Abc Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢍⠙⠁⠀⠑⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⣼⠃⠂⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠂⢹⣄⠀⠀⠀⠀⠙⠮⠤⠲⣄⢀⣼⠀⠀⠀⠀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠜⣀⡀⢠⠌⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡜⠀⠀⢣⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣕⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢠⠀⠀⠈⠁⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⠅⠂⠁⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠸⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠏⢹⠂⠀⠀⠀⠀⠀⠈⠙⠒⠤⡄⣀⠀⠀⠀⣀⣀⣑
⠀⠀⠀⠀⠀⠲⠷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⠁⠃⠀⠘⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠀⠀⡾⠉
⠀⠀⠀⠀⠀⠀⡴⠶⢉⡉⣉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⡗⢀⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⣰⠁
⠀⠀⠀⠀⠀⣠⠇⠀⠀⠤⠠⠀⢺⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠛⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠀⠙⠃
⠀⣀⣠⣤⣀⠻⢤⡀⠑⠀⠊⢠⡞⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⠀⠀⠈⠑⠦⣄⡠⡖⡖⠤⠾⠅⠂⠈⡆
⣰⠇⢀⠈⢹⡃⠀⠙⠶⠖⠦⠞⠁⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠣⣀⣀
⢧⠀⠁⢰⡼⠃⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠃⠀⠀⢀⡠⠞⠁
⠈⠓⠚⠋⡁⠀⢠⠔⠒⠞⠁⠈⣧⡀⠀⠀⠀⠀⣀⡠⠤⠒⠋⠉⢀⠠⠒⠒⢌⡑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⡠⡀⠀⡇
⠀⢀⡀⠘⢻⡖⠛⠀⠠⠀⠂⠀⣉⡩⠷⠖⠚⣉⣁⣠⠤⣀⠀⢠⠁⠀⢀⠔⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠙⠦⣴⠃
⠀⠙⠚⠀⢈⡷⠀⠃⠀⠈⠀⡎⣁⣀⠴⡏⠉⠁⢀⠀⠡⠈⣄⡀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠸⣄⡀⠐⢴⡚⠉⠁⠙⢄⠱⡘⠀⠀⠉⠀⠙⠐⠢⣭⠀⠀⠈⡀⠱⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠳⣄⣀⡇⠀⠀⠀⠀⠱⡈⠳⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠑⠤⠨⠛⡽⡰⠁⠀⢀⡠⠴⠒⠉⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠠⢆⠀⠀⠈⠢⡡⠀⠀⠺⠆⠀⠀⠍⡢⠄⣀⣀⠠⢔⣫⠤⠒⠋⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠁⠀⠀⠀⠙⣆⠀⠀⢀⠠⠚⢉⣀⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡊⢹⣳⠀⢀⡠⠜⢒⣩⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠇⣀⣀⡤⠼⠚⠉⠉⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠖⠒⠀⡀⠀⠀⠠⠤⢄⠀⠀⠀⠄⠀⠄⢀⠀⠀⠆⠐⠂⡆⠀⠐⠂⠀⠲⠆⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠋⠠⠇⠀⠀⠀⠂⠀⡃⠀⠀⠀⠘⠀⠈⡇⠀⠀⡉⡏⡀⠀⠀⠀⠒⠎⠀⠀⠀⢐⣄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢒⠀⢰⠀⠀⠀⠢⠉⡍⠀⠀⠀⠰⠂⡠⠃⠀⠀⠀⠀⠅⠀⠀⠀⡏⠀⠀⠀⠀⠓⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠄⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⣀⣀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠀⡄⠀⠀⠐⠰⠀⠀⠀⠀⠀⠃⠃⠀⠀⠐⠁⠗⠁⠐⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⠀⠔⠴⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠐⠂⠄⢤⠀⠀⠀⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠚⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠤⠀⠀⢄⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠈⢁⠀⠀⡀⠀⠀⠀⠨⠅⠈⠀⠀⠀⡎⠀⠀⠀⠀⠀⠠⠆⠈⠂⠀⠐⠶⠶⠀⠈⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠇⡀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠗⠃⢠⠀⠀⠀⢰⠀⠡⠀⠈⠉⠥⠠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠴⠄⢰⠀⠀⠀⠠⠶⠀⢰⠀⢀⢀⠄⠀⡀⠄⠠⡄⠠⠄⠠⡤⠄⡄⠀⠂⠒⡄⠀⠖⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇⠀⠀⠀⠌⠀⢈⠀⠰⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⠁⡈⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠆⠀⠀⠆⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⢀⡂⢀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⡤⡲⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠒⠒⠒⣲⣤⣤⣤⣄⠀⠀⠤⠄⡏⠉⠉⠁⢀⠐⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⠀⢀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠃⠀⠀⣷⠀⠀⠠⠇⠀⠀⠀⠀⠀⢀⡴⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⠀⢸⡀⠀⠸⠆⢀⠄⠀⠀⣠⠟⠉⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠦⠤⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠐⠁⢈⣥⣿⠇
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⣦⣤⣤⡏⠀⠀⢀⠀⠀⢹⡄⢘⠀⠀⠀⢠⣢⣴⣿⠿⠛⠉⠀⠀⠀⣀
⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠦⠤⡍⠉⣉⣚⡛⠛⠻⠇⢘⣀⣤⣾⠿⠛⠉⠀⠀⠀⢀⡤⠶⠋⢩
⠀⠀⡖⠒⣶⠶⠶⠶⠶⠶⢖⣒⠒⠛⡇⠀⠈⢩⣅⣉⡉⠉⠙⠋⠉⠉⠀⠀⠀⣀⡠⠴⠊⡟⠀⠀⠀⢰
⠀⠀⡅⠀⡇⠀⠀⣀⣀⣀⠀⠈⢳⠀⠃⠀⠀⢸⡇⠀⠀⠌⠛⠛⠓⢒⡒⠒⠆⢻⠠⠁⠘⠁⠐⠀⠀⢻
⠀⠀⡇⠀⡄⠀⠀⠧⠤⠼⠂⠀⣰⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⣀⣘⣀⣀⢀⡄⣀⣨
⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠐⠺⢅⠀⠀⠀⠀⢸⣇⠀⠀⢠⡖⠒⢦⣤⠤⠉⠠⢨⡭⡿⣿⠿⣿⣿⣿⣿
⠀⠀⡃⠀⠀⠀⠀⡎⠉⡦⠀⠀⠀⡇⠀⠀⠀⢸⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⢰⠒⠒⠒⠒⠻⠛⣻⣿
⠀⠀⡇⠀⡇⠀⠀⠉⠉⠀⠀⠀⣠⠇⠀⢠⣀⢸⡇⠀⠀⠈⠓⠂⠐⠢⡀⠀⠀⢰⡄⠀⠀⡠⠂⣴⢋⣿⠒
⠀⡀⠦⠤⠕⠖⠲⠒⠖⠒⠒⠈⠁⠤⠾⢸⢸⢸⣇⡈⢄⡀⠀⠀⠀⢀⣸⠇⠀⢸⠀⠀⡐⢁⣠⠷⠋⠁
⠀⠉⠉⠛⠛⠓⠶⠋⠉⠝⠋⠉⠲⠍⠉⠛⠛⠓⠦⢤⣍⣉⣛⡒⠮⠭⢄⣀⣀⢰⠇⣠⠶⠋⠁⠤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠩⠭⣁⣒⣒⡦⠘⠛⠝⠛⠛⠋

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠙⠛⠛⠲⠶⠶⢤⣤⣤⣄⠀⠀⠀⠀⠀⣾⡿⠛⠛⠛⠛⠛⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣤⠤⣤⣀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣤⣤⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠙⣧⠀⠀⠀⣿⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⣷⠀⠀⠀⣿⣀⣀⣼⠏⠀⠀⣰⠏⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣾⠏⠁⠈⠹⣦⣠⠞⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠀⠀⢀⣴⠋⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣤⢤⣄⠀⠀⠀⠈⢿⡄⠀⢹⡇⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⠀⠀⠀⠀⡇⠀⠈⢷⠀⠀⠀⠈⣿⠀⠘⣿⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⣼⠀⠀⠀⠀⣿⠀⠀⢻⣇⠀⠀⠀⠀⠘⢷⣄⣀⣀⣤⠾⠛⢶⣄
⠀⠀⢠⡿⠀⠀⠀⠀⠀⣾⠉⠉⠙⠻⡆⠀⠀⠀⠀⠈⣇⠀⠀⢸⡇⠀⠀⠀⢧⠤⠾⠃⠀⠀⠀⣰⠏⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣸⠟
⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢻⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠻⠷⠶⣶⣤⣤⣼⡇⠀⠀⠀⠀⠈⣷⣤⣤⣤⣤⣼⡇⠀⠈⡇⠀⠀⠀⢀⣀⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⠶⠶⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⠶⠶⣦⠀⠀⠀⠀⢀⣴⠾⠟⠛⠛⠛⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⢺⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠘⠓⠚⠛⠛⣻⠟⠁⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⢾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⣤⡴⠾⠛⠛⠳⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⢾⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢿⠶⠶⠷⠶⢶⣄⡀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⣼⣧⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣯⣤⣤⣤⡄⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣦⣄⣀⣀⣀⣠⡴⠛⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣶⠶⠾⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠛⠛⠒⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣾⠉⠉⠉⠛⠓⠒⠶⢦⡄⠀⠀⠀⠀⣿⠛⠉⠉⠉⠉⠉⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠦⣄⡀
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡀⠀⠀⠀⢹⡄⠀⠀⠀⢸⡇⠀⠀⢺⠉⠛⢦⡀⠀⠀⣿⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⣾⠀⠀⠀⢸⡏⢹⡄⠀⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⣸⠇⠀⢀⡿⠀⠀⢰⡟⠀⠀⠀⠀⢀⡴⠛⠛⠳⣄⣠⡴⠋
⠀⠀⠀⢀⡟⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⢻⡀⠀⠀⢸⡇⠀⠀⠈⠛⠉⠁⠀⢠⡞⠁⠀⠀⣿⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⠁
⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⠀⢠⡇
⠀⠀⠀⣾⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣷⠀⠀⠀⣧⠀⠀⠀⡶⠶⣄⠀⠀⠀⢻⡆⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⡇⠀⠈⣧⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⢷⡀⠀⠀⠀⢀⣄
⠀⠀⢸⡇⠀⠀⠀⠀⡶⠶⠶⢤⡀⠀⠀⠀⠈⣇⠀⠀⢿⠀⠀⠀⣇⣀⣠⠏⠀⠀⢀⡟⠀⠀⢻⣄⠀⠀⠀⠈⠛⠶⠶⠞⠋⠈⢳⠆
⠀⠀⣾⠀⠀⠀⠀⢠⡇⠀⠀⠀⢧⠀⠀⠀⠀⢻⠀⠀⢸⠀⠀⠀⠉⠉⠀⠀⠀⢀⡾⠁⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠿⣦⣤⣄⣀⣸⠁⠀⠀⠀⠘⣇⣀⣀⣀⣸⡇⠀⢸⠀⠀⠀⠀⠀⣀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠘⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠶⠶⠞⣧
⠀⠀⠀⠀⠀⠀⠀⣰⠖⠒⠒⠒⠒⠲⡆⠀⠀⠀⣠⠾⠛⠉⠉⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⡇⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⣿⣀⣀⣤⣤⣤⠄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣦⡀⣠⣤⣤⣤⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠙⢦⣀⣠⣶⠀⠀⠀⢰⡇⠀⠀⠀⠈⠋⠁⠀⠀⠀⢻⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠁⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢹⡴⠶⠶⠶⣤⡀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠿⠶⠶⠶⠶⠤⡤⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⠀⠀⠀⠸⠷⠶⠒⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⠶⠤⠤⠤⠖⠋⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⢿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠸⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠚⠃⠈⠓⠶⠤⣤⣤⣤⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡶⠶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⣶⢶⣶⡶⢶⣶

⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⠉⣿⢫
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠦⠼⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛⠓




⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠆



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠖⢄⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡠⠀⠀⠄⠠⠀⠄⠰⠠⠄⠀⢠⠀⣆⣄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⣷⣶⣾⣶⣷⣷⣾⣿⣷⣾⣾⣷⣾⣾⠿⣷⣶⣶
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣄⣤⡀⠀⠀⢀⣀⣤⣤⠤⠤⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⡤⠤⣄
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢡⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢣⠈⡆⠀⠀⠀⠠⠊⠁⠀⠀⠀⠈⠑⡄⠱⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⡇⠀⠀⢸⠀⠀⢨⠉⡷⠀⠀⢸⢀⠅⠀⠀⢀⠃⠀⢀⠔⡑⠠⡀⣀⡸⠴⠃
⠀⠀⠀⠀⢸⠀⢀⡄⠀⠀⠘⡂⢱⠀⠀⢸⠀⠀⠈⠁⠀⣀⣴⣿⠥⣀⠀⠀⢸⠀⠀⢸⠠⡇
⠀⠀⠀⢀⠆⠀⡘⡃⠀⠀⠀⡅⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠑⡄⢸⠀⠀⢨⠀⡇
⠀⠀⠀⠰⠀⢀⣧⡇⠀⠀⠀⠣⠐⡄⠀⢸⠀⠀⢰⠉⡟⠲⡄⠀⠀⠘⠀⡁⢸⠀⠀⠸⡀⢣⠀⡤⣔⣶⡤⡄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⢸⣤⡧⠴⠁⠀⠀⠰⢀⠇⠀⡄⠀⠀⠑⠤⠛⠁⠀⡨⢰⠃
⠀⠀⡸⠀⢠⠏⡟⠙⠀⠀⠀⢸⠀⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠘⢄⠀⠀⠀⠀⢀⣴⡳⠃
⠀⠀⠁⠐⠚⠉⠀⠀⠃⠐⠀⠘⠉⠁⠀⠈⠀⠀⠀⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠚⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⢨⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠖⠤⣀⠀⣀⠱⡀⠑⠊⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢱⠀⠰⠁⠀⠀⠀⢀⡁⠠⢀⠘⢄⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠳⣴⠈⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⣱⣬⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣉⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠹⠓⠀⢄⠀⠣⡀⠀⠀⠀⠀⠀⢸⡇⠀⠢⠄⠀⠀⠀⠀⠀⠀⠂⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠄⠀⢀⠀⠀⠈⠑⠢⠌⣀⠀⣸⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⣠⠴⠺⡀⠀⠐⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡙⠂⠄⠺⣄⠀⠀⠀⠀⠀⣠⡴⣽⣶⣶⣶⣶⣶⠁⠀⠀⡰⣾⣿⣿⣿⣿⠁⠀⠀⢀⠴⠋⠀⠀⢂⡁⠂⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠃⠘⢦⡠⢤⡀⠐⠏⠀⣾⠿⠿⠋⠚⠛⠀⠒⠋⠉⠛⠋⠛⢛⡟⠀⠀⡴⠛⠤⡀⠀⠀⠀⢈⣐⣠⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⡤⠢⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢠⣤⡞⠀⣠⠂⠈⠓⣤⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠙⠆⠁⠀⠀⣴⣶⣶⣶⣶⣖⡶⣷⣿⣟⣿⣿⣿⣣⡀⠈⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠛⠛⠋⠉⠉⣡⠿⠿⣿⡉⠉⠉⠉⠀⠘⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣟⣀⣀⣤⣃⣀⣀⣀⣀⡀
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠀⠀⠀⣤⠀⣀⡀⠀⠀⠀⣰⠒⠢⠤⠄⣀⡀
⠀⢀⡤⣼⠁⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠳⡄⠀⠀⢀⣤⠞⠛⠛⠉⠉⠉⠉⠉⠉⠉⢉⣩⠿⠋⣇⠀⢈⠀⠀⠈⠛⢻⠥⠤⠔⠺⡁⠊⢈⠀⠀⣸⠃
⠀⢈⡖⠇⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠙⢦⠾⠋⣇⣀⣀⣀⣀⣀⣠⣤⣤⠶⠞⠋⠁⠀⠀⠸⣆⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠀⠀⢀⡴⠃
⠀⠈⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⠄⣀⠀⡜⠀⠀⠀⡀⠀⢀⣀⡠⠛⠁
⠀⠀⠀⢤⣤⣀⣀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢰⡶⠒⠛⠛⠋⠉⠛
⠀⠀⠀⠀⠀⠈⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⢠⢄⣀⢄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠈⢳⡖⢻⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣅⣀⠀⠀⠉⠁⣠⡾⠛⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠹⠞⠀⠟⠂⠀⠀⣀⡀⠀⠀⢀⠀⠀⢀⠀⢠⠤⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠀⠹
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⡏⢹⡄⠀⠕⢀⡞⠉⠀⠈⢶⠉⠃⠀⠀⠈⢿⣧⣀⣀⣠⡶
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⣀⣿⡄⠀⠈⢷⣤⣤⠦⠀⠀⠀⠀⠀⡀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠐⠠⢅⡘⠀⠀⢀⡖⣆
⠀⠀⠀⠀⠀⠺⣒⡶⠦⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢸⠀⠀⠀⠀⠀⠀⠀⢸⠦⠺⡄
⠄⠀⠀⢐⢐⠄⠈⠇⠀⡀⠀⠀⠀⠀⢸⣹⣏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠
⠀⠀⠀⠨⠀⠂⠀⠀⠘⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠓⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏
⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⠀⠀⣸⣷⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠤⠲⣉⡜⠀⢀⣿⠁⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠃⠀⠀⠀⠀⠀⠀⠼⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠰⡋⢙⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠀⠀⠀⠘⠯⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⢉
⢸⠬⡂⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠐⠗⠁
⠈⠂⠁⠀⣀⡼⠀⢀⢤⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠂⠀⠓⠐⠂
⠀⠀⠀⠀⠉⠀⡠⠧⢸⠀⠀⠀⠀⠀⣠⠤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⢀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠀⣾⠃⠀⢠⡤⠀⠀⠀⠴⠅
⠀⠀⠀⢄⠙⠀⠀⠀⠀⡶⡈⠀⠀⢻⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣑
⠐⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠛⠀⠀⠀⠀⠀⢀⣤⡞⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁
⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠘⢦⡞⠉⠀⢀⡤⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠟⠛⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠁⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿
⠀⠀⠀⠀⣸⡟⠉⠉⠉⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣿⡄⠀⠰⣾⠟⠛⠛⣷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠃⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠁
⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⣀⣠⣶⠟⠀⠀⠀⠀⣠⡿⠁⠀⠀⢸⡟⠀⠀⠀⢠⣿⠃
⠀⠀⠀⣸⡏⠀⠀⢠⣶⡄⠀⠀⢻⣇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠙⠛⠉⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣼⡇⠀⠀⠀⣸⡇
⠀⠀⢀⣿⠀⠀⠀⣼⠟⣿⡀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣤⣀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣇
⠀⠀⣼⡇⠀⠀⢰⣿⣀⣸⣷⠀⠀⠸⣧⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣦⡀⠀⢸⣇⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⣀⣶
⠀⢠⣿⠀⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⢻⣆⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢻⣆⠈⣿⡄⠀⠀⠀⠀⠉⠛⠻⠿⠛⠋⢹
⠀⣼⡇⠀⠀⠀⣀⣀⣀⣠⣄⡀⠀⠀⠈⢿⡄⠀⠀⠀⠘⣿⠀⠀⠀⣿⡋⠉⢙⣿⠀⠀⠀⠀⠀⠈⣿⡄⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⢠⣿⠀⠀⠀⢀⣿⠉⠉⠉⠙⣷⡀⠀⠀⠘⣿⡀⠀⠀⠀⣿⡆⠀⠀⢻⣧⣴⠿⠃⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠉⠻⢷⣦⣤⣤⣤⣤⣴⡶⠟
⢸⡏⠀⠀⠀⢸⡏⠀⠀⠀⠀⢹⣧⠀⠀⠀⠸⣷⠀⠀⠀⢸⣇⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣿⠇⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢻⣦⣤⣤⣴⣿⠇⠀⠀⠈⠻⠿⠷⠶⠶⠶⠶⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠶⠾⠿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠾⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⠶⠶⠾⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠶⠿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠌⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣠⠰⠹⢿⣿⣿⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⢀⡴⠲⣶⣶⢶⣄⡀⢀⣿⡶⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⣠⢤⡀⠂⠈⠹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⢏⡈⡔⢡⣁⠊⠑⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠄⣸⣥⣤⣤⣤⣭⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣷⣾⣿⣿⡿⢃⠀⠁⢹⠛⡁⢁⣤⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣠⡾⠁⢈⡼⢣⡈⠀⠁⠈⣌⠁⠀⠀⢿⣿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢢⢄⡄⠀⠀⢸⠁⠉⡀⠉⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⡠⠈⠹⠧⠖⠋⠀⢀⠑⠀⠀⡔⠙⠀⠀⣤⠈⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠸⣿⣿⣿⡏⢡⢇⡃⠃⠀⠀⠈⠀⠘⣧⠀⣀⣠⠤⠚⠁⠀⠀⠀⠠⣎⡀⢀⣀⠠⠤⠔⡚⢿⢃⡤⠊⠀⢀⠃⠀⠰⠀⡉
⠀⠀⠀⢄⡶⡾⣆⠀⠀⠹⣿⡟⡅⣵⡎⠙⢓⢠⠄⠀⠀⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡸⠀⠀⠀⠀⡇
⠀⠀⠀⠾⣿⢾⣧⠀⠀⠀⠙⢷⣴⡹⡇⠂⠈⠁⠀⠀⠀⣿⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢰⠁
⠀⠀⠀⠰⣿⣷⠁⠀⠀⠀⠀⠀⣿⣇⠈⣺⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠁⠀⢸⡆⠇⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⡌
⠀⠀⢀⣄⠘⣻⡅⠀⠀⠀⢀⣉⠁⠹⢆⣿⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡑⢌⣣⠸⢸⠀⠀⢰⠀⠐⠃⠀⠀⢀⡠⠖⣹⣷⡄⠀⠀⠐⣉
⠀⠀⠀⠏⠳⠹⣗⠀⠀⠈⠙⠛⠋⠀⡜⠛⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⡄⣏⠦⡘⠀⠀⠸⣄⢸⣤⡠⠖⠁⢀⣼⣿⣿⣷⠀⠀⠀⠈⠐
⠀⢠⣶⡆⠀⠀⢋⣄⠀⠀⠀⠀⢰⣾⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣠⠀⠠⢸⠄⠃⠀⠀⢠⣿⣿⣯⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⢠⠂⠠
⠀⠀⠻⠇⠀⠶⡀⠉⠀⢀⡠⠴⢏⡈⠙⠳⢷⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⢀⡧⠔⢻⡄⠀⠘⢃⣿⠻⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⢸⠁⠀⣿⠙⠓⣿⠌⠉⣲⣤⣀⣀⣀⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡧⠶⠀⠸⣶⣾⣿⣷⡀⠀⣸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⣸⡀⢼⡷⠟⠀⣈⢻⢫⣮⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢻⣿⣿⣿⣷⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢠⠟⣡⣤⠀⢰⣯⢓⠾⡀⠡⠊⢀⣀⣀⠀⠀⠀⢀⡴⠴⠦⠼⢄⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⡄⢀⡎⠀⠀⠀⡎⢸⠯⠜⡲⠆⠞⠁⠀⣀⠤⣊⠖⠲⣭⠻⢆⠀⠈⣞⣙⣋⠱⠂⠀⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣠⢿⠀⡜⠀⠀⠀⣸⢁⣤⣦⠞⠀⣴⣶⣶⣿⣶⣶⣶⣾⣷⣿⣶⣾⣶⣶⣿⣷⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣰⣷⡾⣷⠁⠀⠀⠀⠧⣛⣃⣍⠀⠀⠈⠉⠹⠋⠉⠉⣉⣉⣭⣭⠭⢭⣿⡉⠉⠉⠉⠉⢩⣿⣿⠉⠉⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠉⢉⣿⣸⣄⣀⣀⣀⣀⣀⢠⡭⣍⡁⠚⠻⢞⣁⢾⡏⢩⣟⠷⠀⢠⣞⠛⣿⡀⠀⠄⠀⢸⡇⡀⠀⠀⠀⣠⠊⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡠⢀⢽⢏⡀⣤⠀⢀⣐⡄⠀⠀⢹⣯⠆⢤⣴⣾⣿⡇⠀⠀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⢾⡎⣧⡻⠃⠀⠺⠙⠁⠀⣾⠎⢹⣯⣱⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣦⣸⡆⢹⢁⣶⡿⠂⢠⣶⡇⠀⣴⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣇⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣷⣾⣿⣷⣇⡈⢉⣤⠤⠽⡿⠒⠋⠙⣇⠁⠀⠉⢻⣿⣿⣿⣿⣿⣏⠙⣷⢀⠤⠀⠰⠄⠂⢀⣩⣽⡮⠁⠈⠈⠁⠚
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⡰⠉⢦⠀⠀⠹⣆⠀⠀⣾⠉⢿⣿⣿⣿⣿⣦⢹⡄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⠛⠉⠀⡆⠀⢠⡅⠀⠀⠳⡀⠀⠹⣦⣀⣿⠀⠀⠙⣿⣿⣿⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⣇⣀⣀⡈⢻⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⣁⠀⠘⣆⠀⠀⠀⠙⣿⣿⢿⣿⣿⣶⣤⣤⣀⢀⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡞⠀⠀⠀⢸⣿⠻⢿⣿⣶⣄⣀⠀⠈⣧⠀⣼⠀⠉⠛⣻⣿⣿⡿⠋⠈⠋⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠓⠚⠁⠀⠀⠀⠀⠃⠀⠀⠈⠙⠛⠿⠿⠗⠛⠚⠋⠠⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠚⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⣶⣿⣶⣯⣭⣿⣧⣿⣿⡿⣿⣿⡧⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⠟⠹⠿⠟⢻⡟⢻⣿⡶⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡷⡌⣿⣿⡆⠀⠀⠀⢈⠉⠉⠈⢳⡦⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⠀⠀⢺⣿⣿⣿⠀⣸⣇⡇⠀⠀⠀⠀⠀⣶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⠛⢀⣿⠿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠀⢤⣾⣿⣻⢋⣿⣿⣶⣤⣀⡀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢰⣿⡽⣱⣿⣼⣿⡇⠙⠋⠉⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠙⢶⣤⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⠀⢀⣠⣤⣴⣶⠿⣿⡿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠘⡟⢜⢿⣿⣿⣷⡻⣧⠄⠀⠀⣾⣧⣭⣿⣿⣿⣿⡟⣼⣿⢟⣿⣿⣿⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⣰⡿⢸⠘⠿⣿⣿⢿⣟⠛⢦⣠⠏⠀⢺⣿⣿⣿⠟⣱⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣍⠀⠀⠀⢠⣿⢣⣯⣴⡇⠨⣿⣿⡿⠃⠀⠘⠂⢀⠀⢹⡿⢻⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢀⣠⣾⣿⣿⣿⣿⣿⠀⠚⠁⠀⠀⠀⠀⠁⠘⡀⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠘⢿⣇⣀⣩⣿⠟⠉⢻⣿⣿⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢿⣿⣇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢣⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣭⡤⠀⠀⠀⠰⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠶⠿⡥⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⠳⣄⠀⠀⠀⠀⠀⣠⠞⠑⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠖⠉⠙⠦⣀⠀⠀⠀⢸⠁⠀⠈⠓⠦⣄⡀⢰⠃⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⠲⠤⣬⡦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡰⠓⢶⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣠⠶⠚⡇
⠀⠀⠀⠀⠀⠇⠀⠀⠘⠦⣀⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠇
⠀⠀⠀⠀⠀⢢⠀⣀⠀⠀⠈⠁⠀⡜⠉⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢹⡹⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡿
⠀⣴⣤⣶⢀⠀⠈⢇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⡀⣶⣤⣦
⣻⣽⠞⠻⢯⠇⠀⠘⢎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠃⠀⠸⡽⠟⠳⣿
⠙⢯⡀⠀⠸⢤⡀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⠃⠀⢀⡤⠃⠀⢀⡽
⠀⠀⠈⠳⡀⠀⠙⠦⣀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠉⠉⢉⠏⠀⠀⠀⠀⠀⢀⣠⣯⠞⠀⣀⠴⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠙⢦⠀⠀⠈⠳⢄⡀⠙⠻⣦⣄⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠀⠀⣠⣴⠿⠋⢀⡠⠞⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠉⠳⢤⡀⠉⠛⠷⢦⣤⣤⣀⣀⣀⣀⣤⣤⡴⠾⠛⠋⢁⡤⠞⠉⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠉⠳⡶⣄⠀⠀⢘⡇⠀⠀⢸⡃⠀⠀⣠⢶⠞⠉⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⡰⠃⠀⠙⠒⠋⠱⢤⡤⠞⠙⠒⠋⠀⠈⢆⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢗⢀⠃⠁⢐⠸⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣴⡰⣲⡄⠀⣤⡟⣥⡏⠐⢀⠀⠄⠂⣺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢹⠐⣿⠁⣼⡟⠫⣴⠀⢃⠄⠐⠈⡌⠎⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⡜⢳⡆⠀⡖⣿⠀⣞⣀⠢⠉⢐⠒⠠⠁⢀⡂⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⢳⡄⢰⡀⡇⢸⠀⣿⠂⡎⠃⠐⠂⠠⠀⠠⢂⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠻⡄⢳⣼⢸⡄⣸⣆⢣⠁⠀⠀⠄⠀⠄⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠹⡄⠹⣶⠇⠘⣷⡾⡊⠲⠆⢀⠰⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⡄⢿⣷⠀⠘⡿⣵⣬⢁⣂⡲⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡿⣎⠌⢦⠀⠈⢮⠉⢉⠽⠊
⠀⠀⠀⠀⠀⠀⡇⠘⣇⠈⢳⡀⢸⠀⡌
⠀⠀⠀⠀⠀⠀⡇⠀⠻⣆⠀⠙⣯⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠒⠒⠖⠒⠤⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠷⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡰⠋⠑⠀⠀⠀⡀⠂⠀⠀⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⡁⡄⣷⡀⠀⠀⠈⢦⠀⠀⠀⢀⡞⠀⠀⠀⠈⡶⠊⠀⠀⠀⠀⢀⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⣿⣧⠀⠀⠀⠀⢣⠀⠀⡸⠀⠀⠠⠐⠈⠀⠀⠀⠀⡠⠂⠁⠀⠀⣀⡤⠞⠓⠒⠒⠒⡆⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⣧⣿⣿⢧⡀⠀⠀⠀⢳⡖⠉⠚⣅⠀⠀⠀⠀⠀⢀⠚⢄⠀⠀⣠⠞⠁⢣⡀⠀⠀⠀⠈⠙⠢⡈⢢⡁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣏⠁⠘⢷⡄⠀⠀⠀⠱⡀⠀⠘⣦⠄⠀⠀⠀⠂⠀⠀⠑⠴⠁⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⢸⡄⢀⡔⠛⠃⠷⣄⠀⠻⣄⠀⠀⠀⠰⡄⠀⠘⡄⠀⠀⡆⠀⠀⠀⢀⣧⡠⠔⠈⠻⣿⠿⠗⢀⠀⠀⡀⠄⠛⠿
⠀⠀⣠⠒⠉⠁⠙⣇⠬⠷⢀⠀⠀⠈⠳⠤⠈⢂⠀⠀⠀⠘⢄⡰⠃⡏⠈⠁⠂⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⡇⠀⠀⠀⠈⢧⡀⠀⠀⠉⠒⠤⠄⠀⠀⠘⢧⡀⠀⠀⠈⢣⣀⠘⢆⠀⠀⠐⠀⠀⠷⢄⠀⢀⣀⣄⠀⠀⠀⠀⡀
⠀⠀⢣⡀⠀⠀⠀⠎⠙⡇⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠹⡑⡄⠉⠈⠹⠤⠤⠒⡀⠙⣿⣿⣿⣷⡄⠀⠈⠁⠀⢄⣀⡰
⠀⠀⠀⠉⠀⠀⠒⠛⢄⣘⣦⡽⠂⠀⠀⠀⠀⠀⠀⠀⣈⣦⠀⢀⠀⣧⣸⠀⠔⠃⠀⠀⠀⠑⢤⠘⠻⠿⢏⠀⠀⠀⠀⠀⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠄⠊⠑⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠈⠧⠄⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠉⣇⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣍⠀⠀⠀⣿⡈⠀⠀⡀⠀⠀⠀⠀⠀⡀⠆⠀⠔⠈⠀⡇⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡏⠐⢤⣴⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠘⣦⠀⠀⢀⠃⠠⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠋⠉⠁⠀⠈⠙⢻⣿⣿⠆⠀⠰⠂⠈⠀⠄⡀⠀⠁⠐⠠⠊⠀⠔⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⡀⠀⠀⠀⢹⠀⠘⣿⡷⠀⠀⠀⠀⠄⠀⠀⠁⠄⠀⠀⠀⠙⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠠⠁⠀⠀⠀⡆⠀⠀⠡⠀⠀⠀⠁⠂⠀⡔⠀⠀⠀⠀⠀⠀⠀⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢜⠀⠀⠀⣰⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠏⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⣼⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠖⠀⠈⠒⠇⠀⠀⠀⢠⣤⣤⣀⣀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢉⠙⠉⠀⠈⠁⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⢀⠆⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤
⠀⠀⠀⠀⠀⠀⡔⠶⢖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠐⠈⠱⡤⢈⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⢠⣻⣓⢲⣹⡇⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠘⠙⢻⠶⠊⡁⠀⠙⠃⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠄⣿⠡⣤⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠴⠆
⠀⠀⠀⠀⠀⡿⠿⣶⣷⣾⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠿⠜⣿⣧
⠀⠀⠀⠀⠀⠌⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠚⠻⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⢀⠀⠺
⠀⠀⠀⠀⠀⠞⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⣭⣧⣀⠀⣀
⠀⠀⠀⢰⣤⣀⡈⣯⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣖⣐⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⡽⢉
⠀⠀⠀⠀⠉⠙⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣾⣇⣹⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⢤⣶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠙⠋⠉⢉⣿⣷⣴⣿⣦⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢴⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⠁⠉⠉⠢⠀⢀⡐⢀⠀⠀⠀⠀⠀⠀⢠⡟⠘⠛⣿
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠋⠁⠀⠀⠀⠀⠘⠂⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⠆
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⢤⣦⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⣴⣥⠞⠀⠀⡠⢴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠚⠶⡀⠀⠀⠀⠀⠠⢿⣀⠸⣄⣁
⠀⠀⠀⣀⠀⡷⠟⠁⠀⠀⠀⠹⠯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠁⠠⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠈⠳⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡬⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠈⠹⠾⠇
⠀⠀⠀⠀⠀⢻⣿⣶⣤⣀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣇⡀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣮⠁⠀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⡟⠛⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⠟⢋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⠉⠉⠁⠛
⠀⠀⠀⠀⠀⠀⠈⡹⣿⣴⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⣤⣧⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⢰⣥⣤⠆⠈⠙⠂⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⠶⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠘⠀⠜⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠁⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠴⢚⡿⠀⠀⠀⢀⣶⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⢳⡄⠀⠀⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠺⡏⠙⠹⠓⠗⠛⠉⡷⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠇⠀⠀⢀⣠⡴
⠀⣀⡀⠀⠀⠀⠀⠈⢳⡝⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡄⠀⣧⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣾⠤⠶⣾⢕⡠⠶⠚
⢀⣬⡿⣷⣶⡖⠶⠒⠉⠀⠀⠙⡆⠀⠀⠀⠀⢀⡾⠀⡾⠀⠀⢸⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠠⡿⠟⡒⠒
⠀⢬⣭⣻⣯⠶⣠⡤⠦⢤⡀⠀⣷⠀⠀⠀⠀⣼⠃⢸⠇⠀⠀⠈⡷⠶⠶⢶⡞⠀⠀⠀⢹⠀⠀⢻⡄⠀⠀⠀⠀⠀⣸⠃⠀⡴⠛⠉⠉⠉⠉⠙⠛
⠀⠀⠀⠾⠖⠋⠁⠀⠀⠀⣧⠀⢸⡄⠀⠀⢰⡏⠀⢾⠀⠀⠀⠀⢷⠀⠀⣸⠁⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⠀⠀⢠⡏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣇⠀⠀⣿⢄⡀⠘⣆⠀⠀⠀⢸⡄⣰⠃⠀⠀⠀⢀⣿⠀⠀⠀⠸⡆⠀⠀⠀⡞⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⠀⢰⠇⠀⠉⣱⠘⢧⣤⠤⢬⣧⣏⣀⣀⡀⢀⡾⠙⣧⣤⠴⠞⣧⠀⠀⣸⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣇⡏⠀⠀⣰⠏⠀⣎⣵⣤⡴⠷⠾⢤⣀⡿⡾⠁⠀⠘⣇⠀⠀⠸⡆⢠⠏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡿⠀⠀⢠⡏⠀⠀⠀⢈⣆⣀⣀⣀⠀⠈⣹⠇⠀⠀⠀⠘⣆⠀⠀⠙⠞⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠀⠀⣠⡴⠋⠁⠀⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⡞⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢦⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡾⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀⢀⡀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣀⡘⣁⡀⢀⣾⣿⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠖⠾⠟⠀⠀⣠⣾⣿⣿⣿⠟⣿⠿⢿⣿⣿⣧⣌⣉⣩⠿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡎⠉⣩⣤⣔⠀⠈⠀⢸⣿⣿⡟⠉⠀⠀⠀⠀⠈⠿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣿⡇⣿⣿⣩⣽⣦⠑⢠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠦⠀⠀⣨⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣮⣿⣿⠿⠿⣲⣄⠸⣿⣿⣿⡖⣀⡀⠀⢠⣤⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢲⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣶⣩⡽⠛⣋⣵⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⢻⣿⣿⠿⣿⣿⣿⣿⠋⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣿⡿⠋⣿⣿⠋⠵⠚⠉⠁⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠻⠿⠧⠈⠩⠀⠀⢀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣅⠀⡰⠀⠀⢠⣠⣾⣿⣄⣴⠾⢋⠁⣁⣀⠀⠤⠛⣁⢀⢰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣧⣸⣤⣾⣿⣿⣿⢏⣁⠴⠊⠀⢹⡄⠡⠠⢾⣟⢢⣸⣿⠀⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢘⣭⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡿⠉⠂⢀⣐⣢⡶⣾⡇⢸⣿⣨⣿⣿⠿⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⣿⠏⠁⢸⡏⠙⠛⠟⠛⠋⢀⣉⣠⣽⣿⣷⣦⣍⡤⠿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠁⠀⠀⢤⣷⣤⡀⠀⠀⠀⠈⡻⢿⣿⣿⣿⣿⣿⡇⢠⣿⣬⠀⠄⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣭⣶⣾⣾⡇⣤⠀⠈⠋⠁⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⠀⢾⣿⠇⣀⣴⢀⡀⠀⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡛⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⢿⣦⣉⣀⣿⣿⣿⣷⣤⣶⣶⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠒⠠⠘⠟⠀⠀⣸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠹⠿⠿⠿⠿⠒⠾⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡛⠻⠿⢿⡿⠿⠷⠄⠜⠛⠛⣿⣿⣶⡞⠃⠀⠘⣿⠿⣿⣋⣉⠚⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣿⣿⣦⡜⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄⠀⡀⢭⠔⠀⠀⠉⠁⠀⢹⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠻⣿⣿⣿⣿⣿⡀⠀⢀⠴⢤⠄⢀⣴⣋⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠿⢿⣿⣶⣄⣤⠀⢀⣀⣼⣿⣿⡿⠛⠁⣠⢄⠱⣦⣄⣴⡿⢟⣛⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣶⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⣿⣾⡿⢟⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠙⠿⣿⣧⠉⠙⠛⠋⠺⠷⠿⠛⠻⣽⣴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⡀⠤






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠛⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠻⡿⠰⢀⠐⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⣤⣤⣀⣾⠋⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢷⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⣀⣀⣀⣀⣀⣠⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣰⣾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣎⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢡⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁

⠀⠀⢀⠤⡂⠀⠉⠙⡌⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠐⠉⠙⡆
⢀⠔⠁⠀⠈⠓⣄⠀⠸⠀⠀⡜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠈⠙⢗⠢⢌⣒⠒⠁⠀⣀⣀
⡄⠀⠀⠀⠀⠀⠈⣇⠀⡇⡼⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⣚⡉⣉⣥⣴⢾
⡧⢄⣀⠀⠀⠀⠀⢸⠀⣧⣃⡠⠞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡴⣩⠖⠊⠉
⢱⡀⠀⠈⠉⠐⠒⡞⢺⠛⡅⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡞⡴⠁
⠀⠑⢤⣀⠀⣠⠞⠀⡞⢀⡹⠖⠁⠀⠀⠀⠀⣠⠔⠐⠒⢔⠒⠦⢤⡀⠀⠘⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠟
⠀⠀⠀⠀⠉⠉⠒⠋⠉⠉⠀⠀⠀⠀⠀⢠⠎⢀⡉⢦⡀⠈⢂⠀⢡⠈⢣⡀⠘⠢⢝⡒⠶⠤⠤⠴⣒⡪⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡔⠁⢀⡠⢷⠀⢸⠀⠘⠀⢸⢳⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⡠⠃⠀⣀⣄⢸⠀⢠⣀⣸⠼⡇⠀⠀⠀⠀⠀⠀⠀⡠⢚⣅⡢⠾⣿⠷⢦⡑⣄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠸⡇⠀⠁⢀⠾⢄⣀⠈⠉⠉⢀⣀⢴⠇⠀⠀⠀⠀⠀⢠⢊⣴⢷⡏⢨⠞⢄⡜⠃⢼⠸⡆
⠀⠀⠀⣠⠔⠛⢧⡔⠋⠀⠈⢟⠦⡀⠀⠱⣄⠀⢸⠤⣀⠈⠉⠉⢉⣁⣠⠞⠀⠀⠀⠀⠀⠠⢡⣳⠗⢅⡜⠑⠦⣎⠈⡰⢺⠀⡇
⠀⠀⡌⠀⠀⠀⢠⡀⠀⠀⠀⡘⠲⣝⣆⠀⠈⠑⠮⢷⣤⣬⣭⡭⠽⠛⠁⠀⠀⠀⠀⠀⢠⢣⡿⠋⡦⡂⢈⠖⢄⡠⠋⡲⡞⢰⡇
⠀⡜⣸⠦⠤⡖⠁⠙⠦⡠⠴⣄⠀⣸⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⢉⠶⣀⡼⠓⣤⡊⢩⠾⡕⡡⢣⠁
⠀⣏⠀⠀⠀⠱⣄⣀⡜⠀⠀⢠⠋⠈⢦⡇⠀⠀⠀⠀⠀⢀⠤⠀⠲⠤⡀⠀⠀⠀⠀⠀⡇⡧⠉⣦⡎⠑⠴⣁⡜⡳⢊⠔⡱⠃
⠀⠘⣄⢀⣀⠊⠀⠀⠑⢢⠖⠣⣀⠀⡼⠁⠀⠀⠀⠀⢠⠊⠐⠢⡀⠀⢈⣆⠀⠀⠀⢐⢠⡘⠶⣁⣨⡳⠤⢛⡩⢔⡡⠊
⠀⠀⠈⠳⢄⣇⠀⢀⠠⠯⣄⣰⠧⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠆⠊⢸⠀⠀⠀⠌⣬⠶⢋⡠⠴⡒⠉⠁⠂⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣠⠔⠋⢉⡷⠃⠀⣀⡌⢈⡵⢊⠕⠊⠁⠀⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠒⠲⢤⠤⣀⡀⠀⠀⠈⠉⠉⠁⠀⢀⠾⠉⢍⢫⠈⠀⠀⠀⠀⢸⡀⣀⣸
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣀⣠⢤⠴⠤⢦⠈⡍⡗⠀⠀⠀⠀⠀⡰⡉⢦⢱⢸⠎⠀⠀⠀⠀⢀⣼⣖⣗⣮⣄
⠀⠀⠀⠀⢀⠜⢄⠀⡠⠴⠎⠙⠉⠀⠀⠀⠀⠀⠇⢸⠃⠀⠀⠀⠀⡾⠤⡙⡼⡤⠃⠀⠀⠀⠀⠀⣾⢏⡏⢿⢙⢿⣄
⠀⠀⠀⠀⠊⠡⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠑⢄⣈⡷⠁⠀⠀⠀⠀⢀⣎⡟⣹⠓⢼⠉⣍⣷⢆
⠀⠀⠀⠀⠀⠀⢱⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠾⢁⣼⠑⣾⠁⣤⢹⠛⠧⡀
⠀⠀⠀⠈⠢⢄⣼⣠⠁⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠘⣅⠘⡹⠃⠫⣀⣨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠉⠀⠀⢀⡼⡃
⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣀⠀⢀⣴⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢢
⠀⠀⠀⢀⢠⣾⣿⠿⠛⠋⠉⠚⠉⢀⣀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢂
⠀⠀⢀⢲⠟⠋⠀⠀⠐⠲⠶⠛⠛⠛⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⣀⠔⠉⠁⠒⡀
⠸⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠛⠛⠛⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠿⢄⠂⠉⠀⠀⠀⠀⣠⡴⠟⢱
⢀⡧⢄⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡄⠈⡿⠟⠛⠛⢛⣋⣁⣠⣤⠼⠄
⢸⠁⠀⠀⠀⠀⠀⠈⠉⠁⣠⣌⠐⠒⠂⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠻⠿⠛⠉⠑⠒⠚⠉⠉⠉⠉⠉⠉⠀⠀⢀⠼⢦⣀
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢐⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⡤⠶⠶⠒⠛⠉⠉⠂⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠘⢟⠶⣕⣀⠤⠄⠒⠤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⠾⡻
⡇⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⢠⣶⡛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⣷⡆⠩⠝⣛⠒⠒⠒⠶⠶⠶⠶⠖⠒⢚⣛⠩⠍⢒⠋
⢹⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣤⠀⠈⡍⠙⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢧⠈⠀⠀⠐⠂⠀⠠⠤⠤⠄⠀⠐⠒⠀⠈⠁⡸
⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠄⠀⠐⠀⠒⠒⠒⠒⠒⠒⠀⠀⠄⡜⠀⠸⡄⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠀⠐⠒⠂⠀⢀⠀⠀⠀⠐⠒⠀⢨⣇⠀⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠉⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠜⠇⡆⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⢸⠄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠇⠀⠀⠀⢱
⠀⠀⠀⢢⢄⠀⠀⠀⠀⠀⠀⠀⢀⠢⠁⠘⣇⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣜⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠑⢕⡠⣀⠀⢀⠠⡐⠕⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣧⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠠⠊⠁⠀⠐⠀⠀⠁⢂⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠸⠧⠀⠀⠀⠘⠿⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⣀⣀⠀⠀⠀⠄⢃⠁
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⠁⠀⠒⠀⠀⠀⠒⠐⠈⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨
⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣤⣤⣤⣤⣤⣬⣶⣶⣶⣶⣶⣶⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣶⣶⣶⣶⣾⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠑⠂⠁⠀⠈⡰⢖⡁⢈⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠐⠁⠀⠠⠀⠀⠐⠉⠆⠠⠂⠀⠰⠡⠜⠀⠤⠁⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢃⠀⠱⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⡄
⠀⠀⠂⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡸⢠⠁⠀⠀⠀⠀⠀⠀⠀⢰⠐⠲⠶⠳⠃
⠀⠀⠒⢒⣒⣛⣒⠒⠦⢤⣀⠀⠀⠀⠐⢄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⡀
⠈⠀⠚⠒⠤⠤⠤⠤⠬⠟⠰⠀⠀⠀⠀⠀⠉⢃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠞⠤⠤⠘
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠌⠆⠀⠀⠀⠓⠄⣀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⠤⠔⠂⠠⠤⠤⠀⣀⡠⢀⠀⠀⠀⡇⠀⡀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⡡⠒⠒⠺⠭⢉⠁⠒⢌⡂⡅⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠉⠉⠉⠉⠉⠂⠜⠐⡌⠀⠀⡃⠀⠇⠄⢲⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡜⠀⠀⠀⠀⡄⡀⢒⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⡱⠀⠰⠓⢀⠀⠀⢀⠀⢃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠔⠣⣀⠠⢣⠀⠀⡀⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⠀⣠⣉⡉⠀⠀⡇⠀⠈⡀⠀⡀⢀⠀⢂
⠀⠀⠑⠂⠤⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡅⠠⣘⠏⠄⢘⠀⠀⠑⠦⢤⣀⣀⠤⠎⠀⠀⠌⡇⠀⡇⠆⠀⠀⠀⢀⣀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠉⠀⠀⠑⠓⠂⠠⠤⠤⠀⠀⠀⠀⠚⠉⠀⠀⠈⠢⠄⢀⣀⣀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠠⠤⠤⢬⣆⠀⠀⠀⠀⠀⢸⠳⠤⠤⠤⠤⠞⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⠁⠐⠒⠂⠈⠱⢳⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⣾⣑⣿⣿⣟⡫⠉⠚⣷
⠀⠀⠀⠀⠤⠀⠀⠀⠠⠤⠄⣀⠀⠀⡟⠢⠄⣀⣀⣀⡀⠤⢺⠀⠀⠀⢠⠇⡀⠀⠀⣀⠀⠀⢻⡀⠀⠀⠀⢰⠉⠓⠋⠉⠭⠭⠭⡽⠋
⡐⢁⠠⠄⠀⠀⠀⠀⠀⠠⠄⡀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠣⠀⠀⠀⠀⢀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠢
⠏⡓⠠⠄⠀⠀⠀⠀⠠⠤⢔⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠌⢰
⠀⣎⠁⠐⠒⠒⠒⠒⠒⠈⢁⡞⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠢⣤⣀⣀⣀⠤⠊⠀⠀⠀⠀⢸⠀⠀⠀⡀⠄⠂⠁⡠⠊
⠀⠈⠛⠲⠄⣀⣀⣀⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⢀⠔⠈⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⢠⠊
⠀⠀⠀⡀⠄⠸⠐⠐⠤⡀⠀⠀⠀⠀⢘⠢⢀⡀⠀⢀⣀⠠⢺⠀⠀⠀⠀⠀⢀⠀⡸⢠⠠⠄⡀⠀⠀⠀⠀⠀⢁⡀⠀⡇⠀⠀⠀⠀⡠
⠀⠀⠀⠡⢀⣀⣀⡀⠔⠃⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠠⠴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠜⠀⠀⠀⠀⠀⠀⠡⠁⠘⠒⠐⡀⠥⠃

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

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠉⠒⠤⢀⡤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⠀⠠⠐⠈⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢀⣥⣶⠤⣤⣄⡀⠀⠀⠀⣀⣤⡴⢶⣤⣅⠀⢄⡮
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⣶⠟⠁⠀⠀⠀⠈⠻⣄⢀⡾⠋⠀⠀⠀⠀⠙⢷⡁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⣿⠿⠿⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⠀⠀⠀⠀⢸⣷⠾⠿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢘⣿⡀⠀⠀⢴⣰⡆⢀⣿⣿⣆⢠⣎⣶⠀⠀⠀⣼⠟⢦
⠀⠀⠀⢠⡄⣰⠠⢾⣁⡐⠁⠈⠻⢦⣤⣬⣽⡷⠋⠀⠀⠉⢳⣯⣭⣤⣴⠾⠋⠢⠀⢳⣤⣀⢀
⠀⠀⠘⡏⠓⠨⠠⢒⠠⠩⢅⡂⠤⡀⠀⠀⠀⠸⠢⡀⠀⡠⠒⠀⠀⠀⠀⢀⠠⠤⣓⠈⠥⣞⣻⢶⣤
⠀⢀⡯⠓⠂⠁⠉⠂⠈⠁⠂⠌⡑⠢⡑⢦⡀⠀⠑⠈⠈⠐⠀⠀⡠⢔⡨⠔⣊⠭⠔⢂⣽⠉⠀⠙⠺⢄
⠀⠀⠀⠀⢀⣠⣴⣉⡑⠢⠤⣀⡈⠑⠨⣦⡙⢄⠀⠀⠀⠀⡴⡪⢒⡡⠒⣉⡤⠖⣋⡥⠞⡷⠄⡀⠀⠀⠈
⡦⠐⠒⠉⠀⠀⢀⠆⠉⠙⠲⠤⣍⣓⠲⠬⣑⣄⣳⡀⣠⠞⡩⣐⡧⡙⢯⡥⠖⠋⠁⠀⢸⡀⠀⠀⠙⠒⠠
⣇⣀⡀⠤⠴⡖⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⢹⠓⠒⠒⠻⡏⡕⠒⠹⠉⠁⠀⠀⠀⠀⠀⢈⡳⠦⢄⣀⡀
⠘⡀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠒⠒⠒⠒⡇⢷⠀⠀⠀⠀⠀⣤⣦⠀⢰⣿⠢⣀⠀⠀⡨
⠀⠈⢹⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠉⠉⠉⠉⡇⢸⠀⣸⣷⣄⠀⢿⣿⡷⠈⠿⠿⠃⡟⢳
⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡇⢸⡀⠿⠛⠛⠀⠈⠉⠁⠀⠀⠀⠀⢳⢸
⠀⠀⠀⡟⠷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣒⡭⠜
⠀⠀⠀⠈⠉⠳⣖⢭⣝⣒⡲⠤⣄⣀⡀⠀⢸⢸⣄⣈⣉⣁⣽⠸⡇⠀⢀⣀⡤⠴⣒⡭⢵⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠓⣭⣢⣌⡉⠒⠲⠭⢝⣛⣘⡇⠀⠀⠀⢸⠀⢓⣛⠭⠒⣊⢝⣫⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣎⠀⣩⡽⠿⢷⡶⢤⣤⣤⣬⣷⣦⣤⣴⣾⣯⣥⠴⣶⡿⠿⣥⡂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡃⠉⢰⠟⢄⡠⠃⠀⠀⠀⠀⠀⠀⠣⣀⡼⢻⠈⠁⡳⠈⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡄⣿⡀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣬⡻⠟⠋⠁⡱⠒⡑⠊⣁⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡠⠚⣡⣾⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠰⢯⣟⡣⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⣠⡅⣰⠟⠋⠀⢀⣤⠀⠈⣹⠶⡀⠀⠀⠀⠀⢈⡎⠱⡄⠉⡿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢡⡴⠀⠀⠋⢀⠀⠀⢄⢰⠜⢆⠀⠀⠀⢀⣷⢠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡘⠇⠀⠀⠀⠙⠁⠀⣤⣉⠆⠈⣇⠀⢀⣾⣷⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⡄⡰⢊⡁⠀⣀⡠⠤⠀⣿⣠⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠁⠁⠸⣶⣶⣶⣾⠏⢀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡐⢄⠈⠛⠛⢉⢄⣾⣿⣿⣿⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣦⣥⡒⢂⣵⣿⣿⣿⣿⣿⢵⣾⢫⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⡇⠈⠑⠼⡏⠙⠉⠙⢟⠛⠛⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠁⢃⡀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠛⠿⠿⣿⣿⣿⣶⠶⢤⣤⣀⠀⠀⠀⠒⠒⠰⠀⠓⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⠇⠀⠈⠸⣩⢻⢦⡀⠀⣠⡼⢤⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣼⡀⢀⢃⢇⠀⠄⢋⢞⠃⢀⠀⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⢩⠇⡸⠌⠈⡄⣴⠟⡌⣄⣴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡏⠈⠊⡤⢇⣄⣠⠟⢁⣤⡾⡿⡱⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢰⢰⠀⢡⣠⣟⡥⢶⣏⠁⠁⠁⠃⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⡆⠆⢾⣠⡾⠛⠁⠀⠀⠙⣶⡰⡆⠀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⡞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⣥⣼⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠻⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⣀⣴⣾⣶⣦⣀⠀⠀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢿⣿⣿⣿⣿⣿⣿⡿⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡡⠐⠀⢱⠂⠂⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⢂⡊⠀⠐⡱⠄⠄⡪⠊⠡⢁
⠀⠀⠀⠀⠀⠀⢠⡀⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⢠⢅⣄⢨⠐⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠀⠀⠤⠤⠤⠤⠤⠤⠔⠖⢶⠖⠛⠉⢸⠢⡂⠀⡐⡈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⠀⠔⡉⠈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠈⠁
⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠒⠒⠒⠂⡈⠐⠦⢄⡀⠀⣀⠤⠒⠂⠀⠐⠢⡄⡇
⠀⠀⠀⠀⠀⠀⠀⡜⡀⠀⠀⠄⠀⠀⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠃⠀⠰⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠁⠀⠀⠀⡠⠘⠀⢠⠤⠠⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠨⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⡀⠁⡀⠀⠲⡄⠀⠀⠀⠀⠀⠀⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡑⠬⣁⣒⠒⠒⠒⢒⣊⠭⠔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⡀⠈⠉⠉⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣀⠤⣤⣤⣀⠀⠀⠀⠀⢀⡠⠤⠤⣀⣀⠠⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⣾⠟⠁⠀⠀⠀⠙⠧⠀⢀⠌⠁⠀⠀⠀⠈⠻⣶⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠿⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢃⡌⠀⠀⠀⠀⠀⠀⠀⢹⣷⡾⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠊⢹⣇⠀⠀⠀⣔⣲⡄⢀⡦⢧⠀⢠⣲⣦⠀⠀⠀⣼⠗⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡦⠤⣞⠁⡔⠁⠙⢷⣤⣀⣙⣿⡅⠀⠀⠀⠁⢾⣿⣉⣤⣴⡾⠋⢄⠈⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠰⠚⠃⠭⢒⠠⠭⢙⡒⠤⢀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠆⠉⠉⠉⠀⢀⡀⠤⠒⣊⠩⠝⣻⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠌⠁⠒⠤⣁⠢⢍⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡢⠕⣂⡩⠅⢒⡞⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠓⠲⠤⣀⠀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⣡⠴⢚⣩⠵⠆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡟⠫⠭⠵⢺⢂⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈
⠀⠀⠀⠀⢋⠁⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡷⠠⠤⠤⢼⠀⡇⠀⠀⠀⠀⢀⣤⣄⠀⢰⡶⢄⠀⠀⠉⣱⠃
⠀⠀⠀⠀⠀⠐⢺⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⠒⠒⠒⠺⠀⣷⠀⣾⣄⠀⠘⣿⣿⡆⠸⣷⡾⠏⡖⣦⠁
⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⢹⠠⣿⠻⠇⠀⠛⠋⠁⠀⠀⠀⠀⠁⢿
⠀⠀⠀⠀⠀⠀⢸⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⣃⠈
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠭⣓⠀⠤⠄⠀⠀⠀⠀⠀⠃⢨⡀⠀⠀⠈⡇⢸⠀⠀⠀⠀⣀⡤⢴⡀⠩⠕⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡠⣍⠀⠰⠤⢄⣐⡲⠆⢠⠁⠀⠀⠉⡇⠸⠦⢖⣚⠥⢀⡰⣋⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠙⣟⣢⣶⣤⣤⣀⣉⣉⣚⣤⣀⣀⣠⣷⣖⣊⣭⣴⣾⣷⣪⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠙⠓⠂⠙⠗⠉⠙⠋⠉⠉⠉⠉⠉⠉⠋⠉⠸⠋⠐⠂⠏⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⣭⣷⣶⣿⣛⣟⡻⣿⣷⣾⣭⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣾⣿⣿⣿⣿⢿⣿⣿⣧⡘⢿⣿⡏⠹⣷⣾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠻⠿⠿⣿⣯⣴⣿⣿⣿⣿⣿⣶⣮⣍⣀⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠿⠿⠧⠀⠀⠀⠀⠤⠬⠭⡙⢿⣿⣇⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⡿⢁⣤⣤⡀⢶⡀⠀⠀⢀⣤⣀⡀⠀⢿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢁⣹⣿⣿⡇⠘⠋⠀⠀⠀⠁⠀⠀⠉⠀⠈⠉⠀⢸⣿⣿⣄⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⢿⠀⠀⠀⠀⠀⢾⣇⠰⠄⢀⠀⠀⠀⠀⣾⣿⣿⣿⢾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⡇⠀⠀⢀⣤⠤⠀⠶⠦⣌⢳⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠻⢿⠿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⡾⠋⠀⠀⣸⣿⣿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣴⣞⠀⠀⣠⣿⣿⣿⣆⠀⠀⠈⣉⣉⡋⠍⠀⠀⠀⢠⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⠾⠟⠈⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣷⣤⣴⣤⣤⣤⣿⣿⣿⡟⠻⣿⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠃⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⢈⢷⣹⣿⣿⡏⠘⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠙⢿⣿⣿⣿⠟⠛⠁⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢀⣦⡸⡞⣇⢻⣿⣦⡀⠑⠺⢻⣆⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⢸⣿⢿⠟⠀⠀⣀⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣾⣿⣿⣿⣹⡜⣿⣿⣿⣷⣦⣄⡙⠳⡄⠀⠀⢀⣼⠟⠁⢀⣠⣶⣿⡿⠀⠀⠀⣼⣿⣵⠏⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣧⢻⡏⢻⣿⣿⢿⣿⣿⣷⣌⠢⣠⣞⣡⣶⣾⣿⠛⡉⡁⠀⠀⣇⣼⣿⣿⡏⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠃⠈⠋⠛⠁⠂⢻⠛⣿⣷⣽⣏⠋⠉⠁⠀⠈⠀⡐⠀⣆⣿⣿⣿⡾⠀⣤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠈⠀⠀⠐⠀⠈⠃⠈⠃⠘⠛⠀⠀⠀⠀⠀⠘⠁⠀⠛⠛⠛⠛⠁⠘⠙⠋⠐⠛

⠀⠀⠀⠀⠀⠀⢴⡷⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠉⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣤⣤⡃⠮⡀⠀⠒⠀⠀⠀⠀⠠⡀⠐⠲⠞⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⢸⢀⣩⣾⡇⠠⠂⠀⠀⠀⠀⠀⢈⠀⠀⣸⡿⠛⠉⢘
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⡈⣀⣤⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣨⣥⠃⣉⣀⠀⠀⠀⠀⠀⠀⠀⠸⣥⢶⣿⡇⠀⢀⣼⣦
⠀⠀⢹⣷⡀⠀⣀⡀⠔⠳⠾⢿⣕⠾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠛⠋⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠛⠉
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡦⠀⠀⢹⣆⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣆⠦⣀⡰⢿⡃⠀⠀⠈⢿⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⣸⣧⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⡟⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤⠠⠤⠤⠦⠀⠤⠀⢺⠶⠘⠁⠄⢀
⠀⠀⠀⠀⢀⣀⣀⣾⣮⣿⣦⣶⣿⠃⠀⠀⠀⠀⡾⠛⠀⠀⠀⠀⠀⠀⠀⣄⠠⠂⠀⣀⣤⣖⡿⠁⠀⠀⠀⠀⠀⠐⠀⠀⢰⣇⣡⡀
⢀⣠⣀⢠⠟⠃⠀⠉⠙⠛⣿⣿⡏⠀⠀⠠⣤⡄⢹⣶⡶⠦⠀⢀⡀⡀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⡃⠀⠀⠜⠁
⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠈⣙⣻⣭⢦⡤⢈⣛⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠗
⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⢻⡟⠀⠀⠀⠀⠄⠀⠀⠛⠉⠙⠛⠻⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠃
⠀⠀⠀⠀⠰⠋⠛⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚
⠀⠀⠀⠀⠀⢠⣀⡭⠇⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⣤⡌
⠀⠀⠀⠀⠀⠠⢿⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣹⣷⣦
⠀⠀⠀⠀⠀⠀⠘⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⢿⡿⠷⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣿⢟⣧
⠀⠀⠀⠀⠀⠀⠀⢶⣀⣀⠀⠀⠀⠀⢠⣴⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣆⡉⠉⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⣰⣿⠿⠋⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠛⠿⠟⠀⠉⠁
⣄⠀⠂⠀⠀⠀⠀⠀⠈⠷⠀⠀⢠⣿⡟⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄
⠓⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿
⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣥⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⠀⠀⣰⣾⠤⠀⠀⠀⠀⡠⠄
⠀⠈⢄⠀⢀⣀⢀⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⣀⠔⠉
⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⢀⠀⠀⠡⣀⠀⠀⠀⠔⠀⠀⠠⢂⠴⠊⠀⠀⠀⣠⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⡠⠈⠀⢀⠀⠀⠉⠈⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠰⠛⠂⠀⢴⣢⣄⠀⠀⠉⠁⠀⠈⠀⠀⠀⠙⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠁⠀⠀⠀⠈⢪⠘⣆⠀⠀⠀⠀⣦⠀⠀⠀⠠⠀⠀⢀⠔⠉⠀⠀⠀⠞⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣺⠟⠓⠲⡀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⡀
⠀⠀⠀⠐⠤⣤⠠⠔⠀⠀⠑⠤⠀⠀⢠⠏⠓⣾⠇⠀⢇⠀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⡞⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢜⠁⠀⣠⠞⠀⠀⠀⠀⠀⡰⠀⠐⠂⠀⠀⠀⠀⠀⠃⠀⢠⡞⠀⠀⠀⠀⢐
⠀⠀⠀⡯⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠊⠀⠀⢠⣼⡦⠀⠀⢃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠐⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠈⠲⢄⡀⠈⠀⠀⠀⣀
⠀⢸⡀⠀⠀⠀⠀⣠⣾⡀⣀⣀⠀⠀⠀⠀⠈⠁⠘⠉⠉⠀⠀⠀⠀⠴⠠⢰⠄⠀⠀⠀⡠⠀⢀⡴⠶⠀⠀⠒⠁⠀⢠⠀⡄
⠀⠀⠳⢤⠀⠐⠛⠛⠻⠻⣛⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⢀⡀⠀⠀⡐⠂⠀⢀⣠⠤⢤⠀⢀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠣⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡈⠁⠀⢀⣿⠇⠰⣿⣿⡆⠃⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣶⣤⠄⡘⠁⠀⠀⠈⡉⣄⣀⠉⠩⣠⡤⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠹⢿⣿⠂⡴⠿⠁⠀⠀⠀⡇
⠀⠀⠁⠀⣀⠀⢀⠀⠀⡀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⡀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠚⠁⠀⠀⠀⠀⠠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡠⠖⠋⠉⠈⠉⠒⢄⠀⠀⠀⣠⠔⠋⠉⠉⠉⠒⢤⠀⠀⠀⢀⠔⠚⠉⠁⠉⠓⢤⡀⠀⠀⢠⠖⠉⠒⠢⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⡰⠁⠘⢡⡄⠀⠀⠀⠀⠱⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⢰⠁⠀⠀⠀⠀⠀⠑⢦
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡇⠴⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢣⡀⢿⠧⠀⠀⠀⠀⠀⡼⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠸⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠑⢄⠀⠀⠂⠀⠀⣀⠇
⠀⠀⠀⠑⠤⣀⣀⣀⣀⡤⠊⠀⠀⠀⠙⠦⣀⣀⣀⣀⡠⠚⠁⠀⠀⠈⠢⣀⣀⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠙⠢⠤⠠⠔⠁
⠀⠀⢀⡀⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡤⠄⣀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⣀
⠀⠀⡇⠀⠀⣠⠄⠉⠲⢄⠀⠀⠀⢀⣴⠁⢀⣴⣶⣄⠀⢱⣄⠀⢀⡔⠋⠀⠀⠀⠀⠀⠙⢆⠀⠀⡴⠋⠀⠀⠀⠀⡈⠙⢆
⠀⠀⢧⠀⠀⠀⠑⢕⠄⠀⠱⡀⠀⣾⠃⠀⠈⠿⠿⠏⠀⠀⠹⡄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠁⠀⠄⠀⢠⠀⡀⠂⠈⡆
⠀⠀⠈⢆⠀⠀⠀⠀⠈⡦⠀⢱⠀⠇⢠⣤⣄⠀⠀⠀⣠⣤⢀⠇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠐⠑⠁⠀⠇⠈⠌⠀⢂⡇
⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⢘⠀⠈⢾⣿⣿⠆⠀⠐⢿⣿⠏⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⠞⠀⠈⠳⡀⠀⠀⠀⡐⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠀⠀⠀⠉⠒⠢⠤⠔⠊⠁⠀⠀⠀⠀⠉⠒⠶⠤⠔⠚⠁⠀⠀⠀⠀⠉⠓⠲⠦⠖⠚⠁
⠀⠀⠀⢀⠴⠂⠉⠉⠑⠢⣄⠀⠀⠀⢀⡤⢆⣉⠉⠓⠢⣄⠀⠀⠀⢀⡴⠒⠻⠉⠓⠲⢄⠀⠀⠀⠀⠀⠀⡐⠳⢤
⠀⠀⡰⣡⡶⡻⣶⡄⠀⠀⠈⢣⠀⠰⠃⠀⠀⠀⠀⠀⠀⠈⢣⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢰⠄⠀⠀⠙⢄⡀
⠀⠀⡃⣿⠰⢡⣾⡇⠀⠀⠀⠈⠃⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣿⣦⡀⠀⠀⠀⠑⣄
⠀⠀⢣⠈⠛⠟⠋⠀⠀⠀⠀⣰⠁⢣⠀⠀⢀⠀⠁⠀⠀⠀⣰⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⢴⣿⣿⣿⣿⣦⣄⠤⠔⠊
⠀⠀⠀⠳⢄⡀⠀⠀⠀⣀⠔⠁⠀⠀⠑⢄⡁⠀⠀⣀⣀⠔⠁⠀⠀⠑⢤⣀⠀⠀⠀⣠⠔⠁⠀⢀⠀⠙⡿⠛⠉
⠀⠀⠀⠀⠀⣉⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⡀⠀⠀⠀⠀⠁⠈⢀⣀⣀⣀⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠢⡀⠀⠀⡴⠋⠀⠘⣄⠀⠈⠲⡄⠀⠀⡠⠊⠁⠀⠀⠀⠈⠓⡄⠀⠀⡠⠊⠁⠀⠀⠀⠈⠑⣄
⠀⠀⡞⢰⡷⠀⠀⠀⠐⣷⠆⢹⠀⡜⠀⠀⠀⠀⠈⠱⢄⡀⢘⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⠒⠠⣀⠀⠀⠀⠀⠈⠉⠇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⣄⠀⠀⣠⣀⠀⠀⢀⠎⠀⠘⣄⠀⠈⠳⡄⠀⠀⢀⠜⠀⠘⢄⠀⠀⠀⠀⠀⠀⢀⡜⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠈⠑⠶⠬⠥⠤⠚⠁⠀⠀⠀⠈⠑⠢⠄⠼⠤⠒⠁⠀⠀⠀⠀⠑⠢⠤⠤⠤⠒⠉⠀⠀⠀⠀⠑⠢⠤⠀⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠀⠀⢸⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡏⠀⠀⠀⠀⠀⡿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣀⠀⢰⠛⢦⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠶⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠇⢀⡴⠛⠁
⠀⠀⠀⠀⠀⡏⠉⠳⣾⠀⢸⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡴⠶⠦⣄⡀⠀⠀⠸⠶⠋
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣀⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠈⣇
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⡴⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡴⠋⠀⠀⢹
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⢰⣄⣀⡸⠁⠈⠒⠀⠚⠁⠈⠑⠦⠴⠈⠳⢄⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢀⡴⠒⠒⠦⡀⠀⠀⠀⠀⠘⡆⢀⡤⠚⠛⢤⡘⡇⠀⠀⠀⠀⠸⠧⠶⠶⠒⠛⠋⠉
⡏⠀⠀⠦⠼⠂⠀⠀⠀⠢⡄⠀⠐⣦⣤⠜⠀⠀⡎⠀⣠⣤⡀⠹⠀⠀⠀⠀⠀⢹⡏⠀⣶⣶⠀⢷⡇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢁⠀⠀⠀⠀⢧⠀⠙⠿⠃⢠⠇⠀⠀⠀⠀⠈⣧⡀⠙⠋⢀⡿⡇
⢻⡀⠀⢀⠀⠀⢠⠞⠉⠀⠈⠦⠤⠎⠀⠀⠀⠀⠈⠳⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⣧⠉⠒⠒⠉⠀⢹⠀⠀⠀⠀⠠⣶⠒⠒⠲⠶⠤⢤
⠈⣧⠀⠀⠁⠀⡇⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣸
⠀⠈⢧⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠇
⠀⠀⠀⠙⢦⣀⠀⠙⠓⢲⡆⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏
⠀⠀⠀⠀⠀⠉⠛⢦⡄⢸⠇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⣯⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣄⣀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢀⣤⠤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢑⡞⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣴⠋⠀⢰⠋⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡾⢄⠀⠀⠀⢠⠞⠁
⠀⠀⢰⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠜⠀⠀⢠⠏
⠀⠀⠀⢷⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠘⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢠⡞⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠑⢄⡀⠀⢀⡴⣏⠀⠀⠈⠙⠳⢤⣄⣀⣠⡴⠟
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⣢⠞⠀⠘⡆
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣾⣁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⢀⣠⠞⠁⠀⠈⠙⠶⣄⣸⡄

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠿⠶⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡶⢶⣤⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠹⣧⡀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠈⢷⣄⠀⣀⣀⡀⠉⠛⠛⠛⢋⣠⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠙⠛⠛⠛⠛⠛⠻⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠿⠾⠶⠶⠾⠂⠾⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠶⣦⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠹⣇⠀⠀⣠⣤⣤⣤⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⢷⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠙⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠫⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠋⠁⠀⠀⠀⣀⣠⣄⠀⠀⠀⠸⣇⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣴⠶⠛⠋⠁⠹⣦⠀⠀⠀⠹⠷⠾⠛⠛⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⣇⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⣷⠶⠶⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡴⠶⠿⠃




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⣻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣷⣴⣿⣿⣿⣿⡿⢿⣷⣄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣾⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⣨⣿⣿⣿⣿⣿⣧⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡤⢾⣿⣿⣿⡟⠉⠉⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠝⢀⣬⣷⣿⣿⠃⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⣿⠗⣄⣠⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⣶⠋⠁⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣧⣄⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⠀⠀⠀⠀⠀⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠉⠙⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣡⠿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠉⠙⠳⣄⠀⠀⠉⢽⣒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣾⣣⡼⠖⠋⠉⢑⡜⠂⠀⠀⠀⠉⠉⡿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢙⣲⣤⠤⠤⠤⣿⠄⠀⣀⣀⠞⠁⠀⠀⠀⢀⡀⠀⢧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠘⠄⠀⠁⠀⠀⠘⠉⠉⠁⠉⠁⠀⠀⠀⣠⣏⠏⠁⠀⣁⡤⣤⣄⠹⡄⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⢛⡶⠋⠀⠀⣀⣀⣉⣁⣠⠼⠁⠀⣠⠀⠀⣦⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠉⠒⠦⠤⠤⠤⠤⠴⠒⠋⠉⠀⠘⢉⡴⠚⠑⠺⣄⠀⠀⠈⠑⠢⠤⠴⢻⣀⣠⠿⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⣀⣀⣀⣀⣠⠤⠤⠒⠚⠙⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡖⠒⢜⣯⣍⣠⣟⠔⠊⣉⠆⠀⠀⠀⠀⠀⠀⠀⣠⣞
⠀⠀⠀⠀⢀⣴⣾⠏⠁⠉⠹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠸⣉⣱⢇⡠⠤⣽⠏⠇⠠⢐⠄⠁⠀⠀⠀⠈⣦⡠⢾⡿⢿
⢠⠞⡑⠠⡟⠋⠑⣄⣀⣀⡠⠋⠙⠻⣆⠀⠀⣀⠤⡄⠀⢉⣒⣊⣀⣴⠃⠀⠢⢈⡁⠔⠁⠀⠀⠀⠀⣧⢠⠼⠀⠘⠓⡄
⡄⠀⠇⣶⡅⠀⢠⣿⣿⣿⣇⠀⠀⠀⣻⡀⢈⡟⢠⢞⣆⣸⡄⠀⠀⠈⠙⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⢻⠈⢆⣠⠤⠚⠁
⠃⠀⠀⢻⡟⠀⠙⢿⣿⠿⠛⠒⢤⣴⣿⠁⠈⠻⡈⢧⠚⢇⣻⣄⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠚⠛⠦⡄⢡⣊⠙⢶⡄⠀⠀⢄
⠀⠀⠀⠈⢅⠀⠀⠀⡇⠀⠀⠀⢰⣿⠃⠀⠀⠸⢵⡌⠁⠛⠁⠈⠳⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⢺⠉⣇⠀⢣⠀⠈⡆⠱⠀⠀⠑
⠀⠀⠀⠀⠀⠑⠲⠾⢿⣶⡶⠖⠋⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠒⠊⠁⠀⠱⣄⠀⠀⠀⠀⢀⣴⣿⣁⡼⢾⡽⣇⢈⡿⠀⠁⠀⠄⠘⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⠤⠖⠉⠀⠀⠀⠀⠈⠫⣈⡼⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢠⠀⡄⢀⠀⡄⢀⠀⡄⠀⡀⠀⡀⠀⡀⢀⠀⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡿⠀⠀⡆⠀⠀⠀⠤⠤⠤⠄⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣠⣤⠴⠒⠋⠉⢁⣀⠤⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣄⣀⠀⠀⢀⣉⠉⠙⠳⢦⣄
⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⣶⡋⠁⠀⠀⠀⠀⠀⠀⢴⡄⠀⠠⠤⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠶⠶⠦⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠁⢀⣀⣀⣤⣴⠞⠋⡀
⠀⢠⣭⠿⣿⠷⠦⠤⢤⣤⣤⣤⣄⣠⣤⣄⠀⢀⣀⣀⣀⣀⣠⣀⣤⠤⠤⠤⠴⠖⠒⠚⠋⠉⠻⠋⠁
⠀⠀⢀⡆⠉⠙⠓⠒⠒⠠⠴⠶⠶⡤⠄⠀⠀⠴⠲⠐⠀⠀⠀⠀⠤⠖⠠⠀⠀⠀⠉⠀⠀⣀⣀⣤⡤⠴⡖⠉
⠀⠀⠈⠇⠐⠒⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡴⠶⠶⠞⠛⠋⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠃⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⠀⢸⠇
⠀⠀⠀⠀⢿⡔⠀⠁⠀⠀⢀⠤⠤⠤⠄⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁
⠀⠀⠀⠀⢹⡟⠦⢤⠀⢀⡎⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠉⠐⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠉⠀⠀⠀⣐⠶⠖⠷⠦⣤⢄⣀⣀⣀⣠⣤⣤⣤⣤⣤⡔⠚⠒⠉⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⡀⠈⠀⢀⡴⠋⠁⠀⠀⠤⡄⠀⠉⠉⠲⢄⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⢻⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠊⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⣧⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⠁⠀⢸⡀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠂⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠤⠐⠂⠉⣁⣤⠌⠒⠒⠲⠖⠛⠁⠀⠀⠀⠐⠀⠀⠄⡁⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⡀⠀⠘⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⣠⠟⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠛⠁
⠀⠀⠀⠐⢧⣄⣀⣐⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠳⠶⠶⠶⠖⠒⠒⠊⠋⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠄

⣀⠀⠀⣰⠆⠀⠀⠀⠀⢀⢤⠀⠀⢀⣶⠀⠉⠐⢂⣐⣀⠀⡱⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢂
⣠⠇⢰⠏⠀⠀⠀⠠⢀⡀⢂⢣⠀⠋⠹⣰⡷⠿⣿⣱⣠⠏⢱⠏⠀⡀⠀⠠⢄⠀⠀⠀⠀⠀⠀⣰⠷⠿⣿
⠉⢙⡛⠀⠀⠀⠀⣬⣅⣀⠀⣐⡤⢤⢮⣀⠾⠛⠋⠉⠉⢙⡋⠀⠉⠽⡄⣬⣍⣀⡄⢄⡀⠀⢮⣀⠾⠛⠋
⠀⠁⠒⠔⠀⠀⣰⠇⢠⠫⣛⣿⠶⢬⠀⠐⡆⠀⡬⡀⠈⠁⠒⠀⠀⠒⣹⠇⠀⠈⠙⢷⡿⣦⡀⠠⠀⡄⡄
⠀⠀⠀⠀⠀⠠⠏⢐⡆⢁⠍⠠⢄⣀⠀⠀⡇⢀⢡⠃⠀⠰⠡⠀⠀⠰⠏⠀⠄⠠⢄⠠⢝⡁⠃⠀⠘⡸
⠀⠀⠀⠀⢀⡖⠀⠐⠁⡆⢸⠐⢢⣍⣓⣒⢀⠐⠂⠀⠀⠀⠁⠀⢀⡖⠀⠀⠀⡆⢸⠐⢢⣍⣙⣒⢋⠀⣰
⠠⠀⡀⢀⡾⢀⢀⠀⠀⠧⠜⠀⠀⣀⠉⠑⠊⠀⠀⠀⢠⡆⠀⢀⡾⢀⠀⠀⠀⠧⢼⠀⠀⠀⠉⠑⠊
⡀⠀⠀⠼⡅⢠⡆⠀⠀⣼⠁⠀⠸⣰⠻⣄⠀⠀⢐⣐⠞⠃⠀⡠⡅⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢶⠀⠀⠀⠁⡾⠁⡀⠀⠀⠀⠀⠀⠈⠳⡌⢣⢠⠇⡞⠀⠀⠘⠔⣠⡄⠀⠀⠈⠀⠀⠀⠀⡠⢄⣀
⠸⢀⠀⠀⠼⠁⠀⢆⢣⠀⠀⠀⠀⣤⣀⣈⣉⡠⢈⠔⠂⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠄⠁⠽⣭⣙⠣⠄
⣁⠐⠀⣰⠆⠀⠀⠈⠆⡃⠰⣋⣩⣭⣙⣯⡱⢈⡎⠓⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢣⠀⠀⠉⠑⢂
⣠⠇⢰⠏⠠⡄⠀⠠⢀⡀⠀⠀⡀⠉⠉⠉⠙⢧⣠⠞⠁⠀⠀⠀⡠⡢⠆⠢⢀⠀⠀⠀⠈⢂⠀⣰⠷⠿⣿
⡉⢙⡛⠀⢈⡆⠀⣬⣅⣀⣀⣠⣤⡶⠉⡳⠪⣑⠄⠀⠀⢀⣒⠀⠈⣄⠀⣬⣅⣀⠀⠀⣀⠀⣮⣀⠶⠛⠋
⠀⠁⠂⠐⠈⠀⣰⠇⢰⠋⢏⣿⣶⢾⠏⢀⣾⢀⠈⠀⢀⢃⠎⠀⠀⠿⣰⢇⢠⢘⣛⣻⠧⢦⠁
⠀⠀⠀⠀⠀⠰⠏⡀⠘⠉⠍⠡⢄⣀⠀⠋⠘⠓⡆⢧⠀⠈⠀⠀⠀⠰⠏⢸⠿⡀⠍⠠⢄⣀
⠀⠀⠀⠀⢀⡖⠀⠀⠀⡆⢸⠐⢢⣍⣛⣒⢀⠀⠘⢌⢣⠀⠀⠀⢠⡖⠀⠀⠀⡆⢸⠐⠢⣍⣛⣒⢄
⠀⠀⠀⢀⡾⢀⠀⠀⠀⠧⠼⠀⠀⠀⠉⠑⠊⠀⠀⣠⣁⠀⠀⢀⡾⢀⢀⠀⠀⠧⠼⠀⠀⠀⠉⣑⠦⡀
⡀⠀⠀⠘⡅⢠⡆⠀⠀⠈⢈⡖⢠⢩⠂⠈⡅⠀⠈⢣⡀⠀⠀⠘⡁⢬⡄⢀⠀⠈⠀⠀⠀⠰⠀⠒⠊⠁
⢶⠀⠀⠀⠁⡾⠁⠀⠈⠀⠈⠀⡁⡣⢄⣘⠂⠀⠀⡗⢲⠀⠀⠀⠃⡾⠁⠀⠁⠀⠠⠀⠀⣠⢄⣀
⠸⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠽⣬⣙⡣⠄⡇⠸⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠼⣭⣙⠣⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⠫⠉⢍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⠍⠊⠀⠀⠀⠀⠈⠒⢍⡻⢿⣿⣿⣿⡿⠟⢋⠡⠐⠀⠀⠀⠀⠉⡳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⡡⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⠟⡁⠤⠈⢐⡀⠀⢀⡀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⡀⠄⠀⠒⡈⠈⠀⠙⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⠟⡡⠊⠀⠀⠀⠀⠀⠁⠀⠒⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⠄⠒⠀⠈⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇
⠀⠀⢸⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⠁
⠀⠀⠀⠸⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠉⠉⠉⠉⠉⠉⠩⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠇
⠀⠀⠀⠀⢳⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡞
⠀⠀⠀⠀⠀⠳⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠞
⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⣤⣤⣤⣤⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⣤⣤⣶⣶⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⠬⠥⠤⠤⠤⠴⠖⠚⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢻⣿⢟⡿⢛⣛⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⠟⣼⣇⣛⣛⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣴⣿⣯⣭⣭⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡬⢛⣭⢭⣝⢿⣿⣿⣿⠿⣋⣭⣽⡭⢁⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢛⣩⣶⣿⣿⣦⢻⣧⢻⣿⠏⣾⠿⣛⣭⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣛⣭⣦⣙⢿⣼⡿⣸⣿⡸⣿⣿⠿⣛⣥⣮⡙⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣴⣿⣿⣿⣿⣿⣷⣬⡁⠿⠿⠇⣩⣶⣿⣿⣿⣿⣿⣷⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣽⣿⣿⣧⣶⣿⠟⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣛⣻⣿⣿⠇⠀⠀⠀⠀⠈⢿⣿⣛⣛⣛⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣄⢾⣿⣶⣾⣿⢇⡄⣀⣀⠀⣀⡀⣄⢿⣿⣶⣾⣿⢆⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣌⡳⢭⣍⣭⠵⢚⣴⣿⣿⣷⣌⢳⣜⠲⢭⣭⣭⠵⣋⣼⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠿⠿⠿⠷⠶⠶⠾⠿⠿⠏⣿⣿⣿⡆⠿⠿⠶⠶⠶⠿⠿⠿⠏⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⣾⣾⣶⡾⣛⡛⣶⣾⣶⡆⣿⣿⣿⡧⢰⣾⡞⣛⡻⣶⣿⣾⡆⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣿⣿⣿⣧⣛⣃⣿⣿⣿⡇⣿⣿⣿⡇⢸⣿⣆⣛⣣⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣬⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⣿⣿⡟⢨⣭⣭⣭⣭⣭⣭⣭⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠎⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠍⠀⠀⠉⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠞⢲⡄⠀⠀⠀⠠⣏⠈⣀⡀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⣓⣤⠀⠀⠀⠈⠉⠈⠳⠶⠇⠀⠀⢠⠋⠻⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⣶⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠙⠉⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠉⠀⠈⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠏⡷⠀⠀⠀⠀⠀⠈⠑⠢⢤⢀⠀⠀⣀⣀⣈
⠀⠀⠀⠀⠘⠛⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢅⡁⠀⣉⣢⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⢠⠏
⠀⠀⠀⠀⠀⡞⠉⠠⠒⠌⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⣧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠎
⠀⠀⠀⠀⢰⡁⠀⠄⢁⠀⣨⠇⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⠢⣄⡀⠀⣀⣀⣀⡴⡫⠛⡄
⢰⡟⠉⠛⡆⠉⠣⣤⠤⣠⠇⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⠀⠀⠀⠉⠓⠧⣄⠀⠁⠀⠀⢇
⢯⠀⠁⣦⠇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⠀⠀⢀⡨⠟
⠘⠒⠓⣁⠀⢠⠖⠒⠋⠈⢳⣄⠀⠀⠀⣀⡀⠤⠒⠈⠁⡠⠐⠒⠄⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢇⠀⠀⡇
⠀⣠⡀⠉⣟⠉⡀⠐⡀⢀⡤⠤⠛⣊⣩⠥⠤⠄⢄⠀⠈⠀⠀⠔⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠑⠶⠃
⠀⠉⠁⢀⡟⠀⢁⢀⣤⠼⢤⠠⡚⠇⠀⠠⡄⢸⣀⠢⡅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠑⢦⠀⠹⠀⠀⠀⠑⢌⠲⡄⠀⠀⠀⠀⠈⢣⠀⠀⠢⡈⠢⡤⡔⡲⠀⠀⠀⣀⠠⢤⢠⠇
⠀⠀⠀⠀⠀⠈⠙⢻⠀⠀⣄⠀⠀⠡⡈⡀⠀⢠⡄⠀⠀⠦⡀⠀⠀⢀⡠⢐⡡⠤⠒⠉⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠒⠂⠀⠀⠈⢲⠀⠀⠀⡠⠖⠀⣀⡤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡐⠹⣳⢀⣀⠤⢓⣈⠥⠒⠊⠉
⠀⠀⠀⠀⠀⠀⢰⣃⡠⠤⠖⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠙⢷⣦⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⡿⠋⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠷⠶⣶⣶⣶⣾⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣧⣤⣤⣬⣤⣤⣤⣤⣄⣈⣁⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡄⠀⠀⢸⣿⡇⠁⠉⢉⣩⣭⣭⣉⠉⠉⢹⣿⡏⠉⠉⣩⣯⣭⣭⣍⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣾⠟⠁⠀⠀⣾⣿⡇⠀⣴⡿⠋⠉⠉⠻⣷⡀⣸⣿⠇⢀⣾⠟⠁⠀⠈⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣦⡀⠀⠀⣿⣿⠅⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⣿⠀⢸⣯⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠉⠻⠆⠀⣿⣿⠁⠀⠻⣷⣤⣀⣠⣴⡿⠁⣿⣿⠀⠀⠻⢷⣦⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣿⣿⣦⣤⣤⣬⣿⣿⣿⣯⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣌⠉⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠈⢻⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣀⣀⣴⡿⠃⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢠⡈⠳⣄⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⠂⣠⡞⠁
⠀⠀⠀⠀⠱⣄⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡞⠉
⠀⠀⠀⠀⠀⠈⢡⠊⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⠷⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢿⣦⠀⠀⠀⠀⠀⢸⠃⡀⠀⢀⡀⢿⡄⠀⠀⠀⠀⣠⡾⠋⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠹⣷⡀⠀⠀⠠⢾⠀⠁⠂⠈⠁⣸⢧⠀⠀⣴⡾⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠈⠻⢦⡀⠀⢻⡄⠺⣯⡗⢀⡿⠃⢀⣾⠟⠀⠀⣠⠞⣠⣴⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠙⢦⡀⢻⠦⣤⡴⣿⣠⣴⡿⠋⠀⣠⣾⢫⡞⡀⠀⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⠀⠀⠈⢷⡈⢰⣦⣴⠛⠛⠁⠀⢀⣾⠛⠁⢸⠀⣉⣁⡀⠀⢙⠆⠀⢤⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠁⠈⠀⠉⠀⠀⠀⢀⡾⠁⠀⠀⠸⣆⠻⠾⢁⢠⡋⠀⠀⡂⢿⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠈⢓⡖⠉⠸⣀⠀⠀⢹⡄⠀⡼⠁
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣆⣤⣶⣋⢳⣤⡾⠉⠳⣶⠟⠀⡸⠁
⠀⠘⡕⢦⣄⣏⢳⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣻⣿⢋⠀⠀⠀⠙⢿⣿⠀⠤⠤⠄⠒⠒⣲⡾⠁⠀⣼⠃
⠀⠀⠙⣦⡈⠁⠘⣇⡀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣼⣿⡇⢠⡄⡄⢠⡦⠸⣿⣿⡆⢒⣛⣛⣻⠏⠀⢀⡾⠃
⠀⠀⠀⠈⠙⠶⣤⡈⠛⠷⣤⣄⡀⠀⠀⢿⣇⠀⠀⠀⣿⣿⡇⠈⠁⠀⠀⠀⠀⢻⣿⡏⣉⣁⣼⠏⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⠷⣦⣸⣿⠲⢤⣀⣙⢿⣿⡀⢿⣥⣽⠃⣰⣿⠟⢀⣠⡿⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠙⠿⣧⣤⣀⣀⠀⠉⠳⣄⣉⣡⢴⡏⠀⣴⣿⡋⠙⢦⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⡿⠙⢻⣿⣷⣦⣼⠉⠁⢘⣧⣾⣿⣿⣿⣦⡾⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢧⣠⣿⣿⣿⣿⡏⠛⣶⠛⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠉⠻⣿⣿⣿⣷⣾⣿⣷⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢨⣮⣝⣛⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⢻⡿⠃⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡼⣧⢱⡟⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⡄⠀⢿⣷⠁⠟⣼⣿⠀⢠⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⠀⠀⠸⣩⠞⡳⢮⠻⠀⠀⣿⣿⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠆⠀⣿⣿⠀⠀⢀⡻⣌⣇⡿⡀⠀⠀⣿⣿⠀⠠⢾⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⣶⢰⣾⡇⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⣿⢸⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⣿⢸⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣿⠀⠀⢰⣶⣶⢰⣶⡦⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠒⠂⠠⠤⣀⡀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢀⠈⡇⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡑⠢⢄⣀⠀⠀⢀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⣀⠀⣤⠁⡄⢀⣠⠔⠊⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠀⠈⠙⠒⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⡀⠀⡉⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣁⠀⠀⢀⣤⣾⣷⠶⢶⣶⣤⡀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠾⣷⣶⣤⠄⠠⢄⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⡿⠋⠁⠀⠀⠀⠀⠉⠻⣧⡀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠉⠻⣷⣖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣠⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠋⠛⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠙⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣿⣧⠀⠀⠀⠀⢰⣈⣿⣦⠀⣰⣿⣿⣷⡀⢀⣎⣹⣷⠀⠀⠀⠀⢠⣿⠟⢦
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣤⡞⠁⢀⠎⠈⠻⣷⣄⡀⠀⠘⠿⢿⣫⡴⠛⠉⠈⠙⠻⣦⣻⠿⠟⠀⢀⣀⣴⡿⠻⡀⠈⢳⣄⡀
⠀⠀⠀⢀⣀⣿⠦⢸⣄⠉⠛⠢⠤⣇⣀⠀⠀⠈⠙⠻⠿⠿⠿⠟⢏⠀⠀⠀⠀⠀⠀⢈⠿⠿⠿⠿⠿⠛⠉⠀⠀⠙⠄⢀⣹⡽⠶⣦⣠⠄
⠀⠀⠀⠈⣧⠈⠉⠒⠲⠭⢙⡓⠲⠦⢤⣉⠓⠦⣄⠀⠀⠀⠀⠀⠸⠓⢄⠀⠀⢀⠔⡻⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⣋⣩⠤⠴⠚⣋⡽⢿⣧⣤
⠀⠀⢸⡟⢻⡦⠔⠂⠉⠑⣄⠈⠉⠒⠤⣀⠉⠲⢤⡙⠲⣄⠀⠀⠀⠑⠤⣑⣂⡡⠔⠁⠀⠀⢀⡠⠔⣊⡥⠖⠊⣉⡠⠤⠒⣹⠋⠉⠉⠛⠤⣿
⢀⠴⠚⠋⠁⠀⠀⠀⠀⢀⡿⣤⣀⠀⠀⠀⠉⠲⢤⡙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⠴⠊⣡⡴⠞⠋⢁⣠⠴⠞⢻⣄⠀⠀⠀⠀⠀⠙⠲⠤
⠸⠀⠀⠀⠀⢀⣀⠤⠶⢿⢤⣄⡈⠙⠓⠦⣄⣀⠀⠈⠓⢽⣦⠈⢣⡀⠀⠀⠀⠀⣠⢞⡥⠚⣡⡔⠋⣁⣠⠴⠚⢉⣠⡴⠞⢋⡽⠓⠢⢄⡀
⣧⠤⠔⠒⠉⠁⠀⠀⠀⢸⡆⠀⠉⠛⠲⢦⣄⣈⠙⠓⠦⣤⣉⡣⡄⠹⡄⠀⢀⡴⠛⢉⠄⣚⣤⠈⠻⣍⣠⡴⠞⠋⠁⠀⠀⢸⡀⠀⠀⠀⠈⠙⠲⠤⣄
⡇⠀⠀⠀⠀⠀⣀⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣬⡙⢻⠿⣍⣁⣋⣡⣾⠷⢚⣉⡤⢷⡶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀
⢱⡴⠖⠒⠊⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡀⠀⠀⠀⠀⢸⡄⢻⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠉⠉⠙⠒⠶⢤⣀
⠈⢇⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠉⠛⠓⠚⠛⠛⡇⢸⡇⠀⠀⠀⠀⠀⠀⣤⣶⣶⡆⠀⢰⣿⠟⠳⣄⡀⠀⠀⢀⠞
⠀⠀⠓⢺⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠛⠒⠒⠒⠒⠚⡇⠸⡇⠀⢸⣷⣄⠀⠀⢸⣿⡿⣷⡄⠘⢿⣷⣾⡷⢹⡗⣶⠉
⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⡇⠀⣷⠀⣼⣿⣿⣷⡄⠀⢿⡿⠿⠃⠀⠀⠉⠉⠀⢸⡇⢸⡀
⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⡇⠀⣿⠀⠛⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⣷⠸⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⢛⣡⡼⠇
⠀⠀⠀⠀⠙⠒⠦⢬⣍⣛⠳⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡏⠓⠒⠒⠒⠚⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⣛⣩⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣭⡙⢿⡲⠦⢭⣙⡛⠲⠦⢤⣄⣀⠀⣿⠀⡗⠲⠶⠤⠴⠶⣿⠀⢸⡀⢀⣀⣤⠴⠞⣛⡩⣴⠖⢋⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣝⡢⣄⡀⠉⠉⠓⠲⠤⣬⣉⡋⠀⡇⠀⠀⠀⠀⠀⢻⠀⠘⢛⣉⣥⠴⠚⢋⡥⢖⣡⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠙⡝⢓⣿⣿⣶⣦⣤⣀⣀⣈⠉⠙⠳⣤⣀⣀⣀⣠⣾⣶⣚⣉⣥⣴⣶⣿⣽⣞⢋⠝⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠤⠚⣟⡡⢌⡑⣿⡍⠟⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⠛⠛⢏⣽⡗⣉⢤⣙⡟⠢⢤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡀⠀⣨⠏⠳⢤⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⠼⠋⢯⡀⠀⣀⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡰⠀⠀⠀⠘⡝⣿⣿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡃⠀⠀⠀⠀⠴⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠫⠁⠽⢧⠀⠀⠀⢀⣂⣿⣅⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⠀⠀⠀⠀⠀⢀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢸⣿⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠭⢽⣛⣷⣾⣿⣿⡘⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣩⣥⠠⠤⠤⣤⡄⣴⣾⠩⢿⣻⣛⡛⠡⠌⠳⢶⣶⣶⣶⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠂⠀⠙⠛⠛⠉⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⣹⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣖⢿⡿⠛⣛⡉⠉⠥⠤⠤⠭⠥⢬⣭⣝⣛⡻⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⣿⠛⠉⠁⠀⠀⠀⠀⢀⢔⣶⣶⣖⢢⣄⡈⢉⠙⠒⠦⣍⣛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡙⣦⣄⠀⠀⠀⠀⢀⣷⣿⣯⣻⣿⡿⠟⠛⠿⣿⣶⠦⡀⠈⠉⠒⠽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⡇⠙⠷⠶⠶⣤⣧⣿⣿⣿⣿⣏⣠⠀⠀⠀⣿⣿⣿⡷⠤⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠒⠚⠻⡨⠻⡄⠀⠀⢠⣇⣿⣽⣏⢿⣼⠿⠿⢒⣤⣶⣿⣿⢿⡓⠄⠀⠐⠦⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣶⣷⢀⢳⣄⡤⣠⣿⣿⢿⠁⣼⣿⣀⠺⢟⣽⣿⡿⠁⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣶⢴⣿⣷⣶⣿⣿⡄⣦⡙⢻⣾⣷⣾⠿⣿⣧⡐⠶⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⠛⣿⣷⠈⢹⣿⡟⣿⣧⡹⣷⣶⣶⣿⣷⡦⡿⢿⣧⣀⠀⣀⣴⣾⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠶⡤⠞⣳⢶⣿⣿⣦⡀⢻⣻⣼⣿⣿⣎⠻⣿⣿⣿⣧⣳⣾⡿⣿⢿⣿⠛⠏⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⣧⣴⣴⣿⢮⣥⢿⣿⣷⣔⣻⠶⣛⣿⣿⣷⣽⣿⣿⣿⣫⡽⢿⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣄⣺⡤⣾⣿⣿⣿⠑⣻⢞⡋⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠷⣦⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠴⠋⠀⠀⠀⠍⣿⣿⡿⣃⢻⣿⡬⢐⣽⡗⠙⢿⣿⣿⣿⡟⣹⣿⣵⡶⣤⣿⡆⢣⠉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⣀⡄⣹⣿⣷⣿⣌⢿⣮⡻⣿⣷⣤⣀⠙⢿⣿⣿⣿⣿⣿⣿⣤⣿⣷⣾⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠿⠛⢿⣧⡹⣿⣿⣿⣷⣍⣇⠘⣿⣿⣿⣦⣀⡨⢟⣦⣿⣟⣿⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⠛⠀⢸⣿⣿⣿⣿⣿⡿⣿⣧⢸⣿⣿⣿⢋⡶⣫⢾⡟⣿⣿⣶⣿⡿⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣠⠴⠫⠿⢿⣿⣿⣷⡈⢿⣆⡟⣿⣿⣻⣵⢛⡿⡾⡻⠻⣿⣿⠁⠀⠈⠳⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⣧⣤⣀⠈⢻⢿⣿⣿⣿⡇⢣⣿⠟⣿⣿⣿⣿⡎⠀⢿⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⡁⠠⣍⣠⣾⣿⢿⣿⣿⣠⡿⣻⣼⣿⣿⣿⣿⣿⣆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡂⠬⠭⣁⣼⣿⣿⡿⢟⣵⣿⠿⣫⣽⣿⡿⠋⢹⡤⠹⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⣙⡻⣿⣛⠛⠉⠿⢮⡯⠿⢏⣰⣿⣿⣿⣏⠐⢦⡴⢿⢎⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣄⣏⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡴⠛⠁⣉⠛⣿⢿⣷⣶⣿⡿⣿⣛⡭⠀⠙⠶⠶⠖⠘⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠿⢾⣻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⡠⠊⢱⠤⠒⠒⠈⠙⢆⠀⠀⠀⣰⣿⡘⣯⣵⣶⣶⣶⡄⠀⠀⢀⢾⡁⠀⢀⡤⠤⣌⢢⡀⠀⢠⡸⣿⣿⠿⣛⣿⡛⢦
⠀⢠⣇⠀⠀⠣⣀⡠⠤⣄⣈⡆⠀⠐⢿⣿⣷⣝⠿⣟⣛⢛⡿⠀⠀⡎⠀⠉⠉⠁⠀⠀⠀⢣⠇⠀⣿⣿⣶⣶⣿⣿⣿⣿⡎⡇
⠀⠘⡏⠣⣄⢀⡎⠀⠀⠇⢀⠇⠀⠸⣮⡻⢿⡿⣸⣿⣿⣸⣿⠀⠀⢇⠀⣀⣀⡀⠀⠀⠀⡜⡆⠀⣿⣿⠿⠿⣿⣿⣿⣿⢇⡇
⠀⠀⠙⢄⣨⠏⠀⠀⣼⡠⠊⠀⠀⠀⠙⢿⢗⣵⣿⣿⢇⡿⠃⠀⠀⠈⠻⣀⠀⠈⠙⠒⣫⠜⠀⠀⠈⢵⣿⣿⣶⣭⣯⣥⠞
⠀⠀⠀⠀⠉⠑⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉
⠀⠀⠀⣠⡶⠓⠀⠺⣶⣤⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡙⠻⣦
⠀⠀⠈⠁⢀⣤⣤⡆⠀⠉⠀⠀⠀⢀⣾⣿⡟⠛⠛⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⣠⡦⠙⢷⡄⠀⠀⢀⣾⣿⣿⠏⢙⣷⣌
⠀⢰⣦⠀⠸⢿⡿⠇⠀⣠⣶⡆⠀⠈⠻⣿⣅⡀⢀⣽⣿⠟⠙⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣾⣿⡿⠁⣰⣿⣿⠏
⠀⠀⠿⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⢦⣀⠙⠁⠀⠀⠀⠀⠀⠀⢈⠻⣿⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠐⢾⣿⡶⠁⠀⠀⠀⠀⠀⠀⠙⠏⠁⠈⠹⠟⠉⠀⠀⠀⠀⠀⠉⠳⠦⠀⠀⠀⠀⠀⠀⠘⢷⣦⡉⠻⠛⠁

⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣴⣶⣷⣶⣦⡀⠀⠀⠀⠀⢀⡤⠂⠈⠀⠒⢀⡀⠀⠀⠀⢀⢰⣶⣿⣷⣶⠄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠠⢁⠇⠀⠀⡴⠚⠉⠑⡀⠀⣰⡇⣾⣿⡿⢫⣴⣾⣷⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣿⣿⣿⣿⣿⣿⠀⠀⣧⡞⠀⠀⢸⠁⠀⠀⠀⡁⠀⠛⣼⣿⣿⠅⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⠟⠀⠀⠸⡀⠀⠀⠸⡄⠀⠀⢠⠃⠀⠸⣿⣿⣿⡅⢿⣿⣿⡿⠁
⠀⠀⠀⠁⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠈⠂⠄⠀⠉⠶⠒⠁⠀⠀⠀⠈⠻⠿⢿⡦⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄
⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⣀⡠⠄⢀⡀⠀⠀⠀⢀⣿⣧⢀⣀⣀⣀
⠀⠀⠈⢿⢆⠀⠀⠀⠀⡀⠀⠀⠀⠙⣤⡀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠈⢀⠞⠁⠦⡀⠀⠈⢢⠀⠀⣾⣟⣵⣿⣹⢿⣿⣷⣄
⠀⠀⠀⠀⢂⠁⠒⠈⠁⣔⠀⠉⢐⡄⠘⣿⣶⣶⣿⡟⠽⣷⣶⣶⠦⠀⠀⢸⠀⠘⠂⠉⠀⠀⠀⡇⠀⢿⢹⣿⣧⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠢⠀⢀⣀⡁⠤⠀⠀⠀⠀⠘⠿⠿⠿⠷⠽⠟⠛⠛⠉⠀⠘⢌⣄⠀⠀⠀⠀⢀⡔⠀⠀⠘⠯⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁
⣟⣿⣻⣻⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣛⣛⣟⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣤⣤⣤⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠤⢤⣴⣿⣀⠀⠀⠈⠙⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⢩⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠳⠶⠶⠒⠀⠀⠀⣾⡇⠈⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣗⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣶⠶⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣿⡟⠙⠛⠛⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⠙⠶⠶⠶⠶⢾⣿⡷⠈⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣸⡿⠓⠒⠒⢲⣖⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠛⠛⠓⠒⢺⡿⠋⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⣿⠁⠀⠀⢸⣿⣿⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠁⣤⣴⣤⡙⠿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠀⣀⠀⢰⣿⠀⣴⠞⡋⠩⠩⠉⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠸⣿⣿⣿⠃⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⣿⡇⣼⠃⠀⠘⠄⠀⢀⡠⠆⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣭⣥⣤⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡿⢠⡟⢘⠁⠐⠀⠂⡉⠤⣬⠆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠿⠇⠘⣿⡄⢖⠁⠀⡃⠰⣄⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣾⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠲⠤⢤⣤⣤⣼⣿⣶⣤⣘⣓⣀⢤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠖⠚⠿⠟⠛⠋⠙⠛⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⢧⠀⡿⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣛⣛⣛⣿⡿⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠒⢺⣿⠛⢷⣾⣻⣷⠚⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⣿⣟⠋⠉⠉⢁⡀⡸⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣤⣤⣼⣿⡿⠿⢞⣻⣎⠙⣺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢟⣻⣷⣮⣤⣡⣠⣤⡘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣸⣽⡟⣿⣩⡹⡏⡩⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠭⣀⣀⣀⣀⣀⣀⣀⠀⠍⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⠟⢿⣹⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣧⣾⣤⣿⣼⣷⣤⣹⣤⣺⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢻⣎⡈⠀⠁⠀⢼⣏⠛⠛⠛⢿⣿⡿⢡⠇⠠⠤
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⢷⣶⣧⣀⣤⣤⣧⣴⠿⢟⣩⠴⠋⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣸⡂⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⡈⠉⠛⢿⣿⣿⠟⠋⠉⡀⠀⠀⠈⢷⡆
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣏⠉⠉⠉⠉⠉⠉⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠐⠧⠀⠀⠀⣿⣯⠀⠀⠀⠿⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠙⠲⠦⠤⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣿⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣶⣶⣶⣶⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⢀⡀⠀⡀⠄
⠀⠀⣀⠀⠀⠂⢠⡔⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⡀⢤
⠀⠈⢹⠀⠸⡇⠘⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢲⡘⠀⠞
⠀⠐⠀⠀⠀⠤⠄⣠⡁⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢴⡄⠈⠋⠠⠖⠐⢀⠖
⠀⠀⢣⠀⠀⠀⠀⠀⠁⡰⠶⠾⠀⠀⠀⠀⠀⠰⣶⠀⣀⠀⠐⣀⠀⠶⠄⠠⢆⠀⠀⠀⠀⠈⠓⢦⠀⢥⠀⠀⠀⢀⠻⢦⡀
⠀⠀⠀⠓⣤⡀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⠀⠀⠁⠀⠀⠞⠁⠈⣃⠀⠀⠀⠀⠀⢸⡀⠀⠙⠀⠀⡜⠁⠒⠛
⠀⠀⠀⠀⠀⠹⠂⠸⡄⠀⠀⠀⠀⠀⠀⢀⠰⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣐⠆⠀⠀⠀⢱⠄⢀⡠⠴⠁
⠀⠀⠀⠀⠀⠀⣧⠀⢿⡀⠀⠀⠀⠀⠀⣘⡷⠄⠚⠓⠂⠘⠛⠒⠤⣀⠀⠀⠀⠀⢞⠁⠀⠀⠀⡰⠃⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠙⡄⠘⣧⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠳⢄⠀⠀⠈⢓⠀⢀⡞⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢃⡀⢘⣄⣠⠏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠈⠆⠀⠀⣸⣄⠎⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⢰⡞⠉⠉⢹⠇⠀⠀⠀⠀⠀⠊⠁⠙⠀⠀⣀⡤⠚⡁⠀⠀⠸⠀⠀⣿⠏⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡎⠀⠀⠀⣤⣤⠤⠤⠤⠔⠒⠋⠁⣠⣼⡇⠀⠀⠐⠓⢶⣟⡀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡇⠀⠀⠀⢻⣿⣄⣀⣤⣤⠤⠚⠛⢻⡟⠀⠀⠀⢦⡤⠎⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢰⠀⠀⠀⠈⢿⣿⡿⠿⠇⠀⠀⣸⠋⠀⠀⠀⢠⠟⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢳⡀⠀⠀⠀⠙⠓⠀⠴⠖⠊⠀⠀⠀⢀⣴⠋⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠢⣄⣀⡀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠢⠤⠤⣄⣀⣀⣀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠰⠒⠒⠂⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢣⡀⠀⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⠤⠒⣇⣀⣀⠀⠀⠀⠀⠀⠀⢀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⡄⠀⠀⠉⠉⢹⠉⠉⠚⠟⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠀⠀⠀⠸⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠀⠀⠀⠀⠀⠀⣧⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⣳⠀⠀⠀⠀⣠⠜⠁⠀⢠⡄
⠀⠀⠀⣀⠀⠀⢀⣤⠔⠊⠁⠀⠀⠀⢻⣀⠠⠔⠊⠁⠀⠀⠀⢸
⠀⠀⢘⠁⠄⢀⣈⣃⣀⣀⠀⢀⡠⠛⠊⠉⠣⠀⠀⠀⠀⡀⠁⢰
⠀⠀⠈⠁⠀⠤⠤⠤⠤⠤⠀⠿⣈⠀⠄⠀⠀⠰⠀⠤⠄⣛⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⢀⣀⠀⣀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣧⣴⢷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⢿⡆
⠀⢠⡿⢿⣆⣿⣾⣿⠾⣿⣷⠶⣿⣾⣿⡷⢾⣿⠸⣿⠀⣠⠿⣰⠗⢶⡆⢺⠂⣴⣦⠟⢰⡆⠀⠀⠀⠀⠉⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢾⠘⠇⠛⢾⡇⠾⠁⠀⢯⡤⠻⠦⢿⡾⠁⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠁⠈⠀⠙⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣠⠶⠄⣀⡀⠀⠀⠀⠀⠀⠀⢰⡶⣆⢀⣤⡄⠀⠀⠀⠀⠀⠀⣴⠶⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠆⣴⡇⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣀⡀
⠀⠀⠀⠀⠳⡴⠞⠧⠀⠀⠀⠀⠀⠀⠀⠸⡷⠎⢻⠼⠃⠀⠀⠀⠀⠀⠀⠺⡇⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠁⠹⠀⠀⠀⠀⠀⠀⠀⠀⠷⡽⠛⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠆⠀⠀⠀⠀⡀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⡄⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠒⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⡷⢼⣿⡷⣆⠀⠀⠀⠀⠀⠀⠀⢈⣏⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡇⢰⡄⠀⠀⠀⠀⠀⠀⢸⣿⡁⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣇
⠀⠀⠀⠈⠁⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣞⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠠⠈⠉⠀⠁
⠀⠀⡀⠀⠀⠀⠀⠘⠂⠠⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡁⠙⡇⠀⠀⠀⠂
⠀⠀⠠⠀⠠⠆⠀⠀⠀⠀⡆⠀⠀⠀⠢⡄⠀⠀⠀⠈⠑⠦⠀⠀⠀⠀⣀⢤⡄⢘⣀⡀⠀⠁⠀⠀⢴⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠰⣄⠀⠁⣄⠀⠀⠀⠀⠀⠀⢠⠛⠢⠆⠈⠁⠁⠀⠀⠀⠀⠀⠀⠛⢤⡖⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠈⠁⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠂⠈⠛
⠀⠀⠀⣶⡀⣴⣀⣄⣀⡀⠀⠀⠀⠀⠀⢰⣆⢰⣄⣀⠀⠀⠀⠀⠀⠀⠀⡴⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⢰⡞⣦⣠⣀⠀⠀⠀⠀⠀⠀⢠⡞⢳⡄⣀⣀
⠀⠀⠀⠏⠻⠙⠿⠙⠹⠇⠀⠀⠀⠀⠀⠸⠏⠻⠏⠉⠃⠀⠀⠀⠀⠀⠈⠷⠴⠛⠧⠟⠀⠀⠀⠀⠀⠀⠸⠟⠁⣿⠞⠀⠀⠀⠀⠀⠀⠘⠶⢾⡇⠷⣿
⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣈⣋⠀⠰
⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⣿⣼⠃⡖⠂⠀⠀⠀⠀⠀⠀⠀⠛⣦⡰⣧⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⢿⠂⠀⠀⠀⠀⠀⠀⢸⣇⡘⣶⣰⠀⠀⠀⠀⠀⠀⠀⢣⡾⠓⣴⠆
⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⢀⢀⡀⠀⠀⠀⠀⠀⡀⢋⡐⢀⣄⡀⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⡁⠀⠀⠀⠀⠐⢦⡁⠙⠒⠶⣦⡉⠃⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⡎
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠰⣄⣠⣀⣤⡀⣀⢀⠀⠀⠀⠀⠀⠰⣦⡴⢀⣀⠀⠀⠀⠀⠀⠀⠀⢦⡴⢆⠀⣀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⣤
⠀⠀⠀⠹⠏⠿⠀⠻⠻⠏⠀⠀⠀⠀⠀⠰⠟⠳⠜⠻⠄⠀⠀⠀⠀⠀⠀⠈⠇⠈⡿⠃⠀⠀⠀⠀⠀⠀⠰⠷⠦⠾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣬⡄⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⣨⠄⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠞⢣⣽
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠿
⢠⡄⠄⢠⡤⠀⢤⢠⡄⠴⠆⣤⠠⠴⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠶
⢸⣄⡤⢰⣶⠖⠀⢸⣤⡤⠀⣾⣤⠤⠀⠀⠀⠀⢰⡆⣧⡀⠦⣤⠶⣶⣦⡴⢲⣀⡔⢦⢼⡴⠶⣤⣶⡶⢴⡶⠃⠀⠀⢠⡆⠀⠀⣦⡴⠲⣄⡴⢶⢤⡶⠶⢶
⢸⡇⠀⢸⡏⠳⢦⣼⣁⣠⡤⣿⣀⣤⡄⠀⠀⠀⣾⠋⠙⣿⣃⣧⡴⠃⣿⠁⢨⣿⣠⡿⣿⣠⡾⠹⣏⣠⠾⡇⠀⠀⠀⢸⣇⣠⠞⣿⠃⢀⣿⣀⣾⣼⡇⠀⢸

⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⡄⠀⢀⡀⢠⠀⠀⠀⠀⠀⠠⠖⡲⢦⡀⠀⠀⠀⠠⡊⢳⣿⣿⣿⡏⢑
⠀⠀⠀⠀⣤⣷⣿⠇⠀⠀⠀⠀⠀⠈⢃⠀⣾⡿⠟⠀⠀⠀⠀⣈⠂⠜⢠⠃⢽⠀⠀⠀⠀⠙⠺⣿⣿⣿⠗⠁
⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⠀⠠⣶⣾⡟⢀⣤⡀⠀⠀⠀⠀⠘⢕⣒⣣⡈⠎⠀⠀⠀⠀⠀⠀⢉⣿⠁
⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛

⠀⠀⠀⠀⢀⠀⢀⣤⡄⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣧⡂⠀⠀⠀⠀⠀⢠⣤⡄⣀⡀
⠀⠀⠀⠀⢨⣿⣿⡿⠋⠀⠀⠘⢟⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣰⣿⡣⣹⣦⡄⠀⠀⠀⢻⣿⣧⣿⡿⣦
⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⡟⠉⠉⠉⠀⠀⠀⠀⠀⠰⢟⣱⠿⢛⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⡥
⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠞⠋⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⢀⡈⣶⣷⠆⢳⡀⠀⠀⠀⢀⡤⡴⠗⠳⠤⢤⠄⠀⠀⠀⢠⣿⢃⡼⣭⣤⠀⠀⠀⠀⠀⣼⡙⣎⣣⠶⣀
⠀⠀⠘⢇⣈⠉⢰⣶⠀⠀⠀⠀⠀⠙⣷⠀⠀⣴⠃⠀⠀⠀⠀⠰⣟⣶⣽⣷⡝⠀⠀⠀⠀⡼⠡⠗⢉⣤⠶⣉⡄
⠀⠀⠀⠈⠛⠃⠈⠁⠀⠀⠀⠀⠀⠰⠿⠛⠛⠾⠀⠀⠀⠀⠀⠀⠈⠛⠓⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⡿⣶⠄⠀⠀⠀⠀⠀⠘⣿⠇⣴⡿⠃⠀⠀⠀⢐⣴⣿⠟⢻⢹⣿
⠀⠠⠞⠋⡳⠤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⣶⣿⣿⡾⠋⠀⠀⠀⠀⠀⣾⢏⠘⡐⣼⡼⡋
⠀⠀⠀⠀⠁⠢⢈⠗⢦⡄⠀⠀⠀⠀⠛⠛⠟⠃⠀⠀⠀⠀⠀⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠿⠦⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠈⠙⣆⠀⠀⠀⠀⠑⠢⡌⡆
⠀⠀⠀⠀⠀⠀⢧⡀⡨⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⢡⢳
⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠰⣤⣶⣶⠆⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢈⣿⡆⢀⡀
⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⢀⡀⠀⣸⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⢻⣀⣰⣼⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠰⣿⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⢸⠏⠈⠻
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠃⢘⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢸⣄⠀⢠
⠀⠀⠚⠛⠛⠓⠀⠀⠀⠀⠀⠐⠛⠛⠓⠂⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠐⠚⠛⠂
⠀⠀⣠⣤⣄
⠀⠀⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢹⣿⠇⠀⠀⠀⠘⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⢠⣶⠤⡤⢶⡆⠀⠀⣠⣤⣴
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠾⠿⠿⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⢸⣧⣠⣤⣀⡇⠀⠀⠿⠿⠿
⠀⠀⠙⠛⠃⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠉⠛⠛⠉⠁

⠀⠀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⢀⣿⣿⣿⣿⣿⣿⠉⢿⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣷⣶⣶⣶⣾⠗⢲⡀⢀⡀⣀⣈⣉⠉⣀⣠⣤⡀
⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣷⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⢸⣿⣿⣿⣿⣿⣿⠀⣸⡗⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⢀⣤⣽⡁⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣃⣀⠀⠀⠀⠀⠀⠀⠛⢉⣿⡿⢥⡴⠀⠀⠀⠀⢀⣴⣶⣿⣿⣟⣷
⠀⠀⠀⠀⠀⠟⢸⡿⠳⡄⠀⠀⠀⠀⠀⠀⠉⢰⣿⠛⠷⠦⠀⠀⠀⠀⠀⢠⣿⣿⣍⣉⠉⠀⠀⠀⠀⠀⢤⣤⡿⠛⠳⢦⡄⠀⠀⠀⠀⢸⢿⡁⢰⠀⠉⠓⠆
⠀⠀⠀⠀⠀⠀⣼⢻⡆⠀⠀⠀⠀⠀⠀⠐⠶⠾⢛⡦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠘⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺

⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⡄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣀⢨⡗⣤⡀
⠀⠀⠀⠀⣠⣤⣼⡷⠞⠋⠁⠀⠀⠀⠀⠈⣷⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠷⠶⠚⠀⠀⠀⠀⠀⠘⣇⣸⣯⡤⠶⠖⠀⠀⠀⠀⠉⢿⣿⣡⣼⣄
⠀⠀⠀⠀⢻⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠛⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡌⠁⠡
⠀⠀⠠⠞⠋⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡄⠀⠀⠀⠀⠀⢀⣠⡾⠋⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢃
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠈⢷⣰⣆⡟⠁⠀⠅⠀⠀⠀⠀⠀⠀⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠠⠤⠤⣤⣾⡁⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉⣿⣮⠋⠀⠀⠀⠀⠀⢠⣀⡀⣿⡟⢀⣀⡄⠀⠀⠀⠀⢀⣴⠿⠛⢯⡁⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣤⡀⠀⠀⠀⠀⠈⠉⠛⠾⠿⢿⠦⠤⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠴⠛⠁⠀⢠⣬⣷⣤⣀⠀⠀⠀⠀⠐⠃⠉⠉⠉⠉⠄
⠀⠀⠀⠀⠀⠀⡏⠙⠁⠙⠀⠀⠀⠀⠀⣤⣦⣤⣤⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠁⠈⠁⠈⠈⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢹⡾⠗⠒⠂⠀⠀⠀⠀⠀⢀⡀⠀⢰⡆⠀⡀⠀⠀⠀⠀⠁⠀⠙⣟⠋⠀⠈⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⣄
⠀⠀⠀⠀⠀⠒⢾⣷⠒⠂⠀⠀⠀⠀⠀⠀⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠛⠉⠉⠀⠀⠀⣀⣉⢉⠻⡿⠟⡉⣸⣄⠀⠀⠐⠛⠉⠀⠈⠙⣯⠁
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣤⣤⣤⣤⡄⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣼⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⢠⣄⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣶⢄⣠⡁⠂⠀⠀⠀⠀⠀⢸⣷⣿⣠⠤⠀⠀⠀⠀⠀⠀⠙⣧⣾⣴⠇⠀⠀⠀⠀⠀⠀⠓⢦⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡛⠁
⠀⠀⠀⠀⠀⠀⣰⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢦⣁⣠⣿⠟⠖⠃⠀⠀⠀⠀⢀⣀⣉⣉⣽⣿⣁⡀
⠀⠀⠀⢀⣤⠶⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠺⣏⣿⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠈⠀⠀⠀⠀⠀⠨⠉⠉⠉⠉⠉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

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

⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠔⠁⠀⢀⠀⠉⢢⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⠔⣅⠀⠀⠀⡨⠢⡀⠀⠀⢀⣤⣻⣿⣿⣿⢟⣤⡀
⠀⢸⠀⠀⠀⠀⠀⠠⠄⡃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡌⠀⢸⡄⠀⢠⡇⠀⠁⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇
⠀⠸⡀⢀⠀⠂⠀⠀⣠⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠰⡀⡸⠁⠀⠀⢇⢀⠆⠀⠀⠸⣿⢏⣿⣿⣿⡹⣿⠇
⠀⠀⠈⠲⠤⠠⠤⠞⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠈⠣⠄⠀⠠⠜⠁⠀⠀⠀⠀⠈⠻⠿⠿⠿⠗⠁

⠀⠀⢀⠄⠒⠀⠒⠠⡀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⡀⠀⠀⠀⠀⠠⢔⣂⣀⠐⠢⢄⠀⠀⠀⠀⣠⡴⠶⠿⣶⣦⣄
⠀⢰⠁⠀⠀⠀⠀⠀⠽⠆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣻⡄⠀⠀⣐⡝⠁⠀⠀⠙⡄⠈⠂⠀⠀⣰⢫⣾⣿⣿⣮⢻⣿⡆
⠀⢀⠀⠀⠀⠀⠀⠀⡅⡂⠀⠀⢸⣿⣿⣿⣿⣿⣿⢾⡇⠀⠀⠌⡇⠀⠀⠀⠀⠸⣄⠘⠀⠀⢿⢸⣿⣿⣿⣿⣧⢻⡿
⠀⠈⠢⡀⠀⠀⠀⣀⠜⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢜⣦⡀⠀⠀⠀⡨⠁⠀⠀⠈⢷⡻⣿⣿⣿⣿⡷
⠀⠀⠀⠈⠁⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠂⠂⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠋⠁
⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⢀⢔⣿⣷⡆⠀⠉⠦⡀⠀⠀⢀⣴⠋⠉⢽⣿⣷⣤⡀⠀⠀⢀⠎⠁⠀⠐⠆⣌⠱⡀⠀⠀⢀⣾⣿⣿⣯⣹⠻⣷⡀
⠀⠈⠀⠙⠉⠀⠠⣴⣆⠁⠀⠀⢸⣿⣶⣾⣿⣿⠋⠹⡇⠀⠀⡂⠀⠀⢀⣄⠀⠀⠀⢠⠀⠀⣾⣿⣿⣿⠻⣿⣿⣿⣧
⠀⠸⣤⣶⣄⠀⠘⠻⢋⠇⠀⠀⠸⡟⠙⠿⣿⣯⣄⣴⠇⠀⠀⠡⡀⠀⠀⠉⠀⠀⢀⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⠛⠏⠤⠤⠖⠁⠀⠀⠀⠀⠈⠲⠾⠿⠛⠋⠁⠀⠀⠀⠀⠑⠢⠀⣀⠠⠔⠂⠀⠀⠀⠀⠘⠻⢿⣿⡿⠟⠋

⠀⠀⠀⠀⣀⠄⢤⡄⠤⠀⠀⠀⠀⠀⠀⣀⣤⡀⢤⣤⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⢠⠊⠀⢀⣤⠙⢶⠀⠀⠀⠀⢠⣾⣿⡿⢛⣷⡙⠀⠀⠀⠀⠀⡠⠊⠀⢠⠂⢘⠀⠀⠀⠀⠀⣠⣾⣿⣟⣿⣿
⠀⠀⣇⠀⣴⠟⠁⠀⡔⠀⠀⠀⠀⠻⣿⠋⣡⣾⣿⡟⠀⠀⠀⠀⠎⠀⣀⠔⠁⡠⠊⠀⠀⠀⠀⣼⣿⢿⣿⣿⡿⠃
⠀⠀⡉⢳⣄⣀⠤⠊⠀⠀⠀⠀⠈⣷⣝⠻⣿⠿⠋⠀⠀⠀⠀⠀⠳⣈⢀⡠⠊⠁⠀⠀⠀⠀⠀⠹⣿⣿⠿⠋

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

⠀⠀⠀⠀⠀⠀⠀⠰⠾⠗⠗⠀⠀⠀⠀⠀⠖⠗⠆⠶⠺⠺⠶⠆⠀⠀⠀⠰⠺⠺⠗⠆
⠀⠀⠀⠀⠀⠀⠀⠸⠻⠗⠗⠀⠀⠀⠀⠀⠐⠗⠿⠛⠘⠺⠻⡇⠀⠀⠾⠺⠚⠙⠓⠗⠇
⠀⠀⠀⠀⠀⠀⠸⠺⠻⠟⠗⠀⠀⠀⠀⠀⠘⠗⠿⠀⠺⢺⠟⠁⠀⠀⠻⠻⠃⠀⠘⠗⠟
⠀⠀⠀⠀⠀⠀⢻⢻⠇⠙⡟⡇⠀⠀⠀⠀⠘⡟⡟⠛⢻⢻⠀⠀⡀⠘⠛⠻⣤⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⢻⠋⠀⠘⡟⡛⠀⢀⠀⠀⠘⡟⡟⠛⠛⠛⠛⡛⡇⢛⣿⢴⣿⡆⠀⠀⠀⠀⢰⣿⡦⣿⡷⢶⡄
⠀⠀⠀⠀⠀⣛⢛⢑⢒⡛⡟⡛⣛⢻⠛⠀⠘⡛⣛⠀⢀⢘⢛⡛⠁⢈⡏⠀⣙⡅⠀⠀⠀⠀⠀⣙⠀⢘⡁⡜⠁
⠀⠀⠀⠀⡘⣛⠛⠛⠋⠉⠉⠛⣛⢁⠀⠀⠈⡋⡛⣚⢛⠹⠋⠀⠰⢾⣿⠶⣿⡧⠀⠀⠀⣰⢶⣿⡷⣿⡟
⠀⠀⠀⠀⠋⣛⠁⠀⠀⠀⠀⠀⢛⢙⣡⣋⣾⠋⡋⣛⠙⠀⠀⠀⠀⢈⣇⠀⣩⠀⢀⠀⢀⣇⠀⣭⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡇⠀⠉⠉⠀⠀⠀⠀⠀⠘⢿⠺⣿⠗⣿⡷⢾⣿⠺⣿⠟
⠀⠀⠀⠀⠀⠀⣀⣚⡛⠛⠛⣛⡇⠀⠀⣛⣋⠟⣛⣢⠀⢀⣘⡛⣛⣄⠀⠀⢭⡀⣨⡁⢀⣅⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠴⠶⠶⠦⠀⠀⠶⠆⠀⠸⠶⠄⠶⢾⠀⠶⡦⠀⣀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣛⠛⠁⣀⣛⣋⠀⠀⣛⣃⠀⢘⣛⠁⣛⣻⠀⣰⣶⡆⠀⠷⠦⠠⠧⠃⠃⠀⠧⠒⠘⠱
⠀⠀⠀⠀⠀⠀⠶⠶⠶⢶⠞⠱⠶⡆⠠⠶⡶⠶⢴⠞⠀⠰⠾⠦⢾⡟⢠⠀⠖⢰⡆⢄⠀⠰⣏⣱⠆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣰⠀⡆⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣀⡾⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠲⣴⣒⣫⡽⠶⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⣁⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⡿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡼⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣀⣤⠤⠶⠒⠒⠛⠛⠛⠛⠛⠓⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⣴⠶⣄⠀⣿⠀⢹⡆⢀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⣿⠀⠸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡴⠛⠉⠛⠲⣤⡀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢀⣠⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢠⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⡄
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⣷
⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⣀⠀⠀⣠⠏⠳⣄⠀⠀⢀⠿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢸
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡧⣤⣤⠎⠀⠀⠈⠈⠉⠁⠀⠀⠈⠙⠓⢋⠀⠈⠳⠤⣤⣤⣤⠴⣞⠁⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣀⣀⣸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⠴⠛⠛⠓⢦⡀⠀⠀⠀⠀⠀⠘⡆⠀⡤⠒⠋⠉⢶⡀⣿⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠛⠛⠉⠉⠁
⣿⠀⠀⠰⣄⡸⠂⠀⠀⠀⠐⢆⣠⠀⠀⢰⣄⣀⡴⠁⠀⢀⡇⠀⢀⣤⣀⠀⠱⠀⠀⠀⠀⠀⠀⢹⡼⠀⣠⣶⣦⠀⢻⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠸⡇⠀⠺⣿⡿⠀⢀⡇⠀⠀⠀⠀⠀⠈⣧⠀⠙⠿⠛⠀⣸⣿
⢿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠲⣆⠀⢀⡇⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⢹⠳⢤⣀⡀⠴⠋⢹⡄⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⡀⣀
⠸⣇⠀⠀⠢⠀⠀⢰⠋⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⠉⠉⠉⢹
⠀⢹⡄⠀⠀⠀⠀⢸⠀⠀⠠⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⡾
⠀⠀⠹⣦⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣼⠁
⠀⠀⠀⠈⠳⣤⡀⠀⠈⠛⠲⠤⡤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠁⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⠇
⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣲⠶⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⣀⣤⠶⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢉⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢀⡾⠋⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⢀⡾⢄⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⢸⠃⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣸⠇⠀⠀⢠⡞⠁
⠀⠀⠀⢸⡆⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⢠⡟
⠀⠀⠀⠀⢷⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡼⣯⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠉⠳⣴⠏⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⠟⠉⠛⠶⣤⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣆⣴⠟⠁⠀⠀⠀⠀⠀⠉⠛⠶⠟

⠀⠀⠀⢴⣦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⠆⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⢀⣼⣷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⣶⡦⠀⠀⠀⠀⠀⠰⢫⣿⠓⠞⣁⣰⡿⢆⠀⣠⣴⣯⣁⡀
⠀⠀⠘⣻⣿⠀⠀⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡋⠳⠚⠀⠀⠀⠀⠀⢀⡾⠙⢻⠞⣹⣿⠛⠋⠀⣡⣴⡀
⠀⠀⠀⢹⢿⠀⠀⠰⢻⡿⠟⠆⠀⠀⠀⠀⢠⣄⠴⠋⠀⠞⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠏⠉⠻⠀⠚⠋⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣠⣼⣏⡀⠀⣀⣤⣼⡏⠀⠀⠀⠀⠀⠀⢫⣿⣟⡷⠃⠀⠀⠀⠀⠀⠈⢯⣿⣇⣀⡀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠈⣼⠿⣬⠉⠀⠉⣼⢿⣭⠉⠀⠀⠀⠀⣠⠟⠉⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠀⠀⠀⠀⠀⠚⠋⣹⣿⠛
⠀⠀⠰⠞⠁⠀⠉⠀⠀⠞⠃⠀⠃⠀⠀⠀⠀⠀⠁⣀⣀⣠⠇⠀⠀⠀⠀⠀⠀⠠⠞⠁⠈⢿⠀⠀⠀⠀⠀⠀⣤⠟⠉⠳⠄

⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠦⣤⣴⣶⣦⡄⠀⢀
⠀⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⣧⡤⠀⠀⠀⠀⠀⠀⣸⣿⣇⣀⡀⠀⠀⡇⠀⠰⣿⠛⣶⠋⠋⠀⢘
⠀⠀⠀⠀⠀⠞⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣐
⠀⠈⠀⢀⠀⢸⠇⠘⡇⢀⠀⠀⠀⠀⡀⠘⠛⠀⢻⡄⡀⠀⠀⠀⡀⠀⢀⡾⢹⡇⢀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠈⠀⠈⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟
⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠷⣶⠆
⠀⠀⠀⠀⠀⠀⡾⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⢀⠴⠖⠒⠶⠶⠒⠒⠶⠶⠒⠒⠒⠶⠶⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶

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

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

⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⡔⠉⡍⠁⠀⠑⡄⠀⠀⠀⡠⠚⠡⠊⠀⠉⢢⡀⠀⠀⠀⡴⠋⠀⢀⠀⡙⢆⠀⠀⠀⡠⠊⠁⣀⣀⠈⠳⡀
⠀⢸⠲⠀⠀⠐⠐⠐⢽⠀⠀⠀⡇⠈⠦⠀⠀⠐⠀⡇⠀⠀⢸⠀⠀⠀⠈⠠⠄⢸⠀⠀⠀⡃⢰⠋⣶⡆⢱⠀⠁
⠀⠘⣄⠅⠀⠣⡀⣀⡜⠀⠀⠀⠳⣁⡆⠀⠀⠀⣰⠃⠀⠀⠘⣄⠀⠀⠀⠀⢀⡜⠀⠀⠀⢣⡈⠢⠽⠥⠊⣠⠃
⠀⠀⠈⠑⠒⠒⠛⠁⠀⠀⠀⠀⠀⠈⠉⠓⠒⠉⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁

⠀⠀⡠⢚⡽⠋⠉⠲⡄⠀⠀⠀⢀⣴⠉⠉⠉⠑⣄⠀⠀⠀⠀⣠⠖⣩⡙⢉⡲⡀⠀⠀⠀⣀⡠⠤⠤⠤⢤⣀
⠀⢰⢱⠃⠀⠀⠀⠀⣸⠀⠀⠀⡏⢸⠀⠀⠀⠀⡇⡇⠀⠀⢸⠡⠈⢄⠈⠀⠐⢻⠀⣠⢚⠁⠀⠀⠀⠀⠀⢸⡓
⠀⠸⡈⢆⡀⠀⣠⠞⡸⠀⠀⠀⢧⠈⠲⠤⠤⠞⢠⠃⠀⠀⠸⡔⢢⡀⠡⠀⠤⡻⠀⠘⢿⣍⠉⠀⠀⠉⣉⡽⠟
⠀⠀⠙⠢⠬⠭⠕⠊⠀⠀⠀⠀⠀⠑⠦⠤⠤⠒⠁⠀⠀⠀⠀⠈⠳⠤⠦⠥⠊⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⢀⠤⡶⢲⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢤⢒⢢⠛⡿⠾⡆⠀⠀⠀⠀⣠⠴⡶⠖⡤⣀
⠀⢠⠃⠐⠀⠀⠀⠀⢳⠀⠀⢠⡖⠉⠁⠀⠀⠉⠑⢦⠀⠀⠀⢸⣿⢸⢰⢻⣸⠁⠀⠀⠀⡜⢡⠛⢊⡅⠂⡏⡆
⠀⠸⡀⠀⠀⠀⠀⠀⡿⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢻⣾⣾⡾⠃⠀⠀⠀⠀⣗⠰⠐⡆⠐⣩⠒⡇
⠀⠀⠑⠤⣄⣀⡤⠔⠁⠀⠀⠀⠈⠉⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⡿⠿⡇⠀⠀⠀⠀⠀⠘⠲⣥⣔⣷⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⡠⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⠤⠄⠒⡢⢄⡀⠀⠀⠀⠀⠀⢰⠉⡆⠀⠀⠀⠀⠀⠀⠈⢣⣈⣯⡰⠋
⠀⢠⠊⠀⠀⠀⠀⠈⢳⠀⠀⠐⢭⣁⣠⠀⣟⣭⠆⢱⠀⠀⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⠀⡠⠚⠛⠙⠣⣄
⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣲⣷⣖⣧⣜⣋⡇⢸⠀⠀⠀⠀⢀⣎⣀⣧⠀⠀⠀⠀⠀⡜⡐⢡⡀⠀⠈⡘⡄
⠀⠈⠣⣄⡀⢀⣀⠴⠃⠀⠀⢸⣞⣻⢽⣿⣁⠤⣤⠎⠀⠀⠀⠀⢸⠦⠢⢾⠀⠀⠀⠀⠀⢡⡀⠀⠀⢀⠠⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠃⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡋⡸⢶⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⣡⣈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠰⠄⠀⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠘⢀⠀⡤⣤⣤⣤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢼⣿⣇⠀⠀⣰⠻⠟⠻⡇⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⢠⣿⡿⣻⢟⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠻⠆⠒⠉⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠐⣸⡿⢟⠁⠙⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠠⣀⢿⣠⡀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⢿⣿⣷⣭⣬⣵⣿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣁⣻⣇⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⡟
⠀⠀⠀⠀⠀⢾⡂⠈⠉⠉⠉⠩⠅⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣧⣀⡀⢀⣀⣧⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⣿
⠀⠀⠀⠀⠀⠸⣦⣤⣤⣤⣤⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠀⠈⠉⠉⠁⠀⢒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠑⡠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠹⣿⣿⣿⠏⠉⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⡐⠿⠻⣄⣀⠐⠒⠚⢀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠛⠁⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠓⠒⠀⣘⡃⠀⠀⠀⠀⠀⠀⣨⠀⠀⢀⣀⣤⣤⣀⣀⣀⣀⣀⣡
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⣚⠀⠀⠀⠀⠀⠀⢰⣿⣄⣀⣀⣠⣀⣀⣀⣀⣤⣤⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠿⣿⣣⠄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⣿⠃⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣷⠰⠀⠱⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣿⣁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠰⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠴⠾⣖⠛⠰⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⢿⢼⣧⣤⣠⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠂⠈⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⢀⡤⠔⠒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢠⡄⢀⡀⠀⠀⢀⣿⠃
⠀⠁⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢈⠇⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⡄⠀⠀⣀⡀⠀⠀⢄⠈⠢⡀
⠀⠎⠀⠀⠀⢰⠓⢦⡀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣧⡀⠀⢀⣠⣴⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣠⠞⢉⡿⠀⠀⠀⢳⠀⠹
⠀⠀⢠⡴⠤⣈⢳⡀⠳⡄⣾⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⣴⠟⣉⡀⠀⠀⠀⠀⠈⠉⠀⠉⠙⢷⣄⠀⠀⠀⠀⠀⢀⡴⠒⠒⢦⣟⠈⠙⠃⣴⢛⣀⣀⠀⠀⠘⡇
⠀⠀⠀⠱⢦⡈⠳⠟⠁⣹⠿⢰⡃⠀⠀⠀⠀⠀⠀⠀⣸⠇⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣦⡙⣧⠀⠀⠀⠀⠘⠷⠒⠛⡦⠈⠻⣦⠀⠘⢋⣠⡼⠃⠀⠀⡇
⠀⠀⢀⡤⠴⠨⠗⠀⡾⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⢧⣀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠁⠸⣇⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠘⠆⠀⠛⢤⡀⠀⠀⢸⠇
⠀⠀⠈⠑⠒⢲⠖⠀⠁⠀⠀⠰⢏⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡇⠀⠙⠓⠶⠤⠤⠴⠖⠛⠁⢸⡀⠀⣿⡀⠀⠀⠀⠀⠀⢀⡽⠂⣤⣠⡴⠟⠓⠲⠃⠀⠀⠉
⠀⠀⠀⠀⠰⡥⠞⠛⠶⠶⠞⢧⡀⠳⣄⠀⠀⠀⢠⡞⡛⠂⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠍⢳⠀⠀⠀⣰⠏⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠈⢳⡶⠀⠀⣿⣿⣷⣤⣄⣀⣀⣀⣀⣤⣴⣿⡇⠀⢲⣴⠟⠀⢠⡞⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠳⣄⠈⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣗⢀⡴⠋⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣷⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⠀⠀⠀⢹⡟⠿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣇⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⣡⡿⠃⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣄⠀⠙⠳⠶⠶⠞⠋⠀⡀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡀⠀⠈⠳⣦⣄⣀⣀⣠⣴⠞⠁⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠳⠦⣄⣀⣉⠉⠉⠉⢀⣀⣀⣤⠴⠚⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣠⣤⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⢦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠢⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡇⠘⣇⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣧⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠙⣆⠀⠀⠀⠸⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⢀⣠⠶⠛⠙⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⣄⠀⠀⢠⠟⣻⠻⠶⠶⢶⣶⣶⣶⣶⡶⠶⠾⠟⠻⣏⠻⣄⢀⡴⠛⠁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⠶⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⠋⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⠋⠁

⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣖⠱⣭⠎⢤⠀⠀⠀⠀⠀⠀⠘⢦⣙⣋⡼⠁⠀⠀⠀⠀⢀⢠⡴⣐⠿⣠⢦⡄⡀⠀⠀⠀⠀⣀⣀⡀⢀⡠⢄⢄
⠀⠸⣿⠃⣿⠰⣿⡇⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀⠀⠀⠀⠀⠀⠈⢻⡞⢹⣿⠉⣿⡎⠀⠀⠀⠀⡀⠛⠛⢋⡙⠋⣟⢕
⠀⠠⠿⠜⠉⢣⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠿⠻⠃⠻⠇⠀⠿⠗
⠀⠴⠤⠶⠤⠷⠤⠦⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠈⠁

⠀⠀⢠⣴⠶⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⢆⡄⠀⠀⠀⠀⠀⠀⢠⣤⠀⣴⡄⢠⡄⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⣼⣿⢈⠁⣿⣥⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣬⣥⣤⣽⣤⣬⣥⡄⠀⠀⠀⠀⣤⣽⣥⣼⣧⣀
⠀⠀⣿⠛⢿⡟⠋⣿⠀⠀⠀⠀⠀⠀⠀⡼⠿⡀⠀⠀⠀⠀⠀⠘⢿⣿⢻⣿⡿⣿⣿⠃⠀⠀⠀⢀⣁⡿⣧⣼⢧⣄
⠀⠀⠘⢷⣾⣷⡞⠃⠀⠀⠀⠀⠀⣏⣉⣇⣀⣏⣀⡆⠀⠀⠀⠀⢸⢿⢸⣿⡇⢿⡿⠀⠀⠀⠀⠤⠭⠤⠬⠭⠤⠬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢾⣿⡟⠟⣿⣿⠂⠀⠀⠀⠀⣀⢀⣤⠀⡿⠫⠿⠇⠀⠀⠀⠀⡀⠘⢀⣁⠀⠃⡀
⠀⠀⢹⣿⣾⣟⠁⠀⠀⠀⠀⠀⠈⢲⣥⠞⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢿⣹⡇⠀⢠⠀⠀⠀⠀⣤⣶⢦⡄⣤⢶⣶⡤
⠀⠀⣿⣏⢙⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣧⠀⠀⡄⠀⠀⠀⠀⠉⠙⠛⠁⠉⠛⠉⠁
⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠂

⠀⠀⢠⣤⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⡀
⠀⠀⠈⣇⠶⠶⣺⠃⠀⠀⠀⠀⠀⠈⠧⣜⣫⠼⠁⠀⠀⠀⠀⠀⢰⡆⢠⣯⡄⢹⡏⠀⠀⠀⠀⠀⣠⣤⣤⡀⢴⣶
⠀⠀⠀⠻⢷⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡟⠈⣿⠁⡸⠇⠀⠀⠀⠀⠀⠁⠾⠻⠟⠯⠁
⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠜⠇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠈
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠙⢦⡀⠀⠀⠀⠀⠀⣰⠞⠛⠙⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⣠⠴⠖⠛⠛⠛⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣰⢦⡀⢳⡄⠀⠀⠀⠀⢿⠀⢺⠛⠒⠛⠦⡄⠈⣇⠀⠀⢀⡾⠁⣠⠴⠚⠛⠛⠲⣤⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣴⠃⠈⣧⠈⢳⡀⠀⠀⠀⣾⠀⣼⡀⢀⣀⣀⡿⠀⣹⠀⠀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠈⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠏⠀⠀⠸⣇⠘⣧⠀⠀⠀⣽⠀⣈⠉⠉⡉⠉⠀⢶⡃⠀⢰⡇⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠺⠖⠒⠲⠖⠛⠀⠸⡄⠀⠀⢻⠀⢹⠋⠉⠙⠓⢦⡀⠙⡆⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠶⠶⠒⠶⠶⠶⣆⠀⣷⠀⠀⢻⠀⢻⠀⠀⠀⠀⣠⡇⠀⡏⠀⠹⡄⠘⢦⡀⠀⠀⠀⠀⣠⠋⢉⡷
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡟⠀⠀⠀⠀⠀⠀⢹⡆⢸⡇⠀⣾⠀⠘⠛⠛⠛⠋⢁⣀⡼⠁⠀⠀⠙⢦⡀⠙⠛⠓⠛⢉⢁⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠚⠃⠀⠈⠓⠒⠒⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⡤⠀⠀⠄⡀⠀⠀⡠⠄⠀⠄⡀⠀⠄⠠⠤⠀⡀⠀⠤⠠⠠⠀⡄⠀⠠⠀⠀⠀⢤⠀⢀⠠⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠊⡜⢂⢡⠀⠀⡂⡅⣈⡠⠁⠀⠎⠜⠁⠀⠑⠘⠀⠀⠃⠀⠐⡐⠀⠀⣁⣀⣀⠀⠀⠀⢈⣀⣀⠀⢠⢁⠊⠀⠈⠒⠃
⠀⠀⠀⠀⠀⠀⡀⠰⠀⠜⠂⠀⠀⠁⠶⠐⢄⠣⠀⠀⡀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠄⠇⠀⠄⠀⠘⠀⠀⠀⠰⠀⠐⠃⠀⠸⠀⠀⢖⢀⡒⡄
⠀⠀⠀⠀⠀⢀⢃⠋⠉⠉⠱⢀⠀⡆⠦⠀⢐⡸⠀⠱⣕⠢⠄⣈⠔⠀⡀⠆⠀⣊⠔⠀⡀⠦⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠣⣑⠠⠀⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠄⠀⠀⠐⢱⠀⠐⢲⠀⠀⠀⠀⢸⢡⠀⡊⠄⢀⢔⠆⠀⠋⠀⠀⠀⠀⡎⠄⠀⠀⠠⠒⠀⠔⠰⡀⠀⢐⢓
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠢⠀⠄⠆⢸⠀⠀⢸⠀⠀⠀⠀⢸⠐⠀⠅⠖⢡⠊⠀⠀⠀⠀⠀⠀⠀⠂⡌⡄⢀⢁⠈⠀⡀⠺⡌⢆⠨⢘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡋⠉⠉⠁⢸⠀⠀⢸⠀⣀⡀⠀⡈⠀⠀⡇⠔⠢⠱⡀⠀⠄⠀⠀⠀⠀⠄⢣⠰⡌⡘⠀⡂⠀⠀⠈⢌⠻⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠅⠀⠀⢠⡸⠀⢠⡼⠀⠢⢁⣈⠄⠁⠀⣧⠅⠀⠑⡴⠀⢅⣁⣀⡰⠀⣤⠀⠦⠐⠀⣠⠄⢄⠄⠀⠀⠡⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡩⠄⠀⢍⢂⠀⠇⠄⠀⢌⢢⠀⡐⡩⠄⠀⢍⢂⠀⡇⠄⠀⢌⢂⠀⠐⠩⠄⠀⠭⠂⠀⠓⠀⡀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡂⠀⡅⢂⣐⠊⠌⠠⢰⠀⠀⠀⠀⡂⠀⡇⢒⠐⣊⠌⠀⠰⠄⡒⣒⡠⠄⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢂⡀⠀⡰⣠⠀⡇⠅⠀⠀⠀⠀⢄⢄⡀⣎⠲⣠⠀⡇⠅⠑⠌⠆⠀⣠⢄⡀⠀⢸⢐⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠂⠁⠀⠓⠂⠀⠀⠀⠀⠀⠑⠀⠀⠒⠋⠀⠓⠂⠀⠈⠒⠀⠈⠐⠂⠀⠒⠁⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⡤⡀⡠⡀⠀⠀⠀⡄⡀⡠⡄⠀⠠⢄⠀⢀⣤⠀⢀⢄⠀⠀⡠⡀⠀⡠⡀⠀⢀⢄⠀⢀⡤⠠⠤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢘⠀⠀⠀⠀⡂⢠⠰⠀⠀⡘⠐⠀⠠⢀⠀⠃⡀⡄⠀⡘⠀⠈⢄⠠⠌⡐⠁⠀⠡⡑⢤⢂⠎⠀⠀⠁⢈⠖⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢘⠰⠀⠀⠀⠀⡅⠀⢂⠡⡐⢀⠁⠀⠀⠆⡾⠈⠇⢱⢁⠃⠀⠀⠠⢃⡘⡀⠀⠀⠀⢸⠀⠊⠀⠀⠀⡠⢋⠎
⠀⠀⠀⠀⠀⠀⠀⠘⡌⠤⠤⠜⡠⠀⠀⠈⢌⢃⠂⠀⠀⠀⠐⠀⡆⠰⡀⠜⠀⠀⡰⠡⠊⠐⡘⢄⠀⠀⢸⠐⠀⠀⠀⡔⠡⠥⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠁
⡿⢿⠿⡿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣟⣛⣿⣟⣻⣿⣛⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡟⠀⠀⠀⠀⢸⠃⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠶⣄⠀⠀⣀⡤⠶⠒⠚⠉⠉⠉⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡾⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠑⢾⠀⢸⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡴⠶⠦⣄⠀⠀⠀⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡠⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡠⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⡞⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⢠⠙⠦⠀⠠⠞⠑⢄⣀⡰⠳⡄⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⡰⠋⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠁⣠⠤⠤⡀⠀⠀⠀⠀⢠⡀⢈⡑⠒⢖⠹⡇⠀⠀⠀⠠⣞⣠⣤⠤⠶⠖⠋
⠀⠀⠀⠀⠀⠀⣾⠀⠠⠄⠴⠀⠀⠀⢄⡀⠀⢠⣄⡠⠃⠀⡜⠀⣠⣄⠈⡆⠀⠀⠀⠀⢷⠃⣠⣦⡈⢷⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡄⠀⠀⠀⢣⠀⠻⠟⠀⡆⠀⠀⠀⠀⢸⣄⠈⠋⢀⡾⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⢄⡀⢀⠞⠁⠀⠈⠲⠔⠁⠀⠀⠀⠀⠑⠤⠴⠊⠀⠀⠀⠀⠀⠀⡆⠉⠀⠉⠀⢳⠀⠀⠀⠀⢾⡛⠓⠒⠒⠶⡦
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⠀⠀⠰⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⣄⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠢⣄⣀⡀⠀⠀⠀⠀⢸⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠥⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⣆⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⢨⡇⠀⠀⠀⠀⠈⡄⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠙⠒⠤⢄⣀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀⡤⠋⠁⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠁⡞⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡎⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠈⠲⢤⡾⢣⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢣⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⠢⡀⠀⠀⠀⣴⠋⠈⠓⠦⣄⡀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠲⣤⠎⠙⣇⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⣞⡁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⠞⠁⠀⠉⠓⠦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢩⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠨⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣙⢐⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣆⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠻⣿⣿⣿⡿⠃⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣤⣤⣤⣤⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡛⠛⢛⣁⣀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⣛⣉⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠀⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠸⠿⠟⢸⣿⣿⢿⣿⣿⣧⣽⣿⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⢸⣿⣿⡿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣉⣀⣉⣉⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣇⣀⣀⣀⣈⣉⣁⣀⣉⣉⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢛⣛⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⡆⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠠⢾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠘⠛⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠰⢶⡒⠶⠶⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠯⠭⣉⣉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠛⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣤⠤⢄⠀⠀⢠⡬⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⠋⠀⠀⠀⠱⣄⠀⠉⠓⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡏⠀⠀⠀⠀⠀⢹⡀⠀⣀⡬⢍⠂⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⢀⠀⢘⡷⠋⠁⠀⠈⡇⠀⠀⠈⠁⠒⣲⠂⠀⠀⠀⠀⠀⠀⠀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣄⠈⣇⠀⠀⢰⣏⣡⠎⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣌⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠁⠹⣄⠀⠈⠋⣟⣤⠀⠀⢀⡀⠞⠀⠀⠀⡍⠁⢸⣇⣠⢤⣄⣀⠀⠀⠀⠀⢹⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠓⠠⢌⡓⠆⠚⢇⠉⣠⠖⠉⠀⠀⠀⠀⠼⠀⠀⠠⣤⡴⠦⣤⡈⠱⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠱⠀⠀⠈⠿⠁⠀⠀⠀⠀⢀⠎⣰⠀⠀⢀⠀⠉⠙⠋⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⡏⠀⠀⠌⠙⠓⠶⠤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⢠⠀⠑⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠐⣤⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠲⢤⣀⠀⠀⠀⠀⠀⣧⣀⡀⠀⠀⠘⠧⠀⠀⠀⠈⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡀⠐⠃⠄⠀⠤⣼⠑⠢⢄⡀⠀⡟⠉⠀⠀⠀⠸⣷⠁⠀⠀⠘⡄⢿⠲⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣡⠞⠐⠉⠉⠉⠹⣄⡤⢴⠈⠒⠁⠀⠀⠐⡆⠚⠛⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠑⠚⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡍⠙⠉⠉⠉⠉⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠗⠓⠂⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢚⡤⠤⣼⣀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⣾⣤⢶⣹⣽⣭⠉⠑⠒⠒⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠛⠓⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠃