Curly arrows Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⢀⠀⣠⡴⠶⠶⣦⣀⠀⠀⠀⠀⠀⠙⣿⢷⡄⠀⠀⠀⠀⣠⡿⡿⠋
⠀⠀⠀⠹⣄⡀⠀⠀⠐⣿⣿⡇⠀⠀⠀⢹⣿⡷⠂⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠙⠲⠤


⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠈⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠉⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣀⣴
⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⡏
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⣿⣿⣿⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠛⠇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣄⣀⣀⣀⣀⣸⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠤⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣄⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⠿⢿⣶⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⠀⡀
⠀⠀⠀⠀⡀⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠉⠙⠛⢿⣿⣷⣷
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠤⣄⣀⣤⣴⠿⠛⠉⠁⠀⠀⠀⠉⠉⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣷⣤⣀⣀⣀⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠛⠿⠿⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣹⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠘⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⡻⠁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠔⠊⠁⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢀⠤⢤⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⣆⠀⠀⠀⡎⠀⠙⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡠⠃⠀⡠⢤⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠈⠓⠤⠤⢧⣔⣊⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠔⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠷⢤⣀⣀⣀⣀⡤⠴⠚⠉

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣾⣿⣶⠄⠀⠀⣰⣿⠋⠉⠈⠙⣧⠀⢤⣾⣿⣷⣦⡄⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⢀⡀⢙⣿⡆⠀⠀⠀⣠⣴⠶⣿⠷
⠀⠀⢠⣿⡿⠛⠟⠁⠀⠀⣀⣿⣧⠀⠀⠀⠐⠃⠀⠀⠈⠙⠋⢻⣿⠀⠀⠀⠀⢀⣽⣿⠿⠄⠀⠀⢀⣾⣷⣿⡿⠁⠀⢀⡾⠋
⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⣾⠟⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠛⠛⠿⠅⠀⠀⠀⠘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢦⣀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣆⡄⠀⠀⠀⠀⠀⣴⣾⡇⠀⠻⣿⣷⣶⠿⠿⢻⡇
⠀⠀⠛⠿⣷⣤⣀⣀⡀⠀⠀⠀⣿⠿⠿⠋⠈⠀⠀⠈⠻⢿⣿⣦⡤⠀⠀⢻⡏⠀⠙⠻⡿⠀⠀⠀⣠⣴⣾⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠇⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠉⠙⢷⣦⡀⠀⠀⠀⣼⠟⠛⠻⠿⣿⠄⠀⠀⢀⣤⣿⣦⡀⠀⠀⠀⢀⣀⣤⣷⣄⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⢠⣴⣾⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠟⠉⠀⠀⠀⣾⠿⠟⠛⡿⠟⠁⠀⠘⣿⣿⢁⣤⠤⠄⠀⠀⠙⠿⠙⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠐⣿⡷⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⣀⣤⣶⡗⠀⠀⢠⣄⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⡄⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⢢
⠀⠀⠀⠀⢈⣽⢻⡿⠀⠀⢀⣿⣿⢦⠀⠀⡼⣿⢿⣄⠀⠀⠀⡇⠀⠀⠀⡼⣿⣿⡀⠀⠀⢺⡟⣿⠃⠀⠀⠀⠸⡇
⠀⠀⠀⢠⡟⠁⠀⠁⠀⠀⠘⢩⣿⠀⠀⠈⠀⣿⡀⠁⠀⠀⠀⣧⠀⠀⠈⠁⣿⠈⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠸⣇⠀⠀⠸⣦⣿⡴⠀⠀⠀⣿⠀⠀⠀⠸⣧⣞⣻⠆⠀⠀⠀⢰⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⢹⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠹⡏⠁⠀⠀⠀⢿⣾⣷⠆
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠺⠟⠁
⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⣠⠆⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠚⢡⡟⠹⠇⠀⠀⢠⡟⠀⠀⠀⠀⣈⣽⠟⣿⠀⢀⡾⠁⠀⠀⠀⠀⣰⣿⡇⠀⢰⠀⢀⣾⠛⢉⡧
⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⣠⡿⠁⠀⠀⠀⣾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠚⣱⡟⠿⠀⠈⠳⣼⣧⠶⠟⠁
⠀⠀⠀⢠⡟⠁⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⣈⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠂
⠀⠀⠀⠀⡤⢾⣿⡟⠀⠀⠀⠀⠀⠈⠁⠀⣸⡆⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠤⠒⠒⠛⠓⠶⢶⣤⣀
⠀⠀⠀⠀⣴⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠒⣻⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⣦
⠀⠀⢀⡾⠁⢠⠴⢦⠀⠀⠀⠀⣠⢀⣼⠟⠀⠀⠀⣼⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⣶⠶⠀⠀⢀⣙⣿⣿⡆
⠀⠀⠸⡇⠀⠈⣠⡿⠀⠀⢀⣼⣿⣿⡷⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠟⠁⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⢈⡉⠉⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⠄⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⢐⠀⠀⠀⠀⠙⠶⠖⠁⠀⠀⠁⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢤⣶⣶⡟
⠀⠀⠀⣴⠛⣷⡀⠀⣠⡿⠙⠁⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠠⠤⣶⣿⡟⠀⠀⡠⠒⠉⠉⢻⡇⠀⠀⣠⡴⠛⠟
⠀⠀⡼⠃⠀⣿⣇⣴⠟⠀⠀⠀⠀⠀⠀⠈⠙⠶⢦⣤⣤⣤⣶⠾⠛⠿⠀⠀⠈⠀⠀⠀⠀⠈⠻⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠁

⠀⢀⣤⠀⠀⠀⣠⣄⠀⢀⣤⣀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣤⣤⣶⣦⣄
⠀⠘⠛⢷⡀⣴⠟⠋⠀⠈⠉⠙⢷⠀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠂⠉⠉⠀⡴⠋⠉⠉⠉⢀⡴⠟⠛⠋⠙⠻⠋⠁
⠀⠀⠀⠈⠃⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠸⡅
⠀⠀⠲⣄⠀⢀⠴⠂⠀⠀⠚⠓⢄⠀⢠⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣤⣤⣴⡾⠋⣀⣄⣀⣠⠴⠃⢀⣀⠠⠀⢀
⠀⠀⠂⠀⠀⠀⠔⠀⠀⠀⠐⠦⠀⠀⢀⠤⠂⠀⠀⠀⠙⠻⠟⠋⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⣰⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⣴⠁⠀⠀⠀⢸⠇⠀⠀⢠⡆⠀⠿⠋⠀⠀⢾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣀⡼⠁⠀⠀⣀⣀⣠⡿⠃
⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠈⠁⠀⢀⣀⠀⠀⠉⠀⢀⡀
⠀⠀⡏⠀⠹⡆⠀⢠⠀⠀⠥⠀⠀⡆⠀⢹⡄⠀⢴⠁⠈⣷⠀⢰⠁⠀⠛⠀⢰⠉⠉⠓⠀⢰⡋⠈⣣⠀⠠⡆⠀⢹⠄

⠀⠀⠀⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠰
⠀⠀⠀⠀⡠⠃⠀⠀⡠⠐⠀⠀⠐⢄⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡇⠈⠒⠀⠐⠁⠀⠀⠀⢁
⠀⠀⡠⠊⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠘⠀⠀⠀⠔⠢⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⡅⠀⠀⠠⠤⢄⠀⠀⠀⢀⠀⠀⠀⡅⠀⠀⠀⠀⡰⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠘⠤⠀⢥⡠⠊⣀⠤⠒⠁⠀⠀⠀⠐⠤⠀⠠⠐⠁⠀⠅⠉⠁⠀⠀⠠⡤⣀⠀⠀⣀⠀⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣠⣭⣿⣷⠄⠀⠀⠲⠶⠶⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⠆
⠀⠀⢀⡾⠛⣦⢠⡿⠹⣧⡟⠉⠉⠁⢠⠿⠋⠀⠀⠀⠀⠀⠀⠛⠋⠁⣠⠶⠛⠛⠳⠶⠶⠶⠿⢻⡿⠁
⠀⠰⠟⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢂⣤⠶⠖⠒⠒
⠀⠀⠀⠀⠀⣴⠟⠋⠁⠀⠉⠛⢦⡀⠀⠀⠀⠀⣸⣿⣫⡵⠄⠀⠀⠀⠀⠀⣶⣴⠾⠛⠛⠛⠷⢶⣄⡀
⠀⠀⠀⣤⣸⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⣣⡴⠶⠶⠄⠀⠉⢿⡄
⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⣿⢿⣅⡀⠀⠀⠀⠀⠀⢸⡄⠀⡆⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣲⣶⣤⣀⠀⠀⠀⠈⠙⠳⢦⡄⠀⢀⣸⡇⠀⡇⢀⡄⠀⠻⣦⣄⣀⣀⣠⣤⠾⠋
⠀⠀⠀⠚⠛⠛⠛⠋⢉⣽⠟⠁⠀⠀⣴⠛⠉⠙⠉⠁⠀⠈⢿⡇⠀⣷⡾⠁⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠢⢤⡀⠀⠀⠀⠀⠈⠻⣶⠟
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⣠⠟⢷⣄⣾⢿⣄⣼⢿⣦⡾⢿⣄⣽⠟⢹⡄⠀⠀⠀⠀⢀⡿⣿⠷⡄⢠⡟⠀⠀⢀⣀⣴⣶⣤
⠀⠀⠀⠐⠋⠀⠀⠙⠃⠀⠛⠁⠀⠛⠁⠀⠛⠋⠀⠈⠀⠀⠀⠀⠀⠘⠃⢹⡆⢰⡟⠀⠀⠀⠸⣯⣄⡚⠁
⠀⠀⠀⣠⣾⣁⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠈⣿⡿⠀⠀⠀⢠⡶⠶⠾⠿⠆
⠀⣄⠀⠈⠦⠈⠙⢶⣄⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣨⣷⣦⣄⡀
⠀⠸⡄⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠐⠿⢧⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⡉⠁
⠀⠀⠙⢦⡀⠀⠀⡀⠀⠘⣇⠀⠀⢀⡄⣀⣤⠿⠀⠀⠀⠹⣆⡀⠀⠀⢠⣤⣄⡀⠀⠀⢸⣏⣉⠉⠁
⠀⠀⠀⠀⠙⢶⣤⣹⣄⠀⠙⠀⠀⠸⠿⣿⡄⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣻⠟⠁⠀⠀⣤⣬⣭⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠄⢰⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⡀⠀⠀⠀⠀⠔⠈⠈⠐⡈⠉⠐⠆⠀⠀⠀⢀⠠⡀⠀⢀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠂⠀⠀⠐⠉⠐⠂⠈⠁⠀⠀⠀⠈⠀⠀⠐⠤⠁⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠁⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀⠀⠀⠀⠀⡀⠁⠠⠂⠀⢀⡀⠀⠀⠀⡀⠀⢀⡄⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠡⡀⠀⠀⢂⡀⠄⠀⠀⡀⠀⠀⠀⠠⠁⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⢄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠶⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠁⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠈⠀⠀⠑⠄
⠀⠀⠀⢀⠀⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠠⡄⠀⠁⠂⠀⠤⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠠⠀⠤⠐⠁⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢰⡦⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠉⡩⢦⡀⠀⠀⠀⠀⠁⠙⢆⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠈⠋⠢⡀⠀⠀⠈⠈⠑⠤⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠑⢪⣼⠄⠀⠀⠀⠀⠎⡞⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢄⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠐⠚⣡⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⢀⡴⠾⣿⠟⠋⠀⠀⠀⢀⣶⠟⠉⠉⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⠄⠀⠀⠀⠠⠊⠉⠀⠉⠉
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠀⠀⠀⣷⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠹⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠙⠶⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⠈⠛⠶⠤⠄⠔⠃⠀⠀⠀⠀⠀⠀⠉⠿⠛⠋

⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⢦⣄
⠀⠀⠀⠀⠈⠙⠻⠟⠻⢦⡀⠀⠀⠀⠀⢀⡴⠒⠒⢀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣰⡏⠀⠀⠀⠀⠹⣆⠀⠀⣼⣷⡀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⢰⣿⠀⠀⠉⢿⡀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣠⣴⣦⣴⠞⠁
⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠦⠤⠀⠁⠀⠀⠀⠀⠈⠉⠙⠋

⣶⢶⣶⣶⠶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⠶⣶⡶⡶⢶⠶⢶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠭⠆⠀⠀⠀⠀⢀⣹⠆
⠀⠀⠐⠊⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⣄⠀⠀⢰⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠼⢦⣀⠀⠀⠀⠀⠀⠀⢰⣋⠉⠉⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⢀⡤⣀⢐⣇⣩⡾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠙⢦⡀⠀⠀⠀⠘⢮⣷⠃⠀⠀⠀⠑⣼⡞⠀⠀⠀⣧⣏⠤⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠒⠋⠀⠀⠀⠙⢦⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠈⠀⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⡒⠒⠒⠒⠊⠁
⠀⠀⢀⣀⣀⠤⢤⣀⠀⠀⢀⣀⣀⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢭⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣀⣀⣀⡀
⠀⠀⣠⠖⠋⠉⢹⡉⣳⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⠉⡧
⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠟⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠘⠥⠴⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⢚⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢤⡀⠀⠀⠀⡸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡬⠇⠀⠀⠀⠀⠈⡹⠹⠇⠀⠀⣴⣆⠀⠀⡰⡷⡄⠀⠀⠘⠳⣄⠀⠀⠀⠀⠙⠼⣟
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣠⣄⣸⠁⠀⠀⠀⠘⠁⡏⠃⠀⠁⠳⣍⠀⠀⠀⠀⠈⠲⢤⣠⣖⠆⠀⠈⠑⠂
⠀⠀⢰⠋⠉⠉⠁⠀⠀⠀⠀⠀⢠⠋⠀⠀⡏⢳⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠺⡦⢄⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢗⠲⢄⠙⠢⠷⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠾⠿⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣷⣤⡀
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠛⠛⣿⡿⢷⣦⣤⡀
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠙⠻⢷⣤⡀
⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠙⢿⣦⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠘⣿⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣼⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒
⠀⠀⠀⠀⠁⠀⠀⢀⠀⠤⠤⢤⠀⠀⠀⠀⠀⠀⡠⠂⠉⢁⠄⠂⠀⠀⠀⠀⠈⠁⡠⠊⠀⠀⠀⠀⢀⠓
⠀⠐⣀⠀⠠⠐⠈⠀⡀⢠⠀⠀⢀⠠⠆⠀⡠⠊⢀⠠⠔⢅⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⢡⠇⡀⠄
⠀⠀⠉⠀⢀⠄⠊⠁⠀⠈⠀⠐⠁⠀⠀⠐⠀⠠⠁⢰⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠄⠂⢁⠄⠐⠀⠀⠉
⠀⠠⠠⠐⠁⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁⠀⠈⠤⠔⡀⠄⠚⠀⢀⣀⡀⠀⠀⠊⠀⢀⠔⠃
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⡠⠀⠀⠀⠙
⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⡴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠋⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⢀⠛⢀⠄
⠀⠀⠀⡠⠐⠀⢁⠠⠀⠐⠂⠀⠀⠐⠲⠀⢀⠄⠂⠀⠈⠁⡠⠃⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀⠐⠁⢀⠂
⠀⠀⠊⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⣀⡀⠀⠀⠄⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⢀⠀⠀⠉⠐⠄⠀⠀⠀⡥
⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⡀⠔⠈⠀⡰⠆⠀⠰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠐⠀⠄⠠⠄⠐⠈⣀⠀⠀⠀⠑⠄⠀⠠⠚
⠀⠀⠀⠀⠠⡇⠀⠀⢠⡅⠀⠀⢀⠠⠃⠀⠀⠄⠀⠀⣀⠁⠂⠄⠀⠀⠠⠀⠂⠉⠀⠀⠀⠠⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠃⠀⠀⠀⠀⣠⠞⠙⡄⠀⠀⡠⠚⠙⣦⠀⢠⢋⡇
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡇⠀⢠⠃⠀⠀⡟⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣦⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⢸⠀⠀⢰⠇⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⡸⠀⠀⠈⢧⣠⠜
⠀⠀⠀⠀⠀⢀⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⡴⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡯⣄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢄⠀⠀⠀⠠⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠢⣀⣠⠜⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠛⠻⡄⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢣⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠋⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⢀⡏⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠂⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⣾⣿⠶⠤
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⣤⠞⠉⠁⠀⠀⠀⠁
⠀⠀⠈⠓⠲⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠐⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠋⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣠⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠳⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⣀⡠⢶⡶⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠹⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡁
⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠀⠀⠚⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⢀⠰⠁
⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⢠⠴⠒⠲⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠉⠑⠓⠒⢢⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢳⡄⠀⠀⡏⠀⠀⠀⠈⢓⣉⣲⡤⠀⠀⠀⠀⠀⢸⣾⡠
⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠦⠶⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣶⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣐⣦⣤⡀⠀⠀⣀⡤⠶⠒⠛⠛⠶⢦⣄⣄
⠀⠀⠙⠙⢷⣤⣤⣤⡴⠚⠁⠀⠀⠀⠸⣄⠀⠀⠉⠙⠛⠋⠿⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⡶⠶⠶⠦
⠀⠀⠀⠀⠀⣠⣴⠦⠀⠀⢉⡟⡇⠀⠀⠀⠙⢷⣄⠀⣀⠀⠀⠀⠀⢩⠟⠃⠀⠀⣼⠃
⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢻⣾⣷⣄⠀⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢸⣿⡥⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⣧⠀⠀⠀⠻⣷⣤⣀⣀⣠⡿⢿⠁
⠀⠀⠀⠋⠀⣠⣄⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠉⠛⠛⠉
⠀⠀⠀⠀⢰⢿⣿⢆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠰⣶⣶⣖⣀⣀⣀⣀⣴⠆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠘⠊⠙⠛⠛⠛⠉⠀⠀⢀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡿⠋⠀⢀⣤⣴⣆⣀⣤⡴⠞⠁⠀⠀⠀⣼⠇⠁
⠀⠀⠴⣶⣶⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡖⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠈⠻⠉⠙⠛⠻⠷⢶⣶⣤⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡷⠄
⠀⠀⠀⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠙⠛⢷⣤⣧⠀⠀⠀⠻⣷⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠚⠋⠀⠀⣸⠁⠀⠀⠀⠉⠛⠿⢿⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⠃
⠀⠀⠀⢀⣤⡶⠟⠛⠋⠉⠙⣻⣿⣧⠀⠈⠻⢶⣤⣤⣤⠴⠂⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⠿⠛⠹⠃
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⢀⡴⠋⠉⠉⠛⣦⣠⠀⠀⢀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠀⠀⢀⡴⠞⠛⠻⠿⠗⠀⠀⠀⠀⠀⣀⣤⣼⣦⣄
⠀⣾⠀⠀⠀⠀⠈⠻⠿⠀⠀⠈⠓⠲⠤⠴⠖⠋⠹⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠉⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠰⢻⠿⠄⠀⠀⠀⢀⡞⠀⠀⢸⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠰⢿⠛⠂
⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⢦⣧⡄⠀⠀⠀⠘⠦⣄⣀⣠⡴⠋⠈⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣤⢤⣼⣄⠀⠀⠀⠀⠈⠑⢦⡀⢀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠠⢴⣾⠁⠀⠀⠀⠀⠀⢀⣼⣧
⠀⣀⣠⠴⠋⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠠⣿⣾⠀⠀⠀⠀⠈⠳⢤⣄⣤⠴⠋⠘⠀⠀⠀⣀⣀⣤⠽⠟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠺⢿⡷⠶⠦⣤⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢿⡀
⠀⠀⠀⠀⠀⠐⢾⣷⠂⠀⠀⠀⠀⠀⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠛⠲⠮⣷⡦⠀⠀⣀⡀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣤⣼⣷⣄⠀⢀⣠⣤⣄⣀⣙⣿⣿⣸⣷⠀⠀⠀⠀⢀⣀⣀⠀⣀
⠀⠀⠀⡼⠟⠯⢿⣧⡀⠠⠀⣀⡌⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣥⣶⣈⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⠛⠿⠿⠋⢙⣿⢿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡿⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁







⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⣤⣤⣾⣿⣿⣿⣿⣷⣤⡤⠴⠖⠂
⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣥⣿⣤⣤⣿⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠋⠀⠀⠀⠁⠀⠉⠉⠉⠉⠀⠈⠀⠀⠀⠙⠿⡿⠟

⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢲⡄⢹⡆⠀⠀⠀⠀⢰⡏⢠⠖⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠠⠴⢃⣼⠃⠀⠀⠀⠀⠘⣧⠙⠦⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠠⡄⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⣆⢐⠀⠀⠐⠀⠀⢀⣦⠀⢈⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠣⠁⠀⡀⠈⠀⠀⠀⠀⢀⡲⠋⠀⠀⢀⠈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡰⠀⠀⠠⠀⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠞⠒⠂⠀⠀⠘⠀⠀⢰⠠⣧⠀⠀⡰⠦
⠀⠀⠀⢿⡾⢥⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠊⠀⠀⠀⠀⠀⠀⢬⣿⡆⠀⢸
⠀⠀⠀⠀⠌⣢⣽⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠰⠀⠀⠠⠐
⠀⠀⠀⠀⠈⢻⢻⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠖⠀⡀⠀⠀⠀⠀⠀⠀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚
⠀⠀⠀⠀⠀⠀⠸⠈⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⢛⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠋⠳⠄⠀⠀⠀⠀⠀⠀⣀⣠⡁⠀⠐⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠓⡛⠃⠀⠜⢢⠛⢄⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡈⠃⠈⢷⠀⠀⠀⠀⠀⢀⢙⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⣄⠠⠰⠀⢀⡀⠀⡀⢃⠀⠀⠀⠀⡘⠋⠀⡀⠄⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠋⠐⠈⠀⠀⠙⠦⣙⣌⡆⠀⠀⠀⠙⠂⠈⠳⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⠸⡀⠀⡀⠐⣷⡄⠈⠙⠻⡄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠈⠊⠀⠙⠉⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢀⣿⣿⡿⠂⠀⠀⠀⣀⣤⣶⣾⣿⣷⡤⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⢻⣿⣿⠀⠀⠀⠀⣴⣿⠟⠻⠁⠀⠀⢀⣼⣿⠟⠉⠙⠋⠁⠀⠀⠀⣴⣿⠟⠉⠉⠉⠙⢿⣿⣦⡄
⠀⠀⣿⡿⠈⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠘⠿⣿⡇

⠀⠀⠀⠀⠈⠉⢩⣄⡄⠀⠀⠀⠀⠀⠀⠀⢄⠀⣄⡀
⠀⠀⠀⢻⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠐⢼⡇
⠀⠀⠀⠀⠀⠰⠾⠉⢁⠀⠀⠀⠀⡈⢠⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠐⠃⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠠⢄⡂⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠻⣿⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉
⠀⠀⠀⢰⠄⠀⣤⣶⣾⣿⣿⠀⣿⣿⣯⣁⣉⣉⣉⡉⠉⠛⠛⠠⢬⡀⠀⡀
⠀⠀⠀⠀⢸⡈⠿⡿⠛⠋⠉⠀⣿⠉⠉⠈⠀⠉⠉⠁⠬⠁⠀⠀⠀⠘⢀⡇
⠀⠀⠀⠀⢸⡟⠳⠶⠤⠤⢀⣄⣛⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⣿⣿⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣿⣿⣧
⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡗⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⣤⢀⡀⢀⣀⣀⠀⠀⠀⢀⡀
⢀⢀⣤⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠛⠿⠻⠿⠿⠿⠶⠶⠵⠋⠃⠂
⠈⠈⠉⠉⣻⠅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇⠀⠀⠀⠐⠋⠂⠀⡀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠴⣭⠤
⠀⠀⠀⠀⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢀⡀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠀⠀⠤
⠀⠀⠸⠂⢸⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢺⣿⣿⣿⣧⣢⣤⣤⣶⣶⣶⣦⡶⢈⡉⡁⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠁⠶⠤⠤⠄⢛⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣾⠿⠿⠛⠛⠛⠿⠋⠿⠟⠛⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠈⠉⠙⠋⠙⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠉⠀⠈⠉⠙⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⣠
⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿
⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠉⠃⠀⠀⠀⠘⢷⣄
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣤⣤⣤⣤⣄⣀⣀⣠⣽⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⢻⣿⣿⠟⠋
⠀⠠⠤⢤⣤⣤⣤⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⠉⠉⠉⠙⠛⠻⢿⣿⣿⣷⣦⣤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠉⠛⠻⢿⣷⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⣶⣄⠀⡄
⠀⠀⢀⡀⠀⣀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠉⠉⠙⠻⣿⣿⣿⣷
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣼⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣦⣄⣀
⠀⠠⣀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⡉⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠈⠙⠓⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢿⣿⣿⣷⣶⣶⣶⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠙⠲⡄⠀⠀⢸⡇⠀⠀⢠⠖⠋⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣰⠀⠻⠀⣿⢸⡇⣿⠀⠏⠀⣄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⠀⠛⠀⠀⠛⠀⡇⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⢛⠓⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢧⡀⠛⠟⠃⠘⠻⠟⠀⠛⠿⠃⣀⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠉⠉⠛⠒⢲⡖⣶⠒⠚⠋⠉⠁⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣀⣠⠤⠴⠶⠒⠒⢺⡇⣽⠒⠒⠒⠶⠤⢤⣀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠋⠁⠲⠶⠒⠶⠂⠀⠘⣇⡿⠀⠲⠔⠲⠔⠂⠀⠉⠓⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⣀⠀⠀⠀⠀⠲⠴⠦⠴⠂⠀⠀⠀⠀⠲⠤⠶⠤⢆⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠋⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠉⠓⠒⠲⠦⠤⠤⠤⠤⠤⠤⠶⠒⠒⠋⠉⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠲⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠲⠤⣄⣇⣀⣂⡀⠰⠀⣀⣂⣀⣿⣤⠴⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣀⠀⠈⠉⠉⠉⠉⠉⠉⠁⢀⣀⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⣉⡉⠛⠛⠛⠛⠛⠋⣉⣉⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⢰⠀⠰⠀⠄⡄⢰⠀⡰⡀⣔⡂⢠⠀⢐⠀⠀⢔⠀⢰⠀⡆⡆⡐⠐⡄⣄⠂⣆
⣤⣤⣤⣤⣤⣤⣬⣤⣼⣤⣧⣥⣼⣤⣥⣥⣤⣬⣼⣤⣤⣤⣤⣤⣥⣬⣤⣥⣥⣥⣤⣥⣥⣥⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠠⢀⡀⠄⠀⢠⡤⣠⡤⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡄
⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⡀⠀⢀⣷⣽⢻⣷⣻⣶⡄⠀⠄⠀⢀⠀⠀⠀⡴⠂⠀⠀⠘⠡⣄⠠⠈⣴⣿⠁⢌⡿⣾⠁⠀⡌⢠⡀⠀⠀⠀⠀⠀⣸⣤⠏⣺⣿⠃
⠀⠀⢸⡆⠀⠀⣀⡄⣤⠺⠇⠀⣼⣿⢣⣿⢿⡏⠘⠄⠈⢸⣤⣀⠄⠰⠊⠀⠀⠀⠀⢦⠀⡋⠀⢸⣿⠇⡌⣾⠛⠃⠀⠀⠻⣾⣗⡇⠀⢠⢀⣴⣿⣟⡻⡹⠁⢸⡀
⠀⠀⢸⡇⠀⠀⡇⢸⠁⠀⠀⠸⠉⠉⠩⡍⠘⢧⣼⠀⠀⣿⣿⣿⠂⠀⠠⠀⠀⠀⣰⢀⣿⡇⠀⢸⡟⢀⠀⠃⠀⠀⠀⠀⠀⠀⠙⢷⣾⣾⡿⣽⣿⠋⠰⠀⠀⣼⠁
⠀⠀⠸⢧⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⡔⠄⠀⢸⣆⣼⣿⣿⠁⡠⠀⢀⣀⠀⠄⣹⣿⣿⣷⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡿⠃⣼⡇⠁⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠿⢶⡅⢀⢠⣶⣿⡟⠋⠀⢀⠶⢮⡝⢡⠶⣰⣿⣿⡟⠃⢀⢛⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠁⠀⠳⢄
⠀⠀⠀⠀⠀⠀⢰⣦⣤⣴⣶⡟⠀⠀⠀⠈⢧⠘⠿⣧⠀⠀⣰⢏⣠⠏⠀⣸⠶⣿⣿⠹⢄⢴⣏⠙⣿⣽⠀⢀⣆⣸⣧⣥⣤⣤⠞⠀⠀⠀⠀⠲⣄⡀⠲⣠⣧
⠀⠀⠰⠀⡦⠀⠻⣟⣿⠛⠋⠀⠀⠀⠀⢀⣹⣄⠀⢹⣿⣾⣿⠟⠁⠀⡁⢹⠀⠉⠀⠀⠻⣟⠻⣶⡛⠁⢀⣼⣿⣿⣟⠅⠀⠜⢷⣄⠀⠀⠀⠀⠘⣧⣜⣿⡗
⠀⠀⢰⣞⠀⠀⠀⠈⣹⣦⣀⣀⠀⠀⠀⠙⣿⣿⣀⣼⣿⣿⠧⠀⠐⣮⣷⡀⠀⠀⠀⠀⠀⠈⠳⣟⠀⢠⣿⡿⢿⣿⣧⠀⠒⠀⠀⠹⣦⡀⠀⠀⢀⣠⣭⠁⢀⣀
⠀⠀⣸⡏⠂⠀⣠⣾⣿⠏⠛⢛⠶⠶⠶⠖⢋⣿⣿⣯⣿⡿⡆⣀⣀⡈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⡿⠁⠘⣟⠁⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠒⢠⡀⠂
⠀⠀⠛⠃⠀⠸⡿⠋⠁⠀⠀⠀⠳⠀⣤⣤⢾⡝⠃⠈⠙⠀⠀⠈⠛⠅⢿⡿⢷⠀⠠⢱⠀⠀⠠⡄⢸⣿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠠⣴⣶
⠀⠀⣤⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢰⡞⢣⡛⠀⠀⠠⢠⣀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠈⠀⢠⣿⣯⠁⠹⣆⠀⠀⠀⠀⢀⠐⢦⠀⢀⣆⠀⠀⠀⠀⠀⠀⠠⣌⠙⢇
⠀⠀⣿⢹⡆⠀⢠⠀⠀⠀⠀⠀⠀⡿⠉⠋⠙⣷⡀⠀⠀⠠⢌⣡⡀⠀⠀⢡⠀⠀⠀⢀⣴⣿⠟⠁⡀⠀⠈⠀⢠⡀⠀⣸⠆⠘⠃⠈⢻⣷⠏⠀⠀⠀⠀⠀⠈⠑⠆
⠀⢸⡇⢏⠇⣠⠋⠐⡄⢀⠀⠐⠀⣀⠀⢲⣴⣼⣷⢶⣤⡀⠀⣿⣷⠀⠀⡌⠀⢀⣠⣿⡟⠁⠀⠀⠁⠀⡀⢀⣼⣿⣤⣿⣤⠏⠀⠀⠘⠟⠀⠀⠀⠀⠀⢀
⠀⠀⠿⠞⢻⣧⡀⠀⣽⡇⠀⠀⠀⠙⣧⠀⠛⠻⠄⣰⣿⢷⣼⡿⢿⡇⠀⠀⢺⠏⡟⠉⠀⠀⠀⠀⠾⠿⣯⣷⣾⣿⣿⠛⠁⠀⠈⣷⣌⡀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠤⠲⠚⢿⣴⣿⣡⡇⠀⠀⠀⠀⢳⣄⠀⠀⠀⢈⡷⠄⢠⣼⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣬⡻⠿⣿⡃⠀⠂⠀⠀⠙⢿⠛⢀
⠀⠀⠂⠀⠀⠀⠉⣫⠉⠉⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⡥⢠⣾⢏⠃⠀⢠⡄⠐⢶⠶⣻⠃⣴⣿⣴⣿⠛⠀⠁⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢀⡴⠆
⠀⠀⠀⠀⠀⢀⡠⠄⢻⣦⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⣾⣇⣾⣟⡮⣶⣸⠇⠁⠀⠙⢿⣇⢸⡟⠟⠻⠿⣄⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠤⣸⣮⠑⠒⠉
⠀⠀⠘⣁⠘⠁⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⣿⣾⡏⣾⡿⠈⠀⣈⣿⡆⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠙⢷⣄⣠⣾⣷⡁⠀⠀⠀⢀⣴⡿⠟⠟⢧⠤⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠀⡾⣿⣿⣿⣆⡀⠀⠀⠀⣹⣷⣄⡀⠀⣤⣿⣿⠿⢿⠛⠁⠐⠠⢴⡎⠁⠀⠀⡰⠁⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢤⠄⠀⠀⠀⠙⢧⡀⠀⠰⣿⣿⠋⣿⣄⠀⠰⣿⡟⠁⠸⣿⣷⡦⢶⣿⣱⣿⣦⣿⣿⡿⡏⠀⠀⠀⠀⠀⡠⢾⣷⣶⣤⡾⠃⠀⠀⠾⣿⣽⣿
⠀⢸⢀⠴⣀⠀⠐⠄⠃⠀⠀⠀⠀⠰⣦⠁⢀⣴⣿⠈⠀⠻⣿⣟⠓⠀⠀⠀⠀⢨⣿⡁⣼⡿⢋⣿⠟⠙⠏⠀⠀⠀⠀⠀⠀⠾⠄⠀⠹⣧⠀⠀⠀⠴⠳⡀⠴⠿⠛
⢀⢾⣕⢦⡉⠶⣤⢄⡤⠤⢄⣠⠀⢠⡟⢀⠎⠁⠁⠀⠀⠀⠈⠙⢓⣤⣤⣦⣠⡿⠉⠻⣯⠈⠂⠀⠀⠀⠀⠀⠀⠀⣄⣀⢼⣄⡄⠠⠈⠉⠉⠻⣧⣄⠀⠠
⠀⡀⠙⠿⣿⠶⠶⠂⠀⠀⠈⢻⣟⠋⠁⠀⠃⢀⠀⠀⢀⣤⣤⣴⣿⢀⣿⣿⡄⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⣠⡀⣷⣿⡏⢸⣷⡤⢄⠀⣤⣾⣧⢍⡿⢦⠀⠀⠀⡀
⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣷⣠⡿⡿⣿⣿⣻⠛⠿⣿⣷⣄⡀⣠⢲⡄⠘⣧⠀⠀⣴⣿⣿⡿⢿⠁⣘⡤⢃⣼⠛⠿⠿⣿⣃⣽⠃⠀⠀⠀⡇
⠀⠀⠙⠸⡓⠤⠀⠀⠀⠀⠀⠀⣿⣄⠀⢀⣠⣾⡿⣿⠀⠁⠘⠿⣿⣄⠀⠀⠈⣿⣿⣷⡶⢤⣁⣸⣾⣽⠿⡟⠉⠀⣈⣦⢹⣿⡛⠀⣠⠴⠖⢯⡽⣇⠀⣔⢠⡏⠅
⠀⣶⡄⠀⠈⠁⠘⢻⣶⣄⠀⣸⣷⢭⡴⠿⠋⠉⠀⠀⠳⣄⣀⣀⣬⣿⣆⡀⠀⠸⣿⣿⣬⠁⣨⣿⠿⠡⠆⠀⠀⢀⡿⠃⠀⠻⠤⠔⠀⠀⠀⠀⠃⠉⠀⢻⣾⠇⡀
⠀⠺⣯⡀⠀⠀⠠⣿⣷⡍⣠⡍⠛⠀⠁⠀⠀⠀⠂⢀⣶⣿⠿⠋⠉⢛⣿⣧⠐⢄⣿⣷⣠⣾⣿⡟⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⢦⣷⣶⣨⣁⣿⢀⣿⡟
⠀⠀⠈⢿⣷⡤⠔⠋⠀⠀⣠⣿⣥⣴⣦⡆⠀⠀⠀⣸⡿⣉⠀⠀⠀⠋⠘⣷⣀⣨⠷⣿⡿⠏⠻⡀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣀⣷⣿⣋⢽⣻⢏⣼⡿
⠀⠀⠀⢶⣿⣷⡀⠀⠀⢴⣿⣿⣿⣿⡟⢁⣴⣶⣿⣿⡃⠛⠄⠀⠀⠀⠈⠺⣿⣿⡇⠃⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠋⠙⠛⣿⢿⣿⡾⠛⠁
⠀⢀⠀⠀⠹⣿⣧⣴⣶⣿⠋⠛⠏⠿⢻⣿⣿⣟⢻⣆⠹⣄⠀⠀⠀⢰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡞⡿⠃⠀⠀⠀⠏⣼⠏⠁
⠀⣼⣀⣬⣦⣿⣿⡷⠛⣷⡀⠀⠀⢐⣿⢿⣿⣿⡄⢻⡄⠈⢳⣄⠀⣼⡿⠫⠋⠀⠀⢰⠀⠀⠀⠀⠀⡌⣷⡄⠀⠀⢀⢠⣗⠀⠀⢀⢂⠀⠘⠏
⠀⢹⣿⣿⣿⡏⢻⡅⠀⣼⣧⣀⣼⣿⡅⠀⠛⢸⣷⠎⢹⣾⣿⣃⣾⡯⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⣿⠋⠘⡆⣰⣾⠇⢉⠃⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢻⣿⡏⠀⠀⠙⠆⣾⣿⣽⡟⠀⢣⡀⠀⠀⠙⢧⣸⢟⣰⣾⣋⡀⠀⢀⠀⠀⠀⠀⣯⠀⠀⠀⢠⣿⡉⢀⣷⡿⠋⠀⡀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⢀⣶
⠀⠀⢿⣿⡄⠀⠀⠀⣀⠙⠁⠰⠀⠀⠀⠛⢠⡀⠀⠀⣿⣾⣿⣭⢿⣿⠀⠈⣷⡄⠀⣴⠏⠀⠀⢠⣿⣻⣣⡾⣻⠉⡄⠀⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣼⡇
⠀⢠⡄⠀⠁⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠀⠀⢷⠀⢠⣼⣿⣷⠷⠋⣻⣦⣰⣿⣷⣾⡟⠀⠀⣠⣞⣳⣿⡟⠃⠑⡶⢀⢀⠆⠀⠀⠀⠀⠀⠀⣼⢠⣶⡾⠛
⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠰⡟⠀⣼⣇⢿⡇⠀⣸⡿⠿⢻⣿⣿⢏⣤⣾⡾⠃⠼⡧⠸⠁⠀⠘⣧⣟⡴⠁⠀⠀⠀⠀⠀⣼⢿⣿⠋
⠀⢸⠆⢀⢀⡀⣼⡇⢱⡀⠀⠀⠀⠀⠀⠀⠜⠁⣼⠻⡫⠈⢷⡀⣃⠀⣰⣿⣿⣷⣿⣷⣏⠁⠀⢘⠀⠀⠀⠀⠀⢳⡿⠀⠀⠀⣀⠀⠀⢸⠏⠀⡏
⠀⠀⣷⣿⡞⠁⠟⠀⠘⠁⠄⠀⠀⠀⠠⠄⢊⣾⡁⠁⠀⠀⠀⠈⠛⠄⠛⠿⠿⣿⣿⠿⡋⠀⠀⠀⠈⠄⠀⠀⠀⠀⠁⠤⠠⠾⠋⠉⠀⠸⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠦⠄⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⢿⣷
⠀⠀⠀⠀⠀⢀⣴⠟⠛⡿⠟⠉⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠒⠀⠀⠀⠀⢠⠘⠁
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣇⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣿⠁⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠘⣦⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠱⣄⣀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠗⠂⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠈⠛⠿⣾⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠐⠛⠿⣿⡿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⡄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠐⢤⡀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⣰⣿⣁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠃⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠁⢻⣧⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣀⣴⣾⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢿⣷⣶⣶⡶⠋⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠙⠷⣄⣀⣀⡀⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠄⠄⢀⠆⠀⠠⡀⠀⠀⠂⠀⠀⢀⡀⠀⠈⠤⠀⠀⠀⠆⠀⠀⠀⢀⠒⢀⡀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⢀⠄⠂⠀⠀⠐⠀⢸⠁⠠⢤⡅⠀⠀⠀⠀⠀⠀⠈⠄⢠⠐⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠐⠄⠀⠐⢀⠠⠈⠀⠀⠀⠐⠐⠀⠀⠀⠐⠒⠒⠊⠁⠠⠄⠀⠀⠐⢤⠀⠴⠄⠀⠀⠀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⣤⡁⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⠔⢠⣤⠌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠤⠤⡲⠀⢉⠛⠶⢲⠤⠤⠤⠤⣄⣀⡠⠤⠤⢤⡒⠍⢚⠴⢨⡖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⡖⠶⡈⠐⠀⠀⠀⠀⠀⠉⠉⠐⠐⠐⠉⠱⣩⠀⠂⠌⠃⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⠀⠀⠂⠀⠀⠐⡄⠉⠀⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠐⠀⠄⢀⡀⣀⣀⣀⢤⠠⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠑⠂⠀⠀⠀⠀⠀⠠

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠊⠀⢴⣾⣿⣿⠀⠘⠈⠙⠓⠀⠀⠒⠀⠀⠀⠐⠁⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⡿⠀⡀
⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⠀⠀⠀⠄⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠄⠀⠀⠀⠀⠀⠀⠀⠋⡟⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾
⢀⠔⠈⠁⠈⠁⣀⠀⠀⠀⠀⢠⣖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢀⣾⣏
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤⠀⡴⠊⠉⠉⠐⢄⠀⠀⠀⠁⢄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣀⡀⢀⣤⣿⣿⣟⡡
⠁⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠦⣄⡠⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⡀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠑⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡻⣿⣿⣷
⠙⠂⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠴⠊⠁⠀⠀⢀⣿⡟⠃⠀⠃⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀
⠀⠀⠀⠈⢱⣄⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠈⢆⠀⠉⠁⠀⢄⠵⠶⣦⠀⠀⠀⠀⠀⢀⠀⠀⢽⣿⣿⡇⠀⣾⠇⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢀⣀⢀⡀⠉⠉⢻⣿⣿⣧⢠⣿⣷⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠻⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠳⡀⠀⣰⠁⠀⠠⡄
⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⡀⠐⠃⠀⠁⠈
⠀⠐⢄⢿⡄⡀⠀⠀⠀⠀⠕⠀⠄⠀⠀⠀⠀⠀⠀⠒⢂⣩⡴⠋⡉⠀⠙⢷⡀⠈⠀⠀⠐⠒⠒⠄⠠⠄⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆
⠀⠀⠀⠀⠙⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠅⡔⠁⠀⠋⠀⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣴⣶⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠖⠀⠀⠀⠀⠀⠀⠁⠰⣀⠀⢀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⠀⠀⠀⠈⠙⠙⠓⠚⠠⢄⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠉⠉⠒⠆⠒⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣦⢠⠀⢀⣴⣿
⠀⠀⠀⠀⠇⠑⠂⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢺⣧⣠⣿⣿⣿⣿⠏
⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠸⠁⠀⠀⢀⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢀⣀⠀⠀⠀⠈⢻⣿⣷⣀⢠⠀⠀⣤⣿⣿⠋⢀⠀⠠⠠⠀⠠⠄⠀⡸⠉⠐⠙⠧⣐⠀⠤⠤
⠲⢀⠈⠁⠀⠁⠀⠀⠠⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠈⠻⣿⣿⠛⠃⢸⣿⣿⡡⠊⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⠒⠒
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣷⣶⣦⣉⡀⠃⢌⣿⣟⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠐⠚⠉⠉⠉⠻⠛⠛⠛⢻⡿⢿⠁⣠⡆⢫⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⢋⣉⣥⣤⣤⣤⣤⣤⣤⠄⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣡⣾⡿⠿⠛⠛⣻⣿⣿⠟⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⣸⣿⠏⠀⠀⣠⣾⣿⣟⣁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢀⣿⡟⠀⠠⠾⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⣾⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣿⣿⠟⢁⣾⣿⠃
⠀⠀⠀⠀⣠⣾⣿⡿⠟⢛⣋⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣉⣩⣤⣾⣿⠟⠁
⠀⠀⠀⣼⣿⠟⣡⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⢸⣿⡏⣰⣿⠟⠁
⠀⠀⣿⣿⡇⣿⣿
⠀⠀⢹⣿⡇⢻⣿⡆
⠀⠀⠘⣿⣿⡈⣿⣷⡀
⠀⠀⠀⠹⣿⣧⠘⣿⣷⡀
⠀⠀⠀⠀⢻⣿⣧⠘⣿⣷⡀
⠀⠀⠀⠀⠀⢻⣿⣧⢙⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⢒⣒⣒⣒⠒⠦⠬⣍⣓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⣋⣩⣭⠭⠭⣭⣭⡙⠓⠶⣭⡙⠶⣍⡳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⠴⢚⣩⠴⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠎⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢰⡇⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡀
⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡
⠀⠀⠀⢸⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⢸⠘⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡾⢸
⠀⠀⠀⠈⡇⢷⢸⡄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠇⡞⠰
⠀⠀⠀⠀⠱⡘⣆⢳⡘⣆⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠏⡼⢁⠇
⠀⠀⠀⠀⠀⠡⡘⢆⠳⡜⢦⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⡼⢡⠏⡐
⠀⠀⠀⠀⠀⠀⠑⠈⠣⡙⢦⡙⢦⡙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⢏⡴⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠉⠢⢌⠓⠤⢍⡓⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⢠⡴⢋⡵⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣩⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣭⠵⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⣽⣽⣯⣯⣗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣮⡾⠛⠹⠻⠟⠏⠛⢷⣵⡱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠗⡄⠀⢀⣀⣤⣤⣴⣧⣿⡋⠀⠀⣠⣽⣮⢄⡀⠀⢙⣿⣼⣦⣤⣤⣀⡀⠀⢠⠺⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣾⡟⠛⠉⠍⠉⠉⠙⢿⡶⢝⠜⢯⡽⠣⡫⢶⡿⠛⠉⠉⢩⠉⠛⢻⣷⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⡿⣯⣢⠸⡈⠀⡇⡰⢭⠃⣀⣡⣎⣀⠘⣭⣧⢘⠀⠁⠇⣔⣽⢿⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⣈⡚⠿⢇⣣⣤⢧⣽⣷⠞⢋⣉⣉⡉⠻⣾⡧⡼⢬⣜⡸⠿⢓⣁⠠⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⡇⠀⠂⠨⠍⣾⣶⣻⣟⡿⢱⣞⣭⠴⠦⣭⣳⡎⢿⣫⣟⣦⢷⠉⠁⠐⠂⢸⣿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⣵⡿⠻⣷⣄⢉⡨⣉⣷⣿⡽⡡⢎⠻⠬⢣⠎⠱⣜⠥⠟⠹⢬⢯⣾⣾⣩⣅⡉⣠⣾⠟⢿⣮⢕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⣾⠋⠀⠀⣜⢏⠧⠛⣽⠟⣱⠶⡛⡆⠠⡢⣬⡐⢂⣥⣔⠄⢰⢛⡶⣎⠻⣯⠛⠼⡹⣣⡀⠀⠙⣿⡞⣆
⠀⠀⠀⠀⣠⣀⣄⣠⣗⣿⣷⡖⣄⣞⡾⣁⠄⣸⡇⢰⢃⡟⡩⠖⢂⠻⡿⣫⣝⢿⠟⡒⠲⢍⢻⡘⡆⢸⣇⠠⣨⢷⣳⣠⢐⣾⣿⣺⣄⣠⣀⣀
⠀⠀⠀⠀⠙⠉⠋⠙⡯⣿⡿⠅⠋⢿⠷⡋⠊⢹⡇⠸⡌⣧⣑⠦⠌⣴⣷⣝⣫⣾⣦⠥⠴⣊⣼⢡⠇⢸⡏⠑⢉⡾⡽⠙⠬⢿⣿⢽⠋⠙⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣿⣄⠀⠈⢫⣎⡖⣤⣻⣦⡹⠾⣭⠇⠐⠝⢻⠡⠌⡟⠫⠂⠸⣬⠷⢏⣴⣟⣤⢶⣱⡝⠁⠀⣠⣿⢯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⡻⣷⣴⣿⠋⣈⣙⣋⡿⡿⣳⡑⣆⣰⢒⡜⢆⡰⢣⡒⣦⡰⢎⣞⢿⢿⣉⣚⣉⠙⣿⣦⣾⢟⡪⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⡇⠀⠄⠐⣀⢿⠻⣽⣫⣷⡸⢯⣛⠲⠖⣛⡽⢇⣾⣝⣫⠟⡾⣀⡀⠠⠀⢸⣿⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠒⢉⢥⣶⡎⡝⠛⡖⣺⡿⣦⣈⣉⣉⣁⡴⢿⡟⢲⢚⢫⢱⣶⡬⡉⠐⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣷⣟⠝⢰⢁⠁⡇⢰⣛⡄⠉⡹⢏⠉⢠⣟⠞⢸⠀⠀⠆⠫⣻⣾⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⢿⣧⣤⣀⣂⣀⣀⣠⣾⠷⣪⢦⣞⣳⡴⣝⠾⣷⣄⣀⣁⣘⣀⣤⣼⡿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡦⠃⠀⠈⠉⠛⠛⠻⡟⣿⣅⠀⠈⠑⣺⣟⠊⠁⠀⣨⣿⢻⠟⠛⠛⠉⠁⠀⠘⢴⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⢟⢷⣤⣸⣴⣦⣇⣤⣾⡻⡱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢭⣻⣻⣿⣟⡯⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠫⠀⠀⠈⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠐⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠙⠒⠒⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⡀⠀⠀⢀⣀⠀⠀⢀⡄⡤⣄⣠⡀⠀⢠⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⠠⠶⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠴⠃⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠢⠀⠀⠰
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠊⠉⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠾⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠉⠛⠿⣿⣿⣍⡛⠛⠿⠿⢿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀⠀⠀⠉⠙⠛⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣍⠉⠉⠉⠉⠉⠉⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠺⢿⣃⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠦⠀⠀⠈⠑⠳⠾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣠⠀⠀⠀⠈⠋⣲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠗⠈⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣿⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠤⡀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣀⡄⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠰⠀⠀⡦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢧⠸⣿⣧⡷⣿⡧⠖⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠯⠿⠛⠹⠛⢛⠪⡓⠿⠿⠋⠁⣀⣘⣿⣤⣴⣶⣶⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠂⠒⠂⠐⠻⠛⠛⠋⠃⠀⢶⡛⠻⢿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⢄⣀⣀⣀⣀⣀⡤⠼⠛⠛⠋⠉⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠟⠛⠛⠿⠿⠿⠟⠟⠻⠿⠿⠻⠟⠻⠾⠻⠿⠾⠾⠲⠇⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣦⠾⠟⠟⠋⠉⠉⢉⠋⠉⠻⢛⣲⣶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣿⣿⠃⠈⠁⣀⠀⠀⠐⢯⣀⡀⠀⠀⠈⠂⡑⠼⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⢻⣿⣧⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣟⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠏⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡄⣌⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣿⣿⣿⡟⢡⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡄⣽⣇⣸⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⢃⡞⠁⢀⣀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⢠⣧⣼⣷⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠊⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⡁⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡓⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠿⠛⠛⢉⣝⣩⣰⣾⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣸⢇⢴⡿⢻⠂⠀⢈⣾⠐⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆⠀⠀⣾⣧⣤⣾⠃⡞⠀⠀⠘⠏⢺⣿⣿⢠⣿⣿⣿⣿⣿⣿⣧⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⡏⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣽⣿⡿⢻⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣟⣿⣿⣾⣾⣿⣧⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢉⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣽⣯⢁⣀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⣿⣿⣿⣿⣊⠿⣿⣿⣿⣿⣍⣹⣿⣶⣬⣻⣿⠿⠏⠃⠀⠀⠀⠀⢀⣙⠛⣶⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡻⠻⣿⣿⣿⣿⣷⣟⢿⣿⣿⣿⣿⣿⣿⣭⢉⣁⡐⠆⣶⡖⣤⠄⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠝⢿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣁⡉⠉⠁⠴⠶⠀⢳⣀⠙⠿⠿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡐⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣁⠀⠛⠓⣀⠈⠉⠤⠤⠀⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣤⣤⡀⠐⠂⠲⣹⣿⣿⣿⣿⣿⣹⣿⣿⣿⡚⢿⣿⣿⡹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠙⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣏⣹⣙⠛⠛⠛⠛⠏⠐⠒⠊⠉⣽⡿⣿⣿⣿⣖⣻⡟⢯⣹⣿⡙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⢠⣶⣤⣬⣭⣿⣿⣿⣾⣿⣿⣏⠉⠛⠙⠋⠛⠿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠿⢿⣿⡿⠟⠃

⠀⠀⠀⠀⣄⡀⠀⠀⠀⣀⣤⡦⣤⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⣠⣾⣿⡿⠃⠀⢰⡟⠁⠀⢀⠇⠐⠻⢿⢿⣦⠀⠀⠀⠀⣾⣿⠀⠀⠀⣠⣠⣿⡇⠀⢀⡴⠛⠛⠋
⠀⠀⡟⠁⠈⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⢠⣀⣠⡿⠀⠐⠶⠾⠟⠁⠀⠀⠰⠿⢿⠉⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⣀⣀
⠀⢸⣷⣆⠀⠀⠀⠀⠀⣠⣤⣾⠿⠀⠘⣦⣤⣀⠀⠀⢠⣿⠛⣿⣷⠆⠀⠀⢀⣰⣿⡇⠀⠹⠛⠛⠛⢹⠇
⠀⠀⠈⠛⠛⠒⠂⠀⠀⢹⠉⠁⠀⠀⠀⠀⠹⢿⡟⠀⠈⢿⡀⠀⠉⠀⠀⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠏
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠉⢳⣦⠀⠀⣸⠋⠙⠛⠿⠂⠀⣠⣶⣷⠄⠀⠀⣠⣤⣼⣶⡄⠀⣴⣦⡀⠀⠀⠀⢶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣿⣇⠀⡏⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⠀⢸⠋⠉⠘⠁⠀⠀⢹⣿⡶⠋⠁⠀⠀⠉⠀⠈⢻
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣞⠁⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⣷⠈⠉⢠⡟⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⡽⠿⠿⠿⠿⠷⠚⠋⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⣠⣶⡯⠞⠋⡉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⡀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠿⣒⠿⠛⠉⠀⠀⠘⢦⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣦⠀⡰⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣒⣒⣃⣀⣈⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣭⣭⣭⣙⣓⣒⠶⠤⢤⣤⣤⣤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠤⠀⠀⠐⣒⣒⠒⠒⠒⠒⠲⣦⠀⠀⠀⠀⠀⠀⠊⠉⠀⠒⠂⠒⣂⠬⠉⠉⠛⠛⠒⠶⠶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡆⠀⢇⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠘⠀⣀⠔⠁⠀⠐⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣨⠃⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣜⣁⣀⣀⣀⣈⣀⣀⠀⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠩⠄⠀⠐⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⡄⠀⡄⠈⢳⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠭⠭⣅⣐⣒⠒⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣢⠐⠴⠃⠀⠑⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢻⡆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠳⣌⠻⣦⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⠘⢦⡼⠳⠋⠀⠀⢻⣄⣠⠇
⠀⠀⠀⠀⠀⠀⢯⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣠⠞⠁⠀⠀⠀⠦⣈⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⣠⠴⢾⡉⠉⠉⠉⠉⠙⠚⠁⠀⠀⠠⣄⢱⡶⠋⠀⠀⠀⠀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠟⠀⢠⠞⠁⠀⠀⠙⣦⠴⢲⣄⣠⠄⠀⠀⠐⣦⡼⠋⠀⠀⠀⠀⠀⠈⠳⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣆⣤⠄⠀⢠⡏⠀⣸⡋⠀⠀⠀⡀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣾⢠⣌⣀⣀⣀⠈⠓⠀⠈⠁⠀⠀⣼⣃⠀⢸⡆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣏⣹⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⢿⣷⡶⢶⣦⣤⣭⣍⢻⡇⠀⠀⠀⠀⢼⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⡄⢿⣿⣯⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⠏⡾⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣎⠻⣿⣿⣿⠛⢻⣧⣿⣿⣿⡿⢋⡾⠁⣠⠖⣾⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣟⠉⢹⠇⠀⠈⠳⢮⣙⡻⠶⠾⠿⠿⣛⣩⠶⠋⠀⢼⣇⠀⣩⡷⢀⡴⠚⠛⣳
⠀⠀⠀⠤⠶⠶⠶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⣶⡶⠶⠶⠶⠤

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⢀⣀⣤⠶⠖⣛⣫⣭⠥⠶⣒⣒⣶⣯⡭⢓⢦⣀
⣋⣥⡴⠞⣛⣩⡥⠶⢚⣩⡭⠶⢚⣫⡭⠷⣒⣫⢷⡠⣄⢤⡀⢀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⣛⡛⠛⠛⠛⠿⠶⠶⣦⣤⣤⣤⣤⠴⠶⠛
⣩⡤⠶⢛⣩⡥⠶⢛⣩⡥⠶⣛⣩⡴⠖⣋⡭⠶⣚⣷⡈⠷⠙⣊⣃⡤⠴⣚⣫⡭⠶⠚⣛⣛⣉⣉⡛⠛⠛⠻⠷⣶⣦⣤⣤⣤⣤⣴⣶⡾⠿
⠵⢖⣛⣭⠵⣖⣛⡭⠴⣒⣫⡭⠶⣚⣫⠵⣒⣯⠵⣚⣩⣭⡭⠥⠶⣚⣋⣭⠶⠖⣛⣋⣉⣉⣉⣙⠛⠛⠿⣶⣦⣤⣀⣉⠉⠉⣉⣀⣀⣠⣤
⣍⡩⠷⠮⠽⢓⣒⣚⣭⡭⠶⣚⣫⠭⢖⣫⠵⣒⣋⣉⠉⠛⢿⣟⣭⣭⡥⠶⢚⣛⣉⣭⣭⣍⣉⡛⠛⠷⣦⣄⡈⠙⠛⠿⠿⠿⠿⠿⠿⠛⠛
⣉⣉⣉⣉⣉⣉⣭⣥⠴⠖⣛⡭⢖⣪⠽⢒⣋⣉⠙⠻⣿⡆⢸⡟⢰⢒⣒⣛⣩⡭⠤⠶⠦⢤⣭⣙⠻⢶⣄⠙⠻⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠛⠛⠛⠛⣋⣉⣥⠴⢞⣫⠵⣚⠽⣒⣛⣉⠙⠻⣿⡄⢸⡇⣸⠃⡏⣮⡲⠿⠶⣒⣛⣛⣛⡒⠦⣍⠳⣦⡙⢿⣦⣀⠉⠙⠛⠛⠻⠿⠿⠿⠿
⠿⠿⠟⠛⣋⣩⠴⣚⡭⣶⢟⣚⣋⣉⡙⠻⣷⠀⣿⠁⣿⠀⣿⠀⢷⣬⣭⡭⠭⠶⠶⠶⣬⣉⠳⢮⡙⢦⡹⣦⡈⠻⢿⣶⣦⣤⣤⣀⣀⣀⣀
⣤⡶⠾⣛⡭⢖⡯⣷⣟⣯⠭⠥⣬⡙⣷⢀⡟⢰⣿⠀⣿⡀⠙⠷⠶⢶⣒⣛⣛⣛⡛⠶⣦⣉⠳⣦⡙⣎⢳⡌⠻⣦⣀⠉⠙⠛⠿⠿⠿⣿⣿
⣤⠶⣻⢽⣺⣿⠿⠛⠉⠉⠀⠉⢸⡇⡏⢸⡇⠸⣿⣄⠙⠛⣛⣛⡯⠭⠭⠷⠭⢭⣍⡓⢦⣝⠳⣌⢳⡌⢧⡹⣦⡈⠻⢿⣶⣤⣄⣀⡀
⣖⣭⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⢸⠘⣧⠘⢿⣤⣈⣙⣛⡭⢽⣒⡾⢭⣭⣭⠭⢟⣲⢭⡳⢍⠳⣝⢦⡹⣌⢳⡌⠻⣦⣄⠉⠛⠻⠿⣿⣿⣷
⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠙⢷⣤⣬⡭⢽⣒⠯⢗⣺⡭⠽⠷⠶⠯⠭⣗⣛⡯⠷⠽⠮⠶⢕⣌⠣⡙⢦⣌⠛⠿⣶⣤⣄⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣛⣒⣒⣒⣫⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠈⠳⢍⡳⢦⣌⡉⠛⠿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠨⢝⠳⢦⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠛⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠈⠻⣿⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠎⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠃⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⡠⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⢠⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠠⠀⣀⡀
⣰⣄⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⡌⠉⠀⠄⠀⠀⢀⣠⣤⣀⣀⡀⢦⣊⢰⣗⣀⣄⣤⣤⠔⠺⢭⣄⡀
⢽⣭⢹⣅⣀⠀⣴⣶⣖⣤⣴⣶⡿⣴⠦⠀⣀⣤⣶⣛⢶⣿⡻⢷⢆⣼⡿⣿⣽⣛⣋⣽⡛⣗⣩⠝
⠿⢭⣿⣿⢿⣏⣭⣿⠿⣭⣷⢿⡧⢶⣼⣿⣿⣥⢕⣜⣻⣶⣷⣻⣕⣾⢛⣳⣏⣿⣿⡨⣻⣾⣿⣿
⣾⢽⣏⣾⡿⣽⣭⣟⢾⣗⣾⡿⣷⢾⡿⡽⣯⣷⢿⣿⣿⣾⣟⢿⣿⢻⣽⣻⣭⣟⠛⢃⣻⣓⣿⡽
⣟⢿⣽⣿⣕⣿⣿⣿⢿⣻⣿⣭⣾⣿⣿⣿⣿⣏⢺⡇⣬⣼⣿⣼⡶⢯⣽⣿⣹⣭⣿⡷⣻⣯⣿⣾
⣿⣟⣫⣟⣽⣾⣯⣿⣙⣷⣝⣼⣿⣷⠿⣮⡿⣋⠶⢸⣿⣏⣴⣾⣵⡿⢷⣯⣷⢇⡽⣿⣻⡿⣿⢿
⣾⣛⠿⣿⢟⣋⣴⣟⣻⠿⣯⣿⡯⢽⣲⣼⣿⣿⣷⡿⣽⣿⢿⣙⣿⡿⣾⣿⡿⣾⣳⣿⣽⣿⡿⣙
⣷⣍⣾⣿⣼⣻⣷⣧⡿⠷⣾⣵⣚⣝⣿⣾⣿⣿⣿⣿⠿⠿⡏⢻⡾⣿⢿⢿⣿⣡⡶⣭⣽⣿⣿⢹
⣽⣻⣿⣿⣯⢟⣿⣿⣷⣼⣿⣿⣷⣿⣿⣿⣷⣟⢙⣃⣶⣶⣷⣿⣿⣿⣯⣻⠟⢏⡷⢓⣾⣫⣿⣿⡇
⡍⣟⣣⣿⣽⢆⣿⣟⣛⣿⣹⣿⠿⣿⢿⡯⣟⡿⣎⣨⡹⣺⣿⢯⠿⣻⣿⣿⣷⣿⣿⣾⣷⠝⣛⣿⠂
⠷⢛⣻⣽⣻⢻⡵⢎⣷⡿⣙⢿⣠⣿⣿⣿⣾⡾⣵⣿⣿⡿⣯⣻⣌⠭⣑⣿⢩⣥⣿⢛⣵⣿⣿⣿⡄
⢿⣿⢿⣭⣻⡿⡿⣾⣿⣞⣅⠚⢿⣟⣽⣏⣝⡺⢿⣷⣿⣿⣯⣴⣇⣾⣿⣯⠛⡻⣧⣿⢿⣾⣿⣼⡇
⣿⢽⡾⣿⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣾⣯⣿⣽⣿⣿⣶⡛⢖⣽⡾⢿⣧⠿⣵⣿⡿⣾⣿⡛⣿⣿⡇
⣷⣺⣷⣿⣿⣿⣻⣿⣧⣽⣿⣾⣻⣼⣿⣿⣏⠻⣾⣿⣿⣿⣿⣾⢛⢻⣛⣷⢿⣿⣿⣿⣯⣟⣿⣿⡃
⣻⣾⣿⣿⣿⣿⣿⣥⣿⢷⣯⣿⣯⣿⣿⣏⣙⣿⣄⣟⣿⣭⣿⢿⣿⣿⣿⣾⡭⣿⢻⣿⡿⢿⠿⢿⡇
⣿⣭⣤⣿⢛⣧⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣿⣺⣿⣿⣵⣗⣿⣿⣶⣯⣿⣿⡼⠛⣾⣿⣷⣿⡇
⣟⣥⣍⣛⣷⣿⣿⣿⣯⣵⣿⠿⢛⢿⣿⣿⣿⣻⡿⣷⢹⣿⣿⣿⣿⣿⢟⣽⡿⠿⣆⣺⣟⣻⣿⣿⡇
⠙⠉⠛⠉⠉⠈⠙⠛⠛⠛⠋⠛⠛⠋⠀⠛⠋⠛⠙⠑⠛⠙⠊⠉⠉⠑⠛⠛⠛⠛⠊⠉⠛⠁⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⡿⠟⣋⣉⣉⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣫⣭⣶⣾⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⢸⣇⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⣾⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⢿⡟⠁⠀⣠⣶⡟
⠀⠀⠀⢻⣿⣿⣿⣧⣿⣿⣿⣿⢷⠿⢀⣴⣿⣿⠟
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠁
⠀⡀⠀⠀⠀⠀⠘⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⣶⣶⣾⣿⣿⣿⣿⣷⣶⡆⣠⣉⡛⠿⣿⣿⣾⣿⣿⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠐⠒⠒⠲⠶⠶⣦⣤⣭⣙⠛⠿⣿⣿⣿⣧⡙⢿⣿⣷⣦⣍⠛⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣙⠻⢿⣶⣬⣙⠻⣿⣿⣶⣬⣿⣿⣿⣿⣶⡌⠙⠻⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣋⣹⣿⣿⡿⠻⣿⣿⣿⣿⣷⣦⣌⡙⠿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣵⣿⣿⣶⣿⣿⣿⣿⠃
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠻⣿⣿⣾⣿⣿⣿⣿⣿⡟⢻⣿⣷⣤⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢠⡟⠀⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⠈⢻⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⣿⣿⣦⣌⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠸⣧⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡟⢻⣿⣶⣿⣿⡿⢿⣿⣶⣿⡿⠿⣿⣿⣷⣦⣉⠛⢿⣿⣿⣿⠏
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣿⣿⡿⠿⣿⣶⣾⣿⡿⢿⣿⣶⣿⣿⡛⣻⣿⣿⣶⣌⡙⠻⠗
⠀⠀⠀⠀⠸⣇⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣿⡿⠿⣿⣷⣾⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡿⠟⠉⠀⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠛⠙⠷⣤⣤⣤⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⠁⠀⠀⢠⠇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⡀⠀⠋⠀⠀⠀⠘⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⠷⢦⣤⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠢⣾⣿⣏⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⡆⠉⠛⢿⣧⠀⠀⣠⡀⣠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣶⣶⣿⣥⣶⡶⣄⠀⠀⠀⠻⠧⠀⠙⠿⣯⠱⣴⠿⣿⣄⡀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⢠⣤⣤⡴⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠙⠆⠀⠀⠀⠀⠀⠀⠙⠿⣆⠀⠀⠀⠙⢶⠦⣾⡿⠿⠛⢟⠷⣤⣄⣤⠞⠋⠉⠻⠦⢀
⠀⠀⠀⠈⠛⠙⠇⠈⠻⠿⢁⣴⣿⣿⣿⠆⠀⠀⠀⠀⢀⣠⣤⣶⣶⢠⣀⠀⠀⠐⠀⢠⣄⣀⣀⠀⠀⢀⣴⠾⣿⣯⠙⠆⠀⠀⠀⠈⠙⠳⠤⠶⠒⠒⣦⣄
⠀⠀⠀⠀⠁⠠⣶⣾⢿⡄⠈⠻⣿⣿⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡇⠙⠻⠔⠄⠀⠀⠉⠉⠉⠃⠒⠉⠀⠀⢀⣿⠀⠀⠈⠂⠀⣰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠂⠄⠀⠙⢶⣶⣶⣾⣿⣿⣿⣿⠟⣻⢿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠘⠃⡜⠀⢠⠟⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠣⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⠔⠀⠐
⠀⠀⠀⢠⣀⣀⠒⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠉⠓⠀⣠⠀⠀⢀⡶⠛⢉⠀⠈⢀⠀⠀⠀⠀⠀⠈⠻⢿⢿⣆⢀⠀⠀⠀⠸⣿⣿⣿⣤⡴⠂⠐⠃
⠀⠀⠀⢸⣿⣿⣷⡖⣤⣀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠐⠆⠉⢀⡠⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠻⠿⢿⠛⠀⢀⣻⣿⣿⣿⣿⣅
⠀⠀⠀⠘⠻⠉⠉⢙⣿⣿⣿⣶⣿⡆⣀⣄⢸⣿⣧⠀⣠⡀⠀⠀⠀⠉⠺⠿⣿⣿⡛⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⢀⢢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣿⢿⠀⠀⠀⢀⣴⡄⠀⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⣤⡀⠀⣀
⠀⠀⠀⠘⠷⢾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⡄⣸⣿⣷⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠛⠿⠿⠿⣿⡟⢿⣿⣿⣷⣿⣿⣿⣿⣷⣾⣧⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠁⠀⠈⠉⠉⠙⠛⠛⠻⠿⠧⠀⠀⠀⠾⠷⠾⠿⠟⠉⠉⠋⠙⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣿⣟⡻⣿⣷⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣟⣿⣿⠆⠀⢹⣿⣿⣿⣿⣷⣶⣄⣶⣄⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣤⣀⣀⡀⣐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢰⣧⡀⠀⠜⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⡀⠀⠀⠀⢀⡤⠊⠠⠈⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠂⠠⠀⡀⣿⣦⠈⠉⡟⣻⣿⣿⡍⠉⠻⢿⣿⣿⣿⣧⣿⣶⣦⣼⣤⣶⡟⢉⣴⣷⡄⠀⠀⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⡦⢀⣦⣷⣿⣿⢦⡀⠿⠛⢿⣿⣿⡆⠀⠀⠻⣿⣿⡿⢿⣿⢿⡿⠝⠋⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢀⣾⣿⣿⣷⠀⠈⣉⣇⠀⣨⣿⠛⠿⠀⠀⠀⠘⣿⡿⣞⣡⣶⣿⣿⣶⣤⣤⣼⣤⣤⡶
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣷⣶⠤⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣿⣿⣿⠟⣉⠟⠁⠄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⡀⠀⠉⣿⣿⣿⣿⡿⠿⢿⣿⣷⣾⡃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢉⢿⣿⣌⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣌⡈⡿⣿
⠀⠀⠀⠀⠘⣿⣿⡟⠋⠠⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⢠⣯⠾⣿⠂⡄⠀⠀⠀⠄
⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡟⠛⠛⢹⣿⣿⣿⣿⣶⡶⠟⢠⣾⣷⣞⡇⡶⠀⠀⠀⠀⠀⠀⠑⡆
⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⢠⡀⣰⣿⣿⣿⣿⡛⠋⠀⠀⢸⡟⢿⡇⠀⣷⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⠀⢀⠀⠀⣰⣌⣿⣿⣿⣿⣿⣿⣷⣾⠗⣿⣿⣿⣿⣿⠛⣋⣠⣶⣾⣧⣾⠇⠀⠙⠉⠑⠂⠀⠠
⠀⠀⢀⣠⣖⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣤⣇⡀⠸⣏⣙⣿⣿⣾⣿⣿⣿⣿⣿⣏⣐⣀⡀⠀⠀⠀⣰⠁
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢀⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡴⢰⠇⠀⠀⠈⠀⢻⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⡆⢀⠀⠁⢚⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠿⣿⣿⠿⣿⡿⠿⠿⠿⣿⠿⢿⣿⣿⡿⠿⣿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⣁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣮⡿⠇⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⣤⣶⣦⣼⣿⠿⠛⠃⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠀⠀⠈⠉⠙⠻⠿⠿⣿⣷⣶⣦⣤⣤⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣩⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣶⣶⣶⡖⢿⣿⣿⣿⣿⣿⣟⣛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠈⠉⠋⣹⣿⣷⣶⣿⣭⣽⣿⣿⣿⣦⣀⣠⣀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⣿⠀⠀⠀⠈⣜⣻⣟⣛⣛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⠀⢠⣶⣿⣿⣿⡟⣋⠉⢻⣿⣿⢿⡀⣿⣿⣿⣯⡄⡀⠀⣿⡇⣾⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣭⣵⣿⣿⣿⣿⣿⣿⠛⠛⠛⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠌⢁⣈⡹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠘⠀⠀⠉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣟⠫⠴⠆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣹⣻⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠰⢒⣂⣾⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣥⣤⣤⠤⠤⠴⠦⠤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡌⠀⠘⠛⠉⣉⠛⢻⣿⣟⣿⡻⣯⡀⠀⠀⢰⣶⣿⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠰⢦⣤⣶⣿⡾⠧⣷⣿⣿⣿⣿⣿⣶⣿⣦⣦⢹⣹⠛⢛⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠚⣾⣳⣧⣌⣀⣀⣹⣧⡄⣉⣉⣭⣯⣿⣿⡟⡷⣇⣰⣧⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⠁⡉⠈⠉⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠐⠛⢺⡟⠃⠀⠀⡴⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⡾⢷⠀⠠⣄⣘⣁⣨⡇⠘⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⢾⡿⠁⠀⠈⢹⡏⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⣿⣿⣦⣀⠀⢙⡦⢧⣛⠓⢻⡴⠨⢙⡾⠿⣧⣿⣿⣿⢿⡏⣻⣯⢭⡝⠀⠀⠿⠃⠴⠈⢻⡆⠙⠇⠙⠻⣧⣶⡰⠟⠈⣺⠏⠀⣙
⣿⣿⣿⣿⣿⣷⣤⢜⡛⠁⠀⠛⠢⠀⡿⠺⢿⠵⠿⣿⣿⠻⡻⣭⣟⠦⡆⠉⢸⡇⣀⢂⠢⠀⠀⠀⠀⠀⢹⡏⠀⠐⠆⣈⢀⡤⠻
⣿⣿⣿⣿⣿⣍⣿⣶⢸⣿⢤⡤⠀⠠⠁⢰⣦⣟⠛⠿⠟⠺⠻⠾⡮⠘⠀⣴⠾⢿⣽⢾⠄⠀⢤⠀⠀⢠⣀⠃⠀⠂⠀⣸⣄⣤⡿
⣿⣿⣥⣤⣴⠋⣸⣏⣴⡶⢆⣀⡄⠀⣠⣜⠂⠈⠁⠀⠀⠀⠀⠀⠀⡆⠀⢈⡄⢰⠧⠇⢉⡐⠂⠉⠰⣀⣀⠈⠀⠀⢚⡯⠩⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣭⣵⣶⠿⢫⡉⡶⠖⠂⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠉⡰⠧⢄⡄⢻⠁⠈⠀⠈⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡇⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢒⣧⣿⠀⠀⠀⠴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣧⣿⡟⠀⠀⡀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⢀⠀⠀⠿⣏⡛⡷⠾⣷⣳⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡀⠀⠀⠀⠡⣄⡀⠀⠀⠀⠠⠀⠀⠀⣄⠊⠉⠀⡷⠈⣠⡏⠁⢠⠀⠀⠀⣠⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⢛⣋⣪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠈⢐⣀⣠⡘⠋⠸⠁⠀⠀⠀⠀⠀⢈⣿⠝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣭⢆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⢇⡤⢀⡔⠀⠀⠀⠀⠀⠠⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢺⡵⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢶⠀⠘⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⠀⠀⠀⢹⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⡶⠀⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠰⡟⢻⡶⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⠿⡛⠁⣄⡄⠀⠀⠀⢰⢶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢇⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⡶⠤⢌⡮⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢺⣾⠃⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣠⣀⡀⠘⡧⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⠀⡓⠛⢹⣼⠻⢿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⡁⣨⣿⡿⢻⢿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡄⠀⠀⠀⠀⠀⠀⠰⡎⠉⢷⢸⣿⠋⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠡⣖⠒⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀
⠀⠀⣠⣶⠿⠟⠛⣿⠿⠓⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣿⠟⠂
⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⣾⣿⠟⠛⠉⠹⠟⠁⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⢀⣤⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠋⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡄
⠀⢀⣼⠿⠛⢉⡿⠟⠋⠁⠀⠀⠀⠀⠀⢀⡿⠋⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠋⠀⠀⠀⠀⠀⢰⡿⠛⠉⠩⠟⠋⠁
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠂⠀⠀⠀⠀⠀⠀⢀⣤⡶⢟⣛⣛⣳⢦⡀⠀⠀⠀⠀⠀⣠⣶⣾⡿⢷⢶⣤⣄⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣄
⠀⠀⠀⣰⠀⢸⣿⠃⢠⣶⠿⣷⣦⠀⠀⠀⢠⣿⢫⣾⣿⣿⣿⣿⣷⣎⢆⠀⠀⢀⣾⣿⢿⣷⣿⣿⣿⣾⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⠀⢸⣿⡀⠘⠧⠀⢈⣿⡇⠀⠀⣾⡇⣿⣿⣏⢶⣶⡝⣿⣿⡇⠀⠀⢸⣿⣿⣿⣽⣟⣿⣿⣯⣿⣻⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢿⣧⠀⠻⣿⣦⣤⣤⣾⡟⠁⠀⠀⢹⣷⡹⣿⣿⣿⣿⢇⣿⣿⡇⠀⠀⠸⣿⣿⣽⣿⣿⣿⣿⣯⣿⣽⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠻⣷⣤⣀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠻⣿⣶⣭⣭⣶⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣷⣿⣿⣾⣿⡿⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠰⠶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⣰⣿⠟⠉⠉⠈⠉⠛⢿⣦⡀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⠁⣄⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⣴⠟⠉⠀⠀⠀⠈⠙⢷⣄
⠀⠀⢰⣿⠁⢠⣾⡿⠿⣷⣆⠀⢻⣧⠀⠀⠏⠀⠀⣠⠈⠉⠁⢤⠀⠀⠈⡀⠀⠰⠁⠀⢀⠂⠁⠁⠐⡀⠀⠀⢂⠀⢸⡏⠀⢠⡾⠛⠻⣦⡀⠀⢻⡆
⠀⠀⠸⣿⡀⠘⢿⣿⠇⢸⣿⠀⢸⣿⠀⠀⡆⠀⠀⠁⠴⠂⠀⢈⡀⠀⠀⠓⠀⢐⠀⠀⠐⠀⠠⠀⠀⠠⠀⠀⠠⠀⢸⡇⠀⠘⠷⠗⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠹⣿⣦⣄⣀⣴⣿⠏⠀⢸⡟⠀⠀⠀⢄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠇⠀⠀⠡⡀⠀⠀⠀⠀⡀⠁⠀⠀⡨⠀⠀⠻⣦⣀⣀⣀⣠⡿⠁⠀⣼⠇
⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉

⠀⠀⠀⠀⢀⡴⠞⢋⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣶⢟⣫⣭⣭⣒⠄⠀⠀⠀⠀⠀⡠⢖⣫⣭⣭⣛⠶⣄
⠀⠀⠀⣰⡟⢠⡾⢋⣉⣉⡙⠻⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⣱⢏⡵⠒⠲⣝⢷⡀⠀⠀⠀⢊⣾⣿⡿⠿⠿⣿⣿⣎⢷⡀
⠀⠀⠀⣿⠀⣿⠀⠋⠀⠀⠹⡆⢹⡇⠀⠀⣾⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⠀⠀⢸⢸⣧⢻⡸⡀⠀⠀⣸⢸⡇⡇⠀⠀⣾⣿⡏⣾⣿⢿⢜⣿⣿⢸⡇
⠀⠀⠀⢻⡆⠻⣄⠁⠀⠀⣰⠇⣸⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣧⢻⣮⣛⠮⠭⢶⣫⡾⣱⠃⠀⠀⣿⣿⣇⢿⣿⣶⣿⣿⢏⣾⠃
⠀⠀⠀⠀⠻⣦⣈⡛⠛⢋⣡⣴⠟⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⢷⣬⣛⣻⢿⣛⣫⡾⠃⠀⠀⠀⠘⢿⣿⣷⣭⣝⣭⣵⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁
⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⠦⢄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⣰⠏⡠⠚⣉⠭⣉⠓⢄⠱⡄⠀⠀⠀⣴⠋⣠⡴⠒⠛⠲⢮⣳⡄⠀⠀⠀⣰⣿⣿⢛⣭⣴⣦⣍⠻⣦⠀⠀⠀⣠⠞⣩⠶⠖⠶⢦⣝⠳⣄
⠀⠀⠀⡏⢰⠃⡞⢠⡶⡄⢱⡈⡆⢹⠀⠀⢸⡇⢰⠃⠀⠀⠀⠢⡀⠹⣿⠀⠀⢰⣿⣿⠃⣿⢏⣥⣬⠻⣷⢸⡇⠀⢰⡏⣼⢡⡞⣫⣙⢳⡜⣧⢹⡄
⠀⠀⠠⣧⠘⢆⠑⠤⠥⠃⡸⢁⠇⣸⠀⠀⢹⡇⢸⡄⠀⠘⠃⠀⡷⠀⣿⠀⠀⠸⣿⣿⣆⠻⣿⣿⡿⢠⣿⢸⡇⠀⢸⡇⣿⠸⣎⣛⣽⢂⡇⣿⢸⡇
⠀⠀⠀⠳⡑⢄⡑⠒⠒⢊⡠⠊⡠⠃⠀⠀⠈⢿⣄⠙⠦⣤⠴⠞⢁⣼⠏⠀⠀⠀⠻⣿⣿⣷⣦⣤⣶⠟⣣⠟⠀⠀⠀⠻⣌⠳⢮⣭⠴⢟⣴⠏⠸⠁
⠀⠀⠀⠀⠈⠲⠬⠭⠉⠥⠴⠊⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠾⠋⠁⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠾⠛⠁⠀⠀⠀⠀⠀⠈⠛⠓⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠠⢄⠀⠀⣠⠶⢩⠉⠶⣄⠀⢀⡠⠄⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⢻⢍⡲⣽⠻⠘⡈⣸⣤⢡⢃⠗⣯⢖⡩⡟⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣦⣿⣘⡪⣴⠫⣣⡵⡿⢞⡳⣷⢎⣜⠜⣮⣕⣃⣷⣶⣤⣤⣤⣄⣤⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣯⣭⣥⢤⢤⢤⠠⡄⢬⢭⣛⡷⣷⡯⡪⠖⢱⡎⠢⣕⢝⣾⢿⣛⡭⡤⢠⠤⡤⣤⡤⣬⣭⣽⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠃⣿⠪⣦⡧⣧⢥⢧⡵⣸⣀⣈⣽⣿⢏⠰⡄⡏⠱⢠⢂⡱⡿⣯⣀⣀⣇⢧⢬⡬⣬⢼⣴⠕⣿⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣗⠭⣯⣱⣼⡤⢤⠇⣬⣨⣉⡏⡇⣐⠝⡮⢺⡁⢕⠩⡂⢸⢹⣉⣄⣇⢼⡤⢤⣧⣊⣽⠭⣾⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡗⠥⡷⠂⣏⠑⢌⢣⢡⠘⢸⢉⠟⡢⢍⡰⢭⡭⢆⡩⢔⢻⠉⡇⡅⠎⠜⡠⢊⡹⠐⢾⠬⢺⠀⣿
⠀⠀⠀⠀⠀⡠⠔⡒⣸⣿⠀⣍⣐⣋⡉⣯⢍⡒⢵⣷⠿⣼⡸⠐⡡⢺⣅⢲⠖⡩⡗⢌⢆⣇⣧⠼⣾⡮⣒⡩⣍⢉⣝⣂⣹⢀⣿⣅⢒⠢⢄
⠀⠀⠀⠀⠘⡁⡟⢖⡲⡸⣧⢷⠀⢸⡖⢺⣂⣒⣉⣧⢰⣶⡝⢿⣶⣿⣢⣹⣏⣔⣿⣮⡟⢩⣶⡆⣼⣙⣂⣐⡗⢰⡇⠀⡞⣼⣇⢖⡲⢻⢈
⠀⠀⠀⠀⠀⠱⣜⣮⠵⡛⢿⡯⣷⣿⠯⠭⣦⠤⢂⠪⣧⣙⠚⣠⡋⠷⠋⣼⣧⠑⠺⢙⣄⠓⣉⣾⢗⡒⠠⣼⠭⠽⣻⣾⣽⡯⢛⢮⣵⣣⠊
⠀⠀⠀⠀⠀⣠⣛⠢⢝⡾⡻⡪⢋⠱⡔⡔⡌⢎⣡⣊⣴⣽⢫⠈⢾⣳⣣⣃⣘⢜⣞⡷⢡⡽⣯⣯⣑⣌⡱⢡⠣⣢⠊⡑⣕⢽⢗⡩⠔⣓⣄
⠀⠀⠀⢀⡜⠃⠂⣭⡺⢋⢜⣁⡠⠍⡊⣊⡜⣎⢣⡑⣌⣾⣂⣤⠭⢺⠛⣄⣦⠛⣕⠭⣤⣑⣗⣡⣃⡌⣱⢢⡙⣕⠭⣠⣈⡢⡫⣛⣍⠐⠘⢣⡀
⠀⠀⠀⠈⢣⡭⠄⣛⣵⣎⢪⡉⠃⣂⢕⢍⠣⢏⡜⡩⢋⢿⢍⠛⡒⢽⣤⠋⠛⣤⡣⣒⠛⡫⡯⡙⡌⢃⡹⠜⡡⡫⣐⠚⢉⠕⣕⣯⡛⠠⢠⡜⠁
⠀⠀⠀⠀⠀⠙⣭⠔⣪⢷⣵⢕⢌⡰⠫⠢⢣⢎⡙⢍⢻⣻⣜⢀⢾⡽⡙⡍⢉⢨⢯⡷⡘⣳⣿⢟⡩⢋⡱⡐⡕⠝⢄⡱⣫⣪⡮⣑⠠⣭⠋
⠀⠀⠀⠀⠀⡠⢫⢟⠲⣥⣾⣗⡿⣿⣖⣒⡟⠂⠬⢕⡟⣩⣤⠙⣅⠶⣄⢻⡟⣠⢦⣨⠋⡤⣙⢿⡪⠥⠐⢻⣒⣲⣿⢿⣺⣷⣭⠞⡻⡝⢄
⠀⠀⠀⠀⢠⡁⣧⠮⠵⢱⡟⡾⠀⢸⠆⠼⠍⠩⣍⡟⠸⠿⣣⣼⠯⣿⠝⣹⣛⠩⣿⢽⣧⣙⠿⠇⢻⣩⠍⠩⡧⠸⡇⠀⢧⢻⡎⠮⠵⣼⢘⡀
⠀⠀⠀⠀⠀⠑⠢⠥⢙⣿⠀⣋⠩⣝⣁⣟⣊⠍⡺⡿⣶⢻⢱⠡⡑⢼⡋⠼⠦⣑⡧⢊⠎⡋⡟⢲⢿⢗⠭⣐⣋⣈⣫⠍⣙⠈⣿⡋⠬⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡒⡷⠄⣏⡠⢊⡜⡘⢨⢸⢀⣧⠕⣊⠱⣚⣓⠮⣑⠪⣼⣀⡇⡃⢆⢢⠑⢌⣱⠠⢿⢒⢼⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡯⣒⣟⡩⢻⢓⠚⡖⢛⢹⣉⣇⡇⠩⣪⢵⢼⡥⡪⣒⠅⢸⣸⣉⠋⡏⢚⠓⠚⡟⢍⣻⣒⢿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⢔⠛⡗⡟⡚⡟⠳⢸⢉⢉⣻⣿⢎⠠⠃⣇⡰⠘⠌⡱⣿⣟⠉⠉⡇⠞⢚⢓⢻⢺⠻⡢⣿⢰⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣟⣛⠛⠚⠚⠚⠐⠃⠚⣚⣭⡷⡷⣵⢕⠦⡸⢇⠔⡫⣪⢿⣾⣭⣓⠓⠘⠒⠒⠓⠓⠛⣛⣻⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠙⠛⠛⠛⠟⣿⢩⢕⠻⡔⡝⡳⣷⢮⡵⡼⢞⢯⢢⢟⡫⡍⡿⠻⠛⠛⠛⠛⠛⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡐⣼⣊⠵⣻⣴⢠⢁⢹⠛⡘⡌⣦⣟⠮⣑⣧⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠐⠊⠀⠀⠙⠾⣘⣀⠷⠋⠀⠈⠑⠂⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠰⠖⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⡄⠀⠀⠐⠋⠐⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠲⡀⠀⠀⠀⡀⠀⠈⠄⢀⠞⠁
⠀⠀⠀⠀⠹⠀⠀⠀⢀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⡜⠃⡀⠀⡘⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠄⠀⠀⠀⠀⠀⣠⡮⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠀⠀⠀⢱⡄⠀⠀⢀⢻⣤⣄⠀⠀⠈⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠚⠉⠀⠀⠀⢠⢤⣶⠔⢀⡏⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠎⣁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠄⢸⣧⣤⠞⠀⠀⠤⡤⣴⡖⡶⣶⡄⠢⡀⣀⡄
⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠰⠀⢠⠀⠀⠈⠉⠡⠀⠰⠀⠈⡿⠋⠉⠀⣼⠇⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢹⠁⠤⠀⠀⠀⡤⠀⠀⠀⠀⠀⣀⣤⠤⠖⠶⢄⠀⠻⠤⠤⠖⠋⠙⢿⣿
⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠁⠈⠀⠀⠀⢣⡀⠀⣸⡄⣿⣯⠋⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠸⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢋⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠻⣆⡂⠀⠀⠀⠀⠀⠀⠠⢆⡀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣎⠜⢇⡀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠳⠶⢦⠴⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠉⡍⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡤⠤⠊⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⠀⢀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠏⠀⠀⠀⠘⣦⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠠⠤⢀⡀⢀⡀⠀⠐⠀⠀⠀⠀⢀⡴⠖⠒⠂⠀⠀⠀⠀⠀⠘⡁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣇⠀⠀⠀⣠⠶⠞⠁⢀⣦⡀⠀⠀⠀⠈⣣⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣥⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠁⠈⠁⠀⠀⠀⠀⠋⢳⠶⢸⠦⠴⠎⠀⠀⠀⠀⠀⣀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⣤⡞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠰⡄⠀⠀⢆⠀⠠⡀⠀⢞⠑⢶⣤⣤⣴⣯⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣾⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠙⠦⠈⣉⠁⠈⠀⠀⠘⠁⢄⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢔⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣷⣿⣿⣾⣿⣿⣾⣴⣆⣀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠚⢉⣽⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⢿⣿⣟⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠈⠹⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⢠⠀⠞⠀⢀⡄⠀⠀⠀⠀⠀⠀⠿⠛⠟⡿⣿⠟⣿⠿⠻⠉
⠀⠀⠀⠀⠀⠙⠋⠃⠀⠁⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⣶⣦⣈⡓⢶⣭⣓⠤⣍⡓⠦⣄⡑⠢⣄⡀⠀⢤⣾⣿⣿⣿⣿⠯⣿⣿⣿⡆⢿⡄
⣽⠿⣿⣿⣷⣦⣹⣳⢦⣝⠶⣈⠻⢦⡈⠻⣦⡀⠹⣿⣿⣿⣿⣷⣿⣿⣿⣿⠘⣧
⢯⠛⣷⣯⣏⣿⢏⣝⡶⢟⢷⣬⠳⡄⠻⡄⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀⡟
⣆⡘⢻⣝⠿⣿⣿⣿⣯⣶⣧⠻⣷⡙⡄⢹⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣧⡀⢀⠠⢂⢀⡄
⣟⣞⣂⢍⣹⣿⣿⣿⣝⣿⠂⠢⢻⣷⢱⠀⣧⠀⠘⣿⢻⣿⣿⣿⣥⣿⣿⣿⣼⣿⣿⣷⣶⣿⠋⠉
⣿⣦⣍⣘⢉⢃⢿⣷⣬⡜⠆⠘⣾⣿⢸⠀⢸⣆⠀⠈⠻⠿⠟⠉⠻⢿⣿⡿⣿⣏⣹⣿⡿
⣿⣿⣿⣋⡎⣯⣸⠉⢉⣧⣸⣱⣿⠃⠎⢀⣼⣿⣶⣄⠀⠤⣠⣤⣤⣄⣀⣰⣿⣿⣯⠻⣿⣶⣦⣀
⣿⣏⣿⠓⣽⣿⣿⡴⣹⠋⣱⣿⠃⢠⣶⣟⣿⣿⣿⣿⣗⠠⠉⢿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣷⡀
⣗⡿⢛⠀⠩⠟⢙⠑⡣⣰⣿⡇⠀⢿⣿⣿⣿⣿⡋⣿⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣯⣿
⡌⣰⣯⢬⡢⠀⢴⣾⣿⣿⣿⢁⣄⠸⣿⣿⣿⣿⣧⢻⣿⣹⡿⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⡇
⣎⣟⣵⠟⣠⡄⢛⢿⣿⣿⡟⣾⣿⣷⣬⣝⢿⣿⡿⠷⠭⠉⣡⣼⠟⠛⣁⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡉⠉⠉⠉⠁
⠿⠛⣚⡩⣠⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢟⠀⣠⡾⠋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⠣⠅⢀⠀⠀⠀⠀⠀⠄
⠶⣿⠿⠚⣃⡾⢿⠿⣿⡿⠿⣻⣿⣿⣿⢣⣿⣯⢎⣾⡿⠁⣾⠿⣿⣿⣿⢏⣵⣿⣿⣿⣿⣿⣇⣽⣿⣿⣶⡟⡀⢄⡀⠈
⣠⣤⡶⠞⠒⠀⢀⣪⣽⣾⣿⣿⣿⡿⣣⣿⣿⣿⣾⡟⠀⠘⣿⣰⣿⣿⣿⣹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣮⣶⣊⣁⣤⣀
⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⠁⢠⣾⣜⣿⢿⣻⣿⣼⣿⣿⣿⣿⣿⣿⣡⠝⠿⣿⣿⣿⣿⢿⡛⠫⠍⠓
⣿⣿⣿⠿⠿⠿⠛⠛⣋⣩⣴⣾⣿⣿⣿⣿⣿⣿⣏⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣈⠙⢻⣿⣷⣮⡑⠄
⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣷⣦⣦⡉⢻⣿⣿⡂
⡛⡛⠛⠛⠿⣿⣶⣮⣻⣿⣿⣿⣿⣿⣿⣟⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣿⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⡗⠂
⠀⠀⠀⠀⠀⠈⣏⣄⣀⣬⣉⣏⣹⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⡏⠙⡵⣾⡟⡗⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡴
⠀⠀⠀⠀⠀⠀⡇⢐⣾⣿⣯⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡇⢐⣒⣿⡯⡧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⢀⡄⠠⠶⣿⣯⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢸⡇⠠⡯⣿⣛⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⢸⠃⠈⠹⠟⠻⣇⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⢸⡇⠑⠀⢦⣠⠟⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶
⠀⠀⠀⠀⠀⢸⡅⠀⠀⢰⡃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⢱⡖⢨⣿⡏⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠠⠄
⠀⠀⠀⠀⠀⠀⣺⠁⠀⣿⠀⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣿⡟⣿⣿⣿⣿⣿⣿⠤
⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢬⡧⣿⣿⣀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠰⠶⠾⠿⠶⠶⠶⠿⠶⠶⠶⠿⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣦⣻⣧⣤⣤⣤⣔⣛⣠⣀⣀⣛⣃⣀⣀⡹⢻⣀⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣦⡾⢻⡿⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣅⡠⠾⣿⣿⡵⠟⠁⠀⠀⠀⠹⣶⠀⠀⠀⣴⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠊⠉⠁⣠⣶⣴⣤⠀⠀⠀⠀⠀⢀⡀⡀⣠⠶⠋⠑⠀⢦⠀⠤⠄⣠⡀⠀⠀⠀⠀⠈⠉⢿⠾⠁⢀⣶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠛⠁⠀⠀⠀⢠⡾⠛⠉⠀⠙⠷⣤⡀⢠⡀⠛⢩⠟⢁⠀⠠⠃⠄⢀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢀⣶⡥⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠙⠳⣄⡈⠁⠘⠊⠉⠀⠀⠀⠀⣿⣷⠀⣸⣿⣿⠀⢀⡴⢊⠿⠋⠠⠀⢠⠆⡴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣠⠀⡀⠀⠀⠀⠀⠀⢀⡈⢻⣦⡼⠋⠀⡠⠞⠀⢀⣿⣿⣤⣿⣿⣿⣗⠁⠀⠁⠀⠀⣠⠐⢋⣠⣾⡿⠟
⠀⠀⠀⠀⠀⣼⣆⡀⠀⠀⠚⢁⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠈⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⢊⣠⣴⠟⠋⠉
⠀⠀⠀⠀⠀⠙⠛⠿⣿⣧⣰⠋⣶⣄⢀⠀⠀⠀⠀⠀⠀⢠⣟⣁⠀⠀⠀⠸⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣇⣠⣦⠀⢡⣉⠁⢰⣷⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠿⣿⠟⠛⠛⢳⣦⡀⢀⢠⣼⣿⠟⠁⠀⣠⣦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡄⣿⣿⣷⣾⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣄⠀⠀⠀⠀⠘⠿⢾⣿⣿⢁⡀⠀⣄⣿⣿⣷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⢀⡀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠈⠛⠳⣤⡄⠀⠀⠀⠉⠉⠉⠙⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⢀⠠⠀⠊⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠠⣴⣾⡟⣀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣠⣶⣶⠗⠁⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠛⠓⠴⢄⡄⠀⠀⠈⠿⣆⣀⠀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⣎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠙⠿⣧⣶⣦⣨⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠛⠋⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀⣴⠟⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠙⠿⠛⣿⣿⣿⣿⣿⣿⣯⠉⠀⠁⠀⠀⢀⠀⠀⢀⣤⣾⣿⡶⠛⠁⠀⠀⠔⠋⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⠿⠟⠋⠉⠈⠀⠀⠀⠀⠀⠀⠁⠀⠐⠛⠉⠙⠁