Snowman Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡆⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠛⢉⠉⠉⢉⠻⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠀⠀⠘⠛⠀⣀⠘⣃⣠⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠰⢂⡀⠙⠛⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡤⣤⣀⣤⣤⠀⣅⣁⣤⣦⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠓⠦⢤⣀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⢷⣿⣾⣿⣦⠀⣀⣤⠶⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣐⠉⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⢻⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡉⠻⠒⠀⠀⠀⠀⠀⠀⠈⠁⢹⣧⢻⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠶⠈⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠄⣀⣠⡀⢀⠀⠀⠀⠀⠛⠀⠈⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠭⠛⠋⠉⠉⠉⠉⠈⠋⠙⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠠⣴⣶⣿⠶⣾⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣒⡈⠠⣺⣿⣿⣿⡶⣬⣄⣂⣀⡀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠶⠞⠉⠐⠋


⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠋⠀⠸⣿⠆⠀⠀⢾⡿⠀⠈⢻⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣀⣤⣤⡴⣄⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⡇⠀⠈⠉⠛⠛⠷⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡟⠀⠀⠀⠀⢧⠀⠀⠐⠦⠤⣤⡤⠤⠖⠂⠀⢠⠇⠀⠀⠀⠘⡇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠿⣧⡀⠀⠀⢰⡾⡷⢶⣦⣤⣤⣤⣤⣤⣶⣶⠶⠿⣶⠀⠀⠀⣠⡿⠷⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢸⣯⣭⣭⣭⣇⣀⣀⣀⣀⣮⣭⣭⣭⣿⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⣿⣰⣽⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⢹⣼⡇⠀⢠⡶⣦⠀⠀⠀⠀⠀⠈⠁⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⣾⣿⡇⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣻⣻⡇⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⠉⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠸⣧⡿⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠦⣄⣀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠐⡀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠠⠊⠱⡁⠂⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠶⠦⠚⠒⠲⠶⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠢⠀⠀⣁⡤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠚⠉⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠒⠚⠉⠉⠉⠻⡒⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⣠⠤⠒⠊⠩⠥⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢱⡀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣤⠚⠉⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢰⣖⠄⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡓⠦⠤⣀⣀⣀⡀⣀⣀⣀⡠⠤⠖⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠳⢤⣀⣀⡉⠉⡁⢀⣀⣀⠤⠲⡅⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡼⢩⣏⡏⠉⠉⠁⠀⠀⠀⠘⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠀⡼⠀⡾⠰⡇⠠⠈⠀⠀⠀⠀⠀⢹⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⢠⡇⠀⣧⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠋⢸⣠⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠉⠈⠙⠢⡀⠀⠀⢀⣀⠎⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⣀⣀⡤⠏⠉⠉⠉⠙⠦⣤⣀⣠⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣯⣭⣭⣭⣭⣤⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⠿⠿⠛⠻⠭⠽⠯⠭⠟⠓⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣠⣴⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠿⣦⠀⠀⠀⠀⠀⢰⠟⠛⠣⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⢀⣿⠀⠀⠀⠀⠀⢹⣆⣀⣰⠿⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⢙⡛⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣷⠀⠀⠀⠸⡀
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⠼⠿⠿⠟⠛⢀⡄⠀⠀⠃⢀⣤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⢀⠋⢀⣶⣠⣇⢀⣀⣀⣶⣴⣷⣶⡶⠟⢻⠏⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣿⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠰⡃
⠀⠀⠈⠛⠛⠛⠛⠋⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡶⠟⠟⠋⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃⢰⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢣⡀⠀⠀⠀⠀⠙⠛⠷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠟⠋⠀⣠⠏⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⡶⠖⠶⠶⠶⢶⡶⠾⠿⠟⠛⠛⠉⠁⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣄⣀⣠⠀⠀⠀⠀⠀⣯⣤⣤⣤⣶⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⣿⠉⠁⢸⣿⣷⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⡿⠿⡿⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡜⠀⠀⠀⠀⠀⢻⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢰⡶⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⢸⡇⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠈⣇⠰⣿⣿⣷⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⡇⠀⠀⠀⠀⠀⠸⣧⠀⠀⢻⠀⠙⠛⠋⠀⠀⠀⠀⠉⠛⠒⠶⠶⠚⠛⠋⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⠶⠶⠶⠞⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⣄⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣴⢿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣿⣧⣽⡾⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠶⠶⠶⠿⢛⣋⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠟⠿⠟⠛⠛⠁⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠞⠛⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⡙⣿⠛⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠤⠄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⢀⠔⢯⠀⠰⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠀⠀⣀⠠⠄⠀⠤⠤⢠
⠀⠀⠀⠐⠁⡄⢈⠅⢄⢀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⡀⠁
⠀⠀⠀⠀⠀⠈⠢⣳⡄⣐⡥⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠑⠙⠒⠤⢄⣀⠀⢠⡴⠗⢀
⠀⠀⠀⠀⠐⠠⡀⢠⠛⠁⢀⠄⠊⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠂⠀⠀⠀⠀⢒⠂⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠑⢇⣀⠀⠀⠀⣰⠿⡀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠸⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠃⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠃⠁⠀⠀⠉⠁⠠⠄⠔⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⠄⠀⠀⠀⠀⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⣀⡤⣀⠦⠘⠊⠀⡀⠀⠈⠑⠀⢀⡂⠔⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⢁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡄⠈⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⡃⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⠁⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⡁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠛⠓⠦⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣀⡀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠈⠁⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠉⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⢀⣸⠀⠀⢤⠀⠀⠀⠀⠀⠠⠤⠀⣀⠀⠀⢀⡀⡀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢂⠀⠀⠀⠀⠒⠀⠀⠉⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠉⠀⠀⠀⠀⡦⠀⠀⠰⠂⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⣠⠄⠒⠢⢄⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⢠⠁⠈⠉⠀⠒⠐⠀⢣⣄⠘⡄⠀⠀⠀⠀⠀⠀⡀⣀⣤
⠀⠰⠁⠀⠀⠀⠀⢣⠔⢢⠀⢠⠀⠀⠀⠠⡀⠀⠀⠈⠂⠀⠀⠀⠀⠉⠀⢈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠁⠀⠌
⠀⠸⡀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠐⠊⠀⠀⠀⡌⠀⠀⠀⠑⠠⢄⣀⣄⣀⠠⠊
⠀⠀⠑⠄⡀⠀⠀⡠⠐⠃⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠣⣀⠅
⠀⠀⠀⠀⠈⠶⠉⠀⠀⠀⠑⠀⡀⢸⠈⠂⡤⢀⠀⠀⡀⠀⡀⠤⠐⠁⠀⡀
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡨⠛⠢⠀⡃⠀⠀⠀⠃⠀⢀⡐⠀⠀⠁⠙⠢⣄⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⠌⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠀⢀⠀⠀⠀⠀⠄⠘⣄⠈⢁⠞⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⢀⣀⡰⠀⠈⠄⢸⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠸⠁⠍⠠⠀⠂⠀⠀⢰⠌⠦⣀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠁⠁⠐⠂⢠⠄⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢢⣀⣀⡀⣀⣀⣀⣀⠤⠒⠂⠉⠉⠉⠐⠒⠒⠧⠄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠘⠿⠟⣡⠴⢶⡄⠈⠻⠿⠃⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠘⠛⠒⠚⠃⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠺⠶⠾⣿⡀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣼⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣧⡀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠙⣷⣤⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠘⢷⣤⡾⠋⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢰⠖⠲⠶⡭⣄⠡⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠖⠒⠒⠦⠤⣀⡜⠙⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡀⢾⠇⢀⣀⠀⣶⡆⠀⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠺⠂⠀⠠⠀⠅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠑⠤⢀⣀⠠⠔⠁⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠒⠠⠄⡀⢀⠀⠤⠄⡖⢺⠩⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⢜⠦⢄⣀⠀⡀⢀⠀⢠⣀⣆⠴⠾⡉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⢂⠎⠁⢢⢉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠑⡄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠃⡜⠄⢀⣹⠒⠈⠠⢤⡄⠀⠀⠀⠀⠀⠀⢰⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠀⠈⠒⠐⠊⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠀⢰⠉⣷⠀⠀⠀⠀⠀⠀⢰⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠧⠜⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠀⠀⢠⠄⠴⠒⠀⢠⠄⠀⠀⠠⠆⠀⠀⠀⠀⠀⣠⡾⠒⠂⠓⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠈⡀
⠀⠀⠈⠋⠁⣠⠊⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⡅
⠀⠀⠀⠀⠀⢛⠶⡶⢤⡀⠁⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠀⠀⠐⢀⠀⠀⠀⠀⠃⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠈⠑⠌⠟⡹⢲⠄⠐⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⣠⠿⣆⣂⣴⣶⣴⠀⠀⠐⠿⠀⠀⠀⠀⠀⣤⠼⠀⠀⠆⢹⣖⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⢀⠄⡀⠈⡄⠀⠀⠀⠀⠀⠰⠁⠀⠀⠉⣹⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢢⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⡯⢔⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠚⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠴⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠐⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠪⠁⠀⡸⠁⠈⠂⢠⠀⠀⠀⠀⠀⢠⢁⡀⠀⠀⠐⠀⡃⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠈⠀⢄⡆⠈⠉
⠀⠀⠀⠀⠀⠀⠢⠸⡀⠀⠀⠀⠐⠘⠀⠀⠀⣠⠀⠀⠛⠂⠀⡇⠀⠀⠀⠀⠀⣨⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠀⠀⢀
⠀⠀⠀⠳⠀⢀⡀⣀⣠⠄⠀⠀⢤⣤⠤⠀⠂⠈⠀⠀⠀⣇⠀⠀⣄⠀⠀⢀⢠⣭⡔⡁⠴⢀⠀⠀⠓⢀⡀⠀⣰⠄⢒⣀⢔⣇⣀⣀⣠⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠔⠀⠀⡀⠀⠀⠀⠀⠀⠀⡹⠋⠠⡀⡉⠤⡎⢱⡆⠀⠀⠈⠛⠀⠀⠀⠉⡟⢫⠀⠸⠒⠂⠀⠙⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢆⠀⢰⠀⠀⠀⠀⠀⢰⠁⠀⢂⠀⠀⠐⠀⠸⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢡⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠤⡀⠈⠀⢸⠀⠀⠀⠀⠀⢸⠀⠺⠠⠄⠀⠀⢀⠃⡐⠀⠀⠀⠀⠀⠀⠀⢸⡀⣆⡀⠀⣘⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠲⠌⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠠⣀⡤⣢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢤⡄⠀⠀⠀⠀⢠⠤⣤⠎⢷
⠀⠀⠀⠀⠀⢀⡿⠀⠁⠘⣓⠀⠀⠀⢀⣠⠴⠚⠉⠁⣀⠔⠊⣇⠀⠀⠀⠀⣸⠧⠀⠀⢉⢩⠗⠀⠀⢠⣀⢠⡄
⠀⠀⠀⠀⠀⠑⠓⡆⣠⣌⠇⠀⢠⠞⠋⢀⡠⠤⠒⠉⠀⠀⠀⣿⣀⣀⠀⠈⠓⢲⡂⣠⣈⢻⠀⠀⠠⣮⠁⠈⢵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠀⠀⠀⣀⠠⠐⠈⠀⡌⠀⣨⠇⠀⠀⠈⠒⠁⠈⠉⠀⠀⠀⠱⠷⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⢢⡀⠀⢙⣦⠀⠀⢀⣀⠤⠒⣉⠤⠊⠉⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⢀⣐⡃⢠⡏⠀⢈⡉⠡⠄⠒⣉⠀⠀⠀⠈⠳⠀⠙⣆⠀⢠⡞⠳⡴⠚⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠃⠀⠀⠀⣀⠀⡩⠄⠤⣀⠓⠀⠀⠀⢹⠀⢸⡇⠀⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⢄⠣⢄⣀⠼⠀⠀⠀⠀⣸⢠⡞⠁⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢢⡆⢴⡄⠀⠀⠀⢠⠷⣄⠀⠀⠀⠈⢷⣶⠖⠂⠀⢀⣀⣰⡧⠞⠑⢄⡈⠒⠤⡔⠋⠀⡖⠂⠡⣄
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢿⠀⠀⣠⡼⢤⠀⠉⠖⠠⢤⠤⠀⡤⢎⠉⣁⠈⢆⡇⠀⠀⠀⠈⢉⡟⠁⠀⠐⠢⣠⠜⠅
⠀⠀⠀⠀⠀⠀⠀⠹⠃⠛⠃⣠⠎⠁⠀⠀⠑⠢⣄⡀⠘⠀⠀⠠⠀⢡⠀⠀⠀⠱⣄⠀⠀⢀⡞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡀⠀⠈⠉⠁⠂⠀⠓⠈⠫⡀⣀⠠⠘⠓⣤⠏⠀⢰⡰⠶⡞⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⠋⠉⠒⠈⠉⢑⠄⠀⠀⠀⠙⡀⠀⢀⠠⠘⡆⢀⠴⠓⠀⠀⢈⣩⠕
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣽⢆⡀⠀⠀⡆⢠⠂⠀⠀⠀⠉⠲⡀⠀⠀⠀⡋⠁⠀⣀⢴⡇⠈⠘⢻⢅⣰⣠⢋
⠀⠀⠀⠀⠀⠀⢐⠔⠉⢂⠄⣿⠀⠈⠑⠒⠧⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⣉⡁⠀⢸⡇⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠁⢢⠰⠼⠀⢻⠀⠀⠀⠀⠀⠀⠉⠒⠤⠄⠤⠊⠀⠀⠀⠀⠐⣿⡟⠀⠸⠷⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠐⡲⠻⠉⠿⢆⡂⠀⠙⣦⠔⠊⠉⠉⠉⠒⠠⡀⠀⠀⠀⣀⡤⣎⠀⠀⠀⢀⣠⠖⡋⣀⢤⣦
⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⢺⡄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣶⠒⠋⠁⠀⠈⠓⠒⠛⠉⠀⠀⢘⠛⠀⠁⠿⣖
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣠⠟⠑⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣀⠟⠀⠀⢰⠐⠉⢦⠀⠀⠀⠀⠀⢛⢗⣤⡀⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠚⠛⠉⠁⠀⠀⠀⠁⢂⠤⠵⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠒⠈⠉⠙⣄⠀⠀⠀⠀⠈⠉⠀⠒⠒⠀⠀⠠⠤⠤⠤⠤⠤⠄⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠘⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠂⠒⠒⠒⠒⠈⠀⠀⠈⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠉⠛⠂⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠐⠒⠂⠀⠉⠉⢻⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠐⣁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡴⠂⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠒⠂⢁⠀⠀⠀⡀⠀⠀⠀⢦⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡠⠤⠐⠂⠈⠉⠀⠀⠀⠉⠢⡀⠀⠀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠲⠄⣄⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡔⠒⢠⠈⠉⠐⠒⠒⠊⠁⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠁⠶⠈⣀⢀⡀⠀⠀⠀⠀⠀⣀⣄⠀⠇⢀⠅⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠇⠀⠄⠠⠉⢙⡂⠀⢀⣈⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⢙⣤⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠦⣀
⠀⠀⠀⠀⠀⠀⢠⠃⢀⡴⠁⢀⡽⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠺⣅⠈⠱⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⣈⢀⠎⠀⢀⠎⠀⠀⡜⠉⠁⡛⠂⠀⠦⠴⡄⠀⠚⠛⠉⠉⠀⠀⠀⠈⣦⠀⠘⢆⠀⠹⠄
⠀⠀⠀⠀⣠⠞⠉⠮⡀⠀⡎⠀⠀⢰⠁⠀⠰⡇⠀⠀⣾⠀⢣⣀⣀⠀⢤⡤⠀⠒⠊⠉⠈⡆⠀⠈⡄⡰⠳⣄
⠀⠀⠀⡴⠁⠀⠀⠀⠈⠚⠧⣀⢀⡈⠀⠀⠀⠀⠀⠀⢿⠀⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠴⠋⠀⠀⠈⢦
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣬⡀⢀⡀⣘⡀⠀⢩⡄⠀⠀⠀⢤⠄⠒⠒⠉⠁⣧⠀⠀⠀⠀⠀⠈⢧
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢌⠉⠉⠉⠁⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠈⣧
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠈⡆⠀⠀⠀⠀⢹⡄⢀⣤⠄⠀⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠚⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠠⠴⠒⠀⠉⠈⢱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠙⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠷⠶⠶⠦⠄⠂⠈⠋⠁⠀⠀⢡
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡆
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠤⠶⠔⠞⠛⠛⠉⣉⢏⠴⠄⠀⠀⠀⣠
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠾⠶⠈⠓⠋⠁⠉⠈⠀⠀⠀⠀⢠⡏
⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣚⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢐⣡⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢴⣴⣷⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠠⣑⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠖⠒⠒⠻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⣀⣀⣨⣷⣿⣾⣿⣿⣿⣿⠀⠀⢡⣏⠀⠘⠩⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⡭⡥⠼⠿⣿⣿⣿⡟⠉⠀⠀⠀⢼⣂⠀⢐⠚⠺⣖⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣸⣿⠃⠀⠀⠀⠀⠀⠈⠋⠀⠀⠂⠀⠀⠂⠄⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠨⢭⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠬⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣝⣋⣍⣹⣝⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡀⢡⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢣⠈⠀⠀⢁⣀⣀⠤⠤⠔⠒⠒⠒⠒⠚⠋⠉⠛⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠂⣀⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠉⠀⠀⠀⣀⡠⠤⠤⠒⠒⠉⠉⠉⠉⠀⢀⠀⠀⠘⡅⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣠⠴⠚⠉⠁⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠘⡤⠖⠉
⠀⠀⠀⠀⠀⢠⡇⠀⠠⠖⡏⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠜⠷⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⣉⠉⠑⠒⠒⠒⠒⠒⠋⢁⣤⠞⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢙⡖⡲⡶⠒⠒⠒⠋⠁⠀⢳⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⢀⡎⢰⠏⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇⡼⠀⢼⡀⢸⡀⠀⠀⠀⠀⠀⠀⠘⡆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⡴⠁⣏⡀⣸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠊⠉⠉⠲⡄⠀⠀⠀⣀⡞⠉⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣀⣀⣠⠞⠉⠉⠉⠙⠧⢤⣤⣤⠤⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡘⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣼⠀⢳⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡀⠘⢆⠙⢕⡠⢀⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢿⢿⣿⣷⣦⣌⣷⣄⠈⠁⠨⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠄⠉⠛⠿⢭⣙⠳⢦⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣿⡷⠶⣴⣿⣶⣤⣈⠙⠲⠤⣉⣛⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠉⠛⠒⠲⠻⠿⣿⣿⣿⡶⠂⠄⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠶⠶⢶⣤⣤⣄⣢⣬⣉⠛⠛⠓⠚⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠿⣷⣶⣤⣤⣤⣄⣉⠙⠛⠛⠛⠛⠛⠋⠋⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠦⠭⠭⠍⢩⣉⣭⣭⣥⣤⣴⣶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣹⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡀⠀⡀⠀⠀⡀⠀⠀⢀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣤⣤⣴⣴⣦⣾⣷⠾⠿⠛⠁



⣿⡏⢹⣟⠿⣿⢛⢟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣾⣤⡆
⠀⠀⠀⠈⢳⣤⣽⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠿⣶⠿⡏⠁
⠀⠀⠈⠛⢛⡿⣤⢾⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠋⠀⠿⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀⢀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⣳⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡇⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠼⣟⢉⣷⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤⢐⠋⠈⠗⠂⡄⠠⢀⠀⠀⠀⠀⠀⠠⠟⠉⡏⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠈⠃⠒⠊⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠑⠂⠤⠀⣀⣀⣀⠀⠤⠒⠉⠀⠀⠀⠀⠡
⠀⠀⠀⠀⢦⣼⣦⡴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣀⣴⢀⡄
⠀⠀⠀⠉⡽⢷⡾⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠐⢲⣿⣭⣿⡒⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢰⠀⡀
⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⢐⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⡃⠀⠀⠀⠀⠀⠀⡸⠊
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠊⠢⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡠⠊⠖⠒⠒⠒⠒⢒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠈⠉⠉⠉⠃⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⡜⢰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠢⠀⢀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠁⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⣀⣴⠊⠁⢀⣀⠀⠀⠀⠈⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠉⠀⣀⣉⡐⠂⣄
⢀⠞⠁⠀⠀⠀⠀⠀⠀⠉⠐⠠⠤⠀⠈⠶⠒⠈⠀⠀⠀⠀⠀⠈⠁⠐⠠⠄⣀⣠⠔⠊⣁⠠⠔⠈⠁⠀⠀⠀⠀⠀⠙⠲⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠩⠗⠓⡈⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣤⣤⣤⣴⣾⣿⣿⣷⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⡿⠟⠛⠉⠉⠙⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⠟⠛⠉⠁⢀⣤⡀⠀⢰⣦⠀⠙⣆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠀⢀⣉⡭⠔⠊⠁
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠀⡀⠀⠀⠀⢒⠩⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢧⠀⠀⠀⠀⠈⠁⠚⠀⠃⠉⢀⡴⠋⣧⡀⠀⠀⠀⢀⣠⡴⠚⠉⠁
⠀⠀⠐⢤⣤⣬⣷⣀⠀⠀⠀⠀⢰⠋⠲⢄⠑⠠⠠⠀⢀⣀⣀⡤⠴⠚⢉⡠⠚⣡⣷⣠⠴⠖⠋⠉⠉⠓⠦⠄
⠀⠀⠀⠀⠀⠠⠴⠋⠛⠲⢦⣀⡸⡆⢀⠀⢀⠀⡀⠀⠀⠩⣀⠤⢰⣞⠉⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠗⢶⠀⠀⠀⠁⠀⠀⠀⡆⠀⠈⢋⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⡋⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣤⠀⠀⠀⠀⡇⠀⠀⠘⠿⠀⠀⣠⣏⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⡄⠘⠛⠱⢷⣶⡰⠀⠀⠀⠀⢀⡀⠀⠁⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠦⣤⣤⣄⣀⣀⣤⣤⠤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠈⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣷⣲⣶⣶⣶⣶⣶⣶⣶⣖⣺⣯⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣍⣽⣭⣹⣟⣽⣭⣭⣹⣿⣝⣭⣯⣯⣍⣹⣿⣯⣽⣿⣯⣽⣿⣯⣽⣿⣿⣽⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⠤⣄⠀⣠⠶⠋⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣀⠀⣠⠶⢦⣄⡶⠋⠑⢦⡞⢁⠈⢱⣾⣥⡤⠬⠿⠷⠒⠺⡆⢀⡇
⣠⠖⠒⠒⢤⣀⡰⠋⠉⠳⣾⠁⢀⣉⣿⣁⣤⡤⠼⠗⠒⠒⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⡀
⣇⠀⠀⢀⣠⠼⠧⠤⠒⠒⠛⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢹⡆
⠈⠳⢄⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⡀
⠀⠀⡞⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⡿
⠀⠀⠷⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠶⡀
⠀⠀⢰⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡶⠁⠀⠀⣠⣄⣠⡄
⠀⠀⠈⢳⡶⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⡏⠲⡄⠀⢸⠃⠀⠀⠀⠈⠁⠒⢠⡄
⠀⠀⠀⣏⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⣴⠒⠒⠛⢻⣍⠁⠀⠀⠀⣹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣄
⠀⠀⠀⠈⣳⠞⢿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠒⣶⠚⡏⠉⣯⡀⠀⣠⡟⢦⣀⣠⠟⠈⠙⠒⠒⠚⠁⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⣾⠁⠀⠸⡧⣤⡤⠖⠚⣿⣏⠉⣁⡜⠳⢄⡠⠞⢻⡀⢿⠛⠀⠙⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢷⡀⠀⣀⡴⠋⠙⠒⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠷⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡇⠀⠀⠀⠀⠀⠀⡛⠉⠛⠓⠶⣤⣌⠀⠀⠀⠀⠈⠁⠦⣀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⢠⣆⠀⠀⠀⠙⢦⡀⠀⠀⢀⠈⠙⠲⣤⣈⠑⠦⣄⠀⠉⠲⣄⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣀⠘⣿⣷⣦⡀⠀⠀⠛⠚⠿⠀⠀⠉⢑⠒⢬⠑⠦⣄⡙⠶⣄⡈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠉⠳⡌⢿⣿⣿⣿⣤⣤⡤⠀⠀⠀⠀⠈⠛⢦⡈⠓⢬⡉⠲⢬⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⣴⡂⠀⠀⠁⠀⠀⠉⢢⡀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣸⠀⡆⠘⠻⠿⠿⠿⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠀⢀⣉⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠶⣤⡴⣾⠃⠘⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⡀⣿⡄⠀⢰⠀⠀⣀⠉⢲⣦⣤⣤⣤⣤⣬⠷⠄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠉⠹⡇⠀⠰⢷⡀⠈⠱⣿⠟⠛⠛⢿⡿⠋⠀⠀⠀⠀⠀⣠⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢣⠀⣤⡀⠉⠒⢤⠈⠁⠒⠂⠉⠀⢀⡀⠀⡀⡤⠒⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠟⠀⠙⠀⠀⠀⠈⠁⠒⠲⡆⠚⢏⠉⠈⠁⠀⠀⠀⠰⠀⠀⠀⠄⠀⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢳⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠀⠁⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⣿⢸⠀⣀⠠⠄⠚⠦⣀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢐⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢢⣄⡀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⣼⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠢⡄⠀⠀⠀⣀⣨⠀⠀⣼⠃⠀⠀⠀⠀⢀⣠⠞⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠙⠛⢿⣄⠀⠀⠀⠀⠀⠈⠐⠠⠀⠉⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢀⡤⣤⡀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠢⠀⠘⣷⡀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠸⣇⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⠟⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢦⡀⢀⡠⠾⡟⠙⠳⠐⣌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⠳⣌⠀⢰⡌⠒⠉⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣶⡶⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣶⣶⣶⠶⠶⠾⠷⠶⠾⠟⠛⠋⠉⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⡀⠀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣟⣋⣙⣉⣙⣋⣀⣉⣙⣏⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣥⣯⣤⣬⣭⣤⣿⣿⣯⣭⣥⣬⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⢯⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠐⠀⢾⣯⠿⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣶⣶⡀⠀⠀⠀⣀⠔⠲⡀⠀⢰⣿⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠙⠋⠀⣀⠴⠊⠁⠀⠀⣣⠀⠀⠉⠁⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣆
⠀⠀⣀⣀⣸⣇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠾⠀⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⣿⣀⣀⡀
⠀⢸⣏⠉⠛⢿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⠟⠋⢉⣿
⠀⣀⣉⣿⣦⠄⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠉⠁⠈⠉⠁⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⢤⣾⣏⣁⡀
⣾⡋⢉⣀⣠⣤⣴⣶⣄⡈⠛⢷⣤⡀⠀⠀⠀⢀⣴⠾⠋⠉⠉⠒⠤⠄⣀⣀⣀⣀⡀⠠⠔⠊⠁⠉⠛⢶⣄⡀⠀⠀⠀⠀⣠⣴⠟⠋⣀⣴⢶⣤⣤⣀⣈⠉⣻
⠈⠛⠛⠉⠉⠀⠀⠀⠉⠻⢶⣄⡈⠛⠷⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣠⡴⠟⠉⣀⣴⠞⠋⠁⠀⠀⠈⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣤⣤⡶⠾⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⡠⢇⡀⠀⠀⠀⢠⡄⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠐⠣⡜⠐⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣧⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡈⠀⠀⢘⠃⠀⠀⢀⣀⡤⠤⠶⠒⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠈⣀⡥⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠖⠋⠁⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠻⡉⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⢀⣠⠤⠖⠚⠋⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢻⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡀⠀⠀⠀⠀⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠴⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠰⠊⠉⠁⠐⠢⠘⠛⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠉⠉⠙⠓⠖⠒⠖⠒⠒⠚⠛⠉⢀⣠⠞⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠈⠙⠒⢦⠤⣤⣤⣤⡤⠤⠤⠶⠒⠋⠉⢳⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢠⠏⢰⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⠀⢠⠏⠀⡿⠀⢿⠀⠄⠨⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠀⡞⠀⢀⣧⠀⠚⡆⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⢀⡞⢰⠏⠀⠄⣟⠉⠉⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠋⠉⠀⠘⠓⠓⠒⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠋⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⣰⠊⠉⠉⠉⠳⣦
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠈⣷⠶⠶⠶⠒⠺⣇⠀⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠈⠙⠛⠓⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠢⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣡⣏⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢅⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠦⣀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⢹⣶⣸⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⣰⡏⠁⠀⠀⢺⣇⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⢈⠽⠀⠀⠀⠀⢸⠿⠄⢺⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠀⡀⠀⢰⠊⣠⣾⠀⠀⠀⠈⠆⡡⢸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡆⠀⠂⠀⠋⠁⠀⠀⠀⠀⡀⠄⢰⣤⠰⢉⣠⣾⣿⣿⡇⠀⠀⠀⢀⡑⢸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⡂⠰⣼⠀⠙⣃⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⢀⡜⡃⣸⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⡀⠘⢿⣿⣿⣿⣿⣿⣷⣶⣤⣭⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠙⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠸⡇⠀⡂⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠐⠺⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠁⢀⠈⠂⠄⠀⣈⠙⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠠⠵⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⡟⠁⠀⠀⢌⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⠀⠁⠐⠀⠀⠀⠀⠀⢠⣿⣿⣿⣏⣀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⡿⠿⠟⠛⡁⢀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢀⡀⠀⠂⠤⠀⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠀⠀⠀⠀⠤⠀⠂⠉⢀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠻⠿⡿⠛⠛⠋⠁⡠⠀⠀⠑⠀⠀⣀⠀⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠁⠐⠂⠀⠉⣀⠀⠤⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⠂⠈⠀⠀⠀⢀⠀⠉⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣨⠔⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠔⠁⠀⠁⠀⡏⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠉⠁⠓⠓⠒⠛⠃⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠠⠆⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡻⠲⢾⠶⢄⣀⡤⠤⠴⠀⠉⠤⠬⢂⣢⡴⡂⡆⠀⠀⠀⣀⠀⠀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠐⢞⢦⣀⣠⢂⠆⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠄⠀⠈⠉⠉⠉⠉⠉⠍⢻⠷⠓⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠁⠀⡀⠠⠀⠈⠐⠲⠤⣍⣁⠒⠀⠠⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⣠⡞⠀⠠⣒⠄
⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⢧⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠙⠳⢶⠶⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⢀⢉⠁⠬⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣁⡀⠀⠀⠀⠀⠀⠀⢀⢵⡀⠀⠄⠄⠄⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣀⡵⠃⠀⠀⠀⠀⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇⢀⠀⠀⠀⠀⠐⠈⠙⠂⠀⠀⠠⠤⠤⢠⠞⢡⠀⠀⠀⠀⠀⢄⡬⠋⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠈⠣⢁⢀⡠⠂⠙⠲⢦⣀⣀⠀⠠⠠⠠⠄⢂⣸⢄⠀⠀⣠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⡀⢀⠀⠁⠉⠻⡝⠉⠉⠉⠅⠀⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠁⠀⠀⠀⠀⢴⣿⠆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠋⡈⠄⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠃⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⡞⣄⡄⠀⠀⠀⠀⠀⠀⠳⡀⠀⠱⣂⠁⠸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠅⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠤⠂⠀⠀⠀⠀⠀⢀⠔⢇⠀⠀⠀⢀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠢⠀⠀⠘⠬⡷⠁⠀⠀⠀⠀⠀⠀⢠⣤⣤⡌⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⠐⠀⠀⠂⠀⣚⣠⣤⣤⢾⠄⠤⣦⢤⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠊⠄⠂⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⢄⠀⠀⠂⠀⠄⠀⠀⠀⠀⢀⡀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠂⠄⠃⠆⣤⣑⣀⣊⣀⠀⠀⠁⠠⠂⠀⠂⠀⠌⠀⢀⣠⠞⠢⠀⠄⠠⡠⠄⡀⣄⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⡒⣂⠂⠉⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠁⠈⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣀⡹⠶⠖⠒⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠓⠒⠦⡼
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠈⣆⠀⠀⠀⢀⡴⠃⠀⠀⣀⢞
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠴⠊⠁⠀⠀⢀⠀⠈⠑⠢⣄⣀⣀⣽⣀⠀⡼⠁⢀⡀⠀⡼⡇⠈⡇⠀⡰⠃⢸
⠀⠀⠀⠀⠀⠀⡎⠀⡴⠁⠀⠀⣠⠖⠛⠣⣌⠉⠲⢄⡀⣠⣠⣀⢸⠀⡷⠀⡇⠈⢺⡀⡇⠀⡇⢠⠃⠀⡆⢀⠤⢤
⠀⠀⠀⠀⠀⠀⢧⠜⠀⠀⢀⠾⠷⠖⠆⠀⠈⠦⠤⢀⡜⡱⠢⠈⢺⣠⠃⠀⠘⢄⠀⠳⠅⠀⠳⠎⠀⢸⠔⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⢾⡀⠀⢰⣒⡄⠀⠀⠀⠀⠀⠀⠀⣜⣰⠁⠀⠀⢠⠞⢦⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠉⠁⠀⠀⣀⠀⠀⠀⠀⢸⠁⣠⠔⢒⠧⠤⠴⠋⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣖⠃⠐⢇⣀⣀⡤⠤⣀⣀⣠⡆⢀⠴⢏⠉⠙⠢⡀⠀⠀⠀⡔⠚⠚⢕⣬⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⢴⡡⠀⠗⡄⠀⠀⠠⠤⠤⣤⠭⣑⣒⣒⡶⠏⠀⠀⠢⡇⠀⡴⠚⠳⡄⠐⠢⡑⢿⡦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢄⣤⠐⠉⢀⣠⢴⠎⠲⠖⠁⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠁⠀⡇⠀⠀⠀⠀⠀⢹⠎⠀⠀⠀⢘⣆⣀⣈⢢⠙⡍⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡝⠀⠘⠤⣤⢔⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠋⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡤⠞⠁⢠⠞⠀⠀⠀⠀⠀⣀⣀⣀⡠⢴⠾⠃⠀⠀⠀⠀⢀⡯⠤⠒⠉
⠀⠀⣀⡠⠖⠒⠒⠒⢢⠖⠒⠚⠉⠀⠀⠀⠀⡠⢴⠋⠀⢀⡴⠳⠤⠤⠴⠖⠚⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠋
⢀⠞⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⡤⠞⠟⡽⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠀⠀⠀⠀⣠⠞⠁
⠘⠦⠖⠊⠉⠢⢄⠀⢠⠝⠦⠤⠤⠒⠊⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⢆⢀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠉⠉⡩⠛⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢒⠁⡀⠀⠀⠜⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠳⡦⠤⠤⠴⠒⣖⣚⣻⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣉⣉⣉⣉⣉⡠⠤⠤⠒⠒⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣒⡒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢘⣴⣤⣷⣔⣶⡄⣠⣆⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡎⠀⠀⠀⠀⠆⠠⡾⠿⠟⠻⢿⣿⣿⣿⡿⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⠀⢀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⣀⡀⠛⠛⢀⡀⠀⠀⠀⠀⠜⠀⠌⠛⠛⠛⠙⠥⢾⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⢀⠂⠙⠛⠄⠐⠀⣀⠀⣀⢀⣴⣞⣀⠘⠁⠀⠠⠂⢠⡆⢴⣿⣆⠀⠀⠀⠀⠀⠒⠉⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠃⢴⢆⣈⠹⢻⡈⠂⢡⣀⡛⢈⣅⢻⣿⠀⠀⠀⠀⠀⣾⡸⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣦⡔⢢⡀⠀⠁⣀⠛⣿⣿⣿⣿⠏⣸⠂⠀⠀⠘⢆⣛⣿⣿⣽⡿⠓⠁⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡷⢦⡎⠉⠛⠙⠳⢿⣾⢿⣿⠏⠘⠟⠀⠀⠀⢰⣾⢿⣿⣿⣿⣆⣀⢠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣷⡮⣤⣹⣶⣾⣷⠘⢛⡿⢻⣦⣄⠀⠀⠀⠘⠗⣿⠛⣹⢿⣿⣿⣯⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠙⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠋⠀⠂⠸⠂⠸⣮⡿⣼⡿⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠮⣉⣿⡝⠛⣋⣾⡟⢽⣿⣿⠀⣀⠀⠀⢸⠄⢤⡛⠿⢟⢄⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⢿⣯⣿⣿⡒⢪⠘⣧⠹⠷⠀⠉⠶⡆⢀⣤⣾⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣥⣬⣭⣭⣥⣤⣮⣴⣼⣶⣿⣯⠾⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠘⠻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡚⠉⠁⡂⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡠⠦⠖⠀⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠸⠁⡀⠀⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⣤⣴⡖⠒⠒⣤⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡠⠤⠀⢀⠤⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⠋⠁⠀⢠⠻⠿⠳⡀⠀⢸⠀⠀⠀⠀⠀⠀⢤⡀⠀⠠⢄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠳⣆⠀⠀⢦⡀⠣⡈⠂⠀⠀⠱⠀⠎⠀⠀⠀⢀⣠⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠑⢄⡀⠀⢠⡮⢦⡄⠀⠀⠀⢠⠊⠱⢄⡀⣉⠀⠀⠀⠂⣐⣠⡀⠀⠀⠀⠀⢰⡶⢕⡀⠀⣀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠙⠶⣄⢀⣼⠒⢰⣁⣠⠔⣂⣀⣠⠀⠈⠂⠉⠢⡀⣠⠶⠁⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢛⠀⠦⣈⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠊⠈⠀⡏⠀⠀⢰⡁⡠⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠤⠄⢅⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣆⢀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠁⡱⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢒⣛⠓⠐⡄⠀⠀⠀⠸⠤⠂⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠓⠢⠤⠤⠤⠴⠖⠊⠁



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡆⠐⣦⣭⣿⣷⣦⣀⠀⢀⡤⠚⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⣿⣶⡋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⢀⡿⠿⠿⠿⠿⠛⠛⠓⠒⠲⠒⠾⠿⠿⠿⠿⠿⢿⣗
⠀⠀⠀⠀⠀⣇⠈⣾⠀⢣⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠰⡍⠙⡧⠘⠃⢸⡠⠤⡀⢹⠉⠉⠉⠉⠁⠀⣉⡉⠉⠉⠉⠉⠉⠉⠉⠁⢲⠃
⠀⠀⠀⠀⠈⠱⠀⠐⠉⠉⡠⠒⠃⠘⡆⠀⠀⠀⠔⣋⣉⠁⠀⢙⣛⢦⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠑⢤⣔⣺⠃⠀⠀⠀⣧⠀⠀⠀⠘⠀⠈⠂⡔⠁⠀⠃⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⢸⠀⠀⠀⠠⠠⣿⠸⢰⡶⢀⠆⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣾⡇⠀⠣⡀⠁⠈⠀⠈⠁⠂⢠⡄⠀⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⣷⣶⣤⣤⣶⣾⡟⠀⠀⣼⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⢿⣿⣿⣿⠿⠋⠀⠀⢀⡇⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡘⢿⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⡀⠀⠀⠀⣀⣀⡠⠏⠀⠀⡏⠈⠉⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⠉⠉⢹⣿⠀⠀⠀⠀⠀⠑⢇⠀⣠⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣧⡀⣠⣾⣿⣶⢶⣤⣄⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠉⠻⣿⣿⡿⠃⠻⣿⣿⡿⠋⠉⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠴⠖⠋⠁⠀⠀⠀⠀⠙⠓⠦⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⣀⠤⠤⠐⠒⠒⢄⠀⠀⠀⠀⠶⡴⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠤⠄⠀⠀⠠⠄⣀⣀⡈⠒⠠⠤⠤⠞⢀⢸⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠠⣤⡤⢀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠾⣇⢇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⡟⡘⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⡤⠒⣡⠓⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡤⠿⠅⣀⣀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠒⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⠀⠀⠉⠒⠒⠤⠤⠤⠐⠒⣊⡡⠔⠋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⣀⣉⡉⠀⠀⠀⠒⠂⢀⣉⡩⠤⡄⠒⠚⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣀⡀⠀⠉⠉⠉⠉⠙⡇⠀⠀⠀⠱⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠑⡄⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠈⢆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⠤⠤⠤⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠤⠤⠤⠤⠄⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠥⠢⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠔⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢀⣀⡤⠶⠖⠢⢄⢨⠀⠀⠀⠀⠑⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠐⠒⠊⠉⠀⠀⠈⠀⠀⢠⠇⠀⠀⠀⠀⠀⠂⢈⠑⠢⠄⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢿⣋⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠾⡟⠉⠀⠀⢀⠕⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠰⣤⣴⣶⠶⠾⠿⠿⠿⠟⠛⠋⠉⠛⢦⠀⠣⠤⠀⠂⢁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⢏⠁⠀⠀⠀⢀⡠⠔⠊⣁⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣁⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⡹⠛⠛⠀⠀⠈⠙⠛⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⣖⡒⠒⠤⠄⠂⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡟⠛⡿⠿⠿⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠉⠛⠲⠶⣤⣄⣀⣀⠈⠉⠀⠒⠒⠂⠤⠤⠤⠜⠁⠸⣀⠀⠀⠀⠈⡇⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠦⠤⣤⣤⣀⣀⣀⣀⣀⣀⣉⣀⣈⣁⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣵⢏⣿⣿⡇⢹⣿⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⣾⣿⡟⢿⠈⣿⣧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣠⣿⣿⣇⠸⡇⢿⣿⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⣿⠀⢻⣾⡼⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠐⣓⣦⣿⢹⠃⢻⡄⠈⢿⡇⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢭⡽⠇⣿⠀⠈⢷⡀⢸⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⢛⡿⠀⠀⠈⠁⠀⡇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⣋⣱⠆⡀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢾⠋⣢⡄⠀⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⢰⠟⠧⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠈⠛⠦⣂⠤⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠚⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁⠐⠤⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠀⠂⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⢀⣀⣀⠀⠠⠤⠀⠀⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣻⡛⠶⣤⣌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⣬⣯⣙⡷⣎⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡛⠶⠶⣄⣠⠛⠧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣭⣋⡛⠶⣮⠙⠧⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠿⣭⡙⢶⣍⠻⡆⠄⠂⠀⠀⠀⠀⠀⣀⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠉⠁⠀⠀⠀⠀⠀⣀⡴⠞⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠞⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⠨⠐⠁⠀⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠀⠉⢀⣀⠀⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⡀⠠⠄⠀⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣶⣧⣽⣼⣷⣶⣧⣽⣽⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠒⠂⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⠄⠀⠀⠈⠁⠀⠀⢹⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⠠⠀⠀⠀⡒⠊⠉⠥⠄⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⡇⠘⠉⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠀⣨⠥⠄⠐⠒⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠘⠓⠀⠀⠀⠀⠈⢆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⡠⠄⠤⢤⡀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠫⠀⠀⠀⠀⠀⠀⣰⠁⠈⠛⠁⠒⠲⠀⠤⠤⢇⣀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌
⠀⠀⡔⠁⠀⠀⠀⠀⠙⣆⢀⣀⡀⠀⠀⡇⠀⠀⠀⢂⠀⠀⠀⠀⠀⠸⡀⠀⠠⠤⠤⠄⠐⠂⠀⠒⠈⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢠⠁
⠀⠰⡃⠀⠀⠀⠀⠀⠀⠘⠏⠀⡸⠀⠀⠇⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠠⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠐⠐⠂⠉⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠑⠲⢤⣀⣄⣠⡤⠒⠁
⠀⠀⠀⠱⢄⡀⠀⠀⠀⢀⠤⠚⢄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡨
⠀⠀⠀⠀⠀⠉⢦⡤⠊⠁⠀⠀⠈⠳⣄⠀⠀⢸⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠑⠦⣸⠀⠀⠀⠉⠁⠀⠒⠲⠖⠒⠈⠉⢉⠀⡀⠠⠤⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡠⠊⠁⠉⠂⠠⠄⣀⣀⠀⠀⣄⣀⡀⠤⡎⠀⠀⠀⠀⠈⠙⢶⡢⠤⢄⡀⠀⢠⣴⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠆⠀⠱⡀⠀⠈⡹⠋⠀⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠒⠒⠂⡋⠋⣡⠀⠀⠀⢱⠀⢇⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠘⡃⠚⠓⠢⡤⢴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⠄⡀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠈⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠁⠀⡗⠒⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠉⠉⠑⠒⠫⠤⢀⡀⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡤⢶⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠀⠈⣠⠖⣡⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡌⠐⠤⡈⠛⠓⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠔⠂⠀⠀⠀⠀⠀⣀⣀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠶⠾⡁⠠⠴⠾⠿⠋⣉⡤⠤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠵⠒⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢁⣴⣿⡿⠃⣀⣤⣄⠀⠀⠐⠚⣛⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠆⠀⠤⠤⠄⠀⠀⠀⠀⠤⠤⢶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠒⡂⠀⠀⠀⠤⠄⠠⢤⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⡁⣈⢍⠋⠙⣉⢏⣿⣛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣅⠀⢁⣜⠈⢱⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⣨⠶⣁⠈⣡⣼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣅⠄⣨⠖⢡⣾⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠒⢤⡀⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣂⢴⡊⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠙⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣜⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠈⠁⠙⠀⠒⠢⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⡤⠤⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢰⠁⠀⠀⠀⠀⢀⠎⠀⠀⠉⠁⠐⡲⠂⠰⠀⠠⡄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠁⠐⠒⠀⠤⠼⠄⣀⣀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠎⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠸⠏⠉⠉⠁⠒⠒⠒⠘⠂⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠤⠄⠴⠒⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠍⡉⠈⠀⠀⠀⣯⠀⠁⢉⣁⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡜⠀⡇⠀⠀⠀⠀⠛⠀⢰⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⠁⠀⢇⠀⠀⠀⢀⡖⠀⠀⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠢⢄⠀⠈⣉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠎⠉⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⢸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⢀⣀⢚⣟⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣼⣿⣾⣊⣿⡵⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣯⣞⣿⣎⢆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⡿⣪⢶⢤⣰⡦⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣧⡀⣰⣿⣾⣿⣿⣿⣦⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⣿⡏⠉⠉⠉⠛⠻⠯⣽⣿⣿⣿⣿⠿⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣄⡛⣧⣤⣤⣤⣤⡄⣀⣼⡧⣤⣤⣤⣤⣤⣽⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣛⣛⣛⣛⣛⣛⠙⡛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠱⡄⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠐⠒⠲⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢇⡇⠀⡀⠴⠀⠀⠈⡉⠀⠐⠤⣀
⠀⠀⠀⢀⠔⠊⠈⠇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠑⠄⡀⠀⠀⠀⢀⠔⠁⠀⠈⠨⠉⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠑⡄
⠀⠀⠔⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⢀⠆⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠘
⠀⡔⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢤⡀⡌⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢡
⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⡀⢔⡧⠃⡄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠌
⠀⡷⡀⠀⠀⠰⡁⠀⠀⢀⣀⢰⠅⣄⡐⠲⠬⡒⠛⢄⡆⠀⢠⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢸
⠀⠉⠺⠀⠐⢶⠙⠛⢧⡀⠉⠫⡁⠀⠑⢄⠀⠈⠢⣤⠀⠀⠈⡄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠱⣄⠀⠑⢄⠀⠈⠢⡀⠈⠲⢄⠀⠑⠢⡀⡄⠀⠀⠀⢌⠢⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠘⠗⢄⠀⠑⢀⡀⠈⠢⡀⠀⠑⢄⠀⢘⠃⠀⠀⠀⠈⡓⠢⢈⡑⠒⠧⠀⠀⣀⡀⠀⣸⠀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠈⢂⠑⢄⠀⠈⠢⡀⠈⠢⡀⠀⠑⡞⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠐⠒⠠⠄⠤⠌⠭⠩⡬⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠙⢤⡀⠈⠢⡀⠈⠑⢄⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠙⠢⡀⠈⠢⡀⠸⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⢄⡀⠈⠢⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠉⠠⡀⠈⢲⠁⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⢰⣒⣲⣶⣒⣒⣖⣲⣖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣤⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣛⣩⣭⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣉⣭⣥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣴⠶⢖
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⠾⣋⣥
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠛⣥⡾⢂⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡟⣱⡦⢀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣁⣶⢠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣭⣉⣙⣛⣛⣛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠙⠛⠓⠶⣬⣝⡛⠿⣿⣿⣿⣿⢛⣛⢿⣿⠿⠿⠟⢛⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣭⣥⣬⣤⠴⠶⠞⠛⠛⢛⣯⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣆⠀⠀⠀⠀⣀⣠⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⣘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠠⠁⡀⠃⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡔⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⢿⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⡐⠾⢀⠄⡠⠂⠀⠀⡀⠀⠀⠁⠋⢃⠄⠀⠀⠀⢘⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡁⠈⠁⠐⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣠⣾⣿⣏⣶⠀⠀⠀⡎⠠⠀⠀⢆⣀⣷⣤⠑⠀⠀⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⠘⢺⡀⠀⠀⡜⠀⠀⠀⠀⠔⣆⢶⣿⣿⣿⣿⣿⡆⠀⢸⣀⣀⣸⣠⡿⣿⣿⣿⣜⡇⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠁⠸⡇⠀⠀⣗⠀⠀⠀⢰⣨⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢛⠉⠉⠉⠉⠉⢻⣿⠟⠀⠀⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠒⡗⠇⠠⣷⣤⣄⣄⣴⣷⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⡄⠀⠀⠀⠀⣾⡏⠀⠀⢠⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⡖⠘⠛⠀⠀⠈⠙⣥⣤⣤⣴⣾⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢸⣧⣒⢲⡦⠤⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡏⠀⠀⠀⣼⣯⣭⣥⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⢶⣒⣒⣚⣻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⠁⠀⠀⠀⠀⠀⢈⠟⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠧⠠⢽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠇⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣟⠉⢹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣗⠀⢸⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣷⠀⢘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡂⢰⣿⣿⣿⣿⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡼⠛⠋⠉⠉⣁⣀⣀⣤⣬⣷⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣿⠾⠟⠛⠛⠛⠋⠉⠉⠉⠻⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠀⠀⣤⡀⣴⣦⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢈⣀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠯⣉⣉⠈⠉⠀⠉⠙⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠏⢙⠒⠚⠁⠀⢀⣀⡀⣀⡶⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠑⢄⠤⠞⢿⣼⣿⠟⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⢘⠹⣄⣀⣀⣤⣰⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣄⣰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠛⠒⠲⣤⠤⢤⣤⠤⠤⠖⢚⣻⣽⠀⠀⠀⠀⠀⠀⠀⢀⢞⡴⠋⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠈⠉⠈⠳⡦⣄⣀⠠⡤⢀⡤⠊⠁⠀⠉⠓⠒⠞⠲⠶⠶⠒⠖⢻⣻⠉⠀⠀⠈⠢⡀⠀⠀⠀⡴⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠂⢈⠟⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠸⠸⠁⠀⠀⠀⢪⣉⣉⣉⣙⣋⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⢀⢀⠴⡄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢐⡂⠀⢳⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⠀⡠⠸⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠺⡿⠇⠀⠀⠀⠀⠀⢸⡃⢀⣀⡀⠀⠀⢀⠔⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⠉⠉⡁⡅⠀⠀⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⢤⢰⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠒⠁

⣿⢛⡛⣿⡟⢻⣿⢻⠛⣿⢻⡟⡛⣿⢛⣛⢻⡛⡿⢻⡟⣻⣿⢛⣻⡟⢿⡟⡿⢛⡛⢿⢻⡟⢿⠟⣿⡿⢛⣛⡿⣛⡛⣿⠻⣿⢻⢛⣻⡟⣛
⣿⢠⡐⠿⣈⣁⠿⢸⢰⣎⢸⡇⠆⣡⡘⠿⣠⣇⢁⡆⢡⣿⣿⠶⢉⡇⣦⠁⣇⠻⠟⣸⡆⢡⡌⣸⣿⣇⠻⠿⣆⠻⢇⣼⢰⡌⢸⠀⢾⡷⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⡄⠀⢠⡄⠀⠀⠀⠀⢠⡄
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⣇⡗⢳⣰⡞⢺⡇⣶⢰⣦⣞⣻⣵⡾⡶⢰⣷⠀⢸⡟⣷⢸⣷⡞⣺⢴⡞⢺⣷⡞
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠁⠁⠈⠀⠉⠉⠁⠉⠉⠀⠉⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠈⠁⠉⠉⠀⠉⠉⠁⠉
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠤⢀⡀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⡄⠀⢷⣴⣦⡞⣿⠛⡆⣶⢸⡇⣾⣷⠄
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠁⠈⠀⠈⠀⠁⠉⠈⠁⠈⠉
⠀⠀⠀⢹⡛⠿⣿⣿⣶⣤⣍⣛⠻⠿⣿⠗⠒⠂⠀⠐⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢻⣷⣦⣍⣙⠛⠿⢿⡿⠋⠐⠠⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣤⡎⠉⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢻⠛⠿⢿⣿⣷⡶⠁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣶⣦⣤⣉⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⣿⣿⣿⠄⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢟⠛⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⣿⣿⣤⣤⣿⣿⣿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⢦⣼⣶⡦⠤⣤⣠⣤⣤⡤⣤⣤⣠⣄⣴⠆⠀⠀⠀⠀⠐⣮⣙⠿⣶⣬⣝⣻⠟⠲⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠛⡿⢹⣝⠢⣌⡙⠢⢌⣙⠢⢌⣉⢳⠃⠀⠀⠀⠀⠀⠀⢹⡻⢷⣶⣭⡟⠑⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⢇⡙⠢⣍⡓⠦⣌⡙⠒⢮⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣬⣹⠀⠀⢠⠀⠀⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠸⣍⠒⠤⣉⠓⠲⠬⣉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣉⣻⡀⠀⢀⠀⠀⠀⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡑⠢⢄⣉⠓⠢⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⠇⠘⡯⢍⡛⠍⣙⠫⢍⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠒⠦⣌⣉⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠹⣑⠪⠥⣂⠤⢭⡇
⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠲⢤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠬⣁⠒⠨⠽
⠀⠀⢠⠄⢠⢅⠈⢰⣀⠀⠀⠀⠀⠀⠀⠀⢏⠓⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡒⠤⢩⠃
⠀⠀⢸⠂⠸⢦⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠘⣋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠍⡚
⠀⠀⠈⠓⠀⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣶⠋⠛⣆⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣄⠀⠀⣴⠲⣄⠾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣿⠇⠀⣸⠻⣄⡗⢠⡆⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢶⣯⡀⠀⢸⡆⠀⠙⢦⡟⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⡏⠀⣽⠋⠉⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠁⠀⢸⡇⠀⣠⠞⠉⠋⠁
⠀⠀⠀⠀⢀⠀⠈⠢⡀⠈⠙⢲⡾⢤⣼⣧⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢀⡾⢀⡼⠁⠀⠀⠀⡀
⠀⠀⠀⡰⠃⠘⢢⠀⠀⢄⣠⠏⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡞⠁⢸⠁⡠⠁⢀⠖⠈⠳⡄
⠀⠀⠀⠀⠀⠠⠀⠙⠤⢸⡿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠛⢻⣶⡠⢀⠎⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠈⠂⠍⢐⠫⠟⢻⢹⡟⡟⢿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⣠⠴⠞⠉⠀⢀⣠⣴⢿⡛⠷⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⢠⢶⡶⡟⢿⠹⢈⠣⠄⠈⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⢤⣤⣤⡤⠠⠀⠀⠀⠀⢂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⢀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⣀⣀⠤⠤⠔⠒⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠤⣊⠉⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠃⠀⠀⠀⠀⠍⠁⠀⠀⠐⡲⠠⠤⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠉⠐⠒⠀⡸⠠⠠⠄⣀⣰⡀⠀⠀⠀⠀⠊⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠉⠉⠈⠁⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠤⠄⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠃⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠁⠂⠠⠤⠄⠐⠂⠉⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠩⠛⠉⠉⠉⠉⠉⠉⢉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠉⢤⡀
⠀⠀⠀⠀⠠⠤⠄⢠⢴⠋⠀⠃⠀⠀⠀⠀⠀⠀⠰⡁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡰⢄⠂⠐⠂
⠀⠀⠀⠀⠀⢀⡔⢁⠂⠀⢰⠀⠐⠄⣀⡀⠔⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠱⢄⡀
⠀⠀⠀⣀⠔⠁⠀⡈⠀⠀⠀⠉⠂⠤⠐⠀⠀⠀⠀⡠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠢⣤
⠉⢉⠜⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠉