White as snow Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠶⠀⠀⠀⠀⠠⡀⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⣤⣤⡄⠀⠀⠡⠀⢤⠆⠀⢀⡈⠾⣦⡤⣄⠳⣄⡆⠈⠀⣼⣬⢧⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣰⣿⣿⣿⣷⣤⡀⠀⠀⠀⡀⠀⠀⠡⠒⠒⠛⢿⣇⣀⡳⠀⠘⢛⣿⡀⢱⡄⢀⡆
⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢀⡀⠓⠦⣸⣟⢀⠀⠹⣾⠁⠀⠄
⠀⠀⠀⠀⠀⢀⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠰⠄⠀⠀⠀⠀⢀⢀⡚⠦⠤⣹⣿⡈⢷⡀⢿⣒⢀⡗
⠀⠀⠀⢠⣾⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⠦⠰⠆⠀⠀⠀⠀⠀⠀⠈⣿⣷⠾⣧⠸⣧⣸⣇⡀
⠀⠀⠀⣾⣿⣿⠿⠋⣿⣟⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠋⠛⣦⢤⣤⣤⣴⣾⡟⣻⣿⠇⠈⣿⣿⣿⡏⠄
⠀⠀⠀⣸⠟⠁⠀⠀⠀⢈⣻⣧⡀⢸⣻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⡀⠚⣡⠴⠏⠉⠈⠉⠙⠻⣿⣇⠐⣿⣿⠟
⠀⠀⠠⠯⠤⢶⣷⣠⣶⣾⣿⣿⡇⠸⠿⡁⠘⣿⣿⠿⣿⣿⣿⣿⠿⠷⠷⠇⠬⠧⠀⠡⢼⡆⠰⣼⣯⢿⠀⡏⠫
⠀⠀⠀⠀⠀⠀⣹⣷⣤⣬⡍⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠒⠛⠛⠛⠛⠒⠓⠑⠀⠀⠀⣀⣿⣷⣿⣷⠀⢿⡥
⠀⠀⠀⠀⢀⣠⣠⡝⠋⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⣶⣷⣶⣶⠿⢿⡟⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠉⠛⢙⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⡉⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠂⠉⠉⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠈⠉⠀⠂⠒⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠮⠤⠤⠤⠤⠤⠦⢄⡀⠀⠀⠀⠀⠀⠰⠚⠒⡢⠀⠤⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡧⢀⣠⠁⠀⠀⠀⠀⠐⠁⠀⠀⠉⠉⡰⠒⠀⠢⠤⠠⣀⣰
⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⠀⠎⠀⠀⠀⠉⠉⠒⠒⠂⠦⠤⠀⢀⣀⢠⡀⠀⠀⠀⠀⢀⠊⠀⠁
⠀⠀⠀⢀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠈⠉⠉⠀⠐⠚⠒⠐⠇
⠀⠀⠀⡸⠤⢤⡤⠀⠐⠒⠒⠰⠂⠉⠉⠉⠈⡘⠁⠀⠀⠀⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠢⡀
⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⣀⠀⡀⢀⣀⣀⠧⠀⠠⠤⠤⠄⠺⡒⢺⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⢋⠋⠉⠈⠀⠀⠀⠉⠁⠀⠀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡼⣀⠒⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣪⣱⠀⠀⠀⢠
⠀⠀⢎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡹⠙⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⡀
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠉⠐⠂⠐⠒⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⡇
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⠒⠂⠠⡴⠶⠆⠀⠒⣊⠁⠀⡀⠀⠀⡰⢤⣄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⢇
⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⣿⡀⠀⢰⠄⠀⠠⠤⠤⢆⠀⠀⠈⢢⡜⢁⠆⡆⠀⠀⠀⠀⡇⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠰⢏⠀⠉⡙⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠑⡌⠀⡇⠀⠀⠀⠀⠇⠀⢨⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠲⡀⠀⠀⠁
⠀⠀⠀⠀⠌⠀⠀⠀⢀⠃⠈⠉⠈⠁⠥⠕⠀⠀⠀⠀⠘⠀⠀⠀⠀⢡⠀⠱⠤⢀⡀⠤⠃⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢲⢄
⠀⠀⢀⡎⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢱⠤⠀⠔⠁⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠑⠤⣀⣀⣀
⠀⢀⠊⠈⠙⠐⠂⡼⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠀⠀⠀⠘⣄⠤⠐⠐⠈⠉⡄⠀⠀⠀⠀⠀⢈⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠈⠢⡀
⢀⠎⠉⠐⠂⠤⣀⠂⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⢰⣀⡠⠤⠐⠊⠙⡄⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡌⠀⠀⠀⠀⠀⠈⠢⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⣠⠜⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢇⠀⠀⠀⠀⠀⡠⣀⡸⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢆⡀⣤⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠰⡁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠈⠒⠤⠀⠔⠊⠀⢸⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠑⠢⠄⠀⠔⠋⠀⠀⠀⠀⠀⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠉⠁⢹⡁⠀⠀⠀⠈⠉⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⢈⠁⠀⠉⠉⠀⠀⠀⢁⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⢀⡠⠒⡇⠀⢀⣀⣀⣀⡀⢸⠀⢀⣀⣀⣀⣀⠀⢸⠃⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⢀⡴⠛⠈⠉⠉⠉⠑⠢⢄⡀⠀⡙⠈⠀⠀⠀⡀⠤⠈⠛⠒⠀⠤⠌⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠐⠻⢦⣄
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠂⠀⠤⠄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣄⠆⠀⠀⠀⠀⠀⠐⠬⡄⣸⠿⠁⠀⠠⠀⠀⠀⠰⡀⢀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡛⠀⠀⠂⠀⠀⠀⣂⣢⡄⢤⡤⣀⡀⠀⠀⠀⠈⠀⢑⠺⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠂⠂⠈⠌⠨⠩⠽⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠘⠛⢍⠀⠀⢀⢀⠔⢀⠀⠀⠀⣠⠖⠀⠀⠀⢀⠀⢠⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⢠⠊⠳⡄⡀⣠⣞⡠⠆⠀⣠⠚⠁⠀⠀⠀⠐⠀⢀⠀⢉⢉⡑
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡀⡀⠀⣀⠀⠁⠀⠀⠂⠌⠀⠀⡇⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠐⠰⠦⠦⢜⢀⢉⠉⠉
⠀⠀⠀⠀⠀⡛⠒⠚⢂⢈⣉⡍⠛⠁⠀⠀⠀⠀⠀⠀⣠⠄⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠤⠦⠤⢦⢝⠋⠊⠛⠓⠀⠀⢀
⠀⠀⠀⠀⢘⠃⠛⠑⠎⡉⢉⠉⠉⠙⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢠⡤⡠⠤⡤⣼⠟⠜⠚⠳⠎⠁
⠀⠀⠀⠀⠐⠛⠒⠛⠫⠁⠓⠊⠂⠙⠄⠀⠀⠀⡀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⣤⣠⡀⣤⣀⣈⢹⡆⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠓⠛⠊⠚⠯⠶⠤⠦⠴⠴⡶⠁⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠐⠈⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠈⢙⡇
⠀⠀⠀⠀⠁⢱⠇⠘⠔⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠐⠃⠀⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠘⠃⠀⠄⠀⣀⢻⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣌⠄⠀⠀⠐⠠⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠷⢄⡀⠀⠄⠈⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠠⠮⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠂⠄⠂⠁⠂⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠐
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠶⠷⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣤⣤⡀⠰⠀⠀⠀⠀⠀⠐⠀⠀⠔⣤⣠⢌⣢⠀⠀⠄⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢉⠀⢹⠹⡅⠀⠀⠀⢀⠁⠀⠀⠀⢠⠀⡄⣁⣀⣈⠀⠀⠀⠈⡀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠂⠀⢀⠠⠀⠐⠂⠀⠀⠉⠀⠼⠶⠆⠀⠀⠀⠀⠈⢄⡠⠀⠠⢔⡉⡀⢁⡈⠳⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⠈⠁⢢⡤⠊⠀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⠉⠋⠑⠊⠙⠛⢃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠀⠀⠀⡤⠀⢀⡴⠔⠀⠉⢧⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠔⠋⠔⠣⠴⢦⡔
⠀⠀⠀⠀⠀⠈⠠⠀⠀⡉⠀⠀⢀⠊⠀⣤⠘⠀⢲⢒⢲⠒⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⢠⣆⣤⢀⢤⡐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢡⢠⠿⠀⠐⣔⣸⠟⢹⣀⣁⡀⠲⣦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣹⠆⡉⠠⣅⣄⡙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣺⠍⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠖⠂⢄⡴⠂⠉⣾⣝⣋⣁⡘⠿⠛⢿⠿⢧⡨⠤⠭⠌⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢠⠂⢉⠉⠘⠉⠀⠀⠀⠴⣸⣽⣇⣇⠀⣬⣷⣿⠀⠀⡆⣶⣶⢶⡄⢒⠒⢖⢩⢹⣿⣇⡤⡅⠠⠌⡀⢀⣀⢠⢀⢤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠒⠂⠀⣠⢀⠠⠈⢉⣡⡀⡂⢃⣋⣛⠊⡇⠀⢀⡀⠀⠀⢀⠤⡤⠵⠴⠂⡁⠁⠀⢁⣅⢐⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠑⠧⡀⠠⢌⢰⡉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣉⠈⢳⠤⠒⢄⠤⠤⣀⠀⣠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⣤⣄⣴⠞⠉⠁⠀⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣤⣼⡋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠶⠶⠶⢤⣄
⠀⠀⢀⣠⣴⠛⠉⠉⠛⠁⠀⠈⠿⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⣦⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠈⠳⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠞⠋⠉⠛⢷⡴⠶⠶⠶⣤⣸⡇
⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢶⣄
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⡶⡶⡶⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢟⡟⣟⠇⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢽⡮⣥⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠃⠀⠀⠀⠀⢼⣿⡧⠀⠀⠀⠀⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠼⢳⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⣺⢿⡺⠂⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣴⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⠻⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡣⠄⠀⠀⠀⠲⠆⣤⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠾⠰⠀⠀⠀⢀⡄
⠀⠀⢀⣃⠀⠀⠀⢨⡑⢣⠀⠀⠠⠄⣄⠳⠆⠀⠀⢓⡀⠀⠀⠀⢀⡀⠀⠀⠀⣐⡁⠀⢠⠀⠀⡭⠋⡲⠍⡀⠀⣐⠓
⢠⠀⢐⠊⠀⠀⠐⠌⠠⢃⣀⢀⣤⠴⠆⣄⡃⠀⢰⠰⠂⠀⠀⠀⠸⡇⢀⡆⢘⠂⠌⠀⡬⠀⣄⠐⠫⠅⣨⣁⠠⢄⠊
⣸⠀⡄⠠⢁⣳⠖⠪⡥⢠⡠⠀⠤⠀⢀⣈⠁⠀⣚⠓⠾⠀⣶⡀⠯⡀⣸⡔⠢⠌⣒⣠⡚⡂⠰⠚⠀⠀⣀⣬⡐⢀⠉
⡠⡧⠄⣁⢀⣺⠻⡤⠊⠠⠜⠃⠀⡛⠀⠉⠐⣧⠖⡈⢊⡥⢉⣟⠓⣃⢿⣨⠁⢢⠤⠴⣪⢳⣤⡄⠻⠃⠀⢀⡴⢐⠉
⢌⣬⡃⢁⡛⠧⠆⠶⠀⠔⢘⠛⠉⠉⠷⠂⠶⠘⠚⢀⡈⠡⢵⡮⠉⢰⢮⢅⡡⠄⠛⡤⢓⠽⣯⢄⣠⡄⠛⠛⠀⠛⢤
⡥⠂⡄⠂⣼⡛⠁⠶⠐⠲⠛⡶⠖⠃⣀⠀⢠⣄⣨⡵⡀⢁⣯⠙⠉⠀⠉⠩⠹⠄⠦⠐⠛⠓⢀⢈⣁⢠⣤⡄⠙⠓⡞
⢽⡉⠏⣨⠞⠛⣁⠐⠐⢿⡆⠀⢀⣀⡈⠟⠀⠀⢈⣙⣧⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠉⠁⢨⡄⣤⠶⣤⡿
⠀⠀⠁⠉⠻⠶⢖⡂⢶⠂⠚⠃⠈⠉⠁⠦⣀⣀⡌⠁⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠻⠖⠠⠔⠂⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⠄⠴⠛⢦⡴⣉⡈⢤⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠚⠞⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠾⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠀⢀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠴⠆⠀⠀⡠⣿⠄⠀⡔⠒⢄⡀⠀⠀⠀⠀⠰⠆⠀⠀⢀⡄⠀⠀⠀⠀⠀⡰⡡⢂⡒⡕⡀⢐⠁⠙⢄⠀⠀⠀⠁⢀⠀⢀⡀⠀⠀⠀⠀⣤⡄
⠀⢀⠀⠀⠀⣰⡡⠉⢬⡄⠈⠒⠠⠬⢑⡒⢄⠀⠀⡀⠀⠀⣼⣷⠀⠐⠛⠀⠀⠇⠇⠛⠃⡆⡇⠈⠒⠂⢤⠑⢢⠀⢠⢿⡀⠣⢈⣑⠢⡀
⠀⠀⠀⠀⠀⠋⠀⠗⠀⡇⠀⠀⣀⣀⣀⡙⣬⡀⠀⢀⣤⣎⣎⣄⣆⣤⠀⠰⣉⣊⠎⠀⠀⢇⠓⡱⠀⠃⠀⢦⡁⢀⡞⠒⢣⠀⢀⠤⣸⡧⠀⢀
⠀⠀⡆⠀⠀⠀⠺⠀⠇⢀⣠⣻⣳⣾⣾⠉⢧⠀⠀⢸⠀⣤⡀⢠⣄⠀⡄⢀⡇⣔⣲⡀⣔⣶⠈⡥⣒⠕⠂⠻⡷⢤⣤⢲⢴⣎⠕⢭⠒⣷
⠠⡊⣿⡄⠀⠀⣉⢀⡁⠘⠘⠁⠉⠉⠁⠰⠀⡛⠉⠋⠀⠉⠁⠈⠉⠀⠉⠉⡇⠑⠓⣀⡓⠓⠀⠋⠁⠀⣿⠆⠈⢻⠙⠚⢹⢁⣄⠀⢀⡈⣀⠴⠷⢦⡀
⢈⢕⣯⡂⢀⡄⣉⢸⡀⢀⢰⡇⠰⡷⠀⠘⠀⡇⠸⠿⠀⡠⠤⠤⢄⠐⠿⠆⡇⠀⠀⡇⢹⠀⢰⠀⣰⣆⠀⢰⣷⠘⣟⣻⣹⠀⠁⣠⡄⠀⡏⢀⣈⠉⡇
⠴⡪⣟⠅⢸⣗⢠⣂⡆⢸⢀⠄⢠⡄⢠⠏⡆⡇⠀⠀⡌⢀⠀⡇⡀⠃⠀⢠⡧⠀⢰⣟⣻⠀⢸⠀⣾⣿⠀⣸⣿⠈⣴⡦⢼⡀⠀⣺⡇⢐⡇⠘⠛⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠸⠤⠆⡆⠀⠎⠀⠀⢐⣈⢉⡁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⡆⠘⡔⠀⠀⠀⡠⠄⢘⡛⢦⠧⠔⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⡠⠎⠆⠀⠀⣀⠱⠴⠊⢉⡠⠐⠈⠋⢐⡬⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢀⠌⠀⠀⢦⠄⠐⡞⠉⡀⢠⡄⠀⠀⠤⠌⠙⡷⠞
⠀⠀⠀⠀⠀⢀⠄⠂⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠄⣤⣌⡆⡆⢀⠁⢈⡄⠀⠄⠀⢇⠀⢠
⠀⠀⠀⠀⠀⠈⠔⠈⢀⠠⠀⠀⠀⠬⢀⡄⠀⠀⠄⠀⠀⡔⠀⠈⡆⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠐⠀⠦⠤⠼⠤⠼⠄
⠀⠀⠀⠀⠀⠈⢀⠊⠀⢀⠀⠀⢀⡠⠀⡘⢆⠀⠀⠀⡠⠒⡀⠉⠉⢀⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠂⠘⠋⠀⠒⠙⢦⠀⢀⡼⡨⠄⣂⠀⠀⠀⢐⡈⢦
⠀⠀⠀⠀⠀⠠⡄⠸⠁⠀⠼⠆⠀⠀⠿⠀⠰⠀⢈⢊⠔⡡⡔⡤⠀⠠⢆⡐⠨⠄
⠀⠀⠀⠀⠀⠀⠙⠄⠄⠀⠀⠰⠀⠂⠀⢀⠀⠀⢋⠀⠌⠐⢠⡆⠀⠀⣀⡀⠈⠁⠀⠀⡔⠋⠀⠈⠑⢄
⠀⠀⠀⠀⡀⠠⠄⠼⡃⠶⠤⠤⡤⠄⠂⠁⠀⠀⠘⡌⠀⠀⠀⠁⣀⠀⠛⠀⢠⠀⢀⠮⠤⠀⣀⠀⠀⣤⠒⡄
⠀⠀⠀⠘⠓⠀⠀⠒⠚⠒⢶⢰⡆⠀⠀⠀⠐⠀⠀⢀⠀⢀⣀⠀⠒⠀⠀⡠⠚⡰⠁⠨⡄⡐⠂⠉⢲⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠌⠀⡀⠐⠚⠘⣸⣲⠀⠀⠀⠀⠀⢀⠗⡼⠬⠉⣁⠼⠁⣴⠀⢻⣀⡐⠬⠄⢂⣀⡸⠀⠀⢀⠀⠀⠦
⠀⠀⠀⢀⡀⣀⡃⠄⠉⠈⣺⢺⢨⠁⠀⠀⠀⠀⠀⡘⡜⠀⠀⢄⣤⢀⠑⣾⣆⠬⠄⣉⣀⣀⣀⡄⡸⡀⣀⣢⣤⠴⠃
⠀⠀⠀⢺⡀⠀⠈⡢⠤⠔⢇⡈⠀⠱⡀⠀⠀⠀⠀⠙⢃⠀⠒⠐⠜⠨⠁⠀⡏⠀⠀⠰⠀⣜⣰⠀⠃⠈⡄
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠁⡴⢋⠝⠀⠀⠀⠀⠀⠈⠖⠒⢒⠒⢚⠀⠀⡄⠀⠀⠂⠘⠊⢛⣤⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣾⠒⣎⠀⠀⠑⢄⠀⠀⠀⠀⠘⠚⢃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠋⠉⠈⠀⠀⠀⠀⠙⠂⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡼⣤⡆
⠀⠀⠀⠘⢷⡬⢧⡾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⢷⠻⠍⠁
⠀⠀⠈⢉⡽⢷⡖⢯⡉⠁
⠀⠀⠀⠈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⢯⡿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⡿⣔⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡿⡦⠾⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠙⠀⠦⠀⠠⠀⠋⠈⠐⠤⡀⠀⠀⠀⠉⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠉⠉⠒⠠⢀⡀⠀⠀⠀⠀⣀⠤⠂⠁⠀⠀⠐⡀
⠀⠀⠀⠠⣄⣶⣠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀⣠⢀⡀
⠀⠀⠀⢛⡿⣼⢿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠛⠈⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢰⢀
⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⢸⠆⠠⠄⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠠⠄⠠⠾⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⢠⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣄⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠔⢡⢩⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠃⠘⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠒⠄⢈⡀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⢀⣠⠴⠉⠀⠤⢀⡀⠀⠈⠉⠢⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠉⢀⡀⠬⠅⢂⣄⡀
⠠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠓⠀⠁⠀⠀⠀⠀⠀⠉⠀⠐⠀⠤⠤⠂⠡⠤⠐⠈⠀⠀⠀⠀⠀⠀⠉⠓⠦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⠄⠀⠴⡮⢀⡀⠀⠀⠀⠀⠈⠁
⠠⢴⣆⠀⠀⠀⠐⠀⠀⠀⠀⢰⡄⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠸⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠠⠀⠁⠀⠉⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀⠀⠀⠐⠀⠂
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠑⠢⣄⢀⡤⠖⠚⠋⠉⠙⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠾⠄⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⡤⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⡀⠀⠀⣀⠼⣄⣀⠀⠀⠀⠀⢀⣼⡏⣹⡅⠈⢹⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠉⠁⠀⠀⠉⠉⣭⡟⢦⣬⣽⠝⢯⡿⢯⣿⠛⣾⡭⠶⠤⠞⠵⠯⠴⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⠞⣹⢟⡴⠋⢳⣞⢟⣴⡻⣽⡾⠉⢧⢯⣉⠙⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢧⣀⣨⢗⠼⠒⠷⡼⣅⣀⣼⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⢻⢧⡼⣄⣀⡰⣣⣔⣖⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠫⡟⠧⠼⢻⡤⠗⢘⡎⢳⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⡆⢲⣤⡀⢀⠀⠠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⠒⠀⠠⣌⠁⠀⠈⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢂⠷⣒⣀⡰⢧⣾⠥⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠣⠉⠈⠁⠀⠀⠀⠀⠀⣀⡴⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠴⢶⣶⠀⠀⣠⠶⠲⠶⠎⢀⣲⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⢀⡤⠀⡈⠀⠀⡀⠒⠶⢲⣤⣤⠀⢤⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠒⢿⠟⠋⢻⣾⣶⠮⠃⠀⠀⣶⡶⣴⣦⣶⡦⣴⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⣀⣀⡠⢤⣶⣦⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠠⠴⠶⠒⠂⠀⣀⡀⠀⣀⡤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢡⣬⣵⢶⠶⣂⠀⠈⠀⠀⠀⠀⠀⠐⠇⠀⠀⠴⠖⠂⠈⠉⠁⠋⠉⠀⠀⡰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠕⡪⣶⠚⠛⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠒⠦⠶⠿⠟⠓⠀⠐⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣷⣾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⡀⠀⠀⢳⣄⣀⣒⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⣤⣴⣤⣤⣴⣦⣤⣀⣀⠀⠀⠀⠀⠀⣀⡀⣤⣬⡂⠀⠠⣤⡄⠀⠀⠼⠓⠀⠬⣿⣽⣿⣿⣿⠿⣯
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣶⣿⠿⠿⢿⡾⠿⠶⠶⢴⠾⠟⠛⠛⠛⠻⠿⠿⠷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢦⡞⣏⠰⣶⣶⣮⣴⢞⣤⣤⠰⣦⣀⠐⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣾⣿⠖⢤⢀⣀⡨⣀⣀⣦⣗⢰
⢐⡻⡄⠋⢙⠿⣟⣡⠈⢨⢸⡗⣫⠩⡟⠊⡩⡼⢀⣀⣀⢀⣄⠀⣀⣠⣠⠟⣤⢝⡎⢼⠨⣏⣮⠹⣿⠫⡐⢓⢻⠤⢳⠾⣇
⠈⠇⢑⠦⡋⠏⢹⡼⢎⣽⢨⠶⣨⡷⠚⣶⢑⣯⣘⣿⠹⣏⠋⣿⣿⢿⣟⣿⢍⣜⣄⡼⡔⠿⢆⠓⢿⡧⠙⢠⠙⡏⣸⢳⡟
⠐⠀⠾⡖⣩⠓⢞⠋⠂⠶⢊⢌⡽⠋⢔⣠⠋⡐⣬⡱⢏⢀⣀⠈⠗⠞⠣⠊⢄⣿⡸⢆⡲⢌⣆⠛⠶⢦⢘⠀⢅⠱⢗⠊⢍
⠀⠀⣰⠀⡌⡙⠂⣀⠀⠀⠀⠀⠀⠋⠀⠓⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀⣆⠁⢲⠌⢺⡷⠄⠈⠀⠁⠙⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠁⠈⠀⠈

⠀⠀⠀⣀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀
⠀⢠⣾⣿⣷⣶⣶⣾⣯⣿⡆⠀⠀⠀⠀⣰⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣶⣦⡀⠀⠐⣢⣀⡀
⠀⠸⠿⣿⢻⣹⣽⣯⣽⣭⣷⣠⣴⣆⠠⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿⣿⣿⣿⣿⣷
⢰⣶⣶⣿⣾⣿⣿⣿⡿⠿⣙⣿⣿⣿⣧⣤⣧⣤⡄⠀⠀⠀⡀⠤⠤⠤⠴⠶⠶⠶⠿⠿⠿⠿⠿⠿⢿⡿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡄⠀⣀⠐⠂⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢢⣔⡀⠀⠀⠀⠀⠀⣸⡇
⢰⣿⣨⣀⣿⠀⠀⠀⠠⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⡆⠙⠉⠀⠀⠤⠀⠈⠡⠍⠃
⢀⣹⣉⣿⠉⠀⠈⣰⡄⣛⠛⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡿⠻⠇⠀⢈⢀⢀⣀⣁⣉⣀⣈⣃
⠀⠉⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣄⠀⠀⡀⠀⣀⠐⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣴⠀⠀⠀⠀⣄
⠀⣾⣿⣆⣀⣀⣀⣂⣀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⠀⠀⢀⣠⣿
⠀⣤⣿⣿⣿⣿⣿⡿⠿⠿⠧⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣄⡨⠄⣍⣀⣤⣸⣿⣯
⠀⠈⠉⠉⠉⢹⣿⡇⠀⠀⠀⢉⠉⠁⠁⠙⠛⠏⡍⠉⠉⠀⣸⣽⠿⡾⡻⣻⡿⣫⣵⣾⣿⣿⠟⠋⠉

⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀⣆
⠀⢀⡠⠶⢶⠞⢿⠿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡔⢉⠉⢰⡧⢸⣿⣄⣦
⠀⣼⣯⣉⣰⣒⣺⣾⣿⣧⣤⠶⠶⠶⢶⣶⣒⣓⣲⡶⠆⠀⠀⠀⠀⠊⢹⣿⢰⣿⣿⣦⣤⠸⡿⢰⣿
⠀⣶⣶⣶⣶⣾⣿⡿⡿⡿⡿⡷⡲⡻⡳⡶⡿⣯⣥⡒⠁⠀⠀⢀⣀⣀⣀⣥⣼⣿⣿⣿⣿⣤⣤⣄⣋⡀
⠀⠙⠉⠋⠉⠈⠈⠈⠈⠈⠈⠈⠈⠈⠈⠈⠈⠉⠉⠉⠁⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠔⣪⠿⠋⠀⠀⠀⠀⠀⠀⣠⠄⠂⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣉⡼⢋
⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠠⠚⠁⠈⡙⠀⠀⠀⢀⡤⠔⠊⠡⠉⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢰⡆⠀⠀⠀⢼⡇⢨⣡⣶⣮⠈⠒
⢠⣾⠴⣻⠇⣸⠀⠀⠀⠀⠚⣍⡄⢦⠀⠀⠀⠄⣦⠐⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣧⠀⠀⣠⣿⣿⣈⣋⡼⠟⢶⠶⣶⢀⣆
⣿⡿⣊⢃⣲⣼⣇⣤⡶⠚⢈⠉⢰⢌⣁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⡆⠀⠀⣫⣜⠅⠀⡜⢛⡎⢉⣻⣀⣤⠈⢃⡀⠙⢿⣀
⣿⠞⣹⣈⡽⢌⣿⣿⡷⠂⠀⠈⡃⠀⠀⢣⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠂⠘⣁⡙⢶⡀⠟⠁⡴⣄⡘⣿⡏⠳⡌⠙⠷⣾⣿
⠿⠓⣅⡟⢘⣦⣹⡿⠗⠚⠶⠖⠉⠛⠧⣌⠳⣦⣦⣴⣀⣴⣠⡠⢼⡿⢄⣀⣰⣄⣦⣦⣾⣷⣶⣏⢜⡁⢸⠞⢉⡅⢸⡡⠒⠉⠻⡀⠻⣌⣗⣦⣤⣀⠈⠻⣿
⣰⡎⠀⣿⢺⣏⣠⡤⢾⣀⣤⠾⢶⢸⡆⠘⠷⣿⣿⣿⣿⣿⣿⡗⡹⡟⢺⣿⣿⣿⡟⢹⣿⣿⣿⡥⢟⠙⠓⠛⣩⢸⢛⣀⠀⠂⣧⠘⣤⣼⣿⣇⠀⠙⠷⢴⣿
⠴⠳⣀⣿⣶⠟⠉⣀⢀⣉⣇⠀⢨⡽⡟⢦⣀⠸⣿⡟⡟⡿⡿⣉⣠⠉⢈⢻⣿⣿⡴⢊⣻⣿⠋⡠⠴⠗⠶⣦⣽⣇⣼⠡⠤⠖⠛⢿⡀⠘⢯⠉⠁⣄⠀⠀⢹
⢀⣶⡟⣹⣷⡞⠋⢀⣬⠋⠀⡖⠈⠀⢀⡀⠙⠳⣾⣿⡏⣿⠯⠎⣀⢧⡼⠨⢿⡵⡁⠊⢉⡟⢋⠀⣠⢤⠦⣀⢹⣿⣅⠀⣠⡀⠀⢹⣉⠉⠺⣆⡀⠈⠂⢤⣀
⣾⣁⣼⣿⡯⠀⠚⢻⣁⣠⡞⠀⢠⡀⠘⢳⡄⣀⠈⡿⢿⡅⠀⠈⡇⢸⠀⠀⠠⡾⠁⠲⢎⠁⣣⣤⡇⢀⡷⣄⣉⣿⣿⠜⠛⣧⠀⢠⡏⠶⣄⡘⢧⣠⠂⠀⢻
⠀⠀⡽⠃⠀⠀⣀⡤⠞⠉⠀⠀⠀⠛⣆⢨⡗⠛⠓⠇⠘⠓⠐⠋⠙⠛⠒⠀⠀⠈⠀⠀⠀⠁⠀⠀⠑⠁⠀⠘⠛⣁⠆⠀⢈⠉⠓⠃⠀⠀⠀⠙⠻⣯⠁⢀⢈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠲⠀⠀⠀⠙⠻⠇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⠠⠾⠴⣄⡀⠀⢠⣀⣣⡀⠈⣻⠿⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠄⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⣻⣤⡲⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠀⠀⠠⡼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⡆⠀⠀⢠⠟⠞⢃⡾⣹⢧⡹⡏⡜⠛⠁⠀⠀⠀⠀⣀⡤⠒⠋⠘⠁⠠⣶⡀⠀⢸⡞⢻⣀⡀⠀⠀⢠⣷⡄⠀⠀⠀⡩⡀⣥⣾⡀⣠⣿⣄⣾
⢀⣄⢠⣿⠀⣰⡰⡚⠛⣸⣦⣴⣃⣶⣤⣴⣏⠀⠙⠿⠀⠘⠁⢀⡠⢔⣾⡏⠀⠀⠀⠀⠀⢴⣿⣆⠀⠼⣇⣾⡍⠁⠀⠀⣦⢷⣰⢀⠀⢰⡟⢻⣠⡏⢳⣿⣸⣇⢿
⢸⣿⣫⣭⣷⣿⢉⣿⢉⣻⡿⢩⠇⢸⣧⠁⣾⡆⣸⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣎⣻⢸⡤⣀⣽⣏⠹⠶⠀⣠⣤⣿⡉⢼⠁⠼⣷⣚⣡⣇⣸⣧⣹⠙⡛
⢸⣿⣽⡉⣿⠟⠁⣈⢈⡉⢹⣿⣠⣾⣧⡖⢁⣿⣏⠈⡝⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⢿⣌⣥⠈⠾⡟⠳⠇⠀⢈⣡⣯⡛⠆⣉⠰⣾⡿⢋⣍⠁⢹⡻⡦⣿
⢸⣯⣴⣿⡝⠛⠋⠈⣿⡛⠛⣿⣿⣿⡿⣥⣿⢿⣿⣆⣻⣿⣾⣧⣦⣷⣶⣴⣄⣤⣄⡤⠚⣇⣼⣮⣙⣥⡀⡇⠀⣀⣴⡌⢀⣧⢥⠔⢣⡴⢤⣿⣯⣿⣷⣼⣿⣁⣿
⢸⣿⣿⣿⠧⠾⣀⣼⠞⢷⣶⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣯⣛⣧⣿⣿⠖⣉⣿⠈⣧⡙⢯⢻⣿⣟⡣⠾⣙⣿⠅⠞⡔⠢⠗⢤⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡄⣠⠏⠈⣄⠀⢳⣀⣻⡇⠿⠛⢿⠈⠟⠻⡿⣿⠟⠙⠛⠙⠿⠿⣿⣿⡿⢛⣡⣻⠆⠁⣹⡚⠻⡿⢓⠦⠓⠆⣹⢇⡠⠃⡤⠧⡘⠾⢿⡿⡿⡻⠻⠻⣿
⠈⠋⠻⢯⣀⡴⠦⠤⠊⠓⠛⢿⣄⣀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣡⠀⣥⠀⢈⣍⠠⡬⠃⠈⠋⠸⡀⠤⣹⠇⡴⢳⠀⡉⠙⡈⢃⠁⠀⠀⠀⠁
⠀⠀⠦⠴⠁⠀⠦⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⡗⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⠇⠀⢠⣿⢀⠀⡀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣷⣿⢻⣤⣴⣿⡄⠂⣡⡄⠂⣶⠄⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣭⣶⣿⣟⣷⣿⣿⣟⡿⠄⡟⠿⣾⡤⠤⣷⠖⢀⡀
⠀⠀⡄⠀⡠⠀⠀⢠⠀⠀⣤⢈⡿⢿⢿⣿⡟⢛⣧⣤⠃⢸⡇⢰⣿⣤⡤⡧⠄⠠⡄
⡀⠀⣿⣰⡇⣰⢴⣣⣶⢾⠋⢩⣽⡿⠿⠳⠿⠏⠹⠈⠀⠹⡇⣟⣃⣠⢀⡗⠂⢀⣀
⡇⢰⢻⣽⣿⣿⣾⠏⢰⣏⣥⡶⢮⡴⠞⠒⠐⣋⡥⠀⠈⢸⡇⠿⠏⠙⠘⡇⠀⠀⠙⠁⠉
⠠⡜⣼⡿⢻⡣⢾⣺⠟⠩⢁⣠⣿⣉⣠⢵⢾⣇⣐⣀⢀⢸⡟⠀⠃⠀⠼⠇⠀⢠⣤⡀⠀⢀⣀⠀⠠
⠀⣿⢿⣿⡿⣲⣿⣿⣧⣶⣿⣟⣯⣫⣛⣿⣶⣶⣷⣤⣾⣿⣁⣀⣀⣀⣀⡀⡰⠋⠈⢳⣴⣿⣿⣿⣶⣤⣄
⠰⠃⠿⣯⡷⣿⣟⡹⡛⢻⡭⣿⣿⣟⠾⢟⡋⢿⣾⣿⣿⣿⣿⣿⣿⣫⣩⠙⠛⠛⠓⣀⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣴⣿⣬⣿⣹⣭⣍⣺⣀⣀⣻⣏⣑⣀⣚⣒⣻⣿⣿⣿⣺⣿⣿⣿⣿⣿⣷⣶⣶⢽⠿⠿⡿⢻⢻⢿⢻
⠀⠀⠛⠉⠁⠀⠀⠈⠉⠉⠍⠩⠛⠹⠋⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠛⠛⠛⠚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣛⣛⣓⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣤⡀⢻⢀⡤⠄⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⢀⣩⢝⠯⣤⡀⠀⠀⠀⢀⠐⠳⠄⠀⠀⠀⠁⠀⠀⠀⠀⠙⠇⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠉⠁⢼⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠂⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡍⠀⠀⡀⣀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⡇⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠐⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⣃⣁⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡈⠃⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⡤⢤⢤⡀⠀⠀⠁⠐⠃⠀⠁⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠒⢂⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⢀⡡⣆⣾⣶⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢈⠊⠀⠀⠀⠀⣠⢀⡄⠀⠀⠀⠰⢂⠚⢛⢂⡄⠀⠀⠀⡘⡈⠀⠐⠀⣀⠀⠃
⠀⠀⠝⠽⣿⡛⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⡛⠤⠀⡃⠆⠀⠀⠘⠀⠀⠀⠠⠂⢀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⢀⠀⢘⡅⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡆
⠀⠞⡞⢻⡇⠰⣾⣷⢖⡶⡖⣀⣤⣤⡌⢓⣂⣄⢘⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢠⣿⠯⢿⠓⠒⣦⣠⣤⡔⢂⣤⣼⣰⣇⢰⡆
⠀⣛⣥⠘⠉⢛⠿⡟⢙⡄⠁⡩⢨⣗⢩⡍⢹⡟⢊⣩⣬⠇⣀⠀⠀⢀⣤⠀⠀⣀⣀⣀⠾⢠⡮⢳⠈⣼⠨⣯⣳⡍⢿⣿⠯⠀⠛⡚⢇⠤⢳⠼⣧
⠀⡯⠘⢶⣸⢓⡖⢹⣅⣷⠚⡳⢘⣵⠈⣓⡭⠶⣤⠒⣶⡂⢿⣿⢻⡏⠛⢿⣿⣯⣿⡿⣺⣙⢈⢫⠀⣶⡠⢿⢧⠱⠶⣿⣆⠩⢠⡈⢻⠒⠸⢱⡼
⠀⠈⢀⣯⡜⠸⣆⡠⠿⣠⠋⣡⡬⡀⢛⡿⢖⡱⢉⣞⠉⡍⠺⣻⡤⠁⠡⠈⢿⢁⡹⡂⡩⠌⢹⡏⣹⠁⢩⡘⢄⠱⠦⣬⡁⠲⡆⠓⠘⣥⡋⡜⠳
⠀⠀⠀⠙⠀⠺⠤⡘⠀⡀⠀⠉⠐⠉⠛⢡⣄⢱⣏⠀⢢⣸⠓⠈⠁⠐⠒⠀⠈⠀⠀⠈⠁⠉⢚⡙⢉⠑⠏⠉⠒⢇⣠⡁⠉⠠⠆⠨⠂⡌⠔⢠⡉
⠀⠀⠀⠃⠐⠁⠄⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⢈⠧⠀⠘⡟⠠⠩⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣭⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣵⣮⡿⠏⣤⣶⣂⣠⠦⣁⠳⡄
⠁⠀⠐⠶⣤⡉⠹⢉⡀⠸⣤⠟⢀⣀⠀⢄⡀⠀⠀⠀⠀⠀⠁
⣶⠍⠄⠐⠆⢽⣷⢿⠿⢶⢇⠼⣍⢰⣤⣀⠉⢣⡂⠁
⣿⣿⣌⠛⣶⣾⣿⣵⣶⠤⡝⠿⣍⢉⢉⣉⠶⠀⠷⣤⣾⠒⠀⢀⡀⠠⠁⠀⡀⠀⠀⠀⠀⠀⠠
⡁⠹⣟⣛⢿⣷⢿⣯⣄⣐⡶⠂⠘⠻⢧⣄⣻⡂⠀⠁⢾⣥⡴⣯⠷⢂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠐
⠷⠛⣷⣮⡉⣿⣟⣇⣠⡄⣄⠐⢀⡴⢀⠈⢁⠻⣄⠀⡈⢿⣼⣿⣀⠀⠁
⣿⣤⣼⣿⣿⣿⡏⠛⣿⣶⣾⠇⠧⠉⠰⢤⣨⠃⠿⠛⠙⣴⣿⣿⡿⠧⣱⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠅
⣉⠹⠿⢿⣿⣿⣗⣲⠚⠻⢵⣶⡖⣾⢒⡸⣹⠃⢱⠿⡔⣄⠻⢿⣦⠀⠈⠄⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⡄
⣥⣀⡘⢿⣿⣿⣿⣿⣌⣀⣠⡏⠁⡀⠀⡘⠉⣤⠒⠾⣉⣃⢀⠸⢧⡦⣶⣆⡄⠀⢁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠣
⢯⣥⠰⢸⣿⡇⣿⣾⢿⣿⣿⣿⣵⣒⡔⠓⠀⣏⠨⢀⡐⠉⠈⠠⢀⡿⠏⠹⠦⢁⠀⠀⢀⠀⠠⠰⠀⡀⠀⠖
⣘⡋⠀⣾⣿⡯⣿⣿⣿⡅⠉⠠⢈⣵⢺⣶⣿⣟⣀⣽⡫⠛⢧⢉⣾⣿⣦⡄⡆⢉⣇⡄⠀⠀⠾⠀⠀⣹⠃
⣴⣷⣶⣯⣿⣿⣿⣿⣿⣿⣦⣶⣦⣤⣼⡿⣿⣿⣿⣿⣿⣿⣦⣬⡁⠤⠉⣙⠛⡀⠉⠰⣤⠠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠠⣄⣀⣙⣿⣿⢿⠂⣗⣲⣿⣿⡻⠿⣏⢡⡯⠉⠛⣻⠟⠛⠿⠿⣟⣷⣬⣌⣐⢠⣄⣠⣀⠲⠤⢤⣀⠀⠀⠀⠀⣀
⣽⣦⣘⡫⠙⡂⢈⠂⡀⡔⠋⣡⣀⢀⢉⣠⣤⣤⣮⠩⢷⠶⠶⠶⢞⠆⠑⠚⠛⠛⠓⠒⠛⠛⠛⠃⠛⠛⠁⠀⠀⠀⠁
⣿⣿⣿⣿⠿⡿⢿⠟⠟⢛⡛⠻⠟⠉⠉⢁⠉⠀⠀⠂
⣿⣭⣤⣤⣤⣤⣤⠄⠂⠄⠘⠃⡠⠁⠠⠂

⠀⠀⠀⠀⠀⢀⡀⢀⠀⢒⣶⣾⣤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣯⡭⠅⠂
⠀⠀⠀⠀⡰⠛⢳⣿⣿⢋⣴⡿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⢏⣫⡙⠐⠀⢀⣴⡖⡂⣠⣤⣀
⠀⠀⠀⠀⠁⢸⡿⠛⠿⢙⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃⡹⠁⠀⠀⠚⠈⢷⠌⠛⠹
⠀⠀⠀⠀⠀⡜⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠢⢄⠀⠀⠑⠤⡀
⠀⠀⠀⢀⠎⠀⢀⠞⠁⣀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠈⠑⠄
⠀⢠⡴⠃⣠⡶⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠈⠺⠄
⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⡕⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠐⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠲⣧⡟⠛⠛⠾⠼⣵⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠁⢄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⣀⡀⠀⠦⠁⢣⡐⠿⣀⡀⢀⣭⢙⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠓⢲⡝⠀⠈⠭⠅⠚⠪⠥⠎⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠌⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⠏⠉⠠⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢑⠬⢖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⣸⠁⠰⡄⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢣⠈⠀⢀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⠀⠀⠀⠐⠀⢁⠒⢪⠀⠈⠒⠲⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠦⠴⠛⠒⠲⠶⠶⢦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠀⠀⡉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢶⡀⢀⡼⣿⣬⣀⠀⣤⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠘⣷⡟⠸⠋⢨⠉⠿⠈⠉⠙⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢻⣤⣾⢋⡀⢡⡆⠁⠀⢀⠈⢀⡔⣰⠃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠊⠂⣬⠟⡇⢠⢊⠉⠀⡀⠀⢡⣭⡎⢳⣟⠀⠀⢷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣤⠞⢿⣏⠀⢹⣠⣖⡀⡢⢸⡼⢏⣿⡇⠾⣧⢤⣤⣼⠷⣧
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡶⣾⢹⡆⣸⣇⣀⣸⡇⢻⣷⢃⣼⠁⣾⣿⣷⡶⠟⠻⠉⠛⢶⣏⣷⣰⡆
⠀⠀⠀⠀⠀⡰⠿⢸⢏⣤⠿⠿⠛⠿⠾⢷⣿⣷⡿⠙⣦⢿⣶⡿⠋⠁⠀⠠⠖⠃⠀⢀⠹⣮⣟⢳⡄
⠀⠀⢀⣠⣼⣅⣠⡾⠛⠰⠋⠀⠠⠄⠈⠑⠂⢄⠙⠻⣿⣯⣉⣀⠁⠘⠀⠀⠤⣄⡀⠀⠁⠬⠻⢦⣷⣄⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠒⠀⠁⠀⠀⠀⠂⠔⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠄⢀⠠⡵⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣠⠴⠇⠀⠀⠀⢟⠎⠙⢆⣀⠔⠒⠒⠒⠲⢮⣀⢀⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢈⡲⣄⠀⠀⠀⢉⡹⢇⠀⠀⠠⠤⠤⠀⠤⠋⠀⠀⢀⠠⢀⠶⠒⠠⠔⣉⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠞⠁⠀⣈⠧⢤⡀⠚⢓⡶⠋⠀⠤⠪⠅⠐⠀⢶⡀⢀⡄⠀⠀⠀⠘⡀⠀⠰⣈⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠈⠀⠀⠀⠙⣯⡤⣶⠉⠀⠀⠤⢤⣄⣠⠀⠀⢠⡙⣺⢦⣀⣀⡠⢼⡂⠀⠠⠈⠳⢤⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢘⣯⠶⢃⣀⣀⢀⠂⠀⡠⠀⠊⠁⠐⠀⠤⠈⠄⢠⠄⠀⠀⠽⠿⡤⠤⠆⢶⠣⠴⠄⠨⠙⠷⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⡀⠂⠀⢀⣵⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠦
⠀⠀⠀⠀⠈⢁⠀⠀⠈⢇⠀⠀⠀⠀⠄⠐⠐⠇⢀⡈⠃⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠀⠀⠀⣿⠸⢀⢀⠆
⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠳⠂⠐⠒⠋⠉⠉⠀⠀⠁⠀⢀⠭⠐⠠⣄⠀⠀⠀⠀⡰⠆⠗⣇⠀⡀⡀⠀⠩⢅
⠀⠀⠀⡐⠀⢀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⢄⠨⣀⢘⠀⠀⡰⠃⠀⠀⠉⠂⠀⢄⠀⠀⠀⠡
⠀⠀⠀⠃⠐⠈⠰⠚⠂⡀⠀⣀⠀⠀⠀⠀⠀⠈⡅⠢⠎⢰⠤⠔⠂⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⣀⣸⣀⣠⠴⠒⠊⠁⠀⠀⡀⠀⠰⠄⡀⠀⠐⣤⠀⠀⠺⠀⡀⠀⠀⠂
⠀⠀⢐⡒⠀⠀⠠⠤⠨⠓⠈⠁⠉⠀⠀⠀⠟⠦⠓⠂⠉⠀⠑⠊⠈⠀⠀⠀⠀⠀⠀⠒⠒⠒⠠⠸⠱⠈⠑⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⣤⣦⡶⠟⠓⠲⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠜⠤⠶⠢⠆⠴⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣚⣟⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿⣡⣟⠓⣏⠙⠿⢆⢤⠄⠀⠀⠀⡀⣤⡤⣤⡀⠀⢠⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠘⣀⡜⣿⡇⠷⣼⣷⡀⠈⠀⢀⠀⠀⣪⣿⣿⡄⠲⣄⣤⢾⣿⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⢻⡇⠀⠨⣗⠁⠂⠀⠀⠀⠸⠃⠀⣽⣽⣆⠸⠏⢿⠈⢓⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢦⡌⠳⢄⡀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⡀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠈⠑⠦⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠳⣄⣀⠘⣆
⠀⠀⠀⠀⠀⠀⠟⠛⠲⠶⠂⠀⠈⠁⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣄⠀⠈⠻⣧⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⠤⡤⠤⠤⠤⠖⠛⠡⢀⡀⠐⠙⠁⠀⠀⠀⠀⠈⠻⣷⣄⠀⠙⣆
⠀⠀⠀⠐⠒⠒⠂⠈⠉⠉⠉⢉⣁⣀⣀⣀⣀⣀⣀⡤⠀⣀⠤⠴⠴⠖⠋⡹⠀⠀⠀⠀⣀⡤⠤⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠤⠀⠠⠴⢖⣫⣭⡥⠶⠶⠶⠶⠶⠶⣤⣤⣤⠤⣤⠤⠖⠊⠁⣀⡠⠀⠊⢁⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠠⠤⠄⠒⠀⠀⠊⠉⢀⡠⠒⠈⠀⠀⠀⡠⡊⣨⢧⠷⢾⣋⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠤⠒⠈⣀⠤⠔⠂⠀⠄⠀⠀⠀⠀⠠⠴⠻⢚⠏⠑⠛⠰⠖⠠⠀⠀⠀⠀⠒⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣸
⡇⣠⠿⠀⡀⣤⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣿⡉⠀⠺⣳⠀⢸⡟⠀⡄⣸⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⣾⣥⣌⠉⣠⡼⠂⠸⢁⣘⢻⣯⢀⣼⣴⡯⠤⣾⣠⠀⠀⡀⠁⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢿⡶⠂⠠⠤⠀⢀⣬⡍⠼⣥⠀⣿⣿⠛⠂⢹⣿⣄⣼⢁⡀⢀⠁⡀⠀⣰⠀⡀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⡀⣀⠀⢠
⡷⠨⣙⣟⡳⠒⠀⢸⡟⣀⣘⠟⡯⣿⠛⡘⣋⡀⣽⣿⠟⣛⣦⣿⣼⡇⢰⡿⢻⣧⣶⡾⠇⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⣶⣿⣡⡏⣾⣿⣵
⠀⠀⠀⠀⠈⠈⠀⠘⠛⣷⠍⠂⣼⡻⠂⠠⠤⠀⢐⣿⣧⠆⠰⣿⡗⠭⢿⡥⠄⢿⣿⡷⠼⣿⡿⢲⣾⣆⡀⢀⣄⣤⣿⣿⣿⣿⣿⣿⡿⠥⠽⠿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢯⡃⢦⣤⠄⠀⠉⢻⣇⠐⠈⢻⡿⢠⢽⣏⣀⣋⣿⡥⠀⢹⣇⣈⣿⡿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠾⠿⣯⣘⡛⣷⣀⠊⢿⡧⢴⢺⣄⣐⠈⣷⡆⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠚⠛⠶⠿⠿⠿⠒⠛⠉⠉⠁





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠤⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣥⢶⡶⠄⡀⠀⠀⠀⠀⠉⣙⠙⢳⡅⠐⡆⠈⠉
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣥⣵⣯⠔⢁⡀⢠⢀⣀⡄⣠⡠⠶⠿⣣⡀
⠀⢀⣤⠠⡀⠀⠸⡇⠀⠀⠀⠀⠀⠔⠒⠂⠠⠄⠠⡀⠀⢀⠀⠂⠀⠒⠀⠀⠀⠀⠈⠀⢠⣞⣷⢞⣯⣶⠘⠋⠛⠀⠋⠀⠀⠀⠉⠩⠇⣀
⠀⢸⣼⠀⠈⠄⠈⢆⠀⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⠒⠄⣈⣽⣿⠛⠉⠋⣁⡀⠀⠴⠖⠀⠀⣀
⠀⠀⠿⠀⠀⢠⠀⠀⠀⢰⣇⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣇⠀⠀⠀⠰⠿⠻⢿⣷⢿⣿⣻⣷⣾⠀⠀⠀⠁⠀⠤
⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠄⠀⠤⠤⢧⣴⣤⠴⣼⡧⡄⠀⣦⡀⣠⡤⠀⣠⣠⠼⣷⢖⡂⢤⡴⠞⡡⠂⠀⣠⡠⢵⠀⢰⢾⣿⣶⣶⣾⣾⠆
⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡴⣿⣿⠶⠾⠿⠻⠭⠭⠩⠍⠉⠉⣤⡍⢄⣶⠄⠀⠠⠒⠘⠀⣱⡴⣾⢻⣿⢿⣿⢹⡇⠆
⠀⡀⢀⣀⠀⠒⢒⠚⠛⠘⡿⠛⠛⣖⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⣴⣻⡿⢢⣿⣆⠔⠛⣾⡿⢸⣯⠬⠋⣸⣿⢈⣿
⠀⠀⢀⡠⠀⠀⠈⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⣬⡽⡿⠗⣸⡷⢿⠟⠓⢿⡿⢀⣓⠀⢨⢸⡞⢿
⠀⠀⠠⣐⡄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⠘⣹⠇⠀⠀⠁⣼⠃⠀⠀⢀⣘⢸⢧⢈
⠀⠀⠀⠀⠀⠈⠉⡟⠲⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⢀⠀⡔⢛⣉⠀⠈⠘
⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐⠒⠲⠦⠭⠭⠍⠉⠩⣭⣤⠧⠤⡀⢀⣠⣀⠀⠀⡀⡔⣤⠀⣤⣼⣠⣤⣀⢀⡀⠠⡇⣿⡆⠈⠈⠉⠉⠀⠃⢰
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀⠀⠀⠀⠁⠀⣘⣤⠟⠃⠀⠈⠿⠗⢛⡛⠙⠉⠉⢉⠥⠴⠛⠛⡇⢹⡇⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡇⠈⢀⠈⢀⠰⠌⠋⢹⣷⠀⠀⡦⠀⠀⠀⠘⠏⠈⠁⠒⠀⠀⠐⠀⠀⠇⣼⡇⠀⠀⠀⠀⠀⡟⠀⢤
⠀⠤⠄⠀⠀⠄⠶⠀⠀⠰⠂⠀⠸⠾⡇⠆⠛⣶⠘⠒⠉⠁⠘⢉⣿⡇⢀⡀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡀⠀⠀⠂⢹⡇⠀⠀⢠⠖⠂⠅
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠤⣄⢙⠀⣀⠒⠂⠂⠀⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⣧⠀⣀⠐⠠⠀⠔⠉⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠁⠘⢀⠀⠀⣠⣴⣿⡟⠙⠃⠀⠈⠂⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣦⡀⡼⣮⣿⣤⣤⣤⣤⣀⣀⡀
⠒⠒⠒⠀⠙⠛⠓⠂⠀⠀⠀⠚⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠋⣭⠭⠽⠿⢿⠩⠽⠛⣿⠛⠻⠝⠛⠛⠋⠉⠉⠉⠉⠉⣩⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣠⣤⣠⣶⣤⣶⣶⣶⣶⣤⣤⣴⣤⣤⣦⣤⣤⣬⡥⠼⠤⠤⠍⣿⣼⣤⣶⣦⣤⣤⣄⣀⣀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠻⠿⣿⡿⢿⣿⡿⢿⠶⠛⠉⠀⠀⠀⠀⠀⣡⣿⣿⣶⣾⣿⣿⣿⣿⣿⣽⣿⣿⣟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣲⣟⣶⣿⣀⣿⢻⡯⠓⠈⠀⠀⠀⠀⠀⠀⢀⡠⢰⣿⣿⣿⣿⣿⣿⠿⠭⠭⠿⠿⠿⠿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣋⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢡⣿⣿⣿⣿⣿⣿⠾⠛⠛⠛⠀⣴⣀⠀⡀⣠
⣤⣤⣤⣄⣀⡀⠀⠀⠄⠀⣀⣀⣀⣀⣀⠀⠂⣠⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡍⢠⣿⣿⣿⣿⣿⣭⡉⠻⢿⣒⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⡩⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⢀⣿⣿⣿⣿⣿⣿⣿⠽⠟⠻⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣿⣿⡿⠿⠛⠡⠤⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢩⠋⢀⣾⣿⣿⣿⣿⣿⡿⢾⠿⠿⠃⠤⡍⠀⣢⣭⣿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡽⠛⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠒⡿⠒⠂
⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⠖⠁⠴⡏⠀⠀⠀⠀⢀⠀⠔⠠⠏⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠀⠀⢸⣧⠀⡴⢏⣤⠒⢦⠄
⠀⣴⢠⣿⡿⢀⡀⠀⠀⠀⣠⡶⠂⣀⠀⠀⠀⢁⣀⠀⡐⠀⠀⣠⢤⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣸⣷⡄⢿⠛⢿⣣⣀⣀⡄⢀⡀
⣾⣿⣿⣿⣇⣾⠁⡀⢀⢠⠠⠶⢂⠈⠀⠀⠀⠁⢸⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⡀⠀⠀⠸⢻⡄⠀⢸⣿⠟⠷⣦⠒⠀⠈⣯⠉⢉⣸⡇
⢺⣿⠛⢨⣿⣿⣼⣷⣟⣠⠰⠀⡼⠁⠲⡴⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⡀⢀⠞⠿⣁⠀⢙⡀⠚⡀⠲⣧⠔⢦⡘⢶⣤⡙⢻⣴
⢸⢿⣃⣤⢹⣿⣿⣿⠟⣡⡄⠀⡤⢀⡠⠀⢲⣶⣴⡄⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡬⢓⠇⢠⣠⡼⠆⠙⡧⣎⣀⠚⠙⢢⣻⠆⠀⠑⠂⠘⠿⣿⣿
⠠⡾⠋⢃⢸⣿⠟⠋⢁⠇⠈⣀⠀⠀⠀⠓⡀⣻⣿⣿⣿⣷⣶⣼⣴⣶⣠⣄⢀⣠⣴⣶⣼⣷⣶⣾⡶⠣⠤⣘⣇⡠⢢⣈⡶⠉⢀⡄⠀⠀⢻⡃⠀⠀⠠⣄⠀⢈⣿
⢀⣆⠀⠋⢘⣥⡴⠚⠛⠠⠖⠃⠀⠀⣀⠀⠉⢺⣿⢿⣿⢻⣟⣿⣻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡿⠂⢀⡀⠈⠡⣴⠀⢹⡴⠞⢉⡴⣦⠜⢶⡤⠀⠀⠀⠘⠛⠿⣿
⠸⠧⠆⢁⡞⠋⠀⠰⠂⡴⠦⠀⠀⡾⣯⠉⠢⣄⡛⣏⠍⣋⣽⣥⡿⠟⢁⡀⠀⠀⠀⠀⠈⠛⣿⡀⠄⠈⠉⠻⢷⣎⢢⡼⠷⠒⠉⠀⠘⠦⢄⡙⠀⠀⠐⣆⠀⠀⢈
⠀⠀⠀⠈⡽⠋⡀⣀⡔⠀⢀⠌⠛⢇⠘⡶⠀⠈⠉⠉⠉⠉⠏⢀⠤⢾⣧⣽⣷⣤⣀⣀⣠⣤⠌⡀⠀⠐⠂⡐⠦⣽⣿⣯⠔⡠⣆⠀⠀⢦⡄⠈⠛⣤⠀⠈⠁⠢⣌
⠀⠀⢀⡼⠓⠀⠁⠰⢤⡤⠟⠀⠀⢀⡓⠙⡇⢠⣄⢨⠀⠀⠀⠙⠺⠿⠛⠒⠓⠚⠛⠛⠚⠡⠀⠤⠐⠃⠠⠟⢦⣤⡹⠟⠊⠁⡼⡀⢠⠿⠟⠀⢠⢈⣦⣾⠀⠀⢻
⠀⠠⠞⠡⠀⣀⣤⠖⠾⡄⠀⠀⠀⠈⢳⣠⠝⢦⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡀⡀⠙⠈⢢⠀⢄⠀⠻⣆⡀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠚⠃⠐⠊⠉⠂⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣤⠄⠞⠉⠣⠠⡀⠀⢦⡨⠦⠀⢨⣿⢯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠰
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣽⣭⣿⣭⣯⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣶⣾⣿⣿⣶⣾⣶⣶⣶⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢘⣿⣻⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡃⠀⡄⠀⢠⣯⠄⠀⠀⠀⠀⣸⠀⠀⢀⠀⠀⠀⠀⣨⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠠⣿⣿⠿⣿⣄⡀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢢⢠⣇⠀⣰⣿⡇⢰⠀⠀⣴⣿⡷⠀⢀⣆⢰⣿⣇⠀⣾⠀⠀⡀⠀⣼⡆⢀⠀⠀⢀⣼⣧
⠀⠢⢼⣿⣿⣶⣉⡶⢿⣤⠀⠀⣼⣿⣇⠀⢰⠀⠠⣿⠀⠨⠀⢠⣿⣾⣿⣤⣼⣿⣿⣿⠀⢴⣾⣿⡟⠂⢼⣿⣿⣿⣿⣿⣿⣦⣠⡆⠀⣼⣧⣾⡆⠀⢠⣿⣿⠄⢰
⢠⣾⣾⣿⡿⢿⠯⢹⣿⣿⣷⣾⣿⣿⣿⣶⣿⣶⣼⣿⣦⣾⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣀⣿⣿⣏⣼⣷⣿⣿⡿⠟⢟⡛⢿⣿⢿⣿⢈⣿⣿⣿⡇⠀⣼⣿⣿⣇⣾
⠘⢿⣿⣿⡿⣌⣴⣿⠿⠉⣿⡿⠿⠿⠟⠛⠙⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⢿⠟⠓⠚⠛⣵⡎⢿⣾⣿⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠛⠻⠿⣤⣿⣿⢡⠤⡤⠠⠀⡦⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠉⠀⠂⠀⠀⠀⠀⠀⠉⠋⠉⠉⠙⠛⠛⠿
⠀⢺⠙⠇⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⣀⣀⣠⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡄⠤⠀⠀⠦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡦⠀⠄⠀⣴⡛⠍⠑⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉
⠀⠀⠀⠐⠀⠀⢀⠈⣯⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠀⠈⣀⣯⣀⡀⡀⠀⠘⣷⠀⠰⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣀
⠀⠀⠀⠀⠀⢀⣄⠀⣇⢘⡗⠀⠀⠀⢉⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠰⠐⠀⠘⠃⠀⠀⠀⠀⠤⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⢨⠀⠀⠐
⠀⣤⠈⠈⠀⠀⡏⠀⡏⠀⠍⠀⠀⢸⢐⠀⠐⠀⠒⠂⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠐⠂⠀⠂⠀⠀⠀⠂⠈⠑⢲⠀⠄⠀⠀⠀⠀⠸
⢐⡙⣈⣉⠉⠀⣇⠀⣇⠀⣅⣀⣣⢼⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠁⡄⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠈⠀⢀⠀⠀⠈⠀⡃⠀⠀⠀⠀⠈⠁⠀⠐
⠈⠄⠤⠬⠤⠤⠾⠤⣯⠀⣭⢰⡶⠄⢀⣆⠀⠀⠢⠴⠤⠤⠶⣤⠤⠶⠆⠁⠶⠿⠛⠡⠞⠀⠀⠒⠶⠂⠈⠁⠀⢱⡦⠶⠶⠷⠦⠤⠤⠀⠠⠤⠄⠄⠄
⠀⠀⢀⣴⠄⡀⠀⠀⢠⠀⠙⠀⠀⠀⠘⠟⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚
⣀⡔⠿⣿⡿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⣶⡄
⠺⢶⠀⠁⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢶⠀⡀⠀⠀⠹⠟⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡘⠁⠀⠀⠀⠀⠀⠠⠶⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣾⠶⢠⠀⠀⠀⠀⠀⠀⠀⠇⢀⠆⠁⠀⠈⠉⠁⠀⢀⡩⣤⠘⠟⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡼⠀⠀⢀⡀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⡦⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠀⠀⠐⠒⠀⠀⠄⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠄⠁⠱⣄⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠓⠒⠒⠒⠒⠒⠒⠒⠂⠤⢄⡀⠀⠈⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣠⠤⡤⠤⠤⠤⢤⣀⣀⠀⠀⠈⠑⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠘⢤⣠⡏⠂⠀⠈⢦⡀⠀⠀⠀⠈⠉⠒⢄⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣶⠯⣍⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡡⣷⠐⡡⢿⠒⠤⣀⠀⠀⠀⠀⠱⡀⠠⠂⢀⠤⠐⠂⠀⠀⠐⠂⠀⠈⠁⠀⠀⠈⢻⡴⠭⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢧⠈⠀⠀⠀⠠⠱⠄⠈⠉⠁⢢⡀⠙⠤⢀⣁⡀⠀⠀⠀⠀⠀⢀⣤⠤⠖⠒⠒⠒⠒⠻⠛⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠑⢄⡐⠐⠚⠃⠀⠀⢀⣠⠏⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⢀⠀⠀⠀⠀⡠⠐⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠌⣟⠐⠒⠒⠛⠉⠀⠀⣀⡨⠆⢀⠀⠀⠠⠄⠀⠠⠤⢄⡀⠈⠁⠂⠈⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠈⠐⢶⠀⠀⠠⡀⠀⠈⠉⠀⠐⠖⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⢻⣌⡐⠤⠀⣒⠈⠀⠀⠲⣂⣂⠃⠐⠂⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠀⣈⠤⠀⠀⡠⠐⠀⠉⠉⠁⠙⠀⠀⠈⡇⡻⣀⣁⣀⡐⠠⡄⠀⠈⢁⠀⠆⠓⢠⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠘⠤⠚⢦⠴⠥⢰⠄⠁⠡⣀⠀⠀⠀⢀⣀⡤⠴⠚⠁⠁⠙⡀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢎⡤⡤⠀⠒⠁⠀⣀⡌⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉⠒⠒⠒⠋⠁⣨⠴⠒⠉⠉⠉⠉⠁⠒⠒⠲⠤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠵⠄⠉⠂⡀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⠠⠀⠓⠠⠤⠊⠀⠀⠒⢎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⡀⠈⠂⢄⡀⠀⠤⠔⠓⢄⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⠁⠆⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢢⡄⠀⠀⠂⢠⠄⠀⠀⠑⢆⠂⡁⠄⠀⠂⠈⢀⣀⡠⠤⠔⠒⠉⠁
⢷⠠⠄⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠤⠤⣄⣀⣠⠀⠡⠤⠀⠀⠀⣀⣀⡠⢜⣁⡠⠤⠖⠒⠋⠉
⠈⡑⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⣒⠠⠭⠁⠉⠛⢒⣒⣒⠦⠭⠿⠛⠚⠉⠉
⠀⠹⢌⣒⠒⠒⠒⠒⠒⣉⣉⣁⡤⠤⠴⠒⠒⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠆⣀⡀
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠠⢤⢀⢬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡸⠄⡀
⠀⣠⡾⠟⠁⠀⠀⢀⠀⠐⣊⣠⢤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⠀⡾⠃⠠⣄⠒⠆
⠠⠿⠿⠿⠄⠀⠀⠀⠀⡀⠈⣤⠀⢀⠰⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠛⠂⣮⠅⣈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⢨⠀⡠⠀⠺⠇⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠵⠂⠨⡡
⡀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠉⠙⠒⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⠀⠰⠀⠀⠀⢠⣅⣋⣭⡟⠒
⠈⠀⠀⠀⠀⠀⠀⢐⡤⠾⠀⠼⠀⢳⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠄⠿⢶⣶⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡄⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⡀⢙⠀⠀⢸⣿⡿⣿⣿⣷⣾⠿⠷⠐⣿⣿⣿⣿⣮⣅⣼⢏⡃⠀⢈⡄⠀⢨⣿⣿⣿⣿⣿⠟⠁⠁⠀⢛⣀⡌⠙⢷⣿⣷
⣭⣿⣿⡄⠀⠀⢘⡉⠀⠂⠀⠀⢸⡋⠘⡄⠀⣸⣿⣹⣿⣿⡏⢹⠀⠀⠀⢰⡿⣿⣿⣿⢃⣿⡇⠁⠀⠢⠀⠀⢸⣁⣹⣻⣿⣿⣤⡀⠀⠀⢿⣿⣿⣦⣰⡌⠻
⣿⣿⣿⣿⡆⠀⠀⠈⠉⠘⠀⠀⣾⣧⣼⣥⣰⣿⣿⣿⣿⡿⡥⢺⣀⠀⠀⢨⠀⠐⠉⠉⠚⣿⣇⣤⣀⠈⠂⠀⢸⢿⣻⣿⣿⣾⣧⡄⢰⠀⢺⣿⣿⣿⣿⡇⢰
⠛⣿⣿⣿⡇⡀⣀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⣃⠘⠿⠇⠀⣿⣿⣿⣷⣶⣴⣿⡿⠋⠀⠰⣦⡄⠘⣿⣿⣯⣛⣻⣿⡇⢸⠀⠸⢿⣿⣏⡙⠃⠸
⠶⣿⣿⣿⡇⠀⢻⣶⣦⡔⠀⠀⣠⣜⣻⣿⣿⣿⣿⣿⡟⠀⣻⠀⠀⠀⠀⣿⣘⣻⣟⡿⢻⣿⡇⣿⡆⢸⡉⠀⠀⣿⢿⣿⣿⣿⡋⠀⠸⠀⢸⣿⣿⣿⣇⠆⢸
⠀⣿⣿⣿⡇⠀⢸⣏⠉⠧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⢿⠀⣿⡷⠀⠿⣿⣿⣿⣿⣶⣶⡇⣛⠃⠀⣇⠀⠀⣁⣀⣉⢉⣿⣷⠶⢠⡄⢸⣿⣟⣿⣿⡄⢸
⣶⣿⣿⣿⡇⠀⠸⣥⢠⡇⠀⠠⠀⣟⣸⣿⣿⠏⢼⡿⠓⠀⣽⠀⣿⡇⠀⠀⡿⣿⣿⣿⡿⢻⣧⣤⣤⣴⣿⣶⣿⣿⢿⣿⣿⣿⣶⣤⠸⠃⠈⢿⣿⣿⡉⠁⠸
⣿⣿⣿⣿⡇⠀⠀⣿⢀⡁⠀⠀⣸⣿⣟⣿⡏⠀⢠⡁⠈⠀⢾⠀⡿⡇⠀⠀⣧⡆⣽⠙⠣⢿⣯⡟⠉⠉⣀⡀⠠⣴⣶⣿⣿⣿⣿⣿⠀⡄⢀⣴⣯⣿⡋⣿
⣍⣿⣿⣿⡧⠀⢰⣿⣦⢷⣤⣴⣿⣿⣿⣿⠀⠀⢸⡟⠠⠀⢻⠀⣧⣿⣿⣧⣿⣷⣾⣦⣶⣯⡷⡷⠶⠶⣿⠁⠀⢸⣿⣿⣿⢻⣏⠀⠀⠁⢸⣛⣟⣿⣿⣿
⢿⣿⣿⣽⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠸⠗⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⣶⠀⡽⠀⠀⢸⠃⠉⢙⣻⢿⡆⠀⡖⠈⣿⣿⣿⡏⠉
⡋⠉⣿⣿⣿⣿⣿⡇⢚⣗⣹⡇⣿⣭⡿⣛⣛⣿⢻⣿⠿⣶⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠂⣦⣀⣀⠂⠀⣾⣷⣿⣿⣷⣶⣤⠀⡇⠀⡍⣿⣿⠿⢰
⣤⣤⣿⣿⣿⣧⣽⣅⣈⣿⣿⡃⢻⠉⠾⠛⢛⡵⢿⡟⣵⡸⣿⣿⣿⡆⡆⠂⠨⢉⠩⣽⢹⣿⡛⣄⢋⣸⣿⣧⣄⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⣿⣿⣿⣿⡞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣶⣶⣶⣶⣿⣧⣿⣿⣿⣇⣷⣀⣐⡌⠀⣼⡞⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣀⡀⡀⠀⠈⠉⣿⣶⣶⣿⣿⡷⠇⠀⠸⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠀⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⡦⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣋⠉⠉⠁⠈⠉⠉⠉⠙⣿⢶⣾⣿⡿⢇⡒⠀⠀⣿⣟⣻⣿⡄⠀⠀⡆⠤⣼⣿⣿⠀⣿⡟⣿⣿⣷⣿⣿⣿⣿⣯⣼⡏⣁⢿⠙⣿⣿⣿⡿⣿⠿⢿
⣿⣿⣿⣿⡅⢀⠀⠀⢀⣀⣀⣀⣀⣿⠙⠛⣿⣡⠞⠻⡄⠀⣿⡿⢛⡹⢿⠀⠀⠁⠁⠀⣹⣿⠀⣿⠁⠙⢿⣿⣿⢿⣿⣿⡿⠻⠃⠙⠋⠀⠻⠘⠻⡇⠻⢷⣼
⣿⣿⣿⣿⣿⠹⠂⢀⡄⠈⢿⣿⣿⣿⠒⠺⣿⣿⠄⠀⣼⣿⣿⡁⣾⣿⣾⡍⠀⠀⠀⠀⢻⡷⠖⣿⠇⠀⢸⣾⣶⣿⣴⣶⡆⢠⡡⡄⢐⠀⠀⠀⣀⡇⠀⠹⣿
⣿⣿⣿⣿⣿⡀⡀⠈⠇⠀⢺⣿⣿⣿⣤⣴⣿⣿⠀⡆⢸⣿⣿⣧⣽⣿⣟⠀⠀⠀⢀⣀⠀⠁⠀⠹⢠⡆⣿⣭⣭⣿⣭⣿⣶⣾⣿⣷⡼⠀⠀⠀⣧⣴⣶⣶⣿
⠉⠉⠉⠉⠁⠀⣿⡄⠀⠜⠂⠀⠛⢀⣀⣀⣀⣀⡘⣀⣄⣠⣤⣤⣬⣿⡿⠀⠀⠀⣬⠀⠀⢰⣶⠆⠶⠞⢿⡿⢻⣛⡋⠀⠈⠛⣹⠟⡕⠀⠤⠴⠄⠀⠀⠴⠴
⠶⣶⣶⣿⣷⠀⠈⠓⠀⠀⠀⠀⠀⠻⠛⠛⠛⠛⠓⠛⠟⢛⡛⢋⠉⢯⣀⣀⡀⢀⣀⠀⢰⣿⠤⠴⠿⠞⠛⠛⠛⠛⢁⣀⠀⠀⠁
⣿⣿⣿⣿⠏⢀⣀⢀⡀⠤⣆⠀⠀⠀⣀⣀⣀⣀⣠⣽⣿⣿⣿⣟⢛⣋⣉⣉⣁⣈⣉⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠛⠛⠛⠿⠶⠿⠿⠋⠁⢀⡷⠀⠀⠀⠉⠀⢤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⣠⢤⣤⠀⠀⠛
⠀⠀⠀⠀⡜⠁⠀⡺⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠛⠐⠂⠉⠁
⠀⠀⠀⢰⠀⠀⠀⠃⣠⡀⡌⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⢰⡀⠀⢀⡞⡀⢁⣀⡀
⠀⠀⠀⠀⠓⠶⠚⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣻⣿⡟⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠿⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠟⠿⠚⠻⠼⠟⣿⣽⣷⣾⢻⣿⣷⣦⣤⣤⣿⣇⣴⣶⠶⣦⡀⠙⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠁⠀⠀⠀⠀⠀⣠⠌⢻⣶⣿⣻⣿⡈⠉⠉⣉⠜⣫⣤⣴⣶⡈⠻⠷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⣀⠀⠀⠀⠀⠀⠨⢾⣟⣿⡟⠛⠿⠟⠿⣋⣡⣤⣤⣈⠻⣷⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣀⠀⠀⢁⡾⢿⣿⡿⠿⣶⡶⡿⢛⣉⣉⣉⡉⠻⣷⣤⣤⣬⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠙⠉⠁⠀⠀⢛⣛⠛⠾⣷⣦⣤⡶⠟⣋⣉⣉⠛⢿⣦⣄⣈⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠻⢷⣦⣈⣡⡖⢋⣉⣉⡙⠻⣦⣍⡛⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⠛⠛⢶⣬⣉⣥⠀⠀⠀⠉⠙⠳⠤⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⠿⣦⣬⣉⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⢀⡀⠠⠤⠄⠂
⠀⠤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣫⠄
⠀⠀⠀⠀⢠⣄⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣩⢧⠶⠂
⠀⠀⠀⠀⣄⣈⣱⣆⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⣩⣿⣦⣶⠛
⠀⠀⠀⢠⡌⠉⢡⣎⣁⣀⡄⠀⣠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣤⣾⣥⡼⠳⠶⠾⠃⢀⠀⣠⠄
⠀⠀⠀⠀⠓⠚⣯⠉⢉⢁⣠⠀⠋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⡞⠀⠀⠀⢰⠃⠁⢺⣤⠿⢶⣧⡾⢿⣶⠶⠾⠋⠊⠀⠟
⠀⠦⠐⠶⡴⠾⢛⡓⠟⠉⠁⠀⠀⣧⠀⡀⢀⡀⠀⠈⢧⡄⠠⢠⠆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣟⣫⡿⠶⢟⡿⠶⠶⠂
⠀⠀⠶⣦⣀⣴⠞⠛⣶⣄⣼⠻⠇⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣳⣫⣿⣭⣿⣟⣻⡷⢶⡾⠇
⠀⢀⣤⣬⣡⣂⣴⣾⣇⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣽⠶⠖⠺⢛⣿⣷⣤⣤⣶⠄
⠀⠉⠉⠉⠙⡉⠉⣹⡋⠛⠋⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠶⠼⠿⠿⣿⣧⣤⣤⡤⠆
⢀⡝⠛⢿⣍⣠⠾⠻⡿⢷⠆⣦⠆
⠈⣿⠏⣉⣈⠈⣀⢾⣧⣀⠀⡾⠟
⠀⠀⠀⠀⠿⠋⠏⠈⠙⠛⠋⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠲⢦⣄⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣀⣀⣀
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⣻⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡴⢾⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠿⢫⡟⠛⠛⠻⣤⣞⡃
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠙⢦⣤⣀⣀⣠⣤⡞⠉⢳⣦⣤⣀⣀⡀⠀⢀⣀⣤⣏⡿⣠⣭⡗⠀⠀⠀⣿⠉⢿⠄⢀⣄
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⠹⣤⣤⣤⣽⡜⢯⣩⣟⢻⣍⣧⠙⣴⣧⣴⠟⣦⣤⡾⠡⣿⡭⠤⠟⠼⠧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣶⢂⡶⢶⣲⡶⣠⠶⠶⣦⡴⢶⡶⣀⠰⡖⢶⣔⡶⠒⣆⢲⡒⠒⠓⢶⣘⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢾⡉⢰⡇⠀⠀⢸⣗⠛⢰⠋⣷⠙⣻⡏⠀⠀⠘⣧⠛⢶⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢧⣤⣤⣤⠟⡴⠞⠛⠳⢷⡙⣦⣀⣀⡴⣷⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡴⠒⢲⢆⡘⣇⠀⠀⠀⣰⢃⡄⢶⠶⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⣷⠙⢲⣶⠚⢡⡏⠹⣎⢧⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⢁⢺⡄⠙⠶⠛⠹⠷⠖⠋⠀⣸⠂⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠟⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⢿⣿⣿⣿⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⡿⠈⢿⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⣿⣿⠀⠀⠀⠈⠉
⠀⠀⠀⠠⠤⣄⣀⣄⣀⡀⢀⣠⣾⡿⢋⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⣀⣀⣠⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⠶⠦⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣦⣄⠀⠀⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⠿⣿⣷⣄⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣘⣿⣷⣄⡙⢿⣷⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⣛⣿⣿⡿⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠿⠿⢷⣦⣀⣀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⣀⣠⣶⣿⠿⠋⢁⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣤⣴⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠲⠶⢶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣉⠙⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⣾⣿⣿⣿⣿⡿⣿⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⡎⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣼⣿⡿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣿⡿⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⢀⡀⠀⠀⠠⣀⣀⣀⠀⠀⢀⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠠⠤⠤⠤⠿⠿⠿⠿⠷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠀⠈⠉⠙⠛⠲⠶⠤⣭⣽⣿⣿⣿⣿⠿⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⠶⠦⣬⣭⣍⣓⣒⣶⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⢓⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠓⠚⠻⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡺⡟⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠛⣒⡲⢤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢒⡜⠀⠆⠀⠀⢾⢦⡏⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠘⠂⣀⣦⣀⠀⣠⣼⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣧⣉⡉⠁⣈⠥⠚⣽⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠻⣉⡉⣇⣠⠎
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠰⣇⡀⠀⡷⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢳⣀⣤⣀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢐⡷⠯⠞⠁⠀⢀⣠⠴⣊⠥⠒⠉
⠀⠀⠀⠀⠀⠀⣿⣅⣄⡼⡏⢹⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣿⣿⣿⡿⠟⣫⠟⢄⡀⠈⠀⠀⣀⠤⢚⣩⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠙⠾⠷⢖⠙⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠷⠚⠉⢀⡤⢒⡉⠓⢄⣈⠥⠒⠉⠀⠤⠴⡋⠀⡖⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠉⠒⠒⢀⠉⠉⢀⡠⠔⠈⢳⠀⠀⠀⠠⠀⣤⠀⠀⠓⢀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠁⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⢀⡀⢠⠎⡀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⣠⡤⠶⠒⣚⠞⠁⠀⠀⢀⣠⡴⠾⠋⠀⠀⠀⠀⢀⡤⠂⠁⠀⠥⠞⠁⠈⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣴⠋⠉⠀⠀⢀⡞⠁⠀⢀⡤⠚⠋⠁⢀⡠⠔⠂⣙⡶⠊⠀⢀⣀⣀⢠⡀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⠷⠤⠐⠉⣷⠀⠀⠀⠀⣧⣀⣀⠜⣄⢠⠴⠚⢁⡠⠔⠊⠁⣀⠴⠚⢁⡠⠔⣋⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠣⣄⣠⣴⣯⠀⠀⠀⠀⢆⠀⠀⢀⣼⣀⠴⠚⠁⢀⡠⠔⠋⢁⠤⠒⡡⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣎⡝⢢⠀⠀⠘⣿⣿⣿⣆⢀⡠⠔⠈⢹⣿⣿⣿⠀⣀⠤⠚⠉⣀⠔⢊⠡⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡰⠛⣱⠞⠀⠀⠀⣈⡿⠛⠋⢳⡠⠔⠊⠈⣿⣿⢿⠋⢁⡠⠔⡩⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣠⠒⢊⣤⣀⠭⠛⠁⣀⠐⢛⣢⣤⣉⠺⢓⠡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⢉⡩⠛⠉⠀⠀⣠⠴⠋⠉⣉⠝⡋⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣠⠄⠊⠁⠀⢀⡠⠖⠉⢀⡠⢖⡩⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⣀⡤⠒⠉⠀⠀⣀⠴⠚⠁⣀⠤⠚⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⢁⡠⠔⠊⠁⠀⢀⡠⠔⠋⢁⣠⠔⠋⠁
⠀⠀⣀⣀⣤⠴⠚⠉⣀⠤⠒⠉⠀⠀⣀⡤⠒⠉⢀⡤⠒⠉
⠈⠛⠻⠮⠥⠖⠒⠉⠀⠀⢀⣀⠔⠊⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠭⠥⠄⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⣄⣀⠀⣠⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣄⣀⣀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣦⣄⠈⠉⢹⣿⣿⡦⠭⣤⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡀⠀⢻⣿⣷⣶⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡿⠃⠀⠀⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⣀⠀⠤⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡀⣰⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠲⠶⠦⠭⣭⣭⣿⣒⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣟⣓⣲⡶⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⠶⠶⠮⣭⣭⣝⣒⣒⣒⣀⣤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣐⡩⠠
⠀⠀⠀⠠⠴⣄⡠⠀⠀⣀⡄
⠀⠀⠀⡒⣉⠔⠒⠂⠠⠺⠔⠂
⠀⠀⠤⡭⠽⣦⢘⠛⠓⣞⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠤⠤⠚⣹⠒⢶⣯⢤⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠠⠴⠤⣆⡉⠓⠶⠶⣾⣑⢂⠉⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠐⠇
⠀⠶⣤⠔⠛⣳⠶⣤⡤⠁⠈⠉⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡰⢃⡀⣵⣦⠂⠀⢀⣀
⠀⠈⠿⠖⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠄⠘⠁⠄⠀⠘⠋⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢰⠆⠃⣴⠂⠐⡔⠰⠶⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣰⠃⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢠⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠀⢀⣀⡀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠘⣼⡇⠠⠀⡀⢸⣿⢆⣣⠀⠀⠀⡄⡧⠋⢀⠆⠀⠠⠀⠀⠀⣄⡇⢸⣧⠀⢸⢡⠇⢀⡇⢸⠀⢾⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡄⠡⡄⣿⠀⠂⠀⢸⣿⠈⠉⢀⡴⠔⠃⡧⠐⠁⠀⢀⠆⠀⠀⠀⠈⡆⢸⣏⣤⡏⠠⠓⠀⠇⢸⡇⠸⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⢸⡞⠁⠀⠀⣿⣆⠀⠆⠀⠀⢠⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠐⢼⡟⠻⠰⠁⠠⠀⠐⢾⡇⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡄⠀⢷⠀⠀⠀⣿⡿⠐⠀⡀⠀⠸⠴⠶⠚⡋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⣂⠀⠀⢘⡿⠂⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢾⡄⠀⠀⣿⡟⠤⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠐⡈⢋⣁⣤⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢰⣿⣇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣿⠀⡆⢀⢀⠀⠀⠁⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⣿⣯⣄⢀⣀⣥⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢹⠂⣇⣎⣁⡀⠀⠀⡀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣭⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣼⣄⡟⠻⠿⣷⡄⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣿⠃⠀⠀⠀⠀⠀⣀⣴⡾⠛⢿⣿⣿⣿⣿⣿⣿⡜⢱⣄⡀⠈⠀⠠⣿⠘⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⢸⣿⣿⠂⠀⠒⠀⣀⣴⠾⠛⠁⠀⠀⠀⠈⠻⢿⣿⣿⣿⡏⢸⣿⣿⣦⡀⠀⣿⠸⢃⡀⣴⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠹⣷⣾⣿⣿⢀⣠⡴⠟⢋⠥⠘⠀⠀⡀⠄⠀⢸⢠⢀⠉⠻⣿⡷⠇⣿⣿⣿⣿⣷⣿⣸⠀⠹⣧⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡃⠐⠀⢸⣿⣿⣼⠋⠀⠄⢼⣤⢤⣤⣴⣃⡴⠇⠈⠘⢽⡌⣆⣸⡷⢀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠡⠜⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠆⠈⣀⡴⠞⠉⣿⡇⢰⡇⢀⣧⡞⠁⠠⠤⡀⡄⠀⠀⠀⠀⠸⠀⣇⣿⣿⢷⠉⠻⣿⣿⣿⣿⣏⣋⣥⣶⡟⡋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠶⠛⠁⠀⠀⠇⣿⢃⡀⣥⡾⠁⠑⠎⠀⠀⡁⡇⠀⠀⠀⠀⠀⠀⢹⣿⣗⡈⠀⢀⣼⣿⣧⣼⡏⣻⣵⣾⣷⢹⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣴⠾⢛⠁⠀⠀⢲⡀⡆⠀⣿⣿⠙⡍⠁⠀⠀⠀⠀⠀⠃⠇⠐⠀⠀⠀⠀⠀⠘⣿⣟⠃⣰⣿⣿⣿⡿⣿⠃⢿⣿⡏⢻⣈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⠀⠐⠂⠺⠛⠉⢦⣿⣟⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢻⡏⢰⣿⣿⣿⣿⡇⣿⡄⢺⡻⡇⠈⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⢸⠀⠀⠀⣿⣿⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⣼⣿⢸⣿⣿⣿⣿⡇⣿⡆⣿⡇⣧⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⠀⠀⠀⠀⠀⣻⡏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⢀⣾⣿⡇⡄⣿⡿⣿⣿⡇⣿⡇⢿⡇⡿⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⡀⢤⣄⣸⠃⠀⠀⢰⠀⠀⠀⣿⣧⡔⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⣰⣿⣿⣿⣟⣥⢛⣿⣿⣿⣷⣿⠂⠸⡃⣷⡇⣿⠃
⠀⠀⣰⣦⣔⣃⣹⣷⣾⣿⣿⠀⠀⠀⠈⠀⡄⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⣿⡏⠅⣸⣿⣿⣿⢿⣿⠀⡆⠁⣿⠇⡿⡇
⠀⢸⣿⣿⣿⣿⢿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠃⠀⣿⣿⢿⡅⠀⠀⠀⠀⠀⠀⣄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⢸⣿⠚⣿⠀⣿⠀⣿⡇
⠀⢸⣿⣿⣿⣓⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠏⠀⠀⠀⠀⠀⠀⠃⠠⠾⠿⣿⢿⠿⠿⠿⣿⣯⠴⢻⠿⣿⣿⠑⣿⣆⡿⡿⣯⣿⣿⠁
⠀⠀⠉⠉⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠧⢰⠀⠐⢠⢿⠿⠇⠁⠀⡃⠠⢀⡿⠿⠁⡀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢠⠀⠇⠀⠘⠇⠀⠀⠃⠀⢸⣽
⠀⠠⠠⢠⣄⣄⣤⠤⠄⠤⠤⠤⠴⢤⠴⠶⠖⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠛⠛⠻⠿⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠦⢤⣼⡿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⣠⣴⠞⠋⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣿
⠀⠀⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⡟
⠀⠀⠹⣷⣁⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⠀⢈⣴⡟
⠀⠀⠀⠙⢿⣦⣁⡂⠀⠀⡀⠄⠀⢀⣀⣠⡾⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣉⡀⠂⠥⣑⢂⣡⣶⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠻⠿⢶⣶⣶⠶⠿⠛⠯⣅⣂⢐⠠⠀⠄⠀⠀⠀⡀⡀⠰⠐⢜⣿⣯⣐⡀⡀⠀⠀⠀⠀⠀⢀⢀⢠⣼⠟⠁⠉⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⠶⣷⣷⣷⠶⠶⠟⠛⠉⠀⠉⠛⠷⢾⣦⣵⣤⣬⣬⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠂⢀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠄⠀⠀⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⡀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠄⢠⠠⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠐⢀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡀⡀⠂⠀⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⠀⠂⠁⢁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⠐⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠃⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⡀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠀⢁⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠁⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠅⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠠⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡀⢈⠽⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡁⠀⢻⡆⠀⠀⠀⠀⠀⢀⣄⠀⠀⠆⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⣘⣿⣿⡤⢀⡤⠌⢈⣯⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣀⠀⣿⣿⣷⣂⣠⣠⣄⣿⣿⣿
⠀⠀⠀⠀⠀⠙⢳⣽⣷⣟⣿⣤⣘⣧⣛⣤⣹⣿⣿⣿⣿⣶⣿⡇⠁⠀⠀⠀⠀⠀⠈⠭⠄⢀⢤⡠⣬⣿⣿⣿⣠⢠⣈⣄⣟⣿⣟⡁⠁⠈⠅⠀⠂
⠀⠀⡠⠒⢐⣡⠽⢛⣛⡭⠶⢚⣽⠖⢋⣥⠞⣫⢿⣋⣿⠏⣹⠗⣠⠦⢤⡤⣡⣀⣀⣾⡿⢷⣼⢿⠾⣯⣿⣭⣿⡿⣿⠿⡿⠿⠟⣻⠛⡛⠷⠶⠾⣤⣀
⠀⠀⠀⠉⠉⠀⠐⠋⠁⠐⠋⠉⠀⠞⠁⠰⠞⠉⡾⠛⢠⡾⠋⣰⠟⢠⡟⢠⡿⢰⡏⠀⠧⠘⡄⠻⡞⢞⠲⡑⠋⠮⠑⡩⣊⢴⡫⢖⠝⡧⣾⢟⡋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠘⠁⠀⠟⠀⠘⠀⠑⠄⠙⢈⠁⠀⠆⠐⠄⠌⠋⢐⠏⠘⠪⢼⡍⣶⠅
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣁⣀⣈⣀⣁⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣤⣀⡀⢙⠗⠂⠤⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠈⡟⣧⠤⢤⠤⠶⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢏⡩⣠⠊⠀⠃⠀⠀⠀⠉⠙⠭⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠙⣦⡀⠣⢀⠀⠀⣀⣀⠤⠈⢢⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠑⢼⡈⠐⠢⠄⡀⠀⠈⠑⡄⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢰⠉⠉⠲⡖⢺⣻⠁⢀⣩⣸⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⠎⠀⠀⡔⡱⢺⠉⠉⣥⡼⠷⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣺⠤⠐⠉⠀⠀⡜⡔⠁⠇⠀⡠⠊⠥⢄⡸⠛⠒⠶⠶⠤⠤⢤⣄⡀⢤⣄⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⠀⠀⠀⠀⡜⠘⠀⡘⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡘⠀⠠⡰⠁⠀⠈⠢⣀⠀⢀⡠⠐⣊⠝⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⠀⢠⠛⠦⡀⠀⣀⠄⠛⣥⠔⠈⠀⠀⣀⠤⠂⡡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠃⠀⠈⠀⡠⠜⢋⡦⢖⣩⡶⢳⡤⠐⢉⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣠⣤⣤⠗⣉⠤⠊⠁⠀⣰⢭⡲⢋⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⠀⠀⢀⣼⠿⣛⠕⠊⠀⠀⢀⡠⠚⡳⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡩⠔⠊⠀⠀⢀⡠⠒⡡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣉⠔⠊⠀⠀⢀⡠⠒⡡⠔⠉
⠀⠀⠀⠀⠀⠠⠤⠤⠒⣉⠄⠊⠀⠀⢀⡠⠒⡡⠔⠉
⠀⠀⠀⠀⠀⠈⠐⠂⠉⠀⠀⣒⠒⢊⡡⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠟⠛⠋⠉⠉⠉⠙⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠛⠛⢲⣾⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠀⠀⠈⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⠤⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣿
⠀⠀⣿⣇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⣾⠏
⠀⠀⠘⢿⣦⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠄⡀⠂⡀⢂⣥⡾⠋
⠀⠀⠀⠀⠙⢷⣦⣥⣈⣀⠄⠀⢀⣰⣤⡶⠏⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠾⣤⣥⣀⣤⣥⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠙⠲⣥⣬⣈⣠⣂⡄⣐⣀⢀⣅⣈⣤⡬⠿⢷⣬⣄⢄⠀⠄⠤⢀⢠⠠⣠⣴⠟⠋⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠈⠙⠛⠳⠿⠶⠶⠛⠛⠉⠀⠀⠀⡀⢀⠀⠀⢄⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠤⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣣⠆⠀⠪⠃⠊⠠⡆
⠀⠀⠀⠀⠀⠀⢈⣐⡸⠀⠙⠋⠈⢀⢩⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠁⢬⠳⠀⢀⠠⠐⠕⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⢂⡐⠀⠤⡀⣱⠩⡈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠒⢌⠂⠐⡀⠭⠌⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⠮⠂⠄⠌⠔⠀⠙⠈⠃⠀⠀⠀⠀⠀⠀⢀⢐⠔⡎⠄⠒⠠⢑⢄⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠡⢰⠢⠀⠂⠖⠕⢀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠄⡬⠆⡠⡆⢌⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⠀⡤⠀⠀⡞⡕⢂
⠀⠀⠀⠀⠀⠀⠈⠤⠁⠠⣦⠦⠀⢁⠅⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡨⢲⠁⢠⣤⠀⠰⡰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠂⠂⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡏⠑⠂⠀⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠊⠰⠐⠩⠒⠂⠀⠀⠀⠀⠀⡉⠠⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡆⠐⠭⠊⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠑⠨⠃⠀⠀⢼⠡⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⢀⢠⠀⡀⢄⢒⠏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠲⣁⠄⠄⠒⡕⠀⢁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣒⡄⠀⣡⢀⡒⠀⢀⣁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⠘⠠⠰⠂⠠⠩⡎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢂⠜⢀⣀⣄⠀⠐⣑⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣒⡆⠀⠤⡔⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢚⠢⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⢈⠉

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠟⣋⣥⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣤⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⡟⣿⡿⣹⡇
⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣇⣟⣼⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠋⣾⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣧⠸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⣼⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠀⣿⣿⣿⣿⣿⣿⣿⡇⠛⢸⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⢛⣾⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⡇⠘⣿⡿⢋⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣇⠀⠟⣴⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣅⣤⣤⣤⣤⠀⣾⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⡇⠀⣿⠿⠿⠟⠛⠛⠁
⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠉⠁

⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⣀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠂⠐⠀⠀⠀⠂⡂
⠀⠀⠀⠂⠀⠀⣄⠄⠀⠀⠀⠀⠐⠆⠀⢀⡇⠀⠀⠀⠀⠀⣀⡌⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠃⠀⠀⢄⠀⠀⠀⠁⠒⠀⠀⠀⡈⠁⠀⠀⠁⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⡠⣤⠒⠄⢀⠀⠠⠀⠀⠈⠈⠠⡄⠀⠡⡄⠀⠀⠀⠙⠛⠀⣦⣀⡀⡀
⠀⠀⠘⠆⠀⠀⠣⠀⠀⠀⣠⣀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠦⢠⠤⠘⠃⠀⠀⢑⠤⠄⠀⠀⠈⠒⢄⠠⡄⠀⠀⠠⠀⠘⠄⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⡀⣸⡀⠄⡂⠀⢠
⠀⠀⡈⠀⠀⠀⠀⠲⠁⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⢀⡀⡀⠄⠘⡠⢀⠀⠀⠀⠀⠀⠀⢃⠀⢀⢧⠁⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⢀⣈⡁⠄⠔⠈⠂⠉⡀⢠⠴⠦⠀⣶⡤⠀⠄⠀⠁⣀⠀⠀⢾⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠀⣇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠈⠈⠀⠈⠈⠑⢻⡆⠂⠀⢴⡄⠀⠀⠀⠐⠆⠀⠘⠀⠀⠸⠰⠁
⠀⠀⣀⠀⠀⢀⡄⠀⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢐⠀⣄⢀⠀⠀⠠⣧⠈⣻⡇⠐⠂⠐⠂⠀⠘⠀⠀⠀⠀⠈⣀⡀⠁⠀⠀⢰⡀⠀⠐⠀⠀⠒
⠀⠀⠈⠓⡏⠉⠁⠉⠠⠵⢄⡉⠉⠁⢦⠀⠄⠀⠀⠀⠀⠈⠁⠀⣿⡇⠀⠄⠀⠈⠁⠀⠀⢂⣤⡀⠀⠀⠈⠀⠀⡃⠀⠀⠀⠃⢀
⠀⠀⠀⢀⡧⠤⣄⠀⠀⣀⡀⠑⡀⣀⠀⠑⠀⠀⣰⢨⢗⠶⠄⠠⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⢀⠇⠀⠀⠀⠀⠀⣡⡀⣂⠀⡇⢸
⢀⢐⣁⣈⣧⡖⣣⣶⠀⣿⣷⠀⠀⠒⣂⢀⠀⠁⢰⡐⠊⠀⣘⠂⠀⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠙⠁⠉⠈
⠀⠝⡿⢷⣿⣷⠛⣼⣏⢻⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸
⠀⠘⠁⠀⠋⠒⠘⠫⢀⠏⠘⠴⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠄
⠀⠀⠀⠀⠐⠴⠄⠄⠀⠦⠐⠀⠦⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢐⡂⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⠀⣀⢌⣳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⠴⡁⠈⠀⠠⢗⠎⠱⣄⢀⡤⠤⠔⠒⠦⢴⣁⠀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠳⣤⡀⠀⠀⠈⢉⣹⡃⠀⠀⠠⡈⠄⡀⢌⠋⠀⠀⠀⢀⠀⢴⠖⠈⣠⢙⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠂⠀⠈⠻⣅⣀⠠⠶⢭⡤⠃⢀⡠⠒⣐⠖⠀⣤⠀⢀⡐⠀⠁⠈⠐⡀⠀⠠⡌⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡅⠂⠀⠈⠁⢶⣉⣠⡖⠋⠀⠀⣀⣀⣐⢁⠀⠀⣈⠳⢼⣅⡀⠀⢀⣰⠇⠀⢀⡈⠯⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡴⠀⠀⠀⠰⠉⠁⠀⠡⠐⠂⢄⠀⡈⠙⡁⣀⡀⠈⠁⣻⣾⣉⣉⡅⣬⢧⣀⡄⠀⡒⢶⡏⠤⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⡇⡠⠊⠀⠀⠄⢀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣇⠀⠀⢄
⠀⠀⠀⠀⠠⠒⠀⠀⠀⢂⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⢺⠀⠄⠁⠬⡅⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢹⢰⡂
⠀⠀⠀⠀⠀⠈⣒⠀⠀⠀⢣⠠⠤⠤⠤⠐⠰⠂⠀⠚⠀⠀⠀⢂⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⡖⠁⠀⠀⠀⢜⡚⠈⠁⠁
⠀⠀⠀⢀⠀⠀⠑⣄⠀⠐⠀⠀⠀⠃⠀⠀⠐⡀⠀⠀⠀⠀⠏⣀⠀⡀⠉⠤⠀⠀⢠⠏⠀⠀⠛⡄⠀⠀⠈⠀⠈⠠
⠀⠀⠀⡆⢀⠐⢄⡤⠤⠀⠀⠀⠀⠰⠰⠀⠀⠀⠢⢄⣀⠤⣄⠁⡩⠈⠓⠈⠀⣠⠃⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⠀⢰⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠉⠀⣠⣀⠠⠚⠁⠀⠀⠀⢰⠀⠀⠀⠠⡀⠀⠀⢀⠃⠀⠀⠀⡀
⠀⠀⢀⣀⠀⠀⠀⠀⠠⢸⣀⠜⠂⢒⣀⡀⣀⣀⣸⣀⠐⠒⠻⣚⠿⠍⠀⠀⠐⠀⢀⢂⣀⣈⢅⠐⢲⢴⡹⠡⣄⣀⡁⡱
⠀⠀⠀⠂⠐⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢒⡐⠛⣿⣕⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⣬⣽⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢲⡖⡊⣻⣿⣿⣌⣻⡗
⠀⠀⠀⠀⠀⠀⣤⢤⣶⢿⣶⡀⠀⠀⠀⠈⠈⠉⢀⣤⣦⣿⡿⡯⠻⠟⢙⠻⠃
⠀⠀⠀⠀⠀⠰⣥⠶⣟⡙⣻⣷⡄⠀⠀⠀⠐⠚⠋⠹⣿⣍⢫⣷⣶⣾⢧⡤⠦⠤
⠀⠀⡤⠀⠀⠀⠠⠉⡿⠉⣿⡟⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⣙⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⢠⣆⠠⠠⠠⠄⢐⣶⣿⡏⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⣈⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⣶⢇⣐⣴⡄
⠀⣁⡀⠀⢠⠦⠀⡄⢀⣈⣁⣠⣴⣤⠈⠉⠛⠆⠁⠀⠀⠁⠀⠷⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠬⣽⣿⣿⣿⣿⡁⠠
⠀⠉⢀⠊⣩⠘⣻⣀⠀⡀⣉⣉⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠦⢤⡄⣲⣀⠠⠉⠛⠛⠛⠛⠀⡀
⠀⠿⠶⠖⠐⠒⠈⠉⠉⣉⢉⣩⣴⣲⠚⠀⢤⡤⢀⣠⣤⣽⣴⣀⠿⠄⠀⡀⠴⠶⠆⢩⣽⢶⣼⣗⣰⣦⢛⠀⠌⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⠿⠫⠶⡶⣶⣾⡷⢾⠦⠀⠊⠠⠄⠈⠐⠷⠷⢿⡶⣤⣠⣶⣶⣶⡾⣟⣫⣤⣤⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠁⠀⠛⠟⠹⠯⠽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠟⠛⠿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠠⣾⣾⣿⣶⣄⠀⠀⠀⠀⠀⠘⢷⣌⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⢀⠸⢿⢙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣧⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢤⡟⢸⣃⣬⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⡶⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡄⠀⠀⣉⣦⡆⣿⣾⠓⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣴⣶⣫⣅⣀⠀⢾⡇⣽⢾⣦⣻⢿⣞⣿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢛⣼⣋⢠⡀⢰⣛⣸⡇⣉⢋⣹⣻⣿⣍⣭⣦⡀
⠀⠀⠀⠀⠀⣄⠀⡀⠘⠖⣿⢠⡀⠐⠂⣀⡀⠀⠀⣀⡄⣂⡾⣻⢷⢋⣿⣿⣻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠄
⠀⠀⠀⠀⠀⢬⡻⢤⠤⢼⠿⣏⡀⣤⡄⠀⠀⠐⠂⠉⢙⣋⡶⣉⡄⠙⣿⣿⡟⠿⢟⣫⡿⢟⡿⣿⣿⣿⣿⣋⣥⢼⣇⣶⣄
⠀⠀⠀⠀⠀⠀⠠⠈⣤⣤⡤⣿⣧⡄⠳⢄⣤⣤⣀⠲⣾⣿⣴⠏⢠⠟⠹⣿⣤⣦⣟⣉⣷⢟⣿⡟⣿⣷⣾⣿⢻⣿⡿⠿⡝⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣄⠐⠂⠞⢻⣧⣀⢀⣍⠛⢋⣴⣿⣛⣥⡆⠀⣠⣾⠛⢻⣟⣿⣿⣷⢬⣿⣼⣿⣿⣿⢿⡼⣿⡇⣶⣷⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢄⣠⠼⢿⣿⡿⢃⣥⣿⣁⡿⢧⣿⣀⡾⢻⣇⣵⠟⢉⣽⣿⢿⡿⣿⣿⣿⣾⢛⣼⣇⣻⣿⣿⣧⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⣳⣶⣊⣿⠿⣿⣾⣯⣿⣟⣷⢿⣯⢥⣿⡟⣻⣆⢸⣯⣴⣎⣾⣯⣿⣻⡿⠿⣿⡛⣿⣣⣼⣽⣷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣭⣿⠟⣽⣾⡟⣻⡿⠿⢿⣣⡾⣻⡾⢻⣿⡿⣿⣼⣯⡿⢿⣿⠏⣹⡿⣷⠿⣿⡿⢿⣿⣿⡿⠻⣾⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣾⣋⣷⣿⣍⣛⠻⣻⣿⣿⢛⣿⣿⣧⣴⣋⣿⣏⣴⢦⢶⣾⣻⣶⣏⣤⣾⣵⣶⣿⣶⣶⣾⣿⣿⣿⣯⡛⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣟⣻⢶⣿⣿⣹⣷⣾⣏⢛⣿⣿⣩⣿⣿⣻⣿⣽⣯⣶⣿⠛⡿⡟⣿⣿⡿⢿⣿⢿⣏⢉⣿⣽⣿⣿⣿⣿⣽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣯⡽⣿⣿⣯⠵⣿⣿⣽⣿⣿⣏⣴⣿⣿⣿⣿⣏⣴⣤⣧⡆⢩⣼⣀⠀⣼⢛⢿⠻⢿⡛⠛⣍⢿⣿⣷⡿⣯⠛⠩⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠱⠶⢻⣷⡺⣿⡋⢷⣅⣭⣿⣿⣿⣿⣿⣿⣿⠛⢿⡛⠿⣿⡟⣿⣿⡾⢿⣿⣴⣿⣤⣿⣿⣿⣼⣿⣿⣷⣄⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣾⣿⣮⣿⣽⣿⣿⠿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣎⣻⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⣯⣟⣹⣷⣿⣷⣶⣛⣿⡼⢿⣵⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣯⡢⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣡⣯⣍⣬⣯⣙⣿⣿⣋⣶⠾⢿⣿⠟⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣭⣿⣟⣿⣾⣷⣤⠶⠶⢿⡾⢫⡜⢻⣿⣿⣯⡀⠙⠻⢿⡿⠿⣿⣿⣷⣿⡿⡏⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⡿⠋⠙⢿⣯⣷⣶⠞⣻⡅⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⢇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⣾⣿⡟⠀⠀⠈⢀⣀⣀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⢻⡏⠙⠃⠀⠀⠀⣼⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣻⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈