Electrical circuit Emojis & Symbols

⠈⠀⠉⠁⠰⠶⠶⠶⠲⠶⠀⡠⠶⠶⠈⡆⠀⠀⠀⡇⠀⠀⠙⢄⠠⡀⠀⠀⣠⢊⡠⣊⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⢸
⠀⠤⢀⠀⢸⣉⣉⣁⣈⣀⣨⠀⠀⣹⠀⡇⠀⠀⠀⡇⠀⢤⡀⢤⡑⢌⢦⠈⠁⠈⠁⠉⠈⠩⡤⢤⣀⣄⣀⣀⣀⣠⣀⣀⣀⣀⣄⣧⠜
⠠⠄⠤⡀⢠⠠⡆⢤⠠⠄⢤⠠⠄⢤⠀⡇⠀⠀⣄⠇⣀⠀⠘⠂⠙⠂⢹⠀⠀⠀⠀⠀⠀⢐⡒⣪⢔⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⢶⢒⡆
⠀⠀⠀⠀⢰⠀⡇⢰⠀⡄⢼⢠⡄⣴⠀⡇⢰⠄⣅⡃⠉⡠⢊⡍⠁⠈⣩⠀⠀⠀⠀⠀⠀⢨⡭⠔⢫⠢⠒⡒⢒⣶⡛⣉⣋⡀⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠀⡇⢰⠄⡡⡣⣊⠀⢠⡅⡻⠊⣀⠐⢦⡰⢄⠶⡐⢆⠀⠚⠋⢧⠋⢠⡅⠈⠀⠀⠉⢘⣣⡤⢤⢤⡤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠲⠉⠂⢸⠀⡇⢠⠊⠎⠀⣙⠰⡠⢊⠔⠁⠉⠀⠀⠑⢆⡱⣌⣶⢭⣭⠭⣤⣯⣥⣬⣥⠯⡙⣌⡧⠤⣤⡞⣀⢃
⠤⠤⠤⠤⠤⠤⠤⣄⠀⠁⠈⠃⠀⢸⠀⡇⠀⠀⠀⡄⡩⢊⠔⢁⡄⢠⡄⣒⠒⠀⠒⠉⡉⠋⠉⢋⡉⢤⠀⠀⠀⠈⠧⠉⠄⠠⠱⡆⢰⠠⡇
⣀⣀⣀⣀⢌⡢⠀⠀⠀⠀⢀⡀⠀⢸⠀⡇⢠⠐⣢⢊⠔⠁⠴⠊⠴⠁⠀⣭⠤⠤⠤⠬⠥⠔⠋⠈⡥⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉
⠠⠶⣒⢢⢱⣻⠰⢨⡍⠿⢩⡏⠿⢩⡁⠿⢹⠉⠯⢹⠉⠏⢩⠉⠉⢢⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠒⠀⠀⠀⣀⣀⣀⡀⠀⠀⠓⠖⠲⠒⠖
⠛⣕⡌⢸⢹⠘⠶⠤⠄⠔⣂⣀⣒⣂⣀⣒⣊⣀⣒⣀⣐⣒⠂⣀⡀⢸⠀⡏⢘⠀⡋⠈⠉⡃⠘⠀⡏⠀⢉⣉⠁⠀⠀⢈⣋⣀⣁⣀⣀⣀⣉
⠛⣜⡇⢨⢾⠐⠚⠒⠚⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢯⡅⢸⠀⠋⠘⠁⠋⠘⠁⠃⠘⠀⠃⠀⠡⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤
⣉⢗⡇⠘⣀⣉⣉⣉⣩⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡵⠶⢸⠒⡡⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⣶⠒⠤⠤⠤⠔⠒⠒⠒⠒⠒⠒⠒
⠤⢖⠣⣢⡠⣄⡤⠤⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⣋⢸⣉⠔⢁⠔⣒⣒⣒⢒⠒⠒⢟⠁⠀⡉⢀⠀⡀⢀⢀⠀⡀⢀⠀⡀⢀
⣶⠀⠑⠆⢰⠈⠷⠐⠲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣯⣥⢼⢤⡄⡇⠊⣄⠀⣄⠀⢱⡀⢨⠀⠀⡇⢹⠈⡇⠉⢘⡃⠋⢸⠁⠁⢸
⣀⣀⣀⣀⣀⣂⣉⣉⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡷⠶⢸⠆⠒⢁⠃⠁⠀⠇⠀⠀⠀⢸⢀⡀⡇⢸⠀⡄⠀⠨⡅⢀⢸⡄⠀⢸
⠠⠤⠠⠤⠀⠤⢤⠤⢬⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⡛⢸⠂⡦⢥⡄⠁⠀⠃⠀⢠⡀⢨⠈⠁⡆⠘⢄⠣⡀⠀⠈⠂⠛⠒⠒⠓
⣴⢠⡄⣤⠐⠒⠲⠐⠂⠂⢨⡍⠉⢩⡍⠉⢩⡍⠉⢭⡍⠉⢴⠉⠉⢺⣄⡒⠒⠂⠓⠀⠓⠀⠨⠀⢸⠀⠠⢃⣀⢀⡑⠘⠛⠛⠛⣛⢛⣛⠛
⣸⢀⡇⣀⠀⠀⠐⢄⣠⢟⣬⣡⢟⣨⣁⣷⣨⣀⡷⣸⢀⣇⣨⣐⡇⠜⠈⣣⠐⡩⠉⠉⠉⠉⠀⠀⠊⠘⠒⢿⠀⠀⡗⠀⠀⠀⠐⡇⠀⢸⡗
⡉⡈⢅⡈⡀⠤⠤⢊⠤⡪⠊⡠⢊⡴⢡⠞⡡⢉⠜⡱⡢⠃⠸⠀⠣⡀⠀⣻⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡛⠀⠀⣟⣁⡠⢊⣉⡇⠀⢘⣋
⠉⠉⠉⠉⠉⠂⠀⣤⠈⠀⡎⢰⠃⠖⠡⠊⡔⠡⢊⠊⢀⠀⢸⠀⠀⡇⠀⣻⢀⠀⣤⠀⠀⠀⠀⢠⡄⢠⠤⠄⠀⠀⡧⠤⠔⡡⠤⡇⠀⢸⠦
⣀⣀⣀⣀⣀⠖⢊⡴⢈⠀⡇⢸⠀⡃⢈⠀⡃⢸⠀⠀⠅⠁⢸⠀⢠⡇⠀⠛⢄⣑⣒⡒⣒⣒⣒⣒⢄⢸⣶⣂⠀⠀⣗⡒⡆⣔⡓⡇⠀⢸⡓
⠇⢻⠘⢇⣛⣐⣋⡀⢠⠀⠃⠸⡀⠃⠘⠂⣓⠘⠻⠐⣇⡺⠸⡀⢰⡆⠀⠑⠤⠀⠀⣀⢀⠄⡤⠀⢸⢸⡏⠹⠤⣤⣋⠁⡇⠈⠋⠣⠤⠸⠉
⠁⠀⠛⠋⢟⠻⣱⠈⢸⠀⠀⣄⢠⠁⠀⣡⢀⣌⠈⢦⡄⣠⣡⡱⣸⡃⣳⠀⡀⢀⣀⡙⠘⠉⡇⡄⢸⢸⡇⠀⠀⠀⠀⢋⠥⠃⠀⠀⠀⡠⠊
⣈⣀⡈⢌⠢⡁⢸⠀⠰⠀⠀⣀⣀⡀⠀⢀⣀⠈⢣⠀⠄⠀⠀⠀⠉⠁⠉⡜⠋⠈⠉⠀⠀⠀⡇⡇⢸⢸⡇⠀⠀⠀⠀⢸⢸⠡⠆⢠⠚⡀⠛
⠀⠀⠈⡆⡗⠀⢸⠀⢘⡠⠞⠛⠛⠛⢛⠛⠛⠳⣌⠒⠒⠒⠚⠀⠛⠒⠄⡇⠘⠘⢋⠃⠀⠀⡇⡇⢸⢸⡇⠀⠀⠀⠀⢸⢸⠀⠀⢰
⠀⠀⠀⡇⠇⠇⢸⠀⢸⡇⠀⠀⠈⡄⢠⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡇⠀⡏⠸⠀⠀⠀⡇⠃⢸⢼⠇⠀⠀⠀⠀⢼⢸⠀⠀⠸⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⢉⣀⣉⡉⣀⠀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠔⠁⠄⠀⢀⠀⠐⢄⡀⢀⣀⠀⣀⣀⠈⠢⠔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠐⠂⠀⠘⠀⠀⠀⠀⠆⢀⠄⠂⠀⠀⠀⠤⠄⠀⠀⡆⠁⠀⠈⠁
⠀⠀⣀⠀⢀⡐⢄⠒⠒⡠⠂⠀⣀⣀⠈⠁⠀⡎⠉⡉⠈⠍⠁⡀⠀⣸⣀⠀⣀⣀⠉⠈⠉⠁⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠃⠀⠠⠀⠑⠠⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠐⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠤⠤⠤⠤⠤⢄⠀⢸⠀⠀⠀⢩⠁⠀⠀⠑⠤⠤⠤⠤⠤⠄⢀⠄⠀⠂⠀⠀⠐⠤⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢇⠀⠉⣁⣀⠈⢉⣀⠀⠁⠀⠀⠀⠀⠀⠀⠁⡄⠐⢄⡀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠰⠤⠤⠤⢄⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢱⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁


⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣏⠉⣻⠀⣼⠉⢹⡆⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⠛⢻⠛⣿⠛⠉⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⠀⣿⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠀⣿⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣼⣀⣿⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⢀⡶⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠈⢹⠁⠀⠈⠀⠀⠁⠀⠉⠈⣿⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠉⠉⠳⡄
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢯⣭⣭⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠈⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⢀⣠⠟
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡨⢔⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡊⢔⡩⢒⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣊⠕⡪⢐⡡⠒⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠐⢩⠒⠁
⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⠀⠰⠆⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⣤⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⢸
⠀⠀⠀⠀⢸⢠⡜⢛⠤⢂⠄⢘⠧⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠙⠃⢀⡠⢔⡩⢔⡨⠔⢸
⠀⠀⠀⠀⢸⢰⢪⠔⡪⠔⠊⠀⠀⣤⠤⠤⡠⠤⠻⠥⠤⠤⠤⠽⠧⠤⠤⠤⠄⢂⠷⢰⠡⢂⡡⠦⠛⢸
⠀⠀⠀⠀⢸⢸⠀⢸⠀⠀⠀⣄⣀⣀⣀⣘⡏⠈⣉⠉⢉⣍⠉⠉⠉⠉⠉⣉⡉⠀⠀⢸⠀⠈⠁⠀⠀⢸
⠀⠀⣀⠔⡋⠜⡀⣸⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⢹⠀⠈⡇⣐⢗⣺⣒⣗⣈⡁⠔⠛⢸⠀⠀⣦⠀⠀⠘⠁
⠔⣊⠔⡨⢐⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⢸⣠⡀⡇⠀⣀⡠⠄⠀⢰⡆⠀⣀⢸⠀⠀⡇
⡪⢔⡡⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⠤⢒⠡⢀⠻⠒⠁⠀⠀⠀⠀⣭⢸⠀⠀⡇
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡔⣊⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⣨⢸⠀⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠃
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢊⠔⡡⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⠛⠃⡄⡄⣤
⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢔⡩⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⢃⡀⠇⠄⠶⢀⡀⠀⣤⡄
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠰⢊⠡⢂⠇⢺⠥⠒⠒⠚⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⡨⠕⡊⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡃⢇⡄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡊⠔⡨⢐⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣊⠕⡪⢔⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠔⡩⠒⠁

⠈⣈⣈⣁⣄⢀⢠⠀⠀⡀⠀⠀⠀⠄⡀⠠⠤⠀⢀⠦⠀⠆⣴⠂⠄⠠⠀⡀⠀⠀⠠⠰⠂⠆⠠⠀⠀⠀⠀⠆⠢⠀⢰⡀⢀⠄⠆⠀⠀⠀⠰⠀⠲⠐⠆
⠀⣿⣯⣿⣿⠀⢸⠀⠀⠅⠀⠀⠑⠤⠂⠘⢁⢊⠂⠀⠀⡁⠂⠀⠀⠀⠀⠓⣒⢀⣒⡀⠀⠀⢀⠀⠀⠄⠄⠀⠐⠒⢂⠀⢂⡀⢀⠀⠄⡄⣿⣿⣿⣿⣷
⠀⠀⠀⡄⠀⠀⠠⠆⠀⠁⠂⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠀⠒⠙⠁⠂⠄⠄⡁⠀⠀⠀⠁⠁⠀⠘⠀⡜⠁⣿⣾⣿⣿⣿
⠈⠀⠀⡀⠒⠒⢢⠰⠅⠤⠠⠄⠤⠠⠀⡤⢠⠢⠤⠡⠠⠀⠀⠤⢢⠔⠍⠩⠍⠁⠀⠀⠠⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⢀⣶⣶⣮⠸⢹⠁⠙⠛⠛⠛⠋⠀⣀
⠀⡂⠀⠀⠀⠀⢸⠀⠂⠐⠀⠀⠇⢸⡀⠇⠰⡁⠇⠒⠐⠀⠀⠐⢸⠀⡇⢸⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢾⣿⠀⠀⠀⠀⠀⠀⠀⠄⠐⠄
⠀⡅⠀⠂⠂⠒⢸⠠⠀⠀⠀⠀⠁⠘⠀⠁⠘⠁⠃⠀⠀⠀⠀⠀⠘⠀⡃⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠈⠑⠊⣭⣀⠸
⠀⡇⠀⠀⠉⠭⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢈⠀⣠⣮⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⠉⠀⠀⡀⣀⠀⢀⡀
⠀⡇⠀⠄⠐⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⠠⠀⠈⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠉⠀⢁⣤⣤⣤⡈
⠀⡇⠀⠅⠸⠀⣟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢼⠰⠀⠀⢠⡰⠆⠖⣀⠠⠤⠀⠐⠀⢐⣐⣂⣒⣐⣂⡀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⡇⠀⠀⠀⠐⢻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡅⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡇⢸⡄⠀⠀⠁⡋⠉⠁⡇⢀
⠀⡇⠀⠀⠀⠀⣴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠙⠊⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠄⠀⠀⠈⠂⠈⠈⠀⠀⠘⠁⠁⠥⠠⠠⠇⣀⢸
⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠰⠉⠀⠈⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠂⠀⢀⠈⢀⢸
⠀⡇⠀⡀⠀⠀⠙⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠈
⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠀⡆⠠⠁⢌⠀⠀⠀⠀⠀⠐⠀⠆⢰⢀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠀⢀
⠀⡇⠀⠀⠀⠀⠰⠲⠂⠐⠀⠀⠂⠸⠀⡃⠘⠀⠂⠂⠐⠀⠀⠒⠐⠀⠃⣘⠈⢀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡄
⠀⡇⠀⠀⠔⠶⢂⠀⠀⠀⠏⢀⣀⠀⣀⠀⠉⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠃⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠠⠁
⠀⠃⠀⠓⠂⠀⢸⠀⠀⠀⠁⠀⠤⠤⠤⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐
⠀⠄⠀⠀⢀⠀⠘⠀⠀⠀⠀⠐⡆⠀⠀⠖⠳⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⡄⢱⣶⣶⠀⠀⠀⠀⠠⠤⠀⠘⠃⠀⠀⠀⢀⣀⣀⣀⡀⣶⡀⠀⢸⠀⠚⢀⠰⢆⠀⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠇⢸⣿⣟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢻⠇⠈⠀⠁⠁⢸⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⢀
⠀⠈⠉⠉⠀⢀⠠⡀⢠⠀⠃⡠⢤⡀⠘⠁⠹⠿⠾⠿⠇⠹⠁⠐⠀⠃⠃⠘⠠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢠⠀⡄⣤⡌⠀⠀⢰⣿⣇⠀⣟⠀⣿⠐
⠀⠀⠀⡀⠋⠥⠀⠂⠘⠀⠀⠙⠛⠃⢒⡁⢤⡀⠀⠀⡶⠖⠀⠀⠀⠰⠀⠀⠠⠄⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠉⠓⠤⠁⠀⠀⠤
⣤⣤⣤⣤⣤⣤⣤⣽⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣼⣭⣿⣽⣯⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⢀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠀⠀⠀⠀⠀⠐
⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⡀⡀⠀⠘⠈⠐⠃⠂
⠀⠀⠁⡄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠄⠬⠀⢀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⢀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⡁⠀⣀⠀⠙⠁⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠨⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠦⠆⠐⢠⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠠⡦⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⢀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⢀⠂⠀⠐⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄
⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⢘⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⡀⠀⠀⠀⠀⣴⡚⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⢀⠀⠀⠀⡄⠀⢠⠀⡄⢠⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⡀⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⣄
⠀⠀⠀⠀⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⣀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⢀⠀⠀⠀⡀⠈⠀⠈⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠁⡀⠀⡁⠈⠀⠠⢠⠁
⠀⠀⢰⠘⠆⢂⠸⠀⢰⢂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐
⠀⠀⠈⠀⠁⠀⠀⡄⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠉⠨⠅⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣉⣬⣫⣴⣍⣽⣉⣾⣏⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠
⠀⡰⠀⠢⣀⣀⣀⣀⣀⣀⣀⣀⡠⠂⠂⠂⣐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠇⠀⢀⡀
⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠤⠀⠁⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠼⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢀⠀⠀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⢀⠤⠄⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠁⠠⠀⠀⠀⠀⠀⠀⠐⠐⡐⢂⠂⠀⢤⠀⠀⡐⠀⠈⠢⠤
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣀⣀⠐⠐⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠐⠁
⠀⠰⠀⠀⠀⠊⠠⢀⠄⣈⣔⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠒⠒⠒⠒⠒⠒⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠰⠀⠆⠰⠀⠖⠰⠂⠒⠐⠆⠀⠀⠈⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠐
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢤⠀⠀⠀⠤⣀⠤⠀⠀⠤⠠⠄⠠⠄⢠⠀⠠⠄⠠⠄⠀⠤⠠⠄⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢩⠄⢠⠀⠤⠀⠄⠠⠄⠀⠠⠄⠀⠴⠤⠄⠄⠤⠠⠄⠀⡤⢠
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠐⢀⠐⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⣠⠀⡄
⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠃⠀⡄⠀⠀⠀⢀⢲⢲⢲⠂⠀⠀⠀⠆⢰⠀⡀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⣀⣀⣀⢀⡀⢀⡀⣀⣀⣀⢀⣀⠀⡀⢀⣀⠀⡀⠀⢀⡀⡀⢀⠀⢀⠀⢀⠀⠀⡀⢀⠀⠀⡀⣀⢀⢀⣀⠀⠀⡀⣀⠀⣀⣀⣀⣀
⣿⣿⣿⡟⣻⢿⡿⣻⢟⣻⡛⡟⡻⡿⢟⣻⡟⣿⢿⣿⢟⣿⡿⡛⡟⣻⢿⢿⢻⢛⣿⢟⣿⠿⡟⣿⢻⠛⡿⡛⡟⣿⢛⣿⣿⣿⣿
⣿⣿⣿⣧⣾⣬⣧⣾⣼⣽⣧⣧⣦⣧⣾⣽⣤⣽⣽⣿⣼⣽⣧⣦⣯⣿⣼⣼⣼⣼⣿⣕⣽⣼⣧⣤⣼⣤⣧⣫⣧⣿⣕⣽⣿⣿⣿

⠀⠀⡀⠀⠄⠀⠀⠬⠅⠀⠠⡄⠀⠠⠭⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠂⣀
⠀⠀⠇⠀⠀⠀⠂⠒⠰⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡄⠀⣤⠀⠁⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⢠⡀⠀⠀⢠⠀⠀⠀⣄⠠⠠⠀⡄⠀⠀⠀⡄⠁⠤⡄⡄
⠀⠀⠆⠀⠀⠀⠀⠀⠂⠄⠤⠠⠐⠒⠒⠒⠐⠆⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠠
⠠⠀⡗⠀⠀⠀⠀⠀⠐⠐⠐⠐⠐⠀⠆⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⠠⠀⠀⠀⠀⠀⠤⠌⠀⠤⠄⠀⠤⠠
⠰⠆⢇⠀⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣃⠀⠀⡉⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣈⣁⣈⠚⢑
⠀⠀⠀⠀⢠⣤⠀⠁⠀⢰⠒⠒⠒⠒⠃⠀⠀⢄⠀⠄⢀⢠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠃⠘
⠄⠄⡀⠀⠂⠁⠀⠂⠀⠚⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⢀⢨⠈⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠆⢀⠒⢓
⠊⠁⡅⠀⠀⠀⠀⡀⠀⢈⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠲⠖
⠀⠁⡇⠀⠀⠀⠀⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠴⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠤
⠀⠇⠉⠄⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣆
⠀⡄⠀⠚⠀⠀⠂⡀⠀⠞⢂⠀⠘⢂⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠤⠀⠤⠀⠠⠦⢴⠀⠀⠄⠴⠀⠄⠄⢀⠀⠀⠀⠰⠋⠉
⣀⣀⣀⡠⠀⠀⠠⠃⠀⠣⠈⠀⠠⠀⠀⠀⡤⢄⠀⠀⣤⠀⠭⠀⠉⢀⣄⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⢠⠀⠀⠀⢃⢠⠀⡀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡀⡀⠂⠀⣀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠀⣠⡆⠃⠐⠀⢠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⠀⠀⠅⠀⠀⠬⠀⠀⠀⠀⠀⢨⠀⠈⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢘⠀⠀⠀⠀⡃⠀⠀⡀⢀⡀⣀⠀⠀⠀⡃
⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠈⠁⠈⠁⠉⠀⠀⠀⡁
⠀⠀⠁⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⡅⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⡀⣄⡀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⣰⡀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠑⠌⢁⠉⠀⢀
⣀⣀⠀⣸⠀⠁⠐⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⠀⠀⢨⡀⠀⣀⣀⡀
⠀⢈⠀⠘⠂⠀⠐⠒⠀⠀⢘⡃⠀⠀⡀⠀⠀⠀⠀⠀⠠⡟⠉⡅⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢈⠀⠀⠀⠀⠠⢠⣀⡀⠈⠁⠀⠀⡄⠀⠀⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠰⠂⠲⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙
⠀⠀⠀⢀⡀⠀⠀⣀⡙⡓⠀⠐⠀⢀⣢⣒⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠐⡓⢒⣶⣀⣰⣀⣴⣀⣀⣀⣐⣀⣀⠀⢐⡂
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠛⠛⠛⠛⠻⠿⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⣠⣴⠿⠋⠁⡠⠒⠫⠭⣭⣙⣳⣦⣤⣄⠀⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠉⠉⠉⣻⡿⠿⣷⣤⣄⡜⠁⠀⠀⣠⠾⠛⠛⠛⣿⠟⠀⠀⠀⠀⠈⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡖⠦⢤⣼⡟⠀⠀⠀⠈⠙⣷⡄⢠⣾⡇⠀⠘⠛⠓⣙⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⢩⣆⡀⠀⠀⠀⠘⣻⣇⠊⠁⠀⠀⠀⠀⠽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢹⠚⠻⢷⣤⣤⣄⡘⢻⠓⢦⢄⣀⣀⣀⣈⡟⠛⢿⣦⡀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢈⠄⠀⠀⢿⣾⣽⣿⣿⣶⣄⡠⣙⢿⣽⣁⠀⠀⢠⣽⣮⣢⡄⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⠀⠀⢠⢾⣿⡏⠻⣿⣿⣿⣿⣶⣭⡛⢧⣬⣕⣢⣌⡅⠀⠀⠈⡄⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⡀⢠⠇⢸⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣷⣎⣙⠿⣿⣿⠀⠀⠀⢱⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⢡⣾⣦⣼⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠻⣼⣿⣿⡏⢷⡈⢇⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠘⡟⠿⣝⢿⢿⣿⣿⣄⢸⣿⣿⠉⠻⣿⣿⣿⣄⠈⠙⠿⣿⣸⡇⢘⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠱⠀⢹⣏⣿⡟⣿⣿⣿⠿⢿⣷⣄⠈⠙⢿⣿⣷⣦⡀⣬⢻⣷⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣵⡿⢿⣿⣧⡘⣿⣟⠣⡀⢠⡙⣿⣿⣿⣦⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⠀⠀⠀⠀⢀⣼⣿⡿⡟⠀⠉⣛⣿⣿⣿⣿⣷⣌⡢⣤⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡁⢀⣠⠶⠻⢿⣥⣀⣷⡀⠐⠾⠿⢿⣿⣿⣿⣿⣿⣮⣏⢈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡟⠻⣆
⠀⠀⠀⠀⠀⣿⠛⢷⠀⠀⠸⣇⠀⢻⡄
⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠀⢿⡀⠈⣷
⠀⠀⠀⠀⠀⢸⡇⠀⢹⡆⠀⢘⣧⠀⠸⣷⢶⣦
⠀⠀⠀⠀⠀⠀⢿⡄⠈⣿⡖⠋⠹⣧⣴⣿⡾⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡜⢷⣤⡿⠃⠀⢀⣠⡾⠋⠁⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣀⣀⡀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠙⢯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡟⠉⠉⠙⢷⡄⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢻⡀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠤⢤⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠹⣆⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⡾⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⠻⢦⣀⣾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⣹⠏⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠙⠳⠦⣤⣄⣀⣀⣀⣀⣠⣽⠟⠁⠀⠀⢀⡿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠿⣅⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠁⠀⠙⢧⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣌⠳⣄⡀⠀⠀⠀⠀⠀⣀⣴⠞⠁⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣈⡙⣺⡏⠛⠛⠖⠛⠛⠉⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⣀⣤⣤⣤⠾⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⡾⠿⢿⠄⠀⠀⠀⠀⠀⢰⣿⣋⠀⠀⠀⠀⠀⣯⣭⣿⢀⡀⡄⠀⠀⠀⠀⢠⠏⢣⡀⠀⠀⠀⠀⠀⣠⣾⣷⣶
⠀⠀⢀⣧⣀⣰⡀⠀⠀⠀⠀⠀⠉⣿⠋⠀⠀⠀⠀⠀⣧⣠⣿⠸⣃⡇⠀⠀⠀⢠⠏⢺⠀⢳⡀⠀⠀⠀⢺⣿⡇⣸⣿⡗
⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠟⠀⠀⠀⠀⠧⠤⠥⠤⠤⠗⠀⠀⠀⠸⠻⠷⠿⠟⠃

⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⣀⡀⣤⡤
⠀⠰⢖⠿⠶⠿⡲⠆⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⣰⣷⠊⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⣴⡿⠛⢿⡄
⠀⠀⣷⣿⣿⣿⣾⠇⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠒⠋⠀⡇⠀⠀⠀⠀⠀⢀⣾⠞⠀⠀⠀⠀⠀⠀⢿⣦⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⢀⣦⣴⡀⠀⠀⠀⣾⡿⠿⠿⣿⠀⠀⠀⠀⣾⡿⠿⠿⣿⡆⠀⠀⠀⠀⡎⣉⡉⡦⠀⠀⠀⠀⠀⠀⠀⣼⣴⡦
⠀⠀⣷⠀⠀⢻⡟⠀⠀⠀⠀⣿⡐⠀⠂⣿⠀⠀⠀⠀⣿⠁⠈⠀⢹⡇⠀⠀⠀⠀⠇⠛⡧⣿⠀⠀⠀⠀⣤⠀⠀⢻⡿⠃
⠀⠀⠘⠲⠶⠋⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⠣⠈⠁⠛⠀⠀⠀⠀⠙⠶⠶⠾⠁

⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⢀⡠⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄
⠀⠀⠸⡅⠀⢀⠇⠀⠀⠀⢀⢳⣿⡿⣻⣞⠆⠀⠀⢰⡟⠛⠛⠛⡛⣧⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠹⣽⣯⠇
⠀⠀⠀⠸⣤⠏⠀⠀⠀⠀⠈⢾⡟⠒⠚⣷⠇⠀⠀⠸⣇⣁⣀⣀⣁⡿⠀⠀⠀⠀⠰⢇⠹⠀⠀⠀⠀⠀⠘⢳⣯⣽⡛⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠑⠃⠀⠀⠀⠀⠘⠋⠁⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠛⠛⠛⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⡴⠋⣠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣴⠃⢀⣤⡀⠀⠀⠀⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠈⠀⠊⠉⢀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠠⠾⠂⠈⠅⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠐⢇⠀⠳⠀⠀⠀⠈⠃⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠠⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢲⠀⠠⠄⠀⣴⡱⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⣰⣤⠇⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣚⠜⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠉⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠄⠒⠀⠀⠀⠉⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢀⡇⡾⠀⠀⢀⠀⠀⢀⣠⠴⠋⠀⠀⢀⣤⣴⣦⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⢠⡛⠤⣄⡀⣼⢸⡃⠀⠀⠀⣰⠞⠋⠁⠀⠀⠀⣠⠟⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣠⠔⠂⠉⠁
⠀⠀⠀⠀⠀⢨⠙⢦⡀⠀⠉⠉⠉⠉⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⡁
⠀⠀⠀⠀⠀⢻⠙⠒⠤⣄⡀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⢁⡠⢖⡩⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠑⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⣬⠄⠀⠀⠀⠀⠀⠀⡾⢧⣄⠀⠀⠈⣓⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⣶⣦⡴⠃⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⣀⠴⢫⡼⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⠤⠴⠤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⣀⡤⣾⡵⠛⠉⠀⠀⠀⢀⣾⣷⡦
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡚⠁⠀⠀⢠⣞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀
⠀⠀⡨⠂⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠄⣨⡽⠃⠀⠀⠀⣈⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠈⠠⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡠⠚⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠘⠒⠀⠠⠔⠃⠀⠀⠀⢀⡜⠉⡄
⠀⠀⠀⠂⠊⠉⠂⠀⠈⠁⠀⢀⡴⠋⠁⠀⠀⣀⠴⠋⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⣤⡄⠀⠀⠸⣅⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠓⠲⠶⠶⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣴⠋⠁⠀⠀⠀⣀⣹⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⣠⠴⠊⠁⢠⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡠⠔⠋⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⡀⠈⠣⣀⠤⠖⢻⠀⠀⠉⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⣠⢞⣠⠖⠋⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢀⣴⠷⠋⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠔⠒⢢⡀⠘⠀⠀⠀⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠠⡞⠁⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢣⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡞⠁
⠀⠀⠀⠀⢰⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⠄⠀⠈⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠛⠋⠁

⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⢀
⠀⠀⠀⢀⡀⣠⣄⠀⠀⠀⠉⡙⣷⣤⡄
⠀⠀⠀⠘⠳⣿⣷⡿⠒⡉⠉⠑⠁⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⣂⣴⢾⣯⣿⡏⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠖⠙⠂⠈⠙⣿⡇⣷⠠⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢘⣆⣿⣷⢿⠚⠛⠋⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⢀⣨⣶⢿⢻⣿⡷⠟⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣿⣶⠀⠒⠒⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠟⠉⠋⢼⡄⣿⣇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⡂⠀⢀⣅⣀
⠀⠀⠀⠚⠸⣿⣏⣿⠛⠿⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠁⠁⢠⣸⣟⣻⣐⡿⠶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠉⠉⠄⣿⣿⣉⡀
⠀⢀⣠⣶⣮⣿⡏⠿⠆⠉⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢿⡟⠴⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⣤⠄⡄⣿⠛⠙⠓
⠻⡏⠀⡛⢻⣿⡟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⢰⢴⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠋⠈⠉⠉⣻⣿⣮⣀
⠀⠈⠢⢧⠀⣿⡇⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣸⣷⢿⠉⠉⠓⣄⠀⠀⠀⠀⣀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣹⠙⠑
⠀⠀⠸⠁⢱⣿⡏⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠋⠹⢿⡿⣬⠀⠀⠀⠈⠀⠀⠀⠌⠉⠑⠂⣾⣿⣃⠀⠀⠀⠀⢀⠞⠛⢹⣿⣿⣈⡀
⠀⠀⠼⡀⠀⣿⡏⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡦⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⣿⡋⠛⠢⡄⠀⠀⠀⠀⠀⡶⣿⠟⠉⠶
⠀⠀⠇⠀⢤⣿⡇⢂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢹⣧⠘⡅⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⢿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢈⠠⣿⡘⠇
⠀⠰⠂⠀⢸⣯⡇⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢸⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢔⣓⠃⠀⠉⠁⠀⠀⠀⠀⠰⢀⣿⢀⠄
⠀⡴⠈⠦⣸⣟⡗⠤⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢸⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣢⣿⠶⠠⡄⠀⠀⠀⠀⠀⡖⢀⣿⠂⢀
⠀⣆⠀⠠⢼⡟⡧⠐⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⣺⢿⠀⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣏⠰⠀⠀⠀⠀⠀⠀⠀⡄⠘⣿⡤⠈⠄
⢸⣬⠷⣔⢺⣿⣟⢢⣤⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⡄⢼⣾⢦⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠘⢀⣰⣿⡁⣠⣂
⣺⡄⠀⠈⢻⣷⡟⡂⠉⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⣻⣿⡊⢉⣿⠀⢀⠀⠀⠀⠀⠀⠀⡈⢀⣿⢀⡄⠀⠀⠀⠀⠀⣾⠉⣸⣿⡏⠈⣽
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⣀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢒⠂⠀⠀⠐⡄
⠀⢠⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠚⠀⡄⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢨⠀⠀⢣⠃
⠀⠈⠀⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⢀⠸⡿⠀⠆⠀⠀⡇⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⠒⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢋⢺⠀⠀⢸
⠀⢨⠁⠀⣉⠉⠉⡇⠀⠀⠀⠀⠀⢰⠤⠷⠄⠗⠒⠗⠃⠲⠅⡇⠀⠀⠀⠀⠀⡠⢂⡡⠘⣿⠃⠌⡐⢄⠀⠀⠀⠀⠀⠀⠀⢪⠉⠙⡄⢠⣚⡢
⠀⠰⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢨⢁⠂⠊⠒⠂⠒⠀⣤⠸⠃⠀⠀⠀⠀⠈⠂⠁⠀⠀⣿⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢡⠀⠀⠆⠀⠁⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠖⠀⠀⠀⠃


⠀⠀⡠⣄⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠤⢄
⠀⢨⠊⣀⣀⣀⡑⡱⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠔⠐⢀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡄⠈⠉⠁⡀⡌⠀⣄
⠀⢰⡘⠒⠒⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠓⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠐⠁⡕⠄⠋
⠀⠰⢮⣒⣀⣐⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠔⡋⢉⢹⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠆⣈⣉⣉⣉⢁⡠⠀⠀⠀⠀⠀⠀⠀⡆⢤⠔⠠⡂⠀⠁⠐⠛
⠀⠘⠷⠤⠄⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⠂⠒⢂⠁⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⢇⡈⣋⣈⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⣠⣤⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢰⢱⡤⡄⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠙⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⢀⡔⠁⠀⠈⠁
⠈⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠈⠁⠃⠀⡎⠘⢑⠀⠀⠀⠀⠀⠀⠀⠀⢆⣃⣠⡄⡆⠀⠒⠁⠀⠀⠀⠀⠀⠀⠁⠀⡧⡤⠀⠀⢠⢤
⠀⠀⠘⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠓⠚⡀⠀⡀⢄⠀⠀⠀⠀⠀⠀⡩⠩⠀⡅⠣⣭⠁⢄⠡⠈⠂⠀⠀⠀⠠⡲⠓⠂⣇⠁⠀⠀⡠⠊
⡄⠀⠄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠘⠐⢸⡀⠀⠀⠀⠀⠉⠑⣈⠀⡁⢾⡤⠤⠤⠤⠤⠴⠀⠀⠀⠀⠈⠆⠀⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠾⠖⠒⠚⠁

⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀
⠀⠀⢨⣾⡿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣈⢨⡉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⠰⠸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⡀⣂⠈
⠀⠀⢘⠷⣿⠝⡁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢩⢀⡅⢀⡀⢈⠀⠱⠀⠀⠀⠀⠀⠘⣋⠞⠖⣛⡱⠷⣙⡃⠀⠀⠀⠀⠀⠀⣐⠉⠉⡆⢀⠉⣁⠉⢀
⠀⠀⠸⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣃⣀⠁⠠⠀⠀⡆⠀⠀⠀⠀⠈⠉⢘⠃⣭⡘⡃⠈⠁⠀⠀⠀⠀⠀⡎⠤⢑⠀⡇⠀⠀⠘
⠀⠀⠀⢄⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⢈⣀⣠⣀⣈⣀⣀⣀⣀⣈⠀⠀⠀⠀⠀⠠⠠⠾⠈⠭⠉⠷⠄⢄⠀⠀⠀⠀⠀⢻⡶⡞⠀⠁⠀⠀⠈
⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡴⣚⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢚⣷⡀⠀⠀⠀⠀⠀⠀⢀⠴⡛⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⢠⠞⠛⣷⡄
⠀⠀⡞⣸⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣸⠶⢛⣉⡥⣟⠀⠀⠀⠀⠀⢠⢏⡎⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⠈⡇⣿⡇
⠀⠀⢻⡘⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣽⠚⢉⡥⣶⠋⠀⠀⠀⠀⠀⠸⡜⡆⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⡇⣿⡇
⠀⠀⠀⢻⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢉⣯⣼⣧⣭⡄⠀⠀⠀⠀⠀⠀⠹⢄⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⣈⣃⣛⡇
⠀⠀⠀⠈⣳⣶⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃
⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢀⡤⣠⣦⣴⡄⢤⡀⠀⠀⠀⠀⠀⣴⠋⠲⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣶⣾⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⢰⣿⣉⣿⡄
⠀⢠⣮⢁⣽⠁⢰⣯⡨⣵⡄⠀⠀⠀⠀⠈⢡⣶⡿⢮⡰⣀⡀⠀⠀⠀⠀⢸⡇⣿⣿⠁⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠈⠛⢁⡆
⠀⢘⣛⢈⣯⣄⢀⣼⡁⣻⡃⠀⠀⠀⠀⠀⢸⣿⣷⠉⠾⣫⡶⠀⠀⠀⠀⠈⣧⣿⣿⣤⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⢀⡣⠤⣊⡀
⠀⠸⠟⠘⣻⣧⣞⣛⢑⠻⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣦⡍⢰⠀⠀⠀⠀⠀⠘⢿⣿⣿⣼⣿⡿⠁⠀⠀⠀⠀⣴⡇⢸⣿⣾⣿⡇⢸⣦
⠀⠀⠈⠳⠙⠇⠾⠋⠚⠁⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠁⠑⠨⠦⣀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⣿⣷⣾⣿⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⣿⠛⣉⡙⢿⠀⢠⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠈⠙⠲⡀
⡀⣿⣿⣿⣿⢰⣒⣰⡶⣿⡇⠀⠀⠀⠀⠀⣿⣾⣿⣷⣿⡄⢸⣴⠀⠀⠀⠀⢀⣿⣇⣡⣀⣸⣿⠀⠀⠀⠀⢠⡇⠀⣄⢈⣦⣄⠀⠀⢹
⠧⣿⣿⣿⣿⢸⡷⠶⢆⣿⡇⠀⠀⠀⠀⠀⣿⣾⣷⣷⣾⡇⢸⢿⠀⠀⠀⠀⢸⣿⠏⠙⠛⢻⡛⠀⠀⠀⠀⢸⡇⠀⠘⢿⣿⣿⡅⠀⢸
⠀⣿⣿⣿⡿⠸⠯⠉⠅⣿⡇⠀⠀⠀⠀⠀⠙⠛⡟⡟⠛⠀⢸⢸⠀⠀⠀⠀⢸⣿⣇⣁⣀⣽⣟⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⡷⣠⡟
⠀⠉⠉⠐⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠳⠧⣄⠤⠮⠞⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡟⠀⠀⣄
⠀⢀⣠⠴⠆⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣰⡷⣁⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⡆⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⢶
⠈⠰⢦⣄⣤⣄⡉⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⢰⣯⡦⠀⢀⣽⠟⣿⡄⠀⠀⢀⣧⠀⢀⣃⠀⠀⠇⠀⠀⠀⣴⣋⣁⣃⣉⣉⣉⣘⣈⣙
⠀⣀⣀⣀⣙⣿⣿⣷⣼⣦⣼⣧⣄⡀⠀⠀⢠⡟⠁⢻⡆⢸⠇⠀⠈⣿⠀⠀⢠⣿⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡟⣟⢿⣿⣿⣿⡟⣻⢻
⠀⠿⡿⠻⡿⡿⠿⠿⠿⠿⣿⠛⣿⠿⠀⠀⠸⡇⠀⢸⡇⢸⡄⠀⠀⡏⠀⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⠀⠀⣶⣦⣯⣶⣶⣶⣶⣦⣿⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠂⢀
⠀⢀⠀⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠶⠈⠀⠀⠀⠀⠀⠆
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠈⠠⠶⠠⠀⠀⢀
⠀⠀⠊⣉⠗⠀⠀⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠁⣅⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠰⠄⠀⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠴⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⣀⡂
⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⠁⠀⠀⠉
⠀⠀⠀⠀⠋⠀⢠⠐⠀⠀⠀⠂⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠂⡀⠀⢀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠄⠄⠀⠄⠤⠀⠀⠀⡀⠀⠀⠼⠋⠡⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠠⠀⠀⠀⠀⠠⠀⠐⠁⠀⠂⠀⠀⠂⠀⠰⠀⠀⠀⠰⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⠀⠉
⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠰⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠐⠀⠀⠺⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠒⠆⠸⠂⠖⠒⠒⡖⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⡆⠺⠒⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠁⠀⠐⠀⠀⠉⡷
⠀⠀⠀⠀⠁⠀⠐⠂⢰⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠉⠀⡂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⠠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⡇⠀⢠⢀⠀⠀⡄⡄⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠰⠀⢠⡄⠀⠀⠀⠠⠀⠀⠄
⠀⠀⢰⠉⣓⢀⠸⠁⠀⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢈⡀⣈⠀⠀⠀⡃⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠃
⠀⠀⠀⠁⠀⠀⠀⠤⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠘
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣮⣝⣤⣮⣩⣏⣴⣿⣹⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠻⣿⣿⡟⠛⢛⣛⡛⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢸⣿⢹⡇⠀⣿⢻⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⢸⡇⠀⣿⢸⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠿⠿⠃⠀⠛⠛⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣠⣦⣀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⢟⣼⠏⠀⣠⣄⠀⣹⣿⡁⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣄⣀⣼⢯⣾⣇⠀⣴⢟⣿⢿⣯⣬⣿⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠛⢷⣦⣉⣿⣧⣿⡁⢙⣿⢫⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠈⠙⠿⣯⣍⢻⣿⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣟⠛⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠻⣷⠀⢰⣶⣶⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢸⣿⠀⢸⣿⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣿⣸⣿⠀⢸⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠉⠉⣡⣶⣤⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠉⣻⡷⠶⡶⢶⡟⠁⠀⠀⠀⠀⠀⠻⣿⠿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢹⣿⣶⣤⣴⠟⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣾⠛⣷⡀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢀⣴⠟⢹⡇⠈⠁⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⣿⣿⣿⣧⣤⣤⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣴⡿⠁⠀⠘⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⢀⣴⡾⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⢀⣤⡾⠋⠁
⣀⣠⣤⣴⠶⠞⠛⠉⢀⣠⣴⠾⠋⠁
⠉⠉⣀⣀⣠⣤⡶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠇⠀⠀⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠃⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢸⣷⣶⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠘⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢑⣦⣼⣿⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⢸⠟⠻⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣾⣤⣴⡆⠀⠀⢸⣿⣿⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠃⠀⠀⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣾⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣀⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠾⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⢿⣑⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⠉⠉⠉⠉⠛⠉⠉⠁⠉⠉⠀⠀⠀⢀⡄⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⣶⣶⠁⠀⠀⠀⣶⡖⠀⠀⠀⢸⡇⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⢀⣿⡏⠀⠀⠀⣸⣿⠀⠀⠀⢀⣼⠃⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⠇⠀⠀⠀⢸⡟⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣿⡏⠀⠀⠀⣼⡿⠀⠀⠀⢀⣿⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡿⠀⠀⠀⢠⣿⠃⠀⠀⠀⢸⡿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣼⠁⠀⠀⢀⣾⠃⠀⠀⠀⣾⡏⠀⠀⠀⢠⣿⠃⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡟⠀⠀⠀⣸⡿⠁⠀⠀⠀⣼⡟⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⠀⠀⠀⢀⣻⠃⠀⠀⠀⢠⣿⠁⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⠀⠀⢠⠁⠀⠀⢀⣿⡏⠀⠀⠀⢠⣿⠇⠀⠀⢰⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠇⠀⠀⠀⣼⡟⠀⠀⠀⠀⣾⡏⠀⠀⠀⣾⡟⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⡿⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣾⢟⡻⣦⠀⣴⢟⡛⣿⠓⣶⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣊⠭⠒⣆⠀⠻⣮⣵⠟⣀⡻⣶⣵⠟⢸⣏⣻⠇⣨⣝⡲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣫⠵⣋⠀⠀⠀⠘⠔⠒⣈⠹⠉⣙⠉⠋⠀⡤⢄⣈⠉⠰⢿⣼⣟⡀⣹⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡫⠊⠁⠀⠀⢀⣀⠤⠒⠋⠁⠸⡀⠃⠸⠼⠳⣾⣷⣦⣄⣩⢲⢎⡈⡰⠋⠢⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠸⢄⠚⢤⡀⣠⠚⠉⠀⠀⠀⠀⠀⠛⠙⠛⠛⠛⠛⠷⢾⣽⣗⠋⢀⠙⠧⣀⣴⡈⠶⡠⠝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢲⢏⡴⢀⡙⠦⡙⢦⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣮⡢⡀⢼⡪⣗⣈⣷⠞⣡⣦
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠛⠾⠤⢮⣀⡜⡽⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⢪⡶⠛⣇⠘⢫⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠤⢈⠀⡀⠠⣌⡜⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢧⢠⠙⡄⠀⢣⠠⠔
⠀⠀⠀⠀⠀⠀⡸⠰⡀⡀⠀⠉⠋⢸⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⡎⣇⢱⠀⠈⡆⠘⠁
⠀⠀⠀⠀⠀⠀⡇⢸⠉⠉⢩⡭⠗⠋⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠈⢠⣆⣀⣉⠉⢹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠒⠒⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⠆⡏⠀⢓⣀⣀⠰⡄
⠀⠀⠀⠀⠀⠀⣇⠹⠤⠤⣈⣉⣉⡍⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⢲⠃⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⢹⠒⠉⢀⣉⡤⠴⠸⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠇⡜⠰⠦⠤⣄⣀⠸
⠀⠀⠀⠀⠀⠀⠈⡆⣏⠁⣀⡤⠔⢪⡁⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡎⣰⠃⠀⣀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⡀⢀⣀⠀⢱⡄⢹⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⢎⡼⣳⢤⣼⢩⣁⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠠⡜⡋⠖⣉⠜⠃⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣻⠗⠁⠈⠐⢅⠀⣩⠑⣮⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠉⣹⢆⠁⢀⡤⠤⡀⠙⠢⡄⢠⠖⠒⠤⢤⠤⣤⣶⠾⡟⠋⠁⠀⢙⠖⠒⢦⠀⢠⡾⣡⢾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠞⠁⣏⠀⠂⢸⠀⣰⠃⡎⡼⠙⠁⠛⠓⠁⠉⠉⠹⠄⠀⢀⣼⡀⠂⣠⠇⢈⣷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠓⠚⠧⣀⠣⢼⣁⡀⠀⡴⠋⡉⢳⡤⠤⠔⢲⣈⣡⢤⠉⢉⣡⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠭⣑⣚⡂⠤⠿⢤⣠⠜⠀⠀⠀⢀⠿⠐⣴⡷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠬⠥⠤⣄⣀⣀⣠⡤⠤⠴⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣀⠀⠑⢄⠀⠀⠠⠤⠤⠤⠀⠠⠤⠤⡀⠑⢄⣀⡀⠀⠀⡠⢊⠤⠀⠤⠤⠀⠄⠤⠓⠤⠀⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠙⠦⡀⡑⠒⠒⠒⠒⠂⠒⠐⠒⠒⢌⠢⡀⠀⠀⠀⡎⢰⠁⡎⠉⠉⣉⢉⠉⠑⢈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠤⢀
⣈⣀⣀⣀⡀⣀⣀⣀⣀⣀⢀⣀⣀⣀⠈⠢⡑⠌⠂⠀⠀⡇⢸⠀⡇⠀⠘⠀⠀⠀⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀
⠀⠀⢀⡤⠂⠂⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⡇⠀⠀⠀⠊⠀⠘⢄⠈⠢⠄⠀⠈⠢⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠊⡠⠄⡀
⢀⡴⠋⠐⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⢢⠀⢆⠀⠈⠢⠤⠠⠤⠄⡑⢄⠀⠀⡇⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠢⡀⠀⣉⣉⣉⠔⠉
⠉⠀⠀⠀⠒⠒⠒⠒⠒⠒⢄⠀⠀⠄⠘⢄⠀⠑⠒⠒⠒⠄⠀⠀⠈⠂⠱⠀⢧⡀⠉⠂⠀⠐⠒⠒⠀⠐⢲⠀⡇⠀⠀⠀⠀⡈⢢⡀⠀⠀⠀⠀⠂
⠀⢀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⢀⣁⣉⣉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣉⡉⣉⡉⠉⣉⠍⠕⠀⢸⠀⡇⡀⠀⠀⠀⠑⢄⠙⢄⠀⠀⠀⠇
⢄⠀⠑⠒⠒⠒⠒⠒⠒⠢⡀⠀⣠⠂⢰⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠒⠒⠒⢂⠔⠐⠀⠀⠘⢄⠣⡡⡀⢢⠀⠀⠀⠑⡄⠑⢄
⠀⠈⡉⠉⠀⠉⠀⠀⡀⠙⠌⠉⠀⠀⢸⠀⠀⡈⠁⠉⠁⠠⠊⠁⠀⠀⢰⠀⠀⠈⠁⠉⠉⠡⢊⠉⠁⠀⠀⠀⠅⠁⠨⠀⠇⠸⠀⠀⠇⠀⠀⠈⡇
⠀⡘⠁⡠⠀⠀⠀⠀⠈⠂⠂⠀⠀⠒⠁⡠⢊⠄⠀⠀⠀⠀⠐⠁⠀⠂⢸⠀⠀⠀⠀⠀⠀⢂⠅⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢡⠁⠀⡇
⠀⠅⠸⠀⠀⠈⠉⠉⠉⠉⢉⠉⢉⣉⣩⠔⠁⠠⢀⠉⢉⣉⠉⠢⡀⠀⢸⠀⠀⠠⠊⠉⠉⠁⠀⡄⠠⠀⠈⠉⠉⠁⠁⢀⠐⢄⠀⠣⠀⠰⠀⠀⠇
⠀⠁⢸⠠⠋⠀⠀⠀⡁⡔⢁⠀⠀⠀⠀⠒⠀⠀⠀⠂⢄⠀⠀⠀⠇⠀⢸⠀⠀⡆⠀⠀⠀⢠⠀⡇⠈⠀⠀⠀⠀⣀⣀⡀⠑⢄⠑⢄⠀⢐⠀⠀⡆
⠀⡇⢸⢀⠀⠀⡠⠒⡠⠃⠈⠀⠢⡀⠀⠀⠀⠀⠐⠦⡀⡁⠀⡀⡀⢄⠈⠢⡀⢅⠠⡀⠀⢸⠀⡇⢈⠀⡆⠀⠀⠀⠀⠉⢢⡀⠁⠀⠀⢀⠀⠀⡇
⠀⡂⢨⠀⠀⠀⠀⠀⠠⡄⠀⠀⠐⢌⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡢⡄⠈⡌⢣⠈⡆⢸⠀⡇⠀⠀⡇⠀⡇⢰⠀⡂⠀⡇⠀⠀⠀⢘⠀⠀⡇
⠀⢁⠈⠃⠤⠤⠤⠀⠐⠡⠀⠀⢀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣀⡀⠀⢸⠈⠀⠀⢸⠀⠃⠜⠄⠃⠀⠀⡇⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⢸
⢄⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠄⠈⠆⢸⠀⠀⡄⢸⠀⠀⠤⠄⠀⠀⠀⠑⠤⠬⠄⠁⠀⠀⠀⠀⠀⠀⢠
⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠐⢀⠈⡂⠀⠈⠀⡀⠁⢸⠀⠀⠂⠂⠀⠀⠀⠀⠐⠀⠢⡀⠀⠂⠀⠀⠀⠀⢸
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⠙⡄⢸⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⣁⡁⠀⠀⠀⠀⠥⠬⡑⠌⠉⡁
⠢⡀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢄⠈⠀⡇⢸⠀⡀⠀⢘⠀⠠⠁⢸⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠒⠀⠀⠁⠐⠀⠀⢨⠀⠀⡂
⠀⡄⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠘⠀⠀⠇⠸⠀⠁⠀⢸⠀⠀⠀⡸⢀⠄⠀⠀⠊⢀⠤⠤⠤⠤⠤⠤⠤⠔⠀⢀⠀⠀⠰⠀⠀⡇
⠀⡅⠀⠀⠀⢸⠀⢸⠀⠆⠀⠀⠀⠀⢸⠀⠂⠀⢘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠁⡀⠀⢀⠔⡡⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⢀⠀⠀⠇
⠀⡃⠀⠀⠀⠜⢀⠼⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⡄⢠⠀⠄⠀⠈⠀⠀⡁⠀⠈⢀⡔⡡⠊⢀⢀⠀⠉⠉⠉⡁⡉⢉⠉⠉⠉⠀⡨
⠀⠇⢀⣀⣀⡰⠋⡀⠀⠀⠀⠄⠀⠀⢸⠀⡀⠀⢸⠀⠀⡇⢸⠀⢢⡀⠀⠀⡠⠃⢀⠔⡣⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠊⠀⠀⠀⡆
⠀⡇⠀⠀⠀⠤⠜⠀⠀⡀⠀⠀⠀⠀⢸⠀⡃⢠⠨⡀⢄⠈⠢⡢⠤⠭⠭⠭⠤⠔⡡⠊⠀⠔⠁⠀⠀⠀⠀⠀⠄⠀⠀⣠⠔⢁⠔⠋⠁⠀⠀⠀⡃
⠀⡅⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠂⠀⠑⢌⠢⡑⢄⣉⣒⣒⣒⣒⣒⣊⣀⣀⣂⡐⣐⣀⣒⣐⣀⣒⣂⣒⣊⣀⡀⠀⠀⠔⡡⠂⢀
⠀⠈⠢⡈⠢⡉⠒⠒⠀⠀⠀⠑⢄⠀⠈⠢⠤⠤⢀⠀⠑⢌⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⢊⠔⢉
⠀⠀⢀⠈⢢⡈⠂⠒⠂⠀⢀⠀⠀⠀⠀⢄⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠔⠁⠈
⡿⢿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣻⣻⣻⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠐⠄⠘⠀⠸⠀⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠘⠃⠠⠂⠰⠀⣀
⠀⠀⢀⠠⠌⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠲⡉⠀⠀⠀⠀⠀⠀⠀⣀⠒⣀⠐⠇⢀⠀⡀⠈⠀⠉⠀⠀⡄⠀⠔
⠀⣀⠈⠁⠀⠀⠀⠰⠀⠀⠀⠠⠀⠀⠀⠒⠈⠢⠲⠐⠂⠀⠀⡀⠈⢀⡀⠀⠆⠀⠈⠀⠀⢀⠔⠠⠀⠀⠀⠀⠈⣁⡀
⠠⠄⠀⠀⠀⠀⠀⢤⡔⠑⢄⠀⠀⠀⠀⠠⡀⠀⠈⠢⠀⠀⠈⠀⠠⠀⠳⠄⠁⠚⠒⣒⠒⠀⠀⡠⢀⠀⡤⠀⠀⠀⠤
⠖⠀⠀⠀⢀⠀⠀⠀⠉⠃⠀⠀⠈⠀⠀⠙⠀⠢⠀⠀⠀⠲⠂⠉⠒⠀⡠⠾⠂⠀⠀⠀⠀⠀⠦⠀⠀⠀⢀⠐⠀⠖⠐
⠀⢠⠀⠈⠁⣴⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡌⠁⠀⣄⠠
⠐⠒⠒⠁⠄⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠊⠒
⠀⠈⠤⠀⠀⠀⠀⠀⠀⠐⠂⠂⡃⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⢈⢁⠀⠀⠀⢸⠀⢢⠀⠀⠀⠀⠈⠦⠀⡉
⠀⠀⠠⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⠘⠀⠀⡄⠀⠀⠀⠒⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠠⠀⠀⠘⠀⠀⠁⠒⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠘⠂⡀⠀⠀⠀⠀⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠒⠀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠴⠀⠉⠁⠀⠐⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠁⢀⠀⠀⠀⣀⡀⡖⠂⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⡀⠀⠉⠁⠉⠀⢄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢛⡭⠚⠏⣇⠀⠠⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣋⠴⢊⡡⠖⢹⠀⣿⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⣩⠔⠊⢡⠖⠉⠀⣾⡘⡄⢹⠀⢰⣶⣶⣾⠉⣿⢻⢛⣓⢶⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⡴⠞⣩⠔⠋⣠⠀⠀⢸⢸⡇⠀⠛⠁⡇⢸⠀⢾⣿⣿⣿⠀⣿⠀⠀⠀⡃⣏⣿⣷⣶⢦⣴⣞⣯⠽⠆
⠀⢠⣞⣩⠔⢋⡠⠔⢋⠸⡄⠀⢸⠈⠁⠀⠀⠀⡇⢸⠀⠀⠤⠤⢼⡀⣿⣒⣴⣮⠼⠋⠁⣠⢟⣿⢯⡻⣄
⠀⢸⠈⡛⢰⢉⡄⠀⣿⡇⡇⠀⢸⠀⠠⠿⢃⡠⠣⣼⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠀⠀⣰⢯⠟⠀⠀⢻⣽⡄
⠀⢸⠀⡇⢸⢸⡷⠀⠈⠀⡇⠀⢸⣀⡤⠒⢉⡴⠞⠁⠀⠸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⠀⢀⣿⡇
⠀⢸⡇⡇⢸⠀⠀⣠⡀⠀⡇⠀⠀⢁⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⢦⣤⣤⢞⡽⠁
⠀⢸⡇⡇⢸⠀⠀⢛⡡⠖⠁⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉
⠀⠘⡇⡇⠘⡤⠒⠉⣀⡴⠛⠁
⠀⠀⣇⢰⠤⣠⡴⠚⠁
⠀⠀⠙⠚⠛⠁

⠀⡇⠀⢀⠀⢀⢀⠀⠀⣀⣀⣀⣀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣠⠞⠁⢀⡔⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠱⣦⠀⠀⠀⠀⡇
⠀⡇⠀⠈⡆⠀⠁⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⡂⠀⠀⠠⠲⠀⠀⠀⠔⠊⠀⠀⠀⠉⠁⢀⡴⠋⠀⠀⡠⠂⠀⠀⠤⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡇
⠀⢧⠀⠀⡇⠀⠈⠉⠉⠉⠑⠁⠀⠀⠩⠀⠀⠀⡃⠀⠀⢀⡀⢀⠀⠀⣀⢠⠀⠀⠀⢀⡴⠁⠀⠀⡠⠊⠀⠐⠠⡀⠀⠉⢦⡀⠀⠀⠑⡄⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠇⠀⢀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠁⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⢀⡴⠋⠀⠀⡠⠊⠀⢄⠀⠀⠀⠈⠢⡀⠀⠉⠔⠀⠀⡇⠀⠀⠀⠀⡇
⠀⢀⡴⠋⢀⠔⠁⠀⠀⠀⢀⠔⠁⠀⢀⠔⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡠⠊⠀⠀⠀⠉⠢⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠳⡀⠀⠀⠈⠈
⠴⠋⢀⠔⠁⢀⠀⠀⠀⡔⠁⠀⢀⠔⠁⢀⠔⠁⠀⠀⢀⠔⠉⠉⠉⠉⠉⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⠕⠀⠀⠀⠈⠥
⠀⠀⢸⠀⠀⢱⠁⠀⠀⢦⠀⠀⠂⠀⠀⢸⠀⠀⢀⠔⠁⢀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴
⠀⠀⢼⠀⠀⢸⠀⠀⠀⠁⠀⠀⠂⠀⠀⢸⠀⠀⠂⠀⠀⠑⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠑⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⡇
⠀⠀⠉⠀⠀⢸⠀⠀⠀⡔⠀⠀⠀⠀⠀⢸⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡇
⠀⠀⠀⢀⠔⠁⠀⠀⡠⠃⠀⢀⠅⠀⠀⡸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠈
⠀⢀⠔⠁⠀⠀⡠⠊⠀⢀⠔⠁⠀⡠⠊⠀⠀⠀⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠂⠀⠀⠈⠚⢄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠘⠀⣀⣀⣀⣀⣀⣀⡇
⠔⠁⠀⠀⡠⠊⠀⢀⠔⠁⠀⠰⠜⠀⠀⠀⠀⠀⡢⠤⠤⠤⠤⢄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⡠⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠔
⠐⠉⠀⠀⣤⠀⠀⠀⡠⠠⠤⠤⠤⠤⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠊⠀⠀⡠⠊⠀⠀⠀⣀⣀⣀⠀⠈⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡠⠊⠀⢀⠔⠉⠉⠉⠉⠁⠁
⠒⠊⠀⠀⢔⠊⠀⠀⠀⡠⠊⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢸⠀⡠⡔⠁⢀⡤⠒⠒⠐⠂⠒
⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⢀⢀⠀⠀⠀⠀⢸⠀⠈⠀⡴⠋
⠒⠒⢄⡀⠀⠀⠀⠁⠀⠀⠠⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⢐⡂⠀⠀⢘⠄⠀⠀⠀⡠⠊⠁⠀⠀⠀⡠⠊⠀⠀⠀⡇⠀⠀⠀⠀⠋⠒⠒
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡇
⠀⠀⡀⠀⠀⠉⠈⠁⠉⠁⠉⠂⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠢⡀⠀⠀⠐⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣔
⠀⠈⠑⢄⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡠⠀⠈⡆⠀⠀⡇⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⡠⠊⠀⠀⠀⡀
⠀⢀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠨⠀⠠⠢⠀⠀⠠⠂⠀⠀⠀⠉⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐⠁
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⡇⠀⠀⠣⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠢⡀⠀⠙⠦⠤⠤⠤⢀⠀⠀⠀⢔⠊⠀⠀⠀⠀⠀⢸
⠀⢀⠀⠀⠀⡤⠀⠀⡠⠊⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⢄
⠀⠀⠑⢄⠀⠐⠀⠀⠀⠀⠀⠀⠈⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠱⠀⠀⠀⢸⠀⠀⠀⠀⠑
⠑⡄⠀⠀⠑⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠁⠀⠀⠁⠁⠀⠠⠀⠀⠀⠀⠑⢄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠀⠀⢀⡤⠂⠀⠀⠨⢆⠀⠀⠑⢄⠀⠀⠀⠀⠑⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡆⠱⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⢀⣱⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣏⡇
⢀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡇
⢸⣿⣿⡿⠟⠉⠻⠿⠿⠛⠉⠠⡠⠀⢈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡟⡹⣶⠇
⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡗⠀⠈⣿⣿⡿⠋⠉⠁⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠘⠳⢦⣀⠀⠐⠄⠀⠀⠀⠀⠀⣲⣶⠠⣤⣤⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠺⣿⣦⣼⣟⢿⠋⢁⡄⢀⣀⣀⠀⠀⢀⣉⣀
⢠⣤⣤⣈⠓⢦⣄⠀⠀⢀⣀⣤⡁⠈⣧⠈⠻⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⠠⠤⡄⠷⣟⠒⡀⣿⣿⢿⣿⣿⣤⣤⣧⣝⡟⣷⢶⣿⣿⡿⠋⡄
⠠⣍⠻⣍⣀⡀⠙⠙⢦⣰⣿⣽⡆⠀⠘⣿⣄⠀⠄⡦⠀⠤⠄⠀⣠⠄⠠⠂⠂⠀⠀⠠⠈⠀⠀⠀⠈⣨⣯⣭⣿⡇⠀⠘⣿⣿⣷⣿⣷⡹⣇⠀⠀⡟⠁
⠀⠘⢷⣭⣭⣿⣿⣴⣍⠙⠻⢿⣷⣤⡀⠘⣿⣇⢰⣧⡔⠁⠀⣴⢃⣀⣶⡀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠐⡟⠻⠛⢳⣄⠐⣿⣿⡿⣿⣿⡷⢨⣶⠤⠂
⠀⠙⠋⠙⠿⠾⢿⣿⣿⡁⠑⠶⣮⣝⠻⣧⠸⣿⣿⣿⣶⣶⣾⣷⣮⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⣀⠤⠁⠀⠀⠀⠸⠜⢻⣧⣈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣶⣄⠘⠿⠀⣌⡁⢹⣿⣿⠿⣿⡿⠿⠿⠟⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠊⡑⠀⠈⠀⠀⠘⠀⠀⠠⡀⣀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣙⣷⣴⣾⣿⣿⣶⣬⣓⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⣶⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⣠⠖⠉⠀⠀⠀⢀⡞⠁⠀⠈⠙⢦
⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠑⣄⣠⣤⠤⣴⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠁⠒⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⠠⡀⠀⠀⠀⣀⡔⢉⣠⠴⠛⠉⢙⣦⡞⠋⠉⠉⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢄⣓⠀⠀⠀⠀⠈⠑⠂⣬⣦⣴⣊⡥⠾⠟⢰⣦⣴⣮⣟⠁⢈⣲⣤⡤⠤⢤⣤⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠭⠭⠟⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠛⠛⠻⠥⢤⣤

⠈⠁⠉⠀⠠⠦⠀⠀⠀⠠⠦⠀⡠⠀⠶⠈⢣⠀⠀⠀⠀⠀⡇⠈⠣⡀⢃⠀⠀⠀⣀⠔⣡⢞⡡⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠁⠀⠀⠘⡓⠒⠒⠒⠒⠒⣊⠀⠀⢚⠀⢸⠀⠀⠀⠀⠀⡇⣄⠀⣌⠢⡑⢤⡀⠉⠈⠁⠘⠁⠉⣩⡍⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⢉⣠⣀⠄
⢡⡀⣄⠀⢈⡍⢠⠉⣅⢠⡉⣍⢀⡄⣩⠀⢸⠀⠀⢀⠀⠀⡃⠈⠳⠌⠲⠌⠳⠀⠀⠀⠀⠀⠀⠀⠰⠄⢊⠍⡩⡩⠭⠭⠭⠭⠭⠭⠭⢭⣭⣅⣄⢢⡄
⠀⠀⠀⠀⢀⡁⢸⠀⡇⢀⡀⣏⢀⡀⢸⠀⢸⢀⡄⢹⠀⠘⠃⢀⢔⠒⠒⠒⢚⠀⠀⠀⠀⠀⠀⠀⢘⡒⡡⢊⢔⡀⠀⠀⢠⠶⠆⠶⠂⢠⠞⠃⠛⠘⠃
⣀⣀⣀⣀⣀⣁⣈⣀⣁⣈⣁⣉⢈⣁⡉⠀⢸⢀⡇⠙⡨⢀⠔⠁⢘⠡⢄⡠⠋⠀⣄⢠⡄⢠⡀⣠⠈⠁⠤⠇⣆⠔⢳⠐⠘⠃⠀⠛⠓⠺⣀⣀⣀⣀⣀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⣄⠲⡄⢸⡂⢸⠈⡡⢊⠔⠱⡆⣀⠘⡤⡪⠂⠲⠂⠈⠢⡈⠢⡑⠤⠑⠀⠀⠀⠍⠀⠘⠁⠂⠐⠠⡐⢂⣁⣛⣁⡿⠘⡇
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡀⢸⠀⡇⢸⠀⢸⠀⡇⡇⠀⠰⢇⡩⡪⠊⠀⠀⠀⣠⣀⣀⣈⣲⡬⣦⣶⡶⡴⣖⠒⠒⠒⠒⠒⠆⠡⠼⠴⠤⢄⡤⣖⠲⡙
⠤⠤⠤⠤⠤⡀⠀⠀⢢⠀⡇⢸⠀⡇⢸⠀⢸⠀⡇⣇⠘⡤⡪⠊⢀⠴⢂⠴⠂⠴⠄⠀⠀⠄⠴⠀⢀⠄⠤⠆⠱⠄⠀⠀⠀⠈⠉⠉⠉⢉⠝⠡⠛⠬⠣
⠒⠒⠒⠒⢄⢂⡆⢀⣸⠀⡥⢸⠄⣧⢸⡅⣼⠠⡇⢡⠊⡮⢀⠀⠋⠀⠋⡀⠀⣚⠒⠐⠒⠒⠒⢒⡁⠀⢐⡃⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⠠⡉⡄⡇⡧⠁⠸⠀⠋⠸⠄⠙⠸⠇⠙⠰⠇⠙⠀⠇⠘⠀⠶⠀⠀⢱⠀⣩⢉⡍⣩⠉⣅⢩⡁⣄⢈⡅⠀⢄⣀⠄⠀⠀⠤⣠⣀⣀⣘⣁⣛⣘⣃
⡉⢢⡃⡇⡇⣇⢙⡗⠚⢰⢉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠑⣤⡄⢸⠀⣉⢀⡃⢸⠀⡀⢸⡀⣀⢨⡇⠀⠢⠤⠂⠀⠀⠀⢬⠤⠤⠤⠤⠤⠤⠤
⣉⢸⡇⡇⡯⣄⢹⡋⣙⡡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠶⠆⢸⠀⣉⣈⣁⣈⣀⣉⣈⣁⣉⣈⣁⣠⠕⠲⡁⠀⠀⠀⠒⠆
⣅⢸⡇⡇⠧⠀⢸⡅⣭⡐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠗⠒⢺⠊⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡾⡛⠂⠀⠀⠔⠛⠃
⠤⢨⠣⣁⣀⢀⢰⡆⠤⠌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣛⣉⢹⣉⠔⢉⠍⣑⣉⡊⣉⡉⠉⠉⡙⠁⠃⡈⢉⠉⡉⢉⠉⡉⢉⠉⡉⠉⡉⢉
⣒⠀⠑⠶⠠⡆⠹⠇⠲⢊⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣭⣅⢸⣀⡄⠈⡌⢡⠀⢠⡀⠀⣧⠀⠀⠀⠄⡏⢸⠁⡏⠈⠁⠛⢘⠃⡟⠈⠁⢹
⠉⠉⠉⠈⠌⠄⢚⡃⣛⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠦⠤⢼⠤⠔⢁⡇⢨⠀⠨⠀⠀⠀⠀⠀⢀⡁⡇⢸⠀⡇⠀⠀⢀⠨⡀⣥⠀⠀⣼
⢉⣍⣉⣩⡍⢩⣹⣏⣩⡑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠗⠖⢸⠂⣔⣋⡀⠸⠀⢠⠀⠀⣀⠀⠀⠘⠃⡇⠸⡀⠣⡀⠀⠈⠳⠼⠦⠶⠶⠶
⢤⠤⡤⢤⠤⠤⢼⡥⢤⠐⢌⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⡠⠛⠓⢼⡀⠥⠠⠥⠼⠀⠰⠄⠀⠙⠀⠀⠀⣠⠇⠀⠈⠢⠬⠦⠤⠤⠦⠤⠤⠦⠤
⢹⠀⡇⠘⠁⠀⠘⡆⠀⢠⠦⢸⢃⡤⢸⠇⣤⠘⡇⢤⠄⡟⢠⠄⠛⢠⡄⡸⠙⠗⡠⠐⣒⣐⣀⣒⣐⣁⣀⠄⠰⠥⣴⠉⠉⣧⠄⠀⠀⠀⣴⠋⠉⢱⡄
⠺⡀⠇⠸⠂⢀⠀⡀⠝⢉⢚⠝⠉⡰⢋⠝⣩⠞⡱⢋⠝⣩⢘⠁⠛⠘⡉⠀⠀⡸⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠰⠆⠀⡀⠤⠴⠀⠀⢸⠆
⠒⠒⠒⠒⠒⠆⠀⠀⠀⡕⠁⡠⢊⠔⢡⠔⡡⢊⠔⡡⢞⠕⠃⠀⠀⠀⢨⠀⠀⢸⠀⡃⠘⠒⠒⠒⠒⠒⠒⠒⠒⠚⢺⠀⠀⢚⠓⢊⠤⠚⠒⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣀⠜⠃⡇⢸⡁⢸⠀⡇⠀⠀⠈⠀⠁⡇⠠⠠⡀⠀⠀⢸⠀⠀⢸⠀⢇⣘⣓⣒⣒⣒⣒⣛⠀⢸⣉⡱⠀⠀⢊⣉⡁⠞⣉⣉⠀⠀⢸⡁
⡄⢠⠀⡄⢠⠂⣉⠜⠃⡇⢸⡄⢸⠀⣇⢠⡀⣠⠀⣄⡇⢀⠀⡇⠀⠀⢘⠀⠀⢆⠑⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡫⣴⠀⠀⣨⡤⠀⡄⢥⡬⠀⠀⢸⡄
⡃⠸⣀⣱⣬⣤⣭⠠⡀⡇⠈⠁⠈⠀⠉⠈⠁⠉⠀⠉⡇⠙⠀⠃⠰⡀⠸⠀⡀⠀⠁⠀⠐⢰⡂⣒⢲⠒⠀⣿⢸⡇⠈⠒⡖⠃⢃⡀⠪⠀⠀⠑⠒⠊⢀
⠘⠙⠉⠙⠙⢍⠣⡑⠀⡇⠀⠠⠆⠰⠄⠀⠰⠄⠤⡀⠙⠦⠀⠦⠤⠇⣸⠄⣽⠀⣤⠀⣤⡠⠀⡇⠸⠘⠀⢻⠸⡇⠀⠀⡇⠀⢈⠔⣋⠀⠀⠀⢀⠔⣁
⠤⠤⢤⠠⡘⠆⠀⡇⠀⡇⠀⢀⠤⠤⠀⠀⠀⢤⡄⠙⡀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠁⡀⡀⢀⠀⡇⢰⢀⠀⣽⢰⡇⠀⠀⡇⠀⠈⠈⡤⠚⠀⡔⠁⠄⠩
⠀⠀⠀⢱⠀⠀⠀⡇⠀⢣⠴⠋⠈⠉⠉⠉⠉⠉⠙⢦⡈⠉⠉⠉⠋⠈⠋⠉⠢⡀⠈⢉⠉⡙⠀⡇⢸⢸⠀⣿⢸⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⢸⠰⠀⠀⡇⠀⢸⠀⠀⠀⠀⣄⢠⡄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠉⠃⠀⡇⢸⢸⠀⣿⢸⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⡇

⠀⠀⠃⠀⠀⠀⠀⠀⠀⢌⠁⠀⠀⢸⠀⠀⠦⠀⠀⠀⠀⠀⠐⠂⠀⠃⠀⠀⠀⠀⢠⠀⠀⡀
⠈⠀⠀⠈⠠⠀⠀⠀⢀⠀⠀⠆⡀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠃⠠⠂⠀⠁⠀⠠⢆⠐⠀⠀⠰
⠀⠰⠷⠀⠀⢀⡄⠀⠈⠀⠀⠂⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠀⠀⠀⠐⠀⠀⡆⠀⠀⠄⠀⢀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠂⠇⠀⢸⠀⠀⢀⠢⡀⠑⢌⠊⡃⠑⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡠⠊
⠉⠐⠂⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⠀⠀⠈⠀⠁
⠀⠠⠀⠈⠢⡁⠀⠈⠂⠀⠀⠃⠠⡀⠰⠀⠌⢀⠐⠂⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠄⠈⠀⠀⢀⠀⠢⠀⠀⢀⠘⠀⡄⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠀⡃⠀⠀⠀⠀⠀⠀⠐
⠀⢀⢀⡈⠉⢀⠀⠈⠀⣁⠀⠈⢁⠀⡀⢁⡀⠁⠀⠀⡀⠀⠀⠀⠀⠤⠀⠠⠆⡠⠊⢀⠀⡆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢔⠀⠀⠘⠀⠀⠀⠀⠀⠀⠊⢀⠔⠁⠀⡁⠠⣀
⠀⠈⢁⡍⠁⠉⠁⠈⠈⠈⠀⠀⠀⠈⢨⠐⠌⠉⠪⠀⠆⠠⠌⠀⠤⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠀⠀⠙⠀⠂⠡⠀⠄⠤⡀⠀⠀⠃⣄⠀⢀⡀⠀⠀⠀⠀⠀⢀⠄
⠄⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠁⠀⠀⢀⠀⢀⠄⠀⠀⠂⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠔⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠎⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠤⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⡀⠑⠀⠆⠀⠀⡀⠈⢂⠘⠁⠃⠀⠀⠀⡀
⢀⠀⠀⠀⠻⠃⠀⠀⢘⡀⠀⠂⠀⠀⠀⠀⠀⠐⠰⠂⠀⠁⠈⠀⠀⠀⠀⠈⠁⠀⢘⠀⠀⠂⠰⠀⠀⠁
⠤⠤⠭⠭⠭⠭⠭⠥⠄⠤⠈⠀⠀⠀⠀⠄⠤⠤⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄⠁⠀⠀⠀⠔⢡⢀⠀⢀⠄⡀⠐
⣀⡀⡀⠀⣀⣀⢀⡀⢀⠀⠀⡀⢀⠀⣀⡀⠐⢄⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡂⠀⠈⠀⠁⠈⠀⠠
⠀⠀⠀⠀⠀⠀⢄⠈⠈⠑⠀⢤⠠⡀⢄⠈⠢⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⠂⠄⠀⠀⡀⢀⠉⠈
⠀⣀⠀⠁⠤⠠⠀⠁⠈⠀⠀⠆⠀⢸⠀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡐⢌⠂⠀⡀⠀⠀⠁⡁⠀⠂⠐
⠀⠀⠀⠀⠂⠀⠘⠂⢐⠀⠀⡀⢀⠀⠀⢬⠂⡘⠀⠀⣀⢀⢀⠀⡀⠀⢄⢂⠀⡁⢸⠀⠀⡁⠀⡀⣄⠀⡀⢀
⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⢷⡾⢛⣡⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠹⣦⠀⠈⠻⣟⠉⠀⠀⢀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⡤⠞⠙⢷⡀⠀⠙⢧⣠⣶⠟⣩⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⠶⠋⠀⠀⠀⠀⠻⣆⠀⠈⢻⣵⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢙⣷⡀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣦⠀⠀⠀⠀⠀⠀⣠⠶⠋⠈⣻⣦⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠙⢷⡄⠀⣠⡴⠛⠁⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣬⣿⣆⣼⠿⠞⠋⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠉⠉⠉⠉⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣠⡾⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣠⣴⠶⠟⠛⠛⠛⠛⠿⢶⣤⡙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣴⠟
⠀⠀⠀⠀⢀⣴⠟⠁⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡈⠻⣦⡀⠀⠀⠀⠀⠀⢠⡿⠁⣾⠏
⠀⠀⠀⣠⡿⠁⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠘⢷⡄⠀⠀⠀⢀⣾⠃⣼⠏
⠀⠀⣴⠟⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⢿⡄⠀⠀⣼⡏⢰⡟
⠀⣰⡟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠘⣷⠀⢠⣿⠀⣿⠁
⢠⡿⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡆⣼⡇⢸⡟
⣸⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣧⣿⠀⣾⠃
⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣿⡏⢰⡟
⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⡿⠁⣿⠃
⢿⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣾⠃⣸⠏
⠸⣧⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣼⠇⣰⡟
⠀⢿⣆⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⣾⠃⣰⡟
⠀⠀⢻⣆⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⡟⢁⣼⠏
⠀⠀⠀⠹⣷⣜⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡾⠋⢀⣾⢋⣴⠟⠁
⠀⠀⠀⠀⠈⠙⢷⣬⣛⠷⣦⣤⣀⣀⣀⣤⠾⠋⠉⠙⢿⣄⣴⣿⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢻⣦⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⡶⠟⠉⠻⣦⣠⣴⠟⠁

⠀⡤⣄⠀⠀⠀⢠⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣠⠞⠁⠀⠀⠀⢀⡴⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠙⠳⠤⠤⠤⠼⠉⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⣠⠟⠁⠀⢠⣤⡞⠁⣴⣶⠀⠠⣖⡏⢠⢤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢦⠀⠀⠀⣿
⠉⠑⢆⡀⠀⠀⠀⠀⠀⣠⣄⠀⢠⠞⠉⣡⡄⠀⣠⠞⠁⠀⢀⡀⠈⠛⢁⠔⠉⠁⠀⠀⠀⠀⠈⠛⠣⠤⠤⣄⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⣿⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠀⡸⠂⡠⠓⣣⠞⠁⡠⠊⠉⠻⠞⢀⡴⠉⣠⠔⠒⠒⠒⠲⠯⠇⠀⠀⠀⠀⠀⠯⠗⣠⣄⠀⢀⠜⠀⠀⠺⣥⡿
⣀⣀⣀⣀⣀⡠⠒⠒⠒⠒⠒⠊⡠⠊⣠⠞⠁⡠⠊⠀⢰⣳⠀⠀⡏⠀⡞⠁⣠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⡀⠙⠋⠉⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⣠⠞⠁⡠⠊⠀⢀⣀⠀⠀⠀⠀⡇⠀⡇⡜⠁⠀⠀⠀⠀⠀⢰⣖⡆⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠻⠞
⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣠⡞⠁⡠⠊⠀⠀⠀⠻⠞⠀⠀⣠⠞⠀⡰⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢰⣲⠦⠤⠤⠤⠤⠤⢤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠾⠉⣠⠞⠀⠀⢀⠔⠒⠒⠒⠒⠚⠁⡠⠊⢀⠔⠁⠀⣠⠦⠤⢾⡷⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠙⠶
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠚⠁⠀⢀⠔⠁⢀⣀⠔⠒⠒⠒⠊⣴⣶⠁⠀⣠⠞⢁⡠⠠⠀⠀⠀⠀⢠⣶⡄⠀⢰⣳⠦⠤⡀⠈⠳⣄
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠁⠀⠀⠯⠟⠀⠀⠀⠀⠀⠈⠁⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⣠⠭⠤⠤⠤⠤⠤⣀⠈⠢⡀⠈⠳⣄
⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⢦⣀⣀⣀⣀⣀⣀⣀⡴⠒⣒⠒⠒⠚⢁⡴⠋⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⣟⡆⠈⠢⡀⠈⠳⠤⠤
⠀⠀⠀⠀⠐⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⢀⡴⣋⠀⠀⢀⡴⠒⠒⠒⠊⠀⣠⠖⠒⠒⠒⠒⠒⠒⠒⠚⢶⣄⠀⠈⠦⠤⠤⠤
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⡸⠿⠃⣯⠟⠀⠀⢀⣀⣠⠞⠁⠀⢀⣀⣀⣀⣀⣀⣀⣴⢦⠙⢷⣄
⠒⠒⠒⠒⠒⠂⠒⠒⠂⢒⣤⡒⢚⣏⠛⠛⠙⠓⠛⢛⣧⡟⠙⠋⠀⠀⠸⢿⣇⠀⠀⢿⣽⠇⠀⢀⠔⠁⠀⣠⠤⣞⡧⠀⠈⢉⣀⠀⠙⠷⠶⠶⠶
⠀⠀⠀⠀⠀⡠⠊⠉⠉⠉⠓⠃⠘⠚⠁⠀⠀⠀⠀⠈⣻⠁⠀⠀⠀⠀⠀⠀⠈⠓⠚⠒⠛⠒⠚⠁⠀⣠⢞⠝⠊⠛⣁⡐⠐⠛⢞⡵⠋⣩⡉⠉⠉
⠭⢭⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⢉⡉⠉⢀⣀⡴⠋⠉⣉⡩⠯⠭⠭⠿⠯⠽⣭⠭⠯⠖⠁⠀⠀⠀⠳⠛⠉⠉⠉⠀⡠⠓⠋
⠀⠀⠙⠲⠒⠒⠒⠒⠒⢾⡽⢀⣀⡔⠁⢰⣲⠄⠻⠾⣄⠹⠞⠀⠀⠸⠽⠁⠀⣠⠖⠒⠒⠚⠿⠃⢀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠊⢀⣄
⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠯⠟⠀⠀⠀⢯⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠊⠁⣠⠶⠶⠶⠶⠖⣡⠴⠶⠶⠶⠶⠶⠶⠶⠦⣄⠀⠘⠚
⠒⠒⠒⠒⠒⠒⠒⠒⠒⣄⠱⠤⠤⠤⠤⠤⠤⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠜⣡⠞⠉⠉⠉⠉⢢⣤⡀⠀⠈⠳⠶⠶⠶⠶⠶
⠒⠒⠒⠒⠒⢢⡀⠀⠀⠈⣓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢁⡠⠀⠀⠀⠀⠬⠛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡴⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠳⡄
⣒⣛⣛⣚⣛⣛⣛⣛⣛⣛⣓⣒⣛⣛⣛⣛⡛⠛⠢⡀⠀⠀⢾⡳⠀⠀⠀⡠⠊⣀⠤⠤⠤⠤⢄⡀⠀⠀⠈⠳⠋⠉⠉⠉⠉⠳⣄⠀⡇⢠⣄
⠴⠶⠶⠶⠶⠶⠤⠴⠦⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠓⠒⠓⠓⠒⠒⠋⢀⠞⠁⠀⢾⡷⠀⠀⠙⢄⣀⣀⣀⣀⣀⠀⢰⣲⡄⢸⠀⣇⠙⠚
⣀⣀⣀⣀⣀⣀⣠⣄⡀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠳⣄⣉⣠⠞⠀⠈⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠤⠥⠤⠭⠭⠥⠥⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⠲⣄⣈⠻⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠭⠭⠿⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠯⠉⠙⠆⠈⠳⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒

⠀⠀⣤⠺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢢⡄
⠀⠀⢻⣇⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢀⣿⠃
⠀⠀⠈⢿⣆⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣀⣾⠏
⠀⠀⠀⠘⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⡟
⠀⠀⠀⠀⠸⣿⡁⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⣹⡿
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠈⢻⣷⠆⠀⠀⣠⣤⠶⠖⠚⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠋⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠁⢀⣴⠟⢋⡤⠒⠀⠀⠀⠉⠉⠀⠀⠀⠠⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣟⠀⠀⠀⠀⢠⡾⠃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⢣⡀⠀⠀⠀⠀⠀⠀⢘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣾⠁⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢷⡀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢠⡏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣇⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⣿⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢹⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⡇⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⡟⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⡁⠠⢄⠀⠀⢀⣀⣠⣴⠾⠋⡠⠞⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣬⣥⠄

⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⢠⢄⠀⢀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠐⠀⡀⠄⠀⡀⡔⠀⠀⠀⠁⠀⠀⠀⢀⢀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠂⠀⠀⠀⢉⠄⡀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠂
⠀⡠⠀⠐⠀⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠌
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⡀⠀⠐⡀⠀⠀⢀⠠⡀
⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠜⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠡
⢀⠀⠀⠠⠁⠀⠀⠃⠀⠀⠃⠀⠀⣐⠄⠀⠀⠀⠀⠀⠈⠐⢀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⢀⡠⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠑⠀⠀⣄⠀⠀⡀⠀⠀⠀⠊⠀⡀⠀⠀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢂⠀⠀⠈
⠀⢀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠈⠈⠀⢀⠂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠐⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⢀⠀⡀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡑⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡠⡀⠀⠄⡀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠒⠒⠐⠪⠂⠀⠀⠀⢄
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠈⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠠⣄⠀⠀⢀⡠⡀⠀⠠⡀
⡀⠀⠀⠀⡀⠀⠀⡠⠀⠀⠣⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢄⠀⠐⠜⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠃⠀⠀⠊⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠡⠁⠀⠀⠀⠀⢖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠁⠀⠀⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠊⠀⡀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢠⠆⠀⢜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⡀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⠂⠀⢀⠀⠂
⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣪⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣂⣀⣀⣀⣀⣀⣊⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⠶⠿⠿⠿⠿⠿⠿⠿⠷⠶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⢀⣼⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢿⣆
⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣷⡀
⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡀⠂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⠐⠉⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠉⠴⠄⢆⡰⣷⡶⢤⠃⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠀⢹⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⠄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡤⠾⣧⢤⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣹⠄⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣰⠋⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠶⠶⠷⠤⠤⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⠛⠛⢻⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⠿⠶⠶⠾⣧⣄⠀⠀⠀⠀⠀⠁⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠑⠲⠤⣤⣄⣀⣉⣀⣀⣀⣀⣀⣀⣈⣀⣤⣤⠤⠶⠚⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠠⠤⠤⠄⠀⠀⣀⡀⠀⠀⠤⠤⠤⠀⢀⣀⡠⢴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⠛⠓⠲⠶⠶⠴⠤⠤⠶⠶⠖⠚⠛⠛⠉⠉⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠦⣌⣉⣉⠀⠐⠒⠒⠒⠒⠒⠀⣀⣀⣁⣠⠴⠶⢾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠠⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠙⠲⠶⠤⣤⣬⣭⣭⣉⣩⣭⣤⣤⣤⠤⠶⠖⠊⠉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣀⡀⠀⠤⠤⠤⠄⠀⠀⠀⠠⠠⠤⠤⠀⢀⣀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠉⠉⠙⠛⠒⠒⠒⠲⠶⠶⠶⠖⠒⠚⠛⠉⠉⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⠙⠛⠛⠛⠛⠛⠛⠉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⣄⣀⣤⣤⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⣤⠄⠀⠀⢺⠀⠀⠀⣤⠀⠀⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⢦⠀⢸⡀⠀⠀⢽⠀⠀⢀⡿⠀⢀⡇⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠳⡄⠙⢲⡀⣾⠀⡴⠋⢀⡖⠉⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇⣿⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡃⣿⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇⣾⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠤⠤⣄⠙⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⠒⠒⠋⠀⣠⠤⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⢰⡆⢶⡆⣶⡆⣶⡂⣶⢰⣶⢰⣶⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⡴⠊⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢨⣥⣬⣥⣭⣥⣭⣤⣭⣬⣭⣬⣅⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣠⠞⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠳⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠒⠋⠁⣠⠤⠤⠤⠤⠤⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠤⠤⠤⠤⣄⠈⠓⠒⠺⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡄⣿⠀⡇⠀⢰⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇⣿⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇⣿⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡴⠃⣀⠜⠁⢿⠀⠳⣄⠈⢧⡀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⠋⠀⢸⠁⠀⠀⣿⠀⠀⠈⣷⠀⠙⡄⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⠛⠂⠀⠀⢿⠀⠀⠀⠛⠀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇

⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⡇⠀⢆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠦⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠭⠀⠭⠀⠭⠀⠀⠀⠩⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠄⠀⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⢨
⡰⠀⠀⠀⠀⠀⠀⢄⠀⡅⠀⠀⠀⡇⠀⡇⠀⠠⠀⠄⠄⠄⠀⠠⠀⠀⠄⠠⠄⠀⡠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠠⠀⠀⠀⠊⠀⠠⠊
⠀⡠⠊⠀⠠⠀⠈⠂⠀⡇⠀⠀⠀⡇⠀⠃⠀⠀⠀⡄⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⢐⠀⠀⢀⣀⣀⣀⣀⣀⡀⠔⠁
⠊⠀⡠⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠧⠄⠠⠠⠄⠀⠄⠀⠀⠀⠀⠀⠑⠉⠈⠀⠀⡇⠀⠀⠀⠄⠀⢀⡢⠄⠠⠀⠀⠀⠀⠀⠀⠤⢔⠀⠀⠀⠠⡐
⠠⠊⠀⠀⠐⠂⠀⠀⠀⠇⠀⠤⠤⠠⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠄⠰⡢⠀⠃⠀⠀⠀⠁⠀⡠⠀⠀⠤⠠⠤⠤⠤⠤⠤⠤⠄⠠⠄⡀⠀⠀⠐
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠠⣂⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠒
⠑⠂⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⠀⠄⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠
⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢀⢃⢀⢣⢀⢢⠀⠢⠀⠢⠀⠰⠀⡔⡀⠀⠀⠀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⣐⠀⠀⠀⠀⠀⠂⠀⠂⠀⠘⠀⠈⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⡇⠀⠒⠁⠀⠠⣢⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠐⠂⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠂⠃⠀⠀⠀⠀⠒⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠚⠔⠀⠀⠀⠆⠦⠄⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⠀⠀⠀⢸⠀⠨⠕⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩
⠒⠒⠚⠔⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠚⠜⠀⠀⠀⠀⠀⢸⠀⠨⠅⠀⠀⠀⡀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠂⠀⢀⠀⢀⠀⢈⠀⠀⠀⢰
⠀⠒⠒⠒⠒⠅⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠫⠂⠀⠀⠀⠁⠀⡀⠀⢸⠀⠠⠀⠀⠀⠀⠑⠒⠒⠒⠂⠒⠒⠒⠂⠀⠀⠀⠁⠁⠀⠁⠁⠃⠀⠀⢸
⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠭⠂⠀⠀⠀⠀⠀⡀⠊⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠀⠀⠀⢸
⠀⠀⠈⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠨⠀⠀⠀⠀⠆⠀⠠⠀⠀⡠⠊⠀⢈⠂⠀⠂⠖⠒⠒⠒⠒⠒⠀⠂⠐⠁⠀⠉⠀⠨⠀⠀⠀⢰⠒⠂⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠪⠖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠈⠀⡄⡀⢈⠀⠀⠎⠖⠀⠀⠀⠀⠐⠌⠂⠐⠅⠂⠀⠀⠀⠀⠂⠀⠠⠀⡀⡀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠐⠌⠂⠐⠥⠂⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠈⠀⢘
⢀⠀⠀⠀⠀⠀⠀⢂⠖⠀⠀⠐⠂⡄⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡃⠀⢆⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠀⢀⠀⢘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⣴⡄⢠⣦⠀⢠⣦⠀⣴⡄⠠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢦⡀⠑⢄⠈⠳⣄⠙⢦⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢙⠀⠀⢳⠀⠈⡇⠀⠙⡆⠀⢱⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢴⣷⣤⣼⣧⣤⣾⣤⣤⣷⣤⣼⣧⣤⣾⡦⠤⠤⠤⠔⠁⣠⠯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡀⢀⢀⣀⣿⡿⣿⣽⣿⣿⣯⣿⣿⣿⣭⣟⢿⣿⣀⡀⠀⠀⣠⠞⠁⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢀⡴⠋⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⠀⠀⠈⠀⡠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⠋⣠⠖⠒⠒⠒⠚⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠒⠒⠒⠊⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⡠⠤⠤⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠤⠤⠤⠴⠋⢀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡠⠊⠀⠀⠀⠀⣀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⣀⠔⠁⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⢀⡴⠋⠉⠉⠉⠉⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣻⣻⣾⣿⠉⠉⠉⠉⠁⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠋⢀⠔⠒⠒⠒⠲⡿⠛⢻⡟⠛⢿⠛⠛⡿⠛⢻⡟⠛⢿⠗⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢇⠀⠸⣄⠀⢸⡀⠀⢇⠀⠀⣅⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠳⣄⠙⢦⡀⠑⢄⠈⠳⣄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠘⠟⠀⠻⠃⠀⠻⠃⠘⠟⠀⠘⠗

⠀⠀⡀⠀⠀⠀⠀⠠⡭⠁⠀⢠⠄⠀⠀⠭⠸⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠂⣀⢀
⠀⠀⠤⠀⠀⠀⢔⠀⠒⡄⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢤
⠀⠀⣀⠀⢀⡀⠘⠀⢀⡀⠀⠰⠀⠀⠀⣀⠀⠀⢀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⣀⢀⠂⡀⣀⠀⠀⠀⢀⡐⡀⢀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⣅⠀⠈⠁⠀⠀⠨⢄⣀⣀⣀⡀⠄⡭⠀⠄⢬⠀⠀⠯⠀⠀⠀⠈⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠁⠈
⠀⠀⣠⣀⣀⣀⣀⠀⣀⡠⠤⠤⠤⢄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⢀
⢈⡀⣀⢀⡠⠤⠄⢤⠄⠠⠠⠤⠤⠄⠄⠦⠤⠠⠤⠀⠠⠧⠠⠤⠄⠤⠠⠤⠤⠤⠤⠤⠤⠄⠄⠤⠠⠤⠄⠬⠤⠄⠤⠬⠤⠠⣨⢭⢉
⠀⠁⠙⠂⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠰⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠚⠰⣆⢀⣯
⠀⠀⠀⠀⠀⠫⠃⢠⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠒⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⣀⣀
⢑⣒⠀⠀⠈⠂⠀⠈⠁⠀⢩⠀⠀⣶⠄⠀⠀⠁⢀⠀⠈⠀⠦⡇⠄⠀⠀⠀⠀⠀⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠰⠍⠀⣇
⠁⡀⠀⠀⠀⠀⠀⠢⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠘⠙
⠀⠀⣀⠀⠀⠀⠀⠐⠂⠀⠓⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠒⢻⣄⡨⠐⠀⠀⠀⠀⠀⠠⠀⢸⠰⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠇⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣥⡈
⠀⡤⠀⠈⠃⡀⠐⢱⡀⠀⠋⣀⠀⠈⢀⡀⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠄⠀⠶⠤⡂⠀⠰⠠⠆⠠⠤⠃⢠⠀⠀⠀⠠⠏⠈⠦
⡀⣀⣀⣠⠆⠀⠀⡜⠀⠀⠤⠉⠀⢠⠄⠀⠀⣠⢰⡀⠀⢠⡄⠠⡅⠀⡇⢠⣤⢈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠀⠀⠀⢗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠨⠀⠀⠀⠀⠀⣀⠀⠀⣠⠔⠂⠄⠀⠰⠀⠀⠀⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠐⠈⣙⢀⠀⣈⡋⠈⠀⠈⠁⠀⢘⠁⠈⠀⠀⠈⠉⠀⠀⠙⠷⠄⠀⠀⠸⠀⠀⠀⠐⠴⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⢀⠀⢀⡀⠀⢀⠐⠀⣘⠀⠂⠀⠀⠚⠐⠀⠚⠀⠛⠀⠟⠐⠂⠐⠂⠊
⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⢠⠀⠀⠀⠀⠀⠅⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠁⡀⠥⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠀⠀⠀⠀⠀⡁⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠒⠂⠾⡀⠿⢀⠗⠒⠂⠀⠀⠀⠀⠇
⠀⠀⠀⢐⡖⠠⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠶⠰⠀⠰⠆⠀⠀⠈⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⢀⣄⠀⠀⠀⠸⠀⠀⠰⠂⠆⠀⠠
⠀⢠⠄⠀⡄⠀⠀⠈⠁⠈⠀⢨⠅⠀⠀⠄⠀⠀⠁⠀⠀⠀⠺⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠨⠀⠀⣤⡆
⠀⠠⠀⠀⠀⠀⠀⢂⠦⣤⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠡
⣀⣀⣀⣂⣀⣀⣀⣀⣀⣘⣉⣈⣈⣀⣁⣒⣘⣀⣈⣀⣀⣀⣀⣀⣀⣚⣀⣀⣀⣐⣛⣓⣛⣂⣐⣓⣰⣇⣀⣀⣀⣈⣀⣀⣂⣐⣃⣀⣀
⣿⣿⡋⣛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠒⠂⠀⠀⠒⠒⠂⠤⣀
⠀⠀⠀⠀⠀⣀⣠⠿⠶⠒⠛⠋⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄
⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⣰⠋⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⢛⣟⣋⠁⠠⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⡇⠀⠀⠀⢰⣮⡥⠽⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠙⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢰⠃⠀⠀⠀⠀⣀⣤⠶⠶⠛⣋⣉⣉⣀⡤⠥⠄⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢿⡀⠀⢀⣀⣿⠬⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠐⠰⠆⠂⠀⠙⠀⠁⠘⠃
⠈⡿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⣴⣖⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣼⠁⠀⠀⢀⣀⣠⠴⠶⣞⣛⣉⣭⣥⠴⠦⠒⠂⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠈⠉⠆
⢻⡀⠀⠔⠋⣩⡴⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢙⡶⢖⡾⠁⠀⠀⠀⠀⣀⣀⣤⣤⡤⢴⣶⣶⣞⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⢠⡏⢰⡿⠀⠀⠀⣠⡾⠛⠙⠶⠶⣆⡾⠉⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⡇⠀⢇⠀⠀⣠⡟⢸⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⠁⢀⣀⣍⣭⣥⠤⠼⠶⠶⠶⠶⠶⠷⠦⠤⣤⣤⣄⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠎
⣾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠐⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⢸
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡟
⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠄⠀⠀⠐⠃⠀⠀⠀⠀⣠⣧⠤⢤⠤⠴⡾⠁
⠀⠀⠀⠻⡶⠶⠒⠒⠾⠛⠛⠛⢟⣙⠋⢻⣟⠉⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠄⢨⠁
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣂⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⣀⣐⣒⣉⣉⣍⣛⡃⢘⠆
⠀⠀⠀⢀⡿⠄⢀⣀⣉⣉⣉⣉⣉⣩⣥⣤⠴⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠈⠉⠉⠉⠉⠉⢉⣭⣔⣤⡆⢈⡆
⠀⠀⠀⢀⣵⠄⠀⠈⠉⠉⣉⣤⣔⣒⣲⡲⠯⠌⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠉⠉⠉⠍⣛⣛⣛⣃⠸⡄
⠀⠀⠀⢈⣷⠀⠉⠉⠉⠉⠉⣁⣐⣶⣶⣧⣂⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠠⠤⠴⠶⠶⠶⠿⠟⢛⣛⠃⠸⡀
⠀⠀⠀⠘⣷⠌⠉⠉⠋⠛⠉⠉⠉⠭⠭⣭⡓⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠰⣶⣿⣟⣿⡿⢢⠞
⠀⠀⠀⠀⠈⠳⣄⡀⣉⣉⣉⣉⣉⣉⣭⣿⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⢀⣀⡀⠀⡐⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠻⡉⠉⠉⠉⢩⠍⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣙⣫⣽⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣀⣠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢀⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡐⢂⡿⠀⢿⣐⣂⡟⢸⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠐⠿⠢⠉⠉⠀⠛⠷⠟⣰⡟⣷⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃⠀⠀⠘⠀⠀⠀⠠⠄⠀⠀⠀⠆⠉⠰⠀⠐⠂⠀⠀⣀⠈⠙⠋⡄⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢄⡀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⡀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⡘⠂⠄⠀⢠⡁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠡⠖⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠐⠁⢚⠠⣉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠃
⠀⠀⢀⠀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⢀⠀⢴
⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠃
⠀⠀⠸⡆⠁⠀⢄⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠤⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⠀⣤⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠢⠠⣶⠠⠄⡜
⠀⠀⠀⠀⠀⠀⠀⠒⡉⠘⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠓⣄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣠⠇⠀⢀⡀⠒⠀⠀⣀⣀⡀⠀⠀⠐⠀⠀⠀⠣⣈⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠠⠄⠀⣾⠁⠄⢹⠀⠀⠀⢚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⠀⠈⠒⠖⠋⠀⠀⠀⠒⠥


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣶⢶⣾⣿⣿⣶⣶⣶⣶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡏⠙⠿⢧⣤⣝⠿⣿⣯⡂⣿⡟⢙⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡉⣻⣿⣧⣵⣿⡿⣱⣿⣿⢣⣿⣿⡞⣿⣇⢪⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠻⣿⣿⣷⢻⣿⣙⣩⣭⣶⣿⡿⣱⡟⠻⣿⢣⡿⡋⣼⠫⢻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣏⢿⣿⡞⣿⣿⡏⢝⣫⣭⣵⣿⡧⣾⣿⢸⣿⣶⢋⣾⣿⣧⣄⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠙⢿⣿⣿⡘⢿⣷⣝⠿⣿⡿⠿⢟⡻⢿⣷⣔⣸⡎⣿⡇⣿⡿⢐⣽⣿⣇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣷⣭⣛⢿⣷⣍⢍⣿⣶⣾⣿⡿⢿⣶⣭⡻⢿⣷⢹⣷⢹⡿⠙⣿⣿⣜⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣱⣿⡫⠹⣿⣷⣮⣝⣛⣯⣭⣵⡶⣾⣶⣝⡻⣿⡎⣿⣐⡽⢣⣿⣾⣿⣿⣿⣆⢝⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣛⠿⠿⣶⣍⡻⠿⢟⣛⣫⣭⣤⣼⣿⣿⣿⢸⣧⢹⣿⢱⣿⠿⠿⠿⣤⣬⡻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣵⣿⣿⣿⣿⣿⣿⣅⢸⣿⣿⣿⢟⢿⡎⣿⡜⣿⡜⣷⣤⣿⣷⣀⣽⢟⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⠿⣿⣿⣿⣎⠿⣿⡟⣰⣾⣷⢹⡧⠻⣧⢻⣿⣿⡉⣩⣭⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣴⣿⣿⣿⡇⣷⣴⣿⡜⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠛⢿⣿⣷⢹⣿⣿⣅⣹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣄⣿⣿⡟⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿

⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⢄⠀⠐⠀⠀⠀⠄⠀⠠⢄⠀⡠⡀⠀⠀⢀⢄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠄⠀⠀⠀⠁⡀⠈⠁⡀⠀⠀⠀⠄⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⡀⠀⠀⢀⠠⠀⠀⠀⠉
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⣀⠄
⠀⠄⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠭⠀⠐⠕⠀⠀⠀⠢
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠄⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⢐⠀⠀⠠⠢⠀⠐⠀⠀⢀⠀⠀⠁⠀⠀⠀⠐⡄⠀⠀⠩⠂⠀⠢⠀⢐⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠢⠀⠈
⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢
⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⡄
⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠁⠀⠀⠀⠀⠰⠅⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠃⠁⠀⠠⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⡀⢀⡀⠀⠈⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘
⠀⡀⠀⠠⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠔⡄⠐⠁⠈⠂⠐⠂⠀⠀⠀⠀⠒⠀⠀⠠⡂
⠈⠂⠀⢖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠁
⠀⡀⡄⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⡄⡀⠀⠀⠀⠀⠐⠂⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠊⠂⠀⠑⠀⠀⠀⠀⠀⠀⠢
⠠⡈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢀⡀⠀⢀⡄⠀⠀⡀⠈⠆⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠄⠄⠀⠀⠠⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠈⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⡔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠊⠀⠠⠔⠀⠀⠐⠤⠀⠐⠴
⠂⠀⠀⠀⠤⠀⠐⠴⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⡀⠀⠀⠁⠀⢠⠂⠀⠐⠄⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠁⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠠
⠀⠄⠂⡀⠀⢀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠄
⠀⢀⠀⠈⠀⠀⢁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⢀⡀⠀⠀⠀⠉⠀⠠⡠⠀⠀⠐⡤
⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⢐⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⣀⣠⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠟⠂⠚⠛⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⣷⡦⠀⠀⠀⠀⠀⢠⡿⠿⠿⠿⢿⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⡿⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠻⠗⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⠄⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢤⡄⢀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠉
⠀⠀⠀⠀⣀⠉⠁⣴⣶⣾⠀⢻⣿⡀⠀⠀⠀⠶⠆⠀⠀⢠⡄⠀⠐⡛⣶⣶⣷⢋⠄⠀⠀⠀⠀⠀⠀⠘⢆⡴⠔⠚⠁
⠀⠀⠀⠀⠌⣳⠀⠛⢻⣷⠄⢻⡟⠀⠀⠀⠀⠀⠀⡤⡤⠼⠁⠀⡴⣱⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢴⣈⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠐⠇⠈⠉⠉⠉⡅
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠛⠛⠋⠀⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠐⢢⠔⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠘⠓⠒⠀⠀⠒⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠠⠒⢲⠆⠀⠀⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣅⢠⠀⣷⣤⣤⣤⣾⡀⠀⠐⠂⠀⣀⠈⠱⠀⠀⠀⠀⠘⠊⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⣀⣿⣯⣿⠿⠿⠁⠀⠀⠰⡆⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠰⡀⠀⢀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⣀⠊⠀⠀⠀⠠⢀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠠⢀⠤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⣴⠄⣀⠰⣄⡦⠴⣄⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠠⢀⡀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠸⠟⡶⠾⠛⠛⠛⠛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠀⠀⠀⠀⠐⣾⠂⣾⣿⣿⣛⠛⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⠀⠀⠀⠀⠈⢸⣿⣿⣟⣁⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡿⠿⠛⠛⠛⡋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠂⠉⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⡇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡈⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠳⠖⠚⢻⡆⢠⡄⠀⢀⠐⠒⠺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠁⣠⣀⣀⡄⢠⡁⣐⣀⣀⠀⣠⠜⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣀⣀⡀⢠⣀⣀⡀⣀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠁

⢀⣀⣤⣤⣴⣶⣶⢿⣿⡄
⠘⣿⡏⠉⠉⠀⠀⠀⣿⣇
⠀⢻⣧⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⡀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⣿⣇⠀⠀⠀⠀⠀⢹⣿
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣟⢿⣷⣄⡀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⡻⣿⣿⣧⡈⠻⢿⣶⣤⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠹⣿⣿⣿⣦⠀⠈⠉⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠘⢿⣯⡻⣿⣦⡀⠀⠀⠀⠀⠛⠃⠀⠀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠻⣿⣌⠛⠃⣀⣠⣤⣴⣶⣶⡿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠻⣷⠌⢿⣿⣏⠉⢀⣤⣾⠿⢋⣁⣤⣤⣶⣶⣶⣿⣿⠗
⢀⣀⣀⣀⣀⣠⣤⣤⣤⣿⣿⡟⠛⠛⠛⠛⠿⠿⠿⣷⣶⠀⢀⣤⣿⠿⠃⠙⢿⣧⡀⠛⠛⠉⠉⠁⠀⠙⠿⠿⢿⣷⣶⣶⣦⣤⣤⣄⣀⣀
⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⣥⣴⣶⣾⡿⠿⠟⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠛⠋⡉⠉⠀⠀⠀⠀⣠⡈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠀⠀⠀⠀⢀⣿⣿⣷⣽⣿⣦⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉⠀⠀⠰⢶⣶⣶⣤⣝⣻⣿⣿⣿⣿⠟⠀⠙⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⠟⠁⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣷⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⣦⣤⣀⣀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣶⣿⠇
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣻⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠸⡎⠿⢿⠁⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢺⢉⣽⣿⣻⡄⠀⢹⡄⠘⣧⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠘⣇⠙⠁⢳⡹⣆⠀⢻⡄⠘⣧⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⣽⣆⠀⢹⣆⠸⣆⠀⠀⠹⣷⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠹⣿⣶⣿⠟⠳⠿⣆⠀⠀⢻⡗⠿⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⣽⣇⠀⠀⠀⠙⢦⣤⠞⠁⢀⣼⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠷⣤⣤⣼⡿⠀⠀⠀⢀⣠⣤⣴⣾⠿⠛⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠨⣀⣀⣀⣀⣠⣴⣶⠿⠟⠛⠉⠁⠀⠀⠀⣠⣾⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠲⠿⠛⠛⠋⠉⠀⠀⢀⣀⣤⣤⡶⠶⠛⠉⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣤⣄⣀⡀⠀⢀⣠⣤⣶⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣉⣁⡤⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⣥⡤⠤⠶⠶⠶⢤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⣼⣡⡶⠖⠛⠛⠛⠒⠲⠦⣤⣀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢷
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡼⣿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡼⠁⢹⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⡾⠁⠀⠈⢷⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⡾⠁⠀⠀⠀⠈⢷⡀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠙⠶⣤⣀⣀⣀⣀⣀⣤⠾⠋⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣀⣀⣀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⢠⠀⠀⡄⢠⠀⠀⡄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢁⡐⠂⣀⢀⠀⠂⡐⠀⠀⠐⠂⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⢈⠀⠀⠀⠀⡄⠈⠀⠀⠁⠘⠀⠲⠀⠉⠀⠀⠈⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣃⠈⠀⠈⠀⠃⠀⠀⠀⠀⡄⢀⠀⠂⡀⠀⠀⠘⠂⠠⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡡⠊⠀⠥⢈⡰⠂⠀⠠⠀⠀⠀⠀⠠⠈⠠⠆⠀⠀⠀⠀⠈⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠘⠀⠆⠀⢠⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠄⠀⠀⠈⠢⠈⠀⠀⠄
⠀⠀⠀⠀⠀⢉⡌⠀⠃⠀⠀⡒⠀⡀⢀⠀⠀⡄⢩⠀⠀⠈⠁⠀⠠⠄⠀⠀⠒⠀⠀⢀⠄⠉⠀⠀⠤
⠀⠀⠀⢀⠀⠀⠀⠐⠀⢀⠔⠁⠀⠀⠀⠀⢀⠀⡀⠀⡀⠂⣤⠀⠰⠂⠀⠀⠀⠀⠐⠁⠐⠂⠀⠀⠂⠃⡀
⠀⠀⠀⢨⠀⠐⠂⠰⢈⡁⠀⢒⠔⢀⢀⡀⠀⠀⠰⠊⠀⠀⠠⢈⡀⠂⠀⠀⠀⠀⡄⠀⠰⢂⠘⠀⠀⠈⠱
⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠆⠁⠀⠀⠀⠀⢠⠀⠂⠀⡀⠀⠀⠀⡀⠋⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢠⠀⠀⠆⠈⠁⢀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣁⠄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠈⠁⡄⠉⠀⠀⠀⠀⠘⢠⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠃⡄⠀⢀⠀⠀⠀⠀⢀⠠⠄⠀⠀⡄⠀⠀⠀⠀⠐⠄⠀⠀⠤⠪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⣀⠀⠀⠂⢀⠀⠂⠀⢄⠀⠆⠀⠀⠠⡄⠀⠀⠀⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⢁⡀⠁⢀⡉⠀⡀⠀⠀⠑⠄⠀⡌⠁⠀⠀⠊⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠰⠀⠀⠆⠀⠀⠴⠀⠂⠀⠀⠀⠀⠤⠀⠀⠀⠈⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠋⠀⠚⠀⠘⠀⠃

⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠂⠀⠀⢀⠄⠀⢠⢄⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠐⠁⡠⡄⠀⡠⡔⠀⠀⠀⠈⠀⠀⠁⢀⠄⠀⠈⠂⡀⠈⠀⠈⠈⠀⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠐⠀⡠⠀⠀⠀⡠⡔⠁⠀⠀⠁
⠀⠀⠀⡀⡄⠀⠀⠈⠀⠀⠉⠀⠀⠀⢀⠐⠁⠀⠀⠀⠈⠀⠀⠀⠈⡆⠀⠀⠀⠀⠰⡅⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠈⠁⠀⢀⠄⠒⠒⠒⠒⠐⠂⠁⠀⠀⢉⠀⡀⠀⢀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠎⠂⠀⠀⠀⠀⡀
⠀⡀⠀⠀⠀⠊⠃⠀⢀⠄⠂⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠔⠁⢀⠔⠀⠀⠀⠀⠀⠈⠉
⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⠀⠀⠡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠀⠀⡐⡀⠀⠀⢀
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠂⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠔⠉⠀⠀⠀⠀⠈⠀⠀⢈⠄⠁⠀⠀⠉
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠫⠀⠀⠝⠀⠀⠀⠀⠀⠤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⠫
⢀⠀⠀⠨⠁⠀⠀⠂⠃⠀⠃⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠐⠘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠃⠃
⠈⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⡄⠄⠀⠠⠊⠀⡀⠀⡀⠀⠀⠀⠰⢠⠀⢠⠀⠀⠀⢠⡂⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠐
⠢⡀⠀⢔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠂⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⠀⠣⠁⠀⠀⠑⣆
⠀⠈⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⢀⠘⠊⠀⠁⠀⢀⠠⠀⠀⠀⣀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠑⠀⠀⡐⠀⠀⡀⠁⠀⠈⠒⠁⡀⠀⠀⡀⠀⡄⠀⠀⠀⠀⢀⡀⠐⠀⠀⠈⠀⡀⠀⠀⠁⠀⠀⠀⠆⠄⠀⠊
⠀⡀⠀⠀⠄⠠⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠠⢢⠈⠊⠁⠈⠂⠀⠂⠀⠀⠀⠀⠐⠂⠀⠀⢔⠂⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀
⠈⠒⠀⢔⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠒⠁
⠀⠀⡀⠊⠀⠀⠑⠀⠀⠀⡖⠄⠀⠀⠀⠐⠂⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠜⠆⠀⠖⠄⠀⠀⠀⠀⠀⠀⢒
⢀⠁⠀⠀⢰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠰⠲⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠉⠉⠉⠓⠁⠀⠀⠈⠢⣀
⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠠⡀⠈⠁⠀⡀⠀⠠⠈⠀⢨⣀⠉⠉⠁⠀⠀⠀⠈⠓⠒⠒⠒⠲⢿⠆⠀⠀⣠⢄⣈
⠀⠈⠁⠀⠀⠉⠀⠀⠐⠄⠈⠁⠀⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠊⠁⠀⠈⠅⠀⡀⢀⠀⠀⠀⡠⡀⠀⡠⡀⠀⠀⠈⠁
⡀⠀⠀⠀⡀⡀⠀⡀⡀⠀⠋⠀⠀⠀⠐⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢅⠀⠀⠝⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠈⠁⠀⢀⢀
⠈⠁⠀⠀⠈⠁⠀⠈⠁⠄⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠬⠂⠀⠀⢨⠂⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠀⢪⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⠐⠭⠀⠀⠕⠀⠐⠕⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⣀⠄⠀⠀⠀⠩⠂⠀⠰⠅
⠀⠀⠀⠔⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠂
⠀⠢⠁⢄⠄⠀⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠘⠍⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁⠀⠀⠀⡤⡔
⠀⠀⡀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠴⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢆⠄⠀⣀⠑⠤
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠁⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠰⢃⡌⠢⠡⡀⢀
⠑⡐⠕⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠁⠀⣈⠘⡄⠂⠀⠀⠀⠀⠁⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⡙⢷⣅⡀⡑⠄⡀⠀⠀⠀⠀⠄⢈
⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠠⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠈⠀⣹⠐⠂⠀⠀⠀⠀⠀⠀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣔⠌⠀⢀⢀⠀⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⠦⡀⠈⠢⠀⢀⡠⠀⠐⠌⣀⠂⠉⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠙⠧⢊⠀⠂⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠈⣅⠠⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠔⢀⠀⡀⠀⠀⠀⠙⠆⠀⣺⡏⠀⠀⠋⡤⠈⢐⠀⠉⠂⡄⢌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠓⠡⠆⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠪⠂⠁⢀⠒⠐⢀⡊⠀⠀⠔⠁⠀⢀⡶⠂⡁⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠐⢠⠂⡀⢀⠀⠢⡀⠂⡀⠀⠀⠀⠀⠀⠀⡀⢀
⢁⠄⠀⠀⡘⢾⣤⠀⠌⠀⠀⠀⠀⠀⠐⠀⠐⣠⠆⠈⠀⠄⠀⠀⠀⠀⢠⣤⣾⣿⣿⠇⢀⠄⡠⢊⠲⠄⠈⠀⠘⡀⠀⠀⠑⢄⠈⠢⡄⠁⣀⠀⠀⠀⢨⠄⠀⠱⠄
⠊⠀⡠⠞⠁⠀⡙⠂⠀⠀⡠⢆⠔⠁⠙⠁⠚⢁⠀⡡⠊⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠣⠊⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠢⡈⠃⠀⠀⠸⠅
⠀⠀⠀⠀⢀⠔⠁⠸⠓⢊⠔⢁⠀⠀⠀⠀⠐⢁⠦⡀⠀⠀⠀⠠⣴⣿⣿⡿⠋⡡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠀⠀⠀⠀⠃⡀⠐⠄
⠀⠀⠐⠀⠀⠐⠄⠔⠀⡅⠌⠸⠀⠀⠀⣠⡪⣀⠀⡨⠡⡀⠀⣺⣿⡿⢋⡴⠐⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠌⠢
⠀⢴⣷⠉⠐⠁⠀⢠⠀⣉⠀⠠⠀⢠⡀⠑⡀⡀⠱⡀⠐⠌⠀⡀⠀⠀⠨⠀⢀⠀⠀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠁
⠄⠈⠀⡀⠀⠀⢠⠂⠀⠊⠀⠠⠢⠑⠡⠐⠁⠀⠀⠈⠀⠌⠈⢌⠢⠀⠀⠀⠀⢀⠀⠁⠀⠀⢀⡄⠀⢃⠄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠢⠀⠀⠁
⢀⡤⠂⠀⠀⠀⠀⠀⠀⠠⡨⠐⡠⡑⠄⠀⠀⠀⠀⠀⠀⠈⠢⢂⠡⠰⠢⡀⢀⠈⠀⠀⠀⠀⠉⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢻⡷⠒⠂⢀⠐⠁
⢀⠀⠀⢀⠐⠀⠀⡠⡂⠅⡨⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠠⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁
⠁⡠⠀⠁⠁⠠⡐⠍⡈⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠈⢜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⠀⠀⠀⣆
⠊⠀⠀⠂⠀⠈⠢⢕⠌⢔⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠌⠊⢥⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠀⠐⠀⠀⠀⠠⠄⠀⠀⠈⠂⠸⡂⠄
⠀⠀⠀⠀⠀⢀⠐⡈⢪⡂⢅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⢄⢈⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠐⠀⠀⠀⠐⠁⠐⠀⠀⠀⢀⠀⠙⢦
⠀⠀⠠⠀⠀⠀⠈⠄⠁⠺⣥⡡⠑⠡⡀⡀⠀⠀⠀⠀⠀⠠⢄⢈⣢⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈
⠀⢀⠀⠁⠄⠀⠀⠀⠀⠰⠈⠻⢐⡙⡈⢔⠄⠀⠀⡀⢀⠪⠀⠡⠀⡡⠀⠀⠀⠀⠀⠀⠀⠔⠈⡐⠈⠢⠀⠀⠠⠂⠀⢀⠄⠁⠀⢀⡠⠀⠀⠈⠀⠀⠀⠀⠀⣠⣾
⡤⠈⠠⠄⠀⠈⠀⡀⠀⠀⠀⠀⠀⠺⣮⢜⢌⠊⢂⠢⠀⠠⠒⠀⠐⠀⠂⡠⢀⠀⠀⠀⢤⣄⠁⢀⠠⠁⠀⠀⠈⠀⠄⠀⠄⣀⠀⠊⢀⠐⠀⠀⠀⠀⠀⡠⣾⣿⣿
⠀⠦⠁⠠⠆⡀⠐⢤⠀⠀⠀⠀⠀⠀⠈⠃⠡⡠⠑⠠⠀⣀⠀⡠⠈⠐⠌⠶⠃⠀⢀⠖⠀⠙⠇⠀⠀⠀⣰⢄⠔⠀⠄⡠⠞⠋⠐⠀⠂⠀⠀⠀⠀⢀⣽⣿⣿⡿⠃
⠃⠀⠸⡀⢀⠐⡀⠃⢑⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠠⣄⠀⠀⠀⠘⠁⠀⢀⠔⠀⡴⠠⠞⠠⠁⠀⠀⠀⠃⡄⠀⠈⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛
⠀⠀⡀⠀⡁⠀⠀⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡴⠂⢢⡀⠀⠀⠀⠈⠃⠀⠀⠀⠄⠐⠁⡀⢀⠀⠐⠁⠂⠀⠀⠀⠀⠠⢔⠐⡐⢢⠀⠀⠠⣿⣿⣿⠋⡠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⠀⠀⣤⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⡤⠄⣀⣄⡀⡸⢀⣇⠀⢸⠹⠎⠘⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠐⢃⠀⠊⢁⣤⠝⡁⢸⢀⡇⠈⡀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠀⠀⠈⠀⢰⢛⠋⢰⠃⠣⢎⠤⠴⢱⠆⢶⢣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠘⠋⠀⢸⠀⠀⠈⢓⠀⢬⡤⠨⠷⠧⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⣁⣀⢠⠘⠢⢤⡤⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡄⢡⡸⢴⡛⠈⣷⢹⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠧⠞⢀⠐⣯⣀⢹⠾⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠮⣄⣀⣀⠀⠀⠀⠀⠀⢀⠟⠢⡄
⠀⠀⠀⠀⠀⠀⢠⡞⠕⠦⣀⣀⣀⡀⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆⠀⠀⢀⠎⠀⠀⠸⠢⣄
⠀⠀⠀⠀⠀⠀⡌⠃⠀⠠⠤⣀⣀⣠⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⡀⠀⠀⡘⠀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣤⠞⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⣏⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣭⣭⡭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⢹⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢸⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⣿⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⣿⠀⠀⣰⠟⣫⠵⠒⠒⠮⣝⢷⡄⠀⢸⡇⠀⢸⡇⠀⠀⣠⣤⠀⠀⠀⠀⣤⣤⠀⠀⢸⡇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⣧⡇⠀⠀⣿⠀⣸⢯⠞⠀⢀⣀⣀⠀⠘⡆⢿⠀⢸⡇⠀⢸⡇⠀⠀⢹⣿⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣿⠀⣿⣼⠀⠠⣿⠟⣿⡇⠀⡇⢸⠃⢸⡇⠀⣾⠁⠀⠀⠈⠉⠀⠀⠀⠀⠘⠋⠀⠀⢸⡇⠀⢸⣸
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠹⣟⣆⠀⣿⠀⣿⠀⣰⣣⡿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠙⢮⣝⣿⠀⣿⣯⡾⠋⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⢸⡇⠀⣼⣿
⠀⠀⠀⠀⠀⠀⣿⢷⠀⠀⣿⣀⠀⠀⠀⠈⢻⡄⢻⡅⠀⠀⢀⣀⣸⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⣿
⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠉⠉⠛⠛⠛⠛⠻⣇⢸⡟⠛⠛⠛⠉⠉⠁⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⡇⣿
⠀⠀⠀⠀⠀⠀⣿⠸⣌⣡⣤⣤⣤⣤⣤⣤⣤⣿⠀⢿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣃⡇⣿
⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⡇⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠤⢄⣀⣀⣀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒

⣶⠶⠦⠤⠤⠤⠤⠶⠶⠶⢶⣶⣤⣤⣤⣤⣤⢀⣠⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⢴⣦⣶⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⢀⣀
⣒⣂⠠⠤⣄⣀⣀⣀⣠⣤⣤⣤⡤⠶⠒⠒⣒⣚⣻⠿⠿⠟⠋⠛⠓⠚⠿⠿⣛⣓⣒⣒⣾⢿⠿⠿⠯⠭⢭⣭⣶⠶⠶⠶⠤⠴⣺
⠒⠊⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⡘⣫⣧⣼⣿⣿⣿⣭⡭⣽⣶⣾⣧⣤⣶⣶⣖⣿⣿⣷⣶⡶⠶⢶⣶⡶⠶⠶⠶⣶⣶⣶⣦⣤⣤⣤⣴⠶⠭⠽⣿⣿⣾⣿⣿⣻⡖
⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠒⠒⠒⠚⠛⠛⠛⠛⠛⠓⠚⠛⠉⠉⠉⠁


⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⠿⠷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⢀⣤⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠙⣷⡄
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡿⠀⠀⢠⣿⣿⡿⠛⢿⣿⠟⠻⣿⣿⣧⠀⠀⠘⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣄⠀⠀⠁⠀⢀⣼⣿⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⢸⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⡟⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⠛⠛⠛⠛⠛⢻⣧⠀⠀⠹⣿⣿⣦⣀⣴⣷⣄⣠⣾⣿⡿⠃⠀⢀⣿⠛⠛⠛⠛⠛⢻⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⣾⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠉⠉⠋⠉⠉⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣦⣤⣤⣤⣤⣤⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸
⣴⣶⣾⣿⠀⠀⢸⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⢻⣷⣶⣶⣶⣶⣶⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡟⠛⠛⠛⠛⠛⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⣇⣀⣀⠀⠀⢀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠙⠛⢻⣿⠀⠀⢸⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⢀⣴⡶⠿⠿⠿⠟⠁⠀⢀⣴⡿⠋⠀⠀⣠⣶⠿⠿⠿⢷⣦⡀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⢸⣿⣶⣶⣶⣿⠋⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠘⢿⣶⣶⣶⣶⣾⣿⠀⠀⢸
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡷⠀⠀⢹⡇⠀⠀⠀⢸⣿⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⣶⡄⠀⠀⠉⠀⠀⢠⣿⠇⠀⠀⠀⠈⣿⣆⠀⠀⠉⠁⠀⢀⣶⡶⢶⠶⠶⠶⠶⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣤⣾⠟⠃⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣤⣶⠿⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶