Easter Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣬⢷⠚⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢃⠀⢳⡀⠈⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⢀⠁⠒⠄⡀⠀⠀⠀⢭⢄⣄⠷⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣴⡊⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠁⣸⠋⠻⡷⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠸⣤⢠⡏⠀⣂⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠋⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠈⠀⠀⠀⠈⠁⠀⠄⢢⡀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠘⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢉⠡⠄⠐⠂⢀⠀⠀⢀⡀⠀⠀⠈⠻⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠉⠀⠑⠄⠁⠠⠀⢈⠒⡈⡁⠤⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠙⢂⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠑⢌⠂⠀⣀⡀⠂⢀⠀⡀⠠⢄⠀⠠⠀⠐⡤⠀⠀⠀⠂⠀⢀⣠⠐⠘⡄⠀⠀⠈⠉⠘⢦⠈⠐⠉⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠑⠠⠤⠀⠒⢠⠐⠓⠂⠈⢰⠠⢞⡑⠬⠅⢨⠀⢐⢆⠙⢀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠉⠝⠳
⠀⠀⢀⠤⢄⠀⠀⠀⠀⢄⢁⠼⠣⠀⡄⠀⠀⠀⠀⠀⠘⠄⠔⠒⢢⡅⠠⠊⠀⠀⠀⠀⠀⠀⠀⠑⠚⢦⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠐
⠐⠀⠑⠠⠸⠠⡀⠀⠐⠉⢁⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠉⡆⠀⠀⠀⠀⠀⠀⠒⡂⠁⠣⠀⠀⠑⢀⠔⠁⢸⠂⢢⠠⡀
⡘⠘⣀⡠⢠⣄⣀⣀⠈⠀⠉⠀⡰⠍⠄⠀⠀⡐⠲⠎⢱⠀⠑⠠⠴⠁⠀⠀⠀⠀⠀⠈⠄⠈⡒⠀⠀⠀⠀⠈⠀⠰⠉⢐⠉⢂⡠
⠑⠀⠃⢀⠜⠮⠑⠤⠐⢄⠀⠥⠀⢄⡈⠀⠀⢉⡄⢤⡀⠃⠀⠸⢀⢀⢀⠄⠀⠀⢠⣆⠄⠂⢰⣀⠆⣀⠀⠐⠠⣈⢳⡋⠲⡄⢀
⠀⠀⠀⠀⠀⠀⡀⢪⡌⠂⠀⠀⠁⠢⣉⣖⠈⠩⠥⠚⢷⡤⠐⢄⣈⣮⠤⠐⠐⠒⡟⠀⠀⠀⠁⣤⠢⢌⡸⠀⢀⠔⠉⠁⠒
⠀⠀⠀⠀⠀⠀⠙⡄⢼⣆⡀⠀⠠⢀⠈⢹⠀⠀⠀⠁⠞⡫⠋⠢⣄⠧⠐⢤⡵⠃⣟⡠⡠⠃⢰⠏⠁⡚⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠻⣗⠀⠐⠠⡁⢸⣇⠡⡜⡡⠅⢿⠠⠀⣰⠖⣵⠅⠀⢰⠏⠌⠀⠀⣞⣠⠊⠀⢠⠏⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⢤⣀⠀⠀⠀⠑⠌⢧⠀⠀⠈⠈⡆⠐⠐⠑⠂⢹⡃⠤⡞⡘⠁⠀⠀⠾⠐⠀⡀⢰⡏⠈⠆⢀⡏⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠑⠄⢄⢀⠀⠀⢠⢳⠐⠠⡄⣿⢠⠀⠀⠤⢜⡗⠂⢡⠤⠤⠤⢴⢢⡏⢀⠀⢸⠃⠀⣰⡜⠀⠀⠀⠂⠊
⠀⠀⠀⠀⠀⢀⠔⡫⠄⠤⠤⠀⢡⣡⠀⠀⠐⠒⠐⠀⠤⢈⣿⠘⣈⠀⠸⠀⠚⠒⠱⠀⡈⢸⠄⠠⣿⠓⠀⢀⣉⣉⡐⠂⠄
⠀⠀⠀⠀⢀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠚⠉⠉⠀⠀⠀⠀⠀⠉⠀⠠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠉⠉⠉⠉⠉⠑⠒⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠀⠀⠀⠀⠀⢀⡤⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠘⠦⢤⠤⠴⠚⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⠀⠀⠀⠀⠀⢀⠟⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣠⠞⠁⠀⠈⢧⡀⠀⠀⠀⠀⢀⡾⠀⠀⠈⠙⠒⠶⠶⠚⠉⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠁⠀⠀⠀⠀⠀⠙⠲⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣰⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⢧
⠀⠀⠀⠀⢰⣏⡀⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣀⠼⣆
⠀⠀⠀⢀⠇⠀⠙⠦⣄⡀⠀⠀⠀⠈⠉⠓⠶⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠖⠊⠉⠀⠀⢀⣠⠴⠚⠁⠀⠸⡄
⠀⠀⠀⡞⠀⠀⣠⠤⠤⢍⡛⠲⠤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⢀⣀⠤⠖⠛⣉⠤⠤⢤⡀⠀⠀⢻⡀
⠀⠀⠀⠁⢠⠋⠁⠀⠀⠀⠙⢦⠀⠀⠀⠉⠉⠒⠲⠶⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠶⠖⠒⠋⠉⠁⠀⠀⢠⠞⠁⠀⠀⠀⠈⢣⠀⠈⠃
⠀⢠⡆⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⠶⠴⠦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠴⢦⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠
⠀⣼⣅⡀⠘⢧⣀⠀⠀⢀⣠⠎⠀⠀⢠⡎⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢠⠖⠋⠉⠉⠓⢦⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⢧⠀⠀⠈⢧⣀⠀⠀⢀⣠⠟⠀⣠⠼
⢀⡇⠈⠙⠦⣄⠉⠛⠛⠋⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠉⠙⠛⠋⢁⡤⠞⠁
⢸⠷⣄⡀⠀⠀⠉⠲⢦⣄⣀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣤⠏⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⠣⣄⣀⣀⣀⡴⠃⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⢀⣠⠖
⡘⠀⠀⠙⠳⢤⣀⠀⠀⠀⠉⠛⠒⠶⢤⣀⣀⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣀⣀⡤⠶⠚⠋⠉⠀⠀⢀⣠⠴⠋⠁
⡇⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠲⠶⠒⠒⠋⠉⠉⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠖⠛⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣄⣀
⢸⡀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠘⣇⡴⠋⠁⠀⠀⠉⠙⢦⡀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣷⣾⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡀⠤⠖⠒⠒⠶⢤⡀⠀⢀
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣨⣤⠋⠀⠀⠀⠀⠀⠀⠀⠙⣆⣸
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⣀⡀⢀⠞
⠀⠀⠀⠀⠘⣏⠑⢦⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠒⠚⢦⣄⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡴⠋⠉⠀⣸⠏
⠀⠀⠀⠀⠀⠈⢷⡀⠙⢦⡀⣱⠶⠢⠶⣄⡀⠀⠀⡸⠁⠀⠀⠀⠀⠈⠳⣆⠀⠀⣠⠏⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⠤⠶⠒⠚⠷⢴⡋⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢻⠁⠀⠀⠀⠀⠙⠶⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⣰⠇⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⢹⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖⠚⠉
⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⢀⢄⡵⣁⢀⡀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡀⠀⠀⢠⣳⣀⡐⣿⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠤⠄⠀⠃⠀⠺⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠰⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠘⠃⠀⠈⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠂⠒⠒⠀⠂⠀⠄⠀⠂⠒⠂⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢾⢾⣦⡖⣢⠇⠀⠀⠀⠺⠃⠀⣈⡁⠀⠐⠦⠾⢧⡈⠁
⠀⠀⠀⠀⠀⠀⣄⢣⣀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠆⠙⠤⠘⠢⠆⠀⠀⠀⠉⠀⠀⣠⠀⠀⠀⠀⠀⠞⣅⣌⠢⠀⠐⠚⠀⠀⠐⠳
⠀⠀⠀⠀⠀⢦⣰⠲⠃⣾⠟⠁⠀⠶⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡠⢄⠀⠐⠃⠀⠀⠀⠀⡀⠀⠛⠋⠀⠀⠀⠀⠠⠘⢀⠂
⠀⠀⠰⠷⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠂⠀⣤⣠⠀⣄⣤⠀⢸⠀⠀⢠⠀⡄⠀⡌⡼
⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⣠⠑⠀⠀⠚⠿⠃⠸⣠⣤⡄⠀⠀⠀⠀⠙⠃⠀⠛⠃⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃
⠀⠘⠛⠛⠛⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠄⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⣠⡄⠶⢶⠇⠀⢀⣄⠀⠄⠀⠀⠀⡺⡤
⠈⢦⣄⢀⣴⠂⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠸⠖⡗⢿⡇⢆⣀⢼⣀⣼⣉⠆⠈⠙⠅⡀⠀⠀⠀⠈⠁⡤⣀⠀⠀⠄⠀⠁⠀⠀⢠
⠀⠿⠻⠿⠿⠃⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⢐⠀⠁⠀⢀⣀⢠⣀⣀⣀⡀⡀⣀⢀⠀⣀⡀⠀⢀⡀⠀⠈⠻⠂⣁⡟⢵⣶⠀⠀⠐⠂⡠⠀⠀⠄
⠀⠀⠤⠤⠄⠀⠐⠁⠀⠀⠘⠋⠛⠀⠀⠀⠀⠈⠁⠀⠀⠊⠛⠚⠋⠘⠛⠒⠃⠋⠙⠘⠒⠶⠀⠉⠀⠀⠀⠀⠓⠸⡇⠈⠁⠋⠀⠀⠀⠁⠀⠨
⠀⠘⣦⠤⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⣀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠁⠈⠑
⠀⠀⣿⢶⡇⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢀⠘⠿⠿⠁⠀⡀⠀⠀⣼⠁⠀⡋⢠⣤⣤⣼⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠐⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡈⠀⣿⡷⡆⠀⠀⠀⠉⠀⠀⠃⠀⠀⣀⡘⠿⢋⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠀⠐⠀⢰⣿⣿⣿⣿⡧⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠛⠋⠀⢰⣇⠀⠀⠤⠄⢤⠤⠤⠤⠀⢀⣄
⠀⢠⠀⢀⠀⠀⠀⠈⠃⠉⠀⠈⠁⠀⣀⠻⠿⣿⠿⠁⠀⠀⠀⡀⠀⣄⠀⣾⣧⠁⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⣿⡄⠤⠠⢄⢤⠠⠠⠤⠄⠈⠿⠗
⠀⣟⢠⠇⠠⢀⡟⠀⠀⢠⣶⣦⡀⠺⠿⠂⣀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣤⡀⢀⣀⡀⠀⣠⣶
⠀⠛⠘⠀⠀⠊⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠻⠿⠃⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠂⠘⠛⠃⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⡈⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠱⣦⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⢣⡀⠈⢳⡄⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠸⠆⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣤⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢨⣀⣸⠃⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠘⡄⠀⢸⡇⠀⠀⠈⡍⢩⡄⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠎⠀⠘⣷⡄⠀⠀⠀⠸⠃⠀⠀⢸⣇⣸⣿⠀⠀⠀⠀⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠰⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠙⠲⣄⠸⠇⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⡇⠀⠀⠤⠂⠀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡆⠀⠀⢀⡴⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⡠⠊⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⠘⠛⢛⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠸⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣇⠀⠈
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⣀⣤⡾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡺⠀⠈⠋
⠀⠀⠀⠀⢠⡀⠀⠀⢠⡇⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⢀⣀⠀⣠⣴⠶⡛⣴⠶⠞⠁
⠀⠀⠀⠃⠀⠀⠀⢱⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠘⠃
⠀⠀⠀⠂⠀⠀⠀⠀⣇⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⡀⠀⠀⠠⡼
⠀⠀⠀⠘⠂⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠉⠛⠄⠀⠀⢡⡀
⠀⠀⢐⠀⠀⠀⠐⣾⡟⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡃⢄
⠀⢀⡴⠆⠀⠀⠀⠘⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠰⠿⠀⠀⠀⠀⠀⠀⢠⠴⠏⠀⠈⡄
⢰⡏⠀⠀⣰⠄⠀⠀⢈⡄⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⣶⡀⢀⡀⠠⠶⠈⠀⠀⡄⠀⣰
⢸⡄⠀⠘⠃⠀⠘⠦⣈⡧⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⣶⣴⣶⡶⠊⣿⡋⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢠⣧⣼⠃
⠈⢧⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⢀⠂⢿⡁⠀⠀⠀⠀⠀⠀⠐⠀⢀⡄⠀⠠⠐⠉⠀⣿
⠀⠀⢹⠟⠻⠦⢄⣀⣀⡀⢀⡀⠠⠔⠉⠑⠠⠄⢀⡀⠀⠠⡞⠀⢺⢸⡇⠀⡀⠀⠀⢈⡇⠀⠀⠀⣀⠀⠀⣼⠛⠋⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠉⠙⠛⠐⠂⠶⠶⠶⠬⠛⠳⢆⡃⢠⣯⠞⠃⠛⠛⠛⠛⠈⠹⠀⠀⢠⡏⢰⠇⣼⠀⠀⠀⠠⠆⠀⢠⡟⠁
⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢫⣠⠾⠿⠃⠀⠀⠀⠠⠞⠀⢼
⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⣀⣀⠀⠀⠀⠀⠀⣤⣤⡦⢿⣶⠶⠒⠀⠀⠀⠀⠀⢀⡾⠓⠲⠶⢤⣀
⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠶⠒⠀⠈⠉⠉⠉⠉⠉⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠘⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡰⢿
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠀⠀⠴⠶⠶⠄⠀⠀⠛⠛⠛⠛⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⣘⠂⠀⠀⠀⠀⢀⡀⠀⠰⠦⠀⠐⠂⡄⠀⠀⠀⠀⠀⡀⠄⠀⠀⠉⠙⠋⡀⠒⠞⢿⣤⠀⠀⡀⠀⠀⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠐⠒⠋⠐⣦⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤⠖⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠈⠳⣄⣠⡴⠟⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⣠⡖
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠉⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠋⠁⠀⠈⠓⠠⠤⠀⠀⠀⣄⠀⢀⡀⠤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠓⠒⠒⠚⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⠀⠀⢀⠀⠀⠀⠈⠉⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠟⠀⠀⠀⡐⠄⠀⠀⢰⠁⠀⣼⠁⠚⠃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢀⢃⡤⠀⠀⠘⣇⢰⡇⣰⢛⠆⢹⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡠⠂⣾⡠⢄⢀⠄⢹⠈⠃⠻⠄⢢⠟⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠓⠶⠤⠤⠒⠈⠀⠀⠈⠁⠀⠸⣀⠼⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠈⢁⠀⠘⠃⠠⡀⠀⠀⢰⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠈⠀⠀⣀⠀⠉⢆⠀⠈⠀⠃⠀⠀⠀⣬
⠀⠀⠀⠀⢀⡄⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢿⣠⣀⢄⣐⢀⠘⣤⠃⠃
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⣤⠀⠀⢠⠄⠀⠀⠀⠀⠀⡿⠼⠀⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⡄⢠⡦⢀⠀⢀⣰⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⠇⠀⢀⠀⠀⢀⡿⣧⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣠⣼⠛⢂⡄⠺⠇⠈⠹⡿⢶⠶⣄⠀⠀⠠⠈⠻⡅⢠⠀⢀⠀⣠⡞⠁⠀⡄
⠀⠀⠀⠀⠂⠃⠀⠀⠹⣶⣀⠀⠋⠀⠞⠳⡀⠈⠆⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⣵⣄⣀⣼⣴⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠼⣿⣧⢠⣤⣦⡀⠑⡀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠟⣹⠿⠛⠃⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠚⠛⠛⠫⠽⠿⠾⣷⣴⣷⣋⣀⠄⢀⢀⡄⠠⠒⠋⠀⠀⠐⠀⠂⠀⠘⠫
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠋⠀⠀⢀⡈⠀⠀⢀⡄⠀⠀⢀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠒⠢⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠠⠎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢠⡠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣀⡀⠀⠈⢁⡀⠀⠴⠈⠀⠀⠀⠚⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⣀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠈⠙⠳⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠋⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇
⠀⠀⠀⠀⣠⠖⠛⠉⠛⠒⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠓⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠙⠲⣄
⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⡤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠑⣭⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⡤
⠀⣁⣺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼⠀⡸
⠘⡑⢄⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⢀⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⢩⡼⢋⠽
⠀⠈⠢⢁⡈⠓⡄⢀⣀⠀⣀⡀⠀⢀⡀⣀⣤⡾⡡⢷⣄⣈⡎⡆⠀⢸⡹⣄⡏⢶⡦⢔⣳⡼⠏⠛⣘⡳⠤⠤⠊⡅⢀⡔⣶⡚⠱⠃⠶⠁⣳
⠀⠀⠀⠀⢸⣰⠘⠉⠾⣤⡄⠌⠲⠋⠘⣛⠚⠋⠛⠦⠤⠀⣠⡉⣓⠾⡰⠌⠰⢋⡾⠙⢓⡒⡆⠤⡀⠩⠉⡁⠀⠘⢡⠤⠈⢃⠄⡔⠊⠑⠃
⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠔⠂⠤⠠⠄⠠⢄⠠⣄⠢⣄⢲⡠⠒⠊⠓⠓⠂⠒⠐⠉⠚⠀⠀⠀⠈⠉⠉⠉⠐⠒⠒⠂⠀⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⠀⠧⠘⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠈⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠘⠤⠠⠔⠊⠀⡄⠀⠀⠀⢀⠜⢃⠀⠀⠀⠀⠸⠣⢄⠀⠀⢀⡘⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠔⠊⠀⠈⠢⢄⣀⠤⠂⠀⠀⠉⠁⠁⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠢⢄⠀⠈⠑⠂⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⠈⢁⡠⠔⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠄⠀⠩⡐⠂⠄⠀⡀⢀⡀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠤⠐⢈⠅⠂⠢⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡅⠀⠀⠀⢸⠀⠀⡠⠄⠤⣀⠀⠉⠉⠉⢉⡉⠉⠉⠁⠀⣀⠤⠠⢄⠀⠀⡇⠀⠀⠀⢨⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠤⣘⠢⠀⠔⠁⠀⠨⠀⠀⠀⠈⠀⠀⠀⠊⠀⠀⠑⠀⠀⠀⠁⠀⠀⠈⡅⠀⠈⠢⠀⠔⣃⠔⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⢄⠀⠑⠂⠄⣀⠀⠈⠢⢀⡀⠜⠀⠀⠐⣄⠀⠀⣠⠂⠀⠀⠣⢀⡀⠔⠁⠀⢀⡠⠔⠊⢀⡠⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠐⠢⠄⣀⠈⠁⠒⠐⠂⠀⠠⠤⠤⠀⠁⠈⠀⠠⠤⠤⠄⠀⠂⠐⠀⠉⢀⡠⠔⠒⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠠⠤⢀⡀⠀⠀⠀⠀⣀⠠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡤⠐⠂⠤⡀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠈⢂⣀⠔⠉⠀⠀⠀⠀⠀⠈⠓⠄⠀⢀⣀⣀⣀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠈⢦⣁⢀⡀⠀⠀⠀⠀⢠⠊⠁⠀⠈⠢⡀⠀⠀⠀⠀⣀⠤⠬⡖⠉⠀⠀⠀⠈⢢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⢀⠊⠀⠀⠈⠑⢄⠀⠀⡆⠀⠀⠀⠀⠀⢡⠀⠀⡠⠊⠀⠀⠀⠈⡆⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⠀⠸⠀⠀⠀⠀⠀⠀⢣⣀⡇⠀⠀⠀⠀⠀⣸⢀⣠⠁⠀⠀⠀⠀⢀⠃⢀⠠⠤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡑⢄⡡⠄⠠⣀⠀⠰⠁⠀⠈⠑⢄⠀⠠⠊⠀⠀⠈⠂⠀⡠⠀⠀⠦⡔⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡁⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢈⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⢺
⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡎⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⡤⢺⠟⠉⠀⠉⠙⢗⠀⠒
⠹⡄⠈⠙⡲⢤⡀⠀⠀⠀⠀⠀⢸⢃⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠚⠁⠀⠀⠛⠓⢯⡄⠀⠀⠀⠀⠀⠀⠐⣆
⠀⠹⣄⠀⠀⠑⢝⢆⠀⠀⠀⠀⢸⡯⡄⠀⠀⣿⠀⠀⠠⡄⢠⠊⠉⠱⠀⠀⠈⠀⠒⠛⠛⠛⠛⣛⣟⠺⡁⠀⠀⠀⠀⡀⡴⠒⠉⠃
⠀⠀⠙⣦⠀⠀⠈⢯⢆⠀⠀⠀⠀⣧⢷⢀⠀⡟⠀⠈⠁⣀⣸⡄⠀⠰⢤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠈⣀⡤⠀⠀⠘⠁
⠀⠀⠀⠈⢳⡀⠀⠸⡟⡄⠀⠀⠀⢸⡜⠐⣴⠇⠀⠀⢾⡀⠀⣕⢬⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠙⢦⡰⡝⠽⣤⠶⠚⠛⠃⠀⠟⠲⣄⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠖⠂⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⣷⢀⡀⠀⠀⠀⠀⡩⠥⡀⠀⠙⠦⡄⠀⠀⠀⠀⠀⠀⠰⠯⠡⢬⣤⣤⠤⠄⠈⣠⡷⠤⠤⢄⠀⡠⠴⢤
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⡤⠤⡀⠀⠐⢱⣦⣷⣠⠀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢼⠃⠀⠀⠀⠀⠉⠀⠀⠘⠲⠤⢤
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢶⣷⣌⡴⠖⢛⡏⠀⢤⠄⠀⡷⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠿⠤⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢷⠆⠀⠚⣡⠈⠑⠲⡎⣠⠔⠁⢀⣴⠃⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⣀⣄⡀⠠⠆
⠀⠀⣀⡀⠂⡤⠀⠈⠙⢦⡀⠈⠉⠘⠛⢴⡾⢰⠖⢋⣉⡉⠛⠲⢶⣅⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⡅⠀⡹⣤⠨⢄
⠰⡅⠈⣷⠤⢤⡀⠀⠀⠀⠉⣩⠟⣫⠙⠶⠖⠋⠀⠈⢧⢉⡷⢾⡛⣌⣳⢤⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⣈⡴⣥⢀⠼
⢀⠟⠀⠀⢀⡠⠃⠀⠀⣠⠞⢁⡞⠹⡆⠀⠀⢦⠀⠀⣨⠟⠛⠉⠛⠋⠀⠀⠀⠀⠙⢮⠉⠉⠙⠳⢄⠀⠀⠀⠀⠀⠀⠈⡟⠐⠁
⠈⠉⠓⠢⠎⠀⠀⢀⣰⠇⠀⣾⠀⠀⢻⡀⠀⠀⢀⡞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠈⢳⠀⠀⣀⣀⣀⡀⢣
⠀⠀⠀⠀⠀⠀⡞⡩⡤⣠⠤⠭⠷⢤⣀⢳⡄⣠⠏⠠⡀⠈⠀⠀⠁⠀⠀⠁⠀⠐⠀⡀⠈⢧⠀⠀⢀⡨⠖⠋⠉⠀⠈⠉⠛⡄
⠀⠀⠀⠀⠀⠰⣭⣥⣃⠇⠀⠀⠀⠀⠉⠳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣆⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢴⠊⢺⡟⠙⠢⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⣻⠁⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⡬⢦⡴⠓⣤⣼⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡨⠷⡎⠉⢻⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣄⣈⠄⢀⡏⠀⢱⠀⠀⠀⠀⠀⠘⣧⠀⠄⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠄⢀⠸⣄⣀⡷⠀⠲⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⢯⣀⣠⣿⣏⠁⠀⠀⠀⢀⡀⠀⢹⣇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⡳⡄⠈⢎⣿⠦⢔⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⢀⠀⠀⢷⢦⡘⢿⡀⠀⢀⠔⣨⡀⢰⡆⠹⣷⣄⡜⢻⣾⢡⣄⡴⠀⢀⣆⣴⢧⠘⣶⣚⠝⣩⣏⡀⡀⢀⠀⢀⣠⣄⣤⠞⠁
⠀⠮⣛⢦⡾⡓⢝⢆⣷⡴⡣⠞⠄⡙⠇⠙⠀⠈⠀⠀⠀⠙⠀⠁⠻⠁⠀⠁⠉⠈⠓⠿⠟⠊⠀⠉⠓⠱⠊⠞⠡⠞⠻⡵⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠳⢭⣝⣛⡂⢿⣯⣿⠇⠙⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣀⣨⠲⣬⣐⠀⠩⢁⣴⣦⠀⠀⠀⠀⠡⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⡿⠏⠀⠀⠉⠽⢋⠸⠿⠟⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡘⠃⢀⡙⡃⠀⠀⡄⠀⡀⠻⠓⢐⡛⠀⠀⠀⠀⠀⠀⠈⠱⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⡏⣀⠈⠛⢷⠿⠳⠀⠡⠈⠀⢺⣿⣧⡄⡀⠀⢀⣄⢠⢀⠈⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⣀⠈⠉⠁⠀⠀⠀⠀⠈⠡⠈⠁⠈⠙⠃⠀⠉⠛⠁⠈⠀⠩⠄⣦⠲⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣄⠊⠡⠀⠔⣦⡀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⢠⠄⡼⠀⠀⠠⣦⠄⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⡼⡶⠀⢠⣿⢠⣏⢠⡔⡆⣰⢖⣸⣶⠋⠾⠓⣛⡿⠋⢁⡀⠀⠀⠋⠀⠌⠈⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⢻⠁⠘⠋⢩⡏⠀⢰⠇⠀⠀⡞⢹⠃⠀⠉⢹⣷⠀⢈⠁⡈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⢀⡤⠔⠤⡀⠈⠁⠀⠉⠀⠀⢠⡁⠁⠀⢀⣴⡿⠃⠀⠠⠀⠄⠀⠀⣴⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡀⢾⠇⠀⣿⠀⠀⣤⠬⠤⢤⣄⣀⣀⣠⣿⡷⠶⠟⠋⠁⠀⠀⣤⠀⠀⢀⣤⡐⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠸⠿⠛⣀⠀⣀⣿⣦⡌⠃⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⣤⡄⠀⢀⣼⠟⢄⠀⠈⠉⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣷⡆⠒⠋⢡⡾⠋⠀⠀⠀⠀⠀⠀⢠⣲⠀⢠⣿⠃⠀⣸⡟⢁⣴⠞⠁⡠⠋⠀⣠⡆⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣥⣍⠛⢰⡿⠀⠀⠀⣴⠋⢉⡴⣦⡼⢧⣴⠏⢿⣤⡾⠋⠉⠉⠀⠀⠸⢧⣤⠾⠋⠀⣰⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠸⣷⠀⠀⠀⠙⠛⠉⡀⢀⣴⠟⢻⡄⠀⠀⠀⠠⠀⠄⠀⠀⣤⠀⠀⠐⣀⣠⡙⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠃⠀⠈⠳⠶⠤⠴⠖⠋⢡⣾⠁⢀⣾⠇⠀⠀⠀⠀⠈⠄⣡⣄⡈⠀⣟⣿⣭⠵⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣄⡀⢀⠣⠃⠋⠧⠤⠛⠀⡀⢛⠚⢋⣅⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⣂⣀⣐⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡈⠡⠶⢁⡀⢠⡀⠀⢰⣷⣆⠘⡋⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠙⠮⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⢲⠀⠈⢠⡄⠉⣄⠀⠀⠀⢠⣷⡾⠁⠀⠀⠀⠀⠁⠀⠀⢰⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣤⠀⠀⠴⠄⢠⣇⠀⠈⠄⠁⠸⠿⢀⣠⣄⠂⠐⠀⣄⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢠⡄⠰⠊⠘⠿⠠⠪⠶⠋⠀⠀⣻⣿⣷⠦⠀⠀⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠄⠀⢾⡷⢀⣬⡝⠋

⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠄⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣲⣤
⠀⠀⠀⠰⠀⠂⠀⠀⠠⠀⡔⢤⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⢇⠀⠉⢀⡄
⠀⠀⠀⠀⢃⠀⠰⠁⠢⠔⠀⠀⠣⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⠀⠀⠈⠉⢉⠃⠈⠢
⠀⠀⠀⠀⠀⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⡤⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢔⠞⡟⠁⡧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠂⡜⠀⠀⢣⡈⠑⠲⣑⣄⡠⡀⢀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⣠⠃⠀⡇⠀⡁⠀⠀⠀⠑⡄⠀⠈⣦⡱⠁⡯⠷⡔⠚⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠂⢫⠀⠸⢆⠀⢇⠀⠱⡀⠀⠀⢀⣇⣀⡠⣗⣌⠉⠵⢄⠘⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠦⠁⡶⠗⡢⡀⡨⠬⡁⡲⢯⢁⠴⢅⡠⢄⢀⢥⡠⠵⢤⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⠖⢱⠢⠤⠩⡇⠀⢨⠀⠀⡅⠀⠠⠀⢠⢁⠜⡚⠈⠉⠉⠉⠁⠒⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⡄⠸⡀⠰⠀⠈⡄⠀⡇⠀⡈⢀⠜⠁⠀⠀⢀⠄⡔⠓⠄⡀⠁⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠀⠀⣀⣰⣀⠗⠤⣇⠀⠇⠀⠁⠀⠃⡎⠀⠀⡀⢫⠛⠉⠀⠈⢑⠇⠂⢀⠀⢰
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠛⠁⠈⠇⠀⠁⠀⠀⢸⠀⠐⠀⠀⠘⠀⢧⢤⡠⢄⠀⠉⠒⡀⠈⠁⠀⣀⠇⠉⠎
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠱⣀⠈⠢⠒⠐⠄⠔⠑⠊⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠤⠤⠄⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠤⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡉⠉⠀⢀⣀⣀⣤⡤⠽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠋⠡⣤⢶⣛⢉⣡⣴⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠉⠉⡟⠋⠑⠨⠴⡀
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⢣⣀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠙⠒⠲⠤⣤⣀
⠀⠀⠀⡠⠖⠋⠁⠠⢔⣮⡅⠻⢼⣽⣿⣿⡶⠦⣤⣠⣇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣇⣭⣵⠦⣄⠀⠈⠙⠲⢄
⠀⠀⠈⠀⠀⢠⣴⣿⣛⣻⣥⡴⠶⠛⠛⢛⣻⣿⣷⡿⣯⣿⣓⣲⡦⢤⣼⣀⣀⠀⠀⡷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠦⣀⠈⠉⠉⠙⠳⠀⠀⢠⣶⣿⣯⠭⠶⠶⢒⣻⠿⣋⣉⣽⠿⠛⠷⠿⠿⠽⠇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⠀⠉⠁⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠒⠲⠶⠶⠶⠤⠤⠶⠶⠶⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣾⡄⣶⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⢀⣶⣶⠘⠿⠋⣀⠉⢀⠈⠛⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠥⠤⠖⠀⠠
⠀⠀⠈⠀⠐⢌⠻⢿⡿⠂⢸⣿⣿⠿⠃⠀⠀⠀⠀⠁⠀⠀⢁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⢈⠐⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡁⡂⠐⡀⢐⠀⣂⢡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠅⠤⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⢌⢂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⡶⠄
⠀⠀⠀⠀⠀⢂⢐⠐⠂⠐⠀⡃⣈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠙⠋⠈⣡⣴
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⡀⠁⠠⠤⠄⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⠠⠆⠀⠤⡀⠣⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡅⢠⣳⡶⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠤⡅⠛⣀⠈⢀⠁⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠢⠀⠀⠀⠀⠆⠀⠀⠲⠒⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣴⣶⠦⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⣄⣸⣶⡟⣹⡏⢿⡇⠀⠠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠂⠀⢸⡶⢋⣿⠛⣿⡍⢛⠂⠛⠃⠊⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷
⠀⠀⠀⠄⣀⣼⣿⣷⠞⠛⠲⢿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡞⠉⠋⠀⠀⢀⡴⠦⡶⠆
⠀⡀⣰⠋⠀⣠⡄⠐⢲⣷⣦⠀⠀⢳⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢸⣟⢰⠇⠈⠓⡀
⢀⣷⠃⠀⣄⣿⣝⣷⣶⡁⣿⣽⠀⠀⢻⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠋⢹⣿⣤⣛⣾⡃
⢸⡇⠀⠀⠹⣿⣛⠏⠈⠀⣄⠃⡰⡶⠋⠉⢱⠇⠀⠀⠀⠀⠀⠀⢠⠙⢦⣀⠀⠀⠀⣀⣈⣿⡷⣽⠛⡇
⠀⢷⠆⠙⣦⠈⠙⠛⠄⠠⡤⣶⠏⢸⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⣦⠀⠀⠀⠈⠿⠆
⠀⠈⠀⠛⠁⣀⣀⠐⢄⣨⠇⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣿⡀⠀⠀⠀⠀⢀⠀⠀⣀⣴⡄
⠀⠀⠀⠠⡈⠛⠠⡄⠉⠀⢠⠀⠀⠈⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⣿⠉⠀⠀⢀⠀⣴⡃⠀⢿⡽⡀⠹⠂
⠀⠀⠀⠀⣹⣦⡴⣿⣄⠀⢁⠀⠀⢠⣾⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⠛⠁⠀⠴⣦⠛⢧⡀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠁⠐⠋⡉⠁⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢋⣠⠀⠀⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⣠⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣿⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢤⡶⠦⣤⣄⣛⣁⣩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣧⣙⣿⠀⠀⠀⠰⠋⠀⠀⡀
⠀⠀⠀⠀⣹⡾⡇⠀⠋⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⣼⣿⣿⣿⡇⠀⠀⠀⠿⠶⣢⣿⣄⠀⡀
⠀⠀⠀⠀⢨⠟⡠⣷⢖⣼⡷⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣿⣿⡝⠋⠹⣆⢀⣤⣤⡼⠋⠀⠀⠉⠁
⠀⠀⠀⣰⠃⣾⢃⠻⣿⣿⡟⢷⣤⠀⠀⢀⢀⢄⠀⠀⠀⠀⠀⠀⠈⢫⠟⠓⠢⠀⠘⠛⠻⠟
⡀⢀⠠⠋⢝⡻⠈⢇⡈⢻⣷⣤⣿⠀⠀⠀⢿⡙⡇⠀⠀⣠⣤⠀⡟⣿⣠⡀⠀⠀⠀⠘⠁⠄
⠈⠉⠀⠀⠈⠀⢀⡺⠃⢀⢻⣿⣌⢧⠀⠀⢀⢻⡇⠀⠀⢛⠖⣠⡇⢿⡟⠛⣀
⠀⠀⠀⠀⠀⠀⣮⠀⢠⣶⣿⣿⣿⢀⠀⢀⡼⢫⠃⠀⠀⠘⣄⣇⠁⣼⣡⢸⠏⠀⠀⠀⠰⣶⡀
⠀⠀⠀⠀⠀⠀⠻⣷⠷⢿⣿⣿⣿⢆⣀⣤⡿⠋⠀⠀⠀⠀⠈⢺⡤⢿⠗⢉⣦⣤⣄⣠⣶⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣥⣶⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣣⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⡓⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡖⠒⢲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠉⢻
⠀⠀⠀⠀⠀⠀⡠⠟⢤⡀⢹⠀⡜⠀⡸⠙⢆⠀⠀⠀⠀⢠⣄⠤⠖⠢⡀⠀⠀⠀⠀⠀⠀⣧⠈⠓⢾
⠀⠀⠀⠀⠀⢠⠃⢀⣀⠱⣜⣴⣁⠔⠁⣠⠎⢧⠀⠀⠀⠈⢦⢀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡟⠓⢦⣸
⠀⠀⠀⠀⠀⠸⡎⠁⢀⡽⠋⣿⠯⣐⣉⡠⠤⢺⠀⠀⠀⠀⠀⣳⣾⣎⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠙
⠀⠀⠀⠀⠀⠀⠳⣀⠎⠀⠀⡇⢆⠀⠀⠀⣠⠃⠀⠀⠀⢠⡋⠙⠀⢨⢷⠀⠀⠀⠀⠀⠀⢠⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣧⣀⣱⠶⠚⠁⠀⠀⠀⠀⡟⠋⠠⡦⠀⣀⡇⠀⠀⠀⠀⠀⢸⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⡷⠆⢀⣄⠀⠉⡇⠀⠀⠀⠀⠀⢸⣤⡀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⣀⠐⠶⡇⠀⠀⠀⠀⠀⠸⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⢀⣀⡀⠀⠀⠀⠀⢻⣁⠀⡉⢀⣼⠁⠀⠀⠀⠀⠀⠸⠶⣄⡀⠱
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢾⣶⣖⣉⣠⡼⠀⠀⠀⠀⠈⠫⢤⣫⡴⠃⠀⠀⠀⠀⠀⠀⠀⣆⡀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⣹⠛⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠷⡄⠀⠀⠀⠀⠀⠀⠀⡇⠙⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⡄⠀⠙⠂⠀⠀⠀⠀⠀⢀⡇⣀⠤⠼⠀⠀⠀⠀⠀⠀⠀⢸⠦⣄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣤⠤⠼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⡏⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⠃⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣸⣿⠀⢹⠀⢀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠻⠀⠈⠀⡾⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠴⠛⠉⠀⣠⡤⠶⠚⠛⣻⡆⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣀⠤⠴⠚⠉⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣤⣤⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠘⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⡿
⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⢀⣴⠟⠋⠀⢀⣤⠴⠖⠒⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣤⣤⣤⣤⣴⠟
⢠⡟⠁⠀⠀⠜⠉⠀⠀⠀⠀⠶⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⠟⠁
⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠰⣶⣤⣤⣤⣤⣴⡶⠾⠛⠉
⠀⠈⠻⢷⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣸⠁⢀⡆⠀⠀⢿⡇
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⣦⡀⠀⠀⠋⠀⣼⠁⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⡏⠀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠘⣇⣰⠏⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠈⠁⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⣾⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⠖⣶⠃⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣦⣄⣥⣾⣽⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠈⠉⠉⠱⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⢀
⠀⠀⢠⣄⣨⣗⣦⣾⠂⣾⣶⠶⡾⢷⠀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠄
⠀⠀⠈⢙⣿⣿⣯⣥⠀⠋⠰⡶⠀⠛⠿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢠
⠀⣻⣲⡶⠟⠁⢀⠀⠀⡎⠁⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡻
⠈⠉⠉⠀⡄⠀⠀⠀⣼⡀⢦⡀⠘⢇⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠀⠐⡆⢉⡇⢮⣵⡀⡾⠴⠀⠀⠀⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⣴
⠀⠀⠀⠀⠀⠀⣶⣴⡟⠉⠃⢈⡟⠀⠀⠈⠁⠠⢿⣦⠀⢃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⠐⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣤⠴⠋⠀⠈⣹⣶⣟⠁⢠⣄⠀⠀⣠⣤⣿⡆⠀⢇⠀⠀⠀⠄⠀⣞⠀⠀⠀⠀⠀⠀⠀⢲⡇⠀⠘⠣⠶⣗⣀⢸⠿⠂⠀⠀⠘⠒
⠀⠀⠀⠀⠀⢤⠼⠷⣶⠉⣿⢻⣷⣿⡻⢷⠟⠁⠀⢻⣿⠀⢀⣁⠀⠂⢀⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠷⠀⠀⠈⣵⡒⠒
⠀⠀⠀⠀⠀⣤⠄⠈⠙⣤⣨⣼⣿⣇⠀⠀⠀⠀⠈⠩⢹⣷⢾⣇⢀⣠⠟⠛⠒⠂⠀⠀⣀⠀⠈⠑⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣭⡥⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠛⣿⡝⢫⡔⠀⠀⢠⡀⠀⠛⠀⠂⣿⡿⠁⢶⢃⣀⠀⠈⠉⢻⢠⡇⣰⠖⠛⠉⠁⣡⠄⢺⡇⠀⠀⠀⠀⠻⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⣿⣿⣷⣆⠀⠀⠀⠀⠁⠀⠀⠀⢸⠿⣶⢦⡞⠻⠿⣿⠷⣤⣴⣾⣿⠣⠀⠀⠁⣾⣿⠀⢿⡆⠁⢀⣴⠂⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣉⠛⡄⠀⠠⠦⠼⠀⠀⠀⠉⣰⣧⣀⠥⠤⢄⣠⡼⠉⠛⣿⡌⠷⠁⣠⡚⠁⢀⡀⠀⣀⣀⠀⠋⠐⠶⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⡀⠀⠀⢠⡇⠀⠀⠀⠀⣿⡏⡄⠐⠐⣎⠹⣿⣷⣄⡀⢐⣘⣁⠉⠈⠛⠃⠀⢸⢇⡈⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄⣠⣤⣦⢻⣶⣶⣄⠐⠙⠳⠄⠢⡄⠙⢢⣿⣾⠁⡀⠀⠘⢏⢢⣶⣦⣠⡀⠘⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠋⠻⣿⢎⣿⣿⡏⠃⣀⠴⣷⡦⢀⢶⠟⣙⠁⠛⠁⠀⢠⢤⣾⣟⣂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠘⠛⣠⠀⠀⠈⠻⡀⠈⠃⢠⠆⠀⠀⡨⢟⣿⠛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠉⠉⠒⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠊⠳⠄⠀⠀⠀⠀⠲⠉⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢀⠙⠀⡫⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣉⡡⠀⠈⠒⠀⠁⠐⠠⠂⠀⠀⢀⠈⠈⠈⠊⠁⠠⡉⣩⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠒⠒⠚⠈⠉⣀⡀⠀⣀⣀⠀⠈⠉⠀⠇⠒⠐⠁
⠀⠀⠀⠀⠀⢠⠀⠠⠄⠄⠄⠆⠠⠠⠀⢤⠀⠀⠰⠀⠀⠀⠀⠀⢠⠂⢀⠀⠀⠀⠀⠠⠒⠈⠈⠁⠐⠄⠄
⠀⠀⠀⠀⠀⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠌⠐⠀⠀⠒⠀⠀⠈⠁⠀⠀⠈⠈⡁⡀⠀⢀⢈⠈⠁⠀⠈⠈
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢧⡁⢀⠽⠠⠀⠀⢔⠒⠒⠒⡊⢠⢧⢰⢿⡈⡒⠒⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠀⠈⠶⡬⡉⡣⢲⡤⢏⡞⠀⢇⠳⢼⡲⡜⡁⡤⠎⠀⠀⠠⠄⠀⠤
⠀⠀⠀⠄⠠⠃⠂⠀⠀⢄⡀⢀⠠⠀⠀⠀⠣⠐⣀⠀⠀⠑⠒⠈⣡⢔⣀⡀⢀⢠⢭⠴⠀⠀⠀⠀⠰⠮⡭⢀⡀⡀⣐⢠⡈⠐⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢍⠉⠁⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠠⣄⣀⣠⠄⣴⠀⠀⢀⣀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢉⢼⠩⡧⡘⡡⠀⢀⣸⡈⢦⠀⠀⢸⣻⡇⠀⠀⢸⢟⡇⠀⠀⡰⠃⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢸⠀⡇⡛⠁⠀⢸⡀⠳⡀⠱⡀⠀⣿⣟⣠⣆⣻⣿⠄⠀⠜⠀⡜⢁⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⡵⠀⠀⠀⢣⠙⢆⠙⠢⡀⢠⡙⠙⠃⠘⠛⢙⡠⢈⡄⠊⡠⠊⡼
⠀⠀⠀⠀⠠⣶⣀⠈⢂⠀⠀⠌⠁⣠⡶⠄⠀⠀⠀⠀⠀⠀⢀⠸⢲⠥⢴⡛⠀⠄⣗⠦⠤⣽⣏⠛⡈⠳⡄⢠⡖⢁⠗⣩⣮⠤⠤⢺⠁
⠀⠀⠀⠰⠲⣌⢉⢷⡶⠂⠲⣶⡾⠉⣰⠾⠀⠀⠀⠀⠀⠀⣤⡴⣹⠇⠸⢧⠣⠶⠈⢟⠒⣚⠣⣄⠘⡀⡽⢻⡀⡪⢀⠬⣓⠒⣺⠁
⠀⠀⢀⣀⡀⡘⠻⡖⠁⠀⠀⠘⠾⠋⢁⢀⣠⠀⠀⠀⠀⠠⡤⠖⢹⠂⠀⣧⠙⠲⠂⠀⠉⠣⢖⣁⡍⢲⡁⢈⡗⢸⣈⣒⠄⠋
⠀⠀⢸⠀⠈⠙⠒⡗⠀⠀⠀⠀⢓⠚⠋⠀⠈⡀⠀⠀⠤⠀⣀⡠⠋⠀⠀⠈⠓⣠⠤⣹⡄⠀⠀⠀⠈⠉⡀⠀⠈⠉
⠀⠀⠳⢆⢤⢇⡐⡏⠀⠀⠀⠀⢟⣂⡤⠤⠰⠃⠀⠀⠙⠉⠈⠀⠀⠀⣠⠞⢉⠍⡓⢀⢦⠀⠶⡆⢒⡩⡉⠳⣄
⠀⠀⠠⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡰⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡜⠁⠐⢅⠒⠤⢏⢨⠀⡑⠁⠥⠒⡈⠃⠈⡑⡄
⠀⠀⠈⢱⡊⣯⠀⠀⠀⠀⠀⠀⠀⢠⣿⢱⠈⠀⠀⠀⠀⠀⠀⠀⠰⡠⢃⠸⡼⠐⠢⣀⠍⠀⠈⣇⡔⠂⢣⠜⢘⢄⡠
⠀⠀⠀⢻⡟⢋⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⡃⠀⠀⠀⣀⠤⠂⣡⠔⡀⠀⡀⠀⡌⢠⠀⠀⠀⠀⠀⢇⢰⡀⢀⠀⢀⠲⣄⠐⠤⣀⡀
⠀⠀⠀⠈⠓⠬⢧⠀⠀⠀⠀⠀⠀⡾⠴⠋⠁⠀⠺⠩⢤⡶⢛⣡⠞⣡⢾⣁⠜⠑⠋⠀⠀⠀⠀⠀⠈⠊⠑⣄⡷⢄⠳⣬⣙⠶⡤⠌⠵

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠔⠂⠀⠀⠀⠀⠺⣇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢸⠠⡀⠀⠀⠀⠠⣺⠆⠿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠸⠀⠉⠛⠷⠿⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠐⠻⣦⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢶⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣐⠲⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⣰⠋⠃⠒⠂⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠁⢰⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠛⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣐⣤⢀⣽⠃⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠃

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠤⢀⠀⠀⠀⠀⠀⣀⣴⣎⣩⣶⣦⡀⠀⠀⠀⠀⠀⣀⢆⠁⠀⡌⢆⠀⠀⠀⠀⠀⡠⣶⣬⣿⣷⣴⣿⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠂⠁⠀⠀⠉⠛⣿⣿⡄⠀⠀⠀⢰⠌⡁⣈⢁⠡⠄⠇⠀⠀⠀⢠⣴⣿⣿⡁⠀⢀⣹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣟⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠉⠉⠙⠓⠍⣁⠀⠠⠁⠀⠀⠀⠀⠐⠤⣄⡀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠭⠹⠿⠋⠍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠈⠢⠊⡀⠤⠈⡄⠀⠀⠀⠠⠆⠀⠉⠿⠛⠁⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⠷⣽⣿⣛⣛⣛⣫⠭⠇⠀⠀⠀⠀⠀⢄⠀⠠⢄⢁⠄⠀⠁⠀⠀⠀⢸⠓⠲⠶⠤⣤⣀⣀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠠⢀⡈⠃⠀⢃⡦⠂⠀⠀⠀⠀⠘⠉⠙⠛⠒⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠤⠐⠀⠈⠀⠀⠈⠐⠄⠀⠀⠀⠀⡼⢿⡟⠁⢹⡟⠻⣷⠀⠀⠀⠀⠀⣰⣾⣿⣛⣻⣷⣶⡀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠞⠙⢢⠈⣷
⠀⠀⠀⠀⠘⠠⠶⠀⠀⡤⠀⠀⠰⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢀⠈⠙⠛⠛⠛⠛⠉⢃⠀⠀⠀⠀⠀⠀⠘⣄⠸⣦⣐⣁⣼⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡤⡠⢤⠀⠁⠀⠀⡠⠂⡍⠀⠀⠀⠀⠀⠀⠀⠘⡅⠠⠀⠀⠀⠀⠀⠈⡷⠆⠉⠉
⠀⠀⠀⠀⠀⠢⡀⠈⠀⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠞⠀⠀⠀⠣⡀⠐⠢⠤⢤⣀⣤⠤⠴⠎⠁⡠⠀⠀⠀⠀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠆⠙⣿⣿⣿⣿⡿⠃⡓⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⠀⠀⠀⣀⠐⠁⠑⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣋⠌⠀⠀⠀⠀⠀⢠⣾⣻⢻⣟⣞⣻⣿⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣿⣿⣷⣯⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⣰⢶⠇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⢣⡾⢅⡠⠷⡶⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠸⠷⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛

⠀⣀⢀⡀
⠀⡁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠈⠀⡀⠀⠀⠀⣀⡤⠄⢀⣰⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠀⠀⢪⠤⢴⠍⠀⢀⣼⡁⠀⠀⣼⠃⢐⣳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⢠⠂⠂⠀⡋⠀⣈⢻⡿⠖⠛⠛⢳⣦⣾⣿⡇⢳⠀⣠⠆⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠘⢀⣧⢀⡄⠀⠀⠀⠉⠀⠇⠀⠃⠶⣬⣿⢟⣿⡟⠀⠲⠁⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣯⠈⠄⠀⣿⡆⠎⠀⣰⠀⣾⣦⣾⣿⣿⡿⢆⠀⠀⠀⡠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣥⢼⡄⠈⣻⠄⠀⠀⠀⠀⣿⣿⣿⢾⣿⢨⡿⣢⠄⠘⠑⣠⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠘⠳⠤⠇⠀⠈⢱⠀⡔⠀⠑⠁⣸⣿⣿⣾⡟⠀⠀⠀⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⠀⠎⠀⠀⠀⡄⠸⣧⠀⠘⢋⠿⣼⣿⠇⠀⠂⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠀⠀⠀⣄⣧⠀⠉⢄⣤⣯⣤⠸⠃⠀⠐⢡⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠄⢄⠆⠀⠀⠘⠙⢧⠀⠈⠠⣸⡿⠁⣀⠀⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢅⠀⠰⠦⠄⢴⣤⣢⣄⣠⢿⠅⣀⠄⠈⠄⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢀⠀⠀⠀⡩⠋⣉⣸⠅⠈⡀⢄⡾⠃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⣠⡈⣆⠀⠀⡤⠾⠋⠀⠀⢤⡤⠎⡀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⡀⠈⠈⠉⠁⠀⣀⣀⡴⠟⠋⣠⡔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢑⢖⠒⣛⢚⣿⠏⠃⣠⡴⣠⠍⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠚⣇⠀⠄⢈⠤⠟⠉⠁⠀⠀⠀⠀⠁⠔⠐⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠴⠊⠁⠀⠀⠀⠀⢀⠴⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⢇⣁⣶⠒⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢑⠁⠀⢄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠣⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠂⠀⣀⡀⠀⠐⠀⢀⣀⠀⠀⠘⣷⣤⡴⡿⠀⠀⢀⠀⠄⡀⠘⠂⠀⣀⡀⠀⠐⠀⠁⣀⠀⠀⠘⣷⣤⡴⡿⠀⠀⢀⠀⠄⡀
⠀⢸⠉⠀⠘⠀⠀⡴⠪⣥⠆⠀⠀⠉⡁⠀⠀⢰⠦⣴⡟⢡⠂⠀⢸⠋⠀⠘⠀⠀⡴⠪⣅⠆⠄⠀⠈⡁⠀⠀⢰⠦⣴⡞⢡
⠀⠀⠀⣀⠀⠀⡏⠁⠃⠀⠀⠀⠀⠀⠠⠺⠀⡹⢟⣿⢹⠆⠀⠀⠘⠀⢀⠀⠀⡎⠀⠂⠐⠀⠀⠀⠀⠠⠺⠂⡹⢟⣿⢹⠆
⠀⠰⠆⠈⠋⠀⠈⠠⠀⠀⠀⡴⠈⠀⡠⠾⠁⣤⡶⠤⠀⠀⢠⠀⠰⠆⠈⠋⠀⠈⠠⠀⠀⠀⡴⠈⠀⡠⠾⠁⣤⡶⢤⠀⡀
⡶⠂⠀⠀⠀⠺⠃⠀⠀⠂⠀⡀⠀⢄⠀⠀⠈⢟⠓⠚⢀⣿⣿⡶⠂⠀⠀⠀⠺⠃⠀⠀⠂⠀⡀⠀⢄⠀⠀⠈⢟⠓⠚⢀⣿
⠙⠀⠀⠀⠀⠀⡠⠀⣀⡀⠀⠉⠀⠀⡀⠄⠀⠘⠃⠀⣀⡘⠋⠙⠀⠀⠀⠀⠀⠠⠀⣀⡀⠀⠉⠀⠀⠀⠄⠀⠘⠃⠀⣀⡘
⠀⠀⠀⠂⢡⣂⠀⠀⠈⠁⠀⠀⡄⠀⢀⠀⠐⠦⠀⠈⠛⠃⠀⠀⠀⠂⠢⢤⣂⠀⠀⠈⠁⠀⠀⡄⠀⢀⠀⠰⠤⠀⠀⠛⠃
⠈⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡛⠑⣀⠀⠀⠀⠀⠈⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡟⠃⣀
⣢⣀⡀⠀⠀⠀⠀⣅⠀⠀⠀⠀⣈⣀⠱⣶⣇⡀⠉⠀⠀⠀⠰⣢⣀⡀⠀⠀⠀⠀⣍⠀⠀⠀⠀⣘⣀⠱⣴⣆⡀⠁
⢀⠁⠀⢸⣧⠀⠀⢻⣷⡶⠾⠛⠁⠀⠀⠈⠉⠀⣠⣶⣶⣄⠀⢀⠁⠀⢸⣧⠀⠀⢻⣶⡶⠾⠛⠁⠀⠀⠉⠉⠁⣠⣶⣶⣤
⠘⣄⣦⣼⠟⠀⠀⠘⠉⠀⣤⠀⣀⠤⠴⣿⠀⢠⠘⠋⠑⡿⠀⠘⣄⣦⡼⠟⠀⠀⠘⠁⠀⣤⠀⣀⠤⠴⡟⠀⢠⠙⠋⠑⡿
⡀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢸⣅⠀⢀⣬⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⢸⣄⠀⣀⣼
⠀⢠⡖⠒⢠⠀⠀⢐⡲⠀⡀⠀⠛⠿⠯⠉⠀⢀⡀⢀⣡⠆⡀⠀⢠⡶⠂⢠⠀⠀⢀⡲⠀⡀⠀⠛⠿⠏⠉⠀⢀⡀⢀⣡⠆
⠀⢘⠀⠀⠀⠀⡠⠋⠈⢛⠁⠁⠀⠀⠂⣠⡀⢼⣭⣿⢧⡘⠀⠀⢘⠀⠀⠀⠀⡠⠋⠈⢛⠁⠀⠀⠀⠂⣠⡀⢼⣭⣿⢧⡘
⠀⢀⡀⠰⡤⠀⠣⠀⠀⠀⠐⢀⠀⠀⠉⣨⠄⠊⣑⠛⠘⠁⠀⠀⢀⡀⠰⡤⠀⠡⠀⠀⠀⠐⢀⠠⠀⠈⣨⠄⠊⣑⠛⠘⠁
⣀⡈⠁⠀⠀⣠⡄⠈⠀⡀⠀⠋⠀⠀⠊⠉⠠⣿⣏⣩⠀⣦⣸⣀⡈⠁⠀⠀⣠⡄⠈⠀⡀⠀⠊⠀⠀⠊⠉⠠⣿⣏⣩⠀⣦
⢯⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠦⠀⠐⠈⠀⠀⢱⡄⠀⠐⢻⡿⢯⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠦⠀⠑⠀⠀⠀⢱⡤⠀⠐⢻
⠀⠀⠀⡀⠀⠀⠈⠀⠲⠆⠀⠀⠀⠀⠂⠁⢀⣀⠀⠠⣶⡆⠀⠀⠀⠀⡀⠀⠀⠈⠀⠲⠆⠀⠀⠀⠀⠂⠁⢀⣀⠀⠠⣶⡆
⠠⠀⢀⠄⠉⠒⠀⠀⠀⠀⠀⠀⠃⠀⢰⢤⣤⢍⠀⠀⠀⠀⠀⠠⠀⢀⠄⠉⠒⠀⠀⠀⠀⠀⠀⠃⠀⢰⢤⣤⢁
⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢆⣀⡆⠀⠦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢆⣀⡃⠀⠶
⠚⠖⠂⢠⡄⠀⠀⣷⣀⣀⣤⣤⠖⠒⠈⠿⠷⠂⠀⣀⣀⠀⠈⠚⠒⠂⢠⡄⠀⠀⣷⣄⣀⣤⣤⠖⠒⠈⠿⠿⠂⠀⣀⣀
⢰⠀⡀⢸⡿⠀⠀⢸⠿⠋⠉⠀⠀⠀⢀⣤⠀⠀⢺⡿⢻⣿⠀⢰⠀⡀⢸⡿⠀⠀⢸⠟⠋⠁⠀⠀⠀⢀⣤⠀⠀⢺⡿⠻⣿
⠀⠓⠻⠛⠁⠀⠀⠀⠀⠀⠛⢠⠖⠁⠉⠫⠀⠘⠀⠀⠀⠋⠀⠀⠓⠻⠛⠁⠀⠀⠀⠀⠀⠛⢠⠖⠉⠉⠻⠀⠘⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡀⡀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡏⠘⣯⡁⠂⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠣⡀⠈⠙⠲⢤⣀⠐⡸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢱⣤⠀⢀⠀⠹⣿⣾⠇⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠤⠐⠀⣠⠃⢈⠤⠀⣀⣈⡀⠐⢿⡇⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠒⠛⠂⠙⠱⢂⠋⠁⣡⠶⠋⠀⠈⢢⠀⠀⣩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⠃⠀⠀⠀⠀⢨⣷⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⠴⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⣸⠁⢸⣄⠈⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠚⣁⣀⣠⡤⠖⠋⠁⠀⢠⡧⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢦⣶⠖⠒⠶⠒⠒⠉⠓⠀⠀⢀⡴⠞⠋⠉⠉⠁⠀⢀⣀⣤⣴⣿⣿⣛⡳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠢⢤⡀⠀⠀⠀⣠⣶⡛⠁⠀⠀⣀⣀⣤⣴⣾⠿⢟⠭⠋⡙⡉⡍⢐⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠛⠟⡛⠚⡛⠟⠻⡏⢍⠁⠀⠈⠀⣾⣶⣾⣷⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⡶⣤⣄⣠⡄⠀⣀⠀⣀⢀⣄⣀⢡⣈⣠⣇⣴⣥⣼⣿⢷⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⢸⡆⠸⡏⠉⣻⠉⢿⠉⢻⡋⢻⠛⢻⠍⢉⡇⢠⣯⢸⣿⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡄⣷⠀⣷⠀⢹⡀⢿⠀⣼⠀⢸⠁⣸⠀⣸⡇⣸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠰⣸⡆⢻⠂⠸⣇⢼⠣⣸⡅⢸⠆⣿⢈⣿⣹⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣿⣟⣹⣧⠀⣏⣾⡇⣿⣧⣿⢐⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣻⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡼⣿⣿⣷⣿⡟⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣷⣿⣿⣷⣿⣿⣷⣿⣏⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⠿⡏⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⠿⠿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠟⠻⠿⠻⠛⠛⠛⠛⠛⠋⠛⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⢛⣛⣛⡉⣉⠙⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢩⣖⣦⣶⣆⢸⣿⠃⢹⡇⠸⢷⣿⠀⣿⠉⠉⠉⠛⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⣿⢸⡟⠁⠟⢻⠈⠋⠳⠈⠁⠒⢚⣁⣀⣯⣀⣀⣀⣘⠛⢭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠷⡶⠀⠀⣻⣄⣡⣤⡤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠙⠋⠀⣀⡴⠃⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠠⠀⡇⢨⡄⠀⣼⣡⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⡆⠀⠀⠀⣹⣶⢶⡖⢲⢶⡶⡾⢯⣹⡇⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⢸⡇⣇⢸⡀⠀⠉⠁⠀⢠⣤⡤⢤⠤⣤⢲⣶⢿⡁⢹⣌⣿⠀⠀⠀⠿⠋⠈⢷⠇⠈⠻⠃⠀⠙⠃⢸⡇⣿⡇⢠⣤⡄
⠀⠀⣴⢒⠊⠉⠙⠋⠛⠙⢓⠒⢦⡀⠀⢸⣿⡇⢸⣧⣽⠸⣿⠾⡇⠀⠋⠈⠀⠀⠀⠀⢸⡇⠀⢰⣢⠀⠀⣴⣦⠀⢸⣧⠻⠇⠈⠛⠉
⠀⠀⡧⢀⣀⢉⣭⡉⣩⣅⢠⣤⡀⢻⠀⠈⠈⠀⠈⠀⡁⠀⠁⠀⠐⣦⣀⢿⣠⢿⠀⢰⢟⣧⠀⣰⠿⡀⠀⢸⣻⣦⠈⠿⠀⢠⣦⣀⡀⠻⠃
⠀⠀⢷⡟⢻⣿⣸⣇⣟⣻⡿⢹⡇⡿⠀⠀⠀⠀⣶⣾⡿⣰⠀⠀⠀⠹⡉⣂⡡⠼⠀⣯⣵⡿⠀⣿⠃⢷⡀⣾⣭⣼⠇⠀⠺⣼⢿⣻⠅
⠀⠀⣸⣗⠀⣤⠙⠿⣃⠉⢠⣌⣻⠧⣄⢠⡖⠒⢻⣿⡏⢉⣳⡄⠀⡶⣄⢠⢺⠂⠀⢀⡀⣀⠀⢙⡓⠛⠁⠀⠀⠀⠀⢀⣀⡙⠋⠁⣀⢀
⠀⢸⠁⠈⠉⠓⠒⠚⣉⠉⠉⠉⠀⠀⠘⡇⢳⠚⠹⣿⡏⠉⣹⠁⣤⣷⣿⣿⣾⣧⠀⡸⠖⢶⣉⡳⣆⡵⠀⡶⠉⢲⣤⠟⠁⢸⡆⠀⠻⠟
⠀⢸⣴⢶⣄⡞⣷⣼⢻⡆⣾⢻⢠⡟⣦⣿⢸⡀⠀⣿⡇⠀⡟⠀⢸⣏⠋⠋⣭⡏⠀⠁⠈⠁⢀⣉⡉⠀⠀⣷⡀⠀⠉⠀⠀⣼⠃⣶⣤⡤
⠀⠀⣏⠈⠿⠃⠻⡿⠈⠷⣏⠈⢿⡃⣸⡅⠀⠣⢀⠛⠓⠚⠁⠀⠈⣿⣀⣴⣉⡇⠀⠀⠀⣰⠋⠀⠙⣦⠀⠈⠙⠲⢤⣠⡼⠃⠀⠻⠟⠁
⠀⠀⢿⠺⡧⢮⡥⣬⢤⡴⠶⢋⣛⣬⠾⠃⠀⣼⢁⢹⣠⡖⢒⡄⠀⠈⠉⠉⠉⠀⢀⡴⠒⣿⠀⠀⠀⣿⠞⠉⣶⠀⠀⣽⠁⠀⢀⡤⠖⠂⢤
⠀⣠⡀⠉⠓⠒⠒⠒⠒⠛⠉⠉⠀⢠⣤⡀⢠⡬⠽⡿⠻⣿⠏⣤⢰⣿⣤⣶⠀⣤⠞⠳⣄⢿⠀⠀⢀⣟⣠⠤⣿⡁⠀⠙⢦⠀⡞
⠲⡋⠹⡃⢤⢤⣶⣶⡾⣹⠀⡤⣄⢨⣿⡁⠸⡇⠀⣇⢠⡧⠀⢼⢻⣿⣿⡅⣸⠃⠀⠀⢹⣮⠧⣴⠻⡿⠁⠀⠈⣿⠀⠀⣼⠀⡇⠀⠀⠀⢠
⠘⠛⠉⠁⠘⠚⠉⢁⡀⠀⣠⢿⡅⠺⠾⠇⠀⣇⠀⣿⢸⠇⣀⣿⣸⣿⣸⠇⢻⡀⠀⢀⣾⡏⠀⢸⣿⡇⠀⠀⢀⡿⠀⠴⠃⠀⣸⠶⠴⠒⠋
⢸⠖⢦⠀⠀⣠⠚⣵⠿⠀⢑⣛⣁⡔⢰⠀⠀⠈⠉⠉⠉⠉⠁⣀⣀⠀⠀⠀⠀⠙⢶⠋⣿⡄⠀⣸⡿⠙⣦⡴⢛⣀⣀⡀⠀⢠⡇⠀⣸⣷⣶
⠉⠻⠁⠐⢊⣲⠗⠁⣴⠰⣿⣌⠿⠃⠘⢡⣾⠀⠀⠀⢀⡴⠺⣅⡽⢦⡀⠀⠀⠀⠀⠀⠈⢳⣤⠟⠠⠀⡄⡴⠋⠀⠀⠈⢢⠈⢇⠈⠛⡽⠋
⠘⠃⣠⡤⣤⣁⣀⣀⡈⠙⠋⠀⠀⢀⠴⢭⠭⠵⢦⠀⢯⢌⣓⣉⣫⣭⡽⠀⣔⠀⠀⠡⣠⠀⡅⢀⠃⠜⠐⡇⠀⠀⠀⠀⣸⠇⢸⡆⢠⣤
⠀⠀⣿⠀⠖⠀⢀⣠⡾⣷⣀⠀⠀⡾⢉⢚⣩⢉⡹⣄⢸⢸⣻⢹⢸⣿⠃⠀⣾⡆⠀⠀⠈⢳⡁⢀⠎⠀⠀⢻⣄⣀⣀⡴⠋⢀⡼⠀⠙⠛⠁
⠀⠀⢻⣆⣤⡾⠛⢋⣠⠾⣹⠃⠈⣶⣦⡭⡶⣤⡖⡟⠀⠉⠛⠛⠛⠁⡔⠀⠉⠙⠒⢄⡀⠀⣿⠀⠀⠀⢠⠞⠋⠁⠀⠀⣶⡄⠀⣶⣤⠄
⠀⠀⠀⠉⣷⣤⠴⢛⡵⠚⢡⣄⡄⠹⢾⣷⣷⣿⠼⠁⡠⣠⣶⣄⠀⢺⡄⠀⠀⠀⡀⣠⡗⠀⣿⡀⠀⠀⠸⡀⠠⣿⣖⠀⣀⣠⡆⠘⠁
⠀⠀⠀⠘⠧⠔⠚⠉⠀⠀⢮⢿⠗⠀⠀⠀⠀⠀⠀⠀⣱⢺⡟⡞⠁⠀⠘⡏⡏⣿⣏⣿⠃⠐⠁⠀⠀⠀⢀⡇⠀⠁⠀⣠⣯⡀⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣁⣀⣀⣀⣷⣿⣟⣛⣛⣀⣀⣀⣀⣀⣠⣏⣀⣀⣀⣀⣈⣀⣈⣃⣀⣀⣀⣀
⣿⣿⠛⡻⢛⡛⠛⣟⢛⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⣠⣽⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⡯⡀
⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠵
⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠈⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠈⢩⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠋⠟⠋⠉⠻⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⡿⠟⠉⠻⠏⠳⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣼⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⣿⣿⣿⣿⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⣿⣿⣿⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠠⣿⡇

⠀⠀⠀⠀⠀⣀⠤⠀⠀⡤⣀⢐⠉⠂⠲⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠠⣀⡀
⠀⣅⠳⢤⠔⢄⠀⠠⠹⢀⣀⣣⠞⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⠢⠏⠡⠡⠈⡀⠸⢹⡞⠀⢆
⡠⠃⠀⢀⣠⠛⠃⠀⠀⠢⠜⢸⠧⡄⢠⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⡁⣠⣘⢄⢀⢇⢀⣇⣰⡼⢻⡖⠊
⠃⠤⠊⠣⣀⡱⢦⡡⠌⣐⡰⠃⠑⠒⠂⠀⠀⠤⢀⠐⢌⣭⣔⡒⡒⢄⠀⠉⡧⠃⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠥⠤⠤⠴⠄⢻
⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠤⢀
⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠀⠰⠀⠤⠤⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠤⠅⢁
⠀⠀⠀⢸⡄⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠊⠀⢄⠱⠄
⠀⠀⠀⠈⢌⠒⠄⢉⠒⠀⠐⢊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣀⠄⠂⠠⢀⣀⠀⠈⢈⡀⠀⠀⢀⢠⢖⡀
⠀⠀⠀⠀⠈⠱⠤⣀⣀⡩⠝⠁⠀⠀⠀⠀⡠⣄⣀⠀⠀⠀⠢⠀⢈⣁⠀⠀⡀⠐⠈⡄⠀⠀⠈⠀⡑⠏⣠⠲⠊
⠀⠀⠀⠀⢀⠃⡐⠀⠀⠀⠀⠀⠀⣀⠠⠚⠒⠀⠘⣤⣄⠀⠀⠀⡀⠈⠐⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢀⠎⡘⠀⠀⠀⠀⠀⢴⡋⠄⠀⠀⠀⠀⡊⠀⠈⠉⠁⠚⡍⢣⠀⠷⠊⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⢄
⠀⠀⠀⢎⣠⠀⠀⠀⠀⠀⠀⠠⢈⠑⠈⠀⠙⠉⠈⠖⠉⠙⠆⠀⡠⠸⠁⠀⠀⢀⠔⠊⠁⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠚⠀⠈⠓⠀⠉⠓⠈⠀⠀⠀⠀⢀⠏⠀⢀⠔⢋⠑⡦⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⣄⠀⠀⠀⠀⠀⠸⡀⠉⡇⠀⣭⠤⠣⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠲⢚⢉⠉⢫⡤⢀⠃⠀⠀⠀⠀⠀⠙⢤⡛⢮⣀⣀⡧⢏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠂⠉⠀⠑⠄⠀⠈⣎⡤⠊⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢂⠠⡀
⠀⠀⠀⠀⢲⠠⠠⠅⠀⢂⠑⠄⡄⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡘⢆
⠀⠀⠀⠇⠀⡑⢒⠔⠣⠤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃

⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠈⠹⣆⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠃⠀⠀⢦⠈⢿⣤⣤⣇⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⠇⠀⠀⠘⣺⣷⣾⠁⠀⢨⡗⠋⣉⡁⠀⠀⠸⣆⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢈⡇⠀⠀⠀⠘⣁⣴⣇⡀⠀⡾⢿⡿⠭⠀⠀⢠⡾⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⠶⠶⠒⠛⣩⠏⡏⠉⢻⣷⡀⠃⠀⠀⢀⣼⠋⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⢀⡇⠀⠸⡏⢳⡄⠀⠀⢨⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⣻⣗⣀⡴⠋⢻⡀⢀⣹⡄⠙⠳⠶⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⠳⣾⡏⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣿⠌⡌⣷
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⢠⣿⣿⢣⡼⣿⢈⣧⠘⣷
⠀⠀⢠⣄⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠂⠀⠀⢠⢳⣜⣧⠀⠀⣠⣿⣿⠟⣸⡇⣿⢸⣷⢲⠈⠃
⠀⠀⠉⡀⠀⠀⠀⠀⠦⡐⠐⠂⡀⠀⠀⠰⢊⣰⢃⠀⠀⠀⠘⣷⠻⠎⣡⣴⣿⡿⡃⣴⡘⢁⠏⢸⣿⢸⡆⢰⡄
⠀⢀⠁⠁⠀⠀⠈⠘⠀⢣⡠⠀⡞⠢⠄⣀⡀⠀⠀⠀⠁⠀⢿⣿⣿⡷⠿⢟⢻⣾⣷⡙⢡⣿⢠⢲⣏⠸⡇⣧⠁
⠀⠟⢐⠀⠀⠀⠈⠘⠀⠀⠀⠔⠁⡜⠀⠄⠈⠎⠒⠀⠀⠀⠀⢫⣶⣾⡏⣿⠿⡷⠉⣴⣼⣿⢸⢻⣿⢦⣌⢹⡀
⠀⡆⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠙⠖⢤⠴⠣⠀⠀⠀⠀⠀⠘⣣⣙⢃⡌⣴⢰⣿⣻⠆⡟⣾⣻⣿⢸⣿⠘⡇
⠐⠁⣤⠀⢨⠀⢠⠀⢡⡰⡀⡄⠠⠀⢧⠈⠂⠣⠀⠀⠀⠀⠀⠀⠫⠏⣿⢣⣿⢸⡇⡿⡐⢰⣿⢹⣿⢸⣿⠀⣧
⠀⢠⠹⠀⠀⠀⢨⠀⠀⠀⠛⠱⡧⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠸⢹⠸⢡⡄⣿⠈⣿⣼⡏⣿⣿⢀⢹
⠀⡣⠈⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣻⠇⣿⢰⡏⣿⠇⣿⡋⣾⡌
⠀⠀⢠⠃⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⠘⢱⡟⠀⢿⠇⢫⡄
⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡄⡾⠁⠆⠘⠀⠈⡃
⠀⠀⠂⠀⡜⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡇⠀⡾⠀⠀⡼⡀⡁
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢠⣡⠀⡇⢽⡇
⠀⠀⠀⠈⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣾⡏⣴⡆⠻
⠀⠀⠀⡀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢃⣼⡟⣰⡟⠀⠰
⠀⠀⠘⠀⠀⠀⡀⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣾⠟⢠⠟⣴⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⢀⠠⣾⣿⠘⣿⡇
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣽⣿⠸⣿⣿⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠁⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠹⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡤⠴⠒⠋⠁⠀⠀⣀⡤⢾⡇
⠀⠀⠀⠀⠀⢸⠒⠚⠉⠉⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠈⢦⣠⣤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠴⢶⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢝⢢⣀⡠⠴⢲⠶⠦⣄⡀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⡅⠉⠀⣰⠋⠀⣰⠃⠙⣎⣇⠹⣄⣀⣠⣄⣀⡀⠀⠀⣠⠴⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣰⠒⠀⠀⢀⡏⠀⢰⠇⠀⠀⠘⢻⡶⢫⠇⠀⣾⠀⠉⢲⠞⠔⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢼⣘⣿⣠⠴⢦⠀⢸⠀⠀⣾⡋⠉⠭⣛⠿⠀⢸⡀⠀⢹⠀⠀⠀⠐⣃⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡄⠀⡏⢳⡄⠀⠒⠀⠀⠀⣇⠀⠸⡆⠀⠀⢀⠀⠩⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡟⠀⡪⠀⣄⠀⠸⣄⠀⠹⡄⣠⠏⠙⠲⠯⠥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⣢⠞⠉⠙⠲⠾⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠛⠉⠛⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⠿⠛⠿⣷⢄⣀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠀⠀⠀⠀⠀⠀⡠⠀⠀⡴⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢰⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠠⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠈⠀⠀⠀⡀⡇⠀⠐⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠲⣄⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⡸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠄⠁⠀⠀⠀⠄⠀⢄⠀⢰⡀⠄⠀⡠⠊⠁⠀⠀⠸⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠂⠀⠸⡀⠀⠂⠀⠀⠀⠀⠀⢹⢄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢄⠴⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠠⢄⠀⠈⠀⠀⠀⠘⠀⠡⢀⣔⠉⠃⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠘⢠⠀⠤⠀⠀⠀⠇⠈⠀⠀⠀⠀⢂⠀⡄⠀⠠⢀⠀⠀⠆⠀⢠⡆⠠⠀⠙⠛⠁⣴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠑⡀⠀⢄⠀⠸⡄⠀⠀⠄⠉⠛⢄⡇⠀⠔⠁⠀⠀⠀⠀⣼⠁⠀⠀⠡⠌⡑⠁⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡘⡄⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⡜⠀⠠⠚⠻⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⡀⢀⠀⠀⢡⡀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠐⡎⠀⠀⠂⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣁⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⢠⠷⠀⠀⠀⠀⢨⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢺⡗⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⢀⣀⡠⠀⠀⠀⣡⣿⡍⠀⠀⠀⠀⢠⡀⠀⠀⠀⢽⠅⠀⠠⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠠⣼⣷⠄
⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠘⣡⣿⣌⠢⠀⠀⢠⣿⣷⡀⠀⠀⢺⡒⠀⢠⣿⣿⡄⠀⠀⢠⣆⠀⠀⠀⠴⣿⣿⠶⠆
⠀⠀⠀⠀⠀⠖⠒⠂⠀⠀⠔⣩⣿⡝⠢⠀⢀⣿⣿⣿⣧⠀⢐⠱⣝⠀⢠⣾⣿⣄⠀⠀⣾⣹⡀⠀⠀⠾⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣱⣿⡝⠢⠀⣼⣿⣿⣿⣿⣇⢁⡼⣌⠁⠉⣽⣯⠉⠀⣸⣷⢺⣇⠠⠴⠾⣿⣿⣟⣉⣀
⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠚⠁⢺⠈⠂⠸⠿⠿⢿⠿⠿⠿⠀⢸⠀⠀⣾⣿⡿⠷⢠⣿⣷⣼⣿⡄⣠⡾⢿⡿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣻⣷⣦⣽⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠓⠶⣿⣿⣟⣿⣿⣿⣿⣿⣦⣤⡀⠀⢀⠠⢀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣷⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣦⢸⣷⣤⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠻⢿⠿⣿⣿⣿⣿⣿⣿⠿⠷⠿⠛⠀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠟⢻⣿⣿⣷⣿⣦⣀⠀⠀⣸⣿⣿⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⢿⣿⣿⡤⠀⣼⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣨⠏⠀⣿⣿⣅⢀⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣰⣿⣿⣿⣿⣇⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡟⠙⠁⠀⢹⣿⣿⣿⣿⣿⠀⠀⠹⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠴⠶⠷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠍⠀⠒⠀⢉⣙⠉⠉⠁

⣶⡶⠶⠦⢤⣤⣴⠶⠛⠛⠛⠻⠶⢦⣄⡀
⢻⡛⢦⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠸⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷
⠀⢳⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⢤⣤⣙⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⣿⠀⢠⠀⣿⣿⣧⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⢶⣤⡀
⠀⣿⠀⠈⠧⣍⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠝⠀⠀⠀⠈⠙⢷⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠘⠈⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠛⠶⣦⣀
⠀⣿⠀⠀⢀⢀⢀⡀⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⢻⢸⣿⠾⠜⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⢸⡇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀
⢸⡇⢶⢿⣷⢿⡟⠟⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠴⠶⠞⠛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠭
⠈⢿⡜⢏⢫⡋⠀⠀⠘⣟⠳⣤⣀⣠⣄⡙⠛⠓⠛⢻⣤⣤⣤⡤⠖⠋⢉⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉
⠀⠀⠻⣦⠃⠀⠀⠀⠀⠘⠷⣤⣈⣷⡈⠙⠓⠒⠚⠋⢷⡦⠤⠤⠶⠚⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⢻⣄⠉⠓⠒⠶⠴⠶⣾⠓⠶⠶⠶⠒⠚⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⣦⠀⠈⠛⠷⠶⠶⠶⠞⠛⠲⠦⠤⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣃⣀⣤⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣄⣤⣤⣄⣠⠞⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣀⣀⣴⣿⡿⢋⣶⠋
⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣾⣿⣯⣽⣿⣿⠟⢴⡿⠁
⠀⠀⠀⠀⠀⠀⣠⣤⡤⠽⢿⣛⠋⠀⠈⠀⣀⡛⢳⣤⣄
⠀⠀⠀⠀⠀⠀⠉⠉⢉⣿⣿⣭⡶⠿⠟⠛⠋⠉⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠒⠻⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠐⠚⢻⡿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠚⢿⠟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠐⢺⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠂⠐⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⣰⡄⠘⠃⠀⠀⠀⠀⠀⠀⠄⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠤⢾⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠠⠴⢾⣷⠶⠤
⠀⠀⠀⠀⠀⠁⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠰⡦⠈⢻⡿⢁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣰⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠹⢦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⣿⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠖⠋⣁⡤⠴⠒⡦⠀⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠒⢋⣡⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡄⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠃⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠴⠚⠉⢉⡤⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣶⡶⠋
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⣤⣀⣀⣠⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⡀⠀⠀⢠⠇⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⠀⠀⠀⡏⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠐⣇⡼⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠞⠁


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

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤
⠀⠈⠙⡦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⠈⠀⢀⠰⠂
⠀⠀⠀⠈⠀⢠⠉⠓⠶⠠⢄⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠐⠪⠀⠢⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠠⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⣠⡧⣿⡄⠀⠀⠀⡘⠰⠁⠀⠀⠀⠀⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠄⢹⡷⠁⢁⠘⢥⣶⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢷⡁⠀⠀⢰⡝⠒⠀⡀⠀⢀⠐⠀⠀⠂⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡠⠀⠀⠠⠀⢈⡖⠀⠀⡏⠀⡈⠁⠠⢀⢳⡨⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢁⠘⠀⡌⠙⠒⠀⠀⠀⢰⡀⠀⠀⠑⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣿⡌⢸⠀⡇⠰⠀⠀⠀⠀⠀⠓⣼⠀⢰⠒⠲⠅⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠛⢹⠀⠀⣇⠀⠀⠀⠀⣀⣀⠀⠈⣕⢺⡧⠀⠀⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡦⠴⠖⠀⠉⠁⠀⠀⡀⠤⡀⢄⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⡧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⠚⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣧⠀⠀⠐⢄⠀⠀⠀⠀⠀⠃⠀⠐⡘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈⠳⡄⠀⠀⣼⣀⡤⠀⢷⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠤⠂⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠤⡀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠴⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⣶⠰⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢠⡜⠀⠀⠀⠈⠶⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠄⠐⠓⢀
⠁⠀⠀⠀⠀⡽⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠈⡇⢀
⡆⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⡀⠀⠛⠋⠁⠀⠓⡀⠀⠀⠀⠀⠁⠈⠀⠀⣀
⠀⡂⠀⠀⠤⣰⠁⠀⠀⠰⠀⠀⠀⠙⠂⠰⡓⠀⠀⠀⢡⠀⠀⠀⠀⠰⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠈⠐⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡄
⠐⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠘⠀⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡅⢁⠀⠈⠀⠀⠀⠀⠀⠀⠠⠌
⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣀⣼⠿⣿⢿⣤⣀⣄⣄⣠⣤⣤⣤⣶⣿⠿⣿⣧⣍⠒⠀⠀⠀⠀⠀⡈⠃⠀⠀⠀⠤⠀⠀⠀⠀⠄⢀
⣀⣀⡀⡀⠀⢀⣸⡿⠶⠶⠖⠷⠚⠉⠁⠀⠀⠀⠀⠁⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠘⠛⠿⠷⢶⣤⣶⣶⣾⣿⠳⠾⣿⣦⣄⠀⠀⠀⠀⢀⠈
⠉⠙⠛⠛⠛⠛⠥⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢯⣽⣅⣀⣀⡀⠉⠛⠛⣚⣶⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠖⠂⠀⠙⢿⣦⣤⣤⣤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠐⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⡩⠄⠀⠀⢀⡴⢏⡨⠁⠀⠀⠀⠊⢄⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣃⠀⠀⠀⠀⠀⠀⢠⡮⣕⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠋⠀⠀⠀⠀⠀⢰⠗⠥⠀⠀⠀⢈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣀⠀⠀⠀⠀⠀⢀⠢⢀⠄⠀⠀⠀⠀⠀⠐⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠑⠀⡀⢀⠀⠀⠀⠀⠀⢠⠀⢃⠀⠂⠀⠀⠈⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⠀⠀⠄⠀⡀⠀⠀⣔⢂⣨⠜⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠦⡀⠀⠈⠲⠐⠤⠊⠁⠀⡀⢀⠀⠀⠀⠀⠀⠴⢆⣄⠉⠸⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠌⠀⠀⠔⠁⠀⢈⠦⡀⠚⠋⢄⠀⠀⠀⠄⠠⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠄⠄⠀⡠⠀⠀⡀⠐⠁⠀⢀⠰⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠈⠀⠀⠐⠈⠀⠄⠀⠈⠁
⠀⠀⠀⢠⠂⠔⡡⠀⡀⠄⡂⠠
⠀⠀⢠⣏⣀⡨⠔
⠀⠀⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠙⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠈⠙⠂⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢠⣦⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⣀⣀⡤⢦⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠈⠁⠀⡀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠙⠳⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡔⠉⠉⢆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣴⠚⠉⠻⣦⠀⠉⣉⣀⠔⠁⠀⠀⠀⠀⢀⡴⠖⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠛⠛⠻⠶⣄⠀⠀⢰⡏⠀⢀⣀⡨⠛⢦⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⡡⠀⠀⠀⠀⠀⠀⣸⠇⠀⠘⣷⠀⠀⢻⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠉
⠀⢀⣤⠴⠖⠒⢦⠊⠓⠄⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠈⠳⣜⢫⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠖⠋
⣰⡟⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⢈⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⢹⡇
⣿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠻⢍⡀⠀⠀⠀⠀⣀⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠆
⠻⣦⣀⣀⠀⢈⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡏⠹⣎⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅
⠀⠀⠉⠉⠉⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⢯⡛⠄⠹⠀⠜⠣⠢⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠳⠤⣄⣀⠁⠈⠀⠀⠈⠛⠓⠶⠶⠞⡏⢀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢶⡦⣌⢙⠒⠦⠤⠤⠤⠤⠤⠒⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⠄⠀⠀⠀⢀⣀⠀⢣⠃
⠀⠀⠀⠀⠀⠀⢀⠤⠉⠊⠁⠸⡀⠀⠀⠀⠀⠀⢀⡴⠙⠶⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠧⠔⠁⠀⠛⠀⠀⠀⠀⠀⠛⠊⡀⠠⡐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⠔⢣⠰⣬⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠪⢈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡿⠗⠀⠀⠀⠴⣭⠪⡵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⡴⠓⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⢘⢸⡰⠭⣵⢉⠄
⠀⠀⠀⢀⣀⣤⣤⣴⣶⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⣡⣤⣬⣄⠀⠀⠀⠀⠀⢰⣿⠁⣉⣿⠏⠀⠀⠀⠀⠀⠈⠦⣙⣙⡥⠜
⠀⠀⣴⣿⣿⣿⠿⡿⣛⣹⡄⠀⠀⠀⢸⠀⠀⠀⠀⢀⢼⠿⠿⠿⡿⠻⠤⠀⠀⠀⠀⣺⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣶⣷⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⢂⠂⢠⠀⠁⢇⠁⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠢⠤⠼⠼⠌⠀⠀⠀⠛⠿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⢀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⠬⠯⠥⡞⠉⢃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢈⠖⠀⠒⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⡈
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢢⠀⠀⠀⡼⠉⡇⠀⠀⠘⠢⠤⠤⠤⠤⠗⠋
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠚
⠀⠀⠀⠀⠀⢹⡢⣞⣢⢯⠇⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡚⢳⣤⡀
⠀⠀⠀⠀⠀⠀⣷⢾⣉⡾⠀⠀⠀⠀⢠⠞⠡⢀⠀⠈⠀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡞⠙⣦⡴⠛⢏⣠⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠸⣞⣭⠇⠀⠀⠀⠀⠇⠨⢠⢰⣿⠿⣦⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⣠⣴⠚⢣⣠⠽⢏⢉⡷⣖⢋⣱⣶⠋⣱
⠀⠀⠀⠀⠀⠀⠀⢫⡟⠀⠀⠀⠀⠀⡇⢁⠀⢘⠦⠤⠊⠈⠀⠀⡇⠀⠀⠀⠀⠀⣾⢀⡸⢶⠋⣹⣴⠚⢻⣤⠞⢻⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢳⣆⣀⠂⠄⠂⠐⢀⣀⣾⠃⠀⠀⠀⠀⠀⠙⣯⣠⠼⢻⣁⡼⢿⡉⣹⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠷⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠚⢹⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⣾⣟⣼⠄⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⣠⡐⡦⣀⠀⠀⠀⠀⠀⠀⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠘⣷⢣⢠⡍⠀⠀⠀⠀⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⡰⣟⡲⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⣀⢸⡶⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⡗⠀⠀⠀⠀⠀⠿⠮⠙⠁⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠰⣬⡳⠁⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠃⠀⠀⠠⣿⠊⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⢙⡇⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠻⢿⡿⠏⠀⠀⠀⠀⣸⣷⡿⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠾⣟⡀⠀⠀⠀⠀⣴⢿⣿⣷⡄⠀⠀⠀⠀⣀⣾⣿⣦⠀⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⣶⣤⣴⣦⣶
⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠀⠀⠘⠁⣾⣿⣿⡿⠀⠀⠀⠀⠉⠛⣛⣽⠃⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⢀⠄⢼⠷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⢀⠮⠁⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⢀⣯⡀
⠀⠀⠀⠀⠠⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠂⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣾⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣼⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷⠤⠀⠀⠹⠉⠀⠀⠀⠀⢠⣿⣧⡀
⠀⠐⠒⠺⢿⣿⣿⣿⣿⡷⠶⠆⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠾⣿⣿⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⠹⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠻⠋⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣀⠀⠀⠀⠀⠀⠀⠈⢿⡏
⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣇⠀⢘⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣠⠀⠀⢠⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢈⠿⠿⠛
⠀⠀⠛⣿⠟⠀⠀⠹⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠈⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠙⣿⠛⠁⠀⠀⠀⠐⢦⣠⣿⣧⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⢿⡏⠉⠓⠀⠀⣰⣿⣶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠻⠓⠠⢴⣿⣯⠄⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠈⠛⠁⠀⠀⠀⢀⣀⣼⣧⣀⡉⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢡⣤⣾⣧⣤⠄⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢹⡿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⣿⠏⠉
⠀⠐⠒⠒⠿⠿⠿⣿⣿⠿⠿⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣤⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠰⠶⢾⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠤⣤⣿⡤⠤⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠀⠀⠀⠀⠀⠐⠶⢾⣿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠲⠾⢿⣿⡿⠿⠒⠂⠀⢸⡇
⠀⠀⠀⠤⠤⣾⡦⠤⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣦⡤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠠⢤⣼⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⠀⣀⣤⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠶⠶⣿⣿⡷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⣿⣿⡂⢀⠀⢠⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢀⡈⣢⠈⠙⣿⣿⠻⢿⣿⣿⣿⣿⣷⢈⣿⣿⣻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⡆⠀⠁⣤⣹⣿⢄⣎⣿⣿⣷⣾⠿⣿⣶⣤⠟⡾⠻⡍⠙⣀⣄⡤⠖⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣟⣁⡀⡁⠼⢿⣷⣌⠛⢋⣿⡟⠀⠈⠻⣷⣤⣄⠀⠙⢤⠛⢇⠰⣢⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⣻⣻⣷⣴⡄⡈⢙⡀⠻⣿⠁⠀⠀⠀⢹⡿⡿⠛⠻⠀⢆⠀⣴⡟⢩⡀⠡⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣎⢀⡾⢾⡟⢹⣿⣶⡁⡈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⠿⣿⣿⡶⢤⣀⣠⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠰⢛⣀⣤⣾⠗⢞⡿⠄⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⡍⢉⣿⠀⡿⣿⣿⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠷⠶⣷⠀⠼⣿⣼⡷⠚⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣙⣯⡿⣿⣧⢸⡟⠛⠒
⠀⠀⠀⠀⠀⠰⠇⠀⣀⣀⠀⠐⡸⡟⠁⠐⡆⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡟⠙⢿⣿⠿⠠⠁⠒⠲⠄
⠀⠀⠀⠀⠀⠘⠁⠈⣭⢛⣧⢠⢑⣿⠷⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡘⢸⣇⣄⣀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⡏⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡏⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠐⠛⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⣿⣶⠀⢰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡀⠀⠀⠀⠀⠙⠃⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠽⠏⢻⢿⠊⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠉⡟⠛⢳⡀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⣿⣦⢾⣾⣿⠛⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⢾⣙⣿⡗⠀⣸⣟⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡸⣿⣆⠘⠙⢛⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣏⠉⠀⢁⣽⡟⠦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⢦⡸⣿⡄⠐⠁⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠍⠀⠺⡗⠆⠀⠀⠀⠀⠀⣠⣿⠦⣤⣷⠀⠀⣹⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠙⠉⠈⠉⠙

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡃⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠻⠏⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣶⣤⣴⣦⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⡟⠛⠉⠉⠀⠐⠻⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢶⣾⠛⠻⠿⠻⣿⣿⣿⠿⢿⡿⠟⠉⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠂⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠟⠉⠛⠛⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⡛⠃
⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⡿⠿⠿⠛⠉⠉

⠀⠀⠀⠀⠚⠒⠒⠶⠴⠄
⡤⠀⠀⠐⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣠⣤⣀⣀⣠⣤⣀⣤⣤⣀⠀⠶⢶⣶⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣠⣤⣾⣿⣿⡿⠟⣛⣯⣿⠟⣩⣵⣿⣿⣿⣿⣿⣿⣉⣛⠛⠿⣤⠉⠛⠋⠩⠿⠿⠒
⣶⣶⣶⣶⡶⢾⡿⠷⠾⢋⡶⠖⠖⠀⠀⠀⣤⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⠛⠉⣀⣴⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣶⣾⣿⣿⣿⣿
⠁⠀⠀⠀⠈⠈⠃⠀⠀⣠⣤⣠⣦⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢠⣾⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⡇⠀⢀⣤⣶⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠦⢹⡇⢳⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣸⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⡟⠋⠉
⠃⠀⣸⣿⣸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⡈⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡾⣿⣿⣿⣿⣿⣷⣿⡿⠖
⣿⢿⣿⣿⣧⣼⣿⣾⣿⣿⣿⣿⣿⣿⡿⢉⡀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣉⣉⡉⠉⠉⠉⠁
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠰⠀⠀⠀⠈⣿⣦⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠈⢻⣿⣞⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣽⡜⠋⢻⣿⡟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣤⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿
⣴⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠿⢿⠿⢷⣄⠀⠀⠀⠀⠀⠀⢤⡄⣈⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⡀⠀⡀⠀⠀⠈⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠂⠁⢀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣵⣦⡿⣿⣿⣿⣧⣄⣀⣐⡀⠀⣴⣶⣶⣶⣿⣿⣶⣿⣤⣤⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠐⠋⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠧⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠠⣶⡦⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠘⠛⠀⠀⠀⠀⠀⠀⠆⡰⡿⠃⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠆⠼⣠⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠦⣤⣅⠰⠒⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠲⠀⠀⠂⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠁
⠀⠀⠀⠀⠀⣀⠤⡍⠈⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢻⠉⠻⠂
⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠂⠸⠀⡈⡄
⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠈⠈⠁⠁
⠀⠀⠄⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠜⡁⠀⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠄⠀⡀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⢀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢤⠂⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⡁⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠁⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⡄⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢣⠀⠀⠀⠄⠀⠀⠀⢀⠋⠀⠀⠀⡘⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡔⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠘⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⡠⠀⠀⠀⠀⠘⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢀⠀⠀⢃⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⢐⢐⠀⠀⠀⢸⠀⠀⢴⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⢰⡟
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠻⢦⣀⣴⣤⡴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠛⠈⠁⠀⢀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠶⢤⣀⡀⠀⠀⠀⠀⠈⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢲⣦⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⣄⠀⠀⠀⣿⠀⠀⠀⠀⢠⡚⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡿⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠛⢦⣄⣿⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⣠⠟⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣶⣄⡀⠀⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⢀⣠⠴⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠈⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⢄⣀⣀⣀⣀⣀⣀⣀⡤⠤⠒⠚⠉⢀⡤⠖⠛⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡞⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⠖⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⢀⠀⠄⢸⠀⠀⠀⢀⡀⠀⠆⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⠀⠀⠀⠀⠈⠁⠀⢀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣤⣤⣀⣼⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⡏⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⡠⠂⠀⠀⠀⢸⠋⠑⢦⡀⠀⠀⠀⠀⠀⣸⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣇⠀⠀⢀⡴⠒⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠙⢦⡀⠀⢀⡼⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠓⠖⠋⠀⠀⠈⢣⡀⠀⢀⠴⠶⡄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀⠘⢆⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⡀⠀⠀⣀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠶⠋⠁⠀⠈
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⢀⡁⠀⠀⠠⠄⠠⠤⢀⠀⠀⠀⠀⠀⠀⡠⠶⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡒⠈⠁⠀⠀⠀⠙⠃⠐⠒⠀⠀⠀⠴⠀⠑⢄⠀⠀⠀⡞⠤⠂⠒⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⡐⠡⠈⠁⠀⠾⠆⠹⡀⠶⠄⢀⠶⠈⠋⠀⠀⠀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡜⡄⠀⣨⠃⠀⢀⡀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠀⠀⡀⠀⢀⠒⡂⠀⠴⡄
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣄⠀⠀⠀⣠⠐⣌⠂⠆⠚⣣⡈⠉⡀⠰⠆⠀⢃⠀⠀⠀⠀⠂⢸⠧⡈⢠⠀⠀⢁⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠄⠀⠀⢀⠁⠀⢀⣀⠀⠘⢵⣄⠉⠀⢹⠀⢒⠝⠁⠀⠀⠀⠠⡆⠀⠀⡆⠀⠀⠀⠀⠈⠃⠀⠁⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⢀⣄⠀⠙⢿⡆⠜⠀⠒⣰⠶⠚⢉⡁⠀⠀⣀⠀⡇⠀⠀⠀⠀⠀⠲⠠⠄⠈⠓
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠡⠀⠀⠀⡀⠁⠀⠀⠀⠙⡀⠀⠠⠁⠀⠀⠈⠁⠔⠀⠉⡐⣀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⢈⠀⠠⢀⣧⡄⠀⠀⠀⠀⠀⠐⠄⡀⠀⠈⠀⠰⠇⣀⠴⠀⣇⠀⠀⠰⠶⠀⢀⣠⡞⠁⠈⠉⠢⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⢻⠁⠂⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⡐⠀⢀⠌⠀⠀⠐⢄⠀⠄⠠⠀⠀⠀⢄⢠⣠⣴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡥⡄⠀⠀⠀⠀⠀⠀⠁⠂⠒⠛⠲⠀⢄⣉⣥⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠆⠀⠀⠀⢀⠌⠀⠀⠉⠐⠠⣄⠄⠀⠠⠀⠀⠀⢀⠂⠀⠁⠈⠛⠧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢠⠀⢀⣤⡂⠀⠀⠀⠀⢠⠎⠁⠀⣀⠄⠠⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠸⢇⠠⡀⠀⠀⠀⠸⡄⠒⠨⠀⢠⠀⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠑⢔⢄⡀⠀⠠⠐⠀⠠⣤⠄⢀⢰⡞
⠀⠀⠀⠀⠀⡐⠀⠀⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡇⠀⠀⠄⠀⠀⠀⠻⣉⠲⡄⣘⣓⣴⠀⠐⣤⠾⣀
⠀⠀⠀⠀⠀⠁⠀⠐⠢⠀⠀⢀⠊⠀⠐⢄⠀⠀⠀⣠⠀⠂⠁⠀⠀⠀⠐⠀⠀⠈⠑⡄⠀⠀⠈⠑⠲⠤⣀⡈⠒⠚⣁⣠⣤⠓⣄
⠀⠀⠀⠀⠀⠑⠀⡰⠀⡠⠀⠀⠀⠁⠀⠂⠀⠀⠀⠁⠀⠀⣨⠀⠠⠄⡀⠁⠐⢍⠉⠁⠀⠀⠀⠀⠀⠀⠀⢫⠉⠁⠀⠐⢆⠙⢄⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁⠀⢹⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠐⠒⢘⡄⠀⠉⠢⠄⢲⣤
⠀⠀⠀⠀⠀⠀⠀⠑⠐⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣁⣀⣀⣀⢵⡀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢨⠀⠀⠀⡀⠀⠡⡀
⠀⠀⣠⠴⠲⢦⡀⠀⠀⠀⠀⠐⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⣰⣄⠀⢀⣀⣀⠠⠞⢆
⠀⢰⠃⢴⣲⣀⣽⠤⡤⠶⢦⣤⠤⠴⠶⣷⠴⡿⠲⡶⠶⢤⣠⠴⠤⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣦⠀⣰⡀⠘⠮⠂⢉⠉⠉⠀⠴⠶⢅⠈⡆
⠀⠈⣧⣈⠙⠻⣿⠀⣴⢳⡄⢻⠀⣶⣆⣿⠐⡟⢀⡞⡆⢰⡇⢠⣶⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⢸⡉⠻⠽⠂⣸⠂⠻⠼⠁⣾⠀⡏⠉⣿⠈⡇⠀⡇⡇⠘⣇⠘⠿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠑⠲⠶⠚⢻⠀⣶⠒⠚⠛⠒⠃⠀⠛⠚⠛⠚⠃⠳⠶⣟⠙⣾⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀
⠀⠀⠀⠀⠀⠀⠸⠦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢻⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣾⠁⠀⠉⠉⢡⣿⣧⡴⠟⠛⠛⠟⠉⠈⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⡀⣀⣤⡶⠾⠛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣷⣶⣦⣤⣶⣤⣤⣤⣀⣀⣀⠀⣀⡀⣀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣿⣯⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠈⠛⠳⠛⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣿⣄⡀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣁⡽⢀⣀⠈⠛⣦⡴⠞⠋⠁⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣀⠀⠀⠠⡏⣹⠇⢀⡼⣧⣠⣤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⠀⣏⣈⡷⠀⠀⠉⠁⠀⠈⠓⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⢋⠀⠀⠉⡴⢤⡀⠠⡞⢳⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⣏⣹⠀⠀⠙⠦⠇⠀⠉⠉⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠈⠁⠀⠀⠀⣀⡤⣄⠀⢰⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡤⠇⠀⣞⣹⠆⠐⢧⡤⠏⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⣸⣷⡀⠀⠀⢁⣤⣄⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⣠⡾⠋⠀⠙⠷⢦⣼⡧⣾⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠸⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠛⠉⠻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣛⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠸⠀⠘⠀⠐⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢈⢩⡙⠘⠒⠁⠀⠀⠆⠈⠀⠀⠁⠁⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⣄⠢⡑⠀⠀⢠⠀⠀⠀⠂⠈⠀⠀⡆⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠩⡥⠀⠀⠀⠀⠁⢈⠀⠀⠸⡀⠀⠀⠀⢣⠀⠡⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣁⣨⠀⠀⢄⢡⠀⠀⢕⢄⣇⠀⣁⠀⠄⠑⣇⠠⠀⠀⠀⢀⠂⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢀⠔⠼⠢⠠⠀⠊⠀⢣⠀⠀⠦⢻⢀⢀⠠⠌⠦⠧⢀⠀⠀⠀⠀⠀⡠⠜⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⢲⠒⣦⣀⠀⠒⠐⣬⠡⡆⢤⡾⢠⣌⣒⣐⣒⠶⡊⠭⠩⠉⣁⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⠒⠒⠳⠤⠤⠜⠋⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠠⠀⢀⡀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢂⠀⠁⠀⠀⠐⠀⡰⠂⠀⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠤⢀⡀⡑⢄⠀⠀⠈⠹⠀⠀⠀⠀⡏⠁⠀⠀⢀
⠀⡎⠀⢴⡁⠉⠉⠉⢇⣀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠈⠀⠈⠀⠀⡀⠉⡀⠀⢀⡀⠁⢠⠀⠀⣠
⠀⠈⠒⠤⠤⣀⡴⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠰⠤⠄⠀⠀⠠⡚⠀⠀⠠⢀⠁⡀⠉⠁⢠⠀⠀⠈⠐⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠧⢄⣀⠴⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠛⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠉⢣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⡐⠀⠙⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡅⠁⠀⠈⠃⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠰⢆⠀⠠⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣨⠔⠚⣁⢐⡉⠀⠀⢼⢯⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠲⠊⠀⠀⢀⠀⠠⠀⣡⣿⣀⠃⠱⢦⠄⠀⠰⡦⢠⣀⠶⠘⠃⠀⠀⠀⠀⠀⠀⢱⠈⡅⠐⣪⠴⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⣠⠿⠁⠀⠈⡧⠀⠀⠁⠀⠀⠀⢈⠀⠀⠀⠐⢀⠄⢁⠀⠄⠀⠀⢁⠐⢁⠑⠄⢠⡀⡠⢎
⠀⠀⠀⠀⡀⠶⡄⠀⠀⡀⠄⠒⠛⠀⠰⣶⠦⠕⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠠⣈⠀⣁⠀⠀⠄⠀⠊⠀⠈⢡⠌⠠⠁
⠀⠠⡤⠤⣤⠄⠀⠀⣠⢤⣠⠇⠉⣡⠀⢀⣥⠃⠀⠀⠀⠀⠀⠀⠆⠄⠁⠀⠥⠀⠂⠀⠀⠀⠄⠀⠀⠠⠈⠁⠀⠀⠁
⠀⠁⡀⠀⠀⢠⡄⡈⠂⠌⢄⠀⠈⠉⠀⠉⠙⠂⠀⠀⢤⣠⠤⠔⠀⠀⠀⠀⠀⠑⠂⡄⢀⠀⢐⠄⠀⠀⠄
⠀⠀⠒⠠⠍⠂⠀⠀⠀⠀⠁⠀⣀⠄⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣶⡎⢲⣿⣷⣮⠭⢗⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣖⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠈⣀⠤⠀⠀⠀⠀⠈⠛⣷⠖⢚⡹⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠒⠲⡞⠀⠀⠀⠀⠀⠀⠉⢧⣄⣀⣠⠀⠀⠂⠸⢆⣀⠚⢉⠉⡀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠓⠣⠤⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠭⠛⢋⠁⢠⡡⢀⠀⠀⠀⠤⢁⡲⠄⠠⠰⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⡀⠀⠙⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡑⠂⠐⠈⢣⠊⠒⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⠛⠛⠛⠶⣾⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⡀⠑⠀⠀⠀⠀⠀⠰⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⢈⡐⠄⠅⠀⠀⠀⢀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠐⠀⠀⠀⠀⠀⢀⠰⡉⠙⠂⠈⠗⠁⡠⠄⠀⠀⢲⠶⣤⣑⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢨⠀⠀⠀⣀⠤⣰⠁⢄⠄⠑⠄⠗⠚⠉⠀⠀⠀⠀⣸⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠠⠃⠀⠀⡜⠁⢀⢜⠧⢠⢸⠐⢊⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢆⠀⠈⠁⣠⠎⠁⠀⢀⡀⠀⠈⠀⠀⣠⡟
⠀⢠⡴⢒⠒⠶⠶⠴⠋⠁⠀⢢⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠠⡏⠈⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠹⣦⡀⠁⠉⠙⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⡴⠞⠋
⠀⠀⢨⡇⠀⠀⠈⠂⡑⠁⠀⠀⠀⣿⠙⠓⠲⠶⠶⠶⠚⠋⠉
⠀⠀⠈⢷⡀⠀⠀⠀⡄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠉⠛⢶⡄⢇⡘⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣾⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠐⠀⠀⠀⠙⠁⠀⠀⠀⠀⡀⠀⠁⠁⠄⠀⠀⠀⠠⡇
⠀⠀⠀⠀⢻⣿⣡⣹⡿⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠁⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠈⠛⠛⠛⠇⠀⠀⠀⢀⡸⠃⠀⡌⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠁⠀⠀⠾⠏⠀⠀⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠳
⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⠠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢠⡎⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠡⠣⠀⠀⠀⢸⠼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡴
⠀⠀⠀⡞⣲⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⠀⠀⠀⠐⠆⠀⡀⠀⡏
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⢈⡌⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠠⠶
⠀⠀⠀⠀⠰⠆⠛⣀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉
⠀⣠⠛⢠⣄⡐⠀⣉⠀⣀⠈⠁⠀⠀⡀⢀⠀⠀⠐⠀⢈⢿⣷⠐⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⢀⡀⠀⠓⠜⠀⡐⠃
⠀⠈⣀⢀⠈⠁⡀⠉⠶⠉⣀⠀⠐⠂⠁⠈⠐⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡷⠈
⠀⠀⠉⠀⢠⡐⠃⠘⡃⢂⡉⠀⠀⠀⠄⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⢰⠔⠁⠀⢀⠀⠀⠀⡐⢁⠠⠺
⠀⠀⠰⠆⠦⢠⡌⠂⠀⣬⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡤⠼⠉⠉⠀⠀⠀⠀⠐⠄⠀⠃⠁⠀⠀⢰
⠀⠀⠛⠀⣀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠈⠀⠋⠀⠀⠀⢲⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⢐⣶⠾⣿⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠆⠀⠀⠐⠀⠀⠀⠈⢎⡗⠀⠀⠀⠈⠀⠀⠀⠀⠀⠜⠳⣶⠟⠑⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡜⠃⣤⡄⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠂⠀⡀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⣆⠐⠀⠀⠀⠀⠀⢀⣠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠛⢠⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⡿⠋⠀⠀⠀⠀⠛⠛⠿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⡐⠈⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⠟⠁⠀⠀⢀⣼⣿⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣄⠒⢿⣿⣿⣿⠟⠂⠀⠙⠁⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠷⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠁⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠲⡄
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⡸⢭⣙⣳⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢢⡀⠀⠀⠀⠀⠀⢸⠤⠖⠤⢾
⠀⠀⠀⠀⠀⠀⠀⢻⢮⣑⡏⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⡇⠀⠀⠀⠀⢸⡀⣀⠀⢀⡀⢈⠆⠀⠀⠀⠀⣏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⣷⡼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⢹⠁⠀⠀⠀⠀⠀⠙⣄⣍⣡⡸⠁⠀⠀⠀⠀⠀⠈⠓⡖⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣴⡁⣹⡀⠀⠀⠀⠀⠀⢠⠞⠓⠛⢤⠗⠀⠀⠀⠀⠀⠀⣀⣟⣆⡀
⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠙⠦⡀⠀⠀⢠⠞⠓⠒⠛⠓⢛⡆⠀⠀⠀⠀⢮⣀⣀⣀⣼⠄⠀⠀⠀⠀⠀⢸⠶⠤⠤⢧
⠀⠀⠀⠀⠈⠻⣍⣑⣉⣉⣊⣩⠗⠁⠀⠀⢸⠟⠛⠛⠛⣛⣛⡇⠀⠀⠀⠀⠀⢣⣶⣶⠃⠀⠀⠀⠀⠀⠺⢍⣛⣛⣛⡩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡇⣃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⢀⢔⡒⣒⠢⡀⠀⠀⠀⠀⠀⢀⡤⠒⠢⢤⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⢠⢊⡩⣍⠲⡄⠘⡄⠀⠀⠀⠀⡇⡏⣞⠶⡱⣱⠀⠀⠀⠀⠀⣏⢀⡀⢀⠀⣱⠀⠀⠀⠀⠀⣺⣿⣽⣽⣿⡇
⠀⠀⠀⠀⠀⢤⢸⠰⣀⡧⢸⣀⠇⠀⠀⠀⠀⠱⣕⣮⣭⠷⠋⠀⠀⠀⠀⠸⡍⣿⢹⡏⡿⢸⠇⠀⠀⠀⠀⣿⣿⣯⣭⣽⡇
⠀⠀⠀⠀⠀⠈⠣⣳⣬⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⢳⣻⣸⣧⣇⡟⠀⠀⠀⠀⠀⣗⣀⣈⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡉⢢⠀⠀⠀⠀⠀⠀⠀⣠⡼⣝⢢⡀⠀⠀⠀⠀⠀⢺⢀⣀⡅⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⢸⠁⠏⠀⢀⠀⠈⡆⠀⠀⠀⠀⢠⠞⡄⢣⢸⠋⠁⠀⠀⠀⠀⢎⡉⠀⠈⢋⡱⠀⠀⠀⢀⡾⡀⢣⠀⣰⢃⡼⡆
⠀⠀⠀⠀⠀⠘⢄⣀⠀⢀⣁⡼⠁⠀⠀⠀⠘⣍⠢⡵⠜⠁⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠻⡀⠀⠀⠀⠀⠳⢼⠍⠉⠉⣽⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠋⠙⠦⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⢀⣦⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠀⠀⠀⢀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⡄⢀⠀⣶⡧⠀⠀⢀⣿⣿⠟⢳⣄
⠀⠀⠀⠀⠀⠀⠐⡾⢁⠀⠀⠀⠀⠀⠀⢰⢋⠉⠀⠀⠀⢰⡀⡀⠀⠀⣤⠏⠓⡂⠀⠀⠀⠠⣗⢚⡄⢉⠃⡀⠐⢩⣿⣷⡖⠁⠛⢃
⠀⠀⠀⠀⠀⠀⢀⡷⢻⠀⠀⠀⠀⠀⣰⠿⠟⠀⠀⠀⠀⠤⠓⠃⡀⠀⢠⡄⠘⠟⢀⡄⠀⠀⣻⢼⡃⠀⠰⠀⡘⣿⡟⠉⠀⣀⡴⣿⡀⢀⡄
⠀⠀⠀⢀⢀⣰⣿⣃⣀⠁⢠⡄⠀⢀⣁⡄⠀⠀⠐⢶⠀⢼⠃⣿⠁⣶⠈⠁⢀⣀⠀⢳⡴⠞⠓⠐⠛⠦⣄⠀⠈⠛⣡⡶⠛⠁⠠⠸⠃⢀⡧⡀
⠀⠀⡰⠀⢼⣿⡿⢅⣠⡀⡨⢦⡀⠸⡿⠃⣀⡀⣿⡿⠀⣾⠶⣿⠀⠉⠠⣦⣾⡟⢲⣿⣤⣤⣤⡤⠤⠶⠞⣛⡀⢞⠙⡾⠀⣠⠶⠁⢀⣼⠄⢷⡀
⠀⠀⢧⠸⣿⣀⢶⡎⠀⢈⠃⠄⡇⡆⠈⠐⠿⠷⠈⠁⠸⠁⠀⠸⣧⠀⠠⠃⠘⠃⣾⣤⣤⣠⣤⣀⣤⢠⡶⣿⡧⠈⢢⡿⠋⢀⠄⠀⢀⣅⠀⢠⣅
⠀⠀⠘⡇⣾⣽⣔⢑⣄⣡⢈⣤⡠⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢻⣄⠀⠀⠀⠀⠹⣿⣼⡷⣦⡿⠴⠌⠿⣾⠃⠀⠀⠁⢴⠉⠀⠀⣸⣄⣀⣀⣸⣆
⠀⠀⠀⠈⠻⢿⣿⠿⠤⠀⠉⠞⠁⠀⠀⢀⣼⣤⣀⣀⡄⠀⠀⠀⢸⡟⢀⠀⠀⢀⠄⠙⠳⣶⠶⠶⠖⣲⡞⠋⠀⠀⠀⠀⠀⠀⣀⣼⣯⣥⣤⣤⣤⣽⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠉⢡⡀⠀⠀⣼⠁⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠟⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠋⠙⠒⠀⢿⡀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⢐⠃⠀⢀⠠⡀⠄⡀⡀⠀⢠⠀⠀⡄⡄⡀⢀⠀⡄⠠⢀⣠⣀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠰⠸⠁⠘⠀⠃⠘⢘⠁⠀⠠⠀⠀⠁⠀⠁⠈⠀⠅⠆⠘⠈⠀⠐⠸⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠖⢪⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠳⡜⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠗⠀⠀⠀⠛⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⡜⠀⠀⠀⠀⠀⢺⣿⣿⣿⠇⠀⠀⠀⢰⡐⠐⢠⡆⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⡆
⠀⣠⠔⠳⢤⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠱⣤⠊⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⠤⠓⠤⡀
⣰⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⡇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⢇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢠
⢸⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡸
⠀⢣⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠈⢣⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠱⣄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠸⡗⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡏⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠄⠀⢹⠳⠒⠦⠤⠤⠤⠤⠴⡖⡏⠉⢠⠾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⢃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢀⣆⠀⠀⠀⠀⠀⠀⠀⣬⡬⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢰⠆⠙⣆⠀⠀⠀⠀⠀⡼⠃⢸⡄⠙⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢷⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢤⡀⠀⢌⠀⠌⣀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠠⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠑⢐⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⡄⠀⠀⠀⠀⡠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠀⠀⢱⠀⠀⠀⠀⢠⠁⡀⠈⠁⠀⠀⠀⢀⠀⠀⠒⠁⠀⠀⠂⠉⡔⠀⠀⠀⠈⣇⣀⡀⠀⢀⢕⠛⠀⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠔⠀⠈⠐⠆⠤⠐⡀⡁⠐⠆⠀⠀⠀⠀⠘⠀⠀⠸⡄⠀⠀⠓⢄⠁⢀⠀⠀⠀⠸⠀⢀⠴⡁⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣤⠀⠈⠦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣕⢀⠀⠀⢲⠀⠀⠀⠀⠈⠡⠃⠈
⠀⠀⠀⠀⠀⠠⢄⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠐⠈⠖⠀⠀⠀⠠⠈⠐⢅⡢⢘⡀⠀⠀⠀⠀⡇⡸⠤⠀⠀⠢
⠀⠀⠀⢀⣄⡈⠈⠀⠀⣈⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠔⠀⠀⠀⠀⢀⡜⠉⠈⠉⠻⠑⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠉⠓⡰⡀⠀⠀⠀⠀⢀⠌⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠑⠄⠀⡜⠸
⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢂⠀⡇⠀⠀⠀⠀⠀⣀⠀⠡⢄⡀⠈⠑
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢉⠈⠌⣁⣀⣐⣊⣄⣀⠀⠀⠀⠀⠀⠐⠀⠄⠊⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⠰⠄⠀⣀⠀⠙⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡌⠈⠀⠀⠈⢉⠁⠀⠈⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠒⠀⠠⢄⠀⠀⡆⠀⠈⠂⠀⠀⡆⠀⠀⠀⠀⠀⠰⠀⠀⠄⠀⢰⠀⠧⠀⢠
⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠤⠄⠀⡀⠀⡁⠀⠡⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣨
⠀⠀⠀⠀⠀⡀⠅⡠⠄⠐⠀⠀⢀⡈⠋⠀⠀⠀⠠⡄⠀⠂⠀⠀⠀⠈⠙⠄⠀⠀⠀⠠⡄⠀⠹⡀⠀⠀⢀⡀⠄⠐⠂⠀⠐⠀⠦⡀
⠀⠀⠀⠀⠀⡇⠹⠀⠨⠂⠀⠀⠀⠀⠓⡀⠀⠁⠀⠀⠀⠰⠉⠈⠑⠀⠀⠀⠀⠀⠀⢸⠈⠄⠀⠐⠂⠀⠀⠀⠀⡠⠀⠒⠀⠄⢀⠄
⠀⠀⠀⠀⠀⢡⡀⠀⠀⢠⠋⠐⠄⠀⠀⡥⠀⠂⠀⠀⠀⠘⠀⠄⠊⠀⢀⡄⠀⡀⠀⠘⠀⠈⢄⠀⠀⠀⠀⠀⠌⠀⢀⠠⠤⠄
⠀⠀⠀⠢⠀⠀⠑⠒⠖⠉⠀⠈⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠤⡀⠀⠘⠄⠀⠀⠁⠀⠰⠀⠀⠀⢂⠀⠀⢀⠀⡄⠀⠘⠄⢀⠀⠈⠣
⠀⠀⠀⠀⠡⠀⠀⠁⠃⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢄⠀⠀⠢⡀⠁⠀⠁⠀⣀⣀⣀⡁⠰⠁⠀⠐⠄⠀⠀⠐⠀⠀⠦
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠑⠄⠀⠔⠀⣀⠐⠁⠀⠀⠀⠈⠑⢔⠄⡀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠊⠀⡀⢀⡄⠀⠀⡤⠤⠆⠀⠤⣤⢀⠄⠀⠀⠀⢰⠁⠁⠀⠉⠉⠁⠐⠒⠒⠚⠶⢤⠉⠀⠀⢁⡀⠀⠐⠠⠐
⠀⠀⠀⠀⢠⠀⢠⡀⡀⠀⠂⠀⠀⠈⢂⠢⣀⠁⠀⠀⠀⠀⠅⠀⠉⠄⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢂⠀⠇⠃⡈⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⢀⡀⠨⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⣢⢸⡤⡀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠁⠀⠌⡇⠀⠀⠀⠀⠀⠤⠒⠃⠀⠤⡢⡀⠀⠀⢠⠀⠀⠀⠀⠀⡤⠄⡐⣒⣈⡉⠤⠄⠇
⠀⠀⠀⠀⢠⣊⠐⣁⡀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠒⠀⠁⠀⠀⢔⠈⠁⠈⠉⠀⠀⠀⠈⠪⢗⡤⠜⠀⠀⠀⠀⠀⠉⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡉⣆⡀
⠀⠀⠀⠀⠀⠀⠀⡠⣤⠤⣴⣷⣏⣴⢗⡄⠀⠀⠀⣀⠤⠤⠤⠇⠀⠀⠐⢢⠀⠀⠀⢀⣠⠤⢤⢼⠑⠀⠨⢳⡄
⠀⠀⠀⠀⠀⣴⠋⡔⢁⠞⢀⠼⡛⠓⠉⠀⠀⢠⠊⠀⠀⠀⠀⠀⡗⠒⠂⠁⠀⢀⡔⠫⢐⠠⢀⠀⢸⠒⠛⠈
⠀⠀⠀⠀⣸⠃⡜⡰⠃⡠⢋⡼⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⣜⠀⠈⠐⠨⢐⠀⡾
⠀⠠⢔⣶⢿⣜⣰⠁⣔⣡⠟⠁⠀⢀⠄⠒⠚⠂⡀⠀⠀⣀⡴⠋⠀⠀⣠⠰⢖⠳⡨⢀⢐⢨⡰⠟
⠀⠙⢵⠁⡜⡿⠉⠉⠉⠀⠀⠀⠀⠈⠢⠀⠀⢀⠏⠉⠉⠀⠀⠀⠀⠀⠓⣌⠐⡐⡎⠉⠉⠁
⠀⠀⠈⠙⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠀⠈⠢⣄⠈⠉⠓⠲⢄⡀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠙⢦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⣀⠀⠀⠀⠀⠀⡟⠓⠢⠤⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣠⠖⠒⠛⠉⠉⠉⠉⠉⠉⢹⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢚⠇⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠉⠒⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠢⣉⠒⠲⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⡀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡤⠞⠁




⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡆⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⣆⢀
⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⢰⣦⣺⣞⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣟⣿⣢⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣻⣿⣷⣄⡀⠀⣀⣴⣿⣿⣻⣿⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⠋⠀⠈⠊⠀⠈⢻⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠟⣿⡿⣿⣦⡀⠀⠀⠀⣠⣾⡿⣿⡿⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣦⣠⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠂⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢯⢣⠈⢻⣄⠀⣀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡀⠀⠣⡑⣄⠹⡏⠀⠀⠀⠀⠀⠀⡴⣺⣛⠻⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠁⠀⠈⠁⠀⠀⠈⠪⡵⠁⠀⠀⠀⠀⠀⠈⠘⢐⡠⡁⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⡀⠋⠀⠀⡤⠀⠀⠙⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠽⢑⣫⣷⠶⠮⡙⢦
⠀⠀⠀⠀⠀⠀⣀⣀⠨⣧⠈⢗⡄⠀⡀⠀⠀⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡠⡤⡀⡀⡼⡄
⠀⠀⠀⠀⠰⢍⠀⠀⠀⠈⢷⣀⠪⣒⣏⠔⠊⠀⠀⠀⠀⠀⠀⡀⠠⠠⢀⠀⠀⣄⣀⣀⠀⠓⣬⡥⠞⠋⡠
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⢀⠟⠓⠉⠀⠀⢀⠔⠈⠀⠀⠀⠈⠀⠘⠛⠖⠀⠄⠠⠄⣀⣀⣀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢈⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⣀⡥⣐⣂⠄⠶⢦⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁⠀⠀⠀⠀⠀⣀⠄⠂
⠀⠀⠀⠀⠰⠚⠉⠃⠀⠀⠀⡀⢀⠀⢷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡠⠂⠀⠀⢠⠖⠭⣀
⠀⠀⠀⠀⠀⣀⠠⠼⠖⠒⠈⢁⠀⠀⢸⡆⠀⠀⠀⠑⢄⠀⠀⠀⡠⠊⠀⠀⠀⡠⠁⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⢁⠀⢀⣡⠠⠤⠘⣆⠀⠩⣦⠀⠀⠀⠀⠀⠁⠲⠊⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠈⠯⠀⠠⠖⠉⠓⠁⢀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠀⠀⠀⠀⢀⣀⠀⠄⠐⠀⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⠁⡌
⠀⠀⠀⠀⠀⠀⠈⡀⢀⡀⠄⠄⠄⠂⠈⠂⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠠⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⡰⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⢛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠆⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣠⣾⣿⣿⡟⢀⡀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⣀⢀⡀⢀⣩⣭⣍⡛⠀⠀⠉⠉⢉⣉⣙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠙⠋⠁⢀⣼⣿⣿⣿⣿⣧⣿⣿⣿⣿⣻⣿⣠⣶⣷⣶⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣷⣦⣬⡙⠛⠻⠿⠿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿
⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣁⠿⣿⡬⢙⠋⣹⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿
⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠋⢹⡦⢬⡤⠟⡷⢃⣼⣻⣿⣿⣿⣋⡁⠀⠀⠈⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢹⣿
⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢧⡌⠉⠀⠈⠛⢠⡤⢖⣪⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⣻
⣿⣿⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠻⠇⣠⢤⠀⣀⣸⣷⣿⣿⣿⣿⡿⠉⠛⠛⠛⠋⠙⠛⠁⡀⠿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⣿⡃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⢀⣞⣿⣦⡜⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣷⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠸⡿⠟⠛⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⡟⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣦⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣧⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠛⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿
⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⡿⣃⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣉⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠟⠋⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣄⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⣀
⠀⠀⢀⡀⠠⠓⡀⠀⠀⠄⠀⠦⠊⠛⢲⠤⠀⢀⣀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡴⠛⠉⠋⠀⠄⠀⣐⠐⢀
⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠟⠁⠓⠘⠇⠘⠋⢲⠞⠒⠁⠾⠁⠠⠈⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣸⠟⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠅⠀⠉⠒⠂⠀⠰⠀⠀⢠⠤⠀⠦⠀⠀⠀⠴⠂⢤⠄⠀⠚⠁⠘⠉⠉⠁⠀⢀⠀⠀⠁⠀⢸⢥
⠀⠀⠀⠀⠀⠐⠀⠀⠚⠠⡬⠑⠀⠸⠗⠀⢈⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠥
⠀⢀⣀⣤⣄⡤⠀⠂⠀⠈⠀⠀⠀⢀⠀⠀⠀⠉⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠫⡄⠀⠐⠂⠀⠲⠌⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠌⠀⠀⢄⠘⢁⠀⠀⠘⠁
⠀⠀⠀⡐⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡐⣒⠀⠀⠂⢀⡀⠀⡄⢸⡆⡀⠀⢄⠈⠉⠀⠀⢀⡴⠀⠨⠀⠀⠀⠀⠇⠀⠀⠀⣠⡄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⡀⠄⠀⡔⡷⠀⠯⠼⣧⢼⢦⠼⠷⠄⠀⠀⡖⠀⠀⠀⠀⠐⠀⠀⠚⠂⢠⠀⠈⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠎⠀⠃⠞⠚⠀⠀⠂⡇⠀⠀⠀⠀⠀⡄⠀⠀⢠⡀⢠⠀⠀⠀⢀⠆
⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢖⡦⢀⢻⠀⢾⡘⠺⠈⢿⡚⠊⠓⡆⠀⠋⠀⠈⠀⠀⠀⠀⠀⠠⠈⠘
⠀⠀⡀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⡀⠛⢀⡓⠀⣉⠀⠋⠁⢂⡑⠷⠀⠀⠆⠀⠂⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢨⠅⠀⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⡀⣠⠀⠀⠀⢠⡄⠀⠙⣓⠃⣼⠃⠠⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡾⠀⠦⡀⠀⠠⠄⠀⠀⢀⣀⣀⡀⠀⠀⠐⠊⠛⠀⠀⠀⠈⠀⠠⢀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠂⠀⠀⠂⠀⠚⠋⠀⠀⠀⠀⠈⠀⠝⠲⢤⣉⣀⡀⠀⠉⠀⡀⠀⠄⠐⢊⠠⠸⢀⡀⠀⠀⠀⣀
⠀⠀⠀⣮⢧⢆⣄⠀⠀⠀⠀⠀⠀⠈⠫⠉⠁⠀⠐⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⢀⠠⠀⠄
⠀⠀⠀⠁⠁⠀⠁⢐⢄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣼⡃⠠⠠⠀⠀⠀⠀⠀⠘⢞⡛⣭⡴⣄⣶⠀⠀⠄⠀⠨⠀⠀⡆⢸⠀⡆⡆
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠳⣧⣾⣗⣻⡇⡮⠀⠄⠠⠸⠀⠀⠛⠘⠀⠃⠃
⠀⠀⠀⠠⠄⠐⠆⠠⠤⠀⠀⠢⣀⠀⠆⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠷⠍⠗⠀⢦⡤⢲⡀⠠⣆⠀⠀⠄⠲
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠙⡇⠀⠀⢤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⠀⡀⠀⠀⠀⠛⠀⠀⠲⠄⠀⠀⢀⡤⠘⣷⠀⠀⠀⢀⠀⠀⠠⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠾⠛⠛⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠛⣳
⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠛⠛⠛⠛⠛⠛⠷⣦⣀⠀⠀⠀⠀⣀⣠⣼⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡄⢰⢏⡴⠛⠉
⠀⢿⣯⣩⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠀⠀⢀⣠⣽⠿⠟⠛⠋⠉⠉⠁⠈⡴⢇⡄⠀⠀⠀⠀⠀⠀⠀⠘⣡⡴⢿⠀⠀⢸⡇
⠀⠀⠈⠉⠻⣷⣶⠶⢀⣀⣀⣀⠀⠀⢻⡀⠀⣸⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⢗⡀⠀⠀⠀⠀⠀⣰⣿⣿⢟⡾⠀⢸⡇
⠀⠀⠀⠀⠀⠙⢿⣿⢛⣉⣡⡤⠀⠀⢀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⣀⠀⠀⠀⠀⠉⠀⠀⠋⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣥⠄⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠩⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢛⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⢾⣧⣰⣦⠀⣦⠀⠀⢀⡄⢀⡀⠀⠀⠸⣧
⠀⠀⠀⣼⠃⠘⠁⠛⠖⠴⠠⠀⠀⠀⠀⠀⠀⢀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣾⣿⢰⡟⢸⡇⢸⡇⢸⡇⠀⣿
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⣾⡇⢸⡇⢸⡇⠀⢹
⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣄⡀⠀⠀⣰⡿⠋⠻⠿⢿⣼⣧⠀⢸
⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣵⣿⣿⣴⡷⣰⡿⠁⠀⠀⠀⠀⠈⠙⠓⠋
⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⣫⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠿⣾⡿⣷⣤⣀⣀⣀⣀⠀⠀⠰⢦⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠈⠉⠛⠛⠛⢿⣿⣟⠳⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠌⠉⣉⣽⣿⡿⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠉⠙⢷⣤⡀⠀⠀⠀⠀⣴⣾⡷⠶⠛⠛⠛⠾⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣷⢸⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏

⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠔⠉⣀⡤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠐⠒⠒
⠀⠀⡇⠀⠊⡇⠀⣰⠴⢺⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡰⠀⠀⠉⠉⢉
⠀⠀⢴⠀⢀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⡀⢀⣠⡠⠆⣰⠁⠈⠀⠀⠀⠀⡼⠂⢤⠇⡀⢀⢀⡴⠁⠠⠄⠀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡰⡆⣳⡟⠸⠱⡤⠃⠀⠘⠂⠀⠀⠠⠁⠀⡞⠰⠀⢈⡏⣠⠞⡤⠒⣠⠊⠈⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⠤⢤⡄⢠⠀⡆⢸⠇⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠀⢞⡥⠂⡠⢆
⠀⠀⠀⠀⢰⣇⣀⣀⣀⠸⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠠⠉⠙⡖⢁⡤⠊⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠛⠋⠤
⠀⠀⠀⠀⣤⠂⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠋⠉⠙⠛⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠛⠋⠉⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢷⣄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣴⣿⡿⠛⠛⠛⠿⠿⢿⣶⣦⣄⣀⠀⢀⣴⣿⠏⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠋⠁⢀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⡏⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣹⣿⡿⠶⢶⣶⣶⣶⣶⣶⠾⠿⠛⠁
⠀⠀⠀⠘⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⡿⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⣰⣿⠋
⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣀⣠⣴⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣋⣁⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛
⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⠛⠋⠉⠁⠀⠀⢀⣀⣠⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⢿⣿⣿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉




⣿⣿⣿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢤⣴⣶⡚⠭⠡⠃⠒⠂⠄⡀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢒⣚⣭⠴⢒⣋⠉⣁⠽⣬⣼⣅⣒⠀⠀⠀⡁⠀⢀⣾⡿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⣶⣲⡿⠿⡿⠿⢟⣛⡿⢷⣶⣚⣩⠶⢋⡵⢊⡕⣠⢟⣦⣁⢛⢸⠁⠠⣾⣿⣿⣾⣿⣿⠷⣒⡦
⠀⢀⡠⢔⣒⡩⠽⢚⡊⠥⠐⣀⡡⠴⢛⣫⡽⠖⣫⠔⢋⡽⡋⠿⣐⣯⣞⡵⣋⣴⡟⣿⠸⡀⠀⢿⣥⡟⣯⣡⣤⡾⠋
⢓⡞⡚⡩⠠⠖⣊⣉⡤⠔⣛⠉⠀⢔⠋⢁⢐⡋⠀⠖⠫⡠⢊⠔⢉⡤⠙⣟⣥⡞⢁⠘⢻⡟⢃⣛⣿⣯⣿⣿⠃⠀⢄
⠀⠉⠀⠋⠉⠈⠀⠈⠈⠉⠀⠈⠁⠀⠀⠈⠉⠀⠉⠁⠀⠁⠈⠈⠃⠀⢀⠀⠒⠚⣏⣼⣼⢴⣿⣯⣼⡥⣸⠃⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⡊⠄⡴⣱⠞⣵⣿⠟⣹⠿⢿⡓⠁⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀⠀⠀⠀⠜⢡⠞⡵⢅⡜⠁⣈⡝⢇⣰⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠓⠒⡶⣖⡥⠄⠀⠉⠉⣻⣿⡲⡤⣦⣼⡵⠵⠞⢛⣣⣼⣯⠞⠓⡿⠀⠐⣀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠔⢊⠁⠀⠁⠀⠀⠀⠀⢀⢙⡿⣃⠂⢁⠨⠁⠀⢁⣾⣏⡉⠁⠪⣤⣝⡞⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣾⠟⠡⠐⠁⠰⢡⢠⢤⣄⠌⢡⣬⠛⠛⢛⡁⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢞⠩⢊⠞⢁⣴⣥⠤⠚⣠⠪⡠⡠⢫⠔⠀⣀⢠⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣤⠅⠪⠳⠊⠅⠈⠳⠄⠀⠉⠓⠛⠋⠁⠀⢞⡵⠎⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠁⠀⠠⠀⠀⠀⠔⠉⠼⠡⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⡀⢈⡥⠶⠊⡁⠄⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⠫⠝⠻⢀⡤⠊⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡁⠀⠀⣀⡔⠈⠒⠤⢀⣀⡠⠄⠒⠀⠚⠋⠠⡤⠤⡀⠏⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⠑⠢⠀⠀⠈⢉⠥⠀⣄⣀⢀⡀⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⢤⣀⣈⠀⣂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠉⢱⠀⡌⠉⠉⠁⢀⣠⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⣐⡊⠅⠈⠑⠇⠀⢀⣀⠠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠀⢒⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢆

⠀⠀⠀⠘⣧⡀⠀⠀⠀⢠⣤⢲⡴⣲⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠂
⠀⠀⠀⠢⢡⠐⢤⠀⠀⠘⣿⡾⠞⠁⠀⠀⢀⣀⣀⣀⣀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⣀⠀⠀⠈⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆
⠀⠀⠑⢄⠘⠆⠀⠀⢀⡔⢩⠀⠀⠀⠀⠐⠛⢢⡤⠀⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠰⢃⠀⠀⠀⣴⣾⠀⣾⡿
⠀⠀⡀⠈⠁⠀⢀⡴⠣⡈⣿⠀⠀⠀⠀⠀⠚⠃⠒⠒⠀⠤⠅⢀⣤⠀⠉⠁⠀⠒⠠⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠒⢾⣏⣩⠟⠃⠀⠙⠁
⠀⠀⠀⠀⢀⡴⣋⠐⢄⠘⣿⠀⠀⢀⣀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠢⠀⠀⠈⠲⣄⠀⠀⠟⠁⠉⠛⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⡀
⠀⠀⢀⡴⠋⠠⣌⠱⣄⢳⡏⠀⠀⢙⣞⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢁⠀⣤⠌⣢⡀⠀⠀⠀⠀⡀⠀⢤⣞⠓⠀⠈⡿⠇⠠⠅
⠀⢰⡟⠒⠚⠦⣌⣆⠘⣎⡇⠀⠀⢸⠹⣆⣰⠋⣿⠀⠀⠀⣞⡦⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡄⠈⠓⠀⢀⡤⠀⢠⠜⠉⠻⣀⣀⣠⠇
⠀⠀⠙⠦⣄⣀⠀⠉⠳⣿⠇⠀⠀⢸⠀⠙⠃⠀⣿⠴⠚⣹⠋⠀⢴⣏⠩⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡤⠖⠉⠄⠀⠀⢀⣀⢀⣀⣬⠁⠐⢄⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⣿⠭⠭⢭⣛⠲⢤⣠⠏⠀⠀⠀⠾⠋⡜⠑⢩⡟⢛⢶⠲⡶⢶⡶⡖⡻⣏⢹⠙⣄⢰⠺⠆⠀⠈⠒⠚⠲⠀⠀⠀⢰⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠲⣖⣶⣬⡙⢶⠋⢀⡤⠤⣄⠀⠀⠙⠚⠁⣷⠃⢸⣠⣀⡌⢧⠀⡇⠈⠺⠀⠈⠛⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠸⢆⠄
⠀⠀⠀⢴⠶⠒⠒⠒⢒⡶⠖⢦⠀⠀⠉⠒⠾⠭⠿⠃⢠⠏⡴⠶⣌⢳⠀⠀⠀⣀⣤⣄⡈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠐⡧⠀⣤⣀
⠀⠀⠀⠈⠳⣄⠀⠀⣾⡩⠽⠾⠦⣄⠀⠀⠀⢀⣀⠀⠸⡜⡇⠀⠈⢧⡇⢀⣾⠟⠒⢆⢻⠀⠀⠀⢰⣆⠀⠀⠀⢸⠁⠟⠁⠀⢠⠖⢉⡠⢪⠞⢀⠉⠛
⠀⠀⠀⠀⠀⠈⠳⣄⡿⢤⡠⠔⠒⠚⠻⢦⡀⠈⠻⣍⠲⢵⡹⣄⠰⡘⣷⣾⡣⠂⢀⠌⡼⠀⠠⣠⠤⠙⠀⠀⣀⣠⡤⠤⠄⠀⠈⠀⠉⡜⢁⡤⠃
⠀⠀⡋⢋⠢⡀⠀⡈⠓⠴⠛⢦⣀⠤⠤⠤⢽⣖⠺⠿⣅⣀⡉⠻⣧⣧⣿⡟⠁⣀⣴⡾⠥⣤⠆⠀⠀⣴⡙⠒⠻⣄⠀⠀⢀⠀⠀⠀⠀⢈⡉⠤⠤⢀
⠀⢠⠛⢶⣌⠁⠀⣍⢦⠀⠀⠀⠻⡄⣀⡤⠶⢻⡄⠀⡤⠬⠭⠷⢾⠧⠀⣹⣿⣭⣤⢤⠬⠑⣦⠀⢸⡇⠈⠉⢉⠃⠀⠀⢸⠀⠀⠀⡴⠅⠐⠂⠂⠀⠑⡄
⠀⠀⠶⡒⢆⠀⠀⣈⣟⡀⠀⠀⠀⠻⣥⠴⡖⠋⠀⠀⢷⡀⠀⠀⡸⠀⠀⡀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⢠⠏⢧⣀⢀⡼⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠈⠁⠀⠀⡏⢨⠇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠉⠉⠉⡇⠀⢀⠋⠉⠉⡏⠁⠀⠀⠀⠀⠘⢦⠴⠃⠀⠀⠈⢩⡄⠀⠀⡇⠀⠀⠂⡀⠀⠀⠀⡘
⠀⠀⠀⢀⡤⠶⠶⡇⣼⠠⠤⣀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⡇⠀⡘⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠁⠎⠀⢀⠠⠀⠀⡴⠁
⠀⠀⠀⢸⠓⠲⠤⠽⠥⠤⠴⢚⠃⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⢀⣠⣿⡤⠄⠀⣆⣠⣁⣤⠶⠊
⠀⠀⠀⢸⣤⠋⠢⠚⣆⡰⠓⡼⠀⠀⢀⡷⢼⣷⡆⠀⠸⠤⠤⠤⠧⢼⣄⣀⣀⡇⠀⠀⠀⠀⢀⣀⡈⠁⠀⣀⣀⡀⠈⠁⠀⠀⠐⢏⡇
⠀⠀⣠⠼⣇⠀⠀⠀⠈⠁⢠⠇⣀⠀⠈⠿⣤⡼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⢻⠋⠉⢉⣩⣭⣓⠊⠈⢩⣑⢂⠀⠠⠀⠀⠀⠀⢀⣄
⠀⠀⠳⢤⣈⣓⠶⠤⠤⢖⣋⣠⠼⠂⢀⡼⠉⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡇⡞⠀⡰⢹⢋⣭⣭⠳⡄⣿⣼⡛⢠⠁⠀⠀⠀⠀⣸⠀⠙⣻⠷
⠀⠀⠀⠀⠈⠳⣭⣭⡭⠟⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⠀⢇⠘⢆⠠⠀⠢⡀⠀⠀⣇⢧⠀⠱⣼⡜⠿⠿⣣⠇⠀⢠⠁⡆⠀⠀⠀⣴⠉⠉⠳⡞⠁
⠀⠀⠀⠀⠀⣠⣴⣖⠲⣄⠀⠀⠀⠀⢀⡀⠀⢘⠱⡄⢄⠈⠢⡀⠑⣄⠑⠳⠀⣘⣶⡦⠙⢾⣦⣀⠈⠉⠓⠚⠁⠀⢠⠃⢀⠀⠀⢀⠾⡈⠑⠦⢤⡞
⠀⠀⠀⠀⡞⢁⠄⠈⣷⢸⣤⡄⠤⠒⢯⢹⡆⠈⠣⡈⠢⢡⡀⠐⣴⣄⠱⣄⠻⠿⠀⠐⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠁⠀⢸⠀⠀⢸⡓⢌⡑⣒⠞
⠀⠀⠀⠀⢧⠈⠳⠴⠛⠁⠀⠀⣀⡤⠞⠋⠀⠀⠀⠈⠢⡀⠶⣿⠋⠙⡀⠈⠑⠂⠄⠊⠀⠀⠀⠀⢠⡀⢸⠙⡆⠀⠀⠀⠸⠀⢴⠋⠝⡲⠚⠁
⠀⠀⠀⠀⠀⠙⠒⠒⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠔⠁⠀⠀⠀⢀⡀⣀⡀⣹⢆⣀⠷⣄⢑⡗⠐⠀⠀⠀⠀⠈⠳⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣟⣻⣶⣤⣶⣟⣥⣶⣾⣿⣶⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡠⢤⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠀⠉⣴⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣈⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣦⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡤
⠀⠀⠀⣈⣽⣿⣶⣦⣤⣀⢀⣠⣾⡿⢟⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⢠⣿⣿⣿⣿⡿⠿⠿⣿⣿⠟⣱⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⣾⣿⠏⠅⠀⠀⠀⠈⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⢵⡏⣾⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁
⠀⠀⠀⠜⣸⣾⣧⣤⡀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁
⠀⠀⡸⢠⢹⣿⣿⣿⣿⣶⣤⣄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏
⠀⠀⠀⠀⠀⢻⡿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⠄
⠀⠀⠀⠀⠀⠈⠁⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠛⠋⠉⠀⠀⠉⠱⠏⠰⠋⠁