Tarsier Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡄⣄⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⡀⢀⠔⠋⠁⠀⠀⠀⠀⠉⠒⢄⢀⡠⠼⠤⠔⢒⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⠀⢄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠄⠊⡜⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡀⠀⢀⠤⠤⡀⠀⠀⢀⠤⠤⡀⠀⣔⠁⠀⢰⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠃⠀⡇⠦⠆⡹⠀⠀⡇⠦⠆⡱⠀⣆⡠⠔⠁⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⠀⠈⠑⠊⠅⠋⠁⠈⠑⠊⠁⢠⡿⠀⠀⠀⠀⢸⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⡠⠤⢦⡈⠀⠒⢀⣀⠠⡢⢋⡈⠳⠞⢢⣴⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⣀⠀⠀⠨⢅⠈⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠖⠂⠀⠀⠐⢠⠔⢋⡏⠈⠑⠌⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣦⠾⡄⠀⠀⠀⢠⡕
⠀⠀⠀⠀⠄⡄⡄⠄⣤⢠⠀⠀⠀⠀⠘⡄⠀⠀⡜⠀⠀⢀⡜⢙⠍⢀⣀⠀⠀⣿⠇
⠀⠀⠀⠀⠈⠁⠁⠉⠁⠈⠀⠀⠀⠀⠀⠘⢆⡼⠀⢀⢴⣉⠜⣩⠐⡫⢟⣈⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡖⠲⠤⢄⢀⣲⠲⠈⠡⣞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⢍⢢⠀⠀⢸⢀⠇⠀⡰⠃⠑⠩⢌⣤⠈⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⠀⠉⢀⡰⢃⠎⠀⡠⢇⡀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣉⣊⡩⠔⠁⠀⡰⠁⠀⠉⠁⡒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢻⡆⠀⠀⠀⠀⢀⡀⠠⢤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⣌⠀⠀⡇⣌⢣⡄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣶⣛⣽⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣿⡇⠀⠃⣿⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠉⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⣿⣷⢰⣾⣿⡿⣷⣀⣷⡶⢐⠁⢀⣀⣆⣺⣿⣾⣷⣶⣀⠈⢿⣷⡞⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣻⣿⣟⣿⣿⠋⠀⠋⣰⣿⡿⠋⠉⠉⢻⣿⣿⣾⣷⣿⡏⢀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⡖⣿⠇⣿⣿⣷⡄⠀⠄⠀⣹⣿⣿⣿⣿⣧⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡉⣿⣿⣿⠿⡽⣿⣤⣤⣤⣿⣿⠏⠹⠏⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⡛⢻⣿⣿⢿⡜⣿⣿⣇⡛⢿⣿⣿⣿⣿⡏⣶⣆⡀⠛⠚⠃⣿⣿⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣝⣛⣿⣟⠻⠿⢂⠻⣿⣿⣿⡿⠿⢿⣿⣿⣶⣯⣿⣿⣢⣷⣾⣿⡿⠜⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠿⣟⣛⣿⡷⠀⣷⢿⣿⣿⣷⣿⣿⣿⣿⣿⣟⠻⠿⣿⣿⣿⢿⢦⡈⠙⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣶⣶⣾⣿⡁⢹⡬⠂⠀⠈⠙⠻⢿⢿⡿⢿⠿⠿⠊⠁⠀⠴⠞⠛⢷⡏⠙⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⢾⢯⣽⣉⣹⣟⣛⠻⣷⡜⠀⠀⠀⢠⣶⣷⡿⠟⠛⠛⢻⡿⣷⣆⠰⠄⢀⣤⡋⣤⢀⢽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⠖⠲⣶⣦⡤⣭⣝⣟⢿⣿⣆⣧⣠⣿⡿⠋⠀⠈⠁⠈⢿⡿⣌⡙⣿⣶⣞⡟⠑⣾⣇⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢷⡿⠿⠶⠶⢿⣿⣻⣿⣿⣿⡿⠋⠀⠀⠀⠒⠴⠐⢏⡽⢧⡝⠃⠙⢿⣿⣏⣬⣻⣗⣤⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠘⠻⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢈⠠⠄⡉⠹⠿⣦⣴⣻⣿⣿⣧⣉⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⠐⢿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠀⠀⠀⠀⠀⢠⠀⣢⢀⣀⣯⣷⣉⣆⣤⢞⠗⠈⣿⣿⣯⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠈⡀⠀⠈⢁⣸⡿⣿⣿⣷⢸⠓⢤⣬⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢸⣿⢏⣙⢛⣻⠛⢛⣊⣹⣆⠀⠀⠀⠀⠀⢈⠀⠀⡤⠛⠛⣡⣼⠟⣿⢀⣀⣿⢦⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣼⣿⣾⢭⣍⣩⣿⣿⣭⠀⢿⡇⠀⠀⠀⠀⠀⠀⡀⢠⢇⣲⣴⣿⣾⢳⣿⣏⢁⢾⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣾⣿⣶⣾⣿⣿⣿⣾⣧⠀⠀⠀⠀⣀⠀⠫⠄⠀⣹⡟⠈⠻⣮⡛⢰⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡛⢿⣿⣿⣿⣿⡟⢿⣿⡄⢀⠀⢰⣿⣧⠀⠉⠂⢇⠀⢶⡗⣾⣆⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣶⣌⡟⠉⡻⠷⣾⣿⣷⠰⣾⣧⣿⣿⠀⠀⠲⢉⣀⣼⣟⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣝⢷⣟⠻⣿⣿⣿⡿⣿⣷⣛⣿⡏⠁⡀⢄⣠⣯⢩⣤⣾⣿⡿⠃
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣷⣿⣏⠙⢻⣿⣻⣿⣿⣤⡎⣤⣘⣿⣠⣾⣿⡿⠟⠁
⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⡿⠀⢸⣿⠿⠿⣿⣿⣿⡿⠿⠿⠟⠋
⣿⡦⢀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠻⠌⠁⠀⠈⠀⢀⡿⠋⠁
⠋⠀⠀⢳⣤⣼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉
⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⢶⣶⡶⢶⣶⡶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠓⢠⣀⡀⠀⣠⢶⡄⢠⣄⠀⠠⠀⠉⠀⠊⠄⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣞⣾⣿⣎⣻⢹⡷⣠⣶⣠⠙⠀⠀⢀⠆⢀⣄⣀⣠⡱⣤⠀⠀⠀⣀⢀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡤⠼⢿⣿⣿⣿⣷⡀⢀⣴⢆⣾⣿⣿⣧⣵⣿⡃⣳⣦⣽⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠊⣿⣤⣴⣷⡿⣿⣿⣿⣿⣼⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣟⣤⠨⣿⣿⢯⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣻⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⢡⣿⣿⣿⣿⣷⣶⣿⣿⡿⠁⠀⢻⣿⣿⡁⠀⣐⣿⣿⣿⣿⣟⣿⠟⠉
⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣏⠀⢨⡷⢿⣿⣿⣿⣿⠿⠛⠀⣀⡰⣜⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⠄
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣽⣿⠀⢸⣇⠈⢝⣻⣿⡋⠀⠐⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢃⣼⡦
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣄⠨⠟⣿⣾⣿⣿⣷⣦⣬⣿⣿⣯⣿⣁⣸⣿⣭⠿⣟⣡⣾⡧⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⣄⠈⠻⣿⣿⣿⣿⣿⢷⣬⣭⣭⠉⠉⢽⣿⣿⣾⣿⠿⠁⠀⡀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣶⣄⢈⡽⣿⣿⣿⣽⣻⣿⢿⣀⣶⣾⣿⠿⠉⠀⠀⢀⣼⣇⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣩⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⡭⠀⣀⣠⣶⣿⡟⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣤⣌⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠍⣻⣿⣿⠿⠿⠛⠻⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣷⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢆⣾⣙⣿⠁⠀⠀⠀⠀⠉⠙⠋⠙⠻⢿⣧⣿⣿⡛⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⣿⡹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠻⣿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠰⠱⡄⠲⡶⠄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠨⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⣴⣦⣶⡨⣼⢣⠀⣂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⠀⣶⣆⣰⡇⠩⢀⠂⢀⢈⡀⠀⠰⠀⡵⢾⡤⣏⡉⢙⠻⢿⣾⣷⣾⣿⣸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣶⣿⣷⣾⣿⣿⣿⣾⣲⣡⣂⣀⣬⣔⣤⣷⣧⡾⠿⠛⠓⠓⡿⣷⣶⣭⣿⡿⡛⠛⠛⠿⣦⡚⠛⠛⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠛⠙⠛⠛⣛⣮⠙⢿⣿⣿⣽⣿⣿⣿⣾⣿⣿⠟⠃⠀⠀⠀⠐⠀⠀⠀⠉⠻⣿⡏⠀⠀⣀⣠⢈⢻⣦⣤⣿⠅
⠀⠀⠀⠀⠀⠐⢤⣿⡣⠀⠀⢀⣀⡀⣙⣿⣷⣌⣿⣿⡟⢻⢿⣿⣿⣧⠉⠀⣠⣶⣾⣿⣿⣿⣧⣠⢥⡄⠈⠇⠠⣸⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣬⣿⣿⠀⠀⠉⣠⣶⣶⣿⣿⣿⣿⣿⠀⢨⣿⣿⢿⡃⣀⣾⠻⠆⣓⣛⣛⣛⢻⣷⡈⠃⢄⡀⠀⣽⣿⢖⣶⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢘⢿⡿⠶⠀⢼⣿⣿⣿⣿⡀⠛⡿⣿⣷⣿⣿⣿⣯⢠⣾⢋⠴⠛⠝⢿⡏⠙⢷⣿⣧⣄⣺⢠⡀⣾⢿⣏⠙⢿⣿
⠀⠀⠀⠀⠀⠐⠈⣿⣷⡀⣼⣷⣿⡙⢿⣿⣿⣿⡜⢻⣿⣿⣿⣿⠏⠺⠏⢼⣠⡀⠀⠉⠀⠀⠈⣿⣿⣿⣿⣿⠅⣿⣼⣿⡀⢠⣝
⠀⠀⠀⠀⠀⠀⠀⠤⠙⣿⣮⣿⣿⣷⢸⣿⣿⡟⠀⠈⠉⡼⣿⣿⣗⣊⣇⢸⣿⣿⡷⣁⡃⢶⣜⣿⣿⣿⣿⣿⠀⣿⣿⣦⣴⣼⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠽⠿⣿⣿⣿⣿⡿⢤⣾⣀⣶⣡⣃⣿⡛⢍⣿⣎⣻⣿⣷⣶⣷⣾⣿⣿⣿⡿⠉⠁⠀⢿⣿⡿⠿⣊⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠲⠏⠉⠀⣤⣅⢹⣟⢿⡟⣷⣿⡚⢙⡟⣿⣿⣶⣿⠷⠾⠫⠿⠟⠀⠀⢀⡀⠈⣿⣿⣿⡏⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⣀⡈⣙⠻⣯⣷⣾⡟⣿⣷⡷⣧⡙⢻⢿⡦⣠⠇⡀⣤⢷⣿⣮⢡⡙⠲⠘⢿⣟⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠶⠖⣲⣦⡘⠿⣾⣶⣍⠙⣿⢻⣿⣿⢿⢿⠓⡜⠟⣿⡝⢟⠟⣯⣿⣿⣿⠷⣙⣤⣟⣾⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢈⡙⠛⡧⠈⣿⣽⡿⣗⡼⣶⣿⣧⣳⣄⢿⣾⣿⣿⣦⡁⠀⠹⢿⣿⣿⣿⡿⣻⣿⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠈⠛⠀⠀⠀⡙⢳⣥⡈⣏⡈⢃⣵⡝⣿⣿⣿⣿⣿⣿⣿⠶⣦⣼⣶⡾⢟⣾⣿⣿⢹⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠆⠀⣠⠛⠳⣶⠛⢊⠈⠑⠸⣍⠻⣹⣿⣿⣿⣶⣄⣈⣈⣠⣾⣿⣿⡧⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡌⠀⠌⢠⠢⠠⠍⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠀⠠⠀⠀⠈⠹⠂⠀⠏⢻⡛⡿⣿⣹⣿⣿⣿⢿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠘⠑⠃⠃⠈⠘⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡄⠀⠈⢰⡄⠀⠀⠀⠀⠀⢀⣮⠀⠈⣳⠶⠿⢿⣿⠿⠻⠿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐⠀⠀⠈⢳⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⢀⡴⠋⠉⠛⠛⠂⠰⠌⢙⠛⠷⣄⠀⠀⠀⣀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⡧⠀⠀⠈⣆⠀⠀⠀⠸⣿⠟⣫⢮⣾⢏⣠⡤⣄⠉⠁⠀⠀⠒⠀⠱⣦⣸⣿⡏⣁⣠⡴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⡉⠀⠀⣠⣯⠀⠋⣿⢡⢸⡟⠷⢸⡇⣸⡄⣴⣶⡟⣶⠘⣿⣿⢿⠟⠛⢀⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣧⣡⡤⠰⣿⣦⣰⣿⣿⠀⠀⠘⢦⣮⣽⣶⣿⡷⠉⢿⣿⡋⢁⣾⢃⣿⣯⣤⣤⡖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠏⠀⠀⠹⣿⠇⢻⣽⣇⠀⠀⠄⠉⠻⠋⠱⣀⠀⠌⠻⣿⡿⠛⢉⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠂⠀⠀⠀⣿⠀⠈⢻⣿⡆⠀⠀⠐⢷⠈⢲⣤⡤⡤⠄⣿⠃⡞⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠶⢦⡆⢀⣿⠀⠀⠈⠛⠷⣦⠄⠓⠂⠀⡀⠠⠠⣤⠮⠄⠈⠱⠞⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⡑⠂⠀⠈⠹⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠀⠉⠈⠀⡀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⢶⣄⣄⡀⠐⠪⣁⣿⡟⠁⠀⠀⠀⠐⠦⠀⠀⠀⠉⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠉⢿⣷⣴⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡾⠀⠀⠀⠀⣈⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⣻⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢀⢻⣿⣄⠀⠀⠀⠀⠀⠀⢶⠀⠁⠀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣤⠈⠛⢻⣿⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠀⠙⠛⠛⠃⡿⣿⣿⢦⣀⠀⠀⠈⠂⢰⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⣂⣒⠀⠁⢹⣥⠤⠸⠿⢶⣄⣠⡿⠀⠀⠀⢴⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⠋⠛⣯⠀⠀⠀⠀⠀⠛⠉⠉⠁⢀⣴⣾⣿⢸⣏⡝⠉⣿⡇⣢⢈⡙⡇⡿⠋⢝⠋⢝⣻⣩⠟⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣴⣿⣴⣿⣿⢿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠏⢛⢹⡛⡗⡟⣹⢛⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⡿⣶⣶⣿⣶⣶⣷⣾⣾⣛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠛⠛⠛⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢰⡄⠀⠀⠀⡀⢀⡀⢀⠀⡀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⡄⠐⢸⣥⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⢠⣾⣿⡍⣦⡀⠄⠀⣠⣤⣤⣤⡀⠰⣶⡤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⢏⣘⣱⣿⠛⠉⠻⣿⣿⣷⣿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣯⣯⣼⣿⣗⣀⣠⣿⠿⡿⢿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣤⣐⠚⢋⣿⡗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣽⣁⣿⣿⣿⣹⣿⣿⣿⣿⣿⣾⣿⣿⠫⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣟⢲⡏⠉⠛⠿⢿⣿⣿⠷⠞⠉⠩⠞⢷⡞⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣛⣻⠿⢿⣭⣿⣇⢀⢰⣾⡿⠛⠉⢽⣿⠷⣔⣀⣴⣽⣦⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣮⡿⠯⣽⣿⣻⣿⣿⡿⠃⠀⠀⡄⢰⣻⣗⢟⢿⣿⣎⣻⣮⣟
⠀⠀⠀⠀⠀⠀⠀⢼⡀⠘⣿⣿⣿⣿⣿⢿⣿⡟⠀⠀⠀⠀⡀⠀⣠⡽⠛⠶⣿⢿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠁⠉⠓⣻⢷⣿⡏⠧⣈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡸⣿⣭⣻⣟⣻⡽⣧⠀⠀⠀⠈⠀⠰⡛⠩⣼⣻⣧⣼⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣷⣼⣿⣧⣼⡆⠀⠀⠀⠰⣆⠙⣿⠟⣿⡿⣣⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠿⣿⣿⣿⢻⣧⠀⢀⣾⣆⠈⢊⡏⢲⣾⣧⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣾⢤⣯⣿⣿⣯⣿⣿⠋⣀⢙⡶⣞⣷⣿⠏
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⠛⣿⣿⣿⣧⣎⣤⣿⣵⡿⠟⠃
⣿⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⠸⠛⣿⠿⠛⠛⠉⠉
⣿⣿⣤⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠀⠀⠄⢠⣤⣀⠀⠀⠀⠀⠸⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠦⢤⣀⡉⠁⠛⠒⠒⠃⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠶⠃⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣂⢵⡂⢠⡏
⠀⠀⠀⢠⡤⣤⣄⠀⠀⠀⠀⢀⡠⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⠀⡸
⠀⠀⠀⢾⠀⠀⠈⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢺⡇⠀⠀⡸⢠⠇
⠀⠀⠀⠘⣄⠀⠀⠀⠈⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠉⠀⡾⠀⠀⠀⠃⡾⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠳⡀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢠⠈⠀⣸⠃⠀⠀⠆⣸⠇⠘⣙⣡⡴⠖⠛
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⡖⠉⠀⠉⠙⢦⡀⠀⠀⠀⠀⣴⠚⠉⠉⠉⢶⠀⠀⠔⠁⢠⣾⠃⠀⠀⡈⣤⢛⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠀⠀⠀⠴⣺⠇⠀⠀⠀⠁⣼⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠈⠛⠲⠀⠠⠖⠀⠀⠀⠀⠈⠠⢠⣤⡴⠚⠁⠀⠀⠘⣤⠬⠄⠐⠒⢉⣀⠚⠁
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠏⠀⠀⠒⠀⠛⠉⠛⣉
⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⡀⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠼⣇
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠉⠛⢂⡀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠋⠉⠀⠦⠰⠎
⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡠⠄⠀⠰⠞⠋⠁⠤⠀⣌⣀⠀⠀⢐
⠀⣤⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢻⣀⡶⠦⠤⠀⠄⠀⣀⣀⠛⠋
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢈⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⡿⠾⣷⡶⢶⡖⢀⡬⠷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣵⡟⠀⠀⠈⠘⡟⠉⠋⠀⠀⡿
⡄⠀⠀⠀⠀⣠⠖⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡠⠀⠀⣤⡄⢸⠁⠀⠀⠀⢠⡆
⡅⠀⠀⠒⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠙⠓⠚⠾⠶⠿⢇⠀⠀⠀⡄⣹⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠇⠀⠘⠛⠀⠛⠛⠳⢦⡿⠀⠈⣠⠏
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠏⠈⣀⢩⣭⣭⢍⡉⠳⣦⠼⣆⠞⠁
⠈⣅⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡄⠀⠀⢀⡎⢀⣤⠛⠛⣁⠤⢠⡟⣦⣣⡞⠉
⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⡇⠀⠀⠀⡼⡗⠺⡇⠀⠀⠀⠑⣼⣵⠟⠃
⠀⠈⢻⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣮⣱⣇⣀⢦⣀⣀⣠⣶⡟⣤⡀
⠀⠀⠈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠘⠻⠿⠿⠛⣻⡿⠿⣿⣾⣟⣹⡇
⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠠⢶⡶⠶⢦⠶⢾⡷⠶⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⢀⣴⠿⠿⣿⣶⠶⠐⢰⣶⡜⠃⢸⣶⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣻⣏⠉⠀⠀⠐⠙⢷⠀⠀⣾⠁⠁⢈⠉⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⣶⢀⠏⠀⠀⠀⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠘⠀⠀⠀⠆⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⡛⠀⠀⠀⣰⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣾⠁⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢈⡟⠀⠀⣄⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣌⠻⢦⣤⣀⡀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣭⣙⣛⣛⠶⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣴⣿⠾⠿⣽⣿⣿⡿⡿⠿⣿⣷⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣴⣿⣿⣿⠟⠉⢁⠀⠀⠀⣿⠉⠀⠐⠀⠀⠐⢙⠘⢫⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡏⣿⣶⣷⣷⣶⣄⠀⠀⡴⠀⡠⣐⣚⠳⢦⢨⣴⠲⣼⣿⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣦⢼⣧⢹⣽⣿⣿⠟⣽⣧⡄⠀⣼⣿⣿⣏⣻⡄⠸⣯⡿⣹⣅⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⣽⣿⣿⣿⣯⣿⣿⣿⡷⣷⣿⣿⣾⣿⣿⣅⡏⠏⣿⠏⣈⠁⣚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⡪⢙⣿⣿⣿⡇⠉⠻⣿⣿⣟⣻⣯⢿⡾⢣⣼⢇⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣊⣠⠟⣿⣿⣉⡤⠽⠶⠟⢕⣚⣿⡭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢦⠙⠂⢀⣾⡿⣏⣰⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠿⠿⢿⣿⣿⡿⣿⣿⠿⠋⠉⠉⠩⠙⠻⠾⠲⠈⠙⣿⣳⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣛⡍⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⠿⣿⡿⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⠛⣷⣿⣾⠻⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣥⣿⣿⣿⣣⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠃⣬⣉⡉⠻⣿⣿⣿⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣿⠛⠳⠗⢰⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠃⠈⠅⠈⣹⢿⣿⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣥⣶⣷⣶⣤⣠⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣠⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢡⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡃⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⣀⣀⣠⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢰⣠⢠⢄⡀⠀⠀⠀⠀⣂⡀⢠⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠙⠁⠄⠁⠀⠀⠀⠀⠈⠻⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⠀⠢⢄⠘⠀⠈⢻⣿⣿⡿⢦⣽⣵⠶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡠⣾⠃⠀⠀⠀⠀⠓⠀⠀⣠⣿⣿⣿⡗⣸⣿⣿⣂⣼⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢶⣦⣿⡴⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣷⡄⠀⠀⠀⠀⠠⠂⠔⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⣿⡿⢛⣷⣦⣤⣤⣤⣤⣤⣄⡀⠀⠀⢰⣿⣿⡿⠏⣉⣉⠉⢻⣿⣯⡻⣟⣿⣿⠀⠀⠠⠀⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣛⢳⣝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⣿⣦⣶⠞⠻⠂⢴⣿⣿⣷⣿⣾⡿⠀⢠⡙⣴⡟⢰⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⡀⣿⣿⣿⠿⠋⠀⠀⠀⣼⢹⣧⣬⣯⣴⡶⠌⢻⡈⢇⣟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⣶⣿⣿⣶⣤⣿⣾⣏⣉⣩⣿⡃⣰⠟⢿⣬⣟⠙⠳⠄
⠀⠀⠀⠀⠀⠀⢸⣷⣯⠉⡿⠗⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣉⣑⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣽⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃⣆⣸⣿⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢸⣿⡿⣿⡿⣟⠛⠿⡿⠟⣡⣶⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠊⡡⠈⢻⣿⠦⠉⠉⠷⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⠻⣷⡀⠀⣜⡋⠉⠛⠂⠀⠀⢿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⡏⠉⢩⣿⣿⡿⠛⠀⠂⠰⠤⠶⠿⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢘⣐⣿⣷⣤⡛⢿⣦⡁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⢛⣿⣥⣀⣛⠛⠁⠀⠀⣀⣀⣀⣀⣤⣀⣄⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢻⣿⣿⣄⡙⣿⣦⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⢸⣿⣿⠟⠋⢆⢀⣀⠀⠉⠉⠉⠙⠛⠛⠿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠈⠿⣿⣿⣿⣿⣟⠿⣦⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠿⣷⣄⡀⠀⠀⠈⠙⠒⠾⠿⣿⣷⣦⣤⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣿⣿⠻⣷⣶⣶⡿⠿⣿⠿⢿⣿⢀⣸⢀⠙⠻⣶⣤⣄⣀⠸⣷⡴⠘⠩⢽⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠛⠻⢿⡟⠱⠞⠃⠀⠸⠌⢻⠀⠎⠀⠀⠀⠁⠈⠹⠄⠠⠁⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠉⠉⠋⠈⠁⠈⠓⠒⠦⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣀⣤⡄⢠⡇
⠀⠀⠀⠀⠀⠀⢶⡶⢤⣤⣤⣤⣤⣤⣤⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡴⠖⠛⠛⠛⠋⠉⣡⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢯⡐⠤⢄⣀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⡠⠔⠉⡼⠥⢬⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢰⠇⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⢄⡀⠀⠀⢠⠴⠒⠲⢤⡀⠀⠀⠀⠀⣠⠖⠒⠦⣄⠀⠀⢠⡏⠀⠀⠀⢀⡾⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢸⠁⠀⢠⡇⢠⣂⣦⠀⣷⠀⠀⠀⣼⠁⣴⣐⡆⠘⡆⠀⠰⡇⠀⠀⣠⠞⠁⠀⠀⡴⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣤⣼⠀⠀⠈⢧⡈⠛⠁⣠⠏⢀⣀⣀⠸⣄⠈⠋⢁⡼⠃⠀⣾⢴⠖⠋⠁⠀⠀⠀⠀⡽⠿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠉⠙⠋⢡⠖⠙⠤⠊⠁⢪⠉⠛⠉⠀⠀⢀⣧⡟⠀⠀⠀⠀⠀⠀⠀⢟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠰⣀⠐⠒⠋⢀⡠⠁⠀⠀⠀⢀⡜⣹⠧⠤⣦⣄⣀⢄⠀⠀⢸⡏⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠲⠶⠒⠛⠓⠮⣍⣉⢉⣉⣀⣀⡠⠤⠖⢋⡴⠁⢰⣁⠠⠜⢋⠎⡙⢟⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠛⠚⠋⠁⢈⠇⠀⠀⠀⢈⣛⣒⠔⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⣀⣀⡀⢀⣀⡀⠀⠀⠀⣠⣴⣻⠲⠤⣀⠀⢬⣉⠓⢨⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡤⠟⠋⠁⠀⠀⠀⠀⠉⠳⡶⠋⠱⣠⠏⠀⠀⠈⠙⠢⠌⣃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⡏⠀⠀⠀⠀⠀⠀⠀⣔⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⢻⡥⣙⠇⠀⠀⠀⠀⠀⢈⣙⣧
⢤⢠⡄⡤⣄⡄⠀⡤⢠⣄⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⣰⠋⢘⣧⣀⠀⠀⠀⠀⠀⠀⡲⣿⠃
⠸⠸⠇⠿⠇⡵⠄⢏⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢠⡏⠀⠀⠀⢀⡴⠞⠓⡶⠛⢒⣬⡙⠟⡟⠛⠲⠶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣾⠣⡀⢀⠶⠻⠶⠶⠚⢠⣎⡥⠤⣉⣒⣡⣤⡀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠳⡶⠦⢤⣤⣀⡀⠀⠐⠶⣖⣖⠒⠙⣲⡐⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⢸⠇⢰⠇⠀⠀⠀⣨⠟⢦⡻⢟⠲⠌⠉⠩⣭⡽⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠤⡄⢹⡄⠀⠀⠀⡾⠀⡼⠀⠀⠀⣰⠋⠀⠀⠑⠒⢭⣘⣶⠄⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠱⠞⠁⠀⢀⡼⠁⡴⠁⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠈⢁⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⠳⣄⣀⢀⣀⡴⠋⣠⠞⠁⠀⠀⡴⠋⠙⢦⣄⣀⠀⠠⠤⠄⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣈⠉⠉⣁⡠⠞⠁⠀⠀⠀⣸⠁⠀⠀⠀⢀⠉⠉⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠉⠉⠁⢠⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣇⢀⠄⠀⠀⠀⠀⠠⣦⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣄⣠⣷⣿⣯⣯⣿⣿⣿⣦⣄⠀⠀⠀⠀⣿⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣗⣴⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢿⡟⣿⠟⠳⠿⠿⢋⣽⣿⣿⣿⡀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡿⠾⠋⠰⣿⣠⣶⣿⣿⣿⠏⠈⠐⠂⠈⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀⣤⠶⣾⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣿⣿⣿⡿⠟⠉⠀⠀⢠⣾⡏⠀⣿⡟⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠉⠻⢿⣤⣀⣀⣀⣤⣿⣿⠀⢰⣿⣇⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⣸⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠈⣿⣿⣿⣏⠀⠀⣉⢿⣿⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠩⢸⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠄⠀⢀⣹⣿⡟⠀⣰⣿⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣦⢳⣾⣿⠟⠃⠀⣉⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣍⡋⠀⠬⠎⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡶⢳⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠻⣿⣿⣶⣆⡀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣄⠀⠀⣿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣷⣰⡟⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⠇⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣇⣤⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡬⠉⠉⢡⣭⠋
⠀⠀⠀⠀⠀⠀⢠⡿⠓⣠⣾⠛⠃⠀⠀⢀⠀⢀⣀⠐⢴⢄⡀⣠⡄⠀⠀⣀⠤
⠀⠀⠀⠀⡴⠀⠀⣽⣿⡟⠁⠀⡀⠀⢹⣿⣿⣿⣏⣰⣆⡺⣿⠚⣄⣀⠘⠓⠂
⠀⠀⠀⠀⠑⠀⠀⠙⣇⡈⠂⠀⠰⠀⠀⢻⣿⣿⣟⠩⠍⣷⠀⢸⠩⣽⡄
⡆⠁⠀⠀⡮⠊⠀⠀⠩⠾⢴⠦⣩⡀⣷⢾⣿⣿⣿⣷⣟⣻⡇⠘⠓⠟
⡇⠀⡠⠈⠀⠀⠀⠀⠀⠬⢶⠖⣶⡿⠤⠀⠻⣿⣿⣿⣿⣾⣿⣷⠞⠊⢀
⡇⠂⠀⠀⠀⠀⠀⠀⠀⠘⢏⣻⣛⣽⣏⡀⠀⠀⠙⣻⣿⠛⢛⠲⢾⡶⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠂⠀⠄⢻⣷⣾⣷⠛⢲⠀⡀⠀⠀⠉⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⢿⣿⣧⣤⠘⠻⠇⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠑⠀⠀⠀⠀⣽⣧⢚⣿⣤⠁⠀⠪⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣔⡆⢀⢻⣿⣽⣿⣿⡧⠂⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣧⣼⣿⣉⣿⣯⣿⣿⡟⠂⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠉⠹⣎⢿⣿⣿⣧⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⠀⡈⠳⢿⣿⣿⠅⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⠀⠀⢹⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡏⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠸⡌⢆⡀⠀⠀⡠⠴⠲⠖⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠒⠶⠖⠉⠀⠂⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠲⠤⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣲⠦⢄⣀⠀⢀⠀⠀⠆⢰⠶⠀⠠⠔⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⣶⡄⠀⠀⠀⣤⠞⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣄⠀⣸⡿⠂⠘⣄⣄⣉⣀⣤⣴⣀⠻⡄⠀⠈⢀⢠⠎⢀⣤⡄⣀⣀⠀⣶⠀⠛⡿⢋⡀⢸⣇⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣹⣿⣿⠧⣧⣬⣖⣾⣿⣿⠾⠷⣌⢣⡼⠈⠀⣎⣩⡶⣫⣵⣾⣾⣽⡯⠀⢡⡀⣀⢻⣴⡿⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⣿⢟⣹⣿⣿⡟⠀⠀⠀⠘⣷⢻⣚⡀⢀⣏⣼⠋⠀⠀⠀⢙⣿⠉⣦⠻⣴⣿⣿⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⠇⣿⣿⣷⣦⡀⠀⣤⣿⣿⣿⣡⣼⣿⣿⣀⣀⣀⣰⣾⡿⣠⡾⡄⢿⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⢻⠉⠃⠀⠻⢏⣛⣻⣿⣻⣫⡿⢗⡄⢐⣿⡿⢟⣻⣿⣛⣫⢾⠁⡸⠃⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠘⠉⠣⠈⠓⢤⡙⠙⠯⣿⣿⣿⣿⡾⠲⠻⣿⣿⣦⣍⡛⠛⠋⠉⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣲⣶⠀⠀⠀⣬⠛⠄⡛⢋⠉⢙⡿⣤⣦⢠⣿⡁⠈⠁⢉⣀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠄⠀⣄⢀⣿⠻⣛⣶⣶⣌⡛⢀⣘⡻⣶⣬⣙⠦⣤⠴⢛⣵⢲⣿⣫⣥⣶⣁⣄⣐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢤⣾⢼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡟⡂⠀⠀⠀⠠⣦⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣁⣾⣯⣿⡿⠿⠿⠿⠿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠘⠇⠩⠐⡅⢨⣽⣿⡋⠀⠀⠀⡔⢠⠖⠶⣄⣀⣠⠄
⠀⠀⠀⠀⠀⠀⢀⣤⡾⡁⠰⠛⠋⠉⠉⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣦⣀⡓⠐⣷⡛⣿⡁⠀⠀⠴⠊⠠⡏⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⡀⠀⠀⠀⠀⠈⠻⣿⣷⡮⣌⢻⣯⣿⣿⡏⠉⢀⡤⢰⣶⣶⣬⡀⢠⠤
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣸⠅⣦⠘⠙⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⣿⣿⣷⣾⠟⠁⣿⠀⠈⢻⣿⣉⣬⣶⣵⣾⠟
⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠾⣿⡶⠀⡦⠀⠀⠀⠀⣤⠀⢨⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠻⠷⣬⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢀⣗⠂⡤⢀⠂⠔⠈⠀⠘⠁⠀⠁⠀⠀⠈⠀⠀⠀⠲⡀⠀⠁⣧⣙⠀⠀⣈⣀⢰⣿⣳⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⢮⣍⠛⠋⠁
⠀⠀⠀⠀⢠⡬⢡⠀⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠁⢸⠷⢧⡶⣦⣀⣟⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢀⣄⡻⠿⠾⠃
⠀⠀⠀⠀⠘⢃⠟⡀⠉⠀⡀⢀⠄⠀⡀⠶⠀⠀⢠⡂⠀⠀⢊⣠⠀⠶⠶⢸⣦⢰⠿⣿⣿⣿⣯⣭⣍⣹⣿⣿⣿⣿⣷⣦⣼⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠺⢱⣤⣜⢣⣖⣦⢘⠋⢁⣇⢒⡰⡿⠀⢼⡟⠋⠐⡶⡁⡈⠛⣩⣾⣿⡿⠫⢙⡻⢿⣿⣿⡿⠿⢿⠿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣽⣾⣿⣯⣴⣿⣾⣿⣯⣸⡇⢀⡴⢴⡓⣸⣴⣾⣿⣿⣿⣿⣿⣿⣝⡒⢦⣭⣓⠺⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠮⡽⠿⠤⠾
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⣯⡀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠈⢻⢻⡟⠉⠉⣹⣿⣿⠿⣿⠿⠛⢛⣭⠞⣫⣿⠟⠋
⣿⣿⣤⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⠋⠹⠖⠋⠀⠀⠐⠋⠀⠴⠋⠁
⠛⠛⠛⠛⠒⠛⠓

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣗⡄⠀⠀⠀⢠⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣀⣐⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡚
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⢺⣵⡿⢧⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠅
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⢰⣶⣰⡿⣿⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⣤⣄⣼⣿⣟⠓⢺⡿⣷⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣤⣿⣿⣧⡄⣂⣠⣿⣿⡟⢋⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢂
⠀⠀⠀⠀⠀⠀⠀⣼⢹⣷⣿⣿⣿⣿⣿⣿⢿⣽⣷⣿⣿⡟⠔⠰⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠆⠁
⠀⠀⠀⠀⠀⠀⢠⣧⣀⣞⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣷⣶⣷⣤⣤⣠⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⠟⠋⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⡴⠒⠲⠤⣀⡈⠙⠛⢋⣁⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⡇⢀⣤⣀⣤⠍⡳⣞⢋⣽⣿⡛⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⡿⣿⣿⣿⣿⣿⣧
⠀⠀⢠⣴⡿⠛⠛⣫⣵⡽⠞⠛⣼⡿⠿⠿⣧⣹⣿⣿⣉⣀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣄⡀⣨⣍⣍⣀⣨⣭⣽⣿⣿⣿⣿⣿⣿⣋⣄⡀
⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣀⣀⣾⣉⣈⢉⣹⣿⣿⣯⣿⣿⡿⣿⠁⣀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡭⠿⠓⣈⠡⢊⡻⠿⣿⠛⠻⠷⠖⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⢀⠠⠖⣛⠅⠦⠚⣋⣵⣾⠟⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⣄⣀⠀⠀⠀⠊⣡⣀⡴⣟⣋⠁⢀⡴⠊⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠈⠈⢁⠜⠀⣠⢟⠁⠀⠀⢉⡴⠁⠀⠤⣥⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣲⠋⠀⣼⠏⡀⢛⠛⢮⣍⠀⣦⠀⠀⠀⠀⠉⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠀⠉⠉⠉⠁⠉⠑⠒⠂⠐⠐⠂

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣦⣀
⠀⢀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠀⡀⠀⠀⠠⣽⣿⣅⣰⣿⠟⠁⠈⠻⣿⣿⣾⣿⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⠈⠳⣶⣤⣀⡀⠀⠈⠙⠻⣿⣶⡤⢤⣄⡈⠫⠙⣿
⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠈⠛⠿⣿⣷⣤⡤⡀⠈⠛⣃⣤⣭⣭⣗⠻⣿⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡟⢉⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠡⠵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠛⠻⡿⠿⠿⢿⡿⢿⠏⠹⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣚⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣄⣤⠄⠖⣤⢤⣄⡠⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣖⢀⣤⣿⣿⣿⣙⠁⣬⠉⢲⣨⠇⠉⢘⡟⠃⠈⠀⠀⠡⢩⣷⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠖⠀⣵⣿⣿⣿⡿⠿⣻⣿⡿⠋⠉⠻⠐⠋⢩⣼⣿⣾⡇⣄⣀⠀⠀⠀⣿⣿⣿⡿⢿⣷⣤⡀
⠀⠀⠀⠀⠀⣐⠀⣀⣴⣾⠿⠛⠉⠀⠀⢀⣿⡏⠉⠀⠀⠀⡄⠀⣲⣿⣿⣿⣆⢽⣻⣇⠀⠐⣿⢍⠁⣠⣼⠟⣡⣷⣦⣤⣤⡀
⠀⠀⠀⢀⣾⣾⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣧⣄⠀⠀⠧⣠⣾⣿⣿⣿⣿⣏⢿⣷⢠⣷⣿⡌⡸⠿⢫⣾⡿⣿⣿⣿⡿⠁
⠀⠀⠀⣸⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⣧⡀⠀⣿⣿⣿⠟⠁⠀⠀⠻⠿⣜⣛⣻⣿⣁⣤⣿⣿⣵⠿⠋⠁
⠀⠀⠀⢾⣘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⣿⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡩⣿⣿⣿⠋⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣌⢷⣿⡟⠋⠁⠀⠙⣿⡿⢤⣄⣀⢀⠀⠀⠀⠀⠑⠀⠶⠽⠘⣿⠇⣀⡀
⠠⠤⠤⡼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣘⣿⡻⣟⣷⣔⠌⡉⠙⠳⣌⠧⣌⠓⠛⠉⠈⠁⠈⠉⠙⠻⢿⣯⡾⣿⣿⣴⣶⠒⢲⠤⢆⡀⡤
⣴⣤⢦⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣧⣴⣴⣶⣦⣼⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣾⣿⣒⣻⡅
⠻⠿⠿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣿⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⠃⢀⠃⠀⠀⢹⡆⢹⡇⠀⠀⠀⠀⣧⢷⠀⢰⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠝⠻⡀⠀⠀⠀⠀⢀⢹⠇⠀⠀⣿⠛⢿⣿⢷⡶
⠀⠾⠀⠀⠀⠀⠚⠃⠀⠃⠀⠀⠀⠀⢸⣾⠀⠀⡏⣧⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⠀⢰⣞⡇⠠⣠⡀⣼⣿⡆⠀⠀⣿⠀⢀⣿⣿⣷
⠀⢀⠀⠀⠀⢀⣾⡆⢰⣶⡀⠀⠀⠀⠈⠙⠀⠀⠇⠸⠂⠀⠹⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣷⢀⣿⣷⠘⠉⠁⢿⢿⡇⠀⠀⢸⣿⣿⣿⣿⠟
⢰⡏⠀⠀⠀⣸⣇⡷⠟⢻⡗⠀⠀⠀⢠⢠⡄⠀⠀⠀⠠⡄⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡚⣿⢹⠿⡀⢰⣶⢄⣈⣋⡅⠀⠀⠀⠛⣿⠻⠝
⣿⠀⠀⠀⠀⠉⠀⣠⣴⠈⡏⠀⠀⠀⢈⢸⡇⠀⡇⠀⠀⢣⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿⣿⢙⠀⣸⠇⠰⠇⣼⡿⣽⠃⠀⠀⢀⡇⠀⠀⡀
⠋⠀⠀⠀⢰⠆⢸⠇⠘⡀⣷⠀⠀⠀⠸⢠⣆⠀⡇⠀⠀⢘⡄⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣸⣷⠀⠀⢡⠀⠁⡴⠁⢁⣿⡄⠀⠀⠘⢧⣶⣶⠁
⠀⢀⠤⠐⡤⠀⠒⠀⢈⡁⣿⠀⠀⠀⠀⢀⡉⠀⠇⠀⠀⢸⣇⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠁⠀⣇⠹⡄⠀⢀⣝⠀⢼⢰⡿⣻⠇⠀⠀⢠⡀⠈⠛
⠀⠀⠀⢀⡀⢀⡀⠀⢠⡄⢸⠀⠀⠀⠠⢀⡉⠐⠂⠀⠀⢸⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡀⠒⣸⠁⠘⡇⢿⡁⠁⢀⣾⡟⠀⠘⠺⡁⣸⠀⢀⣤⣶⣿
⠀⠀⠀⠹⣇⣼⡧⢀⡟⣿⢸⠀⠀⠀⢹⣾⣿⠀⡆⠀⠀⡎⠀⢸⣿⣿⣿⠓⠒⢒⠂⠀⠉⠀⠀⠋⣠⢠⡷⠀⣷⠀⣼⣼⣁⢰⣶⣴⣧⡏⠀⠘⠿⠋⣷⣿⠆⠀⣤
⠀⣴⠀⠀⠛⠐⡇⣼⠁⡍⢻⠀⠀⠀⣸⣿⢹⠀⢃⠀⢠⠀⠀⢨⣿⠿⠿⠰⠒⢋⣈⠱⡂⡄⢸⣆⣧⣾⠶⢛⡏⠸⠶⠠⠾⠁⢓⢿⠸⣣⠀⠀⠀⠀⣯⡉⠀⠀⠘
⠀⠀⠀⠄⠀⠀⡇⣿⠀⡇⠨⠀⠀⠀⢸⡧⢸⡇⠀⠀⠀⠀⣤⣾⣯⡢⠖⡀⠆⠇⠀⢀⡙⡴⢩⠧⠘⠛⣛⠠⣴⢈⠙⡷⢽⣡⠛⠞⡱⠢⡌⠳⣄⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠇⢻⢸⣧⣰⠀⠀⠀⣩⣧⢸⡇⠸⡿⢣⠋⣼⡜⣫⣱⠞⣉⠀⠠⢠⠒⢊⠓⢤⡠⢄⠡⠈⣀⠙⠲⠚⣰⠲⢄⠻⠶⠁⡚⠳⢆⠋⡵⢀⢽
⢠⠀⠀⠀⠀⠀⠀⠈⢻⢹⡯⠀⠀⢀⢻⡟⣼⣿⠀⡅⣷⣴⣄⣤⣆⠉⠀⣧⢸⡄⡅⢛⣀⣨⣗⡐⠢⡜⣻⠭⢡⣴⡴⠀⠈⡙⠶⠚⡎⠻⠑⠞⢾⣤⣼⣀⠀⠀⣤
⠸⡆⠿⣦⠀⠀⠀⠀⠀⢐⡇⠀⠀⠈⠘⠿⠃⣿⡆⠳⡅⠄⠉⠹⠉⣙⣁⣸⠞⣓⡠⠋⠆⠠⡜⠹⠏⠐⣉⡖⢻⡄⠐⠗⠀⠩⠆⣀⢀⡀⠙⠀⠀⠙⠬⡱⠓⢏⠙
⠀⠛⢰⡝⢆⣠⡀⠀⠀⠘⠷⠀⠀⡆⣷⣾⠀⣿⣷⠀⢫⡲⣶⠖⣴⣿⣯⣴⣋⠝⣯⡀⢀⠘⢱⠧⢾⣆⠻⠇⠿⠐⠛⠀⠰⣗⡉⢙⠸⠋⠓⢄
⡀⠀⠀⠉⠘⢿⣿⣦⡀⠀⠀⠀⢸⣷⣎⡿⢶⣿⠿⣧⡀⣩⠍⠁⣹⣿⣿⣿⡟⠣⣔⣥⡉⣘⢂⠀⠀⠀⠁⠃⠀⠀⣶⠀⠀⢹⣏⠾⠀⠁⠀⠈⠳⣄
⡟⣻⡗⢦⡀⠘⣿⣯⣵⣦⠀⠀⠀⠱⣮⡢⣿⢑⣤⣠⣌⢿⣷⡄⢸⣿⢻⣿⣧⠀⠈⠄⡶⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣧⡶⠺⠀⠀⠀⠈⢳⡀
⠿⠏⢿⣬⣍⣷⣦⣙⠿⠿⠧⠀⠀⠀⠈⢿⣧⣍⡙⣍⡻⣾⣿⡇⣘⡯⣰⣿⣹⣆⡀⡀⢅⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡜⡁⠃⠀⠀⠀⠀⠀⠹⣶⡄
⠀⢶⣶⠇⢿⣿⣟⠛⢻⡷⠀⢠⣗⣄⠀⠈⢋⣸⣷⣿⣿⣜⣿⣟⢜⠣⠛⢺⠹⣽⣧⠁⠀⢠⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣤⣾⠇⠛⢢⡄⠈⠃⣼⡷⠀⢸⣿⡿⢷⣤⡈⢻⣿⣅⣽⣿⣿⣿⣿⣷⣾⢧⣷⡏⠁⢀⣽⣽⣿⣿⣤⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠙⠃⠈⢉⠈⣷⣀⢀⣟⠀⠀⠘⠛⠃⢈⡙⠙⠆⠙⠛⠉⠈⢿⣿⣿⣿⣧⠈⢉⣿⣿⣧⣭⣍⣿⡿⠀⠀⢀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠾⠻⣿⣿⡏⠀⠀⠰⣶⣤⣈⠹⠠⣧⠀⣂⣸⠇⠈⣧⠿⣷⣦⡿⢿⣄⠛⢡⣤⠉⣉⣤⠀⣺⣿⣿⡟⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⣳⠀⠀⠀⠀⠘⠿⣿⠤⠀⣰⠈⠏⢁⣿⣷⣤⣷⣾⡿⣿⣅⣀⣤⣤⣤⢠⡶⣴⢦⡴⠋⢠⣾⣿⣷⣿⣿⣿⣿⡷⠿⢷⣿⣀⡀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠰⢠⣆⡀⠀⠀⠙⠃⠀⣿⣧⡜⣿⣿⣿⣿⣿⣿⣱⣿⣧⡈⠁⠀⠀⢸⣧⠄⠀⢱⡿⣿⣿⣿⣿⣿⣿⣯⣕⡂⠤⠬⠉⠉⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⢠⣿⣿⣿⣷⣄⠀⠀⠀⢺⣿⣿⣿⣠⣹⣿⣿⣿⣿⣿⠟⠁⠀⠘⠀⠘⠀⠀⠃⢰⣇⣿⣿⣿⣿⣿⠟⢋⡁⠀⢶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⣾⣾⣿⣿⡍⢹⡃⠀⠀⢀⣀⠉⠻⣿⣿⣻⣿⣿⣿⡿⠁⠀⠀⠁⠀⠀⠀⠠⠃⠀⠈⠙⣷⣿⡿⢫⠀⠀⠹⠃⠀⠈⡿⠃⠀⠀⠒⠀⠀⠄⠀⠀⠀⠈⠳⢄⡀
⣿⣿⣏⠈⣷⠘⠃⠀⠀⠈⣿⢷⣶⣬⣝⣻⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣿⣿⣝⠂⠀⠀⠀⠀⢀⡀⠀⠺⣿⠉⠛⠿⠿⠿⣿⠇⠀⠀⠱⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠟⠃⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣿⣟⣿⣦⠀⠀⠀⠀⠸⠀⢀⣤⣻⣷⠀⠁⠀⠀⢸⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆
⣿⣿⣿⣷⣾⣴⢆⡞⡴⢦⠠⣬⣍⠹⣿⣶⡈⠀⠸⡧⠀⠠⠀⣴⡞⠀⠒⠂⢠⣴⣶⡦⢶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠻⣛⣍⣉⣀⠀⠉⠈⠉⠉⠉⠉⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣾⡿⠛⣿⣿⡿⢻⣿⣿⣿⣿⣿⣷⣶⢰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⡷⠤⣰⣿⠋⠀⠀⠻⢿⣿⣿⣿⣿⠟⠐⠁
⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⡀⠈⠻⣿⣿⣿⡶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠻⣷⠖⠂⠂⡤⠍⢻⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠓⠀⢿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠈⠹⠗⠶⠦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢀⣠⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠿⢿⣷⣄⠀⢾⡁⠀⡴⢛⣿⣿⣿⠿⠿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⡉⠀⣇⠘⠋⢹⠙⠂⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢽⡂⠀⠢⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⢠⠀⡀⠀⢀⡀⠀⠸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⠀⠀⠄⠀⠀⠗⠀⠈⠁⠀⠀⠹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⡤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠀⠠⠤⠄⡄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⢤
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣘⡤⠄⠀⠀⡀⠸⠠⠀⠀⠀⠀⠂⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠁⠀⠀⠀⠀⠀⠳⠑⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⢀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸
⠀⡇⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⢀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⡀⠀⠀⠈⠐⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⡇⢀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠈⠁⠀⠀⠀⠤⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⢸
⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⢸
⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠂⠀⠉⢼
⠀⡇⠀⡀⡤⠖⠒⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠋⠉⠀⠐⠀⠀⠀⠠⢼
⠀⣧⡊⡁⠀⠀⠀⠀⡤⠶⠶⠴⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡔⠀⠄⠀⠀⠀⠠⠂⠀⢦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣁⣀⠀⡀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠁⠀⠀⠀⠀⠀⠁⣀⠈⠉⠀⠉⠈⠀⠀⠈⠀⠁⠀⠉
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⢀⣀⣀⠀⡠⣴⣿⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⢻⣿⠿⢿⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢠⣤⠈⠁⣠⣄⡀⣬⣽⣿⣿⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡍⡀⠈⢫⣤⡻⣋⣼⣿⣿⣿⣿⣿⣧⠀⠐⠐⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⣤⣿⣶⠟⣛⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⣢⣌⡙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⣦⠴⣦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⢷⣞⣿⣶⣿⣿⠿⣿⣿⣿⣿⣷⣿⣿⣿⣏⣀⣸⣿⣌⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣤⡀⣸⣿⣿⡿⠿⣿⣿⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⣤⣀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠸⠽⢻⣯⢿⣿⣏⠀⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢆⣀⣀⣦⡀⠀⠀⠀⠀⡶⠈⠉⢱⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢿⣿⣟⣿⣿⣿⣟⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⡄⠀⢠⠔⣰⠂⠀⠈⠋⠛⠿⢿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⣿⣶⣣⣤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢼⣿⣿⣿⣿⣿⣶⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣾⣿⣦⡀⠀⡀⠀⠀⠘⠓⠞⠋⠉⠉⠉⢙⡻⢿⣿⣧⣻⣿⣿⣿⣿⣿⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣟⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠊⡓⢈⣿⣟⣿⣿⣿⣿⣿⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡠⠈⠛⠻⢿⣿⣿⣿⣦⣀⣀⡀⠤⠀⡀⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢃⢀⠙⠈⠉⠛⣿⣿⣿⣿⣔⠀⠁⢀⣤⡶⣾⣽⣫⣭⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠹⣧⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⢿⡿⣾⣹⣯⣿⣿⢟⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠁⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣧⣿⣛⢈⣯⣴⣿⣿⣿⣿⣿⣿⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⢿⣿⣿⣿⣿⡯⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣞⣻⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠻⢿⣿⣿⣧⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⡇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⣿⡃
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣄
⠀⢢⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠘⣧⠀⠀⡄⠀⠁⠀⠀⠀⠈⠀⠂⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⡀⠀⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁⠠⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠒⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠠⠤⡄⠀⠂⠢⡰⠲⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡄⠀⠀⠀⠀⠀⠀⠀⠠⠟⠷⡀⠀⠀⠀⠀⠀⢀⢸⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣑⠀⢄⠀⠀⠀⠌⡠⠀⠀⠀⢀⡁⠁⠙⢀⠄⠾⠟⠠⢿⢛⣿⣦⡄
⠂⢀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡲⣤⠸⠯⣆⠀⠀⠠⠈⠀⠀⠠⠀⠤⠊⠀⡀⠀⠂⠸⠈⠀⠀⢀⠂
⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠲⠴⠠⠈⠄⠀⠀⢰⠇⠀⠀⠠⠉⠀⢀⣰⠦⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢋⠉⠀⠀⠤⠁⠠⠴⠁⠈⠦⠀⠀⢂⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣷⣶⣾⣷⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣤⣾⣡⣿⣇⠀⠀⠀⠂⢦⣤⠖⠉⠀⢱⡄
⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⢿⣿⡿⠛⢹⣿⣿⠉⠁⠀⠀⠀⠀⠈⢹⣧⣄⠀⠊
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⡇⠀⢨⠀⡾⣛⣓⠛⣠⣶⡤⠀⠀⠀⢀⣤⣷⡿⡿⣤⡀
⠀⠀⠀⠀⢹⣿⣿⣿⠋⠉⠉⠉⠻⢿⡏⠉⠙⠻⠗⠿⠶⢳⡀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣴⡾⢰⡿⠿⠛⠛⠉⢉⣀⠀⠀⠀⢼⡛⠿⢀⣀⠄⠑
⠀⠀⠀⠀⣼⣿⣿⡟⠉⠐⠒⠶⣤⣄⣠⣀⣀⡀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠊⠉⠐⠀⠀⣀⣴⠶⠞⠉⠀⠀⠀⣲⣿⣿⠷⢟⣇
⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⠈⠉⠉⠙⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⡶⠾⠿⠟⢁⠀⢀⡄⠀⠀⠉⠉⢛⡁⠈⢨⣄⠉⠃
⠀⠀⠀⠀⠙⠋⠁⢀⣠⣼⣯⡿⠀⠀⠀⢺⣿⣿⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠈⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠐⠛⠁⠀⠸⠫
⠀⠀⠀⠀⠀⠀⢠⣿⢉⡙⢭⡄⠀⠀⠀⠀⢸⠚⣛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢘⣿⣞⡡⠀⠈⠀⠑⠤⠀⠁⣰⡟⢟⠋⣸⣖⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡄⣠⡀
⠀⠀⠀⠀⠀⣀⣈⣠⣠⠤⠔⠚⠁⠀⠀⠰⣦⢈⠛⢺⣶⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢲⣤⣤⣤
⠀⠀⠀⠠⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠻⠂⣉⠍⠛⡿⡻⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠉⠀⠀⠀⠘⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⣾⢳⣦⣤⣤⣴⣤⣀⠘⠙⠀⢠⣿⠴⠌⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠏⠙⠛⠛⣡⠞⠀⡀⠙⢛⣭⣭⣶⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢿⣿⣼⣧⡄⠙⣿⣿⣿⣧⡀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⣼⣿⣟⣿⣿⣿⠋⠀⣠⡶⠞⠁⠀⠀⠀⠸⣳⣶⣿⣿⠇
⠀⠀⠀⠀⠰⠀⠀⠀⠑⡀⠺⡿⠟⠛⣁⣴⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⢿⣧⠴⠋⠁⠀⠀⠀⡉⠐⠦⠠⣼⣿⣲⣿
⠀⠀⠀⠀⢀⣀⣤⣤⣾⣋⣀⣀⠐⣚⠁⢰⣶⣶⣿⣿⣿⡀⡂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣴⣿⣤⣤⡀⠀⠀⠉⠙⢛⣷⣤⣶⡄⡍⠻⡋⠁
⠀⠀⠀⠀⢀⣐⣿⣻⣜⢹⣿⢿⣷⣦⣉⠻⣿⣿⡍⠛⢿⣷⡍⠁⠀⠀⠀⠀⠀⠀⠾⣿⣿⣄⠙⠛⠻⣿⣿⡆⠀⠀⠀⡾⠁⠀⠈⠉⠛⠛⡶⠄
⠀⠀⠀⠈⠉⠉⠙⠋⠊⠹⢾⣯⢿⡿⠛⠙⠫⣍⡛⠚⠙⢟⡡⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣀⣠⣿⣿⠇⠀⠀⠀⠹⣤⣀⣀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⣄⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣆⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⣴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⢷⣄⡀⢀⣴⠟⠁⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠳⣄⠀⢀⣠⠞⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡈⢷⡀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣠⠟⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⢦⣝⣶⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣩⠞⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠉⠁⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠉⠁⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠛⣦⡀⠀⠀⣠⠞⣩⠭⣍⡿⠿⣷⣄⣀⣴⣾⠿⢏⡭⠭⣙⢷⡀⠀⠀⢀⡴⠛⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣩⣭⡅⠀⠈⢙⣶⡶⢋⠎⢀⣽⣶⣶⣄⠈⢯⠛⡞⠁⣤⣶⣶⣥⠈⢳⡛⢶⣾⠋⠀⠀⣨⣵⣽⣦
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⢻⣿⣀⠰⣦⡛⣇⢾⠀⣎⣨⣿⣿⣿⡇⢸⢸⠀⢸⣿⣿⣿⣀⡇⢈⡃⣾⢋⣴⠂⣀⣿⡏⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣷⡞⢹⡏⢷⣄⣻⠻⡿⠘⢆⠘⠿⢿⡿⠟⢀⣞⣤⣧⡈⠻⢿⡿⠟⢁⡼⠁⡿⢻⣗⣠⠿⣹⡏⣳⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡹⢾⣷⣀⡙⠻⢧⣄⣀⣈⣑⣦⣤⡄⠒⢩⡏⠀⢿⠙⠒⢤⣤⣖⣋⣀⣀⣠⡾⠟⢁⣠⣿⡾⢫⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡀⠈⠉⠁⠀⠀⠈⠉⠉⠉⠁⠉⠙⠳⢦⣧⣀⣿⡴⠞⠋⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁⣠⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣹⣦⣄⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢀⣠⢾⣋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣡⣴⣛⣛⡛⠛⠓⠲⣶⣦⣤⣀⠀⠀⠀⠀⠎⠀⠀⠀⠀⣀⣤⣴⡶⠒⠛⠛⣛⣛⣻⣦⡉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣟⠉⡀⢀⡔⢶⣿⣷⣾⣭⠷⣤⡀⠠⢀⠀⢀⣴⢾⣽⣶⣿⣡⡶⢠⡀⡄⢙⡿⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⡿⠋⡤⠁⠀⣤⠸⣿⢻⣿⣿⢸⣿⡿⣦⣤⡶⣿⣿⠦⣿⣿⡟⣿⢳⡄⢀⠀⡎⠙⣿⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡎⠁⠚⢠⡿⣧⣽⣎⠛⣿⠰⣿⠷⣏⣿⣇⢻⣷⢶⡟⡛⣻⣧⣾⣷⠘⠃⠘⠠⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⢀⣵⣟⣛⣾⣿⡏⢻⣿⢧⣮⣴⡟⡛⣹⣦⣢⢾⣿⠛⢹⣿⣷⣛⣳⣌⡀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣿⠟⠃⠀⢈⡻⠿⣭⣇⢻⡿⣸⢧⣿⡟⣏⢻⣯⢸⡌⢿⠇⣼⣭⠿⣛⠁⠀⠙⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⢟⡤⢀⠀⠈⢻⣿⠏⣼⠷⣶⣿⢦⡟⣴⣿⣬⢏⡼⣿⣶⢾⣇⢻⣾⡏⠀⠀⠀⣾⢻⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⢧⠀⠀⠀⣸⣧⢾⣿⣆⢛⢃⣿⡉⣿⢿⡿⢹⣧⠙⡋⣼⣿⣦⣾⡇⠀⢀⢀⡟⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⣏⣿⢠⣿⡟⣿⢻⣿⠷⣥⣬⣥⢿⣿⠛⡏⢿⣧⢸⣏⣷⣐⡥⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣧⣛⣰⣧⠻⡟⣸⢿⣿⡿⣎⠿⠃⣿⣌⣋⣼⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⡏⢾⡿⢻⢿⡁⣾⣿⣷⢹⠿⡟⣿⡎⣹⣟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢏⠙⢦⡶⢟⡀⢳⠴⠤⢴⡏⢀⡳⣤⡴⢁⡹⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡏⠀⢿⣿⠋⣴⢟⡀⠀⣐⠿⣆⠻⣿⠇⠀⡷⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣜⣡⡿⢿⡟⠁⠠⠉⢿⡿⢷⣍⡆⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢉⠿⣷⣏⣴⢀⠀⠘⣦⣓⣼⢯⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢻⡁⣼⠈⠀⠀⡧⢙⠏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⣎⠐⣼⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁

⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⢀⡠
⠀⠀⠀⠤⢄⠃⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⣉⣗⣶⣷⣯⣠⡤
⠀⢀⣀⣠⠙⢶⠺⠃⡰⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡄⠀⠐⠒⠐⡆⣜⣈⠍⠉⣿⠟⠟⠁⠀⢤⡆⠀⣀⡄
⠀⠀⠒⠚⠐⠎⢐⠺⣆⣪⠤⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⢠⠀⠀⢰⠀⠀⠀⠀⢸⣆⣤⠀⠋⠀⠀⡀⡿⢠⢠⠖⣳⠺⡿⢟⣡⣄
⠀⠐⠛⠉⠉⡠⢦⠄⠘⠉⢒⡀⠀⠁⠀⢐⠢⠆⡜⠈⣥⠁⣖⡀⠀⠀⠀⠈⠉⠳⢋⢏⡀⡧⠤⢤⠈⣷⠘⢲⣾⣡⠦⡿⡲⠀⠁
⠀⠀⠀⠀⠀⠀⠨⡆⡴⠠⡿⠀⠀⠀⠀⠠⠒⠒⢀⢄⠀⠛⠁⠀⠀⠂⠀⠶⠉⠀⢠⠏⠀⠁⣉⣉⣈⠻⢠⠓⢣⣥⠖⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠈⡟⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠊⠉⠀⠀⠜⢸⠂⠈⠀⠩⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢐⣇⠀⠀⠀⠙⡆
⠀⠀⠀⠰⢄⣲⠂⣥⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠋⠀⠀⠀⠀⠃
⠀⠀⠐⢷⣾⣿⠿⠿⡖⠊⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⡀
⣠⡳⠀⣤⣧⠿⠀⠀⠁⠀⠃⣰⠄⠂⠒⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠲
⡿⡿⣿⣿⣶⣴⣿⠿⢳⠾⢧⣑⡐⢊⠹⠘⠹⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⠑⢲⣦
⣙⡗⣁⣠⠙⡦⢼⣷⡧⠠⢮⣌⠀⢨⡖⢂⡠⡟⡅⡌⡠⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠂⠀⠀⠀⠀⠙
⠉⣄⠮⢊⣹⣥⡞⠟⠠⣾⠞⢲⡾⢻⠀⣈⠿⠁⣹⠋⢡⢀⠠⠹⡇⢀⠀⠀⠀⢀⠐⠁⡀
⠳⠶⣆⡁⠉⠙⣷⢲⣜⢧⠴⣟⣇⣞⠿⠦⠒⠈⠌⠂⠹⡂⠀⠀⠀⠊⠀⠀⣛⠎⢀⣉⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⢶⣶⠶⠶⣶⠶⠶⠶⠶⣶

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


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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⣀⣀⣀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⢀⣤⡖⣀⣤⡀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠐⠁⠈⡏⠹⠅⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠋
⠀⠐⢋⣀⠈⣿⣦⣄⡈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⡉⣿⠟⠋⠙⠳⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⢿⣿⣿⣿⣿⣿⡟
⠀⠈⠀⠂⠀⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡹⠁⠉⢙⣿⣿⣿⣦⣀⠉⠉⠉⣉⡿⠃
⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⣶⣾⣿⠷⣄⡀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣷⣶⣴⣶⣿⣿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠙⢿⣇⠀⢸⣿⠛⢿⣿⣿⣿⡧⠀⠀⠒⠂⠉⠉⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣼⣿⠀⠉⠛⠁⢸⣿⡇⢸⣷⡀⠀⠀⠀⠀⠸⠓
⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⣆⣾⣟⠀⡀⠀⠀⠘⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⢀⣿⣿⠤⣼⣿⣿⠀⣴⠀⠀⣄⣅⠄⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⣅⣥⣤⣥⣄⣀⣉⣿⣿⣿⣿⣿⣿⣇⣀⣠⣶⣾⣿⠃⠀⢛⠛⠁⠀⠉⡠⠬⣯⣿⠀⠀⠀⢀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⠛⠛⠁⣰⡞⠀⣀⢃⣠⣄⠀⠘⠽
⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠙⠛⠛⠿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠋⠙⠂⢰⢠⣿⡆⢀⡁⡞⣰⣿⡷⢦
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠡⠛⠉⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⣇⢸⣯⣀⠙⢉⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⢀⡆⠌⠀⢈⢠⣼⣿⡿⠧⠧⠸⠦⢶⢄⠇⡀
⠀⠀⠀⠀⣴⠞⠙⣿⣿⣿⣿⣿⣶⣤⣴⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠓⠒⢈⣍⣶⠿⠋⠃⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠿⠿⠿⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡟⣻⡟⢟⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⣿⣿⣿⡿⣿⢿⢿⢿⡿⡿⣿⠿⡿⡿⡿⠿⡿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⠛⠀⢀⡀
⣿⣿⣿⣶⣿⣶⢶⣾⣷⣾⣷⣾⣾⡷⣷⣶⣶⣾⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣤⡿⣿⡄
⣿⣿⣿⣶⣶⣶⣾⣶⣶⣶⣶⣶⣦⣶⣶⣶⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⣿⣿⣿⣥⣬⣭⣼⣾⣧⣤⣭⣭⣮⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⢀⠄⠀⣿⣿⣶⣤⣴⣶⠴⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⠿⡿⠗⠀⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⡉⠀⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠸⡿⠋⠀⠀⢠⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠄⠀⠀⣿⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠃⠐⡀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⢀⠀⠀⠀⠀⣤⡿⠈⢈⡤⢃
⠀⠀⠀⠀⠀⠈⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠆⠈⢠⠸⠀⠀⡘⣴⣟
⠀⠀⠀⠀⠀⠀⠈⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠞⢹⡇
⠈⠁⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⡎
⠀⠀⠀⠀⠀⠀⠀⢠⣽⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠄⢠⡾⠀⠀⠀⢾⡁⠀⠀⣿⡄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡄⠀⠀⡀⢘⢀⡀
⠠⡄⠁⠛⠃⠀⠀⠻⠎⠆⠀⡿⠷⠿⠙⠁⠌⠡⠀⠐⠂⠀⠀⠀⠐⠲⠶⠀⢰⡄⠀⠂⠀⠀⠀⠀⢨⠿⠿⠦⠤⠣⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠠⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄
⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠
⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁
⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃
⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄
⠙⠀⢀⣀⡀⠀⠉⠙⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⠀⣀⡀⠀⠋⠉⠀⢀⣀⡀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠛
⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠
⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁
⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃
⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡄
⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⡀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠
⣀⠀⠈⠉⠁⠀⣀⣠⠀⠈⠉⠀⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣄⣀⠀⠈⠉⠁
⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃
⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄
⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠
⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠀⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈⠉⠁
⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠃

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⢦⠀⠠⠁⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠀⠀⠀⠀⢐⡂⠀⠀⠀⡁⠔⠈⠀⠀⠀⡔⠁⠀⠱⡀⠀⠀⠁⠂⢄⠁⠀⠀⠀⠰⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠢⡀⠄⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠆⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸⠅
⠀⠈⠀⠀⠀⠀⢐⢢⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠰⠄⠀⠀⢸⢀⡀⠤⠄⠤⠤⠤⢸⡤⠖⠒⢰⠂⠒⠠⠀⠧⠀⠀⠀⠀⠐⠂⠀⠼⠘
⠀⠀⠀⠈⠁⠀⠀⠀⠁⢀⣴⣄⢠⣆⢠⣦⢴⣶⣶⢨⣆⢠⡦⣠⣄⣴⡄⢠⣄⢠⣤⠀⠀⠀⠀⡀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⣼⣯⣿⡼⣿⣾⠇⠀⣿⠀⠸⣿⣾⡇⣿⠛⢻⣿⣿⡿⣿⡿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠁⣉⠋⣴⠀⠉⠀⡖⠉⠉⣀⠋⣤⠀⠉⠘⠁⠈⠁⠀⠀⢴⠀⠀⠀⠀⠂
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠘⠧⢺⠀⣿⣠⠐⣇⠀⢈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⢐⡃⠀⠀⠮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣟⣛⣟⣛⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⠋⢹⣿⣿⡏⠙⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⣿⣿⣿⣿⣿⣿⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⡟⠀⠀⠘⡇⠀⠙⢿⣿⣿⡿⠋⠀⢸⠃⠀⠀⢻⣿⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⣸⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠠⠄⠁⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢆⠘⠁⠋
⠀⠀⠀⢰⢆⠀⡀⠀⠀⢹⠓⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠐⡾⢉⢦⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠂
⠸⣶⢡⠆⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡐⠛⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⡠⠆⣧⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠤⠀⠀⠀⠀⠒⠁⠀⢀⠀⠀⠀⢠⠀⠀⣠
⢀⡂⠀⣴⢿⠇⡿⢀⡐⣆⣾⢧⡳⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⣖⣦⣶⣤⢴⣞⠟⣀⣤⡌⢷
⠞⣤⣶⣮⢣⣌⢣⣯⢿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠻⢫⡷⣶⡷⢿⢾⣨
⠛⠛⠛⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠟⢛⣛⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⣉⣴⣶⣿⠿⠿⠟⠛⠿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⣿⡏⣥⣴⣶⣶⣾⣿⣷⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⡾⠛⢉⣡⣴⣾⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣲⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣤⣬⣉⣉⠉⠉⣉⣉⣤⡴⠞⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⣵⠞⣫⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣬⣿⣦⣤⣉⠛⠛⠛⠛⠛⣩⣴⣾⣯⣌⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣡⢞⣵⡾⢛⣹⠿⠛⠉⠁⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣞⣡⣿⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣴⠂⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡼⠁⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡟⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⣷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⣤⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢹⡄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠲⣤⣀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣄⣤⠤⠤⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⣤⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠯⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣤⣄⣀⣠⣤⣤⡤⠴⠖⠒⠋⠉⠁

⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢐⠞⡇⠉⣶⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⡴⢿⡁⠀⠀⠀⠀⠔⠋⢳⣤⡴⢢⠀⠀⠀⢀⣠⣤⣦⣀⠀⠀⠀⠀⣄⣂⠀⠀⠀⢀⠤⣂⠻⣏⣵⡄
⠀⠀⣐⡯⢐⡇⠀⣩⡅⠀⠀⠀⡈⢳⣶⡇⠒⠀⠀⠀⡨⠀⣨⠈⠢⡄⠀⠀⢻⣴⣼⣟⣶⡟⠀⠀⠀⡼⠽⢿⣿⣿⡆⠀⠀⠐⠀⠠⠆⠀⠀⢎⠲⢯⣿⡯⠵⡮
⠀⠀⠂⢹⣶⣧⣠⡽⠀⠀⠀⠀⠁⣨⠉⠱⠄⠀⠀⠀⢠⡴⢫⡀⠀⠀⠀⠀⢈⡛⣠⠟⡅⠀⠀⠀⠀⡇⢰⢄⡈⠀⠀⠀⠀⠈⢠⠉⠀⠀⠀⠀⠉⢹⠋⠛⠓⠁
⠀⠀⠀⠀⠉⡛⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⣸⠡⠂⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠘⠯⠩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⡀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣇⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⢘⠣⠄⣠⠀⠀⠀⠀⠠⠊⠀⠀⢱⠀⠀⠀⠀⠀⡿⡛⢻⠏⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⠈⣣⣬⢅⡠⠀⠀⠀⠀⠀⢀⢸⠃⣑⠀⠀⠀⠀⠒⠊⣹⣟⠂⠘⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⢿⠀⢘⠀⠀⠀⠀⠀⢹⡟⠙⠛⠋
⠀⠀⠀⢀⡴⣤⡚⠶⢼⠄⠀⠀⠀⠀⠀⠐⣎⣸⠗⠉⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠘⠶⣦⣦⠞⠀⠀⠀⠀⠀⠸⣆⡜⠀⠀⠀⠀⠀⠈⢦⣠⡄
⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠰⢶⣿⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣣⠇⣀
⠀⠀⠉⢰⣶⡦⠚⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡼⣿⢀⡄⣤⢸⡏⠀⣠⢠⡄⢀⠀⠀⠀⢠⣄⣄⠀⠀⢀⡤⡶⢛⠿⠷⡛⠓⠂
⠀⠀⠀⠞⢉⠃⠲⠄⠀⠀⠱⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⡗⣿⢼⡷⢿⣿⡇⢀⣿⠼⣷⣿⣴⣶⡖⣸⡏⡟⠀⠀⢼⡏⢰⠃⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⢸⠃⣿⡆⠀⠀⢸⣇⡜⠀⠀⠸⣿⠃⠀⠈⠁⠀⠷⠂⠀⠘⠣⠸⢆⣀⣴⢁⣔⠡⠃⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⡀⢀⣄⠉⠀⣴⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⡧
⠀⠀⠀⠐⣤⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⢀⡄⠀⠄⠀⠀⠀⠀⠀⢻⡇⣼⣯⠀⣸⣿⣾⣤⢀⣾⠇⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⢻⣿⣀⡇
⠀⠀⣾⣁⣈⣦⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣧⡏⢿⡠⢿⡟⣱⣿⠙⣿⣸⢿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⡿⠋
⠀⠀⢸⣶⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢸⣟⠻⠏⠀⠀⠀⠛⠀⠀⠀⡄⠀⠐⠀⠔⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠘⠃⠁⠀⠀⣀⢄⠀⠀⠀⠀⢀⣤⣤⢀⡀⣴⡶⢶⡶⢦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣀⠌⢄⣀⠀⠀⠀⠀⠈⠻⠓
⠀⠀⠀⠀⠀⠀⡴⠉⣿⣷⠀⠀⠀⢸⣿⠏⣿⣋⣿⡧⢺⣟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡞⠫⠥⠤⢬⡙⣤⠀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⣷⢏⠀⠀⠀⠸⣿⣆⡿⠇⠛⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠢⠠⠄⠤⠠⠜⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡽⡆
⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡞⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠒⠋
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠞⢽⠟⣃⠀⠀⠀⠀⠀⠄⡀⡶⣆⠀⢠⠀⠀⠀⠀⠀⠤⠺⠰⠇⠻⠂⠀⠀⠀⠀⢀⠀⠈⢠⡤⠀⠀⠀⠀⠀⠀⠈⠃⢠⠇⠂⣀
⠀⠀⢘⡀⣲⣮⣽⠀⠀⠀⠂⢀⣷⣿⣶⣯⣀⣀⠀⠀⠀⠀⠀⠇⠀⢸⡁⢀⡇⠀⠀⠀⠀⠘⢇⠀⠁⠀⡀⠀⠀⠀⠀⠀⢰⣒⣹⡥⡀⠈⠀⠀⠀⢀⣀⡀⠋
⠀⠀⠀⢳⣿⣯⠃⠀⠀⠀⠀⠀⠈⢙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠚⠀⠀⠀⠀⠀⠒⠈⢑⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⠴
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠀⠐⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠈⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠠⠈⠐⠁⠀⠈⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣀⣀⣶⡆⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⣈⢹⣿⣿⣿⣿⣿⣷⣾⢿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⡿⠿⠿⠿⠛⣋⣭⠹⢯⣷⣾⣿⡿⠛⡿⠿⣍⢳⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣤⣤⡤⣤⣶⣬⣭⣤⣉⣉⠉⠁⢠⣾⣿⣖⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣄⠉⣹⢿⣿⣿⣿⡦⢘⣿⣿⠛⠋⠈⣹⠟⣿⠿⢿⠟⠛⢋⣽⣭⣷⣦⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⡀⣀⣠⡄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣏⣀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢠⡿⠻⢿⡿⢻⣿⣿⣿⣷⣾⠟⢿⢿⣽⠛⠿⠿⢛⣩⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣼⣤⡀⢀⣿⣸⣿⣿⣿⣿⣿⡀⠈⠛⠐⠃⠀⠀⠘⠋⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⡟⠛⣿⣯⣙⣿⣿⣿⣿⣿⠖⠐⡲⢷⠞⠒⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⣨⣭⣽⣿⣶⢿⣾⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⢿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠟⣴⣋⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢠⣤⠛⠋⠛⢼⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠒⠂⠀⠀⠄⠙⠛⢹⣿⡿⠟⠛⠿⣿⣿⣭⣾⣷⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⣾⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢠⠈⠀⠀⠁⠀⠀⠀⢸⣿⣷⠀⠀⢀⠈⣿⢟⡭⠇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⣿⣿⠂⢹⣿⡿⠋⢹⣿⣿⣿⣿⠟⠀⠐⠀⠀⠃⠀⠀⢀⠀⡀⠀⣼⣿⣿⣷⣄⣿⡗⣡⣿⠅⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢾⣿⣦⢀⣿⣿⣀⣿⣿⣿⣿⠃⣤⠀⡁⠀⠀⠁⢀⠀⠌⣀⠐⣼⣿⣿⠿⠿⠛⠋⣴⠿⠻⢛⡃⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠿⠿⢿⣿⣿⠿⣿⠙⢿⣿⠯⠆⠀⢣⠀⣡⠒⠯⡴⠶⠈⠙⠉⠉⠀⠀⢀⣀⣀⣤⣠⣤⡞⠉⠁⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢠⣤⣿⣏⣀⣾⣿⣷⣄⣿⣆⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⢀⣴⣶⣿⡿⢿⣿⣿⡟⠿⢿⣿⣿⣿⣿⢿⣄⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠘⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⣠⡴⢾⠿⣿⣿⣿⡏⣠⣿⣿⣿⣷⣀⡀⠉⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⢿⣿⡟⢿⣿⠈⠉⠀⠙⠦⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⠋⠀⠘⣿⣧⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⢿⣿⣿⣿⣿⣿⣿⣯⠅⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣤⣀⣀⣤⣤⣾⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣝⣿⣿⣟⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠛⠿⠟⠿⢿⠛⣿⣿⣶⣤⣶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡉⠀⣀⣑⠀⠈⣀⡈⢿⠿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠩⠀⠿⠛⡀⢼⠛⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⡀⢤⣿⣽⡷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡀⠐⠀⢙⣿⣿⣋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣱⣾⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⡀⠀⠈⠈⠿⠿⠀⠀⠈⣿⣿⣿⡞⠛⠛⠿⣿⣿⣿⣛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⡀⠢⠊⠀⡀⢸⣿⣿⣿⣅⣈⣃⠰⡟⠈⢿⣿⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠉⠀⠈⠛⠉⠘⠉⠛⠚⠢⣭⣶⣿⣿⣿⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⣛⠻⠀⠀⠀⠀⠂⢀⠐⠀⠠⣤⡀⠁⠀⠉⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⠀⠀⠍⠠⠤⠁⣁⡹⢄⣀⣠⣌⣀⣀⠠⠅⠤⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⡤⠐⠀⠐⢦⠀⠤⢤⠤⠄⠀⠀⠀⣤⠤⣄⠀⠀⠤⠀⠁
⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠉⠑⠦⡀⠀⠀⠀⠢⡀⠁⢄⢸⠀⢸⠀⠄⠀⡀⢨⠤⠤⣤⢄⠀⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣀⣆⡀⣃⣇⡠⠊⠁⠀⠐⠒⠒⠋⠉⠒⠤⣀
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⣤⣤⣤⠤⠤⠴⠖⠉⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⣀
⠀⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠑⢆
⠀⠀⢸⡠⠋⠀⣀⣀⠀⣀⡀⡇⢀⣀⡀⢀⠀⡀⢀⣀⡀⢀⣀⠀⡁⠀⠀⢏⡈⢀⣆⢀⠀⢀⢀⣀⣸⠀⡁⢀⣀⡀⢀⣀
⠀⠀⢸⠙⢆⢸⡁⢸⠀⡇⠀⡇⢾⠀⣹⠘⣦⠃⣏⠀⡷⠘⢦⡀⡇⠀⠀⡀⢙⡆⡇⢸⠀⣿⢸⠀⢹⠀⡇⣏⠀⡹⠘⢦⡀
⠀⠀⠈⠀⠈⠁⠉⠉⠀⠁⠀⠁⠈⠉⠁⠀⠈⠀⠈⠉⠁⠈⠉⠀⠁⠀⠀⠉⠉⠀⠁⠈⠉⠁⠀⠉⠉⠀⠁⠈⠉⠁⠈⠉

⠀⢠⠀⣼⢹⠏⠈⠻⠋⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧⠈⠉⡀⣹⢻⣠⡞⠀⠂⢺⣶⠟⠉⣻⢄⢒⡶⢀⡐⡄
⠀⠀⠀⡏⠸⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣘⢧⠀⢭⠆⠈⡩⠃⠀⠀⠀⣙⡄⠀⠀⢬⠃⠙⠸⠇⠼⣦⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⡄⢀⣄⠄⠛⠋⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⡂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⣧⣤⠈⠁⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⢀⠻⢷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⠀⠀⠈⣿⣷⣼
⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⢜⣦⡀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⣠⣿
⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡈⠀⢠⠀⠗⠀⠲⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠂⠀⠀⠀⠀⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠠⣄⠁⣸⣿⠀⠗⠛⢉⠄⣠⠉⠀⢠⣐⠇⠀⠀⢀⣠⡉⠀⠀⠁⢠⢠⣴⣧
⡃⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡔⠀⠀⢀⣓⣾⣿⣆⣠⠀⢁⢰⠃⠀⠀⠀⣻⢄⠀⠊⠉⠉⠉⠂⠀⣴⣿⠘⢿⣟
⣷⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣰⠊⡸⠀⠀⣴⣿⠿⣩⣿⣿⣿⣇⠘⣂⣼⠇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠓⠀⢸⠀⠻⠏
⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠠⠾⠃⠀⠃⠀⠨⠟⠉⢠⣿⣿⣿⣿⣿⠓⠙⡿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣄⣤
⣿⣿⠀⡀⢠⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣿⠘⢿⡇⠀⢡⠠⠀⠀⡅⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⠀⣿⣝
⣿⠏⣠⡇⢸⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠁⠀⠀⠀⢘⠙⠀⠐⡄⠂⠀⡇⠀⠀⠀⠀⠀⢠⣏⣦⡠⣼⡀⢏⣽
⣇⢸⣿⣧⣿⣿⢸⣿⣿⡇⠀⠤⢦⢾⢳⣤⠀⠃⠀⠀⠀⠀⠀⢀⡆⠀⠞⡚⠆⠀⡄⠀⠀⣬⠀⠀⠀⠀⠀⢾⡿⠫⠶⣼⠀⠘⠛
⣿⢾⡿⣽⣿⣿⢸⣿⣿⣷⣄⠀⢀⡀⠣⠋⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⡇⠀⠃⠀⢠⣿⡆⠀⠀⠀⡀⢘⡇⢠⢂⠼⠀⣈⠛
⡿⢟⣼⣿⣿⣿⢸⣿⣿⣿⣟⣣⡬⢥⡀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⢆⠘⡆⢀⣷⠀⠀⢸⡷⠀⠀⢀⣡⡪⠤⠣⠶⠶⠘⢻⠆
⣴⣿⡟⡿⣿⣿⡝⣷⣹⣿⣿⣿⣿⠄⠀⠀⢠⠈⢀⡀⠀⠀⠀⡀⠀⠀⠸⣰⡀⢸⣟⠰⠄⠟⠤⠈⠀⢀⠁⣁⠂⠻⡫⣀⢈⠈⠃
⣟⠟⣄⠻⣿⣿⡂⣿⡆⠻⣋⣭⣭⡄⠀⠀⠀⢂⢸⡇⠸⣃⡀⠃⠰⣆⡀⠨⠅⣈⣫⡎⢍⣛⣦⡿⡄⠩⣠⣤⠮⠂⡀⠤⠀⠉⠒
⠉⠀⠀⣿⣿⡟⣦⢸⣧⠀⢻⣿⣿⣿⡀⠀⣰⡘⣿⣧⡄⠙⠛⢷⣦⣄⠻⣦⠀⠻⣿⢯⣼⡼⣿⡏⠳⠔⠀⠀⠘⠀⢹⠄⠀⠢⡀
⠁⠀⣾⣿⣿⣱⣿⠀⢿⡇⠀⠃⠿⣏⠓⠀⢹⣮⣻⣾⠧⠀⠀⣀⣱⠟⠟⣻⢰⣤⡩⣿⣿⣯⣭⣿⠃⣴⣆⠀⠀⠀⠈⠀⠀⠀⠘
⠀⢠⣿⡟⣻⣿⣿⠂⠈⠛⢁⢀⡀⠀⠀⠀⠀⠙⣿⡐⠲⢆⣄⠀⠉⠀⢷⡇⢨⣅⡣⣈⡌⠻⠧⣾⡻⢚⣡⣶⣶⡆
⡀⠈⣿⡇⣿⡿⣿⣄⠀⢠⣼⣿⢿⡀⠀⠀⠀⠀⠹⣭⢦⣀⠻⣧⢀⣦⡈⠁⣷⣾⣿⣿⡿⠉⠸⠋⣱⣿⣿⠟⢩⡍
⣷⢸⡏⠓⠿⢻⣿⣾⣷⣸⡿⠙⠋⠀⠂⠀⠀⣀⣼⡿⣆⣬⢢⠿⣿⡻⠃⠀⢮⣽⣿⣟⠀⠀⠀⠀⠈⣟⠁⠀⡈⠁⠀⠀⠀⠈
⣽⣮⣿⣦⠀⣼⣁⣽⣿⣫⣟⣧⣀⠀⠀⢠⣤⡿⣠⣤⣸⢽⡿⣿⣿⣦⣀⡀⢸⢦⡀⢁⠀⣀⠀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣫⠖⠛⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠘⠃⢹⡆⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⢀⣤⠼⣋⣼⣶⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣻⠿⢷⣿⣿⣿⣿⡿⠁⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢿⣿⣿⣿⡿⢫⡿⠁⠀⣀⣿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠉⣉⡟⣠⡀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⣠⣤⠏⣴⡿⠃⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⣿⣾⣿⣿⣾⣿⠁⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⢿⣿⣯⣽⣿⣿⡿⢿⣿⣻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠙⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣤⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠿⠿⣷⢶⠠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢉⠻⠿⢿⣷⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠀⠈⠀⠈⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⠀⡄⠂⢄
⠀⠀⠀⠀⠀⠻⡄⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⠀⠀⣤⣤⣤⡠⠄
⠀⠀⠀⠀⠀⠀⢳⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣴⠷⠛⠛⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢫⣵⣄⠐⢤⡄⢶⣀⠀⠀⣴⠿⣹⣟⡥⠀⠂⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣲⡀⡈⠓⠠⣧⠜⠁⠈⡏⠀⢠⣏⣄⡀⠀⠀⠀⣸⣤
⠀⠀⠀⠀⠀⠀⠀⠉⡩⣍⣉⠑⡢⣄⡀⠀⠙⠻⣥⣈⡉⠁⠀⢀⠀⢜⣾⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠹⡇⠐⠂⡀⠤⠉⠳⣼⣷⣾⣿⣟⣛⣥⣾⣶⣽⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢏⡓⣺⡦⠤⠤⢤⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠉⣬⡤⠴⠀⠀⠀⠀⠰⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡄⠀⠀⠀⠀⠀⠻⠿⣲⡅⡬⣿⠺⣿⣿⣿⡿⠞⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠄⠀⠀⠀⠀⠀⣾⣧⢥⣼⡶⣷⠄⣿⣿⣿⡿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⠀⠀⠀⠘⠿⠊⠖⠘⣻⠟⠖⣽⣻⣷⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠰⢩⡆⠀⣠⣾⣾⣧⣤⣰⠟⠀⣄⣨⣿⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⢿⡀⣿⣿⢿⣿⣿⣿⣧⣜⣿⣷⣦⠀⠾⣿⣷⢄⣽⣄⣀
⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠠⢤⡀⠀⠀⠀⠻⢿⣹⣿⡇⣀⠘⠛⠉⠛⠛⠛⠉⣿⣉⢾⣿⣿⡿⠹⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠼⣦⠀⠉⠀⠀⠀⠀⠺⣿⠱⢸⠃⠀⠀⠀⠀⠀⠀⠀⠸⣷⠮⣿⣿⠀⠀⠈⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣠⠄⠀⠀⠀⣴⢉⡼⢈⡀⠀⠈⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣩⠤⢤⡄⢀⠆⠘⠛⠣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣤⣴⣷⣿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠇⢀⣄⠁⠈⠀⠀⠀⠈⣷⠀⠀⠀⠄⠄⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⡀⢀⣀⢀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡉⢂⡀⠈⠉⠂⠤⠀⠀⠻⣆⣄⠀⠀⢯⣿⠟⠋⣁⡉⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠼⠶⢢⣴⡄⠀⠀⠀⣵⡙⠆⣀⠴⠠⠶⠛⠙⠇⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢎⣤⡀⠈⠉⠀⠁⠀⠀⠀⠀⠀⢠⣅⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣶⣤⣄⠄⠀⠀⢀⠀⠀⠈⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠒⡗⠒⠁⠈⠀⡀⠀⠀⠀⢙⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⡀⠀⠀⠀⠀⠂⠠⠁⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠓⠀⠀⠀⠀⠃⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠀⢸⠀⠀⠀⠀⠘⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⡿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀
⠉⠀⢀⣀⡀⠀⠉⠁⠀⣄⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⡠⠀⠉⠉⠀⢠⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⣀⣀⠀⠈
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡄
⣀⠀⠈⠉⠁⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠀⠀⠉⠁⠀⢀⣀⠀⠈⠉⠁⠀⣀⣀⠀⠈⠉⠁⠀⣀⡀⠀⠉⠉⠀⢀
⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⠁
⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀
⠉⠀⢀⣀⡄⠀⠉⠁⠀⢄⣀⠀⠈⠉⠁⠀⣄⣠⠀⠈⠉⠁⠀⣀⡀⠀⠉⠉⠀⢀⣀⡀⠀⠉⠉⠀⢀⣀⠄⠀⠉⠁⠀⣀⣀⠀⠈
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄
⣠⠀⠈⠉⠁⠀⣄⡠⠀⠉⠉⠀⢠⣀⡄⠀⠉⠉⠀⢠⣠⠄⠀⠉⠉⠀⢄⣠⠀⠈⠉⠁⠀⣄⣠⠀⠈⠉⠁⠠⣀⡄⠀⠉⠉⠀⢠
⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙
⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀
⠉⠀⢠⣀⠄⠀⠉⠉⠀⢄⣠⠀⠈⠉⠁⠀⣄⣠⠀⠈⠉⠁⠠⣄⡠⠀⠉⠉⠀⢠⣀⡄⠀⠉⠉⠀⢤⣀⠄⠈⠉⠁⠀⢄⣠⠀⠈
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢠⡄
⣤⠀⠈⠉⠁⠀⣤⡤⠀⠉⠉⠀⢠⣤⡄⠀⠉⠉⠀⢠⣤⠄⠈⠉⠁⠀⢤⣠⠀⠈⠉⠁⠀⣤⣤⠀⠈⠉⠁⠠⣄⡤⠀⠉⠉⠀⢠
⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙
⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀
⠉⠀⢠⣤⠄⠀⠉⠉⠀⢤⣤⠀⠈⠉⠁⠀⣤⣤⠀⠈⠉⠁⠀⣤⡤⠀⠉⠉⠀⢠⣤⡄⠀⠉⠉⠀⢠⣤⠄⠈⠉⠁⠀⢤⣤⠀⠈
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢠⣆
⣤⠀⠈⠉⠁⠠⣤⡤⠀⠉⠉⠀⠠⣤⡄⠀⠉⠉⠀⢤⣤⠄⠀⠉⠉⠀⢤⣤⠀⠈⠉⠁⠀⣤⡤⠀⠈⠉⠁⠠⣤⡤⠀⠉⠉⠀⢠
⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠘
⣟⣿⣿⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣿⣿⣛⣿⣿⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢻⠀⠀⢢⢄⣀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠃⠀⠀⠀⠀⢶⠌⠙⠦⠄⠀⠀⠀⠀⠀⢩⠽⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡓⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⢻⠇⠀⢀⡠⠤⢀⣰⠋⠇⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠥⢄⣀⡿⠠⣞⣭⠤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢶⣦⡄⢰⣉⣤⡶⠚⣻⠷⠈⠣⡉⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠈⣿⠸⣿⡄⠀⠀⠉⠀⠀⠀⢣⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠐⠐⠛⠋⠁⠀⠘⢧⡀⢨⡀⠀⠀⠀⣰⡀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠠⠸⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣜⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣵⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠔⠠⠄⠀⠐⠶⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠄⠀⠀⠓⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠤⠤⠄⠠⠠⠦⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀
⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠐⢨
⠀⢸⠒⠀⠀⠀⠑⢀⠆⠀⠀⠀⠀⠀⠰⠌⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰
⠀⢸⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠸
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⠀⠀⢸
⠀⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⠠⠀⠀⠀⠸
⠀⢠⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢐
⠀⠘⠀⠀⢁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⢰
⠀⠰⠀⠀⠈⠤⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢐⠀⠀⠀⠀⠉⠎⠁⠀⠐⠀⠄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢘
⠀⠸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡦⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠐⠀⢸
⠀⢸⠂⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠋⠓⠀⢸
⠀⢘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢸
⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰
⠀⢘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐
⠀⠀⠁⠉⠀⠈⠀⠈⠀⠉⠀⠁⠈⠉⠁⠉⠁⠉⠈⠀⠀⠉⠁⠈⠁⠀⠈⠀⠉⠀⠀⠀⠉⠁⠁⠈⠈⠁⠁⠁⠈⠉⠁⠈⠉⠈
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⢿⡾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡃⡼⠃⠀⠀⠀⠀⣴⣶⣶⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢤⠀⠀⠀⠀⠈⢃⣀⣀⡸⢱⣀⠤⠙⠛⠛⠛⠿⣿⣿⡿⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢠⣄⣀⣠⠊⠁⠀⠐⢁⠜⢣⠀⢸⣏⣶⣤⡀⠘⣿⣿⣷⡄⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠈⠒⢤⠤⠀⠠⠀⠘⠀⢀⠀⠆⢠⣉⡙⠻⠛⢹⡏⠉⠉⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⢏⠤⠒⠚⢄⠀⠢⠴⢶⡊⠁⠀⢰⠀⡏⢙⡀⠀⠠⡀⠀⠀⣴⠟⣻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠱⣁⣀⢶⣾⠂⢣⡀⠀⠸⣨⠗⠈⠙⠚⠀⠛⠳⡦⡁⠇⠀⠠⠵⣾⣿⣝⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⡇⠛⠿⣤⣽⣿⣿⣇⣀⣰⠁⠀⣀⣀⠀⠠⢆⡀⠀⠙⣄⠀⠀⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢠⣀⡇⠀⠒⢃⠜⠋⢡⣂⡄⠀⣉⠲⠄⠋⢀⣠⣴⠀⣀⠤⡀⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡡⠨⢳⡀⠀⡏⠀⠀⢨⡽⢗⠻⠀⠀⡎⠁⡪⠽⠋⠰⠥⡀⡨⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠰⡅⡀⡇⠙⠂⠖⠂⠘⠁⢀⣎⠀⣀⠔⠋⠉⠑⠢⣾⠼⣀⣈⢣⠸⣌⠆⡀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠳⢌⣘⡦⡄⣠⡀⠀⣤⠈⠈⢶⠁⠠⡄⣠⣶⣴⠈⡞⠀⡏⡆⣠⠃⠊⠐⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠕⠠⢊⠼⢿⠀⠉⣀⣀⣄⠀⠀⠸⠀⠀⢀⠁⢀⡀⠀⢰⠊⠀⠀⢹⠍⠉⡓⣎⠔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠡⡐⠆⠆⠀⠻⠽⠟⠀⠀⠀⡆⠧⡸⠀⠿⠃⠀⠸⠀⠀⠇⢸⠈⢑⠈⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⣶⣶⣶⣿⡖⠒⠒⠚⠧⠁⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠈⠛⠟⠛⠁⠀⠀⣠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣤⣀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢀⣀⡀⠀⠀⠀⣰⣶⣶⣦⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣴⣾⣿⣿⣿⢿⣷⣎⢩⣿⣿⣿⡟⠻⢿⣿⣿⡟⣻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠛⢿⣿⡿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡽⢽⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠈⢻⣷⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠏⢹⣿⣿⡿⠛⠿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣿⣿⣧⣸⣿⠟⠁⠀⠀⠻⣿⣷⢀⠴⣿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠈⠋⠀⠀⠀⠀⠀⣴⡾⢙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣰⣒⣾⣿⠶⠋⠁⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣦⠀⢈⣠⣔⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⠉⢡⣀⠀⠀⠀⠀⠻⠣⣼⣱⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⠈⠃⢀⠀⠀⠀⢂⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⣸⣿⣿⣿⣧⠀⠀⠀⠀⠴⣿⣿⣿⣿⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠂⢄⠊⠻⣿⣿⣷⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⣤⣔⣬⣤⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠻⣿⣧⡄⠐⠀⣿⣿⠿⠟⠛⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⣿⣿⣿⡏⠂⡐⢸⣿⣿⣷⡶⢯⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡷⢦⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⠬⠉⠙⠛⠃⠀⠀⠀⠛⠉⠁⠀⢸⣿⣷⡄⠀⠀⠀⠉⠛⠛⠛⣅⠀⢸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠈⠉⢀⣀⡀⠀⠀⠀⠀⠀⡀⢀⣾⣿⠫⢠⡄⠀⠀⠀⢴⣶⣾⣶⣶⣽⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣶⣿⣿⣿⠇⠈⣴⣿⣷⣤⣤⣿⣿⣇⣈⣐⣠⣤⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⣾⣶⣦⣤⣴⣾⣿⣿⣿⣿⡿⠫⣀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢈⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⡿⠟⠛⠛⠛⢻⣿⣿⣿⣦⣀⠀⢸⣿⡿⠿⠻⣿⣿⣿⡟⠛⠻⠿⢿⣿⠀⣠⣴⣿⣿⣿⠃⡌⠻⣿⣦⣄
⠀⠀⠀⠁⠄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⢺⣧⣄⡠⠆⢻⣿⣿⠃⠀⠀⠀⣠⣼⡛⠻⠿⣿⣿⡟⠈⠄⠁⣿⣿⠿⠛⢹
⠀⠀⠀⠀⠀⠈⡠⠀⠀⠀⠉⠉⠉⠉⡅⠀⢸⣿⣿⣿⣆⠀⠈⠃⠀⠀⣠⣾⣿⣿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠨⠠⠄⠀⠀⠀⢴⣶⣾⣶⣦⣼⣿⣿⣿⣿⠆⠀⠀⠀⠈⢛⢿⣿⣿⣿⡄⣂⣬⣤⣴⠀⠀⠠⠀⠀⠀⢤⠁
⠀⠀⠀⠀⠀⠏⠈⠔⠀⠄⠀⠀⠙⢿⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⡈⠅⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⣿⣿⣿⣿⣿⣆⠀⠀⠀⣸⣿⣷⣶⣾⣿⣿⣿⣿⣿⣟⠋⠲⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⣾⣿⣿⣿⠃⠈⢻⣿⣧⣄⠀⢻⠿⠋⠉⠀⠀⠀⣿⣿⣿⣿⣷⣦⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡏⠀⠀⠈⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⡀⠀⠀⠀⡴⡄⠀⢀⠔⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡧⠊⠹⠝⠀⠀⠃⠀⠀⡌⡄⡌⢰⣡⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠖⠋⠈⣱⠀⠠⡪⠕⠒⢒⡲⠶⡤⡷⢖⡂⠐⠒⢤⡀⠀⠀⠱⠋⠀⢘⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠒⠊⢩⡆⡜⠀⠀⡔⡁⠀⡌⠀⠘⡄⠈⢢⠀⠙⠙⡄⠀⠀⢠⡊⠅⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠑⢤⠚⢱⠀⠀⢠⠁⠀⢀⠁⠀⠀⢁⠀⠀⡇⠀⠀⡇⠀⠀⠉⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠊⠈⠒⠤⢤⠈⡄⠀⠈⡆⠀⠘⠀⠀⠀⠸⠀⢀⠇⠀⢠⠱⠀⢀⡜⠉⠱⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡐⣄⠘⢸⠀⠘⢄⡀⠘⢆⠀⠇⠀⠀⡆⢀⠎⣀⠔⠉⠁⢠⡟⠈⠢⣀⡸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠁⡛⡲⢦⣀⡀⠈⠓⠂⠍⠸⠄⠐⠒⠃⢈⣀⣀⣀⡀⠀⢱⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣈⠀⠀⠀⠀⢄⡀⠀⣠⣀⢴⣤⠒⠈⠁⠀⠀⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢁⡢⠘⢄⣊⡣⠀⠀⡠⣒⠄⠉⠁⠀⡼⢃⢀⠑⣀⡸⢻⠃⠀⠎⠉⡊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠑⠀⠈⠁⠀⠸⣔⡰⣂⠾⠚⢰⢁⠞⢉⢈⠁⠀⢆⡉⠒⠒⠎⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡊⠁⣬⠖⠂⠐⢉⡠⢄⠀⠚⢘⡿⠠⡫⠠⠘⠈⡀⠨⡃⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⠗⠉⠀⡆⣤⡍⡑⢙⢋⠀⣔⠝⡸⢩⢯⠀⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⠁⢹⠀⡇⠸⣽⠋⡙⠊⣀⣸⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⠃⠀⣕⠠⢒⠜⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⠦⢀⣴⠘⣁⣬⠥⠀⣤⠀⠀⢀⣁⠀⠀⠀⢠⠀⠀⠄⠀⠀⢸⣿
⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⡀⠀⠓⢄⣺⣿⡈⠁⠠⢊⡰⠀⠀⠐⣾⠁⠀⠠⠶⠦⠄⠀⢀⣴⢸⣿⡿
⣇⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢠⠄⡎⠀⢀⣴⣶⢿⣿⣿⣿⠀⢾⢃⡄⠀⠠⢿⠓⠀⠀⠀⠀⠀⢠⠘⢻⠈⣿⠶
⣿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣴⠃⠸⠁⠀⣾⠟⢁⣿⣿⣿⣿⡷⠴⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠉⣁
⣿⣶⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⡏⠻⣿⠀⠘⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⣟⣫
⣿⠟⢰⡄⣿⣹⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠀⠅⠀⠏⠂⠀⡆⠢⠀⡇⠀⠀⠀⠀⠀⣾⣧⢀⣸⠀⣟⣿
⣏⢸⣿⣷⣿⡇⣿⣿⡇⠀⠠⢤⢾⢦⡄⠚⠀⠀⠀⠀⠀⢀⡂⠠⢓⠓⠀⠄⠀⠀⣥⠀⠀⠀⠀⢸⣿⢻⠤⣼⠀⠙⠋
⣿⣿⣿⣿⣿⣇⣿⣿⣿⣦⡀⢀⡈⠏⠃⠀⠄⠠⠀⠀⠀⠈⠀⠀⠁⠸⠀⠀⠀⠠⣿⡀⠀⠀⢠⢀⡷⢠⠀⠾⠀⣈⠃
⠟⣫⣾⣿⣿⣇⣿⢿⣿⣟⣥⣖⢦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠇⡱⠀⣿⠀⠀⣸⠧⠀⢀⢠⡴⠗⣚⣒⡟⠈⢹
⣾⣿⠋⣿⣿⣷⢹⡮⢿⣿⡿⡿⠀⠀⠀⠀⠀⡆⢀⣀⠀⡄⠀⠀⠐⡷⠀⣯⡔⣆⣋⠢⡄⠌⣆⢠⢄⡐⠱⠤⠬⣞
⣿⠓⠢⣽⣿⣿⢸⣿⠈⣵⣶⣿⡆⠀⠀⠈⣤⡇⠈⣥⣤⣁⠛⢢⣄⠑⢠⣧⣧⢱⢶⣷⢿⡀⠐⠚⠋⡀⢦⠀⠀⡀
⠖⠀⣴⣿⣿⣹⡏⢿⣆⠘⣿⣿⣿⡀⠰⣗⢿⣟⣯⠀⠈⠙⣻⣦⣿⡇⡈⠻⣷⣾⣾⢿⣧⠈⣀⠀⠀⠀⠸⠋⠀⠀⢄
⠀⢀⣿⡿⣷⣿⡇⠘⢷⠆⠀⠉⠓⠀⠀⠛⣷⢟⣭⡅⠀⠓⠛⢹⣰⠃⡟⢶⠻⡻⣿⣟⣳⡾⡿⢀⣀⡀⠀⠀⠀⠀⠈
⠀⠸⣿⢠⣿⣿⣇⠀⠀⣸⣶⣦⠀⠀⠀⠀⠙⣕⣢⡘⢿⡆⢂⡀⠛⢰⣩⣷⣿⣷⠖⢹⠓⣵⣿⣿⠟⡓⠀⠀⠀⠀⠐
⣧⢰⡟⢿⡿⣾⣯⣷⣸⣿⠻⠟⠃⠄⠀⠀⣠⣿⣯⣝⢄⣷⣾⣿⠀⢨⣻⣿⣿⠁⠀⠀⠀⢻⡛⠉⢀⠃⠀⠀⠀⠐⠄
⣻⣬⣷⣄⢠⣟⣹⣿⣟⣿⣦⣀⠀⠀⣠⣼⢏⣩⣸⣿⡾⣿⣿⣀⣀⣀⣧⡉⢉⠀⣀⠀⣀⣈⡁

⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤
⠀⢨⣿⣿⢟⢿⣿⣧⠀⠀⠀⣰⣞⡛⣳⣦⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠶⢤⠁⠆⠰⠆
⠀⠸⣿⣯⠈⠠⣿⡗⠀⠀⢠⡟⠛⠁⠙⠛⡇⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢿⣤⣬⣇⠁⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⢶⢆⣶⣶⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠀⠤⠤⠤⠆⠀⠀⠂⠀⠉⠉⠈⠉⠈⠀⠀⠀⠠⠄⠀⠤⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠻⡿⠿⠃
⠀⠀⠀⠀⢀⢀⠀⠀⣈⠥⠀⠀⠰⣠⡆⣴⢰⣴⢰⠀⣤⣤⢀⡆⣦⢰⠀⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠐⠻⠳⠀⠀⠉⠁⠀⠀⠈⠁⠀⠈⠈⠈⡈⡀⣁⡈⡀⡅⠀⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⡄
⠀⠀⢠⡀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿⡶⣾⣏
⠀⠀⠀⠁⠈⠁⠁⠀⠀⣶⡄⠀⠀⢠⣶⠀⠀⣀⣻⠟⢉⠙⢿⣃⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣿⠙⢹⣿
⠀⠀⠀⠏⠀⢒⣛⠀⠀⠘⡇⠀⠀⢸⠇⠀⠀⣭⣿⠀⠀⠀⢈⣯⡅⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣿⠀⢸⡟
⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢹⡷⣶⣶⣿⡍⠁⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣶⣾
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣍⠀⠀⠀⠀⠶⠖⠀⣬⣿⡄⠘⠿⠗⠀⢸⣿⣿

⠀⠀⠀⠈⠆⠀⠀⠃⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣤⣤⣴⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡀⣢⣉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢹⣿⣿⣿⣿⢿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢠⣆⢢⣲⣶⣠⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⣜⣶⣿⢿⠎⠑⡛⢽⣿⣟⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⡔⠃
⡀⠀⠀⠀⠀⢠⣟⡫⠇⠈⡀⠀⡇⠈⠈⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠳⡀
⢿⠆⠀⠀⠀⣞⣛⣒⠀⠂⡆⠀⡇⠀⢈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠤⠤⠤
⣾⡆⠀⠀⠀⠴⣖⣚⠀⠀⠹⡿⠇⠀⠈⣙⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⢂⢀⡀⠀⠀⠀⠀⠀⠀⣾⣤⣦⣄⠀⢠
⣿⡇⠀⠀⠀⠈⠟⣶⣧⠀⡀⣐⣀⣀⢠⣻⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠒⠻
⡻⠃⠀⠀⠀⠀⠘⠻⣻⣿⣿⣿⣴⣷⣿⠏⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⠀⠒⠒⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣤⣶⣦⠠⣶⣶⣶⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⣄⡀⡀⡄
⠀⠀⠰⠖⠂⠀⠀⠀⠒⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠼⠍⠉⢼⢗⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⣀⡿⣿⣿⡂
⠀⠀⠀⠀⠈⠡⠻⠓⡈⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠀⠀⠀⠤⣯⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⣤⣼⣿⢚⣛⡁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢲⡞⠂
⠀⠀⠀⠘⡀⢸⠀⠐⠀⡰⠁⠈⠀⠀⠀⠀⠀⡴⢧⡖⠀⠀⠐⠊⠀⠈⠹⣮⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⠠⠀⢠⣥⡀⠄⢰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⣿⡷⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣿⣿⣤⣾⣆
⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⡿⢿⠿⡿⢿⣿⣧⣶⣦
⠀⠀⠀⠈⠁⠙⣿⣿⡅⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠀⡆⠀⢸⣿⣿⡿⠃
⠀⠀⠀⢀⠠⠀⠛⣿⠃⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⡇⠀⠃⠆⠸⣿⣿⣿⠗
⠀⠀⠀⢸⠛⠰⣶⣶⡆⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠂⠈⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⢷⠇⠀⣿⣿⣿⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠆⠀⢀⢀⣤⣶⣾⣶⣶⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢟⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣾⣿⡿⠛⢿⣿⣿⣿⣿⡻⣿⣿⣿⣷⣽⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣶⡄⠸⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠰⡀⠀⠐⠀⠀⣰⣿⣿⣿⣿⡿⠙⠀⠀⠀⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⠇⠀⠀⣀⣴⢶⣯⣤⣽⣿⣿⣿⣧⣠⣧⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢘⣷⡀⢾⡿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢯⢷⡾⢧⡌⠀⣄⠴⠿⣽⣟⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢋⢹⡀⠀⠀⠀⣰⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢦⢷⣾⡆⠀⡿⠚⣻⡿⣿⡟⢻⠟⣿⣿⣝⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠈⣿⣿⡇⠀⠇⣰⠏⠀⢿⢲⣏⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡦⠄
⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⠏⠀⡆⢀⡄⣿⣿⠛⠉⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠀⠀⠈⡀⣧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢁⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠘⣝⡷⠀⠀⠀⠀⠸⢀⠸⣿⡀⠀⠀⡤⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡇⡗⠀⠀⠀⠀⠀⢢⠀⣿⡇⠀⡀⠠⠀⠄⠸⠁⠀⠀⠤⠄⠀⠀⠀⠉⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠂⠀⠀⠀⠀⢸⠀⢺⡇⠐⢁⠘⠛⢦⠊⣤⡴⣷⠀⠀⢀⢦⠀⠀⠈⢻⣿⣿⣟⢿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠃⡰⠀⠀⠀⠀⠀⠀⠆⣼⣇⡴⠙⣦⣄⣀⡈⣼⢾⣥⣤⠔⠋⠀⠀⠀⠀⠈⢿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠃⠠⢿⠚⢟⡿⡟⠁⠀⠉⣼⢏⠀⢀⣰⣷⠀⠀⠀⢻⣿⣿⡿⣿⣾⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠐⣠⡀⠉⢋⠰⢋⣽⡿⠃⠀⠀⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠁⣸⣿⠀⢀⠞⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠽⠻⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⢀⣤⡴⣶⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⢠⣾⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⣛⡛⠓⠿⠀⠀⠀⢀⡀⠀⠁⠐⠂⠀⠀⠀⢿⡿⠿⠃⠀⠻⠿⠿⠃
⠀⠀⣀⠂⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠁⠀⠀⢈⠁⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠒⢠⣤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠶⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠂⠀⠀⠀⠀⢠⠙⢿⠟⣁
⠀⠀⠀⢴⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⢻⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠛⠀⠰⠆
⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠰⠆⠀⠀⠀⢴⠈⠉⠀⠀⠠⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠘⡟⠀⠀⠀⠀⠘⡛⠀⠀⠀⢀⡀⠠⡰⠄⢀⣤⣄⣴⣾⣷⣆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠂⡄⡁⠀⠉⡈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣻⡿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠿⢛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠁⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡄⠀⠠⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡷⢆⣤⣥⣀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣤⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠣⠁
⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⡀⠁⢀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⡟⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉
⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⠛⠿⠿⠷⠿⠿⠿⠿⠛⠋⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⢰⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡟⣆⠀⠀⠀⠀⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠐⠀⠀⠉
⠀⣼⣿⣿⣿⣿⣿⣿⠀⠁⠐⠀⠀⠀⢸⡇⢻⣆⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠻⣿⣿⣟⣿⣿⡟⠀⠀⠀⠀⠀⠀⣾⡇⠸⣿⠆⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠁
⠀⠀⠈⠉⠉⠋⠉⠀⢀⣂⠀⠀⠀⠀⠉⠉⢈⠀⠀⠀⠀⠀⠉⣡⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠐⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⢠⡀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣤⣠⠀⢀⣤⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⣠⢤⢠⣄⠀⢀⣀
⠀⠀⠀⠜⠁⠀⠀⠛⠃⠀⠘⠁⠀⠀⠀⠀⠂⠁⠈⣇⠀⣴⠃⠀⠐⠀⠀⢠⣆⡄⠈⣡⡀⢆⠷⠂⡠⠘⡇⢫⢶⡄⠀⠀⣴⠮⠃⡟⢘⡄⣱⠉⡸
⠀⠐⠀⠂⠀⠀⠀⠐⠁⠁⣠⡦⠤⠦⠀⠀⠀⢀⣤⡌⠀⠈⠂⠀⣀⣀⣠⠾⠊⠀⡞⠁⠀⠀⠓⠂⠀⠀⢧⡀⢨⠃⢹⠀⣧⢀⣠⠇⡈⠒⠉⠒⠃
⠀⠀⠀⠀⢰⣶⡂⠀⠀⢰⢿⣾⠃⢀⠀⢠⣄⣀⠀⠉⠀⣀⢠⣤⠀⡉⠀⠀⠀⡰⠂⠀⢀⡀⠀⠠⠀⣤⠀⣿⣈⡀⠈⢀⣁⣼⡇⢘⠑⢦⡉
⠀⠀⠀⠂⢀⠟⡀⢐⠀⠈⠦⠽⠀⢘⡀⢉⢱⠟⢷⣖⡶⠿⠧⠉⢀⡩⢀⣄⠘⡇⠀⠠⡟⠁⠀⠀⡰⠃⠀⡟⠙⠃⠀⠀⠉⠉⡄⢈⣀⡐⠓⢷⡀
⠀⠀⠐⠀⠁⢠⠈⠀⠃⣀⣴⣾⡇⠀⠘⠠⠀⢀⣠⣿⣄⡀⠀⠠⠂⢀⠎⠸⠃⠀⠀⠀⢀⡀⣼⠋⡀⠀⠄⢶⣿⠶⠀⠀⢀⠀⠀⠈⠛⠤⠄⠚⠁
⠀⠀⠀⠀⠂⢸⡐⠀⠈⢿⡍⠉⢻⠝⠈⠀⠘⠎⠛⠿⠋⠑⠃⢀⠃⠚⢀⡠⠖⠀⣇⠐⠢⠉⠐⠎⠀⠀⠀⢠⣿⠀⠀⠀⠀⠱⠆⠀⠀⣠⡄⠋
⠀⠀⡀⠀⠈⠠⠏⠀⠀⠀⠙⠒⠡⣦⠀⠀⠀⠀⠀⠀⣡⠀⠂⠊⠠⣶⡁⠄⠂⠀⠙⠀⠀⠄⣀⢦⠀⠙⠤⠀⠀⠀⠄⠋⢀⢄⠐⠒⣾⣷⡤⠂
⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⠙⠃⠀⠀⠀⠀⠉⠈⠁⠀⠂⠐⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡶⣒⠶⠶⠶⠶⣶⣶⣶⣶⢒⡒⢲⡖⡒⠒⣖⣶⠀⠀⠀⣇⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⡉⠷⣖⣯⣭⣭⣿⣿⣿⡛⠉⠎⢢⢘⣦⠟⢉⠀⠀⠀⣿⣇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⡄⠉⢷⡒⣟⣻⣯⣾⡷⢚⣦⣾⣿⡿⠶⢌⠀⠀⠀⣿⣿⣿⡇⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢾⣷⣧⣄⢱⡴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠜⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣓⢋⠽⣿⣿⣶⣿⠻⠹⣿⣿⢫⢰⣿⣿⠿⡿⢻⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢏⠛⢮⡽⡿⣿⣿⣧⠰⣼⠋⠆⣾⠽⣶⣥⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢿⣿⣾⢣⡟⣿⣿⣷⣿⣾⣰⣧⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣟⣷⢿⣧⡿⣼⠟⣿⣿⣾⣿⣿⣿⠟⠻⡏⠉⣿⠅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣨⡏⢿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣇⠒⢞⠒⠶⠤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠁⣰⠆⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣇⣽⣟⣿⡿⢿⣿⣿⣷⣿⣿⠿⠿⠿⠿⢿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣤⣴⣶⠆
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣾⣷⣿⣿
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠏⠀⠀⠐⠒⠂⠐⠒⣶⢦⠸⣿⣿⣿⣿⣯⣿⣿⢿⣿⣆
⠀⠀⠸⠀⢀⠀⠀⢈⡁⠐⣸⣿⣿⣷⣭⡻⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠠⣄⠀⠈⢉⠄⡩⠛⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠹⣶⣴⢁⠚⢀⠤⠤⢄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣶⣁⣀⠀⡀⠙⢷⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡁⠀⠀⠀⠀⠀⠛⠋⠹⣇⡀⡀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣯⣆⠀⠀⠀⠀⢦⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠈⠁⠐⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⡿⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⠃⣠⡆⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠹⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢠⣿⣾⠏⠀⠀⢀⠀⠈⠀⠈⢿⣿⣆⠀⠀⠀⠘⢿⡟⠛⠛⠛⠋⠻⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣾⣿⣿⣶⣿⠛⣷⣄⣲⣆⡀⠈⣿⣿⣷⡀⠀⠀⠘⢿⣦⡀⠀⢄⡀⢻⣿⣿⣷⡇⣀⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⢨⣿⣿⣿⣿⢿⣿⠿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣄⢀⢠⢣⣻⣿⣶⣦⣁⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⣠⣾⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠈⠉⠁⣤⣽⣟⣽⣟⣯⣶⣭⡿⠟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣖⣚⣻⣿⣉⣻⣿⣿⣿⣿⣿⠧⠤⣬⣿⣿⣿⣿⣿⡿⠋⠱⠟⢉⣿⣿⠿⠆⠀⠀⠬⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠿⠟⣠⡏⣱⣿⣿⣟⣛⢿⣉⠶⠆⢹⣿⣿⣿⣿⠋⠀⠀⠀⡰⠈⠛⠛⠑⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠛⠉⠉⠉⠉⠀⠀⠀⠈⢿⣿⡿⠃⠀⠀⠏⠱⣬⣤⡀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠑⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢹⠏⠉⠉⠀⠀⠀⠀⢠⡎⠃⠀⡼⠁⠀⠀⠄⠀⠀⢀⢀⠀⢀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠻⠶⠀⣾⠀⠀⣠⠤⢄⡀⠀⣾⠂⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠁⠈⠶⡁⠐⢤⡀
⠀⠀⠀⠀⠀⠐⠄⠁⢄⠰⢀⢀⠃⠀⠀⠀⠀⠀⠀⠚⢻⠟⠚⣼⠁⠀⣼⠃⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⡐⢱⠤⠊⣁⠘⡆⠁⠐⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠁⢘⡢⡁⢠⠀⠏⠀⠀⠀⠰⢤⡴⠏⠀⠀⢿⡴⠊⢿⡤⠸⣥⠤⠂⢧⡤⠔⠀⠀⠐⢠⠀⠄⠀⠙⠦⠅⠀⠀⢀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⣁⠉⢲⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⣀⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣼⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠈⠄⠀⠀⠀⢹⠄⠀⢰⠚⣰⠀⢀⣴⡿⠗⢦⠀⣰⠞⠛⡆⢠⣞⠛⠃⠀⠀⠠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⡾⠀⢀⠆⢰⡏⠀⢠⣟⠀⠀⡼⢸⡟⠒⠊⢁⡀⠉⢻⠄⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠁⠀⠑⠄⠀⠀⠀⠀⠀⠐⠀⠀⡀⠳⠖⠋⠀⠘⠶⠚⠛⠙⠶⠚⠁⠈⠳⠤⠒⠈⠳⠶⠋⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠆⣒⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⢀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⣠⠀⢀⠀⢚⠡⡬⠒⠆⣀⡑⠀⢬⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡴⠄⠐⡲⠁⠄⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⡀⠊⠁⠤⠂⢐⠖⠀⣈⠐⠚⠠⠤⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠉⠁⠀⠀⠈⠡⡀⠈⠦⠀⠷⢀⣈⡡⠤⠔⠐⠂⠀⠀⠓⠀⠢⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠈⠁⢢⡅⢚⡰⠖⠈⢠⠄⠘⠢⠀⠀⠀⠀⢀⠀⠉⠡⢤⠄⣠⡤⡡⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡔⠩⠀⠔⠀⠈⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠂⠒⠁⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠐⠀⠀⠄⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡌⢻⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣶⣿⣴⣤⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⢹⣿⠟⠿⠇⠀⠈⢻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠁⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣦⣀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡶⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠶⠖⠂⠀⠠⣈⠛⠓⠀⠀⠀⠉⠛⠿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠐⢦⡤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣄⣀⠀⣰⣄⠀⡀⠀⣼⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣯⣴⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠘⠋⠈⢋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣄⣤⣝⠈⠁⠀⠀⠀⠤⣴⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡄⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣿⣪⣠⡏⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢀⣄⢀⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠙⢿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⡇⢀⠀⢀⠸⠿⠿⠿⠦⠤⠄⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣀⣀⣀⣠⣤⢶⠿⣿⡿⢾⣧⣄⢒⣦⣄
⠀⠀⠀⠀⠀⣧⠙⢿⣌⡿⠈⣸⡆⢹⢲⣿⣳⢸⡆⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠹⢿⡞⠉⣟⣀⢹⡏⣠⡗⠙⣯⣞⡏⠀⠀⢀⡟⠒⣆
⠀⠀⠀⠀⠀⠀⠙⢇⡀⠨⣽⡶⠠⢻⣅⣸⣟⢹⣿⠀⠀⢛⠆⣨⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠛⣾⣿⣬⣿⣼⣿⡏⠐⣼⣿⣠⣠⠋⢠⣻⣿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⣻⠁⠈⠉⠙⢿⡇⠀⣸⣿⣿⡏⢠⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢈⠤⠹⠀⠀⠀⣀⣰⠇⢰⣿⣿⡟⢀⣷⣿⢻⣿⣤⣤⣀⣀⣀⣀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⢠⢦⣠⡤⢩⠁⠸⢛⡁⠀⣛⠩⠆⠠⠈⠙⢛⠋⠛⠻⢿⣿⠂⠐⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠿⢸⠃⡇⡼⠀⠀⡏⢰⢛⡈⡇⠀⠀⠸⠗⠋⠀⠀⠤⠄⠈⠳⡄⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠠⠄⠟⣠⠏⠀⠀⠀⠉⢸⡀⣧⠐⠀⠀⠀⠈⠀⠀⠀⠀⠄⢙⣄⠹⡄⠌⠈⢧
⠀⠀⠀⠀⠠⠂⠀⠈⠁⢒⣠⢀⣁⠀⠀⠹⠬⠤⠄⠀⠤⠄⠀⠐⠤⠖⠀⠚⠓⠂⣿⣆⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⣿⡃⠀⠀⠊⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⣿⡧⠂⠀⡀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣷⢀⠴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⢀⠈⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⠁⠉⠉⠉⠁⠀⠃⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⣤⣤⣤⣀⣀⣥⣤⣤⡤⠶⢾⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣀⠀⠁⠊⠑⠂⡀⢀⣝⣃⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠫⣿⣿⡄⠢⡈⠉⡗⢒⠿⣹⣽⣯⣿⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣻⢿⣿⣤⡏⠱⡧⠼⣂⣽⣿⣧⣿⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣾⣿⣯⣠⣤⣤⣤⣿⣿⣿⣯⣿⣿⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠐⢿⣿⠉⣿⣿⣿⣿⣿⣯⣻⣿⣯⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡖⢛⣿⣴⣿⣼⣿⣧⣴⡞⡛⠻⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢻⣿⣿⣿⣦⣁⠄⠤⠀⠀⠀⠀⠉⢻⣿⣿⣿⣀⣀⡀⠀⠀⡀⣀⣀⣀⢤⣶⠟⠁
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠠⠆⠀⠒⠄⢨⡾⣿⣟⣿⣿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠙⠉⠍⠩⠉⠉⠃⠐⠏⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡤⠋⢡⣨⠾⠛⢻⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⡬⠗⠛⣿⣿⠀⠀⠀⠀⡀⠀⠠⠋⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠌⠁⢣⠂⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣧⡠⣄⠀⠀⠉⣘⡁⢐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢂⡖⠁⠰⡄⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢸⣿⡋⢉⠁⠀⣸⣯⣵⣿⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠘⡇⢘⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡿⢀⣿⡟⢳⣤⣿⣿⣿⡿⠿⣞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣼⣿⣟⠁⡠⣛⢻⣟⡁⠀⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠂⠤⠄⠘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⠿⠻⡿⠋⠁⠁⠈⠉⠉⠈⠓⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠰⠆⠀⠀⠀⢀⠀⠀⠄⠀⠀⡠⠸⠱⡜⢣⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠈⠁⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣾⣿⣿⣷⣶⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⡏⠹⢿⡿⢿⣿⣿⣿⡿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⠿⠀⢿⣿⢀⠇⡿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⢠⡆⠐⠋⠇⣈⡅⣉⣤⠀⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⣶⠰⠋⡝⢸⡆⣇⢈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⡇⣿⣤⡆⣿⣄⡿⣇⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣷⣿⡼⠧⢾⣶⢻⡏⣿⠝⡼⢛⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⡿⢹⠋⣿⢋⣭⡿⢿⢹⡇⣿⡙⡇⢻⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣟⢪⡇⣿⡇⣾⠋⠘⢸⡇⣿⡿⢲⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣷⣺⡜⣿⢨⣯⡀⢨⠸⡇⢻⡗⣷⣼⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣝⡗⣽⡇⣿⣿⣾⣈⣧⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣼⣿⣿⣿⣤⣷⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⡿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣾⣿⣿⣷⣾⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⢛⣿⡿⡿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⢛⣿⣿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⢺⠿⢹⠃⡇⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⡏⣿⠇⣻⢿⠏⡇⣾⢻⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢿⣶⣤⡆⡇⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⡿⠷⢯⣿⢸⣧⣀⢸⢠⡟⡬⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡍⢿⢿⢿⡇⣷⡿⢚⠁⢟⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠁⢶⠾⠟⣻⢡⣟⡿⣿⣷⣿⢩⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠘⢸⠀⡇⢀⣦⣼⣃⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⢸⣧⣼⡇⡻⢸⢈⠁⣿⡅⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣷⣼⣿⣿⣷⣿⣾⣿⣷⣿⣿⣧⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣿⣹⣍⣿⣭⣅⣽⣿⣿⠏⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⡀⠀⠀⠀⠀⠢
⠀⠴⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠐⢀⠀⠀⠀⠀⠂
⠠⠒⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠄⠊⠂⠀⢀⠀⠀⡀
⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠔⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢄⠀⠀⠉⠀⠀⠈⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠
⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢴⠀⠁⠉⠈
⢀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠂⠀⠀⠀⢣⣶⡜⠁
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠀⠄⡀⠀⠀⠀⠈⠀⠀⠂⠀⠓
⠀⠀⠀⠀⠐⠊⠀⢀⠀⠀⢀⠀⠀⠀⠀⢀⡀⢈⠀⠀⠀⠀⠀⢀⡂⡀⠓⢀⠄⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠁⠈

⣷⡀⠀⠫⠙⠁⠰⠏⣿⣿⡗⠀⣄⡿⠦⢀⣤⠠⣽⣶⡖⣿⡟⠙⠘⢷⡦⠀⢠⢇⣦⡄⠀⠀⢴⣄
⠻⣷⡀⢠⠀⣠⣐⣹⠇⠈⣿⣸⣯⠇⠀⠀⢀⠀⠨⣽⣱⠋⠀⠀⠀⡮⠑⣄⠈⠸⢧⡅⢴⣦⠤⢿⡄⠀⢀⡀
⡀⠹⣷⠐⠂⣉⣬⣱⠄⠒⢈⡡⣞⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠁⠀⠀⠐⡌⠳⠂⠈⠇⢼⣧⡳⣄⣿⣦⠀⠙⢦
⢿⣦⡘⠆⠁⠀⠛⠁⠀⠆⠘⠁⠀⠀⠀⠀⠀⣠⢠⡤⣱⠍⠀⠀⠀⠀⠈⣽⠀⠁⠀⠀⠀⠀⠀⠀⢸⣟⣗⠀⠄
⠀⠉⢻⣦⣂⠀⠒⠀⠀⡀⣠⣤⠀⣨⣅⡰⠤⠉⠓⠋⠁⠀⠀⠄⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡝⠇⠦
⠀⠀⡶⠈⠻⠝⣯⡈⢁⡇⠓⠀⢠⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡆⢦
⠀⠀⢀⣀⠠⠔⠶⣶⢈⣫⠷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠧⠀⠀⠀⠀⠀⠀⣀⣁⠹⠿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠘⠓⢸⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢫⠀⠀⠀⠀⠀⠀⢚⣲⣿⣶⡆⣿⣿
⠀⠈⠃⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢡⡐⠀⠀⠀⠀⠈⣿⣿⠟⢴⣿⡟
⠀⠈⠀⠀⠱⠄⣀⡀⢹⣶⣀⢀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡀⠀⠐⠀⠉⢀⠀⠀⠀⠀⠈⠙⠁⣼⣿⣷
⠀⢘⢆⠀⢀⡀⠀⠙⠪⡗⣿⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠲⠀⠀⠀⢶⣼⣿⣿
⠀⢸⠜⠓⠀⠛⠚⠶⠀⠀⠁⠀⠀⠀⣀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢻⣿⣽
⠀⠀⣦⣤⣶⡶⠖⠛⣉⠍⡺⠲⠆⠀⠀⠀⢠⣤⡄⣤⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠚⠁⠀⢱⠀⠀⢀⣼⡏⢿
⡇⠀⠛⠉⠀⠀⣠⠞⠁⣸⠁⠀⠀⠀⣀⣶⣤⣝⠃⠀⠀⠀⠀⣀⣀⣠⣇⠀⠀⠀⠄⠀⠀⠀⣼⠀⢶⣿⣿⠱⣿
⣥⡄⠂⡀⠀⠚⠁⢠⣦⡏⠀⠀⠀⠀⠀⠐⢧⣍⡀⠀⠀⠴⠚⡉⠉⠋⠉⠛⠢⠀⠀⠀⣠⣴⣿⠀⢸⣿⣏⡾⡛
⣷⣾⣷⣏⠀⠀⣾⢸⢷⠀⣀⠀⠀⠀⠀⢐⣿⣟⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡿⠻⣿⠀⠘⣡⣾⣦⣆
⣿⣿⣿⣿⣃⠀⠻⢺⢸⣰⣿⠀⠀⠀⠀⠉⠹⡇⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠩⠢⠀⠀⣹⠀⠠⡟⣿⠙⠉
⣿⣿⣿⡿⣿⣧⡀⣾⢸⣿⡯⡄⠀⠀⠀⠀⡀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠉
⣿⡻⣿⣿⣾⡏⠓⠜⢸⣽⠂⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣦⣠⣾⣂⣀⣦⣧
⣿⡇⠹⣿⣿⣷⠀⠀⢈⠟⡀⢠⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⡇⠉⣿⠿⠳⣤
⢹⠁⠀⠈⢻⢿⡄⠀⠀⢹⢱⠸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹⡅⠀⣿⣷⣤⢛

⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢪⢧⡀⡇⠀⠀⠆⠡⠀⠁⢀⠀⠀⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⢀⠰⣬⠶⣂⡀⠀⠀⠀⠉⠁⡒⣷⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀
⠀⠠⠂⡠⢁⠆⢵⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠅⢀⢀⠀⠀⠀⠐⠀⠀⠀⠨⠑⢆⡃⣩⠶⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢀⡀⢊⠔⠀⢠⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠃⠘⡣⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡤⠁⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠊⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⣿⢻⡟⠄⠀⠀⠀⠀⠀⠀⠀⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⢰⣦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠷⠇⠆⠀⠀⠀⢀⠅⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠆⠀⠆⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠄⠀⠀⠀⠀⠴⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠺⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠅⠈⠀⠀⠀⠀⠀⠀⢀⢂⡄⠀⠀⠀⢀⠒⠑⢄
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡁⠀⠀⠀⠀⠀⢦⠆⠀⠀⠀⠐⠛⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢀⠠⠀⠈⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⢤
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠈
⠀⠀⠀⠀⡄⠀⠰⢄⠀⠀⠀⠀⠀⠥⠀⠁⠀⠀⠀⢀⡀⠸⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠒⠂⠀⠀⠀⣀⠄⣬⠇
⠀⠀⠀⠰⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠿⣿⣻⣶⡝⢪⢁⢄⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠘⠛⣋⣽⢤⣾⣩⣌⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⡣
⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠙⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⣶⠄⠀⠀⣀⢿⡇⠀⠀⣸⠃⠀⠀⣴⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢀⡾⠋⠉⠙⠷⣄⣠⣿⡟⠀⠴⢦⣿⣤⣥⠴⠞⠁⢀⠀⡘⠛⠉⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠘⠁⢀⣶⠟⣦⢨⢻⣿⢧⣆⡔⣼⣱⣰⢰⣶⡷⣟⣿⢺⡏⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⢡⠂⢸⣿⠘⠋⠗⠛⠉⠈⢉⣀⡀⠉⠁⢻⡇⠀⠀⠀⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠧⠔⣁⣄⡘⢃⣤⠀⠀⣼⠇⢀⣾⢿⠇⢰⡷⡄⠀⠀⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣴⠏⢸⡇⢠⡁⠀⢰⡿⠀⣸⡿⠋⠀⠘⢿⣧⡀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⡀⣼⢠⣿⠃⠀⣿⢻⡉⣿⡇⠀⠀⢀⡞⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⣹⠇⣼⡟⢀⢸⣿⢸⠃⠸⣧⣀⡴⠋⣠⣾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⢠⡏⠀⢿⣧⠃⠈⠿⠋⠀⠀⠀⠁⠀⣼⠟⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⡟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⠏







⡿⠿⠿⠿⡿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿