Among Us Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠉⠉⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣄⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⣿⡏⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠈⢻⡿⢶⣦⣤⣄⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣀⣀⣀⣀⣀⣤⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣴⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠉⠉⠉⠉⠉⠛⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠉⠉⠙⠛⠒⡒⠦⢄⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠚⠉⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠳⣄⣀⡀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠛⠋⠉⠉⠉⠉⠉⢙⡟⠛⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠈⢳⣄⣀⣀⣀⣠⠤⢾⣦⣀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⢀⡞⠹⣄⠀⠀⠀⠀⢸⡀⠈⠉⠛⠓⢲⡾⢯⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⡴⠋⠀⠀⢘⣦⠤⠴⠖⠻⡟⠓⠒⠒⠒⡿⠶⢤⣄⣉⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠲⢦⣶⣋⠀⠀⢀⣠⠏⢹⣆⣤⣤⣶⣷⡶⠶⠶⠾⠷⢶⣶⣶⣤⣥⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢸⡇⠈⠛⣶⡋⢀⣴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣸⠀⠀⠀⡏⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣼⡇⠀⠀⠀⡿⠀⠀⢠⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⣠⡿⠻⣄⠀⠀⠀⣿⡇⠀⠀⢠⠇⠀⣠⣾⣤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣰⡿⠁⠀⠘⣆⠀⠀⣿⠟⢷⣦⣿⠚⠋⠙⢧⡀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⢀⣿⠃⠀⠀⠀⢹⣄⣴⣿⠀⠀⠈⠻⣷⣄⠀⠈⣧⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠋
⠀⠀⠀⢸⡟⢷⡀⠀⢀⡼⠿⢤⣿⠀⠀⠀⠀⠈⢻⣦⠀⣹⣠⠖⠋⠙⠿⣶⣤⣤⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣤⣴⡶⣿⣿⣿⡀
⠀⠀⠀⣼⡇⠀⢷⣠⠏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⣷⠛⠓⢦⡀⢀⡾⠁⠈⢩⠟⠛⠛⠛⢿⠛⠛⠛⠛⢯⠉⢁⣼⠟⠁⣿⡆
⠀⠀⠀⣿⡇⢀⡼⠳⣄⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢳⣿⣄⣀⢠⡏⣀⣀⣀⡀⢸⣀⣠⡤⠤⠬⣷⣾⠏⠀⠀⣿⡇
⠀⠀⠀⣿⣇⡞⠀⠀⠈⠳⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣰⠏⠀⠀⢉⡟⠉⠉⠉⠉⠉⢹⡏⠀⠀⠀⠀⣾⠏⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡿⣄⡀⠀⠀⠀⠹⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⢸⠁⡔⢠⣆⣴⣦⢸⡇⡆⠀⠀⢸⡟⠀⠀⠀⠀⣿⠃
⠀⠀⠀⢻⡇⠀⠻⣄⠀⠀⣠⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠓⠲⢤⣟⣀⣧⣸⣯⣿⣟⣼⣧⣧⡤⠤⣿⠇⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣧⠀⠀⢹⡄⣴⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡏⢡⠞⡟⣿⣿⣿⢿⡿⡄⠀⠀⣿⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠈⣿⡀⠀⠀⡿⠁⠀⢸⣿⣶⣶⣦⣤⣤⣀⡀⠀⠀⣿⡀⠀⠀⠀⡇⢸⠈⡄⣿⣿⣿⢸⡇⡇⠀⢸⣿⠀⣀⣠⣤⣼⣿
⠀⠀⠀⠀⢹⣧⠀⣸⠋⠛⠲⢼⣿⠀⠀⠀⠈⠉⠙⡿⢷⣾⣿⠉⠉⠓⠶⡧⠴⠶⠖⠺⠿⠧⣼⡶⠶⠒⠛⣿⠿⠛⠉⠁⣸⡏
⠀⠀⠀⠀⠀⢻⣷⡇⠀⠀⠀⠈⣿⠷⣶⣦⣤⣤⣴⣇⣀⣈⣉⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣾⣠⣤⣤⣤⣴⣶⡶⠿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣿⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⢉⣉⡉⠁⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⣿⡿⠿⠟⠛⠋⠁⠀⠀⣀⣠⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡆⠀⠀⠀⣿⣷⣶⣶⣶⡶⠶⠿⠛⠛⠉⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠉⠛⡟⠛⠿⠿⠿⠛⠛⠛⠋⣿⡇⠀⠀⠀⣿⡇⠀⢀⣀⣀⣤⡤⠤⠤⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠙⠳⣼⣇⣤⠤⠤⠤⠤⣤⣀⣀⣿⠃⠀⠀⠀⢹⡷⠛⠉⠁⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣼⣀⠀⠀⠀⣀⣀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠈⠻⠿⠶⠶⠶⠶⠿⠛⠉

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⢀⣠⡴⠋⠓⢄⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀
⠀⠀⠀⢰⢋⣀⡤⣵⣄⠀⠀⢠⠔⣋⣠⣥⣿⡀⠀⠀⠀⢀⣤⣼⣤⣼⡀⠀⠘⠴⣗⠂⠊⢉⢱⠀⠀⠀⠀⡏⠀⠁⣠⣘⠄
⠀⠀⣀⡟⣡⠒⠛⠻⣆⠀⠀⢈⡿⢡⠖⠓⠻⢆⠀⠀⢀⣸⢉⡖⠒⠚⢧⡀⠀⢀⡾⢩⠟⠓⠻⣆⠀⠀⠀⣱⢺⠟⠒⠻⢦
⠀⢸⠉⡇⠘⠤⠤⠤⡏⠀⢸⠉⡇⠘⠦⠤⠤⡞⠀⢀⡏⣽⠈⠧⠤⠤⢼⠁⢸⠉⡇⠘⠦⠤⠤⡞⠀⢰⡏⡿⠘⠧⣤⠤⣼
⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⠀⢀⡇⠀⠸⡇⣿⠀⠀⠀⠀⣸⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⢸⡄⡇⠀⠀⠀⠀⢸
⠀⠈⠛⡇⠀⡶⡆⢠⠇⠀⠈⣿⠳⢤⡤⣄⡘⠲⣄⠀⠙⢻⣄⠀⣴⣾⠁⠀⢨⡟⠓⢠⠤⠤⡖⠛⡆⠀⢱⠗⠂⢐⡦⢴⠋
⠀⠀⠀⠙⠚⠁⠈⠉⠀⠀⠀⠈⠓⢋⣀⠀⠙⠲⠚⠀⠀⠀⠹⠧⠏⠁⠀⠀⠈⠓⠒⠋⠀⠀⠙⠖⠁⠀⠈⠛⠛⠙⠒⠚
⠀⠀⢀⡔⠚⣙⢢⠀⠀⠀⠀⠀⡠⠞⠚⠳⣄⠀⠀⠀⠀⠀⣠⣶⠦⣀⠀⠀⠀⢠⣠⠓⠚⡄⠀⠀⠀⠀⠠⡖⡏⠉⢱
⠀⢠⣾⠖⣻⠿⠿⣦⠀⠀⠀⠀⡧⣲⠭⠷⣾⡀⠀⠀⠀⢸⢳⡴⠮⢿⣄⠀⠀⠀⣷⢊⡭⠭⢷⣄⠀⠀⠀⢳⠟⣢⠾⢽⣦
⠀⡖⣿⠘⣇⣀⣀⣸⠇⠀⡴⢺⠇⢧⣀⣀⣀⡗⠀⢠⠖⡿⠸⣆⣀⣀⣸⠂⢠⠖⡇⠸⣄⣀⣀⣸⠀⠀⡖⢺⠀⣇⣀⣀⣈⡇
⢸⡇⣿⠀⠀⠉⠁⢸⠀⠀⡇⢸⠀⠀⠈⠉⠈⡇⠀⢸⠀⡇⠀⠈⠉⠁⢹⠀⢸⠀⡇⠀⠈⠉⠁⣿⠀⠀⡇⢸⠀⠀⠉⠉⢸⡄
⠈⠧⣿⠀⢠⣄⠀⣸⠀⠀⠳⣼⣄⠀⠀⠀⠾⣅⠀⠘⠦⢧⡀⠀⣤⣤⠋⠀⠘⡦⢧⠀⣀⣀⣠⠿⡄⠀⠣⣼⣄⠀⣄⣀⡸⠃
⠀⠀⠹⠤⠼⠘⠶⠋⠀⠀⠈⠳⠤⠟⠉⠙⢦⣈⡗⠀⠀⠘⢿⣀⡟⠛⠀⠀⠸⢧⣤⠜⠁⠈⠳⣤⠟⠀⠀⠧⠤⠴⣧⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢛⣛⣹⣿⠿⠶⠶⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠋⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⣠⠒⠁
⠀⠀⠀⠀⠀⠀⣠⠤⠖⠂⠤⣀⠀⠀⠀⠀⠀⣨⣿⣽⣗⣰⠪⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⡰⢋⣠⣤⠦⣄⣀⠀⠳⡀⠀⠀⡼⠛⢫⡉⠛⠻⢷⣬⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡞
⠀⠀⠀⠀⢟⠁⠀⠈⢳⣄⠈⠂⠀⢱⠀⢸⢣⡄⠀⠱⡀⠘⡶⠛⣷⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠁
⠀⠀⠀⠀⠸⡀⠀⠀⠀⣹⡄⠀⠀⠀⠓⠺⢾⢼⡆⠼⠻⡀⢠⠀⠘⣷⠈⢇⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠰⣁⣠⡘⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⡷⣀⣠⠤⠥⢹⡄⠀⠀⠣⡤⠨⠯⢊⣐⣼⠋⣸⣧⠀⢸⣧⠘⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠤⠀⠀⠀⡟⠉⣧⡷⠀⠀⢀⣀⣤⣼⡿⢦⡀
⠀⠀⠀⠀⢀⡟⠉⠁⠐⠂⠀⠙⠦⣤⣀⣠⡠⠴⠿⣿⢷⣿⡿⠛⠇⢸⣿⢀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⠃⠠⠤⠤⠶⠚⠋⠉⠁⣀⠀⠄⠙⢦
⠀⠀⠀⠀⡎⠹⠀⠀⠀⠀⠀⠀⠐⡡⠊⠁⠀⠀⠀⢀⡀⠈⣱⠓⠄⢸⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢰⡇⠒⡔⢪⠛⠉⠒⠂⡾⠀⠀⠀⣀⣀⣀⠀⠙⢿⡏⠀⢀⡟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠘⡇⠘⠀⡇⠀⠀⠀⠀⣷⠀⠀⠋⢸⣿⡟⠳⠶⠋⣈⡷⢋⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢃⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠙⢆⠀⠸⡀⠀⠀⠀⢻⡀⢀⡀⠀⣿⠛⠳⠿⠿⠛⠊⠉⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⠂⠀⢹⠀⣸⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠑⢤⡙⡄⠀⠀⠀⠱⣄⠑⢄⠈⠒⠲⣤⣤⠤⢤⠤⠤⠶⠒⠒⢛⠉⡅⢸⠀⠀⠀⠀⣀⠴⠛⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠙⣼⡀⠀⠀⠀⠈⠑⠤⣑⣤⠀⠈⢳⡀⢸⠀⠀⠀⠀⠀⢸⣄⡅⣨⣤⣴⣞⡫⠽⠒⠂⠈⠛⢿⣶⣼⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⡇⠀⢰⠇⠀⠀⠀⠈⢹⣧⡀⢠⡇⠈⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⢿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⢀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠤⠞⠀⠀⠀⠀⠀⣼⣉⣿⠜⠀⠀⠀⠀⠠⠖⠋⢡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠸⠳⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠈⠋⠙⠒⠶⠶⠦⡄⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⡆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⡴⢶⡄⢰⠇⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⠀⠀⠀⠏⠸⣦⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⢇⢰⠀⠹⣆⠀⢠⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⡇⢸⡇⡞⠀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠳⡀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠸⠈⢆⠀⡈⢳⡎⠳⡄⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠙⠛⢱⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠂⠘⣆⠀⠸⢤⢠⡇⠀⠀⢰⠙⣿⠀⠀⠀⣀⣴⣍⢆⠀⢸⠀⠀⣀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠰⠀⠈⠣⡀⠀⠛⠻⣄⠀⢸⠀⢻⠀⣠⠞⠛⣄⣼⣼⠀⠸⡆⠀⠘⢿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠂⠀⠘⠢⡀⠀⠈⢳⡌⡆⢸⡆⡇⠀⡴⠋⠉⠁⠀⠀⢳⠀⠀⠠⠉⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣

⠀⡄⣀⠀⡄⡄⠠⢠⠀⡀
⠈⢁⠈⠆⢠⠁⠀⠘⢀⡇⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠁⠀⠈⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢉⣁⠀⠀⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠛⠛⠛⠛⢷⡄⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⣤⣤⣤⣴⠟⠁⠀⠀⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠶⠶⠶⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣀⣀⣠⣤⣤⡄⢠⣄⣠⣤⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢲⣞⣲⡄⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠉⠉⠛⠛⠻⠶⢶⣶⠶⠶⠒⠁⠉⠬⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣤⣤⢤⣤⠀⠀⠀⠀⣿⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⣿⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⣶⣾⡇⠀⣿⣀⣀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠞⠛⠛⠛⠛⠛⠳⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⠋⠁⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡏⢂⡀⢄⣀⠀⡄⠀⠉⠀⠀⠀⠀⠀⠀⢰⡦⢠⠖⢁⠦⣹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⡶⣌⠣⡐⢄⡈⠻⢇⣠⣆⠀⠀⠀⢠⠦⣀⠸⠚⠁⠔⢡⠔⡡⠎⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠐⠀⠛⢳⣌⠃⢼⠒⠤⢀⢉⣁⠀⢈⢁⡁⣤⠐⣊⠥⢘⣡⠾⠓⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢁⡒⠘⠀⠧⠴⠀⠂⣘⣀⣄⡂⣁⣀⡀⡀⢀⠠⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣥⣤⠴⠶⠒⠂⣀⣀⣩⣍⣭⣡⣴⠶⠟⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠻⠶⢦⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡴⢒⣪⣥⡴⢶⠛⠊⠊⢏⣉⣀⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⣠⡶⠯⠃⢅⣠⡄⣺⡾⠧⠞⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠏⢦⣠⠧⣼⠗⢋⣉⣠⠶⣿⡇
⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣿⣸⢦⣠⠖⣉⣤⣞⣫⠙⣝⡦⢹⡇
⠀⠀⠀⣠⣾⡯⠥⠤⠂⣼⣏⣠⠚⣡⡶⣅⢲⠈⠿⠆⢘⠁⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⣼⠛⠛⠤⠶⠶⠷⢿⡟⢡⢾⣍⢷⡈⠟⠁⣠⣴⡾⠟⠋⠉⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁
⠀⢰⣿⣁⣲⠒⠐⣶⡦⣾⣷⣡⢣⠈⠃⠁⣴⡿⠛⠁⠀⡀⣥⣼⠇⢹⣏⠛⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠶⠛⣋⡽⢻⡄
⢀⣿⢁⣟⠉⣧⣾⠋⣳⣾⣧⠉⠋⠁⣸⡿⠋⢰⡟⢶⣦⡀⣻⠟⠀⢀⠉⠻⠦⡴⠷⠿⠉⣹⠿⣯⣭⣭⠉⠀⢠⣤⣤⣾⡏⠀⢸⡇
⢸⡿⣿⣷⣾⠌⢙⣷⡏⣼⡿⠁⣰⡿⠋⠀⡂⣼⡇⢀⠛⠻⠏⢀⣀⡄⠀⣴⠖⢶⠶⠀⢠⡤⣀⡈⠙⠿⢄⣰⠟⠋⠁⠀⠑⠀⢸⡇
⣸⣟⣏⠀⢹⣦⣟⠹⣅⣸⡇⣾⡟⢡⠶⢶⣦⣹⡁⠀⣁⠔⠾⠇⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠁⠐⣦⣄⡉⠂⢀⡀⠀⠀⡀⢸⡇
⣿⠁⡗⣤⣼⢩⢿⣾⠋⣿⣷⡟⢠⢸⣆⣀⡥⠈⣠⡞⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣄⣀⠀⠀⠀⢀⠐⠘⠛⢀⣄⠙⢷⡎⠁⢸⡇
⣿⢠⠋⠈⣹⣤⡋⢿⡔⣿⡟⠀⣢⣀⣸⠏⢠⡌⠀⠀⠀⠂⡠⢄⠀⠀⠀⠀⠀⠈⠁⠐⠀⠚⠐⠂⢄⡀⠀⠀⠈⠍⣶⡀⠱⡀⢸⡇
⣿⡜⢆⣰⠃⠸⣧⣤⡷⣿⠁⢎⠉⢫⠄⢠⡏⣅⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠄⠀⠀⣧⣄⠀⡀⠂⠙⠀⡈⠀⠀⠀⢠⣆⠈⣸⡇
⣿⡷⠊⠹⣬⡆⠀⡝⠀⣿⣦⠼⢗⠀⢀⡉⠀⠀⢁⡀⠀⠀⢠⠀⠈⢋⠁⠀⠐⠀⠀⠀⡁⢌⡾⠁⠀⡀⠄⠀⠀⠀⠀⠀⠼⢆⢸⡇
⢸⣇⣦⣴⠁⢳⣤⣴⠦⣿⣡⣶⠞⠁⣌⠁⢀⠀⠘⠀⠁⢄⢠⡀⠀⠀⢂⠀⡄⠀⠀⠀⡇⡞⠀⠀⢰⢡⣰⠤⠚⡂⠀⠀⠀⣠⣾⡇
⠘⣷⠉⠸⣄⣠⣟⢻⡀⣿⢧⣀⠘⠀⠉⠀⡀⠀⠄⠀⡄⠀⠙⢧⠀⠀⠈⠆⠂⠀⠀⠀⣟⠁⠀⠀⣯⠞⠁⢀⡜⠀⠀⠀⠐⠢⣿⡇
⠀⢹⣇⣾⢻⣧⢤⣴⣥⣿⡆⠻⣄⠀⠗⠀⠁⠘⠁⠈⠐⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⡜⠁⠀⠠⠓⠙⠉⠃⠐⠂⢀⣾⡇
⠀⠀⢻⣤⣤⢤⣤⣤⡤⣾⡳⠞⡀⣴⠂⢻⠏⠈⠋⠘⡿⠂⣤⡌⠑⠄⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⢠⡄⠺⡟⠉⡟⠉⠿⠂⣤⣸⠃
⠀⠀⠀⠻⣮⣋⣋⣄⣯⣿⡧⠾⠀⢠⣄⡸⠦⠼⠦⠼⠆⣴⡇⣀⠟⢢⡀⢀⠀⠀⠀⠀⠀⢀⡔⠛⡀⢠⣀⡦⠰⠧⠰⣇⣤⠁⣼
⠀⠀⠀⠀⠈⠉⠛⠋⠁⢸⣧⡀⠛⠀⡀⣤⢶⠒⠒⠂⠄⠠⣈⠙⠲⡎⣹⡄⠂⠀⠀⠞⡰⢇⢠⠄⠋⣁⣠⢤⡤⢦⠤⡄⣈⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡄⠂⠁⠀⠇⠈⡇⠀⠐⠀⡔⠈⡅⠂⠈⠧⢺⡀⠀⠀⣠⢳⡜⢁⣴⠛⣿⠀⣿⡇⠘⣆⢳⡌⡷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢣⠀⠀⠐⠀⠰⠃⢦⡰⠲⠤⢀⠜⠀⢱⣬⣭⣥⣴⣤⣦⣏⣰⣿⣿⠀⢸⠬⣿⡃⠀⣿⣬⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⠃⡟⠀⠠⠤⡀⠚⠃⠢⡢⠖⠀⠘⣸⣿⠀⠀⠀⠀⠀⣿⢹⡇⣿⣄⠞⠻⡇⢹⣩⠹⡟⡃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⠒⠘⢅⣤⡨⠇⠀⠀⠀⢆⠀⠔⠉⢻⡇⠀⠀⠀⠀⠸⣷⢈⠟⢧⡐⢺⠋⠉⠑⡶⠶⠎⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢡⡀⠀⠀⠀⡌⠈⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠠⠾⢴⣈⠴⠀⠀⠀⠙⠋⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡁⠀⠀⠀⠀⠓⠀⠀⠸⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⣶⡄⠄⠀⠿⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠠⠉⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⣀⣀⣠⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡾⠁⢀⡴⠶⠿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⠁⠀⢾⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠈⠓⠲⠶⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⠀⠀⠀⠀⡀⠀⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⢹⡿⠷⠤⠼⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢤⡼⠁⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣇⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡟⠀⠀⣸⠁⠀⠀⠀⠀⠀⣠⠴⠖⠚⠋⠉⠉⠉⠉⠉⠙⠛⢦⡀⢸⡀⠛⢉⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠻⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠳⠒⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠞⠛⣦⠀⡿⠀⠀⢀⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⡿⢰⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢾⠇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⣤⣄⣀⣀⣀⣤⠴⢶⠟⢁⡴⠶⠿⣭⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣾⠀⠀⠀⠀⣷⠀⢹⡛⣧
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣿⠀⠘⡷⠤⠤⠴⠃⠀⢸⡇⣿
⠀⠀⠀⣰⢻⠋⠉⠉⢻⡄⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣉⡭⠿⢿⣀⢠⡇⠀⠀⠀⠀⠀⠀⡇⢻
⠀⢰⠚⡇⠹⣄⣀⣀⣼⡇⠀⠸⣆⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⡇⢸⡃⠀⠀⠀⡟⠛⠷⢦⣄⣀⠀⠀⠀⣧⡿
⠀⣿⠀⣿⠀⠀⠉⠁⠀⣇⠀⠀⠈⠉⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠙⠶⠴⢾⠁⠀⠀⢀⣤⠿⢻⡄⠀⣿
⠀⠘⠦⣿⠀⠀⠀⢀⠀⢹⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⣼⡇⠀⠀⠀⠀⠈⠓⠲⣄⠈⠀⠀⢸⡷⠶⠃
⠀⠀⠀⣿⠀⠀⡾⣯⡀⢸⡇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠿⣶⡀⠈⠓⣏⣀⣀⡿⠀⠀⣠⡟
⠀⠀⠀⠙⠲⠞⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣧⣀⣠⡟⠉⠉⠓⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣭⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣴⣶⣿⣿⣿⣿⠟⠿⠿⠉⠉⠉⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⡶⠶⣦⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⣿⠁⡞⠙⢻⣿⣿⣿⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⡇⠀⠸⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠚⠁⠀⠀⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⠛⠛⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠘⠀⠀⣀⣀⣤⣤⣶⠶⠶⠿⠟⠛⠛⠛⠛⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⡶⠾⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⠶⠶⠶⣶⣄⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠇⠀⠀⠀⠀⢀⣴⣶⠿⠛⠛⠛⠛⠉⠉⠉⠙⠛⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⢿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣿⠃⠀⠀⠀⠀⢻⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢷⣌⡂⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣦⣤⣤⣤⣤⣤⣶⠶⠿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸⡇⠙⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠻⣟⡛⠛⢿⣛⠛⣿⠛⠙⣿⣩⡟⠁⢸⡇⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣉⠳⣿⣟⢛⣿⢋⣀⣴⠟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢻⠛⠋⠉⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⣥⠄⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⡉⠁⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣀⣀⣀⣀⣤⣼⠃⠀⠹⣷⣶⣶⣤⣶⠶⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⡙⠛⠋⠉⣩⡿⠃⠀⠀⠀⠘⠳⣦⣤⣤⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⡍⠀⠀⠀⠀⣠⡏⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⡜⢟⠛⠉⠉⢹⠉⠓⠲⠤⢤⣼⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡠⠊⠀⢈⣦⠤⠶⠚⡟⠒⠒⢒⡟⠦⢬⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⢳⠻⢤⣀⡤⠊⣨⣶⠶⠞⠛⠛⠛⠛⠛⠛⠓⠶⢶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠀⠀⡿⢦⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣠⣤⠶⢦⣼⡇⠀⠀⡿⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢀⣾⠛⢦⠀⠀⢸⣇⡀⢠⣃⣠⣾⠴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣾⠃⠀⠈⢧⢀⣿⠉⠛⢿⣅⠀⠘⡆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⢠⡿⣄⠀⢀⡼⢯⣿⠀⠀⠀⠙⢷⡀⢹⣠⠞⠛⢶⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣾⣿⡇
⠀⠀⢸⡇⠘⣦⠎⠀⠀⣿⠀⠀⠀⠀⠈⢷⡋⠓⢄⢠⠞⠀⢩⠟⠙⠛⢻⠛⠛⠙⢯⠉⣴⠏⢸⡇
⠀⠀⢸⡇⡴⠉⠳⣄⠀⣿⠀⠀⠀⠀⠀⠘⣧⠀⣨⠛⠲⢤⡯⠤⠤⠤⢼⠴⠒⠚⠚⣿⠃⠀⢸⡇
⠀⠀⢸⣿⡁⠀⠀⠈⣆⣿⠀⠀⠀⠀⠀⠀⢻⣴⠃⠀⠀⡜⠀⢠⢀⣄⢸⡂⠀⠀⣸⡏⠀⠀⢸⡇
⠀⠀⢸⡇⠙⢦⠀⢀⡼⣿⠀⠀⠀⠀⠀⠀⢸⡟⠒⠲⢤⣇⣴⣼⣾⣿⣼⣿⡤⠤⣿⠀⠀⠀⢸⡇
⠀⠀⠘⣧⠀⠈⣧⠞⠀⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠎⠏⣿⣿⣿⠳⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡄⢀⡿⠤⣄⣿⠉⠛⠛⠳⢶⣤⣰⡿⠲⠤⣼⣄⣦⣥⣿⣿⣸⣘⡤⠴⣷⡴⠾⠛⣿⠁
⠀⠀⠀⠈⢷⡜⠀⠀⠀⣿⠶⣤⣤⣄⣼⣀⣙⣃⣀⣀⣸⣇⣀⣀⣀⣀⣽⣁⣠⣤⣥⡴⠶⠾⣿
⠀⠀⠀⠀⠈⠻⢦⣤⣤⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣩⡅⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⣿⣉⣉⣁⣠⣤⣤⠶⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠳⡶⠶⠶⠶⠶⠶⠟⣿⠀⠀⠀⣿⠉⠉⢉⣉⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠑⢲⡧⠤⠤⠤⠤⠤⣄⣿⠀⠀⠀⢿⡚⠉⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢸⠀⠀⠀⠀⠀⢀⣸⠏⠀⠀⠀⠘⢧⣄⣀⣀⣀⣤⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠛⠛⠛⠉⠉⠉⠛⢿⡛⠓⠶⣶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠿⠒⠛⠛⠛⠛⠛⠛⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣿⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⡆
⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣀⡤⠤⣤⣄⡀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⣠⡤⠤⠤⢤⣼⣀⠈⠉⠛⠒⠶⠦⠤⠤⠤⣿⠀⠀⢰⠋⠀⠀⠀⠈⣧⠙⣦⠀⠀⣰⠋⠀⠀⠀⠈⢧⠙⣆⠀⠀⡿⠀⠀⠀⠀⠀⣿⡀⢠⡞⠳⢾⡇
⢠⡏⠀⠀⠀⠀⣾⠉⠙⠒⠶⠤⣤⣤⣀⣀⣀⣸⡇⠀⠘⢦⣀⠀⠀⢀⣟⣠⠏⠀⠀⠘⢦⣀⠀⠀⢀⣞⣠⠏⠀⢰⠇⠀⠀⠀⠀⠀⣿⠓⠋⠀⠀⢸⠇
⢸⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀⠀⡾⠀⠀⠀⣠⡤⢤⣿⠤⠤⠤⠤⠾⠦⠤⢤
⣾⠓⠦⢤⣤⣤⣿⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⡼⠁⠀⢀⡞⠁⠀⠀⠈⠳⣤⣤⣤⣤⣤⣤⣼
⡿⠀⠀⠀⠀⠀⣿⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠈⠻⠛⠁⠀⠀⠀⠀⣼⡁⠀⠀⢸⠁⠀⠀⣄⠀⠀⢻⠀⠀⠈⡷
⡇⠀⠀⠀⠀⠀⣿⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣴⣾⣦⠀⠀⣰⣾⣶⡄⠀⠀⢠⡞⠉⡇⠀⠀⢸⠀⠀⠀⢻⣀⣀⣼⡤⠖⠻⣅
⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠿⠛⠀⠀⠘⠻⠟⠁⣀⡴⠋⠀⣠⣇⠀⠀⢸⡀⠀⠀⠸⣍⣁⣀⣀⣀⣴⡏
⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣀⣀⣀⣀⣤⠴⠚⠉⠀⣠⠞⠁⣿⠀⠀⠘⣇⠀⠀⢸⡁⠈⠉⠉⠀⢀⡿
⢿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⣿⠀⠀⠀⠘⢦⣀⠀⠉⢻⠛⠛⠋⣿
⢸⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠓⢻⣄⣀⣀⡿
⠈⢧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠓⠶⠖⠚⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⠛⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣠⡤⠤⠶⠶⠶⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣤⣀⣀⣀⣀⣀⣤⡤⠞⠁⠀⠀⠈⠉⠉⣉⣳⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣤⣤⣄⣀⣀⣤⣤⠴⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣯⣙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣤⣴⣶⣾⣿⣿⣿⣿⡿⠋⣿⣿⡄⠀⠀⠀⠈⠉⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣉⡻⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⢀⡟⠉⠙⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⣸⠇⠀⠀⠘⠿⢿⣿⣿⣿⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⢀⣠⡔⠋⠓⢄⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀
⠀⠀⠀⣰⣁⣠⣬⣷⡄⠀⠀⡴⢚⣡⣬⣚⣧⠀⠀⠀⠀⣠⣼⣦⣼⡀⠀⠘⠷⣗⢈⡉⣉⣱⠀⠀⠀⠀⡇⠈⣀⣄⣹
⠀⠀⣀⡏⡴⠚⠛⠻⡄⠀⢀⣨⠇⡖⠛⠚⠳⡄⠀⢀⣠⠏⡔⠒⠚⠳⡄⠀⣀⡞⢱⠛⠓⠛⣆⠀⠀⣀⡗⣹⠓⠒⠛⡆
⠀⢸⢸⡇⠙⠦⠴⢶⡇⠀⡞⢸⠀⠑⠦⠴⢾⠁⠀⡞⢸⠀⠑⠦⠴⢾⠁⢸⠁⡇⠘⠦⠤⠶⡏⠀⢸⠉⡇⠘⠦⠤⠴⡇
⠀⢸⢸⠃⠀⠀⠀⢸⡇⠀⢧⢸⠀⠀⠀⠀⡼⠀⠀⢧⢸⠀⠀⠀⠀⣸⠀⢸⡀⡇⠀⠀⠀⠀⡇⠀⢸⡀⡇⠀⠀⠀⠀⡇
⠀⠀⠙⣆⢀⡟⣆⡼⠀⠀⠨⣏⢓⡶⠶⢤⡙⢲⡄⠈⠉⣷⡄⢸⣽⠁⠀⢠⡏⠉⣠⠒⠲⣏⢙⡆⠀⢹⡛⣀⡼⠒⡞⠁
⠀⠀⠀⠈⣉⡀⠀⠀⠀⠀⠀⠈⠉⡤⣄⠀⠙⠋⠀⠀⠀⠐⠓⠋⠀⠀⠀⠀⠉⠉⡁⢀⠀⠈⠋⠀⠀⠀⠉⣁⣉⡉⠁
⠀⠀⢠⢋⣡⣬⣳⠀⠀⠀⠀⢠⠊⢉⣉⠳⡄⠀⠀⠀⠀⡴⠿⢛⣢⠀⠀⠀⠰⡔⣉⣩⣆⡀⠀⠀⠀⢸⡉⡇⠀⣇⡀
⠀⢰⣽⢩⠖⠛⠛⢧⠀⠀⢀⣸⢫⡗⠒⠛⢧⠀⠀⢀⣰⠋⡞⠓⠚⢳⡀⠀⢀⡾⢠⠒⠒⠛⢦⠀⠀⢈⣹⢩⠟⠓⠛⢦
⢠⡏⣿⠈⠣⠤⠤⣾⠀⢠⡏⣿⠈⠣⠤⠤⣾⠀⠀⡏⢹⠀⠳⠤⠤⢾⠁⢸⠉⡇⠘⠦⠤⠤⡞⠀⢰⠏⡟⠈⠦⠤⠤⣾
⠸⡇⡏⠀⠀⠀⠀⣿⠀⠸⡇⡟⠀⠀⠀⢀⡼⠀⠀⡇⢸⠀⠀⠀⠀⣸⠀⢸⡀⡇⠀⠀⠀⠀⡇⠀⢸⡀⡇⠀⠀⠀⠀⣿
⠀⠉⢷⠀⢰⢶⣀⡏⠀⠀⢽⡛⢦⡤⠤⣈⠓⢦⠀⠈⠙⣦⡀⢸⣻⠁⠀⢀⡟⠛⢠⠶⠶⣞⠙⡆⠀⢹⡟⠂⣰⠖⢶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠟⠛⠛⠛⠛⠛⠻⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠋⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡉⠙⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠀⠀⣀⣀⠀⢀⡠⢉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡙⢧⡴⢆⠈⠲⢦⡴⡇⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠾⢃⠔⠉⣠⠞⢱⡞⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠸⢷⣄⠰⢎⠑⠤⡈⠙⠧⠴⢻⡄⠀⠀⢀⡰⣟⠢⠤⠛⢁⡀⠚⣀⠜⢃⡔⠃⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠁⠘⠛⢳⣤⡙⠠⣟⢲⠤⢤⢀⣀⣀⡀⣈⣀⣀⢠⡄⢚⣉⠵⠀⣩⡶⠏⠑⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠲⠠⠇⠸⣁⡤⠀⠷⠀⠃⣈⡀⠒⠉⠀⠀⠀⠀⠀⢀⠀⠐⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢑⣀⣀⣠⣤⡤⠄⠀⠀⠐⠚⠛⠒⠒⣂⣤⣴⣶⡶⠿⠿⠿⠛⠛⠛⠛⠛⠿⠷⠾⣷⣦⣤⣈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⣠⡤⠟⠋⣉⣡⣤⡔⣖⢶⠾⠏⠉⣩⣽⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠐⣋⣤⠔⠿⠟⠋⠛⣀⠀⣅⢘⣦⣴⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣥⡾⠟⢲⠁⠲⣤⢿⣄⣿⠿⠛⠋⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠻⠐⣦⣬⠷⣴⠷⠛⣉⡠⣔⡞⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣿⣀⡷⣀⣡⠴⠋⣠⡴⠛⣭⠛⣙⣧⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣶⢟⣋⣉⣩⠏⣽⡿⢨⣡⠟⢁⣴⡋⢤⡍⠻⣿⡄⠘⠏⢀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣴⣿⣿⠁⣠⣍⣤⣂⣿⣿⠞⣠⡾⠻⡄⠻⣶⠷⠀⢉⢀⣸⣦⣾⠿⠟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⣼⣯⠀⣁⣉⣉⡉⠉⠉⣻⡏⡰⢏⠻⢶⡽⠆⢈⢄⣤⣾⠿⠋⠁⡠⠀⣠⡞⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢶⣿⡏
⠀⢰⣿⢿⣤⣼⡈⠀⣹⣿⡟⣿⣿⢴⣎⣦⡀⢁⣀⣼⡿⠋⡁⠀⠐⠄⢲⣶⡿⠀⠘⣷⣌⣙⠻⠷⡶⣶⣦⣤⣤⣤⣤⣤⣴⣶⡶⠶⠾⠟⠛⠉⣁⣴⠞⢸⣷
⠀⣿⠇⣸⡏⠀⣿⣾⠏⠈⣳⣿⣿⡀⠙⠀⢀⣿⡿⠋⠀⣾⠻⢿⣿⡀⢘⡟⠛⠀⢢⠀⠈⠻⠤⠾⠿⠽⠏⢀⣟⠻⢷⣤⣤⡆⠀⠀⢠⣤⣤⣾⣿⡇⠀⢸⣿
⢸⣿⢿⣿⣧⣾⡌⠙⣷⣼⠇⣿⣿⠇⢀⣾⡿⠋⠀⡘⢠⣿⡀⣈⠛⠻⠾⠁⠀⢀⣀⠀⢤⣴⠤⣶⡦⠤⠤⣤⣀⡀⠀⠙⠻⢷⣀⣰⠾⠛⠉⠁⠈⠱⠀⠰⣿
⢸⡟⣾⠋⠈⣿⣄⣾⠛⣿⠀⣿⡇⣴⣾⡟⢁⣤⣤⣄⠘⡟⠁⠀⠋⡀⣤⣶⠉⠛⠁⠀⠈⠁⠄⠀⠀⠀⠀⠉⡄⠛⠋⠀⣤⣄⠈⠑⠄⠀⠀⠀⠀⠀⠀⠈⣿
⣾⡇⢿⡃⠀⣼⡟⣿⣪⣼⠗⣿⣧⣿⠏⠀⣿⡉⠙⠛⠛⠛⢀⡠⢾⡅⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠉⡉⢿⠦⢀⠈⠻⣤⣤⡤⠂⢀⣿
⣿⡇⢸⠼⢿⣿⠘⣋⣿⡏⢠⣿⣿⡏⢀⠃⠛⢷⡤⠎⠀⠴⠛⠇⠠⡀⠀⠀⠀⠀⠀⡐⠂⠠⠤⠤⠤⠒⡒⠆⡠⠀⠀⠀⠂⠀⠀⠀⠠⠷⢄⠈⠻⡇⠀⠀⣿
⣿⡔⡇⠀⢀⣿⣾⣧⠘⢷⠸⣿⡇⢠⣠⣶⡤⠾⠃⢠⣦⠀⠀⠀⠀⠁⠠⠚⡤⠀⠀⠀⠀⠀⠀⠐⠂⠀⢁⠀⠁⠈⠁⠐⢤⡀⠐⢀⠀⠂⠼⠷⠀⠙⢦⠀⣿
⣿⡇⠱⣄⡾⢁⠘⣷⣵⣾⠻⣿⠁⠻⡈⠉⣥⠀⢰⣆⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠀⠆⠀⠀⢸⣤⡀⣀⡀⠊⠀⠋⠂⡀⠀⠀⠀⠀⣴⣆⠈⢤⣿
⣿⣏⠖⠉⢳⣈⡆⠀⢉⠏⢰⣿⣆⡰⢿⡃⠂⢀⡉⠀⠀⠈⢀⠂⠀⠀⠀⡄⠀⠈⠋⠁⠀⠀⠘⠀⠀⠀⢈⢠⡙⡾⠁⠀⢐⠠⠀⠀⠀⠀⠀⠠⠂⢼⣆⠘⣿
⢸⣏⢦⢀⣼⠋⣳⣄⣀⣤⣬⣿⠏⣥⣤⡿⠀⡘⠃⠀⠀⠀⠸⠁⠂⣀⠀⢁⠀⠀⠈⠄⠀⢀⡄⠀⠀⠀⢸⢀⡞⠀⠀⠀⡌⡀⣤⣁⡴⠆⠀⠄⠀⠀⢈⣤⣿
⠸⣿⡱⠛⣿⠀⠜⣻⣿⡋⢸⣿⡞⠛⠣⡄⠀⠟⠀⠈⠁⠠⠀⠀⠀⠈⠲⣿⡆⠀⠀⠘⢁⣈⠃⠀⠀⠀⢸⠶⠁⠀⠀⣰⢧⡿⠋⠀⠠⠐⠀⠠⠀⠠⠍⣹⣿
⠀⢿⣧⠁⣸⣷⣾⠻⠦⠳⢘⣿⡙⣷⡇⠂⠀⡄⠀⢠⠀⣠⠁⣀⢃⡀⠀⠈⠳⠀⠀⠀⠈⡤⠀⠀⠀⠀⣸⠂⠀⠀⢠⡞⠋⠀⠀⡰⢗⣦⣢⠀⢀⠀⠀⢹⣿
⠀⠘⣿⣼⠿⠱⠿⠞⠿⠻⠶⣿⡇⠉⠳⠄⠀⠉⢀⣀⣀⣀⣀⣀⡈⠉⠀⠀⢀⠀⠀⠀⠀⣻⠀⠀⠀⠀⡾⠀⠀⠀⠎⡠⠀⠀⠋⣉⣀⣀⣀⣀⠈⠁⠠⢿⣿
⠀⠀⠘⣷⣤⣶⢶⣶⣦⣶⢶⣿⡥⠟⣁⠴⣶⠉⠹⡏⠀⠙⠁⢈⡿⠋⢱⣦⠄⠁⠂⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⣶⠊⢻⡏⠀⡟⠁⠘⠟⠁⣦⢼⡏
⠀⠀⠀⠈⢿⣬⡫⢛⡥⣘⣫⣿⡧⠾⡇⠀⢠⣄⣰⡧⠤⠿⠤⠼⠆⣠⣎⠀⢠⠟⢂⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡔⠛⡀⠀⣆⣠⣦⠠⠷⠄⣼⣀⣠⠁⢸⡇
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠋⢹⣇⠀⡼⠆⠉⠁⣀⣠⡤⢤⠤⠄⢀⠀⡁⠘⠳⣤⡜⠛⣄⠐⡀⠀⠀⢰⠃⣴⠈⢁⣀⠿⠚⠉⣀⣀⣀⣤⣀⣀⡈⠙⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⣠⠐⠆⠁⣽⠁⣷⠈⠀⢢⠁⠠⠍⠳⢢⠈⠱⢎⢹⡄⠀⠀⠀⠁⠶⣄⡱⠎⢁⣤⣶⣿⠱⣿⡏⠘⣏⠸⣅⠳⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣫⠀⠀⢠⢘⠁⠀⣹⣀⠃⡌⢀⠑⠀⠘⡅⠀⣄⠈⣥⠾⠀⠀⠀⡘⢣⠜⢁⣴⣿⡇⠘⣯⢰⣿⡇⠀⢻⡆⢹⡆⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢩⣂⠀⡀⠈⠀⠀⠁⠈⢣⡜⠉⠳⠃⠔⠳⢀⠸⣶⡾⠾⠷⠿⠿⠿⣿⣦⣿⡿⣿⠀⠈⣟⣸⠿⣄⢀⣼⣿⣸⠃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢀⠉⠰⡅⠀⠈⠖⢂⠀⠉⠁⠐⠈⠲⠁⠀⠘⣴⣿⠀⠀⠀⠀⠀⠀⣿⡏⣿⠁⣟⢦⠼⠉⢻⣅⣸⣤⠄⠹⢉⡃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠗⠂⠛⣅⣠⣂⠽⠀⠀⠀⠀⣦⡁⢠⠞⠋⠻⣿⠀⠀⠀⠀⠀⠀⣿⡆⢸⠿⢿⡀⠲⡟⠉⠉⠑⣶⠶⠶⠙⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠈⠀⠹⡀⠀⠀⠀⠀⣰⠉⠓⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢿⡗⣠⣖⣨⡐⢊⡅⠀⠀⠀⠚⠶⠂⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡴⠀⠀⠀⠀⠀⠳⠄⠠⠀⢀⡏⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⣧⠁⠀⠈⠙⢧⡀⠀⡀⠀⣰⡆⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠸⠝⠀⠁⠀⠈⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠂⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢶⣤⡶⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣀⣀⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣠⡿⠋⠉⠉⠉⠉⠉⠛⢿⣶⡶⠦⣀⠀⣠⣄
⠀⠀⠀⠀⢠⣿⠃⠀⢀⣤⣶⠶⠶⠶⠶⢿⣿⣦⣸⡟⢡⠏
⠀⢀⣀⣤⣼⡟⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⢻⣯⡴⠛⢲⡀
⠀⣾⡟⠉⢹⡇⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢀⣸⡿⠙⣄⠀⠉⢷⣄
⠀⣿⠃⠀⢸⡇⠀⠀⠀⠙⠿⢷⣶⣶⠶⠾⢻⣿⠁⠀⠈⠳⣄⠀⢸⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠘⢦⡟⠀⠀⠀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠙⣿⡄
⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⣀⣀⣀⣀⠀⣠⣿⡷⠶⣤⡀
⠀⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡾⠟⠛⠛⠛⠉⠉⠛⠻⣿⡀⠀⠘⣷
⠀⠘⠿⠶⣾⡇⠀⠀⠀⢠⣶⣶⣶⠶⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⣠⠶⢛⣛⣛⠛⠳⢦⡀⠸⣿⠀⢰⡟
⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⣿⠸⣿⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁⣾⣷⣾⠟⠋⠙⣷⠀⠀⣯⠀⣿⣴⡿⠁
⠀⠀⠀⠀⠸⣿⣦⣤⣤⣾⠟⠀⠙⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢠⡄⠀⠈⢻⣿⠀⣸⠃⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣧⣀⣀⣼⡛⣉⣩⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠊⢁⡀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠢⡀⠀⠀⠀⠀⠀⠀⠝
⠀⠀⠀⠀⢀⡠⠤⠄⠤⣀⠀⠀⠀⠀⣸⣿⣷⣂⠾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢠⠇
⠀⠀⠀⢠⡣⠤⣖⠢⢤⠀⠣⠀⠀⡼⠉⢯⠉⠛⠿⣮⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡼
⠀⠀⠀⢨⡀⠀⠀⢷⠀⠁⠀⢃⢀⣡⢦⠀⣡⡈⠛⠙⢷⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣇⠀⠀⠘⢣⠀⠀⢠⡈⠉⣿⠎⢉⡶⢸⡄⠘⣧⠘⠀⠀⠀⣶⣿⡆⠀⠀⠀⠀⠀⢸⠖⢆⣛⠛⠛⠛⠓⣲⣤⡀
⠀⠀⠀⠀⡷⠛⠃⠤⠈⠳⣄⣀⢈⣈⣤⣾⣾⣴⣾⠿⠄⣿⠆⠁⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⡸⠀⢉⣁⠤⠶⠚⠋⠉⠁⠙⢦
⠀⠀⠀⡘⠱⠀⠀⠀⠀⠀⢈⠝⠉⠀⠀⠀⢀⡈⢱⠒⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⡜⠉⠉⠐⡆⠀⢀⢠⣤⣄⡀⢻⢇⣀⣰⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡃⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢳⡀⠀⡄⠀⠀⠀⣗⠀⠀⠘⣿⣭⣙⣡⣴⡫⠔⠁⠀⠀⠀⠀⠀⠀⣀⣀⠠⢺⠉⢡⡄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠙⢤⡘⡄⠀⠀⠘⣄⠲⡀⠻⠤⣉⡉⠀⣀⣀⣀⣀⠤⠤⢒⢺⠉⠁⠀⠀⢈⡥⣾⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀⠀⠙⢾⡄⠀⠀⠈⠑⢌⡢⡀⠈⢻⡀⠉⠀⠀⠀⠀⢰⣀⣀⣄⣤⣶⡺⠷⠂⠙⠿⣶⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⡇⠀⠈⢃⠀⢸⠀⠀⠀⠈⢽⣆⢀⡇⠀⠀⠀⠀⢀⣠⣴⠟⠉⠈⠀⠀⠀⠀⠀⠀⠈⠛⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⣇
⠀⣤⠀⠀⠀⠃⠀⠀⠈⠒⠁⠀⠀⠀⢠⡮⢼⣟⡀⠀⠀⠀⠚⠉⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⣿⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⢉⣉⠉⣳⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⢀⡟⣆⠀⠀⠀⠀⠀⠀⢸
⠀⠘⠀⠈⢣⡀⠀⡀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⡇⢹⢄⡇⣰⠟⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠈⠀⠹⣦⠀⠀⠀⠀⠀⠈
⠀⠀⠇⢣⠀⠙⣦⠳⡄⠀⠀⠀⣰⠏⠀⠀⠀⠀⠑⠞⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠈⢦⠀⠳⣄⣆⠀⠀⡎⢿⡀⠀⢀⡴⢮⢢⠀⣦⠀⢀⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠂⠀⠑⡄⠈⠉⢧⡀⢃⢸⡇⡔⠋⢡⣼⡿⠀⢸⡀⠀⠙⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣭⣀⡀⠀⠈⠻⣦⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⠀⠈⠙⢷⣄⠀⠘⢿⡀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠻⣄⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠙⣦⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠋⠙⠛⠛⠻⢶⣤⡀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠘⢧⡀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣈⣻⡄⠀⠀⠀⠈⠛⠷⣶⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⡴⠛⠛⠉⠉⠉⠉⠙⠻⣶⡀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣀⣴⣯⡀⠀⠀⠘⣧
⠀⠀⠀⢀⣠⣤⣤⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠈⢿⣄⠀⠉⢻⣅⠈⢷⣄⣀⣴⠟
⠀⠀⠀⣾⠉⠀⠀⡟⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣠⡿⠀⠀⠉⠉
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠘⠳⢦⣤⣤⣤⣤⠶⠾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠈⠙⠛⠛⣷⠀⠀⠀⠀⠀⣿⠿⢷⡖⠋⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡿⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⣠⣼⠇⠀⠈⠻⠶⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⡍⠀⠀⠀⠀⣠⡏⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⡜⢟⠛⠉⠉⢹⠉⠓⠲⠤⢤⣼⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡠⠊⠀⢈⣦⠤⠶⠚⡟⠒⠒⢒⡟⠦⢬⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⢳⠻⢤⣀⡤⠊⣨⣶⠶⠞⠛⠛⠛⠛⠛⠛⠓⠶⢶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠀⠀⡿⢦⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣠⣤⠶⢦⣼⡇⠀⠀⡿⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢀⣾⠛⢦⠀⠀⢸⣇⡀⢠⣃⣠⣾⠴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣾⠃⠀⠈⢧⢀⣿⠉⠛⢿⣅⠀⠘⡆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⢠⡿⣄⠀⢀⡼⢯⣿⠀⠀⠀⠙⢷⡀⢹⣠⠞⠛⢶⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣾⣿⡇
⠀⠀⢸⡇⠘⣦⠎⠀⠀⣿⠀⠀⠀⠀⠈⢷⡋⠓⢄⢠⠞⠀⢩⠟⠙⠛⢻⠛⠛⠙⢯⠉⣴⠏⢸⡇
⠀⠀⢸⡇⡴⠉⠳⣄⠀⣿⠀⠀⠀⠀⠀⠘⣧⠀⣨⠛⠲⢤⡯⠤⠤⠤⢼⠴⠒⠚⠚⣿⠃⠀⢸⡇
⠀⠀⢸⣿⡁⠀⠀⠈⣆⣿⠀⠀⠀⠀⠀⠀⢻⣴⠃⠀⠀⡜⠀⢠⢀⣄⢸⡂⠀⠀⣸⡏⠀⠀⢸⡇
⠀⠀⢸⡇⠙⢦⠀⢀⡼⣿⠀⠀⠀⠀⠀⠀⢸⡟⠒⠲⢤⣇⣴⣼⣾⣿⣼⣿⡤⠤⣿⠀⠀⠀⢸⡇
⠀⠀⠘⣧⠀⠈⣧⠞⠀⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠎⠏⣿⣿⣿⠳⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡄⢀⡿⠤⣄⣿⠉⠛⠛⠳⢶⣤⣰⡿⠲⠤⣼⣄⣦⣥⣿⣿⣸⣘⡤⠴⣷⡴⠾⠛⣿⠁
⠀⠀⠀⠈⢷⡜⠀⠀⠀⣿⠶⣤⣤⣄⣼⣀⣙⣃⣀⣀⣸⣇⣀⣀⣀⣀⣽⣁⣠⣤⣥⡴⠶⠾⣿
⠀⠀⠀⠀⠈⠻⢦⣤⣤⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣩⡅⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⣿⣉⣉⣁⣠⣤⣤⠶⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠳⡶⠶⠶⠶⠶⠶⠟⣿⠀⠀⠀⣿⠉⠉⢉⣉⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠑⢲⡧⠤⠤⠤⠤⠤⣄⣿⠀⠀⠀⢿⡚⠉⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢸⠀⠀⠀⠀⠀⢀⣸⠏⠀⠀⠀⠘⢧⣄⣀⣀⣀⣤⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠋⠉⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢧⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⠄⠀⠀⢀⣀⣠⣤⣤⣿⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⢀⣠⡴⠖⠛⠛⠛⠛⠳⢦⣴⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡿⠀⠀⠀⢀⣴⠶⠚⠛⠛⠛⠋⠙⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⣽⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠀⠀⠀⠀⢻⣜⣀⠀⠄⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠶⠚⠛⠛⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡟⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠉⠙⢿⡛⠻⢿⣻⣏⣉⣿⡿⠁⣼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⠀⠀⠀⠀⠀⠙⠳⠦⢽⣿⣼⡯⠴⠚⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢠⡴⣤⠴⠷⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡾⠀⢿⣄⣀⣀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡛⠛⠛⣛⡿⠁⠀⠀⠻⢭⣭⣥⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⣠⣾⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⣿⡏⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⢻⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⠋
⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⢹⣿⣷⣶⣦⣤⣴⣶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠟⠀⠀⠀⠙⠛⠛⠛⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⠿⠿⠿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠛⢷⣄⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⢀⣤⣴⣶⣶⡶⠶⠶⣾⣿⣿⣷⡄⣹⡿⠋⣰⠇
⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣟⢀⣴⠿⣤
⠀⢀⣴⣿⠿⢿⣿⡇⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⡁⠀⠸⠧⣤⡀
⠀⣸⣿⠃⠀⠀⣿⠀⠀⠀⠀⠸⣿⣆⡀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡟⠈⠻⣆⠀⠀⠘⠷⣤
⠀⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⣶⡶⠿⠿⣿⡟⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀
⠀⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠙⢦⣀⡿⠀⠀⠀⠀⢀⣴⣾⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⣷⣄
⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣷⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣼⣿⡿⠛⠛⢷⣦
⠀⢻⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡿⠟⠛⠛⠛⠋⠉⠉⠉⠛⠻⣿⣆⠀⠀⠀⣿⡇
⠀⠈⢿⣷⣦⣴⣿⡇⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⣠⣴⡶⠶⠿⠿⠷⠶⣦⡀⠀⠘⣿⣇⠀⢀⣿⡇
⠀⠀⠀⠈⠉⠙⣿⡇⠀⠀⠀⠀⢸⣿⡟⢻⣿⠁⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢠⣞⣋⣥⣶⣿⣿⣷⣄⠀⠈⢹⡦⠀⢻⣿⠀⣼⡿
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢸⣿⡇⢸⣿⣀⠀⠀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣴⡿⠿⠿⠟⠉⠀⣀⣸⣿⠀⠀⢘⣿⠀⢸⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣤⣴⣿⡿⠁⠀⠙⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⣴⠆⠀⠀⠙⣿⣿⠀⢀⣿⠁⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣾⣿⡀⠀⠀⢀⣾⠟⠛⠛⢁⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠋⠉⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢧⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⠄⠀⠀⢀⣀⣠⣤⣤⣿⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⢀⣠⡴⠖⠛⠛⠛⠛⠳⢦⣴⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡿⠀⠀⠀⢀⣴⠶⠚⠛⠛⠛⠋⠙⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⣽⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠀⠀⠀⠀⢻⣜⣀⠀⠄⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠶⠚⠛⠛⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡟⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠉⠙⢿⡛⠻⢿⣻⣏⣉⣿⡿⠁⣼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⠀⠀⠀⠀⠀⠙⠳⠦⢽⣿⣼⡯⠴⠚⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢠⡴⣤⠴⠷⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡾⠀⢿⣄⣀⣀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡛⠛⠛⣛⡿⠁⠀⠀⠻⢭⣭⣥⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠉⠉⠉⠉⠉⠛⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠉⠉⠙⠛⠒⡒⠦⢄⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠚⠉⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠳⣄⣀⡀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠈⠉⠻⣭⡉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠤⠤⣶⡒⠦⠤⢤⡀⠀⠀⠀⠀⠀⢴⣏⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠘⡆⠀⠀⠀⠀⢠⠟⢧⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢠⠃⠀⠀⠀⠀⠟⠒⠒⠻⡄⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠰⠿⠤⠬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⣄⣈⡉⠉⠉⠉⠉⠉⠓⢤⡀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⢿⡤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⠀⠀⡴⠻⡄⢱⠀⡴⢳⡀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡤⠼⠶⠶⠷⠶⠷⠾⠾⠷⠶⠧⠤⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⣄⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠀⢀⡟⠉
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠒⠲⡶⠶⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡤⠟
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠛⠦⣤⣀⣠⣤⠴⠋⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢛⣛⣹⣿⠿⠶⠶⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠋⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⣠⠒⠁
⠀⠀⠀⠀⠀⠀⣠⠤⠖⠂⠤⣀⠀⠀⠀⠀⠀⣨⣿⣽⣗⣰⠪⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⡰⢋⣠⣤⠦⣄⣀⠀⠳⡀⠀⠀⡼⠛⢫⡉⠛⠻⢷⣬⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡞
⠀⠀⠀⠀⢟⠁⠀⠈⢳⣄⠈⠂⠀⢱⠀⢸⢣⡄⠀⠱⡀⠘⡶⠛⣷⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠁
⠀⠀⠀⠀⠸⡀⠀⠀⠀⣹⡄⠀⠀⠀⠓⠺⢾⢼⡆⠼⠻⡀⢠⠀⠘⣷⠈⢇⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠰⣁⣠⡘⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⡷⣀⣠⠤⠥⢹⡄⠀⠀⠣⡤⠨⠯⢊⣐⣼⠋⣸⣧⠀⢸⣧⠘⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠤⠀⠀⠀⡟⠉⣧⡷⠀⠀⢀⣀⣤⣼⡿⢦⡀
⠀⠀⠀⠀⢀⡟⠉⠁⠐⠂⠀⠙⠦⣤⣀⣠⡠⠴⠿⣿⢷⣿⡿⠛⠇⢸⣿⢀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⠃⠠⠤⠤⠶⠚⠋⠉⠁⣀⠀⠄⠙⢦
⠀⠀⠀⠀⡎⠹⠀⠀⠀⠀⠀⠀⠐⡡⠊⠁⠀⠀⠀⢀⡀⠈⣱⠓⠄⢸⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢰⡇⠒⡔⢪⠛⠉⠒⠂⡾⠀⠀⠀⣀⣀⣀⠀⠙⢿⡏⠀⢀⡟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠘⡇⠘⠀⡇⠀⠀⠀⠀⣷⠀⠀⠋⢸⣿⡟⠳⠶⠋⣈⡷⢋⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢃⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠙⢆⠀⠸⡀⠀⠀⠀⢻⡀⢀⡀⠀⣿⠛⠳⠿⠿⠛⠊⠉⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⠂⠀⢹⠀⣸⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠑⢤⡙⡄⠀⠀⠀⠱⣄⠑⢄⠈⠒⠲⣤⣤⠤⢤⠤⠤⠶⠒⠒⢛⠉⡅⢸⠀⠀⠀⠀⣀⠴⠛⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠙⣼⡀⠀⠀⠀⠈⠑⠤⣑⣤⠀⠈⢳⡀⢸⠀⠀⠀⠀⠀⢸⣄⡅⣨⣤⣴⣞⡫⠽⠒⠂⠈⠛⢿⣶⣼⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⡇⠀⢰⠇⠀⠀⠀⠈⢹⣧⡀⢠⡇⠈⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⢿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⢀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠤⠞⠀⠀⠀⠀⠀⣼⣉⣿⠜⠀⠀⠀⠀⠠⠖⠋⢡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠸⠳⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠈⠋⠙⠒⠶⠶⠦⡄⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⡆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⡴⢶⡄⢰⠇⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⠀⠀⠀⠏⠸⣦⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⢇⢰⠀⠹⣆⠀⢠⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⡇⢸⡇⡞⠀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠳⡀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠸⠈⢆⠀⡈⢳⡎⠳⡄⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠙⠛⢱⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠂⠘⣆⠀⠸⢤⢠⡇⠀⠀⢰⠙⣿⠀⠀⠀⣀⣴⣍⢆⠀⢸⠀⠀⣀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠰⠀⠈⠣⡀⠀⠛⠻⣄⠀⢸⠀⢻⠀⣠⠞⠛⣄⣼⣼⠀⠸⡆⠀⠘⢿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠂⠀⠘⠢⡀⠀⠈⢳⡌⡆⢸⡆⡇⠀⡴⠋⠉⠁⠀⠀⢳⠀⠀⠠⠉⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠛⠉⠉⠉⠉⠙⢯⡙⢳⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠀⠀⠀⠉⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⢸⡇⠀⠀⡠⠇
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⡇⠀⠸⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⠈⣧
⠀⠀⣀⣀⠀⡟⠲⠤⢤⣀⣀⣀⡀⣸⠀⠀⣠⠖⠚⠛⢶⢦⡀⠀⢀⡴⠒⠛⠳⡶⢄⠀⠀⡿⠀⠀⠀⢸⡇⠀⡠⣄⡿
⢠⠏⠉⠉⠉⡟⠲⠤⢤⣀⣈⣉⡉⢙⡆⠀⢧⡀⠀⠀⣸⣠⠇⠀⠸⣄⠀⠀⠀⣟⡸⠃⢠⠇⠀⠀⠀⢠⡷⠞⠁⠀⡇
⣼⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠈⠉⠉⢳⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⡞⠀⠀⣠⠤⠴⡧⠤⠤⠴⠷⠤⣤
⡏⠙⠒⠶⠶⡇⢳⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢰⣿⡷⠀⠰⣿⣷⠀⠀⠀⠀⡼⠁⠀⡼⠁⠀⠀⠈⢶⠒⠶⢶⠒⠛
⡇⠀⠀⠀⢸⡇⠀⠹⣄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀⣭⣄⠀⢀⣬⣅⠀⠀⢀⡼⣧⠀⠀⡇⠀⠀⣇⠀⢸⣀⣠⡞
⡇⠀⠀⠀⠀⡇⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠘⠿⠟⠀⠘⠿⠟⢀⡠⠊⢀⣼⠀⠀⡇⠀⠀⢾⣋⣉⣁⣀⡼
⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⣤⡤⠤⠖⠋⢀⡠⠊⢸⠀⠀⠹⡀⠀⢯⣈⡉⢉⣀⡽
⢷⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⢸⡀⠀⠀⠙⠦⣄⣸⡏⠉⢸⡇
⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠶⠖⠒⠋⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠛⠋
⠀⠙⠶⠶⠒⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠲⠖⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠤⠤⠴⠶⠶⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢯⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠚⠋⠀⠀⠀⠀⠠⡖⠋⠀⠀⠀⠀⣀⣠⠔

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⠴⠋⠓⢄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀
⠀⠀⠀⢀⠎⢁⣀⣙⣆⡀⠀⠀⣠⠔⢋⣠⡥⢿⡀⠀⠀⠀⠀⣀⣤⣧⣠⣇⠀⠀⠸⢼⡗⠂⠂⠙⠹⡄⠀⠀⠀⢰⠁⠈⠀⡄⢸
⠀⠀⠀⣼⢋⡵⠿⠿⢯⡁⠀⠀⠘⡞⢩⠽⠿⠿⣇⠀⠀⠀⢀⡟⣩⠵⠮⠿⣄⠀⠀⠀⡿⢩⠽⠿⠿⢧⠀⠀⠀⠘⡦⣺⠯⠭⠿⣄
⠀⢰⠋⡏⠘⣆⣀⣀⣸⠇⠀⣼⢻⡇⠹⣄⣀⣀⣼⠀⠀⡾⢹⡇⠻⣀⣀⣀⡼⠀⢰⠛⡇⠸⣄⣀⣀⣼⠂⠀⡴⢻⡇⢻⣀⣀⣀⣼
⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⣯⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇⢸⠀⠀⠀⠀⠀⡷⠀⣻⢀⡇⠀⠀⠀⠀⢹⠀⠀⡇⢸⠃⠀⠀⠀⠀⣧
⠀⠘⠦⡇⠀⢠⣤⠀⣸⠀⠀⠙⣼⣇⣀⢀⠀⠸⢥⡀⠀⠳⠼⣄⠀⠀⡤⡴⠃⠀⢸⡶⢧⠀⣀⣀⣠⠾⣄⠀⠻⣼⣤⠀⢠⣀⣠⠏
⠀⠀⠀⠳⠤⠞⠘⠶⠃⠀⠀⠈⠳⠤⠟⠉⠉⠲⣄⡹⠀⠀⠀⠛⣇⣰⠗⠃⠀⠀⠸⢤⣤⠞⠁⠀⠱⣤⠞⠀⠀⠻⠤⠴⢾⣤⠏
⠀⠀⠀⢀⡤⠤⢄⡀⠀⠀⠀⠀⠀⢀⣴⣱⣄⠀⠀⠀⠀⠀⠀⠀⣉⣅⠀⠀⠀⠀⠀⠀⠀⢦⣠⡄⠀⠀⠀⠀⠀⢀⣠⡖⠖⣄
⠀⠀⣠⣏⡤⢦⡦⣇⠀⠀⠀⠀⢰⣉⡠⠤⢌⣱⠀⠀⠀⠀⠀⣼⡛⣫⠭⣆⠀⠀⠀⠙⣏⡤⠴⠧⢤⡀⠀⠀⠀⢹⣠⣇⣀⡽⣄⡀
⠀⣐⣿⠃⡞⠉⠉⠙⣧⠀⠀⣀⣸⠁⡞⠉⠉⠙⣦⠀⠀⣀⣸⠃⡟⠉⠉⠙⢧⠀⢀⣀⡟⢰⠋⠉⠉⠻⡄⠀⢀⣀⡟⢰⠋⠉⠛⢻⡄
⢀⡇⢸⠀⠙⠦⠤⠶⡏⠀⢰⡇⢸⠀⠙⠦⠤⠶⡏⠀⠀⡇⢸⠀⠙⠦⠤⠶⡟⠀⣼⠀⡇⠈⠳⠤⠴⢾⠁⠀⢸⠀⡇⠈⠧⠤⠤⢾⠃
⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⢸⡇⣿⠀⠀⠀⠀⢀⠇⠀⠀⡇⢸⠀⠀⠀⠀⢀⡗⠀⢻⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸
⠀⠙⢻⠀⠀⡶⡆⢠⠇⠀⠀⣹⠛⠦⣤⣤⣀⠙⠦⣄⠀⠙⠛⣦⡀⢰⣞⡏⠀⠀⢨⠟⠓⢀⡤⠤⣴⠛⢳⡀⠈⢻⠷⠂⢐⡦⢤⠞
⠀⠀⠈⠓⠚⠁⠙⠋⠀⠀⠀⠈⠓⠚⠁⠀⠈⠓⠤⠞⠀⠀⠀⠹⣧⡼⠉⠁⠀⠀⠘⠲⠶⠋⠀⠀⠈⠷⠚⠀⠀⠘⠒⠚⠛⠶⠞

⠀⡄⣀⠀⡄⡄⠠⢠⠀⡀
⠈⢁⠈⠆⢠⠁⠀⠘⢀⡇⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠁⠀⠈⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢉⣁⠀⠀⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠛⠛⠛⠛⢷⡄⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⣤⣤⣤⣴⠟⠁⠀⠀⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠶⠶⠶⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣀⣀⣠⣤⣤⡄⢠⣄⣠⣤⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢲⣞⣲⡄⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠉⠉⠛⠛⠻⠶⢶⣶⠶⠶⠒⠁⠉⠬⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣤⣤⢤⣤⠀⠀⠀⠀⣿⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⣿⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⣶⣾⡇⠀⣿⣀⣀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⢀⡤⠤⡄⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⢀⣤⠞⠉⠢⡀⠀⠀⠀⠀⢀⣀⣤⠤⡀
⠀⠀⠀⣜⡁⣤⣬⣦⠀⠀⢠⣒⣡⣤⣖⣣⠀⠀⠀⠀⣠⣼⠦⣼⡀⠀⠘⠾⣃⣉⣉⣉⡇⠀⠀⠀⡏⠀⣀⣤⣸
⠀⢀⣠⠇⡞⠉⠙⢳⠀⠀⣀⡟⢰⠋⠉⠛⡆⠀⢀⣠⡇⡞⠉⠙⢳⡀⢀⣠⡇⡞⠉⠙⢳⡀⠀⣀⣼⢹⠛⠛⠛⣆
⠀⣾⢸⠀⠙⠒⠒⢺⠀⢰⠃⡇⠈⠓⠒⠲⡇⠀⣼⢸⠁⠙⠒⠒⢺⠀⢸⢸⠇⠙⠒⠒⢺⠀⠀⡇⣿⠈⠓⠒⠒⡇
⠀⢻⣸⠀⠀⡀⠀⣸⠀⠘⣆⡇⠀⠀⠀⢴⠃⠀⢹⣸⡀⠀⢀⣀⡼⠀⢸⣸⡀⠀⠀⠀⣸⡀⠀⣇⣇⠀⢀⠀⢀⡇
⠀⠀⠘⣆⣸⠹⠤⠇⠀⠀⠺⣍⡽⠚⠲⢄⣙⡆⠀⠀⠿⡆⣸⠿⠀⠀⢸⣁⣁⠞⠉⠻⣄⡽⠀⠐⣏⣡⣼⣉⡏
⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⣰⣲⣄⠀⠉⠀⠀⠀⠈⣉⣁⠀⠀⠀⠀⠀⢠⣄⣤⠀⠈⠀⠀⠀⣀⡤⠤⢄
⠀⢀⣼⡥⢴⣶⣇⠀⠀⠀⠀⣎⡠⣤⣌⡇⠀⠀⠀⠀⣾⣛⣭⣵⡀⠀⠀⠙⣭⠔⣚⣦⡀⠀⠀⠀⣧⡦⢀⡼⣤⡀
⠀⡼⡟⢸⠉⠉⠉⡧⠀⢠⢴⡇⣎⠉⠉⢙⡆⠀⣠⢼⠁⡏⠉⠉⢹⠄⢠⢤⡇⣎⠉⠉⢙⡆⠀⣠⢼⠁⡏⠉⠉⢹
⢸⠁⡇⠀⠙⠛⠉⡇⠀⢸⢸⡇⠈⠙⠋⢹⠀⠀⡇⢸⠀⠈⠛⠋⢻⠀⢸⢸⡇⠈⠙⠋⢹⠀⠀⡇⢸⠀⠉⠛⠛⢻
⠘⢦⡇⠀⣀⡀⢀⡇⠀⠸⣼⣄⠀⠀⠀⢞⡀⠀⠳⣼⡀⠀⢀⣤⠞⠀⢸⣼⣇⠀⣀⣀⡸⣄⠀⠧⣼⣀⠀⣀⣀⡼
⠀⠀⠳⢤⠏⠳⠞⠀⠀⠀⠳⡬⠟⠉⠓⢄⣹⠆⠀⠀⢻⣆⡼⠚⠀⠀⠸⣄⣠⠎⠉⠙⢆⡼⠀⠀⠧⠤⠴⣏⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠛⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢣⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⣷⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣤⣤⠶⠾⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠉⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠁⠀⠀⣀⣀⣠⣄⣠⣤⣤⣀⡀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠛⠿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⣀⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡟⠀⠀⠀⠀⢀⣤⡶⠾⠿⠟⠛⠛⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠾⢿⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⡇⠀⠀⠀⠀⢿⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢷⣬⣀⡃⠐⠀⠀⠀⠀⠀⠀⢀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠶⠶⠾⠿⠛⠛⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠈⠙⠳⠶⣦⣤⣤⣤⣤⣤⣤⡶⠶⣶⢶⣶⠟⣻⢯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠳⣦⡈⠛⢦⣽⣶⢶⣾⡿⠁⣠⡿⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠿⢿⣶⠿⠶⠛⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣏⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢹⡏⠉⠉⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⣀⣀⣠⣤⡿⠀⠈⢿⣶⣦⣤⣴⠶⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣉⠉⠉⣉⣽⠟⠀⠀⠀⠈⠛⠶⢦⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⣴⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠛⠉⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠛⠛⠋⠁⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⡦⠆⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢻⣿⣧⣤⣤⣤⣤⣴⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⠟⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠒⠛⠛⠋⠉⠉⠙⠛⢿⡛⠓⠶⣶⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⠖⠒⠛⠛⠛⠛⠛⠲⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⣀⣀⣀⣀⣸⡏⠙⠓⠶⠦⣤⣄⣀⣀⣀⣀⡇⠀⠀⣠⠞⠉⠁⠀⠙⣏⠳⡄⠀⠀⢠⡖⠋⠉⠀⠈⢿⠛⢦⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇⠀⢠⡶⢦⣸⠇
⢀⡞⠁⠀⠀⠉⢹⠟⠲⢤⣤⣀⣀⠀⠀⠀⠉⠉⢷⠀⠀⢷⡀⠀⠀⠀⠀⡿⢀⡟⠀⠀⠸⣄⠀⠀⠀⠀⢸⠇⣼⠀⠀⣼⠀⠀⠀⠀⠀⠀⡿⠦⠟⠀⠀⢸⠁
⢸⠃⠀⠀⠀⠀⢸⣆⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⠻⡆⠀⠀⠙⠒⠶⠶⠾⠛⠋⠀⠀⠀⠀⠈⠓⠶⠶⠶⠟⠋⠁⠀⢠⡇⠀⠀⠀⠀⣀⣀⣇⣀⣀⣀⣀⣼⣀⣀⣀
⣼⢦⣀⡀⠀⠀⢸⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡖⠋⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠈⠉⠙⠛⢻⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⢀⡾⠀⠀⠀⡾⠀⠀⠀⠀⠀⠘⣏⠉⠙⠛⣏⠉⠉
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢀⣤⣀⠀⠀⢀⣠⣄⠀⠀⠀⠀⢠⡞⣧⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⣿⢀⣠⣴⠃
⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢿⣿⣿⠀⠀⠸⣿⣿⠇⠀⢀⡴⠋⠀⣹⠀⠀⠀⡇⠀⠀⠀⡽⠶⠞⠛⠉⠁⢈⡇
⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠉⠀⠀⠀⠀⠈⠁⣀⡴⠋⠀⢀⡴⢻⠀⠀⠀⣷⠀⠀⠀⡽⠲⠶⠶⠶⠚⠻⣄
⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠖⠚⠋⠁⠀⢀⡴⠋⠀⢸⡇⠀⠀⠘⣆⠀⠀⠳⣤⣄⣀⣠⣤⡴⠋
⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⢤⣄⣀⡯⠀⠀⠀⡇
⠸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⣤⣤⣀⣀⣤⣤⠤⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠖⠃
⠀⢻⣄⠀⠀⢀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠉⠉⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣤⠶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣠⠴⠶⠶⠒⠒⠒⠒⠒⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⣀⣀⣀⣀⣀⣤⣤⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣤⣄⣀⣀⣀⣠⣤⡤⠶⠃⠀⠀⠀⠉⠉⢉⣉⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣤⣄⣀⣠⣤⡤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠛⠋⠉⠉⠉⠉⠉⢹⡟⠛⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠙⢦⣀⣀⣀⣀⣀⣤⣾⣤⣀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⣠⠟⢿⡉⠉⠁⠀⠀⢸⠀⠉⠙⠓⠲⠶⡶⣏⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢀⡴⠋⠀⠀⢳⣄⣤⣤⠴⢿⡓⠲⠶⠶⠶⡾⢧⣄⣉⠉⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠤⢤⣤⣴⠋⠀⠀⠀⣠⠏⢳⣀⣀⣠⣼⣧⣤⣶⣶⣶⣷⣤⣤⣭⣍⣉⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣿⠈⠛⢦⡴⠋⢁⣴⡾⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⡏⠀⠀⢸⡟⢶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣠⣿⠁⠀⠀⢸⡇⠀⠀⢸⠇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⢀⣴⣿⡋⠉⠉⠉⢻⡿⠀⠀⠀⣸⠁⠀⢠⡟⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣾⠏⠀⠙⣆⠀⠀⢸⣿⣦⣄⣠⣧⠴⠖⢿⡉⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⣼⡏⠀⠀⠀⢹⡄⢀⣼⡇⠈⠙⠻⣧⡀⠀⠀⢳⡀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⢠⣿⣆⠀⠀⠀⢀⣷⡋⣿⡇⠀⠀⠀⠈⢿⣦⠀⠈⡇⢀⣤⠿⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡇
⠀⠀⠀⢸⡟⠘⣧⠀⣠⠟⠀⠉⣿⡇⠀⠀⠀⠀⠀⠹⣷⣠⣿⣏⠀⠀⠀⣸⠛⠛⢿⣶⢶⣶⣶⣶⣶⣶⣶⢶⣾⠿⠛⢋⣽⠟⢻⡇
⠀⠀⠀⣸⡇⠀⢸⣾⡁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢹⣧⠀⠈⠻⣄⡼⠁⠀⢀⡞⠁⠀⠀⠀⢹⠀⠀⠀⠀⠙⣆⣠⡿⠋⠀⢸⡇
⠀⠀⠀⣿⡇⢠⠟⠈⠙⢦⡀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢠⡟⠛⠒⢦⣾⠤⠶⠶⠶⠦⢼⡶⠚⠋⠉⠉⢻⡿⠁⠀⠀⢸⡇
⠀⠀⠀⣿⣷⠋⠀⠀⠀⠀⢳⡄⣿⡅⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⠏⠀⠀⠀⣸⠃⠀⠀⡄⠀⠀⢸⡇⡀⠀⠀⢀⣿⠃⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡏⠓⢦⠀⠀⠀⠀⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⣀⡀⠀⡿⠀⡇⢸⢰⣿⣷⢸⡇⡇⠀⠀⣸⡟⠀⠀⠀⠀⣸⡇
⠀⠀⠀⢸⣧⠀⠈⢳⡀⠀⣰⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠈⠉⢳⡧⠴⣳⣾⣿⣿⣷⣿⡿⠗⠚⠋⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠘⣿⠀⠀⠈⣧⡼⠁⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⣼⢹⠋⣿⣿⣿⢹⡟⡇⠀⠀⣿⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢿⡇⠀⠀⣿⣁⣀⠀⣿⡟⠛⠿⠿⢶⣶⣤⣀⡀⢸⣷⣤⣄⣀⢸⡇⢱⠈⡆⢿⣿⡿⢸⠃⠇⣀⣀⣿⣀⣤⣴⡶⠿⣿
⠀⠀⠀⠀⠘⣿⡀⣸⠃⠈⠉⠛⣿⣇⠀⠀⠀⠀⠀⢹⠛⠻⣿⡇⠀⠀⠉⢻⡟⠛⠛⠉⠉⠛⠓⢾⠟⠛⠉⠉⠻⠛⠉⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⣿⡟⠻⠿⠶⣶⣶⣿⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣿⣴⣶⣶⡶⠾⠿⠟⠛⠋⢹⡏
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣄⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠛⠛⠛⣿⠛⠛⠛⠉⠉⠀⢀⣀⣠⣤⡶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣄⣀⣀⣀⡀⢀⣀⣀⣀⣀⣤⣿⠀⠀⠀⠀⣿⡷⠶⠶⠾⠿⠟⠛⠛⠉⠁⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠈⠉⣻⠛⠛⠛⠛⠛⠛⠛⠉⠉⣿⠀⠀⠀⠀⣿⡇⠀⣀⣠⣤⠤⠤⠶⠦⠤⢤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⠲⣿⡤⠤⠴⠶⠦⠤⢤⣄⣠⣿⠀⠀⠀⠀⢻⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣇⣀⠀⠀⢀⣀⣠⣤⣾⠟⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠉⠻⢯⡉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣀⣀⣤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠙⢦⠀⠀⠀⠀⠀⢈⡷⣄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣸⠀⠀⠀⠀⢠⣯⡤⠬⢧⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠈⠙⠲⠶⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⣄⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠤⣀⠀⠀⠀⠀⠀⠙⣦⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣌⠳⡄⠀⢠⣄⠀⠙⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣇⠀⣰⠃⢸⡀⣹⣰⠃⢹⡀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⢰⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⣤⣤⠴⠞⠁⠀⠀⠀⠈⠷⣄⣀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠉⠻⢯⡉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣀⣀⣤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠙⢦⠀⠀⠀⠀⠀⢈⡷⣄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣸⠀⠀⠀⠀⢠⣯⡤⠬⢧⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠈⠙⠲⠶⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⣄⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠤⣀⠀⠀⠀⠀⠀⠙⣦⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣌⠳⡄⠀⢠⣄⠀⠙⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣇⠀⣰⠃⢸⡀⣹⣰⠃⢹⡀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⢰⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⣤⣤⠴⠞⠁⠀⠀⠀⠈⠷⣄⣀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿

⢠⠀⡀⡄⡄⠀⡄
⠀⠄⠈⠰⠀⠀⠁⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡥⠶⠶⢦⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣿⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⡴⠏⠀⠀⣿⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣒⣚⡛⠛⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠀⣤⣤⣶⣶⡄⣴⠤⠶⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠿⣤⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠁⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣤⣤⡄⠀⠀⠀⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣵⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠋⠀⠷⣤⣴⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠛⢿⡛⠲⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢸⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⡠⠤⠤⠤⢼⣀⠈⠙⠓⠒⠶⠤⠤⠴⡇⠀⢰⠋⠀⠀⠀⢹⡉⣦⠀⠀⡞⠁⠀⠀⠈⣏⢱⡄⠀⣸⠀⠀⠀⠀⢸⡄⢠⠞⠲⣾
⢸⠃⠀⠀⠀⢸⠈⠉⠛⠒⠶⠤⠤⠤⢤⣿⠀⠈⠣⣄⣀⣀⣼⡵⠋⠀⠀⠙⢤⣀⣀⣠⡯⠞⠀⢠⡇⠀⠀⠀⠀⢸⠉⠉⠀⠀⡿
⣾⣀⠀⠀⠀⢼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡞⠀⠀⣠⠖⠛⠻⣟⠛⠛⠛⠛⠛⢻
⡟⠈⠉⠛⠒⣿⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠸⣿⡿⠀⠀⢿⣿⠗⠀⠀⠀⠀⡼⠁⠀⢰⠃⠀⠀⠀⠈⢿⠛⠛⢻⡛⠛
⡇⠀⠀⠀⠀⣿⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣤⣄⠀⠀⣠⣤⡄⠀⠀⢀⡞⢻⠀⠀⢸⠀⠀⠸⡄⠀⣸⣀⡤⣞
⡇⠀⠀⠀⠀⢻⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠿⠟⠀⠀⠻⠿⠃⢀⡴⠋⠀⣼⠀⠀⢸⠀⠀⠀⣏⣉⠉⢀⣀⣼⠁
⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣄⣀⣀⣤⠤⠖⠋⠀⣠⠞⢸⡄⠀⠘⣇⠀⠀⣏⠉⠉⠉⢁⣸⠆
⢿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⢸⡇⠀⠀⠘⠦⣄⡈⢹⠋⠉⢹⡇
⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣄⣀⣠⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠙⠲⠶⠞⠃
⠀⠳⣄⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡤⠖⠒⠚⠛⠛⠛⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠻⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⢴⣚⣁⠀⠀⠀⢀⣀⣠⠴

⠀⠀⠀⠀⠀⢠⣶⠶⠷⠶⠶⠶⣶⣤⣀⣀
⠀⠀⠀⠀⢰⡿⠁⠀⢀⣀⣀⣀⣀⣹⣿⣍⠳⣤⠖⡷
⠀⠀⠀⣀⣿⠇⠀⢠⡿⠋⠉⠁⠀⠉⠉⠻⣿⣋⡼⢧
⠀⣾⡟⠛⣿⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣿⠻⣄⠈⠓⣆
⠀⣿⠀⠀⣿⠀⠀⠀⠙⢷⣦⣤⣤⡴⠶⣿⡏⠀⠈⢣⡀⠈⡿⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⡀
⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠙⢦⠇⠀⠀⢠⣴⠟⠋⠉⠉⠀⠀⠉⢻⣦
⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⣀⣀⣀⣀⣀⣀⣼⡿⠶⢦⡄
⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠛⢛⣋⣉⣉⠉⠉⠻⣧⠀⠀⣿
⠀⠈⠛⠻⣿⠀⠀⠀⢰⣿⢷⣶⠂⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡴⢞⣫⣭⣭⡉⠙⢦⡀⢻⡇⣰⡟
⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠘⣿⣀⣀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⠛⠛⠋⢀⣨⡿⠀⣸⠇⢸⣷⡿⠁
⠀⠀⠀⠀⠙⠻⠿⠿⠟⠃⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣠⡟⠀⠀⢹⣿⠤⠟⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠿⠶⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⡟⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆
⠀⠀⠀⠀⠀⢠⣿⣿⠛⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⠋⠁⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢿⣿⣧⣤⣤⣤⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣦⣤⣴⣾⣿⡟⠀⠀⠈⠛⠿⠿⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠾⠿⠿⠿⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠘⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠁⢀⣀⣤⣤⣶⡶⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠛⠻⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⢀⣠⣴⣶⡶⠶⠶⠶⠶⠶⢶⣶⣄⣀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣄⣀⣀⣀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠿⠿⠿⠟⠛⠻⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠋⠉⢹⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢿⡇⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⢿⣦⣅⣈⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⢶⣶⣶⣶⣶⣶⠶⠿⠟⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢸⡇⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠛⢿⡟⠿⠿⣿⡿⠿⢿⡟⠛⠛⣿⣛⣿⠏⠀⣿⠑⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⠷⣼⣿⠶⢾⣿⡿⠁⢀⣼⠏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⢾⣿⣷⣾⣿⠶⠞⠛⠁⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⣶⢶⠿⠶⠂⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣀⣀⣀⣀⣀⣤⣤⣼⠇⠀⠀⠻⣿⠶⠶⠶⠶⠾⠿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⡉⠙⠋⠉⠉⣩⣿⠇⠀⠀⠀⠀⠙⠷⣦⣤⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠓⠶⢦⣤⣤⠤⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠈⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠒⠲⠿⢿⣍⣛⠓⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⣠⠟⢷⡄⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢰⡇⠀⠀⠀⠀⠀⣰⣧⣤⠤⠿⣆⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣄⣤⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠦⠤⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣀⣀⡀⠀⠉⠛⠒⠒⠒⠒⠚⠛⠒⠲⢤⣀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⡙⢲⡀⠀⠀⢀⡀⠀⠙⢻⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢷⠀⠀⠀⡴⠋⣧⠀⢹⡀⣠⠟⢻⡀⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣘⣧⣀⣼⣧⣤⣼⣦⣼⣥⣯⣄⣨⣧⣀⣸⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⢰⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⡏⠁⠀⠀⠀⠀⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣀⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠛⠛⠛⠛⠻⠿⣿⣶⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣍⠙⢦⣄⣰⠾⡆
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣴⣾⠿⠿⠟⠛⠛⠛⠿⢿⣿⣧⣴⡟⠁⣼⠃
⠀⠀⢀⣀⣠⣴⣿⠇⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣠⡾⠛⢶⡀
⠀⢰⣿⡟⠛⢻⣿⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⣆⠀⠈⠛⢳⡄
⠀⣾⣿⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⣦⣄⣀⣀⣀⣀⣠⣤⣾⣿⠏⠀⠈⢳⣄⠀⠈⠙⣷
⠀⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠛⠛⠋⠉⢹⣿⠀⠀⠀⠀⠙⢦⡀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⠾⠿⠿⠿⠷⣶⣤⡀
⠀⣿⡏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠻⣾⠃⠀⠀⠀⢠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣤⣄⡀
⠀⣿⣷⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⣤⣶⣶⣶⣿⠿⠿⠿⠿⠶⣾⣿⡏⠀⠀⠙⣿⡆
⠀⠸⣿⣄⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⢁⣀⣤⣤⣤⣤⣄⣀⠀⠀⠹⣿⣆⠀⠀⣿⡇
⠀⠀⠙⠛⠿⢿⣿⡄⠀⠀⠀⠀⣼⣿⢿⣿⡿⠋⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⢠⡴⠟⣋⣭⣥⣤⣄⠈⠙⠻⣄⠀⢹⣿⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣠⣿⣷⣿⡿⠋⠉⠙⣿⡆⠀⠀⣿⡀⢸⣿⣤⣿⠏
⠀⠀⠀⠀⠀⠐⣿⣧⣀⣀⣀⣠⣿⡟⠀⠹⢿⣶⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⡟⠀⠀⣤⠀⠀⠐⢶⣿⡅⠀⢰⡟⠀⢸⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣤⣼⣏⠀⠀⠀⢸⣿⠷⠶⠟⢁⣰⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣶⣿⣧⣤⡴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠞⠛⠛⠛⠛⠛⠻⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠛⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⢆⠁⣀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⣤⠄⡠⠆⣠⣉⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⣦⠙⢈⠲⣀⠙⠷⣇⣠⣖⠀⠀⠀⢀⣦⡀⢀⡥⠂⣠⠘⣠⠜⣡⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠐⠰⠷⣮⡑⠎⣱⠤⣈⠁⠉⠀⠀⠐⠊⠁⣈⡠⠄⢢⡀⢚⣠⡞⠄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠈⠉⠐⠈⠘⠂⠮⠬⠋⣏⣈⡉⠧⠸⠂⡉⠥⠒⠉⠁⠀⠀⠀⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⣂⣀⣠⣤⠄⠀⠀⠀⠚⠓⡒⢂⣠⣤⣴⠶⠾⠿⠿⠟⠚⠛⠻⠾⠶⠷⣦⣤⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣤⠤⠚⣋⣩⡥⢤⢶⡔⡚⠋⠉⣭⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⢈⡥⢖⠙⠛⢁⠈⣤⣰⣄⣿⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⢏⠉⢡⡈⣗⣺⠷⠛⢋⣩⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡏⣌⠀⣋⡫⠝⢋⡤⡶⢮⢾⡈⢿⡃
⠀⠀⠀⠀⣠⡶⠟⠛⣛⢛⣿⢟⢋⡷⢋⣰⢎⡛⢶⣿⡀⢻⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢀⣾⣯⠛⢨⣉⣥⢸⣿⡴⢃⡴⢿⡙⢦⡿⠄⠉⢀⣴⣴⡷⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟
⠀⢀⣾⡅⣉⣉⣉⣉⡉⢙⣟⡰⢏⠻⢮⠷⠀⣡⣤⣾⠟⠋⢁⠄⢠⡞⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⢶⣿⠁
⠀⣼⡟⣧⡼⣆⢀⡽⣿⢻⣿⠷⣦⠧⠈⣠⣴⡿⢋⣀⣀⡁⠀⣶⣿⠁⠘⠷⣬⡝⠛⣿⣶⣶⢶⣶⣶⠶⠶⠶⠞⠛⠛⠋⠉⣠⡶⠃⢹⡀
⢠⣿⣠⣿⢀⠿⣿⡄⢨⢿⣿⡧⠈⣀⣴⡟⢁⠀⣽⠙⢻⣷⣄⡿⠉⠀⠑⠀⠈⠓⠚⠋⠚⠂⠰⠍⠛⣷⣶⡃⠀⢀⣶⡶⠟⠻⡄⠀⢹⡇
⢸⣟⣿⠟⣿⡇⣠⣿⡯⢸⣿⢃⣠⣿⠋⠀⠀⠐⣿⠆⠂⡄⠉⣁⡠⣴⠆⠀⠻⠋⠛⠋⠉⠱⠶⢢⣤⠄⠉⠛⠶⣟⠁⠀⠀⠀⠈⠀⢹⡇
⣼⡇⡷⠀⢸⣿⣿⢐⣷⣼⣯⣸⡿⠁⣞⠛⢿⠶⣿⠀⢀⣴⠈⠙⠒⠀⠀⠀⠀⠈⠀⠀⠠⠀⠘⠀⠀⠀⠹⠓⣤⡀⠀⢤⣀⡀⣀⠄⢸⡇
⣿⡃⣟⢶⣾⠁⢟⣿⠃⣸⣿⡿⠀⠆⠿⣦⣠⠂⠠⠾⠇⠍⠀⠀⠀⠀⠀⠠⠀⣀⢀⣀⠤⠤⠀⡀⠀⠀⠄⠁⠉⠉⢰⣄⠙⢿⡇⠀⢸⡇
⣿⢰⡁⠀⣸⣷⣯⠙⠗⢻⡿⠁⣨⣤⡤⠿⠀⣴⠀⠀⠀⠈⠀⡴⢦⠀⠀⠀⠀⠀⠀⠆⠀⡁⠈⠀⠁⠀⢤⡀⠠⣀⠐⠠⠷⡀⠻⡄⢸⡇
⣿⡎⢣⣴⠁⠈⡷⣴⡟⢻⡇⠘⣌⠉⠴⠀⣾⡠⢄⠀⠀⠀⠀⠀⠀⢀⢀⡀⡠⠄⠒⠀⠀⣵⢤⣀⣀⠊⠀⠃⠀⠀⠀⠀⠀⠴⣆⠀⣼⡇
⢿⡷⠋⠙⣦⣇⠀⠸⠃⢾⣷⡔⠻⣅⠁⣤⠀⠀⠀⢠⡂⠀⠀⢠⠀⠀⢃⠀⠀⠀⠁⠀⠀⢀⠢⡹⠃⠀⢨⠰⠀⡀⡀⠀⠀⠀⠺⠆⢸⡇
⢸⣧⢦⣴⠉⠸⣧⣤⡶⢾⣇⣴⡶⠋⢠⡍⠀⠄⠀⠈⠀⠁⢄⣠⡀⠀⠀⢢⠀⠶⠀⠀⠀⢸⡸⠁⠀⠀⡆⣄⡷⠔⠙⡀⠀⠀⠀⣴⣾⡇
⠈⣿⡉⠘⣦⣁⢾⣻⡄⢾⡿⣄⡀⠃⠈⠁⠀⠀⠈⠄⠠⠀⠀⠙⢧⠀⠀⠈⠖⠂⠀⠀⠀⢾⠃⠀⠀⢸⡝⠋⠀⣠⠇⠀⠀⠀⠈⠰⣿⡇
⠀⢹⣧⣶⢟⣿⣤⣴⣮⣼⡷⠘⢧⡀⠸⠂⠀⠀⠘⠀⠉⠒⠄⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡏⠀⠀⡠⠃⠀⠀⠜⠊⠛⠙⠀⠐⠀⢠⣾⠇
⠀⠀⢻⣄⣤⣤⣤⣤⣤⣼⣏⠶⢂⣠⡴⠐⣿⠁⠙⠋⢹⠷⠂⣤⡈⠐⠄⠀⠀⠇⠀⠀⠀⠁⠀⠀⠀⢂⣤⠐⢾⠋⢹⠋⠘⠗⢠⣄⣿⠁
⠀⠀⠀⠻⣯⣛⢛⣭⣑⣽⣧⠴⡏⠀⣡⣀⡾⠤⠾⠤⠼⢀⣴⠁⢀⠟⢂⡀⢀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠀⣄⣸⡄⠼⠄⣴⣀⡬⠁⣿
⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⣿⣀⠼⠂⠉⣀⣤⡄⢢⠀⠀⡄⢀⠈⠛⢤⡞⢙⡄⠢⠀⠀⠰⠁⣶⠉⣤⠜⠋⣁⣀⣤⣤⣤⢤⡀⠙⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠤⠘⠁⢰⠃⢸⡈⡀⢱⢀⡒⠙⡓⠄⠘⢧⠽⡄⠀⠀⢀⠛⣤⠛⣠⡴⢺⡏⢸⣿⠀⢻⡈⣧⢙⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡀⠀⠂⠤⠀⡼⠣⡁⠦⢤⣀⠀⣓⠀⢢⣀⣞⣃⣠⣄⣬⣼⢁⣼⣿⠇⠈⣧⣸⡿⠀⢈⣧⢸⠎⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠷⢐⠆⠀⢄⡀⠀⠼⠃⣄⢄⡬⠀⠰⢸⣿⠉⠉⠉⠉⠉⣿⠷⡟⢸⣇⢠⠷⣾⠙⡖⡊⢻⠿⠄⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⡦⠌⢷⡀⡠⢐⡅⠀⠀⢠⡑⠀⡠⠖⢿⡟⠀⠀⠀⠀⠀⣿⠀⣷⣾⠉⢥⡶⠘⠒⢭⣥⣬⠲⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠉⠙⠆⠀⠀⠀⠀⡝⠲⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠆⣡⣀⡅⢒⡁⠀⠀⠸⢧⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡔⠀⠀⠀⠀⠹⠄⠠⠀⣸⠃⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠙⢫⡀⢀⠀⢠⣦⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠘⠋⠀⠀⠀⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⢀⣠⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡁⠀⠀⠀⠀⢀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠛⠛⠛⠛⠛⠛⣿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⣏⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⢠⠿⡗⠒⠚⠛⠛⠉⢹⡏⠛⠶⠦⣤⣤⣀⣀⣽⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⣰⠏⠀⠹⣄⠀⠀⠀⠀⣸⣧⣄⣀⣀⣀⣀⣠⡟⠙⠳⠾⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣠⠞⠁⠀⠀⢀⣽⡷⠒⠛⠋⠉⣷⠈⠉⠉⠉⢉⡟⠙⠓⠶⠦⣤⣽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠓⣶⢿⣅⡀⠀⢀⣠⠞⠁⣹⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣤⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠈⠛⣶⡋⠁⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡟⠀⠀⠀⣿⠙⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣼⡏⠀⠀⠀⢸⡇⠀⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡛⠉⠉⠉⠙⣿⡇⠀⠀⠀⣼⠁⠀⠀⣼⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢠⣿⠏⠈⠳⡄⠀⠀⠀⣿⣧⣄⡀⢠⣏⣠⡴⢾⡟⠛⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢹⡄⠀⢰⣿⠉⠙⠿⣿⣍⠀⠀⠀⢻⡄⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣧⣴⢾⣿⠀⠀⠀⠈⠻⣷⣄⠀⠀⢿⠀⠀⢙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿
⠀⠀⠀⠀⣿⡏⢷⡀⠀⠀⣰⠟⠷⣼⣿⠀⠀⠀⠀⠀⠈⢿⣦⠀⢸⣤⠶⠋⠁⠙⢻⣷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⢿⣿⣿⣿
⠀⠀⠀⢠⣿⠁⠈⣧⣠⡞⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⠛⠛⢦⡄⠀⢠⡞⠁⠈⢉⡿⠛⠛⠛⠛⣿⠛⠛⠛⠛⠻⣏⠉⠁⣴⡿⠋⢸⣿
⠀⠀⠀⢸⣿⠀⠀⣼⢯⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠹⣶⣏⡀⠀⢀⡾⠁⠀⠀⠀⠀⢸⡀⠀⣀⣀⣀⣹⣦⣾⡟⠀⠀⢸⣿
⠀⠀⠀⢸⣿⢀⡾⠁⠀⠈⠳⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣰⠋⠉⠉⠓⣾⠗⠚⠛⠛⠛⠒⢾⡟⠋⠉⠀⠀⠈⣽⡟⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⣞⠁⠀⠀⠀⠀⠹⣆⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣼⠃⠀⠀⠀⢰⡇⠀⠀⢠⠀⣀⠀⢸⡇⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠉⠳⣄⠀⠀⠀⠀⢹⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣀⣀⠀⠀⣾⠀⣼⠀⣿⢼⣿⣷⢸⡇⣥⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠈⣿⡄⠀⠘⣧⠀⠀⢠⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠉⠉⠙⠶⣯⣤⠾⣶⣿⣾⣿⣧⣾⣷⠷⠖⠛⢻⣿⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠸⣇⣰⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡇⢠⠟⡿⢻⣿⣿⣿⢻⡟⣦⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠋⠀⠀⢸⣿⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⣿⣇⠀⠀⠀⢸⡇⠸⡀⢧⢸⣿⣿⣿⢸⡇⡾⠀⠀⢸⡇⠀⣀⣠⣤⣴⣿⡇
⠀⠀⠀⠀⠈⣿⣇⠀⢰⠟⠛⠲⢦⣼⣿⠀⠀⠀⠈⠉⠙⢻⣿⣶⣤⣿⠏⠙⠛⠲⢼⣧⡤⠷⠶⠶⠿⠿⣅⣸⣧⡥⠶⠒⢻⣿⡿⠟⠋⠉⢉⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣤⡟⠀⠀⠀⠀⢹⣿⣦⣤⣄⣀⣀⡀⣸⠃⠀⠙⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⣀⣀⣀⣡⣤⣤⣶⡶⢿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⢸⣿⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⢾⣿⠶⠶⠶⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉⢹⣿⠉⠉⠉⠀⠀⢀⣀⣀⣤⣴⣶⠿⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⡆⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠉⠉⣿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣿⡇⠀⠀⠀⢸⣿⠀⠀⣀⣀⣤⣤⣤⠤⠤⠤⢤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠳⢦⣿⣀⣤⣤⣤⣤⣤⣤⣀⣀⢀⣿⠀⠀⠀⠀⠈⣿⡗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⡿⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⢐⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣤⣤⣤⣴⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣶⣶⣶⡶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠛⠳⢶⣖⠒⠲⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠠⠤⢴⣶⡒⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠰⣏⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⡼⠳⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡞⠀⠀⠀⠀⠀⣾⣥⠤⠽⣦⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⣀⠀⠛⠛⠓⠲⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠤⢤⣀⣈⠉⠉⠁⠀⠀⠉⠉⠲⣄⢀⣠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠸⢯⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡆⠀⠀⢀⡞⣧⠈⢧⠀⣠⠾⡄⠀⠘⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢻⣀⣀⣟⣀⣸⣄⣸⣰⣏⣀⣳⡀⢰⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠃⠀⠀⣆⣀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⢠⡏⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⡦⠴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠶⠞⠋⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠛⠛⠛⠛⠻⠿⣿⣶⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣍⠙⢦⣄⣰⠾⡆
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣴⣾⠿⠿⠟⠛⠛⠛⠿⢿⣿⣧⣴⡟⠁⣼⠃
⠀⠀⢀⣀⣠⣴⣿⠇⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣠⡾⠛⢶⡀
⠀⢰⣿⡟⠛⢻⣿⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⣆⠀⠈⠛⢳⡄
⠀⣾⣿⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⣦⣄⣀⣀⣀⣀⣠⣤⣾⣿⠏⠀⠈⢳⣄⠀⠈⠙⣷
⠀⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠛⠛⠋⠉⢹⣿⠀⠀⠀⠀⠙⢦⡀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⠾⠿⠿⠿⠷⣶⣤⡀
⠀⣿⡏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠻⣾⠃⠀⠀⠀⢠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣤⣄⡀
⠀⣿⣷⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⣤⣶⣶⣶⣿⠿⠿⠿⠿⠶⣾⣿⡏⠀⠀⠙⣿⡆
⠀⠸⣿⣄⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⢁⣀⣤⣤⣤⣤⣄⣀⠀⠀⠹⣿⣆⠀⠀⣿⡇
⠀⠀⠙⠛⠿⢿⣿⡄⠀⠀⠀⠀⣼⣿⢿⣿⡿⠋⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⢠⡴⠟⣋⣭⣥⣤⣄⠈⠙⠻⣄⠀⢹⣿⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣠⣿⣷⣿⡿⠋⠉⠙⣿⡆⠀⠀⣿⡀⢸⣿⣤⣿⠏
⠀⠀⠀⠀⠀⠐⣿⣧⣀⣀⣀⣠⣿⡟⠀⠹⢿⣶⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⡟⠀⠀⣤⠀⠀⠐⢶⣿⡅⠀⢰⡟⠀⢸⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣤⣼⣏⠀⠀⠀⢸⣿⠷⠶⠟⢁⣰⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣶⣿⣧⣤⡴⠶⠛⠉

⠀⡀⢀⠀⣠⢀⠀⠤⢠⠀⡠⠀⠀⠀⠀⠀⡠⠂
⠀⠑⠂⡇⠉⡌⠀⠀⠞⠀⡇⢀⠀⠀⠀⠀⡑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠌⠣⠐⠀⠃⠀⠒⠀⠘⠁⠄⠀⠀⠐⠄⠁⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠋⠉⠉⠙⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⣶⠶⠶⣶⣦⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢸⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠶⠶⠶⠶⠾⠿⠛⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠛⠛⠛⠛⠛⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⣤⣤⣤⣶⣶⠶⠆⠴⠦⠤⠶⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⣻⣆⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠟⠒⠂⠐⠒⠲⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⢸⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡏⠉⣿⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢛⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣸⡇⠀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⠻⢶⣶⡶⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠙⠛⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠛⠛⠛⠋⠉⠛⠛⠻⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠈⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠉⠉⠁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣴⣶⣾⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢫⣿⡿⠟⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡇⣿⡿⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⠀⢿⣧⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⠛⠉⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⠘⢿⣷⣤⣤⣶⣿⣿⠁⠀⠀⠀⠀⢸⣿⣏⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⠀⠀⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⣿⣿⡏⠀⠸⣿⣿⡀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⣿⠀⠀⢀⣀⣀⣀⡀⢸⣿⠀⠀⠀⢀⣰⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠀⠀⢸⣿⢻⣿⠀⢸⣿⣶⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣤⣼⡿⠘⢿⣷⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁

⢀⠄⡄⢠⢠⠀⢠⠀⡀⠀⠀⠀⢀⠐
⠀⠀⠘⠀⡄⢀⠈⢠⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣤⣤⣄⡀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠀⠀⠀⠈⣷⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⣀⢀⣀⣠⡟⠀⠀⣿⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣼⠉⠉⠉⠉⠉⠉⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢀⣀⣀⡀⣀⠀⣀⣤⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⡶⣦⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠉⠛⠻⠿⠾⠶⣿⣷⠬⠭⠉⠉⢭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢲⡖⢲⡆⠀⠀⠀⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⡇⢸⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⠘⠷⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣯⣙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣤⣴⣶⣾⣿⣿⣿⣿⡿⠋⣿⣿⡄⠀⠀⠀⠈⠉⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣉⡻⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⢀⡟⠉⠙⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⣸⠇⠀⠀⠘⠿⢿⣿⣿⣿⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⢀⡤⠤⡄⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⢀⣤⠞⠉⠢⡀⠀⠀⠀⠀⢀⣀⣤⠤⡀
⠀⠀⠀⣜⡁⣤⣬⣦⠀⠀⢠⣒⣡⣤⣖⣣⠀⠀⠀⠀⣠⣼⠦⣼⡀⠀⠘⠾⣃⣉⣉⣉⡇⠀⠀⠀⡏⠀⣀⣤⣸
⠀⢀⣠⠇⡞⠉⠙⢳⠀⠀⣀⡟⢰⠋⠉⠛⡆⠀⢀⣠⡇⡞⠉⠙⢳⡀⢀⣠⡇⡞⠉⠙⢳⡀⠀⣀⣼⢹⠛⠛⠛⣆
⠀⣾⢸⠀⠙⠒⠒⢺⠀⢰⠃⡇⠈⠓⠒⠲⡇⠀⣼⢸⠁⠙⠒⠒⢺⠀⢸⢸⠇⠙⠒⠒⢺⠀⠀⡇⣿⠈⠓⠒⠒⡇
⠀⢻⣸⠀⠀⡀⠀⣸⠀⠘⣆⡇⠀⠀⠀⢴⠃⠀⢹⣸⡀⠀⢀⣀⡼⠀⢸⣸⡀⠀⠀⠀⣸⡀⠀⣇⣇⠀⢀⠀⢀⡇
⠀⠀⠘⣆⣸⠹⠤⠇⠀⠀⠺⣍⡽⠚⠲⢄⣙⡆⠀⠀⠿⡆⣸⠿⠀⠀⢸⣁⣁⠞⠉⠻⣄⡽⠀⠐⣏⣡⣼⣉⡏
⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⣰⣲⣄⠀⠉⠀⠀⠀⠈⣉⣁⠀⠀⠀⠀⠀⢠⣄⣤⠀⠈⠀⠀⠀⣀⡤⠤⢄
⠀⢀⣼⡥⢴⣶⣇⠀⠀⠀⠀⣎⡠⣤⣌⡇⠀⠀⠀⠀⣾⣛⣭⣵⡀⠀⠀⠙⣭⠔⣚⣦⡀⠀⠀⠀⣧⡦⢀⡼⣤⡀
⠀⡼⡟⢸⠉⠉⠉⡧⠀⢠⢴⡇⣎⠉⠉⢙⡆⠀⣠⢼⠁⡏⠉⠉⢹⠄⢠⢤⡇⣎⠉⠉⢙⡆⠀⣠⢼⠁⡏⠉⠉⢹
⢸⠁⡇⠀⠙⠛⠉⡇⠀⢸⢸⡇⠈⠙⠋⢹⠀⠀⡇⢸⠀⠈⠛⠋⢻⠀⢸⢸⡇⠈⠙⠋⢹⠀⠀⡇⢸⠀⠉⠛⠛⢻
⠘⢦⡇⠀⣀⡀⢀⡇⠀⠸⣼⣄⠀⠀⠀⢞⡀⠀⠳⣼⡀⠀⢀⣤⠞⠀⢸⣼⣇⠀⣀⣀⡸⣄⠀⠧⣼⣀⠀⣀⣀⡼
⠀⠀⠳⢤⠏⠳⠞⠀⠀⠀⠳⡬⠟⠉⠓⢄⣹⠆⠀⠀⢻⣆⡼⠚⠀⠀⠸⣄⣠⠎⠉⠙⢆⡼⠀⠀⠧⠤⠴⣏⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣠⠂⣻⣿⣀⣴⡄⠀⠀⠀⠐⣂⡭⢭⣒⠁⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠋⣤⠬⠿⣤⡀
⠀⠀⠀⠿⣿⡁⣀⣈⣟⠛⠀⠀⢀⣰⠃⣴⠒⠚⠳⡄⠀⠀⠀⢠⠠⠈⡦⠀⠴⠁⠀⠀⠀⢰⡟⡟⠈⢧⣀⣀⣼⠃
⠀⠀⠐⣶⣿⡇⢉⣿⣿⡶⠀⠀⡟⢽⠀⠙⠿⠶⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠽⠿⠏⠉⠁⠀⠀⣧⣸⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⠀⠀⠤⠀⠀⠗⠊⠀⣶⡾⠟⠁⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠈⢹⡀⢰⢶⣋⡿⠀⠀⠀⠀⠚⠶⠾⠿⠶⠶⠓⠂⠀⠀⠉⠙⠳⣤⠴⠛⠛⠁
⠀⠀⠀⠀⢲⢊⣨⣥⣆⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⣄
⠀⠀⠀⠀⣀⡏⢠⡖⠚⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢣⡜⢛⣛⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢰⣏⠉⠉⢳
⠀⠀⠀⢸⢹⠇⠘⠿⣶⢶⡏⠀⠀⠀⠀⠀⠀⠀⡴⣾⠀⣿⣄⣀⣹⠆⠀⠀⠀⠀⠀⣿⢸⠀⠈⠻⠿⠿⣟
⠀⠀⠀⢸⢸⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠈⠉⠋⣻⠀⠀⠀⠀⠀⠀⢿⣸⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠈⠹⡆⠀⡶⡞⣸⠁⠀⠀⠀⠀⠀⠀⠀⠧⣇⠀⢀⣀⡄⡿⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⡶⡞⢱⠇
⠀⠀⠀⠀⠀⠉⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠞⠻⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣭⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣴⣶⣿⣿⣿⣿⠟⠿⠿⠉⠉⠉⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⡶⠶⣦⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⣿⠁⡞⠙⢻⣿⣿⣿⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⡇⠀⠸⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠚⠁⠀⠀⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀⠀⠀⡠⠄⢤⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⢀⢤⡞⠉⠢⡀⠀⠀⠀⠀⢀⣠⡤⢤⡀
⠀⠀⠀⣎⠠⣤⣼⡦⠀⠀⢰⣊⠤⣶⣾⡄⠀⠀⠀⣠⡶⠷⢼⡄⠀⠘⠺⣍⣉⣈⢍⡆⠀⠀⠀⡇⢀⣠⣄⡇
⠀⢠⢼⠁⡏⠉⠉⢳⠀⢀⢤⠇⡎⠉⠉⢳⠀⠀⡤⡏⢼⠉⠉⠙⡄⢀⣤⡇⡞⠉⠉⢳⠀⠀⣠⡟⢽⠉⠉⠹⡄
⠀⡏⢸⠀⠙⠛⠛⡇⠀⢸⢸⠀⠈⠓⠛⣿⠀⢸⠁⡇⠈⠛⠚⢻⠀⢸⢰⡇⠈⠓⠛⢻⠀⢸⠁⡇⠈⠓⠒⢻
⠀⠳⢼⠀⢀⣀⠀⡇⠀⠸⣼⣄⠀⠀⠠⣏⡀⠘⠦⣇⠀⢀⣤⠜⠀⠸⡼⡅⢀⣀⣀⠼⡀⠘⢦⣇⠀⢀⣀⡸
⠀⠀⠘⠦⠜⠘⠚⠁⠀⠀⠳⠬⠋⠉⠓⢤⡽⠀⠀⠘⣷⣸⠛⠀⠀⠸⠤⠤⠋⠀⠙⠤⠏⠀⠘⠦⠴⠯⠼⠃
⠀⠀⢀⠴⢒⠢⡀⠀⠀⠀⠀⡠⠏⠳⣄⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⢀⣰⠢⢆⠀⠀⠀⠀⢠⠴⡖⠒⡆
⠀⢠⡾⢒⡿⠿⣧⡀⠀⠀⢸⠄⡶⠶⢾⡄⠀⠀⠀⡾⣤⠶⠾⣦⠀⠀⠈⡖⣨⠭⠷⣆⠀⠀⠘⢲⢓⡴⢿⣦⡀
⢠⠞⡇⠸⣄⣀⣠⡇⠀⡖⢻⠘⢇⣀⣀⡿⠀⢰⠚⡇⠻⣀⣀⣨⠃⢰⠚⡇⢣⣀⣀⣸⠃⠀⡖⣿⠸⣄⣀⣀⡇
⢸⠀⡇⠀⠀⠀⢸⡆⠀⡇⢸⠀⠀⠀⢀⡇⠀⢸⠀⡇⠀⠀⠀⢸⠀⢸⢸⡇⠀⠀⠀⢸⠀⠀⡇⡏⠀⠀⠀⠀⡇
⠀⠙⡇⠀⡶⡆⣸⠁⠀⢹⡛⢤⡤⢤⡘⠢⣄⠈⠛⢧⡀⢰⣲⠋⠀⢨⠟⠃⣠⠤⢴⠚⢦⠀⢱⡗⠂⣰⠦⡴⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠋⠉⠉⠉⠉⠛⣍⣓⣶⣲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠢⣄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠀⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⡇⠀⠈⢣
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⡇⠀⡰⠊
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠑⢤
⠀⠀⠀⠀⢸⢤⣀⡀⠀⠀⠀⢸⡃⠀⢀⠤⠤⢤⣄⠀⠀⠀⡠⠤⠤⣤⡀⠀⠀⡇⠀⠀⢀⡇⠀⣀⢸
⢠⠚⠉⠑⣿⠦⢄⣈⣉⠉⠛⠛⡇⠀⣇⠀⠀⢈⣇⡇⠀⢺⡀⠀⠀⣱⣸⠀⢸⠀⠀⠀⠀⡧⠜⠉⢹
⣜⠀⠀⠀⣿⡄⠀⠀⠈⠉⠉⠉⢳⠀⠈⠙⠒⠋⠉⠀⠀⠀⠉⠓⠚⠉⠁⢀⠇⠀⢀⠤⠴⡧⠤⠤⠾⠤⢤
⡏⠙⠒⠒⡇⠹⡄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠰⣿⡷⠀⠸⣿⠇⠀⠀⢀⡞⠀⢠⠃⠀⠀⠈⣖⠒⠲⡖⠚
⡇⠀⠀⠀⡇⠀⠘⢆⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⣴⣦⠀⢠⣶⡄⠀⢠⠎⡇⠀⢸⠀⠀⢧⣀⡼⠤⠾⡁
⡇⠀⠀⠀⡇⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠙⠦⣀⠙⠁⠀⠈⢉⣠⠔⠁⡠⢷⠀⠸⡀⠀⣹⠦⠤⠴⠺⡁
⡇⠀⠀⠀⢿⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⡤⠊⠀⢸⠀⠀⠳⣄⠘⢲⠖⠒⡞⠁
⢹⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⢤⣀⣀⠤⠤⠖⠊⠁⠀⠀⠀⢸⠀⠀⠀⠀⠉⠙⠦⠤⠃
⠈⠣⠤⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⠖⠋⠉⠉⠉⠉⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠣⠤⢤⣤⡤⠤⠤⠔⠁⠀⠀⠀⠀⠘⠦⠤⢤⣤⡤⠤⠴⠃⠀⠈⠉⣙⠆⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠙⠛⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠛⠛⠛⠋⠉⠛⠛⠻⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠈⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠉⠉⠁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣴⣶⣾⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢫⣿⡿⠟⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡇⣿⡿⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⠀⢿⣧⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⠛⠉⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⠘⢿⣷⣤⣤⣶⣿⣿⠁⠀⠀⠀⠀⢸⣿⣏⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⠀⠀⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⣿⣿⡏⠀⠸⣿⣿⡀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⣿⠀⠀⢀⣀⣀⣀⡀⢸⣿⠀⠀⠀⢀⣰⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠀⠀⢸⣿⢻⣿⠀⢸⣿⣶⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣤⣼⡿⠘⢿⣷⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁

⠀⡀⢀⠀⣠⢀⠀⠤⢠⠀⡠⠀⠀⠀⠀⠀⡠⠂
⠀⠑⠂⡇⠉⡌⠀⠀⠞⠀⡇⢀⠀⠀⠀⠀⡑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠌⠣⠐⠀⠃⠀⠒⠀⠘⠁⠄⠀⠀⠐⠄⠁⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠋⠉⠉⠙⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⣶⠶⠶⣶⣦⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢸⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠶⠶⠶⠶⠾⠿⠛⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠛⠛⠛⠛⠛⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⣤⣤⣤⣶⣶⠶⠆⠴⠦⠤⠶⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⣻⣆⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠟⠒⠂⠐⠒⠲⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⢸⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡏⠉⣿⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢛⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣸⡇⠀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⠻⢶⣶⡶⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠛⠛⠛⠛⠛⠛⠷⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠉⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠯⠈⢁⠀⠀⠀⡀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢠⣄⡀⣠⠔⢀⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣧⡙⠦⠓⣄⠙⠳⣞⡇⠀⣠⠀⠀⠀⠀⢠⡀⠀⢘⡡⠆⢁⠴⢋⡸⢋⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⠋⣷⣄⠛⢤⡓⢤⡈⠑⠚⠽⠆⠀⠀⠤⠛⠍⠒⢉⡠⡄⠉⡤⢋⣴⣉⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡀⠀⠀⠈⠉⠻⠦⡈⠛⢬⠋⡐⠠⡦⢤⠠⠄⢴⠀⣻⠈⠷⠚⡡⠶⠛⠁⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣉⣁⠑⠒⢃⣈⣁⣤⣴⣦⣥⣤⣤⣤⣠⣄⣤⣒⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣴⠶⠶⠛⠋⡉⣀⣠⡤⠤⠤⣦⣤⣶⠿⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⠷⠾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠠⠞⢘⣩⣴⣶⢛⠝⠛⠘⠒⣄⣠⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢂⣴⡾⢭⠂⣅⣀⣆⢸⣷⡿⠦⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠣⣄⣸⣆⣸⡵⠟⠋⡉⣤⢖⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⡁⣦⡀⢩⡭⠚⣉⡴⢾⡛⢞⢷⡈⢿⡀
⠀⠀⠀⠀⣠⡶⢟⣛⣉⡽⣹⣿⢉⢃⠟⢃⣴⠊⣭⠛⢾⣇⠈⠿⠁⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⢀⣼⣿⡟⢁⣍⣡⣄⢹⣿⡞⢁⡴⢻⡍⠳⣼⠦⠈⡁⣀⣦⣼⠿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⣾⡇⢈⣉⣉⣉⠉⠉⢹⡟⡰⢏⠻⢦⡿⠄⢁⣤⣴⡿⠟⠉⠠⠄⢠⡞⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⣾⣿
⠀⣸⡟⣧⣤⣧⠀⣈⢿⣟⢻⣿⢷⣮⣦⡈⢡⣠⣾⠟⢉⡀⢐⠠⠐⣶⣿⠀⠘⡷⣬⡙⠻⢿⢶⣶⣦⣦⣤⣤⡤⢶⣶⡶⠶⠿⠛⠉⢁⣠⠞⠁⣿
⢀⣿⢁⣿⠅⢸⣿⣏⠀⣹⢾⣿⣆⠈⠀⣠⣿⠛⠁⢰⡏⠻⣿⣦⠀⡟⠉⠀⠡⠀⠈⠳⠶⠟⠓⠛⠀⢼⡛⠻⣶⣶⠆⠀⠀⣶⣶⣶⠿⣯⠀⠀⣿
⢸⡿⢻⣿⣾⣷⠀⣹⣷⡇⢸⡿⠇⢠⣿⡟⠁⠀⠅⣼⣧⠠⢌⡉⠛⠃⢀⣠⡄⠀⢲⡖⠲⠶⠒⠒⢢⡤⢄⣀⠈⠛⠳⢤⡼⠋⠉⠀⠀⠈⠂⠀⣿
⣸⡏⣿⠁⠈⣿⣼⡏⠹⣅⣸⡟⣼⣿⠋⣰⢶⣾⣦⣸⡁⠀⢈⡠⠐⢿⢡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⢶⣦⣀⠈⠀⢀⡀⠀⠀⢀⠀⢹⠂
⣿⡇⢻⢄⣤⡟⣹⢯⣾⠋⣹⣷⣿⠃⡀⣿⡀⠈⡥⠉⢁⣴⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠛⠓⢀⡈⠙⢷⣶⠉⠀⣿
⣿⢃⡜⠉⠛⣇⣠⠞⣿⡀⣿⡿⠃⠐⡀⠈⣻⠛⢁⡐⠉⠉⠈⠰⠀⢀⠀⠀⠀⠀⠀⠈⡉⢉⠁⠰⠈⠴⠠⠄⠀⠁⠀⠀⠀⠘⡛⣦⡀⠻⡄⠀⢿⠇
⣿⡘⢇⠀⡼⠛⣿⡣⣈⣧⣿⡇⢰⠺⠿⠏⠉⢀⠞⠃⠀⠀⠀⠀⠈⠁⠛⠀⠀⠀⠀⠀⢀⠀⠀⠐⡄⠀⠀⠀⡠⠙⡦⡈⠐⠀⠀⠉⠑⣀⠘⠆⣼⠃
⣿⡇⣼⠿⡇⢠⠘⠙⢿⠃⣿⡇⢈⣷⡄⡏⠀⠞⠓⠉⠂⢀⠀⠀⠀⠀⠀⠐⡤⠂⠂⠁⡌⠀⠀⠐⠟⡳⣴⠆⠀⠠⠀⠀⠀⠀⠀⠀⠘⢛⣆⠘⣿
⢻⡟⡁⠀⣹⠺⣄⠀⢃⠀⣿⡇⢋⠙⣦⠀⡼⠄⠀⠀⠀⡆⠀⠀⠀⠱⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡆⢱⠎⠀⠀⡰⠈⡀⠂⣠⡀⠀⠀⠈⠙⠂⣽
⢸⣷⢹⢾⡇⢀⠻⣾⡿⠋⣿⡧⠿⢟⡁⠠⡧⠀⠐⠀⡀⠁⠀⠈⠢⣰⡄⠀⠀⢱⠂⠸⠀⠀⠀⠀⣧⡇⠀⠀⢀⣇⣶⠟⠉⢀⠆⠀⠀⠀⡰⠻⣿
⠀⣿⣆⠂⣿⣤⡾⡯⠹⡄⣿⡗⣦⡄⠁⠀⡀⠀⡄⠀⡐⠀⠱⠀⠀⠈⢷⠀⠀⠀⢙⡉⠀⠀⠀⢈⡏⠀⠀⠀⡸⠞⠁⠀⢰⣧⡀⡀⠀⠀⠀⠺⣿
⠀⠸⣿⣼⡟⡽⠷⠶⠾⠦⢿⡇⠛⠣⡄⠐⠃⠀⣀⣈⣁⣈⠁⠑⠀⠀⢀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠃⠀⠀⠜⢁⠀⠀⠚⠃⣉⣉⣁⠀⠃⠀⣴⣿
⠀⠀⠹⣦⣤⡤⣤⣤⣤⡶⣾⣇⠞⢃⢠⡶⠈⢻⠋⠈⠋⠀⡻⠟⠰⣦⡄⠑⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⡁⣴⠂⢻⠏⠈⡟⠀⠻⠃⢴⣄⣿
⠀⠀⠀⠙⢷⣝⠙⣫⢍⣺⣿⡧⠾⡇⠀⢠⣀⣸⠦⠴⠧⠤⠧⢀⣼⠁⢀⠟⢂⡀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠃⠀⣆⣸⣤⠴⠧⢠⣆⣠⡌⢀⡿
⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⢸⣧⣀⠼⠆⠉⢁⣀⣤⠤⡤⠄⢀⠀⣀⠘⠛⢤⡜⢛⣄⠠⠀⠀⠀⡞⢠⡎⠁⣄⠾⠋⠉⣀⣠⣠⣤⣄⣀⠉⠳⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⢠⠐⠂⢁⡏⠸⡆⢁⠀⡆⢀⠎⠻⡢⡀⠑⢏⡹⡄⠀⠀⠈⡰⢇⣸⠞⢁⡴⢾⣟⢱⣿⡇⠸⡇⢻⡘⢦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢨⠀⢀⡿⡜⢠⣀⡌⠀⠀⡧⠀⢆⠈⡖⢓⠀⣀⢠⣋⡞⢁⣴⣿⡇⠈⣇⢸⣿⠆⠀⣿⡈⣷⠉⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣥⠀⡄⠀⡀⠈⠀⢈⣶⢁⢈⡁⡘⠙⢠⢸⣿⠛⠛⠛⠛⠛⢻⣷⢾⡿⣹⠀⢀⣯⣼⡻⢆⠤⠿⣷⣏⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣘⣂⠄⠘⠉⡔⠀⠀⠈⠑⢈⠁⢀⣈⣾⣿⠀⠀⠀⠀⠀⢸⡏⠸⣇⣿⠓⡊⣀⡹⠤⢞⡒⢀⢃⣤⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠋⠀⠈⢢⠲⡔⠋⠀⠀⠀⠘⣦⣰⠃⠀⢨⡏⠀⠀⠀⠀⠀⢸⣧⠠⢋⠹⠄⡩⠏⠀⠀⠈⣟⣉⠃⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢀⠀⠀⠀⠀⢱⡄⠀⠀⠀⢰⠁⠈⠀⠀⣸⠇⠀⠀⠀⠀⠀⠘⣿⠰⠛⠚⢦⡴⠂⠀⠀⠀⢉⠋⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⡀⠀⠉⠀⠁⠐⠋⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢹⣦⠀⠂⠀⠿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠌⠁⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣀⣀⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⣀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠛⠛⠛⠛⠛⠛⣿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⣏⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⢠⠿⡗⠒⠚⠛⠛⠉⢹⡏⠛⠶⠦⣤⣤⣀⣀⣽⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⣰⠏⠀⠹⣄⠀⠀⠀⠀⣸⣧⣄⣀⣀⣀⣀⣠⡟⠙⠳⠾⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣠⠞⠁⠀⠀⢀⣽⡷⠒⠛⠋⠉⣷⠈⠉⠉⠉⢉⡟⠙⠓⠶⠦⣤⣽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠓⣶⢿⣅⡀⠀⢀⣠⠞⠁⣹⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣤⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠈⠛⣶⡋⠁⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡟⠀⠀⠀⣿⠙⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣼⡏⠀⠀⠀⢸⡇⠀⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡛⠉⠉⠉⠙⣿⡇⠀⠀⠀⣼⠁⠀⠀⣼⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢠⣿⠏⠈⠳⡄⠀⠀⠀⣿⣧⣄⡀⢠⣏⣠⡴⢾⡟⠛⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢹⡄⠀⢰⣿⠉⠙⠿⣿⣍⠀⠀⠀⢻⡄⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣧⣴⢾⣿⠀⠀⠀⠈⠻⣷⣄⠀⠀⢿⠀⠀⢙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿
⠀⠀⠀⠀⣿⡏⢷⡀⠀⠀⣰⠟⠷⣼⣿⠀⠀⠀⠀⠀⠈⢿⣦⠀⢸⣤⠶⠋⠁⠙⢻⣷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⢿⣿⣿⣿
⠀⠀⠀⢠⣿⠁⠈⣧⣠⡞⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⠛⠛⢦⡄⠀⢠⡞⠁⠈⢉⡿⠛⠛⠛⠛⣿⠛⠛⠛⠛⠻⣏⠉⠁⣴⡿⠋⢸⣿
⠀⠀⠀⢸⣿⠀⠀⣼⢯⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠹⣶⣏⡀⠀⢀⡾⠁⠀⠀⠀⠀⢸⡀⠀⣀⣀⣀⣹⣦⣾⡟⠀⠀⢸⣿
⠀⠀⠀⢸⣿⢀⡾⠁⠀⠈⠳⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣰⠋⠉⠉⠓⣾⠗⠚⠛⠛⠛⠒⢾⡟⠋⠉⠀⠀⠈⣽⡟⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⣞⠁⠀⠀⠀⠀⠹⣆⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣼⠃⠀⠀⠀⢰⡇⠀⠀⢠⠀⣀⠀⢸⡇⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠉⠳⣄⠀⠀⠀⠀⢹⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣀⣀⠀⠀⣾⠀⣼⠀⣿⢼⣿⣷⢸⡇⣥⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠈⣿⡄⠀⠘⣧⠀⠀⢠⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠉⠉⠙⠶⣯⣤⠾⣶⣿⣾⣿⣧⣾⣷⠷⠖⠛⢻⣿⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠸⣇⣰⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡇⢠⠟⡿⢻⣿⣿⣿⢻⡟⣦⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠋⠀⠀⢸⣿⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⣿⣇⠀⠀⠀⢸⡇⠸⡀⢧⢸⣿⣿⣿⢸⡇⡾⠀⠀⢸⡇⠀⣀⣠⣤⣴⣿⡇
⠀⠀⠀⠀⠈⣿⣇⠀⢰⠟⠛⠲⢦⣼⣿⠀⠀⠀⠈⠉⠙⢻⣿⣶⣤⣿⠏⠙⠛⠲⢼⣧⡤⠷⠶⠶⠿⠿⣅⣸⣧⡥⠶⠒⢻⣿⡿⠟⠋⠉⢉⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣤⡟⠀⠀⠀⠀⢹⣿⣦⣤⣄⣀⣀⡀⣸⠃⠀⠙⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⣀⣀⣀⣡⣤⣤⣶⡶⢿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⢸⣿⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⢾⣿⠶⠶⠶⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉⢹⣿⠉⠉⠉⠀⠀⢀⣀⣀⣤⣴⣶⠿⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⡆⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠉⠉⣿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣿⡇⠀⠀⠀⢸⣿⠀⠀⣀⣀⣤⣤⣤⠤⠤⠤⢤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠳⢦⣿⣀⣤⣤⣤⣤⣤⣤⣀⣀⢀⣿⠀⠀⠀⠀⠈⣿⡗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⡿⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⢐⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣤⣤⣤⣴⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣶⣶⣶⡶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠶⠶⠶⠶⠤⠄⢄⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢰⣾⡍⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⡠
⠀⠀⠀⣔⣩⡤⢄⡈⠑⡀⠀⡴⠛⡛⠻⢷⣕⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠇
⠀⠀⠀⡅⠀⠈⢦⠈⠀⠰⣀⣱⣄⢈⡄⠙⠙⣧⠱
⠀⠀⠀⢰⢀⡀⠈⢃⠀⠀⢀⠙⠟⡈⡴⢊⣆⠘⣇⠁⠀⠀⣾⣿⡀⠀⠀⠀⠀⠱⠛⣸⠉⠉⢉⣙⣶⢄
⠀⠀⠀⣼⠉⠁⠀⠀⠓⠤⡤⠄⠚⠻⠷⣿⡛⠂⡿⡀⠀⠀⠻⠟⠁⠀⠀⠀⢀⡇⠐⠂⠒⠋⠉⠁⠀⠀⠳⡄
⠀⠀⢠⠠⠀⠠⠤⠤⢠⠊⠀⠀⢀⠀⢦⡼⠁⢰⢧⠃⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠸⡀⠀⡃⠀⠀⢸⠀⠘⠹⣿⡳⢖⣁⣖⡫⠃⠀⠀⠀⠀⠀⠀⠀⢴⠛⢂⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠑⢄⡑⡀⠀⠈⢆⠠⠀⢯⣉⡉⠉⠁⣀⣀⣀⢤⠤⢲⠊⠉⠁⠀⣣⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡄⠙⢶⠀⠀⠀⠑⠌⣢⡀⠙⡅⠉⠀⠀⠀⢀⡀⢀⣤⣴⠶⠿⠂⠙⠷⣦⣽⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠃⠀⠈⠆⢀⠃⠀⠀⠀⡿⡄⡗⠀⠀⠀⣀⠤⣶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⠀⠀⠀⠀⠀⠀⡇
⠀⠦⡀⠀⠈⠀⠀⠀⠁⠀⠀⢀⣼⠑⠟⠤⠤⠤⡈⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠀⣿⠀⠀⠀⠀⠀⠀⢃
⠀⢀⠈⢦⡀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠰⢲⢀⠇⣰⠇⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠃⢧⡀⠀⠀⠀⠀⢸
⠀⠈⠰⠀⠳⣄⢇⠀⠀⠀⢀⡏⠀⠀⠀⠰⠼⠸⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠘
⠀⠀⠀⠳⡀⠫⣠⡁⠀⠐⢻⡀⠀⣀⠴⣠⠀⡇⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠑⢄⠈⠙⢦⠰⠸⣇⠎⢁⠴⠿⠀⢹⠀⠈⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⣒⣶⣤⣤⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⢁⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢀⠑⠁
⠀⠀⠀⢀⠴⠂⠊⠐⠂⢄⠀⠀⢀⣼⡿⣿⣼⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⡎
⠀⠀⠀⡮⠂⠙⢯⠑⠆⠈⠆⠀⡎⡀⠳⠀⠨⡽⣷⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁
⠀⠀⠀⢸⠀⠀⠈⣧⠀⠀⠈⠦⠾⣵⡠⠿⡀⣄⠈⢷⠘⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣇⣀⢠⣤⣤⣤⣤⣀
⠀⠀⠀⠈⣣⠤⠐⠀⢧⡀⠈⠲⠀⢋⣥⣶⣡⣼⣆⢸⡇⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⡏⠨⠾⠂⣀⣤⠴⠾⠛⢦⡀
⠀⠀⠀⡸⡇⠀⠀⠀⠀⠩⢓⠖⠊⠉⠉⠛⠻⣯⠌⢸⡇⡄⠀⠀⠘⠋⠁⠀⠀⠀⠀⣰⠁⠈⠁⠉⠁⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⡇⢆⢀⠖⠒⠀⠴⠁⠀⢀⣀⡀⠙⢶⠃⠀⡸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣇⠀⢸⠀⠀⠀⢷⠀⠈⠘⣿⣛⣓⣃⣼⣊⠕⠁⠀⠀⠀⠀⠀⠀⠀⠠⢞⠛⣄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠈⠢⣈⢂⠀⠀⠘⢄⠠⠀⠳⣉⡉⠉⠉⠀⣀⣀⣀⢤⠤⠒⠒⠉⠁⠀⢘⣤⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⢀⠈⠳⣇⠀⠀⠈⠒⢌⡢⡀⠈⢯⠉⠇⠀⠀⠀⢀⣀⡀⣀⣤⣴⡶⠥⠌⠻⢶⣤⣽⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠹⡀⢰⠀⠀⠀⠈⢷⣄⢸⠄⠀⠀⠀⠀⣀⢴⠞⠉⠈⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⠀⠀⠀⠀⠀⠀⠘⡄
⠀⣤⠀⠀⠀⠂⠀⠀⠑⠊⠀⠀⠀⢠⡇⢼⣎⣀⣀⠀⠒⠉⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣠⡍⢩⠆⢠⡏⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⡟⢧⠀⠀⠀⠀⠀⠀⢇
⠀⠸⠠⠈⢳⡀⢠⠀⠀⠀⠀⠀⣾⠁⠀⠀⠸⡀⡿⡼⢠⠛⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠘⠷⡀⠀⠀⠀⠀⢸
⠀⠀⠀⢣⠀⢹⠎⢱⠀⠀⢀⣴⠃⠀⠀⠀⣀⠉⠁⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈
⠀⠀⠀⠈⠣⡀⠑⠾⣄⠀⠀⢸⡇⢀⡴⠞⢣⡇⠀⡇⠀⢦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⢀⠀⠈⢣⡘⠈⣇⡇⢀⠞⠛⠁⠀⢣⠀⠀⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠛⠛⠛⠛⠛⠛⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠉⠀⠀⠀⠀⡀⠀⠀⠀⠢⠀⠀⠀⠀⠈⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢏⢣⡀⠠⣀⣠⡄⠀⠁⠀⠀⠀⠀⠀⠀⡶⠂⠖⣁⠦⣽⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠾⣎⠡⠜⢢⡈⠙⠤⠴⣇⠀⠀⣀⣾⠦⠰⠂⡁⠔⡁⢆⡱⠊⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠁⠙⠳⠦⠁⠾⢑⠂⠄⢤⢀⠀⡀⡤⠰⡂⡧⠕⣊⡵⠟⠉⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣁⣁⠘⠒⢂⣈⣨⣥⣤⣤⣤⣤⣄⣄⣠⣀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣀⡴⠶⢚⣛⣉⣠⣤⡄⠴⢰⣶⡶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⣫⡕⠶⠟⠙⢉⢁⡉⣦⣤⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⠟⠓⡅⢰⢴⣧⡼⠟⢛⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡉⠸⠒⡫⠟⢉⡠⣖⢾⡙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢀⣤⠶⠛⢛⠛⣿⠗⢋⠶⢉⡴⣚⠳⣼⡀⢲⠇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⣠⣿⣽⢃⣍⣡⣘⣿⡶⢁⡔⣯⠱⣼⠆⠈⢁⣰⣤⠷⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⢠⣿⠀⣤⡩⢉⣉⣉⣿⡰⢫⠛⢾⠃⢀⣤⡾⠟⠉⠠⠀⣠⠛⣿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⡾⣿
⠀⣾⢻⡶⢻⣄⡼⠻⣝⣿⠛⢷⠳⢠⣦⡾⢋⣤⣄⡄⠀⣿⣿⠀⠸⠳⣮⢉⣿⣻⡿⠲⣶⣖⠒⢛⠟⠛⠋⠉⢀⣴⠞⠁⣿
⢸⣿⣾⣇⣬⠛⢷⣰⠋⣿⡗⠀⣤⡾⠋⠄⢸⡇⠙⠿⢦⡏⠀⠀⠀⢀⣈⣉⣁⡈⣁⡈⠂⠙⠿⣿⡀⢀⡼⠿⠛⠙⠆⠀⣿
⢸⣷⡟⠙⣿⣰⡞⣻⠈⣿⢠⣼⠟⣠⣤⣄⢹⠃⠈⠂⠀⣴⠒⠟⠁⠈⠋⠈⠁⠀⠀⢫⠙⠗⠀⣄⡉⠛⠄⠀⠀⠀⠀⠀⢻
⣿⠛⡇⣀⡿⢻⣇⡾⢻⣿⣾⠋⢐⣇⠉⢋⠙⢁⡴⠿⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠹⠷⠀⠘⠳⣦⡔⠀⣾
⣿⢠⠋⠙⣷⣨⠺⣇⢸⣿⠃⠀⡀⢙⡗⠃⡀⠉⠉⠀⠀⢀⠀⠀⠀⠁⠀⠀⠑⠉⠍⠠⠀⠄⢀⠁⠀⠀⠘⡛⣄⠘⢧⠀⢹
⣿⠘⣀⡰⠋⢿⣄⣸⣼⡟⢰⠛⠛⡉⢀⡜⣁⠀⠀⠀⠀⠁⠉⠀⠀⠀⣀⢠⠀⠀⢠⣀⠀⠀⠄⠱⠄⠀⠀⠀⠉⣡⡄⢃⣸
⣿⡷⠞⢳⣰⠈⢉⠏⢸⣷⡠⢿⠂⠀⡈⠉⠀⠁⠀⠀⠀⢀⠀⠐⠊⠀⠀⠂⠀⠀⢘⢍⢻⠃⠀⠐⠄⠁⠀⠀⠀⠈⢵⡄⢿
⢹⣗⣄⣼⠉⢷⣠⣤⢼⣟⣱⡤⠃⢠⠃⢀⠀⠘⠁⠀⢄⢈⠀⠀⠐⡀⢠⠀⠀⠀⢸⢰⠁⠀⢀⣁⣰⡤⠚⡀⠀⠀⠀⣤⣾
⠘⣷⠉⢻⣄⣸⡟⣇⢸⡿⣅⡑⠂⠈⠀⠀⠀⠀⠀⡀⠀⠙⣇⠀⠀⠱⠄⠀⠀⠀⢸⠃⠀⠀⣺⠟⠉⢀⣔⠁⠀⠀⠐⠠⣿
⠀⢻⣇⣾⣻⣧⢤⢾⣼⣷⠘⢧⡀⠸⠀⠀⠐⠁⠈⠐⠀⠀⠈⠀⠀⠀⢧⠀⠀⠀⡜⠀⠀⡐⠁⠀⠠⠒⠙⠙⠃⠐⠀⢠⣿
⠀⠈⢿⣤⡤⣤⣤⣤⢴⣿⠞⣃⢴⡆⠘⡏⠈⠋⠈⠟⠃⣦⠌⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡡⡴⠘⡟⠈⠏⠈⠟⢠⡄⣿
⠀⠀⠀⠻⣮⣉⣥⣬⣿⣷⠚⢇⠀⣦⠴⠷⠚⠓⠺⠂⢴⢁⣠⠛⣠⡀⠄⠀⠀⠀⡀⠀⣴⠛⣀⣰⡤⠶⠰⠇⠰⢦⡌⢀⡟
⠀⠀⠀⠀⠀⠉⠉⠉⠀⣿⡤⠚⢁⠠⢴⠶⡐⠂⠀⠄⠠⣄⡉⠲⣉⠵⡈⠀⠀⠘⣁⠻⣀⠶⢉⣠⡤⣴⡶⢶⠶⡄⣈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠂⠈⠀⠞⠀⣧⠀⠀⠀⠌⠈⡎⢂⠈⢆⣳⠀⠀⠠⢍⡶⢁⣴⡏⢻⡀⣿⡃⠸⣇⢳⡸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣄⢀⠀⠁⠐⠁⢱⡜⠙⠔⠠⠣⢀⢵⡾⠶⠶⠶⠾⣾⣴⣿⢻⠁⢸⣓⡿⣅⣀⣿⣼⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡉⢸⡀⠈⠒⡄⠈⠁⠑⠕⠃⢀⣉⣾⡇⠀⠀⠀⠀⣿⠉⣇⣿⠢⠊⡉⣇⡼⠔⠘⢫⣅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠉⠀⠑⠔⢤⠋⠀⠀⠀⠣⢤⠁⠀⢹⠁⠀⠀⠀⠀⣿⡄⢏⠙⢄⠹⠁⠀⠈⣏⡙⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠐⣆⠀⡀⢠⠇⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⡇⠋⠉⠲⡎⠀⠀⠀⣨⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠻⠂⠁⠀⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⣠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠛⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣰⣿⣿⠿⠛⠛⠉⠉⠉⠀⠈⠉⠉⠙⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⡯⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠉⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣄⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⠿⠿⠛⠋⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢀⣀⣤⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⢰⣿⠏⠀⠀⠀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⡇⢸⣿⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⣴⣾⣷⣾⣶⣶⣶⠞⠛⠁⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠈⢿⣷⣄⣀⣤⣴⣿⠏⠀⠀⠀⠀⢸⣿⡏⠁⢹⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠙⠛⠛⠛⢹⣿⠀⠀⠀⠀⠀⣾⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⣀⣀⣀⡀⢸⣿⠀⠀⠀⠀⣰⣿⣿⡇⠀⠈⢿⣿⣷⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⣿⠟⣿⡇⢸⣿⣶⣶⣶⣿⣿⡿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣠⣿⠀⢿⣷⣾⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣩⣤⣤⣿⣿⣿⣿⣿⠛⣿⣯⠉⠉⠉⠉⠉⠙⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⣿⣿⣿⣿⣿⣿⡟⠁⡴⠒⢾⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⢸⡇⠀⠈⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⣸⠇⠀⠀⠻⢿⣿⣿⣿⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠿⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢀⣴⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠉⠉⣿⣿⡇⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠘⠿⣿⣿⣶⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢀⣀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⠇⣿⡏⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢻⣿⠀⣿⡄⠀⠀⠀⢠⣿⠇⠀⠀⠀⣿⣿⡿⢿⣿⣿⠛⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠙⢿⣶⣶⣶⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣇⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣿⣿⠀⠀⣿⣿⣤⣠⣤⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⣿⠀⠀⣶⡶⣶⠂⢹⣧⣤⣤⣴⣾⣿⠟⠀⠀⠈⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣿⠀⣿⣦⣿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠉⠻⢯⡉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣀⣀⣤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠙⢦⠀⠀⠀⠀⠀⢈⡷⣄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣸⠀⠀⠀⠀⢠⣯⡤⠬⢧⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠈⠙⠲⠶⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⣄⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠤⣀⠀⠀⠀⠀⠀⠙⣦⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣌⠳⡄⠀⢠⣄⠀⠙⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣇⠀⣰⠃⢸⡀⣹⣰⠃⢹⡀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⢰⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⣤⣤⠴⠞⠁⠀⠀⠀⠈⠷⣄⣀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡞⠉⠀⣠⠬⠿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⠁⠀⣾⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠙⠦⣤⣤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡇⠀⠀⠀⠀⠀⠀⠀⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣧⡀⠀⠀⠀⢲⣤⣆⡀⢀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⢦⣀⠀⢠⡏⠉⠉⠉⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣸⣇⠀⠀⢠⠖⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠸⣆⠈⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⠉⠛⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡷⠋⠙⣦⠀⡿⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⡟⢰⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⢾⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣤⠤⣶⠟⢁⡤⠶⠿⢯⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⢹⡄⠈⣿⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣦⣄⣀⣠⡾⠁⠀⢻⠀⡇
⠀⠀⠀⢀⣴⡿⠛⠛⠛⣦⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⣛⣶⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡄⣷
⠀⢀⡤⣾⠸⡇⠀⠀⠀⣼⠀⠀⢻⡄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⠀⣴⠋⠁⠀⠙⡷⠶⣧⣀⠀⠀⠀⠀⠀⢸⡇⡿
⠀⢸⠁⢹⠀⠙⠓⠒⠛⢹⡆⠀⠀⠛⠶⠶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠻⣄⣀⣀⣠⠇⠀⠀⠉⠛⣳⣶⣄⠀⠈⡟⠁
⠀⢸⡄⢸⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣧⠀⠀⠀⠉⠉⢻⣄⣀⠀⢰⠟⠉⠀⣿⡀⣰⡇
⠀⠀⠉⢻⠀⠀⠀⣤⡤⠀⢻⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣿⣄⠀⠀⢤⣀⡄⠀⠈⢷⠀⠀⠀⢠⡟⠉⠉
⠀⠀⠀⢸⡀⠀⣸⠙⢧⣄⣼⠂⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠛⣷⠀⠀⠈⣧⢤⣤⣟⣀⣀⣤⠟⠁
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣤⡴⠃⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⡀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠛⢿⡛⠲⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢸⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⡠⠤⠤⠤⢼⣀⠈⠙⠓⠒⠶⠤⠤⠴⡇⠀⢰⠋⠀⠀⠀⢹⡉⣦⠀⠀⡞⠁⠀⠀⠈⣏⢱⡄⠀⣸⠀⠀⠀⠀⢸⡄⢠⠞⠲⣾
⢸⠃⠀⠀⠀⢸⠈⠉⠛⠒⠶⠤⠤⠤⢤⣿⠀⠈⠣⣄⣀⣀⣼⡵⠋⠀⠀⠙⢤⣀⣀⣠⡯⠞⠀⢠⡇⠀⠀⠀⠀⢸⠉⠉⠀⠀⡿
⣾⣀⠀⠀⠀⢼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡞⠀⠀⣠⠖⠛⠻⣟⠛⠛⠛⠛⠛⢻
⡟⠈⠉⠛⠒⣿⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠸⣿⡿⠀⠀⢿⣿⠗⠀⠀⠀⠀⡼⠁⠀⢰⠃⠀⠀⠀⠈⢿⠛⠛⢻⡛⠛
⡇⠀⠀⠀⠀⣿⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣤⣄⠀⠀⣠⣤⡄⠀⠀⢀⡞⢻⠀⠀⢸⠀⠀⠸⡄⠀⣸⣀⡤⣞
⡇⠀⠀⠀⠀⢻⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠿⠟⠀⠀⠻⠿⠃⢀⡴⠋⠀⣼⠀⠀⢸⠀⠀⠀⣏⣉⠉⢀⣀⣼⠁
⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣄⣀⣀⣤⠤⠖⠋⠀⣠⠞⢸⡄⠀⠘⣇⠀⠀⣏⠉⠉⠉⢁⣸⠆
⢿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⢸⡇⠀⠀⠘⠦⣄⡈⢹⠋⠉⢹⡇
⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣄⣀⣠⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠙⠲⠶⠞⠃
⠀⠳⣄⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡤⠖⠒⠚⠛⠛⠛⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠻⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⢴⣚⣁⠀⠀⠀⢀⣀⣠⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠉⠉⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣄⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⣿⡏⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠈⢻⡿⢶⣦⣤⣄⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣀⣀⣀⣀⣀⣤⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣴⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡞⠉⠀⣠⠬⠿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⠁⠀⣾⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠙⠦⣤⣤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡇⠀⠀⠀⠀⠀⠀⠀⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣧⡀⠀⠀⠀⢲⣤⣆⡀⢀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⢦⣀⠀⢠⡏⠉⠉⠉⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣸⣇⠀⠀⢠⠖⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠸⣆⠈⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⠉⠛⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡷⠋⠙⣦⠀⡿⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⡟⢰⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⢾⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣤⠤⣶⠟⢁⡤⠶⠿⢯⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⢹⡄⠈⣿⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣦⣄⣀⣠⡾⠁⠀⢻⠀⡇
⠀⠀⠀⢀⣴⡿⠛⠛⠛⣦⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⣛⣶⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡄⣷
⠀⢀⡤⣾⠸⡇⠀⠀⠀⣼⠀⠀⢻⡄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⠀⣴⠋⠁⠀⠙⡷⠶⣧⣀⠀⠀⠀⠀⠀⢸⡇⡿
⠀⢸⠁⢹⠀⠙⠓⠒⠛⢹⡆⠀⠀⠛⠶⠶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠻⣄⣀⣀⣠⠇⠀⠀⠉⠛⣳⣶⣄⠀⠈⡟⠁
⠀⢸⡄⢸⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣧⠀⠀⠀⠉⠉⢻⣄⣀⠀⢰⠟⠉⠀⣿⡀⣰⡇
⠀⠀⠉⢻⠀⠀⠀⣤⡤⠀⢻⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣿⣄⠀⠀⢤⣀⡄⠀⠈⢷⠀⠀⠀⢠⡟⠉⠉
⠀⠀⠀⢸⡀⠀⣸⠙⢧⣄⣼⠂⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠛⣷⠀⠀⠈⣧⢤⣤⣟⣀⣀⣤⠟⠁
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣤⡴⠃⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⡀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣯⣙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣤⣴⣶⣾⣿⣿⣿⣿⡿⠋⣿⣿⡄⠀⠀⠀⠈⠉⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣉⡻⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⢀⡟⠉⠙⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⣸⠇⠀⠀⠘⠿⢿⣿⣿⣿⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡾⠁⢀⡴⠶⠿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⠁⠀⢾⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠈⠓⠲⠶⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⠀⠀⠀⠀⡀⠀⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⢹⡿⠷⠤⠼⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢤⡼⠁⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣇⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡟⠀⠀⣸⠁⠀⠀⠀⠀⠀⣠⠴⠖⠚⠋⠉⠉⠉⠉⠉⠙⠛⢦⡀⢸⡀⠛⢉⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠻⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠳⠒⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠞⠛⣦⠀⡿⠀⠀⢀⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⡿⢰⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢾⠇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⣤⣄⣀⣀⣀⣤⠴⢶⠟⢁⡴⠶⠿⣭⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣾⠀⠀⠀⠀⣷⠀⢹⡛⣧
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣿⠀⠘⡷⠤⠤⠴⠃⠀⢸⡇⣿
⠀⠀⠀⣰⢻⠋⠉⠉⢻⡄⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣉⡭⠿⢿⣀⢠⡇⠀⠀⠀⠀⠀⠀⡇⢻
⠀⢰⠚⡇⠹⣄⣀⣀⣼⡇⠀⠸⣆⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⡇⢸⡃⠀⠀⠀⡟⠛⠷⢦⣄⣀⠀⠀⠀⣧⡿
⠀⣿⠀⣿⠀⠀⠉⠁⠀⣇⠀⠀⠈⠉⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠙⠶⠴⢾⠁⠀⠀⢀⣤⠿⢻⡄⠀⣿
⠀⠘⠦⣿⠀⠀⠀⢀⠀⢹⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⣼⡇⠀⠀⠀⠀⠈⠓⠲⣄⠈⠀⠀⢸⡷⠶⠃
⠀⠀⠀⣿⠀⠀⡾⣯⡀⢸⡇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠿⣶⡀⠈⠓⣏⣀⣀⡿⠀⠀⣠⡟
⠀⠀⠀⠙⠲⠞⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣧⣀⣠⡟⠉⠉⠓⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠩⠭⠽⠟⠛⠛⠓⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠠⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⡋⢀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⢀⠔⠊⠉⠉⠁⠒⢄⠀⠀⠀⢠⣾⣿⣿⣶⣯⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⣸
⠀⠀⠀⢀⡯⠖⠚⢯⡑⠲⡄⠈⢆⠀⢠⠏⠀⠳⡀⠈⣝⣻⣦⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡏
⠀⠀⠀⠀⣤⠀⠀⠀⠳⡀⠀⠀⠈⣆⣘⣼⣣⠀⣰⡄⠘⠁⠙⣧⠈⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠
⠀⠀⠀⠀⢸⡄⠀⠀⡘⠳⡀⠀⠀⢄⠈⠸⣾⠍⢁⣰⠆⣧⠀⠸⣇⠘⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠀⠀⠀⣷⠚⡆⣟⠋⠉⠉⠙⢛⣲⣤⡀
⠀⠀⠀⠀⢸⡜⠛⠁⠄⠈⠱⣄⣀⠀⠉⢉⣠⣾⣾⣥⣶⡿⢧⠀⣿⠀⠁⠀⠀⢹⣿⣿⠇⠀⠀⠁⠀⠀⢀⡇⢀⣙⣉⣠⡴⠖⠛⠋⠉⠀⠙⣄
⠀⠀⠀⢀⠞⡇⠀⠀⠀⠀⠀⠠⢋⠝⠋⠁⠀⠀⠉⠉⠛⡴⢄⠀⡿⢰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠈⡇
⠀⠀⠀⢸⠀⢄⠄⡶⠒⠲⠤⢴⠁⠀⠀⢀⣀⡀⠈⢳⣾⠁⠀⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢸⡀⠈⢰⠀⠀⠀⠀⣶⠀⠀⠃⢹⣻⠟⢶⠔⠁⣱⠖⣫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢳⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠳⡄⠀⢆⠀⠀⠀⠸⡀⢀⡀⠀⣟⠛⠶⠾⠟⠓⠋⠁⠀⠀⠀⠀⢀⣀⣠⠤⠖⠒⠈⠘⡆⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⠲⣌⢢⠀⠀⠀⠸⢄⠑⢄⠉⠒⠲⣤⡤⠤⡄⠒⠒⠒⠚⢛⠉⠄⠃⠀⠀⠀⢀⡠⠞⢻⣧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⠀⠈⢳⡆⠀⠀⡀⠀⠑⠢⣑⣄⠀⠘⢧⠀⡇⠀⠀⠀⠀⠨⡤⠥⣴⡴⣞⠿⠝⠛⠉⠀⠙⠻⣷⣶⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠈⢱⠀⢀⠇⠀⠀⠀⠀⢽⣧⡀⡼⠀⠀⠀⠀⠀⢀⣠⢶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢠⡀⠀⠀⠀⡇⠀⠀⠀⠑⠊⠀⠀⠀⠀⢠⡿⢼⣷⡁⠀⠀⠀⠐⠚⠉⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⢹⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢘⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠐⠀⠉⣉⡉⠉⡇⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⡄⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢰⠉⣷⢰⠇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠘⠁⠸⣧⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢃⢱⠀⠙⢦⣀⢧⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠸⣤⡏⡾⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢧⠐⠀⣟⠀⡱⠀⠀⢀⢴⣿⠀⠀⠀⠀⡠⢄⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠄⠈⠣⡀⠈⠳⢷⡄⠀⢸⠀⣿⠀⢀⡴⢞⠙⣆⡇⠀⡇⠀⠰⣦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠙⢦⡈⡆⢸⣠⡏⠀⡰⠺⠟⠁⠀⢻⠀⠀⢈⠻⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⠛⠛⠛⢿⣷⣤⣤⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣾⡟⠀⠀⢀⣀⣤⣤⣤⣤⣽⣿⣷⡈⢳⡴⢋⡗
⠀⠀⠀⠀⣠⣿⠁⠀⠀⣿⠋⠉⠀⠀⠀⠀⠉⠛⣿⡟⣡⡾⢥
⠀⣴⣿⠟⢻⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡀⠘⠳⣦
⠀⣿⡇⠀⢸⡇⠀⠀⠀⠹⣷⣤⣀⣀⣀⣠⣤⣶⣿⠃⠀⠹⣄⠀⠈⢻
⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⢸⣿⠀⠀⠀⠈⠳⣄⣸⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠛⠛⠻⢶⣄
⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣀⡀
⠀⣿⡄⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣃⣀⣠⣤⣤⣶⣶⣶⣤⣤⣾⡿⠋⠙⢳⣆
⠀⢻⣧⣀⣸⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠉⣁⣠⣤⣤⣄⣀⠀⠙⣿⣄⠀⢸⣿
⠀⠀⠙⠛⢻⣿⠀⠀⠀⠀⣿⡿⣿⡟⠉⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢁⡴⢛⣩⣵⣶⣦⡈⠙⢳⡄⢸⣿⢀⣼⠇
⠀⠀⠀⠀⢸⣿⡀⠀⠀⢀⣿⡇⢹⣇⣀⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⡾⠛⠿⠋⠁⣀⣹⡇⠀⢸⡇⠀⣿⣾⠟
⠀⠀⠀⠀⠀⠻⢷⣶⣶⡿⠟⠁⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣁⣀⡾⠀⠀⠈⣿⣧⣤⡿⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣤⣴⣯⣡⣤⠴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣦⣤⣬⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⣰⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⠇⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠉⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠟
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣶⣶⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⢸⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⠏⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣉⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠟⠛⠛⠛⠋⠉⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⡶⠖⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⠋⠁⢀⣭⣽⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢉⡿⠀⠀⣼⠋⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢿⣄⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⠉⠙⠛⠋⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣾⡀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢷⡀⠀⠀⠀⠙⣷⠿⣤⣄⣴⠟⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠙⠷⣤⡀⢀⡟⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣿⡀⠀⠀⣴⠶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣼⠇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀⢻⡄⠉⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠳⢾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠻⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠶⠲⣦⠀⢸⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠆⣼⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣴⣿⣀⣿⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⠀⣀⣤⡤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠶⠶⠶⠶⠞⠛⢻⡏⠀⣴⠛⠉⠉⠻⢦⡀⠙⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⠀⠀⠀⠀⢸⡇⠀⢸⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⠀⢹⡶⢤⣤⣤⠞⠁⠀⠈⡇⢸⡇
⠀⠀⠀⠀⣴⢿⠟⠉⠉⠙⢶⡀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⢉⣙⣷⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⢸⡇
⠀⠀⣠⣴⡇⢿⠀⠀⠀⠀⣸⡇⠀⠸⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡇⠀⡾⠋⠁⠀⠈⢿⠶⣾⣅⡀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⢸⡇⢸⡇⠈⠳⠶⠶⠞⢻⡇⠀⠀⠙⢷⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡇⠀⢷⣄⠀⠀⣀⡾⠀⠀⠉⠙⠛⢶⣦⣄⠀⠀⢹⠛⠁
⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡇⠀⠀⠉⠙⠛⢹⣇⠀⠀⠀⢠⡾⠛⠉⢻⡆⠀⣼
⠀⠀⠛⠶⡇⠀⠀⠀⠀⣀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⣬⣇⠀⠀⠀⢀⠀⠀⠉⠛⠳⡄⠉⠀⠀⠀⣾⠗⠖⠋
⠀⠀⠀⠀⡇⠀⠀⣰⢻⡏⠀⢸⡇⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠿⣷⣄⠀⠉⠳⣿⠀⠀⢠⡟⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠳⣤⣴⠏⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⣿⡀⠀⠀⣾⠉⠛⠛⠶⠶⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⢀⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⠟⠛⠿⠿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡶⠿⠿⠿⠿⠿⠷⣶⣦⣄⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣷⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣠⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⠉⠀⠀⠀⠀⠀⢀⣠⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠷⠶⠿⠿⢛⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣴⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣶⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠿⠟⠟⠛⠛⠛⠻⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⠁⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢱⣿⡟⠉⠀⠀⠉⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣤⣴⣦⣤⣤⣤⣤⣤⠶⠖⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣿⡇⠘⣿⣧⡀⠀⠀⣀⣼⣿⠇⠀⠀⠀⠀⣿⣿⡟⠛⢻⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⡇⠀⠘⠿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠘⣿⣿⣤⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣿⡇⠀⠀⣴⣶⣶⡶⠀⣿⣇⣀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠘⠻⠿⠿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇⠀⠀⣿⡇⣿⣇⣀⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣿⠃⠙⠻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡞⠉⢀⣤⠼⠿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠁⠀⣾⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠀⠀⠘⠳⠦⠤⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠈⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣄⠀⠀⠀⢻⣶⣧⣀⣠⠿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠳⢦⣀⣰⠇⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠶⠖⠒⠒⠲⠶⠾⣦⡀⠀⡟⠹⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣲⡿⠀⠀⠀⡟⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠻⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣏⡤⣄⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇⣸⠁⠀⠀⢸⠃⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⢾⣁⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠀⢀⣠⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠚⠋⢙⡏⠀⡞⠉⠉⠙⢳⡄⠙⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣇⠀⠀⠀⢠⡇⠀⢻⠀⣷
⠀⠀⠀⠀⣠⣤⠤⠤⣤⡀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣸⡇⠀⢸⠛⠛⠛⠋⠀⠀⢸⡆⣿
⠀⠀⣀⣼⢹⠃⠀⠀⠈⡷⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠀⣤⠖⠛⠛⢷⣤⣼⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⢸⠉⣿⠈⠷⢤⠤⠞⣷⠀⠀⠻⣦⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡇⠘⣧⡀⠀⠀⣸⠁⠉⠛⠶⢦⣤⡀⠀⠀⡷⠏
⠀⢸⠀⢹⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠸⡇⠀⠈⠙⠛⠛⣇⠀⠀⠀⣴⠞⠋⢻⡄⠀⡇
⠀⠈⠓⢿⠀⠀⠀⣀⡀⠘⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣧⡀⠀⢀⣀⢀⠉⠉⢳⡄⠁⠀⠀⣼⠛⠛⠁
⠀⠀⠀⢸⠀⠀⣼⠹⣄⣀⡿⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠻⡆⠀⠉⢻⣄⣀⣼⠃⠀⣀⡼⠃
⠀⠀⠀⠈⠛⠚⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡿⢤⣀⡼⠀⠀⠉⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠉⠉⠉⠉⠉⠙⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⢀⣾⣿⠟⠋⠉⠉⠉⠉⠉⠙⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⠃⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⣤⣾⡿⠿⢿⣿⡟⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⣸⣿⠏⠀⠀⢸⣿⡇⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣤⣤⣤⣶⣶⣿⣿⣿⣏
⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠁⠀⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢿⣿⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠸⣿⣇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠻⣿⣦⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⡀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢻⣿⡋⠁⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣇⠀⠀⠀⢀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣤⣀⣀⣤⣾⡿⠁⠀⠻⢿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠛⠋⠁