Swing music Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣼⣿⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣹⣿⡇⠇
⠀⠀⠀⠀⠿⣿⠇⡀⠀⠀⠀⠀⢀⣀⣤⡊⠉⡅⢹⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠞⠟⣛⡽⠂
⠀⠀⠀⠀⠀⢴⣾⣷⣄⠀⣀⣴⣿⣿⣿⣧⡀⢱⡀⣿⣿⣿⣿⣦⡀⠀⠀⠀⣴⣿⡶⠲⢶⣤⣤⣀⡐⠁⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣬⣧⣿⣿⡈⢿⣿⣿⣶⣿⡅⠛⠛⠁⠀⠀⠈⠙⠛⢿⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠙⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣽⣥⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠺⠁⠀⠌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠉⠙⢿⣿⣿⣿⣄⠀⠀⠀⠀⢸⡀⠐⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠉⢻⣿⣿⣦⡀⠀⠀⠀⠑⢠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣦⣀⣀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣍⡤⠴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣭⣦⣄⣀⣈⢿⣿⣿⠟
⠀⠀⠀⠀⠀⢴⣶⣾⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⣸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⣿⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⡻⠷⠀⣿⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠰⠊⣴⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠃⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠗⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠋⠬⡆⣹⢦⣀⡲⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠀⠐⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⠉⠈⠆⠀⣉⠢⠀⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣿⡀⠀⠘⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠠⠀⠀⠀⠁⠁
⠀⣀⣴⣾⣿⣿⣿⣿⣿⣧⣿⡇⠀⢐⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⣾⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡇⠀⢐⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⡇⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠠⠔⠋⠁
⢸⣿⣇⠀⠈⠻⣿⡿⢻⢿⡟⠀⠀⠀⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⡁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠑⠂
⠀⠈⠙⠃⣄⣶⣪⣾⣿⣿⠁⠀⠀⠀⠛⣧⡀⠈⠛⠛⠋⠛⠛⠛⠈⠐⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⢀⣠⣝⣿⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣑⣓⡐⣀⠬⣀⣀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠻⠿⣿⠿⣿⣿⣿⡟⠛⢿⣻⣿⠭⢽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⡇⠀⠀⠸⢿⣧⠤⠤⣜⣯⣭⡾⠁⢀⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠉⠉⢻⠿⣷⣿⣿⡷⢄⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠘⡆⠈⠙⢿⣿⣿⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣷⠀⠀⢃⠀⠀⠀⠈⣻⠿⢟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⡿⠟⡿⡛⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠆⡀⠈⠀⠀⠀⢠⣷⡿⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠁⣔⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠮⣿⠒⢶⠖⠀⠀⠀⡞⣠⡴⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⣈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣵⣿⣿⣿⠋⠀⠀⠀⣸⠋⣩⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢒⣛⣿⣿⠛⠁⠀⠀⠀⠐⠁⠺⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠧
⠀⠀⠀⠀⠀⣰⠇⢺⣽⣾⠋⠁⠀⠀⠀⠀⢀⢴⡙⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⢾⣵⡿⠂⠀⠈⠀⠀⠀⠀⠀⠀⠘⠻⢿⣇⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠾⠄
⣀⣀⣐⣢⣾⣉⣛⣛⣉⣉⣉⣉⣙⣛⣉⣛⣛⣋⣉⣙⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣢⣤⣤⣟⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀
⠀⣠⣤⡀⠀⠀⠀⣄⠀⠀⠀⠀⠠⠔⣒⢂⠀⠐⠀⠀⠀⠀⠀⣀⠀⣀⡀⠙⡄⠀⠁⠙⠀⣀⡀
⠀⣿⣁⢰⡔⠖⣺⡧⠄⠀⠀⠀⢰⡟⣉⠐⠳⣀⡖⣰⡄⣤⡆⠙⠇⣀⣹⣀⣌⡶⠛⢿⣾⠰⢿⡷
⢠⣿⣿⣿⣿⣿⣿⡗⠳⠀⠀⢀⣼⣿⡏⣿⣟⣿⢳⣾⣿⣋⣠⠾⣿⣟⠻⠽⣿⣾⣯⣯⢩⣋⣿⣿⡍
⠈⠻⣿⣿⣿⣿⣿⣧⡘⠀⡶⢺⡏⣿⣿⣿⣿⣥⣿⣷⣠⣁⠿⢄⣠⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⡿⠁
⠀⠀⠈⢻⣿⣿⣿⣿⣷⣦⢰⣾⢏⣋⢻⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡿⣿⢻⣿⣿⣧⣿⣿⣿⠃
⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⣾⣷⣇⣙⣷⣿⣿⣿⣽⣻⣿⣯⠇⠈⣿⣭⣤⣼⡌⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⡇⣀⣽⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣦⢠⣿⣿⣿⢿⣿⣿⡿⠛⠹⣿⣿⡆
⠀⠀⠀⣸⣿⣿⣿⣿⡟⢹⣿⣟⠒⢺⣿⣿⣿⣿⣿⣿⠓⣿⣿⠛⣽⣿⡗⣾⣿⣿⠀⠀⠀⠹⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠹⣿⡀⢸⣿⠻⠎⠉⠏⣿⡆⣿⡇⠀⠉⣿⡇⣿⣿⡇⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⢸⡿⠿⢸⣿⣿⠀⠀⠀⠿⠛⠺⠛⠀⠀⠀⠂⠻⠇⠿⠃⠀⠀⠋⠁⣼⠻⠇⠀⠀⠀⠀⠀⠀⠛⠿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢞⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⠲⣦⣀⠀⠀⠀⢹⡆⠀⠀⠀⠘⠀⢠⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠂⠀⠈⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠸⠟⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⣀⣀
⠀⠀⠀⠀⠀⠀⢩⣟⣛⠁⢀⣴⣄⢠⣶⡶⠒⣴⣦⣄⠐⠒⢠⠀⠀⠀⣾⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⣠⣾⡿⠆⢨⣯⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⣿⣿⣷⣾⣿⣦⣼⣿⣿⣿⠂⠀⠈⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⢷⣶⣾⣿⠏⠀⠚⠟⡻⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠉⠘⢧⢹⣿⣿⣿⣿⣿⢀⡁⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⡦⠄⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠼⣿⠀⠀⠀⠀⠈⢨⣿⣿⠀⣮⣴⣾⠁⠀⣺⣿⣿⡟⠁⢶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⣿⣯⣉⣿⣿⣧⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⢀⣤⣀⡀⣿⣛⣿⣶⣿⠻⣿⡇⠀⢿⣿⡇⠈⠀⠾⠛⠀⠀⠀⠀⠀⢀⣾⣿⠛⠳⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⣿⣿⣿⣿⣿⣄⣤⣤⡶⠟⠋⠉⡀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣶⣿⡿⠿⢏⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠀⣸⣿⣏⣿⣿⠿⠛⠛⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⣿⠋⠀⠀⠀⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣄⡀⢂⢀⢹⣧⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣷⠐⠄⢨⣿⣿⣯⣬⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⢶⣚⠃⠀⠀⠀⠀⠚⠃⢹⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠛⠛⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠃⣀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡈⠙⢀⣤⢻⣆⡠⢄⡀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡆⢰⡶⠶⠋⠐⠋⠀⠀⠀⠀⠀⡀⠈⠀⣾⣇⣿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⣼⡆⠘⣿⣿⣿⠛⠀⣸⣿⣿⢰⠇⠀⠈⠁⠂⠀⠶⠚⠋⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢶⣶⣷⣿⠆⢹⣿⣿⡀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⡤⠶⠾⠁⣿⣿⡇⠀⠸⠟⢋⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢸⣿⠟⠡⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡈⢀⣴⡀⠀⠀⢿⣿⣿⠀⠀⠀⣴⣿⣄⠀⠀⠀⠐⠀⠆⠀⠀⠁⢠⠀⠀⠁⠁⢀⠀⠀⠀⣿⣿⣿⠀⠀⡺⠁⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢿⡇⠀⠀⣸⣿⡿⠀⢀⣴⡿⠋⠻⣷⣄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⠀⠀⣿⡄⢠⣄⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⡇⠀⣼⣿⡏⠀⠀⠺⠏⠀⠀⠀⠈⠙⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⣿⠁⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⠇⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠳⡄⠀⠀⠀⠐⣣⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠜⠐⠉⠂⠀⠿⠈⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡶⣦⣀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠉⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠷⠀⠀⠠
⠀⠀⠀⠀⠠⣦⣤⡤⢤⡴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠛⠁⠀⠰⡴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠁⡶⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣤⣤⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠻⣿⣦⡀⠀⣀⣠⣤⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠈⠻⠿⠟⠛⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣏⣉⠛⠷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⢠⣶⣶⣶⣯⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣾⣿⣿⣿⠗⠀⣸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣴⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⣿⣁⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⢿⣿⡿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣜⢿⣿⣿⣯⡻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣩⣦⣴⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠏⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⠛⠁⠈⠉⠉⠉⠁⠈⠉⠉⠉⠉⠻⣿⣿⣿⡽⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⢀⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠠⣿⣿⣿⣭⡀⠀⢹⣿⣿⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠉⠛⣿⣿⣿⣿⡄
⠀⠀⠀⠈⠙⠿⣿⣿⣄⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾⣽⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠀⠀⣠⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠃⠀⠀⢸⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠐⣶⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⣦⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠅⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠰⠛⠂⠀⠀⠀⠀⠒⠃⠀⠀⠀⡀⠀⠀⠀⢠⠤⠒⠆
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⡁⠀⠀⠀⡒⢦⡀⠀⠀⠀⢐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢨
⠀⠐⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠘⠁⠀⠀⠀⠸⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢶⡾
⠀⢀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⣠⡿⠟⠛⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠰⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⢀⣼⣧⠀⠀⠂⠀⠂
⠀⠀⠀⢸⡟⠻⢷⣦⣄⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣴⣾⣿⣿⣿⣇⡀⠤⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⡇⠀⠀⠈⠛⠃⠀⠀⠀⠀⣀⠀⠀⠰⣂⠀⣤⠀⠀⠀⠀⢈⣁⠠⠄⠂⠉⢉⡀⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠶⢾⡿⢻⠇
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⡄⠼⠄⠹⠁⠉⠀⠀⠀⠀⠀⡤⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡞
⠀⠀⠘⠁⠀⠀⢀⣠⣴⠀⠀⠀⠀⠀⠈⠀⠀⠀⢴⠲⠀⠀⠀⠀⠀⠀⣦⣤⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠘⣶⣶⣶⠾⠛⡟⠉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠈⠘⠀⠀⣈⠀⣹⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠹⠏⠀⢠⡐⠿⣙⠿⠿⠂⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⢀⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠀⢀⡀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡴⠋⠁⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠋⠦⠔⠃⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⣴⣶⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣈⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡦⠼⢿⣦⠀⠀⢀⣠⣶⣿⣟⠐⣶⣄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠉⣿⣾⣶⣿⣿⠟⠉⣭⣴⣶⣤⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣅⡀⠔⠽⢫⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠉⠛⣦⣦⣀⡀⠀⢸⣿⣇⡙⣿⣿⡿⠋⣩⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣴⣮⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠹⠿⣿⠿⠿⢿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⣤⡤⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣼⠿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣀⠀⠀⠀⢀⡀⠀⠀⠀⣤⠀⢀⣤
⠀⠀⠀⠀⣀⣀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠬⢋⠷⠦⠄⠀⢸⠆⠀⠀⠁⠰⣿⠿⠂
⠀⠀⠀⣾⢃⣼⠃⠀⣀⠀⣰⠾⠳⣆⢀⣾⡟⢿⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⢘⣿⡟⢀⣤⣀⣤⠶⣠⣤⡀⠦⢄⠀⠀⣰⣦
⠀⠀⠀⠘⠋⣿⠀⠀⡉⠀⡏⠀⠀⣿⣸⡏⠀⣾⠀⠀⡞⢉⠆⣰⠏⣿⢻⡇⠀⠀⠀⠀⠀⠀⠛⠀⠺⣿⣿⣿⣶⣿⣿⣏⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⢷⣀⡼⠃⢿⣅⣼⠃⠀⣼⠋⠁⠀⠃⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠙⢼⣿⡟⣻⣣⡖⠂⣿⣿⣷⢄⣀
⠀⠀⠀⠀⠈⠁⢀⣴⢶⡆⠀⠉⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁⠀⠀⠀⠀⠛⠡⣤⣄⡀⣾⣿⣷⣿⢿⡷⠀⣿⣿⠉⠢⠿⠂
⠀⠀⠠⠄⠀⠀⣿⠃⠈⠃⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣴⠆⠀⠀⠀⠀⢰⠁⢀⠴⣶⠀⠀⠀⠀⢠⣿⡇⢀⣿⣿⣿⣿⣴⣶⡾⠋⣉⠤⠙⢄
⠀⠀⠒⠀⠀⠀⠹⣦⠀⠀⠀⣦⠀⢠⣶⣾⠁⠀⠀⣼⠏⠀⠀⠀⢠⠀⠈⢧⣤⡾⠃⠀⠀⣀⡀⠠⠙⣧⣸⣿⣿⣿⠉⠀⠀⠀⠈⠉⠠⣠⣉⡀
⠀⠀⠀⠀⠀⣄⠀⠈⣧⠀⠀⠙⣧⣿⠉⠛⠀⠀⠀⠁⠀⢀⣤⣦⣸⣇⠀⠀⠈⠀⠀⠀⠀⠚⣿⡬⠜⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠘⠳⠎⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡷⠀⠀⠀⠀⠀⢠⣾⣶⣄⡀
⠀⠀⠀⠀⠀⡀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⢠⡾⣻⣯⣿⣷⣆⡀⢀⣀⣀⣀⣀⣹⣿⣿⠳⠤⠄
⠀⠀⠀⠀⠀⠈⠢⠤⠿⢿⣿⡶⠤⣄⣀⣀⣤⠴⠿⢋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠴⠋⢿⣿⣟⠉⠀⠉⠉⠉⠉⠀⠈⠉⠁⢀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠛⣿⡦⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢻⣧⠀⠀⠀⠀⠀⠀⠀⢀⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠀⠀⠀⠀⠀⠙⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠅⠀⠀⠻⠃⠀⠀⠀⠀⠐⠶⠋⠀⢼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⣿⠗⠀⠀⠀⠂⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠠⠤⠀⠀⢹⣦⣾⣆⡐⣶⣽⣍⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢁⣤⠿⠟⠀⠀⠀⠀⠀⣠⠶⣿⣿⣿⡄⠀⠀⠀⠘⢦⣤⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣴⣿⡟⣯⡤⠤⠄⠀⠀⠀⢘⣷⠀⠀⠸⣯⣴⠟⠀⠀⠀⠐⠂⠀⢠⣿⣿⠋⠙⠒⠀⠴⠆⠤⣤⣿⣧
⠀⠀⠀⠀⠀⠹⠶⠟⠋⣹⡿⠁⣿⣿⣷⣦⠀⠀⠀⠀⠀⠐⣢⣿⣶⢰⣦⠸⣧⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠈⠙⠞⠀⠀⢠⠜⠋⠤⣶⣿⣿⡷⠀⠈⠳⣄⠀⠀⠀⠀⢀⣼⢿⣧⡀⠀⠀⠀⠀⣸⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⠿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠙⢧⠀⠀⠀⡞⠉⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠈⣿⣄⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡜⣏⠀⠀⠀⠀⠀⠀⠸⣿⣃⡰⠂
⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠻⠶⠶⠤⡤⢤⣤⡤⠖⢾⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⢃⡿⣦⣤⠶⠂⢄⡴⢿⣿⡏
⠀⠀⠀⠀⠀⣾⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⣿⡌⠁⠀⠀⠀⠀⠀⢐⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢳⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⢠⡟⠁⠀⠀⠀⠀⠀⣰⠟⢻⣄
⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⠀⠿⠄⠀⠀⠀⠀⠀⠞⠁⠀⠀⢹⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠰⠄⠀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢿⣿⡗⢲⣤⡀⢀⣛⠒⡟⠋⣴⣶⣤⡖⠒⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠈⣴⠧⡀⠙⠷⣌⢹⡷⢧⣰⠿⢿⣟⠚⠁⠑⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣇⠑⠚⠁⠀⠀⠈⠉⠀⠀⣵⠄⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⠁⠀⠀⠀⠀⠀⣠⣶⣦⣶⡀⠈⠋⠀⠂⠀⠀⠀⢀⠔⠋⢻⣧⠴⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠲⠏⠈⡇⠀⠀⠀⠀⠐⡿⠋⢸⣿⣧⣄⡀⠀⠶⣄⠀⠈⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤⣄⣿⡆⠐⠿⢦⣄⣀⣿⠀⠀⠀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠘⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⠉⣿⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣿⣦⡘⢦⣀⠀⠠⠚⠁⢿⣿⣿⣿⣿⢿⣿⣿⡏⠁⠀⣀⠀⠀⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⣼⣿⣿⡓⢌⣧⡀⣠⡀⠈⣿⣿⣿⣿⣿⣿⣿⡌⢧⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠋⠀⢉⡙⣿⣧⣬⣿⣷⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠒⠁⠒⣺⣿⣿⣿⣿⣿⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠛⡟⠃⢉⠹⣧⠺⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⢷⡈⠣⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡿⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣷⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣾⣆⡀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣏⣡⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠿⢻⣿⣿⣿⣿⣿⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣻⣿⠿⣿⣿⣿⣿⣶⣶⣷⣶⠶⠾⠛⠛⠉⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⣀⣶⣶⣤⣄⡀⣀⣤⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠒⠀⠀⠀⠉⢁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⠟⠷⣤
⠀⠀⠀⣈⡴⠀⠀⠀⠀⣤⣀⣀⡀⢀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢔⡗⠁⠀⠀⢸⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃
⢀⡴⢚⣋⣤⣴⣶⣾⣯⣵⣶⣟⠊⠐⠁⠀⠁⢂⠑⠁⠀⡀⠀⠁⠀⠰⠂⠀⠘⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⠋⠀⠒⠠⢀⠀⠀⠀⠀⠀⢀⡼
⢸⠰⠋⢻⠟⠋⠉⠀⠦⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠈⠀⡈⠀⠠⠈⠀⠀⠀⠀⢻⣇⠄⣸⣿⡿⣿⣿⡟⣁⣤⣄⡐⠠⣀⠑⢤
⣠⡁⡚⠉⠀⠀⢀⡄⠀⠄⠀⠌⠠⢐⠄⠀⠀⠀⢄⠂⠀⠌⠀⡱⡀⠀⠀⠀⢀⢸⣿⣾⣿⠋⠂⠉⠁⢸⣿⠆⠈⣻⢄⠀⠁⡀⠑⡄
⠉⠒⠁⠀⠠⠀⠀⠀⠄⠠⢀⡀⠄⠀⠀⠀⠀⠀⠈⠀⡀⠎⠀⢅⠀⠀⡀⠀⢠⣾⣿⡿⢁⣿⠄⠂⠀⠀⠂⠄⣠⡟⢠⠣⠀⠘⡀⠘⡄
⣶⣶⡆⠄⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠾⠠⠈⢄⠀⠀⠀⠢⣰⡿⠟⠉⣲⣾⡏⠀⢀⣀⣤⡴⠾⠋⢶⠀⠀⡄⠀⢀
⢸⡿⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⠓⢄⠉⠂⢀⣾⡏⣠⢴⡁⠈⠟⠃⠀⠀⠐⠲⣶⡄⠀⡀⠄⠀⢰
⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣁⡕⠠⢈⡀⠉⣋⣱⠃⣒⠁⠀⠀⢀⡀⠀⠀⠀⠀⠱⡈⠻⢢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠲⢦⣍⡛⠶⢤⣀⠀⠵⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⡀⠄⠀⠀⠀⠐⠢⢀⣠⢠⣄⣸⠁
⠀⠀⠀⢀⣴⣿⢢⡄⢺⣷⣽⡾⠀⢰⣶⡆⣤⠀⠐⠠⡀⢠⣤⠼⣷⣿⠉⠁⠀⠀⠀⠀⢀⣤⣴⣤⡸⣿⣾⠁⡟
⠀⠀⠀⠘⠿⠟⣋⢥⡴⢹⣿⣇⠀⠻⠿⢃⠑⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠈⠀⠀⠀⠀⠀⣽⣿⠏⠀⣿⣿⢓⠂⠄
⠀⠀⠀⢰⣆⢁⣴⡀⠀⠸⣿⣿⠀⠀⢀⣼⣦⡀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡏⠀⠰
⠀⠀⠀⣿⡇⠀⢻⡇⠀⢠⣿⡿⠀⢠⣾⠟⠙⠿⣦⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⣿⣿⠀⢸⣷⠠⢦⡤⠴
⠀⠀⠀⢘⡇⠀⢸⡇⠀⣿⠿⠀⠀⠙⠁⠀⠀⠀⠉⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠏⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⡿
⠁⠀⠀⠀⠀⠀⢀⣠⣿⣾⣿⠟⠁
⢀⡀⠀⠀⣠⣶⣿⡿⢿⠋⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⢠⣿⡿⠛⠁⢀⣼⣄⣀⠀⠀⠀⠀⠀⢈⣋⡗⠠⢀⡀⠀⠀⠀⠀⣰⠻⡄
⠠⠄⣿⡏⠀⢠⣾⡿⢿⡿⢿⣿⣶⠀⠤⢀⣛⡙⠁⠀⠀⠀⠀⠀⠠⣠⡟⢧⡙
⠀⠀⢻⡀⠀⢹⡏⠀⠸⣇⡀⠘⣿⡇⠀⡛⡛⠉⠀⠠⠄⡀⠀⠀⢀⠊⠻⣘⠧⢀
⠒⠠⠌⢳⣄⡀⠙⠂⠀⡇⠀⢠⡿⠓⠠⠀⣀⣤⣥⡅⠀⣠⣬⣄⠮⠀⠀⠉⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠈⠉⠓⠒⠶⣿⠚⠉⠀⠀⠀⠀⣠⣭⡟⠂⠘⣿⠿⠛⠀⠀⠈⠑⠠⢀⠀⠀⠀⠈⠐⠀⠀⠘⢻⡄
⠐⠂⠤⣤⣤⣤⡀⠀⠀⣿⠀⠀⠁⠐⠠⢀⣍⡉⠀⠀⠀⠀⠈⠐⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⢀⠇
⠀⠀⢸⣿⣿⣿⠟⠐⠠⣾⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠉⠙⠛⠿⢶⣦⣤⠀⠠⣾⣿⡶⠀⠀⠈
⠀⠀⠀⠙⠷⢤⣤⣤⠾⠃⠀⠀⠀⠂⠤⢀⠀⠀⠀⠀⠀⠀⠘⠃⠤⠀⠀⠀⠀⠀⠉⠀⠄⠈⠉⠀⠀⠂⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢴⣶⣦⠀⠀⠀⠀⠈⣐⠠⣄⠀⠀⠀⠀⢱⣤⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠂⠄⢀⠻⠿⠟⠀⠈⠒⠄⡀⠀⠉⠉⠀⣰⠦⠚⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⢤⣄⠀⠀⡀⠀⠀⠀⠈⠉⠓⠄⣀⡀⠀⠈⠉⢑⠂⡀⠀⠀⠀⠀⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠆⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⠀⠼⣃⠠⠤⠌⠀⣄⠁⠀⠰⠃
⠀⠀⠀⠀⠓⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⢄⠠⠄⠂⠆
⠀⠀⠀⠀⠐⠀⠀⢀⡘⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠐⠂⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠀⠠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠄⠀⠀⠠⠤⠐⠃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠠⢠⠀⠐⠀⢀⡀⠀⠛⠀⠀⠀⠀⠀⠂⠀⢤
⠀⠀⢸⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⡤⠀⣀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⣾⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢁⠀⠚⠈⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠
⠀⠀⣼⠙⠚⢶⢀⢀⠀⠀⠀⠤⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡤⠀⠠
⠀⠀⠘⠀⠀⠎⠀⠈⠄⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠆⡉⠀⠀⢀⠤⡂
⠀⠀⠀⠰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠁⠁⡀⠄⠚⠀⠀⠛⠀⡀⡄⠀⠉⠀⠚⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⠀⠀⣀⡘⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠒⡀⠀⠀⠀⠀⠀⣤⡄⠀⠀⡄⠀⠀⢆⠀⣀

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠶⠶⠶⠖⠶⠶⠚⠛⠛⠉⠻⣿⣿⣿⣦⠀⠀⠀⠀⢰⠏⣿⣿⡿⠉⠛⠓⠒⠲⠶⠲⠶⠶⠶⠛⢻⣿⣿⣟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠓⠀⠀⠀⢸⡀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣆⠀⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠻⣷⡄⠀⠀⠀⠀⠀⠀⠘⢿⡋⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⠄⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣤⣤⣤⣤⣄⣠⣤⣀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠻⣧⣤⡄⠀⠀⠰⠚⠋⣿⣿⡏⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠉⠉⠉⠉⠉⠛⠛⠛⠛⠋⠉⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣿⣿⡇⢰⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢿⡇⠘⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢸⡇⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢱⡇⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⠧⠀⠘⠛⠒⠀⠀⠀⠀⠀⠀⠀⠈⣽⢿⡇⠀⣾⠧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠀⠘⠓⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⢀⡾⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⡀⠀⣠⣦⡀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⢀
⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣯⣤⡶⠏⠀⠀⠀⠀⠀⠘⠋⠛⠙⠛⠛⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣸⣿⣷⣦⣤⡶⠋
⠀⠀⠀⠉⠉⠉⢸⣿⣿⣿⠋⠻⣷⣤⠴⠶⠒⠲⠶⠞⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢿⣧⡀⠀⠀⢀⣀⣴⠟⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢺⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠉⠛⠛⠋⠉⠉⠀⠀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⠛⠟
⠀⠀⠀⠀⠀⠺⣿⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⢸⣿⣅⡀⠀⠀⠀⠀⠀⠀⣼⡟⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣀⣀⣀⠀⢀⣤⣴⡶⣄⡀⠀⢀⣀⠤⢄⣠⠴⣆⡀⠀⠀⠀⠠⣄⣄⠠⣀⡀
⠀⠀⠀⢠⢶⣴⣳⠂⢄⢲⡿⣍⣙⣆⠐⡿⠗⠿⠺⠚⣾⠋⡐⠊⢜⡐⣈⢘⠻⣷⡌⢯⢳⡄
⠀⠀⠀⠈⣾⠋⣿⢠⢸⡎⠙⣼⣿⠛⠳⠘⠯⠄⡠⢞⡨⠋⠀⠀⡸⠂⢁⣹⠀⠈⢿⣬⡳⡯⠀⢀⠤
⠀⠀⠀⠸⠃⢀⣿⢾⣸⡁⠀⢸⡁⢈⣸⠀⢀⠞⢢⠄⠀⢀⠉⠩⡧⠛⠒⣻⠿⢲⣄⠉⠀⠀⠀⠐⠒⠊⣀⠀⠈⣆
⠀⠀⠀⠀⠀⢸⡿⣈⠿⠤⠒⡉⣯⣤⡏⠀⠏⡾⠁⠀⣨⣯⣵⡓⠒⣀⠐⢋⠸⣦⢱⣎⣱⡶⠀⠀⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⠞⠉⠆⠀⢸⠓⡟⢹⠕⡌⢿⠂⠀⢸⣿⢏⡉⡙⠐⢯⠈⡟⠀⡾⣞⣘⡿⡗⠃⠀⠉⠑⠀⠀⠀⣿⠆
⠀⠀⠀⠀⢠⠏⠀⠀⡴⠀⠀⢧⡇⣸⡔⢀⠸⠀⣀⣠⣁⠀⣙⠗⠢⠌⠀⢇⠸⠀⠀⠻⣤⣸⠀⠀⠀⠀⣠⣾⢱⣿
⠀⠀⠀⠀⡼⠀⣠⡞⠓⠶⠶⠞⠋⠉⠉⡴⢨⢩⣼⢘⠷⢷⠞⣧⡀⠀⠀⠘⣆⠀⢠⠀⠤⠀⠀⢀⣴⢒⣿⠇⣾⠏
⠀⠀⠀⡾⠱⡀⠀⠑⢄⣀⣀⣀⣀⣀⠞⠀⠀⠀⡄⢸⠀⢈⢎⠆⡇⠀⠀⣾⣿⡇⠀⠁⢀⣶⣆⣿⡏⣼⣿⡼⠋
⠀⠀⠀⣇⠰⠿⠦⣀⣾⠋⢉⣻⠋⣿⠀⢠⣇⠀⠱⢘⡶⢣⠋⠀⠇⠀⠀⠙⡋⢠⣾⡷⣿⣿⣹⠿⢻⣿⠏
⠀⠀⠀⠘⣄⠀⣀⣈⣀⣈⡩⠑⠂⢗⠐⠛⡼⠆⣠⠟⣠⣦⡗⠂⣸⣀⢰⣿⠃⣾⡿⠁⠻⠛⠁⢀⣾⡿
⠀⠀⠀⢀⣼⡿⢿⣛⠉⠉⠙⣆⠀⠀⢧⣠⡇⡰⠋⠐⢛⣭⢠⣾⢣⢿⣿⡿⠚⡛⠁⠀⠀⢀⣴⢿⡿⠁
⠀⠀⠀⠚⠁⢀⣿⡏⠀⠀⢠⣿⡆⠀⢀⣸⡄⢠⣾⠗⣽⣟⡸⣿⡤⠊⠉⠀⠀⠀⠀⠀⢀⡿⢡⡿⠁
⠀⠀⠀⠀⠀⣼⡿⠀⠀⣠⣿⡟⣴⡾⢹⣿⢡⣾⡏⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠋
⠀⠀⠀⠀⣸⣿⠃⠀⣰⣿⣏⢼⣿⠗⠿⠟⠁⠉
⠀⠀⠀⠰⠛⠉⠉⠛⠋⠙⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣆
⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢸⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⠀⠀⠀⢸⣮⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣤⡀⠀⠀⠀⠀⣠⣼⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⢫⣾
⠀⠀⠀⠀⢿⣛⣦⣾⣤⣤⣀⠀⠀⠀⢠⡾⡡⡸⠓⠒⠢⣝⣦⣄⣤⢞⡥⡒⡲⡻⠤⠿⣦⠀⠀⠀⢀⣠⣤⣽⣦⣟⣻⠄
⠀⠀⠀⠀⣴⢛⡿⠷⠒⠦⢭⣛⣦⣴⠋⣪⡶⠞⠛⠻⢶⣄⢙⢿⢟⢕⣴⠾⠛⠛⠶⣦⠈⢷⣤⣾⣫⠥⠒⠢⡿⣟⣳⡄
⠀⠀⠀⣼⡡⣢⣴⠶⠷⠶⣥⡉⠛⠁⢠⣿⠀⠀⠀⠀⠀⢻⣔⠕⠁⣾⠃⠀⠀⠀⠀⢸⣷⢐⢝⠉⣁⡴⠾⠾⢶⣮⡈⢹⡄
⠀⠀⣼⡡⣠⣿⡃⠀⠀⠀⠈⢿⠠⠪⠺⣿⢦⣀⠀⢀⣠⣾⢇⠀⡠⢻⣦⣀⠀⢀⣠⢾⠟⢕⠁⣴⠏⠀⠀⠀⠀⣿⣷⢄⢻⡄
⠀⠀⢷⡈⠸⡘⢧⡀⠀⠀⣀⣾⡷⠤⠪⠮⠦⢍⣉⣩⢟⠕⠌⣅⡀⡠⡻⠭⣙⣯⢅⠞⢔⠕⠕⢹⣆⡀⠀⠀⣠⠟⣙⠐⣰⠇
⠀⠀⠈⣧⠀⠙⢦⣉⣛⣫⠽⠃⠊⢂⣂⣠⣤⣤⣶⣶⣶⡄⠴⠊⠉⡛⣾⣶⣾⣧⣥⣤⣁⣀⠄⠪⠻⢍⣛⣋⡥⣞⡑⢡⡏
⠀⠀⠀⠈⠛⠶⣅⣑⣑⣠⣴⣶⠿⢛⣫⠍⢕⢖⠜⢝⣉⣁⣀⣀⣊⣊⣉⠉⠙⢒⢖⠽⠏⣛⠻⢷⣦⣬⣊⣀⣠⡦⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⠏⠲⠫⡊⢢⣤⠶⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⣵⣇⠠⡪⡀⠈⣷⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠨⢪⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡯⡨⢸⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠿⣠⢀⠛⢭⣛⠶⠦⣤⣤⣀⣀⣀⣀⣀⣠⣤⡤⠶⠞⣫⡽⠫⡪⠸⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣤⣀⡐⠕⠝⠝⠓⠒⡲⡲⡠⠼⡷⢔⠖⢖⢖⠝⠉⠀⠠⣢⣪⣮⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⠦⠬⣬⣤⣼⣤⣤⡥⠴⠷⠶⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣉⡉⣉⣉⣓⠦⣄⠀⢀⡤⢖⣋⣉⡉⣉⣉⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⢟⡫⠿⠟⠳⢯⣝⢿⣮⣳⣫⣾⢟⡭⠿⠛⠻⢯⣛⢷⣜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣠⢏⣾⣣⣿⠖⠛⠉⠉⠙⠻⣷⡽⣿⡿⣵⡿⠛⠋⠉⠉⠛⢿⣷⢹⣦⢷⣀⣀⣄⣠⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡠⢞⣩⣥⠤⠶⠶⣾⣭⣾⡇⣿⠃⠀⠀⠀⠀⠀⠀⠘⣧⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣮⣭⡶⠶⠦⢤⣬⣙⠢⣄
⠀⠀⠀⠀⠀⢠⠞⣴⢟⡽⢚⣉⣭⣽⣶⣝⢻⣷⢻⡀⠀⠀⠀⠀⠀⠀⢠⢏⣿⣇⢧⠀⠀⠀⠀⠀⠀⠀⣸⢣⣿⢟⣵⣚⣩⣍⣙⣶⣝⢷⣌⢦
⠀⠀⠀⠀⠀⡟⣼⢯⣟⡷⠋⠁⠀⠀⠉⠻⣷⢻⣷⣙⢦⣀⣀⣀⣠⠴⣫⣾⠿⢿⣮⡳⢤⣀⣀⣀⣠⢖⣱⣿⢳⡿⠋⠁⠀⠀⠉⠙⣿⣧⢿⡞⣇
⠀⠀⠀⠀⢸⡇⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣷⣶⣯⣽⣶⠿⣛⢵⣿⣷⣽⡻⢷⣾⣿⣿⣶⣿⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⡇⣿
⠀⠀⠀⠀⠀⣷⢻⣟⢧⡀⠀⠀⠀⠀⠀⢀⣌⣼⣿⣿⢛⣽⠶⡖⢚⣋⡵⠞⠁⠙⠻⣿⣻⠒⠒⣿⣽⡻⣿⣿⣞⣆⠀⠀⠀⠀⠀⠀⢠⢏⣿⢳⡇
⠀⠀⠀⠀⠀⠸⣷⡻⣷⣝⡶⠤⢤⠤⢖⣫⣾⣿⣿⢣⣿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣷⢻⣿⣿⣮⣗⡦⠤⠤⠴⣞⣵⡿⣣⡟
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣽⣟⣿⣿⣿⣛⣿⣛⡿⣿⣇⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣾⡿⣟⣻⣟⣻⣿⣿⣿⣿⣽⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⢿⣿⣿⠿⣿⠿⣿⡎⣿⣷⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣡⣿⡟⣼⡿⠿⡿⢿⣿⣿⡿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣩⣍⣋⣴⣿⣿⣿⣷⣬⣙⡲⠦⠤⠤⠤⠤⠶⢚⣩⣴⣿⣿⣿⣷⣌⣛⣭⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣝⡻⢿⣿⣿⣿⣿⣿⠟⣠⣶⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⣟⣭⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣟⡚⢯⠽⢏⣅⣘⣛⣁⣀⣾⣛⣛⣛⣛⣯⣭⣵⣒⣩⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⢬⣭⣭⣭⣽⡿⠿⠿⠟⠛⠋⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠷⠷⠄⡀⠀⠀⡀⠴⠷⢇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠤⠠⠀⠠⢀⣄⠲⠆⣬⠁⣩⡄⠲⢂⣄⠡⠀⠀⠠⢴⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡡⠀⠜⠳⢆⠟⠀⠀⠀⠈⡏⡏⠀⠀⠀⠘⣧⠶⠛⠄⠠⡉⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠘⣿⠀⠀⠀⠀⢗⣄⡀⠀⢀⣿⣇⠀⠀⣀⣄⠇⠀⠀⠀⢸⡗⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠄⣀⣀⢄⣾⡻⠋⠛⠏⠁⠉⠟⠋⠻⣻⣆⢄⣀⡀⢜⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠫⢭⡻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣫⠭⠛⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣽⣿⣦⣄⣀⣀⣀⣠⣴⣿⣿⣅⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠉⠛⣻⣷⣿⡛⠋⠉⠉⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢿⠰⣦⠸⣑⠋⣶⡶⠞⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠈⠛⠳⡑⠃⠀⠙⠁⣩⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠞⠃⠀⠀⢰⠟⣿⣄⠀⢠⡀⠀⠀⠘⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⡄⠀⠀⠀⣴⣿⣿⣿⣦⡧⠘⠳⡦⡇⠀⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⢄⠀⠈⢻⣿⣿⣿⣿⠋⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠂⠛⢿⣼⣷⣶⢀⣿⣿⣿⣿⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠄⢠⣤⡽⢿⣿⣿⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠙⡌⠊⣻⣿⣿⣿⣿⡟⠹⢻⠆⠀⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⡄⠀⠀⠀⠀⠠⠀⠀⠙⠋⠀⠐⡄⠀⠀⡈⠀⠀⠀⠀⠀⣠⠊⠉⣝⠻⠶⡟⠢⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠀⠀⠈⠉⠀⠠⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⢀⢠⣿⣟⡔⡾⠘⠉⠳⣄⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡀⠀⠀⠀⠀⣛⠉⡛⡟⠽⡻⠢⡄⠀⠀⠘⣷⣤⡄⠀⠀⠁
⠀⠀⠿⣦⣤⣤⣴⣾⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⢱⡀⠀⠀⠛⠈⠓⠴⠀⠐⠳⠤⠉⠀⠀⠀⠘⢿⠕
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠒⠂⠁
⠀⠀⠀⣀⡀⠀⢀⡴⠀⠀⢀⡄⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠨⠀⠀⠀⠰⠀⠀⠀⠀⠂⠈⠀⠀⡠⠴⠲⡆
⠀⠀⠀⢹⡯⢽⡿⠀⠀⠀⠘⠛⠙⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⡲⢉⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⡤⠒⠀⢀
⠀⠀⠀⡀⠀⠀⢀⡂⠀⠀⠀⢀⠀⡆⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⢈⠇
⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠘⠒⠐⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠙⠒⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢆⣴⡄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠲⣼⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠿⢿⣦⠀⠈⠀⠀⢠⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢂⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠶⠉⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠾⣷⡀⠙⠛
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⣿⠏⠀⠀⠀⡄⠀⠀⠐⠦⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠛⠀⠠⡶⠀⠀⠐⠀⠀⠈⢿⣄⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣼⠇⠀⠀⠀⠀⣷⡀⢰⡦⠀⠀⢸⡿⠁⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⢻⣦⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⢸⣿⣿⣀⠐⣀⣾⣇⠀⠀⠀⠀⢉⠛⡦⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣾⠋⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⡸⠋⠉⠛⠛⣁⡿⠿⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⡀⠀⠀⠀⢀⡀⠀⠀⢀⣤⡀⠐⢺⠋⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⠶⠚⠛⠁⠀⣾⣿⡁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣞⣿⡇⠀⠀⠀⠀⠉⠙⠁⠈⡽⠁⠈⣿⠰⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣧⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣀⠀⡀⠚⠛⢿⣦⡀⠀⠀⠀⠀⠀⣿⣿⣏⣹⠆⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠶⠚⠁⠃⠀⠈⠉⠀⠀⠀⠀⢴⣿⣃⣀⠀⠁⠀⠈⠛⢦⠀⠀⠀⠀⣿⣿⣟⡋⢳⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠛⣹⡿⠃⠀⠀⠀⠂⠐⡤⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡏⢉⠉⠛⡇⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠒⣿⡏⠀⠀⠀⠀⠠⠤⠇⠀⠀⠀⠀⠀⠀⠘⠓⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣟⠁⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡼⠂⠀⠛⠻⠒⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠶⢤⣤⣌⣿⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣥⣧⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒

⢀⡆⢠⢠⠏⢾⢦⠪⣃⡜⠁⠖⠒⠋⠀⢠⢠⠇⠠⠃⡷⠼⢂⡛⠀⠞⠠⠆⠴⢀⠀⠄⣈⣀⠠⠤⠠⡷⠈
⢈⡀⡉⣜⠦⣼⠾⠀⠁⡀⠰⠐⠐⠬⣄⢏⠆⠶⢤⠛⠁⠀⠇⠈⡆⠀⢷⠘⠛⠛⠃⢠⡀⠲⠄⠠⠤⠄
⠀⡇⠀⡟⢀⣸⠀⡾⢶⠶⠆⠀⣇⠄⢀⠀⠀⣄⠀⡀⠂⢱⠀⢜⠀⠶⠀⠖⠰⠀⠆⣸⠃⠂⠀⠀⣀⠀⡜
⠘⣀⣘⣁⠀⢰⣀⡇⣸⢀⡄⡴⠀⠀⠒⠒⠒⠀⢰⠉⢀⣁⣀⢈⠉⠀⢰⠀⡉⠉⠈⡁⣀⠀⠃⠈⠉⢠⠅
⡄⡂⢀⢀⠀⠆⠨⠤⠅⢈⠁⠖⠛⠠⠂⠆⠰⠐⠂⠀⣉⣈⡠⠀⠀⠹⣙⡆⢀⡤⡄⠀⠠⠀⠠⠖⠒⠀⠰
⠀⡁⢨⢤⡥⠀⠆⠄⠄⢸⠄⠂⠐⠀⠒⠖⠂⠀⠀⠁⢁⠀⠀⠀⠋⠀⢈⠀⡀⢀⠄⠀⠀⠆⠂⠁⠁⠒⠂
⠐⡇⡀⣸⢀⡄⠀⠈⠓⠀⠀⡘⠀⠠⠠⠆⠄⠀⣀⢀⡘⠀⠈⡁⡀⡉⠡⠀⠀⡄⠰⠃⠀⠆⠀⠱⠀⠤⠤
⣀⡀⠀⢀⠀⠠⢤⡘⠀⠂⠈⠁⠰⠒⠀⢀⡀⠈⠀⠠⠤⠤⠀⠀⠀⠠⠶⠂⠰⠁⠀⣀⣀⠀⣀⠀⠠⠠
⠀⠄⠀⡘⠀⠠⠀⠄⠀⠐⠒⠀⠀⠈⠀⣬⠁⠀⠀⠔⠠⠠⢀⣠⡄⠠⠀⠂⢀⡀⠠⠠⠠⠀⡉⠁⠀⢀⠇
⡄⠀⠈⠁⠠⠖⠂⠀⠀⠀⠈⠀⠸⡀⠀⠀⠀⠉⠓⠀⠀⠀⡈⢀⠀⠀⣀⠀⢀⢉⠀⠀⡀⠀⠀⣬⠄⠉⠰
⢠⠀⠀⠀⠄⠰⠀⠀⠊⡁⠀⠀⠀⠉⠀⢀⡀⠁⠘⠀⠀⡄⠁⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⢀⠀⠄⠀⠰
⠀⠀⠀⠀⡤⠀⠀⠈⠀⠀⠐⠲⠀⠀⢀⠁⠄⠀⠀⠀⡤⠁⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠁⠀⠀⡤⠄⠀⢀
⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⢠⠀⠄
⠀⠀⠀⢀⡀⠀⠑⠀⠈⠄⠀⠀⠀⠠⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⠄⠀⠀⠠⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠠⣤⣤⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡆
⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠈⢠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠋⢉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣬⣿⢩⣬⡇⣬⣽⢪⣤⣍⣍⣡⣤⣤⣴⣦⣴⣶⣶⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠸⡿⠛⢿⠟⠹⣿⠛⠙⠇⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡶⠿⠖⠛⠒⢲⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢳⣶⠖⣶⡖⢂⡖⠒⠀⠐⠒⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠱⣿⠉⢺⡏⡁⠀⠀⠀⠀⠀⣠⣤⠈⣇⠀⠀⠀⠀⠀⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⣴⠩⠶⠥⣤⡤⢤⡔⣠⣬⣥⡤⣬⣤⠬⣤⡬⢤⣤⣬⠭⡭⣽⠦⣥⣿⠹⠶⣶⡶⠦⡀
⠀⠀⠀⠀⣠⠖⠂⠐⠢⡀⠀⠈⠳⣄⣀⣀⣘⣶⣶⠶⠶⠶⣿⠰⠶⣾⠃⠐⣏⡈⠲⡄⠘⠛⠻⠟⠛⠛⢛⡛⢿⡿⠘⠛⠛⠛⠋⠁
⠀⠀⠀⠀⣛⡄⠀⠂⣰⡇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢸⡀⣀⣿⠀⠀⡇⠈⣷⣛⡛⣻⡟⠛⠛⠛⠛⠛⢛⡅
⠀⠀⠀⠀⣿⠆⠀⡷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠥⠤⠤⠤⠤⠤⠤⠿⠥⠼⠦⠤⠶⠖⠚⠉
⠀⠀⠀⠀⡿⢶⡤⠟⣿⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⡀
⠀⠀⠀⠀⠇⠈⠁⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣆⣆⢀
⠀⠀⠀⠀⠈⠀⠈⣠⣿⡀⢢⡀⢀⣀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠉⠁⠉⠭⠟⠙⡟⠈⠁⠛⢏⠉⠉⠛⠛⠛⠒⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁⠈⠇⠀⢏⢀⣇⠀⢀⡀⣀⣀⣀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠃⠇⡀⠐⠃⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⢻⠀⢿⡀⠛⠉⠉⠉⠙⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠗⠋⠀⠁⠀⣈⠠⠀⠀⠸⠀⢸⠀⠸⠄⠄⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠰⢲⠒⣼⠂⣸⣀⣴⠀⣀⠀⢆⠀⠀⢰⠁⠀⠀⠀⢹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣰⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠆⠀⢸⠀⢿⠀⢹⣿⢸⠀⡇⢩⣾⡇⠀⢸⡀⠀⠀⠀⡠⠈⠳⣦⡄⠀⣀⡤⣄⣀⣀⣀⣀⣀⣐⣗⣀⣀⣉⣠⣼
⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠰⠀⢸⠀⠀⣿⣼⠀⣇⢎⡏⡇⠀⠀⠈⠐⠐⠊⠀⠀⠚⠁⠀⣼⠫⠊⢙⣽⣿⣿⣛⣛⣙⣛⠛⠛⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠈⣎⠆⠈⠲⣄⣀⢸⡀⠀⣿⠀⢀⡡⢊⢨⠃⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⡅⢐⠛⠀⢠⣾⣿⣦⠀⠈⡆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢯⡢⡀⠀⠀⢹⡃⠁⠿⠉⠈⢁⡼⠃⠀⠀⠀⠈⠉⠉⠀⠀⠛⠀⠄⠀⠘⢿⣥⣼⣿⣿⣶⣾⣿⣟⣉⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⢀⣰⡇⢐⣣⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⠀⢀⣀⠀⣠⣤⣤⡤⠖⠚⠉⠀⣿
⠀⠀⠀⠀⣼⠋⢹⡏⠉⣿⠉⠉⠉⠉⠉⠉⠉⢹⡿⣿⠿⢿⡿⠿⢿⡿⠿⠿⠿⠿⠿⢿⣟⣿⣿⢤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⢿⡀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠠⠤⠀⠄⠀⢠⠠⠠⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⠾⣿⣶⣦⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣥⠶⠾⣷⡀⠀⠀⠀⣚⣁⣤⢬⣞⢻⣿⣿⣿⣁⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⠏⠀⠀⠘⣷⡀⠀⠰⢽⣍⠉⠘⣿⣿⣿⣿⣿⠀⠚⢆⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠟⡾⠀⠀⠀⠀⠈⠻⢷⣷⠶⠂⣶⢸⣿⣿⣿⣿⡿⠄⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢿⣠⠇⠀⠀⠀⠀⠀⠀⠀⢐⣿⣥⣾⣿⣿⣿⣿⣿⣷⡄⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢿⣿⡿⡿⢛⣥⡉⠥⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡠⢪⣿⣿⣿⢻⣷⠿⠶⠛⠩⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⣠⣴⣿⣿⠽⣛⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡿⠻⠿⣆⠀⣠⣾⣿⣿⡿⠗⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⠛⠳⠤⠀⠀⠈⢿⣿⠏⠀⢀⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣛⠛⠛⠃⠁⠀⠀⠀⠀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠒⠶⣿⡿⢏⢭⣵⣷⣚⣛⣀⣀⡀⣠⣾⣶⣄⡀
⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠈⢳⡍⢩⣿⣿⡟⠉⠛⠿⣷⣿⣿⠋⠈⠉
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣼⡇⣸⡿⠿⠁⠀⠀⠀⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⣶⡟⢡⣼⠏⠁⡟⠀⠀⠀⠀⠀⠘⠛⠣
⠀⠀⠀⠀⢠⣀⠙⠉⠊⠉⣁⣴⣿⡏⠀⢸⠃
⠀⠀⠀⠀⠀⠈⠁⠻⢺⣿⣿⣿⡿⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠱⠁⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃

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

⣷⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⣴
⣿⣿⣿⣦⡀⠀⢸⡇⠀⢀⣤⣾⣿⣿⣿⣿⣷⣄⠀⠀⢸⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣀⠀⠀⣿⠀⠀⣠⣾⣿⣿
⣿⡿⠋⠁⠙⢦⣸⣇⡴⠋⠈⠙⢿⣿⣿⡿⠋⠈⠑⢄⢸⢀⡴⠋⠈⠻⣿⣿⣿⡿⠋⠈⠳⣄⣿⣠⡞⠃⠉⠻⣿⣿⣿⠟⠁⠙⢷⡄⣿⣠⠞⠁⠙⢿⣿
⡏⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢀⣽⣏⠀⠀⠀⠀⠈⢻⠋⠀⠀⠀⠀⢈⣿⡁⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⢉⣿⡁⠀⠀⠀⠀⠙
⡇⠀⠀⠀⣠⣾⣿⣿⣷⣆⡀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⠀⠀⢀⣴⣿⣿⣿⣷⣀⠀⠀⠀⣿⠀⠀⠀⣀⣴⣿⣿⣿⣦⡀
⡇⢀⣤⠞⢿⣿⣿⣿⣿⡿⠟⢦⡀⢸⡇⢀⡴⠻⣿⣿⣿⣿⣿⡿⠳⣄⠀⢸⠀⢀⡔⠻⣿⣿⣿⣿⣿⠟⠳⣄⠀⣿⠀⣠⡞⢿⣿⣿⣿⣿⣿⠿⢦⡀
⣷⠟⠁⠀⠀⠙⢿⡿⠋⠀⠀⠀⠙⢾⡶⠋⠀⠀⠈⠻⣿⡿⠋⠀⠀⠈⠳⣾⠖⠁⠀⠀⠈⠻⣿⠟⠁⠀⠀⠈⠳⣿⠞⠃⠀⠀⠙⢿⣿⠟⠁⠀⠀⠙⢶
⣿⣦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣾⣷⣄⡀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣴⣿⣦⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴
⣿⣿⣿⣦⡀⠀⠀⡇⠀⠀⣠⣾⣿⣿⣿⣿⣷⣆⡀⠀⢸⡇⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⣿⠀⠀⣠⣾⣿⣿
⣿⡿⠋⠀⠙⢦⣀⣇⡴⠋⠀⠙⢿⣿⣿⡿⠋⠀⠙⢦⢸⣇⡴⠋⠈⠙⢿⣿⣿⡿⠋⠀⠙⢆⣿⣠⡾⠋⠈⠻⣿⣿⣿⠟⠉⠈⠳⣄⣿⣠⠞⠁⠙⢿⣿
⡏⠀⠀⠀⠀⢀⣽⣯⡀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢀⣽⣯⡀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢀⣽⣏⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⢈⣿⡁⠀⠀⠀⠀⠙
⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀
⡇⢀⡴⠛⢿⣿⣿⣿⣿⡿⠛⢦⡀⢸⡇⢀⡴⠛⢿⣿⣿⣿⣿⠿⠛⢦⡀⢸⡇⢀⡴⠻⣿⣿⣿⣿⣿⠟⠳⣄⠀⢸⠀⣠⠔⢿⣿⣿⣿⣿⣿⠟⢦⡀
⣷⠋⠀⠀⠀⠉⢿⡿⠋⠀⠀⠀⠙⢾⡷⠋⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠙⢾⡶⠋⠀⠀⠀⠹⢿⠟⠁⠀⠀⠈⠳⣾⠞⠁⠀⠀⠘⢻⣿⠟⠁⠀⠀⠙⢦
⣿⣷⣄⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣿⣷⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣿⣦⣀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⣾
⣿⣿⣿⡷⣄⠀⢸⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⢸⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⡇⠀⠀⣠⣾⣿⣿
⣿⠟⠁⠀⠈⠳⣼⣇⠴⠉⠀⠙⢿⣿⣿⠟⠁⠀⠙⢦⣸⣠⠞⠁⠀⠙⢿⣿⣿⠟⠁⠀⠙⢦⣸⣠⠞⠁⠈⠻⣿⣿⣿⠟⠁⠈⠳⣄⣇⣠⠞⠁⠙⢿⣿
⡇⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⢀⣽⣧⡀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣀⣿⣅⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⣨⣿⡁⠀⠀⠀⠀⠙
⡇⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄⠀⠀⢸⡇⠀⠀⣠⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⣿⠀⠀⠀⣠⣾⣿⣿⣿⣶⡀
⡇⣠⠖⠙⠻⣿⣿⣿⣿⠟⠉⠣⣄⢸⠇⣠⠞⠙⢿⣿⣿⣿⣿⠟⠙⢦⡀⢸⠀⣠⠞⠛⢿⣿⣿⣿⣿⠟⠳⣄⠀⣿⠀⣠⠞⠻⣿⣿⣿⣿⣿⠟⠢⣄

⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠈⢸⠂⠙⠀⠀⠀⠀⠀⠄⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⢀⠤⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⠐⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢁⣤⡖⠂⠉⠉
⠀⠠⠀⠠⠀⠁⠀⠉⠁⠀⠀⢐⡿⠀⠐⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢃⣼⠶⢋⣌⠀⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⣠⡾⠋⠀⠀⠆⠀⠀⠀⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⡤⢠⣆⠀⠈⠀⠀⠀⠁⠀⠀⢀⣼⠃⠀⠀⠀⠐⠖⠛⡟⠛⠏⢁⠀⠀⠊⠁⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣟⠀⠔⠀⠀⠀⠀⠀⠀⠈⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡂⣨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡈⠥⣀⠀⠀⠀⠀⠀⢈
⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠙⣧⡈⡀⠀⠀⡀⠀⠀⢠⡀⠀⠛⠀⢀⠀⠀⠀⢀⠀⠀⠀⢈⡓⠀⠀⠀⠔⠁
⢀⠀⠀⠀⠀⠐⠂⠘⠀⠉⠀⠄⢀⡷⢄⠘⣦⡀⠨⢽⣦⡀⠱⢄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉
⢁⠤⠴⠥⢤⣀⡠⠄⠀⠀⠀⠀⣨⠁⠁⢨⠁⠑⠀⠀⠹⡝⠿⡸⣇⠀⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⣠⠛⠀⠉⡇⠀⠀⣧⠀⠘⡜⡆⢡
⠀⠀⠀⠀⠀⠀⠐⠃⠈⠀⠀⠀⠀⡴⠂⠀⠀⡰⠂⠀⡀⠊⠃⢀⠂⣴⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢤⠄⢁⡠⠞⠁⢀⠤⡂⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠑⢲⠆⠀⠀⠈⠔⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠘⠋⠉⠀⠈⢀⣀⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠇⠀⢠⠃⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢤⣾⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠀⠄⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡀⠀⠐
⡤⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠚⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠰⠞⠁⠀⠀⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣉⣷⡄⠉⠂
⠀⠀⠀⠀⠺⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡴⢾⣿⠋⠉⠀⠠⠀⢆
⠀⠀⡀⠀⠀⠨⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠒⠉⢁⠪⠕⠁⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⢀⡀⣀⡄
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⣀⣠⡤⢴⠠⠊⣀⠀⠠⠄⠀⠀⠀⡆⣇⠀⢳⣁⡠⠂⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⡠⢖⣪⡷⠋⢈⡤⠞⠏⠀⠒⠒⠒⠲⠲⠾⠓⠛⠘⠋⠁⠀⠀⠈⢀⣼⣤⠏
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠌⠉⠐⡡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠤⠀⡀⠀⠀⠀⠀⠠⠆⣸⠁⢻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠠⠀⠈⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢀⠄⠉⠀⠤⠄⠀⠀⠈⠀⢀⣀⣀⣉⠀⠒⠀⠀⡀⢀⡀⠀⢤⠶⠊
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡴⠁⠀⠄⡠⠀⠁⠠⠠⠆⠊⠀⠀⠀⠀⠀⠁⠀⠀⠁⠒⢄⣀⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠂⠐⡀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠉⠀⠘⠠
⠀⠀⠀⣀⣠⣤⣤⡤⡜⠉⠀⠀⠁⠘
⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⠄⢀⠀⠀⠀⣶⠚⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢠⣿⣇⣴⡏⠀⠀⠀⠨⠀⠀⣼⣿⡷⢤⡀⠀⠀⠀⠀⠀⠀⠈⠚⢤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⢘⣿⣿⣿⡇⠀⢠⠀⠈⠀⢀⣿⠏⠁⠀⠑⣄⠀⠀⠑⢦⡀⠀⠀⡈⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢭⠿⠿⠖⠀⠉⠻⣿⠃⠀⠀⠀⠀⡠⠋⠀⠀⢀⣤⣾⣿⣧⠀⠀⠀⠈⢶⡀⢛⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⣄⠀⠙⣧⢂⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠢⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⣤⣬⡳⡀⠘⠧⢠⠀⣠⣴⣿⣿⣿⠛⠋⠙⢻⣿⠇⠀⠀⠀⢀⠀⠰⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠃⠤⠀⠀⠀⠀⠀⠃⠀⠤⣅⠀⣀⣼⣿⡿⠟⣉⢔⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠀⠄⢠⣿⣷⢆⣸⣾⡀⠀⠀⠀⣠⣶⠟⢷⣮⡻⣿⡀⠻⢛⣭⣿⣿⣿⠻⠿⠀⠄⠀⠀⠀⠀⠀⠀⠃⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠺⠇⠀⠙⢷⣄⣴⠀⣟⠁⣠⣾⡿⣳⢌⣵⠞⠛⣿⡉⠉⠙⠷⠀⠀⡀⠀⠀⡀⢀⠀⠀⠈⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⣀⠹⣿⡿⢿⡙⣏⠸⣏⡳⠀⠀⢾⡠⣀⠈⠀⡼⠃⠀⠀⠀⠀⠱⢠⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠀⠀⠀⠀⢀⣠⠞⠋⢀⣴⡿⢟⣦⠹⣟⠈⣷⣴⡷⡝⠿⠌⢆⠈⢷⡷⡶⠋⠀⠀⠀⠀⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠀⢀⡔⠛⠁⣠⣶⢟⣩⡴⠛⢟⠷⡙⠈⡿⢮⢿⠊⢄⡲⡼⣅⠀⠻⣦⠀⠀⠀⠀⠀⠁⠘⠡⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣴⡿⢉⣴⠟⠁⠀⠀⠋⠙⢷⣤⣄⣴⡱⣾⣦⠳⢶⡊⣦⠀⠹⣧⢸⡄⣆⢶⠀⠔⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⢠⣿⠁⠀⣀⠀⣶⠀⠻⣀⣈⣉⡑⢶⠋⢅⠀⠀⠀⠘⣧⡠⡘⢿⣹⣿⡻⣓⡶⠲⠦⢤⣤⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠸⣿⠀⠿⠂⣂⣭⣴⣶⢾⠿⠙⠻⠟⠙⣺⣷⡈⠧⠀⣀⡴⢿⡝⡇⠈⣿⣧⣿⣉⣻⣛⡿⠂⠈⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠘⣁⣠⡴⢶⡾⠿⢛⣋⢈⡲⠠⣏⡖⢛⡴⠀⢈⣩⣴⡶⢏⠁⠀⠀⣻⢸⡆⢸⣟⠿⣿⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⡾⠛⠉⠈⡃⢒⣶⢭⣵⠤⠃⠭⠶⠚⢉⣩⠴⠚⣉⡤⠓⣿⡇⣗⣤⣞⠥⠚⢀⣼⠋⣾⢎⡓⢦⣀⠀⠀⢂⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠐⣿⠙⠀⠀⠀⣖⣈⡡⠴⠾⣿⣦⢀⣤⡶⣟⢉⣤⠔⠋⠁⣀⡠⠖⠚⠿⠀⠤⠤⠖⢿⠻⠛⠾⠟⢿⡤⠙⢿⣶⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣿⠁⠘⠾⣧⡤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣧⣿⢹⢳⣿⡿⣿⢸⡟⣿⢸⡇⣿⡈⣿⣸⡏⣇⢹⠻⡇⠀⣷⠀⠀⠀⠀⠀⠀⣰⠇⠀⣠⢞⡥⢖⣊⡩⠭
⣸⡿⡾⡞⣿⣿⡿⣼⠃⣿⢸⡇⢸⡇⣿⡇⣿⢹⢸⡆⠳⢿⠈⠢⣤⣀⠀⠀⢰⡏⢀⣼⢟⣵⣾⣷⠶⢿⣿
⣯⢣⣧⢇⡿⣸⠇⣿⢠⣿⢸⡇⢸⡇⣿⡇⣿⢸⠸⡅⠀⢸⡆⠀⠈⠙⠦⡄⣸⡇⣼⣿⣿⣿⢕⣪⡭⠵⠶
⠃⣼⢝⡾⢱⡟⣸⠇⢸⡟⢸⡇⣼⠇⣿⡇⣿⢸⢠⡇⠀⣼⡅⠀⠀⠀⠀⢌⢻⣽⣿⣿⣿⡷⢋⠤⣒⣨⣭
⣾⢏⡾⣱⠏⢠⡟⢀⡿⢁⡿⣱⠏⢠⣿⢳⣿⣿⡾⠀⠀⡟⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⣱⡷⠛⠉⠁
⡱⢋⡴⠋⣠⠏⣠⠟⣡⠟⣱⠏⣠⣾⣷⢋⣾⠞⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⡟
⡥⢛⡴⢊⡥⢞⣡⢞⣡⠞⢁⣴⣿⣿⣷⡿⠃⠀⠀⠀⢹⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣚⡵⢚⡭⣖⡯⠖⢋⣠⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⣵⣾⠿⣚⣥⣴⣿⣿⣿⣟⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⣽⣶⣿⣯⣅⣈⠀⠀⠈⠉⠛⠿⣿⣶⣤⣀⠀⠀⠀⠐⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⡀⠀⠈⠈⠉⠙⠛⠷⣦⡀⠀⠀⠀⠈⠑⢝⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⡛⠻⠶⣦⣄⡀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢹⣧⣠⡾⠋⠂⠒⠀⠀⠀⠀⠀⠀⢀⢀⣠⠃
⠙⠷⢤⣀⡉⠛⠷⣦⣄⠀⠀⠈⠳⣄⠀⠀⠀⣿⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠠⠀⠐
⠀⠀⠀⠈⠉⠓⠲⢬⡙⢿⣦⡀⠀⠘⢧⠀⣠⣿⠂⠀⠀⠀⠀⠀⠀⠀⢰⣾⢏⠠⠂
⠛⠛⠛⠲⠶⢤⣀⠐⠙⢷⣝⢷⡄⠀⢸⣿⣻⣥⣄⣀⠀⠀⠀⠀⠀⡄⠀⣿⠃⠀⠀⠀⠀⠀⠀⢀
⣭⣭⣭⣕⣢⢄⡈⠓⢆⠀⢹⡎⣷⣠⡟⠡⠄⠀⠀⠉⠙⠲⣄⠀⠀⢹⣾⣏⠄⠀⣀⠠⡰⠄⠊⠀⠉⠉⠉
⣶⠿⠳⠶⢮⡑⢯⣢⡈⢳⠀⣿⣿⣷⣦⠶⠤⣔⡢⠀⠀⠀⠈⠳⡄⠸⣿⢏⣴⠪⠔⠁⢀⡠⣶⠿⣛⣛⣛
⣉⣉⡛⠛⠦⡍⢲⣹⡱⡀⡇⣹⣿⣿⣭⣽⣛⢶⣭⡳⢅⠢⠀⠀⢹⢸⡿⠃⠁⢀⣠⡾⣛⠭⣒⠭⠒⣒⣲
⡤⢭⣉⠓⠦⡈⢆⢹⣧⢱⣧⡿⠉⠀⠀⠀⠈⠙⢪⣻⣮⠳⡱⡀⢸⣼⠃⢀⣴⡿⡫⡪⠔⠉⣀⣴⡿⢗⡯
⠤⢭⣐⠭⡢⡙⡼⡄⣿⢸⣿⣷⣖⡒⠲⢄⠀⠀⠀⢹⣟⢇⢻⣧⣾⠃⣴⣻⡫⡪⠊⢀⣴⣾⢟⡵⣪⠵⣚

⠀⠀⠀⢀⡀
⠀⠀⠻⣍⢃
⠀⠀⠀⢹⣎⠄⠀⠀⠀⣠⠴⣒⡫⠍⠉⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⢻⡖⠀⠠⢊⠕⠋⠀⣀⣀⠀⠀⠀⠀⠀⠉⠒⣍⡲⣄
⠀⠀⠀⠀⠈⢿⡁⢰⠛⢴⣤⡾⢧⣉⣷⣤⡀⠀⠀⣰⠛⠉⢻⣮⡳⡄⠀⠀⠀⢠⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠘⠁⣏⠀⢠⡿⣡⢀⣽⢋⡿⠃⠀⢀⡿⢀⣠⡼⠃⠱⡹⡄⠀⠀⠀⣿⡟⠛⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣦⠹⠁⢀⡿⣡⣾⣥⡄⢠⡾⣡⡟⠉⠀⠀⠀⢷⢳⠀⠀⠀⣜⠀⡴⢷⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠰⡘⣿⡆⠀⠘⡤⢴⡫⠹⠿⠟⠀⣘⣳⣤⣀⠀⠀⣼⣾⠀⢀⣜⣛⢆⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠳⡙⣿⣤⡟⢡⡼⠛⣳⣞⣡⡬⠶⢮⣇⣯⢑⣶⠣⢃⣴⡿⢟⡿⢳⡄⠀⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣷⣿⣠⣜⣏⠉⠁⠀⠀⣀⣿⡽⢟⣡⡴⠟⢋⣴⣋⣤⣾⠷⠿⠟⢟⠿⠟⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣭⣛⠁⠠⣭⣭⣭⣭⡽⠶⠞⠛⠉⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠒⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠴⠶⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⣀⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣟⣭⠿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣟⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⡿⣻⡗⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠈⠙⢿⣿⣿⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠈⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠙⢾⣿⣿⡆
⠀⠀⠀⠀⢾⣿⣛⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣀⠀⠀⢀⣠⢾⣽⣿⣿⣧⣀⠀⠀⠀⢀⣤⢿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷
⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣿⢷⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡏⠛⡏⣷⣺⣶⣖⣿⢹⡛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣾⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠙⠋⠉⠀⠈⠉⠙⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣼⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⠿⠟⠛⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠄⠀⠀⠀⠀⠀⢀⣠⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣞⠳⡄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣡⣄⢦⠀⠀⠀⢱⠀⠀⢀⣈⠳⢀⡴⠤⢄⢀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢿⣿⠁⠀⠀⠀⠘⣆⠀⠀⣄⣀⠈⠀⢦⣶⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠺⣷⣧⣄⠩⣇⠀⠀⢀⡼⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠁⠖⡬⠀⠀⠀⠀⠀⠀⣶⠉⣿⣿⡍⠙⣢⢴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⡇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⡟⡼⢡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠰⠇⠐⠀⠀⠀⠀⠀⠀⠠⠒⠂⢠⠀⠀⠠⠟⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢠⡤⣄⣠⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⣷⣴⣷⠀⠀⠐⠋⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⢀⠦⠄⠩⠃⠀⠠⢀⣠⠴⠚⠁⠀⠉⣁⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢗⡭⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣡⠶⠛⠓⠒⠒⠀⠠⠄⠀⢆⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣫⣥⣶⡿⠛⠛⠛⠛⠛⠃⠀⠀⠁⢤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠌⠹⠂⢼⣿⣯⣾⣿⣿⠿⢿⣿⣶⣀⣠⣆⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣶⣤⣈⠩⣿⣿⠋⠉⠀⣰⣿⡿⠿⢿⣯⣁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠤⠤⢄⠀⠀⠀⢸
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣌⢻⣶⡖⣼⡿⠛⠀⠀⠀⠈⠻⣿⣷⣶⣤⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠒⠚⠆
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⡇⢻⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⡇⠻⠋
⠙⠋⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⡌
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠋⡠⠂
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⣋⣠⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠶⠶⠶⠶⣶⠶⠶⠶⢶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣿⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⢀⠤⠤⠤⠶⡤⡴⠶⠦⠤⡤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠴⠶⠶⣿⠶⠶⢶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⣄⣀⣀⣀⣇⣇⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣼⣠⣄⣀⣀⣿⣀⣀⣀⣸⣀⣀⣀⣈⣉⣉⣛⣻⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⡟⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⢀⣁⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣷
⢰⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠙⠛⠛⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⣿⢺⣿⢺⣿⣇⣀⣠⣤⣤⣤⣤⣦⣄⣀⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠉⠻⡿
⠀⠀⠀⠀⠀⠈⠿⣦⣄⣀⣀⣰⣟⣛⣛⣛⣛⣛⣻⣿⣾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣸⣿⣻⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠀⠈⢁⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠸⠿⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⠶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⣀⣠⠤⠤⠴⠒⠒⢋⡿⠛⠉⠀⢀⣰⣆⣶⣰⣎⣻⡙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⠛⠻⣷⣆⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠁⠀⠀⠀⠀⠀⣸⢿⡶⠾⢿⣷⣋⣉⣉⣉⣙⣉⠉⢹⡝⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⡞⢡⣴⡞⢿⢿⣿⠻⣿⠟⣿⡗⢺⡗⠲⣾⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⡄⠀⡄⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣹⢻⡟⢻⡗⢾⣿⣼⣾⣾⣿⡷⣷⢾⣤⠶⠿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⡇⢰⣶⣰⣷⣰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣶⡆
⠀⠀⠀⠀⠀⠀⢹⣿⡞⣇⠘⠷⠟⣿⢼⢼⣿⣿⡷⡏⢸⡏⣇⢀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣷⢿⣿⢹⣿⣽⣿⣷⣼⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⣿⣷⡈⠓⠶⠦⢿⢾⢾⣾⣿⣷⡇⢈⣷⣇⣼⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡗⣾⣿⢺⣿⢻⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⣄⣤⡴⣿⢸⠈⠉⠸⡿⣧⣼⢻⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⠟⠘⠛⠈⡟⣿⣿⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⡓⢿⣾⠓⠒⠚⢿⣿⡶⠋⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⠋⠉⠉⢹⡏⣿⣿⣷⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠿⠟⠻⠶⠶⠛⠛⠉⢉⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡄⠀⠀⠘⣧⣿⣿⡏⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠛⠛⠛⣩⡟⢸⡇⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣟⡛⠛⢛⣉⣴⠟⠁⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡏⠉⠛⠋⠉⠁⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡼⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⡀⠀⠀⠀⣀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣿⣿⣿⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⣗⣿⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣗⢾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣭⠟⠂⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠘⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢷⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⣠⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⢻⠟⠉⠉⠉⠙⠛⠿⠛⢛⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣳⣾⣷⣿⠟⡡⠚⠁⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠟⠭⠓⠉⠀⠀⠀⠀⠀⠀⠐⠾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠙⠛⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠀⠀⠀⣀⣠⠶⠾⢿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡫⠄⠀⠀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣧⠲⣄⣀⣠⣴⠞⣁⡤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢋⠁⠀⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣄
⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⢿⣿⣿⣿⣿⠿⣿
⣿⣷⣾⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⣂⣠⣄⡀⠀⠀⠀⠀⠀⠐⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠈⢿⡟
⠿⠟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠋⠁⠀⡉⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⠀⠀⠀⠀⢀⢤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⡆⢷⣀⣶⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣿⣿⡜⣧⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⡟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢙⣿⣿⡘⣷⣶⣶⣦⣤⣤⣖⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⢛⣿⣭⣿⣯⣿⣭⣽⡿⢿⣿⣽⣁⡶⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠙⠛⢿⣿⣿⣿⣇⣤⣤⣬⣿⣍⠉⣉⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠉⠻⡅⠈⠁⠚⠋

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⡴⢫⠕⣲⣒⣒⣒⣲⣶⡶⡶⣶⣒⣟⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠙⠷⣦⣄⡀
⠀⠀⢸⠀⡇⢸⠔⠒⠒⠚⢃⣀⣿⣷⢿⣿⣷⡂⠀⢨⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠩⢗⡭⡻⢶⣄
⠀⠀⠸⡄⢧⣹⡓⠒⠒⣒⣳⣶⣦⣼⢿⣻⠷⠶⠶⠗⠊⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣉⠤⠼⠀⠙⢷⠄
⠀⠀⠀⠘⠢⠤⢌⣉⣀⣀⣀⣀⣀⣀⣀⣙⣄⡀⠀⢴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⢞⠕⠊⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠙⠢⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡰⣵⡧⣠⠤⢤⣖⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⠀⠀⠃⠀⠀⢀⢦⠀⠀⠀⠀⣜⡜⣸⡳⢿⢸⢠⢸⢦⡿⢟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⣀⣀⡠⠴⠋⢺⡆⠀⠀⢠⢿⢰⠁⢱⣸⢸⡇⣿⢸⠤⣄⠑⡜⡄
⠀⠀⠀⠀⠀⡠⠴⠒⣒⣒⣒⣂⣉⣉⠉⠩⢽⠩⠭⠭⠭⠤⠤⠤⡴⣚⣿⡇⠀⠀⠸⣼⠣⠭⣟⢸⣸⣇⡿⣸⣏⣁⣃⣱⣧
⠀⠀⠀⢀⢎⡔⢋⡡⢤⣤⣤⣤⣤⣤⣤⡤⠼⣦⠤⢤⡀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⢯⢿⣸⣝⡸⣻⣞⣷⣛⣷⡔⢣⢿⡇
⠀⠀⠀⢸⡜⢰⢻⣶⠾⢿⣋⡇⣖⣿⠿⣿⣿⣛⣻⡟⡍⠉⠉⠉⠒⢌⣿⡇⠀⠀⠀⠈⠫⡻⣻⡶⠺⠰⠸⠒⠛⢻⢟⠟⠀⣀⣀⡠⡄
⠀⠀⠀⠸⣧⠸⣟⣿⣀⣞⣿⣿⢻⣿⣎⣀⣀⠇⠀⡸⡇⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠛⠿⢾⣮⣼⡶⠾⠓⠉⠉⠉
⠀⠀⠀⠀⠹⢷⣌⡺⠷⠶⠶⠶⠶⠶⠶⠶⠯⢽⣋⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⣂⣠⣤⣤⣤⣤⣤⠤⡒⠒⢯⣾⡇
⠀⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠒⠒⣵⣿⠀⠀⠀⠉⠁⢹⠉⢉⣉⣉⢋⡏⢇⣀⣀⣀⣀⠀⠀⣹⠀⠉⠢⣽⠁
⠀⠀⠠⡋⠀⢸⠁⡇⠀⡆⠀⠀⢸⢸⠀⠀⠉⠉⠉⠉⠉⠻⡟⠀⠀⠀⠀⠀⠈⠉⠈⠒⠂⠙⠂⠐⠒⠒⠒⠚⠉⠉⠁
⠀⠀⠀⠑⠒⠚⠒⠓⠒⠓⠚⠛⠛⠿⠶⡤⠤⡤⠤⠤⠤⢤⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠛⠒⠛⠒⠒⠒⠒⠦⠤⠤⠤⠤⠬⠉⣉⣉⣉⣉⣉⣑⣦
⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣼⣷⣭⣿⣥⣵⣯⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠈⠉⣉⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠐⠒⠚⠿⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⢰⣿⡅⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⠉⠛⢷⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠐⠒⠂⠉⠉⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠻⣄⠀⠀⠀⠶⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⢠⠀⢳⡀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⢨⠿⠦⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣤⣄⣀⣀⣀⣀⣀⢠⣤⠔⠋⠁
⠀⠀⠀⠀⢸⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⢸⠶⣽⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠄⣸⠀⠈⠙⣦⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⡏⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⡜⠁
⡄⠀⠀⡆⢹⠖⠒⠒⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠀⠀⠀⡇⠀⠀⠀⠈⠉⠲⠦⣤⡀⠀⠶
⢧⡀⠈⠉⢸⠆⠀⠀⠀⠈⠳⢦⠀⠀⠀⠀⠀⠀⣀⠴⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢦⣀⣀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠙⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠀⠀⠀⡘⠃⠀⠀⠈⠉⠛⠛⠢⠤⣄
⠀⠀⠀⠀⠀⣿⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠙⡄⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⣆⠀⠀⡗⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⢧⣄⠐⠒⠈⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠈⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⣰⡆⠀⠈⣧⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠳⣤⡄⠄⠒⠠⠄⠘⢷⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠈⣿⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠙⠠⠤⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠛⣦⣤⣤⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠈⣤⠁⠀⠀⠀⠀⠀⠀⡍⠀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠁⠈⠁⠈⠀⠈⠉⠀⠈⠉⠁⠈⠈⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣠⣤⣤⣤⣤⣤⣀⡀⠴⠖⠒⠒⠶⢦⣤⠀⠖⠒⠒⠖⠢⣄⡀⠰⠶⠒⠶⠶⣤⣀⡄⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⠃⠀⠀⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣸⡆⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⢀⡆⠀⡄⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠸⡇⠀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⢀⠀⠀⣦⠀⠀⠀⢠⠀⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⢿⠀⠀⠀⠘⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢰⡀⠀⢸⡇⠀⠀⠀⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⢩⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⢸⠁⠀⠈⠀⠀⠀⠀⠇⠀⠀⠸⡇⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⡄⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⢁⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⠇⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠀⠀⠀⠃⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⡄⠀⠀⠀⠀⡆⠀⠸⠀⠀⠀⠀⠸⠀⠀⡆⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⡇⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⢄⠀⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⣀⡿⢧⣀⠀⠀⠀⣀⡿⢆⣀⣀⣀⣀⡠⠘⠛⠲⠶⠶⠶⠖⠉⠛⠑⠶⠆⠉⠁⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠶⡄⠐⠂⠀⠀⢲⡆⠐⠀⠀⠒⠒⠒⢶⠀⠐⠂⠐⠒⠀⠒⠀⠒⣤⠔⠂⠀⠀⠀⠀⢠⢰⣧
⣤⣤⣀⣤⣤⣤⣄⣠⣤⣤⣄⣤⣸⣷⣤⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣠⣤⣤
⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⠈⠟⠁⢹⠋⠈⠿⠀⠀⡴⠶⠄
⣿⣶⡶⠶⠾⠿⠛⠻⠿⢿⣟⠛⠛⠀⢐⣠⣤⣶⠾⠞⣛⣿⢛⣷⠟⢷⡾⢻⣄⡀⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢀⣴⠟⠉⢀⣠⠴⠛⠉⠑⠚⠛⠖⣾⡶⠚⠉⠛⠷⢦⣄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣿⠃⡀⠔⠉⠀⠀⠀⠀⣴⣤⢠⣆⡿⣧⣤⡀⠀⠀⠀⢹⡷⣦⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⡿⢁⠈⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⠏⢡⡿⠈⣇⠀⠀⠀⠈⡷⠈⢿⣧⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⡀⠁⠀⠀⠀⠀⠀⠀⢀⠠⠀⣀⢠⣅⠄⣀⡸⠿⠀⠀⠀⢀⠃⠀⠈⢿⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⣀⣤⣦⠤⣴⠤⢤⠀⣤⣶⣿⢴⣾⢍⡦⡿⢹⡾⣶⠐⣦⣤⣰⣦⣀⠈⣿⣷⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣰⣏⠀⠈⢳⡀⠀⢸⠶⠀⠀⡿⢲⡗⢨⠃⡇⠜⠁⠀⣤⠄⠀⠀⠀⠉⠹⣌⢯⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠻⣿⢧⡀⠸⡇⠀⢸⠀⠀⠀⣿⢰⠁⣘⢘⡧⠀⠀⠀⠆⡏⣦⡄⠀⠀⠀⢸⡎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣝⣲⣧⣀⡈⢀⠀⣀⡧⢸⣸⢯⣀⠁⠀⠀⠀⠆⡃⠁⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠄⠀⠀⠈⣹⠛⠿⣇⠸⠿⠿⡇⠘⣥⣌⠀⠀⠀⠀⢀⠀⡅⠀⠀⠀⠀⠀⣿⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⡀⢠⡴⠋⣀⠀⣧⢀⠀⢀⡇⢠⠀⣀⢀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣀⣼⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠙⠚⠓⠒⠛⠒⡧⠘⠛⠚⡇⣿⠙⢻⢹⠁⠿⠟⢿⠀⢷⡶⠿⠤⠍⠘⢁⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡆⠀⠀⠀⠀⣿⡆⠀⠀⡗⣿⠘⠋⢸⣤⠀⠀⢸⣤⠀⣷⠀⠀⠴⢁⠎⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠹⣄⠂⢊⠀⠛⠂⢰⡚⠃⠀⠀⣸⠓⠀⡟⠀⢊⡴⠋⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠀⠀⠘⢦⡀⠉⠁⠀⢀⣡⠠⠞⣡⠔⠋⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⠀⠀⠉⠐⠚⢛⣉⣴⠶⠋⠁⠀⠀⠀⠜⠁
⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢉⡉⠥⠞⠉⠀⠀⠀⠀⡀⠄
⠀⠀⠀⣻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢏⣠⠔⠚⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢘⣯⣻⢍⡙⠛⠻⠶⠶⠦⠦⠶⠤⠖⠲⠚⠐⠊⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠘⣷⡌⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⡹⣿⡿⠿⠿⠟⠳⠒⠒⠘
⠀⠀⠀⠀⠀⠘⣩⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠑⡆⣀⡀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⡤⠄⠙⠄⠀⡀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣀⠀⠈⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⣴⡏⠠⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠅⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠇
⣶⣶⣶⠶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡾⠛⠀⠀⠀⠀⡜⡔⠙⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⠋⢀⠃⠀⠀⠀⠀⡇⡇⢀⡿⣾⡀⠀⠀⠀⠀⠀⠀⣴⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣴⡇⣼⠀⠀⠀⠀⠀⣿⣫⠜⣿⠉⡇⠀⠀⠀⠀⠀⣴⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣤⢹⣿⡇⣿⠀⠀⠀⠀⠀⢹⣇⠀⣰⠒⣇⠀⠀⠀⠀⣼⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⡲⠈⢧⢻⣧⠹⡄⠀⢀⠀⢄⢸⣋⡥⢻⣾⢹⠀⠀⢀⡾⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠁⠙⢷⣜⢦⡈⣧⢟⠘⣇⣀⠸⢻⡸⡆⢀⡞⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣻⠏⡘⣇⡴⠚⣿⡇⣧⠊⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⡻⣼⠀⢻⣷⠛⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣴⣶⠿⠛⢉⣉⣀⣈⠒⠦⣄⡀⠀⠀⠀⢉⠙⠲⣅⡺⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠠⠟⣩⠴⠒⠉⠁⠀⠀⠈⠉⠒⠦⣙⠲⢤⡄⢸⠀⠀⠀⠙⠲⣝⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢁⡴⠋⠁⠀⠀⢀⠄⠂⢉⣀⠀⠉⠒⠤⣍⡒⠆⢸⣦⣄⡀⠀⠀⠀⠙⠪⣑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⢠⠁⣠⠊⠁⠀⠀⠈⠐⠠⢄⣉⠃⣬⢿⣷⣯⣗⣤⣀⠀⠀⠀⠁⠈⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⢀⡛⣏⡛⢤⡠⢉⠒⠌⡙⠀⠽⣿⣿⣦⢄⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠱⣄⠀⠀⠠⡬⠁⣤⣛⡌⠃⢄⡈⠐⢢⣑⢤⣈⠈⠋⢝⠿⣶⡀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣈⠹⣲⠤⣀⠀⠠⡶⢅⡀⠀⠨⠕⡢⢁⡀⣿⡟⣶⠤⡈⠢⡙⢦⡀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢍⡓⠵⣖⡿⣶⠬⣑⡢⠀⠀⣹⠀⡿⣧⠸⡆⠈⢢⠈⡆⠹⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣦⣭⣓⠺⢾⡿⢗⣦⣍⣂⠿⢿⣀⣇⠀⣸⠃⡇⢀⠇⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡾⣿⠃⠈⠉⠒⣤⣄⡉⠉⠂⠿⣶⡤⠭⡍⠥⠊⣠⠎⠀⠀⢘⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣿⣷⡆⠀⠀⠀⠀⡍⠃⢹⠷⣦⣤⣀⠈⠉⠛⠛⠋⠁⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⢋⣴⣿⣿⣹⠃⠀⠀⠀⠀⠁⢸⠘⢃⡟⣴⠌⠛⠓⠶⠶⣶⣞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠿⣿⣿⡏⣿⠀⠀⠀⠀⠀⢸⠸⡠⣟⣀⠥⣤⡶⠶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢿⡄⠀⠀⠀⠀⠈⡀⡇⢹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣇⢦⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⢀⣿⠋⠁⢹⠀⠀⠀⠀⠀⠀⢀⣏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⡜⠹⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⢀⣾⡿⠀⠀⢀⣠⣄⡰⠀⠀⠉⠀⠀⠀⠀⠀⡀⠠⠆⣤⡄⠰⠖⢀⡆
⠀⣀⣀⣀⣀⣀⣷⣿⣿⣁⣀⣀⣻⣿⣿⣃⣀⣀⣀⣀⣬⠠⠤⠤⠬⠞⠀⠀⠀⢉⠠⠄⠃
⠀⠉⠉⢉⣽⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⡖⣄⠰⠆⠈
⠀⢀⣰⣿⣿⣋⣹⣆⣀⣀⣀⣀⣀⣠⣤⣤⠤⠤⢤⠦⠤⠒⠒⠚⠿⡃⢈⡤⠄
⠀⣹⣿⠟⠉⢉⣽⣿⣶⣦⣄⠀⠀⠀⠀⡰⠚⢛⡎⠀⠀⠀⠀⢀⣦⠏
⠀⣿⣏⣀⣠⣿⣟⣻⣛⣿⣿⣧⣤⠤⠤⠬⠿⠿⠒⠒⠒⠋⠉⠙⡏⡆
⠀⢻⡏⠉⢹⡏⠉⠸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡤⠜⡇
⠀⠀⢳⣄⣀⣛⣄⣀⣧⣠⣼⡿⠤⠤⠴⠖⠒⠒⠛⠉⣉⣁⡀⠁⢀⡆
⠀⠉⠉⠉⠻⠭⢥⣤⢿⠖⠋⠀⠀⠀⠀⣶⣿⡆⠀⣐⣿⡿⠷⠒⠉
⠀⠀⠀⣀⣀⣀⣀⣀⣼⣧⠤⠤⠴⠶⠒⠛⠛⠋⠉⠁
⠀⠉⠉⣹⣿⣿⣇⠀⠀⣧
⠀⠀⠀⢻⣿⡿⠏⠀⣠⠏⠀⠀⠀⠀⠀⠀⣤⣴⡶⠶⠿⠃
⠀⠀⠀⠀⠉⠛⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⢈⣿⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⣰⣿⡿⠁⣠⡾⠁⠀⠉⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣿⣿⠀⠀⠀⢀⣾⣿⠏⢀⣴⠏⠀⠀⢀⣼⠋⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⡟⠁⣠⡾⠁⠀⠀⣠⡟⠁⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣾⣿⠋⢀⣴⠏⠀⠀⢀⣼⠋⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⣿⣿⣿⡟⠁⣠⡞⠁⠀⠀⣰⡟⠁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⢀⣼⠋⠀⠀⢀⣼⠋⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠟⠁⠀⠀⣰⠟⠁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢀⡾⠋⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣰⠟⢁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⡾⠋⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣴⠟⢁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢠⡾⠃⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⣴⠟⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⣿⣦⣄⣠⡾⠃⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠛⢿⣿⣦⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣀⣤⣶⣾⣿⠿⠛⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡀⠀⢀⡤⠀⡀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠠⢽⣂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣼⠋⣀⣘⣷⢾⣃⡀⢣⣬⠟⣀⣀⣀⣠⣤⡶⡊⠀⠼⠀⠀⢿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⢚⡩⡵⣤⣀⣀⢽⢾⢄⣉⣭⡿⣍⣉⣉⡁⢀⣀⣀⣀⣠⠄⠀⢀⣾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣏⣴⣞⣿⣛⣿⡗⢛⡟⠛⣿⡛⢻⣿⣾⡟⠋⣿⡿⠿⠿⠛⠿⠿⣟⣀⣤⣤⣼⣻⠄
⠀⠀⠀⢈⣄⣷⣠⡀⠀⠀⢀⣠⣾⡾⠿⡭⠿⠅⠀⠀⠿⠷⠾⠴⠠⠿⠷⠹⠤⠿⣧⣾⣯⣴⣖⡀⠠⢀⠀⠀⠩⢉⣛⣿⠹
⠀⠀⠀⠈⠙⣋⢙⡯⠉⠉⠉⣭⣭⣭⣭⣯⣭⣩⣭⣿⣿⡟⢻⣿⢿⡿⠿⣷⢖⡒⠚⠛⠳⠲⠟⢿⣳⣦⣄⡀⠀⠀⠉⠛
⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⡇⢸⣇⣇⡔⠉⢀⣀⠀⡼⠧⠾⠷⠸⠷⠶⠿⠸⠷⠼⢿⡗⠶⠦⣄⠈⠻⣧⠉⠳⣤⠲⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⡿⠊⠀⠉⣀⠀⣤⣾⣤⣟⣛⣂⣂⣒⣂⣀⣀⣀⠀⠐⠖⠿⢳⡀⢺⡆⠀⠘⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢿⠃⠀⣰⣧⣀⠀⠸⠿⠿⠥⠿⣾⣟⣸⡽⡏⠀⢹⠀⠱⠀⠰⣾⡇⠀⣇⠀⠀⢹⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⢀⡇⠉⠙⣦⠀⠉⠩⢁⠈⢉⣉⣉⡍⠊⠀⢸⠀⠀⢀⢠⢹⡇⠀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡜⡇⠁⠘⠀⠰⠨⠬⠤⠭⠬⠭⠤⢀⣠⠀⠙⣗⣚⣥⣫⡞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣝⠦⢄⡀⠀⠲⣶⣶⣦⣿⣚⣛⣛⣛⣿⣃⣈⣭⠭⠁⢂⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠏⠙⠛⢛⣛⠉⣉⢉⣉⣩⣭⢡⣀⣀⡤⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠉⠉⠁⠀⠈⠁



⡖⠒⢲⠖⠶⠶⠶⠶⡖⠶⠶⠶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⡶⡶⢶⣶⠶⠶⢶

⠶⠚⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢌⡑⢌⣿⣿⢷⣝⡡⡢⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠶⢛⣉
⠞⣋⣩⡄⠀⠀⠆⣠⠆⣠⠆⣠⠦⣹⠦⣹⠦⣽⣿⣻⢮⣼⠔⣡⡦⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⣋⣥
⣛⣩⣤⠦⠀⠀⠀⠁⠞⣡⡾⣍⡷⣍⡶⣍⡶⣿⣿⣝⡷⣡⣾⢋⡴⣿⣿⣳⣀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣏⣭⣴
⣏⣥⠶⠞⡀⠀⠀⠠⡘⢮⡽⢯⡵⢯⡵⢏⡵⢿⣿⣯⣿⢟⡵⢫⣾⢿⣿⣿⡿⣿⣽⣹⣱⣱⣻⣹⣻⣿⣿⣿⣿
⣽⣟⣾⣿⣅⡠⣌⢳⣌⣲⡌⣫⣽⣯⣽⣯⣽⣯⣹⣮⣱⠊⣠⠊⣠⢟⣛⣻⠑⠳⠳⢣⢣⢣⢣⢧⢯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⢿⣷⠿⣫⠞⣡⠞⣡⣟⣻⣿⠁⠀⠀⠀⠀⠀⠉⠋⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⢁⠜⢁⠜⢁⠔⢁⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢋⡴⢋⡴⢋⣹⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠋⡠⠋⣹⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠢⠢⠘⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠞⣩⣭⣽⣄⣀⣀⣀⣀⣄⣄⣤⣄⣤⣌⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⣽⣿⣿⣿⣿⢿⠝⠿⠿⠟⠽⠽⠿⠝⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⢰⡄⢻⣄⢿⣿⣿⡿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⣶⠈⣷⡈⣷⡈⢷⡈⢷⣬⣛⢿⣿⣿⡿⣫⠿
⠀⠀⠀⣀⠠⣄⠰⣦⠸⣇⢸⣧⢸⣧⡸⣧⠘⣧⠘⣧⠘⣧⣸⣽⣻⢿⣿⣿⣟⣷⠇⠀⠀⠀⠀⠀⠀⢀⡤
⡄⢻⡄⢻⡄⢻⡆⢻⡆⢹⡆⢻⡇⢹⣇⢹⣆⠻⣶⠹⣇⣽⣾⣝⡻⣷⣾⣿⣯⡞⠀⠀⠀⠀⠀⠀⢰⣿⠶⢿⣏
⢿⡈⢿⡀⢿⡀⢿⡀⢿⡄⢿⡄⢻⡄⢻⡄⢻⣾⣿⣶⣿⣿⣿⣿⡿⣿⣯⣿⡻⡝⣆⢧⢳⡸⡎⣷⢮⠶⢺⣋⣿
⡘⣧⠘⣷⠘⣷⠘⣷⠈⣷⠈⣷⡈⣷⡈⢿⡈⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⢧⢹⡸⡌⣇⢧⠹⠘⠶⠞⣋⣻⣿
⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⢻⡹⡜⣇⢧⠹⠸⠜⠃⠃⠉⠀⠀⠀⠀⠐⢛⣩⡤⠶
⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⠆⠃⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⣥⠶⠞
⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⠢⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⠴⠞⣛
⣶⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣌⣿⣯⣷⣽⣣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣴⣖⣛⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⠇⢀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡾⠀⡞⡄⠀⢸⡀⠀⠀⠀⠀⣀⣴⡆⢉⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣫⣍⡁⠀⢸⠑⠃⠐⠾⡇⠀⠀⠀⠀⣿⣿⣿⣞⢩⡿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⢸⣏⢻⣿⣷⣾⣞⣀⣀⣀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⢹⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡟⡻⣿⣿⡇⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣾⣯⣻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⣅⢠⣿⡿⠁⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠈⣿⡗⠒⠛⢛⡻⢿⣧
⠀⠀⠀⠀⠀⠀⢸⡏⣸⡟⢀⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⣿⣿⣷⠙⣇
⠀⠀⠀⠀⠀⠀⣴⢣⠏⠀⢨⣿⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣛⣉⣼⣿
⠀⠀⠀⠀⠀⠀⠺⢾⠀⢀⡟⠙⡁⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⢰⣼⣷⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⡋⢻⠼⣿
⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡟⠀⠠⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⢸⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⡇⠀⢀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢿⣞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡟⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡈⢻⠆
⠀⠀⠀⠀⠀⠀⠠⠶⠿⠋⠁⠀⠹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣼⠇

⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄
⠀⠀⠀⠀⠀⠀⢸⣠⣾⠃
⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⢀⣾⠟⣁⣷⣤⣄⠀⠀⠀⠀⢠⠶⠚⢻
⠀⠀⠀⠘⣿⠰⡟⢹⡍⢻⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠘⠢⢭⣪⣷⠞⠁⠀⠀⠀⣤⠇⠀⠛⠃⠀⠀⠘⡳⡄
⠀⠀⠀⠀⠀⣠⣤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠻⠿⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠀⠀⠀⢠⣀⠀⠀⠀⠀⢸⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⢸⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠘⠛⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠀⠀⠤⡴⠣⠂⣤⣀
⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠀⠀⠀⠀⠔⠃⠀⢀⠼⠁⠀⠀⠀⠈
⠠⠄⡁⠁⠀⢸⠀⠀⠙⠀⠢⠴⠀⠀⠀⠀⠽⠀⢀⠦⡀⠀⠀⠀⣀⡤⠤⠂⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⢰
⠈⠀⠀⠀⠀⠘⠆⠀⠠⠀⠀⠀⠀⠀⠀⠐⢢⡄⠀⠀⠀⠠⠤⢐⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠐⠁⠀⠈⠀⠉⠁⠀⢀
⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠎⠀⢀⠄⠀⠀⠀⡀⡠⠴⠒⠀⠉
⢀⠠⠄⠀⠐⠐⠖⠄⠄⠠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡠⠀⠁⠀⠀⢠⠾⠀⠠⠟⠋⠋⡡
⠀⢀⢀⠀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⡤⠊
⠀⠃⠀⠀⠀⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⡐⠀⠀⡟⠀⠀⠌⠀⠠
⠀⠀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠐⠁⠀⠀⠀⠀⠀⡖⠁⠀⢀⠃⠀⠀⠀⠠
⠀⠀⢠⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠀⠀⠀⠀⠃⠉⠀⠀⠂⠀⢀⠀⠀⠀⢀⣀⢳⡀⣠⠂⠠⡄⠠⠀⠤
⠀⠀⣬⣇⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⡸⡆⠀⠂⢓⠀⠐⠂
⠀⠀⠏⠀⠀⠀⠀⠀⠩⠃⢀⣀⠀⠀⠂⠀⠀⠀⠀⠉⢠⠈⠀⠀⠀⠀⠀⢀⠀⠀⠠⣤⠀⠀⠀⠈⠀⠀⠀⠀⢀⣶⡀
⠀⣸⠀⠀⠀⠀⠀⡰⠁⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠉⠱⡀⠀⠀⠀⠀⠈⣧⠔⠚⠉⠢⠀⠀⡄⣀⢀⠀⠑⠌⠀⠁⡀
⠀⠧⠀⠀⢄⠀⠞⠀⠐⠀⠀⠠⠀⠠⠀⠀⢁⠐⠀⠀⠀⠀⢠⡀⠈⣀⠀⠂⠀⠇⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠘⠣⣄
⠀⠀⠀⢠⠀⠞⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⣤⠔⠂⠐⠃⠂⠤⣀⠀⠀⠂⠈⠉
⠀⡆⠀⠀⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⢀⠀⠢⡀⠀⠀⡤⠤⠰⠂⠀⡥⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠙⠒⠂⠤⣤⡀
⠀⢣⡀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣇⡀⡜⠂⣀⠀⠀⠀⢀⡀⣆⡀⢤⠠⠀⢀⣀⡀⠀⠀⠠⡁
⠀⠀⣧⢠⡅⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡘⠉⠁⠉⠙⢍⡀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⢹⠂⠆⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠄⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⡀⠀⣀⣠⣅⣀⠀⡀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠋⠈⠙⠚⠉⢉⣻⣿⣿⡟⣻⠛⠛⠛⢛⠓⠒⠲⣶⡇⠀⠀⠀⡜⢠⡟⠉⠀⡀⢹⢳⡌⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠈⠲⠾⠶⠿⣿⣿⡿⠿⠿⠶⠷⠚⠀⠀⠀⠈⠁⠀⠀⠰⠁⢾⣀⢴⡜⢩⣷⠈⡇⡇
⠀⣾⣿⣿⣷⣄⠈⠙⠉⠰⣄⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀⣸⡿⣿⣿⣿⣟⣆⠇⡇
⠀⣿⡿⠿⠛⢿⣶⣾⣿⣶⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⢰⠀⢹⣇⢾⣿⣟⣷⣿⣆⡇
⠀⠘⡇⠀⠀⠀⠙⠿⠿⠻⠉⠙⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⣒⣺⣓⠺⢗⢣⠀⠀⠀⠀⠀⣼⠀⢸⣿⣾⣿⣼⡿⢰⡏⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⣮⣼⣧⣽⣆⣀⣷⡀⠀⠀⢄⣀⡇⠀⢸⣿⣯⣽⣿⣳⠿⡇⡅
⠀⠀⠀⠰⠓⢲⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡀⠁⢹⣿⣿⣿⣿⡿⣿⡐⣕⡁⠀⠉⠀⡏⠉⢹⣿⡿⠘⠙⠛⠀⢠⠁
⠀⠀⠀⢠⠞⡫⠅⠒⢘⣯⠥⡶⢶⣤⣀⠀⠀⠀⣶⡀⠀⠀⣿⠖⣺⣿⣛⣻⣿⡿⠟⠸⢳⡇⠀⠀⠀⡇⠀⠀⣿⡑⠤⣤⣠⠵⠋
⠐⠀⡰⠡⠂⠀⠀⠀⠀⠉⠀⢈⣦⣿⣿⣆⠀⠀⠀⠈⠲⢦⣀⣺⢄⣀⢸⠀⣨⠁⠄⡡⠋⠀⠀⠀⣼⠁⠀⠀⢻⣇
⡄⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣽⠟⠀⠀⣆⣀⣠⣶⣤⣭⣬⣭⡭⠭⠽⠒⠋⠀⠀⠤⠄⠼⠧⠀⠀⠴⠧⠿⠷⠦⠄
⢧⠀⣇⠀⠀⠀⠀⠀⢰⡾⣛⢛⣿⣿⢻⠀⠀⠀⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠘⣆⠘⢦⡀⠀⠀⠀⢼⣦⣷⡈⣱⢃⡞⠀⠀⠀⡟⠀⠀⠀⡤⢤⠤⢶⡦⠤⠤⠤⢤⣤⠤⠤⡤⣤⣤⣬⣡⡄
⠀⠈⠳⣌⡛⠦⣄⣀⣀⣻⡵⠟⣡⠎⠀⠀⠀⠀⠇⠀⠀⢀⠀⢸⠀⢰⡀⠀⠀⠀⠀⡏⣿⠉⣻⠉⠈⠛⠛⠟⠒⠒⠒⠒⠒⠂⠒⠒⠖⠲⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⣶⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⣟⠉⠉⠉⠉⠉⠉⠁⠀⠀⢻
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣠⣤⠤⠶⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡉
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢌⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢄⠁
⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠛⣻⢆⣤⣄⢀⣠⣀⡀⠀⠟⣀⣀⠀⣠⣴⡇⢠⢤⠀⣦⠞⠀⠀⣿⠢⡀
⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⢯⡁⠸⣏⡉⠰⡏⡟⣷⢸⡇⣿⠉⡇⢯⠞⣇⠘⢯⠀⠻⠀⠀⠀⣯⠑⠄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠁⠀⠈⠁⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡱⠄
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢆⠙
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢫⡈⢢⠁
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣾⡟⢯⠙⢄⠑⢄
⠀⠀⠀⢰⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡉⢦⠑⣄⠳⡈⠳⡀
⠀⠀⠀⠀⠀⠉⠉⢯⠻⡉⢻⡙⢟⠛⢿⠛⢟⠛⣟⠛⣟⠛⢏⠉⢣⠘⢆⠑⡄⠱⡌⢢⡙⠄
⠀⠀⠀⠀⠀⠠⡌⠆⠣⠱⠄⠱⠌⢢⠀⢣⡈⢣⠘⣆⠈⢆⠈⢣⠀⠳⡈⢦⠈⠦⠈⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠙⠛⠛⠓⠒⠐⠛
⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣋
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠉⠉⠹⠗⠀⠀⡀
⠀⠀⠀⠀⠀⠿⣿⠟⠋⢉⣿⣛⡻⠿⢥⣴⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⣷⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣉⠙⠛⣶⣦⣿⣿⡳⡞⢃⠀⣄⡀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠿⠿⣿⣿⣿⣧⣈⡙⠾⠛⠛⠳⠶⣽⣡⡿⢾⣿⣿⣷⠼⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣤⠒⠿⣖⠾⣿⣿⣿⣿⣿⢧⢤⣤⢶⠶⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣦⣴⡿⣭⣹⣿⠿⠿⠃⠀⠈⠀⠀⢿⣷
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠈⡿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣳⣀⢠⠎
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢌⢿⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠨⠓
⣿⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣯⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠠⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣤⣴⣾⣯⡍⣽⣿⣷⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢠⣝⠁⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣿⣿⡾⠻⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢿⢟⣁⡴⠟⠉⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⠀⡀⢀⣤⣴⡶⠾⣿⣾⠇⠀⠀⠀⠀⢠⡞⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⡏⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢠⡿⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡄⠀⠀⠀⢀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠤⠁⡀⡀⠀⢸⠀⠀⠀⠀⡌⠀⠀⠀⢻⣼⣿⣯⣸⣧⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⣄⢃⠀⣾⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⣀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⡿⣯⢒⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠲⠀⢄⡀⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢫⡀⢙⣄⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠶⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⣿⣿⣿⢿⣼⣦⠀⢀⣀⣠⣤⣤⣶⣶⣾⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣅⠀⠜⣇⠙⠿⠿⠿⠟⠛⠛⠛⠛⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣭⣽⣿⣶⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣴⣶⣦⡀⡀⠀⠸⢗⢸⣿⣿⣀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣿⣿⣿⣷⣹⡶⡀⠀⣬⣿⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢯⣿⣇⠘⣧⣻⣽⣧⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢯⣙⠛⣞⣱⣿⣿⣿⣆⠈⣿⣿⣿⡆⣿⣻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠙⢟⣿⠄⠸⣿⣿⡆⠘⣇⢻⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠙⣿⡇⠀⢹⢼⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣶⣦⣽⡀⠀⣼⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚
⣿⣿⣿⠿⢿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠲⡀
⠀⠀⠈⢆⠀⠀⠀⣀
⠀⠀⠀⠀⠑⢄⣼⡿⣆
⠀⠙⢄⠀⠀⢸⡟⠤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠑⢤⣸⠁⣠⣿⠓⠢⢀⣀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡶⠶⢶⠀⠀⠀⠀⠀⠀⢀⡀⠠⠖⠀⠀⠐⠂⠋⢀⠀⠒⠀⢠⡀⠀⠠⠄
⠀⠀⠀⠀⠀⣨⣷⣿⣇⠀⠀⠀⢸⠉⠁⠀⠀⠚⠉⠁⠰⠛⠂⠀⠀⠀⠀⢠⠄⢠⠄⠈⠀⠀⠐⠃⠉⠁⠀⠀⢈⣠⡔⠂⠀⠈⠀⠐
⠀⠉⠲⣤⣴⣿⢿⠁⠀⠉⠐⠒⢸⠄⠠⠀⠀⠐⠂⠀⢀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠃⠀⠀⠈⠁⠀⠖⠂
⠀⠀⢠⣿⠟⠓⣸⣤⣄⣀⠀⠀⢸⠉⣿⡀⠀⣀⡆⠀⠈⠉⠁⠀⣾⡷
⠀⣀⣿⡏⠀⣼⠿⣿⠻⢿⣧⠉⠹⠋⠁⠀⠐⠿⠃
⠀⠈⢹⡗⠶⢯⣤⣼⣄⣈⣿⠤⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠙⢦⣀⠁⢀⣧⠴⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⠿⠋⡄
⠀⣀⣀⣀⣀⣈⣉⣉⢽⡤⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⠠⡄⠀⣤⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⠰⠆⠁⠰⠃
⠀⠀⠀⠀⣼⣿⣧⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢹⣷⠰⠀⠛⠁⠀⣀⢀⣄⠘⠋⠜⠛⠀⠀⡉⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠻⢿⣋⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡟⠀⠀⠀⠀⠈⠉⣈⡁⠀⠀⠀⠀⠀⠀⡘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠉⠉⠙⠛⠃⠀⠀⠀⠠⠀⠀⠀⢀⠉⠓⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⣤⠀⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣫⣾⣿⣿⠿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣡⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⡾⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⡾⣫⣴⣿⡿⠿⢿⣷⣄⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣾⠟⣡⡾⣫⣾⡿⠋⠁⢀⣠⣀⢹⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣄⠀⠀⣰⢁⡴⠋⣡⡾⣫⣾⡿⠋⠀⣠⡾⠋⢁⣿⣸⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⣶⣜⣿⡛⠦⣿⠋⣠⠞⣡⣾⡿⠋⠀⣠⠞⠁⢀⣴⣟⣵⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣽⣯⠉⠳⣄⠀⠺⣡⣾⡿⠋⠀⣠⠞⠁⢀⣴⢟⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠳⣄⠈⠳⣄⠈⠉⢀⣤⠞⠁⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⣄⠈⠳⣄⠈⠳⣄⠈⠁⢀⡴⣻⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⣿⣿⣿⡗⠀⠈⠳⣄⠈⠳⣄⠈⠺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡵⢋⣼⡿⣿⣝⢿⣦⣱⣄⠈⠳⣄⠈⠳⣤⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣵⡿⠋⠀⠈⠻⣷⣿⣿⣿⣷⣄⠈⠳⣦⣽⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋
⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠹⢿⣦⣤⣤⣤⣴⣾⡿⠋
⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁
⠀⠰⢾⣿⡏
⠀⠀⠀⠙⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢀⡄⠀⠀⠀⠤⠤⠤⠠⠀⠸⠥⠀⠀⠀⠀⠀⠒⠛⠶⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠠⠅⠴⠆⠒⠒⠒⠂⠀⠀⠀⢺⠁⠀⠀⠀⣶⠆⠀⢠⠠⠠⠤⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠓⡆⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠄⠀⠀⠠⠄⠠⠄⢴⠖⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠈⠀⠀⠀⠀⠀⠐




⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⡀⠀⠀⢐⢦⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⣁⡀⠠⠼⠤⠤⢤⣤⢄⣙⣀⣉⢁⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠐⢸⡡⠶⡄⠀⠐⠒⠚⠓⠢⣤⠤⢬⣍⣉⣙⣛⠒⠒⠶⠦⠤⠤⢤⡶⠤⠤⠤⠤⡤⠤⠤⠒⠒⣲⡃⠉⠛⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⢀⢵⡚⠃⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠛⠒⠂⠀⠀⠀⠉⢀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠸⠀⠀⠀⣀⣠⠤⠤⠴⠶⣶⠶⠷⠤⠤⣄⣀⣀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠁⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠤⢴⡿⠶⣾⠿⠟⠿⠯⠭⣖⣒⠒⠶⠬⢭⣄⣀⡀⠀⠀⠀⠉⠉⠙⠛⠒⠦⠤⢤⣄⣀⡉⠉⠉⠉⣉⣡⡄⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⢤⣉⣙⡒⠶⠤⣄⣚⡁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠒⠒⠮⠭⠿⠶⠶⠮⠤⠴⢤⣀⣀⢠⠤⠤⡾⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠾⠶⠶⠶⠿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠶⠶⠦⠶⠶⠆⢿⡆
⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⢸⡇
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⣶⣦⣄⣀⡀⠀⠀⠀⢉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠉⠉⠉⠙⢿⣿⣧⡀⠀⣴⠏⣀⣴⣶⣤⣤⣀⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⢰⣯⣼⣿⣿⠿⠛⠛⠿⠿⠶⣄
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡄⠀⣠⣤⠚⠿⠛⠛⢹⣿⣷⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠲⠿⠋⢀⣠⣤⠀⠘⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠀⠘⣻⠷⢶⣦⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠶⠟⣹⣿⣿⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠙⣾⣿⣿⣿⣿⡿⣿⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠇⡟⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⣀⣤⣤⡤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣧⣿⣤⣿⣿⣿⣿⣿⣄⠀⠀⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣧⠀⣰⣿⣿⣿⣧⡿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⠿⠿⠛⠋⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠻⢿⣿⣿⣿⣷⣄⠙⣿⣏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⣿⣿⣭⣟⠛⣷⢸⣏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣿⣿⣶⣤⣄⡀
⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡆⢸⣇⢘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣘⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣞⠓⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣼
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠛⠋⠉⠁⠀⠈⠛⠋⠀⠀⣿
⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣷⣤⣤⣴⣶⣶⣦⡤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿

⠄⠀⠀⠀⠀⠀⣿⠁⠀⠈⣿⠿⠟⢻⣿⣿⡟⠉⠀⢈⣿⣟⠉⠉⠙⠋⢈⣿⣿⣿⣟⠀⠀⠀⠀⠰⠷⠄⠸⢿⠋⠀⠐⠀⣹⣿⣿⣿⣿⡇
⣇⠀⠀⠀⠀⣰⣿⣷⡖⠈⠀⠀⢀⠘⠛⠛⠻⠶⣾⡍⠉⠉⣠⣿⣷⡶⠈⠉⠙⠿⣄⣰⣶⡖⠀⠀⠀⠀⠀⢀⡽⣿⠏⠀⠐⠀⠀⢹⣿⣿⣶
⣷⡀⣀⣴⣶⡄⠀⠀⢱⡤⠀⠺⡟⠀⠀⠀⠀⠀⠈⡫⠈⠻⣉⣻⣿⡇⠀⠀⠀⠀⠹⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠘⠉⠁
⠻⠿⠿⣯⣿⠃⠀⠀⠀⠁⠀⠀⢰⣄⠾⠀⠀⠀⢠⣧⡈⠂⠈⠁⠀⠸⣶⡦⣴⣶⣿⣶⡾⠟⠃⠀⠀⠀⠀⠀⣠⣎⣀⣀⣀⠴⠒⠂⣀
⣤⣀⠀⠀⠀⠀⣰⣶⡿⠈⠀⠀⣘⢡⣿⣷⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⡿⠦⢿⡏⠉⠙⣀⠀⠀⢀⣿⣶⡶⠞⠉⠉⣿⣿⣿⣦⣤⣴⣿⣿⣶
⣻⡿⠛⠛⠉⢉⣻⣿⡿⠿⠿⠿⠿⠿⠋⣻⣿⣥⣀⣠⣦⣀⣀⣠⣤⡀⠀⠀⣠⣦⣷⠤⠛⠋⠀⠽⢻⡿⠛⠓⢲⣴⠟⠋⠉⠉⠉⠛⠛⢿⡜
⣻⣇⣀⣠⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠛⠉⠛⠛⠛⠛⠉⢉⣶⣿⣿⣏⣁⣀⠀⢀⣀⠐⠛⠃⠀⣴⡿⠿⠂⠀⠀⠀⠀⠀⠀⢀⣷
⣿⣿⠿⠛⠲⣄⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠈⠻⠧⠀⠈⠹⣿⠟⠋⠠⢹⣶⣤⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠿
⠉⠀⠀⠀⠀⣾⠷⠀⣴⣦⣄⠀⠀⠀⢀⣴⣿⣽⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⣠⣆⢠⣿⣷⣦⣴⠿⠛⠦⡀⠀⠀⠀⣠⣆
⣀⣀⣀⣤⠂⠀⢀⣠⣷⣿⣿⡋⠀⠀⠀⠀⠉⠙⢻⡿⠋⠉⢡⠄⣄⣀⣀⠀⢀⠴⠟⠛⠻⠏⠉⠉⠙⠛⠟⠁⠀⠀⢀⡿⠖⠀⠈⠉⠉⠐⠚
⣿⠿⠛⠃⠀⠀⠿⣿⣿⠛⣿⣷⣦⣄⣀⣀⠀⢀⣠⡀⠀⠀⣀⠠⠚⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣿⠉⠀⠁⠀⢹⣿⣿⠋⠁⠀⠉⠋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠗⠀⠀⠤⣾⣿⠿⠀⠀⠀⠀⣠⣿⠿⠿⢦⣄⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣀⣤⡆
⣧⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠁⠀⠀⠀⠈⢋⣠⡤⠀⠶⢾⡏⠀⠀⠀⠀⠈⠹⣿⣿⡅⠀⠉⠙⠛⠋⠀⠈⠉⠙⣄⡀
⣿⣷⡶⠖⠡⠛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣇⡀⠀⠀⠀⠈⢢⣄⣀⣀⣀⡋⠟⠛⠓⢀⡀⢀⠀⠀⠀⠀⠀⢠⣽⡿⠦
⡴⠋⠀⠀⠀⣰⣿⣶⣤⣤⣀⣀⣀⣀⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣷⣶⡶⠞⠛⠐⠉⠁⠀⠀⠙⠂⠀⢀⣀⣠
⣀⠀⠀⠀⣰⣿⣿⣶⡤⠀⢿⣿⣿⡏⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠿⠛

⠀⠀⠀⠀⢀⠀⠀⠀⡀⣤⢰⠒⠐⠄⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⢺⡁⠀⠑⠉⠁⠀⠀⢂⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠦⢄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⢴⠀⠀⠀⢀⠄⠀⠀⣀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠰⠶⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢠⡢⠀⠀⠄⠀⠀⠸⡆⠀⠀⠀⠀⠀⠁⠀⠂⠀⠠⠀⠀⠀⠒⠀⠀⠀⡀
⠀⠀⠀⠀⡸⠀⠈⢀⡴⠞⠁⠀⠀⠀⠀⠠⠀⢠⡠⣐⣒⣀⠄⠀⠀⠹⡁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⢘⡤⡀⠈⠈⠀⠀⠠⠀⠀⠒⠀⠈⠌⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⣋⣉⣩⣻⣏⣉⣉⣹⠀⠀⠈
⠀⠀⢈⣌⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠐⠒⠀⠀⡁⠀⢔⠂⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠲⠀⠠⡀⠀⠀⢀⠀⠀⡐⠀⠠⠘⠐⠁⢄⠖⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢳⠀⠀⠀⢁⢄⠀⡇⠐⡀⠆⢑⡠⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠁⢀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠋⠀⠈⣸⡏⠀⠀⢰⡇⠀⠀⢶⣶⢀⡀⠀⡀⡀⠀⢤⡀⠀⠀⠀⠀⢀
⢀⣀⠀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠲⠤⡁⠁⠀⠈⡿⠂⠀⠀⠀⡒⠀⠀⢁⠰⡀⠀⠙⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢂⢀⣀⡀⢀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠀⠀⠀⠀⠈⠂⡀⠐⢎⠣⠙⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠱⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠱⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠂⠈⠀⠀⠀⠂⠀⠄⠀⠀⠁⠒⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⡎⠀⠀⠀⠀⣀⡤⠀⠸⡇⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠴⠀⣀⡸⠀⠀⣠⠖⠋⡁⠠⠆⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⢀⡶⠀⠀⠚⢀⠀⠘⠟⠃⠀⠈⡀⠴⠀⣡⠤⣤⡤⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠌⢆⠀⢾⠁⠀⡾⠀⠀⢠⡄⠀⠀⠄⠈⠁⠀⣀⠡⢮⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠉⠠⠀⢁⣦⠀⠀⠀⠈⠁⠀⠂⠂⠐⢏⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⡌⠀⠐⠁⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡤⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⢠⡄⠀⠀⠀⠀⡠⠛⠛⠳⢶⠄⠀⠀⠀⢻⣄⠛⢶⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠤⠀⣠⠀⠀⠀⠀⠺⠷⠃⢀⣤⣠⠂⠀⠀⠀⠀⠀⠉⠋⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠀⠆⡞⣵⡢⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⣤⡄⠘⢃⡙⠀⢉⡎⠁
⠀⠀⠀⠀⣀⡀⢠⡀⢠⡞⠁⣄⠁⢄⡈⠉⠀⢀⠈⠁
⠀⠀⠀⢀⡉⢩⠉⢉⠉⣃⠘⠋⠀⠀⠶⠀⠠⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⣢⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣏⣋⢳⠀⠀⠀⠀⠀⣠⣤⡴⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠂⣄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣦⣈⡭⠓⣄⠀⠀⠀⠀⠉⠀⠀⣀⡇⠀⠀⠀⠈⡒⢭⡀⢀⡉⡤⢀⣠⠀⢀⡴⠁⠴⢀⡀⠒⠀⠄⠤
⠀⠀⠀⠀⠀⠉⠀⢠⠖⣒⠦⠐⠀⠀⠀⠀⠛⠀⠀⠀⢴⡾⠀⠈⠛⠁⠀⠀⠀⠀⠙⠚⠱⠎⢠⠀⠛⠛⠀⠈⣀⠛⠀⠈⠁⠛⠠⡤⣀⢚⡀
⠀⠀⠀⣤⠀⠀⠰⠆⠋⠒⣀⣤⠀⠀⠀⢠⡁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⡶⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢠⡄⢀⡄⠀⣀⡴⠚⢁⠀⠖⠀⠀⠀⠀⠀⢛⠁⠀⢀⡀⠻⠃⠐⠂⠀⡄⠒⠒⢀⡙⠆⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠘⠃⠀⢉⠠⠆⠉⠀⠀⠀⣠⠾⣷⠄⠀⠀⠀⢛⠁⢀⣴⠄⠀⠄⠱⠚
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠶⠀⠘⠁⠀⠲⠟⠁⢰⢨⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠡⠁


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

⠀⠀⠀⠀⠀⣇⣃⢰⠀⡀⠀⠶⠐⠊⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡌⠁⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡇⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⡀⠅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣀⣠⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠁⢸⠀⠀⠐⠀⡀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⢸⠀⠀⢀⠀⠈⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⢸⠀⠀⣀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⠁⣀⢸⠀⢰⡋⠀⠈⠂⢀⣈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠃⢸⠀⠺⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⠀⡄⢸⡆⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣿⠀⠁⢸⠀⡃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⡄⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢹⠀⡀⢸⠀⣆⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⠀⣁⡚⢀⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡉⢉⡁⠈⠃⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠊⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠁⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠤⠄⠂⠈⠁⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣀⡧⠤⠀⠀⢀⠀⠀⠀⢆⣀⠤⠄⠒⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢉⠆⠀⠘⡤⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠤⠚⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣯⣽⣽⣿⣦⣭⣿⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣿⣷⣾⣿⣷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣆⠀⠀⠀⠀⠀⣰⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣄⡀⠀⠀⣠⠟⢛⣉⡛⢦⣤⡴⢛⣉⡙⠻⣄⠀⠀⠀⣠⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠟⣋⣩⣙⢋⣾⣿⣿⣿⣷⣤⣾⣿⣿⣿⣷⡙⣋⣍⣙⠻⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣮⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣵⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠓⠒⠛⠛⠛⠒⠒⠛⠋⠉⠁


⠀⠀⠀⢸⠀⠀⠀⡴⠋⠉⢳⡀⣿⠉⠙⣧⢐⡏⠉⠉⠀⣿⡆⠀⣸⡇⢸⣿⢸⣿⢻⣷⢼⣿⡻⠇⣿⡇⢸⣷⢸⣿⣧⢸⣿⣿
⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⢸⠇⣿⠛⢻⡁⢀⡟⠛⠛⠀⡇⢻⣰⠃⡇⢸⣿⢸⣿⠛⠋⣠⡝⢿⣦⣿⡇⢸⣿⢸⡏⣿⣿⢿⣿
⠀⠀⠀⠘⠒⠒⠂⠈⠓⠒⠋⠀⠛⠀⠀⠛⠀⠓⠒⠒⠂⠃⠈⠋⠀⠃⠘⠛⠘⠛⠀⠀⠘⠛⠛⠃⠘⠛⠛⠃⠘⠃⠘⠛⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⣆⠀⢎⢈⠶⡁⡅⡰⢧⢸⢢⡆⢰⠆⠆⡆⠀⠸⢸⢰⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢠⢶⡀
⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⡿⠋⣼⣿⣿⢙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⣸⣼⠇⠀⠀⡷⡄
⣿⣿⣿⣿⣿⣶⣿⣿⣿⠏⣠⠾⢿⣿⡛⣸⣿⣿⡏⣩⣿⡇⠀⠀⠀⠀⠀⢸⠉⣀⡇⠀⣾⢿⣅⡀⠀⢴⡿⠀⠀⣾⠗
⣿⣿⣿⣿⣉⣸⣥⣼⣿⡀⣷⣶⡆⣿⣿⣿⣿⣿⣃⣿⣿⡇⠀⠀⠀⠀⢴⡾⠘⠻⠃⠘⣿⠏⡏⢻⠆⠀⠀⠀⠘⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠚⣧⣾⣿⣿⢿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣵⢻⠉⠀⣀⡀⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⢠⣴⣷⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠙⠛⠋⠀⢸⠟⠃⢸⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⡾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠉⢉⣽⣿⣿⣿⣿⠿⠟⠛⠉⠉⠛⢯⡉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣽⣻⡟⣽⢫⡟⣽⣋⡽⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁
⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠉⢻⡻⣿⣿⣿⣷⡙⣮⠗⠉
⣿⣿⡟⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢱⠀⠉⠻⣿⡟⠁
⣿⡿⠋⠉⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸⠀⠀⢠⡟
⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣀⣠⣤⠴⠷⠤⠤⢄⣤⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⠋⠁⡞⠁⠀⠀⢀⡴⠋⠁⠉⣑⣦⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⢶⣶⣶⣶⣶⣶⣦⠤⢤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣏⢀⣀⣈⣳⣄⣀⠀⢸⡇⠀⣰⡾⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⣿⣷⣦⣤⣾⣿⣿⡿⠛⠉⠁
⢀⠔⠈⠉⠉⠲⣄⣸⣶⡿⢻⠏⣩⣿⠿⠛⠛⠛⣳⣦⣿⣠⠴⢲⢻⢹⣇⠀⠀⠀⠀⠀⡾⢶⣿⣿⡋⠁⠀⠈⠉⠻⣉
⠃⠀⠀⠀⠀⠀⠸⣿⣿⠁⣿⢀⣿⠃⢀⣴⠞⠋⢉⣩⢻⡁⠸⣌⢯⣧⣿⣆⠀⠀⠀⠀⠹⣄⡈⠌⡯⡑⢄⠀⣠⣤⣬⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⣿⡬⣧⢠⣿⡇⠀⣴⠟⡇⠀⠳⢄⣈⣓⡟⠁⠙⣷⡀⠀⠀⠀⠙⣿⡿⠾⠃⠀⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀
⡀⠀⠀⠀⠀⣀⣀⣸⣿⣆⣙⣷⣿⣾⣿⣧⣼⠃⠀⠙⢤⣀⠀⢈⡃⢹⡄⠀⠈⠻⣦⡀⠀⠀⠈⣷⡄⠀⠀⣰⣿⡿⠛⠛⠛⠛⠿⣦⣴⣾⣿
⣿⡄⠀⢀⡎⠀⠀⠈⠙⠿⣟⣋⣁⣠⡴⠋⠈⢧⠀⠀⠀⠈⢉⠋⠙⠻⣷⠀⠀⠀⠉⠳⣄⠀⢀⣿⡿⢶⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⡁
⣿⣿⣄⢸⠀⠀⠀⠀⠀⠠⠚⠉⠁⠐⡄⠀⠀⠀⠙⠢⠤⣤⠞⠛⠻⢶⣼⡆⠀⠀⠀⠀⢙⣷⣿⣿⡠⣄⠈⠩⣾⠛⠷⣦⣀⠀⣠⣶⣾⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣴⡿⠛⣛⣿⣷⡿⠷⣒⣶⣶⡾⢿⣟⠁⠘⣿⣮⣵⣾⠃⠀⠀⠀⠙⠷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠸⡆⠀⠀⠀⠀⠀⠙⠦⣄⣴⠞⠁⣴⢿⠫⠈⠁⠀⣼⡛⠋⠁⠀⠘⣿⣄⣠⣬⣽⣿⣧⣄⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛
⣿⠻⢿⣿⣿⣿⣿⣷⣤⣹⣦⣀⣀⣀⣠⣴⣾⣟⡁⠀⠀⠙⢮⣶⣄⡀⢄⡻⣷⣤⡄⣀⣀⣈⣛⣻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⢿⡄
⢻⣧⡠⢈⣙⣻⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⢙⣿⣿⣿⠿⠟⠛⠉⠉⠉⠋⢹⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣷⠞⢻⣆⠀⠀⠀⠸⣧
⠘⣿⣉⠓⠀⣁⣼⣧⢠⢿⣟⠀⠀⠀⣠⢾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠾⢻⣆⠀⠀⠀⢿⣦
⠀⢿⡟⠷⠤⠉⠀⣿⣼⠘⢿⣦⣤⣾⣏⣿⣿⠁⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣾⣆⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⠟⢻⡄⠀⠀⢸⣿
⠀⢸⡇⠀⠀⠠⠴⠛⣿⣆⠈⢉⣩⡿⢾⣿⣿⠀⠀⠀⢀⣴⣿⣿⠟⠛⠛⠛⠛⠿⡄⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣧⠀⠀⣸⣿
⠀⣸⠷⣤⣀⠀⠀⠀⣿⣷⣒⣺⡿⡗⠺⣿⣿⡄⠀⠀⢸⣿⠏⢀⣀⣤⣤⣄⣀⢀⠇⠀⠤⠀⠀⣰⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⡀⠀⠀⡀⣲⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⢠⣶⣿⣿⣿⣿⣿⡇⠀⠈⣹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠿⠿⠿⠛⠂⠀⠀⠈⣿⣿⣿⣿⡿⠷⠆⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠘⢀⡞⠠⠀⠀⢄⣠⣼⣿⣿⠇⣼⣾⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣿⢴⡞⠁⠐⡀⣠⣾⣿⣿⣿⣿⡿⣽⣿⣿⠃⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣸⡇⠀⣰⡇⣿⣿⣿⣿⣿⡿⣱⣿⣿⡏⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⢉⡀⣰⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⡿⢀⡟⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⣶⣄⠀⠀⠀⣹⠉⢹⣿⣿⣿⣿⠟⠛⠛⠛⣇⠸⠇⠀⠴⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠹⠿⡿⢿⣤⣾⣦⠟⢀⣾⣿⣿⣿⣇⢠⣤⣤⣴⣿⣀⣀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠙⣿⣿⣿⡇⠀⢰⣿⣿⡿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⡇⢸⣿⣿⠟⠁⠀⢸⣿⣏⠀⠹⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡴⠉⣿⣿⠋⠀⠀⢠⣿⣿⣿⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⡿⠁⢠⣴⣧⠈⣦⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢃⡟⠁⠀⠀⣼⣿⠀⢨⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣇⣼⠃⠀⠀⣼⡟⠹⣢⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⡀⣸⡏⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠾⠋⠁⠀⠀⠀⣿⣴⣿⢿⣿⠿⣿⣷⠶⠶⠿⢿⡿⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣾⡿⠗⠋⠀⠀⠀⠀⠘⠧⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⢿⡿⡙⡿⣿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣿⣿⣿⣟⣛⣛⣻⣟⣛⣻

⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠘⣷⡿⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⣔⠂⣀⡡⠄⠒⠁
⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⢁⠏⠁
⠀⠀⠀⠀⢀⣜⠀⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢩⢉⠵⢤⣼⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠁⠢⢦⡄
⠀⠀⠀⠀⣌⣹⠤⣽⣿⣯⢄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡀⠈⠆⠀⠀⠑⢅⢢⣀⠀⠀⠐⢶⠎⠉⢲⣄⠀⠄
⠀⠀⠀⠀⠈⣯⡘⠉⠉⠻⣄⡜⡁⠀⠀⠠⠄⠀⠀⠀⠀⢤⠀⠰⢹⠃⠀⠀⠀⠀⠀⠈⠈⠓⢤⡀⠀⠀⠀⠀⠀⣉⡴
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠈⣧⠀⣴⣷⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠸⠿⠏
⠀⠀⠺⠿⠀⠈⠁⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⠀⠀⢀⣤⡾⣿⡇⠀⠀⠀⣰⢿⡷⢀⣾⣷⠀⠀⠀⣼⠃⠀⠀⠈⠉⠯⣽⠟
⠀⠀⠀⠀⢀⣶⡀⠀⣠⢼⡂⠀⠀⣳⡾⠁⠀⠀⠀⠛⠔⠁⣀⠀⠀⠀⣰⠃⠀⢀⡟⠀⠀⠀⠀⢀⡼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⡆
⠀⢠⣶⣴⠯⠞⠁⠀⠚⠏⠃⠀⡴⢛⣤⣤⡀⠀⠀⢀⡀⣰⠇⠀⠀⠀⠛⠲⠦⠞⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⢀⡔⣢⡀⠀⠀⢀⣤⣄⠀⢀⣿⡅
⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⠀⢸⡇⣏⠱⠈⣿⠀⠀⠸⠿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣀⡀⠀⠹⠬⠞⠋⠉⠀⠀⢠⡞⠛⠋⠀⠘⠛⠁
⠀⠀⠀⡴⢢⣤⣞⣹⠀⠀⠀⠀⠳⠬⣤⡾⠋⠀⠀⠀⠀⠀⠀⣮⠬⠃⠀⠀⢠⡞⣹⠗⠀⠀⢸⢩⡟⠀⠀⢠⡀⠀⠀⠀⠀⠋⠀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠈⠋⠀⠉⣠⣄⠀⠀⠀⠀⠶⣆⠄⠀⣠⠦⠤⣤⠀⠀⢻⠀⠀⠀⠀⢀⡽⠃⠀⢀⣤⡾⠋⠀⠀⠀⣾⠁⠀⠀⣴⣶⡄⣰⠿⠟⠀⠀⡷⠚
⡦⠀⠀⣴⣤⣠⠞⠁⠈⢳⣄⠀⠀⠀⠀⠀⢀⡟⠀⠀⡟⠀⠀⠘⠀⠀⢠⣶⡌⠀⠀⢰⢏⡴⡿⢶⡄⠀⢠⡾⠆⠀⢰⣏⣉⣠⡏⠀⢀⡄⠀⣿
⡁⠀⠀⠈⠋⠀⣾⣶⠖⠋⠈⢷⡀⠀⢀⣤⣼⠁⣶⣾⠃⠀⠀⠀⣶⡶⠈⢿⡀⠀⠀⠸⣌⠃⢃⣰⡏⠀⠈⠁⠀⠀⠛⠒⠶⠟⠀⢀⡞
⠉⠀⠀⡀⠀⠀⠀⣡⣀⣠⠴⠋⠀⢀⡀⠙⠉⠀⠈⠁⠀⠰⣿⠇⠘⢧⡀⣠⠿⣄⠀⠀⣬⠛⠛⠉⠀⠀⡴⣲⠆⠀⠀⡶⢄⠀⠀⢾⣷⠄⠀⠀⠐
⢀⡠⢾⠁⠀⠀⠀⠙⠛⠁⢀⣀⣠⢿⡷⠀⠀⠀⠀⢀⡀⠀⠙⣆⣠⠴⣻⡵⠚⠁⠀⠀⠉⠊⠀⠀⣖⣲⠞⠁⠀⠀⠀⣻⠘⠀⠀⢀⣀
⠈⠀⠉⣀⣤⡀⠀⠀⠀⠀⠻⠟⠉⠉⠀⠀⠀⢀⠴⣻⠀⠀⠀⠈⠳⠞⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣁⣀⣀⠀⠀⢯⡹⠀⠀⣰⠋⠉⢹⡆
⢀⣄⠀⠙⠲⣽⡀⠀⠀⠀⠀⢀⣠⣴⣶⡀⠀⠀⠈⠁⠀⢠⠤⠤⣤⠀⠀⠀⢀⣠⣴⠛⠉⢧⡀⠀⠈⡿⠭⠽⡇⠀⠀⢠⣤⣼⢃⣀⣠⠏
⣛⡿⠀⠀⠀⢿⡿⠀⠀⠀⠐⠋⠁⠈⠉⠀⣤⣤⠀⠀⠀⣾⠋⠉⣿⠀⠀⠰⡉⠀⠘⣧⠀⢈⣷⡀⠀⣷⣶⠀⣧⠀⠀⠈⠛⠁⠈⠛⠋⠀⠀⣠⣤
⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⢀⣶⣦⢸⡏⠉⠀⢀⣠⡇⢰⣶⡏⠀⠀⠀⠹⣄⠺⠿⠃⠘⠟⠃⠀⠈⠁⠀⢻⣿⠆⠀⠀⠀⠀⡴⣆⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⡀⠀⢸⣏⣁⣸⡇⠀⠀⠙⠛⠁⠀⠀⣀⡄⡀⠀⢴⣿⠆⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡀⠀⠑⣻⡄
⠀⣶⢼⡂⠀⠀⠀⠀⠈⠧⠃⠀⠸⠷⠶⠞⠁⠀⠀⠀⠀⠀⠀⠰⢫⡟⠃⠀⠀⡀⠀⠠⣴⠲⡄⠀⠀⣠⣷⠀⠀⣀⣀⠀⡿⠿⠀⠘⠤⠃⠀⢀
⠀⠺⠉⠃⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣀⣤⢤⣤⣀⣴⣚⣷⠄⠀⠀⢀⣀⡀⢾⠿⠂⠀⠈⠙⣯⡄⠈⠛⠋⠀⠀⡟⠛⠀⡇⠀⠀⠀⠀⠀⣤⡾⠂
⠀⠀⠀⢠⠄⠀⠀⣷⠐⠁⠀⠀⠀⢸⠡⠖⡳⣾⡉⠉⠉⠁⠀⠀⠀⢸⡟⠃⢸⡀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⣟⣻⣿⠇⠀⠀⠀⠀⣤⢿
⠀⣠⣠⡏⠀⠀⠀⣿⠀⠀⠀⢰⡶⢸⣦⣊⣠⣾⠃⠀⠀⣰⠇⠀⠀⠘⡇⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠛⠛⠀⠀⠀⠀⠈⣀⣀⣀⡀⠁⠁⠀⠉⠉⠀⠀⠀⢠⠟⣳⠂⠀⠀⠛⠛⠉⠀⠀⣠⣶⣆⠀⠀⠀⢻⡲⡀⠀⠀⣀⣴⠀⠀⠀⣸⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢩⡇⠀⠀⠀⠀⠀⣠⣄⠀⠉⣻⠃⠀⠀⣿⣦⠀⠀⠀⣰⠋⠉⠁⠀⣀⠀⠘⠛⠀⠀⣠⣿⠀⠀⠀⠀⣿⠀⠀⣿
⣰⣿⡦⠀⠀⢀⣀⡾⢀⣤⣼⠀⠀⠀⢀⣤⡄⢻⡏⠀⠀⠋⠀⢀⣤⡗⠃⠀⠀⠀⠁⠀⠀⠀⠘⢯⣳⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⠻⠿⠀⣯⣄
⠃⠀⠀⠀⠀⠘⠿⠃⠈⠛⠃⠀⣠⣶⠈⢿⡁⠀⢹⣆⠀⠀⠀⠘⠛⠃⢀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠟⡆⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠘⢯⠀⢀⣽⣞⣩⠞⠃⠀⢠⠒⣤⣴⣋⠇⠀⠀⡾⠭⣭⡿⠀⠀⠉⣁⠀⠀⠘⣧⠜⠀⠀⠀⢀⡞⠙⠲⣤⣄⡀
⠀⢀⣤⠶⠺⡍⠀⠘⣆⠀⠀⠀⠀⠈⠻⣯⠴⠋⠁⠀⣀⠀⠀⠉⠁⠈⠁⠀⣀⣸⠁⣤⣴⠃⠀⠀⣿⣿⠄⠀⠀⣿⠀⠀⣠⣄⡞⢀⣀⡼⠁⠈⣹
⣀⣈⣳⣀⣀⣻⣄⣀⣽⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣇⣀⣀⣀⣀⣀⣘⣿⣃⣀⣉⣉⣀⣀⣀⣙⣈⣀⣀⣀⣈⣀⣀⣙⣛⣀⣙⣛⣁⣀⣰⣃
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⣶⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠈⠛⠛⢡⣿⣿⠟⠛⠛⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡿⠿⣶⡆⠈⠋⠁⠀⠀⠀⠀⠀⢴⣻⣿⣿⡿⠋⠉⠉⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⡯⣭⣶⡂⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣿⠯⣟⣒⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣗⡾⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢋⣿⣿⡁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠻⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠹⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⢿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣆⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠋⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠋⠉⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⡛⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⣸⣶⡿⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠿⠿⠏
⠀⠀⠀⠀⠀⣠⣾⡿⡏⠀⠀⠀⠀⠀⠀⠀⢾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢾⣿⠟
⠀⠀⠀⠀⣾⡿⠋⢀⣹⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃
⠀⠀⠀⢸⣿⠃⢀⡾⠻⡍⠉⠻⣷
⠀⠀⠀⠈⢿⡆⠈⢇⠀⡇⠀⢀⣿⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠈⠻⢦⣄⣀⣱⣤⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡄
⠀⠀⠀⠀⠀⣰⣶⣦⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠘⢿⣏⡤⠞⠀⠀⠀⠀⠀⠀⢾⡿⠟⠀⠀⠀⢿⡿⠋⠀⠀⠀⠸⣿⠿⠁⠀⠀⢾⡿⠟⠀⠀⠀⢾⡿⠟

⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⡜⠁⠀⠀⠀⠙⣿⣆⠀⠀⢾⡦
⠀⠀⠀⢧⣾⣿⡦⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠈⠙⠛⠁⠀⠀⢠⣿⡟⠀⠾⠗⠀⢸⠀⠀⠀⠀⠀⣀⣧⣼⣶⠀⠀⠀⠀⠀⠷⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⢸⢀⣀⠀⠀⠀⠛⡏⢹⣀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⢸⠉⣿⠇⠀⠀⣴⣷⣿⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠁
⠀⠀⠀⠀⣀⡤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠴⠋⠀⠀⠀⠉⡇⠸⠀⠀⠀⢰⣿⡿⠃⠀⠀⣴⣿⡿⠀⠀⠀⣾⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣂⣈⣉⣉⣽⡷⢶⣤⠀⢶⡶⠀⢰
⠀⠀⢶⣶⣶⣶⡆⢰⣶⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢉⡛⠛⠟⢋⡠⢾⠃⠰⠈⠁⡠⡊
⠀⢰⣦⣬⣛⠻⢷⣸⣿⡀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢧⣿⣿⢶⣤⡷⢟⣣⣤⣤⠾⠃⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⡇⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⢉⣁⣠⣿⣿⡿⠉⣀⣤⢠⠜⣧
⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠃⢀⣘⣯⣿⠆⢀⣠⡄⣀⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⠧⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠛⠋⠾⡴⢬⠅⠀⠘⠓
⠀⠠⠤⡤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⡀⠉⠛⢤⡀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⢠⣿⡓⢄⠈⢯⡔⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣾⡿⣿⡿⣷⡿⣿⠿⣿⡿⣿
⠀⢠⠄⡀⠈⢤⡂⠐⠱⡊⣷⣦⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⡿
⠀⢸⡄⠀⡨⢀⣎⡂⠀⠑⢮⣙⣋⣉⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⣿⣿⣿⣟⣿⣟⣿⣟⣿⣟⣿⣟⣿
⠀⢀⣀⠀⠀⣈⠉⠈⣀⠈⠀⢀⣀⣉⡁⠀⠀⠀⠀⢀⢀⡀⡀⡀⡀⠀⠀⢀⡀⠀⠀⣈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋
⠀⢸⣿⣦⡀⠘⢷⡀⠙⢆⣄⠨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⣻⣋⢿⣠⣼⢿⡝⠤⣙⣻⡣⡥⡏
⠀⢸⣿⡌⠳⣦⡘⢷⠀⠀⠻⣷⡌⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣥⣷⣁⣨⣿⣽⠣⣟⣷⣟⠘⣦
⠀⢸⣿⣿⣆⠙⣷⡌⢷⣄⠀⣸⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⡿⣶⣿⣿⣿⣷⣦⣻⣟⣰⣡⡇
⠀⢸⣿⣿⣷⠀⠀⠻⣿⣿⣷⡈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣿⣿⣿⣿⡟⣾⢏⣿⣧⣝⢣⡔⣃
⠀⠈⠉⠉⠉⠁⠀⠀⠙⠋⠙⠉⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠚⠃⠀⠀⠀⠀⠛⠓⠛⠛⠛⠚⠛⠛⠚⠛⠒⠒⠋
⠀⠘⠢⠘⠿⣿⣜⢿⣷⡄⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠈⠀⠙⠛⠣⡙⢷⡀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⠟⠋
⠀⢰⣤⡀⠀⠰⡀⠀⠀⠀⠙⡄⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢄⠀⠀⠙⢷⣄⢾⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠉⠛⡀⠀⢳⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣀⣿⣿⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠛⠁
⠀⠀⠀⠀⠈⠀⠀⠘⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠿⠷⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠶⠿⠿⠿⠇
⠀⣶⣶⣶⣶⣶⡰⣶⣶⢶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⡶⠂⠀⡄⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⠂⠀⠀⠀⢀⣷⣄⠀⠻⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠛⡶⢲⢦⣆⡀⠒⣠⠁⠀⠃
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣼⣿⣷⡄⢀⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣆⠉⠚⢁⠿⢩⣄⢀⡀⠄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣏⢻⣿⣿⣿⣧⣀⣀⣤⣾⣿⡇⠀⠀⠀⠀⠀⡀⠈⠣⠝⣶⢟⣻⡟⠀⣀⠐⠂
⠀⠿⢿⡿⢿⡿⢿⡿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⠀⠙⢿⣿⠷⠙⢻⡿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠃⣴⠓⠚⠆⠀⠳⠈⠣⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠀⠁
⠀⣰⠆⢠⡶⣶⡶⢂⣤⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⢀⠀⠠⠀⠂⠄⠀⠀⣠⣤⠀⠀⠀⠠⡄⠀⠀⠀⠀⣠⠶⣰⢆⡴⠦⣴⢶⠶⣀⠶⡀
⠀⣿⠀⣼⠀⣿⣿⢋⡾⠟⠳⢶⣍⣏⡻⠇⠀⠀⠀⠉⠔⠣⠀⡔⡂⠀⢀⢌⡳⠆⠀⣱⣾⡇⠀⠀⠀⠀⣩⠿⣽⢮⡵⢿⣽⢿⠿⣩⠿⡅
⠀⣿⣆⣿⡀⢿⣿⣾⠃⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢠⠐⣈⠂⠐⠠⠀⡀⣾⡗⣀⠂⠀⢨⠀⠀⠀⠀⠀⣭⠿⣽⢯⡝⢛⣽⣿⠟⣤⠻⡅
⠀⢿⣿⣿⣷⣄⡻⣙⠷⣤⣤⣾⢃⣿⣿⡇⠀⠀⠀⢦⣷⣴⣷⣤⣷⣦⣿⣿⣿⣎⠡⡈⠠⠀⠀⠀⠀⠀⣤⠛⣼⢫⡜⢋⣿⣿⠻⣤⠻⡄
⠀⢷⡙⠿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣿⣿⡄⠀⠀⠀⢌⣵⡫⣭⣻⣿⣿⣿⣿⣿⣿⣶⢬⣶⡂⠀⠀⠀⠀⣤⠛⣼⢣⡜⢫⣽⣿⠛⣤⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠘⠁⠉⠉⠋⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀