T rex Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡠⠤⣀⢀⠀⢀⡤⠤⢤
⠀⠀⠀⠀⢀⡶⠚⠁⠁⠀⠁⠰⢀⡔⠀⠉⠀⠀⠦⠈⢣
⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⠀⢸⠀⠀⠀⠀⢤⠀⠀⠀⠂⣿⢑⣲⢶⠖⠟⠋⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡⡏⠉⣭⢻⠛⠒⡊⠷⠤⠴⣄
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠊⠢⠄⠀⠀⠈⠑⠹⠽⠾⠀⠀⠀⠀⠀⠈⠙⠻⢆
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡀
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠑⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠶⡆
⠀⠀⠀⠀⢀⣀⣀⢸⠀⢟⢦⡉⠀⠈⢃⠰⠀⠄⠀⠀⡐⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆
⠀⠀⢀⠔⠁⡠⠒⠒⠒⢉⣴⠟⢂⡤⠄⠤⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣄⣀
⠀⠀⠘⠷⣺⡀⠀⠀⢀⡞⢁⡀⠄⠉⠢⢄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠑⠒⠠⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠙⠣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠒⠀⠉⢀⣀⣠⠴⠛⠒⢦⠀⠀⠀⠀⠤⠂⠤⣤⡤⠤⢤⣤⣄⣀⣈⣁⠒⠠⢀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⢀⣀⠈⠑⡆⠀⠈⢇⡀⢀⠀⠀⠀⠀⠀⠉⠓⢢⠀⠀⠀⠀⠈⠉⠓⠢⣝⢢⡀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⢀⡠⠊⣀⠔⠁⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⡖⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣷⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣴⣉⠴⠁⠈⠉⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠄⡏
⠀⠀⠀⠀⠀⠀⠀⠘⠚⠓⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡠⢲⠖⣢⠤⠚⠁⠀⢼⢀⡤⠤⠒⠒⠒⠤⠤⢄⡠⠤⠊⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣡⣼⢀⠎⠢⢀⠔⠋⠀⠉⠉⠉⠉⠓⠒⠦⠤⠤⠤⠤⠒⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣙⣊⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⢾⣿⣦⣤⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢄⢠⠘⠓⠋⠁⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⡾⠀⠀⠀⣠⠆⠀⣷⣄⣀⡤⠄⠶⠲⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠀⠀⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⡜⠁⠀⠀⠈⠻⣭⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⢸⣶⣄⠀⠀⠀⠈⢿⣶⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣼⡿⠋⠙⠢⠤⢄⡀⠙⠛⠲⢆
⠀⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣧⡀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠉⠁⠀⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠁
⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢿⢇⠀⠀⠀⠀⣺⣿⡷⠀⢈⣿⣦⠀⡘⠁
⡇⠀⣀⠤⠶⠶⠷⠶⠶⠿⠿⠿⠿⠿⢿⣿⣤⣿⣆⡀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣀⣼⣿⣧⡘⢿⣿⣟⠙⠄⠀⢀⣀⡀
⠡⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢿⣿⠇⠀⢀⠀⢠⣼⠿⠿⠿⠟⠋⠁⠈⠑⢬⡄⠀⠀⠀⠀⠨⠇
⠀⠑⠝⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢀⣴⣿⣷⡿⠁
⠀⠀⠀⠀⠁⠘⠓⠶⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠚⠻⣿⡇⣸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢅⣤⣠⡄⠀⡼⢡⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠸⢫⠀⠀⢰⣅⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⡆⢸⠀⠀⠈⢏⠁⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣷⣐⡄⠀⠀⢸⡄⣄⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠁⠀⢸⣧⠸⣷⣦⣽⡁⡏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⢾⠋⣝⣯⡅⠀⠀⠀⠀⠀⢠⠘⠻⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠐⠃⠀⠈⠛⠫⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⢀⡀⠀⢀⡀⠀⡀⣠⣤⣀⠀⠀⣀⣤⢒⣋⣥⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⣹⣧⠐⠈⠁⠑⠲⠶⠛⣵⣿⣿⣯⣭⣉⣼⣼⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣰⣩⡏⠁⣷⠀⠠⣄⡀⡀⢠⡿⢿⡿⣏⠁
⠀⠀⠀⠀⠀⠀⢠⢣⡿⢽⡀⠻⣄⠀⠀⠈⠉⠘⢧⡀⠑⠌⠳⣄
⠀⠀⠀⠀⠀⠀⢘⣿⢧⡸⣧⣙⡿⡦⠴⠦⢄⠀⠀⠉⠳⣦⡐⣸⣶
⠀⠀⠀⠀⠀⠀⠈⠉⢮⠧⠈⠻⣿⣿⣶⣶⣾⠇⠄⠀⠀⠀⠘⣋⡉
⠀⠀⠀⠀⠀⠀⢠⡇⢸⣆⠈⠳⣌⠻⠿⣿⣿⠀⠀⠀⠀⠀⠈⠁
⠀⢀⣌⣤⠀⠀⢸⣧⠈⢡⠀⠀⠈⠆⢻⡟⠹⣗⠠⠖⠢⣄⣀⣀⠀⢀⡀⠀⠀⠀⢀⡀
⠄⠊⢻⡟⠀⠀⠸⣿⡆⣏⠣⠀⠁⠀⠞⠰⠶⢎⣃⠴⠀⠁⠀⠀⠀⣀⣤⣤⣤⣀⡀⢀⠑⠢⣀
⠀⠀⢸⣷⠀⠄⣀⣿⣛⠻⢧⣷⣶⣾⠹⣿⠟⠋⠀⠀⢤⣀⠀⠀⢻⡉⣿⣿⣿⠛⢛⢾⣟⣶⣦⣵⣄
⠀⠀⠈⢿⣧⣀⣹⣿⣿⡅⠀⢾⡃⡖⠀⠀⠀⠰⠄⣀⠀⢽⣆⠈⠃⣇⠸⣿⣿⣷⣤⣤⣭⣭⡞⠻⣿⣆
⠀⠀⠀⠀⠈⠉⠉⠹⣿⣇⡀⠀⠁⢧⠀⠀⠀⠀⣾⡿⠃⢰⣯⡄⢸⣹⠀⣿⣿⣿⣟⣛⣿⣿⣿⣶⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡶⠤⠓⠂⠒⢻⣿⢰⣿⠿⣿⡃⣾⣾⠀⣿⠀⠀⠀⠀⠀⠉⠣⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢨⠎⠀⠀⡈⢻⣿⡟⠈⣿⡄⠀⠀⠀⠀⠀⠀⢹⡌⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠁⠰⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣀⣹⠄⠀⢀⠀⣠⣾⡟⠄⠀⠃⡼⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠻⣿⣿⣿⣿⢿⣛⣋⣭⣾⣿⢛⣧⡀⠀⠐⢻⡄⠀⠀⠀⠀⢠⣿⠟⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠈⠛⠛⠛⠁⠸⣿⡟⠚⢀⢀⡇⠀⠀⡀⣠⠟⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⣧⢠⣿⠎⠀⣠⣼⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣴⠋⣿⡿⠃⠀⠀⠀⠀⠀⣀⣿⠁⢻⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣿⣸⡿⡇⠀⠀⠀⢠⠴⠚⠙⢿⣫⣈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡏⣸⡅⣴⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⡅⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠡⣿⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠛⠿⠿⠟⠷⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⢹⠀⠿⡏⠒⠀⠃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣤⣤⡤⢤⣤⡤⠴⠾⠁⣰⠀⠀⢀⣡⡞⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠀⠀⠀⠀⠀⠈⠀⠋⠁⠀⠀⠁⠀⠀⠀⠚⠁⠢⣀⣀⡉⠓⠢⡄
⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⢤⢆⡀⠀⢀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠴⠊⠀⠈⠀⠀⠐⠐
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢴⠮⣻⠺⠠⠣⢻⡀⠀⠀⢠⡖⣀⣤⣴⠋
⠀⠀⠀⣸⠀⢀⡴⠚⠛⠒⠾⢿⣯⣥⡔⠀⡐⣿⣦⡤⠼⠛⠒⢿⡃⠀⠐⠔
⠀⠀⠀⡇⠀⡏⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⣡⠏
⠀⠀⠀⢃⢰⠀⠀⠀⠀⡠⠒⣀⣤⡾⢀⡼⠋
⠀⠀⠀⠈⢯⡇⠀⠀⠠⠁⠾⠁⠰⢷⡎
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣠⡀⠀⠉⢻⡀
⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠉⠀⠀⠈⠘⠀⠁⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠀⢤⢶⢶⣺⡷⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⡀⡀⣀⣄⡁⠉⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣏⠙⠲⡾⢋⣡⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⣿⠟⣿⠄⣶⣤⣴⡗⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⠾⠟⠋⣉⣁⣼⡷⣿⣿⠛⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠐⠚⠛⠋⢭⣟⢿⡟⠛⠢⠘⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠶⣼⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡀⠀⠀⡀⣧⣤⣾⣿⡿⢹⣿⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣰⡀⠋⠘⢿⣿⣿⣆⠾⢿⡿⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠀⠀⢠⡟⢻⣿⣿⣷⣼⣏⠀⠀⠈⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⣿⣿⣿⡟⠋⢁⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⠀⢠⡿⠋⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣶⣶⡁⠀⠀⠀⠀⠀⠀⣌⣙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⣸⣿⠟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡇⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡰⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡾⣧⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⣳⢻⣀⢻⣶⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠁⠻⢻⠟⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠿⣤⣄
⢀⣴⠾⠛⠛⠛⠋⠉⠁⣠⣾⡟⣇⠈⠻⣶
⣾⡏⠀⠈⠀⠀⠀⠀⠈⢙⠻⠵⠟⠀⢠⠹⣧⡀
⣿⣿⣿⣿⣶⣤⣭⣤⣤⣤⣤⣴⣦⣄⣸⡄⣿⡇
⢻⣿⣿⡿⣿⡻⢿⢿⣿⣿⣿⠿⢮⡙⢿⡇⢸⣷
⠀⠀⠀⠀⠀⢠⣸⣾⣿⡿⡃⠀⠀⠀⢠⣿⠄⣿⡆
⠀⠀⠀⢀⣰⣿⣿⡿⡫⠊⠀⣀⠤⣴⣿⠉⠀⡟⣿⣤⡄⢀
⠀⠀⣦⣿⣿⣿⡫⠊⣀⣤⣴⣶⣿⡿⠏⠀⡸⠁⡟⠻⠿⣿⣷⣶⣄⣠⡀
⠀⠀⠈⠻⣵⣿⡾⠟⠋⠹⣿⣿⣿⡁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠉⠛⠿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠠⣄⠀⠀⢠⣏⠀⢀⠀⠀⠀⠀⠈⠻⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⣹⣷⣤⠟⠁⢀⡾⠤⠀⠀⠀⠀⢀⠈⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣽⠿⠋⢀⣴⣿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣿⡿⡇⣴⠿⣿⣿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠙⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠙⢿⣿⣿⣮⣷⣿⣿⠐⠀⠀⠀⢀⣾⣵⣥⣄⣀⡀⠀⠀⠀⠉⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⣶⠷⠀⠀⠙⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢷⠈⠀⠀⠀⠐⣿⣿⣿⣿⣿⠋⢻⣄⡀⢸⡏⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣶⣌⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠸⣟⣁⣀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠈⠙⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⢸⡿⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣾⣿⣟⠀⠀⠀⠀⠀⠀⣠⣾⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⣽⣟⣉⣿⣋⣹⠿⠦⠀⠀⣴⣹⣞⣙⣿⣀⣉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡤⠑⠀⠀⠀⠀⠈⠑⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑⠤⡀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠉⠀⠀⠈⠉⠀⠀⠘
⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢀⠀⠀⠀⢀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠶⠶⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠝⠓⠒⠲⠶⠶⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠐⠎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⣠⠎⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡠⠤⠾⢥⣤⣠⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠤⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⢀⣀⣀⣀⡀⠀⠀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⡤⡤⠏⠉⠉⢁⠋⢡⠄⢀⡠⠈⠓⠊⠁⢠⡄⠘⣇
⠀⠀⠀⠀⢠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣀⣀⠀⠀⢀⣀⣤⣶⣾
⠀⠀⠀⠀⢹⠀⠀⠀⡀⠐⢺⠈⠉⠁⠁⢰⢇⣊⣰⣛⣞⣙⡃⠁⢀⡀
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠈⢢⡃⠀⣤⠌⡇⠉⠛⡛⢻⠦⠤⣶⣄
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠠⠚⠦⣀⠀⠀⠀⠈⠒⠬⣛⣷⢦⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⡀
⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢁⠠⠈⠉⠉⠐⠂⠄⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢦
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠤⣀⠀⢀⡀⠢⢦⠀⠀⠄⠀⠀⡀⠀⢀⡴⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⣀
⠀⠀⠀⠀⠀⣀⡤⠤⠤⠧⠀⣯⠳⣄⠀⠀⢀⣡⠘⠅⠒⠢⠄⢁⠌⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⣀⢀⣀
⠀⠀⠀⡠⠎⢀⡰⠒⠒⠚⠋⢁⣴⠏⠃⣭⠤⠤⠤⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢦⣀⣀⡀
⠀⠀⠀⠻⣇⢼⠀⠀⠀⠀⢠⡟⠁⡀⣐⠈⠑⠤⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠋⠒⠢⠤⠤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⣄⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⠘⠬⠉⠒⠂⠀⠀⠀⣁⡶⠤⣄⡇⠀⠀⠀⠀⠀⢀⣔⣁⠀⠀⡀⠀⢀⠀⠀⠉⠉⠒⠂⠤⢀⡀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣄⠀⠀⠀⠈⠻⢥⡀⠀⠀⢹⡆⠀⠀⠀⠈⠁⠀⠈⠉⠻⠭⣍⡉⠉⠉⠛⠛⠒⠒⠦⢤⣈⡒⢤⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⡶⠀⠀⣸⠀⠀⠀⠳⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣝⢆⠄⠀⠀⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠶⣤⣄⣀⡠⠞⠁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠚⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣋⡠⠒⠑⠂⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠒⠧⠖⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⢖⡲⠤⣤⠴⠋⠀⠀⣼⠀⣀⠤⠤⠴⠶⠤⠤⣄⣀⣀⣀⣠⠞⠁⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠞⠉⣦⢁⡴⢔⠀⢀⣠⠞⠈⠓⠒⠒⠒⠲⠦⢤⣄⣀⣀⠀⢀⣀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠙⠳⢾⡤⠤⡥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠂⡷⠄⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⠄⣀⣀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⡀⠀⠙⠤⠦⢿⡓⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠤⠤⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣤⣀⡀⠀⠀⠹⣶⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠋⠀⠀⠀⠈⠑⠂⠤⠄⠉⠋
⠀⠀⠀⠀⢀⠔⠁⣀⠤⠔⠒⠂⠀⠀⠐⠒⠒⠂⠤⢤⣀⣀⠀⠃⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⡆⠀⣘⣡⠞⠁
⠀⠀⠀⢠⢃⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠀⠀⠀⢰⠃⠀⢀⡠⢴⠒⣇⠠⡡⠄⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⣠⠏⠉⢙⠁⢠⠎⠀⠀⠑⠀⠀⠸⡆
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢠⠖⠉⠉⠉⠀⠀⠀⢅⠀⢀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢂⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢢⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡳⠤⢤⠀⠀⠀⠀⠘⠒⠰⠄⠠⠼⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠠⣽⠂⠼⠤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣼⣶⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡞⠛⠶⠆⠠⣄⣴⣶⣦⣴⣾⣿⣿⣿⣿⡿⣯⣍⠛⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠙⠃⠉⠁⠀⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠮⢻⡻⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣉⢾⣿⣇⠐⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣀⣤⣀⡒⣢⣴⣶⠞⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡟⣿⡄⣷⣤⠦⢿⣧⣀
⠀⠀⠀⠀⢀⡾⠟⠉⠀⢠⡿⢫⣶⣿⣿⠟⠙⠃⣀⣩⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⢿⣿⠳⣀⠙⠟⠿⠿⠓⠘⢿⣮⡻⣷⣿⡿⣿⣥
⠀⠀⠀⠀⣾⣻⡇⠀⠀⠀⠀⣿⣿⣿⣿⢶⡀⠺⢿⣿⠹⣿⡧⣀⠀⢩⡿⢷⢾⣿⣟⣙⣉⣠⡿⠿⣦⣤⣤⠔⠲⢤⢄⣀⣈⡉⢻⣿⣯⣧⡄⠻⣧⠄
⠀⠀⠀⣼⣿⣿⣁⠂⠀⠀⠀⠉⠻⢟⠃⠘⢻⣄⠀⠀⠀⠉⠿⢿⣿⣓⣶⢶⣦⡙⠃⢫⣭⣤⣴⡿⠟⠁⣀⠄⣀⣀⣼⣻⣿⣷⡜⣿⣿⣏⣳⣄⠙⢿⣧
⠀⠀⢀⣿⣿⣿⣿⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⣙⢃⡀⠀⠀⠀⠀⢨⣝⡛⠦⠀⢯⣰⣽⣿⣿⣿⣁⣤⣸⣮⣿⣿⡿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣺⣿
⠀⠀⢸⣿⣿⣿⣿⡤⠀⢟⠀⠀⠀⠐⣦⣀⣀⣀⢘⡍⠐⠀⠀⠀⠘⠛⠉⡵⣮⣙⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⣿⣿⡿⡈⣿⣿⣿⣿⠟⣿⣧
⠀⠀⠘⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣤⣬⣛⣻⡟⣿⣿⣭⢧⡬⢤⣤⣤⣴⣾⣗⣧⣾⣿⡿⣿⣿⣿⣿⣿⣿⡿⡷⣾⡿⣷⡭⢟⠀⢡⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⣿⣿⣿⣿⣷⢸⣿⣿⢸⣇⣿⡏⣿⠻⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⢿⣿⣿⣿⣿⠟⠛⢛⢿⠶⠀⠘⠆⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠹⢿⣿⣿⣿⣦⣹⢿⣼⡟⢿⣧⢽⠀⡷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠐⢯⣉⠒⠄⠀⣀⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠙⠀⠙⠀⠀⠙⠀⠃⠁⠈⣿⣿⣿⣿⣿⢿⣿⢟⣯⣾⡿⠛⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣒⠦⣴⣿⣿⣿⣿⡟⢸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣿⣿⡻⣹⡾⣏⣵⡛⠙⠉⠁⠀⣸⣿⡯⠀⢤⣄⡀⠀⠀⠀⠐⠈⠂⢽⣂⣾⣿⣿⣿⣽⠃⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⡾⡟⢙⣶⢗⣯⣾⣿⡇⠀⠀⠀⠀⠘⣿⣿⣧⠀⠌⠻⠿⢶⣦⣄⠰⣒⣶⣶⣿⣿⣿⣿⣿⡏⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⢿⣛⣽⣶⢾⣋⣶⣿⣿⣿⡿⣷⡀⠀⠀⣠⣾⣿⣿⣿⣶⣶⣖⣤⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢞⣻⣷⡾⢟⣯⣦⣎⣿⣏⢿⠿⠯⣶⣿⣷⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣾⣿⣿⣷⣾⣈⣿⣿⣿⠟⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣏⡁⣰⣴⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠈⠙⠛⣿⣿⣿⣿⢿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⣿⣷⡦⠀⠢⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡰⠰⡈⠉⠀⢀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠀⠀⠔⠁⠀⠻⣿⡋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠐⣷⣄⠀⠈⠉⢷⣴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣴⠟⠉⠙⠒⠠⢄⠉⠙⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⢠⣶⣁⠀⣤⣀⠀⡾⠛⠉
⡆⠀⣀⣤⠤⠤⠤⠶⠾⠿⣿⣿⣆⣰⣄⠀⠀⠀⠀⠀⠙⢶⣦⣄⣸⣿⡅⢶⣿⡟⢊
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⡆⠀⣀⢠⡼⠿⠿⠛⠋⠁⠁⠨⠅⠀⠀⠈⠸
⠀⠁⠉⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠊⠈⠀⠉⡟⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠿⠋⠁⣼⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡆⠀⠀⠘⡁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠕⠄⠀⣷⢰⣌⠢⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠛⠃

⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⠿⠛⠻⣦⣤
⢀⣴⡾⠟⠛⠛⠛⠋⠉⣀⣴⣿⢷⠀⠻⣷⡄
⣾⡏⠀⠐⠃⠀⠀⠀⠀⢉⠻⢭⡾⠀⠀⡌⢿⡀
⣿⣿⣿⣷⣶⣤⣚⣀⣄⣀⣀⣤⣤⣄⣀⣇⢸⣿
⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣝⢿⣿⠀⣿⣆
⠈⠉⠉⠉⠁⠁⣈⣶⣿⣿⢟⠁⠀⠈⠀⣹⣦⢸⣷
⠀⠀⠀⠀⢠⣶⣿⣿⢟⡵⠁⠀⢀⣠⣴⡏⠃⢸⢿⣦⢀
⠀⠀⣄⣶⣿⣿⢟⠕⠋⢀⣀⣬⣵⣾⣿⠃⠀⡞⢸⠿⣿⣷⣶⣤⣤⡀
⠀⠀⠙⢿⣟⣵⣥⣶⠾⠻⣿⣿⣿⡟⠁⠀⠘⠁⠎⠀⠀⠈⠉⠙⠻⢿⣿⣆⣀
⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠘⣿⣿⡗⠀⣀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠈⠻⢿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠹⣧⡀⣠⡟⠁⢀⣖⣀⡀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡐⣾⣿⠏⠀⣠⣿⠉⠀⠀⠀⠀⠀⢰⠀⠉⠹⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠙⠻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠉⠻⣿⣿⣼⣌⢧⣽⣿⡗⠄⠀⠀⠀⠀⣼⢣⠀⠀⠀⠀⠀⠀⠉⠿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣀⣠⡀⠈⠻⣿⣿⣿⣿⣿⣷⡈⠢⠀⠀⢸⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠈⠙⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠹⠏⠁⠀⠀⢸⣿⣿⣿⣿⣿⡿⣆⠀⠀⢸⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣤⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠃⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⡀⢹⣶⠂⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣦⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⠘⢷⣶⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠃⠀⠀⠈⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⣸⠏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣅⠀⠀⠀⢀⣀⣀⣔⣷⠴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⣠⣤⣤⣴⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣟⠇⠀⠀⠈⠉⠃⠙⠛⢫⠀⠅⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣦⣤⣴⣾⠷⣄⡀⣀⣠⡿⠅⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣇⢀⠉⠻⠏⢠⠶⡃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⢛⣿⠆⢱⢇⣦⣶⡏⢳⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⡿⠻⠛⠛⠁⣰⣯⣾⢿⣿⠻⠛⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣉⠁⠤⢶⡿⠟⠛⢿⣿⣾⡿⠧⣄⠘⡮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠐⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⣿⣶⣿⢃⣒⢠⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣘⣿⣻⣿⡷⠙⢿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣾⣟⡀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⡀⣧⣤⣾⣿⣿⠟⢩⣿⣿⡟⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢂⡆⠘⠃⠸⣿⣿⣿⣯⡆⢼⣿⣿⣇⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣾⠇⠀⠀⠀⣼⢿⣿⣿⣿⣦⢈⣿⠆⠁⠀⠘⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⢘⣷⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠛⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠉⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⠋⠁⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⠀⠀⠀⢠⡿⠛⠁⠀⠀⠀⠘⢿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⣤⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡰⣦⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣾⣿⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠲⢧⣿⡆⢻⣦⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⠞⣼⣷⣦⡿⠿⠯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠛⠀⠙⠉⠟⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣼⣶⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡞⠛⠶⠆⠠⣄⣴⣶⣦⣴⣾⣿⣿⣿⣿⡿⣯⣍⠛⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠙⠃⠉⠁⠀⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠮⢻⡻⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣉⢾⣿⣇⠐⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣀⣤⣀⡒⣢⣴⣶⠞⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡟⣿⡄⣷⣤⠦⢿⣧⣀
⠀⠀⠀⠀⢀⡾⠟⠉⠀⢠⡿⢫⣶⣿⣿⠟⠙⠃⣀⣩⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⢿⣿⠳⣀⠙⠟⠿⠿⠓⠘⢿⣮⡻⣷⣿⡿⣿⣥
⠀⠀⠀⠀⣾⣻⡇⠀⠀⠀⠀⣿⣿⣿⣿⢶⡀⠺⢿⣿⠹⣿⡧⣀⠀⢩⡿⢷⢾⣿⣟⣙⣉⣠⡿⠿⣦⣤⣤⠔⠲⢤⢄⣀⣈⡉⢻⣿⣯⣧⡄⠻⣧⠄
⠀⠀⠀⣼⣿⣿⣁⠂⠀⠀⠀⠉⠻⢟⠃⠘⢻⣄⠀⠀⠀⠉⠿⢿⣿⣓⣶⢶⣦⡙⠃⢫⣭⣤⣴⡿⠟⠁⣀⠄⣀⣀⣼⣻⣿⣷⡜⣿⣿⣏⣳⣄⠙⢿⣧
⠀⠀⢀⣿⣿⣿⣿⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⣙⢃⡀⠀⠀⠀⠀⢨⣝⡛⠦⠀⢯⣰⣽⣿⣿⣿⣁⣤⣸⣮⣿⣿⡿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣺⣿
⠀⠀⢸⣿⣿⣿⣿⡤⠀⢟⠀⠀⠀⠐⣦⣀⣀⣀⢘⡍⠐⠀⠀⠀⠘⠛⠉⡵⣮⣙⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⣿⣿⡿⡈⣿⣿⣿⣿⠟⣿⣧
⠀⠀⠘⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣤⣬⣛⣻⡟⣿⣿⣭⢧⡬⢤⣤⣤⣴⣾⣗⣧⣾⣿⡿⣿⣿⣿⣿⣿⣿⡿⡷⣾⡿⣷⡭⢟⠀⢡⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⣿⣿⣿⣿⣷⢸⣿⣿⢸⣇⣿⡏⣿⠻⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⢿⣿⣿⣿⣿⠟⠛⢛⢿⠶⠀⠘⠆⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠹⢿⣿⣿⣿⣦⣹⢿⣼⡟⢿⣧⢽⠀⡷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠐⢯⣉⠒⠄⠀⣀⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠙⠀⠙⠀⠀⠙⠀⠃⠁⠈⣿⣿⣿⣿⣿⢿⣿⢟⣯⣾⡿⠛⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣒⠦⣴⣿⣿⣿⣿⡟⢸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣿⣿⡻⣹⡾⣏⣵⡛⠙⠉⠁⠀⣸⣿⡯⠀⢤⣄⡀⠀⠀⠀⠐⠈⠂⢽⣂⣾⣿⣿⣿⣽⠃⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⡾⡟⢙⣶⢗⣯⣾⣿⡇⠀⠀⠀⠀⠘⣿⣿⣧⠀⠌⠻⠿⢶⣦⣄⠰⣒⣶⣶⣿⣿⣿⣿⣿⡏⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⢿⣛⣽⣶⢾⣋⣶⣿⣿⣿⡿⣷⡀⠀⠀⣠⣾⣿⣿⣿⣶⣶⣖⣤⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢞⣻⣷⡾⢟⣯⣦⣎⣿⣏⢿⠿⠯⣶⣿⣷⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣾⣿⣿⣷⣾⣈⣿⣿⣿⠟⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣏⡁⣰⣴⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠈⠙⠛⣿⣿⣿⣿⢿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⣚⣋⡀⠙⠛⠋⠁⠉⠁⠀⠈⢩⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠠⣾⣿⣽⣿⣷⠆⠀⠀⠀⢀⣀⣀⣠⣽⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠉⠛⠉⣀⣤⡤⡤⠞⢉⡉⣅⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢀⠄⢀⡀⠀⠀⣠⣾⣿⣿⣾⣷⣶⡟⣟⣟⠹⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⢶⣶⣶⣾⣿⣟⠀⢀⣿⠀⠈⠻⣝⠊⣿⣿⣿⣿⡯⠋⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡯⠗⠛⠋⠉⠁⠉⠀⠉⠉⠳⢀⣾⣿⡀⠀⠀⠈⢶⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣄⠀⠀⠑⠙⣿⡟⣣⢳⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣤⣄⡈⠑⠠⡗⢽⣷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠖⣒⡺⢋⣹⠏⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠶⣮⣀⠀⠨⠨⣍⣿
⠀⠀⠀⠀⣠⡶⠛⠉⠁⠀⠀⣉⣤⣶⣿⠃⠀⠀⢻⣷⡀⠀⠀⠀⠀⣠⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁
⠀⠀⢀⡼⠁⢀⣠⣤⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣦⣤⣤⣾⠋⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⣆
⠀⠀⡼⢀⣴⣿⣿⣿⠿⠿⠿⣿⣿⡟⡌⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⢿⣿⡁⠀⠛⣀
⠀⢠⡇⣼⡿⠋⠁⠀⠀⠀⠀⠀⢿⣧⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⠿⠿⢿⣿⢆⠙⠻⣦⡀⠉⠙⢓⢦⡀
⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠁⣤⠿⣾⠀⠀⢘⣿⠔⢦⣹⣦⠇
⠀⠀⠘⢦⣿⣦⡀⠀⠀⠀⠀⠀⢨⡿⠀⡀⠀⢻⣿⢿⣿⣿⣿⣿⡿⢿⣿⣇⡐⣶⣾⡷⠋⠀⠀⠈⠋⠀⠊⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⡿⠀⠈⣿⣿⣿⣿⡇⠙⠛⠛⠉⢀⣾⣿⡏⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⡁⠠⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠓⢠⣿⣿⠟⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠷⠿⠾⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⣉⠑⠂⠤⢤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⡙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣶⡄⢶⣄⣀⣬⣶⣿⣿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣊⡁⡰⣠⣶⣤⣆⠙⣛⡻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠇⠻⣿⣟⣿⡟⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢾⣿⢻⣿⡿⠿⣿⣷⡿⠿⠿⢿⣯⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⠀⠛⠋⠀⠀⠀⠀⠈⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⣚⣋⡀⠙⠛⠋⠁⠉⠁⠀⠈⢩⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠠⣾⣿⣽⣿⣷⠆⠀⠀⠀⢀⣀⣀⣠⣽⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠉⠛⠉⣀⣤⡤⡤⠞⢉⡉⣅⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢀⠄⢀⡀⠀⠀⣠⣾⣿⣿⣾⣷⣶⡟⣟⣟⠹⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⢶⣶⣶⣾⣿⣟⠀⢀⣿⠀⠈⠻⣝⠊⣿⣿⣿⣿⡯⠋⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡯⠗⠛⠋⠉⠁⠉⠀⠉⠉⠳⢀⣾⣿⡀⠀⠀⠈⢶⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣄⠀⠀⠑⠙⣿⡟⣣⢳⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣤⣄⡈⠑⠠⡗⢽⣷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠖⣒⡺⢋⣹⠏⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠶⣮⣀⠀⠨⠨⣍⣿
⠀⠀⠀⠀⣠⡶⠛⠉⠁⠀⠀⣉⣤⣶⣿⠃⠀⠀⢻⣷⡀⠀⠀⠀⠀⣠⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁
⠀⠀⢀⡼⠁⢀⣠⣤⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣦⣤⣤⣾⠋⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⣆
⠀⠀⡼⢀⣴⣿⣿⣿⠿⠿⠿⣿⣿⡟⡌⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⢿⣿⡁⠀⠛⣀
⠀⢠⡇⣼⡿⠋⠁⠀⠀⠀⠀⠀⢿⣧⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⠿⠿⢿⣿⢆⠙⠻⣦⡀⠉⠙⢓⢦⡀
⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠁⣤⠿⣾⠀⠀⢘⣿⠔⢦⣹⣦⠇
⠀⠀⠘⢦⣿⣦⡀⠀⠀⠀⠀⠀⢨⡿⠀⡀⠀⢻⣿⢿⣿⣿⣿⣿⡿⢿⣿⣇⡐⣶⣾⡷⠋⠀⠀⠈⠋⠀⠊⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⡿⠀⠈⣿⣿⣿⣿⡇⠙⠛⠛⠉⢀⣾⣿⡏⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⡁⠠⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠓⢠⣿⣿⠟⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠷⠿⠾⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⣉⠑⠂⠤⢤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⡙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣶⡄⢶⣄⣀⣬⣶⣿⣿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣊⡁⡰⣠⣶⣤⣆⠙⣛⡻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠇⠻⣿⣟⣿⡟⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢾⣿⢻⣿⡿⠿⣿⣷⡿⠿⠿⢿⣯⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⠀⠛⠋⠀⠀⠀⠀⠈⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⣕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢼⠎⠉⠉⠑⠀⠈⠉⠙⣬⠍⢳⣮⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠀⠀⠻⠀⠀⠀⠀⠀⠸⡿⠶⠈⠀⢧⡘⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣽⡱⣤⣄⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⣾⣹⣞⢻⣿⣿⣿⢷⣭⠴⠂⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣻⣿⡿⣿⠀⠀⢀⣰⠀⢠⡆⠘⡆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃⠞⠀⡹⠖⠛⠉⠁⠀⡼⠃⠰⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣄⣴⠾⠋⠀⠀⡠⠤⡤⠼⠗⣢⠆⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣛⠛⠁⠀⢀⠠⢾⣧⣦⣶⣶⠿⠁⠀⡀⠉⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⣻⡟⠿⠖⡠⠀⠀⣶⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⢄⣀⡤⣀⣀⣠⠔⠀⠀⠺⠋⢿⠋⠂⠀⠀⠀⠀⢸⡇⠀⠀⢼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠁⠀⠀⠀⢋⠄⣸⡇⠀⠀⢸⡿⠩⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣶⣶⣶⠿⠟⠛⠛⠋⠀⠀⠀⠀⡠⠀⠉⠙⠶⢤⣠⠤⠴⠀⣏⠖⠟⣤⡤⠁⣸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⠛⢉⢀⣀⣀⣤⣤⣾⡟⠐⠀⠀⢀⡃⠀⣀⠰⠂⠀⠀⠀⢲⡴⠂⠀⢠⣷⣯⠠⢴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⢁⣴⡿⢿⣿⣿⣿⣿⣿⡃⡄⣆⢀⣤⡆⠈⢿⡴⠂⠀⠀⢀⠟⠁⠀⢀⣾⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢠⡿⢫⠚⠉⠀⠀⠀⠀⣿⡇⢻⢹⣸⠟⠷⠿⠂⢿⡔⠀⠐⠂⠂⢤⣀⣩⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣿⢱⠃⠀⠀⠀⠀⠀⠀⣼⡄⠈⢧⣋⡄⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⢸⡆⠀⠀⠀⠀⠀⠀⠏⠇⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⣿⡄⠀⠀⠀⠀⠀⢸⡀⠃⠀⢹⣧⣤⡀⠀⣀⣀⣀⡤⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠙⣦⢀⠀⠀⠀⠀⣼⠃⢀⠀⣼⠙⢿⣿⣦⣍⣭⠿⡿⠟⣻⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠳⡄⢀⠀⠀⡇⢀⠉⢡⣿⠅⠈⠙⠛⠋⠁⠀⢿⡿⢋⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠧⣴⣄⡀⣻⡄⣼⠋⠀⠀⠀⠀⠀⢠⣶⣿⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠀⡽⣇⠀⠀⠀⠀⠀⠘⢿⣯⢹⡆⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠦⣽⠋⠙⠓⠆⠀⠀⠀⠸⡟⠼⡧⠸⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠁⣽⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⢿⡌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠒⣻⣗⢄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠛⠛⠉⠉⠘⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⢀⣀⣀⠀⣀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠢⢀⡀⠀⠀⣀⠠⠐⡂
⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⠈⠉⠒⢤⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠦⠤⠤⠤⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⡿⠛⠻⣟⡰⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢀⡍⠉⠓⢼⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⠤⢤⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⣠⣄⠀⠀⣤⠀⣠⡄⣴⣶⣦⣄⣀⢀⣠⠴⡞⣩⣤⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣽⣷⡄⠃⠀⠀⠈⠛⠳⠛⠋⣴⣿⣿⣿⣇⣏⣨⣸⣷⣷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢉⡟⠉⢸⡄⠀⢠⣀⡀⢀⠀⢸⡿⢿⣿⣿⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣿⣻⡄⠸⣇⠀⠀⠈⠙⠛⠃⢼⣇⠀⠹⣌⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡇⢹⣇⢠⣽⣧⡀⠀⡀⠀⠀⠀⠙⠲⣄⣠⠀⢈⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⢷⠌⠹⣷⣾⣙⣋⠉⠉⠙⣂⡀⠀⠀⠀⠙⢿⢈⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣦⠳⠀⣈⠻⣿⣿⣿⣿⣿⡟⠑⠂⠀⠀⠀⠀⢈⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢿⣧⠀⠙⢧⡘⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⣀⣂⣄⠀⠀⠀⣿⡄⠈⢋⠀⢄⠀⠙⣎⠳⣿⠟⢿⡶⢀⡴⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⡀⠜⠻⣿⡿⠀⠀⠀⡿⣿⠐⡞⢧⡀⠑⠀⠀⣼⠃⣴⣈⡳⠆⢀⡀⠙⠉⠉⠉⠀⠀⠉⠀⡀⠀⠀⠀⠈⠑⠢⣄⡀
⠀⠀⠀⣿⡇⠀⡀⠀⢹⣿⣦⣿⣆⢡⣀⣀⣤⠧⣤⣤⣭⡷⠚⠈⠀⠀⠈⠀⠀⢰⡾⢿⣿⣿⣿⣿⣶⣤⣰⣤⣀⡙⠢⡀
⠀⠀⠀⢻⣿⡄⠉⢲⣾⣯⣬⠍⠛⠲⣿⠟⠟⠒⠻⠛⠁⠀⠀⠀⠉⢶⣤⠀⠠⡄⢷⠘⣿⣿⣿⣇⠁⠜⠻⠧⣿⢻⣿⣿⣦⡀
⠀⠀⠀⠈⠻⣷⣆⣸⣿⣿⣿⡆⠀⠘⢿⠐⡏⠀⠀⠀⠀⠸⠂⣤⡀⠀⢿⡆⠀⢁⣸⡅⢹⣿⣿⣿⣷⣶⣤⣶⣦⣾⠉⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣧⣠⠀⠈⠈⣧⡀⠀⠀⠀⠄⣾⡿⠏⠀⣼⣥⡆⢘⡇⣷⠈⣿⣿⣿⣿⣙⣉⣿⢿⣿⣷⣾⡛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣤⡬⠷⠒⠒⠲⣽⣷⢀⣿⣶⣿⣽⠇⣸⣷⣟⠀⣿⡁⠀⠀⠀⠀⠀⠉⠫⣍⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⢙⡈⠋⠉⠀⠹⢷⣿⣿⠇⠰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢳⣌⣿⡟⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢈⣿⡟⠀⢠⡜⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣤⣤⣛⣀⢀⣀⡀⢀⣶⣿⣟⠂⡀⠈⢁⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡙⢿⣿⣿⣿⣿⡿⣟⣛⣋⣥⣾⣿⡿⢹⣿⡀⠀⠀⠘⢻⡄⠀⠀⠀⠀⠀⡠⣼⣿⢋⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣽⣿⣿⣿⠀⠈⠙⠻⠿⠿⠛⠁⢺⣿⡿⠶⠟⠀⠀⡷⠀⠀⠀⠠⢂⣾⢟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⢀⣿⡼⠃⠀⢀⣴⣷⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⡇⢹⣿⣀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⣿⢅⣾⣿⠋⠀⠀⠀⠀⠀⠀⣀⣴⣿⣅⡀⢸⢋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡟⢨⣿⠸⡿⠿⠀⠀⠀⠀⠀⠔⠛⠉⠉⢻⣯⠤⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⢀⣸⡄⣦⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣌⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢿⠉⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡏⣹⣷⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠾⣿⣶⣾⡿⣧⣽⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠚⣻⣷⣆⠀⠰⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⢿⠀⠷⠿⡌⢈⠀⠈⢔⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣠⠤⠴⠿⠁⢠⡖⠀⠀⠂⢈⣠⡞⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠉⠁⠀⠀⠉⠉⠉⠉⠩⠟⠋⠁⠀⠉⠋⠁⠀⠀⠀⡴⠊⠠⠀⠀⠀⠙⠺⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⡀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡽⠾⠷⠕⠢⠀⣈⠙⠃
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠀⠀⠰⢸⠊⣠⡀⣀⠀⣄⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⣰⠯⠀⠀⠀⠀⡀⠀⢰⠷⠞⣛⠺⠄⢎⢢⢻⡄⠀⠀⠀⠀⣴⠚⣀⣤⣤⡞⠁
⠀⠀⠀⠀⢰⠇⠀⠄⣠⡤⠶⠶⣤⣾⣷⣿⣋⡁⡀⠆⠀⠱⣹⣦⣀⣀⣠⣿⠦⢭⣻⡗⠭⠐⠠⡀⠄
⠀⠀⠀⠀⡾⠀⠀⡞⠁⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⠀⠀⡇⣿⠟⠋⠉⠁⠀⠀⠀⠙⠓⠀⠀⠀⠘
⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢺⡿⠀⢀⣴⠃
⠀⠀⠀⠀⢻⠀⣯⠀⠀⠀⠀⠀⡴⠒⣉⣤⣶⣿⠃⣠⠟⠁
⠀⠀⠀⠀⠈⢷⢹⠀⠀⠀⠀⡰⠁⣼⠏⠀⢰⡏⣦⠃
⠀⠀⠀⠀⠀⠈⢳⡇⠀⠀⠰⠀⣰⢱⠀⠀⠈⠎⢿⡄
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣘⣮⡂⠄⠀⢸⢈⡿⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠍⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠤⠄⠀⠀⠠⠔⠱⣮⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⡄⠀⠀⠀⠀⢰⣏⣀⠛⣳⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⢤⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠓⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣯⣇⣗⣶⢶⣿⣷⣶⣮⣦⠔⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⡿⣷⢀⡀⣠⠆⢠⡆⢱⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠊⣀⠟⠈⠉⠁⠀⡜⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⡴⠟⠁⠀⣠⠒⠒⢚⣫⡴⠃⢸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠍⠀⠀⠀⠈⢻⣿⣿⣟⠋⠀⠐⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴⢻⡤⠀⠊⠀⠘⠃⣾⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠉⠀⠁⠈⠉⠈⠉⠉⠁⠀⠀⠀⠌⠃⠀⠀⠀⢂⠀⡟⠀⠀⢸⡟⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣤⣶⡶⠾⠷⠞⠃⠀⠀⠀⡠⠈⠙⠲⢤⣀⡤⠤⢀⡣⠾⢧⡠⠃⣸⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡾⠋⣉⣀⣀⣤⣴⣾⡇⠐⠀⠀⡎⠀⡄⠐⠀⠀⠀⢸⡶⠀⠀⣼⣾⣀⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡾⢟⠿⠿⠿⠯⣿⠁⡶⡆⣴⡇⣈⠻⣆⡀⠀⠀⠎⠀⠀⡰⡿⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢵⡟⡔⠁⠀⠀⠀⠀⢻⠀⢧⢳⠟⠙⠉⠀⠛⠁⠀⠀⠉⠳⢦⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢸⡀⠀⠀⠀⠀⠀⡿⡆⠀⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣧⠀⠀⠀⠀⠀⢠⠠⠀⠘⣧⣀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢻⣅⠀⠀⠀⠀⣼⠂⠀⢀⡟⢿⣿⣄⣛⣿⣿⡿⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡇⡀⠋⣹⡧⠈⠙⠛⠋⠀⢸⣿⠋⠕⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣱⢠⣟⠀⠀⠀⠀⠀⣴⣿⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠰⣻⣤⣀⠀⠀⠀⠙⣿⡬⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡎⠙⡏⠀⠈⠁⠀⠀⠀⢹⣍⣿⠨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣤⠼⣧⡀⠀⠀⠀⠀⠀⠀⠟⠉⡧⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠓⠾⠟⠛⠑⠆

⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉⠑⢄
⠀⠀⠠⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡔⠒⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠂⠀⠀⠀⠀⠀⠈⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠦⣄
⠀⠀⠀⠢⢀⡀⡀⢀⠀⡤⠐⠆⠰⠁⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠈⠠⠃⠘⣠⡷⠘⠃⠂⢁⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⡌⣾⢁⠌⠆⠱⠀⣠⣔⢁⣀⠀⠀⠀⠀⠀⡀⠀⢠⠂⠀⠀⠀⠀⠀⠃⢀⡠⠖⠂⠈⠉⠁⠐⠒⠠⢄⡀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠉⡠⠊⠀⠀⠀⣀⠑⢄⠀⠈⠀⠰⠀⠸⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠐⠀⡀⠀⠈⠀⡤⠠⠤⠀⠀⢰⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡰⠈⡈⠢⣀⠀⠀⠈⣆⠀⠀⠀⠚⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠉⠉⠙⠉⠓⠶⢠⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠀⡀⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⡠⢀⡄⠔⠁⠈⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠒⠐⠂⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠖⠢⢤⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠒⣄⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣀⠰⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡤⠀⠛⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⣤⣤⣢⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⢠⡿⠿⠟⠿⢷⡶⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⡞⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⠀⠀⢀⣀⠀⣤⠐⠒⠚⠂⠐⠒⠐⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠶⠢⠴⢶⢲⢒⠒⠈⠉⠁⠀⠀⠘⡀⠐⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠁⠀⠀⠀⠀⠀⠀⠡⠈⠠⠤⠉⠉⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡄⠀⠠⣄⣠⣴⡦⠄⠀⠐⠰⠴⠈⠀⠀⠀⠀⠀⢀⡕⠀⠀⠀⠀⢠
⠀⠀⠀⠫⣬⣧⣠⣈⡦⠌⠙⠀⠀⠀⠀⢀⣆⠀⡰⢀⡀⠂⠀⡃⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠸⠿⠟⣶⡶⠋⠀⠘⡶⡾⡀⠀⠀⠀⡑⠺⣡⣇⠀⢀⠀⠁
⠀⠀⠀⠀⢀⣠⣀⣴⠿⠟⠀⠆⡡⠀⠔⢾⣥⣴⠶⠾⢛⡗⠛⠙⠄⢈⢄
⠀⠀⠀⠀⠛⣫⠥⠊⠀⠀⠈⠁⠀⠀⠀⣶⠙⣿⣆⠀⠀⠑⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠹⠁⠀⠀⠀⠀⠀⠀⢀⡌⢠⠀⠀⠀⠄
⠀⡀⠀⠀⠤⠀⠀⠀⣀⣀⣀⡀⢀⣶⠷⠼⣿⣵⡧⠄⠀⠀⠠⠄⠠⠸⠛⢤⠏⣰
⠀⠀⠀⠚⠒⠒⠺⠿⠿⠿⠛⠛⠻⠿⠿⠟⠋⠋⠉⠁

⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠀⠀⢸
⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣷⣶⣄⣀⣀⣀⣀⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢣⣾⣿⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣟⣛⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢻⣿⣿⡻⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣾⣿⣹⣧⠀⠹⢧⣽⡭⣥⣆⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣶⢤⣀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⢸⡛⣿⣮⡛⠻⣿⡉⠙⠿⣿⣿⣾⣟⡷
⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡯⣷⢿⣷⡜⣿⣷⣹⣿⣿⠀⠀⠈⠙⠛⠋⠁
⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢛⣛⡛⣿⠾⣻⡇⢻⣯⣿⣿⣿⣧⣤⣴⡄⠀⣼⠆
⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⣠⣿⣭⣿⣷⣅⣹⣧⣸⡿⠿⢿⣻⠋⠉⠉⢻⠿⠄
⠀⠀⠀⠀⠙⢿⣟⣷⣦⣤⣄⣤⣴⣾⡟⣯⣽⣧⢈⣻⣿⣿⡈⣿⣿⣿⣿⡿⣿⣿⣿⣢⡀
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣹⡽⢯⣾⣟⣻⣿⣿⣶⣿⣿⣿⣇⢹⣿⣿⣿⣽⣿⣿⣿⣇⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⢹⣿⡿⠟⠛⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢰⣇⢸⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⠀⠀⢠⡀⠐⢿⣿⣿⣷⣤⣀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⣻⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⡀
⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠎⠿⠿⠷⠼⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣀⠂
⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⡿⢿
⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡻⢆⣿
⣿⣿⣿⣶⣶⣦⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣞⠛⢃⠈⠀⢀⠀⢠⣾⡷⠤
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠇⠀⠀⢸⣷⡿⢯⠅⣆⠀⠀⢵⠤⣀
⠀⠀⠀⠀⠀⠀⢰⠁⡟⠀⠀⢀⠀⢿⠇⢰⢂⠹⣿⣦⠀⠀⠉⠀⠀⠁⠀⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠸⣌⡀⠈⠀⠈⠀⠀⠁⢸⡿⠀⣿⡈⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢣⣶⣿⣿⣷⣶⣶⡿⢃⣾⣿⣿⣄⡀⠀⣀⠀⠀⢴⢂⡀⠀⠀⠀⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠉⠏⠀⢸⠁⣾⣿⣿⣿⣿⣿⣶⣿⣦⡀⢸⣿⠃⠀⠀⠀⠀⠀⠑⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣇⠀⠀⡾⢰⢿⣻⣿⣿⣿⣿⣿⡿⠿⠗⢸⣿⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠁⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣵⣿⣀⣰⠇⡄⠀⣱⣌⠻⣿⣿⣿⣿⣶⣾⣿⣿⠇⠀⠀⡆⣠⠀⣾⣿⣿⣿⣶⣶⣤⣄⣄⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⠉⠪⢭⡥⠞⠀⠀⠀⢹⡟⣶⣬⣍⡙⢯⣽⣿⣿⣷⣦⣾⣶⣷⣤⡈⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢸⣶⣿⣿⣿⡟⠪⢟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡗⠒⠚⠛⠛⠋⠙⠛⠛⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣿⣿⣿⣿⣦⡀⠀⠀⠈⠉⠉⠁⠉⠻⢿⣿⣷⡌⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣤⣉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠐⡀⠀⠀⠀⠀⠀⣀⠔⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⣰⠁⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⡀⠀⠀⠀⠠⠤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡎⢀⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡀⢀⡄⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⡭⠟⣉⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣰⡧⢈⣷⣄⢈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠿⠳⣇⢸⠟⠓⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠻⢿⣿⣷⣶⠄
⠀⠀⠀⠀⣤⣾⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠙⢷⣬⡙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢻⣿⣦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡦⠀⢿⣿⣟⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠖⠒⠶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠐⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡾⠇⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠑⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠉⣛⠐⡖⠂⡶⠒⢸⠂⠰⡎⢹⠓⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠔⣣⣴⡿⠔⠫⠰⠄⠆⡘⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠒⠒⠒⠒⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣥⠛⠀⠄⡀⢠⢈⠖⠁⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⢄⠁⠓⠠⣏⣀⡇⠔⠁⣀⢤⣐⣊⣁⣀⣀⡠⠔⠀⠀⠀⠀⠀⢸
⠀⠀⢠⣎⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠛⠂⡀⠀⠀⢀⣀⠄⠚⠶⠶⠛⠳⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠘⡄⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡌⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡸⠁⠀⡈⠀⠀⠀⠀⠀⠀⣠⠞⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢇⠀⠀⠀⠀⠀⠒⠠⣤⠞⠛⢄⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣆⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠉⢉⣉⡭⠿⣀⠀⠀⠄⠀⢀⠁⡈⠡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⠉⠉⠣⠀⠀⠀⠀⣰⣧⡤⠤⠶⡞⠋⠁⠀⢀⠌⢀⢆⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⢄⠀⠀⢠⣠⡤⠞⠉⢣⠀⠀⢸⠀⠀⠀⠐⠘⠖⠃⡘⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢹⠋⠉⠀⠀⠀⠀⢈⠀⠀⠈⠢⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⣀⠀⠀⣀⠀⠀⢘⠀⠀⠀⠀⠀⣀⡀⠱⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⡈⠰⡀⠅⠆⠘⢄⠀⡀⠀⣂⠀⢡⡀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⡃⠀⢣⠰⡀⠀⣟⢢⡀⠀⠀⠑⠲⠦⠬⠳⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⢆⠉⠒⠛⠣⠌⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⡠⣊⣝⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡸⠗⢁⠉⠉⠄⠁⠀⢛⣤⠛⢻⣮⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠁⠀⠙⠀⠀⠀⠀⠀⠘⠿⠛⠀⠐⠳⡈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣷⣦⢤⣀⢀⣀⣤⣄⣀⠀⣀⠀⢀⣀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣼⣯⣽⣿⣿⣿⠻⠖⠛⠁⠀⠀⠀⣄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⢿⠟⢿⣀⣄⣠⠞⠀⢸⠁⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣁⡤⠞⠁⠀⠀⠄⢠⣋⡀⡂⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣳⠾⠋⠀⠀⢠⡖⡛⠒⣛⣭⠞⠁⠸⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⠁⠀⠄⠀⠊⠙⣿⣿⣿⣟⠁⠀⠀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠼⣏⠍⠡⠂⠀⠘⠏⣰⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠚⠛⠉⠛⠛⠛⠛⠒⠛⠉⠀⠀⠀⢀⠻⠀⠀⠀⠀⠄⠀⡿⡇⠠⠘⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣁⣀⣄⣤⣤⣶⣤⣦⠀⠀⠀⠀⠀⠐⠲⢤⣈⠀⢠⣀⣀⢠⠄⣠⣇⠁⣸⠀⣿⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡿⠟⠛⠋⠋⣁⣤⣼⠀⡄⠀⢠⡴⠃⠀⢀⠈⠉⠉⠙⣍⣹⠉⠉⢲⣹⡏⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡿⢃⣰⣷⣶⢿⣿⡿⣿⡏⢰⢠⠀⢸⡇⠰⣿⣀⠀⠀⠀⢀⡟⠃⠀⢀⣿⡿⠿⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡟⢠⡾⢫⠕⠚⠉⠉⠉⢻⡇⢸⢸⡘⣿⣧⣤⠈⣥⠦⠀⠠⠬⢄⣀⠠⣞⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡟⡰⠁⠀⠀⠀⠀⠀⢨⡇⠈⢇⡟⣁⠀⠀⠠⠉⠁⠀⠀⠀⠀⠉⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⢷⠀⠸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣆⠀⠀⠀⠀⠀⠰⡄⠆⠀⢹⣦⣀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⡀⠀⠀⠀⠀⣰⠇⠀⠀⣰⡿⣿⣿⣄⣛⣻⢿⣿⠟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡻⣄⢄⠀⠀⣉⢀⠘⢋⣿⡁⠈⠛⠛⠋⠁⠈⢿⡿⢋⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠓⣕⣄⡀⠸⡄⣰⡏⠀⠀⠀⠀⠀⣠⣶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⣸⢃⡀⠀⠀⠀⠀⠙⢿⣏⢱⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⣼⠋⠉⠓⠆⠀⠀⠀⠸⡟⣼⡇⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠈⣼⡄⠀⠀⠀⠀⠀⠀⠀⢻⡟⢷⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣸⣓⣿⣷⣢⣀⠀⠀⠀⠀⠀⠈⠀⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠋⠁⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠃⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣶⣶⣤⡀⠀⢀⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡄⠀⠀⠌⢽⣿⣿⣶⣌⠁⠄⠉⠛⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣦⣤⢿⠄⠀⠀⠀⠙⠿⢿⣿⣿⣷⣶⡖⣄⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠰⣮⡻⣿⡟⠛⢶⡄⠀⠀⠈⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠹⠆⣀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⣤⡈⣿⡏⠁⠀⠈⣿⣶⣦⣴⣾⠶⠦⣄⣀⠀⠀⢀⢠⣼⣿⠶⡿⢻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⢦⣹⣿⣿⣿⣷⠀⠀⠹⣿⣻⡿⣻⣒⣦⣈⠹⠛⠛⠚⠛⠹⠌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠈⣷⢹⣿⣿⣿⣷⡂⠀⠀⠉⠈⠋⠘⠹⣿⣿⣤⣤⡤⠄
⠀⠀⠀⢀⡀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠐⢄⣠⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣄⣤⣈⠰⢠⡏⠉⠉⣄⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⣿⣿⠏⠉⠛⠛⠛⠿⣿⣷⣀⡉⠘⠇⠛⢈⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣹⣿⣷⠟⠘⢶⣶⡖⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠸⣶⣻⡟⠉⠀⠀⠀⠀⠀⠈⠁⣤⣉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣿⣧⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⣧⠀⠀⠀⡜⠁⠀⠀⣀⣀⣀⢐⠒⠂⠒⠖⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣷⡆⠀⢀⣠⠤⠚⠁⠀⠀⠀⠉⠑⠒⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡹⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊