Pancakes Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠲⠎⠉⢳⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢰⠲⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠁⠀⠀⠀⠀⠀⠀⠸⢠⣠⣤⠀⠀⠈⣇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡉⠉⢳⣎⣠⣃⣀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠃⠀⡁⠘⣉⠉⠳⡒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⠭⠒⠒⣏⠀⢀⡀⠀⡁⠀⣰⠯⠭⣍⣓⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢯⠀⠀⠀⠘⠢⠤⠤⠤⠖⠋⠀⢰⣂⣐⠆⣹⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠙⠒⠶⠶⠶⠶⠶⠦⠤⠤⠤⣤⠀⡰⠊⢁⣀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣟⠑⠭⢭⣓⣒⣒⣒⡒⠲⠖⢒⣒⣒⣒⣒⣾⠁⢻⡭⠭⠴⢚⣿⠉⢻⢲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⢶⣤⣤⣀⣀⣀⣀⣀⣀⣈⣬⣭⣭⣤⣤⣬⡇⡿⠴⠖⢒⣩⡟⠀⡇⡼⢠⢷
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⣄⡉⠓⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠗⠒⠋⠉⣠⡗⠺⣥⠇⣞⣼
⠀⠀⠀⠀⠀⠀⠀⠹⣗⢾⣉⠻⢭⣟⣒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠖⢒⣒⣩⣭⣛⣀⣠⣼⠾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠺⣭⣭⣛⣛⣛⣛⣓⣒⣒⣒⣒⣒⣒⣒⣻⣿⠭⠭⠭⠿⠛⠛⠋⠉⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣹⡈⣇⢣⢹⠉⣏⠉⠉⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠾⠶⠶⠾⠾⠦⠶⠶⠒⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⢄⠒⠂⠉⣉⣉⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⢀⣀⣀⡀⠤⡇⣰⠉⠀⠀⠀⠉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠚⠂⠦⠤⢤⡚⠠⣏⠀⠀⠁⠀⠐⠀⠀⠈⠢⡤⠤⢀⣀⡀
⠀⠀⠀⠀⣀⡠⠔⠒⠉⠉⠁⠀⡰⠁⠀⠀⠠⠀⠄⠀⠈⠙⣌⠢⡀⠀⠁⠄⠀⠠⠄⠀⢸⠀⠀⠀⠀⠉⠉⠒⠢⣀
⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢂⠄⢀⠀⠁⠀⢀⡿⠢⣈⠑⠒⠂⠠⠤⠤⠔⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠤⢔⡪⠕⠁⠀⠀⢉⠗⠒⠀⠠⡔⠚⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣔⠤⢑⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢆
⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠂⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡇
⠀⠀⡌⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣀⠔⠊⠱
⠀⠀⢰⡀⠀⠀⠈⠉⠓⠠⠭⢍⣈⡁⠉⠉⠑⠒⠣⠬⠬⢰⣁⣀⣀⣀⣀⡀⠠⠤⠤⠔⠒⠉⠁⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡰
⠀⠀⡎⠈⠓⠤⢄⣀⣀⢀⠀⠀⠀⠀⠉⠉⠁⠚⠒⠐⠒⠒⠒⠂⠀⠤⠤⠤⠤⠤⠀⠤⠤⠤⠔⠒⠊⠉⠀⠀⠀⠀⡠⠒⠉⡇
⠀⠀⡱⣄⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠔⠊⠀⠀⣴⠁
⠀⠀⢇⠈⠑⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠒⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⣀⠤⢊⡎
⠀⠀⠀⣱⢤⡀⠀⠈⠑⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠤⠤⠤⠤⠤⠤⠀⠒⠒⠈⠉⢀⡴⣋⠆
⠀⠀⡎⠸⡀⠙⢕⠢⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⠁⠀⠈⠆
⠀⠀⠱⢄⡙⠢⢄⠉⠒⠬⠕⣲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠒⠊⣁⠔⠁⠀⠀⠀⣤
⠀⠀⢠⠀⠈⠑⠂⠬⣑⡂⠤⢀⣈⠉⠉⠛⠃⠭⠄⠈⣀⣀⣀⣈⣀⣈⣉⣉⣉⠁⠤⠄⠐⠒⠒⢂⡠⠋⠀⠀⢀⡀⠔⠊⠀⡇
⠀⠀⠀⢦⠀⠀⠀⠀⠀⠈⠁⠒⠢⠬⣉⡁⠒⠒⠒⠐⠐⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠂⠈⠉⠉⠀⠀⠀⢀⠔⠁⠀⢀⡠⠞⡃
⠀⠀⠀⠈⠳⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠠⠤⠤⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡤⠔⣁⠤⡴⠚⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠹⣑⠒⠩⢄⣒⡒⠠⠤⠤⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠂⣁⠔⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠉⠉⠁⠒⠒⠠⠤⠭⠬⠩⣭⡍⠉⢉⣉⣉⣉⣉⣉⣉⣁⣀⠠⠤⠒⠉⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠐⠒⠂⠉

⣟⣿⣿⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣻⣿⣻⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⢀⣠⣆⣬⣿⣿⣿⣦⠀⠀⠀⢀⢀⠀⠤⣤⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣓⣶⣤⣤⣖⣲⡄⠀⠈⠮⢻⠿⠟⠋⠉⠁⠀⠀⠀⠘⣜⢷⣾⣿⣿⣿⡄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠
⠅⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⢷⣾⡿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⡠⠀⠀⠐⠒⠒⠢⢤⠀⠙⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠘⣦⣄⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸
⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⠋⠀⠀⠀⠀⡐⢶⡄⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢠⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠣⡀⠀⠀⠀⠀⠇⠀⠀⡌
⢠⠀⠀⠀⣈⠀⠀⠠⠀⠀⢀⢸⡏⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⢰⣻⣭⣭⣑⠒⠶⠤⠴⣷⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣄⠀⠀⢰⠀⠀⠀⠇
⠸⣌⠀⢀⠜⠀⢠⠁⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⡇⢿⣦⣀⠈⠳⢤⣿⣿⡿⢷⣶⣶⣿⣿⠀⠀⠀⠀⠄⣸⣷⣦⠀⠀⠀⠀⠀⣸⢿⡇⠀⠘⡄⠀⢸⠀⠀⠸
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠙⢦⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⢪⣿⡀⠀⢀⣴⣿⣿⡿⠏⠀⠀⠀⠀⣴⡿⣸⠁⠀⠀⢱
⠀⠀⡇⢁⠀⠀⡇⠀⠀⢀⣼⣿⣿⣷⣵⣄⠀⠀⠀⠀⠀⠈⠙⢮⠻⢿⣾⣿⣶⣄⣀⣀⣼⣿⣿⣾⣿⠟⠉⠁⠀⠀⠀⢀⡠⣺⡟⣡⡟⠀⠀⠀⢸⠀⠀⠀⢠⡇
⠀⠀⡇⢸⠀⠀⡇⠀⠀⢸⣿⣿⡟⢿⣿⠻⣕⡤⣀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⣭⡽⠟⠛⠳⣽⡇⠀⠀⠀⠀⣠⠔⣫⠾⢋⣴⣿⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⡇⠀⡆⠀⢳⠀⠀⠘⣦⣿⣿⡀⠹⣗⢄⡙⠮⣝⡒⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⣤⠤⠒⣋⡴⠞⣡⢔⣵⣿⠇⠀⠀⠀⠀⡞⠀⠃⠀⢸
⠀⠀⡇⠀⢡⠀⠈⢧⠀⠀⠈⠳⢽⣾⣄⠈⠳⢭⣒⠤⣉⠛⠶⢤⣤⣈⣉⣙⠒⠒⠒⢒⣈⣩⣭⣭⣿⣷⠖⣋⡥⢖⣩⢶⢟⣽⠋⠀⠀⠀⠀⣼⠁⢸⠀⠀⡏
⠀⠀⠀⠀⢸⡀⠀⠈⠳⡄⠀⠀⠀⠹⣿⣷⣖⢤⣉⠛⠲⢯⣕⡒⠦⠤⢍⣉⣉⣉⣉⣉⣉⣉⠿⡿⣻⣿⣯⡴⢚⡫⢞⣡⠞⠁⠀⠀⠀⢀⡾⠁⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠢⡀⠀⠀⠈⠪⠿⠷⢮⣙⠢⢤⣀⡉⠛⠓⠲⠶⠶⠒⠒⠒⠒⠛⢻⣿⣷⣿⡯⠖⣋⣴⡿⠃⠀⠀⠀⢀⣴⠏⠀⠀⢠⠇⠀⢰⡇
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠈⠙⠓⠶⠬⣭⣍⣑⣒⣒⣒⣒⣉⣉⣩⣭⣭⣵⣹⣷⣟⡿⠋⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⡸⠀⠀⢸
⠀⠀⢸⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠑⠈⢓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠗⠚⠛⠉⠁⣀⣠⢴⡺⠝⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⡀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠭⢒⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢖⡒⠍⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣠⣄⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠿⣿⡿⠟⠉⠉⠉⠉⠙⢛⣿⠿⠶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠀⠀⠀⠀⣿⣅⣀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠉⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡾⠟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣄⣀⢹⣧⠀⠀⢠⣶⠿⠿⢷⣦⡀⠀⠀⣰⡿⠛⠉⠉⣀⣠⣴⣿⣁
⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⣧⡈⠉⠛⢻⣿⠀⠀⣿⣧⣤⣤⣤⣽⣷⣤⣴⣿⣷⠶⠾⠟⠛⠉⣁⣼⠟⠿⣶⣄
⠀⠀⠀⠀⢠⡾⠋⠀⠀⢸⣟⠛⠷⣶⣬⣿⣄⣸⣟⠀⠀⠉⠉⠉⠉⠈⠁⣀⣀⣀⣤⣤⣶⠾⠛⣻⡆⠀⠀⠙⢷⡄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣶⣤⣀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⣀⣤⣶⠟⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠉⠛⠛⠿⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⡶⠶⠿⠛⠛⠉⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⢠⡐⠉⠙⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠀⠀⢺⠀⠀⠀⠘⠀⠐⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠘⠒⠊⡁⠀⠈⢹⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣭⣍⣛⣛⡻⠿⠷⠶⠶⠶⠒⠒⠀⠀⠐⠉⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⣈⡉⠉⠛⠛⠿⠿⠷⠒⠚⠛⠃⠀⠀⠀⢴⠿⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣮⣉⡙⠛⠛⠿⠷⠶⠆⠀⢒⠀⠀⠀⠀⠐⠈⠀⡴⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢤⣉⠛⠛⠻⠷⠶⠶⢶⣤⣤⡤⠀⠀⠀⠒⠀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠙⠻⠶⣶⣶⣤⣤⣤⣤⡤⠤⠄⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣷⣶⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⠛⠉⠉⠉⠈⣻⣟⣻⣿⣿⠿⠛⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣟⠾⡅⠓⣶⡿⡯⠽⣏⣹⣟⣥⣬⣶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠲⢭⣽⣼⣉⣉⣉⣩⣽⣿⣶⠿⠛⣩⢜⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢮⣅⣺⣾⡇⠤⠤⠤⠽⠾⠿⣾⣻⣽⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠷⣌⠹⣿⣿⠭⠭⠭⠿⠿⠟⠋⣋⣊⡭⣛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠤⣈⢹⢿⡷⠬⣭⣭⣙⣭⣬⣭⣷⣶⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠳⢮⣍⣿⣧⣤⣤⣬⣵⣶⡿⠷⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣶⠤⢤⡟⡟⠉⠩⠉⠉⢭⣒⡫⢵⣾⣿⣧⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠐⠁⠀⢀⠴⢾⣿⣔⠝⠒⡿⣯⣭⣭⣉⣭⣥⣴⡾⣛⣭⣿⢿⡋⠒⢄⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣰⢼⡄⠙⠿⣿⣾⡧⠤⠤⠬⢭⣯⣭⣵⣾⣿⣿⣿⣗⡰⣎
⠀⠀⠀⠀⢀⠀⠀⠀⠲⣷⣿⣿⣶⣤⡾⣹⣏⣉⣛⣛⣛⣭⠽⢶⣻⣽⣿⣿⣿⡶⠋⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⢻⢿⣟⠨⠿⢿⣿⣶⣶⢶⣾⡿⢿⢿⡿⠟⠋⠉⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠉⠓⠛⠛⠛⠛⠛⠒⠒⠚⠉⠉⠁⠀⠀⠀⣀⡠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠂⡠⠤⠀⠀⠀⠄⠀⠀⠑⡄⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣄⣀⡄⠠⠀⠀⠀⠀⠇⠀⠐⠁⠀⠠⠰⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⢀⠈⡁⠈⠛⠓⠛⠛⠁⠀⠓⠛⠛⠇⠈⠛⠁⠀⠀⣢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠐⠀⠀⠈⠛⠋⠤⢄⣀⡀⠀⣀⣀⣐⣂⣀⡀⠊⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁⠒⠢⠤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠐⣒⣀⠔⠊⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠅⣀⣀⡀⠀⠀⠀⠈⠉⠙⠀⠉⠉⠉⠉⠉⠉⠉⠀⣂⡴⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠈⠉⠉⠛⠚⠒⠒⠆⠀⠲⠶⠶⠒⠚⠚⠉⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣤⣀⣀⡇⠀⠀⣀⣀⣠⣤⣤⠤⠴⠒⠋⢁⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⣀⡀⠀⠀⠈⠀⡀⢀⣉⣉⣁⣤⣤⡤⠶⠖⠛⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠲⠤⣄⣀⠈⠉⠉⠉⠉⠉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⣤⣀⣀⣀⠀⠈⠉⠛⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⠉⠉⣀⣀⣀⡤⠄⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠩⠭⢉⣛⡓⡒⢒⣒⣒⣒⡒⠒⣒⣻⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⡄⠒⠂⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣈⡥⠆⠀⠀⢄⣀⣀⣠⡀⠈⠀⢤⡄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠄⠀⡀⢀⠄⠚⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢵⠀⢠⣄⣀⣹⠀⠀⣠⣄⣒⡂⠤⠭⠍⠐⠒⠊⠉⢢⢀⡠⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⢀⣀⣀⡀⡉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠒⢟⡈⢀⡨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢀⣀⠁⠀⠀⠀⠈⢱⡀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⠀⠑⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢄⣉⠀⠀⠐⠒⠂⠶⡇⠠⠤⠤⠒⠒⠒⠋⠉⠉⠁⢀⣀⡗⠐⠈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣭⠈⠒⠒⠒⠒⠶⣇⠠⠤⠤⠤⠔⠒⠒⠊⠉⠉⠀⢀⡠⠔⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡓⠤⣀⡈⠑⠒⠒⠒⠂⠆⠀⠠⠤⠤⠤⠤⠔⠒⠚⠉⠽⣧⡀⠀⢀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⢃⠢⢄⡉⢁⠒⠶⠦⠄⣴⠀⣀⣀⣠⣤⠤⠤⠤⠴⡶⠋⠀⠁⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⠋⠁⠀⠙⠶⣼⠁⠀⠀⠰⢤⡤⠤⠤⠤⠤⠤⠤⠴⠶⣶⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⢄⣀⠤⣉⠀⠀⣀⠠⢄⣀⣀⠠⠝⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣠⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠈⠛⠤⣤⣤⣤⣤⣀⠀⠀⣠⣤⣶⠏⠁⢀⡤⠞⠁⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢿⣧⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠂⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠉⠛⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠄⠀⢀⠀⠀⠀⠀⠐⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣤⣦⣃⠀⠀⠀⢀⠐⠀⠀⢤⣄⣀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣴⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣼⢄⡀⠉⠉⠛⠶⢤⣿⡀⠀⠀⡦⠭⠉⣝⣓⣦⣄⣀⡦⣆⣀⣄⣀⣠⣤⡶⣞⣻⣯⣵⠶⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠛⠷⣧⣈⠀⠀⠀⠀⠀⠀⠋⠃⠘⠛⠒⠿⠿⣿⣿⣿⡗⣿⠿⠿⠿⠟⠛⠛⠉⢉⣁⡤⡾⢻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⡀⠈⠉⠛⠻⠷⣶⣀⣾⣤⣤⣀⠀⠀⠤⠀⠀⠀⢠⠀⡀⠀⠀⢀⣀⣠⣤⣼⣿⣽⠷⠾⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⣙⠳⢤⣤⣄⣠⡀⣎⡴⢈⠉⠉⠛⠳⠶⠶⠶⠴⠞⢠⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⢀⣰⣶⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠻⠾⣷⡀⠀⠀⠈⡉⢉⡟⠛⠲⠶⠤⢄⣑⣀⡀⠀⢐⠊⡀⣀⣀⣀⣠⣦⡴⠴⠶⠚⠋⠉⣹⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠉⠑⠶⡆⢰⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠀⣀⣀⣀⣤⡤⠶⠛⠉⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⠿⢦⣀⡒⢀⣀⢃⠀⢡⠈⠉⠉⠛⠲⠲⠦⠤⠤⠄⠒⠶⠖⠒⠒⠋⠉⠁⠀⢀⡀⠀⢀⣄⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣤⡉⠙⠻⠿⠾⢧⣼⣠⣈⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⣉⣀⣠⣶⠶⢿⣛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣤⣀⣈⡙⠛⢿⣟⢿⣾⢶⣶⣴⣤⣤⢤⣶⠶⠶⣾⡿⠿⢋⣡⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠉⠉⠛⠛⠿⠷⠶⢦⣭⣭⣭⣤⣬⣥⣭⣭⠤⠖⠓⠛⠉
⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁
⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠾
⠀⠀⠀⠂⠘⠛⠋⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⢳⣄⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⡀
⠀⠀⠀⠀⣠⠶⠞⣋⣥⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⡀
⠀⠀⠀⠀⣷⣄⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣤⡿
⠀⠀⠀⠀⠻⣬⡉⠛⠶⢤⣤⣀⣀⣀⣠⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣈⣉⣉⣩⣥⡴⠞⠋⣩⣼⡃
⠀⠀⠀⠀⠀⢰⡟⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣉⣉⠉⠛⠛⠛⠛⠉⢉⣉⣉⣀⣀⣀⣀⣀⣀⣠⣤⡴⠖⠋⠁⠉⠙⢳⡄
⠀⠀⠀⠀⠀⣸⡷⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣿⠃
⠀⠀⠀⢀⣞⠉⠙⠶⣤⣉⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋⣁⣤⣾⠋
⠀⠀⠀⠀⣿⠳⠦⣤⣀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣄⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⢖⣻⡿⠿⢻⡏
⠀⠀⠀⠀⢈⣿⢦⣄⣉⠛⠛⠒⠒⠒⠒⠒⠒⠲⠶⠶⠤⣤⣤⣤⣤⡤⠴⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⢋⣁⣤⠾⠿⣤⡀
⠀⣀⡤⠶⢻⣧⣀⡀⠉⠛⠛⠒⠒⠒⠒⠒⠒⠲⠶⠶⢤⣤⣤⣤⣤⣤⠴⠶⠶⠒⠒⠒⠒⠒⠒⠚⠛⠋⠁⠀⢀⣠⣼⡷⠦⣄⡀
⣾⠉⠀⠀⠈⢷⣌⡉⠛⠶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⢉⣥⠟⠀⠀⠈⢹
⠙⠷⣄⣀⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣉⣉⠉⠙⠛⠛⠋⠉⣉⣉⣀⣀⣠⣀⣀⣀⣠⣤⣤⠶⠚⠋⠁⠀⢀⣠⡴⠟
⠀⠀⠀⠉⠛⠓⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠖⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣽⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣭⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠃⠴⡟⡁⠀⠀⠐⠒⠢⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣾⣷⡀⠀⠀⡴⡠⠀⠀⠀⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠂⠉⠁⠀⠀⠒⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢄⡀⠈⠙⠓⠲⠶⠶⠤⠤⣤⡤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠒⠚⠋⠁⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠂⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠙⠒⠶⠤⠤⣬⣭⣉⣁⣀⣀⣠⡤⠤⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠓⠤⣀⣀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢀⠀⠄⢀⣀⣀⣤⠤⠴⠒⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠉⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠁⡀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠉⠓⠲⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠶⠖⠒⠛⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠙⠦⣄⡀⠈⠉⠛⠓⠷⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠊⠉⠀⠀⢀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠛⠓⠶⢶⣤⣤⣤⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠀⠉⠉⠁⠀⢀⣀⡤⠶⠛⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⡀⠀⠀⠀⠀⠉⠛⠒⠶⢤⣤⣤⣤⣤⣄⣀⣤⣀⢤⣀⣀⣀⣤⣤⠴⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⣀⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣠⡤⠤⢶⣖⡖⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠚⠦⠤⠤⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠤⠴⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠊⠀⠂⠠⢶⠂
⠀⠀⠀⠀⠀⢀⠀⠀⢖⣿⡀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠠⠀⠐⠚⠉⠁⠀⠂⠀⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⢣⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠖⠂⠹⣋⠁⠠⠀⣈⡋⠹⠉⠉⠉⡭⠽⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣉⠠⠄⠀⠁⡠⠔⠒⡄⠉⡩⠄⠲⢤⠀⠀⠀⢉⣉⠉⠉⣹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡁⣀⣀⠠⠯⠀⠀⡔⡠⢄⢣⠤⠄⠀⣇⠀⡜⠉⠈⢣⢸⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡿⠍⣙⣗⠀⠠⠰⡀⡇⢸⠀⠆⠀⠒⢇⣴⡇⠌⠉⢸⠸⣀⡟
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⢏⡒⠼⢨⣉⣉⣁⣳⡇⠚⢛⣂⣉⣉⠁⠸⠱⠀⠐⣚⠀⣯⣤⣀⣀⡀
⠀⣠⠴⠒⠋⠉⠁⠀⠘⡇⢰⡀⠱⠼⠒⠂⠠⠶⢹⠄⠄⠀⠀⠒⠂⡆⢸⠂⢁⡨⠟⢷⡄⠀⠈⠉⠉⠓⠢⢤⡀
⣟⣄⠀⠀⠀⠀⢀⠤⠴⢷⡸⠨⠍⠀⠒⠒⠒⣧⡔⠒⠒⣒⠒⠒⠒⠣⠜⠍⠁⢒⣁⠴⠣⠤⡀⠀⠀⠀⠀⢐⢝
⠈⠻⠵⣒⣢⠤⠬⢒⣂⡀⠙⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠖⠒⠛⠛⠉⠁⣀⣀⣀⠡⠤⣤⣒⡪⠝⠊
⠀⠀⠀⠀⠉⠉⠓⠲⠦⠤⣄⣀⣀⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣀⣠⠥⠤⠶⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⢂⡀⠈⣣⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠑⢺⡧⠈⡀⠐⠈⠀⠀⠰⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠤⠐⠒⠀⢰⠛⠓⠆⠀⠄⣿⣧⠌⣤⣤⠄⣤⡷⢀⡠⠄⠀⡀⠐⠒⠠⠶⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢉⠁⠀⠀⠀⠀⠀⢀⡘⡀⢀⡀⠂⠀⠀⠙⡿⠛⡁⠀⠉⠙⣯⠁⠀⠀⠘⠳⠶⢤⣀⠐⠂⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠀⠀⣠⠴⠚⠋⠉⢙⣬⠉⠵⣐⠀⠀⣼⠃⠀⠄⡁⠀⠀⢸⣇⠴⠛⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⣀⠀⢀⡞⠁⠀⠀⠀⠐⠒⠺⣧⣐⢢⣨⣶⣛⣆⠀⠁⠀⠀⢔⣬⢯⠉⠁⠀⠀⠀⠀⠀⠀⡄⢳⡄⢀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⢿⠑⢤⣀⠉⠀⡼⠀⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠻⠿⠦⠌⠛⠛⠁⠀⠀⠀⠀⠀⠤⠤⢔⠃⠀⢸⠇⠉⠀⠀⣠⡴⠛⡇
⠀⠀⠀⠀⠀⠀⡸⢧⠀⠈⠻⣦⣱⠀⢈⡐⠒⠒⢈⡉⠤⠤⠤⠄⠀⠀⠀⠀⠀⣐⣢⣭⣭⣽⣦⣶⣤⣤⣄⡀⠀⠀⠀⢠⢏⣀⡤⠖⠋⠉⢀⣼⣅
⠀⠀⠀⠀⠀⢸⡇⠈⢷⣤⡀⠀⠉⢆⠀⠈⠀⠀⣠⣴⣶⣿⣶⣤⡁⠀⢀⣴⠛⠩⠅⠀⣂⣀⣒⠤⠤⠤⠭⢿⣦⠀⢰⠟⠋⠁⠀⢀⣠⡴⠟⢁⢸⣧
⠀⠀⠀⠀⠀⢹⡙⢦⣀⠈⠛⠷⣦⣬⣥⠀⠀⢰⠏⠀⠀⠀⠀⠀⢣⠀⣼⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣽⣤⣴⠶⠟⡋⠁⠀⣀⣤⠏⣿
⠀⠀⠀⠀⠀⠘⣧⠀⠙⠻⢦⡀⠀⠉⠙⡀⠀⡿⠿⠶⠶⣶⣶⣶⣾⠀⢻⣦⣤⣤⣶⣶⣶⠶⠶⠶⠾⠿⠟⠛⠻⣦⡿⠁⠀⢀⡠⠥⠒⠛⠉⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠙⠶⢦⣼⠀⢰⡁⠈⠀⠀⠀⠀⠀⢸⠄⠸⡇⠀⠤⠀⠀⠀⠀⠀⠠⠀⢀⣀⣤⣤⠤⠶⠶⠚⠁⠀⠀⢀⣠⣴⠟⠁⢸⣧
⠀⠀⠀⠀⠀⠀⢘⢿⡙⠻⢶⣤⣄⡀⢸⡆⠀⡟⠛⠒⠒⠒⠒⠲⣾⠀⠀⡷⠒⠒⠒⠲⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠉⠀⠀⣠⠎⣿
⠀⠀⠀⣀⡤⠒⢹⡆⠳⢦⣤⡈⠉⠛⠻⣷⠀⢹⣤⣤⣄⣀⣀⣀⣿⣀⣴⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⠶⠞⠛⠉⠁⠀⠀⢀⣠⡴⠛⢁⣼⡛⠳⢤⡀
⠀⣴⠞⠉⠀⢀⣾⠻⣄⠀⠀⠙⢦⣀⠁⢸⡇⣼⠁⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠁⣀⣠⡴⠟⠋⠁⢀⣤⠞⠉⣷⡀⠀⠙⢦
⣾⠁⠀⠀⠀⢨⢳⡀⠈⠳⢦⣀⠀⠈⠋⢻⠁⣿⠒⠶⣤⣄⣀⣤⣤⣤⣤⣄⣀⣀⣀⡁⣀⣀⣀⣤⡤⠶⠶⠖⠛⠛⠛⠋⠉⠁⣀⣠⣤⠾⠋⠁⢄⣰⢿⡇
⢿⡄⠀⠀⠀⠸⣆⠙⢦⣄⡀⠉⠛⠷⣶⡇⠀⢿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠟⠛⠉⠀⢦⣠⠴⠛⢁⣼⠇
⠈⢻⣄⠀⠀⠀⠙⢷⣄⡀⠉⠓⢦⣄⠸⣧⣤⡿⠛⠿⠿⠶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⠶⠶⠿⠛⠛⠉⠉⠀⠀⠀⢀⣀⣤⠖⠋⠁⢀⣤⠾⠋⠀⠀⣠⡾
⠀⠀⠈⠻⢦⣀⠀⠀⠙⠻⣶⣤⣀⠈⠙⠢⢤⣀⣀⣘⣂⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⡤⠔⠚⠛⠛⠛⠛⠋⠉⢀⣠⣴⠾⠛⠁⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠉⠳⠶⣤⣀⡀⠉⠙⠻⠷⣶⣤⣤⣄⣀⣀⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣤⣤⣴⠶⠟⠋⠉⢀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣤⣤⣈⣉⡙⠛⠛⠛⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠋⣉⣉⣠⣤⣤⣶⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢭⣭⣛⣛⠛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⣛⣉⣩⣥⠴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡶⠶⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⣹⠏⠀⠀⠀⠀⠀⢸⡏⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠘⠳⠶⠶⠶⠶⠶⠞⠁⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⢻⣄⢀⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢤⣄⠀⣼⣿⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠈⢿⣿⢦⣤⣀⣙⣦⠀⠀⠀⡴⠛⠁⠀⢀⣀⣠⡤⠿⢦⣿⠿⡆⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠛⠶⢬⣭⣙⣳⣤⣞⣛⣛⣛⣋⣉⣭⣥⠶⠞⠋⠁⣸⣷⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⢀⡴⢲⣿⡇⠈⢷⣦⣄⣀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣠⡴⢞⣵⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠸⡀⠸⣏⢷⣄⠀⠙⠻⢯⣝⣛⡛⠒⠶⠶⠶⠒⠚⠛⣋⣉⣤⠶⣻⣿⡿⣳⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⢒⡜⠷⣍⡓⠶⣤⣀⣀⡉⠉⠛⠛⠛⠛⠛⢛⣋⣉⣥⠶⢚⣽⠟⢱⡅⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠈⠳⠴⠚⠛⠳⠶⣬⣭⣉⣛⣛⣛⣛⣛⣋⣉⣭⡥⠶⠾⠿⠖⠚⠉⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣤⣀⣀⣀⣀⠉⠉⠉⠉⠉⠉⠉⠁⣀⣀⣀⣀⣤⡤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡖⠲⣤⠀⣠⣤⡀⣠⣠⡄⠀⣠⡀⠀⣠⣤⠀⣶⢀⡄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠁⣾⣡⢾⣀⢸⠃⢻⢸⣅⣀⣞⡡⢿⣀⣿⣟⡁⢾⡗⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠈⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡒⠒⠒⠒⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠀⠒⠒⠒⢧⣀⣀⣀⣀⣀⣀⠜⠒⠒⠒⠒⠠⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠴⠯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠤⠤⠤⠤⠤⢠⣀⣄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⣣
⠀⠀⠀⠀⠀⠀⠀⠈⡶⠠⠤⠤⠄⢀⡠⠤⠤⠤⠤⠤⠤⠄⠀⠠⠤⠤⠤⠤⠤⠤⠄⠒⠒⠉⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠠⠤⠤⠤⢀⣀⣀⡀⠀⠤⠤⠤⠆⠀⠒⠒⠀⠰⠶⠦⠠⠤⠤⠒⢚⢇⣀⡀
⠀⠀⠀⠀⠀⢠⡖⠂⠙⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠀⠐⢒⣒⣉⣩⡌⢤⡼
⠀⠀⠀⠀⠀⠀⠙⢍⡉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉⠉⠉⠁⠀⠀⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠂⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢿⣷⡆⠘⠃⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣈⠉⠃⣠⡶⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⠿⢿⣿⣠⣷⠌⠉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣏⣀⣾⣿⣿⣿⣷⣶⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠯⣿⣿⣟⡛⠿⣟⠿⡿⣟⣻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⣙⣛⣃⣴⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢶⣶⣤⣤⣀⣀⣈⣀⣛⣀⣀⣬⣿⢻⣿⣶⣿⢿⣿⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣴⡀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⣿⡿⡍⢙⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠛⠲⠶⠦⢧⣀⣀⣀⣬⣤⣤⣼⣿⣷⠞⠿⣿⠋⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣶⣦⣀⣁⣀⣉⣤⣤⣭⣧⣽⣿⣧⣴⣶⣿⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣅⣀⠀⠀⠩⠍⠉⠉⠉⠩⠉⠉⠻⠝⢻⠋⢉⣡⣿⣥⣾⢿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⠶⢶⠶⠾⠷⠶⠾⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⠛⠃⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⠀⠈⠙⠲⣶⡚⣶⣶⣦⣁⣀⡀⠀⠀⣀⣼⣧⣽⣿⣿⣿⣉⣻⣿⣷⣀⣤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠢⠭⠭⠭⠭⢤⡄⢀⡰⡶⠆⣀⣤⣤⣤⣴⠶⠶⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⣺⣩⠗⠒⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡒⠋⠉⠑⠂⠀⠀⠀⠀⠒⠋⠩⠟⣒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⠍⠊⠁⠀⠀⢀⡀⣀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠈⠐⠩⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠊⠀⠀⠀⣄⠘⡀⠄⠸⠉⠃⠀⠀⠒⠚⠇⢈⢁⠆⠀⠀⠀⠀⠑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⡫⠊⠀⠀⣄⣋⠣⠋⠁⠀⢀⡀⠤⠀⠄⠠⠄⠠⢄⠀⠀⠁⠙⠧⡯⢀⡀⠀⠑⠝⢆
⠀⠀⠀⠀⠀⢀⡞⠕⠀⠀⠠⠄⡘⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠹⢁⠦⠀⠀⠊⢳⡀
⠀⠀⠀⠀⢀⡞⠈⠀⢀⡈⠀⠂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠪⢠⠀⠀⠡⢳⡀
⠀⠀⠀⠀⣸⠙⠀⠀⢄⣻⠋⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⣹⡇⠀⠀⠋⣧
⠀⠀⠀⢠⡇⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⢸⡀
⠀⠀⠀⢸⠘⠀⣤⢤⡀⢠⠤⡤⠀⣤⣤⠠⡄⠀⠀⢀⣄⠀⢠⡤⣄⠀⢠⡄⠀⢤⣤⠄⢠⠀⡠⢤⡀⣤⠀⣤⠀⡏⡇
⠀⠀⠀⢸⠀⠀⣿⠀⢿⢸⠖⠀⢠⡀⠀⠀⠇⠀⠀⣼⣹⡄⢻⠦⡟⠀⣾⣿⡀⠀⡇⠀⢸⠠⡇⠀⡇⣿⢡⣭⠀⠀⡇
⠀⠀⠀⢸⣰⠀⠛⠛⠁⠐⠛⠓⠈⠓⠚⠀⠛⠛⠐⠃⠀⠓⠘⠀⠙⠘⠁⠀⠃⠀⠃⠀⠘⠀⠐⠛⠁⠛⠀⠛⠀⢧⡇
⠀⠀⠀⠘⡇⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢻⡠⠀⠀⠨⡇⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣠⣤⠙⠀⠀⢄⡏
⠀⠀⠀⠀⠀⢷⢃⠀⠀⠃⠋⢀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⡐⠢⡈⠁⠀⣜⡞
⠀⠀⠀⠀⠀⠈⢳⡡⡀⠀⠒⢀⣦⢄⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⣀⡎⠉⠊⠀⢀⢌⡞
⠀⠀⠀⠀⠀⠀⠀⠙⣔⢄⠀⠀⠐⠿⢲⡤⢀⡀⠀⠁⠒⠂⠀⠀⠐⠂⠈⠀⠀⢀⣠⢢⡧⠉⠀⠀⡠⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⠄⡀⠀⠈⠀⠠⣀⡅⢰⠤⠦⠀⠀⢤⣠⡒⡴⠈⠄⠐⠀⠀⢀⢄⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⣖⡤⠀⠀⠀⠀⠉⠐⠋⠀⠀⠀⠉⠉⠀⠀⠀⣀⢄⣢⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⢥⣆⣂⣀⡤⠤⠤⢤⣀⣐⣢⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⣉⣉⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⣶⣶⣶⣶⠿⣿⣿⡟⣤⡀⠀⠈⠉⠂⠀⠀⠀⠀⠀⢀⡼⢊⣿⣷⣶⡒⠲⡶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢿⣿⣍⣉⣀⣀⣠⣤⣤⡈⠓⢮⣿⣷⣶⡆⠀⠀⠀⠀⢀⣠⣴⣾⣋⣉⡉⠹⣿⢸⠀⠒⠈⠉⢉⣉⡛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠛⠓⢲⠂⠶⠤⠄⠀⣍⣳⣦⢸⡏⠀⣈⠀⠀⠀⠈⠀⢀⣹⡿⠁⠨⠭⠶⠶⢿⣧⢳⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠂⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⣿⣀⡇⠀⢉⣀⣀⣠⣤⡤
⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠙⠛⠛⠛⠓⠒⠒⠒⠒⠲⠾⠿⠿⠿⠷⠀⠀⠠⠤⠀⠰⠶⣾⠷⠶⠒⠒⠛⢻⣿⣾⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠘⠿⣿⣿⣿⣾⣿⣷⣶⣦⣤⣀⣠⣤⣄⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣀⣀⣸⣿⣷⣤⣤⣴⣶⣶⣶⡶⠀⠀⠀⠊
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠻⠭⠍⢙⡛⠻⠿⠿⠿⢿⣿⣿⠿⠁⠴⠀⠠⠄⠀⣼⣿⠃⠙⢿⠿⠿⠿⠟⢿⡿⠻⢿⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠈⠀⠀⠀⠰⠂⠉⠁⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⢠⡶⠂⠀⠀⠀⠀⠚⠒⠀⢸⣇⠀⠀⠙⠇⠀⠀⠀⢀⠀⠄⠀⡐⠃
⠀⠀⢀⣤⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢩⣧
⠀⢠⠋⢸⣿⣦⣁⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⢻⣶⣄⡀⠀⠀⠀⣀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⢀⣀⣠⣴⣿⣿⣦
⠀⢸⡄⠀⠙⢿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠛⠛⠛⠛⠳⢿⣿⣭⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡟⢀⣾
⠀⠘⣿⡳⢤⣀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⡞⣇⠠⠄⠁⠀⢀⣠⣤⣤⡏⣥⣤⣤⣤⣤⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⠿⢛⡩⠔⢋⡿
⠀⠀⠈⠻⠶⠈⠙⠲⠦⣤⡄⠉⡉⠉⠉⠙⠛⠛⠻⠿⢿⣿⣷⣾⣿⣶⣿⣿⣿⣿⠿⠿⢧⣻⣿⢿⡿⢿⣿⡿⠿⠟⠛⠛⠛⠋⠹⠒⢊⣡⣴⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠒⠦⣶⣦⡄⢈⣙⠛⠒⠶⠶⠶⠶⠤⠤⣤⣤⣭⣭⡭⠉⠠⣤⣤⣤⠤⣤⠭⠤⠴⠄⠐⠒⠒⠛⠁⣀⣤⣤⣶⣤⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠻⠗⠰⣿⣷⠀⣴⣶⣦⡀⢤⣤⣀⣤⣤⣤⠀⣤⣤⠀⣰⣶⣶⣶⡆⢰⣶⣿⡇⠥⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠘⠛⠉⠉⠐⠓⠀⠛⠛⠀⠙⠛⠋⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢁⡀⠈⢁⣡⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠉⠛⠒⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠶⠟⣛⣉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢈⡴⠈⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡎⠀⠈⠔⢀⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠚⠒⠦⠔⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡰⠁⠀⣀⡎⠀⠀⠀⠀⠀⢀⣴⢆⡴⠆⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⢠⢢⠎⠀⠐⠶⢰⠀⠀⠀⠀⠀⣠⢟⣵⡟⢁⣼⡵⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠇⠀⡸⠃⠒⠂⠁⢀⡇⠀⠀⠀⠀⠘⠟⠋⢿⡴⠋⣞⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣾⣿⣿⣷⡄⠀⢸⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣴⣿⣿⣿⡋⠉⠙⢿⣦⡏⠀⠀⠀⠀⢛⡽⠋⣀⡼⠃⠀⠀⠀⠀⠀⢠⢞⡿⠁⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣤⣶⣿⣿⡟⣭⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⣠⣿⡵⢚⡽⢶⠀⣠⡶⣀⣀⣴⠟⣭⠀⢀⣄⡀⠀⠀⠀⣿⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠃⠀⠀⡼⢻⡇⢰⠿⢖⡡⣺⢯⢞⡝⣿⣡⡞⡱⢲⣯⠀⠀⠀⠀⠀⣿⣿⣦
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠘⡇⠈⠙⠉⠓⠃⠘⠉⠀⠉⠀⠋⠀⢧⣤⠴⠃⠀⠀⢀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣬⠤⠶⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡟⠋⠙⠛⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠤⠤⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢩⣆⠀⠀⠀⠀⣰⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⡇⢀⡢⢔⣤⠔⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠒⠀⠀⣏⣛⣵⣚⣁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠂⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠃
⠀⠀⠀⢀⠀⠩⠀⠒⣇⠀⠀⠄⢐⠀⢀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢈⠀⠉⠀⠀⠀⠘⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠄⢂
⠀⠀⠀⠨⠘⠀⡀⣀⠌⡇⠁⠀⠀⢀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⢀⠁⠀⠀⠀⠀⠀⠀⢀⠂⠠⠤⢁⣓⣦⢾⢤⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠁⢀⠐⠓⠀⠀⠀⠀⠀⢀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡠⠤⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⣀⣛⣲⣶⡅⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⢲⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠒⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠀⢸⠻⣴⡇⠃⡆⠆⡂⡆⣷⡄⢸⠁⡀⣶⠠⣄⢹⠀⠀⠀⠀⠀⡆⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠨⠤⡀⠐⠀⠀⡄⠀⢀⠰⠀⠀⠈⠀⠀⠀⠘⠈⠉⠁⠀⠁⠀⠁⠁⠋⠑⠘⠀⠁⠉⠀⠈⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡀⠀⠁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠒⠊
⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠅⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⣀⠀⢠⣀⡄⠀⠀⠀⠀⢀⡀⠀⢤⣀⢄⠀⠀⡶⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠈⠑⠀⠀⠀⠀⠈⢇⠀⠀⠉⠀⠀⣰⡇⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠶⠶⠶⠛⠋⠁⠉⠉⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠈⣉⠉⣉⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠂⠀⠀⠐⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠦⠤⠀⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡈⠀⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⣠⠊⢀⠞⠁⣠⣤⣶⢆⣸⣷⣷⡀⠀⠀⠀⡀⠀⠀⠈⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⣄⣦⠓⢠⠤⣖⡈⠁⠄
⠀⠀⣶⣦⣀⡠⢧⠰⠆⢀⣼⣯⡉⠗⠾⢇⣻⣏⢠⠀⡀⡴⠁⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡱⠤⠶⠂⣁⣬⡥⠥⠥⠐
⠀⠀⠈⠙⠄⠈⠠⠀⠐⠲⢦⣭⣶⣤⣥⣬⡴⣦⠾⠿⠛⠁⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣑⠒⠖⠤⢤⣀⣠⠴⠒⠁⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠢⠤⠤⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣤⣚⠻⢿⣿⣿⣮⣛⢛⣛⣩⣭⣤⣍⢻⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣭⡛⢿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣶⣭⡛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢟⣛⠻⠿⠿⣿⣦⡙⢿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡱⣯⡟⣰⣿⣳⡎⣿⣿⣮⡻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢉⣋⣜⡛⢛⣱⣿⣿⣿⣷⡜⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣜⠿⡽⢏⣼⣿⣿⣿⣿⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⢻⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⢿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⢀⣴⡿⢋⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⣿⣇⠀⠀⢀⣴⡿⢋⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⠟⢀⣴⡿⢋⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠞⢃⣴⠟⢋⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢀⣴⠿⢃⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⢀⣴⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⡄⢠⣾⣿⣿⣶⡿⢋⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣈⣁⣀⣀⣉⣉⣈⠀⣼⣿⣿⣿⠏⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢸⣿⣿⣉⣉⣉⣉⣉⣉⣉⣀⠛⣉⣡⣤⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠟⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡍⢉⡛⠻⢿⣯⣷⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣟⣿⣿⣿⣿⣿⣶⣇⣘⣻⣿⣷⣿⣯⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡾⢿⡟⠛⣿⣿⣿⣿⣿⣾⣿⣿⣯⣯⣭⣽⣿⣿⣾⣶⣿⣽⠛⢻⣼⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠉⣿⣿⣷⣹⣷⣶⣿⣿⣿⣿⣿⣻⣿⠿⣻⣿⣿⣿⣯⠶⣯⣿⣿⣶⣶⣯⣿⡆⠈⠙⠲⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣷⣾⣿⣿⡟⠻⣿⣿⡿⠿⠿⠿⠿⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⠉⠛⠤⣀⠀⠀⠀⠉⠉⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⣧⣽⣿⡿⣿⡇⢰⡿⠉⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠋⠙⠛⠛⠻⠿⠷⢿⣿⡃⠀⠀⠀⠙⠒⠢⠀⠀⠀⠀⠀⠀⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⣹⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⣠⣤⣤⣤⣄⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡄⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠇⢶⣈⣿⣿⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠛⠟⠁⠀⠉⠋⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣾⢰⣆⢻⣿⡇⣸⣿⣿⠃⠀⠀⠀⠀⠀⡀⠴⠚⠉⠙⢷⣦⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢸⡇⠱⠀⠀⠀⠀⠀⠀⠀⣀⢾⣿⣸⠏
⠀⠀⠀⠀⠀⠀⠀⣿⢀⡻⣿⣿⡇⢻⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⣷⠀⠅⠘⢧⣤⣄⠀⣀⣴⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡟⠈⡳⣼⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣸⡿⢀⠇⠀⠀⠉⠙⠋⠉⠁⠀⠀⡞⠀⠀⠀⠀⠠⣾⠶⣣⣾⠟
⠀⠀⠀⠘⡀⠀⠀⣿⠘⢿⣤⣿⣿⡟⢿⣧⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣴⡿⠟⢁⣌⣀⣀⣀⢀⡀⠀⠀⢀⡀⣠⠎⠀⠀⢠⣴⣿⣟⣾⡿⠃
⠀⠀⠀⠀⠑⠀⠀⢸⣆⡀⠉⣠⣿⣿⣾⣿⠷⣤⣀⣀⣄⣀⣀⣠⣄⣀⣀⣤⠔⠋⣠⣤⠀⢴⡞⣡⣾⠟⠛⠁⣀⠰⣄⣤⣼⠟⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⣿⣏⣾⣿⠧⣠⠤⠋⢬⣥⢤⣝⣥⡈⠻⡟⣽⡇⢰⡏⠀⠀⡎⣶⠟⠀⠀⠀⠀⣹⡇⣿⡟⠁⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠱⠒⢣⣀⡀⠢⣈⢳⣤⠔⠛⢳⡼⠇⣅⠸⣇⠀⠀⢣⠁⡀⡀⣀⣠⣾⢟⣴⡿⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠛⠟⠀⣔⢡⣀⣁⡤⣒⡒⡷⢤⣼⣦⣙⡻⣃⠀⠧⣬⣝⣛⣭⣴⡿⠛⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠨⠉⠱⠶⠗⠋⠉⠀⠀⠀⠀⠀⠈⢉⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠐⠂⠀⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⣀⣀
⠀⠀⠀⠂⠀⠀⠀⢈⠘⠓⠓⢑⠐⠀⠀⠊⠀⠀⠄⡀⠈⠀⡆⢀⡀⠀⠀⠧⠃⠀⠀⠀⡰⠀⢀⠄⠠⠀⠀⠨⠒
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⣀⠀⠀⠀⡀⠀⠂⠠⠐⠁⠀⠠⠀⠀⠠
⠀⢠⡦⠠⢄⠀⠀⠄⠠⠁⠀⠂⠀⠀⠀⡔⢉⢀⠄⡐⢢⣤⣾⠀⠀⢠⠤⠀⠢⡀⠀⠀⠀⡠⠄
⠀⢨⡀⠂⣨⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠚⠈⠊⠉⠈⠀⢈⠀⠀⠀⢇⡀⠠⠅⠀⢀⠞⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠻⢰⡑⠏⠘⠑⠆⠃⠑⢻⠀⠀⠀⠀⠐⠀⠙⠆⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠘⠀⠀⢀⡀⠀⠀⠀⠠⣤⠐⡀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠀⠰⠶⠒⠉⠀⠈⠂⠠⠀⢀⢘⠁⠁⠂⢠⠌⠂⢠⠀⠀⡆⠀⢁⡔⠐⠀⠀⢀⠄
⠀⡶⠀⠀⠀⠀⡀⠀⠀⣄⠀⡐⠛⠛⠂⠁⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⢸⠭⠉⢽⠀⠄⠧⠤⠬⠤⠤⠄⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠉⠀⠠⣤⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢂⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠂⠚⠞⠒⠂⠀⠀⣁⠤⠤⠄⠀⠀⠀⠔⠀⠀⡄⡘⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⢰⡀⢀⡰⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠐⠂
⠀⠀⠀⡉⠀⠄⠄⠀⠀⢠⣤⡄⠠⡖⣲⠀⠀⠀⣀⢀⢰⣀⢀⣄⢠⣄⢴⠐⡗⠀⢀⠀⠐⠲⠂⠀⡄⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⣀⠇⠏⠸⠯⠛⠚⠛⠈⡇⠈⠙⠚⠁⠑⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠙⠀⠀⠃⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⡠⠤⠄⠀⢤⠀⠀⠀⠀⡀⠀⢀⠟⢒⠂⡇
⠀⠀⠀⡁⣘⣛⣋⢀⠀⠀⠀⠀⠎⠀⠀⠝⠂⠀⡈⠚⠐⡂⢀⠀⠄⡀⡴⡘⠠⠀⠅⠠⠂⢀⡐⠀⠈⡦⣀⡠⠃
⠀⠒⠀⠁⠀⠀⠀⠀⢀⠈⠁⠀⠄⠀⠠⠤⠀⠀⡀⠀⠸⠀⠐⠀⠀⠀⠀⣀⡀⠀⠀⠁⠐⠉⡀⠀⠀⠤⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠁⠉⠩⠉⢉⠉⡈⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠈⢀⡀⡀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠘
⠀⣄⠀⠀⠀⠀⠈⢁⡜⠁⠀⠀⠀⠀⠀⢈⠈⠉⠉⣉⠀⡀⠀⢤⡤⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠒⠒⢺
⠀⠉⠀⠀⠀⠀⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠒⠂⠘⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠳⠤⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡓⢶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠠⠀⠀⠀⠀⠀⡐⢺⣿⠛⣿⣿⣿⡅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⠛⠹⠄⠈⠙⠂⠀⠀⠀⠀⠀⠚⠻⠟⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⢀⣼⣿⣧⡀⠀⣠⡄⢀⡉⣽⣿⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣴⢾⣿⣿⣿⣿⣿⣿⣷⣬⣵⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣉⠀⡬⢹⣿⣿⣿⣿⣧⣿⡇⠆⢀⡄⠀⠐⠀⠀⠀⣨⣷⢶⢄⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣦⣾⡏⣀⡀⠀⠀⣴⣿⣿⣴⠟⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠈⠙⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⣦⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣿⣿⣿⣏⣀⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠋⠘⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣆⠀⠀⠀⠀⠤⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠈
⣿⣿⣧⠀⠀⠀⠀⠀⠘⢷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢦⡆
⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠇⠀⠀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢻⡟⣿⡆⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠘⢧⣈⠁⠤⠀⣻⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠈
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾
⠀⠀⠀⢀⠀⢉⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠶⠶⠶⠶⠶⠦⠒⠒⠶⠶⠶⠶⠶⠤⢤⡴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠝⠋⠲⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⣸⠉⣹⢀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠘⣌⠉⢁⠜⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠰⠀⠄⡄⢀⠀⢈⣉⢉⣉⠒⠒⠒⠒⠚⠋⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠰⠄⠐⠀⠀⡀⠀⡀⠈⠀⠈⠉⠀⠘⠁⠘⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠤⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠉⠀⠒⠀⠀⠂⢤⠀⠠⢤⢠⡀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠠⠄⠀⡀⢀⠠⢤⠀⡈⠀⠀⠈⠉⠀⠛⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡄⠀⢀⠁⠈⠀⠉⠈⠃⠈⠉⠋⠑⠇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠁⠠⠀⠱⠀⠀⠂⠐⠂⠀⠀⠤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡀⢀⠀⠀⣓⡶⠶⠛⠀⢠⡔⠚⠋⠷⣄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠤⠤⣄⣀⠀⠀⠂⠀⠀⠀⢸⠀⣉⠀⡀⢸⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠲⠾⠷⣬⠁⢰⠿⣶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⣇⢨⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣶⣼⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⢀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐⠒⠉⠀⠀⠈⠑⠒⠒⠛⠂⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⣀⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣈⠒⢆⠀⠀⠀⠠⢶⠀⠀⠀⣀⠠⠤⠤⠄⢐⣈⡡⠴⢦⡉⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⡝⠀⠘⠓⠒⠆⠀⠐⠛⠒⠀⠉⠉⠀⠀⠀⠀⣀⣤⠧⠞⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠃⠈⠉⠒⠒⢇⠀⠐⠒⠒⠒⠒⠒⠂⠈⠉⠁⠀⠀⠐⠠⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠢⠠⠄⢀⣀⣀⣸⠀⡀⣀⣀⣠⣤⠤⠤⠤⠐⠒⠈⢳⡄⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⡓⠀⠤⣄⣀⣀⣸⡄⢀⣀⣀⣀⣀⡠⠤⠤⠖⠒⠂⠉⢀⡠⠔⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⢤⣀⠁⠒⠤⠤⣤⣀⣈⡇⠀⢉⣀⣀⣀⣀⣠⠤⠤⢆⣲⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡦⢈⠙⠒⠠⢄⣀⣀⠀⡃⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠚⠑⠀⠀⠃
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠻⣄⣀⡀⠀⠞⠆⠈⠢⣌⡲⠊⠀⠀⢀⣀⡃⠉⠉⣉⣉⣉⣀⣠⣤⡼⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠈⠷⢀⠀⠀⡐⠊⠀⠀⠀⢀⠀⠀⠀⢀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣄⣀⣀⡀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠁⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠒⠒⠒⠒⠒⠶⠴⠶⠶⠒⠒⠒⠒⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠛⠋⠉⠉⣽⠿⠯⣉⣁⡠⠭⠝⢛⡿⠿⠿⠿⠛⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⣠⡶⣻⠟⠋⠁⠀⠀⢀⣀⠀⠀⠀⠻⢤⣄⣀⣅⣀⡤⠴⠞⠁⠀⠀⠀⠀⠠⢴⣒⠚⠋⠉⠻⠷⣤⡀
⠀⠀⣼⠋⣼⠁⠀⠀⢠⠔⠋⠉⠉⣹⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠈⢻⡄
⠀⢸⡟⠳⢼⣦⠀⢀⡏⠀⠀⢀⡴⠃⠀⠀⢀⡴⠛⠓⠶⣤⡀⠀⠀⠀⢸⡏⠙⠳⣤⡀⠀⠀⠀⠀⠈⠙⣷⠟⣷
⠀⢈⣷⣄⣀⣼⠁⡼⠳⢦⡾⠋⠀⢠⣤⠶⠞⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠳⣄⣀⣈⣿⢦⣄⣀⠀⠀⢠⣇⣰⡏
⠀⢸⣇⠀⠉⡇⠘⢧⣤⣸⣇⠀⠀⠸⡏⠙⠛⠛⠛⠻⠷⠶⠶⠒⢻⠄⠀⠀⠀⠙⡇⠀⣀⣀⣼⠆⢠⡟⠉⢸⡗
⠀⢸⡟⠓⠶⢿⠀⠈⡇⠈⠙⣆⠀⠀⢻⠤⠤⣤⣤⣤⣄⣀⣀⣰⡏⠀⠀⠀⢠⠾⠛⠋⠉⠀⣏⠀⠀⣳⠶⢻⣷
⠀⢸⣧⣀⠀⢸⠀⢠⡟⠓⠶⡿⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠘⣦⣤⠶⠖⢛⡏⠀⢰⡏⣀⣼⣧
⠀⣿⠉⠉⠛⠻⠧⢾⣄⣀⣸⠃⠀⠀⢸⡏⠉⠉⠙⠛⠛⠛⠛⠛⣿⠁⠀⠀⠀⠈⢧⠀⣀⣨⣷⠀⠀⢻⠉⢀⣿
⠀⣻⣧⣄⡀⠀⠀⠀⠀⠈⢹⠀⠀⣾⠿⠦⣤⣤⣀⣀⣀⣠⣤⣤⣬⣧⠀⠀⠀⢠⡟⠉⠉⠀⣿⠀⢠⣯⠴⠚⣏
⠀⣿⡁⠈⠙⠓⠶⠤⣄⣀⣸⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢰⠏⢀⣀⣤⡤⠿⠦⠏⠁⠀⣸⡟
⠀⢹⡿⠶⣤⣀⣀⠀⠀⠈⠉⡇⠀⠀⢳⠶⠤⠤⣤⣤⣤⣤⣤⡼⣇⠀⠀⠀⢸⡟⠋⠉⠀⠀⢀⣀⣤⡴⠞⣿⡁
⠀⢸⣇⠀⠀⠈⠉⠛⠳⠶⢤⣿⣶⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⣼⣡⣤⠶⠒⠛⠉⠉⠀⠀⣠⣿⠁
⠀⢸⡏⠙⠓⠶⣤⣄⣀⡀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠒⠒⠖⠒⠒⠛⢻⠀⠈⢫⡀⠀⠀⢀⣀⣤⠴⠖⠛⠉⣿
⠀⠘⢿⣦⣄⡀⠀⠀⠉⠙⠛⠶⠶⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣼⡆⠀⠀⡷⠚⠋⠉⠁⠀⠀⢀⣀⣴⠟
⠀⠀⠀⠈⠙⠛⠿⠶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠈⣧⠀⣼⠃⢀⣀⣤⣴⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠷⠶⠾⠿⠿⠛⠿⠿⠿⠿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣶⡿⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣾⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣾⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⣾⣿⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⣀⡀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠄⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢰⣿⠋⠉⠻⣿⡿⠋⠀⠹⣿⡇⠀⠀⠀⠀⣠⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣷⠀⠀⠀⠈⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⣀⣀⣤⣤⣶⡾⠿⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠙⢷⣄⠀⢀⣴⡿⠃⠀⠀⠀⠀⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠻⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⠶⠿⠟⠛⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣤⣶⡶⠾⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠚⠛⠁⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠶⠟⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⡶⠿⠿⠛⠋⠉⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠾⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⡟⣿⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⠋⠀⠉⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣶⣶⣾⣿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣀⣠⣤⣶⣾⡿⠿⠿⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣶⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣏⠉⣻⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣿⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠤⠤⠄⠀⠀⠀⠀⠠⠤⠄⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⠄⠸⠀⠂⠀⠀⠀⠀⠀⠘⠀⠚⠀⠣⠀⠇⠈⠂⠐⠈⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⢤⣤⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⠐⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠉⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡡⠔⠐⠒⠐⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢴⣀⠀⠀⠀⠀⣀⠀⠹⡄⠀⠘⠃⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⢉⠴⠁⢀⡄⡒⠂⠀⢒⠢⡄⠙⢆⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠻⢶⣦⣄⣾⠏⠀⢰⡇⠀⠀⢀⡤⠔⠚⠓⠐⠒⠒⠠⢀⡀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠀⡞⠀⠀⣴⣿⠁⠀⠀⠀⠑⢊⢣⡄⠷⠤⠒⠒⢛⡦⠀⠀⠀⠉⠲⣄⡀⠉⠉⢁⣀⣴⡟⠁⢠⠎⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠙⢢⡀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠰⠀⠀⢺⣿⠇⠀⢀⣠⣄⣄⡀⠄⣿⣶⡞⠛⠋⢉⣤⣤⣀⡀⠀⠀⠀⠉⠛⠛⠛⠋⠁⣀⠰⠁⠀⢀⠄⣨⣗⣀⠀⠀⠀⡀⢄⠀⠀⠹⡄
⠀⠀⠀⢀⡀⠀⠀⣱⠀⡼⡏⠀⠀⠀⠿⣿⣿⣁⢂⣿⣿⠇⠀⢀⣿⡟⡛⠙⠷⠀⠀⠀⣀⣀⠄⣀⡸⠯⡈⠀⠀⢀⠎⣾⡟⠋⠁⠀⠀⠐⢆⠈⠆⠀⠀⢱
⠀⠀⠀⠛⠋⠁⠘⢻⣇⠈⠓⢠⠀⠀⣀⣈⠙⣣⣿⣿⡟⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠈⠂⠼⠀⠑⠀⣀⠈⠀⢸⠀⣿⠀⠀⠀⠐⠀⠀⠈⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⠁⠻⠞⠻⣿⡿⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⠀⣀⡀⠀⠀⠙⠀⠈⢹⠀⠀⠈⠅⠸⡆⢀⠄⠀⠀⠀⠘⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣈⠙⠒⠲⠐⠒⠈⠁⠀⠀⠀⠀⡠⠄⠂⠁⠂⠀⠀⠁⠀⠂⠀⢙⡢⣀⠀⠀⠀⢣⠀⠀⠈⠮⡀⠐⠢⠠⠐⠀⣠⠞⢦⡀⢠⠇
⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣠⡨⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⣴⣏⠹⠇⢻⠄⠀⠀⠑⣄⠀⠀⠀⠉⠐⠒⠊⠉⠀⠀⢘⡵⠃
⠀⠀⡞⠀⠀⠀⣀⡤⣤⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⣼⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠀⣸⢿⢀⡀⢸⠀⠣⠀⠀⠀⠑⠢⢤⣀⣀⣀⣀⡠⠤⠚⠉⠀⢛⣲⣟⡁
⠀⠀⠇⠀⠀⢰⠃⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⣀⠀⠑⠀⠀⢰⣏⢨⢠⠉⡇⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣄⣀⣀⠀⠈⠉⠸⠟
⠀⠀⣆⠀⠀⠀⠓⠤⠴⠃⠀⠀⠀⡞⠀⠀⠀⠀⠇⢀⠐⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠛⠿⢸⠹⠇⠀⠀⠀⡆⠀⠀⠀⠀⠀⡊⡱⠂⠀⠠⠀⣉⡛⢷⣄
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢗⠳⠸⡚⡆⠀⠀⠀⠀⢠⠴⠶⠀⠀⣿⡛⠈⠀⠀⠔⠊⠻⡀⠙⣇
⠀⣄⠀⠀⠉⠒⠀⠤⠴⠒⠈⠀⠀⠀⠀⠀⠀⠈⡄⡌⠀⠀⠀⠀⠀⠀⣀⠜⠋⠀⠀⠀⢸⠖⡦⡔⣇⠀⠀⢀⠂⠘⠷⠾⠁⠀⢚⣷⠄⠊⠀⠀⠀⠀⠉⡀⢻⡆
⢰⠏⣅⠀⠀⠀⠀⠀⣀⣄⣠⣾⠛⠋⠻⣄⠀⠀⠡⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢶⡷⣧⣚⠀⡀⠄⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇
⠀⢧⠇⡀⠀⠀⢠⣾⡯⠉⠉⠦⣓⠀⠀⣾⠀⠀⠀⠱⡀⡈⠒⡀⢀⠀⠀⢀⡀⠀⣠⠃⣼⠋⡶⢡⢃⢂⠌⠀⠀⠀⣤⣾⡁⠀⠀⠀⠰⡷⡀⠀⠀⠀⣀⠁⣼⠃
⠀⠀⣾⠀⠀⣠⣾⠯⠀⠀⠀⠀⠈⠻⡟⠁⠀⠀⢀⠀⠘⠮⡐⠌⠀⠀⠈⠁⠈⠉⠉⠀⠈⢉⡩⠋⠀⠁⢀⡠⠂⠁⠜⠁⠀⠀⠀⠀⠀⠐⢾⠲⠖⠰⢧⡼⠃
⠀⠀⠁⠀⢸⡇⠀⠀⠈⣠⣀⣀⣀⣼⠇⠀⠀⢀⡟⠋⠓⢦⠀⠀⠠⢑⡒⠀⠠⠄⠀⠒⠈⠍⠀⠀⡠⠐⠀⣠⠜⠀⠀⠀⠀⣠⠐⣦⠀⠀⠀⠙⠢⠔⠉
⠀⠀⠀⠀⠸⢅⣠⣤⣠⡽⠛⠛⠋⠁⠀⠀⠀⠀⠰⣄⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠹⠶⠟
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⣀⣠⣀⠀⣀⣀⣀⡀⠀⣀⣀⠀⢀⣀⢀⡀⢀⣀⣀⡀⠀⣀⣀⠀⢀⣀⣄⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⣿⠁⣸⣧⡼⠃⣸⡧⠄⢀⣰⣏⣿⡄⣸⣷⠋⠁⢨⡯⡤⠁⣰⣏⣿⡄⠸⢷⣬⡁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠛⠀⠿⠉⠻⠀⠻⠷⠒⠀⠟⠀⠿⠀⠿⠈⠻⠂⠺⠃⠀⠐⠟⠀⠿⠀⠛⠶⠛⠁⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⡾⠧⢺⠐⠯⠀⢠⠾⠄⠀⢸⠗⠦⠦⢴⡃⠾⠄⠀⡾⠣⡴⠧⠴⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⣿⡿⠛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣏⣇⣠⣄⣀⣠⣤⣤⠄⣅⡤⣠⣤⢠⢶⠀⠀⢰⣊⡣⠐⣎⣑⠄⢲⣉⡦⢐⣎⡳⠄⣖⣙⠆
⠀⠀⠀⠀⠀⡏⠀⡸⠉⠙⠄⠏⠛⠛⠋⠈⠛⠉⠙⠉⠉⠉⠈⠃⠀⠈⠀⠁⠀⣁⡈⠀⠉⠈⠁⠈⠀⠁⢀⣁⣈⣄
⠀⠀⠀⠀⠀⠙⠊⠑⣾⠉⣟⡔⢻⣛⢷⡴⠒⠒⢶⡆⠴⣶⢰⢺⡧⢲⠒⠉⣉⣩⠟⡘⢹⣇⠐⢋⣛⠾⢉⠉⣉⠿
⠀⠀⠀⠀⠀⠀⠀⡄⣤⡉⢻⠇⣈⢩⣜⠁⠘⢻⡏⠰⢴⢸⣦⠈⠱⣇⠀⡀⣩⠽⠣⢹⠃⣿⣐⢌⠳⣄⠀⡀⣷
⠀⠀⠀⠀⠀⠀⠐⠄⠉⠡⠾⠄⡼⣆⢻⢇⢘⣛⣷⣆⡾⡀⣿⢀⡷⣹⡆⢁⡿⠀⠧⠟⢅⠽⢝⠳⣂⠟⠀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠠⣀⠀⠁⡠⣤⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢤⡀⠀⠙⢦⡈⠂⠀⡄⢈⡷⠄⠄⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠉⠉⠁⠒⠂⠄
⠀⠀⠀⠀⡠⠐⠚⢁⠀⠲⡀⠑⢀⠔⣸⠃⠀⢂⡴⠋⠀⣼⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡠⠖⠒⠤⡀
⠀⠀⡀⠈⠀⠀⣀⠀⠱⡀⠈⡰⢃⣾⣗⣥⠖⠓⠒⢈⣀⣷⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢰⠀⢠⡞⠁⠀⠀⠀⡝⠄
⠀⢠⠁⠀⠀⡀⠈⠢⠀⣠⠎⣰⠟⠉⠉⠀⠀⠈⠉⠛⠁⠈⠁⠀⠀⠉⠁⠂⢀⣀⣤⠔⠊⡉⠀⠇⣀⡴⡋⠀⠀⠀⠀⣸⠃⢸
⠀⢸⠀⠀⠀⠱⡄⠀⠔⢁⡞⡅⠀⠀⠀⠀⠠⠂⡀⠀⠀⠄⠀⠐⠄⠀⠀⠀⠈⠁⠠⠀⠀⣣⡴⠞⢉⠀⠁⠀⠀⢀⡼⠁⠀⣸
⠀⠈⡳⡀⠀⠀⠘⠦⣴⡋⠀⣇⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⣤⠴⠒⢛⠁⢰⠀⠀⠀⠀⣠⠞⠉⠀⠀⢔⠃
⠀⠀⠈⠪⡀⠀⡀⠀⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠈⠁⠀⠒⠒⠈⠀⠀⢀⠞⠁⠀⠇⠀⠈⠀⠀⠀⣀⡴⠟⠁⠀⠀⢔⡠
⠀⠀⠀⠀⠈⠑⠨⢑⡒⠤⠄⡀⠀⠀⠉⠓⠲⠤⠄⠀⠀⠠⠤⠒⠊⠉⠉⠁⠀⢀⣀⣀⣠⣤⠶⠚⠉⠀⠀⡂⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠀⠭⠉⣑⣒⣒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣂⣈⠉⠥⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡀⠑⢧⠀⡐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠁⠀⢀⠀⠈⠀⠘⡷⠚⠒⠺⡗⠈⠠⠤⢄⡈⠍⠓⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠁⣠⠔⠈⠁⢳⡄⠃⢄⣼⡁⠀⠀⠀⣷⠄⠁⠀⠀⠈⠐⡀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢄⡀⢠⠁⠀⠀⠀⠀⠙⠓⠛⠛⠷⠦⠴⠚⢉⡀⠀⠀⠀⡤⠀⡽⠀⠀⣠⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⣄⠙⠺⡀⠈⠀⠁⣀⣀⣀⠀⠀⣀⠤⠞⠓⢒⣒⣒⣦⣄⠀⣰⠥⠒⠉⣀⠜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠦⣌⠓⠦⣤⡀⠀⡎⠉⠉⠉⢣⢰⠓⠒⠂⠈⠁⠈⠉⣁⣹⢀⣥⠴⠖⠋⢁⡠⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡈⠓⢦⣀⡇⢸⠉⠙⠛⠛⢻⠘⡟⠛⠛⠛⠛⠋⠉⠉⣉⣛⣡⠤⠂⠉⢁⡠⠚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⡛⠶⢤⣄⣇⠘⠒⠂⠐⠒⣾⠀⡗⠒⠒⠒⠒⠒⠊⠁⠀⢀⣀⡤⠴⠚⠉⢀⡴⣿⡀
⠀⠀⠀⠀⠀⠀⢀⠴⠊⢠⢧⡈⠙⢦⡈⢹⠀⠟⠓⠲⠶⠿⠾⠷⠦⠤⠴⠶⠖⠒⠚⠋⠉⠁⢀⣠⠴⠚⢁⡴⢣⠉⠲⡄
⠀⠀⠀⠀⠀⢠⡇⠀⠀⡌⢆⠙⠢⣄⣈⣹⢸⠓⠒⠤⠤⠤⠦⠤⠤⣤⣤⠤⠔⠒⠒⠛⠋⢉⣉⣤⠴⠚⢁⣠⢺⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⢦⡉⠒⠤⣉⢧⣸⠷⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠒⠛⠉⠁⣀⡤⠛⢉⣠⠞⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠉⠳⢦⣬⣁⡒⠀⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠈⠉⢉⣉⣡⠴⠖⠋⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣍⣉⣛⣛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢒⣛⣛⣉⣥⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠭⠭⣭⣍⣉⣉⣛⣛⣉⣩⣭⡭⠭⠵⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⢶⡶⣶⣶⣶⡶⠀⢸⣿⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣶⣶⣶⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣴⡾⠟⠛⠿⣶⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠘⣿⡀⠀⠀⢶⣄⣠⡾⠋⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠹⠟⠁⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⠆⠐⠶⠶⠆⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠙⠛⠁

⠆⠀⠁⠠⠀⠀⠐⠀⢶⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⡀
⢀⠀⢀⡠⠔⠁⠈⠂⠨⠈⠃⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⡀⡀⠀⣀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠑⡆
⠀⠁⠀⠀⠀⠀⢀⠀⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄⠀⠀⠈⠑
⠀⠀⠀⠆⢤⠔⣠⣂⠐⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄
⠀⠀⠃⠁⠀⠨⠀⢠⠎⠠⣀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠀⢻⡿⠃⠀⠀⠀⠘
⠀⠐⡅⡀⠀⠈⠐⢸⣂⠞⣧⠐⠨⠂⠀⠀⡀
⠀⠀⠀⠀⠂⡀⠀⡸⠁⠠⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠦⠡⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢑⡂⠀⠄⢛⠀⠀⠀⠀⠀⠀⠀⠀⡶⠖⠲⠶⢦⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⠃⣜⣷⡶⢢⠉⠶⠀⠀⠀⠀⢌⣀⣼⠀⠀⠀⢤⠀⢸⣷⡄⠀⢀
⢠⠂⢉⡈⠳⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⠰⠷⠌⠛⠾⠋⠘⠁⠄⠂⠀⠀⠶⡏⠨⣹⡄⡀⠀⠊⠠⡿⣿⣿
⠘⡄⠚⠋⠀⡆⠀⠀⠀⠂⠀⠁⠀⠐⢱⢀⠀⠀⠀⠈⠂⢀⠀⣤⠈⣤⡀⠊⠀⠀⠀⡾⠁⠀⠀⠀⠂⠀⠀⠀⠀⢀⠙⡇
⠀⠉⠒⠂⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡐⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⡸⠀⢀⠀⠀⠀⠸⠠
⠀⠐⣦⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡓⠁⠀⠀⠄⢀⡤⠽⠆⠐⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⣀⣼⣣⣀⣄⠄⠀⢀⠂
⠀⠎⠀⢻⠓⣄⠀⠀⠀⠀⠐⠀⢠⠼⠛⠁⠀⠀⣠⠖⡏⡠⠂⠜⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠁⠈
⠀⠀⠀⠆⠀⡞⢣⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢐⢼⠀⢧⡁⠀⡀⠀⡸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀
⠀⠀⠀⠅⠀⢣⠈⠍⠀⠘⠁⠀⠀⠀⠈⠤⠝⠐⠈⠳⢄⠳⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⢀⣐⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠘⠆⠀⠀⠀⠺⢿⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣦⣤⣴⣶⣇⠀⠀⠀⠀⠀⠀⣹⡧⣄⡀⠀⠀⠀⣠⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠁⠽⣿⣿⠟⡿⢷⠦⠴⠦⠔⢎⣋⣠⡂⠉⣓⠛⠻⠿⠔⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⣶⣦⣄⠈⠘⠋⢉⣁⣈⣀⣀⣉⣉⠉⠉⣉⣉⣀⣤⡴⠞⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⠻⠿⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⡿⣿⢿⣻⠟⣉⣤⣶⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠶⢾⣿⣿⣶⣶⣶⣦⣤⣤⣀⠀⠀⠉⣉⣠⣾⣟⠯⠜⠋⢁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣤⣀⣀⣀⣈⣉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠀⠀⠄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠉⣉⣛⣉⣉⣉⡉⠉⠉⠉⠛⠛⠛⢋⣉⣉⣩⣤⣶⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⡿⠿⠛⣇
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⠿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣈⣉⣉⠉⠉⠉⠁⠈⠉⠉⠁⠙⠁⢁⣀⣤⣤⣴⣿⣭⣶⡄
⠀⠀⠀⠀⠀⣰⣝⢻⣿⣿⠛⠳⣄⡈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣨⣿⣿⡻⣟⣅⡄
⠀⠀⠀⠀⠀⠹⡏⠑⠛⣿⣿⣿⠋⠙⠿⣶⣤⣤⣤⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣉⣉⣉⣉⣉⣀⣤⣴⡾⠛⣸⣿⣿⠏⠨⡃
⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠉⠉⠓⢄⣀⠀⠉⠉⠉⠉⠛⠛⠻⠿⢿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠋⣉⠤⠚⠋⠉⢀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠁⠀⠒⠒⠂⠀⠠⠤⣀⠀⢀⠀⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢦⣤⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⠏⠡⠈⠦⠍⠹⠰⠣⠼⠉⠛⠒⠛⠉⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠢⠀⠀⠆⠐⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠿⠿⠛⠙⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠩⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢦⠀⠘⠣
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠄⠀⠈⠀⠀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣤⡄⠀⢀⣤⣤⣤⣄⠀⠈⣷⣄⠀⠀⠀⢠⢤⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⠀⠘⢹⣷⠦⣍⠦⠄⠈⣿⣷⠶⣦⣼⢀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⠏⢡⠁⠀⠀⠈⠃⠀⠀⠀⠀⢀⣿⡝⣻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⡀⢧⣄⣤⣰⡄⠀⠀⠀⠀⠀⠈⢿⡛⢩⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡇⢿⣋⣀⣀⡑⠀⠀⠀⠀⠀⠀⠘⠋⠁⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣧⣹⣯⡅⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⠀⠀⠀⣀⣀⣠⠔⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠃⡀⢀⡜⣸⠃⠀⠁
⠀⠀⠀⠰⢯⡤⠀⠀⠈⣙⣶⣶⣿⣿⡿⠕⠐⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⠖⠋⡕⠀⠃⠉⣠⠆
⠀⠀⠀⠠⢾⠧⣀⡄⣾⣿⣿⣿⣯⣧⣀⠔⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⡂⠠⠄
⢀⠀⠀⠀⠠⣄⠚⣠⣿⣿⣿⣿⣽⠛⠙⣈⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡐⠂
⠈⠁⠀⠀⠠⠘⡍⣹⣿⣿⢿⣿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⠢⣈⠃
⠄⠀⠀⠀⠀⠈⣱⣿⣿⡟⡋⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡳⣽⠫⠮⠙⠢⢀
⠀⠀⠀⣠⣴⣾⣿⣿⠟⠝⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠋⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣾⣿⣿⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⣠⠏⠟⣿⣿⡿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠻⠉⣿⠁⢉⠗
⡁⠀⣠⠿⠟⠀⠀⠀⣠⣿⡿⠋⠀⢛⠭⣿⠿⠍⠀⠘⠏⠀⠀⠀⡏⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠏⠁⠠⠀⠀⡸⠃⠀⠀⣠⠋⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠚⠁⠀⠀⠀⠀⠀⠐⢦

⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡤⢶⣶⣶⣶⣿⣿⣷⣦⣬⣍⡁
⣿⣿⣶⣾⡿⠟⠋⠁⠀⠀⠀⠈⣩⡟⠁⠉⠉⠉⠉⠛⠛⠿⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢰⡀
⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⣠⣶⣿⣶⠀⠀⠉⠻⢦⢔⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⡞⠉⢠⡀⠀⠀⠀⠀⠐⠆⢠⡟⠛⠉⠛⠀⠀⣀⠀⠀⠉⠯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣦⢠⡀
⠀⠀⠀⠀⠀⠘⠤⠇⠀⠙⠃⠀⠀⠀⢀⣠⣤⣟⠀⠀⡄⣀⣄⠀⢯⡀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣯⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⡧
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⡠⠀⠰⠂⠀⠀⠈⠁⠀⠀⠁⠀⠀⠺⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣛⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡛⠻⠶⠊⠁⣀
⠀⠀⠀⢠⣾⣿⡄⠹⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠃⠀⠀⠀⠀⢠⣼⣧⡀⠀⣿⣿⣿⣿⣿⠿⠛
⠀⢀⣴⣿⣿⠷⠙⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡧⠀⢸⣿⣿⣿⢏⣰⠃
⠀⠘⣿⣿⡇⠀⠀⢀⢠⣿⡄⠀⠀⠀⡀⠀⠙⣿⣿⣿⣷⣾⣿⣆⠀⠀⠀⠀⣠⡟⣿⣿⣷⣦⣄⡀⠀⠀⣠⣾⣿⣄⢲⡦⣀⣰⣴⣿⣿⣿⠇⠀⣸⣿⣜⣿⣬⣧
⡀⠀⠘⣿⣷⡀⠀⠀⠃⢙⣿⣦⡄⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠏⠀⣭⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣴⡿⣻⣿⣯⢻⡋
⣷⡀⠀⠻⣿⣿⣶⣶⣾⣿⣿⣿⣿⣶⣶⡿⠋⠉⠹⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠛⠛⠉⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⡿⠏⣁⠴
⠻⣿⣄⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⣠⣤⣴⡾⠟⣿⣟⠛⠋⠢⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⠏⠐⠁
⠀⠙⢿⣷⣤⡀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢉⣙⡉⠀⣠⡾⠷⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠦⠜⠉
⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⠉⠁⠌⠙⠛⠋⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⣄⡀⠀⠀⠀⠉⠙⠻⣿⣿⣷⣶⣶⣶⣤⣤⣴⣶⣶⡾⠿⠿⠛⠉⢁⣀⡀⣀⢴⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖⠊⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠐⢿⣿⣿⣿⣿⣿⡼⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠉⠛⠲⣄
⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣟⠛⢧⡀⠀⠈⠻⠿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣶⡄⠀⠈⠑⢴⣀
⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⣟⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣶⣀⠙⣿⣿⣿⣿⣿⣇⢀⢰⡇⠈⠙⢻⣷⠒⡀
⣿⣿⣿⠿⠛⠁⠀⠀⠀⢀⣀⣠⣴⠶⢛⣻⣧⣾⡿⠿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣬⣷⣿⣏⢁⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠿⠟⠛⠳⠦
⠿⠋⠀⣠⡀⠀⠀⠀⠀⢉⣉⣤⣤⠶⠟⠛⢉⣡⡶⠿⡇⠀⢀⣼⣿⣦⠄⠀⠀⠀⢀⣠⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⣀⣿⣿⡶⠶⠒⠛⠋⠉⣀⠀⠀⢶⣿⣿⡿⠃⠀⠁⣤⡉⠉⠉⠀⠀⣠⣀⠀⣿⣟⠻⢿⣀⣩⣿⣿⣿⠛⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠉⢹⣿⢶⣤⠀⠀⠀⢸⣿⠀⠀⠈⠛⠉⣠⣄⣀⣴⣿⣿⣿⣿⡆⣼⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢹⣏⢺⣻⣥⣶⣤⣼⠋⣳⡄⠐⢾⡛⠦⠈⠉⢹⣿⣿⣿⠙⠉⠿⣯⡁⠀⣿⣿⡋⣩⣿⣿⣿⣿⣿⣿⠏⢹⡿⠿⠿⣿⣿⣿⣿⣷⣿⣶⣾⣤
⣼⠀⢠⡾⠛⣻⣿⠻⠿⠿⢿⡏⠉⠀⣾⣿⡇⠀⣴⠄⢹⣿⣿⣿⣤⡀⠀⠠⡄⠀⣿⣿⣿⣿⣿⣧⡌⣿⡟⠁⣸⣿⣶⣤⣾⣿⣿⣿⣿⣿⣟⠛⠛⠛⠲⣶⠄
⣿⠀⣿⣷⣸⠷⢿⡄⠀⠀⠀⠿⠀⠀⠹⣿⠿⢾⠧⢀⣸⣿⣟⠛⣏⢡⣠⡈⠁⠀⣿⣿⣿⣿⣿⣷⠿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⡶⣤⣴⢛
⢸⣇⠹⣿⣿⣷⣾⣷⣤⣀⣴⡆⠀⠀⠀⠛⠦⠘⠛⣿⣿⣿⣿⣤⣿⣧⣍⣳⣦⠀⠉⢘⣿⣿⡟⣁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠏
⠀⢻⣧⡙⢿⣿⣏⠉⣛⢉⣼⣆⠀⠀⠀⣠⣄⣤⡀⠻⠿⣿⣿⡟⢻⣿⣿⠿⠏⠀⢶⣶⣶⣴⣶⠿⠟⠛⠉⣻⣿⣿⣏⠉⣿⣿⣿⡿⣿⣿⣿⠿⣟⠄
⠀⠀⠙⢿⣦⡻⠿⣴⣿⣿⣿⣯⣀⣛⣷⣿⡟⠉⠁⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣏⣥⣵⣼⡅
⠀⠀⠀⠈⠙⢿⣶⣄⡈⠉⠉⠉⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠿⠿⠟⠛⠉⣀⡤⠞⠁
⣦⡀⠀⠀⠀⠀⠈⠛⠻⢷⣶⣤⣄⣀⣀⡀⠀⠀⣄⣀⢀⣀⣀⣤⣤⠶⠛⠉⠀⠀⢿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠⠤⠲⠆
⠀⠀⠀⢀⠀⠐⠊⠁⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⢀⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡄⠊⠁
⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠏⠃⠀⠀⠐⠯⠁⠀⠀⠀⠀⠘⣄⠀⠀⠀⢰⠁⠀⠀⠀⠀⢺⡏⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠂⠀⠀⠀⠀⢠⠀⡄
⠀⠀⠀⠊⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⢡⠆⠀⠀⠀⠀⢸⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠒⠁⢁⡀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠜⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⢀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠠⡀⠈⠉⠀⢀⠀⠀⢀⠀⡠⠰⠀⠀⠀⠺⡀⠆⠠⡀⠀⠀⠀⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⠀⠆⠀⢣⡀⠐⡀⠞⣁⢘⠁⠤⠁⢠⠈⠉⠂⠁⠀⠁⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠒⠋⠀⠀⠀⢀⡄⠀⠀⠀⠠⠜⠀⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠐⠈⠀⠀⣀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠐⠒⠚⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠂⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⢀⣴⣿⣥⣤⣤⣶⠶⠿⠀⠀⠀⠀⠀⠐⠚⠋
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⣄⠀⠀⠣⡀⠘⠛⠛⠿⠻⠟⠋⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⣰⣀⣀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠿⠈⠁⢩⡱⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠉⢡⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠀⣁⠀⠀⢀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⣐⠒⠀⠈⠁⠀⠬⠖⡛⢥⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣤⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⠐⠂
⠀⠀⠀⣉⣥⠐⠀⠀⠤⠒⠨⠵⠮⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠙⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⢀⡀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠆⢀⢀⠀⠀⡀⠒⠶⠀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⡄
⠀⠀⠀⠀⠀⠤⠀⠒⠀⠈⠁⠰⡄⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠄⠀⠀⠈⠃⠀⣁⠀⠀⡤⠐⠆⠀⠈⠀⡴⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠂⠈⠛⠛⠀⠐⠢
⠀⠀⢁⠀⠠⠀⠙⠀⢐⠀⠈⠀⠐⠲⠀⠀⠀⠀⠀⠇⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢀⡄⠀⣤⡄⠀⢤⣄⠀⠠⠆
⠀⠀⠈⠑⠀⠀⠀⢀⠀⠁⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠏⠜⡀⠀⠀⠀⢠⠆⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠉⠀⣠⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢈⣀⣀⠀⠀⠀⠀⠠⠀⠠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠜⠀⠀⠀⠀⠐⠠⠤⠐⠀⠀⡄⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠄⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠠⠴⡒⠈⢉⣉⠉⣑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠤⠤⠥⠤⡞⢠⠋⠀⢀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⡤⠒⠛⠒⠂⠤⢎⡑⡺⡀⠀⠈⠀⠐⢀⣀⠈⠳⡤⠤⠤⠄⢀⣀
⠀⠀⠀⢀⡠⠔⠊⠉⠁⠀⠀⢀⠎⠀⠀⠀⠂⠀⢀⠀⠈⢳⠑⢄⡀⠁⠐⠀⠐⠂⠀⢈⠀⠀⠀⠀⠀⠈⠁⠢⢄
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡤⠀⡄⠈⠀⣠⡾⠑⠦⣈⠉⠐⠒⠒⠒⠒⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣀⠀⠐⣒⣒⠍⠊⠁⠀⠀⢠⠛⠉⠀⠐⢎⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠮⣒⡸⠀⠀⠀⠀⠀⠀⣠⠔⠒⠚⢄
⠀⠈⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢀⣼⡀
⠀⠀⡅⠀⠉⠒⠤⣤⣀⠀⠀⠄⠀⠀⢀⣀⣀⣘⠸⣀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁⠀⠀⣀⠤⠒⠁⠀⢱
⠀⠀⡸⢦⡀⠀⠀⠀⠈⠁⠐⠒⠠⠤⠄⢄⣀⣉⣁⣐⡒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⣀⢴⠃
⠀⠀⡇⠀⠈⠉⠐⠒⠂⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠛⠓⠀⠛⠃⠈⠉⠀⠀⠀⠀⠀⣀⠴⠋⠀⡸
⠀⠀⡞⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠊⠉⠉⠉⠀⠀⢀⠔⡇
⠀⠀⠑⢄⠀⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⢀⣀⣀⠠⠤⠔⠊⣡⢞⠆
⠀⠀⡔⢋⠙⢦⢄⡀⠀⠈⠉⠐⠒⠠⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠒⠒⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⡤⠚⠒⢪
⠀⠀⢣⠈⠢⡀⠑⠬⢑⡢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡡⠃⠀⠀⠀⡇
⠀⠀⠎⠉⠒⠬⣑⡂⠤⣈⠉⠙⠛⠓⠶⠶⣄⠠⠤⠤⠤⠤⠤⠄⠤⠀⠀⠐⠒⢒⣀⣉⠉⠩⠤⢤⠔⠊⠀⠀⠀⡠⠞⢱
⠀⠀⠘⡄⠀⠀⠀⠈⠁⠒⠤⢍⣐⡒⠒⠠⠤⠤⠬⠉⠉⠀⠒⠒⠒⠤⠬⠭⠥⠤⠀⠐⠖⠒⠂⠁⠀⠀⡤⠊⠁⠀⢀⢾
⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⣀⣤⠖⠊⠁⡸
⠀⠀⠀⠀⠈⢗⠫⠕⣒⡀⠤⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣉⡉⠥⠐⢊⡥⠊⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠉⠐⠒⠂⠤⠤⠍⣉⣀⣐⣒⣒⣒⡒⠒⠒⠒⠒⠒⠂⠉⠁⣀⡀⠤⠚⠁⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⠀⠤⠄⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠠⠐⢀⣀⠤⣤⠄⡀⠀⠀⣤⣄⠀⠀⠀⡆⠀⢀⣀⣼⣁⣀⢀⠀⠀⠀⢀⢀⠀⠀⣨⣯
⠀⠀⠀⢀⣔⠥⠠⣀⡀⡀⠀⠱⠀⠈⠻⡇⠀⠀⢴⣧⢤⣜⣿⡖⣾⠎⠀⠀⠀⢹⠆⣵⣄⠈⢉
⠀⠀⢐⠃⠀⠀⠀⠀⠒⠚⠃⠭⣣⠀⠂⠀⠀⠀⠀⢸⠀⢸⡇⠀⡆⠀⠀⠀⠀⢸⡇⠨⣌⣢⡈
⠀⠀⠀⠹⢝⣛⣛⣛⠙⢚⠉⡲⠞⠀⠀⣶⡶⣤⠀⢸⠖⣻⣇⣦⡆⠀⠀⠀⠈⠈⣟⣃⠛⠉⢉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠀⠈⠉⠁⠀⢰⢎⡏⣰⡭⢃⠀⢀⡀⠀⠀⢹⠤⢾⣓⡯⠟
⠀⠀⣠⠢⠢⠀⡠⢴⡸⠽⣒⣄⠀⠀⠀⠀⠀⠀⠁⠀⢉⣈⣉⡁⠁⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠠
⠀⠀⠂⠀⠊⣸⠒⣾⠑⣢⢯⡔⣳⡄⠀⠀⡶⠀⢀⠖⠁⠀⠀⠀⠑⢄⠀⢀⠖⠤⠀⢀⣽⣿⣼⣣⡀
⠀⠀⠀⠀⠀⡽⢩⠉⠋⠏⠛⢋⠁⠀⠀⠀⠀⢀⠖⠀⠀⠂⠒⠒⠒⠚⡢⠈⠉⠳⢀⢼⣿⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠇⣜⠀⠀⠀⢰⠘⠀⠀⠀⣙⠂⠈⡛⣗⢾⢭⡀⡁⣉⣝⣷⠀⠀⠀⠈⠉⠉⠉⠉⠉⠿
⠀⠀⠐⠶⠀⠀⣸⠀⢰⠀⢸⠀⠀⡀⠀⠉⠁⠘⢖⠩⡭⠭⠭⠛⠑⢒⠖⠁⠀⢀⠀⠆⡐⢢⠒⠀⡇
⠀⠀⠀⠀⢀⠐⠾⢄⣈⣠⢘⡰⠋⠀⠀⠀⠀⠀⠀⠑⠐⠄⠤⠀⠒⠁⠀⠀⠀⠀⠀⢰⣀⣀⣀⣠⠁
⠀⠀⠀⠀⠀⣡⡀⠀⠀⠈⠉⠀⢠⠀⠀⠀⢠⠀⠀⠀⣀⣶⣤⠄⠀⠂⢆⠂⣄⡠⠲⠀⠀⠀⠀⠐
⠀⠀⠀⠆⠀⠉⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠀⢋⠤⡄⡀⠸⠇⠋⠛⠤⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⢀⣀⣀⣰⡏⠀⠀⠆⠀⠀⠀⠀⠀⡀⠛⠀⡠⠋⠈⢧⠀⢁⠀⠐⠀⠀⣀⣠⣄⡀⠹⠁
⠀⠀⠀⠀⠀⠙⠓⠒⠛⠿⠊⡃⠀⠄⠀⡀⠀⠳⠵⢀⠔⠑⠀⠀⢠⠀⠎⠀⠀⠐⣿⣿⣿⣿⣧⡉⠐⠂⡄
⠀⠀⠀⠀⡔⣁⠠⠭⠍⠉⠀⢨⡐⠀⠀⠻⠀⠀⢠⣛⣀⣤⡶⡒⠉⠌⠀⠀⠀⠀⢹⣮⣻⢿⠿⣷⠀⣴⠁
⠀⠀⠀⢠⠀⠀⠁⠀⠉⠀⠁⠀⠠⠀⠀⡤⠔⡄⠘⣿⣿⣿⡙⣄⠎⠀⠀⢠⣤⠀⠀⢿⢿⣿⣧⠽⠾⠃
⠀⠀⠀⠀⠢⠕⣂⠰⠠⠄⠐⠢⠕⠀⠀⠈⠊⠁⠀⠘⠋⠿⠛⠋⠀⠀⠀⠀⠉⠀⠀⠈⠋⠁⠉

⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀
⠀⠀⠬⢳⠤⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠁⠠⡘⠋
⠀⠀⣠⢉⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠂⠀⠀⠀⠐⠀⠀⠆⠐⠂⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠑⢀
⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠈⠀⠁⠀⠀⠁⠓⠀⠀⠒⠁⠀⠘⠁⠆⠐⠂⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠅⠘⢀⠀⠂⠀⣀⡀⠀⢠⠰⢚⠑⠀⠐⠀⠀⠂⣠⠀⠱⠢⠆⣀⣀⠀⠐⠂⠀⠀⠀⠂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⢈⠀⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⠈⠉⠀⠠
⠀⠀⠀⢀⠠⠀⡂⠒⡉⢰⠜⢃⢁⠀⣰⠆⠀⠀⠤⢤⠀⠠⠁⠂⠀⠐⠠⠀⠄⠀⠌⠁⠊⠀⠈⠒⠀⠀⡄⣀
⠀⠀⠐⠂⠈⢈⣀⣈⣁⣀⣁⣀⣈⣀⠁⠀⠀⢀⠀⠁⡠⢀⠀⡈⠀⢈⡀⣀⣈⣀⣀⣀⣀⣁⣀⣀⣂⣀⠁⠀⠂⠄
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠉⠀⠾⠷⠿⠼⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠐⠐⣶⣤⢰⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠐⠀⢀⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢁⠀⠀⠌⢀⡀⠀⠀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠡⠄⠀⠤⠄⠀⠤⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠄⡲⠍⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠂
⠀⠀⠈⠀⠀⠀⡄⠀⠉⠒⠠⢄⣄⠀⠀⠉⠀⠀⠀⠉⡈⠀⠀⠄⠀⠁⠄⠤⠀⠀⠀⣠⠠⠐⠂⠁⠀⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⢆⢠⠉⠐⠂⠤⣀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠄⠐⠈⠁⠄⠀⠀⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠇⠀⣌⠀⡆⠘⠆⠀⢠⠀⠁⡒⠸⠀⠂⠉⠀⠀⢊⠠⠀⠀⠔⠀⠀⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡐⢨⠀⠀⠀⠀⠘⠀⠁⠘⠀⠀⠀⠀⠀⢸⠀⢹⠨⡀⠀⠀⠋⡄⠐⠀⠀⠀⠀⡇⠀⠀⠀⡄
⠀⠀⠈⠀⠈⢀⢁⡤⠃⠀⠄⠂⠀⠃⠀⠂⠆⠈⠀⠀⠁⠀⠂⠐⠀⠀⠀⠙⠀⠂⠀⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠖⠀⢁⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠂⠄⠛⠀⠉⠀⠂
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠕⠀⠄⠤⠀⠀⡄⢀⡀⢀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠾⠿⠿⠿⠷⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⢀⠀⡀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠙⠀⠸⠀⠁⠂⠘⠀⠐⠀⠀⠑⠐⠘⠀⠑⠀⠃⠀⠈⠀⠘⠀⠓⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢛⢛⠛⠛⠛⢛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠃⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⢠⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠠⠔⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠




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

⠀⠀⠀⢠⣀⠶⠀⠂⠀⡁⠀⢠⡖⢠⣌⢠⡄⣦⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⣀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⣜⠛⣻⠀⠘⣷⠄⠀⠀⠋⠃⠀⣠⣴⣶⣶⡄⠈⠳⠶⠮⠑⠀⠀⠀⠀⠀⠄⠀⠙⠿⢥⣤⠜⠁
⠀⠀⠈⠳⠤⠔⠀⠈⢬⡏⠀⠀⠈⠐⠀⠀⠀⠀⠀⠛⣟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢤⣶⡻⣳⣄⠀⠀⠀⢀
⠀⠀⢠⡴⠶⠶⣦⣄⡀⢁⣠⣴⡤⠟⠀⢸⣷⡄⠀⠀⠉⠁⠀⠀⠀⠀⢢⠢⠤⠂⠀⠙⢿⣾⡿⠓⠀⠐⠦⣴⢇⡢
⠀⠀⣿⠃⣾⡂⠈⢽⡗⠉⠀⡀⠀⠀⢰⡟⠉⠛⠀⠀⢀⠀⠀⠀⠀⢀⡀⠓⠒⠊⠉⠀⠀⠁⢀⣠⣶⣶⣤⣈⠉
⠀⠀⢿⣦⡀⠀⢀⡼⠃⢠⡀⠀⠀⠀⠈⠓⠤⠚⠀⠀⠀⠈⠉⠳⣆⠀⣁⠀⣤⣔⠙⡧⠀⠀⣰⡯⣝⢛⣿⣟
⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⢃⣠⠋⠀⠳⠿⠛⠁⠀⠀⠙⠻⠿⠿⠛⠛⠁
⠀⠀⢀⣠⣤⠀⢀⡶⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠈⠁⠈⠁⠀⠈⢉⡀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠘⢿⣿⣦⡤⠀⢴⡶⠀⠀⠀⣴⠒⢀⡀⠀⠒⢦⣄⠀⢰⣿⣿⣿⡆⠀⠀⠐⢶⠉⢩⣽⣿⡂⠀⢸⢹⢿⣷⡄
⠀⠀⠐⠌⢿⣿⣧⣤⠄⠀⠀⠠⣚⣯⣗⡂⠈⠐⠂⢵⠋⠀⠻⣯⣥⣤⡟⠀⠀⠘⢮⣍⣩⣷⡿⠃⠀⠈⠄⣓⢽⠇
⠀⠀⠀⠀⠁⠛⠉⠀⠂⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠦⣄⠀⠐⣆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⡀⠠⠉⠉⢙⣰⠆⢀⡴⠆⠡⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⣽⣿⠁⠠⢤⣿⡬⠟⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣀⣴⣧⣀⣠⡆⠩⡉⣀⢀⠈⠭⠀⠀⢰⣾⠰⢠⡇
⢀⣠⣴⠖⠋⠉⠉⠉⠑⡶⣄⠀⠀⠀⠀⣀⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠸⣟⣴⣿⣷⡀
⢿⣅⠐⠂⠀⠤⠥⢒⡬⢶⣾⣶⣒⣿⣤⢀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⢠⠀⠀⠀⠀⣶⠀⡇⢠⣾⣿⣼⣿⡏
⠀⠈⠑⠒⠂⠒⣴⣿⢿⣯⣟⡡⣿⣶⣿⣿⣶⠿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣼⠀⠀⠀⠀⣿⠀⠹⠌⠉⣿⢻⣿⣿⣶⠂⢀
⠀⠀⠀⠀⣀⢄⢿⣅⣉⣹⣾⣟⣻⡛⣿⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣆⠀⠀⠐⢿⠆⠀⠀⠀⠉⠈⠉⠉⠉⠉⡉
⢀⢄⠴⠚⠨⣧⣑⠈⠙⠛⠶⢿⣍⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⣿⡏⠙⢦⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠜⠘⢃⠄
⣮⡧⠀⠀⠀⣙⠺⠿⢦⢄⣴⠂⠀⠀⢀⢀⣀⣤⣶⣤⣤⠴⠶⠞⠛⠉⢃⡔⡿⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⢖⣕⡄⡠
⠹⣿⡄⠀⠀⢌⠲⢶⣤⣌⡉⠁⠉⠒⠛⠂⠀⠀⠀⠀⠀⢀⣀⣤⡤⡶⠛⡱⠀⠀⢀⣀⠝⠀⠀⣠⣤⣤⣤⡈⠑⠅⠫⠎⠀⢠⣿
⠀⠈⠙⠶⣤⣀⡉⠓⠦⢭⣉⡉⠉⠉⠛⠛⠉⠓⡒⠂⠉⠉⠈⠁⠀⠀⢁⣠⡤⠖⠋⠁⣠⠶⠛⠉⠀⠀⢀⣨⠕⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠶⠦⠤⠤⣤⠤⠤⠤⠥⠤⠤⠦⠶⠒⠚⢋⣉⠤⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣰⣯⡠⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡧⣤⠤⠚⠁⠀⠀⠀⠀⣀⣭⢶⡀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢂⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⡀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠶⠶⠶⠶⠶⠾⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣴⡿⠋⠻⣷⣄⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣴⡿⠛⢿⢦⠀⠈⣿⡿⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣸⡟⠀⠀⠀⢐⣶⠗⠉⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣿⣃⣤⣴⡾⠟⠉⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⠀⢴⣶⣶⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⠠⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠙⢒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠑⠈⠀⣀⠀⠀⠀⢀⣤⣼⣧⣤⡀⠀⠀⠀⣠⠀⠀⠊⢓⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡋⠀⠀⠀⠲⣾⣿⣷⠖⠀⠀⢹⡿⣿⡏⠀⠀⠲⣾⣿⣷⠖⠀⠀⠐⢝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠈⠀⠀⣄⠀⠀⠿⠛⠷⠀⠀⠀⠈⠀⠀⢁⠀⠀⠀⠿⠛⠿⠀⠀⣠⠀⠀⠁⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠂⠀⠶⣾⣿⢶⠖⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠁⠂⢄⠀⠀⠲⣶⣿⣷⠆⠀⠐⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠿⠛⠿⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠿⠛⠿⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢰⡶⢶⡄⢰⡶⠶⠖⢀⣶⠿⣦⠀⣶⠀⠀⠀⠀⣶⣆⠀⢰⡰⠶⣦⠀⢀⣶⡆⠀⠲⢢⡴⠆⣶⠀⣴⠾⢶⡀⣶⣆⠀⡆
⠀⠀⠀⢸⡇⢀⣿⢠⡿⠗⠀⢸⡇⠀⠀⠀⣏⠀⠀⠀⣸⣏⣿⡄⢸⡷⢶⡟⠀⣼⣏⣿⠀⠀⢸⡇⠀⣿⠀⣿⠀⢸⡇⣏⠻⣦⡇
⠀⠀⠀⠸⠷⠾⠃⠸⠷⠶⠶⠈⠷⣶⠟⠀⠿⠶⠶⠀⠟⠉⠉⠧⠸⠇⠘⠷⠰⠏⠉⠙⠧⠀⠸⠇⠀⠿⠀⠻⢶⠾⠁⠿⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⣦⣀⣶⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣶⣤⣶⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠄⠀⠔⢿⣿⠿⠆⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⢀⡀⠄⠊⠀⠀⠰⠿⣿⡿⠶⠀⠠⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠋⠀⠀⣶⣤⣶⠀⠀⠀⢁⠀⠀⡁⠀⠀⠀⣶⣤⣴⠀⠀⠙⠀⠀⣐⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢄⠀⠀⠴⢿⣏⠿⠦⠀⠀⣸⣿⣾⣇⠀⠀⠴⢿⣿⡭⠦⠀⠀⡠⣨⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠇⠢⢀⠀⠋⠀⠀⠀⠈⠛⢺⡟⠛⠁⠀⠀⠀⠛⠀⡀⠄⡬⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣢⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠓⠂⠐⠛⠋⠉⠁