Change Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢈⣻⣿⣿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⣀⡴⠋⠁⠀⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠈⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠌⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣧⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⢦⡀⠀⠰⠆⣠⡞⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣾⡁⠀⠀⢰⣏⠀⣼⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⣿⡙⣄⣉⣶⢠⢎⡙⢿⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡅⣿⠸⣿⡆⠀⠁⣿⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢰⡟⢹⠀⠘⡇⠀⢠⡏⠀⠀⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢸⡇⠀⠀⠀⢸⡇⠀⠁⠀⢸⠇⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣾⡇⠀⠀⠀⠘⣇⠀⡁⠀⢸⠀⠀⠀⢿⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣾⠉⡇⠀⠀⠀⠀⣿⠀⠁⠀⣾⠀⠀⠀⣾⡆⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⣼⠥⠤⠷⠤⠤⠄⠀⠙⠀⠀⠀⠝⠀⠀⠠⠿⣇⣀⣀⣸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⢀⡀⢠⣄⣀⡀⠀⠀⣀⣀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠇⡀⢸⠃⢹⣼⡷⣼⠻⡷⠂⠀⠀⣿⠤⠀⣾⣷⠰⣧⠈⠐⣶⢰⠆⣇⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠂⢸⠈⠓⠚⠉⠃⠈⠈⠉⠒⠀⠀⠙⠚⠐⠋⠘⠛⠋⠃⠀⠛⢸⠙⡟⠏⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡭⣽⠂⠀⠀⠀⠀⢀⡔⠲⡄⢠⡀⠀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠘⢓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿⣼⠳⣌⠀⣿⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⠂⠚⠁⠛⠀⠈⠀⠳⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡴⠆⠀⣠⠀⡄⠀⢀⣤⠀⠀⣄⠀⣄⢀⡠⣄⢀⣤⢤⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⣧⣠⡄⣻⠤⣧⠀⣼⢹⣧⠀⡿⢶⣟⢸⡅⠈⠀⡷⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠁⠉⠀⠁⠀⠉⠁⠀⠛⠒⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠒⠒⠒⠒⠒⠒⠲⡖⠒⠒⠛⣿⡟⠒⠒⠒⣶⠓⠒⠀⠒⠂⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇⣿⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⡿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠦⢼⠛⡟⠒⠒⠚⠳⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣁⣀⠀⠠⠜⠀⠛⠛⠛⠛⠛⠃

⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⣠⣤⢀⣄⢠⢠⡀⣠⢠⠤⢠⣤⡀⣤⡤⠀⣠⠤⠀⠀⡀⢠⠀⢀⡤⣄⢠⢤⡀⢠⣤⢄⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡘⣇⣸⢿⡟⢿⠈⣷⠇⢼⣋⢸⠻⡇⢸⠀⠀⢧⣀⠸⠀⠘⢸⣀⠻⣄⡿⢸⠺⠄⠀⡇⠸⣅⡼
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣠⣤⡄⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣤⣄⠀⠀⡠⢄⢠⢤⣀⢤⡤⢤⠀⠀⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣦⣴⣶⣶⣿⣷⣶⠖⠀⣿⢞⣻⡧⡄⢣⠸⡇⡀⡿⢰⡇⢘⡒⢢⡗⢿⠁⢙⡶⢒⡒⡄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣦⣺⣷⠿⣫⡾⣿⣿⡄⢠⣇⠀⣾⡇⢸⡇⢸⡇⣸⡄⠻⣇⠰⠶⣮⠉⠁⠈⠉
⠀⢸⣿⣿⣿⣿⣿⢿⢿⣿⣿⢿⡿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢉⣭⣶⣿⢿⣯⣿⢿⣷⣿⣯⡿⣿⣿⠉⠁⠈⠉⢉⣡⠞⣋⠻⣍⡟⢙⠳⣤⣀
⠀⢸⣿⣿⣿⣿⣿⣾⣾⣿⣿⣷⣷⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣾⣾⣿⣿⣿⣾⣿⣿⣿⣧⠞⠀⠀⢀⣾⣟⣥⣤⣭⣾⡿⣷⣮⣤⣬⣿⣿⡄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⡿⢟⣿⡟⣋⠫⢋⡛⣿⣿⠿⣿⣟⣴⠀⠀⠈⢿⠙⢋⢹⡟⡛⠯⢛⠳⣎⡑⠟⣿⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣵⣿⣿⣧⣄⠠⢄⣥⣿⣿⣿⣯⡿⣻⠀⠀⠀⣀⠔⢉⡜⣧⣄⠀⢠⣴⢧⡏⠳⣄
⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⡶⣿⢯⣿⣿⣏⣾⣿⣿⣎⣿⣿⣿⣿⡿⣿⠀⠀⠆⡙⣠⡾⣘⢈⡻⠿⢿⡈⣗⢿⣦⠃⡱⠄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⢠⣧⣳⣿⣿⣯⣾⣿⣷⣿⣿⣿⣿⣿⣷⣳⣿⠀⠀⢦⣳⣿⣸⣁⣾⣧⣤⣴⣿⣌⣧⣿⣷⣳
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠿⠉⢈⣿⣿⣿⣿⣿⣿⣿⡌⠉⡿⠣
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠉⠙⠛⠉⠉⠉⠉⠙⠉⠛⠉⠛⠙⠋⠉⠙⠀⠀⠈⠉⠁⠀⠁⠈⠀⠉⠀⠉⠈⠉
⠀⠀⠸⣦⣷⡼⢨⢰⠆⡷⢤⠀⢸⣹⠆⡧⣤⢠⢤⡄⡦⢠⢤⡄⣤⢸⡧⡄⣠⢤⢠⡤⣄⠀⡞⠉⢰⠋⠁
⠀⠀⠀⠛⠘⠃⠘⠈⠃⠃⠘⠀⠘⠀⠀⠃⠙⠘⠚⠁⠓⠘⠚⠁⠚⠙⠃⠃⠙⠚⠸⠗⠋⠀⠙⠒⠈⠓⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠘⠘⡀
⠀⠀⠀⠀⠀⠜⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢹⣷⣬⣦⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠐⠊⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠛⠛⠿⠿⠇⠀⠔⢀
⠀⠀⠀⠀⠀⠀⢐⠀⣀⠠⠶⠘⠃⠀⣰⣤⠴⣶⣄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢀⠀⢀⠀⢂⡀
⠀⠀⠀⢴⠈⠀⠈⠀⢣⡀⠀⠀⠀⠰⠻⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠂⠀⠀⠀⡟⣽⠃
⠀⠀⠀⠘⣆⠀⠀⠀⢈⠧⠀⢡⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⢀⡏⣘
⠀⠀⠀⠀⠈⠶⠐⠈⠀⠀⡐⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠁⠀⢘⡯⠊
⠀⠀⠀⠈⢀⡀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⢀⠤⠄⠠⠀⠀⡀⣠⣤⡦
⠀⠀⠀⠀⠈⠉⣭⠝⠃⠀⠀⠀⣀⠀⠀⢦⣼⣇⣀⠀⠀⠀⠀⣠⠀⠈⠁⠀⠀⡆⠀⠀⠈⠀⣠⡀⠀⠐⠇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⣖⠤⠄⠀⠉⠁⠀⠉⠌⠁⠀⠀⠂⢠⠁⠀⠀⠀⠀⣛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⠊⣡⠓⠈⠃⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠀⠀⢀⠀⣈⣠⠆⣰⣢⣟⡄⠀⠉⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐⠘⠋⠀⠀⠀⠀⠉⠙⢯⠂⠁⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠖⠖⠈⠓⠖⠂⠘⠓⠂⠺⠙⠒⠖⠒⠶⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⡀⡀⣤⢀⣦⠼⣄⣚⠇⡀⠀⣄⠀⠀⢀⣐⠚⢭⡲⢄⡺⣖⢦⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠙⠿⠿⠟⠿⣿⣬⡤⢺⣧⣴⣽⠛⠓⠀⠈⣿⣧⣧⠸⡿⣿⢏⠀⢀⡴⠋⠛⣧⠐⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣏⣉⠙⣷⣷⣍⣶⣟⢡⠉⣾⡉⠻⡮⡀⡾⠀⠀⠀⣿⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠠⣿⠏⠘⣛⣋⣤⡙⠛⠛⠛⣉⣽⣇⣿⣏⡼⣄⣣⡇⠀⠀⠀⡟⠀⣼⢠⡇
⠀⠀⠀⠀⣴⣶⠹⠟⢤⣭⣤⣾⣿⣿⣿⣿⣟⣛⣹⣟⠍⢉⣹⣽⣄⣽⠟⡇⠀⠀⢠⡇⠀⣿⣸
⠀⠀⠀⠀⠻⠟⠉⠀⣟⣿⠛⢳⣚⡟⠙⢿⣯⣻⣿⠿⢉⣡⣴⠄⣉⡥⢤⡇⠀⠀⠈⡇⠀⣷⢻
⠀⠀⠀⠘⡯⢽⠃⢹⡯⣾⠀⢿⠷⡏⠀⠀⠀⠀⠈⠉⠀⠁⠀⢰⠏⠀⠀⢹⡀⠀⠀⣿⠀⣟⢸
⠀⠀⠀⠀⡇⢸⡀⢸⡇⢹⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⣀⣤⡦⣸⠀⠀⠀⣸⠀⠀⠀⠻⠀⠉⠸⡄
⠀⠀⠀⢸⡇⠸⡇⢸⡇⢸⠀⢸⠀⡇⠀⣀⣠⣴⣶⠿⠛⠉⡇⢸⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢸⠃⠀⡇⢸⡃⠸⡆⣾⠀⢷⠸⣿⠟⠉⠀⠀⠀⠀⡇⣾⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢿⠀⠀⣠⣤⣤⡤⠤
⠀⠀⠀⣼⠀⠀⣻⣸⣃⣀⣇⣿⣀⣸⣀⡏⠀⢀⡀⢀⣀⠀⡇⢿⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠘⣾⠉⢻
⠀⠀⣿⣭⣭⣭⠭⠽⠯⠿⠯⠽⠯⠭⠭⣿⠀⠿⠏⠸⠿⠀⡇⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⢸⠀⣿⣷⠀⠀⣟⡇⠀⢸⣿⡆⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⢸⠀⠉⠉⠀⠀⠛⠃⠀⠈⠛⠁⠀⡇⠀⠀⣀⡀⠀⢸⡇⠀⠀⠘⠲⣄⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡏⡇⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠲⣇⣀⡞
⠀⠀⠸⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠷⠤⠼⠷⠷⠤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠒⠶⠦⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢀⠀⠀⠀⠤⣀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠎⠀⠀⠀⠀⠂⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢬⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣥⡀⠀⠀⠐⠀⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠘⠷⣶⣤⢔⡾⠃⣹⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⣿⠙⢦⡀⠀⠈⢻⠖⢶⠁⢸⡟⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣿⠀⠀⠙⣷⡤⡴⠀⢸⣧⠚⢗⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠉⠀⠀⠰⣽⠀⡇⠀⣾⢻⡀⠈⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠀⠃⠁⠸⠁⢠⠏⢸⠂⠀⣴⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⣿⠀⠀⠀⢰⠀⢀⣆⡀⡞⣠⠟⠀⢀⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⣉⡉⠉⣉⣉⠉⠉⠉⡉⠉⣉⠀⠈⠉⠀⠀⠀⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⢘⡳⣤⠀⢹⡅⠀⣿⡉⣽⠀⣷⠈⠁⠀⠀⠀⠀⠀⣶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡁⣹⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⣁⠀⡁⢀⣀⡀⢀⣀⡀⡔⠀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣤⡙⢠⡞⠉⠁⠐⡇⠀⢸⣾⣧⣿⣰⣷⡈⣿⠀⣿⣁⢸⡇⠄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⢽⡌⠻⠶⠒⠀⠓⠒⠘⠛⠃⠈⠛⠋⠃⠉⠀⠿⠤⠈⠷⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⠟⢀⡠⣤⣀⠀⣤⠀⣠⠀⢀⡀⠀⣀⢀⣤⣄⢤⣤⣤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡀⠈⢸⡤⣿⠀⣿⣧⢸⡟⢶⡇⣿⠀⣶⠈⣧⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠃⠀⠘⠁⠉⠈⠉⠉⠉⠁⠈⠁⠈⠙⠻⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣤⣄⣤⡤⣄⣀⣀⣀⠀⢀⣀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⢸⡇⡧⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠠⠶⢻⡇⣷⢀⣠⡴⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠇⣿⠈⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⡼⠀⢻⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠐⠋⢨⡇⠀⠘⣇⠙⠧⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⠄⠒⠉⠀⠀⠀⠻⠤⠀⠀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⡠⠀⠀⠀⢀⡀⠂⠠⠆⢀⡀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠊⠀⠍⣂⡀⠀⠀⠀⠀⠉⠡⠋⠀⢀⣴⡂⡥⠀⣈⠐⠂⠂
⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⡌⠁⠀⠀⣢⡀⠀⠈⠀⠀⣀⡠⠒⠁⠉⢀⡌⡜⠓⣶⡤⢲⠐⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡚⠀⣶⣿⡻⠆⠀⠀⠀⠀⠈⠀⠀⠀⠚⢁⣦⠠⡴⣴⣴⡞⡩⠭⡆
⠀⠀⠀⠀⠀⠀⠀⠂⢠⠌⠁⠉⡉⠉⠋⠀⠀⠀⠀⠀⠀⣁⠤⠚⠇⠛⠂⡠⠿⠏⠦⠟⠺⠤
⠀⠀⠀⠀⠀⠀⠈⡄⠈⠜⠠⠈⠀⠀⠱⣀⣤⠀⠀⠀⠀⢁⡠⠐⠀⠁⠐⢀⣄⠂⠖⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠦⠈⠁⠤⠌⢹⠽⣧⢄⡠⠀⣠⣀⣀⠀⠀⢐⣊⣀⣀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠈⢉⠂⠁⠢⠀⠰⠿⡿⠀⠀⠀⠁⠀⢀⡤⠊⠉⠒⠢⡄⢈⣀
⠀⠀⠀⠀⠀⠀⠀⣂⠀⠈⢷⡦⣄⠠⣤⠄⠇⠠⠹⡖⠀⠌⣁⡄⣠⠀⠠⠄⣲⡈⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠀⠀⠈⠀⢄⠀⢸⡀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⡀⢨⡅⡄
⠀⠀⠀⠀⠀⠀⡤⠀⢠⡌⠰⢶⢰⣡⡄⢯⡶⢺⠃⠐⡄⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠐⠜⠂⠙⠚⠇⠘⠀⠐⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠉⠀⠀⢄⠀⡀⢀⠈⠀⠰⡀⡀⢠⠔⠄⠁⠁⠀⠀⡀⠔⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡮⣠⠨⠟⢀⠁⠀⠁⠀⠀⠀⠂⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠤⠀⢀⡠⠣⣄⣀⠀⠀⠀⠀⠫⣋⠙⠀⠀⠀⠀⠀⠀⡤⠈⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠟⠀⠹⠄⠆⠴⠉⠀⠀⠂⠁⠊⠁⠀⠀⠈⠆⠀⠀⠀⢸⠚⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠂⠀⠈⠒⠐⢄⠀⠀⠀⠀⠀⠀⠀⣀⠠⠘⠂⠀⠉⠠⠐⢃⠂⠀⠀⡄⠁⠀⠐⠈⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠈⢂⠈⠀⠀⠀⠠⠀⠀⡂⠑⢄⠀⠁⣀⡀⠀⣟⠀⠀⠁⠀⡀⢔⠋⠀⠀⠀⠀⡆⠀⠀⠔⠡⡁⠁⠀⠐⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢔⡠⠀⠑⢄⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠈⠒⠄⠐⠠⠀⠄⠀⠀⣀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡀⠀⠀⠀⢀⣤⠴⠚⠙⠡⢀⠑⡄⠀⣌⠀⠨⡀⠐⢦⠀⠀⣀⠑⠠⣀⠀⠂⠀⢀⣠⠒⢂⠴⢊⡕⠄⢈⠁
⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⡒⠀⡠⢂⠕⠀⠊⠄⠂⠀⠀⠐⠈⢢⡷⢈⠄⠛⣀⣀⠉⠀⠀⠐⣠⠔⠊⠉⠉⠀⠀⠊⡡⠂⢉⠠⡤⠉⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠌⡂⠄⠀⠌⠀⢌⠠⢈⡀⡝⢆⠀⠘⠡⠈⢁⡁⠖⠉⠀⡠⡀⠀⠀⠈⠐⡪⠠⠀⠨⠢⠈⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠊⠀⠋⢂⠕⠢⠀⠀⠡⠀⠀⠄⠀⠀⠤⠁⠀⣄⠀⠡⠄⠈⠄⣈⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⣀⠀⢂⢀⣀⠠⠤⠤⠤⠤⠄⠂⠂⠁⠠⣁⠀⢐⡀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠙⢗⣂⣐⣫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠉⠭⠉⠁⠉⠉⠉⠀⢤⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢈⣁⠤⠤⠤⠤⠄⡉⠒⠤⠄⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠔⠊⠁⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠤⠀⣀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠁⠀⣀⠔⠈⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠑⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠞⠀⠀⠀⠊⠀⠀⠀⠀⠀⢰⠐⡡⠁⠙⡄⠦⡈⠳⡀⠀⠀⢣⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢁⡔⠁⠀⠀⣀⠄⠀⣀⠤⢒⢃⠜⠀⠀⠀⢸⠆⠘⢆⠘⡄⠀⠀⢆⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠎⠀⠀⡠⠊⠀⡠⠊⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠄⠀⠘⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠎⠀⠀⡴⠁⢀⣾⣴⣤⡋⠀⠀⠀⠀⠀⠀⣠⠿⠛⠛⠂⠈⣆⠈⠄⠀⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⢰⠁⢤⣮⣠⣀⠀⠉⠃⠀⢠⠀⠀⠚⠁⣀⣤⠾⡾⠊⠙⠀⠐⠀⢠⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⡇⢀⠆⠀⢣⡹⣿⣶⣄⠀⢸⠀⠀⢀⡾⠿⢏⠔⠁⠀⠀⡇⢸⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⢠⠀⡌⠀⠄⠠⣌⠈⠁⠈⠀⠘⠀⠀⠀⠁⠀⠀⡴⠂⢰⠀⡇⠰⠀⠸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠀⠀⠀⡆⠀⠑⠤⡬⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⠢⠔⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⢰⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡅⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠀⠀⠂⢣⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⡠⠃⠀⡇⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⡀⠀⠒⠀⠑⡄⠀⠀⠀⠉⢑⢒⡓⠒⠉⠀⠀⢀⡔⠁⡆⠀⠁⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢡⠀⢈⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃⠀⡇⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠣⠀⡆⠀⠆⠀⢈⠑⠤⣀⠀⠀⢀⣠⠊⡀⠀⡄⠀⠀⠀⠇⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⢰⠀⠠⠀⠘⡀⡆⠘⠉⠉⠁⢸⠀⡇⠀⡇⠀⡇⠀⢰⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡸⡀⠈⠀⢰⠀⠀⡇⠀⢸⠀⠀⠀⠸⠀⠁⠀⡇⢀⢃⠀⠘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠃⠀⠀⠀⠀⠀⠄⢀⠆⠀⠀⠀⠀⢃⣀⣀⣀⣸⠈⣀⣀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⢈⡩⠋⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡊⢉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠸⠁⢢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠁⢸⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢸⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠧⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠤⠔⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⣀⣀⠀⣀⣀⠀⣀⡀⠀⣀⣀⠀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⢻⡯⠭⢸⡏⠙⢸⡏⢹⡇⣿⠀⢸⡏⢹⣾⣯⣽⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠚⠓⠒⠈⠓⠛⠈⠓⠚⠁⠛⠒⠈⠓⠛⠘⠃⠙⠂⠀⠀⠀⠈⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⣿⣻⡆⠛⡟⠃⣷⣸⣆⡿⣴⠛⢷⣸⣟⣳⢴⣧⡾⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⠇⠿⠹⠆⠀⠇⠀⠸⠏⠿⠇⠹⠦⠞⠸⠏⠿⠸⠏⠻⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠐⠀⠀⠁⠉⠈
⡇⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⢀⠀⠀⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⡀⢀⠀⡀⣀⣀⢀⣀⡀
⡇⠀⠀⠀⠀⢸⡯⣟⢸⠀⢀⣟⣇⣾⠉⡁⣷⣏⠀⠀⠀⠀⠂⠀⢹⡾⣿⠏⡷⢾⣿⡇⢹⡇⢸⠧
⡇⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁⠉⠈⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠈⠉⠁⠈⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠴⠒⠒⠋⠉⠉⠓⠒⠒⢤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢱⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⡸⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⢣⠹⡀⠀⠀⠀⠀⠀⠀⡼⣰⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢧⢳⡀⠀⠀⠀⠀⣰⢡⠃⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢣⠀⠀⠀⢰⢃⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱
⠀⠀⠀⠀⠀⢀⡖⠦⢍⣓⠦⢄⣀⠀⠀⠀⠀⠘⡎⢇⠀⢠⠇⡞⠀⠀⠀⠀⢀⣠⠤⢒⣫⠥⠒⢢
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠮⣍⡒⠦⢄⡀⠹⡜⣆⠎⡜⢀⣀⠤⢖⣊⠥⠖⠊⠉⠀⠀⠀⢘⡆⣠⣤
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠬⣝⡓⠈⠘⣋⡭⠔⠚⠉⠀⠀⠀⠀⠀⢀⡴⣺⠗⠋⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⣚⡭⡤⢀⠠⡬⣙⡲⠤⣄⡀⠀⠀⠀⠀⠈⠙⠯⣶⢤⡀⢿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡠⠴⣒⡩⠴⠒⠉⠁⣰⢡⠋⢧⢳⠀⠉⠑⠲⢭⣑⠲⢤⣀⡀⠀⠀⢸⠃⠈⠋
⠀⠀⠀⠀⠀⠀⠷⢒⣩⠥⠒⠋⠁⠀⠀⠀⠀⢰⢃⠏⠀⠘⣆⢧⠀⠀⠀⠀⠀⠉⠓⠢⢭⣓⠢⠞
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡞⠀⠀⠀⠘⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢀⡎⡼⠀⠀⠀⠀⠀⠹⡘⡆⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡜⡸⠁⠀⠀⠀⠀⠀⠀⢳⡸⡄⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡼⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢶⣶⣤⣤⣤⣤⣤⣴⣶⡾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠉⠙⠉⠉⠉⠙⠛⠛⠉⠁⣼⣿⣟⠛⠛⠋⠙⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⣈⣤⣸⣿⣿⣽⣶⢿⣥⣴⣶⡀⠉⠉⠟⠉⠉⢿⡏⣿⣏⣴⡿⠹⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⡟⠉⠀⠙⠍⢛⣗⣤⣹⣿⡟⠁⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⡛⢻⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠗⣩⠁⠀⠀⠀⠃⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⣇⣿⣿⣼⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠁⠀⠀⠰⠈⢳⡀⠀⠀⠀⠀⡀⠀⠀⢠⢀⣾⣿⣿⣿⣿⣿⣿⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣾⣶⣿⣿⣷⣶⣼⠇⠀⠀⠀⠀⠘⠀⢻⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢄⣿⣥⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⣄⢺⠿⡼⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢏⡁⢀⣈⣹⣿⣿⣷⡀⠀⠀⣌⣻⡿⠂⢱⣇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠿⠿⠿⠟⡿⠛⢁⡀⢰⣿⣿⣧⣳⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣰⣴⣠⣿⡗⠀⣰⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⢿⣿⣿⠿⠿⢶⣾⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡿⢟⠋⠃⠈⣿⣶⣤⣦⣴⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⣯⡪⣻⣿⣿⣿⣿⣿⣿⣿⡿⣟⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⡫⡞⠡⠃⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⠔⠁⣻⢇⣿⣿⣿⣿⣿⢫⣼⣿⣷⣬⢻⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⢇⠛⡕⡘⣠⢂⡔⢠⠂⢸⢧⡹⠋⡉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣖⣉⣤⣾⣥⣾⣿⣿⡿⠋⣱⣾⡿⣵⣿⢻⣷⣿⡿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⡼⣿⠇⢨⣾⣶⣄⣏⣘⣜⣾⠀⣿⣾⡀⠀⠀⢫⣕⣬⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡿⠟⠋⢀⣴⡿⣋⢞⡽⡳⠿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣧⣿⣰⣿⣿⣇⣽⢸⣿⣿⣷⣦⣿⡇⠀⠀⡀⡀⣍⢻⣿⣾⣿⣿⣿⣯⣉⣩⡭⢉⣀⣀⣶⣿⣿⣿⣾⠷⣣⣜⣇⡴⣹⣟⣿⣿⣷⡿⣿
⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣜⠳⠞⠀⢀⡈⡛⠰⠂⠐⡆⠠⠶⠶⠈⠋⠀⠀⠘
⢀⠒⠀⠲⠒⠒⠂⢀⢀⡤⠀⠈⠄⠀⠀⠙⠋⠸⡷⠀⠀⠁⡘⢀⣀⡀⠀⠀⠂⢀⡁⠀⠂⠀⠀⠀⣄⣠
⢸⠀⠀⣀⣁⠂⠀⠀⢤⣄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠈⢩⣟⣵⡀⠁⠀⠀⠀⢀⡀⡄
⠈⠀⠀⠀⡀⠀⠀⣠⠇⢨⠉⠀⡀⠀⢸⣍⡀⠀⡄⠀⢐⠘⠘⣏⠁⡔⠂⠀⣈⣇⠤⡄⡀⠀⠀⠀⠈⠀⠁
⠂⠀⠶⠶⡄⠀⠀⠅⠀⡜⠇⠀⠙⡊⢢⠎⠉⢵⠐⠂⠈⠞⠉⢹⠄⠰⠦⣄⡘⠛⢏⣁⣄⠉⢈⠠⡄⢸
⣨⣤⢭⡅⠁⠀⢀⠄⠗⠁⢾⠀⢐⡄⠘⠤⠐⠈⡀⠀⠸⠀⠄⠈⠀⠀⢂⣼⠀⡄⢸⡁⠀⡏⢀⢀⡇⣺⠇
⠀⠀⠀⠆⠀⠁⠈⠑⢄⡄⠘⠒⠈⠀⠈⠁⠀⠉⠉⢰⡶⠞⠀⡌⠀⠰⠐⣘⠳⠱⡶⠁⢨⠺⠀⠙⠐⢬⠂
⠀⠀⠄⣀⠀⠀⠸⡀⡄⠀⠀⢠⢀⢀⢀⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⠀⠀⢀⢁⡀⡄
⠀⠀⠀⠁⢈⠀⠒⢉⠁⠀⠀⠰⢇⣄⠠⠀⠀⡤⢼⡃⠈⠃⠀⠀⠀⠀⢙⠋⠀⠀⢈⡛⠁⡀⢀⣀⠓⠣
⠀⠀⠀⠀⠰⢄⣉⡥⣻⠀⠃⠀⠀⠀⡄⠀⠀⠀⠠⢈⣁⠛⠓⠛⠛⠛⠋⠛⠐⢛⣚⣛⣈⣙⠙⠋⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⡶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠛⣉⡉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠋⠀⠀⠀⡞⠁⠀⠀⡷⢦⡄⣠⠖⣦⢠⣤⡄⠀⣤⢴⣤⣖⣲⡦⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠻⠶⠾⠋⠙⠀⠃⠙⠚⠋⠘⠁⠛⠈⠛⢻⡇⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢀⡶⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢀⡴⠶⡄⢠⠄⢠⠀⣶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠘⠷⠾⠃⠘⠷⠛⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⢸⣦⡀⣰⣶⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⡀⠀⣀⣴⣤⠀⠀⣿⠀⠀⢀⣿
⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⣿⡋⠛⠁⣿⠀⣅⢠⠶⡆⠀⣴⢾⡇⠀⢾⣙⠃⣾⣯⠿⠂⠈⣇⢀⡀⢀⣌⠀⢠⣾⠏
⠀⠀⠀⢠⣾⠋⠀⠀⢀⣤⣶⣄⣀⠙⠁⠀⠀⠛⠸⠧⠘⠀⠛⠘⠷⠾⠧⠘⠶⠟⠁⠈⠛⠛⠀⠀⠉⠉⠁⠀⣁⣴⡿⠃
⠀⠀⣰⡿⠁⠀⣠⣶⠿⠋⠉⠙⠛⠿⢷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣤⣴⣶⠿⠟⠉
⠀⢰⣿⠁⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⣿⠃⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠾⡶⠶⠶⣦⣤⣀
⢸⡟⢰⡿⠁⠀⠀⠀⢠⢦⣀⣀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠈⠉⠛⠳⢦⣤⡀
⣼⣧⣿⠁⠀⠀⠀⠀⢦⠀⠈⢉⡁⠀⠀⠀⠀⠀⢠⡴⠚⠛⠉⠙⣻⠂⢀⣀⠀⢰⡆⠀⠀⠈⠛⢷⣤⡀
⣿⣿⠇⠀⠀⠀⠀⠀⠈⠛⢶⡟⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⢷⣤⣯⣀⡀⠈⠀⡼⠀⠀⠀⠀⠀⠀⠙⢿⣆
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡾⠛⠉⠁⠀⠉⠉⠿⠭⣿⣟⠳⣤⡀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠾⠁⢠⡄⠸⠟⠋⠀⢠⡀⠢⣽⣷⣄⠙⣦⡀⠀⠀⠀⠀⠀⢹⣷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣧⣠⠀⡄⢠⡄⢿⠀⣾⡥⠤⠀⠈⢶⡀⠈⠦⣤⡿⣷⠀⠘⣷⠀⡀⠀⠀⠀⠀⢻⣇
⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠻⢻⡟⠛⠶⢷⣾⣧⣿⣤⣤⣼⣤⣬⣿⠶⢿⠿⠚⡿⠀⠀⢸⣯⠀⠀⠀⠀⠀⢸⣿
⢹⠀⠀⠀⠀⣠⡶⠶⣾⠇⠀⠀⠀⢀⣨⠼⠯⠁⠀⠀⠀⣠⣶⣄⣀⠀⠀⠀⠀⢸⣇⣀⡀⢸⡏⠀⠀⠀⠀⠀⢸⣿
⠘⠀⠀⠀⠀⣿⡠⠲⣿⠀⠀⠀⠐⢋⡴⢶⠶⠀⢀⠀⠀⢠⠿⣿⣍⠙⠀⠀⠀⢸⡟⠋⠙⣿⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡀⢰⣿⡆⠀⠀⠀⠎⠀⠠⠀⠀⡌⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⣿⣿⠛⢆⡿⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠘⣧⡀⢻⡇⠀⠀⠀⠀⠀⠒⠂⣰⡁⠀⠀⠀⠒⠒⠀⢀⠀⠀⢀⣿⡏⢀⣾⠃⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠀⠛⢀⡾⠉⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⢸⣿⣠⡾⠁⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣀⠀⠀⠻⣤⣀⣀⣀⣴⠟⠀⢀⡀⠈⠃⢸⡿⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠃⢠⣀⣀⣀⣉⣉⣉⣤⡴⠶⣿⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠙⣿⣉⡉⠉⠉⠀⣀⣠⡏⠀⠀⢰⡿⠀⠀⠀⠀⢀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢿⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣿⡇⠀⠀⠀⠀⠘⣷⣿⠋
⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠻⣧⡀⠀⠀⣀⠙⠛⠛⠛⠛⢉⠀⠀⣰⣿⠋⡇⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠘⢿⣷⣄⠈⠙⠓⠒⠒⠛⠉⢀⣼⡟⠁⢸⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⡟⠛⠿⢶⣦⣤⣤⣴⠾⣿⣇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠎⠹⣆⠀⠀⣰⠃⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠘⠀⠀⢈⠀⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⢰⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠈⣿⣄⣀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠙⠛⠻⠷⠿⣶⣶⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣼⣦⣤⣤⣶⡶⠶⠾⠿⠛⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣭⣭⣤⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣤⣾⣿⣿⣷⣾⣿⣷⣾⣦⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⢉⡁⠀⡄⡖⠀⣆⣖⠈⣝⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣠⡧⠼⠓⠓⠛⠛⠛⠋⠉⠙⠻⢾⣧⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣀⣀⣈⡀⠀⠀⠀⠀⡙⠷⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⡤⢾⣿⣿⣿⣛⣛⢫⡝⣛⡷⣮⡂⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⢞⣭⣭⣭⣹⣗⣲⣶⣮⣽⣶⣶⡶⣟⣳⡀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣲⣿⠿⠿⢿⣿⠷⣚⠯⣽⣿⣿⣷⣾⣿⣿⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢙⣿⠓⢤⡿⢷⣾⣿⣿⣻⠟⢿⠿⣷⣾⣦⠽⠿⢻⣯⢮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠠⣟⠀⠀⠀⠀⠛⢛⠍⠈⠀⠘⠠⠄⠻⠼⠁⠀⠈⡃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢩⢀⣧⡀⠀⠀⠀⢀⠄⠀⠀⢀⣀⠀⠀⠀⣰⢠⡕⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢿⠈⠑⢣⠀⠀⡈⢙⣻⣶⣞⣿⣉⠁⠀⠀⢡⣾⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣯⣧⠀⠀⣼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⣼⠋⢁⡒⣶⣶⣶⡆⠀⠑⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⣤⣀⡀⠛⢛⠋⠀⣀⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣸⡏⡏⡛⣿⡾⣫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢸⢹⣋⣧⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⢀⠀⠀⣤⣤⢀⢀⢀⠀⡀⠀⠀⣤⡄⢠⠀⠀⢀⣀⡀⡀⢀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠯⠸⠁⠀⠻⠟⠾⠟⠒⠘⡏⠀⠀⠛⠳⠸⠸⠇⠻⠚⠸⠁⠾⠻⠸⠏⠛

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣂⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠉⠙⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⠀⢰⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣧⣼⣿⠻⣿⣿⣿⣿⠋⠀⠀⣰⠀⠀⠞⠀⠀⢀⣀⣤⠤⠤⠄
⣿⣿⡿⢿⣿⡿⢿⣿⣮⣿⣛⣐⠋⠉⠀⣸⡟⣿⣿⣿⠀⠀⠀⣿⠀⠐⢐⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣴⣤⣸⣿⣁⣀⣨⣿⡿⠿⠿⣿⣷⣦⣿⣃⣿⣿⣿⣀⣤⣰⣏⣠⣾⣉⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣷⠊⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠠⣠⠀⠀⠀⡀
⣛⣛⠛⣻⣟⣻⠋⠛⠛⣟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⡛⠛⣻⣿⠛⠛⠛⣻⠿⣟⡛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠋⠙⠛⠉⠉⠉⠛⠛⠛⠋⠛⠉⠙⠛⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁
⣄⣰⣂⣀⣀⣀⣀⣀⣀⠀⢀⠀⡀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣤⣄⣀⠀⣀
⠭⠭⢽⣿⣿⠿⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠛⠛⠉⠙⠛⢿⣻⣿⣥⣄
⠰⠎⠉⠉⠀⠀⠚⠉⠉⠉⠉⠉⠉⠿⠶⠦⠈⠛⠁⠀⠀⠀⠀⠀⠒⠋⢀⣠⠶⠋⠉⢻⣧⣉⠉⠛⠛⠓⠀⠠⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠀⠀⠠⢬⠿⠷⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣷⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠉⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠇⠀⠀⢿⡿⠿⠿⠿⠿⠿⠿⡿⠛⠛⠛
⠀⠀⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⣠⣧⡀⠀⣸⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⣤⣷⣄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡀
⢀⣾⣿⡷⠀⠈⠉⠉⠁⠈⡇⠀⠀⠀⠀⣰⣿⡿⠃⢀⣿⣿⣿⣿⣿⣿⣿⡟⢀⣀⣀⢿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⠋⡟⣡⣤⣄⠀⠀⠀⣰⣿⣷⠀⢀⣾⣟⠉⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⡄⡇⢸⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⢿⣷
⠟⠀⠁⠻⣿⣿⠀⠀⣰⡿⢻⠃⢠⣿⣿⠃⠀⠀⠀⠀⠀⢠⣽⡍⠛⠛⠟⠀⠀⢸⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠆⠀⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢿⡁⣠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠓⣾⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢲⣤⠟⣁⣴⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠙⢶⣁⡤⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⣿⣛⣉⣠⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡉⠛⠶⣿⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡿⢯⣩⢤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣉⣛⣻⣿⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⡇⠀⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣽⠁⢸⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣰⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠳⣄
⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⡼⠁⣇⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⢸⠙⣄⠀⠀⠀⠀⠈⠳⡀
⠀⣠⠞⠁⠀⠀⠀⠀⢀⡼⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⣆⠀⠀⠀⠀⠀⠙⢦⡀
⠼⣅⣀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠈⠉⠓⠲⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡤⠴⠒⠋⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠙⠛⠻⠷⣶⣦⠀⠀⣰⡟⠁⠀⠀⠙⣷⡀⠀⢠⣶⡶⠿⠛⠛⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣶⣟⠁⠀⢰⣿⣶⣶⠀⢰⣶⣾⣷⠀⠀⢙⣷⡆⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣶⣦⡈⠻⣷⣄⠀⠀⠀⣿⠀⢸⡇⠀⠀⢀⣴⡿⠋⣠⣶⣄⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠉⠻⣦⡈⠻⡷⠀⢀⣉⣤⣌⣁⠀⠰⡿⠋⣠⡾⠏⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⡇⠀⠀⠙⠻⡆⢠⣾⠟⠉⠉⠉⠙⢿⣆⠀⠾⠛⠀⠀⠀⣿⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠸⠷⠶⠶⠶⠶⢀⣿⠁⠀⠀⠀⠀⠀⠀⢹⣇⠰⠶⠶⠶⠾⠿⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⢠⣤⣤⣤⣤⣤⠘⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⣤⣤⣤⣤⣤⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣼⡏⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠈⣿⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⣴⠶⠿⠦⠈⠙⠻⠿⠿⠛⠉⠀⠾⠷⢶⣤⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⣷⣤⣴⡇⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡆⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣿⣅⠀⢀⣽⣧⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠟⠋





⡿⢿⠿⡿⡿⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣛⣛⣿⣟⣛⣟⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣦⡤
⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠏⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣀⣀⣈⣉⣁⣀⣀⣪⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢶⣤⠀⠀⠀⠀⠀⢸⠆⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠄⠀⠴⠋⠉
⠀⠀⠀⠀⠀⣀⠁⢀⡀⠙⠛⠀⡀⠀⠀⠀⠀⠀⢠⣬⠉⠀⡀⣀⣀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⢠⣮⣾⣤⣴⠀⣶⣦⡄
⠀⠀⠀⠀⠸⠻⠿⠿⠷⠚⠻⠾⠀⠀⠀⠀⠀⠀⠚⠛⠛⠘⠙⠙⣛⣛⣛⠛⠚⠛⠟⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠐⠑⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⢀
⠀⠀⠀⠀⢀⠀⡤⠓⠠⠆⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⡢⠓⠤⠴⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠋⠀⡝⣰
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢀⣄⣠⣤⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⢲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠮⠛⠛⠻⣷⡂⠈⠁
⠀⠀⠀⠀⠀⠐⠛⠛⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⠀⠈⠉⠉⣄⠖⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠒⠀⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠐⢠⣆⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠉⠉⠩⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠄⠒⠆
⠀⠀⠀⠀⠀⠀⠢⣉⠁⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡒⡀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣸⡄⠀⠐
⠀⠀⠀⠀⢠⣦⣀⢠⣧⣀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠗⣽⣷⢾⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠆⠸⠦⡤⠄
⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣶⡆
⠀⠀⠀⠀⠀⠀⠈⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⣷⣦⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣀⣽⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠶⢶⣶⠶⠆⠀⠀⠀⣠⡶⠶⣦⡀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⢿⣄⣀⣼⠟⠀⠀⠀⠀⢠⣿⣋⣀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿

⠀⠀⠀⠖⠂⢄⠔⠐
⠀⠀⠀⠈⠀⢘⠂⠁
⠀⢀⠔⠀⠁⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⢀⠊⢰⠀⠀⠀⠈⣰⡀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣤⣄⢠⣤⡀
⠀⠀⠀⠀⠋⠀⠀⠉⠣⡀⠴⢀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡥⠿⡤⠁⠥⢼⠤⠍⠉⡸⠧⡤
⠀⢄⠀⠀⠀⠑⢒⡩⢂⢀⠆⡈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠼⣖⠀⠀⠀⠠⠧⠄⠄⠀⠀⠼⠤⠄⠀⠀⠠⠧⠄
⠀⠀⠐⠤⠂⠀⠣⠴⠋⣥⡘⠁⠀⠀⠀⠀⠀⠘⠐⠤⠤⠄⠔⠂⡁
⠀⠀⠀⠀⠀⠀⢆⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠐⡀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀⡀⠀⠊⠁⠀⠀⠀⠓⠑⠄
⠀⠀⢀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠁⠀⠤⠰⠄⠀⠀⠘⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉
⠀⠀⠂⠀⠂⢠⠀⠈⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⢀⠀⠀⢀⡘⠀⠃⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⡔⢢⠠⠩⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠀⡤⡀
⠀⠀⠀⠀⠀⠀⢿⣇⢒⡡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢀⠀⣸
⠀⠀⠀⠀⠀⢠⠤⢅⡈⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠲⠔⢄
⠀⠀⠀⠀⠀⢀⠓⠢⡈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⣠⠎⠀⡔
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠷⠂⠀⠀⠠⣄⠀⠒⣢⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢸⡠⠀⡜⣀⠀⠠
⠀⠀⢀⠆⡠⠀⠱⠤⢂⡠⠤⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⢣⡀⠃⠘⠀⠋⡜⠀⡇
⠀⠀⢸⠊⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠁⠈⠈⠉⣱⠖⡰⠁⢠⠇⠐⡄
⠀⠀⠸⡀⠀⠀⢠⠃⠀⠀⠀⣀⡠⢼⢥⡀⠀⠀⢀⣀⡀⠀⠀⠦⢀⣀⡠⠤⡄⠀⠀⠀⡀⠀⠀⠀⡇⠈⠀⠀⠀⡠⠊⠐⠁⠀⡎⠀⠀⣇
⠀⠉⠁⢸⠁⢠⠋⠀⠀⠀⢊⠥⠒⡃⠀⢻⠀⠀⡀⠀⠀⠀⠁⠀⡀⠐⡀⠴⣀⡀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⡀⠀⠀⠀⠀⠘⠀⠘
⠀⡔⠉⠁⠀⠜⠀⠀⠀⠀⠀⠀⣠⠃⠠⠜⠀⠀⠯⠤⠃⠀⠓⠤⠈⠉⠀⡄⠀⠀⢀⠀⢠⠊⠀⠀⠙⠂⠉⠀⠀⠈⠙⢆⡀⠀⡄⢀
⠀⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠃⠀⠘⠢⢄⡀⠀⠀⢠⡀⠀⠀⠀⣀⠔⠊⠀⠀⡄⠉⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠑⢄⣊⡀⠀⠀⠀⠠⠔⠃
⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣷⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠙⠛⠛⠛⡆
⠀⠀⠀⠀⠀⣤⠴⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠤⢤⣿⣧⣤⣤⣤⣤⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢸⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠓⣒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⡒⢲⠀⠀⠤⣿
⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠁⠀⠀⣿
⠀⠀⠀⠀⠸⣿⣆⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣿
⠀⠀⠀⠀⢀⣿⡏⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠉⢩⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⣷⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⢹⠇
⠀⠀⠀⠀⠀⢛⣷⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠒⠖⢶⠛
⠀⠀⠀⠀⠀⡏⣿⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠐⢻
⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⣷⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠒⢾
⠀⠀⠀⠀⠀⢻⣿⣤⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡧⠤⠤⣾
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⠀⠰⠆⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⣁⣸⡇⠀⠀⣼
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠛⠛⠛⠛⠋⢉⠉⠉⠉⠉⠉⠤⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⣀⣾
⠀⠀⠀⠀⠀⠸⠿⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⡶⣶⠶⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⣤⣀⠈⣿⡇⠀⠀⠀⣿⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⠻⣷⣿⣇⣠⠴⢤⣿⣴⣶⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣬⣿⠷⠛⢿⡏⠀⠀⣀⣽⣨⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠤⠤⠶⠓⠶⠺⢧⠴⠛⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⡂⠀⠀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠈⠁⠀⢰⡃⠀⠀⠈⡀⠁⠄⠘⢠⠀⠀⠀⢀⢿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⡁⠀⠀⢉⠀⡀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠐⠀⠈⠀⠉⠈⠉⠁⠀⠲⡤⢞⡢⡤⠖⢀⣀⡀⠀⠀⠀⣀⡀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⣀⠂⠄⡀⠀⣀⠮⡝⣏⠤⡀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠘⠂⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⣌⣈⠆⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⡂⢰⢄⣠⠠⢄⠀⣤⠄⠀⠀⠀⠘⡍⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⠈⡈⢠⢐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠈⠀⠀⠀⠀⠀⠀⢼⣦⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠐⠊⠣⡀⠀⠰⠀⡀⠀⡄⠠⠂⢰⣿⡆⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⢧⠀⠀⠀⠀⡴⢤⣤⢴⠊⡀
⠀⠀⣀⡤⠄⠀⠀⠀⡀⠀⢀⠀⠁⡀⠀⠀⠀⠉⠙⠉⠁⠀⠐⣢⢤⢄⡤⢠⢤⡠⠠⠠⡄⠀⠀⠀⢠⡘⢆⠇⠀⠀⠁⠈⢸⠈⠀⠁
⠀⠀⠁⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣂⢸⡀⠀⠁⢀⣄⡄⢀⢨⠀⠀⣀⣄
⠀⠀⠀⠀⡤⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⠀⠀⠀⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⢞⠣⡧⠂⠈⠉⡇⠈⣸⡈⠐⠋⠉
⠀⠀⡰⠂⠀⠀⠈⠳⣄⠠⠈⠁⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⣫⠴⠒⠀⠁⠀⠀⠈⢤⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠆⠀⠀⠀⠺⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣀⠀⠀⠀⠐⠂⠙⢦⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠘⠚⠓⠒⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⢒⡽⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢸⡆⢀⣇⠀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⢚⡽⣫⢪⣿⣿⣿⣿⡇⠀⢰⣏⣉⣉⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡴⠴⢴⣤⠠⢂⠅⡟⣻⣿⣿⡿⠀⠀⢸⣍⣉⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣥⠐⣠⣽⡯⠋⠀⠈⠈⠈⠠⠒⠲⠀⠸⠏⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠚
⡶⣶⢶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⢶⣶⢶⣶⣶⣶⡶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢀⣠⠤⠒⠉⠉⠒⠤⣄⡀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⢀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⢀⠀⠉⠓⠦⢄⡀⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⠖⠋⠁⠀⠀⠀⢾⣉⡇⠀⠀⠀⠰⣏⣹⠄⠀⠀⠀⠈⠑⠲⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠉⠒⠤⣄⡀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⠴⠒⠉⢸⠀⢸
⠀⠀⠀⠀⠀⢠⠶⠷⠶⠷⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠾⠶⠾⠶⡄
⠀⠀⠀⠀⠀⢸⠀⠀⢠⠴⢦⡀⠠⡄⠀⣤⠀⢠⠴⢤⠀⢠⣄⠀⡄⠀⣠⠶⢤⠀⢠⡶⠶⠆⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢀⡷⠶⣿⠀⣿⢤⢼⠁⢸⡏⢆⡏⠀⣿⠀⠀⠀⢸⡷⠶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠘⠲⠚⠁⠘⠃⠀⠛⠀⠛⠀⠘⠃⠘⠃⠈⠃⠀⠙⠲⠚⠀⠘⠓⠒⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠶⡶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⢶⡶⢶⠶⢶⠶⢶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⡇⠀⠀⣠⣄⠀⠀⠈⠓⠚⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠢⢄⡀⠀⠀⠀⢇⣸⠂⠀⢸⡇⠀⠘⠧⠼⠀⠀⠀⢀⡠⠔⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠈⠙⠲⢤⣀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡤⠖⠋⠁⣀⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠉⠒⠤⣸⣇⠤⠒⠉⠀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⢀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⢤⡀⠀⠀⠀⣠⠕⠖⠀⠐⠦⣄⠀⠀⠀⠀⠹⣿⣷⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀⠈⢆⠀⠀⠀⢀⣤⡎⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⢦⡀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⢁⣿⢿⣿⡀⠀⠀⡠⠀⠀⠲⠥⣤⣬⡓⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠑⠀⠀⢈⠀⠀⠀⠀⠀⠈⠑⠒⠢⢤⣀⠀⠀⣀⡠⠔⠊⠉⠀⠀⠀⡠⠤⣺⠇⠀⠙⠇⢀⡤⠖⠉⠀⠀⠀⠀⠉⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠉⢲⡀⠀⢣⡀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⢀⡴⠥⠚⠁⣀⡤⢤
⠀⠀⠀⠀⢰⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠁⠈⠓⢢⣤⡄⠀⠀⠚⠁⠂⣤⡤⠴⠚⠉⠀⣠⠔⠋⠁⠀⢠⣇⡀
⠀⠀⠀⠀⠀⢳⡀⠀⢀⡀⠀⠈⡀⠀⠀⠀⠀⣷⣀⠀⠀⠀⠈⠁⠀⠀⠠⣀⣴⡆⢻⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠙⠦⢬⡀⠀⠀⢳⠀⠀⠀⠀⣿⣿⡷⢦⣤⣀⣀⡠⠤⠤⠤⣽⣇⠀⠀⢠⡞⡁⠀⠀⠀⣀⠀⠀⠀⠸⣿⣿⠀⠀⠨⠉⠉⡍
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠂⠀⠓⠄⠀⠀⠻⢿⣿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠙⣆⢰⡟⢸⣿⣷⣄⣀⣈⠑⢂⡴⠄⠘⠿⣦⠀⠀⠀⢀⠘⢠⠄
⠀⠀⠀⠀⡀⠊⠁⣠⠔⠋⠁⠀⠀⠀⠀⠀⠘⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠘⠿⣿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠉⠀⠀⠘⠃
⠀⠀⠀⠀⠳⡀⠸⣅⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡠⠤⠤⠦⠤⣀
⠀⠀⠀⠀⠀⠈⠑⠊⠑⠒⠀⠀⢀⣨⠵⠚⠉⠉⠉⠂⢧⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠁⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⡸⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⠀⠀⢁⣴⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠉⢲⣿⣿⣿⣿⣾⠗⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣿⣿⣿⣿⣿⡟⠉⠉⡀⠁⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⡀⠀⠀⠀⣶⠞⠃⡐⠚⠻⠿⣿⡟⠛⢀⡀⠀⠈⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡜⠁⣠⠘⠋⣰⠀⡄⢘⠛⡀⢠⡁⠀⠀⠀⣤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⠇⠀⠀⠀⠀⠁⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠀⠉⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠲⠒⠒⠲⡆
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣄⣀⣸⣿⣇⣀⣀⣀⣀⣇⣀⡀
⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡤⣤⣤⣤⣤⣤⣤⣤⣄⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣻
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⡇⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢸⠀⠀⠉⢻
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⡿⠶⠶⠶⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠶⠶⠶⠾⡆
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⣇⣿⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣸⡇
⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢈⣿⣿⠷⠶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⢻⠋
⠀⠀⠀⠀⠀⣾⢸⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⢹
⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⣸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠒⢾⡁
⠀⠀⠀⠀⠀⠸⣿⣇⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣼⠃
⠀⠀⠀⠀⠀⢰⣿⣇⣀⠀⠈⡿⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣸⡇⠀⠀⣸⠂
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠷⠶⠶⠶⠖⠒⠛⠛⠛⠋⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣬⣍⣉⣁⣀⣀⣀⣠⣤⣤⣤⣤⣬⣥⣤⣤⣄⣀⣉⣀⣠⣭⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠈⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⠻⢷⣄⢸⣿⠀⠀⠀⠀⣿⠟⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣌⢻⣿⣿⣤⠶⠚⠲⣿⢾⣿⣥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣿⠟⠛⠛⢿⡀⠀⢀⡤⢿⣴⠟⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⠛⠛⠛⠛⠶⠞⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠠⠄⡴⠶⠀⠀⠀⠀⠀⡘⠄⠀⠀⠋⠛⢶⣗⠿⠇⠀⢠⣄
⠀⠀⠀⠀⢘⠂⢀⠠⣾⣷⠀⠀⠀⠦⠘⠢⡀⠀⠼⠚⢻⡶⠦⣄⠈⠛⠂⠀⠀⠀⠀⠀⠀⣀⢠⠐
⠀⠀⠀⠀⠘⠋⠉⠅⠀⢀⣶⣦⠤⠤⢤⣀⣈⣢⣀⠀⠀⠉⠀⣰⣀⠛⢁⣄⠀⠰⡀⠀⠰⠟⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣒⡶⠐⠒⠒⢢⠴⠚⠛⠉⠉⠙⠉⠉⠙⠉⠛⠉⠉⣉⢙⢻⣿⡛⠶⠦⣴⡛⠃
⠀⠀⠤⠤⠄⠒⠊⠁⠀⠀⠀⠀⠀⠃⠀⠀⢰⡤⠀⢀⣀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠈⠓⠢⣀⣀⣹⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠈⢿⠷⠆⠀⠀⠈⢁⣀⡀⠞⣀⣀⡀⢸⣶⡌⠥⠄⣠⠴⠒⠋⢉⢉⣩⠴⠤⣄⡙⠢⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢨⡄⠀⠀⠀⠛⠀⠀⣤⡄⠀⠾⠁⠜⢂⠀⠔⣊⢁⡀⠄⠒⠿⠁⠀⠀⠀⠀⢈⣷⣦⣀⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢙⣉⠀⠰⠮⠀⠀⠀⠀⣠⡶⠋⠁⠀⠈⠙⠢⣀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢺⢟⠂⣤⡀⠀⠀⠀⣄⠘⠻⠀⠀⠀⠀⢀⣴⣧⠀⢰⣾⠂⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⣀⠓⡀⢠⠿⠂⠔⠀⡛⠛⠀⠀⠀⠌⠀⠀⢠⣤⢔⡶⠛⣱⡌⠦⢈⡁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠨⠡⠄⠀⠀⠀⠀⠠⠤⠒⢙⠿⠋⠀⠀⠀⠀⠋⠚⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⡀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠀⠈⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠰⠷⠀⠁⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⡧⠀⠀⠀⠀⠈⠁



⠀⠁



⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠉⠉⢸⡇⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠶⣶⢀⣿⣖⡽⢣⡾⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡟⢰⢏⣼⣇⣾⣿⠁⢀⣿⡷⠋⣰⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣷⡄⠀⢸⡇⠘⠋⠈⠉⣾⠈⠓⠋⠙⠷⠟⢉⣴⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⠛⠆⠘⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠠⢞⣛⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠀⠀⠀⠘⠀⠀⣾⡼⣧⠀⠘⠂⠀⠀⠉⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⠟⢉⡙⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠃⣰⣿⣥⣿⡿⢀⣿⣿⣿⠟⣋⠻⣿⡟⣿⡟⢙⣿⠏⣴⣦⣿⠃⡴⣸⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢰⣿⣿⣿⡿⠁⢘⡷⢸⡏⣸⡟⢀⣿⢠⢿⡆⣼⠏⣼⣿⡿⠃⢈⣵⣿⡿⢀⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡄⢸⣿⣿⢏⣾⠀⣾⡇⠾⣁⣋⣷⠘⣃⣨⣿⣄⣹⣆⣛⣫⣼⣇⠸⠿⢋⣴⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⣌⣉⣵⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁








⣿⢿⠿⡿⣿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣛⣿⣿⣿⣟⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣯⡅
⠀⠀⠀⠀⠀⠀⡀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠁
⠀⠀⠀⠀⡠⠀⠀⠀⡙⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨⠋⠔⠈⠂
⠀⠀⠀⠀⠁⠀⢠⣠⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡐⠃⠠⣛⠚⣖⣣⠀⠁
⠀⠀⠀⠀⠀⠀⠃⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⢀⠍⠉⠩⡱⠀⡄
⠀⠀⠀⠀⠰⣀⢐⠷⠠⣤⡦⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢻⡜⠓⠄⠀⠀⠀⠀⠀⠀⡀⠉⡀⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡐⢀⠀⡈⠂⠈⢀⢠⠀⠀⠀⠀⠨⠤⠄⠁⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠈⣴⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⠓⠁⠂⠂⢺⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣌⠃⡀⠀⣈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⡛⠡⠀⠑⢢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⡄⠀⠀⠀⠸⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢤⡄⠈⠉⠀⠉⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠂⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠒⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣏⡀⠀⠘⣧⣤⢼⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⢙⠟⠞⠁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢛⣿⣴⣿⡿⣿⢚⠁⠀⠀⠀⣡⣀⣀⣠⣿⣷⣤⡤⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⡟⣋⠈⠛⠤⣼⣿⠿⣤⣶⣟⣉⣿⣿⡄⠛⠤⢿⡏⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⢂⡀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣶⠉⣿⡇⠛⠀⠀⣠⣀⠉⠀⠈⣹⠟⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣤⠛⢿⣦⣴⣾⡷⠛⡟⢻⣇⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⣿⠇⠠⣾⣗⣻⣏⣀⣀⣀⣸⣧⣀⢾⡄⠀⠀⠀⠀⣸⢾⣇⠤⢾⣿⣦⣾⣷⡺⣟⠛⠟⠻⠽⠟⠈⠋⠀⡀
⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⡿⢀⣶⣿⣿⠛⠋⠉⢛⣻⣇⣼⡏⠉⠀⢠⣄⠀⢸⡿⣶⠇⠀⠀⠉⠁⠠⢿⡦⠿⠿
⢀⣴⡿⢿⣿⣀⡾⣷⣄⢸⣷⣿⡟⠛⢿⣿⠀⠀⠀⠉⠉⠻⣷⣤⣤⠻⢿⣶⡄⠀⠏⠀⠀⠀⣴⣦⠀⠈⠀⠀⠀⣀⣀⣒⡠⠄
⠈⠻⣧⣼⣿⣿⣦⣾⣿⣾⣿⣿⣧⣀⣾⣿⡤⠂⠀⠀⠀⠀⠀⢙⣿⣤⣴⣿⣥⣤⣤⣤⣤⣤⣿⣙⣶⣦⠀⢠⡜⠉⠀⠉⠑⠂
⠀⠀⠈⠻⣿⢛⠉⢉⡿⠋⠘⠿⠟⠳⠟⠿⠁⠀⠀⠀⠀⠀⠀⠘⠿⠋⠉⠻⢁⣤⠀⠀⠀⠀⠀⠀⣭⠁⠀⢈⣶⣄⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠈⠀⣜⠀⢀⠴⠦⣀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢶⡎⢙⣷⠂⠀⡒⢶⡾⢛⣷⠤⣰⢏⣹⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⠁⠀⠂⠀⠆⠀⠀⠀⠀⠸⠿⠛⣿⣴⠋⢻⣾⣿⠚⠿⡀⠈⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⠋⠿⠿⠟⠀⠀⠱⡸⠆⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠀⠀⠀⠀⠀⠀⢹⣦⠞⣷⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⠶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠂⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠻⠄⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠇⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠛⠙⠳⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⡅⠀⠀⠀⣴⠀⠀⠐⠒⠒⢸⡅⠀⠀⠀⣽⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢸⠋⣿⠀⣀⠀⠀⠀⠀⡷⠀⠀⠀⠐⠃⠀⠀⠀⢸⠆⠀⠀⠀⠀⣤⠙⠶⠴⠞⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠈⠓⠋⠘⣹⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡆⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⡤⠖⠚⠋⠉⠉⠉⠉⠙⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠁⠀⣀⡤⢶⠖⠒⠒⢲⡶⢤⣀⠀⠈⠙⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡆⠀⠀⠀⠋⠀⣠⠶⢋⣁⣤⠾⣡⠴⠖⠋⠀⠀⠈⠙⠦⣄⠉⠛⠀⠀⠀⢰⠖⢒⡒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⢹⡆⡇⠀⠀⠀⢀⡼⢡⠞⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⠈⢷⡀⠀⠀⠀⢸⢰⡏⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⡇⡇⠀⠀⢀⡾⠶⠋⠀⠀⢀⡖⢋⣁⣀⣀⠀⠀⠘⠧⣄⣈⣳⠀⢳⡀⠀⠀⢸⢸⡇⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⡇⡇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠳⣆⠀⠈⠉⠀⣀⠈⣧⠀⠀⢸⢸⡇⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⡇⡇⠀⠀⣿⠀⠀⠀⠀⣠⠴⠶⠶⠶⠤⣄⣠⠴⠞⠀⠀⠀⠘⡏⠙⣿⠀⠀⢸⢸⡇⣿⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠇⣿⢸⡇⢧⠀⠀⢿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡿⠀⠀⡼⢸⡇⣿⠸⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠰⣇⢀⡷⢸⡇⠀⠘⣆⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣰⠃⠀⢸⡇⢾⡀⣸⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⣉⡄⠛⠀⠀⠀⠘⣆⠀⠀⠈⠳⠦⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣰⠋⠀⠀⠀⠳⢤⣉⣡⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠈⠙⠲⢤⣄⣀⣈⣧⣀⣠⡤⠖⠋⠁⠀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠉⠁⠀⠀⢀⣀⡤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠈⢿⣿⣿⣿⠃⣰⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣇⠘⣿⢿⠏⢠⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣈⠙⠛⠿⣿⣆⠘⡟⢀⣿⡿⠟⠛⢉⣠
⠀⠀⠀⠀⠀⣸⣿⣿⣶⣦⣄⡈⠀⠀⠈⣁⣤⣶⣿⡟⠋⣠⡆
⠀⠀⠀⠀⠀⢸⡿⠿⠛⢉⣁⡤⠀⡄⢠⣄⡉⠛⠻⢟⣢⠀⠁
⠀⠀⠀⠀⠀⠀⢤⢶⣾⣿⣿⠃⣰⣷⡀⢻⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠇⢰⣿⣿⣧⠈⢿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠿⠿⠿⠿⠆⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡸⣿⣿⣿⣿⡟⣰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠜⠀⠀⠀⠀⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠹⣿⣿⡿⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠀⠀⠀⢀⠌⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⣠⣙⡻⢿⣿⣿⣧⢻⣿⢡⣿⣿⡿⠿⣛⣡⡀⠀⠀⠀⠀⠀⠀⠀⠠⠕⠠⡀⠀⠀⠀⡁⠀⡠⠀⠀⠀⠀⠄⠨⠄
⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣭⣛⠂⠃⢛⣫⣥⣶⣿⣿⢟⣣⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⡔⠒⢄⠀⠀⠈⠀⠀⣠⠔⠐
⠀⠀⠀⠀⠀⣿⣿⣿⠿⢛⣫⣥⢆⡄⢮⣍⣛⠿⢿⣿⣶⡝⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠠⠀⠑⠤⠊⠒⠄⠀⠀⠀⠉⠒⠠
⠀⠀⠀⠀⠀⠉⣭⣶⣾⣿⣿⡏⣼⣿⡘⣿⣿⣿⣶⣮⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⡁⠀⠑⠀⠀⠀⠀⠑⢠
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⣸⣿⣿⣷⡸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢰⣿⣿⣿⣿⣧⠹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢠⡀⠀⠀⠀⢀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⣶⣶⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⠉⠉⠉⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠟⢯⣭⣍⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢉⣥⣶⠿⢧⣿⣯⣠⣶⣿⣯⣿⣿⣟⠋⣤⡀⠙⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠈⠁⢠⣤⣿⣿⣿⣿⣿⣿⣿⡎⠋⠉⠁⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣥⠾⣯⣦⣤⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠉⠉⠉⣄⠀⠦⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣬⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠈⠙⢻⣿⣿⣿⣿⣿⣷⣤⣴⣦⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣴⡟⣹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⢀⢀⣼⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⣰⣿⣿⣧⡟⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣼⣿⣿⢻⡇⠀⠀⠀⠈⣿⣿⢿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠇⠀⠁⠀⠀⠀⠀⠙⠃⠸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⠶⣶⣴⠶⢾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠀⠀⢿⣿⠀⠀⠙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠉⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣀⣀⣀⠀⣀⣀⣠⡤⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠉⠉⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠴⠧⠤⠴⠤⠤⠤⠤⠤⠤⠼⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⣠⣞⣁⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠋
⡏⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡷
⠀⣭⠽⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⡇⢀
⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠤⠤⢤⠤⠤⡤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡀⠀⠀⢀⣀⡴⠃

⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣄⣼⠟⠉⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠈⠻⣄⠀⣠⡾⠟⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠰⣦⡀⠀⢹⡟⠋⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣟⠳⠞⢁⣀⣤⡶⠟⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣿⠉⣽⠿⠛⠋⠁⠀⠀⢀⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣶⣿⣤⣤⣤⣤⡶⠞⠋⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠠⣾⡉⠁⠀⢀⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠺⠷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠈⠉⠛⠻⠶⢦⣤⣀⡀⠀⣰⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠀⠀⢰⠶⢲⢰⡒⠖⣦⣴⡤⡖⣦⣶⢴⢰⣶⠀⣶⡒⢦⠂⠀⠐⡖⠒⣆⡖⢲⡖⢴⠒⡤⣶⡆⡖⢠⣦⣰⡆⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠚⠀⠀⠀⠂⡀⠄⠀⠀⠰⢁⠒⠀⢀⠂⡠⠀⡀⡀⡄⠄⠄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣶⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠛⣿⣧⡀⠂⡀⠃⣴⡆⠀⡁⠀⡦⠀⣦⡴⠀⢦⡤⠀⠰⠴⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢶⢶⣶⣾⢿⣷⣾⣷⡾⠿⣶⡶⡷⢶⡶⢶⡾⣷⣶⣾⣷⡶⣶⣾⣿
⣿⣿⡇⠐⠀⠈⠁⠰⠟⢀⠘⢃⠰⠆⠐⠀⠀⠂⠀⠀⣿⣷⠆⠰⣤⠀⠶⢀⣽⣏⠐⠖⢀⣴⠀⢶⡆⠀⠀⠸⠀⠐⠐⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣶⣶⣶⣷⣶⣾⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⢿⣿⣿⣇⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⢸
⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⠒⠒⠛⢻⠀⢸
⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⡇⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠛⢻⣿⣿⣿⡟⠛⠛⢻⣿⢻⣿⣿⣿⣿⣿⠟⡟⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⢿⣶⣶⡆⢸⣷⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠸⠿⠷⠶⠶⠶⠶⠶⠶⠿⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⣀⣀⣠⢾⡉⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⢀⢠⣠⠞⠋
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⠆⠀⠀⠀⡰⠚⠃⠀⠀⠠⡏⠀⠀⠀⢠⡠⠁⠄
⠀⠀⠀⠀⠀⠀⣇⡀⠀⢀⡴⠓⠀⠀⣸⠁⠀⠀⠀⠄⠉⣇⠀⢀⡰⠾⠏⠀⠐
⠀⠀⠀⠀⠀⣠⡿⠁⢀⡾⠀⠀⠀⠀⣁⠀⠀⠀⠀⠼⡶⢿⡴⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠠⢿⡇⠀⣸⠇⠀⠀⠀⠀⡆⠤⠀⠀⠀⠠⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀
⠀⠀⠀⠀⠀⠀⢷⣰⠋⠀⠠⠈⢱⡄⣻⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯
⠀⠀⠀⠀⠀⠀⡈⣿⠀⠀⠀⠀⠁⠁⠙⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠄⡀⢄⠀⢠⣴⠏⠰
⠀⠀⠀⠀⠀⠀⣧⣸⡆⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⢸⡇⠀⠀⣾⢄⠁⠀⢶⡴⢚⠉
⠀⠀⠀⠀⠂⠀⠉⠀⢻⡄⠀⠠⣄⠠⠄⢸⠁⠀⠀⣼⠟⠛⠛⠉⢾⣶⠀⠠⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡴⠈⠛⠀⠀⢸⡀⢼⣹⡿⠀⠀⠘⠀⠈⠟⠣⣄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠌⢷⡄⠤⠈⠀⠀⢃⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⠔⠀⠀⠘⢧⣾⡁
⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠈⣿⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠀⢸⣧⠀⠀⢀⠀⠐⡟⠑⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⢤⠈⣿⡄⠀⠀⡐⠛⠻⠀⠀⠆⠀⠀⠀⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣦⣼⣧⠀⠀⠁⢠⡆⠀⠀⠀⠀⠀⢂⡀⠀⣆⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢀⣾⠃⠀⠀⠀⠀⠀⠛⠁⠀⡏⠀⠐⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⣿⣄⣼⡟⠀⠘⠂⡀⠀⠀⠀⠀⠁⢹⠀⠀⠂⢀⠀⠀⣄⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠛⢿⣿⡄⠀⠀⠀⠙⢄⡀⢠⠀⠐⠺⠇⢀⠀⠈⡁⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢣⡄⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠸⣯⡁⠀⣢⠀⠀⠀⠀⠀⣜⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⠀⡆⠀⠹⣿⣦⡀⠀⠀⠈⢧⣴⠃⠀⣐⠀⠀⠰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠘⠁⠀⠀⠈⠻⣿⣦⡀⠀⠈⢿⠀⢰⡏⠀⢮⡼⠃
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⠂⠉⠀⠀⠀⠉⢻⣿⣦⡀⢸⡄⠀⠳⣤⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠠⠀⠛⠓⠞⠛⠛⠻⣿⣿⣷⡀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋

⠀⠀⠀⣀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠄
⠀⠀⠀⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢊⡄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠌⢀⠸⣿⣿⣿⣿⣟⣛⣛⢛⣛⣛⡛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⣿⡿⣿⠛⠛⢻⠟⠛⠛
⠀⠀⠀⢠⠜⢳⣿⣿⣿⢿⡇⣷⣟⣷⡤⣺⣁⣈⠲⠊⠀⠀⠙⠶⢁⣀⣠⣶⣄⡀⠀⠑⠓⣡⣤⠈⠛⠁⣄⠀⢹⡇⣿⠄⠀⢸
⠀⠀⠀⠈⠣⠈⣿⡿⣿⣽⡇⣹⠍⣼⠉⠻⠉⣋⣻⣿⡇⢸⡏⠁⢸⡏⠽⡿⢿⡇⠐⠀⠀⢸⣿⠀⠀⠀⣿⠀⢸⡇⣿⠀⡀⢸⡀⢦⡄
⠀⠀⠀⠀⠀⠀⣿⡇⣿⢻⡇⣽⠀⠘⠀⠲⣴⣿⠙⣿⡅⠼⠃⠀⣿⢁⠀⣁⣈⠣⣧⢀⣀⡘⣿⠀⠀⢰⡿⠀⢸⡇⣿⠠⣷⢼⣿⢻⡇
⠀⠀⠀⠈⠀⠀⢿⡇⡟⢻⡇⣸⠀⠀⢤⡵⣿⡿⣞⢿⡇⠀⠀⢠⡶⠤⠤⠾⠛⣷⠩⠀⣿⣇⣿⣀⣀⣘⣯⡀⣼⣧⣿⡲⢻⣿⡅⣼⡶
⠀⠀⠀⠀⠀⠀⠸⢇⠇⣸⣇⡨⢀⣀⠫⣾⠈⣠⣧⣬⡀⠘⠛⠛⠓⠒⠒⠛⠛⠓⠒⠒⠒⢒⡶⠤⢬⢬⣏⡉⣿⡏⣿⠋⡚⢻⠢⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣆⣬⣿⣿⢶⣿⡆⢰⡄⣻⣿⣟⣹⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⡼⠿⣿⣿⠄⠀⢠⡿⠉⣻⡗⣿⠀⣧⣼⢀⣺⣿⠄
⠀⠀⠀⣠⣜⣿⣧⠈⣿⡧⣯⡝⠿⣧⣼⣧⡝⢿⠅⣿⣧⡛⠛⠛⠛⣿⠀⠀⠀⠀⠀⣿⠃⠿⣟⠀⠈⠉⠈⠈⣿⣏⣟⣀⣯⣼⣯⣉⠛
⠀⠀⠀⣿⠟⠉⠁⢾⢿⡇⠈⠙⣷⢦⣯⡛⣿⣿⣮⡛⣽⣿⣞⣷⠀⠛⠈⠀⠁⠀⣰⣿⣿⣶⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣷⣸⣿⣿⣿
⠀⠀⠀⡟⠀⠘⣶⠿⣶⡇⢄⣼⡙⠺⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣴⣿⣿⡿⢿⣿⣿⣿⡆⠀⠰⣿⡿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠐⠞⣽⣧⣿⣷⣿⣿⣧⣠⣽⠟⣿⣿⣿⣿⣿⣿⣿⣿⠿⢶⣶⣶⣶⣿⣿⡋⠀⠀⣿⣿⣿⣿⣶⣶⣿⣷⣦⣬⡿⣿⣿⣿⣿
⠀⠀⠀⠃⠘⣛⢿⣿⣿⣿⣿⣿⣿⣿⣦⣬⠻⢟⣿⣿⣦⣹⣿⣿⣿⣼⣿⣿⣟⣽⣿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⢿
⠀⠀⠀⣅⠐⠈⠃⡙⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣅⣀⣈⣛⣿⣿⣧⣤⣿⣿⡛⠉⢙⣭⣻⣿⣿⣿⣿⣿⣧⢳⣦⣀
⠀⠀⠀⣾⣀⡤⠊⢙⡛⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢾⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣦⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠾⡿⢿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⠟⠛⣷⣾⣏⢻⣿⣿⣿⣿⣭⣿⣿
⠀⠀⠀⠄⠤⠿⠿⠿⠿⠿⠟⠻⠛⣻⡿⠿⢻⠻⣿⣿⣤⣄⣵⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣦⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠏⡭⠉⠀⠉⢿⡿⣿⢿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠐⢶⠖⠒⠒⠒⠒⠀⠀⠀⠀⠘⠛⠛⠃⠙⠘⠓⠂⢆⠐⢿⣿⣿⣏⠳⢤⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠻⣍⢿⣿⣿⣷⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⠟⠙⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠙⡎⢇⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠘⠮⣷⡄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⠀⠀⠸⠀⠀⠈⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⣤⣤⠀⠀⣸⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠄⠈⠁⣀⣼⠃⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡃⣷⣼⠀⠀⢸⣭⡃⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢷⣷⢧⣸⠑⢀⡝⢸⠏⠛⠒⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⣹⢿⠀⣽⡄⣾⠄⢸⣛⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠘⣿⡸⠀⠈⢳⡟⠀⠸⡺⡐⣆⠀⣀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠉⠀⠀⠀⠀⠉⠃⠀⠀⠈⠁⠀⠀⠓⠃⣛⠠⢈⡻⠦⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠘⠠⡦⢰⡀⠀⣀⣤⠀⡀⠀⡀⠀⠀⡀⠀⠀⠙⠛⠛⠁⠀⠀⢀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣀⡀⠀⠀⠀⠀⠀⣏⠀⠀⣇⠀⣿⢸⠷⢿⠀⣿⡄⠚⡟⠂⣴⣒⠈⠺⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠈⡂⡛⣧⠀⢀⡀⠀⣀⡉⢉⡀⠈⠁⠉⠈⠀⠈⠀⠁⠋⠀⠁⠀⠛⠐⠀⠙⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡶⠎⠀⠸⠤⠘⠛⠇⠿⢧⠸⠳⡿⠰⡅⣤⢸⠇⡷⣤⡆⣖⢉⡀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣠⣄⣠⢠⣠⡄⣀⡀⠀⠀⢀⡀⠀⣀⠀⠈⠀⠈⠉⢃⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠈⠃⠈⠉⠃⠾⠀⠀⠀⠸⠻⠜⠿⡁⣟⠁⡷⣼⠈⠘⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠑⠁⠈⠯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂⠐⠒⠒⣶⡒⠒⣤⠤⠤⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡏⠀⠀⢱⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⠃⠀⠀⠸⡆⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀⣇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⣸⠀⠀⠀⠀⢻⠀⠀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠐⠿⠂⠉⣟⠀⠀⠀⠀⢸⡅⠀⠨⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣁⠤⠐⠒⠐⠒⠂⠄⠑⠒⠀⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡡⠔⠉⠀⣀⠤⠀⠒⠒⠀⠀⠀⠀⠈⠐⠢⢄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢡⠊⠀⠀⡠⠊⠀⠀⠀⠀⢀⢌⠒⢄⢀⡀⢄⠀⠀⠑⡄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠰⢁⠄⠀⠀⠀⡀⠀⢀⡠⡔⡠⠂⠀⠈⣮⠑⢄⠑⡄⠀⠘⡄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⠁⠀⢀⠔⠉⡠⠒⢁⡼⠚⠀⠀⠀⠀⠉⠀⠈⢢⠘⡄⠀⠰⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡐⠀⠀⠠⠁⢀⣬⣤⣔⠋⠀⠀⠀⠀⠀⣰⠾⠶⠆⠀⢃⠘⡀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠇⠀⢠⠁⢤⣎⣀⡀⠈⠓⠀⠀⠀⠀⠞⠁⣀⡤⢶⠓⠉⠀⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠂⠈⢆⡻⣷⢦⡀⠀⠀⠀⢠⠺⠿⠡⠊⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠐⠠⡈⠉⠈⠁⠀⠄⠀⠀⠀⠀⡠⠊⢉⠆⠇⠸⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⡇⠀⠁⠒⠂⠀⠀⠀⡐⠁⠀⠀⠀⠀⠈⠂⠁⢀⡆⠀⠀⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠀⠁⡟⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠃⡀⠀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡄⠀⢀⠘⢄⠀⠀⠀⠤⠴⠒⠔⡒⠤⠀⠀⠀⡰⠁⠀⠃⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠐⠀⠈⠢⡀⠀⠀⠈⠐⠒⠀⠀⠀⢠⠊⠀⠄⠀⡆⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢂⠀⡄⠀⡀⠈⠂⢄⠀⠀⠀⠀⢀⠔⠁⢀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠀⢁⠀⠃⠀⠃⢠⠈⠒⠒⠈⢉⢸⠀⢸⠀⣰⠀⢠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡇⠘⠀⢀⠀⠸⠀⢠⠀⠀⠀⢸⠈⠀⢸⠀⠙⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠁⠃⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢆⣀⣀⣠⠀⢇⣀⡀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⢀⡠⠋⠀⠀⠀⠀⠀⠈⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⡅⢰⠀⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠊⠁⠀⠀⢹⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡇⢸⠀⠀⠀⠀⠈⠁⠒⡄⠀⡔⠉⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⠉⠉⠙⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣀⣄⣀⣀⡤⠶⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣠⠖⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⢉⣙⠛⠉⠉⠙⠛⠛⡛⠛⠛⢛⢛⣛⠛⠛⣛⠶
⡞⠓⠒⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⡇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⢸⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠸⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⢸
⠀⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡦⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣇⠜
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠙⠋⠉⠉⠙⠉⠋⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣀⣀⣀⣤⠴⠃

⠀⠀⠀⠀⠀⠀⣰⢒⠄⠍⢭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠀⡠⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠐⢚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⢀⠀⢸⠄
⠀⠀⠀⠀⠀⢀⡤⢬⡈⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠢⠤⡥⢅
⠀⠀⠀⠀⠀⠀⠓⠠⠈⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⢀⡔⠀⡰⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡵⡤⠀⠀⠀⢀⡀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⢰⢉⠀⡰⠁⠀⠐
⠀⠀⠀⡐⢀⡀⠳⣄⡠⠀⢀⣀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠀⠈⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢇⠈⠎⠠⠃⡟⢱⠀⡇
⠀⠀⢠⡧⠋⠀⠀⠀⠀⠛⠥⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠘⠓⠒⠢⣤⢂⠇⠀⡜⠀⢄
⠀⠀⠸⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠰⠀⠀⢀⠝⢁⠎⠀⢰⠃⠀⢸
⠀⠀⠀⠑⠀⠀⡰⠃⠀⠀⠀⠔⣋⡡⠆⠘⣆⠀⠀⠀⠀⠀⠀⠄⠀⠉⢉⡉⠁⡘⠀⢀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠁⠀⠀⠀⠀⢰⠄⢀⠎⠂
⠀⢀⡤⠔⠀⢀⠇⠀⠀⠀⠀⠈⠀⢠⠀⠀⡻⠀⠰⠦⠀⡄⠀⢇⠀⠰⠤⠆⠈⠉⠉⠉⠀⠀⢀⠔⠀⠀⣾⠡⠄⠂⠈⠲⠤⡄⠀⠀⢘
⠀⠣⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⠔⠋⠀⠉⠀⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠘⢄⣀⣠⠊⠀⣇⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢒⣠⠆⠀⡆⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠄⠀⠘⢄⠀⡠⠄⠒⠉⠀⠀⠀⣰⠀⠈

⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⢀⠊⠀⠚⣃⣁⣀⣀⠀⠀⠀⠀⡀⠃⠈⠛⠉⠀⠀⠀⠀⠀⠀⢀⠊⠀⠙⢋⣁⠀⠀⠀⠀⠀⠀⡐⠁⢈⣿⣉
⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⡄⠀⠀⠀⠀⢠⣴⣶⣤⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⡀
⠀⠀⠀⢨⣿⣿⣿⡍⠛⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠨⢿⣿⠿⠰⠾⠷⠆⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣠⣄⡠⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣀⠄⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠤
⠀⠀⠀⠠⠁⠀⠉⢁⣤⣤⡀⠀⠀⠀⠀⠈⠀⠈⣉⣤⣤⣄⠀⠀⠀⠀⠠⠈⠀⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣭⣤⣄
⠀⠀⠀⠀⢠⣤⣤⣼⣿⠿⠄⠀⠀⠀⢀⣤⣤⣄⣸⣿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠙⠿⣿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇


⠀⠀⠀⠀⣠⠀⣤⡦⠔⠀⠀⠀⠀⠀⠀⢀⡄⠠⣴⠤⠂⠀⠀⠀⠀⠀⠀⣀⠀⣤⡦⠔⠀⠀⠀⠀⠀⠀⢀⡄⠠⣴⠤⠒
⠀⠀⠀⠐⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⣴⠞⠁⠀⠀⠀⠀⠐⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠸⣿⣿⡿⢃⠈⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠑⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠿⠿⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⡿

⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⢀⠊⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠐⠁⣈⡙⣉⠀⠀⠀⠀⠀⠀⢀⠊⢀⣙⡋⢥⣠⠀⠀⠀⠀⠀⡀⠃⠈⢛⠉
⠀⠀⠀⠀⠀⣀⣴⣄⣀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠉⣀⡱⠈⠐⠂⠀⠀⠀⠀⠀⠀⣴⣌⣴⡄
⠀⠀⠀⠀⣻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢓⣾⣿⣷⡶⠇⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠐⠄
⠀⣠⣍⡀⠔⠰⡶⢦⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⢀⠀⠁⠀⠂⢤
⠀⠀⠠⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⠀⠸⠇⠀⠴⠂⠀⠀⠀⠀⡤⠀⠙
⠐⠒⠲⠒⠲⠶⠶⠶⠠⠤⠀⠴⠖⠀⠚⠯⠄⠀⠨⠍⠀⠈⢥
⠀⠀⠀⡪⠓⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠈⠀⠀⠠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⠒⠂⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⢦⠀⠀⠀⠀⠀⡴⠄⠀⠀⣠⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⣰⣾⣁⣀⣀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡰⠄⠐⠀⠀⠀⠀⢀⣼⠟⠉⠉⠉⡁⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣀⡤⠤⠴⠶⠟⠓⠒⠋⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠞⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠇⠀⠀⠀⢀⣀⡿⠴⠛⠙⠒⠤⠒⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠂
⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⣰⣿⠷⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡄⠀⠰⠀⠀⠀⠀⣰⠀⣠⠟
⠀⠀⠀⠀⠀⢯⣄⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠓⠀⠀⠀⠀⠀⣴⣷⠞⠉
⠀⠀⠀⠀⢠⣾⢋⣀⣴⣦⣤⠤⠤⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⣰⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡠⢤⡄
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠙⠒⠒⠒⠒⠀⠀⠂
⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣴⣋⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣝⣭⣍⣹⣭⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄⢈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡿⠀⠀⢹⡇
⠀⠀⠀⠀⠀⢀⣴⣤⣾⣿⣷⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢀⡀⠀⡈⠀⠀⠀⠀⠀⠀⣰⠛⠛⢷⣤
⠀⠀⠀⠀⣰⡏⠘⣿⠁⠈⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⡔⢿⡟⢡⡏⠀⢀⠀⠀⠀⠀⠋⡀⠀⣸⠟
⠀⠀⠀⣴⣿⡗⣸⣿⢸⠀⠀⠂⢹⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠐⣇⢸⣧⣿⠁⢴⠈⢁⠀⠀⢀⣠⡷⠆⣱⣄
⠀⠀⣼⣿⣿⡇⢾⣿⣏⠆⡀⠀⣾⣿⣽⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧⡀⢻⣾⣿⣯⣀⡧⠃⠞⠇⠰⠿⠿⣷⣞⣽⣍⣰⡀
⠀⢠⣿⣿⣿⣇⠈⢿⢿⠀⠼⢦⣸⣿⢟⢼⡀⠀⠀⡄⠀⠀⣀⣾⡝⣬⣾⠀⠻⣿⠿⠉⠃⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣥
⠀⢸⣿⡏⢿⣿⡀⠨⢿⣀⣠⣤⣾⣿⡿⣼⣀⡀⠀⣧⣴⣾⣭⣭⣽⣧⣼⣾⣀⣀⣰⣶⡖⣦⣀⣀⣀⣀⡀⠀⠀⠀⢹⣷⣿
⠀⢸⣿⢁⣰⣿⣿⣅⠉⠀⠀⠀⠘⠻⢿⡖⠸⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣽⣿⣿⣿⣉⠝⠉⡛⣂⢹⣿⠿⣿⣿
⠀⠘⣯⢽⣟⣽⣿⠁⠈⠙⠁⠀⠀⠀⠀⠈⠀⠀⠙⢿⡟⠉⠉⣹⣭⣭⠟⢿⣿⣿⡧⣿⣿⡟⢋⣹⣿⠋⡀⢿⣟⣀⣷⣿⡃
⠀⠀⢰⡛⢿⣿⣿⣶⡶⣄⣤⢀⣠⣿⣮⣠⣀⣠⣶⢾⣿⣷⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠷⣾⣿⣶⣮⣷⣜⣿⣿⡿⠿⠁
⠀⠀⠋⠷⠀⠼⠿⠿⠏⠉⠁⠉⠉⠉⠈⠀⠈⠉⠉⠻⢿⠿⠶⠶⠾⠿⠿⠏⠀⠉⠁
⠀⠀⠀⠀⠐⠒⠶⠒⠶⠿⠚⡓⢒⢶⠖⠒⣲⣒⣲⣖⣒⣒⣲⣒⠲⣲⣖⣖⠒⣶⣒⣒⣶⣖⣒⣲⣒⣒⣒⣒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⣤⣄⠘⠉⠀⠐⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠐⠃⠐⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⣯⡀⠀⢠⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⢸⣿⣿⢯⣤⣼⣿⣿⣷⣿⣽⣿⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣴⡿⠟⣁⣸⡟⢿⣿⡿⠉⠙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣁⣀⠽⠄⢙⣿⣿⣷⠞⠃⠀⣤⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡟⣽⠓⠓⣻⣯⠼⠃⠈⠘⠋⢛⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⡿⠂⠔⠈⡞⢿⣿⣿⠃⠀⠀⠀⢀⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠞⠀⠀⠙⠁⠀⠀⠀⠀⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠔⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⠒⢀⣐⠀⠂⠈⠑⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠐⠒⠂⠉⠖⠀⠀⢄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣷⣤⣤⡠⠤⠄⠀⠀⠀⠁⠀⠑⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠏⠉⠈⠯⠩⠉⠛⠀⠀⠐⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠲⠖⠐⠶⠶⠶⠂⠶⠶⠆⠰⠶⠶⠶⠶⠶⠶⠀⠶⠶⠶⠶⠶⠆⠰⠶⠖⠖⠶⠶⠲⠦⠰⠶⠰⠖⠲⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠒⠒⠸⠒⠒⠒⠐⠚⠃⠘⠒⠒⠚⠂⠐⠒⠒⠃⠒⠒⠓⠒⠂⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠢⢄⠀⠀⠀⢀⣠⠄⠒⠒⠒⠒⠤⣀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠠⠀⠀⠢⠀⢁⠀⡆⠀⠀⠄⢸⠀⠢
⠀⠀⠀⠀⠀⠀⠁⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⣀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⠀⢀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡀⠈⠁⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠐
⠀⠀⠒⠋⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠔⠋⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣒⣒⡒⡒⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠚⠒⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠠⠁⠂⠠
⠀⠀⠀⠀⠀⠀⢀⠔⡉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠁⠀⠛⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠂
⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠄⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠰⢀⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠔⠀⠀⠀⠀⠀⠀⠂⠉⠒⠂⠀⠠⠀⠐⠄⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠂⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠐⢤⣄⡁⠀⠘⣄⣀⡤⠀⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠔⠀⠀⠀⠀⠂⠀⠀⠐⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠖⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⣁⣤⣄⡈⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣁⣤⡶⠟⠋⠉⠉⠛⠻⢶⣤⣈⠙⠻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⢉⣠⣴⠶⠟⠋⣡⣤⡀⠀⠀⠀⠀⣠⣄⡈⠙⠻⢶⣤⣄⡉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⣾⣛⠉⠀⠀⠀⠐⣿⣭⡿⠀⠀⠀⠸⣯⣽⡇⠀⠀⠀⠀⠉⣛⣷⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠙⠻⢶⣤⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣤⡶⠟⠋⠉⣿⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⠿⠷⠶⠶⠶⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠶⠶⠶⠾⠿⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡶⠶⣦⠀⣶⠀⢰⣶⠀⣴⠶⣶⡀⢰⣦⠀⣶⠀⣰⡶⢶⣆⠀⣶⠶⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣉⠀⣿⡷⢾⣿⠀⣿⣤⣼⡇⢸⡿⣷⣿⠀⣿⡇⠈⣉⠀⣿⠶⠶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠷⠶⠟⠀⠿⠀⠸⠿⠐⠿⠀⠸⠇⠸⠇⠘⠿⠀⠹⠷⠾⠋⠀⠿⠶⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⢶⣶⢶⣶⢶⣶⠶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⣠⣤⡀⠀⠈⠿⠾⠏⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⢶⣤⣀⡀⠀⠀⢸⣏⣻⡇⠀⢸⡇⠀⠸⣯⣽⡇⠀⠀⢀⣀⣤⡾⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣈⠉⠛⠷⣦⣄⡉⠉⠀⠀⢸⡇⠀⠀⠈⢁⣠⣴⠾⠛⢉⣁⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡉⠛⠷⣦⣤⣸⣇⣤⣶⠾⠛⢉⣠⣴⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡈⠙⠋⢁⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠚⢛⠟⢛⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⢀⣤⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣄
⢠⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠾⠶⠶⠶⠶⠿⠿⠷⠾⠿⠾⠾⠷⢾⣇⠙⠳⣤⡀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡈⠻⣦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣦⡌⠛⢷⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡄⠹⣦⣀
⣿⡇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠙⢦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡿
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠋
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣴⠟⠁
⠀⠻⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⠶⢶⣶⠶⠶⠶⠶⠶⢶⡾⡿⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠠⣀⠢⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⡹⣆⠀⣿⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠈⠳⣷⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⢶⣄⢇⣠⠶⠃⡠⠆⠀⠀⠀⠀⢝⢿⣆⣿⠀⡠⠀⠀⠀⣼⣿⠰⢀⠎⢀⠔⠀⠀⠹⣷⣤⠂⣠⡴⠋
⠀⠀⠀⢀⠙⢿⣿⢋⡤⡛⠀⢠⠏⠀⠀⠀⠀⠑⢿⣿⡞⠁⠀⠀⠀⠘⣿⣼⡏⡴⠁⠀⠀⠀⢧⢹⣿⣷⠏
⠀⠀⠀⠀⠉⢲⣿⡿⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠘⣿⠧⠀⠀⠀⠀⣗⣏⣿⣶⢐⣀⣀⣀⣀⢘⣈⣿⡏

⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⣤⣤⠄⣠⣄⠀⡄⠀⣄⣠⣤⣤⠀⠀⣄⠀⠀⣠⣀⣤⣄⢀⡄⠀⢠⣠⣤⣄⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⣸⠇⢸⣇⣧⢠⡏⣿⠀⠀⠀⠀⢻⡄⣰⢿⡏⠀⢹⣾⡇⠀⢸⣿⡇⢘⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿⠶⠶⣿⣿⣯⡀⣿⠶⠄⠀⠀⠀⢻⡏⠸⣇⠀⢸⡟⣷⠀⣾⢹⣷⠛⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⠀⠛⠛⠈⠓⠙⠛⠓⠀⠀⠀⠘⠃⠀⠙⠶⠋⠀⠙⠛⠋⠘⠋⠳⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢦⣄⡄⠀⡄⢠⣤⡄⢠⡀⠀⡄⢀⣤⣤⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠛⣇⠀⣇⣾⠀⣿⢸⣷⢠⣧⡿⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣄⣿⠶⣿⣿⠶⣾⢸⡟⣿⡏⣷⠀⢀⣸⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠛⠀⠛⠛⠀⠛⠘⠃⠘⠃⠈⠛⠛⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠙⢧⣄⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣧⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⣿⡿⠻⣿⡟⢻⡟⠛⠛⢛⣿⣿⣿⠛⢿⣿⡟⢻⡟⠛⠛⠛⣿⠛⠛⠛⢻⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⢹⠇⡄⢿⠀⣿⡇⠸⠿⢿⣿⣿⣿⠀⡈⢿⡃⢸⡇⠘⠿⢿⣿⠀⠻⠿⣿⡇⢸⣿⡆⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠈⢰⣷⠈⢰⣿⡇⢸⣿⢿⣿⣿⣿⠀⣿⣄⠁⢸⡇⠸⡿⣿⣿⠀⢿⢿⢿⡇⠸⡿⠃⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣷⣶⣶⣶⣿⣿⣿⣶⣿⣿⣶⣿⣷⣶⣶⣶⣿⣶⣶⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⢋⣉⡉⢻⣿⠙⣿⣿⡏⢻⣿⡿⠉⢻⣿⣿⠉⢻⣿⡏⢹⡿⠋⣉⡉⢻⣿⠉⣉⣉⣹⡟⢋⣉⡙⢿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⣿⣾⣿⠀⣛⣛⠁⣻⣿⠃⣾⡈⣿⣿⠀⣆⠹⡇⢸⡇⢸⣿⠿⠾⣿⠀⣛⣛⣻⣧⣈⡛⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣧⡘⠿⠟⣩⣿⠀⣿⣿⠇⣹⠇⢠⣤⣤⠘⣿⠀⣿⣦⠀⢸⣧⡘⠿⠟⢀⣿⠀⠿⠿⢿⣏⠹⠿⠃⣸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡅⢉⣀⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⠋⠀⠀⠈⠙⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⡀⠀⡆⠀⢸⠃⢠⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣁⣀⡽⠃⠐⠃⠀⠎⢠⣿⣿⣻⣤⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⣄⠀⣸⠿⠋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡟⣡⣀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢄⠀⠀⠀⠾⠿⣿⠛⣡⣶⡊⠁⣀⣀⣀⠀⠀⠀⠀⠐⠀⠀⢿⢿⣞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠽⠓⠈⠙⠃⣿⣘⣛⡛⠛⠉⠛⠛⠿⣿⣷⣾⢧⣀⡀⠀⠀⡀⠀⠀⠁⠢⢄⠀⠀⠀⠀⣀⡐
⠀⠈⢜⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⢀⣤⣬⣳⣀⣿⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢐⡽⠁
⠀⠀⠈⠢⣀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠑⠁⡜⢻⡾⡿⣄⠀⠀⢀⡠⠤⢤⡀⠀⣄⣀⠔⠀⠀⢈⣫
⠀⠀⠀⠀⠈⠳⡃⠀⠀⠀⠀⣶⠀⠀⠀⣀⡀⠀⣀⣈⣖⡁⣁⡈⡅⠈⣿⣶⡃⡠⠔⠀⢳⠉⠠⠈⠣⡘⢿⠀⠀⡄⢠⠋
⠀⠀⠀⠀⠀⠀⠫⡀⢀⠆⠀⣹⡦⠂⠁⣀⢈⡆⠀⠀⠀⢹⠁⠠⡈⠳⠏⢀⡀⠀⠀⠀⠀⢃⠀⠀⠀⠉⢿⣧⣀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⡴⠛⠀⠀⠀⢊⠟⠀⠋⠑⣢⠚⠢⠄⡀⠀⣎⠣⠀⠀⡄⠀⠀⠈⢦⠀⠀⠀⠀⠙⠾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⣰⠏⠀⠀⢀⠞⠀⠀⠀⡀⠉⠋⠉⢣⡀⠀⠸⡄⠀⠀⠈⠓⣄⡀⠀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢑⣦⣴⡾⠋⠀⠀⣠⡟⠀⠀⠀⡸⠉⢁⢿⡂⠉⣷⡄⠀⠘⢦⡄⠀⠀⠈⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⣤⣤⠾⢽⣁⡠⠔⠚⠒⠊⠁⠀⠈⠉⠀⠉⠒⠀⠒⠉⠙⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣒⣒⣒⣒⣒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠈⠉⠉⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠼⠦⠤⠤⠤⠤⠤⠤⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠲⠶⠶⠶⠶⢤
⠀⠀⠀⢠⡾⠓⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣠⣄⠀⠀⢠⡀⠀⠀⢠⡄⠀⠒⢾⡀
⠀⠀⠀⠀⡇⠀⠀⢰⡟⠛⠛⠛⠃⠀⠈⢹⡏⠀⠀⣿⣧⡀⠀⣸⡆⠀⠀⢩⡏⠀⠀⢶⣟⠉⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠃
⠀⠀⠀⠀⡟⠀⠀⠀⣷⣤⣤⡤⠀⠀⠀⢸⡇⠀⠀⣿⠈⢿⡄⣿⠃⠀⠀⢸⡇⠀⠀⠀⠙⢳⣤⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣼⣧⠀⠀⣿⠀⠀⠻⡿⠀⠀⠀⣼⡧⠀⠀⢠⡾⠋⠁⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠙⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠶⠤⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡡⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠶⠆⠀⡆⠀⣶⡄⠀⣶⠀⠀⠀⢠⣶⡆⠀⠀⢰⣶⢰⡆⡀⠀⠙⠛⠃⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⡇⠀⣿⣷⣶⣿⠀⠀⠀⣼⣿⣷⠀⠀⢸⡿⣿⡇⠃⣠⠖⠛⡃⠀⣿⠛
⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣠⡀⠀⡇⠀⣿⡇⠀⣿⠀⠀⢠⡿⠉⠿⠆⠀⠸⠇⠹⠇⣸⣷⣆⣀⡀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠅⠀⠁


⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⣰⣾⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡇⣿⣃⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢱⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠


⠀⠀⠀⠀⣄⣠⣴⣶⣶⣤⣀⣤⠀⠀⣀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠇
⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠰⠶⠶⠾⠿⠿⠿⠿⠿⠶⠶⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⡀⠈⠀⠀⠀⠀⠈⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠏⠁⢰⡀⠀⠂⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣌
⠐⠠⠀⢷⣦⣤⡄⠰⠀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⡀⠐⠚⠀⠀⠤⠉⠃⠆⠀⠠⠀⠐⠂⠀⠠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠁⠠⠄⣄⠀⠀⠀⡾⣷⣦⠀⠀⣄⠈⠀⠀⠀⠡⠄⢶⣄⠀⠀⣀⠢⠄⠠⠄
⠀⠀⠀⠉⠀⠀⠀⠀⠈⠎⠀⠆⡈⡓⣀⠀⠁⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⢀⡤⠃⠘⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠒⠛⠁⠀⠀⠀⢿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⡀⠀⠀⠀⠼⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠱⠆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⡾⠿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠉⠀⣀⡤⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡴⠊⠁⠈⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⣾⣁⠀⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⣠⣾⡿⠥⠒⢲⡄⠀⠀⠈⢩⡟⠀⣠⣤⣤⡾⠁⠀⠀⠀⠀⠀⠙⢷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⢀⣼⠟⠁⠀⠀⢀⣴⠟⠒⠓⣆⠈⠻⠟⠁⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢰⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⢀⣾⠏⠀⠀⠀⠀⠘⠋⠀⠀⣀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠛⠻⣦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⣠⣤⣶⣶⡄⠀⠀⠀⢠⣶⣶⣤⣄⠀⣿⠀⠀⠀⢻⡟⠷⣄⠀⣠⠶⣦⠀⠀⢿⣇
⢸⣿⠀⠀⠀⣀⣀⡀⢰⡾⠋⠀⠀⠀⠀⠀⠚⢉⡥⠤⠤⢄⡀⠀⢀⡤⠤⠤⣌⡉⠓⠈⠻⠶⠶⠟⠁⠀⠈⠛⠋⠀⠻⣤⣤⣾⣿
⣾⡟⠀⠀⠾⠯⢍⡙⠓⠃⠀⠀⠀⢀⣀⠀⢰⠏⠀⠀⠀⠀⠙⡴⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡿⣤⣤⣤⣄⢸⣇⣀⣀⣀⣰⡿⠛⠙⠻⣿⣀⢠⣄⠀⠀⠀⡧⠀⠠⣤⠀⠀⡀⡿⣠⠚⠉⠉⠉⠓⠦⠴⠒⠲⣄⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⣹⠃⠀⠀⠀⠈⣿⡀⠀⠀⠀⠸⣇⠘⠋⠀⠀⠀⣧⠀⠀⠛⠀⠀⢨⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⢸
⣿⡇⠀⠀⠀⣿⢀⣤⡀⠀⠀⠙⠷⣦⣤⣠⡪⠛⢦⣄⣀⣤⡾⠙⣷⣤⣀⣠⣴⡟⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢹⡄⢸
⢻⣷⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠈⡿⢦⣄⠈⠻⣷⠊⠁⠀⠈⠓⠾⠖⠋⠀⠀⠻⣦⣀⣀⣀⠀⠀⠀⠀⠿⠀⠀⠀⣼⠃⣾
⠘⣿⡄⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢀⡼⠃⠀⠙⢷⣄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡇⠀⠀⠀⠀⠀⣠⠾⠃⢠⣿
⠀⢻⣷⡀⠀⠀⠀⢻⡀⠀⠀⠀⣴⠟⠁⠀⠀⠀⣠⠝⠛⠛⠛⠒⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡇⠀⠀⣾⡟
⠀⠀⢻⣧⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⣸⠁⠀⣼⡟
⠀⠀⠀⢻⣷⡀⠀⠈⣧⠀⠀⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣷⣀⣀⣀⣠⠟⢀⣾⡟
⠀⠀⠀⠀⠙⣿⣆⠀⠘⠷⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣰⣿⠋
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⣄⣀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⣠⠴⠦⣀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⢹⣦⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣄⡀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⠿⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣀⠀⠀⠀⡀⠀⡠⠂⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠴⣃⠀⠑⠊⠀⠀⠀⠀⠾⠏⢰⢌⠁⠒⢤⡂⠰⠂⠁⠠⠐⢀⣔⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠊⠑⠁⢀⡀⠃⠰⡤⠀⠀⠀⠀⠀⠀⠃⠘⠁⡀⠀⡠⣎⠅⡰⡋⢀⡴⠀⠉⠀⠑⠠⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠅⠀⢠⠈⠁⠀⠀⢈⣧⡄⢀⠂⠑⠀⠀⣈⣤⠞⠉⠁⡀⡁⣤⢄⠓⣛⢻⣣⡬⢽⠘⢋⡠⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠠⢈⠰⠀⣰⠃⢀⣶⣿⡝⣾⡂⠃⠀⠀⠀⠀⠈⠄⢀⡀⠅⠔⠋⣰⡬⢀⡠⣜⣦⣥⡔⡋⣍⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠒⠓⠒⠿⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠑⠁⣀⣳⡞⠼⠭⠍⢀⣳⣟⢋⣉⣧⣍⡄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠏⡄⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢀⠍⠤⢀⣠⠊⠁⡫⠈⣠⠇⠂⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢘⠅⠂⢑⡀⠀⠀⢙⣶⢶⣂⠁⠀⠀⠀⢈⠤⠓⠁⠈⠀⠀⠈⣡⠣⠌⠉⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠻⠤⠀⠑⠐⠶⠀⢿⠒⢿⠔⢄⡠⠈⢠⣆⡤⣀⠀⠠⠠⣋⣁⣀⣀⣀⣀⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠀⠃⠢⣀⠠⡴⢿⣷⠆⠀⠀⠀⠉⠀⠀⠀⣤⠞⠊⠑⠒⢤⡄⠈⠁⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢷⣦⣐⡀⠀⡀⢠⠐⣇⢈⡐⣦⡤⠀⢀⡒⠊⠁⠀⡀⠀⣀⡀⢥⠀⠻⠇⠂⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡂⠄⠠⠜⠋⢷⡀⡹⠛⠤⡁⠀⢀⠈⢁⡀⢬⠖⢛⠉⠙⠇⠀⠀⠀⠾⠷⢶⠒⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠲⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⡪⡀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡍⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣰⠖⣠⢦⠩⡜⠀⢸⡟⣠⡔⡾⠀⢬⡁⢸
⠀⠀⠀⠀⠀⠀⠀⢘⠉⠈⠐⡏⠂⠈⠙⠀⡏⠻⡆⣻⠏⠠⡷⠀⣐⡇⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠈⢂⠁⠈⢁⡅⠀⠉⠉⠃⡐⠁⠀⠄⡅⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣶⡄⢰⡆⠀⢰⡶⠆⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⢰⡇⣇⢸⣧⠏⠘⡇⠀⠀⠀⠀⠀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡧⢿⠈⣿⡄⠀⡟⠉⠀⠀⠀⢸⠗⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠸⡆⠇⠙⠀⣷⣀⠀⠀⠀⡾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠈⠀⠀⠧⠀⠀⠀⠈⠉⠀⡀⢀⣀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠃⣇⢰⡆⠀⣿⡄⢰⣆⢸⡇⣾⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣸⡇⢸⠋⡇⢸⢿⣸⡇⣿⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠀⣿⢸⡇⣼⠛⣧⢸⠈⣿⡇⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠀⣿⢸⡇⣿⠀⢿⢸⠀⢹⡇⢹⣠⠆⢸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⠘⠈⠁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⢠⣸⡇⢠⠀⠀⢰⡄⢰⡆⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⣇⡇⢀⣤⡀⣼⢹⣼⡇⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⢸⣿⣧⠈⠹⠁⡟⠀⠛⣇⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⢸⣇⠘⠀⠀⡇⠀⠀⣿⠘⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠈⠃⠀⠀⠀⠀⠀⠀⠹⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠲⢾⠀⠀⡀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⠐⡀⢠⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠁⠀⢠⣿⢈⣻⣦⠀⠀⠀⢰⣶⣾⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢠⣌⢫⡁⠀⢄⠀⠀⢰⣾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠈⢣⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢀⣀⠙⠷⣄⣳⠠⣿⠀⠀⠀⠀⠀⠀⠐⣳⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢀⠀⠀⠲⠾⠿⢇⣠⠀⠀⠉⠉⠉⠙⠛⠻⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠎⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠈⠙⠓⠀⠀⣀⠀⠀⠀⢠⣀⡤⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⡲⠟⠛⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⣰⣾⡿⢀⡀⠀⠀⠉⠀⠀⠈⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠸⡿⠿⠁⠐⢦⠔⠀⠀⣿⢋⠀⢜⣿⣦⡀⠐⡄⢰⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠲⢽⣿⣿⣄⠘⡀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠨⢷⣄⠀⢹⠀⢰⢠⣿⡇⠀⠀⠀⢀⣀⠀⠀⠉⠻⣿⣦⣧⣷⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠀⢀⡈⠳⣬⣧⠘⠀⠉⠁⠀⠀⠐⠿⠟⢀⠀⠒⠦⠬⣿⣿⣿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⣚⣿⣷⡄⠀⠀⣀⡀⠀⠀⠴⠿⠀⠀⠀⠀⢀⣘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⠉⠁⠀⠀⢰⣾⠟⠡⡀⠀⠀⢀⣠⣶⠴⠀⠈⠉⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢴⣦⣵⣄⠀⢀⠉⠠⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⢿⣷⣄⣣⠀⢧⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠜⠁⠀⣈⣁⣂⣼⣿⣿⣷⣼⣆⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢰⣶⠀⠀⠤⠤⠒⠚⠛⠉⠛⠻⠶⣦⣤⣤⣀⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣿⢿⢿⢷⢷⠾⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣷⣶⣷⡿⢷⣾⡷⠶⠾⢿

⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⡄⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣤⣼⣿⠇⠀⣠⣶⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⢻⣿⣿⡿⠒⢠⣿⡏⠀⠠⢽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⣤⣴⣶⣶⣦⠸⡓
⠀⠀⠀⠀⠈⠈⣿⡟⠁⠀⠘⣿⣧⣀⣠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⣿⣶⡀⠀⠀⠀⣿⣿⣿⣿⣿⠐⠇
⠀⠀⠀⠐⢳⠶⣿⡕⠉⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⠇⠈⣹⣿⣷⡀⠀⠀⢹⢿⣿⢿⡏⠄
⠀⠀⠀⠐⠉⠀⢸⣇⡀⠀⠀⠐⠀⠹⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡿⡁⠔⣰⣿⣿⣿⣷⡀⣠⣼⣿⣿⣿⣿⣄
⠀⠀⠀⠸⣿⣴⣿⣿⡏⠀⠀⢀⣡⢜⢈⣿⣿⣯⣅⡢⢠⠀⠀⣠⡄⠄⠀⠠⠄⠀⡈⠀⢠⣿⠿⠋⠀⠀⣶⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥
⠀⠀⠀⠀⠙⢿⣿⣿⣧⣀⣄⣈⣿⣿⣿⣿⣿⣿⣿⣷⣾⢷⣶⣧⠷⠀⠀⠀⠀⣂⠐⠿⠞⠁⠀⠀⠀⢠⣾⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠛⣿⣿⡾⣄⣾⣿⠉⠛⠛⠛⠛⠻⠿⣿⣾⠏⠀⣀⣀⣀⣀⣴⣳⡄⠤⣴⣄⠀⠀⠀⠙⢋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡌⠉⠀⠀⣼⠗⠀⠚⠒⠀⠀⢹⣷⣶⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣶⡶⠚⠛⠟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣦⢤⣼⣯⣤⣄⠀⠀⠀⠀⣹⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣶⣶⣾⠴⣯⡇⠀⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⣟⠻⢿⠛⠿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⡤⣶⣿⣇⣀⡿⠿⠿⠿⠿⠆⠾⠿⡟⠛⠻⡏⠉⠑⠀⠀⠃⠀⠈⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠋⠉⠉⠉⠛⠛⠛⠛⠙⠛⠃⠀⠓⠂⠀⠀⠀⠀⠀⠁⠀⠀⠁