Spider Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠲⢾⡉⠉⣩⠝⠛⠋⠙⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠳⣄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣠⠞⠁⠈⠳⣄
⠀⣀⡀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠳⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡷⣄⣠⠞⠁⠀⠀⠀⠀⠘⣧⠀⠀⢀⣀
⠀⠈⠉⠛⠲⠇⣼⠳⢤⡀⠀⠀⡰⠋⡇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢰⠇⠈⢧⠀⠀⠀⣀⡤⠞⢧⠸⠒⠋⠉
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⠳⡶⠁⠀⢳⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡞⠀⠀⠈⢧⡴⠚⠉⠀⠀⠘⣇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⠃⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡠⠧⣀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⡀
⣀⣀⣀⡀⠐⡇⠀⣴⠤⣤⡎⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠉⠀⠀⠈⠉⠓⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⣇⣠⡤⠴⢦⠀⢸⡇⣀⣀⣀
⠀⠀⠉⠉⠉⠁⢰⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⡆⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠀⠀⠀⠀⠀⠀⠀⢈⡟⠉⠀⠀⠀⠀⠀⠀⡼⢀⣀⣀⡀⠀⣧
⠀⠀⠀⠀⢀⣀⣸⡀⣾⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠁⣿⠀⣏⣀⣀
⠀⠀⠈⠉⠉⠉⠀⠀⣿⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⣸⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⢀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⡀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢡⠀⠀⠀⠀⠀⠀⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠀⠀⠀⠀⠀⡼⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢇⠀⠀⠀⠀⢸⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⡄⠀⠀⠀⠀⢸⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠾⡄⠀⠀⠀⡾⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢹⡀⠀⠀⠀⢻⡟⢿⡀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⣼⠁⡜⠁⠀⢀⡼⣷⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣶⢄⡀⠈⢳⣄⠻⣄⠀⢠⡿⠛⠉⠉⠈⠻⣆⠀⣰⢣⠞⠀⢀⣴⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣕⠠⡙⣦⠹⣤⡿⠁⠀⢀⣀⣀⣀⣘⣶⡣⠋⣀⣴⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣝⣷⣼⣷⠾⠛⠛⠉⠉⠉⠉⠉⠻⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣽⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣶⣤⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⡤⠊⢰⠏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠐⡄⠙⠷⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡽⠀⠀⡟⠰⠁⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠘⣆⠘⣄⠀⠘⣧⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠃⠀⢸⣷⡇⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⣿⢛⡇⠀⢸⣆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡀⠀⢸⡆⢧⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣧⠀⡇⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢿⣈⣇⠀⠀⠀⠘⢿⣷⡀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⣿⣠⣧⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢻⣍⢧⡀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⢠⡏⣼⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⢀⠴⡶⢄⠀⠀⠀⠀⠀⡰⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣇⠀⠀⠀⢠⠋⢰⣷⠈⢣⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⣶⡄⠘⡿⠀⣴⠆⠀⠀⣸⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢙⡙⢦⠀⠸⣷⢸⡟⢰⡿⠀⣠⠞⣉⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡳⣄⢹⣆⢃⣾⢁⡴⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⠿⠿⢿⣿⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠲⣦⢶⢺⣿⣤⠆⠐⢦⣽⣿⣶⢶⡶⠲⣶⣶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠿⠈⠃⠈⠁⠀⠀⠀⠀⣠⢺⣿⣵⠏⠈⢷⣽⣿⢢⡀⠀⠀⠀⠀⠉⠀⠊⠸⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⣽⡛⢿⣡⣇⢀⣧⣹⡟⣻⣝⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⡋⠀⣰⠋⡔⢠⣿⣿⣾⣿⢧⡐⡌⢷⡀⠈⡛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠷⠊⠀⢰⡋⡸⠀⢿⠀⠙⠏⠁⢹⠇⠸⡈⣳⠀⠈⠲⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠀⠀⠀⠀⣼⡿⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠹⣿⡆⠀⠀⠀⠨⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠍⠁⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢀⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣁⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇




⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⣀⠘⡄⠀⡆⢀
⠀⠀⠀⣤⡄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠘⣶⡊⠀⠀⠀⠈⠓⣷⣾⠕⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⣤⠔⠁⠀⠀⠀⢦⣤⠖
⠀⠀⠀⠻⠇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠊⣿⠓⠄⠀⠀⠀⠱⣿⣿⢧⠁⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠺⣿⠦⠀⠀⠀⠀⠺⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣀⣈⢑⣄⠀⣰⣽⡩⠭⣍⡐⣄⠀⠀⠀⠀⠀⠀⠐⢤⣀⣇⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣶⠏⠓⠐
⠀⠀⠀⠐⠉⠁⣼⡿⠟⠻⠿⠋⠑⡄⠀⠀⠈⠂⠀⠀⠀⢀⠀⠚⠛⠛⠟⠻⡒⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⡿⢶⡤⢄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠠⠔⠒⠛⠩⠏⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⠀⠀⠀⠀⡠⢚⡹⢯⠓⢄⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠌⢀⣿⡇⠘⣧⡀⠱⡀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠈⠟⢄⠀⠀⢸⠀⢈⣿⠇⠨⢻⣇⠀⣧⠀⠀⠀⡐⡿⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠙⢀⢀⠀⠀⠀⠀⠈⠻⡁⠠⣼⠀⢈⣺⣿⠐⣞⡁⠀⣏⠠⢶⡦⠖⠁⠀⠀⠀⣠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠙⢇⠠⠀⠀⠀⠀⠀⠐⠼⣧⡈⣩⣥⢀⣬⣥⣼⡧⠖⠉⠀⠀⠀⣀⢀⡦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣅⠠⣤⡄⠀⣶⣮⣿⡟⢻⡿⠛⢿⣡⠦⣯⣈⣿⣵⣫⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⡴⣺⢿⣧⣘⢧⣤⣿⡽⣖⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠼⢫⡞⣯⣸⣺⣸⡟⣯⠪⡓⢬⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠛⢁⣣⠎⠐⡏⠙⠙⠁⠇⠈⠣⣴⢆⠈⠣⣕⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠞⠁⢠⢎⠏⠀⠀⠘⠀⠀⠸⠀⠀⠀⠈⢣⡠⡀⠈⠳⢯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⢂⠀⠀⠉⠢⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡼⠁⠀⠀⠀⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⣠⣶⠖⢦⣄⠀⠀⠉⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⣞⡿⢳⡾⠟⢃⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⣧⡀⠐⠛⢳⡶⠛⡣⠈⠆⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠈⢿⣿⣿⣯⣶⣀⣿⣺⣷⣿⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⠙⢿⣿⣿⣿⣿⣿⠿⠋⠁⣀⣀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣿⣿⢿⣿⣿⡶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠾⠿⣿⣶⢿⣿⣿⡿⣿⣿⣷⣦⣶⡿⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⣿⣿⣿⣴⣿⣯⡿⢷⣶⣶⣶⣤⡀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⢀⣿⠋⢿⡍⠉⠿⡥⠗⠀⠀⠀⠈⠙⣷⡀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠘⠓⣶⣿⣿⣷⣼⣠⣤⡀⠀⠀⠀⠀⠀⠐⠒⠐⡆⡇⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⡴⠶⣿⣿⣿⣿⣷⣟⡴⢧⡀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣖⣠⠖⠚⠉⠀⠀⠀⠀⢀⣀⣨⠀⣰⠃⠀⠀⠀⢀⣀⡠⠤⠀⠒⠒⠒
⠀⠐⢁⣤⢾⣿⣿⣿⣿⣯⣀⠀⠙⣆⠀⣠⠋⠉⣿⣿⣿⠿⣟⠛⠑⢦⣀⠀⠀⡔⠊⠹⢋⣧⣦⣧⣀⣠⣔⣊⣁⡀
⠀⢀⡞⠁⢸⡟⣿⠟⠿⡇⠹⣇⠀⠀⠠⠋⠀⠀⠉⢩⠏⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⠿⡍
⠀⡞⠀⠀⢸⠇⣿⠀⠀⡇⠀⠸⡆⠀⠀⠀⠰⠖⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⢻⠀⠘⢄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠋⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢰⡄
⠀⠀⠀⠐⢀⠀⣀⣤⣄⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⣠⣤⡄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡇⠀⠀⣼⠑⡀
⠀⠀⠋⠲⡘⣴⣿⣿⣿⡇⡌⡰⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⠀⡇⠀⠀⡇⠀⣼
⠀⠀⠀⠀⣘⣷⣽⣿⣿⣥⣗⣁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢮⣿⣿⣿⡥⠞⠉⠉⠉⠀⠁⠀⠀⠀⠀⣞⠉⠦⣷⣾⣧⣧⠜⠉⣦
⠀⢀⡴⠋⢸⠙⢻⠟⠻⡟⢹⠉⠳⡀⠀⠀⠀⠀⠀⢀⡴⢒⣿⣿⣿⣿⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⣿⣿⣿⡟⣶⠞⠁
⠀⡌⠀⠀⢸⠀⠁⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢀⠖⠁⠀⡿⠈⠋⠉⠁⡇⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠻⣿⡿⠁⢸
⠀⠁⠀⠀⠈⡆⠀⠀⠀⠀⢨⠀⠀⠈⠆⠀⠈⠁⠀⠀⡞⠀⠀⠀⠀⠀⢡⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡷⢦⠤⣄⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠊⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⡈⡇⠀⢠⠏⠀⠀⠀⠀⠀⠂⠈⠉⠉⠀⢀⡠⢴⠾⠀⠀⠙⠢⠄⠤⠤⠤⠤⢤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⢀⡏⡠⠤⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⣄⣀⣠⠖⠋⠀⣀⣠⠴⠚⠃⠀⠀⠀⠀⠑⠢⠤⣤⠒⠁
⠀⠛⠳⢤⣄⡀⠀⠀⠀⠈⢷⢸⣇⠀⢠⡞⠛⢄⠤⠤⠤⠤⠀⠀⠀⠀⠀⡀⠀⠀⡀⠔⠈⡏
⠀⠀⠀⠀⠐⡌⠉⠛⢷⣶⣾⣿⣿⣷⢟⣀⣀⡤⠵⣤⠠⠄⠚⠀⠰⡄⢀⡨⠛⠉
⠀⠀⠀⠀⢀⣸⠶⣾⣿⣿⣿⣿⣿⠛⠋⠻⠊⢤⢖⣈⣗⣲⡤⣓⠒⣉⠁⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⡀
⠀⠀⢠⠔⠋⠀⢸⣿⣿⣿⣿⣿⠛⣆⡄⠀⡧⠈⠘⣽⠛⡍⠐⠁⣠⠉⠉⠀⠘⠓⠒⠀⠀⠠⠬⡦⣄⣀⡀⠑⢤⡀
⠀⠔⠁⠀⠀⠀⠀⠙⠛⠋⠁⡏⠀⡸⢷⡀⠀⠀⢱⡀⠀⠈⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣇⠁⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⣠⣞⡠⠤⠂⠁⢸⠁⠁⠀⠀⠀⠀⢹⡴⠂⠀⠀⢺⡃⠀⠀⠀⠀⠀⠀⠒⣚⠷⢄⡀⠀⠀⠀⡀
⠀⠀⠒⠉⠉⠉⠉⠑⠂⠀⢘⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠇⣠⠀⠀⠉⠉⠉⠳⣖⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⡔⣁⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠞⠋⠁⠀⠀⠀⠀⠀⠀⠁⠒⠳⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠂⢀⣾⡆⠀⠀⠐⣲⣔⢒⡦
⠀⠀⠀⢀⡠⠖⡲⠤⠭⠠⠔⠀⣤⠖⠁⠀⠀⠀⠀⠀⠠⣀⠀⠀⠉⠀⠀⠈⠲⣤⠀⠢⠄⠭⠤⢖⠲⠄⡀
⠀⣠⢎⡩⠂⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣤⠀⢘⢠⡄⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠐⢍⡱⣄
⢜⠔⠁⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⢀⠀⠀⠄⠀⠁⠠⠒⠄⣀⠠⠈⠀⠀⠀⠀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⡠⡊⠗⠒⠉⠀⠗⡇⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⠀⠉⠂⠺⢑⢄
⠀⠀⠀⣠⢋⠌⠀⠀⠀⢀⡀⡒⢷⠀⠀⠀⠑⠀⠄⠀⠀⠀⠀⠄⠐⠀⠀⠀⡀⡾⢒⢄⡀⠀⠀⠀⠡⡝⢄
⠀⠀⡠⢡⠃⠀⠀⢀⠒⠵⠉⠀⠈⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠁⠀⠉⠮⡒⡀⠀⠀⠘⡌⢄
⠀⠀⢅⠃⠀⠀⠠⢁⠃⠀⠀⠀⠀⠀⠔⠝⠢⠧⢄⣀⡖⢲⣀⠠⠐⠗⠫⠢⠀⠀⠀⠀⠀⠘⡈⠄⠀⠀⠘⡨⡀
⠀⠀⠈⠀⠀⢀⣓⡆⠀⠀⠀⠀⠀⠎⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠱⠀⠀⠀⠀⠀⠐⣚⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⡺⠀⠀⠀⠀⠀⣸⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣇⠀⠀⠀⠀⠀⢗⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⣆⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠻⣦⣄
⠀⠀⠀⠀⠀⢀⣤⠾⠛⠁⠀⠀⠘⢷⣄⠀⠀⠀⠀⣠⠖⠉⠉⠉⠑⢦⡀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠙⠻⢦⣄
⠀⣀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣰⠁⠀⠀⠈⠀⠀⠀⠱⡀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣦⣤⣄⣀⠀⠙⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠟⠁⢀⣀⣠⣤⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠈⠉⠙⠛⠷⠶⠽⣄⠀⠀⠀⠀⠀⠀⡼⠵⠶⠟⠛⠉⠉⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠟⢻⣷⣶⣤⣤⣶⣿⠛⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⣴⢟⣽⠟⠁⠀⢸⡟⠾⣿⡿⠞⣿⠀⠀⠙⢿⣝⢷⣤⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⣴⠋⢐⡽⠃⠀⠀⠀⠘⣇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠻⣵⠈⢳⡄⠀⠀⠀⠀⠀⠘⢧⡀
⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠆⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⢠⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⡤⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠁⠀⡖⠂⠀⢀⠖⡄⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠉⠀⠀⠀⠀⠱⡄⠀⠀⠐⠓⣄⠳⠯⡄⡎⠖⢃⡜⠂⠀⠀⢀⡖⠁⠀⠀⠐⠈⢀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠈⠀⠀⠈⠣⣆⠀⣈⣎⠓⠶⠆⠶⠞⢻⡎⠀⣄⡶⠋⢀⠀⠈⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⣄⡼⢦⡼⠋⠀⠠⣤⡤⠀⠈⢻⣴⠾⡀⣄⣁⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⣴⠇⠀⠉⠀⠀⠀⠈⠁⠀⣧⣤⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣄⣊⢙⡆⠀⠤⠀⠙⠀⠠⠄⢀⣟⢉⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⠀⠠⠀⠠⠠⠤⠄⠐⠈⠁⠀⡩⣏⣙⠦⣀⣀⣀⣀⣀⡠⢎⣙⠯⡀⠀⠉⠐⠀⠤⠤⠀⠀⠤⠌⠠⠆⢀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠉⢁⣾⠿⠋⢻⠛⠻⢷⡄⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠢⣄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡱⣤
⠀⠀⠀⣠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠀⠀⠐⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⡀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣧⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡊⣢⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠢⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠑⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡀⠀⠀⠀⠀⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⣀⠀⠀⠀⢀⣩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁

⠀⠀⠀⠀⠀⠀⠠⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢀⡀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢶⡄⠀⠀⠀⠀⠀⠀⠀⢉⡝⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢷⠀⠀⠀⢀⡠⠤⠠⣯⣤⣤⣼⠧⠄⠤⢄⠀⠀⠀⢠⠇⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⢠⠏⢀⣤⣤⣤⣄⠀⣠⣤⣤⣤⡀⢱⠀⠀⠎⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⣄⣸⡀⢿⣿⣿⣿⡿⠀⣿⣿⣿⣿⡇⢸⣤⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⣧⡈⠻⠿⣿⣷⠀⣿⣿⣿⠟⢁⣞⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⠀⣿⣿⠀⣽⣿⠀⣰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠚⣩⡥⠽⢿⣶⡿⠿⣍⡉⠈⠙⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢁⣤⣶⣾⣯⠀⠀⠀⣿⠀⠀⢈⣿⣿⣶⣦⠀⠸⡖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡥⢼⠁⣼⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⢿⣿⣿⣿⣿⡇⠀⢹⠘⢻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⢀⡎⠀⠘⢿⣿⣿⡿⠁⣀⣤⣿⣦⣄⡈⠻⠿⠿⠟⠀⠀⠈⡆⠀⢎⢧
⠀⠀⠀⠀⠀⠀⠀⢠⠂⡞⠀⣼⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠄⢧
⠀⠀⠀⠀⠀⠀⠀⡞⡼⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠱⡀⢣
⠀⠀⠀⠀⠀⠀⢸⡼⠁⠀⢸⠁⠀⣠⣤⣤⣄⣀⠀⠙⢿⣿⣿⣿⣿⠟⠀⢀⣠⣤⣤⣤⡀⠀⢳⠀⠀⠐⠾⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡟⠀⣾⣿⣿⣿⣿⣿⣿⣶⡀⠉⢹⠉⠁⣠⣾⣿⣿⣿⣿⣿⣧⠀⠸⡄⠀⠀⠀⠙⢦⣀
⠀⠀⢀⣤⠟⠁⠀⠀⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⡇⠀⠀⠀⠀⠀⠹⡍⠂
⠀⠀⠋⠏⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⠿⣿⣿⣿⣿⠏⠀⢀⣼⣆⠀⠈⠿⣿⣿⠿⠛⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⢉⣤⣶⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⢱⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⣹⡂⠀⣀⣀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠀⠀⢸⠲⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠖⠹⣶⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⣿⣦⡌⠀⡎⣇
⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠛⠛⢿⡿⠟⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢰⠸⡄
⠀⠀⠀⠀⠀⠀⢸⢩⠃⠀⠘⣿⣿⣿⠃⠀⢀⣤⣶⣶⣄⠀⢸⡇⠀⣠⣶⣶⣤⠀⠀⠹⣿⣿⡿⠀⠀⠸⡄⢱
⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠹⣿⠏⠀⠀⣼⣿⣿⣿⣿⠆⢸⡇⠀⣿⣿⣿⣿⣇⠀⠀⠈⣿⠃⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⢀⠃⣾⠀⠀⠀⠀⠈⢧⡀⠀⣿⣿⣿⣿⣿⠀⢸⡇⠀⣿⣿⣿⣿⣿⠀⠀⡴⠋⠀⠀⠀⠀⠈⢷⣟
⠀⠀⠀⠀⠀⣨⠾⠃⠀⠀⠀⠀⠀⠀⠙⢦⡙⠿⣿⠿⠃⠀⢸⡇⠀⠈⠻⠿⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣤⣼⣧⣤⣤⡤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⢤
⣠⢖⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣈⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡙⢦⡀⡶⢖⠶⡄⣠⠞⣡⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣧⠙⢡⣾⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣄⣎⡻⢈⠸⢻⣇⡄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠋⠉⠀⢄⡨⠋⡄⢲⠀⡌⢫⣁⠀⠈⠉⠛⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⢀⣀⠄⠀⣅⠂⡡⢬⢄⠁⢈⡂⠀⢄⣀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣠⠟⠁⠀⢸⠄⣸⡄⢛⢠⣧⠁⡆⠀⠀⠙⢧⡀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⣏⠺⢵⢿⣇⠕⢫⠇⠀⠀⠀⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀⠘⢦⡀⠉⢄⡼⠋⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣟⣿⣻⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⣿⣟⣻⣟⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢾⣿⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣻⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡉⣸⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⢦⣥⣾⡇⠠⢀⠾⠟⠋⡤⢁⢴⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⢤⣴⡿⠀⠈⢁⡠⢄⠀⠀⡵⢦⢸⣾⢢⣀⣀⡀⠀⢀⡀⢀⠀⠔⢀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⢹⣏⢀⣚⠿⠗⠂⢰⡍⠀⠺⡃⠀⡇⢈⣿⣻⣿⣿⣿⣶⠃⠈⢀⣀⡠⣠⣾⣿⣿⡀⠀⠀⢀⡔⡋⠙⣿⣿⣀⡿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⡁⠀⠀⠀⠘⣿⠶⢊⡇⠀⣇⣾⣷⣿⣿⡟⣹⣿⣴⣷⣿⣾⣿⣿⣿⣿⣿⠃⣠⡖⣡⢊⣴⠖⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠁⢙⡏⠀⠢⡀⠀⢹⣿⣼⣳⣆⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡁⠈⢿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⢀⠤⠫⢀⣀⠉⣈⣶⢺⣦⣟⡩⢷⣷⣶⣬⣙⣿⣿⣿⣿⣿⣿⣿⡿⣛⠁⢾⣭⣶⣶⠏
⠀⠀⠀⠀⠀⠀⣠⡄⡸⡟⠁⠀⠀⠀⠉⢻⣟⣻⣾⣩⣟⣙⣼⣿⣧⣄⣽⣿⣎⢻⣿⣿⣿⡛⢚⡵⣣⡼⠁
⠀⠀⠀⠀⠀⢐⡁⠀⠟⠀⠀⠀⠀⢀⣠⣴⣿⣿⣏⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣏⡏⣸⣿⣿⣿⣿⣯⢶⣖⡀
⠀⠀⠀⠀⣠⠈⢾⠗⠀⠀⠀⢀⡠⠾⢛⣿⣧⡟⣛⠛⢿⣿⣷⣿⡏⣿⣜⣿⣯⡿⢋⣌⣽⣿⡿⣿⡃⢿⣍⠿⠓⠄
⠀⢀⣤⣄⣈⠘⠃⠀⠀⠀⣴⡉⠀⠔⣲⣿⣿⣿⣿⣿⣶⣤⣈⠻⣧⣼⣿⣿⠿⡓⣼⢿⣿⡯⣥⠿⠓⠈⠛⠆⣾⣿⢷⡄
⠐⠩⠷⠋⠀⠀⠀⠀⣰⠊⠐⢹⡆⠀⠛⠗⣿⣿⣿⣿⣟⣿⣿⣦⢾⡿⠛⠧⢸⣿⣯⠉⠙⠮⢴⣦⠀⠀⠀⠀⠙⣿⡟⠁
⠈⠁⠀⠀⠀⠀⠀⣮⡀⠀⣴⠟⡠⠾⢿⣷⠈⠭⢾⣳⣿⣤⣽⣿⣿⣻⣿⣷⡌⠙⠛⠦⣄⠀⣤⢾⢀⠀⠀⠀⠀⠈⢣⣾⣣
⠀⠀⠀⠀⠀⣰⢧⢠⣽⠆⠁⢾⣷⠄⠈⠀⠀⠀⠀⣁⡙⢛⣿⠏⠁⠉⢿⡿⠁⠀⠀⠀⠀⢈⣷⣼⣄⡀⠀⠀⠀⠀⢸⠿⠟⠆
⠀⠀⠀⠀⣴⡡⠀⣸⠋⢀⢦⡄⠁⠀⠀⠀⠀⠀⠰⠛⠗⢼⣿⢫⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠛⢀⠉⠇⠀⠀⠀⠀⠈⢤⣶⣶⢄
⠀⠀⠀⢠⠃⠁⢸⠃⠀⢈⡛⠀⠀⠀⠀⠀⠀⠀⠱⢴⡆⢨⡟⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⢿⡆⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⡐⢲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠁⢸⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⢸⠃
⠀⠀⢠⠛⠓⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠾⠀⡼⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠺
⠀⠀⣠⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⡿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢱⡄
⠀⢰⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠛⠁
⠀⠰⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡣
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⣻⣉⣝⣛⣟⢋⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡀⡠⠂
⠀⠀⠀⠀⠀⠀⢘⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⣇⡿⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣶⡦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢢⣾⡯⢷⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠂
⠀⠀⠀⢀⡴⠛⣽⡇⢳⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣟⣿⣿⠂⡀⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣏⠡⡀
⠀⠀⠴⠋⠀⡼⢹⡇⡎⢷⠀⠉⠣⠀⠀⠀⠀⠀⠐⠈⠐⢿⣿⡿⠂⠁⠀⠀⠀⠀⠀⠀⠐⠙⣿⣿⠏⠁
⠀⠀⠀⠀⠐⠁⠈⣇⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⣰⠉⢳⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠁⠤⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠺⠰⠉⠆⠀⠀⠀⠀⠀⣶⣏⣳⡖⠀⠀⠀⠀⠀⢀⣘⣁⠀⠀⠀⠀⠀⠀⠹⠺⠈⠁⠀⠀⠀⠀⠀⢨⡀⠗⣈⠂
⠀⠀⠀⠐⠿⠗⠃⠀⠀⠀⠀⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠺⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢘⣏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡉⣯⠩⠀⠀⠀⠀⠀⠀⡑⣇⣿⡋⠀⠀⠀⠀⠀⣾⠃⢷⡄⠀⠀⠀⠀⠀⢸⠦⠿⠀⠀⠀⠀⠀⠀⠠⠛⡈⠓⠆
⠀⠀⠀⢓⣿⡀⠂⠀⠀⠀⠀⠨⠃⣇⡿⢡⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀⠀⠀⠀⡅⠀⠀⣏⠀⠀⠀⠀⠀⢐⠀⠁⠘⡂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⢸⣁⡿⠀⠀⠀⠀⠀⠀⠹⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠴⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠰⣤⣤⡔⠢⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡀⠀⠀⠀⠀⠐⢀⡊⣒⠀⠀⠀⠀⠀⠀⠀⡤⢢⠄
⠀⠀⠀⢐⢠⢰⠂⠀⠀⠀⠀⠀⡜⠀⠂⠀⠀⠀⠀⢀⢀⡻⠻⡟⡀⠀⠀⠀⠀⠀⠈⠀⠃⠔⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠈⢹⡸⢀⠁⠀⠀⠀⠀⠐⠢⢝⢡⠃⠀⠀⠀⠀⠀⢿⡘⣿⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠘⢖⣲⠗
⠀⠀⠀⢻⣒⣚⡗⠂⠀⠀⠀⠀⢶⣌⣰⠦⠀⠀⠀⢀⠁⠪⡄⠼⠉⠀⠀⠀⠀⠀⠀⢇⡼⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢨⣡
⠀⠀⠐⡘⠁⠋⠪⠀⠀⠀⠀⠀⢈⠇⣺⠀⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⠀⠀⠼⠃⠷⠀⠀⠀⠀⠀⠀⠀⠚⠳
⠀⠘⠒⠄⠀⠀⠔⠀⠀⠀⠀⠀⣰⠐⡰⠀⠀⠀⠀⠀⠬⠀⠀⠈⠤⠀⠀⠀⠀⠈⢦⣛⣠⠆⠀⠀⠀⠀⠀⠀⠂⠘⠂
⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢤⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⠘⠆⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣶⣤⡴⡇⠀⠀⠀⠀⠀⠘⢡⠛⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⣖⠀⠀⠀⠀⠀⠠⠌⠀⠀⠠⠄
⠀⠀⠠⠄⣿⠅⠃⠀⠀⠀⠀⠀⢂⠸⠀⡂⠀⠀⠀⠄⠀⡌⠈⣄⠀⠀⠀⠀⠀⠀⣠⡞⠤⠀⠀⠀⠀⠀⠀⢴⡄⠀⣼
⠀⠀⠀⠶⠊⠛⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠑⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢈⠉⠀⠀⠀⠀⠀⠈⢛⣲⣦⣾⣿⣶⣖⣛⠁⠀⠀⠀⠀⠀⠉⡁⠀⠀⢠⣶⣄
⠀⠀⠀⠀⣼⣿⣿⣷⡀⢈⠀⠀⢀⠀⠠⠒⡀⠈⡡⢺⣿⣿⣿⣿⡗⢌⠁⢀⠒⠄⠀⣀⠀⠀⡑⢠⣾⣿⣿⣧
⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠻⠿⠀⠈⠀⠈⢐⡞⣿⣿⣿⣿⢫⡂⠁⠀⠁⠀⠿⠟⠀⠀⠀⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⡄⠀⠀⠀⠀⣰⡶⣴⠋⠈⢿⣿⣿⡿⠁⠙⣦⢶⣆⠀⠀⠀⠀⢠⣼⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠁⠄⠁⡴⠁⠀⢘⢸⣿⣻⡇⠃⠀⠈⣦⠈⠢⠀⠂⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣆⠴⢊⢃⠔⠁⠘⠸⣿⣿⠇⠋⠘⠢⡘⡑⠦⣰⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠛⠁⠀⠀⠀⢠⢿⡿⡌⠀⠀⠀⠈⠛⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠂⠀⠀⠁⠀⠀⠀⡌⢣⠀⠀⠀⠀⠀⠀⠐⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠆⠀⢠⠠⠔⠁⠈⠢⠄⡄⠀⠰⠄⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⡿⡇
⠀⠀⠀⢰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣴⣇
⠀⠀⠀⠀⠙⣿⣿⣿⣽⣿⣶⣤⣀⢀⠰⠃⠘⠆⠀⢀⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣙⣻⣿⣿⣿⣿⣿⣷⡇⠡⠄⠸⣾⣿⣿⣿⣿⣿⣟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⡽⣛⢵⡂⠙⠋⢐⡪⣝⢯⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⡀⢀⣰⡄⠀⣸⢿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢰⢹⣿⣾⣿⣿⡏⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠂⠁⣠⣴⣿⠿⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠭⠭⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣵⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠸⢿⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢢⢂
⠀⠀⠀⠈⠖⡼⢀⣃⡤⢠⡄⣀⠀⢄⡘⠃⠘⠃⣀⠀⢀⠠⡄⢰⣔⣇⢧⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⡧⠀⡄
⠀⠀⠀⠀⠘⡍⣑⡒⠽⡶⠳⢺⢧⣦⡍⠁⠈⢉⣴⡤⣟⠺⢳⡮⠔⡚⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠮⢷⠢⠌
⠀⠀⠀⠀⠀⠀⠨⠦⠎⠑⠘⠋⢋⣹⡄⠀⠀⢠⣏⠙⠋⠋⠚⠹⠴⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣮⡯⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣤⣤⣤⣶⣦⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⡀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣛⡻⠿⠿⠿⢛⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠀⢠⣀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢩⣙⣛⣛⣋⡭⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⣛⣩⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠐⢀⣠⡄⠤⠴⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠔⠁⠀⣠⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠈⠀⠂⠂
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣂⢄⡀⡀⠀⢄⡀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣰⣾⣍⣹⣿⣿⣆⣱⡈⣦⠀⢉⣳⣤⠀⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠄⠂⢠⣾⣿⣵⠿⠻⣿⣿⣿⠛⣹⣽⣿⣿⣛⣿⣏⣽⣉⡀⢠⣶⢿⣿⠛⢦⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡴⠟⠉⠁⠀⠀⠀⠀⢰⢏⣽⣿⡿⠹⣿⣍⡀⣀⡀⣸⣟⠉⠁⣸⠂⠀⠀⠈⢣⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣺⣿⠏⠀⠀⠈⠙⠙⠋⠙⢏⢻⣆⠀⠁⠀⠀⠀⠀⠀⠙⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃

⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⡷⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢾⣿⣿⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⡀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣉⡀⠀⠀⣿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⣀⣠⣾⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣦⣀⠀⠀⠀⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⣰⣿⣿⡿⣋⠹⡏⣼⢹⣿⡄⠀⠀⠀⠀⣰⡿⣿⣮⡿⠩⣿⣿⣿⣧⣀⣀⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⣿⣿⣟⠁⡁⢙⡀⠄⠠⠎⠞⠛⢦⣾⣆⣼⢋⣇⡱⠀⠀⢰⡋⢈⠙⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⣿⣿⠄⠓⠸⠧⠀⠀⠂⣆⡄⠈⣿⣿⣰⣄⡏⡃⡀⠀⠞⠁⠄⠰⠿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠲⣶⣾⣶⡷⡖⠒⢦⣿⣟⡻⢿⣶⣶⣶⣻⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣟⠻⢿⣷⣿⢿⡇⢑⠍⣉⠀⣿⡏⠐⣻⣿⠉⣹⠿⣷⣾⣿⢿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡉⢶⣊⠁⠉⠒⠀⡍⠀⠀⠀⢽⡇⠀⠀⢷⣧⠐⠊⠉⠙⣻⣾⣸⣳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢷⣟⠲⠍⣀⠖⠀⣤⢀⠀⠀⠀⠸⠃⠀⠀⢀⡆⣤⠑⢟⣈⡹⢟⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⣿⣶⢾⣥⢴⣆⠤⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⢿⣬⣶⣶⣯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠏⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣄⠴⣶⢲⡆⢤⣴⣤⠄⣰⢲⡶⢂⣤⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠻⣧⣄⠀⠹⠀⣽⡇⠰⠉⠀⣠⣾⠋⠀⠀⠀⠀⢠⣾⠏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⡄⠁⠏⢀⠁⣰⡿⠉⠀⠀⠀⠀⠀⠀⢊⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⡿⠞⠀⠈⠻⣏⠀⠀⠀⠀⠀⣴⣶⣶⡽⢻⡿⡿⢻⣹⣾⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⣤⣄⡘⢿⣿⠇⠀⢇⠃⠀⣿⣿⠋⣀⣴⡄⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡠⠀⠀⢠⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣦⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡾⣏⡙⣃⢈⡄⠀⠀⠤⠄⢀⠀⠀⡀⢠⣶⡄⢀⡀⠀⠀⡠⠤⠀⠀⠀⢈⣠⣼⣧⣄⡃
⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣟⣯⡭⡄⠀⠀⠀⠀⠀⠈⣓⢉⣿⣿⣿⡉⢉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿⣋⣀⡀
⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⡇⢇⠰⠀⠀⠈⠙⠱⠋⠁⠞⠈⣿⠉⠣⠀⠙⠟⠛⠁⠀⠀⠎⠀⣿⣿⣿⣿⠁⠰⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⡟⢸⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠇⠹⣷⣿⣍⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⡦⢤⣄⡀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⢠⢹⠆⠀⢸⠏⠀⠀⠀⠀⠀⠐⠒⠂⠉⠉⠀⠀⣀⣠⢴⢾⠀⠀⠈⠳⠄⣀⣀⣀⣀⣀⡤⣤⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⣏⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⢠⠏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⠈⠁⠀⠈⠀⠀⣀⡴⠖⠉⠉⠀⢀⣠⢴⠇⠀⠀⠀⠀⠢⢤⣀⣀⣀⡠⠊⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡆⠀⠀⣻⡷⡚⠁⠀⠀⠀⠒⠉⡉⠠⠁⠀⠀⠀⠀⠀⠀⠀⣈⢝⡟⠀⠀⠀⠈
⠀⠀⠈⠛⡓⠦⢤⣤⣇⣀⣈⣷⣼⣿⣄⣴⠏⠀⠈⠾⡉⠉⠉⠉⢀⡄⠀⠀⠀⠐⠦⣄⡠⠔⠉⠀⠘⠁
⠀⠀⠀⠀⠘⣆⠀⣀⣙⣿⣿⣿⣿⣿⣿⣯⡤⢴⠶⠓⠛⢯⣙⣉⠉⣄⠀⢱⣄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠾⢛⣿⣿⣿⣿⣿⣿⣿⠉⠁⠘⣗⠲⡶⢧⣤⣯⣭⣶⣪⣍⣀⣄⠀⠀⠰⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠋⠁⠀⠸⣿⣿⣿⣿⣿⡿⠙⣎⡆⠀⡸⠀⢈⠹⣽⠉⣤⢀⡁⢠⣜⠁⠈⠉⠉⠛⠛⠒⠒⠒⠒⠬⠷⠤⣄⣀⣀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⢸⠃⠀⣸⣷⡀⠀⠀⠈⣷⣁⠄⠈⠋⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⣾⠐⠁⠀⠀⠉⠀⠀⠀⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢀⡼⠁⣀⡤⠒⠉⣿⠉⠢⠀⠀⠀⠀⠘⣦⣠⠄⠀⠀⢈⡾⠁⠀⠀⠀⠀⠀⠀⠠⠤⣾⣇
⠀⠀⠀⠶⠿⠾⠯⠭⣄⠀⠁⡗⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠒⢤⣀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠇⠀⠀⠀⠘⡄⠀⠀⢀⠠⠤⠤⠤⣄⡀⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣌⡓⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠋⣰⠆⠀⠀⠀⠀⠀⠈⠙⢿⠃⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⣞⣡⠀⠀⠀⠀⠀⠀⠀⣀⠈⢧⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣹⡀⠀⠀⠀⠁⠈⢷
⠀⠀⠀⠀⠡⣤⢆⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀⠈⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢄⣀⣤⣾⣶⣾⠟⠁⠀⢸⣿⣿⣤⡄⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⠤⣤⣴⡿⠻⡿⢛⣿⣶⣆⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⢨⠹⢶⣶⣿⡤⢴⠓⡞⣻⣿⣁⣴⣤⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢔⣯⣀⠀⠀⠘⢿⣯⡷⡆⣠⡾⢋⠜⣡⡞⠀⣐⠀⠀⠉⠑⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⣹⣿⣿⡿⢚⣵⣿⣶⣷⡤⠃⠀⠠⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠛⠁⣻⣶⡿⣈⣸⣿⣿⣦⡄⠚⠀⠈⠛⠙⡄⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠹⣿⣯⣃⣠⠿⣿⣧⣄⢴⠳⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠻⣿⣯⣠⣬⠿⣿⣦⣤⠒⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢰⡋⠙⢿⣶⣤⣾⡻⣿⡀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠙⢦⡀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠢⡤⠤⡤⠤⣠⣀⣀⡀⣸⣴⣿⢹⣷⣼⠄⣀⡀⣠⡠⠤⡠⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠘⣦⣽⣿⣿⣻⣭⡍⡏⠈⡏⢩⢙⡹⠻⠙⣣⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⢀⣠⠄⠀⠰⠁
⠀⢂⡛⣯⠛⠘⠫⠝⣿⡛⠅⠣⠀⠓⠘⣛⣚⠠⠛⠈⠋⡏⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⠀⢀⠀⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠉⠈⠂⠀⠈⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⣀⠠⣤⠀⠀⠀⣤⢄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⠁⠀⠀⠀⠉⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠀⠂⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠢⠀⠀⠠⠊⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠂⠺⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡤⠀⢄⡀⠸
⠀⠀⠂⢬⠓⠉⠀⠄⠐⢒⡏⠈⠈⠀⢟⠒⠀⠀⠀⠑⢫⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⠈⠀⠠⠟⢃⡀
⠀⠀⠀⠀⢣⡖⠢⡍⠙⡻⢃⠀⠀⠀⠚⢛⠁⡥⠒⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠃⣀⠘⠄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣰⡇⠀⠀⠀⢳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⣸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢣⡀⠀⢀⠃⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠠⠀⠀⠀⠀⠀⢄⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠇⠀⠀⠀⠀⠀⠰⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢠⢠⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠤⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠆⠉⡞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠓⠀⢃⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠣⡀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢈⠀⠀⠀⠉⠀⠉⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠎⠁⢱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠀⠐⢤⠊⠁⠀⠉⠓⠴⡀⠀⠒⣁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢴⡃⠀⠀⠀⢘⡆⠌⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠆⠀⠀⠀⠀⠀⢆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠜⠁⢂⠘⡀⠀⠀⠀⠘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⢲⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢀⠠⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⢀⠀⡀⠀⣠⣿⣄⠀⢀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣄⠈⢲⣷⣶⠿⠿⠿⣿⣿⡶⠁⣠⠶⠁⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠂⠉⠉⠁⠉⢉⣛⣿⣿⣶⣤⣄⣀⡈⢓⣿⣿⣿⣧⣰⣤⣿⣿⣿⣛⣁⣤⡴⠶⠟⠻⠿⠍⣉⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⣀⣤⣎⣁⣈⣹⣿⠟⠙⢻⣿⣿⡿⣿⣿⡿⠋⠻⠍⠲⣤⣤⣤⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⡤⢻⠛⠀⠀⠀⠀⢸⣿⣟⣛⣿⣿⣷⡀⠀⠀⠀⠈⢦⠉⠲⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣟⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠢⣀⠀⠀⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠖⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠈⠛⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠻⣿⣿⣿⡿⠛⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⣦⠀⠀⠀⠀⠀⢠⡆⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⢻⣷⣄⠀⢿⣠⣤⠀⢠⣤⣸⠇⢀⣴⣿⠃⠀⠀⠀⠀⣀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠙⢿⣷⣼⣿⣿⣿⣿⣿⣿⣴⣿⠟⠁⠀⣀⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠛⠛⠉⠉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠈⠉⠙⠛⠿⢿⣶⣦⣄
⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⣤⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⢿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢠⠤⠠⠖⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡂⠀⠀⠀⠀⠀⡀⢀⠄
⠀⠀⠒⡲⠂⠡⠀⠀⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠶⠀⠀⠀⠤⣤⡀⠙⠆⠀⠠⠐⠃⠀⡏
⠀⠀⠐⠀⢤⡙⠂⢄⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠴⠀⢞⠿⡿⢠⠀⠢⠀⢈⣀⡀
⠀⠀⠐⠂⠀⠑⣄⠀⠉⠓⠄⠐⠀⠀⠐⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠊⠀⢤⠘⠢⠀⠀⢀⠄⠙⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠂⠉⠙⠀⠀⠛⠁⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠄⠁⠀⠀⠈⣃⠄⠀⢤⠁
⠀⠀⠀⡀⠀⠄⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⡤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⢇
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠑⣄⠀⢐⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠲⠅⠀⢊⣀⡈⢄⣌⠀⠤⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⣀⣅⠀⢻⠻⡗⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠴⠖⠋⠁⠀⡀⠾⠛⠉⠣⡀⠀⠀⠀⠙⠓⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠐⠄⢂
⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠑⠈⡀⠀⢠⠄⠀⠄⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⡀⠠⡄⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠜⣤⡐⠀⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⠍⠐⣷⠅⠄
⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠁⠂⠑⠆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⡤⠐⠊⡄⠉⢡
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠖⠀⣀⠠⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠄⠂⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⡼⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠘⠀⢇⠀⠀⠀⢀⡄⢠⡀⠀⠀⠀⡸⠀⠃⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠁⢄⠀⠀⠀⠀⠑⢄⠑⢄⣀⠊⠁⠈⠑⣀⡠⠊⡠⠊⠀⠀⠀⠀⡀⠈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⣀⣀⣀⠀⠀⠁⡤⠉⠀⠀⠀⠀⠉⢠⠄⠀⠀⣀⣀⣀⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⢀⣐⠀⠀⠀⢀⣀⠀⠀⠀⡃⡀⠀⠀⠠⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢘⠔⠈⠁⠀⠀⠀⠁⠢⡇⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⡀⠔⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠠⢀⠁⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠡⠀⠐⠈⠁⠀⠀⠀⡀⠄⠊⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡄⠑⠠⢀⠀⠀⠀⠈⠁⠒⠀⠌
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠔⠈⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡉⠐⠠⢀⠁⠢⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠌⠀⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠘⠀⠡⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠀⡘⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠎⠀⡠⠁⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣠⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣄⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣇⠀⠀⣠⣿⣽⡆⢰⣯⣿⣄⡀⠀⣸⣽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠿⠋⣿⠁⠀⠀⠠⣾⠙⠿⢷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏⡀⢀⣠⣷⢀⣼⣧⠀⣿⣆⡀⢀⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠻⢿⣿⣿⡿⡞⢿⡿⢳⢿⣿⣿⡿⠟⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣀⣀⣠⠄⢼⣿⣿⡿⢿⣿⣿⣇⣤⣄⣀⣀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⡛⠿⣿⣿⠿⠿⠟⠁⠘⠻⠿⣿⢿⣿⠿⢛⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⣇⠀⣧⣭⣄⣄⣀⡀⢀⣀⣠⣤⣴⣿⠀⢸⡇⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⣆⢿⡿⠛⠛⡛⠃⠙⠟⠻⠟⣿⡿⣰⣿⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣸⠇⢼⣷⣤⣤⣤⡇⢠⣴⣤⣴⣿⣏⠸⣇⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⣜⡿⠀⣸⠿⢿⡿⢿⡄⢰⡿⢿⣿⣿⣇⠀⢿⣣⡀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⠏⡀⣾⣿⣤⣠⠀⠀⠀⡀⠀⠀⣄⣦⣿⣶⣄⠩⠅⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣦⡼⠋⢹⣿⣿⣾⣿⣾⣷⣿⣿⣿⣿⡏⠙⢿⣶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣧⠀⠀⠘⣇⠀⠀⠈⢸⡇⠁⠀⢀⣼⠃⠀⠀⣼⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⢷⡀⠀⢿⣿⣿⣷⢾⣷⣾⣿⣿⡿⠀⢀⡾⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⣿⡄⠘⣧⣀⣉⣼⣇⣁⣀⣼⠃⢠⣿⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⣷⠀⠘⢿⣿⣿⣿⠿⡿⠃⠀⣾⠁⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠀⠀⠀⠰⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠂⠀⠀⠀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⡰⠃
⠀⠀⠹⣿⣿⣦⣀⠀⠀⡰⢆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠻⣁⡐⠙⠆⠓⠈⣇⣀⣀⣼⣇⣀⣈⠧⠀⠠⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⢀⠀⠤⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⢠⣴⠖⠋⠉⠙⠄⠈⠀⡄⠀⠁⠒⠂⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠉⠁⠀⠀⠀⡀⣠⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⠀⣀⢤⡆⠀⠅⠂⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠽⠍⠙⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠂⠀⠀⠐⠂⢄⡀
⠀⠀⠀⣠⣴⣶⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠉⢓⡐⠒⠂⠀⠀⠈⠉⠻⣦
⠀⡴⣾⠿⠿⡶⡤⣄⠈⠀⣖⢲⡖⢲⣴⣤⣄⠀⠀⠀⢀⠀⠴⢶⠋⢻⡀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⢀⣻⠄
⠀⠀⣙⠻⡱⣓⡗⠀⠘⢼⠃⣜⠣⡞⠥⠗⢽⣳⠄⠀⠀⠀⠀⠘⢷⠮⢶⣦⣤⣸⣷⣤⣶⣷⣶⣶⡶⠿⠛
⠀⠀⠈⠋⠀⠈⠈⠱⠤⢥⠔⢤⠞⣥⠖⠀⠲⠟⠁⠀⠀⠀⠀⠀⠘⠀⣀⡿⠙⢇⠈⠉⠉⠉⠉⠙⠶⠶⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣴⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠡⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⠀⣰⡓⣐⣄⣶⣷⣰⣄⠀⠙⠻⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⠳⣄⡀⠀⠀⠀⠀⠈
⠀⢀⡏⣴⣆⡀⣿⣿⣍⣽⣿⠏⡷⢧⣀⡄⢋⠁⠦⠀⠀⠀⠀⠀⣀⣤⣠⣴⣤⠴⠊⢉⣿⢟⡶⣺⢿⣷⣾⠉⠈
⠀⠘⢦⡟⠁⠀⠉⡿⠛⠁⠉⠙⠃⠀⠺⢣⣄⠱⠀⡁⠀⠀⣠⣾⣿⣿⡇⣼⡿⢿⢸⢧⡿⣻⠟⢯⡞⠙⡾
⠀⠀⠀⠑⢰⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢠⠄⠀⠈⠙⠛⠉⠉⠁⠁⠀⠀⠉⠉⠉⠑⡄⠀⠀⠠⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣄⠀⣤⣆⠀⠀⠀⠀⣤⡄⠀⣠⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣦⠈⠟⢃⠀⠀⠘⠻⠁⣼⣷⠌
⠀⠀⢀⢠⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢈⣁⡇⠸⣟⣀⣀⣻⠇⢨⣌⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠈⠈⠛⠂⠉⠉⠘⠿⢯⣽⣶⣄⡀⢸⣿⣧⣶⣸⣿⣿⣇⣶⣾⣿⠇⢀⣤⣾⣯⠽⠿⠚⠉⠉⠘⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣅⣱⡀⣿⣽⣿⣿⣿⣿⣿⣿⣽⣿⢠⣎⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠰⣶⡍⠿⠛⠸⠿⢷⢿⡿⢟⣡⣘⠻⢿⣿⡽⠿⠇⠛⠿⢹⣶⠦⣄⡀
⠀⠀⠀⠀⠀⡠⢾⡿⠉⠁⠁⠀⠀⠀⠀⢀⣸⣧⣰⣿⣯⣽⣿⣂⣼⣅⠀⠀⠀⠀⠀⠉⠈⠙⢿⡷⢄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠻⠿⡿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣋⢭⣾⡿⠛⠀⠘⢇⠻⠿⣿⣷⡭⣙⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃⣾⣿⣷⡇⠀⣾⡇⠀⠘⣿⣿⣷⠘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡔⠰⣿⣿⠱⠠⠀⠙⣿⠀⠠⠈⣿⣿⠀⢂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⢿⣯⡦⠀⡀⢀⣿⠀⠀⢰⣿⡿⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⢿⣿⣦⡀⠉⠛⢁⣴⣿⡿⠁⠀⠀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠙⠻⢷⣾⣿⡿⠟⠋⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⢠⣾⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣨⡇⠀⢀
⠀⠀⠀⠀⠀⠹⣤⠿⠋⠿⢷⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡿⢾⣏⡠⠋
⠀⠀⠀⠀⠀⡠⢤⣛⢻⠛⡃⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⣾⣿⡀
⠀⠀⠀⠠⠚⣠⣾⣿⣾⣇⣷⣧⡈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⣿⡇⢡
⠀⠀⠀⠀⢠⡇⠈⠿⡿⠿⠟⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣶⣿⠟⠆
⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡂⡄⣸⣀⠀⡁⡒
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣀⠈⢦⡿⠿⣿⣿⣿⡥⠃⣀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠐⠊⠉⠀⠈⠛⠛⠥⠹⢶⣤⣤⣽⣶⣿⣿⣿⣿⣿⣷⣯⣤⣠⡤⠶⠭⠍⠛⠋⠁⠀⠉⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠈⠉⢉⣉⠏⠉⢡⡟⢻⣿⣿⢿⠛⣿⡟⣏⡉⠐⠂⠚⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠒⠉⡝⣠⠀⠊⣱⣿⣿⣿⣮⠀⠃⢃⢺⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⢾⣿⣿⣿⣿⣿⣷⣄⣸⡿⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢸⠀⠻⣿⣿⣿⠟⠁⡏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠉⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣆⢀⣀⡀⣴
⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢧⣼⣩⣧⠍⠠⡀
⠀⠀⠀⠀⠀⢀⡄⠀⠚⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠴⠾⣿⠷⠦⡄⢡
⠀⠀⠀⠀⠀⠁⠁⠶⠀⠰⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⣰⣄⠋⣠⣆⣆
⠀⠀⠀⠀⠀⢀⠲⡆⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⣟⠀⡻⢈⠈
⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠛⠁⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⣥⣾⣧⣬⣤⡄⠠⣤⠀⡀⠀⢰⠀⠀⠀⡡⠤⠁⠀⠀⠐
⠀⠀⠳⡀⠀⠀⠀⢀⣴⠋⢳⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⢱⡄⠀⠀⠀⠀⠀⠀⣀⠘⢺⠿⢣⡜⠿⡖⠃⣀⠀⠀⠀⠀⠀⠢⡠⣆⠀⠀⢀⣠
⠀⠀⠀⠀⡘⠂⠂⣈⢻⡄⣼⢋⡀⠀⠐⡂⠀⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠛⡿⠋⠉⡄⡀
⠀⠀⠀⠀⠀⠈⠁⠉⢁⠸⢀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠑⣄⡳⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡈⠀⠀⠀⠀⢀⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⢄⣀⠴⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠆⡀⠑⢦⢠⠖⠁⠰⠄⠀⠀⠀⠀⠀⡀⢡⠌⠉⠁⡎⠀⠀⠀⠀⠂⠉⠉⠀⠀⠀⠙⣗⢸⡏⠁⠀⠀⠀⠉⠐⠂⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⢀⡡⢬⡇⠀⣿⠤⣅⠀⠀⠀⠀⠀⠀⠈⠴⠈⠹⠁⠶⠒⠁⠀⠀⠈⠂⠀⠀⠀⡀⠀⣯⢸⡃⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢇⠈⠳⢤⠛⠈⢃⠴⠋⣀⠆⠀⠀⠀⠀⢠⠀⠛⠂⠛⠀⢤⠀⠀⠀⠀⠀⠀⢹⣏⢇⣀⡘⣏⣀⣠⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠙⠂⠂⠀⡉⠀⠒⠒⠁⠀⠀⠀⠀⠀⠄⠈⠓⠐⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⢹⡛⢟⠻⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⠒⠲⠤⠐⣄⣧⣥⡔⠡⠤⠒⠂⠀⠀⠀⠀⠀⡆⠀⠀⡥⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⣶⡐⠙⡆
⠀⠀⠀⠀⠀⠀⠐⢻⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠔⠛⠢⣈⠆⠀⠀⠀⠀⢀⠘⣇⠀⠀⢰⡤⣴⠀⠀⢀⡟⢀⠀⠀⠀⠀⠀⣹⣇⢀⡇
⠀⠀⠀⠀⠀⠀⡠⡖⠋⠙⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠦⠤⠏⠀⠀⠀⠀⠀⠀⠀⢼⡄⢀⣻⣿⣿⢒⡀⣼⠁⠀⠀⠀⠀⠀⠀⣿⣷⣾
⠀⠀⠀⠀⠀⠌⠐⢇⠀⢀⠟⠀⠣⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠸⠐⣄⠀⠀⠀⠀⡌⠸⣇⠀⠙⢿⠿⠋⢀⣿⠞⡄⠀⠀⠀⠀⠀⢸⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢀⢴⡄⠈⠀⠀⠀⠀⠐⢀⠘⡦⠀⠈⠀⠠⡞⢀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠂⡀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠰⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡽⠤⡧⠬⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠗⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠤⠐⠂⢆⡇⠀⠀⠀⠀⢤⡀⠀⠒⠒⠀⢀⡤
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠹⣦⡾⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠴⠖⠢⠔⢣⠤⠀⠀⠀⢰⠒⠇⢹⠋⠉⠉⠸⠐⡆
⠀⠀⠀⢀⠄⠁⠀⠀⠁⠀⠀⠊⢃⠀⠀⠀⠀⠀⠀⡆⡠⠊⠤⠆⠤⠄⠢⡀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⣄⠀⢠⡕⠀⣠
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⢠⠀⡀⠀⠹⠁⠨⠖⠀⠐⠲⠀⠹⠅⠀⣀⢠⠀⠀⠀⠀⠃⡀⠀⢈⠀⠀⠀⠀⠀⠢⡀⢦⠂⠐⡄⢀⠔
⠀⠀⠀⠀⠀⠀⢙⠒⠶⠚⡘⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢹⣧⡀⠀⠀⠀⡀⡀⠀⠀⠀⣠⣿⠃⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠙⢿⣦⣀⣾⣷⣿⣆⣠⣾⠟⠁⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⡶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⣩⣽⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠙⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣴⡾⠟⠹⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⣶⣄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⢻⣆⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢿⠀⠀⠀⠀⠀⠙⢷⣦⣭⣭⣿⠟⠁⠀⠀⠀⠀⢸⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡔⠊⠀⠀⠀⠀⠀⠀⠇⢀⡀⠀⠀⠀⠀⠀⠀⢂⠀⢀⠀⠂
⠀⠀⠀⠀⢐⢀⠂⢐⠀⠀⠀⠀⠀⢉⡜⠐⣗⠀⠂⠀⠀⠀⠀⠐⡗⠀⠀⠀⠀⠀⠀⠀⠖⠁⢠⡄
⠀⠀⠀⠀⢀⡙⠀⠠⠂⠀⠀⠀⠀⠊⡇⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡁
⠀⠀⠀⠀⠃⠀⠀⢀⠓⠀⠀⠀⠈⠀⢇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠘⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⣀⠀⡔
⠀⠀⠀⠀⠌⠀⠐⢁⠁⠀⠀⠀⠀⠀⠀⢀⠨⠦⠐⠶⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⣬⡂⣡⣤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⡠⢊⣠⠞⢈⢡⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠐⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠳⠿⠥⠒⢡⠻⡄
⠀⠀⠀⠠⠖⣋⣽⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠛⠋⠙⠳⠴⠤⠄⠀⠀⠢⡀⠀⠄⣢⡮⠈⠤⠀⠤⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠘⠋⠋⠀⠘⠀⠀⠀⠀⠀⠀⠄⠔⡒⣂⣀⠂⣠⠤⠤⠈⠁⠀⠀⠀⢀⢈⡔⡀⢲⠟⠁⢈⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣂⣀⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠁⠀⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠉⠒⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⡀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠠⠔⠲⠦⠀⠀⠀⠀⠀⢠⠴⠦⢤⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠼⢤⡙⢦⡀⠀⠀⠀⡜⠀⠀⠀⢀⠤⠐⠀⢄⠀⠀⠀⢀⠤⠀⠀⠄⡀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡴⠊⡗⠢⣀
⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠉⠳⣜⣷⡄⢰⠁⠀⠀⠐⠁⠀⠈⣿⣷⡔⠀⠠⠁⠀⢻⣿⣦⠘⠀⠀⠀⢣⠀⠀⣠⠞⣡⠴⠋⠉⠳⢬⡑⢤⡀
⠀⠀⠀⡴⣫⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⠀⠀⠀⠀⠘⣷⣶⣿⣿⡇⠂⢀⢷⣶⣿⣿⡿⠀⠃⠀⠀⢸⣠⣾⡷⠛⠁⠀⠀⠀⠀⠀⠙⢶⣝⢦⡀
⠀⢠⢮⣾⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠻⡄⠀⠀⠈⠢⢈⠙⢛⡩⠊⠀⠀⠢⢉⠛⢋⡠⠊⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢷⣝⢄
⢠⢃⡿⠁⠀⠀⠀⢀⡴⣩⠤⠭⣭⣭⣿⣶⣦⣤⣵⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣴⣶⣶⣿⣭⡭⠭⠭⡟⢦⠀⠀⠀⠀⢻⣎⢧
⣏⡼⠁⠀⠀⠀⢠⢎⡴⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⣄⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⢀⣜⣋⣉⣉⣀⣀⣀⣀⣀⠀⠀⠈⢦⡱⡄⠀⠀⠀⢻⣈
⠀⠀⠀⠀⠀⡰⢣⡞⠀⠀⠀⣠⢖⠋⠉⣉⣉⣉⣩⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣭⣥⣤⣤⣀⣀⡈⣹⢣⠀⠀⠳⡜⢆
⠀⠀⠀⠀⡼⣱⠏⠀⠀⠀⣰⢃⡞⠚⠉⠉⠉⠀⣀⣴⣾⡿⠛⠉⠙⠒⠲⠤⠤⠤⠴⠒⠊⠉⠉⠛⠿⢿⣶⢤⣀⠀⠀⠀⠀⠉⠙⢆⠳⡀⠀⠹⣎⢣
⠀⠀⠀⡜⣴⠏⠀⠀⠀⣰⢃⡞⠀⠀⠀⢀⠴⣚⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣙⣢⡀⠀⠀⠀⠈⣆⠱⡀⠀⠙⣧⣳⡀
⠀⠀⢰⢹⡟⠀⠀⠀⢠⠃⡾⠀⠀⠀⢰⢓⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠀⠀⠀⠀⠘⣆⢱⡀⠀⠸⣷⢳
⠀⢀⡇⣾⠁⠀⠀⢀⡇⣼⠃⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡆⠀⠀⠀⠀⠹⣆⢣⠀⠀⢹⡆⢇
⠀⠘⠤⠋⠀⠀⠀⡸⣰⡏⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢱⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠣⠼
⠀⠀⠀⠀⠀⠀⢠⢣⣿⠁⠀⠀⠀⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⡄⠀⠀⠀⠀⠘⣿⠸⡀
⠀⠀⠀⠀⠀⠀⢸⢸⡏⠀⠀⠀⢰⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⢻⡀⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⠀⠀⠀⠀⠀⠸⡇⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢳⠀⠀⠀⣎⣃⣀⠀⠀⠀⡀⠠⠦⠀⠀⠀⢨⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⣆⠀⠀⣈⣟⠉⠀⠀⠀⠹⠖⠶⠀⠀⢠⠃⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⣱⠊⠀⠉⠉⠈⠉⠉⠉⠉⠑⣄⡤⣮⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠠⡄⠒⢚⡩⠝⠻⡴⠋⠀⠀⠈⠙⡗⠒⠒⡖⠀⠉⠉⠻⣄⠠⡤⣀⡀
⠀⠀⣀⣀⣤⣶⡶⡧⠚⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠙⢲⠚⠀⠀⠀⠀⠀⠘⡟⠁⠢⢌⠙⠤⣀
⡠⡮⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠑⣶⠹⣦⣄⡀
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠀⠀⠙⠛⣕⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⡶⡇⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⣼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜⠀⢣⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠻⡟⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢸⠁⠀⠀⠙⢀⣀⣀⠀⢰⠀⢀⠀⢀⣠⠞⠁⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⡌⠀⠀⠀⠀⠀⠙⠻⠬⣿⣨⡭⠗⠋⠁⠀⠀⠀⢸⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣌⠆⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠻⡅
⠀⠀⠀⠀⠀⢠⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⡵⡄
⠀⠀⠀⠀⣰⣃⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢳⡀
⠀⠀⠀⠠⠇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢂⢐⠞⠂⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⡀⢈⡄⡀⠀⢀⠀⠀⠀⠀⠀⣊⣀⢀⠀⠠
⠀⠘⠓⠀⠀⠈⢐⣁⠀⠀⠀⠀⠀⠀⣲⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣦⡾⡉⡹⡓⠒⠁⠀⠀⢠⠆⠈⣹⠟⠷⡄⠊
⠀⠰⢹⡄⠀⠀⠀⠉⡧⠀⠀⠀⠐⠀⢣⢺⠃⡏⠀⠀⠀⠀⠀⠀⠚⠁⢠⣾⢋⡔⠘⠐⠊⠀⢠⡀⡘⠁⣠⡀⣠⠡
⠀⠀⠹⢄⠀⣀⠀⠄⠁⠀⠀⠀⠀⠠⠊⢹⠡⠁⠀⠀⠀⠀⠀⠊⠁⠀⠚⠕⠂⣸⠀⠀⠀⠠⠚⠀⠁⢀⡈⠀⡤
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠠⠀⡤⡼⠀⠈⠈⠄⠀⠒⠁⠀⠀⠀⠐⠀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⢈⣉⠑⢨⡚⠠⠄⢐⠀⠀⠀⠀⢸⠀⠠⡀⠀⠀⣡⢜⠞⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀⢀⣈
⠀⠀⡔⠉⠇⠀⡡⠝⡠⡍⠁⠑⠀⠀⠀⢸⠀⠀⠁⠀⠀⢦⠈⠆⠑⠌⠀⠀⠀⠀⠠⠀⠀⠀⠤⡚⠈⢀⣤⡀⢀⢠⠄
⠀⠘⠀⠀⠀⠤⠔⣾⠸⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠠⠶⡦⠤⠀⠀⡀⠀⠉⠰⢸⠀⣈⣭⣀⢀
⠀⠀⠀⠀⠀⠠⠔⠁⢀⠀⠀⠀⣰⠀⢰⡴⢻⡆⠪⡁⢠⣞⡹⢠⡎⠀⢸⠇⠰⣉⠂⠀⠁⠄⢰⣾⣛⣭⠾⠯⡲⡀
⠀⠀⠀⠀⠀⠂⠀⠰⠁⠀⠀⡄⢿⡠⢺⠀⢸⡠⢄⣸⠾⢧⡤⠚⢧⡤⠾⠤⢄⣨⡇⠀⠀⠀⠁⡇⠡⢶⣺⠁⠇
⠀⠀⠀⠀⠀⠀⢀⠰⣀⠀⠰⠀⠀⠀⢀⠀⡇⡀⢀⢀⢀⠀⡀⡇⢸⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡉⠁
⠀⠀⠈⠂⢀⡲⠊⠌⢶⠈⠀⠈⠀⠀⠸⠄⠇⠃⠘⠹⠰⠛⠆⠧⠸⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢶⣀⠊
⠀⠁⠀⠉⠀⠁⠂⠀⠼⡁⠂⠒⠀⠈⢠⢤⠤⡤⢀⠀⢀⠀⠀⠀⢀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠐⠀⢽⣿⡅
⠀⡀⠄⠂⠁⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⠒⢩⣥⣄⣩⠇⠀⠁⠞⢦⠼⠧⣄⣤⠤⢄⡀⠀⠀⠀⢀⢚⣘⡶⡀
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡀⠠⣎⣠⠀⠑⡌⠉⠆⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠁⡠⠃⢰⣶⡺⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⢁⣆⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⣴⣆⣠⠂⠀⠀⠀⠀⢠⢼⡖⣄⣈⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠠⡤⠀⡏⠊⠀⠀⠀⣠⡄⠀⠀⠀⠈⣋⠉⠉⡇⢀⡀⠀⠄⣀⣀⣧⠙⢦⣌⣀⡐⣁⠀⠠
⠀⠸⠁⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠁⠀⠘⢢⣀⡯⠂⠀⠀⠈⠰⢼⠀⠠⡎⠁⠀⠀⠀⠀⠀⠸⠇⠴⠉⠁⠙⠈⠂
⠀⠀⠐⠦⠄⡀⠀⡀⠑⢢⡀⠀⠀⠀⠀⡐⡻⣿⡅⠐⠀⠀⠀⠂⢂⠀⠀⠙⡤⠀⡀⠀⠀⠀⠠⠤⠤⢠⣧
⠀⠀⠀⠀⠀⠈⠁⠈⠉⠢⣉⠄⠀⠤⠀⠸⡴⠋⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⡀⠸⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠉⠉⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡠⢒⣭⡑⢄⠀⠀⠀⢠⠁⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⢣⠀⠀⠀⠀⢀⡤⠦⢀
⠀⠀⠀⢀⠔⣫⠖⠁⠀⠉⠲⣝⣦⡀⡇⠀⠀⠀⠀⠘⣷⣆⠀⠐⠁⢸⣶⡄⠀⠀⠀⡇⠀⣠⢔⡡⠖⠉⠢⣕⠢⡀
⠀⠀⣴⣥⠞⠁⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⢻⣾⣿⠟⠀⠈⢷⣿⣿⠇⠀⠀⠀⣧⣼⠷⠋⠀⠀⠀⠀⠈⠳⣮⡢⡀
⢀⢎⡿⠁⠀⠀⢀⠤⠀⠤⠤⣤⣀⡈⢃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠈⠀⠀⢠⣟⣁⣀⣤⠤⠤⠤⢄⠀⠀⠈⠻⣞⠄
⣎⡞⠀⠀⠀⡠⢪⠎⠉⠉⠉⠙⠛⠛⠿⢦⡀⠀⠀⠀⠀⠐⠤⠈⠀⠀⠀⠀⠀⡠⠟⠛⠛⠉⠉⠉⠉⠉⠡⡑⡄⠀⠀⠹⡌
⠀⠀⠀⠀⡔⡵⠃⠀⠀⡴⠒⢊⣉⣉⣽⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠭⢭⣭⣍⣉⣩⠢⠀⠘⢎⢂⠀⠀⠈
⠀⠀⠀⢜⡼⠁⠀⠀⠌⡜⠉⠉⠀⢀⣤⣶⠿⠋⠁⠉⠁⠒⠒⠒⠂⠉⠁⠈⠙⠻⢷⡢⢄⡀⠀⠀⠈⢣⠱⡀⠈⢧⡣
⠀⠀⣼⡾⠁⠀⠀⡌⡼⠁⠀⢠⢞⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡜⡆⠀⠀⠀⢣⠱⡀⠈⢷⡥
⠀⢰⢸⠃⠀⠀⡘⣰⠃⠀⠀⡎⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢧⢱⠀⠈⣧⢃
⠀⠘⠚⠀⠀⢀⢡⡏⠀⠀⠰⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠃⠀⠀⠀⠘⣧⢃⠀⠘⠼
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠀⠀⠀⠀⢻⡌
⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⡀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠓⠁⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⣠⡏⠁
⠀⠀⡿⠛⢦⠀⠀⠀⠀⠀⠀⠹⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠹⠇⠀⠀⠀⠀⠀⠀⡔⠛⢿
⠀⠀⢱⠀⠀⠱⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡸⠀⠀⠀⠀⠀⢀⠎⠀⠀⡎
⠀⠀⠀⢣⡀⠀⠘⢆⠀⠀⠀⠀⠈⡄⠀⠈⢢⡀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢠⠁⠀⠀⠀⠀⡰⠃⠀⢀⡜
⠀⠀⠀⠀⠱⣄⠀⠀⢣⠀⠀⠀⠀⠘⡀⠀⠀⢳⡀⠀⠀⠀⢠⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡄⠀⠀⠀⠀⠞⠀⠀⢀⠇⠀⠀⠀⠀⠜⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠡⣀⠀⠀⠀⠡⠀⠀⠈⠇⠀⠀⠀⢨⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡝⠀⠀⠀⠈⠁⠀⠀⡎⠀⠀⠀⣀⠌⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠤⠙⡄⠀⠀⠀⢇⠀⠀⣁⠀⠀⠀⠀⠙⢷⣄⡼⠛⠢⣄⣠⠔⠙⢧⣠⡾⠋⠀⠀⠀⠀⣀⠀⠀⠸⠀⠀⠀⢠⠛⠠⣴⠉
⢱⡄⠀⠀⠀⠀⠀⠀⠘⡄⠀⢡⠀⠀⠀⢸⣦⣼⠟⠳⣄⣠⠴⠒⠶⢿⣇⣀⡀⢸⡇⢀⣀⣸⡿⠶⠒⠦⣄⣠⠞⠻⣧⣤⡇⠀⠀⠀⡌⠀⢠⠋⠀⠀⠀⠀⠀⠀⣠
⠀⢿⣦⠀⠀⠀⠀⠀⠀⢱⠀⠀⠄⠀⠀⠈⢧⣀⡠⠀⣁⣉⣀⡄⣣⠜⡉⠉⠙⣆⣰⠋⠉⢉⠣⣜⢠⣁⣉⡉⠀⢄⣀⡾⠁⠀⠀⠰⠀⠀⡎⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠈⢽⣷⡀⠀⠀⠀⠀⠀⠣⠀⠈⣶⠲⠤⢄⣭⣓⣂⣉⣉⡀⣼⢃⠎⠄⠀⠀⢹⡟⠀⠀⠠⠱⡘⢧⢀⣉⣉⣒⣺⣩⡤⢤⠖⣶⠁⠀⠜⠀⠀⠀⠀⠀⢀⣜⡿⠁
⠀⠀⠈⠳⣽⣄⠀⠀⠀⠀⠀⢲⡞⠋⠀⠀⠀⠁⠀⠈⠀⠐⠀⠇⠈⠀⡄⠀⠀⣼⣷⠀⠀⠠⠀⠁⠘⠄⠂⠀⠁⠀⠈⠀⠀⠀⠙⢳⡖⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠈⠙⣷⠖⠠⠄⣀⠀⠉⠓⠒⠚⠒⠚⠛⢒⡻⠷⠾⡄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⠷⠿⢟⡒⠛⠒⠒⠒⠒⠚⠉⢀⣀⠠⠄⠶⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⢄⣀⠉⠁⠂⠶⠖⠖⠉⠁⠀⣀⣤⣽⣦⣴⣶⢾⣿⠿⠿⣿⣷⣶⣤⣴⣯⣤⣀⠀⠈⠉⠲⠲⠖⠐⠈⢉⣁⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⡀⣤⣴⠟⡹⠋⢡⠎⣹⠇⡼⠁⣠⣄⠈⢧⠸⣏⠳⡌⠙⢏⠻⣶⣤⢀⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⣡⡾⠁⠆⢸⡀⢧⠀⡇⠰⡇⢸⠆⢸⠂⡼⢀⡇⠰⠈⢻⣍⠱⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣰⡟⠀⢠⢦⠀⢧⠈⢆⠹⣆⠉⠉⣴⠃⡴⠀⠸⠀⡴⡄⠀⣿⣆⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢲⡏⢸⡀⠘⠋⣠⠞⢀⡜⣠⡟⠐⠂⠻⡀⠣⡀⢰⣄⠙⠃⢠⠟⠹⡖⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣰⢸⡇⢀⡿⠀⣞⠁⡴⠁⢠⠏⢠⡞⢳⡄⢸⡆⠈⢦⠈⣿⠀⢏⠀⢸⡇⣆⠀⠠⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣰⠃⠈⢧⡞⠀⣀⠈⢦⡙⢦⠘⣆⠀⠓⠚⠀⡼⢃⡔⢋⡔⠁⣀⠀⢳⣼⠁⠸⣆⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠑⣆⢀⡴⠃⠀⠀⠘⢧⡘⢯⠇⠀⣧⠀⡆⠈⡷⠀⠀⣾⠁⢸⠀⢸⠀⠘⠽⢃⡼⠃⠀⠀⠘⢦⡀⣠⠊⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠛⠁⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠹⣦⢹⣄⡗⢃⡘⢻⣠⣏⣤⠞⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠿⢿⣄⣰⡿⠯⠄⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣼
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢳
⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡆
⠀⠀⠀⠀⠀⠀⠀⢾⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠠⣙⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢋⡄⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡖⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⢰⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡆⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⢃⠀⠑⡄⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠸⠀⠀⠀⠀⠀⢠⠂⠀⡘
⠀⠀⠈⠄⠀⠈⢢⠀⠀⠀⠀⠘⡀⠀⠐⣄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢠⠂⠀⢠⠃⠀⠀⠀⠀⡔⠁⠀⣠⠁
⠀⠀⠀⠘⢆⠀⠀⠡⡀⠀⠀⠀⠱⠀⠀⠈⢆⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠰⠁⠀⢀⠆⠀⠀⠀⢀⠌⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠑⡄⠀⠑⡀⠀⠀⠀⢡⠀⠀⠸⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠂⠀⠀⠀⠃⠀⠀⡌⠀⠀⠀⣀⠊⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠈⢢⡤⠙⣄⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠙⠻⣆⣠⠓⠦⡀⣀⠔⠒⣆⣰⠟⠉⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⣠⠛⢄⡔⠁
⢱⡄⠀⠀⠀⠀⠀⠈⢅⠀⠠⠀⠀⠀⢸⣤⡼⠟⢦⣀⡤⠆⠶⢿⣏⣀⡀⢸⠇⢀⣀⣽⠷⠶⠰⢤⣀⡴⠻⢧⣤⡇⠀⠀⠀⠄⠀⡸⠁⠀⠀⠀⠀⠀⢠
⠀⢿⣆⠀⠀⠀⠀⠀⠈⡄⠀⢀⠀⠀⠈⢦⣀⠄⠀⣀⣁⣤⣈⡴⡋⠉⠉⣧⣸⠉⠉⢙⢦⣁⠤⣈⣀⠀⠠⣀⡾⠁⠀⠀⡐⠀⢠⠂⠀⠀⠀⠀⠀⣰⡿
⠀⠈⢟⢧⡀⠀⠀⠀⠀⠙⠄⠀⣻⠑⠖⠠⣭⢭⣥⠥⠤⢠⠏⠐⠀⠀⠀⢹⡇⠀⠀⠀⠂⠹⡆⠤⠬⣭⠭⣭⠄⠶⠚⣟⠀⠠⠃⠀⠀⠀⠀⢀⢜⡿⠁
⠀⠀⠀⠑⢿⣄⠀⠀⠀⠀⠘⢏⡉⠀⢀⠀⠀⡀⢀⣀⡀⡚⠀⠀⠀⠀⠀⢾⡧⠀⠀⠀⠀⠀⠁⢀⣀⠂⢀⡀⠀⠀⠀⢉⡽⠃⠀⠀⠀⠀⣠⡿⠏
⠀⠀⠀⠀⠀⠸⣟⠁⠒⠠⠄⣀⡈⠉⠉⠉⢉⣉⠭⠛⠛⢣⡀⠀⠀⢀⣀⣸⣇⣀⡀⠀⠀⢀⡜⠛⠛⠭⣉⡉⠉⠉⠉⢁⣀⠠⠄⠐⠈⡻⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠄⠀⠁⢹⠉⠃⠀⢀⣰⣶⡷⢿⡿⣿⢛⡿⠛⠙⢿⠛⣿⢿⡻⢾⣶⣆⡀⠀⠈⠉⡋⠈⠀⠠⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢒⡶⢟⡵⠃⠀⡏⣸⠃⠞⠀⡖⢢⠀⢳⠘⡇⢹⠀⠑⢮⡻⢗⡂⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⡾⠁⢈⠀⢷⠈⣄⢲⡀⠣⠜⢀⠞⣰⠁⡜⠀⡁⠈⣷⡄⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣠⡟⡄⠀⠯⠃⢸⠆⠈⠄⣿⠠⠀⣏⠰⡁⠀⡀⠘⠽⠀⢸⢻⣄⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⢠⢹⠁⠙⡆⢠⠞⢉⡔⠁⡾⠁⡤⢤⠈⢢⡈⢢⠙⠳⡄⢰⠃⠈⡎⡄⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢠⠃⠸⣄⠞⠀⠈⢧⡘⢦⡈⣇⠈⠧⠼⠁⣸⠃⠰⢃⠜⠁⠈⠳⣤⠃⠘⡀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠄⠀⡠⠋⠀⠀⠻⡄⢸⣳⠀⢹⠀⣡⠙⣦⠀⠀⣼⠁⣎⠀⡏⠀⢞⡇⢠⠟⠀⠀⠙⣄⠀⡠⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠚⠊⠁⠀⠀⠀⠀⠙⠢⡀⠀⠸⣧⠹⣄⡣⢂⡐⣿⣠⣏⣠⠇⠀⠀⠔⠋⠀⠀⠀⠀⠀⠑⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠤⠭⢿⡄⣠⡿⠭⠄⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣧
⠀⠀⠀⠀⠀⠀⠀⣰⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⡆
⠀⠀⠀⠀⠀⠀⠀⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻
⠀⠀⠀⠀⠀⠀⠀⣷⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠹⣷⡀⠀⠀⣀⣿⣇⡀⠀⠀⣰⡿⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠀⠀⠹⣿⣦⣼⣿⣿⣿⣿⣤⣾⡟⠁⠀⠀⣠⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⢹⣿⣯⣿⣿⣿⣯⣿⣿⠁⠀⠀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣽⣿⣿⣿⣿⢿⣿⣥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠙⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠛⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡇⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⠛⠿⠟⠿⠟⠋⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡻⢶⠀⡃⠀⠀⣤⡤⠀⣀⠀⠀⡀⠠⢰⣶⡆⠄⢀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠠⣀⡤⣤⣀⡤⠀⠀⠀⠀⠀⠀⠀⢸⠀⡾
⡿⣿⣉⣁⠀⠀⠀⠊⠌⣉⠙⠯⠙⢛⣿⣿⣿⡒⠫⠖⠒⠀⠀⠀⠀⠀⠀⣀⣀⠴⣿⡀⢁⣿⡦⣀⡀⡀⠀⠀⠀⠀⣈⣉⣿
⣿⣿⢡⠸⡀⠀⠀⠶⣶⣤⡴⠖⢂⡾⠻⣿⡟⢷⡐⠒⢦⡤⣶⡦⠀⠀⠀⠈⠁⣼⢩⢿⡟⡉⢷⡈⠁⠀⠀⠀⠀⢠⠃⣾⣿
⣿⣿⢸⡄⠁⠀⠀⠀⠀⠉⠀⠀⠘⠁⠀⣿⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⠟⠄⣸⣃⠠⠺⣧⠀⠀⠀⠀⠔⠀⢀⣿⣿
⣿⣿⢸⡏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠃⠈⢫⡄⢂⠑⢿⡇⠀⠀⠀⠀⢼⠛⣿⣿
⡟⠃⡼⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠁⣀⣼⣆⡀⠀⢈⢿⠀⠀⠀⠀⠘⡄⢿⣯
⠿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⡴⠊⠁⠈⠁⠈⠂⢠⣀⡄⠀⠀⠀⠊⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠁⠀⠁⠐⠀⢀⢀⣤⣶⣄⣠⠄⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⡷⢶⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⠦⠀⠀⢀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡾⣟⡻⣦⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟
⣿⣄⣀⣄⣀⣀⠠⠴⠖⠂⠀⠀⣘⣛⣷⣿⡷⣯⣙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠰⠒⠂⢀⡤⣄⣠⣄⣃
⣿⣿⠉⠈⡁⠀⠀⠀⠀⠀⠀⢰⠁⣿⣿⣿⣿⣏⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠙⢒⡈⣽
⡟⠘⢇⠀⠙⣻⡽⠟⠓⠀⠔⠀⢰⣿⣿⣿⣿⡿⢸⡀⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤⣠⣄⣤⠀⡠⠀⠘⠻⠿⡶⠋⡉⣼⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢻⣿⣿⣿⣿⣷⢸⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣿⣿⠁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⣽⣿⡟⠃⡸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣷⡼
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣧⣤⣤
⡇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⠄⠀⢀⡎⠀⢸⣿⣿⣿⣿⡇⠀⢱⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣤⠖⠈⠀⠀⠀⠀⠀⠀⠁⢀⣤⣿⣿⣿⣿⣿⣿⣦⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣻⡟⠂⠀⠠⠄⠀⠀⠀⠀⠀⠈⡄⢿⣿⣿⣿⣿⡿⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠌⠻⠿⡿⠟⠡⡆
⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠠⣄
⢾⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠄
⠀⠀⠀⠀⠀⢀⣾⣇⡀⠀⠀⠈⢻⡄⢾⡛⢆⠀⢀⠔⣻⡇⣼⠋⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢧⡾
⠀⠀⠀⠀⠀⡴⣿⣿⢄⠀⠀⠀⠀⠹⢤⠭⠿⣿⡿⠯⢥⠴⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣾⣶⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢆⠀⠀⢻⠇⠀⢀⠆⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⢘⣿⣿⡁
⠀⠀⠀⠀⠀⠀⣇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⣀⣀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠛⠿⣿⣿⣶⣶⣞⣳⣶⣶⣿⣿⠿⠛
⠀⠀⠙⢿⣿⣷⣤⣴⣿⣿⡿⠃⠀⠀⠀⠀⣿⣻⡅⠀⠀⠀⢀⣠⣴⣾⡿⢻⡟⢿⣷⣦⣄⡀
⠀⠀⠀⠀⣿⣿⡟⢿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠈⠉⠉⠀⠀⢸⡇⠀⠀⠉⠉⠁⠀⣰⣿⣷⡄
⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠘⢿⣿⣷⣦⣔⣦⣴⣾⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠬⠕⠀⠀⠀⠀⠀⠾⠟⠋⢀⣉⠈⠙⠻⠆⠀⠀⠀⠀⠀⢿⡷⠀⠀⠀⠀⠐⠿⠿⢻⡟⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣷⢆⠀⠀⢀⠴⣿⣻⡟
⠀⠀⠀⠀⠀⢀⣾⣇⡀⠀⠀⠀⠸⣿⣇⠀⣁⣤⣁⢀⣿⡿⠀⠀⠀⠀⢀⡜⢣⡄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣾⢿⢿⣷⠀⠀⠀⠀⣼⡟⠋⠩⠟⠉⠛⢿⡆⠀⠀⠀⠀⢸⣷⣾⡇⠀⠀⠀⠀⢠⣾⣿⣿⣧⡀
⠀⠀⠀⠀⣼⡟⡲⡚⢿⡇⠀⠀⠀⢹⣷⣤⠄⠀⢠⣴⣾⠁⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠠⠿⠛⢻⠟⠛⠷
⠀⠀⠀⠀⠙⠁⠉⠁⠈⠃⠀⠀⠀⡜⠉⠁⠀⠀⠀⠉⠉⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣤⡶⠶⠒⠻⣽⣦⡿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣿⣿⣯⣀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡿⢢⡀⠀⠀⠀⣀⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡈⠛⠻⠿⣷⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣀⣠⣴⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠋⠀⠀⠀⠀⠈⠉⠙⠲⣤⣈⠙⠿⣿⣿⣿⣿⣿⡇⠉⠛⠾⡆⠀⠀⢰⡿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣿⠿⠷⠦⢌⡙⠻⣿⣿⡇⠀⠀⠀⣷⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣫⣾⣿⡆⠀⠀⠀⠉⠲⣌⠙⢿⣦⡀⠀⢿⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠳⣄⠻⣿⠶⢸⣶⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⠆⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⢰⣷
⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠹⢿⣿⠟⠀⠀⣸⡿
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀
⠀⣀⣠⣴⡾⠃⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠟⠛⠗
⣠⡿⣿⠁⠀⠀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢹⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠖⠊⠙⠉⠉⠁⠉⠀⠈⠁⠈⠉⠳⢲⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠴⠒⠊⢉⡉⢦⡀
⠀⠀⠀⠀⠀⠀⡔⣡⣄⣈⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠈⠓⢽⣦⡀
⠀⠀⠀⠀⢀⢜⡔⠁⠀⠀⢸⠋⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⣠⠴⠶⣄⠀⠀⠀⠀⢹⡀⣀⣀⣀⡀⠈⠛
⠀⠀⠀⣠⠞⠋⡴⠒⠒⠒⠛⠀⠀⠀⢠⠋⠀⠀⠘⡆⠀⠀⠀⠁⠀⠀⠘⡆⠀⠀⠀⠀⠁⠂⠀⠀⠱⡀
⠀⠀⠀⠀⢀⠞⡰⠋⠉⠙⢷⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⡏⠉⠉⠉⠳⣕⡄
⠀⠀⠀⢀⣪⠎⠀⠀⣀⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠠⣴⠆⠀⠀⠀⠀⠀⠀⠀⢀⠛⠤⣀⠀⠀⠈⠻⡄
⠀⠀⢠⠟⠁⠀⢰⢋⡤⠤⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠑⠦⣀⠙⡄
⠀⠀⠀⠀⠀⠀⠇⡜⠀⠀⠀⡰⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢟⠀⠀⠀⠈⡆⢧
⠀⠀⠀⠀⠀⣸⡼⠀⠀⠀⡼⠁⢠⠏⠉⠑⠳⠔⠤⠤⠤⠤⠤⠒⠒⠉⠉⠀⠙⢄⠈⢆⠀⠀⠀⠸⣸
⠀⠀⠀⠀⢀⡿⠁⠀⠀⠸⡄⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠃⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠱⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁