Sprout Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡔⠂⡆⠀⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢈⢧⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢌⠿⣤⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⡙⠻⣻⡆⣲⠀⢠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡈⠻⢆⣻⣴⠀⢀⠇⠀⢣⡀⠀⠀⠀⠀⠀⠀⠘⠄⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⢦⢹⣿⠀⡜⠀⠀⣿⢣⠀⠀⠀⠀⢤⠀⠀⣼⣩⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠠⢀⠙⠻⣣⠇⠈⡸⡎⠸⠀⢰⢀⠀⢸⠀⢰⣯⠕⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⠠⠒⠤⠔⣿⣧⠰⡟⢀⠆⠄⢸⠘⠀⢸⣀⣼⡡⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠰⡀⠀⠀⠑⢤⡐⠶⢌⡳⡷⢁⠎⡘⠀⡼⡀⢀⡶⣿⣋⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⠀⠉⠓⢷⣷⣁⠀⠀⠀⡀⠉⠐⠘⣷⡎⠀⡇⢀⣃⢶⣽⣫⣡⠤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢀⠀⠈⠀⠈⢷⡆⢄⡀⠀⠀⠀⠀⠀⢣⠀⣧⣚⡵⠋⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠻⣕⠂⠀⠀⠀⠀⠊⢲⠟⠁⠈⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠐⠒⠒⠪⠷⣧⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⢀⣀⣈⣻⡂⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢸⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡙⣅⡸⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡇⣚⢄⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠇⠐⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡁⠴⠖⠷⠼⠋⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠈⠓⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣦⣬⣏⡿⣧⣝⣛⠂⣀⢀⠀⠀⡁⠑⢾⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣵⣿⣟⢻⣯⢲⢾⢧⣸⠻⠟⢀⡈⠖⠀⠉⠁⠀⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣉⣽⣉⣶⣷⡶⣉⣽⣿⡿⠿⡟⢇⢸⡷⠺⠉⣲⠒⣀⠀⠆⠠⠄⠈⢅⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠙⠛⠲⠌⠽⠿⠿⠛⠛⠻⠋⠉⠟⠲⠖⠻⠯⠭⠞⠁⠉⠁⠈⠉⠉

⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⣲⠒⣲⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢫⡅⣀⣤⣴⣚⣉⡉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣸⠞⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣠⠾⠥⠤⠶⠂⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣀⣠⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠓⢲⣦⣄⣀⣹⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢈⣩⠟⠛⣹⠋⢈⡏⠉⠉⠙⠻⣷⣄⠀⣀⣀
⠀⠀⠀⠀⠀⢀⡞⠱⣲⠖⢻⠇⠀⠐⠃⢀⠞⠀⠀⠀⢀⡤⠼⣿⡻⡿⠯⠗
⠀⠀⠀⠀⠀⣼⢠⣾⠁⠀⠈⠀⣀⣠⠴⠋⠀⠀⠀⠀⣞⣸⠛⠁⢹⡙⡆
⠀⠀⠀⠀⠀⣿⣃⠬⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢳⢹⡀
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣿⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣠⠶⠶⢚⠿⠶⢧⣺⣅⡽⠶⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠦⠀⠉⠻⠿⢽⣇⠀⣴⠤⢷⡶⠋⣤⡄⠀⣦⠈⢧⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠲⣄⡉⠒⠒⠤⢤⢄⣈⢁⡼⠋⠁⠀⠈⣉⠀⠈⠉⠢⠀⠐⠚⠉⠁⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢈⣁⠀⠀⠀⠀⠀⠀⣉⠚⣾⡁⠛⠰⠆⢀⡀⠀⠀⡤⢄⠶⠄⠀⠛⠓⠃⠒⢂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣦⡬⣄⣘⣥⣬⣉⣠⠵⠞⢿⣙⡒⠶⢦⣤⣅⣀⣀⣠⠤⢤⣴⣚⣭⡉⣯⡍⠩
⠀⠀⠀⠀⠀⠀⠈⠣⠈⢓⣒⡚⢃⠤⠶⢾⡿⠚⠆⡴⠿⠁⢀⡉⠩⡍⠓⣦⠰⢯⣉⣁⣀⣾⣂⡤⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠒⠛⠋⠘⠃⠀⠳⠶⠲⠿⠷⠒⠛⠛⠁⠀⠀⠀⠉⠁

⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠂⠀⠉⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⣌⠚⢄
⠀⠀⠀⠀⠀⠀⠀⢈⣨⡔⠀⠀⡠⠀⠉⠐⠀⠀⠀⠀⠀⠤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣀⣀⡀
⠀⠀⠀⠀⠠⠂⢠⣤⠀⠘⡆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⠉⠉⠲⣀
⠀⠀⠀⠀⡇⠀⠀⠈⢁⠀⠀⠀⠸⠀⠀⠀⠀⠴⠦⠶⠠⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠸⡇⠀⠙⠶⣄
⠀⠀⠀⡤⠀⠀⠀⠄⠘⠛⠻⢧⣾⣄⣀⡌⣀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡀
⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⠻⢏⠙⢶⣄⠀⢠⡴⠒⠶⠶⢀⡀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠿⠀⢋⠰⣀⣀⠀⣈⠁⠀⠀⠀⠀⠈⠛⠛⠛⠃⠈⠉⠀⠀⠄⠀⠠⠀⠀⠈⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠘⠋⠰⢋⡈⢠⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀
⡧⠀⠀⠀⠠⠀⠐⠖⠉⣻⠀⠀⠀⠀⠀⠀⣠⠿⣉⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⢀⠀⠀⠁⠰⣿
⠀⡀⠀⢀⣤⠐⠀⠀⠸⠃⠀⠀⠀⠁⣤⠛⠁⠀⠉⢀⣄⣠⣷⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠐⠀⠘⣿⡀
⠘⠇⠀⠉⠀⠀⠀⠀⡶⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠋⢈⡿⠁⠀⠉⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠰⠂⠰⢸⡇
⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢁⠀⡇⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⢠⡄⣴⣂⠀⠀⠀⠀⠀⠀⠄⠀⢘⡦⠀⠠⠈⢤
⠀⢸⡀⠀⠰⠀⠀⠀⠀⠀⠠⣤⠾⠧⠤⡀⠀⠀⠀⢸⣿⡆⠀⠀⠀⡇⠘⢠⣿⣷⡄⠀⠀⡤⠀⠀⠀⢨⣧⠀⠀⠀⣤
⠀⠈⣧⠀⢰⠀⢠⠀⠀⣾⣇⠀⠀⠀⠀⠀⠉⢦⡀⠸⣿⡇⠀⠀⡄⠀⠀⣿⣿⡟⠀⠛⠳⢤⡶⠶⣄⠘⠃⠀⠀⠠⣙
⠀⠀⠈⣶⠋⠀⠘⠀⣠⠛⢿⣿⣷⣦⣘⣦⡀⠀⠐⢦⡙⣇⡀⠐⢁⣠⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⢠⡟
⠀⠀⠀⠻⣀⠀⣿⠆⠁⠀⠀⠙⠋⠉⠙⢻⣟⣇⠀⠈⣿⣿⠟⠛⠋⣽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣱
⠀⠀⠀⠈⢿⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⡞⠉⢷⡾⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡄⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⢀⣾⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣰⡿⠛⠛⠙⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠓⠻⣀⠈⢿⣷⣶⣦⣄⣀⣬⣷⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠂⠀⠀⠀⠀⠻⡷⣼⠿⣦⡉⠙⠻⠶⠈⠀⣉⡙⠛⠳⠾⣇
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠏⠀⠀⠀⠀⠀⠀⠀⢀⠛⢤⡈⠻⣦⡀⠀⠀⡀⠈⣿⠀⠀⠀⠈⠻⡖
⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⠀⠀⠀⠶⣠⡶⣌⠑⠈⠀⠀⣀⠶⢻⣧⠀⠀⣹⠀⢹⡆⠀⠀⠀⠀⠀⢰
⠀⠀⢀⡶⢺⡇⠀⠀⠀⠀⠀⠀⠙⣠⠛⠀⠈⠀⢠⣤⠞⠁⠀⢸⡏⠀⢼⠁⠀⢈⡄⠀⠀⠀⠀⠀⠙⠃⢀
⠀⠀⠚⠀⠘⠇⠀⠀⠀⠀⠀⠈⠁⠛⠀⠀⠀⠀⣠⠏⠂⠀⠀⣸⣷⡀⣸⠃⠀⠘⡃⠀⠀⠀⠀⠀⠈⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡾⠁⠀⠀⠀⢤⠿⡇⠸⠁⠐⠄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡦⠀⠀⠀⢐⡿⠃⠀⠀⠄⠁⠈⢠⠘⠀⠼⠃⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠉⠀⠀⠀⠀⡸⠁⠀⠀⢈⢠⠄⠀⠸⢇⠀⠀⠁⠀⠀⣶⠀⠀⠸⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠃⢸⡀⠀⠀⠀⠀⠀⠘⠀⣿⣤⡄⠀⠀⠀⠿⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠞⠳⡄⠀⠀⠀⠀⠀⠀⡄⠠⣾⠀⠀⠀⠀⠸⠗⠶⠒⢢⣄
⠀⠀⠀⠀⠀⠀⠘⠎⢻⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣀⠀⠀⣼⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⣜⢦⠀⣿⠊⠀⠀⠀⣀⡤⠔⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠌⢷⣠⠃⠀⠀⡴⠋⢁⣠⠎⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣠⡴⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠋⣉⠉⠙⠳⢄⡀⠀⢸⠀⣠⠞⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠴⠥⢤⣌⡉⠉⠉⠉⠙⠛⠦⣵⡀⢸⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠤⠤⠤⠖⠋⠙⢼⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣰⡫⠍⠉⢹⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⢤⡟⠁⠈⠛⠊⠁⠀⠀⢰⢟⣩⣍⠳⡄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣸⠇⣿⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⡏⠓⢤⡀⠀⠀⠀⣸⠃⣠⠞⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⣕⡉⢹⡍⠑⡄⠉⠲⢄⣠⠏⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣤⢼⣌⣹⣏⣹⣿⣉⣦⣠⢞⡥⠾⢥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠡⡞⠘⠐⢧⡞⢢⣉⠴⡏⣩⠗⠋⠀⠀⠀⠈⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⣔⠉⠓⠒⠋⠧⠞⠈⠳⣇⡙⢲⣄⣀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣷⠈⡉⠻⡭⢇⠀⣀⣀⣠⣿⣍⢩⠿⠞⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢯⣀⣈⡿⣤⣓⡾⠴⢋⡙⠷⣯⠱⣞⡆⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠐⡏⣝⢒⢆⠔⢒⡆⠓⠊⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠁⠈⠹⠆⠙⠉⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⢸⡀⠀⠀⣀⣀⡤⠴⠖⠋⠉
⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠟⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣶⣄⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣰⠶⠛⠉⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⣰⡿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⣴⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠁
⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠶⠞⠛⠛⠿⠶⣦⣤⣄⡀⠙⠁⣾⠋⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠟⠁
⣿⣿⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⣀⣤⣴⣶⡾⠿⠛⠋⠁
⠉⠉⠉⠉⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣦⣀⠈⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡿⠿⠛⠉⠙⠿⣷⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣸⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⠿⠟⠛⠻⢿⣿⠀⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠁⠀⠀⠀⠰⢶⣦⣼⣿⠀⠀⣼⠟⠿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣾⣿⠀⠀⠀⠉⠻⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠉⢻⣿⣿⣿⣾⠿⠿⢿⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣼⡿⠀⠀⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣿⡟⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠈⠛⠿⣿⣿⣷⣶⣶⣶⣿⡿⠿⠿⠿⠿⢶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣿⣦⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣰⣿⠛⣿⡿⢿⣿⠿⠟⠛⠛⠋⠉⠛⠛⠻⠿⢿⣶⣤⡀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢠⣿⠇⠀⣿⡇⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣸⡿⠀⠀⠻⣿⡀⠹⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣇⠀⠀⠀⠙⢿⣦⣀⠉⠙⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠸⣿⡆⠀⠀⠀⠀⠙⠻⢿⣶⣦⣤⣤⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠛⠻⠿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⡀⠀⠀⠀⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⣶⣿⣿⣷
⣶⣷⣶⣿⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣿
⣿⣿⣿⣿⣿⠛⠋⠻⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠖⠛⠋⢉⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠁⢀⣀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡉⠙⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣀⠤⠒⠉⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡠⠊⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠉⠑⠢⣄⡀⠀⠙⢷⡀⠀⠀⠀⣸⠃⣠⠊⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠲⣄⠀⢻⡄⠀⢀⣏⡔⠁⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⣄⢷⠀⣸⣟⣠⣤⠤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⣀⡈⢿⡆⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠖⠋⠉⠁⠀⠀⠀⠉⠙⠲⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠆



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠶⠶⠶⠶⠦⢤⣤⣀
⠀⠀⠀⢀⣀⣠⡤⠶⠖⠚⠛⠛⠛⠛⠓⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⢀⠀⣀⣀⣤⠤⠄⠀⠀⣩⠿⠛
⠀⠀⠀⠈⠛⢦⣄⠀⠀⠲⠤⣤⣤⣀⣀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⡼⠃⠀⣀⣠⣶⠞⠋⠉⠈⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠁⠀⠈⠙⠻⣦⣄⡄⠀⠻⡄⠀⠀⠀⢸⠃⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⣷⠀⠀⠀⢺⠀⣰⠏⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⣀⠀⠀⠀⠘⢷⡀⣽⠀⠀⠀⢸⣶⣇⣤⠴⠶⠒⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⢤⣷⢯⡀⠀⢠⣞⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⣄⡾⡾⠁⠀⠀⠀⢀⣠⡤⠴⠶⠶⠶⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠛⠛⠛⠛⠛⠒⠶⢤⣀⠀⠀⠀⢳⣻⢿⡇⠀⠀⣠⠞⠉⠀⠀⢀⢀⣀⣀⣠⠤⠀⠀⢀⣩⠿⠃
⠀⠀⠀⠀⠙⠻⢦⡀⠀⠀⠦⠤⣤⣤⣀⡄⠀⠀⠈⠳⣦⠀⠈⣯⢸⠃⢀⡞⠁⠀⢀⣤⡶⠟⠋⠁⠙⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠙⡷⣦⣀⠀⠈⢳⡀⣿⢸⡀⣼⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠈⡇⢹⢸⡇⣯⠀⡼⠇⠀⠀⠀⠀⠀⣀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⡀⠀⠀⠀⠘⢧⠀⡟⢸⣿⡇⢻⣼⣁⡤⠶⠶⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⣼⣷⣇⢸⣿⣷⢯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⢿⡿⣏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣧⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⢀⣠⡾⠷⠶⠶⣻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢰⣇⣠⠶⠛⠿⠶⠶⠶⢠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⡼⠋⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣰⠿⠤⠴⠶⠶⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢶⣦⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣉⣉⣀⣈⣩⣽⡷⣦⣤⣬⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⣡⠴⠛⠉⣰⠏⠀⣸⠇⠀⠀⠀⠙⠿⣷⣦⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠴⣶⡶⠋⡏⠀⠀⠐⠋⠀⣰⠏⠀⠀⠀⠀⢀⣤⠬⣿⡻⣿⠷⠭⠗
⠀⠀⠀⠀⠀⠀⢰⠇⣠⡞⠉⠀⠘⠃⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣰⠏⣴⠶⠋⠻⡌⢷
⠀⠀⠀⠀⠀⠀⣾⣴⠋⢇⣀⣤⡤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠹⠞⠋⠀⠀⠀⢻⡈⣧
⠀⠀⠀⠀⠀⠀⣿⡷⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣟⣀⡏⢡⡞⠛⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⠛⠓⠶⣦⣤⡴⢿⡅⠀⠐⡚⠩⣍⣙⣶⠟⠛⠉⠀⡈⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣁⡀⠙⠃⠀⠀⠙⠋⡙⡛⢦⣄⡿⠟⠋⢽⣻⠁⠻⣷⡀⠈⠳⠀⠘⢳⣚⡛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣈⠻⢤⡀⠉⠉⠁⠲⠦⠄⣀⡁⢠⠞⠉⠀⠀⠀⠀⣀⠀⠀⠈⠘⠳⠀⠈⠉⠉⡀⡀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠋⡟⠀⠟⠀⠦⠄⢀⡀⠀⠀⢀⣤⣠⠾⡇⠀⠐⠛⠱⠃⠖⠒⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣤⣉⣋⠀⠰⠖⠀⠒⠒⢀⣙⡴⢺⣏⠳⢦⣤⣤⣀⡘⠋⠀⠀⠈⢀⣉⣀⣠⠴⠶⠒⠒⡖⣒⡚⣉
⠀⠀⠀⠀⠀⠀⠀⠠⠦⠄⠸⣧⣤⣉⣿⠏⠉⣉⣩⠿⣟⣿⠋⢁⣤⡶⠛⠛⠲⠶⠶⠾⣭⣉⠛⣻⠿⠭⠭⠍⣻⣟⡏⢙⡇⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠢⣶⠤⣞⣋⣩⣭⠿⣁⡀⠃⣾⠉⠉⣀⣶⣆⣐⣛⣃⣠⡿⠀⠙⠒⠶⠶⠶⠞⠒⠚⠋⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠀⠀⠉⠛⠋⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⣀⣠⣤⣶⣾⠿⠟⠛⠛⠛⠛⠛⠻⠿⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⡇
⢀⣤⣶⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⠀⠀⢀⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠘⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⣠⣶⠞⠁⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢠⣄⡀⠀⠀⠀⣿⣿⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠆⠀⠹⠟⠀⢴⠟⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⣿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠻⣿⡄⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⡀⠀⠸⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣾⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⢶⣤⣤⡀⣻⡇⠀⠀⢸⣿⠃
⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣀⢠⣿⣿⣦⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠉⠻⣿⣦⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠙⢿⣷⣄
⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⡀⠹⣿⣧
⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠈⢿⣷⡀
⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⣠⣤⣶⣿⠿⠿⢿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠃
⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣦⣄⣀⡀⢸⣿⡿⠿⢶⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⡿⠿⠋⠁
⣠⣿⡏⢀⣤⣤⣶⣿⡿⣿⣿⣿⣶⣤⣄⡀⠉⠙⠛⣿⣿⣿⠟⠀⠀⣼⠏⠉⠉⣿⡿⠛⠛⠋⠉⠁
⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⡶⠟⠛⠉⠀⢀⣠⡾⠋⠀⣀⣾⡿⠁
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⢀⣴⣾⣿⣿⣶⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢠⣿⡟⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣦⣤⡀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠈⠙⠻⣿⣷⡄⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⢽⠂⢀⣀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣶⡀⣐⣰⡷⡦⠦⢵⠾⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⡲⠀⠀⠀⠄⠀⠀⠂
⠀⠀⠀⣸⣿⣧⢀⢈⡯⢐⣦⡞⠉⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢬⣭⠄⠀⠀⠀⠀⠀⠈⠶⢦⠐
⠀⠀⠀⣿⣿⢻⣸⣯⣶⠰⣿⣬⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠖⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣏⠸⠿⢿⠟⢧⣬⡷⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡂⠀⠀⠀⠀⢂⠠⣅⠀⠀⣐⠉
⠀⠀⠀⠀⣹⣤⡀⠙⠟⠁⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⢨⣴⠀⣷⠀⡁⣼
⠀⠀⣠⣾⣟⠻⢍⡟⣿⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⢴⣿⣿⣏⢉⣼⢗⡡⠄
⠀⠀⣿⣿⣿⣧⡀⣿⣿⢢⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⡤⠶⠂⠀⠈⠉⢁⣘⠄⠀⢀
⠀⠀⣻⣿⣿⣿⣷⣸⣿⣆⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣴⣮⣛⠛⠻⣿⠧⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠞⠖⠀⠀⠙⠿⠿⠛⠓⠒⠀⠀⠀⠓
⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠙⠌⢦⡀⠀⠀⠀⠀⠀⠀⣤⠼⣿⣩⣤⠄⠒⣰⣖⡢⠆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠁⠐⣀⡄⠀⠀⠾⠀⠀⠣⠀⠀⠈⠃⠠⠤⠦⠀⠀⠀⢡⠀⠨⠞⣠⠚⣡⠜⠋⠁⣀⠚⠛⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⢘⣻⡆⢢⣦⠀⠀⣀⠀⠀⡇⡵⠐⢈⡙⢁⠀⠀⣠⣦⢀⠤⠇⠚⢵⡾⠋⠀⣧⠀⠀⣠⣿⡀⢠⡅
⠀⠀⠀⠀⠀⢰⣶⠎⠁⡄⠈⠚⠻⣿⡷⠀⠈⢰⡄⠻⠀⢀⡇⠦⡀⠀⠃⡜⠃⠺⠏⠀⠀⠀⠀⠀⠈⠇⠀⣴⣿⣦⣎⣀⠈⣤⠀⠓
⠀⠀⠀⠀⠰⣯⡟⠁⠘⠋⠀⣠⡆⠘⢿⠀⠀⣾⡁⢀⠀⢨⠁⠀⠀⠁⠒⠳⠀⠀⡀⠀⠀⠀⠀⠀⡄⡃⢄⠁⠂⠄⠉⣉⠃⢀⠈⣥⡀⢀⡂
⠀⠀⠀⠸⣿⠉⠶⠶⡤⢀⣻⢨⡛⠄⠈⢨⠀⢸⡀⢸⢠⢼⡒⠀⠤⠀⡄⠰⠀⠠⣛⠀⠤⣶⢲⡼⠀⠡⠄⠂⠠⠈⢀⢀⠈⢀⡆⢿⡅⣜⠃
⠀⠀⡆⠀⠉⠀⢰⡎⠀⢠⠇⣀⡉⠃⠀⠘⠃⠈⡷⠾⠚⠛⠟⡂⣄⠐⢡⠐⠅⠘⠙⠶⠤⠀⠉⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⡜⠀⠀⠉⠳⠆
⠀⠀⠀⠀⠀⠀⢸⠁⣀⣠⠀⠛⣡⡀⡀⢄⡀⠉⠀⠀⡀⢤⡀⠀⠠⣛⡄⠙⠀⠀⠚⠤⢀⠂⠀⣀⠙⠇⠀⠀⠀⠀⠀⣠⠄⠀⠾⣄⡀⠀⠀⣠
⠀⢠⡿⠂⠀⠀⠀⠀⠈⠹⠀⠰⠿⣀⡷⠈⣁⠃⢀⠙⡟⠠⠅⠀⠀⠈⠀⠀⠀⠘⠃⠀⢠⠅⢈⠋⠀⠀⠈⠳⣶⣿⣛⠃⠀⡀⠀⣄⠀⡀⠠⡿⠄
⠀⠈⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠀⠓⣂⢡⠴⠗⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⡄⠀⠀⠀⠀⡩⡄⢹⡄⠈⠀⠀⡅⠀⠁⡰⢂⡀
⠀⣠⠗⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠺⠁⠀⠀⠰⢟⣁⣀⣷⣦⣱⣿⠆⠀⠀⠐⠀⠁⠀⣸⡧⠈
⠀⠸⠀⠸⡇⣀⡞⢀⡟⠀⠀⠀⠀⢀⣰⠷⡄⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠃⠀⠋⠸⣷⢞⡉⣥⡩⣹⣶⣦⣤⣀⡀⠀⠀⠈⠅⡀
⠀⢀⣐⣀⣈⣽⣅⣸⠃⠀⠀⠀⠿⠋⠁⢀⡀⠱⣿⡧⠀⠀⠀⠀⡀⠀⠰⢺⣄⠀⠀⠲⠀⠘⠁⢸⡟⠻⠖⠿⠛⠞⠉⠉⠛⠻⠿⣷⣶⠒⢮⣀⡀
⠀⠀⠽⠓⠘⠓⠚⢿⠄⠀⢤⡴⢠⡄⠀⠀⠁⠀⢰⡦⠀⠀⢄⣠⡄⠀⣀⠓⣈⡡⠴⢪⡉⠵⠲⢒⣤⣀⠀⠀⠀⠀⠀⣿⣶⣤⣤⣀⣀⠀⣼⡉
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⡇⠈⠉⣤⠉⠠⡄⠀⠀⠀⠀⠀⢹⣫⢁⣩⠄⠀⠀⠤⢉⠐⠌⢃⠠⠤⠹⠳⡄⠀⠀⢠⣿⣿⣿⣿⡿⣿⡿⢶
⠀⠀⣀⠀⠀⡺⠘⠓⣦⣄⠺⢇⢀⡀⢼⡀⢠⠃⠀⠀⠀⠀⠀⢀⠛⣠⠍⠀⣤⡐⠂⣉⠑⠆⣀⠤⠂⠠⣘⢣⣤⠖⠁⠀⠉⠿⠉⠙⢶⡍⠒⢀⡄
⠀⠀⠓⠁⠀⠀⠀⢀⡁⠈⣾⣻⡈⠅⢀⠁⠀⢠⡀⠀⠀⠙⠶⠾⣦⠉⠐⠒⢠⣄⣂⡈⠌⢠⣭⡀⠾⠛⢡⡀⠙⢦⢄⠀⠀⣰⣦⣌⢂⠱⠞⠁⠁
⠀⠀⢺⣄⢀⡴⡠⠞⠓⠘⠋⢱⡄⠀⣼⠆⠀⠀⡁⠀⠐⣀⣀⠀⡉⢓⠠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠔⢉⠱⣷⠦⠑⠀⠀⠉⠙⣻⡿⢇
⠀⠀⠘⣿⡟⠆⠀⣶⠂⠀⣤⠋⢀⡄⠀⠀⣰⠀⣠⠟⠀⠍⣩⠔⠟⢸⡄⠹⠗⠀⠀⠀⠀⠤⠂⡀⠀⢶⡟⠋⠀⠀⠀⠀⣀⣀⣠⠟⠀⠀⠀⠓
⠀⠀⠀⡿⠀⠀⠀⠈⠦⠀⠛⣦⣬⣿⡦⠀⠈⠁⠈⠃⠐⠦⠛⠃⠠⠜⠁⣴⡀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠉⠚⠯⣤⣤⠎⠙⢏⠀⠀⡠
⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠀⠁⠁⡈⠀⠊⠐⣦⢠⢠⣤⣄⠀⢚⡀⠐⠀⠀⢳⣄⡀⢀⣀⠜⣇⠳⠀⠀⠀⠀⠀⠀⠉⢀⠀⣀⠀⣿⣿
⠀⠀⠀⠀⠀⠘⠒⠋⠀⡏⠀⠀⠀⡌⠀⢀⠀⠈⠡⠋⠁⠀⢨⡀⢀⠐⠁⡆⢀⡹⠿⠛⠇⠀⠸⣬⡀⠀⠀⠀⠀⠀⣰⠞⠋⠀⠀⠉⠀⠀⠀⠐
⠀⠀⠀⠀⠠⣀⣀⠀⢀⠙⠆⠀⠀⠀⢀⡁⠐⠀⠀⠰⠋⠀⢋⡐⠋⠁⠘⠓⢫⢤⡆⠀⢲⠇⠐⠀⠉⢢⣤⣤⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢈⣁⠛⠒⠒⠚⠁⠀⢀⠀⠰⠖⠃⠀⢼⠃⠀⠀⠀⠀⢸⢆⠀⣠⠊⢠⡄⠀⠄⠀⢨⠻⠦⣤⠄⠃⠀⠛⠃⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣟⠀⠀⠀⡼⠉⠃⣤⠃⠀⠀⠀⠀⠀⠀⢸⡈⠿⢄⡖⠤⠵⠶⠶⠀⠁⠠⠆⠉⠛⠂⠡⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠋⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⣼⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣀⣀⣀⣀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣥⣠⡍⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣿⣿⡄⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠉⠙⠻⣿⣿⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣏⠁⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⡴⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣤⣛⣷⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣀⣿⠹⠛⠛⢋⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡁⣤⡤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⢰⣿⣿⡿⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣍⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣄⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⡻⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⡎⢿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣤⣀⢸⣿⣧⣼⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⢀⣏⢸⣿⣿⡏⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣾⡟⢻⣿⣿⠃⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣱⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⢛⣉⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⡥⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠋⢉⡀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣀⠶⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⣁⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠻⡟⢀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣧⠈⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣹⣶
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣛⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣏⣿⣿⣿⣿⣿⣿⡙⠓
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣶⣶⡶
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠙⠛⠿⠿⠿⠿⣿⣿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠛⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠸⡟⣿⠟⠇
⠀⠀⠀⠀⠀⢿⡿⠟⠁⠀⠀⠀⠸⣶⣦⣴⠶⣦⣀⠀⠀⠀⠀⣈⡹⣿⣧⣅⣘⡁⠀⠀⠀⠀⠀⣀⣠⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣾⣿⣿⣟⣻⣿⡷⠺⠿⢲⣦⣤⡿⣿⣶⣿⡿⠛⢿⣷⢾⣯⣼⣶⠁⠈⡿⠀⠘⠋⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠉⠉⠉⠉⠀⠀⠁⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⣠⣊⣁⠀⠀⠉⠑⢆⠀⠀⠀⢀⠊⠀⢠⡀⠁⠀⠊⠀⠈⠀⠀⠀⠀⠆
⠀⠠⠁⢠⠀⠀⠀⡄⠈⠄⠀⠀⠀⠀⡞⠁⠀⠈⠙⢦⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⢨⠀⠙⠀⠀⠰⠀⠀⠀⠸⠀⣠⣴⠖⠒⠒⠶⠤⣄⡀
⢠⠁⠀⠀⠢⠀⠜⠀⠀⠈⡄⠀⠀⠀⡅⠀⠀⠀⠀⠘⡆⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⠀⡄⢻⡇⠀⢀⡴⢷⠀⠀⠙⣦
⠀⢢⣀⡤⠄⠭⠤⢄⣀⠔⠁⠀⠀⠀⢣⠀⠀⠀⠀⡸⠁⠀⠀⡜⠀⠀⠀⢠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⠉⠀⠘⢦⣠⡴⠛
⠀⡤⠄⠀⠀⠀⢀⠀⠀⠤⡀⠀⠀⠀⠀⠑⠶⢖⣊⣀⡀⠔⠊⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠁⠀⠐⡃⠀⠀⠀⠀⠃⢠⠀⠀⠄⠀⡤
⠀⠑⠄⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠠⡀⠀⡠⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠋⠁
⠀⠀⠈⠢⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠑⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠐⡀⠀⡀⠁⠢⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠉⢣⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠐⠀⠋⠁⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢲⠄⣝⣲⢈⣔⣣⠠⠆
⠀⣠⣤⣤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣤⡀⠀⠑⢄⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⣀⡗⠀⠀⠀⠰⢖⡶⠉⠀⠀⠀⠑⣖⡰⠂
⠀⠈⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠑⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⢟⠩⠛⠉⠛⡟⠁⠀⠀⠀⠐⠂⣨⡇⠀⠀⠀⠀⠀⢨⡁⠒
⠀⠀⠘⠿⠿⠿⠋⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠑⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⡀⠄⢸⠁⠀⠀⠀⠀⠀⠘⢑⠗⣄⡀⠀⣀⡔⠳⠑⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⢳⡀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠚⠈⣷⠛⣩⠣⡏⠐⠃
⠀⠀⠀⠀⣇⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠂⣀⠀⠀⠀⠀⠀⠈⢇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⢼⡄⠐⠀⣄⠈⠀⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣶⢦⠀⠀⠙⠁⠀⡾⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠃
⠀⠀⠀⠈⠆⠀⠀⢀⠐⠀⠀⠀⠀⠀⠘⡄⠤⠭⠭⠭⠥⠔⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣄⠈⣷⣦⡀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⡀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⢟⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠛⢃⡝⠛⠛⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⢸⠈⠈⠂⣀⡀⣩⠀⠀⠀⣈⡩⡰⠀⢸⠟⠉⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⢄⢀⣤⠾⡣⠃⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⢀⡅⠀⠀⢈⠔⠊⠁⠀⠀⠄⠀⠀⠀⠀⣰⣿⣿⣧⢀⠂⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠅⠒⠂⠠⠁⠀⠀⠀⠀⠀⠈⠢⡀⢀⣼⣿⣿⣿⠿⠃⠀⠀⢰⡭⢭⣭⣥⡤⣤⣬⣭⣥
⠀⠄⠀⠀⣄⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠡⣚⠃⠌⠔⡛⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠟⠉⠙⠻⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⣀⡀⢸⡇⢮⡀⠀⠀⠀⣴⠀⡇⣤⠤⡤⣤⣤⣤⡤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⣉⣉⠉⠉⢹⢸⡇⠈⠻⠶⠴⠾⠃⠀⡇⡿⢠⢰⠀⠐⠀⠠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢊⣼⣵⠇⠀⢸⠘⢓⣒⣒⣒⣒⣒⣒⣚⠃⡏⢸⠈⢰⠀⢸⢸⡆⣿
⠀⠀⡶⠒⠒⠒⠒⠒⠒⠒⣦⢸⠀⠀⣾⣿⠇⠙⠀⢸⢸⡏⣉⡉⢉⣉⠉⠉⠉⡇⡗⢸⣼⢸⢸⢸⣸⡇⣿⢸⠉⠉⠉⠉⠉⣉⠉⢹
⠀⠀⡇⠐⢦⡲⣄⢦⠻⠀⣿⢸⠀⠘⠛⠋⠀⠀⠀⣸⢸⡇⠿⣾⣿⣥⣿⡀⠀⡇⣯⣬⣤⣬⣬⣬⣤⣤⣿⣸⠀⣰⣮⣿⣿⣿⡂⢸⡆
⠀⠀⡇⠘⢦⡑⢬⠡⣔⠀⣿⢨⣭⣭⣭⣭⣭⣭⣭⣭⢸⡇⣾⣿⣋⣟⣿⣷⠀⡇⣶⠒⠒⠒⠒⠒⠒⠒⣦⢸⠀⣿⣿⡽⠾⠿⠇⢸⠃
⠀⠀⡇⠘⢦⠓⢤⠰⠘⠀⣿⢸⠀⠀⢠⣤⣤⣤⡄⢸⢸⡇⠙⠛⠛⠛⠋⠛⢀⡇⣷⠀⠀⠔⠚⣿⣞⠀⣿⢸⠀⠛⠉⠀⠀⠀⠀⢸⠁
⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠟⢸⠀⠀⠀⠠⠶⠶⠆⢸⢀⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⠀⠀⠀⣠⣿⣿⠀⣿⠈⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣛⣛⣛⣛⡃⢸⣸⡇⢀⣀⣀⣀⣤⣦⠀⡇⣿⠀⢠⣾⣿⠿⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣉⣉⣉⣉⣉⣁⣼⢺⡇⢦⣍⡙⠛⣽⠟⠀⡇⠿⠶⠶⠶⠶⠶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣉⣉⣁⣀⣀⣀⣠⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠤⡼⠀⠀⠀⠀⠠⢄⣀⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⡍⠉⠉⠡⠄⣀⠀⠀⠠⣄⠄

⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⡔⠄⠀⠀⠀⠀⢀
⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣠⠄⢼⣿⠄⣄⠀⠀⢀⣤⣾⣶⣄⠀⠀⠀⠠⠘⠀⠀⠀⡀⠀⠀⢎⠀⠁⠜⠓⡄⠀⢠⠐⠉⠿⠀⢀⠀⠀⢠⠓⠈⠃⠀⢣
⢻⣷⣶⣶⣾⢟⠀⠀⣉⣀⣀⣀⢈⡱⠀⠀⣅⣀⣀⣠⣴⡎⠀⠲⣔⣤⣤⡤⡴⡆⠀⠸⣄⣠⣀⣤⣴⡇⠐⢯⡉⠑⢒⣂⣉
⠸⣿⣿⣾⣿⡇⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⢹⣿⣷⣿⣿⡇⠀⠀⢳⣧⣇⣷⣷⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⣿⣽⣽⣽⡿
⠀⠙⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣶⣶⡆⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⢠⣴⣦⣶
⣠⠄⢶⡷⠄⣄⠀⠀⢀⣬⣿⣿⢄⠀⠀⠀⠠⠛⠁⠠⡶⠀⠀⠀⠊⠈⠀⠼⠢⡄⠀⢠⠔⠛⠛⠛⢄⠀⠀⢠⠓⠭⠌⠁⢧
⢿⣷⣶⣶⣾⢿⠀⠠⡉⣁⡀⣀⠈⡱⠀⠀⣁⡀⣀⣠⣤⡆⠀⠲⣐⣄⣀⡤⡤⡆⠀⢸⣀⣠⣀⣠⣤⠇⠐⢯⡉⠐⠒⢚⣉
⢸⣿⣿⣾⣿⡏⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⢹⢿⣷⣿⣿⡇⠀⠀⢷⣇⣧⡷⣿⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⣿⣹⣽⣽⡿
⠀⠙⠛⠛⠛⠁⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠈⠓⠛⠛⠋⠀⠀⠀⠈⠛⠛⠓⠋⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⢀⠀⣠⣠⡄⡀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⢀⡀⠀⠀⢤⠀⠀⠀⡔⠛⢛⡫⠢⡀⠀⢀⠀⠀⠀⠀⢄⠀⠀⢀⠾⠥⠄⠭⣦
⠿⢶⣦⣴⣶⠿⠀⠀⡉⢉⠀⡈⠉⣡⠀⠀⡀⠂⡂⣀⣤⡗⠀⢢⣠⣁⣀⣠⡤⡄⠀⢸⡀⢀⣀⣀⣤⡇⠠⣾⡒⠒⠂⠒⢛
⢸⣿⣿⣽⣾⡏⠀⠀⢹⣯⣿⣿⣿⡇⠀⠀⢹⣏⣿⣿⣯⡇⠀⠀⢯⡗⣇⣇⣿⠇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠸⣽⣻⣻⣹⡿
⣀⣻⣿⣿⣟⣁⣀⣀⣈⣻⣿⣿⣟⣁⣀⣀⣈⣻⣿⣿⣟⣁⣀⣀⣈⣿⣿⣿⣏⣀⣀⣀⣙⣿⣿⣿⣋⣀⣀⣀⣹⣿⣿⣿⣁
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⡀⠈⢑⠀⠀⠀⠀⠀⠤⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⢄⠈⠁⠁⠀⠈⠀⠀⠈⠀⠀⢸⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠐⠄⡂⠀⠀⠈⠄⡀⠀⠀⢀⠎⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⠀⠑⠈⠂⠀⠀⠉⠉⠆⠀⠀⣠⠖⠁⠀⠀⠀⡠⢐⠨⠁⠀⠡⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠑⣄⡀⠀⠀⠀⡬⡼⠒⠲⠚⠁⠀⠀⢀⠀⡠⠊⠄⠂⠀⠀⢐⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠞⠁⠈⠳⠶⠶⢬⣭⣆⢤⣊⠌⠀⠀⠀⠀⠀⢀⡢⠕⠉⠀⠀⠦⠤⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠱⣄⠀⠀⢀⢌⠑⠈⠝⣛⠶⠊⠁⣈⣀⣀⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠓⣢⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠠⣐⠈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠈⠹⠀⢰⠆⠉⠿⢒⢦⡤⠤⠴⠂⠈⠁⣠⡤⠬⠍⡛⠗⠲⢏⠀⠀⠈⠢⣀⠀⡸
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠁⢲⠀⠀⢠⠀⡟⠀⠀⢀⡀⣀⣈⣉⣙⣛⡋⠉⠁⠀⠀⠐⠁⠀⠀⠀⢡⠀⠄⠂⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠘⠦⣄⠀⡰⠢⠔⠋⠲⡧⠴⠚⠁⠉⠀⠀⠀⠀⠉⠉⠓⠶⠀⡀⠀⠑⢄⡠⠋⢡⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠠⡐⠄⠀⢐⢌⠀⠤⣂⠀⠄⠀⢸⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠢⡀⠀⡿⠀⠀⠀⠀⠠⡂⠐⠁⢀⠠⠀⢒⠥⠀⠀⠀⠈⠈⠉⠉⠑⠢⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠎⠁⠢⠂⠈⠁⠀⠀⠀⠀⣁⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣶⢿⡘⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣷⣲⣶⣿⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⠏⢿⣿⣿⣿⣿⣧⣤⠆⠀⠀⠀⠄⠀⣶⣤⠄⠀⠀⢻⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣦⠈⠿⣿⣿⣿⣿⣆⢐⣤⣆⡀⡀⣴⣿⡿⠠⠄⡀⣀⠟⢉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢽⣿⠦⣬⠙⠿⣿⣿⡌⢳⡶⠟⠻⠛⠋⠀⠀⠀⠻⣟⣡⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣦⣻⣿⣇⣼⣄⢠⣤⣠⣤⣶⣦⠄⠀⢘⡿⠿⠏⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡤⢶⣦⣤⣭⢬⣬⠿⠻⢿⣿⡿⢿⣿⣿⣷⣿⣿⡿⣫⠦⢄⣼⣦⣴⠀⣠⣷⣤⡶
⠀⠀⠀⠀⠀⠀⠈⠛⠣⣍⡔⠀⠈⣷⣶⣾⣧⣷⠿⢷⣮⣷⣿⣿⣿⣿⣟⣷⣾⣿⣶⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣶⣬⠛⣉⠈⠁⠀⡀⠂⠀⠸⣿⣿⣭⣭⡀⣤⢤⡀⠉⠻⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⡇⢿⣷⠀⠈⠃⠀⠈⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⣠⣀⡄⣂⠀⣀⣀⣼⣿⣟⢻⡇⠘⣿⣾⣾⣆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠿⠁⠴⠞⢷⣾⣿⣿⣧⣽⡯⠁⠀⠈⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⠛⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡉⣹⡷⢾⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⢿⡗⠈⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣄⣽⡷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⡟⠛⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠛⣿⣤⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠷⣿⣿⡗⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠤⣶⠜⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⡶⠻⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⠛⣿⣦⢿⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣧⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟⠙⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢾⣿⣇⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠁⠻⠿⠟⠷⣄
⠀⠀⠀⠀⠀⢠⠀⠀⠐⠿⠇⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⢠⣄⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃⣀⠀⠀⠀⢸⠀⠀⠀⢀⡀⠒⠀⠀⠂⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠿⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠜⠛⠻⠷⣶⣾⣄⣀⡠⠈⠁⠀⠀⠀⠀⠀⠐⠛⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢻⣿⡶⢻⣶⣄⠀⠀⠀⠀⣀⠙⠠⠤⢤⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣤⡄⠉⠷⠀⠀⠸⠇⠀⢀⣾⠋⠀⠀⠀⠀⠉⠠⠤⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠉⠀⠀⣀⡜⠃⣠⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠘⠃
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠁⢀⠜⠁⠀⠀⣠⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⣿⠀⠀⠀⠀⠀⠀⢠⡄⠐⠞⠻⡖⠉⠂⠀⠀⠀⠀⠀⠀⠀⣰⣾⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠿⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢰⠿⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⢠⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣤⠀⠀⠀⣾⠋⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣶⡎⠁⠀⠀⠀⠀⢀⣤⢶⣴⡿⠓⠶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⣼⡇
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡈⠁⣴⡟⠁⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠃⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠀⠀⠀⠀⣤⠆
⠀⢠⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⡜⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡄⠀⠈⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠸⣇⠀⠀⠀⠃⢀
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠛⠉⠈⠉⠛⠀⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠁⠀⣀⣸⣿⣿⡿⠃⢀⣤⠀⠋⠀⠀⠀⠀⠀⡟⠃⠀⠀⡀⠘⣿
⠀⠀⠘⣦⠀⢰⡟⠀⠀⠀⠀⠀⣿⣽⣷⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠀⢸⣿⠀⠀⠀⠀⠈⠀⠀⢹⣿⣿⣿⠁⠀⠉⠁⠛⠿⢾⠿⠿⣦⡀⠙⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠈⠢⠈⠀⠀⠀⠀⢀⣀⠛⢿⣿⣿⣿⣦⣴⣶⣆⣀⠀⠀⠙⠦⢈⣿⠀⠀⠀⠈⠀⠀⣰⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⡀⠀⣿⠛
⠀⠀⠀⠀⢰⡆⠀⢰⣦⣠⠞⠁⠀⠀⠙⠿⠛⠛⠛⠛⣿⣏⣱⠆⠀⠀⢿⣿⣿⣿⣶⡶⠶⢂⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⣦⣉⣴
⠀⠀⠀⠀⠈⣷⣄⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣀⡈⢿⣿⣉⣀⣠⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠻⡟⠀⠀⢸⣿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠏⠀⠀⢰⣿⡃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣶⣿⠿⠋⠀⠘⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢾⡇⠀⠀⣿⣿⣁⣀⣀⠀⠀⠀⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠛⠉⠀⠀⢳⣄⠀⣹⣿⣿⡿⠿⣷⣶⣦⣠⡿⠷⠴⣶⣶⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⠋⠘⠻⣷⡄⠈⠉⠛⠛⢠⡀⢤⣤⡀⠉⠉⠛⠛⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⠀⠀⢸⡷⠀⠀⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠻⠏⠉⠀⠀⠀⠀⣠⡀⢀⣀⠀⠒⠀⠀⠀⠀⠀⢃⣀⣼⣿⡇⠀⠀⠘⢣⡀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀⠈⣠⡾⠋⠰⠂⠀⠀⠀⠀⣀⠘⠉⠉⣿⡿⠀⠀⣠⠞⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⣠⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⠉⠁⠀⠀⠀⠀⠠⣶⡎⠉⠀⠀⠀⣿⡁⠀⠀⠁⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄
⠀⠀⠀⠛⠁⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⢀⡀⠟⠁⠀⠀⠀⠀⣹⣷⡀⢀⠖⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⣾⡏⠀⠻⠁⠠⠦⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠄⠉⠁⣤⠀⢠⣄⠀⠀⠀⠀⠈⠠⣤⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡾⠋⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣠⠄⠀⠀⠰⠀⣠⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⢰⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡆⠀⠀⠀⠀⠀⠀⠐⠀⢠⡀⠐⠂⠀⠀⠀⠀⠰⠀⠀⠐⢿⣤⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠙⣅⡀⠀⠀⠀⠀⠀⠸⣷⣀⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣦⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⣤⠸⡯⣠⡍⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣶⡔⣿⠛⠧⠐⠋⠑⠢⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣀⣀⣸⡼⣇⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢⡄⡀⠀⣸
⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠐⣿⣿⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠆⣠⣽⣰⠏
⠀⠀⠀⠀⠀⣿⡇⠀⢀⠂⠀⠀⣹⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⣾⣾⡿⠋⠉⠉
⠀⠀⠀⠀⢸⣿⣏⣱⣾⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⣀⣸⢫⠿⣷⡘⠂⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⠟⠛⠛⠯⠿⠿⢿⣿⣿⣿⣾⣿⣟⠿⣿⣎⣧⠤
⠀⠀⠀⠀⠀⠀⠙⣿⠃⣬⠀⢀⡈⠟⢁⣤⠀⣨⣿⡟⠛⠩⠋⠀⠀⠀⠻⣿⡟⣁⢀⠀⣼⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣦⣸⠏⠉⡁⠠⠏⠀⠙⢻⣿⡇⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣤⠞⠁
⠀⠀⠀⠀⠀⠀⢸⡅⠰⣿⣀⢀⠏⢳⡄⠀⣠⣼⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠽⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣯⡏⠀⠀⣴⠀⣀⣽⠟⣿⣿⣴⣦⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡷⠟⠛⠛⠁⠀⠀⠙⠿⣖⣬⡟⠦⣰⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡀
⠀⣀⠠⣿⡆⣀⠀⠀⣠⡴⢦⣄⠀⠀⠀⠒⠀⠀⠀⠀⠠⠂⠈⠠⠢⠀⠀⡄⠒⠿⠠⠀⠀⢠⠦⠚⠀⢦
⠀⢻⣷⣶⣾⣟⠀⠨⣁⣄⣄⣀⠆⠀⢀⣀⣤⣴⡾⠀⠢⣤⣤⣤⣶⠆⠀⣦⣠⣤⣴⡆⠀⢯⣉⣀⣀⣩⠆
⠀⠘⣿⣿⣿⠇⠀⠀⢿⣿⣿⡿⠀⠀⠸⣿⣿⣿⠇⠀⠀⢿⣿⣿⡿⠀⠀⠸⣿⣿⣿⠇⠀⠈⣿⣿⣿⠏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠
⠀⢀⠀⣴⡄⠀⠀⠀⣀⣿⣿⡀⠀⠀⠀⠶⠀⢤⡀⠀⢀⠘⠛⡱⠄⠀⠀⡠⠿⠿⠆⠀⠀⢀⠜⠋⠛⢄
⠀⢻⡶⣦⣶⢿⠀⢀⣉⣀⣈⣉⡆⠀⢀⣀⣀⣤⣤⠀⢢⣠⣀⣤⣤⠆⠀⣅⣀⣀⣤⡄⠀⢯⡐⠂⣐⣛⠄
⠀⠸⣿⣿⣿⡏⠀⠀⢿⣿⣿⣿⠀⠀⠸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⠇⠀⠘⣿⣿⣿⡟
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣀⡀⠀⠀⠀⢠⣶⣾⠆⠀⠀⠀⠀⠀⢁⠀⠀⢀⠸⠿⢦⡀⠀⠀⢀⡄⠄⢀⠀⠀⢀⡴⣀⠄⡄
⠀⢾⣬⣭⣥⣿⠀⢀⠛⠉⠉⠓⡄⠀⠀⠀⠀⣀⣷⠀⢌⢀⣀⣁⣀⡄⠀⡃⢀⢀⣀⡀⠀⣾⠀⠠⠤⠛⡄
⠀⢸⣷⣿⣾⡎⠀⠈⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⡇⠀⠸⣿⣿⣿⡿
⠀⠀⠙⠛⠋⠁⠀⠀⠈⠛⠛⠁⠀⠀⠀⠙⠛⠋⠁⠀⠀⠉⠛⠛⠁⠀⠀⠈⠙⠛⠉⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡒⠢⢄⣀⣀⡴⣶⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡵⠂⠀⠀⡠⠒⣩⠟⡀⢅⢟⢢⣄⠋⠛⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠼⠃⠀⠀⣠⡴⢊⠄⠐⠧⢌⠳⡱⣇⠉⠢⣄⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣵⠀⠀⠀⢈⠵⢋⢍⠔⠁⢂⡤⠘⠈⢡⠘⡘⡄⠀⠈⠛⢄⠈⠐⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⠞⠁⠀⡠⠂⠀⢀⢾⠋⠐⣄⣼⠀⣄⣀⢘⠐⡇⢹⠀⠐⠀⠀⠑⢦⡀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⣠⢞⠀⠀⢀⢺⠂⠀⡀⢈⠖⠁⠀⢀⡉⢸⠁⢸⡀⠀⠀⠀⠀⠘⠙⠢⡀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⢊⠄⠁⠀⢠⢣⠗⠢⡀⠘⡡⠒⠈⠐⠌⢀⠏⠀⡼⠩⠓⡆⠠⣄⣀⡀⣄⡀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡞⡁⠐⢠⣀⠏⣎⡀⠀⠰⡦⠃⠀⠀⠀⠀⠃⠀⣼⠁⠀⠀⣷⠀⢸⡀⠉⠁⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠸⡃⠀⠱⢄⠣⠐⠃⡖⢀⡞⠀⠰⠳⡀⠀⠀⠹⡀⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠑⢄⡯⠤⠀⡄⢀⠌⠇⡰⠁⠀⠙⢆⣀⠀⠇⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⢄⡺⠀⡀⠊⣠⠊⡀⡡⠃⠀⠀⠀⠀⠈⠢⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢦⠼⠐⡈⠤⢞⣋⠩⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠚⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣀⠄⡄⣄⠀⡄⡄⡤⢠⢠⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠙⠀⠀⠘⠀⠀⠃⠃⠚⠘⠘


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⢀⡀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⠉⠉⠹⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠂⠀⢈⡅⠀⢸⣿⠀⠀⠀⣀⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⣀⣰⣦⣤⡅⠀⢸⣧⠀⠰⠖⠉⠀⠀⠄⠈⠙⣷⣀⠀⠀⠀⠀⢰⡀⠀⠀⠐⢿⡀⠀⠀⠀⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠉⠁⠀⠉⠀⠰⣏⣹⣷⠀⡀⠠⡾⠗⠀⠀⠀⠸⣿⣆⣀⠀⠀⠀⠙⠀⠀⠀⢸⠇⠀⠀⠀⡦⠀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠁⠀⠀⠀⠀⠀⠀⣀⡼⠋⡉⠙⡿⠃⡀⠀⢠⡟⠀⢀⠀⠾⠋⠉⠁⠶⠀⣠⣄⣀⣰⣄⠀⠀⠶⠾⠁⢀⣀⡀⠀⢦⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠁⡄⢰⣾⠁⣀⠈⠀⡤⠉⠀⠀⢀⠀⠀⠀⠀⣹⡟⠿⣏⡉⠁⠀⠀⠀⠀⠈⠙⠻⡆⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠟⠈⢹⣾⠉⡀⢨⣷⠀⠀⠀⠉⢱⣶⡶⠀⠻⠃⠀⠈⠻⢶⣀⠀⠀⠀⠀⠀⠀⠀⡸⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠶⠶⡄⠈⠻⠇⠀⠀⠀⠀⠀⢀⣸⣿⣷⠈⠉⡀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠙⣷⣤⠀⢰⣆⠀⠛⠀⠠⡃
⠀⠀⠀⠀⣾⠀⠀⠀⢰⠆⠀⠀⠀⠀⢿⠇⠀⢰⡆⠀⠀⢀⡴⠛⠉⠉⣿⣆⠀⠱⢄⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢹⡏⠐⢦⡘⠳⣀⠁⣠⡇
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢿⣿⠻⣦⡘⣷⣦⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣻⣴⡿⠻⣿⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⣰⠛⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠋⠀⢙⠇⠀⠀⠙⠳⣀⠈⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⣿⢿⣷⣄⢿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠻⢿⣦⡀⠀⠀⠀⠀⢸⡇⠀⠆⠀⠙⠇⠹⣿⣸⢿⡀
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣾⡇⠀⠀⠀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠀⢀⡀⠙⣧⣄⠀⠀⠀⠈⠁⠀⠀⠰⣷⣀⠀⠸⣿⣾⣿
⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⢀⡸⠃⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⣾⡇⠀⠀⢀⠀⠀⢸⠁⠺⣿⡏⠑⣦⣤⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⣸⡇⠀⠀⢸⣿⣦⡀⠂⣀⠀⠀⠄⠀⠀⠀⠀⠘⣀⡀⠀⢀⠛⠀⠀⠘⠀⣴⡟⠀⠀⠀⠀⠘⠛⠛⠃⣴⡆⠀⡽⠂⠀⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠘⠃⡀⠻⠁⣰⠿⠀⠀⠙⠛⠀⠛⠋⢠⣤⡀⠀⠀⢠⣼⢿⣷⠆⠀⠀⠀⠰⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣤⣄⠹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡄⠀⡹⠟⠋⠀⣠⣄⣠⣤⣴⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⢀⣴⣾⡿⠋⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠁⠀⠙⠛⢛⣤⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡞⠁⠀⣼⣿⠀⠉⠀⠈⠛⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉⢹⡇⠀⠀⠘⣿⣇⣀⡀⠀⠀⢠⣿⣇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢻⣾⡿⠋⢸⡆⠀⠀⣠⠀⠀⣾⣿⢿⣿⠿⣾⠟⠙⣿⡟⠛⠿⣿⣦⣄⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠃⠀⠀⠛⢆⣠⣿⠛⢷⣄⠀⠀⠀⢰⣿⣿⣦⣀⠀⠻⠟⢻⣥⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⡿⠋⢹⣧⠀⠀⠀⠀⢦⣄⣠⣤⣾⡿⠛⣀⠀⠹⣿⡄⠀⠀⠙⣤⡌⠿⣧⣄⠀⠀⠈⢻⣿⡧
⠀⠀⠀⠀⠀⣠⣼⡟⠁⠀⣴⡆⠀⠈⠀⠀⢠⣦⡌⠻⠿⠋⠉⠀⠀⠀⢠⣴⠿⣿⠀⠀⠀⣿⠁⠀⣿⡏⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⡾⠏⣩⡀⠀⠀⠈⠁⠀⠀⣀⣰⣿⣏⡁⠀⠀⠀⠀⠀⡴⢦⣬⠛⠀⣿⣄⠀⠀⣿⡇⠀⢸⠃⢶⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⣼⠀⠀⠿⠃⠀⠀⠀⠀⢰⡾⠉⣻⣿⠀⠸⡆⠀⠀⣀⣾⣶⠈⠉⠢⠀⣸⣿⠀⢶⠉⠁⠀⣸⠀⠀⠠⠀⠀⠀⢸⣿⣿⠄
⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢸⣿⠟⠉⠆⠀⠀⠀⣿⡏⠀⣾⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠏⠹⠆⠀⢀⣴⠏⠙⣦⠀⠰⠶⠿⣠⡿⠁⠀⠻⣦⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⢠⣦⠀⠀⠀⠀⠀⢀⣴⡾⢿⡿⠃⠀⠀⠀⢀⣼⣿⡀⠀⠸⡿⠀⠀⠶⢋⣤⡀⠀⠀⠀⠀⠀⠛⢻⠧⢤⠀⠀⠀⠀⢰⡏⠁
⠀⠀⠀⣅⠀⠀⠀⠀⢀⣾⡟⠀⠘⠃⠀⠀⢀⡀⢹⣿⠀⠀⠀⠀⠁⠀⠀⠀⢸⡟⠁⢶⠀⠀⠀⠀⣿⡁⠀⠀⣠⡀⠀⠀⠘⠃
⠀⠀⠈⠛⠀⠀⠀⠀⣿⡟⢳⡄⠀⠀⠀⡀⠈⠁⣸⡏⠀⠀⠀⠀⠀⠿⠀⠀⠸⠿⠀⠀⠐⠀⠀⠀⢙⠛⠀⠀⠛⠁
⠀⠀⠀⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠹⣦⡄
⠀⠀⠀⠁⠀⠀⠀⠾⠉⢻⣆⠀⠀⠀⠀⠀⠀⠰⠎⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠁⠀⠀⠀⠸⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢳⣦
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡅
⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣾⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠸
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠃
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠻

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⣿⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⣡⠷⣶⢦⢲⣂⢦⡆⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠠⠤⣼⡷⡖⠠⠄
⣿⠀⠀⠀⠮⠴⠋⣯⢑⢬⠐⡀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣠⣄⣾⣷⣠⡤⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⣆⠺⠁⢺⡷
⣿⠀⠀⠀⡁⠢⠁⢿⢐⠅⢑⠁⠀⠀⣿⠀⢸⡇⠀⠀⠀⣻⣿⣤⣥⣽⣧⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣬⡈⣠⢀⡄⠱⠄
⣿⠀⠀⠀⠬⡥⠧⣿⣆⡁⠵⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢩⣿⠿⠟⣬⡋⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣯⠅⠀⠀⠀⠀⡀
⣿⠀⠀⠀⡇⢭⡨⣿⠬⢀⣀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠚⠛⠙⠃⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠁⠀⠀⠖⠠⠠⠵
⣿⠀⠀⠀⠀⠀⠁⠉⠀⠈⠁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢀⣀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢠⣷⣤⣤⡀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣇⡎⡠⣽⡧⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠏⢯⣁⡰⠃⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢀⣾⡿⠛⣿⣿⣿⡄⠀⠀⢸⡇⠀⣿⠀⠀⠀⢘⠀⡤⠋⢵⠃⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣼⢿⣤⣶⣾⣿⣿⣃⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⢄⠃⡀⠔⠀⡸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉
⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢀⣤⡄
⣿⠀⠀⠉⠛⠛⢛⣛⣿⣿⣷⡄⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡿⣿⢸⣿⢩⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢤⣽⣥⠄⣤⣶⣄
⣿⠀⠀⢀⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡇⣿⢸⡇⣾⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠶⣶⡶⠂⠶⠿⠶
⣿⠀⠀⢤⣭⣭⣭⣭⣤⣤⣤⡄⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡇⣿⢸⡇⣿⡆⠀⠀⢸⡇⠀⣿⠀⠀⠀⠲⠶⠶⠂⣚⣿⣓
⣿⠀⠀⢈⣙⣛⣛⣛⣋⣉⡁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡇⣿⣿⡇⣿⡇⠀⠀⢸⡇⠀⣿⠀⠀⠀⢘⣻⣛⠈⣩⣭⣍⠁
⣿⠀⠀⠠⠤⠤⠴⠶⠶⠶⠦⠄⠀⠀⣿⠀⢸⡇⠀⠀⠀⠛⠃⠟⠙⠃⠛⠃⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⠉⠁⠈⢩⣿⠍⠁
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠊⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠢⢄⠀⠀⠀⠀⢰⡄⠀⠀⢸⠧⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠙⢆⠀⠀⢸⠱⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠑⣄⡂⠀⠀⡀⢣⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢅⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⡇⠀⠂⢰⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡆⠀⣾⠃
⠀⠀⠀⠀⠑⡒⠂⠄⡸⠀⡜⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠡⣰⠏
⠀⠀⠀⠀⠀⠰⡀⠠⡘⡿⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠑⠠⣸⠃⣠⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⡠⠔⢊⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡞⡔⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡧⠊⢀⠔⠋⡰
⠀⠀⠀⠀⠀⠀⣀⣀⠼⣿⡠⠮⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠓⢄⡀⠀⢸⢃⠞⠁⡠⠊
⠀⠀⠀⠀⢰⡯⢄⣀⣀⣉⣀⠀⠤⢼⡇⠀⠀⠀⠀⠀⠀⠈⢆⡑⠤⣈⠢⣼⡧⠒⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⡻⠛⠓⠠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠉⠀⠀⠁⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡠⠚⠉⠉⠁⠀⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⣀⡴⠁⠀⠀⠀⠀⠀⠉⠲⠤⣀⣀⣀⣀⣀⣤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠊⠁

⣿⣿⠻⢿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⢦⣤⣤
⠀⠀⠀⠀⣤⣤⡴⠖⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢠⣀⣠⣤⡴⠶⠖⠒⠀⠀⣠⡶⠛⠉
⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠐⠓⠶⢶⣤⣤⣀⣠⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⡀⣠⣴⡾⠛⠉⠁⠀⠑⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠈⠀⠀⠉⠛⢿⣶⣄⣀⠀⠀⠹⣆⠀⠀⠀⠀⢀⡟⠀⠀⢰⣿⠟⠁⠐⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡆⠀⠀⢻⡄⠀⠀⠀⢸⡇⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢸⡇⠀⠀⠀⠸⡇⣰⠏⠁⠀⣀⣀⣀⣤⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⣤⣀⣀⡀⠀⠙⣇⢸⡇⠀⠀⠀⢀⡿⣿⡴⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⣿⡟⣦⡀⠀⢠⡟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢷⡀⡾⣸⠃⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⠀⠀⠀⠀⠘⣏⢿⣇⡟⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⣙⣿⠿
⠀⠀⠀⠀⠀⠿⣿⣉⠁⠀⠀⣀⣄⣀⣀⠀⠀⠀⡀⠀⠀⠉⠛⢦⣄⠀⠀⢹⡜⢹⡇⠀⢀⡼⠋⠀⠀⠀⢀⣤⣶⠶⠛⠛⠏⠉⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⠙⠙⠛⠶⣷⣤⣀⠀⠀⠀⠙⢧⡀⠈⣿⢸⡇⠀⣾⠁⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⡀⠀⠈⣷⠀⣿⢸⡇⢸⡇⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⢸⡇⢻⢸⡇⢸⡇⢀⡾⠃⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⡀⠀⠀⠀⠀⠀⠘⢷⡀⢸⡇⢸⣿⡇⠘⣧⣾⣀⣤⡴⠶⠶⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠶⠦⣤⣈⣷⣼⡁⢸⡇⣇⣼⢫⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣮⡻⣼⡇⣿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣇⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣷⣿⣷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠞⠲⡤⡫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⣀⡀⠀⠈⡆⠀⠈⠰⠂⠀⠀⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠀⠀⠠⡀⢤⣛⢿⣖⠀⠀⡀⠒⠈⡤⢊⠔⠂⠐⣤⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠐⠚⠉⠉⠡⡀⠀⠤⠀⠉⠑⢭⠌⠻⢍⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠛⠃⠀⡠⠀⣠⠐⠨⠁⡄⠀⠀⠀⠀⠈⠛⠳⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠐⠂⡤⢈⠁⠈⠓⠌⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠀⡠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠂⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣀⣤⢤⡠⠤⠀⢀⣀⠐⢒⣠⢴⣤⠴⣦⡿⠃⢀⡀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠉⠉⠓⠦⠀⠀⡤⠟⢀⣠⠤⠀⠉⠉⢉⣉⣉⡁⠀⠒⠚⢋⢁⡀⠤⠴⠢⡿⠁⠁⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣅⠀⠀⠀⠒⠲⠒⠀⠼⢻⡧⠀⢀⣀⠀⠛⠃⢀⣠⠀⣠⠞⠻⢗⠀⠠⢀⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢒⡢⠀⡁⠀⠀⠀⢀⣀⡨⢷⠀⠀⠀⢉⡁⡄⠄⢬⡑⠪⣶⢈⣁⣶⠛⠒⠤⣠⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠙⠒⠋⢉⡤⠒⣊⡩⣙⠢⠖⠀⠀⠀⠁⠀⢉⡘⣧⡈⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣀⠀⣀⣽⣒⠀⠠⠉⢀⠀⠀⠒⠢⠌⠐⠂⢀⣅⠀⠀⢐⠳⣆⣀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣉⣤⠀⠒⠋⠀⠤⠀⠉⠁⠀⠀⠒⠂⠠⠄⡀⠀⠠⠭⠄⣀⠀⠀⠂
⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⡻⢋⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠈⠉⡓⠂⠀⢀
⠀⠀⡴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁

⠀⠒⡴⠂⠀⣠⣤⠀⠀⢰⣶⡄⠀⠀⠀⠐⠀⠀⠀⠀⢲⣶⣶⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣶⣶
⠘⠾⡤⠀⠀⠹⠿⠀⠀⠈⠛⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠉⠀⣶⡆⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠈⢰⣿⣆
⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⢿⣿⣿⠧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⣴⣶⣶⣶⣦⠈⠈⠛⠉
⠀⠀⠀⠀⠀⠘⠿⠿⠟⠁⣶⠀⠈⠉⣉⠀⠀⠠⠁⢰⣿⣿⣿⣷⠴⡄⠀⠀⣰⡄⠀⠈⢙⠛⠛⠁⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠛⠀⠀⠀⠐⠾⣿⣿⣿⣿⠾⠀⠀⠀⢹⣽⠀⠰⡾⠀⡀⠂⠀⣀⣠⣀⣀
⢀⠀⠀⠀⢠⣤⣤⣄⣀⠀⠀⣾⠇⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠸⠇⠀⢘⣿⣿⣿⣿⡭⠃
⠻⠃⠀⠀⠸⠿⠿⠗⠋⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣋⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠛⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠
⠀⢾⣿⣿⠒⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⢀⣤⣤⣄⠀⠀⠄
⠀⢸⣿⣿⠒⠁⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠐⣿⣾⣿⣿⣿⣧⠴⢦⡄⠀⠀⢀⠀⠀⠀⣀⣶⠀⢹⠿⣿⡟⠀⠀⠠
⠀⠈⠉⠉⠀⠀⠐⠚⢿⣿⠯⠁⠀⠐⠒⠂⠀⠀⠈⣿⣿⣿⣿⣿⣀⣠⠇⠀⠠⠀⠃⠀⢀⣿⡇⠀⠀⠛⠛⠁⠀⣤
⠀⠀⡉⠀⠀⠀⡀⠀⢘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣷⣾⡄⠀⣀⡀
⠀⠀⠁⠀⠀⠀⠀⢰⣏⣹⡇⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠃⢘⣿⣏
⠀⠀⠄⠀⠀⠀⠀⠀⠉⠉⠀⢀⣀⣀⠀⠀⠀⣿⣷⠀⠁⣤⣤⣄⠀⠀⠀⠀⢠⠀⠀⣴⣿⣿⣷⠖⣦⠀⠀⠀⠈⠛⠉
⠀⠀⠅⠀⣼⣿⣶⡆⠀⠀⠀⣸⣾⣿⡏⠂⠀⠹⠟⠀⢸⣿⣿⣿⠀⢠⠀⠀⠐⠀⠀⢿⣿⣿⣿⡠⠋
⠈⠀⠀⠀⣽⣿⣿⡇⠀⠀⠙⠿⠿⠿⠛⠀⠀⡀⠀⠀⠀⠉⠋⠁⠀⠛⢀⣾⡆⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⡿
⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⡇⠀⢁⠁⠀⢰⣶⣶⣾⡇⠀⠉⢀⣤⣴⣶⣶⣶⣤⠀⠀⠀⠀⠀⢀⠀⠀⠈⠋⠀⣰⣶⠀⠀⠀⣠⣤⣤⡀⠀⠠⣿
⢉⠁⠈⢠⡀⠀⠸⢿⣿⡷⠏⠀⠀⠈⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠁⠀⡿⠀⠀⢿⣿⠃⠶⠀⠿⠿⠻⠃⠀⠀⠉
⠸⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠄⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣅⣰⡄⣀⠐⠚⠈⠁⣐⠤⠒⣠⠄⠀⠀⡀⡀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⣗⣗⡯⣿⠁⠀⠀⣤⠞⢁⡰⠐⠀⠀⠀⠸⣞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣢⠭⠲⠺⢿⠋⠀⠀⠀⠀⠈⠣⣷⠦⡖⠀⠀⠙⢷⣍⡀
⠀⠀⠀⠀⠀⠀⣠⠁⡶⠞⠀⠀⢁⡄⠀⢀⠀⠀⠘⡾⢉⣉⣀⢤⡤⣤⠄⣀⣸⡥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠈⢃⠈⠈⢢⣀⡠⢸⡛⣿⣉⠞⢭⣽⡳⢂⡿⢵⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣂⡷⢜⣗⢹⣥⣟⡯⢾⣲⣶⡟⢣⡼⣽⣦⠹⣞⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢝⡭⠿⣟⣷⢻⡳⣨⠏⢺⣏⢸⣤⢏⣤⣿⡯⢤⣞⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠤⠬⠰⠛⠷⠞⠩⠒⠃⠈⡉⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠐⠖⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣠⣀⣠⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⣿⣿⣿⣿⣿⡿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢶⡤⡀⠀⠀⠀⠀⣠⣤⣶⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢻⣞⡵⣷⠀⠀⠀⠐⢿⣿⡿⢳⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣙⡀⢫⣿⣷⡴⣷⣤⣴⣿⡿⢰⣯⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣿⣥⠸⡿⢟⣰⣇⡛⢿⢹⠂⣽⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⣒⣤⠠⢍⣰⣿⠳⣤⡆⣨⣍⡡⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣨⠷⠆⠐⡃⢷⣾⣿⢱⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⡖⠾⣻⣷⣆⣤⠈⠒⠒⠪⢤⣈⢋⣷⠅⡭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠞⠛⠒⢻⠌⢉⠉⠿⣻⣻⣄⣤⡀⠀⠹⣼⢿⡿⠁⠀⣠⣴⢢⣤⣶⢶⡶⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠛⠻⠛⢉⣻⡿⣐⡿⣶⡴⢺⣾⡃⠤⣴⠟⠛⣡⠞⠃⠈⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣝⠒⠰⢤⠞⠫⢟⣻⣿⢭⠳⠾⣼⡶⡾⢷⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡴⣋⡩⠤⢤⠧⢶⣸⡏⠓⠋⣹⣄⣤⣿⠇⠙⢸⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⡭⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⡇⡿⡟⣾⡿⣔⠟⡉⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡟⣛⣧⣼⣥⡀⣹⢓⣕⢤⣯⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢣⣄⣥⠾⣆⣸⡏⠑⡸⠌⠐⣅⠄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣂⣭⠘⠃⣽⡉⢻⠆⠖⠲⢆⣸⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠽⣿⡏⣳⣷⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠲⢺⠧⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⡙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠙⢦⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠹⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⡼⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠛⢲⡄⢀⣀⣀⡤⠞⠁⠀⠀⠀⢀⡼⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⡴⠖⠛⠯⣍⡉⠉⠁⠀⠀⠀⢀⣀⡤⠖⠋⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠙⠲⢤⣀⡀⠉⠉⠙⠛⠛⠉⠉⢁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢩⣭⣭⡍⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣭⣭⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⠒⣆⣿⠀⠊⢻⡟⠛⠀⢸⢸⠉⡉⠉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠻⠤⠤⠤⠤⠤⠤⠾⢸⠀⠁⠃⣄⡄⡇⢸⡇
⠀⠀⡤⠤⠤⠤⠤⠤⠤⡄⡇⠀⠐⠀⠁⠀⠀⣿⣾⠉⣉⣉⢉⠉⠉⢻⢸⠀⢄⠓⠒⢂⡇⢸⣷⠛⠛⠛⠛⠛⠛⢻⡆
⠀⢀⡇⢰⢦⣀⣴⠦⠀⡇⣇⣀⣀⣀⣀⣀⣀⣿⣿⠈⠓⡓⠊⡻⡆⢸⢸⣤⣤⣤⣤⣤⣤⣼⢿⠀⢐⣹⢬⡻⠀⢸⡇
⠀⢸⡇⠠⣿⣿⡿⠅⠀⡇⡬⠭⠭⠭⠭⠭⠭⣅⣿⠰⣧⣷⣞⣃⡀⢸⢰⠒⠒⠒⠒⠒⠒⢲⣼⠀⠸⢾⣽⣷⠀⢸⡇
⠀⠰⡇⠘⠊⠀⠉⠛⢀⡇⡇⠀⠖⠀⠒⢂⠀⣿⢿⣤⣉⣭⣭⣍⣤⣼⢸⠀⠀⠠⠀⠄⠀⢸⣿⣄⣀⣀⣈⣀⣀⣸⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⡇⠈⠁⢀⠀⠀⠀⣿⣶⠒⠒⠒⠒⠒⠒⢶⢸⠀⠀⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⣿⣿⢀⣀⢀⡀⣾⡇⢸⢸⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⣿⢸⣿⠋⠋⠛⠃⢸⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣁⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⡿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠈⠁⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣄⣀⠀⠀⢠⠞⠋⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⠈⠙⠷⣤⠏⡠⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠈⠉⠃⣈⡈⠀⢴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⢉⠇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠒⠶⠛⠉⠉⠉⠙⢷⣄⣀⣤⣀⣀⣀⣀⣤⠤⠤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠻⡴⠋⠀⢀⡠⠘⠉⢁⢨⠽⠶⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠖⠒⠒⠧⠤⠤⠶⠚⠉⠉⠙⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⡏⠀⣠⠖⠁⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠶⠒⠒⠒⠚⣛⣺⣥⡀⠀⠀⠀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠙⣆⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠉⠑⠒⠠⠤⠀⠩⢷⠖⠋⠁
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠤⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠁
⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠈⠓⠦⣄⣀⠀⢀⣠⠞
⣶⣶⠶⠶⠶⠶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⣄⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⢠⡄
⠀⠀⢀⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣠⠃⠀⠀⠀⢦⣤⠉⠀⠀⠘⠀⢀⠀⢰⡀⡔⠋⠀⠀⠓⠈⠀⠀⠓⠀⠋⠀⠀⠾⡠⠂⠋
⠀⠑⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⢀
⠀⠀⠠⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣁⠀⠀⠐⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡐
⠀⠈⠁⠀⠀⠀⠀⠀⠘⠀⣤⠀⠆⠀⡄⠀⠐⢲⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣠⢀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂
⠀⠋⠀⠕⠀⠀⠀⠀⠀⠴⠀⠀⠀⠠⠀⠀⢀⣰⠄⢀⡀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⢀⠒⠑⠄⠉⠉⠰⠶⠂
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠄⠄⠀⠁⠺⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⣤⡀⠀⡀⠀⠀⢀⠀⠄⠀⠀⠀⠰⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠂⠀⠀⠀⠀⡤⠀⢄⠀⢖⡀⣁
⠀⠀⠀⠀⠐⡖⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠁⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠⠀⢠⣀⠀⠀⠈⠀⠉
⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠖⠀⡄⠀⠀⠁⠀⠂⠀⠠⠤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⢀⡁⠀⠀⠀⠀⠔⠐⠀⠀⠀⠀⠀⢀⣄⠀⡀⠂⠀⠂⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠃
⠀⠈⠀⠀⠀⠀⠠⠄⠁⠰⠂⠀⢢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠆⠠⡀⢇⠀⠀⢀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠘⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠁⠉⠉⠠⠀⠀⠀⠈⠁
⠀⠞⠚⠠⢖⡀⠀⢀⠄⢀⠀⠀⠀⠺⠁⠀⠁⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠄⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⢰⠖⠠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠙⠀⠀⠀⢂⢀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⡀⢀
⠀⠀⠈⠣⣠⠀⠘⢂⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⢀⡀⠀⠀⡀⣰⢂⡀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⡌⠈⠀⠀⠀⢀⠎⠈
⠀⠀⠀⠚⠃⠀⠀⠁⠈⠀⠐⠀⠀⠀⠀⠈⠆⠀⠀⠀⠄⠀⠀⢾⠋⠀⠘⠀⠘⠀⠤⠀⠰⡋⠁⠘⠀⠀⠀⠀⠁⠔⠀⠂⠀⠿

⠀⢀⣤⡀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⣀
⠀⣾⣿⣿⠉⠁⠀⣾⣯⣿⡂⠀⠀⠰⠀⠰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣀⠀⠈⠀⠀⡠⢠⣶⣶⡦
⠀⣿⣿⣿⡦⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠈⠩⠿⠍⠁⠀⠀⠐⠀⠀⠐⠻⠿⠿⠿⠿⠿⠟⠂⠀⠀⠑⠘⢿⣽⠃⠊⠀⠀⠀⠀⢾⣿⣿⣷⠆
⠀⠻⢿⠿⠃⠀⠀⠈⠛⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠸⠿⠀⠀⠠
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⣀⣸⣿⣿⣿⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠣⢸⣿⣿⣿⡁⠀⢠⠀⢀⣧⣠⠀⠀⢠⣤⣀⠀⡀⣤⠀⢰⣶⡗⠀⠀⠠⠀⠀⢹⣤⣾⣦⣜⠑
⢀⡀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠙⠛⠉⠀⠀⠾⠀⠀⠛⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠬⣿⣿⣿⠧
⠀⠠⣮⣭⣭⣭⣶⢀⠃⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⢄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣸⣿⣿⣿⣛⠁⠀⢀⠀⠀⠘⣿⣿⣿⡅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠙⠿⣿⣿⠿⠋⠁⠰⠆⠀⠀⠀⠘⠃⠀⠀⠀⠁⠀⢰⣿
⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⢿⠏⠀⡀⠀⠀⠀⢈⠀⡀⢂⠀⠀⠀⢸⠂⠀⡤⠀⠈⠙⢛⡁⠀⠀⠀⢀⣤⣷⣤⣀⡀⠀⠀⢀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⠾⢿⣿⣿⣿⣿⣿⠷⠀⠈⠁
⠀⣀⠀⠀⠀⡀⠀⠀⠀⢺⡇⠀⡉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠐⠷⠀⠀⣠⣤⣤⣤⣀⠄⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠉⠀⠀⣠⣇⡀⠀⠀⠈⠁⠀⠉⠀⡠⣴⣶⣆⠂⠀⠀⣿⡟⠀⢰⠀⡤⠀⣿⣿⣿⣿⣿⠔⠁⠈⠁⠀⠄⠀⠀⠀⢀⣄⠀⠀⠀⠀⣾⣿⣿⣿⡷
⠀⠀⠀⠈⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠋⠀⠀⠀⠉⠀⡀⠲⠀⡀⠀⢭⣿⣿⣿⡅⢀⡀⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⠉⠂⠀⠈⠛⠛⠋⠁
⠀⠂⠀⠀⠀⠀⠀⠀⡄⢰⣶⣶⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠁⠀⣀⠀⡀⢀⠀⡈⠁⠀⢸⡇⠀⣤⡀⠀⣿⣿⣿⠐
⠀⠀⣠⣤⣤⣤⣀⠀⠁⠈⣿⣿⣁⠁⠀⠈⠳⣤⣴⣶⣶⣶⣶⣶⡤⢤⠀⠁⠉⠈⠡⠌⠨⠁⠀⠀⣽⡇⠀⠀⠀⠀⢩⣯⠁⠀⠀⠀⠀⣀⣶⢠
⠀⠘⣿⣿⣿⣩⡟⠀⠈⠙⠛⠛⠉⠁⣄⠠⠀⠹⣯⣿⣿⣿⣿⣻⣇⡼⠁⠄⠀⢀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢧⣿⡼
⠘⡀⠈⠉⠉⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠿⠂⠠⢿⠆⠀⠀⢀⡇⡁⢯⠀⠀⠈⠉⠁
⠐⠗⠀⠀⠀⢚⠓⠀⠐⣦⣿⡴⠃⣴⣄⠀⠀⢀⢀⣀⡀⣴⡆⠀⠀⠀⠀⠀⠛⠾⠂⠀⠀⠀⡇⠀⠀⢤⠀⠀⠀⠀⢀⠀⡀⣀⠌⠀⠀⢠⠀⠐
⠠⣄⢄⢀⡏⠈⢷⣄⠀⠘⠿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣄⠀⠀⢠⡀⠀⢰⠀⣇⡇⠀⠀⠀⠀⠉⠁⠀⢻⣷⠃⠀⠀⠀⢨⠀⠀⡠
⠀⢨⣄⠈⠁⠀⣀⣀⠀⠀⠂⠀⠀⠀⢀⠀⡀⡀⠀⢀⢠⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⢧⠿⠁⢀⣀⡀⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠂⠘⠁
⠀⠀⠙⠷⠀⠀⠛⠋⠀⠃⢁⠠⠀⠀⢀⢈⠁⡃⠚⠘⡈⢠⡀⠀⠈⠛⠋⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⣿⡧⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠈⠂⠀⠀⢠⣤⠀⠃⠘⠃⠛⠘⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⢰⣿⣿⠂⠢⠀⠀⢭⣽⣿⣿⣁
⠀⣲⠈⠀⣴⢶⡶⣦⢠⠀⠀⠄⠄⠀⢸⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⡀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⠀⡰⠀⠀⠈⣻⣿⠉
⠀⠘⡀⠀⠘⢿⣿⠃⠊⠀⠠⡞⠁⠀⢸⡿⠀⠠⠀⠇⢾⣾⣿⣿⣿⣿⣆⠝⠀⠀⠘⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠁⣤⠀⠀⠐⠀⠀⠠
⠀⢾⢷⠀⠀⠈⠁⢀⣀⢀⣤⠀⣠⣤⣬⣶⣦⣤⠀⠀⠀⣛⣿⣿⣿⣟⡁⠀⠘⠀⠀⠀⠉⠉⠀⠀⢀⣀⢀⣶⡄⠀⣀⡀⢀⣿⠀⠀⠉⠀⣴⠛⣦
⠀⠘⠛⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⠛⠛⠛⠛⠉⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠁⠀⠉⠀⠀⠉⠁⠈⠉⠁⠀⠙⠁⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢠⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣶⠀⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢾⡏⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣾⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡗⠈⢿⣿⣏⠉⠉⠙⢻⢿⣷⣦⡀⠀⢀⣤⠰⠆⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣅⣀⣤⣄⠙⠉⠁⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣶⣿⣶⠄⠀⠀⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠉⠉⣡⣬⡇⠀⠀⠀⠀⣀⣠⣶⣿⣷⣿⣿⣿⣿⣟⣧⡶⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⠀⠀⢴⣾⡟⠋⢀⣀⣄⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠈⠙⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠛⠠⠾⠛⠋⠀⠙⠷⣶⣾⡿⠿⡛⠻⠛⠉⠛⠻⠛⠻⣿⠏⢹⣧⡜⠂
⠀⠀⠀⠀⢀⠟⠁⠀⣸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠉⢰⠀⠀⠀⡄⠀⠀⢿⠀⠎⠹⠟⠀⢲⣦⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⢡⡔⠀⠘⠂⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠘⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠳⠀⠙⢁⡀⠀⠀⢀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠈⠣⡀⠀⡏⠀⠀⢿⡀⠀⠀⢹⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⠈⡷⠀⠀⠀⠘⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠀⠀⠀⠀⢠⠉⣀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⡀⠀⠀⢶⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠁
⠀⠀⠄⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠋⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠰⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣤⠞⠁⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⠞⠁⠀⠀⠀⣠⠞⢉⣠⠤⠖⠒⠒⠒⠖⠀⢠⣈⡉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡏⠀⠀⠀⠀⡼⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡅⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠾⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣇⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠉⠉⣟⠶⣞⢁⡤⠤⠶⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠘⢦⡀⠀⠀⠀⠙⠦⣤⣀⣀⣴⣛⠉⠉⠓⢦⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠲⢤⣄⣀⣀⣀⣀⣀⣭⠽⠛⠙⣲⢤⣻⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣈⣉⣀⣀⣠⡤⠶⠊⠁⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⢀⣀⣠⡤⠀⠈⢉⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⣄⣤⣤⠤⠖⠚⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠰⠆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⣀⡀⢸⠀⣿⠁⢸⣷⠄⣿⣠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⡭⠉⠉⠉⢹⢸⠘⠛⠋⠈⠁⠀⡷⡇⠀⠒⢦⣤⣶⢸
⠀⠀⣀⣀⣀⣀⣀⣀⡀⡇⠘⣵⡆⡀⠀⢸⢨⠭⠭⠭⠭⠭⠭⡅⡇⠀⢠⣾⠏⠛⢸⣠⠤⠤⠤⠤⠤⠤⡄
⠀⢸⠀⠀⠀⠤⢄⠀⡇⡇⠀⠀⠀⠓⠀⢸⢸⠐⣿⣿⣿⣿⡆⣿⣇⡐⠛⣋⣀⣀⣸⢾⠀⡀⠂⢰⡆⠀⡇
⠀⢸⠀⠈⠐⠃⠀⠀⡇⣙⣓⣛⣛⣛⣛⣛⢸⢸⣿⣿⣿⣿⡇⣯⡽⠭⠭⠿⠿⠿⢯⢸⢸⣷⡀⠀⠻⠀⡇
⠀⢸⠀⠀⠀⠀⠉⠀⡇⡇⠀⣀⣄⠀⠀⢸⢼⣈⣛⣛⣛⣛⣁⡯⡇⢰⠀⣠⣶⣶⢸⢻⣘⣛⣛⣂⣀⣀⡇
⠀⠈⠛⠛⠛⠛⠛⠛⠃⡇⠀⣛⠟⠻⠅⢸⣰⠒⠒⠒⠒⠒⠒⣦⡇⣿⠀⢿⣿⣿⢸⠁⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠁⠀⠀⠀⢸⢾⠀⣿⣧⠀⣠⡄⣷⣧⣉⣀⣀⣀⣁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢸⠠⡿⠟⠀⢿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣤⣤⠟


⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡄
⠀⠀⠠⠤⠴⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠦⠴⠏⠉⠉⠤⠤⠤⠤⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠐⠀⠀⠰⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠙⠛⠋⠀⠈⠐⡀⠀⠀⠀⠛⠛⣿⣿⣿⣿⠿⢿⠭⠁
⠀⠀⠀⠀⠀⠐⠲⠷⠦⢄⠀⠀⠀⠒⠂⠁⢀⡄⠀⢠⠀⢩⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠦⣧⣄⣠⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣀⠀⠀⠀⠀⠠⣸⢶⠋⢀⠆
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠆⠁⠀⢀⠀⠀⡠⠀⠈⠁⠀⠀⡀⠀⠹⠻⠟⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⢀⠄⢀⡀⠀⠂⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠀⠐⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠈⢼⠁
⠀⠀⠀⠀⠐⠀⢠⠀⢠⡠⠈⠀⠀⠀⠀⠀⠀⠁⡌⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⣰⢶⣻⣽⣳⡼⡟⠟⠷⣻⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠈⠛⠙⠸⠤⠋⠉⠙⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⠛⠷⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠸⣄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠋⠀⢀⣀⣀⣤⡤⠶⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣴⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⢀⡴⠟⠁⠀⢀⡴⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠈⢧⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠠⠤⠤⠼⡗⠒⠛⠒⠲⢤⣄⡀⠀⠙⣧⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠈⠻⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⠛⠛⠲⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⢶⡄⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣄⣀⣀⣤⣤⣤⡴⠶⠚⠋⠉⠁⠀⠀⠀⠈⢿⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠐⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡄⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠃⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠐⠆⠀⠀⠀⠈⢿⡄⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣤⠶⠞⠻⢾⣿⠀⣼⠟⠉⢻⣦⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠿⠿⢷⣦⡀⠀⠀⣠⣴⠾⠿⠿⣷⣴⡟⠁⠀⠀⠀⠀⠙⢿⠏⠀⠀⠘⠛⠁⠀⠾⠟⠛⢿⣦⢀⣤⣴⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⠀⠈⠻⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠉⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢶⡶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢋⠀⠁⠄⠀⠀⠈⠑⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢹⣧⠆⠀⠀⠀⠀⠀⢀⣠⡞⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⢿⠀⡜⢁⠀⠀⠀⢺⠀⠛⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣻⣇⠈⠳⢴⡀⣤⠄⢄⠀⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣛⡻⣦⡠⡀⢡⠷⢂⠤⢷⣴⠏⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⡽⣿⡾⣵⣏⡿⣷⣴⣾⡿⠃⠀⠀⠀⢀⣠⣴⡶⠶⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣯⣭⣥⡼⠟⠋⠀⠀⠀⢠⣖⣭⢩⡍⠀⠂⠀⠀⠁⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠐⡁⠳⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⣶⠶⢶⣦⢄⡀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢡⡯⠚⠀⠀⠀⠈⢉⣟⣦⡀⠀⠀⠀⠀⡏⣿⣿⢦⣘⠄⠐⠄⠀⢀⣀⡠⠴⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡯⣽⡞⠱⠎⠀⠀⠀⠐⠃⠀⠀⠘⡄⠀⠀⠀⢷⠙⠻⣿⣿⣾⠛⣙⠋⠀⠀⠀⠀⣀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣧⡿⢀⡧⠀⠀⠀⡀⠀⠀⠀⠀⣶⠒⠀⠀⠀⠈⠳⣄⠈⢻⣿⣿⣯⠶⢀⡠⣤⡴⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⡃⠻⡈⣤⠀⠀⠀⠀⠀⠀⠀⣄⢁⡸⠀⠀⠀⠀⠀⠈⠙⠦⢝⣛⣓⣛⣋⣀⠰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣁⢰⠁⡇⠀⠀⠸⡀⠠⠤⠀⣾⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣜⣧⠈⠶⣀⣀⣹⢀⣀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠷⢾⣿⡿⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡂⠀⠀⣀⠂⠁⠀⠀⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠘⠢⠁⠀⠀⠈⠀⠀⡸⠕⠚⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠘⣧⡀⢀⣀⣴⠀⠀⢀⠠⠋⠁⠁⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠂⣀⢠⣻⣴⣾⣿⣿⣿⣾⣢⠤⠄⠀⢂⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣢⡄⠀⢀⣨⣿⣿⣿⡟⢉⣉⠙⣿⣿⡴⢉⠉⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠊⡀⣀⡀⢘⣿⣿⣿⣧⢴⣿⣿⣿⠸⣿⣿⠊⠍⠒⠋⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠵⢄⠀⠀⣸⣿⣿⣿⣵⣏⣝⣡⣾⣿⣿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠴⠥⡼⠁⢀⠈⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⠽⠤⠄⡀⡠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣴⠂⠀⢀⠜⠙⢣⠟⡉⠯⡻⢟⠉⠉⠉⠐⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡼⣷⠤⠄⣿⠀⠀⠠⠀⠘⡄⠐⠀⠀⠤⠤⠤⠏
⠀⠀⠀⠀⠀⡰⠶⠖⠋⡕⠀⠀⠀⠀⢁⠃⠀⠀⠈⣄⠰⠁⠀⠀⠀⠴⠀⡀⠄⠀⠀⢀⣀
⠀⠀⠀⣠⠞⠁⠀⠀⢐⠀⠀⠀⢣⡀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠦⠀⠀⠀⠈⠀⠀⣴⣿⣿⡿
⠀⠀⠠⠃⢀⠀⠀⠐⠁⠀⠀⠀⠀⢻⢈⠀⢀⠤⠲⠤⠄⠾⢌⡛⠒⠠⠀⠀⢀⣴⡦⡀⠀⢠⣴⢆⣒⡦
⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⢸⠀⠀⠈⠀⠀⠀⠉⠑⢡⡐⠃⠈⠛⠿⢿⠄⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠑⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠑⠄⠠⠀⠀⠐⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣒⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣋⣉⣉⡉⠉⠙⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⢷⡶⢤⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠷⣄⣀⣀⣀⣀⣀⣤⡤⢤⣄⠈⠳⠄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢘⣧⡀⠀⠀⠀⠀⢘⣆⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣤⣤⣄⣀⡀⠀⢀⣠⠴⠖⠋⠉⠉⠓⣦⡴⠛⠛⣏⠉⠁⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⠿⣅⡀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢹⠀⢀⠀⠀⡆⠀⣴⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠧⣤⣤⡀⠀⠀⢀⠀⠀⠀⠰⢦⡀⠈⠹⣆⠀⣰⠏⠀⠀⠀⠀⠀⡾⠀⢸⠀⠀⣿⡾⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⣦⠀⠈⠙⠛⠒⠒⠚⠛⢦⡀⠈⣷⡏⠈⣧⢀⡼⠃⠸⡇⠀⢸⡄⢠⡟⣁⣠⡴⠚⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⣀⣀⠀⠀⠀⢳⡄⢸⡇⠀⢹⡾⠁⠀⠀⠹⣆⠸⣷⠟⠋⠉⠀⠀⢀⣀⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣧⠀⠀⠀⠹⣼⣿⡀⢸⡇⠀⠀⠀⠀⣿⡼⠃⠀⢀⣠⠴⠛⠉⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠙⠓⠒⠒⠒⠚⠛⠛⠛⠛⠛⠓⢿⡄⠀⠀⠀⢻⡏⢷⣼⠃⠀⠀⠀⣼⠿⠓⠛⠛⠋⠁⣠⠀⢀⡄⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢻⡄⠀⠀⣼⠁⠀⠻⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⣴⣯⠖⠋⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠘⢦⣀⠀⠀⣿⠀⠀⠀⠀⠙⢦⣀⡏⠀⠀⠀⠈⢿⣅⣀⣀⣠⡤⠴⠖⠛⠉⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠈⠙⠲⠾⣤⣀⣀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣀⣀⣀⣈⣩⡽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠃⠈⠉⠛⠻⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢠⡄⠀⠘⠇⠀⠘⣿⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣄⡀⢂⠀⢰⡟⠀⠀⣀⠐⠂⠀⠀⠀⠺⢷⣄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠰⣦⡀⠀⠀⠈⠙⢧⣄
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢀⡀⠾⠿⠟⠛⠛⠛⢀⡼⠿⣶⡆⠀⠀⣀⣤⡀⠀⠀⡀⢻⣷⡀⠀⠀⠀⠈⠳⠀⠀⠀⢹⡇⠀⠀⠀⢀⣀⡙⠶⡀
⠀⠀⠀⠀⠀⠐⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⣷⡶⢯⣴⠶⠂⠉⠉⠁⠀⠾⠃⠀⣿⡷⠶⢀⣀⠀⠀⠐⠀⠀⠸⠃⠀⠀⣠⡌⠉⠁⠀⠈⢦⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠉⢀⡀⠙⣶⠦⣀⠀⠐⠀⠀⠶⠀⠈⠀⠀⠀⠉⠰⠿⣷⣦⡾⠗⠰⠶⠂⠉⠁⠲⠷⣶⣄⠀⠙⣦
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠈⠃⡠⢷⣦⠉⣀⠀⠀⣿⠀⠀⠀⠦⣀⡀⣀⣀⣴⡏⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢠⣄
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠰⣿⡅⠀⠀⠀⠀⠁⠈⠛⣾⡛⠠⠾⣿⠀⠀⠀⢀⠙⠛⠉⠉⠻⠃⠀⠀⠈⠙⢷⣆⠀⠀⢀⡀⠀⠀⠀⡌⠛⡄
⠀⠀⠀⣿⠀⠀⠀⠀⢀⡠⠾⠛⠉⠛⣦⡀⠉⠓⡄⠀⠀⠀⠀⣀⡴⠿⣿⣇⠀⠻⠀⠀⠀⠉⠀⠀⠀⢾⡷⠀⠀⠀⠀⠀⠀⢹⣷⣤⡈⠻⣆⠀⠶⡀⠰⡇
⠀⠀⠀⠙⠀⠀⠀⢀⠈⠀⠀⠀⠀⣀⡹⠃⠀⠸⠏⠀⠀⢠⡾⠛⠁⠀⠻⣿⣆⣀⠀⢦⣀⠀⠀⠀⠀⣸⠀⠈⠀⠀⠀⠀⠀⢨⣇⠈⠙⣦⡘⢷⣄⢡⣴⡇
⠀⠀⠀⠀⣰⠀⠀⠈⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⣿⠟⠛⣦⡜⠛⢧⡤⡀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣷⣤⠙⢿⣿⡇
⠀⠀⠀⠀⠻⠀⠀⢠⠀⠀⠀⠀⣼⠛⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠟⠀⠀⣤⠁⠀⠀⠀⠛⣦⣀⠁⠀⠀⠀⠀⠀⠀⡄⢠⡄⠀⢸⡟⢻⣷⡎⢻⣿
⠀⠀⠀⠀⠀⢴⠀⠈⠀⠀⠀⢰⡟⠀⠀⠄⠀⠁⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠹⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢽⣷⣼⠿⡀
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⠇⠀⠀⢀⡄⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡀⠀⠀⠀⠈⠀⠀⠀⣴⣿⣀⠀⢹⣿⣾⣿
⠀⠀⠀⠀⠀⢿⡇⠀⠀⠐⣤⡌⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣿⡆⠀⠀⢀⠀⠀⢠⠀⢺⣿⡏⠙⢦⣤⡀⠀⠀⠀⠀⠀⠘⢿⣷⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⣿⡇⠀⠀⢸⣿⣦⣀⠂⠀⠀⠀⠤⠀⡀⠁⢀⠀⠀⣿⠀⠀⠀⠘⠀⠀⠈⢳⣀⣿⠇⠀⠀⠀⠙⠛⠛⠛⢢⣤⡀⠈⢻⡄⠈⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣰⡿⠃⠀⠙⠛⠐⠛⠛⢦⣤⡀⠀⠂⠀⣿⡾⢿⣤⠀⠁⠀⠀⢠⡄⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⣤⣀⡐⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⡀⠀⠛⣿⡿⠉⠀⢀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⡆⠀⣤⣶⠿⠿⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⢴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⣦⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢦⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⣧⡀⠹⠿⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⠁⠀⢼⣿⡟⠀⠀⠀⠀⠈⢩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣠⣾⣿⡏⠀⠘⡟⠀⠀⠀⢉⣻⣦⣤⡀⢀⣀⠘⣿⣇⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⣿⣿⠟⠁⠘⢃⠀⠘⣿⡆⠀⢸⣿⡟⠻⣿⡿⣿⡏⢸⣿⡏⠉⠛⠿⣿⣦⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡟⠁⠀⠀⠐⠛⠀⠀⠸⡇⢠⣿⠙⠿⢷⣄⠀⠀⠉⠀⣿⠿⢷⣤⠀⠘⠿⠋⢹⣦⡀
⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⡟⠉⠹⣧⡀⠀⠀⠀⠶⣦⣤⣤⣾⡿⠛⠳⣄⠈⢹⣷⡀⠀⠀⠹⣷⡀⠻⣷⣄⠘⠀⠀⠙⢿⡿⠆
⠀⠀⠀⠀⢀⣤⡿⠟⠀⠈⣷⡄⠀⠈⠁⠀⢠⣶⡴⠿⠛⠛⠉⠀⠀⠀⢉⠀⡼⢿⣷⠀⠀⠀⣿⠃⠀⣽⡏⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠀⣴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠰⢶⣀⣿⡇⠀⣿⡄⠀⠀⣿⡇⠀⢹⠃⠰⠀⠀⠀⠀⠈⣿⣦⡀
⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⢰⡾⠉⢹⣿⠁⠀⢠⠀⠀⠀⣠⣶⡖⠉⠹⠇⠀⣹⣷⠀⣾⠀⠁⠀⣾⠆⠀⢰⠄⠀⠀⠀⣽⡿⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣿⡏⠀⠀⠀⠰⠶⣾⡿⠉⣦⠀⠀⣴⠀⢹⣯⠀⣾⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠻⣧⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⢹⡆⠀⠀⢀⣴⠿⠃⠀⣀⠰⠶⣿⣤⡼⠋⠀⣿⡆⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⡿⠏⠀⠀⠀⠀⢰⣿⠃⠀⠀⣼⠛⠀⢀⣿⣏⠁⠀⠀⠈⠁⠀⠀⣿⡟⠷⣦⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⢼⡇⠀⠀⠀⠠⣶⣿⡏⠀⠆⠀⡟⠀⣶⠉⢶⠙⠿⠄⣀⠀⠀⠀⠀⣭⡁⠀⠀⢠⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢃⡀⠀⠀⠀⠀⠰⠆⢠⣿⠀⠀⠀⠀⠁⢠⡇⠀⠀⢠⣦⠀⠙⢦⠀⠀⠀⢻⣧⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠃⠀⠀⠠⡦⠀⠀⢰⣇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢿⣤⣤⠀⠀⠀⠀⢾⣇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠟⢃⡀⠀⠀⠀⠀⠀⠀⠀⡘⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⣤⠀⠀⠀⢻⠟⠳⡄
⠀⠀⠀⠀⠀⠀⠛⠁⠀⢻⡧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⢲⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡀⠀⠐⠀⠀⠱⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⠀⠀⠀⠀⠀⠘⠀⠈⠂⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⠤⣄⡀⢸⠁⠀⠀⠀⠀⢀⠀⠀⠄⠀⠄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡂⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠐⠁⠀⢀⢀⡤⠖⠚⠋⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠑⢄⠀⠀⠐⠒⠂⠀⠄⠹⣄⠠⡀⠀⠀⣰⠟⠉⡠⠐⠀⠀⠀⠀⣀⢈⡳⣄
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠁⠀⠢⢀⠀⠀⠀⠠⠀⠂⠘⡆⠀⠀⡼⠁⢀⠊⠀⠀⢀⡀⠤⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠑⠂⠀⠤⠀⠀⠀⣿⣒⣸⠃⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠑⠆⡈⠈⠀⠀⠀⠁⠀⠀⡿⠈⢹⠀⠀⠀⠊⠀⠠⠁⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠈⠑⠠⠠⠀⠰⠈⢉⠇⠀⠘⡇⠀⠀⠀⡰⠁⠀⢀⠀⠊⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠖⠚⠚⠛⠁⠀⠀⠀⣿⠀⠀⠠⠃⠀⠀⠁⠀⠀⣨⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡢⣀⣔⣀⣩⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣤⣎⣻⣄⡰⢃⡜⠁⠀⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢷⡶⢶⣴⡿⠁⠀⠀⠀⡰⣦⣄⡀⠀⠈⣳
⠊⠛⠋⠓⠈⢻⡀⠀⡀⡀⠄⠀⠀⢈⠓⠑⠀⠀⠀⠀⢀⢄⡾⠟⢋⡀⡂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠙⢿⣧⣀⣀⠴⠈⡁⠀⠀⢰⣿⣿⣿
⠀⠀⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣄⣠⢂⣴⣄⣀⣩⡶⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣾⣶⣿⣥⡀⠀⠀⠀⠀⠀⠘⠣⡺⣄⠁⠆⠀⠀⠒⠆
⠀⢀⠀⠀⠀⠀⠀⣀⣴⡄⣠⣈⠁⠀⢠⠞⠉⠀⠀⠈⠙⣞⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⢻⠛⢻⣻⣿⡆⣤⣀⣀⣤⠀⣴⣴⡘⢦⣄⠄⠀⠀⢷⠐
⡤⢠⣄⢀⣤⢞⠋⠛⠉⠙⢊⣻⡱⡆⡀⠀⡔⠈⠉⠅⠲⡞⠁⠠⡄⠀⠀⠂⠀⣄⢀⡀⠀⠘⠄⠀⠈⠛⠡⢹⡜⣿⣏⢡⡴⣖⣿⡷⢶⣶⡭⠙⢒⡿⠁
⠘⢷⡸⠻⡇⡼⢇⠀⠀⠀⠀⠀⠀⣹⡿⡀⣀⡖⢦⣠⣾⡀⢤⣶⣾⣦⠰⣡⡖⠉⠀⠀⠉⠁⠀⢀⠀⠈⠀⡉⠈⢻⣾⡗⠉⢭⡭⠴⣿⣿⣿⡛⣧⠾⡟
⣴⠆⠀⣋⣼⣾⣜⣯⣀⠔⠒⣀⡀⠠⣷⣮⣯⣿⠿⠛⠀⠀⠀⠿⣿⠝⣷⢿⣧⡀⠀⠀⠀⠀⠀⠀⢶⡔⠋⠀⢀⣿⡿⡀⠀⠀⠀⠀⣿⡿⠻⠲⣿⣸⣿
⠀⠀⢠⡿⠿⠟⠻⠿⠯⠉⠓⣴⢒⡚⢛⠁⠀⠠⡁⠒⢀⠀⠀⠀⠇⠀⠀⠀⣻⠟⠳⠶⠴⣄⡀⠀⠀⢻⣶⠆⠋⠁⠀⠀⠀⠀⠀⠀⠘⠇⠘⠀⡘⠋⠁
⢀⡤⡨⣢⠴⠛⠉⠙⠊⠙⠲⣿⣶⢀⠁⠀⠀⠀⠀⠀⠁⠀⠰⠆⠃⠀⠀⢀⡆⡀⡀⠀⠀⠞⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠳⢶⡄⠀⠵
⣾⠁⠸⢡⠆⠖⠁⠀⠀⠀⣾⠿⠇⠈⠀⠀⠀⠀⠀⠘⣴⣶⣥⣤⣶⣾⣷⡉⢳⡀⠘⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⣤⣶⠗⠀⢀⠯⠴⢯⠄
⠿⣷⣧⡆⠀⠀⠀⠀⣂⡛⠑⠒⢂⡀⠀⠀⠀⠐⢤⣄⣿⣿⠷⣾⣿⣿⣿⣫⣇⡙⠲⡤⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠜⣦⡀⣠⠾
⠛⠊⠈⡏⢿⣶⠄⠀⠚⠉⠀⢈⢀⢣⣂⢀⠀⢠⠸⠛⠉⠹⣿⣻⣫⢿⣛⠛⠟⠻⠻⠟⣃⣩⠄⠀⣶⠀⣀⠰⠿⢦⣴⡈⡀⠀⠀⠀⠀⠀⠀⠟⢁⠠
⠀⠂⠈⠃⢸⠃⠀⠀⠀⠀⠀⢪⠁⠀⠈⣢⣦⡜⣧⠀⠀⠀⠀⠀⠙⡆⡸⠀⢈⡎⠀⠀⠉⢷⣾⣦⣷⣿⡏⠀⠀⠀⠈⠳⡈⠂⢀⠀⠀⠀⠀⢦⡀⠁
⣤⠖⠁⠀⢸⠀⠀⠀⠀⢠⣴⡇⠀⠈⠀⡸⠿⣿⠟⠀⠐⠶⣶⣶⣶⡄⠁⠀⠘⠀⠀⠀⠀⠀⣿⢓⢤⡊⢅⣄⠀⠀⠀⠀⠈⠀⢦⣤⢀⡄⠊⠀⣹⣶⣤
⠿⠓⠴⠤⠤⠣⣤⣲⢮⣾⣿⣷⡦⣴⡾⠁⠀⠀⠀⠀⠀⠀⠘⣿⣁⣶⣶⣷⠖⠀⠀⡀⠀⢠⡟⠂⠀⠨⠳⡝⠳⣤⡀⠀⢀⠀⠀⢛⣸⠐⢶⡾⠋⣔⢌
⠒⠐⠒⠒⠂⠐⠂⠉⣈⣿⣿⣿⣲⢻⣿⡀⠀⠀⠀⠀⠀⠀⢠⡉⠉⠀⠛⠛⠀⠀⠐⣂⢀⣞⠧⠀⠀⠀⠐⢹⡆⣻⡅⠼⢋⠈⣽⣋⢿⣽⠟⠀⠀⠈⢦
⢂⠀⠄⠀⠀⠀⠰⢘⠟⠋⣉⠹⠴⣿⣿⣿⠢⣤⣤⣤⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠑⠀⠀⠘⢀⢌⡇⡇⢣⠀⠈⠂⠀⢁⡠⢛⡆
⠃⠀⠀⠀⠀⠂⠒⠿⠅⠠⠀⠀⢀⢿⡿⢻⠶⣯⣴⡿⠋⠁⢀⠀⠀⠀⡀⠀⣁⠀⠀⠠⠀⣴⡷⠦⠤⢀⢌⡜⠐⣸⣮⡇⠉⠄⠀⠂⡐⡹⠁
⡀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⡘⠃⠀⠂⠸⠏⠀⠀⠀⢽⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣼⣿⡇⣀⠈⠁⠴⠚⠀⠂⠀⠀⢀⣆
⠀⠀⢀⡀⢀⠀⠈⣻⣦⠀⠀⠀⠀⢰⠇⠀⠀⣴⡄⠀⠀⠀⠈⠀⣩⠛⠘⠀⠉⠁⢲⣶⣶⠀⠁⠀⠀⠀⠀⠈⢡⣍⠀⠀⠀⠀⠀⠀⠀⡂⣼⣿⡦⡙⢿
⢰⠛⢿⣿⣿⠶⢦⠜⠛⠷⣤⣄⣠⣨⣴⡷⡾⠻⠻⠴⠾⢷⠀⢀⡁⢠⠔⠀⠄⠀⢤⠿⠿⠇⡀⠀⠀⠀⠀⢀⡟⠉⠉⠀⠀⠀⠀⠀⢀⠂⡟⠁
⠀⠀⠀⠂⠀⠁⠀⠄⠀⠀⠠⠀⠉⠻⠇⢆⡇⡆⠀⠀⠀⢛⢷⡀⢇⠀⣴⣲⣄⣸⣆⠀⠀⠀⠈⠳⣦⣤⣄⣚⠀⠀⠁⠀⠀⠀⠀⠠⢀⣴⡇⠀⢠
⠀⠀⣠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣈⢧⡀⠑⠀⠀⠀⠙⣿⣦⡽⠶⠛⠟⢻⢿⣦⡀⠀⠀⠀⠈⠿⢁⡙⠁⠀⠀⠀⣄⡀⠀⢤⡿⣿⣿⣶⣷
⠻⠿⣧⣀⠀⡀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣄⠳⢦⣠⠄⠀⠈⠿⠿⠻⠀⠀⠈⢠⠀⡅⢁⣦⠀⠀⠀⣿⣧⣟⣴⠙⣦⠀⠀⣀⠱⡸⣿⣿⣿⣿⡿⠖⠒
⠀⠀⠀⠐⣿⡽⡇⠀⠀⡀⠂⠀⠀⠀⠀⠙⢿⣷⣶⡶⠉⠙⢻⣷⡟⠀⠀⠀⠜⠀⡰⢓⣉⣿⣦⣄⡀⢨⣿⣿⣿⠝⠃⠐⠀⠡⡖⣱⡿⣛⡋
⠀⢀⠀⢀⡾⠗⠸⠶⡆⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠉⠉⠻⡟⢻⠃⠀⠀⢔⡤⠞⢁⣴⣟⣿⣿⣿⡿⠃⠁⢹⡟⠁⠀⠀⠀⢰⣿⣿⣟⣿⣿⣶⣤⣤⣄
⡀⠉⠉⠁⠘⢆⠀⠀⣤⡀⠀⠀⠀⠀⣦⣶⠁⠀⠀⠈⠁⠐⠒⣿⣛⠛⠩⣑⣶⣶⡿⠗⠻⣿⠿⣿⠀⡠⠀⠈⡆⠀⠀⠀⠀⣘⣿⣶⣯⡼⠿⠟⠁⢸⠃
⣂⣀⣀⣒⣀⣀⣐⣰⣛⣙⣀⣲⣦⣴⣿⣦⣀⣀⣀⣀⣀⣀⣹⣿⣿⣿⣟⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣐⣒⣂⣈⣂⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣸⣊
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⡠⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠉⠢⣄⠀⠀⠀⠔⠁⠀⢠⠊⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⡀⠀⠀⠀⠈⠣⡀⠌⠀⠀⡔⠁⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠘⢄⠠⣀⠀⠀⠸⠀⢀⡜⣢⠂⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠌⠢⡐⠆⠀⠀⢧⢀⡯⠐⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⡘⠢⡁⢰⡆⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⢸⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠀⠀⠀⠈⠉⠉⠉⠈⡉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠉⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢐⡈⠄⢂⠄⡉⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⢒⠨⠐⡨⠀⠁⠀⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⣊⠠⠐⡁⠔⢀⠀⢂⠄⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠐⢂⠁⠐⡈⠄⢊⠠⠀⡁⠄⡈⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠀⠀⠀⠀⠠⠬⠭⠬⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠡⠄⣂⠡⠐⢈⡡⠄⡈⠔⡀⢔⠐⠀⠘⢄
⠀⠀⠀⠀⠀⠀⡠⠌⠀⠀⠠⢀⠀⠀⠀⠀⠠⠀⠀⠤⠍⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡉⠄⠐⡈⠄⢂⡡⠔⡨⠐⠁⢔⠕⠀⠀⢃⡀
⠀⠀⠀⠀⢀⠜⠀⠀⠀⣀⠀⠂⠀⠀⠀⠤⠉⠉⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⠄⠀⢂⡁⠤⠐⡈⠤⠂⡁⠄⡊⠔⠁⡢⢊⠄⢀⠌⠦⡀⡀
⠀⠀⠀⠀⠳⠤⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠌⠀⠀⠀⢀⡒⠀⠩⠄⢒⢀⠡⢔⡀⠥⢒⠩⡀⠕⡨⠐⠕⡁⢂⡀⡁⡸⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠠⠤⣄⢂⣠⠤⠖⢦⡀⠀⢀⡂⢀⣁⠀⣥⠤⣀⣐⡂⢌⡉⣀⠒⠈⠀⠐⠈⢐⡉⢐⡐⠂⠖⡈⠀⠈⠊⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠀⠁⠀⠉⠀⠈⠀⠁⠂⠉⠊⠉⠋⠉⠐⠉⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠈⠻⢶⣦⣄⣄⡀⣀⣿⣦⡀⠀⢀⠀⠀⠀⠀⡀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⢿⣿⣞⣿⣵⡶⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢹⠏⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠈⠀⠀⠂⠠⢄⠀⠀⠀⡀⠈⢳⣦⣄⡀
⠀⠀⠀⢠⣤⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣤⣴⣶⣶⣤⣴⣷⣤⡀⠳⡐⢤⣬⠽⠟⠒⠀⢤⣄⠀⢀⣤⡄⠀⠀⠀⠀⠀⠂⢄
⠀⠀⢤⣤⣽⣷⣶⣤⣠⣤⣠⣾⣶⣶⣾⢸⣶⣦⣤⣭⣿⣿⣿⣿⣿⣿⣿⣥⢰⣿⣿⣷⣶⣶⣾⣾⣿⣯⣤⡇⢻⣿⣷⣿⣶⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠉⠉⠀⠀⢘⢸⣿⠃⠀⠀⠀⠁⠀⠀⠈⠁⠀⠻⢸⡯⡉⣯⠏⠀⠀⠉⠋⠙⣿⡗⣿⠋⠉⠉⠉⠉⠉⠉⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠬⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠁⠉⠂⠀⠀⠀⠀⠀⠴⠣⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⡰⣸⠃⠀⠐⠤⠄⣀⡀⠀⠀⡠⢒⡀⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⠋⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⢃⣿⠛⠢⡀⠀⠀⠀⠉⠒⠄⡐⠁⡄⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠴⢾⣿⡀⠀⠈⠢⠀⠀⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⣷⠄⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣵⣶⣤⣧⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣾⣏⣀⠤⠀⠀⠋⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣦⣤⣦⣄⣀⡸⠂⢀⠔⠁⠀⠀⠀⢲⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠄⠁⠀⠀⢀⣴⢾⣿⠀⡈⠀⢤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠓⠀⠀⣸⠃⢠⣀⠀⠁⠀⠀⠀⠀⠰⠆⠀⢀⡀⠀⠀⢠⣤⣶⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠉⠀⠀⠘⠛⠛⢤⠄⢀⣀⣀⣼⠃⠀⠀⠀⣿⠀⠀⠛⠛⠛⠿⠿⣿⣦⣤⣤⣀⣈⣁⣀⣉⣉⣥⡉⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣴⠿⠒⢦⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⠀⠀⠈⠻⣦⠀⠙⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠘⢷⡀⠀⠀⠉⢿⣶⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠙⠣⣌⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⢷⣤⡄⠀⠀⠀⠘⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠙⢷⣿⡶⠄⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⡀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣾⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⣾⡏⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠸⣿⡇
⠀⠠⠶⠶⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠇⠀⣿⡇
⠀⠀⠀⠀⠀⢸⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠾⠃⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⡟⠀⠀⠉⠁
⠀⠀⠀⠀⢸⡗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠠⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢀
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠂
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠛⠻⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠚⢯⣿⠃⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⣍⡀⢀⡔⢺⣯⡿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠰⢤⡀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠈⠉⠉⣤⣠⣴⢸⣿⠀⠀⠀⠀⠀⠀⠠⣶⣤⣤⣮⣿⣆⠀⠀⠀⠀⠀⢀⣾⠏⣴⣧⣠⣀⢀⠈⢻⡆⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣧⠈⡟⠀⠀⢀⡆⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢻⡿⠟⠀⠀⠀⠀⠀⠀⢺⣿⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⡿⠿⠿⠿⠚⠁⠀⠀⣈⠀⠀⠀⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠠⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⠧⣄⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣻⣽⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣛⢀⡀⡆⠀⠀⠀⢲⠀⢀⣀⣴⣮⣿⠃
⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⣾⣿⠛⠙⢋⢻⣿⣧⠀⠀⠀⢀⣠⡀⣰⠦⠾⠸⠛⢛⣛⠁⠀⠀⠀⠘⢄⢰⣿⣿⣿⠟
⠀⠀⠀⡀⠀⠈⠣⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⢸⣿⣥⡀⠀⠀⣸⣿⣟⠀⠀⠀⢈⣉⣠⣦⣤⡶⠶⠿⠛⢛⠀⠀⠀⠀⠀⠈⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠪⣿⣿⣷⣤⣾⣿⡿⠃⠀⠀⠀⢘⣉⣉⣧⣤⠴⠶⠞⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣀⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⢤⣀⢠⣄⢠⣤⡰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣐⠦
⠀⠀⠀⠀⢠⣤⣶⣶⡇⢙⣿⡏⣹⠁⠀⠀⠀⠠⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⢤⣘⠊⣏⡁⡀
⠀⠀⠀⠀⠽⣿⣿⣿⣿⣸⣿⡿⠃⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⢶⠓⠢⡊⢿⣄⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠳⡤⠉⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣭⣿⣿