Crying Emojis & Symbols

⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠃⠀⠀⢰⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⣩⣶⣿⢟⣻⣭⠿⢛⣛⣻⣿⣿⣛⣻⣿⣿⣿⣷⣶⣦⣬⣽⣿⣷⣶⣶⣶⡶⠿⣿⣿⡿⠋⢻⡆⠙⢦⡄⠻⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⡿⠋⣴⠟⢉⣴⠿⠛⠛⣉⣉⣉⣉⣛⣛⣛⣛⣉⣙⣛⣿⣿⣿⡿⠿⢛⣩⣴⡾⠛⠁⠀⠀⣼⣿⠀⠀⠹⣦⠹⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠀⣼⠃⣴⠏⢁⣴⣾⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⣉⣁⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⣰⣿⣿⡀⠀⠀⠹⣷⣹⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⠃⣾⠃⣴⣿⡿⠛⣁⣤⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠛⠋⠉⠘⣆⠀⠀⠀⠀⠀⠐⠛⠁⢸⣧⠀⠀⠀⢻⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣧⣼⠃⣼⣿⢏⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠈⠀⠀⠀⠀⣴⣢⣶⣿⠿⣿⡁⠀⠀⠸⣿⣾⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠏⠀⠀⠀⠀⠀⠀⢰⣿⠻⢏⣼⠞⢿⠀⠀⠀⠀⣿⡏⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣿⣿⣿⢸⡟⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⡿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠭⠜⠁⠀⢸⣇⠀⠀⠀⣿⣇⠸⡆⠻⣿⣿⣿⣿⣿⣿⣿
⠇⣿⡏⣿⢸⡇⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢿⡄⠀⠀⢹⣿⣦⣷⡀⠹⣿⣿⣿⣿⣿⣿
⣾⣿⢣⡟⣸⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⢿⣿⡟⣯⢉⣤⡹⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⣧⠀⣴⣸⠇⢻⣿⢷⡀⢻⣿⣿⣿⣿⣿
⢻⡟⣼⢃⡟⠀⠀⠀⠀⠀⠀⠀⠉⠹⢥⣄⠙⢪⡭⠵⠟⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣿⣶⡟⣿⠀⠀⢿⡞⣧⠸⣿⣿⣿⣿⣿
⠘⣿⢏⣾⠻⣦⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠈⡀⠀⣿⣿⡗⢿⣆⠀⢸⣧⢻⡀⣿⣿⣿⣿⣿
⡆⢹⣾⣷⡀⢹⡆⣠⡴⠖⠛⠉⠉⠁⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣿⠋⠀⠀⢹⣇⠈⣿⣼⡇⣿⣿⣿⣿⣿
⣷⠈⣇⢹⣇⣼⠟⠁⠀⢀⣀⣀⣠⣤⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠀⠰⠇⠀⢰⣿⠀⠀⠀⠀⣿⡀⣿⣿⡇⣿⣿⣿⣿⣿
⣿⠀⣿⡸⣫⢋⣀⡤⠖⠋⠉⠀⠀⠈⣷⡄⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢸⣇⣿⣿⠇⣿⣿⣿⣿⣿
⣿⠀⣸⢉⣿⠏⣵⠛⠛⠲⣤⣴⠟⠛⠛⠛⠶⠶⠦⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣺⠃⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⢠⣿⣿⣿⣿⣿
⣿⠀⣿⣾⣇⠀⠸⣆⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⣀⡤⢞⣡⣾⡟⢻⡄⣿⠀⠀⠀⢀⢠⣿⠏⣼⡇⣼⣿⣿⣿⣿⣿
⠇⢰⠋⠈⢿⣷⣄⣈⡿⠋⠀⠀⠀⣠⣶⣶⣶⣶⣶⠶⠶⠶⠀⠀⢹⡤⣤⣶⡾⠵⠞⠋⠉⠁⢀⣾⠃⣿⢀⣄⣖⡞⣿⡟⢰⣿⢁⣿⣿⣿⣿⣿⣿
⢠⣿⣆⠀⠀⠹⣿⡿⠁⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣇⠀⠉⠛⠻⠶⢶⡶⠾⠟⠁⠀⢸⣿⡿⣼⣽⣿⠁⣼⡟⠸⠟⠉⠀⠀⠉⠙
⡿⢿⣿⣦⡀⠀⢸⠃⠀⠀⣾⡿⠁⠀⠀⢀⣀⣤⡴⠾⠛⠁⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⣷⣿⠇⠀⣿⡇⢠⣴⡶⠶⣶⣄
⠃⠀⠙⢿⣿⣷⡏⠀⠀⣰⣿⠃⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠙⢻⣿⠀⠀⣿⡇⠸⠏⠀⠀⠈⣿⠆
⠀⠀⠀⠀⠙⢿⠹⠀⣰⢿⡇⠀⠀⣰⡏⠀⠀⢀⣤⣴⡶⠛⠁⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⣿⠀⠀⣿⣧⠀⠀⠀⠀⣰⠟⢠
⣶⣄⡀⠀⠀⢹⠶⢾⣧⣸⡇⠀⠀⣿⠃⠀⠀⣼⠑⢿⠀⠀⠀⠀⠀⠀⠀⣿⡟⡿⠛⠛⠛⢿⣿⡀⠀⠀⠀⠀⠘⣿⣆⠀⠘⢿⣷⣤⣀⣀⣠⡴⠋
⠛⢿⣿⣷⣦⡀⠀⠀⠙⢿⣇⠀⢀⣿⠀⠀⢸⡇⠀⠀⠀⡶⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⡀⠀⠙⢿⣦⣀⠀⠀⠀⠘⠿⣷⣤⣤⣍⣩⣭⡭⠖⣢⠄
⣷⣦⣈⠙⢿⣿⡄⠀⠀⢸⢻⢀⣾⠘⣇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡄⠀⠈⠉⠙⠃⠀⠀⠀⠀⠉⠉⠉⠉⣁⡴⢟⡥⢃
⠀⠉⠻⢷⣄⠙⣿⡄⢠⣤⣾⠋⠙⣷⣿⠦⣀⡏⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠁⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠴⢞⣛⡭⠖⣫⡴⠋
⠀⠀⠀⠀⠙⣧⠘⣿⡌⢿⣿⣷⡀⠈⣿⠐⠏⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠃⠁⠀⠀⠀⠉⠉⠩⠭⠭⢷⣖⣒⣫⣭⠵⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠋⠀⠀⠀⠀⢠⠔⠢⣄⣲⣶⣤⣀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠉⠉⠈⠑⢿⡌⠳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢰⠻⣼⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢠⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡤⠦⣼⠀⠉⠀⠀⢠⠞⠁⠈⢳⠀⠀⠀⠀⢠⠤⢤⠱⠏⣽⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣼⢠⠶⡌⠀⠀⠀⠀⡏⠀⢰⣯⣿⠀⠀⠀⢰⠃⢀⣀⡇⢸⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡈⢦⡇⠀⠀⠀⠀⠉⡉⠛⠛⠃⠀⠀⠀⠸⠤⣼⣾⠃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⢦⠁⠀⠀⠀⠀⢰⢻⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡀⠀⢀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⢸⡸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡞⡇⠀⠀⠀⣤⠶⠶⣖⣲⣄⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣇⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠔⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠺⡅⠀⠸⡌⠉⠙⠒⠒⠒⠒⠒⢲⠻⣅⠀⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠒⠦⣀⠱⡄⠀⠱⡄⠀⠀⠀⠀⠀⠀⢸⠀⢸⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠳⡝⢆⠀⠘⠦⣀⠀⠀⠀⢀⠞⠀⢸⠃⢧⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠑⢦⣀⠈⠙⠒⠚⠁⢀⡠⠋⠀⠘⡆⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣈⣉⣓⣒⣒⣋⣉⣀⣀⣀⣀⣇⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣠⡀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢳
⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠁⢉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⡆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢈⣿⣿⣿⠧⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⡿⢰⣿⡆
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣾⣿⣿⡿⣧⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⡏⣸⡏⠀⠀⣽⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡟⠉⠿⠀⠀⢠⣿⣷⠈⠙⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇⠀⠀⢿⣇⠀⠀⣄⡆⢹⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣽⡀⠀⠸⠀⠀⠀⢸⣿⣷⡀⠉⠁⢸⣿⣿⣇⠀⠹⡿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡀⠀⠀⢸⡏⣿⣷⠀⠀⢸⣿⣿⣿⡖⠈⢿⠿⣿⣿⣿⣿⡇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠇⠀⠀⠸⣷⢿⡏⠀⠀⢸⣿⢿⡏⠛⣠⣦⠀⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠆⠀⠀⣠⣿⣿⠆⠀⠀⠘⠀⠈⠃⢠⣿⣷⣾⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡆⢰⡀⠀⣿⣿⣿⣧⡀⠀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⡀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⠂⠂⢏⠁⢸⠀⣿⠀⠈⠀⠁⠰⠂⣠⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠈⢧⡀⢧⣰⣼⣤⣼⣤⣿⣤⣧⣾⣤⣢⣾⣁⣨⠟⠀⡰⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢄⠢⣘⢦⣌⠲⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣟⣁⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢦⣀⠠⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣔⡪
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠲⣭⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠻⠿⣿⣿⠻⣿⣧⣤⠔⣀
⠀⠀⠀⠀⢀⣀⠀⠉⠲⢦⣤⣬⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⣿⣿⠀⠈⠛⢿⣿⣅⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⢿⣿⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⢌⠋⡉⢀⣿⡏⠀⠀⠀⠈⣿⣿⣿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣦⡙⢿⣿⣇⠀⠀⠀⠀⠀⠈⢿⣷⣤⣴⣿⣿⣿⣿⣿⣿⠟⢧⠠⡀⣠⣾⡟⠀⠀⠀⠀⣠⣿⣿⡿⢁⠉⢉⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⣛⣿⣦⡙⠻⢦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣹⣿⢠⢨⠘⢠⣼⣿⣿⡿⠋⠀⠀⣀⡤⢾⣿⠿⠛⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠩⢛⣷⣤⣉⠓⠦⣤⣀⡀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣾⠿⢟⣋⡤⠔⣒⣿⢵⡚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢀⠔⠛⣻⣶⣦⣌⣉⣙⠒⠒⠒⠀⠀⠀⢀⣐⣂⣬⣵⠶⡞⠻⡏⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⠉⠀⡼⠋⢹⠋⠹⠏⠙⠋⢻⠟⠉⢻⠁⠈⠏⠇⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡑⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠀⠀⠀⠀⠀⠀⢰⡟⣴⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⣀⣀⣀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⡇⢀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣼⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⡇
⢴⣂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢟⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠘⣿⣧⡀⠠⡀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⡤⠀⠀⠀⠈⡨⠄⣉⠀⠀⢠⡶⠂⠀⠀⠀⠀⠉⠙⠂⠀⠘⠿⣿⣷⣷⠧⠼⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢳⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⠀⠀⠙⠦⡽⢂⡀⠈⣿⣹⡗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⠀⠀⠀⠀⠀⡠⢀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠙⡄⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⠀⠀⡴⣡⣿⣿⣌⢦⠀⠀⠀⢀⡤⠶⢖⠗⠀⣠⠃⠀⠀⠀⢀⣉⣤⣾⣿⣿⣿⠳⡀⠱⢌⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣽⣒⠋⠉⠑⠢⠤⠠⠘⠁⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⢒⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠎⠀⠀⠀⠀⠀⠀⠈⠘⠿⠻⠿⢿⣿⢿⡟⠰⡀⣈⠖⠋⢀⡞⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣠⠄⣀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⠁⡄⠐⠋⠀⠀⠀⡄⠉⠉⠛⠛⠋⠉⠋
⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡐⠀⠀⠉⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡰⠃⠀⠚⠃⠀⠀⠀⣶⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣀⠀⣸⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠞⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⢈⡽⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡄⠀⢇⠀⢀⡤⠖⠒⠦⢄⡤⠄⠛⠚⠒⠘⠁⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⣀⡤⠖⠀⠀⢲⡀⣀⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣭⣥⣤⣤⣤⣤⣼⣷⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣔⣤⣀⡀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠐⠋⠙⠿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠔⣻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣶⣶⣦⣤⣶⣷⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣰⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣿⡟⡇⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠀⡠⠁⠀⠉⠀⠈⠀⠈⠁⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠄⠀⠀⠐⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣤⣶⣿⣷⣿⣿⣿⣶⣶⣾⣿⣷⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢀⣠⡴⠖⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⢠⠿⠋⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠹⣶⠞⠛⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠙⣧⠀⣴⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢙⡿⠖⢀⢎⡤⠤⢼⣀⣶⠀⠀⠀⠀⠀⢸⢶⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠴⠀⠀⠀⢀⡠⠞⠉⠀⠀⢰⠏⠀⠀⢀⣹⡆⠀⠀⠀⠀⣠⠟⠈⠃⠴⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣿⠀⠀⠀⠘⣻⡟⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠘⠷⠤⠴⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠐⠒⠋⠀⣷⣄⠀⠀⠀⠀⢀⣠⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣧⣿⡀⠀⠀⣠⠴⠲⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⠀⣠⠖⠋⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⣿⢁⣴⡶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣈⣀⣀⡤⢾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣼⠀⢈⠉⠓⠒⡶⠶⠶⠶⠛⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⠀⠀⠀⢳⡀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⣤⣤⣤⡼⠇⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣀⣀⣿⠋⢧⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡿⠶⠦⠉⠁⠘⣦⣤⣤⡤⠴⠖⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠒⠲⣮⣤⠞⠁⡼⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠺⢧⣀⠀⠀⠀⠠⠤⠾⡵⠷⠒⢀⣠⢟⣶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣈⣿⡓⠛⣛⣓⣶⠶⣶⣾⠷⣖⣚⣉⣓⣋⣽⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠭⠭⠭⠔⠒⠋⠁⠈⠉⠒⠒⠫⠍⠓⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠉⠒⠉⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠉⠉⠉⠉⣀⡴⠀⠀⠀⢦⣄⡀⠳⣄⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡠⢂⣠⡴⠶⠟⠋⠀⠀⠀⠀⠀⠙⠿⣷⣮⣕⣦⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠃⠐⠙⡋⠐⠉⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⢤⣉⠉⠛⠓⠐⡆⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢀⠂⠀⢠⠦⡇⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡤⠀⡤⠤⡀⠀⢳
⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢏⠁⠉⠿⠟⠁⠀⠀⠀⠀⠀⠈⠁⠈⠹⠿⢣⠀⢀⠀⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠀⢣⠀⢀⠀⠈⠒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠋⠀⢘⠀⠀⠰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠳⠨⡄⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⢀⠐⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢣⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠃⠀⠀⠀⢀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠚⠓⠒⠚⠛⠂⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠣⢀⠄⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠤⣈⠢
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⣀⡠⠖⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⠎⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠦⢄⣀⠀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⣤⠤⠶⠂⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⠁⠒⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡇⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠈⠑⠢⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢄⠀⠀⡃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⡠⠞⡠⠐⠋⠂⣤⡀⠀⠈⠡⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡒⠂⠜⢡⠎⠀⣤⣼⣼⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠌⢀⣷⣾⣿⣿⡿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⢿⣶⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡀⠘⠏⠁⢀⠀⢀⢀⣀⠸⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠈⠀⠀⠂⠉⠠⠀⠉⣩⠄⠋⠀⠀⠀⠀⡠⠀⢄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠅⣁⣀⡠⠀⠐⠪⢥⠄⠀⠀⢂⡉⠠⠄⠧⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠺⠤⠗⠀⠀⠐⣶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠄⢀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⡀⠠⠒⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠢⡀⡄⠀⡁⢡⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⠃⣷⠑⢦⠼⡏⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠂⠀⢆⠀⠘⠀⢸⠀⠀⠀⡀⠆⢀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠁⣇⡡⢀⠀⠠⡢⡤⠀⣧⠖⠋⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣠⠀⠀⡖⠘⡀⠀⠘⣷⣊⣁⠈⠀⠤⠠⢴⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠊⠀⡠⠑⢤⢔⡃⠉⠉⠢⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⢡⠈⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠊
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠐⠲⣤⣀⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠃⠙⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠄⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⠛⣦⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠖⣋⣁⣤⠾⠃
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠛⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠠⠤⠬⠭⠭⠶⠶⠶⠤⠄⢸⡿⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⡠⠴⠶⠶⠶⠖⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⣼⡇⠀⠈⠉⠒⠲⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⣤
⠀⠀⠀⣀⣀⣤⡤⠀⠀⠀⠀⠀⣼⠟⢉⠛⠦⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠉⠾⠿⡛⠓⠀⠀⠀⠀⠀⠀⣘⡛⠛⠷⠶⢦⡀
⠲⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠻⠦⠀⠀⣀⠠⠶⠛⠁⠀⠀⠀⠀⠀⠀⣤⣰⡇⠀⣰⠖⢠⡞⠋⢁⡀⠀⠀⠀⠻⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠋⠀⠀⠉⠁⠿⢠⡾⠋⡁⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⠋⠀⠀⠀⠀⠀⠀⣴⠇⠉⣿⣉⡵⠁⠀⣠⣶⣶⣦⣄⠀⠹⣄⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠈⠁⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⢰⡟⠓⢤⣄⣀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣼⢿⣦⣄⠀⠀⠀⠀⠀⢸⠿⠿⢿⡿⠁⠀⠀⠀⣀⣴⠟⠁⢸⡇⠀⠀⠈⠉⠙⠛⢛⣓⣴⡿⠋
⠀⠀⠀⠀⢀⡴⢚⣽⠟⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⣿⠻⠿⣶⣄⣀⠀⠈⠀⠔⠋⣀⣠⣤⠶⠟⠛⠁⠀⠀⠈⠃⠀⢀⣀⣠⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠘⠷⠋⠁⠀⠀⠸⣇⠀⠀⠃⠀⠀⠀⣰⠏⢀⣿⡇⠀⠀⠀⠀⠉⠉⠒⠒⠂⠈⠉⠀⠀⣠⣴⣦⣠⣤⣤⡴⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢀⣠⠾⠋⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣌⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡤⠀⠀⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⡴⠀⣷⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠉⠃⠈⠉⠛⠛⢿⡁⠀⠴⢶⣶⠶⠶⠶⠶⠿⠛⠋⠁⠀⠀⠀⢠⡿⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣀⡀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣼⠇
⠀⠀⠀⢠⡾⠛⠙⠷⠚⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠉⠛⠶⢦⣄⡀⠀⠀⠀⣸⡟⠀⣀⣴⠟⢣⡄
⠀⠀⠀⢿⡇⠀⠀⣠⡶⠟⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣶⣄⠀⠀⠀⠈⠛⠷⠆⢠⣿⡷⠞⠋⠀⠀⠀⠻⣆
⠀⠀⠀⠘⣧⠀⢸⣿⠀⠀⠀⠻⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠲⣤⡀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠘⢷⡈⢿⣇⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡘⠋⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠹⣦⣨⡻⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣮⠙⢿⣦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠙⢷⣄⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣬⣙⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣄⣈⣀⣀⣀⣠⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠙⠛⠶⢦⣤⣀⣀⠀⠀⠀⣀⣴⣿⠃⠀⠀⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⢿⣿⣿⣿⠿⠿⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⣿⡟⠀⢀⣾⣿⣿⣏⠀⠀⠀⠀⠈⠙⣿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⢰⣿⠀⠀⢸⣿⣿⣿⣿⣶⣤⣴⡷⠀⠀⣿⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⢸⣿⡀⠀⠘⣿⡉⢻⣿⣿⣿⣿⠃⠀⢀⣿⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⠛⠻⠿⠟⠋⠁⠀⢀⣾⠏⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄⢠⣶⠿⠿⠿⠿⣷⣦⣀⡀⠀⠀⠀⢀⣀⣴⣿⡿⠶⠶⣶⣄⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣧⡄⢀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⢀⣠⣼⣿⢿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⣿⣧⠰⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⡟⠛⢿⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢻⣧⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠈⠹⡷⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣬⣛⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠃⠀⠀⠀⠀⣀⡀⠀⣄⣀⠀⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡞⠀⠉⠙⠛⠋⠑⢽⡗⢤⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣀⠀⡞⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢠⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡏⠈⣿⠁⠀⠀⢀⠴⠚⢳⡄⠀⠀⠀⢀⡀⠘⣿⢧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠻⠀⠀⠀⡏⠀⠀⢿⡇⠀⠀⣰⢋⢽⡆⡇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠻⡕⢶⠀⠀⠀⠀⠉⢹⡟⠚⠁⠀⠀⣇⡈⢺⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠞⠁⠀⠀⠀⢀⣀⡈⠻⡄⠀⠀⠀⣶⠈⠁⠀⠀⠀⠀⢸⡯⣁⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⡏⠀⠀⠀⢀⡜⠁⠀⠈⢳⡹⣄⠀⠀⠀⣶⣤⡶⣾⣲⣤⣠⡀⢛⡞
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢫⠳⣧⣀⡈⠀⠀⠀⠀⠀⣙⡷⢫⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⣇⠀⠀⠀⡼⠀⠀⠀⠀⠀⡇⠀⢳⣞⠒⠛⣩⠟⠛⡿⢏⠁⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⢠⠏⠈⠦⡀⠘⠧⣤⠤⢤⡤⣤⠟⠀⠈⠉⠉⠉⠁⢀⣼⣁⡼⠐⠿
⠀⠀⠀⠀⠀⠀⠀⢘⡄⢸⠀⠀⠀⠈⠲⣄⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠔⠋⠀⢸
⠀⠀⠀⠀⠀⠀⡴⠉⠙⢾⡄⠀⠀⠀⠀⠈⢻⡀⠀⠀⠸⡄⠀⠀⠀⣰⡻⡄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠹⡖⠛⠉⠀⢳⠳⡀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢹⢀⣀⣀⠈⠀⠀⠀⠀⠀⠀⡼⣷⣄⠀⠀⠈⠉⠓⢦⡼⠀⠹⣄⠀⠀⠈⠛⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠓⠤⣄⣀⣠⠴⠊⠀⠀⠉⠓⠤⠤⣤⣤⠴⠃⠀⠀⠈⠳⣼⡷⣄⣄⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣀⡒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡀⠀⠀⣀⣤⣶⣶⣬⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣝⣯⣌⣉⣛⣿⡿⠿⠛⠋⠙⠛⠻⠻⠯⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢟⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⠇⠀⠀⠀⠉⠳⠦⠀⠀⠀⣀⣤⠖⠂⠀⠀⠈⢻⡿⢚⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡎⠻⠄⢀⡠⠶⠒⠒⠢⠀⠀⠀⠈⠴⠛⠛⠳⠀⠀⠘⢳⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠐⠠⠟⠸⠆⠲⢀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠎⣠⣔⠒⠐⣦⣄⠈⠂⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⣿⠿⣿⣿⣟⢿⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠈⠈⠁⠂⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⡠⠔⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⡍⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠘⢦⠀⠀⠀⠀⠀⣰⠏⠀⢰⣤⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⣿⣿⣿⣧⠀⠀⠀⠑⢄⠀⢀⠜⠁⠀⢀⣾⣿⣿⣿⣶⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⣾⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⠟⠁⠛⠋⠋⠇⠃⠈⠉⠉⠙⠛⠛⠻⠛⠻⠟⠀⠀⠀⠀⠇

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⢶⢶⣤⠖⢦⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⣇⠀⠁⠀⠈⠀⠀⠀⡸⠛⠛⠓⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡴⠊⠉⠉⠉⠑⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢧⢠⠞⠉⠛⠀⢀⡜⢡⠋⢉⠦⣄⠀⠀⠀⠀⠀⠀⣠⢤⡴⢤⣀⡀⣇⣠⠖⠲⡄⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⢀⡠⠋⡠⠊⢀⠎⠀⡜⠋⠀⠀⠀⠀⠛⣇⠀⡇⠀⡇⠹⡌⠁⠀⢀⡇⢸⠁
⠀⠀⠀⠀⠀⠀⡜⠀⣸⣃⠏⠀⠊⠀⠔⠋⢀⠞⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⡄⠀⠀⠹⡞⢉⠿⡄⢸
⠀⠀⠀⠀⢀⣀⡇⢸⠁⢹⠀⠀⠀⠀⠀⣰⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⢱⡎⢴⢃⡞⠲⣄
⠀⠀⣤⠚⠉⠉⠹⣄⢓⣼⠀⠀⠀⠀⢰⠇⡀⠂⠀⢀⠀⠀⢀⠅⠀⠴⠀⡣⠀⠀⠀⠀⠀⡇⢸⡏⠀⠀⠈⢳⡀
⠀⢸⠁⠀⠀⠀⠤⡹⢺⠁⠀⠀⠀⢀⡾⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡧⣼⡗⠂⠀⠀⠀⡇
⠀⢹⠀⠀⠀⢀⣴⠃⢸⠀⠀⣠⠖⢻⡇⠠⢢⠀⠀⠀⠐⠂⠀⠂⠀⠀⠘⡷⣀⠀⠀⠀⢺⠃⠀⠙⢆⠀⠀⢀⡇
⠀⠸⡄⠀⠀⠀⠀⠀⠸⣄⡴⠃⠀⣼⡀⠈⣈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠷⡈⠳⣄⣠⠋⠀⠀⠀⠀⠀⠀⡞
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠻⡀⠀⣰⠃⠉⠉⠉⠉⠓⠒⠤⠤⠤⠒⠚⠉⠀⠀⢙⣤⡼⠃⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠳⣄⡀⠀⠀⠀⣀⡽⠶⣇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠙⠓⠦⣤⣀⣀⣀⣠⡞⠁
⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⣨⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⡯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠀⢳⠈⣟⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⣸⠀⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠉⠓⠒⠒⠒⠒⠚⠋⠉⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⠓⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠈⢓⡶⠤⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⡠⠴⠚⠉⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⢌⠊⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡘⡀⠀⠀⡆⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠁⠀⠀⠇⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⢀⠄⠀⠌⠀⠀⣁⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠅⠐⠀⠀⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠐⢄⠐⠂⠐⠀⠀⠀⠀⠀⡐⠀⢀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠠⠀⠀⢀⠤⠀⠆⡀⠀⠀⠖⠀⠀⢂⠲⠤⠀⠀⠀⡠⠊⠀⢠⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡀⠈⢆⠀⠀⠀⠀⠇⠀⠐⠈⠉⠀⠢⡈⡄⠀⢀⠔⠈⠀⢀⠄⠆⠐⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⡁⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠊⠀⠀⠑⠂⠠⠀⣀⡘⠤⠂⠀⠐⠒⠁⠐⠊⠀⠀⢀⠆⠌⡠⠊⠀⠀⢀⠀⠀⠐⡈⠅⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠂⠀⠀⠐⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣁⠀⠉⠐⠂⠀⢀⠀⠀⢀⠄⡀⠀⠀⠀⠀⢀⠄⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠠⢊⠔⡡⢂⠔⡠⠁⠈⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠈⠄⠡⢊⡔⡁⠀⠂⢀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢊⠄⡰⠉⠀⠈⠉⠑⠄⡁⡀⠱⡀⠢⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢊⡇⠀⠀⠀⠀⢀⠀⠀⠐⠀⠱⡀⠐⠈⠀⠀⠀⠀⠀⣀⠀⢀⡠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠡⡇⠀⠀⠊⠔⠡⡠⡂⢀⠀⠀⠈⡀⠀⠀⠀⢀⡀⠅⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠹⠀⠀⠐⠀⠠⡬⣀⣁⣁⣀⠴⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠀⠀⠊⢀⠙⢎⠀⠉⠢⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠀⠄⠈⢧⠂⠀⠈⠒⢄⡀⠀⠐⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠈⢆⠔⡑⠠⢀⠈⠐⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠂⠒⠒⠘⢅⠀⠊⠔⠀⡡⠊⢀⠄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣈⠈⠀⠔⡡⢂⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠄⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠠⡄⠀⠀⠀⠀⠈⠢⣄⠀⠑⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⢉⣤⠰⡤⠤⠤⠤⠤⠤⢼⣀⡓⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢠⠀⠀⢀⣤⠒⠉⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣠⠴⠄⠳⣴⠉⠀⡂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⡠⢄⡀⠀⠙⢦⡀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡔⠋⠀⠀⠀⠑⢀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠱⠀⢆⡠⠋⠲⡄⠀⢙⡤⠚⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢢⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠀⠀⠀⣁⠁⢀⡀⡰⠚⠁⠀⠘⠷⢾⠉⠑⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⢂⠀⢀⡌⠀⠀⠀⠀⠀⠺⣦⡀⠲⣄⠀⠀⠀⣀⡤⠀⠀⣈⡼⠇⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠤⠄⣭⠀⠁⠀⠏⠀⠀⠀⡸⠙⢦⣌⠳⠤⠞⠁⣠⠴⠚⠉⢡⠀⡀⠀⢀⡠⠄⣄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠎⠀⠀⡁⠀⡶⠠⡀⠠⠋⠀⡇⠀⣠⣌⡓⢤⠴⠋⢁⣀⠀⠀⡼⢇⡀⠀⠎⠀⠰⡃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⡆⠀⠡⣀⠌⠁⠀⠀⠸⣼⣿⣏⣹⡾⢀⣾⣿⠉⣷⡰⠁⠀⠓⠀⠀⠀⡔⠀⢀⡶⠤⠧⣀⠴⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠙⠿⣿⡿⠛⠁⠀⠀⠀⠒⠤⠴⠁⠀⠘⠓⢲⣤⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣌⣁⢿⡀⠀⠀⠀⠀⠤⡐⢶⠀⣹⡟⠈⠉⣶⠂⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⢷⡀⠀⡔⠀⢠⠁⣀⡛⠁⠰⣄⡰⠉⣄⡔⢫⡈⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢅⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⢳⡀⠉⠚⢦⣷⣁⡇⠀⡰⢎⠁⡀⣈⡤⠈⢣⡔⢹⡈⠷⣄⠀⠀⢀⣴⣴⠏⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣦⡀⠀⠀⠉⠉⠛⠳⢼⢏⣭⡇⢘⣤⠚⠃⢀⡛⣤⣈⣧⠀⢈⡷⢄⠑⠊⢁⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⢰⠈⠙⢦⣄⠀⠀⠀⠀⢸⠸⠀⠈⠉⠉⠉⠉⠉⠉⠀⢀⣠⠜⠋⠀⣈⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠸⠀⠀⠀⠈⠛⢶⣤⣄⣘⢸⡀⠀⠀⠀⣀⣀⣠⡴⠖⠋⠁⠀⠀⠐⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠒⠀⠁⢄⠀⠉⠌⠋⠉⠉⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⡀⠃⠀⢸⠘⡀⢀⠀⠀⠀⢀⡠⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠂⠜⠀⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠤⣀⡇⠀⠀⠀⣀⠀⢀⠀⢠⠀⠀⠀⡀⠀⠀⠀⢀⡞⢀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⢈⡉⠠⠄⢦⠄⠀⠀⠀⠀⢠⣤⣄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢈⡁⠀⢸⠀⠠⠆⡂⠀⠀⠀⠀⢸⡄⡟⢻⡇⣠
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⠠⠤⢀⠀⠀⠀⠋⠀⣠⣴⡁⢸⠀⠀⠀⠃⠀⠀⠀⠀⣠⢄⠀⢈⠰⠀⠀⠀⡀
⠀⠀⠄⠀⠀⡉⢀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢠⣈⠿⢻⠏⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⡇⠀⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⡀⠉⠀⠈⠻⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠠⢤⠆⠀⡀
⠀⠑⠒⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠃⡠⠛⠒⠶⡶⠚⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⢂⣦⡒⠲⡇⠀⡜⠁⠀⠀⠀⠀⠀⠢⠀⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⡙⢠⣿⣿⣿⢰⠁⢰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⢄⡀⠀⠀⠸⡅⠸⢿⣿⢳⡎⢠⠃⠉⠠⠀⠀⠀⠀⠀⠀⣀⠤⠤⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠡⠀⠀⡈⢸⡀⢳⠀⠱⡖⠀⠀⣰⠏⢀⠂⡀⠰⠀⠄⢄⠀⠐⠚⠉⠀⠀⠰⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⡀⢁⠀⠃⢸⠃⡄⠀⠀⠷⠄⠴⠁⣠⠋⠌⢀⡾⠁⢠⠂⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡁⠳⠀⠰⠀⠏⢠⠀⠀⠐⠊⠩⠄⠚⢁⡘⠤⠯⣀⡴⠋⡠⠂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡆⢀⠀⢀⢀⠀⠀⠄⠀⠀⠀⠀⠈⠰⠞⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠰⠛⠀⡐⠀⠀⠉⠄⠘⠓⠂⠀⠀⢀⠂⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠢⣀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣪⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⠊⠀⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠍⠑⠒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠐⠠⡑⢄⠀⠀⠀⢀⣄⠀⠀⡄⠀⠁⠂⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠠⠔⠁⢘⠀⢠⡙⠢⡀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⢸⠀⠀⢠⡀
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣰⡰⠀⠀⠀⠙⢄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⣀⡀⢀⣀⡄⠀⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⢻⣆⣀⣀⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠶⠀⠀⠹⠧⠀⠀⠀⠀⢠⣴⠶⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠈⠻⠷⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⣠⡾⠁⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣤⣀
⠀⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⢰⡇⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠰⣦⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡀⠀⠀⠀⠈⠻⣦⡄
⢀⣴⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠛⠀⠀⠀⠀⠋⠘⢷⡄⠀⠀⠀⠀⠀⠈⠷⠀⣿
⠚⠉⠀⠀⠀⠀⢘⡧⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣀
⠀⢀⡄⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿
⠀⣼⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠰⠶⠶⣶⣶⠄⢀⡾⢁⡾⢁⡤⢰⣶⡶⠶⠷⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣿
⠀⠛⠀⠀⣠⡄⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠛⠀⠛⠀⠟⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⠻⠇
⠀⠀⢿⣆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢰⣷⠀⢀⣾⡆⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡏
⠀⣠⡾⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡀⣸⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣷⡄
⠀⣿⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⢠⡾⣏⣸⡏⣿⠀⣿⢷⠀⢀⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⡿
⠀⠹⣧⡀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠋⠀⠙⢷⣄⠀⠉⠋⠐⣇⠀⣿⠀⣰⡟⠃⠀⢹⣇⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⠃
⠀⠀⠙⠳⣦⣿⡀⠀⠀⠀⠀⢠⡿⠀⣀⣤⣌⡙⢷⣤⣄⣀⣙⣻⣥⠾⣋⣤⣤⣀⠘⣿⡀⠀⠀⠀⠀⢸⣿⣴⠟⠁
⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⣴⡟⢡⡾⠋⠉⠉⠙⢷⡄⠉⠙⠋⠉⣰⡿⠋⠉⠉⠻⣷⡘⢷⡄⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⢿⣤⣾⣇⠀⠀⠀⠀⠈⣿⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣼⣷⣼⡿⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⡾⠋⠀⠙⠻⢶⣤⣤⣴⣿⣤⣤⣤⣼⣿⣤⣤⣴⡶⠟⠉⠀⠙⢷⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⣀⣉⣁⣀⣈⣿⡁⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠛⠛⠉⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣤⡴⠿⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠋⠉⠉⠁⠉⠉⠉⠙⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠛⠿⢷⣤⣀
⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⠀⠀⠀⢿⣇⠀⢀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⣈⣿⣷⡀⠀⢸⣿⢰⣇⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣁⣹⣿⡿⠁⠀⠀⣿⠘⢧⣤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣤⣀⣀⣀⣀⣠⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠛⠛⠻⢿⣷⣦⣄⣀⣀⣤⣶⡿⠛⠉⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠋⠉⠉⠙⠿⣿⣶⣤⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣸⠻⢧⠸⣆⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⠿⠙⠄⣿⢠⣿⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣴⣾⣷⣿⠿⠿⠯⡿⠉⣿⠀⣄⢠⣼⣾⣿⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡿⢼⠛⠘⢻⡄⣿⡄⣿⣿⡇
⠔⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡌⠀⢻⣼⡀⢹⡇⢽⣿⣇
⠀⠀⣼⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⠁⠀⡾⣧⠁⣼⣧⣿⣿⣿⠄
⠀⣸⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠴⣠⣿⠀⢠⣿⠉⢠⣿⡇⣸⣿⣿
⠀⠙⠋⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣿⣷⠀⢰⡇⢰⡏⠸⢃⣿⣿⣿
⠀⢠⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⡏⠀⠈⢠⡟⠁⡄⢸⣿⣿⡏
⠀⢸⡇⠀⠀⠀⢤⣀⠄⠀⠀⠀⣀⡤⠄⣠⣾⣿⣿⠿⠀⡗⠀⢀⣿⡆⢀⠀⣼⣿⣿⡇
⠀⢸⡇⠀⢠⠀⣰⣄⣀⣀⣀⣀⣤⣴⣾⣿⡿⠛⠉⣀⡴⣿⠀⡞⣹⢀⠚⣴⢁⣿⣿⠇
⠀⣿⠀⠀⠎⡀⢻⣿⣿⣿⣻⣿⡿⡿⠻⠟⠀⠀⡰⢟⣵⣿⡎⠀⠃⢎⣶⠋⣸⢻⣿⠁
⠀⡿⠀⠀⠀⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⣴⣿⣿⣿⣧⠂⣸⠜⡁⣴⢣⣿⣿⣇
⠀⠃⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣯⣾⠏⢀⣱⠂⢜⣿⣿⣿
⠀⠀⠀⠄⠀⣿⣿⣇⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⢠⣾⢣⣴⣾⢻⣿⣿⡄
⠀⠀⠀⠀⢠⣿⠏⣿⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠚⠀⢐⡼⣿⣿⣿⣿⠃
⣤⣴⣶⣶⣼⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⡿⢱⣿⢻⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⡟⠡⣼⣯⢛⣯⣿
⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⠟⢁⣼⡿⠃⣸⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠇⡠⡞⠉⣡⣾⣿⣿⣧⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠁⠀⣠⡼⣿⣿⡿⢱⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⢾⣷⠴⠞⣁⣴⣿⡫⣴⡿⣠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣶⣾⣧⡤⠾⢟⠿⠁⢎⣠⣿⡻⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢹⡇⠀⡠⢂⠄⣰⣿⣿⣯⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢲⣿⡧⢴⣷⣯⣞⣹⣿⣿⡿⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠛⡻⢛⡽⢫⣿⡟⣧⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣿⠉⢉⣉⡁⠘⠉⢂⣁⣴⡿⣿⢻⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿⣿⠀⠈⠍⣛⣟⣻⣿⣿⠯⠞⣡⢣⣽⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⠃⣿⣿⠄⣹⠣⢍⣽⡟⡙⢡⣄⡤⣠⣿⣿⠁
⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⡟⣿⡿⣻⡟⠀⣿⣿⣷⠱⣦⣤⣥⡼⢨⣠⠞⣳⣿⣿⣏
⣿⣿⣿⣿⡿⢫⣴⣿⡿⢿⣿⠏⣿⠋⠀⠀⡿⣿⣿⣷⣾⣿⣶⣤⣤⣡⣴⣿⣿⣿⣿
⣿⡿⣿⣧⣼⣿⣿⡟⣄⡼⠃⢸⡿⠐⠆⠀⢣⢹⣿⣿⣿⣿⣷⡿⠵⠿⢿⣿⠋⣹⣿
⣿⡗⣿⣿⠿⢏⢡⣷⡟⠇⠀⣾⠇⠈⢄⠀⠙⢿⣯⣻⣿⣿⣿⣷⣮⣀⠞⠀⢘⣿⣿⡄
⣿⡾⣿⠇⣰⣼⣿⡍⠀⡼⢶⣯⠀⠀⠀⠀⠀⠀⢿⣏⠛⠿⣿⣿⢿⣿⣷⣤⣾⡯⡿⠷
⣟⡷⣿⣶⣿⡛⣯⢿⠘⠃⠈⠀⠀⠀⣀⣀⣀⣀⡌⢿⣦⡀⠀⠉⠓⢾⣿⣿⣿⣿⣿⣧⣄
⢿⣿⣿⣿⠅⣫⣴⣿⣿⣿⠶⣿⠿⠿⠟⠛⠻⠛⠛⠁⠙⣷⠞⠳⢶⣄⠈⠉⠛⢿⠿⣯⣻⣷⣦⣄⡀
⡘⣿⢛⣷⡿⠏⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡜⠂⢌⡙⠲⢦⣀⡀⠘⠻⣿⣟⣻⠟⠷⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣉⣤⣹⣇⣠⣏⣉⣷⣉⣼⣞⣩⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⠉⢩⣒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⠴⠻⠔⠋⠀⠀⣀⠬⠥⢬⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣠⠔⠹⠖⠁⢀⡀⠀⢀⡔⠋⠀⠀⠀⠀⢱⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⢖⠉⠀⠀⠀⠀⡠⢋⣀⡀⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⢠⠏⠀⠉⣳⣼⡇⠀⠀⠀⢀⠎⣠⠤⣄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢷⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⠘⡄⠀⠀⣻⣧⣀⣀⣀⠴⠋⠸⠁⢀⡸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣓⣄⣀⢱⠀⠀⠀⠀⠈⠉⠉⠋⠀⠀⠀⠀⠒⠀⠀⠒⠉⢠⠇⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠙⢶⢦⡀
⠀⠀⠀⠀⠀⠀⠰⡓⡔⡹⠂⠀⡔⠉⠤⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣒⣲⣒⠖⠒⠲⠤⠴⠃⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢳⢳⡀
⠀⠀⠀⠀⠀⠘⠉⠁⡀⠀⢤⢠⣿⡦⠄⢤⡤⠄⠲⢄⠀⠀⠀⣰⠋⣉⣙⣂⢠⣤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡇⠲⣄⣤⣀⢀⠄⢠⠄⡇⡇
⠀⠀⠒⣠⡀⠀⠐⠦⠜⠀⠀⠘⣿⠤⠠⠀⠀⠀⠀⠀⠉⠒⠤⢝⣋⣉⣁⠤⡴⠿⠀⠀⡀⡘⠈⢀⣛⡒⣲⠀⠀⠀⡇⠶⢁⠖⣿⣿⣿⡇⠀⡇⡇
⠀⠘⣃⠤⠄⠀⠀⠀⠀⢰⡮⣁⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠤⠤⣀⣀⣿⠋⠉⠉⠉⠑⣄⡜⠀⠈⠁⠀⠀⠀⣇⠠⠈⠙⠛⠸⠉⠈⢁⣇⡇
⠀⠀⢴⣺⣽⠶⢚⢋⠟⡏⠀⠀⠉⢀⡤⠄⠀⢹⣀⣀⣠⠔⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⣜⡼
⠀⠀⡿⠋⠣⠘⠙⢼⡀⠙⠒⢒⡶⢁⣠⡴⣿⠻⡟⢿⠻⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⣀⣤⡾⠛
⠀⠀⠘⠦⣤⡤⠜⠋⠈⠒⠋⡸⢿⠛⡅⠱⡈⢆⠹⡈⢣⠈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠳⠸⠦⠗⠘⠒⠛⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠀⠉⠡⠞⠧⠤⠦⠤⠒⠲⠶⠄⠒⠶⠒⠶⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠐⠒⠂⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⠤⠤⢀⡀
⠀⠀⠀⡠⠚⠁⣀⣀⠠⣄⡀⢤⡀⠀⠉⢀⠀⠀⠀⠀⢠⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠐⡅⠒⠡⠀⠀⠀⠀⠠⠀⠉⡀⠀⠀⡆⠀⠀⠔⢁⡔⠁⠑⠤⢄⡀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢠⠁⠀⢀⢀⠤⠀⢀⡤⢄⠀⠀⠀⠈⠆
⠀⠀⣠⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢨⠀⠈⠀⢀⡀⠀⠀⠉⢒⡤⢄⠀⠀⠀⠀⠡⠀⠘⠀⡌⠐⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠈⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡼⠀⡄⠀⠘⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠘⡀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡁⡀⠀⡀
⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⢠⠁⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠀⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠃⡰⠁
⠀⠀⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢘⠀⢧⡀⠀⠀⠀⠁⠀⠀⠀⢀⡸⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠑⡂⢶⣰⠴⡆⡰⠒⠣⡀⠀⠀⠀⠈⢀⠀⢉⡱⠶⢤⠤⠴⣚⡺⠉⠙⢄⠀⠀⠰⠀⠀⠈⠢⣀⠀⠀⢀⡀⣤⠔⠒⠥⢀
⠀⠀⠀⠀⢠⠊⠀⠈⠀⠀⠈⠁⠀⠀⠈⡆⠀⠀⠀⠀⢈⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⠀⠀⠀⠀⠜⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆

⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠤⠤⣀⠀⠀⠀⠀⠀⠀⢀⠒⠊⠉⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⠔⠈⠔⠚⠀⠁⠀⠀⠀⠉⠢⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠈⠒⢄⠠⠀⠤⢄
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣇⠎⠈⠀⠀⠀⠀⣀⠀⠁⡄⠀⠀⠈⠀⠀⠀⠠⢊⠄⡠⠔⠊⠐⠢⢄⠀⠀⠀⢻⠆⠀⠈⠂
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠈⠋⠁⠀⠀⠀⠉⠁⠀⠱⠀⠀⠀⡄⠀⠀⣞⡡⠊⠐⠀⠀⠐⠂⠈⠣⠀⠀⠀⢃
⠀⢠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢘⠀⠀⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠓⠒⡀⠀⠃⠀⠀⡟⠀⠀⠠⠀⠀⠠⠀⠀⠀⠧⢀⠀⢸⠀⠀⠆
⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠎⠀⠀⠇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠉⠀⡸⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⡘⠀⡌
⠀⠀⢆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⡴⠁⠀⠀⠀⢨⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⢠⠓⠀⠃
⠀⠀⠀⠑⠦⠄⣀⡀⠀⠀⣀⠠⣔⠊⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⡀⠔⠋⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠁
⠀⠀⠀⠀⡠⠖⠻⠘⠓⠛⢂⠔⠀⠉⠢⠄⠀⠀⠀⠀⠀⢀⣨⠞⠋⠈⠀⠀⠈⢲⠦⢀⠀⠀⠀⠀⠀⠀⢈⠵⠒⡦⠠⠶⠹⠅⠒⠄⡀
⠀⠀⢀⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢠⠃⡄⠑⠰⠆⠂⠀⠒⠁⠠⠀⢣⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠀⠀⠀⠀⠀⣀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⢺⡐⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⡇
⢶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⣀⡀⠀⠀⠀⠀⠀⠀⢉⣑⠒⠘⡟⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠔⠀⠀⠀⣠⣢⠄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠁⢀⠨⡊⠑⠀⠠⣇⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⠂⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠉⠡⡂⠀⡅⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠮⠔⠃⠀⠀⠀⠀⡰⠁⠈⠌⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⠀⠀⠀⠐⣋⡴⠃⠀⠱⡀⠢⣀⠀⠀⠀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡄⠀⠈⠀⢐⠐⠊⠁⠠⠀⠄⠈⠀⡀⠔⠀⠀⠀⠀⠀⠀⢠⠹⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠇⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠈⡄⠀⠀⠀⠀⢠⢰⠀⠀⣎⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠇⠀⠀⠣⠤⠋⣀⠜⠀⠀⠀⠀⡴⡫⠃⠀⡼⠈
⣎⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠤⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡰⠀⠠⠆⠀⠀⢀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⣐⠧⠞⠁⠀⠀⠀⠀⠀⢸⡀⠀⢀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠩⠞⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⢸⣄⣀⣀⠨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠑⠤⠚⠁⠀⠉⠓⠉⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡤⠀⠀⢄⠀⣸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣭⣥⣤⣤⣤⣼⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⣿⣿⡟⣿⣃⡵⢆⢋⠹⣿⢿⠿⢟⣽⢄⠉⢻⢗⣹⠋⠇⠀⠀⣻⠙⢦⠄⣄⠀⡀⠇⣰⣿⢦⣼⡇⠓⠃⣠⠀⡸⣾⣏⠙⠚⠒⢋⣙⢻
⢿⣿⣝⣟⣾⢗⠎⠯⠀⠀⠀⠀⠎⠑⠃⠀⠀⠘⠋⣠⣤⢠⡄⡹⢷⠇⢂⡀⠀⢀⣰⣥⣼⣼⣿⣶⡞⡐⢩⣄⣿⣿⣿⣴⣀⣠⡆⣾⢿
⠀⠀⠉⠹⠏⣈⣌⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠠⠸⠋⠛⠛⠃⣄⠀⢈⣡⡜⠀⠙⣾⣿⣿⣿⣿⣿⣿⡞⡿⣸⣶⣿⣿⣭⣽⣗⣻⣍
⠀⠀⢀⠸⠷⢻⣿⠄⠀⡀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠐⣿⣿⣿⣿⡿⣿⣿⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⡡⢾⣷⣟⡻⡾⠁⠁⠠⠄⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢙⣡⣀⠀⠀⠙⢿⣻⣿⣿⣿⣿⣿⣟⣫⢻
⠀⠀⠀⠈⠓⠀⠁⠜⠘⢂⠀⣴⣿⡶⠁⣠⣴⡟⣿⣾⣧⡄⠀⢠⠀⠀⢠⣶⣦⣾⣿⣾⣿⣿⣿⣿⣷⠆⠀⠞⠻⠿⠛⢙⢻⣿⣽⣷⣾
⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠙⠋⠑⢃⢙⣿⡤⢉⠙⡖⣋⡈⠀⢀⠀⠠⠈⠹⠿⢿⢿⣿⡿⣿⣿⣟⠀⠀⠀⠀⢰⡁⠀⢈⣿⣷⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣆⣀⡀⠚⠺⠄⠈⢉⠁⠘⢉⠂⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠡⣤⣸⣿⣿⣿⣿
⣀⠀⠀⣀⠀⠈⡱⠠⠀⡀⠀⣧⣭⣟⠀⠀⠿⣧⡄⠁⡄⣀⠼⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣿⣿⣿⣿⣿
⡘⠿⠀⠈⠂⠀⠀⠀⠀⠀⠱⠲⢿⠛⣧⢻⣕⣽⣅⢄⣶⣬⢱⡄⡠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠙⢿⣾⢿⠛
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢰⡁⢸⢞⠁⣶⠻⠟⠻⡇⣦⢿⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⡧⡀⠀⣀⡸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢈⡻⠃⠈⠰⡄⢀⡔⠙⠺⠓⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄⡀⠀⢀
⣥⡀⠀⠀⠆⠀⠀⠀⠀⠆⠠⠲⠈⠀⠀⢀⢇⡂⠘⠚⡙⠌⡧⡄⡀⠀⡀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠈
⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠐⡁⠀⠀⡧⡜⠒⣽⣽⠚⠀⠀⣠⠈⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⣿⠺⣤⣈⠀⠒⠀⡀⠁⠀⠀⠈⠀⠀⣰⡗⠁⢠⡄⠒⠰⢿⠛⠈⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛
⡟⠐⠻⣇⣻⣖⡄⡴⠈⣠⠄⠀⡀⣀⢙⣿⠆⠠⡀⡆⠑⠾⠂⠀⠀⠀⠀⠀⠀⠁
⣇⢶⡂⠛⢇⢹⣴⣆⠠⡌⣙⠁⠃⠹⠃⠀⠘⠿⠿⣵⣀⠂⠀⠀⠀⠀⠀⠀⢐⠐⠄⠘⠂⠀⠀⠀⠀⠀⠀⠐
⠶⢢⣽⣩⣷⣀⣠⡰⣦⣼⣫⡅⢠⣴⡀⠀⠄⠀⠀⠂⡸⠀⠀⠈⢠⠀⠀⢅⢤⣠⣀⡜⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠿⠛⠛⠛⠛⠛⠻⠶⢶⣤⣄⡀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⣿⠈⣿⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠿⠛⠁⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡾⡟⠀⠀⠀⠀⠀⣠⢿⡀⠀⠀⠀⠀⣸⢿⡄⠀⠀⠀⠀⢠⣟⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢀⡀⠀⠀⠀⢻⣆⠀⠀⠀⣀⡴⠋⠀⣧⡀⠀⠀⠀⣴⠋⠈⣧⡀⠀⠀⣰⠏⠀⢻⡄⠀⢀⣠⠟⠉⠛⣿⠃⣠⡤⣤⠀⠀⠀⠀⠀⠀⣼
⠀⠀⣿⣉⣿⡆⠀⠀⢹⡗⠒⠛⠉⠀⡀⠀⠈⠻⠦⠶⠟⠁⠀⠀⠈⠛⠒⠛⠁⠀⠀⠀⠙⠛⠛⠁⠀⠀⢸⡇⠀⠙⠓⠛⠀⢰⠆⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⣀⣈⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⣀⠀⠀⢸⠁⠐⣿⣳⡄⠀⣼⠖⠒⠒⢿⡀
⠀⠀⠠⣞⣿⠋⠀⢀⣼⠀⠀⠀⠀⠉⢉⣛⣛⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣟⡛⠛⠛⠉⠀⠀⢸⡇⠀⠈⠉⠀⣰⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠈⠀⠀⢠⡾⠁⠀⠀⠀⠀⣻⠋⠉⠉⢙⡆⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⢻⡍⠙⠛⢻⡶⠀⠀⠀⠻⣤⣤⣤⠞⠛⠛⢃⣠⣴⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡄⠀⠰⡏⠀⠀⠀⠘⣁⢀⣄⠈⠃⠀⠀⠀⣿⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⢰⡶⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠠⣟⠀⠀⠀⢳⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⢈⣷⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⢀⡼⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⢮⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠘⣧⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢼⠁⠀⠀⢀⣠⡾⠋
⣴⡶⠶⠶⠶⠶⠶⠶⣶⠶⠿⠿⠿⠿⠶⣦⣿⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣀⣠⣼⠶⠾⠿⣿⣍⡀
⠙⠻⠷⣦⣤⣤⡄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠷⠶⠶⠶⠶⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠻⣶⡀
⠀⠀⠀⠘⣿⣹⣤⣤⣴⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⣄⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⣷⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⠛⣧⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣸⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠃⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⢻⣿⣾⢟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣾⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠜⠋⠴⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡠⣧⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣾⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⡟⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⣛⣩⣭⣭⣭⣭⣿⣿⣿⣿⣯⣿⣿⣿⡟⢱⣿⣿⣿⣿⡿⢁⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⡿⠟⠋⢀⣸⣿⣿⣿⠏⢀⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣬⣤⣿⣶⣿⠟⠉⠀⠀⣦⠂⢹⣿⣿⡿⢀⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⣿⣿⣷⢏⣿⢟⣿⡟⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⣼⣯⣿⡟⠃⠠
⠀⠀⠀⠀⠀⠀⠠⠾⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣾⣿⣿⣴⢿⡿⠏⣀⣸⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣧⡀⠀⠀⣀⣿⠿⠓⣚⣉⣽⣶⣿⣿⣟⡷⠛⠀⠲⠊⣏⢀⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣴⣏⠀⢀⣾⡿⠛⠾⢷⣿⡟⠀⠀⠀⠀⠀⠴⠍⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠻⣷⣏⠻⠃⢀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⠉⠛⠂⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤
⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠠⠤
⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠛⠙⠛⠻⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⣠⠀⠀⠀⢨⡿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣤⣤⣶⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⣀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⢿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣆⠀⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣷⡀⣿⣿⠆⠘⠛⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⡀⠀⠀⢀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⠙⠛⢿⣿⣿⣿⣿⣿⣿⡃⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠈⢻⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠇

⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠀⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⠂⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⢀⢀
⠀⠀⠀⠠⠊⠁⣀⡀⡀⢄⣀⠀⡀⠀⠈⢀⠀⠀⠀⠀⢀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⡁⠐⠁⠀⠀⠀⠀⠠⠀⠈⡄⠀⠀⠇⠀⠀⡐⠁⡠⠁⠘⠠⠤⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠎⠀⢀⠀⡠⠀⣀⣤⠄⡀⠀⠀⠀⠁
⠀⠀⣠⠁⠀⠐⠂⠀⠀⠀⠐⠀⠀⢡⠀⠀⠰⠀⠀⠇⡀⠀⠀⡁⠀⠀⠈⠐⡂⢄⠀⠀⠀⠀⠰⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⡀⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢰⠀⠸⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⢈⡀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠃⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠘⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠆
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢸⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠊
⠀⠀⠀⠀⠈⠁⣒⢶⡀⠤⠆⠲⠒⠣⣀⠀⠀⠀⠀⠆⡀⢉⣉⠖⠤⠤⠴⢖⡩⠉⠑⠢⡀⠀⠀⠃⠀⠀⠑⣄⡀⠀⠀⣀⢤⡤⠒⠠⢄⡀
⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⠁⠀⠀⠈⢆⠀⠀⠀⠀⠈⡜⠡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠆⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠠⠤⢀⡀⠀⠀⠀⠀⠀⢠⠐⠊⠉⠁⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠔⠊⠐⠚⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡌⠀⠀⢀⠀⡀⠀⡀⢀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠑⠢⡀⠐⠒⠠⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢠⠈⠈⠀⠀⠀⠀⢀⡀⠉⠀⠀⠀⠀⠃⠀⠀⢀⠎⠄⢀⠄⠂⠁⠐⠤⡀⠀⠀⠘⠗⠀⠀⠐
⠀⠀⡌⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠉⠁⠀⠀⠀⠉⠉⠀⢰⠀⠀⠀⢠⠀⠀⣰⢃⠖⠑⠂⠀⠀⠒⠀⠀⡄⠀⠀⠈⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢰⠀⠈⠁⠀⠀⠀⠉⠀⠀⠐⠐⡂⠀⠘⠀⠀⢙⠁⠀⠀⠄⠀⠀⠄⠀⠀⠰⠀⡀⠀⡇⠀⡠
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠇⠀⠁
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠜⠐⠒
⠀⠀⠀⠑⠦⢄⣀⡀⠀⠀⢀⡠⢔⠊⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⡠⠒⠛⠈⠁⠋⠀⠔⠁⠈⠐⢄⠀⠀⠀⠀⠀⠀⣠⡔⠛⠀⠀⠀⠀⠐⠶⢄⡀⠀⠀⠀⠀⠀⠀⡩⠒⠶⠤⠔⠈⠍⠀⠢⡀
⠀⠀⠀⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢠⠊⠀⠐⠂⠀⠀⠀⠐⠊⠘⡀⠑⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣿⡷⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠀⠀⠀⠀⠀⠀⢰⣟⠋⠉⠉⠉⠉⠙⠛⠶⢤⡈⠉⠙⣳⡄⠀⠀⠀⠀⠀⠈⠙⢷⡄⠉⠙⠛⠶⠶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠷⣦⣄⡀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠶⠶⠶⠾⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠛⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡴⠶⠛⠉⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⡿⢦
⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣄⡀⠀⠀⠀⠀⠀⣼⠅⣠
⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⣀⣤⡶⠾⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠉⠛⣛⣷⣶⣶⠿⠞⠋
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠁⠒⠦⢬⡙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⣿⠻⣦⣀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢦⣤⣤⣬⣶⣤⠴⠿⠛⠛⠛⠛⠳⠶⠶⠶⠶⢶⣶⣶⠞⠛⠛⠋⠉
⣿⠀⠀⠙⠛⠶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠁⢸
⣿⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠛⠳⠶⠶⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠚⠋⠉
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⢀⣤⣴⠦⣴⣴⣦⣤⣤⣴⣶⣦⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣹⣾⣿⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⠿⠁⠀⠐⣠⣿⣿⣿⣿⣿⣿⣶⣤⣶⣦⣤⣀⣠
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⢠⣾⣿⣿⣿⡏⠀⠠⣿⣿⣿⣮⢹⣿⡽⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣤⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢸⣿⣿⣿⣿⡷⡶⠶⢿⣿⣿⣿⣼⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢼⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⡻⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡃⠀⢨⣿⣿⣿⠃⠿⣿⡿⣛⣛⣿⣏⣽⢿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣙⣶⠿⠟⠻⢗⣛⣉⣩⣾⣿⣿⣿⣇⠀⢸⣿⣟⢿⡻⡿⠿⣿⢿⡟⠋⠻⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣱⣎⠘⠁⠀⠀⡿⢸⡇⢀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢝⢙⣡⠄⠀⠀⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡀⡄⣿⣿⡆⠀⠀⠀⠘⠸⠇⠈⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡀⣠⣴⣿⡏⠁⠀⠁⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠰⠆⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⡃⠁⠀⠀⠀⠀⠰⣿⣿⣿⣇⣿⣿⠿⡏⠙⣡⣼⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠉⠁⠀⠀⠀⠀⣀⣰⣶⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⠻⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠈⠀⣹⣏⣿⣿⣿⣿⣿⣿⡏⣤⣤⣶⠂⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠋⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⣠⣾⣿⣿⢼⣿⣿⣛⣿⣿⣿⣿⡿⠉⣀⣀⣀⣽⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⠀⣸⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠁⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣠⣤⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠋⠉⠀⠀⠀⠈⠁⠉⠟⠻⠛⠟⠛⠛⠋






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡭⢽⡟⠛⠛⠛⠛⠛⢛⠻⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠈⠀⠠⡨⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢔⠅⠀⠀⠀⠠⢀⢔⣉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⠀⠀⠫⣎⣎⡴⠂⠈⠀⠠⢋⠥⠐⡀
⠀⠀⠀⠀⠀⠄⠀⠁⠀⢀⠠⠀⠀⠀⠒⢌⠉⠰⡃⠀⠀⠀⠁⠀⣀⠌⢑⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠠⠀⠂⠒⠠⡀⠢⡀⠀⠀⠀⠀⢀⠆⠀⠀⠉⠒⠤⣀⠈⠁⠀⠀⠢
⠀⠀⠀⠀⠀⢀⡞⠀⠀⡐⠁⠀⠀⠀⠀⠀⠈⢂⠀⢄⢀⣠⠴⠋⡄⠀⡘⢦⡀⠀⠀⠉⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣼⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠉⠡⡀⠀⠉⠀⢳⡀⠙⢦⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⢠⡏⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠱⠀⠉⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⢸⡇⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣰⠀⠀⠀⠀⢙⢳⣄⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠂⠉⠳⢤⣠⠞⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣤⣴⠀⠁
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠹⡄
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢠
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢹⣷⣤⣤⣤⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

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

⠀⠀⠀⢀⡴⣷⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⢀⡾⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⢀⣾⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡾⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⣿⡁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⣿⣅⣴⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⠀⠙⠋⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⢰⡿⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡆⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⡿
⢸⡇⢀⡞⠀⠀⣴⣿⡿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣠⡾⠁
⢸⣧⠞⠀⠀⠀⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠁⢀⣴⠋
⠀⠻⠿⠶⠶⠶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠒⠒⠒⠦⣴⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠐⢀⣀⣀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢳⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢴⣶⣦⣄⠀⠀⣠⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠁⠀⠀⠀⢠⠞⠀⠀⡞
⠀⠀⠀⠀⠀⠸⠟⠋⠀⢀⡏⠀⠀⠀⠀⠘⡖⠋⠉⠉⠉⠒⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⢶⡁⠀⢀⡜⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⣶⠋⠀⠺⠷⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⠀⠀⠀⠈⡅⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢧⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢡⠀⠀⠒⠶⠿⠾⣷⡄⠀⠀⠀⣀⣀⡀⠀⠀⠾⡿⢭⣤⣄⠀⠈⣧⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠤⣄⡀⠀⠀⢸⠀⠀⠀⢦⠀⢰⡀⠀⠀⣴⠋⠁⠈⠙⢦⠀⠀⢱⠀⠀⡇⠀⠀⠸⠚⠉⠉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢤⡙⢦⣀⠎⠀⠀⠀⢀⠅⠀⡇⠀⢰⠃⠀⠀⠀⠀⢸⡆⠀⢼⠀⠀⢸⠀⠀⠘⢴⠷⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⡁⠀⠀⠀⠀⠀⠀⡏⠀⣴⠁⠀⣾⠀⠀⢀⠀⠀⢸⠀⠀⠈⡆⠀⢣⡀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣃⠀⠀⠀⠀⠀⠀⣱⠀⠈⢦⠀⣿⡴⠋⢉⠟⠀⣾⠀⠀⢼⠁⠀⢸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠀⠀⠀⡖⠁⠀⡴⠋⠀⡟⠀⠰⡇⠀⠀⡇⠀⠀⠈⢢⠀⠈⢦⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣷⠀⢀⡷⠀⠀⣧⠤⠶⠛⠛⠛⢛⡇⠀⢠⡏⠀⠀⡎⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣇⡀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢳⣀⣤⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⠤⢤⣤⣤⠤⠴⠶⠖⠛⠋⠁

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠂⢰⣤⣾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠃⠀⠈⠀⠀⠀⠈⠘⠀⠠⠆⠀⠺⠖⠛⠃⠸⠦⠿⢼⣹⣿
⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢶⡀⠀⠀⠀⠀⢀⠂⠰⣄⠉⠈
⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠀⠀⠂⠀⠀⠑⢄⠁⣄⡺
⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⣁⣵
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠠⠀⠀⠀⠀⠀⠀⠟⠀⠀⢹⣯
⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠘⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢼
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠚⠀⠀⠀⠀⢀⡀⠀⢠⡀⠀⢰⠌⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠬⠀⢀⠏⠀⡀⢩⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢦⡀⠀⢲⣁⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣿⡄⢨⢡⣤
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⣿⠬⠉
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠠⡘⢣⡄
⡆⠢⡈⠚⠃⠀⠀⠀⠀⢠⠴⠆⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢋⠡⡦⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡆⠰⣦⠁⠀⠁
⠁⠛⠱⠆⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠠⠠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡱⠾⡄⠈
⠀⠠⠀⠀⠐⠱⢆⠀⠀⠀⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⣿⠁
⠀⠋⠀⢀⠀⠀⠉⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⡀⢐⣅⣆⠀⠀⠤⠀⢀⠀⠀⠀⢀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⣴
⢀⡀⠀⠀⠀⠀⠠⠀⢀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠚⠨⣀⡀⠀⠀⠐⠋⠿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠉⠀⢈⠀⠀⠀⠋⠀⢿
⠈⠀⠈⣅⡀⠀⠀⠀⠀⠂⠀⠈⣠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠔⣁⠒⣧⠀⣆⣤⡄⠀⢀⡀⠂⠀⠀⠀⠀⠀⡀⠀⣀⢠⣌⠀⠀⠀⡀⠀⣽

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

⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⢶⣤⣤⣀⡀
⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄
⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠁⠀⠀⠀⠀⠀⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⣿⡟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣿⡇
⣿⡇⠀⠉⠻⠷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣟⣋⣁⣀⣿⣇⣤⣤⣤⣤⣤⣀⣀⣀⣀
⣿⡇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⠷⠾⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢶
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠙⠷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠾⠿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⢠⠀⠄⠀⠀⠀⠘⠙⠛⠈⠀⠀⠀⠘⣺⣿⠇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠀⠐⢀⠐⠆⢗⡀⠁⠒⠀⠀⠠⠀⣀⠀⠀⠀⠐⠁⠈⠾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠄⢀⠤⠁⠀⠈⠉⢁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠨⠀⡇⠠⠀⠀⠀⠀⠀⠁⠁
⠄⠀⢈⡀⢀⠀⠀⠀⠀⠠⠀⠀⠐⠒⢨⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠤⠰⠆⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡀⠀⠁⠈⠀⠀⠀⠠⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡁⡀⣒⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠐⢁⢂
⠀⣀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠉⠛⣠⢂⠀⣄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉⠐⠖⢨⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠁⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⢨⣳⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⠀⠀⠀⠁⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠴⡀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠂⠀⠀⠀⠈⠘⠃⠀⠀⢌⠀⠄⠀⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⣦
⣦⣤⣤⣤⣤⣤⣤⣤⣴⣤⣦⣤⣤⣤⣤⣤⣤⣤⣮⣦⣤⣶⣦⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣿⣴⣴⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢦⠀⠀⠀⠀⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢱⣿⢹⣿⣿⣿⣿⣿⠟⠛⠛⠛⠿⠿⢿⣻⡽⠋⠛⠛⠛⠛⠛⠉⠉⠉⠉⠙⠳⢮⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡧⣿⣿⢾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠀⠒⠒⠶⠤⠤⣀⠀⠀⠀⠀⠉⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⢸⡇⠀⢀⡀⠤⣶⠶⠶⠞⠛⠉⠉⠉⠛⠻⠿⠿⣿⣿⣿⣿⠿⠋⢀⠀⣼⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⢸⠇⠀⠀⠀⠉⣻⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠊⣡⣾⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣦⣤⣤⣴⣤⣄⠀⠀⠀⠀⠀⢀⠾⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⡉⠀⠀⠀⠀⢠⡃⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠟⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⠃
⣟⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡵⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣦⣄
⣿⣿⣿⣿⣯⡙⠻⢿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⢀⣀⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣄
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⢋⣩⠥⣤⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⠞⠻⠿⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⣰⣿⣷⣮⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠏⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠁⢀⣴⠂⠀⠀⢠⣾⣿⠟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠴⠛⢹⠀⠀⢠⣋⠝⠁⠀⠀⢠⣮⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⢀⡞⠀⠀⡘⠁⠀⢦⡀⢀⢎⡏⠉⡹⠉⣹⡿⠛⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡰⠋⠀⠀⢰⠁⠀⠀⠀⠙⠚⠈⢡⣘⠤⡠⠋⢱⠀⠀⠀⠱⡄⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡳⠀⢶⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⣼⠐⣹⡀⠀⠀⠀⠘⡆⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢱⢄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡍⢳⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣎⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠀⠠⢄⠀⢴⡤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⡀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠠⠀⠀⠤⠴⠒⠉⠀⠀⠀⠠⢵⠢⣄⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⢀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠘⠇⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⠠⠘⠈⠣⣠⠚⠢⠀⠀⠀⠀⠀⢀⡾⠔⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⣴⠀⠀⠂⠀⠉⠂⢀⠗⠂⠤⡀⠀⣼⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⣇⠀⠀⠀⠀⠀⡊⠀⠀⠀⢈⠜⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⠀⠈⠓⠄⡀⠀⠀⠘⠄⠀⠐⠁⢀⠄⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠰⢮⣉⣉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠠⡀⠁⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠂⢌⠀⠤⠤⠀⠀⡞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⡡⠄⠀⠀⠀⠀⠀⢠⠁⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⢀⠴⠢⡌⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠓⠁⠀⢠⠷⡀⠀⠀⠀⠀⠀⠁⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⢀⠎⠀⠀⣰⠃⠀⠀⠀⣇
⠀⠀⠀⠰⠀⣠⠤⢤⡄⠰⣄⠀⢀⠌⠀⢀⡼⠁⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠚⠁⠉⠂⠀⠉⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠛⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⢿⣿⣿⣧⠀⢀⠞⣁⣠⠏
⠀⠀⠀⠀⠀⠀⣰⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠈⠋⠉
⠀⠀⠀⠀⠀⢠⣿⠇⣼⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠀⠘⣿⣷⠀⢠⣴⠛⠛⢳⡄
⠀⠀⠀⠀⠀⣼⣿⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⡆⠀⠈⠙⠓⠛
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢳⡀⠘⢛⠻⣆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⣤⡿⠀⠀⠀⠀⠀⢀⣀
⣠⣤⣤⣄⡀⠘⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢰⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣰⠏⠉⢻⡶⢶⣄
⠳⣤⠤⠞⠋⠀⠹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⢿⣾⡟⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢻⣶⠟⠛⢻⡏⠀⢠⠏⠀⢀⣿⣄
⠀⠀⠀⢀⡠⢤⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⡀⠀⠳⡖⢧⡀⣠⠊⠁⢉⡇
⠀⠀⣴⠁⣰⠇⠀⠀⠈⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⣿⠘⣧⡀⠀⠁⠀⠙⠀⣠⡶⠋
⠀⠀⠈⠛⠁⠀⠀⠀⠀⢰⠏⡤⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⡏⣠⠟⠁⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⢿⣿⡿⠆⠀⢀⣾⠟⠁⠀⠀⢠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠞⠉⠁⠀⠀⣠⣾⡁⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢾⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⡾⠋⠀⠻⣆⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⣴⣿⠀⠈⢷⡈⠙⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⢞⣻⠟⠀⠈⠲⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢘⣧⣀⣀⣀⣸⣇⠀⠀⢿⣤⣤⣤⡼⠿⣿⡛⠛⠛⠛⠻⠿⠿⠶⠛⠋⠁⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠠⡟⠁⠈⠉⠉⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠛⣶⠖⠒⠚⠛⠀⠀⢀⣤⣤⣤⣤⣤⡤⠶⠿⠖⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣤⠶⠞⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠛⠛⣯⠉⠉⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⣠⣴⠶⠛⠋⠉⠉⠀⠀⠀⠀⣿⡀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠟⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠉⠛⢶⡶⠶⠶⠶⢾⠋⠉⠀⠀⠀⣿⠀⠀⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠏⠛⢷⠶⠶⠶⠾⠿⠒⠶⠶⣿⠀⠀⠀⠀⠀⢸⠟⠛⠛⢻⣡⣏⢼⠟⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⡄⠠⠄⠤⠠⠤⠶⠶⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢀⣇⢹⠶⢦⣤⣤⣤⣤⡴⠟⠀⠀⠀⠀⠀⠀⠙⠶⠶⠖⠚⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡺⠼⣦⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣠⡿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣾⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠛⠛⠛⠛⠛⠛⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠶⣦⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⢰⣟⠻⠿⠇⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀
⠀⠀⠀⠀⣹⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⢀⠀⠀⢻⡄
⢠⡿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡾⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⣷⠀⢸⡄⠀⠈⣿
⣼⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⠁⠀⠀⣸⠀⠀⠀⣼⠀⠀⠀⡇⠀⠸⡟⡄⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢠⡞⠛⠦⡀⠀⠀⣸⠇⠀⠀⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⡇⠀⠀⢰⡇⠀⢰⠇⠸⡀⢸⣇⣀⡀
⣿⠀⠀⠀⠀⠀⠀⢹⢿⠉⠉⠀⣰⣿⠀⠀⠀⣰⡇⠀⠀⠀⡾⠀⠀⠀⡼⠀⠀⠀⣸⣇⣠⠞⠀⠀⠇⢼⡯⠤⠿
⢻⡄⠀⠀⠀⠀⠀⢈⠸⣄⣠⠾⠁⣿⣀⣀⡴⠙⣇⣀⣠⣾⠁⠀⢀⣴⡇⠀⠀⣰⠇⣀⣀⠀⠀⠀⣴⢾⡇⢀⣄⣄⡀
⠸⣧⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⠀⣨⣽⣷⠶⢦⡈⠉⠁⠈⠓⠚⠋⠀⠙⠒⢚⠵⢋⡽⣍⠙⡆⠀⢠⣼⠇⠈⠓⠶⠃
⠀⢻⡄⣾⠛⢛⠢⣄⡧⠀⠐⢂⣜⣡⠾⠟⠳⣤⡇⠀⠀⢀⣤⠤⣤⡀⠀⠀⠘⠲⣏⠉⠙⡞⠁⠀⠀⣿⡀
⠀⠈⣷⠘⠲⢬⣗⠀⠀⠀⠀⠀⠀⢙⠀⠀⢞⠀⠀⠀⣰⠋⣀⣀⡀⠙⣆⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⣾⠁
⠀⠀⣿⠀⠀⠀⠈⠳⢚⠇⠀⠀⠀⢿⠀⠀⡼⠀⠀⠀⡟⠉⢁⣤⠿⠀⢸⡄⠀⠀⡧⠀⠈⡇⠀⢀⣴⠏
⠀⢠⡿⠀⠀⠀⠀⠘⠛⠳⢤⣀⠀⢰⡀⠀⢸⠂⠀⢀⡀⠀⣀⢈⣦⣠⣤⠇⠀⢰⡁⠀⠘⣧⣴⣟⠁
⠀⢼⡇⢀⣾⠁⠀⢰⠀⠀⠀⡉⠛⠶⢦⣀⣸⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⢀⣥⡤⠞⡋⠀⢻⡄⣀⣴⠾⠷⠤⣤
⠀⠈⠛⠛⠛⠷⠶⠛⠻⠶⠞⠷⠶⢦⢶⣬⣭⣛⡷⠶⣄⠀⠐⠶⠶⣶⢶⡖⠛⣫⣡⠶⡼⠟⣶⡾⠟⠋⣠⡴⠾⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⠉⣳⢄⠈⠙⣦⣴⠚⠁⣀⡽⠛⠻⠶⠖⠚⠋⣁⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⣠⣤⡏⠈⠳⠞⠁⠈⠳⠚⠉⣇⣀⣀⣤⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡾⠋⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠛⠦⣄⠀⣼⠃⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣀⣀⣀⣀⣀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣹⠉⠉⠉⠉⠁⢹⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⡿⠀⠀⠀⠀⠀⠸⣇⣿⡄
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣾⣧⡀⢠⣤⣬⣻⣿⣿⣿⣿⣿⢿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⠐⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣷⠚⢿⠁⠈⠀⠀⠀⠐⠀⠀⠶⣾⡏⠙⠛⠂⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⣀⡲⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣈⡆⣦⣀⡠⠆⠀⠀⠀⠀⠀⠀⣖⢿⡟⣣⣌⣷⠄⠘⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣟⣍⣠⣿⣿⣿⣿⡷⣿⡿⢀⣤⠀⠀⡀⠀⠀⠀⠀⠀⠙⣿⠿⠋⠀⠀⠈
⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⡛⣟⠋⠀⠀⣀⣿⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⡾⠻⠋⣀⣶⣿⡟⠛⠻⣿⣷⠀⢸⡆⢀⡀⠈⠁
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠘⣻⣽⣿⣿⣿⣿⣿⣾⣿⣿⣟⠛⢳⣤⣄⣹⣿⣿⠁⠀⠀⠘⣿⡷⠀⠙⠏⠛⠠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣯⡄⠈⡻⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢯⡟⠛⠻⣿⡿⢸⣿⣿⡶⠂⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⣻⣿⣿⡈⠺⠓⠚⠉⠀⠞⠛⠏⠁⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡟⠻⣿⣿⣿⣿⡟⠁⣀⠀⠀⠀⣴⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⡿⢿⣿⣦⣚⠁⡀⢸⣿⣿⡅⢠⣾⡯⠐⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⢿⠻⠛⠿⠗⠀⠉⠻⡿⠿⠁⢾⣿⣿⣷⢹⣙⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡿⡿⢿⣌⠻⢷⣄
⣽⣿⣿⣿⣿⣿⣽⣿⡿⠂⠀⡘⠁⠀⠀⣤⣦⣤⣴⣆⠀⠀⠹⢤⣶⡟⠛⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠶⢿⣛⣻⢟⢦
⠀⠀⠀⠀⠀⠀⣠⡤⠶⠤⣤⡀⠀⢀⣴⣻⣟⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⣿⣏⣧
⠀⠀⠀⠀⢠⠞⢁⣴⣶⣶⣦⡙⢧⣼⣿⣿⣿⡎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿
⠀⠀⠀⠀⣿⠀⣿⡏⣠⠖⠛⢿⣾⣿⣿⣟⣝⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃
⠀⠀⠀⠀⢻⣠⣿⣿⣿⣦⣤⡀⠉⠉⠉⠉⣿⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣿⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣿⣿⡞⣿⡟⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠴⠶⠶⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣦⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢷⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣶⣶⣶⣼⣿⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡈⠙⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⢀⣠⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⣦⣀
⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢿⣆
⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠘⣿⡄
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢰⡇⠀⠀⠀⢸⡆⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⢸⣧
⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡅⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⣸⠇⠀⠀⣿⢷⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠙⣦⡄⠀⠀⢠⡿⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡏⠀⠀⠀⠀⣿⠀⠀⢀⡿⠈⣧⠀⠀⣿⠄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⠉⠉⠁⠀⣠⣿⡇⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣾⠁⠀⠀⠀⢰⡇⠀⠀⣸⠃⠀⢹⠄⠀⣿⡶⠶⣤⡀
⢻⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⢿⡀⢀⣠⠾⠁⣿⡅⠀⠀⣠⡾⢻⡅⠀⠀⠀⣰⠏⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡾⢧⣤⡶⠋⠀⠀⢸⠆⠸⣷⠶⠶⠾⠃
⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠛⠁⠀⠀⠘⠷⠶⠾⠋⠀⠘⢷⣤⡴⠞⢣⡀⠀⠀⣠⡾⣿⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢈⣤⢴⣿⠀⠀⣀⡀
⠀⣿⡆⢀⣤⠦⣴⣆⠀⠈⣧⠀⠀⠀⠀⠀⢀⣠⠶⣶⣝⡛⠶⣆⠀⠀⠀⠀⠈⠛⠓⠛⠉⠀⠘⠷⠶⠞⣫⡶⢛⣉⣉⠙⢶⡀⠀⠘⠁⢸⡏⠀⢾⣍⣉
⠀⢹⣧⠘⣇⠀⢠⣌⠳⢦⡾⠂⠀⠀⠒⢠⣟⠀⣾⡿⠾⢷⣄⣸⡆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠾⣁⣠⡿⠦⣿⣆⣬⠇⠀⠀⢿⡿⠁⠀⠀⠈⠉
⠀⠀⣿⡆⠈⠳⣤⣾⡃⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⣠⠟⠉⠀⠀⠀⣰⠖⠋⠉⠉⠻⣦⡀⠀⠀⠀⠉⢹⡄⠀⠀⣼⠁⠀⠀⠀⢸⣷
⠀⠀⣿⡇⠀⠀⠀⠈⠹⣦⣠⣴⠆⠀⠀⠀⠀⡴⠂⠀⠈⢣⡀⠀⠀⠀⣼⣁⣠⣤⣤⣤⡀⠈⢷⡀⠀⠀⠀⣼⠁⠀⠀⣿⠀⠀⠀⠀⢸⡿
⠀⢠⣿⠁⠀⠀⣠⣴⠲⣿⢁⣯⡀⠀⠀⠀⠈⠳⡄⠀⠠⡞⠀⠀⠀⢰⠟⠉⠀⣀⣠⡼⠟⠀⠸⡇⠀⠀⠀⢷⡀⠀⠀⢿⡀⠀⠀⢀⣿⠃⣀⡀
⢀⣿⠇⠀⠀⣴⣏⠹⠆⣹⠟⢻⠿⣦⣀⠀⠀⢼⠃⠀⠀⣹⠆⠀⠀⠹⠀⠀⠀⠉⠹⣆⠀⠀⠀⣿⠀⠀⢀⡞⠁⠀⢠⡞⠀⢀⣴⡿⣡⡞⠉⣷⣤⡀
⢸⣿⡀⣀⣄⠻⣎⠀⠀⠀⣀⣶⣄⠀⠙⠳⢦⣼⡁⠀⠀⢧⠀⠀⠀⠘⠀⠋⠙⠦⠔⠛⠻⠛⠛⠃⠀⠀⠘⣆⠀⠀⢀⣵⠶⣿⣯⡞⠹⡇⠘⠋⣼⡃
⠀⠙⠛⠛⠛⢷⣾⣷⡴⠞⠉⠀⠙⢦⡀⢀⡀⠉⠙⠻⣶⣮⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡴⠾⠛⠁⣀⣼⣿⡀⠀⠀⠀⠘⣩⡟
⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠙⢿⣧⣀⣰⡆⢀⣈⣽⠟⠻⣦⡀⠀⠀⠰⠶⠶⣶⢶⣶⠾⠛⠛⢉⣥⣀⣤⠾⠟⠋⠀⠈⠻⣦⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠳⣤⡀⠙⠷⣤⣠⠴⠞⠁⠀⢙⡷⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⡾⠋⠹⣦⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣄⣀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⢀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⡀⠀⠀⣠⣶⣄⠀⠀⢀⣀⣠⣤⣤⠦⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠛⠛⠛⠋⢸⡏⠛⠛⠋⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⠀⠀⣸⠃⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣋⡉⠉⠛⢛⣿⠛⠛⠛⠛⠛⢷⣦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣶⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣦⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⠀⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣰⣫⡤⠋
⠀⠀⠀⠀⠀⢸⣿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢿⣿⣿⡄⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⣿⣿⡀⠀⠙⠲⠤⠞
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠂⠘⣿⣇⡀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠘⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⠄⠀⣋⣿⣿⣿⣿⣀
⣎⣉⣱⠆⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⠟⠻⣦⢤⣄
⠀⠀⠀⡀⣄⠈⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⠷⡟⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢹⣿⠉⠙⡏⢀⡜⠁⢀⠿⣄
⠀⠰⣏⡠⠃⢀⣬⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣁⣀⡀⠀⠀⠀⠈⣿⣷⠀⠈⠏⠣⡔⠁⣀⡾
⠀⠀⠀⠀⢀⣿⣿⣿⣿⢛⣉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⢠⡟⣻⠇⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠸⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡿⢿⣿⡷⠀⠀⣼⠟⠁⠀⢀⡞⠉⠁
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠖⠉⠀⠀⣠⡾⣅⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠋⢻⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠉⢀⣈⡷⠋
⠀⠀⠀⠀⠀⠀⠰⣏⠀⠉⠙⡆⠀⢳⣄⣈⣙⣷⣶⡦⠤⠴⢶⣶⣾⡯⠷⠛⠁⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢻⠉⠀⠀⠉⠉⠀⠀⠘⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠉⡿⠊⠉⢉⣀⣀⡴⠶⠶⠶⠶⠖⠛⠛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣀⣤⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣥⣀⠀⠀⠀⣀⣀⣤⠴⠚⢻⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⠦⣤⣀⣀⣉⣿⠛⠋⢹⡇⠀⠀⠀⢸⣧⣤⣤⡟⡴⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⠀⢸⠅⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⡇⣀⠀⣉⣁⠽⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡄⢰⣙⠶⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠘⠷⠶⠖⠒⠒⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠓⢳⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⠞⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠘⣿⣇
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⣀⣀⡀⢹⣿
⢸⣿⣇⣀⣀⣠⣤⣤⣤⣶⣶⣾⡿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿
⣾⣿⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡉⠛⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⣁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣬⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣤⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⣶⡆⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⡀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠻⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⣰⣿⠏⣰⣶⠀⠀⠀⠀⠀⠀⠀⢠⣶⡈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣰⣿⠋⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠈⢿⣷⡀⠀⠀⠀⢀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣿⣿⠃⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠈⢿⣷⣤⣴⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⣼⣿⠃⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⢻⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣼⣿⠃⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢻⣷⣤⣾⣿⣦
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣼⣿⠃⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⢻⣿⡿⠿⠏
⠀⠀⠀⠀⠀⢾⣿⣿⡇⢸⣿⣃⣀⣠⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣄⣀⣀⣻⣿⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠈⠙⠋⢁⣼⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣿⡟⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⣰⣾⣷⣦⠀⠀⣿⣿⣿⡷⠀⢠⣾⣷⣦⠀⠀⢀⣶⣿⣶⡀⠀⠻⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠻⣿⣿⠟⠀⠀⠈⠛⠋⠁⠀⠘⠿⠿⠏⠀⠀⠘⢿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢠⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⣿⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠘⢿⣿⣦⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠟⠋⠀⠀⣤⠀⠀⠈⠻⣿⣷⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠈⢿⣿⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣿⣦⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠛⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠉⠛⠻⠶⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣟⣛⣷⣞⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣻⡿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⢛⣿⡴⠛⠉⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠘⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠙⢛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠘⡷⠋⠉⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠘⣻⠷⠂⣠⣂⡤⠤⢼⡀⢰⠄⠀⠀⠀⠀⠀⢹⢶⡟⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠄⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⣵⠏⠀⠀⠀⡘⣆⠀⠀⠀⠀⠀⣠⡟⠀⠃⣠⠞⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠿⣿⢦⣤⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣬⡧⠀⠀⠀⢿⣄⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⣉⠠⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⡆⠀⠀⠀⠀⢀⣀⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⡄⠀⠀⠀⣀⡴⠞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠣⣄⣀⣠⠞⠉⡉⣉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠞⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⠎⠜⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣀⣀⡀⠤⠚⡷⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡀⠉⠛⠒⡒⠶⠶⠚⠛⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⣇⣀⣀⣀⡨⠧⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢐⣏⣉⡉⠓⠀⠹⡀⠀⠀⢀⣀⣀⣤⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣄⣀⣠⠄⠀⣠⠟⢻⢏⡏⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠁⠀⠀⠙⠛⠛⠁⢠⠏⣼⢁⡀⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⣍⣛⣶⣤⣀⣀⠀⠈⠙⢛⡟⠉⣉⣠⣴⣞⣵⢿⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⠤⢽⣮⣭⣥⣬⠭⠟⣋⡿⠿⣟⡻⠭⣤⣤⣭⡤⠿⣚⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠚⠉⠁⠀⠀⠈⠉⠉⠒⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠘⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢦⡄⠀⢄⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠉⠀⢸⢦⣀⣀⣤⠖⠁⠀⢀⣀⡀⠀⠀⣀⠀⠄⠤⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⢯⣀⣀⠈⠉⢉⠠⠂⣏⠔⠚⠈⠑⢦⠑⡄
⠀⠐⠒⠒⢀⣴⣃⡀⢀⣴⠞⠩⠥⢒⢈⡠⠒⠉⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠘⠉⠁⠀⢹⡾⢸⠄⠁⠉⠈⠀⠀⠀⠀⠀⢀⣀⣠⣤⣼⣥⣧⣤⣤⣀⣀
⠀⠀⣠⠞⠀⣴⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠀⠀⠀⠀⠀⠈⠉⢹⡇
⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣮⣍⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡆⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠚⠉⠉⠉⠙⠲⣄⠀⠀⣠⠤⠒⠒⠦⢄⡀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⢠⠋⠀⠀⠀⣦⣿⡆⠀⠈⢳⠞⢧⣿⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣄⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠤⠤⠤⠶⠚⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠄⢤⡀⢠⡄⠀⠤⠤⠈⠛⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⠤⣄⢀⣀⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣸⠀⠀⠀⣀⠤⠀⢤⠀⠙⡤⠸⠦⣄⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢿⣀⣤⣮⣬⣤⣤⣼⣤⣤⣤⣤⠤⠦⠤⠦⠤⠤⠷⣤⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣤⣤⣤⣤⣤⣤⡴⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⢀⣀⠀⠀⠂⠀⠀⠀⢀⠀⢀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⢀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡅⠈⢐⠀⠀⠀⠀⠀⠰⠄⠁⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠋⠀⠈⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠁⠀⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡿⠂⠀⠀⠀⠤⣤⡐⠂⠒⢒⣇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠈⠑⠊⠀⠀⠀⠖⠀⠾⠉⢶⣀⡕⠿⠁⠋⠀⠀⠀⠀⠀⠀⠈⠄⠀⠠⠂⠣
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠄⠠⠠⠀⠊⠀⠀⠒⣰⣷⡶⢀⣦⡆⠀⠀⠀⠀⠀⠰⠇⠁⠀⠐
⠖⠂⠂⠀⠀⠀⠀⠴⠆⠀⠀⠀⡀⠠⠉⠐⣚⠁⠀⠃⠀⠓⠀⠀⠀⠀⠀⠀⠍⡁⠀⣀⠱⠀⠀⠈⠁⠀⠀⠀⡀⠄
⠀⠀⠠⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢌⡟⠻⡍⡅⠔⠁⠀⠀⠈⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠖⡂⠀⠐⠤⢽⣃⠪⠂⠀⠐⠠⠀⠄⠈⠀⠈⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠎⠸⣃⠠⠠⠶⣜⠲⡗⠁⠐⠀⠈⠁⠀⡆⠀⠀⠀⠀⣠⡒⠀⠆⠀⠀⠠⠐⠦⠉
⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⠀⠁⣃⡤⣀⠀⠲⢀⡈⠀⢤⠈⠀⢀⢠⠀⠀⠀⠀⠐⡰⠈⠔⢿⢄⡠⡑⠂⠁⠄⠆⠀⠐⠦⡀
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠘⠉⠀⠀⠀⠀⠀⢠⣄⣀⡈⠀⠀⠠⠀⠑⠀⠀⠰⣦⣤⡈⠑⠀⠐⠀⣰⡉⠉⠉
⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⣀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠴⢀⠀⢰⢃⠀⠀⠐⠠⠀⠄⠀⠀⠀⠀⠈⠉⠀⠁⠄⠀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡀⢄⠠⣄⣀⣀⣀⠀⠀⠀⠀⡠⠖⠁⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⣀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠢⡼⠁⢀⠤⠤⣄⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣀⠀⠈⢳⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃⠀⠀⢸⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⠉⠉⠙⢦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⡞⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡤⡶⠁⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡜⠁⢠⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢀⣤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠢⡆⠀⠀⠀⠀⠀⣧⡞⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣇⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢸⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⢦⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⠀⣀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡍⠑⠒⠤⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⠉⠉⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⢦⠖⠉⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠈⠒⠶⣤⠤⣌⣧⠀⠀⣠⠖⠋⣁⣀⣀⣀⣀⡈⢧⠀⢀⡤⠒⠛⠉⠛⠲⢤⡀⠀⢰⠷⠒⠒⠒⠒⠚⣁⡀
⠀⢀⣠⡤⣤⣀⠀⢀⡞⠁⠀⠀⠙⠀⡜⠁⠈⠉⠉⠀⠀⣠⠬⠽⣿⡇⣾⠶⢯⣉⠉⠉⠓⠒⠙⢦⠀⠀⠀⠀⠀⠈⠙⢯⡉⠙⠲
⡞⠁⢀⡴⠋⠀⢀⠎⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋⢰⠃⡇⠙⠲⢬⣀⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠑⢤⠴
⠙⠒⠋⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠒⠚⠉⠁⠀⠀⡰⠋⠀⠹⣄⠀⠀⠀⠉⠙⠒⠒⢀⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⢀⡞⢹
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠈⠙⠒⠒⠚⠉⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⣦⣀⡀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⢀⣀⣤⢾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣷⣯⣽⣟⣶⠶⢦⣤⣤⣤⣤⣤⠶⣶⣛⣯⣿⣾⣿⣿⣿⡿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⠾⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠸⣿⡀
⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⣀⡀⣻⣇
⢸⣿⣀⣀⣠⣤⣤⣤⣶⣶⡶⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿
⣿⡟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣠⣤⣶⡾⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠷⣶⣦⣤⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠈⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⢠⣶⠀⠀⠀⢰⡆⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣾⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠉⠁⣾⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣿⡀⠠⣿⣁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡏⠀⢿⣧⣤⣽⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣇⠀⣼⡏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠔⠒⠒⠈⠉⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣒⡚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⣼⠋⠠⡌⢳⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⣿⠀⠈⠁⣸⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⡞⠉⠛⠵⣶⡼⣀⣀⠀⠀⠀⠀⡜⣁⣤⣶⠿⢧⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⣿⠀⠀⠳⣄⠀⠀⠀⠉⠑⠒⠭⢵⣒⠮⠝⠋⠉⠀⠀⠈⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢻⡀⢠⣤⢸⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⠳⠤⠴⠋⠀⠀⠀⠀⢫⠉⠙⠒⠒⠒⠛⢅⣀⣀⣠⠞⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⣀⣠⡴⠟⠊⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⣠⡴⠞⠛⠉⠉⠉⠛⠳⢦⣄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⣦⡄⠀⠀⠀⢸⡇⠀⡠⠲⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣿⣿⠀⠀⠀⢸⡇⠀⣿⢐⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠁⠀⠀⠀⣾⠃⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⢠⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⡄
⠀⠈⣧⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠉⠻⣦⣄⣀⠀⠀⠀⣀⣠⣴⠟⠁⠀⠀⣼⠁
⠀⠀⠈⠳⣄⠀⠈⠛⠶⢦⣤⣄⣀⣠⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⡟⠛⠉⠉⢹⠉⠙⠛⢻⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠈⢉⣻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠛⠓⠲⠷⠶⠶⠶⠾⠶⠶⠶⠚⠛⠛⠉⠁⠀⢰⡏⠉⠛
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠛⠳⣤⡴⠚⠓⢦⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣀⣾⠤⠤⣤⠲⠶⠶⠶⢦⠤⠤⢷⣄⣀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⣿⠁⠀⠀⠀⣠⠞⢹⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠉⠳⣄⠀⠀⠀⠈⢿⣆
⠀⠀⠀⣿⣤⣤⣤⣤⣾⣦⣼⣧⣤⣤⣤⣿⣤⡤⡶⠶⠾⠶⠶⠶⠶⠿⠶⠶⠟⠛⠛⠛⠛⠛⠛⣻⡆
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡏
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠴⠄⠀⠈⠉⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⣴⠛⠋⠀⠈⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠈⠁⠒⢤⡀⠀⠀⠀⠀⠀⣠⣤⡝⠁⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠘⠛⠁⠙⠛⢦⣄⡀⠀⠙⠆⢀⣠⠞⠛⠀⠈⢹⠄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠁⢀⣤⣤⠀⢀⡀⠀⠈⠉⠲⣄⠀⡟⠁⠀⠀⠀⠀⠘⢀⣄⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡤⠚⠉⠀⠀⠘⠣⢾⣆⢀⡀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠉⠠⠤⠤⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⢀⣀⠀⠀⠀⠀⠙⢧⡕⠂⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠔⢻⡇⠀⠀⠀⠂⠀⠙⡄⠀⠀⠀⠀⠐⠛⢢⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣴⣷⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣄⠶⠶⠆⢴⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⡴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠰⣟⣠⠿⢆⠰⠦⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠾⢿⡏⠀⠈⡇⠀⠀⠈⠛⣥⣶⡆⠀⠀⠀⠀⡄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⢸⡆⠀⠀⠀⠀⠈⠠⠆⠀⠀⠀⣧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸⠷⠶⠶⠶⠶⠟⠳⠶⠒⠶⠿⣅⡀⠀⢻⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢿⡀⠀⠙⣦⡤⠐⠠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢹⣿⡴⠟⠁⠀⠀⣿⣄⠀⠀⠀⠉⠳⣆
⠀⠀⢀⣤⣤⣤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠀⠀⠈⢷⡀
⠀⣰⠿⠁⠀⣄⠀⢈⣉⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡆⠀⠀⠀⠀⠀⠻⡄
⢀⡇⠀⠀⠀⢏⣠⠞⣡⣴⣦⡼⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣤⣤⣶⠶⢶⣦⡼⠟⢸⡇⢀⠀⠀⠘⠀⠀⢻⡄
⣼⠃⠀⠀⠀⢸⡏⠀⣿⡀⢀⣤⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⢀⡴⠀⠀⠀⠀⠀⣰⠏⠀⢾⠀⠀⠀⣽⠀⠈⢣⡀
⢻⡄⠀⠀⠀⣿⠁⠀⠀⠛⠛⢡⠀⠸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣣⡴⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⠀⠀⠀⠹⠀⠀⠘⣧
⢸⣧⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢙⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⠟⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⠀⠀⢻⡀
⠀⢹⣦⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠣⣤⡀⠖⣀⠀⠀⢀⣤⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⠀⣿
⠀⠀⠈⠙⡿⠀⠀⠀⠀⠀⡀⠀⣄⠀⡟⠢⣀⡌⠃⡘⠛⠛⠛⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⣿⠀⠀⠀⠹⡀
⠀⠀⣠⡿⠀⠀⠀⢠⠀⠀⠁⠀⡉⠋⠁⠀⠉⢧⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡆⠀⢀⣤⣴⠺⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⣧
⠟⢀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣷⠀⠀⠀⠀⠀⠙⢣⡀⠀⠀⠀⠀⣀⣠⠞⢫⠀⢿⣿⠛⢀⠘⠃⠐⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿
⠀⠈⠑⣦⡀⠀⠀⡘⠀⢀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠾⠿⠋⠁⠀⢸⠀⢸⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠻⡀⢰⡅⠀⠈⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠘⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠓⣶⡟⠲⢾⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡇⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⣇⠀⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠼⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⢄⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣸⣏⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⡀⣈⡛⠁⠀⠀⠀⠀⠄⣀⡛⢿⣆⠀⠀⠀⠀⣰⠟⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠙⢷⠦⠶⠾⣟⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⡤⣴⣛⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣹⡿⠛⠳⠶⠶⠖⠙⣿⠉⠀⠀⠀⢀⣄⠈⣋⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⡴⠫⡝⠛⠋⠀⠀⣸⠀⠀⠀⣤⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⡾⠀⠀⠘⣄⠀⠀⠀⠉⠑⢶⡀⣠⠘⡏⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢺⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠹⣧⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠼⣇⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣽⡆⠀⠀⠀⠀⠀⠀⠈⠻⠷⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠹⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣿⡇⠀⠀⣿⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠳⠶⠾⠿⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⢸⡿⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠛⠸⠿⢦⣴⡾⠷⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠿⠄⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣠⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣼⡷⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⣡⣴⣶⣶⠶⠶⠶⠶⠶⠶⢶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⣴⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠘⢿⣄⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⠛⠿⠿⠯⠍⠉⠙⠋

⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠴⠐⠒⠒⠛⠡⠀⠀⠨⠀⠉⢻⣿⠂⠔⠋⠁⠁⠀⣸⠿⣿⣿⣿⣷⣿⣿⠓⣋⠛⢻
⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⠽⠄⠀⠀⠀⠀⠀⠀⠱⠀⠉⠙⡿⠊⠉⢻⣿⠟⣟
⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠚⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⠾⣯⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠀⣃⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⡀⠀⠀⠀⠀⠶⠀⣛⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠴⣿⡖⠀⡙⠆⠠⠀⢠
⠐⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⣉⣿⣳⣶⢾⣾⢧⣭
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣠⣿⣄⢀⠄⣠⠀⠀⣠⡴⣉⢛⣌⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠐⠁⢠⣾⢶⣿⣿⣾⠃⢀⣿⣷⣼⣽⣿⣿⣯⣿⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⣀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣯⣤⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢁⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠹⣿⣿⡌⢿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢷⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠙⠿⣧⠀⠙⢿⣿⣷⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠳⣤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠛⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠁⠀⠀⠈⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣿⠀⠀⠀⠀⣉⡷⠦⠀⠀⠀⠀⠀⠀⠀⣴⡞⠋⠀⠀⠀⢀⡿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠄⠀⠀⣀⣤⠤⠤⢤⣀⠀⠀⠉⠁⠀⠀⠀⢸⣇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣿⡇⠀⠀⢀⣠⢴⡾⣿⠶⡄⢠⠲⣾⢿⡢⣄⠀⠀⠀⠀⣼⣿⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡴⠖⠉⣠⢏⡼⣡⠞⡳⣞⠳⣜⢧⡱⣌⠙⢦⣀⣰⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⢀⡼⣡⢏⡼⣣⣾⠃⠘⣦⣜⢦⡳⣜⢧⠀⢉⣿⣿⡇⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢻⡞⠁⠁⢟⡼⢡⠞⠀⠀⢳⡘⢮⡳⠈⠈⢷⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⡀⠀⠈⠀⢿⡴⠤⢤⣤⡿⠈⠁⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢻⡟⢻⠏⠀⠀⠀⢠⡟⠘⢿⣿⣿⣿⣿⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠲⢦⣀⢠⣇⣸⣀⣠⠶⠚⠙⢦⡀⠈⠿⠙⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⣿⣭⣽⣟⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢠⠏⠙⣿⣿⡿⢧⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠛⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠦⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠙⠶⠃⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣠⡴⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠚⠚⠛⠳⢤⣀⣠⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣤⡤⠖⠀⠀⠀⠀⠀⠙⠶⣤⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠈⠁⠀⠒⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣟⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣻⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣷⣋⡷⣄⠀⠀⠀⠀⣰⣞⢷⣝⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⣹⣿⣿⣿⣷⣾⣧⡀⠀⣼⣫⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠿⣳⣿⣿⣿⣿⣿⣿⢏⣷⣴⢯⣹⣿⣿⣿⣿⣼⡿⢟⣻⣩⣵⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⣷⣿⣾⣿⣿⣿⣿⣿⣯⣾⣻⣼⣿⣿⣿⣿⣿⣷⣾⣯⣛⣥⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣾⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠁⠉⠉⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢹⣿⣏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⢹⣿⣿⣿⠀⣀⠁⢀⡀⠀⢢⣤⣼⠇⠈⣿⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⡈⣇⢿⠸⡞⠳⣾⠁⠑⠀⠀⠈⠇⠀⢠⣿⣯⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣾⢷⠈⢌⡀⢻⣄⠈⠀⢀⡀⠄⠀⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⣿⡎⣷⣌⠳⡄⢿⣧⡀⠀⢔⣒⠄⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢰⠀⣿⣷⢸⡟⣆⠹⡄⣿⠻⢶⣤⣀⣠⣾⡟⠸⡏⠉⠛⠷⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢀⣿⡿⢘⡇⣿⡄⢡⠘⣷⣀⠙⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠁⡾⠙⢰⡎⠃⣿⣇⢸⠀⢻⡽⣧⢈⠇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣸⠁⠀⣸⠀⠀⠛⠟⣸⠀⣿⡀⣿⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡏⣰⠀⣿⠀⣰⠂⡀⣋⠀⡿⣧⡟
⠀⠀⠀⠀⠀⢀⡟⠀⢀⠰⣧⡟⠀⣿⡄⣿⡄⠁⢿⠀⠡⠘⢧
⠀⠀⠀⠀⣠⠊⠀⠀⢨⠀⣿⡇⠀⣿⣶⢻⠃⠀⢮⡀⠀⠀⠀⠀⠀⠒⢄⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆⣿⡗⠀⠘⣿⠸⡀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢻⡆⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢠⣄⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠛⠛⠛⠛⠲⠦⠠⠦⣄⡀
⠀⠀⠀⠀⠈⠉⠓⠷⡄⠀⠀⠀⢀⣤⠾⠛⠁⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠟⠳⣄⠀⠀⠀⠀⢀⣠⣤⣖⣋⡥⠴⠋
⠀⠀⠀⠤⠤⢤⣀⣀⡀⠀⢠⣿⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠻⣄
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⢸⡯⠀⠠⢤⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⣀⣤⣤⣤⠤⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⣾⠀⠀⠛⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦
⢀⣀⣤⡤⠶⠒⠀⠀⠀⠀⣾⠉⢭⡛⠀⠀⠀⠀⣠⡴⠋⠁⠀⠛⠛⠉⣀⠀⢀⣀⠀⣨⠍⠉⠛⠛⣦⡀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠉⢁⡤⠖⠉⠁⠀⠀⠀⠀⠀⠈⠳⠟⠀⠺⠁⡞⢠⡴⠆⠀⠀⠈⠛⠲⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠞⠉⠀⠀⠀⠀⣠⠎⢻⣟⣻⠂⢀⣠⣤⣄⡀⠑⣏⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⣴⠃⠀⠀⠉⠀⠀⣾⣿⣿⣿⠏⠀⠈⠉⠁⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⣰⠇⣿⠙⠲⠤⣄⣀⣀⡀⢀⣴⠟
⠀⠀⠀⠀⢀⣠⢴⡶⠀⣾⠁⠀⠀⠀⠀⠀⣰⠏⣿⣶⣤⣀⠀⠀⢾⣙⣻⠏⠀⣀⣠⣴⠾⠋⠀⢻⠀⠀⠀⢀⣠⣤⡶⠟⠁
⠀⠀⠀⠀⢯⠖⠋⠀⠀⣿⠀⠀⠂⠀⠀⣠⠏⢰⡿⠀⠉⠙⠛⠲⠦⠤⠐⠚⠋⠉⣠⣄⣀⣀⣠⣤⡴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⢀⣠⠴⢋⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣰⠂⠀⡿⣦
⠀⠀⠀⠀⠀⠀⢸⣏⠻⡷⠶⢤⣤⣤⡀⠀⠀⣀⣀⣀⣀⣀⣤⡴⠞⠁⠘⠁⣿⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⢧⡈⠉⢉⡉⠉⠉⠉⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⣆
⠀⠀⠀⣴⠟⠛⠦⠆⠻⡄⠀⠀⠀⠀⠀⠙⠢⣄⠉⠛⠲⢤⣄⡀⠀⠀⢀⡿⠀⣀⡴⠻⡄
⠀⠀⠀⣿⠀⢀⣤⠞⠃⣀⣀⣀⣤⣤⣤⣤⣀⣈⣳⣄⡀⠀⠈⠙⠳⢀⣾⠷⠚⠉⠀⠀⠹⣦
⠀⠀⠀⠹⣆⢸⣷⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠘⢧⣙⠣⣤⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠷⣮⡻⢶⣄⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠙⢷⣄⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣭⣿⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⣤⣬⣄⣠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠙⠓⠶⢤⣤⣤⣤⣤⣾⠟