Stitch Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠑⠢⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⡱⡄⠀⢀⠔⠉⠁⠀⠀⠀⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠉⠢⡀⠀⠀⠘⡀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡹⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⢄⠀⠀⠐⢄⠀⠶⡀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠁⠀⠀⠠⠀⠀⠈⢨⠀⢀⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡩⠂⠀⠀⠀⠀⠀⠱⡒⠤⣀⣘⠈⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⣤⣶⣶⠶⣤⡀⠠⣀⡈⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠉⠛⠦⣄⠀⠀⠀⠘⡀⠀⠀⣾⣿⣯⣿⣦⣼⣿⣎⠻⡇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠈⠑⠄⠀⠀⠱⢀⠀⠘⠿⣿⣿⣿⣿⡿⠛⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⡄⠀⠀⠀⠀⠀⠁⠂⠠⠈⠉⠉⢁⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⣀⣀⠀⢀⣀⣠⣶⡿⠷⠀⠀⠲⢄⠀⠀⠀⠀⠀⠐⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⢠⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠌⢢⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠡⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠑⠄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡎⠀⠄⡆⠀⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠈⢂⠀⢹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣇⣀⡀⠀⠀⠀⠀⠀⡄⢸⠁⠃⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢼⠀⠀⠀⠀⠐⠒⠒⠛⠋⠁⠀⢠⢥⠚⠉⡹⢆⠀⡇⠨⠤⡈⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡀⠀⠀⠁⠂⢀⠴⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣄⣀⠀⠀⠀⠀⠀⠨⠊⠀⡼⠍⡓⣸⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣙⣫⠔⠉

⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠘⠷⠶⠦⣄⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣰⡄⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣤⢠⡔⠂⠉⢉⡁⠈⠉⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⣠⠞⠁⠘⠀⠀⠄⠈⠁⠐⢂⠀⠀⢀⠼⠛⠛⠳⣄⠀⠀⢀⡏⠈⣧⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡼⠸⡀⢰⠟⢻⣧⡐⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⡴⠲⣶⣦⡌⢳⡄⣸⠇⠀⢻⡀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣏⠀⡿⣼⣿⣿⣿⣣⡄⠀⠀⠀⠀⢀⣴⣄⡇⢸⣿⣿⣿⣿⣿⡆⢻⡟⠀⠀⢸⡇⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⣧⠀⠇⢻⣿⡿⠫⠙⢿⡀⠀⠀⠀⣾⡿⠏⠐⢄⠻⢿⣿⣿⡿⠃⠘⡇⠀⠀⣼⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠋⠉⢹⠇⠀⢽⢸⠇⠀⠀⠀⠀⠀⠈⠁⠀⡄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢻⠀⢠⣏⡴⢾⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⣼⠀⢀⠠⠄⠒⠂⠳⢌⠨⠁⠉⢀⡐⠒⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠠⠟⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣽⠰⡎⠤⠀⠄⠀⠀⠀⢀⠐⠂⠐⠀⢀⣁⠀⢀⡤⠁⠍⠙⢉⠇⢰⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡌⢢⡀⢠⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⣤⠀⢤⠆⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⢄⣸⠋⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠣⡄⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⡤⠚⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠾⠓⢄⡒⠸⠦⠸⠐⣄⠀⠦⠖⣂⣡⠴⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⠶⠂⠉⠉⠀⠈⡑⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡈⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⡏⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡐⠀⠀⠀⠈⠗⢠⡐⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⢰⠊⠙⡀⠀⠀⠀⠀⡠⠖⠂⠐⠓⠢⣄⠀⠀⠀⠀⠀⠀⠈⢴⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡤⣈⠱⡀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢠⠀⠀⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠢⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⢉⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢧⣀⠠⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢉⠆⠀⠀⠀⢈⡀⠶⢀⣀⣀⠀⢀⡺⠳⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⢀⠀⠈⠴⣬⠭⠵⠉⠉⠉⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⣀⣤⠷⣤⣄⡀⡷⠚⠒⠂⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠘⠋⠁⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠁⠈⠉⠙⠂⠚⠁⠉⠀⠀⠃⠙⠐⠈⠀⠁⠁⠛⠓⠀⠀⠘⠉⠋⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⣤⡄⠴⣄⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠇⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠻⡕⠦⢀⣤⣀⠀⠀⠀⠀⠈⠓⠴⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⡤⣴⢮⡶⡻⢇⡀⠀⠀⠀⠀⠀⢀⠀⠙⠒⠉⢉⣿⢦⣀⡀⢦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⢉⣙⣋⣿⣀⣙⣃⣠⡀⠀⠀⠈⠀⠈⠑⠀⠀⠀⠀⢻⣿⣿⠁⠀⠙⣥⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠉⠉⠀⠀⠀⠀⠉⠉⠓⢤⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠈⢱⣆⠄⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⠀⠀⡿⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠞⠀⠀⢀⣤⠄⠀⠀⠀⠸⣏⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣦⡀⠙⢿⡷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠋⠁⠀⠀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢒⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⣠⠶⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠉⠓⣒⣶⡾⠯⠥⠴⠄⠀⢀⡶⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⣀⣀⣤⡤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⡰
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣾⠃⠄⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠙⢆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⣧⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠐⠀⠀⢀⣀⠀⠀⠀⠀⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠉⠀⠉⠳⠀⢤⠈⢐⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡀⢀⢀⠀⣤⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠂⠐⠒⠂⠀⠀⠀⠀⠀⠴⠃⠈⢾⠉⠃

⢰⣶⣶⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⣦⣄
⢸⡇⠀⢘⡿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡠⠘⠁⠀⠀⠁⠀⠈⠉⠑⠲⣄⡀
⢸⡇⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⣴⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⢦⡀
⢸⣧⣤⡖⠛⢢⣤⣼⡇⠀⠀⠀⠀⣾⠁⣠⣦⣌⣆⢀⡴⠚⠉⠉⠑⠢⣼⡾⣷⣆⢱⡀
⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⡇⢸⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠸⣿⣿⣿⣿⡿⠿⣦⡀⠀⢠⠟⠻⣿⡿⠿⢁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠈⢦⣀⣩⣥⡊⠀⠤⠤⠭⠻⠦⠤⠤⠤⠭⣭⣅⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⡰⢦⣔⣺⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠓⠋
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠞⡇⡆⠀⡋⠉⠉⠉⠳⡀⠀⠀⠀⠀⢹⣽⣷⣄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⡰⠃⣀⡤⠞⠁⠀⣷⠁⢀⡅⠀⠀⠀⠠⣇⣀⡀⠔⠋⠈⠛⠟⠃
⠀⠀⠀⠀⣰⡵⠚⠁⠀⠀⠀⢀⡟⠀⡌⠀⢣⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠒⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡸⠁⡜⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠑⢆⠑⠄⠀⢀⣀⢴⠉
⠀⠀⠀⢸⠅⠀⠀⠠⢄⣀⡴⠁⡜⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⣿⣿⣺
⠀⠀⠀⠘⡇⠀⠀⠀⡆⠀⠀⡸⠁⠀⠀⠀⢰⠀⠈⠓⢦⣀⣀⣀⣀⢄⣱⠀⠀⠟⠛⠛
⠀⠀⠀⠀⢳⡀⣀⠞⠁⠀⢠⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠡⠉⠉⡁⠀⠀⣤⣠⢾⠂⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠟⡁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠁⡠⠄⣠⠎⠀⣣⣤⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⣏⣑⣒⣶⡶⠾⠛⠁⠀⠉⣉⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠠⠤⢔⣿⠀⠀⠀⠀⠘⠿⣦⣴⣦⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠶⢶⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⡄
⠀⠀⠀⠀⠀⠰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⡴⠷⠠⣠⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢻⡆
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣷⠟⠋⠙⠓⠤⡀⠀⠀⠀⠀⠀⠀⢹⡄⣿⡀
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣀⣀⠀⠈⠢⠀⠀⠀⠀⠀⠘⣧⢻⣧
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣢⣤⣤⣿⣓⣄⠀⠀⠀⠀⣠⠚⢹⣿⣿⣆⠀⠀⠀⢀⡀⠀⠀⣿⣾⣿⣤⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⣿⣿⡄⠀⠀⠀⢠⣶⠟⠳⡄⢀⣸⡾⠛⠋⠉⠉⠻⣿⣿⣧⡆⠀⢀⣿⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣆⠀⣿⣿⣿⣿⡶⠚⠛⠛
⠀⠀⠀⠀⠈⢷⣿⣿⣿⣄⠀⢠⣾⠃⣀⡀⠈⢰⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠈⠻⣿⣻⣿⣶⣾⡇⣼⣀⣵⡀⣼⣄⣀⢀⡀⣠⣾⣿⣿⣿⣿⡿⡀⢸⣿⣿⣿⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⢡⠀⠈⠉⠙⠉⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⢹⣿⣿⣿⡎⠻⣿⣿⣿⣿⣿⣿⣿⣟⣁⣠⣤⣥⣶⡶⣴⣶⠶⠾⢿⣿⣿⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⢿⣟⡿⠇⠀⠙⣛⣿⣿⣿⣿⣟⠋⣹⣿⣿⣄⠀⣀⣾⣿⣷⣤⣾⣿⣿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⢈⣁⣤⣶⠿⣿⣯⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡙⣿⣏⣿⡿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣋⠀⠀⣿⣿⣿⢿⣿⠿⠟⠛⠛⠛⠛⠁⢀⣼⠃⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠿⣿⣯⠞⠙⣦⣤⣤⢤⣤⣶⠞⢻⡟⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠀⠀⠈⡿⠃⠀⠘⠧⠄⠀⢀⣴⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⢷⣦⣤⣤⣠⣤⣤⣴⡶⠟⠁⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⡄⢙⡛⠋⠉⢸⠃⠀⠀⠀⠀⢾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠛⠀⡀⢠⣄⠀⢀⣤⣾⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⢀⠀⣠⠞⠀⣸⠿⠃⠉⠀⠀⢠⣴⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣤⣄⠀⠀⢠⡆⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣟⣉⣉⣙⣿⣿⣿⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠀⢠⣿⣧⣤⣄⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣿⣿⡿⣶⣿⠿⢫⡥⣤⣹⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣁⣂⡴⣿⣿⣧⡻⠿⠟⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠁⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣦⠑⢸⡏⠀⠀⢄⣴⢦⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣮⣀⣉⢁⣤⣼⣿⣋⣹⡟⠉⠙⢿⣿⠿⠻⠿⣿⣿⣿⣿⣹⣾⣷⡀⡈⢞⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⠿⠛⠿⠿⠟⣻⣿⡿⢿⣿⣷⣴⣶⣿⣿⣷⣶⣶⣿⣿⣿⢿⣿⣿⣿⣧⣥⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠉⠰⡿⠋⠉⠛⠋⠁⣾⠟⠙⠛⠉⠀⠀⠀⠉⠛⠻⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⣄⡇⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡆⡞⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠇⠀⠀⠀⢠⢎⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⠃⡼⠀⣠⣤⡤⢤⠀⠲⠤⢤⣦⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⢠⠇⢀⡧⠊⠁⠀⢙⠆⠀⠀⠀⠀⠈⠁⠘⣄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡼⣇⣏⢆⡜⢠⢊⣴⣾⠟⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠞⢻⣌⣷⡃⢸⣿⣿⣶⣿⣎⡤⠤⠶⣿⠶⠀⠀⠀⡠⠒⠺⣧⠀⠀⠀⡼⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠯⣭⠏⢻⠈⠇⢧⡘⢿⣿⣿⣿⣇⠀⠀⠀⠀⠑⡄⣠⠊⣀⣀⡀⢹⠀⣠⠊⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⡴⢾⡲⡏⢹⡘⣷⣮⣷⣶⣋⡀⠻⡄⠀⠀⢀⣀⣿⣵⣿⣠⣿⣷⢸⡜⠁⡼⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣅⡼⠀⢧⠹⣿⠿⠷⣾⣿⣷⣿⣷⣚⠛⢡⢿⣿⣿⣿⣿⠇⡟⠀⡼⠁⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠒⢒⡿⠳⣜⢮⣳⠀⢉⣿⣿⣿⣾⣷⢮⣦⣙⠛⠋⢁⣴⢃⠞⠁⣀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠚⠉⠀⣰⡞⠳⢍⡻⢇⣠⣄⠀⣩⡛⣿⣿⣿⣭⠍⡩⠿⣥⣤⡠⢋⡽⣲
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠏⠀⠀⠀⠉⠓⠫⣭⣞⣓⣛⣚⣋⣩⣕⣫⠭⠭⣍⣁⡴⠉⣻⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢄⠉⣙⣯⡭⠷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⠤⠞⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠜⣈⡉⣷⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠞⠁⠀⣰⠋⠉⠉⠉⠙⠓⠒⠶⢤⣀⣀⣀⣠⠴⠒⢄⣽⡌⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠋⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠱⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡤⠖⠋⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠼⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣸⠹⡆⠀⠀⣠⡴⠚⠛⠉⠉⠙⠛⠶⢄⡀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡇⠀⣇⣠⠞⠉⡇⠀⠀⠀⠀⠀⠀⠀⡰⠿⣦⠀⠀⠀⢀⡟⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠁⠀⣿⣃⣀⠀⠁⠀⣤⣶⣦⡀⠀⡜⠀⠀⠈⣇⠀⣠⢟⡇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠸⡆⢀⣿⣿⣦⡇⣶⠋⠀⠀⠉⠳⡘⢠⡒⢲⣄⢸⣴⠃⣸⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣳⢸⣌⢿⣿⢇⢷⡀⠀⠀⠀⣠⡇⣿⣿⣿⡟⢸⠇⢠⠇⣠⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⢻⣶⣒⣈⣀⣑⣦⣤⣞⠋⣱⠽⢿⡋⢤⣾⣴⣧⣤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣌⠀⠉⣶⠆⠀⠀⠐⠂⠙⣓⣒⣶⡿⠋⣸⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠀⢀⡇⡇⢀⣴⠀⠀⠀⠞⠁⣿⠀⠤⠋⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣠⣎⡴⢶⡀⠸⡇⠀⠀⢣⡰⠼⣄⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⣧⠀⠀⠀⠀⠀⠙⠢⡈⠓⢶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠢⠄⣀⣀⣀⣠⢔⠃⠀⠀⠀⠀⠈⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣅⡀⢀⣀⣠⡤⠟⠋⠉⠉⠉⠉⠓⠦⣄⣀⣤⣄⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠳⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠀⠀⠀⠉⠓⠶⣤⣀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡴⠿⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠚⠻⣦⡀⠀⠀⣾⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣇⢷⠀⠀⣠⠟⠀⠀⠀⠛⠀⠀⢀⠤⠶⠦⢤⠀⠀⠈⠀⠀⠀⠈⢷⡀⢀⡇⣸⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⠘⣇⢠⡏⢀⣤⣤⣄⡀⠀⠀⠐⢚⣉⣉⠒⠀⠀⠀⣠⣤⣤⡀⠈⢷⣸⠁⣿⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢸⡄⠘⣿⢀⣿⣿⡀⣸⣷⠀⣰⠞⠉⠉⠉⠙⢦⡀⣼⣿⣅⢀⣿⡆⠸⡏⠀⡟⠀⣀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⢷⠀⣿⠸⣿⣿⣿⣿⣿⢰⠃⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣿⣿⡇⠀⡇⣸⠃⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡬⣧⣿⠀⠙⢿⣿⡿⠋⠘⣇⠀⠀⠀⠀⠀⢠⠇⠈⠿⣿⡿⠟⠁⠀⣿⡯⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣄⣄⡀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠖⠉⠀⠀⠀⠀⠀⣀⡀⣸⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣍⣉⠉⠉⠉⠉⠭⠭⠭⠭⠭⠽⠋⠉⠉⢉⣉⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠻⡛⠛⠛⢛⠛⠛⠛⠛⠛⣻⠛⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣀⣀⣹⣄⡀⢾⣦⠀⠀⢀⣰⣃⣀⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠘⠋⠉⠁⠈⠉⠛⢮⠿⣡⠞⠉⠁⠀⠈⠙⠶⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠀⠀⠀⠀⢸⡇⡏⠀⠀⠀⠀⢀⣀⢀⣀⣸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣗⣀⣀⣤⡼⠋⢷⣄⢀⠀⢀⡞⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠛⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⡿⢿⠿⣿⠿⣿⣿⠿⣿⠿⠿⣿⣿⡿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣿⣏⣿⣿⣯⣷⣿⣾⣋⣿⣿⣹⣶⣽⣿⣿⣿⣯⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟⢀⣴⡶⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢛⡷⣼⣿⠀⣀⡀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⠤⠴⠒⠒⠒⠲⠶⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢠⠜⠁⠈⢀⣠⣨⣿⡟⠋⡼
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠊⠀⠘⢛⠀⠀⠟
⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠀⠀⡦
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢦⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳
⠀⠀⠀⠈⠂⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣆⠀⠀⠀⠀⠀⠀⠀⠰⣄⡸⠿⣷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠯⣍⣉⠉⠉⠉⠙⠓⠒⠲⠤⣀⣣⠈⢆⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣒⠢⠤⠤⠤⠤⢤⣌⣣⣄⡀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠀⠀⠀⣀⣀⣀⣀⡀⠈⠲⢌⠉⠓⠦⡀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠋⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠣⠐⠂⠼⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⢸⡇⠀⠀⠀⠀⠀⡟⠉⠙⣿⣿⣿⣿⣿⣿⣷⠀⡆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠁⠀⠙⠤⡀⠀⠀⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⠏⡠⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠤⠬⠉⣩⣭⣿⡅⠘⠀⠀⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡎⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠒⠒⠒⢒⣈⣻⣿⣭⡥⣀⠀⠀⠀⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢠⠎⠁⠀⠀⠀⠀⠤⠾⣿⣿⣿⣿⣿⣿⣷⡌⠣⠀⠀⠅⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢿⠀⠀⠀⠀⠀⢸⣄⣀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⠃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⡰⢠⢀⡴⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⡀⠀⠀⠈⠉⠉⠉⠉⠁⣀⠤⠊⢀⡠⠞⠁⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠭⠵⠶⠒⠂⠒⠚⠛⢒⡶⡻⠁⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣤⣞⣉⣁⣀⣀⣄⣠⣤⣤⡤⠶⠶⢺⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⡠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠸⣿⠿⠟⠂
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣀⡸⠋⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞
⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦
⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢢⡀⣰⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⡆⢠⡀⢈⣉⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⡟⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠧⠀⠙⠛

⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃
⠀⣭
⠀⣿
⠀⣿
⠀⣿
⠀⣿
⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢻⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡀⠙⣆
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢂⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⠀⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠋⠻⣆⢀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠘⢦⠀⠀⠀⢀⣠⡔⠚⠉⠙⠀⠀⠀⠀⣩⠞⠛⠳⣦⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢇⢀⡴⠋⠛⠀⠀⣀⡀⠀⠀⠀⢠⠋⠀⠀⠀⠈⠻⣄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⡠⠚⠓⠃⠢⠀⠀⡀⢀⣴⣿⣉⣳⡀⠈⣧
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢀⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⠇⠀⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣿⠗⠀⠻⢿⣿⡿⠏⠀⠀⠂⢱⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⡀⠙⠛⠋⠈⠓⠀⠀⠠⠟⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠒⠀⠈⡀⠀⠠⠄⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢰⡄⠀⠈⠙⠦⣄⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⢦⣀⣠⣠⢾⡆⠈⠢⢀⡀⠀⠈⠙⢦⣀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠷⡤⣄⠀⠀⠉⠐⠀⠀⠙⢷⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠑⠲⢤⣰⡏⠀⠀⠀⠀⠀⠀⠉⠂⠙⣆
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠈⢼⣇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠿⠐⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⡱⠳⠶⣤⣤⣀⣀⣨⡿
⠀⣿⠀⠀⠀⠀⠀⠀⡠⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⣄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠐⠀⠈⣱⠠⣄⣀⡀⠈⠉
⠀⣿⠀⠀⠀⠀⠀⡞⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡄⠀⣇⠀⠀⠀⠀⠀⠈⠓⠶⣤⠀⠀⠀⠀⠀⠁⠀⠩⡤⠼⠂
⠀⣿⠀⠀⠀⠀⠈⠲⡶⠋⠀⢈⡹⠋⢙⡝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⠀⠀⠀⠀⠀⢰⡏⠰⢃⠔⠘⠉⠙⢠⡤⠛
⠀⣿⠀⠀⠀⠀⠀⢀⣤⣊⡴⠋⠀⢀⠎⢀⡠⠒⠁⠀⠀⠀⣀⣀⡔⠀⠀⠀⠀⠀⠀⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⣿⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⣯⣴⠏⢀⣀⠴⠆⠘⠁⣠⠋⠀⠀⠀⠀⠀⣠⠔⠁⡄⠘⣧⡀
⠀⣿⠀⠀⠀⠀⣤⠴⠞⠀⠀⠀⠀⠀⣧⣖⣥⠤⣤⣤⣤⣤⡏⠀⠀⢠⡤⠖⠉⠀⠀⠀⠈⠢⡉⣿⡆⠀⠀⠀⠀⠀⢠
⠀⢿⠀⠀⢠⡘⠻⣀⣰⠄⣄⠒⣇⠤⠴⠍⠁⠀⠀⠀⠀⠀⢄⡠⠊⠀⣱⠀⠀⠐⡀⠀⠀⠦⢈⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⡄
⠀⣶⠀⠀⠀⠀⠈⠉⠁⠀⠴⠖⠀⠄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣈⣙⣳⣤⠾⣛⢣⣴⣞⣛⣁⣀⣀⣀⣀⡀⠀⠀⠀⠤⠤⠤⠀⠀⠘⠁
⠀⣿
⠀⣿
⠀⣿
⠀⣿
⠀⣿
⠀⣿
⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠈⠉⠀⠁⠈⠀⠋⠈⠉⠁⠀⠈⠉⠈⠙⠃⠀⠀⠈⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠁⠀⢳
⠀⠀⠀⠀⢀⡞⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⣸⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠐⠛⠓⠛⠒⠶⢤⡀⠀⠀⠀⠀⠀⡾⠘⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠷⢦⠀⠀⢠⡇⠀⢡⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢠⡾⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢸⠃⠀⠈⡀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠰⠆⠘⣆⠀⣼⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠚⢳⣆⢹⡄⠀⠀⡇⠀⠀⢀⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠆⠀⠈⢦⡇⠀⣴⣿⡀⢈⣦⠀⠀⠁⠀⠀⠀⠀⠀⠐⡄⣿⣶⣿⣿⠀⣧⠀⠀⠃⠀⢠⡞
⠀⠀⠀⠀⠀⠱⡄⠀⢀⠀⠘⡀⠀⠘⡇⠀⢿⣿⣿⣿⣿⡇⣆⡀⠀⠀⠀⠀⠀⢰⠇⣿⣿⣿⡿⠀⢿⠀⠘⢈⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠋⢉⡇⠀⠈⢄⠀⢣⡀⠈⠻⣿⣿⡿⠟⠈⠷⣄⠀⠀⠀⡠⠋⠀⠈⠙⠋⠀⣒⢾⡦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣔⡒⠓⣾⢅⡀⢠⠔⠉⠑⠢⢀⣀⠈⠁⠰⠄⠄⠀⠀⠀⠀⡠⠼⠇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡇⠀⠡⢌⡐⠐⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⡰⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡀⠀⠀⠙⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⢀⡬⠄⠀⠀⠀⠀⠀⠀⠸⠀⠀⣰⠒⢤⣈⠂⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠙⠳⠦⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠙⠮⠤⠄⣄⢂⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⡀⠀⠀⠀⢀⠤⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠸⡅⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⣀⣀⣈⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⢳
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⣄⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⡴⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠈⠳⡀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⡼
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢠⠞⠀⢀⣀⠀⠘⣿⣿⠟⠉⠉⠉⠉⠉⠛⢿⠇⣠⠞⣻⣿⣦⠹⡄⠀⢠⣿⣿⡇⠀⠀⠀⣀⣀⡰⠁
⠀⠈⣇⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⡜⠀⣾⣿⣏⣙⣦⠘⠃⠀⠀⠀⠀⠀⠀⢀⡈⣦⣿⣿⣿⣿⣿⠀⢹⡀⣼⣿⣿⡇⠀⠀⠻⣍
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⢰⡇⠸⣿⣿⣿⣿⣿⣷⢷⣶⣄⠀⠀⠀⢀⣾⣿⠙⠿⣿⣿⠿⠋⠀⣸⣷⣿⣿⣿⠇⠀⠀⣠⠋
⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⢿⣿⣿⣷⣼⣧⠀⠙⠿⠿⠿⠟⣁⣾⣿⣿⣧⣀⣀⣼⣿⣿⣿⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⣤⣶⠟
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣼⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣾⡿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⢀⠔⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢻⣢⠀⠀⠀⣹⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠙⠻⠁⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠠⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣿⣿⣿⣿⣿⣿⣷⠀⠈⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⡶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠁⡀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠟⠛⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠹⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡄⠀⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⢾⡟⢛⠿⢿⣿⣿⣿⣿⣿⡿⣖⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣧⡀⠘⢁⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠉⠻⢏⡿⠓⠼⠋⠁⠀⠉⠙⠻⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣄⢻⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠘⠀⠀⢤⣵⣤⣬⠿⠟⠀⡹⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢺⣾⡎⠻⣻⡧⠖⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠧⢤⢒⣊⣀⠁⠀⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢱⡍⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠳⠤⠰⠳⢎⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠮⡝⠀⠀⠀⠀⠀⠀⠊⣠⠴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣆⣄⣀⣀⡀⠀⢆⡈⢰⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢡
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡇⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢠⡄⠀⠀⠀⠀⠀⠀⣠⠋⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠠⣟⠈⠁⠒⢄⡀⡼⠁⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡆⢠⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡇⢠⠇
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⢣⣰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢳⠀⠀⢇⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⢆⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣐⠀⠀⢀⠀⠀⣰⣽⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣀⣓⣀⠀⠐⣿⣧⣵⡄⢀⠊⠀⠀⠀⠀⢱⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠤⠜⠛⠿⡿⠘⢄⠀⠀⠀⢀⠜⣘⠝⠁⠀⢠⢡⢀⣀⣠⣄⡰⢂⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠈⡰⠈⡖⠒⠓⡈⠉⠢⢤⡴⠗⣶⠻⡭⠛⢊⢙⣀⣀⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⠰⣠⢴⢟⡴⢰⠟⠈⠀⡅⠀⠢⢀⠀⣏⠻⠁⢠⠞⠙⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠒⠉⠮⠅⠀⢀⠔⠁⣀⣎⡁⣀⡄⠀⢡⠊⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢼⠀⠴⠒⠂⠀⠈⠁⢠⢞⢉⠝⠉⠉⠁⡠⠆⠃⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠃⠑⡄⠀⢠⠀⠀⠢⣑⠦⠀⠈⠉⠀⠀⠀⠀⠈⢀⣏
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⠀⠀⠐⢄⠀⠀⠑⠋⠀⠀⠌⠀⠐⠀⢀⠖⠦⢡
⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠠⢂⣀⣤⠀⠀⠒⠀⠀⠐⠊⢠⠃⠀⡠⠀⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠒⠁⠀⠀⠈⠢⢄⣀⣀⣀⠔⠉⠉⢢⠃⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠙⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⢟⠁⠀⠀⠈⠛⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠲⣷⠀⠀⠀⠀⠀⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⢟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠐⠢⣄⣀⠀⠀⢀⣾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢋⠓⠤⢀⣈⣤⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⣻⣷⣤⣤⣿⣿⣿⠛⠀⠀⠁⠀⠀⢀⠀⠂⠙⠂⠀⠤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠶⢾⣿⣿⣿⣿⠿⠻⠛⢆⠀⠀⠐⠀⡎⠤⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢻⣿⡿⢗⡀⠂⠀⠀⡇⠀⠀⡎⠀⣤⣶⣬⠀⢠⣶⣷⣶⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠙⠐⠛⡄⠀⠀⡠⠣⡀⠀⠀⠀⠙⢿⣿⣧⠺⣿⣿⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣷⣦⣤⣄⠀⢠⠟⠂⠀⣦⣦⣤⣤⠆⢀⠀⠀⠒⠀⠀⣈⣉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⣿⣿⣇⠀⠀⣀⣀⣼⣧⠸⢛⠁⠀⠀⠀⠀⠀⠀⡀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠁⠀⠀⢀⠀⠀⠀⢐⡴⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⣸⣿⣿⣿⠟⠙⠀⠀⢸⣿⠀⠀⠀⠀⡤⠀⠂⣩⠃⢸⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢈⣿⠆⠀⠀⠀⢷⠴⠖⠗⠉⠈⢂⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣛⣿⣧⠥⠰⣶⣲⣶⣿⠿⠯⢤⡆⢴⡆⠋⠁⠀⠀⠞⠃⠀⠠⠰⠶⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠉⠀⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣞⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡄⠀⠀⠀⠀⠀⣴⣟
⠀⠀⠀⢠⣞⣻⣿⡆⠀⢀⣤⣿⠿⠟⠻⠧⠀⠀⢀⣠⣄⢀⣦⠀⣤⠾⠃⠀⠀⠀⠀⢈⣽⣿⠟⠻⣄
⠀⠀⣴⣾⡟⣩⠉⠁⠰⠛⠉⣾⣿⠿⣿⡦⠀⣴⡏⣦⣿⣿⠛⠸⠇⠀⠀⠀⠀⠀⠀⠐⣿⡿⣽⣶⣯
⠀⠘⠿⡿⡷⠿⠿⠂⠀⠀⠘⠛⠀⠀⠋⠀⠀⠈⣿⣻⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠙⢿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⢠⡆⠀⡀
⠀⣰⡆⠀⢀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠿⠆⠀⠀⢸⢿⣿⣉⢲⡄⠀⠀⢺⡵⠤⢤⢠
⠀⢿⣧⣚⣿⣿⣂⣼⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠿⢿⣞⣥⡀⠀⠀⠀⢀⡀
⠀⠈⢻⣉⣿⣿⣩⠟⠀⠀⠀⠀⠀⢀⡀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⢸⡟⠉⠀⠀⣴⣾⣿⣿⣧⡆
⠀⠀⠸⡿⠀⠈⣿⠇⠀⠀⠀⣄⡴⠟⢿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡿⢿⡿⠇
⠀⠀⢴⡷⠀⠰⢿⡆⠀⠀⠲⠿⣇⣉⣸⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠄⠉⠘⠋⠀⠀⠀⠀⢠⡄⣶⣿⠂⢠
⠀⠀⠀⠠⣄⣆⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠟⣿⣿⣿⣿⣿
⠀⠀⠀⣰⠛⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠓⠋⠀⣾⣮⣥⢢⣿⣄⠀⠀⠀⠀⠐⣿⣷⠂
⠀⠃⠰⣉⠘⡿⢮⣡⠄⣄⠀⣀⠀⠀⢠⣿⣿⣻⣦⡀⠀⠀⠀⠉⠁⠀⠋⠉⠀⠀⠀⢰⠔⠋⠙⠢⡆
⠀⠀⢹⣿⠀⠀⠸⣿⠆⠀⠰⡟⠃⠀⠈⠛⡿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠀⠀⣷⣧
⠀⠀⠀⠥⠐⠒⠂⠌⠀⠀⠀⠀⠀⠀⠘⠟⠣⢼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣦⠄⠀⣼⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠴⣴⣶⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⡀⠘⠋⠿⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⡊⠃⠘⠛⠀⠀⢀⣠⣿⠇⠀⠄⠀⠀⠃⠀⠀⠀⢀⠄⣈⠁⠀⠀⠀⢢⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠶⣶⠄⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠙⢤⠁⠸⢷⠿⠈⠆⠄⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠠⠿⠿⠷⠀⠀⠐⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⢠⢠⡀⠰⠀⠇⡈⠹
⠀⡀⠀⠂⠉⠀⢀⡀⢀⠀⠀⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⠀⠀⠈⠁⠐⠌⢯⠉⠛⠉⠀⡀⢈⠠⠂⠀⢀⡠⠀⣤⠆⠐⢟⣀
⠀⠀⠀⠀⠀⢀⠀⠐⠀⠱⣤⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠋⠓⠕⠦⣀⢠⣡⠟⠂⠀⠀⠠⡀⠀⠉⠀⠀⢀⡁
⠀⠀⠀⠀⢠⣿⣿⠐⠂⠀⠁⠀⠀⠀⢿⣿⠒⠄⠀⠀⢨⡀⡀⠈⣱⡄⡤⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠂⠄⡠⠈⠀⠀⠉
⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⡈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢁⣿⡿⠄⠀⠘
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢐⠀⢀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⢀⠀⠁⠄
⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡐⠂⠁
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠀⢀⠔⠀⡠⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠄⠡
⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⢄⠀⠀⠀⠘⠀⠀⠐⠀⢀⣠⠀⠁⠀⠀⠀⠀⠀⣔⡄⠀⠀⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢳⠀⡀⠀⠄⠀⠀⠀⠐⡃⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠨⡄⠁⠈⠄⠰⠀⠐⠺⠀⠡⠀⡆⠀⠀⠀⠀⠀⡧⣀⡄⡀⣴⠀⠀⠀⠀⠀⠐⠀⣡⣀⣠⠛
⠀⠀⠀⠀⠘⠢⠀⠀⠔⠀⠀⠀⠐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠛⠠⠄⠀⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⡀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣀⣀⠠⠤⠐⠁⠀⠠⠀⠠⠧⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢳⡀⢀⠀⠀⡿⠀⡘⠠⠀⠀⠀⢰⣿⣤⠀⠀⠀⠀⠀⠧⢲⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠿⠋⠛⢾⡇⠀⠈⠂⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠢⣘⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡰⠃⢀⣠⡾⠁
⠀⠀⠀⠀⠀⢠⡟⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡄⡀⠀⠀⠀⠀⠀⠈⢇⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠉⢡⡷⠚⠋⠁
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡑⠢⠄⡀⠀⠀⠀⢡⠀⢀⠂⡁⠀⠀⣀⠀⠀⢠⢻⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠚⠻⠷⡤⠀⠐⠠⡀⢸⠓⢄⡀⠁⣀⣀⡀⣤⡐⠁⢈⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡾⠫⠷⠀⠀⠀⠀⠀⢠⠞⠛⠳⡦⡈⡦⠀⠀⠀⠀⠉⠍⢡⣄⣥⡶⠚⠛⢲⣤⣀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠿⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠎⠀⠀⠀⠓⡀⠀⠈⠲⡈⠀⠀⠀⠀⠀⠉⠉⠉⠃⢿⣁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢳⣰⣇⠤⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠔⠘⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⣤⡀⠀⠐⠀⢻⣇⠠⠄⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⢐⡇⢠⠃⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢂⢸⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠈⠁⢀⠾⢏⠰⣌⡶⡀⠀⠀⠀⠀⠀⡠⠛⢶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠤⢤⣹⡁⠂⠁⠀⠀⠑⠦⣀⣀⡰⠏⠠⡐⠔⢏⣀⡀⠑⢄⠀⠈⠑⠒⠒⠒⠏⡀⡷⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⡿⢤⡤⠤⣤⠤⣉⠶⣿⠀⠄⢸⠃⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡐⢁⠀⠀⠀⠐⠶⢞⡃⠂⠀⣘⠀⠀⠀⠞⠀⠀⠐⠁⠀⠀⢀⠂⠁⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⡋⠙⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠢⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⡀⠜⠢⢄⣀⠀⠀⣀⢜⠃⡄⠀⠀⢠⠱⠀⠀⠀⠀⠀⠠⠥⠄⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠉⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⡀⠀⠠⣀⠀⠀⠄⠀⠀⠀⠀⠀⠡⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡜⠀⠀⠢⠈⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠐⡒⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣴⡇⢀⣀⠠⠤⠤⠤⣤⣤⣤⣀⣀⣀⣀⢀⠀⢴⠶⠿⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠉⢹⠇⣀⠀⠀⠀⡻⣄⠀⠀⢸⡃⠠⠀⠄⠀⠀⠀⣈⡝⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⠀⠀⢀⡆⠀⣶⠆⠋⠉⠀⠀⠀⠀⢸⡏⢁⣀⡀⡀⡄⢻⠆⠀⠀⠙⠓⠶⣤⣄⣉⣈⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⣤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡉⠀⠀⢉⠀⠀⢈⠀⠀⠀⡁⠈⠀⡉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣶⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠉⡿⣿⠉⡿⡏⠹⣿⠏⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢹⡟⣿⣛⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢰⣶⡀⣶⣶⠀⣶⣆⢰⣶⡆⣲⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠏⠹⠻⡿⠿⡏⠿⣿⠿⢿⡿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⣿⣿⣿⠦⢙⡀⠇⢰⠸⡀⠷⡇⡆⢈⠠⠤⠦⢙⣿⣿⣿
⣿⣿⡟⠉⠀⠀⠀⠈⠙⣿⣿⡇⠀⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⣿⣿⣿⣿⣿⡟⢻⣿⠟⣿⣿⠛⣿⡿⢻⣿⡟⢿⣿⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢰⣧⠤⠬⠬⣬⣤⣷⠀⠀⣿⣿⣿⣿⣭⡅⢨⣩⠀⣍⣩⠀⣭⡅⢨⣭⡁⣩⣭⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡤⠤⠤⠠⠤⠠⣾⠀⠀⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣶⣿⣷⣾⣿⣷⣾⣿⣿⣿⣿
⣿⣿⣄⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠳⢶⣶⣶⣶⠶⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠐⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣄⠀⠰⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠔⢊⣤⠀⠀⢈⡶⣅⠀⢡⣿⠏⠹⣿⠿⠛⣿⣥⣤⣍⣉⢳⡀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠢⡀⠀⠀⣠⣷⠘⠀⠀⠀⢠⣿⣧⣾⣆⠶⠊⠀⠀⠁⠘⠄⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣿⠟⠢⡀⡐⠘⠈⡻⠿⠿⠋⡀⠀⠀⢄⡀⠀⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠂⣨⠀⠀⢠⠸⠒⠖⠉⠲⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⣨⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠃⠘⢞⡓⠈⣉⡈⠉⠁⠛⠛⠾⢂⢀⠦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠑⠂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠑⢀⡀⠀⠀⠒⠀⠉⢋⠀⠈⣿⣿⣿⡉⠀⣀⠄⠀⠀⠀⠌⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠳⠀⠀⡄⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠷⠒⢄⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠀⠀⢂⢸⣿⣿⣿⣿⣷⣀⠠⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⢀⠁⠀⠀⠀⠠⠀⢺⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⢐⠄⠀⠀⠀⢠⠃⠀⠘⢿⣿⠿⠿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠧⠐⠎⠓⠲⣠⣤⠁⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢠⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⡀⠀⡀⠖⠁⠀⠀⠀⠀⡁⠀⠀⠀⠰⡅⠀⠀⣼⠂⢄⡁⠀⠀⠀⠀⠀⠀⢀⠥⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠁⠀⠀⠀⠐⠭⠀⠨⠷⢲⠤⣀⠒⢊⠁⠀⠂
⠀⠘⠒⠐⠚⠁⠒⠒⠒⠐⠒⠚⠃⠒⠒⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⣴⡟⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠌⠰⠋⣙⣷⡶⠆⡅
⠀⠀⠀⠀⢀⡠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⡀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠀⢛⡇⠀⠇
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢠⠃⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠃
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⠀⢀⠀⣼⣥⣄
⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠶⢖⣚⠛⠒⠒⠒⠤⠤⣀⣃⠱⠀⠀⠀⠀⠀⠈⡏⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠒⠶⠤⠤⠤⣭⠦⣥⡀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⣠⣤⣶⣶⣤⣄⠑⢄⢈⡑⣄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡏⠀⠀⠀⢰⠟⠻⣿⣿⣿⣿⣿⡄⠂⠈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠑⠄⠀⠀⠀⠠⢴⣿⣿⣿⣿⡿⢃⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⣨⣽⣿⣄⠁⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢻⡖⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⠴⡆⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⡟⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⣿⡿⠟⠋⠀⠀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡤⠒⠈⠁⠀⣠⣤⣶⣿⣿⣿⣇⠢⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣸⡀⠀⠀⠀⢨⣀⣸⣿⣿⣿⣿⣿⠆⡇⠰⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠘⠿⣿⣿⣿⣿⠿⠋⡠⠰⢡⠎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⣀⣀⣀⣀⣤⣔⣨⡤⠒⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣒⣉⣀⣀⣀⣀⣀⣤⢤⠖⡰⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣨⡜⠁⠀⠀⠀⠀⠀⠘⠁⢿⠿⠓
⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠋⠱⡀⠀⠀⠀⠀⠀⠀⠰⡎
⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢀⠀⣉⠆
⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⢠⡈⣒⡻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡟⢻⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡾⠛⠙⠒⢄⠀⠀⠀⠀⠀⢱⣸⣇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⣄⡀⠀⠐⠋⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠘⣇⣿⡄
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣀⡤⣄⠀⢀⣯⡶⠟⠻⢿⣾⣧⡀⠀⢰⣥⣼⣿⣿⡆⠀⢀⣴⣄⠀⣿⣿⣷⣠⡤⠴⠆
⠀⠀⠀⠐⣤⣿⣿⡄⠀⣰⠏⣀⠈⠂⠏⠁⠀⠀⠀⣸⣿⣿⣧⠀⢸⣿⣿⣿⣿⡟⠀⠀⣿⣿⣶⣿⣿⣿⡃
⠀⠀⠀⠀⠈⢿⣿⣿⣶⣟⢸⣬⣧⣠⣤⣀⣀⣠⣼⣿⣿⣿⣷⠀⢹⣿⣿⣿⠿⠁⠀⣸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⢸⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡿⠄⠢⠀⠀⠈⠀⣀⣤⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢿⣿⣿⠀⠿⢿⣿⣿⣿⡿⢾⣾⣿⠛⠉⣹⣿⣍⣩⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⢉⣠⣴⠾⣿⣏⣽⣿⣿⣿⣿⣿⣷⡾⠛⠻⣿⣻⡿⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣄⣀⣿⣿⢿⣿⠛⠛⠉⠛⠉⣠⣼⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠙⠻⠏⠈⢿⡶⠒⢾⡏⠉⠋⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢤⣄⣈⣁⣀⣀⣠⡴⠚⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠉⠉⣻⠛⠉⠿⠀⠀⠀⢠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⢁⠄⣰⣄⣠⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠴⠋⠀⠋⠁⠀⠀⠀⣿⡇⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣆⠘⣿
⠀⠀⠀⠀⠀⠀⢠⣴⣆⣶⡀⠀⣴⠀⠀⠀⣸⣿⣿⣆⠀⠀⠀⠀⢀⣿⡿⢿⣭⣬⠭⠿⣿⣦⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣤⣼⣿⣷⣷⣼⣿⣿⣿⣯⡀⠀⢠⢰⣿⣻⣿⡿⠋⢰⣿⣷⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⢿⣤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⡐⢸⠇⠀⣠⣶⣾⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⢠⠶⢿⣿⣦⣤⣤⣶⣿⣥⣾⣁⣈⣹⣿⣉⡉⣿⣿⣿⣼⣿⣧⡔⣡⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠉⠉⠑⠟⠋⣽⠟⠿⠿⢛⣿⠿⠿⠟⠛⠉⠻⠿⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡿⣤⢤⢤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡇⠀⠀⣸⣇⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣯⣿⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣽⣿⠟⠃⢀⣇⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣽⣾⣿⣿⠇⠀⢠⣼⠏⠀⣿⣿⣿⡿⠿⣿⡿⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢳⣿⣿⣿⣿⡿⢠⡷⠟⣁⣠⣄⣿⣿⠋⠁⠀⢉⢴⣦⣤⣿⣿⣿⣿⣙⠛⠛⠻⢿⡿⢿⣿⢙⣦⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⢯⢎⠿⣿⣿⠿⣿⡷⠋⢠⡾⠛⢉⣉⣿⡛⢱⣾⣶⣦⡀⠀⠸⠇⣽⡿⠋⢻⣿⣇⠠⠈⠱⣄⣼⣿⣿⢻⣿⡟⣾⣷
⠀⠀⠀⠀⠀⠀⡼⣅⣄⠐⢉⡁⠀⠐⡾⠁⢀⣿⣀⣸⡧⣸⣧⣤⣴⠿⠿⣷⠹⣿⡗⢲⠆⡀⠀⠚⡟⣿⣇⠀⢶⣾⡿⣱⢏⢲⠲⠹⡻⣾⡇
⠀⠀⠀⠀⠀⡼⠉⣭⡇⢠⣽⣷⠟⢻⡇⢇⠘⡩⡙⣹⣡⣿⡿⠿⠛⠛⠳⠊⠃⠋⢻⡄⠈⣿⣄⣛⣀⣤⡏⣰⣿⡟⠀⠃⠀⠣⢢⠡⣱⣽⡇
⠀⠀⠀⠀⣰⣷⣬⣟⣽⣿⣷⣋⢡⣸⣇⢜⣔⣼⡶⠛⠙⡆⡄⠀⠀⠀⠀⠀⠀⣀⠈⠛⢷⣶⣶⣿⡿⣿⣾⢻⡟⠀⠀⠀⠀⠁⠀⠱⡳⣹⠁
⠀⠀⠀⢀⣯⣿⣿⣿⣿⣿⣿⣋⣈⣥⣽⣶⡾⢋⣀⡀⢀⠀⠁⠠⣀⡀⠀⠀⠘⡱⠛⠓⢦⡙⢿⣍⣼⡇⡿⢸⠃⠀⠀⠀⠀⠀⠀⠡⢡⣏
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡟⢀⡁⣤⣶⠖⢳⢶⢮⡁⠀⡘⠀⠀⠀⠀⢳⡈⢿⠋⣿⠇⣿⣤⣠⠀⠀⠀⠀⠀⣰⠿⣿
⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣿⣿⣽⡇⠀⠀⠀⠀⢾⣿⡴⢠⣾⠛⢳⡄⠀⣧⠈⠰⢋⢈⣿⣿⡃⠀⢸⣿⣷⣾⣳⣶⣾⡇
⠀⠀⠀⢸⢺⢿⣿⣿⣿⠛⣿⡿⠟⣛⣿⣆⠘⠛⠫⠻⣷⡀⠀⣠⣶⣶⣾⢣⣿⣿⣿⣼⠇⠀⡿⠀⣠⠎⣼⣏⠭⢊⣤⠞⡋⠉⠈⢉⣿⣿⡇
⠀⠀⠀⢸⣎⣿⣿⠄⢿⣿⣿⣾⣾⠿⢿⢻⡓⠢⣤⣀⡙⣳⠾⠿⠿⠋⢡⠈⢿⣿⣿⠏⠀⣰⠃⠀⣧⣾⣭⢴⣾⣿⣴⣶⡟⣲⣿⣧⡐⢹⠁
⠀⠀⠀⠸⡿⢯⢯⣶⡎⢉⡍⠉⣱⣶⣌⣧⢻⡛⠛⡧⢭⣿⣖⠲⢤⣤⣀⣑⡂⠀⠀⢀⣂⡥⢻⣰⡿⠧⣤⣤⡉⠢⡘⣿⡿⢀⣩⣝⣷⣿
⠀⠀⠀⠀⢻⢶⣿⡿⠯⣽⣧⠀⣿⠉⠛⢿⣷⣝⡲⢏⡙⣮⠥⢯⣉⠛⢦⣤⢘⡻⠯⠛⢁⣤⠞⠋⣇⣀⣸⣿⣿⣶⣵⡘⢻⠛⠩⣿⢻⠇
⠀⠀⠀⠀⠈⣿⣿⠿⢶⣏⡙⢠⡏⡁⢀⠀⡀⣹⠟⣳⣦⣭⣅⣀⣉⣀⣈⣩⣤⣤⡶⢿⢻⣷⠀⠀⣿⣯⡱⠛⠻⣿⣿⡟⣿⣴⢟⣿⡟
⠀⠀⠀⠀⠀⠘⣞⢿⠿⣿⡵⢿⣯⢛⣿⢿⣿⢏⣀⡇⠁⡏⠟⠉⣯⣿⠉⠉⡏⠉⠀⠘⢶⣿⡄⠀⢻⣿⣷⣤⠾⠛⣿⣿⣼⣏⣂⡞
⠀⠀⠀⠀⠀⠀⠈⢧⡾⠟⣡⣶⣼⡿⡥⣾⠟⣁⠈⡀⠀⢣⣘⣴⣭⡟⣡⠞⠉⠁⢀⣀⡻⣌⣿⣦⡀⠻⣿⡟⣆⣤⠾⣿⣿⢯⠞
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠷⠚⠻⢰⡏⠀⠻⢦⡘⡄⠸⣿⣿⠾⠊⠋⠠⠞⠁⣾⠀⣽⡝⣿⣿⣿⢷⡸⣧⣿⣧⣱⣼⡷⠋
⠀⠀⠀⠀⠀⢀⣀⣿⢻⠽⠁⠠⢺⣷⢿⡴⠊⠙⠲⣽⡇⠀⡟⣷⣆⣤⣤⣀⠀⠀⠘⠓⠋⣹⣿⡿⠿⣿⣷⣮⡿⢻⢻⣿
⠀⠀⠀⠀⢰⣿⡍⠛⠓⣀⣤⣀⠘⣻⣼⢧⣤⠏⠁⠺⡄⣰⡇⠈⣿⣿⠿⢟⠀⠂⡀⢴⣾⠅⠁⠀⠈⢿⣭⣿⣷⡦⠛⢻⡀
⠀⠀⠀⠀⠈⠻⢿⡄⢸⣿⣿⣿⡆⣀⣸⡆⢠⣤⣠⡀⢰⣿⣷⡀⠈⠻⠷⢭⡀⣾⣻⣾⣿⠀⠀⠀⠀⠈⠹⠟⢉⡠⠼⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠈⢷⡈⠻⠿⣿⣿⣉⣩⣁⡀⢀⣀⣀⣻⣭⡻⣿⡄⢠⣀⣀⣙⣻⣿⣵⢿⡆⣼⡃⣀⠀⠆⢰⣿⣿⠀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⠿⠿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⠟⠉⠉⠉⠉⠉⠁⠈⠛⠿⢿⣿⣿⣇⣀⠫⠿⣫⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠧⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⡉⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢰⡟⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣀⠈⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣾⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠳⣶⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⢸⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠘⢿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢻⡿⠇⠀⢀⢀⠀⠀⠀⠀⠀⣀⡄⢰⣀⡀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⡆⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢀⠀⠀⠑⠂⣴⣿⣾⣿⣿⣿⣿⣷⣿⡦⠠⢰⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⣷⡀⠀⠐⡿⠿⠋⠉⠙⣻⣿⣿⡿⠀⠀⠀⠘⠿⡿⠟⠁⠚⣛⣽⠋⠉⣻⣶⣿⣿⠋⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠹⠆⠀⠁⠀⠈⢍⡻⠀⠀⠀⠀⠀⠀⠀⢠⠆⡀⠀⠀⢈⡉⠁⠀⣰⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠚⢷⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢹⣧⣤⡀⠀⠀⠀⠀⣰⠀⠀⠀⣠⣴⣶⡄⠀⢀⠀⡽⢋⡟⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢉⢯⣿⣦⢀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⢼⡸⣟⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠚⣿⣟⣿⠀⠀⠀⠀⠹⠿⠿⠛⠁⢀⠀⣠⡀⠀⠋⢻⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠻⢳⣤⣀⣀⣠⣄⣠⣤⣴⠾⠿⠿⠃⠀⣴⣠⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣉⣩⣩⣤⡀⢀⣤⠀⠀⣀⣜⢋⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⠇⠡⠌⠻⠙⠡⠄⣨⣵⡞⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡊⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣳⣤⣤⣤⣠⣤⣀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠂⠀⠀⠂⢐⠀⠂⠐⠀⠂⠐⠀⠂⡐⠀⠂⠐⠀⡂⠐⠀⠂⠐⠀⡂⠐⠀⠀⠐⠀⠐⠀⢂⠐⠀⠂⠐⢀⠂⠐⠀⠂⠐⢀⠂⠐⠀⠂
⠀⠀⠀⠀⠑⠄⠔⠁⠀⠑⠄⠔⠁⠈⠠⠀⠌⠁⠈⠢⠀⠊⠀⠈⠢⠠⠊⠀⠉⠂⠠⠊⠀⠑⠄⠠⠈⠀⠑⠄⠔⠁⠀⠑⠀⠔⠁⠀⠑⠀⠔⠁
⠀⠀⠀⠐⠤⠂⡦⡂⡢⡂⡢⡂⡢⡖⢠⠔⢐⢔⢐⢔⢐⢔⠒⢤⠒⡤⠂⡢⡂⡢⡂⡢⡆⡢⡖⢲⢔⢐⢔⢐⢔⢐⢴⠐⠴⠂⡦⡂⡢⡂⡢⡂
⠀⠀⠀⠀⠄⠀⠄⠠⠀⠠⠄⠠⠀⠠⠀⠄⠀⠤⠀⠤⠀⠄⠠⠀⠠⠄⠤⠀⠠⠀⠄⠀⠤⠠⠄⠀⠄⠠⠀⠠⠄⠤⠀⠠⠀⠄⠀⠤⠠⠄⠀⠄
⠀⠀⠀⠀⠰⠀⠰⠀⠰⠀⠰⠀⠰⠀⠰⠀⢰⠀⠰⠀⠰⠀⠰⠀⢰⠀⠰⠀⣰⠀⡰⠀⠰⠀⠰⠀⢰⠀⡴⠀⣴⠀⡴⠀⢤⠀⢦⠀⣦⠀⡶
⠀⠀⠀⢀⠃⢡⠃⢣⠁⢡⠃⢡⠃⢡⠁⢡⠃⢣⠁⢣⠁⢡⠃⢡⠁⢡⠁⢣⠁⢣⠁⢧⠀⢡⠁⢣⠁⣣⠁⣦⠀⢤⠀⣤⠀⣤⠁⣴⠀⣴⠈⠆
⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀
⠀⠀⠀⠰⡆⠀⢶⠀⠰⡃⠠⢎⠀⠶⡁⠰⠎⠀⢶⠀⠰⡆⠀⢾⠀⠴⡁⠰⠎⠀⢶⠀⠰⡇⠀⢎⠀⠶⠁⠰⠆⠀⢶⠀⠰⡃⠀⢎⠀⠴⡁
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠁⠀⠈⠀⠈⠁⠀⠁⠀⠈⠀⠀⠁⠀⠈⠀⠀⠁⠀⠁⠀⠈⠀⠀⠁⠀⠈⠀⠈⠁⠀⠁⠀⠈⠀⠀⠁⠀⠈
⠀⠀⠀⠨⠲⠀⠨⠪⠸⠩⠪⠈⠱⠎⠀⠕⠇⠇⠕⠅⠍⠗⠅⠬⠺⠹⠨⠪⠨⠸⠪⠠⠵⠊⠅⠕⠅⠅⠕⠅⠍⠗⠅⠨⠺⠩⠨⠪⠨⠸⠪⠨
⠀⠀⠀⠀⠀⡠⠂⠀⡠⠀⢀⠔⠀⢀⠔⠀⡠⠂⠀⡠⠀⢀⠔⠀⢀⠄⠀⡠⠂⠀⡠⠂⢀⠔⠀⢀⠄⠀⡠⠂⠀⡠⠀⢀⠔⠀⢀⠄⠀⡠⠂
⠀⠀⠀⠈⠢⠀⠑⢌⠀⠑⠄⠈⠢⠁⠈⠢⠀⠑⢌⠀⠑⠌⠈⠢⡁⠈⠢⠀⠑⠌⠀⠑⠄⠈⠢⡁⠈⠢⠀⠑⠌⠀⠑⠄⠈⠢⠁⠈⠢⠀⠑⠄
⠀⠀⠀⢠⣠⡀⣄⢤⡠⡄⢄⢠⡠⣄⢤⡠⡀⣄⢴⡠⡄⢄⢠⡠⣄⢤⢠⡀⣄⢤⡠⣄⢄⢠⡠⣄⢤⠠⡀⢄⢤⡠⡄⢄⠠⡠⣄⢤⡠⡀⣄⠤
⠀⠀⠀⢈⠈⡁⠁⠈⢀⠁⡉⢈⠀⢁⠈⡈⢁⠁⢈⠀⡁⢉⠈⡀⠁⡈⢈⠁⡁⠈⡀⢁⠈⡈⠀⡁⢈⠈⡁⠁⠈⢀⠁⡈⠈⡀⢁⠈⡀⢁⠁⢈
⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠇⠸⠀⠠⠀⠄⠨⠀⠁⠀⠄⠸⠀⠀⠀⠄⠠⠀⠃⠀⠀⠸⠀⠄⠀⠄⠠⠀⠅⠘⠀⠰⠀⠄⠀⠄⠠⠀⠇⠸⠀⠠
⠀⠀⠀⢠⡄⢢⡄⢠⡄⢠⡄⢠⡔⢠⡔⢠⡔⢠⠔⢤⠔⢠⠔⢤⠔⢤⠔⢤⠐⣤⠐⣤⠀⣤⠀⣤⠀⣤⠀⣤⠀⣤⠂⣤⠂⡤⠢⡤⠢⡤⠢⡤
⠀⠀⠀⠂⠈⠃⠘⠃⠘⠃⠘⠃⠘⠁⠘⠁⠘⠁⠘⠁⠘⠀⠘⠁⠙⠀⠙⠀⠙⠀⠙⠀⠙⠀⠛⠀⠛⠀⠋⠀⠋⠀⠋⠀⠋⠀⠊⠈⠃⠀⠂⠈⠂
⠀⠀⢐⠉⠠⠉⡆⡊⠁⠈⢱⠀⢙⢐⠉⠄⠉⡂⡊⠁⠌⢱⠀⢙⢐⠉⠄⠉⡂⡊⠁⠌⢱⠀⠙⢰⠉⠄⠉⡂⡊⠁⠈⢱⠈⠁⢰⠉⠄⠉⡂⡊⠁
⠀⠀⠐⠛⠒⠛⠒⠘⠓⠚⠓⠒⠛⠂⠛⠒⠛⠐⠘⠓⠚⠓⠒⠓⠒⠛⠒⠛⠐⠚⠓⠚⠓⠒⠓⠒⠛⠒⠛⠐⠘⠓⠚⠓⠚⠓⠒⠛⠒⠛⠐⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠏⠉⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⢀⡏⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣻⣿⣿⣻⣿⣿⡄⢰⠋⠁⣰⠃⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣯⣿⣿⣏⣿⠇⡇⠀⢠⠏⡇⢀⣤⡔⠚⠉⠉⠙⠢⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠋⠀⡇⠀⢸⠀⣷⠋⠀⡇⢀⣀⡀⠀⡰⠛⠳⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠉⠀⠀⠀⠹⣄⣸⢀⢷⣯⣵⡗⠊⠉⠓⣴⣔⣲⡄⢇⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠿⣽⣮⡿⡿⠳⠀⠀⣠⢿⣿⡿⠃⣼⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣨⡘⠛⣧⡀⠩⠛⠳⢮⣭⣵⠞⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠜⡄⢤⠀⠀⡜⠹⡇⠐⠉⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠱⠤⠤⠞⠋⢹⡌⠃⠀⠙⢎⡳⣄⣀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠱⡄⠹⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡄⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣁⣳⣤⣄⣀⣀⣤⣞⣀⣀⡇

⠀⡏⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢙
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠱⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡰⠃⠀⠀⢸⣀⣠⠔⠒⠒⠒⠒⠂⣌⠳⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣀⠜⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣠⠏⢀⣤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠰⢅⣀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣐⠃⢰⣿⣿⣄⣼⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠉⠀⢾⣿⣿⣿⣿⠐⣦⠀⠀⠀⠀⠀⠈⠀⢀⣴⡶⢦⡀⢹⠀⢀⡔⢡⡃⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⡀⢋⠀⠀⠀⠙⠛⠛⠁⠀⢻⡀⠀⠀⠀⣠⡴⢣⣿⣿⣦⣼⡇⢸⣤⠎⢀⢫⠁⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⢻⡆⠰⠖⠞⠻⡒⠒⠒⠦⠠⣤⣀⠚⠋⠀⠘⢿⣿⣿⣿⡅⢼⣅⣀⡏⠉⣇⣀⢠⠆⡰⠁⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢌⡁⣀⠀⠀⡀⠀⠀⠀⡙⢄⠘⠶⠀⠀⠀⠁⠀⡀⠀⠈⢍⠐⢠⡀⠀⢀⠝⠁⠀⠀⠀⠀⠀⠀⠁⣡⣦⠊⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠘⠲⡄⠤⠀⢀⡀⠄⢀⠆⠀⢱⣄⠉⠀⡁⠀⠀⠀⠀⠀⠈⠀⠘⠉⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠄⠉⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡞⣳⠰⠀⠀⢉⠞⠃⠉⠒⠊⠁⠀⠈⠐⠀⠁⠒⠀⠤⠄⠤⢶⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⡐⠒⣀⡱⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠥⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢦⡀⢀⢀⡠⠚⡍⠀⠀⠰⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠣⠔⠁⠀⠀⠀⠀⠉⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⡄⠛⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡶⠠⠶⠄⠚⠋⠉⠀⠈⠣⣄⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⣀⠀⢀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠤⠖⠺⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⢀⠀⠀⡀⣄⠀⢠⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣘
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠈⠁⠉⠀⠈⠈⠈⠁⠈⠈⠀⠀⠉⠈⠙⠉⠀⠁⠈⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠺⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢰⣧⠀⠀⠀⣀⡤⠴⠾⠿⢄⡀⠀⠀⠀⠀⢀⡇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⢸⢀⡴⠻⠁⠀⠀⠀⠀⠀⡸⢷⡀⠀⠀⣸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠃⢸⣟⡄⠀⠄⣰⠶⣦⠀⠈⠀⠀⢱⠀⡼⡻⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣘⡆⣸⣿⣶⣧⡏⠀⠀⠈⢳⣰⣧⣿⠌⡟⢠⠇⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠷⣿⣞⣛⠍⠳⣄⣀⠼⢛⡻⣿⠋⣴⣥⣊⣸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠋⠛⣯⠍⠉⠉⠉⢛⣶⣾⠟⢩⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠁⢠⠟⡀⢴⡀⠀⠘⠁⢇⠀⠋⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣤⠿⠊⢳⠈⠃⠀⠈⠪⡙⠢⣄⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠢⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠧⡀⠀⠀⠀⠀⢀⠂⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⣈⡶⠶⠶⠚⠶⢄⣀⠀⣀⢈⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠙⠢⠤⣀⠀⠀⠀⡄⢀⠤⠴⠒⠒⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠂⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠂⠀⠀⠀⠀⢣⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⡔⣨⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠣⡀⢠⢣⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠀⠀⠀⠀⠠⠀⠀⢠⡇⢈⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠙⠖⠤⣤⣈⣃⠉⢄⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⣴⣿⣿⠛⢦⣕⢄⣦⣝⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠉⠙⠛⠦⣄⠀⠀⠀⠘⡀⠀⠀⢿⣿⣷⣿⣷⣾⣿⣷⡙⢿⣪⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠈⠓⠄⠀⠀⠑⢄⠀⠈⠻⢿⣿⣿⣿⡿⠟⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠨⠉⢁⡠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠖⠀⠐⠒⢄⠀⠀⠀⠀⠀⠀⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠂⡀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠌⠢⡔⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡁⠀⠉⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠑⠀⠀⠘⣆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢁⡿⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠇⠀⡏⠛⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠀⠀⠠⢤⡤⠾⠛⠉⠁⢈⣁⠔⠃⢰⢆⠀⠀⠸⣁⠀⡲⡄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠃⠠⠀⣠⢿⠔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠅⠀⣰⡃⠄⢸⠀⢀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠂⠂⠀⠀⢀⠀⠀⠀⠻⠒⣡⠞⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⡏⠀⠀⢀⣰⣶⣒⢶⠉⠛⡑⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄
⠀⠀⠀⠀⠀⣄⠀⠀⠘⣇⠀⠀⡿⡇⣠⠖⢁⡀⠀⠀⢱⠀⠀⠈⠉⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⡆
⠀⠀⠰⣦⣠⡟⢧⡔⣷⢻⡧⣀⡇⣽⢇⣼⣿⣿⣷⣦⣸⠁⠀⠀⠀⠀⠀⠀⢙⣄⠀⠀⠀⠀⠠⠁⠀⠀⠀⠇
⠀⠀⠀⣿⡌⠁⠀⠁⣯⣀⡙⣌⢿⣿⣸⣿⣿⣿⣿⣿⣯⠤⢾⣿⣷⣄⠀⢠⠊⢻⡇⠀⠀⢀⠃⠀⠀⠀⢰
⠀⠐⠾⣦⣧⡀⢀⡘⠁⠀⠈⠪⣿⣤⡿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⢻⣠⣧⣤⡀⡇⠀⣠⡎⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠙⣏⠀⠀⠀⠀⠀⠸⡟⣷⠦⣉⣉⠉⠙⣿⠄⠀⠀⢀⣸⣿⣿⣿⣿⡷⢪⠟⠃⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠱⡜⢦⣈⡛⠛⠓⠚⠷⢦⣾⡿⢿⣿⣿⣿⣿⠖⠁⠀⡴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⣸⣦⣙⠷⣦⣀⣀⢀⣀⣻⡿⣶⡭⠟⠟⠃⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢺⣿⠁⢈⣹⣶⠯⠽⣭⢿⠓⠊⠉⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠨⣿⣿⠀⠀⢧⠸⣄⢀⠄⠂⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠈⠉⠀⠀⠘⣆⠈⠇⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠇⠀⠀⠀⠀⠀⠀⠘⢦⣇⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠓⠾⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⣈⠲⢄⣀⣀⠀⢀⣀⠄⠊⠀⡀⠊⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢦⣀⣀⠈⠹⡷⠒⠚⠛⠓⠒⠒⠚⣧⢀⣀⣀⡔⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣤⠿⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠽⣤⠷⠌

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⡀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠋⠓⠚⠓⣺⡿⠦⣤⣀⡇⠀⠃⠀⠀⠀⣿
⠀⠀⠀⠀⡾⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣠⠼⠋⠀⠀⠀⠀⠀⠃⠀⠀⠀⠙⣇⠀⢸⠀⢺⡍⠁
⠀⠀⠀⠀⢧⣄⠀⠹⣆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⡀⠀⠀⡀⣼⣿⣿⡄⠘⣄⡌⢀⢠⡟
⠀⠀⠀⠀⢾⠁⠀⠀⠹⡶⢦⣄⡀⣼⠃⠀⠈⢂⠀⠀⠀⠀⠀⣼⠜⢿⡿⠃⠄⠸⣃⡵⠋
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠑⣄⠈⠙⢿⠀⣴⣿⣦⡱⣤⡀⠀⠀⠛⢀⣠⡔⠲⡾⣠⠏
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠳⣄⠀⢆⠹⣿⣿⠟⠀⢉⣠⣼⣾⠆⠑⣀⢞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⣤⣤⠌⠵⠾⣇⠀⣀⣀⢒⡑⣉⣀⢠⣔⡮⠖⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠓⠶⠶⡶⠀⠒⢚⠉⠠⣄⢤⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠀⢹⣇⣀⢺⡁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠐⡀⠀⠀⠈⡯⡀⠉⠃⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⠁⠑⠂⠀⠀⠁⠀⠄⠤⢰⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠞⠩⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠈⠉⡶⠊⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠁⠀⠀⡀⠀⠀⡀⠐⠁⠀⠈⠁⠂⠀⠘⢦
⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠠⠀⠀⠘⢧⣀⣀⣠⠴⠶⠒⠒⠒⠒⠒⠲⠶⠦⠤⣤⡄⠀⠀⡠⠯⢁⡀
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠤⠤⠬⠭⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠈⠉⠉⠀⠐⠊⠁


⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠀⠀⠤⠀⠄⠀⠀⡀⠀⠀⠠⠀⠠

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀
⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠐⠪⢟⠄⠀⣠⡏⢹⡄⠀⢀⣶⡞⣿⠃⠀⠠⢤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠛⠃⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⣤
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⣀⠀⠀⣤⣤⡄⠀⠀⠀⠀⢀⠤⢾⠤⣄⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠤⠀⠰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠤⠀⠀⠹⣿⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠄⠠⠝⠁⠀⣤⣤⣀⣀
⠀⠀⠀⠀⠄⠀⠀⠐⢀⠀⠀⢻⠸⡇⠀⠸⠿⢿⠃⠀⠀⢸⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠁⠀⠀⢒⢀⠀⡙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠈⠤⠉
⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠋⠈⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⠘⡛⠓⡀
⠀⠀⣀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠚⠿⠿⠻⠥⠿⠷
⠀⠀⠻⠿⠃⠀⠻⠿⣿⠷⠀⠡⠆⢤⠁⠀⡈⢤⣃⢠⠄⠀⢿⣿⠆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠠⠦⠀⠀⠀⠠⠄⠀⠀⠀⡠⣤⡄⠀⠀⠀⡠⡶⡄⠀⠀⠀⢀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠰⡐⠀⠐⠀⠀⠀⠀⠀⠀⠂⠚⠍⠀⠀⢴⠟⠐⣷⠄⠀⢰⣿⡯⠿⠁⠀⠀⠘⢒⠴⣶⠀⠀⠸⠟⠛⠓
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⣾⣿⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢷⠐⣆⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠐⡆⠀⠸⣿⣿⡟⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠺⠦⠟⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠒⠀⠀⠙⠀⠐⠺⠓⠂

⠀⠀⢴⣀⠀⣐⠆⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⣤⢠⣦⠀⠀⢸⣶
⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⠉
⠀⠀⠀⣄⣀⣠⠀⢀⣠⣤⣀⡀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣠⣶⣴⡄
⠀⠀⠈⠙⠿⠋⠀⠈⠻⠿⡿⠿⠈⠱⠆⠶⠀⠀⡈⢶⢘⡀⣴⠀⠻⠿⠇⠀⠀⠀⠀⠀⢀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠄⠈⠉⠘⡷⠐⠤⢀⠀⠀⡴⠁⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⡇⠄⠀⠀⣠⠊⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠺⡁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⡇⠘⡄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢇⠀⠸⡃⠕⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠘⡄⠀⠁⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⣌⣦⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⣈⣂⡀⠀⢺⣿⣽⣆⠀⠞⠁⠀⠀⠀⢱⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠛⠻⢿⠎⠦⠀⠀⠀⠀⢊⡹⠋⠀⠀⡀⣀⣀⣠⣄⣰⠂⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⣀⣹⠈⣞⠋⢊⡁⠁⠒⠶⢞⡲⣛⠷⠝⢣⣉⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⡀⣢⣺⠞⠾⢺⠋⣀⡠⠄⠂⢀⠠⣸⠝⠃⠀⡎⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠒⠊⠁⠘⠐⡀⠀⢈⣀⣤⣦⣄⡴⢊⠀⠎⠀⠉⣁⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡒⠐⠃⠀⠉⢈⢀⠈⠀⢰⠯⠄⠋⢀⣀⠠⢘⡠⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠉⠀⠘⠄⠀⠶⡀⠈⠑⢌⣢⠀⠀⠀⠀⢀⠀⠀⣐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⠀⡀⠀⠈⠂⢀⡀⠀⠀⡠⠂⡀⠀⠀⠘⠉⠃⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣀⣀⡨⠒⠓⠓⢄⡀⠀⠀⠀⢀⠼⠤⣠⡎⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠈⢆⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠈⠁⠢⠀⢀⢀⣶⣾⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣹⣿⣿⣿⡟
⠀⠀⠀⡠⣤⣤⣤⣤⠠⡀⠠⢀⠀⠀⣀⠀⣤⠄⠀⠀⠛⠻⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⢹⣿⣿⣿⡟⡄⠑⠀⠀⠀⢀⣉⣁⣤⡄⢤⣀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⣀
⠀⠀⠀⢸⣿⣄⣁⡇⡆⠀⣶⣤⡠⠸⠿⠿⣫⣾⡎⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⣾⠿⢿⣿⡇⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢇⡟⡉⠐⠘⠁⠙⠀⠢⢄⠂⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠈⠈⠁⠀⡇⠀⡿⠛⡟⣟⣟⣿⢻⣿⡆⠂⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣧⢀⠻⣿⣿⣿⣿⣿⣿⠟⣤⣀⠀⠰⠠⠲⠀⢒⠀⠄⠂⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣿⣌⠉⠉⠉⠉⠁⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠸⠛⠛⠟⠸⠿⠏⠔⠀⠉⠉⠁⠰⢄⠃⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠀⣀⣂⠀⠀⡀⠀⠐⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠈⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⡇⣶⠿⣚⣓⡛
⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⢸
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠈⠀⣊⠡⠄⡀⣀⠀⠀⠀⠀⠀⡄⢀⠇
⠀⠐⠈⠀⠀⠀⡀⠀⠀⠀⠀⠤⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣵⢖⣋⡠⠞⠗⡑⠌⡀⠀⣿⣄⢰⡝⠉
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⡀⠈⣳⡟⠤⠤⣤⡀⡀⠀⠀⠈⠀⢯⣞⣑⡏⡿⣳⠿⠀⠱⡀⣿⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠑⠋⠉⠁⠀⠀⠀⠠⠀⣼⣯⣁⡀⠋⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠰⡠⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠋⠉⠀⠄⣄⢀⣶⠀⠐⠒⠒⠒⣸⣷⠟⠁⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠛⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠇
⠀⠀⠀⡴⠉⠒⠚⠀⠀⢀⡞
⠀⠀⣸⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠳⣄
⠀⢀⡇⠀⠀⠀⠀⠀⡰⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⡟⠛⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⡆
⠀⢸⠁⠀⠀⠀⠀⠠⠇⠀⣇⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢹
⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⢹⠀⠀⢀⡼⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⡇
⠀⢸⠀⠀⠀⠀⠀⠇⠀⠀⢸⠄⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠛⢷⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⡇
⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀⢸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⣠⠏⢸⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢧⠀⠀⠀⢸⠀⠀⠀⢸⠃⣴⡟⠉⢣⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠘⡇⠀⣰⠃⠀⡌⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠈⢧⠀⠀⠈⡄⠀⠀⡏⢰⣿⣿⣶⣾⡇⡔⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⣼⡁⠀⣹⣷⡀⠀⢿⡰⠃⠀⢠⠃⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠈⠳⣌⠀⠲⠀⠠⡇⠘⣿⣿⣿⣿⡇⢧⡀⠀⠀⠀⠀⠀⠀⠀⡁⣸⣿⣿⣿⣿⣿⠇⠀⢸⠃⠀⢀⠎⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠈⠙⠦⢄⡼⡄⠂⠈⠛⠟⠋⠁⠘⢇⠀⠀⠀⠀⠀⣰⡿⠁⢿⣿⣿⣿⣿⠟⠀⠀⡇⠀⢀⠞⠀⠀⣟⠓⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⢣⣀⠀⠀⠀⡀⠀⡀⠁⢠⡄⠀⠚⠉⠀⠀⡠⠍⠻⢍⡁⠀⠀⠘⢧⠴⠅⠀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⡀⠀⠈⠉⠑⠲⣈⣀⣠⡄⣀⠵⢠⡞⠉⢻⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠣⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⡶⠊⠁⠀⠀⣟
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠠⠎⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣀⠀⠐⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣚⡤⠖⠋⠹⡆⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠐⠺⢦⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠛⠛⠛⠛⠋⠉⠉⠓⠦⣤⣀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣷
⠀⠀⢠⢀⢀⣤⣄⠠⣄⠀⠠⠛⢶⣅⣤⣤⣤⣤⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠦⠴⠓⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣶⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢩⠷⢿⣇⣀⣀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠒⠚⠋⠉⠙⠒⠒⠒⠲⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠊⠀⠈⣠⠦⣾⡿⠋⢰⠁
⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠠⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠁⠀⢉⡽⠀⢘⠁
⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⡀⠀⠘⠁
⠀⠀⠐⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⣀⡀
⠀⠀⠀⠀⠈⠉⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠶⠶⠦⠤⠤⢄⣀⣀⠀⢳⠘⠆⠀⠀⠀⠀⠀⠀⠘⡖⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⢀⣀⣀⠀⠈⠉⠚⢧⠈⠄⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠀⠀⠈⠉⠉⠉⠉⠙⠫⡛⠓⠤⣄⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡾⠋⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⣤⡈⢢⠀⠄⣱⣄⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣾⠀⠀⠀⠀⠠⡟⠛⢻⣿⣿⣿⣿⣿⣿⡀⠃⠀⡄⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠁⠙⠢⣀⠀⠀⠀⠐⢤⣾⣿⣿⣿⣿⣿⡿⢀⠇⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠠⠤⠭⠉⣻⣿⡯⠔⠁⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣦⡀⠀⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢎⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠇⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠉⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡠⠄⠒⠂⠀⠉⣉⣭⣭⣶⣾⣿⣶⡐⢄⠀⠀⡇⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⢠⡏⠀⠀⠀⠀⢀⠊⠉⢻⣿⣿⣿⣿⣿⣷⠈⡄⢀⠃⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣧⠀⠀⠀⠀⠸⣷⣶⣿⣿⣿⣿⣿⣿⡟⠀⠇⠘⢀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠉⣠⠎⠘⣰⠎⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⣤⣤⣤⣀⣤⣴⠦⢭⣤⡖⠋⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣠⡔⠚⠉⠀⠀⣀⣀⣀⣀⣠⣤⡴⢊⡜⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⣠⠤⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢰⣡⠞⠀⠀⠀⠀⠀⠀⠀⠘⠉⣷⣶⠶⠦
⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡾⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄
⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⢦⠀⣶⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣀⣀⣀⣀⣀⣀⣠⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡀⢰⡀⣉⡹⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⡏⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠢⢤⠄⢦⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡬⠁⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣀⠀⠀⠀⠀⠀⠀⠘⢟⢄⣀⡀⠀⠀⠀⠐⠤⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣧⡾⡴⢿⡧⠀⠀⠀⠀⠠⡈⠋⠉⣽⣠⡤⠠⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠒⠒⠓⠐⠓⠢⣀⠀⠄⠀⠀⠀⠀⠈⢻⠃⠀⠸⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠘⠢⡀⠀⠹⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⠀⠀⣶⣀⣠⡄⠸⣤⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠘⠤⢤⣤⣄⣒⡉⠉⢠⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠁
⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠁⠀⡶⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠒⠄⢀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⡤⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠐⠃⠀⠃

⠐⠲⡀⣰⠒⠤⠀⢤⢀⣀⠐⠰⡆⠂⠀⠶⢶⣖⠐⠂⡴⡀⠀⠀⠔⢰⣦⡀⠀⣶⠆⡀⡄⠀⠀⠠⠀⡰⠀⠀⠀⢀⡀
⠀⠀⠀⠌⠐⣠⣄⣀⠀⠈⠂⠚⢉⠀⠀⢠⣴⠂⠀⠀⡀⠃⡀⠀⢌⠀⡰⠀⠀⠙⠁⠉⠉⠁⠐⠂⢀⠀⠀⢀⠠⠁
⠀⠀⠀⠀⠐⠛⠀⠹⠁⠃⢀⡐⠆⡀⣀⣀⠔⠶⡦⠀⣀⠀⠁⠀⢀⠂⠀⡠⠄⢐⠂⠞⠢⠀⡀⠁⠀⠉⠀⢀⣤⠀⣀⣀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⡠⡷⠀⠀⠀⣐⣣⡄⠀⢀⠄⠀⠐⠦⠀⠀⠂⢀⠀⠀⠈⠁⠈⠀⣤⠈⠐⠁
⠈⡆⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠐⢾⣸⠀⣆⣁⣈⠃⠀⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⠄⠄⠀⠀⠀⣷⡄⠀⢰⣀⠀⠀⢀
⢰⠁⠀⠀⠠⣁⡠⠀⡄⠀⠰⢀⡘⠃⢋⣐⣋⠉⠐⠀⠀⠀⠄⠁⠁⠀⠈⢦⠀⠤⠄⠀⠀⠠⠂⠀⡀⠀⢶⣾⣉⠀⠀⠀⢬
⠈⡆⠀⠠⡌⠡⠄⠀⠀⠀⠀⠁⠀⠀⠉⠉⠈⠐⠰⢌⣑⣤⠆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠒⢭⡋⠂⠀⠀⢀
⠰⡆⠀⠀⢨⡀⠀⠀⠀⠀⡀⢀⠰⠀⠀⣴⡶⠶⠄⡀⠀⠀⠀⡀⣀⢀⠀⠈⠃⠀⠀⠀⠀⠘⠀⠈⠁⠐⠀⠀⠀⠀⢆
⠀⠚⠀⠁⠘⠀⠀⢀⡈⠂⠱⠈⠈⣦⠸⠉⢋⢠⡄⠊⠀⢿⡘⠇⢐⠁⠀⠀⠀⠀⠄⡀⠀⢠⠀⠀⠀⠁⠀⠀⠁⠀⢈⠧⠈
⠀⠀⠂⠀⠀⠠⠀⠠⡄⠀⠀⠀⠀⠀⠦⠀⠈⠐⠃⠠⢀⡖⠓⠛⢠⡍⠀⠀⠒⠀⢤⠁⠀⠀⠀⠀⠀⠀⡀⢠⠀⠐
⠀⠀⠀⠠⠌⣖⣦⣀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠠⡄⠀⠳⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠃⠉
⠀⠀⠀⠀⠒⠒⠨⠙⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡐⠄⠀⠀⣀⠀⠀⢀
⠀⠀⠠⠉⠠⡤⠁⠀⠂⠀⠀⠀⠸⠤⠄⠊⣀⠀⠀⠀⠀⢀⠌⠀⠀⠤⠀⠀⠀⣠⣄⠀⠀⠀⠐⠐⠳⠀⠛⠃⡖⠆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠇⢈⠀⠼⠀⠀⣖⠁⠄⠒⠀⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠁⠀⣀⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⢀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠶
⠀⠒⢢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣁⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠻⠠⠜⠀⠀⡄⠀⠀⠀⠀⠀⣤⠀⠒
⠀⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡄⠄⠀⠀⠰⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠙⢦⠀⠄⠐⣠⠀⠀⡀⠇⠀⠦⠀⠀⠸⠾⠀⠈⠀⠈⠻
⠀⠄⠀⠀⠀⠀⠼⢆⠀⠚⠋⠓⠂⠂⠁⠀⠀⠀⠀⠀⠈⠠⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⢰⡇⠀⠀⠀⠂⠀⢀⠀⢀
⠀⣀⠁⡀⠀⠀⠒⠘⠀⠀⠀⠀⠀⠈⠀⢀⢄⡄⠐⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠤⠀⣈⣹⠉⠀⠠⠀⠀⠀⢀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⢬⠴⡤⠤⢠⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢊⣀⣌⠉⠀⠀⠀⠀⠀⠠⣏⠉
⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢭⠀⠀⠀⠀⠖⠀⠂⠘⣠⠡⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣸⠶⠋⠀⠸⠁⠀⢀⠀⠀⣽⡀
⠀⠶⠦⠴⠟⠀⠀⠦⠶⠴⠄⠀⠑⠂⠖⠋⠀⠂⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠻⠶⠴

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠠⠄⠠⠤⠀⠐⢒⡒⠂⠀⠀⠭⠉⠉⠉⠉⠭⠉⠩⠉⠉⠍⠀⠀⠉⠀⠄⠒⣒⠀⠤⠤⠤⠤⠄⣀⡀
⠀⢀⡀⠤⠒⠂⠉⠑⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠈⢳
⠀⢺⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⢀⠤⠒⠩⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠲
⠳⢄⡀⠀⠈⡆⠀⡀⠀⠀⣀⣈⣡⣤⡬⠥⠤⠄⠀⠒⠒⠒⠒⠀⠈⠉⠀⠉⠉⠉⠉⠀⠀⠐⠒⠒⠂⠀⣬⣥⣄⣀⣀⠄⢰⠇⠀⣀⠴
⠀⠀⠈⠳⡆⠘⠦⣔⣚⣙⣑⡑⣣⣢⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣛⣔⣤⠽⠟⠋⠀⡞⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡩⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⢍⣀⠠⠀⠀⠀⡇
⠀⠀⠀⠀⣇⠀⠂⣀⠥⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠪⢤⡇
⣶⣶⡶⢶⠾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢲⠀⠀⠀⢠⡄⠀⠀⠀⣴⠀⠀⠀⢠⡀⠀⠀⠀⣴⠄⠀⠀⣦⠀⠀⠀⢻⡄⠀⠀⢠⡄⠀⠀⣠⡀
⠀⠐⠒⠒⡿⠓⠒⠒⠛⡿⠶⠶⠶⣿⢦⣤⣤⣼⣷⠶⠿⠶⡿⠳⠶⠒⢿⠛⠻⠟⢻⡿⠿⠓⠾⡷⠶⠶⢿⣧⣤
⠀⠀⠀⠰⠇⠀⠀⠀⠰⡇⠀⠀⢠⡇⠀⠀⠀⢼⠇⠀⠀⠠⣷⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠸⠗⠀⠀⢼⡏⠈


⠀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣈⣿⣤⣤⣾⣇⣀⣀⣀⣹⣧⣀⣀⣞⣁⠀⠈⢻⣄⢀⡴⠿⠀⠀⠐⢆⠀⠀⣠⡟⠀⠀⠰⣆⡀⠀⣰⠾⠂
⠉⠉⠉⠁⣠⣿⣍⠉⠁⠀⠀⢈⣽⠋⣋⠉⠉⠉⠉⠉⣿⣿⡛⠛⠛⠛⠛⠛⣿⣟⠛⠛⠛⠛⠛⠛⣿⣟⠛⠳⠆
⠀⠀⠀⠐⠉⠀⠙⢦⠀⠀⠀⠘⠁⠀⠙⠇⠀⠀⠀⠈⠁⠀⠻⡄⠀⠀⠀⠾⠉⠙⢷⡀⠀⠀⢠⣾⠋⠙⠷⡆
⣿⡿⠿⠿⠿⢿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⣠⡿⠋⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⣧⠀⠀⢸⣿⡇
⠀⠀⣰⣿⠁⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠘⣿⠀⠀⢠⣿⠁
⠀⠀⠻⢿⡀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⢿⣷⡄⠀⠰⢤⣄⡀⠀⠉⠀⠀⠀⢻⡆⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠘⠻⠄⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠸⣇⠀⡾⠁
⠀⠀⣴⠞⠁⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⣦⡀⠀⢿⠈⠁
⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠈⢿⡀⠘
⠀⠀⢿⣆⠀⠀⠀⠀⠀⠈⣿⡌⢿⣦⣿⡇⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠘⡇
⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⢻⣷⡈⢿⣿⠁⣰⣿⠟⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣴⣼⡇
⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠈⣿⣷⡀⠻⠄⣿⡇⣠⡀⠀⡀⠙⣦⠀⠀⣠⣶⣿⣿⣿⣷⣤⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⣀⣈⣿⣷⣄⠀⠸⡇⠻⣿⣶⣿⣦⡈⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣷⣆⠀⠀⣀⡴⢖⣛⡧⠖⠂⣀⣽⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠉⠀⠀⠉⠀⠈⠛⠿⠿⠟⠀⠿⠛⢿⣿⣿⣿⣿⠟⢀⡴⠃⠀⠀⢠⣿⡿⠶⣯⣥⣖⣭⣿⣶⣿⢿⣿⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣾⠃⠀⠈⠛⠛⣋⣡⠴⢋⣠⠤⢒⡣⠘⣁⠐⠾⣿⣿⡿⠟⠻⣿⣿⠎⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣠⡾⠋⠉⣿⣿⣿⣿⣶⠄⠀⢉⣩⠭⠖⠊⣉⡤⠞⢉⡤⠚⢹⣷⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢰⠋⠀⠀⠀⠛⢿⣿⠻⢿⡶⢋⡭⠶⠶⢀⠔⢋⡠⠞⠁⠀⣰⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⢠⠞⣠⠋⣀⣤⡄⠡⠖⠉⠀⠀⡀⠠⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣴⠶⠊⠤⠴⢶⠟⠚⢡⣾⣿⣿⠇⠀⠀⢀⣠⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⡄⠀⠀⠀⠀⣀⣴⠁⣠⢖⡠⠉⠉⠀⣴⣶⣿⣿⣿⣿⠏⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡟⠁⠀⠀⠀⢸⣆⠀⠀⠛⠿⣿⣷⣯⠀⠀⠀⢰⣿⣿⠿⠛⠋⣰⢞⡛⠻⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠯⢡⣶⣶⣦⡀⠀⠸⣿⣦⣄⠀⠀⠀⠙⠉⠀⠀⣠⣿⣿⠃⠀⠀⠀⠁⣤⣤⣄⠉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠀⢺⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⡿⠀⠀⠀⠀⢼⣿⣿⣿⠘⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣅⡀⢙⡛⠛⣁⣠⣤⠄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠠⣄⡀⠈⠛⠛⢁⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⠷⠿⠛⠉⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠛⠿⣶⣾⠿⠋

⠀⠀⠀⠀⠀⠀⡠⠒⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠢⡀
⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢄
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⡄
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠙⣿⡆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠈⠁⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣠⠮⠥⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⢕⣄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⠘⠄⢀⠞⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠉⢧⠀⠀⡎⡇⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢸⠀⠆⡌⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠃⠸⠀⡇⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢸⠀⢸⠀⢠⣿⣯⣀⣵⡀⠀⢀⣠⣤⣭⣤⣄⠀⠀⢀⣆⠀⣿⣷⡄⠠⡆⠀⡇⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢌⡀⠀⠘⡆⢸⠀⢸⣿⣿⣿⣿⣷⣠⣿⣿⣿⣿⣿⣿⣷⡄⣸⣿⣿⣿⣿⡇⠀⠀⡸⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⣀⠽⠯⣑⠳⣘⢃⠘⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠁⢼⢠⠧⢒⡲⠿⢄⡀
⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠉⠚⢇⠑⠌⢙⣛⠩⠈⠀⠻⣿⣿⣿⣿⣿⠟⠀⠪⢙⠛⣋⠠⠊⡼⠀⠂⠁⠀⠀⠀⠈⠲⡄
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣅⠀⠤⠄⢀⣀⣀⣀⣉⠹⠉⠁⠀⠀⠀⠀⠀⠀⣂⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⢠⣶⣎⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠀⠒⠀⠄⠤⠤⠤⠤⠐⠂⠠⠄⠠⠀⠒⠈⠓⠤⣀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠠⣱⣶⣦
⠀⣴⠾⢆⣮⡄⢠⠤⡀⣠⡝⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣤⠀⡤⣄⢀⣽⣰⠿⣶⡀

⠀⠀⠀⠀⠀⠀⠋⠀⢰⠀⠉⡲⡀⠀⠀⠀⠀⣴⠑⢀⢆⠀⠀⠀⠉⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠡⣤⡤⠚⠉⠾⠀⠀⠀⢸⢃⠀⠀⠈⠢⢴⠃⠠⠀⠀⢃⠀⠀⠀⠀⠀⠀⠠⠀⠈⠄⠀⠤⠀⠢⣀⡀
⠴⠒⠛⠒⠲⢤⡀⠀⠈⠓⠒⠢⠊⠀⠀⠀⢸⠀⠀⠉⠉⣳⠀⢄⠀⠀⠈⠸⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⢀⡠⡋⠹⣇
⠂⠀⠀⠀⠀⠀⠉⠢⡀⠀⢢⡐⠋⠀⠀⠀⠀⠣⡂⣀⡀⠀⠀⠀⢅⠢⣢⠃⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⡎⠀⢠⠁⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠤⣣⣤⣠⠭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠆⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠁⠀⠀⠀⠀⠸
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⠤⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡴⠡⣆⠀⢸⠁⡠⠖⠀⢀⡤⠒⠉⠉⠉⠀⢳⠀⠀⠀⠀⠀⢀⠠⣰⡶⢤⣀⢀⡄
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢨⢃⣀⡈⢳⡾⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⣧⡀⡴⠁⢳⡀⢀⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠑⠴⠤⠤⠍⠋
⠉⠩⠉⠍⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⢄⠀⠂⠀⠀⠡⠹⡄⠀⠀⠀⠀⠀⡀⠤⢤⣄⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠄
⠈⡟⡢⠀⠀⠀⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⡄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡠⠊⠃⠀⠀⠀⠀⢼⢀
⠀⢀⠈⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠘⠀⠱⣄⠀⡀⠀⠀⢀⡠⠊⠀⠀⠀⠀⢸⠀⠢⠄⣁⠀⠀⠀⠸⡀⡀
⠤⠸⠀⠀⣰⠴⠁⠀⠀⠀⠀⠠⠦⠀⠐⠀⠈⠈⠈⠢⠄⡄⠀⠁⠓⠒⠋⠁⠀⠀⠀⠀⠀⠀⢸⢠⡴⠒⢻⠇⠀⠀⠀⠑⢌
⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⣀⡇⠀⢀
⠄⠀⠐⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢂⠖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠝⡄⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⢠⡪⢧⣀⠘⠀⠄⠀⠀⠀⣠⠖⠋⠉⠍⠍⠓⢦⡀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠂⠀⠀⠀⠀⠀⠀⢘⡁⠀⣈⣿⠊⠀⠀⠀⡜⠁⠐⢆⠀⠀⠀⠀⠠⠙⡆⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠂⠁⠁⠂⠀⠀⠀⠀⠀⠐⣼⠉⠀⠀⠀⠀⠀⢰⢠⡀⠀⠀⢽⢣⠜⠈⠈⢱⣽⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠋⠀⢸⠀⠀⠂⠀⠀⠀⠀⢦⠄⠀⠀⠘⠁⠀⠀⠀⠀⠘⡄⢄⠀⠀⠐⠀⠀⠀⠀⢨⠇⠀⡼
⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡐⠤⠀⠀⠀⢀⡧⠊⠀⠀⠣⠤⣀
⠒⠊⠁⠀⠀⠀⢀⡀⢀⢀⡀⠈⠑⠂⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠤⣀⠀⠀⠀⠀⠈⠁⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒

⠈⠉⢙⠲⢤⣠⡖⠆
⠀⢐⣻⠛⢆⡷⡖⣿⣵⢮⣶⣏⣴⡶
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣶⣶⣶⣿⣷⣦⣤⣶⣾⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠛⠿⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⡄⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⣀⠀⠀⠀⠈⠙⠛⠛⠓⢒⣦⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢻⡗⠋⠉⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⠙⠻⣦⡀⠀⠀⢀⢿⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⢻⣦⣠⡟⠀⣧⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣠⣴⣤⡀⠈⣧⣻⠀⠀⣿⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⣄⠀⠀⠀⣸⠃⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾⢿⣿⣿⣿⣆⢸⡇⠀⠀⣿⣀⡤⠖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠛⠲⣤⡿⠛⠉⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢰⣀⣸⣿⣿⣿⣿⢸⡟⠀⡰⠋⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠳⡄⠀⠰⣋⡥⠤⠀⠀⢣⡘⣿⣿⣿⣿⣿⠟⣸⠃⠈⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⡄⠀⢀⡶⣾⣿⣶⣄⠙⡄⠘⢁⡤⠖⠒⠒⢄⠳⣽⣿⣿⣿⠵⠚⠁⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⣇⠀⢸⣅⣼⣿⣿⣿⣷⡜⣴⠋⠀⠀⠀⠀⠈⡆⠈⠉⠀⠀⢀⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⢻⣆⠘⣿⣿⣿⣿⣿⣿⣿⡏⠢⡀⠀⣠⠴⠒⠓⠒⢤⡤⣖⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⢻⡳⢌⣻⣿⣿⣿⣿⡯⠟⠀⢨⠟⠁⣀⠤⠤⣄⠀⢹⠘⡓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⣈⠉⠉⠉⢁⣀⠤⠴⣾⢠⠏⠀⠀⠀⠀⢳⡞⠀⣧⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠛⣞⠉⠉⠻⢦⣀⣀⠤⠖⠋⠀⢀⡸⢦⡤⠤⢤⡽⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⣤⠤⠒⠒⢋⠽⠿⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⡿⠔⠒⣷⠖⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣇⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⢧⣀⠀⠀⠀⠀⠙⣶⢤⣀⣀⣀⡴⠔⠋⠀⠀⠀⢹⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠀⠀⠈⠉⠙⣒⢦⣶⡧⠤⠤⢭⠥⠤⢤⡤⠶⠖⠚⠋⡟⠛⠓⠲⢄⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⠖⠋⠁⠀⠀⣉⣓⣤⣴⡄⠀⠀⡇⠀⠀⠀⠀⡧⠀⠀⠀⠀⠙⠈⡝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡞⠀⠀⠀⣠⡟⢋⣉⣈⠀⠹⣦⣀⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣜⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣄⠀⠸⡏⢹⠉⠀⠈⠙⡄⢸⣿⠃⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢫⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠷⣄⠑⠶⠲⠚⢀⡼⠛⠺⠛⠧⠤⠤⠤⠤⠤⠤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁

⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣷⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣆⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⢁⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣀⡀⠙⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⠟⠆⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣿⣿⡛⢢⡈⣿⣿⣿⣿⣿⣿⡿⠛⠛
⠀⠘⢿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣷⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣌⠿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣭⣥⣶⣿⣿⢋⡾⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣛⣿⣻⣟⣿⣿⣿⣿⣿⣧⣫⠾⠕⠒⠒⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⡛⠿⠿⠿⣿⣿⣿⣟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⠿⢿⢁⢾⣷⠀⠀⠀⠙⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⣸⠸⡄⠀⠀⢀⣤⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣙⠢⣄⣙⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⣴⠛⠛⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⢾⠆⠀⣿⠤⠄⠀⠀⢸⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠸⠁⠀⢷⣤⣤⡄⠀⠸⣤⣤⡤⠀⠀⢧⣤⣤⠀⠀⠘⢦⣤⠜⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣤⢤⣄⡈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠊⣉⢤⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣞⠀⠀⠀⠙⠳⣄⠈⠳⣄⠀⢀⣀⣀⣀⣀⡀⢀⡤⠚⢉⡤⠖⠋⠁⠀⠈⡣⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠧⠀⠀⠀⠀⠀⣠⠗⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠰⣉⠀⠀⠀⠀⠀⢀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠰⡆⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡼⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠲⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⣸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡤⠝⠦⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠊⠉⠀⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣽⣯⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣘⡇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠏⠉⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⣼⢳⠀⠀⠀⠀⠀⣀⣠⣤⠶⠷⠿⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⠀⢰⠇⠘⡇⠀⣰⠶⡟⠁⠀⠀⠀⠀⠀⠈⠙⣦⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡇⠀⠀⣾⠀⠀⣧⡞⠁⠀⢭⠀⠀⠀⠀⠀⠀⠀⡰⠛⠛⢷⠀⠀⠀⣼⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀⣿⠀⢠⡟⣴⠶⡄⣾⣀⠴⠿⢮⡅⠀⡜⢁⣀⠀⠈⡇⠀⣼⣿⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣤⣸⡀⣼⢸⣿⣶⣿⡟⠁⠀⠀⠀⠈⣶⣵⣏⣹⣷⡄⢻⣼⢁⣿⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣭⣃⣿⣌⠿⡿⣿⠻⡆⠀⠀⠀⣠⣾⣿⣿⣿⡿⠀⣸⢃⡾⢹⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⢹⣶⣮⢥⣤⣭⣶⢶⣞⣋⣨⠿⠿⢭⡤⢺⣿⡾⣤⣼⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠳⡀⠀⠙⡶⡖⠀⠒⠒⠒⠈⠑⣒⣣⡾⠟⠁⣽⠋⠉⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⠃⡇⢀⣴⠀⠀⠀⡰⠃⢸⡇⠀⠜⠉⠓⣆⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣠⣊⠴⠾⡄⠹⣦⠀⠀⠻⣄⠠⢷⠀⠀⠀⠀⣸⢾⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠋⠁⠀⠀⢿⠀⠀⠀⠀⠀⠙⢶⡌⠳⠦⣤⡴⠋⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣦⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⣆⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠈⠻⣼⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠳⣤⣀⣀⣀⣀⣀⣠⡴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠘⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠾⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠾⠃

⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⠒⠵⣄⠀⡠⢤
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣠⣀⣰⠋⣴⡉⢶⡘⢏⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠐⢇⠀⠀⠹⡌⣧⣸⠀⠀⠀⠀⣀⣀⣀
⠀⡇⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢿⡘⣇⠀⠀⡠⠞⠁⠀⠈⢆
⠀⡇⠀⠀⠀⠀⠀⠎⠉⢣⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠹⡀⣨⢳⡘⣄⡜⠁⠀⠀⠀⠀⣾
⠀⡇⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⣀⣀⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢻⣁⡤⢿⠟⠀⠀⠀⠀⠀⠀⡟
⠀⡇⠀⠀⠀⠀⠀⡆⣴⠏⣴⣿⣿⣥⣿⣦⣠⠄⠘⠀⠀⠀⢀⠤⠒⠉⠁⣠⠏⠀⠀⠀⠀⠀⠀⡼⠁
⠀⡇⠀⠀⠀⠀⠀⠈⢻⡀⢻⣿⣿⣿⡿⠁⠀⠠⠀⠀⠀⠐⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⡼⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⣀⡤⠔⠉⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⡎⢢
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡖⠀⠄⠀⡤⠀⠒⠀⠉⠒⣵⠦⢄⣀⣀⣀⣠⡴⠚⢧⡉⠲⠤⠴⢃⡞
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠈⣆⠸⡄⠀⠉⡶⢶⠖⠋
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠑⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⢦⡙⠦⠤⠇⢸
⠀⡇⠀⠀⠀⠀⠀⢀⡤⠔⠛⠒⠛⠀⣠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉⠲⠤⠖⠃
⠀⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡄⠰⠃⠀⠀⡐⠰⠎⠈⠙⠢⡀⠀⠀⠀⠀⠘⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠒⢦⠀⠀⢰⡏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠥⢹⡤⠂⣀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⣀
⠀⡇⠀⠀⠀⠀⠀⠐⢏⡀⠀⠈⠈⠒⠡⠤⠶⣀⣀⣀⡤⠤⠤⠤⢀⡠⠤⠚⠉⠀⢀⣈⠇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠒⠀⠀⠠⠠⠤⠤⠀⠀⠐⠒⠒⠒⠈⠉⠁
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠄⠤⠂⠆⠀⠄⠂⠄⠒⠢⠀⠤⠄⠀⠠⠤⠄⠀⠆

⠁
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠑⢄
⠀⠀⠀⡠⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢢
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢃
⠀⠀⠃⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⢀⠠⠠⠄⠊⠘⣺⡐⠀⠄⠠⢀⠀⠀⠀⠀⠀⠠⠱⠀⠀⢀⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⠴⠋⠡⢐⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠉⠰⢄⠀⢀⠃⠀⠀⠀⠈⠃⢄
⠀⠀⠱⡀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠑⣌⠀⢀⠀⠀⠀⠀⣰
⠀⠀⠀⠙⡆⠄⡀⠐⡀⡼⠀⠀⡀⠤⢀⠀⠀⠀⢀⠢⠤⣀⠀⠀⠀⢀⢤⠄⡀⠀⢸⡄⠌⢀⡠⠔⡚⠁
⠀⠀⠀⠀⠈⠐⢄⡀⠙⢱⠀⠘⠒⠃⠀⠃⢀⡆⠁⠀⠀⠀⠑⡇⢀⠃⠊⠀⠈⠀⠈⢛⠁⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢆⠐⠤⣀⣀⠀⡸⠁⠀⠀⠀⠀⢀⠷⡘⣀⣀⡠⠈⢀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢁⡀⠀⠀⠈⠀⠈⠐⠤⡤⠔⠁⠀⠈⠀⠀⠀⣈⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠑⢅⠒⠲⠴⠂⡛⢋⣉⢛⡁⠲⠴⠒⢀⠕⠁⢀⠔⠁
⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⢈⠑⡠⣀⢉⠒⠶⠅⣠⡀⢀⣀⣀⠵⠖⠂⣁⡠⠔⠁⠀⠀⡀
⠄⠂⠁⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⠃⠀⠀⠉⠀⠒⠒⠀⠒⠒⠂⠉⠁⠘⢇⡉⠁⠀⠀⠀⠀⠑⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠐⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠒⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢃⠀⠀⠀⠀⠱
⠀⠀⠀⠀⡴⠶⠕⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠠⠖⠢⠗⢖⡄
⠀⠀⢀⡞⠂⡀⠤⠤⢀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠔⢁⠤⠠⢄⠀⢳⡆
⠀⠀⠀⡗⠀⠀⠀⠀⠀⠡⢁⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠘⠐⠁⠀⠀⠀⡁⢐⡇
⠀⠀⠀⠈⠢⡑⠄⡀⠀⠔⡼⠘⠀⠀⠀⠀⠀⠀⢮⠉⠉⡨⠂⠀⠀⠀⠀⠀⠑⢤⡰⢄⠀⡠⢔⡠⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢡⠳⠆⢻⣀⠤⠄⠀⠦⣠⠇⠀⢅⠔⡄⠀⠤⣀⡘⠢⠾⣢⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠩⠏⠀⠘⠃⠀⠃⠀⠘⠼⠀⠈⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡙⠁⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⠀⣠⠽⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⣿⣿⡿⣿⢠⠃⠀⡾⡀⢀⣀⠤⠴⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏⢸⠀⢸⠀⡷⠋⠁⠀⡀⠀⠀⠛⢦⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠀⠀⠀⢧⣸⣠⢻⣧⣖⠈⠉⢢⣤⣲⡄⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠾⢮⣟⢙⣤⣤⣚⠿⣟⣱⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⠈⠀⠘⠃⢀⠀⠉⠖⡎⠱⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠱⣀⡠⠖⠲⡘⠂⠘⢄⠣⣀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠱⡌⢣⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⣇⠀⠀⠀⠀⣹⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠚⠒⠚⠛⠒⠒⠛⠓⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠖⠒⢠⣀
⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⠉⢽⠟⣇⠈⠈⠀⠰⠄⠀⠀⠀⠀⡆⢀⡆⡀⣁⣰⣧⣬⢷⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⡠⠴⠶⠿⢤⣄⠠⠀⠈⡇⠀⠀⠀⡇⢬⣀⡀⢀⡀⠀⠀⠀⢹⠀⢀
⠀⠀⠀⠀⠀⠰⠀⠚⡀⣸⢫⣶⡄⠀⣠⣤⠘⣇⠀⠀⡷⠄⠀⠀⠗⠈⠱⠉⠉⢉⠀⠀⠀⠀⢧⠀⠀⡀
⠀⠀⠀⠀⣀⠈⠀⠀⢠⡇⠀⠉⠀⠁⠈⠋⠀⣿⣟⣻⣿⣛⣟⣻⠛⣶⡀⠀⢨⣶⠄⠀⠀⠀⢸⣇⠐
⠀⠀⠀⠀⠈⠀⡇⠀⠀⣹⢶⠚⢱⡶⣫⡷⣚⠍⢻⣿⣷⣧⣥⣟⣷⣿⡟⢿⣿⣧⣶⣶⠦⢤⣤⣍⣉⠑⠒
⠀⠀⠀⠀⣀⡀⡧⠀⠀⣿⠄⠀⠉⢿⡟⠰⣭⣳⠞⠉⠁⠄⠀⠉⢻⣷⡟⠽⣻⣿⣏⠀⠂⠀⠀⡘⢹⠂
⠀⠀⡠⠜⢚⡻⣧⡀⠐⡌⣱⣴⢲⡿⢷⡅⢻⠃⠀⣿⡇⠀⣿⡇⠈⡟⠛⣾⡿⠷⠼⠿⢀⡐⠀⠡⡘
⠀⠀⢟⠐⣁⠘⢀⣁⠀⠀⠀⠈⠻⣻⠶⣤⣾⠀⠀⣿⠇⠀⣿⠇⢰⣧⡞⢁⣴⡀⠀⠀⠀⠉⠲⣔⠙
⠀⠀⠈⢰⠃⠀⠀⠉⠀⢸⣿⡷⠀⢰⣶⣟⠿⢧⣀⠉⠀⠀⠉⣠⠞⣹⠀⠻⠾⠟⡀⠀⣀⣤⡐⠘⡆
⠀⠀⠀⠘⡄⢜⣿⡇⠐⠂⠀⠀⡦⠛⠚⠻⣅⠃⢛⡷⠶⢲⠮⠁⣠⠟⠣⣀⠀⠈⠛⠀⠿⠿⠃⢰⠇
⠀⠀⠀⠀⠀⢄⡉⠠⣀⠠⡐⠉⠰⢇⢀⡤⢈⡟⠉⢀⠀⠄⡀⠄⠁⣠⣾⡿⠃⢢⡤⣤⣤⣤⠶⠿⣄⠄
⠀⠀⠠⠂⣒⠘⠿⠦⠀⡀⠉⠄⣀⠈⠈⠁⢈⣷⠄⡶⠘⡿⠿⠀⠐⠛⠛⠃⠈⠙⣷⣋⢹⡇⢶⠇⣺⠀⢄
⢀⣤⡸⠀⠉⠀⠀⠛⠀⣶⣶⣾⠟⣋⠀⠃⣉⠙⣿⣩⣺⡀⠀⠀⠀⠀⠀⠀⠀⢀⡗⢛⣥⣿⣶⣶⠋⠀⠈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⢹⣾⡟⢈⠛⠀⠀⠙⠏⠀⠀⠘⣿⣧⠀⠀⣀⣉⠉⢩⣿⣿⣏⠐⠃⣨⡉⠙⢄
⠀⠀⠐⣄⣀⣀⣀⢀⣤⣾⠿⠷⠬⠗⠰⣏⡘⠀⠀⠀⠀⢹⣯⣧⠀⠻⠟⠀⣾⣷⢾⣧⣵⠞⠈⡉⠀⠀⡃
⠀⠀⡉⢀⡘⢿⣿⣿⠻⠁⠀⠐⠂⠀⠀⢶⠁⠀⠀⠀⠀⠀⣯⠏⠑⠲⢴⣾⡿⠀⠀⠀⠈⠳⢆⡀⠤⠀⡁
⠀⠀⠠⡞⠙⠺⣆⢘⢶⠠⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⣠⡟⠀⠀⠠⣿⣽⣷⡠⠀⠰⠄⠀⠀⢙⣦⡚⠁
⠀⠀⢀⠦⣄⠀⠈⢁⢸⠐⠂⠀⠀⠀⠀⠀⠀⠧⣶⢿⣽⣍⠀⠀⠀⠀⣷⣿⣿⡵⣿⠦⣄⡀⢀⣪⠋
⠀⠀⠘⢢⡜⠁⡀⢀⠞⠃⢠⣤⣤⠤⠀⢢⣶⣆⠻⣾⣿⡓⠀⠀⠀⠀⠹⣁⣿⠉⣿⠛⣬⣭⠝⣃
⠀⠀⠠⡋⠀⠀⡠⠀⠀⡴⠧⣽⠏⣠⣤⣘⣿⠟⢁⠛⣾⣿⡀⠀⠀⠀⠀⠙⢍⠘⢻⡚⢿⢴⡇⣬
⠀⠀⢰⣿⣶⣞⠦⣤⠎⠀⠀⡘⣏⢿⣿⣿⠀⠀⠀⠐⢁⣈⠁⡄⠀⠀⠀⠘⠀⡷⠆⢹⣸⠀⢘⡇
⠀⠀⢸⠁⠈⠻⣷⡎⢰⣿⠸⡿⠘⡢⡰⡁⢀⣤⣄⠀⠿⠭⠀⠈⢢⣌⣁⡀⠔⠁⠀⡼⡿⡆⠈
⠀⠀⠀⠢⡀⠀⠘⣇⠀⠀⠀⠀⠀⠗⣿⠀⠘⠳⠋⠀⠤⠀⠀⡤⠾⢽⣃⠀⣴⡦⢰⠁⢰⠇
⠀⠀⠀⠀⠀⠁⠈⠙⢢⡄⠀⣄⠃⠀⠈⠱⣄⡠⡄⠀⠀⣠⠋⠁⠤⢶⠌⠻⠶⢤⠃⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠃⠌⠀⠁⠀⠂⠀⠈⢉⠉⠁⠀⠀⠀⠀⠀⠁