Meteorite Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠀⣠⣶⠟⠁⣰⣿⠀⢀⣠⣶⠟⠁⣠⣶⣿⣿⣿⠿⠋⠁⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⣰⢾⠟⠁⣠⣾⡿⢃⣴⣿⣿⣇⣠⣾⣿⣿⡿⠋⠁⠀⡀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡾⡁⠿⡴⣞⡵⢋⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣼⠇⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣺⠏⠀⣰⠏⠀⣡⡴⠛⠉⣠⢿⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⣿⠏⠀⠈⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡞⠁⢀⡼⠃⠀⣴⠋⠀⣠⠞⠡⠝⣻⢟⠼⠿⣿⣿⣿⣷⣶⣾⣿⠟⠁⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢾⣀⣠⠞⠁⠀⠀⠙⠲⠛⠁⠐⠀⠁⠠⠈⣤⠀⣩⢾⣿⣿⠿⢋⣡⣶⠟⠁⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠀⠀⣰⠋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣾⡷⠛⠉⢀⣴⣿⣿⣥⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣠⢞⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⡫⢕⣚⣭⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠉⠛⠛⠓⠶⠶⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠉
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣶⣿⠆⣀⡀⠀⠀⠙⠛⠒⠒⠶⢶⣶⣄⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉
⠀⠀⢀⣴⠟⠁⢈⣉⡀⠸⠿⠟⠁⠀⠉⠀⠀⠀⢀⣠⡀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⢰⡏
⠀⠀⣿⠁⠀⣴⣿⣿⡿⠀⠀⢀⣤⣶⣶⡀⠀⢰⣿⡿⠁⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡇
⠀⠀⢹⡀⢸⣿⣿⠟⠁⠀⣴⣿⣿⣿⣿⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⢀⣴⠟
⠀⠀⡼⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣤⠞⠋
⢠⡞⠁⠀⢀⣴⣾⣿⠀⠈⠛⠛⠋⢀⣠⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠉
⠘⣧⠀⠀⣿⣿⣿⠏⢠⠄⠀⠀⠀⠛⠛⠁⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁
⠀⠘⢷⡀⠛⠛⠁⠀⠀⢀⣀⣤⣴⣶⣶⣤⣴⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠈⢻⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠁⠀⠤⠤⢄⣀⣉⠉⠑⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡩⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⡠⢚⣥⣶⣿⣿⣿⣷⡄⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣶⣦⣌⠓⢤⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡼⢡⡾⢋⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡝⢆⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡇⣿⠃⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠻⣿⣿⡌⣇⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠃⣿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⣽⣷
⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣿⡆
⠀⠀⠀⠀⣿⡇⢠⣶⡀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⢀⡄⢿⡀⣿⡇
⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠋⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⢿⡇⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡼⠀⠀⠀⠀⡾⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠁⠀⠀⠀⠀⠁⠀⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣆⣿⣿⣆⠀⠀⠀⠀⠀⠀⢆⠱⣝⠿⣿⣿⠟⠀⠀⠀⠀⣀⡀⣀⣼⣧⡾⠃⠀⠀⠀⠀⠀⡀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣞⣿⣇⠀⠀⠀⠀⠀⠀⠑⠮⢉⡂⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⠓⠒⠒⠀⠀⠀⠜⣱⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣷⣦⣀⠀⠀⣄⡀⠀⠀⠀⠀⣶⣶⣶⣄⠀⢀⡄⠀⠀⠀⣸⣿⠟⣡⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣍⡻⢿⣿⣿⣟⡻⣦⣄⡀⠀⠈⠉⠉⠉⠀⠈⠀⠀⢀⣠⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣶⣶⣶⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣟⣛⣛⣛⣛⣻⡯⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⡠⠀⠀⠀⣴⢀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠆⠆⠀⠛⠀⠃⡴⠆⢠⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠀⠁⠀⠀⠀⠉⠚⠢⣶⡍⢿⠶⣆⣀⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠑⠨⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠔⠒⠀⠁⠀⠘⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡆⠀⠀⠺⠂⠰⢀⠐⠟⠚⣀⡄⠀⠠⢂⡠⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡞⠁⢠⠀⠀⢈⠀⠈⠃⢀⡀⡼⣗⠀⠀⠈
⠀⠀⠑⠀⡄⠀⢾⠿⢀⡀⢛⣤⣽⡿⠃⠀⠀⠀⠀⠀⡴⠲⠷⢆⡄
⠀⠀⠀⢦⠉⣠⡄⠐⠀⣴⣼⣿⣿⡟⠀⠀⠀⠀⠀⠘⡀⠀⢈⠠⣮⠀⠀⠀⠀⠀⠀⢀⡄⠴⣧⣴⣄
⠀⠀⠀⠀⠑⠙⠧⣾⣷⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠋⠀⠀⠀⠀⠀⠀⠻⣤⣽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠞⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠀⠀⠀⠀⠀⠀⠉⠻⡇⠀⠀⠀⠘⢦⣤⣴⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠷⣄⠀⠀⢀⣤⠖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⣿⣧⠀⠀⠀⠀⠀⠀⣼⠃⢠⣶⣶⡈⣷⠀⡾⠁⢠⣶⢲⡄⢻⡀⠀⠀⠀⠀⠀⡂⠢⡸⣧⣤⣤⣤⣀
⠀⠀⠀⠀⢀⣠⡴⠶⠾⠛⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⠟⢁⡿⠀⢿⡀⠘⠿⠿⠃⣾⠁⠀⠀⠀⠀⠀⠁⢀⠅⠙⣧⠀⠈⠹⣧
⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⠶⠛⠁⠀⠈⠛⢶⣦⣶⣿⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢻⣆
⠀⢠⡞⠁⠀⢀⡴⠋⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⢀⡟⠀⠀⢀⠎⠀⠀⢰⢇⣀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⣿
⣼⠇⠀⠀⢸⠀⢀⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⢡⡏⠉⠙⠀⠀⠘⢧⣄⣀⣀⣀⣀⣀⣤⣼⡿⠀⢠⡴⠿⣟⠛⠃⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⠀⠀⠀⢸
⣿⠀⠀⠀⠈⢻⡉⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠉⣟⠉⠁⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣠⠞⠉⠻⣤⣀⡤⠊⠀⠀⠀⣾
⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⠀⠀⠀⠀⠀⠀⢇⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠂⠀⢰⡏⠀⠀⠀⢹⠀⠀⠀⠀⠀⣴⡿
⢻⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠁⠀⠀⢸⡄⠀⠀⣠⠟⠀⠀⠀⣠⣾⠟
⠈⢿⣆⠀⠀⠀⢀⡞⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⢀⣴⣾⠟⠁
⠀⠈⠻⣷⣀⠀⠘⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠈⢻⣧⡀⢳⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢄⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⢹⣷⡀⠙⢦⣤⡴⠃⠀⡀⠀⠀⠀⠀⠀⣰⣀⣀⣎⣀⣠⡂⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣣⣾⡟⠁
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠸⡀⠈⠲⡀⠀⠐⢯⣉⡉⠈⠉⠉⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠟⠉
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠟⣁⡴⠚⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⠚⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡴⠋⠀⠀⠉⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠀⣠⡶⠋⠀⠀⠀⢀⡄⠀⠀⣠⣿⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡼⣡⡞⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣼⡷⠃⠀⣠⡖⢀⣴⡿⠃⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⣠⠞⠁⠀⠀⠋⢀⣠⡾⠋⣰⢋⡾⠁⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡞⠁⣸⠁⣠⠞⠁⠀⠀⠀⠀⡰⣫⠏⠀⡼⣡⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣷⠏⠀⠀⣿⠞⠁⠀⣀⡄⢀⡤⢊⡼⠁⣠⢞⡼⠁⣠⡞⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠸⣃⣀⠀⠀⠁⠀⣠⢾⣯⠖⠉⠀⠈⠁⠔⠁⠚⣡⣾⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⠴⠋⠁⠀⠀⠀⠤⠞⠁⠋⠁⠀⠀⠀⠀⠀⠀⡠⠞⠉⠁⠀⢀⣴⡷⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⣫⠴⠖⠒⠒⠛⠛⠲⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⢺⡏⠀⠴⣄⠀⠀⠀⠰⡄⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⣰⢏⠜⣡⠞⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠖⢸⡇⠀⠀⠰⠋⣠⠟⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⡏⡞⣼⠁⠀⡄⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⣰⠋⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⡼⣱⢡⠟⠀⠀⠃⠀⠀⠀⣄⠀⠗⠀⠀⠀⠀⢴⠋⢀⡼⠁⠀⣠⠃⠀⠀⠀⣠⠞
⠀⠀⠀⢀⡞⢁⣿⡏⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⡾⠀⠀⠀⠁⠀⠀⠀⡴⠃
⠀⠀⠀⡞⠀⣾⠀⢳⡄⠀⢿⡀⠀⠁⠀⠀⠀⠀⠀⢀⠰⢋⣀⡼⠃⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢸⡇⠀⠸⡆⠀⢹⠀⠀⠉⠀⠀⠀⠀⠀⣀⡬⠁⢰⠏⠁⢀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢷⡀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣈⣽⠿⠭⠤⠴⠋⣠⠴⠃⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠹⢦⣀⠀⠀⣀⣉⠛⠛⠉⠉⠀⣀⣤⣤⠴⠚⠁⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠈⠙⠓⠶⠖⠋⠁⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢂⠔⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣡⠖⠁⠀⡴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠔⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠔⠁⠀⡠⡢⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⢊⠔⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡠⠊⠀⠀⠀⢀⠔⠈⡠⠃⢀⠔⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠂⠈⠀⠀⠀⠠⠈⠁⠀⠊⠀⠀⠊⢈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⡅⠀⠠⠊⠀⡠⠊⠨⠀⠁⠀⢀⠔⠁⠀⠀⠀⣀⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠀⠘⠐⣁⠠⠒⠁⠀⣀⡀⠀⠀⠠⠆⢒⠄⠀⠀⠀⡡⠊
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠎⡠⠒⠆⠄⠂⢉⡀⠤⠐⠊⠁⠀⡩⠃⠀⠀⡠⠃⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠰⠈⠔⡡⠊⢀⠠⠀⠒⠈⠉⠐⠒⢄⠀⠀⢐⠆⠀⡠⠊⠀⡠⠒⠁
⠀⠀⠀⠀⠠⠁⢠⠊⡠⢊⡡⠀⠠⠀⠀⠀⠀⠢⡀⠡⡠⠂⡠⠊⠀⠔⠉
⠀⠀⢸⠑⠁⡰⢁⠎⡔⠁⠀⢀⠌⡠⠀⠀⠌⠀⢡⠀⡇⢌⠀⠰⠥⢤
⠀⠀⢘⠀⢠⠁⠆⠈⠀⢀⠔⠡⠊⢀⠀⠈⠀⠀⠠⢀⠃⠌⡀⠀⢠⠂
⠀⠀⠘⡀⠀⠀⡄⠐⠔⠁⠀⠑⠒⠊⠀⠈⠢⠐⠁⠌⠀⡔⠁⡠⠁
⠀⠀⠀⠡⠰⡀⠰⡀⠀⠔⠈⠉⠁⠈⠑⢂⠀⢀⠜⡠⠊⠀⠊
⠀⠀⠀⠀⠡⡈⠢⡈⠢⡑⠠⠄⠀⠤⠐⢁⠠⡢⠊⡠⠒⠁
⠀⠀⠀⠀⠀⠈⠂⢄⡑⠂⠅⢀⣀⣂⠨⠕⣊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣀⠀⠀⠀⣀⣀⠀⠐⠛⠋⠙⠒⠂⠐⠶⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠸⣿⣧⠙⣧
⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢻⣿⡇⢹
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠙⠁⢀
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⣼
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⣳⠀⠀⠀⠀⣿⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠉⠙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣄⣀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⡿⠟⠋⠉⠉⠙⠻⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣻⣿⣿⣿⣿⣟⣛⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⡖⠢⠤⣄⣀⠀⠀⡀
⠀⢈⡆⠀⠀⠀⠉⠒⠿⠑⢄
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀
⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡀⠀⠉⠒⠤⣄⡀⢠⣀
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢯⠑⠦⣀⠀⠀⠈⠙⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⡆⠀⠈⠑⠲⠒⠢⢄⡀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠉⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠦⠀⠀⠸⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⢠⡓⠀⠀⠀⠹⡑⠦⣀⠀⠀⠀⠀⠀⠈⠲⠒⠤⣀⠈⠑⢄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⢄⠀⠀⠀⠱⡄⠀⠙⠢⢄⡀⣄⣀⠀⠀⠀⠀⠙⠲⢄⡈⠛⠀⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠳⣄⠀⠀⠙⡄⠀⠀⠀⠈⠉⠀⠉⠒⠖⠠⣄⠀⠀⠈⠲⢄⠀⠀⠀⠀⠈⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡍⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⠤⠒⠊⢉⣉⠐⠒⠤⢄⡀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⢦⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡤⠒⠉⣁⠠⠄⠀⠈⠀⠀⠉⠁⠀⢀⡈⠒⠢⣄⠀⠙⠋⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣵⡄⠀⢶⠊⠀⠀⠀⠀⠐⠉⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠆⠀⠈⠓⠤⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠙⣄⠀⠀⠳⡀⠀⣠⠎⢀⡠⠊⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠘⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢦⡀⠀⠈⡶⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠃⠀⠀⠘⡄⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠑⢄⣠⠃⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡹⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠤⡀⠀⠸⠤⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⠀⡇⠀⠓⠂⢰⡀⡄⠀⡀⠀⡀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⢱⠀⠠⠒⠂⠌⡀⠀⠃⠤⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡜⢀⠎⠈⠂⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡆⢰⠀⠀⠀⠀⡀⠀⠀⠐⠂⠒⣄⠀⠀⡈⠖⠒⠒⠶⠊⠀⡎⠀⠀⠀⠀⢸⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⡇⠀⡇⢠⠒⠒⠁⠀⠧⣀⣀⠀⢈⡆⡞⠀⠀⢂⠀⠠⠒⠄⠈⠱⠴⠃⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠙⠋⠀⡜⠉⠉⠑⠲⢄⠉⠉⠀⠈⠒⠊⠁⢠⡃⣀⠀⡠⢄⠀⠀⢰⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠳⣄⠀⠀⠣⡀⠀⠀⠀⠀⠱⠀⡴⠊⠁⠉⠢⢄⠉⢠⠊⠀⠀⠅⢀⠇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠑⢄⡀⠹⡄⠀⠀⠀⡜⠘⡄⠀⠀⠀⠀⠀⠇⠈⠑⠒⢀⡴⠋⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠙⠦⡈⠀⠀⠀⡡⠀⠈⢦⣀⣀⡀⠈⠀⣀⡠⠖⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠑⠢⠌⣀⡀⠀⠀⢉⣁⠤⠔⠋⠀⠀⢀⡠⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣒⣤⣀⣠⣭⣭⣤⣤⣤⣀⣀⣒⣊⣁⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣴⠀⠈⠈⠉⠀⢄⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠊⠀⠁⠉⢀⣠⠀⠁⠀⠀⣴⡖⢀⡀⢤⡵
⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⡄⡠⠀⠀⣾⠆⢸⠃⢀⣀⡀⠀⣨⣙⠟⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡠⣀⠈⠀⢄⠀⠀⠀⠀⠀⣠⠆⣀⠁⠋⢀⣀⣈⠀⠀⠀⠙⢉⣤⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⡂⠀⠐⣀⠀⠀⠀⠀⠉⠙⠗⢿⣷⠈⢻⡜⢿⣃⣨⣌⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣘⣥⣶⠩⠛⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠔⠡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠀⠀⠐⠅
⠀⠀⠀⠀⠀⣠⠔⠛⠃⠀⠁⠀⠀⠈⠛⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠁⠊
⠀⠀⠀⠀⡘⠁⠀⠀⢰⣶⠀⠠⣄⠀⢀⣴⣦⣵⡀⠄⠀⠀⠀⢠⠄⢇⠔⠊⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣯⠀⠀⢀⠀⠁⢀⢀⠃⣧⡀⠭⠀⠀⠵⢾⡀⠀⠈⠉⡶⠲⠉⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡴⠃⠀⠀⢈⠄⠐⠁
⠀⠀⠀⡏⠀⠀⣦⠀⠀⢀⢀⡀⠀⠈⠉⠀⣄⠀⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠠⢀⠄⠀⠀⢔⠅
⠀⠀⠀⢳⠀⢀⠀⠀⢸⣿⣿⠇⠀⢀⡻⢦⣨⢙⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠⠆⣾⣶⡦⠐⢀⠔⠀⠀⠀⠀⠁
⠀⠀⠀⠢⠀⠸⠇⠀⠈⠉⢁⡀⠓⠀⢸⣿⣿⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢀⡉⡵⠘⣋⡷⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠤⡤⠠⣄
⠀⠀⠀⠀⠙⣇⡀⣦⣷⠀⢈⡁⢀⣿⣾⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠡⣅⠈⠠⠴⢰⢫⣞⠰⠃⠀⠀⠀⠀⠀⠀⣀⡾⢀⢻⠞⣻⣻⣷
⠀⠀⠀⠀⠀⠈⠑⢉⣯⣼⣯⣿⣶⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣦⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣛⣝⣛⣩⣛⣻⣛⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⡤⣤⡶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠉⠁⠀⠀⠉⠉⠀⠀⠾⠿⡟⠛⠓⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⢀⣤⣦⣄⠀⠀⠀⠀⠀⠀⡀⠀⢤⣤⣀⣠⣀⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠁⠀⠀⠀⠀⢸⣟⣻⣿⠇⠀⠀⠀⠀⠀⡀⠀⠈⠛⠻⣿⣷⣷⡌⢻⣯⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⢨⣶⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⡆⠁⠿⠊⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠖⠃⣽⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡤⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⡎⢷⡀
⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⠀⠀⠀⢺⣿⡗⠀⠀⠀⣼⣽⣶⣶⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡁
⠀⠀⠀⠀⠀⠀⢸⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠿⠿⠿⠽⠏⠀⠀⠀⢤⡟⣿⣿⣮⡻⡆⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⠿⠐⠀⠀⠀⠀⠀⠀⡄⢻⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⢸⡁⠂⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⢿⣷⠞⠀⠈⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⣿⣿⣿⣿⢹⠇
⠀⠀⠀⠀⠀⠀⠘⣇⣄⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⠿⠟⣩⡾
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠃⠀⠘⢿⣿⣿⣿⣾⠀⠀⠀⠀⣟⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠂⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡄⠈⠛⠿⢿⣿⠧⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⣿⣿⠀⠀⡀⠈⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡔⠁⢠⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠛⠛⢯⡿⠏⠀⠀⣀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣔⠀⠙⠻⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠠⣿⣿⣤⣴⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠆⢀⠈⠛⠿⠿⠿⠛⠃⠀⠀⢀⠀⣡⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠥⠴⠦⢶⣿⣿⡿⠿⠷⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢒⣒⢢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⠤⢤⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠞⣡⠶⠷⢿⣷⠠⣟⣥⡐⠢⡀⠀⠀⠀⠀⠀⢀⣾⢹⡇⢸⢟⠀⡾⢽⢻⡿⣏⠹⢷⡦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣤⡁⠰⡴⠊⣋⣰⡯⠁⠙⣠⣿⣆⠀⠀⠀⢀⠼⣃⠘⣿⡆⠉⠀⢓⡿⢻⢇⣹⣷⣀⡴⢧
⠀⠀⠀⠀⠀⠀⢸⣯⣭⡋⣸⣄⡳⠦⠈⠹⣟⣀⣽⢿⣾⡿⠿⡀⠀⠀⢼⣦⣽⠴⠋⠀⠀⠀⠈⠈⠁⠾⣿⡟⡛⣣⠈
⠀⠀⠀⠀⠀⠀⡾⢿⣭⣿⣿⠻⣿⣿⣾⣿⣿⣿⡻⢏⣭⠘⡡⠃⠀⠀⢾⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⢿⡇
⠀⠀⠀⠀⠀⠀⢯⣷⢻⢿⣿⣿⣿⣯⣤⣾⣿⣿⠃⠻⡮⠴⠀⠀⠀⠀⠘⣿⣏⢰⠶⢶⣴⠮⠖⠀⠠⢿⣻⣗⠀⠸⡸
⠀⠀⠀⠀⠀⠀⠀⠻⠼⢿⣿⠿⣿⡟⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠛⠎⠛⠢⠄⠀⠖⠛⠉⠍⣿⣗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣻⠿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⢀⣠⣭⡿⢻⣧⠛⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠭⠽⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⣀⣈⣀⡨⣽⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⢯⣿⣻⣃⣠⣀⠀⣿⣿⠛⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣥⣀⡀⠀⠀⡠⢊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁⣸⣿⣿⢛⣿⣿⣿⣶⡑⢬⢁⣀⠀⠀⢀⣰⣶⣋⡿⣦⡉⠛⣿⣿⣋⡙⣯⡾⢿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⣼⡿⢛⡟⢼⣿⣻⣽⣿⡇⣿⣼⢹⠀⠀⠸⡛⠿⣭⣴⣌⡻⠾⣋⣿⣿⣿⣟⣿⣷⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠠⣿⡟⠇⣈⠻⠟⢡⡾⢣⡎⢉⣉⣉⣼⣱⣿⣿⡾⠀⠀⢀⣿⣶⡏⠻⢿⣿⡿⠿⣿⣿⣿⣿⣷⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠙⣝⣿⣶⡝⠑⠙⠣⠦⠖⣚⡋⢀⣿⠏⠀⠀⠀⢸⡿⣿⣿⣶⣶⣾⠁⠐⡙⠮⠩⠟⣫⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠘⠋⢼⢿⣶⣴⣶⣦⣹⣿⣿⡼⠃⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣧⣤⡶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣟⣴⣧⣍⠛⣈⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣻⣻⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣤⣦⣾⣷⣾⣵⡇⠉⠁⠀⠀⠀⠀⠀⣀⢄⡤⢢⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⢟⡿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⠀⡀⣠⡞⣡⡟⡄⡡⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⡀⠚⢷⡮⠌⣾⣿⡯⠉⠉⠀⠀⠀⢚⣵⠋⢾⣟⣴⣿⡼⠁⠀⠀⡠⢀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⠰⡿⠃⣷⠄⠀⠈⣨⡿⠋⠀⠀⠀⣠⣾⣠⣹⣷⢟⣿⣭⣿⡿⠁⠀⠀⡀⣱⢿⣿⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⣄⠐⢴⡦⠀⢀⡼⠋⠀⣠⠔⣡⣾⣷⣿⣿⣿⣿⡿⣿⣿⢟⡔⠀⠀⣤⢞⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠉⠀⠀⢚⣵⣮⠿⣻⡿⣫⣿⣿⣵⣳⡿⣿⠟⢀⣔⣾⣿⣻⣿⣭⢿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡻⠋⢡⠞⠉⠜⢡⣿⣿⣷⣿⠅⠀⠀⢰⣯⣿⡟⣿⣿⣻⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠟⣀⡴⢀⡴⢃⡴⠀⣩⣿⢯⣿⠋⠀⠀⣰⡿⢻⡿⠀⠿⣷⣟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⢀⣤⣾⣿⣿⣿⡿⢋⡀⠘⣹⣻⡟⠁⠀⢀⡞⠉⡰⠟⣠⡀⣴⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⠛⠛⠻⠿⣿⣿⣷⠋⠀⣰⣿⡟⠀⠀⢠⢋⣴⠟⢃⡘⢿⢁⡃⢺⡟
⠀⠀⠀⠀⠀⠀⢞⡟⣡⣤⠀⠦⠀⣴⣦⡌⢻⣷⠏⣼⣿⠏⠀⠀⠀⢣⢋⣀⠤⢻⡿⠀⠿⠃⣸⠁
⠀⠀⠀⠀⠀⠀⡎⠐⠿⠋⣴⣶⣶⠈⣛⠁⠀⣡⢦⣿⠋⠀⠀⠀⠀⢀⠸⠟⣴⣶⠄⠀⠀⢇⠏
⠀⠀⠀⠀⠀⠀⣇⠀⣶⡄⠙⠛⠋⠈⠉⠀⢀⣿⠟⠁⠀⠀⠀⠀⠀⠈⢾⡃⠹⡅⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠹⣆⠉⠁⠐⠂⠀⠀⠀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠦⠤⠤⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣤⠴⠖⠚⠛⠉⠿⠿⠛⠀⠉⠉⠹⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⢻⠦⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠉⠀⢄⣤⣶⣶⣾⣶⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⡈⡉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠀⠀⢀⡄⠿⣿⡿⠿⠿⣫⡾⡏⠀⠀⢁⣤⡾⣯⣾⣿⣿⣶⡄⠀⠀⠈⠣⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠈⠛⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠠⣿⠸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠻⢾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠻⠿⣳⣶⣦
⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣛⣭⡾⠇⠀⠀⠀⠠⠀⠐⢾⢹⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢰⢻⣇⠀⠀⠰⠀⠀⣼⡄⠀⠁⠀⠀⠀⠺⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⡘⣿⡷
⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡞⣿⠂⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⣾⣷⠾⠃
⠀⠀⠀⠀⠀⠘⢿⡦⠀⠀⠀⠀⢸⣿⣿⣧⢀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠈⠀⠀⢻⣿⣿⣿⣤⡀⠈⠛⠋⣭⣻⡯⣿⠋⠀⠀⠀⠀⠰⣿⣿⣿⡿⠃⠀⠀⠀⠀⣁⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡆⡀⠐⠀⠙⠻⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⢠⢞⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣴⣃⡿⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣣⣟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢤⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⠐⢈⣡⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣤⣀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠸⠿⠯⠍⠀⠁⠀⠀⠀⠀⢠⣽⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣚⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⡶⣶⣶⣤⣿⣻⣧⣠⣽⣯⣥⣀⣠⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠿⣭⡽⠟⠁⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⢀⡤⠚⠁⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⠀⠀⣀⠴⠚⠁⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡡⢋⡠⠔⠋⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⣠⠾⠛⠉⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣀⡤⠖⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠯⠖⢚⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣁⡤⠖⢉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠥⠖⠋⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣚⢥⡖
⠀⠀⠀⢀⠴⠋⠀⢀⡤⠖⠒⠉⠉⠀⠀⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⠋
⠀⠀⡰⠋⠀⢀⠔⠁⡠⠴⠒⠋⠉⠑⠒⠲⠤⣄⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⡜⠁⠀⣠⠋⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⣸⠁⠀⢠⠃⠀⢹⣀⣀⡤⠖⠚⠉⠉⠑⠒⠒⠚⠁⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⡇⠀⠀⡍⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⡇⠀⠀⡇⠀⡇⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⡴⠋
⢳⠀⠀⢳⠀⢱⡀⠀⠈⢳⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢠⠃⠀⡞⠀⠀⠀⢀⡴⠋
⠈⢧⠀⠀⠳⡀⠳⡀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⠏⢀⠞⠀⠀⢀⠴⠋
⠀⠈⢣⡀⠀⠈⠲⣌⠒⠚⠁⠀⠀⠀⠀⠑⠤⡠⠤⠚⢁⡴⠋⠀⣠⠖⠁
⠀⠀⠀⠙⢄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠉⠑⠒⠒⠒⠊⠉⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣠⡤⠖⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡟⠁⠘⠗⠐⣲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠛⠙⠉⠀⠀⠀⠀⣴⠿⠁⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⣛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢴⠃⠀⠀⠀⠀⠀⠀⠈⠁⢠⡾⣡
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠃⠀⣠⢏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠐⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠔⠀⢀⣴⣶⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢞⡼⠻⠋⣰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢈⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⣴⡷⠟⠀⢀⣹⡿⠟⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⢀⡴⣭⠟⠀⠀⢀⡜⠋⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠹⣿⢄⡀⠀⠀⢀⣤⣶⡟⢁⣀⡴⣫⡾⠁⠀⢀⡴⠏⠁⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠸⣿⣿⣶⣿⣿⣿⣃⣼⡿⣫⣾⠟⠀⢀⣤⠞⠁⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⠟⣫⣾⣿⣡⣴⣶⡟⠁⢀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⠂⠐⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠀⠀⠒⠤⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢘⠀⢠⠄⠂⠀⢀⣾⢱⠀⠀⠀⠀⠀⠀⠀⣼⠇⠠⠞⠁⠀⠀⠀⢈⣧⣄⣀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⡗⠐⠀⠀⢀⢑⣡⢂⣾⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⠀⢀⡀⠀⠠⠈⢹⠄
⠀⠀⠀⠀⠀⠀⡅⠠⣀⠀⣀⣀⣤⠶⢟⡞⠁⣼⠏⠀⠀⠀⠀⠀⠁⠀⢻⡍⠀⠒⠋⠀⠀⢀⢈⡤⠀⠐⠂
⠀⠀⠀⠀⠀⢄⠷⣄⢉⣉⡥⣜⣶⡾⠋⢀⠾⣉⡰⠂⠀⠀⠀⠀⠉⠀⠀⠘⠶⢭⣈⣬⣥⠴⡋
⠀⠀⠀⠀⠀⡇⢀⠈⠉⠓⠺⠟⠉⠀⢠⠋⠌⠹⣿⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠣⠈⠃⠀⠈⠀⠀⢀⠔⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠁⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠤⠦⡀⠀⢀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠰⠂⠀⠀⠀⠂⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠠⣿⡼⡧⠀⠀⠠⠛⠓⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡄⢀⠕⣄⡠⠖⠰⠀⠀⣀⢤⠃
⠀⠀⠀⠀⠀⠉⠀⠯⠵⣅⣤⠴⠀⠐⠒⠠⠡⠄⠀⠀⠀⠀⠀⠀⠀⠘⠎⠠⠄⠀⡇⢀⠒⠫⣺⠏
⠀⠀⠀⠀⠀⠃⠀⠠⠒⠀⠀⠲⠀⠒⠂⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠠⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠱⢤⡀⣀⠀⢈⠁⣁⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠜⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠁⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⡀⢘⡃⠠⠀⠐⠄⣠⠐⠇⠀⠀⠀⠀⠀⠫⢤⢧⣠⣤⣽⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢤⠁⠈⢰⠀⠀⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠤⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠥⣀⣀⠹⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣤⣤⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣻⣭⣿⣿⠿⣿⣵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣞⣉⠀⠀⠀⠀⠀⠀⠀⢠⢂⡁⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⢾⣇⡲⠿⠿⠟⣻⣿⣿⣫⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⡠⠀⣴⣿⡿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢀⡼⠘⣿⢸⣿⣿⣼⣿⣿⡀
⠀⠀⠀⠀⠀⣴⣿⠇⣠⣶⡜⢿⣿⣦⠚⢿⣿⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⠟⣫⣿⠋⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠶⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⡾⠉⣥⣤⡀⢻⣿⣿⣻⣿⣆⠾⠗⣫⠞⠁⠀⠀⠀⠀⠀⠀⣴⣾⡍⠛⠽⢃⣼⢟⡡⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠂⣀⣠⣿⣿⣿⣷⣿⣿⣶
⠀⠀⠀⠀⢳⠀⣤⠙⢃⣼⣿⣿⣿⣿⣿⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⡀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⣿⢣⣶⣿⣽⣿⣿⣿⡿⣹⣿⡿
⠀⠀⠀⠀⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡜⣿⣿⣛⣿⣿⣿⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡔⠋⠑⢄⠀⠀⠀⠀⠀⠈⠺⠿⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⢀⠀⣀⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⢷⣿⣿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢨⣝⣿⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠅⠀⣠⣤⠀⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠀⠠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⢀⡀⠀⠲⠈⣿⣿⣤
⠀⠀⠀⠀⠀⠀⣠⡴⠸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡉⢀⡈⣴⣾⣻⣟⢻⡇
⠀⠀⠀⣴⠏⠀⠋⠀⢠⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⣳⣄⢢⠀⠀⡀⢥⠀⠀⣬⣿⡷⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠟⢁⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢠⣄⠀⢸⡆⢈⣻⣻⣻⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣩⣾⣿⣿⣰⣀⣀⣐⣶⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣤⣶⣿⣿⡿⣨⣿⣿⠃
⠀⠀⠀⠈⢿⡄⢨⣷⣾⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠠⣶⣤⣼⣿⢿⣿⣗⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣛⡿⠿⠿⠿⠙⠋
⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢔⣀⡠⠴⠟⠛⠛⠛⠳⠿⠿⠿⠦⠽⠦⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂

⠀⠀⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⠀⠀⣠⢴⠆⠠⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⢀⣸⣭⡖⠀⠀⡂⠁⠀⠀⢸⡷⠎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣤⠀⠀⠀⠀⠀⢨⢭⠉⠉⠁
⠀⠀⠀⠈⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⠷⠶⠊
⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⣀⣤⠄⡀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⠀⠀⠀⠀⠀⠀⣤⡶⠒
⠀⠀⠀⠀⣼⣿⡇⠀⠈⠀⠀⠀⠀⢸⣿⡟⠀⠀⢠⠀⠀⠀⢀⣾⣿⠖⠚⠋⣻⠀⠀⠀⢸⣿⡀⠤⠂
⠀⠀⠀⠀⠙⢿⣷⣶⠞⠀⠀⠀⠀⠘⢧⣴⣄⡀⠀⠀⠀⠀⠻⠽⢿⣦⡄⠀⠁⠀⠀⠀⠀⠙⠿⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢀⣀⠀⣠⣀⡤⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⠀⠀⠀⢀⣠⡤⠄
⠀⠀⠀⠀⢰⣛⣿⠣⢐⠁⠀⠀⠀⢡⡌⠀⡉⣉⡀⠀⠀⠀⠀⠀⠋⣠⠚⣹⠎⠀⠀⠀⣾⣿⠓⠀⠐
⠀⠀⠀⠀⠈⠿⠿⣉⡁⠀⠀⠀⠀⣼⠇⠀⢣⠀⠹⠆⠀⠀⠀⠀⣰⠟⠿⠕⠁⠀⠀⠀⠘⠿⠿⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠒⠸⢿⣷⣶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠶⠋⠀⠀⠀⣺⠟⣩⣿⣿⣿⣿⣟⠛⠛⠻⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⣾⠋⠁⢘⣿⣿⣿⣧⡀⣰⢇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠀⠐⠉⠁⠀⣰⣿⣿⣿⣿⣿⡷⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣾⠿⣋⣿⣿⡿⢋⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⢁⣴⣿⡿⣋⠔⣡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⣾⡿⠟⡡⢊⣥⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⣡⠔⣉⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⣩⣖⣤⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⢤⣀⣀⣠⡬⠥⠖⣚⣩⣴⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠀⠃⠈⠃⠈




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⡴⠶⣚⣛⠋⣁⠐⢢⢱⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⠿⠿⠛⠋⠁⢠⠈⣆⠀⣬⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⢜⡜⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⢿⣿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⡅
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠉⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠋⠁⠀⠐
⠀⠀⠀⠀⢀⡴⣫⣾⠟⠁⠀⠀⠈⢀⠀⠀⣀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠐⠁
⠀⠀⢀⡴⡁⠀⡍⠸⣀⣀⠀⣀⣤⣴⣷⣿⡿⠛⠉⠁⠀⠀⠀⠀⢀⠄⠊
⠀⠠⢱⠰⡀⠐⠀⠒⣒⣒⣭⠿⠟⠛⠉⠀⠀⠁⠀⠐⠒⠂⠀⠈
⠀⠐⠠⠅⠤⠉⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠖⠛⢋⣉⠙⠓⠦⣄⠀⠀⠀⢀⣆⠀⠀⠀⢀⡤⠶⡟⢹⠋⠛⠲⢤⡀⠀⠀⢤⡞⣦⠤⠀⠀⣠⡴⡺⢛⠟⢉⠗⢶⣄
⠀⠀⢠⠞⡁⠶⠀⠻⠞⠀⠀⣶⠈⢷⡀⠙⣯⣨⡟⠁⣰⢛⢒⢒⠁⠘⠤⠤⠤⠤⠽⢆⠀⣼⠛⠻⠀⢀⡾⠉⢁⠀⠄⠒⠁⡰⠁⣨⠷⡀
⠀⠀⡟⢠⠔⠦⠀⠘⠂⠆⢠⢤⠐⠀⣧⠘⠋⠈⠓⢰⠏⠉⠈⠀⢉⡇⢠⣦⠠⣖⣒⣛⡆⠀⠀⠀⠀⣾⡤⠊⢁⠔⠂⠈⢉⠤⠊⣀⠴⢻
⠀⠀⡇⠘⠲⠚⠀⢠⠚⢲⠈⠉⠀⠀⣿⠀⣀⣀⡀⢸⣋⣉⡉⠉⣉⠀⣀⠤⠤⠤⠤⢤⡇⢀⠤⢄⠀⣿⠔⣒⠥⠐⠒⠬⠅⢒⣊⢅⡮⣿
⠀⠀⢻⡄⣞⡆⠀⡈⠛⠋⠀⠰⠆⣰⠇⢰⠋⠬⢳⠀⢷⡐⠋⡈⠋⠀⠑⠒⠒⠒⢒⡾⠁⠺⣘⡺⠀⠘⣯⣊⠕⡀⠬⠄⠉⣀⠠⡀⢭⡟
⠀⠀⠀⠙⢦⣀⠀⠁⠀⠰⢂⣠⠾⠃⠠⡈⠓⠒⠋⠀⠀⠻⢭⣭⠭⠭⠭⠝⢀⣯⠟⠁⠀⠀⠀⠀⢄⠀⠈⠳⣏⡴⢊⠩⠤⠀⣂⡴⠋
⠀⠀⠀⡰⠀⠈⠙⠛⠚⠛⠋⠁⠐⠄⠀⠀⠄⢀⣤⢠⣄⠀⠀⢉⠙⠛⠛⠛⠉⠀⠜⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⢋⡁
⠀⠉⢊⠁⣉⠈⠀⠀⠀⠀⣴⢶⡄⠐⠉⠐⠀⣾⢤⣻⢾⠀⠢⠀⠀⠀⠀⠀⠳⡈⠀⠈⡀⠒⠂⠠⠀⡒⢀⠀⠠⢿⡿⠆⠀⠻⠟⠠⠶
⠀⠀⠄⠉⠑⠄⣀⣀⣀⣀⡈⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠐⠀⣀⣀⣀⡀⠀⠤⠒⠄⡇⠀⠐⠂⢿⡽⢀⠀⠀⢉⣋⣀⣀⡀
⠀⠀⠀⢀⡴⠾⢉⡐⠀⠈⠉⣳⣤⡀⠀⢠⠂⡡⠐⠶⢶⣶⡶⠛⠩⠭⠭⠟⠻⢶⣄⠀⠈⠀⠀⠘⠀⠂⢀⡴⠞⠉⠉⣉⠉⣉⠓⢦⡀
⠀⠀⣰⠋⠙⠢⢀⡀⠀⠀⠀⡔⡤⠳⡄⠸⡀⢆⠡⡀⠻⡛⠒⠒⠦⠤⠤⠤⠤⠖⠚⢧⠀⠀⠺⠒⠀⢠⣞⡀⡈⠁⠈⡐⠯⣊⠂⣶⠹⣆
⠀⠀⡿⠤⣀⡀⠀⠈⠉⠒⠒⠒⠒⠒⣷⠀⠑⢄⠑⢬⣦⣈⠙⠶⣒⣒⣒⣒⣒⣉⣉⣹⣧⡀⠀⠀⠀⣾⠘⠭⠀⠀⠶⠀⠀⡀⢀⣤⠀⢹
⠀⠀⣇⢠⣶⡄⠉⠉⠀⠒⢂⣀⡉⠉⡿⠀⠀⠀⠑⢤⡉⠋⠭⡦⢄⣉⠙⠲⢄⣈⡀⢠⣿⢿⣷⡄⠀⢿⠀⢠⠫⠕⡄⠀⠀⣁⠀⠠⠄⣸
⠀⠀⠹⣄⠉⠄⠒⠈⣀⠀⠀⣤⠄⣼⠃⠀⠀⠀⡀⠀⠻⡑⠦⣌⡙⠂⠌⠐⡢⠤⢀⣈⢁⡴⢈⠜⡆⠘⣧⠰⠉⠊⠁⠀⡎⠡⢱⠄⣰⠏
⠀⠀⠀⠈⠳⣆⣉⡀⠆⢀⣉⡶⠞⠁⠀⢋⠐⢨⠁⢠⠀⠙⠷⣤⣛⡓⠦⣤⣄⣈⡉⠁⠀⠀⢁⡠⠃⠀⠈⠳⢤⣀⣛⠀⢈⣁⣥⠞⠁
⠀⠘⠃⠠⠆⠀⠉⠉⠉⠉⣁⠔⢀⠀⠠⠆⠒⠲⠆⠀⠀⠄⠀⠀⢈⡉⠉⠉⠡⠄⠀⠈⠉⠉⢠⣲⡀⠺⡗⠀⠀⠈⠉⠉⠉⠁⠀⠀⣴⡄
⠀⠀⠀⡁⠈⠐⠀⠀⠀⠈⠂⢀⠠⠁⠀⠀⡜⢢⠀⠈⡀⠀⠀⠐⠄⡐⠀⠘⢄⡀⠓⠠⠄⡤⠒⠁⠓⠠⠠⠄⠐⣶⠆⠀⠀⠀⢠⠀⠉⠁
⠀⠀⠀⠘⠀⢀⣠⣤⣤⣤⣈⡀⠈⠠⡔⠊⠀⠀⠑⣠⠀⠀⠀⣀⣨⣤⣤⣄⣀⠠⢶⠀⠀⢀⠀⡀⠀⠐⠁⠀⢀⣠⣤⣤⣤⣀⡀⠀⠺⠂
⠀⠀⠀⣠⠞⠉⠓⠒⢱⠄⠀⢹⢦⡀⠀⠑⠄⠠⠋⠀⠀⣠⠞⡉⢃⠵⠸⣄⢉⠿⣦⡀⠀⠆⠁⠐⠢⠠⣠⣞⣛⣀⣀⣒⣊⣠⠝⢳⣄
⠀⠀⣰⡇⠀⣀⣠⠔⠚⠀⢀⣻⣂⣿⡄⠀⠘⠁⠀⢀⣾⡁⠀⢠⢖⢠⡐⠋⢼⢰⡉⢳⡀⠀⠀⠀⠀⣰⡇⠒⠤⣄⣀⣀⣀⠤⠒⠁⢘⣆
⠀⠀⡇⠑⠌⣓⠤⠤⣀⠀⣏⣀⠀⠈⣿⢀⡖⢦⠀⢸⣅⠸⠤⢌⡢⠥⠖⢲⠀⣇⢉⣹⡇⠀⠈⠀⠀⡿⢭⣙⡒⠒⠰⠶⠶⣒⣒⣿⣗⣻
⠀⠀⣧⠀⠀⠘⡄⠀⠀⡑⠀⠈⡇⠀⡟⠀⠙⡋⠀⢸⡄⢹⡆⢤⠃⡀⠀⠘⠤⠬⠅⢾⠇⠀⠀⠀⠀⢿⡒⠲⠮⢭⡽⢿⣛⣉⡭⠖⢋⣿
⠀⠀⠘⢦⡀⠀⢸⢀⡔⠁⠀⠀⢹⡜⠁⣴⢋⡍⣷⠀⠻⣬⠥⠤⠤⠃⠠⡄⢒⠴⣴⠏⠀⢠⣼⣧⡄⠈⢷⡩⠍⣂⠒⠤⠤⠤⢆⣈⡽⠃
⠀⠀⠀⠈⠙⠦⣬⣚⣀⣀⡤⠖⠋⠀⠀⠙⢶⡴⠟⠀⠀⠈⠲⢶⣄⣐⣤⣹⠾⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠙⠷⢦⣐⣒⣂⣴⠶⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠛⣴⡄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢀⠷⡄⠀⠀⠤⠐⠀⠀⠀⠐⠒⠀⠀⠀⠸⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢀⣤⡀⠀⠀⠟⠃⠀⠀⠀⠊⡠⡄⠀⡄⠄⠀⠀⠀⠀⠀⡆⠀⠘⡀
⠀⠀⠠⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠐⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠆⠀⡜⡀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⢀⠀⠒⠀⡠⠗⠀⠀⠀⣣⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠀⠂⠀⠌⠀⠀⠀⡄⠀⠀⠐⣇⡀⣀⠆⠀⠘⢂⠊⠀⠀⠀⢤⠀⠀⠈⢅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡦⠀⢠⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠠⠃⠈⠀⠀⠀⠀⠀⢰⠆⠂⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⣴⡮⠁⢀⣠⠤⠤⠀⠀⠀⠀⣰⠎⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣌⠰⢣⠎⠁⣀⣀⣴⡿⣡⠖⠛⣒⣒⣒⣪⠟⠀⠀⣠⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢁⡖⠂⣱⠋⢉⡽⠛⢋⣠⠃⣰⠋⣉⣁⠀⠀⠀⣀⢴⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⣩⠥⢞⡭⠶⠖⠃⠀⢿⠷⠛⢉⠁⣰⢏⣮⠞⡠⠀⣀⡼⠓⢋⡼⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠪⡎⢀⢠⠏⠀⠀⠀⠒⠒⠀⡀⠀⣀⡴⠃⡠⣲⠞⣡⠛⣩⣖⣫⠍⣀⠤⡟
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⣀⣠⣯⣧⠏⣠⠴⠀⠘⠀⠀⢰⣾⣯⠴⠶⠚⢡⠇⠠⣇⣤⠉⠉⡼⢋⠔⠊
⠀⠀⠀⠀⠀⠀⠸⠁⠀⣾⡿⢛⠽⠋⣴⣡⠇⠀⢀⡤⠴⠛⡿⠃⢠⣖⣮⣵⣣⢀⣤⠎⡠⠔⢡⠏⡎
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠛⠋⠉⠀⠘⠛⠁⠀⢀⣧⣔⠀⣸⠀⠀⡞⢿⣿⠋⠉⠉⣠⠤⠴⡖⣵⡾⠃
⠀⠀⠀⠀⠀⢸⣤⢤⡄⠀⢀⠀⠀⠀⢀⠇⠀⠈⠛⠋⠙⠃⢀⠔⢡⠆⡇⠀⠀⣟⢁⡴⠾⢞⡽⣵⠁
⠀⠀⠀⠀⠀⣼⡇⡎⠀⠆⡁⠀⠀⠐⠁⠀⠀⠀⡠⠂⠀⠀⠲⠒⡹⢀⡇⠀⣠⣿⣿⠀⣴⢉⣴⠟
⠀⠀⠀⠀⢸⢹⡗⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠀⢀⡔⢋⡤⠿⠠⣎⣽⣿⡇⢸⢿⡟⡟
⠀⠀⠀⠀⣿⠀⠀⠆⠀⣀⣤⠶⠶⠦⠤⣀⠀⠀⠀⠀⡀⢸⣷⡏⠀⢀⡠⠴⢺⣿⠃⠃⡠⠚⠁
⠀⠀⠀⠀⠳⣄⠀⠁⣼⠃⢀⣀⡀⢀⠀⠈⠓⠀⠀⠀⠀⡠⠟⠁⠀⣻⠄⣰⠞⠁⢠⣎⡄
⠀⠀⠀⠀⢀⡟⠀⠀⣧⣾⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠈⢀⣠⠀⠾⢳⣴⠇⠀⢀⡼⠋
⠀⠀⠀⠀⠀⢻⡀⠀⢻⡏⠉⠙⢿⣿⣿⣷⣀⠀⠀⠀⠀⠈⠀⠀⠀⠊⢁⡤⢖⠋
⠀⠀⠀⠀⠀⠀⠻⣷⠀⠑⠀⠀⢀⣿⣿⡿⠀⠀⣰⠀⠀⡐⢀⡔⣤⡤⣘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⢀⠉⠛⠛⠛⠀⠀⠀⠁⢀⣴⠿⠞⠀⢈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠴⢶⣤⣄⡠⠀⢀⣀⣡⣤⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠒⠀⠹⣿⣿⣿⣷⠶⠦⣉⠁⠠⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⡠⠄⠀⠈⠁⢀⠀⠀⠙⠆⠻⣦⣀
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⡤⠀⠁⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠈⠣⣦⠤⠀⠀⠀⠀⠙⠂⡀
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠆⠘⠃⠀⠀⢐⣦⠀⢮⡀⠀⠀⠀⠀⣔⠙
⠀⠀⠀⣼⢂⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⣶⠀⠀⠀⠀⠑⢀⣤⢸⡿⠀⠐⠘⡦⠀⡄⠀⠸⣆⠘
⠀⠀⢰⣿⠠⠀⠀⠀⠠⣀⠀⠀⠁⠐⠂⠀⠓⡀⠀⠀⠀⠸⠞⢿⠏⢁⣤⠀⠀⣐⠀⠙⠀⠀⠻⢀
⠀⠀⣾⣯⢐⠠⠀⠀⠀⠉⡗⠀⠶⡐⡈⠉⠇⠀⠰⠗⡄⠀⠒⡀⠀⢈⠈⠃⣾⣿⡆⠀⠠⢠⠀⠸⡇
⠀⠀⣿⣷⠀⠀⠀⡀⠀⠀⠀⢀⠀⣤⣉⠀⠋⢰⣄⠈⣅⠀⠬⠈⠃⠀⢀⡀⢈⣅⡀⢄⡀⠈⠧⡄⠀⡄
⠀⠀⣿⣿⡄⠀⠀⠀⠀⠠⡐⢪⠀⠁⠙⠂⠠⡈⠉⠁⠀⠝⠀⠀⠃⢀⠀⡧⠠⠀⠙⠒⢯⡐⡆⠀⠀⠁
⠀⠀⢿⣿⣷⠄⠀⠀⠀⠀⠙⠦⢀⡀⠀⠀⠀⠑⠀⠲⣬⠙⠈⠁⠰⡌⠈⠉⣆⡂⠀⠓⠂⠀⢰⠂⠘
⠀⠀⠸⣿⣿⡦⠈⠀⠀⠀⢈⡆⣀⠁⠈⠀⠀⠙⠘⠢⠤⠀⣠⣀⠠⠀⠐⠀⠀⣮⠁⠀⠀⢠⠃⢠⡎
⠀⠀⠀⢹⣿⣷⣤⢰⠌⠀⠀⠇⠮⠙⠶⠐⢏⣦⠀⢠⢀⡀⠀⠛⠂⠙⠂⢀⠀⠈⠂⡀⠀⠀⢰⣾⠃
⠀⠀⠀⠀⠻⣿⣿⣴⢢⡄⠁⠀⠀⠺⠀⠀⢴⢮⠀⠠⠌⠐⠶⠀⠀⠀⠰⠦⣄⠀⠀⠀⠀⠀⠺⠃
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⣈⠀⠁⠀⠀⠀⠨⠴⠀⡀⠀⠀⠀⠲⠄⠀⠀⠁⠀⢀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣦⡀⠀⠀⠂⠀⠀⣜⠀⠀⠉⠣⡀⠀⠀⢀⣬⡉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣦⡓⠘⣄⡲⡐⠒⡀⠀⢠⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢿⣿⣿⡿⠶⠶⠛⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠩⠁⠀⠀⠉⠉⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⠀⠠⠣
⠀⠔⠂⢈⠭⠍⠩⠥⠴⠆⢐⡖⠀⡀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢣
⠀⠑⢄⠈⠢⢄⠀⠀⠀⠀⢀⠅⠈⢀⠁⠀⠀⠈⠪⠿⠁⠈⠉⠁⠻⠧⠃⠀⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠁⠢⢄⡉⠒⠤⣀⢸⠂⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠂⠀⠖⠀⠠⠁⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡈⠑⠂⠤⣄⡠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠠⢄⣈⠁⠒⠢⠄⣀⡀⠀⠀⠊⠀⠈⢀⠀⠀⠀⠀⠰⠁⠒⠭⣒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠂⠀⠉⠒⠂⠤⣄⣈⠉⠙⠛⠠⠄⣀⡀⠀⠁⡰⠃⠀⠀⠀⠀⠉⠒⢅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠠⠄⠀⠤⢀⠀⠈⠛⠒⠒⠠⢤⣀⣉⠉⠑⠒⠂⠠⠤⠤⠀⠀⠀⠕⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀⠀⠀⠀⠤⠄⠀⣀⠤⠊⠁⠀⠉⠁⠀⠐⠒⠒⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⡠⠖⠚⠛⢻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡓⣦⣄⠀⠀⠀⠀⠀⠀⠀⣰⣒⠫⠛⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⡀
⠀⠀⠀⢈⠁⠀⠀⠀⠀⢲⢹⣿⣆⠀⠀⠀⠀⠀⠀⠐⠀⠘⠗⠛⣿⣷⡀⠀⠀⠀⢠⠏⠉⠛⠁⢄⠈⣙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢿⣿⡄
⠀⠀⢸⠌⠀⣀⠀⠂⡀⠉⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⣭⠸⠇⢔⣽⣿⡇⠀⠀⠀⢷⣀⡈⠀⠀⠀⣹⣿⣿⣿⡄⠀⠀⠀⠀⣀⣄⣐⣦⣤⣠⣾⣿⣿
⠀⠀⠰⠀⠀⠉⠀⠀⠉⠧⣨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⡈⣵⣯⣿⣿⠇⠀⠀⠀⠘⠿⣿⡇⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⢍⣍⣿⣯⣽⣿⡟
⠀⠀⠀⠁⢂⠀⠐⣠⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠆⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠐⢻⣧⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠆⠀⢘⡋⣡⣿⠟
⠀⠀⠀⠀⠀⠁⠁⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⢲⢶⣤⣄⣴⣶⣶⡀⠀⠀⠀⠀⠐⠂⠂⠲⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣷⡄⠀⠀⠀⠀⠀⠀⠀⠔⠡⠋⣹⣿⣦⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⣿⣷
⠀⠀⠀⠀⠒⠶⢶⣶⡖⢶⣟⣿⡿⠀⠀⢀⠀⠀⠀⠀⠈⣠⠞⢋⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣠⣨⣵⡿⠁⠀⢠⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠐⠂⠉⢛⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠁⠀⠀⠀⠀⠁⠈⠉⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⢷⡄⢀⠀⠀⠀⠀⢀⣠⢉⡀⠰⡄
⠀⠀⠀⢀⡀⠀⠀⣾⠀⢠⡆⢀⡖⠀⠀⠀⠃⢸⡇⠈⢺⠀⠀⠀⠈⡇⠈⠀⢸⡇
⠀⠀⠀⠀⠸⣶⡄⢿⠀⢠⣧⢫⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠤⠈⢿⠗⠀⣘⠷⡁⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⢀⠀⣀⣘⣼⡇⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠐⠒⠚⠱⠾⠻⠟⠁⠀⠀⠀⠀⠀⠘⠷⠘⠁⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⠆⡀⠀⠐⠃⠀⠀⠰⠀⠀⠀⠀⡁⠀⠀⠈⠕⠄⠀⠀⠐⠀⠀⢀⡈⡀
⠀⠀⠀⠀⠀⢹⠀⠀⢀⣾⠁⢲⠀⠀⠀⠀⠉⠦⠀⡀⢀⠀⠀⠀⢰⠀⠀⠈⠀⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⠋⠀⠀⠀⠀⠀⠀⠀⣷⡌⠀⠀⠀⢸⠀⠀⠸⠸⠀⠀⠀⠀⠀⠛⠀⠀⡀
⠀⠀⠀⠀⢸⡦⣀⠔⢺⣷⡎⢠⡾⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠸⡀⠀⣬⡼⠀⠀⠀⠀⠀⠟⠀⠸
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⣷⠀⠀⠀⢀⠀⠀⠁⣠⡀
⠀⠀⠀⠀⠁⠀⡴⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠚⠥⠐⠊⠁⠉⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⣤⡶⠛
⠀⠀⠀⠀⣯⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⠶⣻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣡⠴⠞⣫⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⠞⢋⡄⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣊⡤⠞⠻⠟⠉⠀⣈⡵⠞⠋
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⣀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠈⠧⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠿⠴⠋⡡⠂⠀⠈⠁⣀⡽⠃⠠⠖⠁⠀⠀⢀⡜⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣆⣠⡴⠋⠀⠀⠀⠀⠀⣀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠠
⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠶⠞⠉⠀⠉⠡⠔⠀⠀⠠⠂⠀⣨⡴⠋⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡾⠛⢛⠛⣛⢶⣤⡀⠀⠀⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⡟⢡⣟⢈⡴⢶⡌⠿⡃⢹⡇⠀⣘⡵⠋⠀⣀⠄⠀⠀⠀⠀⢀⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⣇⠰⣿⢀⠙⣋⡀⠸⠟⣼⡏⢈⡿⠀⠠⠊⠁⠀⠀⠀⠀⠀⠹⠔⠚⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⣷⣌⣛⣣⣼⣶⣿⡶⠋
⠀⠀⠀⠀⣠⠀⠀⠀⠘⠷⢦⣍⣉⣩⡖⠛⠁
⠀⠀⠠⡖⠉⢳⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡦
⠀⠀⠀⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⡱⡻⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣊⡁⠀⡜⠀⡇⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡝⢆⢸⠁⣸⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢸⡈⠑⠊⠑⠢⡄⠀⠀⠀⡌⠀⠀⢠⠁⠀⡟⠊⡸⠀⢉⡻
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡎⠈⠑⠢⢄⡜⢡⠀⠀⠀⡇⠀⠀⡎⠀⢰⠁⢀⠇⠀⣞⠃
⠀⠀⠀⠀⠀⠀⢸⡒⠤⡜⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⠀⠀⢸⠁⠀⡎⠀⡸⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀⠀⠀⡇⠀⡇⠀⡎⠀⢀⡇⠀⢸⠀⢀⠇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⡆⠀⠀⠀⠀⡇⠀⢇⢠⠃⠀⣸⠀⢀⠇⠀⡸⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢱⠀⠀⠀⠀⣷⠀⢸⡸⠠⠀⡇⠀⣸⠀⢀⡇⢀⠇⣀⡤⠴⢲⣒⡶⢶⢆
⠀⠀⠀⣰⡶⣖⠶⠦⢼⡄⠈⡇⠀⠀⠀⣿⠀⢸⡇⡇⢸⠀⢀⠇⠀⢸⠀⣜⠉⣀⡤⠒⠙⢦⣠⣃⣸
⠀⠀⠀⡇⢱⠀⠙⣲⡆⣧⠀⢹⡀⠀⠀⢹⠀⠈⣿⣏⣾⡒⠉⠑⢤⣇⠴⣗⠉⠁⠀⠀⠀⡴⢁⡴⠋
⠀⠀⠀⣇⣀⢧⠚⠁⠸⡘⡆⠈⡇⠀⠀⢸⠀⠀⡿⠋⢹⡉⡲⠒⠉⡇⠀⢈⣦⠀⠀⢀⡜⣀⠟
⠀⠀⠀⠑⢄⠀⠳⡀⠀⠙⣷⠀⢹⣀⡠⠿⠤⠾⢼⣠⠤⠛⠳⠤⢄⡧⠖⠁⠘⡆⢠⠎⡰⠃
⠀⠀⠀⠀⠀⠑⢤⣘⣦⠤⠚⠋⠉⠀⣀⣠⠤⠒⠋⠹⡄⠀⠀⠀⠀⢱⠀⠀⠀⣱⠿⡎
⠀⠀⠀⠀⠀⠀⣰⠋⠒⢤⡤⠖⠚⠉⠁⠀⢀⣠⠴⢚⡇⠀⠀⠀⠀⠀⣇⠀⡰⠁⠀⢣
⠀⠀⠀⠀⠀⣴⣫⠔⠊⠁⢳⠀⣀⠤⠖⠊⠁⠀⣀⢼⡤⠤⣤⣀⣀⣀⣸⣼⡡⠤⣶⠞
⠀⠀⠀⠀⠀⠙⠫⣍⠉⠉⡽⠉⢀⣠⡤⠖⠾⣉⠀⠀⢳⡀⠀⠀⢀⡴⠊⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠒⠋⠉⠓⠢⢤⣀⡀⠉⠒⠤⣷⡠⢚⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠞⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠴⠶⠶⠶⣶⡦⠤⢤⣤⣖⡒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡤⠖⠚⠉⢁⣀⣀⣀⡀⠀⠰⠋⠉⠉⠁⠀⠀⠈⠉⠛⠻⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣻⡿⠛⠁⠀⣠⣴⣾⠉⠁⠀⢹⠟⣿⠀⠀⠀⢀⣴⣾⡟⠓⢦⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠞⠁⠀⠀⣠⣾⣿⡿⠛⢀⣠⠖⢁⣼⡟⠀⠀⠀⡿⣿⣿⠋⠀⢨⣷⠀⠀⠒⠲⢦⡈⢲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⠞⠁⠀⠀⠀⢸⠿⠿⠿⠖⠚⠉⣠⣴⡿⠋⠀⠀⠀⠀⠀⠈⠉⠳⣾⠿⠋⠀⠀⠀⣀⠤⠥⠼⠋⠻⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠋⣠⠞⠁⠀⠀⠘⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⢤⣤⣄⡹⣆⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠦⡀⢾⣿⠄⢱⡘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⢠⠞⣻⣿⠋⠉⠛⢮⡳⠤⣾⢧⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢰⢃⡞⠁⢹⠙⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡟⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠏⢰⣿⣿⡄⠀⠀⠀⢿⣌⠀⢸⡇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣄⣸⢀⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⣝⡻⣷⣴⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠿⠆⠀⠀⣸⠘⡄⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⢠⡇⠈⠻⣿⣥⡾⠁⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⢥⣄⣤⣴⠃⡼⠁⠀⣿⢸⣿⡗⢶
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠵⠋⢀⡄⠀⢸⢹⣿⣷⢸⡇
⠀⠀⠀⠀⠀⡴⢻⡇⢀⠄⠀⠀⠀⢀⡴⠛⠉⠓⠦⡉⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣠⠖⠊⠉⠉⠱⢤⡀⠀⠀⣿⠀⠀⠈⣼⣿⡏⢸⡇
⠀⠀⠀⠀⠘⡄⠸⣇⣿⠀⠀⠀⠀⡾⡄⡀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠈⠉⠉⠉⠁⢀⠀⢠⣴⢏⠉⠙⢻⡄⠀⠘⠓⠚⢁⣿⣿⡇⣼
⠀⠀⠀⠀⠀⡇⠀⣿⡙⠦⠂⠀⠀⡏⣷⣷⡆⠀⠀⠀⢷⠀⡆⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⣷⡷⠀⠀⠀⢃⠀⠀⠀⡖⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠸⡄⢸⣷⡀⠀⠀⠀⢳⣻⣿⣧⠀⠀⠀⡟⣿⡇⠀⠀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⣷⡸⣿⣿⡇⠀⠀⢀⡇⠀⡄⣼⢣⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⢳⡀⣿⣷⡀⠀⠀⠀⠙⢿⣿⣦⡤⠞⣴⡿⠁⠀⠸⣇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢿⣧⣙⣿⣇⣠⠴⠋⠀⣼⣷⢯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣷⡄⠀⠀⠀⠀⠙⠳⠶⠞⣋⣀⣀⠀⠀⠙⠳⠶⠂⠀⢠⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢠⠆⢀⣾⣿⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⠒⠛⠉⠉⠙⢉⣿⣣⣤⣤⣍⡉⠻⢶⡶⠤⠖⠃⠀⠀⠀⠀⠀⢀⣀⣉⣻⣷⣄⠹⣶⣿⢟⣵⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀⠀⠸⣿⣇⠀⠀⠀⠙⢢⣾⣿⡄⠀⠀⠀⠀⠀⢠⣾⣽⡁⠀⠉⢻⣿⣾⢟⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⣿⣿⣷⡤⠀⠀⠀⢻⣿⡇⠀⠀⠀⠈⠷⣿⣿⡟⠀⠀⠀⣸⣯⣶⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣿⣟⡧⠀⢀⣠⣿⣟⣡⣆⣀⣠⣤⣤⠼⠟⣷⣤⣴⣾⣿⣿⣿⠿⠯⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣦⣭⣭⣭⣿⣿⣷⣶⣾⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠾⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡠⢾⠉⡹⠻⡉⢹⠦⡀⠀⠀⠀⠀⢀⡴⠋⢧⣀⣀⣰⠋⢢⡀⠀⠀⠀⠀⣠⠔⠋⢹⠙⠢⣄⠀⠀⠀⠀⠀⢀⣤⠔⠚⢹⠉⠒⠦⣄
⠀⠀⠀⣠⣎⣀⣸⣞⣁⣀⣙⣾⣀⣘⣦⠀⠀⠀⢸⠉⢳⠋⠀⠀⠈⡗⠉⣿⠀⠀⠀⣾⠣⣤⠔⠛⠢⣤⠜⢳⠀⠀⠀⠀⡼⠉⡳⠒⠋⠑⠲⡞⠙⣆
⠀⠀⠀⠈⠳⡀⠀⢧⠀⠀⢠⠇⠀⡰⠋⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⣿⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠥⢴⡃⠀⠀⠀⠀⢹⠤⢼⠄
⠀⠀⠀⠀⠀⠈⢢⡘⡆⠀⡞⡠⠊⠀⠀⠀⠀⠀⢸⠀⣸⡀⠀⠀⠀⣇⠀⣿⠀⠀⠀⣿⡠⠾⢄⡀⡠⠷⢄⣸⠀⠀⠀⠈⢇⠀⣣⣀⠀⢀⣠⡏⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣼⠞⠁⠀⠀⠀⠀⠀⠀⠘⢯⡁⡽⠒⠒⢺⡁⡹⠋⠀⠀⠀⠈⠳⢄⡀⢹⢀⡠⠖⠁⠀⠀⠀⠀⠘⠻⢄⣀⢹⠁⣀⡬⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢤⣤⡤⠄⢀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠀⢀⠀⢸⣟⣀⣮⣿⣿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢀⣀⡀⠐⠷⠶⠼⣟⣉⣽⣿⣿⣿⣿⣿⣿⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⣀⡄⠀⠈⢒⡿⠝⣁⣀⠄⣌⠛⣿⡾⠦⣿⣿⣿⣿⣿⣷⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⢴⣿⣷⠞⠀⠸⢿⢲⡆⠸⠿⠎⠀⠀⠙⠅⠘⠛⠏⠾⢿⣿⡿⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣍⣊⣽⣛⣁⠑⣠⢄⣴⣿⠇⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠉⣉⠑⢪⣿⣤⣀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢨⣿⣷⢷⣿⣿⣿⣾⣞⣽⣿⣱⠂⠑⢀⣴⡴⣠⠇⠂⠀⠀⠘⣋⠀⠐⣿⣹⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡌⠃⣟⠋⢀⣿⣿⡿⢛⣻⣿⣟⡏⠀⡀⠀⠘⠟⠐⠂⠀⠀⠀⠰⠊⠀⠀⢀⣝⠛⡿⢿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠿⢷⣿⣿⣶⣿⣟⠋⠀⠘⠀⠀⣀⠈⠀⠀⣁⠀⠉⠀⣀⡐⠀⢸⡇⠠⠀⠨⣿⠆
⠀⠀⠀⠀⠀⠀⠀⡄⢢⣸⣦⣰⣞⣿⣿⣿⣿⡟⣦⠀⢀⣀⠼⢿⣷⣾⡿⢡⠄⣤⠃⠀⠀⠀⠠⠁⠀⠨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠈⢻⡏⢤⢘⢯⣛⣿⣿⣿⣳⣏⣿⣶⣾⣿⣿⡁⠁⢮⣅⠀⠀⠀⠀⣄⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⢻⢆⣾⣠⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣇⣼⣿⣿⣦⡄⠀⠈⣿⣶⣀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⠀⠀⠈⢛⣿⣟⣻⣿⣿⣿⠟⠛⠛⠿⣿⣿⣯⢯⡝⠋⠁⠀⠀⠀⠏⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣏⠁⠀⠀⠃⣘⡿⡿⣿⠃⠒⠠⠀⠀⠘⣿⡿⠌⠠⠆⠤⠀⣀⠀⠀⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡔⠂⠘⠻⠡⠺⢿⣆⠀⠀⠀⠠⣤⣿⣥⡠⢄⡀⠀⠄⣀⣴⠾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⢤⣀⠀⠠⣨⢛⣂⠆⢸⣿⣿⣿⣿⣾⣿⣞⣿⣿⣿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⢊⣙⢿⠿⢯⣼⣛⣿⣿⢚⣻⣽⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠓⠛⠛⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡿⠟⠉⣩⣷⢶⠚⣉⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠿⠿⠿⠋⠛⠩⠝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⣀⣴⠾⠋⢀⣤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡐⣀⣈⣁⣀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠾⠛⠋⢀⡤⢞⣫⠞⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠿⠛⠛⠛⠋⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢃⣠⡴⣚⡭⠖⢋⣥⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣆⠐⠀⠀⠐⠂⠀⠀⣀⣠⠌⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠞⠋⠙⠫⣩⣤⣶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠳⢭⣽⣁⡬⢩⣥⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠉⣹⣳⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣢⠑⠊⠑⠁⠓⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣄⠀⢀⣴⡟⣱⣦⠀⢣⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠠⠂⣀⡀⠀⡀⠀⠠⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡣⠘⠚⢶⣿⣿⡆⠀⡇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠃⠀⠈⠠⡀⡁⠘⠀⠀⢆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡉⠤⡄⠀⠈⣟⡻⠗⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⢂⠈⠢⠀⠠⠊⢀⠂⡍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣄⣰⣿⣦⣜⣡⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠆⡑⠀⠀⠀⠐⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠊⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠸⡠⠑⠊⠋⠢⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡠⠊⠁⠠⠒⠁⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠁⠀⠐⠨⡝⠳⣄
⠀⠀⠀⠀⢐⡩⠄⠀⠈⠛⠓⠀⡼⠀⠔⠐⠚⠀⠀⠀⢁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⠀⠀⠀⠀⠐⠘⠌⢧
⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⡇⠒⡀⠀⡀⠂⠉⠂⢈⠆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠕⢄⢤⠀⠀⠀⠀⠀⠀⠀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠀⠈⠊⠉⠁⠈⠙⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⢘⡆⠀⠀⠀⢠⠈⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣐⠒⠁⠑⠠⢄⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡬⢀⠀⠀⡴⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢀⡠⠔⠉⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡽⢁⡠⠒⠉⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⡥⠞⠊⠁⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⡠⢊⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢈⠕⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣁⠤⣒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠯⠒⠉⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⡁
⠀⠀⠀⠀⠀⡠⠒⠁⣠⠤⠒⠂⠉⠉⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠞
⠀⠀⠀⢀⠜⠁⢀⠞⡠⠔⠂⠉⠉⠉⠒⠒⢄⡈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠎⠀⢠⠁⢘⠀⠀⣀⠠⠤⠤⣀⣀⠔⠃⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠸⠀⠀⠇⢠⣈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠈⠆⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⢠⠀⠀⠀⢸⠈⠢⡀⠀⠀⠀⠀⠀⣀⠜⠀⠀⢸⠀⠸⠀⠀⠀⠀⡠⠊
⠀⠀⠈⠆⠀⢣⠈⢄⠀⠈⡆⠀⠀⠀⠊⠀⠀⠀⢀⠆⢠⠇⠀⠀⡠⠊
⠀⠀⠀⠘⢄⠀⠑⢌⡢⠤⠃⠀⠀⠀⠣⣀⣀⡤⠊⡰⠃⢀⡔⠋
⠀⠀⠀⠀⠈⠢⡀⠀⠙⠦⡀⠀⠀⠀⠀⢀⡠⠔⠉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠉⠁⠈⠉⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠒⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠾⠿⠿⠛⠻⠿⠿⠷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠋⠁⠈⠙⠛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⢀⣤⣶⠶⠿⠛⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣠⡾⠟⠉⢀⣠⣤⡶⠾⠟⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣠⡾⠋⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⣴⡿⠃⣼⡇⠸⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⣠⡾⠋⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄
⠀⠀⠀⢀⣼⠟⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡾⠟⠁⠀⣠⣾⠏⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠈⢿⣆
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⢀⣴⠟⠁⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⢻⣆
⠀⠀⣾⠃⠀⠀⠀⢀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡏⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⢀⣀⣤⡾⠋⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⢀⡿⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⢉⣩⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣤⡶⠾⠷⣦⠀⠀⠀⠀⢠⣾⠏⠘⣧
⢸⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⢠⣿⠁⠀⠀⢠⡿⠃⠀⠀⢿
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⡿⠁⠀⠀⣰⡿⠁⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⡿⠋⠀⠀⢀⣼⠟⠀⠀⠀⣠⡿⢻
⣿⠀⠀⣀⣤⣶⠶⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣿⣀⣀⣤⣶⠟⠋⠀⠀⠀⣠⣾⠋⠀⠀⠀⣴⡟⠁⢸
⣿⣠⣾⠟⠁⠀⣠⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⣠⣾⠋⠀⢠⣿
⢹⡟⠁⠀⣠⡾⠋⠁⠀⠀⠀⠈⠉⠛⠿⢶⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⣠⡿⣿
⠘⣧⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⠀⣴⡟⢁⡿
⠀⢻⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣠⣶⠟⠁⠀⠀⣠⣾⠋⠀⣼⠃
⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁⠀⢀⣤⡾⠛⠁⠀⠀⣠⡾⠟⠁⠀⣰⡏
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠁⠀⣀⣤⡾⠟⠉⠀⠀⣠⣴⠿⠋⠀⠀⠀⣰⡟
⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠉⠀⣀⣤⣶⠿⠛⠉⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⣀⣴⡶⠟⠋⠁⠀⣀⣤⣶⠾⠛⠉⠀⢠⡀⣠⡄⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢀⣿⠃⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣠⣶⠿⠛⠉⠀⠀⢠⣦⢠⣿⠱⠿⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⡇⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⣿⠃⠈⠁⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⣼⡏⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⠀⠀⠀⣰⡿⠃⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢾⣿⣤⣤⣤⣤⣿⣥⣤⣤⣤⣤⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⠀⠀⠀⠈⢉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣤⡀⠀⠈⠛⠂⢱⣤⠔⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣧⢀⠀⠒⠀⠈⠀⠀⠀⡔⣰⠄⠀⢱⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡠⢾⣿⡄⠉⠀⢰⠉⠙⣷⠀⠀⠀⠀⣆⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁
⠀⠀⣴⠟⠁⠸⣿⣿⣂⣀⡈⠃⡚⢃⣤⣶⣤⣿⠿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢘⠉⢄⠀⠀⠛⢛⣛⣩⣭⡲⠖⠛⠋⠉⢱⡄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣤⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⣠⣤⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠃⣀⣴⣿⠁⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣯⠓⡀⠉
⠀⠀⠀⠀⢃⡐⠙⠀⢿⣶⣿⣷⣿⣿⣿⣿⡉⠀⢉⣄⡀⠁⠀⠀⢠
⠀⠀⠀⢀⡄⠀⠀⠐⢿⣿⣿⣿⠹⢿⣿⠟⠛⠂⠈⠛⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣾⢠⣶⡀⠀⠈⠙⢻⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⣾⣿⣿⣷⣠⣤⢈⣿⠉⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⢿⣿⣿⣿⣿⠙⠟⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠐⢀⡻⣿⡏⠀⠀⠀⠈⠀⠀⠒⠒⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⣾⣅⠀⢳⠤⠀⠀⠀⠀⠳⣾⠣⠟⣹⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⢿⣷⣤⣤⣤⣾⣶⡤⠖⢃⣄⠉⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠟⠓⠄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠾⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠠⡤⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠴⠾⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠀⠴⠀⣀⣢⣄⣄⡀⠀⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⢀⣽⡏⠉⡀⠀⢀⣨⢿⣶⣄⣤⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠖⠒⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢈⡟⠙⢦⣤⡄⢻⠇⠡⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⠀⠀⠂⠀⠀⠀⠀⠘⢦⠀⡀
⠀⠀⠀⠀⠀⢠⣼⡃⠀⣿⠉⠀⠀⣷⣄⡀⠀⣨⣿⣷⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣚⡆⢉⠠⠤⣈⡳⠾⢧⡀⡀⠀⠘⢂⠀⠀⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⡶⡄⣤⣼⠁⠉⠻⣯⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠑⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠳⣤⡀⠻⢄⣀⣀⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠉⣷⠀⠀⠘⡿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⠠⡀⠉⠿⣀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢏⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠆⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠂⢉⣉⠉⠉⠉⠉⠉⠐⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⣻⣯⠀⠀⠀⠀⠀⣠⠄⠀⠀⠲⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣥⡀⠀⠀⣠⣤⣄⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣠⣴⣾⣿⣿⠶⠄⣆⠀⠀⡀⠀⠀⠉⢉⣛⣩⡼⠀⠀⢻⣿⣿⡧⣀⠀⠈⢷⣕⢄
⠀⠀⠀⠀⠀⠀⡔⠁⠐⠀⠀⢰⣿⣿⠿⠋⠀⠀⣸⣿⠀⠈⠁⠀⡄⠀⠀⠉⠉⠀⠀⠀⠳⣌⣉⣀⣿⡇⠀⠈⢿⣷⡑⡄
⠀⠀⠀⠀⢀⠎⠀⣠⡤⠀⢀⠸⠋⠁⢀⣀⣤⣾⣿⣿⠀⠀⠀⣠⣀⠀⠀⠰⣟⡧⠀⠀⢠⠈⠙⠛⠛⠀⠀⢰⣿⣿⣿⣎⢦
⠀⠀⠀⢀⠎⠀⠀⠽⠋⠀⠀⠹⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢘⠋⣡⠄⠀⠀⠀⠀⢀⣀⡐⠲⣤⡀⠀⠀⠀⠸⣿⣿⣿⣿⣦⢣
⠀⠀⠀⡎⢀⡄⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠴⠂⠀⣀⠈⠛⠋⢀⠀⠀⢀⣶⣿⣿⡟⠀⠘⣿⣆⠀⠀⢀⠉⢻⣿⣿⣿⣆⢇
⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠀⢠⣾⣿⠿⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠈⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⡄⠰⣿⡗⢸⣿⣿⣿⣿⡘⡀
⠀⠀⡇⠀⡴⣦⠀⠀⠀⠀⠀⠨⣭⣴⡾⠃⠸⠇⠀⠀⣀⣤⣤⣄⠰⡷⠀⠀⠘⢿⠟⠁⠀⢀⣴⣿⣿⠃⠀⠀⠁⣸⣿⣿⣿⣿⣇⢃
⠀⢰⠆⠀⠲⠃⠀⢠⣦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⣿⣿⢿⣫⡄⠀⢀⠀⠀⠲⠶⣶⣾⣿⣿⠟⠃⠋⠀⠀⣠⣪⣷⡘⣿⣿⣿⢸
⠀⢐⠀⠠⠀⠀⠐⣜⣻⠇⠀⠀⠀⠀⣾⠗⠀⠀⠀⠰⣶⣶⣿⡿⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢇⣿⣿⣿⠘
⠀⠘⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢀⡄⠀⢀⠀⡈⢿⣿⢟⣼⣿⣿⣿⢸
⠀⠀⠇⠀⠓⠀⠀⢠⣶⣄⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠘⠶⠟⠁⠀⢀⣼⣿⣦⣴⣿⣿⣿⣿⡏⡘
⠀⠀⠸⠀⢦⡀⠀⣸⣿⣿⡟⣆⠀⢰⣟⣛⣼⡇⠀⢠⣉⣩⠀⠀⢰⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⢀⣀⣛⠿⣿⣿⣿⣿⣻⣿⣿⢃⠃
⠀⠀⠀⢃⠈⠷⠀⢣⡙⠿⢃⣿⣇⠀⢻⣿⡿⠃⠀⠈⠛⠋⠀⠀⠘⡿⠿⠛⢛⣫⣶⡟⠀⠀⣔⣽⣿⣿⣷⡘⣿⣿⣿⣿⣿⠏⡜
⠀⠀⠀⠀⢆⢀⡀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠿⣿⣿⡿⠟⣀⣴⡆⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⡟⡘
⠀⠀⠀⠀⠈⢪⢻⣶⣤⣙⣿⣿⠟⠀⠐⠂⢀⣠⣄⣀⠀⠲⠀⠀⠀⠉⠀⢀⣤⡠⣾⣿⣿⣷⡙⠿⠿⠿⢋⣼⣿⣿⣿⠏⡜
⠀⠀⠀⠀⠀⠀⠱⡝⣿⣿⣿⣿⣶⣦⣤⢰⣿⣿⣿⣾⣷⡀⣤⣴⢢⣶⣾⣷⡙⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⢡⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠪⡻⣿⣿⣿⣿⣿⣇⠻⣿⣿⣿⡿⢣⣿⣿⣮⣛⣛⣻⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡿⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢝⡿⣿⣿⣿⣷⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡩⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠽⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⠭⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠊⠩⠽⢛⣛⣛⣛⣛⣛⣛⡛⠭⠍⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣔⡢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢊⣥⣶⢶⣯⡅⢨⠯⣑⠢⢄⠀⠀⠀⠀⠀⠀⠀⣴⢻⡟⠀⡿⡇⢸⣟⡿⣿⣿⠉⢷⣦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣆⡘⠀⣄⡤⠫⠃⢤⣏⠉⠳⢨⡷⡄⠀⠀⠀⠀⣸⠟⠘⡿⣄⠙⠁⠸⣾⡵⣷⠘⣷⣄⢉⣼⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣛⡻⠸⣙⡰⣤⡄⠚⢿⠟⠀⡶⣶⣝⣿⣧⠀⠀⠀⣸⣧⣹⣠⡜⠉⠀⠀⠀⠋⠒⢡⣿⣿⡿⡿⡅⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⣾⢿⣿⣶⣦⣶⣾⣿⣟⣷⢜⣋⠴⣀⠇⠀⠀⣼⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣟⣼⣷⡀
⠀⠀⠀⠀⠀⠀⢿⢮⠻⣿⣿⣷⢾⣿⣋⣹⢿⣿⡽⠃⣾⣋⣠⠁⠀⠀⠀⠘⣿⣿⢂⣠⣠⡀⣤⣤⠄⠀⣰⡶⣦⠌⠁⡌⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣑⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡜⠀⠀⠀⠀⠀⠀⠀⠙⢿⡞⢮⣄⠿⢤⡁⠀⣀⣬⠟⢛⠲⣦⢜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣽⡿⣶⣿⣿⣟⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡀⠀⠀⠀⢴⣲⡦⣦⣰⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠶⠳⠭⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠾⠿⣿⡱⠿⣧⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠶⠒⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⢯⣤⢶⠖⠒⠒⠫⡿⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠒⠂⠀⠀⠒⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⣈⣾⣷⣿⣴⡶⢦⡘⢟⠿⠌⡅⠀⠀⠀⠀⣀⡠⢤⡔⠾⣿⣿⣷⣶⣤⣤⢴⣨⣾⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠋⠁⣴⣿⣿⡇⢸⣿⡿⢿⣿⠀⣿⢰⣶⠀⠀⢠⣾⣿⡧⠏⠛⢦⣀⣼⢿⣧⣶⣼⣿⣽⣹⣷⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⠀⣠⣾⡿⠃⣼⡁⡿⣷⢭⡿⢻⢃⣟⡾⣸⠀⠀⠈⣧⣉⣿⣿⣿⣮⣝⣱⣾⣿⣿⣿⣾⣻⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣩⣤⣬⣉⠠⡾⠃⣿⡆⠆⡄⣰⡿⠾⣿⣿⠏⠀⠀⠀⣿⢿⣷⣉⢙⣛⡿⠋⣻⡿⣿⣿⣿⡇⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠻⣽⡿⣷⣄⠁⠈⠛⠺⣥⣴⡄⢸⡿⠁⠀⠀⠀⠰⣿⣾⣿⣿⣿⣿⣁⣀⡰⠙⢃⣊⣡⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣉⣐⡝⢻⠷⣿⡿⢷⣼⣿⡿⠞⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣴⣿⣶⣄⣡⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠛⠿⣮⣧⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⣿⣏⢽⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢲⠖⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠢⢤⡀
⠀⠀⠀⠀⠀⡜⡁⠂⠘⠛⠀⠰⠌⢣⠀⠀⠀⠀⢠⡋⠀⢈⡘⠠⠤⠤⠽⡄⠀⠀⠀⢀⡾⢉⠀⠀⢂⡡⠂⡘⢦
⠀⠀⠀⠀⢸⠁⣊⡀⠀⣁⡀⠶⠎⠀⡇⠀⠀⠀⣧⠀⠀⠠⠌⠐⠂⠪⠁⢿⠀⠀⠀⢸⠆⡁⠀⠁⠠⠐⡁⠔⣪⡇
⠀⠀⠀⠀⠘⣆⡠⡄⠀⠣⠞⠀⠄⢠⠇⠀⠀⠀⢳⡴⠆⠒⠀⠊⠉⠡⠀⡟⠀⠀⠀⠘⣦⢂⠀⠁⠀⠒⢀⠈⣺⠃
⠀⠀⠀⠀⠀⠘⠮⣀⠈⠀⠒⣠⠴⠃⠀⠀⠀⠀⠀⠻⢭⡭⠭⠤⢇⡰⠞⠀⠀⠀⠀⠀⠘⠷⣤⣂⠁⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⡴⠆⠁⢉⠉⡓⢦⡀⠀⠔⠀⠠⠶⣶⠖⠛⠋⠙⠓⠦⣄⠀⠀⠀⠀⠀⢀⡴⢚⠉⠉⠉⠒⢤⡀
⠀⠀⠀⠀⢀⡏⠈⠒⠄⣀⡀⠀⠀⢹⡀⢂⠂⠠⡘⠫⣙⣒⣒⣒⣒⣂⢉⣧⠀⠀⠀⢠⠏⡤⠀⠀⠘⠓⠁⠶⢳⡀
⠀⠀⠀⠀⢸⠉⣒⠀⠀⠤⠠⠤⠄⠠⡇⠀⠑⢄⠛⠖⣨⡁⠠⢄⡀⠀⠒⢺⣷⣄⠀⢸⠀⠨⣠⠈⠀⠐⠀⢃⠀⡇
⠀⠀⠀⠀⠈⢇⡉⠀⠀⠀⠀⠠⠄⡾⠁⠀⠀⠀⠹⡆⠬⡐⠋⠀⠀⠈⢁⡈⠡⠉⠱⠈⢆⠜⠂⠂⠀⡪⠐⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⣠⠵⠊⠁⠀⠀⠀⠀⠀⠈⠳⠮⢝⣲⡤⠄⠈⠁⠀⠠⠔⠀⠈⠓⠦⣬⣀⣤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⠚⠉⠀⢱⠂⢈⠗⣄⠀⠀⠀⠀⢀⡴⠛⠋⠐⢈⡌⠝⣦⡀⠀⠀⠀⠀⣠⠎⠥⠔⠂⠥⠙⡳⣄
⠀⠀⠀⠀⢠⠣⡀⢄⠂⠁⢀⠜⠃⠻⡆⠀⠀⠀⡼⢀⠀⢎⢐⡀⡘⡎⠢⣷⠀⠀⠀⢰⠧⢅⠐⠒⣐⣂⣉⣤⣸⡆
⠀⠀⠀⠀⢸⡀⠀⢂⠀⠑⡂⠁⠢⢀⡇⠀⠀⠀⣏⢲⠁⡑⠀⠀⠃⣙⡂⣿⠀⠀⠀⢸⡊⠴⠂⣠⠴⠒⣋⠕⢺⡇
⠀⠀⠀⠀⠀⠳⣀⠀⡆⡔⠀⠀⢸⠞⠀⠀⠀⠀⠘⢮⠀⠀⠂⠰⡀⣄⡴⠃⠀⠀⠀⠀⠳⣀⠀⠀⠀⠉⠠⣨⠟
⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠎⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠤⠔⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⣨⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠨⠟⠋⠙⣯⠀⣿⣿⣿⣿⣿⡠⡟⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣘⠃⠆⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⠠⠤⠰⠀⠲⠶⠋⣙⠛⠋⠉⠉⣿⣿⣿⣿⣤⡥⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⠀⠂⠀⢸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠈⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠧⣀⡀⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠈⠁⠂⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⠂⠈⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⡞⣷⡘⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣰⡹⠧⣿⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉⠈⢟⠀⠀⢀⣼⢃⢃⣶⡟⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⡤⠀⢾⡟⢋⡌⠦⣿⣻⣭⣿⡿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⠈⠁⠀⠀⠀⠀⠀⠻⣟⡼⣴⣏⣷⣿⣿⡔⢛⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣼⣿⣿⣿⣼⣿⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢧⣴⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣬⣿⢺⣡⣾⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠴⠒⠒⠚⠛⠛⠉⠛⠋⠑⠒⠒⠦⠤⣤⣤⠒⠒⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⢀⣤⠤⠒⠒⠦⣄⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢫⠞⠁⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠊⠁⠀⠀⠀⠀⡴⠖⠒⠦⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⢪⡔⠁⠀⠀⠀⢀⡴⠋⠀⠂⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣀⣀⠟⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⢠⣎⠖⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢦
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣤⠒⢦⡀⠀⠀⠀⠀⠀⠀⢠⠞⠙⠏⡲⣄⠀⠀⠀⠀⠀⠉⢣
⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⣴⣄⠀⠙⠧⣤⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣀⣀⡜⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠈⠊⢳⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡞⠀⠀⣰⠛⠁⢸⠄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢰⠇⠀⠀⣧⠀⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠷⣤⣤⠴⠏⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡀⠀⠀⠙⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢂⡴⠊⠁⠩⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠠⢠⠖⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠸⣶⣦⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡇⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⢧⢣⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠈⢦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠳⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⢲⠀⠀⠀⠀⠀⠀⢠⠾⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢠⣾⡁⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠀⢠⠟⠀⠀⠀⠀⣀⡔⠛⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⠀⠈⠻⢌⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⢀⡠⠞⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠉⠑⠺⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⠤⡶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠹⠤⠤⠐⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠹⣄⡀⠈⠓⠀⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⢰⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢸⠆⠉⠀⡐⠲⡦⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣰⠚⢷⠀⠀⠀⠈⢝⠆⠐⠆
⠀⠀⠀⠀⠀⢀⣼⣿⣷⢤⠘⠥⠒⠀⣉⠈⣀⡨⣀⡴⠞⠟⣻⣷⡄⠀⠀⠓⠀⠈⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣮⣿⣷⣶⣟⢗⣯⣥⣶⣿⠀⠀⠀⢸⡿⠁⠀⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠿⣧
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣤⣧⣽⣷⡍⣢⠤⢶⣦⠀⠈⠀⠀⠀⡼⠛⢻⣷⠀⠀⠀⢆⠀⠘
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⣿⣶⣦⡄⡰⡄⣰⣴⡶⠀⠀⢃⡀⠀⠉⠀⠀⠀⠀⠑⠊⠀⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⡀⣀⢁⣀⣤⣀⣀⢀⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠸⣿⣿⡙⢿⢿⣿⣿⣿⣿⣈⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⠄⠀⡌⠹⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⡀⣴⣿⡷
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣉⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣛⣩⣭⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⢿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠿⣻⣿⣛⣿⣭⣷⣶⣶⡶⢶⣾⣭⡭⣉⡉⢉⡉⢉⡝⢛⠛⠛⠛⠛⠛⠻⠿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡏⣼⡟⢡⡿⢡⡟⠁⢇⡎⠀⣼⠁⣶⠆⣤⢀⣤⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣠⣟⢠⣾⠘⣀⣼⠟⣠⡟⣸⣿⣾⢟⣼⡿⡽⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠘⠷⢀⠀⠀⠀⠀⠉⠉⠉⢉⣙⠛⡛⠛⠿⠿⠿⠿⣿⣿⣿⣼⣷⣶⣿⣷⡶⠿⠿⣛⣫⣵⣿⣿⣿⡇⠸⣧⡀
⠀⢀⣀⣀⣀⣤⣾⣿⡿⠇⠀⠠⠛⠠⢤⠀⠀⠠⠀⢀⡄⢀⡼⠉⠐⣻⠃⣿⡿⢛⣛⣿⣿⣶⣶⢶⣶⣶⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⠶⣤⣄⣀⣀
⣿⣿⡟⡟⢿⠟⢛⣁⣴⠄⢀⣘⠂⠨⠁⠀⣠⠊⣠⢎⡀⣆⡀⠀⣴⠶⢀⣿⠇⣛⡽⣶⣶⡾⢿⣶⣿⣏⣿⣿⣿⣿⣾⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣧⡴⠷⢟⣋⣥⣾⡿⠆⣀⠔⢡⣾⠇⣸⣧⠋⡴⠎⢀⣴⡾⢣⣾⣥⣭⣽⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⢸⣿⣛⣛⣛⣋⣉⣉⡐⠲⠶⠿⠿⢾⣻⣇⡈⠛⠃⠤⠁⠘⠛⠋⠻⣿⣿⣿⠿⠿⠿⢿⣿⣿⡟⢿⠿⠿⢿⣿⠿⠿⠿⣿⣯⣹⣿⣟⡻⣿⣻⡿⢛⣙⡻⢶⣿

⠀⠀⠀⠀⠀⠀⠠⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⣠⠈⢳⡄⠈⡆⠈⢦⠀⠀⠀⠀⢀⣀⠔⣀⠈⠙⢂⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡘⠷⣄
⠀⠀⢰⡟⠀⡼⠋⠁⢴⡀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠖⠂⠈⡀⠀⢸⣦⠀⠀⠀⠀⠀⠀⢀⠀⡋⠎⠇⢧⡀⠀⠀⠀⠀⠀⢠⠃⡼⠉⠰⡈⠄
⠀⠀⠘⠿⡸⠀⠀⠀⠀⢻⠺⣇⠀⢀⡿⠶⠴⠋⠀⠀⠀⠀⠈⠓⠰⢎⠁⠀⠀⠀⠀⡰⠃⡸⠁⠀⠰⡄⠱⡄⠀⠀⠀⠀⠚⡎⠁⠀⠀⣻⢶⡄
⠀⠀⠢⡀⢇⠀⠀⠀⠀⢸⡀⠸⠀⠸⢦⡀⠂⠀⠀⠀⠀⠀⠀⠘⢀⡠⠟⠀⠀⠀⡼⠀⡴⠀⠀⠀⠀⠹⣄⠐⡀⠀⠀⠀⡇⢻⠀⠀⠀⢰⢠⠇
⠀⠀⢠⡞⠺⣆⠀⠀⢀⠄⢿⡄⠀⠀⢦⣟⠀⠠⣄⡀⠀⣀⡴⠖⠋⠑⠀⠀⠀⣸⠃⠘⠀⠀⠀⠀⠀⠀⠘⣆⠳⠀⠀⠀⢦⠿⡀⠀⢀⢶⡳
⠀⠀⠀⢇⠀⢈⡠⠖⡏⠀⢸⠃⠀⠀⠈⠳⠄⠀⢠⡉⠓⠴⡤⠤⠔⠁⠀⠀⢰⠟⣲⡦⠤⠤⠀⠀⠤⠤⠔⣲⡛⢶⡀⠀⠘⣄⣑⣤⣈⣠⠁
⠀⠀⠀⠀⠀⣘⣇⠀⠹⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠉⠀⠀⠀⠀⠀⠈⠉⠁⠘⠓⠒⠂⠀⠐⠒⠛⠁⠁⠉⠀⠀⠀⠈⢫⡈⡏⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢐⣇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠀⣀⠠⡀⠀⠐⠒⠦⢀⠀⠄⢀⠀⠀⠀⠀⣴⠂⡰⣄⢐⠂
⠀⠀⠀⠀⢀⣈⢆⠹⡎⢇⠀⠀⠀⠀⣴⠁⢨⣙⣍⡳⠤⣠⣈⠙⠐⠲⠄⠀⠀⢠⣁⠀⠙⠢⠄⣀⢀⠀⠋⢀⡈⠄⠀⠀⠀⠿⡇⠀⢈⡟⠂
⠀⠀⠀⠠⠉⢡⠂⠁⢷⠈⢣⠀⠀⠀⣉⡄⠘⠁⠀⠈⠃⠀⠈⠱⢀⡀⠀⠀⠀⠀⠈⠿⠋⠂⠀⠀⠉⠙⡆⠈⠣⣄⠀⠀⠀⠲⠾⠳⠉⠴⠂
⠀⠀⠀⣤⡔⠃⠀⠀⠀⢧⡈⡄⠀⠀⠙⠋⡹⠄⠀⠀⠀⠀⠀⠺⣉⠼⠁⠀⠀⡁⠀⠀⣆⠀⠀⠀⠀⠀⢳⠀⠀⢘⠄
⠀⠀⢠⠀⢐⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⢎⠳⣄⠀⠀⣀⠔⢈⡁⠀⠀⠀⠀⡙⢆⡘⠉⠆⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠨⠤⢌⠐⡄
⠀⠀⠘⡳⠿⡀⠀⠀⢀⣈⡦⠇⠀⠀⠀⠀⠀⠑⢰⡌⠛⢯⠴⠊⠀⠀⠀⠀⠀⠐⡈⠀⣀⠀⠀⠉⠁⠀⣤⡉⠅⠂⠀⠀⠀⢘⡁⠀⠀⣁
⠀⠀⠀⠘⠦⠘⡓⢒⣾⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠶⣤⣀⡠⠊⠀⠿⠙⠀⠀⠀⠀⠻⢉⠂⠊⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⠀⢲⡠⠄
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣤⠠⠂⠈⠉⠙⠣⠠⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⢀⣤⠀⠀⠀⣼⣋⠀⠉⠀⠀⠀⠀⣄⣈⠣⠀⠀⠀⠀⢀⢻⡄⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡎⠉⣤⡀⢤⠐⢐⠒⠤⢤⣤⡀⢷⡄
⠀⠀⢀⠤⠼⠃⠈⠉⠁⠀⠉⠈⣇⠰⡄⠀⠘⠅⣻⠷⠂⠶⢄⣁⠀⠐⠀⣀⠄⠀⣧⡀⠠⠀⠀⠀⠀⠈⠳⡀⠃⠀⠀⠀⠀⠀⠀⠀⢸⢳
⠀⠀⠘⢄⣠⠁⠀⠀⠀⠀⠀⠀⠙⣄⢃⠀⠀⠀⠀⠈⠁⠀⠈⠁⢀⡀⠈⠁⠀⠀⠉⠀⠕⠤⡐⢀⠀⠀⡀⢡⡀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠠⡀
⠀⠀⢘⠉⠹⡀⠀⠀⠀⠀⠀⠀⡀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢷⣆⠀⠀⠀⠀⠀⠁⡍⠀⠀⠘⠶⠈⠉⠉⢉⣈⢥⣤⣀⡉⠙⡛⠘⠁
⠀⠀⠈⠶⠤⠦⠤⣄⡀⠀⠤⠐⠷⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠁⠠⢄⠀⠐⣦⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠛⠉⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠂⠀⠀⠀⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠕⠈⠀⠈⠁⠂⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠠⠤⠤⠥
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡀⠀⠀⠀⠑⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡁⠀⠡⠀⠀⠀⠀⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡦⠀⢀⡉⠉⠐⠠⠄⢀⠀⠀⠀⠀⢳⠀⠀⠑⠄⠠⠀⠀⠀⠀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠂⠀⠁
⠀⠀⠀⠉⠢⡀⠀⠉⠀⠐⠂⠄⢈⡁⠒⠠⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠐⠂⠀⠀⡁⠠⠀⠤⠤⠤⠀⡄
⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⢀⡠⠔⡠⢁⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠁⠀⠀⠀⠀⢀⡀⠄⠐⠂⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⡠⠐⠂⠉⠀⢈⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠒⠒⠊⠉⠀⡠⠔⠁⢀⠔⠁⠀⠀⢀⠠⠐⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠈⠂⠐⠒⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⢔⠒⠠⠄⢀⣀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⣉⠀⠀⢀⣄⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⢳⠀⠃
⠀⠀⠀⠀⡇⠀⠀⣞⠉⠉⠓⣒⠋⠁⢸⣿⣍⣳⠀⠀⡉⠀⠘⠀⠀⠀⢀⠀⠉⢧⠀⠈
⠀⠀⠀⠀⣧⠀⠀⠘⢿⠄⠀⠉⢠⡄⢤⡙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢲⡜⠦⣄⡀
⠀⠀⢸⡀⠘⣆⠀⠀⠈⠳⡄⢠⠀⠀⠀⠉⠑⡒⠀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣤⡿⠀⠀⠙⠢⣄
⠀⠀⠀⠙⢄⠘⢦⠀⠀⠀⠘⢿⡈⣇⡀⠂⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣙⠿⣷⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠓⠷⠼⣦⣴⠀⣄⢳⡀⠐⠂⢀⠀⠀⠀⠠⡦⠀⠈⢉⡁⠀⠀⣤⠈⠉⠙⣒⣒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢧⠀⠠⣿⣯⣢⡀⠀⢠⠀⠀⠸⣷⣾⣦⢀⠀⠋⠀⠹⣾⣷⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣐⣮⣟⣛⠁⡀⠀⢀⠑⠦⠄⠉⠋⠀⠐⠂⠀⠈⠀⣁⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠿⠽⠦⠬⢥⣥⣼⣮⠷⠦⠶⠶⠷⠒⠚⠉⠁⠀⡠⠋⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠈⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣤⢖⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠖⠚⣩⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣀⡤⠞⣉⠴⣀⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⡵⠞⠉⠛⠁⢀⣠⠴⠛⠁
⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠞⠉⠀⢀⠔⠀⣴⡋⠁⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠄⠀⠀⣠⠞⠙⠋⠁⠚⠁⠀⠀⣠⡴⠋⠀⠈⠁⠀⠀⠀⢾⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠻⠴⠋⡁⠀⠀⣀⠀⠠⢖⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠃⠀⠀⠀⠀⢀⡴⢋⣭⣤⣤⣤⣄⡉⠀⠀⠈⠁⠠⣶⡋⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⢠⣼⢱⡟⠅⣀⡂⢴⡏⢻⡆⠀⢠⢄⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡅⣹⡇⠺⠥⠟⠨⣶⢈⣿⠠⣶⡋⢀⡠⠚⠁⠀⠀⠀⠀⢞⣁⣽⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⢧⡙⣷⡆⠲⠷⣀⣄⣼⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣨⡛⠛⠛⣫⡽⠟⠁
⠀⠀⢀⡤⠻⢤⠀⠀⠀⠀⠉⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠗⠒⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠽

⠀⠀⠀⠀⠰⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠁⣮⠊⠀⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⡀
⠀⠀⠀⠀⠀⠚⠛⣤⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⡄⠑⠂⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇⠰
⠀⠀⠀⠀⠐⢲⠂⠸⠿⠷⠇⠀⠁⠀⠀⠀⠀⠀⠀⠊⠀⠰⡀⠀⠄⢀⠀⢤⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢈⠒⠀⠀⠀⠀⡀⣐⠀⠀⠀⠀⠀⠈⡐⠰⠀⠀⠀⠰⠱⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨
⠀⠀⠀⠀⠠⢾⡌⠄⠀⢀⡀⣘⠋⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠀⠀⠀⠀⠀⠀⠀⠂⢜⠀⢀⣀⡁
⠀⠀⠀⣠⢀⡉⠡⠿⢐⠃⠬⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠙⠇⢤⡤⠹⠒⠶⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠀⠀⠀⠀⠁⣀⠀⠀⢀
⠀⠀⠀⠘⠐⠀⠀⢵⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠠⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠁⠀⠀⠀⠀⠉⢀⣰⠀⡌⢉⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠔⣰⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡶⠂⠀⠈⢻⠷⠄⠀⠀⠀⢰⡒⠺⠉⠀⠚⢉⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢀⣄⠀⠀⣤⣠⡄⠀⠀⠀⠀⢨⡀⣄⠀⠀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡟⠉⢀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠉⠳⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⣄⠀⠀⠙⠀⠀⠀⠀⠀⠈⠧⢀⣄⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


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

⠀⠀⣶⣶⣶⣶⣶⣶⡶⢶⣶⢦⣤⣤⣤⣀⣠⣤⣄⡀
⠀⠀⠻⣿⣿⣿⣿⣟⣷⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀
⠀⠀⣄⣷⣿⣿⣿⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣶⣶⣦⣄⣀
⠀⠀⠿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠛⠟⠋⣿⣍⠉⠁⠀⠈⢛⢿⠻⣿⣿⣯⣥⢾⠡⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⡿⣶⢂⠀⢀⣼⡏⣨⣿⣿⣿⣿⣿⣦⣮⣤⣭⣮⣩⣉⣛⢛⠛⠛
⠀⠀⣿⣷⣢⠀⠲⠆⠀⠀⠀⢄⠢⠀⠀⠀⠀⠾⡿⣡⡌⠀⣼⣥⣾⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷
⠀⠀⠟⣿⠋⡄⠀⠱⣤⣦⡰⡜⢧⣤⠀⠀⠀⠚⠀⠹⠿⢿⣿⣿⢿⣟⡿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢙⢣⣷⣿⠆⢧⠑⢶⣖⠈⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣤⣼⣻⣿⣿⢿⡲⣦⠉⠒⠛⢷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣷⣦⣮⣤⣀⡀⢈⣹⣿⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣄⣄⠀⠀⠀⠩⣡⣀⣐⣶⡀⠲⣶⢀⡠⡜⠾⠾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠀⢡⣄⠀⠀⠀⠘⠿⣿⡏⢻⠆⠉⣄⠉⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡧⠀⠹⠆⠀⠀⠀⠀⠈⠇⢨⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠋⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⢄⠀⠸⠏⠀⠀⠀⠀⠁⠁⠀⠈⠣⣀⣀⠠⠃⠀⡁⠀⠀⠀⠠⠀⠀⡀⠀⣄⠀⠁⢀⠄⠈⠀⠀⠁⡀⠀⠀⢡⠀⠀⠔⠀⠡
⠀⠃⠀⠀⡠⠂⠐⠠⠀⢏⠩⠢⡀⠈⠁⡄⠂⢀⠀⢄⡀⠈⢀⡀⠀⠀⠀⣀⢀⠈⠁⠀⡠⠤⡀⠑⠤⡀⠠⠂
⡐⠀⠀⠐⠀⠀⠀⠀⢁⠈⢄⠀⠀⢀⠐⡀⠀⢀⠃⠀⠀⠀⠈⠁⡠⠊⠀⠀⠀⠘⠀⢰⢀⢂⠈⡀⠀⠀⣀⡀⠀⠂⠀⢀
⣁⣀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠢⢂⣸⠀⠀⠉⢀⠀⠐⢆⠀⠀⡌⠠⠀⠀⠀⠀⠠⠀⠈⠢⠎⠊⠀⢠⠁⡀⠈⢂⠀⠑⠤⠐
⠄⠂⢂⠈⠄⠀⠀⢠⠄⢀⠤⠀⠤⡁⠀⠀⠀⠌⠀⠀⠀⠱⠀⢃⠀⠀⠀⡀⠒⢁⠄⠀⠀⢄⠀⠀⠚⠀⠀⠀⠀⠑⡄
⠠⠅⠘⠀⠀⠁⡈⠁⠀⡂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢈⣤⠀⢀⠁⠐⠀⠂⠀⠂⠰⡀⠈⠀⠀⡀⠀⠚⠂
⠢⠀⠀⠆⠁⠠⠉⠂⠀⠐⠢⢀⣀⠀⠈⣄⠈⠀⠀⢀⠄⠀⣀⠀⠐⠁⠄⠄⢸⠀⠀⠀⠀⠀⠀⠀⠈⡉⠄⠠⢀⠀⠀⠠⠂
⠜⠀⢠⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠉⠀⠘⠋⠀⠀⠀⡗⠉⢣⠀⢠⠀⠰⡀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠠⠀⠈⠂⠈⠄
⢠⣄⠀⠑⠄⠀⠀⠀⠠⠄⠀⡄⠘⠢⠀⠀⠠⠈⠉⡀⠐⢀⠀⠺⠾⠵⠊⠀⠀⠈⠉⠉⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀
⠂⠀⠈⠢⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⠊⠍⠒⡀⠀⠀⠑⠤⠀⢁⣀⠔⠁
⡀⠂⠈⠀⠀⠀⠆⡉⠁⠀⠂⠀⢂⠂⠇⠠⠄⠀⠐⠀⠀⢀⠀⡐⠁⡀⠑⡀⠀⠘⡀⢀⠱⠁⠀⠀⠀⣀⡀⣀⠀⢀⠶⡀
⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⠀⠁⠂⠐⠀⠉⠀⠀⠀⠀⠀⠑⠀⠀⠈⢀⠀⠀⠀⢀⠀⠘⡠⠀⠈⠃⢡⢀
⣀⠀⠙⠇⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠠⠊⠌⢠⠀⠀⠀⠾⠀⡀⠀⠀⠘⠀⠇⢀⠀⠁⠀⠐⠀⠀⢡⠀⠀⠐⢤⠈⠝⠃⣄
⠀⠑⠀⡀⠀⠐⠀⠀⠤⠔⠃⡰⢆⠀⠘⢄⣂⠔⠀⠀⣀⣀⢀⠀⠀⠉⠀⠉⠀⠀⠀⢀⠀⠀⠀⡠⠂⠀⠀⢀⠀⠠⡀⠀⢡
⠀⠄⣒⣩⠀⠀⣀⣀⡀⠀⠘⠐⠐⠃⠀⠀⠀⠀⡠⠊⠀⠐⡌⠀⠰⡻⠀⣐⡄⠉⠀⠄⠀⠀⠉⠀⢴⡒⠀⠀⠀⠂⠈⢠⡀
⠄⢀⠀⠀⢰⠙⠀⠄⡁⠀⢸⠀⡠⠋⠇⡇⠀⡞⢂⡀⠐⠈⠀⢀⠄⠛⠐⠚⠵⠀⠀⡠⠐⠒⠢⡀⠀⠀⠐⠠⢀⣀⠠⠊⠁
⠀⠀⠐⢄⠈⠓⠥⠔⠁⡀⠀⠒⠶⠥⠂⠀⠀⠁⠀⢀⡀⠀⠀⠦⡀⡂⠔⠊⠁⠀⠊⠀⠀⠀⠀⠰⠀⢀⣀⡀⠀⠀⠀⡠⠂
⠀⠀⠀⡼⠀⠀⢠⠀⠁⠀⠀⠢⡄⠀⢠⠆⠈⠉⠀⠄⠈⠆⠀⢀⠀⠀⠀⠀⠐⠃⠀⠀⠌⠀⠒⠁⠀⠭⠄⠊⠂⠀⡈
⢀⠀⠂⠀⠀⠀⠀⠀⡄⠁⠠⠀⢁⠀⠰⡀⠉⠀⠀⠀⠈⠀⢐⠀⠀⠀⠁⢀⠀⠀⠀⣀⠀⡀⠀⠀⠈⠃⠤⠅⠒⠀⠁
⠁⠀⡤⡄⠀⠀⠃⠀⠀⠀⠐⢀⠜⠀⠀⠈⠀⢄⠀⢀⠁⠀⢀⠀⠀⠀⠐⠀⠀⠀⠣⠌⠀⠀⠀⠈⣠⡄⠀⡤⢀⠀⠀⠀⠈
⢀⠊⠀⠀⠀⡀⠀⠑⠂⠀⠐⠃⢀⠄⠚⠣⡀⠀⠙⠃⠀⠀⠀⠣⡀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠁⠉⠀⠀⠠⠠⠒⠁⡤⣲⡄
⠈⡀⠀⠈⠠⠁⠀⡄⠀⢄⠀⠀⠆⠀⠀⠀⠑⠀⠀⠀⡀⠠⢀⠀⠈⠓⠀⠂⢀⠔⠉⠀⠈⠇⠀⠀⠓⠀⠀⠱⡀⢠⣠⢀⠂
⠀⠀⡀⢀⠀⠀⠸⡀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠢⠀⠀⠰⠁⠀⠀⠀⠀⡤⠀⡈⠀⡀⠢⠀⠁⠓⠉⠉⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠈⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠊⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠁⠀⠀⠈⠂⠐⠠⠀⡀⠘⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡴⠊⠁⠈⠉⠂⠒⠢⣀⠤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠘⠃⠀⠀⠪⠀⠠⠤⠄⢀⡈⠉⠉⠀⢀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠂⠤⠬⠐⠒⠂⣔⠒⠒⠲⠀⠀⠀⠀⠀⠀⠤⡒⠒⠒⠀⠀⠀⠊⠀⠀⠀⠈⢹⠉⡆
⠀⠀⠀⢠⡄⠤⠤⠀⠤⠤⠤⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠒⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠸⢃⠠⠖⠛⠀⠠⠀⠣⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠂⠤⠤⡄⢀⡀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⠿⠀⢀⣠⡍⠀⠾
⠀⠀⠀⠐⠈⠶⠂⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠁⠀⠑⡀⠀⠄⠀⠀⠈⠄⠈⠂⠀⠀⠀⠀⠛⠀⠈⠀⠀⣈⠀⢥⠀⠈⡱⢂⡰
⠀⠀⠀⠀⢷⠀⢙⠳⠄⠀⠑⡈⠂⠐⠄⠒⠀⠠⠀⠀⢄⠀⢄⠀⠀⠐⠄⢀⠀⠀⢀⠡⠀⠒⢢⡄⡀⠀⠁⢐⡏⠀⢓⠆⢈⠶⠂⡏
⠀⠀⠀⠀⠰⡁⠀⢁⡄⣠⠄⠀⠄⡀⠀⠀⠈⠢⡑⢄⡀⠀⣠⣄⣀⣀⡠⠤⠐⠈⠠⠄⠐⠀⡄⠀⢈⣄⠢⠷⠀⠀⠈⡖⠘⢂⣉⡇
⠀⠀⠀⠀⠔⠀⠀⠨⠇⣀⣀⡠⠄⠰⠦⠀⠀⠂⣈⠁⠁⡃⡄⠀⠉⠀⠀⠐⠀⠁⢀⠀⠀⠀⠁⢈⡂⠀⠐⣔⠃⠀⢀⡘⠤⡈⠠⠆
⠀⠀⠀⠀⠀⢸⠀⠒⣀⠀⠉⠀⣀⠀⠀⠀⣄⠀⠀⠀⢀⢉⠀⢠⠏⠉⠀⠀⠀⠀⠙⡅⠈⠀⠈⡼⠇⠈⢫⠙⡅⠀⠸⢀⠀⣰⢂⠁
⠀⠀⠀⠀⠰⠀⡠⠈⠁⠀⠆⠀⠋⡄⠀⢀⠀⡄⠀⠀⠆⢠⠂⠘⢠⡀⠀⣨⠀⢲⠁⢳⠀⢀⢽⡅⠀⢸⠂⠹⡂⠈⡤⠈⡇⡰⠎
⠀⠀⠀⠀⠀⠀⠼⠂⡩⠇⢀⠦⠀⣄⢗⡁⠰⡇⠀⢲⠄⠘⢄⡂⠈⣆⠀⢸⠀⡧⠀⠠⡃⢈⠖⠀⠠⠆⢑⠘⣲⠀⡱⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠣⠈⢆⢬⡃⡀⠁⠈⠇⠈⠱⢹⠜⠀⢠⠏⠁⠀⠘⠯⠀⢆⠃⠀⠀⢸⠊⠁⠀⣴⠁⠀⠧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠀⠹⠀⠆⠈⠉⠀⢚⠀⠀⠀⠘⠀⠀⠚⡄⠀⠀⢈⠖⢀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠋⠀⠀⠀⠀⠁⠈⠉

⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠠⠀⠀⡄⠀⠁
⠀⠐⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⢀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠐⠀⠀⠀⠀⡄⠀⠄⠈⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠄⠚⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠐⠀⠀⠀⡀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠔⠁⠀⢀⠀⠀⠀⢀⡄⠠⠌
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠃
⢀⡠⠄⢒⠋⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠐⠀⠀⠀⢠⠉⠀⠀⠠⡀⠀⠀⠘
⠉⠂⢀⠂⠀⠀⠈⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠠⠀⠁⠀⠀⠠⠀⠀⢀⡇⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠀⠀⠉⠒⠐⠂⠚⠀⠀⠀⣐⠁⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡⡀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠒⠀⠈
⠀⢡⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡼⠂⠀⠀⠀⠀⠀⠁⠀⠤⠄
⠀⢀⡄⠤⠀⠠⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄
⠰⠁⠘⠁⠀⠐⠀⠁⠀⠀⠃⠀⠔⠀⡄⠀⠀⠀⠀⠀⠈⠄⢀⠆⠀⠄⠀⠀⠠⠀⠀⢀⠀⠀⠃⠀⠀⡀⠁⠀⠀⢀
⡂⠡⠀⠀⠀⢀⠆⢈⠀⠤⠀⡀⠠⠀⠀⠠⠀⠀⡐⠆⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⢀⡄⠀⠀⠃⢠⠀⠔
⠐⢂⠃⠐⠰⡀⡠⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⢀⠞⢀⠀⠀⡀⠐⠀⠀⠀⠀⢂⠀⠀⠀⠐
⠀⠀⠀⠈⡀⠈⠀⠀⠀⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁⠀⠈⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠊
⠀⠀⠀⠈⠈⢀⠀⠀⠀⠁⠀⠀⠆⡠⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⠅⠀⠀⠆⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠐⠀⡇⠀⠀⡖⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⢀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⠙⢤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡢⠌⠀⠀⠘⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⣊⡀⠀⠎
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠫⠟⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢠⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣀⡴⠊⠀⣠⢄⣴⠀⠀⣴⢟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢫⣧⠞⠙⠋⣀⡴⣺⡿⣺⠃⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠈⠀⣀⡴⠚⠁⠀⢁⡴⠁⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⡀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣰⠋⠀⠀⣠⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠄⣠⠞⡇⣠⡇⠀⠁⠀⠀⠀⢀⣞⣵⠄⠀⠶⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠩⠿⠊⠁⠘⠋⣸⠁⠀⠀⠀⠀⠰⠟⢁⡞⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡀⠀⠀⠀⢠⠞⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⣾⠃⠀⢀⡴⠋⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡤⠞⣡⠏⠀⠀⢨⡟⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⠉⠀⠴⠟⡿⠀⣰⡟⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⣴⠷⢫⠟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡟⠁
⠀⠀⠀⠀⠀⠀⣠⣏⣤⣤⡴⠶⢤⣤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⣴⠆⠀⣀⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⢀⣎⠘⣧⢠⠄⠀⠀⠈⠀⠀⠉⠑⢦⠀⣸⠃⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⡽⢠⠟⠘⣦⠀⠀⠀⠀⣠⣤⠀⠼⠀⢿⡀⠀⠀⢀⡴⠋
⠀⠀⣼⠁⢸⡆⠀⠈⣽⠀⠀⠀⢠⡈⢳⡄⠀⢸⡇⣀⡴⠋
⠀⠀⢹⡁⢸⡇⠀⠀⠛⠒⠲⠀⠀⣀⣠⠗⢀⣾⢠⡏
⠀⠀⠀⠙⡇⠙⠛⠳⣦⡀⢀⣀⡀⠉⣡⡴⢋⡵⠊⠁
⠀⠀⠀⣼⡵⢲⣀⣤⡈⠛⡉⠉⠛⠛⣡⠖⠛
⠀⠀⠀⠉⠀⠘⠋⠐⠗⠊⠹⡶⠛⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣊⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠠⠂⠀⠂⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠜⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦⡄⠀⠀⠀⠀⡇⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠆⠀⠈⠁⠀⠈⠉⠻⣿⠀⠀⠀⠀⠻⣄⣀⣨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣯⣀⠀⠀⠀⢀⣤⠴⠶⣤⡈⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⡆⠀⠀⠀⠀⠀⠀⣰⠏⠁⣠⣤⡉⢷⡀⢰⡏⠀⣠⣤⣄⠙⣆⠀⠀⠀⠀⠀⠀⠄⢄⠸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠟⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⡀⠘⢿⣷⠇⣸⠇⢺⡄⠀⢿⣷⡾⠀⡿⠀⠀⠀⠀⠀⠀⢃⠀⡃⠹⣏⠉⠙⠻⣷
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠾⣷⣤⣀⣠⡴⠏⠀⠈⠻⣤⣀⣀⣤⣾⣁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠧⠀⠀⢻⣇
⠀⠀⣰⠏⠀⠀⢀⡴⠒⢶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠐⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⣼⠃⠀⠀⣰⠋⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⢸⡇⠀⠀⢰⡇⠀⠀⣰⠋⠛⠀⠀⠀⠀⠀⠀⠐⢚⡿⠿⢦⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⣠⣴⣶⡶⠄⠀⠀⠀⠀⠀⠀⡤⠂⠉⠐⡄⠀⠀⠘
⣿⠃⠀⠀⠘⢦⡤⠞⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠙⠛⠶⢶⠶⠶⣶⠿⠿⠛⠁⠀⠛⠉⠈⢧⡀⠀⠀⠀⠀⣠⠤⢼⡀⠀⠀⣠⠃⠀⠀⢀
⣿⡀⠀⠀⠀⠈⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⡾⠁⠀⠀⢻⠒⠋⠁⠀⠀⠀⣼
⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢦⣤⣀⣀⣀⠀⠀⠐⠲⠶⠛⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠀⠀⢸⠃⠀⠀⠀⢸⠁⠀⠀⠀⢀⣼⡟
⢸⣿⡀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠘⢆⣀⣀⡴⠃⠀⠀⣠⣴⡿⠋
⠀⠻⣷⡀⠀⠀⠀⡿⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣦⣤⣤⣤⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣾⡿⠋
⠀⠀⠙⢿⣦⡀⠀⢻⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠙⢿⣆⠈⢧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠲⡄⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⣿⣆⠈⠛⠶⠶⠛⠀⣠⠄⣀⠀⠀⠀⠀⣼⣤⣤⣯⣤⣴⣇⣀⡤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠣⡀⠀⢱⠀⠀⠘⠷⢤⣀⣀⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣶⣶⣶⣶⣶⣾⣿⠿⠟⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠩⠤⠀⠠⠄⠀⣀⣭⣙⣷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠡⠒⠁⠐⣦⡄⠒⠂⠀⠀⠀⠀⠀⠀⢿⣀⠉⠙⠻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡵⢂⣀⣀⣤⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠦⣌⣻⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠁⠀⠈⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⣿⣿⣿⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⡼⠛⠋⠀⠀⢰⡆⠀⢠⣶⠿⣛⣿⣿⣷⣦⣤⡆⠀⠀⠀⠀⠀⣄⠀⠙⣷⠀⠈⠻⣧⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⡜⣠⠀⠀⠀⢠⠞⠀⢠⡟⣥⠞⠉⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣄⠀⠀⢈⣿⣷
⠀⠀⠀⠀⡘⣰⡇⠀⠀⠀⠀⢀⣴⡟⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⠀⢹⣿⣿⣿⡇
⠀⠀⠀⢠⢡⣿⠀⢀⡀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣿⣿⡀
⠀⠀⠀⡌⣾⣿⠀⡾⠋⠁⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠠⡄⠀⣠⣿⣿⡇
⠀⠀⠀⡇⣿⠃⠀⣇⣀⠀⠀⠀⠀⠈⢻⣤⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⠀⠀⢻⣿⣿⢠
⠀⠀⠀⣷⣇⠀⠀⠈⠉⠀⠠⡄⠀⠀⠀⠙⠛⠛⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠙⡟⠀⣰⣸⣿⣿⡟
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⡇
⠀⠀⠀⠘⣿⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠀⠀⣿⣿⠁
⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢠⡆⠀⠀⣸⣿⠏
⠀⠀⠀⠀⠀⢿⡆⠘⣄⠀⢠⠃⣀⠤⠒⠀⠀⠀⣀⣤⠼⠶⢦⡀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠈⣁⠀⣿⣇⡴⣳⣿⡟
⠀⠀⠀⠀⠀⠀⠻⣄⠨⣧⣾⡞⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠁⠀⢶⣿⣿⡀⠙⣫⡾⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡘⡛⢧⣀⠀⠀⠀⠀⠀⠳⣤⡀⢠⠞⠀⠁⠀⠀⠀⣠⣤⣀⣠⣴⣿⣿⢿⣿⣿⣟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣉⠳⣄⡀⠀⢀⠀⠀⠉⠀⠀⠀⣀⣀⠀⠚⠻⢿⣿⣿⠿⢋⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⠉⠓⠦⢅⡀⠀⠐⠚⠛⠉⠁⣀⣠⣤⣾⣟⣥⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣤⣶⣶⣶⣤⣿⣶⠾⠿⠟⣛⣛⣻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠶⠶⠦⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠴⠚⠉⠀⠀⢀⡤⢖⣋⣙⣓⣒⣒⣮⡙⠻⢧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣡⠞⢁⡤⠤⣀⣀⣀⡾⢶⣃⠦⠤⠤⠤⠀⢝⡻⢆⠀⠉⠻⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢀⣄⣀⣀⣠⠜⠋⠀⣰⠉⠉⠉⠏⢻⡉⠙⢆⠈⠳⣖⠢⢬⢧⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⢀⡠⠞⠁⠀⢀⡴⡰⠃⠀⠀⠀⢸⡀⢧⡀⠈⠣⣄⠀⠀⠠⣄⢳⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠐⠋⠀⠀⠀⠰⠋⣼⠁⣠⠆⠀⠀⠀⡧⡄⠈⠦⠀⠀⠙⠢⠀⠈⠃⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠚⠁⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⢰⡀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣆⠻⠀⠀⠀⢀⡇⠀⣠⠖⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢳⣸⠀⠘⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⣀⣀⠀⠀⣸⠗⠊⠁⠀⣀⣤⡀⠀⠀⠚⠉⠙⠓⠲⡄⠀⣇⢸⠁⠘⣦⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡏⡔⠺⡳⣖⠥⠒⠒⠋⠙⢦⣀⠙⢦⠀⠀⠀⠀⠀⠀⠈⢳⣘⣼⠤⠶⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠻⡔⡄⠙⣽⡖⠒⠒⠦⠀⠀⠈⠉⠙⢦⠀⠀⠀⠀⠀⠀⣰⠏⡴⠚⠙⡷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣞⠂⠸⣿⣀⣀⠀⠀⠀⠀⠀⢀⡈⢧⡀⠀⠀⢠⡞⣡⠞⠀⠀⡀⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠋⠁⠀⠈⠓⢄⣀⠀⠀⠀⠉⠛⠦⣀⣰⢏⡴⠃⠀⠀⠚⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡓⢦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣙⣇⠘⠇⣠⡴⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣙⡓⠲⠦⠤⢤⣭⡭⠯⠴⠞⠛⠙⠳⠦⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡟⣦⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠄⢹⣿⢽⣷⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠆⠁⠄⠀⠀⠠⠄⠀⠀⢀⠄
⠀⠀⢸⣴⢀⠀⣄⠀⠀⠀⢠⠀⠀⢸⣿⣯⣯⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠽⢹⠀⠀⠀⠀⠀⡄⠀⠀⣽⣾⣼⣙⣙⣷⠀⠀⠀⠀⡗⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⢀⠐⠁⠀⠀⠀⢀⠁⠀⠀⢿⣽⣯⣿⣿⣵⣄⠀⠀⠀⠡⠨⢷⡈⠀⠀⠀⠀⠀⠀⢀⡠⠬⠐⠂⡇
⠀⠀⠈⢀⠀⠠⠀⠀⠀⡌⠀⠀⠀⣿⣾⣷⣥⣿⣾⡟⠀⠀⠦⠄⠉⡁⠦⠀⣀⠀⠀⠀⠀⢦⢰⣛⡹⢃⠦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠳⠀⠀⠀⠈⡛⢉⠃⡛⠁⠀⠀⠀⠈⠃⠁⠀⠀⠀⠁⠀⠀⠀⠈⢣⣗⡝⡖⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⡀⠀⠀⠀⠂⠀⢈⠁⡲⢱⣠⠀⠀⠀⠀⠴⠂⣂⢀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠘⢀⠓⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡰⣀⢀⠀⠈⡰⠑⢂
⠀⠀⠀⠀⠪⠀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠓⠐⠀⠅⠽⣠⣦⠃⠐⠶⣤⣀⣠⡤⠀⠀⠐⡈⠀⠄⡌⡡⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀⣠⣴⣿⣿⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠠⠼⠟⠛⠛⠙⢿⣷⣦⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢄⡈⢳⣤⣄⡀⠀⡄⠀⠀⠈⠛⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠽⠿⠛⠻⣆⠀⠀⠀⠀⠀⠀⠘⣿⡏⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢀⣄⣀⡀⠈⠃⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠧⠹⠃⠀⠀⠀⠀⠀⠀⡶⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠙⠿⠧⠈⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⠀⠈⠻⣿⣶⡄⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠁⠀⠀⠘⣯⢳⠀⠀⠀⠀⠀⢠⡌⢻⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⠞⠁⠟⠀⠀⠀⢀⣤⡄⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢠⡄⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⢹⣶⣄⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠉⠉⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢠⣾⣿⣿⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⢰⠆⠀⠈⠃⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⢸⣇⢀⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⣸⡿⠿⢃⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣤⣤⣤⣈⠻⣿⣧⣤⠤⠀⠀⠀⠀⣠⣄⢀⠀⠈⠉⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠋⢿⣷⡌⠻⣿⡦⠀⠀⠀⣼⣿⡟⢸⠄⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠟⠁⠀⠈⢻⡇⠀⣿⣷⠂⠀⠀⠛⢛⣡⠟⢠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠹⣿⣿⣿⠃⠀⠀⠀⠀⣾⠀⢸⡿⠿⠇⠀⠀⠀⠈⠁⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⢘⣦⡙⠿⣿⣷⣀⣀⣀⣼⠇⣠⡿⠁⠀⠀⠀⠀⠀⢀⣾⠟⣩⣿⣿⣿⠆
⡀⠀⠀⠀⢀⣰⡟⠻⠿⠛⢿⣦⣄⣤⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⡽⣿⣷⣾⣿⣿⣿⣭⣴⠞⠛⠇⠀⢀⡄⠀⠀⢠⠟⢁⣼⣿⣿⣿⠟
⠙⢿⣿⣿⠿⠿⠦⠀⠠⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⢤⠤⠞⠁⠀⠀⠰⠛⠽⠟⠛⠛⠟⠻⡇⠀⠀⠀⠀⠈⢃⣠⡄⠀⣰⣿⣿⣿⡿⠋
⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⣀⠤⠀⠀⠀⠀⠀⠀⣸⣷⣀⣠⣴⣿⣿⠿⠛⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⠓⠀⢠⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣶⣦⣤⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿