Drunkard Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠠⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠨⣽⡦⠂⠀⠀⠈⠀⠒⡰⠟⠁⡢⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣀⡀⠐⠦⠁⠀⠇⠁⠀⠀⠢⠂⠀⣠
⠀⠀⠀⠀⠀⠀⣀⡠⡄⠀⠀⠀⠀⠀⠀⠐⢰⡇⡠⠋⠃⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣰⣿⠃⠈⠀⠀⠈⠂⠀⠀⠀⠚⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣾⣿⣶
⠀⠀⠀⠀⣾⡟⡁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⠐⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣽⣿⣧
⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠛⠛⠻⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⡟⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⠁⠂⠠⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢻⣇
⠀⠀⠀⣠⣶⣶⣶⣶⠦⣤⣤⣤⣀⣀⡀⠀⢀⣜⡿⠁⢀⣖⡂⠀⠀⠀⠀⠉⠻⡆⠀⠀⢠⣾⢿⣷⣼⣿
⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠉⢿⣷⣜⡟⠀⠀⡌⠁⠀⠀⠀⢀⣠⠢⠀⠁⠀⠀⢼⣿⣾⢻⣿⣿
⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡙⡇⠤⢄⠣⣀⠀⢀⠀⠈⠣⠀⠀⠀⠀⠀⠸⣿⢿⣛⡻⣽⡄
⠀⠈⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣾⣿⡷⠶⠇⣧⡷⢤⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⡂⢤⣟⠇
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣀⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠝⠁
⠀⠀⠀⠀⠉⣩⣟⣷⣾⣿⣿⣿⣿⣿⡇⠈⣯⡿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣿⣁⢘⡟⣆⠀⠀⠀⠀⠀⢀⡴⣾⠝⠋
⠀⠀⠀⠀⠀⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣗⠠⠄⠀⣀⣉⢳⡣⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⠀⣮⠁⠀⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠙⠈⢳⣤⡇⢹⣿⣿⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢿⡁⠀⣿⣿⣿⣯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣇⠀⢸⣿⣿⣿⣷⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠀⠘⣿⣿⣿⢟⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣾⣿⡀⠀⠻⣿⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠛⠛⠓⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⢿⣿⣿⠁⠀⠑⠄
⠀⠀⠀⠀⠀⢠⣿⠏⠉⠉⠀⢀⠀⢈⠛⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣷⣶⣷⣾⣿⣷⣾⡇⠼⠁⠀⣀⣄⡀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠀⠀⠘⠹⠿⣏⠁⠀⠀⢀⠔⡸⠀⢦⣀
⠀⠀⠀⠀⠀⣿⣿⡇⣗⢮⡙⣿⣿⡁⠸⣧⠀⠀⠀⠀⢈⣡⠴⠢⠃⣴⣷⡀⠀⠈⢳⢤⡀
⠀⠀⠀⠀⠀⠹⣿⣿⣮⠺⢯⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠡⢲⡖⠚⠛⠛⡂⠀⡄⠈⠃⠛⢆
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠉⠢⠜⡁⠈⠻⡟⡈⠰⢦⣌⡑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠡⣄⠐⠒⠿⢷⣮⢾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⠃⢿⡇⠙⠛⠷⢶⠆⡴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠈⢣⣹⠟⢩⠄
⠀⠀⠀⠀⠀⠀⢀⠏⠳⡄⠀⠸⣷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢠⣢⠀⠀⢸
⠀⠀⠀⠀⠀⣀⠞⡄⠀⠙⠷⣄⣽⣆⠀⠀⢀⡞⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣆⣠⠴⣇
⠀⠀⠀⠐⠋⠁⠀⠘⢆⠀⠀⠈⠙⠛⠤⣀⡜⠉⢢⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡜⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠃⢊⠃⢺⠏⠀⠀⠀⠀⢀⣀⠀⣠⣾⣷⣦⡀⠦⠀⢀⣀⣀⡀⠈⠀⠀⠀⠰⠐⠂⠲⡄⡀⠄⢰⠄
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠂⠙⠁⠸⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⢿⠙⡁⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠈⠀⠰⢤⡄
⠀⠀⠀⣾⣿⢟⡁⢀⣀⠀⠀⠈⠀⠐⠀⠀⣀⡓⠀⠀⢀⣼⠙⠻⡙⠛⠻⣾⠋⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣠⡿⠃⠈⠀⠀⠀⠀⢠⣤⡈⠙⢳⣄⣩⠅⢀⠀⠘⣿⣄⣟⣁⡀⠀⠶⠐⠀⣠⠀⢸⣿⣿⡗⠀⠀⠀⢀⠀⠀⢸⣁⢟⠂
⠀⠀⢘⠁⠀⡄⠀⠀⠀⠰⠈⡹⠓⠤⠼⠋⢩⡄⠑⠀⠟⣹⣷⡉⠀⠀⣰⠆⣤⡄⣿⠀⢸⣿⣿⣿⠀⠀⠀⠈⠀⡄⢸⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢾⡇⠀⠒⠈⢸⡇⡍⠄⠀⣿⣿⣿⣶⣷⠀⣾⣿⣿⡎⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠁⢸⣏
⠀⠀⠀⠀⠀⠀⡤⢠⣥⣾⠛⠺⣝⡶⠀⠈⢸⡋⠉⠉⠀⣻⡟⣹⣯⣉⣾⣿⣿⣿⣹⣦⠀⢻⣿⢿⣷⠿⠀⠀⠀⠀⠘⠇
⠀⠀⠆⠐⣀⣭⣶⡞⣿⣷⡌⠙⠘⠛⠒⠠⢾⣧⣖⡆⡀⠸⣏⡄⢹⣿⣿⣿⣿⣏⣾⡟⢿⡌⡿⠙⡉⠀⠀⠀⠀⢀⡈⠀⠀⢄⠀⠠
⠀⠀⣸⣦⣤⠈⠀⠀⠈⣿⡇⠀⠀⠀⠀⢀⣼⣿⡷⣇⠡⠀⢹⡟⠄⣿⣿⣧⠙⣼⣿⣿⣶⣿⡜⢺⡇⠀⠀⠀⠀⠛⠑⠶⠶⠈⠀⣤⡀
⠀⢻⢿⣿⠹⠀⠐⠒⠈⠉⠀⢰⢾⡧⣷⣾⠏⢹⡟⣿⠀⠀⣄⠀⠀⠉⠀⠈⢶⣿⡿⠹⣻⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢈⣠⣇⡿⠀⡴⠋⠀⢠⣦⠀⠛⠈⠀⢱⠄⠘⡏⠙⢛⠁⠀⠀⠀⣀⡤⠤⠤⣠⣶⡶⣿⣿
⠀⠀⠀⠀⠀⣲⣶⣄⡋⠀⠀⠀⠀⠀⣠⣴⣿⠟⠟⠀⢀⠁⠀⢸⣿⣿⣿⣆⣀⠀⠀⠃⠀⡼⢀⠈⠄⠐⠒⠉⠀⠀⣠⣜⣋⣽⣿⣿⡏
⠀⠀⢀⣴⣿⣿⣿⣿⠛⠀⠄⣠⣴⣾⣿⣋⡀⠀⠀⠀⣸⡆⢰⣿⣿⡇⠻⣿⣯⠀⠀⠘⠶⣖⣦⣄⣀⠀⠀⠀⠀⠉⣽⣿⠓⣸⣴⡟
⠀⠰⠋⠁⠀⠘⠿⠟⣧⣾⣿⣿⣿⡿⡿⠟⠂⢀⣠⣶⣿⣷⣿⣟⣿⣅⣰⣿⣿⣄⡀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠿⠝⣇⡶⠛⠃
⠀⠀⠀⠀⠀⣀⣤⣾⠿⡿⠁⠈⠃⠀⠀⢰⣶⣿⠾⣿⣿⣿⣿⢿⡿⣿⣿⣻⣿⠪⣧⠀⠀⠀⠀⠘⣿⢿⡦⢀⠀⠀⠉⠂⠁
⠀⠀⠀⠀⠺⠛⠵⠓⠘⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠈⣴⠛⠻⣶⠖⠉⣻⢸⣿⡷⠶⠖⠀⠀⢀⣀⠋⣐⣢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣄⠀⢡⣶⣾⢻⡎⠁⠀⢀⣠⣤⣾⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⣿⢠⣶⣶⣿⣿⣿⣦⢸⣿⣧⣶⣷⣾⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣼⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠛⠛⠛⠙⠋⠚⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⠿⢡⣞⣷⠨⡄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠿⠾⠇⣩⡼⡴⣧⣾⡉⢉⣉⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣿⢤⡄⠈⠿⣿⣄⣼⠹⠟⢧⣌⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣺⣿⢛⠛⠲⠊⡍⣿⢛⢿⣧⠐⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⣿⡆⢠⡀⣯⠈⢦⠠⠙⠻⣤⣀⠀⠀⢀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⢷⠄⠰⣸⣿⣿⣿⣿⣮⣙⠘⢦⣸⠀⠀⠀⠈⠛⠻⠲⠦⠴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡏⠀⠐⢁⡛⣇⠿⢿⠾⣿⣿⢥⡄⣱⠀⠀⠠⣐⠢⣄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠫⣄⡝⠀⠘⣿⣿⣿⣿⢟⣻⠏⠀⠠⠈⣌⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠴⠒⠿⢽⣿⡿⢿⡟⠀⠒⣄⠀⠀⠚⠿⠽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣶⣿⠀⠁⠀⠘⠓⠒⠾⠷⡶⣬⣉⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⢿⣭⡁⢤⠄⢀⠄⠀⠀⠀⠀⡈⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠏⠥⠀⠀⠀⠀⠀⠀⢲⡎⡰⠐⠀⠀⠀⠈⠀⢉⡿⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠈⠈⠉⠐⠀⠀⠀⠐⠒⠒⠤⣬⣙⣻⣧⠆⠀⠀⠀⠀⠀⠈⣆⣤⣴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⡀⠀⠀⣠⣄⡤⠤⣶⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠻⢏⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠐⢶⡺⣯⣤⡿⠶⣿⣋⣡⣴⣶⠿⠛⠻⣷⣆⠀⠀⠀⢰⣴⡆⣷⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠘⡇⠈⢻⣆⠸⡟⠋⠉⣿⣿⡶⠀⠀⠈⠹⣷⡀⠀⠐⠂⠊⠿⠻⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣠⡼⠃⠀⠈⣿⡆⠻⠀⠀⠸⣿⣿⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⠀⡽⠀⠀⠀⠀⠸⣷⠀⢀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠈⠉⠻⣷⣶⣥⣀⠀⠀⠘⢳⡄
⠀⠀⠀⣀⡀⠀⠀⠀⣼⡇⠀⡾⠁⠀⠀⠀⠀⠀⢻⡆⢰⡄⠀⠐⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡻⢿⣶⣤⡀⠀⠙⢦
⠀⠀⠈⢿⣯⣶⠔⠶⣿⠁⣰⣇⣠⣤⣠⣤⡄⣤⣼⣧⠀⢷⣤⣴⣾⣿⣷⣤⣤⣤⣤⣤⣤⠄⠈⣿⣷⡀⠙⠟⢻⣶⣎⠸⣶⡄
⠀⠀⠀⠀⠙⠻⣿⣷⣌⠁⣻⣶⣾⢶⣿⣿⣶⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣦⣤⣤⣬⣁⣀⡀⠀⠀⠉⠻⣷⣞⣍⠓⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠻⢿⡟⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⠾⠿⠿⠿⠟⠿⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣷⣽⣿⠙⠀⡤⠋
⠀⠀⠀⠀⣀⣠⣶⣿⣿⠿⠿⠏⠉⠉⠉⠀⠈⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢿⣟⡴⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠐⠂⠐⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠀⠂⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠏⢹⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠋⡄⢀⣄⣬⣡⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢪⠟⢛⠛⠻⡝⠉⠀⠿⣦⣼⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⠅⠈⠀⠀⠀⠙⡠⠰⠄⠺⢻⠷⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢱⠏⠀⠀⠒⠁⠀⠀⠀⡠⡆⣰⣮⡜⠁⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⠀⢀⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⡋⣀⡟⠈⠀⠈⡸⠄⠐⠄⣴⣡⣵⡙⣾⣀⠶⣆⠀⠀⢠⠀⠰⠀⠀⠈⣴⠏⢠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣟⢁⣤⣹⢷⡒⠀⠉⢨⣯⣿⣄⡂⢀⡸⠆⢀⡐⣌⢻⢻⡿⠋⠉⠁⠀⠈⠉⠉⠃⠰⠶⠤⠾⠿⢾⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠲⢷⣼⣿⣶⣷⣾⣿⡯⢭⡉⣙⣳⣄⣬⣿⡟⢾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⣉⡭⠋⠀⢀⡞⠘⡟⠈⠳⣮⣛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠒⠻⢻⠃⠀⠻⣤⣐⣯⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣀⢸⡀⠀⡤⠀⠉⣿⣟⣿⢿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠠⢤⡘⡆⢧⠘⠁⠀⠀⠙⡈⣿⣼⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠉⣷⣼⠀⠀⠀⠀⢀⡙⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢙⣿⠀⠀⠀⠀⠀⠹⡟⠻⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣤⡎⠀⠇⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠠⠴⣦⠞⠀⠀⠈⣦⠀⠀⠀⣇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣴⡞⠉⠀⠀⠀⠀⣧⠀⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢈⣽⠇⠀⠀⠀⠀⠀⠈⠳⠄⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⡀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠈⡂⠄⢹⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⣹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⢵⣟⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠹⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⢿⡀⠀⠀⠀⠀⢸⣶⣴⣤⣏⣰⣯⡀⢤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠐⢿⡄⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⡈⣻⡁⣿⣧⣶⠧⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠊⣀⣽⣾⣷⣤⣶⢿⡿⠿⠿⠛⠛⠋⠙⢷⣌⢻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠥⠄⠘⠛⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠄⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠉⠙⠛⠛⠙⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⣣⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣀⡀⠀⠀⣀⣤⣄⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⡿⠿⢻⣿⠈⠿⠳⠆⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠉⡁⠀⠀⠀⠀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣣⢀⡖⠙⠛⠉⠳⠀⠀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠷⠀⠂⠀⠘⠁⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠈⠉⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣄⣀⣀⣾⠟⢸⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⣿⡟⠋⠋⠀⣸⠇⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡹⣧⠙⠃⠀⢀⡴⠋⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣿⣿⠿⢠⡽⠳⠀⢻⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠋⠁⠀⠀⠹⣟⢷⣈⣿⡄⡿⢢⡿⠶⠋⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡞⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠂⠉⠀⠀⢈⡁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢀⣀⣀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠈⣉⡀⠀⠀⠀⣌⣠⠍⣦⡤⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡵⠚⠂⠀⣀⠀⠀⠀⢸⢿⠁⠄⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡉⠉⠒⢄⠀⠀⠉⠀⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠐⠂⠀⢠⡞⠀⠀⠀⠀⣸⠀⠀⡀⠀⠀⣀⣀⣀⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣁⠒⢚⣠⣴⠁⢠⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⣈⢀⢀⣾⠁⢀⣀⣀⣀⣟⠀⣀⣵⣾⠛⠀⠂⠤⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠓⡀⡴⠛⠏⠀⠀⣸⢷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡀⢩⣼⡾⠃⠀⠈⡯⠉⠉⠉⠛⠉⠉⠉⠐⠒⠤⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⣀⣤⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⡿⣱⣿⣿⡄⠀⢳⣤⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢁⣛⠛⠉⠁⠤⡼⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠹⣿⣀⣁⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠄⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⡄⢀⣀⣄⣤⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠘⠻⣿⣟⠟⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣿⣶⣦⣜⠛⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⡀⠀⠀⣀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⠇⢹⡿⠿⠛⠋⠈⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣯⣶⣶⣶⡄⠀⠘⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣽⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠑⠀⠀⠀⠈⠉⢫⣹⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣿⣿⣽⡟⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⢀⣀⣀⣀⠀⠀⠀⠀⠰⠶⠿⠿⣿⣷⣷⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⣰⣿⣿⣿⣿⣿⣦⠀⠀⣄⣠⣤⣤⣯⣭⡋⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣹⠇⣿⢟⣿⣟⣻⣿⣿⡇⠚⣿⣿⡿⢿⣿⣿⣿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠉⠟⠙⣛⢏⣽⣿⠃⢀⣿⣧⣶⣾⢿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⠁⠈⠀⢸⣿⣿⡄⠤⣾⣿⣿⣿⠏⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⠁⠀⠀⢈⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠄⠠⠀⢠⡎⠀⠀⠀⢀⣿⢿⣷⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⢸⡟⠻⢶⣶⣿⣿⣿⣿⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⣎⡀⠤⠠⣤⣤⣈⣙⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡼⢿⣽⠁⠀⠀⠴⣴⣤⣤⣿⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⣀⣒⣰⣦⠀⠀⠀⢠⡇⠀⠈⢻⡤⠀⠀⠻⠧⣿⣿⣿⡿⠀⠻⣦⡀
⠀⠀⠀⠘⠳⠦⠤⣴⣴⣈⣹⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠈⠻⣦⣤⣶⣾⣿⣿⡿⠁⠀⣼⠈⠳⣤⡄
⠀⠀⠀⠒⠦⠤⣄⣼⣀⣉⣉⣿⣸⡇⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⢸⡇⠀⠀⠀⢠⣀
⠀⠀⠀⠰⢤⣤⣤⣭⡤⢼⣿⠿⠟⠁⠀⠀⠀⠀⠘⠂⠀⠀⣠⠄⢈⡿⢋⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠉⢻⣄
⠀⠀⠀⠐⡤⢬⠿⡷⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢼⢃⣀⣘⢣⣾⠃⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⠿⣡⡞⣡⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣭⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣫⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣾⠟⣫⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣵⣿⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢋⡵⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠉⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⣦⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⢁⣠⣀⢀⣨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡋⠁⠈⠉⡉⢈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣑⡆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠏⠀⠀⠀⢠⣴⡏⣰⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢹⣿⣥⢆
⠀⠀⠀⠀⣀⣤⠚⠿⣴⠲⠀⠀⠀⢀⡀⠰⣿⣿⣿⣿⣿⣷⣦⣀⢀⣀⣠⣶⡇⠀⢸⡏⠻⣯⠷⣄
⠀⠀⢀⣜⢧⣀⢠⣠⠆⠀⠲⠀⠒⠻⠇⠀⠘⣿⣿⣿⣿⣿⣏⣴⣿⡟⣱⣍⣿⠀⢈⣷⡀⠈⢀⣘⣦⡀
⠀⠀⢸⡇⠠⣿⣿⣿⣿⠆⠐⠣⡀⠀⢀⡄⠀⢻⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⡟⠁⡔⠼⠉⣨⣷⡄
⠀⢀⠉⠃⠀⢿⣿⣿⣿⣄⠘⢦⣹⣆⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⢶⣿⣌⢻⣯⣂
⠀⣼⠋⢁⢃⣸⣿⣿⣿⣿⣷⣮⡿⠻⣧⡀⠀⠀⣿⣿⣿⠇⠀⠈⢻⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠣⣻⣿⠿⠋
⠀⡃⠠⠈⣿⣿⣿⣿⣿⣿⣇⣉⠛⠷⠾⢿⣷⣼⣿⣿⣿⣷⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⣀⣀⡰⢿⣿⣿⣿⣿⣿⣿⠭⠙⠂⢀⡈⢿⣿⣿⣿⣿⣿⣿
⠻⠿⣻⠰⠸⢿⣿⣿⣿⣷⡏⠀⢀⢬⣀⢉⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠷⠲⠤⢽⣿⣿⣿⣿⣿⣿⣷⣮⠑⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠚⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣄
⠀⠀⠀⠀⢠⣾⣿⠠⡀⡈⠉⠿⢿⣿⣿⣿⣿⡿⠿⢿⣿⡟⣿⡿⣿⡛⢿⡆
⠀⠀⠀⠀⠌⣽⡟⠀⠈⠛⠂⠀⠀⠸⣿⣿⣿⡗⢶⣌⣿⣿⣿⣿⣇⣹⣷⣰⡦⡀
⠀⠀⠀⢠⢀⣿⣁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢿⣟⣿⣿⣾⣿⣿⣴⣿⣧⣼⠳⣮⠲⣀
⠀⠀⠀⠸⠋⠙⢿⠋⠱⠄⠀⠀⣴⣿⣿⣿⣿⠉⢋⠹⡝⢿⣿⡿⡟⢛⣦⡙⢶⡀⢹⠏⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣌⠁⣸⠙⣿⣿⣿⣿⡗⣊⢡⡄⠌⠛⠿⢴⣝⣢⣼⢿⣉⣻⣀⢾⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠙⣿⣿⣿⣷⠉⣄⠡⡄⠃⣀⠀⠈⢹⣿⣿⣽⡧⢏⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣇⡉⢆⠠⠄⠃⠀⠀⠈⢦⣍⣉⣣⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡛⡈⣤⠰⡖⠃⢀⠀⠸⣿⣋⡙⣦⡽⣏⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡌⢦⠰⣶⡏⠀⠀⠘⢦⣶⠙⣶⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢱⣿⣙⠛⣷⣾⣿⠟⠁⠀⠀⠀⠙⡉⣀⢸⡻⣟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢀⠋⣸⢛⢿⠋⠀⠀⠀⠀⠀⠈⠻⡉⣄⣷⡜⣿⣿⠓⣤⠀⡀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢦⣄⣤⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢽⡉⢳⣽⣿⢧⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⠞⣟⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠞⣋⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠁⢸⣧⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣁⡐⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠛⣿⣾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣤⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⢿⣿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢄
⠀⠀⢸⣷⡏⠀⠀⣿⣺⡁⠀⢘⣶⣆⡦⠀⢀⣿⣂⣤⣤⣄⣻⡀⠀⢀⣺⢃⡀⠀⠸⣇⠀⠀⠘⣶⣆⡦⢀⣈⣿⡎
⠀⠰⢻⡇⠀⠀⠺⣿⣧⠀⠀⢸⣿⣀⠀⠀⢸⡿⡅⠀⠀⠈⣹⡿⠀⠸⡟⠋⠁⠖⢊⣿⠇⠀⢸⣿⣁⠀⠋⢠⣿⣧
⠀⠀⣸⠟⣆⠀⠀⢸⣿⠀⠀⢀⡟⢹⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢀⡟⢹⠀⠀⠈⡧
⠀⠀⠁⠀⠉⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⢠⣤⣤⠂⠀⠀⠀⢀⡾⠆⠐⢻⣄⠀⠀⢀⣴⣖⢛⠀⠀⠀⢀⣴⣄⣠⡗⣤⠀⠀⢀⣶⣀⡀⠀⠀⣰⣆⣠⡄
⠀⢀⡾⣿⣯⣄⡀⠀⠀⢸⣟⡲⣭⠍⣽⠂⠀⠀⣹⠟⢘⡆⠀⠀⡞⡟⠛⠛⠛⢻⡄⠀⢿⣿⣿⣿⡀⠸⣿⣿⣿⣇
⠀⠈⠀⠉⠉⠉⠉⠁⠀⠈⠉⠁⠉⠈⠉⠉⠀⠀⠉⠀⠈⠉⠀⠀⠉⠁⠈⠁⠈⠉⠁⠀⢸⣿⣿⡏⠁⠀⣿⡟⣿⠉
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣀⡠⠀⠀⢀⣄⠀⠀⠀⣠⣄⠀⠀⠀⣀⢀⠄⠠⣣⡤⢀⡈⠉⠉⠁⠀⠀⠉⠁⠈
⠀⢀⣼⣿⡃⢤⣀⠀⠀⢠⣿⣿⠁⠀⢠⣾⣿⠿⠀⠺⢿⣷⡄⠀⠘⣿⠗⠀⠀⣻⡏⠉⠁⠀⠀⠀⠀⠀⡄
⠀⠈⢸⣿⠄⡿⠿⢷⠀⠀⢽⣿⠄⠀⠀⢽⣿⠄⠀⠀⣼⣿⠁⠀⢰⣿⡍⠀⠀⠛⣿⠀⠀⠀⣀⣴⣶⣤⣤⣀
⠀⠀⠸⠿⠀⠀⠀⠈⠀⠀⠸⠸⠀⠀⠀⠸⠸⠀⠀⠀⠘⠿⠀⠀⠼⠁⠧⠀⠀⠀⠿⠀⠀⠉⠉⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣏⣿⣿⡷
⠀⠀⠀⠀⠀⣠⣶⣿⠿⠟⣛⣿⣿⣿⡁⠈⠁
⠀⠀⠀⠀⢚⡉⣠⣴⣶⣿⣿⣿⣿⡈⣷
⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠆⠀⢀⣤⣀⠀⠀⠀⠀⣀⣰⣤⣾⣁⡠⡷
⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠛⠀⠀⣤⠼⢿⠀⠠⠀⠂⠉⢻⢧⣾⣿⡔⣠⡆
⠀⠀⠸⣿⣿⣿⣿⠿⠿⣿⣿⡇⠀⠀⠠⠀⠀⠀⠀⠀⢠⢀⣀⠀⣈⣽⢿⣿⣿⠟⣸⠔
⠀⠀⠀⣿⣿⣿⣇⠋⠳⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡟⠛⠃⠀⠻⠀⠀⠀⠈⠂
⠀⠀⠀⠸⣿⣿⣿⣆⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠒⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠁⠘⢻⣄⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠀⠙⠳⢦⣄⣀⣀⠀⠀⠀⣠⣤⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠛⠉⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠀⠤⠒⠋⠉⠠⣤⣄⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠒⠦⠤⠤⠤⠤⠤⠤⠤⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⡠⠒⠚⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠒⠒⠦⢤

⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣄⣠⣀⣤⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠛⠃
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡉⠹⠸
⠀⠀⣿⣻⠿⠿⠿⢿⣿⣿⡷⠀⠀⠀⠒⢶⠔
⠀⠀⢿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣀⠶⠤⠀⠀⢀⠀⠀⣄⢀⡀
⠀⠀⠈⢿⣿⣿⠀⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⢆⣀⠀⠀⢨⣁⠀⠀⠀⠀⠀⡄⠼⢦⣠⣷⠂
⠀⠀⠀⠈⠻⢿⣷⡎⠑⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠺⣋⣐⣶⣶⣶⡄⢠⠶⠾⠼⡿
⠀⠀⠀⠀⠀⠈⢿⠃⠀⠈⠳⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠪⡉⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠁
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢸⡄⢀⣀⣀⣀⠤⠦⡀
⠀⠀⠀⠀⠀⡤⠊⠐⠀⠀⠀⠀⠀⠠⠏⡻⠀⠁
⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠣⡄⠀⠀⠀⠀⠀⠀⠘⠢⣀
⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣀⠀⠀⠀⠀⡌⢷⡀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⠢⣀⣀⢣⠘⣮⣳⢤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠱⠷⣌⡋

⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡏⠙⠿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣤⣤⣌⣉⠛⠿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡝⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠉⠉⠿⠋⠋⠁⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠏⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⢤⡾⠟⠻⢿⣷⣦⣤⣀⡀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⢻⡿⠀⠀⠀⠀⢰⣏⣤⣤⡤⠬⢿⡿⡿⠟⠀⢰⣿⣛⡛⠋⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⢷⠀⠁⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠘⠁⠀⠀⠀⢸⠍⠙⠉⠑⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⢀⣤⣤⣀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢦⠙⣋⠙⠛⣛⠳⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⢀⠀⠀⠀⡜⠃⠀⠀⠐⠁⠊⠁⠀⣁⠛⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠑⠀⠀⠀⠠⠀⢡⡴⠂⠒⠒⠒⠖⠒⠊⠉⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⡘⠃⢀⠐⠀⠀⠀⠀⠐⠶⡶⠖⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡇⣤⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⣿⢹⣷⣿⣿⣿⣿⣶⣶⣦⣤⣤⣶⣿⠇⢹⡌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣰⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠛⠁⠀⢸⡇⠀⠈⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠐⠏⠀⠀⠈⠛⠿⠟⠉⠉⠉⠉⠛⠀⣸⠀⠀⢸⡇⠀⠀⠀⢸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡿⠁⠀⠀⠀⢸⡇⠈⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠃⠀⠀⠀⠀⢸⠇⣠⡶⠚⠛⠛⠛⡉⠀⠋⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠘⠀⠉⢿⣿⠟⢀⢀⡀⠐⡄⢨⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠳⣄⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠋⣀⣤⠋⢠⣶⡄⣏⣀⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠈⠳⣤⠐⠀⣴⡇⠀⠀⠀⠀⠀⠀⡴⠋⠁⠐⢚⣿⠿⠄⠈⢀⡰⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢿⣿⣆⠀⠀⠁⠀⣼⣿⠟⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠹⣇⠀⠀⠀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠘⣿⣿⣧⣀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡹⣶⡶⠶⠶⢾⣿⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠛⠻⠿⠿⠻⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣛⣛⣙⣛⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣯⣛⣽⣿⣟⣻⣛⣟⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡟⠋⠃
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠰⢴⣢⣀⣬⣷⠐⢄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠤⠇⠁⠀⠀⠀⠀⣈⣤⣶⣶⡷⠉⠻⠿⠯⠶⡌⡄
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⠙⠂⠀⠀⠀⠀⢆⣋⣠⠤⠟⠛⠿⠽⠿⠛⠁⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣜⠂⡀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠋⠻⢤⣀⣀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠣⡀⠀⠀⠀⠠⡆⠀⠐⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⢂⠀⠈⠒⠒⠤⢤⡈⣿⡏⠀⠀⠀⠉⠁⠒⠒⠒⠀⠀⠀⣰⠂⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠙⠢⣀⠀⠀⣿⣝⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠢⡀⠀⠀⡇
⠀⠀⡠⠂⠁⠀⢄⡀⠀⠀⠀⠀⠀⠈⠉⠁⠈⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠌⢉⣩⠇
⠀⠐⠁⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⣠⣦⠥⠄⠀⠀⠀⠀⠀⠑⠨⣀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢸⠏⠉⠉⠒⠂⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣷⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⢀⣲⣦⡀
⠀⠀⠀⢀⣤⡄⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠹⢿⡇
⠀⠀⢀⣿⠉⠀⣀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣾⠃⠐⠛⠓⢺⡇
⠀⠀⢸⣷⠄⠀⠤⠴⢼⣿⡇⠀⣠⣤⣶⠂⠀⠀⠀⢢⣾⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠄⠰⠆⢀⣠⣤⣤⡉⠀⠀⣿⠋⠀⠀⠻⣿⣧
⠀⠀⢸⣿⠀⠀⢠⠀⢈⣿⡇⠀⣿⣋⠉⠀⠐⠒⠒⣾⣿⣿⣿⡟⠇⠀⣠⣤⠄⠀⢤⣤⡀⠈⢻⣏⠀⠀⠀⣀⣼⣿⣿⣿⠧⠀⠀⣿⠀⠀⠀⣠⣸⣿
⠀⠀⠘⣷⠀⠀⠀⠀⣼⣿⠃⠀⠈⠙⣶⠶⠴⠾⣷⣿⠟⠉⠀⠀⠀⢸⠇⠀⠤⢻⣎⠻⣿⠀⠀⠙⠿⡁⠠⣘⣻⠟⠙⠀⠐⠀⠀⢻⡆⠀⠀⢁⣿⡏
⠀⠀⠀⠈⠷⣄⣸⣦⡿⠁⠀⠀⠀⠀⠻⢤⣤⣦⡾⠟⠀⠀⠀⠀⠀⡿⠃⠦⣐⣢⣼⣿⣿⡆⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢲⣿⡟⠋
⠀⠀⠀⠀⠀⠸⣿⠇⠀⢀⡀⠀⠀⠀⠀⠘⢦⡿⠃⠀⠀⠀⠀⠀⠀⢳⡀⠺⠟⠿⣎⣽⡿⠃⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢀⣠⢀⣸⠀⢀⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⣠⠀⠀⠀⠀⠀⠀⠈⠉⠲⣿⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣼
⢀⢠⡷⠟⠋⠉⣻⠀⢨⠒⢟⡷⢶⡶⣄⠀⠀⡇⠀⢿⣁⠉⠄⠠⢤⣄⠀⠀⠀⣿⠀⠀⠀⡀⠒⢶⠠⠀⢰⠇⢰⣤⣿⠆⠀⠻⣾⣤⠆⠀⢹⠀⠀⠰⢦
⠻⠂⠁⠰⡖⠐⠙⠃⠈⢹⡿⠇⠈⢳⣿⠐⠈⢻⣶⣦⠀⠀⠀⠀⠀⣿⠂⣤⠐⠙⣦⣤⠐⡄⢀⡟⢠⣻⠚⢷⣦⡄⠀⠐⢊⣽⡧⣤⡄⠒⣹⣷⣶⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠈⠁⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢂⣴⠏⠀⠀⠈⠉⢀⡒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⣷⡋⠁⠀⠀⠀⠀⠀⠀⠙⣦⠛⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⢀⢈⣷⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⢀⣤⣴⣶⣚⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣤⣀⠐⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢿⡟⠛⣿⣿⠋⢹⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠧⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠉⠒⢎⣍⠀⢸⠀⣱⡶⢤⡀⢀⣤⣓⠓⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⡟⡏⠐⠋⠁⣰⣧⠀⠻⠏⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢻⣄⠀⠉⡁⠿⠀⠀⠄⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⡞⠙⠁⢤⠀⠀⠙⠀⣤⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⡟⢹⣿⣏⡶⠚⠀⠀⠈⠙⠀⡆⠘⡄⢹⢻⣷⠤⣄⠐⠇⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢿⡆⣀⢴⣯⡈⢟⡟⠻⣿⠃⠀⢿⡙⢷⣦⣤⣤⣤⡄⠀⣿⠀⠀⢸⣏⠁⠀⠀⠀⠀⡀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡖⠫⠀⠑⣜⡆⠀⡛⠀⠀⢸⣧⠀⠈⠻⣏⡜⠀⠀⢿⡀⠀⢸⢿⣿⣶⣦⡂⠀⢨⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠈⣿⠀⡁⠀⠀⠈⣿⠀⢀⣠⣯⣴⣦⡀⢸⡇⠠⣾⣄⡀⢠⣿⡅⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢸⡇⣿⣶⠀⠀⠛⠀⠉⢻⣿⣿⠃⠁⢸⡇⠀⠈⠿⢷⣾⣇⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣘⣷⢹⠋⠀⠀⠐⠀⠀⠀⣿⣿⣆⠀⢸⠀⠀⠀⢀⣀⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⡀⠀⠀⢇⠀⢰⣿⣿⣿⠀⡟⢀⣀⣤⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣾⣶⣾⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣱⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⡾⣧⣤⣤⣀⠀⢀⣦⣠⣄⠀⠀⡁⠹⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣼⣶⡷⣿⣽⢺⠸⢯⣯⢻⠡⠀⠂⡠⢼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢵⣿⡇⠀⢳⣥⡼⠗⠀⠀⠀⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣯⡾⡦⠀⠈⠓⢄⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠈⠀⠀⠀⠀⠂⢿⠖⠁⠀⠈⠊⠀⠀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⢛⣈⡀⢀⠀⠀⢀⢰⣷⡄⢀⣀⣠⣤⠄⢀⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⢹⣿⣿⣿⣿⡿⣼⣿⣿⡿⣯⠀⠋⠀⡼⢸⣿⣿⣿⣼⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⡀⠘⠛⠓⣿⠙⢿⡧⢿⡀⢀⡼⠃⢸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⠙⠒⣲⣶⣿⣼⡷⠦⣤⣥⡾⠶⡄⢸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢽⣿⣿⣟⠁⢀⡏⠀⠀⠀⠹⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠘⠃

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⢄
⠀⠀⠀⠒⠉⠘⠀⠀⠀⠰⢄⣀⠈⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠
⠃⠀⠁⠐⠤⢀⠁⠀⠀⢀⠠⠏⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠀⠀⡄⠀⢠⠀⠀⠡⠜⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠃⢂⣴⡀⢄⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢂⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠀⠈⠉⠉⠀⠒⠠⣤⢀⠀⠀⠐⡶⠣⣤⡄⢫⠀⠀⠀⡠
⠀⠀⠀⠀⠄⠀⠀⠄⠀⠠⠀⠀⠀⠈⠁⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠃⡶⠋⠈⠙⢷⠀⢈⠶⠂⠤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠒⠈⠁⠁⠶⡀⣸⠑⠁⠀⠀⠀⢆⣁⠀⢑
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠂⠤⠎⣅⠈⠁⠈⠢⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡖⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⣀⡀⠀⠀⠀⢀⣠⡖⠊⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣿⡿⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠓⡁⢀⡉⠂⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⡀⠀⠄⣀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢀⠈⠀⡸⠂⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠉⡉⠹⠿⠿⠋⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢊⢀⡀⠀⠊⢃⡀⠔⠈⠆⠘⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⠀⠀⠠⣄⠀⠀⠀⠀⠀⢠⡀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠈⢀⠀⠀⢧⠀⡁⠊⠳⡀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠘⠄⠀⠀⠘⡄⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠜⣛⠀⠀⠀⠈⣓⡤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢙⠁⠀⠀⠈⢒⣀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠎⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣷⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⠿⠿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣏⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠹⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡿⢋⠙⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⢷⠀⠀⠀⠀⠀⠀⠞⠁⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⡟⠁⠀⣠⠾⣷⣄⣀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡏⠁⠙⠃⠀⠀⠀⠀⢀⡾⣁⣠⠶⣿⢀⡟⠀⢩⣿⠟⠀⢀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣇⡀⠀⠀⣠⣴⠋⢀⡿⠀⣠⣄⡠⠷⠶⢻⡿⠄⠚⠉⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠐⠀⢨⠝⠋⢀⡾⢁⣼⣧⣤⣄⣀⣀⣀⣤⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⠛⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡀⠀⠉⢿⠀⠀⠉⠉⠀⠙⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣤⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⡇⠀⠀⢸⡀⠀⢰⠦⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⡇⠀⠀⠘⡇⠀⡾⠀⠈⢙⣶⣤⡿
⠀⠀⠀⠀⠀⠀⢠⣞⣩⠽⠿⠿⢿⣿⡿⠋⠀⠀⠀⠈⠻⣿⣏⣙⣷⢿⣿⣿⣴⠇⠀⠀⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠠⣶⠒⠀⠀⠀⠀⠉⡀⠀⠠⠀⠀⠀⠀⠀⠀⣚⡅⠀⠀⢈⣱
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡿⢟⣀⡀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠀⠩⣀⣀⠀⣀⠰⠁⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢱⢿⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠑⠦⣀⡉⢙⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡖⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠀⠀⢆⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠊⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣼⣿⣿⡏⠙⠀⠀⠈⢻⡶⣄⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⢿⣹⣦⣶⣔⢀⠀⠀⣽⠛⢮⣧⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⠛⠻⢿⣿⢀⢰⠏⠀⠀⠉⢷⡀⠀⠀⣿⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⢻⡀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⢹⣶⣤⣀⠘⢇⣻⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠈⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣊⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸⣢⡀⣠⠀⠤⠘⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠨⡙⠻⣿⡇⠀⡄⠜⢢⣀⣊⠁⠀⠀⠀⠀⠐⡿⡒⠂⠀⠈⣿⡇⠀⠀⠀⢸⠀⢀⠠⠐⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠻⢀⠀⠈⠚⠀⠁⠀⠀⠗⠀⠀⠀⠀⠰⡀⠁⠀⠀⣿⡇⠀⠀⠀⠀⢐⠀⢱⡄⠘⢀⠠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣠⡏⠀⣄⡓⠒⠊⠀⠀⠀⠀⠀⠀⣀⠘⢧⡀⠀⠀⢹⡇⠀⠀⢀⡠⡘⠢⠌⠒⠉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⡄⠀⠈⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⢿⣧⠀⠀⣎⠀⢸⠀⠀⠀⠀⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣦⣄⣀⣀⣀⣀⠟⠛⣻⣿⠀⠀⠈⢳⠂⢺⡛⠛⠋⠉⠀⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣿⢻⣇⠀⠀⠸⢤⣼⣁⣀⣈⡀⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣍⡙⠷⠶⠦⠼⠦⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠉



⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢿⡇⢠⡀⣘⡄⣌⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣶⣿⠅⠿⠃⠋⢿⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠉⠁⠀⡀⠀⠀⠙⠰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⡀⠀⠀⠶⠆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠐⢶⠋⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠐⠞⠃⠀⣠⠀⠈⢳⠒⠚⠉⢀⠀⠀⢈⠟⠛⠳⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢴⣞⣁⣀⠔⠁⠀⠀⠀⣸⠀⠡⠂⠀⠔⡌⠀⠀⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠀⠐⠀⠀⡀⠔⠋⢈⣷⣥⣄⣠⡸⣇⡀⠀⡤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⢀⠠⢒⡥⠖⠉⠉⠉⡹⠛⣟⢻⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣐⣄⠀⠀⠀⠀⠠⠈⠊⠀⠀⡠⠔⠊⠀⠀⣸⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠠⠍⠉⠑⢦⡀⢀⡀⠤⠔⠂⠁⠀⣀⠄⠨⠚⠁⣸⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⡀⢀⣀⢸⠟⢦⣀⠀⠠⢔⡲⠭⠓⠁⠀⣀⠔⢹⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⠀⠀⠀⣼⠋⠀⠀⠙⢷⣤⣄⣀⠀⠀⠀⠀⢀⡴⢿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢳⣦⣤⣤⡤⠴⠚⠁⠀⣷⢀⠀⡀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢂⡇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⣠⡴⠞⠁⠀⠀⠀⠀⣠⡴⠿⢍⠀⠀⣰⠊⠀⠀⠀⠀⠠⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠈⠀⣠⠶⠋⠁⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⣾⠃⠀⠀⠈⠉⠀⠁⠀⢠⣞⠁
⠀⠀⠀⠀⠀⠀⢀⡖⣵⣚⣏⢀⡤⠞⠁⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣠⢾⡳⣖⠊⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⢤⣤⠶⠈⣼⠃⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⢎⠃⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠸⡿⣾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⣀⣀⣀⣴⡏⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⣧⠀⣠⡴⠃⠘⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢻⡇⠀⠀⠀⠀⠠⠞⠋⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⢀⣀⣠⡴⠞⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⣀⢀⣊⣀⠀⢅⠀⣸⠀⡀⠀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⢲⣤⣾⠃⣔⣰⠘⠱⣄⡀⠈⠣⡀⠄⠀⢀⠀⡌⡠⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⣏⠎⡞⠏⠀⠀⡷⠎⠀⠘⢿⠆⠀⠀⠂⠙⠀⠀⠊⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠥⠛⣖⠂⠠⢀⠀⠈⠁⠇⠀⠀⠠⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡆⠀⡖⠁⠀⠀⡨⠃⠀⠀⠄⠀⢰⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⣰⠇⣀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠑⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⡀⠈⡕⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠘⣄⣧⠖⠂⠀⠀⠀⠀⠈⢁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣠⣤⡼⠀⠀⠀⠀⠀⠀⠀⡄⢈⡄⠥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⠟⠠⠀⠉⠛⠀⠀⠀⠶⠶⠆⠀⠁⠀⠀⡀⠠⠄⠂⠉⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠚⠓⠒⠂⠀⠀⠀⠀⠀⠐⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠂⣄⡀⠀⠀⠀⠀⠀⡆⠀⡶⠖⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣶⠏⣀⢆⡁⠠⡀⠀⠀⠀⠀⠘⠁⠀⢇⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⡄⢷⡶⠊⢁⠤⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡖
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡎⢀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⣏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠜⠂⠲⠿⠓⠶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠔⠛⣈⡗⠐⢢⠒⡚⢦
⠀⠀⠀⠀⠀⡀⢒⣿⢤⡅⡀⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠐⢆⠉⠣⡤⢄⠁⢸⠋
⠀⠀⠀⠀⠀⠀⡎⠀⣸⡁⢀⣄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠈⢿⣀⠀⢡⠀⣁⠸⢂⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠚⠓⠀⠀⠉⠉⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣽⣿⡿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⢟⣯⣿⣿⣿⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⣒⠶⡀⠀⢈⣙⣷⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠜⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⡠⠎⢁⣀⣀⣀⡟⡷⢷⣿⠿⣛⡟⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠒⠛⠛⠀⠀⠀⡀⠀⠀⠀⡀⣤⣾⣿⣿⣿⣿⡟⠀⠈⠋⠛⠝⠚⠛⠿⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢫⣟⡋⠿⠂⠀⠀⠀⠀⠀⠀⢦⠐⢛⢁⣀⣠⠿⠷⠿⢛⣟⣘⣿⠿⠗⠛⠑⠄⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠘⢬⣅⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢉⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⣶⠾⠓⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠉⢻⣦⣀⣀⠀⠀⢀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋⠀⠀⠀⠁⠋⠉⠉⠉⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⢣⡀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣁⠀⠀⠙⠢⢄⣀⡀⠀⠀⠀⠻⣴⣷⡶⠂⠀⠀⠀⠙⡖⠲⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡄⢰⠇⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠈⠣⣀⠀⠀⠀⠈⠉⠉⢛⣶⣄⢳⣿⡇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⠾⡀⠸⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⢸⣧⡙⢻⣿⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⠀⠀⠀⠀⢷
⠀⠀⠀⠀⢀⠤⠒⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠈⠻⢦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡈⠓⠶⠶⠶⣻
⠀⠀⠀⡔⠁⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠈⢦⠑⢬⡊⠕⠢⠤⠖⠃
⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣁⠀⠀⠀⠀⠀⢀⣴⣊⣥⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣉⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⢠⡾⠿⠷⠶⠤⠤⠤⠤⠴⠒⠛⠓⠒⠒⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⡏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⡠⠄⢂⡉⠉⠐⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⢪⣀⡀⣀⠀⡀⠤⢀⡀⠀⠈⠑⠢⠤⣄⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⠠⣀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⢀⠴⢋⣀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠠⢔⠅⢰⣤⠇⠣⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠱⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠘⢄⠀⠀⢀⡀⠀⠀⢀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠑⠂⠀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⠀⣸⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⣀⠀⠀⢀⣀⡠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⠀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢠⣄⣀⣀⣀⣀⠤
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⣿⡇
⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⣈⠀⡅⠀⠀⠀⠀⡈⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⡇⠀⠀⠀⠀⠲⣲⣾⡆⠀⠀⠀⠶⣿⣿⡟⠃⠀⠀⠀⠀⠀⡁⣹⠃
⠀⠀⡄⣀⣤⣤⡼⠀⠀⠀⢂⠲⠇⠀⠀⠀⠀⠃⠻⣿⣇⠀⠀⠀⠀⠈⢛⠇⣀⠀⠀⠀⠀⣠⠀⠀⣦⡀
⠀⠀⡇⠙⠛⣻⡷⠀⣀⣀⣿⣿⣯⣉⡅⠀⠀⣄⣀⣻⣿⡇⠀⠈⠠⠖⠀⠀⠈⠇⠀⢀⣀⣤⣤⡠⢀⢤⣄
⠀⠀⡇⣿⣿⣿⡇⠀⣿⡏⣿⠟⠹⠿⡇⠀⠀⠈⢉⠉⢹⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⡎⣿⣿⡟⠁⠀⠀⢿⡆
⠀⠀⠗⠶⠿⣿⡇⠀⣿⣇⡟⡞⢟⣻⡇⠀⠀⣶⣶⣶⣾⡇⠀⠀⢀⠀⠘⣿⠇⡀⠀⣧⣿⣟⡃⠀⠀⣄⣼⡇
⠀⠀⠁⠀⢉⠉⢹⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠻⣿⣿⠀⠀⠀⠀⠉⠉⠉⠁⠄⡆⠹⣝⢿⣉⣠⣤⣽⣿⠁
⠀⠀⡤⢇⡀⠳⡼⠀⢠⣤⣿⣯⣭⣭⡅⠀⣤⣾⣾⣿⣿⡆⠀⠀⡀⠀⠀⣀⢐⣰⠇⠀⠹⣷⢎⢻⣿⡿⠁

⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⠛⠛⠛⠲⢦⣄⡀
⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠔⠄⠀⠀⠈⠻⣦⡀
⠀⢀⡾⠁⠀⢴⡄⠀⠀⠀⠀⠀⠀⢄⠌⣀⡀⠀⠀⠈⢷⡀
⢀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⣸⣧
⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣇⣀⠠⠀⢠⠂⠀⢂⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠶⢾⡇
⣿⠁⠀⠀⠀⠈⠤⠤⠊⠀⠀⠰⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⣿⡤⠤⠀⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⣿⣄
⢻⡄⠀⠀⠀⠀⠀⠀⣠⠊⠉⠈⢢⡀⠀⠀⢅⡁⠀⠀⢠⡟⠈
⠸⣇⠀⠀⠀⠀⠀⢠⠃⠂⠉⠀⠀⢃⠀⠀⠀⠀⠀⠀⣾⢽
⠀⢿⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸⠀⢰⣒⡖⠀⢸⠇⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡤⠤⡀
⠀⠸⡇⠘⡆⠀⠀⡸⡆⠀⠀⠠⣶⠇⠀⠈⠈⠁⢀⡿⣤⠜⠀⠀⠀⠢⠆⢠⠏⢱⠀⣴⣣⠤⠖⠁
⠀⠀⣿⠤⣷⠒⠀⠳⣜⣲⣤⡶⠋⢀⣀⣀⣀⣀⣸⣷⠏⠀⠀⠀⣀⡠⠔⠋⢀⣾⠤⠖⠒⠛⠓⡆⠀⠂⡀⠀⠀⠀⢀⠠
⠀⠀⣿⠒⡿⠉⢄⠀⠈⠉⢉⣴⣟⣛⣉⡛⣍⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⡀⢀⣈⡥⠴⠾⠷⠒⠒⠒⣒⠆⠀⠃⠈
⠀⢀⡟⠀⠁⠁⠘⠀⠀⠀⣼⡿⠟⠒⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠛⠫⡄⠐⠯⣩⣏⣙
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠂⠒⠒⠶⠶⢶⣋⣀⠀⠀⠀⠈⠁
⢰⡏⠀⠀⠀⢀⠤⡀⠀⠀⢸⣧⣤⣀⣐⣁⣀⣀⣀⣁⣀⣀⡀⠀⠀⣄⠀⠈⠉⠀⠂⠒⠠⣄⠀⣀⣀⣀⣀⣈⣹⠆⠠⣰
⣼⠀⠀⠀⠀⡁⠀⢨⠀⠠⢸⣿⣤⣴⡶⠿⠛⠛⠛⠿⢿⣯⠉⠉⠛⠓⠤⣄⡀⠐⠲⡤⠤⠼⠂⣀⣀⣀
⣿⠀⠀⠀⠀⠈⠁⠁⠀⠂⠂⠙⠛⠉⠀⠀⠀⠀⠀⠒⠒⢼⡇⠀⠀⠀⠀⠀⠉⠓⠤⠏⠀⠀⠀⠉⠢⢄⣹
⣿⠀⠀⠀⠀⠀⠀⣁⡱⠀⠀⠀⠀⠀⠀⢀⠀⠀⠪⠅⠀⠀⣷⠀⠈⠁⠄
⢹⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠀⠀⠀⠀⣿
⠀⢻⣄⣨⣦⡤⠤⠤⠀⠀⠀⢄⡠⡄⠀⠈⠀⠁⠀⠀⠀⣸⠇
⠀⠀⠙⢶⣤⠷⠶⣒⠀⠀⠀⠈⠷⠉⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠉⠛⠶⠶⣤⣤⣤⣀⣀⣤⣤⣤⣤⠶⠞⠋⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢁⣀⠄⠀⠀⠀⠀⠀⠀⣛⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣶⣾⣿⣿⣿⠶⠀⠀⠈⡘⣻⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣍⣻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣿⠃⠙⠈⠳⣍⠉⠙⠛⠛⢛⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣹⣤⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣯⣽⣿⣿⣯⣿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣭⣿⣿⣿⣷⣬⡆⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣠⣴⣿⣶⣶⣶⣤⡄⠀⠀⠀⠀⠈⠉⠁⠀⠙⡿⠿⣿⡇⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣤⣴⣶⣶⣾⣷⣶⣤⣹⣿⡿⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢸⣯⢸⣿⠏⢿⣛⣛⣻⣿⣿⣿⡆⠺⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠈⠛⣾⠛⣿⢿⡟⢹⣿⣿⠁⠀⢸⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠈⠐⠈⢁⡿⠛⡏⠀⠀⣿⣿⣏⡙⠛⠋⣸⣿⣿⣿⣿⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣻⣿⣿⣦⠉⠛⠻⢿⣛⣿⣿⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣏⡀⠁⠀⠀⠀⠀⣹⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠄⡀⠀⠀⢠⡞⠁⠀⠀⠀⠀⣸⣿⡟⣷⡄⠀⢀⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⠘⠀⠀⣿⠷⣶⣤⣀⣠⣴⣿⣿⣴⣿⡇⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⣿⡶⠄⠈⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠸⢀⠀⣼⣏⠠⠤⠤⠤⠤⣤⣤⣄⣈⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡼⢿⣭⡟⠁⠀⠂⢤⣤⣤⣤⣄⣠⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⢀⣄⠁⠀⠀⠀⠀⢐⠃⠀⠙⠳⣤⢀⣀⠀⠀⣼⣍⢿⣿⣿⣿⣿⣿⠁⢻⣇
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠛⠀⢤⣤⣴⣶⣾⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣾⠈⠄⠀⠀⠉⣺⣿⣿⣿⣿⠇⠀⢈⡏⢷⣄
⠀⠀⠀⠀⠀⠙⠛⠳⠶⠾⢷⣿⣄⣈⣿⣿⢿⣿⠇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⠇⠀⠀⠰⠇⠀⠙⠦⢤⡀
⠀⠀⠀⠀⠲⢦⣤⣄⣀⣠⣇⡀⣈⡉⢹⡇⣸⣿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⢰⡟⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⡀⠀⠉⢉⡉⣉⣙⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠚⣿⡿⠛⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠙⠛⢷⡄
⠀⠀⠀⠀⣈⠉⠛⠿⣿⣿⣛⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣸⡏⢀⣦⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂
⠀⠀⠀⠀⠈⠛⠲⠾⠿⠿⢿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢠⠿⢧⣶⣤⡤⢐⣿⠏⠁⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠿⠟⣠⡾⢁⡄⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⣿⡟⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⣩⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣾⡿⠟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣩⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⣡⡾⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⠿⠿⠿⠻⢿⠟⠙⠿⢿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣛⣻⣟⣿⣿⣿⣟⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠰⣦⠀⣧⠀⡼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⠀⢈⣤⣤⣄⠀⠰⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠀⢰⣏⣤⡴⢿⣷⠀⢠⡞⠳⡆
⠀⠀⠀⠀⠀⢠⡴⠿⠿⢦⡄⠀⠀⠀⠈⠉⠳⣤⣤⠟⠀⠈⠓⠾⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⢀⡾⢻⡆⠀⠀⠀⡴⠛⠛⢦⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⢀⡾⢡⡟⠀⠀⠀⠈⢧⡴⠶⣆⠻⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⡾⢡⡟⠀⠀⠀⠀⣠⡞⠁⣠⠏⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢸⣇⣀⣀⣸⣿⣡⣟⣀⣀⣀⣀⡴⢋⣤⣞⠻⣦⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡏⠉⠉⢹⡯⠭⠭⠭⠽⠿⠯⠾⠿⢭⡽⠗⠈⢷⡤⠶⠛⢹⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡿⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣸⠃⠀⠀⣰⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡗⠒⢲⡶⠚⠛⠉⠀⠀⠀⠀⢠⡏⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠛⠛⠛⠒⠶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠘⠷⠶⠶⠾⠷⠶⠶⠾⠷⠆⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣀⣀⣀⣠⣤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⣶⣿⣿⣿⣋⡀⣀⣀⣀⣈⠻⣿⣿⡯⠞⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠛⠉⠀⠀⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠄⠦⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠛⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢈⣠⣴⣾⣖⣦⣶⣾⣿⣿⡿⠟⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢻⣿⣿⣿⣟⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠛⣽⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⡏⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠁⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⠏

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

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣖⡲⢿⣶⣶⣶⣶⣷⣆
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠃
⠀⠀⠀⠀⣰⣿⣿⣯⣿⣭⣯⣛⣿⣟⠋⢹⠍⡇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣤⣄⡀⠠
⠀⠀⢀⣷⣮⣝⣉⣛⣋⣛⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠌⠟
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⢀⣀⡒⠒⠒⠒⠀⠀⢀⡀⢀⠐⣄⠒⣄
⠀⠀⠀⠘⣿⣿⣿⣿⠁⠁⠦⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠀⠐⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠀⢂⢨⣭⣄⡁⡝⡤⠆
⠀⠀⠀⠀⠈⢿⣿⣿⣦⣀⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠶⠋⠐⠒⠂⢄⡸⡿⠁⣠⣤⣤⣤⡄⠬⠉⢤⣀⣸⡣⣿⣗
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠲⠶⠼⠭⠿⢿⣿⣄⢠⣛⣉⣙⢃⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠘⢧⣄⢀⣀⣀⡀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡀⠲⡶⠶⠒⠶⠋⠉⠳⠆
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠛⢸⠃⠀⠁
⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡮⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀
⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀
⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⢻⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠑⠦⡀⠀⠀⠀⠀⢹⠀⢻⢢⡀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠓⠦⣀⣀⡈⢇⠘⣷⣭⡳⢤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠙⢮⣣⣈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⣶⣶⢶⡶⢶⣶

⠀⠀⠀⢀⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣠⡄⠀⢀⣄
⠀⠀⢀⣼⠷⠛⠘⠺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠤⠄⠰⠦⢼⡇⣄⣨⣧
⠀⠀⠸⣿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠰⣀⣾⣿⠻⠯⡼⠴⣦⠤⠀⠀⠀⠹⣿⡀⠀⠀⣴⣾⠷⠀⢸⡿
⠀⠀⢀⡿⣷⠀⠀⢸⣿⡄⠀⠀⠀⠀⡟⠛⠿⡇⠀⢈⢶⠁⠀⠀⠀⠀⠀⢹⡏⠀⠘⠋⢿⠀⠀⢸⣇
⠀⠀⠘⠁⠋⠀⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠂⠀⠘⠙
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠰⢦⣼⣿⠼⠀⠀⠀⠀⢘⣿⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣻⣷⡖⠒⠀⣀⣀⡘⢾⣏
⠀⠀⠀⠀⢺⣇⠀⠀⠀⠀⠀⠸⣻⣇⠀⠀⠀⠀⠠⣾⣿⣿⠟⠀⠀⠀⠘⠁⠈⣿⡄⠀⠉⠉⠙⣿⠟
⠀⠀⠀⠀⣼⢻⡆⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠰⢦⣿⡂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⡿⢷⣤⡀⠀⠀⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⢉⣿⣻⣗⡀⠀⠀⠀⠀⣿⣧⣤⣴⣿⣇⣀⡇
⠀⠀⠀⠀⠀⢸⡇⠻⠀⠀⠀⠰⠏⣿⣿⡄⠀⠀⢀⡀⠬⠋⠙⠋⠁⠀⠀⠀⠈⠋⠉⢻⠍⠉⠉⠉⠋

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

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣥⣭⣭⣿⣿⣿⣦⠀⠀⢠⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⢸⣦⣸⡿⢿⢿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⡿⠋⠉⠀⠘⠯⢛⣿⡿⣟⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⠃⠀⢠⣄⠀⠀⠀⠀⠉⠉⠉⠉⠀⠁⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠉⠀⠀⠈⠻⠷⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡏⠁⠠⠀⠀⠀⠀⠀⠐⠂⠀⠀⣌⠙⠀⠀⠐⠆⠄⠀⠀⠀⠓⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣄⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣱⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣿⣿⣿⠇⣠⠀⢄⢀⠀⣀⠀⢸⡿⠻⢿⣿⣿⣿⣿⣿⣿⠿⢆⡀⠀⠀⠀⠀⠀⢸⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⣿⣄⣉⠀⠘⠣⠀⠈⠂⣼⠃⠀⠀⠙⠿⣿⣿⡿⠁⠀⠀⠈⠢⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣝⢿⣿⣿⣷⣶⣶⣶⣾⡟⠀⠀⠀⠀⢀⡨⠭⣁⢀⣄⠀⠀⠀⠀⠉⠲⢄⣘⠀⠀⠀⢠⠤⠖⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⠿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⣀⡠⠖⠊⠁⠀⠈⠉⣀⡗⠛⠓⠢⢄⡀⠀⠀⠘⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣋⣉⠤⢄⡀⠀⠀⠀⠀⠀⣲⠀⠀⢀⣀⣈⠁⠒⠐⠒⠒⠉
⠀⠠⠖⠒⠚⠋⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠛⠁⠀⠀⠉⠓⠒⠶⠤⠤⠟⠀⠀⢸⢰⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣚⡛⠇⢰⣆⢀⣦⠆⣢⡟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢷⣾⣾⡇⠸⠟⠘⠋⣏⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠐⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠠⣤⡴⠂⠀⠀⠀⠈⢤⡀⡀⠤⠀⠀⠚⠛⠓⢲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⡜⢀⠆⠴⠁⠀⢀⠜⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡽⠇⠄⠀⠀⠀⠀⠀⢀⡴⢧⡌⢀⠃⠀⡈⡆⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⡨⠻⣶⣦⣤⣇⣿⣤⣀⣠⠇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠤⠊⢥⠎⠊⠀⠀⠀⡰⠋⠻⣍⣹⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⡁⠀⠀⠀⠀⠀⠀⠜⠊⠁⠀⢀⡠⠔⠉⠀⢀⢄⡹⡏⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⠐⢄⠀⠀⣀⡀⠤⠖⠋⠁⠀⢀⡠⠂⠴⠋⠀⣧⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠟⢤⡀⠀⠀⠀⠤⣒⣭⠧⠊⠁⠀⣠⠜⣿⠀⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠊⠀⠈⠙⠤⣀⠀⠀⠀⠀⠀⠀⠐⠉⢀⣴⡿⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠹⣉⠉⠀⠀⠀⣀⠠⠔⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠟⠉⠛⠉⠉⠀⠀⠀⠀⠀⠅⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⣠⣴⠟⠉⠓⠆⠀⣠⠟⠀⠀⢀⣀⡀⡠⠂⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢂⡉⠁⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣞⣁⠡⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⢑⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢁⠲⡖⠋⢻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣄⣀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠳⡜⡆⠸⡀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠹⠶⡔⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⡀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⣦⡀⠀⢀⣠⠀⠰⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠾⢿⡇⠀⠀⠀⠀⠀⢀⣤⠖⠃⠀⠀⣼⣧⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠈⠁⢀⣠⡴⠞⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠠⠶⢿⣗⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠲⣿⠟⠁⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣠⠶⠖⠒⠓⠐⠀⢤⢶⣿⣽⣿⣄⡀⠀⠀⣤⡉⢢⡀⠀⠀⠀⠠⠰⣿⣿⣿⠇⣴⡄⠀⠀⠀⠀⠀⠀⣳⡀
⠀⠀⠀⠀⢀⣀⣲⠾⣽⠑⠂⣰⣷⢄⢠⣤⣴⣺⠛⠋⠁⠀⠀⠉⠲⣄⠈⢷⡀⠻⡀⢠⣤⡀⠑⠈⠁⠀⣀⣼⣯⠀⡄⠀⠀⠀⠀⣼⡇
⠀⠀⠀⣶⣏⠀⠣⢀⣼⡇⠈⣿⣿⣿⠸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠙⠦⡘⣮⣿⠷⡀⠀⠀⠀⠹⣿⣿⣷⠗⠀⠀⠀⢀⡃⡟
⠀⠀⠐⡇⠈⣤⣴⣶⣿⣝⣂⣻⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡙⠳⢶⣀⢠⣁⢀⡿⠃⠀⠙⠛⠛⣩⣦⣀⣙⣻⡇⠀⠀⢸⡏⢴⠇
⠀⠀⠀⠁⣠⣿⡿⠏⠻⢉⡍⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⢠⣶⣿⣿⣿⣿⣿⡿⢷⣤⣤⣿⢓⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣳⣄⣁⠈⢛⡼
⠀⠀⠀⠀⠀⠀⠂⠈⣀⣉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠒⠲⠤⠤⣿⢿⣷⠽⠿⣿⣿⣿⣿⣟⣻⠵⠋
⠀⠀⢀⣚⣣⣖⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⠻⣦⠄⠀⠛⠛⠉⠉
⠀⠀⢸⡿⠋⣩⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢄⡀⠀⠀⢀⠀⣀⠀⠠⣀⣼⣿⡷⠂
⠀⠀⢸⡷⠀⠾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠡⣶⢾⣛⣯⣭⣥⠚⠋⠀⠘⣛⣫⣽⣿⣆
⠀⠀⣸⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⣸⣣⣾⣿⣻⡿⠁⣠⣄⠀⠿⠛⠛⠉⣼⣿⣷⣄⡀
⠀⠀⣿⡀⠀⣾⣿⣿⣿⡇⠀⠀⢀⡴⠋⡁⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠁⢐⣿⢿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣦⣤⣄
⠀⠀⣿⠀⢀⣽⣿⣿⣿⢷⣤⡴⢏⣠⣾⣿⣾⣴⣿⣿⣿⣿⡿⢿⣿⠁⢠⣾⣷⠘⠀⠀⠀⢠⡿⠈⠘⠋⠛⠟⠿⡻⣿⣿⣇
⠀⠀⣿⠀⠀⣿⣿⣿⠏⣼⠃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣿⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠀⡄⠁⠘⠙⣿
⠀⠀⢿⣶⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⣷⣶⣿⣾⣷⣆⣦⠀⢸⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⠇⣸⣿⣿⣾⡃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿
⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⡅⣼⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠁⠚⠙⠳⢿⣿⣿⡿⡿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣖⡀⣀⣄⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢀⡀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⡿⢀⡇⠀⣼⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣟⣿⡇⠈⠀⠀⣿⣿⣿⣻⣿⡆
⠀⠀⠀⠀⣸⡄⠀⠸⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⡟⢢⢀⠀⢀⣠⣤⣠⣀⠀⡤⠘⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠄⢠⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⢀⣸⣷⣾⣸⣦⣾⣿⣿⣿⣿⡄⡀⠀⠀⠀⢠⣄⠀⠀⠐⠂⠤⢀⢸⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠰⣚⣛⣙⣿⣻⣿⠿⢿⣥⣌⣉⠹⣿⣟⢲⣀⣀⠠⠙⠿⣦⡄⠀⠀⠀⠸⣿⣿⣧⣣⡿⠿⠛⠛⠛⠛⠿⣿⣿⣧
⠀⣿⠉⡭⠩⣿⣿⣴⣾⠿⢿⣿⣿⣿⣿⣿⠟⠻⢶⡗⢦⣼⣿⡆⠀⠀⠀⢹⣿⣿⣿⠀⣠⣤⠆⠲⣴⣤⣄⣘⣻
⢨⣿⠀⠃⠀⠈⠙⠋⢁⡀⠀⣸⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⢸⣿⣿⣿⣾⠋⠀⠀⢰⣿⣿⢿⡿⠿
⢸⣿⠀⠒⠀⢀⡒⠀⠒⠀⠀⢻⠒⠒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣇⠀⢀⠄⣾⣿⣿⣾⣿⣿
⢸⣿⠀⠀⠀⠘⠂⠀⠀⠀⠀⣾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⢻⣄⡌⠀⣿⣿⣿⣿⣿⣿
⡿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⡂⠂⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⠀⠀⢸⣿⣿⣿⣿⣿⣳⣠⣿⣿⣿⣿⣿⣿
⠘⡿⠀⠁⠀⢠⠄⠀⠀⠀⠀⢼⠅⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠺⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿
⢸⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⡃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠸⣿⣿⣿⣷⣶⣶⣶⣿⣩⣭⣽⣿⣿
⢸⣿⠀⢀⣀⣁⣀⣀⣀⣀⣠⣿⣍⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿
⠸⣿⣀⣻⣿⣿⣿⣿⣿⣿⣟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣿⣿⣟
⠀⠉⠛⠛⠻⠿⠿⠿⠿⣿⠯⢤⣤⣼⣿⣿⣿⣿⣿⣛⣯⣭⣿⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⡿⢿⠿⣯⣿⡉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣬⣭⣭⣿⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠓⠦⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡤⢤⣀⣀
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠁⠉⠳⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠲⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀
⠀⠀⠀⣏⢀⣤⣠⣤⣤⣠⣤⣤⣆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⡸⠁⠀⠀⠀⡀
⠀⠀⠠⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠙⠶⠤⠼⠋⠧⣄⣀⣤⠞⠁⠈⢹⠁⠀⢀⡇
⠀⠀⠀⢙⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⠀⢠⠋
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢣⣤⣤⣄⣀
⠀⠀⠀⢠⣿⢠⠓⢦⠠⢀⠀⠒⣆⣀⣠⠐⠂⢲⣄⠀⢀⣀⠤⢤⡤⠔⠢⠐⠆⢸⡇⠄⢸⠁⠀⠈⠉⠳⣦
⠀⠀⠀⢸⣿⢸⠀⢈⠀⠀⠀⠀⠘⠿⠋⢰⡄⠘⠿⠿⠋⠀⠀⠀⡆⠀⠀⠀⠀⢸⡇⢀⡿⠒⠲⢦⡀⠀⠈⠳⣄
⠀⠀⠀⢸⣿⢸⠀⠘⢄⡀⠀⠀⠀⢀⡴⠃⠳⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⢸⡇⣸⠁⠀⠀⠀⠙⢦⡀⠀⠘⢧⡀
⠀⠀⠀⡚⣿⠀⠀⠀⠀⠈⠁⠁⠉⠁⠀⠀⠀⠈⠓⠀⠀⠔⠚⠁⠀⢲⣦⠀⢸⢸⡇⢿⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠳⡄
⠀⠀⡠⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢸⠈⣧⠈⠳⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⣆
⠀⣸⠁⠀⡇⠀⢠⡾⠋⠙⢲⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⠀⠈⠀⣿⠀⠀⢧⡄⠀⠀⠀⠀⠀⠘⣦⠀⠀⠙⣆
⠀⢻⡀⠀⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢹⡄
⠀⠘⢦⢰⡇⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠃⢿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇
⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠈⠑⠢⣄⢠⢸⡇⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡿
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢸⡇
⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠂⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⢀⣤⠶⠶⣤⣤⣤⣤⡴⠞⠁⠀⢀⣾⠁
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢄⠀⠀⠀⠀⠀⢀⡜⢡⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⢀⡴⠛⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣤⣶⠃⠀⠑⠲⠤⠤⠖⠋⣀⡴⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟
⣼⠁⠀⠀⠀⠀⠈⠑⠂⠤⠄⢀⡀⢀⣀⣀⣀⣀⣉⠉⠁⣀⠀⠀⠤⠄⠒⠊⠉⠀⠀⠀⠀⠀⢹⡆⠀⢀⣠⣴⠾⠋
⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠓⠛⠛⠉
⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠉⠻⣷⡶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢦⣬⣭⣭⣍⣭⣍⣭⣭⣭⣭⣤⠾⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠚⢳⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠛⣋⣠⠎⠀⠀⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠢⠜⠀⠀⠀⠀⢾⣃⡆⠀⠀⢀⠖⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠑⠂⠀⠀⠀⢀⣤⣤⠰⠶⠶⠒⠒⠒⠒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⢀⠒⠢⡄⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠛⣄⣠⠗⠀⠀⡰⠆⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠙⠦⠴⠂⠀⢀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡤⣄⠀⠀⠀⣀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠙⠃⠀⠀⣎⠉⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠉⠱⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣷⠀⠐⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⠆⣀⡀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠘⢦⣀⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣽⣿⠗⣦⣄⣀⠇⢀⡶⠟⠛⠛⠳⢤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠈⠛⠛⠋⣡⡟⢠⡟⠃⠤⣄⡀⠀⠀⢡⠀⣸⠀⢠⡶⠛⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠀⠤⠀⠀⠚⠉⠀⢸⡇⠀⠀⣿⣟⣳⣦⣼⠀⡿⠀⡟⢰⠎⠩⡉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠁⠒⢢⣄⠀⠀⠀⠀⠲⣆⡀⠀⠀⣱⡄⠀⠈⠉⢉⣴⠏⣴⠁⠀⠳⣌⠓⠒⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠀⠈⠉⠀⢰⠇⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠉⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⢠⠞⠁
⠀⡔⠀⢠⡞⠁⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠁⠀⡎⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⡟⠲⣤⣄⣀⣀⡀⢀⣀⣀⣀⠀⣠⡤⠐⠂
⠀⠀⠀⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢻⡄⠀⠀⣉⠉⢹⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠈⢷⡀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠻⣤⡋⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡛⠛⠛⣶⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⣴⠞⢻⣷⠤⠾⣯⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠚⠛⠁⠘⠋⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠋
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡰⠏⠉⠒⠲⢦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣽⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣧⡀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠙⠲⠶⠤⠴⠾⢧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠛⠛⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⣤⢀⣀⣀⡀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡆⠀⠙⣆⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣸⠃⠀⠀⣼⠁⠀⠉⠁⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⣆⠀⠀⠀⠀⠘⣇⠀⠀⢰⡇⠀⠀⢀⠏⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⣇⠀⠀⠀⠀⠙⣦⠀⣼⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⠙⠓⠶⠦⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢋⡀⠀⠀⠀⠈⢳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⠈⠻⢶⣦⣀⡀⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠛⠛⠉⠉⠲⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠰⠿⠤⠤⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⢶⣤⣤⣤⣤⣠⣤⡴⠶⠞⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⣭⣍⣉⣩⣭⣭⣄⣩⣍⣿⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣤⣾⣿⣿⣴⣤⣧⣼⣷⣦⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠒⠚⢿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠒⣿⣿⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣸⣿⣿⣷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢴⡄⢠⡤⠀⣤⡀⢀⣤⠀⣤⡀⣠⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⣿⣟⠁⠀⠘⣿⣿⠁⠀⠘⣿⣏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⠋⢻⡆⠀⣾⠟⢻⣦⠀⣼⠏⠹⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢻⣿⣿⣷⣶⣶⣾⣿⣿⣿⠏⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣈⣛⣿⣿⣿⣿⣿⣿⣿⣭⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⡆⣤⣉⣿⠖⠋⠺⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡇⠀⢻⣿⣽⡟⠠⢿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡠⡎⠰⠂⠀⠉⠙⡗⠒⠚⡾⠉⢛⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠡⠣⡈⢀⢀⠤⠀⢳⠀⠀⢻⢦⡎⠀⠀⠀⠻⡶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠈⠢⣳⣄⡠⠊⣆⠀⠈⢿⠿⣗⠂⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣠⣷⣄⡄⢾⡫⣷⢠⣏⡽⠃⠀⠀⠘⠳⣦⠤⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⠥⠟⠀⢷⡁⠀⠉⠛⠋⠉⠀⠀⠀⣤⠀⠀⠈⠓⠦⠤⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠤⢪⠀⢈⠳⣄⠀⠀⣠⠄⣠⠟⠉⠉⠉⠓⠲⢤⣄⣠⠀⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣠⣯⠀⠀⠉⠛⠳⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠾⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⠾⠃⠈⠛⢦⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⡹⢆⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⣷⡀⠀⠊⣷⠦⣤⣤⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⢀⡏⠀⠋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣌⣢⠤⠖⡿⠃⠀⠀⣐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣄⣀⣬⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠉⠀⠢⣄
⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⢰⠋⡠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠈⠁⠒⠲⢄⢀⣶⡶⣰⠀⠀⠀⣀⠠⠤⠐⠒⠒⠒⠒⠒⠢⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣀⡤⠀⠀⠀⠀⠉⠈⢙⡿⢷⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠱⣶⡌⠉⠒⠋⠀⠀⠀⠀⠀⠎⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⣉⣠⠔⠀⠀⠀⠈⠀⠀⢀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢦⣀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⣀⣼⡄⠀⡠⢊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠉⠁⠀⠘⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠉⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡈⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠛⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠈⠉⠀⠐⢶⠀⠀⠀⢀⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠀⠒⠀⠀⠈⣇⠉⠲⢶⠄⠀⠀⠀⠀⢀⣜⡉⠄⠐⠒⠦⣀⠀⠀⠀⣀⡔⣁⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢹⠀⠀⠈⠳⡄⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠉⠐⠋⠉⠀⢤⣀⠀⠘⢄
⣀⣀⣀⡠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⢀⠀⠈⠻⠶⠌⡄
⠓⢠⣤⠖⠚⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱⠀⠀⠙⠄⠀⠀⠀⢰
⢠⠿⡤⠋⡱⢊⠟⡹⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡏⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠁⠺⠤⠦⠾⠟⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠂⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⢀⣀⠀⣀⠜⠀⠀⢀⠃⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠸⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢂⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢇⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡞⠁⠀⠀⠀⢸⡴⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⢠⣴⠏⣰⠇⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⣤⠟⢣⣀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠉⠀⠞⢋⣀⠤⠔⠒⠉⠁⣵⡒⠚⠻⠿⢞⠦⢾⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⡾⠦⠀⠀⠀⠀⠀⠀⢀⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣼⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠉⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠢⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⢶⣶⣶⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⠀⠉⠿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠸⣿⡇⢦⢟⠄⠁⠐⠒⠢⠤⣀⡀⢠⢤⠤⠤⠤⢤⣤⣄⣀⡜
⠀⠀⠀⠀⢀⠀⡄⠀⠀⡇⠀⠀⠀⢀⣐⣻⣿⣿⣿⢠⣊⡀⠀⠉⠉⠁⠀⠉⡽⠋⠉⠉⡆⠀⠉⡆⠀⠀⠉⠃⠈⡄⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⠐⠒⣃⣀⣀⣁⠤⠤⣄⠀⠙⢿⣹⠋⠉⢰⠀⠠⠤⣀⡀⠀⠀⢠⠇⡠⠀⠀⡇⠀⡴⠁⠀⠀⠀⢀⡔⢣⡀⠀⠀⠀⠀⡞
⣅⠀⠀⢀⠠⠎⠁⠡⠀⠤⠴⠀⠘⡆⡴⠋⠙⠀⢤⢸⠉⠒⠲⠀⡙⠂⠐⠿⡮⠒⠶⡀⠷⠏⠀⠁⡀⠤⠒⠁⣀⡤⣋⡕⠀⠀⢠⠃
⠈⠓⣄⠳⠴⢖⣀⣀⣀⣠⡤⠤⠖⠙⠶⠀⠀⢩⡓⠊⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣹⣶⡞⣿⡿⠿⠃⢀⠇⠀⠐⢾⡀
⠀⠀⠀⠂⠑⠢⢄⡁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⡆⠀⠀⡖⢸⣿⣿⠿⠋⠀⠀⠀⣠⠴⠵⠶⠖⠒⠻
⠀⠀⠀⠄⡆⠀⠀⠉⠓⠦⣄⣠⠀⠀⠀⣀⣀⣀⠤⣤⡔⠒⠚⠉⣭⣿⣿⣿⣗⠀⠀⡗⢈⠔⠁⠀⠀⣠⠔⢋⣤⠄⠐⠒⠒⠛
⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⡁⠀⠀⠀⢿⡇⠀⠀⢠⠏⠹⢭⡯⢸⠀⠀⣃⡀⠀⠀⠛⣻⣽⠇⣾⣿⠃⠀⠀⠀⣿⡟
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⣠⠃⠀⢠⠎⠀⠸⠀⠀⠉⣌⣣⣄⡀⠀⠙⠷⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⡈⠲⣼⡧⠰⢁⠀⢀⡞⠀⠀⠀⠢⠤⠤⢟⣨⢟⣹⠶⣄⡀⠀⠉⠓⠀⢀⠀⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢌⠢⡈⠋⠻⡗⢕⡿⠀⠀⠀⠀⠘⢦⣀⢀⣀⡈⢸⠀⢸⢹⣇⠠⠊⣀⣠⠃⢁⡀
⠀⠀⢀⡓⠈⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣷⠀⠀⠱⢜⣄⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁⠀⠚⠀⡘⠜⠛⠆⢀⠟⠁⠀⠉
⠄⠀⠿⠇⠉⠿⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠗⠓⠒⠒⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠓⠒⠐⠒⠊⠁
⠀⠀⠀⣀⣀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣔⣒⣀⠒⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⣽⠟⢉⣩⣤⣤⣤⣤⣤⣬⣿⣒⠂⠀⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠯⠛⠁⠢⢴⡿⠟⠙⣓⡚⢓⠛⡛⠳⠮⢤⣀⣄⡐⠻⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⡫⠂⣰⡆⢴⣆⣤⣤⣈⠛⠿⢛⠉⠁⢀⣅⢀⡀⠀⠈⠙⠻⣦⣌⠐⠕⢄
⠀⠀⠀⠀⠀⠀⣠⣿⢿⠏⠠⣺⠟⣡⠀⠸⠟⠉⣤⢶⣳⣬⡛⢿⠿⣶⣦⣬⣉⠒⢦⡀⠈⠻⣷⣄⠲⡡⢀
⠀⠀⠀⠀⠀⣰⣳⠋⠁⢀⡼⢁⠞⡱⠃⡨⢤⣼⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣙⢾⡀⡈⢿⣷⣔⡹⣷⡀
⠀⠀⠀⠀⢰⢳⡏⢀⢠⡿⢠⢃⠠⠀⠐⣁⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣄⢩⣍⡈⠛⠻⠎⢻⢳⡀
⠀⠀⠀⠀⣿⢿⠇⠆⡟⠁⠋⢁⡄⡸⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣆⢻⡟⣦⣶⠀⠈⣏⣧
⠀⠀⠀⠀⣿⡞⢠⠁⠀⠁⠠⣿⢣⠃⣿⡇⣀⡤⡄⠀⠀⠀⠀⡠⣄⣀⣀⣃⡀⠄⠀⠀⢸⡘⡈⠗⢇⡀⣴⢻⢸⣿⡀
⠀⠀⠀⣶⣿⡇⡀⢸⣠⡆⣄⣈⠘⢢⠟⠋⠁⢀⠇⠀⠀⠀⡜⠀⢿⣿⣶⠏⡘⠀⠀⠀⠈⠓⠐⣿⢹⠆⣿⠸⢸⣿⡇
⠀⠀⠀⣿⣿⡇⣷⠈⢿⡇⡇⢻⠞⠁⠀⠀⢀⠎⠀⠀⠀⠀⣇⠀⠀⠀⣠⠜⡤⠊⠙⠀⡘⢠⠰⣿⠈⡄⡿⢀⢹⣿⡇
⠀⠀⠀⢻⢿⠀⢸⣇⠸⣟⢰⣸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⣜⣠⣄⡸⡰⢃⠃⣦⠁⠘⠄⠁⡈⣸⣻⠃
⠀⠀⠀⠸⣾⡇⠈⢏⡆⢿⣖⠗⣷⡀⠀⠀⠈⠷⢄⠀⠀⠶⠮⣥⣦⠀⠀⠈⠉⣩⡞⠁⢃⣼⣿⠃⠈⠀⢠⢡⠇⡿
⠀⠀⠀⠀⢿⣿⣆⠘⣺⡜⢿⢆⠻⡷⠀⠀⠀⠀⠀⠉⠒⠦⠤⢤⡤⠤⠤⢶⠻⠗⢀⡀⠾⠙⠁⠞⠀⠐⣿⠏⡼⠃
⠀⠀⠀⠀⠈⢻⣎⢆⠱⡹⣎⠻⣧⣿⠀⠀⠀⠀⠀⠀⢀⡠⠤⢶⡲⢤⣴⣋⣤⠴⣪⡵⡣⢦⠄⠀⠀⠠⢊⡾⠁
⠀⠀⠀⠀⠀⠀⠛⢯⣧⡙⢿⢧⡈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣤⣤⠴⠾⣋⠤⠖⢁⠔⡹⢋⡴⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠪⡻⣟⠎⠳⣝⡻⡆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠷⠾⠋⣀⠤⣚⡵⢊⠕⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣤⡀⠙⢳⠀⠀⠀⠀⢸⠍⢉⣳⣄⣀⣴⣛⡤⢄⣠⣶⠟⢉⣪⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡻⣶⣧⠀⠀⠀⠈⣗⣒⡲⠞⠒⠒⢒⣉⣉⣥⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡀⠀⠀⢸⣽⡿⠿⠟⠛⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣵⣄⡀⠀⢀⣥⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠙⠛⢿⣦⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⣶⠿⠛⠉⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣀⡤⠿⠛⠟⠉⠍⠀⠀⠀⠀⠀⠀⠀⢀⠭⠙⠻⠻⠧⢤⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣴⣿⣿⣿⡿⠶⣶⣿⣷⡀⠀⠀⠀⠀⠀⡔⣡⣾⣿⣶⠾⢿⣿⣿⣷⢦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣴⣿⠋⠀⠀⠀⠀⠙⢻⣿⠀⠀⠠⡄⢠⢰⣿⡟⠁⠀⠀⠀⠈⠻⣿⣬⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⣤⠨⣿⠀⠀⣀⣀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⢠⣯⣉⣉⣿⠸⣿⣖⠲⠖⠒⠒⠒⣲⣿⣿⡿⠟⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠉⠛⠻⠷⠶⠤⢶⣿⠿⠁⠈⠿⢿⡿⠟⠀⠙⢿⣷⡶⠦⠶⠾⠛⠋⠁⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠀⠀⡀⠈⠒⡦⠥⠼⠤⠄⠀⠂⠁⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢲⠒⠢⢤⡀⠀⠀⠀⠘⠢⢄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢲⡖⠒⠃
⢠⠊⣹⣿⣿⡷⠒⢦⣄⡘⡃⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠀⢸⠁
⠀⢺⣿⣿⡿⠁⣴⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠀⠀⢀⣀⣀⣀⠀⢀⠀⠀⠤⠒⠊⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠙⠏⣠⣾⣿⣿⠟⠀⡍⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠄⠠⠤⠤⠤⠠⣄⡀⠀⠀⠀⠀⠀⠀⢀⡞⡱
⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⢸⠚⠑⡤⠀⠀⣄⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⡀⠀⠀⣴⠋⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⣾⢠⠀⠀⡿⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⣇⢀⢀⣈⡷⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⣏⣤⣄
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⢸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⡆⠀⠀⠀⠾⠻⡿⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡟⠋⠉⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⣀⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣏⣿⣿⣶⣶⣿⣿⣿⣶⡶⢂⣀⣾⡄⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡇⠉⠉⠉⠉⢹⣿⣿⣿⠁⠉⠹⢖⣤⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢘⣭⡻⣇⣄⠀⠀⠀⣼⣿⣿⡇⠀⠀⣠⣾⣿⣷⣄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠙⠃⠁⠀⢀⣠⣿⣿⣿⣁⣤⣾⣿⡷⠿⣿⣿⠇⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢻⣿⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣇⣤⣤⠤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣷⣮⡉⠙⠛⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣍⣿⣿⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠙⢿⣿⣿⣷⡄⠀⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⡟⣺⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠙⠿⠋⢴⣶⣤⠀⠀⠻⣯⡻⣿⣿⡄⠀⠀⠀⠀⠉⠛⠛⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢧⠄⠀⠈⣛⣊⣻⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠈⠠⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡗⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠲⠦⢤⣤⠤⠖⠒⠛⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠠⣤⠞⣩⣥⡀⠀⠈⠣⠤⠶⠒⠲⣄⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡴⠁⣠⢾⠟⣧⠀⠀⠀⠀⢠⣤⡀⠈⠓⣾⠁⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⢳⡿⢲⠟⠃⠀⠀⣠⢺⠟⣧⠀⠀⠹⡄⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣤⡴⢋⡤⠀⠀⢸⢻⡿⢳⠟⠀⢠⠞⠁⢀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⠀⠈⠀⠀⠀⠸⣦⡴⠋⠀⠀⣸⢀⣠⠟⢦⠀⢰⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠳⢤⣄⣤⠴⠂⠀⠀⠀⠀⠘⠛⠉⣾⠁⣸⠃⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠭⣷⣞⣡⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⠈⠹⣟⠓⢒⣲⠞⣻⠋⠉⠀⠹⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡏⠀⠀⠈⠉⠉⠀⡼⠃⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠀⣸⠁⠀⠀⠻⠇⠀⣼⠃⠀⠀⠀⠀⢠⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣍⣑⡟⠀⠀⢀⣄⠀⣰⠳⠤⣄⡀⠀⠀⡟⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹⡇⠀⠀⠘⠞⠁⢈⡗⠶⢤⣍⣙⣺⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡼⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⣴⡿⠤⣤⣀⡀⢀⡞⠀⠀⢀⡞⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡚⠁⠀⠀⡼⠛⠛⠲⠶⠦⣭⠟⠀⠀⢠⡟⠖⠒⠒⣒⣛⣩⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⡾⣣⠖⣠⠞⠁⠀⢀⣰⡴⣪⡅⠀⠀⣠⠏⠉⠉⠉⠉⠉⠣⣄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠻⠶⠗⠋⠁⠀⣠⠖⠋⢯⣾⢟⣕⣡⠞⠁⠀⠀⠀⠀⠀⠀⢀⡼⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⠀⠘⢦⡙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⡤⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⢻⣸⠂⠀⠀⠉⠲⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⣤⣀⣸⣄⠀⠀⠀⠀⠶⠶⠶⠶⡶⠚⠋⠉⠀⠀⠀⠀⠈⣇⣀⡞⡷⣠⣄⠀⠱⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⢤⣤⣤⣀⣁⣀⣠⣤⣤⠤⠴⠖⠚⠃⠉⠙⠳⢧⣇⣀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣉⠛⠛⠛⠛⠻⢷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠈⠉⠉⠉⠉⠉⠛⢶⣤⡀⠀⠀⠙⢿⡉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣄⠀⠀⠀⠻⣆⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢻⡄⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣤⠒⢶⣿⣿⠁⠀⠀⠀⢈⣿⣿⠛⠶⠶⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠆⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠻⠶⢤⠤⠶⠀⠀⠀⠀⠘⠓⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠛⠛⠛⢷⣦⣀⣠⠞⠛⢷⣦⣀⣰⠞⣿⠉⠁⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⢀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣴⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢦⣀
⠀⠀⠀⣠⡄⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠋⠀⡀⠈⠙⠳⣄⠀⠀⠀⠀⠰⠦⠠⠤⠴⠆⠠⠠⣤⡀
⠀⠀⠀⠿⢀⣀⠠⠤⢤⣄⡀⠉⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠒⢂⣀⢠⡤⢤⡤⠤⢀⣀⡀⢀⣈⠃
⠀⠰⠶⢶⣍⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠹⠀⠀⠀⠀⠀⢉⡽⠋⢹⣆
⠀⣦⠀⠈⣿⠛⢶⣤⣤⡄⠀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⢀⡀⣀⠠⠴⢤⡄⠉⠹⠇⠀⢸⡇
⠀⠸⢧⣤⣿⡄⠀⠈⠁⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠋⠁⠀⠀⠐⢢⠀⠆⢸⣧⣤⠞⠁
⠀⠀⠀⠈⣿⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢁⠠⣤
⠀⠀⠀⠀⢸⡆⠀⠉⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⢀⡾⠁⠰⣿
⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠈⠛⠷⣶⣄⣠⣄⣀⣀⣀⣀⣠⣤⣤⢤⣤⡴⠞⠋⠀⠀⢀⠘⣿⠀⣠⡟
⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠋⠀⠀⠀⠀⠀⢸⣾⠃⠀⣿
⠀⠀⠀⠀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⠀⠀⣿
⠀⠀⠀⠀⣿⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠋⠀⢠⠟
⠿⠛⠶⣶⣌⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢰⡇⠀⠀⠀⣀⣠⠶⠖
⠸⣧⠀⠀⢉⡿⠓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣿⠀⠀⢸⣤⡴⠶⠊⠉⠁⠀⢠
⠀⢹⡆⠀⢀⡧⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠹⠖⠛⠣⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠸⣷⠀⠀⣁⠤⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡁⢠⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⣇⣾⠿⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡃⠴⠴⠿⣦⠀⠀⠀⠀⢠⡏
⠀⠀⠘⣿⣇⠀⠀⠀⢰⣤⡐⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣤⠟⠀⠀⠀⠀⣾⠁
⠀⠀⠀⣿⣿⡄⠀⠀⠀⠈⠛⠷⣶⣟⣛⣁⣤⣤⣤⡤⠤⠤⠀⠀⣀⣀⣀⡠⠤⠄⠁⠀⠀⢄⡹⠂⠀⠀⠀⣠⠋
⠀⠀⠀⠸⣿⢻⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠒⠚⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⡿
⠀⠀⠀⠀⣿⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⢸⣇⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⠆⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢰⡯
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣹⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢰⣋⣀⠠⠴⠤⠴⠶⠶⠴⣦⡀
⣤⡖⠋⠉⠉⠀⠀⢈⣩⡿⠟⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠗⠀⠻⢿⣥⣤⣤⣤⣤⣤⠤⠶⠊⠁
⣾⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣦⣤⣤⣶⣶⣶⣶
⣿⣿⣿⣿⠿⠋⠹⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠰⣶
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⠀⣶⡶⠸⡆⠀⣸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⢦⡀⠀⢻⠟⠀⠙⢦⣽⣥⠾⠁⠀⣦⠀⢀⣇⠀⢰⠆⠀⣦⠀⢀⣆⠀⠀⠀⢠⡄⠀⣠⣇⠀⣾⠀⠀⢰⣀⠀⠀⣀⠀⡀⠀⠀⢀⣄⠀⢀⡆
⠀⠈⠀⣀⣻⣋⣠⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⢦⣙⣟⣤⠟⠀⠀⠘⢦⣙⣟⣠⣄⡀⠀⠹⣦⣙⣯⡴⠃⠀⠀⣙⣿⣤⠴⠋⠀⠙⠶⣤⣘⣟⣠⠞⠁
⠀⠀⢸⡍⣿⣿⠀⠀⠀⠀⢀⣼⠋⠻⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠙⠂⠀⠀⢹⣿⡇⠀⠀⣞⠹⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡇⢀⡀
⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⡾⠁⠀⠀⠙⣧⠀⠀⠀⣿⢻⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠙⠀⣿⠻⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠐⠀⠀⠐⠠⠌
⠀⠀⠀⠀⢠⡾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣄⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⣿⢋⡿⠋⠙⠁⠀⠀⠀⠀⠀⢐⣯⣽⡛⣿⡏⠛⠁⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠳⠀⠘⠀⢰⡃
⠀⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⠛⢷⣄⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡄⠄⠀⣠⣤⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⡀⠀⢈⣻⡆⠘⢿⣿⣿⣿⣷⡿⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠟⠁⠀⠀⠀⠀⣾⣿⡄⠀⠀⣾⣿⣇⠀⠀⡌⠻⣷⣶⣸⣿⣿⣏⣀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⣦⣤⡻⢿⣋⣠⡄⢟⢆⢸⡿⣿⣻⡟⣿⣿⣿⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣯⡿⣧⣬⣭⣥⣴⡶⠟⠋
⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⣿⣟⣯⣴⣮⣥⣼⣿⢿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⢙⣛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣻⣷⣸⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⡷⠶⠶⠾⠀⠀⠸⠶⠶⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⠙⣿⣹⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⣿⣿⣿⢸⣿⢸⣿⢹⣿⢻⣿⠟⠘⠿⠘⢛⣿⠟⣿⡏⠁
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⠁⠉⢸⣿⢸⣿⢸⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠉⢸⣿⢸⣿⠀⠀⠀⠀⠐⠿⠃⠿⠃
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⠘⠛⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⠒⠚⢃⡼⠇⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠻⣤⣼⠀⠀⠀⠀⢠⡶⢆⠀⠀⠀⢀⡴⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠲⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠶⠶⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⠋⠀⠀⠀⠛⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣀⡠⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣦⣀⠀⠀⠀⠀⢾⡁⠀⣳⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠙⠚⠁⠀⠀⠸⣇⡀⣹⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢾⣭⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠸⣇⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⣤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢿⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠀⠲⢤⣄⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠘⠶⣤⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣿⠟⣶⣤⣀⣿⠀⣰⡾⠛⠛⠛⠳⢦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⠛⠛⠛⢉⣽⠇⣸⠏⠠⢤⣀⠀⠀⠀⢱⡄⢸⡇⠀⣴⠞⢛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠤⠀⠤⠐⠛⠁⠀⣿⠀⠀⢸⣿⡟⣷⣤⣼⠇⣾⠀⣾⠁⡼⠋⣍⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠁⠀⠀⠀⠐⠒⠒⠒⠒⠲⣤⡀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠘⣇⠀⠀⠙⠛⠋⣠⡟⢠⠟⠀⠻⣄⠻⠆⠜⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠉⠓⠲⠒⠉⠉⠉⠰⠶⠶⠚⠉⢠⡟⠀⠀⠀⠈⠑⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣰⠟
⠀⢀⠀⠀⢀⡄⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠚⠁
⢠⡎⠀⢰⠏⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠋⠁
⠀⠁⠀⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢻⡌⠛⠳⠶⠦⠀⣤⣤⠄⢤⡶⠶⠖⠛⠋
⠀⠀⠀⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣶⠀⣽
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠈⣧⠀⢀⠟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠈⠳⣾⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡍⠉⠉⣷⠄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⣠⠾⠛⣻⡷⠶⠾⣧⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠀⠛⠁⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠋
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠋⠓⠒⢦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠶⣤⣀⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⡀⠉⠉⠉⠀⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡆⠀⠰⣆⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡟⠉⠒⠒⠒⠢⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠙⣆⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣼⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠸⣇⠀⠀⠀⠀⠈⢷⡀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠈⢷⠀⣼⠃⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠉⠉⠙⠛⠒⠤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⡄⠙⠻⠶⣦⣄⡀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⡀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⢀⣠⠤⠴⠖⠲⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡁⢀⣔⣲⠄⠀⠀⢠⣖⣢⡀⣈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡄⢸⠈⠁⣀⠀⠀⠀⠀⣀⠈⠁⡇⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠸⣄⣀⣁⠐⠂⠐⠀⣈⣀⣠⠃⣟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⣈⠛⠒⠒⠛⣁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⢏⠝⠉⠉⠉⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠡⠃⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠙⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠉⠓⠲⠶⠶⠖⢚⣉⠀⠀⣠⣄⠀⠈⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⢾⠁⠀⠀⠀⠀⠀⠔⠤⠀⠀⠘⡇⠀⠀⠀⢻⡶⠒⢒⡄⡧
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⡾⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡇⠀⠀⠀⢸⣯⠭⢴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⡇⣇⠀⠀⠀⠀⠀⠀⢔⢰⠄⠀⠀⡇⠀⠀⠀⣸⡿⠢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣱⠸⣄⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠉⠉⠉⠉⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠼⠀⢳⠉⠓⠒⠶⠶⠤⠼⠦⠤⠶⠶⠒⠚⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⡀⠀⢸⡇⠀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠈⠉⠉⢹⡏⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠋
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⡀⠀⠀⢰⣿⣤⣶⢿⡿⢿⢿⣶⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣇⠀⠀⠀⠀⢀⣧⠀⠀⢸⣿⠿⠿⠿⠷⠾⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⠂⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣀⣠⣤⣼⣿⣤⡄⢸⣿⠀⠛⠃⠀⠀⢰⣇⠀⣿
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣧⣭⣿⣿⣿⣿⣿⣷⣼⣿⣶⣶⣾⣿⣷⣾⣿⣴⣿⣦⣶⣶⣶⣶⣴⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠟⠻⣿⠛⠋⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠙⠛⣿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⢀⣿⡀⠀⠀⢀⡏⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠺⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⠗⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⣿⣶⣿⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠒⠒⠒⢻⡄⠀⠀⠀⠀⠀⢸⣿⢀⣀⣀⡀⠀⠀⠀⢀⣿⣿⣿⣠⡟⠒⠒⠒⠒⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠤⠤⠤⠤⣿⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⣿
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀⣼⣿⡟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⣋⣡⣶⣿⣿⣿⠟⠋⠁⠉⠉⠁⠻⠿⠿⠀⠙⠻⠿⢿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

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

⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣾⢿⣶⣶⡆⠀⠈⠀⠀⠀⠀⠀⢀⡷⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣽⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿
⠈⠻⣌⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠀⠀⡀
⠀⠀⠈⢿⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣜⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⣞⠋
⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠿⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢀⣤⣤⣤⣤
⠀⠀⠀⠒⠚⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠓⠂⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠂⠈⠛⠛⠛⠛


⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣙⠃
⠀⠀⠀⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⣴⣿⣿⣷⡄⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⡇⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⣩⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⡇⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢻⣿⡏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢀⣀⣀
⠀⠀⣿⣿⣿⣿⡇⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿
⠀⠀⣿⣿⣿⣿⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿
⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉


⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣀⢸⣷⢀⡀⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣾⣧⣿⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣾⣿⣦⣤
⠀⠀⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢟⣭⣽⣾⣵⣶⣤
⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⣿⣽⡿⢿⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣡⣿⣿⣿⣿⣇⠀⢹
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠛⠛⠛⣵⣿⣿⣎⡟⠛⠛⠆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣠⡾
⠀⠀⣿⣿⣿⣿⢀⣠⣤⣶⡷⠀⠀⠀⠀⠻⣷⣶⣶⣦⡸⢿⡿⢏⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠾⠷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠛⠛⠛⠋⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠸⠇⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠈⠣⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢸⠀⣠⢀⠀⡠⢀⢄⣀⠀⣀⣤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠛⠾⠖⠧⠘⠴⠛⠋⠛⠶⠛⠆⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣓⣒⠶⠤⣤⣤⣤⣤⡤⠄⢸
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠉⠹⣿⠁⠀⠀⠀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⢽⠠⠾⠳⢤⡀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢹⣧⠀⢀⣀⣀⣠⣤⣤⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢹⠀⠀⠀⡀⠳⡀⣰⣟⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⣼⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣭⣭⣿⣍⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢹⢠⡀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⡞⣿⡿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⢻⠿⠿⣴⠶⢶⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣧⣤⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣻⠀⠀⣾⣿⣿⣦⣼⣿⡇⢿⠿⠋⠉⠉⠉⠉⠉⠉⠁⠀⠈⠻⣿⣿⣿⣿⡿⠋
⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⡿⠿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣄⢀⠐⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠳⠀⠁⠠⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⠆⠀⢀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡣⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣄⢀⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠀⠀⠀⠀⠀⠀⢀⡤⠒⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡈⠀⠀⠀⠀⠀⡰⠋⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡇⠀⠀⠀⢀⠞⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠄⢸⡇⠀⠀⢀⡸⠓⠲⢄⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⡺⠧⠒⠉⠁⠀⠀⣀⠘⠑
⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠠⠐⠠⠶⠋⠁⠀⠀⠀⣀⡤⠖⠉⠈⠃⠂
⠀⠀⠀⠀⡯⠦⠷⠛⢰⡄⠀⠀⢀⣀⠤⠐⡖⠩⠉⡀⠀⠀⠐⢤⣸⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⠔⠋⠀⠀⢰⡃⡆⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⢀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠇⠠⡄⠀⠀⠀⠀⠀⠎⡇⠀⠠⢀⡼⠧⠀⠈⢷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢿⠉⠀⠀⢳⡀⢵⣠⢯⡀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⣇⣴⡒⠉⠀⠀⠈⠣⣈⣀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡜⢻⡄⠀⠀⠀⠀⢻⠈⣃⠈⠳⡀⠀⠇⠀⣳⠙⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠀⢀⣹⣆⠀⠀⠀⠀⠀⠀⠀⣀⣽⣀⠴⠋⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢤⣤⠤⠔⠒⠉⠁⠹⣦⣄⣀⣀⣤⠶⠛⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣼⠛⠿⠏
⠀⠀⠀⠀⠀⣴⠾⠿⠛⡙⣩⣥⣾⣿⡟⢿⡄
⠀⠀⠀⠀⢀⣥⣀⣶⣿⣿⣿⣿⣿⣿⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⢤⣤⡄⠄⠀⠀⠀⣄⣴⣷⠶⣏⣠⠼⠗
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠋⠀⠀⢵⠴⢿⡇⠀⠂⠐⠀⠈⠹⣟⣾⣿⣷⡆⣠⡆
⠀⠀⠈⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡔⢂⣀⠀⢈⣭⣿⣿⣿⣿⠇⣿⠔
⠀⠀⠀⢹⣿⣿⣿⡇⠞⠳⠈⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⡾⠿⠻⠀⠸⠭⠒⠀⠉⠑⠆⠀⢀
⠀⠀⠀⠈⣿⣿⣿⣷⡀⠴⠶⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠊⣩⠥⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣶⣄⠀⠀⡸⠂
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠃⠛⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣻⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠉⠛⠶⣶⠶⡄⢂⡀⠐⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠐⠒⠉⠁⠀⠀⠳⠶⠤⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠒⠒⠶⠤⠤⠤⠤⠶⠤⠤⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢀⠴⠒⠋⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠶⠶⠶⠶⠤⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣩⣭⣻⣿⡟⠈⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⣀⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⢠⡀⠀⠀⠀⠀⠐⠳⠻⠿⠟⣺⣿⡛⣯⣧⣬⣥⡌⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠙⣦⣤⣀⣀⣀⡀⠀⠀⠀⠈⠙⠙⠻⠿⠿⢿⠻⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠛⠵⣄⠀⠀⠀⠈⢣⣄
⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠓⠦⡀⢰⠙⢺⠈⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⢿⣷⠄⠀⢠⣀⣀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠒⠘⠁⠉⠉⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣏⣀⣤⠤⠀⠀⢀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆

⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⡀⡐⠀⡀⠀⠀⡔⢋⣲⣄⣀⣀⣴⠒⠀⠀⠀⠀⠀⠀⠀⠼⠆⠀⠀⢰⣤⣶⣦⣆
⠀⠀⡴⢾⢒⡆⡆⡀⡀⠀⠀⢀⣷⡾⣶⣇⠀⠀⠳⢬⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣠⡶⠉⠂⠀⠀⠀⣿⣿⣟⣿⣭
⠀⠀⡇⢸⢸⡇⡇⡇⡇⠀⠀⠸⣿⠇⢿⡿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢀⣴⣝⡟⠁⠀⠀⠀⠀⠀⣿⣿⡽⣿⣿
⠀⠀⠙⠺⣬⣇⣇⣇⡇⠀⠀⢠⡆⠀⠀⣥⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠣⡸⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⢰⣿⣟⡴⠢⡀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⢸⣤⣀⣼⠀⠀⠀⢸⢩⣭⣭⣩⣍⣭⢹
⠀⠀⢠⣀⣀⡄⣿⣿⡇⠀⠀⠀⢸⣭⣭⡗⠃⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠴⣿⣿⣿⣿⡿⠆⠀⢸⢩⣍⣭⣩⣍⣭⢹
⠀⠀⠀⠻⡟⠁⣿⠀⠀⠀⠀⠀⠸⣿⡿⠇⠀⠀⠀⠀⠉⢹⡏⠉⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢸⣩⣭⣭⣩⣍⣭⣹
⠀⠀⠀⠰⠇⠀⠿⠿⠇⠀⠀⠀⠀⠼⠤⠀⠀⠀⠀⠀⠠⠾⠷⠄⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠸⠉⠉⠉⠉⠉⠉⠹

⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⣄
⠀⠀⠛⣦⣼⣧⣤⣤⡄⠀⠀⢀⣀⡀⠀⣿⣇⠀⠀⠙⢻⣿⣿⡟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣳⡴⠴⠤⠦⢦⡞
⠀⠀⠀⠈⠙⠿⠿⠋⠁⠀⠀⢸⣿⡇⢸⣿⣿⡆⠀⠀⠈⢻⡟⠁⠀⠀⠀⠈⣿⣧⣿⣷⣄⠀⠘⢇⢸⡇⡆⡆⡆⡎⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⠀⣸⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠆⠀⠈⢻⡅⠇⠇⠇⠇⡇
⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠛⠀⠘⠛⠛⠁⠀⠀⠐⠛⠛⠂⠀⠀⠀⠀⠛⠉⠙⠛⠉⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⠖⡆⠰⢲⠀⠀⢰⣖⣒⣒⣲⡆⠀⠀⣰⢶⡖⠒⢶⢲⡀⠀⢀⣀⠀⠀⠀⢀⡀
⠀⣠⢠⡄⣤⢠⣀⠀⠀⠀⣞⠉⣳⠁⢱⡋⢈⡆⠀⣼⠛⠛⠛⠛⣧⠀⢠⡟⣿⠛⠛⠻⡟⢧⠀⢺⣗⢀⠀⣀⣸⡇⡇
⠀⣿⢸⡇⣿⢸⣿⣤⡀⠀⡁⠄⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡄⣧⠀⠀⢀⡇⣸⠀⢬⡧⠀⠀⠀⢸⡇⡇
⠀⠛⠘⠇⠿⠘⠋⠉⠁⠀⡉⠍⠉⠉⠉⠉⠍⡇⠀⢸⣿⣿⣿⢿⡇⠀⠀⢿⣹⣏⣉⣿⣻⠇⠀⠼⣗⠀⠀⠀⢸⠧⠃
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠠⠋⠓⠑⠛⣆⡀⠐⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠂⠈⢳⡀⠀⠐⠯⡘⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⢐⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⠈⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡄⠀⠈⠀⠀⠉⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠜⢁⠀⠀⠀⠀⠈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠋⠀⠀⠀⠀⠀⠈⠀⠀⠐⢇⠀⠀⠀⠀⠀⢠⠴⡀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠂⠁⡰⠃⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤⠁⢐⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⡨⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠅⠤⠒⠁⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠐⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⣀⣀⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡇⠀⠈⠢⡀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⠀⠀⠀⠀⢱⠀⢀⡠⠦⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⢀⠎⠀⠀⠀⠀⠈⠏⠁⠀⣀⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠉⠦⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠤⢠⠆


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡶⠲⢀⣤⣶⡆⠀⠀⣶⣶⣆⠲⡀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⡿⢈⡑⣱⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣌⢸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⡿⠛⠋⠙⣿⣿⣤⡍⢼⣿⣿⣿⣽⣷⣶⣤⣿⠿⣿⣿⣿⣾⣹⡿⣛⠋⠉⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠸⢧⣶⣼⣿⣏⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣽⣿⣾⣽⣻⣟⡻⣿⣿⣶⡆⠀⠈⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⣀⢘⣣⣤⣾⣛⡛⢻⣯⣿⣿⣷⣿⢿⡋⠑⠀⠈⠀⠀⡉⠙⢿⣿⣿⣏⣷⣴⢿⣯⣤⣴⡟⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⡉⠜⠉⢡⡾⠋⢩⣿⣿⣿⣿⣿⣿⢿⠀⣿⣿⣷⡄⡆⢠⣶⣶⣶⡿⣿⣿⣿⣿⡿⣿⡊⠁⠙⠛⠛⠛⠁⢄⠁
⠀⠀⠀⠀⠀⡠⠾⠉⢙⡄⠀⠊⠀⠀⣠⣿⣷⣤⣴⣿⣿⢻⣿⣿⣿⢸⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⣧⠻⢹⣿⣿⣿⣷⣽⡦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⢗⣾⢛⣾⠛⠁⠀⢩⣿⠛⡾⠘⣿⣿⡟⢺⡆⢿⣿⣿⠇⠀⢘⣿⣿⣿⡇⠀⢘⣿⣿⡛⠙⠻⣆⢱⣤⣤⡤⡀⠀⠀⢀⣄⣤⣄
⠀⠀⠀⠀⠀⣠⠞⢠⠔⠀⠈⠳⠶⠋⣀⣤⣾⣿⣿⣦⠃⣰⣿⣿⣷⡼⠃⣼⣿⣿⣆⠀⢸⣿⣿⣿⣿⡀⣨⣿⣿⣣⠀⣸⣿⣿⣦⣀⠙⢿⣟⣢⡼⢿⣿⠟
⠀⠀⠀⠀⣾⡃⢀⠄⠀⣤⡶⠞⣾⣿⣿⣿⣿⣿⢿⢿⣷⣿⣿⣿⣿⠷⢺⣿⣿⠿⡿⣶⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣋⣰⣿⣟⣷⠏⠉
⠀⠀⠒⢠⣻⣤⣬⠁⠐⠛⠉⠘⣿⣿⡿⠓⠉⠀⠀⠀⠀⠀⠈⠃⠙⠈⠀⠁⠈⠀⠀⠀⠸⣇⠉⠉⠁⠀⠀⠺⠷⢬⣬⣙⡋⠉⠉⠙⠛⠿⢿⡽⠟⠻⠧
⠀⠀⠀⠈⣬⠯⣿⣤⣴⡶⠠⣶⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⣩⡉⣕⢦⡀⠸⠀⠀⠀⠲⣄⡀
⠀⠀⠀⠀⢻⣷⣶⣿⡾⢿⠿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⡀⠀⠀⣼⣿⡡⠚⠃⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢄⡀⠀⠀⠀⠘⢷⣆⢠
⠀⠀⠀⠀⢼⣿⢁⣤⣤⣈⣀⠩⠹⣿⡀⠀⠀⠀⠂⠠⠀⠀⣾⣻⣿⣾⠃⠀⠀⠉⠀⠀⠐⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⠠⠀⢸⡟⣿
⢰⠶⣾⣷⣿⣿⣿⣿⡛⣹⣿⡧⠀⣿⡇⠀⠀⡠⠠⠛⠛⢷⣿⣿⣋⡁⠀⠀⠀⠀⣆⢀⣤⠆⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠙
⠘⠓⠉⠆⣿⣹⣿⣿⣿⠿⢫⠁⣠⣿⣇⡄⠈⠂⡀⠀⢀⡜⢫⡴⠾⡏⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢀⣀⠀⠀⠀⠀⡀⠀⠈⠙⢿⠄⠀⢠⣤⣦⡀⠀⠐
⠀⠀⠀⠘⣷⣿⣿⣿⠧⢺⣽⣿⣿⠿⣿⡇⠀⠀⠉⠤⠆⡿⠿⣦⢾⡇⠀⠀⠈⠁⠀⠀⠀⠐⠀⠠⠆⢀⣿⠓⡶⠖⠀⣈⠀⠀⡀⠀⠀⣠⡏⣿⣟⣿
⠀⢠⣾⢾⣿⣿⡿⠁⣽⣿⣿⣟⣿⣷⣷⡄⠀⠀⠀⢸⡷⠀⠀⠈⠉⢁⠀⠀⢙⠢⡀⠀⠀⠀⠀⠀⣤⠏⢈⣤⣀⠒⠀⡈⠉⠀⠀⠀⠀⣀⣀⢠⣿⠉⠁
⠀⠀⢿⢿⣿⣿⡇⠀⣿⣿⣿⡟⠙⠿⣿⣷⣆⠀⠠⠀⠀⠀⠀⠀⢀⣜⡢⠄⡃⣸⣷⡄⠀⠷⠠⣌⠛⣾⣿⣿⣿⣷⣦⣀⡀⣀⡀⣀⠀⣀⠁⡹⣟⢾⡄
⠀⠀⠈⠀⢻⣿⠃⣾⣿⣿⣿⡫⣄⠠⠉⡿⢻⠀⠀⢀⣤⣦⡴⠶⠢⠮⠥⠌⠠⡉⠈⠁⠀⢀⣀⣒⡂⠸⣛⣻⣿⠛⠉⠛⠁⠁⠘⠁⠔⡥⠪⣚⠿⠁⠄
⠀⠀⠀⠀⢄⣿⣧⣿⣿⣿⡏⢈⣿⣳⣶⡷⣾⣤⠐⢾⡛⣯⡄⠀⠀⠂⢘⣂⣀⣘⣠⡴⠶⢼⣿⣿⣟⠋⠉⠉⠁⠀⢀⣤⣀⡨⠟⠓⠮⣦⠔⢡⠀⠄⢄⡀
⠀⠀⠀⠀⠀⠻⣿⡟⣿⣿⣟⡀⠰⢿⣿⣧⣿⡿⢳⣺⡇⣿⠃⠒⠛⠛⠋⠉⠉⠀⠀⣀⣀⡄⠈⢻⣿⡀⠀⠀⠀⢀⣿⣿⡿⠁⢠⣦⡄⣭⡴⣀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠹⣷⡼⢻⣶⣶⠞⣠⣾⣿⣿⣿⣿⣯⣙⠛⠂⠀⡀⠀⠀⠀⣤⣶⣿⣿⣿⣷⡄⠸⣿⣷⡆⠀⠀⠀⢀⣿⣇⣠⣾⣾⠖⠿⠆⢬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣿⣃⣾⣿⣿⣈⣛⣨⣿⡛⢾⣦⣶⠶⠾⠀⠀⠀⡈⣿⣿⣿⣿⠿⡏⠁⢹⡿⣧⠀⠀⠀⢾⣿⣿⡟⢛⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⣌⣍⠉⠁⠙⠿⣶⣽⣿⣶⣤⣴⡀⠀⠈⢹⣿⣿⣏⢴⣿⡀⣸⣿⠻⣆⣰⣿⣿⣿⣿⣤⣤⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣤⣤⠤⢤⡄⠉⠻⠿⠁⠈⠠⣤⡤⡞⢩⣿⣿⣷⣿⣩⣿⣿⣻⣾⣯⢿⡁⠉⠳⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠴⣷⠆⡠⠄⠠⠥⠉⠈⠉⣉⢸⡟⢹⣼⣿⣿⣿⣿⡿⠟⠛⠓
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣉⣬⣼⣿⣿⣿⣟⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⡿⠿⠿⠿⠿⣷⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠉⠻⣦⠀⡀⢹⣆⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⡶⣸⡇⠀⠀⠀⣿⡇⣿⢸⣿⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⣠⡾⠿⣦⣴⣏⣼⣿⠟⠀⠀⢀⣴⣿⣿⡿⠿⠋⣠⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⢀⣿⢰⠶⣼⣿⣿⠋⠀⠀⠀⠀⣨⣥⣴⣶⣶⣶⣟⣯⡴⠟⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡘⣿⠈⣾⡏⠹⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⣀⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡙⢷⡈⠛⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠰⣆⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠋⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠁⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠞⠁⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⢻⡿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣾⠿⣿⠳⣶⣶⣶⣶⣾⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠹⠿⢋⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢋⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⡙⠻⢶⣦⣤⣄⣀⣰⠆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠋⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠉⠛⠳⢦⣤⣭⣉⣹⡟⠀⠀⠀⠀⠀⠀⣸⡿⠋⠙⣿⣦⡶⠟⠛⢿⣦⠀⠀⣠⣴⡾⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣃⣤⡾⠟⠉⠀⠀⠀⠀⠙⣿⣿⠋⠁⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⡀⠀⠀⠰⠟⠋⠉⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠑⠻⠾⣶⣶⣶⣶⠗⠸⣿⠀⠀⢠⣤⡄⠀⠀⣤⣼⣿⣦⣄⣬⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠰⢟⣠⣿⢀⣠⣶⢶⣌⢻⣎⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢬⣝⣛⣛⣿⠇⢹⣯⠙⠇⠙⠁⢉⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⠹⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠙⠛⠻⣿⣿⣦⣤⣀⣲⣾⣽⣿⣿⡾⠟⢿⣧⣤⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢰⡿⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⡉⠛⠛⠉⠉⠉⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠸⣷⡀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⣹⣷⣄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⢀⣰⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣠⣾⣿⠟⢿⣷⣄⠀⠉⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣤⣴⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣷⣶⣶⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⡀
⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣉⠀⠀⠉⠉⠙⠳⢦⡀
⠀⢀⡼⠃⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠃⠀⠀⠀⠀⢀⣠⠖⢻⡄
⣴⠿⠶⣶⣴⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⢶⡶⠶⠖⠛⠋⢻⡄⣼⠃
⣿⣀⣙⣻⠍⣻⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⠈⢁⣴⠀⠲⠂⠸⣷⡏
⠈⣿⠉⠉⠀⣻⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⣤⣿⣇⣀⣀⣠⣶⡿
⠀⠹⠶⢶⣶⠿⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢤⣌⣉⡉⠉⣹⠇
⠀⠀⠀⠀⣿⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⣉⣠⡶⠋
⠀⠀⠀⠀⠸⣧⠀⠀⠙⠷⣤⣀⡀⠀⠀⢀⣤⣴⡶⣾⠋⠉⣿⡶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠳⠟⠻⠟⠳⠟⠳
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠉⠙⠛⠛⠿⠃⠈⠀⢸⣧⣤⡿⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣤⣄⣤⣄⣠⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⡀⠀⠈⠙⠛⠶⢦⣤⣄⣀⣀⣀⣀⣤⣴⣿⣿⡿⠀⠀⠀⠈⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠦⣤⡄⠀⠀⢸⡇⢸⡇⠀⠀⢸⡟⠷⣤⣄⣀⠀⠀⠀⠈⠉⠉⠉⠉⠹⣷⠀⣿⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⢸⡇⠀⠀⠈⣷⠀⠀⠈⠉⠛⠛⠳⠶⠶⠶⠶⠦⢤⣿⣿⣛⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⡇⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⣤⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⢸⡇⢸⡇⢀⣤⣤⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⢸⣇⣸⡇⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠶⠶⣤⣼⡏⢹⣧⣤⠴⠶⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢀⣤⡶⢶⣄⡀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣴⠟⠁⠀⠀⠈⠻⣦⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢹⣆⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⣴⠟⠘⢷⡄⠀⠀⠀⠀⢻⣄⠀⠘⣧⡀⠀⠀⠀⣰⠟⠀⢀⣼⠋
⠀⠀⠀⠀⢸⣿⠶⢶⡆⣿⠀⠀⠀⠀⠀⠹⣦⡀⠘⢷⡄⢠⡾⠋⠀⣠⠟⠁
⠀⠀⠀⠀⢸⣇⠀⣸⡇⣿⠀⠀⠀⠀⠀⠀⠈⠳⣶⣛⣿⠋⣀⣴⠟⠁
⠀⠀⠀⠀⢸⡟⠛⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠙⡿⣿
⠀⠀⠀⠀⠀⠻⠶⠶⠾⠃⠀⠀⠀⠀⠀⣠⡾⠋⢻⡄⠈⠛⠻⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠐⡍⠀⠀⠋⠃⠀⠀⠀⡤⠠⠀⠀⠀⠀⠨⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢤⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠦⢤⡄⠀⠀⠀⡀⠀⠀⠄⠉⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⣄⠀⠀⠀⣠⠐⡀⠀⠀⢀⠔⠁⠐⠀⠀⠀⠀⢀⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢄⠁⢂⡤⠐⠀⡆⠀⠘⠉⡐⠂⠤⡰⢶⣀⠈⠒⠃⠀⠂⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠚⡌⠀⠀⠀⠐⢡⠀⠀⠀⠁⠀⠐⠚⠀⠐⠐⠃⠀⠊⣀⠀⠀⠘⠁⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⣀⠠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢁⣀⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⡀⠀⢠⠀⠀⠀⠑⣀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠉⠀⡀⠈⠈⠀⠀⠀⢀⡤⠤⠀⠉⠀⡀⠙⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣴⠾⣛⣫⣭⠭⠭⠭⠭⣭⣽⣛⡷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠊⣷⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢬⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⣀⣀⡀⠀⢠⣶⣄⡛⠀⠙⢶⡝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⣥⠀⢀⡄⠀⠀⠀⠀⠈⠙⠻⣿⡿⡿⢟⡊⠉⢛⠟⠀⠀⠀⠙⣮⢻⣆
⠀⠀⠀⠀⠀⠀⣰⡟⡼⢡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⢀⡾⡵⠖⣿⣦⡀⠀⠀⠀⠈⢧⢹⣆
⠀⠀⠀⠀⠀⢠⡿⣸⠃⠈⠀⠀⣀⣀⣀⡀⠀⠀⠀⢰⣿⣿⣭⣴⣶⣶⠿⣿⣿⣄⠀⠀⠀⠘⣇⢿⡄
⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣾⡙⠿⡿⠟⠋⠁⠀⠈⠻⣿⣷⡄⠀⠀⢻⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠸⣿⣷⣽⣿⣿⣿⣿⣷⡙⠀⡀⠀⠀⠀⠀⠀⠈⠫⣾⣇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⢿⣿⠉⠉⠛⢻⣿⣿⡇⠀⢳⠀⠀⢀⠀⠀⠀⠀⠈⠹⣷⣼⢸⡇
⠀⠀⠀⠀⠀⠘⣷⢹⡄⠀⠀⠀⠀⠸⣿⠀⠀⠀⢰⣿⣿⠃⠀⣸⡇⠀⠀⠀⣀⣤⣤⣤⣄⢃⡏⡊⠁
⠀⠀⠀⠀⠀⠀⠹⣧⢳⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠱⣶⣶⣆⢀⣶⣾⣿⣾⣹⣿⣿⢟⡜⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣄⣤⣤⣾⠿⠿⠀⠀⠀⠀⠀⣈⣩⣿⡾⣿⡿⣟⣋⣜⠉⣠⢟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠿⣍⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣷⣾⠿⣿⣿⣿⡟⣣⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣛⢦⣄⣀⠀⠀⠀⢀⣿⡿⠿⣿⣿⣿⠘⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣭⣝⣛⣒⣒⣚⣛⣚⣩⣴⡦⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠶⢶⣚⣿⣿⣿⣿⣿⣿⣶⣤⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣭⣿⣿⣿⣿⠿⣿⣿⣿⣯⣭⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣋⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣶⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣾⣿⣿⣷⣄⣤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣷⣽⣿⣿⣯⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠹⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠙⣩⣠⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣆⣯⡋⡋⣿⢢
⠀⠀⠀⠀⠀⢠⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣷⠏⣿⣸⢁⢸⡇
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠩⢶⣵⣫⣞⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⢈⠹⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢈⡶⠦⣤⣀⣀⠤⠈⠂⣰⠏⢳⡐⠆⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢌⡁⠀⠈⣩⠀⠀⠀⠀⠂⠀⠀⠑⠀⢤⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣙⠀⠀⠀⣆⢹⠀⡀⠀⢤⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢸⡄⠀⢸⡄⢸⡣⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣷⠀⠱⣤⡀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡆⡾⠀⠀⣸⡟⢀⡴⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⠣⠀⢰⡟⠀⣼⢣⣾⡡⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⣀⢾⡀⠀⢣⡟⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠸⠀⡠⠏⠈⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠁⠀⠀⠁⠀⠀⠁⠀⠀⢀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣀⠀⠀⢧⡰⢦⡀⠀⠀⢀⡎⢠⣿⠋⠀⢀⡀⣠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢦⡀⠀⢰⡇⠀⠀⣾⠀⣾⠇⠠⠒⠋⢻⡆⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⠁⠀⠀⠇⢸⠋⠀⠀⠀⠛⣾⡿⠢⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣤⣤⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡊⠉⢹⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠄⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠶⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠛⠛⢻
⡠⠒⠓⠒⠶⣄⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠚⠋⠉⠉⠀⣀⣠⡤⠖⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠣⠤⠔⠈⠀⢀⣠⣴⠀⢀⡔⣋⣁⣀⣀⣀⣠⡤⠴⠒⠋⠉⠀⠠⢤⠤⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆
⠀⠀⠀⠀⡰⠋⢠⡇⠀⠈⢿⡉⠉⠉⠉⢀⣤⡖⠀⢀⣀⣠⣄⠀⠉⢻⣦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣇
⠀⠀⠀⠰⣇⢀⡾⠀⠀⠀⠈⢻⣆⣴⡾⠛⠁⣙⣲⣏⣥⡤⠾⢓⣫⡁⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠹⣿⠙⠋⢉⣭⠿⠷⠶⣤⢸⠉⠀⢻⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠋⠇⠀⠀⠀⢸⠇⢀⣐⡊⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠒⢒⡞⣰⠋⠉⢈⣡⢾⡇⠀⠀⠀⢀⡼⠁⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⣤⡤⠶⠶⠛⢉⣠⠜⠃⠀⠀⠀⡾⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡴⠚⠉⠙⠛⠒⠒⠦⠴⠒⠀⠀⠈⠉⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡴⠖⠚⠶⣄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⡇⠀⣀⣀⣠⠴⠋⠁⠀⢹⠀⠀⠀⡴⠛⠳⠞⠀⢻⢀⡤⠤⡄⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣴⡆⡇⢠⡇⠀⠀⠀⠀⠀⠀⠈⠳⠖⠊⠀⠀⠀⠀⠀⢸⠎⠀⠀⢸⠀⢸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢉⡔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⡸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⠊⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠃⣠⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢠⡀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⠔⠁⡴⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡙⠫⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡠⠊⠀⠀⠀⠀⠀⠈⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠖⠚⠉
⠀⠀⠈⣀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠐⠿⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼
⠀⠀⠀⠀⢻⣄⠉⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⢶⣦⣤⣤⣤⣶⠶⠶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠉⠛⠶⠦⢤⣤⣤⣄⣀⣀⣀⣤⣤⣤⡤⠴⠶⠖⠋
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⣎⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠛⡗⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀
⠀⠀⠀⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣒⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠬⠭⠍⣵⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⣀⣠⣋⡛⠒⠒⠖⠴⡇⠀⠀⠀⠀⠈⠁⠛⠃⠀⠀⠀⠀⠀⠉⠲⠤⠼⠾⣀⣀⡄⠀⠀⠀⠀⢠⠞⠉⠀⠉⠙⠢⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡉⠉⡉⠐⠒⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣠⠒⠒⠹⡄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⠡⢀⡤⠤⢷
⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢾⡏⠉⠙⠲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠤⠞⠛⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣸⠀⠀⢠⣶⡄⠀⠀⢸⣧⠀⠀⣀⡗⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣰⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⣰⠃
⠀⠀⠀⠀⡤⠠⢤⣠⠔⠒⢢⠀⠀⠀⠀⣾⡷⠤⠤⠤⡏⠀⠀⣾⠇⢷⠀⠀⠘⣿⠒⠋⠁⢠⡶⠒⠢⣄⠀⠀⢿⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢙⠾⡅
⠀⠀⠀⠀⢇⠀⠀⠁⠀⠀⣸⠀⠀⠀⢐⣿⠇⠀⠀⢰⡇⠀⣼⣯⣤⣼⡇⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠈⡇⠀⠈⣿⡞⠁⠀⠀⠀⣠⢄⣠⢤⠀⠀⠀⠳⣏
⠀⠀⠀⠀⠈⠳⣀⠀⠀⡰⠃⠀⠀⠀⠸⣿⠀⠀⠀⢸⠀⢰⣿⠀⠀⠀⢹⠀⠀⢿⡆⠀⠀⢸⣇⣀⣠⡴⠃⠀⠀⣾⡇⠀⠀⠀⠀⠙⢄⣡⠞⠀⠀⠀⠀⢸⡄
⠀⠀⢠⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⣼⡏⠉⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠻⠃⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣴⡞⠉⠓⢦⠀⠀⠀⢸⣧⠀⠀⣰⡞⠛⠲⡄⠀⠉⠉⣿⡏⠉⠀⣀⠀⠀⠀⠀⢸⡇⠀⠙⢦⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⣠⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣸⠀⠀⠀⣼⡇⠀⠀⣿⡇⢀⣠⠇⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⢸⠇⢸⣷⠀⠀⠘⡇⠀⠀⠀⠀⠈⣿⡄⠀⢠⠇⠀⠀⢸
⠀⠀⢀⡀⠀⠀⠀⢸⣷⠶⠚⠧⣄⠀⠀⣿⠇⠀⠀⣿⡿⣍⠁⠀⠀⠀⠀⣿⠀⠀⢸⣧⣀⣀⣼⠀⠈⣿⠀⠀⢠⡇⠀⣰⣿⡀⠀⠘⣿⣀⡞⠀⠀⠀⢸
⠀⠀⠁⠑⠙⠆⠀⠈⣿⠀⠀⠀⢸⠀⠠⠿⠄⠀⠀⣿⡇⠈⠳⠀⠀⠀⠀⠿⠀⠀⣿⡇⠀⠀⡿⠀⠀⣿⣀⡠⠏⠀⣰⡟⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣠⠞⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢀⡇⠀⠀⠙⠉⠀⠀⣰⡟⠉⠙⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡶⡄⠀⠀⠰⠟⠀⠀⠀⠾⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⡆
⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡉⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠄⠀⠀⠀⠀⠀⠀⣞⠑⠞⢱
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⠉⢳⠦⣄⡀⠀⠞⠀⠀⠠⠖⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣠⠤⠴⢆⠀⠀⠘⢦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠘⡏⠑⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⣋⣉⣩⣤⡤⠖⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠
⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠀⠸⡆⠁⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣁⡨⠤⠔⠒⠋⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠙⠁⠀⠀⠀⠀⢸⡀⢀⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠉⠀⠀⠀⣀⣠⢤⡤⢴⣛⡦
⠀⢀⡤⢤⡀⠀⠀⠀⠀⢠⠗⠋⠀⠀⠀⠀⠀⠖⢦⣀⣀⡀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢸⣓⣮⣽⠯⠽⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤
⠚⠉⠀⠀⠙⠢⠤⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡛⢿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⡽⠃⠉⠙⠻⢷⠗
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⠃⠀⠀⠤⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⣠⠔⠃⠸⣄⠀⠀⠠⢄⠁⠀⠀⣤⣐⣐⡒⢢⡀
⠀⠀⢀⡠⠂⠀⢷⠀⠑⣄⠘⢿⣦⠤⠄⠀⠀⠀⣧⠀⠀⠀⢸⠽⡆
⢀⠞⠁⠀⠀⢄⠘⡆⠀⣈⠳⡘⢉⣧⠀⠀⠀⠀⢸⠀⠀⠀⠈⣯⡇
⣾⠀⠀⠀⠀⠈⢷⡙⠚⠁⠀⠁⠈⠐⢦⠀⠀⠀⠈⠓⢤⡤⠀⠑
⢻⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢠⠀⢳⡀⠀⠀⣰⢣⡑⡼⠁⠀⠀⠀⣀
⢸⢷⡄⠀⠀⠀⢀⣀⣈⢦⡀⠀⠀⢸⢀⣤⣛⣦⡠⠛⢄⠙⠣⠀⠀⠀⡀⠁⢀⣈⢣⠀⠀⠀⢀⣀⣀⣀⣀⣀
⢸⠇⠙⢦⡀⠀⠀⠉⠉⠁⠉⠑⠲⠼⠭⢀⣀⣞⡁⠀⠀⠩⠏⢀⡀⠀⡏⠉⠉⢁⡨⠖⠚⠉⠨⡅⠀⠀⠀⠈⠙
⣸⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠹⡆⠀⠀⠀⢐⣮⠀⠑⠂⠐⢅⠀⠈⠁⠢⠄⠀⠀⠀⠀⠠
⣏⠀⠀⠀⠀⠀⠉⠒⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣭⣶⣦⡤⠐⠀⠀⠀⠀⢀
⠈⢣⡰⣄⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠭⠭⠤⠤⠤⠤
⠀⠘⢿⣾⣷⢢⣤⣗⡒⢲⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠒⠒⢒⣒⣒⣀⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠒⠛⠳⠗⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠀⠀⢀⡀⠀⠀⠢⠚⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⣶⣆⠉⠓⠋⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠦⠀⠉⠀⠀⠀⠈⣷⡂⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠛⠀⠀⢠⣐⡒⠀⠈⢴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⠀⠀⠀⠀⠀⢀⢊⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠙⠋⠁⠀⢀⣤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠆⠼⠉⠛⠛⠉⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⠀⠀⠘⢧⣤⣤⠴⠚⠉⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⡆⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⠇⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠄⠀⢸⡀⠀⠀⠀⠀⣸⠟⠛⠲⣄⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⣠⢾⣧⡤⠶⠛⠉⠁⠀⠀⠀⡸⢟⡽
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠖⠋⠀⠀⠀⢀⣠⣴⡾⠗⠋⠁⠀⠀⠀⠀⢀⣠⠴⠻⣶⢮
⠀⠀⠀⠀⠀⡰⡫⣀⠴⢊⠀⢀⡴⠛⠉⠉⠙⠋⠁⠀⠀⠀⣀⣠⣤⡶⠚⠉⢠⠀⠀⢹⠸⡆
⠀⠀⠀⠀⠰⡧⠵⠽⠎⠉⢹⡯⠂⠀⠀⠀⢀⣠⠴⠖⢻⡏⢩⠀⢄⠄⠀⠀⠀⠳⢤⣀⡇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⣰⠞⠉⠀⠀⢀⡾⠃⡆⠀⠀⠆⠀⠀⠀⠀⠀⠉⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢘⡗⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡁⠀⠀⠀⠀⢀⡔⠊⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠋⠁⠀⢱⠀⠀⠤⠤⠤⠀⠀⠸⠸⣇⣀⡔⠓⢶⡞⠉⢢⡀⠀⢸⠟⠻⣗⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠙⣄⠤⣽⣠⠿⣆⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢠⣴⠖⠊⠁⠀⠀⡈⠳⣄⢻⠉⡀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⣦⠛⣿⠋⠳⣄⠀⠀⠀⡇⠀⠸⡎⢻⣇⠴⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⡜⡁⠙⣧⡀⠀⠀⠀⠀⠀⠻⠄⠚⠆⠘⠈⢳⡀⠀⠁⢀⣤⠿⠀⢷⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠈⠀⠀⢀⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣀⣠⡤⠴⠚⠋⠁⠈⢿⣦⡀⠀⠀⠀⣀⣤⠶⠛⠉⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠛⢉⣱⠆⠀⢻⠋⠀⠀⠀⠀⠀⠀⠈⢹⠃
⠀⠀⢠⣀⣀⣀⣠⣤⠀⠀⢀⣠⡀⠀⠀⢤⡀⠀⠀⠀⠸⠀⠀⠀⣿⠀⠀⠀⠳⣬⡭⠥⠬⢗⣸⡿⢃⣀⠀⠀⣀⣀
⠀⠀⣸⠩⡉⢉⣧⣿⠀⢰⣿⡟⠓⠲⠖⠒⢷⠀⠀⠀⢠⡀⠀⢠⡏⠀⠀⠀⠀⠙⢧⣄⡀⢀⡽⢁⠋⠉⠉⠉⠉⠻⡆
⠀⠀⢻⡅⠀⠀⠁⣿⠀⣸⣯⣀⣀⣀⡀⠀⢸⡀⠀⠀⢸⡧⣧⣼⡇⠀⠀⠀⠀⠀⠀⠙⡤⠏⠀⡌⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠸⣧⠀⠀⣰⠇⠀⣿⠋⠉⠉⠙⡇⠀⢸⡇⠀⠀⠘⠇⠠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠙⢻⣿⠏⠀⠀⢿⠀⠀⠀⠀⠃⠀⣸⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⣀⣀⣿⣿⡿
⠀⠀⠀⠀⠁⠈⠀⠀⠀⢸⡀⠀⠀⠀⢦⣤⡿⠀⣰⣫⣭⣅⣀⣁⣀⣨⣆⠀⠀⠀⣀⡀⠴⢤⠄⡀⠈⠉⣙⣛⠛⠉⢰⡆⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣿⠇⠀⣿⠋⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠁⠒⠚⠓⠐⠁⠀⠀⠀⡊⠀⠀⢸⣷⡀⠀⠀⠀⠤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢨⣿⠀⠀⣿⣷⣦⣤⣴⣶⡄⢰⣿⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣧⡀⢀⣀⣀⢠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡏⠀⠀⡏⠀⠀⠈⠉⣻⠀⢸⣿⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⡟⢿⣿⡷⣾⣿⣿
⠀⠀⠀⣀⡤⣤⣀⡀⠀⠀⢸⠀⠀⠀⣸⡇⠀⠀⡇⠀⠀⠀⠀⢹⠀⢸⣿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠚⠷⠾⠟⠧⠀⡇⢸⡏⠀⢻⡏⡿
⠀⠀⠂⠘⠓⠚⠒⠊⠁⠀⢸⣷⠶⠾⢿⣧⠀⢠⡇⠀⠀⠀⠀⣸⠀⢸⣿⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠋⠀⢸⣇⡀⠀⠀⣠⣿⢀⣸⣿⡶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⣇⠀⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⠿⠿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠿⠶⢿⠟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠿⠥⣉⣹⣿⡤⠴⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠋⠁