Pig Emojis & Symbols

⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⢠⠔⠈⠹⡄
⠀⠀⠀⠀⢸⣏⠢⣄⠀⠀⠀⢀⢿⣆⡀⠀⢣
⠀⠀⠀⠀⢸⣿⠂⠘⠲⠖⠒⠺⠈⢿⣾⡅⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠤⠤⠀⠀⠀⠀⠂⠀⠀⠠⠤⠀⣀⡀
⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠟⠉⠘⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⡀
⠀⠀⠀⠀⡻⠁⠀⠀⢲⣾⣷⡀⠀⠐⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦
⣀⣄⣤⡊⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⣿⠗⣿⠏⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⠿⢶⣟⣛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠈⠙⠓⠒⢶⣀⠀⠀⢀⠄⠀⢀⢠⠴⡄⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⡀⠁⠀⠌⣠⣁⣌⡀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠋⣡⡀⠁⠀⠀⠀⠀⢀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣾⣧⣽⣿⣿⡘⠧⠀⠀⠀⠀⢰⡟⠈⣖⣡⣴⣾⣥⣤⡄⠀⠀⣠⣤⣿⣿⡄⠀⠀⠀⢀⠊⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⠻⠂⠀⠀⠀⡰⠛⠛⠿⠿⠿⠟⠿⢿⣿⣴⡷⠟⠛⠉⢻⣿⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠿⢀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⡇⢇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⣨⠀⢸⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢠⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⡼⡟⢀⠃⠀⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⡾⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠟⠁⢠⣾⣦⡾⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⣿⣧⣠⠾⠇
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⠤⣤⣄⣀⣀⡀
⠀⠀⠀⢰⡸⠭⠇⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠉⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠠⠤⢺
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠇⠠⡤⠔⠃
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡄⠠⠦⠠⢦⠁⣤⢟⢧⣷⢠⠴⠀⣤⢤⠤⠤⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡀⠁⠞⠁⠐⡒⠄⠙⠸⠜⡧⠓⠯⠥⡈⠠⠭⠄⠀⠀⠠⠬⠐⠴⠤⠉⠂⠀⠾⠂⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⡸⣆⠀⠠⢸⠋⠒⠢⠤⠄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠢⢠⣀⡀⠀⠊⠀⠀⠃⡀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠂⡴⠁⠸⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⠙⠀⠀⠀⢃⠀⠀⠉⠐⠒⠂⠶⠬⣀⢒⡞
⠀⠀⠀⠀⠀⠀⠀⡆⠈⣼⠀⠀⠀⠱⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡎⠳⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠀⠀⠱⡈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⣆⠀⠘⣄⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠓⠒⠛

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣧⢀⣀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢹⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⢶⣾⠁⠀⠙⠷⣤⡀
⠀⠀⠀⠀⢰⣿⡿⠛⡛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠻⣄⠈⠛⠷⣦
⠀⠀⠀⠀⢸⣿⣧⡀⠈⣨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡳⣴⠿⣦⠀⠀⣿
⠀⠀⠀⠀⢸⣟⢿⣟⣛⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠳⢤⣄⣀⡀⠀⠀⢸⢇⡴⠆⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀⠉⠉⡹⣦⠘⠷⣴⠏
⠀⠀⠀⠀⠀⠹⣦⡌⠙⠋⠉⠙⠛⠛⠛⠛⠛⠛⠟⢛⡟⠀⠀⠀⠀⠈⠉⠉⠉⠉⠠⢦⡄⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⣦⡿⠘⢷⣄
⠀⠀⠀⠀⢀⣾⡋⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⡟⢠⠞⠁⠀⡴⠋⢷⠀⣾⠳⢄⠈⠳⡄⠀⠙⢷⡀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣼⠁⠀⣿⠀⠹⡄⠈⡇⠀⠹⡄⠀⠈⣿
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠒⠈⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠹⣤⡴⠃⠀⠀⠉⠛⠁⠀⢠⠇⠀⠀⣾⠁
⠀⠀⠀⣿⠂⠁⠀⠀⠠⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣄⠀⠀⠀⠈⠉⠓⠲⠶⠶⠶⠖⠊⠁⠀⠀⢀⡾⠋
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣦⣤⣤⣤⣤⣤⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡤⠀⣀⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⡏⠉⠓⣦⣤⣤⣀⣀⣠⡇⠀⠀⠀⣼⡗⠋⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣦⣉⣽⡄⠀⠉⠉⠉⣧⠀⠀⢰⡿⣷⠄⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢙⣧⠉⠉⠀⠀⠀⠀⠀⢻⣅⠀⢸⡇⠿⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡔⡻⢶⢀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠓⠒⠦⢄⡀
⠀⠀⠀⠀⠳⣌⣊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣵⢤⠤⠐⠒⣻
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠫⠼⠀⢤⡤⠞⠁
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠆⠀⢀⠸⠸⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠀⢀⠐⠂⠀⠀⠀⠈⠀⠀⠎⠃⠂⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⣰⡆⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡊⠀⣴⠀⠀⢐⢑⡶⠤⣄⣈⠀⠀⠀⠁⠀⡀⠀⢀⠀⢠⠀⠀⠀⢀⠀⡀⠅⠀⠀⠄⢀⠀⢠⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⡰⠉⣧⠀⠀⣼⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠒⣶⢆⠀⠀⠈⢰⠋⠙⠒⠤⠀⣀⡀⢀⡑⠄⢀⡌⣻
⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢀⡜⠁⠀⠸⣄⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⣄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠁⠀⠀⠀⠘⡆⢀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⠇⠈⢣⡠⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢺⡀⠀⠀⠀⠀⠙⣌⣚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⣦⠀⠀⠳⡌⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠓⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣷⣶⣦⡀⣦⣀⢀⡀⠀⠀⠀⠀⠀⢼⣿⢘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣴⣦⡀⠀⠀⠀⠀⣠⠸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⡗⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢟⣵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⣿⢾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⢎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣭⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢸⣿⣿⡟⣿⣿⣷⠀⠀⢸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣼⣿⣿⢠⣿⣿⣿⠀⠀⢸⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠿⠟⠿⠛⠛⠛⠛⠿⠅⠛⠿⠀⠒⠈⠛⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⠀⠀⠀⠠⠤⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣾⡿⡫⣄
⠀⠀⠰⣌⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⡉⠀⠀⠘⠿⠞⠁
⠀⠀⠀⠈⠉⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⢩⡿⠁⠒⠲⠀⠈
⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣦
⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡤⠀⠀⠀⠀⠀⡐⠺⠦⣥⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⠀⢠⣴⡾⢏⣀⣀⡀⠠⠤⠀⠐⠠⢀⠀⠀⢀⢁⣨⡋⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠿⣷⣶⣾⠿⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣷⣻⣿⣿⣿⣩⣿⣛⠀⠂⠀⠀⠄⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣾⣿⡿⠉⠉⠙⠛⠛⠛⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⠿⢇⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡂⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠁⠀⠀⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣸⣁⠀⠀⠸⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣠⡀
⠀⠀⠀⠰⠒⠒⠲⠆⠐⠒⠎⠛⠉⠛⠚⠃⠈⠉⠉⠉⠙⠉⠙⠓⠂⠀⠀⠀⠉⠛⠉⠁⠉⠉⠉⠉⠉⠀⠈⠛⠒⠒⠒⠢⠤⠤


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠈⢿⣿⢷⣍⠑⣄⡀⠄⠒⠓⠀⠂⠀⡠⠂⢁⣴⡿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠠
⠀⠀⠀⠀⠐⢿⣿⣧⠌⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⣹⡏
⠀⠀⠀⠀⡀⠀⠹⡟⢀⡀⠀⠀⠀⠀⠀⠀⣀⢸⡿⠏⠀⡀⠀⠀⠀⠀⢀⠁⢀⣀⠀⠻⠠⠊⠀⠀⠂⠀⠀⠐⠢⣄⢀
⠀⠀⠀⠀⠀⠀⠒⠃⠘⠛⠀⠀⠀⠀⠀⠘⢻⠘⠃⠐⠀⠀⠀⠀⠀⠀⢞⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠺⢖⠀⠀⠀⠀⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢄⣤⣄⡤⠂⠀⢠⠃⠀⠰⣶⣤⠶⣿⡇⠀⠀⠀⠉⢫⢁⠀⠀⡀⠀⢸⠇⠀⢀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⡲⢤⣀⠀⠉⢽⣂⡤⠖⠁⢀⣀⠀⡹⠛⢁⡌⠉⢻⣿⣶⣤⠀⢠⠹⠋⠃⠀⡼⠓⠒⡟⡇⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠠⣉⠁⠀⠉⢉⠀⠀⠀⣸⡟⠀⠉⠣⢾⣧⣾⣀⣿⣿⡟⠀⠈⠀⡀⠁⢸⠀⠀⣔⣱⠇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣶⣤⣶⡏⠀⠀⡰⠋⠀⠀⠀⠀⠈⣿⡟⠉⣻⣻⠀⠀⠘⠚⠀⠷⠊⠀⠀⠉⠙⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠉⠁⠀⠐⠁⠀⠀⠀⠀⠀⠈⠙⠁⠈⠁⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣆⣈⣰⠅⢤⠐
⠀⠀⠀⠀⠀⠀⠘⣿⠟⠀⠀⠛⡾⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⣠⢀⣤⣄
⠀⠀⠀⠀⠀⠀⣰⣟⠃⠀⠀⠀⢈⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠲⣴⠊
⠀⠀⠀⠀⠀⢰⣿⣿⣯⢀⣀⣀⠨⣿⣿⣿⡀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⠄⠀⠀⠀⠊⣰⡿⣿⣿⠟⠤⠶⠶⠄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⣀⡀⠈⠠⣿⡿⠀⠂⠂
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠀⢠⣰⣿⡯⠀⠀⠀⠀⠀⠈⣿⡄⣼⡏⠀⢀
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⢱⣿⣿⣿⡇⠉⠛⠻⠷⣦⡂⠠⢙⣿⣷⣶⢂⣤⣾⣿⣿⣾⣿⣿⣿⡀⢸⣷⣧⣖⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⢊⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⡧⠌⣿⣛⣿⣿⣿⠉⠀⠀⠉⠉⠉⠋⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣼⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⡏⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⢨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠈⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶

⢰⣿⣦⣀
⠀⢻⡧⣉⠙⠛⠓⠒⠲⠦⢤⣀⡀
⠀⠀⠹⡎⠓⢄⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⣿⠀⠀⠑⡄⠀⠀⠀⣀⣠⠤⠤⠽⠶⠶⠶⠤⣤⣄⡀⠀⠀⠀⣀⡤⠶⠒⠚⠛⠛⠒⠒⠶⠦⢤⣤⣤⣤⢾⡆
⠀⠀⠀⢸⠀⠀⠀⢸⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣴⡿⠋
⠀⠀⠀⢸⡀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢀⡞⠁
⠀⠀⠀⢀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡟
⠀⠀⢀⡞⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡞
⠀⠀⣼⢀⣀⣻⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠟
⢀⡴⠋⠉⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠿⠵⠤⠤⢤⣤⣀⣀
⡞⠀⡠⣄⠀⠀⢀⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⢧⠈⠦⠞⠀⠐⣍⡽⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⢀⣤⣴⣤⡀⠀⢀
⠈⠳⣄⡀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢠⣿⡋⠉⣿⣷⣠⣿
⠀⠀⠀⢻⡉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⢷⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠹⣗⠦⣄⣀⣀⣀⣀⣠⠴⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣧⠀⠉⠉⢽⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠘⣲⠞⢀⡔⠀⠀⠀⠀⢀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣭⠥⠖⠛⠛⠛⠛⠛⠋⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠳⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣼⠒⠒⢻⡏⠁⠈⢧⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡄⠀⠀⠀⠀⠀⣰⠃⠀⣠⠞⢛⠒⠒⢺⡆⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⡝⠒⠒⣻⠀⠀⠀⠀⢠⠏⠰⢯⣥⠴⠃⠀⢀⣸⣧⣀⣀⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡶⠊⢀⣀⣠⡿⢤⣤⣀⣠⡟⠀⠀⠀⠙⠛⢛⣭⠟⢉⡴⠃⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣭⣟⣋⣠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠉⠿⣯⣤⠤⠴⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠠⠄⠂⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⣀⢞⠄
⠀⠐⡑⡀⠀⠀⠀⠀⠀⢀⣠⠌⠈⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡨⠄
⠀⠀⠣⡈⠢⣀⡀⠐⢊⢽⠁⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⠆
⠀⠀⠠⡘⢢⠋⠀⠀⠈⠼⣴⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠺⡀⠀⠀⠀⡀⠀⠙⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠈⣃⠀⠀⠐⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⡠⠒⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠉⠀⠀⡀⠐⡅⠀⠀⠀⠀⡜
⠀⠀⠀⢜⠂⠃⣁⣀⠄⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⠀⠀⠀⠰⠦⠤⠤⠄⠄⠀⠒⠈⠉⠣⡀⠸⡄⢀⡠⠔
⠀⠀⠀⠀⠿⠝⠁⣀⣀⣀⣀⡀⢤⠚⠁⠘⠇⠈⡄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡅⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠴⠁⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡘⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⡂⢀⠍
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣽⣿⣿⣭⣿⣽⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⡇⠀⠀⣔⡆
⠀⠀⠀⠀⣶⡃⣖⡎⣧⠴⠒⠚⠉⠛⠓⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⡞⣇⠴⢊⢾⠃
⠀⠀⠀⠀⠘⠣⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠓⠈⡽⠋⠀⢀⡞⡸⠳⡖⠁⡼
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡰⠋⠀⠁⠀⠘⣾⠁
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠊⠀⠀⠀⣀⠀⠀⠸⡄
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠌⠀⠀⠀⣳⡀⠀⡀
⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⡊⣹
⠀⠀⠀⠈⢏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣀⠀⠀⢀⣀⣏⡽
⠀⠀⢸⠩⠋⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠩⠀⠀⠀⠀⡀⠀⣠⡤⠴⠖⠒⠲⠭⢝⡏⠁
⠀⠀⣸⠀⢀⡴⠒⠊⠉⠒⠦⡀⠀⠀⠀⡧⣄⣀⣸⠀⠀⢀⡾⠟⢿⠉⠀⠱⡀
⠀⢾⢛⣁⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠸⠀⠀⡎⠀⠀⠈⠒⢤⡀⠈⢢⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡀⢀⣧⡀⠀⣴⣄⡜⠀⠀⠀⠀⠀⠀⠹⢿⡯⣑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠬⠃⠀⠘⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣣⣾⡿⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⣿⣿⣿⣇⠀⢠⡀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⢀⣴⣾⠟⠀⣿⣿⣾⠷⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⠸⣿⣿⣷⠀⡞⢣⡀⣠⣶⠶⠂⠄⠈⠿⣶⣦⣼⣿⣟⡊⢠⣿⣿⠁⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣉⠀⠻⣿⣿⡀⣰⣿⠛⢋⠡⣀⠁⠀⠀⠓⠀⠉⠃⠙⣿⡇⣸⣿⡯⠀⢠⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⠀⣹⣿⣷⡟⠀⣸⣏⠐⠟⠃⠀⠄⠀⠀⠀⠀⠀⠙⢰⣿⣿⣆⠀⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠂⣠⣼⣿⣿⢁⣾⠯⠽⠒⢿⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⣲⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⢠⣆⣤⠀⠽⠶⣶⠀⠸⣼⡇⡼⠇⠀⠀⠠⢎⡀⢀⣷⡦⢈⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢍⡝⢿⣿⠄⣿⣿⣯⡀⠀⠻⠃⢠⠀⡀⠀⠀⠿⣟⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡘⢀⣼⡇⠀⠛⣁⠀⠈⢣⡄⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⣄⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⣺⣿⠀⢰⢯⠗⢀⠴⠉⠁⣀⣤⠀⠀⠀⠀⠀⢠⣥⠀⢙⡀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⢫⣿⡏⠀⣸⠁⢰⡿⠀⣰⠟⢋⣉⡀⠀⠈⠲⠀⠈⠈⠀⢘⣥⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠤⢟⣿⡇⠀⣸⠁⣾⠃⠀⡿⣶⠛⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⠶⢾⡇⠀⠛⠀⠟⠀⢀⡴⢁⣴⡿⠃⠀⠀⢿⣿⣦⠀⠀⡠⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣾⡇⠥⣼⣆⠸⣆⢁⠀⣿⠁⠈⠉⣀⣀⠀⢀⣀⠀⠼⠀⠀⠛⠂⣈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢳⣛⣡⣭⣷⣌⠺⠁⢸⡄⠀⠸⠿⠋⠀⠘⠛⠛⡁⣀⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⡭⠄⣐⣋⡹⢻⣶⣦⡑⢀⣀⣀⣀⣠⣤⠄⢊⣤⠃⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠩⣟⣃⣀⣉⣷⣶⣿⣟⢻⣷⣄⣩⠍⠉⣀⠲⢈⢷⣲⡆⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣛⣻⣶⣷⣤⣾⣽⣟⣽⣯⡟⠀⠠⣜⣷⣋⣛⣴⣷⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢉⣩⣭⠉⠭⠟⡋⣽⣧⣾⣳⡆⢘⠦⢛⣦⣉⣻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠭⣿⣶⡆⣰⣊⠃⢻⡟⣿⠀⢈⠷⣄⣼⠚⡡⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠈⠸⢿⣷⣿⣷⣄⠘⠻⠻⣿⣾⢿⣛⠮⠁⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⠀⢡⡮⢿⣿⡇⠀⠀⢀⣿⣯⣆⠁⠀⢠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡷⢻⠀⣱⣿⡇⣇⠀⠀⠈⣽⣿⣟⠁⠀⢸⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠈⣇⣨⣟⡿⣿⠀⠀⠀⣿⣧⣽⡇⠀⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⣈⢈⡄⠀⠀⣿⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⣿⡯⠈⠃⠀⠀⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠓⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣰⣄⡜⣽⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⣤⡀⡀⠀⠀⠀⠀⠘⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣶⣿⣥⡀⠀⠠⠄⠠⣤⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⢻⣿⣿⣿⣿⣾⠇⢰⠟⢻⣿⣿⡿⠔⠀⠀⠀⠛⠀⢀⠴⠿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣿⡿⠟⢻⠀⠀⢠⡟⠻⠏⠁⠀⠀⣠⣤⣤⠖⢻⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣾⠀⢰⡆⠀⢰⣤⣀⡀⠀⢰⡟⣴⣶⣿⣷⣏⣻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⣴⠀⣸⣿⣦⣩⣿⣿⣇⣾⣿⣯⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠿⠷⢶⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣤⠤⣤⡄⠀⠀⠀⢀⢀⢄⠄⠁⠀⠈⠉⠀⠉⠀⠀⠈⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⢰⡇⠘⠧⣄⣁⣈⣀⣉⣉⣷⣦⣠⡦⠀⠀⠐⣿⣿⡵⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠇⠀⠢⡦⣤⠤⡤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⢀⣀⣀⣀⣤⠴⠒⠋⠉⠉⠉⠛⠲⣄⠀⠀⣀⡤⠖⠚⠋⠙⠃⠀⠈⠉⠉⠉⠓⠲⢤⣀⣠⠴⠛⠉⠁⠀⠀⠉⠉⠙⠒⠂⠄⢲⡦
⠀⠀⠀⠙⣗⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⠖⣫⠏
⠀⠀⠀⠀⠈⠣⡀⠉⠙⠛⠉⠉⠉⢹⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠘⡇⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢦⡀⠀⢸⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⣶⡄⠀⢠⠀⠀⢀⣀⣠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠦⠤⢴⡇⠀⠀⡟⣴⠒⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⣳⣆⠃⠀⠈⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣀⣀⣿⣿⡿⡿⠀⠀⠀⠀⣈⣉⡀⠀⠀⠈⠿⣿⣏⡯⠼⠄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠄⠀⠀⠀⠈⠉⠁⠀⠀⢀⠞⠛⠛⠛⠓⠓⢄⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡴⣦⠀⠀⣰⠶⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⣀⢇⠀⠂⠜⠀⣀⠘⠄⠁⡰⠢⠒⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⣠⠏⠙⠦⣄⠀⠀⠀⠀⠀⠀⠉⠒⠺⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⢠⠏⠀⠀⠀⠈⠙⠒⠦⢤⣤⣤⣀⣀⠀⠀⠀⠀⣀⣀⣤⠴⠖⣿⠹⡄
⠀⠀⠀⠀⠀⠀⣧⠈⠳⠁⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠉⠉⠉⠉⠉⠉⠁⠀⠀⢠⠏⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠠⡐⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣔⣀⣀⣠⡴⠚⣇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣹⣷⠀⠀⠀⠀⣸⠁⠉⢰⠋⠀⠀⠈⢣⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⣿⠀⠀⠀⠀⢿⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⣹⢀⢸⠀⠀⠀⠀⠸⡼⠆⠤⠜⠀⠀⠀⢸⠁⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡄⠀⢃⠀⠀⠀⠀⠀⠀⠸⣀⠀⢰⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠐⠃⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⡶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠢⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢆⠈⠳⣄⠀⠀⠀⢀⣎⡔⠂⠀⢀⡴⠚⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡄⢸⡄⠀⡹⠖⠒⠛⠉⠉⠛⠒⠶⣏⠠⠎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣝⠋⠀⠀⠀⠀⣠⠴⠦⠄⠀⠀⠀⠀⠶⠶⢄⠀⠙⣦⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡤⢄⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠀⠀⠀⠀⠀⢰⣯⣶⠒⣿⠀⠀⠀⠀⢸⣾⡃⣷⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠱⠃⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⠀⠀⠀⠀⡘⣿⣿⡿⠇⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡀⠀⠀⠀⠀⠖⠀⠀⠈⠙⠟⣡⣢⠴⠒⠒⠻⢮⡁⠀⠀⠀⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⡥⠤⡀⠀⢠⠒⣝⢦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣇⣀⠇⠀⠙⠴⠅⢸⠃⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⡡⠴⠛⡲⠦⠖⠁⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⡏⠀⡠⠖⠋⠉⠉⠙⠲⣌⣦⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣹⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡀⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣞⠁⣀
⠀⠀⠀⢰⣀⢔⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣈⡛⢦⡀⠀⠀⠀⠀⠠⡇⠀⣠⠋⠈⡉⠘⣷
⠀⠀⠀⠀⠙⠪⠽⠭⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢤⡼⢹⡆⠙⢦⠀⠀⠀⠀⡇⠀⣇⣀⠐⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⢤⣤⣀⠘⠀⣸⢉⡾⠤⠴⠚⣇⠈⢉⡀⣹⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠲⠷⠊⠀⠀⠀⠀⠈⠛⠛⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠉⠉⠉⠁⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠒⠦⠤⠄⠀⠀⠀⠠⠤⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣴⣾⠟⢥⡀⢀
⠀⠀⠰⣄⡀⠀⢚⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣉⡁⠀⠀⢻⠷⠋
⠀⠀⠀⠈⠉⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠏⣼⡏⠑⠒⠇⠀⠁
⠀⠀⠀⠀⠀⠀⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡄
⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⠀⠀⠀⠀⠀⢀⡒⠶⢬⡜
⠀⠀⠀⠀⠀⠀⠀⠹⣗⠁⠀⠀⠀⠀⠀⣠⣶⡾⢋⣀⡀⠀⠤⡄⠀⢐⠀⠀⠀⠀⠈⢂⣽⡉⠀⠀⠀⠀⠀⠐⣿⣿⣿⠿⠿⣷⡶⠿⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⣧⣭⣯⣽⣿⡃⠐⠂⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⢠⣿⣿⡟⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣄⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⢀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣧⡄⠀⣤
⠀⠀⠀⠒⠓⠒⠒⠂⠐⠒⠒⠛⠈⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠈⠉⠀⠀⠈⠉⠁⠀⠉⠀⠉⠉⠁⠀⠙⠓⠚⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡶⢶⣶⣶⣶⡶⢶⣶⠖⠖⠒⠒⠦⠤⣀⡀
⠀⠀⠀⡠⢤⣄⣰⡿⠛⠉⠉⠉⠁⡀⠄⣬⠑⣊⣁⠄⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠸⣿⣇⣿⠟⠁⢀⠤⠂⠔⣋⠅⣀⣀⡴⡊⣁⢀⠤⠐⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢿⣿⠾⡛⠛⢋⣹⠝⠁
⠀⠀⢀⣿⣿⣿⠀⠐⠡⠶⢴⣾⡣⣾⠞⠁⡨⠖⢁⠠⣊⣵⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⣾⣁⣴⣿⣟⡻⠗⠂
⠀⣰⡿⢻⣿⣧⠀⠀⢠⠔⣉⠔⠊⠁⠁⠀⠀⠀⣰⠴⢿⣻⡵⠂⠀⠀⠀⠀⠀⠀⠀⠲⡾⣚⠫⢿⣿⣿⣿⣿⡄
⣾⡼⠃⠸⣿⣡⠆⣀⡤⣾⣿⣨⠀⡀⢀⠀⣂⣽⣣⢖⣭⣯⣷⡵⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠀⣿⠇⠙⠃⡿⢷⡀
⠟⠀⠀⠀⣿⣿⣿⣻⠟⠉⣩⣽⣏⣫⣴⣾⣵⣷⣖⢛⡹⣨⢿⣿⣗⠀⠀⠀⠀⠀⠸⣿⣧⠄⠀⣝⣶⣾⣟⣤⣬⡼⢢⣤⣤
⠀⠀⠀⠀⠘⣿⣿⣿⣆⣬⣰⣴⣾⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⠿⡋⠦⡄⠀⠀⠀⢻⣿⣶⣦⣤⣿⣿⣿⣿⣟⣛⣻⢷⣶⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣟⣿⡿⢿⣿⣧⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣏⠀⠀⣀⡼⣿⣿⣿⡿⠿⠛⠛⠛⠛⠋⠋⠋⠉⠁
⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⣻⣿⡿⠇⠀⠀⠉⠉⠉⠉⠀⢸⡏⠀⠹⡆⠀⢹⠁
⠀⠀⠀⠀⠀⢹⣿⣯⠀⠀⠀⠀⢹⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⡘⢁⠆⠀⠹⡄⢿
⠀⠀⠀⠀⠀⠀⢿⣾⣆⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⢻⣬⣆
⣀⣀⣀⣀⣀⣀⣈⣻⣿⣆⣀⣀⣀⣈⣙⣻⣃⣀⣀⣀⣀⣀⣀⣀⣓⣳⣀⣀⣈⣙⣺⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣫⣛⣩⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢌⠙⠂⠀⠀⠒⠉⠙⠛⠲⢤⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠈⢉⠉⠉⠓⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⢀⡇⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠸⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠑⢀⡼⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠈⢧⡀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⣉⣁⣀⣀⠉⠙⠆⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢆⠀⠀⠀⠀⠑⠀⠀⠀⠐⠉⠉⠀⠀⠉⠛⣆⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⠈⠳⣤⣀⠀⠀⠀⠀⢠⠀⠋⠛⠀⠀⠰⠦⠘⠂⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⠃⠀⠀⠀⠈⠉⠉⠀⠀⠘⢷⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⠏⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠙⠻⠿⣯⣭⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢷⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⡀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣦⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠸⡷⠛⠛⠉⠉⠉⠙⠛⠓⠶⣤⡼⠋⠙⢷⣄
⠀⠀⠀⠀⣾⣿⠗⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢦⠈⠛⢶⣄
⠀⠀⠀⠀⣿⣧⣀⢈⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⡾⢷⡀⠀⣿
⠀⠀⠀⠀⢿⡻⢯⣉⣉⣀⣀⣀⡀⠀⠀⠀⢀⣀⡼⠛⠲⠤⣄⣀⣀⣀⡏⠴⠂⠀⠀⠀⢀⡤⠤⠦⢤⣀⠉⢭⣻⡌⠻⠶⠋
⠀⠀⠀⠀⠈⣳⠄⠈⠉⠉⡍⠉⠉⠉⠛⠙⠉⡽⠁⠀⠀⠀⠀⠀⠉⠉⢠⢲⣆⠀⣠⠞⠉⢀⣄⠀⢀⡈⠙⢾⠃⠙⢦⡀
⠀⠀⠀⢀⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⡴⠁⠀⡴⠁⢸⠀⢯⠉⢦⠈⠳⡀⠀⠻⣆
⠀⠀⠀⣾⠁⠀⠄⠀⠀⠀⠀⠑⠄⠀⠠⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡇⢀⡼⠀⠈⠦⡼⠃⠀⣿⠀⠀⣿
⠀⠀⢸⡧⠀⠀⠀⠐⠈⠀⢀⠀⢀⢀⡀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠉⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⡟
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡇⠀⠀⠈⠓⠲⠤⢤⣤⡤⠤⠖⠋⠀⠀⣰⠟
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⠶⠶⠶⠶⠶⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢹⠦⣀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⣆⣠⠔⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⣄⠌⢿⡗⠶⠶⠶⢾⠀⠀⢀⣿⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠼⣿⠛⠛⠃⠀⠀⠀⢸⡧⠀⢼⡟⣯⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠟⠀⠀⠀⠀⠀⠀⠀⠛⠶⠾⠃⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴
⠀⠀⠀⠀⠀⠀⢸⣷⣶⡿⠋⠉⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣤⣾⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠈⢻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⡿⢫⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣄⣀⡀⣀⣀⣠⣼⣿⣿⡎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⣿⣿⡟⠀⢸⡏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣷⡘⣮⡑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⣦⣾⣿⣿⣷⣐⠸⡇
⠀⠀⠀⠀⠀⠀⠻⣄⣉⣅⣩⣍⣭⣩⣭⣽⣿⣿⣧⣿⣿⡷⢹⡆⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣭⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡗⢺⡦⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⢻⣿⣇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠵⠿⠁⣴⠟⣉⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣞⡻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡭⠟⠉⣩⠛⣩⣵⣾⣿⢁⣴⣿⣾⣿⣿⣦⡐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠘⠉⣩⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠗⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠇⢀⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡽⢣⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⢀⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣰⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⡎⠈⣿⣿⣿⠇⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣀⡀⠸⣿⡆⣿⣸⣿⣿⠿⠟⢿⠿⠿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢸⡇⢀⡿⠹⡿⠀⠀⠀⠀⠐⠈⠈⠀⠀⠠⢐⣴⣿⣷⣤⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡰⠀⠀⣻⡃⣾⢃⢰⣿⠀⠀⢠⣴⣶⣀⠰⠛⠶⣿⣾⣋⠁⢙⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⠁⠀⣰⣿⣷⡇⢸⠀⠻⣷⣶⣦⣤⣥⣀⣤⣤⣶⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⣿⣿⣿⣿⣤⠀⣤⣙⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⡇⠘⣻⣿⣿⣿⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣤⣀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠻⢧⠺⠟⣿⡿⠿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠖⠒⠚⠯⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⣀⣤⣴⣀⣠⣤⣄⣤⣤⣤⣴⣶⣶⣦⣠⣰⣄⡤⣼⣗⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⢠⣶⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣿⣿⣿⣿⡟⢃⡒⠙⠪⣇
⠀⠀⠀⠀⠀⠀⢲⣄⣀⡾⢁⣤⣠⣶⣯⢻⡋⠰⣿⣿⣿⣿⣿⡿⣟⣉⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⣦
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣖⢿⣿⣿⣿⣋⣠⣶⣧⣹⣿⣿⡿⠿⡷⢿⣿⡶⣿⣯⡟⢛⣿⣿⣿⡟⠛⠻⣿⣿⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢻⣿⣿⣿⣇⢹⣿⣿⣿⣿⣧⣤⣶⣤⣿⣿⣿⣾⣿⡿⠋⢻⣿⣷⣤⣼⣟⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣷⡈⢃⣿⣿⣿⡈⣿⡿⠛⠛⠻⠿⠿⠿⣿⡿⠿⠿⠛⢳⣶⣶⡏⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡀⠻⣿⣷⠾⠋⠉⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠚⠉⣀⣀⣠⣤⡖⠀⣿⣀⣀⣠⣤⡀⠀⠀⢴⣶⣶⡦⢶⣽⣿⡴⠟⠿⠆⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠎⠠⠞⠛⠛⠋⠉⠁⠁⠀⠀⠀⠀⠉⠁⠊⠉⠁⠀⠀⠀⠠⠭⠏⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠖⠉⠙⠢⣄⠀⢀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠴⠊⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢠⠃⠀⠀⠀⠀⠀⢱⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢣⣀⣀⡤⠤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠈⠗
⡇⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠃⡔⠢⠱⠀⡇
⡇⠀⠀⢀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠱⣑⡴⢁⣏⠔
⢇⢀⡔⠁⡇⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠈⠣⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡒⣊⡡⠊⠁
⠈⠉⠀⠀⡇⠀⠿⠿⠃⡠⠒⠂⠐⠒⢄⠀⠿⠿⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢳⠀⠀⠀⢰⠁⢶⠀⠰⠆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠳⢄⡀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⢦⡀⠀⠀⡄⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠑⠲⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⡇⠀⠀⠀⡼⠉⠉⠉⠉⠉⠉⢏⠉⠉⠀⣿⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⡸⢧⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠻⡀⠀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢆⠤⢀⡀⠀⠀⣀⣘⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠢⢌⠓⡄⠀⠀⠈⠉⠙⠒⠤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡄⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠊⠩⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠉⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠲⠲⠛⠁⠀⠀⠀⠀⠀⣇⢉⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠦⠄⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⣀⡤⠖⠋⠘⣇⠀⠀⠘⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⣶⠲⣟⣉⠁⠀⠀⠀⠀⢹⡀⠀⠀⢧⡀⠀⢳
⠀⠀⠀⠀⠀⠠⡀⠀⠈⠷⣿⠾⠛⠁⠀⠀⠙⠂⠀⢀⡀⠀⠀⠀⠈⠳⣄⡀⢸⡃⠀⠀⠀⠀⣧⠀⠀⢸⠑⣼⠙⠇
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣀⡀⠀⠀⠉⠛⣻⡟⠀⠀⠀⠘⣆⡶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠄⠚⠋⠀⠀⠀⠀⠘⠃⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠤⡀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⢳⠤⠓⠒⢘⠃
⠀⠀⢀⣀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢎
⢀⣀⢅⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡀⠀⢀⡀
⠈⠁⠈⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠿⠂⠈⠈⠙⣼
⠀⠀⠀⠀⡷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸
⠀⠀⠀⢠⠁⠘⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠼⢁⡰⠖⠋⠉
⠀⠀⠠⠃⠀⠀⠈⢢⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⣀⣀⡠⠔⠊⠁
⠀⠀⡇⠀⠀⣀⡠⠄⠓⡄⠀⠀⢀⠧⠤⠀⣀⣀⣀⠀⡇⠀⠀⢀⠾⠓⠉⠉⠙⡀
⠀⠀⢆⢀⣏⠀⠀⠀⠀⢰⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠆⠀⢀⠎⠀⠑⠢⢄⡀⠐⣄
⠀⠀⠀⠉⠛⠁⠀⠀⠀⠈⠑⠢⣀⢈⣦⡀⠀⠀⣴⡉⢀⠴⠃⠀⠀⠀⠀⠀⠈⠂⢬⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⢶⠶⣶⡶⠶⢶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣛⣩⡿⣟⡻⣛⠋⡉⢉⠙⡛⠛⠛⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⣿⣿⣿⣿⣿⠉⠀⢂⡙⢋⣻⣷⣶⣤⣩⣷⡤⠐⠘⠙⠻⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⣿⡇⠀⠀⠀⠀⠠⣿⣿⠁⠀⡠⣌⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢛⣼⣯⣿⣷⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠂⣠⣾⡿⠐⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⡿⠿⠛⡉⢹⢯⣿⣇⠀⣀⣠⠀⣶⣿⣿⣿⣿⣿⡿⡶⣿⠆
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⡍⢲⣀⣿⡏⡋⠀⣱⡀⠀⠀⠀⠀⢾⣿⣿⣯⣽⣷⢄⣨⣏⣱⣄⣿⣿⣿⡉⢠⡬⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠠⠶⣿⣧⣤⣴⠟⣿⠁⠀⠙⠩⡳⣾⠇⠀⠀⠀⠀⢢⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢬⣻⣷⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⢸⢛⣴⠱⠾⠠⢂⣠⣽⣿⡿⠋⣸⠆⢠⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣶⡛⢻⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣟⣸⣿⡆⢸⣿⣿⣿⣿⡿⢧⡏⠁⠀⣿⠉⠉⠉⠉⠉⠉⠙⠿⠟⠛⠋⠉⠀⢻⣿⣿⣿⠲⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢼⣭⢽⣿⣦⣼⡿⠟⠉⠁⠀⠀⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠈⠻⢶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠠⣤⣻⡿⠟⠋⠉⡀⠀⣀⡀⠀⠰⠄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠻⠿⢿⣿⣿⣿⢇⣀⣚⣿⣾⣷⣾⣦⣷⣄⣄⣤⣤⣶⣶⣿⣄⢉⣛⣏⣴⣶⣤⣰⣦⣼⣧⡙⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠈⠁⠁⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⠋⠀⠾⠿⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣴⣿⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⣿⣤⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣐⢻⣿⣿⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⣤⣤⣤⣼⣿⣷⣶⡄⠉⠁⢀⠀⠀⠀⠀⠀⠀⢀⡸⢿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣦⠀⠶⠈⣇⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣻⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⢧⠀⡄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⣻⣿⣿⠀⠀⠀⡄⠶⠶⠂⠀⠀⠛⠁⢸⢇⡇⢸⣿⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⢏⡼⠁⢸⡿⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠲⠾⣿⣿⣿⣿⠃⠀⣼⡃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠷⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣠⣾⠗⢠⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠉⢷⣤⡀⠉⠀⣤⣬⣭⣿⡿⠟⣁⠴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣿⣦⡀⠈⢻⣿⣦⣄⡀⢁⡐⡦⠖⢈⣤⠞⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠈⠁⢹⠍⠙⠻⠷⠤⣤⠤⠤⡤⡽⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⢤⣶⣿⠏⠩⠿⠿⠟⠫⠉⠋⠹⢻⠟⠻⡿⠿⢿⣻⢻⣿⡶⣶⣆⠠⠄⣀⣀⣀⣀⡀
⠀⠀⢸⣯⡙⣣⣠⢶⣿⠛⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⣁⢼⡽⢷⣟⡆⠀⠀⠀⠀⠙⣿⣿⣷⣦⣀⣀
⠀⠀⡀⣯⢿⣿⠟⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⢹⣿⣿⡿⠿⣿⣿⡺⠿⠦
⠀⠀⠀⠁⣾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣉⢤⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⡯⣽⠁⠀⠀⠀⠀⢀⣿⠉⡇⠀⢫⠉⢴⣢⣀⣤⣏⣖⡋
⠀⠀⠀⢸⣿⡈⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠈⠏⠀⢿⠀⣿⣷⣄⣉⣽⣿⡟⠁
⠀⠀⠀⢸⠋⠡⡒⠀⠀⠀⠀⢰⠀⡀⣾⣍⣾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠀⠀⠀⢉⠊⠐⣧⡆⠘⣿⣿⣿⣿⣿⡇⠄
⠀⠀⠀⠘⣯⡆⠹⣦⠀⠀⡀⠈⠀⠀⢀⣿⣿⣿⣿⣿⣥⢡⠀⠀⠀⠀⠀⡠⠀⢀⣄⣰⣾⡇⠀⠀⠀⠀⠀⢀⢾⠀⢸⣿⡇⣠⠸⣿⣟⠻⣽⡟⠈⢐⣿
⠀⠀⠀⠀⠹⣷⢀⠀⠢⠊⠴⣠⠀⣪⣭⡷⢾⣶⣴⡭⣦⣥⣍⣀⡀⠀⠀⢀⣠⢻⣟⣿⡿⠡⠎⠀⠀⠀⠀⢸⣦⣡⣾⣿⣿⣟⣰⣿⣿⣮⣭⣩⣽⠿⠋
⠀⠀⠀⠀⠀⢹⣯⣃⠀⠐⠴⣧⣾⢿⡟⠁⠀⠉⠛⠛⠻⠧⠯⠿⣯⠥⠴⠤⠶⠶⠿⠿⢠⣴⡇⠀⠀⠀⠀⠈⡿⠛⠉⠈⠉⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠈⢻⡟⡀⢰⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⡸⠀⠀⠉⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠆⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⣟⠂⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⣣⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⠄⠀⠀⠀⠀⠩⡀
⠀⠀⠀⠀⠀⠱⠀⠀⢠⣤⠄⠠⠹⢧⡀⠱⠔⠆⠠⠱⠖⠒⠒⠰⠲⠐⠂⢀⠐⣁⠚⠓⠘⠁⠚⠉⠁⠀⠍⠀⠓⢦⣄⠐⢘⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠑⠒⠀⠐⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠘⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣿⡟⣦⠀⠀⠀⠀⢠⣀⣸⣿⣿⡏⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣿⣿⣧⡿⠿⠓⠒⠀⠀⠙⢷⣿⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⡧⣶⣂⠆⠀⠀⠀⠀⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠉⠉⠉⠉⠉⠙⠉⠹⣿⣿⣿⡟⠋⠀⠻⠿⠇⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠳
⠀⠀⠀⠀⠀⢀⣴⢠⡎⠁⠀⢠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢰⡛⠠⣾⠠⡷
⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣾⡄⠙⣦⣄⠀⠀⠀⠀⠀⢿⣿⠷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⡄⠹⢿⣷⣶⣶⣦⣶⣮⠙⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢿⣧⡀⠀⠀⠀⡀⢸⡁⠀⠀⠀⣺⣿⣿⣷⣜⠛⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣸⣿⣇⠀⠀⠈⣧⢸⡁⠀⠀⢘⣿⣿⣿⣿⡟⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⣿⣿⣷⣶⣄⣿⡼⣄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⣀⣿⣿⣿⣿⡟⠛⠿⢷⣷⡀⠀⣿⠿⠿⠟⢻⣿⡟⢘⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣼⢻⣿⣿⡟⠀⠀⠀⢸⣿⠇⠀⣿⠀⠀⠀⢸⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⠀⢻⣿⣧⠀⠀⠀⢸⣿⣷⠀⣿⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⣿⡀⠸⠻⣿⡄⠀⠀⠀⢻⣿⡀⡇⠀⠀⠀⢸⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣇⠘⢶⣿⡿⠆⠠⠄⢾⠉⢙⣧⣤⣤⣤⣼⣀⣤⣵⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠶⣿⡿⠟⠉⠁⠀⠉⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠛⣷⣶⣦⡀⣦⣀⢀⡀⠀⠀⠀⠀⠀⢾⣿⢈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⣠⠸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⢿⣿⡷⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢟⣵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⢎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣭⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢸⣿⣿⡟⣿⣿⣷⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣼⣿⣿⢠⣿⣿⣿⠀⠀⢸⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠿⠟⠿⠛⠛⠛⠛⠿⠅⠛⠿⠀⠒⠈⠛⠈⠓

⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠤⠤⠀⠀⠀⠠⠀⠀⣀⡤
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠋⢢⣀⢀
⠀⠀⠑⠦⠬⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⣶⠆⣀⡀⠻⠁
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠈⠃⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠐⢺⢬⡜
⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⢠⣴⣞⣠⣄⠀⢠⣄⣀⡂⢀⡀⢀⣀⣤⣍⠀⠀⠀⠀⠀⣽⣿⠿⠻⠿⠶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣯⠌⠀⠀⠠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠈⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢧
⠀⠀⠀⣀⠀⢀⠀⠀⠹⣾⢤⣀⣈⢻⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⢀⠀⢈⣷⡀⢠⣄⣀⡀
⠀⠀⠈⠉⠈⠉⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠦⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣗⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡤⣌⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠈⣣⠈⠃⠐⠂⠉⠉⠉⠉⠒⠁⠐⠃⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢒⣠⣤⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⢠⣴⢴⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠉⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⢤⢴⢶⠃⠀⠀⠀⢐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣬⠄⡄⠀⢠⠀⠤⠠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠲⠶⢺⡃⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡸⠀⠀⠀⢀⠈⡈⠀⠀⠀⣀⣀⣀⠀⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⡤⠐⢒⣾⣇⣉⣿⣿⣃⣀⣀⣲⡀⠘⡄⠀⠀⠀⠈⢆⡈⠊⠔⠕⠐⢐⡴⠃⣀⠀⠀⢈⡈⠁⠀⢀⣍⠩⢁⣄⢈⣩⣁⣀⣀⣈⠑⣂
⠀⠀⠀⠀⠀⠀⣿⠒⠺⡾⡧⢼⣟⠂⠤⠧⠶⢿⡇⠀⠈⣦⡀⠀⠀⠀⠈⢁⡒⠲⠒⣋⡠⠚⠀⢀⠠⠋⠀⠀⠀⠈⣏⡛⠀⣛⣛⣹⡇⠠⡿⣿
⠀⠀⠀⠀⠀⠀⢾⣍⣹⣟⡗⠲⢿⣉⣐⣛⣛⣻⣧⠀⠀⠂⢙⡢⡀⠀⢀⣀⠈⠉⠉⠀⡀⠀⡀⡀⡀⢸⠀⠀⠀⠀⣶⠄⢨⣭⡭⠷⣯⢉⣯⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠢⣤⢭⣭⠿⠟⠒⠀⠲⣄⡐⡠⠊⠔⠋⣽⣿⡏⠫⠨⠊⠌⠄⠂⠼⠀⢰⠮⠭⢁⣠⡴⡬⣿⣻⣷⢤⢷⠟⠚⠌⠚⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠇⣀⣀⣴⣳⡍⠙⠋⠛⠋⠍⠈⠝⠒⠶⠲⠖⠞⠋⠐⠀⠘⠗⠲⠲⠒⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠬⢥⠥⠶⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⢠⣴⣶⣻⠉⢿⠿⠿⡿⢏⠙⠍⠻⢻⡿⡻⣿⢿⢿⣿⡻⣶⣶⢶⣖⡀⠤⢀⣀⣀⣀⣀
⠀⠀⢸⣿⠛⢷⣀⢴⣾⡟⠋⠉⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠈⠃⠋⢁⣨⣿⢿⣽⣷⠀⠀⠀⠀⠈⢻⣿⣷⣦⣤⣀⡀
⠀⠀⠀⣻⣵⣿⡟⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⢿⣿⣿⡿⡿⣿⣿⠶⣶⡦
⠀⠀⠁⠉⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢣⣴⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⣸⣋⡟⠀⠀⠀⠀⠀⢸⣿⠹⡇⠀⢟⠋⢥⢤⡀⣀⣹⣰⠞⠁
⠀⠀⠀⢠⣿⡆⢡⠏⠀⠀⠀⠀⠀⠀⠀⠁⠘⠟⣈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠁⠀⠀⠀⠀⠀⠸⡏⠀⡇⠀⣿⣧⣄⠛⣻⣿⣿⠋⠁
⠀⠀⠀⢸⡟⠃⡴⠄⠀⠀⠀⠀⣆⠀⢠⡶⣲⣾⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡆⠀⠀⠀⠀⠀⠀⢓⠘⢠⣯⡆⠹⣿⣿⣿⣿⣿⡟⣀
⠀⠀⠀⠘⣏⡆⠙⣤⡀⢀⠀⠀⠛⠨⠉⢽⣿⣿⣿⣷⣴⣠⢂⡀⠀⠀⠀⠀⢀⠀⠀⣠⢀⣼⡷⠁⠀⠀⠀⠀⠀⢀⣟⠆⢾⣿⡆⢀⣹⣿⣿⣿⣻⡿⠀⠂⢴⡆
⠀⠀⠀⠀⠹⣿⡄⠈⠤⡰⢊⡄⠀⠠⢖⣚⣭⣯⣍⣩⣛⣋⣊⡒⡀⠀⠀⠀⠁⢀⣼⣿⣿⣿⡟⣠⠆⠀⠀⠀⠀⣿⡜⢀⣿⣿⣷⡿⢀⣿⣿⣷⣟⣛⣒⣾⠿⠃
⠀⠀⠀⠀⠀⢻⣾⣧⠀⠁⢄⣼⣣⣾⣿⡟⠉⠉⠛⠿⠿⣿⣟⣛⣿⣗⣒⣀⣈⣩⣥⣿⣿⡏⣀⣽⠀⠀⠀⠀⠀⠹⣿⠿⠛⠙⠛⠻⠿⠿⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠠⢿⡷⠇⢠⣈⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⢠⠀⠃⠒⠖⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠈⠟⢏⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⢟⠉⠂⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⡿⠃⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠣⠉⠀⢐⠀⠀⠀⠱⣧⠀⠹⣆⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠤⢠⣤⠸⠷⣈⡶⠀⠂⠀⡤⠘⣤⣄⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠡⠀⠀⢿⠏⠠⢀⡉⠛⠠⢬⠌⠀⠌⠌⠁⠀⠀⠈⠈⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠶⠌⠁⠄⠀⠹⠷⠄⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡟⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⢉⣻⣿⣿⣷⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣼⣿⣿⣿⡟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⣙⡻⣿⣿⣿⢰⡎⣦⠶⠟⢹⡇⢸⣿⣟⠶⢖⣷⡇⣿⣿⣿⡽⠗⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⢯⣬⣿⣯⢈⣿⣿⣤⠤⡎⠀⠈⢹⡟⣾⢟⣿⡱⣿⣿⣽⡽⢇⣶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣶⣶⣝⣿⣯⠚⡛⠁⠀⠀⠀⠀⠸⠀⠈⠁⠈⢉⠙⢿⣿⡻⠿⠿⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢈⢸⣿⣤⠆⣴⠺⠀⠀⣀⣠⣤⢀⣀⡀⡞⣢⡀⣨⣿⡥⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠻⢿⡇⠼⣿⡷⢂⡳⠷⠋⠙⠈⣿⠁⢻⢟⠷⢺⡿⠳⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣾⠁⡘⠍⠠⠖⠉⠀⣤⣠⣄⠈⠲⣄⠈⣥⣀⢻⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⢠⡅⠸⠃⠀⠆⢀⡴⠋⠀⠉⠉⢷⣤⠹⡆⢨⡋⠸⣧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⢠⣖⡁⠀⠀⢊⡴⠖⠛⠛⠓⠦⡀⠄⢸⡼⢡⠀⣿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠈⠙⠁⠀⠠⠸⢶⣿⠇⠀⣿⡷⠾⢤⠀⠁⢿⠂⣿⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⡆⠁⣤⠀⣶⡘⠆⠀⠀⠀⠈⠀⠘⣾⠆⢀⠎⠠⣿⡂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠁⣷⣿⣿⣇⣀⣵⣶⣶⠾⠷⣶⣶⣾⡟⣻⡙⣿⣿⡉⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠠⠾⠿⣛⣿⣟⣌⡉⠻⠶⠶⠏⢘⣰⣎⣛⣻⣿⢥⣉⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⣿⡳⣟⠰⠺⠿⣿⣿⣿⣄⣠⣶⣿⣿⣯⣋⣱⠄⣸⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣿⣟⠓⠂⢶⣿⡿⣿⣿⣿⣿⣿⣿⣮⡋⣩⣿⡿⣃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠊⢻⣿⣷⣷⣾⣿⡃⢺⡇⣹⣝⣏⣲⣶⢿⣿⢖⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠷⢼⣿⠻⠿⣿⣷⣎⣿⣿⣿⣿⣿⣿⡟⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡿⣷⣶⣬⡿⢿⣿⣫⣿⣧⣿⡷⠄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⠛⣿⢿⡇⠈⣿⣿⡿⠟⢿⡯⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠏⣽⡇⢰⣿⣻⣃⠀⢀⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⠀⣀⣿⡇⠰⢶⡿⠯⠀⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⢻⣿⠀⣸⣿⠗⣶⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠿⠿⠷⠿⠿⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⢷⡄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠸⣿⠿⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠿⢶⣤⣠⣾⠛⠉⠛⢷⣄
⠀⠀⢰⣿⣿⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⠀⢰⡀⠙⠿⣦⣄⡀
⠀⠀⣿⣿⡯⠁⠠⡙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠁⢹⣆⠀⠈⠙⢻
⠀⢀⣿⣿⣗⡤⠤⢜⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⣦⡿⢻⣧⠀⠀⢰
⠀⠀⣿⡻⣿⣟⡛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠶⣤⣀⡀⠀⠀⠀⠀⠀⣸⢀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠉⢙⡙⣿⡄⠙⢷⣤⣾
⠀⠀⠘⣷⣄⠙⠻⠿⠿⠿⢿⠿⠶⢶⣶⣶⣤⣤⣶⣶⡶⣾⠏⠀⠀⠀⠉⠉⠛⠓⠲⠶⠶⠛⢈⣁⡀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠈⠙⠳⣤⣎⣹⡎⢿⣦⡀⠉⠁
⠀⠀⠀⣨⡿⠛⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢈⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣸⣷⠀⠀⣴⠟⠁⠀⣠⠴⣄⠀⢀⣤⡀⠈⠙⣿⠁⠀⠙⢷⣄
⠀⢀⣼⠟⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⢀⡞⠁⠀⠀⡼⠃⠀⣿⠀⢸⡄⠈⢲⡀⠈⢳⡄⠀⠀⠹⣷
⠀⣾⠏⠀⠀⡁⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢠⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠃⠀⠀⡿⠀⠈⢷⡀⠀⣷⠀⠀⢹⡄⠀⠀⠸
⢸⡟⠀⠀⡰⠁⠀⠀⣀⠠⠄⠲⡄⠉⠒⠖⠚⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣇⣀⡼⠃⠀⠀⠀⠙⠛⠁⠀⠀⣸⠇⠀⠀⢠
⣿⡧⠐⠊⠀⠀⠠⡋⠀⠀⠀⣠⠃⢀⠄⠤⡀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠈⠑⠒⠈⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⠀⠀⣀⣀⣤⠶⠋⠀⠀⠀⢠⣾⠋
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣴⠟⠁
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠋
⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢹⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⢃⣠⡴⠞⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⢸⡀⠀⢉⣿⡶⣶⣤⣤⣤⣤⣼⡇⠀⠀⠀⢰⣿⡏⠁⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣯⣁⣹⣧⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣿⢻⣧⠤⠤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣖⠒⠚⢿⡍⠉⠉⠁⠀⠀⠀⠀⠀⠸⣿⠒⠒⢺⣿⢸⣷⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣾⡟
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣠⣤⣤⣿⣿⣀⡴⠋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣇⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠉⠉⠁⣿⣿⣭⠄⠚⣷⣿⡍⠱⣶⣄⠀⠀⠀⠀⣰⣿⣤⠄⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⢙⣽⣿⣼⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⣴⣿⡀
⠀⠀⠀⠀⠀⠻⣶⣤⣤⠴⠶⠶⠿⠿⠿⠿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⠷⠀⠈⠙⠿⣿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣀⡀⢺⣿⡅⣷⣰⠹⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⣀⠈⠛⠛⠺⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠟⠛⠿⣷⣼⣿⣠⣫⠅⠀⠀⠀⠛⠉⠛⠿⢿⡛⠛⠿⠟⠛⠛⠒⠾⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⢶⠶⣶⣶⠶⢶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡿⣛⣪⡿⣟⡋⢛⢋⡉⢉⠉⡛⠛⠛⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⡿⢿⡿⣶⣿⠁⠀⢈⡙⢋⣳⣶⣶⣤⣩⣵⠤⠀⠘⠙⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⣿⡇⠀⠀⠀⠈⠀⣿⣿⠁⠀⠠⣌⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢀⣼⣯⣿⣷⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠂⣠⣮⡿⠐⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⠿⠟⠛⡉⠙⠏⣿⡇⠀⣀⡠⠀⣶⣞⡿⣿⣿⣿⠿⡶⣿⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⡅⢲⣀⣿⠇⣋⠀⣱⡀⠀⠀⠀⠀⢾⣿⣿⣭⣭⡷⢄⡨⣇⡠⣄⣿⣿⣿⠁⢠⡄⠀⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠠⢾⣿⣧⣤⣴⠟⣿⠁⠂⠙⠩⠳⣼⠇⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀⢀⣽⣷⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⢸⢛⣴⠳⠾⠀⢀⢠⣴⣿⡾⠋⢸⠆⢠⣷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣶⡛⢻⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⣿⠇⢸⣿⣿⣿⣿⣿⠇⡍⠁⠀⣿⠉⠉⠉⠉⠉⠉⠙⠻⠟⠛⠋⠉⠀⢻⣿⣷⣿⠲⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢼⣭⢽⣿⣦⣼⡿⠟⠉⠁⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠻⢷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠠⣠⣻⡿⠟⠋⠉⡀⠀⣀⡀⠀⠰⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠚⠿⢿⣿⣿⣿⢇⣀⣚⣿⣾⣷⣶⣦⣷⣄⣄⣤⣤⣶⣶⣿⡄⢉⣛⣏⣴⣶⣤⣰⣆⣼⣧⡙⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⠁⠈⠁⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⠁⠀⠾⠿⠛⠒

⠀⠀⠀⢀⡀⠀⠀⠀⠀⢻⠦⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠈⢿⠓⠒⠲⠦⢼⡆⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠈⢧⠀⠀⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠈⣠⠴⠋⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠀⠀⠀⠀⣀
⢀⡴⣖⠚⠛⠉⠁⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⡎⢹⠆⠀⡀
⡯⠀⢼⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣧⠏⢰⣯⠏
⠳⣤⡞⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠙⢧⣀⣠
⠀⠀⠈⠳⠤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡼⠉⠈⠉⠛⠒⠒⠒⠒⠒⠒⠚⠙⢦⣀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣰⣆⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠾

⠀⠀⠀⢾⣿⣾⣌⠒⢄⠀⣀⠠⠔⠖⠠⠀⣀⢀⠄⠂⣡⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⣴⣿⣧⣀⠉⠀⠀⠀⠀⠀⠀⠀⠁⣀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⡡⠗⠂⠐⣻⡏
⠀⠀⠀⠀⡀⠀⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣟⢀⠆⠀⠀⠄⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠼⠀⠿⠆⠀⠀⠀⠀⠀⠰⢿⠸⠇⠁⠀⠁⠀⠀⠀⠀⢀⢇⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣣⠄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠀⠃⢀⠀⠀⠀⡆⠀⢀⣀⠀⣀⣠⣆⠀⠀⠒⠀⢤⡤⠐⠀⠀⠀⠀⢰⡆⠀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠀⠈⠹⠿⢟⠁⠀⣠⠎⠀⠀⠈⢿⣿⠭⠘⠻⠤⣤⣄⡀⠀⠑⠐⢤⡤⡆⠀⢸⣧⣀⣤⡏⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠳⠦⠀⠀⠵⠞⠋⠁⠀⢠⣶⠀⠲⡥⢠⣿⢀⡀⢻⣿⣿⡇⠀⢱⢸⠀⡄⢠⠃⠀⠀⠏⡽⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣄⡀⠀⣀⡴⠀⠀⢀⣾⠃⠀⠀⠈⠙⣷⣿⡧⢾⣿⡟⠁⠀⣌⣠⠀⣁⣸⠀⠀⠾⢾⡁⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠿⠿⠿⠄⠀⢀⠎⠀⠀⠀⠀⠀⠀⣼⡿⠀⡰⢣⡏⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⡿⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⣠⡄
⣿⣿⣿⡏⡻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉
⣿⣿⣿⣿⣿⠀⢰⣶⣦⣤⣤⣤⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢘⣛⡏⠛⠛⠛⠛⠛⢿⣿
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⢛⠦⣀⠀⢀⡞⡁⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡘⣆⠼⠒⠘⠉⣿⠀⢸⣄⣀⣀⣀⣀⣀⣠⣤⣤⢶⠾⠟⠛⠉⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⡹⠃⠀⢀⡀⠀⠀⠠⠾⠋⠁⠉⠉⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢿⣧⣀⡀
⠀⠀⠀⢰⠒⠊⡀⠀⠀⠀⠂⠁⠀⠀⠀⢄⢤⠢⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⢄⢮⠂⠀⡰⣽⣿⡇⣿⠗
⠀⠀⠀⠘⠤⣬⣔⠊⢁⣀⢀⢀⠀⠀⠊⠁⠁⠀⠀⡀⢄⢀⢠⡠⡐⣔⢮⣮⡫⡁⠀⢀⣮⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣾⣮⣷⣷⡰⣴⡄⠐⣜⣾⣮⣧⡳⣝⣾⣮⡳⣝⠏⠀⠀⢕⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⢿⣿⣮⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣻⣿⣧⠐⣿⣿⠙⠛⠛⠛⠛⠛⢿⣿⣿⡿⡆⢘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠃⢸⢀⣿⠇⠀⠀⠀⠀⠀⠀⣸⢈⡟⠀⡇⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣿⠀⡟⢰⡿⠀⠀⠀⠀⠀⠀⢠⠏⣸⠇⢠⠇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠣⠴⠋⡼⠁⣾⠇⠀⠀⠀⠀⠀⠀⠋⠂⠋⢠⠏⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉

⠀⠀⠀⢰⠦⣄
⠀⠀⢀⡟⠀⠈⢳⡀
⠀⠀⢸⡇⠒⣦⣀⢻⡙⠛⠲⢤⣀
⠀⠀⠸⡇⠀⢻⠉⠻⣤⡀⠀⠀⠈⠳⣦⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢿⠀⠸⣇⠀⠀⠹⣦⠀⠀⢀⣬⡿⠟⠛⠛⠉⠉⠉⠉⠛⠳⢦⣴⠛⠉⠉⠉⠉⠙⠲⣤⡀
⠀⠀⠀⠈⣧⠀⢻⡄⠀⢀⣨⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠈⢷⡀⢹⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣧⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢠⡏⢀⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣲⢤⣄⣀⣀⣀⣀⣀⣤⡴⠛⠀⡿
⠀⠀⠀⠀⠀⣾⠁⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣧⠀⠉⠉⠉⠉⠉⢁⣀⣤⠾⠃
⠀⠀⠀⠀⠀⣿⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⢈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢹⡆⠀⢿⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⢷⡀⠸⠿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⣾⢠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁
⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⢀⣽⠿⠷⣶⠶⠀⠀⠀⣀⣿⣸⣿⣿⣿⣠⡀⠀⠀⠀⠀⠀⠀⣼⠃⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡾⣡⡆⢠⡈⢧⠀⠀⠀⠉⠉⠁⠉⠉⠛⠧⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⡀⠈⢳⡄⠀⢀⣤⢶⡦
⠀⠀⠀⠀⠀⠀⢹⣄⠀⠻⣧⡛⠀⠸⠇⢸⡇⠀⠀⢻⡷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠀⠀⠹⣤⣿⠤⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠙⠳⢦⣤⣼⣇⣤⡴⠛⠀⠁⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢹⣤⣶⢦⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⣀⠀⠀⠉⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣯⠻⠞⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⡇⠀⠀⠀⢸⡏⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡾⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡾⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠙⢧⣄⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠟⣀⡴⠟⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠛⠶⣾⠁⠀⠀⠀⠀⢾⠟⠛⠉⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⢦⣄⣀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣤⡴⠆⠀⠀⢉⣽⠟⠓⠒⠶⠦⣤⡀⣰⣏⠙⠛⠛⠛⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⣞⢁⣀⡤⠀⠀⠀⢀⡽⠋⠙⠦⣄⣀⣷⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠦⣤⡤⠾⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠒⢄⠀⠀⠀⠀⠀⣠⠖⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠑⠢⢤⡀⠀⢸⣄⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠀⠀⠺⣄⡀⠀⠀⠀⢀⡤⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢙⢴⡆⠰⡷
⠀⠀⢀⢄⡠⡀⠀⠀⠀⣀⡤⠴⠖⠚⠛⠛⠛⠛⠒⠶⢤⣄⣀⠀⠀⠀⠀⠀⢀⣸⣷⠤⠀⠀⠀⠀⠀⠀⠀⠢⠶⠓⠀⠀⠀⠀⠀⠀⠸⣄⣠⣤⣤
⢐⣒⣂⠸⣉⠇⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⢲⠞⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢁⣼⠃
⠀⠁⠀⠳⣌⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠤⠤⠞⠁⠀⢠⠟⠁
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣶⠟⠋
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠃
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣄⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⠶⠻⡟⠛⠉⠙⢻⡗⢤⣀⡀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⢹⠇
⠀⠀⡇⠀⠀⠀⣾⠏⠉⠀⠀⠀⢹⠀⠀⠀⠀⠳⡄⠈⠉⠙⠛⠛⠛⠛⡄⠀⠀⠀⠀⠀⣼⠻⡋⠀⠀⠀⠀⣸
⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⣿
⠀⢸⠁⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠙⠳⡄⠀⢀⡈⢣⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⡟⠀⠀⢿⠀⠀⠀⠸⡆
⠀⠈⢻⠀⠀⠀⠀⢼⠆⠀⠀⠀⠀⠀⠀⠙⠶⠤⠿⠛⠁⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣾⠃⠀⠀⢸⡀⠀⠀⠀⠙⢄
⠀⠀⠘⣄⠀⠀⢠⣈⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠸⡄⠀⠀⠀⠙⢦⠀⠀⢠⣀⣧
⠀⠀⠀⠀⠙⠒⠾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⠀⠀⠀⢻⡀⠀⠀⠀⠈⠓⠶⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⢄⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⡀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠂⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠶⢶⡾⢶⣿⣿⣷⠾⠋⣀⣀⣀⣰⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣧⡆⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⢰⡦⠀⠉⢻⣿⡿⡄⠀⣿⣿⣄⠀⠀⠀⠀⠀⣠⣿⣿⣆⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣠⠃
⠀⠀⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠈⢦⣽⣿⣄⣿⣿⣿⣆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣠⠘⣿
⠀⠀⠀⠀⢠⣎⡀⠀⠀⠀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⣿⣿⡆⠀⠈⠙⢿⣶⣯⡷
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉⠉⠁⠈⠉⠉⠁⠈⠹⣿⣿⠏⢳⡀⢀⠿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⠀⣠⣿⠟⠀⠀⠤⣤⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⣦⣦⣤⣀⠀⢿⣿⠃⢸⡆⡜⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠋⣀⣄⡀⠀⠀⢀⠜⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠻⠿⢷⣤⣾⣽⣀⡜⣡⠇⠀⠀⠀⠀⠀⠀⠈⠹⠿⠟⣝⠙⠻⠛⠛⠉⠉⠙⠛⠲⠾⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⣠⠶⠚⠛⠶⣄
⠀⠀⡏⢠⠞⢻⡆⢹⡆
⣤⠤⠧⠼⠶⠋⣀⡾⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⢀⣤⣤⣄⣀⡀
⠙⠓⢲⡖⠺⣫⣽⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⣧⠀⠉⠛⠻⣷⣦⣀⣠⣤⣤⣄⣀⠀⣀⣤⣤⠤⠴⠖⣻⡿⢿
⠀⠀⠀⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠉⠙⠛⢩⡴⠶⠶⠶⠛⠉⠀⣼
⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡼⠈⠁⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⢀⡼⠃
⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⢯⠀⡴⠶⢦⡀⠀⠀⢀⡤⣄⢸⣀⣀⣠⡟⠁
⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠀⠃⠀⠀⠈⠲⣾⣿⡏⠉⠉
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇
⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣠⠞⠉⠙⠲⣄⠸⣿⡀
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢸⡀⠀⠀⠀⠘⢧⣸⣇⠻⢗⠸⠟⡾⢀⣿⠃
⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢳⡀⠀⠠⡀⠀⠉⠛⢿⣋⣩⢏⢠⣾⠟
⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⣼⠓⢄⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠦⣀⣀⣀⡩⢕⣿⡟⠁
⠀⠀⠀⠘⣿⡀⠀⠀⠀⢰⡿⢦⣄⡑⠦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠴⣾⡿⢫⡇
⠀⠀⠀⠀⣨⡷⠀⠀⠀⢸⡿⠋⠉⠉⠛⠻⠷⠦⠤⢤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⡿⠁
⠀⠀⢀⣾⢻⡇⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠰⣄⣀⣀⣠⣤⣤⣤⣤⣶⡿⣫⡾⠋
⠀⢀⡜⣳⡘⢧⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠉⢹⢫⠇⠀⠉⠉⣡⡾⠋
⠀⠈⠛⠋⣿⠶⢿⡆⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢸⢸⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠻⢶⣾⣃⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣼⡟⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⣏⣷⡞⠛⢿⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⣿⢳⣀⠀⣶⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣷⣤⣼⠷⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣤⠀⠀⢻⡟⡏⠉⠹⣏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡟⠙⠿⠛⣧⠻⠶⣶⠿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡼⢤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠔⠂⠉⠉⠳⢂⡾⠀⠂⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠀⠀⣀⣀⠈⣁⠴⢶⡆⠀⠀⠘⢿⣿⠇⠀⠀⣴⣿⣿⣷⡦⠤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠾⠿⢏⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⣘⠀⠄⠀⠀⠐⠿⠃⠀⠐⠋⠀⠀⠀⣾⣿⠆⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢤⣅⣴⡤⠤⠆⡀⠀⠀⠠⣾⠇⠀⠈⠁⠀⢀⡁⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣴⣀⣄⠠⠄⠘⣶⠾⢿⠿⠷⠀⠀⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⠐⠁⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠠⡄⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢷⢦⣍⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠠⠼⣿⡷⠸⣣⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣾⣿⡷⡖⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠨⢁⣿⡏⣀⠿⠛⠒⠟⠚⠑⠘⠑⠛⢶⠀⣿⣿⣯⡅⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⢰⣿⡷⠂⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠜⣿⠇⣠⢦⠀⠀⠁⠀⠂⠀⠀⠀⣴⣄⠐⠧⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠀⣷⣂⠀⠁⠐⡆⠈⠀⠈⠀⣴⡾⠐⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⡽⠃⡌⠉⠀⢀⠘⠀⠉⠀⢋⠼⠀⠉⠓⣇⢹⣯⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⠏⢰⠁⡀⠀⠀⢠⡶⠗⠳⢦⣄⠘⠄⠁⢸⡈⣿⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⠏⠀⠏⢀⠀⠀⠼⠃⣀⡀⣀⡂⠙⢆⠐⠀⠘⡁⣽⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⡀⠀⠀⠀⠀⢔⣋⡀⠀⣀⠀⠂⣧⢀⠀⠃⢹⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢤⠀⠀⣢⠘⡛⠛⠁⠘⠛⠛⣤⡟⠀⣀⡿⠋⠂⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠲⠄⠘⢦⠡⣤⣤⣤⣤⢈⡴⣡⠤⠛⣁⣤⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠄⠉⠀⠀⠉⠁⢀⡁⠀⣤⣄⣄⣠⣤⡤⠾⠏⠀⢶⣯⠍⠂⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣰⡃⠀⠐⢻⣯⠿⣿⣾⣥⣤⣥⣬⣥⣴⣿⣿⣿⣷⠶⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⢋⡼⣄⠀⠬⠶⢚⡟⣻⠹⢿⣿⡿⠿⣿⣿⠿⢖⡶⢒⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⠸⣧⡀⠀⠻⣿⣽⣾⣾⣿⣵⣿⣿⡟⠻⠯⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣿⠁⠱⡀⠀⠙⣿⣿⠉⠉⢹⡟⠉⢨⣷⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠱⢠⣀⣿⠃⠀⠀⡀⢀⣼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⢼⣿⡇⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠿⠁⠀⠀⠈⠼⠟⠁

⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠈⣿⣿⣿⣮⣅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣟⣻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡦⡀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡢⣿⣿⣿⣿⣟⠛⣇
⠀⠀⠀⠀⢠⣧⣈⣿⣿⣿⣿⣿⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣻⣿⣿⣿⣍⣀⠏
⠀⠀⠀⠀⢸⣌⡙⡹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣋⡁⠀⠄
⠀⠀⠀⠀⢸⣦⡭⣽⣿⣿⣿⣫⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠋⠀⠴
⠀⠀⠀⠀⠀⠳⢦⠙⢿⡿⠿⣟⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣚⣻⡿⣋⡓⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠁⢾⡈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⠟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣩⡆⠉⣀⡀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡼⢃⣤⡿⠿⠿⣷⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠕⠙⢿⠇⠀⠀⢸⣿⠷⠀⠀⠀⠄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣄⣀⣀⣀⣀⡀⠀⠀⡼⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⣿⣿⣿⣿⣿⡿⠓⢊⡀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣤⣴⡟⠋⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣋⡁⣀⣀⣠⣴⣶⣦⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁

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