Birthday Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢷⠀⠀⠀⠀⠀⠀⡟⠈⣷⠀⠀⠀⠀⠀⠀⢰⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡼⠀⠀⠀⠀⠀⠘⣇⣀⡿⠀⠀⠀⠀⠀⠀⢸⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⡀⠀⠀⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⡄⠀⠀⣿⠀⠀⠀⣼⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠿⠶⠶⠾⠿⠿⠷⠶⠶⠿⠶⠶⠶⠿⠿⠿⠶⠶⠾⠷⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣴⠶⢦⡀⠀⣴⠶⣦⠀⠀⢠⡟⠉⠻⣆⠀⣼⠏⢿⡀⠀⡿⠙⣧⠀⢰⡿⣆⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠃⠀⢸⡇⢀⡿⠀⢸⡇⠀⣼⠁⠀⠀⠙⠶⠏⠀⢸⡇⢸⡇⠀⠘⠷⠾⠃⠙⢧⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⠞⠁⠀⠀⣷⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡀⣀⢀⣀⢀⣀⣀⢀⡀⢠⣀⢰⢀⣀⣄⣠⣀⢀⣠⢀⣀⢀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠓⠟⢹⠾⢻⠿⠋⡿⠁⠘⠞⠛⠛⠁⠳⠛⠘⠙⠾⠒⠟⢸⠏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⣀⢠⡀⢀⢀⠀⡀⡀⢀⡀⡄⢀⢠⡄⣀⡀⡤⣀⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠀⠘⠁⠀⠁⠁⠈⠁⠁⠀⠈⠀⠉⠀⠁⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠐⠒⠤⡀
⠀⠀⠀⢀⠐⠉⠀⠀⠉⠰⠁⠀⠀⠀⠀⠀⠀⠈⠳⡊⠉⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⡖⠁⠀⠀⠀⠀⠀⠀⠈⢖⠈⠉⠈⠁⠢⣄
⠀⠀⡐⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂
⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡱⢒⠤⠤⠐⢎⡁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠕⠢⠤⠤⠐⣌⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠈⠁⠐⠖⠀⡩⠀⠈⠀⠉⠈⠩⠉⣀⣐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⢰⠂⢈⠡⠀⠀⠀⠁⠈⠏⠡⣀⡒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣇⠘⠉⠣⠀⠀⠀⠀⠀⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠦⠀⠀⠀⠀⠀⡂⠘⠃⢀⠀⠀⠐⠋⠧⡀⠹⠍⠛⠀⠀⠠⡀⠚⠃⡄⠀⠀⠀⠀⢀⠴⢎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠗⠂⢀⠀⠀⠀⠀⢃⠠⢲⣤⠄⠰⠁⢰⠄⢸⠀⢴⠄⠰⠀⢤⡇⠄⠶⠀⠀⠀⠀⠀⡀⠐⠢⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠛⠶⣤⠖⡏⠀⠸⠀⠀⣷⣄⡀⠀⠈⠀⠀⣀⣠⡇⠀⡅⠀⢸⠓⢦⣤⠶⠛⠁⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣄⡀⠈⢻⡇⠀⠙⠉⠈⣿⠏⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⠀⢱⠀⠀⠈⠀⡖⠐⢮⠀⠀⠀⡸⠀⠹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⡆⠀⠀⢀⡇⠀⠘⡆⠀⢠⠇⠀⠀⠙⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠃⠀⠀⠀⠀⠳⣄⣠⠼⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢲⡶⠒⠲⣶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⢸⡇⠀⠀⣿⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⠿⠿⠿⠇⠀⠀⠿⢿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⢠⠐⠈⡁⠁⠉⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⠀⠀⢫⠀⠀⠀⠠⠌⠀⠈⠀⠀⠀⠀⢂⠐⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢏⠀⠀⠀⠀⡀⠀⠓⠳⠢⡀⠀⠀⠀⠐⠆⠀⠀⠀⠄⠁⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⠄⠀⠀⠀⢀⠀⡐⠃⠉⠂⠀⠽⡃⠀⠀⠀⠀⠀⡀⠠⢆⠰⠀⠈⠀⠀⠐⠁⡘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠦⣁⡇⠘⣠⣀⠀⡌⣅⠀⡀⠘⠀⠇⢀⠀⢠⠂⠘⠀⠀⠈⠀⡇⠈⠐⡎⠀⠀⠀⢊⠀⡀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⢀⣁⠉⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠁⠀⠀⠀⠉⣐⠴⠂⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠊⠁⠤⠨⠀⠀⠀⠀⠀⠂⠀⠀⠀⠅⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠊⠉⠁⣲⢄⡀
⠀⠀⠠⠀⠃⠑⠂⢠⡠⠚⠗⠂⢐⢲⠀⠀⠐⠒⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⡤⢠⠀⠤⣶⣶⠄⠀⠰⠁⢁⡨⠂⠀⡁⢡
⠀⢀⡀⠄⠀⠀⠚⠆⡐⠁⠀⠀⠈⣚⠄⠀⠀⠀⠀⢀⡆⠙⢲⠀⠀⠀⠀⡎⠀⠎⠐⢠⡀⠀⠀⠀⠀⠈⠀⠀⡤⠈⢱⡈
⠀⠀⠀⠠⣠⠌⠼⡀⠳⡄⠄⠀⡜⠁⠀⠀⠤⢠⡚⢁⠛⢆⡀⠑⠊⠑⠊⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠂⠃⠀⠀⠀⠀⠰⡊⠀⡰⠆⢚⡙⠁⠐⠀⠈⠀⠀⠠⠄

⠀⢠⠄⠀⢠⠄⠀⠀⠀⡀⠀⠀⠀⠠⡂⠀⢠⠄⠀⠀⡀⠤⡄⠠⠄⡀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⢠⠀⣀⣀⢀⡀⣀⡀
⠀⡔⠃⢀⠌⡑⠄⠀⡈⠆⡀⢠⢲⠐⠃⠀⢘⣃⡄⠰⠈⠁⣾⠈⣰⠃⢄⠀⣿⢁⡽⣈⠇⢨⡇⣯⡋⣿⡇⡠⠂⠐⢄⡀⠤⢌⡀⠥⠄⣀⠄⠀⠠
⠀⢐⠀⠀⢈⢌⡄⠈⡥⠔⢀⠸⠐⠚⠀⠘⠌⢤⠠⢀⠬⡲⠍⠹⣤⡀⠤⠁⠻⠿⠿⣿⣿⡿⠿⠿⠿⠛⠀⠃⠰⢤⠸⢁⣰⡀⠑⣠⣀⠙⠀⣦⡄
⠀⠢⠸⢀⠂⠈⢥⠢⣒⢐⠈⠀⢘⠌⠊⠐⠤⠄⠊⠀⢨⡄⠃⢀⠘⠁⠀⡰⢄⢀⠀⠀⠛⠁⡘⡂⠀⢠⠄⠡⢈⣁⠠⠈⠒⢁⡌⠓⠉⡰⢀⣉⡁
⠀⠀⢀⠶⠀⡀⠤⢀⠀⠠⡢⠠⢊⢍⠢⠀⠀⢐⡄⠀⠉⡀⢀⠃⢀⠔⠈⠁⠁⠀⢰⠀⠀⢠⢜⠦⠀⢠⣜⠀⠀⠁⠀⠈⠒⠁⠈⠑⠋⠀⠈⠁
⠀⠔⠱⢆⠈⠁⠆⡐⡠⢒⣓⢔⠀⢡⠄⡇⡠⢚⠢⡀⠀⠀⠀⠀⣻⡈⠀⠤⠈⠀⢈⠓⢠⢸⠀⢸⠀⡧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢄⠃⠂⠄⠐⡰⠀⠅⣉⣈⢈⠘⠀⠊⠀⠰⠀⡰⠀⠰⠒⡂⠪⣈⠒⠒⢐⣀⠩⠄⠐⠁⢸⠀⢸⠀⢃⢈⡇⠠⠰⢆⠀⠸⠝⠀⠀⢉⠟⢄
⠀⠀⠈⠁⠀⠀⠀⢀⡂⠥⠥⠮⠀⠉⡝⠀⠂⠤⠄⠁⠀⠱⠁⠀⠀⠀⠀⣀⢸⡆⠄⠀⠀⠘⠂⠊⠀⣆⠠⠅⠀⠀⠁⠠⠀⠠⠀⠀⡖⡀⠈⠄
⢀⠄⠀⠠⡄⡀⠊⠀⣈⡢⠐⢙⠗⢖⠒⢒⠶⠒⠒⠒⠶⠒⠐⡲⠫⡀⠀⡄⠈⠁⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⡄⠀⢠⠀⠀⠸⠁⢁⠂⡈⠄
⢘⣠⣤⣤⢸⠙⡀⣾⣿⣿⠁⠀⠀⠈⢧⠎⡀⠐⢄⠌⠀⠙⠴⠃⠀⠀⠲⠀⠀⡂⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡐⠈⠑⠈⢱⠀⡇⣀⢀⠁⠀⠸
⠈⣿⣿⣿⠏⠀⠈⠚⠛⠫⣇⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢀⠠⠤⢐⠶⠒⠶⠤⢤⣀⠐⡀⠀⠀⠀⡸⠉⠀⠂⠱⣑⠀⡀⡄⠀⠀⠀⠀⢀
⠀⠈⢩⠉⠀⠀⠀⢀⠄⠀⢈⠷⡠⢀⣀⣸⢄⣀⠀⠀⠀⢠⡇⠀⠀⠀⠐⢠⠀⡄⢈⠀⢗⡈⠲⠒⠊⠀⠀⠀⠀⠀⠳⡀⠐⠁⠀⠄⠀⠘⠋
⠀⡀⢼⠤⡀⠀⠠⠃⠀⠁⡌⠈⠀⡁⠀⠈⠀⠀⢘⠀⠀⡖⠀⠰⠒⠐⠔⠠⠂⡇⢨⠀⠁⠂⠀⠀⡄⠀⠀⢀⠜⠀⠀⠑⠀⠀⠀⢄⠸⠄⠀⡠
⠀⠀⠈⠀⡀⡀⢨⠀⠀⠀⣨⠀⡎⠐⡠⡀⠀⠀⠔⢱⠀⠳⠀⢂⠀⢁⢀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠘⠋⠈⢀⠒⠐⢂⠀⠀⠀⠂⠐⢄⠈⢄⡀
⠠⠤⠀⢰⠻⡀⠐⡄⠀⠀⡖⢀⣃⠋⠀⠂⠐⠂⢈⢘⠀⠈⠖⡔⠀⠀⠉⠈⠁⠀⠉⣄⠖⠀⢀⠀⠀⣀⣀⣘⠁⠀⠉⣄⣀⣀⠂⠀⢀⣀⡀⠁⡀
⠀⠆⢀⠋⠀⠱⠀⠡⢀⢀⠃⢎⠣⢌⡀⠀⠀⣀⠠⢜⡁⠀⠀⠈⠀⠓⠐⠒⠒⣉⣀⠀⠀⠀⠟⠂⠘⢿⡟⠁⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠐
⠀⠀⡞⠀⠀⠀⢣⠀⠉⠀⣀⣠⣁⠀⡔⠀⠀⠒⠐⢉⡀⢤⡔⢀⠀⠀⢀⠐⠨⠂⢀⠄⣉⢀⣠⡀⠀⡊⡅⠐⠀⠀⠐⠀⢸⠢⠀⠔⠒⠉⠉⣉⠢
⠀⢸⡀⡀⢀⡀⡀⡇⠀⣸⠀⠈⠁⠈⠋⢁⠀⠀⣠⠊⠄⠐⢀⢀⡀⡀⠐⡮⠥⣐⡥⠊⠀⠈⠚⠡⠀⠀⠁⣀⠀⠀⢀⣠⠁⠀⢠⡀⠙⠁⡂⠡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡄⠂⡂⡂⢨⠀⡰⠃⠀⠀⠂⣈⠜⠃⠀⠀⠡⠀⠀⢃⠀⢀⠄⠀⢖⠦⠀⣨⣀⣽⣼⣧⣠⡇⠀⠀⠁⠂⠀⠐⠀⠁
⠀⠀⠀⠘⠻⢃⡀⠀⠐⠦⠘⠐⡀⠂⠀⡈⠸⣥⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠑⠂⠬⠔⠁⠰⡷⢀⣀⣀⣈⣉⢙⣛⡋⠉⠁⢀⣀⡀⠀⣀⠠⢿⠂
⠀⣴⠋⢲⡶⣃⡱⢀⠀⠀⢀⢀⠀⠀⠀⢀⡀⠀⠀⠀⡸⠖⠉⠉⣣⡴⠒⠒⠀⠀⠀⠠⠀⠀⠁⢀⠇⠀⠞⠈⠀⠀⡅⡏⢉⠉⠈
⠀⡖⠝⠋⠉⣑⢡⠨⠁⢂⠀⡀⠀⠀⠰⡈⠈⠐⠀⢨⣑⠢⠤⢀⣀⠇⡀⠀⢠⠀⠀⠀⠘⠄⠀⠘⠋⠑⠇⠰⠐⠠⠃⠷⠛⠦⠀⠖⠀⠒
⠀⣀⠀⠨⠁⠀⠠⢨⠀⣠⣀⠀⠀⢀⠀⢓⢵⠃⠀⠀⢀⡀⠐⠀⠞⡰⠙⡄⠈⢱⠀⠀⡀⠀⢤⠀⢤⠀⡤⠀⠀⢀⢀⠀⢀⢀⢠⢀⡤⠀⢀
⠀⠈⠢⢴⠀⠤⠒⠊⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢣⡈⠁⡜⠀⠘⡐⠓⠒⡺⠀⠀⡀⠀⢈⠃⢸⠐⠐⠂⠀⢨⠅⠀⣨⠌⠀⠂⠀⠀⡀
⠀⠔⠒⠂⠀⠀⠐⠂⠠⢠⠣⠀⠀⠀⠀⠀⠃⠇⠀⠣⠀⠀⠐⠀⠀⠀⢙⠀⠀⡄⠀⠀⠀⢀⠈⠀⠀⠀⡀⠈⡀⣉⢀⡀⢁⠀⠈⠁⣀⡀⢀⡀⣀
⠀⠀⠀⠸⠉⠇⠀⡠⢀⠀⠀⠁⠀⠀⡄⠀⢀⣀⢀⣀⣀⣀⣀⣀⢬⠼⢆⢢⡰⠀⠀⢨⠀⡀⠀⢀⡃⡇⠀⠘⠁⢘⠂⢰⠀⠈⠂⠠⠡⠄⠀⡂⠁
⠀⠓⠀⠀⠀⠀⠀⠋⠀⠈⠒⠀⠈⠉⠀⠀⠘⠀⠈⠒⠒⠒⠒⠒⠒⠐⠀⠀⠀⠀⠉⠀⠁⠘⠁⠙⠀⠃⠀⠃⠀⠈⠀⠈⠈⠈⠁⠀⠀⠈⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⣀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⠌⠙⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠆⠞⢤⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠙⢂⢀⡖⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠡⠀⠁⠀⠀⠀⢀⣀⡀⢄⠠⠤⡠⣤⠒⠲⡖⠂⣼⡃⢠⢤⠆⠤⣤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡁⢮⡽⣽⠵⣈⡓⢡⢶⢑⢇⡈⠊⠱⢎⢒⣃⠮⢜⣛⡍⠌⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⠀⠀⢡⠀⣴⣡⠇⣈⡗⢡⠲⠑⠮⢟⡃⡰⡗⢿⡺⢈⡛⠧⠊⢰⢢⠓⡧⡀⢎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠆⠀⠀⠀⠡⣇⡤⡘⠒⡡⡑⠃⡐⡲⢧⡫⡈⡗⢄⠤⠘⣬⢲⢢⠈⣚⠀⣉⠚⡠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢱⡌⢱⠉⡉⡚⢠⢻⢡⢴⢭⠋⢫⡁⣚⠦⢝⡡⡯⠮⠼⢦⢠⣄⡭⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⢀⠂⠀⠀⠄⠙⢹⠀⣶⢥⡇⢸⡼⡁⢸⠀⠈⠑⠁⠀⠘⣬⠃⡶⢫⣸⢸⢸⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡠⠁⠀⠀⡐⠀⠀⢸⡄⠈⠉⠀⢸⠋⢯⣿⠀⠀⠀⠀⠀⠀⠉⠒⠁⢸⡐⢸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡠⠈⠀⠀⠀⡐⠀⠀⠀⠀⢣⡀⠀⠀⢸⠸⣵⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠈⢣⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡠⠀⠁⠀⠀⡀⠔⠈⠀⠀⠈⠶⠂⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠠⠄⠂⢁⡀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠠⠘⢷⠐⠲⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣖⡐⠂⠀⠉⠀⠀⠀⠀⢀⡀⠠⠀⠂⠈⠀⢀⠠⠘⠀⢈⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠀⠀⠀⡀⠀⠀⢀⠄⠦⠴⠊⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⢶⡤⠀⣤⡄⣤⠀⠐⣠⣀⠤⣄⣀⠤⠀⠄⠀⠤⠤⡤⢤⠠⠤⠄⣶⣄⣢⣴⢄⣰⡖⠶⠶⠒⠒⠒⢒⣲⣶⣶⡶⢶⣶⠶
⠈⡈⡡⠀⠠⠁⠢⠄⠜⣠⠴⢫⠥⡀⠉⠺⣩⢈⢳⣃⠜⡀⠀⠀⠈⠋⠁⠐⠚⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢰⠟⠻⠋⣴
⠀⡤⣠⠒⠉⠉⠉⠓⢤⠁⠈⠉⠁⢣⡀⠈⠐⠀⡰⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠍⣩
⠀⢧⠃⠀⠀⠀⠀⠀⢘⡦⡀⠀⠀⢀⠉⠒⠒⠎⠑⠁⠀⠀⠀⢨⢧⢻⢀⡈⢰⢴⡧⠇⠑⡠⠀⠀⠀⠀⠀⠀⠀⠀⢋⡏⣿
⠀⡿⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⢠⣶⢰⠉⡎⠀⢸⠁⠀⠀⠀⢀⣀⡀⠀⢀⡘⠒⢹
⠈⡇⠂⠀⠀⠀⠀⡼⠁⡰⢳⠀⠀⡸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣁⣁⡈⠉⠘⣀⣁⠀⠈⠀⠀⠀⠀⢎⠀⠈⢲⠋⢹⠀⢸
⠀⠞⠆⣄⣠⠴⠊⠀⡰⠃⡜⢀⠰⠁⠀⠀⠡⢦⠈⣷⣤⠀⡐⣶⠁⢹⣄⡀⠉⢃⢦⡑⡄⠀⠀⣠⠀⠬⢦⡀⠀⢀⠎⡀⠼
⠀⠀⡅⢺⠓⡤⠀⠔⠁⢠⢯⠏⠀⠀⠀⠀⠀⠋⢖⠡⡌⠀⡽⠊⢰⢸⡔⢽⠀⠸⢀⠃⡇⡹⠆⢸⣀⢀⠀⢙⠶⠊⢟⡬⠂
⠀⠈⡢⠸⣄⠀⠀⠀⢠⠓⠋⠀⠀⠀⠀⠀⣄⠗⡨⢠⡇⠰⠇⠀⠼⠸⠗⠸⣀⡗⣋⠞⠸⢧⣾⣼⣾⢸⡀⠘⠄⣀⡠⢣⢷
⢸⡄⡠⠸⠈⠃⡶⠊⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣴⣏⠁⣠⣯⠎⠸⠆⠀⠀⠀⠀⢺
⠈⣿⠡⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠰⠚⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡳⠀⠠⠓⠀⠀⠀⠀⢸
⠀⣇⠂⡞⠛⠚⠶⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠙⡇⠀⡔⠀⠀⠀⠀⢰
⠰⣹⢰⡇⠀⠀⠀⠈⢳⡥⠦⣄⣠⠤⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡈⣿⠀⠘⠇⢠⢈⡆⠀⠘
⠀⠛⡉⠣⣎⣉⠭⢽⣾⠀⠀⣏⣀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣀⠈⣉⠀⢀⠠⢄⠀⢀⠤⡬⢀⠋
⠀⠈⠐⠀⡇⣏⠉⠉⠛⠓⣾⠓⠛⢷⠢⠬⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠘⠲⠃⢰⠤⣬⠂
⠀⠠⠐⠚⡛⣿⠀⠀⢀⠀⣿⠀⠀⠼⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢅⡂
⠀⠀⠀⠀⠁⡿⠀⠀⢸⠀⡏⠀⠀⠇⠀⣎⣩⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠛⠋⠭⠭⠭⠭⠭⠉⠛⠃⢈
⠀⠀⡆⠀⢠⡇⠀⠀⢈⢀⡇⠀⢸⠠⡄⠀⠀⣀⡈⠉⠛⠛⠒⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⣡
⠀⡀⢘⢾⠋⣇⠀⠀⠀⢸⠁⠀⣈⢀⠃⢰⢰⠃⠙⠉⠓⠄⠒⠑⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⢸⡁
⠀⠀⠜⠒⠢⠭⠿⢿⣿⠛⠒⣒⠉⠸⠤⠬⠥⠤⠤⠀⣀⣀⣀⣀⡧⣀⠀⣀⠀⠀⠀⠀⢜⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢣
⠠⠀⠚⢿⠥⡤⠤⡤⠶⠶⣶⢖⡟⠉⣓⠠⠼⠿⠷⠶⠶⠶⠶⢒⡠⡿⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠁⠊⠙⠈⠀⠈⠃⠃⠊⠘⠘⠲⠊⠘⠀⠀⠒⠋⠟⠙⠂⠓⠈⠀⠓⠖⠀⠀⠲⠒⠒⠒⠒⠈⠉⠉⠉⠉⠁⠒⠒⠂⠒⠋
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠⠲⡦⠀⠀⠂⠤⠠⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠄⠀⠀⠀⠀⢦⣤⡶⠆
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠁⠀⡀⢢⡢⠀⠈⠀⢠⡀⠀⠾⠓⠆⠀⢰⠸⠁⠀⠀⡀⠀⠀⠀⢀⠰⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣅⠀⠀⠀⠀⢁⡼⠀⠁⣼⠁⠀⠀⠀⠄⢷⣄⠀⠀⣀⣴⡟⠀⠀⢠⠜⠁⠀⠀⠀⠀⠊⠀⠀⠀⡄⡘⠀⠀⠀⢀⠠⠘
⠀⢀⠠⠆⠀⠀⠀⢀⡷⡤⢠⣈⡀⠒⠖⠒⠛⠀⠀⢠⠇⢠⠀⠀⠆⠘⠢⡉⠙⠛⠛⠉⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣧⡇⠀⢀⢀
⠀⡁⠀⠀⠈⠄⢀⣤⣠⣴⣾⣿⡿⠒⠀⠀⠀⠀⠀⡾⠀⠈⠀⠀⠀⠀⠦⠀⠱⡖⡲⠲⣶⠂⡀⠀⠀⠀⠀⠀⡙⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠣⠄
⠀⠁⠤⠤⠞⠀⠸⣿⠿⠿⠛⢉⠑⠁⠀⠠⠆⢠⡄⢠⡄⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⢀⠉⠀⠲⡀⢠⡀⠀⠀⣓⡀⠀⠁⠀⠀⠀⠀⠀⠸⠀⠘⣧⠀⢻
⠀⢀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠦⡀⠀⢐⠎⠁⠀⡈⠀⠀⠀⠀⠠⠬⠐⠀⠀⢠⡀⣤⡀⠀⠀⠀⣄⡁
⠢⠈⠥⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣄⣀⠀⠃⠀⠀⠀⡀⠀⠰⠞⠒⣆⠳⡄⠀⠀⠀⡠⠄⣤⡀⠀⠀⠀⡛⠀⠀⣞⠸⡃⠕⢸
⠀⠃⠀⡼⠻⣦⠀⠀⠀⠀⢂⠲⠙⠶⠠⠁⠉⠀⡀⠀⠠⠀⠀⢂⠀⠀⠀⠈⢧⠙⠆⢠⠊⠀⠀⣿⠇⠀⣤⣤⠀⠀⠀⢰⠀⠁⠈⢨⠀⢀⠄⠀⠀⠃
⠀⠀⠰⠛⡁⠘⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠠⠄⠀⠀⠈⠓⠒⠃⠀⠀⢠⡿⠀⠀⣉⣉⡇⠀⠀⠐⠄⡣⣠⠞⠀⠘⠀⠠
⠀⠀⠀⠀⠤⠄⢧⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠂⠀⠀⠀⢤⢨⠄⢲⢚⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣤⣤⠄⠀⠄⠀⠀⠀⠀⠄⢁⣲⡀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠂⡀⠀⢸⢐⠀⡠⠴⡕⢾⡄⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋
⠀⠀⠐⠀⠀⠀⠀⠙⠓⠛⠀⠀⢂⠀⠀⠀⠀⠀⠘⠧⠀⠘⢨⠈⠳⠊⢀⣸⠃⢀⠆⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠐
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⣟⠋⠁⠀⠂⠀⢀⡿⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠰⣶⣶⣴⣶⡦
⠀⢠⡄⠘⠃⠀⠀⠰⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣽⠀⢠⡃⠀⣠⡾⠁⠀⠀⠀⢀⡀⠁⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⡆⠀⢀⡀
⠀⠈⣗⣄⠀⠀⠀⠀⢫⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠀⠀⣠⣄⠓⠒⠋⠀⠀⠁⠚⠛⠁⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠘⠒⠒⠒⠚⠀⠟⢻⣿⣿⣦
⠀⠀⢋⡈⣳⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⡎⠙⠏⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠤⠄⠀⠀⠋⠈⠉⡀
⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⢰⣲⠆⢠⠀⠐⢶⣯⠈⠛⠁⢀⣀⠄⠀⠤⠚⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⢃⠀⠀⠀⠠⠂⠁⠢⠀⠀⠀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠙⠀⠘⠉⡀⠈⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣫⡇⠀⠃⠀⠀⣠⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⢀⣀⡀⠀⣶⣖⠄⠐⠒⠂⠈⣁⠠⠼⠀⠀⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠂⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠠⠂⡀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⣠⡀⠀⠀⢀⠄⠒⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠂⠄⠀⠐⠚⠙⠈⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠘⣀⡀⠀⠀⠈⢀
⠀⠉⢁⠰⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠂⠀⣸⣷⠟⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣷⣿⠀⠀⠸⣭⣡⠴⣼⠁
⠀⠉⠀⠊⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠠⠤⣤⠄⣄⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⡏
⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠆⢰⠀⠀⢠⣋⡴⠃⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⣠⢲⢓⢀⡀⠀⠀⠴
⠈⢠⣴⣦⡀⠀⠀⠀⠀⠂⢀⡀⠒⠂⠉⢁⡀⠀⠀⠀⠈⠀⠀⢢⡄⠀⠀⠄⢀⠀⠘⡄⠀⠀⢠⠃⢰⠆⢀⠔⠲⠀⠀⠀⢹⢀⢂⠀⠃⠀⠀⠀⠀⠡
⠀⠘⣏⣼⠇⠀⠐⠠⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠘⢢⠀⠉⠀⠄⠁⠈⠀⠘⠇⠀⠀⠁⠀⣤⡶⢾⡿⠿⢿⠀⠀⠰⠒⠣⠼⠃⠠⠶⠤⣤⣤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠤⠤⠚⠁⢴⡒⢪⣹⡇⠀⠀⠀⠀⠀⠠⠜⠀⠲⢿⡟⠀⠀⠀⠘⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⢘⠖⠲⠘⠳⠚
⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⢁⠀⠂⠐⠁⣠⠦⠀⠐⠀⠀⠀⠀⣧⠀⠀⠇⢀⣟⢟⠣⠀⠀⠀⠁⢀⠀⠐⡂
⠀⠈⠈⠁⠀⠠⠂⠚⠉⠀⠀⠀⠀⠀⠀⠬⠱⠤⢀⠀⠀⡠⣦⠀⠀⠘⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⢀⣨⡤⡄⠒⠀⢀⡀
⠀⠀⠀⠀⢀⣤⠤⠀⠐⢠⠀⠀⠀⡄⠀⠀⠏⠊⣹⢇⢼⠉⢉⡇⠀⠀⠉⠁⢠⣶⣶⠀⠀⠩⣤⡤⣧⠀⠀⠠⠀⠀⠈⠑⠠⠆⡰⠔⠃⠀⠻⣿⣾⣿
⠀⠀⠀⠀⠈⢿⡀⠀⡠⠋⠀⠀⠀⠀⠈⠀⠀⠀⠍⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⢄⣁⠤⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣁⣴⣁⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠘⢍⡹⠃⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠧
⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣺⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢒⠢⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⠾⠥⠭⣭⣉⡆⠀⠀⠀⠀⠚⠶⠆⠀⠀⠀⠀⠓⢤⣀⣧⡇⠀⡀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢯⡉⢉⠐⠒⠒⠢⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⠁⠀⠀⣠⠤⠞⢧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠜⠉⠁⢀⠤⠼⡆
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⡏⠉⠉⢢⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠳⡤⠊⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇⠀⠀⢸⠁⠀⣰⣷⡀⠀⠸⣷⣀⣠⠼⠁⣀⡀⠀⠀⢻⣆⠀⠀⡜⠀⠀⠀⠀⠈⠲⢤⣀⣠⠏
⠀⠀⠀⢼⠉⠑⠖⠁⠈⡇⠀⠀⠀⣿⠋⠉⠉⡿⠀⢠⡿⠀⣧⠀⠀⣿⠉⠀⠀⣿⠉⠉⢳⡀⠀⢿⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠸⣽⡆
⠀⠀⠀⠈⢦⡀⠀⠀⣠⠃⠀⠀⢰⣿⠀⠀⠀⡇⢀⣿⠋⠉⠹⡄⠀⢿⡄⠀⠀⣿⠀⠀⣠⠇⠀⢈⡿⠀⠀⠀⠀⢏⠓⣹⠂⠀⠀⠈⡆
⠀⠀⣀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠉⠀⠀⠈⠁⠸⠏⠀⠀⠀⢧⠀⠈⠁⠀⠀⣿⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣴⡏⠙⠳⡄⠀⠀⢸⡇⠀⢰⣾⠙⠳⡄⠈⠉⢹⡏⠁⢀⣀⠀⠀⡀⢸⡇⠀⠙⡄⠀⠀⠀⠀⢶⡄⠀⠀⢰⠀⠀⡸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠀⣾⠃⠀⢸⣟⣀⠴⠃⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠸⣷⠀⠀⢹⠀⠀⣀⠀⠘⣷⡀⢠⠇⠀⠀⡇
⠀⠀⠤⣀⡄⠀⢸⣿⠉⠉⠲⡄⠀⣿⠀⠀⢸⡟⠳⣄⠀⠀⠀⣼⡇⠀⣼⡷⠦⢼⠇⠀⣿⠀⢀⡞⠀⣼⠟⡄⠀⠘⣧⡞⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠈⠉⠁⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⠿⠖⠋⠀⣼⠯⠤⡇⠀⠀⢹⡇⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠻⠦⠖⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠻⠀⣠⡀⠀⠀⢴⠏⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦
⠀⠀⠀⠀⠀⣠⡀⠀⣀⡁⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⡞⠳⠊⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠀⠀⠀⡇⠙⡖⠦⣄⡀⠋⠀⠀⠖⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣸⣄⣧⠤⠔⢲⠀⠀⠘⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡀⡇⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡭⠤⠔⠲⣚⣉⠽⡆⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠰⡶⠀⠀⠀⠀⢡⠀⢣⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⠒⠉⠉⠀⠀⣀⣱⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⠀⠀⡧⣤⢤⣖⣲⡭⠿⠽⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠴⠊⠀⠙⠦⣀⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢟⠏⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠀⠐⠂⠀⠔⠀⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠈⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠂⢄⡄⠀⠉⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠴⠀⠄⠈⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⣉⢨⢁⣀⡀⠀⠘⠄⠀⠀⠀⠌⠀⠀⡃⡆⠀⠠⠀⠐⠀⢒
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⠀⠀⠂⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢁⠈⢔⢤⠀⠐
⠀⠀⠀⠀⠀⢁⡹⠈⠉⠁⠠⣹⠀⠀⠉⠀⠈⡀⣄⡀⠀⠀⢀⡨⢃⠇⡈⠛⠛⠀⠀⠁⠐⠊⠀⠠⡀⠆
⠀⠀⠈⠀⠀⢒⠀⣄⠀⠀⠀⠚⠀⠀⠀⠠⢚⠧⠀⠣⠤⠦⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠅⠀⠁
⠀⠀⠀⠈⠀⠀⠡⠌⠄⠂⠁⠀⠀⠀⠄⠁⢠⡤⠟⠒⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠐⠒⠤⡀
⠀⠀⠀⢀⠐⠉⠀⠀⠉⠰⠁⠀⠀⠀⠀⠀⠀⠈⠳⡊⠉⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⡖⠁⠀⠀⠀⠀⠀⠀⠈⢖⠈⠉⠈⠁⠢⣄
⠀⠀⡐⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂
⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡱⢒⠤⠤⠐⢎⡁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠕⠢⠤⠤⠐⣌⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠈⠁⠐⠖⠀⡩⠀⠈⠀⠉⠈⠩⠉⣀⣐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⢰⠂⢈⠡⠀⠀⠀⠁⠈⠏⠡⣀⡒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣇⠘⠉⠣⠀⠀⠀⠀⠀⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠦⠀⠀⠀⠀⠀⡂⠘⠃⢀⠀⠀⠐⠋⠧⡀⠹⠍⠛⠀⠀⠠⡀⠚⠃⡄⠀⠀⠀⠀⢀⠴⢎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠗⠂⢀⠀⠀⠀⠀⢃⠠⢲⣤⠄⠰⠁⢰⠄⢸⠀⢴⠄⠰⠀⢤⡇⠄⠶⠀⠀⠀⠀⠀⡀⠐⠢⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠛⠶⣤⠖⡏⠀⠸⠀⠀⣷⣄⡀⠀⠈⠀⠀⣀⣠⡇⠀⡅⠀⢸⠓⢦⣤⠶⠛⠁⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣄⡀⠈⢻⡇⠀⠙⠉⠈⣿⠏⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⠀⢱⠀⠀⠈⠀⡖⠐⢮⠀⠀⠀⡸⠀⠹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⡆⠀⠀⢀⡇⠀⠘⡆⠀⢠⠇⠀⠀⠙⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠃⠀⠀⠀⠀⠳⣄⣠⠼⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢲⡶⠒⠲⣶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⢸⡇⠀⠀⣿⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⠿⠿⠿⠇⠀⠀⠿⢿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⢈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⢲⡖⠒⢦⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠃⠀⠘⣦⠤⢤⣀⠤⠤⠼⣄⡤⠦⠤⢄⡠⠦⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡄⠀⢰⡇⢠⠀⢻⠀⠐⠃⢈⡇⠀⠒⠀⡷⣄⠉⢁⡤⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠓⠒⠿⣧⣀⣸⡀⡴⡆⠘⡆⠀⣖⠋⣇⠀⢰⢚⢁⣸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠠⣏⢩⡏⠩⠙⣏⠉⣹⠉⠏⢻⠉⡙⡿⢉⢹⡌⢋⡹⠂
⠀⠀⠀⠀⠀⠀⠀⣇⣀⣘⣠⣏⣨⣇⣀⣸⠜⣆⣿⣰⣆⣼⣀⣡⢇⡴⣄⡿⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⣞⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⢛⡗⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀
⠀⠀⠀⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣒⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠬⠭⢍⣵⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⣀⣠⣛⡛⠒⠲⠶⠴⡇⠀⠀⠀⠀⠈⠁⠛⠣⠀⠀⠀⠀⠀⠉⠲⠤⠼⠿⣀⣀⡄⠀⠀⠀⠀⢠⠞⠉⠁⠉⠙⠢⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢈⡉⠉⡉⠙⠒⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣀⣠⠖⠒⢹⡄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⠡⢀⡴⠤⢷
⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢾⡟⠉⠙⠲⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡤⠞⠛⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣸⠀⠀⢠⣶⡄⠀⠀⢸⣧⠀⠀⣀⡗⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣰⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⣰⠃
⠀⠀⠀⠀⡤⠤⢤⣠⠖⠒⢢⠀⠀⠀⠀⣾⡷⠶⠤⢤⡏⠀⠀⣾⠇⢷⠀⠀⢸⣿⠒⠋⠁⢠⣶⠒⠶⣄⠀⠀⢿⣇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢙⠿⣅
⠀⠀⠀⠈⢇⠀⠀⠁⠀⠀⣸⠀⠀⠀⢀⣿⠇⠀⠀⢰⡇⠀⣼⣯⣤⣼⡇⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠘⡇⠀⠈⣿⡞⠁⠀⠀⠀⣠⢄⣠⢤⠀⠀⠀⠳⣏
⠀⠀⠀⠀⠈⠳⣄⠀⠀⡰⠃⠀⠀⠀⠸⣿⠀⠀⠀⢸⠀⢰⣿⠀⠀⠀⢻⠀⠀⢿⡇⠀⠀⢸⣇⣀⣠⡴⠃⠀⠀⣾⡇⠀⠀⠀⠀⠘⢄⣡⠞⠀⠀⠀⠀⢸⡄
⠀⠀⢠⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⣼⡏⠉⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠻⠃⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⣴⡞⠙⠓⢦⠀⠀⠀⢸⣿⠀⠀⣰⡞⠛⠳⡄⠀⠉⠉⣿⡋⠁⠀⣀⠀⠀⠀⠀⢸⡇⠀⠙⢦⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⣠⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣸⠀⠀⠀⣼⡇⠀⠀⣿⡇⢀⣠⠇⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⢸⠇⢸⣷⠀⠀⠘⡇⠀⠀⠀⠀⠈⣿⡄⠀⢠⠇⠀⠀⢸
⠀⠀⢀⡀⠀⠀⠀⢸⣿⠶⠚⠧⣄⠀⠀⣿⠇⠀⠀⣿⡿⣏⠁⠀⠀⠀⠀⣿⠀⠀⢸⣧⣀⣀⣼⠀⠘⣿⠀⠀⢠⡇⠀⣸⣿⡀⠀⠘⣿⣀⡟⠀⠀⠀⢸
⠀⠀⠁⠙⠛⠇⠀⠈⣿⠀⠀⠀⢸⠀⠠⠿⠄⠀⠀⣿⡇⠈⠳⠀⠀⠀⠀⠿⠀⠀⣿⡇⠀⠀⡿⠀⠀⣿⣆⣠⠏⠀⣰⡟⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⠈⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣠⠞⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢀⡇⠀⠀⠙⠉⠀⠀⣰⡟⠉⠙⡯⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡶⡄⠀⠀⠰⠟⠀⠀⠀⠿⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⡆
⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡉⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⡄⠀⠀⠀⠀⠀⠀⣞⠑⠞⢱
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢽⠉⢳⠦⣄⡀⠀⠞⠀⠀⠠⠖⠓⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣠⠤⠴⣆⠀⠀⠘⢦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠘⡏⠙⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⣋⣉⣩⣤⡤⠖⢒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠
⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠀⠸⡄⠁⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣁⡨⠤⠖⠒⠋⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠙⠁⠀⠀⠀⠀⢸⡄⢀⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⠉⠀⠀⠀⣀⣠⣤⡤⢶⣟⡦
⠀⢀⡤⢤⡀⠀⠀⠀⠀⢸⠷⠋⠀⠀⠀⠀⠀⠶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⢸⣓⣮⣽⠯⠽⠗⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤
⠚⠉⠀⠀⠙⠲⢤⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢻⡄⠀⠀⠀⠀⠀⠀⣾⠙⣧⠀⠀⠀⠀⠀⠀⠀⢰⠏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⡇⠀⠀⠀⠀⠀⢸⡇⠀⣹⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡞⠁⠀⠀⠀⠀⠀⠈⠳⣶⠋⠀⠀⠀⠀⠀⠀⠀⠙⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⡄⠀⠀⠀⣿⠀⠀⠀⠀⣴⣄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢾⣿⣿⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⣠⣄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⣴⠟⢷⡄⠀⢠⡞⢳⣄⠀⠀⣰⠏⠈⠹⣧⠀⣸⠏⢹⡆⠀⣸⡏⠹⣇⠀⢸⡿⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠁⠀⠈⣷⠀⣼⠃⠀⣿⡀⠀⣿⠀⠀⠀⠙⠷⠟⠀⠈⣷⠀⣿⠀⠀⠙⠶⠾⠁⠙⢷⣄⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⠾⠋⠀⠀⢸⣇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢴⣇⣶⡆⣖⣦⣶⣲⢶⣴⠀⣽⣲⣼⣶⡖⣿⢸⡷⣦⣖⣿⣰⣦⢦⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠋⠁⠋⠁⠘⠁⠀⠈⠉⠀⠈⠀⠈⠈⠀⠁⠈⠁⠈⠁⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠶⠄⠰⠤⠗⠀⢠⠤⠠⢄⠄⠰⡆⠇⠀⠆⠗⠤⠦⠰⠢⢴⠤⠆⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠⠐⠆⠀⠀⠀⠠⣔⠃⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⠶⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⣀⠠⠰⡏⠀⠀⠀⣦⠀⠋⠙⠀⣸⠈⠀⠀⡤⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⢀⠀⠀⠀⢐⣀⠀⠂⠀⣀⣀⡴⠃⠀⠸⠀⠀⢀⡀⠌⠳⢤⣴⠾⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣰
⠐⠀⠀⠀⡀⢀⣈⣉⣼⣿⡧⠄⠀⠀⠀⢠⠇⠘⠀⠀⠀⢠⠁⢢⢤⠤⣤⠄⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠄⠴⠀⢸⡿⠿⠛⢉⠐⠀⠠⠄⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⡘⠀⢆⠀⡄⠀⠀⣂⠀⠈⠀⠀⠀⠀⠈⠀⢸⡄⢘
⠀⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠐⡀⠀⠖⠀⠀⠄⠀⠀⠀⠐⡂⠀⠀⢠⡀⡤⡀⠀⠀⠄
⠁⠀⠀⣦⡀⠀⠀⠀⠀⣀⢆⡈⠔⠤⠈⠀⠀⠀⠂⠀⠉⠀⠳⡜⢄⠀⠠⠒⠰⣶⠀⠀⠀⠅⠀⢙⠈⠀⠅⠇⠀⠀⠀⢀
⠀⠀⡼⠅⠹⡀⠀⠀⠐⠀⠈⠀⠅⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠙⠬⡴⠁⠀⢸⡏⠀⠚⢛⡄⠀⠀⡀⠆⢠⠇⠰⠁⡀
⠀⠀⠀⠨⠄⣇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⡤⡂⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠉⢁⣤⡄⠀⠁⠉⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢠⢀⢀⠴⡶⢲⡀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠚⠛⠛⠁
⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⡀⠀⠀⠀⠀⠘⠀⠈⢐⠈⢉⣠⡼⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢀
⠀⠀⠀⡇⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡇⢀⠄⠀⢠⡟⠀⠁⠀⠀⠀⠀⠀⠄⠈⠛⠛⠛⠛⣀
⠀⢻⣄⠀⠀⠀⠰⡂⠈⠀⠀⠠⠀⠀⠀⠂⠀⢀⡀⠧⠼⠃⠈⠂⠴⠟⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠡⠤⠤⠤⠁⡴⢶⣶⣦
⠀⠀⣋⢳⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⣀⣄⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠃⠉⢉
⠀⠀⠉⠁⠀⠀⠀⠀⢰⣶⠀⣆⡀⢺⠧⠘⠉⠀⠴⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⢀⣀⠈⠀⣀⠠⠄⠀⡀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠟⠀⠀⠠⠤⠆⠀⠀⠀⠆
⠀⠀⠀⠰⣶⣶⠀⠘⠛⠁⠀⠤⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠀⠀⠀⠀⠀⠀⡄
⠀⣀⠀⠀⠀⠠⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡀⠀⠀⠀⠖⠒⠈⠀⠀⢀⡔
⠀⠉⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣸⡷⠃⠀⡤⠀⠀⠀⠀⠀⠀⠉⠀⠠⣶⡇⠀⠸⠭⠥⡴⡏
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡖⣰⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠹⠁
⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠈⠀⠂⠀⠐⠒⠁⠀⠀⠈⠄⠀⠀⢀⠀⣀⠈⢀⣀⠀⠀⢰⠉⠀⣢⠀⠀⠁
⠀⢾⣏⡷⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠚⠂⠀⠀⠀⠀⢼⠀⠀⠊⢀⣡⣴⣶⣧⡄⠀⢸⠴⢂⡄⢀⣄⣀⣀⣱
⠀⠀⠉⠁⠀⠀⠀⠀⠁⡠⠀⠀⠤⡤⠞⠠⡎⢐⣻⡆⠀⠀⠀⠀⠠⠃⠰⣾⡆⠈⠁⠈⡇⠀⠃⠀⠀⠀⠀⠀⠐⠄⠬⠩⠴
⠀⠤⣀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⡀⠀⠀⠙⠉⠁⠀⠀⡀⠀⠀⠚⢠⣴⠀⠀⠀⠀⠀⠧⠀⠐⠀⠛⢛⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⣙⣀⣤⠀⡴⢷⡀⠀⠀⠄⠀⣀⡀⠀⠤⠀⢀⠀⠀⠀⠀⠀⢇⠀⠲⠒⣈⠁⣠⣄⣠⡀
⠀⠀⠀⠀⣿⠁⠀⠰⠂⠀⠘⠀⠀⠁⠀⠊⢮⠂⠐⠃⠀⠀⠀⠘⣿⠇⠀⠈⠛⠛⠃⠀⠈⡀⠀⠀⠀⠱⠉⡀⠀⠘⢿⠿⠁
⣀⣀⣀⣀⣈⣂⣔⣀⣀⣀⣀⣂⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⢶⡤⠄⣤⡔⢠⠀⠀⢠⠀⡠⢤⣀⡠⠤⠤⠤⠤⠤⣤⡤⡤⠤⠤⢤⣖⡀⣢⣤⣄⣰⡶⠶⠶⠒⠒⠒⢒⣲⣶⣶⡶⠶⣶⡶⠦
⠈⡈⡁⠀⠨⠡⠶⠄⠠⢇⡥⠞⡉⣁⠈⠣⢟⡉⡙⣖⣀⠔⠄⠀⠀⠘⠋⠀⠀⠚⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠙⢒⡿⠿⡛⣡⡾
⠀⣀⢄⠔⠊⠉⠉⠓⢤⡉⠀⠉⢁⠘⡀⠀⠀⠐⠁⡌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠜⢍⡇
⠀⣗⠋⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠘⣲⠤⢴⠊⠐⠁⠀⠀⠀⠸⢆⢽⢀⡁⢰⢰⣮⠂⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣫⢹⡇
⠀⣿⠀⠀⠀⠀⠀⠀⢠⠇⢱⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢨⣇⢰⠊⡝⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠚⡇
⠀⡇⠄⠀⠀⠀⠀⢠⠏⢀⡿⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠃⠚⠛⠺⠀⠃⠀⠘⠀⠀⠀⠀⢰⠉⠉⢢⡞⠙⡆⠀⡇
⠀⡵⡦⡀⠀⣀⠴⠃⢀⡞⢠⠃⢀⡜⠀⠀⠐⢨⡁⠒⡄⡀⠀⢤⣴⠙⢻⠁⠐⠒⠏⣉⠢⡀⠀⠀⠀⠀⣘⣦⠀⠈⠀⢰⠃⢀⡇
⠀⠀⡂⢽⡯⣀⠀⣀⠎⠀⡼⣶⠃⠀⠀⠀⠀⠰⢃⠴⢉⠋⠘⣦⠟⡄⢈⡉⣳⠀⢸⠈⡇⡗⠶⡤⠨⡇⡇⡇⠑⣤⡴⢷⢌⡢⠈
⠀⠐⢅⠰⡂⠋⠈⠀⠀⣰⡱⠁⠀⠀⠀⠀⢀⢰⡄⠃⢸⠁⢸⡇⠀⣷⢸⡆⣻⠀⡧⡜⡰⢳⣯⣰⠰⣵⣤⡇⠠⡇⠀⠀⡹⣰⡀
⢠⠠⢂⠀⠑⠧⣤⡀⢌⠁⠀⠀⠀⠀⠀⠀⠘⠒⠒⠁⠈⠀⠀⠀⠀⠁⠈⠁⠐⠾⠧⠚⠁⣠⡾⠛⠛⡻⡹⢑⣤⠀⠉⠉⠐⢩⡇
⠸⣷⠒⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢕⣖⡪⠟⠁⠀⢀⠀⠀⠀⠀⠘⡇
⠀⢙⣨⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡀⢀⢠⠀⠀⠀⠀⠀⡁
⠀⡌⣀⢠⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠈⠀⡌⠀⠀⠀⠐⠁
⢀⢷⠀⡏⠀⠀⠉⠑⢦⠸⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣨⠎⠀⣜⠀⡀⡀⠀⠀⡃
⠈⣾⡴⡇⢀⠤⠤⢤⡈⡟⠉⢳⠖⠛⠉⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠶⠮⠗⠚⠂⠂⠛⠐⠂⠚⠄⣠⡐
⠀⢣⠄⠈⡗⣲⣦⣔⣻⣅⣀⣼⠶⣆⡀⠤⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣤⠒⢄⡠⠂⠐⡄⡠⠒⡑⠁⡌
⠀⠀⠈⢠⣧⣿⠀⠀⠀⡁⢹⠉⠉⠙⡏⠓⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠉⠈⠉⠉⣀⡗⢲⠊⠰
⠈⠀⠁⠈⡍⢹⠀⠀⢠⠀⢸⠀⠀⢸⠃⠀⡠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠇⢀⣀⣀⣀⣀⣀⣀⡐⣰⢄⣑⠦⡀
⠀⠀⡀⠀⠀⣾⠀⠀⢸⠀⣾⠀⠀⡌⠀⠹⠤⠾⠦⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠒⠒⠒⠂⠉⠁⢀⠼
⠀⠀⢇⢀⣰⣿⠀⠀⢸⠀⡟⠀⠀⡇⢲⠀⡀⢀⢄⡀⣈⠉⠉⠉⡉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠉⣡⠎
⠀⢄⢈⠻⠃⢿⣀⡀⢸⢀⠃⠀⢠⣀⡎⠀⣇⡜⠀⠉⠈⠑⠊⠉⢘⡶⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⣇
⠀⠀⠌⣉⣒⡒⠛⠛⢿⠋⠛⢋⣅⣂⡣⠤⠐⠒⠂⠤⠤⠤⠄⠀⡰⠧⣄⣀⢀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⡆
⠠⠂⠙⣛⠒⣲⣶⣶⢒⠲⣲⠶⡺⠃⣉⡯⠋⠯⠭⠿⠷⠶⠶⠛⢉⢵⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣉⣂⣙⣊⣒⣀⣑⣘⣊⣈⣉⣓⣚⣁⣁⣐⣐⣊⣙⣋⣙⣈⣈⣁⣈⣓⣒⣒⣒⣒⣒⣒⣂⣉⣉⣉⣀⣀⣀⣉⣉⣒⣒⣒⣊⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠤⠄⠀⢀⠰⠆⠉⠀⡀⠀⠀⠀⠚⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂
⠀⡀⠀⠀⠀⠀⠘⣱⠀⠀⠀⠀⢠⡌⠁⠄⠙⠠⠀⠀⠐⠀⠣⠀⠒⠀⠀⠀⠀⠤⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⡀⠓
⠀⠐⠀⠀⠀⠂⠀⠁⠁⠀⡀⠀⠰⠀⠜⠀⠄⠁⠂⠠⠀⠀⠀⠣⡰⡢⣔⠀⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⡀⠐⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠐⠀⠀⠒⠆⠀⠀⠀⠉⠃⠠⠀⡀⠂⠐⣀⣍⠤⣄⠁⠀⠹⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⡀⢀⠤⠀⠀⡀⢀⠄⢫⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢄⠸⡁⣂⠀⢀⠀⠤⣌⡡⣈⢨⠀⢀⠁⠀⠈⣡⠀⠠⠀⠀⠀⠈⢀⡄⠈⠉⢣⠀⢃⠀⠀⠀⢁⡀⠁⠀⡰⠀⣀⠚
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠀⠆⠀⡸⢀⠎⣠⣤⡀⠱⡄⣇⣐⣠⠀⡀⢀⠸⠎⠀⢀⠀⠜⠀⣼⠀⠀⠀⠈⡀⢸⠀⠀⠀⠺⠀⠄⠁⠀⠈⣁⠀⡀⠈⠐⠈⠀⠆
⠀⠀⠀⠐⠈⠀⠀⠐⠀⠂⠀⠀⠐⠀⠀⠀⠀⠉⠀⢀⢀⢀⡀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡉⠉⠁⠀⠀⠀⠀⠁⡀⠀⠄⠀⠀⠀⠀⠀⠀⠪⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠉⢹⠀⠀⠀⠀⠀⠄⣘⠰⠀⠀⠇⠰⠂⠄⠆⠀⠀⠀⠀⠈⡇⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣭⡤⠴⠲⠡⢄⡀
⠀⠀⠀⠀⢀⣸⣰⡀⠀⠀⠈⠁⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈⣀⠀⠤⣭⠢⡄⠀⠘
⠀⠀⠄⠐⠀⢃⠀⢉⠡⠘⡆⠚⡉⠝⠁⠀⡨⢸⠀⠀⠀⠉⠉⠁⠀⠙⠉⠩⠉⠀⠀⠀⠀⠀⠀⠀⡲⠒⡶⡀⠘⠻⡿⡿⠇⠀⢀⠘⢄⠁⣤⠈⠀⠀⣀⠀⢷
⠀⢀⢀⠀⡤⠀⠀⠐⠚⠖⢁⠞⠁⠀⠀⢀⠁⠿⡆⠀⠀⠘⠀⠁⠀⣰⡆⠘⠓⡆⠀⠀⠀⠀⢐⡞⠁⠰⠋⠑⠤⣀⠀⢀⡀⠐⠁⠀⠈⠂⠀⢈⡅⠈⠡⡆⡉
⠀⠀⠀⠀⢀⠀⠀⡎⣹⠀⢸⡄⠀⢀⠐⠀⠄⠊⠁⠈⠀⠀⠀⠠⢞⢉⠹⡄⠀⠘⡦⡖⠓⡤⠚⠀⡐⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⠀⠀⠈
⠀⠀⠀⠀⠈⠚⠉⠀⢀⠦⣀⠈⠉⣁⣄⢘⠂⠀⠀⠀⠀⣃⣀⠒⠒⣁⠀⣨⡶⢄⣄⢀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠛⠀⠈⠀⠀⠀⠀⠀⠀⠙⢄⡢⢤⠝⠇⢝⡥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⣀⠄

⠀⢐⠀⠠⡂⠀⠀⠠⠀⠀⠀⠠⡇⠀⣴⠀⠀⢀⠠⡀⡠⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠄⠠⢠⠄⡄⢀
⠀⠈⠀⢐⢅⠂⢠⠐⠠⠀⠈⣈⠁⠀⠭⠖⠈⢀⣀⢇⡠⠋⠢⠀⣿⣴⣥⣇⣴⣷⣧⣸⡇⠀⠀⠀⢠⠀⠂⠄⠐⠠⡔
⠀⡄⡀⠀⠀⠆⠀⡂⡁⠀⢢⠡⡀⠀⠈⠀⠀⠣⠸⠀⢳⠆⠈⢀⠙⠛⠛⢻⠟⠻⠉⠉⠀⠀⠸⠗⠁⢔⡇⠨⣖⠆⡁⠸⠗
⠀⠀⢀⡂⠀⢘⠈⠂⢠⠀⠐⠆⠀⠀⠈⡀⠀⠚⠃⠠⠃⠀⠀⠉⠂⠂⡄⠀⢀⣠⡀⠀⣉⠀⠐⠂⠁⠠⠄⠃⢠⠐⠁⠒⠈
⠀⠔⠤⠀⠂⠄⠐⠠⠘⠠⠌⢊⠀⠀⠀⠃⡀⠀⠀⠂⢰⡄⠂⠀⠀⠀⠣⠄⢸⠀⠀⢰⠁⠆
⠐⡐⠐⠠⠀⡐⠀⢂⣉⠀⠐⠀⠊⠀⠀⠀⠀⠀⠒⠀⠅⠓⠐⠒⡀⠀⠀⠊⢸⠀⡇⠘⠀⡇⠠⠴⡒⠀⠽⠀⠀⠸⠻⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡀⠉⠍⠀⠂⠂⠀⠀⠒⠀⠀⠀⡀⡀⢾⠀⠀⠀⠘⠂⠁⠰⠐⠇⠀⠀⠀⠀⠀⠀⢀⢂⠀⠱
⠰⠀⠀⠒⡤⠁⣠⣤⡄⠘⠋⠻⡉⡙⠋⠉⠉⠛⣍⢩⠋⠀⠀⠀⠀⡀⡄⢀⠂⠀⠀⠀⠂⠀⠀⠐⠀⡀⢆⠀⡐⠄⠀⠀⢀
⠀⣾⣿⡦⠀⠢⢻⣿⣧⠀⠀⠀⠙⢠⠀⠐⠂⠀⠈⠃⠀⢀⣈⣀⡀⠀⠀⠠⠀⠀⠀⠀⡤⠄⠐⡀⠀⠀⠈⠀⠃⠀⠀⠀⠈
⠀⠻⡛⠃⠀⠀⢀⡀⠈⢦⠄⠀⠀⡞⠀⠀⠀⠀⢠⠂⠉⠉⠀⢀⠉⡉⠋⢦⠀⢤⠤⠈⠁⠀⠀⠐⡀⠐⡄⠀⡀⠀⠶⠂
⠀⠀⣧⢀⠀⠠⠆⠈⢂⠀⠁⠂⠉⠁⠉⠀⠀⠀⡌⠠⠄⠀⠄⠨⠀⠀⡆⠐⠅⠀⠀⠀⠀⠀⡐⠀⠘⠢⠁⠀⡀⠠⠀⢀
⠀⠀⠀⢀⠀⢨⠀⢀⠀⡆⡔⠁⠠⠀⠀⠤⢳⠀⠧⠐⠀⢁⢀⡀⠀⠀⠀⠀⡄⠀⠀⠓⠀⠀⠀⠐⡄⠀⠀⠀⠐⠄⠠⣀
⠀⠂⠀⡟⢇⠀⡆⠀⢐⠀⡥⢉⠐⠂⠘⠀⢙⡀⠈⠳⡀⠀⠀⠈⠀⡀⠠⠖⠀⣠⠀⣀⣠⡬⠁⠀⠱⣤⣠⡂⠀⠠⠤⠈⠄
⠀⠃⡌⠀⠘⡀⠁⠤⠊⠘⢄⡂⠀⠀⠀⠀⡪⠂⠀⠀⠀⠀⠈⢉⠁⠀⠄⣄⠀⠉⠀⠙⡟⠀⠀⠀⡀⠸⡟⠁⠀⡀⠀⠁⡀
⠀⢰⠀⠀⠀⠘⡀⠀⡔⠒⠒⠠⠧⠀⠀⠀⡰⠂⡙⠁⠂⠀⢐⡠⠈⡤⠊⠐⠐⠲⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⠁⠤⠠⠴
⠀⠉⠐⠐⠂⠀⠁⢠⠃⡀⠄⠀⠀⡂⢀⡜⠁⠁⠀⢂⠖⠀⠀⠃⠉⠙⠀⠀⡀⠀⣠⡀⢀⡉⣲⣰⡊⣡⠀⠈⠃
⠀⠀⠀⠲⠂⡀⠀⠠⣀⠃⠀⠃⠁⠁⢎⡀⠤⠐⠊⠁⠀⠀⠀⠀⠂⠠⠤⠊⠠⡦⢀⣀⣈⠛⠛⠛⠛⠋⠀⠀⠀⢀⡀⢼⠆
⠀⣜⠑⣶⣆⡱⢀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡰⠂⠀⢰⡤⠒⠂⠀⠀⠀⠀⠀⠁⠸⣀⢸⠉⠀⠈⠉⠉⠉⠉
⠸⠙⠉⣀⠨⠰⢸⠀⠀⠠⠂⠀⠂⠀⣀⠁⠐⠌⠐⠀⠠⡄⣠⠀⢦⠀⠈⠀⠃⠀⠈⠉⠙⠐⠈⠐⠀⠊⠑⠀⠂
⠘⢅⠀⠂⠀⣀⡘⠀⠒⠄⡀⠀⠀⠙⠃⠀⠀⡀⠤⡀⡈⢰⡀⣇⢀⡇⠀⠀⠀⢲⡐⡆⠐⡀⠀⠰⠢⠀⠆⠐⡰⠂
⠀⡀⠈⠃⠈⠠⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢆⠐⠂⡀⠀⠀⢢⠀⠐⠂⠀⠀⠀⠐⠀⠃⠀⠐⠀⠚⠀⠰⠁⠀⠆
⠀⠀⠀⡐⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⡌⢄⡸⠀⢀⡂⠀⠀⠰⢠⠀⠰⠂⠳⠈⡄⠁⠂⠀⢉⠀⢠⠊
⠀⠆⠀⠄⠀⠀⠃⠈⠐⠀⠜⠈⠀⠀⠋⠀⠓⠒⠒⠒⠒⠀⠂⠈⠁⠀⠒⠀⠐⠀⠋⠘⠀⠒⠀⠊⠐⠁⠒⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢂⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠛⣶⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠐⠟⠀⠀⢻⣤⢤⣤⣀⣀⣤⣤⢴⣄⢀⣤⣤⣤⣄⣢⡤⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⣸⡏⠀⠀⠸⡇⠀⠰⠆⠈⢿⠀⠀⡦⠀⢹⣄⠈⠳⠋⢁⣱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣀⣾⡏⠀⠀⣿⠁⢈⡃⠀⢿⠀⠀⣀⡤⢿⠀⠀⢀⣠⠾⠈⡇⠀⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢩⠉⢻⡶⢶⡿⣤⣟⣹⣤⣼⣤⠤⣷⣤⣸⣧⣠⣼⠤⢤⡴⢧⣤⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠐⢿⡄⣼⡇⠐⢂⡧⡄⢠⡿⠀⠃⢘⡇⢰⡌⡟⠠⠈⢷⡄⣡⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣈⣠⢾⣡⡼⣇⣠⣌⡇⢿⣸⣧⣸⣇⣸⣇⣈⡠⢧⡴⢧⡼⠧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠧⠆⢰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⢀⡅⣦⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⠀⠀⣟⣠⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠠⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠶⢴⠂⠀⠌⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣂⣀⡀⢸⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⠀⠀⠀⣠⠔⣢⢶⣹⠮⡉⢝⡹⢀⠠⣻⠀⢴⠳⣀⠾⣫⡍⡩⢻⡶⠶⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠄⠀⢸⡱⡢⠙⣟⡱⣉⠱⡲⢄⣯⠃⢫⣲⣄⣀⢏⣆⠔⡲⢉⠱⡒⡇⠁⡖⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡈⠀⠀⠸⠄⡞⠷⢁⡔⡢⢰⣩⠃⡉⣪⢤⠤⣭⠈⠣⠊⡴⢌⠊⠀⢫⣡⠈⢗⣢⠱⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠁⠀⠀⠃⠈⢷⢞⡆⣩⣔⠪⡁⢰⡭⠉⠧⢤⣼⣍⠄⣓⠨⣋⠹⡽⡠⢡⠀⢶⠀⣞⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠂⠀⠀⡈⠀⠀⠸⢆⣰⠀⠇⡬⣤⠋⠦⣊⠗⡆⠈⢶⢬⠞⠙⡤⢎⡏⢑⣹⢳⢰⢣⡖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠂⠀⠀⡀⠀⠀⠀⠃⠈⢸⠇⠻⣞⠜⢀⣖⣃⣈⡇⠀⠀⠁⠀⠀⠱⣎⢸⠏⢱⠼⣸⢸⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠄⠀⠀⠀⠌⠀⠀⠘⡇⠀⠀⠀⠠⡍⣘⠾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⢫⣌⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠁⢀⠔⠁⠀⠀⢀⠌⠀⠀⠀⠀⠀⣆⠀⠀⠀⢎⠣⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠂⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠊⢹⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠄⠊⠀⠀⢀⠠⠒⠁⠀⠀⠀⠹⠃⠒⠒⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠤⠐⠈⣀⠀⠄⠒⠈⠀⠀⠀⠀⠀⢀⠠⠐⠱⡒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣂⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⣂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠐⠁⠀⡙⠉⠉⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠁⠀⠀⠠⠤⠀⠀⠀⠠⠄⠀⠒⠀⠁⠀⠀⢀⠔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠤⠀⠀⠀⣀⡀⠀⢀⠄⠤⠤⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉

⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⣀⢀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠰⠀⠂⠃⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀
⠀⠀⠈⠀⠀⠸⡃⠀⠈⠁⢀⠒⠀⠐⠀⠁⠀⠀⠤⠈⠄⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠣⡴⣠⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⢀⠀⠉⠀⠀⠀⢀⠀⣬⠠⢄⠀⠘⣤⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠄⢀⠀⡠⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡈⠬⡄⢰⠄⠒⠂⠲⠬⠀⠀⠀⡌⢰⡂⠀⠀⠀⡀⢠⠂⠀⠉⡆⢡⠀⠄⢀⠄⠀⠄⠂⡠⠈⠁⠀⠀⠄
⠀⠀⠀⠀⠄⠀⠀⢀⠈⠢⢩⠶⠃⠀⠚⠒⠂⠓⠘⠂⠐⠀⠀⠂⠁⠐⠀⠘⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⠀⠆⡀⢀⠐⠂⠂⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠥⠂⢰⠀⠀⠀⠀⠀⡆⠀⠄⠂⢰⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣂⣉⡤⠆⡀⠀⠀⠀⠈
⠀⠀⠀⢀⣰⣰⠈⠀⠀⠃⢸⠀⠀⠀⠀⠀⠁⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⢀⡀⠨⡑⢦⠀⠐
⠀⠀⠀⠀⠁⠀⠉⡀⠧⢈⠉⠉⠀⢨⢸⠀⠀⠈⠉⠁⠀⠙⠀⡎⠀⠀⠀⠀⠀⠀⡗⢸⠃⠘⠻⠿⠟⠀⠀⠘⢈⠠⠔⡀⢀⡄⠀⡆
⠀⠠⠄⠒⠀⠀⣌⡙⢠⠊⠀⠀⠠⢀⣝⠇⠀⠀⠁⠀⢀⢼⡀⠉⢇⠀⢀⠀⢀⠏⢀⠊⠀⠁⠤⠀⠄⠀⠀⠀⠈⠀⣀⡖⠀⢸⠄
⠀⠀⠀⠐⠤⠄⠐⢣⠈⠳⠄⠀⠀⠎⠀⠀⠀⠰⠀⣎⡁⠔⠙⣄⡀⠉⠀⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠖⠈⠃⠀⠀⠀⠀⠘⢏⠄⣠⠶⠘⣏⠍⠉⠀⠀⠉⠀⠀⠀⠆⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⢠⣿⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⣾⡿⢠⣞⣥⡀⠀⠁⠀⠀⠀⠀⠀⣀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢹⣷⢀⣿⡇⠀⠀⢀⣾⡿⠁⠀⠉⢻⣿⢠⣶⠋⣼⡆⢰⡇⠟⠀⣼⡏⠀⠀⠀⠀⠀⣀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣸⡏⠸⣿⠀⠀⠀⣾⡟⠀⠀⢀⣠⡿⠋⢿⣇⠘⠉⡀⢸⣿⠀⢰⣿
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢠⣿⠇⠀⠙⠂⠀⠀⠙⠁⠀⠈⠉⠁⠀⢀⡀⠉⢡⡾⠁⠘⣿⡇⠀⠉⠁⢠⠄⡄
⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⢀⣾⡿⠀⠀⣀⠀⠀⠀⠀⣀⠀⣴⢠⠆⠀⢸⣿⠀⢸⡇⠀⢀⡿⠁⠀⠀⠀⣿⡌⠁
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⣼⡿⠁⠀⠀⣿⡆⠀⠀⣠⡍⢸⣿⠀⠀⠀⣼⡏⠀⠀⠑⠀⠈⡀⣀⠀⠀⠀⠹⣿⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⣸⣿⠁⠀⢀⣿⠇⠈⣿⣇⠀⢰⣿⠁⢠⣄⠀⢠⡞⢀⣾⠂⠀⡀⠀⠘⣿⡆⠀⠈⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⢠⣿⠇⠀⠀⢸⣿⠀⠀⢹⣿⠀⣾⡏⠀⣸⡟⠀⢿⣧⠈⠁⢠⡾⠀⠀⠀⣿⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠀⠀⢸⣿⠀⢿⡇⢠⣿⠃⠀⠀⠉⠉⠀⠘⣷⠀⠀⢠⠏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⣿⣿⣧⠀⣿⣿⡟⠛⠃⢠⣾⣿⡿⠛⠿⠇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⠁⠀⣿⣿⣷⡶⠀⠀⠙⠻⢿⣦⣤⡀⠀⠈⠉⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣼⣿⣿⠇⠀⢹⣿⣥⣤⡄⠀⠰⣶⣾⣿⡿⠃⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀⠀⠀⢀⣀⣀⠀⠀⢀⣀⠀⠀⢀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⣾⡟⠀⠘⠛⠃⠀⣾⣿⡿⠻⠿⠀⢸⣿⣤⣤⣿⣿⡇⠀⣿⣿⠟⠛⠀⢰⣿⣿⠟⠛⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣾⣿⠁⠀⢸⣿⡇⠀⠈⠛⠻⣷⣄⠀⢸⣿⠟⠻⣿⣿⡇⠀⣿⣿⣶⡆⠀⠈⠛⢿⣷⣄⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⡏⠀⠀⢸⣿⡇⠀⢾⣷⣶⣿⡿⠀⢸⣿⠀⠀⣿⣿⡇⠀⣿⣯⣤⣤⠀⠀⣤⣴⣿⣿⠆⠈⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠀⠉⠉⠁⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠉⠁








⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣄⠀⡀⠀⠘⢿⠀⢃⣤⡀⠀⡖⠀⠀⠀⠄⢐⠠⢴⣦⠀⢱⣶⡇⡐⢸⡇⠀⡀⠜⠛⠀⠿⢀⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡖⢰⡆⠀⠆⢴⣀⠗⠆⠻⠧⠀⠒⠛⠀⠺⢰⡆⢦⡀⡄⡄⡿⢷⠏⢁⡌⣡⣄⣠⡤⣤⢚⠐⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⠠⠤⢤⣈⣡⣿⠁⠀⣰⠊⠾⣷⢰⣀⡌⠧⠀⢹⣷⣬⣷⠏⢰⡸⠇⠘⠿⠿⢀⡉⣹⣴⠟⣻⠆
⠀⠀⠀⠀⠀⠀⠠⡶⢁⠈⠢⡄⠀⠉⠉⠀⠀⠺⣿⢆⣰⢡⡟⢿⣤⡴⠂⠈⠛⢉⡀⠁⡞⠓⢲⠀⢰⣦⡀⣽⠟⣵⣌
⠀⠀⠀⠀⠀⠀⠀⢌⠀⢟⡎⢀⣴⡆⠀⣿⣶⠶⣿⠏⣽⡰⠇⡌⣿⣁⣤⢷⡄⣸⠋⢉⠻⣟⡸⠛⣿⣿⡿⠃⣜⠴⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢶⢿⠧⣧⡌⢿⣷⣾⣿⡿⠀⠙⠛⠋⢠⡴⠃⢸⣿⣿⢰⣿⣿⠀⣸⡏⠛⠃⣸⣿⡟⢡⠞⢁⣦⣴⣌⡁
⠀⠀⠀⠀⠀⠀⠂⢀⣠⣷⡈⠣⢾⡌⠻⣿⣤⣤⠀⢀⣄⠀⣿⣰⠞⣿⣇⣿⢸⡇⣤⣻⡄⠸⠢⣿⡟⡴⠁⣠⡾⠟⡱⠋
⠀⠀⠀⠀⠀⠀⣀⡀⠙⣍⠻⢆⡈⠻⣆⠈⢻⣿⣤⣾⡟⠀⣼⢃⡇⢿⣼⣏⣁⡀⠈⠉⠁⢠⣴⣿⡟⠀⠈⢁⡴⠚⠡⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠙⠢⢽⣦⣙⢷⣄⠹⣿⣿⣇⡼⠁⢸⡇⢸⣿⡇⣼⠻⡀⠰⣦⣄⣿⣏⣠⣤⠞⠋⠐⡀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠻⣿⠻⠿⠷⠿⠿⠿⢷⣶⣿⣷⣾⣿⣿⣿⡶⠿⠿⠿⠿⠟⠛⠛⠉⣽⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠐⠆⢀⠅⠀⠀⠹⣧⠠⣶⠦⡴⣶⠀⡴⠤⣄⠀⠀⠀⠀⠀⣾⠃⠀⢠⡄⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠆⠀⠀⠀⠀⠀⢹⣧⠙⢦⡀⢸⡇⣇⠔⠋⢀⣾⠉⣆⠀⣿⣀⣴⠟⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠈⠛⠇⢀⡴⢦⢸⣿⠀⡇⢠⣿⠋⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⣠⢺⣧⠀⠀⢸⡇⢸⡎⢿⣦⣵⠏⣿⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢱⡇⠁⣸⡿⢦⡄⢸⡇⢸⠁⠈⣿⡿⠖⢻⠀⠎⢹⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⡇⣴⠏⠀⠈⣿⣼⡇⡟⠀⢠⡏⠙⣆⢸⡞⠀⣼⠀⢀⡀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡠⠀⣿⠏⠀⠀⠀⣿⢻⡟⠀⠀⣾⢀⠀⢸⡞⢿⠾⠃⢰⣋⡻⣦⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠁⢠⢿⠀⡠⢤⠀⣿⡾⣷⡀⣸⢻⣯⣀⣼⠇⠀⠰⠶⣄⠛⠁⢿⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⠏⢸⣼⠁⠘⢰⠟⠀⠙⠛⠁⡀⠉⠉⠁⠀⣤⣼⢀⠹⣧⠀⣸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢠⡟⠀⣾⢻⣆⣠⠏⢠⢤⠀⣠⣄⠱⣄⣀⣄⠀⡇⠘⣇⠙⢻⡄⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷⣴⠏⠀⠩⢤⡐⣦⠛⡐⣯⠈⣧⠘⣿⡻⣧⣿⡄⢻⡄⢸⣧⣿⢲⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⣱⠛⣦⠰⡈⣇⢸⣞⢻⡜⢧⣹⠀⡏⢳⡜⣯⢷⣼⡇⠀⣿⢻⣦⠇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢿⢦⡘⣧⢹⡟⢸⡇⡆⣿⠀⢹⣦⣠⠀⠻⣼⡄⢻⣷⣼⡿⠀⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠘⠷⠇⠸⣾⡟⢼⡇⢹⣿⡄⢠⠈⢻⣧⠀⢻⣿⣸⡟⠙⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢹⣇⠈⣷⡀⢿⡇⠀⣠⡄⢻⡷⢼⡇⠻⠃⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠘⡌⢧⠹⣌⠈⢷⡄⠙⢧⣼⠇⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠈⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠶⠶⠶⠤⠤⠤⠤⠤⠤⠶⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⣠⡤⣄⠀⢀⣤⠤⣄⡀⠤⢰⣶⠄⠀⢠⡴⠦⠄⠀⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⣀⠁⠀⣼⡏⠀⢹⠀⣿⡇⠀⠈⣷⠀⢸⣿⠀⠀⣿⡤⢤⠀⢰⣿⡇⢹⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣸⡿⢥⠼⠃⢰⣿⠀⠀⢸⡄⠹⣷⡀⠀⠀⠀⢸⣿⠀⣰⡟⠓⠚⠁⢸⣿⠇⡼⠁⠀⢰⡗
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠤⠤⢼⠀⢀⡈⢻⣦⠀⠀⢿⣿⠀⢿⣇⠀⠀⣠⢸⣿⡋⠁⠀⠐⢋⣀⣄⡀
⠀⠀⠀⠀⠀⣀⣤⠭⠀⠀⠀⠙⠷⠤⠔⠀⠸⠟⠀⠀⠸⠀⠈⠳⠴⠟⠀⠀⠸⠿⠀⠈⠻⠷⠶⠋⠘⠿⠙⠂⠀⠓⠲⣦⣄
⠀⠀⠀⠀⠈⠁⣰⡾⠂⠀⠀⣴⡄⠀⠀⠀⣠⠐⢲⣶⠒⢀⣴⠖⢦⡀⢠⣶⠀⠀⣄⠀⢠⣴⢶⡄⢀⣴⠖⢦⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣿⠀⠀⡀⠀⣿⠀⢸⣿⠀⢸⣿⠀⠠⠇⢸⣿⠀⠀⣿⠀⣿⡇⠸⠇⢾⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⠀⣿⠀⢸⣿⠀⠈⢿⣧⡀⠀⢸⣿⠀⠀⣿⠀⣼⡿⣿⠆⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡟⢀⡇⠀⢸⣿⠀⠀⣀⠹⣷⡀⢸⣿⠉⠉⣿⢸⣿⠀⠀⢠⠄⢀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠿⣅⡼⠁⢀⣸⣿⡀⠀⠻⣤⡿⠃⢸⡿⠀⠀⠿⠈⢿⣆⡠⠏⠀⠸⣇⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⡄⠀⠀⠀⠀⠀⠀⡠⠒⠙⡦⠀⠀⠀⣠⣞⠁⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠲⠿⢧⣴⣚⣁⣀⣀⣀⣀⣠⣾⣥⡤⢾⣥⣴⡶⠺⠿⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡉⠙⢦⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣤⢠⣤⣤⡄⣤⡄⢤⣤⣤⠴⣤⣠⣤⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣼⡯⣿⣇⣿⡇⠜⢻⣿⠄⠟⠀⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠛⠃⠘⠛⠛⠃⠙⠛⠛⠁⠀⠘⠛⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢠⣶⠀⠀⠀⠀⠀⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡿⠀⠀⠻⠦⢤⣿⢻⠃⢻⡇⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠸⠁⣴⢷⡆⠀⣾⣯⠃⠀⡾⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⠀⣴⠀⢿⡜⠀⢀⣿⠏⠀⢰⠇⠀⡀⠀⢠⣾⢻⡟⠀⢠⣾⣿⡇⢀⣼⡟⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⡇⣿⣸⡟⢀⣼⡟⠀⢨⣏⠀⢠⡿⠀⣼⡇⢠⡿⢣⣿⡃⠀⣿⣿⣿⢡⠎⣽⡷⢋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢰⡏⠸⣧⠎⢸⡇⡠⠋⠻⠄⠋⣴⡼⢻⠁⣸⠷⠋⠸⣇⠜⠛⠃⠿⠋⠀⠈⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣸⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠗⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠄⢠⣤⢤⣄⠀⢠⣤⠀⣠⡄⣤⡤⢤⣠⣤⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢰⡿⠀⠀⢹⣿⠟⠡⣿⡃⣸⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠙⠛⠛⠁⠀⠀⠘⠋⠀⠀⠛⠓⠋⠈⠛⠂⠛⠁





⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡴⠒⠒⠒⠊⠛⠊⠉⠉⠉⠉⠙⠀⠀⠈⠏⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠘⠭⠭⠤⡝⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⠭⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣃⣀⣄⠀⢀⣀⣀⠤⢄⣀⡠⢤⡜⣤⠤⠤⠤⠴⠶⠶⠤⣤⢸⠒⠒⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⡟⠉⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣧⠀⠀⠀⠀⠀⠀⣠⣼⠷⢿⢢⠀⠀⠀⠀⠀⠀⢸⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⢰⡿⠧⠤⠼⠿⡆⠀⠀⠀⠀⠀⠀⡇⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠤⣠⠤⠤⠴⠛⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠈⠁⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠠⠀⠐⠓⠂⠠⠆⠀⠈⠁⠀⠲⠀⠀⠀⠉⠁⠙⠀⠀⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⠚⠀⠀⠠⠀⠐⠁⠂⠀⠂⠀⠀⠂⠀⠐⠂⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠐⠒⠒⠂⠀⠈⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠄⠀⠀⣀⠀⠰⠀⠀⠀⡄⠀⠂⠀⠀⠄⠀⠚⠀⠐⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⢰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣜⠁⠀⡂⠀⣁⢠⡀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀⠀⠀⠜⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣠⠀⢀⣉⢈⣀⣁⣈⢉⣀⡀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠶⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣀⣀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢞⠉⠀⣴⡆⠀⠈⠱⡆⠀⠀⠀⣠⠤⠒⠚⠋⣉⠙⠛⢳⣿⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢸⠀⠀⣿⠁⠀⠀⢀⡿⠀⠠⠊⠀⠀⠀⠀⣾⢡⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢸⠀⢸⣿⡤⠶⣦⣾⡁⠀⠀⢀⣀⡀⠀⠀⣿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢿⡏⢻⣤⠏⠀⣼⡏⠉⠉⠀⠈⢷⠀⢠⡟⢁⠇⢀⠼⣿⠀⠀⢸⡏⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠈⠛⢻⠇⠀⢠⣿⠁⠀⠀⠀⠀⢸⡟⢻⣏⣁⠔⠁⠀⣿⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡎⢠⡟⠀⠀⣼⠏⡤⠖⠒⠲⢤⣿⣁⡀⢉⡅⠀⢠⠔⣿⡏⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠋⢀⠀⢰⡟⠘⢧⣤⣤⡴⠟⠀⠀⠀⢸⡇⢰⠃⠀⣿⠇⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢠⡞⠉⣹⠿⡅⠀⢀⡄⠀⠀⣠⣤⠀⠀⣾⠁⠘⢦⡴⠟⠀⠀⢸⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠾⣷⡛⠁⢀⣱⠴⢋⡀⠀⠀⣿⡟⠀⢠⡿⢀⡀⠀⢠⡶⢦⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⠀⠀⠈⠉⠛⠉⡽⠀⣙⠁⠀⠀⣿⠁⠀⢸⠟⢁⡿⠀⣿⠔⠁⡰⠋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠸⣆⠀⢰⡆⠀⢀⡇⢀⡿⠀⢀⠔⢿⡇⠀⣾⠀⢸⣧⠞⠷⠤⠚⠀⢀⣸⣧⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⢻⡆⠀⣿⡄⡼⠀⠸⣧⡴⠃⣀⣼⣧⣀⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⠈⠻⠞⠉⠛⠁⠀⠀⢀⡖⠋⠁⢸⣿⠈⠙⠲⠀⠀⠀⠀⠀⠘⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⣄⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣟⣀⣀⣀⣉⣛⣛⣡⠤⠖⠁⣀⡀⠀⣤⠀⣰⡞⢙⡦⠊⣽⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠋⠉⠉⣿⠋⠉⢉⣉⣁⠀⠀⠀⠀⠀⠜⣹⡇⢠⣿⢰⡟⠉⣩⠃⠸⣏⠠⠿⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⢰⡟⠀⣰⡿⠤⠼⡗⠀⠀⠀⠀⠀⣿⣁⣾⡇⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠊⠀⠀⠀⣼⠇⠀⣿⡁⣀⠜⠀⠀⠀⠀⣀⣀⣈⣁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠈⠉⠁⠀⠀⠀⣴⠟⠉⠀⠀⢨⡟⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⠞⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀
⠀⠀⠔⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠂⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠀⠀⠘⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠡⣀⠀⠀⠇⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠉⠉⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⡀⡔⠑⡄⠀⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⢀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠌⣓⣃⠀⢀⠀⢄⣂⠀⠀⠠⠀⢀⠀⠀⠀⠌⠀⠈⠂⠊⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠄⣀⠀⢸⠀⠀⡋⢩⠇⠀⠈⠀⢿⣽⡗⠀⠀⠰⣯⣿⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠅⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠐⣌⠲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠦⢈⣑⡦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⣶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣴⣶⣦⣶⣦⣾⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡷⠀⠰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠘⣶⡂⠀⠀⠀⠀⠀⢀⢹⡟⣹⠻⡿⡿⢻⡙⣿⢁⠀⠀⠀⠀⠀⠀⣲⡞
⠀⠘⡷⣄⢤⣄⠀⠁⣵⣷⣀⠀⠀⡄⢸⣾⡌⢿⢛⣙⣛⢻⠏⣼⣾⠀⡄⠀⢀⣰⣷⡅⠁⢀⣤⢄⡴⡟
⢀⣠⣬⡟⣤⣝⡇⠳⣦⠰⢧⣀⠀⢻⣼⠿⠞⠓⢹⡾⣿⠑⠻⢿⣿⣬⠃⢠⣠⠗⢠⡶⠃⣟⣥⡼⣯⣤⣀
⠈⠉⠀⣠⠞⠁⣸⡿⠻⣄⡐⠻⠁⡘⠁⡿⣣⡷⠂⣁⡃⠲⣧⡻⡇⠙⡀⠹⠓⣀⡼⠻⣿⡀⠙⢦⡄⠈⠉
⠀⠀⠀⠀⠀⠉⠁⠐⠋⠁⠀⠁⠳⠀⠀⠀⠋⠁⠀⠀⠀⠀⠉⠃⠀⠀⠰⠃⠁⠀⠉⠓⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠨⠂⠁⠅⠀⠀⠉⠘⠀⠐⠐⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⡀⠀⣤⣀⠠⠤⣀⠀⠠⡔⠀⠀⠀⣆⡀⠀⠀⠀⠀⣀⡆⠀⠀⡐⡤⠀⢀⡤⠤⢀⣠⡄⠀⡀
⢀⡀⠀⠙⢳⣄⣬⠷⣶⠋⠰⣾⡄⢱⡀⢿⡍⠿⢄⡭⣁⠼⠏⣽⠇⣰⠁⡼⡶⠈⢳⡶⢯⣄⣴⠛⠁⠀⣀
⠀⠉⡉⣷⠋⣡⠇⡶⠋⢰⣏⠈⠀⡾⢻⣿⣾⡴⣼⣷⣿⡴⠼⣞⣿⢻⡆⠈⢈⣷⠈⠳⡆⢧⡉⢳⡏⡉⠁
⠀⠰⠿⠋⠘⠁⠀⡀⡩⡿⠀⠀⠀⠃⢸⢻⠣⣾⡦⣥⡥⣾⡦⢹⢻⠀⠃⠀⠀⠸⡯⡁⡀⠀⠙⠈⠻⠶
⠀⠀⠀⠀⠀⠀⠠⠿⠇⠀⠀⠀⠀⠀⠀⣸⣧⣽⣶⣿⢷⣾⣥⣿⡄⠀⠀⠀⠀⠀⠀⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⡷⠄⠴⣿⢿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⠋
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⣀⣀⣤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠿⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⣀⣀⣠⠤⠤⠒⠊⢉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⡀⠀⠀⠀⠀⠈⠉⡡⢀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣇⠈⣇⠀⠀⠀⣿⡏⠀⠀⢀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠹⣆⡻⠀⠀⣠⣿⡇⠀⢠⠎⠀⠀⠀⢀⣤⡤⢄⠀⠀⠀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢀⡴⠋⠀⠀⣠⡶⠒⢦⠀⠀⠈⣷⣤⡜⠁⠹⠇⠐⠁⠀⠀⣠⣾⡿⠁⠀⢸⠆⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠨⣿⣇⠔⠋⠀⠀⠀⢸⣿⠃⠀⡼⠀⠀⡐⢀⠻⣷⣄⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⢀⡞⠀⠀⠀⠸⣷⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⢸⣿⡠⠞⠁⢀⠌⠀⡼⠀⠘⣿⡆⠀⠀⠀⣼⣿⠃⠀⠀⣠⠊⠀⠀⠀⠀⠀⣿⣄⠃
⠀⠀⠀⠀⠀⢀⡜⠁⢿⣿⠀⡴⠲⣦⣔⠈⠻⣄⠠⠔⠁⠀⢰⡇⠀⠀⢸⣿⠀⠀⣼⣿⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠘⣿⡄⡇⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣸⡟⠀⢰⣿⡏⡠⠚⠁⠀⠀⢠⣶⡟⢙⡆⠀⡜⢻⣷⡀
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠹⣷⡇⢰⠇⣿⡇⠀⠀⠀⠀⢠⣄⠈⠳⠤⠴⠟⠁⠀⣿⡿⠋⠀⢀⡀⠀⠀⣾⣟⣠⠞⠀⡼⠀⠀⢿⣷⣀⣠⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠈⠃⢸⡄⣿⠃⠀⠀⠀⠀⠛⠛⠀⢀⡀⠀⠀⠀⢀⣿⡇⢠⠞⢹⣿⠆⠀⢿⡏⠀⢀⠜⠀⠀⠀⣸⣿⣯⠀⠀⠀⣿⠟
⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣠⣿⡗⠀⠀⢻⡄⠀⢀⠔⠉⣿⣧⠃⠀⣾⣿⠀⠀⡼⠳⠔⠋⠀⠀⣠⠞⠁⢻⣿⡄⠀⠀⠉
⠀⠀⠀⠀⠀⢿⣁⣀⠠⢴⣿⡷⠀⠀⠋⠵⡖⠊⣿⡟⠀⠀⢀⠔⢻⣶⡁⠀⠀⠹⠟⠀⠀⣿⡇⠀⣠⠃⠀⠀⠀⠀⣰⠏⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⣼⣿⠆⢀⡇⠀⠻⠧⠤⠖⠁⢠⠎⠹⣿⣆⠀⠀⠀⠀⠀⠹⠧⠔⠁⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥⠞⣿⡟⢀⡜⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢦⡀⡠⠖⢶⣄⡴⠚⠉⠉⢳⡀⣀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡀⠀⠛⢀⣄⠀⠉⠀⠀⢀⠀⠈⠛⠁⠀⠈⣧⠖⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⡇⠀⠀⢸⢸⠀⠄⣾⠆⡼⠀⠀⠆⠀⠀⢀⣤⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⡇⢠⣧⠘⡾⣴⠀⣿⣠⡧⣿⣴⣰⣶⣇⣞⣰⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⢸⡇⡎⢻⣰⠇⣯⡼⣾⡏⠁⠋⠛⠈⠉⠋⡩⢾⠛⣡⡴⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠉⠀⠛⠁⣈⠋⠀⠀⡀⣠⣰⣦⣆⡆⠀⠀⠸⣥⠟⠀⠙⣋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠃⣀⠀⠀⣼⠉⡇⠀⠀⢉⡾⢙⠉⠉⠃⠀⡀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⣏⢠⠃⡴⡄⢘⣡⡏⢠⡏⣠⢀⡅⣤⢰⢤⡏⣸⠇⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢰⡇⠹⡄⠹⣾⢴⡷⡧⠔⡟⡠⣿⡠⣏⢾⠇⡟⢾⡼⠞⣸⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠻⣤⠃⠸⠟⠀⠀⠛⠁⠉⠀⠉⠀⠀⠀⠀⢠⠎⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡆⠀⣀⣰⣄⡆⡄⣠⡄⠀⡀⠸⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣩⠍⠀⢀⡷⣶⡴⣼⢁⠈⠁⣏⢾⢺⡷⣏⠄⠀⠓⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠖⠀⠀⠘⠃⠉⠉⠙⠃⠀⠀⢁⡀⠀⠀⢠⣆⣀⣀⣀⣤⡾⠏⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⠔⣻⠀⠀⢀⡀⢠⣿⠇⠰⢚⣿⠉⠉⠙⠉⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢸⡷⠃⣰⠿⣄⢠⡿⠃⢸⣏⢀⠔⣿⡇⠀⠀⡶⠀⠀⢠⠠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⠃⠘⢁⣤⣿⢻⣀⡔⢡⣿⠁⠀⢿⣇⣠⡟⠁⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠠⡏⢀⡴⠋⣸⡇⠈⠁⠰⣧⡟⣠⢀⠈⠉⢉⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⡾⠀⢠⡟⠀⣀⠀⠀⠀⣰⠇⡞⠶⠀⢸⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠳⠴⠛⢀⡼⠻⣄⠀⠸⠋⠸⠃⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣠⠴⠋⠀⠀⠸⢦⣤⠾⢦⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⣐⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀⡄⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢟⣋⣿⣿⣷⡀⠀⠀⠀⢣⠀⠄⡁⡀⡄⢄⡀⢐⠃⠀⠀⠀⠀⠙⠈⠉⠁⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡘⣿⣷⣶⢟⣽⣿⡾⠞⠃⠀⠀⢰⡆⡆⣶⠰⢂⢴⣞⣆⣮⢲⠀⠀⠀⠀⡀⢀⢀⡀⡀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢹⡄⣿⠙⣗⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠈⠃⡇⢸⠀⡇⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⡄⢸⠆⠿⠘⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⣨⠄⠀⠀⠀⠀⠁⠈⠀⠁⠁⠈⠀⠁⠀⠀⠈
⠀⠀⠀⢀⡤⠾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣂⣀⣀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠉⠈⠀⠀⠐⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡨⢐⠠⠌⠀⠀⠀⠀⣤⠤⠭⣥⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢡⠒⣈⠀⣀⢀⢀⢠⡀⣘⡛⣛⣛⣛⠂⠀⠀⠀⠀⠠⠄⠀⠂⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣥⢅⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠿⠸⠘⠺⠃⢇⠒⠲⠶⠆⠀⠀⠀⠀⠀⢂⠀⢀⠀⠀⡄⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⢭⣭⠉⠋⠀⠀⠀⠀⠀⡴⡈⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠐⡗⠃⠂⠐⠀⠀⠀⠀⠀⠀⡀⢀⢠⣸⠇⡤⡃⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠠⠀⠐⠿⠭⠔⠤⠤⣴⣾⠀⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠁⠓⠒⠃⠋⠀⠀⠀⠀⠀⠀⠐⠐⠂⠁⠒⠀⠊
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡶⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠖⢲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⣤⠤⢤⡤⢤⡤⢤⡤⠤⠤⠤⠤⢤⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠒⠺⣇⠀⢀⣇⢸⣇⢸⡇⠀⠀⠀⠀⣸⠗⠒⢻⠀⢸⠗⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠈⠉⠉⠉⠉⠉⣹⣏⠉⠉⠉⠉⠁⠀⠀⢸⠀⢸⠀⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣼⠁⣤⣤⣤⣤⣤⣤⡀⣷⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠘⠛⣧⠀⠀⠀⠀⣸⠛⠋⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠛⠛⡟⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⢻⡟⠛⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⣤⣤⣧⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣼⣧⣤⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠉⠙⡏⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⢹⡏⠉⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠧⠤⠴⠧⠤⠤⠤⠤⠤⠿⠤⠤⠤⠤⠤⠼⠧⠤⠼⠦⠼


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠡⡆⣆⠀⣆⢸⡀

⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⣤⡁⠀⠀⠀⠀⡀⠀⠄⢠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠
⠈⠂⠀⠐⡀⠑⠀⠀⠀⠀⢲⠉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣰⣂⣈⡅⠀⠑⠀⠀⠀⡀⠀⢀⠀⠀⠀⠄⠀⢀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠤
⠀⠀⠀⠀⢀⡀⠀⠀⠀⡄⠐⢄⣀⠦⠂⠀⡄⠈⠉⠀⠀⠀⠀⠀⣾⠂⠄⡉⠀⠀⢁⠀⢀⠀⠀⠠⠄⢰⠀⠀⠀⠈⠀⣀⠂⢆⠀⠀⢀⠀⡄⠀⣀⠁⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠄⠀⢀⠀⠀⠀⠀⠀⠀⠐⠦⣈⢐⢲⠀⠃⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠰⠈⠀⠉⠄⠈⡄⠁⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠁⢀⡀⠀⠀⠀⠂⠀⠀⠀⠄⠤⡀⠘⠀⠂⠰⠀⠡⡀
⢀⠀⠀⠰⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠁⠈⠀⠠⠀⠀⠀⠄⠠⠀⠀⠐⠂⠀⠆⠀⠈⠈⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠈⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠃⠀⠄⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠐⠀⠀⠀⠀⣅⡤⣴⠄⠂⠀⠀⠀⠤⠀⡀
⠀⠀⡀⠀⠐⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢦⠐⠇⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠂
⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠄⠠⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠘⣇⣸⡅⠔⣓⣆⠰⡦⢤⡀⣶⠤⣄⢠⡄⠀⡄⠀⠀⢹⢉⡱⠀⠦⢠⣤⢤⡜⢻⠛⠀⣧⢤⡄⢠⠤⣼⠰⣚⣦⠀⢤⠀⢠⠄
⠀⠀⠀⠀⠀⢠⡇⠸⣇⢮⣉⣿⠨⣇⣠⠇⣿⣀⡼⠀⢱⡼⠀⠀⠀⣨⡀⠀⢤⣧⢀⣇⠀⠀⢸⣄⢠⡇⠀⣇⢇⣀⣼⠸⣍⣹⡄⠈⢧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⣿⠀⠀⠘⠞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢈⢢⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⢁⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃
⠀⠀⠢⢀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠨⡄⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⠠⠀⠀⠠⠀⠄⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠱⠀⠀⠀⠊⠠⠀⠄⠀⡀⠀⠈⠀⠒⠀⠁⠀⠀⢀
⠀⠀⠀⠒⠂⠂⡀⠙⠒⠂⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐
⡀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠁⡆⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠐⠀⠂⠊⠐⠀⠂⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⣄⢀⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢢⡄⠀⠂⠀⠠⠀⠠⠀⠀⠀⠂⡄⠘⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠒⠂⠀⠀⠀⠀⠌⠁⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⡎⠀⠀⠀⢰⡓⡂⠀⠀⠀⠁⠀⠂⠀⠀⠄⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠠⡀⠘
⠄⡀⠀⠀⠀⠀⠀⠁⠁⠂⠀⠎⠀⠐⠀⠈⠀⡉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⡀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡅⠔⠊⠀⠀⠀⠀⠀⠀⣴⡾⠛⠆⠀⠀⡘⠻⣿⣄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⡅⠀⢀⠴⣦⡀⠀⠀⢸⣿⣇⡠⠃⠀⢠⠃⠀⠈⢿⣷⣤⠐⠒⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡎⠀⣿⡇⠀⠀⢸⣿⡇⠀⠀⢀⠂⠀⠀⡠⠊⢹⣿⡆⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢸⠀⢰⣿⣇⣀⠀⢈⣿⣇⠀⡠⠃⠀⠀⢰⠁⠀⠀⣿⡟⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⡐⣿⡿⠁⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠘⢄⣀⣠⠟⠁⠀⠀⠈⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠚⠋⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡇⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠘⢿⣿⠟⠁⠀⠀⠒⠒⠒⠒⠒⠒⠀⠈⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠁⠀⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⣿⠀⢀⠀⠀⣿⠀⠀⣾⡁⠘⠀⠀⣿⠀⢰⠀⠀⣿⠀⠀⠀⣾⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⡇⢸⠀⠀⣿⠀⠀⠹⣧⠀⠀⠀⣿⡄⢸⠀⠀⣿⡄⠄⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⣷⠸⠀⠀⣿⠀⠀⠀⢹⣧⠀⠀⣿⠀⢸⠀⠀⣿⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣿⡆⠀⠀⣿⠀⠀⡀⠀⣿⠀⠀⣿⠀⠸⠀⠀⣿⠀⠀⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠹⠇⠀⠀⠿⠀⠀⠘⠶⠋⠀⠀⠿⠀⠀⠀⠀⠿⠆⠄⠀⠑⠴⠋




⣿⣏⢹⣟⠻⣿⠛⢟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣠⠶⡄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣰⠸⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣬⠌⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣬⠷⠤⠤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢃
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⡀⠀⠀⠀⠲⡄⠀⣀⣀⠀⠀⢀⣀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣲⠂
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢰⠏⠙⠷⠾⠀⠀⠙⠚⣋⠙⢷⣼⠟⠙⢷⣤⣿⠀⠀⠀⠀⠀⠀⢠⠖⠢⡄⠀⠀⣀⣀⠀⡸
⠀⠀⠀⢸⠃⠀⢀⣀⡀⠀⠀⣸⢀⡀⠀⠀⠀⣿⠀⠀⣿⣁⠀⢸⣇⠀⢀⡿⠁⢳⠀⠀⠀⠀⠀⠘⠾⠃⠹⠀⠐⠤⢼⡟⠁
⠀⠀⠀⠇⠀⢰⡟⠉⣛⠶⠶⠃⠈⣿⣀⣀⡠⠋⠙⠚⠁⠈⠉⠁⠈⠉⠉⠉⠒⢸⠇⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠐⢻⡀⠀⢻⡦⣄⡤⠞⠁⠀⠀⣀⣀⣤⡤⠤⠶⠖⠒⠒⠙⠂⠁⠂⠉⠁⠁⠀⠉⠉⠁⠀⠀⠀⡀⠔⠉⡠⠤⠒⠒⠶⣄
⠀⠀⠀⠀⣇⠘⠇⠰⠊⠀⢀⣠⡤⠶⠚⠋⠉⠁⢀⡦⢤⠀⡄⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⢹⣎⣀⡤⠖⢻⠉⠀⡀⡀⠀⡟⠙⡆⢸⠁⢸⠇⢷⡴⢿⠀⠀⢀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠡⠛⡄
⠀⠀⠀⡠⠔⠋⢡⡄⠀⢸⡀⣾⠀⣷⠈⡇⣴⠇⢸⠐⢫⡆⣴⢀⡏⡔⠀⡟⠀⠀⠀⢀⣀⡟⠀⣀⠄⡄⠀⠀⠀⡄⠀⠀⠀⠀⠰⠖⠁
⢀⡴⠈⣤⣄⡤⠋⣧⡴⠾⡇⠻⠞⠙⠀⣧⠀⠀⠸⠃⠀⠙⠖⠋⣼⡧⠄⣷⠎⡇⠠⡏⢠⡇⢰⠃⣰⡇⢠⣀⣼⡇
⣾⠀⠀⠀⠉⠀⠘⣧⠀⠀⠿⠀⠀⢀⠴⡟⠒⡆⠀⠘⡃⢰⡏⠓⢸⡇⠠⡟⠀⠿⠀⠓⠋⢛⣈⡛⠭⠥⠤⠭⣾⠇⠤⠄⠤⠄⢤
⠛⠶⠖⠀⠀⠀⠀⡿⠀⠀⠀⠀⢰⡃⡀⡇⠼⠳⠤⠀⣿⠸⡇⠀⠘⠃⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⠁⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠁⡇⠀⠀⢀⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⣤⣤⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⠶⠶⠶⠶⣤⡀⢀⣤⡴⠶⠶⠶⢦⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠛⣇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⢷⢸⡏⠀⠀⠀⠀⠀⠙⡆⠈⣧⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡏⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿⢰⡇⠀⠀⠀⠀⢀⣰⠇⠀⢿⡀⠀⠀⠀⠀⣾⢻⠄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⣀⣸⣧⠀⠀⠀⣾⣤⣤⣼⣷⠆⠀⣿⠶⠦⠶⠶⠞⠋⠀⢸⡷⠶⠴⠶⠶⠋⠁⠀⠀⠸⣇⠀⠀⠀⣼⠃⣼
⠀⠀⠀⠀⠀⠀⡿⠛⠛⠋⠉⠉⢹⠁⠀⠀⣼⠃⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡼⠃⠀⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢰⠏⠀⠀⠀⠀⠘⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠻⠀⠀⠀⠀⠀⠀⢻⡀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⠴⠋


⠀⠀⠀⣠⢀⣤⣤⣄⠀⠀⡄⢀⣀⣤⡤⣤⡀⠀⢀⣀⣀⣤⣠⣤⣤⣤⢀⡄⠀⠀⠀⣠⠀⡶⠶⢤⣀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⠉⠀⠀⣸⠇⠀⡇⢻⠁⠀⠀⢀⡇⠀⠈⠉⠁⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⣾⠠⡇⠀⠀⠈⠳⣆⠀⠀⢠⡏⣧⠀⠀⠘⡄⠀⠀⠀⢰⡿
⠀⠀⠀⣿⠤⠤⠾⠓⢤⠀⡇⢸⣀⣠⠴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⢹⠀⠀⣞⣀⣸⡄⠀⠀⢧⠀⠀⢠⠏⡇
⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⡇⢸⠉⠳⣤⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⠛⠙⠉⠉⣿⠀⡇⠀⠀⠀⢠⡟⠀⣸⠁⠀⠈⣧⠀⠀⠈⠳⡤⠏⠀⡇
⠀⠀⠀⣿⣀⣀⡤⠞⠃⠀⡇⢸⡀⠀⠀⠉⠳⢦⠀⠀⠀⢹⠀⠀⠀⠀⢺⠀⠀⠀⠀⣿⠀⡇⠀⢀⡴⠋⠀⢠⠇⠀⠀⠀⠸⡄⢇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠿⠀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢦⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠋




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣆⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣠⠴⣤⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⠖⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣿⣿⣿⣿⣽⡇⠀⠀⠀⢸⢹⣿⣧⢠⠞⠁⣴⣾⡇⠀⠀⢠⣿⠿⣿⢷⡄⣼⡥⢞⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⡿⣷⣿⣼⣯⣛⠷⣿⠀⠀⠀⣿⣼⡟⢻⣿⣶⣿⣿⣿⡇⠀⠀⢸⣷⣾⣿⣿⢻⠇⠴⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠿⣦⣙⣿⣿⣝⢳⡏⠀⠀⠀⡿⢿⣿⣾⣿⣿⣷⢉⡟⠀⠀⠀⠘⣧⣾⣿⣿⣿⣦⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢷⣦⣉⠉⠛⠿⡿⠁⠀⠀⠀⢻⣿⣿⣷⡙⢿⢷⠞⠁⠀⠀⠀⠀⠹⣿⣿⠟⡫⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣬⣿⣷⣦⣰⠁⠀⠀⠀⠀⠸⣿⣿⣿⣇⣰⠋⠀⠀⠀⠀⠀⠀⠀⠻⣤⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⣧⠀⠀⣴⠟⡠⠖⢩⡆⠀⠀⠀⠀⢀⣼⠁⣼⠟⠀⠀⠀⠀⡴⡿⠀⠻⠟⢁⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣷⣄⠸⢀⣾⡿⠊⣠⣴⠟⠁⠖⠀⠤⠤⣾⠇⣼⠏⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠙⠻⡿⠀⠀⢠⡆⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠋⠉⠀⠀⣼⡟⠰⢿⣟⠁⣠⡾⣀⢷⡖⣸⠏⢰⠏⡰⣿⣰⠟⣶⠇⣴⠶⣴⢀⡞⢠⡆⡠⠄⢀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⢰⡟⠀⢀⡠⢾⣿⠀⠉⠁⠺⠀⠿⠔⠿⠈⠸⠇⠫⠀⠘⠀⠛⠊⠛⠋⢉⡿⠋⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠛⠁⡀⢀⡴⠋⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢰⠃
⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠉⠀⠀⠀⠃⠘⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠍⣟⣛⣛⣛⣛⢛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰⣁⢱⠀⠀⠀⢠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⢠⣟⡇⠀⠀⠠⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣴⣲⡤⣼⣓⣧⣤⣤⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣶⠖⢿⣿⣇⠉⠋⠀⠻⠭⠽⠀⣨⣝⣿⠿⣿⠦⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠛⠋⠀⣼⣓⣛⣶⠀⠀⠺⠀⠀⣼⢯⣛⣿⡄⠀⠀⢿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠁⣠⣦⡅⠘⠛⠁⠀⡴⣶⣦⠀⠈⠙⠛⠛⢡⣤⣄⠠⠏⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢇⢠⣤⣤⣝⠿⠃⠀⠸⠆⠀⢿⣟⠝⠀⠀⣤⠀⠀⠯⠽⠿⠁⣤⣴⠚
⠀⠀⠀⠀⠀⡤⣖⣟⣿⣿⣿⣿⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⣦⢀⣿⣿⡀
⠀⠀⠀⠀⢸⣽⢻⠓⣾⣿⣿⣿⡀⣿⣿⣿⡇⢀⣷⣶⡄⠀⣿⣧⣼⣷⣤⣿⣿⣿⣿⣿⣽⢷⣦⡀
⠀⠀⠀⢀⣾⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣝⣿⣷
⠀⠀⠀⠈⣿⡍⠛⢇⣀⢤⡿⣥⣿⣿⣿⡿⣿⡋⠙⣿⣿⠟⢏⣋⠽⡿⠻⢤⣸⡀⠀⣾⠟⢻⣿⣽⠃
⠀⠀⠀⠀⠘⢿⡦⣴⡙⠺⠷⠜⢿⣿⡿⢶⣿⣷⣶⣿⣿⡠⢹⢫⣸⡷⠤⠞⣵⠎⠉⠉⣁⠤⣪⠏
⠀⠀⠀⠀⠀⠀⠙⠢⣍⣓⠲⠤⣤⠖⠦⣀⠉⠁⠀⠀⠎⠙⢛⣛⣉⣀⣠⡤⠴⢒⣊⠭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⠿⠯⠭⠭⢭⣉⣉⣉⡭⠭⠭⠥⠴⠖⠒⠋⠉

⠀⠀⠀⠰⡀⠀⠀⠀⢠⠀⠀⠐⢀⠐⢠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠤⣓⣂⠘⠠⡀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠀⠀⠀⠁⠀⠀⠀⢠⠀⠁⠀⠀⠀⠇⠀⡆⢸⠀⡁⢀⠀⠄⢠
⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡇⢸⠄⡇⢸⠀⠦⣜
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠤⠀⠀⡁⠈⡀⢁⠈⡀⠡⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢐⠒⡦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⠀⠐⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠀⢀⠀⢠⠆⠀⠀⠀⢠⡞
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⣿⠀⡄⡀⠠⣿⠄⣿⣀⠀⣠⣤⡟⢀⣤⠀⠀⣀⠀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣴⡞⢷⡶⣇⢠⡏⢼⠠⣏⢸⠥⣟⢠⡆⠀⡏⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⣀⣼⣧⣿⠴⠓⠻⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⠀⡄⠀⠐⡒⠂⠁⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⠀⠉⠙⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⡀⠉⠀⠄⠀⠠⠀⢁⠀⠸⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠤⠀⠀⠄⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⡈⠂⢀⠀⠀⠀⠤⠤⠐⠂⠰⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢠⣈⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢈⡉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠈⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⣿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⡏⢰⠆⠠⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠘⣿⢀⡇⠋⠀⠀⠀⠀⢀⣴⣿⠟⠛⣉⡛⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⢿⠘⠁⢀⡏⠀⡾⣰⣿⠟⠠⠞⠋⠉⠛⠆⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠄⠀⢀⣤⡀⠀⠀⠀⣼⠁⢰⠇⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠏⢠⣿⠀⠀⢿⡅⢹⠀⣀⣰⡏⢀⡿⠀⠛⠀⢸⠇⠀⠀⠉⠀⠀⠀⠀⣼⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⣾⠷⣄⠐⠈⠛⢾⣌⠀⣿⠋⣹⣣⣦⠀⣀⡿⢀⣤⡀⢀⠀⣠⠀⢠⡟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⡇⠘⠃⠀⢹⣆⡇⢀⠇⡿⢰⡟⠀⣿⢃⡟⡼⢹⡇⣯⢾⣡⣇⡴⣿⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣿⠁⣴⠗⠀⣸⠿⣇⡜⢸⢃⢸⣇⠀⠋⢸⡇⠳⠃⠉⠀⡈⠀⠉⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⣿⣀⣠⡟⠀⠉⠀⠘⠃⠀⠙⠂⠀⠘⠇⠀⠀⢀⣀⠀⡴⠚⢹⡇⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠁⠈⣉⠉⠀⣄⠘⣿⡄⠀⣴⡆⠀⣿⠀⠀⢀⢠⡏⠙⠸⣅⣴⠟⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⣿⠀⣿⡇⡄⢻⡇⢀⡏⣴⢰⡿⠀⣿⡄⣀⣀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⢸⣿⠀⢹⢷⡇⠘⣷⠺⡇⢿⠾⣅⢀⣼⣿⠉⠹⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢸⣿⠀⣿⠘⠆⡼⢻⠀⠀⠀⠀⣠⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢀⡏⠀⠀⠑⠋⢀⡀⠀⢠⡏⠀⣠⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠾⠁⢀⡆⣠⠀⠈⠀⠀⠈⠷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡇⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠀⢻⣿⣿⡋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡀⢠⠤⡄⢦⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣶⠀⡼⣧⠀⣿⠴⠃⢺⠚⠁⠀⡏⢠
⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠦⣄⠀⠀⠀⢹⠉⠿⠰⠋⠙⢂⠛⣰⣻⠈⠀⠀⠀⠀⡞
⠀⠀⠀⣠⠊⠁⠀⠀⠀⣰⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣇⠇⠀⠀⠀⠀⢀⡇⠀⠀⣀⢀⠀⢠⠀⢠
⠀⠀⣰⠃⠀⠀⠀⢄⠀⡇⠀⠀⡼⠀⠀⠂⠀⡟⠀⢀⣼⡯⢸⣿⡤⡄⠀⣠⠊⢾⠀⢀⡎⠈⡏⠀⡞⠀⣼
⠀⠀⡇⠀⠀⠀⠀⢸⢸⠃⣀⠜⠁⠀⢰⠂⢀⢷⡀⠀⡿⠀⣼⡟⢀⡇⢠⠇⠀⡎⠀⡼⠀⢰⠇⢠⡇⢀⡇
⠀⠀⢧⠀⠀⠀⢀⡜⣹⠉⠉⠓⢄⠀⣼⠀⡸⢀⡇⢸⠃⢀⡟⠀⣼⠀⣼⠀⢰⡇⢰⡇⢀⣾⢀⢾⢀⢾⡷
⠀⠀⠈⠓⠢⠒⠋⠀⡟⠀⠀⠀⠈⡇⡇⢠⠃⣸⢀⢿⢀⣼⠇⠀⣇⡜⠹⡤⠋⠷⠃⠓⠊⠈⠋⠀⢁⣾
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⡇⠧⠃⠀⠙⠋⠈⠉⠈⠀⣀⠀⢠⠄⣠⠶⣦⠀⡆⠀⣾⠀⢠⠃⡇
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡞⠠⢶⡖⠂⣴⠛⢳⠀⠀⠀⠘⢷⠋⠀⡇⠀⣸⠀⣇⣀⡿⠀⠈⠚⠁
⠀⠀⣴⠉⢉⡲⠮⣄⣀⡤⠔⠋⠀⠀⢸⡇⠀⣯⣀⣼⠀⠀⠀⠀⠸⠀⠀⠙⠚⠃⠀⠈⠉
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠽⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⠀⠀⢠⣶⠀⠀⢠⡦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣠⣴⡀⠀⠀⠀⢀⣀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠒⠀⢠⣤⣾⡆⠀⠀⠛⢋⣩⡄⠀⠀⠀⣈⠁⡃⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠾⠿⠛⣋⡅⠀⠀⠘⠂⡟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠐⠲⠾⠿⠟⠋⠀⠀⠀⠊⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠛⢛⣛⣛⣙⣙⣑⠀⢸⣀⡷⢠⢶⡀⣖⢒⣤⡒⣢⠳⣴⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⡟⢛⠒⡖⠲⠲⠟⠀⠸⠀⠗⠞⠉⠧⠏⠉⠘⠋⠁⠰⠃⠀⣴⢶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠒⢠⠀⠀⠀⠀⠀⣤⢀⢴⠀⠀⠀⠀⡞⡇⠀⢸⣟⣷⢿⡝⣉⠇
⠀⠀⠀⠀⠀⠀⡴⠊⢡⠇⢀⡠⠊⠀⠀⠐⠒⢸⠃⡟⡜⠀⠀⠀⢸⠀⠐⠿⢿⣿⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠒⠃⠀⣄⠀⢀⠀⠀⡼⢸⡵⠁⠀⢀⢀⡧⢀⣀⢀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠊⠀⠀⡜⢸⢸⠈⠀⡇⢸⠐⡆⢠⠃⠘⡇⠇⠋⢾⠐⠁⡇
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡠⠞⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠁⠀⠀⢀⠄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡖⢠⠒⡆⠀⢢⢦⠖⣦⠂⡆⠀⠰⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠒⠃⠀⠘⠀⠓⠃⠓⠃⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣴⣦⣴⣧⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⡿⠋⠙⠋⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⢸⣿⣿⡇⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⡇⠀⠀⣿⣿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡂⣰⡀⢀⣀⢀⡤⣄⢀⡤⣄⢠⣄⢀⢥⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⣿⠯⣿⡿⢿⡿⣛⠻⡿⢛⠻⣟⢿⡿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣧⣿⣧⡼⣿⢸⣾⣿⢿⣾⣿⠏⢿⣿⠏⣸⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⠙⠀⠛⢊⠀⡇⠁⠀⡀⠁⠀⣮⠀⢈⣼⠃⠀⠘⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠇⠿⠿⡇⠿⠨⠉⠁⠸⠉⠁⣴⠟⠁⠀⠀⢙⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⣾⣀⡀⣸⣀⣷⣶⣿⣷⣶⣿⠋⣠⣾⣿⣷⠦⣾⣿⣿⣿
⠀⠀⠀⢠⡤⣄⠀⢀⡀⠀⢠⣀⣠⣀⣀⣠⢀⠀⣠⡀⡆⣀⣀⠀⠜⢃⢠⠀⠀⠀⣿⣿⣿⢟⢻⢿⣿⡟⣿⡿⡿⢿⠿⡿⡿⢿⡿⣿⠟⢿⢹⢿⠿⣿⢦⡿⣿⣿⣿
⠀⠀⠀⣼⡋⢻⠀⡔⡅⣠⡬⡁⢼⡏⢢⢹⣿⠀⡈⣛⠀⢙⣞⡈⣻⣎⠁⠀⠀⠀⣿⣿⣿⠂⢶⠄⣿⣉⢻⠛⠓⢾⡂⣦⣝⡆⠘⣿⢷⢬⣿⡄⠣⣿⢌⠰⣼⣿⣿
⠀⠀⠀⣚⣿⣿⡄⠭⣗⢽⣬⠅⣸⣇⣿⢾⡋⢹⠁⠉⢧⢘⣨⡇⠘⣿⠀⠀⠀⠀⣿⣿⣿⠤⢈⡈⢻⡐⢸⡐⠂⣳⡁⢸⢈⡡⡆⢴⣶⣇⢹⡏⠇⢻⣧⢠⣿⣿⣿
⠀⠀⠀⠰⣁⣀⡟⢸⣇⣾⠧⣆⠸⢿⣿⢹⡀⣏⣀⡠⡾⣟⡻⣷⠀⣿⠀⠀⠀⠀⣿⣿⣿⡏⢿⠟⢸⡔⢸⠀⣏⢻⣇⠀⣰⡶⡇⠸⠿⣟⣀⡠⡄⠸⣿⠀⣿⣿⣿
⠀⠀⠀⠙⠟⠙⠁⠘⡛⠿⠈⠘⠳⠾⠐⠈⢁⠲⠒⠋⠴⠹⠁⠃⠂⠘⠃⠀⠀⠀⣿⣿⣿⣦⣤⣿⣿⣧⣤⣀⣷⣯⣽⣠⣿⣷⡧⣭⣥⣾⣳⣆⣿⣿⣿⣥⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣴⣾⣷⣤⠀⠰⠄⠀⠀⢀⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⠋⠁⠉⢻⣿⣙⣿⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠉⠀⠀⣴⣿⣿⣿⣿⣿⠂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠛⠻⣾⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠤⠂⠈⣿⣿⣿⣿⠟⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣻⣽⣷⠀⠀⠀⠀⣴⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠙⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠙⣿⡇⠀⠀⣴⠟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣸⡿⠁⠀⣼⡏⠀⠀⣀⠀⠀⠀⢠⣶⠂⠀⠀⢀⣴⠆⠀⠁⢀⣀⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠷⠶⣾⡿⠀⣠⡾⢛⣿⠂⢀⣿⡵⢫⣿⠀⣾⡧⠊⣿⠆⢻⣿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⠃⢰⡟⢀⣾⡇⢀⣾⣯⢤⣾⠏⣼⣿⢄⣼⠟⢀⣿⠃⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⣿⠀⠀⠀⢿⣄⠈⠛⠁⠙⠛⣹⡏⠙⠋⠁⢰⡿⠙⠛⠁⠀⠈⠛⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⣴⠚⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⡀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣴⡆⢀⣴⡗⠀⠀⢰⣄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁
⠀⠀⠀⠀⠀⢠⣶⠿⣿⡟⠉⠙⢦⠀⠁⢀⣤⠈⠉⠉⠛⠛⢳⣾⢿⣴⣿⣯⣤⣀⣠⣼⠟⠀⣸⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠹⠅⣰⣿⣀⣀⣤⠏⢀⣠⣌⠉⢰⣛⡆⠀⠀⣾⠏⢠⡿⢁⣬⣭⡍⢉⣡⣤⣴⡟⠀⠀⣠⣴⠦⣤⠀⢀⣴⠆⢠⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⢹⡄⢹⡿⠁⢀⣼⢛⡿⠀⣸⡏⠀⣾⡷⢋⣿⠋⣴⠟⠉⢠⡟⠀⢀⣴⡟⢁⣼⠇⠀⣾⠏⣠⣿⠃
⠀⠀⠀⠀⠀⢠⣿⣁⣀⣀⣤⠟⠁⢿⣥⠶⠋⢰⣿⣥⢾⡿⠀⢰⡟⠁⢸⣇⡤⢿⣤⡶⠻⣧⣴⠟⢿⡥⠊⣿⡤⢺⣯⠔⣿⠏
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠘⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣤⠄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣿⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⣶⢶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⢀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢿⠀⣿⠼⠀⠈⠀⠀⣀⣴⡾⠿⠻⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠇⠇⢀⡆⠀⡆⣴⡿⢋⠴⠚⠛⠳⠄⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡞⢻⠆⠀⣠⣄⠀⠀⠀⣼⠁⣸⢹⡿⠁⡀⠀⠀⣀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡜⢀⡿⠀⠀⣿⡈⡇⣠⣠⣏⣠⡏⠈⠁⢀⡇⠀⠀⠀⠀⠀⠀⢸⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣾⠛⣦⢘⡈⢙⢧⠀⣼⠉⣼⡵⡆⣠⣼⢡⢶⡄⡄⢀⣦⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢸⡿⢀⣁⠀⢸⣾⡇⡘⣸⢠⣿⠀⡟⣸⢷⣃⠿⠻⠻⠞⠷⠋⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢼⠏⠀⣾⠙⠖⠀⡧⠂⢿⡄⠀⢿⡀⠁⠀⠀⠀⢀⡤⢾⠇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠘⠳⠞⠁⠀⢰⣄⠀⢀⣀⠀⣦⠈⠁⠀⣰⢻⢠⡏⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⢸⡄⢠⡇⠘⣿⢀⢸⡟⠀⡏⣤⣰⠇⢻⡆⠀⠉⠉⠀⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠃⢸⡇⠀⣿⡾⠀⢷⠼⡇⣯⢿⡀⣨⣿⡛⠻⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⢸⡇⢀⡏⠓⢰⢻⠀⠀⠀⠀⡼⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣇⢸⠃⠀⠈⠉⢠⡀⠀⢸⠁⢀⡞⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡼⢰⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⢦⠀⢸⢎⡇⠀⠀⣀⣀⣀⣀⣀⣀⡀⣸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠁⠀⡾⢸⢠⣾⠾⣄⠀⠟⠁⠀⠀⢀⣀⡈⢹⢳⠷⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢻⢹⡞⢸⠃⢀⡼⢡⠏⠀⠉⡧⢸⡴⣻⣻⣻⢀⡿⡿⢃⣏⡏⠀⠈⠳⣤⣼⡿
⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⡞⣼⢣⣿⣰⠛⣧⠏⣀⣤⣾⠵⠋⢧⣯⣭⣷⣼⡇⢳⢸⣸⣤⢆
⠀⠀⠀⠀⢠⣯⡇⢀⠀⣰⢃⡇⠀⠉⠀⠀⢀⡴⠒⣻⣦⠀⣰⢦⠀⢰⢿⠁⢻⢸⠂⢉⣾⣿⠇
⠀⠀⠀⠀⠘⢿⡶⠋⢠⠃⡼⠀⣾⢷⠀⣰⢋⠀⡾⡟⠋⠀⡏⡾⠀⠘⢾⣤⠾⠋⠀⠀⢇⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠁⣼⡟⣸⣰⠃⣬⡅⢷⢹⡀⣸⢱⢃⣤⡀⢠⣶⢻⣦⠀⣀⡼⢧⢹⡛⠛⣟⡆
⠀⠀⠀⠀⠀⠀⠀⡼⢰⢃⡼⣹⢡⣿⠇⢰⢣⠇⠸⡆⣇⡏⣾⢿⢇⡇⡇⣷⠟⣯⣾⡏⠀⢸⣧⠇⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢧⣿⠟⠀⢻⣸⠏⠀⢺⣸⠖⠀⣇⡏⢧⡟⡞⣼⢠⠟⠚⠛⠁⢿⣇⣀⡼⠋⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠛⠓⣺⡿⣄⣀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⡏⡟
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠙⠒⠦⢤⣀⣀⡀⠀⠀⠀⠀⢀⣠⣴⡯⠚
⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⣤⡤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢼⢠⢷⢸⠽⢺⠕⢱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⡀⠀⠀⠀⠠⣄⡀⢰⣿⠋⠈⣿⣦⢸⡿⠀⣴⡟⠉⠙⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣀⣀⣀⣀⠘⠗⠀⣿⣷⠀⣤⡀⠀⢹⡷⠈⠛⠦⠤⣿⣿⠋⠀⠀⠻⠷⠀⢠⣿⡗⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠁⢠⣤⠉⠉⠐⣿⣿⠀⣿⣿⠴⠛⠁⠀⠀⢀⣠⣿⡟⠀⣠⣶⢟⣿⡆⢸⣿⡇⣰⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡤⣤⡀⠙⣃⡀⢺⣿⠁⠀⢠⣿⡟⠀⣿⣿⢀⣤⡄⠀⣴⡿⢹⣿⡇⢰⣿⡏⡸⣿⡇⣼⣿⡠⢳⣿⡏
⠀⠀⠀⠀⠀⣴⣿⠁⢸⣿⡄⡜⢠⡿⠃⠀⡻⠇⠈⠿⣦⡄⢸⣿⡇⢰⣿⣇⠃⣿⡿⢸⣿⣇⠞⣿⣧⠞⢿⠟⠁⠙⠛⠀⠉⠀⣼⡟
⠀⠀⠀⠀⠀⠘⠛⠂⢸⣿⣧⠱⣯⣁⠀⢸⣿⡇⠰⢸⣿⡇⢸⣿⡇⡜⢿⣿⠀⣿⣇⠈⠛⢋⣀⠀⠀⠀⠀⣴⡞⠉⣶⡀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠈⣿⣧⠸⣿⣇⠇⠈⢿⠧⠃⠙⠋⠀⠀⠀⠀⠘⣿⡤⠊⠈⣻⡧⠀⠀⠘⣿⡄⠲⠿⠃⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢀⣿⡏⠀⢉⡉⠀⠀⠀⠀⣠⡞⠉⣶⡀⠀⠀⣠⠎⠛⠶⠖⠛⠁⠀⠀⠀⠈⠛⠶⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣤⡾⣋⠀⠐⠏⣻⣷⠀⠀⠀⣿⡆⠰⠿⠃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠉⠒⠒⠛⠁⠀⠀⠀⠈⠛⠶⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⢀⢀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠠⠇⠘⠇⠧⠼⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣫⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣯⣿⣯⣿⣿⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⢀⠄⠂⠤⡀⢀⡀⠀⢂⠀⠀⠀⠀⢀⠠⢀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠘⠀⠀⠀⠞⡿⠥⡀⠀⠲⠀⠀⠀⠈⠛⠟⠶⣋⠀⠀⠀⠀⠀⡀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⣀⠉⢒⠠⢤⠴⠠⠀⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡗⠢⣀⠀⠀⠀⠈⠐⢾⣡⠆⠀⠀⠉⡆
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡞⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠂⠈⢧⠀⠀⠀⠈⠁⠈⠒⠢⠤⠚⠁
⠀⠀⠀⠀⡞⠀⠀⠀⠀⡸⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢦⠀⠂
⠀⠀⠀⣸⠁⠀⠀⠀⡰⠣⠀⠀⣼⠀⡀⠀⡀⠀⡀⠀⡀⢀⠀⢀⠀⡀⢀⡀⠀⠀⠀⠀⠘⡀⡑⠢⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠤⣀⢀⡀⠄⠀⠀⠀⠠⠃⠰⡁⢼⡁⣸⢃⡰⠃⡾⢀⠜⠠⠃⢸⠁⠀⠀⠀⡘⢠⢧⠈⠠⠤⣄⣀⣠⠔⠁⠁
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢰⠁⠀⠀⠀⠀⠏⠀⠀⠀⠈⠀⡼⢸⠀⠛⠀⠒
⠀⠀⢸⠀⡄⠠⠐⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⠃⠘
⠀⠀⠘⣰⠃⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡊⠀⠀⡏⠀⡀⡀
⠀⠀⢀⡏⢠⣄⠁⠀⠤⠀⠀⠀⢰⠃⢰⠃⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠹⢯⡁
⠀⢀⡜⢤⠀⠈⡃⢠⠀⢠⠐⠆⡏⠀⡿⢀⡄⢠⠄⣰⠁⡠⠀⡄⠀⡆⢠⠆⠀⠀⢀⠀⠀⢘
⠐⠊⠐⠰⠐⠊⠀⠻⠀⠋⠀⠘⠃⠐⠁⠸⠀⠻⠀⠳⠀⠃⠘⠇⠘⠂⡸⠀⠀⠀⠈⠀⠀⠈⠂⠠⠃
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣧⠄
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣒⣢⣤⣤⣤⣤⣤⣐⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠋⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⠀⠀⠀⣰⡿⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢸⣿⠁⠀⣼⠟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣃⣀⣼⡟⠀⣠⣤⣤⡀⠀⣾⢏⢤⡄⢀⣾⢋⢤⡀⣠⣶⡖⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⠋⠉⢩⣿⠁⣼⠟⢡⡿⠀⣸⡟⢁⣾⠇⣼⡟⢁⣾⠃⣸⡟⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⡇⠀⢿⠔⠹⡧⢴⡟⠿⠾⠋⣰⡟⠿⠿⠋⠀⢿⠴⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠈⠛⠀⠀⠈⠙⠂⠀⠀⠀⠀⣿⠃⠀⠀⢀⣿⠁⠀⠀⢀⡤⠴⣶⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠋⠀⠀⠀⠈⠃⠀⠀⠀⠙⠷⠟⠋⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣁⠀⠀⠀⠀⠀⣠⡄⢀⣴⡦⠀⠀⢦⡀⠀⣰⡄⠀⠀⠀⠀⠀⠑⠻⠟
⠀⠀⠀⠀⠀⣤⡶⢾⣿⠛⠛⢦⠀⠉⢉⡍⠉⠉⠛⠛⠶⣾⣿⣤⣾⣯⣀⣀⣠⣿⠇⢠⡿⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠻⢠⣿⣃⣀⣤⠞⢀⣠⡌⠁⣾⣳⠀⠀⣰⡟⢀⡿⢁⣭⣭⠍⣉⣤⣤⣾⠁⠀⢀⣴⠶⣤⠀⢠⡶⠂⣴⡆
⠀⠀⠀⠀⠀⢀⣾⠋⠉⠁⢸⡆⣸⡟⠀⣠⢞⣻⠇⣠⡿⠀⣼⡷⢋⡿⢃⣾⠋⢁⣼⠃⠀⣰⡿⢁⣼⠇⢠⣿⠁⣼⡟
⠀⠀⠀⠀⠀⣼⣏⣀⣠⣴⠟⠁⠿⠶⠚⠁⠾⣥⠾⣿⠃⠀⡟⠀⠸⠧⠜⠷⠶⠛⠻⠶⠞⠻⠷⠊⠿⠖⠻⠧⢪⡿⠁
⠀⠀⠀⠀⠀⠀⢉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠴⠶⠶⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠷⣶⣾⠿⠷⠶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠾⠷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⢁⣀⣤⣤⣤⣤⣌⡉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⠇⠀⠀⠸⣦⣀⡀⠀⣀⣁⣤⣶⡿⠟⠛⠉⠉⠀⠈⠉⠻⣷⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢻⡇⠀⢻⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⠀⢀⣀⣀⢀⣴⣿⠷⠀⠈⣿⡘⣿⡀⣿⡆⣰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠻⡄⠀⠀⢀⣠⣤⣤⣶⣄⢀⣠⣤⣦⡄⣾⣯⣙⡛⢠⣿⡟⠀⠀⠀⢸⠇⡿⠀⠟⢁⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠙⠓⠦⠀⠀⠀⣸⣿⣇⣼⣿⢃⣿⡿⠾⠛⣤⣍⣻⣿⠟⠸⠿⠛⠁⠀⢠⠟⠘⠁⠀⠐⠋⣉⣉⣉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣠⣤⠄⠀⠀⠀⢀⣿⡿⢉⣿⡿⠈⠿⠿⠟⠁⠈⠉⠉⠀⠀⠀⠀⠀⡤⠖⠉⠀⠀⠀⠒⠛⠛⠛⠛⢛⣛⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣠⠄⠀⠀⠼⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⢀⣠⣴⣦⣄⣾⣯⣙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⡿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡶⠂⢀⣠⣤⣀⢠⣿⡿⣾⣿⢇⣿⡿⠾⡛⣠⣝⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⠀⠀⡔⠁⢀⣠⣤⠀⣶⣾⡇⣰⠿⢳⣾⡷⢸⣿⣧⣽⡁⣾⣿⢡⣿⣿⠈⠿⠿⠟⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠀⢸⠀⠀⠘⣿⣿⣰⢿⣿⣿⠃⠀⣼⣿⢣⣶⣭⡿⠟⠱⠛⠛⠀⣉⣁⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠸⡄⠀⠀⣿⣿⠃⠸⡿⠃⠀⠐⠛⠋⠀⠀⠀⠀⣀⣤⣶⡾⠿⠟⠛⠛⠉⠉⠛⠛⠻⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠉⠁⣠⣤⣶⡾⠿⠿⠿⠶⠦⣤⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣠⣤⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁







⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣼⡇⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢿⣿⡄⠀⣿⡇⣴⡿⠀⠀⣠⡌⢿⣶⠋⠙⢿⣆⠀⢰⣿⡀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣷⢀⣿⣿⢟⣴⡟⢳⣿⠃⢸⣿⡆⠀⣼⣿⠀⣾⣿⠙⢻⣦⠀⠃⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣸⣿⣿⢾⣿⡇⢸⣿⡀⣺⡏⠀⢸⣿⣧⣼⣿⡟⢠⣿⡟⠀⣸⣿⡇⣰⣿⠃⡾⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢸⣿⡇⠘⠛⠛⠙⠿⠄⢸⣿⡿⠿⠋⢀⣾⣿⣃⣠⣿⡿⢠⣿⡏⢸⣇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣾⡿⠀⠘⣿⡇⠀⢀⣀⠀⠀⠀⣾⣿⠇⠀⢀⣾⣿⠏⠙⢛⣯⣄⠘⢿⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣴⠾⠛⠁⠀⠀⠉⠁⠀⣿⣿⠀⠀⣼⣿⡟⠀⠀⠘⠿⠋⠀⢠⣿⣇⠀⢀⣤⣿⠃⣠⡄⠀⠀⢰⠋⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⢿⡿⠁⢀⣶⣶⠀⢠⣶⣦⠙⠻⠿⠟⠛⠁⣰⣿⡟⠀⠀⠸⣄⠀⠘⣿⡆⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠒⠲⣄⠀⠀⣾⣿⡿⡴⠲⡄⠀⠀⠀⣾⣿⡇⢀⣿⡟⢸⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠈⠁⠀⣿⣿⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣿⠀⠀⠀⣿⣧⢸⣿⣿⠁⣇⠀⡇⠀⠀⠀⣿⣿⣀⢸⣿⡇⢸⠀⠀⠀⣤⡶⣾⣿⡿⢀⣾⡿⠋⣲⣿⠀⣿⣿⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢸⣿⠀⠀⣴⣿⡟⠈⢿⣿⡀⣸⠟⣷⡿⠃⠴⣿⡏⠉⢸⣿⣷⠃⠀⠀⣾⡟⠀⢿⣿⡇⢾⣿⡇⢠⣿⡏⠀⢿⣿⣦⣤⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢸⣿⠀⠿⠟⠻⣤⡀⠈⠙⠛⢡⣾⡏⠠⢄⡀⠙⢷⣀⣸⣿⡷⠚⢳⣆⢿⣿⣤⣼⣿⣧⠈⠻⠷⠾⣿⣧⣀⠀⠉⠉⠁⣿⣟
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣾⣿⡄⠀⠀⠀⠀⠹⣧⡀⠀⣿⣿⠀⠀⠀⣧⠀⠀⠀⢸⣿⡇⢀⣼⣿⠈⠉⠛⠉⣈⣛⣿⣚⠀⠀⠀⠉⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⡀⠻⣿⣷⣤⡴⠃⣀⠀⠀⣾⣿⢃⣾⣿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⠀⢠⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠈⠉⠉⢠⣾⡟⠀⢸⣿⠏⠘⠿⠋⠀⠀⣸⡿⠋⠉⠉⠛⠻⢿⣿⣿⣿⣷⡀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣾⠿⠃⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣶⣿⣿⣿⠟⠁⠀⠀⠀⢠⣿⣿⣃⡀⢀⡔⠀⡞⠉⠙⣧⠀⠀⠀⠘⠶⣄⡀⠀⠀⠀⠀⣀⣨⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⣩⣴⣶⣤⣀⠀⣠⣾⣿⡟⠉⠁⣾⠃⠀⠳⣤⣤⣼⣧⠶⠂⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⢸⣿⡇⠀⠀⣿⣧⡀⠀⠀⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠹⣿⣿⠀⠀⠹⢷⣄⣀⠘⠿⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢀⣿⡟⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠙⠶⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣿⠁⠀⢰⠉⣿⠀⠀⠀⣀⣤⣤⣀⠀⠀⣼⣿⡟⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⣿⠇⠀⠀⡏⣰⡟⣠⣦⣴⣿⣿⡉⢻⣿⣴⣿⣿⠃⠀⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢻⣆⣀⣸⡷⠋⢰⣿⣿⠃⠙⠛⠛⠋⢻⡟⣿⣿⠀⠀⢿⣿⣇⠀⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⢉⣿⠏⠀⠀⢸⣿⣿⡄⠀⠀⠀⢀⣼⠇⠘⠿⣷⣶⡾⢿⣿⣧⣤⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⠿⠃⠀⠀⠀⠀⢻⣿⣿⣶⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⣀⢀⣀⢀⣀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡏⣏⢾⡙⢸⢃⡾⢿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡈⠀⡀⢀⢠⠀⠀⠁⢸⠀⡴⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣸⡟⠤⡇⣼⠘⢳⡆⠀⠀⣠⣷⢀⡤⡄⣤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠉⠀⠀⠈⠀⠀⢷⠄⠘⢄⠿⠸⠀⡧⠿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠀⠈⠀⠀⢰⠋⠀⠀⠀⡄⢀⠀⠀⠀⠀⣸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢷⣄⠀⠀⢸⠀⡆⢰⢸⡇⢸⡀⠀⢠⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠓⠀⢙⡇⠀⢸⠁⠃⢺⡸⡇⢸⡀⠀⠸⠄⠱⡗
⠀⠀⠀⠀⠀⠀⢀⠠⠤⡀⢀⣀⡀⠀⢉⡞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠈⠀⢸⡇⢱⠀⡆⣆⢴⡆⠀⡴⢲⢰⣦⣶⢠⢼⡇
⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⠀⠘⡏⢈⡃⠷⠛⠘⠇⠀⠳⠘⠊⠁⠻⠓⠘⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⢰⢢⠘⠁⡏⠀⡀⠐⠁⠀⠀⢸⠇⡀⠀⠀⠆⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢠⡶⢼⠆⡴⠆⣧⣬⠷⣤⢠⡶⣤⢸⠀⣭⠀⣤⡄⣤⢠⡄⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠸⠆⠺⠄⠷⠀⠇⠜⠀⢿⡸⠄⠧⢸⡄⢿⠘⢧⠍⠛⠰⡇⠀⠆


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⣄⢀⠀⠀⠸⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠙⠁⠀⠀⠀⠀⠘⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⣀⣤⣀⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⢠⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⣿⡼⠆⢀⡟⠀⠀⢠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣙⡻⢿⣄⣾⠃⠀⠀⢸⠆⠰⡇⢘⠩⡆⢸⠉⡇⢸⠉⢳⠸⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢙⡃⠈⠻⠏⠀⠀⠀⠘⠀⠀⠃⠙⠒⠃⢸⠒⠃⢸⠒⠋⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠘⣧⣷⠀⠀⠀⢠⠶⢢⡀⠂⠀⣀⣠⡀⣆⣀⠀⢀⣀⡆⢀⣀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣆⣘⣀⣴⠀⠀⢸⡓⢺⡄⡇⢸⠁⢸⠀⡏⠈⡇⣏⠀⡇⣨⠴⡇⢹⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⣴⠀⢼⡿⠛⢉⡀⢶⠄⠈⠉⠉⠀⠁⠈⠀⠈⠁⠁⠀⠁⠈⠉⠁⠈⠉⠁⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠉⢹⠷⠆⣀⡘⠞⠃⢐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣳⣤⣤⣤⠈⢿⣓⣔⣶⣚⣧⡺⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣤⢼⡿⣭⢳⡾⠇⢿⣽⠀⢘⡛⠃⣛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣇⠐⠛⠂⢠⡿⢶⣴⠖⢼⠁⠹⠟⢧⣶⠛⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠒⢿⢳⣶⣿⠾⢀⠘⠋⣴⠘⢿⣷⣶⣷⣏⠘⠏⣥⠆
⠀⠀⠀⠀⠀⠀⠀⢠⣷⠸⠷⠏⢾⡿⢻⣤⡶⠙⢿⡟⢿⠄⣀⣿⠆⠈⠛⠑⠛⣴⣶
⠀⠀⠀⠀⠀⠀⢀⠛⢛⣷⢞⠀⢰⣆⣈⣤⠝⣷⡎⠑⢓⣰⣻⡦⠺⣿⣦⣢⣴⢯⣟
⠀⠀⠀⠀⠀⠀⣿⣃⠈⠁⠿⡶⠲⢿⠛⡿⢠⣿⠻⢿⣿⠏⣠⣾⡇⠈⣿⣵⠉⠺⠿⠆
⠀⠀⠀⠀⠀⢾⠇⠿⣷⡾⠟⠠⣦⣈⣻⡄⣬⡉⣦⠸⡏⣤⡌⢸⡿⠛⢈⣉⡘⠃⢰⣾
⠀⠀⠀⠀⣦⠐⠷⠸⠟⣀⠛⠀⣿⠛⣿⠀⣦⣼⠛⣿⠋⡤⠠⣤⣠⣾⡇⠻⣿⡿⠿⣿⡄
⠀⠀⠀⢰⡟⢷⡾⣃⡀⣿⣇⡀⢈⣟⣠⣄⢿⣯⣦⣠⣰⣿⠗⠸⠿⣉⡟⢀⡻⠇⠴⣏⣡⡄
⠀⠀⢀⡰⠆⣈⣁⡈⢽⡿⠻⣻⣿⣋⣠⢀⣿⡵⠻⢙⣿⠉⠀⣷⣤⣼⡗⠙⢥⣤⣴⣿⢀⣤
⠀⠀⣿⣿⠀⠛⠻⣁⡶⠀⣤⣛⠁⣛⠙⠀⣉⢸⣇⠘⠻⢤⠆⠛⢉⡿⠂⠛⠁⠻⠏⢙⣧⢀⡀
⠀⢠⣿⣛⣿⢦⣾⡿⠛⣶⡉⢋⣅⣹⡷⢾⡏⢸⣿⣤⣄⣶⡖⠻⠻⠇⣀⢻⣿⣤⣤⣾⡟⣈⣩⡄
⣤⣉⡋⡀⠨⣶⡟⠶⠧⢿⠻⣿⢡⣬⡤⢈⠁⠾⡗⠙⣽⡏⢀⠻⣷⢾⣿⠀⢿⣿⠉⠲⣿⡘⠋⣃
⠋⠛⠀⠙⠀⠉⠀⠛⠁⠈⠛⠀⠀⠋⠉⠈⠃⠀⠙⠋⠈⠁⠙⠀⠛⠀⠉⠀⠈⠁⠙⠁⠈⠛⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⡀⠀⠀⠋⠃⠀⠀⠈⠀⠀⠀⠘⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡔⢢⡀⠀⠀⡴⢤⠀⡴⠞⠛⠛⢻⡶⣦⣤⣠⣴⠶⣄⢀⣠⣿⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⡎⠀⢸⡇⠀⠀⢻⢼⡦⢤⣀⠀⢠⣿⠇⠀⢨⣿⠛⠛⡿⠛⠋⠁⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣸⠀⢠⡿⠁⠀⣠⠈⢱⠀⣼⣿⠀⣸⣿⠀⠀⣾⡏⢀⡜⠁⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⡇⠴⢿⡁⠀⢸⣿⢀⡞⢰⣿⡏⠀⣿⡇⠀⠀⣿⠇⢉⣄⠀⠀⣠⣤⣄⣿⡇⣀⣤⣤⣠⡆⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⠀⠀⠈⣿⣄⡼⠿⠞⠀⣾⡿⠀⡈⣿⡇⠀⡼⣿⣰⢃⣿⠆⢸⣿⢋⡼⣿⠱⣿⠋⡴⣿⡇⣿⣇⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠃⢀⣠⠤⣿⡏⠀⠀⠀⠀⢿⡇⡰⠁⠘⢧⡼⠁⠙⠋⢸⣿⠀⡎⠙⠋⠀⠻⡄⠛⠚⠀⠙⠇⠈⠛⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⢀⡿⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡼⠀⠀⣀⡤⠔⠒⢤⡀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡼⠃⣀⣿⣀⣤⣀⠀⠀⣀⠀⢀⡀⣠⣠⣄⠀⢈⡛⠁⣠⣾⠋⠀⠀⠀⢠⣿⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠠⠊⠀⠀⠉⣿⠀⢸⣿⠃⠀⣿⣀⢼⠻⣇⡿⢸⣣⢿⡃⠀⣿⡇⠀⠀⠀⠙⠛⠁⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠁⣼⠀⠈⠁⠈⠁⠈⠁⠀⠈⠳⠤⣀⡀⢀⠠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠘⠛⠒⠒⠲⠤⣠⡃⠀⠀⣀⣤⠴⠖⠒⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⢈⣷⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠁⠀⠀⢠⡾⠁⠀⠀⠉⠑⠒⠤⠤⠤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢬⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⣄⠈⠉⠀⣠⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠁⠀⠈⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⠿⣶⣤⣤⣤⣤⡄⠀⡴⠿⣛⣁⣤⣤⣄⣀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣤⡴⠶⠒⠈⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣾⠟⠁⣀⣠⣤⡶⠾⢿⣿⣿⣦⣤⣴⣶⣶⣦⣀⠀⠙⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⢠⣾⢟⡿⠒⣾⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣦⠸⣿⣿⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⠀⣾⡧⣿⠇⢠⡿⠃⣠⣿⣿⠿⢿⣿⠟⠻⣿⠂⢸⣿⡇⢻⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⡀⢸⣷⣿⠀⢸⣶⠄⠉⣉⡁⢰⠀⣿⠀⢃⣿⠀⣴⣾⡇⠀⠙⢿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⡇⠈⣿⣿⠀⢸⢡⡆⠀⣼⡀⢨⣴⡿⣆⠀⡟⢀⣿⣿⠀⠀⠀⠀⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣧⠀⣿⣿⣷⣿⣦⣤⣶⣿⣷⣌⣵⣅⣈⣼⣇⣈⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣿⣿⣿⠀⣿⣣⠘⣿⠙⣟⠀⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣿⣿⢀⡿⢰⣿⢸⣦⣿⣿⡇⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣰⣿⣿⡟⢸⣿⣮⢸⡇⢸⡏⣼⢩⡏⢽⡇⠉⡏⢆⣵⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣿⡿⠁⠀⠻⣿⣦⣡⣘⣱⣿⠸⡛⢈⣰⣸⣁⣿⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿