Camel Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⣤⠤⢤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⣾⣶⣦⡀⠀⠀⠀⠀⠀⣠⣼⡟⡭⠒⢿⣶⣻⢄⣀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⡀⠀⠀⢨⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⣿⣛⡿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⢘⣿⠿⣷⣄⠀⠀⠀⠀⣿⡟⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣡⡄⠀⠀⠀⠀⠀⠈⠻⣿⣷⣮⣿⣷⣄⠀⠀⠘⣷⠸⡏⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠙⣿⣿⣿⣇⠀⠀⠸⣇⠙⡌⢿⣿
⠀⠀⠀⠀⠀⠀⣼⠃⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⢿⣿⣿⣿⡄⠀⠀⣿⠀⢹⡜⣿
⠀⠀⠀⠀⠀⣰⣿⠃⢸⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣤⠘⣿⣿⡿⣿⣦⣴⡏⠀⠈⣷⣿⡄
⠀⠀⣀⣠⡶⠋⢿⡀⢸⣆⢻⣷⣄⡀⠀⠀⠀⠀⠀⢸⡿⠠⠹⣧⠘⣿⡇⠠⣍⣉⣠⠀⢠⣿⣿⠁
⠀⣾⣿⠁⠀⠀⢸⡇⢸⢿⣦⡙⢿⣿⣶⣤⣤⣤⣴⣿⠃⠀⠀⠙⢠⣿⢻⣴⡹⠿⠏⢀⣼⣿⡟
⠀⠹⣿⣿⡄⠀⢸⡇⢸⣰⠟⣿⣷⣿⣿⣿⣿⣿⣋⣼⣆⡀⠀⠴⢠⣿⢨⣿⣿⣶⣶⣿⠿⠋
⠀⠀⠘⠿⠁⠀⡿⡇⣼⡏⠀⢿⣿⣿⡿⠉⠉⠉⠉⠛⢿⠁⠀⠀⣿⣷⢿⣷⣶⡶⢿⡁
⠀⠀⠀⠀⠀⠀⣧⢀⡿⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠸⡜⢰⡅⡿⠃⠈⠛⢯⣙⠀⠳⡀
⠀⠀⠀⠀⠀⢠⣟⣼⠁⠀⢠⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠉⠙⠿⣉⡢⡀
⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡇
⠀⠀⠀⠀⠀⢸⣼⠁⠀⠀⠹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⢀⡿⡿⠀⠀⠀⠀⢱⡽⡄⠀⠀⠀⠀⠀⠀⠀⣇⢀⡇⠀⠀⠀⠀⠀⠀⣰⠋⡟
⠀⠀⠀⠀⣾⡄⡿⠀⠀⠀⠀⠀⢇⠘⡆⠀⠀⠀⠀⠀⠀⢿⣸⠁⠀⠀⠀⠀⠀⣠⡏⢸⠁
⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠈⡧⠈⣲⣄⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢷⡤⣾
⠀⠀⠀⠸⡧⣴⡼⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠀⣏⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣿⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠠⠄⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢥⣀⣀⣀⡀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⡠⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠉⠓⠒⠶⠒⠋⠁⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⢃⣤⣀⣀⡠⠤⠔⠊⠁
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⣿⠟⣍⡿⠶⢤⣤⣤⣤⠤⢴⡀⢰⡟⠁⠀⣔⡠⠾⣯⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⢰⡏⠀⢀⣠⢾⣿⡏⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡼⠛⠦⡀⠈⢧⡀⠀⠈⠹⣿⣆⣀⣠⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⠞⢁⠔⠉⠀⢸⣿⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡼⠁⠀⠀⠈⢢⡀⠱⡄⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠁⡰⠃⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠁⠀⠀⠀⠀⠀⠙⠀⠙⡀⠀⠀⠀⠀⣴⠟⠻⣏⠁⠉⠀⠙⣿⠻⣧⡀
⠀⠀⡀⠰⠁⠀⠀⠀⠀⠸⣆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢸⠃⠀⠀⢻⠀⠀⠀⢀⠟⠀⠈⣇
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⡀⠀⠰⠃⠀⠀⠀⠸⠃⠀⠤⠋⠀⠀⠀⠸
⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣹⡄
⢰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⡀⠀⠀⠀⠀⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢳⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠞⠋⠀⠠⠞⠃⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠙⠋⠁⠶⢄⡀
⠀⠀⠀⠀⠀⢀⡾⠭⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆
⠀⠀⠀⠀⠀⠸⢤⣒⣠⣤⢄⣀⠀⠀⣀⡠⠂⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠙⢿⣏⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢰⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢨⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣾⡀⣀⣠⣤⠴⠾⠧⡀⠀⢦⣄⣤⣤⣤⣿⠟⣸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣼⠉⢏⠉⠉⣿⠀⠀⠀⠙⢄⠀⠙⠻⠟⢻⡿⣏⠁⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣼⠃⠀⠈⡇⠀⢻⡀⠀⠀⠀⠈⢧⠀⠀⠀⢸⡇⠈⠳⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⠀⠈⣧⠀⠀⠈⡇⠀⠀⢧⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣼⠁⠀⠀⠀⠳⡄⠀⡏⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠈⢧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠏⠀⠀⠀⠀⠀⢳⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠸⡆⠘⡆⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣷⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡆⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⢸⡀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡀⠸⡇⠀⠀⠀⠀⠀⣸⠄⠀⣸⡆⠀⠀⢀⡟⠀⠈⡇⠀⠀⠀⠀⠀⣸⠃⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢁⣴⡿⠀⠀⠀⠀⣰⣃⣀⡼⠋⠀⠀⠀⢸⠁⠀⣠⡷⠀⠀⠀⠀⢰⣇⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⠎⠀⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⣤⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠁⠈⣁⡴⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢉⠲⣄⠀⠀⠀⠀⠀⠀⡼⠇⠀⡰⠉
⠀⠀⠀⠀⠀⢀⣴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⢳⠈⠳⠦⠤⣤⠴⠊⠁⠀⡠⠃
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⣤⡤⠤⠖⠋
⠀⠀⠀⠀⢀⣿⣿⣿⣦⠀⠀⠀⣿⣧⣀⣀⣀⡀⣀⣠⣀⣰⠀⠀⠀⠞
⠀⠀⠀⢀⣾⠟⢙⡝⠁⢣⡀⢀⠇⠉⠙⠛⠛⠛⠉⠁⠀⣿⣷⠖⢄⡈⠢⡀
⠀⠀⠀⡼⢃⡔⠁⠀⠀⠀⣧⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠛⠀⠀⠙⠢⡈⠢
⠀⠀⢺⣰⠋⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠄⠀⠀⠀⠀⠃⠜
⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠈⠲⡰⡀⠀⠀⠀⠀⠀⠀⢸⡘⠀⠀⠀⢀⡾⠂
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⢳⠃
⠀⠀⢿⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣦⣀⠀⠀⠀⢸⣑⢄⡀⠀⠙⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣬⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠚⠛⠀⢀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠅⢻⣿⣷⠶⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⠿⠃⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠣⣤⣴⣾⣟⣁⣀⣈⠀⠐⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠁⠀⠀⢀⡏⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠟⠀⠀⡇⠀⣠⣿⢡⡄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⢠⣷⣾⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⢣⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⠀⠀⠙⣿⣿⣿⠇⢸⣿⣀⣀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠘⡇⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⣿⣿⡿⠀⢺⣿⣿⣿⣿⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⢀⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣿⣿⣧⣄⢸⣿⣿⣿⣿⣿⣟⣻⣿⢿⣿⣆⠀⠀⠀⣼⠇⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣷⡄⢸⡟⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⡿⠿⠶⣾⣿⠿⣿⣿⠛⠳⣿⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⢿⣷⡸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠉⠁⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠘⣿⣇⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⢨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⠰⠀⠀⠀⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢸⡟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⣼⣷⡆⠀⠀⠀⠀⠀⢀⣄⡀⢤⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣤⣤⣶⣿⣿⣶⣿⣿⣧⣀⣀⣀⣀⣠⣬⣉⠉⠹⠤⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠳⠦⠤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠦⣬
⠀⠀⠀⠀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⠟⠛⠛⠉⠉
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢿⡀
⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠟⠀⠀⠀⠀⢀⣘⣷
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡆⣤⠀⠀⠀⠀⠀⠀⠈⢱⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠤⢤⣤⡤⠴⠶⠛⠁
⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠉⠛⠓⠲⠶⠶⠶⠶⡖⠀⠀⠐⠀⠀⠀⠀⣼⠋
⣿⠀⢠⣧⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡤⠀⠀⠀⣼⠃
⠙⢶⡿⣿⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⡇⠀⠀⣸⠃
⠀⠀⢀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⡇⠀⢠⡏
⠀⠀⢸⠇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⠀⠀⣼⠁
⠀⠀⢻⡀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⠀⢰⡏
⠀⠀⠀⠻⣄⠀⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡏⡿⠀⣼
⠀⠀⠀⠀⠹⡆⢸⣇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡇⡇⠀⡟
⠀⠀⠀⠀⠀⢿⠀⢿⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢘⡆⠘⢿⠇⢰⡇
⠀⠀⠀⠀⠀⠘⡇⠀⢀⣀⣀⣸⠗⠀⠀⠀⠀⠀⠀⢾⣁⠀⠀⡀⠸⣧⣀⡀
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠁⠀⠀⠈⣹⡆
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⡀⠀⣆⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣿⣿⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⣁⣉⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⠀⠉⠀⠀⠀⠠⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠒⣶⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⠃⠀⠀⠀⠨⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⡴⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠰⢶⠇⠀⢠⣾⣧⠀⣀⣐⣀⡀⣴⣦⣄⣀⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠉⠛⠦⣤⣠⣄⣀⢀⣀⣦⣔⣴⣼⣯⠿⡄⢿⣩⡿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠁⠀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠁⠛
⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠼
⠀⠀⠀⠀⠀⠀⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⠁⠛⠂⠂⠀⠀⠀⠐⠐⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡸⠁⠀⢪⣼⡿⠋⠉⠉⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠈⠀⣀⣠⣴⡒⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣶⠃⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⢠⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⡇
⠀⠀⠀⣠⣔⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣠⡿⠀⠀⠀⢠⠇
⠀⠀⠀⣸⠋⢸⣄⠀⠀⠀⠀⢠⣿⣷⡀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡟⠋⠉⠛⠋⠀⠀⠀⣠⡟
⠀⠀⢰⣿⠀⢸⠙⠀⠀⠀⠀⣾⣿⣿⣿⣶⣾⣿⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⢂⠀⠀⠀⠀⣠⣼⠟
⠀⠀⠸⣾⡆⢸⠀⠀⠀⠀⢰⣿⡟⠛⠉⠙⠻⢿⣿⣿⣿⣷⣶⣴⣶⣶⣶⣦⡄⠀⠀⠀⠀⣼⣿⣿⣿⠿⠶⠶⠶⠚⠋⠁
⠀⠀⠀⣿⡇⢸⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣷⡇⠀⠀⠀⣸⡿⠋⠁
⠀⠀⠀⣿⡇⢸⡇⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⡆⠀⠀⢸⠛⠁
⠀⠀⠀⣿⡇⣾⡇⠰⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⣾
⠀⠀⠀⠁⢠⣿⡇⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⡇
⠀⠀⠀⢀⣿⡿⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿
⠀⠀⢠⣾⠟⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡷⠀⣿
⠀⠀⢸⣿⡞⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣇⢀⡿
⠀⠀⢸⣿⢿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⢿⠇
⠀⠀⢸⣿⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⢸
⠀⠀⢸⣿⡇⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⡇⢀⢸⡀
⠀⠀⠸⣿⣇⣿⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⣇⣸⠈⢃
⠀⠀⠘⢿⣿⣿⡆⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠿⢿⡇⠙⠲⠦⡄
⠀⠀⠀⠀⠀⠀⠉⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠁

⠀⠀⠀⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠻⠂⠀⠠⣀
⠀⢀⣀⠠⠌⢛⣔⣚⠇⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡔⢄⠐⠈⠁⠀⠤⡀
⢆⡀⠀⠀⢄⠀⠿⡟⠀⣍⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠄⡀⠀⠀⠘⠢⠀⠀⠀⠀⠀⣼⠿⠄⠸⠀⠤⣲⡛⠢⠄⠺⣦
⠀⠀⢤⣀⠀⠀⠀⠀⠒⠊⠃⡀⠀⠀⠀⠀⠀⠀⠀⡠⣩⣰⣾⢣⡞⠀⠀⠀⠘⠀⠀⠀⠀⢈⠐⠀⠀⡑⣕⢈⠙⠆⠢⠤⠈⣧
⠀⠀⠈⢠⣠⠠⣤⣴⡞⣽⡇⣶⠀⠀⠀⠀⠀⠀⠾⣲⡯⠇⠰⠜⠘⠀⢉⣀⠀⠀⠀⠀⠰⢭⡀⠀⡀⢱⡜⢆⠀⠈⠀⠀⠀⢸⡆
⠀⠀⢠⡇⠽⠓⠀⠺⠂⣬⠁⠏⠀⠀⠀⠀⡠⠀⠀⢀⡄⠀⡀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⢤⣨⡉⡃⠀⠙⠄⡄⢀⠀⠀⠀⢤⠭⢦⡀⡀
⠀⢀⣿⡶⠢⣠⡄⠀⣼⣁⣜⢀⠀⠠⠒⠁⠈⠁⠀⠤⠀⠀⠀⠤⣂⠀⠀⡀⠀⠀⠀⢤⡐⠪⣷⠳⡈⠳⢄⠀⠀⠀⠁⠀⠀⠀⠁⣠⣱⡍⠓⠤⡀
⠀⠘⠉⡾⠀⠉⢡⡖⠁⠈⣉⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠸⣁⡞⠐⠀⣀⠶⡀⠘⢏⠂⠠⣅⠘⢎⠢⠑⠀⢠⠀⠈⠲⠀⠀⣬⡻⣿⠲⣤⣀⣳⡀
⠀⠀⢴⠁⣦⢻⠏⡃⡠⡀⡿⠱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡄⢿⠃⠀⠀⠁⠀⠀⠀⡰⢄⡳⠂⠁⠀⠁⣀⣿⣸⣴⠐⢮⡁⠀⠈⣯⠀⠀⣽⡈⢻⣷
⠀⠀⢾⣰⢻⠀⠀⠈⢯⠹⣤⠀⠀⠑⠀⠀⠈⠳⠤⠀⠀⠐⠀⠙⠺⡰⣤⠀⠁⢄⠠⡦⠘⣄⠹⣦⣠⣷⣿⣿⠀⢿⣿⡄⠑⠄⢠⣜⡞⠃⠐⠘⡇⠀⢿
⠀⠀⠀⠹⣌⠸⠀⢐⠜⠂⡃⣶⡤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⡄⠹⡝⠳⡝⠾⣄⢷⠀⢎⠁⠈⢻⣿⠘⠃⢀⣾⣿⡷⢶⠄⠈⢿⡿⠀⠀⠀⠁⠀⣼
⠀⠀⠀⠀⠈⠧⡈⠂⠑⡴⠈⠈⢷⠄⠀⠈⠀⠀⠀⠀⢄⠀⢸⡀⡇⠀⡀⠆⠂⠁⠀⢷⢄⠘⣅⠲⢧⡏⢠⣾⢟⣼⡯⣿⣶⢤⣀⣶⣽⡄⡀⠐⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⢦⡆⠇⠀⢳⡀⠂⠀⢸⡄⠂⠀⣾⡇⠡⣾⡴⠀⠀⣄⠘⢄⢅⡀⢍⣛⠂⠁⢟⣡⠾⠟⠂⢿⡹⣦⡹⣿⡿⢷⡁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡟⠠⢰⡸⣧⢠⠊⣸⡤⣶⠶⣤⣦⣤⣈⣂⠂⠄⠉⡷⣦⠴⠚⠋⠀⠀⠀⠀⠈⢿⡛⠿⡎⡋⣰⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠁⠘⢫⣶⠣⢰⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣏⢨⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⡀⠠⣿⢿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣆⢿⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡏⠀⣆⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣿⠀⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⣁⠘⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡸⣯⠀⡿⡟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠁⠀⠀⠀⠘⢦⡀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣽⣇⠀⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡶⢹⡿⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣀⢹⣌⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⡟⠀⡼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠋⣄⡎⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣊⢁⡞⠁⠐⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣴⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⡟⠃⡀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣶⣖⣚⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣉⣻⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣭⣽⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣰⣾⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡍⠀⠀⠀⣿⣿⠋⢬⣄⠀⠀⠀⠀⠀⢀⣤⣌⠻⣿⣿⣿⣿⣿⡽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠛⠃⠀⠀⠛⠁⠒⠢⣶⣷⢀⠀⠀⠀⣾⣿⣿⣧⡿⢥⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⣃⠀⡀⠀⠀⣀⣎⣇⡀⠄⠀⠙⡟⠀⠑⣄⣰⣿⣿⣿⣿⡿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⣻⣿⣷⣄⣦⣴⣿⣦⠶⣝⣾⣼⣯⣷⣾⣆⠸⣿⣿⣿⣻⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢱⠃⣧⣮⣷⣿⣿⡿⣿⣴⣿⣽⣶⡯⣿⣷⣤⣿⣿⣿⡆⢹⣿⣿⣯⣿⣿⠏⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠶⣿⡀⣿⣿⣿⣿⡍⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡟⠁⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⣀⣘⣿⣿⣿⣿⣿⣿⣷⣐⣶⣴⣿⣿⣿⣿⡥⠀⠀⠐⠐⢶⣶⡾⢶⣶⣦⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⠷⠶⢦⠶⠾⠂⠀⠐⠚⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠈⠉⠙⠛⠛⠛⢫⣍⠹⠻⠿⣿⣿⡿⠿⠯⠉⠿⣿⡿⣿⠿⣟⣻⣿⣿⡧⢀⣴⣿⣶⠒
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣶⣾⣿⠁⢽⡿⠟⠛⠛⠛⠉⠀⠚⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠄⠀⠻⣯⣽⣿⠿⠿⣯⣷⡀⢐⠌⠉⠨⠍⠭⠏⠑⢒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠈⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡶⠲⠤⣀⠀⠀⠀⠀⠀⣰⡃⠈⠛⢏⣳⣤
⠀⢀⠶⢂⣠⣾⣟⣿⣷⣀⠀⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠠⣙⣦⢀⣴⣞⡏⠀⠀⠀⠈⣿⣿⣧
⠀⠻⢿⣷⣤⣭⣿⣿⣯⣿⣇⠀⠀⠀⠀⠀⢸⡏⡀⠀⠀⠀⠀⠈⠃⠛⠻⣻⡅⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣴⡾⣧⢻⣶⣆⢒⠔⠃⠀⠀⠀⢨⣷⠀⠀⢁⣸⣿⣿⣿
⠀⢀⣾⣿⣉⢸⣿⣷⣿⣿⣿⣿⣇⣼⣿⣿⣿⠟⠓⢋⡝⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⢿⠏⠉⠝⣳⣦⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠃⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠩⢿⣿⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣿⣿⣟⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⣸⣿⡇
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⣾⣾⢓⣆⡀⣀⡀⡀⠀⠀⠀⣀⣼⣿⣿⣿⡄⠀⠀⣴⣿⣿⠃
⠀⠀⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⠟⠛⠻⡿⠿⣧⣄⠰⣿⣿⠘
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣟⣻⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⢹⣿⣧⣈⡛⣧
⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣹⣧
⠀⠀⠀⠀⠀⠀⠙⠟⢻⡿⢿⠋⠁⠀⠀⠈⠻⣿⣿⣿⡿⢿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠎⢿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠃⠀⠸⣿
⢀⢀⣀⠀⡔⠀⠀⠀⡄⠐⠐⠄⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⡇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⣦⡇
⠀⠀⠀⠄⠈⢲⠒⠀⢀⣀⡀⠂⠉⠙⠓⠐⠿⠿⠿⠇⠖⠀⠻⠿⠿⠶⠰⠒⠠⠴⠃⠽⠛⠠⠤⢠⣴⢞⣹⡤
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣠⣴⣿⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣥⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢀⣴⡿⡋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡃⠀⠀⠈⠓
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠹⣿⣿⣿⣿⡇⠹⣿⣿⣿⣿⣇⣤⣤⣧⣂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣼⣿⡆⠀⠒⠁⠠⠂⢬⢿⣿⣿⣷⣽⡟⣿⣿⣿⠛⠉⠉⠙⠋
⠀⠀⠀⢰⣦⡄⢀⣴⣍⢻⣧⠀⠀⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣴⣆⠀⣮⣿⣿⣿⡿⠃⣻⣿⣿⡆⠰⠾⣷⡦
⠀⠀⠀⠀⣤⠆⣾⡸⣷⣦⡨⣦⣤⣿⣷⣶⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⠿⢿⣿⣿⣧⣤⣿⣿⣿⡏⢀
⠀⠀⠣⣼⠁⠠⠋⡏⠿⠻⣿⣿⡻⢻⣿⣿⣿⣇⠹⣿⠛⢻⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⠟⠉⠀⣰⡿⣹⣇⣼⠿⠀⣾⣿⢑⣿⣿⣿⣿⣿⣷⣾⣿⣅⡀
⠀⠀⠉⠀⢽⣴⣕⣴⣤⣶⠚⢿⣟⣿⣿⣿⣿⠋⠁⠿⢒⠀⣿⣿⠁⠀⠀⠀⠸⣿⣿⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⢸⣿⡏⠁
⠀⠀⠀⠀⠀⢀⣀⢀⡈⣩⣷⣯⣍⣙⠓⠈⣙⣙⡂⠚⠛⢻⣿⣿⠀⠀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⡀⣠⣴⣾⣿⡿⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠙⠿⠿⠿⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣏⣻⣟⠛⣛⣛⣛⡛⢛⢛⣛⡛⠛⠁⠀⠀⠀⠀⢠⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠙⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⠊⠒⠀⠁⠈⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠋

⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢢⣤⡀
⢀⣼⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣾⣿⣗⣅⣟⣷⠀⠀⠀⠀⠀⠀⣼⣿⣟⣁⡈⢩⣷⡄
⠈⣿⢙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⡋⣰⣄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣿⡀
⠀⣯⠬⠏⠛⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿⡿⣻⢿⣿⣿⣿⣿⣿
⠈⣿⣯⣾⣷⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣧
⠀⢸⣿⣿⣻⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡎⡛⠋⣶⣽⣿⣿⣿⠟⠻⣿⣷⡀
⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣰⣄⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣄⡀
⢀⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢪⣿⣷⡄
⠀⢻⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⢸⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⡉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡼⣿⡿⣎
⠀⠀⢻⣿⣿⣿⣿⣷⣤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⠋⠀⠉⠻⣿⣿⣿⣿⣿⡿⣦⣿⢣⣧
⠀⠀⠀⠛⢻⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣏⠸⣯
⠀⠀⠀⠀⠈⠙⢻⣏⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣿⣿⡟⠅⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡐⣿
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠿⠛⠛⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢻⣿⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣏⣿⣾⠃
⠀⠀⠠⠀⠐⠲⢖⣶⣶⣿⣶⣾⡿⣿⣶⣶⣾⣿⡿⣀⣼⣿⡿⠼⢾⣿⣷⣦⣶⣤⣄⣀⣠⣤⣴⣿⣾⣿⣿⡟
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠽⠿⠿⠿⠛⠛⠛⠛⠁⠀⠀⠀⢀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣀⡀⠀⢠⡤⣤⣦⣄⣬⣔⣿⣿⣦⣼⡾⣦⣤⡤⠤⠐⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⡠⠤⠤⠖⠚⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠉⠉⠒⢄
⣞⠁⠀⠀⠐⠂⠀⠀⠘⡄⠀⠀⠀⠀⠀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢄⡀
⠈⠉⠉⠢⣀⠀⠀⠀⠀⠹⡀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠙⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠳⡄⠀⠀⢀⠀⠀⠀⢀⣀⣀⡠⠤⠒⠊⠉⡆⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠋⠱⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠘⢆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⡆⠀⢰⢤⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠇⠀⠀⠀⠈⢣⠀⠘⡄⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠙⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡸⠀⠀⠀⠀⠀⠈⢇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣰⠁⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠳⡈⢆⠀⠀⠀⠀⠀⡸⢠⠃⠀⠀⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⡆⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣀⣸⠀⢠⡒⠉⣠⠃⠀⠀⠀⠀⠀⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣤⡀⠀⠀⢀⣤⣿⣿⠁⡀⠚⠂⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠁⠒⠀⢺⡄⠀⢸⣿⣿⡉⠈⢡⡆⠡⠀⡊⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠍⠐⡇⠙⠂⠀⢩⠀⣿⣟⣏⠓⠉⠛⠃⢼⣦⣧⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠆⠀⠀⠁⠀⠀⠀⠀⢿⣿⠋⠁⠀⠀⠀⠀⠤⠀⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠤⢠⣴⡟⠗⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⠿⠉⠙⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡰⠂⠀⠁⠀⠀⠀⠀⠀⢊⠈⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠠⠀⢀⣺⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⢀⣼⣿⣻⡶⣴⣶⣾⢋⣀⣦⡉⠂⢄⣀
⠀⠀⠀⠀⠀⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠘⠳⠀⠀⠀⠀⣿⠋⠉⣷⣶⣿⣟⢿⡎⠉⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⣴⡟⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⣼⠇⠰⠀⢹⣿⣟⣿⡄⢀⡃⠀⢠⠄⢃⣳⡆⠰
⠀⠀⠀⠀⢀⣿⣟⢃⣴⢣⣏⡶⢀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡞⠐⠀⠘⠀⣸⢟⣙⣿⣆⣜⠻⢶⣦⣿⢶⣍⢀⠖
⠀⠀⠀⠀⢻⣿⣿⡟⠇⢰⡟⣿⣿⡅⠀⠀⠀⠀⠁⢀⠲⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⣐⢠⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣹⡘⣯⠹⢾⣿⢃⣶⡿⠁
⠀⠀⣴⢦⣿⣿⠇⠁⠀⣿⢣⢞⣿⣧⠀⠀⠀⠀⠞⢥⣾⠋⠀⠈⠀⢀⠀⢀⠆⠀⠀⠉⠡⢘⠀⠀⡰⡟⢰⠀⠀⠀⣸⡏⠀⡝⠆⠳⣝⣿⡟⠁
⠀⢀⣿⣾⣹⣏⠘⠀⢀⣽⣿⣆⣷⢻⡿⡃⠁⠀⢀⠾⣧⠀⠀⡠⠌⠀⠀⠈⠀⠀⠀⡄⠀⣺⠀⠀⡇⣷⡎⠀⠆⡄⢻⠇⣆⣷⠀⠀⢻⣿
⠀⢸⣿⡿⣿⠃⠸⠀⠘⣿⡟⣯⣯⣾⣽⣿⡁⡞⢩⣛⣓⣰⢆⣴⡇⠌⠀⠀⠀⡆⠀⢠⠀⢩⠂⠀⡰⠉⡟⣴⠁⠀⢰⡄⡿⡄⢱⠤⣾⣿⠁
⠀⣯⣿⡟⣿⢸⠇⠀⢸⣿⣿⣻⣿⣿⣷⣿⣳⣶⣎⣿⡟⠅⠈⠁⣄⠀⠂⠀⢀⠇⠀⡅⠀⠈⠀⠰⡀⠀⢹⠀⠀⡏⢸⣿⠀⢹⡆⢺⣇⡝
⠀⢹⣿⢹⡟⢉⡀⠀⢨⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡌⢁⡨⡄⢶⣜⣵⣶⠇⠀⠠⠀⠀⠃⢰⠈⠀⠀⠃⠸⡟⠀⠀⣷⢸⡟⠁
⠀⠈⠁⠈⣿⣾⢢⣿⣼⣿⠁⢸⣿⣤⣹⣿⣿⣿⣿⣿⣟⡀⠁⢀⠈⠀⣡⠙⣿⣿⡈⣶⡂⡴⠀⠀⢀⡇⠀⠀⣀⠘⠇⠹⣸⡖⣾⡷
⠀⠀⠀⠀⠸⣿⣿⡿⣿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⠁⠀⠂⠩⢰⢿⣿⣏⣹⢿⣧⢼⣆⢸⣄⣴⡖⠏⠀⢣⠀⣿⡿⠏
⠀⠀⠀⠀⠀⣿⣼⣿⡇⠀⠀⠀⢹⣿⣿⣿⡟⠻⢿⣿⣯⠗⣧⠀⠀⢀⠀⡈⠀⣿⣿⡘⣾⢿⣶⢹⠇⡟⠱⣷⣦⡄⠀⣷⣼⠁
⠀⠀⠀⠀⠀⣿⡋⢸⡇⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠙⢿⣾⡅⠐⠀⠈⠠⢇⠀⣹⣿⣱⣽⣨⢿⢻⣄⣧⢰⣿⣼⣧⣗⠛⠁
⠀⠀⠀⠀⠀⣿⡇⣼⡇⠀⠀⠀⡿⠂⢹⣿⠀⠀⠀⠀⠸⣿⣿⣼⢳⠀⠀⠈⠂⢸⣿⣿⣹⣿⣾⡆⣽⣿⣼⡿⣿⡿⠉
⠀⠀⠀⠀⠈⣿⠷⣿⡇⠀⠀⠀⢿⣀⣴⣿⠀⠀⠀⠀⠀⢿⢻⣏⠘⠀⣀⠃⠀⢘⣿⣿⣿⣷⣶⣿⣋⣹⡽⠞
⠀⠀⠀⠀⠀⢿⠘⣿⠃⠀⠀⠀⠀⣷⠙⣿⠀⠀⠀⠀⠀⠈⢻⣿⢢⣇⠹⠀⠀⢸⣿⡿⣿⠿⠟⠋⠀⠉
⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠸⡆⢹⡇⠀⠀⠀⠀⠀⠀⠹⢷⣸⣗⣾⡿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⢹⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⣿⣿
⠀⠀⠀⠀⠀⠀⡇⢻⡄⠀⠀⠀⠀⠀⢸⡆⠈⢧⠀⠀⠀⠀⠀⠀⠀⡇⠹⡇⢀⣿⣿
⠀⠀⠀⠀⠀⢰⡀⢸⣷⠀⠀⠀⠀⠀⠈⢧⡀⣨⣶⣄⠀⠀⠀⠀⠀⡇⢸⡇⣼⣿⣿⡄
⠀⢀⣀⣀⣀⢸⠟⢿⣻⡀⣤⣤⣶⣦⡆⣘⡧⢤⣾⣿⠁⢀⣤⡄⢀⠁⠸⡇⢿⣿⣿⣇⡀
⠀⠈⠛⠉⠻⠛⢎⣹⣏⡁⢶⣿⣷⣶⣾⣿⣷⣿⣥⣴⣿⣭⢤⡄⢰⡄⠀⠓⣼⣿⣿⡿⠟⠀⣤⣤⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠻⠐⠒⠶⠦⠖⣗⠠⡼⡾⠏⣉⣃⣺⣤⣶⣽⣿⣴⠶⠾⠿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠀⠈⠉⠉⠉⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡁⠀⠀⠀⠀⠀⠀⠊⢹⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠺⠠⡄⠈⠀⠀⠀⡀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠀⠀⡐⠀⠁⠀⠼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐⠀⠀⠘⠒⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢸⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠄⡀⢰⣦⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠤⡼⣿⣿⣿⣯⣥⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣿⣿⣿⣿⣄⣀⣠⣾⣿⣇⣀⣀⣀⣼⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⣀⣀⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠛⠛⠋⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣴⡖⠀⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣍⠳⠀⣼⣿⢏⣷⢠⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⠀⠈⠀⠀⢰⡿⠃⠀⠀⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⢀⣴⣧⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⢀⣤⠴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠂⠀⠀⠀⠉⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⣦⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠟⢿⣿⡿⢷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠈⣿⣿⡐⣆⣤⣦⡟⡁
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢻⣿⣿⣆⠀⠀⢀⣼⡄⠐⠃⠀⠀⠀⢠⠀⠀⢰⣿⠀⠀⣬⢟⡉⢿⣿⡏
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢸⣿⣿⣿⣶⠃⣸⣿⠀⢠⠀⠀⠃⠀⠈⣴⠀⢻⣯⢀⡴⣯⣼⡀⠻⡏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⢸⣿⣿⣿⣿⣄⣿⣿⡷⠟⡈⠀⠀⠀⠘⠁⠀⠞⢻⠋⠴⣿⠟⡐⣾⠇
⠀⠀⠀⠀⠀⠀⠿⢻⣇⣀⣸⡿⣿⣿⣿⣿⣿⣿⡁⠶⠑⢰⣿⣶⣄⠀⠀⠀⠀⠐⢀⣿⠀⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠁⢸⣿⣿⣿⣿⣿⣧⠈⠀⠾⢻⣿⣾⣦⡆⣸⣠⠶⠊⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢈⣿⣿⠉⠛⢿⣿⠆⠀⠀⠸⣿⣿⣿⣿⡏⢹⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢸⠟⣿⠀⠀⠘⣿⣾⡆⠈⠀⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⠃⠀⠀⠿⣿⠀⠀⠀⠹⣿⣄⡶⠀⣾⡿⡿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠛⡄⠀⠀⠀⠉⣿⣿⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⣀⠁⠀⠀⠀⠀⠈⡟⢠⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠰⣾⡇⠀⣠⣀⠈⣶⣿⡆⡀⠀⠀⠳⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠋⠛⠛⠻⠿⣿⣿⡿⢉⣐⣆⢀⣿⢿⠟⣄⣤⣤⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠋⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠈⠳⢶⣶⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣡⠁⠐⣀⡁⠀⢠⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢈⡛⠁
⢀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠘⢃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠑⢄
⡧⢈⠂⢀⠐⠂⠠⠃⠀⠄⠁⢈⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢡
⡅⠀⠀⢩⠀⠀⠀⢀⠌⠀⠒⢉⠜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢁⠀⠀⣸⠀⠀⠀⢰⠁⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠈⠦⠤⠋⠦⣀⣀⠎⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠳⠤⠎⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢢⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠶⠶⢦⠤⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡇⠀⠀⠀⢰⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠁⢣⠀⠀⠀⡾⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⢳⠀⠀⢸⠉⠙⠛⠛⠛⠉⠉⢡⠀⠀⢸⠀⠈⢦⠀⠀⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢾⠀⠀⠈⢧⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⡅⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠀⠈⡆⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔⢰⠁⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡐⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸⡄⠀⠐⠲⠀⠀⣠⠂⠀⠀⠀⠀⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⢣⠀⠀⡠⠁⠀⠘⢄⠀⠀⠀⠉⠉⠀⠀⠤⣤⠄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠀⣠⠠⠚⠀⠐⡀⠀⡂⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠗⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣘⣀⣕⣀⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣚⡸⢷⣶⡄⡀⠀⠀⠀⢱⠀⠀⠀⠀⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠀⡞⣃⣹⣿⣷⡴⡛⠏⠀⢈⡀⠀⠀⠸⠀⠀⠀⠐⢿⣷⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⢶⣿⣿⣧⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡾⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠰⠇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⣟⠀⠘⢼⠁⠀⠀⠀⠀⠀⠀⠀⣰⡿⠙⠟⠷⠖⠒⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⣾⡁⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣤⠀⠘⢿⡀⠀⠀⣀⣰⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⢀⣀⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⣠⣄⣀⣀⣀⣠⣤⣾⡿⢋⣾⣧⢿⣧⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣧⣤⣀⡀⠀⢀⠀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⠿⠒⣿⣿⣿⠇⢯⡷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⣤⠀⢽⣾⣷⡿⣿⡟⠛⠛⠋⠁⠀⠀⠀⠸⢿⣿⡀⢬⣷⣾⡀
⠀⠀⠀⠐⠀⠀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣿⣿⣧⡐⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⣷⠀⢸⣿⢷⠀⠀⢀⡠⢀
⠄⠀⡀⠤⡴⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⢰⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⢿⠋⠈⢠⡷⠊⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣿⠁⠐⠰⠋⠉⠀⠀⠂⠀⠀⢀⡠⠃⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⡀⢀⣀⣀⠄⠀⠀⠀⠀⣸⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠈⠂⠃⢀⠁⡠⠀⢈⡀⠀⠀⠀⢀⡺⢻⣏⣠⣿⣿⡄⣀⢀⣀⣀⣀⣀⣀⡐⢿⣿⣤⣤⣴⣿⣇⡀⢀⣀⠀⢀⣀⢁⣶⣦⣀
⠀⠀⠈⠀⠀⠈⠁⠀⠐⠊⠡⠄⠒⠀⠠⢤⠶⠶⠛⠛⠻⠷⢎⠹⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⢿⣿⠧⠿⠟⠛⠉⠉⠉⠉⠉⠀⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⡖⠰⠂⣀⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⠟⡔⢰⠀⡾⣎⠟⠲⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠄⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠁⠀⠈⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢚⡟
⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⠀⠀⠈⠀⡔⠀⢀⡾⠁
⠀⠀⠀⠀⢀⢎⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡼⠁
⠀⠀⠀⠀⢈⢋⡇⠀⠀⠀⢮⣢⡠⡀⠀⠀⠀⠀⠀⠀⣜⢦⣷⡀⠀⠀⠀⠀⠠⢸⡇⡆⠀⠀⠀⢀⣺⠗⡠⠊
⠀⠀⠀⣠⡎⢸⡇⠀⠀⠀⢸⣿⡿⣾⣷⣤⡀⠀⠀⠀⢌⣳⡿⠁⠀⠀⠀⢠⢇⡿⣶⠿⠶⠶⠞⠯⠒⠋
⠀⠀⡸⢱⠇⢸⡇⠀⠀⢀⣿⣿⣿⡷⠀⠉⠉⠙⠓⠒⠦⠍⡇⠀⠀⠀⣰⣿⣿⠀⢸
⠀⠀⠃⡸⠀⠸⠀⠀⢠⢾⣿⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⡜⠁⢻⣿⠀⢸
⠀⢈⠔⠁⣠⠃⠀⡴⠋⢀⡿⠈⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠁⠀⠈⢿⠀⢸
⠀⠀⠀⢰⡏⠀⢰⠁⠀⡸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡌⠀⠀⠀⢸⠀⣄
⠀⠀⠀⠸⡇⢀⡾⠀⠀⢷⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡃⠀⠀⠀⢸⡄⠘⡄
⠀⠀⠀⠀⣷⢸⠁⠀⠀⠈⢻⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⢰⠃⠀⠀⠀⠈⢻⣦⡇
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⢳⠸⡄⠀⠀⠀⠀⠀⠀⠀⡟⡡⠁⠀⠀⠀⠀⠀⠀⢿⢷⡀
⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠈⢇⠱⣄⠀⠀⠀⠀⠀⢰⢷⠇⠀⠀⠀⠀⠀⠀⠀⠘⣄⢣
⠀⠀⠀⢰⡇⠸⠀⠀⠀⠀⠀⠀⠸⣄⠈⠦⢀⡀⠀⠀⡞⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠃
⠀⠀⠀⠈⣷⠀⣧⡀⠀⠀⠀⠀⠀⠈⠧⣄⠀⠙⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⠀⠒⠒
⠀⠀⠀⠀⠙⢿⠆⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒
⣶⣴⣶⣦⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣤⣶⣤⣤⣶⣶⣤⣴⣴⣦⣶⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⠀⠀⡤⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⢖⠒⣄⠀⠀⠀⢸⠁⠀⠈⠙⢦⡀⣜⠀⠀⠀⠈⠲⠄⢄⡀
⠀⠀⠀⣀⠄⠀⠈⢈⡀⠀⣀⠄⠄⠀⠈⡆⠀⠀⢸⠀⠀⠀⠀⠈⢳⡧⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⢣⠤⠀⠀⠀⠀⠀⠠⡭⠆⠀⠀⢘⡄⠀⡰⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠄⠁⠀⠀⠀⢠⣿⠐⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢢⡤⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢰⠃⠀⡴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⡗⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⢵⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⠈
⠀⠀⠀⠀⠀⠀⠈⣗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⢸⡄⢠⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢌⠶⡀⠀⠀⠀⠀⠀⠸⡏⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠐⠄⠀⠀⠀⠀⠀⢷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠗⣤⠢⣻⢧⡀⠀⠀⠀⠀⠀⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣗⠀⠀⠀⠀⠀⡙⢳⣤⣈⣠⠀⡔⣀⣠⡦⠧⠖⠋⠀⠀⠳⡄⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⡴⢇⠡⠀⠊⠉⣽⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢸⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⠀⠀⣇⠈⡢⠀⠀⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠈⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡟⢠⠁⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠒⠄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⢀⡇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠁⠀⢠⢠⠂⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⣨⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⣴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣷⣤⣤⣀⣤⣀⣼⡻⡆⢢⣀⣀⣄⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢻⠁⣹⣿⣿⣿⣿⣿⣿⡇⠁⣨⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁⠀⢹⣿⠃⠉⠛⠛⢋⠁⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡇⠡⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠸⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠸⠇⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁



⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠟⠛⠛⠛⢻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠈⠁⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⠇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣧⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣀⠀⠀⠘⠻⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡭⠉⠉⣩⣭⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄
⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⡀⠀⡰⠁
⠀⠀⠀⢀⣴⡿⢧⡀⢠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠦⣤⡀⠀⠀⠀⠀⣰⣆⣠⣀
⠀⣠⣾⡿⠉⠙⣦⣼⣷⢋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠄⠀⠀⠘⠋⠉⠉⠉
⡄⢿⠿⢰⣥⣾⣿⡋⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⡇⠀⢘⣿⣿⣿⣿⡷⠀⠀⠁⠀⠀⠀⠀⢀⡦
⣇⠑⣼⢿⣿⣿⠉⠀⣀⣠⠀⢀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡇⠂⠀⣾⣿⣟⣀⡀⣿⣿⡄⠈⠻⡿⠇⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⡄
⠀⠀⢠⣿⡟⢿⣾⣿⣿⣿⡅⠀⠰⠞⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠈⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠹
⠀⠀⠀⢿⣾⣻⣿⡿⣿⣿⢇⠀⢠⢦⡆⣀⠏⡘⠇⠘⢦⡄⠀⢀⡀⢀⠰⢀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠃⢀⣿⡀⠁⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣿⣿⣼⣶⢈⠈⠚⠀⠪⢰⢷⣏⣱⠁⠀⠀⠈⢻⣄⠀⢾⣇⣘⡫⢷⣱⣧⣄⣠⢰⣥⡄⠀⠀⢠⣿⣿⣧⡈⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣶⡄⠈⠰⣠⣟⣍⣿⣿⠆⣀⣠⡌⠹⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⢷⣾⡟⠀⣠⣿⣿⣿⣿⣿⣆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣷⡿⠀⠀⢿⣿⣿⡏⣡⣤⣄⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠉⢿⣿⣿⣿⣿⣿⡖⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠸⣿⣿⣷⣾⣷⣇⡀⠀⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠘⢿⡄⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢧⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢀⠀⠀⠀⣾⠀⣸⡇⠀⠸⠀⠀⠀⠀⠀⢤⣀⠀⠈⠆⠚⠀⠚⡟⣠⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣯⣿⣤⣩⣽⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠾⢷⣶⣿⡯⠾⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡖⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣧⢤⣅⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⣿⣿⡄⠘⣿⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠄⣼⣿⣿⣇⣠⣿⡟⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠋⠿⢛⣟⣼⣿⣿⣷⣿⣼⣄⠀⠀⠀⠀⠀⠀⣤⣤⡴⢲⡶⢒⣿⠻⠦⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣾⣫⢽⠉⠉⠻⣿⣿⣿⢻⣆⠀⠀⠀⢀⣼⡛⣡⠒⠻⠿⣏⣽⣈⣤⡶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣉⠅⣰⠃⣼⣆⠀⠙⣷⣘⣿⠂⠀⠀⠙⢻⣿⡟⠒⠊⢙⣿⣫⣿⠏⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣧⣴⣧⣾⣿⣿⣷⣄⠈⠻⡿⠳⡀⠀⠀⢻⣿⣾⣶⣶⣿⡟⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣏⠙⠿⠿⠿⠿⣻⣿⣿⣿⣿⣿⣴⣶⣦⡈⢢⡀⠘⢿⡎⢿⡿⣿⣿⣦⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢵⣻⣟⣫⣟⣶⣿⣿⡭⢟⡻⣿⣿⣿⣿⣿⣿⣉⠦⣈⢿⡌⢳⡈⢿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢹⣿⢖⣙⣦⢔⢦⣠⠳⡟⣈⣿⣥⠴⠒⣋⠿⡻⢟⡿⣿⡀⠈⠻⣿⡀⠹⣆⢻⣿⠎
⠀⠀⠀⠀⠀⠀⢀⣞⢃⣿⣿⣷⣥⣤⣙⣉⣙⣺⣿⣟⣽⠟⣷⣏⡱⢫⠞⢁⣴⣿⣷⣴⡆⢸⡇⠀⢹⣼⣿⡄
⠀⠀⠀⠀⠀⢰⣏⡘⣌⣿⣿⣿⣽⣟⣿⣺⣗⣿⣿⡿⣁⠘⠩⣿⡵⢋⣶⡿⣃⣇⣩⡛⣿⣿⠃⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⢨⣿⣷⣾⣿⡟⡿⣾⣿⣿⣽⣯⣿⣿⣿⠉⢠⣾⡿⣷⢻⣯⣵⣾⣇⠀⣉⣉⣁⣤⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣠⡾⢻⡇⢸⣿⡄⡄⣁⣉⣉⠉⠈⢈⠈⣿⣤⣿⣿⠁⠳⠾⠏⠀⣿⣿⣄⣌⢿⣿⠟⠀⣸⣿⣿⠃
⠀⣠⣶⠞⠋⠀⠈⣿⠘⣿⣤⣁⡁⠋⡿⠘⠙⠙⠋⣿⣿⡿⣿⠀⠀⠀⠀⠈⣿⡇⢻⣿⣦⣤⣤⣾⣿⡿⠁
⠀⣿⣿⣄⡀⠀⠀⢿⡇⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣿⣦⣀⠀⠚⢃⣿⣇⣾⡟⣛⣛⣿⡟⠉
⠀⠘⢿⣿⣷⠀⠀⣼⡇⢸⣷⠇⠸⣿⣿⣿⣿⠛⠛⠛⠛⠛⠻⢿⠁⡀⠀⠈⣿⡿⢻⣿⡿⢿⡌⢻⡄
⠀⠀⠀⢹⠏⠀⠀⡟⠣⢸⡿⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣎⠃⢳⢀⡿⠁⠀⠈⠙⠶⣤⣄⣽⡦⣄
⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⠃⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣶⠘⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⢦⡮⢱
⠀⠀⠀⠀⠀⠀⠀⣼⣃⡿⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡼⠃
⠀⠀⠀⠀⠀⠀⢸⡏⠉⡿⠀⠀⢾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣰⠃⠀⠀⠘⢿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡟
⠀⠀⠀⠀⠀⠀⠀⣾⢿⠀⠀⠀⠀⠈⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣸⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⠁
⠀⠀⠀⠀⠀⠀⢠⠏⢸⡀⠀⠀⠀⠀⠈⢷⠈⢦⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠀⠀⠀⠀⠀⢸⣟⠁⣸⡄
⠀⠀⠀⠀⠀⠀⢻⡷⢸⠃⠀⠀⠀⠀⠀⠈⢷⡌⠳⢤⣀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⡽⠒
⠀⠀⠀⠀⠀⠀⣸⠇⠸⣄⠀⠀⠀⠀⠀⠀⠈⠧⠴⢯⡟⠃⠀⠀⠀⠀⡏⣹⡆
⠀⠀⠀⠀⠀⠀⣿⢦⣶⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣉⡽⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣾⣾⣉⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⢤⣦⢹⣿⣿⡄⠀⣀⣀⠀⠀⠀⢢⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣃⣬⠡⠿⣿⣿⣿⣿⣿⣿⣗⠀⠀⢸⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠉⠀⠈⠙⣷⡖⢩⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⢿⣿⣤⣤⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡟⡠⠐⣀⣄⠀⠀⠘⠀⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢸⣿⠇⣸⣿⣿⣱⣶⣦⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣇⣼⡿⠟⣻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠹⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡏⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢻⣧⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣸⣿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃
⠀⠀⢀⢀⢀⡀⣀⢀⢀⣀⣀⢀⠀⠀⡀⠀⢀
⣿⣿⢛⡻⣛⡛⣛⣟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠖⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠰⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠈⠀⠁⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢲⡄⠀⠀⠀⠰⠖⠒⠒⠈⠁⢸⠀⠀⢣⠀⠀⠀⠀⡀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⡄⠀⠀⣷⡀⠀⠀⢧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡆⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡞⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠁⠐⣁⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡴⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡄⠀⣰⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣠⣿⣿⡿⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣿⣿⣟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠋⠁⣾⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣦⡀⣠⣶⣄⠀⠀⠀⠀⠀⢀⣀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠛⠋⠉⠁⠀⠀⠀⠀⣾⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣾⣿⣿⣿⣦⠙⢿⠻⣿⠿⣿⡿⠏⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⢿⣿⣿⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⢼⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠘⣿⡟
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢠⣿⠃
⠀⠀⣿⡏⣿⡇⠀⠈⠉⢹⣿⣿⡿⠛⢿⣿⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⣸⡟
⠀⠐⣿⠀⢿⡁⠀⠀⠀⠀⢿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠀⠀⠀⣰⣿⡇
⠀⠀⢸⡄⠈⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⠛⠿⠛⠃⠀⠐⠿⠿⠿⠇
⠀⠀⠈⠷⠆⠘⠓⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠢⣤⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠘⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠋⠀⢈⣠⠦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠦⡀⠀⠀⠀⠀⠀⢀⡾⠀⠀⡞⠁
⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⢧⠘⠓⠤⠤⡤⠶⠋⠀⢀⠜
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⡂⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⣟⣿⣄⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⠤⠴⠚⠉
⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠨⣿⣦⣠⣀⣀⣤⣂⣤⣀⣶⠀⠀⠀⡋
⠀⠀⠀⢀⣾⠟⢹⠟⠀⢧⠀⢰⠀⠉⠙⠛⠛⠋⠉⠀⢰⣿⣿⠲⣄⠈⢢⡀
⠀⠀⢀⡜⢁⠜⠁⠀⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠑⢦⠁⢀
⠀⠀⢺⣰⠃⠀⠀⠀⠀⠀⢃⠀⡆⠀⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠈⠡⠂
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⠲⡱⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⣰⡗
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢔⢳
⠀⠀⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⣢⣄⠀⠀⠀⣇⣃⣀⡀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠟⢦⠀⢐⣿⡿⠦⣄⢀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠓⠈⠁⣸⣿⠍⠘⠋⠸⣶⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⠀⠀⠀⠠⢄⣼⠿⡄⠀⠀⠀⠀⠀⠠⠣⠀⠀⠀⠀⠀⠀⢀⢴⠖⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡃⠀⠀⠀⠀⠀⠃⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⣤⡴⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⢰⡟⢻⣭⣿⢿⡜⠋⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⢂⣀⣡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⢆⠀⣿⢿⡇⢰⣀⣰⣄⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⣸⣿⣷⡀⠀⠀⠀⢀⡀⠀⠴⠀⠀⠀⠀⠀⡀⠀⠀⣠⠏⠀⠀⢠⡗⡟⢿⣷⢨⡿⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡃⠀⣿⣾⣿⣆⡀⠄⠘⣿⠊⠀⠀⠀⠀⡆⠀⠈⢀⡄⢠⣾⡣⠀⠀⣾⡑⡟⠈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠄⠀⣿⣿⣿⣹⣷⠀⢴⣽⣇⠀⡃⠀⠀⠀⡀⠀⠸⡃⠀⡜⡿⡜⠀⣹⣹⠓⣀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣡⠃⢠⣿⣿⣿⣿⣿⣶⣾⣿⠏⠈⢡⠀⠀⢠⠃⠄⠀⠁⠐⠀⡘⠁⠄⣹⡆⢱⠸⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⣤⣄⣼⣿⠻⣿⣿⣿⣿⣿⣿⣆⠔⠠⠘⢺⣿⣿⣃⢀⠀⠀⢠⠀⠀⢠⠽⣠⡌⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠃⢾⣿⣿⣷⣴⡄⣊⣴⠸⠀⢀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⡇⠀⠀⢸⣿⣿⠉⠛⢿⣟⡆⠀⠀⢠⠀⣿⡾⣿⣿⡟⡹⣈⣿⣦⡼⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⡇⠀⠀⣾⠙⣏⠀⠀⠀⢿⣧⣶⠀⢈⠀⢻⣿⣿⣿⣜⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⡇⠀⠀⠘⣴⣿⠀⠀⠀⠘⣿⡇⡀⡬⠀⣵⣿⣿⣷⡿⠻⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠇⠀⠀⠀⢡⢻⠀⠀⠀⠀⠘⢷⣳⣴⣦⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠈⡈⢇⠀⠀⠀⠀⠀⡿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣧⠀⠀⠀⠀⢇⢈⣄⠀⠀⠀⠀⠆⣽⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⣛⣿⠠⣄⣴⡄⣨⢏⠽⢏⣀⡠⠀⠀⢾⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠛⠈⠛⠛⠻⠿⢿⣷⡟⠳⡒⣈⡆⢈⣾⡿⠟⣇⠰⣦⣔⣂⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠛⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣦⠀⠀⠀⠀⠀⢰⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠸⣄⠀⠀⠀⠀⣸⠃⢹⡀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠈⠓⠶⠶⠞⠁⠀⠀⠑⣦⠀⠀⠀⠀⣿⠙⣯⣈⣭⣾⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿⠀⢸⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⡳⠤⠴⠇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣻⠀⠀⢠⣿⣷⣾⣶⣦⣤⣾⣷⣿⠀⠀⠀⢠⣿⣧⡀⠀⠀⣠⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢰⣿⡏⠛⠻⢿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⣿⣿⡏⠁⠉⠉⠛⠉⠉⠁⣿⢂⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡹⠁⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣾⠃⠈⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⢰⣷⣿⣾⣿⢿⣷⣾⣷⡿⢿⢿⣿⡿⠿⠿⣿⠿⠿⡿⠶⣿⣿⢶⢾⣿⣿⣿⣷⣶⣶⣷⣾⣾⣶⣦⣤⣤⡄⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣹⠁⠀⢀⠈⢿⠀⠀⣀⠀⢀⡀⠀⠀⢸⡁⠀⠀⠀⣼⠁⠀⣤⠀⠀⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣾⣷⠐⢀⣿⡀⠐⠂⠀⠈⣧⡀⢀⣀⢈⡋⠀⠀⣸⣀⠀⣀⢘⣿⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠛⠛⢛⠛⠆⠈⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠖⠀⠀⠀⠀⠒⠿⠿⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⣠⠐⠉⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠘⠛⢁⡄⠀⠀⠀⣀⣀
⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⢀⣠⣴⣶⡀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⢙⡿⠀⠀⣿⣿⣿⣿⣷
⠻⠿⠿⠇⢀⣀⣤⣶⡺⢟⡿⢟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠋⠙⠛⠛⠶⠆⠀⠀⡸⠃⠀⠀⠀⠀⠀⣴⡿⢁⣴⠀⣸⣿⣿⡏
⠀⠀⠴⠚⢿⡿⣟⡭⢞⣩⠖⠛⣠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠛⠛⠃
⣶⣶⢶⣲⠽⢋⡭⠞⢋⣤⡶⠛⣁⣠⡶⠶⠄
⠯⠗⣫⡵⠚⣉⡴⠟⠉⠠⣴⡾⠛⠃⣀⣼⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠦⠴⠂
⠞⣋⣥⠶⠛⠁⣀⣴⠼⠛⠁⣀⣠⣶⠟⠋⠀⣀⣤⣬⠛⠃⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠞⠋⠁⢠⣴⡾⠛⠁⣀⣀⣾⡿⠇⠁⢀⣠⣾⠿⠛⠁⣠⣴⣿⠿⠋⠓⣢⣶⡦⠄⣀⣤⠄⠀⢤⣄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣠⣾⣿⣏⣁⣀⣠⣴⣿⣟⣉⣀⣀⣴⣟⣛⣀⣀⣤⣿⣿⣿⣓⣀⣀⣾⣿⣋⣀⣴⣿⣿⣃⣀⣶⣶⣖⣠⣀⣿⣃⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣦⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⠤⣤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣰⡛⣋⠣⢾⣾⡶⢾⠨⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠉⠀⠀⠈⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣷⠋⠀⠀⢩⣷⡿⣾⣿⣟⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠶⠖⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣤⣾⡿⠟⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠀⠀⠀⠀⠀⠀⣤⣼⣯⣙⠻⣷⣄⡀⠀⠀⠀⢻⣇⢻⣿⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣴⡶⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣆⠀⠀⠀⢿⡌⢿⡘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠈⣿⣿⣿⣿⡆⠀⠀⠘⣷⠀⢳⡘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⣸⠀⠈⣷⢹⣷
⠀⠀⠀⠀⠀⠀⣸⣿⠃⢸⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⣠⠈⢿⣿⣿⣿⣷⣤⣤⡿⠀⠀⢹⣾⣿
⠀⠀⠀⠀⣀⣴⠟⣿⠀⢸⣇⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⢹⣦⠈⣿⣿⠀⢉⡛⠋⢁⡀⠀⣸⣿⣿
⠀⣰⣾⠟⠉⠀⠀⢿⡆⢸⣿⣆⠹⣿⣿⣦⣄⣀⠀⠀⣀⣠⣿⠃⠀⠀⢹⠄⣸⣿⣆⣌⢿⣿⡿⠁⢀⣿⣿⡟
⠀⢻⣿⣧⡄⠀⠀⢸⡇⢸⠏⣻⣷⣮⣻⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⢀⡀⣿⡇⢹⣿⣬⣉⣀⣠⣾⣿⠟⠁
⠀⠀⠻⣿⣿⠀⠀⣾⡇⢸⣴⠏⢸⣿⣿⣿⣿⢿⣿⣿⣷⣶⣿⣧⡤⠀⠙⢁⣿⢃⣾⡟⠛⢿⣿⡿⠛⠁
⠀⠀⠀⠟⠁⠀⠀⡟⠇⣼⡏⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⢀⠀⡄⢸⣿⠟⣿⣿⣿⣏⠛⣇
⠀⠀⠀⠀⠀⠀⠀⣇⢀⡿⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⡌⠀⡇⣼⠋⠀⠈⠙⢷⣍⣀⢙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⣏⣼⠁⠀⠀⡸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⡟⠀⠀⠀⠀⠀⠈⠙⠻⣅⣙⢦⡀
⠀⠀⠀⠀⠀⠀⡟⠀⣿⠀⠀⣸⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢸⠇
⠀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠀⠸⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠋
⠀⠀⠀⠀⠀⠀⡿⡿⠀⠀⠀⠀⠘⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠇
⠀⠀⠀⠀⢀⡾⠁⣇⠀⠀⠀⠀⠀⢹⡞⢦⠀⠀⠀⠀⠀⠀⠀⠘⣷⢠⡇⠀⠀⠀⠀⠀⠀⠀⣼⠁⡞
⠀⠀⠀⠀⠘⣿⢢⡏⠀⠀⠀⠀⠀⠀⢧⡈⢧⡀⠀⠀⠀⠀⠀⠀⣷⣼⠀⠀⠀⠀⠀⠀⢠⡾⠇⢸⡇
⠀⠀⠀⠀⣰⠇⠘⣆⠀⠀⠀⠀⠀⠀⠈⣇⣀⡽⣖⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣶⣻⣃
⠀⠀⠀⠀⢿⢲⣷⠾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢠⣇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣭⢿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⠴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⣴⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣿⣿⣿⣧⠀⠀⠀⠀⣠⣾⣿⣷⣿⠿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣤⣿⣿⣿⣧⡀⠀⠀⣰⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣷⣤⣀⣿⣿⣿⡏
⠀⠀⠀⠀⢀⠴⠋⣿⣿⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⢠⠞⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠙⠻⠿⠿⣿⢿⣿⣿⣿⡿⠿⠿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⠇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⢸⠀⢻⡀⠀⠀⠀⠀⠀⠀⢨⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠾⠧⠀⠻⠄⠀⠀⠀⠀⠀⢾⣄⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠘⠷⠆⠀⠀⠀⠀⠀⠀⠙⠻⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡶⡶⠿⠛⠓⠀⠀⢢⣤⣀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣻⣷⣷⣴⣶⣶⣶⣄⡀⢸⣿⡏⢳⣄⠀⠀⢀⡸⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⡟⣹⣿⣿⣿⣿⣯⢟⣿⣿⣿⠀⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⡾⠀⣿⣿⠟⣠⣿⡿⠿⣿⣿⣷⠿⢿⣿⣷⣾⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⣿⡟⠀⠀⠀⠀⠀⠀⢸⡏⠙⢿⣧
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠾⠀⠀⢠⠋⠀⠀⠀⠠⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣿⣦⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⡀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⢟⡀⠀⠀⢀⠔⣿⡏⠀⢀⣀⣀⣁⣴⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠀⠀⠧⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣳⣤⣴⠃⣼⣿⣷⣼⣿⣿⣿⣏⣿⡟⢻⣯⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⣼⣿⣻⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⠦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠉⠉⠉⠉⠉⠙⣿⣷⠈⢻⣷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡾⣿⣾⣇⣉⣁⠁⠀⢸⣷⣄⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣞⣿⣿⣿⡟⣿⣿⣿⣷⣼⣿⣽⡆⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠓⢾⣵⣿⣏⠿⢿⣿⣿⣿⣿⣿⣽⣳⡿⣻⠘⣿⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠈⠉⠛⠛⠉⠉⠉⠿⠷⠶⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣸⠄⠀⠀⣀⡔⠃⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⣀⣀⡀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⣄⠀⢀⣀⣨⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠈⠻⢿⣿⠇⠀⠁⣈⠁⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣀⣨⣤⡜⠷⠄⠀⠘⢿⣷⣾⣿⣿⣿⣷⣬⠻⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠛⣿⡇⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣟⡛⠂⠀⠀⠠⠚⠟⠻⢿⣿⣿⣿⣿⡿⠁⠀⠘⡿⢠⠘⣷⠀⠀⠀⠀⠀⠀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣤⣤⡄⣣⣤⣄⣀⣨⣿⣿⣭⠉⠁⠀⠾⢆⠀⠸⡇⢹⡀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡯⠿⣿⣿⣿⣯⣭⣀⡀⢀⠀⠀⠀⠀⠀⣾⣀⣆⢱⠈⣧⠀⠀⠀⠀⣼⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣽⣯⣾⠀⢿⡀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠀⢸⣇⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡟⣰⣜⢿⡄⢸⣿⣦⣼⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠆⣿⣿⣦⡀⢸⣿⣿⣿⣿⠋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⡁⠀⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⣿⣿⡝⢿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠀⣿⣿⣿⣆⠀⠐⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠘⠻⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⠴⠞⠉⠙⢦⡀
⠀⠀⠀⣀⣀⡴⠋⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⢠⣞⠉⠙⣏⠴⠀⠀⢀⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⣞⠁⠀⠀⢨⠊⠙⠚⡎⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠘⠒⠛⠳⢶⠀⠀⣸⠃⠀⠀⠀⠹⣄⣀⣀⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠈⠙⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠚⠛⠉⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣀⡴⠶⠦⠶⠶⠒⠚⠋⠁⢸⡆⠀⠀⠀⠀⠀⢸⣏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⠉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢰⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣿⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⠏⣿⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⠏⠀⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠃⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢷⠀⠀⠀⠀⠀⢀⣴⠋⣰⠃⠀⠀⠀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢸⡄⠀⠀⠀⠸⢯⣤⠴⠇⠀⠀⢀⡰⠃⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣠⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠴⠋

⠀⣀⠀⠀⣀⠀⡄⠰⣤⡍⠲⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠳⢦⣀
⣜⣉⡁⠒⠉⠘⠛⠁⠦⠄⣿⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠈⠃⠘⠢⢔⣦⣀⡀⠀⣠⠈⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄
⠀⠀⠀⠀⠀⠈⠉⣿⢻⠸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⢳⣳⡀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠙⢿⣦⣀⣀⣀⣀⣤⡾⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⡼⠁⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⣆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⡄⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣴⣶⠿⠿⣇⠀⠀⣠⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠈⣧⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⠇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⡄⠸⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⡀⠐⢟⣷⣀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣶⡾⠿⣿⣿⣿⠀⣷⠀⠃⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠸⣅⣸⣨⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⢡⠏⠀⠀⠈⢿⣿⡆⢸⡆⠀⠀⠀⡸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⡟⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣧⠀⠀⢸⣿⣧⠠⣽⡄⢀⡀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠆⣰⢿⡀⢻⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣾⠋⠈⠳⠿⢿⡈⠳⣱⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣯⡾⠁⠀⠙⣎⢧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⠀⠀⠀⠈⢷⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⢰⠟⠀⠀⠀⠀⢸⡎⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣼⡇⠀⠀⠀⠀⠀⠘⣿⡀⢷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢠⠏⠀⠀⠀⠀⠀⠐⡃⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠹⡽⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠋⠀⠀⠀⠀⠀⠀⠀⠱⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢷⠄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⡰⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣽⠆⠀⠀⠀⠀⢰⠞⣡⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣥⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢎⠩⠽⠧⠀⠀⠠⣾⣭⡾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣡⣿
⣿⣿⡟⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⠀⠀⠀⠀⠄⣸⠍⠀⢀⣺⣷⣿⠛⠛⣻⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⣿⣿⣷⡾⠈⠁⠀⣼⠡⣤⣤⣭⣿⣟⡙⠓⠦⢠⣿⣿⣿⣾⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣡⣿⣿⠀⢠⣼⣥⣤⣶⣿⡿⠙⣿⠟⠃⢀⡈⠹⠿⡿⣿⡿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣿⡻⣿⠀⠘⠿⢆⠉⠘⠛⠁⠈⠀⠀⠀⠀⢀⣼⣒⣒⠂⠒⣒⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠉⠀⠁⡈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠄⣚⡭⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡏⠀⠀⠀⠛⢤⣀⡀⣀⣀⢀⣀⣀⣀⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠉⠉⠛⡿⠿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣁⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⣈⣰⠋
⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⢠⡜⠁
⠀⣀⣀⠤⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⣼⠋
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⣀⡤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠀⠀⠆⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠩⢤⣀⣀⡀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡤⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⠦⣀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠄⠈⠙⠒⠒⠒⠋⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠠⢋⣰⣤⠤⠤⠄⠒⠊⠁
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣾⡿⢩⡭⠛⠲⠤⠤⠤⠤⠖⠦⠀⣿⠃⠀⣰⡤⠖⢻⡄⠀⠀⣤⣴⣦⡀⠀⠀⠀⢀⣴⣶⣤⣀
⠀⠀⠀⠀⠀⣸⠇⠀⣠⠴⣿⣿⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠋⠓⢄⠀⠹⣄⠀⠀⠈⢿⣧⣄⣤⣶⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⢀⡴⠋⡠⠊⠀⠀⢸⡟⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣰⠃⠀⠀⠀⠑⢄⠈⢦⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠋⢀⡞⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠇⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⣴⠟⠙⣯⠀⠀⠀⠈⣿⠙⢷⡀
⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠸⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⠀⠀⠀⢰⠃⠀⠀⠸⡃⠀⠀⢠⠟⠀⠀⢧
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢦⠀⠐⠃⠀⠀⠀⠘⠃⠀⠐⠃⠀⠀⠀⠘
⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣧⣀
⠀⠸⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⠀⠀⠀⠀⠸⠿⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⣀⠔⣁⠉⢂
⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠠⡀⠀⠢⣀⡠⢃⠜
⠀⢀⠠⠐⠀⠀⠉⢄⠀⠘⢿⠷⠂⠀⠀⠀⠈
⠀⠵⠤⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠄⠈⠁
⢠⠀⠀⠀⠀⢀⠠⠀⠠⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠤⠤⣀
⠐⣤⠄⠐⠂⠁⡀⠄⠒⠲⠀⠐⡆⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠉⠀⠀⠁⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣬⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⢀⡀⠀⢀⡀⣀⣀⢰⡄⠶⠛⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡄⠀⠀⢂⠀⠀⠀⠀⠄⠈⠃⠙⠈⠋⠈⠉⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⡀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠠⡀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⡀⣀⣀⠀⠄⠃⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠡⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⢄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣆⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢂⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠁⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠀⡐⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢧⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢠⠢⠑⢆⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠥⠠⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠚⠒⠈⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⠁⠓⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠁