀⠀⣀⠶⠴⠀⠀⠀⠈⡟⢧⡀⠁⣴⠃⢀⣀⡄⠀⠰⠀⠀⠈⡇⠀⠀⠀⠀⠘
⠀⣼⠁⠀⠀⠀⠀⠀⠀⣠⡇⠀⣡⠀⠉⣇⠀⠉⠀⠀⢀⠀⠀⠀⡇⠀⢂⣀⡀⠚⠀⠀⢠⡀
⠀⣧⠀⠀⠀⠀⠀⣀⣴⠞⠻⠿⣿⠀⠀⢸⣦⣀⣤⣦⣾⡄⠀⣠⣧⡀⠀⠀⠀⠀⣀⣠⡟⠁
⠀⠙⠿⠿⠿⠿⠿⠏⠁⢀⣶⠟⢹⣀⣴⡟⠉⠉⠉⠀⠈⠿⠿⠟⢻⣿⣿⠿⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢠⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡄⠀⠀⠀⠀⡀
⡀⠀⠀⠂⠀⠀⠀⣴⣿⠾⠋⢡⡿⠀⠀⠀⠈⡟⠲⢤⣄⠀⠀⠀⢠⢸⣿⣷
⠁⠀⡀⠀⠀⠀⢰⡏⠷⠶⠶⠟⠀⠀⠀⠀⠀⢧⠀⠀⠉⢻⣶⡄⢠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⢰⣷⠀⠀⠈⠻⠶⠿⠛⢁⢄⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠄
⠈⠈⠀⠀⡀⠀⢸⣿⡄⢀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⢦⣬⣽⣿⡟⠃
⠀⠀⠀⠀⠀⡀⠀⠹⣿⣿⣦⣆⡀⣿⣷⠀⡀⠀⠀⠀⣼⣷⣾⣿⣿⠏
⠀⠃⢀⠀⠠⠐⠠⠄⠈⠻⠿⣿⣷⣮⣉⣾⣧⣿⣷⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡄⠀⠀⠀⠀⢈
⠀⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⢀⣸⣿⣿⣿⠉⣻⣯⣽⡿⢿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣔⡠⠀⠂
⢀⣼⡾⣦⡄⠠⣀⠀⠘⠀⠀⠀⣿⢹⡏⣿⠀⣹⡇⢸⡇⢸⠃⠀⠀⠀⠀⡀⢠⣿⢿⣿⣷⡄
⢹⢿⠃⠀⠹⣦⠀⠀⠀⠀⢀⣼⠃⣿⢸⣿⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠠⠁⣸⠃⠀⢸⣿⣿⠰
⢻⣿⣆⠀⠀⠘⣧⣤⣤⣴⠟⠁⣠⡗⢸⡇⠀⣼⡇⠀⣷⠘⣷⡀⠀⠀⢀⣴⠇⠀⠀⢨⣿⣿⢀
⠀⢿⣾⣷⣤⠀⠀⠈⠉⠀⢠⣰⠟⢀⣿⠇⠀⣿⣇⠀⢻⣧⡈⠳⠾⠷⠟⠁⠀⠀⠀⣿⣾⠇⠚
⠀⢡⣿⣿⣿⣿⣾⣶⣦⣷⡾⠉⢀⣾⡿⠀⠘⣿⣷⠀⠈⢿⣿⣦⣤⣤⡀⣤⣠⣴⣿⣿⠇⡈⠰
⢰⣿⣿⡁⠈⠀⠉⠉⠉⠁⢀⣴⣿⣿⠇⠀⣾⣿⣿⣧⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⡁⠀⢀
⠈⢻⣯⣷⣮⣁⣤⣤⣄⣤⣿⣿⡿⠃⠀⠀⣿⠇⢿⣿⣧⣄⠀⠀⠈⠛⢿⣶⣦⠄⠠⠉⠀⠈
⠀⠀⠉⠿⠿⠿⠿⠿⢿⣯⣿⠏⠀⠀⠀⠈⣿⠂⠀⠙⢿⣿⣿⣦⣶⣤⣾⣟⣿⡇⠀⠀⠠
⠀⠂⠐⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⣄⣸⡿⠂⠀⠀⠀⠈⠉⠛⢻⣿⣿⠿⠛⢁⠀⠑⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣷⣤⣶⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨
⠁⠀⠀⠏⠀⠀⠀⠈⠀⠙⠿⠿⠿⠿⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠃⢠⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣴⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⣀⢸⣇⡀⠀⣿⡇⣿⣿⣿⢻⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡟⢿⢻⣿⢸⣿⣿⡇⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⣿⡇⠀⣿⣿⣿⡇⠀⣿⡇⣿⣿⡟⠀⢿⡇⠈⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢠⣤⣤⣤⡀⢸⣿⠀⣿⣿⣷⣿⣾⣿⣼⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⣿⡇⠀⠙⢻⡟⠃⠀⣿⡇⣿⣿⣧⣤⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣾⣿⠀⣿⣶⣶⣶⣶⣶⣶⣶⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣷⣶⣶⣾⣷⣶⣶⣿⡇⢿⣷⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⠤⡤⠤⠤⠤⠀⠀⠀⣄⣠⣠⣄⣄⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣇⢠⣷⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢦⣭⣭⣬⣥⣭⣭⡤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠛⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⢶⡶⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢦⡀⠀⠀⠀⢀⣀⣐⣀⡀⠀⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠿⠷⠾⠀⠠⠿⠿⠿⠆⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠾⠿⠇
⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣩⣭⣭⣭⣭⣭⣭⣭⣭⡍
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣛⣛⣛⣿⣿⣿⡇⣿⡷⠷⠾⠶⠾⠶⠷⣿⡇⣿⡇⠀⣠⣤⣤⣄⠀⢽⡇⣿⡇⠀⠴⠶⠶⠦⠀⢸⡏
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠋⢻⣋⣟⠙⠋⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⡟⠛⣛⣛⣛⣛⠛⢻⡯
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⣿⣿⣿⠀⠀⣿⡇⣿⡇⠀⣤⣤⣤⣄⠀⢹⡇⣿⡷⠶⠶⠾⠿⠶⠶⢾⡯
⠀⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣴⣾⣿⣷⣦⣤⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⣇⣀⣛⣛⣛⣋⣀⣸⡧
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢂⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠒⠋⠀⠀⠀⠀⢠
⠀⠑⢀⡀⠈⠐⠠⠀⠀⠀⢐⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠁
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣴⠋⠙⣆⡞⠉⢹⡄⡏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠲⠞⠁⠙⠲⠚⠁⠳⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣰⣇⢰⠋⡂⣶⡃⣞⢹⡀⣿⠢⡎⢱⢸⢰⢰⢦⡆⣞⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠉⠀⠀⠁⠈⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠁⠈⠁
⠀⢀⢀
⠀⠰⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠠⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠂⠤⡀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠋⠁⠀⠈⠙⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⢀⠠⠊⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣋⣉⣤⡤⠶⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣋⣛⡫⠿⣧⣀⣤⠶⣛⣥⠶⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢃⣎⣋⠒⠄⠴⣈⡼⠁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⣂⣵⠤⠬⠒⢊⣡⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢶⠖⠚⢛⠛⠓⠒⢚⠙⠶⠶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢛⠉⣂⡖⠶⠚⣃⠐⠂⠴⠦⣩⡓⠒⢄⡀⣭⡉⢙⠶⣶⡀
⠀⠀⠀⠀⠀⢀⣀⡶⣛⠛⠵⡞⢁⡼⢦⡈⡁⠀⣖⠂⠐⢂⠀⡠⠤⠴⡄⠠⢍⡃⠍⣌⢹⢻⣄
⠀⠀⠰⡶⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠲⠲⠶⠶⠶⠾⠷⢶⡆
⠀⠀⠀⠹⣦⡒⠐⠒⠐⠒⠀⠂⠐⠂⠒⠂⠐⠂⠐⠂⠐⠒⠐⠒⠂⠒⠀⠐⠂⠐⠂⠐⠂⠒⠀⢲⡞
⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢊⢁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣥⡴⠿⠛⠁⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠁⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠃⠀⠠⠀⢀⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢀⠀⢠⣾⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢿⣄⠀⠀⠀⠀⠀⣀⣶⣶⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠈⢙⣦⣶⣠⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠀⠀⠀⠀⡠⠤⣹⡿⠛⠙⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣠⣤⣴⠊⣠⠔⠀⠺⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣡⣴⣿⡿⠛⣡⡞⢡⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣖⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠒⢠⣶⣶⡿⢛⡩⢋⣴⣿⡿⢁⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⣿⣿⠿⡿⢡⡞⠋⡡⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠃⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉
⠀⠀⠀⠀⠀⠋⣙⡛⢥⣼⠭⢴⡴⢡⡿⠷⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠟⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠁⠹⢠⠋⠀⠀⣠⠔⢋⠄⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⢄⡴⠚⠁⠀⠀⠀⠀⠐⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃

⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢿⣝⣶⢯⡙⠛⠉⠉⠽⠛⡆
⠀⠀⠘⡎⠻⣧⠉⠓⢦⣤⡀⣼⠁
⠀⠀⠀⢱⠀⠈⢧⡀⢤⡉⠋⠙⠲⢤⣀
⠀⠀⠀⠸⡇⠀⠀⢻⡜⠍⠀⠀⣀⠀⠈⠓⢦⣄
⠀⠀⠀⠀⡧⣠⠞⠁⠙⢆⠀⠀⠈⠙⠂⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠙⢢⡀⣸⢢⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⠀⠖⣨⡴⠊⢄⠉⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠾⡝⢒⡲⡄⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢮⡉⠐⠀⢀⡀⠀⠲⢄⣀⠐⠲⢴⡦⣴⣬⣅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⣀⠀⠑⣄⠢⠠⠀⠠⢄⠐⠈⠪⡲⣳⣔⣍⡂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⡶⡀⢈⠻⣿⣆⠈⠲⣥⡀⢅⡈⠫⢌⡙⠻⢧⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠛⣽⠦⣄⡀⠈⡓⢄⡘⢪⠑⢿⡯⣦⢄⠑⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣈⠳⣍⠹⡷⢄⠀⠱⣄⠑⣤⣙⡀⠘⠓⠀⠙⠒⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣌⡖⣳⡌⢷⣀⠐⡌⠉⠐⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⣥⢷⡀⠳⣕⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠻⢿⡟⠠⢙⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠃⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡂⠈⠀⠀⡈⠀⠠⠀⠀⢀⠀⢀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠠⠠⠄⠀⠂⢀⠀⡀⠀⠀⠈⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢠⠔⠁⠀⠀⠀⠀⠀⠀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢐⠜⠁
⠀⠀⠀⠀⠀⣠⠁⢰⠉⠄⠀⠐⠃⠀⠐⠋⠀⠈⠁⠀⠀⠉⠀⠒⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠘⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢙⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢾⣱⣾⣿⢰⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⣬⡀⠀⠀⠈⢻⠛⣼⢻⣿⢼⣿⣱⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⢛⠁⠀⠀⠀⢠⣿⢸⣿⣿⠸⣫⡩⢾⡿⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣴⠊⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⡾⠇⣾⣿⣿⣿⣾⡿⡌⣶⣿⣷⡿⢻⠟⣿⣿⣿⣿⣿⢋⠀⡁⠺
⠀⠀⠀⠀⠀⠀⢠⣶⠏⢠⠂⠀⡀⠀⡄⠀⠀⠀⢈⡀⠀⢀⠃⠀⠀⠀⠀⠀⢹⣷⣧⣿⣿⣿⣾⣿⣶⣿⣿⣿⠟⠁⠌⠀⡰⠃
⠀⠀⠀⠀⠀⣠⡾⠋⣰⣃⣠⠞⢁⠀⠀⢀⠀⠀⣀⣠⣖⣁⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡿⠿⢟⣛⠭⡀⠈⢀⡸⠊
⠀⠀⠀⠀⠐⠯⠁⠾⣿⠟⢁⠐⠁⢀⣾⠋⠀⠈⠀⠀⠀⠀⠉⠉⠓⠒⠒⠀⠘⠲⠒⠒⠒⠒⠒⠋⠁⠀⠀⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⡆⠀⠀⠚⢿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠉⠉⠈⣙⡢⠀⠀⠀⡞⠁⠈⢳⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡐⠈⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠃⠀⠀⡟⠀⠀⠀⣀⠀⠒⠂⠀⠠⡀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⢠⠀⠁⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢁⠀⠀⠀⠀⠋⠇⢀⣠⠔⠁
⠀⠀⠀⠀⢦⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⡄⠐⠒⠚⠁⢀⡔⠀⠀⢀⠿⠋
⠀⠀⠀⠀⠀⠑⠦⣀⠀⡐⣧⡌⠑⠂⠦⠆⠞⠛⣲⠤⠤⠐⠁⢀⡤⠐⠉
⠀⠀⠀⠀⡀⠤⠀⠀⢙⡟⠐⠚⠓⠂⢄⣀⣀⣀⡄⠀⢀⣴⣞⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠩⠉⠛⠀⢰⡿⠋
⠀⠀⠀⠐⢀⠀⠀⠀⠀⠊⠉⠠⠰⠶⠉⠑⢰⡇⠀⢾⣥⠔
⠀⠀⠀⠀⠀⠀⢰⠖⠀⠁⠁⠀⢀⡐⠈⠉⡝⢱⣄⠙⠥⢀⢀⡀⣀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⢨⠝⠁⠀⠀⠀⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠣⡀⠀⠀⠀⠀⠎⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠑⠄⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠎⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡯⠀⠐⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡺⠁⠀⠈⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣢⠀⠀⡹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠛⠛⠻⣷⣦⣄⠀⠀⠀⢻⡾⢗⡂⠀⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠸⣷⣻⣷⣄⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⢿⣿⡷⢾⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣧⠀⠸⣟⢒⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⠀⠀⢿⣁⣙⡖⡆⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢀⢽⣯⣉⣧⠴⠆⠀⠀⣠⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣄⣀⣀⢀⣴⡿⣯⣿⠃⢀⡈⣽⣿⡕⣺⠒⣴⡆⢸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⡁⢀⠘⠩⡧⣿⣿⠉⡱⢤⣤⡘⣿⣿⣧⡀⢀⣠⣤⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢀⣤⣿⣿⣻⣿⡟⠉⣿⣿⠞⢛⡟⢴⣿⣿⠏⡐⢧⣈⣱⡘⢿⣿⣿⣻⡿⠋⠁⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢠⠼⢏⣘⣭⣽⠏⠀⣰⣿⠿⠓⣍⣯⣼⡏⣻⣷⠞⢡⠊⠝⢇⢠⣿⣿⣿⣿⢷⣄⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣷⣶⠋⣉⣹⡏⢀⣴⣿⣿⠗⢋⠱⢠⣿⠇⢸⣤⣤⣌⡹⠒⠿⣿⣿⡆⠹⣯⡓⠒⠿⡄⠀⠀⣤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣤⡴⢗⡛⣻⣿⣿⣿⣿⡧⡤⠊⡈⢘⣿⠀⢸⣃⠀⣨⢓⣦⡴⣿⣿⣇⠀⢹⣏⠁⡴⢶⠄⣼⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠇⣏⣑⣸⣞⠹⢿⣿⡿⠁⣌⣐⣨⠆⠊⠽⡷⠀⣿⠏⠁⢁⢢⣀⣀⣿⣿⣿⡄⢸⣋⣁⡔⠲⠇⣿
⠀⠀⠀⠀⠀⠀⣼⣿⠀⣟⠁⣉⠾⡉⣟⣿⡀⢸⠋⠍⣠⠜⡒⢾⡇⢠⣿⠷⠶⠇⢊⠀⠉⢛⢿⣿⣿⣿⣙⡈⠐⠒⠆⢹⣇
⠀⠀⠀⠀⠀⢸⢕⡇⠀⣿⡋⠍⣡⢿⣉⣋⣧⡾⠙⠛⠁⠢⠠⢴⣧⣾⣧⡄⡔⠂⠘⠓⠪⡿⢸⣿⣿⣏⣁⠀⠚⠒⠆⠈⣿⣆
⠀⠀⠀⠀⠀⢓⠇⢳⡀⠸⣿⡟⠩⢉⡼⢭⣸⣷⠦⠶⣃⢇⢀⣸⣿⡏⠀⣂⡀⢰⣤⣀⢠⡆⣼⣿⣏⣀⡠⠀⠂⢸⠃⠀⢹⡙⣆
⠀⠀⠀⠀⠀⠀⢂⠀⠹⠦⣿⣿⣿⡟⢩⠙⠂⣧⢀⢀⡴⢀⢩⡿⠛⠉⠉⠉⣀⠀⠐⠀⡙⢰⣿⣁⣀⠀⠄⠚⠒⡟⠀⠀⣼⠸⣗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⠆⠘⠁⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⡀⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡶⠰⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢄
⠀⢊⠀⢀⠀⠀⠀⡈⠀⡄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠰⠁⢉⠁⠒⡆⠀⠀⠀⠀⠀⢀⠂⠂⠀⠈⠢⡀⠡⠀⠀⠸⢤⠈⠂⠁
⡇⡇⠀⠋⠀⠀⡐⢀⠎⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⡀⢄⠀⠀⢀⠠⠂⡀⠀⠀⠀⠀⠘⣄⠑⠄⣀⣀⠠⠂⡀
⠡⡈⠀⠀⠐⠀⠠⠃⠀⠀⠀⠀⠀⠈⠢⡀⠈⠉⠁⢠⡆⠀⢀⠁⠀⠀⡀⠀⠰⡄⡀⠁⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⠀⠊
⠀⠀⠀⠒⠂⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⢠⠆⠀⡜⠀⠐⣄⠠⡀⠀⠐⠤⠤⠄⠀⠀⠠⠌⢀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠔⠁⠀⠈⠒⠒⠀⠐⠒⠀⢀⠀⠠⠀⠐⣄⠈⠳⣌⠢⠀⠀⠑⠄⠀⠀⠀⠀⡈⠈⠠⡀⠢
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠰⡀⢃⠀⠰⢀⠈⠳⣄⠘⢶⠠⡄⢀⠀⡀⢀⠈⠐⢷
⠀⠀⠀⠀⢀⠄⢀⠠⠀⡆⠀⠀⢀⠠⠂⠁⠀⠀⠀⢀⡠⠀⠐⠈⠄⠀⠀⠁⠢⠈⢧⠈⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⣸
⠀⠀⠀⠀⢂⠨⠀⠜⡠⠃⠀⠀⠂⠀⠠⠂⠀⠀⠉⠁⠀⠀⠀⡀⢘⠀⠀⠀⠀⠁⠈⡡⠀⠀⠀⠉⠹⠆⠀⠀⣷⠀⠈⢄
⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⢄⠀⠀⠁⠐⠀⠀⠀⢀⡅⠀⡒⠃⢃⠠⡐⠠⠄⠀⠊⢀⠵⠀⠀⢂⠀⢮⡍⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠱⡄⠀⠁⢃⠚⣁⠔⠀⡀⠀⠀⠀⠠⠀⡐⠀⠰⠈⠀⠈⠐⠀⠀⠂⠁⠀⠐⠀⠀⠑⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠸⡀⠡⠀⠀⠀⡀⠔⠀⠀⠀⠀⡉⠠⠁⠀⠀⠱⡀⡀⠀⠀⠠⠤⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠒⠆⠀⢀⠀⠈⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡀⠀⠌⡀⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠋⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠉⠐⠁
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠷⣦⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠰⣍
⠀⢀⡾⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⣋⣀⠀⣤⡿⠀⠀⠀⢸⣿⢀⣴⣶⣄⢠⡶⠛
⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢸⣛⠉⠉⢻⡄⠀⠀⠀⠠⣿⡇⣼⠇⠈⣿⠏⢳⣄⡀
⠀⠀⠀⣸⡇⠠⠀⠀⠀⠀⠀⢸⣊⡀⠀⣸⡇⠀⠀⠠⣼⡟⠀⠘⠂⢀⡿⠅⠀⠈⢭⢂⡰⠞⠛⠛⠿⣶⣄
⢠⣶⣶⣿⣄⠀⠀⢠⣴⣶⣶⣾⣿⣴⣊⠿⡁⠀⢀⢡⡟⠀⠀⠀⠠⡈⠊⢠⡾⣿⣛⣸⠄⠀⠀⠀⠀⠈⣿
⠀⠉⡹⡻⣿⠇⢠⣿⣿⠟⠛⠛⠉⠉⠻⣮⡝⢷⡂⢸⡇⠀⠀⣈⠳⡄⢠⣟⡳⠋⠉⠁
⡰⢩⣉⠶⠋⠀⢒⡻⣿⣄⠀⠀⠀⠀⢀⣾⠏⣸⣃⠐⢇⠀⠶⢭⡿⠀⡿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝
⢿⣿⣴⡀⡀⠀⠈⠓⣮⡽⠿⣦⢀⣴⡏⣡⠞⢣⠘⠗⡻⡔⢛⡚⣷⠀⣇⣿⢰⡀⠀⠀⠀⠀⣀⠀⣄⢲⣾
⠀⠹⣿⡷⢶⢀⠀⠀⣡⡹⡞⠻⣿⣿⠤⣯⢠⡄⣟⠻⡞⢻⡉⣭⠼⣧⢰⡜⣦⠳⡀⠄⠀⣾⣍⢓⣴⠟⠁
⠀⣰⣿⢉⣟⡡⠀⠀⣼⠀⣻⠙⣿⣿⡶⠻⡖⢳⣼⠛⣷⠛⢳⡤⢶⠛⣿⣧⣸⣧⡜⢦⣠⡦⣼⢺⣇
⣾⣿⣤⣿⣉⣧⣴⣾⣿⡇⣿⢠⣿⣿⣿⣎⢹⡆⣿⣗⣻⣗⣹⣷⣞⣻⣼⣿⣷⣾⣻⣮⣿⣷⠶⣆⣻⣦⣀
⣿⣷⣺⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡉⣿⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⣴⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⣀⠀⣒⣀⠁⡝⠻⣿⠦⣝⢛⡠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡢⠂⣂⡏⣼⡎⢶⢑⠂⣸⣃⠈⠅⠉⠻⣽⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡑⡐⢳⣬⣵⠋⠀⠅⣠⣈⡑⠄⡙⠳⠄⠈⠛⠲⠕⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣛⢃⠀⢆⠠⠈⡏⣥⢠⣯⢫⣯⡲⣅⠱⣦⡒⠶⣌⡀⠵⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⢠⢙⠋⡘⣧⡾⠶⢭⠟⠙⢮⣕⠂⠙⠪⠚⡟⢳⣤⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣧⡟⠙⢉⠂⢆⠀⠀⠈⠛⠢⠀⠀⠈⠲⡡⣭⡙⣥⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⣤⠈⢢⠀⠀⠀⠀⠀⢀⡀⠀⠈⠈⠛⢿⣧⡈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡡⠄⠠⢂⠀⠀⡀⡰⣄⡳⣳⡀⠀⢤⠈⢿⣧⠀⠠⢉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣄⣧⣳⣽⣿⣧⣻⢢⠈⣇⢈⢫⣟⠓⢶⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣰⠂⠀⢌⡹⢟⣷⡄⠀⠈⠈⡟⡍⠑⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⢉⠹⣿⣿⢰⠸⡇⠐⣏⠀⠑⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⢠⠠⠈⣻⣹⠐⣿⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎⠠⠀⠉⠽⢯⣼⣷⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⡀⢈⡟⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⡀⡰⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠄⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠂⠀⢀⠀⠀⠀⠁⠘⠀⠀⠄

⠀⠀⠀⠀⢏⠓⠦⢤⣤⠤⠤⠤⠤⢤⢤⡀
⠀⠀⠀⠀⠈⣷⣦⡀⠈⠉⠂⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢸⣿⣿⡢⣄⠀⠀⠀⠐⠤⣄⣧
⠀⠀⠀⠀⠀⠘⣿⣿⠙⢮⡳⣄⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠙⣮⡳⢤⡀⠀⠀⠀⠈⠙⣦⣄
⠀⠀⠀⠀⠀⠀⠘⠦⣝⣒⣄⣈⣿⣦⡛⢦⡀⠀⠀⠀⠈⠙⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠢⣝⢶⣄⠀⠀⠀⠚⠉⠙⢲⡀⠀⢀⡠⠔⣊⠭⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⣿⠗⣿⣄⠀⠀⠀⣓⠚⠻⠶⢮⡥⠤⠴⠮⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠥⣼⠷⡍⡛⠯⢿⡷⢾⣟⠉⢉⡷⣮⡳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢿⣿⣿⡲⢬⡪⣿⣲⠟⠉⠙⠎⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢧⡻⣦⢻⣳⣭⡚⢿⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠟⢨⡇⡟⡇⣏⡇⢹⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢸⠰⡁⣇⠻⣄⡀⡇⣷⣀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣿⣝⢏⡀⠹⠤⠖⠛⠛⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠁⠉⠒⠚⠿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⠿⣿⣿⣿⡿⠿⠶⢄⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⢿⣻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣴⡿⢛⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣠⡾⠋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣴⡾⠟⠛⠛⠛⠛⠿⣶⣤⣀⡀⠀⠀⠀⣀⣴⠏⢀⣾⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⢠⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⢻⣿⣿⡟
⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣤⣼⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⡤⠖⠛⠉⠉⠉⠐⢶⣤⣤⣀
⠀⠀⠻⣿⣶⣤⣄⣀⣠⣾⣟⣉⣠⣤⣭⣟⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷
⠀⠀⠀⠀⠉⣙⣿⢿⡿⠽⠿⠻⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⢏⣭⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⠀⠀⠀⢀⡾⠋⢀⡿⣁⣤⠶⣾⡿⠃⠉⠀⢀⡾⣿⣿⣿⣟⠈⠁⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢸⠁⢀⣞⡟⠉⠀⣼⡟⠀⠀⠀⠀⡾⣽⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⢸⠠⠋⠘⠀⠀⣼⠟⠀⠀⠀⢀⣤⣿⢟⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠈⠀⠀⠀⢀⣼⠏⠀⢀⣰⡾⠟⣿⠁⠨⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡾⠛⠁⢀⡼⠃⣠⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠄⠊⠁⠀⡴⠋⠀⠀⠐⣩⠴⠛⠉⣼⠏⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠠⠊⠁⠀⣠⡼⠋⠀⠈⠻⣿⣶⣤⣀⣀⣀⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉

⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣿⣶⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⡶⠒⢶⣶⠆⠀⠄
⠀⠀⠀⠼⣿⣿⣿⣿⣿⣯⣾⣿⢟⣝⣿⣾⡟⡽⣿⣿⣿⣿⠷⠿⠓⠙⠲⢦⢁
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣾⣷⣯⢞⣿⡿⣿⡟⡒⡢⢸⢠⣄⠀⠻⣄
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣟⣭⣿⣿⢞⠵⣣⣸⡀⢻⣆⢀⠩⣠⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⠯⠿⢯⡜⡭⠿⣷⣄⠙⢦⡀⠱⠖⠚⠀⠛⡫⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠻⢿⡿⠿⠟⠋⠁⠀⠀⠀⠉⠓⠾⣓⣶⠷⠢⡙⠎⠢⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⢳⣡⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⣿⣟⣛⣛⣛⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣄⣠⣀⣄⣀⣀⣀⠀⣠⣤⡦⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⡾⢷⣤⣾⣶⣿⣸⠭⢹⠛⣻⣿⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⠭⢵⣜⣯⡷⠿⣏⢵⣿⡿⣋⡙⡀⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⢶⡦⠨⠗⠂⠀⠩⣍⣉⣉⣈⣉⠉⠀⠀⠈⠀⢈⣷⡑⠀⠀⠠⠤⠴⠦⠒⠲⠆
⠀⠀⠀⠀⠀⠀⢲⣤⠖⠀⣿⣖⠚⠑⠶⡄⠁⠀⠀⠈⠛⠝⠢⣀⣀⠀⠠⡀⣶⣥⣹⣿⣤⣀⣀⣀⠀⢀⣼⠀⠀⠀⡀⠀⠻⠦⣄
⠀⠀⠀⠀⠀⠀⠛⢻⣵⡿⣄⠀⠱⠆⢄⡀⠈⠳⡤⢀⠀⠈⡓⢹⣶⡟⠞⠀⡎⠁⠁⠹⣿⣿⡟⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢠⣤⣕⠤⣈⡻⢿⣞⣿⠆⡬⢉⣠⣶⢤⠈⣥⡜⢿⣼⣿⣇⢄⠘⢀⠀⣂⠀⣿⡏⠙⠄⠀⠀⠀⠀⠰⠤⠄⠀⠀⠀⠀⡼⡐
⠀⠀⠀⠀⠉⠋⠻⢿⣶⣭⣍⣛⡛⠿⠷⠚⠻⣯⣉⡃⠿⠛⠂⠈⠻⢿⣯⣑⠢⢤⣈⣠⣼⣧⣴⣦⣄⠀⠀⠀⠀⣤⣀⠀⠁⢐⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣯⣤⠀⠤⠄⢒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠬⠉⢛⠛⠛⠛⠛⠛⠒⠛⠛⠒⠒⠊⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡽⠾⠯


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡗⠐⠂⢲⠀⠄⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⢇⠸⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠐⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠛⠠⡘⠳⠀⠒⡦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⡀⡀⠀⠀⠀⠆⠀⣆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠈⣶⡦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣄⣤⣤⣤⣤⣶⠁⠀⠀⠀⠀⠀⠈⠙⠛⠒⠓⠻⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠰⣿⣷⣿⡿⢽⣿⣿⣯⣿⣿⠷⢾⣿⣷⠾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢸⠂⢉⡛⢛⠓⡻⠿⡿⠿⠿⣿⣏⣀⣦⣜⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢸⣿⣭⠟⠾⠃⠐⠊⠙⠁⠉⠉⠉⠉⠉⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡁
⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣥⠨⠟




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⢠⠞⠃⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⣼⠀⣀⣀⣀⠳⠶⢶⠤⣤⡤⣀⢄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⢲⡀⠀⢀⡄⢰⠃⠐⢄
⠀⠀⠀⠀⢠⠛⣼⣯⣢⡿⢥⠑⢀⠙⠾⠟⣓⡛⠐⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠁⠈⠨⠟⢮⠁⣨⠠⠴⠚⣦⢤⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠜⢲⡈⣥⠤⢤⡴⠎⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⡘⠲⠒⠲⠋⠃⠀⡆⢰⣅⠀⠂⡴⠃
⠀⠀⠀⠀⠀⠀⠻⣄⡤⠤⠀⠻⢆⣠⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣆⣀⠀⢸⣷⡷⣌⣉⣾⣿⣠⣼⢀⣰
⠀⠀⠀⠀⠀⠀⠀⣟⠀⠐⢃⣴⠞⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣧⠈⢻⣏⣢⣄⡹⢷⠀⢸⣿⣤⣠⣟⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⢙⢷⠾⠓⣾⣠⣽⣿⣦⣭⣵⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡳⠶⠶⠞⢁⠞⢬⠭⠫⠤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⢠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠾⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠖⠛⠛⠛⠉⠉⢉⣉⣉⣀⣀⣀⣀⣀⣉⣉⠉⠉⠉⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⢉⣀⣠⣤⠴⠶⠶⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠳⠶⢦⣄⡀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣠⡴⠶⠛⠋⠉⠀⢀⣀⣠⣤⣤⠤⠶⠶⠶⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠾⢿⣷⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢀⣠⡶⠛⠉⠀⠀⣀⣤⡴⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠛⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⣼⠃
⠀⠀⠀⢀⡾⠁⠀⢠⡟⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⢀⡼⠃
⠀⠀⠀⢸⡇⠀⠀⠘⣧⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠁⠀⠀⣠⡶⠋
⠀⠀⠀⠈⢷⡀⠀⠀⠈⠻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠛⠋⠉⠀⠀⢀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⠀⠉⠙⠛⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠚⠛⠛⠉⠁⠀⠀⠀⣀⣠⣤⠶⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠶⠚⠛⠉⠁⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡛⠛⠒⠲⠶⠶⠶⠶⠶⠒⠒⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡖⢩⡷⠂⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠐⡄⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣠⠤⠤⣀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠨⡤⠗⣀⡀⠠⠑⠦⣤⣀⣠⠞⠒⠒⢶⢤⡀⠀⠀⠀⠙⡗⠒⠒⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣲⠘⠻⣿⢌⡁⢜⣀⢀⠔⠋⢘⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠘⡄⣼⠃⠀⠉⢢
⠀⠀⠀⠀⠔⠒⢦⡇⡄⢱⣢⠀⣸⠀⠀⣠⠜⠁⠀⠀⠈⠢⢤⠆⠀⠀⠀⠘⡄⠀⠀⠀⢜⣿⡀⢏⡀⠀⢧
⠀⠀⠀⢸⠀⠒⠤⢧⡘⠘⠦⢖⠁⠤⠊⠁⠀⢀⣤⠤⠴⠚⢿⠀⠘⡀⣀⡺⠳⣄⠐⠀⠀⠙⠳⠤⠇⠀⡹⠉⠓
⠀⠀⠀⠈⠣⣑⠄⠀⠙⠶⢤⣀⣤⣠⠤⠔⢚⡝⠁⠀⠀⢀⡸⠷⠛⠉⠉⠀⠀⠈⠓⠤⣀⣀⡀⡀⣀⡴⡟⡠⠔
⣀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠑⠽
⠀⠀⢀⡴⢋⡥⣄⡉⠑⠒⠒⠒⠒⠊⢁⠠⠀⢀⡤⠚⠁
⠀⠑⠒⠈⠀⠀⠀⠉⠓⠲⢤⣤⣀⣀⡤⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠄⠀⠀⠀⠀⠑⠀⠆⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠠⠐⠀⠁⠔⡠⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠁⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠒⠂⠄⢰⠀⠀⠀⠀⠊⠀⠀⠒⡀⠐⠂⠂⠐⠀⠀⠄⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⠃⠈⠀⠈⠂⠀⠀⠒⠈⠀⠀⠀⡠⠋
⠀⢀⠈⢠⣎⠀⠒⠋⡀⠀⠀⣀⠀⢀⣀⠠⠮⢅⣀⡀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠬⠀⠀⠀⢀⣀⠤⠒⡀⠀⣀⠠⠊⠁
⠰⠀⠀⠃⣰⠂⠠⠈⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠀⠉⠉⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠂⢠⠀⠁⠀⠀⠘⠀⠑⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢀⠀⠁⠀⠁⠀⠀⠐⠆⢈⠁⢠⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣟⣴⣹⣿⢰⣦⢤⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠔⣉⡒⠄⠀⠈⠙⣿⠟⣼⢟⣿⢸⣿⢃⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡘⠷⠃⡀⠀⠀⡀⢈⣆⢷⡞⣿⢸⢏⣞⣡⣿⡿⣹⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⡤⠪⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⢀⠀⠀⠀⣾⠇⣾⣯⣿⢰⣼⣿⡌⢫⣽⣿⣉⣈⣨⡍⣿⣻⣿⣿⣿⣿⠁⠘⠀⡇
⠀⠀⢀⣤⠆⢀⠁⠀⢀⠁⢠⠀⠀⠀⢀⠎⠠⠀⢸⠉⠉⠉⠉⠙⠛⢻⣏⣾⢸⣿⣿⣏⣵⣿⣥⣿⣿⣿⣿⠟⡑⠂⠀⣲⠁
⠀⢠⣿⠏⢀⠎⢀⣠⠂⠀⠏⠀⠀⠔⠁⠔⢡⠄⠎⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠁⠀⠠⣄⠖⠁
⣴⠿⠁⣴⣧⡶⠋⣁⡔⠀⣀⡴⠄⠠⠤⠒⠓⠒⠦⠤⢄⣈⣀⡒⠀⠠⠈⠙⠛⠛⣛⣛⣋⡭⠥⠒⠉⣇⡡⠴⠒⠁
⠙⠀⠘⠙⢿⠀⡜⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠁⠸⡘⠄⠆⠀⠊⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠂
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠈⠀⠛⠉⠛⠙⠋⠉⠀⠈⠓⣄⠀⠀⠀⠀⠀⣠⣾⣿⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠟⣛⣭⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴⣾⠿⠛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣾⠟⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⣼⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⠿⣶⣦⣤⣤⣠⣤⣴⠾⠋⠀⣠⡿⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿
⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣰⣿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⢿⣿⣿⠏
⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠁
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣄⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⣘⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣠⡤⠶⠶⠒⠶⠤⢤⣀⡀
⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠙⠻⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⡀
⠀⠀⠀⠙⠿⣿⣿⣶⣶⣦⣴⣿⢳⣶⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣉⣽⡿⣿⡿⠱⠛⠛⠛⣽⣿⢟⣯⠿⠛⠛⣽⣿⣿⣿⣿⢋⣴⠄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿
⠀⠀⠀⠀⢀⣼⠋⠁⢰⡿⢁⣠⡴⢶⣾⡟⠃⠈⠀⠀⢀⣿⣻⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣸⠃⠀⢠⢿⡵⠋⠁⢀⣾⠿⠀⠀⠀⠀⠀⣼⢳⣿⣿⣿⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣿⠀⣰⠋⡞⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⠘⣧⣿⣿⣿⣿⠪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠠⢄⠊⠁⠠⠀⠀⢀⣾⠋⠀⠀⠀⢀⣰⣶⣿⠟⠡⣿⣿⡿⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⣤⣼⠿⠛⢹⡏⠀⠐⠿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⠿⠋⠀⠀⣠⠏⢀⣄⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⣰⠟⠁⢀⡀⠴⠊⣡⡶⠟⠉⣹⡏⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⣰⠟⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⢎⠀⢠⡤⠴⠞⠉⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⢀⠀⠀⠠⡦⠥⡠⢄⣠⢤⡄
⡠⠶⠿⠇⢼⠺⢬⠤⢶⠬⠂⠁⠱⠹⠕⠤⡤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣠⣤⣤⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢠⠀⢸⡏⡄⡄⢹⡇⡄⡆⣿⡇⠀⠀⣀⣤⠤⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠒⠒⠚⠓⠒⠒⠛⠓⠒⠒⠋⠁⠐⠓⠂⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡴⠦⠴⠖⠒⠒⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠈⠉⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀⡠⠠⠀⣚⣉⡥⠤⠤⠒⠒⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣺⣯⣽⣯⣿⣽⣽⣭⠿⣷⣦⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣝⡸⢿⡟⣽⣷⡯⣧⣫⡻⢿⠯⣿⣾⢽⣟⣕⡆
⠀⠀⠀⢀⣴⣶⡶⠀⣠⣤⣤⣤⣤⡀⠰⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠁⢀⣿⣿⣿⣿⣿⣧⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠈⠀⠼⢿⣿⣄⢸⣿⣿⣿⣿⣿⣿⠠⠾⠿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⣉⣠⠤⠐⠂⠉⠁⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢶⢒⣋⡩⠤⠤⠄⠒⠒⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⣿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⠊⣠⠖⢉⡤⠝⣷⣤⣀⠀⠀⢀⣴⠟⡹⠋⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣱⣱⣃⡞⣡⠞⣁⠔⢋⣡⣬⡿⠃⢀⡾⢃⡞⠀⣰⠋⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠩⠭⢝⣛⡻⢾⣥⣖⣉⢤⣿⠀⢀⣾⢁⡞⠀⣰⠃⣠⠎⡴⣿⠏
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠉⠑⠮⡙⢷⣾⠃⠀⣼⢇⡞⢀⣼⠃⣰⠇⢀⡾⠃
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠣⡙⢷⣤⣿⣟⣤⠟⣡⡾⢃⢠⡿⠁
⠀⠀⠀⣤⣿⠀⠀⠀⠀⢼⣟⣹⡄⠘⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⠭⠖⢁⡿⠁
⠀⠀⠀⣿⡙⠶⠂⠀⠀⠈⠛⠋⠀⠀⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣒⣒⡂⢸⡇
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⣤⡑⠢⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠄⠐⠁⠀⣠⡾⣿⠮⣛⢶⣄⠀⣀⣴⣿⢧⣄⠈⢿⣿⡳⣦⡙⠢⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿⣋⣀⣈⣿⣮⣿⣿⣾⣏⠑⢬⡓⣭⣿⠌⢿⡻⣆⠙⢦⡀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢏⣿⣯⡙⢮⡑⢝⢷⣹⡶⠟⠋⠁⠀⠈⣷⡘⢷⡈⠻⡄⢈⡲⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣷⡙⢦⡙⢮⣻⣿⠀⠀⠀⠀⠀⠀⠘⣷⡈⢳⡀⠙⣆⢹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢮⣿⣦⡙⢦⡙⣿⡄⠀⠀⠀⠀⠀⠀⠘⢷⡄⠳⡄⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⣯⡢⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠖⠒⠒⠒⠲⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢉⡁⢀⡶⢀⡴⠀⢠⠞⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣱⠂⣰⠋⢠⠏⠀⡞⠀⢠⡏⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⢁⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⡤⠖⠛⣏⠁⠈⣇⠀⠀⠸⡍⠉⠹⡗⠦⣄⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠞⠉⠀⠀⠀⠸⡆⠀⢸⡄⠀⠀⢻⠀⠀⢻⠀⡌⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⣧⠀⠀⠘⡇⠀⠸⡇⠙⠸⡆⠈⢧⠀⠀⠀⠀⠀⣠⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡄⠀⠀⢿⠀⠀⣧⠀⠀⣷⠀⠈⣇⠀⢀⣠⠞⢁⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣶⣿⠳⡄⠀⠀⠀⠀⠀⠀⣷⠀⠈⡇⠀⠀⢸⡀⠀⢹⠀⠀⢸⠀⠀⢹⠖⣫⡤⠖⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠻⣿⡴⠃⠀⠀⠀⠀⠀⠀⢹⠀⠀⣷⠀⠀⠸⡇⠀⢸⡄⠀⢸⡆⠀⢸⡆⠐⣒⣛⣉⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣦⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⢸⡀⠀⢻⠀⠀⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠨⢭⣍⣉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡉⠁⠈⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠋⠓⠶⢤⣈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇⠀⢸⠇⢠⡏⠀⠀⠀⠀⠈⠙⠦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣀⠀⡇⠀⢸⡇⠀⣸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠐⠦⠄⠀⢸⡇⠀⣾⠀⠛⢰⡇⠀⣸⣥⠖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣙⠓⠶⠤⠼⠤⢤⠿⠤⠴⠞⠛⢋⡁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣀⣆⠀⠳⠄⠙⠦⠀⠙⠂⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠛⠁