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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⣀⣀⣠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⢶⡏⢿⣿⣿⢿⠛⠋⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣶⡦⢯⣿⣷⣄⡀⠚⠟⠀⣰⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡌⠹⣿⣿⣿⣶⣶⣾⣿⣿⣿⠿⠯⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣆⠈⠙⢿⣿⣿⣿⣿⣿⣿⡲⣄⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⠏⠙⢻⣿⣶⣀⣀⣉⠙⢛⣻⣷⣹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠟⠀⠠⠘⢋⣿⢿⣿⣿⣷⣿⣿⣳⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡿⢻⣿⣿⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠸⠛⢛⣿⠟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣧⣀⣐⣾⣂⠉⠀⠀⠀⠀⠀⠶⣤⣤
⠀⠀⠀⠀⠀⠀⡰⠂⣀⠀⠀⠀⠀⠀⠀⠰⠁⣼⣿⣯⣙⣛⣿⣬⣵⣦⣤⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⠿⠋⠁⠹⠡⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⣌⡽⠏⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢠⣿⠋
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⢀⡛⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣟⣀⣤⠄⣀⣀⠀⠀⠀⣀⣀⠽⣧
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣅⣀⠀⠀⢩⡏⣁⠀⢠⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⢀⡘⠛⠛⠛⠛⠛⠛⠒⠀⠀⠸⠷⠾⠿⠿⠿⠿⣷⡘⣆⠀⠀⠀⠀⣡⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠄⠀⠼⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢶⣒⡲⢤⡀⠀⠀⠀⠀⣠⣴⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡵⠯⠭⠯⣉⣳⣽⠄⠀⠀⣼⠯⣖⣶⡤⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡇⠈⠀⠐⠀⠘⢺⠀⠀⢰⡏⡼⣿⣻⠇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣩⠔⠒⠒⣣⣀⡐⢃⡠⠖⠉⠀⠀⠈⡟⣭⣓⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠋⠁⣀⣴⡎⠀⠈⠻⣽⠄⠀⠀⠀⠀⠀⢸⣯⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⠃⠘⠢⣀⡔⠙⢧⣀⣀⣀⡠⠤⠾⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠈⢢⣄⡀⢀⣀⠤⢄⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣀⠈⠒⠤⣀⣀⠀⡴⠁⠀⠉⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢀⡔⠀⣀⠀⠀⠀⢈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⠀⠈⢹⠦⠤⢇⣀⣘⣄⣨⢮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⣄⢉⠗⡞⠀⠀⣰⠋⠳⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣘⡏⠀⠙⠢⣀⣀⠴⠁⠀⠀⠙⢦⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣴⠊⠳⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡹⠾⠗⢋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠈⢦⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⢀⡀⠄⠒⠂⠁⠈⠀⠠⢆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⡀
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢁⠀⠀⠀⠀⠐⠆⠓⠀⠀⠈⠉⠁⠀⣠⡌⠃⠀⠀⠀⠀⡠⠄⠀⠀⠀⡀⠀⠈⠑⠢⡄
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠼⠃⢸⠘⡄⠱⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⡘⠀⠀⠀⢠⡪⠐⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈
⠀⠃⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠉⠀⠈⠀⠄⡤⠂⠀⢄⠀⠀⠀⠀⣶⠄⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠠⡀⠀⠂
⠀⠘⡀⠀⠔⠀⢈⠄⠀⠀⠀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⠸⡄⢀⠀⢀⠀⢠⣀⡀⠀⠀⠡⡀⠐⢀⡄
⠀⠀⠘⢄⣄⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠛⠀⡀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⣀⠠⠔⠋⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠀⠀⠐⠂⠈⠓⣄⡼⠀⠀⠀⠂
⠀⠀⠀⠀⢧⣥⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⣀⠀⠔⠀⠑⢄⠀⠀⠀⠁⢡⢠⡄⠀⠀⣴⠀⠀⠀⠀⠀⠀⢈⠂⠁⠀⠈
⠀⠀⠀⢀⠄⠈⠉⠂⠄⠀⣀⣀⣀⡀⡤⠂⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⠄
⠀⠀⢀⠂⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠠⡀⠀⠀⠨⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠢⡀⠀⠀⠁⠀⢀⠀⠀⠓⢨⡀⣪⠀⠀⠐⠁
⠀⠀⡎⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢸⠊⠈⡁⠄⢠⡃⠀⠉⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⡰⠐⠈⠁⠀⠀⠀⠠⠀⠉⣽⣩⡻⠀⣂⠕⠁⠀⢣⠀⠁
⠀⠀⣧⡏⠀⠀⠀⠛⠒⠒⠒⠒⠂⢸⡀⡎⠄⠀⡀⢈⣄⣴⣄⠀⢠⣠⡄⠀⠀⠀⠀⠀⢼⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⢙⠄⢠⠀⠀⠀⢠⠧
⠀⢰⠃⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠜⠶⠗⠊⠁⠀⢀⡉⠉⠉⠉⢛⣲⣖⣠⣄⠅⠀⠀⠸⡄⠀⢢⣤⠐⠀⠀⢰⡋⠀⠤⠀⠀⠀⢸⠘⡄
⢀⡜⠀⠀⠀⠙⠓⠒⠒⠒⠒⡦⠤⠦⠛⠀⠈⠙⣂⠤⠤⠴⣒⣮⠭⠖⠚⠉⠁⠀⠀⡏⢯⠴⠐⠁⠸⣄⠀⠁⠀⠀⢀⣼⠁⠀⡀⠀⠀⠉⠞⠀⢇
⢹⢀⡥⠆⠤⠤⠒⣤⣄⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠉⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⢀⡠⠀⠈⠉⠓⠛⠈⠋⣏⠴⠊⠀⠀⠀⡈⠀⠀⢸
⢸⠁⠀⠀⠀⠠⠈⠀⠀⠈⠈⠉⠁⠒⢤⣑⢦⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠋⠀⣔⠁⢀⡄⠀⠀⢠⠂⠀⠉⠀⠀⠀⣀⡰⠊⠀⠀⠀⡘⠀⠀⡀⢀
⠈⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠉⠑⠢⣄⡇⠀⠀⠀⠀⢀⠕⠁⠀⢠⠓⠘⢢⠈⠂⠘⡇⠀⠀⢿⣀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⢴⠁⠒⠋⠁⡀⠑⡄
⠀⠘⢦⡀⠘⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠁⠀⡞⠀⠀⠀⠈⠀⠀⠀⠙⠂⠀⠱⠤⣀⡐⠉⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⢐⠘
⠀⠀⠀⠙⠛⠓⠦⠴⠷⢤⣄⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣆⠀⠇⡀⠀⠀⡠⣣⡀⠀⠀⠀⠃⠀⠀⠈⠃⠀⠀⢀⠔⠚⠡⣀⣀⠠⠔⠋⠙⠆⡀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⢦⣀⣀⠀⠀⢀⡾⠗⠋⠉⠈⠒⠼⠮⠀⠈⠈⠁⠑⠄⡠⠤⢤⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡰⠎⠀⠀⠁⠚⠂⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢃⡜
⠀⠀⠀⠀⠀⡀⢀⣀⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠒⠩⠕⢒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢸⣭⠭⠴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢸⣿⣿⣿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⣿⣿⠛⠛⠃⠈⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣧⠀⠀⠀⠀⢷⣶⠿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠹⠿⠏⢉⡉⠉⠓⡶⠒⠚⡖
⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⣉⣉⣏⡗⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⡟⠁⣀⠀⠀⠀⠘⣆⠀⠦⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⢸⠁⢸⠀⠀⠀⢠⢦⡱⣄⠀⠀⠀⠸⣇⣀⡟⠦⠤⠴⠖⢻⣀⡤⣼⠏⠁
⠀⠀⠀⠀⠀⠀⡴⠃⢸⣀⠀⢸⡠⠋⠀⠀⢠⠏⠀⠙⢎⠳⡄⠀⠀⠈⡇⠲⠀⡀⠘⠀⠀⠉⣂⠞
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠉⠉⠀⠀⠀⢠⠿⠤⢤⣀⡀⠳⣌⢢⡀⠀⠹⣀⠀⢶⣟⣹⠀⡰⠃
⠀⠀⠀⠀⠙⢳⠒⠒⠲⠤⠤⠤⣤⣀⣀⠞⠒⠋⠉⠉⢹⠀⢸⡟⠁⢠⠖⠻⣍⡳⠿⡷⠀⣹⠶⢤⡀
⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⣿⠭⠔⣒⣒⣪⠭⠭⣷⡋⡇⢺⣿⠀⠀⢹⣾⠏⠉⠛⢁⠄⠀⣷
⠀⠀⠀⠀⠀⢸⠀⢸⣈⡏⠙⡆⠀⣏⠭⠽⠒⢲⠛⠉⠉⠁⢸⡇⢸⠉⣿⣬⣯⢉⡟⠲⢤⠏⠀⣰⢿
⠀⠀⠀⠀⠀⢸⡇⢸⣈⣏⠙⡇⠀⣿⠤⠶⠒⢺⡀⠀⠀⠀⢸⡇⠈⣷⢇⣀⣨⡟⠓⠦⣄⣀⠴⠃⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⠁⠀⣿⠤⠴⠒⠚⠉⠙⠒⣤⣼⡇⠀⢩⢶⡶⣶⡟⠲⠤⣤⣀⣀⣠⠼⠓⢦⡀
⠀⠀⠀⠀⠀⠈⠓⠲⠤⢤⣀⡀⠀⣿⣀⣤⣤⣶⠶⠿⠟⠛⠋⠁⠀⢯⣀⡔⠈⠀⡴⠀⠀⢠⡀⠀⢲⣀⠜⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣍⣓⡾⣧⠤⠤⠤⠧⣴⣾⠵⠶⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠦⠀⣼⣯⣿⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⢹⠀⠷⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⢓⣾⣿⡄⢀⠠⡀⠀⠀⣠⡂⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣍⠴⠃⠀⢀⢭⡙⠉⠃⣿⠇⣀⠀⠀⢀⠀⠀⠀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠿⠀⣴⡲⠄⠀⠹⡷⠀⠁⢾⣿⣟⠷⠎⠀⠀⣾⣷⣍⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠗⠐⡏⠿⣄⡤⠂⠁⠀⠀⠀⠙⠧⢴⣾⡿⣇⣠⡋⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣠⣤⣤⣴⣶⡖⠈⠳⠾⡅⠀⠀⠀⢠⣷⣶⣤⣼⣿⣮⣻⣿⠇
⠀⠀⠀⢀⡠⠔⣠⣦⡄⠀⠀⠀⡆⠀⠀⠀⠀⣠⢞⣨⣷⢿⣿⡿⠛⠿⣟⠣⠄⣼⣿⠀⠀⠀⢀⣿⡿⢸⠟⠉⡍⠙⠉⠃⢀⡀
⠀⠀⠀⠀⠈⠙⠛⠛⠻⢮⢾⠀⠁⠀⠀⠀⡰⠛⡿⠃⢡⣿⣿⡅⣀⣀⡈⠂⢀⣿⣿⠀⠀⢀⣾⣿⠇⠏⡄⠀⠀⠀⠀⠀⣿⡏⢀⢀⣀⡀
⠀⠀⠀⠤⢠⣴⡶⢤⡆⢸⠠⡀⠄⠄⠀⠃⢠⠈⠀⣀⣾⣿⠇⠀⠈⠉⠉⣷⣿⣿⣿⢀⣠⣿⣿⡿⠐⠀⠁⠀⠆⠀⠀⠀⠈⠙⠛⠛⠛⠻⢄
⠀⠀⠀⠀⠈⢿⡇⠀⠁⠈⠀⠧⠍⡠⠀⢀⠉⣴⣿⣿⡟⠿⣀⡉⠀⠀⣼⣯⣿⣿⣿⣯⡿⣿⣿⡇⠰⠁⠀⠀⠆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⡇⠀⡃⠀⠀⠀⠈⠐⢂⣬⣿⣿⣿⠿⣿⠖⠈⠀⣀⣭⢿⣿⣿⣿⡟⠋⡴⣿⡿⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⣠⣴⣾⣿⣿⡿⣿⡇⠀⠿⠂⠀⠀⠀⣉⣠⡌⣿⣿⣿⠆⣾⣹⠁⠀⠀⠀⠂⠀⠀⠀⠦⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡿⣿⠟⠁⣠⡿⠛⠄⠀⡀⠂⠀⣼⢟⣿⡿⣭⣿⣿⡂⠙⠻⢶⣦⣤⣤⣄⡀⠀⠀⠀⠀⢀⣠⠐⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⣿⣿⣿⠃⠀⠈⠘⠁⠈⠀⠀⠉⠙⣄⠻⣟⠉⡁⠈⣿⣿⡇⠀⠀⠀⠉⣿⣿⣟⣛⠛⠒⠶⣏⡵⠂
⠀⠀⠀⠀⠠⣤⣦⣀⡀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠊⡣⠽⣿⣿⡇⠀⢀⣀⣀⣀⣙⡖⠒⢀⣀⣀⣉⠃⠈⢷⣺⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣰⣿⠿⠦⣿⡥⠀⠀⠀⠁⠀⠈⠛⢷⣄⣀⣿⡦⠈⠉⠙⠓⠢⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣶⣼⣝⡁⠘⠉⠀⣙⠀⡀⠀⡿⠏⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⠛⡏⠃⢠⣤⣶⡄⢰⠘⣇⠀⠀⢠⠿⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠄⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣿⠀⠀⠉⠙⢛⣺⣤⣿⣿⡯⢼⠠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⣃⣤⣤⣶⣶⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠉⠛⠁⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣏⣀
⠀⢀⡀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣿⣿⣿⣿⡿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠈⠙⢿⡿⢿⠿⠿⠟⠋⠁⣼⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⣾⠿⠟⠛⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠀⢀⡴⠚⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⢁⡀⠙⣿⣿⡇
⠀⠀⠀⠀⢸⡀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢰⠏⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠘⢧⣤⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⢢⣤⡄⠀⠀⠀⣠⣤⠔⢾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠘⢷⣤⣭⣤⣤⣤⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣙⠿⠿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦⢤⣤⣤⣀⣀⣀⣀⠤⠤⣤⣶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡃⠀⠀⣸⠟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢰⡏⠙⠖⠚⠁⣶⠀⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡏⠀⠀⠀⠀⠀⢿⣀⣠⡿⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⣬⠁⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣦⣤⣤⣤⣤⣴⣾⣿⠏⠀⣠⣇⣀⣤⠤⣤⣀⣠⣴⣿⠏⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⢰⣿⣿⣿⠋⠁⠀⠀⠀⠀⢀⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢆⡼⠿⠛⠓⠚⠒⢶⡖⠲⠖⠀⠙⢻⡿⣆⣨⠟⠛⠋⠀⠀⠀⢀⣠⣶⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⢰⠀⠀⠀⠀⠹⣦⣁⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠻⠿⠟⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⡟⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣄⣀⣀⣀⣠⣤⣴⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠛⠛⠋⠉⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⡄⠀⢀⣤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢿⣧⣰⠟⠁⠀⣀⡈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⣿⣏⠀⢀⡜⠉⢹⡆⣻⣤⣶⣶⣿⣿⣶⣶⣦⣤⡾⠉⠀⢀⡉⠻⣄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣧⣘⣇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⠋⠱⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡇⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣄⡀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⡇⠀⠘⣇⠀⠀⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢳⡄⠀⠙⠦⠞⠁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣤⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⡴⠋⢲⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠈⠃⢸⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠸⡇⠀⢀⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠙⢦⠞⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠉⠓⠢⣀⠀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣀⡀⠀⠐⠠⣴⠮⠅⠚⠁⠀⢡⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠘⠒⠒⠊⠁⠀⠊⠀⠐⠀⠪⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡀⠀⠣⣀⡀⠀⠀⠀⣀⠀⠀⠀⠐⠂⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⠁⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠈⢳⠤⠄⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠄⠴⠀⠈⠢⣀⠀⠀⡘⠉⢄
⠀⡔⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠰⠀⠀⠀⠀⠀⠀⠢⡀
⠀⢀⠊⢀⠠⠐⠂⠀⠁⠀⠀⠤⠔⠆⠀⠀⢈⠀⠀⠀⠀⠀⠀⠐⠀⢠⠀⣀⣀⡠⠀⠢⡤⠃⡠
⠀⠈⠀⠂⠠⠀⡰⠀⢰⠁⠀⠀⠐⠒⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⡀⠤⡀⢻⠥⡔⠀⠀⠀⠀⠀⠀⣀⢠⣤⡄⣀
⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠔⠉⠁⠀⠈⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⣠⣾⣦⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠒⠒⠦⠤⠤⢤⠤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠛⠀⠀⠀⠘⠟⠛⠀⠀⢸
⠀⠀⠀⠀⢀⠴⠋⠀⢸⠀⠀⠀⠘⢤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⣀⣠⠀⠀⠀⢀⣶⡎
⠀⠀⢀⡴⠃⠀⠴⠉⠀⠢⣀⠒⢒⠉⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⡜⠂⢄⠀⠀⠀⠀⠀⢀⠤⠆⠀⡽⠀⠈⠳⢜⠻⠿⠃⠀⢀⡾⠋
⠀⣠⠋⠀⠀⢀⠖⠠⠀⡔⠉⠒⠊⠁⡀⠀⠀⢀⡼⠳⡄⢀⡠⠚⠠⢀⠀⠹⠀⠀⢀⠖⠁⠀⢀⠟⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁
⣜⠁⠀⠴⠂⠀⠀⠀⠈⠁⠀⠀⠀⠒⠡⠐⠚⠁⠀⠀⠉⠁⠀⠀⠀⠈⠣⢄⠀⠈⠱⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⢀⡤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⢀⣄⠀⢀⣰⣶⡏⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢠⣀⠈⠠⣼⡶⠄⣾⣿⡆⢸⣟⡟⡦⢀⣴⡆⠀⡀⠀⢀⣤⠖⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡹⣄⡄⢸⣿⣷⠀⣿⠇⠀⣈⢋⣡⡈⡞⠀⠀⠙⡿⠏⢠⣛⡶⢋⡀⠂
⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⡁⠈⠙⠃⢸⣽⡄⢠⡜⠙⣿⡿⠁⣠⡄⠤⢤⡞⡿⠋⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠙⠀⠈⠉⢡⣧⠀⠄⡠⣿⣿⡇⢰⣼⣛⡿⠁⠀⡏⠀⣟⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠈⡄⠀⡇⢈⣅⣼⠃⠀⠂⣹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢳⢄⡐⡇⠘⢛⠃⠀⣁⠐⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⣷⣮⡇⢠⠇⠠⠞⠋⠀⠆⠀⠀⠀⠀⠐⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢃⠈⠉⡅⠈⠀⠄⠁⠀⢀⡆⠀⠀⠀⠀⠘⠟⠻⠟⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠄⠀⠢⡠⠞⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣠⠆⠀⠀⠀⣰⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⠀⠀⠀⠀⣿⣿⣿⠿⠦⠀⠀⠀⠀⣀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠆⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠾⠀⠀⡀⠀⢐⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⣌⡁⠒⠠⢾⣃⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠶⠦⠄⠀⠉⠃