Fresas Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠍⢁⡒⠂⠀⠀⠒⠂⠀⠂⠉⢀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠔⠒⠒⠂⠀⠈⠁⠀⡀⠀⠀⠀⠐⠀⢄⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⡀⠠⠄⡠⠔⠀⢠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠐⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡠⠔⠂⠀⠱⡀⠀⠀⠀⠀⠀⣠⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠒⢄⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⣠⠤⠖⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿⠃⠀⣀⣤⡴⠖⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠻⡆⠀⠀⠀⣴⠟⠁⣼⣃⡴⠞⠉⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⠀⢀⡞⠁⠀⣸⠟⠋⡀⠀⢀⣠⡴⠞⠋⠉⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣀⣸⡇⣧⠀⡼⠀⢀⡼⢋⡔⠉⣠⣖⣋⣡⣤⣤⣤⣄⣀⣀⣀⣤⡞⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠉⠛⢿⡘⣾⠁⢀⡞⢠⡟⠀⠚⣋⣉⠉⠀⠀⠀⠀⠀⢈⣩⣴⠟⠘⢷⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⡤⠞⣷⡙⣦⡸⢡⣟⣠⠶⠋⠁⣀⣠⣤⡴⠶⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⣴⠞⠋⣁⣠⡤⠴⠾⢷⣌⣷⢘⡟⠁⢠⡞⠋⠉⠀⠀⠀⠀⣷⡄⠀⠀⢿⡆⠀⠀⢸⣦⠀⢸⣇
⠀⠀⠀⢠⡞⠁⠠⠚⢁⣀⣤⣴⠖⣴⠟⢁⠈⠀⠀⠀⡇⠀⢰⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣿
⠀⠀⢀⡟⢀⣠⠴⡾⠋⣹⠟⢡⠞⠁⢠⡏⠀⠀⠀⢸⡇⠀⠈⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⡆
⠀⠀⣾⡶⠛⠁⣼⠃⣸⠏⠀⠏⠀⣰⠋⣷⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⠀⣦⠀⠀⠸⡇⠀⣿⡇
⢠⠾⠋⠀⠀⢰⡇⠀⡿⠀⠀⢀⡼⠁⠀⠙⣷⡄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⣿⡇
⠁⠀⠀⠀⠀⣾⠁⠀⣷⠀⠀⣾⠁⠀⢰⣄⠈⠛⢷⣄⢸⡆⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢹⡄⣸⠇⠀⠀⠈⠛⠀⠀⠀⠙⣷⡇⠀⠀⠙⠃⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⢻⣧⠀⠘⣿⡀
⠀⠀⠀⠀⠀⣿⠠⣄⠀⣧⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠁⠀⠀⢹⣇
⠀⠀⠀⠀⠀⢿⣇⠻⠆⢸⡇⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠇⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠸⡷⠀⠀⠀⢰⣄⠸⣷
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠲⣦⠀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⣶⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠟⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣦⣄⣀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠸⣷⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣶⣾⣿⣭⣥⣤⣤⣤⣤⣤
⣿⣿⣡⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠟⠳⠶⣤⣄⡀
⠀⠀⠀⠀⢠⣾⡿⢋⣽⣿⣧⠀⠀⠀⠀⠀⣴⣿⠟⠋⠁⣼⣿⠋⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⢸⣿⣷⣿⡿⠛⢿⣧⡀⠀⢀⣾⠟⠁⠀⠀⣼⡿⠁⠀⠀⠀⠀⣴⣦⡄⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠙⠛⠻⢿⣦⡀⠻⣷⣄⠘⠁⣰⠀⠀⢰⣿⣁⣀⣀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠛⠷⠶⠏⠀⠀⠘⠉⠛⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡝⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣻⣷⠀⠀⠀⣀⣀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠞⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠿⠛⠋⠉⠀⠀⠀⠻⠿⠆⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⣀⠀⠀⠀⢐⠟⠛⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣠⣶⣿⣿⣆⠀⣰⣿⠁⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣠⣾⡿⠛⠁⢻⣿⣄⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠿⣟⠉⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⢿⣷⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠙⠿⠗⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠠⣶⣦⡀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠘⠿⠿⠀⠀⢀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡾⣷⠀⠀⠀⣀⣤⢶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢻⡄⠀⠀⠀⠀⢰⡟⢷⡀⣰⡟⠀⢸⣇⢠⡾⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷⠀⠀⠀⢀⡿⠀⠈⢿⡟⠀⠀⠀⢿⡟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠘⣧⠀⠀⢸⠇⠀⠀⠀⢳⡀⢀⠀⢸⠀⢠⣀⣠⣾⣧⣤⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠈⢻⣄⠘⢷⡀⣿⠀⠀⠀⠀⠈⢧⢸⠀⣸⠞⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠸⣯⠉⠉⠛⠛⠳⠿⢷⣌⠻⣿⠀⠀⠀⢀⠀⢸⡄⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⠸⡀⠀⡿⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⢠⠢⡀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⡀⠀⠀⠈⢧⠀⠀⠀⡇⡼⠁⠀⠀⠀⠀⠈⠀⠀⡖⣶⡄⠀⠀⠀⠂⠬⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠀⠈⠢⣄⠀⠈⠳⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⣀⣴⠶⠛⠋⠉⠉⠙⠲⢤⣤⣌⣱⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠒⢒⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠠⡀⠀⠀⠀⠀⡒⠄⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠈⠙⠛⣶⡶⠒⠒⣻⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠢⢈⡄⠀⠀⠀⠀⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⢴⠃⠀⠀⠀⠀⠀⠟⠁⠰⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠶⠛⠉⣿⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠍⡂⠀⠀⠀⠢⠡⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢄⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠐⠠⠅⠀⠀⠀⠀⠀⠏⢂⠀⠀⠀⠀⠐⢈⠀⠀⠀⠀⠁⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⠤⠤⢄⡀⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠴
⠀⠀⠀⠀⠐⠉⠤⠠⠀⠉⠉⢹⡿⢿⢧⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢡⠖⢂⠐⠲⢄⡀
⠀⠀⠀⠠⠄⠀⠒⠀⠀⡀⠐⠋⠀⠃⢂⠁⠀⠐⡆⠀⠀⠀⠀⠀⠀⣙⣿⡿⣅⡴⠀⠀⠤⢃⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠁⠀⠀⠀⡀⠀⡀⠰⠀⠀⠀⠀⢀⡤⠀⠀⠁⡸⠻⡍⠇⡀⠀⣉⠉⢀⠓⠈⠄
⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠁⠀⠈⠁⠀⠁⣀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⠀⠁⡈⠐⠀⢀⡀⠈⠀⡄⠰
⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⠘⠀⠀⠰⠂⠀⠁⠄⠀⠀⠀⠀⠁⠔⢀⠀⠀⠁⣄⠀⠘⠀⠈⠁⠀⢄
⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⣠⠀⠀⡤⠀⢉⠌⠀⠀⠀⠀⠀⠠⡄⢀⠀⠁⠀⠀⠀⠀⠘⠆⢀⡀⠀⢤⢸
⠀⠀⠀⠀⠀⠁⠀⣠⠀⢀⡄⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠃⢀⡀⠀⢀⠀⠁⢠⡀⠈
⠀⠀⠀⠰⠀⢀⡀⠀⠀⡄⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⡀
⠀⠀⠀⠢⡀⠈⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢶⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⣦⢿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣿⣌⣿⣿⣷⡄⠀⠀⠈⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡌⣿⣿⣿⣿⣿⣿⣆⠀⠀⢹⣿⠓⠸⣿⡀⠀⠀⠀⠀⢠⣾⣿⣿⣇⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣷⣾⣿⣿⣿⣿⢿⣿⣦⡀⠈⣿⡃⠀⢸⡇⠀⠀⣠⣶⣿⣿⡿⢩⣿⣿⣿⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠻⣿⣿⣿⣿⣦⣀⠈⣷⠀⣿⠀⠀⣿⠀⣠⣾⣵⣿⡿⠋⢠⡟⠛⣿⣿⡇
⠀⠀⠘⢻⣦⣤⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠻⣿⣇⠙⢿⣷⣿⣿⣿⣷⣾⣧⣾⠀⠀⣹⣶⣿⣿⡏⢀⡌⡠⠋⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠉⠛⠻⠿⠶⠮⢭⣿⣿⣶⣶⣶⣶⣦⣭⣷⣦⣟⣛⣋⣭⣭⣭⣤⣉⡙⢛⡛⢿⣿⣿⡿⠿⠞⢁⣠⣤⠾⣋⣤⣤⣤⣤⣄⣀
⠀⠀⠀⢤⣀⡀⠀⢀⣀⣤⡾⣿⣯⡿⠋⠈⠛⣚⠋⣹⣿⠟⣿⣥⠿⠋⣽⣿⣿⡝⠛⣡⣼⠟⠙⠿⠷⣮⣩⣽⠿⣯⣥⣤⣬⣹⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⢈⣽⠿⠛⠋⢿⡀⠈⠁⢴⣿⢠⣿⣿⠃⠻⠋⠀⠙⣡⣤⣤⣿⣷⣿⡅⣠⣿⣿⠀⣠⣶⣦⣤⣝⢷⡦⡀⢀⣈⠛⠛⠻⣍⡉⠙⠛⠻⠿⠷⠶
⠀⠀⠀⠀⣾⢁⠖⠀⠀⣀⠀⢰⡏⠘⣋⡸⢷⣫⣾⡆⣴⡆⣰⣿⡗⣈⢻⣿⣿⣾⣿⡟⠻⢿⣿⡇⣾⣿⣿⣿⣦⡓⣼⣿⣧⣰⡿⠾⠝⢦⣄
⠀⠀⠀⢰⡟⢠⣦⠀⠐⣵⠟⢨⡿⢸⣿⣷⣿⡇⡸⣷⢿⣧⢹⣿⣿⣿⣸⣿⣿⠙⣿⣷⣸⣿⣿⣿⣾⣿⣿⠀⣹⣷⢈⣉⠛⣿⣿⡀⣆⣈⠻⢷⡄
⠀⠀⢀⣿⠀⢙⡏⠀⠸⣷⣣⣿⣀⠈⢿⣿⡟⢡⣽⣤⣿⡿⣀⣽⣿⣿⠟⣿⣿⣆⣻⣿⣿⣿⣿⣿⡟⢻⣿⣧⣻⣿⡘⣿⣿⠿⣿⣧⣽⡻⢷⣦⠹⣆
⠀⠀⣼⠟⠀⠘⠃⣄⠀⠘⠋⣼⣿⣷⡙⠃⢀⣜⢻⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣇⢻⣿⣿⣿⣿⣅⡙⠋⣀⠹⣿⠉⣿⡄⢿⡇⣿⡄
⠀⣼⠁⠜⠃⠀⣼⢻⡇⢸⣷⣄⠹⡿⣷⣤⢾⣿⣦⡈⢿⣏⣴⣬⣽⣿⣿⣾⣿⣿⣿⣿⣟⢰⡟⣿⣿⣿⣿⣿⣿⡟⠹⣿⡄⣿⣿⣿⡇⢿⣇⠸⡇⠹⣧
⢰⡏⠀⠈⢀⣤⡌⠁⡅⢸⡇⢸⣇⢰⣿⣿⣦⢣⣸⣧⣸⣿⣷⣿⣧⣿⣿⣿⣿⡇⣉⢻⣿⣮⣿⣿⣿⣿⣿⡏⢻⣧⢺⣿⣷⣤⡿⠻⣿⣾⣿⣷⡀⣶⣽
⡜⢸⠆⠀⢸⣿⢁⡄⢠⣌⠻⣾⠇⣸⡿⢿⣙⠃⣿⡿⠟⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣇⢸⣿⣷⣽⣿⣿⠀⣾⢻⣿⢉⠻⣷⠹⢻
⡇⠀⠀⠀⠈⠻⢋⣄⠘⣹⣷⡀⠰⣿⡄⣄⢹⡇⢸⣧⣾⣶⣽⣿⣿⣴⣬⣻⣿⣿⣿⣿⡿⣫⣽⣿⣧⣞⣻⣿⣷⣿⣿⣿⣿⢿⣧⡙⢻⣿⢾⣷⡟⠀⣸
⣿⠀⠀⣾⣧⡀⢸⣿⢧⡘⢿⡇⣤⣮⡍⠹⣿⠥⠿⢿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣇⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣿⣿⣿⣿⣦⣄⡀⣿⡿
⢸⡄⠀⠹⣯⣷⢀⡻⠾⠟⠀⠸⣿⣀⣿⠈⣱⣦⡀⢺⣿⣿⣴⣤⠹⣿⣿⣿⠏⣠⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⢻⡇⢸⡇
⠀⢷⡙⠀⠈⢫⠸⣿⢦⡀⢘⣦⣌⣙⠉⢰⣯⣸⡇⠸⠿⣿⣤⣿⣷⣿⢿⣿⣸⣿⣷⣿⣿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⢿⡿
⠀⠈⢷⣶⠀⠈⢷⡝⠾⠗⢸⣧⠰⠏⣿⠀⣿⡟⣡⣤⣄⡙⢻⣿⣿⣧⣦⣹⣿⣿⣿⣿⣿⡇⢾⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢉⠿⣿⣾⠃
⠀⠀⠘⣿⠠⡄⠀⣿⣦⡀⠈⢿⣶⣤⣿⡄⠙⠀⢿⣏⠻⣿⣸⣿⣿⣿⣿⣿⣿⣿⣇⣤⡹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣺⣷⣿⠇
⠀⠀⠀⠘⣏⢳⡘⢮⠻⣿⠀⣶⣤⡉⠻⠇⠰⣦⣈⠻⣿⣿⣿⢉⣉⠻⣿⣿⣿⣿⣿⣼⣇⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⠏
⠀⠀⠀⠀⠙⣦⢿⣦⠀⢻⡘⣿⣿⣿⠆⢀⡀⢿⣟⣷⠈⣿⣿⣿⣻⣇⠙⡟⠛⡀⢹⢛⣿⣿⣿⣟⣯⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠘⣦⠈⡇⢶⣇⠈⠛⠛⠀⢻⣿⣿⣿⣏⣼⣟⣿⣿⣿⣿⣶⣿⢿⡟⠋⡸⠿⠿⠿⣿⣷⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠘⣦⠘⠦⣿⣦⠻⣿⠛⣦⡀⠁⠙⢿⣿⣹⣿⣿⢉⣿⣿⣿⣿⣷⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡆⢧⡘⣷⠹⣷⣾⠁⢀⣿⣶⣿⣏⢿⡃⢼⣹⣿⣟⣿⣿⣿⣿⣟⣩⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⣿⡻⣦⣿⢿⣦⢈⡙⢿⣌⣿⠂⣿⣾⣿⣿⣿⣥⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⡁⢿⣟⣀⢻⣼⡷⠀⠉⢩⣴⣿⢦⣽⣿⣿⣾⣿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡘⣮⡛⢿⢟⡀⢠⣴⣆⣠⠙⢿⣾⣿⠿⠿⣿⣿⣿⣶⣎⣿⣿⣿⢉⣿⣿⣿⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡌⠛⢷⡌⠃⣈⣛⠿⠟⢁⣿⣿⣷⡶⢶⡌⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⣿⣧⠹⣿⣧⠰⣿⣯⣄⠸⣷⣿⣷⣿⣿⣿⣯⣭⡙⣿⣿⡟⢫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⣍⠀⠈⢁⣶⣤⣫⣿⣇⣿⡟⢋⣤⣉⣿⣭⣿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠻⠏⣻⣛⢿⣿⣷⣴⡟⣹⣿⣭⣾⢯⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣅⣾⣶⣿⣿⢋⣿⡿⠿⢿⣿⡿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣈⣙⠿⣿⣷⣿⣦⣾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀⠀⢰⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠉⠉⠉⠁⠈⠉⠚⠠⠟⠛⠛⠩⣽⣛⠛⠛⠿⢷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⡶⢶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⣬⣙⢦⡀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⠏⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣆⠀⠀⠙⠳⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⡏⢠⡾⠋⠉⠉⠉⢳⡶⢀⡴⢶⣠⠟⢷⡄⢻⠀⠀⠻⡅⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⣼⡟⠀⠀⣴⡻⣇⡞⠀⠀⠀⠀⠀⢸⠇⡾⠁⠈⠋⠀⠀⠹⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⣼⡟⠀⠀⠀⠈⠀⠘⠃⠀⠀⢰⠄⠀⢸⡀⡇⠀⢰⠦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⡇
⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠓⠷⠀⠈⠃⠀⠀⢰⡓⠀⠀⠀⠀⠀⠀⠀⠷⠁⠀⠀⣿⡇
⠀⠀⢸⡇⠀⠀⢯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠘⣷⡀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠘⢷⣄⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣓⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠸⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢠⡦⡀⠀⠀⠀⠓⠁⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣤⣴⣶⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⢶⣤⣄⡀⠀⢠⡴⠋⢻⡆⠀⠀⠀⠀⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⠙⠳⣿⠀⠀⠀⢻⡄⢀⣴⠟⢋⣁⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠘⢿⣄⠀⠀⠀⠂⢌⢣⡀⠀⢸⢗⣫⡴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠒⡆⠀⠉⠳⢦⣤⣤⣤⣝⣷⣷⣾⠟⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠘⠛⠁⠀⢀⣴⡿⠛⠁⠐⠒⣻⡿⢿⡻⢄⡈⠀⠀⠈⠻⢷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣴⢉⡇⠀⠀⠀⢶⣾⣟⣁⠀⢀⣀⣤⣾⠟⣷⡀⠈⢢⠙⢶⣶⣶⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠉⠉⠀⠀⢀⡤⢄⠈⠙⠛⠛⠛⠛⠋⠀⠀⠹⣿⣦⣀⠀⠘⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢾⣤⠇⠀⠀⢀⠤⢄⠀⠀⠀⢀⡤⡌⠙⠛⠿⠶⠾⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⡎⣽⠀⠀⠀⠀⠀⣀⠀⠀⠀⢿⣤⡟⠀⠀⠀⢸⣤⡟⠀⠀⠀⠀⣾⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠛⠁⠀⠀⠀⠀⡎⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⡀⠀⠀⢿⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠔⣦⠀⠀⠛⠋⠀⠀⠀⠀⢀⡴⠓⡆⠀⠀⠀⢰⡏⣸⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠞⠁⠀⠀⠀⠈⠛⠃⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⡷⠀⠀⠀⢀⡀⠀⠀⢀⡤⢤⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠐⠙⡆⠀⠀⠀⠀⠙⠛⠁⠀⠀⣾⢁⡹⠀⠀⠿⠶⣫⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡘⠶⠃⠀⢀⣀⠀⠀⠀⢀⣀⠀⠉⠉⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⢰⣇⡼⠀⠀⢰⣏⡼⠁⢀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣬⣉⣀⣀⣀⣠⣭⣶⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣴⠞⢁⣠⠤⣾⣿⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠙⠲⣅⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⣿⣾⣫⣴⣾⢋⣤⢞⣡⠂⢀⠀⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡠⠇⡑⣄⠀⠀⢀⡀⠀⢿⢿⣧⣿⠿⠿⠛⠛⠉⠉⠉⠀⠀⠤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢾⠋⠀⠈⢢⠀⠀⠀⠉⢲⣿⢿⣟⠓⠤⢀⡀⢀⣀⠀⠐⣒⣚⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣈⢶⣄⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡏⠀⠀⠀⠀⢇⠀⠀⠀⠀⠻⣆⢿⣽⣦⣤⣤⣴⣶⣾⣿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡴⠋⠀⠀⠀⡼⠀⠀⠀⠀⠀⠸⡄⠀⣀⡀⠀⠛⠪⢿⣯⡭⢯⣽⣿⡟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣎⣠⣤⡄⠀⢰⠃⠀⢀⣰⣎⡇⠀⣧⠀⠘⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⢿⣟⡛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠁⢀⠏⢠⣤⣈⣿⣿⣿⡄⣿⣴⣿⣿⣷⠀⣠⣀⣧
⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠟⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⢢⣾⣿⣿⣿⡿⣿⣷⣾⣿⣿⣿⣿⡀⣿⣿⡟⠀⣠⣴⠗
⠀⠀⠀⠀⠀⣾⣿⣷⣶⣿⣿⣿⣿⡟⢋⣾⠏⣼⣿⠁⢹⣿⣿⣿⡿⠏⠃⠀⠘⢻⣿⣿⣿⣞⣿⣷⣼⣿⣯⠛⠁⢈⣹⣖⣸⠫
⠀⠀⠀⠀⢸⣟⣿⣽⣿⠿⠋⣡⡼⢱⣿⠏⣸⡟⢻⣇⠀⣻⡿⠍⠀⠀⠠⠄⠊⠿⠿⠿⠿⠿⣿⣿⣿⣋⣠⣤⣾⣿⠟⢈⡇
⠀⠀⠀⠀⣾⣿⣟⡯⣠⣴⡿⢋⣴⣿⣥⣾⣿⣧⣬⣿⣾⠟⠁⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠁⠀⣤⣶⡐
⠀⠀⠀⠀⠉⠙⠋⠛⠛⠳⠶⠟⠛⠁⠀⠀⠋⠿⢿⣿⡟⠘⠀⠐⠀⠀⠀⣀⣀⡀⠀⠐⡅⠠⠄⠀⡸⠿⢿⣿⣿⣆⣀⢸⣿⡷⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠜⠠⠀⡀⠆⠨⢀⣤⣠⣤⡀⣠⢶⣶⣾⣅⣷⣆⣿⣿⣿⣿⣿⡟⠋⢁⡀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠠⠂⣖⣰⣶⣿⣷⣷⣮⣿⣵⣾⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡟⠉⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡇⠀⠁⣠⣶⠟⢋⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣷⡔⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣾⣿⣿⡇⠀⠘⠁⣠⠖⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣿⣿⡇⠀⠀⠉⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⣿⠛⠉⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠫⠉⠁⠀⠀⠀⠀⠀⠂⢠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠫⠽⠿⠿⠟⠛⠻⠿⠿⠿⠟⠛⣿⣿⣿⠟⠛⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⢀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀
⠐⠀⠀⠀⠀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⢁⠀⠀⠀⠀⠰⠀⠀⢀⠴⠃⠉⠀⠀⠀⠀⠀⠰⠋⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠁
⠃⠀⠀⠀⠀⠠⢀⡄⣀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⡀⠀⠀⣾⣷⠋⠀⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣆
⠀⠀⡀⠑⠦⢠⠘⠊⠐⢀⠠⠀⠀⢸⡅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠎⠙⠓⠓⠖⠰
⠀⠀⠈⠉⠓⠢⢄⠀⣰⣿⣀⡀⠀⠚⠦⠤⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠛⠻⢧⠀⠀⠑⢑
⠀⠀⠡⠀⠀⢤⠊⠙⠉⠏⠏⠉⠀⠀⠀⢠⡀⠉⠑⢄⠀⠀⠀⠀⢠⣄⢀⠴⠚⢲⠋⠀⠀⠀⡇⠀⠀⠐⣇
⠀⠀⠀⠀⠀⡀⠀⠦⠄⢀⠀⢀⢀⠀⡀⠀⠈⠁⠀⠀⠑⡀⢀⡴⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠘⣄⠀⠀⠈⠂
⠀⠀⠀⠀⠁⠆⢀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠸⠢⠄⡸⢦⣷⠊⠀⠀⢰⠃⠀⠈⠀⠀⠀⠺⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢽⣆⠟
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠉⠓⠠⡄
⠀⠀⠀⠀⠀⠄⠀⠐⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈⠰⠂⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠑⠀⠄⠐⠁⠀⠀⠀⠀⠀⠠⠀⢀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡾⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⠀⠀⢀⡏⠀⢰⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣄⣀⣘⣦⣀⣸⣃⣠⣞⣀⣀⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢶⣤⣬⣷⣤⣼⣥⣴⣯⣤⣴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠛⠋⠉⠉⠉⠉⠛⠛⠳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢋⣉⣥⣤⣤⣤⣤⣤⣤⣍⣉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠻⠀⠀⠀⠀⠀⠀⠀⠘⢠⡾⠋⠁⣀⠀⠀⠀⠀⠀⢀⡀⠉⠛⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣧⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⠀⠀⠘⠀⠀⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣏⣿⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⠀⠀⠀⠰⠄⠀⠀⠘⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣿⣿⣿⡟⣿⣿⣿⣏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠲⠀⠀⠀⢠⠀⠀⠀⠰⠆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣛⣿⣿⣿⣿⣿⣟⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣤⠀⠀⢀⠀⠀⠠⡄⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⣿⣷⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢤⠀⠈⠀⢠⠄⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠰⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠴⠞⠋








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠚⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣀⠀⢳⠀⡇⢀⣠⣤⣀⡀⢀⣤⡄⠀⠀⠀⠀⢀⣠⠴⠾⠥⢤⣈⠉⠒⠤⣃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣀⣀⡀⠈⠑⠺⠄⡟⠁⠀⠂⠈⠹⣏⠀⠹⡄⠀⢀⡴⠋⠀⠀⠀⣀⡤⠶⠛⠒⠂⠈⠀⢨⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢉⡼⠋⣀⡤⠒⢠⠀⢄⠰⢤⣀⡉⠉⠙⢿⣧⠀⢹⣠⠏⠀⠀⠀⢠⠼⠿⠶⠶⠶⢲⠖⢀⠀⢀⠀⢉⠙⠛⠦⣀
⠀⠀⠀⠀⠀⢠⠏⢀⣀⠻⠖⠋⢹⠃⣰⢻⠀⠈⠷⣄⣈⣿⢿⣶⣦⣽⡆⢸⣟⣀⣤⣄⣀⠘⠀⠀⠀⠀⣴⣫⠞⠉⡄⢸⢦⡀⠙⢶⠠⣤⣑⣦
⠀⠀⠀⠀⠀⡿⠀⠸⡽⠂⠀⠀⣼⣴⠃⠸⡆⠀⣧⣟⣁⣀⣀⠀⠉⠓⠧⠸⠋⠀⠐⠀⠉⠁⠒⢦⡀⠘⠋⣡⠀⠀⣇⢸⠀⠑⣄⠀⢳⡘⣧⠈⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠃⡴⢦⣹⠞⠁⣡⠟⢁⣠⠔⠂⡄⠠⡀⠢⣤⣈⠉⠉⠛⣍⠉⢫⡀⠀⢻⠔⠀⢸⣼⠀⠀⠈⠳⣼⡇⢹⡆
⠀⠀⠀⠀⠀⣷⠀⠀⠀⡶⣄⠀⠀⠀⠘⡽⠃⣀⡐⠷⠚⠉⡏⢀⡜⡇⠀⠹⢦⡀⠙⣟⠳⠶⢬⣧⡀⢹⡄⠀⠀⡀⠀⠿⠀⠀⠀⢰⠺⠁⢸⡇
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠳⠃⠀⠀⠀⢸⡇⠀⢿⡗⠀⠀⠀⣧⡞⠀⢳⠀⢸⠀⠹⣦⡘⣆⠀⠀⠘⠤⠀⢻⡀⠨⡘⠀⠀⠀⠀⠀⠀⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡤⣼⠀⠀⠀⠀⠀⠀⠀⠛⢠⠶⡌⢧⣸⠀⠀⠀⠙⠿⠀⡤⡀⠀⠀⢸⡇⠀⠀⠀⢰⠒⡄⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠓⢻⡇⠀⠀⢰⢦⡀⠀⠀⠀⠋⠀⠀⠙⠠⡖⢦⠀⠀⠀⠳⠜⠀⠀⣸⠇⠀⠀⠀⠘⠚⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢰⡢⠀⠀⠀⢿⡀⠀⠈⠟⠀⠀⡤⡄⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢀⡿⠐⢢⠀⠀⠀⠀⢀⣄⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣳⠀⠀⣾⠃⠘⠃⠀⠀⠀⠀⠀⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠐⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠈⠁⠀⣼⠇⠀⠀⠀⢔⡆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠠⣀⠀⠹⣆⠀⣖⠄⠀⠀⠀⠀⠀⠹⠃⠀⠀⢠⢦⠀⠀⣼⢿⢶⠀⠀⠀⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠓⠶⡿⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⣼⠋⠈⠋⣠⠄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠸⡅⠀⠀⣶⢦⠀⠀⠀⠀⢀⡼⠋⠉⠉⠙⠁⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⢄⡀⠈⠃⠀⣠⠶⢤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠳⢶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠩⢉⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄
⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡇⠈⣇⠀⠀⣀⣤⠶⠒⠛⠒⠶⣤⡀
⠀⠀⠈⣇⠉⠓⠶⠤⣄⣀⡴⠚⠋⡉⠙⠳⡎⠙⠲⠾⢥⣄⣹⣄⡾⠋⠀⠀⠀⡀⠀⠀⣈⡿⠂
⠀⠀⠀⠹⣄⠀⠀⠀⣰⠧⢤⣄⠀⠀⠉⠲⢧⡀⠀⢄⡀⠀⠉⠻⣄⠀⠀⣠⠎⠀⣠⠞⠳⣄⣀⢀⣀⣀⣠
⢠⣤⣀⣀⣈⣷⠦⠤⠄⠒⢒⣘⣷⣦⣀⠀⠈⠙⣆⠀⠙⢦⡀⠀⠘⣖⠋⣀⣠⣾⣭⣍⣒⣀⣉⣉⡭⠞⠁
⠀⠙⠲⢤⣄⣀⣀⣀⣘⣋⣉⡤⠶⠛⠉⠛⠛⠛⠻⣦⣀⣈⣧⣀⡤⠟⠉⠉⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⢀⡴⠋⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣷
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢀⠀⠸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠁⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠀⢰
⢸⡆⠀⠃⠀⢀⡀⠀⡀⠀⠀⠀⠤⡀⠀⠀⠀⡎⡧⠀⠠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢀⡿
⠀⢻⡄⠀⠀⠀⠁⠀⠴⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⢠⠂⠀⣾⠃
⠀⠀⢻⡄⠀⠅⠀⠀⢢⠀⠀⠠⡀⠀⠀⠠⡒⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠂⠀⡤⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠹⣦⠀⠀⠀⠉⠀⠀⠘⠞⠀⢠⢄⠙⠁⠀⠀⠢⠀⠀⠀⠦⠇⢀⡀⠉⠀⠀⡠⠄⠀⠔⣾⠃
⠀⠀⠀⠀⠈⢷⡀⠐⠀⠀⠠⠢⠀⠀⠀⠘⠀⠀⠀⣄⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠈⢀⠄⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠹⣄⠀⡀⠀⠋⠀⠀⠁⢂⠀⠀⡀⠁⠀⠀⠁⠈⠀⠌⠁⠀⠠⠈⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠂⠀⠀⠀⢀⠀⠀⠃⠀⠈⠁⢀⠀⠀⠀⠠⠀⠊⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⢉⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠈⠀⠁⠁⠀⠒⠂⠀⢀⠀⠉⠠⠊⡀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠠⠀⠀⠐⠀⠀⠀⠐⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠐⠄⠀⢒⣢⡶⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⠀⡈⢢⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⡒⠒⣀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⡏⠀⠀⠱⡀⠀⢀⠔⠋⠀⠀⣰⣯⠖⣊⠉⠉⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠉⠱⡴⠁⠀⢃⡰⠁⠀⣰⣡⢚⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⣱⡀⡔⠠⠁⡇⢠⠏⠀⠈⠁⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠘⢅⠀⠀⠱⠉⠉⢹⢃⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠤⠤⡀⠀⠠⠔⣒⢒⣙⣂⣀⠠⢄⡄⡀⠀⠠⠘⣌⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠙⢄⠤⠀⠀⠂⠀⠥⠦⣉⣀⣈⠙⠿⠒⢍⠣⡀⠀⠀⠛⡇
⠀⠀⠀⠀⠀⡠⡊⠀⠁⠠⣒⣅⣀⠄⡆⠀⠀⢢⠤⡼⠟⡇⠀⢰⠀⠀⠑⠀⠀⠀⡀⠇
⠀⠀⠀⠀⢠⠃⠁⠀⠀⠀⠀⠀⠀⠀⢆⡸⠢⠼⢠⠈⠄⠃⣠⠎⠀⢀⣀⡠⠖⠀⠀⢀⡀⠲⣄
⠀⠀⠀⠀⢸⠐⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠤⢰⠊⠁⠀⠀⠓⡺⠒⠁⡄⢀⡈⠀⠰⡙⠭⡟⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⢈⡁⡀⢂⠆⠀⠀⠠⠁⠸⠤⠒⠊⢇⠋⠈⠒⠠⣹⠉⡁⠤⡈⢂
⠀⠀⠀⠀⠀⠸⣠⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⡡⠋⠀⠀⢀⠃⠀⠀⠀⠃⠀⠈⠀⠀⠀⠤⠀⠀⢠⢠⠀⣀⠆
⠀⠀⠀⠀⠀⠀⡄⡀⡀⠀⠀⠐⠂⠂⠀⠆⣠⠊⠀⠀⠀⠀⠸⠀⠄⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠦⠀⠈
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⡄⠀⢢⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠄⢠⠐⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠄⠠⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠈⠀⠀⠀⡀⠐⡢⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠠⢄⡠⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⡀⢢⠀⢀⡀⠀⠀⠀⠀⡂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⠀⠰⠀⢘⡀⠜⢉⠜⠠⠤⠀⠀⠀⢄⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⡷⡄⠆⠸⢀⠔⢠⣁⡀⠤⡰⠂⠀⠐⠀⠀⠈⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣜⢦⣒⣤⠰⢒⡀⠔⠊⠄⠀⠀⠀⠂⠀⠀⠈⠂⠈⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢨⠩⢉⣆⠎⢹⠣⣬⡀⠑⢄⠀⠠⠀⠀⠐⠄⠀⠀⠀⠈⠀⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⡳⣿⡈⠗⣁⢐⠒⠀⠀⠘⠓⠀⠀⠀⠀⠀⠂⠀⡀⠀⠒⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⣠⣢⠊⠀⡌⠰⠀⡌⠀⡄⠄⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⣀⠀⠐⠌⢢
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠠⠀⠀⠀⠀⠀⠂⡀⢈⡀⠀⠀⠀⠀⠀⠲⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠣⡄⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠁⠀⠀⠑⠀⠠⠄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠀⠀⠀⠀⠀⠀⡀⠀⡀⠉⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠠⡀⢈⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠐⠀⠀⠀⠈⠀⠀⠄⠈⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠁⠀⠀⠂⠀⣀⠀⠀⢠⣀⣀⣲⣤⠀⠥⠤⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠈⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣦⣠⡿⢋⣀⣀⣀⣤⡶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣻⣾⣿⣿⣿⣯⣉⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣶⣿⣶⣶⣾⣿⣿⣟⣿⣿⣿⡏⣟⣛⣿⣿⣿⣿⣿⣛⣟⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⢀⣾⣿⣿⢯⡿⢿⣿⣿⣯⣿⢿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣗⣽⣿⣿⡿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⢰⣿⣿⠋⢹⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠈⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⠉⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⢸⣿⠟⢻⣿⣿⣿⣿⣿⣏⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣏⠈⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁

⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⣀⣄⣤⡂⠤⣄⡀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⡾⠛⠒⠛⡛⠻⢿⠿⡀⠀⠉⠻⠮⠿⣷⣤⣀⡀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⢴⡷⠋⠀⠫⠀⠐⡂⠈⠁⠐⠓⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣶⠀⠸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⡠⠃⠀⠀⠤⠔⠒⣀⣾⣿⣿⠗⡀⠀⠀⠀⡨⢍⠉⠛⢿⡏⣡⣰⣶⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢡⠞⣠⣀⠀⠀⠀⠀⠸⣿⠛⠛⠾⠋⠀⠀⠀⠴⠶⠊⢀⣔⣴⣷⣬⣿⢿⠘⢷⡄
⠀⠀⠀⠀⠀⢶⣤⣤⣴⣿⡓⡡⢋⣿⠟⠁⠀⠀⠀⠀⢳⣅⠀⠀⢸⣆⠀⠀⢴⡞⠛⠸⣿⡿⠟⠿⠿⢶⣶⣿⣷⡄
⠀⠀⠀⠀⠀⠘⠿⠿⡿⢋⠀⣠⣻⢋⠀⢀⣄⠀⠀⣠⢿⡿⠀⠀⠈⠻⡆⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠉⢹⣿⣿⣿⣷⠾⠿⠻⠁⠀⠀⠀⠀⠐⠄⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠟⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣠⣷⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣾⣿⡿⠀⠀⡰⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⡇⠀⠀⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣀⣀⣈⡆⠀⡀⢻⣿⣿⡿⡄⠀⣼⠃⠀⢀⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠇⠙⢿⣿⣿⡄⡘⣦⣿⡿⢳⣿⡄⠁⣢⢔⣩⣤⣄⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣠⣤⣤⣤⣤⣍⣻⣏⠉⠉⠁⢠⣿⣿⣷⣿⣶⡌⠛⢫⣤⠉⣛⡿⣿⣿⠓⠢
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⢘⡿⣿⠙⠛⠻⣿⣄⠀⣿⡀⠃⢀⣀⠀⠙⠷⣄
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢦⡸⠃⠙⠀⢀⣴⡄⠘⢧⡿⣄⠀⠀⠙⠓⠀⠸⣿⣷⣄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⢠⡶⣄⠀⢸⡗⠁⠀⠸⣯⡿⠁⢠⣄⠀⢿⡌⠉⢿⢿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣻⣷⡄⣯⡿⠃⠀⠀⠀⢴⡶⡄⠉⠁⠀⢸⡛⠂⠈⢱⣶⡄⢸⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⡿⠁⡴⡆⠀⣠⣤⠀⢻⡅⠉⠀⢘⢟⡂⠉⠀⠀⢨⣹⠳⣺⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀⠸⠛⠃⠀⢿⡻⠁⠀⠉⠀⠀⢮⣁⠀⠀⠀⢤⣄⠁⠘⢫⣤⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⠀⣼⣿⣧⠈⢁⣠⣄⠀⡰⢶⠀⠉⠀⠀⠀⣾⡟⠀⠀⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡃⠟⠧⢿⠀⢩⣗⡟⠀⠷⡎⠃⢀⣴⣶⠀⠉⣀⠀⠀⠙⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣧⣶⠀⠀⢀⠀⠙⠃⠀⠀⢀⣀⠘⠿⠟⠀⢰⡿⠁⣾⣿⠏
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⡟⠀⣰⣹⡷⣠⠾⡳⠀⣿⣿⠀⠀⢀⣄⡈⠁⠀⠋⡽
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢟⣩⣠⠀⢙⣾⠋⠁⠛⠁⠀⠘⠃⠀⠀⢸⠟⠁⣼⣷⣼⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⢾⣿⠆⠁⠀⢠⠖⠒⠀⢀⡶⣦⠀⠀⣠⡀⠻⣧⡏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⣾⠋⢀⣤⣴⠃⣿⡿⠴⡜⣿⠉⠀⢸⣿⣣⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣷⣾⣿⡙⢧⡄⠀⢀⡐⠂⣠⣶⠀⠈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⢿⡿⠛⠈⠁⣀⣀⢾⡻⠇⠐⠿⢿⣽⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣅⠀⠀⣼⣿⡇⠈⠁⣴⣶⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣧⡿⣷⠀⠸⠿⡇⣄⣈⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⡿⣞⣦⣿⣧⡾⣿⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣟⣿⢸⣿⢿⣿⣿⣿⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⠿⠴⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣦⠀⢀⣀⠀⠀⢀⣤⣾⠟⠛⠛⠟⠿⣿⣶⡀⠀⠀⠀⠐⣦⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⣴⣴⣶⣤⣌⠁⠀⣰⣿⠋⠀⠘⠀⠂⢂⣰⡈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⠟⠛⠛⠉⠙⠿⣿⣾⡿⠁⠀⡄⠀⠘⡀⠘⠑⠛⠀⢻⣿⠸⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢀⡀⠀⠤⡀⢀⡈⣿⠓⠀⠀⠀⠄⠉⠁⠀⠀⠁⢀⡘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠐⠀⠳⠀⠁⣹⡀⠂⠉⠀⠈⡀⠀⠀⡔⠀⠈⠁⣿⠁⠠⠾⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢻⣧⠁⠸⡀⢀⠀⠀⠐⢾⣿⣧⣀⣾⣿⣿⣿⣷⣴⡄⠀⠠⢸⣿⡂⠀⣰⠆⠴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠃⠘⣿⣆⡀⠁⡀⠀⠀⣤⣾⣿⣿⣈⡛⠋⠈⢻⣿⣿⣧⠀⣨⣿⣿⣃⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠻⣿⠷⢶⣶⡶⢞⡛⠋⣠⣌⠹⠋⢾⠇⣉⣯⣵⠾⣿⡿⠛⢻⣄⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⣾⣿⠠⠿⢿⡜⠛⠙⡆⢠⠬⡁⣽⣿⠁⣸⡟⠀⢀⠀⢻⣧⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⠀⢠⣿⣿⡷⠀⢺⣿⠆⠀⢓⠈⢳⡄⠬⡁⠀⢹⡇⢠⣄⠀⠀⠹⠳⣆⠀⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⡆⣉⡘⣻⠶⠶⠿⠁⢾⣿⡟⢂⢾⡹⣦⡀⠀⠸⣧⠀⢿⣷⣄⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡮⠍⣩⡲⠤⢤⢀⡀⢉⡀⠙⠂⣽⣿⣇⠀⠀⣿⣆⡀⠀⢻⡄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⠀⠀⢠⡿⠑⠚⣿⣿⣷⣯⣦⢸⣋⣵⣦⣾⣿⣿⠿⡷⠈⢸⣿⣿⣶⣶⣿⣶⡄⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡿⠁⢀⣿⡟⠡⠤⠄⠠⠄⢀⠀⠙⢹⣧⢹⠁⠑⠋⣼⣿⣿⣿⣿⣿⣿⣿⡌⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡾⠇⢀⣼⣿⣿⣿⣷⣤⣄⣀⣈⡀⢤⠀⢻⠄⠒⢉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⠀⣾⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣷⣶⠶⠿⠟⠛⠋⠉⠉⣿⣿⣿⣿⣿⣿⡇⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣾⡃⠂⠠⠄⠀⠀⠄⠀⡉⠛⢿⣿⡋⡀⠀⠤⡀⠐⠂⠀⠁⠀⢸⣿⣿⣿⣿⣿⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⣿⣷⣶⣦⣄⠀⠀⠹⣧⣤⠀⠀⠀⢶⣾⣿⣿⣤⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠄⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⡿⠿⠿⠟⠋⠠⠁⣰⣿⣿⡇⠐⣤⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⡇⠰⡄⠠⠄⠐⠐⢃⠐⢾⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠰⣶⣶⣷⡀⢂⠈⠛⢻⣿⡧⠀⡇⠀⠛⢻⣿⣿⣿⣿⣿⡿⢁⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠀⠁⠀⣸⣿⣿⠃⠀⠃⠠⣤⡉⠀⠀⢀⣀⣱⠈⠉⢻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⢸⣷⣿⣿⣿⣿⣤⣤⣾⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⡀⢀⣉⣻⣇⠀⣿⣷⣿⠉⢻⣿⣿⠋⠙⣿⣯⣀⠀⢀⡀⢀⡀⠀⡀⠀⢀⠜⣁⢠⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣤⣤⣤⣶⣿⠿⠿⣮⠹⡟⠉⠀⠀⠀⠉⢿⣿⠀⢺⣿⡟⠀⠋⠀⠀⠛⠋⠉⠙⠋⠙⠋⠛⢛⢉⡒⣛⣿⡌⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣟⠛⠾⠛⠁⣀⠀⠀⠀⣾⠷⠹⣶⣶⢿⣷⣤⣤⣿⡴⠀⣿⣁⢀⣴⣷⣶⣶⡶⣶⣶⣶⣄⠀⠀⠀⢈⠉⠛⣿⡇
⠀⠀⠀⠀⠀⢀⣮⣭⣀⣀⣤⣤⣴⣿⣄⣠⣴⡿⢻⣦⠙⣦⡀⠀⢙⡟⠻⣧⠀⠙⠻⣯⣧⣄⣠⣤⣤⣤⣤⣬⡿⠷⠴⠿⠛⢷⣤⣼
⠀⠀⠀⠀⠀⣿⣽⠋⠉⢉⣉⣩⣤⣤⣨⣭⠁⠀⠈⢻⣧⣌⡻⢦⣄⡈⠀⠌⠻⢶⣦⣤⣤⣤⣤⣤⣼⣶⣥⣄⡝⢷⣆⠀⠁
⠀⠀⠀⠀⠀⠛⢿⣿⣿⣟⣿⠿⠋⠉⠉⠻⠃⠀⠀⠀⠙⠻⣷⣦⣁⡼⠻⠶⢦⣦⣤⣤⣈⣉⣩⣉⣤⣄⣤⣿⠇⣸⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢤⢶⣶⣮⣥⣬⣍⣭⣭⣯⣌⣤⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⠤⠬⢿⣏⠒⠢⢤⡀⣸⠀⢀⣾⣃⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⠟⠛⠉⠉⠁⠰⠶⣾⣉⡉⠉⠉⠛⠻⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣤⣶⣶⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡈⠙⠳⣦⡀⠀⠀⠀⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢊⣵⡿⠟⠋⣡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡍⠉⠉⠛⠲⢤⣱⡄⠀⠀⠀⠀⠈⠙⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣼⠏⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⢰⡏⠀⢠⣾⠟⠛⠉⠉⠛⠛⠷⣶⡤⠀⠀⣠⣶⡀⢀⡾⣿⣦⠀⠈⣷⠀⠀⠀⢸⡛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⢠⣾⡿⠁⠀⠀⢀⣀⣿⠁⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⡾⠋⠘⣷⡾⠁⠈⠻⣷⡀⢹⡆⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⢠⣿⡿⠁⠀⠀⠀⣟⡹⠻⣆⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣾⠁⠀⠀⠘⠁⠀⠀⠀⠈⢷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⢀⣿⡿⠁⠀⠀⠀⠀⠉⠀⠀⠹⡇⠀⠀⠀⠀⣠⣄⠀⠀⠘⡇⠀⡇⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡆⠀⠀⢷⡀⣷⠀⠀⠸⣧⡍⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡆⠀⠀⠀⢈⣿
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠆⠀⠀⠈⠀⠀⠀⠀⢸⣏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⢀⣿
⣾⡟⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⣿⡛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢶⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⢧⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠇⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⣶⠳⡄⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣦⣤⣀⣀⣀⣠⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠦⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡦⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⡀⠈⢀⠀⡀⡀⠀⡀⠀⠀⡀⡀⢀⠈⣈⠁⢀⢀⢀⠀⡀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠟⠇⠀⠿⠄⠸⢸⠀⠇⡇⠀⡇⠀⠀⡇⡅⠈⣇⢿⠡⢸⠠⢸⠀⡇⠈⠳
⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠜⠦⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡟⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣹⡾⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⢀⣀
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣀⠀⠀⠀⠀⢠⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠉⠉⠁
⠀⠠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠟⠀⠀⠠⠤⠼⡧⠤⠤⠤⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⢀⣐⣁⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣀⢨⣿⡿⠇⠒⠀⠘⡿⠦⡀⠀⠀⠀⠀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢘⡉⠁⠀⢰⡀⠀⠘⠁⠀⠀⠀⠀⠀⠰⣃⠻⠁⡀⣫⢕⣪⠁⠀⠀⠈⢛⡖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠐⢀⡤⢉⠱⣄⠀⠀⠀⠀⠀⠀⠀⢠⢠⠂⠄⢋⡐⠃⠁⠀⡀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⢀⠀⠈⠀⡀⠐⢹⠆⠀⠀⠀⠀⠀⠀⠰⢴⠆⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠠⠃⠀⠁⠈⠠⠂⠀⠀⡎⢸⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠤⠮⣤⣔⣁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⡀⠀⠐⢀⠀⠐⠁⢀⡀⠐⡀⢢⠓⠀⠀⠀⠰⠤⣆⡤⢌⡫⠚⠉⠉⠀⠰⠀⠁⠀⠏⠠⡄
⠀⠀⠀⠀⠀⡈⠀⢀⡀⠁⠠⠂⠀⡈⠀⠀⠁⠀⠀⠀⠐⣃⠄⡴⢈⢙⠋⠀⠰⠀⠀⠇⠀⡀⠈⠀⠘⠐⠄⠂
⠀⠀⠀⠀⡈⣠⠀⢉⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⢡⠠⢿⠘⠀⢠⠀⢀⠀⠀⠂⠀⠀⠀⠀⠁⢼
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠂⠞⠂⠀⡈⠀⠠⠀⠰⠀⢰⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⡃⠀⠀⠀⠁⠀⡄⠀⡄⢠⠄⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⢀⠄⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈⠰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣘⢃⡀⠀⠀⠀⣐⠋⠨⠍⠉⠐⠌⠆⠀⠀⠀⠄⢄⣀
⠀⠀⠀⠈⠀⠀⠀⠉⠀⠉⠁⠉⠁⠉⠀⠀⠀⡀⠀⠀⠀⠀⢐⠲⣷⣦⢄⡀⠀⠀⠀⠉⠛⢿⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡠⣠⠅⠀⠀⠰⠆⠁⢠⠊⠡⠀⠀⠬⠁⠀⠀⠀⠀⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠿⡿⡃⢰⡄⠰⠖⡄⠶⡀⠀⠊⢐⢰⠄⠀⠀⠀⠀⠘⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡖⠁⠀⣼⠁⢸⠄⠘⠉⠗⢤⠰⠀⢘⠀⡘⡖⠀⣤⢴⡾⣵⣾⡄⠀⢀⣵⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠐⢥⠘⢀⠀⠆⠩⡅⠾⠀⠐⠝⠈⣀⠁⠀⣀⠉⢠⠀⢉⣻⢸⣁⠋⠹⢹⡝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠘⠀⢠⠀⢠⠀⡀⠰⠆⠀⠀⠀⠈⠁⠀⢠⡄⠄⠠⠐⡠⣑⡾⢣⡘⠇⡌⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⡄⠂⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠋⣤⠁⠉⠘⡈⢁⠃⠆⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣂⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠁⠈⡔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣤⢠⢀⡄⣀⢠⣤⡀⣤⡄⢠⡤⠀⣤⣄⠀⠀⢠⣤⢠⢤⡀⣤⠤⢀⡤⣤⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⡏⢸⢼⡇⣿⢸⣤⠇⣧⡿⢸⠶⠀⡇⢸⠀⠀⣿⠈⢸⣼⠃⣿⠆⢸⣧⣼⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠃⢸⠘⠇⠿⠸⡇⠀⠯⠀⠸⠤⠄⣧⠞⠀⠀⢻⡴⠸⠘⠆⠿⠤⠸⠇⠸⠸⠇⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠆⠀⡆⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠘⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⡻⠀⠀⠀⠁⠀⢰⠀⠀⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⢀⡔⠁⠀⢀⠌⠀⠀⠀⠀⠀⢸⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠚⠁⠀⢀⠠⠋⠀⠀⠀⠠⠀⢀⠌⢠⠃⠌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢀⠔⠁⠀⠀⠄⡀⠔⠁⡠⠂⡴⠃⢠⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠑⠀⠀⠀⢀⠠⠔⠊⣀⠄⠊⣠⠀⠀⠀⢠⠀⢰⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢀⠂⠀⠈⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠊⠀⢀⠠⠐⣈⣉⣀⡠⠤⠔⠊⠁⠀⠀⠀⡀⠔⠁⠀⡠⠀⢀⣼⡅⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡥⠚⠉⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠀⢀⡠⠊⡠⠞⠁⢸⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠉⠀⠀⠠⠒⠀⠒⠒⠒⠀⠉⠀⠀⠀⠠⠔⠊⡁⠀⠈⠀⠀⠀⡸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠄⠐⢒⡀⠀⡈⢉⣉⠥⠄⠒⠒⠒⠀⠁⠀⢀⠔⠀⢀⡴⠁⠀⠀⠀⣾⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠃⢀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠴⠋⠀⠀⠀⢀⡜⠁⢇⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠈⠀⠀⢀⠤⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠖⢹⠀⠀⡸⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠀⡀⠀⢠⠞⠉⠉⠓⠒⠢⠤⠤⠤⠔⠂⠁⠒⠁⠀⠀⢀⠀⠀⠁⠀⠀⠀⣠⠃⠀⣠⠃⢀⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠐⠈⢙⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠁⠀⠀⢀⠤⠊⠀⠀⠀⠀⣀⡤⠚⠁⢀⠔⠁⡐⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠁⢀⣠⠴⠒⠋⠉⠀⠀⣠⠆⠀⠀⠈⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⡠⠒⠉⠉⠉⠉⠁⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣠⡤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣔⣋⡠⠴⢾⡉⠙⠂⠀⠛⠉⠀⠀⠀⠀⣠⣴⣒⣋⣉⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣄⣀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠚⠛⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠛⠀⣿⡁⢘⣀⣀⡤⠢⡀
⠀⠀⠀⣀⠤⠤⠄⣀⠀⠀⠀⡰⠊⠀⢀⡤⠤⢄⡀⠈⣧⠀⠀⠀⠀⠀⡖⠲⣄⠇⠀⣸⣆⢀⢧⡏⠈⠀⠸⠁⡜
⠀⠀⡼⠁⠀⠀⠀⠀⠉⠲⠎⠀⢀⡔⠁⠀⠀⠀⢻⠀⢸⠀⠀⠀⣠⡉⠣⡈⠻⡅⠀⢩⢿⣏⠀⠛⡄⠀⠀⢰
⠀⢰⡇⠀⡔⠉⠙⠓⠦⡄⠀⢠⠯⡀⠀⠀⠀⠀⡸⠀⢸⠀⠀⢮⡈⠿⡆⠀⠀⠀⠀⠀⠜⢿⠀⠀⠃⠀⠀⠈⡇
⠀⠈⡇⠀⠱⡀⠀⠀⠀⢇⠀⠊⠀⡃⠀⠀⠀⠀⠇⠀⣼⠀⠀⠀⠈⠢⣄⠀⢀⠠⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠹⡀⠀⠱⡀⠀⠀⣨⠂⠀⡰⠦⣀⠀⠀⡸⠀⢠⡇⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠙⣄⠀⠙⣤⠞⠁⢀⡞⢦⠀⠈⠑⢶⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠈⠣⣀⠀⠀⢠⡎⠀⠀⠑⣤⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠹⠤⢖⠁⠈⠓⠒⠊⠀⠀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⡤⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣀⡠⠴⠶⠊⡉⠉⠉⠩⠉⠉⠙⠓⠲⢤⣀
⠀⠀⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⣠⠔⠚⠉⠉⡉⠉⠉⠉⠓⠒⠦⢤⣀
⠀⠀⠀⣹⠓⠒⠒⠂⠒⠒⠂⠂⠒⠒⠒⠒⠀⠒⠒⠀⠀⠀⢧⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠸⡇⠀⠀⠀⠀⠑⠁⠀⠈⠐⠀⠀⠀⠀⡀⠀⠀⠀⠹⡄
⠀⠀⡠⠏⠀⠉⠈⠁⠁⠀⠀⠂⠀⠀⠀⠔⢎⠐⠂⠁⠀⠀⠘⢲⠀⠀⢳⡄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⣿
⠀⠈⡷⠈⠓⠀⠀⠄⠄⠀⠀⠄⠂⠄⠀⠠⠐⠄⡀⠂⠀⡢⣤⡼⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠉⢻⡐⠒⠉⠑⠠⠔⠀⠄⢀⣀⠖⠒⠠⠴⠐⠐⠊⣠⠎⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠙⠒⠦⠤⢦⣄⣠⣤⣀⣀⣠⣀⣠⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠊⠉⠁

⠀⢀⣤⢲⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⠀⠄⢀⠉⠘⠋⠃⠀⠀⠀⠀⢀⣴⣲⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⠀⠀⢀⠈⠘⠋⠃
⠀⢸⣯⣍⠁⠀⠀⣤⡀⠙⠟⠆⠀⠠⠀⠀⠡⠀⠀⠀⠀⢀⠀⠀⠀⣾⣯⣍⠁⠀⠀⣤⡀⠙⠟⡄⠀⠠⠀⠀⠡⠀⠀⠀⠀⢀⡀
⠀⢈⠁⠀⠁⠀⢀⠰⠀⠀⠀⣀⡴⢣⣄⠀⠄⠀⠀⠀⠁⢦⡀⠀⠀⢸⠁⠀⡀⠀⢀⠰⠀⠀⠀⣀⡴⢧⡄⠀⠄⠀⠀⠀⠁⢤⡄
⠀⠀⠑⠀⠋⠀⠈⠀⠀⠀⠞⠇⣈⠀⠀⠀⠀⠀⠀⢒⡀⠉⠺⠀⠀⠀⠑⠀⠋⠀⠈⠀⠀⠀⠞⠇⣈⠀⠀⠀⠈⠀⠀⢳⡀⠉⠃
⠀⠀⠀⠀⢠⠀⠱⣾⠃⠀⠀⠀⡠⠲⠠⠈⠀⠀⠒⠊⠛⢦⣄⠒⠠⠀⠀⠀⢠⠀⠱⣾⠃⠀⠀⠀⠀⠴⠠⠈⠀⠀⠒⠊⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠄⠀⢰⣕⣶⣄⠀⠢⠘⠉⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠄⠀⢱⣕⣶⣄⠀⠢⠘⡁
⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠡⠚⠻⡄⠀⠀⠀⢰⣶⡄⠀⠀⢤⣄⠁⠀⠀⠀⠀⠠⠄⠀⠀⠈⠡⠚⠻⡄
⠀⠀⠠⠤⠶⠤⠤⠀⠀⣀⠀⠀⢀⠀⠀⠀⢀⠄⢠⠁⠁⠀⠐⠃⠀⠁⠀⠤⠶⠤⠤⠀⠀⣀⠀⠀⢀⠀⠀⠀⢀⠄⣀⠃⠁
⠀⠀⠀⣀⡀⠀⠀⠀⢠⣼⣇⠀⠀⠀⠒⠀⠀⠿⢠⡠⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣼⣇⠀⠀⠀⠒⠀⠀⠿⢠⡠⡀
⠀⢠⣾⣼⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣼⡄⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠁⠤
⠀⢸⠗⠢⠀⠀⠀⢳⠂⠀⠉⠃⠀⡜⠀⠀⠈⠀⠀⠀⠄⠐⠀⠀⠀⢻⢟⠢⠀⠀⠀⢳⠂⠀⠉⠁⢀⡜⠀⠀⠀⠀⠀⠀⠤⠐⠂
⠀⠐⢄⠀⣤⠀⠠⠈⠀⠀⣀⡴⠋⠑⠂⠀⠁⠀⠀⣀⠀⣽⢦⠀⠀⠘⡄⠀⣤⠀⠠⠈⠀⠀⣀⡴⠋⠑⠂⠀⠁⠀⠀⣀⠀⣵⡆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠁⠐⠀⠀⢀⠀⠀⢀⣸⣄⡀⠙⢀⠀⠀⠀⠀⠁⠄⠀⣀⡄⠀⠉⠑⠐⠀⠀⢀⠀⠀⢀⣸⣄⡀⠁
⠀⠀⠀⠀⠸⠀⠘⣟⡀⠀⠀⠀⠤⠉⠈⣀⣀⡀⠉⠁⠈⢙⣶⡀⠐⠀⠀⠀⠰⠀⠘⡟⠀⠀⠀⠀⠤⠉⠈⣀⣀⡀⠈⠁⠈⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠈

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠁⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⢁⡌⠀⠀⠀⠀⠀⠀⣈⡶⢀⠀⡀⠀⠀⠀⠀⠀⠰⣩⢹⡑⡒⠀⠀⠀⠀⠀⠀⢀⠀⣩⠏
⠀⠰⠀⠤⠀⠰⠌⠰⠀⠀⠀⠀⠸⠁⢀⠀⠈⠥⠀⠀⠀⠀⠀⠰⡃⢱⣢⢠⠀⠀⠀⠀⠀⠀⠉⠙⠚⠉⠅⠀⠀⠀⠀⠀⠴⣤⠚⠕
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠊

⠀⠀⠖⠒⢒⠒⠒⠆⠀⠀⠀⠀⠀⢀⠠⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡄
⠀⠀⠀⠂⠤⢤⠀⠀⠀⠀⠀⠀⢀⠚⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⣔⠙⢄⡙⠈⠀⠀⠀⠀⡱⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢠⠪⣩⠷⢱
⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠘⠉⣉⡉⠙⠀⠀⠀⠀⠀⢠⡐⢆⠱⠄⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⠙⢬⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠚⠒⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠠⠒⠢⡈⠂⠀⠀⠀⠀⠐⣁⠄⡄⠡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⠀⠀⠀⠀⠞⠀⣀⢀⣀⠐⠷⠀⠀⠀⠀⠠⡮⡖⠿⠶⢄
⠀⠀⠈⢂⡂⡂⡊⠁⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⢾⢠⠤⠘⠀⠀⠀⠀⠀⠈⠀⢤⠤⡄⠂⠀⠀⠀⠀⠨⣀⠅⠀⠀⠀⡠
⠀⠀⠀⠨⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡸⠜⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠀⠈⣄⠀⡠⠊
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢱⠊⠀⡀⢀⡞⠀⠀⠀⠀⠀⠀⢰⠦⠭⢴⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡱⠀⠀⠀⠀⠀⠘⠚⠛⠚⡃⠀⠀⠀⠀⠀⠐⠛⠄⠎⠈⠆
⠀⠈⠅⠈⠁⠉⠉⠆⠀⠀⠀⠀⠀⠠⠀⠀⠴⠀⠀⠀⠀⠀⠀⡀⠊⢥⡤⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠐⠀⠂⠂⠀⠂
⠀⠀⢾⡦⠰⣶⠄⠀⠀⠀⠀⠀⠀⠀⡁⠀⡁⠀⠀⠀⠀⠀⠈⠢⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⡉⠉⡁

⠙⣝⡀⠃⠘⠈⠀⠀⢀⢀⠤⠠⠿⢤⣀⡀⣿⣽⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠯⠚⠃⠀⢄⠈⠒⠒⠒⠉⠀⠀⢀⣧
⠀⣏⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⢿⡷⣄⣀⠀⠂⠀⡈⠆⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠘⠚⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠁⠀⠀⠀⠀⠀⢽⡛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡆⠀⠀⠀⠀⠀⠐⣠⡖
⠀⠈⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠐⠚⠿⣪⡀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⡠⠞⠋
⠀⠀⠄⠀⢀⣈⣦⠀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠁⠀⠠⠶⠈⠁
⢀⡀⠀⠀⠸⡏⣠⡤⠶⠒⠒⠖⠦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡦⡴⣦⣤⠤⣄
⢿⣯⠀⠀⠶⣹⣇⡠⡀⣀⢀⡠⠂⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠘⠿⠀⠀⠈⠀⠐⠉⠁⠀⠀⢱⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠊⢠⣠⣄⣻⣟⠋⣷⣶⠾⢧⣐⡀⠀⠳⢤⡄⠾⠛⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢧⠄⠀⠀⠀⠀⢀⡴⠀⠀⠑⠈
⣄⡠⢻⡽⠅⢾⡀⡾⠁⠀⠀⡪⣿⡄⠀⠀⠀⠀⠀⠀⠀⢈⡴⠛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠢⠰⠀⠀⢀⡾⠗⠠⠀⠀⢠
⠋⠉⣘⠷⠖⡆⠉⠻⠀⠀⡫⢡⣿⠃⢀⣀⡠⣤⡀⠀⡴⠂⠀⠀⢸⢀⠀⠀⠀⠐⠄⣀⠴⠀⠀⢀⠀⠀⠀⠈⠒⠂⠈⠙⠀⠀⠀⠀⠈
⠀⡼⠉⠃⠈⠀⠀⠀⢃⣀⣱⠞⠁⠀⠁⠀⢤⣺⡀⡾⠃⣀⠔⢲⣧⡴⢞⠻⢶⣄⠀⠀⠀⠀⠁⠤⠀⠈⠒⢀⠀⠠⠀⢄⠀⠀⣴⡄
⠞⠀⠀⠀⢀⡠⠦⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠝⣡⣛⢷⣾⢶⣿⠃⠀⠈⣜⠈⣿⡄⠀⠀⡄⠀⠀⠑⡆⠀⠸⠀⡠⠀⠈⠀⠀⠉⠁
⠀⠀⢠⡜⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠤⠀⠉⠧⢿⠧⣀⠈⢧⡀⠀⠁⠆⢼⡁⠀⠀⢡⡀⠀⠀⠘⢷⡤⡬⠁⠀⠀⠇⠀⠀⠀⠘
⢀⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡉⣁⣲⡾⡄⠉⢋⡁⠁⠐⠠⠬⠞⠀⠀⠀⡀⠙⠧⡤⠤⣼⣿⣇⢀⢀⠀⠀⠀⢠⣀⡠
⠛⠀⠀⠁⠀⠀⠀⠀⠐⢀⠇⠀⢤⣀⣀⡨⠁⠀⠀⠩⡉⢷⢾⠏⠅⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉
⡀⢀⠆⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⣄⡺⠃⠀⡷⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉⠀⠀⠃
⡡⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢹⠀⠀⢿⡄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⣄⣀⣀⡄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡏⠀⠀⠄⠀⠀⠮⣛⠿⣦⡀⠈⡄⠀⠀⠣⡀⠀⠀⠀⢀⣜⡃⠀⠀⠈⠀⠀⠙⠁⠀⠑⠄⠀⠀⣀⣤⠞
⠀⢠⠤⡀⠀⠀⠀⢀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⠉⢛⡱⠀⠃⠀⠀⠀⠑⢤⣀⠀⠸⢎⠀⠁⠀⠀⠀⠀⠁
⠝⠁⠀⢨⠀⠀⠐⠀⠀⠀⠀⢻⡎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠁⢀
⠀⣀⢠⣜⣈⣴⣦⣄⡀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠀⠊⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠄⠂⠀⡸⠏⢠⠀⠀⠀⠠⠔⠁⠠⠉⢉⢘⡏⢠⡾
⣟⣥⣾⠏⠁⠑⢺⠙⣷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣦⡄⠀⡀⠀⠀⢠⠂⠐⠀⠀⢀⡼⠑⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠗⠼⢧
⣏⠉⠹⡆⠀⠀⠓⠀⣻⠀⠀⠀⠀⠐⠄⠈⠐⡄⠀⠀⠉⠁⠀⢀⠀⢀⠀⠀⠄⢀⣰⡏⠀⠀⠀⡀⠀⠀⢾⡖⠀⠀⠀⡀⢀⡀⠘⢟⣸
⠁⠷⠶⠝⠒⠤⣀⢀⡹⠀⠀⠘⠀⠀⠈⡶⠀⠀⡆⠐⠂⠠⠀⠀⠑⠀⠀⠀⠀⢸⡿⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⢤⣤
⠇⠤⠖⠆⠀⠀⠀⠈⠀⠀⠠⠰⠀⠀⠠⠱⠆⠨⠠⠜⠁⠀⠂⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠐⠄⠀⠆⠀⠀⠠⠀⠀⠀⠒⠇⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠷⣶⠆⣀⣤⣶⣦⡈⠛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇
⣿⣿⣿⣿⣿⣿⡏⣿⣿⠿⠀⠀⠘⠦⠤⠄⠉⠡⢤⣼⡿⠋⠉⠁
⣿⣿⣿⣿⣿⣿⠟⣛⣒⣒⣒⠂⣲⣤⣤⣾⣿⣷⣶⣤⡀⠲⠆⠀⡀
⠾⠛⢯⣭⣶⣾⣿⣿⠿⠿⣿⠿⢿⣿⣭⣭⣭⣭⣉⣻⣿⣤⣀⠀⠁
⣶⣿⡿⠟⠛⢡⡄⠉⠶⠏⣠⣴⣿⠿⠿⠛⠛⢛⡻⣿⣿⣝⢻⣷⡆
⠛⢭⣀⡤⠞⠡⠦⠘⣫⣾⠟⡉⠁⠀⠤⠆⠘⠿⠿⠿⣿⣿⣦⡘⢿⣦⡀
⠀⠀⠉⠀⠀⠀⠀⣰⣿⠇⠀⠀⠛⠀⠄⠐⣠⣶⣶⣄⠐⢿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⢏⠀⠀⠀⠀⠂⢠⣾⠟⠋⠁⠀⠀⡉⠻⢿⣿⣿⠛⢿⣶⡄
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⣿⠁⠊⠀⣄⠀⣠⠁⢠⣾⣿⣷⣀⣈⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⣿⡟⠀⣾⡛⢻⣿⣏⠈⢻⣿⢿⣦⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣿⣧⣾⣿⣿⣿⣿⣿⣁⣶⣿⠸⣿⡀⠀⠀⠀⣼⣿⣀⣤⡀
⠀⠀⠀⠀⠀⢀⣤⡾⠆⠀⠀⠀⣿⡇⠀⠀⣠⣶⣿⣿⠋⢻⡟⠛⠛⠙⢿⣿⠃⣿⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⠇
⣀⣤⣤⣴⡾⠿⠋⠁⠀⠀⠀⠀⣿⡟⢠⣾⠟⡋⠸⠃⠀⢻⡇⠀⠀⠀⠸⡇⣸⡏⠀⢿⡇⠀⠀⠀⣿⣫⣿⠏
⠛⣋⣭⣥⣴⣶⣦⣤⣤⣤⠤⢀⣿⠛⠿⠁⣴⠁⠀⣀⣀⣹⣇⣠⣾⠟⢀⣿⡟⠁⡄⢸⡇⠀⠀⠀⣸⡿⠃
⡛⠋⠉⠁⠉⠁⠉⠉⠉⠁⠀⠼⠁⢀⣤⡾⣫⣷⣾⣿⣿⡿⢿⣿⣿⣆⣸⣿⠁⠀⡧⢸⡇⠀⠀⠀⠉
⠛⠀⡀⠀⠰⠶⢶⣄⣀⠀⠀⠦⠞⠋⣴⣿⠟⠋⢁⡿⠁⣠⣾⠟⣻⣟⣿⡏⠀⣴⢡⣾⠃
⣴⣿⣟⣿⣦⡀⠀⠉⠙⠛⢷⣦⣴⣿⡟⠁⢀⣴⠟⠁⢰⣿⣷⣾⣿⣿⠏⠀⠀⣠⡿⠉
⠛⠛⠛⢛⣿⣷⣄⠀⠀⠀⠀⠈⠙⣿⣧⢀⡿⠃⠀⠀⢸⣿⠉⠻⡛⢿⣄⣠⣴⡿⠁
⠀⠀⣴⡿⠋⠈⠛⢷⣦⣄⣀⣀⣀⣸⡿⠟⠁⠀⠀⠀⠘⢿⣆⣼⠇⠘⣿⣻⣏⣀
⠀⣾⡟⠀⠀⠀⠀⠀⡸⠋⠉⠉⠉⠁⠀⠀⠈⠛⠖⠀⠀⠦⠿⠃⠀⠀⢸⣿⣿⣿⠿⠶⠐⠄
⢸⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠠
⢻⣿⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇
⣘⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⣦⡄
⠿⢿⣿⣷⣆⣀⠀⠀⠳⢶⣟⣿⣯⣉⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠻⣦⡀
⣤⣶⠿⢿⠿⢿⣿⣿⣦⣄⠉⠉⠛⣿⣿⣴⡈⠷⠀⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠟⠁⠀⠀⠁⠀⠘⣿⣌⣻⢷⣄⠀⠈⠧⠹⣷⠀⠀⠙⣿⡉⠛⠛⠛⠛⠛⣶⡆⠠⠁⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⠀⢹⡇⠀⡶⢀⡿⠀⠀⠀⠈⠻⣦⠀⠀⠀⣴⢛⡜⠀⠀⠀⠀⠉⡷
⣿⣤⣤⣤⣤⣶⣿⣏⠾⠋⢀⣸⣧⡾⢷⣏⠁⠀⠀⠀⠀⠀⠙⠷⣤⠾⣯⠏⠀⠀⠀⠀⠀⢠⡿
⠈⠉⠉⠋⠉⠉⠙⠻⠷⠾⠿⠛⠁⠀⠀⠹⣧⣀⡀⠀⠀⠀⠀⠀⢀⡘⠁⠀⠀⠀⠀⢠⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢹⡿⣖⠂⠠⡤⠎⠁⠀⠀⢀⠀⠀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠞⠀⠛⠷⣶⣤⣤⣠⣶⡟⠋⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠿⢷⣦⠀⠀⠀⠀⠙⠿⠉⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⢸⡄⣶⡆⠀⠀⢠⡄⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⣿⠀⢸⡇⠟⠁⠀⠀⢸⡇⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣴⠟⠁⠀⣿⠀⠈⣿⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⣨⡟⠛⠛⠛⠛⠁⠀⠀⠀⠀⣿⠀⠀⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢻⣧⡀
⣀⣀⣀⣤⣾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⣦⡀⢳⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⡀
⠛⠛⠋⠉⠛⠛⠿⠷⣶⣤⣄⡀⢀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣾⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠰⢤⣄⣉⠙⢿⣿⣷⠀⢸⣿⠀⠀⠀⠙⠃⠀⠀⢹⣆⠀⠀⠈⠐⡇⠀⠀⠀⠀⠀⠀⠈⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣿⣷⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⡴⢋⣀⠈⠁⠀⠁⢈⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠙⠳⢦⣤⣼⣿⠀⢿⣿⡀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢀⣄⠀⢸⣿⠁⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⡃⠀⢹⡆⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡹⢷⣄
⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣤⣤⣬⣿⣄⣄⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣆⣙⣧⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⡽⠛⠋⠛⠛⠓⠶⢤⣄⣀⢀⣀⣠⣤⠶⠶⠶⢦⣄⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡏⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣰⣦⠀⠀⠙⢦⠀⠀⠀⠙⢷⣄⣀⠤⠤⢤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡿⠀⠀⠀⢸⣾⡿⠀⠀⠀⣄⢠⡄⠀⠀⠈⠛⠛⠀⠀⠀⠈⢷⣄⢀⡤⣾⡁⢠⣤⡄⠛⠉⢀⣠⡍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⡯⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡹⠿⠗⢈⣥⡄⢀⠾⠶⠀⠾⠿⠀⠰⠿⠉⢢⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠞⠃⠀⣀⣠⣤⣤⣤⣴⠶⠦⢤⣄⠀⠀⠨⣧⠀⡼⠁⠰⠶⠆⢡⣗⠀⠶⡶⢀⣴⡌⠛⠓⠰⣿⠀⢳
⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡴⠋⣡⡴⠚⠛⠉⠉⠙⠛⠲⢬⣳⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡟⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⢷⡀⢸⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀
⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⢀⣀⠈⠃⠘⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢸⡇⠀⣾⠀⠀⠚⠛⠉⠀⠀⠀⠹⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣶⠒⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠁
⠀⠀⠀⠀⣧⠀⡟⠀⠀⠀⠀⠀⠀⠛⠳⠆⠘⠿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠨⡆⠘⠤⠊⠉⠓⠤⠤⢤⡀⠀⠀⠀⣠⠖⠦⣀⠀⠀⡰⠋⢸
⠀⠀⠀⠀⠸⡆⢿⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⣤⠤⠶⠋⠁⠀⡀⣣⠀⠀⠀⠀⠀⣠⣀⠀⢧⡀⢀⡴⠃⢀⣄⡀⠉⠉⠀⠀⡎
⠀⠀⠀⠀⠀⢹⡜⣆⠀⠀⠀⠀⠀⠈⠻⠂⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠛⡿⣿⠀⠀⢦⠀⠘⢷⡿⠀⠀⢌⡤⠀⠀⢿⡿⠇⠀⢰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣠⣴⠇⠀⠀⠀⠘⠷⠀⠀⢸⠇⠸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠙⠲⠶⢤⣄⠀⠀⠀⠀⠀⠉⠀⠀⠈⠻⣆⢀⣀⡀⢀⡟⠀⠀⢹⡀⣈⣄⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠙⠾⠤⣴⠚⠺⠏⠉⠉⢧⠀⠸⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣝⣓⣲⠒⠚⠋⠁⠙⣦⣀⠀⢀⣠⠾⢦⣀⣀⣀⡴⠛⠒⠒⠀⠤⠤⠤⠀⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁




⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍⠉⠛⠳⢦⣠⡟⠁⠘⣧⠀⠀⣠⡶⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠘⢷⡀⠀⠀⠀⢈⢣⡀⠀⢸⡤⣚⡥⠶⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⢠⠀⠙⠦⣄⣀⣀⣙⣷⣴⣼⠿⠿⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠀⠀⠛⠋⠀⣀⣴⠿⠋⠁⠒⢺⡿⢿⠳⢌⠀⠀⠈⠛⢶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⣡⠇⠀⠀⠲⢾⣯⣅⣀⣀⣤⡾⠟⣷⡀⠀⠀⠹⣶⡶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡴⢲⠀⠈⠉⠉⠉⠁⠀⠀⠈⠿⣶⣄⣀⣹⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⢤⠀⠀⠀⠀⠓⠋⠀⠀⣴⢉⡆⠀⠀⢠⠚⡆⠀⠉⠉⢉⠍⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠞⠀⠀⠀⢠⡖⣢⠀⠀⠘⠛⠁⠀⠀⠘⠛⠃⠀⠀⠀⢸⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡠⣄⠀⠘⠷⠃⠀⠀⠀⢀⡴⢤⠀⠀⠀⢠⠎⡢⠀⠈⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⣧⡟⠀⠀⠀⠀⠀⠀⠀⠾⠶⠋⠀⠀⠀⠘⠛⠁⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣏⡹⠀⠀⢀⣀⡀⠀⢀⠄⢢⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠰⠉⡧⠀⠀⠀⠈⠉⠁⠀⠐⣯⡤⠃⠀⠙⢚⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠙⠁⢀⡔⡆⠀⠀⡠⢶⡀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⠶⠃⠀⠀⢓⣋⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠋⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣭⣬⣭⣯⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠦⠀⠀⠀⢀⠀⠀⠀⠐⠂⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⡄⢢⠀⠀⠀⠀⠀⠈⠀⠅
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢋⠀⢱⢸⡆⠀⠀⢀⡆
⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠤⠬⠼⠥⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄
⠀⠀⠀⠠⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢁⢠⡀⠀⠀⠀⠀⢀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠠⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣈⡀⠐⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠁⠒⠒⠉⠀⠀⠀⠀⠀⠄⡄
⠑⠄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⢤⢄⡀
⠀⠀⠀⢀⣢⣄⣿⣤⣼⡃⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⡐⠈⢸⣸⠿⣇⠀⠀⣐⣿⡿⠇⠀⠀⠀⠦⣷⢿⣿⣿⣧
⠀⠀⣴⡃⡜⢈⢹⣻⣿⡳⠶⠆⠘⠢⣾⣾⣼⠠⣠⠀⣰⠇⣆⡿⠗⢚⡿⠀⠀⠳⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣵⣿⣶⣄
⠀⢠⠋⡁⠱⣸⣭⣿⣿⣿⠀⠀⠠⣌⡉⠽⢿⣧⡇⢀⣿⣼⣟⣣⠍⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠈⠁⠀⣪⣿⣿⢾⡇
⠀⢸⣁⠠⢸⣽⣿⣿⣿⠟⠀⠀⠀⠈⠓⠊⠉⠉⠳⠘⠛⠛⠁⠀⠀⠀⠀⢀⢴⣴⣷⣀⡴⣄⡈⠀⠀⠀⠀⠀⢈⡵⣿⣿⠃
⠀⠈⢤⣭⣾⣿⣯⠏⠉⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣒⣀⡀⠀⠐⠿⢿⣿⣁⡤⣿⣿⣭⣶⣟⣅⠀⠈⠀⣿⡉
⠀⠀⠈⠙⠋⠁⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⠹⣿⣷⢖⣫⠀⠀⠀⡟⠠⡸⣵⠿⣼⡿⣏⠛⣿⣷⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠠⣦⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠃⠛⡇⠈⠀⠀⠀⢗⣰⣿⣿⡠⠉⠷⠋⣻⣿⣿⠇⠀⠀⣄⠠⠶
⠀⠀⢀⣭⢿⡶⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⢿⡿⠿⠗⠈⠄⣼⣿⣿⡟⠀⠀⣾⣏⡗⢀
⠀⢰⡿⠐⠆⠹⠆⣿⣿⣦⠀⣤⢢⣙⠀⠀⠀⠀⠀⠀⣄⣀⣠⣧⠴⠀⠀⠀⠀⠀⠀⣴⣡⣄⣀⠀⠚⠿⠋⠀⠀⠀⠉⠉⠁⠉
⠀⢺⣦⢉⡘⣧⣿⣿⣿⣿⠀⢲⡈⢿⣷⡀⣂⠀⠐⢲⣿⣿⣿⠟⡶⢦⡀⢀⣲⢶⣶⠟⡐⠀⠜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⣿⡤⠹⣿⣿⣿⣿⠏⠀⠀⠁⠽⣿⣷⠃⠀⢰⠋⣁⠈⣉⡀⠐⠊⢻⠀⡅⠀⠖⠈⠛⠂⠀⡀⢣⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠻⣿⣿⡿⠟⠁⠀⠀⠀⢀⣀⣤⠽⠀⠀⠸⡄⠀⠄⠙⠇⢘⠀⢸⠀⠻⢦⣄⣁⡈⡁⣁⣀⣨⠀⢀⣤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⠉⠃⠀⠀⠀⠀⠙⢦⡀⠂⠀⠀⢰⠃⠀⠀⠙⠤⠿⣟⠿⠟⠋⠀⠈⢿⣼⣯⡿⢋⣤⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⠛⠁⠙⠼⠿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠎⠃⣘⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠰⡏⠜⠀⣶⡆⠠⠀⢏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣿⣽⣆⠈⡗⢂⣀⠂⠂⣄⡸⢠⠀⢩⠉⡆⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣴⣽⣯⡿⣷⣿⣼⡆⠙⠊⣀⠙⢋⣏⠐⠄⡷⢫⠌⢣⠠⣿⣿⣿⣿⣿⣿⣷
⠐⡚⣓⣒⡲⢤⡀⣔⣭⣶⢸⢸⣿⣷⣿⣷⣿⣾⣯⡇⠀⠎⢍⠱⠔⢳⡀⡀⠉⣠⠐⠊⣸⡟⣛⣿⣿⣿⣿⡏
⠀⢣⢻⣿⣿⣿⣾⣿⣿⣟⡎⠘⠯⢧⣟⣤⣵⢿⣽⢿⠁⣆⣨⡄⠃⢈⠑⡜⠉⠁⡠⠊⠉⣚⣿⣿⣿⠿⠋
⠀⠀⠑⣿⣿⣿⣿⣿⠛⠈⠀⠀⠈⠛⢳⣎⣽⡛⠁⠀⢹⠐⠬⠈⠁⣸⠂⠇⢠⠞⢀⡴⣿⣽⢿⣶⢿⣭⠷⣄
⠀⠠⣾⣿⣿⣿⢿⠀⠉⠒⠂⠂⠤⠄⣙⢣⠀⠀⠀⠀⡬⠓⠂⠀⠉⠉⡀⡰⠃⠀⣶⣿⣽⡿⣿⣫⣿⣻⣿⡽
⠰⣌⣛⣛⣭⣵⣥⣤⣤⣀⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⡇⣿⣶⣄⠀⡼⣱⠁⠀⣦⣾⢨⣿⣜⣻⣯⣿⣯⠟⠁
⠀⠀⢀⣶⣿⣿⣿⡿⢻⣏⣷⡤⠒⠂⠀⣤⢘⣄⠀⠀⢳⡻⣿⣿⣾⢡⠇⣠⠞⠁⠸⡇⠻⠿⠽⠟⠋⠁
⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠃⠀⣤⣤⢴⣻⣋⠙⡄⠀⠈⢏⠈⠁⠃⣸⡼⠁⠀⠀⢀⣠⣤⡤⠦⠴⠶⢶⡶
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⢀⣴⣖⡶⣦⢹⣿⣥⡜⢆⠀⠈⡆⢠⢀⡟⠀⠀⣰⠞⠋⣁⣀⣤⣤⣴⠄⢸⣷
⠀⠀⠀⠀⢠⣤⣽⣦⣶⢠⣿⣾⣯⣧⣱⣿⣼⣧⣿⠈⠢⠀⢡⢘⣼⡇⢀⣞⣥⣾⣿⣿⣿⣿⣿⣿⠀⣾⠇
⠀⠀⠀⣰⣿⣿⣟⣿⣿⡘⣷⢿⣽⣿⣹⣿⣹⣇⡟⠂⠤⡑⡀⠂⣿⡇⣿⣿⣿⣿⡿⣿⣾⣿⣿⠇⢰⡟
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠘⢿⢯⣽⣯⣽⣏⡝⠁⠀⠀⠀⠙⠲⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡟⠁
⠀⠀⠀⢿⣿⣿⠿⠋⠁⠀⠀⠀⠙⠧⠿⠖⢋⣠⡤⣴⣶⣶⣶⣤⣽⣿⣿⣯⣿⣿⣿⣿⣿⣯⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣵⣾⣿⣿⣿⣿⣻⣭⣿⣿⣿⣶⣮⣝⡻⣿⣿⣿⣯⡳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢀⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣯⣽⢿⣿⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⣾⣿⣿⣽⣿⣿⣿⣿⣿⠟⣡⠛⣆⠹⢿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢼⣿⣿⣿⡿⠿⠿⠛⢋⣥⠞⠁⠀⠈⠳⣄⡉⠛⠛⠛⠛⠛⠛⠋⠉⣀⣤⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⣤⣤⣤⣤⣤⡴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠈⠛⠿⠶⢶⡶⢶⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢠⣿⣧⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣌⣿⣿⡿⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣶⠿⣸⣿⣿⣯⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢌⣱⡞⢿⠛⠟⢻⣿⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠐⡚⠛⣋⠩⣴⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠛⢷⣶⣴⣾⠖⢠⣼⢹⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠐⢴⠃⢌⣭⡾⠷⢺⣛⣱⡿⠈⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡕⠊⠉⠀⠀⢘⣠⡞⢁⣀⣤⡾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠉⠉⠙⠲⠖⠒⠉⠙⠛⠿⠛⠉⢶⣶⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠐⠐⠄⢠⠀⢀⡀⠀⡀⠀⡠⣦⡔⢾⢙⣧⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣠⠀⣆⢔⣀⣀⡆⠀⡇⣰⡆⠹⠳⡿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢇⢻⡀⣄⠙⣿⣀⡿⢁⡗⣾⢦⣷⣼⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢼⡾⡏⣭⠓⢿⣀⣧⣾⡧⣼⣾⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣧⣷⢻⣧⣼⡍⣿⣸⣏⣿⣹⣿⣿⡗⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢼⣧⣹⣟⣿⣻⣿⣿⣿⣿⡿⠽⣋⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⡗⠻⢭⠄⠊⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡴⡆⠰⣊⡥⠎⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⠃⣀⠈⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣤⡄
⠀⠀⠀⠀⠀⡀⣇⠣⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣤⠾⠉⠻⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣟⣻⡿⢾⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣵⣁⣼⠀⠀⠀⠀⠀⠀⠀⣭⣤⣤⣥⣤⣤⣤⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣷⣽⣛⣿⣥
⠀⠀⠀⢀⣼⣿⣉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣤⣤⣤⣤⡀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣟⣯⣿⠉
⠀⠀⢀⣺⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠙⠛⠛⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣄⣈⣙⣿⡇
⠀⠀⠈⠉⠙⠷⠿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠾⢯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⡴⠛⠻⠋⢓⣦⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠠⠀⠠⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⣋⣭⣴⣾⣿⣿⠄
⠀⠀⠀⣾⠛⠀⣶⢀⣨⣭⡇⠀⠀⠀⠀⠀⠀⠘⠳⠤⣄⡀⠀⠀⠀⢀⡴⣚⠁⠀⠀⠀⠀⠀⣴⣭⣶⣾⠿⠟⠋⠁⠈⠹⡏
⠀⠀⠀⠻⣾⠂⣴⡏⢥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠰⠿⣶⣍⡲⠤⢞⣭⣾⣿⡄⠀⠀⠀⠀⢺⣿⣿⠁⠀⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠙⠳⠾⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣻⠿⣛⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠻⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠰⢿⣶⣤⣉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢲⣄⣿⢰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡈⠛⠁⠀⠀⠀⠀⠀⠀⠰⡖⢾⠸⡇⣿⢸⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣷⣶⣶⡄
⠀⠀⠀⣿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣬⣶⣷⣷⣾⣧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣀⠀⠀⡟
⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣾⣿⣦⣶⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⠟⢻⡇
⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⣠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠐⠀⠀⠤⠤⠠⠔⠂⠀⢀⠤⠔⠂⠉⠉⠉⠑⠄⠀⠀⠀⠒⠄⣆⠀⠐⣷⡄⣀⢀⣀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⢄⠾⢛⡌⣍⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣸⠁⡏⠰⠙⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠄⠁⠀⠀⠀⠈⠐
⠐⣤⠀⠀⠀⠀⠀⠤⠔⠩⠀⢉⠶⡀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸
⡘⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠃
⣟⣙⡋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣁⣰⠦⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢣⠀⠀⠀⡀⡤
⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⡘⠆⠀⠃⠀⠁⠀⠀⠀⠀⠀⠈⠐⠤⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠱⠤⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣬⡇⠀⣠⡁
⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠚⠁⠀⠉⠂⠉⢲
⠀⠀⠀⠀⠀⠈⢳⡞⠡⠄⠀⡀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢦⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡦⣄⠀⠀⠀⠀⠀⢀⡀⣠⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠉⠙⠆⠀⠀⢇⣀⢈⣆⠃⠘⣆⠀⢀⢀⣀⣀⠀⠀⠀⠀⠘⢄⠀⠀⠀⡀⠔⠁
⠠⠄⠀⠤⠀⠀⠂⠁⠀⠀⠀⠀⠀⡀⠛⠉⠉⠃⠒⠛⠒⠿⢭⡃⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⢤⡀
⣟⣀⣠⠼⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠛⠻⡄
⣙⠏⠉⠁⠀⠀⠁⡀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢀⠀⠀⠀⠀⠀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠠⡄⡌⢰⠀⣜⠊⠀⠀⠂⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣽⡶⠶⣧⣄⣙⣼⠀⠔⢀⠊⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠩⠀⠀⠀⢀⠀⠀⠂⠁⠉⠣⠤⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠄⠀⠈⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢰⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠰⠁⠀⠘⣼⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠐⠀⡄⠀⢰⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣆⠀⠀⢸⡀⠁⠈⠐⡆⠀⠀⢀⠏⠁⠀⢹⠀⡀⠀⠀⠈⠀⠀⠀⠀⡄⢀⣐⠀⠠⠴⡅⢀⠐⠄⠀⠀⢰⠄⠀⢀⠈⠀⠈
⠀⠀⠀⠀⠀⢳⠀⠒⠀⠈⠦⠄⠀⠁⠀⠀⠈⠀⠀⢀⣎⣠⠤⠒⠚⡇⠀⠀⡠⠖⠉⠀⠸⡀⠀⠀⠀⠀⠾⠺⣄⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠓⢤⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢀⠼⢢⡤⠊⠀⠁⠀⠀⠀⠈⠢⠤⠄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢠⠃
⠀⠀⠀⠀⠀⢠⠖⡉⠁⠀⠀⡀⠀⠁⠀⡄⠀⠢⡀⠐⠒⠈⠀⠀⢀⠄⠂⠀⠀⠁⠀⠀⠐⠀⠠⠀⠐⠃⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠰⠁
⠀⠀⠀⠀⢠⠃⡘⠁⠀⡠⢚⠀⠀⠀⢸⠀⡀⠀⠀⠈⠈⢻⠙⡎⠀⠂⠀⡀⠀⠈⠀⠠⠀⠁⢀⣀⠠⠔⠂⢀⠤⠀⠀⠂⠀⠔⠐⠦⠅⡀
⠀⠀⠀⠀⠆⠸⠠⠲⠊⠐⠈⡄⠀⠀⢸⠀⢇⠀⠀⠀⡼⠋⠀⠰⠠⠀⠀⠁⠀⡀⠀⠓⠒⠂⠀⠂⠀⠀⠒⠁⠀⢠⠀⠀⠀⠀⠀⠠⢀⡀⠈⠁⢠⣤
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠈⡆⠀⠑⠂⠚⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⢀⠀⠀⠠⠙⠲⠤⣀⠀⠀⠀⠀⠴⠒⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⣀⡀⠀⠈⠂⣀⡀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠠⠀⠀⠀⢄⡟⠂⡒⠂⣀⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠀⠐⠀⠀⠄⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⢴⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⣀⠀⡀⠱⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠔⠁⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠐⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠒⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⠉⢩⣿⡯⡉⠛⢿⣿⣯⡝⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢲⣶⡆⠀⣲⣶⣄⠀⠀⠒⢦⣀
⣿⣿⣿⣿⣿⠀⠸⠏⢀⣿⠀⢘⣿⣿⣿⡆⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣇⣾⡟⢸⣿⡇⠀⠀⠈⢿⣦
⣿⣿⣿⣿⣿⠀⠀⠀⠸⠋⣠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣧⡾⠟⠁⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⢠⡀⠙⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣆⠀⠀⠀⠀⢸⣿⠃
⣿⣿⣿⣿⣿⠀⠘⣧⡀⠳⡤⠼⣿⣿⡿⢃⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡇⠻⣷⡘⣿⣂⠀⠀⣠⡿⠋
⣿⣿⣿⣿⣧⣤⣤⣽⣿⣶⣭⣦⡀⠉⠲⠿⠿⢟⣿⣿⣿⣿⠀⠀⠀⠐⠚⠛⠛⠂⠀⠙⠒⠻⣿⣾⣍⣀⣀⡔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠛⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠉⠁⠀⠀⠹⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⣤⣄⣄⠀⢠⠀⣀⡼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣄⣀⡀⡀⢀⢠⢀⣼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠙⠛⠚⠛⠋⠀⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠓⠶⠶⠴⠤⣤⣦⣦⡤⠼⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⠷⢶⣴⣴⣴⣠⣀⣆⣄⣶⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢸⣸⣠⢀⢀⡃⣀⡰⠈⠉⠉⠩⠅⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠯⠍⠉⠉⠛⠛⠛⠳⠶⡖⣴⣴⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⣯⡝⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⠏
⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⢀⡀⠀⠀⠀⠀⠸⣅⣸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠍⠀⢀⣀⠀⠀⠀⠀⢸⣇⣿⠀⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣉⡽⢿⡚⠳⢿⡵⣦⣤⣄⣒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠛⠻⠿⠿⠿⣶⣶⣯⣁⣀⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢙⣄⡤⠷⡖⠛⠻⣅⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⢀⠤⠄⠀⠢⠈⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢉⣧⡤⠞⢾⠉⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⢀⠀⠐⠔⠀⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⡉⢀⣳⣤⠴⠷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢀⡀⠀⢤⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠛⢯⠁⣘⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠒⠀⠁⠀⣐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡖⠚⠻⣅⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠢⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣦⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⢀⣿⠀⠀⠀⠐⠁⠀⠀⠀⠀⠻⢿⣆⠀⠼⠃⠀⠀⠉⠘⣻⠗⠂⠘⠉⠑⠂⠀⠀⠀⠀⠀⡸⠄⠀⢀⠀⠀⠀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠘⡄
⠈⠏⠉⠃⠠⢀⡄⠂⠀⠀⠀⠀⠀⠁⣠⡝⠷⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⡦⠀⠀⡀⠀⠈⠃⠀⠃⠀⠀⠀⠀⠀⠘⢦⣀⡀⠄⠦
⠂⠀⠀⠀⠀⠀⠀⢑⡄⠀⠀⠀⠀⠠⣿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣤⣤⣀⠀⠀⠀⠈⠻⠷⠖⢀⠀⣀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⣽⠁
⠀⠀⠐⠀⠀⠀⣠⡾⢀⣀⣀⢠⣰⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡁⢚⣷⠈⠃
⠐⠀⠀⢈⣠⡾⠋⠈⠀⠈⠋⠋⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠉⠁⡄⠻⣆
⣭⣯⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⣤⠀⣄⢀⠀⠀⠀⠀⠀⠀⠰⡸⣤⠄⠀⠀⠀⠀⠀⠀⢀⡦⠂⠀⠀⠀⠀⠠⡠⣄⡀⡻⠓⣦⠄⠀⠀⠀⠀⠈⠻
⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⡘⠛⠈⠁⠀⠡⠉⢻⡇⡄⠀⠀⠀⠀⠀⠑⡘⢷⣂⣀⠀⠀⠀⢠⠎⢀⡀⠀⠀⠀⠀⠰⠟⠲⣌⣷⠾⢷⠐⢾⣏
⣀⣤⢼⡷⣦⣄⡀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⡙⠋⠀⠀⠀⠀⠀⢠⣭⣙⡶⣤⡾⠋⣀⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣀⠈⠙⣿⣿
⢋⡼⠉⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⠛⢦⠤⣄⠀⠀⠀⠀⠀⢀⡉⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⢀⣠⣟⠋⠀⠀⠀⢀
⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠠⠀⠀⠠⠰⠛⠧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣼⠟⠛⠀⠀⠀⠀⠀⠂
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⢵⡆⠀⠀⢁⠀⠈⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣄⣀⣀⣤⡤⠖⠀⠀⠀⡠⢐⣬⡽⠶⠂⠐⠲⠊⠀⠀⠀⠀⠈⢉⡀⣾⠇⠘⠀⠀⠀⠀⣀⠀⠑⣤⠀⠄⠀⠀⠀⠀⠹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠉⠉⠋⠁⠀⠀⠀⠀⢠⣴⡿⠋⠙⣲⠈⡠⠐⡂⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠄⠀⠀⠀⠉⠃⠀⠀⢃⠀⠀⠀⠀⠀⠀⠹⣿⡀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠘⡿⠉⠀⠀⠀⠀⢠⡀⠘⢳⡄⠀⠀⠀⠀⠀⠀⠘⢅⣀⠀⠀⠀⢀⣀⣀⣤⡴⠋⠄⠀⠀⠀⠀⣀⣀⢿⡄⠀⠚⠀⡄⠀⠒⠂⠤⠤⢀⡀
⢠⠄⠀⠀⠀⠀⠀⣴⣧⠀⠀⠀⠀⠀⠈⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉⠉⠑⢜⠢⣤⡀⢀⣀⣰⡟⣧⠈⠛⠃⠀⠀⣇⠀⠠⠦⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢏⠵⠦⣀⢀⡄⠀⡀⠤⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠁⠨⠛⢻⠿⠿⠗⠈⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠁
⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⡀⠀⢑⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⡀⠀⠐
⠿⠉⡀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⠄⠀⠀⠀⢀⢀⠸⢤⣀⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣴⠆⠀⢀⣠
⠈⠀⠙⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠀⠀⠀⠀⡴⠂⡘⢉⡿⣗⣄⡤⠀⠀⠀⠀⠨⠛⣦⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠁⡄⠀⠀⢀⠀⠀⠀⠀⢻⣤⠀⠘⠇⠈⢹⡏⣑⡾⠛⣟⡿⠀⠀⠀⠀⠀⠀⠀⣸⢛⠈⠀⠀⠀⠀⠀⠀⠀⢐⡸⠗⠚⠙⠓⠥
⠀⠐⠈⠈⠘⠻⡇⣸⠦⠋⠀⠀⠀⠀⠐⠿⣦⣀⣈⡶⠻⠛⡟⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣽⣿⠀⠀⠀⠀⠀⠀⠰⣿⠉⠀⠈
⠁⠀⠀⠀⠀⠀⢜⣏⢂⣤⠀⠀⠀⠀⠀⠈⠘⠿⠿⡷⠻⡄⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢠⣼⠟⠃⠀⠀⠀⠀⢀⣀⣼⢿⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠶⢴⡛⠉⠃⠀⠀⠀⠀⠀⠀⠉⠑⢤⡷⣁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠂⣀⠰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠻⠀⣾⠳⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠙⠷⠻⠌⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢒⠎⠀⠈⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⡤⢀⢈⢷⠀⠀⠀⠀⠀⢠⡄⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀
⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣤⣁⠀⠀⠠⣄⠀⢄⡙⠀⠀⠀⠀⠀⠀⢀⠁⣠⡿⢁⡀⠀⠐⠉⢢⠀⠀⠀⠀⠀⠀⠈⢇⣬⡶⠚⠉⠁
⣀⣀⣐⣃⣀⣀⣀⣀⣀⣀⣀⣰⣆⣐⣤⣀⣃⣀⣀⣘⣻⣗⣤⣖⣉⣒⣀⣠⣀⣀⣀⣀⣀⣀⣀⣺⣏⣀⣀⣁⣀⣁⣀⣙⣀⣀⣀⣀⣀⣀⣀⣺⣃⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠉⠑⠂⢄⡀⠀⠀⠀⣀⠤⠖⠒⠈⠀⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⣀⠠⢤⣄⠀⠀⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡄⠀⢀⠔⠉⠀⠀⡞⠀⠑⠤⣀⠀⠀⠀⠀⠀⠈⠀⣀⠤⢄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠇⣰⡇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠉⠐⡖⠒⠒⠊⠉⠀⠀⢸⠑⢄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⣌⣀⡀⠀⣠⣿⣷⣤⣤⣤⣼⡄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠑⢄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⡀⠈⠉⠛⢿⣿⠿⣿⣶⣦⣤⣤⣤⣾⣧⣄⣀⡀⠀⢀⣠⣿⣦⣤⣄⣀⣷⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠎⠀⠀⠀⢀⠀⠈⠓⠤⣏⠀⠈⠉⠉⡿⠋⠙⠛⠛⢻⣿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣦⣄⣁⣀⣀⣀⣀⣀⣤⠜
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⢀⠀⠈⠙⠒⠤⠤⠗⠒⠉⠉⠉⠉⠉⠉⠉⠉⠀⠛⠒⠒⠒⠛⠓⠒⠉⠉⠉⣉⠕⠋
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠆⠀⠀⠂⠀⠀⠀⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠂⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣍⣫⣬⣉⣽⣩⣿⣻⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⣽⣿⡆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣾⣿⡿⢁⢔⣿⡈⢇⠀⠀⠀⣀⡀⠤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡴⣶⣿⡿⢇⣽⣿⡟⠁⣸⠀⠀⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢒⣯⣫⣷⠟⠋⢻⣥⣿⡿⣙⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⡵⠿⠿⠛⠋⠛⠁⠀⠐⠈⠻⢟⣹⣿⡿⠀⠤⠀⠀⠀⠀⠀⠠⢐⣼⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⣡⢄⣒⣀⠀⠀⠤⣄⠀⠂⣀⣹⣇⠀⠈⡐⢒⣤⣄⢀⢀⣦⢶⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠚⣵⣿⣿⢷⠆⠈⠡⠂⠲⣈⣻⣿⣿⣷⡄⠀⢨⣽⢻⣿⣾⣻⣿⣿⣿⣿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢒⠀⢻⣶⣷⣏⠐⠉⢠⣒⣀⡽⣶⣿⣿⣿⣿⡿⠃⠀⢀⣨⣵⣿⣾⣯⣿⣿⠟⠋⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠮⣴⢂⣐⣴⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⢏⠀⢀⣰⡀⢀⠸⣿⣿⣿⡿⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠋⠙⠛⠛⠛⠛⠻⣿⣿⣯⣴⣷⣷⠟⠁⠠⣤⣀⣿⣿⣿⠀⠀⠀⠀⣀⣅⣝⣽⣷⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣻⠿⣿⠏⡁⢰⢲⠲⣦⣿⣿⣿⠟⠀⠀⠀⢲⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡜⢁⡜⠁⢠⣿⣯⣾⣾⣿⣿⣿⠋⠀⠀⡴⣸⣷⣻⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣨⣷⡌⠀⠀⢿⢶⣙⣫⣙⣿⣿⡏⠀⢂⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⢯⣹⣿⣗⣴⣿⣭⢹⠿⠿⣿⣿⣿⣿⣮⣿⣽⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠀⠀⠟⠀⠀⡈⠙⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢠⢌⡹⠊⠒⠢⠤⠭⠿⠻⣿⣿⣿⣿⣽⣬⣥⣷⣧⣿⠿⡟⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⣋⠡⣮⠿⢄⡤⠤⠤⠴⠶⠤⠤⠼⠛⠛⠻⠿⠛⠛⠋⠀⠀⢱⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠟⠊⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠤⠶⠶⠖⠒⠒⠶⠶⠶⢶⣤⣤⣬⣄⣐⣒⠂⠠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠷⢶⣶⣤⣤⣤⣥⣍⣅⣁⣥⣤⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠢⠤⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢰⣤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣿⡏⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠉⢲⠇⣼⢸⠿⡂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡩⢷⡰⠀⠂⢐⣿⢸⡆⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣼⠁⠀⡹⠁⠀⢾⣿⠈⡆⠀⠠⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢐⢺⡇⠀⠀⡇⠀⠀⠘⣿⠀⢿⣄⠀⠊⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠄⠐⣄⠀⠳⣄⠀⠙⠹⣧⡈⢿⣼⣄⣀⡼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⢠⣶⠶⢈⡉⠒⠺⣟⣶⣶⠶⢷⣆⡈⠃⠒⠒⠺⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠿⣼⠁⠀⠀⢀⢀⡀⠈⠉⠛⠁⠠⠤⢀⡀⠀⠀⠒⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⢧⣄⠈⠢⠤⡔⠋⠀⠙⠲⢄⡀⠀⠀⠀⠀⠉⠲⣏⣿⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⠤⢤⣤⣀⣈⢙⡛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣀⣀⠙⠓⠾⣦⣠⡆⡀⠈⢉⠑⡒⠂⠢⠤⠈⠉⢉⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⣿⡦⠤⣤⣭⣭⣿⣷⣦⣤⣤⣤⡴⠶⠞⣮⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⡇⠀⡇⠀⣿⠀⣾⠉⢹⠇⠀⡿⠀⢸⡇⣼⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠀⢁⠀⣿⠀⣿⠀⢸⠀⢸⡇⢀⣿⢠⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡇⠘⠀⢹⠀⡿⠀⡼⠀⣼⡅⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⢧⠀⠀⢸⠀⣷⢠⣧⣰⣿⢡⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⡆⠓⢺⣶⡿⢸⡟⣿⣿⣿⡿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠋⠓⠚⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡶⠶⢿⡟⠛⠛⠉⢻⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⢿⠛⠋⠉⠹⣇⠀⠀⠈⣧⣀⣠⣤⣼⡷⠾⠿⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠟⠛⢿⡁⠀⠀⠘⡇⠀⣀⣠⣿⡶⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⢀⣤⣴⡶⢿⡟⠋⠁⠹⡆⠀⠀⢘⣧⣠⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠸⣿⠀⠀⠈⢧⠀⣀⣠⣿⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠶⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠹⣧⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠌⠁⠈⠻⠀⠀⠀⣀⣠⣤⠴⠖⠛⢿⣆
⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠈⢿⡆
⢰⡟⢹⣧⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣾⡇⠀⣿⡆⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⣿⠀⠀⠸⣷⠀⠀⢻⣧⠀⠀⠀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⣿⡀⠀⠀⢿⡆⠀⠀⢻⣶⠚⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⢻⡇⠀⠀⠘⣷⠀⠀⠈⢿⡄⠀⣠⡾⢁⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⢸⣧⠀⠀⠀⢻⡆⠀⠀⠘⣷⡀⠉⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣿⡀⠀⠀⠘⣷⠀⠀⠀⢹⣧⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣠⣶⠆⠀⢿⡆
⠀⢸⣧⠀⠀⠀⢻⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣤⡷⠀⢿⣤⣀⠀⠘⣿⡀
⠀⠀⣿⡆⠀⠀⠘⣿⡀⠀⠀⠈⣿⡀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠈⣿⣷⣄⠀⠉⠹⣷⠀⢹⣧
⠀⠀⠸⣷⠀⠀⠀⢹⣇⠀⠀⠀⠸⣷⠀⠀⠻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣦⡀⠀⣿⡀⠀⠀⠀⠘⣿⠙⠃⠀⠘⠋⠀⠀⢿⡆
⠀⠀⠀⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⢻⣇⠀⠀⠀⠉⠻⢶⣄⡀⠀⡀⣀⣄⡀⠀⢰⡟⠀⠀⣿⣧⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠘⣿⡀⠀⠀⠸⣷⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠙⢿⡌⣿⡟⠙⢷⡄⠘⢷⣤⣴⡿⠙⠃⠀⠀⠀⠀⠀⢀⣠⡤⠶⠂⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢹⣇⠀⠀⠀⢻⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠘⣷⠸⣷⡀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⣿⡀⠀⠀⠀⢹⣇⠀⠀⢀⣀⣀⣸⡟⠀⠉⠁⠀⠀⠀⣀⣠⣤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⢰⡆⠀⣰⠀⣀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠸⣧⠀⠀⠀⠀⢿⡀⠀⠈⠙⠛⠋⠀⠀⢀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⣿⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢻⣆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⢿⡄⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠘⣷⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠹⣧⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢻⣇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡆⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⣿⡀⠀⠀⢿⡆⠀⠀⣀⣠⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠸⣧⠀⠀⠸⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣇⠀⠀⣿⡄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⢿⡟⠋⠉⣷⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠈⣿⡄⠀⢻⡇⠀⠈⠳⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠻⣏⠉⠀⠀⠈⣷⣠⣴⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢸⣷⠀⢸⡇⠀⠘⠳⢮⡻⠆⠀⠀⠀⢀⣠⣤⣴⣶⠟⠛⠉⠙⣧⠀⠀⢀⣹⣦⣴⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⢿⡇⣾⡇⠀⠀⠀⢀⣀⣤⣴⠶⢿⡟⠋⠉⠀⠸⣇⠀⠀⣀⣼⣶⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣁⣤⣶⡾⠛⢻⡅⠀⠀⠀⢻⡄⠀⣀⣤⣿⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉⠁⠘⣧⠀⢀⣻⣤⣤⣴⡾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⣶⠿⠿⠛⠛⠉⠁

⠀⠀⠀⢰⡿⣠⡶⣻⣿⢶⡄⠀⠀⠀⠀⠀⣠⡶⠿⠟⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠿⠶⣦⣀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣷⡶⣤⡀
⠀⠀⠀⠀⣰⢏⡾⣩⣍⢧⢿⡄⠀⠀⢀⡼⠋⢀⣤⣴⣤⡀⠙⣿⡄⠀⠀⠀⠀⣼⢫⣾⠟⠛⢿⣮⢻⣆⠀⠀⠀⠀⣼⣷⣯⣾⣿⣯⡻⣽⣆
⠀⠀⠀⠀⣿⣼⣽⠋⣿⢸⢸⡇⠀⠀⣼⠇⣰⡟⠉⠀⠙⣿⡄⢸⣿⠀⠀⠀⣸⢣⡿⣡⡾⠿⣆⢻⡇⣿⠄⠀⠀⢸⣯⣯⣿⣟⣯⡟⣿⣿⣻
⠀⠀⠀⢀⡋⠋⡃⠀⠙⢙⡍⠃⠀⠀⣿⠀⡿⠀⠀⠀⠀⢸⣇⠈⣿⠀⠀⢠⡇⣾⢡⡟⠀⠀⢿⠸⣧⢸⣧⠀⠀⡿⢿⣹⣿⣾⠛⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠐⠃⠀⠀⠐⠃⠀⠃⠀⠀⠛⠘⠃⠀⠀⠀⠀⠘⠛⠀⠛⠀⠀⠘⠉⠋⠘⠃⠀⠀⠘⠀⠛⠘⠛⠀⠀⠛⠛⠛⠛⠛⠀⠙⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⡀
⠀⠀⠀⢀⣴⡿⠟⠛⠿⣷⣄⠀⠀⠀⠀⢀⣶⢞⣩⣭⣝⠻⣷⡀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠙⠻⣷⡄⠀⠀⠀⠀⢠⠎⢁⣤⣤⣄⠙⢦
⠀⠀⠀⣾⡏⠴⠆⠹⠋⣀⢻⡆⠀⠀⠀⣿⢁⣿⠋⠉⠻⣷⠹⡷⠀⠀⠀⠀⢰⡿⠁⢀⣤⣤⡄⠀⠹⣿⡀⠀⠀⠀⡏⢠⣿⠟⡉⠻⣷⠈⣇
⠀⠀⢰⣿⠸⢶⡿⠿⣷⠙⠉⣧⠀⠀⢸⡇⣾⠇⣼⣿⡄⢹⣇⢿⡇⠀⠀⢀⣿⠃⢀⡿⠁⠀⢹⡆⠀⣿⡇⠀⠀⢸⠁⣾⠇⣾⣿⡆⢹⡆⢿
⠀⠀⢸⡏⠦⣿⠁⠀⢹⡚⠧⣿⠀⠀⢸⠧⣿⢸⠇⠈⣧⢸⣿⢸⡇⠀⠀⢸⣿⠀⢸⡇⠶⠏⠈⡇⠀⣿⡇⠀⠀⣸⢀⣿⢰⣿⣿⡇⢸⡇⢸

⠀⠀⠀⠀⠀⠐⣀⣀⣐⠠⡀⠀⠀⠀⠀⠀⢀⣤⣶⣾⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣒⣓⢦⡀
⠀⠀⠀⠀⣠⢞⣡⣤⣌⢳⡀⠀⠀⠀⠀⢰⣿⢟⡵⣛⡛⣮⢿⣧⠀⠀⠀⠀⠀⢰⣿⡾⣫⣭⡻⣿⣷⡀⠀⠀⠀⠀⠀⣼⢣⡾⠋⠙⣿⢷
⠀⠀⠀⢰⢣⡾⢫⢭⡹⣧⢧⠀⠀⠀⠀⣿⣯⣾⡾⠛⣿⣼⡘⣿⡆⠀⠀⠀⢠⣿⡿⣱⣋⡹⣇⣿⣿⡇⠀⠀⠀⠀⢸⣇⡟⠀⠀⠀⢹⢸⠆
⠀⠀⠀⡏⣾⢡⠁⠀⢡⣿⣸⡆⠀⠀⢸⣿⡏⣿⢁⡀⢸⣿⡇⣿⡇⠀⠀⠀⣸⣿⢳⣿⣿⣟⣿⢿⣶⣇⠀⠀⠀⠀⣾⣹⠃⠀⠀⠀⣸⢸⡃
⠀⠀⠘⠃⠛⠀⠀⠀⠈⠛⠃⠃⠀⠀⠘⠛⠃⠛⠈⠁⠘⠛⠃⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠋⠚⠀⠀⠀⠀⠚⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡽⣦⡀⠀⢻⣶⣄⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣜⣿⣿⣿⡄⠈⣿⠹⡆⠀⢀⣴⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢹⣿⢿⣿⣯⣉⣆⠋⠠⣇⣴⡿⠟⠽⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠷⣶⣤⣤⣽⣧⣽⣟⣻⣟⣓⣲⢿⣿⡶⢆⣠⠞⢡⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⠖⠎⠙⢫⣤⣾⠸⠋⢛⣅⣿⣿⣰⣿⣡⣭⣻⡯⢁⣲⠿⡟⠛⠷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣀⠀⡤⢸⢸⣮⡟⣷⣇⣿⣷⣹⡿⣿⣭⣿⣾⣿⢳⡜⡻⣾⣉⣱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠽⡀⠳⢳⣌⠟⠱⣶⣿⣾⣿⣹⣿⣾⣿⣿⣏⣿⣿⣇⠻⠛⣷⢏⢲⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡐⠛⣼⢪⢻⣶⡛⣆⣿⣶⣿⣿⣿⠻⣧⣾⣿⣿⠿⣯⣧⣻⣿⣿⣜⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⡯⠠⢎⠛⣼⠻⡍⣟⣙⣿⣟⣻⣿⣿⣿⣿⣟⣿⣾⣿⣿⣯⢾⣿⣽⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⣶⡐⣷⡜⢣⢾⡙⡗⢻⣿⡻⣿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢆⡈⢡⣷⡄⡮⣉⡸⣿⠚⢻⣿⣾⠻⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡈⣷⡄⠳⢼⡆⠑⢿⣷⣼⢿⣿⣿⣯⡽⣾⣿⣿⣿⣿⣿⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⠆⠁⢿⡷⢠⣸⣶⢻⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠸⣦⣶⣮⠙⡻⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣻⣽⢿⣈⢿⣿⢳⣽⣿⣏⣿⣷⣮⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣽⡶⡟⣡⣄⢻⣿⠿⣿⣿⣽⣿⣟⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡹⣄⢾⡉⣾⡛⣿⣿⣿⣟⡻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣄⠰⢾⣿⣿⣱⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⡟⣯⣿⣝⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠙⢻⡿⢻⣿⠛⠛⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⣠⣄⠀⠀⠻⠿⠂⠴⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠲⠖⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠸⠆⠀⠀⠀⡖⠁⠠⠄⠈⠉⠀⠀⠀⠀⠈⠑⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⣿⣿⡇⠀⠀⣼⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢀⡘⠿⠖⣤⡾⢣⣄⠀⠀⠀⠛⠋⠀⠀⠀⠻⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠺⣿⡆⠿⠿⢷⣄⠈⠁⠚⠛⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠏⢀⣶⣍⣀⣀⠀⠀⠈⠇⠀⠀⠴⠞⠛⠀⣀
⠀⠀⠀⠀⢸⡆⠀⢠⡆⠀⠀⠀⠻⣿⠋⠉⠉⠁⢶⡆⠀⠀⣀⠀⢴⣦⡀⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠶
⣄⠀⠀⠀⠸⣧⠀⠈⠳⣤⣤⣤⣴⣿⣷⣦⡀⢀⣾⣧⣤⠞⠋⠁⠀⠘⠿⠀⠙⠃⠴⠦⣤⡤⠤⠄⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⠋⣿⡿⣿⡟⢁⣤⠛⠃⠀⠁⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣬⡀⠀⠀⢀⣤⡄⠸⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠙⣧⣤⡀⠀⠀⡹⠇⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢹⣷⣤⠀⠀⣀⠀⠀⠀⢀⣉⡙⠿⠷⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠶⠶⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠏⢀⡌⢉⣦⠀⠀⠀⠉⠿⠀⠀⠉⠉⠉⠉⢻⣿⠖⠲⠒⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡄⠘⣧⡈⠙⣶⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠙⢳⡄⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠻⠓⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠒⠛⢿⣧⣤⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢸⡇
⠀⠀⠀⠀⢀⠀⠀⢠⡖⠀⠶⠶⢀⠀⢰⣶⠀⢰⣿⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⡄⠸⡇
⠀⠀⠀⠀⢸⠇⠀⠈⠳⠶⠶⠶⠿⣿⣿⣯⠀⢘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠘⢧⡌⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡿⠉⣿⣿⣿⡄⢸⡟⠀⠀⠀⠀⠀⠀⢀⠛⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣤⠛⠀⠀⠈⠁⣿⣿⠈⢡⡄⠀⠀⠀⠀⢀⠟⠀⢠⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⠁⠀⢸⣇⠀⠀⠀⠀⡿⠀⠀⣿⡇⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠸⠂⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⠛⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⢻⡀⠀⣤⠁⠀⠀⣼⡄⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠛⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⢱⡄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣼⠇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠛⠛⠛⠛⠛⠓⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠹⣶⣤⣴⠖⠒⠛⠛⠛⠓⢠⣤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣶⣶⣶⣶⣶⣾⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣩⣤⣴⣶⣶⣶⣶⣶⣿⣧⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠁⠈⠉⠉⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢺⣿⣿⣿⣿⣿⠇⠀⡶⣦⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠘⠻⠿⠟⠛⠁⠀⢠⡿⠋⠉⠈⠉⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⢻⡟⠋⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠇⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⣿⢷
⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⡤⠖⣿⠛⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⡇⠀⡿⢸⡇
⠀⠀⠀⠀⠀⠘⡇⠀⢠⡏⢠⡞⣁⣤⣤⠤⣄⠈⢷⡀⠀⢀⣠⣤⣿⠀⠀⠀⠀⠀⣰⢇⣼⣷⢿⡇
⠀⠀⠀⠀⢀⣄⢻⡄⠈⢷⣿⡦⢹⠇⢠⣤⡀⠀⠀⠙⠓⠚⠛⣫⡙⢷⣤⣤⣤⣾⠹⣿⠟⢁⣼⠃
⠀⠀⠀⢠⠏⠙⢦⡙⢳⠺⣏⢀⣼⣀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡿⢈⡇⠀⣿⣿⠀⡷⠞⣹⠏
⠀⠀⠀⡿⠀⠀⠀⠳⣿⢀⡿⣄⠀⠉⠉⣤⠶⠒⠒⡀⠀⠀⠘⠛⠓⠛⠇⠀⣿⡟⢸⣧⠞⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠙⣾⡁⠙⣦⡀⠘⠇⠘⠀⢈⣁⡤⠀⠀⠀⠀⠀⠀⣠⣿⠇⡿⠁
⠀⠀⠀⠻⣄⡀⠀⠀⠀⠈⠳⣾⠋⠙⠳⠦⣤⣄⣀⣀⣠⣤⣤⣤⢴⡶⠛⢹⡟⣼⠃
⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠈⢳⣄⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⡾⠁⠀⣸⣴⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⡀⠀⠀⠙⢦⣠⡟⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠈⠻⢦⡀⠀⢀⡟⠀⢀⣤⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠙⢦⣼⠁⣴⠋⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⢀⣠⣤⣀⡹⣆⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠁⠘⣧⠀⠀⠀⣠⠟⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⡏⠀⠀⠠⠴⠦⣤
⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣀⣤⠶⠚⠛⠛⠛⠛⠛⠓⠶⢼⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⣠⢴⡿⠋⠀⠀⣶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠸⠷⡴⠟⢀⣀⣀
⠀⠀⠻⣾⣇⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⡟⠒⠒⠛⠋⣉⣹⠆⠀⢀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣴⣿⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣼⣿⣿⣇⠀⠀⢁⡔⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣖⢰⣶⣶⣴⠀⢠⡘⣿⣿⣿⣦⠀⠏⡀⢀⠴⠿⠟⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠿⠛⠉⠀⠈⠻⢿⣧⠤⠹⠟⠋⣼⣿⣦⣤⡚⠷⣿⠿⠲⢶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣷⣾⣿⣄⠀⠀⠸⣿⣿⠿⣿⣿⣦⠀⢹⣧⠐⠞⠙⠛⠡⣌⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠟⠿⠀⠀⢨⠙⢷⣀⣗⠀⠀⠲⣦⡄⢨⣽⣦⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡗⠙⠋⣀⠀⠀⣴⡟⠃⠀⢿⣶⡦⠀⠀⠀⢠⡄⠿⢿⣷⡄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣧⡀⣾⣻⠗⠀⠘⠁⣠⣄⠈⠻⠀⠀⡿⡤⠈⠳⣠⡈⢧⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⣉⡁⠀⠀⡀⠐⣿⠘⠆⠀⣴⣤⠳⠀⠀⢀⠻⡟⢬⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠉⠰⡿⠇⠀⣿⣿⠀⠘⠇⠀⢠⡗⠜⠀⠀⢀⡀⠛⠀⠾⣏⡇
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣶⡄⠙⠃⠀⠀⠀⣀⡄⠙⠊⠀⠀⢸⣿⠆⠀⢸⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⣿⣿⠀⢪⢿⡄⠸⣦⠹⠀⢀⣤⡄⠙⠃⠀⠀⠘⣿⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠀⠀⠀⠈⠻⠀⠀⠈⢀⠀⢾⡽⠃⢀⣿⡇⢠⣶⡿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⠀⣠⣾⣆⣠⢶⡆⢰⣿⡷⠀⠀⢀⡈⠉⠀⠛⢳⠁
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣁⠀⢹⣿⠛⠙⠞⠁⠈⠛⠃⠀⢀⣿⠏⢠⣶⣄⡟
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢩⣽⣷⡌⠃⠀⢠⠆⢆⠀⣠⢦⡀⠀⢀⡀⠻⢏⡾⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢼⡿⠛⢀⣤⣴⠁⣟⡇⢢⢻⡏⠉⠀⣿⣻⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣏⣿⡛⢦⠅⠀⣀⠒⢀⣴⡆⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⢿⡿⠛⠈⢁⣀⡰⣿⡿⠇⠸⠿⣳⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣠⠀⠀⣾⣿⡇⠈⢰⣶⣷⡾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠻⠟⠇⣠⡜⢿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⢷⡴⣿⣾⢳⣿⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣭⣵⣿⡿⣿⣿⣿⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠟⠒⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⢛⣛⣷⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⡿⠹⠛⠛⠛⠃⠘⠛⠛⠛⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠀⠀⠰⣆⡀⠀⠀⠀⣤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡋⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠙⣢⡀⠀⠀⠀⡀⠀⠔⠋⠈⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢋⡴⠋⣿⣇⠀⠀⣸⣟⠲⠄⠀⠀⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢡⠊⠀⣀⠹⠟⠓⠈⠉⢉⡄⠄⣄⡀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡇⠀⢸⡟⠇⡦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠸⣧⠰⣧⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠞⠋⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⡰⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢡⣦⡀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⡟⠈⠙⢻⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠫⣭⣿⡇⠀⠀⠀⢀⣀⡤⠂⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠒⠛⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠿⠶⢶⠶⢺⣿⠿⠛⠛⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⠀⠘⣇⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⢯⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠛⢆⡀⠀⠀⢾⡋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⣧⠀⠀⠀⠙⠿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠲⠤⡤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢐⠁⠀⢤⠈⣀⠠⠄⠀⠀⠈⠙⠓⠢⠤⠄⠀⢀⡀⢀⠤⠔⣚⡙⠉⠛⠳⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠀⠀⠀⠃⠄⠁⠀⠤⠂⢀⡀⠀⠀⠀⠁⣀⡠⠄⠠⠀⢀⠐⠊⠹⣿⣿⡂⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠂⠌⠀⠈⠀⠈⠈⢁⠤⠀⠄⡀⠂⠀⠤⠀⣛⠿⠀⠠⢙⠛⠉⠀⠀⠀⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠰⠀⠀⡥⠀⡈⠠⠄⠀⠀⠀⠀⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠰⣢⡀⣀⠀⠂⣀⣒⢁⣀⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⡁⠀⠉⠉⠄⡄⠠⠃⠀⠀⠀⠀⢀⡀⠀⡰⡘⠌⣰⠞⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⡠⠀⠆⡂⠀⠀⠀⠀⣡⢀⠈⠁⣠⠄⠀⠀⠀⡁⠂⢀⡀⠀⠀⢬⡜⠒⣀⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣹⣿⣷⣮⢈⣵⣻⣇⠒⣄⣣⣴⡊⣸⣻⣿⣿⣶⣾⣷⣷⣟⣶⣀⠘⢱⡟⠻⣭⣬⣀⣒⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠛⠛⠿⠿⠶⠤⠮⠥⠤⠠⠬⠥⠤⠄⡉⣍⣯⠉⠉⠉⠙⠢⠤⢤⣄⡀⣤⠀⠉⠁⠁
⠀⠀⠀⠀⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠠⠤
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠑⠒⠤⠄⠤⠀⠄⠤⠆⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠃⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢾⣄
⠀⠀⠀⠀⠀⠀⠀⣰⢻⠻⡐⠀⠀⠀⢠⡟⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠰⣟⣲⠿⣋⣩⡝
⠀⠀⠀⠀⠀⠀⠀⠉⣥⣀⣤⡀⣤⣤⣠⠁⠀⣠⡮⣭⡁⠀⠘⡆⠀⢸⣿⣿⣫⣭⣽⡿⣻⡆
⠀⠀⡠⠒⠚⠓⠶⣄⠉⣿⣏⠉⣉⣿⠟⢠⠞⠉⠀⣠⠼⠶⠴⢧⡀⠐⣿⣷⣶⣶⣶⣿⣉⠀⠀⣸⢷⣤⡀
⠀⢸⡁⠀⠀⠀⠀⣽⡆⢻⣿⠿⣿⣿⠀⣮⠁⠀⣴⠃⠀⠀⠀⠀⠨⡀⢻⣞⣽⣟⣩⣿⠇⠀⢸⡼⣊⡿⢽⣄
⠀⠀⠇⠀⠀⠀⠖⢾⡀⢸⣿⡟⣿⡟⠀⠀⡏⣶⠻⡄⠀⠀⠀⠀⢸⡇⠀⣿⣯⣭⣿⡏⠀⢲⡟⣓⢻⡆⣽⣷⡆
⠀⠀⢰⣠⢀⣶⣤⡞⠁⠈⣷⡟⣿⠇⠀⠈⠳⣿⣤⢈⣖⠒⢘⣿⡿⠀⠀⢸⣟⠟⣿⡇⠀⠙⣷⣷⣦⣭⣽⣶⠃
⠀⠀⠘⣭⢻⣽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠋⠀⠀⠀⠘⣯⡿⣿⠀⠀⠀⢻⣿⡿⣷⠺⡟
⠀⠀⠀⢆⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡏⠀⠀⠀⠀⠀⢿⠿⣿⠀⠀⠀⠸⣾⡷⢿⢿⠇
⠀⠀⠀⢸⠷⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣶⢛⠃⠀⠀⠀⠀⠀⢸⣶⡏⠀⠀⠀⠀⢹⣿⢾⡟
⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⢀⠀⣀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠤⠤⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣶⣰⣦⠀⠀⠀⠀⠀⠀⢐⠀⠄⢂⠈⢀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⣠⠐
⠀⠀⢀⣠⣤⣴⣶⡆⠀⠸⠀⠈⠹⠀⠀⣠⠀⠐⣥⣤⣤⡄⣤⡄⠀⡂⠀⣀⠄⠁⠀⠀⠣⠀⠀⠠⠰⠀⠀⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠐⡐⠈
⠀⢸⡿⢟⡿⣱⣼⡇⠀⠠⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠁⠀⠀⠀⠄⠀⠀⣠⣴⠀⡄⣐⡥⠤⠄⣀⣤⠀⠆⠐⢀⣀⠐⠓⠒
⠀⢸⡷⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⣻⠀⠃⠀⠁⠈⡛⠛⠁⠠⠀⠀⢿⢸⠠⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠸⠂⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣹⡴⠛⠁⠀⠀⠀⠀⠙⠃⠄⠈⠀⠀⠈⠈⠉⠀⠀⠁⢰
⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣞⣁⣀⣺⣆⠀⡅⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡿⠋⢀⡄⠀⠀⠀⢄⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠈⠀⢼
⠀⠸⢯⣿⣿⣽⠻⠇⠀⠀⣾⠙⡋⣩⡇⣜⡷⠀⠀⠀⠠⡰⠖⠊⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠺
⠀⠈⠂⠤⠠⠄⠐⠁⠀⢀⠈⠒⠻⠟⠛⠛⠁⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⣄⠐⠑⠄⠀⠐⠐⠁⠀⠀⠐⠀⠀⠀⢐⡹⢄⠀⠀⢘⠀⠀⠀⠀⠀⢰
⠀⠀⢀⡀⠀⠀⠒⠨⠊⠀⠁⠂⠀⠀⠀⠐⠈⠀⠈⠐⠀⠀⠀⠐⠊⠀⠀⠀⠈⠁⠐⠓⠈⠀⠀⠐⠊⠁⠂⠢⠀⠀⡐⢃⡄⠀⠐⠀⠀⡀⠀⠀⠄
⠀⠀⠈⠉⠀⠀⠄⠲⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠄⠀⠀⡀⠀⠀⠈⠄⠂⠀⢞⣘⠀⢈⠒⡆
⠀⠀⠃⠂⠀⠀⡀⣀⡤⠖⠉⠀⠀⠀⢸⡿⠛⠛⡃⠀⠀⠀⠀⠀⠀⣷⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠰⠾⠃⠁⠀⠀⢀⡀⠠⠤⠄⠠⠄⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠃⠀⠀⠀⢸⣧⣀⠘⠓⠒⠰⠆⠂⠲⠂⠙⠀⠈⣹⠃⠀⠀⠀⠀⠀⠀⠀⡰⢂⣀⠀⢰⡀⠀⢀⠀⠀⠀⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣀⣄⣀⣀⣀⣀⣀⣈⣙⣀⣀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠑⣆⡠⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⣜⢁⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠆⠀⢀⡁⠀⠐⠉⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⣾⡶⡎⠁⢸⠀⠀⠨⠀⠒⠀⠀⢒⣀⣠⣴⣶⣖⡒⠂⠒⠆⠠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠀⠀⠀⠀⠤⠤
⠀⠀⠄⢀⠀⠀⢾⡏⠀⠐⠁⠀⠀⢜⠀⣠⠶⠿⠟⢋⡙⢫⣼⠰⢜⡆⠀⡁⠀⠀⠀⠀⢰⠰⣴⠀⡄⢀⠅⢸⡇⣇⡿⠀⣼⡟⠁
⠀⠀⡀⠀⠀⠉⠉⡀⢀⣀⠀⢀⠀⠀⠀⢧⣛⣣⣦⣦⣵⣷⣶⠿⠋⠀⠀⡇⠤⠠⠤⠠⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠄⡈⠀⠉⠀⠀⠀⠀⠀⠀⣼⠂⠐⠀⠈⠉⠛⠛⠋⠉⠁⠰⣯⣩⡿⠀⡆⡠⠀⠀⠐⠀⣀⡀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠐⢠⠤⡄
⠀⢈⣈⣁⣀⣀⣈⣉⣉⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣰⠺⡄⠅⢔⠐⠊⡀⡆⠀⠀⠀⢀⠀⠀⠀⠈⠄⠣⠀⠰⠂⠃
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⣄⠔⢨⡅⠖⡄⠀⡆⠔⠀⠑⡆⢦⠀⠣⡀⠁⠀⠀⠀⠈⠁⡐⢀⠠⠀⠈⠀⠈⠁⠂⠀⣠⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⢨⠀⠀⠀⠉⠀⠀⠁⠁⠀⠁⠁⠂⠐⠉⠉⠀⠀⠈⠢⠄⠀⠀⠔⠊⠀⠀⠀⠁⠒⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡈⠐⠁⡀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢰⣀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⣀⣤⣤⣀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⠿⡿⣷⡄⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠸⣿⣥⣭⣿⢈
⠀⠀⠀⠀⠓⠲⡀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣿⣶⣷⣿⣇⡀⠀⠀⠀⠈⠀⢠⣤⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠
⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠠⠀⡀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠠⠀⠐⠄⠀⠀⠀⠀⠴
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠃⠀⠀⠂⠀⠄⠀⠐⠁⠀⠈⠉⠀⠒⠈⠀⠀⠀⠀⠈⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣉⣉⡐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⣨⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⣦⣤⣀
⠀⠀⠀⠀⣿⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⣦⣄⢠⡿⢦⣀⠀⣸⠇⠀⠀⣿⡀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄
⠀⠀⠀⠀⢿⡀⠀⠈⠉⠛⠳⠶⢤⣴⠞⠋⠁⠀⢀⣀⡀⠉⢻⠁⠀⠉⠛⠛⠶⠶⢦⣼⣧⣼⠟⠀⠀⠀⠀⠀⣠⠔⠃⠀⢀⣴⠾⠛
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢠⣾⡥⣤⣄⡀⠀⠀⠀⠉⠓⢾⡄⠀⠀⠢⣀⠀⠀⠀⠈⠻⣯⡀⠀⠀⠀⣠⠞⠁⠀⣀⡴⠛⢷⣄⡀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⢀⣈⣀⣀⣠⣍⠻⣦⣀⠀⠀⠀⠀⠙⢶⡄⠀⠈⠳⣦⡀⠀⠀⠈⢻⣤⡴⠞⠁⠀⣠⣶⠛⠳⠦⣤⠈⠙⠛⠛⠛⢛⣽⠟⠁
⠈⢿⣟⠲⠶⠶⠒⠛⠛⠋⠉⠉⢁⣀⣤⠶⠖⠛⢛⣷⣦⣤⣄⣀⣀⣽⡆⠀⠀⠈⢷⡄⠀⠀⠀⢻⣄⣤⡤⠞⠛⠛⠛⠿⠶⠶⢶⣶⣶⠶⠞⠋⠁
⠀⠀⠙⠳⠶⣤⣤⣀⣀⣈⣉⣉⣀⣀⣀⣤⡴⠞⠋⠁⠀⠉⠉⠉⠉⠉⢿⣤⣀⣀⣘⣧⣀⣤⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠀⠹⣧
⠀⢀⣾⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠄⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠑⠀⢹⣧
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠁⠀⠀⠀⠀⡄⠀⠀⢿
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠡⢄⡼⠁⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡄⠀⢸
⣾⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠀⠀⠈⠋⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢘
⣿⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠊⠂⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⢸
⣿⡀⠀⠠⡄⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⣼
⢹⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⣁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠁⠀⠀⡠⠀⠀⠀⢀⠁⠈⡄⢠⠀⣰⣿
⠈⣿⡀⢀⠘⠀⠀⠀⣀⠀⠀⡉⡀⠀⠀⠀⢠⠒⣆⠀⠀⠀⠀⠸⣇⣸⠀⠀⠠⠂⠲⠀⠀⠀⠀⢀⠎⢀⠀⠀⠀⠀⠀⠂⠀⠀⣶⣀⠀⠀⠁⠀⢠⣿⠃
⠀⠸⣷⡀⠆⠀⠀⠀⠙⠀⠀⣥⠄⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣠⠞⠁⢀⣾⠏
⠀⠀⠹⣷⡀⠀⠀⠦⠀⠀⢒⡄⠀⠀⢀⠤⠀⠀⠀⠀⠀⠊⣉⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⣀⢁⡀⠀⣼⡏
⠀⠀⠀⠘⢷⡄⠈⠃⠀⠀⠘⢌⠇⠀⠀⠰⡙⢦⠀⠀⠀⠀⢷⣈⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⣴⣠⠃⠀⣴⠋⠀⠀⡐⠁⠀⣼⡟
⠀⠀⠀⠀⠈⢻⣆⠀⠀⠂⣄⠀⠀⠀⠀⠀⠙⠞⠀⠀⢤⣄⠀⠉⠀⠀⠀⠀⠉⡈⢰⠀⠀⠹⠤⠇⠀⣀⣀⠈⠀⠀⠀⢀⣤⠀⠀⢡⠞⣽⠟
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠪⡆⠀⠀⠀⡤⡀⠀⠀⠀⠘⢈⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣤⠄⡠⢏⡀⠀⠀⠉⠁⠀⠅⠘⣀⠀⢢⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠱⡼⠀⠀⢀⣀⠀⠀⠀⠀⠈⢨⠻⠄⠀⠀⡞⠡⡄⠀⢀⣤⠀⠀⠀⢈⡄⠀⠀⠚⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢠⡀⠀⠈⠀⠀⠀⠀⠃⣹⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠎⠰⠀⠀⠀⠦⠆⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠑⡄⠈⠁⡆⠀⠀⠀⠀⠡⠸⡆⠀⠉⠬⠀⠀⢀⠀⠀⠀⠀⠠⠀⠰⠍⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠑⣄⠀⠀⠀⠀⠀⠀⠉⠐⡄⠀⠀⢀⡀⠀⠀⠐⠁⠀⠀⠀⠂⠀⠀⡠⠦⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠀⠀⠒⢄⠀⠠⠄⡀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣀⠀⠀⠀⠀⠰⠁⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⡀⠀⠀⠉⠀⠐⠊⠒⠀⠀⠀⠈⠐⠁⠀⠟⠁⡠⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠐⢄⠀⠀⠀⣀⣀⠰⠀⠀⢀⡤⠄⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠘⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠘⠓⠀⠀⢈⣩⣴⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠒⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⢀⠎⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗
⠀⠀⠀⠀⢆⣁⠤⠔⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠈⢅⠀⠀⠉⠂⠀⠀⠀⠄⠀⣰⠶⠾⢿⣿⣿⣿⡆⠀⡀⠀⢀⡆⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⠙⠿⣿⠇⣰⣿⣿⣿⡇⠀⠀⢸⣦⡄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⣿⣦⡀⠈⢰⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠓⠙⢦⣸⣿⣿⡟⣿⣿⡇⠀⢀⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠹⣿⣿⡇⣿⠟⠁⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠈⢯⡁⠏⠀⠀⣼⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡱⡼⠀⠄⠉⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⣿⣿⣿⣿⣿⣻⢿⣿⡟⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣄⣀⠀⠤⣾⣷⠈⠻⣿⣿⣿⣿⣷⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣷⣶⡤⠤⣤⣤⣉⣛⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣴⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠋⠁⡼⠋⠁⠀⠉⡿⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⣀⣡⣿⣟⣵⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⡘⣿⣿⣠⣾⠉⣫⠾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⠾⣿⣿⣿⣿⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣦⠀⠀⠀⠙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠒⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡏⣩⣽⣏⣽⣯⣉⣩⣿⣏⡉⣩⣍⣉⣽⣍⣿⣘⣋⣯⢨⡟⣥⢭⣻⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣭⣽⣯⣬⣅⣿⣿⣭⣽⣭⣯⣼⣧⣬⣭⣤⣿⣿⣥⣭⣭⣯⣨⣽⣯⣩⣬⣿⣭⣻⣥⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⡿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡐⠻⠖⠛⠾⠒⠓⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣠⠶⠶⠶⣦⡼⠿⠶⠶⣦⣴⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠒⠶⠆⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠋⠁⠀⢀⠀⠀⣰⡄⣰⡏⠉⠙⠛⠛⠋⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣉⣠⡖⠁⠀⢀⣾⣿⣏⣸⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⣤⣾⠛⠉⢿⣿⣿⣿⣹⡟⠀⢀⣠⠏⠁⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠷⢒⣇⢀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⡀⢙⠉⠉⠉⠳⠤⠄⠀⢀⣠⣄⡉⢙⠋⠀⠐⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣠⠔⠋⠁⡤⠀⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⠉⠀⠀⠀⠀⠐⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣦⣤⣤⣤⣶⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠋⠙⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠻⠿⠿⠏⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣤⣀⣀⣤⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢙⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⣀⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠀⡏⡇⠈⠙⣒⠤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡇⠑⠖⠋⠉⡷⠀⠀⠉⣉⡒⠲⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠣⣤⠴⠋⠀⠱⣀⡠⠔⠒⢦⠉⠉⠙⣒⣶⠦⠤⠤⣄⣑⣄
⠀⠀⠀⠀⠀⠀⢧⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠑⠒⠉⠀⠀⠙⠒⠶⠤⠖⠛⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⢾⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠒⣈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠏⢸⠀⠀⢱⢄⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⠀⡟⠀⢸⠀⠀⠈⠚⠝⡲⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣆⣇⣂⡇⠀⠸⠁⠀⠉⠑⠄⠘⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣇⣆⣲⣿⡿⠉⠀⠀⠀⠀⠀⡀⢠⠀⠀⡇⢸⣶⠀⢀⠀⢀⠀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⡶⠒⡟⣷⣿⡟⠀⠀⣀⠤⠀⠀⠀⡠⠋⠀⠜⠀⡿⣒⣾⠒⢀⣰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣿⣷⣶⣿⣿⡇⣠⠞⠁⣀⣠⠔⠊⠁⠐⠋⠐⠚⡇⢻⣿⣶⣸⠘⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠛⣿⣧⣄⣿⡉⠉⠉⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⡰⠁⢀⣿⣿⣿⣺⡛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡧⢄⣿⣟⣀⣀⣠⣤⡴⠖⣋⠠⠀⠀⣠⠞⠁⢠⢿⠹⣾⣾⠻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠍⠟⢿⡁⠀⠀⠀⠉⠀⠀⠀⠀⢀⣠⠞⠁⢀⡴⠃⣸⠀⣹⠻⢿⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣥⣿⣃⠀⠀⠀⠀⢀⣀⠤⠖⠋⣀⣤⠖⠋⢀⡴⠋⢀⣿⣦⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡌⠉⠙⠛⠛⠻⠶⠶⠒⠚⠋⠉⣀⡤⠖⠋⠀⢀⡞⠀⡏⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢽⣇⠀⣀⠀⠀⢀⣀⣀⡤⠖⠋⠉⡁⠀⠀⢀⡠⠋⢀⡼⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣿⠻⢭⣝⣲⠶⠖⠒⠚⠈⣀⣠⣄⣒⡯⠶⠚⠁⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡄⠀⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣓⠶⠤⠤⠤⠤⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠁⡀⠒⠂⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠂⣀⠐⢀⡀⠐⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠀⣀⠐⢂⣀⠐⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⢁⣀⠒⢂⣀⠉⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣁⠤⠒⢂⠤⡉⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣁⣉⣉⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⠿⢿⠿⢿⣿⠿⠿⡿⠿⠿⢿

⠀⠀⠀⠀⠠⠠⠀⠐⢄⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠑
⠀⠀⠰⠀⠀⠀⠀⠈⠀⠆⠂⠀⡂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢀⢀⢀⡀⠀⡔⠓⣀⠰⠃⠀⠀⠈⠀⢀⡈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈
⠀⠀⠀⠀⢀⠄⠀⠂⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢱⠠⢍⠉⡠⡀⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⡉⠀⠀⠑⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠐⠒⠑⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠤⠠⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠓⠒⠶⠼⠧⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠡⡀⠀⠀⠀⠠⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⡆⠀⠀⠀⠘⠄⠁⠁
⠀⠀⠀⠨⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⡌⢐⠨⡟
⠀⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠑⢤⡀⠀⠀⣠⠄⠀⢀⡀⡎⠀⠀⠈⠙⠓⠒⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢧⠀⠀⠳⣄⠔⠀⠀⠀⣾⠀⠁⠀⢀⡞⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠘⢦⡄⠀⣻⠀⠀⠀⠠⣿⠀⠀⢠⡞⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⣦⣿⠀⠀⡀⠀⠙⢆⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠉⠛⠳⢿⣿⡀⠀⠸⡄⠀⠀⠡⣸⡤⣂⡴⠒⠁⠀⠀⠀⠀⠀⠀⢀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⡄⠀⢷⡆⠀⠀⠹⡛⠋⢀⠀⠀⠀⢀⡤⠖⠊⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⣇⡄⠀⠀⣷⠀⠀⠠⣀⣰⠏⣰⠇⠀⠀⡖⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠹⡀⡻⠒⠲⠦⠿⠦⠔⠒⠉⠁⡞⠁⢸⢀⡌⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⢠⡤⠀⠸⢀⡀⣼⣊⠀⣠⠾⠁⠀⠀⠤
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠴⠤⠀⠁⠀⣠⣴⣿⣭⣥⡴⠚⣁⣀⡤⠀⠀⢀
⠀⠀⠀⠀⢀⡏⠀⠀⠂⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣄⡀⠀⣧⠀⠀⠀⠀⠉⠛⠈⢀⣀⠖⠁⡴
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠉⠙⠛⠿⣿⣃⠀⠀⠀⠀⠉⢁⣠⡞⠁
⠀⠀⠀⢰⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠂⠀⠀⠈⠑⠾⣗⢆⡀⠀⠁
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠣⣙⠒
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⠲⠶⠶⠶⠦⠔⠒
⠀⠀⣿⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀
⠀⣿⠃⠀⠀⠀⠀⠄⠁⠀⠀⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠓
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⡏⠀⠈⠀⠀⠀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡰⠋
⣿⡇⠀⠀⠀⠀⠅⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⡴⠞⠉
⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⢿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠛⠉
⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠔⠒⠋⠉
⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣀⣀⣤⠄⠤⠐⠒⠈⠉
⣶⣶⣶⢾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⣟⣿⣿⣿⣿⣿⣿⣧⣾⣿⣟⠛⢏⣤⢀⣒⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣽⡇⢀⡀⢀⡀⠀⠩⠅⠀⠀⡀⢀
⠠⣿⣿⣿⣿⣿⣿⣿⣮⣟⣻⢿⡷⣄⠈⣯⡍⢸⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠯⣵⢄⠀⠀⠀⢀⡀
⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⣿⢁⠈⣉⣼⢿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⡀⠀⠐⢿⡆⠈⣤⠀⠀⢼
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣈⠀⠘⡄⠸⠟⠛⠓⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣐⡄⠀⠀⠀⣠⣿⣿⡄
⠀⠀⠿⣿⣿⣿⣿⣿⣿⢻⣯⠀⠘⠟⠀⠀⠀⠀⠀⣠⣄⡀⠀⢻⣷⣿⣿⣿⣿⣿⢣⠇⢹⡌⡧⠄⢀⠘⢋⡈⠁
⠀⠀⣶⣮⢿⣿⣿⣯⣿⡝⠋⠀⠀⣶⡄⣿⡄⠀⡸⢟⣩⣿⠆⢸⣿⣿⣿⣿⣿⣿⡸⣄⠀⢀⠁⠀⣿⢠⡎
⠀⠀⡈⣡⡀⠁⠀⠙⠛⠁⠈⠑⠀⠉⢠⣄⠀⣀⣀⡀⢉⣀⣴⣦⣤⣙⠻⣿⣿⣿⡟⡄⠀⠈⢀⠀⣅⠀⡦
⠀⠸⢿⠟⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣠⣿⡟⢁⡾⣿⣿⣿⣿⣿⣦⠈⢻⣿⣿⢿⣾⡇⣸⠀⠟⢀⣁⣤
⠀⠀⢰⣦⠸⠗⠀⠀⠀⠀⠀⣈⣛⡀⠀⡀⢹⡏⠀⢾⣿⣿⣿⣷⣍⠿⠿⠀⣾⣿⣿⣿⢿⡇⢀⣤⣤⡀⠀⠙
⠀⠀⠀⠉⠀⢿⡷⠀⠀⠀⠰⠠⠙⠋⠀⠛⣿⣿⣦⠀⠹⢿⣿⠛⢃⡀⠀⣸⣿⣿⣿⣿⣾⡇⠈⠿⡿⠁⠀⠐⠠
⠀⠀⠀⠀⠰⣶⡄⠀⠀⣤⠁⠀⠆⠠⠀⢸⣿⣿⣿⣷⣦⡄⢹⡄⠈⢧⡀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢶⣿⡿⠇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣇⢸⣿⡄⠈⣿⣝⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣠
⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣬⢵⣬⣿⣿⣓⣿⣿⣿⣿⣼⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡶⣠⣄
⠀⢸⣿⠄⠀⠀⢀⢠⣴⣼⣾⣾⡿⣽⣎⠀⣱⠎⠀⠛⠛⠿⠟⠛⢹⣿⠛⠙⠋⠁⢀⠄⠀⠀⠀⠀⠀⠀⠈⠙⡿
⠲⢤⢻⣴⢀⣀⣿⣿⣿⣿⣿⣿⣠⣿⣏⣿⣃⠀⠀⠀⠀⠀⠀⡔⣨⡿⣤⠀⠀⠀⠀⠄⢀⡀⢀⣠⠆⠀⢄⠔⠁
⣿⣶⡈⣿⠻⡿⠿⠈⠷⠟⠋⠉⠀⢨⡥⠀⡽⠀⠀⠀⠀⠀⠀⠃⠉⠁⠙⠀⠀⠀⠀⠀⠀⣰⢸⣿⠤⠓⠀⣠⠇
⢠⢿⣇⠀⠀⢸⠶⠀⠀⠀⠀⠀⠂⠀⠀⠀⠋⠀⠒⠒⢀⡄⣀⣠⢠⣀⢀⢀⣄⡀⠀⠄⢞⣡⣿⣿⣶⠴⠟⢻
⠬⠿⢷⠶⠶⠿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⡾⢻⣿⡏⠀⠀⠀⠀⡼⠁⠈⢻⡿⠄⠀⠌⡆
⠀⠸⠓⠀⢂⡞⠀⠀⠀⠀⠀⢀⣤⣤⢄⠀⠀⠀⢀⠀⠀⠀⠸⡿⣿⣿⡟⣿⠀⠀⠀⢰⠀⠰⣄⣾⣿⣦⡀⠀⠁
⣐⢀⡀⡐⢂⣇⡀⠀⠀⣀⡴⠾⣱⣟⡶⣧⡀⠀⡿⠒⠀⢰⣥⣧⣾⣿⡿⠃⠀⠀⠀⠀⢠⣦⣾⠋⠙⢻⣷
⠷⢂⣀⣻⣿⣿⣿⣿⣖⣩⣤⣾⡿⣮⣴⡿⠗⠺⠧⠄⠚⠁⣿⢙⣯⣿⡇⠀⠀⠀⠀⠈⣿⡟⠁⠀⢃⣼⣿
⠠⡾⣿⡾⢻⣿⣽⣿⠋⠀⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢻⠏⠋⠀⠀⠀⠀⠀⢸⣏⠀⢀⠀⢠⣿⠏⡀
⠄⢠⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⢀⣿⡿⠀⠀⣰⠟⠉⠛⢿
⣠⣿⣿⣿⡿⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢁⣤⠞⠁⠀⠘⠁⠈
⣿⣿⣿⡿⠃⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⡿⠁⠀⠀⠀⠀⠀⠐⣦
⣿⣿⣿⣷⣤⡀⣉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠌
⠟⢻⣿⡟⢙⢣⡏⡀⠀⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠂⠀⠸⢧⠇
⢰⠟⢻⡏⣤⠸⠯⣇⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠛⠂
⡾⠀⠀⡄⠘⠉⠀⢤⣛⣦⣄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢀⠰⠂
⠀⠀⠈⠀⢀⣤⣀⠘⠉⠿⠋⠷⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢺⣄⡈⣤⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⡀⣠⠂⠀⠸⣟⠉⠀⠀⠀⠀⠀⠈⢻⡟⠻⣿⠀⠀⠀⠀⠀⠀⢘⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠀⠀⣸⣧
⣱⡯⠖⠀⠀⠈⠀⠀⣀⣶⠃⠀⠀⠘⠷⣤⣠⡄⡃⠈⠄⠀⠀⠀⠀⣦⣤⠀⡠⡄⣀⣀⠀⠀⠠⠉⠒⠄⠈⢧⠝
⠋⠀⠀⣤⡴⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠙⣧⣿⣶⠁⠘⠃⠀⡛⠛⠂⠀⠐⢻⠟⠃⠀⠀⢠⣴⣼⣦⣒⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⣀⣠⣾⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠠⣿⡟⣠⣾⡿⢟⣋⣥⣶⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣽⣿⣶⣴⣿⡿⠿⠿⠿⣿⣿⣿⣛⠋⠽⢿⣻⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢀⣴⡾⠟⣻⣿⣿⣿⠿⠋⢉⡤⠶⢶⣿⣷⣶⣦⣭⡛⢷⣄⠉⠴⢚⣛⣿⣿⣿⣷⣦⡀
⠀⠀⢀⣼⠟⠁⢰⣿⣿⣿⠟⠁⠀⠀⠀⠐⣋⣭⣿⣿⣿⣿⣿⣿⣷⣝⣧⡀⠩⠖⣚⣿⣿⣿⣿⣿⣦
⠀⣠⣿⠋⠀⠠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠠⢖⣻⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠬⣿⣿⣿⣿⣵⣸⣿⣧⡀
⢠⣿⠃⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣦⠨⣿⣿⣿⣿⣽⢣⣿⣿⣧
⣾⡏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⠿⣿⠾⢿⣿⣿⣿⣿⣿⣷⣾⣿⡆
⣿⡇⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢀⣴⣟⣋⡁⠀⠀⠀⠀⠀⠐⠲⣄⠉⢸⣿⠀⣸⢻⠃⢉⣿⣿⣿⣿⣿⣧⣀
⣿⡇⠀⠀⠢⢄⣀⠀⠀⠀⠀⣀⣴⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⢀⣀⣿⣷⣜⣿⣦⣯⣿⣀⣼⣿⣿⡟⠉⠛⠛⠋⠛⢶⣄
⢸⣧⠀⠑⢦⣑⠪⢭⣛⣢⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢟⣿⣿⢿⡻⣿⣿⣿⣿⣿⣿⣿⡛⠿⣷⣟⠞⡿⣿⣿⣿⣷⣄
⠀⢿⡆⠀⠓⢬⣛⢶⡾⠋⠀⠀⠀⠀⣤⣴⣷⣿⠾⠟⠛⠛⠛⠛⣛⣻⣿⣽⣿⣿⣿⣿⣿⡿⢿⣿⣶⣮⣽⣿⣿⣾⣿⣿⣿⣿⣿⣆
⠀⠈⢿⣄⠀⢑⡚⣿⠃⠀⠀⢠⣼⣿⣿⡿⢋⠥⠀⠀⠀⣀⣴⢞⣿⠿⠛⡽⢟⣽⢟⣿⣿⣿⣷⣄⠘⠙⢛⡿⢟⣽⢿⡿⣿⣿⣿⣿⣧
⠀⠀⠀⠻⣧⡀⢹⣿⠀⠀⣰⣿⣿⣿⠏⣔⡾⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢚⡫⠿⣿⣿⣷⣄⠀⠐⠩⠞⣫⢞⣻⢿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⢿⣗⠀⣀⣿⣿⣿⠇⢼⡳⠅⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⡽⠿⣿⣿⣦⠀⠀⢩⠴⣛⡵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⣿⣿⡿⢠⡳⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣭⣾⣿⣿⣇⠀⠐⣚⣭⠾⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⡇⢘⢯⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠴⢿⣿⣿⣿⠀⠀⠡⠴⣟⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠸⣷⢽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣚⣽⣿⣿⣿⠀⠀⢒⣛⣭⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⢯⡳⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣽⣾⣿⣿⡏⠀⠨⠭⢷⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠙⠾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢶⣿⣿⣿⡟⠀⢀⣒⣻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣿⣽⣿⣿⠏⠀⠤⠴⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⣀⠀⠀⣀⣀⣀⣐⣲⣶⣶⣶⣶⣾⣿⣿⢟⣁⣐⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣿⣭⣭⣿⣿⡿⠿⠿⠿⠶⠞⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠀⠀⣠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⣰⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⣿⣿⣿⠃⠀⠀⢰⣿⠇⠀⠀⣀⣴⣶⣿⣿⣷⣶⣄⠀⣿⣿⣧⣀⣀⣠⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⢠⣿⣿⡿⠀⠀⠀⣿⣿⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⠁
⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⢸⣿⣿⠇⠀⠀⢰⣿⣿⣾⣿⣿⠟⠋⠉⠀⠉⢻⣿⣿⣿⠀⠈⠙⠛⠛⠛⠉⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⡿⠟⠹⣿⣿⣷⣤⣤⣤⣴⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠌⠀⠪⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢉⠀⠳⣄⡀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢢⡀⠀⠈⢳⣦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢀⢤⠀⠤⢀⣀⡁⢐⢿⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠁⠛⠁⠉⠙⢒⠉⣠⠞⠉⠀⠑⣄⣀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡞⠀⡇⠀⠀⠀⠀⡟⢻⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⠴⢃⣀⣠⠴⠚⠀⣘⡇⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡖⠒⠴⠒⠒⠂⠀⣀⡤⠖⠋⠉⠉⠀⣀⣤⣴⣿⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠲⢤⣤⣤⣴⣿⣅⣀⣀⣤⣶⠶⡿⠛⠝⣃⢈⣨⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢤⣀⡀⢀⠀⠀⠈⠀⠈⠈⠎⠁⡡⠀⣀⣢⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⡌⡏⢹⡗⢺⠓⡟⠛⡟⢻⠿⣿⠛⡏⢹⣡⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠑⢹⡈⣇⠨⡇⢳⠠⡇⢸⠀⡇⢰⡇⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣾⡇⣿⠀⣧⣸⢰⣇⣸⣀⣧⣼⣹⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡇⣿⣿⣝⡟⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠤⣤⣶⠟⠋⠉⠓⢾⣿⣟⡵⠚⠉⠙⢿⣦⡤⠴⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⣼⡃⢰⣏⠳⡄⠀⠛⠀⢠⡻⠗⢨⡇⢺⡀⠿⣳⠀⠈⠋⠀⢰⠚⣹⡆⢸⣇⠀⣤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⡛⠛⠷⠬⠥⠚⠁⠙⠲⠓⠊⠀⠀⠀⠀⠀⠉⠛⠉⠀⣀⡉⠋⠁⠀⠀⠀⠀⠈⠓⠓⠒⠋⠈⠳⠬⠥⠟⠛⣛⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢠⣾⠋⠀⠰⢛⣿⡇⢀⣿⡟⠀⣽⡟⣠⠞⣿⡷⠘⣷⣆⠀⢴⣤⠀⣀⣀⣀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⠇⡘⠀⢀⡾⠁⣿⡏⠀⢀⣿⠇⠀⠀⠀⣼⡿⢀⣾⡟⢀⡾⣫⣞⣁⣼⡿⠁⠀⣿⣧⠴⠛⠁⣿⣏⢠⣾⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⣾⡇⢀⣾⠷⢶⣿⢁⡀⣼⣿⣤⣤⣠⠶⣿⣥⢾⣿⡤⠏⣼⣟⠀⢸⣿⣥⠄⣴⣿⠁⠀⣴⡦⠙⢿⣧⠀⣜⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢼⡿⠀⠘⠛⠋⠙⠉⠀⠀⠉⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠛⠦⠴⠛⠁⣤⣍
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⡦⠀⣠⣶⣿⡿⠟⣛⡁⢠⣶⠀⠀⢉⡏⢉⡷⠀⢹⡏⠉⠋⠀⢠⣤⠀⣒⠻⢿⣿⣶⣤⡀⢰⣶⣿⡷⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠻⠿⣫⣶⣿⠏⠀⠀⠀⠀⠀⢸⡇⠉⢹⡆⢸⠋⠉⠀⠀⠀⠉⠀⠉⢻⣷⣬⡻⣿⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⢿⠟⠁⠀⠀⠀⠀⠀⠀⠘⠓⠒⠋⠀⠛⠓⠚⠋⠁⠀⠀⠀⠀⠀⠹⣿⡷⠀⠀⠀⠀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣤⠀⠰⣶⡶⠶⢦⣤⠀⠀⣴⣆⠀⠀⠀⢰⡆⣠⣤⣤⣤⣤⣤⣤⡰⣶⣶⡄⠀⠀⠀⠶⣶⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⡿⢻⡄⠀⠀⣼⠇⠟⠀⠀⣿⠀⠀⠉⠁⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠛⢛⣿⠶⠀⣿⠟⠛⠓⠀⠀⢸⡇⠀⢻⡄⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣼⣿⠀⠀⣿⠀⠀⠀⢀⡀⢸⡇⠀⠀⢻⣆⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡿⢀⣿⣀⣀⣤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡉⠀⠉⠀⠙⠛⠛⠛⠛⠛⠁⠸⠇⠀⠀⠀⠙⠿⠀⠀⠀⠀⢿⠀⠀⠀⠚⠿⠷⠞⠛⠛⠁⠉⠉⣉⠥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠬⢓⣦⣄⣀⠀⠀⠀⠀⠀⠀⢠⡖⢻⣿⠀⢨⣿⡆⠀⣿⠇⢚⣿⠏⢹⣷⠀⠀⠀⢀⣠⣤⠶⠯⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣒⣤⣤⣤⠭⠁⢠⣶⡄⠀⣴⣏⣠⣿⠇⢠⡟⢿⡇⣸⠏⢀⣾⠏⠀⣼⡏⠰⣟⡦⠀⠲⠶⠶⠶⣒⣀⣉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣀⣠⣤⡴⠖⠂⠀⠉⠀⣾⡏⠀⢿⣿⠴⣿⡅⠸⣷⡏⢠⣼⣏⣠⠾⠋⠀⠀⠀⠀⠀⠙⠲⠶⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⡡⠔⠊⠁⠀⠀⢀⣀⡀⢀⣤⣄⠀⢀⣤⠀⠀⠀⠀⣰⡆⣠⣤⣶⣦⣄⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⣿⠀⠀⣿⠋⠃⠀⢹⡏⠀⢸⡟⢷⡀⠀⣼⠛⣧⠈⢰⡇⠀⢹⡧⠀⠈⣿⠛⠀⠀⠀⠈⢻⡟⠳⠶⢤
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣠⣿⠀⢰⡏⠀⠀⠀⢸⡇⠀⣿⠀⠈⣷⣼⠃⠀⣿⠀⢸⡇⣤⣾⣇⠀⠀⡟⠀⠀⠀⠀⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⠉⠉⠉⣿⠀⣼⠁⠀⠀⠀⢸⠇⠀⣿⠀⠀⠸⠟⠀⠀⣿⠀⢸⡇⠀⠀⢹⡇⠐⣇⠀⠀⠀⢀⡀⢸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⡿⠀⠸⣇⣀⣀⣠⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣀⣠⡾⠃⣠⣿⣀⣀⣠⡾⢣⣼⣧⣤⠴⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣈⣙⣉⡉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠈⠉⠉⠁⠀⠀⢈⣉⣉⣉⠁⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⣯⡽⠰⠌⠛⠛⣛⣿⡽⠰⠆⣴⡶⢦⣴⠶⣶⡶⣶⣶⣶⢠⡆⣰⠆⠰⠆⢯⣿⣛⠛⠛⠡⠆⢿⣽⣛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢶⣤⠀⠀⠀⠀⣠⡾⠋⢩⣿⠁⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣉⣡⣴⠿⣿⠀⠀⢠⣾⠏⠀⠀⢸⣿⣤⣶⠿⠟⢋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠉⠀⠀⢿⡆⢠⡿⠁⠀⢀⣴⠿⠛⠉⠀⠀⢀⣾⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢸⣷⡿⠁⠀⣰⡿⠃⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡙⢷⣌⣿⣇⣠⣾⣋⣀⣀⣤⣴⡾⠟⠉⠀⠀⠀⢈⣿⡏⠀⠀⠙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠟⠛⠛⠛⠛⠛⢿⣾⡿⠛⠛⠻⢿⣿⣯⡀⠀⠀⠀⠀⣀⣤⣾⠟⠀⢠⠶⢦⡄⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠈⠻⣿⣦⣶⣶⡿⠟⠋⠁⠀⠀⢾⡀⢸⡇⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣤⣤⣤⣤⣶⡾⠋⢠⣿⠻⣧⡀⠀⠀⠀⠀⠘⣿⣏⠁⢠⠞⠲⣦⠀⠀⠀⠙⠋⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠉⠁⠀⠀⣰⡿⠃⠀⣽⣷⣄⠀⠀⠀⠀⠹⣿⡄⠸⣄⣀⣽⠃⠀⠀⠀⢀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢸⣿⡟⢷⣦⡀⠀⠀⣿⡇⠀⠈⠉⠁⠀⠀⠀⠀⣿⠉⣧⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣀⣴⡾⣿⠇⠀⠀⠀⠀⠀⣿⡇⠀⠙⠻⣶⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠟⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣶⣾⠿⠛⠉⠀⣿⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⡟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⣾⠻⣦⠀⠀⠀⠀⠀⢸⡏⠹⣆⠀⠀⢀⡀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⠋⣼⠛⢳⡄⠀⢻⣤⣿⠀⠀⠀⠀⠀⠸⣧⡼⠃⠀⢀⡟⠙⣦⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣴⠞⢶⡄⠀⣿⣀⣴⡿⠋⠁⠀⠻⠷⠾⠃⠀⠀⠀⠀⠀⣾⠛⢳⡄⠀⠀⠀⠀⠀⠸⣇⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣯⠀⢨⡇⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣄⠀⠀⠀⠀⢀⣤⣄⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⣴⠛⢷⡀⠀⠀⠀⠀⣰⠞⠛⣦⠀⠀⢠⠟⢳⡄⠀⠀⠠⣧⠀⣿⠀⠀⠀⠀⢸⡇⢹⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠹⣦⣸⡇⠀⠀⠀⠀⠙⠶⠶⠟⠀⠀⠙⠶⠾⠃⠀⠀⠀⠙⠛⠃⢠⣤⠀⠀⠈⠙⠛⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡇⠀⣀⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⡟⢻⡄⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣦⣤⣀⠀⠀⠀⠛⠶⠶⠟⠀⢀⡴⢦⡄⠀⠀⠀⠀⠀⠈⠻⠾⠃⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣷⣶⣤⣤⣄⣀⡀⢸⣇⣀⡿⠀⠀⠀⠀⣀⡀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣶⣶⣶⣶⣿⣭⣽⣦⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⠀⠀⠀⢸⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠛⠚⠛⠋⠉⠓⠦⣼⠀⣰⣿⣶⠶⠶⠾⣛⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠛⠷⢦⣄⡀⠈⠉⠙⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠞⣿⣿⡿⠟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠶⠶⢤⣌⡛⢦⠀⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠈⠙⠻⣧⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀
⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⢀⡿⠁⢀⣴⣶⠶⠶⠶⠶⣤⣄⣀⠀⠀⢀⣠⠀⢀⣶⣦⡀⠈⢿⡀⠀⠀⢰⠶⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢸⡇⢀⡾⠋⠀⠀⠀⠀⠀⠀⣽⡟⠀⣴⠟⠹⣧⡾⠉⠙⢷⡄⢸⡇⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⢠⣿⡟⠀⠀⠀⣴⢛⠿⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⣼⠏⠀⠀⠻⠁⠀⠀⠈⢻⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⢠⣿⡟⠀⠀⠀⠀⠙⠉⠀⠻⡇⠀⠀⠀⠀⣀⡀⠀⠀⣿⠀⣿⠀⠀⢀⣤⡀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣱⠀⠀⠹⣆⣿⠀⠀⠸⣇⡅⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⠀⠀⠀⠀⣿
⢸⣿⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠃⠀⠀⠈⠀⠀⠀⠀⢿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⣿
⣿⡏⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠸⣿⡄⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠹⣿⣆⠀⠀⠀⠀⠀⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⠄⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠘⢧⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢛⠇⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⣿⠳⡄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣶⣶⣶⣾⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣓⠒⠦⠤⣄⠀⠀⠀⡠⢋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠤⢤⠤⠤⠤⠤⠤⠤⠭⠽⠦⠈⢧⣠⠞⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⡘⠒⠒⠋⠉⣀⣀⣛⣂⠀⠀⠈⠁⠺⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠙⠓⠚⠋⠉⠉⠉⣠⠋⣁⣀⠀⣀⠀⠀⢀⠈⠙⡲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⣾⠟⠀⠀⠀⢠⠞⡵⠋⠁⢀⠔⣿⠀⡆⠈⣧⠀⠙⠦⣄⣈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣤⠴⠚⠁⠀⠹⣄⠘⠀⣸⠓⠤⣄⣀⣀⣤⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣞⡟⠀⠀⠀⣠⣦⠀⠀⠀⠀⠉⣠⣤⠀⠀⠀⠀⠈⠳⡴⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⢠⣾⠇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠀⠀⢀⢴⠄⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠾⠋⠀⠀⢀⣤⠀⠀⣰⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢰⡷⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⡴⡿⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣤⡄⠀⠀⣠⣶⠀⠀⠀⠉⠀⠀⠀⠀⠋⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⠊⠀⠀⠀⠟⠁⠀⠀⠀⢠⡾⠃⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣠⣶⠀⠀⣾⠏⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡙⠁⠀⠀⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠏⠀⠀⢀⣠⣤⠶⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠀⠀⠀⠀⣠⠞⠋⣰⠏⣠⡴⠞⠋⠁⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⠀⠀⢀⡞⠁⠀⢰⣿⠞⠉⠀⠀⠀⢀⣠⡶⠟⠳⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡇⣿⠀⠀⡞⠀⠀⣠⠞⣡⠔⠂⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⣹⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠷⣾⣿⡸⣆⡼⠁⠀⡼⠃⡴⠃⣠⣾⠿⠶⠛⠛⠛⠛⠛⠛⠒⠒⢒⣻⠟⣦⡀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⣧⠹⣇⠀⣸⠁⣼⠁⢀⣤⠶⠒⠒⠀⠀⠀⣀⣀⣤⣤⡶⠟⠉⠀⠈⠃⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠛⠋⠹⣧⠙⢧⡁⣼⣧⡾⠋⢁⣠⣤⠶⠾⠛⠛⠋⣉⠉⠀⠀⣠⡀⠀⠀⠀⣀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⣴⠟⠉⢀⡤⠶⠖⠛⠛⡛⢷⣼⡿⣸⠋⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠘⠟⠀⠀⠀⢿⡇⠀⠸⣷
⠀⠀⠀⢀⡾⠁⠀⠘⢁⣀⣤⣴⡶⠛⣵⠟⠁⡄⠀⠀⠀⠀⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡆
⠀⠀⠀⡼⢁⣠⡶⢿⡟⠁⣴⠏⢀⠞⠁⠀⣼⡇⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⡇
⠀⠀⣼⣵⠟⠉⢀⡿⠀⣼⠏⠀⡏⠀⢠⠞⢸⣇⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠀⠀⢴⣄⠀⠀⠹⠇⠀⣿⡇
⢀⡾⠛⠁⠀⠀⣼⠃⢰⡿⠀⠀⠀⣰⠏⠀⠀⢻⣦⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⣿⡇
⠉⠀⠀⠀⠀⢠⡟⠀⠸⣇⠀⠀⣼⠏⠀⠀⣤⡀⠈⠻⣦⡀⠸⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⢰⡟⠀⠀⠀⠙⠷⠀⠀⠈⠻⣦⣧⠀⠀⠘⠿⠃⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⣿⣆⠀⠘⣿⡀
⠀⠀⠀⠀⠀⢸⡇⢀⡀⠈⣧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠘⠋⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢸⣿⠘⣷⠀⢹⡟⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢿⣧⠈⠀⠈⡇⠀⠠⣤⡀⠀⠀⠈⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⢀⡀⠸⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠸⣿⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⢀⣀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠁⢸
⡉⠏⠁⠉⠁⠁⠁⠁⠁⠉⠛⠿⢷⣀⢈⠛⠛⠈⡢⢘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⢸
⡐⠠⠀⠠⠀⠤⠤⠤⠖⠀⠀⠠⠈⠛⠿⢷⣶⣶⣬⣤⡂⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢀⣾
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⣙⠛⠿⠿⢿⣶⣤⣤⣀⠀⠀⠉⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠻⢷⡄⠀⠀⠻⣷⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⡎⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⡔⠁⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠱⡄
⢧⠀⠀⠀⣄⡇⣀⠀⠀⠀⣘⠀⠀⠀⠀⠈⣣⡤⠒⡐⠒⠢⣄⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠈⠳⠤⠴⢯⡀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠵⢀⣀⠁⠀⠀⠈⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡷⠦⣄⡀⠀⠀⠀⠀⠀⣀⡠⢴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⢳⠒⠛⠙⠿⡤⠞⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡜⠀⠀⠀⠀⠒⠚⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⡀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢇⠀⠉⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⣡⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣄⡉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢰⡁⢰⡋⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠉⢒⠄⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣈⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⢈⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⡰⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⣁⠴
⠀⠀⠀⠀⠀⠀⠸⣈⠒⠃⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⠀⢁⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⢰⠋⠉⠉⠒⢤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣅⡴⠚⠋⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠸⡀
⠀⠀⠀⠸⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡄
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⡀
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣈⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠙⠓⠲⢬⣉⠒⠦⣄⣀⠀⠀⠀⢀⣠⠜⢠⠃
⡠⠒⠒⠒⠂⠉⢉⣀⣀⡤⠤⠖⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⣞⣁⡠⠤⠤⠤⠤⡀⠉⠒⠦⣄⣈⣁⣉⣁⣠⠴⠃
⠱⢦⣠⣀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠉⠛⠧⣤⣄⣀⣤⣤⣤⠤⠤⠤⣄⠀⢀⢀⣸

⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠸⠄⠤⠀⠠⠄⠼⠀⠀⠘⠈⠠⢄⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⡇⠀⠀⠀⠠⠐⡈⠄⡐⠣⡀⠀⣔⠂⠉⠉⠉⠉⠉⠉⠁⠐⡄⠧⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⣀⣤⣤⣴⠀⠀⠀⠀⠀⢻⣄⡀⢘⠀⠠⢌⣁⣀⣄⢈⣡⡀⠀⠆⠀⠀⡤⠉⠀⠀⠸⣁⠀⠐⡄⢨⠉⠁⠐⠒⠒⠒⠂⠉⠉⠁⡇⠀⠀⠄⠤⢠⠘
⠀⢰⡾⣿⢿⠏⣯⣽⠀⠀⢠⢀⠈⠀⠀⠉⠙⠀⠁⠈⠉⠉⠉⠈⠉⠀⡀⡇⠀⠛⠀⠀⠀⢄⠀⠀⠀⢀⡄⠀⠀⡠⣊⣀⣀⠁⣢⠀⢰⠀⠇⠀⠀⠴⠮⠅
⠀⢸⣧⣏⡾⠾⠛⠛⠀⠀⠈⠈⢉⣉⣁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠠⠀⠀⠀⠀⣠⣾⡟⣧⠀⠀⡏⠇⠰⠮⠿⠟⠀⡄⠀⣰⡏⣇⣐⣒⡂
⠀⠘⢋⡁⠀⠠⠀⠀⠀⠀⢎⡁⠀⠀⠀⠀⠀⢈⡃⠀⡏⠉⡍⠨⡅⠨⠀⠀⠀⠀⠀⠀⠀⢰⠾⡿⣤⠟⠋⠀⡃⠃⠀⢿⣿⣀⠀⢁⠁⠀⡇⠿⠏⠁⠠⠄
⠀⠀⠀⠍⠁⠀⠄⠀⠀⠀⠀⠀⣤⠬⡉⣩⡅⠀⠁⢠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣻⠟⠁⠀⠀⠀⢠⠈⠨⠀⠀⠥⠌⡘⠀⠀⡇⢀⠀⠐⠤
⠀⢰⡦⣤⣤⣤⣤⣴⠀⠀⢀⣴⣷⣷⣿⡿⣻⣦⠁⢸⠀⠄⠀⣀⣠⢰⣆⠀⠀⡄⠀⠀⠀⠘⠁⠠⠚⠆⠀⠀⠀⠑⠠⠀⠀⠠⠐⠁⠀⠀⡇⠄⠀⠀⠀⠀⡁
⠀⠘⡛⠛⠚⠓⠒⡹⠀⠀⠘⢿⣸⣖⣾⣷⣯⡟⠃⠘⠀⠀⠱⠋⠁⠀⢸⠀⠀⡇⠀⣀⠀⠀⠀⠃⣠⠀⡀⠀⢀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠈⠉⠉⠁⢀⣀⡀⠠⡀⠉⠉⠉⠉⠁⢀⠆⠀⡄⡃⠀⠀⠀⠀⡸⠀⠀⠷⠁⣀⠑⣀⢀⠩⠐⠈⠀⢀⢠⡀⠀⠀⢸⠖⡓⠄⠀⢰⠅⠀⠀⠀⠀⠀⢽
⠀⠀⢠⣄⡀⠄⠚⠁⡚⠀⠀⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠄⠂⠉⠀⠀⠀⠘⠀⠀⢤⡭⢞⠀⢈⡉⣀⠤⣀⠀⠀⠊
⠀⠀⡄⠀⢀⠤⠔⡊⢓⢠⢤⡄⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠣⠀⠁⠐⠀⢀⣠⡄⡂⠀⠀⠒⠉⠀⠸⠥⣇⠀⣨⢹⠆
⠀⠀⠏⠐⠐⠄⠄⠠⣴⠶⠃⡀⠀⠀⠀⢸⣿⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⣿⡇⠀⠀⠀⠄⠉⠀⠀⠸⠛⠓⠁⠇⠀⠀⠀⠀⠠⠠⠄⠀⠈⠄⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠈⡇⠀⠀⠀⢸⣿⣄⠈⠛⠒⠒⠖⠂⠐⠒⠂⠙⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡖⢣⢠⠄⠸⡤⠀⣀⣀⡀⠀⢀⣀⣀⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⣏⠈⢀⣤⣀⡀⣄⣀⣀⣀⣈⣹⣀⣀⣈⠃⠀⠀⠀⡇⠀⠀⠀⠀⣐⣇⡠⠀⠀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣠⡛⢀⠄⡄⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢤⣈⠀⣀⢁⡠⠖⠉⠀⠀⠈⠲⣀⠀⠀⠃⠀⠃⡠⠊
⠀⠀⠀⠀⠀⠀⢰⣿⣥⡟⠁⡇⠀⠀⢰⠀⠒⠀⠀⠒⠀⣀⣀⣀⣐⡒⠂⠀⠐⡄⢀⢀⣀⣀⣀⣀⣀⣀⣉⣁⣀⢀⣀⢀⢀⠀⠀⡀⢁⣀⣁⢀⣁⢀⣀⣀⢤
⠀⠀⣀⠀⠀⠀⢨⣿⢏⡠⠔⠃⠀⠀⡸⠀⢀⣬⣴⡾⡿⠛⠿⣫⡏⢥⢱⡄⠀⡇⠀⠀⠀⠀⠀⡄⣄⣔⢰⠠⢠⠀⢰⡆⣆⢲⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⠀⠀⠨⠀⣾⢰⢷⢠⣠⣛⣰⣭⣽⡶⠞⠁⠀⡇⣀⢀⣀⡀⢀⠃⠈⠃⠘⠀⠛⠀⠘⠃⠉⠋⢠⣿⡏⠀⠀⠈⠀⠀⠀⣀⣀
⠀⣐⠩⠅⠱⠎⠀⠉⠀⠉⠉⠉⣰⠀⡨⠀⠘⠳⠿⠿⠿⠿⠛⠋⣽⣶⢖⣦⠀⡇⠀⠀⣀⠠⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⡀
⠀⠠⠼⠤⠤⠤⠤⠤⠼⠥⠬⠼⠏⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠛⠛⠃⠂⠃⡈⢥⣤⡃⠾⢚⡭⣤⢦⢱⡀⠀⠀⠀⠀⢤⠀⠀⠀⡏⣹⠑⠄⣹⣸⡆
⠀⢰⠒⠒⠒⡒⠒⠒⣒⠒⠒⠒⢶⠀⠀⢀⢀⠤⠤⣀⡀⠀⢀⡀⢀⠤⢄⡀⡀⠈⡇⠚⠭⠹⢩⠭⠢⠭⠘⢸⠁⠀⢀⠠⠔⡠⠤⢀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠀⢿⢩⡘⠃⠬⣸⠀⢸⣨⣅⠀⢀⠇⠽⠀⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⡖⠊⠄⣀⠀⠀⠀⠨⠀⡐⠛⠁⠈⠈⠛⢂
⠀⠀⠀⠀⠀⠒⡆⣲⠖⠀⠀⠀⢸⠀⠀⣤⣀⡀⠁⡀⠀⠀⠀⠀⠈⠉⠁⠀⣤⡄⠀⢀⡈⠡⠭⠭⠍⢁⠀⠀⠁⠀⠀⠉⠀⠀⡀⠀⠀⡇⠈⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠤⠀⠁⠤⠐⠀⠀⠸⠀⠀⠃⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂⠀⢸⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠃⣠⢶⠶⣶⣄⢰
⠀⠀⠀⠀⡀⠀⠠⡀⠠⢀⠀⠀⠀⠀⠀⠇⠀⢀⣾⣿⠻⢛⡿⢻⢻⣿⡆⠀⠀⠄⠀⢸⠀⠒⡄⡈⠁⠸⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⡆⠻⢷⣶⡶⠿⢸
⠀⢠⠀⠀⠉⠉⢦⣈⠴⠊⠀⠀⢰⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⡅⠀⢸⠀⠀⣴⣶⠂⢰⠀⠀⠀⠠⠀⠸⠀⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀⠸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠰⡇⠀⢸⠀⠠⠄⢤⠀⢸⠀⠀⣀⠐⠀⠐⠀⢀⠠⠘⠀⢣⠀⠀⠀⠀⠀⡜
⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠃⠀⠈⠐⠂⠠⠀⠒⠈⠀⠀⠈⠉⠀⠛⠈⠁⠀⠀⠀⠀⠉⠀⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠨⢃⠐⠓⢹⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⠁⡄⠀⠀⠀⢘⡀⠀⠄⠈⣂
⠀⠀⠀⠚⠤⠲⣼⠁⠀⠀⠀⠀⠀⣇⠀⣀⣂⣠⠤⠒⠒⢦⡄⠀⠁⠁⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠂⢰⡆⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠤⠠⠞⠐⠃⡀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡴⠀⠀⢂⠀⢀⡄⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠆⠤⡦⠄⠀⠀⠠⡂⠀⠀⠀⡀⢀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠐⡟
⠀⠀⠐⢤⡀⠠⠀⢀⣀⣤⠀⢐⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠲⠄⠀⠀⡌⡻⢻⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⠄⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠤⣶⠗⠚⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⣐⣚⣀⠀⠀⠊⠩⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠂⠈⠈⠀⠁⠀⠀⠄⢀⣍⣉⣥⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢁⠂⠉⠉⡀⠀⠀⠤⠥⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠶⡁⡀
⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢸⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠬⡛
⠀⡂⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠈⢤⡀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤
⠀⡀⢀⠒⠀⡄⠀⠀⠀⠀⠀⠶⢠⠀⠀⠘⣽⡀⠠⠀⠄⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠢⠀⠀⠀⠀⠸
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠉⠉⠪⢣⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⢳⣇⠀⠀⢀⡤⡾⠜⠉⢪⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠲⠄⣰⠾⠋⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡄⠀⠀⠀⠀⠵⡰⡼⠁⠀⠀⠀⠀⢠⢪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⢦⠀⠀⠀⢧⣿⠇⠀⠀⠀⠀⣠⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣣⡀⠀⣽⡫⠀⠀⠀⡴⡊⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢺⣿⠁⢀⣴⡫⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡿⣤⡹⠊⠀⠀⠀⢀⣀⣤⡴⢶⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢼⠀⠀⢀⣀⡤⠋⢯⡀⠳⡀⠣⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡵⠷⠏⣿⢟⠈⠢⡀⠑⣄⠘⢆⠱⡀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣦⡀⠀⢀⣔⡤⠃⢠⡞⠣⡀⠑⢄⠘⣆⠈⢦⣈⠀⣷⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠃⢈⠟⢧⣽⡉⣀⣀⣠⡉⢢⠘⢆⠀⠓⢨⢦⣤⣿⣿⡿⠛⢩⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠆⢀⠎⢀⡎⠀⡟⠉⡟⢩⠃⠀⠳⠤⢯⣽⣻⣿⣿⣛⣁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⡜⠀⡜⠀⡸⠀⣸⠀⢸⠁⡏⠀⠀⣾⣷⡾⢿⣯⣤⣿⣿⣯⣿⣿⡿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⡤⣭⠹⠚⣧⠴⡅⣠⡇⠀⡇⠀⡎⢸⠁⠀⠈⣭⣼⣷⣿⣿⣿⣿⣿⣿⡿⠻⢭⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣴⣿⣦⣟⢻⡧⢴⡀⣫⣅⠷⣊⣳⡜⣽⡾⠀⠀⢸⣿⣿⣿⡟⢻⣿⣿⣿⣿⡷⣄⣸⣹⣿⣿⣿⣿⣷
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣼⣿⣄⣹⣾⡁⣻⣮⣹⣇⠀⠀⢀⣿⣾⣾⡅⠈⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⡿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣾⣮⠀⠀⢹⣿⣿⣿⣿⠛⢿⣉⣙⣁⣈⠈⠁
⠀⣸⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⡟⠻⡿⢿⠿⠏⠀⠀⠀⠈⠛⠉⠀⠀⠀⢻⠏⣩⠿⠚⢉⣁⣀⣀⡀
⠀⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⠁⢸⣷⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣾⣿⣿⣿⣿⠃
⠀⢟⣋⣻⣟⣹⡿⠾⣿⣿⣿⣿⣿⡏⠀⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠁
⠀⢀⣤⣄⣀⣉⡙⠓⢿⡉⣿⣿⡟⠀⠀⠀⠉⠉
⠀⠀⠻⣿⣿⣿⣿⣷⣄⠈⠻⠋
⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠆⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠒⠤⢄⣸⠀⠱⡄⡐⠄⢀⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣉⠒⢌⠑⡄⠘⡁⡴⢠⣾⣮⣏⣁⣀⣀⠠⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠊⠁⣀⡠⠭⣻⠷⠓⠃⠿⡧⠀⠃⠀⠁⢠⣤⣤⡤⠶⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠀⡭⠁⢤⣔⣋⣀⣠⣴⠂⡜⠀⠸⢘⡌⠻⠫⣒⠌⠙⢦⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠰⠇⠀⠀⡠⠀⠀⠇⠀⠰⠂⠠⠄⠀⠀⡜⠈⢆⠀⠹⡌⠒⠤⢬⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠃⠄⠀⠀⠃⠀⠀⡴⠊⠀⠀⠈⠀⠐⠈⢰⠍⠀⠙⡲⠬⠖⠂⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⠀⠀⢠⠀⠀⠀⠂⠀⢀⡀⠀⢰⠅⠀⠈⠀⡀⠀⠇⠀⠀⠌⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⠀⠘⠀⠀⠤⠀⢰⠇⠀⠀⠘⠀⠀⠀⡜⠀⠀⠀⡴⠀⠀⢠⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡘⠝⡠⠀⢘⠀⠀⠀⠀⡀⠀⠀⡄⠁⠀⠁⢀⡒⠀⠁⣀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢀⠀⣧⠀⠈⠀⢠⠉⠀⠇⠀⠀⠀⠀⠌⠂⠘⠀⢀⡄⠁⠀⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢷⠀⠀⢐⠂⠘⠀⠀⠀⢀⡌⢡⠈⠀⢀⡂⠀⠋⠀⢀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠸⠀⠀⠀⢠⠁⠘⠀⠀⡀⠄⢸⠁⠀⢠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⠀⠀⠀⡀⠀⠈⠀⣀⠀⠸⠃⠀⠀⢠⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠄⠻⠀⢀⠄⠁⠀⠄⠀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡑⠀⠀⠘⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠊⠑⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠋⣁⡠⠶⠖⠳⣄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠒⠊⠉⠀⠀⠀⠀⠀⠣⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠄⠉⠀⠀⠈⠳⡖⠒⢦⣄⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⣠⠞⠋⠙⠳⣄⣧⣴⠤⢤⣀⠀⠀⠀⡇⠀⠀⣨⣅⡀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⠀⠀⣸⢁⣀⣤⠤⠤⠤⣄⠀⠀⠀⠈⠉⠛⠳⣇⡴⠛⠁⠀⠙⢦⣤⣬⣇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠠⣿⣤⡀⣠⠟⠋⠁⠀⠀⠀⠀⠈⠳⣤⣤⠴⠶⣏⢉⡽⠛⠋⠉⠉⠛⠳⢦⡀⠸⡇
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⣷⠒⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠇
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⡾⢧⣄⣀⣀⣀⣀⣀⣈⣹⣆⣀⣏⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘
⠀⣠⠞⠉⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣦⣤⣴⠚⢉⠉⢻⡄
⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠇⠀⠀⠀⢰
⣠⠟⠀⠀⠀⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⣾⡁⢠⡄⠀⠀⢀⣤⠀⠀⠀⢠⣄⠀⠀⠀⢀⣤⠀⠀⢠⣿⠀⠀⠀⠀⣼
⣏⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠈⢷⢾⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣆⠀⠀⠀⢹
⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⡇⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⠀⠀⢸⡷⠈⢳⡄⠀⠘
⠀⠈⢹⡶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⢺⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⣠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠄⠀⠀⢠⡆⢹⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠳⣄⣠⠾⠁⠀⠹⣶⠶⠶⠓⢦⣀⣤⣄⠀⠀⣠⣤⡶⠋⣧⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡜⢸⠀⢠
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠢⡀⢀⡠⠌⠃⢾⠀⣾⠋⣼⠁⠀⣿⠘⣧⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡇⢸⣤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⢢⡀⠀⠒⠉⠃⠄⠀⢠⡟⢠⡇⣼⠃⠀⠀⢸⡆⢻⡀⠈⣷⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣼⠃⢸⠁⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⢂⣀⡀⠠⠈⠉⣹⠃⢸⣷⠏⠀⠀⠀⠈⣷⠘⣧⠀⢻⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⢀⡟⢠⡏⢸⡟
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠉⠢⠀⠀⣰⠏⢀⣼⡏⠀⠀⠀⠀⠀⠸⣇⠸⣇⠈⢣⠀⠀⠸⡆⠀⠀⢸⠇⠀⠀⠀⡈⠁⠀⡘⢀⡾⢠⡿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠐⢤⡀⠀⠶⠈⠉⠙⠓⢛⡿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣦⠈⢣⠀⠀⠙⡀⠀⠀⠀⠀⠀⠰⠁⠀⡜⢁⡾⢡⡿⠁
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠑⠠⡀⡀⠄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡘⢷⡄⠑⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠊⣠⠏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠘⠢⠀⠈⠉⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢁⣴⠏
⠀⠀⠀⠀⠀⠀⢸⡆⠐⢀⠘⠓⠂⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣈⠉⠓⠒⠶⠖⠚⠛⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠑⠶⠆⠈⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠦⠤⠀⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠢⢤⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢠⠀⠀⢀⡀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⣴⠋⠀⠀⠈⢧⠀⠀⠀⠀⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠣⠀⠀⠀⢀⣀⣤⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣳⣦⣤⣶⣤⣤⣶⣶⣶⣚⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠂⢀⡤⠒⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠉⡶⠋⠀⠈⢳⡀⠀⠀⠀⢀⡤⠒⠉⠀⠀⣠⠞⣁⠤⠖⠛⠻⠍⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠤⢵⠀⢠⠄⠀⢣⠀⢀⡴⠉⠀⢀⠄⢀⡴⠟⠋⠐⠶⠒⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢧⠏⠀⠀⠈⢦⠎⢠⠀⢠⣋⠴⣉⣀⡀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀⣄⣧⠀⡼⠀⡌⠀⡇⠀⡼⠃⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣅⠀⠀⠈⠱⡆⠀⠁⠀⢣⠜⠓⠒⢺⡆⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠱⣄⠀⠀⠘⠄⠁⠀⠀⠀⠀⠀⢸⡐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒⠒⠊⠑⠢⡄⠀⠔⡉⠤⢐⣒⣶⡶⣥⣤⣀⡚⠶⣇⡄⠀⠐⠊⠁⢳⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠈⢳⡤⠖⠂⠂⠈⠁⠈⠐⠚⢦⣀⣀⣠⣀⠈⠻⠛⠳⢌⠱⢄⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠘⠀⢀⡔⢊⠀⠀⣀⣤⠀⢠⠀⠢⣀⣤⣽⡯⢻⠁⠀⢸⠄⠀⠀⠑⡌⠂⠀⠀⢸⠸
⠀⠀⠀⠀⠀⠀⢰⠁⠂⠀⠀⠀⠀⠉⠉⠙⠋⠁⣏⠀⣸⣄⠀⣧⠀⠡⡀⠸⠀⠀⡸⠁⠀⠀⠀⠀⢀⡠⠀⡜⠘⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠃⠈⠁⠃⠚⠀⠰⠀⡠⠖⠁⠀⢀⠤⢒⡒⢉⡀⠀⠀⠀⠴⠂⠀⠹⡦⠤⢀⣀
⠀⠀⠀⠀⠀⠀⣇⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⠀⠀⠚⢠⠋⠀⠀⠀⠀⡨⠉⡡⠋⠁⢀⡅⠀⣤⡀⠀⠀⣦⡙⠲⣏⠁
⠀⠀⠀⠀⠀⠀⠸⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡁⠀⠀⠃⡜⠀⠀⠀⢠⠊⠀⠬⠤⠴⠲⠃⡇⡞⠀⠙⠶⠦⣘⡏⠋⣉⢠⠄⡈⢆
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠘⢁⠞⠀⠀⠀⠀⡏⠀⠀⠀⠀⠤⠀⠀⠙⠀⠀⠀⠀⢀⠈⠁⠀⠉⠀⡈⠃⠈⢇
⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠛⠀⠀⢆⡴⠋⠀⠀⠀⠀⢸⠀⠀⠠⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠂⠋⠀⠲⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⡄⢠⠀⠀⠀⠀⠉⠀⠉⠀⠘⢁⡴⠋⠀⠀⠀⠀⠀⠀⠘⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠃⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀⡄⠀⠒⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠰⠆⠀⣀⠻⠙⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠁⠀⠀⠀⠀⠠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⡀⡀⠉⠐⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠘⠃⠘⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⢠⠀⠘⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠁⠀⠀⠀⢀⡀⠀⡰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠐⠈


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠄⣀⣤⣥⣟⠒⠛⠖⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⣊⣤⣶⣿⣿⣟⡻⠛⢿⣷⡆⠀⠐⣦⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠄⢀⣴⡾⠛⠋⣀⠈⠀⠁⠀⠀⠀⢹⣷⣗⡄⣸⡄⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣣⣴⣿⣿⡉⠀⠐⠀⠀⢈⠐⢶⠁⠀⢸⣿⣿⣵⠏⣧⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠉⠀⠻⡄⠀⠈⠂⠐⠁⠀⠀⠒⠀⢸⣿⢿⡁⠀⠘⣄⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣿⣷⣬⣤⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⣾⡿⠗⠉⠋⠉⠉⠁⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠘⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠖⠉⠉⣿⢻⣦⡀⠀⠀⢰⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠞⠋⠁⠂⢄⠀⢿⣆⠉⠻⠷⣾⡿⠇⠀⢻⣦⠀⠀⠄⠀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠬⠻⠧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⣸⣿⣷⣶⣦⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⠃⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠂⠀⠀⠀⠀⠀⣼⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢳⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⣿⣧⡀⢀⣠⣴⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠒⠦⢄⣀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢻⡟⠀⠉⢀⡜⢰⡿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠠⠤⠤⠤⣍⡁
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢧⣤⡴⠋⠄⠀⠡⣄⠀⠀⢠⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠋⢴⣤⠐⠆⢶⡀⠁⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠙⣆
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣢⣵⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢫⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⣀⠄⠀⠀⠈⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠈⢧⠀⠀⠀⠀⢐⠇⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠄⠀⠈⠛⠿⢦⣄⣀⣀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠘⢆⠑⢄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠢⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⢀⡄⠙⠦⡀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠄⠀⠀⠀⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡐⠐⠂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣤⣠⣀⣄⣀⡀⡄⣤⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡐⠀⠀⠈⠁
⢀⠄⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈
⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠀⠀⠀⠀⠈⠱⠶⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠳⣄⠀⢀⠠⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠰⠃⠉⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⢀⡀⠤⠈⠁⠰⠀⠀⠀⠀⠀⡀⠙⠓⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠏⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠂⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⡠⢀⣠⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣮⣵⣦⣴⣧⣼⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⣠⠤⠒⠂⢼⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠑⠦⠤⣤⡯⠤⠖⠁⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣤⣤⣀⣀⣤⣤⡴⠶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠤⠤⣀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⡀⠀⢠⠀⠀⠁⠀⢀⠀⠀⠉⠲⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀⠤⠀⠀⠉⠀⠘⠀⠀⠈⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠬⠤⠤⠤⣤⣄⣠⣤⣤⣀⣠⣤⣤⣤⣀⣀⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠳⢶⣤⣭⣿⣍⣀⣀⣀⣠⣴⢦⣤⣤⡶⠂⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣀⡀⠉⠉⠉⠉⠉⠉⠁⣉⣠⣴⠖⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⣿⡀⠀⠉⠉⠛⠓⠚⠛⠛⠛⠉⠁⢀⣠⠄⠀⠀⠀⠈⠻⠷⣦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⠶⠞⠋⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣠⠤⠒⠛⠋⠉⠉⠉⠉⠛⠛⠻⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⣁⣀⣀⣀⠠⢤⣤⣄⣀⣀⡀⠀⠀⠀⣸⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣀⣈⣙⠛⠛⠛⠉⠻⢶⣄⡈⠉⠉⠁⠀⠀⢠⣿⣿
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢶⣶⣤⣈⠉⠛⠿⣷⣦⣄⠀⠀⠉⠻⠷⠄⠀⠀⢀⣾⣿⠇
⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⣴⠟⠁⠘⠳⢦⣄⡉⠛⠿⢷⣦⣄⡉⠛⠿⣶⣄⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠀⠈⡙⠷⣤⣀⠈⠙⠻⢷⣦⠈⠙⠋⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣀⣀⠀⠀⠀⠀⠀⣀⡴⢿⣇⠀⠀⠀⠀⠀⠀⣀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠙⠛⠳⢦⣄⣼⡏⠀⠀⢻⣆⠀⠀⢀⣴⡾⠟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠹⣷⡀⠀⠀⠀⠀⡈⠻⡆⠀⠀⠀⣿⢀⡴⢛⣡⣤⠶⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠘⠿⣄⡀⠀⠀⠈⠒⢼⣆⢀⠀⣟⣥⣾⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢰⣁⣽⠀⠀⠈⠛⣶⣶⣶⠶⠦⢿⣿⣿⣟⡉⢉⡉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⠀⠀⠈⠉⠁⠀⢀⣴⣾⠟⠉⠀⠒⠉⣹⣿⠻⢏⠓⢤⡀⠀⠀⠀⠉⠻⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⣎⣨⠇⠀⠀⠀⠶⣾⣿⣉⣀⠀⣀⣀⣤⣾⠟⢿⣆⠀⠉⢄⠙⣶⣶⣶⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠉⠁⠀⠀⠀⣠⢄⠀⠉⠛⠻⠿⠿⠛⠋⠁⠀⠘⢿⣦⣄⠀⠀⠘⣧⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢸⣁⡼⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣀⣀⠙⠻⠿⣶⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠛⡆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⣏⢀⡗⠀⠀⠀⢰⡇⣸⠆⠀⠀⠀⠀⣴⠢⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠿⠾⠃⠀⠀⠀⠀⡴⠚⡆⠀⠀⠀⠙⠋⠁⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⣿⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠀⠀⠀⣷⣴⠃⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⢠⠔⢢⠀⠀⠙⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣠⠇⠀⠀⠀⠀⣿⣤⡞⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⠾⠃⠀⠀⠀⠀⣀⣄⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣼⠃⠀⠀⢀⣠⣀⠀⠀⢀⡔⠒⡆⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢠⠋⢹⡀⠀⠀⠀⠀⠈⠋⠁⠀⠀⢰⣏⣀⡼⠀⠀⠻⠷⢋⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡎⠳⠞⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠉⠉⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⢰⠃⣼⠀⠀⠠⣞⣁⡟⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣘⡛⠁⠀⠀⣀⣉⣭⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠛⠋⠉



⣤⣦⣦⣦⣦⣴⣦⣴⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤
⣿⣿⣶⣾⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⣦⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⣿⣿⠻⣟⣿⣿⣿⣿⣿⢀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣟⣿⣿⡀⣟⣿⣟⠈⣿⣷⠫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣾⢻⣿⣿⣿⣾⣿⣿⣾⣿⣿⣽⣿⣦⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⠟⣛⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣯⣵⡿⣛⡿⠉⢹⠇
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠭⠉⢹⣿⣿⣾⠀⠀⠁
⠀⠀⠀⠀⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣜⣋⢈⠉⠉⠉⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⠿⠿⠛⠛⠿⡿⠿⠿⠷⡶⠾⠟⣛⣛⡳⠿⠿⠿⠿⣯⡽⢭⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢷⣷⢿⣿⣿⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⣓⡶⢶⣦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠿⠛⠿⠼⢦⣽⢿⡖⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣬⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁