Driving Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠒⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⢀⡠⠄⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡞⠅⠐⠢⠤⡀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠑⠄⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠢⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⠀⡀⠠⠤⠀⢀⠢⡀⣀⠃⠸⠀⠀⠀⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠀⠠⠄⠰⠤⠤⠬⠧⠀⠀⠀⠄⠬⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡀⡀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠀⠀⢀⡃
⠀⠀⠀⠀⠀⢀⠜⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠐⠁⠔⠀⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⢄⠐
⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠩⠍⠉⡁⠀⠐⡒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣈⠉⠩⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠐
⠀⡀⠀⠈⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠀⠀⠀⠀⠈⠀⡀⠀⠀⠜⠀⠀⡀
⡎⠁⠀⠀⠀⠐⠂⠠⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠠⠄⠐⠂⠀⠀⠀⠀⠉
⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠁⠒⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠁⠁⠂⠉⠁⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠈⠀⠑⠈⠈⠀⠂
⠀⠀⠀⠀⠀⠦⠀⠢⠄⠂⢢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠠⠔⠐⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠉⠐⠢⠀⠄⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡠⠊⠠⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠⡀⢀⡈⠛⠉⡅⠀⠀⠠⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠈⠒⠂⠀⠀⠈⠀⠀⠀⠀⣀⡀⠅
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠐⣤⣤⣤⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠰⡂⢙⡦⠤⠈⠀⠀⣈⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠈⠀⠒⠂⠚⢂⠜⠁⠀⠀⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢲⠀⡎⠀⠀⠀⠀⡄⠀⠀⠀⠘⡄⠀⢀⣾⣿⠋⠘⡌⢷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣿⢸⡀⠀⠀⠀⠘⡄⠀⠀⠀⠜⠲⠿⠿⣅⠀⠀⢱⠘⡄⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⡈⠧⠀⣀⡤⠖⠦⣀⠀⣰⠀⠀⠀⠰⡟⢤⡀⠀⣇⢡⠀⠀⠘⢦
⠀⠀⠀⠀⠀⢀⡀⠤⠤⠜⠂⠒⠒⠓⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠀⠨⠪⠵⠦⠽⠦⠼⠬⠦⠤⠤⠤⣱⣀⡀
⠀⠀⠀⠀⣴⡁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⣼⣓⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⣶⣾⣇
⠀⠀⢰⡇⠰⠲⠀⠀⣀⣀⣤⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⡘⣜⣀⣀⣻
⠀⠀⣼⠁⠀⢁⣴⣿⣿⠿⠛⠿⢿⣿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⡿⠿⠻⠿⣿⣿⣦⡀⠀⠀⠣⠽⣖⣂⣸
⡆⠀⠉⢰⠀⣾⣿⢏⠔⢉⠀⢈⠑⠌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡡⠊⡡⠀⡉⠢⠹⣿⣿⠀⠀⠀⠄⠉⠁⠈
⠣⠤⠤⠜⠚⣿⣿⠈⠠⠁⠀⠀⡁⢘⢸⣿⡗⠒⠒⠒⠒⠀⠀⠀⠀⠀⢻⣿⡇⡇⠌⠀⠀⠈⠀⡁⣿⣿⠒⠒⠒⠓
⠀⠀⠀⠀⠀⢿⣿⣌⠄⡑⠐⠒⡡⢊⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡱⢌⠒⠒⢊⠔⣡⣿⡟
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣭⣥⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣬⣭⣴⣾⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡄⢀⣀⣀⣀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣡⣼⠏⠠⣀⠀⠈⡋⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡉⠁⠀⠈⠃⠠⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠤⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠈⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠃⠀⠀⡀⢀⣴⣭⠐⠀⠀⠀⡀⠀⠀⠀⣠⠔⠈⠁⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢸⣿⡄⠀⡤⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠢⡀⢀⠒⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⣴⡁⠀⠀⠀⣀⣀⠀⠀⠂⠰⢚⣃⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⢒⡀⠀⢱⡀⠑⢄⠀⠀⠈⢻⣿⠀⠀⠀⡘⠀⠉⠀⣠⠊⠀⠈⢳⣦⣤⣄⣨⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⣉⣀⡇⠀⠀⠁⠀⠀⠀⠹⡇⠠⠀⣃⣀⠤⠽⢿⣿⠂⣴⡡⢾⠟⢫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣠⠆⠀⣆⠀⠀⠀⠀⠠⡄⠀⠀⠚⠈⡶⢿⠀⠀⠀⠙⣓⡿⠟⢿⣍⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢁⠀⠰⠝⠓⠀⠀⠀⠄⠜⠁⠀⠀⠀⠇⢀⣛⠶⠞⠿⠛⠋⠀⡠⠋⠻⢦⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠆⢠⣤⠆⠀⠺⣧⡀⠁⠀⠀⠀⣀⠴⠈⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠰⠶⠤⠀⠀⢠⣄⢠⣩⠆⠀⠀⠀⠀⠉⠐⠂⠂⠉


⣶⣶⠿⣷⠶⢶⣶⡶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠒⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠗⠀⡄⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣷⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡇⢸⣇⡀⠀⣶⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢁⡀⣠⠉⠀⠀⠀⠲⢀⡰⠂⠀⠢⠄⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⣀⠁⠀⠀⠀⡀⠠⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠐⡀⠀⠀⠂⢹⠕⠻⠿⠴⢿⠹⡆⠀⠀⠀⢀⡤⠖⠒⠒⠒⠒⠐
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⡔⠪⠝⡟⣗⠬⠽⠄⠰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠚⠒⠢⠂⠁⠛⠛⠛⠚⠊⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⡤⠀⠃
⠀⠀⠀⣐⠐⠠⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠲
⠀⠀⠀⠈⠂⡆⡇⡆⠀⠀⠀⠀⢀⠐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠉
⠀⠀⠀⠀⠀⠈⠁⠣⠇⠀⠀⠀⢈⡁⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠴⢁⣤⠖⠒⠒⠒⠲⣷⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢌⠀⢀⢶⡿⠋⠠⠤⠄⠀⢀⣀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠈⠁⠀⠀⠉⠁⠰⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠐⢄⠀⠀⠒⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠈⠀⠀⠉⠱⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠐⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡀⠠⢾⣷⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⢈⠁⢄⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⠄
⡄⠀⠁⠀⠑⡄⠀⢀⠢⠄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⡠⠺⠅⡐
⡇⠢⠤⠀⠀⠈⢦⠀⠱⡄⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⡠⠃⠚⢄⠀⠀⡴⠊⠉⠓⢄⡠⠀⠀⢀⢘⠁⠃
⡇⠀⠀⠢⢄⠀⠘⠆⠀⠈⠢⡀⠀⠀⠀⠹⣿⡄⠀⠀⢀⡃⠀⠀⠀⠤⠮⠤⡄⠀⢀⠬⢛⢯⣽⠶⠚
⢠⠀⠀⠀⠠⠤⣄⠇⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⠀⡂⢨⠤⣤⠐⠒⠛⠿⣿⡉⠠⣥⡞⢹⠟⣀⣣
⠈⣧⠀⢀⡴⠀⠀⣆⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐⠃⠁⡣⠻⡀⠀⠀⠀⠈⢙⣉⡭⠛⢾⣭⡈⠉⠳⢤⡀
⠀⢸⡰⠋⠀⠀⢔⡬⠐⠤⠀⠀⠀⠠⢤⠜⠀⠀⠀⠀⢈⠇⠀⡙⢶⣤⠖⠪⠗⠕⠂⢀⢄⠝⠙⢶⣄⡀⠙
⠀⠀⡇⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⣀⣀⣴⠄⠀⠓⠋⠀⠀⠀⠀⠀⣀⠕⠁⠀⠀⠀⠈⠻⢦
⠀⠀⠰⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⠋⠀⠀⠀⠈⠪⢄⡀⡀⠠⠀⡀⠤⠊⠁
⣀⣀⣀⣈⣀⣉⣙⣒⣂⣀⣀⣒⣐⣀⣶⣶⣁⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡿⠟⠛⠛⠛⠒⠶⣦⣤⣄⣀⠈⠙⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣦⠈⢻⣿⣿⣿
⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠈⣿⣿⣿
⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⣿
⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⢻⣿⣿
⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿
⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠃⠀⠀⠂⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠀⢸⣿⣿
⣿⣿⣿⠀⠸⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠀⢸⣿⣿
⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡀
⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⢠⣿
⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠛⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡗⠂⠀⠘⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠃⠀⠃⠈⡠⠰⠀⠀⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⡀⢀⠘⠉⣰⡄⠀⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣀⠈⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⣀⠀⠀⠀⢀⡀⢳⠀⠀⠀⠒⠦⠀⣤⠀⡄⠐⡃⣠⡶⢋⣀⣤⠤⠂⠀⠀⠒⠂⠀⠉⠈⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠨⠥⠀⠁⠀⠉⠙⠉⠁⠀⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢻⢀⡀
⠈⠂⠀⠀⡘⠢⠤⠤⠤⣄⣀⣀⣀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼⡘
⠀⢠⡄⣒⡨⠭⠭⠭⠔⣒⣒⡠⠄⠩⠥⡄⠀⠂⠀⠀⠀⠒⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⣴⠃⠁
⠌⠀⠐⠂⠈⠉⠉⠉⠁⠒⠒⠒⠨⠤⠭⠥⢀⡀⠀⠀⠀⢀⣀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠂⠀⢠⡟⢻⡇⣿
⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⢧⠟
⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡈⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠠⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⠄⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⣀⠚⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⠀⠀⢰⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠂⠀⡀⠀⡌⠀⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⣀⣐⣒⣉⠀⠀⠀⠄⠴⠤⠤⠄⠹⠁⠁⠀⠀⣀⠀⠀⠚⠛⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠂⠤⠀⠆⠀⠈⠇⠀⠀⡀⠀⠀⠈⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⠉⠀⠀⠇⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠋⢻⣧
⠀⠀⠠⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠒⡉⠁⡄⠀⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠊⠀⠀⠀⠀⡀⠀⢄⡸
⠀⢠⠐⡆⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠀⠀⣠⣶⠶⣿⣿⡄⠀⠀⠉⠁⠀⠀⣀⠤⠒⠊⠁⠠
⠁⢀⠈⠙⡞⠁⢈⣩⠽⠓⠤⠴⠈⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢻⣿⣄⣀⠤⠔⠊⠉
⠀⠀⠀⠉⠛⠫⠥⢀⡀⠈⠀⠒⠤⠄⣄⢛⠀⣀⡀⠀⠀⢠⠎⠙⡆⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠐⠒⠈⠉⠓⠒⠤⢄⣀⠀⠀⢀⠒⠂⠀⣏⠈⢂⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⣶⡾⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠓⠒⠒⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠎⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⡋⠉⠉⠉⠉⠉⠉⠙⢦⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡜⠀⠀⠀⡠⠄⠒⠢⢄⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣸⠁⠀⠀⢰⢐⢄⡀⠀⠀⠃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠃⠀⠀⠰⠃⠀⢀⡓⠄⠀⢠⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⡯⣀⠀⠀⠰⢆⠀⡿⠟⣆⠄⠁⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡜⠠⢹⡵⡀⠀⣴⡆⠇⢀⠦⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠃⣀⣰⡀⠤⠤⠧⠤⠮⠤⠤⠏⢩⠥⣤⣄⠸⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠉⠁⠀⢠⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⡎⣉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡆
⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡇
⠀⠀⠀⠀⠀⡧⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⡇⠔⠄⠀⠀⠀⠀⢠⠖⢋⠩⠭⣉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⠭⠍⡙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣇⣁⣁⣀⣀⣀⣠⠃⡐⢡⠒⠒⢮⢣⠘⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠁⡜⡠⠒⠒⡌⠆⢹⣄⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠹⡀⢣⠡⣀⣀⡜⡸⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠣⣀⣀⠆⡖⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⠒⠑⠊⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠑⠒⠒⢋⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡴⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠑⢄⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣢
⠀⠀⠑⣄⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⢣
⢀⠤⠒⠉⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠁⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠒⠄⡀⠀⠀⠀⠃
⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠉⠒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡤⠤
⠒⠄⠀⠀⠀⠀⠀⠀⠀⢐⣀⠤⠤⠒⠊⠉⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⡀⠤⠐⠒⠉⠁⠀⠀⠀⠑⡄
⣀⣀⢠⡠⠤⠴⠒⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⢃⠀⠒⠂⠈
⠢⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⠉
⠰⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⢀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠖
⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠈⠁⠀⠐
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢤⠀⠀⢀⠙⡴⠢⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠐⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣶⠒⢂⠀⠀⠈⣠⡴⠂⡀⠂⠀⠀⢤⠄⠠⠀⠀⠀⠐⠀⠥⠤⠎⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⣦⢠⡀⢸⠀⢸⠀⠀⡀⠓⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⣀⠄⠰⠫⠄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣬⣭⣛⠺⡁⠀⡙⠎⠀⠄⠀⢀⡸⠠⣀⠈⠀⠀⠀⠀⡄⠀⠀⠦⠀⠊⢡⣈⠀⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠉⠀⠀⢸⠏⠙⠖⡄⠀⠀⠁⠐⠀⠀⠁⠀⠀⠀⢀⠀⠄⠰⢅⠀⠀⠀⣠⠦⠀⠀⠍⠛⡐
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠄⠘⠵⢦⠋⠀⠀⡀⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠎⠀⠀⠀⠁⠒⣦⠀⣾⢁⠃
⠀⠀⠀⠀⠀⠀⢸⡸⠀⢀⡠⠚⠁⢀⡠⢊⢴⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠋⢊⠃⠄
⠀⠀⠀⠀⠀⠀⡈⠠⣄⡠⠭⠭⠀⢐⣈⢔⣣⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢲⠂⠀⠀⠀⠀⠀⣇⠌⡐
⠀⠀⠀⠀⢀⠎⠘⢆⢤⣉⠭⢿⡯⠭⢀⣻⣹⠄⠐⠂⠀⠁⠀⠀⠀⠀⠀⡐⣱⠒⠒⠚⡆⠀⠀⠰⣿⣆⡼⣰⠃
⠀⠀⢀⠀⠧⠤⢀⣀⣁⠀⠀⠀⠉⠒⡊⢁⠟⡀⠀⠀⠀⠀⠄⠀⠀⡀⣘⠢⣸⣐⣛⣙⣃⠛⠀⡀⣛⣛⢃⠏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⢓⠂⠄⢤⡆⢀⡀⠠⠠⠐⠐⠀⠉⠁⠀⠈⠢⡈⠢⡀⠀⡏⠀⠀⣀⢧⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠢⡂⠀⠫⢄⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣯⣽⣽⣻⣿⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⠃⠙⢻⣿⣿⣿⠛⠛⠋⠉⢸⠉⠉⠉⠙⢻⣷⡉⠻⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠁⠐⣷⣶⣶⡾⠿⠷⣶⣿⣿⣿⣿⡿⠶⠶⡦⣿⣤⢦⣴⠀⠀⢹⣷⣀⢸⣏⣿⣿⣶⣄
⠀⣀⣰⣂⠈⢉⡁⠰⠶⠶⠂⠐⠶⠶⠶⠶⠖⠒⣦⢄⣀⣉⣀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠉⠉⠁⣉⡀
⢸⣎⠉⣭⠉⢹⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⡟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠔⠞⠋⠴⠋⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣝⡷⠋⠑⢾⣧⣤⠀⠀⢀⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⡄⠀⠀⢀
⠀⠃⠛⠉⠀⠀⠈⠁⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠹⠏⠧⠀⢉⠈⠀⢀⡈⣵⠺⢙⣿⣿⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⢛⣥⣿⠇⠀⠀⠈
⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣤⡼⠃⠁⢴⣿⢾⡏⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⣿⣿⣍⡋⢹⠋
⠀⠀⠀⠀⠹⣿⣿⣿⣛⣿⣟⣿⣿⠛⠉⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣧⣆⢰⣦⡨⣸⡟⠛⠛⠿⠿⠿⠿⠿⠛⠉⠉⠉⠹⣿⣿⣿⣜⣣⡟
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣤⣭⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀
⠠⡀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠠⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠑⡆⠂⠉⠀⠒⠒⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠉⠁⠀⠈⠐⠤⡀
⠐⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠤⣀
⠀⠐⡄⠀⠀⠀⠈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁
⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠑⢄⡀⠀⠀⢈⣆⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠑⢄⠘⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣠⠦⠆⠐⠐⠒⠒⠒⠒⠒⢄⡀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠁⢀⡔⠉⠉⠂⠆⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⣀⠠⠀⠘⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⣀⠔⠁⠀⠀⠀⡀⣀⠠⠤⠄⠐⠓⢤⡀⠀⢠⢞⠘⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠢⡀
⠀⠉⠉⠁⠀⠀⠀⠒⠂⠤⠔⠠⡀⢀⣣⣤⠮⠤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⢈⠟⠀⠈⠛⠁⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠎⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢰⠀⢀⡀⠠⠠⠀⠒⠂⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡠⠔⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠊⠐
⢀⠄⠀⡒⠨⠆⠒⠉⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠃
⠐⠈⠁⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠆
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠃

⠀⠀⠀⠀⠀⢀⡴⠖⣒⠲⣤⠀⠀⠀⢀⡤⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⢧⣀
⠀⠀⠀⣠⣠⡏⡴⠋⠉⢱⠈⡇⠀⠀⢯⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠂⢣⠘⡄⠙⢦⡀
⠀⠀⣘⣧⡙⠃⠣⣀⡤⠞⣰⠇⠀⠀⠘⡆⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠘⡆⢱⠀⠀⠈⢦⡀
⣠⠞⣩⠴⠦⡀⢀⠰⣖⠛⠁⠀⠀⠀⠀⢹⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⡉⠳⢄⠀⢸⡈⣇⠀⠀⠀⠙⣄
⣿⢸⠁⠀⢀⡇⣼⠳⣌⠳⣤⠴⠒⠒⠊⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡋⠓⠚⠓⠒⠓⠚⠒⠒⠒⠒⠾⠦⠤⢄⣀⡀
⠙⢮⣓⣚⣩⡼⠃⠀⢈⡿⡅⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠈⠉⠀⠀⠀⠀⣞⢐⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⠿⠮⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣓⣒⢷⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡎⡾⠽⠭⠽⣇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⠉⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠐⣌⡫⠭⠭⠭⣿
⠀⠀⠀⠀⠠⠤⠴⠧⢄⠀⢰⣿⣿⢟⡥⠒⠒⠒⠪⡙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⡥⠒⠒⠒⠨⡙⢿⣿⣷⡀⠀⠀⠀⡄⠉⠉⠉⠻
⠀⠀⠀⠀⢄⠀⠀⠀⢸⣠⣿⣿⠃⠎⢠⠊⠉⠙⢦⠘⡎⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢰⣿⣿⠃⠎⢠⠊⠉⠑⢆⠘⡌⣿⣿⣇⣀⣀⣀⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⣿⣿⡀⡆⠸⡀⠀⢀⡴⢀⠇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⡄⠰⡀⠀⢀⡜⢀⠃⣿⣿⠇⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠢⢈⣉⣉⠤⢊⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡘⠢⣈⣉⣁⠤⢋⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣶⣾⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠉⢩⡍⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣀⣈⣁⣀⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⠴⠲⡔⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣭⠉⠙⢐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠫⡝⠛⠛⢫⠋⠙⠛⢳
⠀⠀⠀⠀⠌⠨⠀⠈⠅⠀⠨⠈⠀⠠⢄⠀⠀⠀⠀⠀⠊⣀⣀⠀⠀⠀⠀⠀⣀⣀⠐⠂⡀⠀⠀⠀⢀⠈⠁⠉⠉⠁⠈⠉⠉⠉⠉⠁⢠
⠀⠀⠀⠲⣠⡶⣦⣀⣀⣀⣀⡴⡲⣄⡀⠂⠀⠀⠀⠸⠿⠋⠛⠷⠤⠤⠤⠾⠛⠙⠷⠬⠇⠀⠀⠀⠻⡴⠛⠻⣦⣤⣤⣤⡴⠛⠳⣤⡼
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠂




⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠤⠦⠄⠀⢦
⠀⠀⠀⣀⣄⣀⢀⣠⣌⠑⠀⠒⠉⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡤⠤⠤⠤⠄⠀⢘⣆
⠀⠀⣄⢀⡤⢤⡀⠀⠀⠀⠀⣠⠤⣄⠀⣠⠀⠀⠀⢠⢀⣤⣤⡀⠀⠀⠀⢁⣤⣄⠀⢱⠃⠀⠀⠀⠀⠀⣄⣠⢤⣀⣀⣀⣠⠤⣄⣩
⠀⠀⠈⠋⠄⠀⠙⠛⠛⠛⠛⠣⠀⠘⠛⠋⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣤⠤⣤⣤⡀
⠀⠀⠀⠀⠀⠰⠋⠉⠑⢼⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢎⠀⠀⡷⠀⠀⡰⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⡊⠉⠙⢱⠦⡀
⠀⠀⠀⠂⠈⡀⠉⠉⠉⠉⠀⠉⣀⠀⠀⠂⠀⠀⢸⣿⠁⢀⣀⠀⠁⠉⠈⠁⢈⣁⡀⠀⢠⠀⠀⠀⠊⣉⣤⣉⠉⠉⠉⠉⠉⣁⣭⣁⠈⢂
⠀⠀⠀⠒⠏⠈⠓⠒⠒⠒⠒⠊⠁⠙⠒⠂⠀⠀⠀⠙⠶⠋⠉⠷⠶⠶⠶⠶⠟⠉⠻⠶⠆⠀⠀⠀⠺⢟⠁⠙⠷⠤⠤⠤⠾⠋⠈⠻⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣷⣶⣶⡦⠤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠾⠶⠋⠀⠀⠀⠰⠿⠭⠽⠿⠖⠁⠀⠀⠀⠀⣀⣀⣠⡄
⠀⢀⡀⠀⢐⣯⣅⣀⠉⢉⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣶⣶⣤⣠⣤⣀⣀⣀⡀
⣚⣽⣿⣿⡿⣫⣿⣭⣻⣿⣏⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣍⣽⣿⣟⣽⣶⣍⢿⣿⣷⣶⣶⣶⠧
⠀⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣼⠿⡿⠿⠿⠛

⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢄⠀⠀⠑⠀⢀⣀⣀⣇⠀⠂⠁⠀⠀⣠⠀⠀⢠⠃⠀⠀⡴⠁⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⡠⠷⡊⠉⠉⠀⠀⣀⣈⣦⣀⣀⡀⡔⠁⠀⢀⠎⠀⢀⠞⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣏⡠⠔⠊⠁⠀⠀⠘⡤⠒⠒⠉⠁⠀⠀⠂⠀⠈⢻⠒⡤⣋⠀⣠⠋⠂
⠀⠀⠀⠀⠔⠚⣇⡇⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⡀⠀⠈⠀⠀⢜⣔⠁⢀⡽⠧⣀⡀⢀⢂⠀⢀⣀⡠
⠀⠀⠀⠀⠉⠐⠪⠄⠀⠄⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢄⢀⡴⠋⠈⣱⠮⣄⡀⠀⠈⢸⠁⠉⠄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣠⠜⠫⡀⢀⡜⠉⢣⠀⠉⠓⢦⣞⣀⣀
⠀⠀⠀⠀⣀⣤⢤⠧⠴⠦⡄⢀⣀⣰⠚⡟⠛⠋⠉⠉⠀⠀⠀⡼⠋⠀⠀⢨⡀⠀⢀⡜⠀⠀⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡏⠉⢇⠀⠀⡇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣸⠈⠑⠼⡀⠀⠀⠀⠀⢀⠢
⠀⠀⠀⠀⡀⠤⡔⢳⢊⣹⣇⣠⡼⡤⠤⢵⠴⠶⠶⠖⠚⠁⠀⠈⠠⠀⢠⠃⠀⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣱⠋⠉⠀⠳⡀⠀⢱⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠠⠌⠀⠈⠣⡀
⠀⠀⠀⠀⠀⢠⠟⠦⣀⠀⠀⢘⣤⠔⠇⠀⠀⠀⡜⠀⠉⠒⠤⣀⣠⠃⠀⠀⠀⠐⠀⠁⠀⠀⠀⡀⠘⠢
⠀⠀⠀⠀⢠⠏⠀⠀⠈⢢⡔⠁⠈⠣⡘⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠑⠢⠄⣀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠳⣤⣄⣀⡙⡇⠀⠈⡄⢀⣀⣀⣠⣃⣀⣠⣤⣤⡤⡭⠶⠤⣤⡶⠖⠒⠛⠉
⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠉⢹⠋⠉⠉⢁⠏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠉⠢⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠢⠂⠃⠂⠘⠞⠚⠘⠂⢀⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠈⠁⠈⠀⠈⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠼⠔⠀⠉⠁⠈⠀⠀⠐
⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠂⢄
⠀⢀⠄⠪⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⢸⠀⠀⠀⢀⠄⢀⡀
⠀⠈⢄⠀⠀⠀⠈⠐⠢⠤⡀⡀⠤⠐⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠘⡀⠀⠀⠀⢸⠠⠐⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⣰⡤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⡀⠀⠀⠀⠀⢀⠤⠐⠈⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⢢⡤⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠁⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠄⠀⢀⠠⠐⠈⠀⠀⠠⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠁⢙⠁⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢁⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⡏⢹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⣴⣿⣿⣿⣿⣿⠟⢋⣥⣶⣶⣿⠃⠘⣿⣶⣶⣬⡙⠻⣿⣿⣿⣿⣿⣧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣷⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⣿⣿⣿⣿⠏⣴⣿⣿⣎⠛⢿⣿⡇⣀⢀⢸⣿⡿⠛⣱⣿⣿⣦⠹⣿⣿⣿⣿⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣧⡀⣸⠃⠈⠓⠘⣇⢀⣼⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⠥⠿⠟⠛⠛⠉⣍⡁⠀⡖⣡⣌⠢⠀⡬⠉⠉⠛⠛⠻⠿⠬⣿⣿⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣿⣷⡒⣶⣤⣤⣄⣀⣉⠉⠀⢦⣛⣛⡴⠀⠓⣀⣀⣠⣤⣤⣶⢲⣾⣿⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡿⠁⢹⡄⢠⡀⢠⡏⠈⢿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⣿⣿⣿⣿⣆⢻⣿⣿⢟⣠⣶⣿⡇⠐⠁⢸⣿⣶⣄⡻⣿⣿⡟⣰⣿⣿⣿⣿⡿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⢿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⠁⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢻⣿⣿⣿⣿⣿⣦⣌⡛⠿⢿⣿⡄⢠⣿⡿⠿⢛⣡⣴⣿⣿⣿⣿⣿⡟⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣇⣸⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⢁⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠤⠤⠤⠥⠬⠤⠭⠉⠥⠭⠭⠭⠭⠭⡉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡎⠀⠀⡀⠤⠤⡀⠀⡇⡃⠀⠀⠀⠀⠀⠘⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡘⠀⠀⡰⠑⢄⠀⠈⢢⡇⡅⠀⠀⠀⠀⠀⠀⠘⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠁⠀⠐⡁⢠⣮⡄⢀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⠟⢷⣆⠀⣡⣴⠁⣩⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠎⡀⣼⣤⠔⠧⠶⠤⠴⠩⠵⠤⠤⠀⠧⠤⠤⠠⠤⠤⠤⠤⠤⠤⠼⠀⠹⡄
⠀⠀⠀⢀⡤⠴⠒⠋⠉⠀⠀⠰⣀⣀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢸⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⣯
⠀⠀⠀⢸⠴⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢸⠶⠵⠀⠀⠀⡔⡩⢒⣒⢌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡩⢒⣒⢬⠳⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠓⠒⠒⠒⠺⡁⡆⡁⢀⣇⠇⡟⠒⠓⠚⠚⠓⠛⠚⠛⠛⠛⠻⡄⡗⡁⢀⡕⡇⡟⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⡚⠓⣉⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠚⠓⣊⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠒⠀⠀⠠⠤⠤⠄⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠈⠉⠉⠉⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡊⠁⠀⢠⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⢴⠄⠠⡄⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⢀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣆⠐⡁⠀⢸⠂⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡠⠄⠰⠀⢀⡼⠇⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⢠⡄⠂⠂⣤⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⢘⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠄⠀⠀⠀⠀⢀⠀⠀⠄⢸⡄⣀⢀⠈⠉⠂⢈⡠⠀⢐⠐⣉⣀⣼⢛⣁⣠⡤⠤⠇⠀⠀⠀⠉⠁⠉⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢁⠠⠂⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠈⠀⠐⠀⠀⠈⠈⢀⡨⠤⠀⠀⠀⠀⠈⠉⠁⠀⠀⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣀⡈⠂
⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣧⡆
⠐⠄⠀⠀⠀⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡟⡟
⠀⠀⠀⢠⣒⣒⡂⠤⠬⠭⠍⢉⣛⣓⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣼⢇
⠠⠈⠃⡐⠒⠲⠤⠭⠭⢅⣐⣒⣒⡒⠒⠩⠭⠄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡈⠛⠋
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠉⠉⠉⡃⠶⠀⠠⠀⠀⢠⣶⣦⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠂
⠀⠀⢲⣶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡟⠁⢻⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⢸⠁⠀⡟⠘⠋
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣾⠣⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣹⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡛⠿⠛⡻⠿⡿⠟⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⢀⠀⢂
⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠉⠡⣄⡀⡀⠀⠀⠀⠂⢄⡰⢡⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠀⢀⣄
⡀⠀⠀⠀⡀⠀⡀⠐⠂⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠉⠀⠐⠃⠁⠀⠸⣦⣀⣀⢠⠀⠰⠿⠥⠄⠀⠀⠄⢤⣀
⠠⠐⢀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠐⠀⠀⠀⡀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀
⠀⢀⠀⠉⠀⠞⠀⠂⢀⠔⠁⠀⢀⠀⢀⡀⠉⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⢠⠀⢀⡀⠀⡐⠢⡀⠀⠈⢆⡰
⠀⠈⣥⡀⠀⢤⠀⠀⡌⠀⠀⠂⠀⢀⠀⠈⢂⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠌⠀⢀⡀⠀⠢⠘⡆⠀⠈⠃⠠⠀⠀⢀⡀
⠀⠀⢹⣿⣷⣶⣦⣠⡇⠀⠐⠀⠀⢅⠅⠀⢐⠀⠀⠙⠂⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡄⠦⠘⠀⠀⠀⠇⠼⠀⢀⠂⠙⠀⠀⠀⠃
⠀⠀⠀⠙⠿⣿⣿⣧⠀⠀⠀⠂⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠷⠀⡀⠀⠐⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡤⠖⠚⢹⡇⠉⠒⠦⣄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢷⣄⣀⠤⣾⡇⠠⢄⣀⣴⠟⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢈⠿⣿⣦⣿⡇⢠⣾⡿⢏⠀⠈⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣘⣁⣀⣈⣀⣈⣉⣻⣇⣼⣿⣷⣾⣦⣤⣼⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠹⡉⠛⢻⠛⣻⣿⠋⣿⣦⣠⡀⢠⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢈⣿⡿⠛⠀⣿⡟⠻⣿⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢟⠉⠈⠙⠀⣿⠇⠉⠈⢙⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠒⠤⠄⣿⠤⠴⠚⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲
⠀⠀⢈⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠐⠂⠀⠀⠀⢄⡈⠀⠂⠀⣀⠠⠀⢀⠄⠀⠀⡠⠜⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠤⠈⠁⠀⠀⠠⠊⠀⠀⠀⠀⠂⠀⠀⠤
⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠴⠂⠒⠂⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⢰⠂⠀⠀⠐⠠⠁
⠀⠠⢀⡈⠰⠂⠀⠘⠀⠀⠀⠀⠀⠈⠱⠃⠀⠀⠀⠀⠀⠀⠈⠵⠀⠀⠂⠀⠅⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠁⠀⠀⠀⣀⠀⠂⠐⠤
⠐⠆⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠐⢛⠃⠄⠉⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⢠⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠔⠀⠀⠴⠆⠀⣀⡀⠀⠀⠼⠄⠂
⠀⠄⣀⡉⠐⠂⠀⠯⠗⠀⡀⠀⠐⠀⠈⠈⠂⠀⠀⠀⠶⠄⢀⣑⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠈⠀⠀⠀⡀⠈⢀⠆
⠀⡀⢠⠀⠙⠁⠀⠀⠀⢀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠀⠈⠈⠀⠀⠉⠆⠂⠀⡀⠀⠀⠂
⠆⠂⢀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⡀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠂⠀⠄⠀⡀⠀⠀⠀⠀⠛⠐⠀⠈⠀⠰⠖⠒
⠀⠀⠀⠀⠀⠀⠂⣀⠠⠀⠀⠀⢠⠄⠐⠐⠂⠁⠄⣀⠀⢀⣌⠀⠀⠀⣀⠉⠐⠐⠂⠀⠀⠀⠀⠢⠀⠀⠒⠐
⣤⣤⣤⣬⣥⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣬⣭⣤⣤⣤⣤⣤⣬⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣮⣥⣤⣤⣶⣦⣴⣦
⣿⣿⣴⣭⣶⣥⣿⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⠔⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠂⢄
⠀⠀⡠⠉⡤⠠⡀⡠⠤⣄⢠⡶⢤⡦⣤⡤⣤⠤⣤⡴⣤⡦⠀⠀⣶⣦⡔⠐⡦⣴⠆⠀⡠⠤⡀⢠⠤⢄⠀⠡
⠀⢠⠀⠸⡀⢀⠕⢅⠀⡸⠲⡽⠿⠶⠶⠷⠿⢶⠟⢧⠿⠏⠆⠀⠷⠮⠧⣆⠶⣬⡷⠈⣄⢀⡜⢇⠀⡨⠀⠀⠇
⠀⢸⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⢸
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡀⢀⠀⠀⠀⠈⡄⠀⢸⠀⠸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠘⠀⢰⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⢄⣀⠀⡀⠀⠀⠀⠁⠈⠑⣾⠀⡇
⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣀⡌⠛⠻⡓⠀⠂⠀⠀⠀⣿⠀⠇
⠀⠀⠀⢸⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠐⠂⠼⢖⡚⣦⠀⠀⣿
⠀⠀⠀⢸⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⣿⢀
⠀⠀⡶⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⢻⡘
⠀⢠⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠃
⠀⡈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘
⠀⣧⠊⠁⠈⠑⡄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠊⠁⠈⠑⢄
⠀⠿⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⡘⡀
⠀⠀⠁⡢⢔⠊⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⡄⠁⡢⢔⠊⠀⡅
⠀⡇⢸⡀⠀⡅⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠸⡀⠀⡕⠀⠁
⡄⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠂
⡇
⠃⢤⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⡤
⠀⢸⠈⠒⠉⠁⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⠊⠉⠉⠁⡇
⠀⠈⡌⠒⠉⠐⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠑⠂⠁⠒⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢡⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢣⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣣⢤⣤⣤⣬⣧⣀⣀⡀
⠀⠀⠀⠀⠤⠂⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠒⢤
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⡎⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣁⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢁⣈⠑⡄⠀⠀⠀⠀⠀⠀⠀⣈⡱
⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⢣⠀⠢⠊⢠⠃⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠹⡀⠣⠜⢀⠎⠉⠉⠉⠉⠉⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠉


⣶⣶⡶⢶⣶⠶⣶⣶⣶⢶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣷⣵⣶⣶⣾⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠉⠀⠈⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠀⠀⣠⣤⣤⣤⣤⣤⡀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠋⠁⠰⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⣈⣉⡉⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⢀⡀⠤⢠⢐⡀⡆⣂⢂⣐⣐⢒⡐⠂⡀⣄⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⡀⠄⢂⣡⡴⠼⠋⠉⢀⣀⠀⠠⠤⠌⠉⣍⠹⢓⠶⠬⣓⢤⡀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡠⠢⣀⠶⠚⠓⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠉⠙⠺⣆⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡰⠎⠡⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠐⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡔⢀⡶⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠎⣿⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠂⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⡬⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⢠⠃⣀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠭⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠁⠨⢁⡫⠤⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠨⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣓⠂⠀⠀⠀⠀⠀⠄⠈⠀⠁⠀⠀⢠⠀⡨⠋⠘⢲⡌⢽⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠥⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢌⣡⡞⠫⢽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠱
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣨⡄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢀⠞⠀⠀⠀⠀⡠⠀⠐⠁⠀⠀⠀⠀⠠⢤⠄⠀⠀⢠⠃⡙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡯⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⠒⠈⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠐⡶⢯⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⢥⠀⠁⠀⠀⠀⠀⠀⠀⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠊⠾⠹⠜⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠢⡀⠀⠀⠑⠀⡀⠀⠀⠀⠀⢠⡧⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠔⢢⠶⠚⠆⡶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠲⢄⡀⠀⠀⠁⠂⠤⢀⣈⡁⠀⠀⠀⢀⣀⠠⠄⠒⠛⠉⠁⠀⠀⠀⢀⡄⢂⠁⠈⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠙⠂⢀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠡⠐⠀⡢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠈⠉⠒⠢⠠⠄⡄⡀⢀⠄⡤⡤⠤⠒⡈⠡⠀⠀⠣⠀⣠⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣄⣀⡀⠂⠀⠀⠀⠂⠠⠈⠀⢂⠈⣀⣥⠰⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡉⠈⠐⠒⠓⠒⠒⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠄⠊⠠⠂⠀⠐⢀⠄⠂⠡⠀⡠⠀⠀⠔⠀⠠⠂⠈⠄⠂⠀⠐⠀⡠⠒⢁⠔⠈⠄⠀⠔⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠩⠄⠉⠉⠉⠁⠀⠈⠀⠄⠉⠀⠀⠒⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡘⠐⡀⢰⡀⠀⠀⠀⠈⠀⢀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠁⠂⢃⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠂⠄⠁⠀⠀⠈⠀⢠⠄⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡁⠀⠀⠄⠄⠄⠀⠀⠀⠀⠀⠤⢀⠁⠀⠈⠑⢄⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⢀⠙⠢⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⡄⡆
⠀⠀⠀⠠⠒⠀⠀⠉⠉⠁⠀⠀⢀⣀⡀⢉⣉⣉⣉⣉⣉⣉⣉⣉⣁⡀⠁⠑⠒⠒⠒⠛⠲⠯⠤⢀⣀⣀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠐⠒⠒⠠⠤⢄⣀⡀⠉⠛⢄
⠀⠀⣠⠴⠒⠛⠋⠉⠉⠁⠢⡀⠀⢀⠤⠠⠤⠀⠠⠤⠤⠤⠤⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⠙⠓⠮⣧
⡇⠀⠁⠠⢀⠀⠂⠤⡀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⢈⡀⠀⣨⢁⣤⣲⣤⠤⣍⠳⣄⠈
⡆⠀⠀⠐⠀⠔⠠⠀⠉⠂⢀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡇⠑⢈⠑⢀⠡⡀⠂⢨
⠱⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠔⠁⠀⠀⠣⣀⡀⠀⠀⠀⠐⢀⠆
⠀⠈⠒⠤⠤⡤⠤⠤⠤⠤⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠠⠤⠤⠤⠐⠐⠒⠒⠒⠒⠲⠤⠤⢌⣉⣉⠉⠉⠁⢀⡜
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢉⠉
⠀⠀⠈⠀⠠⠀⠤⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⢀⣀⣀⠤⠂

⠈⢆⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠱⠀⠀⠀⠀⠀⣸⡀⠀⠀⠌⠀⠀⠀⢸⡀⠀⠀⠀⡞⠀⠀⠀⢠⠞⠁⠀⢀⠜⢶
⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢳⣀⠤⠔⠒⠒⠊⠉⠉⠈⢣⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡰⠃⠀⠀⣰⠋⠀⠀⠀⠁
⠀⠀⢀⡷⠀⠀⢀⣠⠴⢒⠁⠙⢆⠀⠀⢀⣀⣤⠤⠖⠒⠻⠉⠒⠲⠦⣏⣀⠀⠀⡴⠁⠀⢀⣼⢁⠀⠠⠎⠐
⠀⠀⢸⣠⡴⠚⠉⠀⠀⠀⠀⠀⠈⢷⡊⠉⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢸⡀⢩⠾⢄⡀⢠⡞⠀⠁⢄
⠴⠚⠹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠠⠄⣀⠀⠀⡊⠀⠂⠄⣜⣡⠋⠀⠀⡽⠻⢄⡀⠀⠀⠑⠀⠀⠀⠀⢀
⠒⠒⠦⣞⢁⠀⢀⡀⠄⠀⠀⠉⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⣠⠞⠉⠙⢦⣞⡁⠀⠀⠉⠉⠉⡏⠉⠙⢉⠉⠁
⠀⠀⠀⠈⢩⠂⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠂⢙⣦⠞⠁⠀⢀⡴⠣⡈⠙⠳⢦⣄⡀⢠⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣀⣠⡤⠖⠋⠀⠱⣄⣠⠟⠀⠀⢱⠀⠀⠀⠈⢙⡿⠶⠦⡧⣤⣄⣀
⣠⣤⠤⠴⠷⠒⠒⠲⣆⠀⣀⣀⣹⠉⢿⢉⢉⠉⠁⠀⠐⠒⢂⠀⢠⡞⠃⠠⠀⠀⢼⣅⠀⠀⢀⡞⠀⠀⢀⠁
⠀⠀⠀⠀⡆⠀⠀⠀⡏⠉⢹⡀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⡵⢏⠀⠀⠀⠀⠀⢸⠀⠑⠢⣞⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⣀⣧⠤⠴⢻⠃⠀⠀⢧⠀⡀⢘⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠑⡀⠀⠀⢀⡇⠀⠀⠈⠈⠑⢦⣠⠀⠀⠀⢠⠃
⠒⠉⠩⣅⣸⡤⠶⠻⡖⠚⠛⠛⡏⠉⠉⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠞⠀⢑⠾⢤⣀⠀⢶⣞⠳⢦⣴⠇⠂
⠀⠀⠀⡼⠀⡆⠀⠀⠘⢦⠀⠀⢱⣀⣀⣇⣀⣤⠤⣤⣀⡀⠀⠀⠀⠀⠠⢠⡍⠠⢤⣉⠀⠠⠈⢹⠾⢄⠙⠦⠙⢦⠨
⠉⠉⣹⠛⠶⣄⠀⠀⠀⠀⣳⡤⠔⢇⠀⠀⠀⠀⢰⠃⠀⠉⠑⠢⢄⣀⢀⠎⠀⠀⡀⠀⢀⠂⠀⠁⠀⠀⠐⠄⡀⠀⠑
⠀⣰⠃⠀⠀⠈⠳⣄⡠⠚⠁⠙⢄⠸⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢈⠟⠒⠤⣄⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⣰⠇⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⠣⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠉⠛⠢⢤⡀⠀⠀⠀⢀⣀⣀⣤⣤
⣏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠦⢤⣽⣀⣀⣀⣧⣤⣤⡤⠤⢤⡾⠴⠶⠶⠶⠒⠺⡖⠛⠛⠛⠛⠻⢭⡉⠉
⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠰⠇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠑⠦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⡤⠀⠄⠀⠈⠛⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⠿⠷⢶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⠖⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡴⠄⣀⣠⠤⠖⠋
⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠋
⠀⣼⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡞
⢠⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⡶⢶⣺⣷⣦⣤⣀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⢹⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣀⡙⠛⠻⢿⣿⣿⣿⣷⣦⡀
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣨⣿⣿⣿⣿⡿⠟
⣿⠁⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣅⣀⡀⠀⠶⣿⣿⡿⠿⢛⡉⣾⡄⢠⡄
⠀⠘⢰⡎⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠉⠉⠉⠉⠙⣏⢭⣍⢤⣶⡔⣾⣿⣹⠧⣛⣵⣿⡇
⠀⠈⠐⠈⠀⣰⣦⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣼⣆⣙⣃⣙⣛⣬⣽⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠴⠿⠟⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠦⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣷⡌⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠓⠋⠉⢠⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣍⠘⠀⠀⠘⠿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠊⠉⠉⠉⠉⠉⠉⠉⠐⠒⠢⠄⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⡀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣈⠳⡄⠀⠀⠄
⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⡉⠂⣰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠐⡀⠀⠀⠀⡄⢸⡀⢹⡀
⠀⠀⠁⠀⠀⠀⠈⠀⢄⡀⠀⠀⠁⢰⡏⠀⠀⠀⠀⠀⡄⠀⠤⠆⡰⠑⠋⢽⠟⠀⠒⡇⠂⠀⠄⢀⢀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢻⠀⡀⠤⠖⠚⠉⠑⣰⣤⢠⣤⣌⣄⠊⠀⠀⢸⡇⠀⠀⠀⡀⠜⠃⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠰⢾⣥⡟⠘⠈⢿⣿⣿⣆⢢⡼⠃⠐⠈⠩⠀⠀⠀⡀⠄⣇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠶⠿⠿⠿⠇⠐⠈⠀⠀⠀⡠⠂⠁⠀⣀⣀⠈⠻⡁
⠀⠀⣠⠔⠊⠉⠁⡸⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⢄⠀⢻⡄⢱⢀
⠀⡜⠁⢠⠈⢢⢀⠁⠀⢾⣟⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⡕⠁⡄⢸⠓⠬⣄
⢸⠀⠀⠈⠚⠿⠼⠀⢨⠭⡗⠒⠀⠀⡠⠒⠉⠁⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⣰⡁⠸⣀⡴⢁⡇⠀⠄⠈
⡀⠟⠀⢀⠿⡄⠀⠀⣺⡟⢆⢰⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣀⠤⠐⠊⣁⠤⠒⠉⠈⢧⣀⣀⡤⠞
⠈⠒⢤⣘⠲⠇⡀⠀⠐⡊⠁⣨⠦⡀⠀⠀⣠⠴⠋⠉⠙⡲⡀⠀⠂⠀⢀⣀⠄⠒⢉⠠⠀⠀⠀⠀⠀⠉⠁
⠀⠣⡀⠈⢙⣶⠤⣌⣘⠓⠈⠀⠀⠝⠙⠋⠡⠂⠀⢱⠀⡇⠸⠤⠤⠒⠉⠀⠀⠀⠁⠀⠄⠁
⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠓⠲⠦⡤⠔⠀⡃⡆⢀⡜⢠⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠑⠼⠋⣠⡟⠀⠀⠠⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠄⠐⠒⠒⠀⠀⠉⠉⠈⠀⠉⡀⠀⠐⠒⠒⠂⠤⠄⠀⢀
⠀⠀⠀⣀⠤⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡂⠅⠀⠀⠈⠉⡀⠀⢉⡍⠁⣶⠪⢐⠢⡀
⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠩⠎⠐⠒⠚⣹⣀⡈⠔⠛⡀⠀⢀⠧
⡌⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡲⠤⠞⠛⠞⠃⢙⣋⢻⠋⠉⠙⢳⠜⡀
⠁⠂⠄⠀⠒⢲⡀⡈⠉⠀⠙⣸⠁⠀⠈⠁⠁⠂⠀⠀⠈⢪⡁⢧⠆⠀⠀⠀⢸⣀⡀⢘⠒⡀⠀⠀⠀⠇⡃⠐⠒⠳⢠
⠀⡄⡀⠀⠀⠀⠇⠁⠀⠀⠀⡇⡀⠀⠀⠘⠘⠂⠀⠀⠐⣽⠞⠈⡼⡀⠀⠀⠰⣙⠀⢀⠀⠀⠀⠑⠀⢸⠀⠀⠀⠊⠉⠉⡅
⠀⠇⢠⠀⠀⠀⢰⢠⠀⠀⠀⢠⠀⠀⠀⠀⢁⡈⠀⠔⠚⠉⢃⠀⢰⢣⠀⠀⠀⢰⠚⢠⠈⠁⠀⠁⠀⠈⡜⠀⢠
⠀⠀⠀⠄⠀⠀⠀⡄⡄⠀⠀⠈⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠘⡆⠀⢡⠘⢄⢰⡀⠀⠀⠀⠀⠀⡇⡆⢨
⠀⠀⠀⠐⠀⠀⠠⠂⠃⠀⠀⠠⠃⠄⠀⠀⠀⠇⣇⠐⠀⠀⠀⠀⠀⠘⠱⠀⠀⠀⠀⠉⢁⣤⡀⢀⠄⡀⢱⡀⠘⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠆⠀⠀⢠⠀⡀⠢⣧⠼⠐⠒⠑⠚⠚⠉⠉⠈⠉⠛⠨⢑⠪⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠉⢻⠇⡊⠁⠀⠀⠀⠀⠁⠒⠠⠀⢀⠀⠀⠀⠀⠀⠀⠈⠒⢍⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠈⢢⠈⢢⣀
⠀⠀⡒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣌⠂⠐⠒⠀⠁⠁⠀⣀⡏⠈
⠀⠀⢡⠀⢀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡆⣄⣲⣒⡩⢥⣒⠍⢳⣤
⠀⠀⠀⠀⠉⠄⢘⢋⡙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠼⠁⣷⠿⠓⠋⠝⠒⠉⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠄⣴⠁⠐⠀⠀⠀⠤⠀⡀⠀⠀⠠⢀⣀⠀⠀⠃⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⣀⣰⢀⣁⣠⣤⣴⠶⠾⠛⣛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠩⠉⠁⡀⠀⠘⡿⢋⡙⠿⠛⠐⢲⣶⠿⠿⠛⢛⣉⣥⣴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠸⡄⢀⣼⠢⢇⣤⡴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠀⠀⠀⠉⠅⢨⠄⠀⠀⠠⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⣵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⡀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐
⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⢀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠸⠿⠿⣇⡀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣷⡞⠉⠉⢹⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠛⠿⣧⣤⣤⣼⠻⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠶⠶⠀⠀⠀⠀⠘⠛⠛⠻⠀⠀⠀⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⢈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠄⠀⢀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠂⠀⠀⡠⠈⠀⠄⠀⣐⣀⣀⡀⠀⠀⠀⠀⠀⠔⠁⡠⠂⢁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣠⣿⣿⣿⣿⠋⠀⠀⠀⠀⠘⠀⠠⠊⠀⠂⣤⣤⣀⣀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠛⣛⣛⣛⣯⣭⣭⣭⣛⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣵⣶⠾⠿⡷⡀⢿⠿⣿⡿⠛⠉⠉⠀⠀⠀⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠌⠁⡸⠀⠀⣀⣇⠳⡸⣀⣿⣥⣤⣤⢀⣒⣒⣲⣶⠦⠼⠦⠶⢦⣤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠾⠶⠶⠿⠿⠿⠛⠛⠳⢷⠻⠿⠿⠛⠻⢿⣛⠶⠖⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢯⣗⠂⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠊⠑⡒⠒⠒⠒⠖⠀⠤⠠⠤⠠⡦⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢠⢻⡲⡦⣼⣗⢈
⠀⠀⠀⠀⠀⠀⠐⠀⣾⡟⣳⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⣀⣭⣛⡪⠁⠒⠒⠀⠀⢀⣜⡙⠦⢀⠀⠀⠚⠛⠉⠁⠠⠘⣋⣥⠈⠻⠋
⠀⠀⠀⠀⣀⣴⣿⣳⣿⣾⡉⡆⠀⢢⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣎⢂⠀⠀⢰⣾⣶⣤⡆⠀⣤⣴⣶⣿⣿⣿⡆⣸⣻⣷⢶⠇
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⠦⢤⣄⣀⡀⠀⡄⠀⠀⠀⣿⣿⣾⠟⣿⣿⣿⣆⢃⠀⠈⠓⠒⠋⢰⣾⣿⣿⣿⣿⣿⠃⠁⠿⠟⣻⡌⠀⡂
⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣻⣿⣿⣿⣿⣶⣮⣭⣙⣛⠒⠠⢄⣿⣿⡏⢀⠀⣿⣿⢿⡄⢰⣤⣤⡆⠠⣛⣿⠿⠿⠏⣽⠅⠀⠀⠀⠀⢻⣄⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠈⠀⣿⣿⣿⣧⣠⣍⣁⡀⣀⠀⠀⠄⠀⠀⣿⠩⣠⣴⣶⣿⣿⣿⣿⣟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣿⣿⣓⣦⣴⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⢀⣘⢦⡀⠀⠀⠀⠄⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⣀⠞⢁⡈⢳⠩⠔⠒⣈⠁⢉⣀⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⢀⠴⡕⡬⢌⣻⠀⠿⣃⠾⠔⢂⡡⠔⠒⠒⠎⠀⣀⣀⠉⢷
⠀⠀⠀⠀⠀⡆⠀⡇⡇⠀⠉⢳⣨⠤⠒⠛⠛⠒⠒⠒⠲⢤⣠⢄⡀⠑⠁⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⡧⢜⡽⠁⣀⣠⡎⡸⠀⠀⠀⠈⣷⡄⠀⠀⠀⠈⠳⣌⠲⡤⠤⠤⠒⠋⠁⠀⠀⢹⢦
⠀⠀⠀⠀⠀⠉⠉⠈⢉⠙⡿⢠⡇⠀⢀⣠⣞⣎⠇⠀⠀⠀⠀⠀⣈⡳⢌⡑⠤⠤⣀⣠⠤⠔⠋⢈⡇
⠀⠀⠀⣀⠤⠤⠤⠤⠾⢦⠇⣼⢫⡻⣛⠒⠒⡲⠶⠶⣋⡉⠉⠉⠉⡲⠈⠙⠲⠤⣀⣀⣀⡤⠶⣋⡀
⢠⠖⠉⠀⠀⡠⡴⡶⠒⡏⢰⠷⣄⡑⠜⢧⠸⡄⠊⠛⡄⠈⠙⡕⣶⠁⠀⢀⠤⡚⠍⠒⠀⠉⠑⠒⢌⡑⢆⠀⣀⣀⡀
⠣⣤⣀⠤⠜⠏⠌⠀⣼⢁⡇⠀⠜⢳⡄⢦⡑⡵⢕⣒⣁⡤⠔⢱⠓⠒⢲⠃⠊⢀⣀⣀⡤⠤⠴⠒⠒⠋⠉⠉⠁⣷⢸
⠀⡇⠀⠀⢸⠐⡀⠀⢧⣼⠀⠀⠀⢸⣿⠰⠙⢌⠢⡀⡀⢀⣤⠯⠤⠒⢛⣉⣉⣉⣀⠤⠤⠤⠤⠔⠒⠒⠒⠚⠋⢹⣯
⠀⡇⠀⠀⠀⢆⢣⠀⠀⠀⠀⢀⢀⢼⢿⠜⠀⠀⠑⠪⠀⠀⠀⠀⠭⠭⢥⠤⡤⠤⠤⠤⠤⠤⠤⠴⠖⢲⠒⡶⠒⠚⠛
⠀⠘⢄⠀⠀⠈⠣⢕⣰⠦⢤⣖⠵⡫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⡀⠀⠀⠀⠀⢀⡴⠃⡰⠃
⠀⠀⠀⠑⠢⠤⣀⣀⣈⣉⠩⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢭⣀⣒⣀⣈⠥⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠃⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠐⢠⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠀⠀⠚⠛⢿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⡐⠒⠂⠀⠀⠀⠤⠀⣄⣘⠇⠀⠀⠀⠀⠀⠸⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⢠⠀⠆⠀⠘⡄⠀⢀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠈⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⣿⡄
⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠉⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠐⠀⠄⠀⠀⣀⣀⣤⣄⠀⠀⠠⠔⠂⠀⠀⢀⡀⠄⠂⠀⠲⠃
⠀⠙⠘⢤⠖⠹⢒⣦⣄⠀⡀⠄⠀⠀⠀⠀⠀⠀⠼⠋⠉⠻⣿⣆⠀⠀⣀⠤⠒⠊⠁
⠀⠀⠐⠺⠶⢒⡉⠀⠀⠠⠀⣀⡀⠾⠀⠀⠀⠀⢀⡔⠲⡀⠙⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠀⡀⠀⠀⠠⠂⠂⢸⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⢶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡥⣤⡤⣤⣤⣤⣤⠴⢾⡄⠈⠂⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠓⠋⠳⠿⠛⣄⠀⣀⣰⠇⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠉⠁⢉⠆⣀⡈⠀⠀⠀⠈⠑⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠘⡀⠀⠈⠀⢈⣀⠀⠀⠀⠀⠀⠌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣊⢀⡀⡼⢷⣀⡀⠀⠈⣃⠀⠒⡀⠴⢆⠂⣀⣀⣀
⠀⢀⣠⣀⠤⣄⠀⠁⠀⠀⠀⠀⠀⠈⠙⠻⣇⠟⣗⠈⠲⠀⠄⠀⠀⠀⠀⠈⣇⣀⠀⠈⢳⡄
⢠⡟⢸⠀⡍⢂⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣸⡌⠀⠃⢀⠀⠀⠀⠀⠀⢸⠠⠘⠀⠀⡇⠀⠀⠀⠀⡀
⡌⣿⣿⢤⣧⡜⡆⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⣤⢄⠈⠀⠈⠀⡀⠀⠸⢀⠈⠁⢀⡗⢰⢦⣠⡶⡍⠕⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠠⡀⢀⠔⠉⢰⡀
⡧⣯⡿⢾⣻⡇⠆⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢶⡂⠬⠅⠀⠀⠀⠀⠐⠄⡀⢀⠞⠁⢸⣛⡦⣟⣳⠐⠀⠱⡴⠒⠊⠁⠀⠠⠠⠀⠤⢤⠰⡣⠤⠤⢀
⠘⣦⣅⠸⢉⡁⡃⢸⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⢀⣠⠴⠒⠁⠀⠀⣑⣍⣁⠈⠅⠀⠀⠀⣳⠤⢤⣄⡄⠉⠉⠉⡃⢀⣀⡼⠀⡏⠈
⠀⣿⣿⣿⣶⣄⡇⢨⣼⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⣀⣀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⠒⠒⠒
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠻⣚⠻⢿⣿⣶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣴⣿⣿⡗⢞⡛⠻⣿⣿⡀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠓⣋⠑⡌⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣟⢚⡉⢱⢹⣿⣧
⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣧⡀⠉⠄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣆⠈⠡⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣤⣾⣿⠇
⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣦⣽⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣧⣂⣮⣥⣭⣭⣭⣌⣥⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣒⡥⢵⠀⠄⠒⠒⠒⠚⠛⠛⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡭⡤⠄⢸⡈⡀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣀⣈⣳⣀
⠀⠀⠀⠀⣠⣀⡐⠛⠻⠿⠤⠶⠶⠶⠃⠻⠿⠛⡛⠛⠉⠉⠉⠁⠀⠀⠀⠈⠉⠁⠒⣒⠲⠶⢤⣤⣤⣤⣄⣤⠤⠄⢀⣀⡀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣤⣬⣐⣚⣲⣶⣄⠈⠙⠲⠞⠛⠛⠛⠉⠛⠿⣷⣶⡞⠱
⠀⠀⠀⢫⣿⢡⢹⢛⣛⣫⣭⣽⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢡⠀⠀⠀⣀⣀⣀⣤⣤⣤⣬⢻⣄⡜
⠀⠀⠀⠀⢻⣧⠛⡿⢿⢿⣿⣿⣿⡿⣿⠿⠿⢿⣯⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣀⣠⣿⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠆
⠀⠀⠀⠀⠀⢯⣋⣿⠦⢤⣀⡀⠂⠴⠟⠀⠀⠀⠘⣿⣿⠃⣺⣫⣵⣆⢻⣿⣿⣿⡟⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡃⣝⡋⣱
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⢹⣿⠀⣿⠀⠈⣿⣼⠂⠉⠻⠿⠿⠿⢓⣻⣯⢰⠬⠉⢉⣀⡲⠧⠝⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⢿⡀⠻⡄⢀⢟⠃⣶⣤⠤⠤⠤⠥⠴⠒⠲⠬⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⠵⢋⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⡀⠀⠀⠀⡎⠀⠈⠦⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠁⠀⣠⣤⣤⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀
⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⢈⡀⠀⠀⢀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠟⠀⠀⠻⠟⠀⠙⠂⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢐⣂⠀⠀⠂
⠀⠀⠀⠀⢈⣈⣉⣉⣉⣉⣉⣉⣁⣀⣀⣈⣉⣉⣉⣉⣀⣩⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣏⣁⣀⣀⠀⠀⠀⠀⠈⠉⠉⠉⣁⣐⡒⠂⠀⣤⠜⠀⠄
⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠐⠆⠀⠠⠾
⠀⠀⠀⠈⠀⢀⡠⠄⠒⠐⠒⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠤⠀⠒⠚⠓⡺⠂⢄⠀⠀⠀⠀⠐⠶
⢀⠀⠀⢀⠔⠁⠀⡀⠄⠀⠀⠠⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⠈⠀⢀⠀⠀⠀⠐⠧⠀⠀⠁⢆⠀⠀⠐⠐⠆
⠀⠁⢀⠂⠀⠀⡁⠄⠂⠀⠈⠀⠂⢄⠀⠀⠀⠑⠤⠤⠄⠶⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡧⠤⢠⠊⠀⠠⠂⡠⠐⠀⠀⠀⠐⠠⠈⠢⠀⢳⠍⠀⠨⠇
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡊⠀⠀⠀⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠡⢀⢀⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⡀⣀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠊
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⡉⠉⠉⠉⠉⠁⠀⠐⠒⠒⠢⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢆⠕⠐⢀⣀⡠⡄⢴⢲⠰⡤⡤⢤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⠁⢀⡠⡒⣉⣦⡷⠾⠾⠟⣓⣓⣛⠺⠞⢲⡿⢇⣲⣠⡄⣀⠀⠀⠀⠀⠈⡒⢤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⢆⣩⡶⠛⠋⣁⢥⡞⢁⣨⠿⠽⠯⠯⠭⠭⣽⣟⣗⡾⢟⣿⢭⣗⡦⣀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡴⠁⠀⣠⢎⡱⠞⢃⡤⢾⣯⠟⠚⠉⡁⠐⣶⣹⠀⠀⠀⠀⠞⣯⣝⠙⠲⠤⣽⡷⣿⣻⢷⣤⡀⠀⠕⡈⢦⡀
⠀⠀⠀⠞⠀⢀⡴⣩⡾⠁⡰⢋⡴⠊⠀⠀⠈⠀⠀⠀⠛⠛⠀⠀⢀⣾⢄⡗⠈⠀⠂⡠⠀⠉⠛⢾⡹⠫⡟⢦⣈⢔⡤⠙⣦⡀
⠀⠀⠌⠀⢀⠾⣵⠃⢀⡾⡷⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢯⠴⢸⣓⠀⠀⠀⠀⠀⠀⠠⠄⠉⠢⡈⢢⡛⡬⢊⠕⡈⢷⢄
⠀⡜⠀⠀⡼⣹⡛⢠⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠃⣂⡣⣼⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⣜⡄⡪⢒⠈⣟⣆
⢠⠁⠀⢰⠳⡏⢠⢃⡞⠀⠁⠀⠀⢀⠀⢀⠤⠂⠀⠀⠀⣾⢃⠾⠩⠁⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠹⣮⢻⡔⠥⡢⠸⠬⣇
⠨⠀⠀⡧⣹⠂⣾⡿⠀⠀⠀⠀⠐⠩⠒⠁⠀⠀⠀⠀⣰⢡⡶⣚⢭⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡘⡆⢣⠪⢐⡀⡗⢼⡀
⡆⠀⢠⣳⡇⢰⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣲⣹⢡⡤⢙⣯⢸⣿⠀⠀⠤⢤⣤⣤⣤⡄⠀⠀⠀⠈⡟⠋⠇⢸⣿⢐⡥⢂⢸⠳⡇
⡇⠀⠸⣽⠅⢈⣸⠀⡁⠀⠀⠀⠀⠀⠀⢀⣀⠤⢛⡇⠘⠷⠶⠿⠛⣾⢶⣶⡲⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡧⣊⠅⢸⣝⡇
⡇⠀⠀⣿⠅⣻⣿⠀⢆⣀⠀⠀⠠⠶⠾⠿⠾⠿⢿⠀⠀⢀⡴⢀⡾⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⡆⢕⠭⠸⢬⡇
⢡⠀⠀⢿⡀⡸⢿⠀⣻⡿⠄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⣾⡏⡟⠛⠿⣦⣄⠀⠀⠀⠀⣀⢀⠔⠂⠀⠀⠀⠄⢀⣦⢁⠅⡊⡟⢾
⢸⠀⠀⠘⣆⢸⠈⡆⠩⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⣠⡟⢻⣧⢁⠀⠀⠀⠈⠀⢀⠤⠊⠖⠁⠀⠀⠀⠀⠠⠁⣸⡟⢴⡪⣰⡙⡎
⠀⣧⠀⠀⠘⣌⣧⣴⡈⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⡓⠀⠀⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⢋⠗⡩⢰⢇⢹⠁
⠀⠘⣧⠀⠀⠘⢾⣯⣷⣄⠠⠀⡀⠀⠀⠀⠀⡟⠀⣴⡓⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠒⣰⣧⢞⣯⢶⠷⣌⡇
⠀⠀⠡⡱⣄⠀⠀⠙⢷⣎⡳⣄⠐⠠⠀⠀⢀⠇⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⢀⣘⣛⠛⣋⢠⡟⢦⡟
⠀⠀⠀⠹⣜⠣⡀⠀⠀⠙⠻⣿⣗⢦⡈⠀⢼⡞⡌⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⢀⡴⢋⢜⡥⡋⣠⠣⣘⠎
⠀⠀⠀⠀⠈⠣⣍⢳⢄⠀⠀⠀⠉⠳⢌⣓⣬⣐⡈⠀⠐⠀⠠⠀⠤⠀⠀⢻⣥⠀⠂⠘⠀⢀⣠⢴⣻⣶⢗⡵⠊⣴⠙⣦⠏
⠀⠀⠀⠀⠀⠀⠈⠺⣌⡝⠦⣄⠀⠄⢀⡈⡉⠓⠻⠿⢶⣒⡒⠂⢤⣤⣤⣤⣤⠰⢒⣒⡩⠿⢚⠟⡫⣶⠕⣫⠚⣌⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣸⡹⠲⡮⣌⣐⡡⠢⠔⡤⣂⠄⡩⢍⡩⢉⠍⣉⠍⣠⢔⡠⣺⠕⢉⡪⡔⢫⠈⡧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⢥⣸⡉⡏⠖⢲⠠⠬⡤⣭⢤⢥⡈⣵⢯⠤⡥⢾⠓⡉⢏⢣⡸⠖⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠚⠂⠦⠵⢼⣌⣆⣣⣘⣄⣧⡴⠼⠖⠛⠉⠁
⠀⠀⠐⠭⢪⢕⡩⢒⡩⢐⡡⢔⡢⢒⠤⢂⠤⣢⠔⡠⢒⠔⣠⠔⡠⢀⠤⢀⠤⢀⠄⣀⠔⣂⠔⣠⠔⡠⢂⠔⡢⢒⠔⡪⣪⢔⡡⣪⢞⠔⡠

⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⠻⣿⡜⣿⣿⣧⠸⣿⣿⣿⣏⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣿⣿⡸⣿⣿⡄⢿⣿⣿⣿⡌⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣷⣇⢻⣿⣷⠘⣿⣿⣿⣷⠘⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢹⣿⡌⣿⣿⡆⢻⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⣿⣧⠸⣿⣷⠘⣿⣿⣿⣧⢻⣿
⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⢸⣿⡆⢿⣿⡆⢻⣿⣿⣿⢸⣿
⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡌⣿⣿⢸⣿⣧⠸⣿⣿⣿⠘⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣖⣲⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⢹⣿⡆⣿⣿⠀⣿⣿⣿⡇⣿
⠹⣿⡿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⠻⠿⠆⠀⠀⠀⢿⣿⣿⣿⣿⠸⣿⡇⢿⣿⡇⢻⣿⣿⡇⢸
⡆⢻⣷⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠉⣿⣟⣿⠀⣿⣿⢸⣻⣧⢸⣿⣿⣷⢸
⣿⡜⣿⣧⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⣿⣿⡀⠀⣷⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣦⣶⣦⣿⣿⣿⡇⣿⣿⠘⣿⣿⡘⣿⣿⣿⡀
⣿⣷⡸⣿⣏⢿⡿⣿⣿⡷⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⢛⣧⣼⣿⡋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠙⠋⠿⠇⢿⣿⠀⣿⣿⡇⣿⣿⣿⡇
⣿⣿⣧⠹⣿⡎⢿⡹⣿⣶⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⢿⣿⣿⣿⠛⠻⠿⠂⠉⠉⠙⠛⠋⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠙⠻⠿⠇
⣿⣿⣿⣆⠹⣿⡌⣷⠹⣾⣇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣼⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁
⣿⣿⣿⣿⡄⢻⣷⡘⣧⠹⣿⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⣿⣿⣿⣿⣷⡀⢻⣷⠘⡇⠹⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠈
⣿⣿⣿⣿⣿⣧⠀⢿⣧⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣋⣉⣩⡍⢩⣭⣉⣓⠒⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣩⠴⠚⠋⠉⠀⠀⣧⢸⡄⠀⠈⠉⠓⠦⢬⡙⠲⢤⣀
⠀⠀⠀⠀⠀⢀⣀⡴⠚⠉⠐⠛⠒⠒⠲⠒⠒⠒⠒⠛⠘⠷⠶⠶⠶⠶⠶⠶⠾⠷⠆⠈⠙⠒⠒⠲⠶⠤⠤⣄⣀⡀
⢀⡴⠒⠒⠛⠉⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠉⠓⠦⡀
⣾⠀⠀⠀⠀⠀⠀⢠⣾⠕⣛⣭⣟⡺⣕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⡽⣚⣯⣝⡛⢷⣦⠀⠀⠀⢹
⠹⣀⠀⠀⠀⠀⢀⣿⢣⠎⠀⠀⠀⠹⡜⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⡞⠁⠀⠀⠘⣆⢿⡇⠀⠀⢸
⠀⠈⠉⠙⠓⠒⠾⠻⡜⣆⠀⠀⠀⢠⢇⡿⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⡏⣇⢧⠀⠀⠀⢀⡟⡼⠿⠤⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣓⣒⣚⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣝⣒⣒⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢡⡗⠀⠀⠉⠓⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠰⠋⠀⠀⠀⠀⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢋⣀⣤⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⠁⠀⠀⠀⠀⣀⣠⠤⠴⠒⠈⠈⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡤⠀⡤⠶⠶⠶⠀⠀⢐⠟⠉⢻⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠹⠂⠀⠀⠶⠖⠀⠉⠀⡀⢚⠁⠸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⢙⡆⠀⠀⠀⠈⠀⠀⠀⠀⢡⠀⡀⠰⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠁⠀⠀⢀⠠⠞⠁⢀⡀⣀⣀⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡿⡀⠀⠣⠘⠋⠥⠶⠶⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⢄⠀⠀⠀⠀⠒⠚⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣞⠢⡀⠈⠒⠤⣀⣀⣠⠤⣿⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢁⠀⢻⣆⠨⠲⢄⡀⠀⠀⣠⣞⡁⢽⣎⠳⡖⠒⠦⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢡⠃⠸⠀⠀⢻⣇⡌⣀⣛⣅⣤⢰⣧⣦⣼⡿⡆⠁⠀⠁⡢⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⡠⢠⡏⠀⠀⠀⠀⠀⢿⣿⠋⠁⠀⠀⠀⠀⠙⠂⣰⣧⣀⣀⣜⣁⣀⡀⠀⠀⠰⠐⠄
⠀⠀⠀⠀⢄⠀⠀⠀⠀⢰⠃⠀⠙⠒⠀⣀⡀⠀⠈⢼⣆⡀⠤⠐⠊⠉⠀⣀⠀⣀⡀⣀⡀⠀⠀⠀⠉⠉⠒⠠⢀
⠀⠀⠀⠀⠀⠑⠄⠀⠀⠈⠀⢀⡠⠖⠋⠁⠀⠀⠈⠻⡅⠀⣀⠄⠔⠠⡏⡅⢠⣽⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⡀⠈⠲⡖⠒
⠀⠀⣀⣀⣀⠠⠤⠔⣂⠖⠁⠀⠀⠀⠀⠀⠀⠈⢲⡀⢸⢁⡄⣂⠀⢀⡶⠓⠚⣿⠒⠒⠒⠢⠤⣄⡀⠀⢠⡞⠉⣲⠊⠀⣀⠈⠳
⠛⠉⠁⠀⠀⠀⠀⡜⡏⠀⡆⠀⠀⠀⢀⡀⠙⢦⠔⠀⡁⡷⢿⡉⢻⢫⢳⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠢⡀⠑⡦⠀⠠⠞⢁⡤
⠀⠀⠀⠀⠀⠀⢸⠁⢳⠀⠘⢤⡤⠤⣄⣉⠖⠀⡠⠊⠀⢹⣿⣧⠀⢫⣇⢇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠙⠒⠒⠒⠋⡠⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠺⠃⠃⡌⠀⢀⠏⠀⠀⡜⠁⠀⠀⢸⣿⣟⣇⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠃⠉⠤⠊
⠀⠀⠀⠀⠀⠀⢙⣀⠔⠀⠰⠁⠀⠛⠀⠀⠘⠀⠀⠀⠀⠈⠉⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⣀
⠀⠀⠀⠀⢀⣠⡴⠖⢻⠛⣦⠀⠙⠓⢄⣶⡉⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠐⠦⡀
⠀⠀⠀⠐⠀⠘⠓⢄⣈⡙⠁⠀⡀⠀⢀⠄⠀⡶⠙⠂⠀⡦⢀⠀⠀⠀⠀⠀⠐⠀⣀⡘⠁⢠⠀⠀⠀⡄⠂⠄⠉⠁⡀⠴⢤⡈⢢
⠀⠀⠀⠸⡄⣠⣤⠀⠀⣉⠑⠢⣤⣤⣈⣐⠀⠁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠰⢀⡀⠑⢉⣙⣄⡀⠓⠊⠀⠀⠈
⠀⠀⠀⠀⠈⠻⡛⠠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⡆⣾⡉⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⡀⢠⡾⠉⢦⠀⠀⢀⠠⡄⠀⢀⣠⡴⡩⠂⠀⠀⠀⠑⢻⣋⡃⠀⠀⢀⣰⡓⠀⠀⠀⢀⠀⠀⠀⢀⣀⣤⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⢨⡅⠀⠐⠈⠇⠀⠛⠉⠤⠖⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⣿⡿⠀⠀⡉⠻⠌⠀⠙⠛⠛⣥⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠥⠀⠀⠀⠁⠀⠸⠶⠲⠛⠋⠉

⠀⠀⠀⠀⠀⣀⣀⣄⡀⠠⠴⣂⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠰⠀⠁⢦⡤⠄⠰⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⡒⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⢀⣆⣀⠃⠀⠀⠀⠀⠁⠒⠂⠠⠄
⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡂⠈⠀⢈⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠈⢡⡇⢂⠠⠂⠀⠐⠒⠉⠀⣀
⠀⠀⢸⠀⠀⠀⠀⢀⣀⠀⢸⢘⠀⣄⠠⠔⠊⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠰⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⣲⠏
⡀⠀⠀⠉⠉⠁⠐⠃⡈⠒⠺⠀⠁⠀⠀⠀⠀⠁⢂⣠⡆⠀⠀⠀⠀⠀⠀⢐⠀⠈⠛⠛⠛⢲⣓⡄⠀⠀⠀⣠⢦⡀⠠⣀⠀⢤⣼⣟⡏
⠹⠾⢂⠀⢀⡀⢀⡤⠄⡀⠀⠀⠀⢩⢋⡢⠀⣸⡸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⣀⠀⠀⠉⠀⠀⠀⠀⠿⣞⡗⠀⠁⠀⠀⠉⠁
⠘⠒⠼⠿⣛⣲⠏⠉⠉⢀⡠⡀⠀⣦⢸⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠘⣭⣾⡍
⠀⠀⠈⠀⠀⠀⠩⠉⠉⢀⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠒⠀⠀⠀⠀⠀⠀⡶⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⢶⣄⡀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢃⠀⠀⠀⠀⠀⠀⠀⠡⠠⡄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢀⡿⠶⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣶⠀⠚⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⣹⠓⡁⠈⠓⣄⣀⣀⣤⡶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣎⢹⡟⠀⠀⠀⢠⡞⢁⠰⠟⣋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣹⠿⣤⡕⣶⡖⠚⠛⠛⠋⡡⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡇⠀⢰⢠⠈⠛⠋⢀⣾⡏⣿⠀⡰⢁⣴⣦⠀⠀⠀⠀⠀⠀⣸⠟⡡⢤⢢⡝⡄⢻⣖⣿⣧⣤⣤⣴⡂⢲⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡆⢸⠘⢠⠠⢤⣴⢿⡟⢿⠟⠀⣡⣿⣆⡟⠀⠀⠀⠀⠀⠀⡿⢸⠁⣸⣿⢀⠂⠼⠛⠻⣄⡀⠠⡔⢁⠿⢇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣲⠖⠀⠀⠰⢾⡿⣸⡇⠈⠛⠛⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⢿⡘⠴⣧⡭⠋⠀⠀⠀⠀⠀⠉⠀⠱⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⣀⣚⣶⣂⡀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡬⠵⠚⢛⣿⣉⣤⣯⣤⣉⣿⡛⠒⠮⣅⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡵⢾⣧⠴⠖⠋⠉⠘⣀⣠⢿⣄⣀⠋⠉⠙⠲⢤⣹⣷⢭⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⡵⢋⡴⠊⠉⣀⢤⣲⡬⠷⠓⠛⢸⡗⠒⠮⢥⣖⠤⡀⠋⠳⢄⠙⢮⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣣⣿⣴⠋⠐⣦⣮⠞⠉⠀⢠⠀⠀⠃⢸⣧⠀⢀⠄⠈⠙⠪⣵⣴⠊⠳⣄⣷⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣱⠃⡼⠉⢠⢮⠞⠙⠷⣄⡀⠀⢧⠀⠀⢸⣿⢀⡞⠀⠀⠄⣠⠞⢣⡳⡐⠙⢏⠙⡎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⠃⡸⠁⢠⣧⠏⠀⠀⠑⠌⠻⣶⣜⡷⠀⢸⣿⣿⠁⠂⣠⡾⠃⠀⠀⢹⡵⡀⠈⣆⠸⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⢶⡧⠀⣆⡏⠀⠐⠲⢤⣈⣂⠈⠻⣿⡀⢺⣿⠃⣰⣿⣟⣠⡤⠖⠂⠀⢳⡱⢀⣸⣶⣧⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣺⣇⠇⠀⡇⢸⣀⣰⣼⣥⣤⣤⣶⣶⣿⣿⣷⣦⣬⣷⣼⣷⠾⠛⠉⠉⠑⠂⠀⠀⠀⠼⢯⣀⣸⡇⢹⠀⠀⣿⡓
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠋⡏⢻⠉⢹⢯⠍⠩⠭⠉⣉⡉⠉⠉⣉⣭⢿⡿⣟⠿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠛⢻⡏⢹⠩⠀⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⡇⣷⣾⡖⠀⡞⡇⠀⢀⡠⠴⠚⣻⣿⠟⢡⣾⡇⠹⣷⣄⠙⢛⠳⠦⣄⡀⠀⣸⢳⠀⢼⣷⡾⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⡀⢧⠀⠰⡿⡄⠀⠀⢀⣼⠟⠁⢔⣿⣿⡇⠀⣿⠻⣷⣄⠢⠀⠀⠈⢰⢧⠃⠀⡞⢨⢇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢳⡈⢧⢀⠱⡿⣄⣠⠟⠁⠊⠀⡼⠹⣿⡇⢠⠙⣇⠈⠙⠷⣄⢀⡰⢫⢂⢀⡼⢀⡏⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠳⡿⠣⡀⢈⡾⡷⣄⡀⠀⠰⠁⠀⣿⡇⠘⠀⠘⠄⠀⢀⡨⢿⢷⡁⣠⠿⣷⢏⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣝⢦⡙⢦⡀⢈⠚⠽⣲⠦⣤⣀⣹⡇⣃⣀⣤⠴⣞⠭⢃⠁⣠⠜⢁⡴⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢝⢦⣾⠗⠦⣀⡀⠉⠘⠃⢻⣧⠋⠘⠂⠁⢀⣠⠴⢿⣧⠴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢑⡢⢤⣉⣹⣿⠒⠶⡿⠖⢺⣷⣋⣉⡤⢖⡫⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠭⠩⠟⠛⠿⠛⠫⠭⠭⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡗⠂⠀⠐⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠃⠀⠃⠀⡠⠰⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⡀⢀⠀⠉⣐⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠒⠦⠀⢤⠀⡀⠐⡃⣠⠖⠋⣀⡤⠤⠀⠀⠀⠒⠂⠀⠈⠈⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠤⠀⠁⠀⠉⠙⠉⠁⠀⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢻⢀
⠈⠀⠀⠀⡘⠢⠤⠤⠤⣀⣀⣀⣀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼⡙
⠀⢠⡄⣒⠨⠭⠭⠭⠔⢒⣒⡠⠄⠉⠥⡄⠀⠀⠀⠀⠀⠒⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⣴⠃
⠈⠀⠐⠁⠈⠉⠉⠉⠁⠒⠒⠒⠨⠤⠭⠥⢀⡀⠀⠀⠀⢀⣀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟⢻⡇⣿
⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⢧⠟
⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢏⣵⠶⠶⣦⡹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣷⣾⣷⣾⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⣿⣿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠿⠛⠛⠛⠛⠿⠷⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⢀⣀⠤⠤⠄⠄⠀⠄⠤⠤⣀⡀⠈⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡤⠊⠁⠀⢠⡀⠀⠀⠀⣀⣀⣰⣆⣀⣀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⡴⠋⠀⠀⠀⠀⢸⣷⡶⠉⠁⠀⠀⢸⡇⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠙⢦⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠎⠀⠀⠀⠀⡠⠚⠁⠁⢣⡀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠱⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⠋⠀⠀⠀⢀⠞⠀⠀⢠⡀⠀⠱⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠳⡀⠀⠀⠀⠙⡄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡎⠀⠀⠀⢀⠊⠀⠀⠀⠀⠙⢦⣄⡱⡖⠚⠉⠉⠓⠲⢄⣀⡴⠋⠀⠀⠀⠀⠑⡄⠀⠀⠀⢱⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢰⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡨⠋⣠⣾⣿⣿⣿⣿⣶⣄⠙⢅⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠐⢺⠗⠻⠿⠿⠿⠿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⠿⠿⠿⠿⠺⡗⠂⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢡⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡌⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠘⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢸⣦⡈⠛⠻⠿⠿⠟⢟⢁⣴⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢣⠀⠀⠀⠈⢣⠀⠀⠀⢀⡴⠋⠀⠈⠑⠒⣤⣤⠒⠊⢣⠀⠙⢦⡀⠀⠀⠀⡜⠁⠀⠀⠀⡜⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⢧⠀⠀⠀⠀⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢣⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⡴⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠳⡀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⣤⣠⠖⠁⠀⠀⠀⢀⠞⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⢦⡀⠀⠀⠀⠀⠉⠒⠦⠄⣀⣀⣸⣇⣀⣀⠠⠄⢾⣿⣿⣆⠀⠀⢀⡴⠁⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡦⡀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠿⠀⠀⣠⠔⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣢⢄⡀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⢀⡠⣖⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⣗⡢⠤⣀⡀⠉⠉⠉⠈⠁⠈⠉⠉⠀⣀⠤⢔⣺⣽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢮⣭⣭⣤⣄⣠⣤⣭⣭⡵⠶⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⢀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠒⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠆⠀⠈⠡⢀⣘⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⢒⣂⠀⠀⢉⣀⠀⠀⠁⢈⣷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⣤⡠⠍⠁⠠⠄⠀⠀⠐⢉⡉⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⢲⡒⠒⠒⠒⠒⠉⣉⣁⣀⣠⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⣴⠀⠀⢀⠀⠀⠉⠙⠋⣈⣉⣯⣩⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠄⠀⢸⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢆⠠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠒⠒⠒⠒⠒⠒⠶⠦⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠠⡀⠀⠂⠋⢸⠁
⠀⢀⠀⠠⠖⠋⠁⠀⢀⠀⠤⠤⠤⠄⠀⠠⠤⠤⠤⢄⣀⠈⠉⠳⡌⣁⣀⡀⠉⠉⠀⠀⠐⠒⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠇⢀⡖⠎⠓⠀⠐⠲⣤⠀⠀⣠⠤⢤⢤⡀⢠⡤⠛⡆⠀⡏⠀⠀⠈⠒⠒⡀⠀⠀⠰⠀⠀⠀⢠⡧⡀⠀⣀⣀⣀⣸⡤⠤⠄
⠀⠀⠀⠃⢸⠁⠀⢀⡠⠨⠛⢣⡄⢰⣁⡔⠒⠄⡼⠁⠀⠀⢰⠀⢻⠀⠀⠀⠀⢀⠇⠠⠀⠀⠀⠀⠀⣎⠁⠰⠀⠀⠀⠀⠉⠙⡆
⠀⠀⠀⢲⠈⡄⣊⡡⠀⠀⠄⡱⠃⠨⡁⣤⣤⢀⡅⠀⠀⠀⢸⠀⢸⢀⠤⠔⠒⡉⠀⠀⠀⠀⡀⠀⢠⣈⠀⠀⠂⠀⠀⠀⠰⠀⡇
⠠⠄⠁⢹⡄⢷⠋⡔⠉⠁⠰⠏⠓⡄⢉⡤⠤⠎⣤⠀⠀⠀⣸⠀⢸⠁⠀⠀⠀⢄⠀⠘⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠐⣇⠸⡮⡀⠦⠶⡴⠨⣠⢳⡄⠀⣠⠊⠀⠀⠲⠂⢨⠀⢸⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠸⠄⠁⠀⠀⠀⠀⠀⢀⠀⡇
⡀⠀⠈⠀⠰⡀⢷⠾⠦⠂⣴⠻⡙⠁⢼⠶⠯⠄⣼⠓⠓⣄⢰⠀⢸⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡅
⢀⠔⠒⠶⢄⣃⠘⡧⠈⠃⠋⠐⢺⣷⠮⠤⡴⠃⠉⠑⠲⡍⢺⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠌⠀⠀⠀⠀⠀⢸⠂
⠘⢄⣀⣀⣠⢝⡂⠸⣆⣼⠤⠤⠶⠿⠼⠴⠼⠤⠴⠧⣄⣘⣌⠀⢸⢀⡐⠂⠐⠂⡀⠀⠀⠀⠀⠀⠀⠈⡏⠐⠒⠲⠤⠤⠤⡼⠀⠀⠁
⠀⠀⠀⠠⠄⢀⡽⠒⠊⠉⠉⠲⣄⠀⠀⠀⠀⠀⢠⠔⢊⠉⠁⠉⠛⠔⠲⢀⣀⡰⠃⠒⠒⠒⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⡧⠀⠀⠦
⠀⠁⠈⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠐⣶⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⠀⠀⣀⣀⣀⠀⠀⣃⠀⠘⣆⠀⡀⠀⣷
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠳⠈⡇⠀⠀⠀⠀⠀⢀⠀⢘⡃⠀⠀⣠⡊⢠⣄⠀⠀⠀⠀⠀⢸⠀⠈⠁⠀⠂⠀⠉
⠀⠠⠀⠄⠤⠠⡀⠀⠀⠐⠈⢀⡼⠀⠃⠀⠆⠱⡀⠀⠀⠀⠐⠀⢂⡝⠀⠀⠀⠀⠑⠀⠀⠘⠀⠀⠀⠀⢸⠀⠀⡆⢠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⡉⢀⣠⣤⣖⣩⣤⣄⣀⣀⣀⡀⠙⠲⠦⣀⣀⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⠀⠁⠀⡀
⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠲⠦⠤⣧⢀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⢹⡤⣤⣤⣤⣄⣀⣟⠒⠐⠒
⠀⠀⠀⠀⠉⢲⡄⠤⠰⠒⣶⠒⡶⠒⠒⠒⠒⠶⢤⡤⣤⣀⣀⠀⠀⠀⢘⡀⠀⠀⠀⠀⡔⠀⠀⡤⠚⠉⠀⠁⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠘⠀⣿⠀⢣⣀⣀⣀⣀⠀⢰⠀⠁⠀⠁⠉⣛⠂⠉⠀⠀⠀⠀⢸⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⢀⣀⠀⡛⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠒⠒⠚⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⠀⠀⠀⠀⠉⠉⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠄⣠⠤⠤⠤⢼⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡠⣾⠋⠀⣤⠀⣀⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⠈⠀⠒⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠐⠈⠙⠶⢂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⢻⣿⡀⠀⠀⠀⠂⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⣂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⢀⢄⡀⠀⠀⢸⣿⡇⠀⠁⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⠀⣨⡟⠥
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠤⢀⠀⠱⡄⠠⡀⠀⠀⠘⢿⣿⠀⠀⠀⠰⠑⠦⠀⢀⠔⠒⠢⣄⠄⠀⠀⡂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠓⠀⢳⠀⠈⠢⠀⠀⠈⢻⡆⢀⠀⠅⠀⢐⣶⣷⣦⠀⡤⣪⣿⠿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣨⠑⢻⠀⠀⠀⠀⠠⡀⠀⠑⠼⠐⣭⣏⠉⠀⠙⠳⢼⣿⢶⣗⠒⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡞⣁⠠⡼⠷⠄⠀⠀⠀⠨⠂⠀⠀⠀⡇⢈⢦⣤⢴⡾⠿⠂⡠⡙⠻⢦⣈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠶⣆⠈⠉⠀⠀⠀⢀⠄⠋⠀⠀⠀⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠤⠤⡀⠀⢀⣀⢀⣘⡅⠀⠀⠀⠈⠛⠐⠐⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀

⠸⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣾⣿⣿⠸
⠀⠀⢆⢻⣿⢟⢸⢛⠾⡿⠛⡿⠽⠿⣿⢛⠻⡻⢻⢳⠻⣿⡟⠀⠀⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠈⠆⢿⣿⣾⣿⣿⣾⣮⣿⣷⣦⣿⣿⣷⣽⣿⡿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⣾⠀⢠⡄
⠀⠀⠀⠘⡌⢿⣿⡇⣿⢿⠿⠿⣽⣿⣿⣿⡿⠷⠟⠇⠇⣼⡇⠀⠀⠀⠀⠀⢀⠀⣀⢡⡂⠀⠀⠂⠀⡉⠃⢀
⠀⠀⠀⠀⠐⡘⣿⣦⢿⣈⣤⣎⣭⣩⡍⣿⣷⣶⣒⣿⣷⡾⠇⠄⠦⠠⣤⣿⠔⠠⢤⣄⣀⠋⠡⠂⠙⠒⡀⠀⠂
⠀⠀⠀⠀⠀⠱⠸⣿⣾⣿⣿⣿⡟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠫⢝⡁⡑⢸⣶⠀⣁⠄⠒⠂
⠀⠀⠀⠀⠀⠀⢣⠹⣿⣿⣿⣿⣅⡀⠘⠟⡙⠲⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠁⠈⠁⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢇⠻⠿⠟⠛⠛⣉⢰⣤⣀⠀⠂⠀⡙⠳⢬⡐⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠁⠂⠀⠀⢀⣀⣤⣄⡠⠤⠒⠊⠈⠻⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢠⠀⣼⠏⠹⡐