Hydration Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠇⠀⢀⣤⣄⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠟⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⢸⣇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⣤⣄⡀⠀⠀⠀⠀⣀⣈⣉⣀⣀⡴⠋⠉⣷⠀⠀⠀⠀⡿⢩⠭⣍⠓⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⠤⠤⠤⡀⢻⠋⠉⠉⣉⣉⠉⠉⠀⠀⠘⠂⠒⠉⠉⠉⠉⠙⠃⠸⣀⣠⠀⣏
⠀⠀⠀⠀⠀⢠⡞⠩⢬⠀⣁⠤⠔⠇⢸⠉⠉⠋⠀⠀⠱⠊⠉⠙⠲⠒⠛⠲⠞⠛⠒⠉⠉⠳⢢⣀⣠⠌⢉⡧
⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠉⠙⠒⠚⠘⠦⠤⠤⢄⣀⣀⣀⣀⣀⣀⠤⠤⠤⠴⠖⠒⠒⠚⠉⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡒⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠁⠒⠒⠤⢌⣉⣑⡒⠒⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⢒⣒⣚⣉⠭⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠒⠒⠒⠒⠒⠂⠉⠉⠉⠉⠉⠁⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠙⠒⠲⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠒⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⠤⠜⠓⠐⠀⠀⠀⠰⡇⣦⡔⡉⠤⠠⢾⠀⠀⠀⣀⠃⠀⠀⠈⠈⣡⠃⠀⠈⠀⢀⠤⠚⠃⠒⢀⠀⠀⠸⡑⣤⢐⠩⠄⠠⡎⠀⠀⠀⡐⠁⠀⠀⠉⢈⡔⠁
⢿⡃⠀⠀⠀⣠⣾⣄⠀⢀⠜⠁⢀⠤⠄⠀⣨⢀⡠⢴⡉⠡⠖⠊⠉⠈⠉⠉⡹⠶⣾⠁⠀⠀⠀⣠⣿⡀⠀⣠⠋⠁⢠⠤⠀⢀⡌⢀⠠⢞⠉⠰⠒⠊⠉⠉⠉⢉⡵
⠀⣱⠖⠦⠐⠋⠈⠉⠙⡿⠓⠒⠛⠓⠢⣤⠼⣏⠀⠀⠀⠀⠀⠴⠶⠦⠐⠾⠀⠀⠀⡶⠖⠆⠘⠉⠉⠉⢙⡟⠒⠒⠛⠒⢦⡤⢿⡅⠀⠀⠀⠀⡠⠶⠶⠆⠰⠮
⠨⢂⠀⣀⡴⠤⢤⣤⠜⠁⢀⣠⠄⣄⣀⣀⣠⠌⠉⠟⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠹⣀⠀⣀⡴⠤⢤⡤⠞⠀⣀⣠⠤⣄⣀⣀⣠⠈⠉⠟⠉⠀⠀⠀⣀⡀
⠛⠋⢉⣼⣄⠀⣀⣠⠀⠉⠈⢂⠀⠀⠀⠀⠴⠞⠀⢀⣀⡤⠔⠋⠉⠉⠀⠀⣨⠚⠛⠋⣁⣼⡀⠀⣀⣠⠂⠁⠙⢄⠀⠀⠀⠀⠴⠇⠀⢀⣀⡤⠒⠉⠈⠉⠂⠀⡥
⢴⡊⠀⠀⠈⠉⠁⠘⣦⠤⠐⠈⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢀⡠⠐⠒⠚⠳⠦⣴⠊⠀⠀⠉⠉⠀⢹⣄⠄⠒⠋⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⣀⠤⠒⠒⠛⠲
⣀⣧⣀⡀⠀⢀⠠⢘⣻⠶⠟⠋⠀⠀⡠⠴⠦⣾⡤⠾⠿⠛⠞⠉⢿⠀⠀⠀⢀⣀⣈⣧⣀⡀⠀⢀⠤⣚⡷⠶⠚⠁⠀⢀⡠⠴⢴⣦⡴⠾⠟⠳⠞⠙⢗⠀⠀⠀⣀
⠀⠀⠀⠈⡹⡡⠞⠛⢦⡤⠖⠙⠒⠋⠀⠀⢀⡏⠀⠀⢀⡴⡀⠀⠀⠈⣻⠋⠁⠀⠀⠀⠀⠈⡟⡴⠚⠛⢤⡤⠊⠙⠒⠉⠀⠀⢰⠃⠀⠀⢀⠜⡀⠀⠀⠙⡿⠉
⢄⠀⢀⡴⠗⠁⠀⠀⣠⠗⠊⠀⢀⣀⠀⣠⠞⠀⢀⣄⢀⡈⡤⠖⢉⠚⠧⠤⣠⠄⠄⠀⢀⠼⠊⠀⠀⠀⣸⠗⠁⠀⣀⣀⢀⣠⠋⠀⢀⡆⢀⠀⡤⠚⢁⠛⠧⢄⣠
⠔⠛⡋⠀⠀⣀⡤⠚⠁⣀⠔⠈⠀⡘⠉⠛⠦⠒⠋⠉⠠⠀⣸⣤⣾⡀⠀⠀⠀⡠⠚⠛⡃⠀⠀⣀⠄⠛⢁⣠⠀⠁⢀⠘⠉⠓⠄⠚⠉⠉⡤⠀⣧⣤⣆⡀
⣠⣒⠁⠐⠈⢿⠆⠉⠀⠉⢧⠀⡸⠁⢀⠔⠀⠀⣀⡀⠤⡦⠋⠁⠀⠈⡣⠐⠔⢁⣴⣒⠥⠐⠉⡿⠊⠁⠈⠙⣆⠀⡞⠀⣠⠄⠀⠀⣀⡠⢤⠜⠉⠁⠀⠉⡦⠂⠊
⠀⠀⠀⢀⡤⠻⣀⣀⣀⣤⣊⠴⠁⣲⣁⠄⠚⠉⣡⣴⠊⠀⠀⠐⠥⠺⠤⣤⠔⠉⠀⠀⠀⢀⠔⢧⡀⣀⣠⡴⣣⠾⢐⣞⣁⠔⠚⠉⣠⣴⠃⠀⠀⢀⠕⠺⠤⣤⠞
⠀⠀⡠⠊⣀⡔⢹⠁⠀⠀⣠⠖⠋⠉⣡⠤⠒⢈⡡⠋⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⡐⠁⣀⡌⢹⠁⠀⠀⡤⠚⠉⠉⣠⠔⠂⢉⡵⠋⠀⠀⠀⠀⣀⣤⡾⠃
⢠⠞⠀⡈⠘⠁⣼⡀⠀⣠⡧⠀⠲⢔⣡⢶⣯⠥⠤⠤⢤⣀⠠⠊⠀⣠⢧⡠⢤⡄⡠⠎⠀⡁⠙⢀⣾⠀⢀⣼⡤⠒⠦⢎⡠⣶⣯⠤⠤⠤⢤⣀⠔⠈⢀⡼⢇⡠⢤
⣴⣀⣘⣀⡴⣚⣀⣉⣉⣙⣦⣐⣚⣋⣠⣮⣌⣿⣀⣀⣀⣠⢂⣐⣉⣀⣤⣠⣞⣁⣄⣀⣚⢠⡖⣋⣀⣉⣉⣻⣤⣒⣛⣉⣴⣧⣬⣟⣀⣀⣀⣸⣂⣚⣉⣀⣄⣰⣊
⣿⢿⠿⠿⢿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣛⣿⣟⣿⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓
⣦⠤⠦⠤⠤⠤⢤⡤⢤⡀⠖⠒⠶⠤⠦⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠛⠒
⠀⠶⠶⠶⠦⠠⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠦⠤⠤⠄⠀⠀⡀⠠⠄⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⢀⠀⣤⣤⣄⣀⣀⣀⣀⣀⡀
⣦⣿⡿⠛⠿⠯⠿⠿⣿⣿⣿⡟⠛⠒⠒⠛⠙⠛⠉⠉⠉⠉⠉⠛⠛⠉⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠍⠩⠛⠛⠓⠀⠛⠉⠛⠛⠛⠛⠛
⣿⣿⣿⡿⠶⠶⠶⢶⡶⣖⣀⣠⣀⣀⠀⠀⠀⠀⠤⠄⠀⣠⣤⣀⣀⡀⢀⡀⠀⠄⠀⠠⡄⠀⠠⠄⠀⠤⠤⠄⠀⢀⡀⠤⠠⠤⠤⣤⠄⢀⣀⡀⣀⣀⣀⣀⣀
⢠⣤⣤⣄⣀⣀⣴⠔⠀⠀⠀⠤⠤⣤⣤⣤⣠⣤⣤⣄⣠⣄⣠⣄⣀⣀⡀⣀⣀⠀⣀⣀⡚⠛⡛⠚⠛⠒⠒⠂⠲⠤⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠬⠷
⠀⠀⠀⣀⣈⣱⣶⠶⠶⠶⠶⠶⠆⠀⠐⠶⠄⠀⠠⠩⣭⣴⣶⡦⢤⣭⣯⣍⣭⣉⣉⣉⣙⣛⣛⣛⠛⠓⠒⠀⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠘
⠀⠀⠶⠿⠿⠟⠉⠉⢉⡙⠙⠋⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⢀⠀⠀⠈⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⣿⡟⠒⠶⠦⢤⡄⠀⠈⣄⡁⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⠐⠂⠈
⠐⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⠄⠄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠠⠤⠒⠀⠠⠤⠤⠤⠤⢤⠀⠒⠒⠒⠀⠠⠤⠄⢠⣄⠀⠀⠲⠴⠀⠠
⠤⠄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠁⠀⠀⠀⢀⣀⠀⣀⣀⣀⣐⣒⣶⣶⣦⣤⣄⣹⡟⠛⠙⠀⣐⣒⣲⣶⣶⣶⣶⣦⡴⠀⣀⣠⣄⣘⣓⠀⠠⠬⢤⣭⠙
⠀⣀⣀⣀⣀⣀⣀⣲⣤⣤⣤⣤⣤⣤⣤⡶⢷⣾⣿⣻⡿⢛⠛⠛⠶⠶⠶⠶⢤⣤⣄⣀⡛⠛⠛⠛⠿⠃⠠⢤⣤⣤⣤⣍⣉⣛⣉⠉⠙⠚⠛⠻⠗⠒⠒⠂
⣭⣭⣭⣍⣉⣙⣛⡛⠿⠿⠶⠶⣶⠿⣿⣿⣶⣾⣯⣭⣭⣭⠽⠽⠿⠐⠒⠶⠶⠶⠾⢯⣭⠉⠉⠙⠿⠶⠶⠶⠶⠶⠾⠍⠉⠉⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⢀
⠆⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⣄⣤⣤⠤⠶⠶⠷⠿⣿⣿⣟⣛⣛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢂⠀⠀⠁⠂⢂⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠐⢤⡏⠈⠡⠂⠠⡂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠈⠀⣹⠀⠀⡀⠘⠀⠀⠀⠀⠀⣀⠀⢈⡘
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀⡀⠤⠀⠀⠀⢐⠀⠀⡄⠀⢠⡤⠂⠉⠁⠀⠀⠉⠀⠔⠄⠀⠀⡢⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠂⠐⡜⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣵⡴⡄⠈⠀⠈⠀⢣⠀⡀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⡈⢀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠀⠘⢰⠓⠄⠊⠀⠍⠀⡀⠀⠒⠀⠆⡗⢢⠔⡠⠂⠠⢈⡒⠡
⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⠃⡀⢄⡀⠒⠀⠀⢠⡟⡜⡀⠀⢠⠄⣡⠫⠐⠍⠀⠴⢆⠖⠁⠀⠠⣈⡬⠀⡛⠠⠂⢁⠰⠀⡜⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢠⣄⡢⠀⠠⠠⠀⢢⣄⣀⣠⠋⢉⠀⠉⡒⢡⠚⣋⠤⣄⠈⢤⠲⠧⠤⠤⣤⣈⣼⢡⠨⢥⠈⡁⠡⠤⠂⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⡋⠙⠂⠀⠁⡤⣄⣀⣈⣸⠆⠀⠉⢈⣉⣀⢀⠀⠐⡀⠀⣢⠂⢀⢹⣴⠃⣾⠷⠧⣔⡁⠁⠐⡀
⠀⠀⠀⠐⠐⠀⡀⠀⠀⠈⠀⠙⠢⡄⢀⣾⡁⠶⠛⡦⠀⢀⡀⠴⠊⠈⠙⠲⠖⠁⠛⠊⢈⡇⠀⠀⡀⠀⠍⣀⠀⢀
⠀⠀⠀⠀⠂⠀⠈⠀⠁⠀⠁⠀⠁⠈⣑⡄⢠⣖⣟⣁⣀⠨⣁⡴⠖⡀⢉⡐⠂⠁⢀⠠⢀⠀⠀⠐⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠂⠄⠀⠈⠘⠀⠂⢐⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠄⠉⢁⠄⠴⠿⠍⠒⠛⠀⢀⠀⡐⠀⠂⠀⠀⠉⢉⡉⢀⢀
⠀⠀⠘⢀⠀⡨⠘⣯⠁⢂⠀⠀⡠⣞⠀⠁⠀⠀⢐⠃⣼⣫⡝⢀⡀⠀⠔⠀⠑⡄⢁⠀⠆
⠀⠀⠀⠘⠐⠻⢿⡁⠀⠈⠉⢉⠐⠀⠀⠀⠀⢓⠡⠊⠁⠀⠀⠀⠀⠀⠀⠈⢀⠁⠨⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⣇⠀⠀⠀⠃⠛⠀⠄⠐⠈⠁⠀⠰
⠀⠀⠠⠀⠀⠀⢀⢈⡷⡂⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠠⣀⠼⢋⢛⢂⠀⡀⠀⠁⠀⠤⠔⠸⠄⢐
⠀⠀⠀⠀⠚⢿⠨⠐⠂⡐⠂⠀⠄⠀⠀⠀⠀⣀⠒⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣒⡒⠖⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⡌⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠉⠀⠀⠀⠒⠒⠠⠤⣀⠀⠀⠀⠀⠸⠀⠀⠙⢄⠀⢠⣚⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⣲⣦⣤⣤⣤⣀⣀⠀⠀⠀⠈⠑⠤⡀⠸⠀⠀⠀⠈⡆⠉⣠⡴⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⣻⠿⠛⠛⢿⣿⡶⢦⣄⣀⠈⠑⣄⠀⠀⠀⢡⠀⠀⠈⠓⠊
⠀⠀⠀⠀⠀⠀⣄⠀⢸⡆⢀⡆⠀⠀⠀⢸⠁⠀⠈⠀⠉⠀⠀⠀⠀⠀⢠⢝⡛⠛⢢⣌⢆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠙⠂⠈⠁⠘⠃⠀⠀⠀⢸⠀⠀⠞⢹⠄⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⢿⣿⣆⢠⠁
⠀⡤⠒⠒⠒⠀⠀⠠⠤⢤⣤⣤⣤⣤⣄⣬⡀⠀⠀⠀⢀⡄⠀⠀⠀⠘⠁⠱⠀⠀⠀⢸⣿⡟⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠻⠙⢿⣿⣿⣟⠲⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⢸⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⠁⢸⣿⠀⠰⠒⣹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠊
⠈⠢⠤⠤⠤⠄⢀⣀⣠⣿⣄⠀⠀⠀⠀⣾⡯⠊⠉⠋⠥⣀⣀⣀⣀⣀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢢⠀⠀⠀⢡⡤⠴⡖⠛⣿⣧⣀⣀⣠⣤⣾⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡆⠀⠀⠀⢳⡈⠸⢠⣼⠿⣛⣛⢍⠩⡍⠙⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⡀⠀⠀⠀⠙⠛⠉⣷⢋⠰⠀⠀⣀⠈⠂⣼⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠓⡄⠀⠀⠀⠀⠀⢸⡎⡇⣀⣈⢙⣡⡾⢋⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⣶⢶⠒⡛⣷⣭⣵⠾⣛⡉⠊⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠙⠉⠁⠀⠀⠀⠁⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⠀⠘⠁⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡔⠀⠀⢠⠄⢈⠐⠀⢀⠀⠘⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣇⣾⡇⠀⣠⠏⠀⠀⠀⠀⠀⠐⠊⠁⠔⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣄⡀⢀⠀⠀⠀⠀⠀⡀⢠⣿⡿⠃⢸⣏⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊
⠀⠀⠀⠀⠀⠼⢳⣞⠀⣤⣀⣠⣾⣷⢋⣵⣦⡴⠚⠋⠀⠀⠀⠀⠀⠀⠉⢱⣄⠀⠀⠀⠀⠀⠘⠁⠀⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣼⣿⣿⠟⠻⢣⣿⡟⠉⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖
⠀⢠⣤⡄⠀⣼⣿⣿⡏⠙⣿⡙⣷⣿⣏⣤⣾⣿⠀⣀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠉⠓⢺⣯⠭⠛⠂⠿⠇⠸⠯⠿⠟⠛⠋⠿⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠒⠒⠉⠤⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⣙⣷⡑⢿⡀⣆⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠈⠙⠟⢮⡁⣺⣿⣿⠀⠀⠄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⣆⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⠃⠈⢻⣿⣿⣾⢠⡿⠂⠀⠀⠀⠀⠀⠀⠘⡀⠐⡗⡀⠀⠀⠀⠀⠀⠀⡀⣜⢷⣿⣿⡁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣎⣧⠀⠠⣿⣿⡇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⣼⡷⡄⣠⣀⢀⣿⣿⠗⣾⠟⣁⡀
⠀⠀⠀⣤⡤⣠⣀⣠⣶⣿⢿⣿⣷⣄⣿⣿⡄⢻⣿⣷⣤⣐⡤⣄⠀⠀⢠⣤⡄⢻⣿⣿⣍⢫⡿⠟⢱⡷⣸⣯⣞⣁⣠⠀⢀⠤
⠀⠀⠀⠙⠺⠭⠍⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⢙⣛⡋⠁⠉⠀⠀⠀⠉⠓⠋⠉⠉⠛⠛⠛⠛⠛⠛⠋⠭⠭⠛⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⣼⡿⠁⠈⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣧⣾⡿⠁⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠟⠋⠉⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣿⣧⣴⡷⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⠀⠀⠰⣷⣤⣿⣧⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠋⠀⠀⠀⠀⠀⣠⣿⠟⠁⠙⢿⣧⡀⠀⠀⠀⠀⠈⠻⢿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣆⠀⠀⠀⢸⣿⡀⣿⣧⡀⠀⠀⠀⣼⣿⠀⠀⠀⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠈⢿⣧⠀⠀⠀⢻⣷⣌⠛⠁⠀⢀⣴⣿⠃⠀⠀⢰⣿⠏⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⢸⣿⡇⠀⠀⠀⠙⠻⠿⣿⠿⠿⠋⠁⠀⠀⠀⣿⣏⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠋⠉⠛⠛⠿⠿⠿⠛⠛⠉⠛⠛⠿⠿⠿⠟⠛⠋⠙⠛⠻⠿⠿⠟⠛⠋⠉⠛⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠀⢀⣀⣤⣤⣤⣀⣀⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠋⠉⠙⠛⠿⠿⠿⠛⠛⠉⠙⠛⠿⠿⠿⠟⠛⠉⠙⠛⠻⠿⠿⠛⠛⠉⠉⠛⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⢀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⢿⣧⠀⠀⠀⣰⣿⠋⢻⣷⡀⠀⠀⢠⣿⠏⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⢀⣸⣿⠀⠀⠀⣿⣧⡀⣠⣿⡇⠀⠀⢸⣿⡀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠀⠀⠈⠻⠿⠟⠋⠀⠀⠀⠀⠙⠿⠿⠛⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⣿⡿⣛⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣦⣴⣶⣶⣦⣤⣤⣦⣶⣶⣦⣶⣦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢟⣩⣥⣭⣙⢿⣿⣿⣿⣿⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣭⢅⣾⣿⣿⣿⣿⡆⢩⣭⣭⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⡜⣿⣿⣿⣿⣿⡟⠸⠿⠿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣷⣜⠿⠿⠿⢟⣵⣶⣶⣶⡇⠀⠸⠿⢛⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣷⣦⣝⡻⠿⠿⠿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣨⣭⡶⡦⢤⣤⡴⠶⠛⠉⢉⣁⣭⣭⡽⠶⠦⣤⣤⠴⠶⠛⠉⢉⣠⣤⣬⡭⠷⠦⠤⣤⣤⠴⠞⠛⠉⣁⣠⣤⣭⡭⠶⠦⠤⠤⠴⠞⠛⠉
⠀⠀⠀⠀⢀⣠⣤⣴⠦⠴⠶⠶⠶⠿⠛⠋⠁⢀⣠⣤⡴⠶⠶⠶⠶⠶⠿⠛⠋⠁⢀⣠⣤⡶⠶⠶⠶⠤⠶⠾⠟⠛⠉⠀⣀⣤⣤⡶⠶⠶⠶⠶⠾⠛
⠀⠀⠀⠀⢉⣉⣠⡤⠴⠖⠒⠒⠶⢤⣔⣒⠛⠛⢉⣁⣤⠶⠒⠒⠒⠶⢤⣐⣚⠛⠛⢉⣁⣤⠴⠒⠛⠓⠲⠦⣤⣒⠚⠛⠋⣉⣠⡤⠖⠒⠛⠒⠶⠄
⠀⠀⠀⠀⢉⣉⣀⠒⠛⠛⠻⢶⣦⣤⣈⣉⣙⣋⣉⡁⠘⠛⠛⠿⢶⣦⣤⣈⣉⣉⣉⣉⣁⡀⠉⠛⠻⠷⣶⣤⣀⣉⣙⣛⣉⣉⣀⠈⠙⠛⠿⢶⣦⣄
⠀⠀⠀⠀⣈⡉⠛⠻⠷⣦⣤⣤⣄⣉⣩⣭⣍⣉⡉⠛⠻⠷⣶⣤⣤⣄⣈⣭⣭⣭⣍⡉⠙⠻⠷⣶⣤⣤⣤⣈⣉⣭⣭⣭⣉⡉⠛⠻⠷⢶⣤⣤⣀⡀
⠀⠀⠀⠀⣈⠙⠓⠶⠤⠤⠴⠞⠫⢥⣤⣤⣄⣉⠙⠓⠶⠦⠤⠶⠒⠩⠥⢶⣤⣤⣈⡉⠛⠶⠦⠤⠤⠶⠚⠭⠤⣦⣤⣄⣉⠙⠛⠶⠶⠶⠖⠚⠩⠤
⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠶⢶⣦⣤⣀⡀⠉⠛⠛⠓⠲⠒⠒⠲⠶⣶⣤⣄⡀⠉⠙⠛⠳⠶⠶⠒⠒⠶⢶⣦⣤⣀⡀⠉⠙⠛⠛⠒⠒⠒⠲⠶⣶⣤
⠀⠀⠀⠀⠴⠒⠚⠛⠛⠲⢦⣤⣀⣉⣙⣛⣻⠽⠒⠛⣛⣛⠓⠶⣤⣀⣈⠉⢛⣛⡯⠕⠒⠛⣛⡛⠲⢦⣤⣀⣉⣉⣉⡩⠽⠒⢛⣛⣛⠳⠶⣤⣀⡁
⠀⠀⠀⠀⣴⠾⠛⠋⠉⣉⣀⣀⣍⣉⣉⣡⣤⣴⠾⠛⠋⠉⣉⣁⣠⣬⣍⣉⣉⣤⣤⡶⠟⠛⠉⢉⣉⣀⣤⣬⣉⣩⣤⣤⡶⠿⠛⠉⠉⣉⣁⣠⣬⡁
⠀⠀⠀⠀⢀⣤⣴⡶⠿⠛⠉⢉⣀⣤⣤⣤⣤⣀⣤⣴⠶⠿⠛⠉⢁⣀⣤⣤⠤⣤⣤⣠⣤⣴⠾⠟⠛⠉⢁⣠⣤⣤⢤⣤⣤⡤⠶⠾⠿⠛⠉⣁⣠⡤
⠀⠀⠀⠀⠠⠄⠒⠶⠶⠶⠞⠛⣉⣤⣴⠶⠶⠬⠍⠓⠲⠶⠶⠞⠛⣉⣤⣴⠶⠶⠆⠤⠐⠲⠶⠶⠶⠛⢋⣡⣤⡶⠶⠶⠬⠉⠓⠲⠶⠶⠛⢋⣩⣤
⠀⠀⠀⠀⠶⠶⠖⠒⠒⠒⠚⠛⠋⠁⣀⣠⣴⡶⠶⠚⠒⠓⠚⠛⠛⠋⠁⣀⣠⣴⡶⠾⠛⠛⠛⠒⠒⠛⠛⠉⢀⣀⣤⣶⡶⠟⠛⠛⠛⠛⠛⠛⠉⡁
⠀⠀⠀⠀⣠⣤⠶⠖⠛⢛⣉⣙⠛⠻⢉⣉⣁⣀⣤⡴⠾⠛⣋⣉⡙⠛⠫⢉⣉⣁⣀⣤⡴⠞⠛⣉⣉⣉⡛⠛⠋⣉⣉⣀⣠⣤⠶⠟⢛⣉⣉⣙⠚⠉
⠀⠀⠀⠀⠠⢤⣶⣊⣉⣉⡉⠉⠛⠷⢶⣤⣍⣩⣤⣴⣄⣉⣉⠉⠙⠛⠷⢶⣤⣭⣭⣤⣴⣬⣭⣁⡈⠉⠙⠻⠶⣤⣬⣉⣥⣤⣴⣬⣅⣀⡉⠉⠛⠗
⠀⠀⠀⠀⢤⣤⣀⡀⠉⠙⠻⠷⢶⣤⡤⠤⢤⣤⣤⣀⡈⠉⠛⠻⠷⠶⠦⠤⠴⠶⢶⣤⣄⣀⠉⠙⠛⠿⠶⡶⠤⠤⠴⠶⣦⣤⣀⣈⠉⠙⠛⠷⠶⠦
⠀⠀⠀⠀⢤⣤⣉⠛⠻⠶⠖⢂⠠⠴⠶⠶⠶⣤⣌⣉⠛⠛⠶⠒⡂⡄⠴⠖⠲⠶⢦⣤⣉⡙⠛⠶⠶⢒⣀⠤⠶⠒⠶⠶⣤⣌⣉⡛⠛⠛⢚⣂⠤⠆
⠀⠀⠀⠀⣀⣈⠉⡛⢛⡛⠛⠛⠛⠿⠶⣦⣤⣀⣈⣉⣛⣛⣛⡉⠙⠛⠛⠿⣶⣦⣄⣀⡉⠛⣛⣛⣋⠉⠙⠛⠻⠷⣶⣤⣄⣈⣉⣙⣛⣉⡉⠙⠛⠓
⠀⠀⠀⠀⠉⣉⣉⣉⣉⡙⠛⠷⢶⣤⣄⣀⠈⠉⣉⣉⣉⣉⣉⠛⠻⢶⣦⣤⣀⣈⠉⡙⠛⠋⠉⠉⠙⠛⠳⠶⣦⣤⣠⠌⢉⣉⣭⣭⣉⣙⠛⠿⢶⣦
⠀⠀⠀⠀⠛⠉⣉⣠⣬⣭⡕⡲⠦⢤⡤⠴⠖⠛⠉⣁⣠⣤⣬⠽⠶⠦⢤⣤⡤⠶⠞⠋⠀⣀⣤⣤⣤⠴⡶⠦⠤⠤⠶⠞⠛⢉⣠⣤⣤⣭⣿⡶⠦⡤
⠀⠀⠀⠀⠶⠿⠛⠉⠁⣀⣤⣤⡶⠶⠶⠶⠶⠶⠟⠛⠉⠁⣀⣠⣴⡶⠶⠶⠶⠴⠶⠾⠓⠃⠀⢀⣀⣤⣶⠶⠶⠶⠶⠶⠞⠛⠛⠉⢀⣀⣤⣶⠶⠖
⠀⠀⠀⠀⠰⢤⣞⡛⠛⠛⣉⣠⣤⠶⠞⠛⠒⠶⢤⣚⣛⠛⠋⣉⣠⣤⠶⠚⠛⠛⡲⢦⣔⣛⠛⠛⢋⣁⣠⡴⠖⠛⠛⠓⠶⢤⣝⣛⣛⣉⣁⣤⡴⠖
⠀⠀⠀⠀⠙⠓⣈⣉⣙⣋⣉⣁⣠⣴⡶⠿⠛⠛⠁⣈⣉⣉⣉⣉⣁⣤⣴⡶⠿⠛⠉⠉⣀⣉⣉⣙⣋⣉⣀⣤⣶⠾⠟⠛⠉⢀⣀⣉⣉⣉⣉⣀⣤⡦
⠀⠀⠀⠀⠾⠟⠛⢉⣉⣉⣭⣍⣉⡠⢤⣤⣴⡾⠟⠛⢉⣉⣩⣭⣍⣉⡠⢤⣤⣴⠾⠟⠋⢉⣉⣤⣭⣭⣉⣁⠤⣤⣤⣶⠾⠛⠋⢉⣁⣤⣭⣅⣀⡀
⠀⠀⠀⠀⠴⠖⠛⠫⠭⢤⣤⣤⣈⡉⠓⠶⠤⠤⠶⠚⠫⠥⢤⣤⣤⣉⠙⠓⠲⠤⠤⠶⠚⠫⠥⠴⣦⣤⣄⡉⠛⠲⠤⠤⠴⠶⠛⠭⠥⢤⣤⣤⣈⡉
⠀⠀⠀⠀⠰⠶⠶⣶⣤⣄⡀⠈⠙⠛⠷⠖⠶⠶⠶⠶⣦⣤⣀⡀⠉⠙⠛⠓⠒⠒⠒⠒⠶⢶⣤⣄⣀⠈⠙⠛⠻⠶⠒⠒⠒⠲⠶⣦⣤⣄⣀⠉⠙⠛
⠀⠀⠀⠀⠲⠶⣤⣀⣈⣙⣛⣻⠷⠞⠛⠛⠛⠲⠶⣤⣀⣉⣉⣛⣻⠷⠛⠛⠋⠛⠛⠶⣤⣄⣈⣉⣛⣛⣻⠶⠛⠛⠛⠛⠳⠶⣤⣄⣈⣉⣉⣩⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢐⠒⠒⠒⢦⡀⡴⠁⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣆⡈⢦⢹⡇⢸⠀⠘⣦⠀⠀⣸⠀⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠉⠙⠻⢧⣸⡄⠀⣽⣤⠾⢃⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣴⠀⠀⠀⠾⠁⠀⠀⠀⠈⠑⣄⠻⠓⠚⠳⠶⠦⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⠀⣠⡤⠀⠀⠛⠃⠀⠀⠈⠡⠊⠀⣰⢂⠀⢻⡟⠛⠻⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⣧⠈⠦⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣴⠀⠀⢠⠆⡀⠀⠒⣃⠄⠀⠀⢚⡡⠂⠀⣀⠀⡇⢻⢿⣦⢄⣀⢙⡂⠄⠀⠀⠀⠀⠀⠀⠀⢀⡞⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠫⠂⠀⣿⠄⢹⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣤⣀⢸⠀⣿⡜⢉
⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⢞⠄⠀⠰⢆⡄⠀⠀⠻⠷⠂⠀⠴⢖⡠⠀⢀⠄⣼⠃⠀⠂⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠈⠻⣆⠘⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠀⠁⢠⠶⣀⠀⠀⠀⢀⣈⣡⠴⣊⣵⠞⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠐⢦⣀⠀⠀⠀⠘⣧⣁⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⠁⠂⠀⠀⠀⠨⢴⣒⣺⣭⠭⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢄⣠⠽⠛⠉⠀⠀⢀⠀⠀⠈⠻⡶⢬⡉⠉⠒⠒⣂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡶⠊⠁⣀⠄⠀⣠⠶⠋⢀⠀⠀⢀⠹⡆⠈⡓⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⠝⢋⡠⠖⢋⣤⠶⠋⣁⣤⠖⠹⠀⠀⣸⣸⡿⠦⠤⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠁⢠⣶⣭⠶⢛⣩⠴⠒⢻⠁⠈⠁⠀⠀⢀⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⡠⠀⡤⠈⠀⠞⠀⠀⣀⣀⣠⣤⠴⠖⠋⠉⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⣤⡤⠴⠶⠶⠶⠚⠛⠛⠏⠛⠒⠈⠉⣀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠴⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢀⠔⠈⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠁⠂⠀⠈⠁⠀⡀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀⡆⠀⢀⣀⣀⣀⠟⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⡀⠀⠀⠈⠑⠀⢀⠰⣂⡁⡄⠀⠀⡤⢃⢾⠌⠏⠹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢍⠂⢈⡉⠠⠀⠀⠀⠠⡦⣀⣤⠄⢀⠀⠈⣀⣁⡈⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⡀⠐⠄⠀⠲⠒⠒⠊⠛⠁⠀⠋⡑⢉⠁⠊⠠⢼⢶⠧⠤⠇⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠔⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠠⠦⠴⠶⡴⠒⠒⠉⠁⠀⠘⠀⠁⠁⠙⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠒
⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠯⠥⢤⣱⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣀⡀⣀⠀⡀⠀⣶⠀⠲⠀⠐⢁⡠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⢲⠀⢷⠀⢸⠀⠀⡆⠀⠀⢨⢸⡁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠒⠈⠚⠈⠊⠈⠊⠀⠉⠀⠈⠋⠑⠁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⢤⣖⣒⣛⣛⣛⣛⣛⣛⣛⣒⣶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⠀⠀⢸⣤⣒⣒⠉⠛⠛⠛⠉⠑⣒⣒⣦⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠠⠭⠍⠀⡇⠀⣠⠖⠉⠉⠲⢤⣤⡤⠖⠋⠁⠀⠀⡇⠀⠀⢸⡀⠀⠉⠉⠉⠉⠉⠉⠉⢉⡁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠥⠖⠀⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣒⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠧⠤⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠤⠤⣄⡀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠙⠲⢤⣙⠀⡧⠒⠉⠑⢶⣴⠞⢳⡀⠀⠀⣠⠔⠋⠉⠉⠉⣒⣦⣤⠉⠺⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡤⠛⢛⡿⠛⢀⡠⠀⠈⠀⢀⡀⠀⠠⠴⢿⣆⠀⢳⢀⡾⠁⠀⠀⢀⣴⣯⣥⣤⣤⣤⠀⠀⠘⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠰⣯⠴⢚⠏⢀⣦⠀⢱⣄⠉⢳⣶⣤⣄⣹⡆⢸⡾⠀⣀⠀⠀⠧⠀⠀⠀⢀⣞⡡⠚⡀⢸⡀⠑⢦⡄⣈⡒⢄
⠀⠀⠀⠀⢠⡏⠀⣟⡆⠀⠀⢸⣠⠏⢸⡀⢸⣨⠟⠉⠀⠉⠙⠫⣽⢸⠗⠉⠀⠉⠓⠂⠤⡀⠀⠟⢋⠀⠀⡇⢸⠈⢦⡀⠹⡌⢿⡉⠃
⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠸⠇⡴⢄⣳⠞⠉⡽⠋⢉⡠⠄⡀⠀⡀⠤⣀⠐⠒⠒⢖⡚⠻⡄⠀⢸⡄⠀⢸⣸⠀⠀⠙⢦⣿⠘⣇
⠀⠀⠀⠀⢸⡇⠀⠀⣠⢤⠀⠀⠀⠙⡼⠁⣀⠸⠷⠚⢹⠁⡰⣇⠀⠹⢦⡈⠻⡓⠶⢤⣵⡄⠙⣆⠀⠀⠀⠈⠿⠀⠀⠀⡶⠟⠀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⠎⠀⠀⠀⢸⠃⠀⣯⠇⠀⠀⣾⡼⠁⢹⡀⢸⠀⠻⣦⡹⡄⠀⠀⠣⠄⢹⡆⠀⡌⠀⠀⠀⠀⠀⠘⠁⠀⡿
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡤⣾⠀⠀⠀⠀⠀⠀⠘⠁⡞⡆⠳⣼⠀⠀⠈⠙⠷⢠⠄⠀⠀⢀⡇⠀⠀⠀⢰⢳⠄⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢹⡆⠀⠀⣶⢦⠀⠀⠀⠉⠀⠀⠉⠀⣖⢲⠀⠀⠈⠒⠃⠀⢸⡇⠀⠀⠀⠈⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⡵⠀⠀⠀⢿⡀⠀⠈⠃⠀⢰⢦⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠀⠀⠀⡾⠰⣉⠀⠀⠀⠀⢰⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⣀⠀⠈⣷⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⠃⠀⣼⠃⠀⠁⢀⠀⠀⠀⢈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠓⠀⠀⠸⣧⠀⢀⡀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⠀⢨⠇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠦⣄⣘⣧⠸⠜⠀⠀⠀⠀⠀⠈⠁⠀⠀⢾⡷⠀⣰⠏⢯⠃⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣧⡀⠀⢄⠀⠀⢀⣀⠀⠀⠀⠈⠀⣴⠷⠤⠤⠖⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠉⡀⠀⠘⠜⠀⢀⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠾⠲⢤⣄⣴⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⡿⠿⠿⢿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠶⢶⣶⡶⠶⠾⠿⠿⢿⢿⡿⠿⠿⠿⣷⢶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⣿⢸⡀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡏⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣀⣧⣷⣀⣀⣀⣀⣸⣠⣇⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣿⣸⣀⣀⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣤⣀⡀⣀⣀⣀⡤⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⡄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⡉⠉⠉⠉⣁⣠⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠹⣄⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠙⣦⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⢧⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠈⢳⣽⡇
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⡤⠖⠛⠓⢦⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⢠⣿⡀⠀⢀⡞⠁⠀⠀⠀⣸⠃⠀⠀⠀⡟⠀⠀⠀⠹⣄⠀⠀⠀⣴⠖⠒⢦⡀⠀⠀⠀⣿⠷⠦⣄⠀⠀⢠⠶⠒⢦⡀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⡟⠙⠛⠉⠀⠀⠀⠀⠀⠻⣄⠀⠀⣠⠇⠀⠀⠀⠀⠙⠲⠤⠞⠃⠀⠀⠀⣇⠀⠀⢸⡏⠀⢀⡟⠀⠀⢸⠀⠀⠀⡇⢀⣼⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣻⡇⠀⢸⣇⠀⣀⡼⠀⠀⠀⠉⠉⣿⠃
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⣿⢿⣆⣴⣾⡆⠀⣀⠀⠀⣿⠇⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⠈⠛⠁⢸⣇⠀⣩⡀⠀⣿⠀⠀⣿⣴⣿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠹⠇⠀⠀⠸⣿⠀⢿⠇⠠⡿⠀⠀⣿⠉⠻⣦⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣀⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⣀⠀⠀⠀⠈⠀⡎⠀⠀⠀⠀⠀⠳⠀⠐⠀⠀⠐⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⡀⢀⡠⠁⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⢧⢀⠀⠀⣀⠜⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠅⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⢊⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⣤⠔⠂⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠂⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠈⠑⢦⠀⠀⠀⡀⠀⠠⠀⠀⠈⡖⠀⠀⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡
⠀⢀⠀⢄⠀⠀⢀⠠⠼⡀⠀⠀⠀⠀⡨⠂⠂⠄⠀⠀⠂⠀⠀⠀⢆⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠠⠤⡠⢄⠀⠀⠀⠀⠀⠀⠀⠍
⠀⠀⠀⠀⠂⠀⠄⠀⠀⠐⣄⢀⡀⢠⠁⠀⠀⡠⠀⠀⢠⡠⠀⠀⠀⠁⠀⣠⠤⠠⠤⡔⠁⠀⠢⠀⠀⢐⠒⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠤⠃⠀⠀⠀⠑⠀⠐⠁⠀⢠⠁⠀⠀⢀⠀⠀⡜⠁⠀⠀⠀⠡⡀⠀⡠⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠑⠔
⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⠂⠀⠀⢆⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⡨⠀⠀⠐⠀⠀⠀⠀⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠒⡁⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡠⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠂⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⡠⠤⣠⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠤⠒⡆⠀⢀⢀
⠀⠀⠀⠐⠁⠀⠀⠦⠤⠄⢢⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠲⡄⠀⠀⠈⠎⠀⠁⠀⠐⢅⡱
⠆⠀⠀⠣⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢄⣀⡀⡀⠈⠉⠀⠀⢀⠀⠀⢄⠀⠀⠘
⡀⠀⠀⠀⠀⠔⠉⠉⠢⣀⣀⠀⠠⠒⠒⠀⠀⠀⠀⠈⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠈⠀⠀⡀⠀⠀⣂⠀⠀⠀⠅⠀⢀
⣈⣋⣀⣀⣀⣄⣀⣀⣈⣀⣀⣈⣁⣀⣀⣀⣁⣀⣀⣐⣂⣀⣀⣀⣰⣊⣉⣉⣑⣠⣂⣀⣢⣀⣀⣀⣀⣈⣀⣀⣈⣂⣀⣐⣁⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⢳⣄⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢷⣝⢦⡀⠀⠀⠀⠀⢀⡾⣏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⠙⣯⣻⣆⠀⠀⠀⣼⠁⣿⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠘⢧⡈⢿⣽⣧⡀⣸⠁⠀⢸⠀⠈⡇⢀⡤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡀⠓⢦⣿⣿⣷⡏⠀⡀⣾⣷⢰⣿⠋⡴⠁⠈⠉⣹⣭⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⣧⡁⡠⣌⢿⣿⣇⣷⣷⣿⣿⣿⠇⣼⠇⠀⣠⣾⠟⠋⠙⠳⠶⣦⠴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣶⣿⣿⣾⣿⣧⣿⣿⢟⣫⠁⣀⣈⠛⣯⣶⣖⣯⣶⣿⠗⠂⠀⣠⡔⠛⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣯⣷⣾⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣾⣿⠶⠿⠿⢿⣦⡀
⠀⠀⠀⠀⢀⣤⣶⣶⡟⠀⢰⠋⠁⣴⣥⡾⣻⣿⡟⣻⠏⣝⣿⡳⡝⢿⣿⣙⠉⠀⠂⠈⠉⢢⡀⠀⠈⠁
⠀⠀⠀⣴⣿⢝⣽⣿⡇⠀⢼⣀⠀⣿⣿⣿⢯⢿⣼⣿⣄⠈⠙⢳⡀⠀⢿⣿⣦⣴⣶⣿⣿⣶⣿⣦⣀
⠀⢀⣴⣿⡷⣋⣿⣿⣷⣴⡘⣜⡀⣿⣿⣿⠀⣾⠏⢠⠟⢦⡀⠂⢧⠀⣸⡇⠻⣶⠈⠡⠞⢷⣿⡭⢻⣷⣄
⠀⢾⣯⠵⢚⣿⣿⣙⡟⠻⠿⣮⠇⣿⣿⡸⢸⡏⠄⡀⠈⠀⠛⣆⠘⠀⡟⠀⠊⠁⠰⠆⠳⠌⠠⢞⣹⡿⠹⣆
⠀⠀⠀⠀⣾⠓⠮⠐⢇⠁⡒⠝⢷⠟⢻⣧⣸⠃⠁⣿⡆⠀⠀⢹⡄⢸⡗⠂⣿⣷⠀⢸⡇⠴⠾⣿⢯⡩⠽⠻⣆
⠀⠀⠀⣸⣿⠵⠠⠆⣾⠀⣩⡄⠙⠻⠋⠿⠏⣿⡆⠘⠁⠀⠀⠀⡙⠻⠀⢀⠁⠁⠈⢀⡀⠀⢶⣯⡀⢂⣴⡀⣿
⠀⠀⠀⡇⠐⠊⠈⢷⠄⡌⢧⣿⠀⠦⠀⠀⠀⠉⠀⠀⠐⣶⡄⠀⣁⣀⠀⠿⠇⠀⠀⠀⣄⠀⢬⡷⠢⣗⡻⠂⢻
⠀⠀⠀⣿⣾⣖⣛⠃⢨⣀⠀⠀⣠⣶⡄⠀⠀⣶⢶⠀⠈⣷⠇⠀⠘⠋⡀⠀⠀⢂⡀⠀⠛⠀⠈⠔⠃⢖⣴⡄⢻
⠀⠀⠀⢸⠀⠲⡜⢳⢸⡅⠀⠀⢿⣿⠀⠀⠀⠹⠾⠀⠀⠀⠀⢰⡀⠀⢸⣧⠀⠿⠇⠀⡄⠀⣦⡭⣀⡐⠉⠩⢼
⠀⠀⠀⠘⣧⠀⠾⠤⠀⢡⠃⣰⡄⠀⠀⣴⡄⠀⠀⢘⣷⠀⠈⡾⠃⠀⠀⠀⠀⢀⠀⠀⠠⡏⠕⢂⣛⢠⣶⢠⡗
⠀⠀⠀⠀⢿⣀⡄⢉⢲⢶⣃⣿⡷⠀⠈⢷⣿⠀⠀⠸⠿⠁⠀⠀⠀⣿⠁⠀⠘⢿⠃⠀⠀⠀⠀⣸⢂⡄⣁⢰⡇
⠀⠀⠀⠀⠈⢿⡿⠀⠘⠾⣖⡀⡀⢴⣦⠀⠀⠀⣂⠀⠀⣸⣧⠀⠀⠀⢠⣄⠀⠈⠀⠀⣰⡄⢀⣁⠈⣱⠇⣾
⠀⠀⠀⠀⠀⠈⢷⡀⣶⡔⠈⣴⡧⠘⠿⣠⠀⢰⣟⡇⠀⠻⠼⠀⠀⠀⠴⠋⢀⣰⡆⠈⠉⢡⠎⠙⠀⣈⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣎⣡⣖⠙⡿⠃⠀⣽⣷⠈⠙⠁⣴⡄⠀⠀⣼⡆⠀⠀⠈⠙⠃⣀⣠⡕⡐⡁⣸⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣏⢱⡄⢰⠔⢈⣩⣦⠀⠀⠿⠟⠀⠀⢉⠁⠀⢠⡦⠀⡀⣛⡶⠰⠷⣄⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡓⢎⠀⣤⠚⠟⠀⠀⠀⣦⠀⠀⢸⣧⠀⠛⠃⢀⡃⣠⣀⣦⣌⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡄⠻⣅⢀⣽⡆⠀⠙⠁⠀⠀⠀⠀⠀⠠⠙⡁⠻⢁⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣣⡂⠻⠯⠀⣸⣷⠀⣸⣧⠀⣷⡴⠛⠀⠿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣶⣦⠀⢈⡋⠀⢨⠅⡜⠉⠤⠰⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡀⠠⠀⢠⣾⠀⡀⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠦⢾⣥⠶⠟⠉

⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠠⢤⠍⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠛⠒⠾⠛⠋⠛⠋⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣶⣤⠶⣄⣀⣄⣀⡀⢤⡄⠀⠀⠀⠀⠐⠒⠄⠬⣿⣤⣤⣤⠤⣤
⠀⢀⠀⣠⣤⣄⡀⢀⣀⠀⠀⡀⢀⣀⣠⠤⣐⣤⡤⠀⠤⠶⠶⠒⠖⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠁⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⣄⣀⣀⣀⣀⣀
⣭⣤⣤⣤⣀⣐⣒⣠⣤⣶⣶⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠈⠭⠍⠉⠉
⣛⣛⣛⣻⡿⠟⠛⠛⣿⣿⣿⣿⣿⣷⡚⣶⣶⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢑⣢⣤⣤⣤⣤⣤⣤⣀⣀⣀
⡉⠉⢹⣿⣟⣻⣟⣭⣭⣭⣭⣭⡍⠉⡉⠉⠈⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣿⣿⣿⡶⠶⠶⠶⠶⣦⣔⣒⣒⣐⣒⣒⣒⣺⣿⣿⣿⣿⣿⠿⠿⠿⠻
⣿⣿⣿⣿⠿⠟⠓⠶⠶⠶⠶⠶⢶⣤⣤⣀⡒⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠙⠿⢛⣛⣛⣉⣉⣉⣉⣛⣛⣛⣻⣿⣶⣦⣤⣤⣐⣒⠒⠒⠒
⠋⠉⠙⠒⠂⢤⣤⣀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⣀⣀⣠⣤⡶⠶⣛⣋⣉⣉⣩⣥⣤⠀⣤⣤⣶⣶⣶⣶⣶⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣛
⣂⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠙⣛⣛⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠛⠛⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠷⠒⠂⠀⠀⠀⠉⢉⣉⣛⣻⣷⣶⣶⣶⠶⠶⠶⠶⠒⠒⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠤⠶⠆⠀⢀
⠁⠉⠀⠀⠒⠒⠒⠒⠒⠶⠶⠂⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣈⣉⣙⣀⣀⣚⣛⣿⡿⠛⠛⠛⠛⠉⠉⠉
⠛⣻⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⢿⣟⡒⠒⠀⠒⠒⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⢄⣀⣀⣀⣀⣀⣀⢀⢙⠛⣛⡓⣒⣒⣚⣶⣶⣶
⠿⠿⢿⣶⠶⣿⣿⣿⣿⣿⣟⣻⣿⣿⣭⣤⣤⣤⣤⣤⣶⣶⣶⠿⠿⢿⣿⣿⣿⣿⣿⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⢉⣉⣈⣥⣤⠤⠤⣤⣤⣤⣬⣭
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠉⠙⠛⣉⣉⣉⣉⣉⣉⣉⠉⠙⠛⠛⣂⣀⣀⣉⣉⣉⣛⣛⣻⣿⡿⢶⣶⣶⣶⣾⣶⣶⣶⣶⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⢉⣉⣀⣀
⣿⣿⣟⠛⠙⠟⠛⠿⠿⣿⣿⣿⣿⣍⣉⣉⣉⣉⣉⠉⠉⠉⠁⠀⠀⢀⣉⣉⣉⡉⠭⠭⡭⠼⠟⠛⠛⠉⠉⢉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠛⠫⠙⠛⠛⠛⠛⠛⠋⠀⠀⠈⣉⣉⣩⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟
⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣶⣶⣿⠿⠿⠟⠛⠛⠛⢛⣛⣛⣿⣿⣯⣭⣭⣭⣭⡽⠿⠿⠿⠿⠿⠛⠛⠋⠉⠙⠛⠛⠛⢋⣉⡉⠉⠉⠉⠁
⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣦⣤⣤⣤⣴⣶⣾⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠶⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⣀⣀⣀⣀⠀⣀⣠⡄⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀
⣭⣭⣭⣥⡤⠤⠤⣤⣤⡶⠶⠶⠶⠖⠒⢟⣻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠏⠙⠛⠉⠛⠚⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠒⠉⠉⠉⠁⠀⢀⣀
⣿⣿⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⢀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀
⠉⠉⠉⠁⢀⣀⣒⣒⣒⣒⣚⣛⣃⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣭⣌⣀⣚⡛⠛⠛⠻⠿⣿⣿⣛⣛⣋⣉⠛
⡶⢶⣶⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⢀⡤⢶⣶⣶⠶⠶⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⣹⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢉⣉⣉⣛⣛⡛⠛⠛⠻⠿⠿⠿⠿⢷⣶⣶⠶⠶⠶⠶⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣷⣶⣿⣿⣶⣶⠶⠶
⠀⠀⠀⣀⣀⠀⠀⠠⠤⠤⠤⠴⣾⣿⡿⠛⠛⠛⠻⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⣤⣀⣤⣀⣀
⣶⣶⣶⣶⣿⣵⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠒⠚⠓⠒⠒⠒⠛⠛⠛⠿⠯⠭⠿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣠⣤⣤⣤⠤⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⠿⣾⣿⣿⣶⣿⣿

⠙⣏⠐⠀⠃⠁⠀⠀⠀⠄⠸⠧⣄⣀⣿⡵⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠶⠝⠛⠀⢠⠈⠑⠒⠂⠁⠀⠠⡽
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠷⠤⠄⠈⢀⣄⠃⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣯⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⣵⠟
⠀⠘⠀⠀⠂⡀⠀⢀⠀⠀⠀⠀⠠⠂⠁⠂⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⡼⠁⠐⣀⠤⠒⠋
⠀⠀⠀⠠⣶⢋⣀⣠⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠁
⣾⡆⠀⢠⡕⣎⢉⡀⠀⠀⡠⠀⠄⠀⠀⠁⠀⠀⠀⠀⠰⠿⠀⠀⠂⠉⠘⠛⠀⠁⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰
⠚⣁⢀⣐⣾⠛⢷⣶⠾⣎⣀⠀⠐⠄⡀⠾⠷⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⡄⠀⠑
⣄⡨⢫⠏⠸⣆⣼⠁⠀⣘⢽⣇⠀⠀⠀⠀⠠⠀⠀⡡⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⢠⡽⠂⠀⠀⢠
⠉⢁⣿⠟⡓⠀⠉⠀⠀⠅⣼⠇⠀⠤⠄⣴⠀⣰⠏⠀⠀⠸⠀⢀⡀⠀⠂⠠⠔⠀⠀⠀⢀⡀⠀⠁⠀⠀⠁
⢠⠋⠀⠀⠀⠀⠀⠡⠤⠞⠁⠀⠀⠀⠰⢷⢸⣏⣠⢖⣹⡷⠚⠭⡛⢷⡄⠀⠀⠀⠈⠂⡀⠈⢠⡄⠀⠀⠆⠀⠸⡶
⠁⠀⠀⣠⣴⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⢸⣿⠙⠻⡆⠀⠀⢆⠸⡇⠀⠀⠇⠀⠀⠘⣤⠀⠠⠎⠀⢀⠀⠀⠀⢀
⠀⠀⠙⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⢷⣦⠀⠀⣭⣏⠳⠶⠝⠂⠄⡀⢈⠇⠀⠀⠘⢦⡀⣀⣈⣿⡟
⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢐⠊⠀⠙⣛⢻⣤⡞⠂⠀⠀⠀⠁⠀⠀⠀⠂⠈⠈⠁⠉⠙⠛⠒⠊⠀⠀⠀⠙⠃
⠀⢸⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠉⠁⠀⠀⣠⠾⠀⢹⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠂
⡕⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⡠⠀⢸⡀⠀⢷⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⣤⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠪⣟⢳⣦⠀⡇⠀⠀⠣⡀⠀⠀⢀⣼⡃⡀⠀⠀⠀⠈⠁⠀⠐⠀⠀⢠⡴⠞
⢀⡴⠂⡀⠀⠀⠠⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠈⠥⠁⠀⡀⠀⠀⠀⠢⠄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⡇⠀⡀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡤⡀⠀⠀⠐⢀⠄⢀⠠⠤⣴⠀⢠
⡤⢂⣾⠖⠺⢛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠎⠀⠂⠀⠀⠈⠁⠀⠀⠀⠲⣾⣸⣏
⡟⠛⢿⠀⠀⠸⠁⢿⠀⠀⠀⠀⠄⠀⠠⡀⠀⠘⠛⠀⠀⠀⠀⠋⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⣤⠀⠀⠘⢀⠀⠀⡾⢹
⠳⠦⠬⠶⠠⡀⠀⣹⠀⠀⠆⠀⠐⢦⠀⢠⠄⠠⠀⡄⠀⠡⠁⠀⠀⠀⣿⠃⠀⠠⠈⠀⠀⠀⠉⠀⠀⠀⢷⣭⠄⠀⣉
⠇⠴⠲⠀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠸⠆⠨⠠⠂⠀⠂⠀⠀⠀⠀⠀⠘⠋⠈⠀⠀⠐⠀⠠⠀⠀⠠⠀⠀⠡⠸⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠞⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢸⡆⠀⡇⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣾⠀⠀⢸⠀⠀⣿⠀⢸⡇⠀⢸⣀⣀⣧⣤⣧⡤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣸⣀⣠⣽⣤⠶⠷⠛⠛⠉⠉⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢷⡖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⣄⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢀⡼⠃⢀⣀⣤⡤⠴⠶⠚⠛⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢠⡿⠷⢿⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠿⣦
⣿⠁⠀⠀⠀⠈⠉⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⠋⠉⠁⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⢤⣀⣘⠆⣀⣀⣤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢸⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⡄⠰⡟⣷⠞⣹⠆⠸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢸⠀⠀⢰⠲⡆⠀⣾⣆⠈⣏⢿⢻⡘⡇⠀⣷⠀⢠⣏⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠙⢶⠇⠹⡆⢻⢸⣼⡇⣿⣀⣽⠀⣶⣝⢦⡀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⠀⢀⡀⢹⣼⡎⣿⣧⣈⣠⣿⣧⡽⠘⠾⠁⢸
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⡟⣧⢘⣿⣦⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠚⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⣿⠀⠀⣒⠦⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⢠⣭⣟⡒⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠈⡇⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⢹⡀⠀⢇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⣧⡀⠈⠳⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞
⠀⠀⠀⠀⠀⠉⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣤⡴⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⣸⣤⡶⠞⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠕⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⡱⠣⡠⠤⠂⠐⢍⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠍⢋⡤⠔⡂⠤⡀⠸⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⢀⠈⠑⠘⡆⢱⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣇⠀⢌⢓⢲⠀⡇⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢢⠸⡄⠀⠘⡜⡜⠀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠀⢹⠀⠈⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡇⢸⠀⠀⠸⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡰⢁⡜⠀⣠⢠⠇⠧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⢀⠦⠀⠀⠀⠘⣒⣚⡀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢋⡠⢚⡡⠞⢀⡨⢕⡫⢊⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣩⠴⢒⡩⠥⠒⠚⠉⠉⠭⠭⠭⠉⠉⠉⠓⠒⠲⠤⠤⢭⣭⡤⠭⠴⠒⢉⡴⠚⠉⠴⠋⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠔⡩⠔⠊⠁⢀⢀⡄⡠⠖⠋⠉⠭⢭⡍⠔⣢⠤⣀⠀⠀⠀⠀⠀⠀⡀⡄⡰⠁⠀⠀⠀⠀⠀⡤⡚
⠀⠀⠀⠀⠀⠀⠀⡴⣋⠔⠋⠀⠀⠀⠀⠋⠞⣾⠁⠀⠀⠀⠀⠀⠈⠑⠢⢝⠎⠙⠲⢤⣈⢁⠁⠁⠑⠌⠒⠂⠒⠒⡒⢲⠈
⠀⠀⠀⠀⠀⠀⢠⠜⢁⠠⠩⠑⠶⠤⣄⡀⠀⠘⠢⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠱⣤⣉⠛⠿⢵⣒⣠⣤⣤⣴⡶⠖⢃⣀⣀⡀
⠀⠀⠀⠀⢀⡴⠃⡴⠥⠒⠚⠿⢓⣒⢤⡉⠓⠤⣠⢄⡀⢀⠀⡀⢨⢳⢀⠠⠤⢤⡀⠈⠙⠯⣐⡂⠠⠬⠭⠥⠐⠒⢉⡉⢀⡸⠃
⠀⠀⠀⢀⠞⣀⡤⠤⠤⠠⠤⠤⢄⣀⣁⠕⠀⠠⡈⠑⠫⢵⣊⣡⣪⠞⠸⣶⣄⡠⠃⠈⠂⠤⠄⠉⠙⠒⠲⠤⠭⠭⠗⠚⠉
⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⡴⠋⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣷⣿
⠀⢸⡿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢟⣭⣴⢿⣿⢿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⠿⣻⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢽⣶⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣏⣽⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣄⣀⠀⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢀⣾⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⡇⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠻⣷⡀⣼⡟⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣷⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡄⢻⣶⣿⠁⣿⣿⠀⠀⢿⣿⡇⠀⢸⣿⣇⠀⠀⠀⠀⢸⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠇⠈⠻⠃⠀⣿⣿⠀⠀⢼⣿⡇⠀⢸⣿⣿⣶⣶⣶⡆⢸⣿⣇⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣧⣧⣿⣿⣿⣿⣿⣿
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠙⠉⢉⣭⣍⡙⠿⢶⣶⣶⣶⠶⠋⠉⠻⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠯⡭⠤⠤⣤⣀⡘⠻⣿⣇⠀⠈⠛⠛⠋⠠⣿⣆⢠⡀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢡⣿⠇⢠⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⣄⠀⣿⣀⠀⠀⣀⣠⣤⣤⣀⡀⠈⢆⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡄⣿⠀⠀⠉⠁⠈⠛⠛⠛⠙⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⢻⣻⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⠟⡀⠀⠀⠀⠀⠀⠀⡧⠞⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣾⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⣤⣤⣿⣧⣼⣿⣥⣤⣤⣤⣤⣤⣼⣿⣥⣤⣷⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣵⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠹⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢠⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣷⣶⣴⣶⣾⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣶⣤⣤⣤⣶⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⡿⠋
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣤⣀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⡞⠀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡆
⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢦⣄⠀⠀⠀⣤⡄⠀⠀⠀⠀⠂⣸⢇⡀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠤⠀⠈⡛⠀⣋
⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠄⠈⠳⠀⠀⠀⠀⠈⠙⠒⠈⠉⠀⠻⠀⠀⠀⢰⠟⡄⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⢶⡟⠁⠖⠶⠴⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣾⠀⠁⡀⠙⠳⢄⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠰⡅⠀⠀⠈⠉⠙⠒⠀⠀⠀⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣤⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⠋⠂⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠊⠉⠉⢽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡋⠈⢷⡀⠀⠴⠀⠁⠀⠀⠀⢈⣿⣿⣿⣿⡿⡟⣻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠒⠉⠀⠀⠐⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⢧⣄⢀⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣷⣻⣿⣤⣿⣧⣼⣿⣿⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠰⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢲⣷⠆⠉⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⡾⡁⠀⡒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠄⢸⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡐⠒⠒⠛⠋⡛⠛⣻⠚⡃⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⡀⢡⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣷⡄⠀⠀⢠⡏⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠀⠁⢠⡾⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠡⡁⠀⠰⠀⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠙⠗⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢦⣤⣤⣀⠀⠀⢀⣴⠞⢻⣇⠀⠀⠀⠀⢀⣠⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠈⠉⠛⢦⣾⡃⠀⠀⢻⡆⠀⣀⣴⠟⠋⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠹⣷⡀⠀⠀⠀⠠⣈⢧⡀⠀⠀⣧⢞⣩⡴⠞⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠤⡄⠈⠛⢦⣄⣀⣀⣀⣑⣷⣴⣴⡷⠿⠷⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠳⠾⠃⠀⠀⣠⣾⠿⠋⠉⠭⢿⣿⣿⠿⣄⠉⠀⠀⠉⠻⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡔⢲⡄⠀⠀⢠⣤⣴⡿⠋⠁⠀⠀⢀⣠⡾⣿⡀⠑⢀⠑⢦⣤⣤⣤⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⠗⠋⠀⠀⠀⣀⡈⠛⠿⠷⣶⣶⠿⠟⠋⠀⠹⣷⣄⠀⠁⠈⢿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣞⢁⠇⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠘⠻⢿⣶⣤⣬⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠒⡄⠀⠀⠀⠀⠙⠉⠀⠀⠀⣼⠁⣽⠀⠀⠀⢰⡏⣹⠀⠀⠀⠀⢩⡤⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠻⠾⠃⠀⠀⠀⢀⡔⢲⡀⠀⠀⠘⠛⠁⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⢸⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⠀⠀⠸⣷⡾⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⠒⡄⠀⠈⠉⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣠⠇⠀⠀⠀⠀⣷⡴⠃⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠁⠀⠀⠀⣠⠤⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣀⣄⠀⠀⠀⠀⠀⣯⣴⠇⠀⠀⣠⠴⢦⠀⠀⣰⠊⣩⠂⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⡃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠞⠀⠀⠙⣋⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡉⠉⠀⢀⠔⠆⠀⠀⢀⡴⢲⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⢿⡴⠃⠀⠀⠸⠶⠞⣀⣤⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣤⣤⣶⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣩⣬⣩⣿⣹⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡞⠉
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠖⠢⠀⠐⠊⣿⠃⢠
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠴⠄⠈⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠂⣀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠃⠄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠳⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠰⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡲⠀⣀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠠⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠒⢻⠷⣄⡈⠀⢐⠻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⡄⠀⠤
⠀⠀⠀⢠⢦⡤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠐⡶
⠀⠀⠀⠀⠗⢦⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠈⠓⠠⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⢠⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣦⢀⣀⡀
⠀⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠐⠠⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠻⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡤⠀⠘⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⣠⣿⠖⢲⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣤⣄⣟⠃⠀⠀⠀⠀⠀⠀⢤⣴⣄⣁⡀
⠀⠀⢠⣍⠀⠀⠀⠀⠂⢿⠀⠀⠀⠀⠀⠀⠐⠰⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠇
⠀⠀⠘⡇⠀⠀⠀⠀⠈⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠣⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠉
⠀⠀⠀⠀⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⠟⠁⢀
⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡸⣿⣫⣉⣉⣛⠂
⠀⠀⠤⠞⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡅⠻⢿⣗⣳⣂⣁⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠑⠂⠀⠀⠀⠐⠀⠀⠀⡃⠀⠀⠈⠛⠶⢌⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

⣿⣿⠿⢿⡿⢿⠿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⣀⡄⠀⠀⠀⡆⠀⠀⠠⠃⠀⢀⠀⠀⠀⠟⢀⠁⠀⠌⢀⣤⡀⠀⠀⢐⣀⡀⠀⠔⠃⠀⠀⠀⠀⠀⠂⡀⠀⠠
⣀⣠⠠⢄⡀⠀⢼⠃⢠⠩⣄⡠⡄⠥⡀⠀⠡⡏⢀⡌⢄⣀⢤⠴⢵⠖⠓⠿⠓⣾⣷⣶⣶⣾⣷⣶⣿⣿⣿⣶⣿
⢙⡉⠀⣼⠤⠐⢂⠀⠬⠀⠈⡋⠀⢠⠥⠄⠒⡀⠠⠁⠀⢉⠁⠀⣾⡖⠒⣂⣂⣉⡉⢛⣛⣿⣾⣿⣿⣿⣾⣯⣿
⠀⢰⡤⠷⠀⠂⡼⠀⠀⡤⠀⠀⡦⠼⠄⠐⠠⠂⠀⢦⠄⠀⣨⠴⠇⠐⠀⠟⠀⠰⡤⠉⢰⣥⠿⠀⠂⡹⠃⠀⡤
⡀⠠⠀⠀⠉⠐⢳⠃⡀⢺⠀⡀⠅⠀⠈⠀⠛⡏⣀⠐⡆⠀⠨⠀⠈⠁⠘⠾⢀⡑⣷⢀⠠⠅⠀⠉⠐⠳⠇⡀⢺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠓⠐⠒⠲⠤⠖⠒⠲⢤⠴⠒⠒⠒⠊⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⠀⠀⠐⠲⠶⠶⠶⠶⠒⠒⠒⠒⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⣤⠒⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠉⢧⡀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢶⣄⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠳⢦⣀⡰⠎⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠹⣆
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⡙⢇⠀⢠⠻⡆⠀⠀⢸⠋⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡉⡇⠀⣀⡤⢶⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠸⠃⠈⢷⡎⠀⠻⡀⠀⠘⠀⠇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡆⠰⠞⠁⣠⠏
⡇⠀⠀⠀⠀⠀⠀⠇⣠⢦⡀⢀⣤⡀⢣⡀⠀⡆⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⣞⠁
⡇⠀⠀⠀⠀⠀⢰⢀⡉⠀⠳⠎⠀⢳⠈⢧⠀⣇⢸⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⡇⢸⣧⠘⠦
⣿⠀⠀⠀⠀⢀⡇⡜⠁⠀⠀⠀⠀⠀⢧⡈⡇⣿⢈⠀⠀⣇⠀⠛⠛⠛⠂⠒⡄⠃⠸⠈⢧⠘⢣
⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⠇⠈⠛⠀⠀⠘⠓⠒⠲⠖⠒⠋⠀⠙⠃⠀⠈⠳⠞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠐⠒⠒⠲⠶⠶⠶⠶⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠁
⡇
⢣
⢸
⢸⡆
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟
⠀⠀⠻⣷⣶⣤⣤⢤⢤⣤⢤⣤⣤⢤⣤⣤⣤⣤⣤⡤⣤⡤⠤⣤⡤⠤⠤⢤⡤⠲⠲⠖⢶⠖⠒⣩⡟⣻⠟⠁
⠀⠀⠀⠈⢿⣀⣳⣀⠀⠳⠀⠈⠃⠀⠘⠃⠀⠉⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣞⣡⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣮⣭⣐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠿⣿⣿⣷⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡅⠁⠀⠈⠋⠻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠇⠀⠀⠀⠀⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠠⠀⠀⣄⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⢸⠁⠿⡿⣷⣾⣦⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠈⠷⣆⠀⢈⠝⡿⠁⠶⠀⠀⣀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠠⠤⠤⠀⠂⢒⣒⣂⣀⣈⣩⣭⣩⣡⠈⡆⢰⣼⠁⣄⣀⣐⢶⢁⠠⠤⠤⠄⠀⢠⣤⣤⣄⢀⣀⡀
⠀⠀⣀⠤⠒⣀⠭⠙⠉⠈⠁⢀⡠⣠⡴⠞⠛⠉⣉⣡⠤⠔⢒⢂⣤⠐⠀⣰⠃⣡⠷⠤⠤⢤⣤⣍⣉⠉⠉⣓⠲⣤⡠⠀⠀⠈⠉⠐⠂⠍⣉⠐⠒⠤⣄⡀
⠐⠉⠀⢠⡎⠁⠀⠀⠀⠠⣒⢩⣞⠁⠀⢰⣾⠛⠁⠀⠀⠰⡁⠀⠐⠒⠊⠁⠀⣀⣐⠳⣤⣀⡀⠠⡌⠛⡷⣭⡀⠈⠻⢷⣤⡢⠀⠀⠀⠀⠀⢛⡦⡀⠀⠈⠐⠤⣀
⠀⠀⠀⢺⢁⡀⠀⠀⠀⠨⡒⠽⡧⠀⠀⠐⠽⣖⡠⢀⠀⠀⠉⠒⠠⢄⣀⡀⣀⣈⡛⠒⡒⠕⠁⠤⠊⢀⡿⠙⡇⠀⠀⠈⡍⣋⠀⠀⠀⠀⡠⢕⠌⡳⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠣⣆⡀⠀⢀⢀⠀⠉⠙⣔⡠⡀⡀⠈⠉⠃⠶⣴⣰⣡⢤⣤⣭⣁⣀⣶⣲⣦⣤⣤⣤⢔⢔⣊⠩⠒⠁⡠⡤⡢⣑⠌⠀⠀⢄⠢⡈⢆⡳⠃
⠀⠀⠀⡀⠀⠈⠙⠓⠃⠃⢊⣎⠄⡀⠙⠺⠔⠔⠖⠄⠀⡀⡦⠭⣉⣉⣙⣚⠛⠌⣋⠛⠛⠊⠭⠈⡁⣤⡔⠖⡑⣑⠴⠚⠁⢄⠄⢆⣆⡧⠚⠉
⠀⠀⠀⠉⠢⢄⣀⠀⠀⠀⠀⠉⠙⠒⠓⠶⠦⢦⣄⣀⣀⢈⠉⠉⠓⠒⠛⡿⠿⣽⣛⠾⠿⡴⠘⠖⠒⢊⣈⡉⣀⣀⣄⠶⠼⠘⠚⠉⠀⢀⣀⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠠⠤⠤⠄⢀⣀⣀⡀⠀⠉⠉⠉⠚⠛⠛⠛⠋⠉⠉⠑⠒⠒⠓⠒⠚⠉⢉⣉⣀⣀⠠⠤⠄⠀⠒⠂⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⣈⠉⠀⠀⠀⢈⣀⡀⠀⢀⣀⠀⠠⠤⠤⠀⠐⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠤⠄⠀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣻⣽⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⢿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⠆
⠀⠀⠀⢀⡠⠔⠒⠋⠉⠀⡀⠈⠉⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⢸⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⡄⠸⠂⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢌⠀⠞⠀⠀⠀⠀⠀⢸⠧⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠃⠀⠀⣠⡀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⡄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⣠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠐⠴⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠳⠄⠀⠀⠀⠀⠀⠀⠀⣀⠴⠆⠀⠀⠀⠈⠉⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠈⣁⠀⠀⠀⠀⠀⠀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⢢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⢀⠰⢀⡀⣀⡐
⠀⠀⠀⠀⠠⣤⣠⢆⣙⠄⠒⠀⠀⠀⠀⠛⢤⡀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠐⠋⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⡎⠉⣄⠀⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠈⠂⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣔⠀⠉⡔⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢉⣉⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣧
⠀⠀⠀⢼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡿⠀⢿⡄⠀⠀⢀⣠⡴⠶⠶⠲⠶⠶⣤⡀
⠀⠀⠀⢸⡈⠛⠶⣤⣄⡀⠀⠀⣠⡴⠖⠛⠛⠳⢦⣼⠛⠦⣄⣼⣁⠀⠘⣧⢀⣴⠟⠉⠀⠀⠀⠀⡀⠀⠀⢙⣧
⠀⠀⠀⠘⣧⠀⠀⠀⠈⠉⣹⣞⡁⠀⠀⠀⠒⠢⣄⣿⠀⠀⠀⠈⠉⠙⠓⢿⣿⠃⠀⠀⠀⢀⡴⠋⠀⣠⣶⡋⠁
⠀⠀⠀⠀⠘⢷⣄⡀⠀⠐⠋⠉⠙⠳⣦⡀⠀⠀⠀⠙⢦⡀⠀⠑⢦⡀⠀⠀⠙⢧⣀⣠⠴⠋⠀⣠⡾⣯⣀⠙⠲⠦⠤⠴⠶⣶⠟
⠰⣶⡶⠶⠶⠶⠾⠛⠛⠛⢋⣉⣡⡤⠾⠿⣷⣤⣄⣀⣀⣹⣆⠀⠀⠙⣦⠀⠀⠈⢿⣁⣠⡴⠞⠻⠶⠶⢦⣤⣤⣤⠴⠶⠛⠁
⠀⠈⠛⠶⢦⣤⣤⣀⣀⣈⣀⣉⣠⣤⠶⠛⠉⠀⠉⠉⠉⠉⠻⣦⣄⣀⣹⣆⣤⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢀⡶⠋⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠳⡄
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⢹⣄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠢⠀⠀⠀⠀⠀⠀⢿
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠤⢀⠆⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⣿⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠎⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢀⠀⡓⠀⣸
⢸⡇⠀⠐⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢰⢒⡄⠀⠀⣠⡀⠀⠐⠀⠀⡀⠤⠀⠀⠀⠀⠆⠀⢀⠐⠀⠈⠀⠃⢠⡿
⠀⢿⡄⠄⠀⠀⠀⠇⠀⢐⡂⠀⠀⠀⠣⡼⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠀⡜⠐⢁⡤⠀⢀⣿⠃
⠀⠈⢷⡈⠀⠀⠄⠀⠠⢈⠁⠀⠀⡀⠀⠀⠀⠀⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠚⠀⠀⣾⠃
⠀⠀⠈⢻⣄⠈⠂⠀⠀⢫⡇⠀⠀⢰⠳⡀⠀⠀⠀⣧⣹⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⢠⡌⠄⠀⠔⠃⠀⠈⠂⠀⣼⠇
⠀⠀⠀⠀⠹⣦⠀⠀⠀⡄⠀⠀⠀⠀⠓⠃⠀⠠⢄⡈⠁⠀⠀⠀⠁⠈⠠⠀⠘⠲⠃⢀⡀⠀⠀⡀⠀⠠⠄⠀⠠⢄⣽⠃
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⠀⠀⠀⠰⡄⠀⠀⠈⠰⠇⠀⠠⠤⣄⠀⠀⠀⣠⠔⠂⠘⠁⠀⠀⠀⠀⠀⠃⣡⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⠀⠀⠑⠁⠀⠀⠒⢤⠀⠀⠀⠐⠈⠁⠀⠘⠀⠃⠀⡴⠓⠀⠀⢀⠒⠀⠈⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠀⠀⠀⢄⠀⠠⡀⠘⠀⠀⠀⠒⡄⠀⠔⡒⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢢⡈⠀⠀⢁⠀⠀⠒⣀⠈⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠁⢀⠤⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡁⠀⠀⠄⠀⡀⢀⠁⠀⠀⠈⠉⠑⠀⢀⣀⠀⠀⠀⠀⠃⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⡄⠀⠀⠁⠀⠉⠀⠀⠀⡀⠑⠀⠀⠋⠠⠄⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠙⡀⠀⠀⠠⠂⠈⠀⠀⠒⠂⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠠⣄⠀⠐⠒⢄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣤⡶⠾⠛⠁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⡀⠀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣄⠜⠛⠁⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄⡀⠀⠈⠀⣀⡀⠀⠀⢴⠄⡶⢀⠠⠄⣦⡔⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠁⠀⢠⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⠦⠀⠂⣿⠁⠀⠀⠀⠀⠀⠀⡁⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⣀⡀⠀⠀⠻⠒⠲⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠰⡄⠙⢿⠢⢤⡀⠠⣀⢀⣀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠐⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠉⠀⣀⣀⣤⣴⢦⡄⠀⠄⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠉⠓⠦⡀⠀⠀⠀⠀⠠⠀⣁⣤⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣠⡀⠄⠀⠀⠀⠀⠀⡆
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠶⠠⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣠⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢀⠸⢿⡀⠔⠂⠀⠀⠀⠀⠚⠇⣀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠤⠶⠶⠋⢣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⣿⣿⢿⣿⡏⣿⣿⣉⣿⣿⢿⣿⡏⢻⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⠙⢦⡀⠀⠀⠠⡤⠈⠙⡃⢀⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠓⠦⠄⠀⠀⠘⠿⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠈⠂⠀⠀⠑⢄⣀⡀⠠⠂⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⡀
⠀⠀⠠⢄⣀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠈⠛⢤⣀⠱⢀⠴⠖⠀⠠⣄⠀⢠⣤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣦
⠀⠀⠀⠀⠀⠀⠈⣹⠦⠉⠀⠀⠀⠀⠌⢢⣌⠉⡓⠈⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠐⢶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠂⠀⠀⣀⠤⠶⠞⠉⡻⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⡟⠀⠀⠉⠛⠢⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⠉⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡐⠀⠀⠈⡾⠗⢂⠀⡉⠘⠍⠊⠁⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠠⠖⠚⠉⠁⢈⠉⠹⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⢛⡀⡀⠀⠀⠠⠈⣳⣀⠀⠀⠄⠀⣠⡆⠀⠀⠀⠲⠖⠒⠒⠢⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢉⠴⠛⠉⠀⠀⠀⠀⠀⠀⠉⠑⠦⢤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⣀⠀⠄⡀⠀⠀⠑⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⠇⠀⠙⠳⠄⠁⠀⠀⠀⠈⠆⠀⠀⠘⣿⣷⡀⠀⢂⠀⠀⡠⠴⡀⠀⠁
⠀⠀⠀⠀⠀⡀⠑⠄⠑⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠄⠀⠀⠈⣠⡟⠻⡇⢀⡀⠀⠉⠙⠳⠦⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠲⡀⠠⣄⠀⠀⠈⠳⣄⠀⠀⠀⢀⡠⠂⠊⣀⠤⡀
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠖⠀⢸⡿⡃⣶⠊⠉⣠⠔⠉⠀⠀⢧⣄
⠀⠀⠀⠙⠆⠆⠀⠐⡄⠀⠀⣿⣶⢤⣀⣀⠠⠤⢭⣧⠈⢀⡜⠁⠀⢀⠀⠀⠸⣿⡇⠀⠀⠠⠈
⠀⠀⠀⡀⠀⣀⠔⠀⠈⠀⠀⣙⠻⠀⠀⠁⠀⠀⠀⠈⢢⡎⢸⣿⣦⣤⣬⠴⠂⠙⠳⠄⠀⢠⠁⠂
⠀⠀⢦⡀⡎⠀⠀⠀⠀⢀⠂⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⣃⡠⠭⢉⡀
⠀⠀⠀⠉⠉⠁⠀⢀⠤⠒⠉⠉⠀⠣⡀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡀⠆⠀⢀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣀⣴⣽⣴⡃⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠⡴⠃⠤⠿⢿⠿⠀⠀⠀⠤⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠊⡠⠚⠀⠠⢸⠃⠨⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⢨⠀⢠⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠚⢻⠛⠉⢹⠉⠉⠏⠉⢹⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣤⠼⠦⠶⠾⠖⠒⠛⣛⣋⣉⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⠽⢦⡀⠀⠀⠀⠀⠀⣾⡏⠀⠙⡆⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠚⠁⠀⠈⠳⣄⠀⠀⠀⠀⠻⣿⣦⠾⠁⠀⠀⢀⣈⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠛⠛⠛⠛⠒⠶⠶⠿⣶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡤⠤⠶⠶⠖⠒⢹⡇
⠀⠀⠀⢠⣟⣛⠓⠒⢶⣄⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⠖⠒⠒⠢⠤⣀⣀⣇⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⢧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡜⣷⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⢀⡇⠀⣄⣀⣀⠠⠄⣶⢸⣿⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⢾⡇⠀⠀⠀⢸⡇⢸⡏⠉⢹⡜⠇⠙⠈⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣧⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠉⠙⠒⠒⠒⠊⠉⠉⠉⡏⣿⠀⠀⠀⠀⢸⡇⠀⠀⢠⠖⠳⣄⡰⠃⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠉⢆⠀⡴⢺⡏⢦⣀⠜⠀⠀⠈⠀⣀⠀⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⢸⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡟⠉⠓⠶⢤⣄⣸⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣭⣒⣒⣒⣤⡤⢤⣔⣚⣥⠞⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⡮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⣀⣀⣀⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣀⠀⠀⠀⠐
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠐⠂⠒⠒⠛⠛⠽⠶⠒⠶⠆⠻⠤⠤⠤⣤⣤⣭⣤⡛⠚⠛⠛⠒
⣒⣂⣈⡉⠹⠄⣀⣠⣤⣶⣶⣿⣿⣾⠿⠷⠦⠴⠄⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠛⣓⠒⠒
⣿⣿⣿⡿⠿⠟⢻⣿⣿⣿⣿⡿⢷⣶⣾⣷⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠁⢐⣢⣤⣤⣤⣀⣀⣀⣀
⣍⣉⣛⣿⣿⡯⠭⠭⠽⠿⠟⠉⠉⠉⠉⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣽⣿⣿⡶⣶⣲⣶⣶⣖⣂⣀⣒⣒⣒⣾⡿⠿⠿⠿⠛⠛⠛
⣿⣿⣟⡛⠋⠉⠛⠛⠛⠛⠓⠒⠢⠌⠉⠉⠉⠉⢉⣉⣉⣁⣤⣄⠀⠀⠀⠀⠀⠀⣈⣛⣩⣭⣭⣭⣥⣬⣭⣭⣽⣿⣷⣶⣶⣤⣭⣭⣉
⠀⠀⠀⠈⠹⠶⠶⠶⠾⠿⢿⣷⣤⣤⣤⣶⣶⣾⠿⠯⠷⠶⠶⠶⠶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿
⣶⣿⣿⣿⣿⡦⠤⠀⠀⠀⠒⠛⠿⠿⣯⣭⣥⣤⣤⡤⣤⠤⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⢛⡛⢋⣀⣤⠘⠋⠉
⠉⠋⠀⠒⠒⠒⠠⠶⠶⠄⠀⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣒⣒⣂⣀⣒⣲⣷⠾⠒⠒⠛⠛⠛
⣛⣻⡿⣿⣿⣿⣿⣻⣛⣛⣛⣛⡛⠛⠛⠛⠻⠿⢿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡤⠀⠀⠀⠤⢤⣄⣀⣀⣀⣈⣛⠛⠛⠺⢿⡿⢿⣿
⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣷⡶⠶⠶⠶⠶⢿⣿⣟⣛⡛⠻⠿⣿⣿⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣉⣡⣤⣤⣴⣶⣖⣶⣶⣶⠶⠶
⣤⣤⣤⠤⣤⢤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠦⠄⠀⠀⠒⠶⠶⠶⠶⠶⢚⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣭⣭⣭⣥⣤⣤⣴⣶⣶
⠛⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣶⣶⣶⣶⣶⣤⣦⡾⠿⠿⠳⠿⠿⠿⠶⠆⠀⠀⠒⠚⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣂⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣶⡶⠶⠶⠒⠒⠒⣒⣲⣾⣿⣧⣤⣤⣤⡶⠶⠶⠿⠷⠞⠛⠛⠛⠛⠛⠛⣉⡀⠛⠋⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣤⣴⡶⠾⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠠⠤⠀⠀⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⡶⣦⣤⣤⣤⣤⣤⡤⠤⠤⠦⠀⠠⠠⠀⠤⠤⢤⣤
⣶⣶⠾⠛⠉⠉⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠛⠛⠛⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣚⡛⠻⠿⠾⠿⠿⣿⣿⡿⠿⠶⠶
⣤⣴⣶⣾⣿⣿⡿⠿⠿⠿⣿⠿⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣲⣶⣶⣖⠒⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠬⢭⣭⣭⣭⣉⣙⣛⣛⣛⣿⣿⣟⣛⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣈⣭⣿⣿⣿⣿⣷⣶⣤⣤⣤⣌⣉⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⡛⠛⠛⠛⠛⠉
⣀⣠⣤⣴⣆⣠⣭⣭⣭⣭⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠿⠯⠽⠿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣄⣀⣀⣀⠀⡉⣉⣉⣉⣉⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂⠠⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠳⣀⡞⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⠛⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣇⠀⡜⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢻⡠⠁⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣸⠃⠀⣸⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠛⠛⠓⠒⢃⠀⣀⠀⠀⣰⠋⠀⠀⠈⠃⠐⠡⢐⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢕⣴⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⢆⠠⠀⠀⠀⠀⠃⠀⠀⠀⠐⡰
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠢⡀⢀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠣⣀⠀⢸⠘⡄⠀⠀⠀⢈⠠⠒⠔⠖⠲⠚⠓⠒⠀⠨⠖⠠⣀⠀⠠⠀⢴⣮⠞⠠
⠀⠀⠀⠀⠀⠀⠀⠉⠛⣆⠡⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢀⢃⣇⣀⣠⣬⠽⠛⠫⠄⠀⠀⠀⠀⠐⠲⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠊⠉⠫⢁⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠁⠒⠒⠀⠐⠀⠀⠚⠑⠠⠁⠒⠀⠀⠀⠀⠐⠀⠡⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⢹⡏⠉⠁⠀⢈⡽⡅⠀⠀⢿⣯⠉⠉⠉⢉⡟⡏⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣿⠀⠀⠀⠀⡇⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⣤⣤⣤⣴⣷⣧⣤⣤⣼⣷⣤⣤⣤⣼⣷⣧⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣿⢦⣄⣀⣀⣤⠴⡎⣿⠀⠀⠀⠀⠀⠀⠀⣼⢳⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣤⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠱⡄⠀⣷
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⣆⢹⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⢮⣷
⠀⠀⠀⠀⢠⡏⠀⠀⣠⠖⠋⠙⣆⠀⠀⠀⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⢸⡧⢤⠴⠁⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠹⣄⣀⣠⠋⠉⠑⡄⠀⢀⡟⠉⢳⠀⠀⡞⠉⢱⡄⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠓⠤⢼⡇⠀⣏⠀⢀⡇⠀⠈⠓⢺⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠉⠉⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣴⣦⠀⣠⡄⠀⠀⠀⣶⠀⢠⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⠘⠟⢹⡇⠐⣃⠀⣿⠀⢸⣤⡾⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠃⠀⠀⠿⠀⠟⠀⠟⠀⢸⠏⠻⣆⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⠶⠟⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠾⠛⠋⠉
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⡟⣿⠳⠈⢻⢿⡆⠀⣠⢚⣿⠟⡷⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⡖⣷⠘⡂⠀⠈⣼⢨⣤⢋⡯⠋⡸⢱⣇⢠⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣿⣿⣤⠀⢣⠀⠀⢹⣼⣿⣞⢁⡶⣡⣿⣿⠟⠖⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⣿⠄⠀⢳⣦⠈⣾⣿⣿⢛⣵⣿⣿⣵⠂⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣽⣿⣿⣿⣾⣷⣿⣿⣿⣿⣯⣾⣿⣿⣝⣦⣤⣾⣿⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⠻⠿⣿⡿⠟⣋⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣦⣀⢀⠀⣰⠆⠈⢿⡟⠀⠀⠀⠀⡀⠀⠀⣶⣿⢻⢻⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡒⢄⣙⣿⣯⠀⠻⣇⡀⠀⠻⣤⡀⢰⣿⠏⠀⠰⣿⣿⣬⣼⣾⣿⠟⠀⠀⢀⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣫⣭⣷⣿⣿⡿⠛⠛⠛⠛⠛⠓⠺⢿⣿⣇⡀⠈⠁⠈⢹⣿⡟⠙⢁⡴⢃⠁⡸⢁⣰⠤⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡀⠀⠀⡾⠁⠁⣰⣿⡁⠀⡰⠀⠋⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⡲⠤⠤⠀⠠⣄⡀⠙⣇⠀⢰⠀⠀⣰⣿⡯⣷⣾⣁⣀⠀⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⣶⣶⣶⣶⣷⣄⠀⠀⢰⣿⠁⠀⢻⣦⣸⡇⠀⢿⠹⣿⣇⣠⢅⣤⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡞⠛⣸⣿⣻⢻⡿⠄⠀⣼⣿⠀⠀⠈⣯⣿⠇⣴⣣⣿⣶⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⣾⡇⢠⠟⣿⣟⣿⢿⣆⣼⣿⠋⠀⠀⠀⣿⠋⣼⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⢶⣿⣿⣿⣯⣾⣿⡋⠀⠀⠀⠀⠀⢿⣿⠃⠀⣠⢶⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣴⣒⣾⣿⣿⡟⢉⣥⡟⣼⠧⣤⠀⠀⠀⢸⣿⢠⣴⡟⣄⠃⠰⣽⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠟⠉⠀⠀⠙⣇⢸⣿⣶⣯⣌⣽⠀⠀⠀⢸⡇⠨⣿⣧⣿⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⣿⠛⠟⠋⠀⠀⠀⣸⠁⠀⠀⣽⡿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⣦⠀⠸⣆⢻⡀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⡄⡟⣆⠀⠈⢩⣷⠀⣰⣫⠄⢰⣏⣠⠞⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠶⣻⣇⣻⣷⣤⣄⣹⣧⡟⠁⠀⡞⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣤⣼⣿⣿⡿⠋⠙⠻⣷⣀⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢻⡇⠀⠀⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡼⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⣠⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣰⠏⠀⠀⠀⢉⡷⠦⣄⣀⣀⣀⣀⣀⣀⡤⠶⢯⡁⠀⠀⠀⠳⣄⠀⢀⣀
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⣟⠁⠀⠀⠀⣰⠋⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⣿⠉⠉⠉⠙⠲⢤⡀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢰⠃⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⠀⢳
⡞⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠘
⣧⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢠
⠹⡄⠀⠀⠀⠀⠛⠶⠶⠞⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠛⠶⠶⠞⠁⠀⠀⠀⠀⡼
⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠈⠙⠦⣄⣀⣀⣀⣀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣀⣀⡤⠞⠉
⣶⣶⠶⠶⠶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⠏⠀⠀⣀⣤⡴⠖⠛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡆⠀⠀⠀⣠⠞⠋⣰⢏⣠⡶⠛⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠃⠀⢀⡾⠁⠀⢰⡿⠟⠁⠀⠀⠀⣠⣴⠟⠛⠓⠲⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⣿⡸⡇⠀⡼⠁⠀⣰⠟⣠⠖⢁⣠⠶⢛⣉⣀⣀⣀⠀⠀⠀⠀⣈⡟⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⠻⢿⣇⢳⡼⠃⠀⡼⢁⡼⠁⠰⠿⠛⠛⠉⠉⠉⠉⠉⠉⠙⢋⣩⡟⠱⣦⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣠⣿⣎⢷⡄⢸⢃⣾⠁⣠⡶⠚⠉⠉⣀⣀⣠⣤⣴⡶⠾⠛⠁⠀⠀⠉⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢉⣁⣀⣿⣆⠹⣆⢸⣷⠟⠁⣠⠴⠖⠛⠋⠉⠁⢠⣄⠀⠀⠀⣦⡀⠀⠀⢠⣄⠀⢸⣇
⠀⠀⠀⠀⣠⠞⠁⢠⠴⠛⠉⠉⣉⡥⢹⡿⠛⠘⠁⠀⠀⣿⠀⢀⡀⠀⠀⠀⠈⠻⠂⠀⠀⠙⠁⠀⠀⠘⠿⠀⠀⣿⡄
⠀⠀⠀⢰⠏⠀⢀⣠⣴⠶⣺⡿⢋⡴⠋⠀⡖⠀⠀⠀⠀⣿⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢠⢏⣴⠾⠋⡿⠁⣰⠏⢠⠞⠀⢀⡾⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⡀⠀⠀⢸⣆⠀⣿⡇
⠀⣠⣿⠟⠁⠀⣼⠃⢰⡏⠀⠘⠀⣠⠏⠀⢿⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⣿⡄⠀⠀⠋⠀⢻⣧
⠴⠋⠀⠀⠀⢠⡟⠀⢼⡇⠀⠀⣴⠃⠀⠀⠈⠻⣦⣀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣸⠏⠀⠀⠸⣷⠀⠈⠙⣷⡈⡇⠀⠀⢸⣷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣄⠀⠸⣿⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢷⡀⡿⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⣿⠀⠀⠀⠉⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠘⠿⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡇⢷⡄⠘⣿⡇⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠸⣿⡈⠟⠀⢻⠀⠀⣀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠘⠀⠀⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠰⣷⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠻⣶⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⢼⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣦⣤⣀⡀⠀⠈⠛⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠸⣷⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠛

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠠⢤⠍⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠙⠒⠿⠛⠋⠛⠋⠉⠋⠛⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣠⣶⣤⠶⣀⣀⣄⣀⣀⣤⡄⠀⠀⠐⠂⠐⠒⠄⠨⣯⣠⣤⣤⢤⣤
⠀⢀⡀⢤⣤⣤⡀⢀⣀⠀⠀⡀⠀⣀⣠⣤⣂⣤⡤⠀⠤⠴⠖⠒⠒⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠁⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⢄⣀⣀⣀⣀⣀
⣭⣥⣤⣤⣄⣐⣒⣠⣤⣶⣶⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠭⠍⠉⠉
⣛⣛⣛⣻⡿⠟⠛⠛⣿⣿⣿⣿⣿⡿⠒⣶⣶⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⣢⣤⣤⣤⣤⣤⣤⣀⣀⣀
⡉⠉⢸⣿⣿⣿⣯⣭⣭⣭⣭⣭⡟⠋⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⣉⣩⣭⣉⣉⣉⣉⣉⣩⣿⣿⣿⣶⠶⠶⠶⠶⣶⣖⣒⣐⣒⣒⣒⣒⣺⣿⣿⣿⣿⡿⠿⠿⠿⠿
⣿⣿⣿⣿⠿⠟⠓⠶⠶⠶⠶⠶⠶⣦⣤⣀⣀⡐⠒⠒⠒⢚⠛⠛⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠿⢛⣛⣛⣉⣉⣉⣉⣛⣛⣛⣻⣿⣶⣶⣤⣤⣐⡒⠒⠒⠒
⠋⠉⠙⠒⠢⢤⣤⣀⣀⣀⣠⣤⣤⣤⣄⠀⠀⠀⣀⣀⣠⣤⣶⠶⣛⣋⣉⣉⣩⣥⣄⠀⣤⣤⣶⣶⣶⣶⣶⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣻⣿⣛
⣒⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠙⣛⣛⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠷⠒⠂⠀⠉⠈⠉⢉⣉⣛⣻⣷⣶⣶⣶⠶⠶⠶⠶⠒⠛⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡥⠴⠶⠀⠀⢀⡀
⠉⠉⠀⠐⠓⠒⠒⠒⠒⠶⠶⠲⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣈⣉⣛⣀⣀⣛⣻⣿⡿⠛⠛⠛⠛⠋⠉⠉
⠛⣻⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⢿⣟⡓⠒⠀⠒⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣈⠛⢛⣛⡓⣒⣒⣛⣿⣷⣶
⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣭⣤⣤⣤⣤⣤⣶⣶⣶⠿⠿⠿⣿⣿⣿⣿⣿⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣉⣉⣉⣤⣤⠠⣤⣤⣤⣤⣬⣭
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⠉⠙⠋⣉⣭⣅⣀⣀⣈⣉⡉⠙⠛⢛⣂⣀⣀⣉⣉⣉⣙⣛⣻⣿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠿⠿⠛⠛⠛⠋⢉⣉⣁⣠
⣿⣿⡟⠛⠛⠟⠛⠿⠿⢿⣿⣿⣯⣭⣍⣉⣉⣉⣉⠉⠉⠉⠁⠀⠀⢀⣀⣉⣉⡉⠭⠭⠥⠾⠟⠛⠛⠋⠉⣉⣉⣉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠙⠛⠛⠛⠋⠉⠉⠁⠀⠈⣉⣉⣩⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟
⣉⣀⣀⣀⣀⣤⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⠿⠿⠟⠛⠛⠛⢛⣛⣛⣿⣿⣯⣭⣭⣭⣭⡽⠿⠿⠿⠿⠟⠛⠛⠛⠉⠛⠛⠛⠛⠋⠀⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣦⣶⣦⣤⣤⣶⣶⣤⣤⣤⣴⣶⣾⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣾⣤⣄⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⣀⣀⣀⣀⠀⣀⣠⣀⠀⠀⣀⡀⣀⣀⣀⣀⣀
⣭⣭⣭⣭⣤⠤⠤⣤⣤⣶⠶⠶⠶⠖⠒⣛⣻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠏⠉⠉⠙⠛⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠀⠀⠀⠚⠉⠩⠉⣁⣒⣀⣀
⣿⣿⣟⣉⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠉⠉⠉⠁⢀⣐⣒⣒⣒⣚⣛⣓⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠴⣶⣶⣷⣿⣻⣛⣿⣟⣿⣛⣟⣿⣉⣉⣛⣛⣛⣻⣿⢿⣿⣿⣟⣟⣛⣛⣛
⡶⢶⣾⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠶⠷⠾⠿⠿⠿⠟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠠⠤⣶⣶⣶⠶⠖⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢉⣉⣙⣛⣛⣛⠛⠛⠻⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣾⣿⣷⣶⣶⣶⠶
⠀⠀⠀⢀⣀⠀⠀⠤⠤⠤⠤⠴⣾⣿⡿⠛⠛⠛⠻⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀
⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠒⠚⠛⠓⠒⠚⠓⠚⠛⠿⠭⠭⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣤⣤⣤⣤⠤⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⠿⣾⣿⣿⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⡤⠔⡋
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⡆⠀⣠⢀⠠⠀⠀⠀⣴⠟⠉⠁⠋⣀⠴⢈⠜
⠀⠀⠀⠻⢷⣄⡀⠀⠀⠀⠀⢁⡀⠼⠋⠀⠀⢀⡾⢁⣠⡴⡾⡍⡀⢠⠎
⠀⠀⠀⠀⠀⠈⢫⣷⢤⣀⣠⠞⠁⠀⠀⠀⠠⢋⣷⠟⠃⢄⣀⡠⠔⠋⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣧⣀⠉⠙⠻⣷⡦⣤⡴⠾⠯⣭⣭⣉⣭⣤⣤⠤⣴⣾⣍⣉⠉⠉⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠰⢻⡌⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠉⠑⢦⣀⢀⣀⣸⡄⠙⠈⠛⠦⣄⠈⠉⠛⢦⣄⣀
⠀⠀⠀⠀⠀⠀⢣⠊⢷⡄⠚⢆⠀⣠⣬⣧⣤⣄⠀⠀⠀⣠⢯⣵⠾⠈⠙⠲⢦⣄⠀⠀⠙⠐⢶⡎⣅⢉⣙⣲⠦⡖
⠀⠀⠀⠀⠀⠀⠘⡁⠀⠻⣆⠈⢳⡏⠈⠉⠡⠌⡟⢦⣀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣀⠀⠠⠤⠀⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠹⡄⠒⡇⠀⠀⠀⠀⠈⠂⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⢰⠀⣿⠀⠀⠀⠀⠀⠀⢑⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢢⣠⠇⠀⠀⠀⠀⠀⠀⠈⣨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠇⠀⠙⢤⡀⠀⠀⠀⠀⢀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡄⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⠉⠓⠒⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢖⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⢐⣧⡤⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠡⠟⡡⠀⢀⢀⠤⢀⢦⠄⠀⠆
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠒⡀⠀⢀⡀⣾⡦⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠠⠆⠩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠒⠂
⠀⠀⠀⠀⠀⢠⡄⠐⢤⡷⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠐⠀⢀⢠⣾⡃⠀⠐⣷⣠⠀⣠⡶⠀⢐⣤⠀⠀⠀⠺⠆⠆
⠀⠀⠀⠀⠀⠀⠉⠁⠘⢷⡀⠛⠛⠋⠉⠉⠁⡶⠋⢄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠑⠖⠊⠁⠰⠀⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠼⠤⢠⣄⣠⣰⡀⡇⣰⣶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⠁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠐⠔⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠋⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠳⣄⣀⠠⠤⠖⠒⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣠⡠⠤⠔⠒⠈⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠀⠀⠈⠉⠉⢉⡍⢹⠀⢀⡀⠀⡄⠀⡟⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣀⡀⢀⠀⢀⠀⢸⠀⢸⡇⣼⠁⠀⠇⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠸⠁⠃⢸⠀⣿⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠈⠀⠛⠀⢸⠋⢷⡄⢀⡀⠀⣠⡠⠴⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠄⠒⠒⠒⠒⠒⠒⠒⠀⠁⠀⠀⠬⠭⢼⠗⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠓⠒⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣿⣷⡄
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠈⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⢾⣿⣿⣿⣿⣿⣿⠆⢾⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠈⠛⠛⠛⠛⠛⠁⠀⠀⣼⣿⣿⣦⣄⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⢀⣤⣶⣶⣶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠙⠻⣿⣿⣾⣿⡿⠛⠉⠙⠻⣿⣿⣾⣿⡿⠟⠉⠉⠻⣿⣿⣿⣇
⠀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⢿⣿⡆
⢿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⣴⣶⣶⡄⠀⠀⠘⣿⣿⠀⠀⢉⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠙⠛⠛⠁⠀⠀⠀⢻⣿⣧⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⢀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠻⣿⣷⣄⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠻⠿⠿⠿⠟⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⠿⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣭⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠖⠒⠒⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⣀⠀⠀⢀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⣿⣿⣷⣦⡀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⠿⣿⡇⢰⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⠟⠋⠁⠀⠀⢀⣤⡀⠀⠘⡇⢸⠁⠒⠀⠤⠤⠤⠤⠤⠀⠚⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡦⠀⠈⠁⠀⠀⠀⠀⠀⣼⣿⣟⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣆⠀⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢀⣤⣄⡈⠛⠿⠻⠿⣿⡿⠃⠀⡆⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⢀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠸⢿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⢛⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⢀⠜⠀⠀⢸⣰⢀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠢⠤⠤⠼⠿⠿⠟⠛⠒⠁⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠖⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠰⠤⢀⠀⣠⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠋⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠃⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⡇⠀⠀⠀⢠⣦⡤⠚⠉⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⡀⠀⠀⡇⣷⣿⣶⣷⣿⣭⡄⠀⢀⡀⠀⠀⡰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡦⠤⠦⠶⢿⡟⢉⣉⠉⠉⠀⠀⢀⠌⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⢣⣀⣀⣀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⢳⣴⣾⣾⠛⠀⠀⢸⣷⣶⠶⠖⠚⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⡷⠶⠟⠛⠋⡠⠋⠀⠀⠀⢠⡟⢻⡄⠀⠀⠒⠤⠬⠶⣄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣰⠴⠚⠛⠉⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢸⡇⠈⠹⣆⣀⠀⠀⠀⢀⣉⣳⡀
⠀⠀⠀⠀⢰⠇⠀⠀⣀⣼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠉⣅⠀⠀⠀⠉⠉⠙⣛⣦
⠀⠀⠀⠀⣾⣀⣤⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡠⠈⠠⡀⠀⠀⠀⠉⠙⢿⣇
⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠻⠾⠷⣧⡀⠀⠛⠦⡀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠀⠉⠓⠂⠂⠀⠂⠒⠂⠃⠀⠁⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⡄⠐⠂⠂⠰⡄⠀⠀⣩⣷⣦⠀⠙⢦⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⣠⠀⠆⠀⠀⠀⠀⠀⢀⠀⠻⠀⠘⠃⠁⠈⢧⣄⢀⡹⣶⣄⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡄⢁⢤⠄⣠⠂⠀⠂⠀⠈⠀⠘⠰⠺⠃⢈⠀⠈⠉⠑⠓⢾⡿⠷⠶⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡴⠈⠓⠈⠀⠒⠰⡄⢈⠀⠀⡀⣔⢢⡄⠀⠀⣤⠄⠘⠁⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠐⠢⠠⠀⡀⢀⠀⠁⠈⢄⠘⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⣴⠋⢥⠽⣄⣈⣨⣅⢄⣘⡊⠛⠙⣷⣖⡡⠶⠒⠃⠤⠆⣈⠂⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠁⠀⠀⠀⠀⠉⠀⠀⠠⡜⠓⠆⣶⢄⡈⡀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⢀⠀⠀⢰⡄⠀⠀⠈⢠⠔⡏⠀⠁⡈⠀⡴⠀⠀⠀⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠰⠔⢁⣽⠔⠀⠀⠠⠟⠀⠀⠀⠀⠘⠣⡙⠶⠀⠀⢦⠜⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠁⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⠈⠠⠀⣈⢀⣀⠎⠀⢆⠓⠀⠀⠀⠀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⡀⠀⠀⠀⠚⠛⠀⢀⡀⣤⠦⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠂⠀⠠⠶⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⢀⡒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠜⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢰⠋⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡄⠀⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢤⡀⣄⠔⠃
⠀⠀⠀⠀⢀⣀⣠⢤⠄⠀⠀⢀⡶⠁⠀⠀⣿⣿⣦⣄⣤⣄⣀⣀⣠⣄⣀⠈⣀⣠⣆⣀⣀⢀⡀⡀⣸⡇⠀⠀⠀⠀⠹⣿⣿
⢀⣀⣻⣶⠙⣣⣤⣿⣶⡒⣆⣰⣇⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⠀⠀⣐⢻⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣛⣿⣟⣋⢉⣉⣹⡿⣿⣿⢿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠉⠉⠛⠛⠛⠿⠻⠿⠿⣶⡾⣿⡿⡿⣯⡿⢿⡿⠿⠃⠊⠙⠉⢠⠁⢸⡴⡄⣠⠘⠋⣹⡿⣷⠿⠋⢉⡉⠉⠋⠛⣷⡛⣿⢟⠏⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⡏⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⡛⠀⠀⠈⠀⠀⠀⢀⠘⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣮⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣾⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡰⠊⢐⢀⠀⠂⡭⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆⠀⠀⢼⠀⠄⠃⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡄⠁⠀⠀⠀⠮⠁⣠⠖
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠁⠀⠠⠀⠘⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢨⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠢⠐⢠⣀⢀⡘⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠀⠂⠀⠀⠀⠂⠀⠀⢠
⠀⠀⠀⠐⠈⠢⢀⠀⠠⠄⠁⠀⠒⠿⣿⣿⣷⡄⠀⣠⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣷⣴⣀⠉⢩⠀⠀⠀⠆⢀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠀⡁⠔⢺⠗⠛⠗⠉⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⡀⠀⢻⠛⠛⢠⠍⠀⡀⠀⠈⠈⢳⣧⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⠀⠁⠀⠀⠀⠀⠂⠀⠘⡏⠙⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡈⢄⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠈⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠁⢀⠀⠉⠂⠤⠘⠰⣦⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢠⡴⠂⠘⠃⣐⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⢀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠄⠀⢼⣿⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠈⠰⣻⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠂⡖⠀⠈⠑⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠠⠀⠀⠀⠀⠄⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠡⠐⠡⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⡕⠄⠀⠀⠀⠀⠀⠀⠀⠌⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⡆⡌⡰⠀⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠁⢬⣿⣧⣤⠁⠀⠀⠀⠁⠀⢀⣀⠠⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡔⠂⢈⣷⣯⣴⠂⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠏⠉⢉⠉⠀⠀⠐⠀⠀⠀⠋⢠⣦⣴⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⡒⢿⣟⠋⢈⡉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠁⠄⠈⠻⡍⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠔⢫⠄⡀⣸⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⢆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠇⠀⢀⣀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠴⠁⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠉⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠠⠾⠀⠐⠂⠀⠰⠉⠀⢀⠀⠀⠀⠀⢨⠂⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠴⠁
⠀⠒⠛⠄⠀⠀⠀⠠⠣⡦⠀⠠⠌⠀⠀⠀⠐⠄⠀⠀⠠⠅⢴⠒⠀⠤⠁⠀⠚⠙⠇⠦⠀⠀⠐⠢⡖⠂⠠⠬⠀⠀⠀⠈⠃⢀⠀⠠⠅⢴⠒⠀⠤
⣤⡔⡲⠚⠓⡄⠀⠀⠹⠅⠀⡇⠘⢦⣤⣒⠔⠛⢢⠀⠀⠈⠏⠀⢸⠀⠓⣤⡔⡦⠒⠓⡌⠀⠀⠹⠅⠀⡇⠘⢢⣤⣲⠔⠛⢢⠀⠀⠈⠯⠀⢸
⠐⣊⠀⠀⣬⠤⠆⠐⢂⠀⣠⠄⠀⠀⢚⡁⠀⢠⡥⠴⠀⠓⡀⢀⡤⠀⠀⠐⣈⠀⠀⣬⠤⠖⠘⢂⠀⢤⠄⠀⠈⢘⡁⠀⢠⡥⠶⠀⠒⡀⠠⡤
⠀⠀⣆⣠⣶⠀⠠⠀⣸⠄⠀⢠⣀⡀⠀⢰⣂⣴⡆⠀⠄⢀⡧⠀⠀⣄⣀⠀⠀⣖⣠⣶⠀⠠⠀⣸⠄⠀⢠⣀⡀⠁⢰⣀⣴⡆⠀⠄⢀⡧⠀⠀⣄
⠀⠀⠩⠀⠀⠴⠄⢤⣥⡄⠀⢌⣃⠀⠀⠘⠍⠀⠠⠦⠠⣬⣤⠄⠠⣙⡄⠀⠀⠩⠁⠀⠴⠄⢤⣥⡄⠀⢌⣃⠀⠀⠈⠍⠀⠠⠦⠠⣬⣤⠄⠠⣙
⠀⣄⠙⠀⠀⠀⠈⣠⡘⠀⡤⠀⣭⠁⢠⠈⠂⠀⠀⠈⢀⣄⠋⢠⠄⢨⡅⠀⣄⠙⠀⠀⠀⠉⣠⡘⠁⡤⠀⣭⠁⢠⠈⠁⠀⠀⠀⢁⣄⠋⢠⠄⢨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⡿⣷⣄⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣜⣿⣿⣿⣧⠀⢸⣟⠹⡇⠀⠀⢠⣶⣿⣥⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣉⠳⡄⡇⢀⡇⣠⣶⣿⠏⡽⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣤⣶⣤⣀⣀⣈⡻⣌⣻⣿⠿⢿⠷⠧⣤⣿⣿⣯⣄⠄⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⢿⡿⠋⠙⣛⢻⡟⣿⡽⢻⣿⣿⢚⣼⠟⠻⠦⣾⠿⠭⣬⣹⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠑⢀⡄⢟⣾⣿⡌⣄⢠⣶⠺⣿⣧⣼⠿⣴⡟⣶⣾⣇⢠⣶⣉⣽⠤⡈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡦⠀⡼⢣⠗⣿⣿⠏⠿⣿⠼⣿⣧⣿⡏⢿⣶⣿⣿⣿⣯⢹⡇⣍⣻⣧⢤⣝⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠃⡀⠙⢻⣶⡼⠉⡸⣿⣿⣶⣿⣏⢿⣿⣿⣿⢿⣿⣸⣿⣿⣇⡙⢋⢻⡟⣏⢻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢁⡘⠻⢸⢧⡝⣿⣞⠟⣆⣿⣶⣾⣿⣿⣿⠿⣿⣾⣿⣿⣿⢿⣏⣿⣘⣿⣯⣿⡜⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⠀⢸⣇⢀⣌⠻⢃⡟⢯⡛⡿⡛⢿⣿⠿⣿⣿⣿⣿⣿⣿⠛⣿⣼⣿⣽⣿⣱⣿⣏⣻⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣄⢱⣦⡸⣇⣈⡓⢾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣻⣷⣽⣿⣛⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⢻⢦⣝⠋⢘⠧⠿⢰⢦⢘⣿⣶⣌⣿⣿⣡⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢺⡻⠇⣿⠵⡶⢹⢟⣤⣘⢻⣿⣯⣹⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⠿⣆⢈⡛⢿⠄⡈⢷⣽⣿⠿⢿⣿⣿⣗⣎⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡿⠆⠁⠻⣿⠆⣤⣿⡷⢹⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⠼⣦⢶⡦⡍⠛⢿⣟⣿⡟⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢾⣏⣿⣇⠸⣿⢿⡽⣘⣿⣿⠛⣿⣿⣬⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠹⣿⣙⡾⠎⠉⣴⣯⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠿⣝⠆⡻⠷⢮⣿⣯⣭⢿⣿⣿⣿⣿⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡸⠦⠻⢆⠻⣧⡹⣿⠿⢿⣿⣭⣿⣿⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡘⢟⣿⢿⣧⣼⣻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣟⠻⣽⣿⣝⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⡀
⠀⠀⠀⠀⠠⣄⣈⣿⣀⣰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⢣⣿⣿⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⣤⣦⣾⣿⣷⣿⡄
⠀⠀⢀⡴⠏⡏⠙⢻⢿⣿⡷⣤⣤⠀⠰⣐⣼⣎⡌⡆⡀⠀⠀⢠⠇⡄⣸⣿⡥⢾⡇⠀⠀⢯⡿⡇⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⢟⣽⣦⣤⡀
⠀⠀⣾⠶⠘⡃⣧⠳⣺⣿⣿⡄⠀⠀⢀⠒⠚⢻⣷⣇⣷⠁⢸⣿⢰⣷⡯⠤⠖⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⠖⠀⢈⢿⣿⣯⣻⡆
⠀⢰⡴⠘⠁⣱⢾⣿⣿⣿⣿⡇⠀⠀⠘⢻⣃⣩⣭⢿⣿⡄⢸⣷⣿⡟⠛⠉⠠⠀⠀⠀⣀⢀⣄⠀⠀⣀⠀⡠⠊⠀⠀⠀⠀⠀⡴⣫⣿⣿⡍⠛
⠀⠘⡷⢤⡇⣸⣿⣿⣿⢿⠍⠁⠀⠀⠀⠀⠁⠐⠂⠀⠈⠁⢬⣀⣀⣀⠠⠀⠀⠀⠀⢰⣻⣾⣭⡖⠶⢹⣶⣄⡤⠀⣀⡤⠀⠀⡴⢣⣿⠿⡈
⠀⠀⠱⣷⣾⣿⡿⠶⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢻⣿⣿⡭⠤⢥⡀⠀⠘⠛⣻⠿⡤⣶⢺⡿⣿⣾⣿⣯⣦⣄⠀⠀⠐⠷⡄
⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠸⡿⣿⡯⢜⡂⠀⠀⠀⡟⡐⡎⢷⡟⢳⣿⡿⣯⡉⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠰⣦⣴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠃⠋⢋⠀⠙⠀⠀⠀⣟⣱⢿⣿⣧⠬⠘⠟⠋⢹⣿⣿⡿⠀⠀⠀⣄⠢⠶⠆
⠀⠀⠀⣈⡽⣷⢦⣿⣿⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⣿⡿⠿⠖⢀⡌⣴⣿⣿⣿⠃⠀⠀⣿⣋⡟
⠀⢠⢾⡍⢴⠈⢢⡌⣽⣿⣦⡀⢀⡀⢔⠳⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣖⣀⡄⠀⠀⠀⠀⠀⠀⣠⠖⣀⡀⠀⠂⠭⣿⠟⠁⠀⠀⠀⢛⠋⠃⠐⠃
⠀⢸⣏⠰⠂⠶⡀⣶⣿⣿⣿⡇⢨⣏⢺⣿⣤⠈⠤⠀⠀⣀⣸⣷⣿⣿⣯⢤⣤⡀⠀⠀⣤⣠⣠⣿⠏⠭⠙⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠸⣿⣇⠺⣺⣯⣿⣿⣿⣿⠃⠀⠹⠂⢽⣿⣶⡼⠀⠀⣠⠾⠍⠻⠛⠁⠉⣉⠿⡆⠐⠛⠉⢉⠁⢴⣆⠈⠤⠸⡆⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠙⢯⣅⣹⣯⣿⣿⠟⠁⠀⠀⠀⠀⠉⠻⢿⠃⠀⠀⡏⠀⠃⠀⢦⡇⠀⡀⠀⣿⠀⣧⠀⠈⠠⠀⠤⠀⠐⠀⠸
⠀⠀⠀⠈⠛⠾⠿⠛⠁⠀⠀⠀⠀⢀⣤⣶⡶⠊⠀⠀⠀⠹⡄⠀⠃⠀⠃⠠⠀⢀⡇⠀⠉⡻⠶⣦⣤⣤⣤⣤⣤⠔⢀⣠⠶⣷⣦⣀⠤⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⡀⠈⠁⠀⠀⠀⠀⠀⠙⠦⣄⡁⠀⠀⢀⡟⠀⠀⠀⠈⠓⠚⠯⠝⠛⠋⠁⠀⠀⠹⣾⣿⣾⠛⣰⡶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠙⠞⠟⠁

⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣂⢁⣩⠁⠐⠒⠄⢀⠀⠀⢆⠆⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣅⠁⢨⠃
⠀⠀⠀⠀⠀⢀⠄⢦⠤⢠⣀⠄⠀⣠⠄⡬⠉⠐⠈⡇⠀⠠⢃⠶⡄⠀⡸⠀⠈⠒⠁⠠⠂⠉⠀⠀⠑⠠⡀
⠀⠀⣀⣄⠌⣤⠀⠀⠲⠚⣁⢍⠀⠀⠈⠀⠐⠀⠀⡀⠰⠧⠌⠚⠃⠴⠠⠴⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⣅⠈⠂⢁⠅⠀⠐⠒⠣⢸⠀⠀⠀⠀⠀⠀⢈⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠑⡌
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⢊⠰⠴⠛⠒⢈⢀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠰⣤⡀⠠⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠡⡀⢀⠌⢐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡠⠤⣀⣐⠀⠀⠀⠀⠀⢂⡀⠠⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⡇⠀⢰⣲⠚⢠⣤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢁⠈⡉⢁⠉⡀⡀⠂
⠀⠀⠀⠀⡇⠀⠀⠉⠒⠙⠋⡀⠀⠀⠀⠀⢸⡠⠓⢄⠨⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠘⠛⠛⠻⠄⠛⠆
⠀⠀⠀⢀⠃⠐⠂⠀⢤⠄⠄⠬⠦⡀⠒⠀⡚⠀⠀⠊⠰⡀⣀⣀⣀⣄⣀⣀⠀⠑⠌⣃⣀⣀⣀⣀⣀⣀⠁⠌
⠀⠀⠀⠂⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⠢⢸⣥⣡⠊⠀⠀⠀⢠⡤⠤⢤⠀⠀⢠⡤⠤⣤⠀⠀⢠⡤⠤⣤
⠀⠀⡌⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠫⠃⠀⠖⠒⠺⠀⠀⠀⠖⠒⠺⠀⠀⠰⠖⠒⠇
⠀⠀⠉⠂⠄⠀⣌⣀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠐⠈⠀⠀⠀⠨⠉⠉⠉⡀⠀⡘⠉⠉⠉⠀⠀⡈⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⠀⠀⠀⢠⢤⠀⠀⠀⠀⠡⢤⠀⠀⠀⠀⢣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠐⠂⠀⠀⠀⠤⠴⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠠⠘
⠀⠀⠁⠂⠄⠠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠐⠈⠀⢰⠚⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠚⢒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⣤⡥⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠤⠖⠂⠀⠀⢀⠀⠀⠀⠀⠀⢀⣞⣡⠄⢻⣿⡣⡁⠀⠘⣿⣂⠀⠀⠀⠐⠂⠘
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠀⠀⠰⢆⡀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠰⠔⡅⠞⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⢠⠀⠡⠀⠀⠀⠊⠀⠀⢳⡄⠀⠀⠀⠀⠀⢩⢠⠈⠤⠓⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠐⠁⠂⠄⠁⠀⡞⡶⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⣄⣀⣆⣀⠔⠀⠀⠀⡀
⠀⠀⠀⠀⠈⡀⠀⠐⡀⠀⠂⠀⡀⠠⠁⠖⠂⠀⠀⠰⢤⣄⡬⢐⠴⠚⠘⠀⠄⠀⠁⠹⠁⣄
⠀⠀⠀⠀⡀⠁⢀⠀⠁⠐⠀⡀⠀⠀⠁⠀⠀⠀⢛⠄⡐⢨⢉⠁⠀⠂⠀⠃⠀⡀⠁⠀⠁⢀
⠀⠀⠀⠀⠠⠂⢀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠁⠀⢛⠈⠀⠂⠨⠀⠀⠁⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⡉⠉⠀⠠⠀⠠⠀⠈⠀⠃⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠃⠘⠀⡄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠐⠊⡚⠂⠠⠔⡄⠀⠀⠀⣀
⠀⠀⠀⠁⠀⠐⠒⠀⠛⠋⠋⠙⠀⠁⠀⠀⠀⠀⠀⢀⠰⣶⡆⢀⠀⠀⠉⠉⠲⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⠀⠀⠀⠗⠀⠰⠊⠆⠀⠠⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠛⡿⡄⠶⣀⣟⠦⠒⠄⣀⠃⡁⠆⠀⠀⢀⠀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢀⡀⢾⠀⠘⠢⡡⢙⠘⠈⢀⠠⠠⠘⠁⢶⠘⠛⢿⡗⡄⢠⢾⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡁⠀⠐⡀⠀⠑⡈⠀⠀⠀⠠⠆⠀⠐⢀⢐⣀⢐⢇⡷⠀⣌⠘⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢘⠀⡀⡀⢠⠁⠀⠀⠀⠀⠀⠀⢋⠀⠔⡀⠂⠚⠆⠃⠄⣅⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠉⠀⠀⠘⠈⣀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠓⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣿⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣄⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡫⠟⠻⣷⡄⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣫⠕⠋⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⣠⣶⡿⣟⠵⠊
⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⣀⣴⡿⢟⡽⠚⠁
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡯⠞⠁
⢀⣾⠃⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⢸⠇⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠉⠛⣿⣷⡀⠀⠀⠀⠀⠀⠘⣧
⣾⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣿
⢻⡄⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⢀⡿
⠈⣷⡱⣄⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠈⢷⣝⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠙⢷⣝⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠈⠛⠶⢮⣤⣄⣀⣀⣀⣤⣤⣶⡿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢻⣿⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠷⠒⠒⠒⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢰⣶⠀⠀⢠⣶⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⣿⣄⣀⣸⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡏⠉⠉⢹⡏⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⡀⠀⠈⠁⠀⠀⠘⠃⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣶⣤⣤⣤⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄
⣀⠀⠾⢻⣷⣤⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠛⣂⠀⠀⢀⡀⠙⠶⠄⣽⠧⠶⠾⠓⠀⠀⠀⠠⣄⠀⠐⠚⠲⣄⠀⣀⣰⣾⣿⣿⣁
⠀⠀⠀⠀⢀⡀⠀⢄⣀⣀⠢⣄⡀⠀⠀⠀⠄⠀⠀⠉⠀⠀⣀⠀⣉⠹⠍⠛⠻⠟⠛⠦⠴⢄⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠒⣀⡀⠄⠈⠉⠩⠙⠻⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⡈⠀⠀⠀⠉⠠⠤⠀⠀⠈⠀⠀⢁⡙⠙⢋⠃⠈⠀⢈⡛⠋⠂
⣠⣄⠈⢉⡙⠿⠿⢿⠓⠦⣀⠉⣁⣀⠋⢩⣥⣦⣤⠤⠶⠛⠛⠁⠀⠈⠉⠤⢤⠾⠷⠦⣤⣀⡀⠀⠀⠀⠀⢀⡠⠶⠤⠈⣁
⣀⣀⣬⣶⣷⣤⣤⡘⠂⢀⣠⣤⣀⠙⠓⠀⠀⠈⠉⠙⠛⠙⠿⠿⠿⠥⠤⢤⣤⠀⠄⠀⠉⠡⠦⠄
⠟⠛⠻⠿⠿⢿⣿⠿⠟⠛⠛⠻⠟⢛⣛⠛⠓⠒⠀⠀⠀⠀⢀⣤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣀⣤⠴⠒⠀⠀⡄
⠠⠶⣶⣶⣶⣶⣶⣶⣤⡄⠀⠠⠄⠀⠀⠤⠴⣤⣔⡈⢉⣀⡀⠐⠛⠚⠿⠂⠀⠠⠤⠤⠶⠖⠛⠛⢳⡴⠖⠒⠀⠀⠀⣀⣴
⠀⢾⣿⣿⣿⣤⣄⣀⣀⡉⠳⠶⣄⣀⠀⠠⠤⠄⠁⢀⣀⣀⠁⠀⣤⣀⣠⣤⡶⠒⠓⠒⠂⠐⣲⠖⠛⠛⠀⠐⠛⠉⠉⠉
⠀⢀⠀⢤⣄⣀⣀⣉⣹⡿⠿⠶⠶⠌⠁⠠⠶⠲⣶⣭⣀⣤⣤⣤⣬⣭⣍⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣀⣀⣀⣨⣭⣥⣴
⣿⡿⠿⠶⣤⣈⣉⣉⣁⣀⣀⣤⣤⣉⣉⡀⠈⠉⠉⠉⣩⡵⠖⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠄⠀⠀⣛⣛⣋⣉⣭⣤
⣶⣶⣶⣿⣿⣿⣉⣉⡙⠛⠉⠀⠀⣈⣩⣉⣁⣀⡤⠄⢀⡐⠒⢛⣋⣁⣀⣤⠤⠒⠂⠀⠀⠀⠠⠒⠒⠀⠀⠀⠙⠛⠛⠋
⣿⠟⠋⠉⠉⠉⠉⠉⢉⣉⠁⠐⠊⠉⠉⠉⢁⣀⣤⣤⣤⠀⠈⠉⠀⠀⠐⠒⢒⠞⠁⢒⡀⣀⣀⡀⠀⠀⠠⣶⣤⣀⡀
⠀⠀⣀⡀⠀⢀⡠⠀⠀⠀⠀⠒⠋⠀⠛⣻⠿⠿⠿⠛⣩⠴⠛⠛⢀⡴⠖⠺⣷⠆⠈⣁⡀⠉⠿⠿⠂⠀⠶⠿⠛⠛⠛⣃
⠀⠰⠛⠉⠉⠁⠀⠐⠋⠁⠀⠀⠀⠒⠋⠤⠔⠀⠐⠛⠁⠀⠀⠉⠁⠀⠀⠊⠁⠀⠀⠀⠉⠀⠀⠀⠠⠶⠶⠀⠀⠀⠛⠉⠙

⠀⠀⠀⠀⠀⠠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⢠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠹⢆⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠳⣾⠁⠀⢀⠂⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠉⠙⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢹⡆⢀⠏⠀⠀⣴⠏⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣷⡜⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣿⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⠛⠛⠶⡄⠂⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠂⠀⠀⣔⠢⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣕⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢷⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠢⢡
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠳⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃
⠀⠀⠀⠀⠀⢠⠈⠀⠀⢠⠒⠆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣳⡀⠀⠈⠢⡀⠂⠀⠀⠀⠀⠀⢀⢀⢏⠇⣀
⠀⠀⠀⠀⠀⠈⠃⠤⣀⣸⡀⢣⠀⠀⠀⠀⡠⠒⢁⠆⠹⠉⠑⠄⠉⠉⠉⡸⢹⠑⠢⠤⣈⣐⣀⣭⠷⠋⠐⠢⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣣⠈⠆⠀⠀⠁⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⡠⢃⣦⣤⣤⣶⣶⠚⠉⠓⠠⢀⠀⣀⡀⢀⠉⠑⠾⠃
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢳⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡡⠊⠈⠒⠍⡀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠚⠀⠒⠒⠀⠴⠀⠀⠐⠛⠢⠌⠑⠒⠂⠠⠤⠤⠄⠂⣈⠥⠊⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣤⣴⣴⣤⣶⣴⣴⣤⣶⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠀⠀⠀⠈⠁⢀⣆⡀⠀⠀⠀⠈⠀⠀⠀⣁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠑
⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠐⠿⡗⠀⠀⠀⠀⢀⠐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠚⠖⠀⠀⠀⠒
⠀⠀⠀⠑⢆⠘⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⡀⣠⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣠⣷⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣾⣿⡿⠀⠀⡰⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⡇⠀⠀⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣀⣀⣈⡆⠀⡀⢻⣿⣿⡿⡄⠀⣼⠃⠀⢀⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠇⠙⢿⣿⣿⡄⡘⣦⣿⡿⢳⣿⡄⠁⣢⢔⣩⣤⣄⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣠⣤⣤⣤⣤⣍⣻⣏⠉⠉⠁⢠⣿⣿⣷⣿⣶⡌⠛⢫⣤⠉⣛⡿⣿⣿⠓⠢
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⢘⡿⣿⠙⠛⠻⣿⣄⠀⣿⡀⠃⢀⣀⠀⠙⠷⣄
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢦⡸⠃⠙⠀⢀⣴⡄⠘⢧⡿⣄⠀⠀⠙⠓⠀⠸⣿⣷⣄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⢠⡶⣄⠀⢸⡗⠁⠀⠸⣯⡿⠁⢠⣄⠀⢿⡌⠉⢿⢿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣻⣷⡄⣯⡿⠃⠀⠀⠀⢴⡶⡄⠉⠁⠀⢸⡛⠂⠈⢱⣶⡄⢸⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⡿⠁⡴⡆⠀⣠⣤⠀⢻⡅⠉⠀⢘⢟⡂⠉⠀⠀⢨⣹⠳⣺⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀⠸⠛⠃⠀⢿⡻⠁⠀⠉⠀⠀⢮⣁⠀⠀⠀⢤⣄⠁⠘⢫⣤⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⠀⣼⣿⣧⠈⢁⣠⣄⠀⡰⢶⠀⠉⠀⠀⠀⣾⡟⠀⠀⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡃⠟⠧⢿⠀⢩⣗⡟⠀⠷⡎⠃⢀⣴⣶⠀⠉⣀⠀⠀⠙⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣧⣶⠀⠀⢀⠀⠙⠃⠀⠀⢀⣀⠘⠿⠟⠀⢰⡿⠁⣾⣿⠏
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⡟⠀⣰⣹⡷⣠⠾⡳⠀⣿⣿⠀⠀⢀⣄⡈⠁⠀⠋⡽
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢟⣩⣠⠀⢙⣾⠋⠁⠛⠁⠀⠘⠃⠀⠀⢸⠟⠁⣼⣷⣼⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⢾⣿⠆⠁⠀⢠⠖⠒⠀⢀⡶⣦⠀⠀⣠⡀⠻⣧⡏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⣾⠋⢀⣤⣴⠃⣿⡿⠴⡜⣿⠉⠀⢸⣿⣣⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣷⣾⣿⡙⢧⡄⠀⢀⡐⠂⣠⣶⠀⠈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⢿⡿⠛⠈⠁⣀⣀⢾⡻⠇⠐⠿⢿⣽⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣅⠀⠀⣼⣿⡇⠈⠁⣴⣶⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣧⡿⣷⠀⠸⠿⡇⣄⣈⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⡿⣞⣦⣿⣧⡾⣿⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣟⣿⢸⣿⢿⣿⣿⣿⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⠿⠴⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠠⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⢀⡂⢼⡉⠁⠓⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⢀⣁⠀⠀⠀⠀⢠⡀⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⣀⠀⠀⠀⠰⠀⠣⠄⠀⠀⠂⠀⠀⠈⠀⠀⠆⠈⢴⡒⠁⠀⠀⠀⠠⠀⡐⠕⠀⠀⠠⠂⠀⢀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢢⠣⡀⠀⠀⠀⢪⠠⡀⠀⢀⠷⣚⠆⡀⠀⠀⠀⢆⢠⠀⡑⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣀⠂⠀⠀⠀⠈⠘⠋⡀⠀⠀⠂⠐⠀⠀⠁⡘⡰⢉⠆⠐⠊⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠂⠈⠠⢈⠀⡠⢠⢯⠏⢀⠀⡀⣂⣔⠀⢀⡂⠀⢙⡁⠁⠀⠀⡂⢼⠇⡬⠀⢀⢀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⣁⣤⣖⠊⠈⠷⠤⠔⠧⠤⡀⠀⢬⣡⡍⠔⠚⠒⠒⠊⠋⠋⡛⠹⣗⢲⠟⣦⣒⠆⠰⢒⠚⠈
⠀⠀⠀⢀⢄⠀⠈⠀⠀⠕⠮⣄⠀⠀⢀⡜⠑⢤⡶⠴⠃⠀⠀⣠⠢⣔⠀⣀⠬⣆⡠⢯⡀⠤⠺⠎⠸⡟⠉⠚⠂⠊⠀⠐
⠀⠀⠀⢀⡁⡀⡄⠀⡀⠠⠀⠨⠙⠤⠾⠒⢈⣠⡝⠁⠠⠆⢉⡁⠤⠠⢉⡉⠠⠌⠠⠐⠁⠀⠀⠀⠀⠀⡢⠀⠲⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠈⠄⠄⠀⠀⠀⠀⠀⢰⠀⠀⠻⠓⠢⠖⠀⠓⣯⣥⣈⣴⠂⢀⠤⠒⠉⡀⠄⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⢡⡦⢄⠀⠐⠀⢀⠔⠠⠀⠀⠀⡄⠠⢆⢭⠉⠁⠈⢀⠄⢔⠀⠀⡀⡀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⢐⢠⣦⣤⠇⠀⠢⠤⠔⡛⠂⠀⠀⢠⠔⢣⠞⠚⠋⠐⠃⠈⠀⠠⠀⠆⠔⠈⠀⠠
⠀⠀⠀⠀⠀⠢⠹⡄⠀⠀⠠⣢⡄⠀⡀⠠⠔⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠔⠁⠀⠀⢠⠀⠀⠀⠐
⠀⠀⠡⠀⠀⠀⡤⠚⠖⠐⠀⠀⠡⠀⠀⢀⢄⠄⠠⡀⠂
⠀⠀⠀⠀⠤⡎⠀⠤⠀⠤⠈⠠⠀⠄⠀⠁⠀⠠⠠
⠀⠀⠀⠈⠠⠈⠀⠀⠉⠠⠀⠀⠀⠄⠀⢀⣪⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⡤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⣠⢞⣁⡀⠀⠰⢲⡀⠲⠤⡉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠤⢤⣀
⠀⠀⠀⠀⠀⢰⣯⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠒⢠⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣋⠉⠴⠀⡘⢁⠀⠔⠐⠊⣳⡀
⠀⠀⠀⠀⠀⡇⠹⣄⠁⠀⠀⠀⠀⠀⠀⠲⢤⣠⡄⢀⣵⠄⠀⠀⢹⡳⣄⠀⠀⠀⢀⡴⠋⡡⠂⠙⠀⡇⠀⣀⡴⠋⠀⠀⠐⡉⢛⣧
⠀⠀⠀⠀⢰⡇⠀⠙⢧⡀⢤⠀⠈⠀⠒⠚⠻⢿⡀⣿⣥⡤⠤⠄⠈⠽⠈⢳⣀⠔⠋⠔⠀⠚⠶⣤⡤⢛⢸⡿⠤⠆⠀⠀⠀⠀⡞⣹
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⢤⡀⠀⠀⠀⠀⠐⠈⠉⠙⡌⠑⠦⣀⠀⠀⠑⠂⠹⡐⡋⣀⣤⡴⢖⡾⢳⣎⠉⠣⠀⠄⠀⠀⣡⠌⢠⡏
⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⢀⡄⠀⠀⠹⡀⠀⠈⠳⢄⠀⠲⢀⡇⠀⠀⢀⡴⠋⠀⠹⠀⠀⠀⠐⢀⡠⠞⠁⢀⡼⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢬⣁⣀⡘⠢⠀⠱⠄⢀⠠⣾⣤⠂⠴⢋⠀⠀⠀⠀⠐⣃⡬⠖⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡔⣿⡦⢤⣥⣯⣤⣤⡶⠒⠋⠃⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣿⠌⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡮⠤⢐⢿⡇⠀⠀⠀⠉⠙⠛⠛⢏⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠤⠤⠤⠴⠤⠤⠤⠒⡞⠋⠀⠀⠀⢠⠏⢸⡂⠀⠶⠀⠈⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⣆⠀⠀⠄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠁⠀⢰⠙⢦⠀⠀⠀⠐⠄⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠴⠁⠀⢀⠏⠀⠀⠑⢄⠀⠀⠘⢠⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣠⠚⠁⢀⡤⠒⠁⠀⠀⠀⠀⠀⠉⠢⡀⠀⣧⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⠀⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋


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

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠉⢢⡀⢠⠿⠁⠀⢀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠉⠙⠛⠻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠹⣿⠀⠀⢠⠆⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠹⡇⠀⡎⠀⠀⣰⣿⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣿⡼⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⠃⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⠿⠿⠆⠤⠼⣁⡀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠐⠎⠩⠝⠒⠤⢀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠁⠒⠮⣕⠀⡀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣿⣷⠐⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠈⠠⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⢧⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡜⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅
⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⡇⢏⠀⠀⠀⠀⠀⠀⠂⣲⠄⠤⡤⣤⡤⠽⢄⣀⣀⠈⣳⣌⡁⠀⠀⢀⡀⠀⠐⣤⠴⣱⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⣤⣇⠈⡆⠀⠀⠀⠀⠔⠊⠀⡘⠀⢳⠀⠉⠂⠀⠀⠀⢀⠇⡇⠈⠑⠲⠤⠤⣥⣤⠶⠛⠁⠈⠑⠀⠄⣁⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡄⠘⡀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⣰⣧⣤⣴⣶⢿⡛⠉⠉⠓⠢⢀⡀⣀⣀⠀⡀⠉⠙⠞⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠁⠈⠲⢄⡀⠀⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠐⠃⠀⠤⠤⠄⠤⠤⠀⠀⠞⠓⢤⣉⠒⠂⠠⠀⠀⠀⠠⠤⠀⠚⣉⠔⠋⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⢢⡀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠉⠁⠈⠳⡔⠁⠀⠈⢱
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣄⣀⡴⠒⠐⠒⠤⡀⢅⠀⠀⠀⣦⣿⣤⢀⣀⣼
⠀⠘⠛⠒⠒⠺⠿⠷⣶⣵⣤⣤⣤⣾⣷⣿⣿⣉⠀⠁⠀⠀⡴⠊⠉⠙⠻⣿⣧⣿⡿⠋⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⣻⠙⠁⠈⠳⡄⠠⠈⡇⠀⠀⠀⠀⣸⠋⠻⠿⣄⠀⠀⣸⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡟⠀⠀⠀⠀⢡⣀⡀⠑⠒⡤⠴⢻⠁⠀⠀⠀⢘⠗⢒⡗⠀⠀⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠐⠀⠐⠤⠄⣀⡠⠂⠈⠉⢯⣛⣓⣒⠲⠷⢄⠀⡠⠮⠤⣿⡇⠂⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠗⠤⡀⠀⠀⢉⠀⠀⠀⠀⠙⠢⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠹⠀⠀⠀⠈⢢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠄⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠠⠈⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠶⠶⢶⠖⠚⢻⡛⠛⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⣸⣄⣀⣸⣧⣤⣿⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡖⠛⠛⠛⠋⠉⠉⠉⠁⣠⡴⠶⣦⡀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣡⠞⠻⣄⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠈⡷⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠔⠋⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠘⢿⣷⣶⠞⠁⠀⠀⠀⣀⣀⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠓⠒⠲⠶⠶⠶⠶⢤⣤⣤⣌⣷⣄⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠴⡟
⠀⠀⠀⠀⢀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠔⠊⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣧⣤⣉⣉⣹⢿⣦⡀⠀⠀⠀⠀⠀⢸⡏⠓⠒⠒⠒⠒⠛⠉⠉⠉⠉⠙⠒⠦⠤⣿⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⡞⣷⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⠸⣿⣿⠿⠿⠿⢿⣟⣛⣛⣿⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⢀⣀⠠⠄⢺⡄⣿⣿⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⢾⣷⣿⣶⣖⣶⣤⣤⣤⣤⣤⣤⣤⣤⣿⣣⣼⡇⠀⠀⠀⠀⠀⡇⠀⣿⠙⠋⢹⡀⡇⠸⠇⠙⠈⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⢿⡘⣇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⢸⡇⠀⠀⠀⠀⠀⡇⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠸⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠤⠤⠿⠼⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡜⣸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣀⠀⠀⢠⠋⠙⢦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡇⣿⣀⡀⠀⠀⠀⢸⣇⡀⠀⠀⡴⠉⠘⢧⡴⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠀⠳⣀⢀⠞⢹⡇⠹⣄⡴⠃⠀⠀⠀⠀⢀⡀⠐⣂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⠀⠀⠈⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡿⠳⢦⣤⣀⠀⠀⢸⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⠦⣄⣀⣀⠀⠀⠀⠀⠀⣀⡤⢊⡼⠃⠀⠀⠀⠉⠙⠛⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠮⣭⣭⣭⣭⣭⣭⡵⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⣉⣉⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷
⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢸⡇⠀⢻⡆⠀⠀⠀⣠⣴⠾⠛⠛⠛⠛⠛⠷⣦⡀
⠀⠀⠀⠸⣇⠈⠛⠶⢤⣄⣀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠶⣴⠏⠻⢦⣤⣟⣀⠀⠈⣿⠀⣠⡾⠋⠀⠀⠀⠀⠀⡀⠀⠀⠈⣻⣦
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⠉⢙⡾⠋⠀⠀⠀⠐⠲⠦⣄⣸⠀⠀⠀⠀⠈⠉⠙⠓⢾⣿⠏⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⣞⠉
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠟⠛⠛⠳⢦⣄⠀⠀⠀⠈⠙⢧⣀⠀⠙⠦⣄⠀⠀⠀⠙⢷⡄⠀⣀⡴⠋⠀⢀⣴⣟⡁⠙⠳⢦⣤⣤⣤⡤⢶⣶
⢠⣤⣤⣀⣀⣀⣨⣿⡷⠦⠴⠒⠒⠒⢒⣚⣻⣷⣤⣀⠀⠀⠀⠙⣧⠀⠀⠈⢳⡄⠀⠀⠈⢻⡟⠉⠀⣀⣴⣿⣥⣬⣉⣑⣒⣀⣀⣀⣤⠶⠛⠁
⠀⠙⠷⣤⣁⡀⠀⠀⠀⠒⠐⠲⠒⠋⠉⣁⣠⡴⠟⠛⠛⠿⠿⠿⠿⣧⡀⠀⠀⢻⡄⠀⣀⣴⠟⠛⠋⠁⠀⠀⢀⠀⠈⠉⠉⠛⢿⣍
⠀⠀⠀⠀⠉⣹⠟⠛⠻⠿⠷⠾⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠈⢷⡀
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⣿
⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠸
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠍⠀⠀⠀⠀⠀⠀⠄⢀⡆⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠁⠀⠀⠀⠀⢲
⣾⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣸⠦⡄⠀⠰⠋⠀⠀⠀⡏⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⣿⠀⠀⠀⠀⠀⡠⠀⠠⠂⡄⠀⠀⡞⠳⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠄⠀⠀⠀⠃
⣿⠀⠀⢠⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡔⠦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠠⠀⢀
⢹⡆⠀⠈⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⡠⠂⠀⠀⠠⠁⢸⠀⣴⠀⣼
⠘⣷⡀⠀⠘⠀⠀⢸⡀⠀⢀⢀⠀⠀⠀⠀⡞⢦⠀⠀⠀⠀⠈⣇⡽⠀⠀⠔⠓⠣⠀⠀⠀⠀⡘⠁⡈⠀⠀⠀⠀⢡⠀⠀⡾⣀⠃⠈⠀⠀⣸⡿
⠀⠸⣧⠈⠄⠀⠄⠀⠁⠀⠨⠼⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⣴⠊⠀⢠⡿⠁
⠀⠀⠹⣧⡀⠀⠞⡄⠀⠈⠠⡀⠀⠀⠐⢀⠀⠀⠀⠀⠋⣠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣀⠀⠀⠀⡨⠀⢀⣿⠃
⠀⠀⠀⠘⢷⡄⠈⠁⠀⠀⠐⠼⠀⠀⠀⢌⠳⡀⠀⠀⠀⠳⣬⠇⠀⠀⢀⡀⡀⠀⠀⢠⡈⢦⠀⠀⠀⠸⡤⠂⠀⠼⠃⠀⠀⠚⢁⣀⣾⠃
⠀⠀⠀⠀⠈⢻⣆⠀⠈⠠⢄⠀⠀⠀⡀⠈⠙⠀⠀⠲⢦⡀⠀⠀⠀⠀⠀⠰⠄⠁⠀⠀⠓⠚⢀⠠⠤⠀⠀⠀⠀⠠⠖⠂⠀⠰⢫⡾⠁
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠒⠀⠀⠀⠴⠢⠀⠀⠀⠈⠲⠇⠀⢀⠠⢠⡀⠀⠀⠀⣠⠴⠖⠀⠋⠀⠀⠀⠀⠀⠀⠃⢂⡄⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢀⠀⠀⠀⠚⠁⠀⠀⡤⣄⠀⠀⠀⠀⠀⠙⠀⠀⠘⠁⠰⠀⢀⡔⡂⠀⠀⡀⢖⠀⠀⠁⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠇⠀⠀⢀⠀⠀⢀⠑⠚⠁⠀⠐⡖⢄⠀⠀⡤⢴⠀⠀⠀⠈⠀⠁⠀⠀⠙⢪⠄⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢀⠀⠑⠀⠀⠃⠀⠀⢠⢀⠀⠚⠁⠀⠀⠁⠀⠠⠆⠀⠀⢀⠰⠀⠀⢁⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠑⠄⠀⢀⠐⠀⠀⠀⠨⠃⠀⠀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡀⠀⠑⠀⠊⠀⠆⠀⢠⠤⡀⠀⠁⠀⠤⡒⠂⢠⡴⠀⠈⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠂⠀⢀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠈⠀⠎⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠱⠀⠀⠀⠚⠂⠀⠀⠀⠈⠉⠀⣀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⡀⠀⠀⠤⣄⠀⠀⠋⢒⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣤⣶⣶⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠈⠀⠈⠁⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠤⣰⠟⠂⠡⠔⢢⢊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠀⠈⠈⠀⠀⢱⠠⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣆⠀⠀⢀⡢⠀⠀⠈⠖⠀⢀⡀⠰⢀⣨⠔⠓⠀⠊⠉⢊⡁⠠⡄⠀⢀⢌⠀⠀⠁⠀⠰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠈⠑⠠⢍⢌⢆⠀⠀⠀⠀⢎⠂⡌⠀⠀⠈⣇⣠⡀⠸⠀⠀⠁⢚⠀⡀⠠⢪⠉⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠠⢀⡔⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡆⢑⠀⠀⠄⠀⠐⣸⣆⡪⠔⠍⡓⠁⠀⠀⢤⠀⡌⢢⢇⡠⢐⠄⠀⡀⠮⢆⡀
⠀⠀⠀⠀⠀⠌⠈⠁⢒⡀⠀⠀⢈⠀⢁⠀⠠⠀⠀⠀⢰⣗⠌⠀⠀⡀⡠⢂⠏⡠⠂⠀⣠⡐⡤⠃⠀⢀⠐⣠⠁⠼⠃⡩⠐⠀⠌⠨⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡢⢄⡀⢀⠁⠂⢩⡢⠀⠔⣡⠟⠊⠘⡢⣄⣪⡴⠗⣂⠈⠐⣂⢤⣎⣀⣀⣂⠕⢸⠏⢐⣂⠈⠀⠘⢁⢄⡨⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢟⠳⡴⢖⠥⠀⠄⢋⡒⠊⠑⠒⣭⠀⠐⠦⠴⠐⠉⠉⠉⢨⠁⠁⢄⡇⠀⢫⣩⡏⣽⣮⡝⢀⠋⢩⠡
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠝⠲⣆⠀⠀⢀⠞⣉⡲⣟⠒⠋⠀⢀⣀⠶⠵⢽⣁⣠⠒⣦⠔⠻⡄⠐⠈⢛⡀⢻⠁⠈⠉⠈⠁⠀⠉
⠀⠀⠀⠀⡄⢠⠲⠀⠤⠀⠆⠈⠠⠙⡴⠛⠋⢈⣠⠼⠁⠀⠖⠀⣠⣀⠀⠦⣈⡤⠐⠂⠀⠚⠁⠀⢠⠂⠀⠁⣂⠂⠀⠓⠀⠀⠀⠀⠀⢀⡀
⡠⠀⠀⠠⢠⠄⡀⠠⠀⠀⠀⠀⠀⠀⢰⠊⠀⠛⠚⠲⠶⠊⠙⣚⣯⢕⣒⡬⠃⢠⠠⢒⠉⡶⠗⠒⠤⠼⠬⣦⠰⠆
⠀⠁⢠⠀⠀⢠⢈⣴⠦⡀⠀⠐⡠⢀⡞⠠⠀⠀⠈⣠⠀⡾⡬⡍⠉⠁⠀⢀⠤⢖⢀⠀⡠⡀⠀⠀⠀⠰⠂⠙⠟
⠀⠀⠀⢀⠂⣢⣄⠽⠀⠰⠤⡤⠔⡛⠀⠀⠀⢠⡠⢊⡼⠗⠛⠃⠒⠒⠈⠀⠄⠈⠄⠵⠀⠁⠠⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠪⡙⡆⠀⠀⠀⠀⢠⠅⠀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠹⣄⠀⠀⠈⠁⡠⠊⠁⠀⣀⠀⠀⠉⠠⠄
⠀⠀⠐⡀⠀⢀⢠⣠⣞⡩⡀⠀⠀⢆⠀⠀⠀⡈⡀⠀⠀⠤
⠀⠀⠀⢈⢀⣦⢚⡡⠣⣁⠀⠤⠀⠀⣁⠐⠚⢀⠓⢡⠊
⠀⠀⠠⠡⡍⠙⠐⠊⠉⠤⡁⢀⢀⠀⠀⠄⡉⡥⠬⠁⠃