Helianthus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⠀⠀⠀⠘⢃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⢀⠀⠘⠀⢂⢀⠀⠃⠠⠀⠀⠰⠊⠀⠀⢀⠄⡚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠇⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠠⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⢀⠀⠊⠀⠀⠀⠀⡀⠁⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⢰⣀⣤⣤⡴⣇⣀⠀⢀⠎⠀⠀⠀⢀⠤⠚⠁⠉⠀⠐⠁
⠀⠀⠀⠀⠠⡶⠤⠄⠀⠒⠒⠓⡀⠀⠀⠀⢀⡴⠚⡏⠉⠓⡬⠀⠈⢛⢓⢪⡀⠀⠀⠀⠁⠀⡀⠀⠠⠮⢀⡀
⠀⠀⠀⠀⠀⠘⢄⠐⠀⠀⠀⠀⠈⠒⢄⢈⡿⠑⠠⠠⢜⠊⠠⡆⣁⠍⠰⠰⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠒⠒⠂⣼⢁⢀⢂⠴⡬⣙⡀⠚⡠⠆⣁⠘⢉⠄⢧⢀⠀⠤⠀⢀⣀⡄⠊
⠀⠀⠀⠀⠒⢉⠉⠁⠀⠀⠀⠀⠀⠀⠉⡟⣁⠁⣛⠖⠢⠡⠬⡿⣭⠓⡍⠡⠬⠦⢼⡀⠀⠀⠀⠀⠀⠀⠈⣩⠶
⠀⠀⠀⠀⠀⢀⣈⠔⠂⠀⠄⠀⠋⠀⠐⣿⢉⠐⠍⡴⠇⢲⣊⠵⡈⠥⡴⠐⡒⠒⣺⢁⠀⠀⠀⠀⠀⠠⢆
⠀⠀⠀⠀⠠⣁⠀⠀⠀⠀⠀⠐⠂⣀⠥⠻⣎⡐⢒⣁⠘⠀⢶⠙⢤⠀⠈⠮⡁⣰⣿⣄⡀⣀⠀⠀⠀⠀⠀⠈⢑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠒⠉⠀⡠⠊⡹⠷⢮⣰⣆⡃⠠⠆⢦⣈⣃⣤⠖⠋⠑⡍⠐⠄⠈⠑⠒⢖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠊⠠⠊⠀⠀⠀⠘⠉⢛⠋⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⣠⡁⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠘⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠀⠀⠀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⡌⠁⠢⡀⢀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠈⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠃⡠⠚⠀⠀⠠⡀⠀⡇⠀⠑⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠈⠀⠀⣀⡗⠁⠈⢄⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⡆⠀⠊⠁⠠⡆⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠈⠀⢀⡇⡌⠀⢠⠤⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠑⢦⣿⣿⣿⣷⣤⡂⠀⢀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢲⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢈⣵⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡠⠀⠀⢉⣿⣿⣿⣿⣿⣿⡿⠓⠠⡀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⡢⠒⠛⡻⢿⣿⢿⠛⠣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡜⠀⠀⡀⠀⢰⠇⠘⠀⠀⠘⠂⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢊⡅⢀⠼⠀⠀⠷⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠉⠁⠈⠁⠀⣠⣀⡆⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠈⠁⠁⠀⠀⠀⠀⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠄⡀⠀⠀⢀⡴⠊⠈⠉⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠂⠶⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⠀⡇⠀⠀⣠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⡿⠀⠀⠘⣿⡀⠀⠀⠘⠃⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢶⠀⠀⢿⠆⠀⠈⢻⡀⠀⠀⡟⠀⣀⡀⠀⠂⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣷⣤⠀⠀⠀⠀⠀⢳⡀⢀⠁⣸⠏⠀⠀⠀⠰⡿⢃⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠈⠁⠀⠀⢳⣄⣾⣿⣿⣴⣿⣞⣵⣶⡦⠾⠛⠛⠙⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠛⠂⠵⣦⣄⢬⣿⣛⣻⣿⣽⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣶⢤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣠⣴⣶⡶⠶⠂
⠀⠀⠀⠀⠀⠀⢀⣤⠮⠾⠛⠙⠃⠀⠸⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣭⣥⣴⣮⣭⣀
⠀⠀⠀⠀⠀⠐⠋⠉⠀⠂⢠⣤⣤⠴⠾⠟⢋⡿⣿⣿⣿⣿⣿⣟⣿⣿⡒⠈⠑⠀⠙⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⣠⣴⠋⢠⡟⣿⣿⠉⣿⠹⣷⣄⠉⠓⠶⣶⣶⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢡⣤⣶⢋⠘⠁⠀⠈⢀⠁⠉⠀⠉⠀⠈⠹⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠛⠋⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⣷⡀⠠⠆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠀⢠⠀⠀⠀⠀⠸⣆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠁⢸⣷⡆⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠡⠼⠲⠀⢲⣦⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⡠⣖⣡⣼⠟⢂⣽⣶⣷⣿⡷⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣠⡶⣿⣿⣿⣖
⠀⠀⠀⠀⢘⡶⢾⣿⣭⣾⠿⠛⠋⠉⠙⠻⢦⡀⠀⢸⡟⠃⣀⠴⠊⠀⠀⠀⣿⣷⡟⢿⣶⣅
⠀⠀⠀⣌⣽⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⡄⢸⡇⢰⠃⠀⠀⠀⠀⠀⠌⣝⣿⡆⣻⡟
⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡇⡿⠀⠀⠀⠀⠀⠀⠹⢜⣿⡯⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡃⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠀⡅⢣⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⣆⠱⠈⡡⠲
⠀⠀⠀⠀⠠⡀⣓⢠⢚⡈⠋⢡⡤⣔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠉⠀⠀⠠⣉⣤⡂⠂⠙
⠀⠀⠀⠀⠒⠀⠐⠰⡀⠛⠔⡂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡐⠒⠈⣲⣾⣿⠿⡇⢊⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⢄⣀⢀⠀⠀⠀⠀⢘⠄⠀⠰⣾⣿⠿⠛⣶⠶⣧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠌⠀⡰⢶⠊⠉⢀⡄⠂⡀⠀⠡⣆⢡⡘⠻⢋⣡⣌⣤⣴⢡⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⡠⠤⠄⠀⠀⠀⠀⠔⠒⠤⣄⣨⣧⣼⣶⣦⣈⠀⠐⢣⢀⠠⠀⠊⡞⠀⠆⠉⠁⠷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢠⠐⠂⠀⠀⠐⠦⡀⠘⢋⠠⣄⣼⢫⣵⣾⣷⣯⢻⣦⣐⠁⢂⠄⠀⠀⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⡠
⠀⠀⠀⠀⠐⠈⠑⣂⠀⠀⣷⠃⠀⠈⠑⠒⠊⠉⠀⠔⣓⠀⣠⣿⣹⣿⣿⣿⣿⢿⣿⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⠔⢋⠉⠀⠀⢓⡠
⠀⠀⠄⣉⣀⣀⡠⠈⠘⢆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠒⠻⣮⣹⡻⣟⣫⣾⠿⡂⠠⠐⠂⠀⠀⢀⠔⢈⣑⣂⠀⠀⢹⡇⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⡠⠔⢟⠉⠟⠙⠉⠀⢂⠘⡆⠁⠀⠀⠄⣉⣀⣀⡠⠀⠈⢄⢾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣧⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣈⡄⣀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸
⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠛⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡟⠀⠀⡔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⡇⡰⠊⢁⡀⠀⠈⣒⠄⠀⠀⠀⠀⠀⠸⣄⠈⠘⠃⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠦⢀⠀⣹⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠖⠊⠀⠈⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠢⢄⣿⠀⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢀⣈⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⢦⣠⠴⣦⠞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢾⡟⢦⣼⢃⣼⠃⠀⢸⢠⡗⢻⣂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠶⢾⡶⣼⡄⣄⡇⠀⠙⣾⡇⠀⢀⣾⠋⢀⡾⠋⢸⡤⠤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠼⠶⢽⣷⡈⠙⢾⣷⡀⣆⢸⡁⡆⣼⢇⣠⠏⠀⠀⣼⣀⡴⠧⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠽⠦⣄⡀⠈⠙⣶⣄⠙⣧⢸⣾⣷⣧⣿⣿⡏⢀⡄⢠⠏⠁⠀⣠⠾⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⣄⠀⠉⢳⣶⣸⣮⣿⣟⣟⡯⣯⡿⡿⣿⡷⢋⡴⠟⠒⠚⠛⢻⡿⢠⠟
⠀⠀⠀⠀⠀⠀⠛⢯⣁⠀⠈⠙⠒⠾⣿⣿⣿⡿⣗⣷⣻⣿⡿⣿⣞⣿⡥⣒⣁⣀⡤⠞⠉⠉⢙⡳⠖
⠀⠀⠀⠀⠀⠀⣀⡤⠞⠛⠓⠒⣚⣿⣿⣿⣲⡿⣟⣞⣿⣻⣯⣟⣷⡻⣿⣿⠿⠿⣶⡶⠶⠶⢭⡀
⠀⠀⠀⠀⠀⠀⣹⣶⠶⠒⢛⣩⠽⢿⣿⣿⣞⣟⣻⢺⣿⢿⣻⣿⣾⣽⡿⣟⣛⣂⣈⣹⠷⠦⣤⣟⠃
⠀⠀⠀⠀⠀⢀⡴⠋⠉⣹⢋⣀⣠⣤⣴⡿⢿⣾⣿⣻⣿⣿⣽⣾⣿⡇⣀⣹⡾⢭⣀⣀⣤⣶⡿⠞⠛
⠀⠀⠀⠀⠀⠈⠉⢉⣟⣉⣭⢥⡶⠋⣀⠠⠼⢧⣈⣻⣿⣿⣿⣅⣀⠹⣏⣙⡓⠦⣌⡻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠥⣤⣾⠤⠤⣤⣤⣤⡼⢿⢻⡇⢸⡟⡟⣏⠙⠹⣆⠉⠑⠀⠳⣤⠷⠄
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⡧⠶⠖⠒⠚⠹⡇⠀⢸⡃⢸⢁⣧⣈⠃⠀⣏⠙⠛⠛⠛⠳
⠘⢿⣍⠉⠁⠤⠤⣤⣌⣉⡉⠉⢛⠲⢤⣀⠀⠙⠦⣼⡇⠀⢸⠁⠈⠛⠶⢼⡆
⠀⠀⠉⠳⣄⠀⠀⠀⠘⠛⠛⠓⢾⣤⣀⠉⢷⡀⠀⠈⢳⡀⣿
⠀⠀⠀⠀⠈⠳⢦⡀⠀⠐⠚⠉⠉⠉⠙⠷⣄⣷⡀⠀⢸⡟⢿⠀⠀⠀⠀⣀⡴⠖⠛⠛⣛⡛⠛⠓⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⢀⣀⣀⣼⣿⠙⢦⠘⡇⢸⡀⠀⢀⡾⠁⠀⠀⣠⣾⣥⠴⠖⠒⠂⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠳⡌⢻⡇⢸⡇⠀⣾⢁⣠⠴⣟⣉⡉⠉⠉⠁⠀⠀⠀⣠⡴⠖⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⠸⣧⠞⣿⣋⠁⠀⠀⠀⠉⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢁⡶⠋⠉⠛⠲⠦⠤⠤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣍⣧⣽⣭⣯⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡆⣀⣀⡀⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢦⡀⢻⣿⣿⣿⣿⡞⠁⠀⠀⠤⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠘⠓⠶⣤⣹⣿⣿⣿⣿⣿⣿⣷⣿⠷⠂⠀⠀⡠⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⢆⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⠄⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠚⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠳⠖⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠖⠉⢁⡬⢿⣿⣿⣿⣿⣿⣿⣿⡿⣤⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⢁⣠⡴⠊⠀⢉⣿⠿⢛⡟⠋⠻⣿⠇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣠⣾⡇⠀⠘⣿⡄⠀⣈⠣⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⣀⠈⢰⠀⠿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⢸⡇⠀⠀⠀⠀⢿⣷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⡇⠀⠔⠈⠁⢀⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡄⠻⡿⢿⣿⠇⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣟⡷⠀⠀⢊⣘⣶⣄⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡶⢦⣀⠈⠻⠿⠟⢸⣿⡄⠀⠀⠀⣤⣴⣶⢶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠙⠢⡀⠀⢸⣧⡇⠀⠀⣼⣿⣥⣀⠈⠙⠛⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡟⠀⠀⠀⠿⢿⣟⡙⠛⣧⣤⠀⣧⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠻⠟⠛⠒⠀⠀⢺⡇⠀⠀⠀⠀⠀⠈⠙⠿⣦⣝⢿⣮⣿⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣽⣦⡾⠿⠞⠷⠶⣶⣼⣷⠀⢀⣀⡀⠀⠀⠀⠀⠈⠛⠷⣿⣻⣿⣷⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠞⠁⠀⠀⠀⠀⠀⠀⠈⢹⡷⠀⣬⡉⢻⣷⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠲⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⡫⠀⠀⠈⢣⠀⢨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡖⡀⠀⠀⢀⢬⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣾⢿⣷⡄⠘⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠊⠳⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠑⡄⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠙⡆⠀⣀⣼⡀⣁⠂⣠⣊⡰⠁⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⣾⣆⣴⠿⢛⡻⣭⢭⣉⣻⠿⣿⣯⡄⢂⢀⡀⠈⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢵⣷⡟⢠⡔⠉⢠⣤⣶⣾⡋⢳⡼⣿⣿⠄⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠈⣿⠁⢸⡇⠸⣿⣿⣿⣿⣿⠅⢹⡾⣿⣒⠈⠉⠁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣽⣧⠸⣧⡀⠛⠻⠿⠾⠋⠀⢸⣿⣿⣏⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣊⣾⣿⣦⣜⢷⢶⣤⣤⣤⣤⠞⣛⣽⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠉⢉⠿⣶⣶⣶⣷⣴⡾⣾⠟⠛⠏⡀⠀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠸⠉⡟⡿⠁⠈⢆⠀⠀⠑⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠈⠀⠘⡇⠀⠀⠀⢂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠐⡄⠀⠀⢸⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⠠





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⡀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠁⠂⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠐⠀⢀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠠⠀⠀⢠⡀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠰⣄⠀⠀⠀⡷⠀⠈⠃⠀⣦⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠐
⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡄⠀⣃⣠⣀⣠⣠⣽⣼⠸⠁⣠⡆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠈⢦⡀⢱⣾⣞⢿⢻⣿⣾⢟⣻⣿⣿⣷⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⣹⣿⢿⢯⣷⣟⣿⣼⣻⣽⣭⣿⠟⡽⢷⡖⠉⠀⠂⡀⠐
⠀⠀⠀⣀⡠⠒⠀⠀⠉⠉⠁⠀⠀⠀⠠⣄⣀⣀⢈⣽⣿⣿⣽⣽⣿⣯⣿⣿⣿⣿⣿⣷⣌⣻⣯⣿⡀⠔⠂⠀⢀⣀⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢨⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⢵⣿⣧⢤⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣟⣿⣯⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡽⣧⣍⣻⡂⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠚⠚⣿⣣⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣯⣗⢺⣯⣉⣁⡀⠀⠠⠤⢄⣀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠔⠁⣸⢷⣽⣉⢿⡿⣯⢷⠷⣟⣿⢿⣽⣿⠟⠑⠤⣁⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠖⠘⠉⠀⠀⠀⠀⠚⠀⢠⢟⣿⣶⣽⣾⣿⣿⣿⣿⡿⠿⠙⠃⠀⠀⠀⠉⠂⠠⢀⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠁⠊⠙⠀⣿⠙⠉⢻⠉⠀⠀⠈⠆⠀⠀⠀⠑⣄⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣄⠰⠙⠣⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣟⣛⣟⣿⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣭⣽⣿⣿⣿⣭⣿⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠆⠀⠀⢈⠀⠀⠀⠀⢀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⡾⠟⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡇⢰⠁⠀⣴⠋
⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢸⣎⠀⢘⡇⣾⢆⣾⢇⠄⠀⡠⠆⠀⠀⠀⠀⢀⣠⣴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢤⡈⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⡋⡁⠂⠀⠀⠀⠀⠀⠋⠉⠀⠈⠀⠋
⠀⠀⠀⠀⠰⠒⠂⠀⠀⣀⠀⠉⠐⠢⢄⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣗⣀⣔⣀⣀⠀⠀⠀⢀⠠⠆⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒⢚⣒⣀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣓⠁⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡑⠒
⠀⠀⠀⠀⠠⠤⠴⠖⠀⠙⠃⠀⠀⠀⠠⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣍⣁⠀⠀⠠⢴⠤
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⣠⠶⣿⡿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡄⠉⠛⠛⠢⠄⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠈⠒⠂⠄⠠⠀⠀⠀⠀⠁⠐⠋⠀⢠⣿⠛⢿⣿⣿⣿⣿⡿⣿⠛⣿⡜⡿⠄⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠋⠀⠀⠘⣇⠁⠘⡿⢳⠙⣇⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠁⠀⠀⡴⠀⠀⠀⣀⠀⠀⠁⠐⡅⠀⠀⠀⠈⠀⢈⠀⠀⠈⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠑⠀⠀⠀⠈⠂⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠈⠀⠀⠀⠀⠀⡆⢠⠀⠀⢂⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠀⠀⠄⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⢄⡠⠂⠀⢂⠀⣠⠔⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠉⠓⢤⡜⠀⠀⢈⠃⠀⠀⢈⠞⠁⠀⠀⠘⡆⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠠⠤⣄⣆⠀⠀⠀⠀⢁⠀⠀⢸⠀⠀⠀⡜⠀⠀⠀⣠⡼⠹⠌⡉⣿⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠙⣆⠀⠀⠀⠘⡀⠀⢸⠀⠀⢠⠃⠀⠀⠀⢹⣰⣦⣤⠛⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠓⠦⣄⡀⠈⠳⡀⠀⠀⢱⡀⢸⣀⠀⢸⠀⠀⠀⢀⡞⠁⠈⢀⡠⠔⠚⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⠢⣀⠀⢣⣤⣿⣄⣼⣆⠀⣠⡟⠀⣠⠖⠁⠀⠀⠀⠀⣀⣠⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣄⣀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠞⢁⡀⠤⠐⠒⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠋⠉⠉⠉⠙⠓⠲⠦⠤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠶⠒⠒⠒⠒⠒⠒⠒⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⣀⣠⠤⠔⠒⠒⠒⢒⡒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⡀⠈⠑⠒⠠⠤⢄⣤⡤⠤⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⣠⠟⢿⣿⣿⣿⣿⣿⡿⢿⡋⠉⠀⢈⠑⠦⣀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⠶⠊⠉⠉⠀⠀⣠⠞⠁⢢⠊⠀⠀⢸⢻⠉⠀⠀⠙⣄⠀⠀⠀⠀⠈⠓⢄⣀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡜⠁⠀⢠⠃⠀⠀⠀⢸⠘⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⢫⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠂⢀⣤⠏⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠸⡓⢄⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢁⠏⠀⠀⠀⣼⠀⠀⠀⠀⠀⣿⠀⢠⠀⠀⠀⠀⠀⠇⠀⠈⠲⢄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⠴⠊⠃⠀⠀⠀⠀⡼⣿⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⢤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠀⠀⡡⠞⠀⡟⢆⠀⠈⢲⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠢⡀⠀⣀⠀⠉⠑⠒⠢⠤⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⡇⢸⣦⣂⡌⠈⠂⠼
⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣁⠢⣀⣀⢀⡀⠀⠉⠲⠤⠐⠒⢦⡀⠀⠀⡇⠀⡄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠂⠤⢈⡀⠐⠠⢄⠀⠀⠀⢸⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⣍⣦⠀⡏⠀⠀⡇⢸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣳⡀⠀⠀⢸⢀⠔⠊⠀⠀⠀⠀⠀⢀⡀⠉⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠀⢸⡆⠀⠀⠐⢁⡀⠐⠀⠉⠁⠀⣀⠤⠤⠤⠀⠉⠒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠸⣀⣼⡃⣉⣁⣀⣀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⢻⣷⠇⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⢾⡀⠀⠀⣄⠀⠟⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣾⣧⢾⣠⣿⣠⡁⠀⣴⠃⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⣼⣿⣿⣿⣿⣿⣧⣾⡿⠛⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠑⢮⣶⣿⣿⣷⣿⣿⣿⣯⣿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢤⣤⣤⠴⠞⠛⢿⣿⣿⣿⣿⣿⣿⢿⣝⠷⠮⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣤⠂⠀⣹⡿⠿⣻⡟⡉⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⡔⠚⠛⠁⠀⡏⠃⠣⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢡⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⠄⡀⠀⠀⢸⡇⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠛⠉⠀⣠⠞⠁⠀⠈⠳⣄⢸⡇⠀⠀⠁⠀⢠⣶⡄⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠘⢸⠃⣀⠴⠒⠒⠒⠽⣿⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡖⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠒⠉⠀⠀⠀⠀⣀⠀⠒⠒⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣰⡔⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⠀⠀⢐⣴⠾⠞⣋⢺⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⢀⣰⠟⣡⠼⠇⠁⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⣸⢣⡾⠃⠀⠠⠀⠀⠀⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢀⡁⡾⠁⠀⠄⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣁⢠⠀⢠⣄⡠⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡾⠟⠛⠒⠋⠉⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡀⠀⠀⠂⠀⢸⠇⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢱⡀⠘⣇⠀⠈⠀⣀⢨⠀⢀⣴⢁⠔⠀⠀⢀⠔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣀⢵⣄⣸⣶⣶⣾⣿⠾⠦⣾⣿⡗⣀⡤⠒⠁⠴⠚⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⠞⣻⣭⣍⠓⠊⣿⣿⣟⣴⠖⠂⠀⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⢐⣂⣐⣻⣿⣿⣿⠃⢶⣿⣿⣿⣿⡆⢹⡿⣿⠅⠒⠂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⢙⣿⣿⣿⡇⠼⣿⣿⣿⠿⠃⢸⡇⣿⠗⠢⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢀⡀⠴⣋⣽⢿⣿⣿⣶⣄⣈⣤⣤⣴⢛⣽⣿⠗⠁⠀⠀⠀⠈⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢁⠐⠉⠙⢿⣿⣿⣿⣿⣾⣿⡿⠿⣧⡀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣾⢿⣻⠏⠙⢮⠀⠀⠡⠁⠐⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⡜⠰⠀⢣⠀⠀⠈⢧⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠠⠀⠀⣦⠀⠀⢸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠃⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⡠⠃⡇
⢸⠀⠀⣰⠁⡄⢿⠀⠀⠀⠀⡾⡄
⡌⢀⢠⠇⣴⣇⢸⡄⠄⠀⣸⢃⠹⣄
⠁⠀⣾⠀⣿⣿⢸⡟⠀⢠⡇⣾⡌⠘⢦⡀⠀⠀⠀⠀⢠⣾⠀⠀⠀⣠⡾
⡀⠀⢻⡀⣿⣿⣼⠃⠀⢸⠁⡇⠀⠀⠈⢳⡀⠀⠀⣰⠋⢻⠀⢀⡞⢡⡇
⠀⠀⠀⢳⣿⣿⠇⠀⠀⠸⡆⡇⢀⠀⡄⠀⢻⢀⡼⠁⠀⢸⣴⠏⡐⢠⠀⠀⢠
⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⢇⠀⢸⣆⣅⣤⣼⠟⠀⠀⠀⢸⡇⣸⡁⢸⡆⠀⣾⡀⠀⠀⠀⢀⡴
⠑⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⡄⠸⣿⣫⡿⠃⠀⠀⠀⠀⢸⣷⣿⠁⠈⣇⣰⠃⣧⠀⡠⠂⣸⠃
⢠⠀⡄⢰⡇⠀⠀⢀⠀⠸⠀⢷⠀⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⡾⢁⠀⡼⠊⠀⢠⠇⠀⢀⣠⡔
⢸⠀⢳⡾⠀⠀⠀⠀⠀⠀⠀⠘⣖⡿⠁⠀⠀⠀⠀⢀⠀⢸⣿⣏⡴⠋⢀⡼⠋⠀⠀⠀⣼⡤⠚⠉⡜⠀⢀⡴⠀⠀⠀⠀⡴
⢸⡄⢸⠇⢰⠀⠀⠀⡀⠀⡆⠀⣿⠃⠀⠀⠀⠀⠀⠈⠀⢸⣿⠏⣀⡴⠋⠀⠀⠀⠀⠀⣿⣶⠁⣰⡡⠒⠁⢸⠀⠀⡠⠾⠁
⠈⣇⡿⠀⡜⠀⠀⠀⠃⠀⢳⠀⢻⠀⠀⠀⠀⠀⠀⡄⠀⢸⣏⣾⠟⠁⠀⠀⠀⠀⠀⢸⣿⠿⠒⠉⠀⠀⠀⣸⠤⠊⢠⡇
⠀⣿⡇⠀⡇⠀⠀⠀⡀⠀⢸⠀⣼⡄⠀⠀⠀⠀⠀⠃⠀⣸⡿⠁⠀⠀⡀⠀⠀⠄⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⣴⠏⡾
⡄⣽⡇⠀⡇⠀⢰⡄⠇⠀⢸⣴⣿⠇⠀⠀⠀⡜⠸⠀⢠⣏⠄⠀⢀⠄⠀⢀⠎⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡼⣁⠀⠀⢀⠤⠆
⢳⣹⣿⣆⢻⣼⣠⡿⢠⢀⣾⣿⣿⡆⠀⠀⣰⢁⠇⢀⣾⣵⠁⡠⠃⠀⢀⠎⢀⣼⣧⡤⠆⠴⠂⢐⣀⡤⠞⠓⠉⠁⢀⣤⠞⣓⠶⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣙⣷⣶⣷⣯⣯⢀⣾⣿⢏⡜⠁⠀⢠⠇⣠⣾⣿⣿⣶⠿⠖⠛⠉⠀⣀⠀⠀⢀⣴⠟⡩⠚⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡴⣫⣬⠞⡡⠃⣴⣿⠿⠛⠉⢀⡠⠴⠊⠁⠀⠀⠀⣠⣿⣩⠾⢤⠖⠀⠀⠀⣀
⢿⡟⣿⣩⣬⢻⡟⣻⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣣⡾⣡⡾⢋⣠⡴⠞⣉⣤⠖⠂⠀⠀⠀⣠⡞⢉⡀⠀⣠⠇⡠⠀⡺⠋⠁
⡎⣏⡻⢧⠼⣏⡹⢭⣿⣻⠿⡟⢻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣽⣿⣿⣥⠶⠛⢉⠄⠂⠀⠀⢀⣴⣿⡷⠧⠴⠾⠿⠧⠴⣪⠶⠒⠈⠁
⢷⣼⣷⣴⣿⣥⡽⣿⣴⡿⢶⡷⢾⣷⢻⣋⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡥⢶⡨⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁
⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢻⣨⡋⡶⡗⢺⣽⣟⣿⣿⣿⣿⡿⠿⠛⠊⢁⣠⣴⣾⣿⣿⣆⣁⠠⠀⢀⣀⣴⣾⣍⣉⣁⠀⠒
⣽⣿⣯⣿⣿⣿⣿⡿⣿⣿⣿⣿⣻⣾⢻⡟⡻⠻⣤⡼⣿⣿⣿⣿⣷⣶⠶⠿⠿⠛⢛⣛⣛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⢛⣀⣠⠴⠶
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⡟⣺⣯⡟⡿⣿⣿⣿⣟⣡⣤⣲⣟⣋⡠⠤⢀⣀⣒⡀⠠⠤⠴⠶⠂⠀⠠⠀⢀⡠⠴⠾⠿⠿⠍⠄⠑⢤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⡿⣤⠯⡷⢿⣿⣿⣿⣿⣿⣿⣟⠛⢙⣉⣩⡥⠄⠀⢀⣀⠤⠒⠉⢀⣠⣶⣻⡶⠒⠒⡲⠶⠒⠀⠀⠀⠀⠀⣠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⠭⣧⡿⠬⣳⠷⣮⣿⣿⣿⣿⣿⣿⣛⣋⣉⣉⣤⠤⠖⠊⠉⣀⣠⠴⠚⠛⠛⠯⢥⣤⣖⣋⣀⣀⣀⣀⣤⠤⢖⡞⠁
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡜⢺⣅⢼⣭⣿⣿⣿⣯⡉⠉⠉⠉⣁⣀⣠⡤⠶⢶⣿⣿⣷⣶⠶⠶⠶⠤⠄⠀⠀⠉⠉⠉⠁⠀⣀⡴⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⢧⣴⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣳⣖⠲⠤⢤⣀⠉⠙⠓⠿⣷⣒⠒⠒⢒⣀⣩⠥⠖⠊⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⡿⠳⡜⢺⢷⣾⣼⣿⣿⣿⣉⠛⠿⢍⣒⠲⠭⠟⣓⣷⠶⢤⣍⣁⠂⠒⠀⠉⠛⠿⣿⡟⠵⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⡀⠀⣰⠋⠘⡆⠀⣠⠖⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣄⠀⠀⡾⠘⣇⠀⡼⠀⠳⡇⠀⠀⣷⡞⠁⢰⡇⣠⠖⠉⣀⣠⠴⠒⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠳⣄⣷⠀⠸⣦⡇⠀⠀⠹⡄⠀⢸⡀⠀⣼⡞⠁⠀⢀⡋⠀⠀⣰⠃⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠤⢧⣀⠀⠈⠻⣄⠀⠘⡇⠀⢀⠀⢹⡄⢸⡇⣠⠟⠀⠀⠀⢸⠁⠀⣰⡷⠚⠋⢉⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⢧⠀⠀⠈⠙⠶⣄⡈⢷⡀⣿⠀⠈⡄⠀⢿⣼⣷⠏⠀⢠⠃⠀⡿⠀⣼⠃⠀⣠⡶⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣏⠓⢦⣌⢳⡀⠈⠢⣀⠈⠙⢶⣿⣿⡄⢀⣷⣀⣼⣿⣿⡀⣤⡏⠀⣼⣣⡾⣁⡤⠾⠛⠉⠉⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠙⠻⣦⡀⠈⠳⣤⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⠁⢀⡠⠐⠀⣠⠞⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠰⡒⠒⠶⠿⠦⣤⣤⣈⡻⣦⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠚⠁⠀⣠⠾⠃⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⡤⠤⠴⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⢞⣁⣠⠴⠞⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢞⠉⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠦⣤⣤⣤⡤⠤⠴⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣀⡀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠤⢄⣀⡀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠰⡖⠒⠒⠚⠛⠋⠉⢉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣠⣤⡔⠊
⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣤⡴⠞⣋⡽⠟⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣯⣍⡉⠉⠉⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⣠⠞⠉⠀⣀⠴⠞⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣆⠀⠙⢿⣍⠛⠛⠳⣶⠶⠦⠬⠆
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⠞⠁⠀⠐⠉⢀⣀⡤⠾⣻⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠓⢄⠀⠙⢶⣄⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⠖⣺⡿⠋⢠⡞⣻⠃⠀⡾⠙⢈⡿⣿⠋⠙⣿⠀⢹⡟⣯⠻⢦⣀⠀⠁⠀⠈⢻⡉⠳⢤⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢠⠟⢠⡏⠀⠰⠁⢀⡾⢱⡿⡇⠀⢹⠀⠸⣇⠈⢷⡀⠉⠓⠦⣄⡀⠀⢳⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣁⣠⡴⢾⠏⠀⢸⠁⠀⠁⢠⣾⠁⢸⡇⢹⡀⠈⡀⠀⣿⣄⠀⠙⣦⡀⠀⠀⢿⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢠⠏⠀⠀⣸⠀⠀⡰⠋⡟⠀⠈⡇⠀⢣⡀⠁⢀⡇⠹⡆⠀⢿⠙⢦⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠤⠖⠋⠹⠄⠊⠀⢸⠇⢀⡼⢿⠀⠀⢱⡄⣸⠁⠀⢹⡄⡾⠀⠀⠙⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠴⠋⠀⢸⡆⡠⠋⠀⠁⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⢀⠔⠦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠈⠙⢏⠠⡀⠀⢀⡞⠀⠀⢹⡍⠀⠀⣠⠔⢺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠦⣄⡀⡴⠋⠓⢦⡀⡇⠀⠀⠀⠱⣇⣠⡾⠀⠀⠀⠀⣇⣠⠊⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⠙⢧⡀⠀⠀⠙⡇⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⢻⠁⠀⠀⠀⠸⠀⣀⣤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⠀⠀⠀⠀⠉⢦⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⡄⠀⠀⠀⠀⠀⢣⠀⢸⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠇⠀⠀⠀⡜⠀⠀⠀⢀⣠⣥⡤⠤⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠚⠳⡜⢆⠀⠀⠀⠀⠈⡇⠀⢣⠀⠀⠀⠀⡇⠀⠀⠀⡴⠋⠀⠀⢀⠞⠀⠀⣠⣶⠭⠔⠒⠒⠒⠒⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⢦⠳⣄⠀⠀⠀⢸⡄⠈⢧⡀⠀⡀⣧⡀⣀⣾⠁⠀⢀⡴⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠦⣄⠀⠀⠀⠀⠳⣌⠳⡄⢀⢀⡛⠃⠻⢹⡋⠁⢈⣟⢉⠻⣄⡴⠋⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠈⠙⠦⣄⡀⠀⠀⢙⡾⠊⠛⠄⠀⠀⠈⠁⠀⠉⠀⠞⠀⠀⢲⣄⡼⠁⣀⡤⣶⡶⠶⠶⠖⠛⠀⡹⠂
⠀⠀⠀⠀⠀⢀⣴⡋⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣉⣳⣦⡜⠇⠀⠈⠀⠀⠀⠀⠄⠂⠀⠀⠀⠠⠂⠄⠘⢧⡾⠛⠉⠀⠀⠀⠀⠀⢀⡴⢅
⠀⠀⠀⠀⠀⡤⣬⣉⣑⣲⠖⠲⠦⠤⢄⣀⠀⠉⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠀⠁⠀⠀⢀⣿⣀⡤⠤⠤⣄⡀⠀⣠⣏⡀⠀⠑⡄
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⢿⡆⠀⠀⠀⠀⢈⠄⠰⠲⠘⠁⠀⠁⠀⠀⠀⢀⢈⣟⡁⠀⠀⠀⠀⢉⡟⠳⣌⠉⠑⠢⢨
⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡿⠋⠀⠀⣀⡤⠚⠧⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠖⢋⣉⣁⣀⡀⠬⠭⠽⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⠼⢿⡛⠛⠋⠁⠀⠀⠀⠈⢦⣀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡺⠋⠉⠀⠀⠀⠀⢀⣠⡶⠾⡿⣱⡄⡀⠀⠀⠀⠀⠀⠀⠀⠂⣰⠾⠃⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡼⣽⠋⠀⠀⠀⠀⣀⡶⠞⢉⣠⡴⠟⠋⠉⢙⣷⡦⠶⡦⣠⣤⣦⣴⡦⢧⠀⠀⠀⠀⠀⠈⠻⡍⠻⠁⠒⠒⠠⠤⠂
⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⠀⣀⡤⠚⠁⣠⠔⡟⠁⠀⠀⠀⡰⠋⠀⠀⢀⣼⠋⠀⠸⠇⠀⠘⡗⠶⠤⠤⠒⠒⠉⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣼⣀⠴⠋⡟⠀⡠⠞⢁⡞⠀⠀⠀⣠⡾⠁⠀⠀⣠⢟⠇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣇⡞⠁⠀⡞⠀⠀⢀⠞⠁⡇⠀⠀⢰⠃⢸⠀⠀⠀⠀⡇⠀⠀⢹⠤⣀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⠁⠀⣠⠋⠀⠀⢧⠀⠀⡎⠀⠈⣆⠀⠀⠀⡅⠀⠀⠸⡄⠈⠉⠓⠒⠐⠠⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠌⠀⡰⠩⡄⠀⢀⠾⡄⢸⠀⠀⠀⠈⣦⡀⠀⢧⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠃⠀⢣⢀⠞⠀⠙⢾⠀⠀⠀⢰⠁⠑⣄⠘⡝⢤⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠋⠀⠀⠀⠀⢣⡀⢀⡏⠀⠀⠈⠙⠁⠀⠉⠒⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠐⠀⠀⠔⢶⡂⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⢃⠢⡄⠀⢀⠉⠀⢸⡇⠀⠆⠀⠀⢃⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠈⢀⠈⠀⠀⢸⡇⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣧⠀⠀⠈⠀⠀⡄⠁⠀⠀⠀⠀⠆⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠀⠀⠀⠸⡀⡀⠀⠀⡘⠀⠀⠀⢀⡄⠀⠀⠀⠄⠐⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢒⠛⠀⠘⠄⠠⣄⠀⠀⠀⠀⢦⡀⠀⠀⣠⣦⣷⣤⣰⣃⣤⣀⣴⢏⡴⠂⠀⠀⠀⠐⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠢⠈⠳⣄⡀⠀⠀⢱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠋⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠈⠁⠈⠒⠬⢝⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⣀⣠⠄⠀⠀⢀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣥⡄⢀⠀⠀⠀⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠠⠤⠤⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠢⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠒⠒⠈⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠒⠒⠒⠂⠁⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠀⠀⠀⠀⠀⡠⠐⠉⠀⣰⠛⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠈⠑⢦⡀⠀⠀⠀⢀⣈⣑⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⠀⠀⢠⡾⠋⣰⠃⠈⠁⣩⢹⡏⢻⣾⡄⠀⠀⠀⠀⠀⡈⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡰⠃⠀⠀⠀⣿⠈⠇⠀⢻⠰⡀⠱⡀⠀⠰⡀⡀⠠⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠀⠅⠀⠙⣄⡀⣿⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⡀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠘⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠘⠃⢀⡇⠄⠡⠀⠀⡀⠲⠄⠀⠁⠃⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠘⢶⠇


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡀⠀⠀⢀⣄⡀⠀⠈⠉⠐⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠄⠀⠀⢀⡎⠀⠐⢿⣦⠀⠂⠈⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠌⠀⠀⢀⣾⣷⣤⣄⡀⢻⠀⠀⠀⢀⠀⠘⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣀⠀⠀⠀⢀⠎⠀⠀⢀⠾⣿⣿⣿⣿⡷⠌⠀⢴⣾⠇⠀⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠒⠠⡏⠀⠀⢀⡎⠀⠈⠻⣏⠁⠀⠀⠀⠀⠿⣇⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⡀⢀⠞⠉⠲⢄⡀⡏⠀⣀⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠊⠀⠀⠀⠀⠈⠁⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠤⠐⠒⠂⠈⠉⠉⠉⠉⠐⠒⠒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡼⠦⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠴⣧⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣽⠛⠂⠀⠀⠀⢠⠄⠀⠀⠀⠀⣠⡤⠄⠀⠙⠆⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⢄⡈⠛⣧⡄
⠀⠀⠀⠀⠀⣿⡫⠁⠀⠀⢀⡠⠞⣁⠀⠀⠀⠀⠈⠀⣠⣤⣴⡆⠀⠀⠀⠀⠀⠀⠘⠀⢠⡄⠀⢲⣍⠒⠺⣧
⠀⠀⠀⠀⣼⣛⠁⠀⠀⠉⡵⣠⣾⠇⠀⠀⠀⢀⢠⣾⣿⣽⣿⣤⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠈⣿⣣⠈⢿⡆
⠀⠀⠀⢰⣟⣵⡀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠰⠃⠀⠉⠛⠋⠙⢫⠇⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛⢃⣿⣟⠀⢾⣧
⠀⠀⢠⡿⠻⡿⢡⢸⠀⠀⠸⣿⣧⡔⠀⠀⠀⠀⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⡂⢾⣿⣿⡆⠘⣿⡆
⠀⢠⣟⠁⠀⢠⠇⡎⡀⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠎⠀⠀⠀⠀⠀⢠⣺⣷⣖⠒⢲⣯⣾⣿⣿⡇⠀⠨⢿⡄
⠰⣟⢋⠀⡄⠀⠀⠠⠁⠀⠀⢱⢿⡇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠠⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⡏⢿⣿⡇⠀⠐⣤⣟
⠼⣿⡃⢰⢀⠀⠀⠀⠀⠃⠀⠀⡟⣷⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⠟⠀⢸⡿⠃⠀⠠⣼⡟
⢸⣿⡇⠀⠘⣷⣶⣠⠀⠀⡄⠀⢸⣻⣧⣀⠀⠴⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣾⡟⠿⠀⠀⣼⠃⠀⠀⡄⣿⡿
⠘⢻⣿⡇⡀⠘⠿⣿⣇⠀⠹⠀⠀⣿⣿⣿⣠⠀⢁⣶⣿⣶⣄⡀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣦⣀⣴⢯⠄⠀⢠⣿⡟
⠀⠀⠘⢿⣷⣀⠀⠈⠹⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣏⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⢸⡟
⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⣰⣻⣿⣿⣿⡟⠀⠀⠘⢿⣯⡻⣿⣿⣿⡆⠀⠀⠈⠀⠀⠈⠟⣿⣿⣿⡾⡀⢸
⠀⠀⠀⠀⣼⡿⠏⣿⣆⠀⢼⣿⣿⣿⣿⠟⢀⡴⠂⠀⠈⠛⠿⠾⠿⠿⠻⣆⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⡃⢸
⠀⠀⠀⣺⣿⢃⡄⣏⠙⠶⢿⣿⢯⠋⠀⣰⣯⠖⠀⠀⠀⠐⣤⣤⣤⣤⣤⡙⠿⢦⠤⢤⡴⣿⡇⢘⣿⣏⠳⠛
⠀⡠⣾⣿⣿⣟⠀⢿⡆⠀⢺⢣⡇⠀⢀⣿⢏⣞⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣤⠤⠴⢞⢹⡇⢨⣿⣿⣅⡀
⠀⣰⣿⣿⣿⠏⣰⠘⣿⡄⠸⣾⡇⠀⠘⣿⣿⣿⡆⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⠁⠀⢰⣼⣿⠇⠀⣿⣿⣷⡆
⢠⣿⡿⣿⠙⢰⢻⡀⠈⣷⣦⠉⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠽⡿⣿⡏⠟⠁⠀⡀⢀⣿⡿⠋⠀⠀⠈⢿⣷⡀
⣼⢻⡇⡏⠀⣿⣼⠃⠀⠁⡿⢧⣰⡀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠃⠘⠁⠀⠀⡶⣿⣾⠏⠀⠀⠀⡀⢀⠀⢻⣧
⣿⠈⡇⠁⠀⢻⣿⣆⠀⠀⠀⠈⠻⣿⣧⣈⣑⠤⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⠳⠃⠀⡘⠂⠀⡇⢸⣾⣸⣿⡄
⠸⠀⠑⠀⠘⠘⣯⢷⡀⠀⠀⢀⡀⡙⠻⣿⣿⣭⡀⠀⠀⡘⡄⠀⠀⠀⠚⠉⠀⠀⠀⢳⡷⠀⠰⠃⢸⣿⢻⠋⡇
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠂⠀⠀⠹⣌⠣⡀⠈⠛⢿⠥⠀⠘⠦⠀⠀⠠⣄⣀⡀⠀⠀⠘⠇⠀⠀⠀⡼⠋⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠙⢦⡀⠀⠀⠈⠲⣄⡀⠀⠴⠶⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠈⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠶⠀⠻⠉⢂⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⢮⣍⠀⣀⢈⠵⠊⢡⣑⠠⠈⠘⠋⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠱⢆⡁⠀⠑⠁⠀⣀⣔⡏⠠⠀⠡⠊⢹⡄⣄⡁
⠀⠀⠀⠀⠀⠀⢠⢊⡴⠒⠒⣲⢚⡛⢻⡝⡄⣤⠋⠉⠉⣠⣴⠄⠽⠛⠃⠔⢱⡙⢦
⠀⠀⠀⠀⠀⠀⢸⠈⡔⠀⣀⡠⠤⣈⠢⡇⡇⢸⠀⠂⠎⢰⠏⠠⠂⠴⣀⡀⠐⠈⠆⢧⣀
⠀⠀⠀⠀⠀⠀⠈⣽⠀⠈⢃⡤⠄⠀⢀⠁⠀⠀⢀⣄⣀⣀⣠⣀⡀⣀⠀⠫⠁⠂⠀⠪⣑
⠀⠀⠀⢀⡀⠔⢻⡥⠂⠐⣭⠴⠒⠿⣿⢖⡮⠟⡄⠋⠈⠁⢻⢟⡁⠀⢀⠀⠀⢘⠀⠐⢬⢣
⠀⠀⢩⠁⡀⠐⡀⠀⡀⠀⠁⡆⠀⣀⠀⢿⡈⠀⠀⠀⠀⠀⠀⠈⠉⠓⣌⡀⢢⣀⣎⠀⠸⢸
⠀⠀⠀⡜⣴⠀⠼⠈⢆⠀⢀⡘⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⡉⠈⠐⠀⠈⠑⢦⡀
⠀⠀⠀⠘⠊⢀⢠⡀⠈⠀⠊⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡆⠀⠀⠀⠐⠀⠀⠀⠃⠀⢠⠈⡅⠂⠀⠃
⠀⠀⠀⠀⠀⠻⡀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠳⠥⠄⢌⡲
⠀⠀⠀⠀⠀⠀⠩⢄⢄⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⢠⢄⠑⠒⠒⠀⠂⠈
⠀⠀⠀⠀⠀⡆⠀⠀⠁⠂⠑⢄⠀⠀⠀⠀⠀⡠⠒⠁⠀⠈⠓⠒⠀⠨⠲⠀⠃⡀⠣
⠀⠀⠀⠀⠀⠀⢈⡶⠊⠡⠀⠈⢦⣤⣠⠔⠛⠀⠀⠀⠀⡀⣀⡀⡠⠃⠉⠂⠠⠴⠚
⠀⠀⠀⠀⠐⠀⢸⠁⢠⡈⠈⠢⠀⢄⠀⡎⠓⠐⠂⠀⠊⠁⠀⢀⠀⠂⠤⠤⡀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠓⠀⠀⠈⠀⠃⠀⢃⠀⠀⠀⠀⠓⠄⠀⠁⠀⠀⠀⠃⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠺⠏⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠓⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠋⠀⡀⢀⡾⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢺⡀⠀⠀⠉⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⡀⡀⠀⠠⡾⠀⢨⣵⣄⡀⠀⠀⠀⠀⣀⣬⣮⡳⠘⣿⡀⠀⠈⢆⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠋⠀⠀⢸⡇⠰⠻⠿⡿⠁⠀⠀⠀⠀⠘⡿⠿⠛⡢⢹⠀⠀⠙⠂⠷⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣠⣢⠀⢸⠀⠀⠁⠀⠀⢰⣿⡿⢿⣗⡄⠀⠀⠀⠀⢸⡇⠀⢤⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠡⠃⡄⣼⠀⠀⠤⠄⠀⠘⣿⣷⣾⣿⠃⠀⠀⠲⠀⠈⣧⠀⠈⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⢚⣴⣿⠀⡆⡄⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⣦⢰⠀⢻⣦⣐⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣟⡀⣟⡀⣧⢻⣦⣀⡹⠛⠻⡟⠻⢯⣀⣴⡟⡸⠀⣸⢀⣹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⢛⠇⠘⢆⠻⣟⣧⠀⠀⠀⢀⣼⣛⠟⡼⠀⢠⠏⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠹⠃⣌⠳⣌⣙⠳⣦⣶⠿⢋⣡⡞⢠⡘⢠⣀⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣦⣠⢀⠀⣈⠄⠈⠉⠛⠲⠒⠚⠋⠁⠀⠀⠁⠀⢈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣾⢰⣿⣿⣦⣷⣿⣀⣤⣾⣦⣠⣦⣆⣠⣠⣀⣠⡄⣰⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠳⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠹⣷⣻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⢛⣿⣿⠟⢁⣠⣤⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠈⢿⣷⣯⣭⣟⣛⣿⣿⣿⡿⢛⣵⡾⢻⠿⠇⠀⢀⡴⠚⠉⠉⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⠀⠀⠀⢸⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⡞⠀⠀⠸⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⠀⠀⠀⠈⠀⠰⠦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⡿⠃⠀⠀⠀⠀⠀⠀⣿⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⡀⢰⣶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠠⠁⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠎⠀⢀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢢⣀⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡾⠀⢀⣸⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢣⣈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠻⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠈⠉⠉⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣡⠄⣠⣤⠀⡟⢁⡤⣼⢃⣤⡀⣤⣠⡄⠀⢀⣴⣯⣼⢁⡤⡄⣼⠇⢰⣄⠀⣤⢀⣤⡀⡤⣤⢠⣤⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⣸⣇⠞⣸⣇⣿⡴⣇⡼⣶⣡⠏⢼⡁⠀⢾⡾⠁⣯⡸⣷⡡⣯⡠⠋⣏⣰⣇⡿⣞⣸⡥⢋⡿⣎⡴⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠂⠀⣀⠀⠀⠀⢠⣢⡘⠋⢈⠷⣣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸
⠀⠀⠀⠀⠀⢤⣈⠂⠀⠀⠎⠁⣏⠹⢗⣋⢁⠙⠧⢔⡄⠀⠀⠠⠺⠇⢀⠀⠀⠀⠀⠈⠁⣠⣞⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠙⠁⠛⢣⣄⣓⢬⠄⣬⡒⠇⠀⠠⠀⠀⡀⠀⢉⠖⠀⠀⠾⢿⡟⠉⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢶⢄⣤⣼⢀⠁⠾⠧⠕⡀⡄⠀⠀⡀⣠⢴⠛⢋⠠⢂⠀⠤⣀⡄⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠐⠂⢌⠉⠰⠆⠁⠀⠈⠉⢿⡁⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠈⠑⠂⠤⡀⠀⠀⠁⠈⠼⠀⠀⠀⠈⠙⠷⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠢⣄⠉⠒⠄⣐⠂⠀⣆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠄⡠⠀⠀⠤⠀⠀⠀⠠⢠⠐
⠀⠀⠀⠀⠉⠀⣠⣿⡟⠓⠚⢷⣾⡚⠛⠋⠙⠲⠀⠀⠀⠠⡀⣠⡆⠀⠈⢹⣦⡇⣀⠀⠂⠠⠠
⠀⠀⠠⠊⢀⠾⠛⣿⠷⠒⠂⠀⠀⠘⠯⠶⠲⢾⠆⠀⠐⣎⠂⠀⠀⠀⠀⠈⠨⠛⡧⢶⣠⣇⣰
⠀⠀⠀⠈⠁⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⢀
⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠖⠦⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢡⣶⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣦⠀⠉⠀⣐⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⠀⠀⢄⠀⠀⡇⠀⡇⠀⡇⠀⢰⠀⠀⡞⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠐⣆⠈⢆⠀⠸⡀⠀⡇⠀⡇⢀⡇⠀⡇⠀⡼⠀⢠⠂⠀⡠⠋
⠀⠀⠀⠀⠠⡀⠀⠀⣄⠈⢣⡀⠈⢆⠘⡆⠀⢇⠀⢧⠀⡇⢸⠀⢸⠀⣰⠁⣰⠃⢀⡜⠁⢀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠢⣄⠈⠣⡀⠑⣄⠈⢆⠘⡄⠸⡀⢸⠀⡇⣸⠀⡇⢠⠃⡰⠃⣠⠊⢀⠔⠁⢀⡴⠊
⠀⢀⡀⠀⠀⠤⡀⠈⠳⢄⠈⢢⡈⢢⡈⢧⠹⡀⢇⢸⠀⡇⡇⢸⢀⠏⡰⠁⡴⢁⡴⠋⣀⠔⠉⢀⡤⠂
⠀⠀⠉⠒⠤⣀⠈⠑⢤⡀⠑⢤⡙⢦⠑⣌⢧⠱⠘⠈⠀⠁⠃⠃⠞⡰⢡⠎⡠⠋⡠⠞⢁⡤⠚⠁⣀⠤⠒⠉
⠀⠀⠠⠤⣀⡀⠉⠒⠤⣈⠓⢤⡙⠦⡑⠈⣠⠔⠚⠉⠉⠉⠉⠑⠲⢄⡁⠊⡴⢊⡤⠚⣁⡤⠖⠋⢁⣀⡤⠄
⠤⢤⣀⣀⠀⠉⠙⠒⠤⢄⣙⠲⢬⠃⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠘⡡⠖⣋⡡⠤⠒⠊⢉⣀⣀⠤⠤
⠀⢀⣀⣀⣉⠉⠑⠒⠒⠤⠬⢍⠃⢰⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢐⡩⠥⠴⠒⠚⠉⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠉⠉⠉⢉⣉⣑⣒⣲⣤⣿⣤⣤⣤⣿⣿⣿⣾⣶⣷⣴⣶⣤⣶⣦⣼⣿⣒⣒⡚⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠐⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈⠙⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡐⠉⠙⠒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣴⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⡾⠉⠙⢁⡲⣦⣄⡀⠀⣀⡠⠤⠖⠂⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠙⢿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠘⢧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣾⣿⣷⣀⣀⣀⠀⠀⢹⣼⠀⠀⠀⠀⠀⠀⠀⢀⠜⠊⠉⢂
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⣿⣿⣿⣿⣙⡻⣿⣷⡄⠸⣿⠀⠀⢀⣀⣤⠞⠉⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣾⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡼⠻⣮⢙⡿⣿⣿⣿⣾⠿⠒⠠⠐⠒⢿⣿⡿⠀⠀⠀⠀⠀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⢆⣤⢀⣴⠋⠀⠀⠀⠀⠀⡜⠁⠀⠘⠿⡹⣏⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⠀⠈⠙⢳⡀⠀⠀⠀⢀⣾⣄⠀⠀⠀⠀⠈⣻⡆⠀⠀⠀⠀⠀⠀⠀⣀⡝⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⢣⠀⠀⢀⡾⠁⠈⠙⠢⣄⠁⠠⣯⡇⠀⠀⢀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣮⣧⣀⡾⠁⠀⠀⠀⠀⠈⠙⠲⢬⣥⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⢰⣿⡄⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⣿⣿⣶⠶⠿⠿⠿⠶⣾⣿⣿⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡾⠛⣁⣤⣴⣶⣶⣶⣦⣤⡉⠙⢶⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣶⣿⣿⣿⣤⣽⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣛⣛⣛⣂⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⠍⠉⠉⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣭⣭⣽⣯⣬⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣯⣿⣿⣭⣿⣯⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢈⠀⠀⣠⠀⡀⠀⡀⠀⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢰⣖⠀⢀⠀⡆⠀⡃⠀⣸⣤⡾⢁⡔⢁⠞⢀⠞⣠⡾⠃⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⡅⠀⠙⢧⠸⡄⣷⠀⡀⣠⣿⡿⢁⡞⡡⢋⠄⣠⡼⠋⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⢘⢦⡀⢀⣳⣷⣽⣶⣿⣿⣿⣧⣾⣾⣇⣴⣾⢅⡠⠀⠀⢀⣠⠄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢷⣮⣹⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢟⣡⡤⠒⠈⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⣿⡟⣋⣹⠦⠤⠀⠀⠈⠁⠀⠈⣲⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⢀⠀⠀⠀⠀⠀⢻⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⣩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠯⠌
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣀⠀⠛⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠛⠋⠉⣭⣥⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢯⡿⣿⣿⣿⣿⣿⣆⠈⠙⠒⠆⢄⣀⣘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⡉⠻⣿⣧⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⢠⠞⢋⣿⣿⣷⣿⣾⣿⣿⣿⣿⣏⠿⡇⠀⠀⠈⢿⣿⣦⣀⣻⡄
⠀⠀⠀⠀⠀⠀⡤⠈⠀⢀⠠⠚⠁⢠⡾⢫⢿⣿⣿⡏⣿⣿⢿⡘⣿⣦⡀⠀⠁⢠⣸⣿⣿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⣿⠃⡟⠘⡟⢙⠀⢸⣿⠘⡇⣿⣿⣿⣶⣤⣬⣿⣿⣧⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠟⢸⠇⠀⠁⢺⠀⣿⣿⠀⡇⣿⡿⣏⡟⢹⣆⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈⠀⣿⡏⠀⢧⡉⠁⠈⡃⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠋⠀⠀⠀⠀⠀⠈⠛⠋⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠸⠆⠀⠀⠀⠘⠃⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣴⠛⠲⠶⣤⣤⣀⣀⣀⡈⠁⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣧⠀⣼⠃⠀⠀⠀⠀⠀⠈⢩⡟⠙⡷⣤⡀⠀⠀⠉⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⢩⡿⡶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡟⠀⠀⠁⠈⠙⠳⢦⣤⣀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠰⣤⣄⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣰⣿⡷⣦⣄⡀⠀⠀⠀⠀⠀⠉⠙⣛⣶⡶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⣼⡟⠛⢳⠛⠞⠟⣷⣦⣀⣂⣴⠾⠛⠉⠀⠀⣿⠀⠠⠶⠶⠂
⠀⠀⢀⣀⡀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢰⡟⠆⠀⢀⣾⣿⣿⣅⢂⠑⠀⠠⠈⠻⢻⡏⠈⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠈⠉⠁⢀⡾⠁⠀⠀⠀⠀⠀⢀⣈⡿⠀⠈⢀⣾⣿⣍⡉⠿⣷⣤⡀⠂⠚⠀⣾⠁⠀⠀⣀⣤⡴⠶⠞⢻⡄
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⣄⡾⠃⠀⢀⣾⢿⢿⣦⣍⠘⡆⠉⢿⣷⣤⣀⣿⣤⣶⣿⣿⠃⠀⠀⠀⠀⢻⣄
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢄⡾⠇⠈⠀⣼⢟⠂⢂⠳⢻⣿⣦⣙⣢⡼⢞⠛⠛⠉⠘⣿⣿⠀⠀⠀⠀⠀⣀⣹⡆
⠀⠀⢸⣿⣶⣦⣤⣀⠠⠀⢀⢀⡾⠇⠀⠀⣸⡿⢮⣍⡈⢂⠘⠛⣾⣿⠁⠈⠀⠀⠀⠀⠀⢹⡟⣀⣠⡴⠞⠛⠉⠁
⠀⠀⠀⢿⡉⣉⡙⡻⠿⣶⣥⣿⠃⡈⠁⢠⡟⠀⠀⠉⠻⢦⣼⣏⢻⣿⠀⠀⠀⢀⠀⢄⣤⡴⠟⠉
⠀⠀⠀⠸⣷⣤⣠⣀⢑⠋⡻⣷⣔⠀⠂⣿⠁⠀⠀⠀⠀⠀⠙⢿⡄⣿⢀⣠⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠷⢾⣤⣶⡿⣆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠑⢄⢠⠋⠆⡠⣆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢄⢀⡤⠀⡀⢀⠲⢼⡀⠄⠟⠀⡿⡤⠃⢠⠔⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡉⢿⠈⢻⠁⢏⣧⡉⢣⡀⠉⠪⣧⢸⢸⠁⢀⡾⠘⠃⣩⣃⢠⠖⢹⡠⠊⣍⠤⠖⣺⡢⠒⠈⠉⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠤⠤⠤⢤⡈⠢⡈⠙⢷⠀⠀⡆⣸⣭⡉⠁⠳⢌⡂⣹⣾⣿⣶⣾⠐⢁⣰⠇⣀⣞⠀⢸⠀⢘⡁⡠⠚⠉⡹⠞⠓⠐⠧⠤⡤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢠⡯⣉⠀⠛⢤⣴⣶⣿⣻⣧⠤⠬⠷⠬⣐⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⣀⡭⡗⢸⣴⣿⣷⡤⠄⠚⠓⢢⠀⢀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⢀⣀⡠⠤⠈⠳⠤⣈⢮⡳⠦⣽⣿⣿⣿⣿⣥⣤⣤⣐⣲⣼⣿⣿⣿⣿⣿⣿⡖⠀⠍⠛⢥⣈⣻⣯⣿⣿⢛⡋⠉⠲⢞⡇⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⠀⣠⣊⣀⠀⣠⣼⣯⣿⣿⣿⣋⣀⣀⣠⠔⠋⠜⣻⢿⡿⢿⡟⠙⠢⣤⢤⡤⠭⣿⣿⣿⡍⠋⠙⠶⡤⠬⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠈⠉⢩⣋⡝⠁⢀⡞⠙⣿⢻⡏⣽⡰⠁⢀⣀⡼⠁⢸⠀⠈⣧⠀⠀⠱⣤⣱⠀⠈⠆⡁⠈⢦⡀⠀⢹⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠫⠴⢶⣩⡄⢠⠇⠀⣷⣄⠛⠿⠅⡇⣴⠀⡌⢣⠀⣬⢹⢳⢤⡅⠀⠀⣀⣂⣧⡀⠀⡏⠒⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠓⠃⠘⣠⠣⢌⡶⠀⠀⢈⡍⠣⠄⠀⡷⡄⠃⠘⠀⠉⠑⠋⠹⣄⣿⠋⠢⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣁⠴⠋⢣⠀⢠⠊⠀⠀⠀⢀⠇⠀⠀⢠⡀⠀⠀⠃⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⢀⡤⠊⠀⠀⡠⠃⠈⠑⠢⢄⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⠒⠊⠉⠀⠈⠒⠤⣰⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⢠⠀⠀⠀⠀⠀⠀⢦⠤⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⡀
⣠⣿⣜⡁⠀⠀⠀⠀⡜⢶⣄⠀⠀⢀⣤⣧⣌⡁⠀⠀⠀⢀⢫⣍⣛⡋⠁⠀⣠⣼⣴⡁⠀⠀⠀⢠⡐⣦⣄
⣿⣿⣿⣿⣆⢄⠐⠀⠍⢐⠂⠀⢘⣿⣿⣿⣿⣿⡤⠄⠐⠈⠉⣉⢇⠀⢀⣿⣿⣿⢿⣿⣦⢤⠐⠀⠍⢐⠀⢀⣹
⣿⣿⣿⣿⡧⢈⠀⢼⣶⣽⡀⠈⠭⢿⣿⣿⣿⣿⡇⣀⠀⣶⣴⣵⠀⠀⡭⠿⣿⣿⣿⣿⡷⢈⠀⢸⣶⣽⡀⠀⠽
⠋⠙⢉⠁⡀⠒⣻⣟⣿⣿⠅⠧⠰⠔⠉⠙⢉⠁⡀⠒⣿⣻⣿⣿⠴⢥⢒⠤⠋⠉⠋⡉⡀⠒⢻⣟⣿⣿⠥⠧⠠
⠚⠢⠌⢐⢠⣿⠀⠻⠿⠋⠄⠉⠀⠀⠚⠢⠈⠘⣤⠃⠄⠻⠿⠁⡄⠀⠀⠀⠐⠳⢌⠀⣢⡟⠀⠹⠿⠋⠄⠉
⠀⠀⠀⢹⣼⢃⠖⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣧⡏⠜⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢧⣾⣡⠆⠀⠀⠀⠁
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡁⣀⡀⠀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠶⠛⠃⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣞⣿⣟⣿⡦⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠰⠀⠐⠉⡡⠀⠀⠀⠀⢀⣤⣤⣴⡦⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣼⣿⣿⣟⣱⠏⠀⠀⠀⢈⠇⠈
⠀⠀⠀⠀⠀⠀⡄⠀⣴⣎⠠⠂⠀⠀⢠⢦⡌⣿⣿⡿⣮⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠋⠛⠛⠀⠀⠀⠀⠘⢸
⠀⠀⠀⠀⠀⠜⠁⣸⢿⠏⡜⡁⡄⡀⠆⠸⣿⣾⣿⣿⣿⠃⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠆⠀⠀⠀⠐⢤⡀
⠀⠀⠀⡀⠀⠀⠐⠁⣿⠀⠀⠑⠸⡇⢀⡾⡈⠹⠟⢃⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠃
⠀⠀⡰⠃⠘⠀⠀⠘⡇⡀⠀⠜⠀⢣⣼⠉⠡⣤⣤⣞⠑⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠈⢌⢳⡄
⠀⠸⠁⠀⠀⠀⠀⠀⣧⠇⠀⠀⠀⠸⣯⠀⠀⠈⣩⣽⡗⣠⣏⢀⠄⠀⢀⣠⣤⠴⠞⠛⠲⣤⠀⠀⠐⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠈⡄⠀⠀⠄⠀⣿⣿⣷⠀⠀⠀⢻⡇⠀⠈⠉⠉⠚⣿⠃⠀⢀⣰⢟⣄⡀⠀⠀⢀⣠⡜⣧⠀⠀⠀⠀⠀⠀⢠⠀⡜⡿⣶⠀⠀⠀⢠⡄
⠀⠀⠀⢀⠇⠀⠀⠀⢸⣿⣹⣷⡀⠀⠈⣷⡀⠀⠀⠐⠛⣿⣤⡀⠀⣿⣿⣿⣿⣿⣷⡙⠛⢛⣿⠀⠀⠀⠀⠀⣴⡟⢸⣿⣌⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠈⠀⠀⢠⣀⣼⡿⣿⠿⣷⣰⠀⠘⢿⣆⠀⠀⢴⣿⣿⠦⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⣾⣤⣿⢿⣿⣦⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢰⢏⡼⠀⢹⠃⣿⡿⣷⡀⠘⣿⡄⠒⠂⢠⣾⣷⣶⢯⣿⣿⢿⣿⣿⣿⣿⠿⣿⠄⠀⠀⠀⡘⠃⠸⡏⢾⣿⣿⣿⠂⠐
⠀⠀⠀⠀⠀⠀⠈⠛⠳⠀⠀⡴⣿⣧⣿⡇⢠⣿⣷⣷⣦⣌⠋⡩⣷⣾⣯⣶⡞⢻⣷⣿⣿⣿⣿⡆⡶⢀⣴⡄⠀⠀⠀⠘⣻⢿⡉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣦⠘⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠄⣿⣯⠇⠀⠀⠀⠀⠀⣿⠟⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠿⠟⢡⣿⣿⣿⣿⣿⣿⣿⣶⡦⣤⣼⣧⣿⣿⣿⣿⣿⡿⠿⠊⠀⢻⠇⠀⠀⠐⠀⠀⠀⠁⠀⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢣⣠⣿⣭⠛⣿⣿⣿⣿⣿⣿⣷⣍⣿⡿⠿⠛⠉⢻⠁⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣾⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠣⠇⢿⣦⣉⡻⣷⣭⣻⢿⣿⣿⣿⣿⣷⡀⠀⠀⣀⠴⠀⠈⠂⠀⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠹⣯⡙⢜⠫⣿⣧⡻⣿⣿⣿⣿⣷⣄⠀⠛⠀⡆⠀⢀⠜⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡇⢀⣷⣀⠀⢰⡄⢢⡽⣯⣛⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡗⢻⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡾⣷⣿⣿⡇⣠⡜⢳⡄⠧⢹⣿⢦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⠀⠀⠀⠀⠄⠀⠀⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⣱⣿⡿⣿⣇⣻⣴⠀⢿⣼⡀⢿⣟⣷⣿⣿⡟⣿⢿⣿⣿⣿⣿⠠⠤⢀⡶⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣽⣾⣿⣿⣿⣿⣿⣦⡼⠻⡇⠿⢛⣉⣭⣝⣿⣀⣾⣿⣿⣿⢡⣶⡖⡙⠃⡄⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣹⡿⢿⣿⣿⣿⣿⣯⣴⠃⠛⣼⣿⣋⣙⡛⢿⣿⣿⣿⣏⣷⢦⡉⠉⠁⣠⠀⣠⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠘⡆⠹⣿⡘⢿⣿⢿⣿⣿⣏⢀⢾⠟⠋⠭⣭⣴⣿⣿⣭⣾⣿⣿⣴⣤⣴⣶⣦⣤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠾⢀⠀⠀⢿⣷⠈⠛⣇⢻⣿⡏⣠⣶⢞⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡣⠛⠻⣷⠸⡇

⠀⠀⠀⠀⠀⣇⡴⠪⡀⣨⡶⢋⡵⠊
⠀⠀⠀⠀⠀⣿⠗⣠⢟⡡⢞⠍⢀⠂⠀⠀⢈⠤⠀⢀⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢺⣷⢷⣷
⠀⠀⠀⠀⠀⣿⣾⡫⠋⠈⣀⣤⡶⠞⢁⠆⢀⣤⠔⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢾⣿
⠀⠀⠀⠀⠀⣿⣿⣴⠞⢛⣉⣵⣶⣤⠾⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣿
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⠀⢻⣿⣼⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⢹⣿⢺⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿
⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⣄⠀⠀⠀⡠⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⠀⣀⠈⢧⠀⠐⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣞⠀⠀⠀⠀⠀⠱⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠍⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡍⠠⠇⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⠀⠀⠐⠉⠀⠀⢀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⢘⠂⡢⠀⠀⠀⣇⣸⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠈⠱⠀⠀⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠀⠀⢠⣀⠀⠁⠀⡀⠀⠀⠀⢀⣀⠀⠀⠄⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠚⠋⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠠⠀⢠⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠈⠀⠀⠎⢀⡀⢀⠀⠆⠀⣀⣀⠇⠀⠀⠄⠂⠀⠒⠐⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⢀⠔⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠶⠒⠒⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠰⠀⢀⡁⢠⡖⠁⠀⠉⠀⠀⣶⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⡄⠘⠆⠀⠀⠈⠁⠈⠀⠀⠈⢻⣷⡄⠀⢀⣿⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣉⣠⠖⠋⠀⠀⠀⢀⣠⣰⠿⠛⠁⣨⣿⠿⠃⣀⠙⢷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢋⣤⣴⣶⣶⠿⠗⠛⠋⢀⣠⣤⣾⣿⢻⡆⠀⣿⡀⠘⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⣿⣿⣡⣈⣡⣤⣤⣄⣤⣾⣶⣿⣿⠿⠛⠋⠘⠛⠀⠈⣿⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⣤⣤⡬⠉⠛⣻⡿⡿⠛⢻⡟⣯⡉⣰⡭⠿⠻⢗⠒⠒⠚⢽⡟
⠀⠀⠀⠀⠀⠀⠀⠠⣠⡴⠛⢏⡴⠚⡿⠿⠿⣦⢀⣼⠿⣿⠇⠸⣷⣤⡀⠀⠻⣤⠖⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⡼⡿⠁⠀⣴⠆⠀⡿⣿⠀⠀⠿⢀⠀⢸⣯⠉⣷⣤⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢉⠹⣷⠀⢘⡉⢀⡄⡼⣢⣷⡿⢿⣷⣿⡅⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃⢈⣃⣀⣈⠀⠃⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞⠛⠋⠛⢻⣆⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⠟⠛⠛⠛⠷⢦⣽⡄⠀⠀⠸⣿⡇⠀⠀⠀⢠⠂⣠⡴⠂⠀⡀⠀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣴⢿⡿⠿⠿⠟⠛⠒⠚⠓⠦⣄⠀⣿⡇⠀⠀⢀⣀⣼⣁⡠⠞⢃⣤⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣩⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣷⠀⢀⣾⣿⣿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣸⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⣀⠠⡄⢀⣾⠟⠁⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⣉⣤⠿⠛⠛⠛⢻⡀⠠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠋⠛⠁⠀⠀⠀⠀⠈⢧⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣇⣠⣴⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠙⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣋⣿⣛⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢂⠥⠞⠛⠓⠲⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠀⠀⠀⢀⣄⣠⣄⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠃⠀⠀⣠⣼⣋⣄⠉⠑⠀⠀⠀⠀⠀⠀⢽⣦⠶⢄
⠀⠀⠀⠀⠀⢰⣚⡛⠋⠹⣤⣀⣀⡀⠀⠀⠀⢹⠻⢿⠿⣧⣀⠀⠀⠀⠀⣼⡄⢺⣇⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣿⡻⣧⣰⠏⠀⠀⠀⠀⠀⠀⠘⡀⢀⣠⣼⠿⠛⠶⠄⢀⣿⢿⡼⠇⠘⣌⠺⣿⣄
⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⣀⡀⠀⠀⠢⡀⠀⠀⠘⠦⢉⣡⡄⠀⠀⠀⣸⣎⡘⠁⠀⠀⣿⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠠⣹⣄⡁⠂⠠⠄⠀⠀⢳⣄⠀⠀⠀⡀⠉⠉⠀⠀⢀⡇⡽⠁⠀⠀⢀⠇⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⡿⢦⣀⠀⠀⠀⠉⠀⢤⣀⠈⢢⡀⠀⠀⣼⣼⠇⠀⠀⣰⣾⡸⠋⣍⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠄⢀⠐⠋⢉⣍⠉⡷⢶⠖⠒⣲⣾⡇⠈⣧⠀⠀⣿⢋⠃⠀⢸⠃⣿⣡⡞⠿⠋
⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⣔⣽⢧⡿⠓⠲⣿⠿⣿⡷⠀⠸⡇⢀⣠⣿⡌⠀⢀⣠⣾⡏⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣙⣶⡾⠛⠛⠒⠚⠁⠀⠀⠀⠚⢻⡏⠻⠛⠚⢋⢹⣿⡇⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣿⠟⢶⣾⡍⠀⠀⠘⠁⠀⠀⠀⢸⡾⠛⠀⠀⠀⢸⠁⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠁⠀⢸⠏⣧⠀⠳⢤⣀⢱⠀⡀⠈⠀⠀⠀⠀⢀⡇⠀⠀⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠸⡇⠈⣀⡟⠀⢰⠀⠙⠲⠟⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡐⣆⠣⢻⡄⣿⠇⢀⡜⣀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢳⣼⡆⣌⣏⣿⠀⣿⣿⠇⣠⠀⠀⢀⣄⣴⡟⡱⠃⠀⠀⢀⢻⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⠻⢿⣿⣏⠀⠉⣿⣾⠁⡆⣠⡾⠛⠟⠉⠀⠀⠀⠀⠈⣿⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢰⠃⠀⠀⣼⣫⠏⠀⠀⠘⢿⠀⢷⡏⠀⠀⠀⠀⠀⠀⠀⣸⡼⠋⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡀⢀⡾⣋⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⠋⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠘⢼⣟⣡⣤⣤⠖⠀⠀⡈⢷⠀⣀⣤⠞⠁⠠⠊⠠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠰⣿⠟⢻⠃⡆⠀⢀⡿⣼⣟⣩⠴⠒⠁⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠄⢷⡀⡾⠁⣉⣡⡤⠤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠈⢣⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⡰⠁⠠
⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠀⠀⡂⢀⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠂⠀⠀⠁⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠑⠠⢐⠠⠂⢁⠠⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⡀⠀⠈⠀⠀⠀⡐⠀⠀⢀⠔⠁
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠂⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠠⠀⠀⡀⠐⠀⠀⢀⠔⠁
⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠌⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠐⠠⠀⠑⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠐⠀⠈⠀⡠⠊⠀⠀⠀⠀⠀⠁⠐⠀⢀⠠⠐⠈
⠀⠀⠁⠂⢀⠀⠀⠀⠠⠀⠀⠁⢄⠀⠀⠀⠀⠡⡂⠀⠁⠀⠀⠁⠀⠘⠀⡄⠀⡈⠀⠀⢀⠇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠘⢆⠠⠄⠀⠄⠠⠠⠄⠁⠠⠀⠀⣠⠃⠀⠀⠀⡠⠈⠀⠀⠀⠀⠂⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⢠⠄⣑⢄⠠⠀⠈⠁⠀⢀⠀⠁⠀⠀⠉⠀⠒⠤⢄⠀⠜⡢⠈⠀⠀⠠⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠐⠀⠀⠤⢀⠀⠀⠂⠀⠀⠀⠀⠂⢄⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⡀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠤
⠀⠄⠀⠀⠀⠀⠈⠐⠠⠄⣈⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⢀⣀⠀⠀⠀⠐
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠂⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡄
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠠⠠⠤⠄⢄⢤⢠⢀⢠⢠⠠⣠⠀⡄⣤⣦⠧⠤⠤⠤⠤⠤⠤⠸⠠⠠⠤⠤⠤⠦⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⠒⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠈⠁
⢀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀
⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠠⡄⠀⠀⠀⠀⡏⠀⠀⢠⡆⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⡄⠀⠀⠀⡇⠀⠀⣾⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠘⢦⡀⠈⢧⡀⢀⡀⢳⡀⢶⠀⡇⠺⢰⠇⡔⠀⡴⠃⠀⠀⣠⠞⠃⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠙⢦⡀⡑⣄⠱⡄⢣⠸⠀⡇⠆⡌⡼⢁⡞⢠⠜⣠⠞⠁⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠢⡙⠢⡈⠣⡀⠀⢀⡀⠇⡀⠈⣠⠋⠔⡡⠊⢁⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⢦⣤⣀⠀⢬⡑⠬⡂⠀⠠⠂⣠⠤⠄⠢⠄⡁⠐⠄⢀⡠⠖⣉⠤⠒⢀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⣤⣤⣀⣀⣀⠀⠈⢉⡒⠈⠑⢈⠟⢠⠊⠀⠀⠀⠀⠀⠈⠳⡔⢅⠀⠪⠄⠒⠊⠁⢀⣀⣠⡀⣀⣀⣀⣴⠖⠶⠤⠤⠤⠶⠶⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠈⠉⠉⠉⠑⠒⠒⠤⠌⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠂⠀⠐⠒⠊⠉⢉⡝⠒⠛⠁⠈⠉
⠠⡤⠶⠒⠒⠒⠚⠋⠉⠀⠀⠀⠉⠉⠳⢄⣀⡉⠉⠉⠀⠐⠀⢇⠀⠀⠀⠀⠀⠀⢀⣀⡧⠬⠥⠤⠬⠭⣱⠖⠋⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠤⣄⣠⠤⠸⠓⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⢀⣠⠼⠃⣀⠖⠋⠀⠀⠈⠉⢁⣠⠤⠤⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠐⠂⠁⠁⠐⢦⡀⣀⡀⠀⠀⠀⠤⡀⠀⡀⢠⣳⣖⡒⠒⠠⠤⠤⠤⠤⠤⣴⠞⠉⢉⡀⠐⠬⠈⠀⠴⡆⡀⠾⣉⣉⠁
⠀⠀⢀⣄⠀⣤⠄⢤⠄⠀⣠⠀⠤⠤⠬⠭⠥⠴⠦⠤⠤⠤⠴⠶⠿⠖⠂⠀⠀⠀⣤⠼⢃⢰⣀⠉⡤⡀⣀⠠⠀⣠⠔⢁⡽⠄⠈⢫⣉⣙⡤⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⡼⣃⣤⠾⠷⡼⠖⠛⠶⢅⣀⣀⣀⣜⣠⣤⣅⣐⣀⣈⣉⣄⣁⢇⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡖⠒⣒⠲⠤⠶⠻⢛⣛⣋⢀⣤⣄⠤⠤⠤⠤⠤⠶⠤⠭⠭⠁⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⣀⣴⠶⠒⠒⠚⠛⠚⠛⠛⠒⣾⣉⡉⠀⠀⠀⠈⣡⣤⣵⣐⠒⣒⣒⣃⡀⠀⠀⠀⠀⠀⠤⠤⠤⠤⡤⠤⠤⠔⠀⠀⠦⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠄⠰⠄⠘⠀⠀⠘⠉⠀⠈⠉⡤⡀⠠⡖⢐⡄⠁⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⣣⡄⠀⠀⠐⠒⠒⢄⡀⠀⢃⠀⠀⡀⠀⠀⠀⢠⠀⠐⡆⠀⠀⠀⣠⡘⠦⠍
⠀⠀⠀⠀⠀⠀⠙⠷⡀⣏⠀⢀⠀⠀⠀⠀⠚⢫⡴⢂⡀⡀⢠⠀⢠⡘⢎⣾⠀⣰⡇⠀⢀⣠⠁⠀⢠⠇⣀⣀⡰⣬⡙⠃⠀⠀⠀⠀⡀⠀⡗⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠀⣸⠂⡴⡖⠀⢠⡆⠀⣽⠀⠣⠀⠀⢀⢙⣾⣿⣿⣿⣿⣷⣾⣵⠠⠐⠀⢀⣠⠊⠀⠀⢤⠀⠀⡖⡆⢸⡁⠀⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠁⠀⡽⠁⠀⢸⠞⠀⢨⠦⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠐⠈⠁⠀⣸⠖⠘⢾⡀⠀⠹⣆⠀⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢁⣤⠖⠃⠀⠀⠀⢠⠄⣛⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠀⠀⠉⠀⠀⠀⠀⠓⢦⣄⠘⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠀⠀⠀⠀⠠⣇⡀⠀⠼⡛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠷⢆⡤⠄⠞⠃⠀⠀⠀⠈⠎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡐⠊⠀⢉⠟⡟⣿⣿⣿⠿⢏⣅⠄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⢧⡧⢤⠔⠁⠘⠀⠙⠙⠘⠀⠀⠈⢂⠀⠲⣾⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠂⠈⠀⢀⠘⠇⠂⠀⢀⠀⠀⠀⠣⢤⡜⠀⣙⠛⠉⠋⠱⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠛⠀⠀⠠⡄⠠⣤⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⢠⢠⡀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⡾⠁⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⣴⡶⡀⠙⡄⠂
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠷⠏⠀⠁⠀⠀⢀⣨⣴⢙⣿⡿⣿⣟⣿⣾⢿⣿⡇⠀⠑⠳⠽⠇⢲⡿⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠙⢯⠠⠑⢶⣶⣬⠭⣤⣥⣭⣤⣼⣿⣿⣣⣬⣛⢿⣿⣇⣐⣀⣖⣚⣿⣷⣾⣷⣿⣿⣦⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠶⣛⣽⣒⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⡭⢙⣮⣡⣌⣿⣿⣿⣿⡯⠿⢿⣏⡷⠝⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠁⠀⠈⠉⠋⠉⠋⠉⠚⠋⠉⠙⠛⠋⠋⠉⠁⠉⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣷⣤⠀⠀⠀⡤⠔⢣⠀⠁⠀⢨⠇⠉⡃⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠃⣤⠦⠀⠚⢢⣷⣤⣦⣼⣄⡤⢀⡠⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢟⢿⡟⠛⠈⠓⠨⠥⠦⠀⣺⣿⣿⣿⣿⣿⣷⡚⠉⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡜⠀⠀⣠⠟⡉⢙⣿⣿⣿⠿⠏⠀⠠⣄⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡎⠱⠊⠀⠜⠙⠇⠈⠳⠀⠠⢀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⡇⠀⠀⠈⠀⠧⢰⡅⠐⠃⢀⢧⠸⠁⠰⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡮⠀⠀⢻⠀⠀⠀⠀⢀⡟⢉⣄⣰⠎⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠫⠀⠀⢸⡄⠀⠀⠀⣼⠵⠫⠁⠁⠀⠀⠀⢀⠀⠀⢀⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢴⡀⢀⢈⡧⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡢⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⠈⢇⠀⡀⢙⡌⡄⣼⠀⠀⠀⠀⠀⢀⡴⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢀⡘⣷⠁⣨⠀⣴⡿⠀⠀⠀⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢀⡙⣿⠻⣦⣴⡇⠀⠀⢀⡼⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⣷⣿⣻⡃⠀⢀⠞⠀⡀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠚⠙⣿⣿⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠋⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣶⣦⠈⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠂⢩⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣄⠀⠀⣄⣀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢸⣿⣿⣼⣿⡿⣿⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⢸⣿⣿⠟⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣾⣿⣿⣿⣿⣡⣿⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠜⣉⣾⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣦⡄⢀⣀⣽⣿⣿⣿⣿⣿⣿⣿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⠆
⠀⠀⠀⠀⢀⣼⡿⢸⣿⣿⣿⣇⣿⣆⡀⠀⢾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣇
⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⣿⣿⣷⠀⠙⠻⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣦
⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣦⣀⡀⠀⢀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⡆⢠⣿⠉⣿
⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠉⠟⢿⣅⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣷⣼⣿⡆⠘
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠉⣤⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣸⣿⣿⣿⣧⠐
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡏⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⡤⠀⠀⢰⠞⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣢⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⣰⠂⠀⠀⠀⢀⣤⡀⠘⣿⣿⣿⣿⣿⣸⣻⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⢻⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⣿⣿⣾⣿⠀⡄⠀⠀⢸⠛⠁⢀⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⢟⠃⠀⠀⠈⠉⠙⠟⠣⣿⣿⠋⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⡇⣀⣴⠋⢠⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣡⣿⢠⡿⠋⢠⣾⣿⣿⣿⡟⠠⣨⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⢫⣾⣿⠿⡾⣧⣾⣯⣿⣿⣿⡿⢡⣸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠙⣿⣿⣿⣿⡟⣥⣾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⣹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣴⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠢⣄⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⠳⡄⠀⠀⢸⡟⣆⠀⠀⠀⡼⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠙⢦⠀⢸⡇⠈⣦⠀⢸⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⢧⠀⢧⣀⡼⠀⠸⣄⠀⠀⠀⠀⠀⡿⠀⡤⠞⢡⠋⠀⠀⠀⣀⡤⠴⣲⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡒⠲⢦⡀⠳⣤⣤⢞⣀⣤⠤⠶⠶⠒⠚⠷⠶⢶⣶⡚⠁⣞⠀⢠⠏⠀⣠⠴⠋⠁⣠⠞⠁
⢀⣠⡤⠖⠒⠒⠒⠒⠒⠶⠤⢤⡀⠹⣄⣀⡟⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣟⠋⢠⠞⠁⠀⢀⡴⠃
⠉⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠙⣦⠈⢩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣄⣀⡴⠋
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣾⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢰⠒⠚⠒⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢦⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡀⠉⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡴⠛⠉⠉⠉⠁⠒⠲⢤⣄⡀
⠀⠀⠀⠀⣠⣴⣚⣉⡉⠀⢙⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠉⠙
⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠶⠤⠶⠚⠉
⠀⢀⡴⢚⣉⣀⣀⣀⣀⣠⡤⠞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠞⠓⠲⣄⡀
⠴⠛⠋⠉⠉⠉⠉⠁⠀⢀⡴⠲⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠳⠦⠤⠤⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣁⣠⠼⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠲⢤⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⢀⣠⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠘⢦⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢙⡆⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡟⠉⢣⠀⠉⠑⠦⣤⣀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⠉⣠⠞⠛⢻⡓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⢋⣀⡀⠓⢦⡈⡇⠀⠀⠀⠀⠈⠙⠮⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡼⠀⡴⠛⢳⠉⣩⠿⠛⠛⠛⠻⢅⠀⢠⠞⠉⠉⠙⣦⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⠞⠁⢀⡇⢀⡾⠀⡇⠀⠀⠀⠀⠀⠘⡇⠈⢧⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠞⠁⠀⠀⣸⣡⠞⠀⠀⢻⡀⠀⠀⠀⠀⢀⡇⠀⠈⢳⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠷⠋⠁⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⢻⡀⠀⠀⠀⣸⠁⠀⠀⠀⢳⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⠏⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠃
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣀⠣⡲⢄⡀⢐⠁⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣘⡄⠀⠈⠳⡄⠹⠁⠀⢀⠿⢠⠆⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢦⠀⠀⢣⠀⠇⠀⡆⠀⢸⣶⠟⠁⢀⡂⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣀⠀⠿⠶⢤⣄⠀⢡⣤⣸⣷⣾⣾⣧⣤⠊⠀⢀⣀⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣙⠻⢷⡀⠀⠀⢄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⣉⡌⠁⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠚⠳⢄⠀⠉⠓⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠉⠉⠉⠉⠑⠦⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⠀⠚⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣥⣄⣀⠴⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠓⠒⢤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣀⡀⠀⠀⢀⡤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠁⠀⡼⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠓⣄⠈⠙⠦⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⣶⢿⠄⠀⣼⠟⠙⠿⢿⢻⢟⠿⠻⣄⠁⠀⠈⠳⡤⠤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢠⠊⢠⣾⠁⠀⠀⠀⣸⠀⡀⠀⢠⢸⢦⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⠀⠊⢹⠀⠀⠀⠀⢹⣸⠀⠀⣸⠘⠀⠈⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⡙⠃⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠱⢃⡴⠖⠶⢤⣀⠀⠀⠀⠀⠀⢠⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⢌⠳⢄⡀⠀⢀⣼⣜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠏⠉⠉⣩⠍⣓⠳⢤⣵⡒⣮⠻⠟⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣆⣀⣈⡴⠲⢤⣵⢤⠤⠃⣼⡷⠖⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⡙⠷⣤⡗⣿⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⡷⡟⢸⠀⠀⠀⠀⠀⠀⣴⣋⠭⠖⠒⠂⠈⠁⠀⠉⠀⡨⢿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠟⠀⠛⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣤⣄⣁⣀⣀⣀⣀⣀⣀⣸⣇⠀⠠⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡉⠙⠯⠍⠉⠙⠛⠛⠛⠉⠉⠩⠽⣶⣬⢹⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡓⠆⠀⠀⠀⠀⣀⠤⠤⠶⠤⣄⣀⡀⠀⠸⣧⠿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣠⠞⠁⢀⣠⣤⡀⠀⠙⣦⠀⠀⢰⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢭⣿⣧⠀⢿⣿⣿⣿⣷⣿⠁⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⡢⠔⠛⣦⣬⠉⠛⠿⠋⠡⣪⠟⢩⠤⢌⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣗⡀⠀⠀⠙⠳⠶⠶⠖⠛⠁⠀⠠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠩⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⣀⣀⣤⣤⣄⣀⣀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⣤⣌⡒⠦⣄⡀⠀⠀⠀⠀⠀⠸⣯⣀⣉⣛⠙⠛⠛⠛⠉⢙⣻⣿⠇⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⠬⠙⠓⠶⣭⣓⠦⢄⡀⠀⠀⠀⠈⠉⠙⢛⣛⠛⢛⣛⣋⣉⣁⠀⠀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢙⡻⢶⣮⣀⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠢⡈⠙⠽⠳⢶⣄⡀⠀⠀⠈⠑⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⢦⣄⣐⣐⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣄⣭⣤⡁⢂⣡⡼⣁⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⠛⠋⠥⠤⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆

⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⢀⢸
⢀⠀⠀⢠⠂⢸⠀⠀⠀⠀⣀
⡸⠀⢠⠇⣸⠘⡆⠀⠀⢠⠛⣆
⠇⢃⡼⢸⣿⠀⣷⠈⠀⡏⣦⠘⢦⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⠄
⠀⠈⡇⢸⣿⣇⡏⠀⢸⠃⡏⠁⠀⠳⡄⠀⠀⢠⠞⣿⠀⢀⡔⣹
⠀⠀⠘⣼⣿⡟⠀⠀⢸⡄⡃⠀⢀⠀⢹⡄⣰⠋⠀⢿⣰⠋⠀⡇⠀⢀
⠀⠀⠀⠘⣿⠃⠀⠀⠀⠇⠀⢿⣈⣠⣄⡿⠁⠀⠀⢸⠁⣎⠀⣇⠀⣸⡀⠀⠀⠀⢠⠆
⠃⠀⠀⢠⡏⠀⠀⠀⢀⠘⡀⢸⣟⣵⠏⠀⠀⠀⠀⢸⣾⡏⠀⢹⣠⠏⢣⠀⡠⠊⡞
⠀⠀⡄⣾⠀⠀⠀⠀⠸⠀⢧⢸⣿⠋⠀⠀⠀⠀⠀⢸⣿⡇⢀⡼⠃⣀⡼⠋⠀⣸⠀⢀⡠⡖⠁
⢰⠀⣷⠇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⡵⠋⣠⡼⠃⠀⠀⠀⡿⢚⠁⠰⠀⡀⢶⠀⠀⠀⣰⠂
⢸⡀⡿⠀⡇⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡟⣠⡴⠋⠀⠀⠀⠀⢸⣿⣇⣠⠗⠊⠀⢸⠀⡠⢞⠇
⠀⣷⡇⢰⠁⠈⠀⢀⠀⢠⠀⣿⠀⠀⠀⠀⡀⡆⠀⣼⣼⠏⠀⠀⠀⠀⠀⠀⡾⠛⠉⠀⠀⠀⠀⢼⢊⡅⣿
⠀⣿⡇⢸⠀⠀⡀⡄⠀⢸⢰⣿⠀⠀⠀⢠⠀⠂⢀⡟⠁⠀⢀⠀⠀⡠⠁⣸⠁⠀⠀⠀⠀⠀⠀⣼⡟⣱⠃⠀⠀⠀⣀
⢇⣿⣧⡸⣆⡄⣷⠀⠀⣼⣿⣯⠀⠀⠀⡆⡘⠀⣼⡪⠂⡠⠂⠀⡰⠁⣰⣇⣀⠄⡠⠀⠀⢀⣠⠿⠾⠃⠂⣠⡴⢭⡤
⣾⣿⣿⣷⣿⣿⣿⣴⣾⣿⣿⣿⣦⣴⣾⣳⡀⣼⣿⣏⡴⠁⠀⡰⢁⣴⣿⣿⣵⣶⠴⠖⠋⠉⠀⠀⠀⣴⠞⡫⠚⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡵⢪⣠⢞⡔⢡⣾⡿⠟⠋⢁⡠⠤⠂⠀⠈⠀⣠⣾⣫⠎⡤⠆⠀⠀⢀
⢿⠻⣟⣧⡝⣿⢻⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣥⢏⣴⠛⣁⡤⠖⣋⡤⠖⠀⠀⠀⢀⡴⢉⡀⠀⣰⢁⠄⠐⠚⠁
⡮⢭⠟⠧⢻⣩⢣⣿⣽⠿⡛⣋⣹⣿⣿⣿⣿⣿⣿⣿⣷⣫⣿⣿⣧⠶⢋⡡⠐⠀⠀⢀⣴⡿⠿⠷⠖⠚⠛⠓⣚⠵⠒⠈⠁
⣳⣾⣷⣾⣷⣾⣿⣶⣟⣻⡟⣿⢞⡯⢽⠛⣿⣿⣿⣿⣿⣿⣿⣋⢥⡲⠴⠀⢀⣠⡶⢋⠁⠀⠀⠀⠀⢀⣤⢊⠁
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡷⣾⣼⣻⣩⡟⢯⣿⣿⣿⣿⣛⠋⣁⣤⣴⣾⣿⣿⣿⣤⣤⣤⣤⣴⣾⣿⣦⣤⣤⣀⣀⣀⣄⡀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣽⣉⡷⣿⣿⣿⣿⣿⡿⠛⢋⣭⣭⠀⠀⠀⢒⡒⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠾⢉⠁
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣼⠛⣯⣏⣿⣿⣿⣷⣿⣿⣿⣶⠮⠭⠶⠒⠒⠀⠙⠉⡉⠄⠀⢈⣠⣖⣉⣉⣉⣉⡠⠁⠈⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣟⣿⣻⣟⣭⣯⢿⣿⣿⣿⣿⣿⣷⠶⠖⠒⠋⣉⡤⠔⠂⠉⣀⡤⠶⣿⣗⢋⣀⠄⠊⠁⠀⠀⢀⣀⢤⠖⠁
⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣳⢦⡛⣴⣛⣿⣿⣿⡛⠛⠛⠓⠋⠉⣉⣀⣤⣴⣶⣿⣥⣤⣤⣄⣀⡉⠉⠒⠛⠛⠋⠉⢉⡤⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢲⣏⣼⢛⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠦⣤⡌⣉⠙⠛⠶⢶⣒⠲⠶⠒⠀⣒⡡⠤⠒⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⡜⢺⢧⣯⣿⣿⣿⣏⡛⠿⣟⡒⠭⢽⢟⣲⡦⢤⣌⣁⠒⠀⠈⠙⠳⢿⡟⠿⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣄⣀
⠀⠀⠀⠒⡒⠦⣤⣀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⢮⡺⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⣀⣐⠒⠦⢭⣓⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠳⡽⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢾⣽⡻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢣⢻⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠤⢄⣀⠭⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠄⢐⢤⡐⣜⣾⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠶⢬⣍⣒⠮⣝⡾⣽⣿⣿⣧⡀⠀⠀⡀⠴⣲⣯⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⣛⠲⠶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣟⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠳⠶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣫⡭⠽⣿⣿⢿⣿⣿⣿⣿⣿⡿⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⢥⣲⡾⢟⣭⠶⣻⣽⣿⣿⡿⠋⠀⠀⠀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣤⣴⣞⣯⣵⠾⣫⣵⣿⣿⣿⣿⠏⠀⠀⠠⣐⣾⣿⣿⣿⡈⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠈⠉⠋⠝⠛⠿⣿⣿⣿⣿⠿⣋⠵⢋⣽⣿⣿⣿⠟⠁⠀⠀⠐⣫⠕⣫⢞⣿⣿⠇⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛⢽⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠐⠉⠄⠩⠐⡡⢊⢀⡴⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣋⢵⡿⣻⡿⠀⠀⠀⠀⠀⠃⢽⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠁⠊⢰⣻⢿⣿⠁⠀⠀⠀⠀⠀⠀⠚⠵⢋⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡹⠿⠿⠿⢷⡁⠉⠻⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⡏⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⣀⣀⣤⣄⣀⣀⣠⣤⣤⣶⡾⠿⠦⠀⠉⠒⠤⠀⠉⠹⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⣉⣂⣬⠶⠋⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠔⡳⠀⠀⠱⠀⠀⠀⠀⠡⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢣⠀⠀⠀⡘⠀⣀⣀⡠⠀⠀⢀⠂⠀⠠⠈⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠤⠄⡈⠀⠀⠀⠸⠆⠀⡁⠈⠑⠂⠠⠧⣠⡛⢢⣾⠛⠛⠋⠻⠛⢻⣻⣯⡎⠀⠀⠙⣼⣟⡛⠛⠛⠛⠛⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠈⠗⠂⢦⠘⠂⠀⠀⠀⠀⢀⡿⣶⢻⠁⠉⠈⠻⠶⣶⣶⠿⠟⠿⠛⠃⠀⠀⠀⠛⠻⠻⠿⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣀⠃⡰⠐⠄⠀⠀⠀⠀⢸⡷⢁⠄⠀⠀⠂⠀⠰⢈⠟⠛⠒⠶⢴⡃⠀⠀⢸⢦⠴⢶⡓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⠄⠠⡀⠠⠀⠀⡀⠀⣸⠗⠀⠀⠁⠀⠀⠁⠀⠀⡇⠀⢀⡠⠜⣣⠀⢀⡂⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⢀⣀⣀⣤⡀⢀⠀⣤⣌⠋⠊⡿⠣⡄⠀⠉⠀⠘⠀⠀⠉⠑⡄⠈⠹⡿⢤⠀⠀⠄⠀⠀⢀⢢⠛⠀⠀⢈⠇⠘⢿⣇⣿⠟⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣠⣦⣭⣭⣽⣷⣞⣷⡟⢻⠟⠈⠀⠀⣄⠀⠡⠀⠇⠀⢆⠀⠐⠌⠀⠀⠈⠑⠐⢟⢠⡚⡈⠈⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣭⣍⣙⠻⠏⠀⠈⠿⠃⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣔⢂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢻⡿⠛⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠡⠘⡄⢀⠳⣦⠀⢀⢀⣀⣀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠳⡀⣥⠀⢉⠄⠀⠆⠁⢄⠉⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⡀⠀⠓⠀⠀⢀⠈⠧⠘⡌⠻⡊⠄⠑⠆⠀⠸⠁⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⠲⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠀⠂⢀⠀⠂⢤⠀⡅⠠⠡⠀⣠⡔⠂⠀⠚⢃⠀⣾⡷⡄⠁⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠠⠀⠀⠀⠀⠂⠓⠀⠀⠀⢀⣀⠤⠀⠂⠉⠉⠀⢀⠸⡁⡇⢰⢦⡄⠰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⡀⠉⠐⠀⠤⡀⠀⠀⠀⠶⠆⡀⠄⠠⠀⠀⠂⠠⠀⠀⠀⠈⢇⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⡇⠠⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⢀⣠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡛⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠄⠋⠲⠅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠎⠰⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡾⠛⠉⠉⠉⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠤⣾⣏⣠⣤⣤⡄⠀⠀⠀⣀⠹⣷⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣽⣿⣷⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⡿⠟⠶⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠺⠿⠿⠿⠿⠿⣿⡟⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⠿⠟⠉⠉⠉⠉⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣄⠀⠀⠀⠀⠀⠀⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠶⠦⠴⠶⠿⠟⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠉⠉⠉⠙⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡂⠀⢐⣾⠂⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⢀⣼⣻⡀⠟⣃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣷⣼⣯⣿⣷⣶⣼⣦⣤⣶⣶⣴⣧⣴⣶⣿⣿⣿⣷⣶⣿⣿⣿⣤⣤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠁⠈⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣠⠊⠙⢂⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣤⣤⣀⣀⣀⡀⠈⠉⠉⠀⠀⠈⠀⠀⠀⠀⠠⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣷⣶⣄⣀⠀⠀⠀⠀⠴⠀⠀⠠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢻⣿⣿⣿⣶⡶⢤⡤⠤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠚⠿⠿⠿⠿⠟⠷


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⣄⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⣻⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡴⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠠⠔⠃⠀⠀⢀⠴⠋⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀⠀⠀⠉⠉⠛⠛⠛⠶⠀⠀⠈⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠚⠛⠛⠛⠳⠀⢀⡤⠶⠛⠋⠉⠉⠉⠉⠙⠛⠷⣦⣀⠀⠘⠉⠀⢀⡴⠋⠀⠙⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⠀⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠰⠋⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⣠⠞⠁⠀⠰⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠛⠒⠒⠒⠲⠶⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣤⣤⠤⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⢛⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢


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

⠄⢣⣶⢶⡄⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⠻⠆⢣⣾⠻⣆⠀⠀⣰⡿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠈⠻⡾⠃⠀⠀⠙⣻⠟⠀⠀⠀⠀⠀⠀⣾⣿⣧⣛⣚⠃⠀⠀⠈⣛⠛⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠟⠉⠀⣀⣀⢾⡁⢰⠄⠀⠀⠀⠀⠀⠙⠛⠃⠛⠁⠂⣤⣄⢺⣁⢰⠆⣀⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠺⣉⣹⠆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠃⠉⠁⢺⣏⢹⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡄⣄⣼⣗⠶⠖⠒⠒⠒⠒⠒⢦⠒⠒⠚⠓⠖
⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⡆⠈⠁⠀⠀⠈⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢷⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⡠⢄⡀⣤⣶
⠀⠀⠀⠀⠀⢿⠶⡄⠀⢘⡃⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠉⠀⠈⠛⣀⡄⠀⠀⠀⠀⠲⣿⡵⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠾⡇⠀⢀⠀⠀⠠⠐⠊⠁
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⣄⠀⠀⠸⣿⡂⠀⣀⠀⠀⠀⢰⣾⠚⢗⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣷⣰
⠀⠀⠀⠀⡅⠀⠀⠀⠘⠻⠃⢻⠀⠀⠈⠉⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠰⣤⢧⠆⠀⠀⠀⡉⢟⣿⣻⢏⠛
⠀⠀⠀⠀⠛⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠛⠞⠀⠀⠀⠀⠀⣼⠈⢑⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⢠⡄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⣆⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠐⢆⠀⠈⠳⡀⠀⠀⠘⣆⠀⡄⢸⡇⡆⢰⠇⡤⠀⣠⠋⠀⠀⢀⡴⠆⠀⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠀⠀⠀⠑⢤⡀⠙⢄⠘⣆⠘⡄⡇⢸⠀⠃⡏⡼⢁⡴⢁⡔⢀⡴⠋⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⢠⡙⢮⠢⠣⡈⠂⠁⠀⢸⠀⠀⠐⢡⠎⡠⢋⠔⠋⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⢉⠲⢌⠢⠀⠀⢈⠀⠂⣀⣈⣈⠀⠐⢅⠈⠀⢁⡤⠞⢁⡠⠀⠀⣀⣠⠴⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠲⠤⣉⠂⠍⢢⠔⢁⠔⠉⠀⠀⠀⠈⠒⢄⠡⡒⠁⠐⢊⠡⠤⠒⠉⠁⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠶⠦⠬⠥⣀⣀⡀⠂⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⠀⢈⣀⠀⠤⠴⠖⣒⠿⠥⠖⠚⠓⠋⠀⠀⠉⠉⠉⠁⠀⠈⠉⠁
⠀⣀⣀⣀⣀⣄⣤⠴⠒⠒⠒⠒⠒⠶⢤⡀⠀⠀⠒⠀⠀⠀⠉⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⡒⢀⣠⠼⠃
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⡀⠀⠀⠈⠀⢣⣀⣤⣤⣄⣀⡤⠴⠚⠉⠉⠉⠉⠉⢠⡞⠁⣀⠴⠀⠐⠂⠖⠂⠀⠀⠀⠀⠀⢠⡄⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠚⠫⣉⢀⣀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠤⠴⠚⢉⠰⠲⠁⢀⣀⠀⢀⡤⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠒⠂⠠⠤⠄⢈⡓⠁⠐⠀⠓⡻⣲⣭⣀⠉⠉⠉⠉⠉⢩⠟⢁⠀⠀⠀⠀⠉⠀⠀⠈⠓⡂⢮⠖⠲⣤⠤⢤
⠀⠀⠐⠒⠀⠛⠃⠈⠃⠀⠐⠂⠈⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣰⡟⠉⡴⡀⢰⣐⣋⡂⠆⠀⠀⠐⢉⠀⠜⠅⠀⠐⠳⠶⠎⠡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠚⣁⣀⣜⣫⡶⠛⠉⠙⠋⠁⠉⠉⠳⠶⠶⠶⠦⠖⠛⠒⠲⠦⠶⠶⠶⠶⠧⠿⢦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠤⠴⠶⠶⠚⠭⠍⠭⠽⡟⠉⠉⢰⡄⠒⠐⠒⠒⠋⠉⠒⠒⠊⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠰⠾⠋⠉⠉⠁⠀⠀⠀⠀⠉⠹⠦⢤⠀⠀⠀⠀⠐⠶⠞⠻⠭⠥⠥⠄⠠⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠒⠒⠛⠋⠀⠀⠙⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠒⠒⠂⠀⠐⠒⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠀⠰⡆⠀⠀⢀⣀⢉⢲⣄⣄⢀⣀⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⠇⠨⠧⠦⠆⠦⠽⠶⠤⠤⠰⠒⢳⣳⣋⡭⠶⠷⢿⠛⠿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜
⠀⠀⠀⠀⢰⣅⡰⢀⢠⣀⠴⢬⣀⢀⣠⢀⡴⠖⠉⠈⣃⠀⡀⡄⠈⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠱⠚⠓⠊⠉⠓⢳⢹⣔⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠶⢦⣀⡋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡴⠛⠂⠉⠒⠀⠤⡀⠈⠑⢆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡅⠤⣠⣤⡀⠀⠀⠀⠐⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠉⠙⠢⣀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠑⠒⠂⢤⡀⠀⠀⠹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠶⠴⠶⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣀⠀⠀⠀⠈⠒⢴⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠉⠒⠤⡂⠄⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠠⠄⣀⣤⣈⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠳⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠂⠁⠠⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢑⠆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢦⠀⠀⡀⠀⠈⢀⠀⠰⡆⠁⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠤⠚⠃⠀⠀⠁⠀⡃⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣋⣩⣥⡤⠤⠤⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣋⡐⠛⠩⠵⠶⠶⣶⣤⡈⣿⣆⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡛⠛⠛⠻⠿⠿⣶⣦⣤⡀⠈⠳⠜⢿⣦⠀⠀⠀⣠⣾⠟⣉⣤⡴⠆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠉⠙⢿⣦⡀⠀⠀⠀⠀⠈⠙⠻⣷⣶⣾⠿⠟⠁⣠⣾⢟⣵⠟⢋⣁⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⢀⣤⣤⡄⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣶⣾⣿⣵⣿⡶⣟⣛⣛⠉⠁⠸⣿⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠸⣿⣧⡜⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿⣛⡛⠛⠛⠿⢷⣦⠻⣷⡀
⠀⠀⠀⠀⠀⠹⢿⣦⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣄⢸⣿⢿⣏⡛⠻⠶⣦⣄⠈⠳⠙⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⢀⣀⣀⣀⣸⡿⠁⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠙⢿⣿⠻⣷⣌⠛⠶⣤⣀⠉⠓⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣛⣛⠛⠁⠀⣀⣀⣤⣴⡿⢿⣍⠻⣷⣄⠀⠀⠻⣷⣌⠻⢿⣦⣄⠈⠙⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⢿⣿⢿⣿⠿⢿⣿⠉⠻⣦⣙⠳⣌⠻⣿⣦⠀⠈⢿⣷⣄⠈⠛⠻⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⣇⢿⣯⡻⢷⣦⠻⣷⣄⠈⠛⠿⣶⣤⣬⣿⣧⠀⠀⠙⠿⣷⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⠈⢿⣿⣶⣿⣷⠉⠻⠿⠿⣿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠻⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣿⣿⠆

⠀⠠⠤⠤⠤⡤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣄⣾⣿⣿⣇⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠿⠛⡿⠿⠿⠿⠿⠟⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠺⠀⠐⠉⠘⠛⣿⣿⣿⡟⠙⠁⠀⠠⠀⠀⠀⠀⠀⠀⡹⠯⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⠒⠂⠐⠀⠂⠀⠀⠀⠀⠒⠀⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠈⢳⡀⠀⢠⠖⠉⢻⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠲⣄⢠⣄⠀⡇⠀⠀⡀⣷⣰⠋⠀⠀⢸⣆⡴⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢻⠀⠙⢧⡄⠀⣷⠃⠹⣄⠀⠀⢸⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣟⠒⠾⣄⣄⠀⢻⠀⠀⠀⠹⣄⡇⠀⠀⢻⠀⡀⢸⠆⠀⡠⢀⣯⠤⢶⡆⢀⡀
⠀⠀⠀⠀⠀⡖⠒⠒⠻⡄⠀⠀⠉⠳⣜⣆⢀⠀⣆⢹⡇⡀⢀⢸⣰⢀⡏⢀⡴⠛⠉⠀⢀⡜⠉⢉⡟
⠀⠀⠀⠀⢀⣹⣤⠤⠴⠿⣄⠀⠀⠀⢌⢻⣆⣣⣼⣼⠿⡷⣾⣾⣣⠞⡴⡫⠀⢀⠀⣠⠞⠋⠉⠉⢙⠆
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⢧⣑⢤⣀⣱⡿⠋⢁⣀⣤⣤⣀⡈⠙⢺⣟⣠⢖⣡⡾⠁⣀⣀⣀⣰⠋
⠀⠀⠀⠀⠀⣙⣦⡤⠤⠤⢤⣄⣉⡓⣾⠏⢀⡴⣋⣹⠶⠶⣯⣙⢦⡀⠙⣿⠿⠛⠋⢉⣉⣀⠀⠉⢉⡽
⠀⠀⠀⢶⡉⠁⠀⠀⠀⠀⠐⠒⠨⢿⡟⠀⣺⢁⡏⣾⠛⠙⣷⢹⡈⣗⠀⢹⣖⣋⠍⠉⠉⠉⠉⠉⠉⠓⠲⣤
⠀⠀⠀⠀⣙⡶⠤⣄⣀⣀⣀⣠⣤⣾⣇⠀⢽⡈⣗⡻⣤⣤⢟⣺⢁⡯⠀⣸⡥⠤⠤⠄⠀⠀⠀⢀⣠⡴⠊⠁
⠀⠀⣠⠚⠁⠀⠀⠈⠉⠁⣠⡤⠴⣺⢿⣄⠈⠳⣌⡙⠖⠲⢋⣡⠞⠁⢠⡿⠷⠶⣶⠶⠶⢶⣾⠍⠀⠙⣆
⠀⠀⠈⠉⢛⡶⠒⢒⣶⠞⠁⠐⠈⠀⢼⡿⣦⣀⠈⠉⠛⠛⠉⠁⣀⣴⣟⠿⣶⢄⡀⠀⠀⠀⠈⠙⠶⡊⠁
⠀⠀⠀⠠⣏⣀⣀⣠⡏⢀⣀⣠⢤⡾⢡⢎⡴⡟⢻⢶⣶⠶⢶⢾⣿⣿⡌⠑⢌⠑⢤⣁⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⢠⠎⠀⣻⠋⠉⠋⢀⡞⠠⢃⡞⠘⠀⡏⣸⢻⠀⠀⠇⢿⡘⣌⢄⠀⠁⠀⠻⡟⠋⠛⢻⡛⠋⠉⠁
⠀⠀⠀⠀⠘⠒⠒⡏⠀⣀⣠⣼⠀⠀⣸⠀⠀⠀⢠⣿⠘⠀⠀⠀⢸⠁⠈⠢⣀⠀⠀⠀⢹⡤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡇⠀⢀⣿⠀⠀⢠⠞⠙⡆⠀⠀⠀⢸⡀⠀⠀⠘⡗⠲⠤⣤⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠉⢻⣀⡴⢻⡀⠀⣸⢆⠀⠀⣼⠙⢦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡴⠛⠞⠁⠀⠙⠶⠇⠀⠀⠈⠓⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠉⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡆⠀⠀⠀⡠⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢠⡤⣀⠀⠀⠰⣄⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣇⠀⠀⠀⠈⠑⠂⠀⠙⣷⡿⢿⣿⡿⢀⣠⠠⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠀⠀⣀⠀⠘⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠂⠀⠉⠐⠾⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⢀⡤⢶⣶⣾⣿⣷⣉⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠈⢳⠆⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣰⣟⢠⣟⣻⣿⣿⣇⠙⠛⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢦⠀⣸⠟⠉⣾⣟⠺⢿⣿⡟⠀⠀⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠲⠆⣐⠦⠀⠀⠀⠄⠃⠀⠀⢹⣧⣴⣿⣿⠇⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⡌⢻⣿⡿⠋⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢇⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠒⠀⡀⠀⠀⠀⠀⠀⢀⠈⡈⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⠀⠀⠀⠑⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⣠⡄⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⡇⠀⠀⠘⠧⠀⠀⠄⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢰⠁⠀⠀⠀⡀⠳⣄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⢀⣄⠀⠀⡆⣾⠈⡌⠀⠀⡰⠃⠀⠈⠱⣄⠀⠈⠢⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⡄⠀⢸⡇⣠⠃⠀⠐⠁⠀⠀⠀⠀⠈⢷⡈⢄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣷⠀⣼⠀⡏⠀⣴⡷⠃⠀⠀⠀⠀⠀⠈⣷⠼⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠄⢀⠸⣧⡏⢠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⣆⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢠⠄⠘⣧⡉⢀⢸⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡇⠈⠨⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡀⡏⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠄⢹⣏⣋⡟⡿⢛⣉⣛⣏⣽⢛⣙⠋⣿⠋⠛⢉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣿⣟⣻⣟⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠓⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠂⢀⠀⠁⠀⠀⠀⢠⠂⠀⠀⠀⡀⠀⢻⠁⢀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠁⠀⠀⠈⠳⠄⠀⠀⡌⠀⠀⡠⠀⠁⠀⢈⠀⢈⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠈⣆⠀⡇⠀⡰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠤⠤⠄⠀⠀⠠⡀⠀⠀⠀⢆⠀⠀⠀⠀⢸⡆⡇⢸⡇⠀⠀⠀⠀⡆⠀⢀⡴⠂⠈⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⢄⠀⠀⠢⣄⠀⣀⣼⣷⡷⣼⣧⣄⡀⣠⠎⢀⡴⠋⣀⣀⡄
⠀⠀⠀⠀⢶⡚⠋⠀⠀⠀⠐⢄⠀⠑⢤⣀⣼⣿⣿⣿⢷⢿⣿⣷⣿⢿⣷⣴⡿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠐⠦⢄⣾⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⣟⣻⡤⠔⠂⠉⠉⠀⠀⠀⠀⠰⢄⡀
⠀⠀⠀⡀⠀⠈⠈⠲⠤⠄⠀⠀⣠⣤⣼⣿⣷⡯⣷⣹⣿⣿⣟⣿⢻⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠛⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⢿⣏⣯⣟⣿⢿⣿⣿⠛⠒⠦⠤⠀⠐⠂
⠀⠀⠀⠀⠉⠓⠤⠀⠀⠀⠀⢀⣠⠾⢋⡿⣿⣿⣮⣟⣿⡿⢯⣿⣟⣿⣿⠿⠉⠍⠉⠓⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣀⠴⠋⢀⠤⢻⢷⣯⣿⣿⣿⢿⣿⠋⠉⠙⠢⡀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠒⠂
⠀⠀⠀⠞⠀⠠⠀⠀⠀⠠⠒⠉⠋⠀⠰⠁⠀⠀⠀⡏⣆⡟⢸⠸⡄⠀⠀⠀⠑⠘⡄⠀⠀⠀⠀⠁⠀⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠃⢣⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠙⠀⠀⠀⠀⠣⠀⠀⠀⠀⠈⠀⠠⠤⢄⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⠀⠀⠀⡠⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠀⠀⠈⠀⠀⣀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢀⠏⠀⠀⢃⠀⠀⡞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⠊⠀⠀⠀⠱⡞⠀⠀⠀⠈⡄⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡄⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⡏⠀⠀⠸⠀⠀⠀⠀⢀⡤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣲⠟⣻⣀⣤⣄⠀⢀⠔⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣴⢛⣭⠵⠛⠉⠉⢀⣽⠔⠁⠀⢀⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠳⡀⠀⠀⢸⡀⡠⠒⢠⣾⣿⣿⣿⣯⣥⣤⣶⠶⠞⡟⠁⢀⠀⣠⢋⣤⠞⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠹⡄⠀⠀⠉⣿⡆⢸⣿⣿⣧⣿⣿⣃⢼⣿⢇⡀⠀⠰⠃⣼⡵⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠠⠚⣿⢏⠈⠙⣻⠟⠻⢿⣿⢛⣥⣻⣷⠀⢁⡾⠋⠀⢀⡞⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⣀⡀⠈⠻⢦⡀⠀⢀⣀⣬⣧⡔⣛⣱⣶⠶⠚⢷⣿⣽⡿⣼⣴⠟⠀⠀⣀⡾⠞⠉⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠻⢦⣀⡿⣿⣷⣞⠻⢿⣿⣻⠷⢾⢻⣿⡾⣿⢁⢀⣤⠾⠉⠀⣠⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣛⣶⡶⠶⠶⠶⠶⣶⣿⣦⠼⣭⣿⡓⣮⣾⠛⢻⢟⡆⠹⣾⢇⣼⠟⠃⣀⣴⡾⠟⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠒⠊⠉⢁⣀⣽⣍⢿⣫⣥⣦⡟⡡⢶⡃⡩⠼⡿⢨⣾⣿⣴⠿⠿⡟⠁⢄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⣫⣿⣿⣆⣶⣻⣶⣦⣽⢛⣿⣡⣋⣵⣿⠿⠋⠀⠀⡼⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠋⠉⠉⠀⠀⣠⡴⠛⠛⠻⣿⣧⣬⣥⣿⣭⣤⡞⠋⠉⠀⣸⠋⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠋⠹⣤⡴⠶⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⣠⣾⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠒⠋⠀⠘⣷⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠂⠀⠐⢲⣦⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣤⡖⠂⠀⠑⣲⣆⣀⢀⣀⣀⣀⡀
⠀⠀⣯⣉⣉⣛⠛⠿⡿⠿⢛⣛⣛⣛⣻⣯⣟⣻⣛⣯⣿⡷⠀⢠⣯⣉⣉⣛⠛⠿⡿⠿⣛⣟⣛⣛⣻⣭⣟⣛⣻⣽⣿⡇
⠀⠀⣭⣭⣭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠛⠛⠋⠉⠉⠉⢛⠛⠛⠛⠙⠛⢛⡉⠛⠛⠛⠛⠛⠃⠀⠈⠛⠛⠉⠉⠉⠙⣟⠛⠛⠋⠉⠉⢙⠉⠛⠛⠙⠛⠛⠃
⠀⠀⠀⠀⠀⣦⠀⣠⣾⠀⠀⠀⠀⠀⢸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⣿⠀⠀⠀⠀⠀⣿⣄⢰⡇
⠀⠀⠀⠀⠀⣹⡞⣫⣾⣇⠠⠤⢤⡀⢸⣯⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢞⣡⣿⣄⠤⠤⣤⡄⢿⣯⣻⣧
⠀⠀⠀⢀⠔⢻⣾⣿⠧⠀⢴⡶⠾⠯⠤⢿⣿⣿⠳⣄⠀⠀⠀⠀⠀⡠⠞⣿⣾⡿⠅⠀⠤⡴⠯⠭⠌⢿⣿⣏⠳⣄
⠀⠀⠖⠁⣴⣿⡿⠁⠀⠀⠀⠠⠤⠤⠾⠯⣿⣿⣷⡎⠳⡄⠀⠠⠊⢠⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠻⢯⣿⣿⣷⡌⢳⡄
⠀⠀⣴⣿⡿⣿⡉⠉⠉⣉⢉⡉⢉⢉⠉⣉⣛⣻⣿⣿⣇⡈⠀⠀⣶⣿⣟⣟⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣻⣿⣿⣧⡁
⠀⠀⣿⣟⣼⠩⠤⠤⠄⠀⢀⣀⣀⣀⣀⡈⣈⣸⣿⣿⣿⣷⠀⠀⣿⢏⡾⠥⢤⡤⠤⠄⢀⣀⡀⣤⡀⠀⣤⣼⡿⣿⣿⡇
⠀⠀⣟⡾⣉⣀⣀⣀⣀⠀⠀⠐⠀⠀⢀⣤⣄⡍⢭⣿⣿⡿⠀⠠⢏⡟⠁⣀⡀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⠭⢭⣽⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣴⢯⣉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠛⣦⡼⠟⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠳⠶⢿⠁⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠳⠦⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣴⠎⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣱⣾⡄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢿⣯⡼⠛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠘⣃⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡿⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡾⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠈⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣿⣾⠟⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠷⠟⠈⢇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠴⠖⠛⣛⣛⣛⣋⣉⣉⣉⣉⣍⠩⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠴⠶⠶⠶⠶⠶⢶⣟⣛⡳⢶⣤⡀
⢠⡞⢻⡷⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠉⠙⡆
⢻⡄⠈⠳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠞⠋⠁⠀⠀⠀⢹
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⣄⠀⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⡇⠀⠀⠀⠀⣠⠛⢳⡀⠀⣸⠀⠀⢧⣀⣠⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡄⠀⠀⠀⢰⠋⠉⢻
⢸⡇⠀⠀⠀⠀⣿⠆⠈⠳⠞⠃⠀⠀⠈⠉⠁⠀⠀⠀⢨⡇⠀⠀⠀⣠⠞⠋⠛⠳⣄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⢀⡄⢀⡼
⣾⠀⠀⠀⠀⢸⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢠⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣹⣦⣤⡴⠾⠛⢻
⡿⠀⠀⠀⠀⣿⠿⠦⠤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠂⣾⠀⠀⠀⠘⡷⠒⠒⠲⠖⠛⠷⢶⡄⠀⠀⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠱⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣤⠴⡇
⠀⢹⠶⣮⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⠤⠤⠤⠤⢾⡀⠀⠀⠀⣸⠓⠚⠛⠛⠉⠉⠁⠀⠀⢸
⢀⡟⣁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⣈⡉⠉⠉⡁⠀⢠⡀⢀⣀⡀⢀⡀⠛⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣿⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡆⠀⡟⠉⢹⠀⠘⡛⠳⣼⣇⢸⡦⠀⠀⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁
⠀⠈⢳⣾⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠛⠀⠙⠶⠞⠀⠀⠁⠀⠈⠋⠈⢉⣉⣀⡀⣥⣤⣤⣤⣤⠤⠄⠶⠶⠒⠉⠉⠀⠀⡇
⠀⠀⡿⠂⠀⠈⠉⠉⠉⠛⠋⠙⠛⠛⠒⠋⠘⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⣟⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠈⠙⣿⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠛⠋⠉⠹⡆
⠀⠀⠀⠸⣧⠀⠈⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠸⣧⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠃
⠀⠀⠀⠀⠀⠈⢹⡷⢦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠊⠉⠉⠸⠁
⠀⠀⠀⠀⠀⠀⠘⣶⡠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠚⠛⠛⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡟⣩⣉⣐⣀⡜⣁⠀⣠⣀⡜⣠⠆⣠⠆⣤⣤⣼⣷⠷⠏

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣷⣦⣄⣀⡀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⡿⣶⣶⣿⣿⣿⠿⠿⠿⠿⣯⣍⠫⠭⠍⠹⠯⠽⠿⠿⠿⠿⠛⠟⠶⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢢⣿⣿⣿⣦⡠⠤⠒⠀⠀⢀⣀⣀
⠰⠶⠴⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠨⣿⢿⣿⣶⡖⠒⠒⠚⠂⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢐⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠺⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠂⠀⠀⠉⠁⠀⠀⠨⠥⠀⠀⢀⢀⣈⣉
⠐⠛⠋⠉⠉⠉⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠐⠃⠙⠛⠛⠛
⢶⣶⡶⠶⢶⠦⢤⣤⣤⡤⠤⠤⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⢠⣤⣤⣄⡀⢄⣀⣐⣲⢶⣶⣖⡀⢰⣶⣶⣶⣶⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⠿⠛⣛⣛⠻⠿⢿⣿⣽⣿⣿⣭⣿⡂⠀⠈⠉⠻⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠿⠿⠿⠿⠻⠟⠛⠋⠁⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣀⠀⠙⠋⡿⠟⠿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⠴⢶⣦⣶⣄⣠⣤⣝⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣯⣥⣤⣀⠘⠾⣽⣬⣤⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠁⠀⠈⠐⠉⠙⠛⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣯⣭⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠶⣶⣭⣭⣟⣻⣯⣵⣶⣤⣻⣝⢿⣿⣿⣿⣿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠐⠒⠒⠒⠚⠲⠚⣿⣶⣦⣽⠷⢶⣤⡈⠙⢽⣿⣿⣿⣿⣿⢟⣉⠉⠀⢈⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣋⣉⣡⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣚⣁⣀⡀⣾⣿⣦⣌⣉⣤⣤⣤⣀⣀⡉⢿⣿⣿⣿⣿⣷⣦⠤⠭⠹⢿⣿⣿⣯⣤⣤⣌⡛⠿⢿⣿⣾⣿⣿⣥⣤⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠛⠛⠋⠋⠀⠙⠛⠉⠻⡿⢿⣿⣿⣿⣿⣶⠤⠤⠀⠀⡤⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣾⣭⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⢦⣶⣶⡿⣿⣿⣶⣤⣮⣥⣤⣤⣀⠀⠀⠀⢠⣤⣶⣶⣦⣬⣤⣤⣤⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⢡⠃⠆⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠧⠊⡜⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴
⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⡌⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡂
⠀⠀⠠⠀⢄⠀⠀⠀⡜⠀⠀⢸⣿⣿⣿⣿⣿⢉⣩⣵⡦⣭⡙⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠑⠂⢀⠔⠁
⠀⠀⠡⣀⣀⣧⠤⠊⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣥⣪⣱⣢⣽⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣛⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣇⣾
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠉⠑
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣡
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⡇⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⡣
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⣡⠖⣡⡝⢤⣼⢿⢿⡄⠀⠀⠀⠀⠀⠀⠌
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣠⠾⠿⠐⠙⣌⠳⡇⠘⣄⢿⠀⠀⠀⠈⠀⡘
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡠⢌⠛⠃⠀⠀⠀⠈⠓⢼⠀⢹⠐⠀⠀⠀⢠⠀⡇
⠀⠇⢀⣠⠤⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠀⠀⠀⢠⣷⠀⢀⣸⠀⢸⠀⠀⠀⠀⠀⠢⡱
⠔⠚⡅⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⡜⢹⠀⠘⡟⠀⠀⡆⠀⠀⠀⠀⠀⠑
⠀⠀⠈⠒⠤⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠁⣿⣷⠖⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢀⡱⠖⠉⠀⠀⢇⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⡘⠂⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⢠⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢂⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣤⣤⣤⠋⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣹⡷⠴⣠⣄⠱⣿⣶⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣚⠋⠶⣦⣝⣿⣷⠘⣿⠇⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⠉⠐⢿⣦⣈⣿⣷⣻⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠏⡀⠀⠐⠄⠙⡿⣮⣿⠛⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠦⡀⣊⣢⠟⡫⠃⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⠭⠁⠜⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠤⠄⠠⡇⠀⣤⠀⠤⠤⠤⠤⠤⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣂⣉⣀⣲⡤⢶⠤⠃⢀⠰⣶⠦⠴⠄⠀⣀⣀⡀⠀⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠴⢏⣙⣇⣸⡠⡧⠼⣦⠀⠈⠐⢦⣤⠤⠤⠤⢤⣄⠀⠙⠢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣶⢮⣉⣉⠭⠄⣀⠀⠠⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢑⣤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣽⣂⠈⣉⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⡄⠐⣁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣝⡻⣟⠀⣴⡂⠀⠀⠀⢠⣶⡄⢰⡯⢦⡀⢂⡀⣇⢈⣀⡥⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢈⢀⡇⠁⠈⠋⢮⡇⠀⠀⠂⢨⠟⡻⢿⠺⠾⠟⠛⠋⠙⠁⠃⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠀⠀⠀⠀⢀⠀⠀⢀⠓⢸⡃⢌⢂⢃⠀⡀⠠⠠⠀⠀⡘⢰⠀⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⣠⣆⠀⠤⠅⣼⡷⠶⠶⢄⠀⠀⠁⠆⡀⠀⠃⡈⠀⠁⢈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⣠⡾⠃⠈⠳⠶⠞⣦⣀⠀⡀⢋⣆⠀⠀⠠⠀⡘⢀⠃⠃⠠⢸⢠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⠀⣔⠝⢁⡀⠠⠠⠤⠤⣴⣿⣤⡟⢀⠄⠘⣧⡀⠀⠈⠁⠸⢰⡖⠓⠮⡈⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉⠠⢄⠀⣠⣶⣯⢁⣿⠃⠀⠀⣀⠘⢟⡄⠀⠀⠃⣼⠀⠀⠀⠡⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠆⠀⠨⡥⣀⡠⢶⣦⣙⡿⣿⠀⢀⡄⠀⠀⡜⡌⠀⠀⢀⠻⠀⣄⠀⠀⠀⠠⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣁⠀⠔⢸⠷⣶⣝⣿⢷⠻⡃⠈⣠⠂⡘⡘⠀⠀⢨⡘⢀⠶⣈⡁⠾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠴⠐⠀⠀⠀⠀⠰⠘⢆⠶⠻⠷⠼⢋⢾⡈⠤⠁⠐⠁⣲⠌⠀⠀⠀⠀⠃⡈⡀⢁⠁⠆⠀⢠⡸⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠱⠈⠖⢎⢦⡀⠋⠀⠀⠀⠖⢠⡳⠁⠀⠠⢀⠂⠈⠰⢡⠁⠄⡘⠰⠀⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠚⠭⠴⠶⠖⣂⣀⣀⣰⠏⠀⠀⢀⠂⠌⡀⢀⢃⢃⠆⡠⢁⢃⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠐⡐⡀⢀⠎⠎⡰⢁⠎⣀⠎
⠀⠀⠀⠀⠀⠀⠐⠢⠀⠂⠀⠊⠑⣠⣉⠂⠑⢊⠔⡠⠂⠂⠐⠀⠁⡠⢁⠌⠔⠜⠀⠀⠎⠈⠀⣤⠞⣣⠀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢂⠠⠀⠄⢉⡰⠛⡰⠦⣤⢀⣀⣀⢀⢀⡀⣀⡀⢀⡤⠀⠄⣐⢞⠕⢁⠈⡡⢊⠐⢁⠔⡡⢂⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠡⠒⢁⠔⢉⠔⢊⠤⠂⠠⠀⠀⠀⡁⠀⡠⠂⠔⠠⠂⡠⢁⠄⡡⠊⡄⠁⠔⢁⠘⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠊⠐⠀⠐⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢤⡀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊⠚⠐⠛⠁⠙⠖⢭⣽⠫⢕⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⢢⢴⣿⣶⢾⣤⡄⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠈⠀⠶⢂⠀⢀⠀⠀⢀⠠⠒⠍⠌⠈⠆⠃⠀⠀⢈⡛⢮⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠬⠄⢀⣀⡀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡄⡄⠀⠊⠀⠀⡀⠈⠀⡰⢟⡹⠇⠆⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡄⠊⠀⡠⠂⡄⡀⠀⠀⠉⠉⢁⠀⢀⠁⡀⠇⠀⠀⠀⢀⠀⠀⠀⠀⡄⣆⠴⠛⡀⠠⠄⠀⠀⠈⠢⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠁⠀⠁⠖⢀⠠⠂⠠⠀⠃⠁⠀⠀⠀⠀⠀⠀⢀⣠⢀⣡⣞⠍⠄⠀⠀⢀⡀⠀⠤⠉⠀⠀⠑⣄⠀⠀⠀⠀⡀
⠀⠠⠐⠀⠀⡀⣜⠃⠐⡂⠴⠂⠀⠀⠀⠀⣀⠀⢊⡕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣨⣴⠿⠉⠀⠀⠂⠂⡈⠀⠈⠀⠂⠀⠀⣐⠄⢀⡵⡄
⢈⠂⠀⢀⠔⠐⠘⠀⠄⢈⣐⠮⡀⢀⠰⠊⠅⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠠⢊⡅⠊⢀⢎⢃⠀⠑⠤⡀⣀⢀⠀⢀⡀⠀⠐⠋⠚⢈⡍⠆⠒⡀⠀⠈⠁
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠑⢦⢵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢭⠚⠁⠀⠀⠌⠊⡜⠐⠐⡄⠀⢡⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠘⡄
⠀⢠⣣⡀⠀⠀⠁⠀⡀⠀⠀⠀⠘⠐⠁⠀⠀⠀⠀⠀⠈⠀⠀⠔⣠⠖⠛⣳⣄⡌⡀⠘⡀⠈⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠑⠪⣐⠠⢀⠊⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡴⠪⠥⠠⠀⠀⠖⠓⢦⣠⠁⠀⠀⠘⠀⠰⠀⠄⠀⠈⠀⠀⠲⢄⠀⠀⠀⠁⠀⡀⠀⠂⣼⡀
⠀⠀⠀⠀⠀⠉⠢⢅⡠⠄⠀⠀⠀⠀⠀⠈⠀⠀⠔⡨⠞⠋⠀⠁⠬⠀⠁⠀⠀⠀⠀⠈⠳⢵⡴⡄⠀⠆⢤⠇⠀⠀⠠⠀⠀⠀⠁⠀⢀⠀⣀⢡⠰⢀⣽⡒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣀⠠⠀⠄⢀⣠⣖⣋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣐⠀⣸⠀⡀⡄⠄⡄⡄⠀⢂⣀⣈⣤⡤⠶⠮⠭⠅⢀⣒⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠭⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⣧⣥⣤⣴⣖⣊⣉⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣒⣒⣒⡒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠃⠀⡆⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣇⢄⢀⣡⣤⣤⣤⣷⣀⡅⣴⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠢⠀⠀⠀⠈⠲⣬⣿⣿⣯⣿⣿⡯⣿⣿⣿⣿⡀⡀⠄
⠀⠀⠀⠈⡤⠀⠤⠀⠀⠀⠀⣀⠀⠀⠢⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⡹⣿⣷⡄⡀
⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣯⢠⠔⠚⠁⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢯⣽⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡟⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣙⠂⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠀⠀⠀⠊⢀⠿⣿⣾⣿⣿⣾⣿⡿⢿⠛⠀⠀⠉⠑⠀⠀⠀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠈⠈⢸⠏⠉⠛⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡰⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⠀⠀⠀⠀⢀⣴⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣷⣄⠀⠀⣾⣿⠃⠈⢿⣿⣄⠀⠀⣴⣿⠟⠁⠀⢻⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠙⢿⣷⣴⣿⡟⠀⠀⠘⣿⣿⡀⣾⡿⠁⠀⠀⠀⣸⣿⠀⣀⣤⣶⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡿⠟⠋⢉⣿⣿
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣤⣤⣄⡀⠀⠈⣿⣧⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣿⡉⠛⠛⠿⢿⣿⣷⣤⡸⣿⣆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡟⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠈⠙⠻⣿⣿⣿⣄⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⠃⠀⠀⣸⡿⠁⠀⠀⠀⠀⣠⣾⣿⣯⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠻⣿⣆⠀⠀⠘⢧⠀⠀⠀⠀⣿⠀⠀⠀⠟⠀⠀⠀⠀⢀⣴⡿⠿⠛⠛⠋⢉⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⢀⣠⣤⣤⣷⣤⣤⣀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡐⠋⠁⠀⠀⢀⣤⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⡿⠿⠛⠓⠂⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣤⣾⣿⣿⣭⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣤⣤⣤⣀⣄⣠⣤⣶⠾⠛⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣈⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⢿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⣀⣠⣴⣿⠏⠀⠀⠀⣰⠊⠉⠙⠛⠛⠛⠉⠁⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣁⣀⣤⣤⣶⣾⣿⣿⠿⠋⠁⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠈⢿⣿⣷⣤⣀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠛⠛⢛⣿⠏⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⢰⡆⠀⠀⠀⠈⣿⣆⠀⠀⠀⠻⣿⣿⣿⣿⣷⣶⣦⣤⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣠⣾⡿⢁⣿⠁⠀⠀⢸⣇⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠙⣿⣧⠈⠙⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣀⣴⣾⡿⠋⠀⢸⣿⠀⠀⠀⣾⣿⡀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠿⠛⠉⠀⠀⠀⢸⣿⡆⠀⣼⣿⣿⣧⠀⠀⠀⠀⣿⣿⣧⣄⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣼⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⠙⢿⣷⣤⣀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⣹⣿⡃⢿⣿⣦⠀⢸⣿⡇⠀⠀⠈⠛⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠈⠻⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠈⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣘⠛⠛⠻⢿⣿⣿⣿⣷⣶⣄⡀
⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣀⣤⣶⣾⣿⣯⣭⣉⠛⠛⢿⣿⣿⣶⣤⡀⠀⠉⠛⢿⣿⣿⣿⣦⡀
⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⣼⣿⠟⠋⠉⠉⠙⠻⣿⣿⣦⡄⠀⠉⠻⢿⣿⣦⡀⠀⠀⠉⠻⣿⣿⣷⡀
⠀⢠⡀⠙⢿⣿⣶⣤⣄⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠉⠻⣿⣆⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⢿⣆⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠠⣿⣿⣿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠸⣿⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠿⣿⣿⣦⣿⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠤⣤⣄⣀⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣦⣄⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣶⠶⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⡀⣀⡠⠄⠠⠄⠀⠀⠀⠀⠀⠒⠈⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠁⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠄⢀⡀⠀⢀⠀⡆⠀⠀⠀⠂⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⡀⠀⣤⠠⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⢠⡄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⣆⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⢆⠀⠈⠳⡀⠀⠀⠘⣆⠀⡄⢸⡇⡆⢰⠇⡤⠀⣠⠋⠀⠀⢀⡴⠆⠀⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠑⢄⠀⠙⢆⠘⣆⠘⡄⡇⢸⠀⠃⡏⡼⢁⡴⢁⡔⢀⡴⠋⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⢠⡑⢌⠠⠣⡈⠂⠁⠀⢸⠀⠀⠐⢡⠎⡠⢋⠔⠋⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⢉⠲⢌⠢⠀⠀⢈⠀⠂⣁⣈⣈⠀⠐⢁⠈⠀⢁⡤⠞⢉⡠⠀⠀⣀⣠⠴⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠲⠤⣉⠂⠈⢂⠔⢁⠔⠉⠀⠀⠀⠈⠐⢄⠠⡒⠁⠐⢊⠁⠤⠒⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠶⠦⠬⠅⣀⣀⡀⠂⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⣀⠀⠤⠴⠖⣒⠿⠥⠖⠛⠓⠋⠀⠀⠉⠉⠉⠁⠀⠈⠉⠁
⠀⣀⣀⣀⣀⣄⣤⠴⠒⠒⠒⠒⠒⠶⢤⡀⠀⠀⠒⠀⠀⠀⠉⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⡒⢀⣠⠼⠃
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀⠀⠀⠈⠀⢣⣀⣤⡤⣄⣀⡤⠴⠚⠉⠁⠉⠉⠀⢠⡞⠁⣀⠴⠀⠐⠂⠖⠂⠀⠀⠀⠀⠀⢠⡄⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠒⠪⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠚⢉⠰⠲⠁⠀⣀⠀⢀⡤⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠒⠂⠠⠤⠄⢈⡓⠁⠐⠀⠓⠻⣲⣭⣀⠉⠉⠉⠉⠉⢩⠟⢁⠀⠀⠀⠀⠉⠀⠀⠈⠓⡂⢬⠖⠲⣤⠤⢤
⠀⠀⠐⠒⠀⠛⠃⠈⠃⠀⠐⠂⠈⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣰⡟⠉⡴⡀⢴⣐⣋⡂⠆⠀⠀⠐⢉⠀⠞⠁⠀⠐⠳⠶⠎⠡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠚⣁⣀⣜⣫⡶⠛⠉⠙⠋⠁⠉⠉⠳⠶⠶⠶⠦⠖⠛⠒⠲⠶⠶⠶⠶⠶⠧⠿⢦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠤⠴⠶⠶⠚⠭⠭⠍⠭⠟⠉⠉⢰⡄⠒⠐⠒⠒⠊⠉⠐⠒⠊⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠰⠾⠋⠉⠉⠁⠀⠀⠀⠀⠉⠹⠦⢤⠀⠀⠀⠀⠐⠶⠞⠺⠭⠥⠥⠄⠠⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠒⠒⠛⠋⠀⠀⠙⠛⠛⠛