Gem Emojis & Symbols

⠀⠀⠀⠀⠀⣠⠖⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡂⢀
⠀⠀⠀⠀⡎⠘⠀⠈⡏⠃⠀⠀⠀⠀⠀⠀⠀⠖⢁⠄⠘⠁⠠⡈⠰⠀⠀⠀⠀⠀⠀⢀⠔⠡⠀⠈⠌⠢⠀⠀⠀⠀⠀⠀⠀⠀⡞⡄⠈⠁⢠⢳
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠐⡇⠀⠀⠰⠂⠰⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢇⢤⠀⢀⣅⡄⠀⠀⠀⠀⠀⠀⠀⠦⡈⠀⢠⡄⠐⢉⠴⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠓⢄⡠⠘⠼
⠀⠀⠀⠀⠀⠘⠢⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖


⠀⠀⠀⠀⠴⡀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡰⢆⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣀⢀⠆⠰⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠡⠀⠀⠀⠀⢀⣊⣀⣤⣊⣀⣀⣑⣠⣀⣑⡀⠀⠀⠀⠀⠘⡄⠋⠉⠉⠙⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢨⠂
⠀⠀⠶⠆⠁⠀⠀⠀⠀⠈⠰⠶⠀⠀⠀⠀⠁⠀⠁⡀⠀⠀⢀⠌⡠⠊⠁⠀⠀⠀⢈⡁⡇⠀⠀⠀⠀⢸⢈⡁⠀⠀⠀⠀⠀⠀⠰⠰⠆⠀⠆⠆
⠀⠀⠀⢂⠐⠀⣀⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠁⢔⡀⢀⡢⠊⠀⠀⠀⠀⠀⠀⠀⢨⠓⣄⣀⣀⣀⠚⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢘⠄
⠀⠀⠀⠀⠲⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠰⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏


⠀⠀⠀⢀⠰⠒⠐⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠒⣢⣴⠲⣄⠀⠀⠀⠀⠀⠀⠀⣀⠰⠶⠀⡀⠶⠦⣀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠰⠆⠤⢀
⠀⠀⠀⠋⠘⠃⠀⠀⠘⠀⠙⠀⠀⠀⠀⠀⢠⠚⠟⡥⠐⠂⢤⠻⠓⡄⠀⠀⠀⢠⡞⣁⢀⣄⣊⣁⣠⣀⣈⣳⡀⠀⠀⠀⠀⢌⣑⣤⠚⠓⡣⣊⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠰⠀⠀⠀⠀⠆⡿⡁⠀⠀⠀⠈⠢⡀⠀⢃⠀⠀⡀⠀⢀⠜⠁⠀⠀⠀⠐⠆⢾⠀⢰⠾⠀⡷⠠⠆
⠀⠀⠀⣄⢠⡄⠀⠀⢠⠀⣠⠀⠀⠀⠀⠀⠘⢤⣦⡓⠠⠄⢚⡴⡴⠃⠀⠀⠀⠀⠀⠈⠢⡈⠄⠰⢀⠔⠀⠀⠀⠀⠀⠀⠀⢁⡠⠚⢤⡤⡕⢄⡙
⠀⠀⠀⠈⠰⠤⠠⠄⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠙⠦⠟⠳⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠰⠆⠒⠈


⠀⠀⠀⠀⡴⠦⠀⠀⠴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⡒⢒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠒⠀⢄
⠀⠀⠀⠌⣠⠀⠈⠑⠀⣆⠡⠀⠀⠀⠀⠀⠀⢀⠔⠁⡰⢄⠈⠢⡀⠀⠀⠀⠀⠀⠰⠋⠂⠚⠂⠀⠓⠐⠙⠆⠀⠀⠀⢀⡈⠀⣀⠀⠀⢀⠀⣀⠀⢑⡀
⠀⠀⢾⡈⠐⠀⠀⠀⠀⡇⢁⡷⠀⠀⠀⠀⠰⡇⠰⠎⠀⠀⠱⠄⢸⠆⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠈⠢⡀⠈⡀⠀⠀⠀⠁⢀⠔⠁
⠀⠀⠀⢀⠙⠀⢄⡠⠀⡏⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠠⠌⢀⠔⠁⠀⠀⠀⠀⠀⠰⣀⠄⢦⠀⠀⡴⠀⣀⠆⠀⠀⠀⠀⠀⠈⠢⡐⠀⢀⢂⠔⠁
⠀⠀⠀⠀⠳⠖⠁⠈⠲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠥⠬⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠀⠉⠁⠀⠀⠀⠁⠈⠉⠀⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠔⢋⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⢄⡀
⠀⠀⠀⠀⣠⠞⠁⠀⡼⠁⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡷⣤⣄⣙⠲⣄
⠀⢀⡴⠋⠀⠀⠀⣰⠃⠀⠀⠈⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⣧⠀⠈⠉⠛⠺⠿⣦⡀
⢰⠋⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⣹⡶⡶⠦⠤⠤⣤⣤⣄⣀⣀⣀⣠⣤⣤⠤⣤⣶⡒⠋⠉⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢳
⡏⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈
⣇⠀⠀⠀⠀⡼⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀
⠹⡄⠀⠀⣸⠃⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡜
⠀⠱⡄⢰⣏⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⣇⠀⠀⠀⣠⠞
⠀⠀⠙⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⢀⣠⠞⠁
⠀⠀⠀⠈⠙⢷⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠙⠦⣈⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠻⣟⠓⠶⠶⠦⠤⠤⠤⠤⣤⣿⡥⠤⠤⠤⠴⠶⠒⠚⢩⠟⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠙⢆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⠳⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢦⡀⠀⠀⢸⡆⠀⠀⣰⠏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣝⣦⠀⢸⡇⢀⡴⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⣷⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢄
⠀⠀⠀⠀⠀⢀⡴⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⠀⠢⠀⠉⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢄⢀⠤⡀⠀⢳⡀
⠀⠀⠀⠀⢰⠇⠀⠴⠀⠳⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡞⢡⠐⠤⠛⡄⠀⠀⠀⠀⠀⠀⢸⠀⢀⠁⠀⠈⡀⠀⡇
⠀⠀⠀⠀⢺⡈⠑⠴⠄⣠⠆⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⡱⢄⠌⣠⠃⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠄⠁⡇
⠀⠀⠀⠀⠀⠉⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠁⠂⡄⠈⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⡠⠂⣀⠔⠄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⢀⠶⡒⠒⠒⠒⡒⠒⡒⢆⠀⠀⠀⠀⠀⠀⣠⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡌⠈⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⡠⢒⠒⠒⠂⠒⢦⡀
⠀⠀⠀⠠⡏⠀⠰⡄⠀⠀⠈⡦⠀⠀⡧⠀⠀⠀⠀⡰⠃⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢠⠓⠀⠀⢃⠄⡇
⠀⠀⠀⠀⠑⡄⠀⠁⠀⠀⠠⠀⢀⠜⠁⠀⠀⠀⢠⠃⠀⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠇⠸⠁⠀⠁⠀⢇⠀⠀⠀⠀⠀⠀⢘⠀⠀⡐⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠈⢣⡁⠐⡴⠁⠀⠀⠀⠀⠀⠘⡇⠑⣀⣀⠌⠁⡞⠀⠀⠀⠀⠀⠀⠈⠓⢄⡁⠐⣠⠜⠁⠀⠀⠀⠀⠀⠀⢸⠐⠈⠢⠀⠰⡈⠐⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⣀⡥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡌⠤⠤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠙⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣁⢙⡄⠀⠀⠀⠀⠀⢀⡤⠒⠊⡉⠈⠹
⠀⠀⠀⠀⢰⠃⡀⣤⠳⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⡄⠀⠀⡐⢹⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌⢡⠃⠀⠀⠀⠀⠀⢸⠀⡲⠈⠀⡈⠀⡄
⠀⠀⠀⠀⠸⡀⠀⠀⠢⣧⢖⠒⣦⠀⠀⠀⡼⠀⢈⢤⠂⠀⠈⠘⠀⡀⡇⠀⠀⠀⠀⠀⠀⡸⠁⠐⠀⡼⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠝⠂⣠⠇
⠀⠀⠀⠀⠀⣷⠀⠀⡜⠁⡈⠚⡞⠀⠀⠀⢣⠈⠀⠀⢂⠀⠀⠆⠀⢀⠇⠀⠀⠀⠀⠀⠀⡇⡤⠀⢀⡇⠀⠀⠀⠀⠀⢰⠀⢀⠔⣡⠔⠊⠁
⠀⠀⠀⠀⠀⠘⠮⣏⣯⣞⣤⠎⠀⠀⠀⠀⠀⠱⡄⠠⠂⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢸⣀⠔⠉⠀⠀⠀⠀⠀⠀⣼⡵⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⢄⠀⠘⡾⠀⠀⠀⠀⠁⠁⠁⠀⠈⠣⣀⠀⢀⠜⠀⢈⠀⠀⠀⠀⠠⠀⠀⡆⠀⢀⠀⠨⠀⢀⠔⠉⠀⠀⠉⠀⠀⠀⠈⠀⠀⠠⠔⠈⠡
⠀⡇⠀⠀⢀⠄⠐⠠⡀⠀⡏⠱⠢⠀⠈⠉⢀⠤⠤⡀⠢⡀⠀⠒⠀⢀⠔⠁⠀⠈⠉⠉⠉⠀⠀⠠⢄⠀⠰⢀⡂⢀⠔⠀⠀⡀
⠠⠀⠀⠀⠈⠀⠐⠀⠘⠄⠐⡀⠀⠑⢄⠀⠅⡀⡀⠰⠀⠈⠀⠀⠈⠁⢀⠔⠀⠈⠀⠉⢢⠀⢴⠀⠆⠙⠀⠀⠀⠀⠀⠀⠠⡄
⠋⠀⠀⢸⠀⠄⠀⠀⠀⠂⠀⠘⢄⠤⢸⠀⠉⠐⠂⠁⢀⣠⡀⠀⠀⠐⠁⠀⠁⠀⠀⠀⡰⠀⠲⢁⡘⠄⠃⠀⠖⠈⠉⠢⠀⠈⠢⣈⠠
⠈⠙⢤⠈⣄⠀⠀⠀⢀⠄⠀⢀⣀⡈⠛⠀⠀⠀⢀⠊⠀⠀⠁⣄⠀⡇⠀⠀⠀⠐⢀⠔⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠑⠄
⠁⠀⢀⡀⠈⠢⠀⠤⠊⠀⡌⠁⠀⠈⠢⡀⠀⠀⡌⠀⠀⠁⠀⡌⠀⠈⠂⠀⠀⠂⠁⠠⠈⠁⠀⠀⠑⡀⢀⡂⠠⠄⠀⠀⠀⢈⣦
⡈⠉⠀⢀⠠⠀⠰⢄⠀⠀⢆⠀⠀⠀⠁⠐⡀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⡄⠚⠇⠀⡇⠈⠀⠀⠀⠀⠁⠀⠱⠤⠄⠀⠒⠈⠀⠀⠀⡠
⠨⠀⠀⠉⠠⠀⠁⠀⠈⢢⠀⠁⠐⠂⠤⠀⢰⠄⠐⣄⠀⠘⠁⠀⡦⡤⡔⠈⠘⠘⠀⡇⠀⠀⠀⡀⠀⠀⠀⢠⠐⠀⠈⠁⠢⣀⠀⡎
⠊⠀⠀⡄⠐⠀⠀⠀⠈⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢍⢠⣈⡄⢠⠇⠀⠡⣄⣀⣈⣀⠜⠀⢀⠁⠀⠀⠀⠂⠀⠈⡄⠐⠂
⢰⠦⢀⠀⠑⠄⣀⡀⠀⠔⠀⠀⠇⠘⠙⡀⢀⡀⠊⠀⢀⠀⠉⢢⠈⠙⠛⠒⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠄⠐⠀⣀⠈⠀⠀⠅
⠃⠀⢀⡁⠆⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠣⠀⣀⠀⢀⠀⠀⠀⠎⠐⢆⡉⡄⠀⠀⠈⠢⠄⠀⢠⠔⠁
⡀⠂⠀⠀⠀⠀⠰⠁⡡⠀⡉⠢⡀⢢⠂⠰⠀⠦⡀⠀⠂⠈⠀⢀⠂⡐⠁⢀⠈⢂⠀⠀⠡⡈⡀⠔⠀⠀⠀⠀⢀⡀⠤⢀⠀⡰⢢⡀
⠈⠂⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠈⠐⠆⠒⠀⠁⠌⠀⠀⠀⠀⠘⢂⠀⠀⠁⢀⠀⠀⡀⢀⠀⠈⣁⠌⠀⠘⡈⠀⢀
⡀⠀⠘⢾⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢔⠩⠒⡄⠀⠀⠀⣎⠀⠀⠀⠀⠈⠂⠸⠂⡠⠊⠁⠄⠐⠀⠀⢱⠀⠈⠐⠦⡀⢙⠟⢁⣀
⠀⠑⢄⠀⠀⠐⠄⠀⢀⣀⠰⠃⢠⣄⠀⠐⢀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠁⢀⠁⢀⠀⠀⠀⠐⢀⠌⠀⠀⠀⠀⣀⣀⠀⠀⢄
⠠⡀⠠⠙⡀⠀⠀⠀⠀⠀⠀⠰⠠⠠⠆⠀⠀⠉⠀⠀⡀⠀⠉⢩⡙⠀⠠⠖⠆⠂⢄⠈⠂⣀⡈⢀⠠⠒⠁⣀⡤⠀⠀⠁⠠⠀⠑⢄⠈
⠀⠀⠉⠉⠁⡤⡊⢉⠙⡂⠀⣠⠀⢀⠦⡆⢤⠀⢠⢎⠀⠀⡠⠘⠁⠀⢀⠽⠤⢩⠿⡀⠀⠀⢀⠠⠤⢀⠀⠈⠑⠠⢀⠀⠠⠀⢀⠜⠃
⢁⠈⠢⡀⠀⠧⡰⠀⡨⠃⠀⠈⣄⣣⡔⡈⠋⠀⠚⠀⠂⠁⠀⠀⠀⡈⠑⡀⠀⣠⠔⠀⢀⠴⠁⠐⠀⠈⢡⠀⠀⠀⠀⠈⠐⠊⠀⠀⡠
⠀⠀⠠⠘⠂⠀⠀⠉⡁⠄⠂⠄⡀⠀⠉⠀⢀⡀⠤⠄⠂⠓⢠⡀⠀⠉⠂⠒⠀⠀⠀⣠⠂⠀⠀⠠⠐⣀⠌⠀⠠⠒⣒⢄⠀⠀⡴⠁
⠀⠀⡠⠚⠀⠀⠀⠃⠀⠀⠄⠀⠈⠇⠀⢀⠁⠠⠄⠀⠘⠀⠠⠀⢀⠔⠂⠒⠤⡀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⡇⠃⠠⢀⡀⠰⠄
⡤⠊⠀⠀⠀⠀⢰⠀⠐⠀⠀⠈⠀⢸⠀⠈⠢⡀⠀⠀⠀⠀⠃⠀⠠⠀⠐⠀⠀⡈⠄⠀⢠⠔⡆⠒⠂⠀⠠⡀⠈⠘⠁⠈⠁⠀⠈⠀⢄
⠀⢀⠜⠣⡀⠀⠈⠂⠀⠀⠀⠀⡠⠊⠀⢀⡀⠀⠑⢄⣀⡔⠀⠀⠰⡀⠀⠀⠀⢀⠘⠀⠀⠐⠀⠤⢀⡀⣀⠬⠆⠀⡶⠂⢄
⣠⠁⠀⠀⡈⢦⠀⠀⠙⠀⠀⠈⠁⢠⠔⡉⠉⢂⠀⠀⠉⠁⠀⠀⠀⠑⢄⠐⠀⠀⠸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠁⢱⠶⡹⡄
⠘⡄⠁⠀⢁⠆⠀⠠⠐⠂⢤⠀⠀⠆⠀⠐⠀⠈⠀⠀⠀⢀⠠⠠⠄⡀⠀⠁⠂⠊⠁⡠⠊⠀⠄⠈⠃⠀⢀⠛⢄⠀⠈⢆⢀⢦⣰⣀
⠀⠈⡄⢀⡈⠀⠀⢇⠂⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠒⠀⠀⠠⠊⠀⠀⠀⠀⠀⡄⠀⡘⠀⡀⠱⡄⠈⠉⠊⠉⠁⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠘⢣⠦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣔⠳⠀⠀⢒⠊⠀⠀⠀⠉⠁⠀⠀⠘⡀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢶⠀⠀⠀⠉⠀⠀⠀⠁⢘⠂⠀⠍⠁⠀⠀⠀⠀⠃⠀⠐⡀
⠀⠀⠀⠀⠀⠐⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠈⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⣄⠉⠂⡀⠀⢤⠀⠀⠐⠉⢀⠀⠀⠺⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢠⡁⠀⠀⠘⠂⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠁⠂⠀⠀⠀⠀⢠⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣤⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⡼⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⢠⠎⢸⠈⡇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⠲⠤⢤⠋⠀⡞⠀⢧⠠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢭⠙⡲⠤⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⡏⠳⣀⡇⣠⢼⢤⣀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠘⣄⠈⠑⠈⠉⠒⣤⠀⠀⠀⠀⡼⠀⠀⠀⣸⠀⠀⣹⠋⠀⡇⠀⠈⣍⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡼⠀⠙⠲⢤⣀⡸⢹⡀⠀⠀⠀⡇⠀⠀⢠⠇⠀⢠⠇⠀⢰⠁⠀⡜⡌
⠀⠀⠀⠀⠀⠀⠀⠰⡧⢄⡀⣰⠁⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⢸⠁⠀⠀⡼⠀⠀⡼⠀⠀⡏⠀⠘⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⡇⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⡾⠀⠀⢰⠃⠀⢰⠃⠀⢸⠁⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢹⠀⠀⠀⠀⠀⠀⣧⠀⢸⠀⢀⠇⠀⠀⡞⠀⠀⡞⠀⠀⡇⠀⢆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⣇⠀⠀⠀⠀⠀⣿⠀⠸⡄⣸⠀⠀⢸⠁⠀⢸⠃⠀⢸⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡀⠀⠀⠀⠀⢿⠀⠀⡇⡏⡤⠀⡏⠀⠀⡟⠀⠀⡏⠀⡸⢁⣀⡤⠖⠚⣟⣉⠽⢿⢷
⠀⠀⠀⠀⣶⣶⡒⠶⡤⠤⣽⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⢿⢃⠃⢰⠃⠀⢸⠁⠀⢸⠃⢠⡛⠉⢀⣠⠴⠊⠻⣄⣠⠋⠊⡇
⠀⠀⠀⢠⡏⢇⠈⠓⠦⣠⠋⣇⠀⠸⡄⠀⠀⠀⢸⠀⠀⢸⡬⡆⣼⡠⠔⠛⢤⡀⡞⢀⣾⠵⠚⠉⠀⠀⠀⠀⡸⠋⣩⡝⠁
⠀⠀⠀⢸⠁⠘⡆⢀⠔⠉⣎⢻⡀⠀⢧⠀⠀⠀⢸⠀⠀⢸⣿⠔⢻⠲⢤⣀⡠⠟⡏⠉⠈⢦⡀⠀⠀⠀⢀⡼⠁⡾⠋
⠀⠀⠀⠸⡖⠒⠛⣇⠀⠀⠘⣆⣇⠀⠸⡄⠀⠀⣼⡇⠀⡄⡇⠀⠈⣇⡴⠁⠀⠀⡇⠀⣠⠔⢣⠀⠀⢢⠞⢀⠞⠁
⠀⠀⠀⠀⠙⠦⡀⠈⢣⡀⠀⠘⢿⡄⣀⣷⠤⠔⠛⠓⠚⠓⣳⡴⠚⠉⠉⠛⠒⠢⣿⠋⠀⠀⠈⡆⢠⠏⡰⠋
⠀⠀⠀⠀⠀⠀⠈⠢⣄⣹⡤⠖⠚⠉⠁⠀⠀⣀⣠⠴⠒⠋⠁⠹⡄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡱⠟⢾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠢⢄⣠⠤⠖⠚⠉⠁⠀⠀⢀⣠⠴⢚⡇⠀⠀⠀⠀⠀⠀⢳⠀⠀⡼⠁⠘⢸
⠀⠀⠀⠀⠀⠀⢠⠾⣀⡤⠖⠉⢣⠀⠀⠀⣀⡤⠔⠚⠉⠀⠄⣸⡁⠀⠐⠂⠀⠀⠀⠈⣇⡜⢁⣀⣠⣼
⠀⠀⠀⠀⠀⠀⠻⣞⠷⠤⠤⠤⢼⠶⠒⠉⠁⠀⣀⣠⠴⠖⠋⠙⣏⠉⠉⠉⠉⠉⠉⣹⢟⡩⣍⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡀⢠⢏⣀⣤⣶⡾⠋⠁⠈⠓⠦⣄⡀⠘⢆⠀⠀⣀⠴⠋⣐⠽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠉⠙⠲⠦⢤⣀⡀⠉⠓⠺⡦⢊⡡⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⢠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣵⢀⠀⠀⠀⡂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠣⠀⠀⠙⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢀⡆⠀⠀⠘⠆⢁⠀⠀⢀⠀⡐⠊⠹⠂⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠫⡀⠀⠀⣾⠉⠀⠐⠞⠀⠀⠀⠀⡠⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣀⠀⠀⠀⠀⠁⡁⡀⢀⠇⠀⠀⠈⣄⡀⠀⠀⠐⠂⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠉⠢⡀⠀⠀⠀⠀⢀⡎⠀⠀⡰⠊⠁⢻⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⠂⠀⠀⣀⢨⠃⢀⣀⠀⠀⠀⡲⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⢮⠁⠈⠈⠃⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⢘⠀⠀⠀⠀⠲⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣄⠰⡽⠂⠀⠀⠀⡀⠀⡄⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠛⢣⠀⠁⣳⠀⠀⢐⠀⠰⡀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⡯⠀⠀⠀⠘⠈⢠
⠀⠀⠀⠀⠀⠀⠘⡀⠈⠉⠀⠀⠀⠀⢸⠝⠃⠻⣉⡀⣄⢸⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣀⡰⠃⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢀⡇⢀⣿⠀⠀⠀⠶⣇⠐⠀⢨⡏⠗⢘⣼⠴⠀⠀⠀⠀⠀⠀⠀⠀⣫⢾⢙⣬⡰⣾⠋⠖
⠀⠀⠀⠀⠀⠀⠠⣹⡟⠙⠀⠀⠨⢠⣽⡄⠦⡬⣇⣬⢩⡿⠂⠀⠀⠀⣤⡄⠀⠀⠀⠛⢾⠿⠅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠈⠙⠢⠠⠟⠉⠁⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢢⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⣾⠀⠹⠊⡅
⠀⠀⠀⠀⠀⠀⣷⢠⠂⠀⠀⠀⠐⠂⠉⠀⠀⠀⠄⠀⠀⠈⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣄⠚⠧⡜⠇⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⢀⣀⣀⡄⢛⠀⢻⣷⠃⣀⠀⠀⠀⠀⠀⢠⡟⢀⣰⡎
⠀⠀⠀⠀⠀⢾⢇⣀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠾⣿⠿⢗⡤⢦⠸⡗⠀⠁⠀⠀⠀⠀⠠⣌⣻⡿⠻⠃
⠀⠀⠀⠀⠀⠘⢮⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡻⠷⠉⣧⠀⠳⡥⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠰⠤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⣰⢻⣦⠀⣅⢡⠀⠀⠀⠀⠀⡀⣠⢁⣄⠀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣴⠀⠀⣸⠀⠀⠀⠀⢠⠃⢸⣿⠀⠘⢺⡄⠀⠀⠀⠀⢹⡏⠰⢳⠀⢀⡇
⠀⠀⠀⠀⠈⠉⣢⣀⠀⢸⡇⠀⠀⢻⠆⡴⡧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡅⠀⠀⠀⠀⠈⡇⢠⢰⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠈⠻⣿⣧⡈⡇⠀⠀⣿⠟⡴⠃⠀⠀⠀⠀⠀⠂⢸⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠸⠈⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠠⠄⠈⢻⡟⠃⠀⣉⡻⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⡆⠀⠀⠀⠀⠀⡀⠀⢀⣀⠓⣾⡿⠀⠀⠀⠀⠀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠤⠤⠰⣟⣤⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣯⡔⢸⠃⠀⠀⠀⠀⠀⠁⠀⠼⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡄
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢴⠇⠀⠀⠀⢀⡄⠀⠀⠀⠀⢐⠃⠀⠀⠀⠫⣑⣄⠀⠀⠀⠀⢄⠀⠈⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠉⠉⣧⠀⠀⠐⠀⣇⣄⠀⡈⡅⠀⠀⠀⠀⠸⢆⡀⠀⠀⢠⠁⠘⠀⠀⠀⠀⢸⠀⠀⠀⢳⠒⡖⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢀⡀⢹⡀⠀⠀⠀⣿⠇⠀⣸⠁⠀⠀⠀⠀⠰⠀⠛⡀⢠⡄⢀⠃⠀⠀⠀⠀⣼⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢻⣧⠀⢃⠀⠀⢰⣿⠀⠘⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣼⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⣿⣀⠀⠀⣥⢼⣿⣤⡒⠀⣤⡖⠀⠀⠀⠀⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⠏⠒⠪⠀⢸⡿⠿⠁⣸⠿⠁⠀⠀⠀⠀⠈⠂⢤⡠⠿⠁⠀⠀⠀⠀⠀⠘⠢⢀⡼⠟⠋⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⢦⣠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠉⠀⠀⠹⡿⡄⠀⠀⠀⠀⠒⠀⠀⠀⣴⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢀⢼⠁⠀⠀⢀⠠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠐⠮⣏⠤⠴⠚⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⢠⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡀⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠟⠋⠙⠯⠀⣿⣿⣿⣿⣇⠼⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⡃⠂⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠐⠐⠃⠐⠛⠁⣭⠉⠁⠈⠸⣿⣿⣿⣷⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⡀⠀⠀⢿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⢀⠸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⠑⠶⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢻⡇⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣠⠐⠃⣸⣿⣿⣿⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣯⢾⡸⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⢾⡷⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣮⡿⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡟⠋⠉⢿⠀⠀⢀⡞⣹⣲⣶⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⠤⠀⢾⡛⣡⠰⢼⣟⣯⣿⡿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣺⡇⠁⠀⠀⠀⠀⠈⠻⣧⣣⠾⣹⣾⣿⣗⡩⠿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣿⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠻⣿⢻⠾⢷⣤⡀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣾⣽⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⣽⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠰⠀⡀⢀⠀⠆⠀⢾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠰⠆⠀⠀⠀⠰⠄⠘⠻⠿⠿⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣄⣀⣄⣀⠀⠀⠀⠀⠠⠀⠀⠀⣠⣶⣦⠀⠀⠀⡀⠀⠀⠄⠀⠀⢀⣠⣤⣤⣀
⠀⠈⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⣸⣿⣿⣿⣧⠀⠐⡂⠀⠀⠀⠀⠐⢯⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⠐⠀⠸⠿⠿⠿⠿⠿⠀⠀⠂⠀⠀⠂⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠂⠀⠈⠻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣼⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡁⢸⣿⣶⢫⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⢠⡄⠑⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠄⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘⣿⣿⣽⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠀⠀⢠⠀⠄⠈⠉⠐⠈⠀⠀⠀⠐⠈⠅⠀⠀⣀⠰⠊
⠀⠀⠀⢸⣷⢇⢸⠀⠰⡤⠠⠀⠀⠀⢰⠀⠀⠠⢐⣿⢮⣿⣼⣦⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄
⠀⠀⠀⠈⡌⡏⣹⠁⠀⠁⠀⠀⠀⠀⣸⠀⠀⠀⢘⡷⣿⣤⠏⢿⠝⣿⡀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠢⢤⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣏⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⡚⣿⡿⢾⣿⣾⠛⣈⠀⠀⠀⠀⠀⠻⡀⠠⣄⡀⢹⠁⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠘⡄⣡⡠⣆⠢
⠀⠀⠀⢀⠁⠶⠀⠀⠀⢀⠁⠀⠀⣸⠀⠀⠀⠀⢣⡿⢾⡻⣯⣷⣿⢿⣿⣦⠀⠀⠀⠀⠈⠅⡌⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢙⣉⣀⠄⠺⠐
⠀⠀⠀⠈⢁⡀⠃⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⠀⣼⣿⡿⣷⣯⣴⢛⣿⣽⠏⠀⠀⠀⡶⠦⠄⢀⡀⠰⠦⠠⢌⡄⠐⠀⠀⠀⠀⢾⠈⣾⠋⣉⡝⢀⣷⡈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣄⠀⠰⠄⠀⠈⠻⠿⠙⠯⠰⠾⠋⡉⠈⠀⠀⠀⠐⠶⠉⠂⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠈⣂⣹⡬⢩⢭⠖⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠈⠁⠂⠀⠀⠂⠐⠂⠐⠂⠐⠋⣁⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠬⠚⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⡃⠂⢄⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢄⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠌⢀⡐⠋⠑⢲⡆⢷⢠⠀⠀⠀⠀⠀⠀⢤⡔⠰⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠋⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⣾⡀⠛⠡⡑⢄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⢀⡄⠀⢄⠀⠘⠀⠇⡘⢃⣀
⠀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢄⣀⣀⣀⠀⠀⠀⠱⡄⢸⡄⠀⠈⡆⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⠙⢦⡀⡆⠀⠀⣴⠃⡀⢠⠦
⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⠀⠦⢤⣷⣠⣾⡴⠁⠀⠛⢷⣤⢀⠀⣤⣶⠀⠀⠀⠀⢒⠀⡁⢠⢄⡜⣡⣤⠿⠞⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⢠⢖⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⡀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⢦
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠰⠀⠐⠀⡠⠀⠠⠉⠉⠁⠀⠀⠀⠀⠁⢎⠀⠈⠀⠀⠀⠈⠁⠀⠓⠂⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠦⠄
⠀⠐⠄⠀⠀⠀⠁⡀⠀⠀⠐⡀⠀⠀⠀⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠴⠖⡄⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠂⠀⠀⠀⠀⢷⢀⣠⡇⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢄⠰⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠐⠂⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⢀⠀⠀⠐⠄⠈⠁⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠁⠸⠀⠘⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠚⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⢠⠀⠠⠀⡰⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠈⠛⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠐⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠁⠀⡇
⠀⠀⠴⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠁⠶⠉
⠀⠀⢤⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⡁⠘⠀⠀⠀⠠⠀⠀⢤⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⢀⠌⡲⠄⠀⠀⠆⠠⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡷⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢦⡴⠂⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠤⠄⠀⠀⠈⠋⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠄⠀⠈⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠀⠀⠙⠊⠉⠁⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠦⡀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢈⠓⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠂⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⢀⠘⠉⠀⠈⠀⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⢁⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠤⠄⠀⠒⠉⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠔⢃⡴⠂⠢⡄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡏⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢤⠴⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠱⠆⠄⢤⠆
⠀⠀⠀⠀⠀⣀⠄⠈⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠆⣀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠈⠁⡀⠀⠀⡛⠛⡆
⠀⢀⠀⠀⠰⠫⠂⠀⠉⢉⠷⠀⠀⠀⠀⠀⠁⣀⠤⠠⢄⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠆⠀⠠⠀⠀⠆⠀⠇⠀⡇⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣂⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠘⠛⠁⠠⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠐⢈⠀⡂⠀⠠
⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⡠⠁⠤⠀⠖⠀⠀⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠋⠉⠁⢙⡀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠉⠈⠡⠆⡑⣈
⠀⠀⠀⠋⠀⠀⠙⠂⠀⣄⠀⠀⣀⠀⠀⢄⠀⠉⡀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠙⠶⣦⠶⠟⠀⠀⠀⠠⠀⠐⡀⠃⠀⢁⡀⠁
⠀⢠⠂⠀⠀⠤⠀⠁⠀⠬⠀⠀⠀⠀⢀⡄⠓⠀⢀⠙⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠆⢐⡢⠄⠄⣀
⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠰⠏⠳⢀⠀⠔⠁⢊⠁⢂⠀⠀⠳⠀⠀⠀⣰⠎⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⡀⠀⢄⣀⡇⠀⠲⠢⡙⠰⠀⠀⠈⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⣠⠀⢤⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⡠⠂⠀⠁⠀⠂⠀⠀⠀⠀⠂⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠂
⠀⠠⠁⡄⠁⠉⠠⠐⠀⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡀⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⡆
⠀⠀⠃⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠄⠆⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠁⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⠀⠀⠀⢀⡤⠤⠀⡀
⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠠⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠴⠡⡀⠄⠀⠈⡄⠀⠀⠈⠀⡀⠀⠹⠀⠀⡀
⠀⠐⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠤⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠄⠀⡁⠀⠈⠆⠀⠀⠀⠐⡇⠀⠈
⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠦
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⡠⠊⠀⠀⠀⡄⠐⢀⠀⠀⣤⡀⠐⠒
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠁⠀⠈
⠀⠀⣀⠤⠐⠞⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠈⠀⠠⠀⠀⠀⠀⢠⠋⠐⠀⠠⣀⠀⠀⠀⠀⠢
⠴⢍⠀⠀⠌⠀⠐⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⡀⠂⠀⠀⢠⠃⠀⢡⠀⠀⡈⢱⠀⠀⠀⠀⠀⠀⢀
⠘⠀⠉⠶⢄⣀⠀⣀⡀⣣⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠁⠀⠀⠀⢻⠤⠠⡀⠀⠀⠁⢸⠒⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠰
⠀⡇⢠⠀⠀⠈⠀⡀⠀⠁⠀⠀⠀⠠⢌⠀⠀⠢⠀⠂⠀⠀⠀⢠⠀⢀⠀⡀⠔⠀⠀⠀⠀⠀⢣⠀⠈⢀⠀⠀⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠰⣆⣠⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠴
⠀⠀⢀⠤⣤⠀⠤⣀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⡠⢄
⢀⠔⠉⡠⠀⠀⠠⡄⠙⠄⠀⠀⠰⠀⢀⡀⠄⢃⠀⠀⡀⠀⠀⠠⠠⠘⠀⡀⢀⠀⠂⡀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠽⠀⠀⠀⢀⠈⠁⠀⠑⡀
⡈⠤⠈⠀⠀⠀⠀⢂⠀⠰⠀⠀⠀⠀⠀⠁⠀⠘⢀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠛⠀⠀⠁⠀⠀⡠⠊⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠸
⠇⠀⢂⠀⠀⠀⠀⠊⠑⠤⠀⠘⠑⠰⠄⠈⠀⠀⠀⠐⠉⠀⢨⡈⠃⠀⠀⠀⠀⠀⣠⠀⠀⠰⡅⠠⠂⠀⠀⠀⠈⠀⠖⠀⠀⠀⠁⠀⠆⠒⠃
⠘⠋⡉⠀⠈⠒⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⡴⠋⢀⠀⠊⢀⠔⠈⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠜
⠀⠀⠈⠀⠈⠀⠘⠁⠀⠀⠀⠀⠁⠒⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠉⠐⠁⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠋
⠀⠀⠀⠀⠊⠑⠄⠀⠀⠀⠀⠘⠁⠀⠀⣄⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠈⢛⠀⠀⠀⡄⠒⠂⢘⠢
⠀⠀⠀⠁⠀⠀⠄⠂⠀⠀⠀⢄⠀⠀⢀⠀⡞⠀⠀⠈⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⡀⠀⠀⠀⠀⡀⠀⠀⢸⠈⠢⡀⠈⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⣄⢛⠠⢀⠀⠟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠂⠑⢄⡀⠀⢠⠁⠀⠀⣀⠀⠀⢀⠁⠐⠂⢘
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢤⠀⠀⠈⠈⠸⡄⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠐⢁⣈⠳⠊⠀⠀⠀⢉⠀⠀⡄⠀⠀⢀⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡀⠁⡄⠀⠇⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠾⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠁⠀⠀⠎
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⣠⠈⢳⡄⠈⡆⠈⢦⠀⠀⠀⠀⢀⣀⠔⣀⠈⠙⢂⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡘⠷⣄
⠀⠀⢰⡟⠀⡼⠋⠁⢴⡀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠖⠂⠈⡀⠀⢸⣦⠀⠀⠀⠀⠀⠀⢀⠀⡋⠎⠇⢧⡀⠀⠀⠀⠀⠀⢠⠃⡼⠉⠰⡈⠄
⠀⠀⠘⠿⡸⠀⠀⠀⠀⢻⠺⣇⠀⢀⡿⠶⠴⠋⠀⠀⠀⠀⠈⠓⠰⢎⠁⠀⠀⠀⠀⡰⠃⡸⠁⠀⠰⡄⠱⡄⠀⠀⠀⠀⠚⡎⠁⠀⠀⣻⢶⡄
⠀⠀⠢⡀⢇⠀⠀⠀⠀⢸⡀⠸⠀⠸⢦⡀⠂⠀⠀⠀⠀⠀⠀⠘⢀⡠⠟⠀⠀⠀⡼⠀⡴⠀⠀⠀⠀⠹⣄⠐⡀⠀⠀⠀⡇⢻⠀⠀⠀⢰⢠⠇
⠀⠀⢠⡞⠺⣆⠀⠀⢀⠄⢿⡄⠀⠀⢦⣟⠀⠠⣄⡀⠀⣀⡴⠖⠋⠑⠀⠀⠀⣸⠃⠘⠀⠀⠀⠀⠀⠀⠘⣆⠳⠀⠀⠀⢦⠿⡀⠀⢀⢶⡳
⠀⠀⠀⢇⠀⢈⡠⠖⡏⠀⢸⠃⠀⠀⠈⠳⠄⠀⢠⡉⠓⠴⡤⠤⠔⠁⠀⠀⢰⠟⣲⡦⠤⠤⠀⠀⠤⠤⠔⣲⡛⢶⡀⠀⠘⣄⣑⣤⣈⣠⠁
⠀⠀⠀⠀⠀⣘⣇⠀⠹⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠉⠀⠀⠀⠀⠀⠈⠉⠁⠘⠓⠒⠂⠀⠐⠒⠛⠁⠁⠉⠀⠀⠀⠈⢫⡈⡏⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢐⣇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠀⣀⠠⡀⠀⠐⠒⠦⢀⠀⠄⢀⠀⠀⠀⠀⣴⠂⡰⣄⢐⠂
⠀⠀⠀⠀⢀⣈⢆⠹⡎⢇⠀⠀⠀⠀⣴⠁⢨⣙⣍⡳⠤⣠⣈⠙⠐⠲⠄⠀⠀⢠⣁⠀⠙⠢⠄⣀⢀⠀⠋⢀⡈⠄⠀⠀⠀⠿⡇⠀⢈⡟⠂
⠀⠀⠀⠠⠉⢡⠂⠁⢷⠈⢣⠀⠀⠀⣉⡄⠘⠁⠀⠈⠃⠀⠈⠱⢀⡀⠀⠀⠀⠀⠈⠿⠋⠂⠀⠀⠉⠙⡆⠈⠣⣄⠀⠀⠀⠲⠾⠳⠉⠴⠂
⠀⠀⠀⣤⡔⠃⠀⠀⠀⢧⡈⡄⠀⠀⠙⠋⡹⠄⠀⠀⠀⠀⠀⠺⣉⠼⠁⠀⠀⡁⠀⠀⣆⠀⠀⠀⠀⠀⢳⠀⠀⢘⠄
⠀⠀⢠⠀⢐⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⢎⠳⣄⠀⠀⣀⠔⢈⡁⠀⠀⠀⠀⡙⢆⡘⠉⠆⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠨⠤⢌⠐⡄
⠀⠀⠘⡳⠿⡀⠀⠀⢀⣈⡦⠇⠀⠀⠀⠀⠀⠑⢰⡌⠛⢯⠴⠊⠀⠀⠀⠀⠀⠐⡈⠀⣀⠀⠀⠉⠁⠀⣤⡉⠅⠂⠀⠀⠀⢘⡁⠀⠀⣁
⠀⠀⠀⠘⠦⠘⡓⢒⣾⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠶⣤⣀⡠⠊⠀⠿⠙⠀⠀⠀⠀⠻⢉⠂⠊⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⠀⢲⡠⠄
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣤⠠⠂⠈⠉⠙⠣⠠⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⢀⣤⠀⠀⠀⣼⣋⠀⠉⠀⠀⠀⠀⣄⣈⠣⠀⠀⠀⠀⢀⢻⡄⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡎⠉⣤⡀⢤⠐⢐⠒⠤⢤⣤⡀⢷⡄
⠀⠀⢀⠤⠼⠃⠈⠉⠁⠀⠉⠈⣇⠰⡄⠀⠘⠅⣻⠷⠂⠶⢄⣁⠀⠐⠀⣀⠄⠀⣧⡀⠠⠀⠀⠀⠀⠈⠳⡀⠃⠀⠀⠀⠀⠀⠀⠀⢸⢳
⠀⠀⠘⢄⣠⠁⠀⠀⠀⠀⠀⠀⠙⣄⢃⠀⠀⠀⠀⠈⠁⠀⠈⠁⢀⡀⠈⠁⠀⠀⠉⠀⠕⠤⡐⢀⠀⠀⡀⢡⡀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠠⡀
⠀⠀⢘⠉⠹⡀⠀⠀⠀⠀⠀⠀⡀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢷⣆⠀⠀⠀⠀⠀⠁⡍⠀⠀⠘⠶⠈⠉⠉⢉⣈⢥⣤⣀⡉⠙⡛⠘⠁
⠀⠀⠈⠶⠤⠦⠤⣄⡀⠀⠤⠐⠷⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠁⠠⢄⠀⠐⣦⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠛⠉⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⡶⢖⠒⠚⠂⠒⠒⢀⠔⣦⠀⠀⠀⠀⠀⢀⣴⠏⣴⠫⡄⢴⡀⠀⠀⠀⠀⠀⣠⠞⠿⠞⠛⠉⠛⠛⡻⢶⣄
⠀⠀⢸⠙⠂⠂⠀⠒⠃⠀⠆⠐⢯⡇⠀⠀⠀⢀⣾⣁⠀⠀⡄⠀⢀⡰⡀⠀⠀⠀⠀⣿⠣⣄⠀⠀⠀⠀⠀⣀⢼⣻
⠀⠀⢸⠀⢐⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⣼⠟⠉⢀⡀⠁⣀⢘⡁⣵⠀⠀⠀⠀⡏⠀⠈⠓⡴⠀⡖⠋⠀⠀⢿
⠀⠀⣼⣧⣎⡀⠀⠀⠀⠀⠀⣆⣾⡇⠀⠀⠀⣿⣦⣤⠘⢁⢀⠁⢼⡧⣾⠀⠀⠀⢀⣧⠀⣀⠀⡽⠚⠃⠀⠀⢀⣿
⠀⠀⢻⣿⣽⣤⠒⠐⠐⢤⣽⣿⣷⠇⠀⠀⠀⠹⣿⣿⣷⣼⣿⣼⣿⣿⠏⠀⠀⠀⠈⣿⣟⣁⠊⠀⠀⠀⢱⣌⣿⡿
⠀⠀⠀⠙⠛⠛⠛⠛⠺⠿⠟⠛⠉⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠶⠾⠿⠿⠛⠁

⠀⠀⠀⠀⡀⠀⠀⠔⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⣀
⠀⠀⠀⠘⠁⢁⡀⠄⠀⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⢏⠀⠈⠀⠀⠀⢘⠉⠁⠄
⠀⠀⡠⠂⢡⠀⠀⠀⠀⠈⢂⠁⠀⡀⠀⠀⠀⣴⠖⢰⠖⠰⠆⠀⡖⠀⣆⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⣷⡦⢦⠀⠀⠀⣠⠸⣖⡟⠀⠀⠀⢠⠛⡆⡌⣆⡘⠁⠰⢸⢀⠘⡀⠀⠀⠀⣿⡷⢠⠀⠀⠀⠀⣀⣈⣤⡾
⠀⠀⠀⠘⢧⣴⣿⡉⣹⣿⣶⠟⠀⠀⠀⠀⠘⠲⠞⠓⠚⠓⠚⠳⠶⠿⠶⠆⠀⠀⠀⠘⠷⣾⣿⣿⣿⣷⣿⣯⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⡄⢀
⠀⠀⢠⠚⠈⠠⡀⠀⠉⠀⣨⡶⢤⠀⠀⠀⠀⠀⣀⠀⠀⠘⠁⠀⡀⣀⠀⠀⠀⠀⠀⢀⣴⠉⠀⠀⠁⢁⠈⠠⢀
⠀⠀⡇⠹⠆⡀⠀⠀⠂⠀⢥⣠⣿⠇⠀⠀⠀⠀⠌⠢⣈⢰⠆⣀⠔⠉⠀⠀⠀⠀⠀⡞⠸⣤⡴⠚⠉⠑⢦⣀⢟
⠀⠀⣯⠀⢀⡇⠀⠀⠀⠀⢸⡿⢿⡆⠀⠀⢠⠬⢤⣬⢍⣺⣴⣉⣤⣥⣀⡄⠀⠀⢀⣶⡏⢹⠁⠀⠀⠀⢸⡇⠙⣿
⠀⠀⣧⣵⠾⣧⣀⣀⣀⣠⣾⣦⠋⡇⠀⠀⠀⡰⢺⣵⣎⡟⣿⣦⣯⢽⣿⠃⠀⠀⠀⣿⣷⡿⣇⣀⠀⣀⣾⢷⣾⡏
⠀⠀⠹⣧⣤⣿⡋⠁⠉⣻⣦⣽⣿⠃⠀⠀⠐⢾⣭⡟⡻⢿⡿⣟⣿⣷⡟⠀⠀⠀⠀⠘⣿⣴⣾⡟⢙⣿⣥⣼⡿
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠉⠓⠿⠿⠷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠿⣿⣾⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠑⠀⢂⠘⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠸⣧⣀⠀⠈⠈⡄⠹⡀⠀⠀⡴⠋⣗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⡆⠀⠈⠙⠂⠀⠹⣄⣳⣤⠀⠀⠀⣸⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⠇⡄⠀⠀⠀⠀⢰⠉⣰⡇⠀⠀⢠⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡆⠀⠀⠈⠀⢇⠀⠀⠀⢠⠃⡰⢸⡿⠀⢀⢻⢷⠢⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣧⠀⠀⠀⠰⢸⠀⠀⢠⡟⣰⠋⡜⡇⢀⡌⡼⣾⠀⢆⠼⡟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠉⣀⠈⠛⡙⡆⠀⣦⡀⣼⠀⢀⣾⣱⠋⣎⣱⣇⣞⣸⡟⡝⠑⡀⠀⠰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⣧⣴⡇⠙⣽⣇⣾⣷⡇⢙⣿⡿⠛⠁⠎⢯⠙⣇⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢀⡀⠀⠀⣼⣿⡇⠀⠸⣿⣿⠟⡀⠹⡇⠀⠀⠈⠢⣤⣠⣿⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⡻⠠⠤⣘⣿⣧⣀⠀⣿⣿⡞⠀⢰⣄⢸⡀⠀⣴⡿⣿⣹⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠛⠛⠛⠛⠻⠷⡿⠻⠾⠦⠞⠉⢿⣷⣾⠿⠲⠿⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠚⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢩⠏⢯⡉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⣾⠲⠤⡽⠤⠤⠤⠤⠤⠤⠤⠴⣯⠤⠞⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡓⠲⠤⣴⠧⠤⠤⠷⣤⠴⠒⢻⢦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⣇⡠⠊⠀⠀⠀⠀⠀⠈⠲⣀⡏⠀⢳
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠴⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⢤⡀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡽⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡟⠁⢀⠇
⠀⠀⠀⠀⠀⠀⢻⡞⠉⡽⠛⠛⠛⠛⠛⠛⠛⠛⢯⠙⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢠⠇⠈⠳⣄⢀⣀⣀⢀⣠⠊⠀⢧⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠧⠤⠤⠤⠤⠤⠤⠤⠤⠼⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠛⠉⠙⢯⠉⢉⠟⠉⠙⢓⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠬⡷⢯⠤⠶⠚⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢧⣀⡤⠞⠦⣄⣠⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡜⠀⠀⠀⠀⠀⠙⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠘⢦⠀⠀⠀⠀⠀⢀⠞⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡿⠢⡾⠀⠀⠀⠀⠀⠀⠀⠸⡤⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡜⠉⠉⠉⠉⠉⠙⣆⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠤⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠤⠤⣷
⠀⠀⠀⠀⠀⠀⠀⣷⠖⢷⠀⠀⠀⠀⠀⠀⠀⢰⠓⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢣⡀⠀⠀⠀⠀⣠⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢆⠀⠀⠀⠀⠀⢀⡞⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡞⠉⠓⢶⠖⠋⠙⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⡞⠉⠉⠉⠉⠉⠙⣆⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠾⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠴⠶⠶⠶⠶⠶⠶⠼⠟


⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣿⠿⣿⣿⣿⣿⣿

⠀⠀⣠⣾⣿⡿⡲⣄⣠⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣶⣄⡀
⠀⢠⠛⠉⠉⠈⠙⠾⠛⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣷⣦⠀⣠⣶⣶⣶⣶⣶⣶⣦⡀⢠⣶⣷⠀⠀⠀⠀⠀⠀⣴⣿⠛⠛⠛⠛⠛⠛⠋⢻⣿⣄
⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⣿⣿⠀⠀⠀⠀⠀⢰⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠈⣿⣾⠂⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡀⠙⠿⠿⠿⠿⠿⠿⠟⠁⣸⣿⣿⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠈⠋⣿⣿⣦⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠀⠀⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠙⢿⣿⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⣟⡷⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⢏⣀⣠⣿⣿⡿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣾⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣏⠉⠉⠉⠀⠀⠉⠉⢉⣹⣿
⠀⠀⠀⢠⣾⡿⠻⢿⡿⠟⢿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⢀⣿⣿⡇⠀⡠⢂⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⣰⣿⡿
⠀⠀⣼⣿⣿⠇⡴⠁⠃⠂⠸⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⢠⣾⣿⠟⠁
⠀⢠⣿⡟⠁⢰⡐⠂⠀⠀⡄⠈⢻⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠟⠁
⠀⢸⣿⣄⠀⢘⠀⠀⠀⠀⠱⠀⣰⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀
⠀⢸⡟⣿⣶⠏⢃⠀⠀⣀⠐⠐⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢻⣦⣀
⠀⠘⣿⣾⣿⣏⠤⠄⠲⠄⣂⢀⣹⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⢸⠇⠀⠉⠻⣷⣄⡀
⠀⠀⠈⢿⣿⣿⣷⣦⣼⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠴⣋⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⠀⠀⠀⠙⠻⠿⢿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⠉⢣⣄⠀⠀⣠⡄⠀⠄

⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⣙⣿⣿⣿⣿⡟⠻⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⢠⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠻⢿⣿⡟⠁⢀⣶⣤⣤⡀⠀⠀⠀⠀⢠⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣾⣿⣿⣷
⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⠦⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣷⣤⣶⣤⣴⡿⣿⣿⣿⣿⣿⣿⣿
⢹⡟⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣏⢿⣿⠏⠀⠈⢻⣿⢿⣿⣿⣿
⠀⠁⠀⠀⠀⠐⠂⠀⠐⠚⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⠫⠥⠤⣀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣙⣋⣂⣀⣀⣷⣽⣿⣿⣿⡟
⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣭⣥⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣆⠀⠀⠶⢿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠈⠙⠃⠀⠀⠈⠉⠙⠻⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇
⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢠⣤⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢛⣿⣿⣿⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀
⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⣀⣰⣦⣄⡀⠀⠀⠀⣠⣴⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⠿⠛⠀⠀⠘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⣿⣿⠀⠀⢀⣾⣿⣇⠀⠀⢠⣿⣿⡷⠀⠀⢰⣿⣿⡇⠀⠀⢠⣶⣶⣦⣄⠀⠀⢰⣿⣿
⠀⠀⠀⠸⣿⡿⠀⠀⠘⣿⣿⡿⠀⠀⠀⢿⣿⠃⠀⠀⠘⣿⣿⠇⠀⠀⠛⠿⠿⠿⠛⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⢸⣿⣷⠀⠀⠀⢻⣿⡇⠀⠀⠀⣿⣿⠁⠀⠀⠀⣿⣿⠄⠀⠀⠐⣿⣿⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠸⣿⡇⠀⠀⠀⠸⣿⠇⠀⠀⠀⢻⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠰⣿⣇⢠⣶⠀⠀⠀⠀⣠⡀⢸⣿⢀⠀⠀⠀⠀⠀⣴⣄⣿⣿⠀⠀⠀⠀⠀⠐⣿⣰⣿⡆
⠀⠀⠀⠀⠹⣿⣿⣿⣠⠀⠀⠀⠹⣿⣾⣷⣿⣃⠀⠀⠀⣤⣽⣿⣿⣿⣶⡄⠀⠀⠈⢳⣿⣿⣿⣃
⠀⠀⠀⠘⢿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⠿⡿⠋⠀⠀⠀⠙⢻⣿⣿⡿⠿⠆⠀⠀⠺⠾⢿⣿⠟⠋

⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣾⣿⡶
⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠈⠉⠉⣿⡿⠃⠀⠀⠀⠀⠘⠛⣿⣿⠟⠀⠀⠀⠀⠀⠸⢿⣿⠋
⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣀⡀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⢀⣾⣿⣇⣀⣀
⠀⠀⠀⠀⠛⢿⣿⣷⣦⠀⠀⠀⠀⠘⣻⣿⣿⣟⡀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠘⢻⣿⣿⠟⠁⠀⠀⠀⠈⢹⡟⠁⠀⠀⠀⠉⠁⣸⣿⡟⠁
⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⣼⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⢠⣿⡿⠿⠛⠛⠿⢃⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠈⣿⠿⠟⢋⣉⣤⣤⣶⣾⣿⣷⡀⢺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣿⣿⠇⠹⣿⣿⣿⣿⣿⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣈⣉⣙⢋⣠⣄⡙⠛⠻⠿⠟⠀⠹⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣦⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣧⠀⣉⣉⣉⣙⣛⠁⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⠻⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡛⣛⣛⡛⢛⣻⣿⣿⠿⠿⢿⡿⠿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣆⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣿⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⢀⣿⡇⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⡤⠞⠁⠀⠀⢀⣴⡿⠟⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⣿⠁⢀⠜⠀⢀⣤⣤⣾⡟⠉⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣶⡾⠟⠋⠁⠀⢸⡟⠀⠁⠀⠚⠁⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣧⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣀⣀⡀
⠀⠀⢰⠟⠀⠀⠀⣠⡟⠁⠀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⢠⣾⣿⡟⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠈⠁⠈⢳
⠀⠀⡻⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⡤⡼⣷⣴⣶⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⢻⣷⣴⣶⣶⠶⠶⠶⣦⣀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠃
⡠⠞⠁⠀⠀⠀⢻⠀⠀⠀⢀⠞⠁⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠘⠀⠀⠎⠀⠀⢀⣀⣠⣤⡶⠶⠟⣿⡟⠋⠉⠙⣿⣿⣆⠀⠀⠀⠀⠙⠷⠶⣤⡀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠏⠀⠀⢠⣿⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠘⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣤⣤⠤⠤⢄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⣿⣇⠈⠉⠛⠿⢿⣧⣄⠀⠀⠓⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⣰⠚⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣇⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⠿⢶⣶⣤⣤⣤⣄⣀⣤⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠉⢠⡞⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⢻⣆⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⣫⣿⣿⠟⠀⠀⣿⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠋⠁⣠⣾⣿⣿⠁⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣾⣿⠟⠁⢻⣇⠀⠀⠀⠈⠻⣆⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⣴⣿⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠉⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣸⣿⠇⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣆⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠙⠦⣀⠀⠀⠀⠀⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠞⢻⣿⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠷⠴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⡶⠒⠛⠛⠙⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠏
⠀⠀⠀⢠⡇⡰⣊⠩⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⡟
⠀⠀⠀⢸⡇⠁⠁⠀⠙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠘⠒⠒⠲⢦⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⠛⠉⠉⣹⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣹⠇⠀⠀⠀⡜⠀⣀⣀⡀⠀⠀⠀⣴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⢉⡟⠀⠀⠀⠀⣼⠃⠀⠀⢀⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣯⣤⣄⠀⠀⠀⢲⡏⠀⠀⠀⠀⠉⠉⢉⡽⠃⢀⢀⡼⠁
⠀⠀⠀⣿⣀⣠⣤⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⣏⣴⡶⠟⢋⡏⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣢⡟
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⣁⣀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠟⢛⡿
⠀⠀⠀⠀⠀⠰⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢠⠏⠀⠀⠀⠀⠿⠛⠒⡖⠀⢠⡟
⠀⠀⠀⠀⠀⢸⡧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡤⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠟
⠀⠀⠀⠀⠀⢸⡇⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋
⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠠⡇⢷⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡴⠶⠖⠒⡒⣲⠆
⠀⠀⠀⠀⠀⢰⣶⠛⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢀⡇⠈⢣⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⡶⠛⠁⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⢠⡶⠞⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡞⠉⠀⠀⢀⢂⡴⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣰⢏⠀⠀⠀⠀⢠⣿⣃⣀⣀⡀
⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⣭⠇⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠐⠉⠉⠉⣩⠞⠁
⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧⣤⡄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠠⣞⠃⠀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠓⢲⠀⠀⠀⠀⠀⣸⠀⢀⡀⠀⢠⠞⠀⠀⠀⢰⡯⠶⠖⠚⣿⠀⠀⠁⣴⠋
⠀⠀⠀⠀⠹⣆⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡜⡀⢸⠀⠀⠀⠀⠀⠙⠋⢹⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡄⠀⠀⠀⠀⠀⢀⡟⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠹⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡇⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⠼⣷⣶⣶⣾⣿⣍⣛⣿⣿⠯⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣂
⠀⠀⠀⠀⠀⠀⣈⠉⠛⠻⠛⢉⣀⡦⠤⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠴⢷⣤⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⣾⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⢠⣄⣠⣀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⠁⠁⠀⠀⣠⣼⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠂⠀⠂⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣿⣥⣵⣄⡐⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠳⣤⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣠⠜⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢠⣼⣿⣇⡂⣠⡇
⠀⠠⠀⠀⠀⠀⠀⠀⢠⣤⠼⠱⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⢹⣷⣦⡀⠀⠀⠀⠸⡈⠀⠀⠀⠉⠙⢿⣿⠙⣿⠁
⠀⠀⠀⠀⠀⡀⠾⢦⡸⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠑⠀⠀⠀⠀⠘⣆⢀⡀⠀⠀⢨⣧⡤⠁
⠀⠀⠀⠀⠀⠀⠤⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠙⠻⠦⠴⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⡰⢹⢹⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⣔⠁⡌⠈⡆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠆⠩⠒⠤⣀⡀⠀⠀⠀⠘⠀⠀⢰⠁⢣⡥⠖⠗⠢⢵
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⠲⢄⡀⢠⢻⠀⠀⠀⡇⠀⠀⡆⠀⡸⠀⢸⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠤⣀⡜⠀⠀⠀⠈⢹⠈⡄⠀⢰⠁⠀⠸⠀⢠⠃⢀⠇⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⡇⠀⠀⠀⠀⢸⠀⡇⠀⡘⠀⢀⠇⠀⡜⠀⡸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⡀⠀⠀⠀⢸⠀⢰⠀⠇⠀⡸⠀⢠⠃⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⠀⢸⠀⢸⢸⢀⢀⠇⠀⡌⠀⢸⠀⡸⣀⡠⠤⢲⣒⡶⠶⡄
⠀⠀⠀⠀⢰⡷⢖⡶⠒⢾⡀⠸⡄⠀⠀⢸⠀⠀⡇⡂⢸⠀⢰⠁⠀⡆⢠⡏⣁⠤⠒⠉⠦⣰⣁⣱
⠀⠀⠀⠀⡸⠘⡀⠉⡲⡅⣇⠀⢧⠀⠀⢸⠀⠀⣿⣇⣷⡊⠉⠑⣼⠤⠺⡉⠀⠀⠀⢀⡔⣡⡖⠁
⠀⠀⠀⠀⣧⠤⠷⡊⠀⠘⣸⡀⠸⡄⠀⢨⡆⠀⢻⠁⠸⣈⠗⠉⢸⠀⢀⠽⡄⠀⢠⠎⡠⠋
⠀⠀⠀⠀⠈⠳⣄⠙⢆⠀⠘⣧⣀⠧⠄⠚⠓⠛⣚⣶⠚⠉⠑⠒⠲⡛⠁⠀⢣⢠⢏⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠑⣤⡓⠉⠁⢀⣀⠤⠔⠚⠉⠀⣈⡆⠀⠀⠀⠀⢣⠀⠀⡰⢋⢫
⠀⠀⠀⠀⠀⠀⢀⡼⢀⡨⠓⡍⠁⠀⢀⣀⠤⠒⠉⢰⠃⠀⠀⠀⠀⠈⡆⡴⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠺⣾⠥⠤⠤⡵⠐⠊⠉⣀⣠⠤⠖⠙⣏⠉⠁⠒⠒⣒⠟⣃⡩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣴⠥⠴⠾⣏⣁⠈⠑⠢⢄⣈⣆⢀⠤⢚⡡⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢌⡽⠕⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣤⡀⠀⠀⠀⠀⠀⣀⢴⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⡠⠊⢇⡜⠉⢢⡜⠑⢄⠀⠀⠀⡾⢤⠗⠒⠒⣥⠼⡆⠀⠀⣰⣊⢁⠼⢄⢉⣢⠀⠀⠀⢀⡞⢅⡠⠷⢄⡨⢳⡀⠀⠀⢸
⠀⠀⠈⠫⡉⠹⡉⠉⢩⠏⢉⠝⠁⠀⠀⡇⢸⠀⠀⠀⢸⠀⡇⠀⠀⡇⠀⡇⠀⠀⡇⢀⠀⠀⠀⣼⢠⡏⠀⠀⠀⢱⡄⣧⠀⠀⢸
⠀⠀⠀⠀⠙⢦⣣⠀⣎⡴⠁⠀⠀⠀⠀⣇⣸⡀⠀⠀⣼⣀⡇⠀⠀⢧⠤⠣⣀⡠⠣⢤⠀⠀⠀⠸⡀⡱⢄⣀⡠⢎⢠⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠙⢤⣏⣉⣉⣆⠜⠁⠀⠀⠀⠑⠦⣸⡠⠖⠁⠀⠀⠀⠀⠙⠲⠤⣯⠤⠔⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠐⠫⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠆⠀⠀⠀⠀⣰⣿⣿⡶⠛⠀⠀⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠼⢿⣿⡿⠋⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢈⡽⠟⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢀⠐⡁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠁⠌⠁⠀⠀⠀⠀⠀⠐⠁⢠⢌⠁⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⢃⠔⠃
⠀⠀⠀⠀⢀⢀⡘⠂⡰⠀⠀⠀⠀⠈⠀⡪⠐⠁⠀⠀⠀⠀⠈⣱⠃⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⢀⠔⠁⠈⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢴⡩⠇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠠⣸⣁⣀⡀⠀⠀⠀⡠⠋⢠⣎⠁⠀⠀⠀⣠⠊⢘⡂⠖⠀⠀⠀⠀⢠⠎⣠⠄
⠀⠀⠀⠀⠰⢓⢖⡴⠋⠀⠀⠀⠈⣩⡿⠒⠁⠀⠀⠀⠀⣩⠏⠋⠀⠀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠰⠎
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣽⣯⣿⢷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⢀⣀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣿⣿⡏⢘⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⡿⢿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣾⣿⣿⣿⡆⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠾⡿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⠿⡿⠟⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠒⡗⠂⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⡀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠁⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠒⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠰⠀⡀⢀⠰⠆⠀⢾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠰⠆⠀⠀⠀⠰⠄⠘⠿⠿⠿⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⡀⠀⠀⠄⠀⠀⢀⣠⣤⣤⣀
⠀⠈⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠠⠀⣸⣿⣿⣿⣧⠀⠐⡂⠀⠀⠀⠀⠐⢯⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⠐⠀⠸⠿⠿⠿⠿⠿⠀⠀⠂⠀⠐⠂⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠐⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠆⠀⠈⠻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣎⠁
⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀
⠀⠀⠀⠀⠐⠛⠛⠋⠉⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⡶⠾⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣀⣀⣀⡄⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠉⠉⢀⡇⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿
⠀⡀⠀⣠⡶⢻⡄⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠙⣦⠄⠀⠀⠀⠀⠀⠘⣿⠙⠛⠳⠿
⠀⠱⠞⠁⠀⠈⢷⣀⣴⠟⠉⣷⠀⠀⣠⠔⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⢠⣤⣄⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠘⣧⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡇
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⡈⠀⠠⠄⠈⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⠐⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⢀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠠⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠀⠒⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠁⠀⠁⠈⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⡀⠐⠀⠀⠀⠀⠈⠆⣀
⠀⠀⠀⠠⠐⠈⠠⠄⠀⠀⠀⠄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠂⢀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠄⠀⠀⠀⠠⠀⠤⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠤⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠐⠂
⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⠀⠀⠀⠂⠀⠓⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣿⣯⣿⣋⣏⣽⣹⣼⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠂⠀⠀⠁⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⢰⣿⣶⡆
⠀⠀⠀⠀⠀⠀⣼⣿⡟⢁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣾⣿⠟
⠀⠀⠀⠀⠀⣼⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣼⣏⣀⡀⠀⠀⠀⢰⣿⣯⣤⡄
⠀⠀⠀⠀⠰⢫⣿⣿⢏⣠⠄⠀⠀⠀⠀⢰⡿⢀⣠⡄⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠐⠛⣻⡟⠀⠀⠀⠀⠞⢻⣿⡿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⢛⣿⣿⠃⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠚⢁⣿⣿⠃⠀⠀⠀⠀⠀⠟⠋⣽⡟⠀⠀⠀⠀⠀⣸⣿⣿⡶⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣸⣿⣃⡀
⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠟⣿⡿⠁⠀⠀⠀⠼⠿⣿⠁⠀⠀⠀⢀⣿⣿⡟⠁
⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣹⡟
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣶⣶⣶⡶
⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⣼⣿⣿⣿⣶⡦
⠀⠀⠀⠀⣰⣿⡟⠀⠀⣀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣀⠀⠀⠘⠛⢻⣿⣿⣿⠁
⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣤⡄⠀⠀⢀⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠛⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣷⣶⠂
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠾⢿⣿⡿⠁⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⣿⡶⠀⠀⠀⠀⠉⢹⣿⣿⠃
⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢉⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⣴⣶⡟⠉⠹⣿⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢊⣉⣩⡍⠙⠛⠻⣆⠸⣿⣧⣼⣿⣗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢁⡒⠛⠛⠿⢿⣧⢠⣆⣿⡛⣯⡭⠏⠛⠉⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡈⣽⣵⣁⡃⢀⣸⣿⣦⡿⣿⣿⣷⣶⣶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⢿⢺⡇⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣸⣘⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⢁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡟⡕⡻⢻⣿⣿⣿⣿⠙⢿⣍⠢⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⢏⠌⠀⠉⣟⢅⠙⣆⠻⣢⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡎⣀⡀⢀⣬⣺⣶⣌⣷⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⣶⣾⣿⣿⣿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡿⣿⢸⣿⡟⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣷⣿⣽⡿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠹⡇⣿⣿⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⠀⢘⡇⠻⠋⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⡇⠄⢸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⠇⠀⢸⡄⡄⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⢸⠀⠀⠈⡇⡇⠀⣿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣷⡇⠀⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠘⣿⠀⠘⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢹⠀⠀⢸⡼⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣃⣀⣀⣀⣀⣀⣈⣀⣀⣀⣓⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⢿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣻⣷⣿⣼⣿⣷⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣿⣿⣿⡿⣫⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣯⣻⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⢟⣽⣿⣿⣿⢿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⢞⣽⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣽⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣝⢿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣮⣿⣿⢻⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⡿⣿⣯⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⡟⣿⣯⣿⣿⣿⣯⣟⣛⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣻⣿⣿⣿⣟⣿⣿⢿⣟⣿⣿⣿⣿⣿⢽⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡯⣿⣿⣿⢿⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣯⢟⣿⣿⡿⣿⣿⣾⣟⣿⣷⣽⣿⣿⣿⣿⣿⢿⣿⣿⡿⣻⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣞⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣵⣿⣿⣿⣿⡿⣟⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣟⢿⣺⣿⢾⣿⣷⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣾⣿⣿⡟⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡷⠂⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⣼⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠠⢾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢶⠟⢷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⢛⡥⠊⡁⠀⠀⠙⠮⡙⢿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⢛⠟⠷⣏⣠⠖⣉⠴⠊⠀⠀⠀⠀⠀⠈⠲⣝⣿⠶⠛⢟⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠉⠀⠂⡼⣇⠀⠀⠀⠈⠙⠳⠴⣁⠀⠀⠀⢀⣠⣴⡚⠉⠀⠀⠀⢈⠷⡄⠀⠈⠙⠻⣶⣤⣄⡀
⠀⠀⠀⠀⣀⣤⣶⣾⢟⣽⠟⠁⠀⢀⣠⠞⠀⠈⢱⣄⠀⠀⠀⠀⢀⡠⠟⣶⣾⣿⣧⣌⠻⣦⠀⣠⠞⠁⠀⠘⢦⠀⠀⠀⠙⢶⣭⡛⢷⣦⣄⡀
⣀⣤⣶⣿⣿⣿⣿⣶⡟⠁⠄⠂⠉⣠⠏⢀⠤⠂⠁⠈⠓⣄⡤⠖⠉⠀⠀⣿⣿⣿⣿⣿⣷⣬⠞⠁⠀⠑⠂⢀⠀⠱⡦⠀⠀⠀⠙⢿⣿⠶⢬⣽⣷⣦⣄
⠹⣿⣿⣍⠛⠻⢿⢷⣴⣒⣒⠒⠒⠳⣎⠁⠀⠀⣀⠤⠚⠉⠳⡄⠀⠀⠀⣿⣿⣿⣿⣿⠟⠓⢕⠠⢀⠀⠀⠀⢈⡲⠞⠐⣀⣤⣤⡿⢻⣶⣶⣾⣿⣿⡟
⠀⠙⣿⣿⣷⣄⠸⣆⠈⠻⣿⣿⣷⣶⣬⣷⣔⣈⠀⠀⠂⠀⠀⠘⢦⠀⠀⣻⣿⣿⡿⠋⠀⠀⠀⠑⢄⣈⣱⣶⣯⣶⣾⣿⣿⠟⠁⢠⣿⣿⣿⣿⣿⠏
⠀⠀⠘⢿⡿⣿⠿⣿⣆⣀⡈⠛⢿⣿⣿⣿⠀⠙⢿⣶⣦⣤⣄⣀⠀⠱⡄⢻⡿⠋⠀⣀⣀⣤⣴⣶⣿⠟⠁⢹⣿⣿⡿⠟⢁⣀⣤⣿⣿⣿⢟⣿⠏
⠀⠀⠀⠈⢿⣮⠢⠈⢿⣿⢿⣷⡶⣽⣿⡧⣀⠀⠀⠙⢿⣿⣿⣯⠉⢓⣾⣾⡗⠓⠉⠁⣿⣿⣿⠟⠁⠀⠀⢈⣿⡯⠴⠚⠉⢡⡿⠏⡴⣣⣾⠃
⠀⠀⠀⠀⠈⢻⣆⠀⢨⣿⣆⠉⠛⠷⣾⣿⠀⠉⠑⠒⠤⠙⣿⣿⣶⣿⣿⣿⣿⣷⣦⣼⣿⣏⡀⠤⠒⠈⠁⣰⡏⠀⠀⠀⣰⡟⣠⢎⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠻⣧⡐⣇⢿⣦⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢹⠉⠻⣿⣿⣿⣿⣿⡿⠋⡸⠀⠀⠀⠀⠀⢠⢻⠇⠀⡀⢠⡟⣠⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣹⡌⢿⣆⠀⡀⠘⡏⣆⠀⠀⠀⠀⢸⠀⠀⠈⠛⢿⡿⠋⠀⠀⡇⠀⠀⠀⠀⢀⠇⡾⠀⠀⢠⡟⣠⡿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣽⠈⢻⣆⡇⠀⢻⡸⡄⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠀⠀⠀⡇⠀⠀⠀⠀⡜⣸⠃⠀⢠⡟⣰⢏⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣢⣻⣇⠀⠈⣧⢳⠀⠀⠀⠀⣇⠀⠀⠀⠀⠂⠀⠀⢸⠁⠀⠀⠀⡸⢰⡟⠀⢀⣾⡽⣡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⣿⣆⠀⢸⡎⣇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⢁⡿⠀⢀⣾⢋⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡌⢿⣆⠀⢿⡸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠌⣾⠁⢀⣾⢡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡻⣆⠈⣧⢱⠀⠀⢸⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠐⣼⠃⢀⡾⣡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣆⠸⡆⣇⠀⠈⡇⢇⠀⠈⠄⠀⢸⠁⡐⠀⣼⠏⢀⣼⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⢻⡼⡆⠀⢻⠈⠆⠸⠁⠄⣼⢠⠇⢠⡟⢠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣷⢻⡀⢸⡆⠘⢄⡆⢀⡇⡜⢀⡿⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⢧⠐⣧⠀⢸⡇⣸⠃⠀⣼⣧⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡆⢻⡄⢸⡅⡟⠈⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡜⣧⢸⣿⡇⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⠀⢀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣃⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⡆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⡏⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⠶⠶⠟⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⣿⣄⠀⠘⠿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⠾⠀⢀⣀⣼⠇
⠀⠀⠀⠀⠀⠈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠐⠲⠶⠤⠤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡶⠛⠉⠁⠀⠀⠀⠉⠙⢳⣄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠻⢷⣄⠀⠀⠀⠘⣷
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⠇⠀⠀⠀⠀⠙⣧⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣸⠇
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠃⠀⠀⢠⡟
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⣀⡴⠟⠁⠀⠀⢠⡿⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣴⠟
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁
⢰⡟⣿⠀⠀⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠈⣿⣛⠛⠛⠋⠉
⠸⣷⠇⠀⠀⠀⠸⣄⣀⣠⠇⠀⠀⠀⠀⢸⡁⠀⠈⣷⠀⠀⠀⠀⢰⡇⠀⠀⢙⡇⠀⠀⠀⠀⢹⡉⣷
⠀⣿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⠀⠀⠀⠙⠲⠶⠛⠀⠀⠀⠀⠀⠀⣿⠋
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⢸⡏⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠺⣧
⠀⠈⠻⠶⣶⣶⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠶⠿⠋

⠀⠀⠀⠀⠰⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠁⣮⠊⠀⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⡀
⠀⠀⠀⠀⠀⠚⠛⣤⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⡄⠑⠂⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇⠰
⠀⠀⠀⠀⠐⢲⠂⠸⠿⠷⠇⠀⠁⠀⠀⠀⠀⠀⠀⠊⠀⠰⡀⠀⠄⢀⠀⢤⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢈⠒⠀⠀⠀⠀⡀⣐⠀⠀⠀⠀⠀⠈⡐⠰⠀⠀⠀⠰⠱⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨
⠀⠀⠀⠀⠠⢾⡌⠄⠀⢀⡀⣘⠋⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠀⠀⠀⠀⠀⠀⠀⠂⢜⠀⢀⣀⡁
⠀⠀⠀⣠⢀⡉⠡⠿⢐⠃⠬⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠙⠇⢤⡤⠹⠒⠶⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠀⠀⠀⠀⠁⣀⠀⠀⢀
⠀⠀⠀⠘⠐⠀⠀⢵⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠠⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠁⠀⠀⠀⠀⠉⢀⣰⠀⡌⢉⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠔⣰⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡶⠂⠀⠈⢻⠷⠄⠀⠀⠀⢰⡒⠺⠉⠀⠚⢉⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢀⣄⠀⠀⣤⣠⡄⠀⠀⠀⠀⢨⡀⣄⠀⠀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡟⠉⢀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠉⠳⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⣄⠀⠀⠙⠀⠀⠀⠀⠀⠈⠧⢀⣄⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


⣿⠿⠿⠿⡿⣟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣻⣿⣿⣻⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣰⣦⠀⡄⠀⠀⠀⠠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⣴⢿⣿⠿⣿⡳⡄⠀⠀⠀⢀⣼⣏⠀⠀⠀⠈⣼⡿⣠⣶⠐⡟⠿⡻⣿⡆⠀⠀⢱⡻⢉⣾⣾⣄⠀⠀⠀⠀⢀⣾⡟⣭⣱⡄⠀⠀⠀⢠⣿⡀
⠀⠀⢴⣷⣴⣾⢀⣼⣷⣧⠀⠀⠐⢿⣿⡯⣄⠀⠀⠠⣬⣛⠀⢸⣄⣴⡾⣾⣿⠃⠀⢰⣾⣁⠈⢾⣿⣿⡅⠀⠀⠀⣖⣴⣿⣷⣿⣿⠀⠀⠀⣼⣯⡁
⠀⠀⡖⢻⡿⠀⢺⣿⣿⣿⣄⠀⢠⣾⠋⢻⣕⢀⣿⣦⠛⠋⠀⣰⡍⣻⣴⡾⠃⠀⠀⠀⣙⡷⠒⢿⣿⣆⣿⡄⠀⠀⢻⣇⣯⣍⣿⠿⣷⣶⣦⡇⠀⡁
⠀⠀⡔⣸⣇⣤⢾⡛⠭⣻⣿⣿⣿⡅⠀⠀⠙⣷⣿⣿⣁⠀⣨⠻⠿⡿⡟⠁⠀⠀⠀⠀⠸⡿⣶⣴⡿⠳⠁⠀⠀⠀⡠⠟⠀⣿⣈⡾⠻⣿⣿⣽⣶⣥
⠀⠀⠀⠈⡯⢫⣄⠀⠰⡌⢻⣿⡿⠆⠀⠀⠀⠈⣿⣿⠿⡿⠧⣹⣾⠏⠀⠀⠀⠀⠀⠀⠐⠘⢻⣿⠊⠀⠀⠀⠀⠀⡇⢄⠀⠹⡻⡿⠾⡦⣊⣁⠰⠟⠂
⠀⠀⠀⠀⣿⣈⣗⣇⡵⢣⠎⠋⣹⡀⠀⠀⠀⠀⠐⡇⠀⠀⣀⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠹⠈⢳⡶⠃⠠⠜⢛⢽⣅
⠀⠀⠀⠀⢰⣈⣯⠿⠒⠋⣀⢐⣯⣿⡄⠀⠀⠀⠀⢣⣤⠴⢃⣯⣿⣦⡀⠀⠀⠀⠀⢤⡊⠀⠈⠀⠀⠀⡄⠀⠀⠀⠈⡇⠛⢐⣈⣠⣴⣋⣆⣿⣦⡀
⠀⠀⠀⠀⠈⠻⠇⠀⠀⠸⠙⣾⣿⣿⣿⡀⠀⠀⠀⠀⣧⣄⣘⣽⣿⣿⣿⣆⠀⠀⠀⠿⢢⡄⡀⠄⡦⡤⠁⠀⠀⠀⠀⠈⠙⠛⣹⣿⣿⣿⢿⠿⣧⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⠛⡿⠒⠀⠀⢨⣽⣏⡌⠛⠃⣿⣿⣆⠀⠀⠀⠈⠙⠛⢱⠂⣜⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠛⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⣽⣿⣿⣤⣤⣤⠀⠘⣯⣛⡔⣡⢰⣿⣿⡟⠀⠉⠀⠙⢲⣄⠂⢈⣩⢣⠄⣠⣤⡀⠀⠀⠈⠁⠰⠥⠄⢚⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠀⣇⠀⠁⠀⠀⠚⣷⡌⠞⢿⠛⡍⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠉⠢⣅⠠⢀⠀⢠⣤⣶⣿⣆⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠁⠀⠀⠀⠀⠀⠉⠀⠀⢠⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠘⠶⣭⡀⡀⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⠀⠀⡄⠀⡆⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⣿⣴⣤⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣸⣾⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠀⢸⠀⠀⠀⣨⠓⢾⠁⠀⠀⠀⠀⠀⠀⠐⢇⠀⠀⠀⢤⣙⢧⠀⠑⠢⣌⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠁⠀⠀⠀⢿⠈⠓⠀⠀⠘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢿⠂⠀⠀⠀⠀⠀⠀⠚⠀⠐⠐⠀⠐⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠀⠈⠀⠀⠃⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠇⠀⠇⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠰⠀⠀⠈⢷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡇⠃⠀⠀⠀⠀⠀⠀⢨⢰⠃⠀⠀⠠⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢧⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⡶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣗⡊⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⣶⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⣶⡂⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣤⡶⠀⣾⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣄⡀⠀⠉⠹⠟⠽⣿⣿⡿⠟⠘⢿⣿⡿⠈⠁
⠀⠀⠀⠀⢀⣼⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣴⣿⣏⠀⣴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⡿⣻⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣿⣇⣴⣶⣶⣦⣤⣀⡀⢀⣸⠄
⠀⠀⢀⡟⢰⣿⢿⡿⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡀
⠀⠀⠸⡀⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⠟⣽⠟⡁⡈⠉⠀⠉⠛⢿⣿⣿⡿⠿⠋⣼⡿⢫⠟⠁⠘⣿⣿⣿⣿⣿⣄
⠀⠀⠀⢳⣿⣿⣿⣿⢇⡀⠀⠀⢸⣿⣿⣿⢁⣴⡏⠀⠻⣿⠳⢿⡦⠶⢤⢛⠛⢷⠐⠚⠉⣠⣤⠶⠖⢿⣿⣿⣿⣿⡻⢿⣧
⠀⠀⠀⢸⣿⡿⣿⣿⣿⣯⡆⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠸⠎⠀⠀⠀⠀⣼⣯⡷⢲⣧⣼⣿⣿⣿⠇⠁⠀⢻⣧
⠀⠀⠀⠘⣿⠀⣿⣿⣿⣿⣧⠀⠀⠈⠘⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢸⣿⣿⣿⠟⠀⠀⣆⠀⣿⡆
⠀⠀⠀⠀⢹⡆⣿⣿⣿⣿⣿⣤⡄⣼⣷⠙⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠃⢀⡄⠀⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⣀⠀⠀⢤⣴⣿⣿⣾⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡸⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣟⣿⡏⢷⡀⠀⠀⠀⠀⠰⡙⠳⢶⣤⣄⣠⠔⠉⣠⣿⣷⣶⢀⣤⣦⣬⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⡘⣿⡄⠱⣄⠀⠀⠀⠀⠈⠀⠠⠉⡉⠀⠀⣴⣿⣧⣄⠻⣿⣿⣽⣿⣿⡿⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠿⣧⡌⠛⠓⠘⠦⡀⢀⣴⣆⡔⣠⠆⣀⠂⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⢂⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣙⣿⡿⢐⣇⢰⣿⣿⣿⣿⣿⢟⣽⠿⠋
⠀⠀⢀⣠⣴⣾⠟⣻⠇⣾⠃⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⡶⠶⣒⠉⠀⠙⣿⡧⡿⠈⠁⠁⠀⠄⠀⡀⠀⠀⠀⠤⠀⢤⡄⡀
⣴⣾⠿⡛⣭⣶⣾⠏⣸⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⣿⣧⠀⡠⠛⠉⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠄
⣿⣧⣱⣼⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⣄⡀⠘⠿⠏⠀⠀⠀⠀⠀⠀⢠⡇
⣿⣿⣿⣿⡿⠛⠁⡀⠀⠀⠄⠀⠀⠀⠀⠿⠷⠦⠀⠀⢺⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⠏⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⣿⠟⠁⠀⠐⠀⣹⡇⢀⠇⠀⠀⠀⠀⠀⠀⢐⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡾⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⡟⢷⡸⠀⠀⢀⣼⡟⠃⢴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡷⡿⢳⠀⠀⠀⠀⠀⠀⠸⣦⣄
⠀⠀⠀⠀⠀⠈⣽⣿⡇⠀⠰⠿⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢧⡿⠛⡇⠉⠀⠀⠀⠀⠀⠀⠀⢿⣏
⠀⠀⠀⠀⢰⡿⢻⣷⠀⡼⢋⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣯⡿⠚⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣸⠀⢸⣿⡶⠁⡿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣥⡿⠺⠄⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣶⡆⣿⣷
⠀⠀⡿⠀⣿⡟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⡿⣏⠠⠔⠁⠀⠀⠀⠀⠀⢀⢀⣠⣶⣆⣼⣿⡇⣿⣟⡴⠃⡀
⠀⠀⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠛⠁⢠⣤⣀⣀⡀⣤⢠⡄⢸⣿⣿⣿⣿⣿⣿⣿⢀⣿⣫⡴⠟⠁
⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠀⠀⠀⣴⣿⢻⠋⠒⣰⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣄⡀
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡇⠀⠀⢠⣸⣷⢾⠃⢠⣴⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀
⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢷⡄⠀⢸⣧⣽⡟⠋⢠⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣍⡉⠉⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡱⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⡴⢁⡇⢳⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠫⠤⠤⢀⡜⠀⢸⠃⢸⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⡟⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡸⠱⡄⡸⠀⣠⣇⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢣⠈⠓⠪⠙⠲⢤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠃⠀⢘⠗⠋⢰⠃⠈⢑⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡎⠙⠦⣄⡀⠀⡼⢻⠀⠀⠀⠀⡎⠀⠀⠀⡞⠀⠀⡼⠀⠀⡞⠀⢀⢎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⡼⠀⠀⠀⠀⠉⢻⡇⢸⡀⠀⠀⢠⠃⠀⠀⢰⠃⠀⢠⠃⠀⢰⠁⠀⡞⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠑⢾⠁⠀⠀⠀⠀⠀⢸⡇⠈⡇⠀⠀⡸⠀⠀⢀⡏⠀⠀⡞⠀⠀⡟⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⡆⠀⠀⠀⠀⠀⠘⡇⠀⢧⠀⠀⡇⠀⠀⣸⠀⠀⢸⠃⠀⢸⠁⢠⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢸⠁⠀⢀⡇⠀⠀⡏⠀⠀⡎⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⡇⠀⠀⠀⠀⠀⡇⠀⠸⡆⡞⠀⠀⣸⠀⠀⢸⠁⠀⢸⠁⠀⡜⠀⠀⢀⣀⣤⡤⠤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢸⡄⠀⢹⡀⠀⠀⠀⠀⣷⠀⠀⣧⠇⡇⢀⡇⠀⢀⡏⠀⠀⡟⠀⣰⠥⠖⠚⠉⣀⢼⡖⠚⢉⡞⢹⡀
⠀⠀⠀⠀⠀⠀⡿⣏⠳⣝⡋⠉⢹⢧⠀⠈⣇⠀⠀⠀⠀⣿⠀⠀⣿⢰⡁⢸⠀⠀⣸⠁⠀⢰⠇⢠⡷⢀⡠⠔⠊⠁⠀⠙⢦⣮⠤⢴⠇
⠀⠀⠀⠀⠀⢀⡇⠸⡄⠀⠉⡳⣏⢾⡄⠀⢹⡀⠀⠀⠀⣿⠀⠀⢸⣧⢇⣼⣒⠉⠀⠙⢦⣼⡤⠾⣎⠁⠀⠀⠀⠀⠀⣠⠋⣠⡶⠁
⠀⠀⠀⠀⠀⢸⡃⣀⣱⡤⠊⠀⠘⡄⢷⠀⠈⣇⠀⠀⠀⢹⠀⠀⢸⡿⠋⠸⡌⠓⡦⠖⠋⢱⠀⠀⠈⣦⠀⠀⠀⡀⡴⠁⣸⠏
⠀⠀⠀⠀⠀⠘⢯⡉⠀⠹⣄⠀⠀⠘⣼⡆⠀⢹⡀⠀⢸⣻⣀⣀⡇⡇⠀⣀⣷⣾⣀⡀⠀⢸⣀⡴⠊⠉⡇⢀⢀⡞⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢦⡀⠀⢘⣿⡤⠤⠓⠚⠉⠁⠈⢉⣉⡽⢿⠉⠀⠀⠀⠉⠉⢻⡁⠀⠀⠀⢹⢀⡞⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣤⠷⠚⠉⠁⠀⠀⣀⣠⠤⠖⠚⠉⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣰⠛⡉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠉⢲⣤⠖⠚⠉⠁⠀⠀⠀⢀⣠⠴⠚⢩⡇⠀⠀⠀⠀⠀⠀⠸⡆⠀⣰⠃⠀⠃⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣃⠴⠚⠁⠈⡆⠀⠀⣀⡤⠖⠚⠉⠀⠀⢂⣼⣀⣀⣉⣐⣀⣀⡀⠀⢳⣼⣁⣠⠤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣓⠒⠒⠒⠒⡾⠚⠉⠀⠀⣀⣠⣴⠶⠛⠉⠈⢧⠀⠀⠀⠈⠉⠉⣩⢟⡩⣔⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣜⣁⡤⢴⣞⡛⠁⠀⠈⠙⠲⢤⣀⠈⢧⠀⠀⣠⠴⠋⣀⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⣀⠈⠙⠺⡷⢊⣡⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠋⠉