Moneybag Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⡤⠖⠲⣄⣀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡇⠉⠀⠀⠘⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠆⡄⠀⡗⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢩⠃⠸⠂⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠛⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⡿⠿⣿⣿⣧⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢸⣿⣿⡀⣿⣿⡇⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⣀⡀⠈⠉⠀⠀⠀⠀⠀⠈⠄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠄⠊⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠻⣿⣿⡇⠀⠀⠀⠀⢀⠤⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⣿⣿⡇⠀⣰⣿⣿⡇⠀⠀⠀⠁⠄⠒⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠑⠀⠀⠀⠀⠈⢿⣿⣿⣦⣿⣿⣷⣾⣿⣿⠟⠀⠀⠀⠀⠀⢀⠡⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠦⠀⡄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠐⢈⠠⠔⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⡄⠈⢁⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠤⠤⠤⠤⠶⠶⠒⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⠟⠁⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⢲⣄⢀⠀⠀⣄⠀⠀⠀⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠙⢿⣷⡀⢺⡆⢀⣤⡀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⢸⣿⣿⣮⣷⣿⣷⣏⡀⠸⣆⡀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⡴⣶⣿⣿⣿⣿⢿⠟⠋⠙⠿⣶⣾⣿⣷⣶⣶⣦⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⢁⣾⢋⡿⢹⠁⡏⠘⠁⡀⠀⠀⡆⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣾⣷⣾⢣⠏⠀⣠⠀⠈⠀⡆⢀⣡⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⢀⣠⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠌⠀⢀⣿⣄⣀⣰⣠⡿⠿⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⣀⣠⣔⣯⣽⣯⣴⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠄⠀⠀⠈⡛⠛⠛⠁⠀⠀⣗⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠃⠄⠀⠀⠀⣰⣧⡀⠠⣠⠀⢰⣿⣤⣤⣤⣤⣴⡶⠋
⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⡟⢿⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⣠⣾⣿⣿⣿⣶⡶⢟⢫⢁⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⡼⡿⠃⠈⡏⠛⠉⢹⡇⢸⠀⠀⣿⠛⠉⠀⠀⠀⠀⣤⣶⣿⡿⠀⠀⠀⠀⠰⣿⣿⢹⡇⢤⡁⠀⠀⢀⣿⠆⢀⣀⣀⣀⣰⣸
⠀⠀⠀⣇⠀⡤⢠⠀⣄⣸⣸⣿⢸⡄⠀⢸⣾⣷⣶⠦⠼⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣾⣇⠈⣿⣶⣤⣾⡿⠿⠿⣿⣿⣿⡿⠿⡀
⠀⠀⢠⣿⣤⣶⣿⣾⣿⣿⣿⣿⡈⣇⠀⠀⢿⣯⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⠀⠀⠸⣿⣿⠿⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡇⠀⠀⢿⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣿⠀⣿⡆⢻⣿⡆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡀⠀⠘⡇⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣿⣀⣿⣧⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡇⠀⠀⠀⠀⠘⢹⣿⣷⣤⣀⠀⠀⠀⠀⠀⠙⠻⣿⡿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃
⠀⠀⠀⠈⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠃⠀⠀⠀⠀⠲⣼⣿⣿⣿⣿⣽⡖⡀⠀⠀⠀⠀⠛⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣾⣷⣶⣶⣤⣤⣤⡄⣀⢀⣀⣀⡀⠀⢀⣠⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣍⣉⣍⣩⣭⣥⣤⣤⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⡉⠉⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⡄⠀⠀⠀⠀⡆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣽⣀⣴⣀⣀⣧⣿⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡹⠿⠿⢿⡿⢿⠟⢏⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⡼⠁⠀⠀⠈⠃⠀⠁⠈⠳⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢴⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠞⠀⠀⠀⠀⠀⠀⠀⢑⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢦⣠⠀⠀⠀⢀⣀⣸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠑⠡⠀⢠⡟⠉⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⡴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠐⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠸⠆⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠚⠏⠘⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢰⡏⠰⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⡃⠀⠀⠀⠀⠛⠶⣤⣀⣤⠀⠀⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠠⢊⠖⡴⡠⢢⠄⡄⠀⠀⠀⠞⡜⠡⠃⠀⢀⣴⢤⣤⣻⣤⣤⣶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣤⣄⣀⣈⣈⣁⣠⣤⣤⣤⣤⣄⣀⣀⣠⡴⠞⠋⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⡀
⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠈⠑⠚⣩⠟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠁⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⡤⠴⢖⠶⠦⣄⡀
⠀⠀⠒⠂⠀⠀⠈⢳⣀⣈⣀⡜⠁⠀⢀⡠⠖⠉⠀⠈⠁⠉⠉⠁⠈⠓⢄⡀⠀⠀⠙⣄⣀⣀⣀⡞⠀⠀⠠⠖
⠀⠀⠀⠀⠀⢀⡤⠚⠻⠛⠟⠣⣄⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢀⡼⠛⠿⠛⠛⠳⡀
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⠖⠉⠉⠒⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⡰⠁⠀⠀⠀⡖⠉⠂⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢣⠀⡔⠉⠂⠀⠀⠀⠈⢣
⠀⠀⡇⠀⠀⠀⠀⠉⠒⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡼⠀⠉⠒⢢⠀⠀⠀⠀⢸
⠀⠀⢣⠀⠀⠀⠀⠐⠶⠋⠀⠘⣆⠂⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠐⠶⠊⠀⠀⠀⢠⠏
⠀⠀⠢⢳⢄⣀⣀⠀⠀⠀⣀⣀⣨⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣇⣀⠀⠀⠀⠀⢀⣠⠔⣁⣀
⠀⠀⠀⠀⠐⠉⠜⠉⠜⡡⠋⠵⢋⠔⠡⢏⡝⡹⠋⡹⠋⡹⢋⡝⣩⠟⡽⠁⠋⠐⠱⠋⠉⠟⠝⠁⠊⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠉⠙⠻⢷⣦⣤⣤⣶⠾⠟⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⣴⡿⠁⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡍⠉⠁⠀⠀⣿⡆⠀⠀⠀⠀⣴⡿⠋⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣼⣷⣤⣤⣤⣼⣯⣤⣤⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⣤⡄⣤⡀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢀⣾⣿⠟⣿⡏⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣿⡇⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⡟⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⡇⣿⠇⣸⣿⡿⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⠀⠀⠀⠀⠀⠈⣿⡏⣿⡏⠀⠀⠀⠀⠀⢀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢤⣄⣤⠶⡻⠲⢤⢤⣤⡶⣛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡚⠾⣯⡮⣳⡗⣐⣱⡱⣡⡟⣊⣿⡓⡒⡲⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢭⣿⠋⠕⣻⠾⠾⢽⡇⠀⠉⢉⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢦⣿⡆⢰⣸⣀⠀⣿⣶⡔⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡬⠗⣲⠿⣧⣼⡿⠿⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣻⢿⡿⢳⢞⣹⣥⣇⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣾⡷⡷⡿⠻⢯⢿⡇⠋⠛⡶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠊⡸⠋⠀⠀⠀⠀⠈⠂⠙⢦⠀⠀⠰⢡⠋⠗⢢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡁⡄⠀⠈⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢃⠔⢉⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⢠⠂⠁⠀⠀⣀⢤⠄⡦⡼⡻⡪⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢣⠊⡠⢛⢦⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠸⠜⠀⠀⠀⠀⣼⠕⢕⣱⣞⡺⡫⣪⣜⢝⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠔⡡⢊⡵⣄
⠀⠀⠀⠀⡠⠊⠀⡀⡄⠁⠀⠀⠀⠀⢸⢕⣵⡟⠁⢸⡯⡾⡟⠲⢵⣿⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⡥⢊⠔⡹⢆
⠀⠀⢠⠎⠀⡄⠆⠁⠀⠀⠀⠀⠀⠀⠸⣷⢝⣷⣄⣸⡪⣪⡇⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠔⣁⠞⡵⢡⢧
⠀⣰⠃⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⣝⠯⡪⣺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡡⠊⡰⡱⢋⣇
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⡾⣻⢋⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢊⠜⡡⣣⣻
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢸⡫⣪⡏⠻⣕⢕⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡴⢋⢜⢔⡕⣽
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⡽⠻⣄⠀⢸⣾⣾⠇⠀⢹⣟⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠖⡵⣫⣮⢞⢾
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡪⣺⡷⡿⣻⡿⡦⡶⣿⢿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡵⣫⢞⡵⡵⣣⢿
⢸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢾⡯⡫⣪⣮⣬⠿⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡡⢚⡵⡣⢊⠜⣡⡏
⠀⢣⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣩⠔⡡⢚⠔⡡⢊⡴⠁
⠀⠀⢣⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡔⡠⠘⢁⠞⡡⢊⠔⣡⢊⠔⣹⠗⠒⠒⠒⠒⠀⣀
⠀⠀⠀⠱⣄⠃⠇⡄⡄⠄⠀⢀⠀⠀⡀⡠⢠⢎⡴⣣⠔⡡⢊⡤⢊⡤⢃⠌⡠⢣⢎⡔⡱⡳⢁⠎⡰⢫⠊⡵⡣⠾⠥⠥⠤⠬⠤⠭⠭⠭⠭⠬⠤
⠀⠀⠀⠀⠈⢳⣄⡉⠃⠆⠇⠸⠐⠰⠰⠡⠃⠊⠐⠁⠊⠐⠁⠐⠁⠚⠡⠊⠔⡡⢊⢌⡜⡠⢃⠎⡔⣡⠾⠎⠩⠩⠭⠍⠩⠭⠭⠭⠭⠭⠭⠉⠉
⠀⠀⠀⠀⠀⠘⠛⣛⣓⣦⣤⣤⣤⠔⢶⣶⠶⣶⣶⣶⣾⣿⣭⣭⣭⠍⣉⣀⡀⣔⣱⣋⣞⡰⠧⠾⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⣽⢋⣁⣀⣉⡭⠭⠭⠭⠭⠿⠍⠭⠿⠾⠿⠉⠹⠿⠿⢿⣭⣭⣭⣯⠭⠭⠭⠭⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⠒⠂⢾⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣿⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠐⡆⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁⢹⣿⣿⠀⠀⠀⠀⡸⠄⠀⠀⠀⠘⣷⠀⠀⢰⠁⠀⠀⠀⠀⢿⡌⠿⢶⡂⣠⡤⣤⣤⠉⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠸⣄⠠⢰⣿⣿⡏⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⢷⡟⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣀⣤⣀⢉⠲⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣌⣿⡇⠀⠀⠶⢖⠂⢤⣐⡀⠰⠀⢀⣠⣤⡴⠦⠤⠦⠸⣿⣉⠀⡀⠀⠘⣿⣿⣇⡀⢠⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⣿⠁⠀⢀⠀⣀⣤⠴⢞⠿⠛⡺⠋⠁⠀⠀⠀⠀⠠⠄⠀⠈⠑⢮⣠⣄⠹⣿⣿⡇⣠⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⣿⣋⣁⠀⡨⠟⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⣧⡘⠏⠀⢰⠈⠉⠉⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠿⠿⣤⣤⠟⠀⠀⠀⠀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠹⣷⡄⠲⣈⢠⡍⠙⠃⠓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣄⣤⣤⠃⠀⠀⠀⣰⡿⢿⡿⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠹⣿⣿⣿⡑⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⣼⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣿⣿⡿⢏⣉⡀⠬⡄
⠀⠀⠀⢀⠀⠀⠀⠀⢀⢼⣅⡀⠀⠀⠀⣀⣴⠀⠀⢿⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠟⢻⣷⡄⠠⢀⣖⠁
⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⡀⠉⣉⢉⣉⣁⠤⢣⠀⠀⠙⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣾⣿⠟⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⠀⢀⠀⠀⠀⠀⢿⡇⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡆⠸⡿⠁⢀⡷⣤⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⣁⠐⠒⠂⠓⠀⠀⠀⠀⠐⠈⠀⠀⢶⡀⠸⡇⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢠⡁⠀⠀⣰⡿⠟⢛⠻⢿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠃⠤⢤⠬⠀⠀⠀⠐⠂⠀⠀⠀⠀⣆⠻⢶⣷⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⣼⣀⣠⡾⢻⡁⣄⣉⡉⠂⣿⣿⡿⠁⠠
⠀⠀⠀⠀⠀⠀⣞⣀⡒⢒⡏⣀⣉⣀⣈⡁⠀⠀⠀⠸⣆⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⣠⣾⣿⣿⣿⣷⣍⡑⠬⣭⣭⣶⣿⡏⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠉⠭⠶⠄⢤⣬⡤⠤⠄⢚⠀⠀⢻⣷⣄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡄⣰⣿⣿⡿⠊⢙⣿⣿⣿⣿⣿⣿⣿⣷⣾⣵⡿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠠⠀⠐⠀⠻⠷⣶⣾⣿⣿⣷⣤⣀⡆⠀⠀⠀⠀⠀⠀⠆⠙⣿⠟⢁⣴⣿⠟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⣿⠥⠯⣀⡀⠀⠀⣈⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⣴⣿⣿⢡⠠⠿⢦⡙⣶⢺⣾⡿⠁⠈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠉⠻⣿⣦⡑⠿⠟⣡⣿⡿⠛⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠆⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠿⠿⣒⠮⢭⣴⣾⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⡸⣧⡀⠰⢶⡄⢤⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⠻⣽⣇⢻⠀⠉⠙⢻⠃⣀⣬⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢶⣿⢿⣿⣇⠀⣠⣡⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢞⡶⡿⢃⡿⢹⠟⠻⢏⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⣵⠏⠈⢀⣾⠃⠀⠀⠀⠈⠳⢄⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⢋⣵⡞⠘⢃⣾⠁⠈⠁⣶⣄⣘⣷⣆⡀⠀⠢⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⣴⣿⠟⠁⠀⠈⠁⠀⣠⣾⣿⣿⠿⢿⣿⠛⠛⠂⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⣠⣿⠇⠀⠀⠀⠀⠀⠠⣿⣿⢿⣿⢀⣸⣿⣤⣄⡀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣾⣤⡄⢶⣾⡀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠛⠻⣿⡆⠀⠀⢠⣄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢹⣿⠀⣼⣿⠀⣠⣿⣿⠀⠀⠘⣿⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠘⣿⣿⣿⢹⣤⠀⠀⠰⣶⣤⣾⣿⣠⣿⣿⣾⣿⡿⠃⠀⠀⠈⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠉⢿⣿⠸⡿⣦⡀⠀⠀⠙⣿⡿⢿⣿⡿⠛⠉⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢀⠈⠀⠃⠁⠀⠳⠀⠀⢸⡿⠁⠸⠟⠁⠀⢀⢀⣰⣿⣾⠀⢀⡔⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣶⣆⣄⣀⣀⣀⠀⠀⠈⠁⠀⠀⠀⡠⠾⠛⢿⣿⣿⣯⣤⣾⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⠿⠿⢿⣿⣷⣤⣤⣀⣀⣠⠴⠧⠶⠦⣤⣽⡵⠧⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣦⣀⣠⣤⣴⣶⣷⣾⣷⣦⠀⢀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣿⣉⠉⠁⠀⣠⣾⣯⠵⠞⠛⠉⠉⠉⣈⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡉⠉⠉⢉⣽⣿⠿⠛⢻⣄⣠⣴⣿⣾⣶⣶⣤⣤⣶⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢿⣿⣶⣾⣿⠿⠟⠋⢉⡾⠉⠉⠉⠉⣩⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠻⣷⣄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣾⢟⣀⣤⣴⠶⠾⠷⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⠶⢶⣶⣤⣤⣤⠶⢿⣻⣿⣿⣯⣤⣶⣶⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠉⠙⠛⠿⠿⠶⠶⣶⢶⣦⣤⣶⡾⠟⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣠⣼⣿⣾⡿⢿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠉⠙⣧⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠈⢷⡀⠀⠀⠸⣇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡆
⠀⢀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣤⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⡁⠀⠀⠘⣷⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠸⣇⠀⠀⠀⢹⣧⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣶⣤⣿⣶⣶⣾⡿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠘⢿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⣉⣖⠒⠂⡶⡞⢛⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠸⠦⢸⠃⠋⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⠀⠀⠈⢀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡬⠉⠉⠭⠥⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣅⡿⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠉⠉⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢶⣁⡀⠀⠉⠀⠀⢀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⢹⣆⠀⠀⠻⡟⣷⠀⠀⢼⢏⡵⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⣴⣷⢿⣶⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⡠⠶⠛⠂⠀⢿⠉⢦⠀⠀⠹⣾⠀⢀⡴⠋⠂⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⢸⣷⣼⡸⡇⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠆⠳⡀⠀⠀⢀⡈⠳⠮⢷⡀⠀⢘⣶⠫⢐⣠⢗⣪⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⠃⠀⠀⠀⠉⢻⡿⣷⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⡄⠑⡄⠔⠎⢉⣠⡤⣺⡗⠈⢀⣿⣺⡽⠚⠉⣀⣬⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠏⠀⠀⠀⢀⡀⢸⡃⡟⣿⡆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠘⠌⢦⠈⣆⣠⡤⢶⣻⣽⣧⠤⡞⠁⠀⠹⣶⠎⣫⣵⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠸⣿⣾⣶⣿⡿⠁⠀⠀⢰⠀⢹⡀⠀⠀⠀⠀⠀⠈⢦⠱⠿⡖⠛⠉⢁⣠⠤⠖⢻⡎⠀⠀⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⢀⠀⠀⠀⠀⠀⠟⠹⠃⠀⠀⠀⠀⡼⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⣦⢉⣠⡤⢖⣩⠼⠷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⢀⠈⠈⣆⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⡽⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢿⣤⡤⠶⠲⠤⠴⠶⠶⣤⣤⣤⣤⡴⠶⠛⠒⠋⠉⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠛⠋⠁⠀⠀⠀⠀⢠⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⢰⠀⠀⠀⣰⠋⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣟⣭⠿⠷⠤⣾⣿⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣠⣤⣴⣶⣶⣤⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢁⠼⠁⠀⠘⢧⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢀⣸⣷⣼⣷⣄⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢠⣿⢿⣿⠹⣿⠛⠃⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣿⡀⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠙⠁⠀⠀⠀⠀⠀⢀⠞⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣋⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠛⠛⠻⠶⠶⠶⠶⠶⠿⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠶⠦⠇⡑⠆⢠⡄⠘⢔⠀⠀⣡⢂⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣴⣀⣤⣀⣷⣋⣚⣂⠾⠟⢤⣯⣭⣶⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠒⠉⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⣶⣶⣶⣶⣶⡶⠶⢶⣶⠶⠶⠒⠋⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠁⢿⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⢦⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⡤⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠤⠤⠶⠖⢲⡄⠀⠀⠀⣠⡞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠒⠒⠀⠐⣆⠀⠛⡀⠀⠀⠀⠀⠀⡀⡇⠀⣠⠞⠉⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡈⢧⠰⣆⠀⠀⠠⠘⢆⠀⡇⠀⠀⢀⠈⣐⠌⠑⠾⣍⡀⢀⠀⠀⠀⡠⠊⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⢧⠀⢀⡴⠖⠒⡈⢧⣳⢤⡴⠀⠘⠉⠀⠀⡀⢤⢝⣦⠑⣤⠞⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⢀⠷⠚⠁⠉⠀⣀⣀⡿⠛⢶⣖⠤⣀⠀⠀⠍⢂⠎⡘⠁⢸⣤⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⣧⠅⠀⡰⠶⠾⠿⢛⠯⣄⡀⠀⠈⠑⠪⣆⢀⢎⢎⡼⣧⣤⠾⢿⡅⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠿⣦⡔⠁⢬⣆⡴⠉⠀⠳⢬⣒⣄⡀⠀⠈⢳⣧⠾⠛⢋⣤⠾⠋⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠢⣌⡙⠲⢿⣫⣤⣤⣀⣀⢀⣀⣀⣼⣧⣀⠤⠿⠶⠟⠋⠁⣠⡴⠋⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠉⠁⠀⠠⣉⣉⡉⢉⣉⡁⠀⠀⢀⠤⠤⠤⠶⠖⠚⠋⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⠁⠀⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣀⣤⡤⠶⠚⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣤⡤⠶⠶⠛⠁⠀⠀⠀⠀⡄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠹⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠀⢀⡠⠖⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡤⠞⠋⠉⠉⠛⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠛⠒⠚⠓⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢻⣿⣿⣿⣿⣿⣿⣿⢏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣤⣄⢨⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣾⣿⣿⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠇⠸⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏⠁⢀⡀⢀⡀⠈⠻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⡇⢸⣿⣄⣠⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠁⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢠⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⡇⢸⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠁⠈⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠀⠈⢁⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠔⠉⠐⠂⠀⠂⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠆⡠⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡈⠢⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠊⣢⠤⠒⠒⠒⠢⢤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⢠⠎⠁⣤⣀⣤⡀⠀⠀⠈⢦⠢⠀⠀⠀⠀⠀⠀⠀⢀⠐⡠⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⡡⢋⠔⠀⠀⠂⡏⠀⠀⣼⡟⠙⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢚⡠⢉⠐⠁⠀⠀⠀⠘⡄⠀⠀⠻⢷⣶⡿⢿⣦⠀⠀⡸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠔⠀⠀⠀⠀⠀⠀⢀⢣⡀⠀⠀⠀⠀⣤⣾⡟⠀⢠⢃⠀⡠⢂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢤⣀⠀⠀⠈⢀⣠⠔⠁⠠⢊⠔⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⢂⠁⠀⠀⣀⠔⡁⠁⠀⠀⠀⠀⡂⠁⠀⠂⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⠚⠓⠉⠁⠀⠀⣂⠁⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠱⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⠊⠀⢀⡀⠄⢀⡰⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠇⢳⡈⠢⡀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠨⠥⠒⠢⠤⠔⢒⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡢⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠒⠢⢤⠬⠦⡔⠂⢀⠤⡄⠂⢎⣄⢉⢁⣀⣀⣀⣀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠈⠐⠻⠦⡈⠒⠁⠔⠁⡙⣄⠀⠹⠿⠿⠋⠀⠀⢀⠜⡉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠆⠁⠀⠀⠈⡊⠑⠢⠤⣤⡤⠤⠒⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠅⠀⠀⠄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⠊⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡱⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠈⢂⠤⠶⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣷⣶⣮⣷⣦⣄⣀⠀⠘⠋⠙⠈⠀⠀⢀⣠⣴⡞⠉⠀⠀⠀⠀⠒⠒⣂⡶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⡏⠀⠉⠐⠒⣤⣴⣬⣬⣉⣉⣁⣀⡀⣀⠄⠐⠚⠫⠤⣖⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡀⠴⣟⡛⠙⠛⠧⢤⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠦⠤⣉⣙⣻⣿⣟⣿⡇
⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠉⠉⠁⠀⠀⠀⠠⣿⣷⣦⢄⡀⠀⡉⠛⠛⢿⣿⣿⠿⠟⠛⠿⠷⡖⠦⢬⣝⣿⣛⣽⣷⠄
⠀⠀⠀⠀⠀⠀⣇⡉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣬⣕⢺⡟⠉⠁⠀⡤⣉⣙⣲⣾⡿⣉⠓⠶⠶⣿⣿⣿⡟⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢻⡉⠑⠂⠀⠉⠑⠲⢶⣶⣿⣿⣿⣿⣿⣿⣿⣯⢸⡁⠀⣀⣀⣵⠤⢬⣝⣛⣋⣭⣉⠓⠶⣿⠿⣿⣇⠒⠶⣶⣶⣿⣏
⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠲⢿⣿⣿⣿⣿⣿⣿⠿⠷⣼⣋⡽⠟⠋⢛⠒⠶⢶⣿⡿⠦⣀⣉⣙⣿⣿⣿⣏⣈⣛⡿⠿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣉⠒⠢⠤⢌⣛⣭⡿⠛⠋⣁⣤⣶⣾⣿⣿⣀⣠⣴⣭⡙⠒⠶⣾⡷⠖⠢⠤⣭⣿⣯⣽⣷⠦⣭⣽⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⣴⣎⣉⠑⠒⠦⢄⣀⠀⠀⠀⠈⠉⣭⣷⣿⣿⣿⣿⡟⠉⣀⠥⡧⢌⣉⣛⣻⣿⡛⠡⠤⣤⣬⣭⣽⣛⠐⠶⣾⣿⣯⡿⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠓⠲⠤⣄⣀⡈⠐⠀⠴⢞⣫⣵⣿⣿⣿⠿⠊⠁⠀⠁⠀⠈⠉⠛⠛⣩⣉⠒⠲⣿⣿⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠧⣄⡀⠀⠀⠀⠀⠈⠉⣙⠒⣚⣭⢶⣻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⠤⣀⣉⣩⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁







⣿⢿⠿⠿⡿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢪⣵⠖⠒⠛⣩⠭⡄⢐⣒⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣪⠋⠁⠀⠀⠀⠀⠐⠻⠈⢠⠚⣡⡾⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⠙⠅⠉⠉⠉⠛⠽⢶⣄⠀⠀⢈⣴⣿⢿⣫⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣿⣿⣿⣯⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠔⠉⠀⢢⠀⠀⠉⠭⡻⢒⠶⣤⣄⡀⠀⠄⡌⣾⣿⣿⣿⡟⢗⢀⣴⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣫⠕⡾⠅⠀⠀⠀⠀⠀⠙⠢⠤⠤⠴⠔⢊⢟⣥⣿⠈⢞⣼⢿⣿⠿⠗⣠⡾⣿⡿⡿⡧
⠀⠀⠀⠀⠀⠀⣺⣅⠀⠲⠋⢡⠀⠀⠬⠄⠀⠀⠀⠀⠀⠀⠀⢀⠤⣪⣵⣽⣿⣿⠄⣽⣿⡿⠿⠥⠾⣿⢾⣝⣝⡴⠋
⠀⠀⠀⠀⠀⠀⣿⠪⣍⣙⠳⠶⣭⣑⠢⢌⣀⠔⢒⣲⡖⠐⣪⢵⣺⣿⣿⣿⣿⣟⣨⡾⠭⠁⠀⠀⡄⣿⣫⣫⣾⠣⣄⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠩⢝⡳⢶⠬⢿⣶⠤⣒⣫⢴⣾⣽⣾⣿⣿⣿⣿⠿⠿⢎⣁⣀⣀⠀⡄⣶⡃⣾⣿⠿⠧⣭⠁⠘⠿⠓⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⡒⠬⢅⡋⠃⠊⢹⠒⠾⢵⣟⣻⣿⢻⠿⠻⠉⠉⢁⣀⠤⣞⡽⡷⣽⢧⠻⣟⡿⠶⠒⢙⡧⢠⡁⠞⢚⣠⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣶⠬⣝⡛⠴⡬⠍⣽⣿⣿⠛⠫⠏⠀⠈⠉⠁⡠⢮⣾⣾⡇⡎⢦⣞⠁⠀⠀⡘⠀⠈⠒⠭⢗⣿⣿⣯⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠿⠓⡡⢍⣉⠛⠴⢼⠿⠭⠅⠈⠉⠀⠀⠀⢀⢔⣔⣟⣽⣿⡇⣦⠏⠀⣀⠤⠊⠀⠀⠀⠀⠀⠒⠀⠉⡏⠉⡓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣶⠥⠤⠪⠁⠀⢃⡀⠤⠬⠷⣒⠂⠀⢀⠤⠄⢲⠖⢒⣵⡷⣳⣫⣿⣿⠛⠍⠁⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢀⠘⣄⠀⠣⢋⡤⢞⣥
⠀⠀⠀⠀⠀⠀⠀⣯⠍⣉⣀⣒⠒⠂⠠⠬⠍⢉⣙⣒⠊⠥⠤⠬⠥⢒⡽⣫⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠤⡺⠴⣚⡥⢖⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣒⣒⠒⠈⠭⠭⠭⠀⢒⣒⣒⣶⣚⣒⣟⣤⣥⣾⢾⣿⣿⣷⣴⡤⠐⠶⣶⠠⢄⡀⠀⣀⡠⠄⣂⡨⠱⣐⣭⣶⣿⣷⣾⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢱⠶⡰⢬⠭⣭⣩⣀⣐⣒⣒⡒⣲⢒⡒⣒⢒⣚⣺⡿⢕⠅⠀⠉⠺⢗⡦⢭⡙⣂⣨⠭⣔⣲⡯⢷⣿⣿⣿⣟⠿⠒⣉⠤⢖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡓⠉⠢⠕⠦⣑⠂⠊⠴⠩⢚⡕⣨⠌⡁⢩⢌⠄⡹⣷⣵⠀⠀⠀⠈⠛⡗⠪⣻⣿⣯⣼⣾⣿⠿⠟⣋⠡⢔⣚⣭⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠂⠀⠀⠀⠀⠈⠑⠺⢦⡤⠤⠔⠐⣤⣄⣠⢔⣾⣶⣟⣽⣷⣄⡀⠀⠀⠅⠈⡿⠿⣟⡫⣭⣖⣾⣍⡘⠭⠓⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠒⣽⣦⣜⣛⣩⣤⡾⣻⣿⣿⣟⢿⠭⠊⠉⠒⠤⣀⠀⣿⡽⡼⠾⠛⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠢⡢⠄⠑⣯⣿⢿⣯⡷⠗⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⢀⡘⠀⠸⣿⠗⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠠⡠⢔⠀⡀⠐⡨⢀⠁⢊⠔⠁⢔⠀⢂⠔⢁⠄⡀⢂⠔⡀⠀⠠⢀⠔⠠⢂⠄⠀⡠⢒⠔⢀⠄⡠⢂⠔⡠⢈⠔⡡⢂⠔⡀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠡⢊⠤⢂⠤⡢⠐⡡⢊⠥⢊⠔⡈⢐⡥⠊⠔⡠⠀⡡⢂⠔⡠⡪⢊⠔⠁⠐⡡⢊⠔⡡⢊⠔⢡⠎⡔⠡⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠐⠁⠐⠁⠊⠀⠉⠐⠡⠂⠠⠊⠄⠁⠊⠎⠀⠀⠘⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠲⢄⠀⠀⡠⠒⠈⠁⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⣸⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠱⡀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠤⠤⠶⠴⠥⣾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣀⡠⠤⢤⡤⢀⡀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠁⢃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣠⠞⢹⡏⡟⢳⡄⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⡀⢸⢃⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⢻⢾⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⢸⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⢦⣯⣾⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⢀⠤⢄⡀⠀⠀⢀⣀⣤⣀⣀⡀⠔⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡯⣥⣀⠀⣠⣤⣤⠚⠿⠖⠒⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣤⡤⠴⢒⡿⠛⣧⠘⡏⠉⣛⣶⠛⠛⡹⢃⡤⣴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠢⢼⡉⠉⠉⠉⠉⠉⢁⣾⠊⣰⢗⠕⠊⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡬⢷⣄⣻⡀⠀⠀⠀⣠⡏⡧⡼⢳⢤⡔⢲⣪⠋⣔⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠋⣭⡴⠊⣠⠋⢓⡮⠥⠤⠬⠷⠿⣟⣋⠹⣟⢦⡉⠳⢄⢀⡼⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣼⠋⠀⣰⢃⡴⡋⠀⠀⠀⠀⠀⠀⢀⡜⡱⠓⠷⣮⣒⣐⣫⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢰⠇⣠⠞⠁⠚⠋⠁⢠⡄⠀⠀⣤⠀⠘⠋⠁⠀⠀⠀⠁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠃⠀⠀⣼⡾⠋⠀⠀⠀⠀⢀⣸⣧⣤⣤⣿⣄⣀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠰⠞⠉⠀⠀⠀⠀⢀⣴⠿⣿⠋⠉⢩⡿⠛⢿⡷⠀⠀⠀⣠⡟⠀⠀⠀⣀⠈⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⣿⠀⠀⢸⡇⠀⠀⠁⠀⠀⠀⠉⢀⣤⠴⠚⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⣿⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠙⢦⡀⠀⠀⢠⣶⡀⢸⡇⠀⢰⡏⠀⢀⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠉⠀⠀⠈⠙⠿⣿⣶⣶⣾⣷⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠖⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠉⡆⠐⢲⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣥⣄⣀⣠⣤⣞⣉⣉⣀⣀⣀⣨⡵⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢃⣼⡛⡶⠀⠉⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢊⣡⣶⣓⣤⠟⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠒⣩⣤⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⣏⡳⠂⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⠀⠉⠛⠿⣍⡙⠛⠲⢤⡀⠀⠀⠀⠀⢀⣠⣶⣯⣤⠗⢋⡤⢞⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⣋⣽⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡙⣦⣀⣤⣶⣿⡿⠟⣋⡤⢞⣩⡴⢟⣋⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢒⣉⣤⣴⣾⣿⣿⠿⠟⠻⣏⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣛⣥⣶⣿⢷⣚⣭⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⣡⣤⢲⢞⣏⣸⠭⠟⠋⠉⠀⠀⠀⠀⠘⠳⣄⡀⠉⠻⢷⣦⣀⠀⠀⠀⠀⣀⣠⣴⢸⡿⢿⣻⡿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠈⠑⠢⢌⡉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠾⣛⣻⣿⣶⢰⣿⣿⣿⣿⢸⣯⡽⢾⣻⣽⢿⣟⣯⣯
⠀⠀⠀⠀⢀⠀⠀⠀⡐⠬⣑⠲⢤⣀⠀⠀⣀⡤⠴⠺⠋⣫⣻⠿⢛⣫⣥⣶⣿⡿⢿⣛⣿⢸⣿⣿⣿⣿⣸⢷⣛⣯⣷⣾⣿⣿⣿⣥
⠀⠀⠀⠀⠈⠲⢤⣐⣤⣑⠢⢍⡒⠬⢙⠲⢬⣙⠻⠞⣋⣥⣶⣾⣿⣿⣻⠭⣗⣪⡽⢖⣻⣸⣿⣟⣿⣿⣾⣿⡿⣟⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣬⠉⠂⠄⠀⠈⠙⣿⣿⣿⣿⣿⣿⡿⣞⣻⡭⠶⣚⣭⣽⣿⣿⣿⠿⣛⣭⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠠⡉⡛⢽⣻⢶⣤⣀⠀⠀⣿⣿⣿⣿⡿⠿⣛⣭⣴⣾⣿⣿⡿⢟⣫⣭⣶⣿⣿⢿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡷⣦⡪⠚⠁⠈⠛⠾⣝⣻⠶⠟⣛⣭⣴⣾⣿⣿⣿⠿⢛⣫⣵⣾⣿⣿⠿⣛⢽⣺⢽⣻⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢷⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣛⣭⣴⣾⣿⣿⡿⢟⠫⣓⡭⣞⣯⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⡈⡻⢦⣄⢸⣿⡿⠟⣋⣥⣶⠿⣛⣯⣷⢿⡻⣕⣪⢗⣫⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⡚⢆⠙⠿⣧⣶⠿⢛⣩⣶⣿⣿⣿⣿⠽⣺⣽⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠈⠻⣾⣿⣿⣿⣿⣿⣿⡷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠟⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣦⣀
⣼⣿⣿⣷⣤⡀
⣹⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⡟⠁⡠
⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⠃⢀
⠻⢿⣿⡿⠄⠛⢢
⠀⠀⠉⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⢀⣀⣀⡠⠄⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠹⣟⠁⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⠛⣤⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠈⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠪⠀⠻⡀⡓⢤⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢸⠀⣀⠀⠀⠀⡄⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠀⠀⠄⠀⠠⠀⠀⠀⢹⠀⡴⠁⠀⠀⡇⢠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠂⠂⠀⠰⠀⡀⠀⠈⠀⠂⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠂⠀⠰⠀⠀⠀⣸⠀⠇⠀⠀⠀⡇⠐⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡀⠀⢐⠀⠀⠀⢸⠀⡃⠀⠂⠀⡇⢐⡁⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁

⣶⣶⡶⠶⠶⢶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠐⠂⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠃
⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠶⣏⡉⠉⠀⠉⠑⠢⠼⣲⣦⠀⠀⠀⢀⣠⣴⣋⣤⡽⢟⣂
⠀⠀⠀⠀⣭⣙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠺⠿⠥⠒⠤⣀⠂⣠⣤⠤⠁⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢱⢤⣉⠓⠢⢍⣓⠶⠴⢶⣶⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡿⠿⠟⠉⠩⠅
⠀⠀⠀⠀⠸⢆⠀⠁⠀⠀⠈⠉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠴⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠚⣭⣒⠤⠀⠀⠀⢹⣿⠿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠑⠢⠍⣐⠢⠥⠤⣐⠿⢛⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⡒⠒⠒⠀⢠⣤⡀⠀⠀⠀⠉⣐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠴⠋⠀⠀⠀⠀⠀⢰⠢⢈⡁⠀⠀⠀⠀⠛⠓⢂⡀⡤⠤⠂⢰⣶⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢤⣤⣶⡂⠀⠀⠀⠀⠀⠀⠀⠘⣍⠀⠈⠁⢲⣶⣾⣿⣿⣿⡯⣇⣀⣤⡼⣿⣿⡶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠽⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⣻⡿⠟⢛⣩⣽⣿⣉⣠⣴⡿⠟⠃
⠀⠀⠀⠀⠐⣐⠿⣿⠕⠨⢽⣿⣿⡇⢀⣐⣢⡄⠀⠀⠀⠐⡧⠤⢅⡒⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠁
⠀⠀⠀⠀⢐⡒⠬⣿⡯⠍⣐⣿⣿⡏⢒⣻⣿⣿⡄⠀⠀⠀⠣⠀⡀⠀⠉⠁⠒⣺⣿⠿⠋⠁
⠀⠀⠀⠀⢐⠠⢭⣿⡯⠁⣒⢿⣿⡿⣐⣺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠈⠙⠛⢳⣂⣺⣿⣿⡟⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠾⠋⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢀⠀⠀⠀⣰⠇⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢸⡆⠀⢠⡟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣼⣷⣴⡿⠶⣾⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⣼⠃⠈⢻⡇⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠋⠀⠀⠈⢿⡀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢿⡟⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⢸⡇⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⡷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣶⣶⣶⣶⣶⣶⡶⠶⠶⣶⣶⣤⣤⣤⡶⠟⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⠉⠀⠉⠻⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⠉⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⠉⠉⠉⠙⣿⡏⠉⠉⠉⠉⣿⡟⠉⠉⠉⢹⣿⠋⠉⠉⠉⠙⣿⡏⠉⠉⠉⣿⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡄⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⣤⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⣄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠇⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⢿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣿⡇⠀⠀⠀⠀⣿⣷⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡀⠀⣀⣀⣤⣤⣦⣤⣀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠛⠛⢋⣉⣉⣙⣛⡛⠛⠋⠉⢉⣴⣟⡥⠶⠟⠛⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⠛⠛⠛⣫⣿⡿⠟⢿⡆⢀⣠⣿⣽⣶⣄⣀⣠⣤⣴⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠹⣿⣶⣶⣾⣿⠿⠛⢉⡼⠉⠉⠉⠉⢉⡿⠋
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠙⢿⣄⠀⠀⠀⢀⡾⠁⠀⠀⢀⡴⢋⣀⣤⠶⠶⠶⢶⣶⣦
⠀⠀⠀⠀⣼⢋⣿⣿⡿⠛⠛⠛⠋⠙⠉⣍⠉⠀⠀⠀⠀⠀⠀⣀⣤⣽⣛⡷⢶⣿⣧⣤⣤⣄⣠⣤⣤⢴⣿⣿⣿⣧⣴⣶⣶⡿⠿⠋⠁
⠀⠀⣠⣴⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⣶⣾⣷⡄⠀⢀⣠⣶⡿⠟⠁⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠾⠿⠛⠻⢦⣄⡀
⠀⣸⡿⢋⠉⠉⠀⠀⢀⣀⡀⠀⠀⠀⣈⣀⠈⣷⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄
⠀⢹⣷⣿⣷⡄⠀⠠⣿⠟⠁⠀⠀⠀⠃⣡⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠙⢿⣿⡿⠀⠀⠈⠀⢙⡥⠂⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⡀
⠀⠀⠀⣼⢋⣽⣇⠀⠀⠀⠛⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢆⣿⡀
⠀⠀⠀⠹⣦⡀⠋⢀⡄⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣩⣼⣇
⠀⠀⠀⠀⠈⠛⠛⠙⢷⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⣈⣷⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⡶⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⡿⠟⠛⣿⠉⠉⠛⠿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢿⡏
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢻⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢰⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣷⣤⣴⣶⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⢟⣵⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣾⠁⠘⠿⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⡏⠀⠀⠘⣧⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣿⠀⠐⠿⣾⣙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠈⣷⠀⠀⠀⢸⣧⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⣄⠀⢒⣶⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣾⣷⣶⠿⠿⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠙⠷⣮⣭⣿⠃⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣙⡟⢿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⡟⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣻⣿⣷⣿⣾⢷⡿⣾⣿⠋⠉⠙⠛⠻⣿⣿⣛⣻⣟⣻⣿⢿⣽⢿⣿⣯⣿⣄⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⣶⣛⡼⢏⣽⣩⡟⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⡻⣾⠿⣽⣷⣟⣿⠷⣿⣦⡾⠋⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⡟⣷⣟⣱⢿⣼⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧⡿⣿⣷⣿⣧⣴⣿⣟⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣧⣟⣳⣾⣹⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢿⣿⣿⣿⡿⠃⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠻⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣿⣿⡿⢦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣾⣷⠄⠀⠀⠀⠰⣷⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣦⣌⠻⣿⣄⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢀⠀⠈⣹⢻⣝⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣌⣛⣛⣋⣀⣁⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠈⢉⣉⣉⣉⣉⡉⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣈⣉⣉⣉⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣛⣿⠿⠒⢢⡄⢀⠈⢉⣉⣉⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⡐⠢⢤⣭⣭⣥⣤⣶⣿⣿⣀⣉⠉⢉⣉⡁⢸⣷
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠠⠤⠶⠶⠂⢸⣿⢀⣉⣉⣉⣉⡅⢸⣯
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢈⣙⣛⣛⠁⢸⡟⠠⣤⣈⣉⣥⣤⢸⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠤⢬⣭⡥⠄⢺⣷⠀⣤⣀⣀⣠⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠶⠶⠶⠂⢸⣿⠀⠀⣀⣈⣭⡤⠼⠿⠒⠚⠀⠲⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⣐⣲⡶⠿⠷⠚⠛⠋⠉⠛⠲⢤⣀⣄⠀⠒⠯⢤⡴⢖⠈⠉⠛⠷⢶⣤⣄⣀
⠀⠀⡀⠤⠤⠖⠒⣊⡉⠩⢐⣛⡳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣄⡀⠀⠀⢘⣮⣝⣱⠀⠉⣉⡛⢓
⢰⠀⠠⣀⠀⠢⣙⣲⣿⡏⡁⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣳⣮⡥⠴⠖⣒⣋⠭⢕⡒⣺⡇
⢸⣦⡀⠈⠓⢤⣈⠉⠙⠒⡼⢛⡛⠶⣤⠤⢒⡂⠬⠑⠂⢀⣀⣤⠤⠶⠒⠋⠉⠁⢹⠀⠈⠡⠐⢒⣉⣡⢤⣿⠇
⠈⣇⠉⠲⣄⡀⠈⠑⠦⣀⠘⠪⣽⡷⠿⢖⣋⣤⡴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠔⠒⠉⣉⣠⡤⢼⣿
⠀⣇⡉⠢⣄⠙⠦⣄⠀⠀⠉⠂⣠⠴⣞⡻⠭⠀⣀⣀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠒⢛⣉⣭⣤⠶⢺⣿⣄
⠀⠁⡈⠲⢄⠑⠢⠈⠑⠦⣀⠀⣿⡭⠵⠖⣚⣭⠵⠖⠒⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠻⣍⣝⣦⣵⣾⡿⠿⠛
⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠈⠑⣿⠶⠛⠋⠁⠀⠀⣀⡀⣸⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⣿⣀⣠⢤⡶⠾⠛⠉⢀⣸⣤⣶⣾⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⣿⣇⣠⡤⣖⣧⣶⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⡭⠖⠛⠉⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡶⡿⡿⣿⣿⣶⣶⣦⣄⣀⣄⡀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣄⠑⣿⣯⣳⣶⡈⠉⠀⠀⠀⢀⠍⢉⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣧⠈⣳⡀⠀⠀⣴⡧⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣯⣿⣇⢻⣧⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⣻⣾⣿⣿⣿⣿⣿⡤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠟⢛⣿⣿⣿⣯⣭⣭⣡⣤⡞⢔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣀⣴⣿⣿⣿⣿⣿⢃⡏⠀⠻⣿⣆⠑⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⠃⠼⠃⡀⢀⡙⠈⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⢀⣤⣿⣼⣧⣄⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⢰⣿⣿⣿⢻⣿⣿⣷⡄⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣿⣿⣿⠀⠀⢿⣿⣿⣾⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣟⣶⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠻⠿⣿⣿⣿⣥⣄⡀⠀⠀⣿⠟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⢠⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠔⣷⣿⡇⣿⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠠⠼⢿⣿⣿⣿⣿⡉⠛⠿⣶⣶⣦⣤⣤⣄⣀⠀⠐⠀⠀⢀⣠⡤⣿⣿⣷⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠜⣇
⠀⠀⠀⠀⢀⣀⣀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣥⡶⠞⠋⢹⣿⣿⠈⣿⠏⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣭⣯⣿⣿⣿⣿⣿⣷⣾⠿⢛⣡⣤⣤⣴⣾⣿⣿⡷⠢⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠉⠉⢻⣿⣶⣤⣤⣤⣤⣉⡉⠉⠙⠻⠗⠊⠉⠁⠀⣀⣨⠝⣻⣿⣯⣆⠤⣀⣧⣄⣀⣀⠠⠄⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⣯⣯⣿⣿⣿⣶⣦⣤⣤⠀⠈⠁⣀⣀⣼⣿⣿⣿⣶⠒⣙⣛⣻⡓⠀⣠⣶⠶⠛⠁
⠀⠀⠀⠀⢸⣿⣶⣶⣤⣤⣄⣀⠀⠀⠈⠉⠙⠛⠻⢿⣧⠴⣒⣋⣭⣽⡿⠿⠿⣿⣿⣿⣯⣯⣿⡏⠨⠟⠋
⠀⠀⠀⠀⠈⠛⠛⠷⠶⢿⣿⣿⣿⣷⣶⣶⣤⣤⣤⠞⠂⠉⣉⡠⠤⠖⠃⠀⠀⢠⣀⠀⠀⠀⢸⠓⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢿⣧⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⢰⠣⢿⠅⠠⠾⣍⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣿⡂⣐⡛⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣼⡥⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣴⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠈⠉⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣂⣠⣄⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠈

⡏⠉⠉⠉⠉⠉⠉⠁⠈⠉⠀⠉⠉⠉⠁⠉⠀⠀⠀⠀⠈⠉⠉⠀⠉⠁⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹
⡇⠀⠀⡤⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⢸
⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠇⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡰⢪⠔⢈⠥⠨⠉⠐⢝⢦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢨
⡇⠀⠀⠃⠀⠀⢀⢔⡕⠒⠂⢕⠄⠀⠀⣸⠰⠁⠀⣀⠻⠀⠀⠀⠀⢂⢃⠀⠀⢠⢪⠔⠒⠪⡳⡀
⡇⠀⠀⡆⠀⠀⢸⠈⠀⠀⠀⡨⡸⠀⠀⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⠀⣇⠁⠀⠀⠀⡁⡇
⡇⠀⠀⡇⠀⠀⠀⠳⢄⣀⣀⠕⠁⠀⠀⠸⡄⠀⠐⠌⠨⠠⠂⠀⢀⢆⠆⠀⠀⠈⠢⣄⣀⡨⠞
⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠈⠊⠀⣀⠵⠂
⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠁⠀⠀⠁
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⢳⡀⠀⠈⣇⡠⠤⠤⣤⣤⣤⠴⠶⠖⢲⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⡉⠉⣽⣦⠽⠶⢦⣧⣠⣦⢟⣀⡀⠀⢀⡴⠛⣦⠀⢀⣸⣶⣿⣶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠊⠿⣇⡾⢅⠈⢦⡀⠀⡙⣯⡿⣯⣤⣿⣤⠯⣄⣸⢯⣱⣿⣇⠀⠀⢻⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠼⣄⣀⢹⡛⢦⡀⠀⠹⣾⣩⡿⠿⠛⠉⠀⠀⠀⠀⠈⠛⠧⢞⣙⣆⣖⣺⣧⣼⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠂⣩⡿⠋⠁⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠋⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠉⠐⠀⢀⣀⣀⣀⣀⣤⣴⡶⠿⡿⠋⠁⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⠐⠖⠛⠋⢹⡄⠀⠀⠀⠀⠀⢀⣠⣄⠉⠉⠉⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⣶⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣿⠛⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⢹⣿⣿⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⣼⣿⣿⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠋⠁⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣤⢠⠖⢒⡖⠒⣲⣶⣶⣶⣶⣰⠖⣰⣶⣴⣶⣶⣶⣶⡆⢹⠱⠜⠚⢾⣰⡶⣶
⠀⠀⠀⠀⠀⠀⠀⡠⡰⠋⠉⠈⠀⠀⠀⠀⢀⢈⣴⢇⡆⣥⡎⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⢿⡟⣿
⠀⠀⠀⠀⠀⠠⡪⠊⠀⠀⠀⣝⢪⠂⠀⠀⣷⣿⣋⢊⢸⣿⣇⠀⠇⠀⠀⠿⡿⢿⠏⠀⠀⠀⢠⠃⣸⣿⣿
⠀⠀⠀⠀⡐⣕⠁⣀⡀⡀⠀⣀⣠⠀⠀⠈⣿⡿⠡⣿⢸⡾⡃⠎⠀⠰⠄⠀⠠⠄⠴⠴⠶⣢⢣⡷⣹⣿⠇
⠀⠀⠀⣌⣘⣿⣿⣯⣬⣥⣵⣛⣂⣚⣛⡻⣿⣱⢁⣛⣸⣛⣻⣿⣿⣗⣶⣿⣒⣚⣋⣯⣥⣥⢿⣷⣿⠃
⠀⠀⠀⣹⣿⣟⣱⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡭⠿⣿⣉⣉⣉⣒⣒⣶⣴⣿⣿⠏
⠀⠀⠀⠹⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⣿⣽⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢻⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠴⢿⡄⠀⠀⠳⠻⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⢀⡴⠶⢤⣒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣴⠋⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠑⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢫⠀⠿⡀⡛⢦⡁⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠐⠃⠀⠀⠀⠀⠀⠀⠀⠉⠆⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠁⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠐⠀⢲⠐⠀⠀⠀⠠⠄⢲⠀⢀⡄⠀⢀⠀⠀⣀⠐⢀⠀⢀⢀⡆⢀⡄⣀⠀⠀⠀⣠⡐⢀⡆⢠⠐⠐⠀⠀⠂⡒
⠀⠀⠀⠂⠀⠀⡆⠀⠀⠀⠀⡀⡄⢀⢀⢰⠀⠀⢸⠀⡼⠀⠀⠀⣇⠈⡇⠀⠀⢠⠈⠀⣁⠈⠀⠠⠀⠀⠂⠀⠀⡆
⠀⠀⠀⠸⠀⠀⡇⠀⠀⠃⠀⡄⡇⢀⢸⢸⠂⠀⢻⠀⡟⠃⠀⠘⣏⢀⡇⠀⢸⢸⠀⡀⢸⠀⠀⠪⠀⠀⡞⠀⠘⡇
⠀⠀⠀⠐⠒⠒⠃⠀⠀⠒⠒⣀⡇⢀⣸⠘⠒⠒⠚⣀⡗⠒⠒⠂⢻⡀⠓⠒⠒⢸⣀⡀⣸⡐⠒⠒⠀⠀⠒⠒⠒⠃
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡇⢀⢰⠀⡁⠀⢀⣀⡇⠃⠀⠂⣹⢀⠀⠀⢈⢸⣀⡀⢸⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⡇⠀⢨⢰⠀⠀⢺⠀⣇⠀⠀⠀⣯⠠⡖⠀⠰⢸⠀⠀⢼⠀⠀⠠⠀⠀⡐⠀⠀⡆
⠀⠀⠀⠸⠂⠂⡇⠀⠀⠂⠐⠆⡇⠀⠰⢸⠂⠀⢻⠀⣟⠀⡄⠀⡷⠀⡗⠀⢸⢸⠠⠄⠴⠀⠀⠺⠀⠀⠚⠀⠐⡇
⠀⠀⠀⠐⠒⠒⠃⠀⠀⠒⠒⠒⠇⠐⠚⠘⠒⠒⠚⠒⠏⠀⠀⠀⠓⠒⠓⠒⠚⠸⠂⠀⠘⠒⠒⠒⠀⠀⠓⠒⠒⠃
⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠐⠒⠀⠓⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠐⠚⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢸⣕⠋⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⠟⠉⠉⠉⠙⢶⡀⠀⣼⣍⠛⠓⠒⠚⢛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠮⣤⣤⣤⣤⣴⣾⠀⠀⡿⢮⣍⣛⣛⣫⣽⣿⠀⠀⠀⠀⠀⢀⣠⡴⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⡻⠲⠤⣤⣤⢤⣾⠋⠀⠀⠙⠦⣤⣤⣤⣤⠾⠋⣀⣠⡤⠶⠚⠉⠥⠖⠳⢬⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⡙⠓⠒⠒⠚⣻⡿⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⣍⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣯⡭⠴⠶⠚⠛⠉⠉⠁⠀⣠⠙⢿⣿⣿⣷⣤⡈⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣷⣄⡀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠙⢿⣿⣿⣿⣦⡘⡇⠀⠀⠀⠀⣀⡤⠞⣋⣽⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠷⣄⠈⠛⢦⡀⠀⡀⠀⠀⠀⠙⠿⣦⣄⣙⠻⣿⣿⣿⣦⣀⣤⠴⣚⣭⢶⣛⣭⣽⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣌⠳⣤⡀⠙⢦⣉⠲⣄⣀⣀⡀⠀⠀⢁⣀⣬⣿⣿⣿⣿⣾⡿⢟⣛⣭⠵⣺⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡙⢮⡳⣮⡛⢦⡀⠙⠳⡬⠥⠶⣖⣚⣿⢿⣿⣿⣿⣿⣿⡯⠶⣚⣭⠵⠞⢋⣭⢶⡶⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡙⢦⡙⠦⠶⠖⣛⣫⡭⠶⣚⣩⡥⢖⣻⣿⡿⠟⠋⠁⠀⠀⠀⢸⣅⣃⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡙⠶⠖⣋⣭⠴⢖⣫⡭⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⢿⣦⣉⣉⣛⣉⣉⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⣚⣫⡭⠖⠛⠉⠀⠀⠀⠀⢀⣠⣤⡤⠤⣤⣄⡀⠀⢸⠳⠦⣬⣭⣭⠽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠵⠃⠀⠀⠀⠈⣻⠀⠈⠓⠶⠤⠤⠤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡛⠒⠶⠶⠒⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣾⢿⣿⢷⣍⠳⣄⠤⠀⠂⢤⡀⠀⣀⡀
⠀⠀⠂⡀⠠⢴⠀⢸⣿⣿⡜⣷⡿⠿⡖⠀⠀⠀⠀⡿⠋⠀⠈⠑⢤⣀⠤⣄⡀
⠀⠀⠀⠈⠂⠄⠀⣿⣿⣝⠷⢫⠇⢠⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⡿⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣿⡟⠃⠈⠀⠀⠀⡴⠈⠁⠒⠄⠀⢰⠇⠀⠀⠀⢀⡟⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠄⢀⠀⠉⢘⠀⠀⠀⠀⠀⢈⡀⠀⠀⡄⢀⠀⣼⠀⠀⠀⠀⡼⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⡀⢀⡀⠀⠀⠉⠒⢛⡡⠋⢠⡇⠀⠀⠀⡼⠁⠀⠀⣠⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠹⣷⣶⣶⢿⣿⣂⣀⣼⣆⣀⣠⡞⠁⠀⢀⣼⣿⢿⣟⣿⣿⡷⠆⠂⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⣻⠟⠟⠀⠉⠹⡝⣿⣿⠋⠙⠛⠶⠒⣿⣿⣿⣣⢿⣿⠏⢠⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⣆⠀⠀⠘⡧⡈⠻⣿⣶⣿⣿⠀⣿⡷⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢆⠀⠀⠀⠐⡀⠘⢿⣿⡏⠀⠟⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣸⢃⠀⠃⠀⠈⠀⢹⣦⡀⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⡛⠷⠶⠾⠟⣋⣭⣀⣀⣄⡼⠳⣠⠥⠚⠷⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠰⠦⠭⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⢤⡔⠚⠳⠤⡤⡴⣛⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡉⠛⠳⣿⡥⣴⣌⣾⣧⠽⠯⢭⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡹⣧⠈⢸⠋⠩⣟⣀⡠⠴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣌⡻⠤⡿⣇⣸⡿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡻⢶⠗⢞⣹⣭⣶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢷⡿⠻⠻⠙⢟⠳⡈⠉⢓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠠⠋⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠂⠈⡙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠔⠈⠀⠀⣀⣀⣀⣿⢝⡆⠀⠀⠀⠀⠀⠀⠀⠐⠡⠂⢈⠦⣄
⠀⠀⠀⠀⠀⡠⠊⠀⠜⠀⠀⠀⣠⠍⢀⣰⣒⠊⢕⡝⠶⣄⠀⠀⠀⠀⠀⠀⠀⢑⡡⢊⢌⢦⡀
⠀⠀⠀⡠⠊⢀⠠⠀⠀⠀⠀⠀⣇⣴⡏⠀⡿⣦⡟⠒⢶⡿⠃⠀⠀⠀⠀⠀⠀⠀⢐⠅⡠⢊⢗⡄
⠀⢀⠎⢠⠆⠂⠀⠀⠀⠀⠀⠀⠻⣯⣿⢦⢟⣕⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠔⡡⢣⡻⡄
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢯⢙⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⡔⡑⣷
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⢛⡟⠺⣕⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⢊⠌⢾⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⠻⣆⠀⣷⣾⡇⠀⣹⣫⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢔⢕⢕⢕⢼
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣼⢻⣿⠿⣳⢞⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢕⠕⡡⡣⡠⣫
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣧⣾⠗⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡨⢔⠵⡪⡪⢊⢔⠇
⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢊⠔⡡⡪⢊⢔⢵⡿⠤⠤⠤
⠀⠀⠙⢄⠃⠄⠀⠀⠀⠀⠀⠀⠀⢀⢆⠔⠀⡀⢀⠄⢀⢀⠄⡠⡡⡣⠢⡲⢡⢊⢜⠔⡡⡡⠾⠥⠤⠭⠤⠼⠯⠗⠒
⠀⠀⠀⠀⢱⢄⣉⠐⠐⠀⠀⠂⠃⠃⠃⠊⢘⣀⣁⣈⣀⣁⠊⠊⢔⢔⡕⡔⡡⣡⣢⡞⢋⣉⠁⡈⠉⠉⠉⢉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⢛⣒⡶⠆⠨⠻⠿⠿⣿⣿⢿⣶⠶⠖⠒⢤⠤⣥⣯⣾⠾⠛⣉⣐⠒⠀⠔⠒⠒⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠚⢋⠁⠀⠐⣦⣀⡐⢂⣀⣀⣀⠛⠋⠙⠉⠛⠋⠀⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠊⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡆⠀⠀⠀⠀⠀⠀⠐⠐⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⠳⡀
⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢢⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠀⠙⣄
⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠚⢧
⠀⠈⠀⠀⠈⠯⢍⡛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⡇⢹⠀⠀⠄⠈⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⢀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠭⠇⠀⢀⡤⠶⠶⠶⢤⡀⠀⡇⠀⢽⡇⢨⡄⠀⠀⠀⠀⠀⡠⠀⠀⢀⣀⣤⣶⠾⣷⠀⠒⠘⡄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢦⣀⢀⠒⢍⢢⣃⠀⣸⡇⣼⠗⠛⣉⣙⡓⢦⠀⢰⣿⣟⠯⠑⠚⠉⠁⠀⠀⠄⢻
⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠡⣄⠙⠳⢾⣷⣵⣍⢠⢏⢀⡔⠂⣉⣤⠾⢃⡜⢄⠀⠀⠀⠀⠂⢀⠀⠀⠀⡀⠰⢺
⡇⠂⠀⠀⠀⠀⠀⠀⠂⠀⣐⠀⠀⠀⠀⣈⠁⠒⠤⡀⠘⢋⠳⠾⠟⠻⣟⡉⣥⣒⠥⣔⠘⢈⡗⡄⠀⠀⢠⢀⢠⠀⠀⢒
⡇⡀⠂⠄⠀⠀⠆⣥⡐⡂⡠⠄⠐⠷⠀⠀⣴⢞⡩⠂⣹⠆⣾⡄⠞⢷⣆⠙⣦⢫⡫⡉⢀⢳⢌⢡⣐⠀⠤⠌⠼⠸⠦⣙⠲
⢱⠈⣗⢠⡡⠄⠤⢈⠐⠂⢀⡂⠉⠃⠆⡞⡡⡁⢀⣴⠏⣸⠊⢣⠘⣨⣽⢷⡘⣇⠰⠾⠓⡞⠂⠔⢲⡀⠖⢸⣁⠄⣀⠋⢰
⠘⡐⠆⡀⠆⡄⠌⠡⢔⣀⠐⡈⠄⡀⢹⢇⣶⡷⠟⢁⣴⠃⢀⡈⢆⠈⠳⣿⡇⣿⢸⣆⢌⣦⣼⡷⣰⣤⣷⢯⣌⣤⣷⡄⣾
⠀⢳⠂⡷⠩⠰⠂⡀⢮⠅⡂⠁⢀⠩⠀⢤⢥⠶⠞⠉⠄⢰⣶⡄⠨⢷⣀⣨⠠⠤⠤⡤⠷⠟⠿⠽⠿⣿⣿⣿⣿⢿⣟⣻⣿
⠀⠘⡇⢞⠀⠠⠈⡄⢤⠃⢈⣴⣿⡗⠈⠀⠀⠄⠀⠈⠀⣿⣿⠃⡤⡄⡙⢻⡑⠆⣢⣝⡱⡘⠗⠳⠖⠏⡜⠣⢯⡏⢉⣿⠟
⠀⠀⠹⡄⢨⣖⢢⠵⢠⣴⣿⡿⠋⠀⡰⠠⠀⠀⠀⠀⠁⣿⣿⠀⣅⢰⠚⠊⢗⡀⢿⣯⢳⣌⡒⣠⠂⡌⠡⠁⠍⢁⣾⠏
⠀⠀⠀⠹⣄⠳⠑⣵⣿⡿⠋⡀⠈⢀⠀⢀⡀⠠⠈⣀⡃⠿⠿⠀⡆⠂⠘⡌⢩⠀⠀⠻⣧⡻⡜⢡⢂⡐⡀⠂⣠⡾⠋
⠀⠀⠀⠀⠈⠲⡍⠦⡀⠀⠐⠀⠀⠀⠌⠀⠀⠉⣁⠐⠀⠀⠀⠠⠵⠄⢀⡘⡈⠀⠀⠀⠘⢿⡿⠤⠠⠖⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⢤⣑⠠⢀⠠⠤⠐⢀⠁⠀⠀⡐⠠⠌⠭⠨⠁⠀⠀⠀⡒⡀⠄⠐⠀⢐⠠⠂⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣜⣐⡀⠀⠂⠂⡄⠉⠨⠉⠄⠀⠀⠀⢁⠃⠂⠈⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣶⣶⣤⣤⣶⣶⣭⣥⣤⣤⣶⡶⡾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⢀⡤⠄⢀⣀⡤⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⡥⠂⠨⣋⡑⠂⠀⢤⣀⣠⠈⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠉⠁⠈⠉⠁
⠀⠀⡠⣔⣚⣅⡉⡙⠉⣇⣆⣩⠟⠋⠀⠉⠐⠉⠅⠒⠀⠀⠀⠀⠀⡀⠐⠒⠘⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠈⢳⡒⠤
⠀⠈⠁⠀⠀⠀⠈⠈⠐⢋⣤⠤⠤⠄⠀⠀⠀⢀⡬⠁⠀⠀⠀⠀⠐⠀⠀⠀⠁⣼⣀⣀⠀⣀⡀⠀⠀⠀⢀⣃⢀⠁⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠫⣀⠉⠉⠃⠀⠀⠌⠈⠀⠀⠀⠔⠀⠀⣙⠶⡌⢠⣞⠁⠀⠀⠰⢾⠛⠇⠘⠂⠋⠩⡍⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠬⠤⠐⡨⠂⠀⠀⠀⠀⢀⠀⠀⠈⠚⠛⠋⠡⠈⠀⠁⠀⠀⠒⠀⠉⢁⡖⢟⢷⢦⠜
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⣀⢅⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⢆⡄⠈⠎⠀⠀⠀⠀⠐⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢬⣀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠐⠶⠁⠀⠀⠀⠀⠠⠤⣤⠶⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠕⣒⠄⠀⣬⠗⠒⢦⠤⣤⢂⢦⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠐⠒⠀⣰⠤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠚⢝⠊⠉⠀⠀⠈⠋⢗⡔
⠀⠀⠀⠀⢀⠀⣀⡠⠤⠤⠄⢄⠀⠓⠀⠷⠤⢄⣸⣀⢻⠈⠒⠦⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⣀⠀⠀⠁
⠀⠀⠀⢐⠁⢀⣙⠑⠈⢠⣦⣎⡱⠀⠀⠀⠀⠀⠀⠉⠐⠐⠒⡤⠖⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉
⠀⠀⠀⢦⣈⡰⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⣏⠁⢉⣉⢢⡐
⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡌⠩⢽⠝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣁⠠⠀⠙⠢⢀
⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣤⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡷⢚⡶⢻⡗⢻⡧⠽⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠆⠸⢣⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⢁⡞⢠⡟⠀⢀⣤⣄⠀⢹⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⢠⠂⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣯⣾⣥⡏⠀⠀⠂⢈⠋⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣾⣽⣷⣯⣴⣋⢉⡑⣌⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠖⠰⢈⠲⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣿⣇⠛⢙⢿⡟⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠘⠚⠉⠀⢀⠀⠀⠀⠀⠤⣿⣿⣿⣿⠋⠀⠘⠻⣓⠒⠉⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⢴⠀⠀⠙⠁⠀⠈⠢⠆⠉⠀⣤⠉⣥⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠄⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠊⠀⠀⢀⠀⡀⠀⠐⡓⡘⠃⡀⡀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠨⠀⠀⠈⠄⠁⠁⠀⠁⠁⠄⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⠀⣂⠀⠀⠀⠄⠀⠁⠰⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠁⠀⢀⠀⠀⠀⡁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⢐⠀⠐⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠀⠀⠀⠂⠈⠈⠀⠠⠁⡀⠀⠀⠤⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠈⠂⠀⠀⠀⠠⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠅⠘⠦⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠚⠚⠀⣂⣀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠰⣾⣿⢛⠁⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠡⠀⠠⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⡀⠠⠀⡂⠀⠈
⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠁⠀⠀⢀⡔⠉⠀⢀⠀⠀⠀⢄⠀⠀⠀⠀⣀⠀⠀⠠
⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾⡏⠁⠀⠀⠀⠀⢀⣄⠱⡄
⠀⠀⠀⠈⠁⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠉⠹⠿⢿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⠿⠛⣳⣒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠉⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢠⡾⠛⠻⡆⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢷⣤⣄⠁⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⣄⠀⢘⡇⠀⠀⠀⣀⣴⡷⠶⠶⠒⠛⠛⠲⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠙⣷⠛⠁⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣹⣷⣤⣄⣀⣀⣀⠀⠀⠀⠀⣿⠷⣤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣤⡴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠶⣄⠀⣿⣄⡀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⣿⡈⠙⠛⠲⠶⠶⠶⠶⠶⠶⠞⠛⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠶⢦⣤⣤⣀⣀⣀⣠⣤⣤⡴⠶⠛⢹⡇⣿⠛⠶⣤⣤⣀⣀⣀⣀⣀⣠⣤⡴⠾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢿⡇⣿⢦⣄⡀⠀⠈⠉⠉⠉⠉⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠉⠛⠛⠓⠶⠶⠶⠖⠛⠛⠋⠉⠀⣸⡇⢿⣀⠉⠙⠛⠛⠛⠒⠚⠛⠛⠛⠉⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⠛⢻⡇⠀⠙⠻⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠉⠛⠓⠶⠶⠶⠶⠶⠶⠛⠛⠉⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟
⠈⢿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⢀⡾⡷
⠀⠈⣳⣄⠉⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⢀⡠⠖⢉⣼⣥
⠀⠀⠙⣍⠓⠦⣄⣀⠀⠉⠉⠉⠓⠒⠢⢤⣀⠀⠀⠀⠀⢀⣤⣶⡿⣿⡿⣿⣾⣛⡛⣿⢀⠴⠊⠁⣀⡤⠴⠒⠫⢭⠄⡠⠞⡱⠃
⠀⠀⠘⢿⠳⢤⡀⢨⡭⠭⠙⠛⠒⠒⠦⢄⡈⠙⢦⡀⣴⠿⠋⢡⣾⡿⠿⠟⠛⠉⣷⡟⠁⣠⠖⠋⠁⠀⢀⠤⢖⡁⠀⣠⣾⡇
⠀⠀⠀⠀⢙⣦⣀⠀⠉⣗⠒⠂⠀⠀⠀⠀⠈⠳⢄⠙⢌⠳⢤⡢⣳⣄⡀⠀⠀⢸⡟⢀⠞⠁⠀⠀⠤⠤⣶⠒⠉⠐⣊⠵⠋
⠀⠀⠀⠀⠈⠛⠭⣙⣂⠀⠉⠹⠭⠥⠤⢤⣀⣠⣤⣁⡈⢧⠀⠙⠺⣿⣿⣄⡇⢸⣷⣆⠀⣀⠴⠊⠉⠉⠀⣴⡶⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠧⢤⣄⣀⣀⠀⠙⠻⠿⠿⢿⣶⣶⣾⣿⣿⣿⣿⣿⡿⢷⡄⢀⣀⣴⡶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⣛⡷⠖⠛⠋⣙⣩⣿⢿⡟⢸⣧⠻⡄⠙⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⢾⣛⣿⠿⠛⠁⠚⠀⠀⠏⠃⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠏⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠶⠶⠶⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠄⠂⠀⠀⠈⠀⠀⠀⠀⠋⢤⠀⠀⠀⠀⠗⠂⠀⢀⡀
⠀⠀⠀⣤⠀⠠⠀⠂⠀⠁⠀⠀⠈⢀⠄⠤⠀⢄⡀⠀⡀⠀⠀⣀⡀⠀⠀⠸⡁⠀⠀⠰⡢⠤⡄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠰⠁⢐⣢⠀⠀⠑⠀⠀⠀⠀⣧⡱⠀⠀⠀⠃⠀⠐⠀⠙⠁
⠀⠀⠀⠀⠄⠀⠀⡖⡇⠀⠀⠀⢡⠀⠀⠀⡆⡂⢀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠓⠀⠸⠂⢠⠘⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠑⠄⣉⡮⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⠦⠒
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠈⡀⠤⠀⠤⠤⠒⠀⠀⠀⠈⠀⠀⠀⠀⠁⠘⠁⠀⠀⠒
⠀⠀⠀⠀⠈⠧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠐⠀⠀⠤




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡾⠻⢷⣦⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣛⣉⡉⠉⣀⣤⣤⡴⠶⠶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣀⠉⠛⠋⠁⠀⠀⠀⢠⣾⣯⣴⠶⠿⠛⠛⠿⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣄⠀⠀⢀⣀⣰⣿⡿⠿⠶⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠟⠛⠿⠿⠯⠽⠟⠙⢿⣦⣄⡀⠀⠀⠉⠛⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠙⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣆⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣸⣿⣄⡀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠉⣿⡟⢿⣶⡄⠀⠀⠀⠀⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠘⣿⡆⣿⡇⠀⢹⣿⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣿⡇⣿⡇⠀⠾⠋⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⢾⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢹⣿⡻⣷⣦⡀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⢸⣿⠀⠈⣿⣇⠈⢻⣷⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⣿⡇⠀⢹⣿⡀⣸⡿⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣹⣿⣀⣀⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡟⠉⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⢠⣿⡇⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠙⠿⢶⣶⡶⠿⠿⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢀⡤⣀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⢀⣀⣀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⢼⣥⢤⡀⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣐⢛⡀⠀⢓⣒⠒⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣦⠀⠀⢠⣶⣶⣖⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠏⠀⡼⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⢤⠀⠀⠀⣤⠤⠼⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠘⠉⠒⠦⠊⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⠓⠤⠔⠋⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⠒⠙⠒⠶⠐⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠉⠉⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⣴⠛⠋⠉⠙⠛⠳⣦⣀⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⣷⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠾⠛⠻⣤⣀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠀⠀⠀⠀⣿⠛⠉⠁⠀⠀⠀⠀⠀⠠⡤⠤⢄⡀⠀⡤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡖⢤⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢳⡜⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⢠⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠋⠀⠀⠀⠓⠉⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣃⠀⠀⢘⡓⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡽⠗⠀⠀⠀⠿⠿⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣛⠀⠀⢘⣙⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⠀⠀⠀⡖⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⣠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠠⠏⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⣶⢠⢄⢀⠀⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠤⠤⣄⣀⣀⣀⣀⢀⡀⢈⡉⢙⣡⡀⢀⠇⠀⠌⢛⡚⣃⠆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⡀⠀⠀⣀⡠⣀⣀⣀⠀⡇⠘⡠⢸⣧⠇⢸⠠⠤⡀⢰⡇⡾⢠⠃⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠉⠉⡛⠉⠀⠉⠛⢠⡅⠃⠐⡇⢸⣿⠀⣮⢀⡿⠂⡜⢸⠇⡎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⡀⠀⠀⠍⠀⣠⢤⠀⢺⠀⢸⠘⡇⢸⡇⠀⡇⢺⡇⢀⠇⢿⢴⠁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⡗⠤⣤⠀⠀⠈⠩⡄⢃⡀⢸⠀⠤⠈⡇⠀⡇⠾⡅⢸⢀⣇⡾⠚⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡹⠀⠀⠤⠀⢠⢾⡄⠀⣷⠘⠀⣰⠀⡆⢀⣇⣴⠄⠚⠉⠁⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠓⠐⠓⠂⠿⠭⠦⠤⠭⠄⠬⠷⠐⠃⠛⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⠠⠃⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠠⠤⠒⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⠀⠉⠁⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⠂⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠤⠐⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⢶⣄⠀⠀⠀⠀⠀⠀⢀⠰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠶⠀⠀⠀⠀⢰⣿⣿⡏⣿⡇⠀⠹⡷⠀⠀⠀⠀⠀⠈⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⣤⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢿⣿⣿⣿⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⠣⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⢸⣿⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠐⡀⠠⠀⠠⠠⢀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⡀⠀⠀⠐⠒⠒⠒⠀⠐⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡄⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣀⠙⠲⢄⣀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠉⠉⠉⠓⠲⣌⡙⠓⠂⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⣠⡴⠊⢁⣠⡄⢸
⠀⠀⠀⣀⣀⣀⣀⣤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠠⠤⢤⣤⣀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡴⠛⠁⣠⠖⠋⢸⡇⢸
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣆⠈⠳⣦⡀⠀⠳⡄⠀⠀⠀⠀⠀⡇⢀⡴⠋⢀⣠⠞⠁⠀⠀⠈⡇⢸⡇
⠀⠀⠘⢦⣄⣀⡀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁⠀⠀⢴⠈⠳⣶⠈⢳⡄⠀⠹⡄⠀⠀⠀⠀⣷⠏⠀⣰⠟⠁⠀⠀⠀⠀⠀⣧⠀⣇
⠀⠀⠀⠀⠀⠉⠉⠻⣍⠉⠉⠉⠀⠀⠀⠀⠀⣀⡤⠀⠹⣟⠈⢟⠀⢹⡄⠀⢳⠀⠀⠀⡴⠃⢀⡞⠁⠀⠀⣠⠤⣤⡀⠀⢸⡄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢦⡤⠶⠒⠚⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣆⣠⠞⢁⡴⠋⠀⠀⠀⡼⢡⣶⡄⠹⡄⠈⣇⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⢶⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣠⠞⠀⠀⠀⠀⠀⢧⠻⠾⣿⡆⡇⠀⢹⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠤⠤⢴⣶⠶⠶⢖⣫⠟⠁⣀⡀⠀⠀⠀⠀⠈⠳⣝⣛⡴⠃⠀⠀⢳⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠚⣉⣠⠴⠞⠉⢠⠞⢩⣉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⢉⣉⣉⣉⣤⠴⠒⠋⠁⠀⠀⠀⠀⣼⢠⡿⣿⣋⣀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⢯⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢹⠈⠛⠻⣯⣿⠃⡧⠀⠀⠀⠀⠀⠀⣰⠋⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧⠀⢰⢋⣴⡤⠙⢦⠀⠀⠀⠈⢳⣘⠛⠻⢃⡴⠃⠀⠀⠀⠀⢀⡼⠁⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡄⠸⡞⠿⣷⣷⢸⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⡴⠋⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣧⠀⠱⣜⣛⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠒⠛⠉⢉⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⣠⠴⠚⠉⣁⣠⡤⠶⠖⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢀⡴⠋⠁⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⠟⠉⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣉⣉⣉⡉⠉⠉⢉⣉⣉⣉⣉⣉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣛⣛⡛⠛⠀⠀⠛⢛⣛⣛⣛⠛⠃⠀⠀⠛⢛⣛⣛⣛⠛⠁⠀⠘⠛⣛⣛⣛⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣭⣥⣄⠀⠀⣠⣬⣭⣭⣭⣥⡀⠀⠀⣠⣭⣭⣭⣭⣤⡀⠀⢀⣤⣭⣭⣭⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣉⣉⣉⣉⣉⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣈⣉⣉⣉⣉⣉⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠤⠶⣦⡀⠀⣀⣠⠴⢺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⠁⠀⠙⢿⣛⡉⠅⠀⠀⣷⠉⣹⠋⠁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠙⣦⠀⠀⠀⢸⢀⡟⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠀⠀⠀⠘⠉⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣽⣦⡴⠶⠶⠖⠒⠒⠚⠛⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠷⣿⣛⣁⣀⣀⣀⣀⣄⣤⠴⠖⠛⠉⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣿⠟⡿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⠟⠁⡼⠁⠀⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⠔⠊⠀⡀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠀⠐⡇⠏⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠦⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⡄⢨⢀⡅⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠚⠈⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⢀⡀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠐⡁⠨⠠⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠉⠉⠉⠉⠉⢉⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠉⠉⠉⠉⠉⠉⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒⠒⠒⢲⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⡖⠒⠒⠒⠲
⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠈⣅⣀⣀⡨⠁⠀⠀⠀⢅⣀⣀⣨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⠇⠀⠀⠀⢩⣀⣀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡖⠲⠒⢲⣾⣿⣿⡇⣴⠠⠦⠠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠠⡆⢸⣿⣿⣿⣤⠀⠦⠠⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⢀⡀⣸⣿⣿⣿⡇⣿⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⡇⢸⣿⣿⣯⣿⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣟⣀⣖⣐⣣⠀⠀⠀⠀⠀⠀⠀⣞⣀⣖⣐⣣⢸⣿⣿⣷⣟⣀⣶⣐⣳⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢸⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡤⠤⠤⢤⣼⣿⣿⡇⣠⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⠤⡄⢸⣿⣿⣿⣤⠤⠤⠤⣄⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⡐⠀⡞⠁⢆⠀⢸⠀⠀⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⣿⠀⠉⠈⡇⠀⡧⠤⣧⠤⢼⠀⢹⠀⠉⠈⡇⢸⣿⣿⣿⣿⠀⠉⠈⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣦⣼⣿⣿⣿⣧⣿⣤⣤⣤⣧⠀⣇⠀⣇⠀⣸⠀⣽⣤⣦⣤⣧⢸⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢸⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡠⠍⠉⠉⠩⠀⠀⠀⠀⠍⠉⠉⠩⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠉⠇⠀⠀⠀⠸⠉⠉⠉⠅
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠶⠶⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠒⠋⠉⠀⠀⠀⠀⠀⠠⠶⠤⠬⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⠟⠤⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢻⡑⡁⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠉⠉⠉⠉⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣴⠋⡀⠀⠀⠠⠤⠤⣴⡾⢟⡽⠋⠀⠀⣀⣤⠄⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠇⠘⠀⠀⠀⠀⣹⣿⠖⠙⠁⠀⠀⠀⠀⠉⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣾⣤⠀⠀⠀⢀⠔⠁⠘⠧⠀⠀⠀⠀⠀⠀⢀⡄⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣣⣶⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⡻⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣿⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⣀⡽⠛⠛⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡟⠀⠸⣧⠀⠀⠀⠀⠀⠀⠉⢛⡶⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⣹⠁⠀⣇⠀⠀⠙⢷⣄⠀⠀⠀⠀⢠⠞⢷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣼⠁⠀⠀⠙⢆⠀⠀⠈⠙⢷⣦⣄⡴⠋⠀⣦⠈⢦⡀⠀⠄⠐⠒⠀⠉⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣸⠃⣀⣤⣦⠀⠜⣧⠀⠀⠀⠀⠈⢹⣧⠀⠸⠇⠉⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠻⠛⣹⡟⠉⠀⠀⠙⢧⠀⠀⠀⣰⣿⣟⣷⡆⠀⠔⠈⠃⢢⠐⠈
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢾⣧⡀⠀⠐⠀⠀⠈⢳⣄⣴⠻⣷⡝⢸⠓⣄⢀⣀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠃⠀⠀⠀⠙⣧⠀⠈⣿⣟⣄⠙⠀⠙⠀⠙⠇⣀⢀⠀⠴⢣
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣄⠀⢂⠀⠈⢆⠀⠳⣿⣿⡀⠃⠀⠀⠀⠀⠈⠘⠀⠀⠡⡀
⠀⠀⠀⢸⡇⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⣿⡄⠹⣧⡈⠀⠀⠘⣿⠳⣦⡙⢷⢰⠀⣠⠏⠰⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⢸⡇⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢹⣷⠀⠘⣿⣤⠂⠀⠘⣦⡌⠻⣦⣯⠶⠁⠀⠀⠀⠀⢸⡆⣿⣀⣀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠱⡀⠀⠀⡀⠀⠀⢻⣷⡄⢡⠙⢿⡄⠀⠘⡻⣆⡸⠁⠀⠀⠀⠀⠀⠀⢸⡷⢿⡏⢹⡇⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⢻⣇⠀⠈⢄⠀⠡⡀⠀⠀⠀⠀⠀⠹⣷⡀⢳⡈⠻⣆⠀⢳⣿⠃⠀⠀⠀⠀⠀⢀⡴⠛⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠈⣿⡄⠀⠀⢦⠀⠲⡀⠀⠀⠀⠀⠀⠙⣷⡈⢧⠀⢹⣆⢀⡏⠀⠀⠀⠀⠀⣠⡟⠁⠀⣿⠀⣷⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢹⣿⡄⠀⠈⢣⡀⠱⡀⠀⠐⠀⠀⠐⡈⢿⣆⠆⠀⢻⣾⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿⣤⣿⠞⠋⠉⠹⣇⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠱⠀⠱⡄⠀⠀⠀⠀⠑⡀⠻⣧⠀⠀⣯⠀⠀⠀⠀⠀⠘⠷⠶⠾⠛⢻⡅⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⣿⠟⣿⣆⠀⠀⠐⡄⠘⢄⠀⠈⢆⠀⠐⢆⠹⣷⣀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠹⢿⣧⡀⠀⠘⢦⠈⢆⠀⠀⠂⠀⠈⢂⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⢸⡇⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠸⢿⣷⣄⠀⠀⠳⡈⠳⡀⠀⠀⡀⠀⠑⠈⠻⣷⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⣧⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢻⣻⣷⡄⠀⠙⢆⠙⣄⠀⠘⢄⠀⠈⠂⠹⣷⣄⠀⠀⠀⠀⠈⠻⣦⣤⣿⡶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⢸⣿⣦⡀⠀⠳⡈⢣⡀⠈⠢⡀⠀⠳⡌⠛⢿⣆⠀⠀⠀⠀⠀⠀⢻⠀⠿⠀⠀⠀⠀⠀⠀⠀⠠⢃⠜⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠋⡿⢿⣦⡀⠘⢀⠙⢄⠀⠑⢄⠀⠀⠂⠀⠙⠻⣶⣄⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠔⠡⠉⢀⡔⢸⡆
⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⠀⠀⠀⠀⠀⠋⢴⠹⣿⣦⡀⠑⢌⠳⣄⠈⠳⣄⠀⠀⠀⢀⣴⣿⠆⠀⢀⡴⠋⢉⡏⠀⠀⠀⠀⠁⠀⣠⣴⠋⣠⡿
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢿⣦⡉⠀⡈⠢⡀⠈⠳⢀⡴⠋⣠⠟⠳⠚⠋⠀⢀⣾⢁⣴⣿⠷⠶⢺⣿⠉⡹⠟⢹⠁
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡇⠹⢿⣦⡌⠢⠙⢆⠀⡞⠀⡴⠋⠀⠀⠀⠀⠀⠘⠋⠋⠁⢀⣠⣤⠞⠛⣋⣄⣴⠃
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢨⡷⢙⣿⣦⡀⠂⢻⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣋⡵⠛⢛⣻⡿⠋⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⣦⢹⣿⣶⣼⣷⣦⣷⣤⣀⣀⡀⠀⠀⠀⣶⣿⣿⣿⡿⠛⠛⠁
⣀⣀⣀⣀⣀⣹⣆⣀⣀⣀⣃⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣋⣻⣿⣸⣇⣈⣙⣿⣟⣙⣟⣿⣿⣿⣿⣿⣟⣻⣛⣻⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠰⠂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣤⣤⣤⢠⢠⣠⣤⣠⣤⣤⠄⡄⠀⠀⠀⠀⠀⠀⢸⠟⠉⠉⠙⣷⡄
⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⢻⢹⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⣇⣇⣸⢿⣼⣿⣿⣿⢶⣿⠂⡇⠀⠀⠀⠀⠀⢀⣈⣀⣀⣠⣴⣿⡃
⠀⠀⠀⠘⠃⠀⠀⠀⠘⢿⣿⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠙⠙⠘⠋⠙⠉⠉⠋⠛⠃⠀⠀⠀⠀⠀⠀⠠⣤⣾⡿⠿⠯⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⢹⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠓⠀⠀⠀⠘⠛⢾⢾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡄⠀⠀⠀⢹⡀⠀⠀⢸⡇⠀⠀⢀⡾⠀⠀⠀⣰⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠻⣄⣀⣠⣤⣷⣴⣤⣾⣷⣤⣤⣞⡁⠀⠀⣰⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠹⣄⣠⣴⠞⡻⠉⢠⣾⣿⣿⠟⢈⢨⣿⣿⣿⣿⡟⠺⣧⣀⣠⠟⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⣴⠟⠉⠀⢰⠁⠀⣼⣿⣿⡇⠐⠚⠸⢿⣿⣿⣿⡇⠀⢸⡍⠳⢦⣀⣠⠋
⠀⠀⠀⠀⠀⠀⢦⣀⣼⠟⠁⠀⠀⠀⢸⠀⠀⢻⣿⣿⣿⡶⠶⠀⢸⣿⣿⣿⠁⠀⣸⠁⠀⠀⠙⢧⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠟⢻⣆⠀⠀⠀⠀⠸⡄⠀⠈⢿⣿⣷⣄⣴⣰⣿⣿⡿⠁⠀⣰⠏⠀⠀⠀⠀⣠⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⣤⣀⠀⠀⠙⢄⡀⠀⠙⠻⠿⠿⠿⠛⠉⠀⣠⠞⠁⠀⢀⣠⡴⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣉⡛⠲⠶⣤⣽⣶⣤⣤⣤⣤⣤⣤⣶⣿⡥⠴⠖⢛⣩⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣍⣛⠒⠶⠤⢤⣬⣭⣭⣭⣤⠤⠤⠶⠖⢚⣋⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠂⠀⢀⡠⣤⣒⡄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⢤⣤⣭⣭⣥⠽⡇⠀⠀⠀⠀⢰⠏⠉⠠⢤⡤⢴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠂⢀⣸⠄⡀⠀⣀⣀⣠⣴⡗⠖⠂⠈⠉⡈⢙⣦⡀⢠⠶⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⢀⣍⣙⣄⣀⣀⣀⣀⣀⣼⣏⠉⠉⠉⠉⢉⣁⣷⠀⠠⠴⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⢠⣨⣿⣆⡀⠈⣉⣉⣉⢥⣟⡈⠉⠈⢉⣉⣭⠛⠀⠴⠶⠷⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⣀⣀⣾⡀⠉⠉⠙⠀⠒⢚⣿⡄⠉⠙⠛⢉⣻⢓⠠⠴⠦⢷⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣄⣈⣙⣿⡆⠉⠈⠚⠚⠋⢩⣿⡁⠀⠘⠙⣹⡿⠻⠀⠠⢶⢻⣯⡤⠤⣤⢽
⠀⠀⠀⠀⠀⠀⢀⡀⠤⣐⣦⠒⣊⢭⣁⣩⡕⠊⠉⠁⠉⠙⠉⠉⠉⠉⠈⠉⠑⠚⢛⣯⡉⠀⢘⢋⣫⡗⡮⠄⠤⡬⠞⣿⡆⢰⢴⣿
⠀⠀⠀⠀⠀⠀⠚⠙⠛⠲⢾⣧⣶⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠖⠊⡩⠉⢉⠉⠋⠻⣛⣛⣛⣾⣀⢤⣤⣶⣯⣤⣼⢾⣧⢰⡽⠀⣠⣉⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣻⠀⠀⠀⢀⠀⠁⠀⠀⢰⣿⣿⣖⣒⠂⠂⢥⡀⢌⡡⢤⠤⠒⢻⡋⣉⣠⣉⣠⣈⣉⣭⡧⢾⣿⣿⣿⡗⠒⡾⣿⣾⣧⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣤⣀⣠⣤⣄⣺⠀⡐⠀⠀⠐⠀⠄⠀⢸⠝⠚⠉⠛⠻⠷⠾⠭⣭⣲⠶⣛⠯⣽⣿⣥⣴⣧⣤⣤⣿⢿⡷⡞⠛⠛⠻⣿⡶⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠙⠛⠿⢆⡁⠀⢄⢄⠄⠠⠂⢸⡅⢒⠨⣁⡀⠀⠀⠀⣟⠉⠅⢈⠉⠀⠁⡈⢼⡏⠭⠩⠩⠰⡆⠁⠐⢊⣛⣿⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣁⢀⡘⣿⣶⣤⣤⡀⠀⠀⠀⡇⢀⠨⠐⣈⣤⢬⣖⣺⡯⠥⠤⠤⠤⠄⠉⠛⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠫⠽⢻⣶⣶⣯⣵⣾⣿⣿⣟⣻⢭⡭⠥⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣉⡀⠠⢄⠀⠀⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡁⠄⠂⣿⡋⣿⡇⠂⢈⡐⠈⢶⡉⠓⠲⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣤⠀⠈⠠⠀⠁⠀⠀⠀⠹⠧⠟⠁⠀⠀⠈⠀⠤⠙⠰⢤⣀⡀⢌⣫⣙⠩⡉⠑⠀⠑⢦⡀⡀
⠀⠀⠀⠀⢨⣹⢤⣐⣃⣠⣴⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠉⠛⠛⠓⠒⠒⠒⠚⠀⠀⠉
⡠⢠⠤⣄⣀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡆⢰⠀⠀⡂⠀⠀⠀⠀⡀⠀⢰⠀⡀⠀⢰⠀⠂⠀⠀⠀⠀⠀⣀⣠⠀⠠⠤⡤⢀⠔⠂
⠙⢿⣦⣸⡏⠙⠦⠀⢀⣠⠴⢚⣱⠈⠀⠀⠁⠈⠁⠂⠀⠀⠂⡇⠀⢁⡀⠅⢀⣥⣀⡤⠤⡤⢶⣞⣋⠁⣀⣀⡤⠖⠉
⠀⠀⠈⠉⠋⠛⠓⢷⣋⣘⣴⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡦⢧⣤⠀⢀⣀⣁⡤⠾⠛⠛⠉
⢠⣆⣖⠒⣦⣄⡀⠚⠛⠋⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⡀⡇⠀⠀⠀⠈⠢⣊⠉⠛⠓⠒⠶⢶⡶⡶⠒⠒⠒⠀⠲⢤⠀⠄⡀
⠀⠙⠻⢷⢯⣄⣈⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠔⠦⠤⠥⢤⠽⠦⠴⠤⠤⠴⠒⠛⠀⠁
⠀⠀⠀⠀⡀⡬⠽⣯⠤⠤⡀⢀⠀⢀⠀⠀⡀⢀⡀⠀⠀⠀⠀⡇⠀⡄⠀⡀⠀⡂
⠀⠀⠀⢸⣷⣿⣶⣿⣶⣶⡿⠬⠤⠤⠥⠬⠤⠬⠽⠀⠀⠀⠼⠥⠤⠭⠤⠥⢼⣯⣀⡞⠛⠛⠛⠻⠛⢿⡛⠟⡛⠓⠂⠰⢤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣶⣤⣤⣤⣴⣶⣿⣶⣷⣶⣶⣶⣮⣤⣥
⣀⣀⣀⣘⣛⣿⣿⣻⣿⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠀⢀⠙⠀⠀⠀⠀⠀⣀⡤⠶⡆⠀⠀⠀⠀⠀⠀⠀⡈⠀⡖⠀⢀⠖⠁⠀⠀⠀⠀⠐⠁⣠⠤⡄
⠀⠀⠀⠨⣓⣄⠁⣒⡦⠴⡇⢉⠀⠀⠂⠁⠀⠀⠀⠀⠠⢂⣀⣀⡘⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢘⠤⠨⠝
⠀⠀⠀⠀⠈⠁⢙⠡⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠜⢀⠂⠁⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣪⠵⠒⢒⢦⠀⢠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣉⣀⠀⠀⠀⠚⠈⣔⣫⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡒⠉⠉⠀⠀⠉⠉⠛⠦⠤⣠⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠⠞⠉⠉⠙⠒⡢⠤⣄⣀⡀⠀⢀⢸⣿⣿⣿⠟⢉⣽⡄
⠀⠀⠀⠀⠀⠀⡀⠄⣐⠍⡶⠁⠀⠀⠀⠑⠢⠤⠤⠂⡺⣿⣽⠈⣦⣾⣿⡏⢉⣾⣿⣿⣇
⠀⠀⠀⠀⢠⡧⠤⣍⣡⢄⣀⠂⠀⠀⡀⢀⠀⣀⣔⣼⣿⣿⣿⠀⣿⡿⠓⠚⢻⣿⡿⡷⠃
⠀⠀⠀⠀⢸⡍⠓⣶⠭⣙⣲⣭⣖⡡⠖⣫⣔⣯⣿⣿⣿⣿⡿⠞⠉⠀⢀⡴⢸⣿⣿⣉⠓⢲⡤⢀⡀
⠀⠀⠀⠀⠘⠠⢀⣀⠭⢍⡒⠉⢻⠿⠿⣿⣻⣿⣿⠟⠙⠁⣀⢭⢿⣷⣽⠟⣾⡯⠶⠚⡧⣠⠠⢖⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⡮⣭⣓⠾⣩⣿⣿⠋⠛⠁⠀⠁⡠⣿⣿⡗⠎⣴⠃⠀⡠⠃⠈⠑⠛⠿⢿⣿⣇
⠀⠀⠀⠀⠀⢠⣔⢊⠍⠉⣆⠐⠨⣍⡋⠂⠀⢀⢀⡀⡠⣪⣾⣿⣿⣧⡟⠀⠐⠊⠀⠀⠀⠤⠀⠀⠀⠂⢄⠉⢐⣆
⠀⠀⠀⠀⠀⢼⡒⣂⠈⠥⠀⠀⠈⢓⡳⠒⠎⠠⠎⢥⣾⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠠⡣⠔⡪⢕⣻⠆
⠀⠀⠀⠀⠀⠘⡧⠤⠒⢊⣁⡠⠄⠀⢤⠶⠃⠶⠦⣥⣾⣿⡿⢷⣦⡐⠲⣆⠠⢄⡀⠄⣀⣢⣜⣢⣭⣶⣿⡾⢟⠏
⠀⠀⠀⠀⠀⠀⣸⡃⢙⢞⡲⠲⠖⢗⢞⠟⠹⡻⠻⠩⠿⣍⣅⠀⠈⠹⣧⣢⠥⢶⣾⡿⣯⣿⣿⣿⣟⣭⣵⣾⡽⠆
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠁⠉⠂⢤⣄⣀⠡⠈⣈⣀⣁⣴⣼⣿⣄⡀⠀⠈⠃⢶⠶⢒⣖⣛⢟⡛⠟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠺⡷⠴⣊⣥⣼⣻⣿⣿⡿⠟⠉⠐⠠⢀⣹⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠹⡆⢨⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠜⠋
⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠔⠀⡠⠀⠀⢀⠐⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠂⢔⠔⡠⡊⢐⠄⡀⡨⠀⢐⠀⡠⠂⢀⠀⢀⠕⠀⡠⠊⠀⠄⠕⠡⠊⠊⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠉⠙⠻⢿⣦⣄⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣀⣿⣯⣀⡀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣾⣿⠟⠛⠿⣿⡦⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠰⢶⣶⣶⣶⣶⡶⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢶⣶⣶⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣷⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠙⣿⣷⣦⣴⣾⣿⠏⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⣿⣇⠀⠀⠀⠀⠉⢻⡟⠉⠀⠀⠀⠀⢠⣿⠃⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠘⣿⣆⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣿⡏⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠘⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⡟⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠉⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⣤⣤⣀⠈⢿⣆
⠀⠀⣼⡿⠁⠀⠀⠀⣠⣤⣶⣶⣶⣶⣾⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⣿⣆
⠀⣸⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣄⠀⠀⢸⣿⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⢻⣿⡋⠉⢹⣿⣿⡿⠃⠀⠀⠀⠘⣿⡄
⢠⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⠈⢙⣻⣿⣿⣿⡿⠋⠁⠀⠀⣿⡆⠀⠀⢸⣿⣿⣿⣿⡀⠀⠈⣿⣇⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⢹⣷
⣸⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤⣀⣿⡇⠀⠈⠻⣿⠟⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣿⣿⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠘⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠉⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⢹⣿⡄⠀⢹⣿⣿⣿⡟⠀⠀⠀⣿
⣿⡇⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⡧⣼⣿⠀⠈⣻⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠃⢿⣧⣠⣾⣿⣿⣿⠃⠀⠀⠀⣿
⢹⣿⠀⠀⢻⣿⠿⠿⣿⣿⣿⣷⣤⣿⣿⣤⣶⣿⣿⣿⡿⠁⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢰⣿
⠘⣿⡆⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⢀⣾⡟⠘⣿⣆⠀⠀⠈⢻⡿⠋⠉⠉⠛⠛⠛⠋⢻⣿⠁⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣄⣀⣀⣀⣀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣶⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⡀⢠⠤⠤⢄⢠⠄⠠⡀⠖⡖⢲⣤⠖⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⡶⠆⣸⢸⠀⣷⠘⣾⠀⠀⠹⠆⡇⠘⢁⠎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⡌⠑⡎⢀⠬⣄⢹⣸⣧⣀⣀⣇⣰⣌⣇⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠖⠒⠒⠚⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⣸⠉⠙⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⠤⢤⠤⠤⢤⠀⠀⡏⠀⠀⣀⠀⠀⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⢀⠤⠃⢄⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⡀⠈⡇⠀⠀⡀⠀⢀⡁⠀⠀⣤⠀⠀⣿⠀⢸⠀⢆⠐⢍⡒⠃⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣇⠀⣿⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⡎⠀⠀⠑⠠⡈⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⢸⠀⠀⠤⠀⠠⡄⠤⠄⠤⠀⠠⡇⠀⡇⠀⠸⡉⠤⢃⠆⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠇⠀⠀⠘⠤⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠰⠀⠐⠆⠀⠐⡃⠐⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢶⠀⠰⠂⠐⠆⠒⠐⠖⠒⢺⠀⡎⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢸⠀⠘⠀⠐⠃⠀⠐⠂⠀⠛⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡇⠈⠉⠛⠓⠒⠓⠒⠒⠒⠒⠂⠀⠇⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⢄⡀
⠀⠀⠀⢀⡠⠤⠔⠂⠉⠀⠀⠀⣠⠤⠒⠉⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⣀⠠⠚⠀⠀⡠⠤⠖⠒⠀⠉⠉⠉⠉⠁⡄⠉⠉⠙⠒⠒⡆
⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⡏⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⢉⡠⠔⠂⠀⡰⠁⠀⠀⠀⠀⣀⣀⣀⣀⡰⠀⠀⠀⠀⠀⠀⡇
⠀⠈⡏⠩⠭⠭⣍⠉⠁⠀⠀⢱⠀⠋⠉⠉⠃⠀⠐⠁⠀⠀⢰⠀⠀⢸⣀⡠⠂⠀⠉⠁⠀⠀⠀⠀⡆⠀⣀⠂⡇⠀⠀⠀⠀⠀⠀⡅
⠀⠀⡇⠀⠀⠀⠁⠀⠀⢀⣀⣸⠀⠁⠀⠀⠁⠀⠈⠁⠀⠀⠚⠀⠀⠈⠁⠀⠀⠀⠃⡤⠤⠤⠤⠤⠤⠤⠤⠄⠇⠐⠂⠉⠀⠈⠀⡇
⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⡠⠄⠒⠒⠀⠋⠀⠒⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡃
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠔⣒⠭⠒⠊
⠀⠀⡇⠈⣀⣀⣀⣀⣀⣀⣀⣸⠀⠇⠀⠀⢠⠄⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⢀⣄⣓⣂⣀⣘⣋⠁⠤⠭⠥⠶⠒⠉
⠀⠀⠳⠤⠬⠤⠤⠤⠤⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠚⠉
⠀⡁⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢀⣉⣍⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠨⢉⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢘⠆⠀⠀⠆⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠀⣀⠒⠈⢌⡐⠂⠤⢀⣀⠠⣤⠼⠉⠠⠶⠏⣤⣀⡀⢐⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠉⠅⢘⡂⠸⠁⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣤⣠⠀⠐⢊⠓⠟⠇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠂⠀⠐⠢⠖⠚⡇⠀⠀⠀⠀⠀⠀⢀⠂⣅⡉⠉⢙⠃⠀⠀⠐⠛⠛⠉⠲⠦⠤⠀⡠⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠖⠒⠒⠠⠴⠀⡄⠸⠂⠀⠀⠀⠰⠤⠜⢃⣀⡀⠄⠤⣄⢰⢒⣋⡕⣒⠷⠶⣣⣅⣒⡦⠤⡁⠀⠉⠓⢈⡉⢄⠔⢒⠉⠉⡅
⠀⠀⠀⠀⠀⠃⠤⠀⠠⠼⠁⡅⠰⠦⣀⣀⣀⣀⣀⡠⢞⠈⠉⢈⠢⣿⠸⠀⠒⠨⠍⠛⠁⠀⠬⣁⡈⠉⠀⠍⠐⠽⢒⠉⢉⠩⢀⠀⠀⡇⡀⣠⢀
⠀⠀⠀⠀⠐⠣⠤⢤⡗⠟⠋⠭⣝⠄⠀⠀⠀⠀⠀⢀⡼⢄⠀⠀⡥⣴⠶⢄⠤⣠⣤⣀⣤⣄⣤⣄⡀⠀⠀⢀⣤⠤⠶⠎⣒⣩⡅⠖⠓⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣐⣀⣠⣆⣀⠀⠀⠀⣙⣰⠞⠓⠲⠒⢚⢭⢆⢲⠂⠀⠀⠀⠀⠈⠙⠙⠻⠽⠀⡠⠤⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⢪⡁⠒⠀⠐⡒⠂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠐⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⠈⡀⠢⠀⠘⡄
⠀⠀⠀⠀⠀⠪⠐⢇⠀⠳⠀⠘⠁⡀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⢄⠈⠣⠀⠁⠀⠀⠀⢄⠀⡀
⠀⠀⠀⠀⠀⠐⠂⠣⣄⠀⠀⠄⠐⠂⠠⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⡀⠀⠒⠠⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠆⠐⠶⠀⠠⠈⠉⠀⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠐
⠀⠀⠀⠀⠀⠀⠀⠜⠓⠚⠂⠠⠤⠀⢀⠀⠐⠀⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⠔⠁⡀⢁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠰⠆⠀⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⡀⠀⠀⢀⠜⣸⠠⠐⡡⠊⠀⣀⠌⠐⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠐⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⠀⠀⠀⠉⠉⠀⡰⠁⠄⠈⠀⠀⠀⠁⢀⣴⠁⠐⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢁⡀⠁⠀⠈⠁⠀⠁⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⢄⠀⠒⢀⠖⢨⡀⣀⡀⠀⠀⠁⠀⠀⠁⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠌⢠⠆⠑⠐⠒⡒⣄⢀⠆⠁⠀⢀⡤⠀⢀⠀⠁⠀⠠⠀⡀⠀⠀⠄⠀⠀⠀⠆⠀⣀⣀⣀⣀⠁⠜⠒⠚⠓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⠞⠀⠓⠈⠁⠉⠉⠀⠀⠀⠀⠘⠧⠞⠋⣹⠀⠀⠀⠀⠀⠀⠰⠀⠄⢰⠎⠀⣀⡀⠀⠐⠶⠦⠄⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠄⠊⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠉⢁⠤⠄⣀⡔⢁⣰⡧⠊⠀⠀⠀⠠⣈⡑⠈⠙⠢⠤⠤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⢀⣴⠒⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣪⠀⣠⢄⡀⠀⠀⠀⠶⠀⠀⠀⢤⠐⢀⡀⠙⠂⠀⠁
⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠘⢧⣹⡾⢏⡙⣧⠀⠀⠀⠀⠰⠄⣀⡠⠒⠉⠀⡃⠰⠊⡈⠐⠀⢊⠀⢀⠀⠒⠐⣆⠀⠉⡁⠀⠁
⠀⠀⠀⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠾⠛⠀⠀⠀⠀⢀⠔⢉⠀⠀⠀⣈⣴⢠⡎⡡⠐⡁⣸⠂⢠⠁⠹⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠁⠒⠤⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡨⠀⢀⠔⠊⠁⠀⠔⢃⠀⠃⠘⠃⡀⠁⠄⠃
⠀⠀⠀⠀⠨⠈⠀⠀⠀⠀⠉⠙⠋⠁⡀⠀⠈⠄⢀⡴⠁⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠑⠠⠒⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⢄⠨⡠⠆⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⢘⣀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠛⠛⠛⠉⠁

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢉⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠙⢦⠑⢄⢀⡀⠤⠤⠤⠤⡀⠊⣰⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢀⣀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⣈⣭⣭⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢠⣤⠤⠇⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⠶⢖⡃⠀⠀⠀⠸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠆⠀⣲⡧⣉⣿⢟⣃⣀⣀⣢⠀⠱⡀⠀⠀⠀⠣⣈⠀⠔⠄⠀⢀⡔⠁⡄⠀⠀⡠⠂⠀⠀⣞⠯⠥⠤⢪⣸⡆⣀⣀
⠀⠀⠀⠀⠀⠈⣇⢒⣟⣷⠴⢿⠒⠀⠳⣖⣻⠀⠀⠸⢄⡀⠀⠀⠀⠈⢑⣐⣘⡉⠔⠃⠀⠠⠊⠁⠀⠀⠀⡯⠉⣀⣹⣹⣽⡆⢲⣳⡇
⠀⠀⠀⠀⠀⠀⠧⠬⣯⣿⡘⣺⡭⠈⣏⣉⣽⡦⠀⠀⠀⠉⠀⠀⡀⣄⣀⣀⣀⣀⠀⠀⠀⠠⠀⡂⠀⠀⣀⣹⠂⢰⢶⡖⣺⡇⠨⢷⡦⢤⠄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠞⣛⠉⠉⠀⢳⢤⣤⣈⣂⣀⣼⢿⣇⡐⠐⠐⠑⣈⡐⠁⠐⣇⠒⠠⠰⠒⣺⣯⠿⠗⠚⠛⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠂⠤⠴⠧⣣⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⠉⠉⠀⠐⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣲⡟⣾⣹⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠚⠙⠁⣉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠦⠤⢤⣯⣛⣒⣦⣄⣀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣠⠤⠴⠖⠒⠚⠛⠛⠉⠉⠉⠙⣆⠈⠉⠉⠛⣿⠲⢤⣀⠀⠀⢀⡴⠒⠒⢦⡀⠀⠀⣰⢊⣍⡈⠙
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣤⣀⠀⠀⡟⠀⠀⠈⠙⡆⢾⠀⠻⣤⠀⡷⠀⠀⣇⠉⠧⡟⡲
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠴⠶⠖⠛⠛⠀⠀⠀⣿⠘⠛⠀⢰⠷⣷⠀⠀⡼⠁⠈⠦⣄⣡⠔⠃⠀⠀⠈⠲⠤⠭⠕
⠀⠀⠀⠀⠀⠈⡇⠀⠀⣴⡟⠉⢙⣷⠄⠀⠀⣿⣿⠄⠀⣾⡄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⣙⣛⣉⣁⠀⠀⠀⣿⠁⠀⣸⠛⠁⢀⡼⠁⡠⢒⡒⠢⡄⠀⠀⡼⢡⡀⡶⡌⢣
⠀⠀⠀⠀⠀⣠⢾⠀⠀⢸⣯⣀⣀⡽⢃⡴⠲⣿⠆⢠⡇⠀⢀⠞⠀⢰⠡⣽⡕⡲⢸⠀⠀⢳⡀⠇⠓⢃⡜
⠀⠀⠀⠀⣸⡷⢟⣋⣭⠭⠭⣭⣍⣓⡚⠧⣤⡏⠀⡞⠀⣠⠏⠀⠀⠀⠳⢄⣉⡥⠋⠀⠀⠀⠉⠓⠚⠉
⠀⠀⠀⢠⣏⠔⠋⠁⠀⠀⠀⠀⠀⠈⠉⠓⠦⣍⠻⣅⡴⣇
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⣿⣸⠀⢠⠞⢩⡍⠳⡀
⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⡟⠀⠘⣆⠘⠀⣠⠃
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠉⠉
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⢠⡟⠹⣇⠀⢠⡿⠉⣷⠀⠀⠀⠀⠀⣀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣧⣤⣀⡿⠁⠀⢹⣶⠟⠀⠀⠸⣇⠀⠀⣠⠾⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⢦⣤⣠⣿⠀⠘⠿⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⢿⡶⠟⠁⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⣴⢻⠉⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠛⠛⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠞⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣠⡽⠼⠂⠀⠀⠓⠒⠛⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡦⠀⠀⠀⠀⢠⢹⠀⠀⠀⢀⣤⢦⡄⠀⠀⣶⣚⡹⠋⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⣸⠘⣿⠀⠀⢿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⢇⠘⡄⠀⠀⠀⠉⠙⠃⠀⠀⠈⠉⠅⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡷⠀⠀⠀⠀⠘⢦⣙⢦⣀⣀⣀⣀⣀⠀⠀⢀⣤⣄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠐⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⠹⡆⠀⠈⠷⡌⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠻⠧⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⢧⠿⠃⠀⠀⣰⠃⠀⠀⠀⢀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡟⠀⠀⠀⠀⠀⠀⣀⢤⠔⠒⠚⠛⠁⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢹⠀⣇⠀⠀⢀⣀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠶⢲⣶⠀⠀⠀⠀⠈⠦⠭⠿⠛⢯⠹⡆⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣉⣉⠭⠏⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⣿⠀⠀⣀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠛⠶⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠞⠉⠀⢻⣆⠀⠀⢀⣴⢶⡀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⢻⣆⣰⠟⠁⠀⠹⣦⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⠻⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣿⣷⡄⠀⠀⣠⣶⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⣉⣉⠉⠀⠈⠉⠉⠉⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⢠⣴⣶⣶⣦⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⢠⣿⣿⣿⣿⣿⣷⠀⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠙⠛⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠛⠻⠿⠽⠿⠷⢾⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠭⠿⠿⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣤⣤⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⣭⡭⠭⣭⣭⠭⢭⣭⣭⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣯⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⣀⣿⣿⣀⣠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⡀⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⡿⢂⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣎⠿⠛⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣀⣤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⠶⠋⠫⣭⡁⠀⠀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⣃⣇⣮⣿⣦⠄⠈⢷⡀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⢧⣄⣆⠈⢧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⡾⣈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠛⠳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡤⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠛⠁⢠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉⠀⠀⠀⠀⠀⣻⣦⣤⣴⣿⣦⣤⣤⣤⣀⠀⠀⠀⠀⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⣠⣴⣿⡿⠿⣿⠛⠛⠻⣿⡋⠛⠛⠃⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠹⣧⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⢹⣧⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣤⣤⣤⣤⣤⣼⣿⣶⣶⣾⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⢿⡏⠉⠹⣿⠉⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⣿⠀⢸⡿⠀⠀⣀⣾⡿⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⠀⢸⡟⠀⣾⣧⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡈⠳⣄⡋⣐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⡿⢿⡿⠛⠉⠁⠀⠀⢀⠀⢸⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡈⠻⣷⣤⡿⠓⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣾⠃⠀⠀⠀⠀⠀⠸⠀⠈⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣌⠙⠿⣶⣍⣩⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠙⠷⣦⣌⡉⠻⠶⢯⣤⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣉⣉⣛⣻⣶⣯⣤⣞⣭⣿⣉⣉⣩⣡⣄⣠⣤⣴⠶⠟⠛⠫⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⣤⣬⣭⣍⣉⣁⡀

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⣶⠶⣶⠶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⢀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⢀⠀⢐⣾⡟⠻⣿⡆⠠⢀⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡠⠉⠀⣀⠀⠀⠀⠀⠤⠐⡀⢀⡀⠐⠈⠀⠀⠸⣿⡷⠘⣿⡟⠀⠀⠀⠂⠀⣀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠂⠀⠀⠀⠠⠍⢀⠀⠀⠀⠤⠉⠿⠾⠋⠄⠀⠀⠀⠀⠀⠠⠀⠲⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⢾⡓⠀⠀⠀⠀⠀⠈⠢⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠂⠀⠀⠀⠀⠀⠐⠾⠇⢀⠄⠀⠀⠀⠀⠀⠀⠘⠈⠉⠀⠀⠀⠀⠀⠁⠁⠈⠀⠈⠁⠀⠈⠉⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀⣀⠞⠁⠈⠀⠀⢀⡀⢀⠄⠐⠀⡋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡉⠀⢹⠀⠀⠀⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠒⡁⠀⠠⠈⠉⠂⠐⠀⠄⠀⠤⡀⠀⡸⡇⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢄⠀⢠⠤⠠⠤⠇⠀⠀⠀⠀⠀⠘⠠⠤⠤⠤⠄⠀⢠⠤⠤⠤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠘⠀⠘⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠐⠀⠚⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⣾⣀⠈⠉⡹⠁⠒⠐⠒⠒⠂⢠⠒⢻⣿⡉⠉⠉⢉⠉⠉⠀⠒⠒⠈⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣬⣀⠠⠄⠀⠀⠀⢀⣁⣀⣀⣙⣿⣤⡤⠃⠀⠀⣀⣀⣀⣐⣋⣀⣈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡶⠶⢶⣷⣶⣤⣬⣭⣿⠿⠿⠿⣿⣻⣿⣯⣭⣭⣭⣽⣿⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣻⣿⣭⣭⣭⣿⣿⣿⣛⣛⣛⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⢒⣈⠩⠄⠰⡀⣻⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⢐⣂⡩⠥⠤⣒⡀⠉⠀⠀⠀⠀⠀⠑⠂⠒⡈⡀
⠀⠀⠀⠀⢀⡀⠠⠄⠐⣂⡉⠭⠀⠒⢊⠜⠉⢀⣴⣄⣀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⢁⢹
⠀⠀⠀⠘⡀⠰⡀⠪⠁⠀⠀⠀⠀⢠⠃⠀⢠⣿⠻⣯⠙⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⡈⡆
⠀⠀⠀⠀⢃⢀⠥⠊⠀⠀⠀⠀⠀⡆⠀⠀⠈⠻⢶⣿⣦⣄⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢡⢠⡀
⠀⠀⠀⠀⠈⡈⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⣯⠙⣿⡄⠀⠀⠆⠀⠀⠀⠀⢀⠔⡈⠀⣽
⠀⠀⠀⠀⠀⢡⢡⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠠⣦⣤⣿⣶⠟⠁⠀⠜⠀⠀⠀⠀⣀⠨⠄⠘⢀⣸
⠀⠀⠀⠀⠀⠘⡄⡄⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠉⠙⠃⣀⡤⠪⠄⠒⣂⠉⠥⠀⠒⠈⣉⡁⢸
⠀⠀⠀⠀⠀⠀⣧⠰⠐⠠⡀⠀⠀⠀⠀⣀⠀⠤⠙⣛⣉⣭⣤⠖⠂⢉⠍⠀⠀⠀⠀⠀⠈⠠⣆⠘
⠀⠀⠀⠀⠀⠀⢸⡄⠘⠆⠐⢒⣀⠩⠄⠐⠲⣈⠉⠉⠉⠛⠁⣀⣴⣂⢀⠠⠤⠀⠐⢒⣈⡀⢡⢤⠃
⠀⠀⠀⠀⠀⠀⢸⡗⢲⠈⢫⠀⠀⣀⡀⠀⠤⠄⠑⠒⣒⣈⣩⠭⠄⠀⡲⠂⠈⠉⠁⠀⠀⡀⢸⢸
⠀⠀⠀⠀⠀⠀⢸⢃⢀⣃⣈⠩⠥⠀⠀⠒⠀⠓⢍⣀⠀⠛⢀⣀⠤⠊⠀⠀⠀⠀⠀⠀⡎⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠸⠤⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠥⠬⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠶⢶⣦⣤⣀⡈⠉⠉⠉⠒⠒⠶⣦⠀⣴⢒⣲⠤⣤⣤⠞⡩⠞⢑⡘⡜⣧
⠀⠀⠀⠀⠀⠀⠀⡴⠁⢸⡿⢀⣴⢀⠂⠭⢙⡛⠿⠷⣶⣭⣷⣃⣿⣿⡟⣁⣸⡼⢋⡥⠊⢀⡤⢶⢾⣙⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣼⠃⠎⠀⠀⠀⠀⠈⠐⣢⠬⢙⡛⠿⢿⣷⣴⣋⡴⠋⢤⠀⢸⡆⣠⠟⢠⡼⠊⣳⡆
⠀⠀⠀⠀⢀⡀⠀⢀⣾⠏⣼⠏⠌⠀⠀⠀⠀⡀⠄⣀⣤⣥⣶⣄⡉⠒⠢⢍⣛⠻⠷⣶⣥⣄⣠⣴⠞⢉⣠⣾⠟
⠀⠀⠠⣴⣿⣟⣷⡿⢃⡾⢃⠎⠀⠀⠀⣠⡊⢠⠞⠉⡤⠔⠂⠤⡉⠳⣄⠀⠀⠉⢔⠲⠬⢍⣙⠛⠳⠿⢿⣥⣄⡀
⠀⠀⠀⠈⣹⡿⠋⣰⠟⡡⢃⣤⠶⣦⠌⠛⠁⢿⣄⠘⠲⣤⣙⠻⢎⡂⠘⡇⠀⢀⡀⠀⠀⠁⠐⠈⠋⣶⢢⠀⢠⣿⣿⣶⠄
⠀⠀⢰⣾⠋⢠⡾⡫⠊⠀⣾⠁⣠⡿⠠⠀⠀⠲⣭⣻⣶⣄⡉⠳⣦⠃⢀⡇⢀⣯⠇⠀⠀⣠⡄⠀⡐⡱⠁⣰⡿⣿⣿⡟
⠀⠀⣸⣏⣀⠀⠬⢤⣄⣀⠛⢛⡋⠀⠀⢴⣄⡈⠪⢙⣛⡡⠛⠀⡸⢀⡼⢡⣿⠏⠀⣰⠏⣹⠇⡀⡜⠀⣼⣯⣿⣿⡟
⠀⠀⠈⠻⢿⣿⡿⣶⣦⣌⣉⠒⠯⣗⢤⡈⠫⣛⠳⠶⠤⠤⠴⣚⡵⣊⣴⠟⠁⠀⠀⠙⠛⠁⢘⡜⠀⣼⣿⣿⣿⡟⢀⡠⡀
⠀⠀⠀⠀⠀⢍⡻⢶⣌⡙⠻⢷⣦⣌⡙⠺⣗⡤⣉⠚⠡⠤⠭⠴⠞⠋⠁⢀⣠⣀⠀⠀⢀⢊⠎⢀⣼⣿⢿⣿⡟⠀⠈⠁
⠀⠀⠀⠖⣩⣶⣬⣀⣈⠙⠳⢦⣌⡛⠿⣶⣤⣉⠓⠯⣗⡦⢄⡀⠀⠀⣰⡏⠉⢻⠀⡔⡱⠃⣰⣿⠟⣡⣿⡿⣻⣳⣶⠂
⠀⠀⠀⠀⠀⣈⠉⠛⠻⠿⣷⣦⣌⠙⠲⣤⣙⠻⢿⣶⣤⣉⠓⠮⢅⡀⠙⠷⠖⢡⢎⠎⢠⣾⡿⠋⣴⣿⣿⢟⡖⠉⠃
⠀⠀⠀⠀⢠⡟⠭⠭⠭⠭⢽⣛⣛⣿⣶⣤⣉⠛⢶⣬⣙⠻⢿⣶⣤⡈⠓⠮⡀⡱⠃⣴⣿⠟⢡⣾⣿⢟⣵⣿⣿⣿⡀
⠀⠀⠀⠀⣼⢧⢡⡖⠀⡠⠄⣤⡀⢈⠭⠛⢛⣷⣶⣬⣽⣿⣶⣮⣝⣿⣷⣦⣀⣀⣾⠟⠃⣰⡿⢋⣵⣿⣿⠟⢡⣿⠁
⠀⠀⠀⢠⡿⡄⠛⠇⠀⠣⠾⡫⠞⢁⣤⡾⠛⠛⣿⣶⣦⣭⣙⠻⠿⣿⣿⣿⣿⣿⣷⣶⡾⢋⣴⣿⣿⠟⢁⣴⠟⢻⣧
⠀⠀⠀⠾⠷⠿⠷⠶⠶⡶⠊⣠⣶⣿⣯⡶⠾⢛⡭⠢⠄⠙⠻⢷⣦⣄⡙⠃⠀⠉⣙⢉⣴⣿⣿⡿⠃⣴⣿⠿⠾⠷⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡈⠛⠿⣶⣦⣄⣉⣉⠛⠛⠋⣠⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣯⣽⠿⠂⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣶⣿⣶⣤⣤⣤⣄⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣥⠐⣯⣿⡟⣛⣛⡛⠛⠛⠙⠛⡁⠙⣛⠛⠓⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣽⣛⣿⣖⠛⢷⡀⠀⠀⠀⢀⡔⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡄⢨⣷⠀⠀⢀⣾⣟⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⢿⣷⣿⣷⡘⣿⡇⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢉⣉⣻⣿⣿⣷⣿⣿⣿⣷⣌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠟⣻⣿⣿⣽⣏⣋⣉⣈⣡⣤⡶⢐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡉⠀⢠⣾⣿⣿⣿⣿⣿⡟⣽⠁⠘⣿⣷⡄⠑⠝⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⠏⢠⡿⠀⠀⠈⠻⠙⠆⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠏⠠⠈⠂⢰⡆⣸⡇⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣿⠃⠂⠀⣠⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣯⣿⡏⠀⠀⣸⣿⣿⢿⡇⣿⡿⡿⠿⠇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⡇⢠⠀⢹⣿⣿⣷⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣿⣿⣿⣿⢱⡀⡀⠈⢻⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠿⢿⣿⣿⣿⣽⣇⡀⠀⠀⠃⢸⣿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⠉⠉⠉⠉⠉⠀⠠⢶⣼⣿⠀⣿⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢘⣫⣟⣿⣟⣿⣷⣾⠠⢶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣿⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣄⣤⣹⣹⣿⣿⣛⣿⣿⣶⣶⡄⠁⢂⣈⡤⣤⣶⣾⡙⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⢀⣄⣤⣤⣤⣤⣽⣿⢿⣿⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿⣷⠾⠋⠁⠀⢸⣿⣿⣇⠺⡿⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣴⣮⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣤⡴⠶⢶⣶⣿⣿⣿⣯⡝⠂⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣤⣤⣤⣄⣀⣠⠀⠉⠛⠻⠗⠊⠉⠀⠀⠀⣀⣤⠉⢻⣿⣿⣶⠀⣀⠽⣧⣤⣀⣀⡀⠨⠀⠀⠀⠀⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠐⠛⠻⠿⠿⠿⣿⣿⣭⣯⣟⣿⣿⣶⣶⣤⣤⣠⣤⠖⠋⠁⢀⣀⣸⣿⣿⣿⣯⣴⢊⠳⠻⠿⡿⠐⠒⣀⣮⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠻⣶⣦⣤⣀⣀⣀⠀⠊⠉⠉⠉⠛⠛⠿⠿⣿⣿⣏⣠⣤⠶⢚⣋⣹⣿⢿⣿⣿⣿⣿⣿⣏⣻⣻⣿⠂⣻⡿⠟
⠀⠀⠀⠀⠀⢺⣿⣯⣭⣍⣛⣿⣿⣷⣦⣤⣤⣀⣀⠀⠀⣀⣹⡯⠵⠖⠚⠋⢉⣉⠏⠀⠈⠉⠉⠉⠉⠉⠉⢉⣿⣁⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⡟⠀⣀⣠⠶⠒⠋⠉⠀⠀⠀⠀⠀⣻⠢⣤⠤⠀⣸⠷⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣿⠃⢀⣉⣿⣂⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⣿⡁⠨⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣾⡶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠉⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⣀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠿⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣂⠤⠀⠤⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠿⠿⠿⠿⠿⢷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⠉⢀⣀⣤⣤⣤⣤⣤⣄⣀⠈⠙⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣿⡆
⠀⠀⠀⠀⠀⠀⣸⣿⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠁⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⢀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣄⠈⠙⠶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠉⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⡈⠉⠙⠛⠛⠛⠛⠉⠉⣀⣠⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢷⣶⣶⣶⣶⠿⠿⠟⠛⠉



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