Mushròom Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢶⠶⠶⡤⢤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⢣⢀⣠⣤⣄⢀⣀⣊⡉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢌⣰⣾⣿⡿⣿⣿⣿⣛⣳⣄⣠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠈⢯⣻⣿⡇⠀⣿⣿⣟⡟⠛⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⡛⣹⡁⢰⣿⢿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣤⣶⡶⠟⣻⡶⣄⢀⡀⢠⣔⣮⣷⣿⣿⣷⣇
⠀⠀⠀⠀⠀⢀⣴⣿⣷⣷⣾⣿⣿⣿⣿⡿⠿⠋⣁⠈⠠⢀⣤⣿⣛⣻⣿⣻⣿⡆⣈⠁
⠀⠀⠀⠀⠀⠊⠁⠚⣻⣿⣿⣿⣿⣟⠋⠉⠁⠠⠀⠀⢠⡾⣿⣟⣿⣿⣦⣉⠙⢛⢿⣿⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣿⡇⣿⠿⠀⠀⠀⠀⣠⡀⠈⠑⣻⣿⣿⢻⣿⣿⠋⠀⢸⣿⣟⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠀⠀⣤⣴⣾⣿⣿⣄⠈⠉⠉⡟⢸⠋⠀⢀⣴⣿⣿⣛⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠨⡑⠿⣿⣿⠿⠟⠁⣶⡆⠐⠁⠰⢾⣿⣿⠟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠘⠏⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⣾⡿⠀⠀⡰⠀⠀⠀⠘⠻⢿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡆⢀⡄⣰⢀⣿⣿⢁⣼⠁⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⢐⣷⣘⣿⡿⢸⣿⣯⣼⣏⡠⠀⠀⠀⠀⢳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣳⣾⡿⣾⣿⣿⠀⢀⣠⣤⣶⣾⣿⣿⣦⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⢶⣿⡿⢿⠟⢿⣿⣿⣿⣿⣿⣿⡷⢞⡿⠁⠉⠛⡇⠘⣏⠙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠶⠋⠉⡧⣼⠀⠰⢇⠈⢿⠈⣿⠙⠀⢺⠃⠀⡼⠶⠁⠈⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠙⠀⠀⠀⠤⠃⠁⠰⠀⠎⠀⠸⢠⡋⢃⠀⡄⠀⡴⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠁⠈⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⢠⡀⠑⠈⠁⠈⠀⣀⣀⠀⠀⠀⠀⠀⠦⠰⠢⠠⠀⠀⠀⠀⠀⠠⠈⠁⠢⠄⠀⡀
⠀⠠⠀⠈⠀⠘⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠄⠀⠀⠂⠀⠐⠤⠀⠄
⠀⠀⢀⠀⠀⠀⠠⣀⡠⠀⠀⠀⡰⠀⠀⠀⠲⠇⠀⠀⠾⠀⠀⠀⠂⠀⠀⠱⠔⠀⠀⠘⠂⠀⠀⢨⠄⠀⢤⠇⠀⢀⣨⠁
⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠈⠓⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠢⠌⠀⠂⢤⠀⡼⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⢀⡀⢠⠠⠀⠶⡒⠇
⠀⠀⠐⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠀⠀⢢⣄⠀⠦⠀⠀⠀⡈⠀⠀⢁⠀⠀⠀⢠⠇
⠀⠀⠀⠈⠀⠀⠀⠑⠦⠤⠤⠞⠀⠀⠀⠀⠈⠃⠀⠠⠴⠀⠀⠀⠀⠀⠠⣸⢿⠀⠀⠀⠀⠀⠐⠄⠠⠜⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠃
⠀⠀⠀⠈⠐⠂⠀⠀⡀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠄⠄⣤⠄⠄⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠂⠂⢸⡇⠒⡄⠆
⠀⠀⠀⠀⠀⡀⡀⠀⠁⠰⠀⠂⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠜⢹⠓⠚⠩⣤⡆⠀⠀⠀⡀⠀⣺⣁⠔⢀⠀⠄
⠀⠀⠀⠈⠀⠙⠃⠉⠀⠀⠀⠀⠄⠀⠠⡴⠃⠀⠀⠀⠀⠙⠊⠀⠀⠘⠂⠀⠘⠶⠚⠐⠚⠀⠀⠀⠉⢀⣤⣽⠇⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠶⢖⠛⠛⠛⠒⠶⠦⣼⣍⡉⠉⠉⠉⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠙⠳⢶⣄⡑⠄⠀⠀⠀⠀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡁⡠⠀⠀⠀⠈⠹⡗⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠤⠄⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠛⠛⠛⠛⠓⠲⢦⣧⠀⠀⠀⢈⡉⣀⠤⠀⠚⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⡛⠒⢦⠀⠀⠀⢀⡤⠖⠿⠃⠀⡾⠛⠙⠙⠛⠛⠛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠃⠀⠀⣼⣷⠞⠛⠋⠉⠛⢛⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠉⠛⠷⣤⣸⣆⠀⢹⡛⣶⡄⠀⠀⡤⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣛⡫⠭⠤⠭⠶⢽⣷⣴⣇⣀⣀⣀⡀⠀⠀⠀⠀⠒⠠⠤⠠⠬⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠒⠉⠀⠀⠀⠀⠀⢀⢷⡿⠛⠉⠉⠉⠉⠙⠳⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠘⠟⠉⠈⠁⠀⠀⠀⠀⠀⢰⢡⡿⠤⡀⠀⠀⠀⠀⢀⢀⠤⠽⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢘⡆⠀⠀⠀⡼⠧⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠤⠤⡈⠀⠀⠀⠰⠁⢀⣬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠠⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠄⠀⢠⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢴⠶⣚⠛⠂⢤⣶⠖⣿⡵⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠀⣀⡤⠄⠒⠂⠀⠐⠁⠀⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠑⢦⣄⢀⡀
⠀⠀⠀⠀⠃⠀⢀⣰⠆⢐⡢⠠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⠁⠀⠁
⠀⠀⠀⢀⡠⠔⠋⠱⠚⣉⣀⣞⠁⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠉⠀⠀⢀⡀⠀⢉⢀⢈⠄⡀⣀⠀⢔⠀⣴⠃⢀⣀⣀⣀⣐⣦⡀⢠⣤⣄⣀⣈⠣⡤⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠛⠁⢠⣇⣀⣶⣿⣷⣿⣠⣾⣦⡟⠰⣿⣿⣿⣿⣿⣿⣿⣏⠙⢿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣿⠟⠁⠈⢿⣿⣿⠃⠀⣿⣿⣿⣿⡿⠟⠋⢈⣾⣿⣭⣿⢻⡁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠈⠻⣭⡀⠀⠈⠛⠛⠉⠀⠀⠀⣾⣿⣿⠀⠀⠀⢳⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⣶⢰⠶⣤⣶⣾⡤⠀⠀⠉⣁⣀⠀⠲⠄⠉⠉⠉⢰⣇⣀⡍⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠟⠀⠀⣼⠿⣿⣿⢿⣶⣿⣿⠄⠙⠒⠂⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣀⣶⣤⡄⢠⣿⣿⣿⡟⣾⣿⡆⢻⣿⡞⣿⣿⠄⠀⠀⣾⡇⠨⠨⠠⠤⢹⡿⠛⠿⠆⠐⠦⠤⠤⡄⠶⠒⠈⠁⠁
⠀⠀⠀⠀⠹⡏⠀⠈⠉⠁⠀⠈⢻⣿⡜⣿⣷⡄⢹⣿⡈⠻⡀⡀⠀⠁⠐⠀⠀⢀⠀⣾⢁⣿⣤⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣷⣿⣼⠷⠀⢢⡁⠀⠀⠀⠀⠀⠀⠀⢧⠸⣿⣏⣼⣤⣴⠂⣀⣤⣶⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣾⣿⡻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⣼⣶⡿⡟⠛⠛⠁⠾⠟⠿⠿⠋
⠀⠀⠀⠀⠀⠀⢰⡶⣾⣿⣷⣦⣍⠁⠉⠉⢋⡿⢶⣦⢄⣤⣤⣤⡾⣷⣾⠾⠿⠻⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⡤⠄⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠐
⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠁⠀⠀⠀⠀⢰⠀⠀⠠⣠⡶⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠉⠉⠀⠀⠠⠤⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠉⠉⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠠⠠⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠇⢨⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢎⣁⡀⢢⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⣂⡤⠀⠀⠢⠈⠇⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠃⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⡔⡀⠀⡠⡀⠀⠀⠀⠽⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠁⠀⠀⠉⡀⠘⠁⠱⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⡨⠀⠀⠠⠀⢀⡀⠀⠀⠄⠂⠀⠀⠀⢸⠀⢐⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠒⠒⠊⠉⠀⠀⠀⠂⣀⣀⣀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠂⢠
⠀⠀⠀⠀⠤⠦⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠢⠔⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠨⣳⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠋⠉⠉⠉⠉⢛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠰⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠉⠀⠀⠀⠀⠀⢀⣀⡀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠁⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠈⢢⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠀⠀⠎⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣄
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢆⡀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠒⠁⠀⠀⠀⠀⠀⠘⢦
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠤⠐⠒⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⠈⢧
⠀⠀⡼⠁⡀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠈⢧
⠀⣸⢣⠊⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⠴⠁⠀⠘⡇
⢀⡏⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠳⢄⡀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠇
⢹⡀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢦⡀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣠⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠙⢦⣀⣀⣀⣀⣱⣦⠤⠤⠴⠟⠒⠒⡶⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⢻⠓⠒⠒⠦⠤⠾⢤⣠⣴⣂⣀⣀⡤⠊
⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢀⣞⣀⣀⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣴⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣯⣁⣹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⠉⢉⡉⣀⣪⣱⡈⣄⡀⣀⠵⠩⠉⠙⠛⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣀⣌⡀⣐⠀⠘⢿⡟⢩⢉⠙⣿⣦⣶⣿⣶⣤⣲⣦⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢻⡟⠂⠀⠀⢻⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠶⡴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡂⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⡞⠀⠀⢠⠀⠀⢸⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢸⡼⢁⡄⢰⡿⠀⢠⣾⡴⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣾⣇⢸⣧⡇⣇⣦⣮⣼⡷⣫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⢻⠻⠸⠀⠟⠿⠉⠋⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⣀⣀⠀⠀⢀⡤⠠⣄⠀⠀⠀⢀⠠⡄⠀⣀⡀⠀⢠⡤⣤⡀⠀⠀⠀⠀⣤⡀
⠀⢀⣼⣇⣀⣀⣿⡄⠀⡜⠈⣿⣿⣧⠈⠗⢺⡏⠀⠀⢀⠈⢉⠁⢴⣥⣷⠠⣿⣀⣸⠏⠀⣤⡀⠘⠿⠇
⠀⣼⣥⣽⣿⡿⠛⢋⢼⣻⣷⣭⠋⠁⠀⠑⠚⣡⠔⠈⠙⢷⣄⠀⠀⢸⠀⢤⡈⠉⠧⠀⢀⣁⡿⣆
⠀⠁⠟⡟⢹⢧⠀⠈⠛⠾⠃⢹⢒⣄⢀⢄⠘⢿⣤⣄⣀⡸⠿⢶⡀⠀⠒⠾⠋⠀⡋⢀⣲⡄⠠⠿⠆⢠⣄
⠀⠀⠸⡇⠉⡇⠀⠀⠈⠀⠀⢘⢿⠋⠛⢺⠆⠀⠘⠋⠟⠋⠁⠈⠁⠀⠀⢸⠀⠐⠃⠈⠉⠀⠀⠀⢴⣛⣿
⠀⠀⠀⡇⠀⡇⠀⠀⠀⢳⣦⡜⡌⠀⠀⢽⠀⠀⢄⡾⢀⠀⠀⢤⣄⠀⠰⡜⠀⠀⠀⠀⠀⠀⢰⡆⠈⠙⠋
⠀⠀⡀⠷⣶⠇⡄⣠⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠞⠙⠩⣷⣦⣼⠶⢓⣤⣔⠒⠒⢦⡀⠀⠀⢀⡆⢀⢨⡄
⠀⡞⢿⡀⠀⠀⠈⢉⡀⠀⠀⡀⠠⡰⣤⠉⠉⠀⢀⣀⠀⠀⢰⠀⠀⠻⣟⠛⠻⢶⣶⣿⣄⠚⠊⢀⣈⣧
⢀⡇⢸⣧⠀⠐⡲⠈⠁⠀⡸⡧⡑⣽⠻⡎⠀⢠⣿⣻⣷⡀⠘⡄⠀⠀⠀⠙⣺⠛⠛⠉⠁⣴⣶⡄⠉
⠘⠷⣾⠟⠃⠀⠀⠀⣤⠀⠈⢺⣿⢿⠨⠆⠀⢾⣾⣽⡿⠋⣤⣊⠉⣷⣦⠠⣽⠀⠀⠈⠻⢿⡶⠷
⠀⠀⠾⠀⠀⠀⠀⠀⠀⣴⠀⢴⡄⠘⡄⠀⠀⠀⠀⠈⡇⠀⠛⠻⣻⠟⠋⠀⣿⠀⢶⡷⠀⠈
⠀⠀⡄⠀⠀⠀⠈⠉⠀⠻⠿⠗⠃⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠁⠀⣆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠷⠶⢤⣠⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠙⢳⣄⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⡤⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣤⠶⠓⠀⠑⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⢶⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣥⡀⠀⢠⣶⣵⠞⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠤⠤⠶⠶⠶⣶⣿⠇⠀⢻⣶⣿⣟⠩⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣠⠜⠛⠻⠟⠇⠀⢸⡿⠵⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠂⠉⢇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀⡶⠿⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠀⢠⡞⠁⠀⠀⠀⠡⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢿⢲⡏⠳⣈⣰⣤⣠⡄⠀⠀⣰⣟⣀⠤⠀⠀⠠⠠⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠟⠉⠀⠈⠁⠀⠀⢟⡫⣀⣠⡴⠖⣤⣀⠼⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠃⠀⠸⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢱⠀⠀⠀⢸⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠧⠄⠤⠼⠁

⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣦⣶⡇⠀⣀⠀⢀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠛⠁⠺⠁⠃⠀⠛⠻⠈⡌⠉⠛⣄⠀⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠄⠀⠀⢀⡈⠀⢹⡅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⡆⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢸⣿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠘⡇⠡⠀⠘⠀⠀⠀⠀⠀⢀⡠⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡦⠀⠨⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠸⠁⣀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠰⡆⣤
⠀⠀⠀⠀⠀⢶⡴⠘⠀⡄⠀⠛⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⠁⢸⣇
⠀⠀⠀⠀⢀⣾⡷⠀⠀⢣⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠈⣠⣤⣬⣯⠤⠄⢀⡀⢠⠁⠸⣿⣷
⠀⠀⠀⠀⣾⣿⠂⡀⠀⠘⠀⠀⠀⠀⣠⣤⠤⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⠯⣟⠯⠁⠀⠀⡰⠁⢘⡄⢸⣿⣿
⠀⠀⠀⠀⣿⣶⠀⠁⠀⠀⠀⠀⠀⣠⡏⠛⣀⡴⣿⣿⣍⣫⣹⣾⣾⣿⣿⠅⢚⡭⠀⠀⠀⢀⠀⠀⠀⠀⣄⠘⣿⣿⠃
⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣶⡯⣩⣵⠾⢿⡿⣿⡿⠿⠟⠋⣘⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⢱⣿⣿
⠀⠀⠀⠀⢸⣿⡇⢤⠀⠀⠰⣿⣿⣿⣯⣄⠀⠀⠈⣡⣾⣵⣶⣷⠶⡾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠉⠙⠛⠛⠛⠲⠀⡾⠛⠛⠛⠛⢿⡀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠸⣿⣷⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡇⠀⠀⠀⣀⡕⠀⠂⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣷⡈⡓⢀⠀⠢⠀⢄⣀⠀⠀⠉⠀⠀⡌⠀⣇⠀⢠⣾⣇⠀⠀⠀⠀⠀⢰⠖⢹⡟⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠿⠄⣀⢀⣿⣆⠀⣀⡀⠀⠇⠉⢿⣆⠈⢿⣿⣧⣄⡀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⣫⣤⣿⡞⣿⣿⡿⢻⣿⣢⠇⠀⢸⠇⠀⡀⢁⡾⠻⣯⠋⢉⣵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠿⣿⣿⣏⠙⠿⢅⣐⣼⣧⣄⣡⠖⠁⢀⣼⡇⢸⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠆⠸⣿⣿⣿⣿⣿⠿⠼⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⣛⡛⠛⣻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠋⠉⠛⠻⠷⢶⣄⡀
⠀⠀⠀⠀⢀⣠⡞⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣶⣦⣶⣤⡄
⢀⡾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣧⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⣿⣿⡆⠘⠈⣿⣿⠏⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⢿⡷⠀⠀⢉⣉⣐⣿⣿⠂⠀⠀⠀⠀⡴⢶⣾⣿⣿⠏⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠛⠂⠀⠀⢄⣠⠾⠟⣻⣿⣟⠋⠁⠀⠀⣠⡺⣿⠦⠌⠋⠻⠷⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠙⣿⣷⠀⠀⠀⠐⣙⡛⠻⠄⠀⣀⠀⠐⣜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢾⣿⡇⠀⠀⠉⠙⠡⠶⠂⠀⠙⠷⠸⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⣶⣤⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⡇⠀⠀⠀⠀⠠⢄⣄⠀⠉⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣹⣿⣧⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠙⠛⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢽⣿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣿⣧⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢨⣿⣿⡄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣼⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣺⢙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠟⢽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣃⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣾⢛⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡼⣣⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣵⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠃⢹⣿⣷⣀⢲⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢠⣿⡄⠀⠀⠀⣀⠂⠀⠀⢀⣀⠀⠀⠀⠀⠛⠘⠃⠉⠉⠀⠉⣍⠉⠳⠦⣄
⠀⠀⠀⠀⠀⠀⣰⠟⣀⣤⣤⣤⡞⠛⢯⡻⣶⡾⠻⡿⡶⢾⡷⣿⣿⢷⠶⣾⠷⣿⡾⣧⣠⣶⡶⠀⡀⠀⠀⠤⠘⠓⢄
⠀⠀⠀⠀⠀⣸⣷⠶⠫⠌⣀⡐⠀⠀⡂⢙⢮⡃⠁⠈⠞⣤⠃⢷⢸⡘⣇⠻⠀⣦⢡⢃⡜⢉⠟⣻⢿⣶⡤⠀⣶⠀⡀⠳⡀
⠀⠀⠀⠀⠀⣟⣁⠀⠐⠀⠤⢈⡑⠂⢤⡑⠢⠸⣶⣌⠄⢱⣿⢸⡆⣷⣌⣣⣾⣧⡡⣊⡔⢉⡾⠓⡉⢀⡽⢺⣟⣦⡀⠀⢱⡀
⠀⠀⠀⠀⠀⢷⠀⣒⠒⠠⠤⢄⣒⣡⠔⣨⡑⠦⣄⡹⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣛⣡⣔⣪⣴⣍⣂⣥⣚⡿⣇⠘⠋⢃
⠀⠀⠀⠀⠀⠈⢷⡍⢁⣄⣄⣠⣤⣤⣉⡙⠿⣿⣿⣿⡏⠀⠀⠀⢹⣿⢿⣿⣿⣉⣉⠉⠉⠙⠋⢙⠻⠟⠽⠚⠉⣷⡼⡗⠛⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠣⣴⢒⣂⠭⠍⢛⣛⣛⣷⣿⣿⡇⠀⠀⠀⢸⠃⢸⣿⠿⢿⠿⢿⠿⣿⣯⡭⣭⢤⣀⣒⣛⠭⠄⣺⣿⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠶⣿⢛⣉⣭⢶⣿⣿⠀⠀⠀⠀⢸⠀⢈⣿⣶⣌⠘⠄⠈⠢⢝⠻⡲⢌⠊⣝⠋⠛⣥⣿⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢳⣾⣿⠀⠀⠀⠀⠀⣦⠘⣿⣿⣿⡕⢄⠀⠀⠠⠑⠌⢆⠑⣌⣣⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⢀⣇⢰⡿⣿⣩⣯⣬⣶⠶⠞⠛⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⣀⣼⣿⣸⡇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⢙⠿⠟⠙⢿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⡀⢰⡏⢰⣷⣄⡌⠻⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣴⣵⣿⣿⣿⣿⢿⣿⣷⣥⣮⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡋⠀⠀⣠⠀⢀⣾⠿⠟⠋⠁⣾⢸⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠉⠛⣿⠁⠀⠀⠀⠀⡈⢈⠇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣶⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠠⢸⡆⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⣾⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡦⠤⠀⣙⣵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠋⠀⠂⠀⢀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠤⠄⠀⠈⠀⠒⠁⠐⠀⠀⡌⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠈⢁⡨⠬⠔⢲⡖⢲⢒⢖⢲⠂⠄⠬⣀⡉⠡⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠴⡘⢪⠑⠠⣀⣠⣼⡗⢷⣦⣾⣿⣦⣄⡤⠀⠀⠁⠛⠐⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠁⠐⠖⠀⢀⡠⠼⠿⢿⡇⠀⠈⣿⣿⣿⣟⡛⠛⠀⢀⡠⠖⠚⡓⠲⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢤⣀⢀⣀⣀⠀⠀⠒⠀⠇⠀⠀⢸⠟⠘⠈⠊⣀⡴⠛⠀⠀⠀⠁⠀⠀⠂⠝⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠚⠺⢤⢍⣉⠉⠍⢉⠉⠐⠁⡆⠀⠀⣼⠁⠉⠉⠁⡼⠗⠠⢂⣀⣠⣤⣬⣤⣤⣤⣬⣭⡑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡉⠱⠀⠀⠀⠄⢀⠝⠉⠒⢧⡀⠀⠢⠄⠀⠀⡟⣧⠀⢀⣺⠴⠒⠛⢭⢿⡏⠉⢻⣿⣿⢷⣥⣌⡿⠇
⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⣀⡀⠀⠈⠂⠈⠀⠁⠀⠀⢄⣁⠽⠳⡞⠀⠀⢸⠯⣏⢣⡘⠧⠮⢤⡦⠖⠒⣃⠀⢠⠉⠉⠡⡄
⠀⠀⠀⠀⠰⠉⠆⠀⠀⢀⡀⠈⠀⠀⠠⣀⡸⠀⠀⠀⠘⠀⠀⠠⣵⠀⠀⠸⣀⣨⡽⡥⠴⢲⣿⠁⣀⡵⠃⢀⣞⠓⠀⠄⢾⡀
⠀⠀⠀⠀⡏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡒⠂⠐⡼⠂⠂⢡⠻⠁⢁⢄⣀⣸⣟⣼⠯⠤⣄⡼⢹⡏⢄⣠⠞⠁
⠀⠀⠀⠀⠰⠉⠀⣀⡤⠶⠶⣶⣶⡟⠛⠛⠛⠙⣽⡉⢈⠠⠄⠊⠁⠀⠀⡬⠠⠼⣿⣿⠋⡽⠋⠁⢀⠼⠁⠀⠔⠂⠉
⠀⠀⠀⠀⠀⠈⠃⠀⠠⠤⠤⠤⠀⠆⠀⠀⠀⠀⠀⠠⠀⠀⡆⠂⠀⠀⢠⠃⠲⠈⠀⣯⠜⠀⢀⡴⠋⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⢀⣑⠀⠠⡐⠀⠀⣘⠖⡁⢹⡴⠋⠀⢠⠎⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠁⠀⠀⠀⠀⢠⣨⡇⠀⠀⢿⣐⣠⠖⠁⠀⣠⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢅⠳⡄⠀⠀⠀⠀⠀⢻⣧⡆⢀⠠⠿⡇⠀⢀⣴⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠨⣑⠻⡄⠀⠀⠀⢀⠀⠉⠙⣍⢁⢐⣁⣰⣾⠃⣜⡅⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣢⣄⣱⠟⡖⠒⠦⠁⠀⠒⢹⡄⡀⡿⠿⠋⠙⠉⢳⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠉⢲⠇⠀⠓⠰⣖⣁⠀⢀⡸⠗⠻⣁⢤⡴⠒⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢏⠀⠀⠀⠀⣃⣨⡽⠯⠥⠤⠤⠤⠼⠷⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢊⡩⠓⠉⠉⠉⠙⠢⡀
⠀⠀⠀⣀⣤⡴⣶⢶⣴⣾⣞⣷⣿⣿⣿⣿⣭⣟⣿⣷⠀⠀⠀⠀⡠⠔⠂⡍⢠⣞⠍⢈⠔⠁⠀⠀⠀⠐⠒⠢⡀⠁
⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⣞⠀⠀⠀⠀⠈⡀⠂⠁⠀⢁⡀⠀⠀⠀⠀⠀⡁
⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢀⡀⠀⢶⡥⠐⠓⠀⡀⠀⠁
⠀⠀⠘⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣉⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢀⠥⠐⠀⠴⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⡿⣿⣿⣧⣾⣿⣶⣴⡤⢖⣢⣄⠀⠀⠀⠀⠀⠀⢰⡕⠒⠂⡄⣀⠈⠋⠁⠉⣙⣛⣿⡿⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⠤⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣯⣯⡿⠟⠋⠀⠀⠀⠀⠀⢠⡀⠀⠀⠠⣀⠀⠀⠀⠀⠈⢉⡑⠋⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡄⠀⠀⠀⠀⠀⠃⠀⢀⣎⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣾⣯⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣿⣿⣿⣿⣿⣯⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⢠⡄⠀⠀⠄⠀⢀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡻⠟⣿⣿⡿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠺⣧⣹⣄⣇⡀⠀⣼⠶⠖⡓⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠓⠛⠋⠛⠷⠒⠁⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡄⡤⣘⣁⡀⠀⢄⡤⡞⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⡈⢀⠋⠐⠋⢣⡭⣤⡾⠁⢀⣀⠨⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠲⠀⢶⡰⣤⠅⠃⣦⡗⢀⢂⡤⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⢉⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠙⠄⠃⠸⣧⠘⠢⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⢻⡶⠓⠆⠀⠋⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠺⠃⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⡄⠀⡀⠀⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠈⠂⠀⠀⠀⠀⣼⣅⠂⠀⠼⣄⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠁⠰⠀⠀⠀⠀⣀⠄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠴⠚⡤⠀⠄⠀⠀⡀⣠⠄⢸⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡇⢀⠳⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠⠞⠠⢶⣦⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⣈⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠒⠀⢠⠀⠀⠀⡀⠊⠀⠀⠐⠂⠈⠀⠀⠀⠀⠑⠀⠆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢴⣶⣶⣶⣶⣶⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠀⠀⠀⠀⣀⠀⢤⣤⣤⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣠⣄⠙⢶⣤⣤⣤⣤⣄⣀⣀⣠⣽⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⣿⣿⣿⣿⣤⠀⠉⠛⢻⣿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠓⣡⣴⣶⡾⣿⣷⣶⢶⡇⠀⡾⢋⣹⣯⣴⡿⠃⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⢾⠿⠿⡿⢇⠹⠟⠉⠈⠁⢀⣰⣾⣴⣾⡓⠙⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠃⠀⠀⢀⠀⠈⠉⠉⠉⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡀⠇⠀⠀⣼⡀⠀⡀⠀⠀⢀⠐⠁⠄
⠀⠐⠀⠠⠀⢄⡀⣬⠻⠟⣿⣶⣀⣄⣿⣿⣄⣿⣠⣰⠏
⠀⠀⠀⠀⠀⠸⠟⠛⣷⣾⣿⣿⣷⣌⣿⡿⡛⠋⠹⠛
⠀⠀⠀⠀⠀⠸⣟⠁⠉⢟⣳⢿⡛⡛⡛⠁
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠤⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠸⠧⠄⠣⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠊⠉⠀⠀⠀⢔⠊⠁⠒⡌⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⢌⡩⠇⠀⠀⠀⠀⠈⠀⠒⠊⠁⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⣠⠞⠕⠊⠉⠉⠑⡄⠀⠀⡠⠖⠒⠒⠒⠲⣄⠀⠀⢀⠔⠒⠒⠒⢤⠀⠳⡀
⠀⠀⠀⠀⢀⠞⠁⠐⠄⢠⠤⠤⠚⠁⠀⢸⠀⠀⠀⠀⢀⣠⠏⠀⠀⠈⠀⠀⠀⠀⢀⠇⠀⠙⢄
⠀⠀⠀⢠⠋⠀⠀⢀⣀⠠⠤⠄⣀⠀⠀⠈⠒⠂⠉⠉⠁⠀⢀⠠⢄⡈⠲⠤⠖⠚⠁⠀⠀⡠⢬⣣
⠀⠀⠀⡎⠀⠀⡞⠁⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠣⣀⠟⡇
⠀⠀⠀⡇⠀⠀⠣⠀⠀⠠⠤⠒⣉⡤⠤⠲⡖⠒⡖⠒⠒⢒⠚⡖⠒⡲⢲⠤⣄⠐⣅⠉⣢⠀⠀⠀⡇
⠀⠀⠀⢳⠀⢠⠤⣄⠀⣠⠔⠋⠤⣈⡐⢤⡈⢆⠇⠸⠀⣎⠜⣠⡪⢔⡡⢒⡡⠝⠢⡉⠁⢀⢤⣀⠇
⠀⠀⠀⠀⠑⢄⠀⠊⢰⠃⠀⠬⠵⣶⣬⣕⣚⡦⠗⠒⠓⠛⠺⠿⣞⣓⣪⣥⢴⠖⠄⢽⠀⢥⡼⠋
⠀⠀⠀⠀⠀⠀⠑⠦⣘⢯⡉⠭⠭⢍⡙⢿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣟⣒⣀⣈⣉⣤⠾⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣷⣿⣿⣿⣶⣿⣾⣓⡞⠀⠤⠐⣤⡄⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣬⣶⡿⠟⠶⣛⠯⢴⣖⢠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⢺⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠈⣝⣺⣝⠛⠷⣥⣽⡖⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠁⠀⠼⠛⠅⠘⣿⠟⠉⠈⠙⠹⠿⠿⣿⠟⠋⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠙⠛⠻⢯⡬⣑⡢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠻⢷⣤⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣑⣦⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣶⣤⣤⣤⠤⣄⣀⣒⣒⣃⣀⣀⣀⣈⢿⠿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣷⣾⣾⣿⣿⣿⣿⣿⡿⠛⠟⠛⠀⠀⠹⣿⣿⢷⣾⡿⢜⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⡶⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠁⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⠆⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣙⣟⣛⡻⣋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡵⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡂⣠⠶⠆⠲⠀⠺⢿⣿⣿⣶⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠉⣻⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠻⣿⡎⠸⠀⠀⠀⠀⡅
⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⣼⣿⡙⠁⠀⠀⡞⠉⠁⠿⣷⣦⣦⣀⣠⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⢸⡄
⠀⣰⣿⡏⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⡿⠻⢿⣤⣤⣼⣿⣧⢤⣴⣄⡀⠀⠀⠉⢆
⠀⣿⣿⠀⠀⠀⣠⡴⣾⣿⣿⡇⠀⠀⠀⠀⠸⡄⠀⣼⣿⡏⠀⠀⠀⠸⣿⣿⣿⡇⠈⠈⠹⠇⠀⠀⠀⠀⠳⠀⠀⠀⠀⡚⢰⡏
⠀⢻⣿⣀⣹⣿⣿⠀⠀⠙⢿⣷⣦⣦⣤⣀⣸⣯⣼⣿⣁⠀⠠⠀⢀⣀⣿⣿⣧⡀⠞⠛⠻⣦⠀⠀⡀⠀⠀⢁⠀⠀⣈⠃⣾⠀⢀⡤⠀⠀⠁
⠀⠀⠉⠉⠀⢻⣿⡀⢀⣠⣴⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⢧⣼⣿⣿⣿⣿⣿⣦⣀⡀⠃⣠⣄⣤⣧⣾⣾⣤⣀⣁⣠⣿⠀⣥⣴⣠⣠⡄⢀⣀⠄
⠀⠀⠀⠀⠀⠠⢿⢿⣿⡟⣟⠋⣋⡀⢘⡿⢿⠿⠿⠟⠛⢻⢿⠻⢿⠡⠾⠛⠛⢿⢿⣶⣷⣶⣿⣿⣾⣿⣿⣿⣿⣯⣭⣿⠹⡾⠋⢹⠿⠛⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⠈⠁⠁⠀⠋⠈⠛⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⡴⡶⡛⣻⠉⠉⣿⢍⢟⢻⢶⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢿⡌⡜⡰⢸⡄⠀⣿⡌⣆⣣⠷⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠙⠲⠭⣝⣛⣻⠁⠀⣸⠭⠽⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡟⠀⠀⠀⠀⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢠⡇⠀⢠⠇⢀⡤⠖⠊⠁⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢶⣟⣹⡟⠉⣟⢒⣶⡄⢸⠄⠀⠀⠀⡞⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢭⡇⠀⣯⣭⠭⠴⠋⠀⠀⠀⡼⠁⠀⢰⠃⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⡏⠀⠀⠀⠀⠀⡝⠙⡶⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀⠀⠀⢀⡏⠀⠀⡾⠀⠀⠀⠀⢀⡞⠀⣸⠁⠀⣀⡠⠔⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠀⠀⠀⣸⠀⠀⢠⡇⠀⠀⠀⢠⠎⠀⣰⠃⢰⢋⣁⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠦⣄⠀⠳⡀⠈⢳⡀⠀⠀⡏⠀⠀⢸⠀⠀⠀⢠⠏⠀⣰⠃⠀⠈⠮⣓⣮⠋⣱⠦⣄⠸⡄
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠙⢦⠹⡄⠀⠹⣄⢸⡇⠀⠀⢸⠀⠀⠀⡟⠀⢠⠇⠀⠀⠀⠀⡸⠃⣰⠯⠭⠭⠞⠁
⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⢀⣀⡠⠞⠀⠹⡄⠀⠘⢾⡇⠀⠀⢸⡀⠀⣸⠁⠀⢸⠀⠀⢀⡤⠊⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠉⢇⠀⠀⠀⠀⢳⡀⠀⠘⡇⠀⠀⠈⣇⠀⡟⠀⠀⣿⣠⠖⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠳⢤⣀⣀⡀⢧⠀⠀⢳⠀⠀⠀⢹⡄⡇⠀⠀⢸⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣹⠺⡆⠀⠈⢧⡀⠀⣰⠃⢧⠀⠀⢸⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⢧⣀⣀⡞⠉⠉⠁⠀⠘⠦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⢷⡶⢤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠁⠀⠀⠈⠀⠉⠒⠌⠀⠀⠉⡓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠘⠀⠀⠀⠀⠀⢀⣠⣶⠿⢛⡷⢾⣆⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠃⠀⠀⠀⢀⣀⠤⠒⠻⠁⠈⠀⠀⠀⠜⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣠⣴⠦⠘⠫⠁⠀⠀⡖⠀⠀⠀⠀⠀⣀⣤⡶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢄⣿⠀⠀⠀⣴⣾⣿⡿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⣀⡀⢀⣀⣤⣤⣤⣴⣾⡎⠙⢳⣤⣾⣿⣟⡃⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣉⠈⣀⣶⣿⣿⣿⡇⠀⢸⣿⣟⣩⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠒⠟⠺⡇⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠈⠘⢿⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡇⠀⠀⠀⠁⠀⠓⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣾⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⣠⡿⠉⠁⠻⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣤⣄⣦⣌⡗⠤⡀⠈⠄⠀⠀⠸⠀⣼⠏⠀⠀⠀⠀⠈⢅⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⣿⠁⠹⣶⣿⠷⢾⠞⠀⠀⣿⣿⡔⠊⠈⡁⠐⠐⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠈⠀⠀⠀⠀⠹⠜⡶⣶⡿⠉⢹⣶⣞⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⢠⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⡀⠀⠰⠀⠀⠀⠀⠀⠀⢰⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⢦⡀⠆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡇⠀⠀⠀⠀⣦⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢹⡀⠀⠀⢸⣧⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠦⠴⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠻⠻⠿⢩⣵⠿⡏⡟⠀⡇⢹⡏⢛⣦⠉⠙⠌⠛⠿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠿⡻⠁⠐⠀⣰⣿⠹⣴⣗⡇⢼⣇⡟⢀⡿⠛⣿⡟⠠⠀⠀⠀⠔⠈⠟⡿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣋⣿⣿⡟⠋⠁⠀⠀⠀⠀⣟⣿⣼⣿⣹⣧⣟⡼⢁⡿⢃⣴⡿⡿⣄⠀⠀⠄⠀⠀⠀⠀⠉⢛⣿⣿⣯⡛⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⢯⠉⠀⠀⠀⢀⠀⠂⠁⠀⣿⣿⣿⣧⣿⣟⡞⣡⠟⣠⡾⠫⣺⣿⡏⠀⠀⠀⠀⠙⠦⢀⠀⠀⠀⠈⣹⢿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠙⠈⢈⠿⠋⠉⠀⠀⠈⢦⡀⠀⠀⢠⣿⣿⣿⣿⣿⣫⡾⣣⡼⣣⣾⣿⡿⢋⣷⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠻⢏⠀⠐⢙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠛⠂⣠⠴⡄⠠⠤⠤⠤⢤⣤⣤⣌⣙⣿⣿⣿⣝⢷⣾⣿⣿⣿⣯⣼⣛⣯⣾⣿⠿⢿⡇⠀⠄⡀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠨⠷⢠⡀⠙⠿⣿⣿⣿⣿
⣿⣿⣿⡧⡁⣠⣾⡉⠀⠀⠀⠠⠀⠀⠀⠀⠈⢹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⢺⣿⠷⢨⣿⣿⣷⣦⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣹⣦⠀⣡⣿⣿⣿
⣿⣿⠿⠋⠡⠝⠉⠉⠀⠠⠃⠀⠀⠀⠀⠀⠀⠈⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣼⠁⢀⣸⡏⠸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠣⠀⠈⠈⠋⢥⡉⠹⣿⣿
⠿⢿⣤⣾⣅⡀⣀⠔⠃⠀⠰⣦⣠⣄⠠⢮⡦⠐⣿⣿⣿⣿⣿⣿⣿⡿⢿⢟⣿⣿⣿⡟⣻⠏⠁⠀⢀⣿⡇⢰⣿⣧⣋⡻⣿⣷⣄⠀⠀⠀⠈⠓⣄⠀⣀⣿⣤⣾⠿
⢀⠊⠉⠙⠓⠻⠟⠅⠀⠀⠀⠸⢿⡿⠀⠈⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⠀⢀⣰⣾⣿⠁⣼⣿⠟⣿⣯⣦⣬⣿⣷⣤⡀⠀⠀⠙⠽⠒⠛⠉⠉⢀
⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣼⡆⠠⠀⣀⣤⣶⣿⡆⢿⣿⣿⣿⣿⣾⣿⣿⣷⢿⣿⣾⠏⠀⢸⣿⣿⢟⣾⣿⣿⣿⡿⠋⠉⠉⠛⠻⣿⣻⣶⣄⠀⠀⠐
⠁⢒⠠⠄⣀⠀⠀⠀⣠⣶⠟⣁⣤⣶⣿⣿⢿⢿⣿⣿⠈⠁⠀⠀⢉⣿⣿⣿⣿⣯⣿⣿⡀⡀⢸⣿⠋⢈⣿⣿⡏⠉⠀⢀⠀⣤⣴⣄⣿⣿⠿⡻⠷⡄⠀⠀⠤⡐⠊
⠀⠀⠀⠀⠀⣀⣴⣿⣽⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⣿⣷⣷⣟⣋⣴⣿⣿⣿⣷⣶⣧⢯⣝⣿⣿⣯⣿⣿⣼⡶⠂⢿⡆
⠀⠀⢀⣤⣾⠿⠟⠛⠛⠋⠉⠉⠉⢩⣿⠛⠛⠻⠿⣿⣿⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⣯⣿⣿⣿⣿⠿⢁⣶⣶⠿⣿⠀⠀⢀
⠀⢸⠙⠥⠧⠤⠤⠠⢄⠂⠀⠀⠀⢸⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⣁⣴⣾
⠀⠘⣇⢠⡶⡶⠶⣞⣛⣲⣒⣂⢀⠔⠛⢿⣿⡽⣷⡄⠀⠀⠀⠀⠀⠘⣯⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⠋⣻⣿⣿⣿⡧⡀
⠀⠀⣿⣷⣶⣿⠾⠟⠿⣿⣿⣭⣤⣤⣿⠃⠀⠀⢸⣿⡄⠀⠀⢀⣤⣾⣿⣿⣿⡁⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣴⣾⣷⣿⣿⣿⣿⣿⣾⣼⣦⣤
⠀⣠⡻⣯⣿⣧⣀⣀⣀⣾⣟⣉⣬⣿⣿⠀⠀⠀⠈⢿⢿⡄⠀⢿⣻⣾⣿⣿⣿⢃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣤⣶⣷⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠿⠛
⠀⠙⢿⣗⣚⣒⣒⣚⣛⣓⣒⣒⣒⣚⣶⣦⠀⠀⠀⠈⠃⠈⠀⠀⠈⠉⠉⣱⣷⣯⣯⣽⣿⣿⡇⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠻⠾⠿⠿⠿⠁⠀⠀⠀⠀⠀⠉⠛⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠡⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⢶⣶⣤⡀⠀⢹⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠹⣿⣿⡄⠀⠃⠀⣐⡺⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠠⢀⣴⣿⡿⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠠⠶⠶⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⣄⣠⡴⠏⠀⠀⠀⢺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠂⠙⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠂⣀⢦⣴⣆⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠾⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠛⣿⣏⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⣀⠀⠀⢀⠀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠈⠀⣘⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠎
⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⣠⣀⣀⠀⠄⢄⣠⣤⣤⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠒⠒⠖⠐⠒⠒⠠⠄⠒⠚⠓⠋⠉⠉⠉⠉⠙⠳⢖⡀⠀⠀⠀⠀⠀⠀⠀⢩⡏⠙⠻⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⡀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠓⣀⠀⠉⢃⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠠⠄⠤⠤⠄⠤⠬⠑⠎⠉⠁⠘⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠟⠿⠿⢿⣿⣿⣿⣷⣷⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢀⠀⠀⠉⠀⠐⠀⠀⠉⠈⠉⠙⠿⠿⠿⠛⠟⠛⠻⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀
⠀⢀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡎⠀⠀⢿⣿⣿⣿⡇
⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣻⣿⣿⣿⡀⠠⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣇⠀⠀⠻⠿⠁⣤⣴⡆⠀⠀⠀⠀⠀⣀⣐⣿⣿⣿⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠙⠋⣀⣤⣰⣶⣶⡿⠟⠃⠀⠀⢀⣤⣜⠉⢽⡷⣿⣋⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠍⠁⢸⣿⣿⠀⠀⠀⠀⠴⣷⣽⡋⠉⠀⠀⠈⠉⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢚⣿⡆⠀⠀⠀⢶⡦⢀⡉⠀⠰⢦⡀⣠⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⢿⣷⠀⠀⠀⠀⠀⠉⠁⠠⠄⠈⣃⠙⠃⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⠀⠀⠀⠀⠀⠒⢲⣦⠀⠀⠈⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡄⠀⠀⡀⠀⠀⠾⠃⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢺⣿⣧⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡏⣿⣿⡄⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⣿⣇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⠍⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢷⢫⢺⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠛⢶⡟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢟⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣽⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣖⣲⣶⣶⣶⣶⡄⢀⣶⣶⣾⣯⣴⣶⣶⣶⣶⣶⣶⣶⣶⠆⡼⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⡿⢿⣏⣭⣭⣿⠟⢻⡿⠿⠛⠛⠀⠈⠁⠚⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⢻⣿⢿⣿⡇⠰⣿⣿⣿⣿⠋⠁⢀⣠⠄⢀⣀⠀⠀⠀⣠⣶⣶⣄⣠⣄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⣴⢶⢶⣄⢷⣄⠙⠿⠃⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠸⣿⣿⣿⠟⠀⣻⡷⠀⣸⣷⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢹⠏⠁⠀⠀⣛⣥⡶⢰⠂⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⢠⣶⣤⣾⣿⡿⠙⠘⢀⣼⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣯⠈⠻⣯⣿⣿⠿⠛⠛⠻⣶⠳⠶⢾⣿⣧⣀⠀⠀⠀⠀⠘⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡼⠋⣠⠀⣹⡟⠁⢂⣀⡀⠈⠉⠀⠀⠠⠉⠛⠿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡀⢻⣾⠟⠁⢆⠀⠈⠁⠁⠀⠀⠀⠀⠁⠸⠗⡄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣙⣡⡮⠨⠀⠈⢀⠀⠀⠀⠁⠀⠀⠀⠐⠀⣀⡐⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⣦⣤⠀⠀⠑⠂⢀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠠⢸⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣼⡇⠀⢿⣿⠓⢄⠀⠀⠊⠻⠷⣤⣤⡤⠠⣾⣷⣆⠀⠀⠙⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡇⠀⢸⣿⡔⣆⢀⢀⣀⠀⠀⠀⠀⠀⣤⣼⣿⡘⠂⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣠⣼⣿⣥⣬⣿⣿⡛⠱⣤⣤⣠⣶⣿⢩⣿⣧⠄⠁⣬⠸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡟⣿⣽⢻⣿⣿⣿⣿⣿⣥⣌⣉⣁⡿⠿⣿⣿⣿⢻⡄⣢⠽⠺⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠙⠛⠿⠒⠛⠁⣿⡟⣿⣟⡉⠀⢈⣿⣿⣿⣿⣿⢻⡇⠀⠂⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⣖⣲⡆⢀⣇⢀⡳⠄⠀⢀⣀⠈⠉⠉⠉⠋⠸⠇⡰⣤⣨⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⠉⢡⠊⠉⠁⠉⠀⠀⠉⠉⣻⠀⠀⠈⠀⠀⢈⡟⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠀⢠⡀⢽⣷⣶⣶⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠙⠛⠏⠉⠏⠱⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣴⠉⢱⠮⠙⠛⠶⠲⢤⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⡾⠷⠂⠀⠀⢰⣷⡤⢾⣫⡘⠟⢢⣽⣋⡻⣯⡴⢛⠢⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠏⣦⠰⡴⣚⠿⢿⣧⡿⠻⠤⠟⢲⣋⠀⠀⣟⠀⣉⢿⡟⠀⠙⠁⠉⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⢐⣠⠋⠀⢦⣵⠶⠛⠁⠀⠀⠀⠀⠘⢯⣷⣆⠈⠃⠽⣦⠙⢛⣧⣙⡀⣝⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢰⡥⠞⠒⠀⢴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣦⣤⣿⣈⣦⣽⡿⣇⠉⠀⣼⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣤⣹⡳⢄⡰⣿⠞⠁⠀⠀⠈⠙⠛⠀⠦⣄⠀⠀⠀⠀⠈⠛⠉⠉⠁⠈⠙⢿⣧⡆⣽⡽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠋⡎⢉⣁⣸⡏⠀⠀⠀⠈⠁⠈⠁⠀⠂⠄⣉⣀⠂⡂⠀⡀⠀⠀⠀⠀⠀⢨⣻⠧⡟⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣤⠛⡾⢱⢻⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠠⢀⠀⠀⠀⢿⡋⡴⠡⠚⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢾⣃⣜⠀⠳⣿⠞⠁⠀⢀⣶⣶⣭⣶⣷⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠴⠻⣅⠂⠨⣯⣿⡷
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠙⣿⠁⠜⣇⠀⢀⠋⣈⡡⠤⣭⡙⠿⠛⢧⠀⠉⠀⣃⣤⣤⣗⠒⠆⠀⠀⣻⣾⡗⢦⣤⣼⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣽⣿⣏⡔⠃⠀⠙⠂⠉⠂⠠⣧⠿⠂⠁⢨⠀⠰⣾⠟⢉⣉⣈⠹⡷⠀⠀⣿⣿⠉⣖⠻⣮⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢹⡸⣧⠙⠉⢋⠞⠀⠀⠛⠲⠄⣠⡤⠶⠀⠀⡜⠀⢸⡏⠀⠛⠈⢩⣿⣦⣄⣀⠿⠁⣆⣽⠏⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠈⡿⣎⠀⠀⠸⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⣠⠃⠀⣾⠀⠑⠀⠀⠌⠉⠉⠉⠀⢰⠀⠛⢠⣾⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠀⠀⢳⠀⠀⢠⠞⠁⠀⠀⠀⡆⢸⡇⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠐⣿⡀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠺⠀⢠⡎⠀⠀⢀⡰⠃⠉⠋⠻⣶⣾⣿⣷⢄⠀⠀⠀⠀⣀⠄⣼⠃⠀⣰⠿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⠀⣸⠃⠀⠀⠁⢀⣄⣀⣀⡰⠅⠈⠉⠀⠈⠆⠀⠀⠘⠁⠀⣿⠀⠀⠈⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⡏⠀⠀⠀⢠⠎⠉⢍⡉⠛⠚⠓⠦⣤⠀⠆⠀⣴⠃⠀⢸⡇⠀⢀⠚⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡀⠀⠀⠀⠀⠀⠉⠀⠀⣤⠈⠉⢉⡉⠁⠸⠄⠀⡰⠋⠀⠀⣸⠃⢀⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⢀⣼⠃⠀⠀⣰⠟⠀⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠉⠛⣄⡀⠀⣀⣀⣀⠀⣼⣷⣶⡿⠁⠀⠀⠀⡇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠠⠀⠀⠈⠉⠉⠉⠉⠙⠛⢻⠟⠉⠀⠀⠀⣠⠞⠀⠀⣾⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⣸⡃⢌⠒⢤⡉⡁⠀⠀⠀⠀⣀⣠⠾⢀⡴⠒⠈⢉⡕⢀⣠⣾⣿⣿⡿⢿⣆⣀
⠀⠀⠀⠀⠀⠀⣠⢖⣿⠋⠀⠴⠁⡇⠀⠙⠶⣄⠁⠁⠀⠀⠀⠉⢀⣴⡀⠀⢀⣠⣿⠶⠛⠉⠁⠀⠀⢀⣾⣻⣿⠿⠦⢤⠤⢄⡀
⠀⠀⠀⢀⡴⢋⣴⠟⠁⠀⠀⠀⡴⢇⠀⠀⠀⠀⡉⠒⠶⠶⠶⠞⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⠞⠛⠋⠀⠀⠀⠀⢹⣎⡭⠒⢦⣀⣀⡀
⠀⠀⣰⠋⢀⣾⠃⢠⣄⣀⣤⠊⠀⠈⣦⠀⠀⠀⠉⠓⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢀⡤⠚⠀⣀⠤⠚⣿⣷⣄⠐⣻⣭⡙⣷
⠀⣼⠃⢠⣿⣏⠀⠀⠀⠀⠈⠑⢤⣀⠈⠣⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⠉⠀⠀⠀⡀⠔⠉⣠⣰⡵⠉⠀⣼⣿⢻⣿⠻⣿⣮⡙⣿
⡼⠁⢠⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠉⠢⠀⢰⡄⠀⠀⢀⣠⠴⠞⠉⠁⠀⠀⠀⢀⣠⠖⠈⠀⢀⠄⣰⠟⢀⡴⢡⣿⠏⣸⣿⠀⢻⡌⢿⣿
⢇⠀⢺⠉⣿⣿⡍⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⢀⡤⠐⠋⠀⠀⣠⠔⣡⠞⠁⡠⠊⣰⣿⣿⢠⣿⡟⠀⣿⡄⢸⣿
⢸⡆⢸⠀⢻⣿⣻⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣾⠡⠚⠁⢠⠞⢀⣴⣿⡿⠁⢸⣿⠁⢠⣿⠇⢸⣿
⠘⣇⢸⡆⠈⢿⣿⠹⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡔⠶⠛⠉⠀⠀⣀⠔⠁⣠⣿⣿⡿⠁⢠⣿⣏⠀⣾⣿⣥⠟⠁
⠀⢻⡄⢧⠀⠘⢿⣧⠀⠉⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠀⢀⠰⠒⡃⠀⣀⣼⣹⣿⡟⠀⢀⡿⠛⠃⣸⣿⠏⠁
⠀⠀⠹⣄⠳⡀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠒⠚⠒⠛⠒⠒⠒⠂⠀⠈⠛⠃⠒⠉⢀⠔⢁⣱⢿⠞⠀⠀⣘⣁⣠⡴⠛⠁
⠀⠀⠀⠈⢧⡙⢄⠙⣿⣷⢤⣀⠀⠀⠶⠦⠤⠴⠶⠂⠒⠒⠚⠛⠛⠃⠂⠐⠒⠀⠃⠀⢀⡤⠖⠁⣠⠞⣡⠋⣠⠴⠛⠉⠁
⠀⠀⠀⠀⠀⠙⢦⡱⣄⠉⠳⣌⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡠⠔⠊⢁⣠⣴⣞⡡⠜⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢮⣉⠀⠈⠀⠀⠈⠛⠲⠖⠒⠘⠛⠉⠉⢠⡤⠶⠒⠛⢉⣤⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣭⡶⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣲⣶⣶⣿⣛⣻⣛⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣸⣯⣹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡆⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⢰⠖⠒⠒⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⢷
⠀⡇⠀⠀⠀⠀⠀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⠀⡇⠀⢀⣀⣀⣀⣿⡦⠴⣦⣤⣀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⡤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸
⠀⡇⠀⢠⣿⣿⣿⣧⡄⢾⣿⠟⠟⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢠⣤⣼⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢸
⠀⡇⠀⠀⠀⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⡇⠀⠀⠺⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⡴⢻⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⢸
⠀⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣰⠋⢰⡟⢻⣿⢿⡀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⡇⢸⠂⠀⡴⠁⠀⠉⠀⠀⣿⠁⢧⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢠⣄⣤⣼⣿⢋⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⡾⠁⠀⠀⠀⠀⠀⡙⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢩⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠐⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠹⣀⠀⣇⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⠀⠀⠀⠀⠀⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁

⣿⣿⣿⣿⣿⠹⣷⡜⠻⣦⡹⣿⣄⠻⣆⠈⠻⢷⣶⣦⣤⣭⣿⣿⣿⣿⣷⣿⣿⡏⢠⣾⣿⣯⣾⠟⣋⣴⣿⣥⣶⣿⡿⠋⣠⣾⣫⣾⠏⠀⣰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⢻⣿⣄⠈⠻⣿⣿⣷⣼⣿⣦⣄⡈⠉⠛⠻⣿⣿⠛⢿⣿⣿⣿⣰⣿⣿⡿⣫⣶⠿⢛⣛⣿⣿⣿⣿⣶⣿⣿⣿⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠹⣿⣦⠀⠘⣿⣿⠛⠻⠿⣿⣿⣷⣤⡀⠸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣾⠟⣡⣾⣿⣿⣿⡿⠿⠛⠻⣿⣿⢁⣴⣿⣿⠟⣩⣿⠏⣿⡟⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣧⠀⣿⡇⣴⢦⣤⣀⠉⠛⢿⣿⣦⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠋⠁⣠⣤⢶⡆⢿⣿⣿⣿⠟⠁⣰⣿⠏⢸⣿⢱⣿⣿
⣿⣿⣿⣿⣯⢻⣿⣧⡀⢹⣿⣾⣿⢡⡿⢴⡔⢙⠳⣄⠀⠈⢿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠿⣿⠟⠁⢀⡴⡛⢡⣐⠢⣿⢸⣿⡿⠁⣠⣾⡿⠃⢠⣿⢃⣾⣿⣿
⣿⣿⡻⣿⣿⣧⡙⣿⣷⡄⢿⣿⣿⢸⡇⡟⢫⣝⣻⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢕⢽⡿⣏⠆⢹⠀⣿⣧⣾⡿⠋⠀⣠⣿⣧⣾⣿⣿⣿
⣿⣿⣧⢹⣷⡙⢿⣮⣿⣿⣾⣿⣿⢸⡇⣿⣴⣛⣫⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣚⢿⣟⣮⢸⢀⣿⣿⠋⢀⣠⣾⣿⣿⡿⣫⣿⣿⣿
⣿⡿⣿⣆⢻⣷⡈⠻⣿⣿⣿⣿⣿⣞⣧⢫⣷⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣯⢁⣾⣾⣿⣧⣾⣿⣿⡿⢟⣩⣶⣿⣿⣿⣿
⣿⣿⣮⣿⣾⣿⣿⣦⣈⠻⣿⡿⠿⠿⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠹⠿⠿⣿⣿⣿⣭⣶⣿⣿⠟⣡⣾⣿⣿
⣿⣧⣍⠛⠻⢿⣿⣿⣛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠛⣿⣿⣿⣵⣿⣿⣿⣿⣿
⣿⣥⣤⡴⠶⢶⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠛⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⡞⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣤⣤⣿
⣿⣥⣶⣶⣾⣿⣿⣭⣭⣭⣝⡛⠦⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⠂⠙⣆⠀⠀⠀⠀⠀⡾⠁⣸⣇⠀⠀⣹⠀⠀⠀⠀⠀⠀⠘⢋⣭⣭⣭⣽⣿⣿⣿⣿⣿⣭⣿
⣿⣿⡿⢟⣿⣿⣟⣋⣭⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⡇⠀⢹⣿⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣍⣛⣿⣿⣭⣙⠻⢿⣿
⣿⢋⣴⣿⢟⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠿⡤⠾⠁⠀⠀⠀⠀⠀⠙⠦⠼⠧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣯⣛⠶⣿
⣿⡟⣫⣴⣿⣿⠏⢀⣤⡴⢖⣶⣶⣶⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⣯⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⣶⣶⣶⢶⣤⣄⡈⢻⣿⣿⣿⣿⣷⣿
⣿⠿⣻⣿⣿⣏⣾⠋⢁⣴⡿⠋⠁⠀⣰⣿⡟⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⣿⣿⡄⠀⠈⠙⠳⣦⠉⠻⣦⣿⣿⡟⣻⣿⣿
⣿⣿⣿⣿⣿⣿⠃⢠⡿⠃⠀⠀⢀⡼⠟⢹⡇⠀⠀⠀⠙⠛⠶⠦⣤⣤⡔⢺⣿⡲⢤⣤⡤⠶⠞⠛⠉⠀⠀⠀⢹⡙⠻⣆⠀⠀⠀⠘⢧⠀⢹⣿⣿⡿⣿⡟⣿
⣿⡿⢿⠁⢸⣿⡀⣾⠁⠀⠀⠀⠉⠀⢠⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⡏⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠧⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣰⣿
⣿⣿⣿⡄⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣧⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⢹⣿⣿⣿
⣿⣿⣿⣷⡀⠘⣿⡀⢸⡄⠀⢠⡤⠶⠛⣹⣿⡇⠀⠀⠀⠀⠀⠀⢠⡟⢠⡾⡟⢧⠘⢷⡀⠀⠀⠀⠀⠀⡀⣿⣿⡝⠛⠶⠄⠀⠀⣰⡇⢰⡟⠸⠃⣸⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠈⠣⠸⣟⠷⢤⣤⣤⣾⡿⢻⣧⡇⠀⠀⠀⠀⢠⡟⢠⡟⠀⡇⠈⢧⡈⢷⠀⠀⠀⠀⠀⣧⣿⠻⣿⣶⣤⣤⡴⢞⡿⠁⠟⠀⢀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣬⣷⣶⣾⣟⣁⡀⠀⢻⣇⡸⠀⠀⢀⡟⣰⠋⠀⠀⡇⠀⠈⠳⡌⣧⠀⠀⠘⣆⣿⠏⠀⢀⣉⣿⣶⣶⣿⣥⣤⣤⣶⣿⣿⣿⣿⣿⣿
⣿⣝⠻⣿⣧⠉⠙⠛⣻⣿⣿⣿⣯⣍⡉⠻⣦⡈⢿⡇⠀⠀⢸⣿⡇⠀⠈⢀⣧⠀⠂⠁⣽⣾⠀⠀⠀⣿⡏⢠⡾⠛⢉⣭⣿⣿⣿⣿⡛⠛⠉⢡⣿⣿⢟⣵⣿
⣿⣿⣧⡘⢿⣧⢀⣾⣿⡿⣿⣟⢿⣿⣿⣦⠹⣧⢸⣷⣄⠀⠘⣿⣧⠀⠠⠈⠉⢠⢀⢀⣿⡿⠀⢀⣴⣿⠀⣿⢁⣾⣿⣿⠟⣿⣿⢿⣿⣆⢀⣿⡟⢡⣾⣿⣿
⣿⣿⣿⣇⠈⢿⣿⣿⣿⡥⢽⣿⣸⣿⡟⣿⣷⣿⣸⡏⠈⢳⡀⢻⣿⡈⠂⢀⣧⠈⠈⢸⣿⡇⣠⠞⠁⣿⣼⣿⣿⣟⣿⣿⣸⣿⡁⣸⣿⣿⣿⡟⠀⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠈⣿⣏⢹⣿⣿⣿⣿⣿⡃⣸⣿⣿⣿⠃⠀⠀⢻⣼⣿⡇⢰⣀⠀⣑⠀⣼⣿⣰⠋⠀⠀⢹⣿⣿⣿⡣⣸⣿⣿⣿⣿⡿⣋⣿⣿⠀⢰⣿⣿⡿⣿
⣿⢿⣿⣿⡆⠀⢿⣿⣌⣸⣿⡇⢘⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣇⠈⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⠿⡻⠄⢽⣿⣗⣼⣿⡇⠀⣼⣿⣿⠇⣿
⣿⡄⠻⣿⣿⣄⠘⢿⣿⣿⣡⣦⣄⣷⣶⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣡⣧⣹⣿⡿⠟⠀⣰⣿⣿⠏⣠⣿
⣿⣿⣷⣿⣿⣿⣷⣦⣬⣭⣛⣛⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣹⡀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⢟⣛⣩⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⠲⠐⠀⠀⠐⠐⠀⠀⠀⠂⠀⠀⠀⡄⣰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠒⠊⠀⠀⠀⠁⠀⠀⠠⠄⠤⡄⠀⠀⢀
⠀⠀⠒⠒⣒⢒⡒⠒⠒⣂⣀⠀⣀⢀⠐⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⡔⠁⢹⡆
⠀⠀⠀⠎⠀⠀⠈⠢⠸⡀⢀⠇⢅⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⣤⣄
⠀⠀⠘⠀⠀⠀⠀⠀⢠⠚⠑⡀⠖⠑⠄⠀⠀⠀⠀⠀⡐⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⡀⠀⡁
⠀⠀⠀⠑⠄⣀⡠⠊⠈⠂⠐⠀⠑⠒⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠉⠉⠁⠀⠁⠀⠁⠀⠀⢀⠀⢀⡀
⠀⠀⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡅⡃⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⢀⠀⠐⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠶⠁⠀⠀⠀⠀⠀⠀⠀⢀⠶⠛⣏⡻⠳⡄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠂⠐⠀⠔⠢
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠸⡜⠀⢸⠱⣂⡇⢠⠊⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠑⠶⠶⠿⠛⠁⠀⠢⣀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠤⠤⠄⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠿⠿⢿⡿⠿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠙⢷⡄⠀⠀⠀⠀⠸⣧⣀⠀⢀⣽⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⡿⢿⡅⠀⠀⠀⣸⡇⠀⠀⢀⣤⣤⣌⡛⠛⠛⠉⠀⣰⡟⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠈⠻⠶⠶⠾⠛⠀⠀⣴⠟⠁⠀⠙⢿⡄⠀⠀⠀⣿⡀⠀⠀⠈⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠻⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣄⣀⣀⣀⣼⣇⠀⠀⠀⠈⠻⢶⣶⠾⠋⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣀⣼⣷⣶⣶⠿⢿⡿⠛⠛⣿⠉⠉⣿⠋⠛⠛⣿⠛⠛⢿⡶⢶⣤⣤⣀⡀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠟⠻⣏⠀⠹⡄⠀⠷⠀⠀⠻⠀⠀⠸⠀⠀⠀⠟⠀⠀⠸⠁⠀⣸⠏⠙⢻⣷⣦⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣄⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠋⠁⠈⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⢀⡖⠀⠀⢀⡀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡆⠀⠀⡀⠀⢠⡀⠀⣱⣦⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣦⣾⣥⣤⣤⣿⠀⠀⠀⠀⠀⢹⣧⣠⣤⣷⣴⣶⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⣻⡿⠀⠀⠀⠀⢶⢸⣿⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠂⡟⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⡼⠸⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣸⠁⡆⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢀⡏⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠎⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠁⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣰⣾⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠂⠀⠀⠀⠐⢲⣛⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣠⢄⣀⣤⣾⣿⣎⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⢤⡎⠁⠸⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⣰⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⢧⣿⣿⣿⣆⠀⠀⠀⠀⢳⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣶⣶⣾⣿⣿⣿⣇⡾⣼⢟⣿⣿⣿⣆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡿⠞⠅⣠⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢏⡵⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠀⢰⣇⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡏⠈⠋⠂⠀⠀⢀⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢀⡀⡰⠃⢀⣾⢇⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡟⠁⠉⠀⠀⢀⣾⠏⣾⣿⣿⣿⣿⣿⣿⣿⣟⡿⣬
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢾⣧⣾⡆⠀⣴⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⡘⠂⠋⡀⣸⢿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢸⣷⣎⢠⣵⡿⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣻⣛⣋⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⢠⠞⠛⣄
⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⢹⡄
⠀⠀⠀⠀⠈⢧⡜⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠛⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠈⠑⢄
⠀⠀⠀⠀⠂⠀⢸⠁⠀⠀⠀⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢈⠇⠐
⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠘⠃⠈⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢋⠙⠳⣄⠀⠀⠀⠀⠀⠀⣴⠟⢉⠙⠳⣄
⠀⠀⠜⣃⡀⢀⠤⣄⢑⣄⣀⣀⣀⣀⡊⢀⠤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢺⠺⡁⠸⠀⠀⠀⠀⠀⠠⠇⠐⢪⠮⡁⠿
⠀⠀⠀⠉⠁⠹⢤⠜⠈⠉⠉⠉⠉⠉⠁⠸⠤⠜⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢠⠄⠀⠀⢀⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘
⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡠⠤⠦⠤⢦⡬⠤⠤⠤⠄⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⢀⣴⠊⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡴⠆⠀⠐⠃⠀⠀⠐⠚⠂⡀⢀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⣀
⠀⠀⡘⠁⠀⣠⣄⠀⠈⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠐⡻⠁⠀⢰⡀⠠⠟⠂⠀⠀⢠⣄⠉⠁
⠀⠀⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠋⠀⠀⣀⠠⠁⠀⢾⠦⠐⠉⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠰⠦⠀⠀⢀⡤
⠀⠀⠻⠄⠀⢀⡀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠁⠘⠃⠀⢀⣤⢤⡄⠀⣤⣤⣤⣤⣀⣰⣏⡼⢀⠀⠀⣠⢤⠀⠀⠀⠘⠺⢇⡀⠀⣉⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⣾⠇⢈⣋⠀⣨⢍⢩⣿⢭⡄⣾⣰⢒⠛⢮⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠸⠿⢠⣿⢸⣾⣧⣸⣾⣿⣞⠱⠧⠻⠄⢺⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣠⠿⣏⠟⠙⠳⢋⣈⣥⡿⢷⣋⣉⣱⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠘⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀⠀⠀⠀⠀⠀⠀⣠⢇⣈⣉⠠⠄⣄⠀⠂⠀⣀
⠀⠀⠀⠚⢱⡄⠘⠁⠀⢀⣠⡀⠀⠘⠿⠀⠀⠀⠀⢀⠠⠞⠁⠠⡶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⣿⠞⣉⠀⠀⠤⠀⠀⣀⠀⠁
⠀⠀⢸⣇⠀⠀⣀⠀⣤⡄⠁⢠⣤⣄⠠⢢⠆⠀⢠⡇⠐⠂⠀⠀⠀⠘⠀⠈⠉⠀⠙⠂⠀⠀⠀⣾⣶⡿⢷⠛⣛⠛⠛⠻⣄⣠⡗
⠀⠀⣾⣿⣿⣦⣦⣤⣠⣤⣄⣀⣀⣤⠴⠏⠀⠀⡰⠀⠈⠉⠀⠀⠀⠄⠰⣆⠀⠂⠀⠀⠀⠀⠀⣿⠋⢠⣄⠈⠋⠀⠠⣤⠀⠙⢆
⠀⠀⠙⣾⣶⣤⠆⠈⠉⢉⠀⣀⣰⣿⣧⡾⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⡆⢀
⠀⠀⠈⣛⡛⠛⠉⠙⠛⠛⣻⡏⠉⠁⣀⣀⡤⠀⠀⠀⠀⠲⠀⠀⠀⠀⠘⠀⠈⠁⠠⠒⠂⠀⠀⣷⠉⢀⡀⠀⠀⠙⠀⢀⠀⡆
⠀⠀⢘⡹⠋⢹⣗⠛⠛⡿⢓⡖⠚⠛⠙⣋⡀⠀⠀⠀⠀⣀⠀⠠⠔⠒⠀⠂⠀⠀⢀⡀⠀⠀⠀⠘⡆⠈⠋⠀⠤⠀⠀⠀⠁
⠀⠀⢾⡿⣻⡗⢶⢤⡶⠶⠶⠶⠚⢋⣍⠡⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡆⠀⠀⠈⠁⣰⠂⠀⠀⠈⠲⠄⣀⡀⠐⠖⡠⠖
⠀⠀⠀⠛⠻⠷⠦⠍⢁⣀⣠⠤⠤⠤⠽⠚⠁⠀⠀⠀⠀⢤⠀⢤⠄⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣽⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠟⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⣙⣿⣿⡟⣿⡟⠗⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠹⣿⣿⣿⣿⠟⠛⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠹⡟⡇⠔⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡰⣶⣿⣿⠿⢁⣀⠀⢶⣿⣿⡿⠟⠛⣿⣿⡿⠿⠛⠉⠈⠀⠀⠀⠈⠀⠀⠀⠢⠀⡀⠀⡀⠐⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡆⢸⡿⠿⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣠⡄⠀⠐⢿⣿⣿⣿⣿⣷⣾⠿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⢀⠀⠖⢠⡄⢰⣾⣿⣿⣾⣇⢩⣾⠿⠟⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠲⢤⠄⠀⠀⠀⠀⠀⠀⣾⣿⣼⠋⢀⠄⣤⣴⣾⣿⣞⢿⣿⡿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡆⠨⣿⣿⣿⠿⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠉⡙⠟⠛⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣼⠁⠀⢠⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠠⠤⠖⠁⠀⣀⣀⢀⠤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⢶⡶⣿⣿⣿⢿⣿⣿⡆⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣻⣿⣿⣿⣷⣿⣿⣿⠁⠀⠄⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣰⡟⠉⢋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⢢⠁⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⣶⡄⣼⣿⡟⠠⢃⡀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⢀⠄⠀⠀⠀⡀⠀⣠⣿⣿⣿⣿⣧⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⡿⣿⠀⠀⠱⠀⠀⠀⠀⠘⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠿⠶⠐⠃⢸⡆⠀⠃⠀⢰⣠⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣄⣀⣰⣠⣴⣿⡇⠀⢠⠀⠀⣿⡀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⢧⠀⠙⣿⣄⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣧⣀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠒⠈⠉⠉⠉⠉⠀⠀⠙⠒⠲⢶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⢠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠿⣿⣦⡀
⠀⠀⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣾⣿⣿⣿⣦⡀
⠀⠀⢀⣾⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⠿⣿⣿⣿⣷⡀
⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣿⣿⣶⣿⣿⣿⣿⣷⡀
⢰⣿⣿⣀⣄⡀⣤⠄⠀⢀⣀⣀⣠⣤⣤⢤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣼⣽⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⡯⠯⠷⡻⢿⢋⡍⣩⡟⠕⠋⠵⠛⢵⡿⣿⣿⠃⠀⢸⣿⣿⣟⣒⢯⠊⡉⡒⢬⢒⠨⡛⢿⣽⣿⡻⣿⣿⣿⣿
⠻⢿⣿⣧⣤⣨⣄⣅⣍⣨⣫⣠⣬⣨⣮⣴⣯⣼⣿⡇⠀⠀⠀⣿⣿⣃⣲⣁⣋⣪⣪⣢⣳⣕⣌⣳⡕⣌⣻⣮⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡇⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣉⢩⡙⡡⠛⣏⡉⠛⡛⠳⢚⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣷⡦⢞⠷⣾⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⡶⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠎⠀⠀⠀⠀⠁⢣⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⣈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣄⠄⣰⣤⣴⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⢿⣿⣾⣿⣿⣿⣿⠻
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣸⣁⣙⣟⣟⣙⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠐⢚⣤⠓⠂⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢨⠯⠅⠀⢺⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣠⣴⣤⣦⣄⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⡏⠉⡏⠉⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⢾⡀⠀⠁⠀⠃⠀⢸⡇⡏⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠹⡀⠜⡌⢷⣧⣤⣤⣤⣶⠏⡴⡘⢰⠋⢙⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⠃⠀⠹⣌⠈⢆⢻⣿⣿⣿⠏⡜⠁⣴⠋⠀⠈⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⠴⢤⣄⠹⣦⠈⢦⢻⣿⢏⠞⢀⡾⠃⠀⡄⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⣓⠀⠀⠉⠓⣼⣷⡴⠶⠛⠺⠤⣿⡁⢀⡾⠁⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢹⣴⢶⡶⠞⠛⠉⠁⠀⠀⠀⢀⣀⣀⣩⣿⣧⣤⣄⣀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡟⠀⢸⡁⠀⠀⣠⠔⢀⣠⠞⢹⡏⠹⠁⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⡀⠀⢸⠁⠀⠘⣧⠶⠋⣠⡴⢿⣧⣀⠘⣷⠀⠃⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⢤⣤⣀⣹⣷⣾⡋⠀⠀⣿⠟⠷⣿⣇⣀⣀⣧⣀⣤⣤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠈⠀⡴⠀⠀⠂⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠙⢆
⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠀⣀⡀⠠⠤⠜⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠤⠤⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣄
⠀⠀⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⠏⣐⢦⠌⢳⠀⠀⠀⠀⠀⣾⢁⡰⡤⠈⣇
⠀⠈⠐⠶⠢⡏⢙⠀⠷⠶⠶⠶⠶⠂⣏⢙⠄⠶⠆⠀⠀⠀⠀⠀⠈⠀⠰⠉⠃⠈⠀⠀⠀⠀⠀⠉⠀⠚⠈⠁⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⠀⠈⠀⡀⢂
⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⢁⠈⡄
⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠵⠚⠒⠒⠲⠖⠒⠒⠒⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠒⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠐⠀⠀⠀⠀⣤⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣤⡤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⢿⢿⠻⠏⠿⠿⢿⢿⣷⣦⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠟⠛⣉⣡⣌⣤⣤⣤⣴⣶⣶⣄⣄⠁⠛⠙⠿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢋⣈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣬⣍⡻⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣟⠋⣟⠈⣋⠡⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⢟⡀⣽⡧⠈⠘⠁⠴⢧⣬⣿⡿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣛⣽⣧⣶⣙⣿⣿⡆⢰⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠏⣇⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣂⣉⣙⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠀⠁⢸⡟⠻⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⣿⠿⣿⣿⣿⠿⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣡⣤⣶⣶⣤⣄⣀⠢⡀
⠀⠀⣠⢔⣾⣿⡿⠋⢀⣉⣤⣶⣤⣴⣦⣴⣶⣤⣮⣙⡻⠆⠀⠀⠀⠀⠀⣧⠀⢠⣿⠀⠀⠀⠀⢀⣠⠀⠀⡰⠶⠿⠿⣿⠿⠿⠿⠿⠿⠿⢿⣷⣝⢢⡀
⠀⢰⣵⢿⣫⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇⠐⢸⣿⡀⠀⠀⠀⣿⣷⣶⣷⣶⣶⣶⣷⣶⣷⣶⣛⣿⣻⣗⣾⠶⠤⣬⡙⣆
⠀⡟⢋⣼⣿⣿⣿⣻⣻⣤⣬⣥⣿⣿⣾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⡁⠀⠀⠐⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⣖⠠
⠀⠰⣽⣿⣿⣿⠿⠿⠛⠉⠛⠻⡯⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⢹⡇⠀⠀⠀⢋⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⠿⠟⢻⣿⣿⣿⣿⣷⣞⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢡⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠀⠀⡷⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠀⠉⢻⡾⡇⢰⣾⣧⣶⣿⣿⣿⣿⣿⣿⣆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⢸⣷⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠇⠸⠟⠉⠙⠻⠿⢿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣴⣾⣹⣟⡻⢿⣛⣿⣻⣦⣄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣣⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣾⡷⢿⡿⠿⣿⡿⢛⣿⣿⣛⣋⣋⠃⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣿⠠⠈⠳⡀⠀⠀⠀⠀⠠⢽⣠⠀⣷⣾⣿⣿⣿⠿⣿⠎⡿⣿⣿⡿⠿⠇⠀⠀⣿⡇⣀⠀⠀⠀⠀⢠⡀⣟⠉
⠀⠀⢸⠇⠃⣠⠀⠀⠀⠀⢒⠀⢁⠀⠘⣿⣧⠸⣗⠀⠀⠀⠀⢈⢻⣠⡄⣿⡙⣿⣿⣿⠀⣹⢷⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢹⠄⠀⠀⠀⠘⡿⠟
⠀⠀⠠⡴⠆⠉⢀⣄⠀⠀⠘⠁⠀⠁⠀⠈⢿⣦⡙⡄⠀⠀⠀⢉⢹⣀⣀⣿⠃⠁⠋⢻⠀⣿⢸⠀⢠⣿⡀⠀⠀⢀⣾⡯⠀⡰⠀⠀⠐⣿⣾⣷
⠀⠀⠀⠀⣤⣤⣼⡍⠀⠀⠰⠡⠤⠁⢁⠀⠀⢻⡗⠈⢮⣂⠀⢉⣹⡅⠉⣿⠂⠀⠀⢸⠀⡿⢸⠀⠲⣿⡅⠀⢀⣾⡿⠁⢰⠃⢀⣤⣄⣸⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠛⠉⠀⣤⡖⠀⠀⣲⠀⠘⣀⠀⠀⢻⡀⠘⠿⢣⠈⠙⡧⠄⣿⠀⢸⠁⣼⢀⣷⡟⠀⣛⡇⠀⢀⣾⡏⢠⠰⡞⠀⠀⠀⣿⠛⢋⠀⠒⠡⡀
⠀⠀⠀⠀⠀⠀⠒⢃⡱⠁⠤⡄⠰⣂⢼⠿⠀⠀⣀⢷⠾⢤⡈⣷⣴⣧⣤⣿⢠⢺⣧⣿⣾⠃⡇⠀⠉⡟⢳⣿⠟⠀⠀⡘⠀⢸⣇⣠⡶⢀⡈⠛⡀⠒⠑
⠀⠀⠀⠐⠶⠀⠰⢣⠕⠀⣺⣏⠈⢛⠂⢀⣤⢀⣽⣷⠶⢼⡗⣼⢿⣿⣿⣯⡼⢸⣿⡹⡟⢠⡍⠙⢀⣧⣾⢏⡜⠀⡾⢠⡄⠾⣾⡇⠀⢺⠔⡠⢁⢀⡀
⠀⠀⠐⠷⠈⢠⡄⠉⢙⡚⣥⢾⡧⠰⢂⣌⢙⠉⣰⣟⠀⣺⣿⣸⣷⣿⣿⣿⡇⣿⣿⣷⢂⡼⢳⣾⣿⡟⢇⡾⠑⢸⠋⠀⡗⠀⠘⣇⣟⡀⢛⢀⡘⠚⠃
⠀⠀⠀⠀⠀⠛⢼⠧⠘⡻⠏⡄⢱⠀⠀⣻⢦⣤⣽⣯⠀⣿⠏⠁⠉⣿⣿⣿⣿⣿⠋⣡⣾⣧⣿⣿⡿⢀⢾⠃⢠⣾⣷⣴⣳⡾⢄⠈⠀⡟⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣁⢐⠀⢛⠀⡽⠃⣩⣤⣿⣿⣧⣠⣿⣦⣠⡀⣿⠋⠈⣿⡧⢾⣿⣿⣿⣿⣿⠃⠀⠠⢀⣼⣿⣿⣿⣿⣿⣾⣧⣼⣇⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⣧⣶⣿⣿⣿⣻⣟⣹⣿⡉⠈⢷⣿⣆⣼⠏⠀⠀⢠⣾⣿⣿⣟⠀⠄⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡷⢦⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⣮⢹⣿⣠⣴⣶⣿⣿⣿⣿⣿⣤⣶⣿⡿⣿⣿⢿⣿⣿⡿⠿⠿⠋⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠛⠿⣿⣉⣻⡿⢿⣿⣿⡿⠧⣀⣀⣾⣎⠹⣯⣀⡀⢹⠈⠛⠛⠀⠈⠉⠋⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠁⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣾⣿⣿⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⢰⣿⣿⡟⣿⣿⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣦⡀⠀⠀⠈⠛⠿⠿⠿⣿⠿⠿⣿⠛⠛⢉⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢿⣿⣿⣿⢿⣿⣆⠀⠀⢀⣀⣀⡀⡇⠀⠀⡿⢀⣴⣿⠟⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣴⣿⠟⢿⣿⣧⡀⠀⣷⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⣰⣿⣿⣿⣷⣿⣿⣿⣷⢸⣿⡿⢿⣿⣿⡟⣻⣿⣿⣹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣹⣦⡀⢸⠀⢸⠀⣰⣿⣿⣿⣿⢻⣿⣿⣿⣿⣇⣿⠿⣿⣿⠿⠿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣿⡿⢟⣿⣷⡌⣦⠸⡀⠻⢿⠿⠿⣿⣶⣿⣿⣿⣿⠏⡏⠀⢀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⢑⣀⣀⢴⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢀⡇⠀⣸⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢹⡀⠙⡄⠀⠀⠀⡇⠀⢸⠃⠀⣀⢸⠀⢠⠇⠀⣠⣿⣾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣱⣾⣷⣄⣷⠀⢱⠀⠀⢠⠇⠀⢈⣴⣻⣿⣧⠀⡞⠀⣼⣿⣿⣧⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣿⣿⡄⠀⠆⠀⣸⠀⢰⣿⣿⣿⣹⣿⡇⠀⠀⢨⠏⠙⠉⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠙⡏⢹⡀⢣⠀⣼⢿⣷⡀⢸⠇⠏⢈⡏⡹⠃⠀⢀⡎⡸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣇⢱⠈⢧⠸⡈⠛⠏⡟⠁⣸⡸⠀⣰⠋⠀⢀⢀⢮⠐⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢣⠀⢧⡇⢰⡀⡇⠀⣿⠃⢼⠇⠀⡠⣢⠆⠈⠳⣤⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡄⠱⡈⢧⠀⠳⣼⡇⡇⡰⠃⢠⡏⢀⣉⢊⠥⠊⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠘⠦⠙⠈⠳⠀⠈⠁⠋⠀⠀⠛⠉⠁⠀⢀⡠⠞⠁⠀⢀⣴⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠸⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⢀⣿⣿⣧⠀⠀⠀⣤⣶⣷⣶⡄⠀⠀⠀⣿⣿⣧⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⡿⠃⠀⠂⠸⣿⣿⣿⣿⣿⠀⠂⠀⠻⢿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣭⡥⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢰⣿⣿⣿⡆⠀⣁⣘⢶⠃⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⣿⡝⣿⡇⠀⠺⡩⠡⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⡖⡶⣄⡶⣖⠂⠀⣀⣀⣀⣀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣀⡄⠀⠀⣴⣾⠳⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠓⠃⠙⠀⠓⠂⠀⠨⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠿⠶⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣾⡏⢀⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢃⡞⠁⠀⠀⠈⠁
⠀⠀⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⢤⡄⢀⣀⡀⠶⠆
⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠠⣤⠀⢤⡄⠉⢠⡤
⠀⠀⠀⠀⠃⠀⠀⠐⠁⠀⠀⠀⠀⠰⠦⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⣤⡀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇
⠀⠀⠀⠀⠸⢿⡿⠏⠀⠀⠀⠙⠿⠇⠀⠙⠟⠀⠀⠿⠛⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠸⠇⠈⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⠋⠙⠟⠁⠀⠈⠛⠁⠘⠛⠀⠀⠀⠀⠀⠆⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁
⠀⠀⠀⠈⠁⠀⠀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⢠⣤⣤⣤⠀⠀⣴⣦⣤⣄
⠀⠀⢠⣀⣀⡀⠀⠙⠛⠛⠁⠀⢲⠶⣶⠆⠀⠀⠀⠈⠀⠀⠀⢸⡋⠈⢻⠀⠀⠉⣭⣍⠉
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⢀⠀⠀⠀⠀⠈⣷⣶⡿⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡇⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠈⠿⠟⠻⣦⣄⢀⣀⣀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⢀⡀⣀⣀⣼⣿⣿⣿⣿⠀⢸⠀⢠⣤⣤⣤⣤⣴⣶⣶⣶⡇⠀⢸⠀⣤⣶⣶⡀⠀⠀⠀⠀⢠⡀
⠀⡇⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⣿⣤⣤⣶⣶⣿⡇
⠀⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣸⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠤⠤⠤⠠⠤⠄⠤⠤⠤⠤⠄

⠀⠀⠀⣀⣀⣀⣀⣀⣤⡄⠠⣤⣴⣄
⠀⠀⠀⠉⢛⣂⡸⢻⣟⣷⣢⣞⣩⣟⢦⡀⠀⠀⠀⢠⣦⣄⠀⠀⠀⠀⢀⣴⣤⣀
⠀⠀⠀⠀⠈⠉⠤⠌⢙⠫⠟⣿⠛⢹⣞⣷⣤⣄⠀⠀⠻⠟⠀⢀⣤⠖⡝⣟⢻⣁⣀⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠸⠁⠦⣈⠉⣩⠉⠁⢀⡔⢺⣿⣻⣯⣿⣬⢟⣽⡿⣿⣿⠙⢇⡠⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠘⢷⡀⠃⢚⡀⠸⡀⠆⠸⡁⠧⠐⠦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣤⡦⠀⠀⠀⠘⠀⠃⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡀





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠅⠀⠀⠀⠀⠉⠉⢢⠀⠉⢰⠁⡠⠀⠈⢢⡀⠀⠀⡰⠁⡠⠆⠄⠀⡝⠌⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠐⠈⠆⠸⡠⠁⠀⣀⠤⠄⡤⢤
⠀⠀⠀⡀⠀⠀⠠⠄⠲⢥⡁⠀⠐⣄⠀⠁⠤⡀⠰⡀⠀⡅⢀⡀⢀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⡐⠀⠀⠀⠁⡜⠀⢠⣈⠁⠘⠗⠤⠤⠍⡏
⠀⠀⠀⢰⣐⠀⠀⠀⠀⢂⠽⠀⠀⠈⠢⢄⠀⠌⠢⠇⠀⠀⢎⣕⡲⠀⠀⠀⢀⠂⡀⡀⢸⠀⠀⡐⠀⠀⠀⣡⠊⡔⠀⠀⠈⠢⠀⡄⠀⠀⠀⡇
⠀⢠⠀⠀⠄⠀⠐⠈⠁⣠⠤⠤⡠⠠⠀⣄⠉⠐⠀⢠⣞⡃⢨⣊⠼⠀⠀⢄⡠⠃⠀⢱⠄⠈⢠⠠⠄⢀⠔⠁⠀⠸⠓⠤⠴⠄⠀⠁⠐⠒⠁⡀
⠀⠈⠃⠀⠨⠇⠀⠴⡃⠠⠀⠐⠡⢁⣂⡠⢕⡄⠀⠘⠋⠀⠀⢷⠇⠀⠀⠲⢇⠀⠀⢰⠦⣐⠈⠂⠐⠁⡐⡠⠀⠐⠦⠤⠀⠀⡀⠴⠈⡀⠀⠈
⠀⠀⡔⠲⡄⠀⡔⣀⡒⢒⣢⢁⣁⠼⠃⢊⡍⠀⣔⠒⠓⠼⢄⠘⠀⠀⠀⠀⢐⠀⡍⠀⠉⠀⠀⠀⠀⠀⠐⠁⢴⠄⠀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣷⠀⠘⠄⠀⠢⠄⠄⠤⠤⠴⠒⠚⠉⠀⢄⡇⠀⠀⠀⡇⠀⠌⢀⠁⢀⠼⠰⠁⠀⠀⡠⣶⠿⣿⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠚⠐⠆
⠀⠀⣇⠨⡁⢸⠀⠀⠀⢤⠤⢄⠀⠀⢀⣀⣤⠈⢧⠠⢄⡘⠁⠀⠈⠨⠆⠀⠀⠀⠂⠀⠈⠉⢻⡒⠛⠛⠛⠳⠀⠁⠀⠀⡍⠀⠈⠓⠒⠊
⠀⠀⠘⠦⠴⠊⢀⠄⠀⠈⠂⠤⠀⠤⠄⠔⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠑⠒⠁⠐⠠⢖⠒⠒⠁⠀⢹⠉⠀⠀⢀⠤⠄⠠⠄⡀
⠀⡠⠀⢠⠀⡰⠁⠙⠀⠘⡀⠀⠀⢀⢀⣄⢠⢤⢰⡿⠞⢱⠀⡠⠩⠐⠒⠐⠒⠪⠔⠁⠀⠠⠄⠀⠈⠀⠠⠀⣀⠒⠀⠐⠀⠰⠃⠀⢈⠤⢤⢃
⠀⠙⠣⠁⠠⠁⠀⠀⠀⠐⢀⢤⠀⠠⠀⠐⠚⠈⢉⠠⠒⡱⠘⠏⠙⡠⣲⠖⠁⠀⠀⠀⠄⠀⠴⠀⠀⣀⠀⠀⣁⠀⠀⠀⢠⠃⠀⡔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠈⠐⠂⠀⡈⠀⢀⣊⡭⡴⠦⠒⠋⣡⡀⠀⠀⠀⠀⡜⠀⠀⣠⠐⠇⠩⠠⠅⠩⠈⠣⡀⠑⣀⠽⠆⢀⡀
⠀⢀⠀⠂⠐⠙⢄⠀⠀⠀⠀⡲⠁⠤⠄⠀⠀⠊⠀⠈⠀⣠⡀⠀⠀⡺⠭⠃⣄⢀⠨⠊⣀⠀⠀⡀⠀⠄⠈⠉⠉⠀⠈⡀⠁⠀⠀⠀⡜⠀⠈
⠀⠘⠤⠀⠀⠈⢀⡄⠀⠀⠐⠚⡞⠠⠀⠀⣰⠶⠞⠛⠀⢛⡧⣤⡀⠉⢀⠔⠈⠀⠀⠀⠈⠀⠀⡆⠁⠀⠀⠀⠁⠈⠀⠈⡇⠀⠀⠠⢃⠐⢀⡁
⠀⢀⡀⠐⢊⠔⠃⠠⡀⠀⠂⠁⠉⠀⠀⠜⠁⠀⠀⠀⠐⠌⠈⢁⡀⠈⠀⢄⠆⠀⠀⠒⢀⠣⠈⠑⠀⠀⠐⠒⠒⠒⠊⡊⠝⢀⠀⠀⠀⠀⢀⠁
⠀⠰⠀⠉⠀⠘⠀⠠⢂⠄⣀⠐⠠⠀⠀⡀⠀⠀⠀⣀⣄⠀⠌⠀⠀⢂⠀⠀⠀⠀⠐⠀⢁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡮⡆⠀⡒⠒⠊
⠀⠀⠣⠬⠄⠂⠁⠀⢇⢸⣁⡐⠀⠢⠀⣁⡀⠀⠉⠉⠀⢌⠀⠀⠀⢸⠀⠘⠀⠀⠁⠊⡀⠁⠀⠁⠠⠐⢒⠂⠠⡎⠈⠂⢀⠈⠁⠀⠧
⠀⠀⠄⡠⡀⡠⢆⡀⠀⡆⢀⠤⠄⠊⢀⠇⠈⢁⠁⠠⠁⠀⣄⠀⠀⡾⠀⠰⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠂⠀⢉⢱⠤⣀⠤⠊⠀⣀⢀⠀⠆
⠀⠠⠂⠂⠃⠓⠀⠖⠀⢈⠥⠤⡀⠀⠢⠄⡶⡇⠀⢀⠀⠐⠈⠀⠀⡜⠀⠈⠀⢤⠀⠀⡰⠋⠁⠀⠀⠀⡔⠁⠀⠀⡴⢁⠀⠀⢀⠹⠗⠎⠈
⠀⠀⠀⠀⠰⠀⠄⠒⠀⠀⠐⠒⠊⠀⠀⠀⠀⠠⠀⠀⠑⠄⠠⠔⠚⠀⠀⠀⢄⡀⠠⡘⠄⠦⠄⠠⢭⠒⠤⣤⠤⢚⡀⠝⢀⠀⢈⠀⢀
⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠘⣠⠠⠁⠀⠁⠀⡠⠤⠴⢆⠀⠀⢄⠀⠠⠉⠈⠑⢊⠉⠐⠒⢒⡀⠉⢀⡀⠈⢁⡀⠀⠐⠀⠀⠁⠀⠀⠜⠔
⠀⢀⢀⠐⣀⢀⡀⠄⠀⢠⠁⡠⠤⠀⠁⠀⢎⣉⠆⠱⠀⠀⠚⠀⠀⠊⠀⢠⡀⠀⣀⠀⠀⠀⠐⣃⠟⢰⢁⠘⠐⢁⡑⠀⢀⣀⠄⠤⠤⢀⠄
⠀⠈⠚⢀⡀⠄⣀⠀⠀⠀⢨⠀⠀⡠⠤⢄⠈⠀⠀⠐⠒⠒⠂⠀⠐⠀⣤⠄⠀⠈⠉⠀⠠⡄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠨⠉⡀⠀⠀⠀⠈⡹
⠀⠀⡔⢽⢃⢴⠋⠂⢠⠦⠈⡠⠂⠀⠀⢨⠅⠀⡠⠂⢁⣈⡰⡄⠀⠀⠀⠠⠰⡆⠀⠀⢀⠠⠐⠀⠐⡴⢶⠖⡂⠀⠀⠀⠈⢢⠄⠀⠀⢀⠔⠁
⠀⠀⢯⠴⠐⠁⠀⡄⠀⠀⠈⡀⠀⣀⡠⢊⡀⢰⢀⠜⠁⠀⢄⠈⠂⠤⠤⠔⠊⠀⠀⠂⢁⠀⡀⠀⠔⠁⠀⠐⢄⠀⠀⠀⠠⠄⠁⠀⠀⠀⡠⡲
⠀⠀⠀⠁⠒⠒⠒⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠐⢀⠂⢌⣲⣄⠀⢀⡴⣂⣴⡖⠒⢒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠻⢷⣬⣻⣆⣾⣿⡛⠭⠝⢲⠢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡂⠄⠉⠀⠀⠀⠀⠈⠉⠻⠛⠻⠁⠀⠀⠀⠀⠉⠙⢛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠠⠔⠂⠒⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠐⠐⠉⠈⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⣒⣡⡦⠄
⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠙⣄⠀⠀⠀⠀⠀⢀⡠⠐⢂⣉⡱⠖⠓⠉⠉⠁
⠀⠀⣸⣷⣶⣶⣦⣶⣤⣖⣒⣶⡖⢲⣦⣤⣤⣤⣴⣴⣲⣦⣤⣿⠀⠀⠈⢧⡀⠀⣠⣔⡩⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠷⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡀⠀⠀⡀⢄⢀⣀⣻⠄⢀⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠂⠀⠀⠐⠢⠤⠄⠀⣘⣇⣴⠗⠋⠉⠄⢂⣸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠖⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⢃⢀⣹⡽⠚⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢄⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠒⠐⢛⣍⣠⠵⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀⠀⠀⠑⢤⡄⠀⠀⠒⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠉⠐⠀⠠⢀⡀⠀⠀⠇⢀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠘⠓⠓⠒⠛⠛⠓⠠⠤⠬⠏⣀⠈⠦⠤⠤⠤⠤⠤⠤⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⣿⠿⣿⣦⣀⣤⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣶⣾⣷⣨⣿⣿⣿⣛⠙⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⠛⠛⠛⠉⠉⠉⠉⠛⠻⢿⣿⣧⡀⠙⢷⡄⠘⣿⣿
⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⡀⠀⠈⢿⣿⣆⠀⢿⣤⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢰⣿⡿⠁⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢻⣿⣇⢘⣿⣿⠋⠻⢶⣶⣶⠶⠿⠛⠋⠉⠉⢉⣽⠏
⠀⠀⢀⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣾⣿⠿⠶⣤⣤⣀⣀⣀⣤⣴⠶⠿⠿⠿⠋
⠀⠀⢸⣿⡇⣴⣿⠟⠛⠛⠟⠋⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠏⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠘⣿⣿⣿⠁⠀⠀⢀⡄⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⠏
⠀⠀⠀⠹⣿⣿⣄⠀⢀⣾⡿⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⢋⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣷⣄⣀⣀⣀⣴⣿⣥⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠐⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠭⠁⠠⠤⠄⠍⠦⠀⠁⠀⠀⠘⠉⢱⠒⠂⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⣀⣀⡄⠸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡃⠀⠀⠙⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢚⠀⠀⠀⠀⠠⢄
⠀⠀⢸⠉⠉⠉⢉⡉⣉⠉⠉⠉⠉⢉⢀⣀⠀⠀⡀⢀⡐⢲⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⢠⠊⠁⠀⠀⠉⠢⡀⢰⠁⠀⠈⡆⢌⠀⠀⢘⢘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢱⠈⠓⠤⠐⠁⠘⢂⡐⠊⢸⠀⠀⠈⠀⠁⠀⠀⢸⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠂
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⠙⡆⠜⠁⠈⢱⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⢸⠀⠘⢆⡀⠀⠀⠀⡠⠃⠈⠢⠄⠴⠁⠐⠤⠤⠚⢸⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠤⠤⠤⠬⠭⠬⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢐⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠒⠂⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⢻⠁
⠀⠀⠀⠀⡀⠀⠀⢃⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠲⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢸
⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⣼⢁⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⡒⠒⠲⢌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⢘
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠰⠁⡀⠈⠂⡀⠄⠀⢱⡀⠀⠀⣠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡇⠈⠈
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠑⠄⠀⠀⢘⡀⢃⠀⠀⠠⠀⠀⢠⡇⠀⡎⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢀⠄⠀⠀⠀⠣⣀⠀⠀⡄⢊⠀⠔⠀⠀⢇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠀⠁⠀⠀⡠⠒⠢⡈⠑⠉⠈⠂⠁⠀⠀⠀⠈⠓⠲⠔⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⡄⠀⠀⡁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⢁⠀⠀⠀⢀⠄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠐⠀⠀⠀⠤⠠⠠⠀⠀⠀⠈⠢⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⡀⣠⣴⣶⣶⢶⣦⡀⣑⣒⣀⣀⣠⣶⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣴⣶⡎⣿⡏⣹⠛⠀⡌⠓⠺⠛⠛⢛⠛⣛⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢋⣿⣏⣱⣷⣪⠭⠂⠀⠒⠀⢲⡤⠤⠤⡽⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠋⠉⢀⡄⠀⠀⠀⠀⠉⠀⠀⠀⠈⠲⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⣶⣴⡳⠞⢶⠆⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠦⡄⠁⡠⠀⠠⠋⢀⠀⠀⠀⠀⡄⠂⠀⢀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠖⠚⡗⠒⠛⢶⠤⣄⣀⣁⣠⣄⣤⡵⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠘⠂⠤⡄⢀⡇⣀⠀⣉⠈⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠄⡀⡀⢨⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠦⢤⣀⡀⠀⡇⠀⠀⣀⡤⠚⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠓⢻⠚⡏⠉⡇⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠇⠀⠇⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠇⠀⢠⠀⠀⢠⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣾⣿⣆⠘⢰⡀⠂⠀⢀⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣶⣾⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢰⡆⠀⡐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡤⢧⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⢺⡄⠀⠠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠟⠛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠓⠒⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠛⠛⢩⠉⠁⢀⣀⣠⣤⣴⣾⠏⡄⠀⠀⣤⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⠀⠀⠀⣆⠀⠰⠀⡀⠀⠐⣀⠰⢶⣾⣾⣿⣿⣿⣿⣿⡿⠋⢸⣷⠀⢠⣿⠀⢚⠛⠃
⠀⠀⠀⠀⠀⠀⣸⡇⢰⣼⠧⠊⢙⠯⢆⡄⢘⡓⠊⡉⠄⢛⠸⠛⠋⠉⠀⢁⠈⠥⠦⣀⡈⢉⠒⠼⠿⡆⠋
⠀⠀⠀⠀⠀⠀⣿⠓⢈⠀⠀⠔⠃⢠⠀⠀⢀⡀⠀⠋⠉⠁⠀⠄⠂⢉⡀⣿⠀⠠⠄⠀⠈⠿⠲⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡜⠂⢀⠀⠀⠀⢰⡆⣀⠄⠁⣸⣧⡿⠧⠠⠖⠀⠀⠀⠀⠆⠀⠸
⠀⠐⠀⠤⢀⠀⠀⠀⠐⠀⠺⠿⠯⠿⠆⠀⠉⠁⠐⠃⠸⠧⠈⡉⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠈⠰⣶⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠲⢢⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄
⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠒⠦⠤⢀⣀⠀⠀⠀⠈⠠⠄⠀⠀⠀⢤⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣤⣴⣤⣦⡀
⠁⠀⠀⠀⠀⠀⠀⢀⠐⠒⠒⠂⠀⠀⠀⠠⠅⠀⠀⠏⠁⠂⢤⠀⢀⣀⣤⠀⠈⠀⠒⡄⡀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠄⠀⠘⠛⣉⡀⠅⠂⡐⡤⢰⠐⣦⣤⠂⠤⣲⣶⣷⣿⣿⡏⠿⠉⠓⠶⠛⠛⠄
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⢀⣀⣀⠀⠁⢠⠄⠀⠈⡉⠽⠁⠀⠉⡳⠂⣈⢆⡤⣫⠛⣝⣿⣿⡟⠃⠁⠀⠀⠀⠀⠀⡀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠜⡂⣀⠘⢩⠄⠓⣄⠫⠀⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠈⠉⠀⠀⢐⣄⠈⠀⡊⠀⢒⠄⠀⢳⠑⡀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⢳⣀⠀⠀⠂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠄⠐⠂⠀⠉⠀⡠⠃⠀⠀⠀⠁⣸⢠⠸⡒⠀⠀⢽⣿⣿⡀⠀⠠⡄⠀⠀⠀⢿⠀⠀⠀⠰⠀⠄⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠄⠂⠁⢈⡁⠀⠄⡵⢊⡵⢢⠈⠅⠀⠰⡙⣿⣿⡇⠀⠀⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢁⡠⠧⠀⠔⡫⠞⣡⢥⠘⠒⠀⠘⠻⣿⠇⠀⠀⠀⠘⠂⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⡠⠊⡡⠄⢀⠈⠁⠚⠁⡣⣄⠙⠢⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄⢉⠀⠀⠈⠔⡇⢠⣨⡈⠴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⣤⠀⠉⠙⠃⠠⠦⠤⡶⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣷⣠⣷⣴⠶⠀⠀⠤⠤⢤⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠶⠶⠶⠶⠿⠿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⡼⠛⠀⠀⠀⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢆⡇⠈⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⣴⣾⣁⡉⣠⣤⠎⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⡆⡀⠘⠻⢿⣦⣀⣄⡀⠀⠀⢠⡦⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⢠⡟⢰⠀⠀⠀⠀⢈⢩⡅⢀⡔⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⣸⢰⢹⠇⠀⠀⠀⢸⠘⢠⠏⠘⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣾⣷⣿⡟⠁⠀⠀⠀⠠⠃⠀⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠡⠶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⣆⣠⡄⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣢⣶⣿⠿⢋⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡾⣿⠹⠟⠉⠀⠀⠨⠁⢄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⠂⠋⠌⠁⢀⠀⠀⠀⠂⢘⠀⠈⠈⡀⠀⡀⠂⠀⣀⠠⠄⠂⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠄⠐⠀⠠⠐⠰⠄⠀⠂⠰⠀⠤⠀⢤⣀⣪⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⣀⡔⣀⣀⣀⡀⠀⠀⠀⠀⠑⠒⠬⡶⠞⠛⠛⠉⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠃
⠀⠉⡀⢰⣁⠕⠋⠀⠀⠈⣆⠀⠀⠀⠀⠄⠀⠘⠓⢤⠀⠤⢤⣤⢀⡀⣀⢀⡰⡄⡁⠀⠀⠀⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠘⢟⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠁⠉⠉⠂⠒⠤⣠⣀⣀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣾⡟⠃⠲⠦⢷⡆⠀⠀⠀⣧⠀⣺⠀⠀⠀⠀⠀⢷⣤⣤⠤⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠟⠋⠀⠀⠀⠀⣰⡇⠀⠀⣴⣿⣼⣿⣦⡀⠀⠀⠀⠀⠀⡀⣂⠒⠄
⠀⠀⠀⠀⠀⠀⠁⠃⠋⠀⠀⠀⠀⠀⠀⣒⡉⣀⡀⡸⠛⠙⠙⠛⠛⠃⠙⠢⠤⠤⠜⠻⠿⠖⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⢰⠆⠐⠒⠠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠈⠙⢃⣄⠀⠀⠀⠄⠀⢀⡐⠀⢻⡀⠀⠀⠀⠀⠀⠀⡀⠄⣈⣴⡎⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢤⡀⢰⠋⡓⠄⠀⢈⣾⡇⠀⠀⢂⡀⠈⠃⢀⠫⠁⠀⠀⠠⣦⠀⠀⢡⡏⠉⣟⢻⠶⡀⠂
⠀⠀⠀⠀⠀⠒⠁⠀⠤⣝⡲⢭⡨⣝⡊⠓⠀⠈⠉⠀⠀⠀⠀⠘⠚⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⢹⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡒⠦⠝⠲⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⣀⠀⡄⠀⠀⠀⠀⠀⠈⡧⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡅⠀⠀⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠋⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠞⠳⠃⠀⠙⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠘⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⠉⢀⠀⠀⠀⢀⠰⠔⠳⠄⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡇⠘⠊⢸⠀⠀⠀⠀⢁⠀⠀⠄⠠⠀⠀⠀⠀⠀⠠⢀⡀⣠⠂⠀⠀⠘⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠃⠒⣀⠆⢀⡃⠐⢠⠀⠀⠀⠀⢸⠇⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡛⠁⠦⢠⠔⢀⡰⢀⡠⠀⠀⠀⠀⢠⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡸⠁⠀⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠘⠈⠛⣐⡃⠀⣃⡀⠀⢨⡄⠀⢤⠆⠀⠀⠀⢸⡆⠀⢶⣶⠆⡀⠀⠀⢀⠀⠀⠀⠀⠁⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⠀⠁⠾⢃⡉⠀⠁⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠾⠃⠈⡇⠀⠀⠀⠀⡧⠛⠉⣭⢻⡆
⠀⠀⠀⠀⠀⠀⣠⠠⢄⣀⣤⠆⠒⢄⡠⠞⠀⠀⠋⠀⠀⠀⠀⠀⣀⢧⡄⠀⠠⠌⠖⠀⠀⠀⠂⠄⠀⠀⠐⠐⣆⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠘⠁⠈⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠲⠒⠶⠋⠋⠝⠉⠋⠙⠉⠀⠨⣬⣥⡭⠆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠂⢀⡈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠁⠀⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠰⠅⡆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣛⡛⠢⢍⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢘⠗⣸⢀⠀⠣⢠⢠⢸⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠻⠦⡉⠁⠀⠀⠈⠀⡊⡈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣮⠑⡄⢀⠀⠀⠀⠀⠀⠐⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢾⠀⠁⠒⡡⠂⠀⠀⠀⠀⠀⢀⠁⣁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣢⡀⠀⣿⣻⢰⠍⡦⠂⠀⠀⠀⣀⣴⣶⣾⠿⠛⠃⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⡄⣶⢾⣿⠹⡄⠘⣾⣆⠈⢁⣠⠴⠚⣽⡿⠋⠀⠀⠀⠀⢀⣞⡟⢉⡽⢧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠽⠓⣺⣦⣧⡿⣿⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⠾⣥⠤⢚⣷⡀
⠀⠀⠀⠀⠀⢀⣿⣷⠸⣿⠿⢷⠘⣄⣱⢳⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⢞⡽⡖⢉⢞⣷⡀
⠀⠀⠀⠀⠀⠸⣿⡟⢐⣾⣯⡘⠣⣻⣿⣏⡆⠘⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⣀⣯⢟⡿⣯⠔⢻⡄⢊⡿⣧
⠀⠀⠀⠀⠀⠀⠙⢧⣿⣿⠛⠀⠀⢹⣟⢻⣧⠀⠀⠀⠈⠀⠀⠀⢺⠀⠀⠘⢫⣹⡲⣧⡷⣂⡠⢷⣊⠀⣻⣀
⠀⠀⣠⣶⢿⣿⠛⣷⡺⣿⣦⣠⢄⡀⠈⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢋⣾⣟⣥⡤⠼⢃⠀⠁⠸⠧⡄
⠀⢸⣲⠏⣨⣍⢡⠟⠛⢙⡺⣽⣿⢽⣦⣻⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠏⠆⠈⠘⢻⣧⡴⠚⠑⢻⣅⡠⠴⠿⡀
⠀⠸⡟⣷⡰⢆⣜⣛⠷⣶⣖⣿⣿⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⠀⠙⣯⡗⣦⠁⠀⢹⡆⠀⠐⠛⢀⣀⣀
⠀⠀⠙⠺⠷⠾⠿⠛⠋⠉⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⠶⠤⢿⣽⣧⠤⠤⣿⡁⢸⣻⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠉⠛⠲⢧⣸⠯⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠈⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡛⠀⠠⠦⠀⠀⠀⠈⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⣀⣤⡶⠶⠛⠋⠉⠁⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠮⠇⠀⠀⠀⠰⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⣄
⠀⠀⠀⢠⣾⡋⠀⠀⠀⠀⠀⠤⠀⠀⢠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡀⣀⣷
⠀⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⡶⢚⡩⠝⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣽⣟⠲⠶⣦⢤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠲⠖⠒⠂⡈⠉⠁⠤⠚⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠾⠷⢶⣤⣽⣦⣄⣀⣀⣴⡀⢠⡴⠷⠞⠓⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⡛⢓⠒⠀⢂⣩⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⢠⠀⢹⣿⡟⠚⠃⠉⠙⡆⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠱⣀⠂⢸⡟⠀⠀⠀⠀⠀⢹⠀⠀⡏⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠠⡽⢦⣸⠇⠀⠀⠀⠀⠀⠀⠃⢸⢃⡎⢰⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣃⣷⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⡮⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢢⣿⣿⢻⠀⣀⠀⡈⠀⠀⠀⢸⡿⢸⠁⣸⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣾⢸⡇⣸⠃⡏⢠⠀⠀⠀⠀⢸⡇⡞⢠⠇⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣻⣿⣧⢻⣤⠁⡄⠀⡄⠀⡄⣾⣟⣴⢟⣋⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⢿⣿⣾⣿⣆⢱⠀⣇⣤⣷⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⠟⠛⠛⢯⣍⡉⠉⠛⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⡹⠶⣤⣀⡀⠀⠈⠙⠛⠶⠶⠶⠟⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣠⣋⣀⣀⣀⠉⠛⠳⠶⠶⣤⣤⣤⡤⠶⠶⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠾⠛⠛⠛⠛⠛⠻⠿⣶⣦⣤⣤⣤⣀⣀⡀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣳⠆⠀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣯⣉⠙⠛⠛⠋⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠸⠀⠈⠧⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠖⠲⠶⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠛⠉⠳⢄⡀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠪⣍⣙⡛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠓⠦⢄⣀⡙⠒⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⠉⠛⠳⠶⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⡶⠞⠋⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠒⠲⠤⣤⣄⣀⣀⣀⠀⠈⠉⠉⠉⠁⠀⠀⢀⣠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠶⣤⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠉⠙⠛⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷⣌⠉⠉⠉⠉⠉⠉⠀⠀⢿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⣼⠟⣿⣦⣄⣀⣀⣀⣀⣀⣤⣤⠶⠛⣿⣟⠳⢦⣤⣄⣀⣠⣴⠞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠛⠶⣤⣄⣀⣀⣀⣀⣤⣼⠟⠀⢹⣷⡈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣹⣿⠀⠀⠀⠈⠉⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠉⠉⠉⢉⣼⡟⠀⠀⠀⠻⣿⣿⣒⣒⣲⣖⣒⣒⣿⣿⣿⠏⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠶⣶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠉⠛⠶⠶⣤⡴⠶⠟⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⣠⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⢼⢑⡢⡰⡄⠀⠀⠀⠀⢰⠿⡎⠋⡾⣷⠀⠀⠀⠀⠀⢛⡟⢻⠛
⠀⠀⠀⠀⠀⠀⠸⠿⣛⠿⠇⠀⠀⠀⠀⠀⣮⣿⣿⣷⡆⠀⠀⠀⠀⠀⣿⠙⠸⢿⡏⠀⠀⠀⠀⠀⣻⣏⣹⣋⠄
⠀⠀⠀⠀⠀⠀⠰⡿⠂⡾⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠃⠄⡄⡄⡿⠀⠀⠀⠀⠰⣾⢍⡸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⣥⣶⣤⠅⠀⠀⠀⠀⠀⠈⠥⠁⠝⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠈⠑⠛

⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⣀⢠⣄⠀⠀⠀⠀⢀⣤⠀⡀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣷⣾⣴⡀⠀⠀⢹⣿⣿⣦⣴⢴⣦⣾⣿⣿⡅⠀⠀⢸⢻⡿⢅⠀⠀⠀⠀⠀⠀⣞⡙⢋⣷
⠀⠀⠀⠀⠀⠀⣼⠿⠈⢿⣦⠀⠀⠀⠀⠙⣼⠿⠘⢿⡞⠀⠀⠀⠀⠀⡼⢾⣟⠻⡄⠀⠀⠀⠀⠀⡿⠥⡬⢿
⠀⠀⠀⠀⠀⠀⡥⢼⣤⡵⠾⠀⠀⠀⠀⠀⠸⣧⣬⣽⠁⠀⠀⠀⠀⠀⢰⣟⢛⡷⠀⠀⠀⠀⠀⠀⣿⡓⢓⣻
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠰⣦⣿⣠⡆⠀⠀⠀⠀⠀⢠⣴⣢⣤⠀⠀⠀⠀⠀⠀⠠⣄⣆⡤⠀⠀⠀⠀⠀⠀⣄⣠⣦⣠
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠛⠁⠀⠀⠀⠀⡿⣿⢹⡿⡆⠀⠀⠀⠀⠀⢨⣼⡤⣭⠀⠀⠀⠀⠀⠀⣉⡙⢟⣉
⠀⠀⠀⠀⠀⠀⠀⢉⣭⡍⠀⠀⠀⠀⠀⠀⣟⣛⢘⣛⣇⠀⠀⠀⠀⠀⢸⣶⠱⡘⠀⠀⠀⠀⠀⠀⢿⠃⠸⣿
⠀⠀⠀⠀⠀⠀⣴⠁⠉⠨⢽⠀⠀⠀⠀⠸⣆⡋⡇⣓⡼⠀⠀⠀⠀⠀⢸⡧⠤⣿⠀⠀⠀⠀⠀⠀⢣⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣇⡾⠁⢸⣧⠟⠁⠀⠀⠀⠀⠀⠈⠛⢯⣍⣧⠀⠀⢀⣤⡄⠙⢿⣿⡄⢹⣽⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⠟⣿⠁⢠⠟⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⠷⣄⠀⢉⣷⣶⣦⣿⣿⣼⠃⠀⠀⠈⠳⣇⢹⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣴⠿⣰⣿⠏⠀⢿⣠⢋⡀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⢷⣼⡍⢻⣟
⠋⠈⠁⠉⠛⠦⣍⣿⣯⣤⣿⣇⠀⠀⠘⣧⠀⣰⠏⢀⣤⠴⠶⠖⠒⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⡀⠀⠙⣧⠏⠁
⠔⠀⠈⠉⠀⠀⠈⢹⣿⡾⠋⠛⠦⣤⣀⢻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿
⠐⠉⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠉⢻⣧⣀⠤⠤⠴⠖⠒⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠈⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⡄⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣀⣀⡀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⡇⠀⠀⠀⠀⣿⡄
⠀⠀⠤⠶⠾⠛⠛⠛⠉⢻⣿⠁⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⡇⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⠉⠀⢹⣷⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣻⣿⡏⠀⠀⠀⢸⣷⢰⣦⡀⠀⠀⣾
⠀⠀⠀⠀⢀⣀⠐⡀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠿⠻⠟⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿⣾⣿⣿⣦⠀⣿
⠀⠀⠀⠀⢀⣿⣿⣷⡶⠶⠀⠘⣿⣧⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⢸⣷⣦⣹⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣽⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠸⣟⠉⠻⢷⣄⠀⠘⣿⣇⣀⣀⣀⡀⠀⠸⣿⡆⠀⠀⠰⣶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⠛⣿⣿⣿⣷⣿⣿⣿⣿
⣀⣈⣷⣠⣤⣤⣿⣤⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⡇⠀⠀⠀⠋⠀⢠⡿⢿⣿⡿⠿⠛⠛⠛⠁⢋⣿⣭⡿⠄⠀⠀⠀⣀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠓⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣾⣿⣿⣿⣿⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣄⠀⠀⠀⠰⣿⣿⣥⣿⣿⣿⣿⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠉⠉⠉⡏⠉⢹⡇⠀⣠⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣯⣿⣿⠀⢀⣴⡾⣷⣾⡇⠀⢸⣥⣾⣿⣯⣨⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡏⢹⠋⠉⠁⣴⣿⣿⣦⣾⣿⣿⡄⣾⣿⣿⣿⣿⡿⢿⣿⡿⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢲⣄⠀⢁⠀⡆⠀⣾⣿⣿⣿⢿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⢿⣿⣧⠈⡄⠇⠸⣿⣿⣿⣿⣮⣿⣿⣿⣿⢳⠅⠀⡙⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢛⠛⠋⢐⣀⡀⡆⠀⠀⠀⢸⠀⢈⡇⠀⠀⢸⠀⢀⠇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⢣⠈⢣⠀⠀⠀⡀⠀⢰⠀⢀⣀⠞⠀⡜⠀⢀⣾⣾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣬⡆⠀⡆⠀⠀⠇⠀⣨⣾⣻⣿⣆⢰⠁⢰⣿⣽⣷⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⡿⢷⠀⠠⣀⣸⠀⢸⡿⣿⢯⣿⣿⠀⠀⢀⠏⠉⠉⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡄⢱⠈⡇⣼⣿⣿⡆⢸⢃⠃⢰⡠⠋⠀⢀⡎⡐⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡶⣧⡱⠈⢣⢣⠀⡃⢸⠀⣼⠎⢠⡏⠀⢀⢀⠘⢆⡀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢷⠛⡅⢣⠈⢻⡀⡇⢸⢀⡟⠀⡞⠀⠔⠱⢋⠄⢀⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⡘⢄⠳⡀⠙⠇⠸⠊⠀⡼⠅⠐⠀⠈⢀⠔⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣿⠄⠀⠀⣉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⠀⠀⠰⣿⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠂⢀⣿⣷⡄⠀⠀⢀⣤⣶⣤⡀⠀⠀⢠⣾⣿⡀⠐⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠁⠐⠀⣿⣿⣿⣿⣷⠀⠂⠘⢿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠐⠀⢉⠑⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠫⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠈⠄⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⢀⣄⣸⣃⠀⢀⡠⣀⡠⣀⣀⠌⣀⣀⡠⣀⣠⣀⣌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢛⡉⠉⠉⠈⠉⢻⠀⠈⠉⠀⠀⢀⣋⣀⣠⠠⠭⠝⢛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⣏⠤⠤⠢⡤⢄⣈⡇⠀⠀⠀⠐⢈⠀⠀⢀⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⣠⠤⣶⠤⢤⣤⣄⣀⣈⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢣⠀⠱⠊⠉⠙⠢⢬⠀⠀⡏⡉⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⠏⢠⡢⠀⢀⣤⠴⠆⣧⠀⣷⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⢀⠎⠀⢆⡤⢾⡇⠀⢷⣳⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠐⢁⡎⠀⠀⠈⠒⠤⡇⠀⢸⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡀⠀⠀⠀⠀⡘⣇⠀⠀⠀⠀⢠⠇⠀⠘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡃⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠸⣤⣄⣠⢇⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠄⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⢄⣀⡈⠢⡙⠦⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⠄⢙⠂⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡈⠀⠄⢈⠘⠐⠣⠰⡀⢠⡀⠀⠀⠀⡄⠀⠀⠠⢀⢀⠀⠀⠀⠀⡐⣆⢀⢢⣎⣾⣇
⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⠁⢰⣦⣤⣤⣉⢀⡁⢀⡁⣀⣀⡠⣀⣀⣀⣁⣈⠀⠉⢉⣈⣀⣉⠠⠃
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⣤⠠⢠⠠⠆⠖⠠⠂⡴⢀⢄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸⠉⠉⠘⠛⠷⢽⡍⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠗⡌⢠⣠⡦⡴⣤⣠⣦⡤⢂⠡⢢⢐⠀⠀⠀⠀⠀⢇⠀⠀⢸⡗⠦⠠⡀⠀⠘⠐⢟⡇
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠬⢥⡿⠟⠀⠀⠀⠀⠸⣿⡷⠖⠁⣀⡐⣀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠙⠖⠳⠞⣾⡟
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣰⡃⢽⡇⠀⠀⠀⠀⠀⠀⠻⣷⣆⠀⠀⠀⢰⡦⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⡼⠀⠀⠀⠀⠀⠀⠀⣰⣦⠥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠈⠉⠑⠻⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠹⢶⣮⢻⣿⠀⠀⠠⣄⣀⡀⠀⠀⣹⣦⡍⡉⣐⡛⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢟⢔⢿⣤⠀⠀⠀⠀⠈⢢⣾⣿⠝⠻⠦⠀⠀⠀⠀⠀⡼⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠌⡾⡆⡿⠀⠀⠀⠀⠀⠀⠀⢺⠂⠁⠀⠀⠀⢀⡠⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣆⡀⠤⠔⠂⠉⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⣀⠀⠀⢀⣀⡌⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠲⣤⡀⠆⢣⣿⠀⠀⠀⠀⠀⠀⣾⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠞⠋⠁⠀⠀⠈⠀⠐⠨⣽⣼⣼⣿⠎⠰⠂⠀⢠⠀⢻⣿⣼⡅⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣣⠞⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡀⠸⢠⢀⠘⣀⣿⡁⠟⡄⡘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢀⠟⢸⡇⡿⠏⡷⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⢂⠀⠠⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⡀⡆⠙⡇⡇⢱⠂⠄
⠀⠀⠀⠀⠀⠀⠈⠀⡀⣿⢸⢸⡀⠀⠀⢰⠀⢀⠀⠀⢠⠀⢳⠂⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⠙⣇⠘⡃⣷⠘⠖
⠀⠀⠀⠀⠀⠀⣃⠐⠳⡜⣰⢸⠀⡇⠀⢻⠀⢨⠄⣶⡞⡀⣿⠀⠠⠀⠀⠃⠁⠂⡀⠀⠀⠀⣰⢃⡗⢃⠸⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠉⠈⠀⠓⡿⠞⡔⣇⢻⢸⣧⠉⣆⣿⠰⣿⡛⠃⠾⠀⠂⠀⡀⢠⣼⣤⡼⠛⠁⠀⢳⠁⠀⠀⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠁⠀⠇⠘⠀⡀⠃⠆⢬⠈⣸⠀⣿⢼⣇⣄⠼⠀⡀⡔⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠀⠁⠁

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠁⠀⣿⠤⡀⡆⠀⠀⠀⠀⢀⣧⢄⠀⡇⣶⡄⢸⡤⠄
⠀⠀⠀⠀⠀⠀⢸⠶⠶⢾⡶⠶⠶⡷⠖⠷⡇⠀⠀⠀⠀⢸⡷⠶⠶⣷⠷⠶⢮⠶⠶⠶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠷⠈⡟⠁⠀⡇⠀⠀⠀⠀⢸⡇⠉⠀⡿⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⡟⠛⠉⡞⡛⠛⢳⣛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⢸⡇⣚⣀⣇⣁⣂⢸⢋⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⡟⣭⠁⣙⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⣶⣶⣤⡶⠒⠃⠀⠀⠀⠀⣯⠭⠤⡭⠭⠤⣥⡤⠤⢼
⠀⢰⡀⠂⢀⣀⣤⣶⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡠⠀⢳⠀⠀⢸⠀⠀⣠⣔⠂⠁⢀⣀⣀
⠀⠖⠛⠋⠉⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡗⠒⠒⡖⠒⠒⣾⠒⠒⢺⠀⠀⠈⠙⠳⠾⠯⠙⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣭⣁⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠘⡇⢀⣀⡃⠀⠀⣻⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣿⣷⡤⠤⠽⣶⣶⠒⠛
⠀⠀⢀⣀⠀⣶⣦⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⢀⣠⡄⠀⠶⡀⣀⣹⠶⣶⡔⠀⠀⠀⠀⠘⣷⣰⣤⣤⠬⣃⠶⣶⠛⠣
⠀⠐⢿⣿⣿⣿⣿⣦⣭⣟⣛⠉⢛⡳⢐⣻⣅⡈⠻⣤⡒⠂⠈⢳⠄⣤⡜⠋⠪⣟⢀⣀⣀⠛⠋⠉⠈
⠀⠀⠀⠈⠛⢿⣯⡉⠽⠿⣿⣿⡵⠖⠉⠀⠛⠂⠀⠙⣿⣾⣝⠃⣀⣙⣆⣴⣶⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠸⡟⠃⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠆⠘⠀⠀⠀⡀⠀⠀⠀⠠⣷
⠀⠀⠀⠀⠀⢀⠈⢁⡓⢄⠐⠊⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠄⣠⠁⠀⣠⣴⢿⣄⢻⣿⡷⠃
⠀⠀⠀⠀⡀⠉⠐⡀⢘⠣⠛⢀⠓⢼⣤⢄⣀⠀⠀⠀⠀⠀⠀⢘⠡⢀⡀⠘⣷⣾⡿⠋⣠⣿⠿⠋
⠀⠀⠀⡈⢡⠀⡆⣀⠨⠀⠀⠈⠓⠘⣷⢀⠈⠁⠀⠀⠀⠀⠀⡬⢙⣶⣿⣦⣿⠏⠀⠀⢀⡜⠀⠁⠾⠶⠀⠐
⠀⠀⠀⠈⠠⡀⠆⠘⠠⠉⡆⠘⠛⠂⣦⠿⡄⠢⣤⡀⠀⠀⢈⠢⢉⣽⣿⣿⡟⠀⠀⠀⠈⠀⠀⠀⢀⠂⡀
⠀⠀⡅⡸⠀⢠⠘⠃⠀⡰⣅⢢⣠⣴⠈⠳⠈⣄⠀⠀⠀⠀⢰⣟⣙⣹⡿⢟⠇⠀⠀⠈⢲⠈⠢⣀⣼⠃⠀⠁
⠀⠀⠀⡆⢰⠀⠀⡀⢀⠰⠈⡀⣁⢉⠒⢿⣷⠀⢁⠀⠀⢠⣟⠙⠿⢿⣿⢻⠀⠀⠀⠀⠘⡄⠀⠫⡉⠳⢤⣤⠛
⠀⡀⠄⠇⠀⠀⠈⠀⣉⠂⠁⠘⠲⡌⢢⣿⢾⡿⠠⠙⠂⢸⣿⣆⣠⡟⣻⣿⠀⠀⠀⠀⠀⠈⠄⠀⠹⣆⠀⠚⠷⠊
⠀⠀⠀⡀⠃⠘⡀⠈⡀⠐⠄⣤⣠⢡⠨⣝⣉⠻⢷⣬⣁⠈⠙⣫⣼⡥⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀
⠀⠋⡁⠀⠐⠄⠣⠄⠘⢀⠠⣤⡈⢟⠰⡥⡌⢳⡆⠉⠛⠛⠟⡿⠿⠾⠿⣿⣅⠓⠂⠐⠂⠀⠉⠲⣄⠀⠐⠉⠉⠒⣀
⠀⢠⢃⢰⡀⠘⠆⠀⢃⡀⠀⡽⣌⢻⡻⢦⣌⡀⠻⣼⣛⠒⠶⠴⣶⢤⣤⣤⣽⡧⠈⠓⠄⠀⠁⢚⡀⠀⠀⠁⠀⠀⠈⠂
⠀⠠⠆⠊⠁⠀⠘⠀⡄⠃⣤⢰⣨⠀⡻⠛⠻⢧⣄⠀⠙⢫⣄⠐⠂⡠⠄⠤⢷⡄⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠱⠄⠀⣠⡀⠀⠀⢀
⠀⠀⢠⠶⢀⠠⡀⠙⢠⡀⡏⠺⠋⠀⡴⢼⣇⠈⠑⢯⡒⢤⡈⠳⠦⠀⢰⣦⡶⠀⠀⠱⠀⠉⠀⢀⡴⡆⠀⠐⠃⠀⢀⠀⠁⠤⠀⣠⠜⠀⠠
⠀⠀⠈⣰⠌⠃⠀⠀⠈⠧⢿⠀⡠⣙⠾⡄⠿⣗⣤⡀⠙⠣⣤⡁⣬⣷⣬⣿⠁⠘⢄⠀⠀⠀⠂⠀⠘⠇⠀⠀⢠⠀⡀⠐⠀⠀⣠⠊⠀⡄
⠀⠀⠀⡅⢀⠀⣠⢰⡄⠀⡈⠛⣌⡳⠇⢈⠃⠘⢿⣟⣷⢢⣄⡙⠻⢟⣿⠱⠀⠀⠀⢡⠀⠀⠀⡀⠴⢦⡀⢀⡄⣨⣡⣄⣠⠎⠀⠀⡔
⠀⠀⠀⣇⢸⡆⡿⡀⢰⣄⠙⣷⣿⢳⠄⠘⠱⣤⡀⠉⠻⢾⣿⣿⢷⡦⢍⡂⡀⠀⠀⠀⠑⠆⠀⠱⢄⡀⠙⣿⢻⠟⠀⠀⠀⣠⠖⠊⠁
⠀⠀⢀⡉⠀⡇⠀⢧⠈⠄⣻⡌⣍⠘⠑⢄⠀⠀⠹⣶⣄⡀⠈⠻⢆⠙⠊⠋⠙⠦⠀⠀⠀⠈⠲⣔⠀⠀⠀⠈⠻⡄⠀⠀⠠⡁⢢⡄
⠀⠀⠈⢣⠄⠱⠃⣌⢇⣸⣷⡍⡈⠓⢄⠀⠀⠀⡀⠀⠘⢿⣷⡖⠤⢁⢀⠀⠀⠀⠀⠀⣠⡾⡡⠈⣻⢖⣶⣄⡠⠈⠂⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⣦⣉⢲⣸⣀⠏⠁⢆⠀⠑⢤⡀⠈⠑⢄⡀⠙⢿⡄⠀⠉⢲⡄⠠⢄⠐⠋⠀⢄⣎⣡⣾⣿⣿⣿⣄⠲
⠀⠀⠀⠀⠀⠀⠛⡘⠛⠃⠉⠀⠣⡀⠑⣄⠀⠙⢶⣄⠀⠻⣷⣄⡙⢶⣄⡄⣀⡀⣠⣤⣀⣦⠳⣿⣿⣿⣿⢿⣌⠻⢷⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠢⠑⡀⠱⡄⠈⠳⣄⠀⠙⣧⡀⠹⣿⣿⣦⡙⢷⣭⡴⠶⠟⠋⢿⠀⠈⠛⢿⡛⢧⡙⢦⡀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⠀⠀⠀⠈⢄⠀⠈⢧⡀⠘⣿⣄⠹⣿⣿⣷⣌⣦⠀⠀⠀⠀⠈⣇⠀⠀⠀⠁⠈⢷⠀⠈⠀⠈⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⡀⢂⠀⢢⡀⠈⢿⣆⠘⣿⢦⡿⠃⠈⢿⣿⡀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠸⣆⠀⣷⡀⠘⣿⢇⠸⣼⣿⡆⠀⠀⢿⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢷⣿⡄⢹⣷⠀⣿⠈⡆⣿⣿⢷⡀⠀⡸⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⢉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣧⣸⣿⡆⣋⠐⣰⣿⣿⣦⡇⠘⠀⠀⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣿⣿⡿⢿⣿⡟⠾⣿⣿⡿⣱⡇⠀⠑⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣠⢟⡿⠁⣹⣿⣟⢸⠏⢿⡆⠻⠀⠀⠀⠀⠉⠢⡈⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣹⢁⡞⡱⣾⣿⠟⢻⠈⠀⠩⠛⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢿⣸⡼⡃⠉⠋⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢙⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠒⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠼⠃

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣲⣞⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡔⠐⠀⡀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠀⢠⡀⠤⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⣄⡔⠁⢁⠠⠔⠻⢧⣰⡾⠀⠀⠀⠀⠀⠀⠀⠆⡀⠈⠀⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢨⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠢⡔⠠⢄
⠀⠀⠀⠠⠹⢷⡀⢁⢀⠀⣀⠄⠩⢥⡀⢠⠄⠀⠀⢀⢰⢮⠀⠀⠀⠂⠐⠢⠀⠀⠀⠀⠀⠀⠀⠄⢀⠘⢥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠆⠃
⠀⠀⠀⠁⠀⢀⣯⣄⢰⡟⠉⠗⠐⡺⠁⠟⠂⠀⠀⠈⣿⠀⠀⠀⠈⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠉⣳⡀
⠀⠀⠀⠀⠀⠙⢿⣧⡦⣙⠉⣋⠶⠆⢶⣺⠂⡄⠀⠀⣙⠂⠀⠀⢰⠢⡔⣼⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡧⠠⠄⠀⠀⠀⢀⠀⠀⠈⢀⣀⢁⠄⢀⣯⠄
⠀⠀⠀⠀⢠⠀⠀⠙⣷⠹⠀⡏⡲⠊⣿⣉⠾⢋⡄⠀⢨⡄⠀⠀⠈⠲⡇⢸⠦⡄⠄⢀⠏⡁⠀⣠⠀⢠⣀⠳⠀⠀⠀⢐⣾⠀⠈⢉⠘⠈⢐⣀⢈⠉⠓⠄
⠀⠀⠀⠀⢂⠀⠀⠀⠈⠑⠠⠆⠰⠢⠿⠗⠊⠌⠀⠀⠀⠙⢄⠀⢲⠃⢸⡟⢺⠁⣴⢯⡀⠂⡠⠀⠀⠘⢫⢧⡤⠐⡄⠨⣯⠀⠀⠀⢀⠀⢸⣷⠗⠋
⠀⠀⠀⠀⠀⠑⠠⡀⢀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠱⠄⣧⣸⢇⡆⡜⢀⢿⠶⠂⠀⠀⠀⠀⠀⠛⠰⠦⣤⣛⣻⠀⡐⡂⢊⠤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⢀⠀⡖⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⢰⣷⢙⡇⠿⠻⢑⡩⠄⢛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⡁⢀⠀⡀⠀⠀⠑⠦⠀⠀⠀⠀⠀⠀⠀⢀⠄⠲⠂⠂⠀⠀⠀⠁⠂⢄
⠀⠀⠀⢀⣸⡔⠁⠁⢀⠔⠊⠀⣴⢿⡿⡆⠀⠀⠀⠀⠀⠴⠄⠀⡃⣺⣾⣁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⣧⢠
⠀⠀⣠⣌⡝⠀⠀⢰⣾⣤⡸⢒⡆⢩⣥⣦⠀⠀⠀⠀⠈⠀⠀⠀⣸⡿⢿⣿⣷⡠⣴⠤⠀⠀⠀⠀⠀⣠⡈⣀⠀⠠⠄⠀⠳⡄⠀⠀⠀⠀⡆⠀⠈⢸⡄
⠀⠀⠻⢻⡇⠀⠀⠻⠏⢛⢠⣾⡿⣏⡿⢻⠀⣤⠀⠀⠀⠀⢁⢠⣇⣻⡦⡨⡈⠃⣸⣿⣦⡀⠀⠀⠀⣿⡄⠀⠬⡥⠈⠃⠀⢿⣄⠔⡀⠘⢥⠀⠀⣿⡇
⠀⠀⠀⣼⡟⠀⠀⠀⢄⠳⡉⠉⣧⠞⣶⣆⠺⠁⠄⠀⠀⠉⠜⣯⢧⠀⠐⣿⣿⢄⣙⣋⠍⣄⣂⠀⠀⢹⡆⢾⠃⠁⠀⠄⠀⠁⣯⠄⠾⡂⠀⠰⣄⡞
⠀⠀⠉⠟⠙⡄⠀⠀⠈⠳⢧⣰⡇⣰⢩⣇⣤⢠⠆⠀⠐⡄⠀⠒⠛⠢⡀⠀⣡⣜⣿⠋⢼⣿⠏⠀⠀⠀⠑⡈⠂⠀⣠⣈⠙⡧⣼⣤⡸⠷⡏⠃⣋⣈⠆
⠀⠀⠀⠀⠈⠈⠢⢄⠀⠠⣀⠈⠉⠉⠉⢋⠔⠁⠀⠀⠀⠈⠢⡀⢀⠀⠈⠙⠒⠧⠾⠤⠆⠟⠀⠀⠀⠀⠂⢤⢫⡐⢸⠋⠀⠅⠉⠁⢀⢀⡧⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠂⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠤⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠳⠶⠦⠴⠑⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣅⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡈⢖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡆⢍⣦⣄⡀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠸⣧⣄⠱⢄⠀⠀⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣈⡿⢠⣤⣵⣤⣾⡿⠾⠶⠄⠂⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠖⠶⠶⠶⣤⣸⣿⡶⠶⠒⠖⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣠⡾⠋⣰⢻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⢀⣒⣾⣿⣿⠿⠛⠁
⠀⠉⢀⣀⡀⠀⠀⠀⣀⠀⣸⣷⣶⣿⠷⠁⠈⠐⡋⠵⣌⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠴⠐⠒⠭⠿⠋⠁
⠀⣿⣿⣿⣿⣶⣆⡞⠁⠰⣿⣿⡇⠻⠀⠟⠀⠀⠁⠀⠈
⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣶⣶⣶⣶⣤⣀
⠀⣿⣿⢩⣍⠻⣿⣿⣿⣦⡄⠀⠀⢴⣶⣶⣤⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣦⡀⢀⣀⠀⠀⠀⣠⣴⣲⣶⣶⣾⣧⣿⣿⣿⣿⣿⣿⣿⣻⠽⣯⣍⠻
⠀⣿⣿⣶⣿⢿⡿⡿⣿⣿⠿⣧⣄⢀⠉⠛⠋⠁⠘⣿⣿⣷⣶⣶⡶⠖⠐⠋⣼⣿⣿⣿⣟⡘⢛⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⡻⠛⣟⣹⠟⠋⣠⣽
⠀⠉⠋⠛⠋⠋⠁⠙⠛⠛⠓⠉⠻⠿⠿⠿⠿⠿⠷⠶⠿⠭⠭⠀⠐⠚⠛⠛⠛⠉⠉⠀⠴⠞⠻⠿⠿⠟⠛⠛⠏⠽⠾⠟⠟⠿⠛⠀⠀⠀⠀⠁⠀⠀⠸⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠉⠉⠉⠉⠉⠙⠓⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⠁⣤⣀⠄⠐⠰⠆⠀⠰⢶⣾⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠶⠾⠃⠚⠠⠆⢰⡀⠁⠀⢀⡀⠘⠟⠲⠖⣤⣶⣯⡙⠢
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡔⠀⠈⠁⠀⠀⣠⠄⠴⠀⠀⠀⠋⠃⠀⠀⠿⠰⣦⠀⠙⠻⢿⠟⠀⠀⠀⠙⠉⢁⢀⣴⣤
⠀⠀⠀⠀⠀⠂⠁⡠⠎⠀⠀⠀⠀⢠⡖⠁⡠⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⠃⠘⠿⣿⠟⠻⣦⣄
⠀⣠⠆⡤⠀⣤⡀⣤⠀⠀⠀⣠⠞⠃⢀⠀⢠⠆⠀⠀⠀⢰⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣳⡆⠰⢿⣿⠛⡉⠒⢦⣄⡀
⡀⢡⠺⠇⠒⢻⣷⠹⠏⠑⠋⠧⠤⢶⣬⣾⡿⠦⣤⣴⣶⣿⣷⣤⡀⢠⣇⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⢀⠀⠉⡁⠀⠀⡀⠀⡀⢀⠀⠈⠛⠲⢤⣀
⡄⠠⠀⠐⠀⠤⠈⠓⣤⣰⠾⢶⣆⠉⠻⠛⠁⢠⡾⣿⠶⠟⠉⠉⠟⢛⡛⢿⠷⠾⣰⣦⣴⣶⣀⣀⣀⣈⡀⠀⢰⠀⠀⠹⡆⢧⡘⣧⡐⣤⣶⣦⡝⣷⣄⡀
⠠⠄⠀⠀⠀⠀⠀⠀⠝⠧⠀⠀⠉⠀⢠⡤⢀⡀⠀⠁⠀⠘⠛⣠⡶⠙⢛⣗⠋⢠⡽⣿⣿⣼⣿⣿⣏⣻⣿⣶⣾⣶⣤⣾⣷⣤⣇⣈⣷⠙⠻⢯⡻⢾⣿⣿⣦⡀
⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠚⠛⠋⠙⠁⠀⠈⠛⠀⠚⣿⣿⡋⢰⡜⢿⢻⣿⠿⠟⢿⢿⣿⠿⠝⣻⣿⡉⠻⠟⢻⣶⣼⣦⣿⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠋⠘⠃⠀⠃⠙⠃⠀⠈⠉⠉⠟⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⠻⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣿⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠓⠁⠞⠀⠀⡉⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢴⡾⣧⡜⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⠀⠈⠳⣘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣠⣤⣤⣤⣜⣉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠉⠁⢉⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣤⣿⣿⡏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿