Russians Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣠⣶⣟⣻⣶⣤⡀
⠀⠀⠀⠀⢀⣾⣿⣟⠝⠫⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀
⠀⠀⠀⠀⠈⣿⡏⠿⠀⠀⠽⢽⣿⠇⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⢿⣷⡄
⠀⠀⠀⠀⠀⣟⣧⣀⠠⠄⢀⣼⢻⡁⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⣲⣶⣦⡄
⠀⠀⠀⠀⣼⣿⠯⣿⣹⢟⣹⠽⣟⣧⠀⠀⠀⠀⠀⠀⣧⠈⠁⠀⠉⣸⠇⠀⠀⠀⠀⠀⢸⠋⡀⠀⡉⣿⠀⠀⠀⠀⠀⣀⠴⠶⢦
⠀⠀⠀⣼⣷⠯⠿⣿⠝⠃⠿⠟⠽⣾⣧⠀⠀⠀⠀⣀⢿⣷⣤⣤⣴⣿⢆⠀⠀⠀⠀⠀⢸⢿⠀⠀⠸⣋⠀⠀⠀⠀⠀⡷⠀⠀⠠⡇⠀⠀⠀⠀⣠⠴⠶⣄
⠀⠀⢰⢫⡌⠲⣱⣯⡿⢿⣽⣏⠖⢩⡝⠆⠀⠀⣴⣄⣼⢿⠛⡝⣻⢿⣄⣶⡄⠀⠀⢠⣾⣷⡯⢮⣶⣿⣆⠀⠀⠀⢀⣹⣇⣀⡾⣇⠀⠀⠀⠀⣿⠂⠐⣿
⠀⠀⠀⠈⠙⣹⣿⡇⠠⠆⢸⣟⣧⠋⠁⠀⠀⠈⢻⡿⡶⣿⠚⠙⢾⡷⠿⡽⠃⠀⠀⣞⡟⣿⣥⣶⣿⡟⣛⡄⠀⢠⣯⣿⣿⣽⣿⣿⣷⠀⠀⠀⣿⣢⣄⣻⠄
⠀⠀⠘⠉⣙⠅⠹⣟⣶⣴⣻⡏⣨⣩⡉⠃⠀⠀⠀⢿⣿⠏⡈⢇⠈⣿⡿⠃⠀⠀⠐⡯⢻⣿⢿⣿⢿⣿⠨⡇⠀⢸⣿⢿⠿⣶⢿⣴⣽⡇⠀⠀⢿⡏⢹⣿
⠀⠀⠀⠀⡴⢋⠀⡈⣛⢛⠏⡀⣉⢦⠌⠀⠀⠈⢿⢲⣿⡀⠙⠛⠀⣽⡷⣻⠇⠀⠀⠻⣟⢹⣿⣿⣇⢹⡿⠁⠀⠸⣿⣿⣥⣶⣼⣦⡱⠀⠀⠀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠊⠏⠑⠙⠈⠊⠡⠟⠁⠀⠀⠀⠀⠈⠛⠿⣿⡍⣘⣼⡿⠟⠁⠀⠀⠀⠀⠸⠥⣷⣾⡦⠟⠀⠀⠀⠀⠙⢿⣿⣿⣧⠜⠁⠀⠀⠀⢽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⢀⣠⣄⠀⡀
⠀⠀⠀⠀⠀⣠⣿⠟⠉⠙⢻⣿⡀
⠀⠀⠀⠀⠀⢻⣏⣄⠒⠀⣑⢽⡋⠀⠀⠀⠀⠀⠀⠀⣤⡶⠾⠷⣶⣄
⠀⠀⠀⠀⠀⣿⡇⠉⠀⠈⠉⣸⡇⠀⠀⠀⠀⠀⠀⣸⡏⣤⠀⠠⡌⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣰⣟⡋⢀⣀⣠⠈⢙⡿⣆⠀⠀⠀⠀⠀⢸⣇⠂⠀⠀⠒⣾⠁⠀⠀⠀⠀⠀⡾⡭⠉⣽⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⣼⣿⣗⢹⣽⣏⣹⣭⢿⣾⣿⡆⠀⠀⠀⠀⣼⣿⣷⠶⣶⣿⣿⣄⠀⠀⠀⠀⠀⣧⡀⠀⢀⣾⠀⠀⠀⠀⠀⣾⢿⠛⣻⢿⡄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢰⡿⡭⡿⠚⠫⠍⠉⣏⡉⣯⣽⣿⠀⠀⠀⠈⠹⠉⠀⣀⡈⢩⠛⠛⠂⠀⠀⠀⠀⣿⣿⣾⣿⣯⠀⠀⠀⠀⠀⣿⡀⠠⢀⣸⠇⠀⠀⠀⠀⣾⡟⠛⣿⡄
⠀⠀⢸⣷⣿⣅⠀⢶⣾⠺⠞⠋⣼⣷⣽⡆⠀⠈⣀⢀⣾⡿⢿⡿⢿⣶⠀⡀⠀⠀⠀⠀⣹⣛⣉⣻⣏⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣄⠀⠀⠀⠀⣿⣄⣀⣼⡃
⠀⠀⠸⣿⣿⡿⠀⠬⡛⠁⠀⠰⣿⣿⣿⠀⠀⠘⢶⡦⢹⡇⠀⠀⠘⠋⠴⠻⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀⠀⢀⣞⣿⣯⠶⣮⡿⣿⣄⠀⠀⣼⠗⣿⣛⡿⣷⡀
⠀⠀⠀⠛⢻⡋⠁⢀⠐⣠⠀⡆⢰⡟⠋⠀⠀⠰⣦⣤⣦⡴⠀⠰⠄⣦⣤⡴⠀⠀⢸⣈⣿⣿⣿⣟⣩⣉⡇⠀⢸⣯⣿⣷⣾⣶⣿⢹⣾⠀⠀⣑⣼⡏⠙⣿⣔⡀
⠀⠀⠀⠀⠘⢧⣠⡌⢰⡆⠰⢆⡾⠀⠀⠀⠀⠀⠘⣿⣶⣇⢀⣀⠀⣁⡿⠀⠀⠀⠈⠿⡽⡿⠿⣿⣯⠟⠁⠀⠘⢿⣯⣻⠿⢟⣣⣿⠃⠀⠀⠀⢀⠛⢿⠃⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠈⠀⠀⠈

⣀⣀⠀⠀⠀⢀⠀⣀⣀⣀⡀⡀⡀⣀⣀⣀⣀⢀⢀⡀⡀⢀⣀⣀⣀⡀⠀⢀⡀⢀⡀⣀⡀⢀⢀⡀⡀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⡀⣀⣀⣀⣀⠀⢀⣀⣀⣀
⢽⠋⠉⠀⠀⠀⠀⠉⠛⢩⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠀⢠⢀⠀⠀⠀⡄⠀⠇⠈⠀⠸⣶⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠸⠚⠉⠉⠀⠀⠁⠈⠙
⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣦⣤⣤⣤⣴⣤⣴⣶⣶⣶⣶⣼⣿⣤⣴⢢⣤⢦⣤⠤⣤⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣴⣶⣶⣶⣦⣶⣶⣿⣷⣿⣶⣶⣷⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠂⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢆⣤⣤⢤⡀⠁⠀⠀⠀⠀⠀⠐⠒⠋⠀⠀⠀⠐⠀⠀⣀⡀⡀⡠⠀⢤⠤⡀
⢠⠒⠀⠀⡀⠀⡄⢀⠠⠄⠬⠗⠀⠸⠄⢸⡦⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠂⠂⠂⠀⠂⠠
⠈⠀⢓⣐⠾⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠔⠠⣉
⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣴⠂⠀⢀⠄⠒⠂
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠚⠀⠀⠀⠉⠈⠁
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⣀⠀⠀⠀⠀⠀⡀⠆
⠀⠘⠢⠀⠀⠀⠀⡠⠀⠤⠤⠬⠀⠀⠀⠀⠀⠐⠤⢄⠀⢀⠄⡀⠔⠠⣀⡀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠣⠀⠀⠀⠀⠰⠁
⠀⠀⠀⢠⠇⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠰⠀⠀⣺
⠀⠀⠀⠐⠄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⠌
⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡿⠀⣶⠀⣦⢰⡖⠂⢰⡖⠒⠀⡆⠀⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡆⠀⣿⠀⣿⠈⠻⣦⠈⠻⣦⠀⡇⢰⡏⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣽⣦⣽⣾⣯⣴⣶⣯⣴⣶⣯⣤⣧⣼⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢂⣉⣤⣤⣤⣤⣤⣄⣉⡀⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣡⣴⣾⣿⣿⠿⠛⢻⠛⠟⠿⢿⣿⣷⣦⣌⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⣾⣿⠟⡫⠉⠀⠀⠀⠄⢰⠀⠀⠀⠉⠻⡻⣿⣷⣄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣼⣿⡟⡡⠊⠀⠀⠀⠠⠊⢀⡆⠀⢄⠀⠀⠀⠈⢊⢻⣿⣧⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⡏⠘⠀⣀⠠⠀⠂⠀⡠⠂⠈⠄⠀⠁⠂⠤⢀⠀⠑⣻⣿⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡮⠐⠉⠀⠀⡀⠄⠊⠀⠀⠀⠀⠑⠠⠀⠀⠀⠈⠐⠼⣿⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⣀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠊⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⡄⠀⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠀⠀⢠⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⣿⡿⠁⠾⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠲⡄⠙⠿⣿⣷⣤⣄⠀⡀⠀⠀⢀⠀⣠⣤⣾⣿⠿⠋⢠⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠂⠤⠃⠸⠷⠈⠝⠉⡠⠀⡁⠀⠈⢈⠀⢄⠉⠻⡁⠾⠇⠈⠤⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠆⢠⠊⠉⠑⠄⠈⠀⠐⠀⡠⠋⡰⠶⠉⢀⡀⠁⠀⠐⢀⠊⠉⠑⡄⠰⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠊⠙⢾⠀⠀⠺⠊⠀⠀⠀⠀⡠⢤⡀⣆⡔⠄⠀⠀⠀⠀⠈⢳⠀⠀⡷⠃⠑⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠂⣼⣆⠓⣀⣅⠂⠐⠂⡤⠠⡄⢠⠇⠠⠔⠌⠐⠂⠐⣢⣀⠚⣰⣧⠐⠤⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢴⣶⣤⠟⣛⡸⣿⡟⠐⠿⠂⠁⡠⠂⡈⠰⠘⢄⠈⠐⠿⠂⢻⣿⠇⣛⠻⣤⣶⡦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣨⣿⢣⣿⣽⣽⡆⣿⣿⠖⠚⠳⡄⠠⠁⠀⠂⢠⠞⠓⠲⣿⣿⢰⡯⣯⣿⡞⣿⣅⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣦⡻⠿⢞⣵⣿⡄⠀⢄⡠⢃⠄⢠⣤⠀⡐⢄⡠⠀⢠⣿⣮⣳⠿⢟⣵⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⢸⠿⠋⢻⣿⠉⠉⠙⠆⠰⡦⠂⠀⢠⣥⠀⠐⢴⠆⠰⠋⢉⠁⣿⡟⠙⠿⡇⠙⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡄⠀⠐⢤⡁⠀⠴⠤⢃⠔⠗⠂⠒⠌⢡⠔⠂⠲⡦⡘⠤⠴⠀⠈⡄⠂⠀⢰⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠢⠔⣃⠑⠤⡼⠔⠁⠀⠢⠤⠀⣸⣇⠀⠠⠔⠁⠈⠀⢦⠤⠊⣘⠢⠔⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣶⠄⡈⠔⠈⡄⠒⢀⠀⣶⣦⣤⠿⠿⣠⣶⣿⠀⢀⠔⠲⡄⠢⢁⠀⣶⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢡⠂⠐⠈⢄⡀⠈⣠⣬⡟⣱⣾⣿⣦⢻⣥⣄⠈⠀⣀⠜⠔⠀⢫⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡘⠤⣀⣀⢠⠴⠋⠙⠛⣳⡹⢿⣯⠟⣼⠟⠋⠉⠳⣤⢀⣀⡠⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⢸⡀⠀⡁⢸⠿⠛⢶⣶⠟⠿⡷⠠⡀⠀⣸⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣬⣍⣀⣀⣀⣀⠘⠋⣀⣀⣀⣀⣬⣬⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠙⠈⠉⢡⣄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠀⠀⠀⠠⠄⠀⠲⠀⠀⠀⠀⣹⣆⠈⠉⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢰⣟⠢⣐⠢⣀⣀⠀⡀⠀⠀⢀⣀⣠⣦⣿⢸⢿⠿⠟⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍⠉⠙⠒⢞⣛⣿⣻⣉⣷⡾⢿⠟⣫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠄⠀⡄⠄⠈⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠠⠀⠤⠤⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡙⠈⠀⠀⠀⠀⠀⡄⣘⣁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡼⠾⣷⣾⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡭⠀⠒⠀⠈⠐⣗⠁⡀⢈⣳⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄⠀⠠⢉⡇
⠀⠀⠀⠀⠐⡷⠴⣶⠆⠀⠓⠀⠀⡀⠀⡀⠍⠉⠉⠙⠿⠀⠀⠀⢀⡬⠦⠀⠀⠀⠀⠀⠓⢒⠶⠼⡧⣴⠒⢂⠀⠀⠀⠀⠀⠀⠀⢂⣨⣿⣧⡀
⠀⠀⠀⠀⠀⢠⡀⢸⡅⠀⠀⢸⠀⡇⠀⡧⢰⠀⡃⢸⡇⠀⠀⠀⡼⡆⠄⣴⠀⠀⠀⠀⠀⠟⠀⢶⣷⣿⡾⠟⠂⠀⠀⢀⠄⠀⠀⠀⠀⠂⡈⡇
⠀⠀⠀⠀⠀⠰⡇⢸⡇⠤⠀⠬⠠⢥⣤⢷⣶⠀⠂⢸⣣⣀⣀⠀⠀⠀⠈⡛⠀⠀⠀⠠⠀⠀⠉⠉⠩⡄⢠⠤⠒⠀⠀⠀⠀⠀⠀⠀⡄⠄⢠⢼
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠀⠈⠆⠀⠀⠀⣤⠀⠀⠀⠉⠙⠛⠿⣷⠶⠇⠤⣀⠀⠀⠀⠈⠉⠓⠒⠋⠒⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢠⡄⠠⣴⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢰⢳⠄⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡷⢷⠀⠀⠀⠠⠤⠠⠄⠀⠀⠀⠀⠀⠀⠃⢀⠀⣀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣉⢄⣀⢀⣀⣄⠐⢀⠀⡀⠀⢠⡀⠀⠈⠁⢺⡆⠀⢀⣀⣀⡠⢆⡀⢀⢀⣀⣀⣀⣀⣿⣘⣿⠦⣿⣤⡴
⠀⠀⠀⠀⠀⠀⢤⣖⣲⠟⠶⣾⣟⣸⠿⡷⢺⣿⣿⣟⠻⣶⠿⣿⣿⣷⠀⠈⣿⠛⣷⣲⣼⠁⠀⢿⣿⡿⣛⠉⡋⢹⡋⢻⣇⣂⣙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣩⣤⡤⠭⠭⢩⣁⠹⠉⢹⣯⣭⡭⠭⢍⣉⣉⣉⡠⠬⠉⠉⠉⠉⠛⠤⠤⢬⣭⣽⠿⠏⢿⡎⠁⠉⠉⣉⣉⣩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠁⠀⠼⠂⠿⢶⣼⠿⠶⠾⣿⠉⠁⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣃⢸⡶⠟⠛⠻⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣥⠀⠀⠀⠀⠀⢦⠄⠀⠀⠀⠉⢿⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⣀⡀⠀⠉⠛⠛⠀⠉⠐⢄⡀⠠⠄
⠀⠀⠀⠀⠀⡖⠋⠉⠹⠇⠀⠀⢀⣖⡤⡈⢀⣄⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⢛⣓⡀⠀⠀⠀⠀⠀⡀⠀⠽⠄⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣤⣯⣭⣷⡿⠿⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠻⣞⢋⣻⡆⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣿⣿⠂⠘⣶⡒⠒⢒⡏⢠⢤⣠⠄⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠂⠐⡂⢈⣈⣀⡀⠤⠼⠥⠤⠬⠧⠤⠤⢥⠀⠁⠁⣁⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡄⠀⣹⠆⠀⡆⠀⠒⠈⠳⡶⢒⣚⠒⠓⠲⠒⢒⡓⠳⡞⠀⠀⡞⣵⡿⣗⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣆⠀⢾⡁⠠⣿⠆⢒⠀⠒⣧⡏⢘⢃⣠⣶⣆⠳⠙⣼⡗⠀⠀⠁⢧⣰⣡⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣯⠘⣆⣀⠀⡴⠋⢦⠀⢠⠎⢙⡟⢼⣂⡝⢟⡃⣚⡝⣼⣹⠀⣸⠰⢂⣥⢥⣘⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣽⠈⡷⠐⣏⣸⠇⠙⣶⠋⡸⠄⠓⠋⠉⢢⢄⣒⣛⣉⣡⡞⠉⠁⣰⢇⡴⣡⣸⢇⣬⠳⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣢⡷⠒⢾⡑⣸⠂⢠⠟⡆⠀⣄⣹⣃⡄⠸⣄⣀⣀⣀⡤⠇⠀⢰⠏⡼⢤⡟⣱⢢⣙⣒⠻⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣁⠼⠉⠁⠀⣞⣀⡼⡄⠉⠽⠍⠁⢀⣨⣇⣐⣂⣧⡀⠀⢸⠈⡇⣌⢳⡍⣈⢵⠫⣼⡇⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⠆⡀⣒⠰⡶⢼⡥⠭⠤⣽⠀⡄⠀⠀⠸⣤⣴⣲⣤⣦⣼⠨⠘⣆⢣⡙⢸⠞⣉⡲⠇⡸⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡳⢤⣠⢷⣼⠲⠞⠶⢻⢀⣿⡀⠀⡴⣤⢄⠀⢠⠀⠀⣤⡄⠈⠳⢭⣒⣠⣤⣖⣪⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠆⡇⣼⢡⠏⡞⣳⢶⠸⢰⡏⠭⠽⢦⠀⣀⡠⣌⠉⠀⠀⣽⡏⠀⣠⠤⣄⠀⡴⡄⠀⢠⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢷⣒⣿⡾⠤⢷⢱⡋⣱⠸⣖⠒⣲⡞⢸⠑⠛⠈⠒⠒⠒⠒⠒⠚⠁⠛⠈⡇⢹⠑⢯⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢰⢩⣧⡨⢼⡠⢏⣡⠤⣸⢽⢸⠀⢻⠴⠶⠾⠦⡀⠀⢠⠤⠶⠶⠶⢤⡇⢸⡈⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⠛⠚⠛⠚⡛⢓⠛⠉⠘⠀⢸⣒⡊⠛⢀⡇⠀⢸⡀⠛⠀⢒⢺⡇⣈⠷⣼⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⡿⠀⠀⠠⢳⣿⡯⠀⡄⠄⡀⢸⠠⠦⠆⢸⢠⣤⡄⡇⠠⠰⠀⢸⠃⠙⠚⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⢠⠉⠃⠀⠀⠘⣷⠃⢸⠀⠀⠀⢸⣘⣛⣃⡇⠀⢀⠀⢸⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠤⠀⢬⣿⡄⠸⣄⠇⠄⠀⠯⠭⠽⠁⠘⠘⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡌⡉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠒⠂⠀⠂⠐⠀⠂⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠷⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⡄⡀
⠀⠀⠀⠀⠴⠠⠾⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠇⠃
⠀⠀⠀⠀⢀⣤⣠⣤⠟⠁⠀⠀⠀⠀⣠⣤⣤⣶⢶⣾⢶⡶⠲⠦⢤⣀⡀
⠀⠀⡀⢀⣼⠿⣿⠁⠐⠋⠀⠀⠀⠀⣉⢠⠉⢰⡄⢰⣾⡇⠀⠀⠀⠀⠓
⠀⠀⢸⣿⣿⣯⠞⢶⢣⣴⠶⠆⠀⠀⣇⠘⠀⠘⢃⠸⣿⠇
⠀⠀⠈⢻⣿⡿⢆⣹⠟⡁⠒⠀⠀⠀⠸⠀⠀⠀⠀⠁⢋
⠀⢠⣶⣯⣿⣿⡿⠻⠿⠛⣡⠛⠃⠀⠀⠀⠀⢠⣤⠀⢸⠀⠀⣤⠀⠀⣦⣔⣆
⣀⠘⢻⣿⣿⣿⣾⣿⣶⣷⣖⣴⣶⣤⡆⠀⠀⢰⣿⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⠄⣀
⠀⠀⠈⠛⠉⠉⠙⠛⠛⠙⠛⠉⠙⠛⠛⠓⠁⠈⠙⠐⠒⠀⠀⠀⠀⠀⠛⠛⠿⣦⣽⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⣀⢀⣀⠈⠛⠓⠓⠂
⠀⠀⠀⠀⠀⢠⣤⡄⢠⣤⣤⣤⡤⢶⣶⣶⣶⣶⠖⠀⢺⠛⠛⠛⠉⠉⠉⠉⠉⠀⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣵⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠏⢀⡷⡀⠀⠀⠀⢸⡺⣿⣿⣿⣯⣻⡇⠀⠀⠀⠠⢎⠀⠹⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⣀⣀⢀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⢄⣀⡀⠈⠂⠀⠄⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢠⣿⣿⣿⣿⡠⠊⡁⠉⠉⢌⠁⢀⣿⣿⣿⣿⡤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣷⡀⠀⠄⠘⣿⠇⣹⣿⣆⡈⠀⠀⠀⠀⢁⣴⣿⡏⢸⡿⠃⢢⠀⢀⣾⡆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣿⣼⣿⣷⣄⣂⡈⣷⠙⣯⣽⣽⢿⣦⠀⠀⣴⣿⣯⣏⣿⠫⣞⣁⡰⢠⣾⣿⣳⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣻⣝⢻⣽⣿⣦⡈⠑⠁⠀⢻⣮⣶⣿⡇⣸⡷⣮⣵⡏⠀⠘⠊⢀⣴⢿⣭⡿⣫⣯⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⣱⣽⣫⣬⢹⡯⢿⣷⡀⠀⢰⣾⣷⣷⣿⣿⣿⣷⣾⣾⣶⡆⠀⢠⣿⡟⢾⡏⣥⢝⣵⣫⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣙⣮⡫⣷⡼⠏⣾⣿⠿⠃⠀⢸⣿⠋⠉⠉⠻⢿⠦⢏⠙⢿⡇⠀⠘⠿⣿⣷⡹⢦⣾⣻⣵⣋⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣲⣭⣻⣬⡺⡧⣿⣿⣀⣠⣠⣼⣿⣇⣶⠀⣹⡟⢠⡦⡀⣤⣷⣄⣄⣠⣿⡿⣹⢇⣤⣯⣽⣞⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⡷⣩⣜⣻⣧⣛⣛⢿⢟⡿⣯⣙⠃⣰⡀⣜⠛⠀⢸⡏⣿⡻⡿⣛⣫⣾⣟⣫⣍⣮⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠁⢰⣯⡍⣽⡴⢟⠿⣟⢿⣻⣿⡿⣿⣿⡛⠉⣽⡆⢸⣿⣿⠿⣻⢟⡻⢸⣧⣭⣱⣮⣿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠧⣹⣿⣵⣶⣶⢻⡆⣟⣬⡿⣿⡈⢟⣉⢧⣈⠉⡱⠇⣿⣿⡄⣛⢨⡟⣴⣶⣯⣿⣿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠋⣸⡿⣻⡟⣿⠿⡟⠟⠙⢿⣿⣿⡻⣟⣵⣿⡿⠛⠟⢿⢻⣾⢿⡟⢿⡇⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠟⠁⠛⠀⣰⣶⣤⡼⣿⣿⣿⣿⣿⣿⢤⣤⣶⡈⠈⠛⠈⢓⣎⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣏⡵⠶⣾⡉⠙⣿⣿⠋⢙⣷⠶⣾⣹⠀⢀⡠⣉⣩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠉⣷⡿⠏⣡⡶⣟⣿⢶⡌⠻⣷⡮⡉⠢⣰⣶⣾⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⣤⣄⣼⣿⣬⣵⣿⣥⣤⣮⠀⠀⠉⠃⠉⢀⣰⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡀⠀⣠⣾⣿⣿⣿⣿⢿⡟⣿⡿⣿⣿⣷⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣷⢸⣿⣿⢻⣟⣻⡻⣿⣿⡓⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠿⠁⡼⢻⡟⠧⠉⠿⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠂⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠠⠇⠀⢀⠀⢀⠀⠀⠀⠤⢀⡄⠠⣄⡠⠀⠀⠀⠀⠠⠀⠈⠀⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠠⠀⠀⡀
⢀⠀⠀⠠⢤⡠⡀⠠⠀⠀⠀⠀⡐⠀⠛⠁⠀⡈⡀⠀⠁⠐⠨⡁⠒⡅⠨⠄⣏⣀⠀⢀⠨⢀⠜⠠⠀⠢⡀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀
⠄⠀⠀⠠⠔⠂⣘⠦⠤⠤⠀⢉⠀⠘⠀⠀⡀⠀⠀⡀⠀⠀⠀⡁⠠⡃⢑⠄⣅⠀⢀⡤⠴⠓⠚⣁⣀⣀⠈⠒⠶⠞⡁⡀⠀⠀⡀⠄⠊⠀⠀⠀⢀⠌⠀⡀⠀⠀⠒
⠰⠀⠘⠠⠖⣉⠤⠴⢶⠖⠒⠦⣤⣁⠲⢿⡀⠀⠐⠁⠀⠀⠀⠁⠄⠋⠙⠂⡀⢐⣩⠔⠂⠉⢉⠐⠨⡉⠉⠈⠐⠆⠀⠁⠤⠀⢀⡒⢓⡀⠀⠀⠀⠀⠀⠁
⢸⡠⠀⠰⠋⠻⣀⠁⠂⠈⠀⠀⠀⠈⠁⠢⣑⠀⡀⡀⠐⠀⠀⠀⡸⢀⠀⢊⠔⠋⠀⠀⠀⠀⠀⠈⢂⠈⠄⠀⠀⢀⡐⠀⠐⠢⡰⢦⠈⠉⠛⠃⠀⠀⠀⠄
⠂⠔⠃⡄⠉⣇⢈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⢤⠉⠒⠒⠘⠃⣈⡤⠎⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠄⠀⠀⠀⠈⡀
⠀⠘⣀⠉⡩⣄⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡉⠋⠅⠀⠈⢃⠉⠀⡴⠈⠂⠀⠉⠀⠀⠁⡠⠃⠀⠄⠃⠈⢀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠈⠁⠠⠀⣀⠔
⠀⠈⢀⡅⢄⠨⡀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢢⡈⠢⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠀⠁⠢⡀⠀⠀⠀⡠⠂⠀⠀⠒⠴⠊⠤⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠈⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡀⢀⡀⢀⣤⡀⢀⠀⣠⢀⡀⢀⢀⡀⠀⢀⣤⣄⢀⣄⢀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢯⡀⡟⢺⡇⣏⢀⣿⢼⠿⣇⢸⡗⢾⣸⣇⡀⢾⡀⣸⢾⣿⣾⣿⣰⠯⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡈⠁⡁⢈⠁⡈⠉⣁⠈⡀⢈⠈⠁⠈⡀⠉⠉⠀⠉⣁⠈⠁⠁⡁⣉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠉



⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⡠⠐⠂⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡄
⠀⠤⢉⠴⠂⠀⠀⠀⡠⠋⠀⠀⠀⠈⠐⠄⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡆⠀⢀⠀⠒⢄⠣⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠈⡃⢐⢸⢁⡀
⣀⠀⠀⠀⠑⢀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⡄⢰⠀⠀⢠⠀⠀⢀⠀⣀⠂⠀⢐⠊⠀⠠⠰⣄⣀⣁⡐⠤⣰⠃⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡧⢈⠯⣠⠥⠄
⡇⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢁⠀⠀⠀⠀⠀⠀⢀⠐⠊⢁⠤⠄⠠⠤⢀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠂⠰⣀⠹⠤⠘⠠⠆
⠃⠀⠀⠀⠊⠀⠀⠀⢠⣦⣤⣀⡑⠂⠐⠄⠂⠊⠀⠀⠀⠘⢄⠱⢄⠀⠀⠀⠀⢀⡠⠚⠅⠊⠀⡂⠀⠀⡀⠄⠀⠀⠑⢌⡁⠀⣀⡀⠀⠀⠀⠀⠠⠌⣷⡤⠂⠀⠋
⠀⠀⠈⠀⠠⠀⠀⢀⠀⠀⠀⠠⠤⠈⣉⠓⢢⠁⠒⠦⠀⢤⣄⣑⡠⢬⣅⠠⢘⣩⠔⡁⠐⣦⣴⠀⢠⠊⠀⠀⢀⠔⠀⠀⡿⠶⠌⡙⠒⠊⠒⠟⠛⢊⡡⠖⠃⠄
⠤⠤⠀⠀⠈⠀⡘⠁⠀⠀⠀⡴⠊⠀⠀⠁⠀⢠⠴⠒⠦⣀⠀⠀⢠⠴⠲⠆⠩⠁⣀⣸⠚⠄⠠⠃⢠⠀⠀⠀⠈⢀⢀⠈⠀⠂⢄⠀⠠⠐⠚⢛⠛⣤⠀⠒
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⡐⠁⠌⠀⡀⠀⠀⠀⢸⠐⣄⣨⠒⢠⡀⠀⠀⠀⠀⡄⠀⢀⠤⡀⠎⠀⠀⠀⠀⠠⢈⠉⢉⠂
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⢤⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⠂⠈⡀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠅⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⡀⠀⠀⠘⢋⣛⣛⠻⠂⠀⠀⡀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠰⠶⠷⠦⠀⠀⢾⠿⢿⠆⠀⠠⠶⠷⢶⠀⠀⡌⠉
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠌⠀⠙⠄⠠⠿⠿⠄⣤⠞⡁⠀⠀⡙⢦⡄⠼⢿⠧⠀⠘⠁⠈⠄⠀⠀⠄
⠀⠀⠀⠀⠀⢌⢯⠎⠢⡀⠀⠀⠰⠙⠻⡜⠂⠀⣀⠋⠀⠀⠀⠈⢃⠀⠀⠘⡼⠛⠳⠀⠀⠀⡠⠊⢬⢏⠄
⠀⠀⠀⠀⠀⠠⡑⠅⠀⠈⠆⠀⠤⠖⠑⠒⠶⠂⢸⣤⣀⢀⠀⣠⣴⠂⠲⠞⠲⠐⠦⠄⠀⡌⠀⠀⠕⡡
⠀⠀⠀⠀⠀⢄⠈⠀⠀⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⣸⣠⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄⠀⠈⣀⠤
⠀⠀⠀⠀⠠⠀⠈⠀⠐⣌⠀⠀⠠⠌⠧⠀⠀⠀⠠⠈⠁⢃⠋⠉⠀⠀⠀⠀⠐⠟⠤⠀⠀⢈⡔⠀⠀⠐⠨
⠀⠀⠀⠀⠠⢄⠀⠀⠀⡀⠀⠀⠀⣶⠀⠀⢰⠂⠀⠀⢁⣀⠀⠁⠀⠀⢢⠀⠀⢰⡆⠀⠀⠀⡀⠀⠀⠀⠤
⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠘⠂⠀⢸⠀⠀⠈⢢⠾⣴⠂⠀⠀⢸⠀⠀⠚⠀⠀⠀⠠
⠀⠀⠀⠀⠉⢩⠙⠉⠀⠀⠘⠡⠀⠀⠀⠀⢸⠀⠀⣀⠀⣙⠟⠀⠀⠀⢸⠀⠀⠀⠀⠠⠙⠀⠀⠈⢑⠢
⠀⠀⠀⠀⠀⠀⢠⠈⢐⢂⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢀⡄⠡⡄⠡⠄⢸⠀⠀⠀⠀⠀⠀⢀⢐⠈⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠈⠀⢀⡚⢲⠀⠃⠀⢸⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠰⠀⠈⡀⠳⠤⠤⠤⡀⡡⠥⠤⠴⠃⠐⠄⠰⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠀⡼⠀⠀⠀⠂⠘⠀⠒⠀⠀⠐⡌⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠤⠀⢀⡀⠀⠤⠀⠀⠀⠰⠄⠀⡀⠉⠤⠄⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠒⠐⠾⠀⢸⠀⠈⠖⠐⠒⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀
⣿⡆⣆⠁
⣿⡷⢿⣦⠀⠀⢠⢐⠂⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⣿⣷⣞⠐⠂⠀⠁⠀⠀⠀⠀⢀⣀⠀⣸⣿⣆⠀⠀⣨⣇⠀⠀⠀⠀⢰⡄⢨⣿⢊⡀⠀⠀⣠⠄⠐⢃⠸⠻⠿⠦⡀⠀⠀⣠⠄⣴⢿⣝
⣿⣿⡟⠑⢀⠰⣿⣀⣤⣄⠰⣏⣿⣷⣿⣿⣯⣤⡏⢉⣹⣦⣠⣦⣴⣾⣁⡞⠿⣠⣾⣧⣬⣀⣀⢀⣤⣀⠿⠶⠆⢴⣎⠉⣁⡼⡿⠇⠈
⣿⣿⣿⣴⣶⣾⣿⡿⠑⠀⢳⡿⠯⠽⠛⠟⠙⠛⠓⠂⠦⠙⠛⠛⢜⣋⠉⠁⠀⠈⠀⠀⢠⣷⣤⣶⣿⡾⠂⣶⣶⠚⠟⠋⠉⠀⠀⣿⣲
⣿⣿⣿⡟⠉⡽⣿⣧⣤⣠⣴⣧⠐⠂⢀⡀⣀⣆⣀⣠⠶⢓⣦⣶⣾⣿⣮⡀⠉⠿⡍⠹⣿⣿⣿⣿⣿⣷⣆⣀⣀⡀⣀⣀⣀⣀⣀⣹⣟
⣿⣿⣽⣿⣷⣦⣿⣿⡛⣿⡟⣻⣚⣃⣈⣉⣈⣑⣉⣽⣿⣿⣿⡿⣿⣿⣿⣿⣀⣀⣶⣿⣿⣉⣿⣿⣭⣽⣿⣛⣿⣽⣛⣿⣿⣿⣫⣿⢙
⢸⣿⣿⡂⠀⠈⣹⣿⣷⣿⣿⣿⠿⣿⣛⣻⣿⠿⣿⣿⠿⠿⠋⠙⠉⠡⠲⡌⠋⣹⠭⠿⢻⠿⣿⣜⣹⣿⠿⠙⠿⣻⢛⠿⣿⣿⣿⢿⣿
⣿⣿⣿⣇⣀⣠⣾⣿⣿⣿⣿⣥⣽⣿⠿⣿⣷⠖⠲⠂⠈⠁⢀⠁⠂⠐⠠⠤⡶⡛⣶⣾⡿⠁⠈⠙⢟⣻⣽⣿⣳⠾⣯⣯⣥⡰⠷⢿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣶⣶⣤⢰⣶⣄⠀⢄⠀⠀⠀⠠⠶⢦⠼⠛⢛⠑⠂⠀⡴⠶⣵⠟⠦⣭⠄⠥⠀⢲⡶⠚⡛⢋
⠸⠟⣛⣻⡿⣿⣿⣿⣿⣽⣅⢿⣿⣿⣭⢾⣿⣿⢏⠺⣧⠄⣈⠙⡾⠒⢠⡠⣔⣡⣶⣿⣀⣡⡦⠀⠀⠒⢾⣠⡜⢃⠂⣿⡕⠿⣾⢶⢋
⢠⡾⢯⣤⠛⠉⢹⡿⠿⣳⣿⣿⣿⢿⣟⡻⡇⠿⠁⠙⠀⠖⠊⠀⠂⠀⢠⡱⠏⠀⣛⠛⠆⢁⣈⣉⣛⢯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣔
⣼⣷⣶⣮⣅⣤⣌⣤⣴⣧⣿⣧⣯⣭⣬⣷⣄⣀⣀⣀⣀⣀⣒⣉⣀⣐⣀⣀⣴⣀⣀⣰⣿⣷⣉⣛⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢟⠻⣟⡛⢻⡿⣻⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⣄⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠁⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄⠀⠀⠀⢀⣴⠃⠻⡍⢁⠈⢹⠀⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡡⡀⠈⠢⡀⠀⢸⢀⡆⡆⡟⡧⠤⣠⡄⠄⣀⣔⠌⢉⡆⠀⠀⠀⢀⡡⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠿⠾⠾⡦⢆⠀⠘⠉⠍⠙⣛⠁⠠⣀⠞⠺⣽⠉⠉⢽⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡀⡀⣶⡶⣈⢢⠀⡀⢀⠀⢾⠀⠰⣥⣄⣦⣿⡧⡄⣼⣤⠀⠀⠀⠁⠉⠈⠀⠑
⠐⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢀⡀⢀⡀⡾⡅⢡⡹⣇⠙⣾⠟⠀⠀⠚⠒⠧⣀⣨⠉⠉⠹⠃⠒⠐⢂⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⡜⡧⠠⢤⡀⠠⣧⠤⠽⣀⠀⠀⠀⢀⣌⡉⠉⠀⠀⢐⠀⠀⡀⢈
⠀⠀⠇⠀⠐⠀⠀⠀⠀⠀⠈⠀⠘⠀⢀⣿⣁⣣⠗⠀⠀⠨⠷⡄⠀⠀⠘⢇⠠⠸⠸⣇⠀⠲⠔⠁⠈⡆⢰⡏⠈⡀
⠀⠀⠀⠤⠘⠤⠀⢤⣄⣤⣄⢠⣴⠠⣼⣉⡷⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⢢⠀⣀⠀⠀⠀⡔⣀⣂⣡⠃⢀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⡛⠘⠁⠀⠁⠂⢐⣀⠉⠁⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠓⠒⠒⠒⠲⠶⠶⠄⠴⠀⠒⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⢠⠀⢀⢀⡠⠀⢀⠤⠀⣤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢎⠸⣀⡼⢈⣁⡆⣈⣰⠄⣧⡀⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠈⠁
⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⠐⠢⣄⠃⠹⠊⠝⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⣚⡷⡿⣶⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠽⡂⣇⣠⣴⠿⠻
⠀⠀⠀⠀⠀⠂⢲⡰⢃⢦⣽⡯⢋⣥⣼⣿⣿⠿⠿⢈⡩⠝⢵⣿⣯⣘⣻⣿⣏⡛⢫⡿⢿⠉⡿⣿⣿⣿⣿⢋⣼⢱⣿⣿⢑⠀⢰
⠀⠀⠀⢀⠀⡀⠂⠀⣱⣦⢻⣷⠎⢯⣿⣿⠋⠀⠐⢏⡬⠁⣾⢋⡉⣽⣿⣯⣙⠄⠰⠶⣟⠶⠁⠘⠛⣿⣿⠿⣿⣿⡟⣽⣿⠧⢂
⠀⠀⠀⠈⠐⠁⢄⠈⠁⠙⢻⣿⢃⢸⣿⡯⠠⣲⡉⠐⠀⢸⡏⡼⣿⣿⣿⠦⠉⠁⢀⠀⡀⠓⢉⣾⠿⠿⣿⣷⣿⣿⣿⣿⣾⢂⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣿⣮⣻⣿⠑⠀⠙⠀⠀⡀⣿⢮⡧⣿⠟⠀⠀⠀⠀⠀⠄⢁⢒⠘⣋⠭⠍⣩⣿⣿⣿⣻⣿⣯⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⣿⣯⣾⣶⣉⢀⡞⠅⢹⣯⣿⣿⣀⣀⠀⠀⠀⠀⠀⠱⣧⠭⡴⣀⢛⡷⣻⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⡿⢻⣏⡿⢀⡀⣸⣿⣿⡕⢉⡉⠁⠀⠀⠀⠀⠁⡹⠁⠠⠧⢉⡱⠻⣿⣿⣿⣟⡯⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⢀⣈⡇⢠⣠⣼⢹⣿⠟⠇⣨⣁⠀⢀⠀⠀⠀⠀⢙⠗⣀⡀⠀⠀⠀⠊⠹⣿⣿⡞⠑⠍
⠀⠀⠀⠁⠀⠀⠀⣀⣠⣾⣿⣿⣅⣿⣿⣮⣤⣡⣬⣭⣿⣿⣿⣷⣶⣾⢯⣴⣿⣴⣥⣤⣼⣍⢤⢤⣼⣷⢂⡿⠀⠀⣿⣿⡇⠂
⣀⣤⣴⣶⣾⡿⢛⣋⡀⠀⣯⣽⣟⣿⣿⣿⢭⢉⡉⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⠄⠀⠀⢸⣿⣧
⠿⠿⠿⠿⠿⠥⠼⣿⣀⣠⢿⠷⣧⣿⡏⣿⣏⣟⢾⣿⣿⠟⢷⣟⣿⣿⣿⣿⣿⣿⡟⠛⠛⠟⣩⣿⢢⣿⡁⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⡿⢿⡿⠿⣿⣿⡀⠻⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢚⣽⣼⠃⠀⠀⠀⠀⢽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣿⣿⣿⠀⠰⡍⠻⢿⣿⣿⣿⣿⣷⠀⠀⢀⡀⢸⣿⢂⠀⠐⣀⠀⣗⣿⡇
⢠⢀⢀⠀⣀⢀⣀⠀⠤⠴⠤⠄⠰⠤⡄⠻⣿⣿⡟⣿⣷⠚⠂⠁⠀⠘⠉⠁⠀⠀⠈⠉⠛⠁⠀⠈⠉⠉⠂⠀⠉⠻⠿⠛⠛⠒
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⣽⣿⣿⣿⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠂⠚⠋⠛⠉⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⠛⠉⠛⠛⢿⣿⣧⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⡁⠀⠁⣐⢢⡄⠈⢀⣍⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣶⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣻⣷⣿⣿⣿⣽⣿⣦⠘⠣⠖⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣁⣤⠚⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⠿⣿⡿⠻⣿⠏⠛⠿⠟⣤⠀⣿⣿⣷⣿⣿⣯⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢄⠀⠈⠀⠖⣶⣾⣿⣿⣿⠃⢀⣹⣿⣿⣿⣿⡟⠋⠄⣼⣿⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⣀⣘⡁⠘⠃⡠⢿⣿⣿⣿⣿⢡⡄⠻⣿⣿⣿⣿⣿⣧⣤⣾⣿⣫⣾⣿⣿⠂
⠀⠀⠀⠀⢀⣴⣶⣿⣷⣿⣿⣿⣩⣷⠠⠄⡙⢄⠈⠝⠉⣤⣴⣦⡄⣄⢩⡉⠉⢹⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⢸⣷⣿⢫⠒⠉⠈⠪⣻⣿⠿⣦⠶⠸⡇⢲⡸⣿⣺⣺⡷⢀⠔⡁⠆⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⣾⢿⣇⠇⠀⢿⠗⠀⢇⣿⣿⠏⠀⡤⢻⡜⠲⠋⡟⠉⡁⢾⣿⣿⣷⣦⠙⠿⠃⠈⠉⠉
⠀⠀⠀⠀⠻⢿⣿⣮⣲⠄⢄⣪⣾⡟⣿⠆⢈⣀⣿⠀⠀⢈⡅⡊⠁⣌⠛⠟⠉⣁
⠀⠀⠀⠀⠀⠘⣿⣹⣿⣿⡟⣿⡟⡛⢩⣾⣿⣿⣿⡗⣦⠈⣒⢁⡀⣵⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢛⣫⣀⡹⠿⠿⣿⣿⠿⠛⠃⠦⡱⠾⡕⣿⣼⣽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢩⢽⣧⠚⠉⢀⡀⢴⡾⡻⣧⡙⠄⢳⠀⣉⠁⢂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠃⠀⠀⠈⠀⠻⣯⣥⡿⠃⠈⡳⠤⡐⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠈⠑⠓⠤

⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⠟⠁
⠀⠀⠀⠀⠀⣠⡾⣿⠟⠁
⠀⠀⠀⣠⣞⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀
⠀⡠⣾⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣵⣶⠿⠿⣶⣮⣶⢄
⣾⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣿⠏⠀⠀⢀⡀⡻⣿⣆⡄
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣟⡨⠴⠒⠒⠈⠑⢼⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡏⠸⠗⠀⠀⠺⠏⢠⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣏⡉⠀⢹⣂⣐⡏⠀⢉⣹⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡦⣝⣋⡿⠏⠹⠿⣙⣋⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⢿⣿⡇⣀⣿⣿⠿⠿⣿⡿⣶⣿⣿⡿⢟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡙⠿⠲⡇⠋⠀⠚⣃⠀⢚⢧⣄⢸⠖⠾⢋⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣝⣛⣟⠀⠀⢰⣦⣿⢴⣷⠞⠋⢁⣿⣛⣫⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⢻⢿⠷⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⣅⣙⡋⠂⠀⠀⠀⠀⠿⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠹⣏⠁⠀⠰⣀⠙⢀⣄⢀⠞⡀⣴⠏⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣻⡄⠀⡀⠙⢠⣬⡁⢠⣄⢠⣟⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠜⡛⠀⠘⠛⠀⢈⠡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡰⢴⡦⢄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⢶⠆⠀⠘⠢⣀⢶⡷⣀⠔⠃⠀⢰⡆⠀⠀⢀⠄⡀⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠊⠑⠀⠀⠀⠀⠰⣝⣽⣝⣳⠄⠘⣮⣾⢷⣵⡇⠠⣜⣩⣯⣫⠆⠈⠀⠈⠀⠋⠱⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⢰⡄⢀⠁⠀⢠⡀⠀⠻⠞⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠳⠟⠀⢀⠄⠀⠀⡀⢠⡄
⠀⠀⠀⠀⢄⡀⠄⠈⠀⠡⠀⠀⡀⠐⠅⠦⠤⠀⣀⢴⠏⠀⠀⠀⠀⠹⡤⣀⠀⠤⡔⠨⠂⢀⠀⢀⠍⠀⠑⠠⢀⡠
⠀⠀⠀⠀⠀⠙⢄⠂⠑⣠⠀⢀⠓⠃⣠⣤⣶⣆⡶⡆⠖⠖⠀⠀⠲⠲⢰⢶⣰⣶⣤⣄⠘⠊⡀⠀⣄⡊⠐⡠⠋
⠀⠀⠨⠀⠓⢌⡂⢑⣮⣇⢠⢄⠀⠀⠣⠀⠉⠉⠳⠨⣾⡖⡄⢠⢲⣷⠅⠞⠉⠉⠀⠔⠀⠀⡠⡄⣸⣵⡊⢀⡠⠚⠀⠅
⠀⠠⠀⠀⠦⢀⠈⢀⣿⡉⠲⢇⢠⠀⠀⠀⠀⠀⠀⠱⢸⠐⣤⣤⠂⡇⡌⠀⠀⠀⠀⠀⠀⡄⡼⠒⢉⣿⡀⠁⡀⠴⠀⠀⠄
⠀⠀⡀⠠⠄⠀⠈⠘⢯⣉⢱⡚⣓⠑⢀⠀⠀⠠⡐⠐⣆⠻⡸⢇⠗⣰⠃⣂⠄⠀⠀⠀⠊⣚⢒⡊⣉⡽⠃⠁⠀⠠⠄⢀
⠀⠀⠀⡤⠀⢀⣀⡈⣳⠄⠐⣙⡧⠀⠀⠀⠁⠈⠃⠈⢬⠀⢐⡀⠀⠁⠀⠉⠁⠈⠀⠀⠀⢼⣋⠆⠠⣞⢁⣀⣀⠀⢤⠐
⠀⠀⠀⠀⡤⠄⠀⠀⢻⠖⠂⠿⣽⣀⢀⠀⡀⢀⠀⠀⢞⡟⣦⣁⠄⠙⢂⠀⡀⢀⠀⡀⣠⣯⠿⠐⠲⡟⠀⠀⠠⣤
⠀⠀⠀⠀⠀⡤⠄⠀⠘⢛⣏⣠⠚⠞⢯⠿⣵⢯⠀⠙⠘⡾⡎⡟⠦⠗⠾⠠⡿⣮⠿⡹⠳⠓⣄⣹⡛⠓⠂⠠⢤
⠀⠀⠀⠀⠀⠀⠠⠊⢀⡀⠉⠳⠚⣤⠞⣀⣦⣠⠀⠠⠆⠀⢿⣍⠉⠙⢠⡤⣄⣴⡀⠳⣤⠳⡞⠉⢈⠀⠑⠆
⠀⠀⠀⣠⡴⢢⠁⠀⠋⠀⠴⠁⢈⠄⠄⠝⠀⠙⠘⣫⣄⡈⢌⠻⡀⢸⠞⠁⠉⠀⠫⠠⠠⡐⠈⠦⠀⠙⠀⠘
⠀⠀⠫⢉⡀⢞⠀⠀⠀⠀⠀⠂⠀⠀⠈⣀⡜⢈⠀⢧⡁⠷⠈⣉⣓⠈⠂⠀⡁⠓⣀⠁⠀⠁⠐⠀⠀⡀
⠀⠀⠀⠀⠁⠉⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⡘⠧⠆⣀⢀⣰⡃⢈⡀⡀⣤⠰⢌⢭⠱⡤⠀⠀⠀⠀⣘⣟
⠀⠀⠀⠀⠀⠀⠠⠐⡀⠀⠀⠀⠀⡀⡰⠎⠀⠐⠈⠁⠘⡗⢈⠘⠳⠃⠉⠁⠒⠒⠷⢆⢀⠀⢀⠀⣨⣭⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⡋⣠⡀⠀⠀⠀⠆⠾⠞⠊⠂⠂⠀⢩⣄⣴⠌⠀⠐⠐⠑⠳⠗⠠⠀⠀⠹⠚⢣⢴⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠥⣴⠎⠀⡀⠀⠤⠀⠐⠁⢨⠶⢊⡏⢿⠓⠲⠁⠨⠀⠀⢆⠀⠀⠀⠀⠐⣢⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠸⡆⠊⠀⠀⠢⡀⠴⠀⢤⡀⠰⠁⠘⠄⠀⡤⠐⠦⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠂⠀⡀⡆⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠒⠁⣺⣆⡰⡆⠀⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠻⣵⠀⢀⡰⢆⡀⠀⠄⣴⠆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⡀⢾⡆⣾⣻⣷⣄⠁⣀⡈⠁⠈⢁⣀⠅⣠⣾⣻⣿⠀⠾⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⠀⠀⣿⣿⣿⣿⠺⣿⣿⣧⣼⣿⣿⠟⣿⣷⣿⣿⠀⠉⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠙⠀⣴⣿⣏⣙⠚⠃⠸⢿⣿⣿⣿⣿⡿⠇⠙⠛⣋⣽⣿⣦⠀⠋⣩⠀⠘⠩
⠀⠀⠀⠀⠀⠀⢿⡜⡇⠀⢀⣤⣤⣻⣿⣿⡿⠀⠠⠄⠠⣖⠉⠉⠀⠀⠠⠄⠀⢿⣿⣿⣟⣤⣤⡠⠂⠐⣡⣄
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡿⢿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢉⣀⣀⡀⠀⠀⢠⡔⠊⢿⣿⣿⣿⡿⢿⣤⣤⣭⣅⡀
⠀⠀⠀⠀⢀⡈⢿⣽⣻⣿⣷⠘⠛⠋⠱⣀⠀⢠⣶⣿⣷⣿⣿⣿⣷⣾⣿⣶⡄⠀⠀⠈⠙⠛⠃⣟⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠈⡛⡀⡙⣿⡛⣋⡀⠀⠆⠀⣵⣿⣿⣿⠿⠛⢉⢉⡉⡉⠛⠿⣿⣿⣿⣦⠀⠰⠀⢀⣉⢛⣟⠋⠠⣬⡛⠃
⠀⠀⠰⠬⠀⢀⡀⠸⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣄⡑⠈⠀⠀⠁⢊⣠⣿⣿⣿⡟⢰⠰⢄⣿⣿⣿⣿⠇⢀⡈
⠀⠀⠀⠀⠰⢎⡁⠀⣉⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⢺⣿⣿⣿⣉⠀⢈⡱⠆
⠀⠀⠀⠀⠀⡈⠁⢰⣿⣿⣿⡿⠐⠎⣻⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⡆⠈⠁⠀⡒⠆
⠀⠀⠀⢠⣮⡟⠀⣠⣿⣥⣉⠁⠀⠼⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣯⣿⣿⣿⣿⣿⣿⡿⠶⠀⠈⣩⣬⣿⣬⠈⣬⡀
⠀⠀⠀⠀⠀⣠⣾⢿⣿⣿⡽⢠⣴⣄⡀⠉⢹⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡏⠉⢇⣠⣤⡄⢿⣿⣯⣟⣷⡈⠁
⠀⠀⠀⠀⠀⠈⢙⣛⠛⠛⣷⣿⣿⣿⣿⣷⡤⠍⠉⡁⠻⠟⠁⠈⣻⡟⠈⠉⠉⢀⣾⣿⣿⣿⣿⣾⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠙⢋⠄⠠⠊⠛⠛⣽⣿⣿⣷⠀⠘⠀⠀⢀⣀⣄⡴⠂⠐⠂⠀⣾⣿⣿⣯⠛⠛⠁⠀⢸⠼⡷
⠀⠀⠀⠀⠀⠀⠀⣂⡄⠀⡏⣠⠀⠻⣿⣏⣩⣤⣄⢰⣿⣿⣿⣿⣿⣷⡆⢠⡤⣭⣻⣿⢟⠀⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⠀⣿⣿⢿⣿⣴⣿⣿⡟⢻⣿⣿⡦⣿⣿⣿⣿⠀⠐⡁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⠀⣿⣯⡿⠋⢐⠉⢁⡀⢀⡈⠉⢀⠙⢿⣯⡿⠸⡷⠈⠐⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠟⠐⠀⠈⠱⠎⠁⠐⢟⣶⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⠀⠀⠀⡀⢢⠆⡀⠈⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡉⢽⠍⡁⠀⢰⡄⠞⠆⣴⠀⠠⡉⢽⠍⡅⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠛⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠁⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠁⠠⠤⣐⡀⠶⡀⠐⠀⠀⠀⠂⠂⠲⠂⣐⡠⠤⠀⠁⠠⠀⠀⠀⠀⡀⠈
⠀⠀⠈⠀⠀⠈⠢⣇⠠⠠⠀⠀⠀⠀⠀⠀⠑⠠⠼⠀⠀⠀⠰⠤⠐⠀⠀⠀⠀⠀⠀⠠⠠⢀⡧⡊⠀⠀⠈
⠀⠀⠐⠠⠀⠀⡱⣌⠁⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠔⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢉⡴⡁⠀⠠⠐
⠀⠀⠀⠀⠀⠀⡣⠄⠀⣌⠉⠈⠀⠀⠀⢀⡀⠈⠇⠁⠘⠀⠁⠏⠀⣐⠀⠀⠀⠈⠈⣉⡅⠠⠔⡃
⠀⠀⠀⠀⠤⠀⡑⠂⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢒⠀⠠⠄
⠀⠀⠐⠂⠀⠀⢨⡏⡀⠐⠴⢀⡀⢀⠀⠀⠀⡀⠻⡍⢶⡄⠀⠈⠀⢀⠀⠀⠀⣀⠰⠐⠀⡈⣯⠀⠀⠀⠂
⠀⠀⠀⠐⠀⢀⠀⠈⠧⠴⢀⠂⢀⠙⠘⠒⠀⠉⡀⠝⡀⡍⠐⡀⠃⠐⠚⠘⢁⠀⢂⠰⠤⠏⠀⠀⠀⠂
⠀⠀⠀⡀⠀⠁⢀⠄⠀⠈⠁⠲⠂⣠⠣⠴⢀⡀⠀⠀⢱⡄⠀⠀⠀⠰⠔⢧⡀⠳⠂⠉⠀⠀⢄⠀⠁
⢀⠤⠖⢉⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠈⠒⢠⡀⢀⢩⡀⠈⠀⠀⠀⠀⢀⠀⠠
⠈⠒⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢁⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠠⠛⠀⢠⢠⠀⠀⠁⠀⢂⠘⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡄⠒⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡶⡟⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠈⠙⠃⠶⢀⠀⠀⠀⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣷⣿⡆⠀⠀⠀⣀⠀⠀⠈⣤⣤⣤⣀⣠⣄⢀⣠⣐⣾⣶⣶⣶⣴⡆
⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⣶⣿⣶⣿⣷⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣄⢀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠙⠂⢀⣀⢿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣿⠿⠃
⠀⢲⣶⣦⡀⣆⣴⣶⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⢰⣇
⠀⠈⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⡆
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠹⠁
⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣏⠆
⠀⠀⠀⠙⠿⢿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠁⠉⠉⠀⠀⠀⠀⠀⠉⣹⡇
⠀⠀⠀⠀⠀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀
⢀⠀⠀⠐⣀⢪⡥⠀⠀⠀⠀⠀⠀⡀⠄⠠⠉⠀⠉⣐⡈⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠠⠀⠀⠸⠄⠰⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠀⡿⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣂⠀⠀⢠⣤⠤⠆⢰⡀
⠀⠀⠀⠀⠀⠠⠄⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠉⠀⠀⠀⠴⠀⠀⡀⡀⠀⠀⠈⠿⠂⡀
⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠁⠀⠀⠃⠀⣠⣤⣄⣀⠀⠈⠓⠛⠂⠀⠀⠀⠀⠈⣅⠒⠲⠀⠀⠲⡐⠰⡒⣤⡧⠀⠀⠀⠀⠀⠀⣄⣀⢁⣤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠁⠀⠀⠀⠀⠦⢀⣀⠂⠠⢀⡀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠆⠽⠏⢀⡀
⠀⠀⠀⠀⠀⠠⠀⠤⢤⣄⠀⠀⠀⠀⠁⢄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠈⠀⠄⣀⠐⠀⠀⢀⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠒⠀⠀⣤⢀⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠀⡤⠆⠀⠀⠀⠀⠈⠀⠀⠀⢠⡶⠦⣤⡈⠃⠠⠈⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠁⠀⢠⣤⣤⠀⣞⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠑⣔⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠆⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠿⡀⠙⠑⣨⡄⠀⡀⠐⠀⠀⠀⠀⠁⠲⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⡔⠁⠀⠀⠀⡆⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⠀⠀⢈⢀⡆⠀⠀⠀⢀⠆⠀⠄⢤⠁⠀⠀⠀⠀⠁
⠋⠀⠀⠀⠀⠀⠘⠁⠀⢸⡇⠐⠀⠤⠀⢤⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠅⡀⠀⠀⠈⠠⠄⠀⠀⠈⠐⠂⠀⠈⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀
⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠴⠖⠒⠀⠀⠒⠒⠒⠒⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠔⠂⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⢤⣰⡶⣦⣤⣤
⢄⣀⣀⣀⡤⠄⠀⠀⠀⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠛⠀⠠⠀⠀⠠⠀⠀⠁⢀⡀⠀⠀⣤⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠠⠭⣙⠉⠉
⢛⣻⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠘⠃⢀⣀⡀⠀⠙⠿⠂⠒⠐⠃⠋
⠀⠉⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠂⠀⠀⠀⠈⠀⠁⢸
⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣷⢸⣇⢸⡇⣿⢸⡇⣿
⠒⠒⠋⢹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⢿⣀⣸⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡤⠖⠉⠀⠀⠀⠀⢰⣂⣣⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⢡⠁⢀⠂⠀⠀⠐⡆⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡀⢳⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠐⡀⠀⣰⡣⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⡼⡈⢈⠌⠔⣄⠀⢀⣀⡌⢣⠏⣶⠊⣧⠑⡔⠏⢔⢵⡀⠀⠀⢰⡾⡄
⠀⠀⠀⠀⠀⠀⢐⠁⠐⠡⢊⠔⠀⠃⠀⣈⠋⠉⠉⠉⠉⠙⡟⠌⢌⢢⢢⢹⠀⠀⢜⣧⢱
⠀⠀⠀⠀⠀⠀⠘⢒⣒⣒⣘⣚⣒⢂⣔⠘⣄⡀⠀⣀⠀⢀⣱⣚⣚⣒⣚⣺⢠⠞⠕⠜⠝⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠇⠀⠀⠀⠇⢿⢬⣧⢼⡶⣿⠀⢾⡇⠸⣏⠀⠀⢀⡁⠸⡬⠬⠬⢎⠄
⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⣀⣈⣀⠐⠂⠀⠚⠀⠀⠀⠀⠀⣬⣁⣁⣆⣁⣁⡄⢙⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢻⠁⠈⠎⠀⢹⠼⠥⠦⠽⠄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⡮⠵⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⢀⡀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⠂⠀⠀⠐⠂⠀⠀⠀⠚⠀⠘⠃⠀⠛⠀⣼⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠤⠔⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⡰⢁⡾⠛⢉⡹⠳⣂⠲⡀⠀⠀⠀⠀⠀⠀⢠⠊⣠⠶⠿⠿⠶⣄⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⢏⡉⠓⢦⡈⢂
⠀⠀⠀⠀⠀⡀⡾⠾⣿⠁⢠⡷⢼⡆⠀⠀⠀⠀⠀⠀⠀⡆⢘⠩⣤⠄⢠⡤⠍⡇⢠⠀⠀⠀⠀⠀⠀⠀⢰⠧⡊⠀⠈⠛⡁⢷
⠀⠀⠀⠀⠈⠃⢣⡒⠀⣀⡀⠐⣶⠃⠃⠀⠀⠀⠀⠀⠀⡇⠘⡀⠀⢤⡄⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢠⣤⠀⢀⡜⠀⠁
⠀⠀⠀⠀⡠⠐⢀⠙⠖⣄⡔⠞⢁⠐⠠⡀⠀⠀⠀⠀⢠⡃⠀⠈⠐⠂⠐⠂⠁⠀⢘⡄⠀⠀⠀⠀⢀⠄⠀⠈⠳⢢⣠⠢⠋⠀⠀⢄
⠀⠀⠀⣔⠐⠀⢦⣀⠔⡿⡑⢄⣠⠀⠐⢑⡀⠀⠀⢠⠕⣂⢱⢀⠂⢄⡀⠐⢐⡎⣰⠪⡄⠀⠀⢀⣊⣦⣀⣀⣠⣾⣿⣦⣀⣀⣀⣎⣢
⠀⠀⢀⣓⠤⠍⠐⣪⠓⠁⠙⢧⡒⠈⠅⢔⣃⠀⠀⣧⠄⠎⣀⣄⡀⠀⠀⢀⣀⣀⢱⠠⣼⠀⠀⣼⣿⡿⠿⠿⠛⠁⠈⠙⠛⠿⠿⣿⣿⡆
⠀⠀⢸⡟⠏⣩⡉⠀⣾⣷⣿⡆⠈⣩⡙⡟⣿⠀⢸⠁⢨⠀⣹⣟⠀⣠⣄⠈⣿⡟⠀⡄⢈⡇⠀⣿⣿⠁⢠⣾⣻⢷⣴⢿⣿⣦⠀⢹⣿⡇
⠀⠀⠸⣷⠂⠛⢃⢀⠈⠛⠋⢀⣀⠛⠃⢲⡟⠀⠈⡇⠛⢆⠶⠿⠂⣹⣏⠠⠿⠵⡐⠛⠸⠀⠀⢻⣿⡀⠸⣞⠷⣾⣿⡷⢟⡾⠀⣸⣿⠇
⠀⠀⠀⠹⣧⡔⠀⠁⠀⡠⡂⠙⠛⢀⣴⡿⠁⠀⠀⠀⣤⡌⠢⡀⠐⠾⠾⠀⡀⠔⢡⣤⠁⠀⠀⠈⢿⣧⡀⠙⠷⣌⣃⡤⠚⠁⣠⣿⠏
⠀⠀⠀⠀⠙⢿⠷⣧⣤⣤⣠⣤⡷⢿⠟⠁⠀⠀⠀⠀⠈⢶⡤⢤⢉⢀⡈⡉⠤⢤⡖⠁⠀⠀⠀⠀⠈⠻⣿⠆⡤⣈⣉⡀⡤⢾⡻⠋
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢠⣾⣻⢽⠓⠛⠽⣻⣦⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⡴⣶⣶⢦⡄⠡⡀⠀⠀⠀⠀⠀⠀⠀⠔⣁⠶⠞⠛⡷⣦⡑⠄
⠀⠀⠀⠀⠀⣿⣽⣤⣡⠈⢲⣦⢽⣽⡇⠀⠀⠀⠀⠀⠀⡌⢰⢫⣤⡄⢠⣤⡛⡆⢡⠀⠀⠀⠀⠀⠀⠈⢠⡯⢜⡒⠁⣀⠄⣷⠈
⠀⠀⠀⠀⠘⣿⣃⠤⠉⡀⠈⠡⢄⣻⡇⠀⠀⠀⠀⠀⠀⡇⠨⡰⠈⠀⠀⠁⢆⠇⢸⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢁⣀⠉⠀⡸
⠀⠀⠀⠀⢰⣿⣿⣴⠤⡄⡤⣴⣼⣿⣧⠀⠀⠀⠀⠀⢀⠃⠀⠐⠢⠀⠁⠔⠁⠀⠘⡀⠀⠀⠀⠀⠀⠄⠀⠉⢦⢤⢁⢤⠎⠁⠀⠄
⠀⠀⠀⣠⣿⣿⣿⣿⠶⣋⠳⣾⣿⣿⣿⣧⡀⠀⠀⢠⣂⠉⢒⠂⠄⢄⠀⠤⠐⠒⠉⣑⡀⠀⠀⢀⠄⠀⠀⠀⡀⢞⣟⠆⡀⠀⠀⠈⢆
⠀⠀⢠⣏⣍⣍⡭⠤⠚⢉⠙⠢⠬⣍⣍⣍⡧⠀⠀⣾⡿⣟⠿⢿⣶⣾⣿⣶⣿⠿⣻⣿⣷⠀⠀⠨⣽⠉⣯⠙⣦⡾⠹⣦⡞⢩⡏⢹⡭
⠀⠀⢰⠀⠐⠂⡄⢠⣞⠡⢙⣦⠀⡄⠒⠀⢸⠀⢸⡟⣼⡛⣿⡜⣿⣿⣿⣿⢣⣿⢻⡧⢻⡆⠀⡿⠻⠖⠛⠛⠉⠀⠀⠈⠙⠛⠗⠾⠳⡇
⠀⠀⠈⡈⡀⢀⠧⣿⢝⢝⢝⢽⡥⢧⠀⡊⡌⠀⠈⣿⣼⣻⣹⣽⣿⣿⣿⣿⣧⣯⣻⣥⣿⠁⠀⢧⣤⣤⣄⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⡇
⠀⠀⠀⢢⠐⠄⠑⣀⡻⢷⠿⣁⡰⠁⡔⢠⠃⠀⠀⠹⣿⣿⣿⣿⢻⣏⣹⡗⣿⣿⣿⣿⠏⠀⠀⠘⣦⣘⣆⢠⢌⢩⡉⢯⣈⣤⢀⢦⡜
⠀⠀⠀⠀⠱⡈⣐⣈⡂⠁⠑⣊⣐⣈⡐⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣭⣹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⢦⣤⣭⣤⣬⣥⣭⣤⣥⣤⠎
⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠉⠉⠉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⠈⢷⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣴⣦⣀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⡁⢤⠀⡄⢠⠀⠀⠒⢠⣄⢠⠀⠂⠀⠀⠀⠀⣿⠀⢹⡆⠘⢧⡀⠀⠠⠛⠶⠀⠀⠀⠂⠀⠀⠀⣠⠶⣥⣛⠶⣮⠃⠀⠀⠀⠀⠀⠀⢀⣰⢶⣄
⠀⠀⠉⠙⠉⠁⠘⣄⠏⠸⠀⠀⠰⠶⠶⠶⠶⠛⠀⠀⠀⠀⠻⠇⠈⠁⠀⣰⠇⠀⠀⠤⠰⠶⠔⢠⠀⠀⠀⠰⢫⣾⢱⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⣾⡗⣬⠟
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⠶⠞⠉⠀⠀⠀⠀⠀⠀⢄⠶⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠢⡀
⠀⠀⠀⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠾⠂⢠⠀⠀⠀⠷⣿⣷⣿⠿⠃⠀⠀⠀⠴⠀⠉⠒⢄⢀⡀⠀⠀⠀⢰⣶⣶⣶⣾⣧
⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⣮⠙⠃⠀⠀⠀⠀⢷⡆⠉⠀⡠⠋⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣾⠃⣀⡀⠙⠷⠀⠀⠀⠈⠉⣙⠿⡇
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢰⠈⠁⠈⢁⡀⠐⠀⠀⠀⢀⡀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⠀⠰⠏⠁⣀⣉⣁⡀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠉⠛⠉⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠰⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠁⠂⠀⠀⠀⢠⡀⠀⢛⠿⠀⣀⠀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⢴⠁⠐⠀⠀⠀⠀⢸⡇⠀⠀⠙⠂⠀⠐⠀⠈⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠉⠁
⠀⠀⠀⠀⠀⢨⣯⡹⡭⠀⠀⠀⠁⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠟⡷
⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢐⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣦⠀⠀⠀⠀⠀⢀⡀⠲⡀⠚⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠛⠃⠀⡘⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⢁⡇⠀⠀⠀⠄⠘⠃⢀⡵⠚⠃⠀⠤⠀⠀⠈⠂⠀⠃⠀⠀⠀⡟⠻⠿⠿⠛⢋⢳⡆
⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡄⠀⠀⣤⠀⠀⠀⠀⠀⢤⡄⠀⠠⢦⣤⠇⠀⠐⠲⠖⠲⠟⠁⠀⠀⠀⠀⠲⠐⠆⠀⢠⡤⠄⠀⠀⠀⠈⠢⠄⠀⠴⠋⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⣮⠀⠀⠀⠀⠀⠈⢀⠀⠐⠀⠀⠀⠀⠀⢀⠄⠴⣿⡟⠀⠀⢀⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠒⢠⡆⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⠀⢀⡤⠈⠀⠀⠀⠈⠀⣄⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⣄
⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⠀⠠⢾⣥⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠊⠀⠀⠀⠀⠀⠀⠉⠉⡆⠀⠀⠉⠀⠀⠀⠈⠀⠂⠰⣆⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠊
⠀⠀⠀⠀⠸⠷⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢟⡻⢿⣧⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠰⠾⠦⠀⠀⠀⢰⠆⢀⡛⡄⠀⡀⠀⠀⠀⣠⣶⣶⣴⡆⠐⠓
⠀⠘⢶⣶⣄⣤⣴⣶⡞⠀⠀⠈⠛⢧⣼⣿⡶⠟⠀⠀⠀⡀⠈⠁⠈⠀⡀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠂⠀⠰⠃⣠⢻⡿⠓⢾⠉⢓⡄⠘⠿⠶⣤⡞
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠞⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⢾⣤⠴⠛⠓⠋

⠀⠀⠀⢀⣤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠤⣴⡄⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖⢠⡀⠀⠀⠀⠀⠀⠂⠀⡈⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠄⢀⡤⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢲⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓⠇⠀⠀⠄⠀⠀⠀⠙⠷⣶⣶⠶⠟⠁
⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠆⠈⠄⠀⠑⠄⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠀⠀⠀⣤⣙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣧⡄⠀⢀
⠀⠀⠀⠴⠆⠀⣤⣾⠃⠀⠀⠤⠤⠤⠌⠉⢫⠀⠀⠀⠀⣤⣹⣿⣧⣄⠉⠀⠀⠀⠀⠀⢠⡄⠐⢳⡄⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢠⡤⠲⡦⠴⠶⠀⠀⠂
⠀⠀⠀⠤⠄⠻⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠋⣻⡑⢫⣧⠀⠀⠀⠀⠤⠸⠃⠶⠊⠀⠀⠀⠀⠿⠟⠀⣀⢠⣦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠐⠛⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠉⠀⠀⠀⠈⠤⢀⣀⣀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⠉
⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡦⠄⠀⠀⠀⣀⠐⠂⠀⢠⡤⠀⠀⠀⠀⠠⠶⠶⠦⠀⢀⠀⠀⠀⠀⠛⠏⠀⠀⣤⢶⠒⣄
⠀⠀⠀⣤⣴⣶⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠀⠀⠀⠀⣴⠿⠛⠉⠀⠀⠀⠘⠀⠀⠁⠀⣄⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡌⠄⠀⠀⠀⠁⠂⠂⠀⠐⠫⠜⠋
⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠟⠃⠀⠀⠀⢈⣿⡷⠲⠶⠿⠓⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⡿⢿⣿⡿⠛⢿⡿⣿⡿⣿⠿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣥⣤⣼⣷⣠⣾⣠⣴⣷⣬⣴⣿⣥⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣛⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠠
⠀⠀⠀⠠⠁⠠⡀⠀⠀⠀⠀⢀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠅⠈⠀⢀⡀⠀⠀⠠⠠⠀⡠⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠐⢀⡐⠶⠦⠀⠈⠁⠀⠁⠀⡠⠀⠀⣀⠀⠀⠀⠀⠀⠅⢈⠀⠥⠀⢠⠄⠘⣃⣉⢁⣁⣀⠈⠐⠒⠉⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠌⠀⡀
⠀⠀⠈⠐⢋⡥⠒⠒⠻⠒⠒⠲⠤⡐⠻⢅⠀⠀⠁⠀⠀⠀⠀⠀⠊⠈⠀⠠⢀⠤⠂⠀⠉⠀⡀⠢⡀⠀⠈⠓⠀⠀⠐⠆⠀⠈⢉⣀⣀⡀⠀⠀⠀⠀⠀⠄
⠀⠐⠀⠀⠁⠑⢈⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠠⣀⠀⠀⠀⠀⠀⡀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠉⠁
⠁⠈⠀⣀⠀⠆⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⢈⠀⠀⠈⠠⢴⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠀⠀⠄⠤⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢈⠁⠀⠀⠀⠁⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠂⢂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠂⠀⠀⠀⠒⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣠⠆⢴⣀⡶⣰⠒⢦⢰⣦⡖⢰⣆⣰⢰⡆⠀⣴⠒⢦⢰⡆⣴⡆⢰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠧⠻⠀⠗⠙⠦⠞⠸⠏⠳⠸⠇⠹⠸⠧⠤⠻⠤⠞⠸⠹⠋⠧⠟⠙⠇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⢀⠄⢈⠄⠀⠀⠀⠠⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⣀⡀⠔⠀⠀⢀⠀⠀⠀⢀⣁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠒⠄⠀⠐⡀
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠛⢃⠈⠁⠀⢀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠰⡁⠈⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⡀⠀⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠔⠊⠐⠈⠀⠁⠀⢀⠀⠈⠐⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⡈⢆⢀⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠉⢉⡀⠒⠲⠄⠀⠀⠤⠀⠀⡈⠂⠈⢐⣀⠀⠐⠊⠁⠂⠠⡀⡠⠀⠀⠀⠀⠀⢀⠄⠀⢉⠦⠌⠑⠲⠤⠠⠴⠶⠖⢊⡥⠆⡀
⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⡡⠶⠤⠀⠉⠉⢁⣀⠠⡔⠈⠁⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⢀⠀⢀⠀⠀⠒⠖⠉⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⡁⠀⡀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⡴⠉⠁⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠈⠙⢧⡄
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⠀⠀⠘⡷
⠀⠀⠀⠸⡀⠰⠂⠀⠀⠐⠆⢀⠇⠀⠀⠀⠀⠈⣿⠀⠶⠀⠀⠀⠰⠂⣸⠇⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢻⡄⠰⠂⠀⠀⠰⠆⢠⡟
⠀⠀⠀⢀⡑⢄⡀⠀⠀⢀⡠⣊⠀⠀⠀⠀⠀⠀⠈⢳⣤⡀⠀⠀⣠⡶⠋⢂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠹⢦⣀⣀⣀⣀⡴⠏⡀
⠀⠀⠀⣛⠁⠀⠀⠀⠀⠀⠀⠈⣛⠂⠀⠀⠀⠀⡀⠈⠀⠀⡠⠀⠀⠈⠀⡀⠀⠀⠀⢀⠘⠝⠂⣴⢷⣶⠾⡄⠸⠼⢁⠀⠀⠀⠀⣶⣷⠀⣼⢿⡿⠷⠀⣾⣖
⠀⠀⢴⡩⠹⠄⠈⠁⠀⢁⠀⡏⠍⡶⠀⠀⠀⣤⣷⣴⡠⡀⠈⠀⠠⣰⣼⣦⠄⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠁⠀⠠⠀⠀⠀⢀⣷⠠⠑⠁⠀⣸⣇⠀⠈⠈⠄⣾
⠀⠀⢴⡉⠁⡀⠂⢐⢠⠐⢀⠈⢉⣦⠀⠀⠘⢻⢯⠿⠅⡀⢰⠀⡀⠿⣷⢿⠃⠀⠀⠀⠀⠠⠀⢠⠀⠀⠠⠀⠠⠀⠄⠀⠀⠈⠁⢴⣶⠀⣤⠀⠀⣤⠀⣶⡆⠈⠁
⠀⠀⠈⡁⠂⠀⠀⣀⢀⣂⠄⠐⢈⠁⠀⠀⠀⠀⠀⠰⠀⡀⣠⢀⠀⠠⠀⢀⠀⠀⠀⠈⠁⢀⡀⢠⣼⢾⣧⠀⡀⠀⠈⠁⠀⠀⠀⢀⣵⣨⢇⣴⡤⡼⣄⣬⡀
⠀⠀⠀⠀⣤⣁⢸⡑⢊⡇⣈⣤⠀⠀⠀⠀⠀⠈⠀⠀⠰⢿⣟⣿⠆⠄⠀⠍⠀⠀⠀⠀⠀⠐⠁⠈⠻⠳⠋⠀⠘⣀⠀⠀⠀⠀⠀⠠⠾⡏⡾⢹⠇⢷⣹⠷⠄
⠀⠀⠀⠀⠀⠉⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣭⣭⣭⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠓⠘⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠉⠛⣦⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠰⠄⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⢵⠀⠶⠀⠀⠀⠴⠀⢸⠇⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢻⡀⠰⠄⠀⠀⠰⠆⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⢤⣦⠀⣴⣶⡶⢦⠀⣴⣤⠀⠀⠀⠀⠰⠟⠁⣼⣿⡟⣿⣿⡀⠙⠶⠀⠀⠀⠀⢀⠀⠃⠀⠀⠄⠀⠀⠁⢀⠁⠀⠀⠀⠀⠮⠷⢈⣽⣿⡿⣯⠁⠿⠗
⠀⠀⣦⢉⠁⠀⠀⠘⠃⠀⠀⠌⡉⣼⠀⠀⠀⣜⠍⣮⠉⡉⠈⠈⡉⢱⠊⢻⡄⠀⠀⢀⣰⣦⡄⡄⠀⠋⠀⠄⣤⣾⣀⠀⠀⠀⠁⢀⠠⠈⠡⠘⠃⠄⠁⠄⡄⢀
⠀⠐⠋⢠⣶⠀⠤⠁⠈⠄⠀⣶⡄⠙⠀⠀⠀⣌⠛⠁⠠⠌⡐⡀⠤⠀⠛⢫⡄⠀⠀⠚⣿⣽⢿⢀⠀⡀⢂⠈⢿⣿⡟⠂⠀⠀⠁⠀⢤⣦⣀⠀⠀⣀⣴⡤⠀⠈
⠀⠀⠀⠈⠫⢀⣆⣤⣄⣠⡀⠙⠁⠀⠀⠀⠀⢙⠂⠌⢁⠒⡀⡐⢀⠡⠄⣛⠀⠀⠀⠀⠀⠀⠄⠐⠀⡅⠈⠀⠆⠁⠀⠀⠀⠀⠛⠀⠘⣿⡿⡩⡉⢻⣿⠃⠀⠚
⠀⠀⠀⢀⣴⡏⣼⢻⡇⣷⡻⣦⡀⠀⠀⠀⠀⠀⠀⣘⠀⣟⠡⢙⡂⣈⡀⠈⠀⠀⠀⠀⠉⠀⢀⠠⣿⣻⣯⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠹⣧⣋⣃⡼⠏⠁⡀⠁
⠀⠀⠀⠀⢶⣥⣁⣃⣐⣈⣬⡶⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠉⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⢰⣤⣀⣋⣛⣁⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⣰⠋⢳⡄
⠀⠀⠀⠀⢀⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⣩⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⣤⠐⠿⡞⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞⠛⣡⢼⡛⠷⢯⣷⡀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠒⠚⠉⠀⠀⢸⡆
⢀⡞⣹⠷⠒⠿⣄⠀⠀⠈⠓⠦⢤⣄⣀⡄⠀⠀⠀⣸⣴⣣⢾⠷⠶⢿⢻⡞⠁⢧⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠛⠛⠳⣄⠀⠳⣄
⠉⠉⢻⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⣀⠿⣽⠀⠀⠀⢻⠙⠛⠻⠶⠶⢾⠏⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡼⠀⢸⠀⠀⠀⠀⣹⠀⠀⠈⢳⡀
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠉⠛⠛⢦⣴⡆⠀⠀⠀⠈⢦⠀⠈⠁⣰⠋⠈⠀⠀⠀⢻⡀⠀⠀⠀⣰⠋⠀⠀⠈⠳⢤⣤⠴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣤⣤⠤⢿⣸⠇⠀⠀⠀⠀⠈⢧⡀⣰⠃⠀⠀⠘⠀⠠⠈⣇⠀⠀⠀⢿⡀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⢀⠀⠀⠀⢸⡆⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⠀⠈⠀⠀⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠙⢦⣀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢰⢡⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⣠⠤⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⡟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⣀⠀⠀⢀⡞⣠⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠙⣦⠟⠳⣦⡟⣏⠹⣞⣦
⠀⢠⠶⠶⠶⠶⠚⠓⠓⠒⠒⠒⢲⡄⠀⠀⠀⠀⠀⣞⣛⣛⣛⣛⡇⠀⠈⢇⢹⢀⣤⣄⣠⡿⠋⠀⠀⠀⣏⣛⠛⢦⣞⢹⢠⡿⣆⠘⢧
⠀⠉⢻⠉⠉⠉⠉⠉⠉⠉⠉⢉⡏⠁⠀⠀⠀⠀⡴⠛⠉⠉⠉⠉⠑⢦⠀⠞⢀⢸⣄⠈⢹⡇⠀⠀⠀⠀⢀⣈⡟⣆⠈⢻⣸⠃⣼⣄⣨⣷
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⣞⠉⠙⢿⡳⠞⠁⠀⠀⠀⠀⠀⢻⠉⠉⠙⠛⠛⠉⠉⠁⢠⡇
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠶⢿⡶⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣀⣷⣠⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⡏⠐⠈⠙⣏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠒⠒⠒⠶⠟
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠻⠶⠶⣶⡿⢦⣧⡴⠋
⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠓⠲⠶⢤⣄⡀
⠀⠀⠀⣰⠿⢞⠳⠮⣍⡹⣯⣽⣇⣤⣀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠶⠒⠒⣖⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⣠⠀⠈⠉⠳⢤⡀
⠀⢀⡞⠁⠀⠈⠀⡄⠀⠙⢦⡸⢭⣳⣈⠱⡄⠀⠀⠀⠀⣴⢋⡀⠳⠀⠶⠀⠡⠆⢈⠳⡄⠀⠀⠀⠀⠀⢸⡷⣤⡈⠉⠓⠦⣤⡄⠀⠀⠙⢦
⠀⠸⡆⠠⠀⠀⠀⠀⠀⠂⠀⠹⡄⢿⣽⣇⢹⠀⠀⠀⠀⢷⣌⣁⣀⣀⣀⣖⣀⣈⣋⣁⣹⠀⠀⠀⠀⠀⢸⡷⢈⡇⢀⣩⡤⣤⣙⠶⣞⠀⣈
⠀⠀⠘⠦⣀⠈⠁⠀⢀⠀⠈⠃⠹⡄⣹⢾⣼⠀⠀⠀⠀⣸⣭⣭⠭⣍⣉⣩⠽⢯⣍⣩⠿⡄⠀⠀⠀⠀⢸⠟⠋⢠⣯⡴⡖⣟⣮⠷⠞⠋⠉
⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠠⠄⠀⢷⡷⢺⠃⠀⠀⠀⠀⠹⣦⠤⠶⠶⠿⢶⣶⠶⠶⠖⢺⠁⠀⠀⠀⠀⢸⠶⣄⢘⣦⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣄⣸⡴⠃⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⣈⣹⣦⡴⠋⠀⠀⠀⠀⠀⢾⠴⠛⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠒⢠⡀⠀⠀⠀⡾⣿⣿⣿⣿⣷⠀⠀⠀⢀⡄⢒⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠋⠀⡀⡀⠀⢻⣿⣿⣿⣿⠏⠀⢀⡀⡀⠉⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢄⣿⣿⣿⣆⠐⠉⠋⠛⠉⠀⣸⣿⣿⣷⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣧⡀⠠⢈⣻⣋⣽⣷⣌⠀⠀⠀⢀⣠⣾⣯⣹⡟⡁⠄⢀⣾⡇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢿⣾⣿⣷⡌⠤⡟⡈⠷⡷⡟⢷⡄⢠⡿⠻⢾⠺⢑⢯⠤⣡⡾⣿⣿⡿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠠⣌⢿⣺⣿⡳⣿⣿⣦⠀⠀⢀⣻⣾⣻⣷⣾⣟⣟⣏⡀⠀⢀⣴⣟⣷⢎⢾⢟⠟⣠
⠀⠀⠀⠀⠀⠀⠀⣀⡻⣟⡿⣏⣫⣿⣽⣿⡇⠀⢸⡿⠟⠛⢿⣿⣻⠟⢿⡇⠀⢾⣿⣾⣿⣟⣝⢿⡯⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣽⣟⣍⢷⣿⣿⣅⣀⣀⣼⣿⣠⡀⢸⡎⢠⠄⢈⣵⣀⣀⣸⣿⣿⣾⣩⣻⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣵⣭⣞⣿⣞⣟⡿⣟⣟⣏⣋⣰⡎⣝⡂⠀⣿⢹⡻⢿⣻⣷⣟⣫⣭⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠋⡁⢸⣾⡧⡷⢛⡽⣯⢿⣿⡿⢿⣿⡏⢁⣿⢀⣿⣿⡿⣽⢯⡓⢿⢸⣵⣾⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣜⡿⣿⣿⣯⣷⣭⣾⡿⣷⣬⣥⣱⣤⣠⣽⣼⣿⣶⣭⣾⣽⣿⡷⣿⣿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡿⠁⡟⢹⠏⢃⣁⠈⣿⣿⣯⣿⣿⣟⠁⣀⡙⠹⡏⢿⠘⠷⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡿⣫⣯⡟⠻⣿⣿⠟⢯⣿⣝⢷⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠛⣷⡿⢋⡴⣿⣿⣤⡛⢷⣾⡛⠀⣴⣴⣷⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢨⣦⣬⣿⣮⣵⣿⣤⣴⡀⠀⠑⠀⠉⣠⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⣴⠿⣿⣿⣿⣿⣯⣿⣿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢿⠿⢹⣿⣿⡝⢿⡧⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⣼⡧⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⢀⡤⠖⠛⠋⠙⠓⠶⣄
⠀⠀⢀⡞⠀⡤⠒⠙⠑⠒⣄⠈⣧
⠀⠀⢸⡇⠨⢀⣀⠀⠀⣀⠈⡇⢹⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀
⠀⠀⢸⡇⢠⡀⠉⢠⡀⠁⢠⠃⢸⠀⠀⠀⠀⠀⣰⣋⣠⠤⠴⠤⡈⠹⡄
⠀⢀⡞⠀⠀⡡⠦⠴⠤⠶⡁⠀⠈⣧⠀⠀⠀⠀⡇⢸⢁⡀⠀⢐⡘⡦⣿⠀⠀⠀⠀⢀⡴⢚⣉⣉⠓⢦⡀
⢀⡞⠀⡀⠸⢀⡴⠋⠳⢄⠸⠀⠀⢈⢧⠀⠀⢀⣇⡰⡀⠁⡤⠈⢠⠃⢼⠀⠀⠀⠀⣾⢰⠯⠈⠉⠝⡆⣷⠀⠀⠀⠀⣠⠴⠒⠲⠦⡀
⣸⠻⠓⠁⠉⠁⠀⠀⠀⠀⠈⠁⠙⠻⢻⡆⠀⡼⠁⢀⠜⢲⣐⠒⢳⠒⠘⣆⠀⠀⠀⣿⢨⡈⠁⡄⢁⠌⢽⠀⠀⠀⢰⣇⡶⠉⠉⢶⢹⡄
⣿⠀⠀⠀⠀⠄⠢⠀⠀⡘⠂⠄⠀⠀⢸⡇⣼⣃⣙⠨⠕⠋⠀⠙⠮⠅⣀⣘⣇⠀⣰⠃⢀⡞⣲⣖⠃⡀⠘⣆⠀⠀⢸⠇⢄⠡⠌⡸⠸⡇
⢸⡈⡤⠀⠀⠃⠀⠁⠀⠀⠀⠁⠀⡼⢸⠁⡇⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣿⢰⡧⠄⠀⠋⠁⠈⠙⠂⠠⢼⡆⢠⡏⠠⢎⡽⢯⡱⠀⢳⡄
⠈⣇⠈⠢⡀⠀⠀⠀⠀⠀⠀⣀⠔⠁⡟⠀⣧⢂⠀⠀⠙⠀⠀⠀⠀⠄⠀⡀⡿⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⣾⠋⠉⠀⠀⠀⠈⠉⠹⣷
⠀⠸⡆⠀⠈⠑⠂⠐⠀⠒⠈⠀⠀⣼⠁⠀⢹⡈⠢⡀⠀⠀⠀⠀⠀⣀⠖⢰⠇⠘⡏⢄⠀⠀⠀⠀⠀⠀⡠⢺⠇⢻⣆⠀⠠⠀⠀⠀⠀⣰⡏
⠀⢸⣍⠒⠠⠤⠄⢀⡀⠤⠤⠐⢚⣹⠀⠀⠀⢷⠀⠈⠁⠂⠒⠒⠈⠀⢀⡟⠀⠀⢹⡀⠑⠂⠠⠤⠐⠊⢀⡟⠀⠘⣇⠑⠤⠀⠀⠄⠊⣸⠁
⠀⠀⠈⠙⠒⠶⠤⠴⠦⠤⠶⠒⠋⠁⠀⠀⠀⠈⠓⠲⠦⠤⠤⠤⠴⠖⠋⠀⠀⠀⠀⠙⠲⠦⠤⠤⠤⠖⠛⠀⠀⠀⠘⠲⠦⠤⠤⠴⠖⠃

⠀⠀⠀⠀⠀⣠⣶⣿⣽⣷⣶⣄
⠀⠀⠀⠀⢸⣿⢿⠅⠉⢩⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⢸⣿⠘⠃⠀⠘⢁⣿⡃⠀⠀⠀⠀⠀⣼⡿⠋⠉⠙⢿⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣸⢯⢷⣤⣤⣤⢾⣼⡇⠀⠀⠀⠀⠀⢻⠃⡄⠀⢠⢘⡗⠀⠀⠀⠀⠀⣸⠿⠛⠳⣇
⠀⠀⠀⣰⣻⣯⣽⡶⣟⢾⣏⢿⣿⡄⠀⠀⠀⠀⢸⣧⡀⠀⢀⣼⡅⠀⠀⠀⠀⠀⢧⡐⠀⢂⣼⠀⠀⠀⠀⠀⡞⠉⠉⢂⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣟⠋⡩⣵⢷⣤⣼⣤⣉⠟⣿⡀⠀⠀⣐⠉⣿⣿⠿⣿⣿⠁⣀⠀⠀⠀⢀⣮⣅⣀⣈⣵⡀⠀⠀⠀⠐⣧⠂⠀⣼⠀⠀⠀⠀⣼⠉⠉⣷
⠀⠀⠀⠘⠤⣴⣿⠉⣈⢙⡿⣤⠼⠃⠀⠀⠸⣟⣿⣿⡦⠶⢶⣿⣿⣿⠇⠀⢀⡾⣟⡟⢩⣿⣻⢷⡀⠀⢀⣾⣿⡿⣿⣽⣧⡀⠀⠀⣽⢀⡀⣿
⠀⠀⠰⠒⣖⠙⣿⢤⣠⣴⡿⢛⡖⠲⠀⠀⠀⠹⣶⣾⠃⠶⠘⣷⣾⠇⠀⠀⢸⡿⣾⣿⣿⣿⣷⢟⡇⠀⢸⢿⣿⣟⣿⣯⣻⡇⠀⠀⣿⣟⢳⣿
⠀⠀⠀⢈⡝⠂⠘⠿⠟⠟⠁⠓⣭⠀⠀⠀⢰⡦⣽⡇⠘⠶⠃⢸⣧⣶⠆⠀⠘⢶⣛⢿⡿⣯⠻⣶⠃⠀⢸⣷⣿⣨⣅⣯⡙⠅⠀⠀⢸⣷⣾⡇
⠀⠀⠀⠀⠀⠯⠛⠘⠎⠓⠳⠉⠀⠀⠀⠀⠀⠙⠾⣿⣞⠐⣳⣷⠷⠋⠀⠀⠀⠀⢿⣬⢭⡭⡽⠀⠀⠀⠀⠻⣿⣾⣿⣉⠏⠀⠀⠀⣹⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⣠⣤⡀⡀
⠀⠀⠀⠀⢀⣼⡟⠉⠉⡹⣿⡄
⠀⠀⠀⠀⠈⣿⢤⡈⠀⣈⢺⡇⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⢷⣤
⠀⠀⠀⠀⢠⣿⡈⠀⠀⠉⣼⣇⠀⠀⠀⠀⠀⠀⣿⠰⠄⠀⠆⢻⡆⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⣠⣟⣧⣄⣤⢤⣄⣤⣿⣦⠀⠀⠀⠀⠀⣿⣌⡀⠀⣨⣿⠁⠀⠀⠀⠀⢸⠳⠀⠰⢻⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⠀⢀⣿⣿⣇⣶⣷⣶⣶⢭⣿⡿⣇⠀⠀⠀⠰⠿⠿⠛⠻⢿⣿⣧⡀⠀⠀⠀⢸⣧⣄⣠⣾⠀⠀⠀⠀⢰⡟⠃⠀⠛⣿⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⢨⠝⣿⠉⢀⣨⣀⣹⡦⢻⡟⣽⠀⠀⠀⠀⢁⣠⣴⣦⣴⣂⠉⠁⠀⠀⠀⠸⡿⡿⢿⣿⠀⠀⠀⠀⠀⣿⣤⣠⣴⡏⠀⠀⠀⠀⣿⠃⠘⢻
⠀⠀⢿⣿⣿⣆⠘⢿⡯⠁⠀⣾⣿⣿⠀⠀⢴⣂⠺⣿⠉⠉⢹⡿⣀⣦⠀⠀⠀⢰⣷⣶⣶⣿⡀⠀⠀⠀⣼⣿⢟⣛⣿⣿⡆⠀⠀⢀⣿⣷⣶⣿⡄
⠀⠀⠘⠿⣿⠇⠈⠠⠄⠀⢠⢛⡿⠟⠀⠀⣌⣛⣁⠛⡀⢀⡈⣀⣉⣀⠀⠀⡴⢺⣿⣿⣿⠟⠃⡆⠀⢸⡟⣽⣏⣍⣿⡞⣟⡀⠀⠻⣡⡷⠾⣇⠙
⠀⠀⠀⠀⢻⡀⡀⠃⣌⢁⡅⣸⠁⠀⠀⠀⠈⢿⣯⣿⠁⠀⠁⠚⣿⠁⠀⠀⠹⣟⣿⣯⣿⣾⣻⠃⠀⠸⣿⡹⢿⣿⠿⣹⡿⠀⠀⠀⠉⢷⣶⠏
⠀⠀⠀⠀⠀⠙⠉⠀⠉⠀⠘⠁⠀⠀⠀⠀⠀⠈⠙⠛⠶⠒⠒⠛⠁⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠈⠛⠓⠓⠛⠋⠁⠀⠀⠀⠐⠀⠈⠒⠁

⣀⣀⣀⡀⡀⢀⢀⣀⣀⣀⣀⡀⠀⣀⢀⡀⣀⡀⡀⣀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⡿⠛⠋⠘⠙⠋⠋⠋⢐⡀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⡏⠁⠀⠁⠀⠈⡁⢈⠀⠹⢈⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠩⠋⠙⠉⠉⠉⠉⠛⠛
⣀⣀⣀⣈⣘⣒⣓⣛⣛⣒⣒⣀⣀⣐⣂⣀⣒⣂⣒⣒⣛⡀⠀⣀⣀⣀⣀⣀⣀⣘⣛⣀⣀⣀⣂⣂⣒⣐⣂⣀⣂⣀⡀⣀⢀⣐⣀⣚⣓⣒⣒⣒⣂⣈⣀
⣿⠿⠿⠿⡿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣛⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠙⢢⡀⣠⠤⠤⠄⣀⠀⣀⠤⠒⠀⠉⠉⠉⠐⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠤⠄⠿⣀⡍⠀⠉⠂⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⢀⠀⠈⠦⠊⠀⠀⠀⠀⢆⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⠉⠂⠀⠀⠀⢢⡀⠀⠀⠈⠣⡀⠀⠀⠀⠁⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⠀⠀⠙⠢⠤⠀⡽⠶⠀⠀⠞⠉⠓⠰⠶⠊⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠲⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠀⠀⠀⠐⠋⠉⠑⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠆⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢠⠊⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠓⢄⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⢉⠶⠤⠄⣀⣀⢀⣀⡀⠤⠐⢏⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠎⠀⠀⠀⣀⠠⠺⢄⡀⠀⠀⢀⠶⡀⠀⢀⣠⠜⠐⠂⠤⣀⠀⠀⠱⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⢘⡁⠀⠀⠀⠀⠈⠉⠉⠁⡀⠈⡉⠁⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠋⠡⡀⠀⠀⠀⠀⠘⡀⠉⠀⢠⠃⠀⠀⠀⢦⢀⠀⣬⠁⠀⠁⠚⠣⠤⠄⠠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠀⠀⢠⠷⠄⡖⠀⠀⠀⠈⠓⠴⠁⠀⠀⠀⠀⠈⡄⠉⠀⠈⠐⠂⠠⠤⢤⡀⠀⠀⢀⡸
⠀⠀⠀⡠⠀⠂⠈⠉⠀⢀⣤⠔⠊⠀⠀⢀⠁⠀⠀⠀⡠⠄⢴⠂⠀⡂⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⣇⠀⠀⣀⠔⠛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠤⢀⠀⠜⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⡐⠓⠠⠤⠤⠀⠒⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠂⠂⠐⠂⠉⠀⠀⠁⠂⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⣠⠔⢆⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠲⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠊⠉⠀⠀⠀⠈⠐⠢⡄⠐⠂⠉⠃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠱⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠈⢄⠀⣠⠾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣀⢼⠻⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠀⠀⠈⢦⣄⢠⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⢀⠴⠈⢦⡀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⢠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠥⠬⢍⡁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣁⠴⠿⢍⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⠀⠀⠀⠀⠈⢂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠏⠀⠀⠀⠀⠈⢙⢷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠂⠀⠐⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠒⠂⠀⠘⠂⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠀⠀⠀⠀⠀⠀⣤⠺
⠀⠀⠀⠀⠀⠀⢀⣷⡄⢀⠀⠀⠀⠀⢀⠀⣴⣧⠀⠀⠀⠀⠀⠀⠀⢀⠁⠚⢀⢸⡶⠐⠒⢀⠉⠁⠁
⠀⠀⠀⠀⠀⢀⢸⠁⡇⢸⠁⠁⠂⠀⢸⡆⣽⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⡷⢺⣷⣼
⠀⠀⠀⠀⠀⠌⠠⠠⣷⡈⠢⣀⣀⣠⠈⣀⡿⠂⠌⠂⠀⠀⠀⠀⠂⢒⡀⠀⠈⢫⣁⡀⡹⠿⡀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠒⠀⠒⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠈⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⡤⠚⠉⠒⣄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⣴⡻⠹⣳⡄⠀⠆⠠⠀⢠
⠀⠀⠀⠀⠀⡄⠀⠀⠡⠂⢇⠀⠀⠀⡕⠠⡀⠀⠀⡄⠀⠀⠀⠈⡀⢤⠀⠃⠄⣗⠢⠠⠳⠇⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠑⠒⠉⢁⠀⠁⠀⡐⠀⠀⠀⠀⠀⠐⠀⠤⠘⠀⠈⠀⠀⠀⠀⠄⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⢁⢀⣂⣀⠁⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠈⡴⣤⣄⣈⣀⣈⣁⣀⣬⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⠤⠭⣭⣭⠭⠽⠿⠛⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡠⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢀⠠⢐⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⣀⣢⢠⣈⣀⣥⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡿⠂⠀⠀⡐⢁⢲⡀⠀⠸⠀⠀⠀⠀⣠⠤⠶⠶⠿⠿⢶⡄
⠀⠘⠈⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠾⠀⠀⠀⠀⠀⠛⢾⡡⠀⢁⡆⠀⠀⠀⢹⠀⠀⠀⠄
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠠⠀⠀⠀⠀⣶⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡄⠀⠀⠐⠀⠀⠀⠐⠒⠘


⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⠀⢀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢘⠆⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠰⣆⠀⡀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⡄⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠠⠂⠀⠀⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠲⢎⠣⣄⠀⠀⠈⠀⡃⠈⠠⠈⠀⠠⠀⠑⠠⠀⠀⠀⢀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⢙⡧⠄⠀⠀⠀⠀⠐⠨⠤⠒⠀⠡⠀⠀⠀⠀⡁⢈⠀⠠⠋
⠀⠀⠈⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣠⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠊⠀⣀⣤⣤⣀⡈⠀⠀⠀⠀⣿⢿⡄⢸⣟⠖⠁⠀⠀⠀⠀⢀⡨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄
⠐⠀⠂⠀⡰⢛⡅⠈⠀⠁⠀⠀⠰⠀⠀⢨⠉⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⢋⣀⣠⡠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠨⡀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠠⡬⠀⠀⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢀⠀⠀⠀⠀⠀⢀⣠⠄⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢀⠂⠈⠂⠀⠀⠀⢠⡏⠃⠀⠀⠀⠙⡆⠀⠀⠀⡀⠔⠒⠂⠀⡀⢀⠠⠀⠀⢀⠔⠀⠀⠀⠑⠄
⠀⣀⠀⠀⠐⠚⠛⠛⢲⠇⠀⠀⢀⠈⠀⠂⠂⠀⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⢈⠀⠀⠒⡄⠶⠀⠒⢄⡜⢂
⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢆⠤⠁⠔⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠘

⠀⣀⠀⠀⠀⠀⡀
⢀⠀⠀⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⣰⣤⣤
⠀⠀⡀⠙⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠃
⠀⠀⡇⠀⢣⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⡜⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠦⡀
⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠶⠒⠃
⠀⠀⢀⠀⠸⠀⠀⠠⠀⠘⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠄⠄⠤⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠙⠍⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⣠⣴⡖⠲⠶⠶⢤⣀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢀⡴⠋⠂⠑⢌⠀⠐⠀⠐⣮⢳⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡞⢐⠁⠀⠀⠀⠀⠠⢈⡀⠀⣈⢻⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣸⠇⣁⣀⠀⠀⠀⠀⢀⣀⣀⠉⠉⠙⣷⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢻⠀⡉⠉⠃⠀⠀⠀⠋⠉⣉⠀⠀⠀⣼⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠹⣄⠀⠀⠠⠀⠀⠄⠀⠀⠀⣠⠏⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠞⠳⣦⣄⣀⣀⣀⣠⣴⠞⠃⡀⠀⠈⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠐⢀⠀⠁⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⡈⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⡂⢀⡀⠀⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⢀⢀⠀⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠠⡀⠁⠀⠀⠀⠀⠒⣈⣀⠂⠀⣀⣂⠀⠀⠀⠀⠌⠀⠠⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡔⠁⢀⠀⠀⠀⢸⠀⠀⠈⣇⡜⠉⠀⢰⠀⠀⠀⠀⠃⢂⡞⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⡆⠀⠄⠄⠀⢀⣳⣤⡀⠘⠁⢀⣠⠞⠀⠀⠀⠀⠉⢙⢦⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⡃⢠⠀⠀⠜⠁⠀⠀⠀⡀⢀⠁⠈⠉⠑⣄⠀⠀⠘⠤⡈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠜⠀⠀⠀⢐⠢⠤⠖⡽⠀⠀⢗⠦⣀⠤⠌⠀⠀⢀⠀⠈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠢⠀⠈⠂⠰⠆⢧⠀⠀⡼⠀⠄⠀⠘⠃⠀⡋⠂⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠠⢇⡀⠀⢄⠀⠀⡀⢱⠜⠀⠀⠄⠀⡀⠀⣠⠞⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠻⡀⠀⡄⠐⠌⢸⢠⠀⠄⢂⡜⠀⡸⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⡡⠀⠀⠆⠁⠸⣼⠀⠨⠄⠀⠀⡀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠚⠠⢘⣂⠀⠀⠼⠼⠄⠀⠀⢐⣀⠭⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⡀⠀⠀⠀⠉⠉⠉⠁⠁⠉⠉⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣤⣀⣀⣀⣠⣀⣠⣤⠤⠖⠋
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠃⠀⢸⢇⣦⠶⣆⣶⣷⣲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡇⠀⠈⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢱⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣶⣦⣴⣴⣧⠀⠀⠀⠀⠀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣆⣻⡉⣽⣍⣽⠀⢀⠀⢀⣾⣿⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣠⣿⣶⣟⣿⣿⡹⢿⣻⠏⢨⣼⣆⣿⣿⣿⣿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠻⣿⡗⣿⢋⣧⣾⣿⣸⠟⢛⢿⡏⢽
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⣿⣰⢶⡇⠀⠀⠀⠀⢀⣾⣿⣿⣷⣠⣾⣿⠷⠾⢿⣿⣿⡍⣠⡼⣾⣶⣿⡇
⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⢨⣿⣾⣿⣷⣿⡇⠀⠀⠀⠸⣼⣏⡿⠾⢥⣷⣿⠛⠀⠘⠿⠻⣷⡟⣾⣟⢻⣿⣿
⠀⠀⠀⣀⣸⣿⣷⣀⣠⣤⣴⠔⠐⠀⠦⣿⣇⣴⣤⡄⠘⣿⣿⣷⣾⣿⣣⣀⡀⠠⠀⠀⠀⠈⠛⢿⣿⢸⣿⡇
⠀⠀⠀⠉⠋⠛⠹⠋⠛⠛⠚⠆⠌⠀⠀⣿⣿⢯⣿⣷⣯⣷⡾⡷⡶⠦⠀⠱⡀⡰⠀⠀⠀⠀⠀⠀⠱⢾⣶⣧⡀
⠀⠀⠀⠀⠀⠀⢀⢀⢸⡠⠀⠀⠀⠀⠠⣟⣩⣍⣯⠟⠻⣽⣶⡃⠓⣤⡠⠀⣅⠀⠀⢀⣱⠀⠀⠀⠀⣤⡽⣿⣟
⠀⠀⠀⣀⣎⣭⣇⣄⣹⣀⣄⡀⣠⣀⣀⣿⣿⣷⣿⡹⣧⠇⢼⠁⠤⢼⡧⣦⡧⣠⡠⠸⢿⠴⠦⠴⠤⠾⠶⠾⠟
⠀⠀⠀⠗⠏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⢹⠁⠄⠒⡗⠂⠀⣠⠰⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⡀⠓⠶⢦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣤⣍⣙⣛⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣤⣄⠹⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣾⣿⢿⣿⣡⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⣀⣾⡿⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢀⠀⠀⠀⠀⠈⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢲⡀⢀⡀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⡑⠠⡀⠀⠀⠀⠀⠀⢳⣐⠂⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠈⡀⠑⢄⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠁⠀⠀⠃⠀⠀⠑⠄⠆
⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢣⡀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠴⢅⠈⠉⢵⠀⠀⠀⠀⠀⢀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠄⡀⠀⠀⠀⣀⡠⠐⠁⠀⠀⠡⡀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐
⠀⠀⠀⠀⠄⠀⠄⢀⠔⠀⠀⠀⡄⠁⠐⠄⠀⠀⠀⠀⠀⡉⠢⠀⠄⠄⠁⠊⠙⠠⡀⠀⠀⠂⠠⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠁⠀⠠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⡄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢃⠀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠈⠡⠀⠀⠈⢠⠤⠄⠀⠂⠉⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠈⠑⠀⠠⠂⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠒⠄⡀⠀⠀⠀⣀⠊⠀⠀⠀⠰⠋⠀⠀⢀⣌⣠⠁⠔⠂⠉⠐⢧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠄⠀⠄⣀⠓⠀⢀⡀⠀⠈⢀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⢀⠊⠀⡀⠀⠀⠁⠲⣀⣂⡀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢀⠠⠄⢒⠀⠀⠀⠀⠀⠈⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠔⠉⣆⠀⠀⠒⠶⠂⠒⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢁⠊⢀⠔⠐⠂⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⠀⡄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣃⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉

⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠐⢲⢀⠠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠂⠘⠁⠘⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠢⡰⣀⠀⢆⣇⢠⡐⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠀⠉⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠒⢒⣠⠒⠂⠀⠠⠄⡐⠀⠀⠘⠻⠛⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⣀⣀⠀⠀⡔⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠈⠁⠀⠀⢀⠀⠁⠀⠈⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡀⠺⡏⠺⢄⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠐⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣧⣾⡀⢀⠄⠙⣦⣆⠀⠒⢚⣡⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠄⠠⠀⠰⢀⢤⠀⠄⠀⠠⠠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠠⢼⡿⠛⣦⠀⡄⠒⢹⡇⢄⠀⠀⠉⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠠⠀⢠⠀⠀⠻⡇⡠⠇⠀⠐⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠠⠇⡀⠀⣠⣌⣞⠀⠒⡊⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣉⣁⠀⠤⠬⠝⠋⠙⠒⠒⠉⢉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⢀⣞⡉⡁⡀⠀⠂⣀⢀⣾⣿⣿⣄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠁⠀⠈⠁⠀⠉⠉⠉⠉⠙⠉⠛⠋⠉⠉⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣨⣤⣴⣶⣶⣦⣤⣄⣀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⣴⣿⣿⠿⠛⠉⠹⠙⠉⠛⠻⣿⣿⣦⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⠟⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠫⡻⣿⣧⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠡⠂⠀⠀⡀⠐⠁⡐⠃⠀⠀⠄⡀⠀⠈⠊⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⣿⣑⠠⠀⠀⠀⢀⠀⠂⠀⠀⠀⠄⡀⠀⠀⠀⠀⣸⣿⣷⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠂⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⡀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠀⠀⢀⣿⡿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⡆⢈⡻⢿⣷⠶⠀⠠⠀⠀⢤⠀⠶⣾⡿⢟⡁⢰⠉⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠤⡙⠃⠐⠁⡐⠀⠡⢀⣀⢌⠀⠠⠀⠠⠘⢋⠤⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢤⣰⠁⠀⣘⠐⠀⠀⠀⠀⠀⠈⡁⠄⠐⠀⠀⠀⠠⣅⠀⠈⣆⡄⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⡄⠤⠀⠀⠀⠀⠀⠀⡘⢃⡟⢃⠀⠀⠀⠀⠀⠈⠠⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡿⠿⢰⣾⡇⢰⡦⠈⠀⡔⠈⠁⢨⠀⠀⢰⡆⢸⣷⡆⠿⢿⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣻⡏⣴⣿⣳⡹⣶⡶⠒⠲⡍⠀⠀⠀⠀⢩⠖⠒⢶⣶⢏⡞⣿⣦⢹⣟⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣣⡻⠿⢞⣼⣯⡀⠠⣀⠄⠔⢠⣄⠡⠠⣀⠄⢀⣽⣯⡳⠿⢛⣜⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠿⠋⢻⡿⠈⠉⠱⠀⠦⠈⠀⢠⣥⠀⠀⠴⠀⠎⠉⠁⢿⡟⠙⠿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠠⡁⠀⠖⠊⠀⡚⠁⠁⢂⡠⠊⠉⢪⠢⡑⠲⠀⢈⠄⠀⠀⡅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⠂⠡⠈⡒⠃⠀⠀⢈⠒⠀⣼⣧⠈⢐⡁⠀⠀⠘⢒⠁⠌⠐⡈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⡀⢈⢰⠈⠉⠄⠘⣿⡶⣫⣋⠺⣿⠇⠀⠌⠉⢢⢀⢠⡘⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡀⠀⠈⠓⣠⠴⢾⣿⢸⣗⢏⡷⣻⣿⠦⢤⡐⠁⠀⠀⡸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠀⠀⠘⠁⠠⠀⣾⡦⣽⣭⢵⣿⡄⠀⠀⠙⡀⠀⡨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣌⣒⠊⠀⠉⠀⠘⠏⠀⠈⠁⢀⣒⣮⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡄⢀⠐⠁⠔⢸⡄⠀⠀⠀⠀⠀⠀⠁⠀⣵
⠀⠀⠀⢀⡠⠈⠋⠆⢰⠆⣝⠀⠀⠀⠐⠐⠶⠚⠙⠿⠿⣖⡂⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡼⠎⠀⠀⡀
⠀⠀⠈⠐⠂⠀⡧⠐⠒⡠⠡⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠚⣿⡷⠀⣤⢠⠌⣍⢀⣀⣈⣉⡀⢀⡀⠀⠀⠈⠙⠒⠒
⠀⠀⠀⠤⡀⢶⠸⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⣿⡇⠀⠈⠻⠴⣧⣰⣄⣤⣠⡷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠃⠀⢰⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣷⣄⣤⣾⣿⣿⡿⠀⠀⢀⡀⠡⠔⠤⠀⠀⠀⡇⠀⠀⠀⠐⠒⠀⠡⡀
⠀⠀⠀⠀⠀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠁⠀⠀⠀⢀⣀⠀⢐⠇⠀⢠⠃⠀⣄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠸⠀⠀⠹⡇⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⣀⣴⠋⠀⠀⠘⢄⣀⢀⣠⣠⣶⡞
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠻⣷⣶⣾⣿⢃⡖⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠨⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠖⠋⠀⠀⠀⠔⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⢂⣿
⠀⠀⠀⠀⠀⠑⠀⡾⠀⠀⠐⢦⣀⣧⣀⣴⡷⠃⠠⢂⣱⣯⢧⠷⠾⣷⣄⠀⢐⠀⣏⠀⠀⠈⠻⣤⣀⣀⣀⣰⣦⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠃⠁⠈⠉⠆⠀⠀⠈⢻⡆⠀⠀⢹⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠡⠀⠀⠀⢴⡇⠀⠈⠒⢤⣄⣠⣼⣶⠿⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣤⣀⣠⡶⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣾⣎⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣄⠀⠀⠏⠀⠀⠀⠀⠠⠟⠃⠙⠁⡧⠠⠄
⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣟⠓⠀⠈⠳⣦⣄⣀⣀⣀⣀⣀⣴⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢲⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠤⢤⠞⠁⠀⠀⣸⡀⠀⠀⠙⢦⠤⢤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⢸⡦⠴⠖⠋⠁⠉⠓⠶⠤⣾⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⣀⢸⡄⠀⠀⠂⠀⠀⠂⠀⠀⣼⠀⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡀⠦⣄⣀⣀⡤⠆⣰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⡿⠲⠤⣤⡤⠴⠺⡷⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⡼⠁⠀⠀⣖⡆⠀⠀⠹⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⠁⠀⠀⠀⣈⡀⠀⠀⠀⠹⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠤⢤⡤⣤⠤⠤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠇⢿⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣶⣶⣬⣍⣉⣉⣉⣉⣉⣉⣀⣀⣈⣉⣉⣉⣉⣩⣭⣥⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢤⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠙⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⡋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⡅⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣒⡛⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣭⡍⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡶⠀⣾⠁
⠀⠀⠀⢀⣤⠖⠒⢦⣄⣿⡸⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡺⠃⣸⡷⠒⠒⡆
⠀⠀⢰⡏⠀⠀⠀⠀⠉⠻⣷⣾⣴⣶⡚⠓⠖⠂⠐⠒⠒⠋⠉⢁⣾⠏⠀⢀⠀⠇
⠀⠀⠸⡄⠀⠀⠒⠀⠀⠂⡈⢿⣵⡂⠀⣤⠶⠒⠛⠲⣦⡀⠀⣼⡏⠀⠀⠸⡆⢸⡀
⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠁⣼⠛⢿⣦⣝⠒⠒⠀⠒⠋⣡⠞⢹⡇⠀⠀⠀⠐⠸⡇
⠀⠀⠀⠀⠀⠑⣤⡄⣀⡠⣴⣋⠀⠀⢻⣿⠿⢶⣤⣾⣿⠃⠀⠸⣇⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠉⠛⠢⠄⣿⢀⠀⠈⢹⣷⣄⡀⠀⢿⡀⠀⠀⠀⠀⠘⣦
⠀⣀⡴⠶⠶⢾⣅⡀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠣⠤⣼⡀⠈⠛⠶⣌⣷⠀⠀⠀⠀⠀⠘⢷⡄
⣰⠏⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⢸⡇⠀⠀⣿⠈⡓⢤⡀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠙⠦⣄
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣸⣇⠀⠀⣿⠀⢘⠂⣿⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠦⣿⡄⣀⡴⠋⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠙⢷⣄⠙⠰⠦⣀⡀⢀⣠⣀⡀⢠⡿⠛⠁⠀⢨⣟⠉⠀⠀⠀⠀⢠⠏⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⣀⣈⣷⠴⠶⠟⠛⠉⠀⠈⢻⣆⣶⢷⣶⣾⡿⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⢰⠞⠛⠁⠀⠀⠀⠀⠀⠲⠀⠀⢀⡾⠉⡿⠻⣿⡿⠺⡏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡾⠿⠶⠾⠿⠶⡶⠶⣾⣿⣶⣶⢦⣤⣄⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢷⡀⠀⠀⠀⠰⠖⠻⢯⣭⣧⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣹⣿⣿⡿⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠈⠻⢦⣄⣀⣀⡄⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠿⠛⠛⠋⠉⠁⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢷⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠘⣿⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣤⣤⣤⣶⣾⡶⠊⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣅⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠙⢧⡀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠈⠻⣦⣼⡿⠁⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣶⡿⢛⣤⠚⠛⢻⡆⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠋⢡⣾⣋⣀⠀⣸⠇⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢿⣿⣿⣿⠞⢁⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣦⡉⠉⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⡦⢴⣶⡄⠤⠾⠶⣤⡤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠒⠋⠉⢙⣦⣄⠀⣼⠷⠀⠀⣠⣼⣄⠀⠉⢻⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠛⢡⣠⠖⠛⠈⣯⣀⣀⣼⣦⣤⣤⣼⣅⡀⠘⠿⠧⣄⠈⠓⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡎⠉⣴⡞⠛⣤⣤⣶⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣶⣧⡀⠈⠻⣦⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⣿⠉⢠⣶⣿⡿⠿⠿⠿⠟⠁⠀⠀⠙⠻⠿⠿⠿⢿⣿⣷⡀⠈⢳⡀⠹⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⣾⠁⣸⡿⠋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⣿⣄⠀⣵⡤⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⣠⡏⢀⠟⠀⠐⠀⠈⠉⠁⠲⣦⡀⠀⠀⢠⡶⠋⠉⠉⠁⠀⠀⠈⠻⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⠈⠀⠀⠀⠖⠐⣿⣛⣷⣄⠀⠀⠀⢀⡴⣾⣿⡿⠐⠆⠀⠀⠀⠁⠀⣀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠻⣦⡀⠀⠀⠀⠈⠳⢟⣋⣀⠜⠁⠀⠀⠘⠆⣈⣛⠻⠆⠀⠀⠀⠀⠀⠁⢻⠁⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢴⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢛⡓⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠈⢉⠛⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⣀⠈⠁⠀⠀⠙⠿⠟⠁⠀⢀⣤⣤⡀⣀⣄⣠⡀⠀⠙⠿⡿⠇⠀⠀⠀⠘⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠋⠀⣀⡤⠐⠛⠁⠀⠀⠘⠳⡶⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣄⠀⠈⠳⣦⠴⠖⠀⠒⠂⠰⢤⡀⠙⠻⠆⣨⠋⢠⠀⠶⠆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠈⢢⡀⠀⠀⣀⠀⠲⠄⠀⠠⣤⣀⠀⠠⠔⠋⠘⠃⡀⠐⢆⡀⠘⠦⢀⠀⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣘⡛⢷⡜⢛⠶⢄⠉⠰⠄⠸⣀⣀⠀⠉⠳⣄⠈⠳⢆⣀⡙⠶⢌⠉⠙⢦⡈⠻⠆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣁⢸⡷⠛⡷⠺⣷⣄⣈⠉⠀⠛⠦⠈⠀⠰⠄⠈⠳⡄⠈⠁⢀⣠⡀⠀⣠⡖⠀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠙⠋⢿⠂⣤⣈⠛⠛⠻⠿⢠⣶⣦⣄⠀⣀⡤⠶⢦⠀⠠⠞⣟⠀⠴⠆⣴⠟⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⣰⡾⢿⣿⡄⠀⠀⠀⣼⠀⠈⠉⠀⠈⠿⠦⠼⠷⡄⢻⣄⣉⡷⠀⠘⠷⠶⠾⠁⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣟⣠⣿⣿⡗⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⠿⠿⠋⠀⢰⣾⣿⣿⣦⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⠀⠀⠀⢀⡴⢾⣿⡋⠀⠀⢹⣿⣿⡶⠾⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠀⠀⠀⠀⠀⠟⠀⣿⣿⣿⠀⠀⢀⣤⣿⣄⠀⠀⠀⡇⠀⠀⣼⡿⣿⣿⣧⠀⣰⣿⠀⠀⠉⢿⣤⣀⠘⣿⣿⠀⠀⠹⣷⡀
⠀⠀⠀⠀⣾⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⢘⣿⠿⠟⠁⠀⢠⣟⠙⣿⣿⡇⢀⣼⣿⣦⡀⠸⣆⣹⣿⡟⠀⠿⠉⢻⡿⠛⢿⣿⡿⠛⠉⢻⣿⡶⠶⣿⣧
⠀⠀⠀⠀⣿⡇⠀⢻⣧⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢧⣼⣿⡿⠃⢸⡏⢻⣿⣿⠀⠈⢻⣏⠁⠀⠸⣦⣼⣧⣄⣀⣹⣧⡀⠀⠸⣿⠀⠀⠘⣿⣆
⠀⠀⠀⠀⢹⣿⡀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠀⠀⠘⣧⢾⣿⠟⠀⠀⠀⠁⠀⠀⠀⠉⠹⡟⠁⠙⢻⣿⣿⠷⢦⣴⣿⡿⠶⣾⣿⡀
⠀⠀⢸⡆⠀⠻⣿⣦⡀⠈⠛⠿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣷⡶⠦⣤⣿⠁⠀⠀⢹⣿⡀⠀⠘⣿⣧
⠀⠀⠘⣷⡀⠀⠈⠻⢿⣶⣤⣀⣀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⣆⠀⠀⣋⠙⢯⡀⠀⠈⢻⣷⣦⣤⣤⣼⣿⠟⢷⣿⣿⡄
⠀⢤⡄⠈⠻⣶⣄⣀⠀⠈⠙⠛⠛⠿⠶⠶⣶⣦⣄⣀⣀⠀⠈⠉⠛⠿⣿⣦⡀⠀⠀⠀⢸⡧⣸⣿⣿⠂⠈⣿⣶⣾⡿⠟⠻⣿⡇⠀⠀⢹⣿⣇⠀⠀⠻⣿⣇
⠀⠈⢿⣦⣀⡈⠉⠛⠿⠿⠿⠷⢶⣤⣤⣄⡀⠈⠉⠙⠻⢿⣶⡀⠀⠀⢸⣿⠇⠀⠀⠀⢸⣴⠿⠟⠃⠀⠀⠈⣁⠙⣧⣄⣀⡈⣷⣦⣤⣄⣩⣿⡿⠿⢷⣿⣿
⠈⢿⣦⣈⡛⠻⠷⣶⣶⣦⣤⣀⣀⠀⠀⠙⢻⣦⠀⠀⠀⢈⣿⠇⠀⢀⣾⡟⠀⠀⠀⠀⠛⠁⠀⢀⣀⠀⢀⣼⠟⢳⣾⡟⣿⠛⠉⠻⣿⡀⠸⣿⣇⠀⠈⢻⣿
⢶⣦⣄⡉⠛⠲⠶⢦⣤⣄⠈⠙⣿⡇⠀⣠⣾⠟⠀⠀⣠⣾⠏⠀⣠⣿⠏⠀⢀⣀⠀⠀⠀⠀⠀⠘⠛⠁⣾⠛⢦⣄⣽⣿⢻⣶⣤⣤⣼⡿⠷⣿⡿⠃⠳⣾⣿
⣾⣿⣿⣿⣿⣷⡄⢀⣿⠃⢀⣴⠏⣠⣾⠟⠁⠀⣠⣾⠟⠁⢠⣾⡿⠁⢠⡜⠻⣿⣿⡇⠀⠀⣀⠛⠂⣘⠛⣷⣾⢿⡏⠛⣿⣏⠀⠈⠻⣧⡀⣹⣧⣀⡀⢹⣿
⣿⣿⣿⣿⣿⠋⣰⠟⢁⣴⠟⢡⡾⠟⠁⠀⣠⣾⠟⠁⢀⣴⡿⠋⠀⠀⠸⣧⣴⣿⣿⠇⠀⠸⠿⠇⣸⡋⢳⣾⢻⣾⠛⢿⢉⣿⡷⠶⢶⣿⡿⠻⣿⠛⠙⢻⣿
⣿⣿⣿⠏⢀⣾⠃⣰⡟⢁⣼⠟⠁⠀⣠⣾⠟⠁⢀⣴⡿⠋⠀⠀⠀⠰⠟⠛⠛⠛⠉⠀⠀⢰⡦⢀⣿⠓⣾⠿⣿⡛⢻⣾⠿⣿⣇⣀⣀⢙⣷⣄⣻⣷⣼⣿⣽
⣿⣿⠃⣠⡿⢁⣼⠋⣴⡟⠁⠀⣠⣾⠟⠁⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⢸⡟⠻⣿⣿⡟⠛⣿⣿⡶⣾⡿⠛⢻⣿⠃⠈⢻⣿⡿⠇⠈
⣿⠇⢠⡟⢁⡾⢃⣾⠏⠀⢀⣾⡟⠁⠀⣴⣿⠟⠁⣠⣾⣏⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢿⣶⣿⢾⡟⠉⠻⣧⡀⠸⣿⡦⠀⠙⠿⠒⠀⠁⠀⢀⣶
⡟⢠⡟⢁⡿⢡⣾⠃⠀⣠⣿⠋⠀⣠⣿⠟⠁⠀⠀⣿⢀⣿⣿⡿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢿⣅⣀⣙⣶⣶⠝⠛⠀⠀⠀⠀⠀⠀⠀⢐⣤⠘⠷⣀
⢁⡾⢁⡾⠁⣾⠏⠀⣴⣿⠃⢀⣼⡿⠋⠀⠀⠀⢀⣿⠿⠿⠟⠁⠀⠸⣿⣿⠀⢠⣦⠀⢰⣶⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢠⠀⠀⢩⣤⠘⠷⣌⠙⢶⣤⠛
⠜⢃⡼⠃⣼⠟⠀⣸⡿⠁⢠⣾⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⢠⣀⠠⢶⡄⠻⢷⡀⠉⢓⣄⣈⠿⢮⡉⠓
⠀⣸⠇⢠⡿⠀⢸⣿⠃⢠⣿⠏⠀⠀⣀⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⠀⠀⠀⠀⠀⠀⠀⣄⢀⢴⣦⠘⠻⣆⡉⣦⣄⣸⠷⣶⡟⠷⣎⡉⠛⢶⣄⣙⣷
⠰⡿⠀⣿⠇⢀⣿⡇⢀⣿⡟⠀⠀⢠⠟⢹⣿⣿⡆⠀⣠⣄⠀⢠⣤⠘⠟⠀⠀⠀⠀⡀⠘⣤⡖⠙⢫⣀⡸⠿⣶⠉⠙⢯⣍⠛⣦⣄⠱⣦⣌⠻⣦⠖⠛⢣⣤
⠀⠀⢰⡏⠀⢸⣿⠀⣼⡿⠀⠀⠀⠘⣦⣼⣿⡿⠁⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢡⣞⠉⠓⣤⣌⠉⠳⣦⣀⠹⢷⣤⠙⠻⣏⠙⢦⡀⠙⣧⣀⢷⣶⠋⠉
⠀⠀⣼⠇⠀⣿⡏⢀⣿⠇⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠉⠳⣦⡉⠉⢳⣶⠈⠙⢧⡀⠉⣶⣄⣈⢷⡔⠿⡶⠉⠻⡀⠰⣦
⠀⠐⠟⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢤⡌⠛⢦⣾⡉⠙⣷⣄⠀⠓⣤⠈⠛⣧⠀⠙⣁⠀⢛⣄⢰⣦⣤⠿⡆⠉
⠀⠀⠀⠀⢸⣿⠁⢸⣿⠀⠀⠀⢀⣴⣤⡀⠀⠀⡀⠠⣶⠀⠛⠃⠀⠀⠈⢠⡀⠾⠙⢶⣞⠉⠻⣾⡁⠘⢣⡄⠉⢠⡀⠰⢶⠀⠙⢛⠉⠙⡇⠘⣀⠀⢋⡀
⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⢸⣿⠻⣿⣿⡆⢾⣿⠂⠀⠀⠀⠀⠀⠠⠄⣀⠿⢦⣠⡜⠉⠻⣦⠈⠹⣦⡈⠓⣄⠘⣿⠀⠀⢇⡀⠘⣄⠀⣤⣤⣼⡆
⠀⠀⠀⠀⢿⣿⠀⢸⣏⠀⠀⠀⢻⡴⣿⣿⠃⠀⠠⡦⠀⠀⠀⠀⢦⠀⠸⠿⣄⣀⡟⠳⣤⣶⠈⠳⣦⡘⠳⣀⣽⠇⠀⢷⣠⡾⠟⠀⠛⡀⠈⢡⡀⠛
⠀⠀⠀⠀⠘⣿⠀⢸⣿⠀⠀⠀⠈⠻⡿⠀⠀⠀⢀⣤⡀⠀⢠⠀⠀⡿⢧⡀⠈⡿⠷⣄⡘⠛⣆⢀⠞⢧⠀⣿⡁⢰⣄⢾⡏⠀⢸⣦⠘⠿⠆⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢠⣤⠈⠛⠁⡄⠀⢸⣷⡀⠀⢙⣿⣆⣠⠟⢷⡀⠘⢿⡀⢀⣿⠈⢃⣠⣿⠀⠉⣤⠞⢻⠀⠀⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢠⣶⣦⠀⠁⠀⣀⠀⠰⣦⡀⠀⢉⣶⣏⡀⣘⠿⣆⠀⢻⡇⠀⢰⡏⠀⢇⣸⣏⠉⣦⠀⢿⡄⠀⢿⡆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣉⠁⠀⢠⡀⠀⢶⡄⠀⠙⣶⣞⠁⠈⠿⣇⠀⠘⣿⠀⠀⣶⠈⠹⣀⣼⡏⠘⢂⣸⡧⠀⠱⣤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠉⠀⣄⡠⠿⢇⣀⡘⣷⢟⣀⠈⡿⣟⠀⡈⢿⡀⠀⣶⡄⠘⣇⡰⣿⠀⢰⣄⠿⠇⠀⣄⣠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣿⣧⣄⣼⡻⣯⣤⣈⠻⢯⣀⣈⠿⣁⠀⣰⡖⠀⢣⣄⣻⣇⣀⣶⣴⣿⣴⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⢛⡟⠛⣧⠈⢛⠛⣿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣍⣉⣉⣉⣉⣉⣉⣩⣿⣿⣟⣉⣙⣋⣉⣉⣉⣛⣉⣉⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠶⠀⠉⢉⠉⠉⠉⠉⠉⠁⠐⠖⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⡡⠄⢠⣀⠎⠁⠀⠈⣱⡊⠁⠀⠉⢀⣀⡄⢠⡉⠐⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢀⠀⡎⠀⢀⠠⣼⠶⠒⠀⠉⠹⠉⠉⠀⠒⠾⣥⠄⡀⠈⠂⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⣀⠂⠈⢀⠳⠒⡩⠒⠁⠀⠀⠀⢀⠆⢠⡄⠀⠀⠀⠈⠂⢑⠢⢟⠀⠀⠲⠄⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣄⠀⡴⠃⡠⠊⠀⠀⠀⠀⠀⢠⠉⠀⡎⠱⡀⠀⠀⠀⠀⠈⠑⢄⠑⢄⠀⣀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠊⠀⠘⠏⡠⠊⠀⠀⠀⠀⠀⢀⠴⠁⠀⠰⡄⠀⠐⢦⡀⠀⠀⠀⠀⠀⠢⡀⠛⡁⠀⠃⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⠀⢠⠁⡔⠀⠀⠀⠀⢀⠠⠚⠁⠀⢀⠔⠁⠐⢄⠀⠀⠈⠒⢀⡀⠀⠀⠀⠈⢆⠰⠀⠀⡇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⠚⠳⢆⠚⠀⡤⠒⠈⠉⠀⠀⠀⢀⠔⠊⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠉⠐⠂⢀⠈⠠⠳⠞⠢⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⠀⢰⡼⠂⠁⠀⠀⠀⢀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠀⠉⠐⢿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢣⣀⣘⠀⠀⣀⠤⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⣀⠀⠀⠀⣁⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡆⠀⢨⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⠁⠀⠀⠀⠀⣴⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣷⡄⠀⠀⠀⠀⢲⠀⠀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⠖⢃⠀⠀⠀⠀⠹⠿⠞⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠁⠀⠀⠀⠀⡎⠲⡉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠇⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣤⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⡤⠄⠒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⡐⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠂⠤⠤⠟⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠘⠣⠤⠤⠊⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⣿⡆⣾⣿⠀⠀⠀⠣⣀⠀⠀⣸⠂⠀⠤⠄⢠⠀⠀⠤⠀⢸⡇⠀⠀⡀⠂⠀⠀⢸⣿⡄⣼⡗⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢿⡟⣱⣶⣦⢹⣿⠃⠀⠀⠀⠈⢁⣤⣶⣄⣀⡀⠞⢣⣄⣀⣠⣮⣀⠀⠁⠀⠀⠀⢿⣿⢧⣶⢦⡙⣿⠟⠰⠆
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⣾⡷⣙⠗⢚⣴⣷⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣶⣿⣞⠲⢞⡱⣿⡦⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⡿⠋⠻⠇⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⢹⣿⣿⣿⣷⠈⠻⢿⣿⣿⣷⡀⠀⠀⠀⠀⠿⠋⠻⡇⠀⠀⠀⡀⢡
⠀⠀⠀⠀⠀⠀⡘⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠏⣯⠀⠀⠀⠸⣿⣿⣿⡇⢀⠀⠀⠀⡼⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⠊⢀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⢀⠔⠁⢀⠀⢿⠀⠀⠀⠀⢹⣿⠟⠀⠀⠑⠀⢸⡇⠰⠀⠑⢤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⡀⢠⡦⠀⠀⠀⢁⠘⠀⣀⠠⢘⡇⠀⠀⠈⠀⠌⠰⡀⢄⡀⠈⠀⠀⢀⣀⠔⢠⠘⡀⠀⠀⠀⠀⡿⠂⠄⣀⠰⣀⠀⠀⠀⢠⡆⠀⡆
⠀⠀⠀⠀⠀⡷⠀⣀⠀⠀⠐⠂⣹⠃⠀⠀⠈⠀⢂⠰⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⢀⠔⠁⠀⠇⠀⠘⠀⠆⠀⡄⠀⠀⢻⡍⠐⠂⠀⢀⡄⢰⡇
⠀⠀⠀⠀⠀⡇⠀⠿⠀⠀⠀⢠⠁⢠⠀⠀⠃⠀⠘⡆⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠁⠀⢀⠈⢠⠀⠀⠀⠸⠃⠀⡇
⠀⠀⠀⠀⠀⠃⢠⠀⠺⠀⠀⡄⠀⠈⠀⠛⠀⢀⠔⠑⡀⠀⠀⡄⢠⠌⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⠀⡠⠙⢄⠀⠈⠁⠘⠀⠀⠆⠀⠰⠄⢰⠀⡇
⠀⠀⠀⠀⠀⢠⡌⠀⠀⠇⡤⠀⠀⠀⢿⣀⡔⠁⠀⠀⠈⠢⢀⣡⠂⠀⠀⠀⡄⡀⠀⠀⠀⢣⣇⡠⠊⠀⠀⠀⠙⣦⢼⡇⠀⠀⠀⠂⡆⠀⠀⣴⠁
⠀⠀⠀⠀⠀⢸⡧⠤⠄⢼⠦⠤⠀⡐⠉⠀⡇⠰⠦⠀⠀⠀⠠⠙⠠⠄⢀⣀⣰⣅⣀⠀⠠⠜⡁⠄⠀⠀⠀⢶⠄⠂⠀⠀⠒⠀⠀⠾⠦⠤⠄⣿
⠀⠀⠀⠀⠀⠈⢷⠒⠀⡸⡆⠀⠂⠀⠐⢀⠃⠀⠀⠀⠀⢀⢀⡸⠀⣰⣷⣄⠀⢀⣴⣷⡄⠐⢀⢀⠀⠀⠀⠀⠀⠇⢠⠋⠀⠠⠀⢰⡆⠐⠰⠆
⠀⠀⠀⠀⠀⠀⢹⠃⠘⡇⠙⢄⡀⠀⣰⠂⢠⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠸⣄⠀⢀⡴⠃⠈⠁⢺⠃
⠀⠀⠀⠀⠀⠀⠀⡆⠀⡃⠀⢀⣈⡉⠀⠀⠈⡄⠑⠒⠀⠰⣶⣶⣶⡞⢃⣤⣶⢦⣌⠹⣶⣿⣿⠆⠀⠐⠒⠂⡙⠀⠀⠈⣉⣁⠀⠀⢀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢇⠀⠀⠀⠈⡇⡤⠒⣧⡀⠀⠀⠀⠈⠻⣿⡁⣿⣧⠶⡎⢻⡆⣽⡟⠋⠀⠀⠀⠀⢠⡗⠲⢀⡌⠀⠀⠁⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠳⢤⢀⣴⠃⠐⠀⠎⠑⡄⠀⢀⣴⣿⣿⣇⠘⢷⣗⣦⠟⢡⣾⣿⣷⡄⠀⠀⡐⠈⠣⠐⠈⠑⣤⡀⠤⠞⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢀⠀⣈⠋⠠⠤⡈⠢⡀⠉⠉⠉⢹⣷⣶⡤⣤⣾⣿⠉⠛⠋⠁⣠⠚⣀⠤⠀⠉⡁⢀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⡀⠈⠀⢈⡇⢀⣀⠈⢦⡙⠦⣀⠀⢸⣿⠟⠁⠘⠿⡟⠀⢀⡠⠞⢠⡞⢀⢀⡀⢮⠁⠀⠀⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡁⠀⠋⢰⠀⠀⠀⢈⡗⠀⠀⠉⠀⡤⣤⡄⣠⣤⡄⠈⠁⠀⠀⢉⠀⠀⠀⢸⠀⠓⠀⣙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⠀⠑⠆⠐⠟⠀⡀⣦⠀⠀⠀⠀⢹⠃⠀⠈⠀⢀⡄⡁⠈⠷⠂⠖⠊⢀⡄⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉⠐⠂⠤⢼⣤⣠⡇⠉⠒⠄⠐⠋⠓⠢⠀⠒⠁⢫⣄⣴⡆⠄⠒⠈⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠒⠒⠒⠒⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠠⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠀⠒⠂⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠙⣿⠛⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠰⣁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⠔⠉⡆⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠪⣗⡤⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⣀⡜⠉⠀⠀⠀⠈⢹
⠀⠀⠀⠀⢶⠐⠋⠿⠈⢧⡴⠄⠖⠃⠀⣼⠂⢷⣄⣀⠀⢰⣫⠀⠒⠉⠀⠀⠀⠀⢀⡠⠤⠓⠒⡆⠀⠀⠀⠙⠁⠀⡤⠒⠐⠛⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⣠⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠚⠒⠦⣤⡀⣠⢾⣿⣤⡖⠚⠀⠀⠀⠀⠀⠓⡤⠔⠀⠂⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠠⡞
⢺⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢂⢇
⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠈⠱⠄
⠣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠘⢦⡀⢙
⠠⢏⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⡀
⠀⠀⡼⠀⠀⣠⠔⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠘⣿⣄
⠀⠀⢹⠀⠀⢃⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠸⣅⡷
⠀⠀⠸⣃⠀⡟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠉⢦⣀⠀⣀⠀⠀⡇⢻⡆
⠀⠀⠀⠘⠋⠁⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠚⠒⢄⠨⠉⠉⠒⠒⢄⡀⡠⠖⠚⠒⠁⠀⠀⠀⠀⠈⠛⢩⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠗⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠚⠉⠳⠤⢰⠀⠰⡋⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣮⣍⣤⣬⣭⣏⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠸⣿⡇⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⡏⡃⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⣤⣤⣤⣤⣉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣰⠾⣛⡭⣾⡯⣙⠺⢷⣄⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣾⠗⣛⡭⠖⠁⠙⠮⣝⣲⠬⣷⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⡗⠫⠤⠄⠀⠀⠀⠀⠠⠬⠙⢾⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣼⢠⡖⢶⡶⠀⠀⠀⠀⢶⡶⢲⡈⢧⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠇⡄⠀⠒⠀⠀⠀⠀⠀⠀⠓⠀⢠⠛⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣶⡘⢦⡀⠀⠠⣬⣤⠄⠀⢀⡴⢃⣶⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⡙⢀⠓⣀⡉⠒⢠⣤⣤⣤⠒⢉⣀⠎⡀⢉⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠈⠀⠉⢀⡞⣽⠷⣾⣦⢱⡀⠉⠀⠁⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⢠⡤⠄⠖⣛⣭⡆⢃⡼⠳⡜⢰⣭⣓⠲⠢⢤⣄⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⡛⢨⢇⡴⠞⢉⣠⣽⠷⠶⠶⠾⢯⣄⠈⠳⢤⠸⡄⢟⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⣧⣾⠻⠓⣴⠟⠁⣀⠄⠂⠐⠠⡀⠈⠻⣦⢚⠻⣷⣽⡉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠺⢿⠧⠔⠀⢸⠂⣽⣦⠄⢠⡖⠠⣼⣯⠐⡇⠈⠦⠼⡿⢷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠳⠼⠀⠀⢀⡜⠀⣼⡷⡀⠀⠂⢀⢾⣆⠀⢣⡀⠀⠀⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⢲⡖⢲⡇⠉⠚⠋⣧⡑⠰⠀⢊⣼⠛⠒⠁⢹⡖⢲⡶⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢦⠈⢳⡀⠀⣠⣴⡂⠙⠋⠰⢦⡄⠀⢀⡟⠀⡼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⢷⡈⠻⣦⣉⠙⠁⠀⠀⠀⠂⣀⣴⠏⢀⡾⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠹⢦⣀⠉⠛⠶⠶⠶⠖⠛⠉⣠⡴⠋⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠉⠑⠳⠦⠶⠶⠴⠞⠋⠁⠀⠀⠀⡠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠑⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣈⠉⠉⠐⠂⠀⠀⠈⢉⣁⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠆⠉⠉⠉⠉⠉⠉⠉⠁⠰⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⡈⢣⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠙⢦⣳⡄⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣹⣷⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠳⠦⣄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢻⣇⠀⠈⠹⢦
⠀⠀⠀⠀⢀⡼⠀⠀⠀⢀⢿⡇⠀⠀⢠⡎⠀⠀⠀⠀⠀⢀⡴⠛⣀⠀⠀⠀⠀⠀⠀⢀⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢸⡿⡀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⡸⠃⠀⠀⠀⢸⢸⡇⠀⠀⡞⠉⠁⠀⠀⠀⠉⠉⠀⠀⠉⠑⠶⠶⠶⠶⠂⠉⠀⠀⠈⠉⠁⠀⠀⠒⠀⠉⠉⢳⠀⠀⢸⠇⡇⠀⠀⠀⠘⢇
⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⢃⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡈⠀⡇⠀⠀⠀⠀⢻
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣶⠟⠉⣻⠀⠀⠀⠀⣀⠴⣿⡛⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⣷⠦⣀⠀⠀⠀⠀⣟⠙⠛⣤⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⠁⢀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣿⣿⡄⠸⠀⠀⠀⠀⡆⠀⠀⢹⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣷⡀⠀⠸⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⢀⠇⠀⣠⣾⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢀⡟⠀⠀⠀⠂⠀⠀⣸⠁⠈⠑⠲⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠖⠋⠁⠀⣇⠀⠀⠀⠀⠀⠀⢻
⠀⡾⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⡆⠀⠀⠁⠀⠀⠀⢷
⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⢧⡀⠀⠀⠀⠀⢳⣈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠛⠳⣶⠖⠒⠒⠒⠲⠲⡶⠟⠻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⡖⠀⠀⠀⠀⢀⣼
⠀⠀⠉⠓⠶⠶⠶⠞⠉⠉⠁⠀⠀⠀⠀⠀⣀⣤⠶⠊⠙⠋⠀⢀⠀⠀⠉⠁⠶⠶⠈⠉⠀⠀⡠⠀⠙⠋⠐⠶⢤⣀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠁⠀⠀⠉⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡼⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠳⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⢀⣠⠞⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⣹⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣏⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀
⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢶
⣇⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠉⠓⢦⡀
⠈⠳⠶⠲⠶⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠙⢦⡀⢴⠶⠒⠞
⠀⠀⠀⠈⠷⠋⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠙⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠈⠉⠁⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⠀⣀⣀⡀⣤⡤⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠓⠒⢤⣤⣤⣤⣤⠄⠒⢶⠂⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠢⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣀⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡄⠀⣠⡴⠚⠉⠉⠉⠉⣙⠲⢤⡀⢀⡤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠣⠴⣮⣿⠋⠁⠀⠀⠀⢀⣰⠾⠋⠀⠈⢯⡖⠛⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡤⢄⢈⣉⣽⡿⠁⣠⣤⣤⡀⠀⠘⠉⣠⣤⣤⡀⠀⢷⣉⡑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠤⡟⠁⠸⣗⣉⣾⠇⢀⡄⠀⣿⣊⣸⡇⠀⢸⣁⣉⡛⠉⠑⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⠋⢻⠀⠀⠉⠉⠁⢀⠀⡁⢀⠈⠉⠉⠀⠀⣸⠭⣅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠊⠀⣤⡼⠉⢧⡀⠠⠾⠖⠻⠉⠋⠟⠓⠷⠤⠀⡰⠳⡄⠈⠉⠙⠦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡷⢦⣀⣀⣀⣀⣀⣀⣀⣀⡤⢾⡤⣄⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣁⡽⠓⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠐⢻⣁⠉⠲⣤⡀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡄⠀⠈⠻⣶⣄⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠀⠀⠀⠀⠠⣾⠄⠀⢰⣯⣿⣲⣄⣠⣴⣻⣯⡇⠀⠀⢼⠄⠀⠀⠀⣀⠜⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢣⠄⠀⠀⠀⠀⢠⣿⠄⠀⠈⢿⢿⣿⣿⣷⣿⣿⣷⠃⠀⠀⢾⠆⠀⢾⣾⠁⠠⣸⠉⢦
⠀⠀⠀⠀⠀⢀⣤⡶⣏⠀⠀⠳⣅⣄⣠⠾⠛⣹⠀⠀⠀⠀⠻⣻⣿⣿⣿⡻⠁⠀⠀⠀⢺⠑⠢⣄⣀⣄⠵⠁⠀⢸⠷⣦⣄
⠀⠀⠀⠀⠀⠈⢀⡴⠟⣷⡖⠒⠚⣩⣤⡀⠀⣇⡀⠀⠀⠀⠀⠈⠺⠿⠊⠀⠀⠀⠀⢀⣸⡆⠀⠀⠉⠙⠒⠲⣾⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠛⠟⢧⣰⠙⠓⢶⣀⣠⠀⢀⣀⣀⣀⠀⣀⣀⣶⠞⠃⣧⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢤⡀⠀⠀⠉⠉⠛⣹⢹⠙⠉⠉⠁⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢦⡀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠀⢹⣻⠂⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢸⠁⠀⢧⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣠⠠⠀⠄⣠⡞⠀⠀⠸⣤⠀⠄⠄⢠⣰⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠉⠉⠉⣹⠁⠀⠀⠀⢫⠉⠉⠉⠉⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣀⣀⠴⠃⠀⠀⠀⠀⠈⠳⣄⣀⣴⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣩⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠉⠉⠉⠁⠀⠀⠈⠉⠁⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠰⡪⢶⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣠⡾⢝⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣸⠇
⠀⠀⠀⢀⠔⠊⢉⠄⡿⠁⠀⠔⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢋⠀⠈⠁⠢
⠀⠀⠔⠁⠀⠔⠁⠠⠀⠀⠊⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⣄⠌⣆⠀⠐⠀⠀⠠⡀
⢀⠎⠀⠀⠀⠀⠀⡇⡀⡟⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢸⠀⠀⠀⠀⠀⠱
⠈⠀⠀⠀⠀⠀⢠⡇⠁⡇⠀⠀⠀⠀⠦⠀⠀⠈⣀⠀⠀⠀⠄⠀⠰⠁⠠⠈⡀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠀⢡
⡇⠀⠀⠀⠀⠀⢸⠇⠀⢧⠀⡠⠂⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠄⠀⠸⠀⡜⡇
⢇⠀⠀⠀⠀⠀⢸⠘⣤⠚⡊⠀⣰⢿⢿⣿⠛⣧⠀⠀⠀⠀⠀⣸⢿⣿⠙⡿⣆⠈⢆⠓⢤⠁⡇⠀⠀⠀⠀⠀⡸
⠈⢆⠀⠀⠀⠀⠈⢇⢠⢀⠐⠀⢻⠸⡘⠿⢃⡞⠀⠀⠀⠀⠀⠳⡘⠿⢃⠆⠟⠀⠋⠀⡀⡰⠁⠀⠀⠀⢀⡴⠁
⠀⠀⠙⠂⠤⡀⠀⠀⢊⠢⣀⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠔⢁⠃⠀⢀⡠⠐⠉
⠀⢀⠊⠀⠀⠈⠐⠄⠈⡀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠀⢸⠀⠀⢁⠀⠀⠀⠠⡀
⢠⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠒⠂⠤⢄⣀⡀⠀⡀⣀⢠⠤⠀⠒⠉⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠑
⢸⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠔⣥⡖⠒⣂⡖⠓⣢⣸⠢⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠂⠀⠀⠀⢠
⠀⡧⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⢀⠔⠁⡐⠀⠉⠁⠇⢸⠈⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢼
⢰⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⡠⠈⠀⢀⠀⠀⠄⠄⠠⠀⠀⠄⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡆⠉⠢⡀⠀⠈
⠘⠦⠀⠁⠀⠀⢠⠀⠀⠀⡠⢆⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⢀⠵⢀⠀⠀⢀⡇⠀⠀⠈⠀⡴
⠀⠀⠂⢄⠀⠀⢸⠀⠀⠸⠀⠄⢉⠖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠲⡁⡤⠀⠃⠀⢸⡀⠀⠀⡤⠈
⠀⠀⠀⡸⠀⢀⡜⠀⠀⠀⠀⢈⡵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠁⠀⠀⠀⠈⢧⡀⠀⠇
⠐⠂⠚⠓⠊⠁⠀⠀⠀⠀⠠⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡇⠀⠀⠀⠀⠀⠉⠁⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠲⢤⡀⠠⠔⠒⢢⠤⣀⡀⠀⢀⣀⣠⠶⠅⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢸⠀⠈⡅⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡡⢒⣒⠒⣹⠀⢰⡇⢰⢒⠒⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⠀⠀⢸⠀⢰⡍⠀⠀⠈⢀⡇

⠀⠀⠀⠀⣠⠴⠚⠛⠉⠛⠶⢤⡀
⠀⠀⠀⡾⠁⣠⠔⠒⠖⠒⢦⠀⢹⡄
⠀⠀⢠⡇⢰⠁⠀⠀⠀⠀⠀⢱⠈⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⢸⡇⢸⠀⠉⢁⡀⠉⠁⡸⠀⣿⠀⠀⠀⠀⠀⣠⠞⢉⣀⣤⣄⡉⠳⣄
⠀⠀⣼⠃⠀⠑⣤⣀⢁⣠⡔⠁⠀⢹⡀⠀⠀⠀⢀⡏⢸⠃⠀⠀⠀⠘⣆⢹⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⣄
⠀⣴⠃⠀⠠⡊⢀⡴⠰⣄⣈⡦⠀⠀⢳⡄⠀⠀⢸⡇⢪⠈⠓⠀⠘⠃⡙⢸⡇⠀⠀⠀⢀⡏⣡⠚⠛⠙⢲⡈⣇⠀⠀⠀⠀⠀⣀⣤⢤⣄⡀
⢸⢧⠦⠀⠀⠒⠉⠀⠀⠈⠑⠒⠠⠤⢧⢷⠀⠀⣸⠋⠀⢡⢤⠩⡤⣞⠄⠘⣇⠀⠀⠀⢸⡇⡇⠳⠀⠐⠆⡇⣿⠀⠀⠀⠀⡞⣡⠶⠶⢦⠙⡆
⢻⠀⠄⠀⠂⠀⢀⠀⠀⠀⡆⢀⠀⠀⠠⢸⠄⣴⠣⠤⠴⢤⡴⠛⠦⡤⠆⠀⠘⣦⠀⠀⣸⠁⢈⡦⡬⡤⣞⠁⢹⡀⠀⠀⢸⡇⡋⠆⠀⠀⡇⣷
⢸⠰⠀⠀⡀⢄⠀⠡⠀⠘⠀⠠⠀⠀⡐⢸⢰⡟⠏⠉⠉⠁⠀⠀⠀⠈⠉⠙⠹⢻⡄⣼⠃⠀⠚⠰⠋⠳⢜⡂⠀⢻⡄⠀⡼⠁⡩⢦⣥⠮⡀⢻⡀
⠘⡇⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡟⢸⡇⡁⠀⠀⢠⠈⠀⠀⠀⠀⠀⢀⢸⠇⡿⠉⠀⠀⠀⠀⠐⠀⠀⠈⢙⡇⣸⡧⠄⠑⠋⠈⠛⠁⠤⣿
⠀⢻⡀⠈⠲⢄⡀⠀⡀⠀⡀⠴⠊⠀⣸⠁⠀⣇⠣⠀⠀⠀⠀⠀⠂⠀⠈⠀⠎⣼⠀⣷⠄⠀⠈⡀⠀⠀⠄⠀⠀⣸⡇⣿⡄⠀⠀⠀⠀⠁⠀⠀⣾
⠀⢀⡧⣀⠀⠀⠀⠉⠈⠁⠀⠀⢀⡰⣇⠀⠀⠸⡄⠑⠶⣀⠀⣀⠀⣀⠔⠊⢠⠇⠀⢸⡌⠢⡀⠀⠀⠀⠀⠀⠈⣸⠀⢸⡕⢄⠀⠀⠀⠀⢀⠔⡿
⠀⠘⠷⣌⣉⡃⠐⠒⠒⠂⠐⣋⣉⡥⠏⠀⠀⠀⢳⣀⠀⠀⠈⠀⠁⠀⠀⣀⡞⠀⠀⠀⢳⡀⠈⠉⠁⠉⠀⠀⣰⠇⠀⠀⢳⡀⠉⠒⠒⠊⠁⣰⠃
⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣷⣾⣿⣯⣥⣤⣤⣤⣤⣤⣭⣿⣷⣶⣾⣿⣯⣥⣤⣤⣤⣤⣭⣿⣷⣷⣿⣯⣥⣤
⣿⣿⣉⣭⣫⣬⣉⣿⣫⣿⣻⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⢊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⣀⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⠉⠉⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿⣤⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣶⠄⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣿⡿⠋⠀⠄⠈⠘⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⣾⡟⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣿⡇⠀⣴⣶⣦⠀⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢠⣿⣷⣹⣿⣿⣿⢳⡶⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢸⣿⣿⣿⣿⣿⣵⣿⡇⡅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⡏⠇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣥⣴⣶⣶⣿⡃⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⠿⠛⠉⠐⢿⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⠯⠭⠥⡭⣿⡇⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⣿⣿⣛⣚⣒⣒⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣷⣮⣦⣼⣿⡇⠀⠀⣾⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⣿⣿⣭⣥⣶⣶⣿⣇⠀⠀⢸⠀⠀⡏⢸⣷⠆⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠨⠀⠀⣧⣼⣿⣤⣤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠘⢻⣿⠿⠿⠿⠿⠿⠿⠃⠀⢸⠀⠀⣿⢹⡿⠃⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢠⡇⡀⠉⡲⣄⠀⢠⠄⠀⣀⣀⠀⠀⠀⣿⣿⡈⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣿⣸⠁⠐⠀⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⠚⠉⢹⠟⠋⠀⡀⠀⢉⡇⠀⠀⣿⣿⡂⢽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣿⣼⣿⣀⣌⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢀⣤⡆⣆⣀⣁⠙⣻⠾⣠⠆⠀⣿⡿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣀⡴⠃⠀⠀⣿⣹⣿⠋⠙⠋⢉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠢⠬⠭⠷⠚⠛⠋⠁⠀⠀⠈⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠐⠒⠁⠀⠀⠙⠛⠛⠃⠐⠂⠛⠊

⠀⠀⠀⠈⠙⢿⡗⢉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⡀⠀⣀⣀⣀⣀⣊⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠉⠉⢉⣉⣻⣍⣉⠉⠹⢿⣿⠟⠻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢷⣿⣿⠿⠿⠿⠿⠿⠟⠉
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢾⣿⡷⠷⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠞⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣼⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⠀⣀⣤⣀⡀⠀⢀⣀⣿⣿⣿⣿⣿⣠⡄⢀⣤⣶⣦⣄⡀⢠⡄⣴⣀⣾⣿⣿⣿⣿⣷⠀⡀⢠⠀⣸⣆⢀⣀⣀⣼⣿⡄⣀⣀⣀⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⡟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣼⣥⣾⣾⣿⣿⣦⣾⠯⣿⣿⣧⣥⣽⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⣿⣻⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡗⣂⢀⡂⣻⣿⣿⣿⠷⣾⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣇⣊⣈⣁⣹⣿⣿⣧⣠⣼⣿⣿⡿⣿⠷⢿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣀⣇⣾⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣶⣿⣿⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣦⣤⣴⠶⠿⠻⠿⠿⠷⣶⣤⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠛⠛⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠛⠻⠿⠃⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠀⠀⠀⠀⠀⠀⢠⣿⠋⠙⠻⢷⣤⣠⣤⣤⣤⣀⣤⣴⡶⢶⣄⠀⠀⠀⠛⠛⠻⢶⣦⣀
⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢹⣿⠀⠀⢙⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⢀⣾⠟⠁⠀⣠⡴⢀⠀⠀⠀⠀⣠⣼⠿⢷⠶⠶⠿⠛⠛⠿⠿⠿⣿⣤⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣀
⠀⠀⠀⠀⣼⡏⠀⠀⣼⠋⣴⠋⠀⠀⣠⡾⠋⣁⣠⣤⣤⣴⣶⣶⣶⣤⣤⣤⣀⣉⠙⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⣄⠀⠉⠻⣷⡀
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠷⣶⣤⣙⣿⣆⠀⠀⠈⢳⡌⢷⡀⠀⠘⣿
⠀⠀⠀⠀⠈⣿⣆⠀⢀⣄⡀⠀⠈⠋⠁⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡆⠀⠀⠀⠁⠈⠃⠀⠀⣿
⠀⠀⠀⢀⣾⠟⠁⠀⠀⢙⣿⣶⣦⣶⣶⠿⠛⢿⣦⣤⣀⣀⣠⣴⡾⠿⣷⣄⡀⠀⠀⠀⢀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⢀⣿⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣀⣀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋⠉⠻⢷⣦⣤⣴⣾⠟⠀⠀⢺⣯⡀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⡇⠀⠀⢀⣾⠋⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⣷
⠀⠀⠘⣿⣀⠀⠀⠀⠀⣿⡇⠀⠀⠸⠟⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠈⣿⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢈⣿⡿⠂⠀⠀⢻⡇⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠻⠁⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣧⠀⢿⣄⣀⢉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⣾⠃⠀⠀⣀⣤⣾⠟
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣄⣀⣠⡿⠀⣰⡟⠀⠀⠀⠙⢿⣅
⠀⠀⠘⢷⣤⡀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡿⠛⠁⠀⠀⠀⠀⠀⠰⣾⠟⠃
⠀⠀⠀⠀⣠⣿⠏⣀⣀⠀⠀⠀⠀⠀⣀⣤⣾⠻⣷⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⢰⡟⠁⣸⠛⠇⠀⢀⣠⣶⠿⢛⣿⡏⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⠏⢹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁
⠀⠀⠀⣿⠃⠀⠈⠀⢀⣴⡿⠋⠁⢀⣾⢻⣷⠀⠀⠈⠛⢷⣶⣤⣤⣶⠾⠛⠁⠀⣸⣿⣏⠙⢷⣤⠀⠀⠸⡿⡆⠹⣿⡄
⠀⠀⠀⢻⡇⠀⠀⠀⣾⠿⡄⠀⢠⣾⠃⠀⠻⢷⣶⣶⠶⠿⠛⠛⠿⣷⣤⣀⣀⣰⡿⠉⣿⡄⠀⠙⣷⣄⠀⠀⠋⠀⢹⡇
⠀⠀⠀⠈⣿⣄⣀⣼⣿⡄⠰⣦⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢸⣧⠀⠀⡼⢿⡆⠀⠀⠀⣸⡇
⠀⠀⠀⠀⣨⣿⠟⠁⠘⢿⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠆⢀⣾⣇⠀⠀⣰⡿⠁
⠀⠀⢀⣾⠟⠁⠀⠀⢠⣾⢻⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⡿⠋⠙⣷⣾⠟
⠀⣰⡿⠃⠀⠀⠀⣰⡿⠁⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣆⠀⠀⠈⢻⣦
⢰⡿⠁⠀⠀⠀⣼⡟⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢻⣆⠀⠀⠀⠻⣷⡀
⣿⡇⠀⠀⢠⣦⠈⣿⠀⣾⡇⠀⢰⠆⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⣆⠀⠀⠀⠹⣧
⠹⣷⣤⣴⡿⢿⡾⠏⢀⣿⠀⠀⠘⠰⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡦⢸⠀⠀⣿⡇⢰⡿⠋⣀⠀⠀⠀⣿⡆
⠀⠀⠈⠁⠀⠀⢀⣴⡾⠟⠘⢶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠃⠙⠀⠀⣿⡇⠸⣧⣼⣿⡄⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠞⠃⠿⣷⣄⠈⠉⠘⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⣶⣿⡀⠀⠀⠀⠈⠛⠀⠲⠶⠀⠠⣤⠄⠰⠶⠀⠘⠋⠀⢀⡀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⠟⠹⣷⣀⠀⣀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣿⣿⣤⣤⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠈⠛⠛⠛⣹⡿⠿⣶⣤⣀⣤⣴⣾⣿⠿⣶⣤⣴⡾⠋⠹⣯⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡛⠆⣀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠉⠉⠉⠁⠀⢹⡇⠀⠈⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⣼⣿⣷⣄⠈⠻⠂⢤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢀⣀⠀⠞⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡓⠈⠉⣁⣠⣾⣿⣷
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⣂⣡⣌⡐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣈⣈⣁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠔⣀⣌⣅⡂⢄
⠀⠀⠀⠀⠌⣴⣫⡄⢊⣭⣳⠁⠀⠀⠀⠀⠀⠐⢠⢞⢉⠋⣉⠷⠈⠀⠀⠀⠀⠀⢀⢀⣎⠍⠑⠬⢙⣆⠂
⠀⠀⠀⠀⠗⢧⠌⢁⡈⠡⣽⠲⠀⠀⠀⠀⠀⠀⠸⠈⢁⣀⠉⢈⠁⠁⠀⠀⠀⠀⢠⠸⡁⠀⣀⡀⠁⡕
⠀⠀⠀⠠⠐⢈⠲⢤⡠⠖⡁⠂⠄⠀⠀⠀⢀⡄⠀⠀⠂⠁⠐⠁⠀⢂⠀⠀⠀⠀⡈⠀⠑⠢⣄⠤⠊⠀⠠⡀
⠀⠀⢠⠁⠀⠆⢄⣹⣏⡠⠰⠀⠈⡄⠀⠀⠞⢣⠽⠔⠀⠄⠐⠰⢥⠋⢆⠀⠀⣠⣸⣄⣤⣴⡿⣷⣤⣄⣼⣥⡀
⠀⠀⣾⡧⡭⠬⢚⣁⣈⡑⠥⠬⣼⣷⠀⠸⠋⠎⢴⡶⠀⠀⠠⣴⡄⠃⠛⠄⢠⣿⡟⠛⣩⣥⡀⣠⣭⡉⠻⣿⡇
⠀⠀⢿⡡⠾⠆⠈⠻⠿⠃⠰⠷⢈⣿⠀⢰⠠⠄⣼⣧⠸⣿⢀⣛⡆⠠⢤⠀⠘⣿⡇⢸⣿⣮⣿⣯⣿⣷⠀⣿⡇
⠀⠀⠘⣷⡤⠐⠇⢠⡆⠸⠇⢠⣾⠃⠀⠈⢆⣈⠦⡀⠸⠿⠄⠀⠔⣀⠌⠀⠀⠻⣷⡀⠻⢦⣿⣧⠾⠁⣸⡿⠁
⠀⠀⠀⠈⠿⠷⢦⣤⣤⣴⢾⡿⠃⠀⠀⠀⠀⠳⡤⠬⠅⠀⠌⠤⡴⠊⠀⠀⠀⠀⠙⢿⠦⠄⠭⠥⠤⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⡠⠐⣈⣉⣀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠔⣀⣭⣅⡂⢄
⠀⠀⠀⠀⣼⣟⣩⡑⢢⣌⣿⣷⠀⠀⠀⠀⠀⠐⢠⢟⡉⠉⣉⠷⠈⠀⠀⠀⠀⠀⢀⢂⡞⠡⠐⠉⢝⣆⠂
⠀⠀⠀⠀⣿⣇⠌⢁⠈⠡⣼⣿⠀⠀⠀⠀⠀⠀⠸⠤⠁⢀⠉⠬⠁⡂⠀⠀⠀⠀⢠⠘⡀⠈⣀⡈⢀⡝
⠀⠀⠀⢠⣿⣿⣶⢤⡠⢶⣿⣿⣄⠀⠀⠀⢀⣄⠀⠀⠂⠀⠐⠁⠀⣀⠀⠀⠀⠀⡈⠀⠙⠲⣌⠴⠊⠀⠀⡀
⠀⠀⠠⠿⠿⠿⢟⡫⢌⡻⠿⠿⠿⠆⠀⢀⣶⣤⣅⣈⣀⣤⣈⣀⣥⣤⣦⠀⠀⡨⠀⠠⢤⠀⣿⡅⢠⢄⠀⠰
⠀⠀⠚⢉⡏⣉⣉⢔⠢⣍⡉⢩⠉⠛⠀⢸⢯⡽⣯⣻⣿⣿⣿⣿⡽⣿⣻⡆⠠⣽⣧⣿⠴⠛⠁⠙⠳⢼⣥⣯⡄
⠀⠀⠄⠆⠀⠄⣯⠲⣶⢿⡠⡀⠸⠐⠀⢸⣮⡳⣿⣽⠿⣻⢿⣿⡷⣟⣿⠇⠀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠘⡄⢄⠃⣘⢻⡟⣋⠐⡠⢢⠂⠀⠈⢿⣿⣿⣯⣿⣹⡷⣿⣿⣿⡟⠀⠀⠱⡸⡯⣩⢍⡍⢽⣉⡭⠡⡴⠁
⠀⠀⠀⠈⢢⣬⣄⣀⣀⣠⣵⡔⠁⠀⠀⠀⠀⠻⡿⠿⠶⠷⠾⠿⡿⠋⠀⠀⠀⠀⠑⢶⠶⠶⠶⠶⠶⠶⠞
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⣠⠶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢨⠉⡃
⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠄⠸⠀⠀⠀⠠⠀⠀⠀⠒⠀⠀⠀⢸⣶⣆⠀⠀⠀⠀⠀⠀⢀⠀⣠
⠀⠀⠀⠀⠀⠰⠀⠸⠃⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠄⠀⠀⠳⣄⠀⢀⠀⠀⠀⢀⡄⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠄⢀⣀⢠⠈⠀⠈⠀⠠⠀⠈⠁⠀⣴⠿⠿⠿⣦⡀⠀⠀⠀⠀⣰⠿⢿⡀
⠀⠀⠀⠀⢀⡠⠛⠛⣆⡀⠀⠀⢀⣼⣹⣿⣦⡀⠀⠀⢀⣀⠀⣀⣄⡇⢐⠀⠀⠀⢰⠀⢰⡃⢀⡀⠀⠈⣷⠀⠀⠀⣠⣥⣤⣤⣱⣦⡀
⠀⠀⠠⣶⣿⣶⡶⠶⠿⣿⣷⠄⡀⠻⠛⠛⠿⡇⠀⠀⠗⠺⠛⠁⢹⡇⠀⠀⠀⠀⠈⠀⢸⡷⠟⠛⠛⠷⣿⠀⠀⢠⠟⠁⠉⠉⠙⠿⡃
⠀⠀⠀⡔⢂⣀⣒⡐⣰⣄⣸⠀⢠⠤⠀⠄⠤⡇⠀⠀⢄⠠⠤⢠⠸⠀⢀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⣿⠠⡇⣞⠀⠀⠀⠂⠀⠈⣿⡆
⠀⠀⠀⢻⣷⣈⣉⠸⣿⢿⣿⠀⢸⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⢸⣦⣤⣤⣤⣤⡿⠀⠰⣿⣦⣤⠀⣠⣤⣾⡿⠃
⠀⠀⠀⠚⠛⠓⠈⠑⠛⠛⠛⠂⠈⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠈⠛⠛⠛⠛⠛⠁⠀⠀⠈⠛⠉⠀⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠾⣧⡔⠀⠬⣽⠷⠖⠚⠂⠀⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⠤⠒⠚⠒⠦⠀⠀⠀⢀⠤⠄⠀⠤⣄⡀⣦⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⡜⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠲⡈⢳⡌⢷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣵⡀⢻⡀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠐⠃⠀⣠⣶⡴⡁⠀⠀⢀⠠⠁⠐⣧⠀⠀⠙⣎⢳⡌⣇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣹⠇⠀⠀⡴⢡⢟⡎⠀⠀⡴⢃⣠⣤⣀⣘⢧⠀⠀⠸⠇⠀⣵⣄⢠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠼⠀⠀⣜⡤⠀⠚⣴⠋⡀⢀⢀⣉⣻⡗⠀⠐⡇⠀⠘⣿⣏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠯⣶⢠⡇⠀⠀⠀⠹⠁⠀⢀⡟⢾⣟⢸⢻⡿⡟⠀⠀⠀⢘⠀⠀⢹⣻⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⢈⡗⠋⠀⣷⡆⠀⣶⣸⠀⣷⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡤⢸⣇⡄⣀⢰⠂⠀⠀⣿⣿⠉⠉⠿⠻⣶⢉⣧⡄⡇⠛⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠀⣿⣇⣿⢸⠀⣴⣄⢛⢿⡑⠒⠒⡻⠋⢸⣿⠁⠁⠀⠀⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⠻⠏⠀⢸⡟⣿⠀⠁⢰⠀⠀⠀⣼⠃⠀⠀⢰⣦⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⣧⠀⠀⠀⢸⣿⣾⣇⠀⠘⢀⢠⣬⣇⣠⡀⣤⢸⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⣇⣶⠀⣿⡇⢼⠿⢳⣿⣼⣿⣟⠸⣿⣻⡿⣾⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⣻⡄⠀⠀⠈⡇⠙⠿⠉⠀⠸⠏⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠀⣉⣉⣉⣉⣉⣉⠐⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣤⣾⣿⡿⠻⠟⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⢿⣿⣷⣦⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⣠⣿⣿⠟⣩⠎⠁⠀⠀⠀⡐⠀⠘⠃⠀⠀⠀⠀⠁⢈⠻⣿⣿⣄⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣼⣿⡿⢃⠞⠀⠀⠀⠀⡠⠄⠀⠐⠆⠀⠐⢄⠀⠀⠀⠀⠑⢌⢿⣿⣧⠀⢂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⡿⠡⠁⢀⡀⠄⠒⠉⠀⢀⠔⠁⠀⠢⡀⠀⠈⠐⠠⠄⡀⠀⠨⣿⣿⣧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣣⠄⠊⠁⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠁⠂⢽⣿⣿⡀⠁
⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⠁⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⡠⠊⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠑⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⡄⠀⠀⠀⢾⣟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⠀⠀⢸⣿⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⣷⡀⠀⠀⠀⠉⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣾⣿⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠈⠛⠹
⠀⠀⠀⠀⠀⠀⠀⡈⡤⠊⠉⢢⠀⠙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⡀⢠⣤⣶⣿⣿⡿⠋⠀⡰⠋⠑⢤⠂
⠀⠀⠀⠀⠀⠀⢠⢱⠀⠀⠀⠜⠀⢾⡦⠈⡹⠋⠁⠀⠈⠁⠀⠀⠈⠁⠀⠀⠙⢛⠁⢼⡷⠀⠣⠀⠀⠀⡏⡀
⠀⠀⠀⠀⠀⢀⠃⠈⡄⠀⡴⠊⠙⠆⠀⠀⠀⠠⠊⠀⡀⠃⢤⠤⠘⢀⠀⠀⠀⠀⠐⠀⡰⠋⠑⢦⠀⢠⠁⠐⡀
⠀⠀⠀⠀⠀⡌⣠⠔⠰⣸⠀⠀⠀⢌⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⡀⠁⠀⠀⠀⠀⠐⢤⡀⠀⠀⣇⠦⠢⣄⢡
⠀⠀⠀⠀⢰⠀⣅⠀⠀⢸⡆⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠛⢺⡗⠓⠈⠀⠀⠀⠀⠀⠀⠄⢁⡄⢠⡇⠀⠀⣨⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⣠⣶⣆⠀⣠⡀⠐⠁⢘⠆⠀⠃⠰⠋⠉⠂⢀⣤⡀⣰⣶⣄⢠⣿⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡇⠀⢿⣿⡶⢋⣭⣅⡛⢿⣃⡈⠛⢁⡀⠠⠜⠀⠀⠀⠀⠳⠄⢀⡈⠛⣁⣘⣿⢟⣩⣭⡙⢶⣿⡿⠀⢸
⠀⠀⠀⠀⡏⣃⣤⣿⠡⡿⣳⡏⣿⢘⣿⡿⠋⠉⠉⢢⠀⠀⠀⠀⠀⢀⡔⠉⠉⠙⢿⣿⡃⣿⢹⣦⣿⠄⣿⣤⣘⢹
⠀⠀⠀⠀⠁⠙⠛⢛⣦⡛⠾⠶⢋⣼⣧⡀⠀⠀⣀⠔⠀⠀⢠⣤⠀⠀⠣⡀⠀⠀⢀⣼⣧⡙⠶⠷⢛⣴⡛⠛⠋
⠀⠀⠀⠀⢠⠘⠃⣸⣿⠟⢸⣿⡏⠙⠛⠛⡄⢠⣦⠠⠁⠀⢈⣍⠀⠀⠂⣤⡄⢠⠛⠛⠉⢹⣿⡇⠻⣿⣇⠘⠃⡄
⠀⠀⠀⠀⠘⠀⠀⡏⠀⠠⢄⠙⠁⠐⣁⢀⠇⢀⣌⠤⠤⢄⠘⠛⣠⠤⠤⣅⠀⠸⡀⣨⠂⠈⠋⠀⠀⠀⠸⠀⠀⠃
⠀⠀⠀⠀⠀⠃⠀⢣⡀⠀⡸⠰⣀⠀⡁⢀⠔⠁⠆⠀⠀⠀⢁⡜⠀⠀⠀⡨⠀⠀⠀⣈⠉⣠⠆⢇⠀⢀⡜⠀⠘
⠀⠀⠀⠀⠀⠘⡀⠀⣈⠉⠰⠆⢈⡩⠃⠀⠀⠀⢀⡁⠀⢀⣾⣷⠀⢀⣉⡀⠀⠀⠀⠙⠉⡁⠰⠆⠉⣁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠡⠘⠿⢃⠀⠂⠁⠐⠋⠉⠁⠀⠸⣿⣷⠾⣛⣛⠰⣿⣿⠇⠀⠀⠈⠉⠒⡈⠐⠤⡘⠿⠃⠎
⠀⠀⠀⠀⠀⠀⠀⠱⠈⢰⠉⠀⠑⠘⢦⣀⢀⣠⣶⣾⠇⣾⣫⠭⢷⡌⣷⣶⣄⣀⡀⣠⠞⠀⠁⠈⢱⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⠳⢀⣀⣀⢠⠔⠉⠉⠙⢛⣆⠻⢞⣧⠟⣱⡟⠛⠁⠉⠑⢦⢀⣀⣀⠠⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⢆⠀⠀⢁⠀⣿⡿⠓⣶⣶⡞⠿⣿⡆⠀⠁⠀⢀⠆⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣬⣑⡒⠁⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⢑⣒⣭⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠟⠁
⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣡⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⢠⣄
⠀⢀⣙⡉⠛⠉⣉⡄⠀⠀⠊⠉⠀⠀⠀⣿⣭⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠐⠠⠘⠋⠙⠈
⠘⠈⠃⠀⠀⢀⠐⠐⠃⠂⠀⠀⠀⠀⠀⠙⠀⠉⠙⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡠⠂
⠀⠀⠀⠻⠶⠟⠀⠀⠀⠀⠁⠀⠡⠀⠀⠀⠀⠄⠀⠀⢀⣶⣿⣷⣄⠀⠀⠤⠀⠠⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⢀⠀⠀⠀⢸⡉⠉⠉⣟⠀⠀⣴⣶⣶⣦⠀⠀⢀⠀⢀⡀
⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠘⠁⠂⠀⠙⠀⢸⡟⠉⠉⣻⡇⠀⠀⡉⠉⠉⠁
⠀⠀⠀⠺⠿⠇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠸⠋⠘⠋⠻⡇⠀⠀⠑⠒⠚
⠀⢀⠐⢈⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⠀⢀⣀⡀
⠀⠀⡀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣾⣧⡀⠀⠀⢿⣶⣾⡇⠀⠀⠀⢀⢀⡀
⠀⠀⠚⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⠀⢸⠏⠉⠛⠷⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⡏
⠀⢀⠈⠀⠄⠠⠄⠀⠀⠀⠀⠀⠣⠀⠈⠉⠁⢹⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⡄⠀⠀⢀⡾⠉⠙⣦
⠀⠀⠠⠀⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠳⢄⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⡠⠦⠀⠒⠚⠛⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⡀⣼⠁⠙⠓⠒⠒⡄⠉⠑⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠉⠀⠈⠑⠛⣀⠀⡰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⡠⠆⠀⠀⠉⢀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⠁⠘⢄⠀⠀⠀⠳⣄⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⢈⠛⠓⢄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠆⠀⠀⠀⠑⠢⡤⠀⣬⠷⠢⠄⠐⠋⠀⠉⠒⠒⠒⠉⠀⠀⠀⠆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⠀⠀⠀⠀⠴⠂⠐⠢⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠙⠀⠀⠀⠀⢸⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠓⡀⠈⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⣰⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠱⣄⠀⠀⠀⠀⠀⠱⢤⣀⣀⣀⡠⠴⠋⠀⠀⠀⠀⢀⡔⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢁⠶⠴⠄⣀⣀⣀⣀⣀⡀⠤⠔⠻⡁⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⢀⡀⠤⠧⣀⠀⠀⠀⠀⣠⣇⠀⠀⠀⣀⡤⠋⠒⠠⠄⣀⠀⠀⠈⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠀⠀⠀⠠⡞⠈⠀⠀⠀⠈⠙⠓⠒⠚⠁⠀⠛⠒⠛⠉⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠀⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢒⡶⠧⠀⠀⠀⠀⠀⠀⠰⡆⠐⠞⠁⠈⡇⠀⠀⠀⢀⡀⠀⠀⢀⠏⠉⠒⠠⣴⣎⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢣⡀⢀⡀⠀⠀⠀⠑⢄⠀⢠⠞⠀⠀⠀⠀⠈⠏⠲⠤⠟⠢⠄⣀⡀⠀⠈⠁⠉⠀⠉⠀⠈⢳
⠀⠀⠀⠀⠀⠀⡀⠠⣤⠔⠊⠁⠀⠀⣀⠴⠊⠙⠙⠇⠀⠀⠀⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⢤⡀⠀⣤⠎
⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⢀⡠⠶⠋⠁⠀⠀⠀⠔⠀⠀⠀⠀⢠⠒⠂⠞⠁⠀⠇⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⢸⡀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠓⠄⡀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠉⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⣀⡠⠎⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡀⠀⠀⢀⡀⠤⠒⠙⢦⣀⠀⠀⠀⢀⡠⠔⠀⠀⠉⠉⠉⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⢀⣀⡤⠚⠳⢄⡀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠉⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠉⠛⠲⡄⠐⠛⠁⠘⢄⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠈⢢⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠱⡄⠀⠀⢠⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢈⢶⡉⠃⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠶⠙⠀⠳⣄⠀⠀⠘⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠈⠳⢶⠜⠁⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠴⠃⠈⠷⢄⣀⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡄⡤⠂