Cool bio Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠉⠀⣀⠀⠰⠂⠃⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠀⠐⠂⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣴⠀⠀⠀⠰⠎⠂⠀⣀⠀⠀⠀⣿⠀⠀⠀⣰⣞⡙⣆⠀⠀⠀⠴⠀⠀⠀⠀⠁⣀⠈⠫⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣿⡿⠀⠀⠀⠀⠀⠀⠐⢱⠄⠀⠀⠃⠀⠀⠀⢩⠜⡁⠘⠀⠀⠀⣠⡆⠀⠀⠀⠠
⣯⠁⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⠀⠀⠀⠀⠉⠀⠀⢣⡀⠀⠀⢠⣿⡟⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣀⠰⡶⠉⠀⣨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠛⠀⢠⠖⠢⠀⠀⡀⠀⠀⠀⠐⠂
⢆⠀⠀⠀⠀⠀⠈⠻⠳⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⡽⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⡀⢄⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠡⠖⠨⠍⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⠆⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢂⠀⢀⡖
⢳⣸⡧⢄⡀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢂⠀⠰⠂
⠎⡯⡃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠂⠀⢤⠀⠀⠀⠀⣄⠀⠀⢀⠀⠠⠀⠘⠂
⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡀⠀⡀⢰⡄⠀⠀⠢⣄⠀⢉⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⠀⢠⡀
⡄⠁⠘⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠙⣦⣀⠈⠀⠐⢀⠇⡠⠆⠀⠲⠀⠐⢾⠟⠁⠒⠢⡀
⠰⠀⠃⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠺⠀⠀⠊⢃⡀⠄⠠⠀⠀⠁⢔⠰⠁⠌⠓⢄⠀⡼⠀⠀⠀⠀⠀⡀⠀⣏⡀⠀⠀⠉⠁
⠀⠀⠠⣀⡇⠀⠐⠒⠚⠉⠀⠀⠀⠈⠀⠀⠀⠀⠎⡽⠛⠂⠁⠀⠀⣀⡈⠓⠀⠀⠀⠈⢹⠃⠀⠀⠀⢀⠠⠀⠀⠈⠃⠀⠰
⠀⠀⠀⢸⠉⠉⠉⠓⣄⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣀⠄
⠀⢠⠄⠈⢆⡀⠀⠀⣹⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⡀⠂⠀⠀⠀⡀⠘⢆⠔⣀
⢀⡏⠀⠀⠀⠉⠓⠲⡿⠶⠶⣄⠀⠀⠀⠈⡗⠀⠈⠀⠸⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠈⠠⣸⢛⡯
⠘⠁⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠑⠄⡀⠄⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⣀⣤⡀⣥⣤⡄⠀⠈⠛⢲⡿⠶⣤⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠸⠇⠀⠁⠙⠻⣀⠄⠀⠀⢻⡀⠀⢸⡇⠀⠀⠀⠁⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢾⡇
⢀⠀⠀⠀⠀⡧⠀⠀⠀⠄⠀⠈⠒⢾⡧⣄⠀⠀⠈⠀⠀⡀⠈⠉⠀⠀⠀⠈⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠘⠁
⠈⠉⢀⠈⠛⠁⠀⠀⢠⠇⠂⠀⠀⠘⠧⣼⠀⠀⠀⠘⠻⠿⠿⡷⠤⢄⡀⠀⠀⠀⠀⠉⠉⠉⠙⠂⠂⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⢠⠀⠐⠀⠰⢶
⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣃⣠⣈⣅⣀⣀⣀⣁⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠸⠿⠿⡁⠀⠀⣶⡦⠀⣠⠖⣿⣬⡍⠘⣾⣿⠁⠀⠘⠷⠀⠀⠀⠙⠛⠛⠉⠀⠙⠛⠋⠁⠈⠛⠒⠚⠁⠈⠛⠒⠛⠀⠙⠒⠖
⠀⣠⣤⢈⣶⣶⡀⣀⠀⣿⣀⣿⣁⣙⣀⣉⣉⣀⠀⠀⠀⠀⠀⠴⠁⠘⣦⡞⠁⢳⡴⠃⠘⣦⡜⠁⢹⡴⠃⠈⣧⡞⠁⠹⡶⠃⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠘⢋⡈⠻⠛⠁⠁⣠⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠘⣷⠀⠀⣽⣇⠀⠀⣷⠀⠀⢸⣇⠀⠀⣿⡀⠀⢸⣧⠀⠀⡀⢠⣤⡀⢀⡤
⢾⣿⠈⢡⣶⡆⢀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠚⠘⠂⠐⡁⠙⠂⠚⠉⠃⠐⠃⠘⠂⠘⠈⠃⠀⠃⠈⠃⠘⠁⢹⣿⣿⣿⣿
⠠⠀⠀⠀⠉⠁⠐⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠂⠀⡀⢠⣩⣄⣸⣅⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠖⠆⠀⢠⠻⣿⣿⠟
⣤⡤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣽⣿⡻⣿⡅⠀⠀⠀⠀⢀⣀⠀⠀⠐⠂⠠⣄⢀⣼⣿⣿⢿⣿⣿⣈⣷⣄⡤⢀⡀⢀⣴⣴⣄⠀⣠⠈⣁⠀⣤⢠⠀⣀⢠
⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣻⣶⣯⡇⠀⠀⠀⠀⠀⠈⠃⠀⠆⠂⠀⢠⣿⣿⣷⡄⠰⡼⣽⠿⢿⣿⡖⠉⠀⠘⢿⣿⠏⠀⢸⠀⠛⢠⣽⣼⣤⣤
⣭⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠚⠓⠛⠛⠋⠀⢀⣠⣤⡶⣟⠁⠀⡰⣦⠙⣚⡿⢿⣿⡷⠻⣿⣿⢦⣵⣿⣿⠤⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⠀⠈⢩⣤
⣛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢩⡀⣉⠀⠀⠀⠀⡁⠀⠚⠁⢠⠝⢿⣾⣿⣷⣢⣿⣿⣾⣟⣉⣷⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⢠⣷⡄⠀⠀⠘
⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⢀⣼⠁⢈⣾⡶⢾⣏⡁⠀⠂⠄⠂⠀⠊⢻⣿⣤⣿⣿⣿⣾⠿⡃⠀⠁⠀⡠⢀⣄⣠⣤⣴⣤⠀⠘⠲⠤⡄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠺⣤⠀⡋⠀⠀⠀⠀⡁⠀⠀⠃⡄⠀⠀⠊⠈⠉⢹⠋⠋⠹⡄⠁⠀⠀⠀⠀⠁⠀⣀⣤⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡇⠀⠀⠀⣼⠀⢈⣷⠶⠾⢟⡁⠀⠀⠀⣀⣀⠀⠁⠀⡀⢀⣤⣄⠀⠀⠀⠀⣠⣤⣤⣶⣾⣿⣿⠿⠟⠋⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣤⣴⠋⠀⣅⠀⠀⠀⢀⡡⠀⠀⠀⠙⠁⠰⠄⠀⠀⠸⣿⣿⠇⠀⠀⠴⠺⠣⠼⠛⠁⠀⠀⠀⠀⠐⠶⣤⣄⣱⣶⣦
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠈⠀⠀⢻⠀⢈⣽⠷⠟⠋⠀⠐⠀⠀⠌⠀⠀⠀⠀⢠⡄⠈⣁⠀⠀⠀⠀⠀⠰⠷⠶⠾⠠⠔⠚⠁⠀⣤⡉⢩⣌⠛⠛
⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠾⠁⢉⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⣀⡀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⢀⠁⢠⣶
⠐⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⣠⣶⣦⣠⣌⠋⠀⠀⠀⣤⣤⣤⣤⡄⣛⠀⠀⢿⠿⠅⠀⣶⣾⣷⣦⣆⠀⠀⠀⠀⠀⠒⠂⠲⡀⠀⠀⠀⢈⠀⠈⠛
⠀⠀⠀⠀⠀⢀⣀⢀⡶⣛⣦⡀⠀⠀⠀⠘⠛⠋⣘⡋⠐⣿⣷⠄⢸⣿⣿⡟⣷⣿⠇⢀⣤⠀⠀⢰⣿⣿⡿⣿⣯⠆⠀⠀⠀⠑⠄⠀⠀⠅⠀⠀⠀⠀⠀⢀
⠀⢈⠉⠉⠃⠠⠎⣹⡶⡹⢼⡃⠄⠀⠀⢀⣴⣤⡛⠁⠀⠸⣿⣧⠈⠉⠛⠁⠈⠛⠁⠀⠉⠠⠦⠀⠛⣿⣿⡟⠙⠁⠀⠡⠀⠀⠀⠈⠀⠀⢀⠐⢛⠘⠇⡀
⠀⢺⡇⠀⠀⠀⢰⡟⢃⠶⣿⠁⠀⡄⢀⣸⠿⠿⠃⣠⡄⣿⡿⣷⣿⣿⣶⠄⠀⠠⢾⣚⢥⠀⠀⢰⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠄⠘⠀⡄⠃
⠂⠸⠇⠀⠀⠀⣼⢰⣿⣻⠋⡀⠀⠄⣘⡋⠰⣿⠆⣽⣧⡏⠁⢿⡛⠲⣏⠓⠀⠀⠛⠼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⣤
⡀⠀⠀⠀⠀⠀⡘⠓⠚⠁⠀⠀⠀⠀⠉⠁⠘⠗⠀⢸⣿⣿⡀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠁⠀⠀⠀⣺⡇⠉
⠈⠄⠀⢴⣦⣤⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⢺⣄⠀⠀⢿⣿⣧⣐⣿⣚⡿⠟⠁⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠒⠀⢀⣠⣄⠀⠀⠀⠀⠂⢐⠀⠀⢀⠀⠛
⢀⡆⢀⣤⡈⠉⠁⣠⡀⠀⠀⣼⣿⣿⠿⣿⣿⣿⣖⠁⠈⢿⣿⣿⣯⣩⣤⣄⠀⠠⠾⠄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠿⠟⠀⠐⣠⣴⣿⣿⣿⣷⣦⡐⢃
⠈⡇⠀⣈⠁⢸⡇⠈⡁⠀⠀⣿⣿⣧⣤⣋⣿⢻⡟⠒⠀⢰⣿⣯⣿⣾⣎⣿⣤⣀⠀⠀⠄⠀⠐⠾⠀⠺⣿⠇⠀⣴⡄⠀⠀⢰⣿⣯⣿⣿⣿⣷⣿⣿⡄⠂
⠘⡇⠘⠿⠁⠈⠃⠀⣿⠀⠀⠈⠻⢿⣿⣿⡿⡟⠣⠀⠀⢿⣿⣿⣿⣿⣏⣉⡛⠛⣀⣀⠀⢠⣄⣀⡀⣠⣧⡀⠀⣨⣅⠀⢂⢺⣿⣿⣿⣿⣿⣿⢿⣿⡇⡐
⠀⣤⠤⡤⠤⣀⡤⠤⢬⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⢤⡄⠠⣤⣌⡉⠛⠿⠿⠇⠸⣿⣿⡷⠀⣬⠿⠃⠻⡿⠏⠈⡻⠟⣀⠀⠈⢻⣿⣾⣿⣿⣯⣾⠟⠠
⢾⣿⠚⣷⣶⠭⡞⣿⠰⡎⡕⡯⡂⠀⠐⠀⠀⣰⡄⠀⠉⠀⣠⡈⠁⣀⣀⠀⠀⠀⢈⢉⠐⠀⠉⡀⡀⢾⡷⠀⡈⠛⠀⠻⠃⠈⠠⠈⡛⠻⠛⡛⠡⠀⠃⣤⣶
⡵⣿⣧⣗⡪⠞⠺⠱⠈⠢⣷⡷⡶⠃⣠⣤⣼⡟⠀⠸⠆⣴⠏⠀⠛⠉⠉⢳⡴⠛⠉⠉⢳⣶⠋⠉⠙⣦⡼⠋⠉⠙⣦⡞⠋⠙⠁⠀⠁⠈⠀⠀⠀⠀⠸⣯⠿
⢠⣶⣄⠀⠀⠶⠶⠶⠀⠀⠀⠀⣤⣠⣿⣿⣿⣏⠀⢠⡄⢠⣴⠆⠀⠀⠀⣠⣏⡀⠀⠀⣸⣇⠀⠀⠀⣼⣁⠀⠀⢀⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠂⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡄⠀⠀⡼⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⢸⡄⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢁⡀⠈
⠀⠀⠀⠠⠀⠐⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠒⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⣀⡤⡀⠀⠀⣀⠄⡀⠀⢀⠀⠀⠀⡀⠀⠀⡀⣀⡀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠙⠀⠀⠀⠁⠘⠀⡈⠀⠀⠀⡀⠉⣤⠸⠁⠁⣸⠁⢈⠩⠀⣀⠃⡇⢸⠉⠉⡭⠄⠀⢹⠀⠀⠀⣆⠀⠶⠈
⠀⠐⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠐⠉⠐⠃⠀⠚⠀⠋⠐⠁⠀⠚⠁⠒⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠈⠈⠙⠛⠉⠿⠯⠽⠿⠟⠯⠡⠮⠤⠤⠤⠶⠶⠶⠿⠀⠨⠁⠀⢖⠀⠄⠀⡰⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⡤⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢄⠄⠠⠀⠀⠀⣀
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠵⠚⠈⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⢠⣴⣦⡀
⠀⠀⠀⠀⡀⠐⠛⠛⣀⠀⠀⠀⠀⡼⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠲⠎⢉⡈⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⢣⡈⣥⠛⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠉⠀⠄
⠀⠀⠀⡀⠰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣄⣀⠠⣿⠧⠀⠀⠀⠀⠇⠀⠀⠂
⠀⠠⠄⠀⠌⡹⠉⣀⠀⠀⠀⠠⠀⢀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠉⠋⢠⡆⠀⣤⡄
⠀⠀⠀⠈⢀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡀⠀⢀⠀⠀⠀⠐⢿⢾⠀⠉⣀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣉⢓⢠⠀⠀⠀⠀⠀⠸⠠⠚⠿⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠫⠆⠒⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠎⠀⠀⠀⠀⠀⠙⣆⠹⣄⠀⠀⠀⠀⡄⠀⢀⠀⠀⠁⠀⠀⠀⠀⠈
⠈⠀⠀⢠⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠘⠁⠖
⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠐⠀⢄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⡿⠡⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠛⠀⠀⠀⢀⠄⠀⠀⠀⢹⠀⠀⠀⠀⢀⣀⠀⠠⠤⢤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠉⠀⡉⠀⠀⠀⠀⢈⡀⠁
⢰⠂⠀⠀⢠⠖⠒⠒⠃⠀⠀⢀⣤⣤⠀⠀⠀⠀⠆⠀⠀⠀⠱⠈⠁⡈⠀⠀⠀⠾⠷⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀
⢸⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠄⢀⡀⠀⠄⠈⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠉⣀⣠⣄⠀⠒
⠀⠳⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠰
⠀⠀⠈⠙⠒⠶⠤⠂⠀⠀⠀⠐⠠⠾⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄



⠀⠀⠀⠀⢀⣀⣀⣤⣴⣤⣤⣄⣠⣤⣤⣤⣤⣤⣀⣠⠀⠀⠀⠀⠠⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⠿⣧⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣃⡀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠈⢁⣀⡀⠀⠀⠈⣿⣿⣿⣷⣤⣴⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠈⣿⣿⣿⡁⠤⠄⡀⠈⠉⠙⠾⠀⠀⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣀⣀⣀⣼⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠈⠀⠠⡐⠀⠀⢙⣿⣿⣿⣿⣿⣇⣐⣸⣿⣿⣿⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈
⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⡀⠀⠀⠁⣀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⢋⢀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⠛⡅⠀⠉⠙⢿⣿⣿⣷⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢄⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠢⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣦⣤⣄⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⢠⡀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠰⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠘⠀⠠⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣅⣼⣦⡀⠀⠀⠀⠀⠀⠀⢸⣦⠀⣸⣿⠀⠀⢈⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣷⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⡟⠀⢠⡿⢻⡇⠀⣤⠀⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⡉⠉⠉⣙⠳⣆
⠀⠀⠀⠀⠀⠠⣤⣙⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠘⠁⠘⠇⠀⣿⣼⠃⠀⠀⠀⠙⢿⣿⠿⠟⠻⠁⢀⠀⠁⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠲⠭⣻⡖⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣧⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⣁⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣵⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠈⠻⡇⠀⠀⠐⠋⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠰⠿⠷⠾⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣴⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣏⠳⣝⢦⡀⠀⠀⠀⠀⣿⡛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⡇⠀⠀⠀⣤⡈⠻⣦⠀⢿⣿⣿⠃⢠⡾⠋⣠⡄
⠀⠀⠀⠀⠀⠀⠀⡴⢍⠻⡉⣿⡟⠿⠶⠷⠶⠀⠀⠀⣿⣉⣉⣽⣿⣿⠷⠶⣿⣿⣿⡿⠿⢿⡇⠀⠀⠀⠈⠻⣆⠈⢷⣄⠀⢀⣴⠏⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠢⡑⢌⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⢾⣿⣿⣿⣿⣷⣶⣶⣟⣛⣿⡇⠀⠀⠀⠀⠀⠙⢷⡄⢙⠀⢘⠁⣴⠟⠁
⠀⠀⢀⣠⣤⣀⣀⣿⡖⢌⠢⣙⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠫⡙⢟⠻⣿⠶⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⣿⣿⣿⣿⣿⣿⣶⣾⠛⠛⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣹⡅
⠀⠀⠀⠀⠀⠉⠢⡑⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡇


⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣴⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⠠⠥⠤
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢲
⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⢈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠂⠀⠑⠄⠀⢸⠀⢸⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣬⠒⢪⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡄⠀⣨⠇⠀⠀⠀⠀⣤⣤⣬⣤⣤⠀⠌⠀⠄⢣⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⠁⠀⠀⠀⠀⠀⠘⠻⠿⠟⠃⣼⣶⣶⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⣹⠟⠲⣄⠀⠉⠠⠀⠀⢠⢄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣷⠜⠋⠘⠠⠘⠳⢅⣢⢝⣦⣸⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠀⢂⣲⣞⣁⡤⠀⠀⠀⠀⠀⠈⢳⣌⣷⣿⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡿⢡⠞⠁⠀⠀⠀⠉⠀⠚⠙⠉⠀⠀⠉⢿⡙⢷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡽⣿⣿⠄⠀⠀⠁⣤⢤⠀⠀⠶⠈⠛⠀⠀⠀⠈⠛⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠟⢘⡛⣿⡀⣀⠀⠀⠈⠲⡀⠆⠀⠀⢀⣄⢀⡀⠀⠰⢿⠇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣀⢸⡗⠈⠉⠃⠁⠠⠟⠂⠀⠉⠐⠁⠈⢀⠠⣻⡞⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢣⡄⠀⡔⠀⠆⠈⠣⡄⠐⣀⠀⣤⡤⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠙⣧⠀⠀⠀⠀⠀⠀⢀⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠻⠦⠀⠀⣤⣼⠛⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢦⠀⠰⠎⣀⠉⠁⠀⠀⠀⠀⢀⡄⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⣦⠀⢈⡀⣠⡀⢠⡄⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⢤⣖⠀⣤⡄⢐⣚⡥⠬⢯⣉⠉⠑⢾⣧⡴⣦⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡦⠂⠀⠠⠈⣙⣿⠋⠰⠛⢿⡿⠃⠀⡙⠲⠤⡀⠈⠷⢫⣉⡀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠐⠀⢐⣿⢿⣿⣧⠤⢀⢀⡀⢴⣁⡤⠄⠋⠡⢤⣃⠈⠻⣶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⠋⠀⠀⠈⢉⡀⠀⠀⠀⠉⠁⠀⠀⢉⣳⣆⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠄⠠⠄⠞⠻⡏⠦⠀⠛⠛⠆⠠⠈⠈⡩⢿⠟⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢛⠀⣠⣤⡀⠀⢀⠀⢀⣀⠤⠀⣀⡀⠺⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡇⠚⣿⠛⠋⠀⠀⠉⠉⠁⠀⠀⠀⠈⣡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⡞⠋⢠⡀⠀⠀⡀⢹⢯⣟⠔⠚⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠈⠁⣠⠏⢀⠴⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣤⠿⢤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣦⡀⡀⠻⣘⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⣐⠀⠀⠚⠛⣮⣀⠈⡚⠁⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⣰⠏⢽⣻⠂⡤⠋⠹⠂⢰⡕⢮⣙⠡⢀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠙⠾⠛⣴⣤
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢀⡴⣠⠖⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⢠
⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⣀⠉⠅⢁⢀⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠘⠐
⠀⠀⠀⡀⠒⠀⠀⠀⡴⠞⠃⠀⠀⡈⡛⡅⠻⠄⠀⠀⠀⣀⠔⠀⠠⡀⠀⢀⣠⢶⡷⡟⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠃⠀⠀⠀⠀⠳⠀⠀⠀⠀⢻⣿⡁⠘⠣⣄⠀⠒⠁⠀⠀⡠⠒⠉⠋⠙⡗⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡟⠙⢄⡃⠀⠈⠏⢀⡀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠠⠤⠾⠇⠀⠀⠉⠳⣦⡀⠈⠑⠣⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡔⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⡀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠇⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠠⠄
⠀⠀⢀⣀⠀⠀⠀⠁⠐⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠠⠘⠃⠀⠈⠀⠁⠀⠀⢄⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀⠀⠃⠀⠨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠁⡐⠐⠄⠀⢀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠊⠀⠀⠀⠀⠀⢈⠈⡃⠀⠀⠀⠀⠁⠀⠙⢷⠀⠅⠅
⠀⠀⠸⠄⠁⢁⠠⠀⠀⠂⠀⠀⠀⠉⠀⢐⢣⠶⠄⠐⠒⠀⠀⡀⠀⠀⠀⠀⠀⢓⢚⢚⡛⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠴⠀⠦⠀⠀⠀⠀⠀⠘⠠⠀⠄⠈⠒⠊⠠⠐⢀⡀⠀⠇⠀⠐⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠐⠀⠠⠄⠀⠄
⠀⠊⠉⠀⠀⠀⠀⠀⠄⠀⢀⡀⠒⠀⠢⠄⠀⠠⠀⠁⠂⢀⡀⠀⠀⠀⠀⠈⠀⠀⠧⠼⢛⠈⠁⠀⢉⠀⠦
⠀⠂⠠⠂⠀⠀⠀⠀⠀⢀⠀⠁⠀⠃⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠂⠀⠶⠀⢐⠦⠠⠒⠁⠐⠂⢀⡑⠁⠈⠂⠀⣄

⠀⢀⠆⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠆⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡇⠐
⠀⠈⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠄⠀⠇
⠠⠐⡐⠠⡀⠀⠀⠀⠈⠈⠁⠁⠆⠀⠀⠀⠀⠉⠐⠚⠉⠂⠀⢀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠠
⠀⠀⡁⠠⠀⠀⠀⠀⠀⠀⠐⠰⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠊⠀⠐⠂⠈⠘⠀⠐⠀⠀⠂⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐⠁

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠐⠟⠁⢙⠀⠀⠠⠄⢀⠀⠀⢀⠀⠀⠀⠀⣠⠶⣶⣶⣤⡀⠀⠀⢴⣴⠀⠀⢐⣶⡄⠀⢋⠄⢶⠄⠁⢄⠀⢰⡿⠿⣦
⠀⠀⠀⠀⠞⠁⠏⠀⠈⡠⠀⠀⡈⢡⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣛⣶⣄⡈⠹⠀⠉⢫⡝⠀⠆⡰⢞⢳⣿⡆⠀⠁⠘⢿⣀⣽⡇
⠀⠀⠀⠀⠈⠈⠁⠀⣿⣈⡉⣧⠤⣄⠀⠄⠀⠀⠻⣿⣿⡿⣿⡟⢛⣳⠾⣿⣷⣄⡈⠚⠛⠀⠀⣷⠉⠁⠉⡰⣦⡄⠀⠘⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡚⣧⣮⢭⢅⣙⠲⠀⠀⠀⣄⠀⠈⠛⠿⠿⣷⣯⣭⣷⢽⣿⣿⣷⠀⠀⠀⣤⣭⣧⠄⡰⠃⢻⡷
⠀⠀⠀⠀⠀⠀⠀⣉⡉⢫⠾⠿⣛⠿⠂⡆⠀⢻⡷⣿⠇⠒⡢⢤⡈⠙⠿⠿⢿⠿⠃⠀⠀⠀⢸⠏⠀⢨⡉⣍⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠘⠾⣷⣶⢯⡜⡀⠀⠀⠀⠙⠶⢤⢤⣠⠂⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⠿⢀⣀⢸⡇⠀⠀⠀⢀⣄⡀
⠀⠀⠀⢀⠀⠹⣆⠀⠙⠂⠉⠀⠀⠉⠀⠀⢀⣀⡠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢲⣿⣿⡆⣻⡄⠀⠀⣿⢿⡇
⠀⠀⠀⠠⠉⢒⣌⢣⡀⠀⣄⡀⠀⠀⠀⠀⣾⠛⠙⠉⡃⢻⡇⠀⠀⠀⠀⢀⡄⢨⡆⠀⠀⠀⠀⠀⠊⠳⣿⣿⣿⢿⡇⠀⠐⣿⣿⠇
⠀⠀⠀⠐⠲⢤⡩⢷⣈⠢⡈⠛⠃⠀⠀⠀⢻⣜⣻⡷⠻⠿⠃⠀⠀⠀⠀⠀⢧⠸⠀⠀⠀⠀⠀⠀⠀⢇⢻⣿⣿⣾⣿⠂⠀⠙⠁
⠀⠀⠀⠀⠀⢀⣉⡒⢿⣳⡿⢧⣄⣴⣤⠤⠈⠉⣩⣶⡆⣿⣷⣶⡀⠀⠀⠀⠈⢆⡄⠀⠀⠀⠀⠀⠀⠀⠑⢝⠿⡿⠏
⠀⠀⠀⠀⣾⢋⡸⢛⣻⣿⣡⡍⢿⣯⣿⣴⠆⠘⣿⡕⢡⣸⣿⣿⠅⠀⠠⠀⠂⠀⢧⠀⡀
⠀⠀⠀⠀⠀⠘⢡⡟⢡⢍⠙⢮⡧⢹⣿⣾⣯⡀⠙⠳⠞⠃⠉⠁⠀⠀⠀⠀⠀⠀⡞⢸⣿⠇⠀⠀⠀⠀⠠⠀⣀⢀⣀⠄
⠀⠀⠀⠀⣠⣤⠀⣰⣣⣤⣳⣿⢻⣟⠾⡿⠏⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⡀⡈⢃⠄⠀⠀⠀⠀⢠⣾⣻⣿⣾⣧⡐⡀
⠀⠀⠀⠸⣿⢹⡇⠀⣋⣝⢻⠁⠾⠀⡀⠄⠀⠀⠀⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠰⣷⠁⠈⠀⠀⠀⠀⠀⠘⣿⣭⢾⣿⣿
⠀⠀⠀⠀⣿⣸⡇⢘⣧⠉⠈⠀⢀⡀⠶⠄⢛⢐⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⡀⠄⠀⠀⠀⠀⠀⠁⠐⠻⠾⣻⣿⡄
⠀⠀⠀⠀⠿⠟⠀⠈⠃⠀⠀⠀⢸⠁⠀⠀⠉⣈⡄⠀⠀⠀⡀⠀⠀⠀⠀⢀⡼⠋⢈⠓⡲⢀⠀⠀⠀⠀⠀⠀⡰⣀⠄⡉⠘⠁
⠀⠀⠀⠀⠀⢠⠴⠖⠦⣄⠀⠀⢸⠀⠀⠀⠀⠘⠰⠆⠘⠀⢁⠀⠀⡤⠊⠉⠀⠀⠨⠀⢨⡆⠀⠀⠀⠀⡀⠁⠀⠊⣈⠌
⠀⠀⠀⠀⢀⠏⠀⠤⠄⠉⠑⡄⠈⠃⠀⠀⠀⠀⠐⡎⠹⠀⠈⠀⠀⠀⠀⠀⢀⠉⡀⠀⠈⠡⠀⢀⣾⡟⣻⠆
⠀⠀⠀⠀⢸⡀⠀⠀⡤⢀⠀⡗⢀⠴⣶⣶⠶⠲⣦⡀⠢⠴⢮⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⡀
⠀⠀⠀⠀⠘⠡⠀⠀⢀⠀⢨⠃⢸⢶⢢⣄⣤⣀⡁⠃⠀⠀⠀⠈⢢⠀⠀⠀⢀⡠⣤⡀⠀⠰⣤⣀⣀⣴⣂⢐⣳⣦⡴⠖
⠀⠀⠀⠀⢸⠸⠀⠂⢉⢡⡇⠀⠈⠛⠛⠛⠻⠙⠃⠀⠀⠀⠀⢀⡀⠀⢀⣀⠉⠀⠀⠙⠦⣤⡤⠼⠟⢋⣩⠵⣢⣴⣶⡀
⠀⠀⠀⠀⢸⠀⢀⠃⠀⣼⠀⣠⢶⣤⡶⣦⢀⠀⠀⢀⣰⣶⠖⡿⣳⠟⢻⡏⣶⠿⣦⠀⠀⠀⢀⣠⠞⠋⣁⡀⢉⡺⠋⠋⣠⣦
⠀⠀⠀⠀⢾⠁⠈⠀⣠⠋⠀⣻⣿⣙⡛⠻⣟⣷⠀⢿⠛⢿⡾⣥⣿⢾⡿⢷⣹⣄⣾⠁⠀⢠⠎⢀⡠⠖⠉⣅⠉⠁⠀⣸⣿⣿
⠀⠀⠀⠀⠈⠳⠾⠂⠁⠀⠀⠉⣿⣏⢛⣶⠏⣯⠀⠸⣧⠾⠑⠷⣿⣭⠳⣼⠧⠉⠁⠀⣰⠃⡀⢸⡀⠀⠀⠈⠶⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⢉⣿⣳⠀⠀⠀⠀⠘⠛⠊⠙⠙⠛⠁⠀⠀⠀⠀⠙⠆⡑⢼⡁⠀⡀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⢀⣤⡺⣿⣿⠀⠀⠀⢀⡀⢉⣶⣤⡞⢳⡄⠀⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠈⠱⣎⠁
⠀⠀⠀⠀⣿⡿⢁⡀⢻⡿⠃⠀⠘⠟⣧⡿⣾⠷⣾⣿⡷⠀⠰⠘⠲⢤⣄⡐⢄⣀⡀⡠⠀⠀⠀⠀⠀⠀⡤⠀⢀
⠀⠀⠀⠀⠙⣖⣩⣾⡇⢀⣤⣄⠀⠀⠻⣤⣿⣾⣏⣽⠆⠀⠀⠀⡐⢁⣉⣉⣽⣿⡿⠧⠄⢠⣾⣀⣔⠈⢠⣔⣁
⠀⠀⠀⠀⠀⠈⠉⣩⣴⡞⢻⣵⡆⠀⠀⠈⠁⠈⠉⠀⠀⢀⡠⠀⠁⠀⠙⠀⠀⠃⠠⠔⠀⠉⠀⠀⠉⠤⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢈⠙⠋⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡀⠀⠀⠀⠀⢂⡶⣾⠵⢀⡶⠂⠀⠀⠀⠰⠀⠀⠘⠋⠄⠀⠀⠀⠁⠀⠀⠀⠒⠉⠑⢄⠀⠀⡀⠀⡤⠤⠤⢤⠀⠀⠀⠀⢀⣀⠈⢃
⠀⠀⢰⠖⣫⠓⠀⠌⢻⠛⠄⠞⠁⠀⠀⡀⠀⠀⠀⠄⠁⠁⠀⠀⢀⠰⠀⠀⠀⠀⠋⣀⠰⠦⠁⠂⠈⠀⠀⠀⠀⠈⣧⢀⠒⠍⠀⢈⠀⠈⠠
⠀⠀⠈⢾⡛⢶⡃⠀⠤⢀⡰⢠⡀⠀⠂⢀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⢢⡄⠀⢀⠕⠉⣑⢍⠠⠁⠀⡀
⠀⠀⠀⠀⠈⢀⣀⠔⠀⠈⠑⠛⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠜⢢⠆⢡⠂⠀⡤⠋⠁⠀⡀⠷⠉⣤
⠀⠀⢲⣤⠀⣋⠁⠀⢠⣀⡄⣠⠀⠀⠐⡀⠀⡀⠀⣤⡤⣬⠄⠀⢈⡤⠄⠀⠀⠀⠀⠂⠀⠀⣀⠀⠂⠀⠀⠀⠰⠤⠊⠸⡳⡆⠠⠈⠱⡾⠇⢤⠂
⠀⠀⠀⠀⠰⠄⠀⠀⢸⣿⢻⣧⠀⠀⠀⠉⠠⠃⠐⠋⠤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⠒⣿⠂⠀⣀⣤⠁⠐⠳⠬⢄⣠⠤⡀⠀⠈⢁⠀⠁
⠀⠀⠀⠰⡤⠀⡀⠀⠘⠷⡿⠛⠀⠀⠀⠀⠀⠀⠰⠶⠄⠀⠈⠃⠀⠀⠀⠀⠀⠀⢶⣬⣿⠃⠤⠀⢠⣯⣌⠒⠇⠀⠀⠀⠉⠛⠉⠀⠀⣸⠀⡐
⠀⠀⠀⠒⠠⠀⡎⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠠⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⢨⡱⠆⢠⠦⠞⠀⢠⠤⠄⡀⡀⠈⠠⢀⠐
⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢞⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠿⡱⣦⠄⠀⢀⠀⡀⢀
⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠸⠛⠘⢛⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠤⠀⠀⡢⠀⠉⠊⠀⠀⠀⢠⠀⠂
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢬⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⠰⠀⠀⠀⠀⠈⡮⠀⠈⢓⡀⠀⠘⠀⠈⠐⡄⠀⡴⣀
⠀⠀⡆⢃⠀⣷⣆⣤⣤⣶⣛⡁⠀⣷⣄⠀⠸⠀⠀⠀⠀⠢⠒⢲⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⡀⠈⠀⠀⠃⠌⠑⠐⠀⠀⠁⠈⠀⢀⠸⣎⣿⠃
⠀⠀⠇⢈⠸⢿⣿⠿⢛⣛⣽⠀⠈⠑⠚⠛⢃⠈⠁⠊⠁⠂⢰⠈⠀⠀⣄⡀⠀⠀⠀⠄⠀⠀⠀⠅⠀⠀⠀⠀⠀⢀⠀⠒⠂⠐⠆⠀⢈⢢⣼⣦⡀
⠀⠀⡀⠀⠀⠀⠉⠛⠉⡁⢂⠶⠀⠴⢂⠀⣠⠀⣠⢤⠁⠀⠀⠀⠀⡀⠀⠐⠐⠃⠀⠀⠒⣂⠀⠀⠀⠀⠡⠤⠤⠟⠀⠀⠄⠀⣸⠁⠀⠈⠻⡽⠁
⠀⠀⠀⣦⠤⢀⠀⠀⠀⠁⠀⠃⠀⣘⡥⠀⡍⠀⠓⠒⠁⠛⡸⠀⠈⠁⠁⠠⠀⠈⠀⢠⠟⠉⠻⣷⠀⠀⡀⠂⠀⠀⣠⠀⢛⠛⡉⠀⡢⠠⣾⠽
⠀⠀⢀⠈⢀⠁⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⡓⠳⠦⠤⢤⡤⠃⠀⠀⠢⢶⡇⠀⠄⠀⢸⣇⣀⣠⡿⠀⢘⠏⢧⠴⠀⠄⠙⠀⠶⡯⠈⢠⠄⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⠈⠉⠁⠀⠀⠀⠒⠈⠀⠛⠁⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⠂⢰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡯⣷⣾⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣇⣨⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣶⣤⡀⢸⠤⠀⣾⡇⢀⣤⣶⣿⣿⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣴⣾⣬⡹⣿⣿⣾⠂⠀⢺⣧⣿⣿⣿⣿⡯⢹⣌⠙⢷⣄
⠀⠀⠀⠀⠀⠀⡠⢢⣾⣿⡝⣿⣿⠯⣿⡟⢿⣀⣼⡟⣸⣨⡿⢿⣿⣿⢬⣫⢈⠌⠻⣦⡀
⠀⠀⠀⠀⠀⡔⣱⣿⡿⣿⢿⣹⣿⣾⣿⣷⠘⣟⣋⣁⣷⣮⣽⣿⣿⣿⡇⠩⢦⢰⡟⣻⣿⣆
⠀⠀⠀⢀⣨⣾⣿⣿⣷⣮⣿⣿⡿⣿⣿⣿⡍⣹⣿⣿⡿⠟⠛⠛⠿⠟⠓⢤⣻⣿⢳⠉⡻⣿⣄
⠀⠀⠀⢠⣿⣿⣿⣯⣽⣿⣿⣯⣵⢁⡽⠟⣠⣿⣿⠇⠀⠀⣠⣶⣶⡴⢀⡿⢯⡩⠿⡏⢻⢻⣿⣆
⠀⠀⣠⣿⣿⣿⣿⣿⣟⢿⣿⠙⢿⢸⡇⢀⣿⣿⡏⠀⠀⢰⣿⡿⣷⣶⣦⣲⣷⣶⠷⢶⣀⣽⣻⢿⣆
⠀⢰⡟⣿⣿⣿⣡⣟⣛⣟⡙⣶⣯⠏⢣⠀⠉⣿⣷⠀⠀⢸⣿⣤⣀⡙⢿⣧⣛⠿⡟⢓⠁⠀⢒⠁⣽⡆
⠀⣿⣿⣿⣿⣻⣟⣿⣿⣿⣻⣿⣿⠀⠀⠀⢰⣾⣿⠀⠀⠀⠀⠹⢿⣿⣶⣿⣿⣷⡶⣮⣔⡢⠄⢋⠠⢱⡀
⠀⣿⣿⣿⣿⣻⣽⣞⢿⣻⣿⠿⣿⠗⢀⣼⣾⡿⠃⠀⠀⠀⠀⠀⠸⣷⢹⣿⣿⣿⣿⢿⣿⣿⡷⣾⣷⣿⣧
⢸⣿⣿⣷⣟⣷⣿⣿⣿⣿⣶⣾⢿⣦⣿⣿⢿⢱⠤⠀⠀⠀⠀⠀⠀⣽⣦⣻⣿⣿⣿⣣⣿⣿⣯⣿⣿⡧⣿
⢘⣿⣝⣿⣿⣿⣵⣿⣿⣿⣾⠩⣾⣿⣿⣷⣶⠸⠃⡀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣟⡿⣿⣿⣿⢻⣷⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢺⣿⣅⢙⣻⣯⣿⡾⠀⠀⠀⠀⠀⡠⢻⣜⣿⣿⣿⣿⣿⠷⣿⣿⣮⣌⣻⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⠶⣺⡇⢠⣿⣿⡿⠿⣿⣄⣠⣄⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿
⢸⣿⣿⣿⠿⣿⢿⣿⣛⣣⣼⣀⢔⣴⣿⣿⣿⡇⠀⠀⠉⠙⠛⣿⣿⣿⣿⡿⢿⢿⣿⣥⣽⣟⣹⣿⣾⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⡀⠚⢈⣁⣤⣾⣿⣿⣿⣿⡿
⢸⣿⣿⣿⡿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠛⠛⠛⠛⠻⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠷⠀⠸⠗⠀⢶⣶⣴⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣀⣀⣀⣀⣀⣿⡏⠀⠉⠉⠛⠻⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣦⣤⣀⣠⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⣶⡿⠿⠆⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⢀⣴⡿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣶⡿⠋⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⡄⠀⣠⣤⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⡟⠁⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⣿⡆⠀⠀⢿⣧⣴⡿⠋⠀⢀⣴⣶⠿⠿⠛⠋⠉⠻⣿⣤⣴⡿⠋
⠀⠀⠀⠀⠀⠀⣼⡟⠋⠉⠀⠀⢿⣧⠀⠀⢸⣿⠋⠀⠀⠀⣿⡏⠀⠀⠀⠀⣀⣠⣼⡿⠉⠉
⠀⠀⠀⠀⠀⠀⢻⣷⣄⣤⣤⣶⡾⣿⣤⣤⣼⣿⣀⠀⠀⠀⠙⢿⣶⣶⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠈⣿⡟⠉⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠻⣷⡄⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⣾⡟⠛⢿⣦⡀⠀⠀⠀⠙⣿⣆⠀⠀⠙⣿⣆⠀⢿⣧⠀⠀⠘⢿⣦⠀⣠⣴⣾⠿⠛⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⢿⣦⠀⠀⠀⠈⢿⣧⣀⣀⣼⡟⠀⠈⢻⣷⡀⠀⣈⣻⣿⠟⠉⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣾⡿⣷⣄⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠹⣿⣾⠟⠛⣿⣦⣴⣾⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣿⠏⠉⠈⠙⠻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣠⣾⠟⠿⣷⣦⣄⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆⠘⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡾⠟⠁⠀⠀⠀⠉⠛⠃⠠⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⢰⠂⡋⠰⠀⠀⢀⣠⣤⣶⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠈⡝
⠀⠈⠰⠙⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠶⠈⢀⡀⠘⠁⠀⠀⢠⡄⣤⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⠘⠁
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠰⠀⠖⠊⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠴⠔⠠⢤⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣠⣾⠟⠀⠀⡼⠃⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠠⢀⣸⣧⠀⠀⠀⠀⠀⠀⢀⠾⣷⠄⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠂⠀⠁⠀⡀⠐⠈⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢐⡂⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀⠄⠀⠀⠐⠀⠀⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⡉⢠⠀⠀⠀⠀⢈⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢟⠁⠀⠰⠓⠀⠀⠀⣠⣄⡄⠀⠀⡰⠛⠀⠀⢠⠀⠀⠀⠠⠊⠢⠘⡤⠚⡦⠐⢀⠀⠀⠀⠀⠀⣠⢣⡿⣤⡇
⠀⠀⠀⣲⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠰⡄⠀⠀⠀⠀⢶⡌⣾⣄⡠⠊⠀⠆⠀⢀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠈⠂⠉⠀⠀⠀⢴⣿⡇⣄⢹⣍⡁
⠀⠀⠠⡍⠀⠀⠀⠐⠉⠭⠉⠉⠠⠀⠀⠐⠚⠁⠐⠀⠀⡠⠖⠙⣄⣀⠀⢨⡖⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠐⠖⠋⢳⣝⣠⡏⢳
⠀⠀⡥⠁⠀⢪⣦⠈⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠂⠀⠐⡆⢀⠞⠁⣠⠀⠈⠃⠖⠀⠀⢀⣔⡛⢖⠀⠀⠀⠀⠂⠈⠀⠀⠀⠇⠀⠀⠲⠞⣿⣷⣧⠠⠙
⠀⢠⡣⠀⠀⠈⢁⠀⠀⠀⣤⠀⠁⠀⠀⠂⠀⠀⠀⠀⢠⡄⠋⠀⢠⡌⢢⡀⠰⠞⠀⠀⠈⠄⠁⠀⠀⠀⠰⠷⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⢻⠘
⠀⢀⢇⠀⠀⠀⠐⠤⠤⠀⠁⠀⠀⠀⢀⠀⠀⠰⢖⠹⣠⡞⣡⡀⣿⠃⠈⣳⠀⠀⠀⠀⠓⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⡀⢤
⠀⢘⡋⠀⢒⣶⡄⠀⠀⠀⠀⢀⠋⠁⠘⠦⠄⠈⡎⠰⠉⠋⢀⣼⢿⡄⢆⡋⠀⠀⠀⠀⢀⡀⠀⡞⣷⠀⠀⠀⠀⠀⠤⠀⢂⠀⠈⠀⠐⠈⢁⠈⠰⠆
⠀⠘⠃⠀⣨⠙⠀⡀⠀⠀⠀⠤⠀⠀⠃⢐⠀⠀⠹⣄⠀⢱⡞⡱⠃⢛⡼⠁⠀⣖⠲⣤⣎⡝⠀⠀⢿⠁⣀⠀⠀⠒⣀⣀⢈⠠⠀⠀⣀⠀⠈⠅⠧
⠀⢴⣶⡖⠻⣶⢤⣀⡀⠀⠀⠑⠧⠄⠁⠈⠀⢀⠀⠙⢦⣟⠂⡠⠰⠞⠁⠀⠀⠉⠜⡻⢿⠴⠂⠀⠀⠀⠈⢀⠀⠀⠀⠙⠛⠓⠉⣀⣻⡴⠆
⠀⠀⠉⠁⠀⠰⠟⠋⠀⠀⠀⠠⢐⡠⠤⢴⠆⠁⠀⠀⠀⠙⠠⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⢿⠇⠀⢀⡴⠋⠉⠉⢹⡆
⡀⠀⠀⠀⢀⡆⠖⠀⣀⠀⠶⠒⣈⡩⠤⠾⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠘⠁⠀⠀⠀⢸⡇⠀⠀⣀⡼⠁⢠⣄
⠸⡓⡄⢰⡟⠁⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠈⠄⠀⠀⡀⠀⠀⠀⠄⠀⡠⠀⠀⠀⠰⠯⣈⡁⠀⢾⠇⠀⠀⠀⢀⣴⠶⢾⣷⠶⠛⠉⠀⠀⠃⢻⡄
⢰⣷⣼⡀⣤⠖⠀⠀⠀⠂⣁⢐⠠⠌⠀⠡⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠉⢰⡞⠀⠀⠀⠀⣾⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⠃
⠈⠻⢾⡞⠉⠈⠀⠀⠀⠄⠀⠂⡀⠁⡀⠁⡀⠀⠀⠀⠀⠀⠒⢤⣠⠔⠉⠂⠀⠀⠀⠀⠄⠀⢌⠁⠀⠀⢀⣤⣼⣷⠶⠛⠁⠀⣀⣌⣳⢀⣀⡀
⠀⠀⠀⠃⠀⠀⠀⠰⠄⠐⠤⠁⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⡄⡀⡄⠀⠀⣀⠒⠂⠰⠀⡄⠙⣀⠀⠀⠀⡟⠀⠀⣹⠆⠀⠀⣄⢹⡿⠟⠛⠉⢿⣆⡀
⠀⠀⢠⡄⠀⢤⠀⠐⢀⡀⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠀⢀⠀⠰⣄⠀⠀⠢⢐⣂⠀⠀⠀⣀⣧⡤⠖⠋⠀⡀⠀⠈⠁⡶⠀⠀⠀⠀⣩⠃
⠀⠀⢹⡏⠀⠈⣦⠀⠀⠁⠀⡤⠄⠀⣀⡠⡶⠶⠒⠒⠂⠻⠛⠀⠀⠀⠀⢀⣠⣤⣴⣤⣄⠀⠀⠀⣾⣩⡟⠀⠀⠀⡄⣿⠀⠀⠀⠳⣴⡆⠠⠴⠷
⠀⠀⠈⠁⠀⠀⠈⠢⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠒⠚⠛⠛⠛⠉⠉⠀⠀⠠⠴⠟⠉⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠉⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⢀⡥⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠘⠃⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠺⠛⠛⠋⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠀⠀⠀⠀⠀⡐⠈⠐⡀⠀⠀⠠⣿⣛⣷⠀⠀⠀⢰⣍⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢱
⠀⠀⠀⠄⠀⠀⠀⠀⠠⢀⠠⠀⠀⠀⠀⢹⣿⠿⠀⠀⠀⠈⣻⣿⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠓⠤⠚⣄

⠀⠀⢰⣦⡀⠀⠀⠀⡤⠶⢤⡄⠀⠀⠀⢀⣤⡀⠀⠀⠀⢠⣶⣶⣦⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⡇⠀⠀⠘⣇⠀⣠⡗⠀⠀⠀⠹⣿⠃⠀⠀⠀⢸⣿⣀⣿⠀⠀⠀⢷⠀⢀⡾⠀⠀⢀⡁⠀⠀⢁
⠀⠀⠈⠃⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠉⠉⠉⠉
⠀⠀⣀⢀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠚⠀⠀⢑⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠠⡄⠀⠀⠀⠠⠅⠀⠀⡇
⠀⠘⠢⠤⠊⠀⠀⠀⠻⠿⠿⠇⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠽⠿⠋⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠑⠰⠐⠁

⠀⣞⢑⣄⠀⠀⠀⠀⣾⣿⣷⡀⠀⠀⢠⡟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠓⠄
⠀⢸⡻⠧⠕⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⢻⣿⠿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⠀⠀⠀⠀⢠⢶⢦⠀⠀⠀⠀⣴⠶⣦⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⣠⣴⣤⣄
⠀⠀⠀⡄⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⢿⣿⣿⠂⠀⠀⠘⢯⣽⣿⠀⠀⠀⢷⡘⠏⣼⠁⠀⠘⢿⡛⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠶⠞⢿⡿⠳⠶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⠒⠺⠤⠤⠤⢤⣤⣤⡷⠖⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚
⠀⠀⠀⠀⠀⠀⠀⣶⡂⠀⠀⠀⠀⠀⣿⣿⢀⣀⣀⣀⣤⡄⣠⣤⣄⡀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣺⣷⣿⣿⣿⣿⣛⣿⣷⣿⣿
⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠘⠺⠿⠛⠿⠏⠻⠿⠟⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⠂⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢿⠻⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠰⣆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠨⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡱⠀⠀⠀⠀⠰

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⡆⠀⡀⠒⢋⡤⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠬⠀⡈⠃⠈⠀⠄⠀⠀⣈⣦⣎⣀⠀⠃⠜⠃⠂⠀⠀⡀⠼⡑⢀⢥
⠀⠀⠀⠷⠶⠀⠀⠀⠀⠀⠠⠀⡂⠀⠀⠀⠁⠀⠘⠀⠐⢨⡃⡙⠀⠁⢂⡐⠀⠀⠉⠀⠀⢉⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠑⠄⠅⢠⡷⠆⠡⠄⡼
⠀⠀⠐⠂⡲⠀⠀⠀⠤⡄⠀⠀⠉⠀⠐⠀⠈⠁⠀⠀⠀⠠⣄⠨⣀⠀⠀⢀⢠⢠⠀⢠⡄⠘⠁⠀⠄⠀⠠⠄⠠⣀⢠⠃⠉⡄⢠⠀⠉⠑⠒⠊⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠑⣂⠄⡠⡀⠀⠀⠘⢀⡀⠀⠀⠀⠀⡁⠐⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠈⠀⠀⠀⠀⢀⢀⠃⠘⡄⡀⠁⣀⣄⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠠⢊⣴⢀⠀⠐⠤⠀⠐⠀⠀⠀⠐⠀⠀⠐⠉⣉⣀⠠⠤⠊⠀⠀⠀⠂⠀⠀⠀⠋⠉⣦⠀⠀⠁⠈⠀⠘⢀⡀⠙⢷⡄⠸⡉⡱
⠀⠀⠀⣸⠀⠆⠰⠀⣤⠀⠀⢩⡬⠀⠀⠀⡴⠶⡀⢠⣤⡄⣠⡀⠀⣄⣤⠀⡄⠊⡀⠠⠀⠀⢠⠀⠀⣐⣒⣒⣳⣖⣲⡀⠀⡘⠒⠀⠂⡀⠈⠁⠀⠈⠄
⠀⠀⠀⠉⡓⠰⠂⠔⠛⠀⠀⠀⠀⠈⠀⠤⢉⠈⠀⠰⣄⠟⣩⠁⢀⡀⢀⠐⡄⢰⡆⠍⠆⠈⠀⠁⠀⠅⠦⠶⠴⠦⠀⠨⠀⠈⢁⠈⠈⢉⠁⠠⠖⠂
⠀⠀⣁⡀⠚⠃⠚⠧⠀⠀⡀⠤⠀⠀⠀⡫⠚⠀⢴⣀⠈⠉⠁⠐⢦⠁⠡⡄⠀⡸⠀⡀⠀⢁⠀⢀⠐⠀⠀⠀⠀⣠⣄⣶⡀⠀⠀⠀⡊⠒⠈⠦⠤⠀⠂
⠀⡜⠉⠙⡄⠸⠀⠂⠀⠀⠰⠀⠀⢀⠀⠙⠇⠀⠣⡠⠃⠈⠠⠄⠚⠈⠃⢀⣈⠀⠀⠀⠀⠀⢀⠘⡀⠀⢼⡧⠼⠛⢃⡍⠀⠂⠈⡓⠥⢿⠀⠔⠀⠀⠆
⠀⢧⠒⢀⠇⠀⠀⠀⢀⡄⠀⠀⠀⠐⠛⠀⠰⡦⠀⠀⠀⠀⢠⡄⠀⠁⠀⢨⢬⠀⠸⠕⠀⢠⣄⠀⢀⣤⡄⢀⡤⠒⠁⠤⠄⠀⠐⠝⠁⠐⡷⠀⠈⡀⢀
⠀⠀⢉⡁⠀⠀⠀⠳⡄⠀⠀⠀⠊⠉⠉⠁⠀⠐⣠⠀⢠⠀⠀⡕⠀⠐⡀⠐⠀⠀⠈⠰⠂⢈⣃⡀⠈⠒⢀⠈⠀⠀⠒⠀⠂⠐⣿⡆⣒⠐⠀⠊⠙⠛⠈
⠀⠀⣜⣗⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠈⠋⠠⠀⢀⡠⢄⢨⠃⠀⢰⠁⠀⢸⠀⢴⠱⠨⠈⡄⠠⠀⠉⠀⢻⠂⠈⠁⠀⠀⠐⢃⠂
⠀⠀⠛⠉⠀⣀⠀⠀⢀⠀⠀⠀⢀⣀⡀⠀⢀⠆⠈⠀⠁⠀⢀⢠⣤⣄⣀⠄⠀⠀⠀⠀⢀⠑⠐⠣⠀⠁⣊⡐⡁⠊⠀⣰⠀⠀⠸⠀⠀⠀⡐⢀
⢀⣐⢒⠔⠆⡀⠀⠘⠈⠀⠀⠛⢹⠂⠁⠰⣃⡐⠀⠁⠀⠐⠉⠼⠞⠛⡙⠆⠀⠁⢀⣀⠀⠐⠀⠀⠂⣤⡀⠈⠄⠐⠲⠣⠀⠀⠂⣀⠀⠀⠈⠁
⠀⠀⠘⢡⢀⠉⠀⠀⠐⠀⠀⠀⠘⠀⢠⣀⣌⣀⠀⠀⠀⢀⣀⡀⠀⠁⠀⠁⠀⠂⠈⠷⠂⢀⢰⠄⡘⠗⡧⠘⠤⣃⣐⡠⠄⡈⠨⠤⡅⢅⠀⠀⡀⡀⠐
⠀⠉⡱⠀⠌⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠃⠀⠸⠛⠆⠀⠠⠀⡀⠀⠀⢀⣇⠀⡀⠀⠀⡐⠀⠄⠤⡀⠠⠀⡖⢤⠀⡈⢁⠅⡀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⢸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡄⠸⡿⠃⠀⠀⠀⠀⠀⠀⠉⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠁⢠⣤⡀⠈⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⠸⣿⠏⠀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠤⠀⠀⠀⠀⠀⠀⠀⠐⠆⣴⣿⣆⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠾⢇⣀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡴⠷⠀⠙⠛⢃⣀⠀⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⢀⣀⡠⣾⣧⣀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣶⣤⣾⣿⣿⡁⠛⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣴⣶⣿⠿⠇⠸⣿⠟⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣀⢉⣿⣟⢁⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⡿⠋⠁⢀⣤⠀⢿⠗⠀⠘⠻⠋⠀⠀⠛⠀⠀⣀⡀⠀⢀⡀⠀⠸⢿⠿⠋⠻⠋⠿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣾⣿⡟⠀⠘⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠉⠉⠀⠀⠀⠺⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠹⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣶⣶⡿⠿⠟
⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢿⣛⣫⣭⣷⠶⠛⠁
⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠛⠛⠛⠋⠉⠁
⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣤⣤⡄⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡤⠟⠉⠉⠁⠓⠶⠶⠦⠤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠂
⠀⢸⣿⣿⣿⣿⡿⠋⠁⠀⠈⠉⠻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂⢠⠆
⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⣿⣿⣷⣄⡀⠀⠀⣀⣴⣿⣿⡇⠀⠈⠋⠉⠉⠉⠉⠉⠉⠋⠙⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠢⠤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠉⠉⠉⢉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢀⡴⠋⢀⣀⡠⣤⡤⠤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠈⠉⠳⢄⡀⠰⠃⠀⠀⠀⠀⢠⢋⡤⠚⠉⠁⠀⠀⠀⢀⡠⠤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢀⠴⠊⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠉⠁⠀⠈⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠤⣀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠐⠒⠒⠒⠀⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠘⠻⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣈⢁⣠⠤⣄⠀⠀⠀⠀⠀⡸⠃⠀⡤⠤⠚⠙⢦⠀⠀⠀⠀⠀⢠⠎⠘⠂⢤⡀⠀⠸⡄⠀⠀⠀⠙⢏⡉⠑⢦⣇
⡀⡄⠀⠀⠈⠀⠀⠀⢔⡢⠀⠀⠛⠁⡠⠖⠉⠀⠀⠀⠀⣴⠁⣠⠊⠀⣀⣄⣤⣈⠇⠀⠀⠀⠀⣏⣠⣠⣄⡀⠙⢆⠀⡁⠀⠀⠀⠀⠀⠙⢄⠀⠉
⠙⠃⠀⠀⣎⢹⠆⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⡆⣼⡵⢊⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡙⠦⣥⢹⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⣤⠁⠀⠆⠀⠀⠀⠀⠘⢇⣀⣀⠞⠑⢦⡀⢰⠃⠀⢰⡁⢠⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣶⡄⢈⠆⠀⠈⣆⠀⡠⠊⢳⡤⠀⠼
⠀⠀⢀⠖⠉⠈⠉⠐⢢⠀⠀⠀⠀⠀⠀⢨⠀⢤⣀⡿⠚⠀⠀⠀⠉⠉⠉⡵⠊⠉⠑⣤⠤⣤⠖⠉⠉⢲⡉⠉⠁⠀⠀⠀⠀⢹⣠⠖⢸⡇
⠀⠀⡠⢿⣏⣿⠛⣻⢧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢱⠦⡴⠖⠃⠀⠈⠓⠦⡴⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣟⠢⠤⣿⡔⠁⠀⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢈⡻⣆⠀⠀⠀⠀⠀⢠⣷⡁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸
⠀⠀⣯⣉⣈⣿⡍⢻⠀⣇⠀⠀⠀⠀⠀⠀⢧⡀⢀⣸⡄⠀⠀⠀⢀⡴⠊⠁⡤⠊⢑⠖⠒⠶⠊⠓⠄⠀⠉⠒⢄⠀⠀⠀⠀⠟⠢⠴⠋
⠀⠀⢹⡦⠿⠤⠴⠦⢧⠈⠻⡦⣀⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡎⠀⣀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣄⡀⠀⢈⡇⠀⠀⡜
⠀⣰⠃⠀⠀⠀⠀⠀⠀⢣⠀⠇⠀⠉⠓⠲⠶⠤⠤⠤⠤⢷⡀⠈⠓⠋⠘⠤⠞⢭⣷⡔⠉⠒⣋⣩⡟⠃⠈⠉⠁⠀⠀⡼⠁
⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⢀⠾⡀
⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⣤⢉⡒⠤⣀⣀⣀⣀⣀⣀⣀⡤⠔⣊⣤⠒⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠳⠦⠠⠤⠄⠤⠤⠠⠴⠖⠒⠒⠊⠉⠁⠙⡀⠁⠀⠀⠈⠙⢌⡃⠸⠁⠀⣸⠅⢻⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⠦⣀⠀⠈⢻⠇⢀⠞⠁⠀⡈⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠑⢄⠀⣆⠇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠱⡿⠀⠀⠀⢀⠜⠓⢤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⣏⠀⠀⠀⠙⡄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠒⠛⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠲⢶⡛⢽⣆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⠒⠒⠶⠶⠶⠒⠲⡏⠈⠙⠉⠁⢹⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠋⡆⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠇⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠀⡰⠀⢠⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⢳⢠⠋⠀⠀⠀⢱⠄

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣤⣿⣦⣤⣤⡀⣠⠞⠉⠀⠀⠀⠀⠀⣀⡴⠖⡛⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠷⠶⠶⣄
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡴⢋⣴⡿⡿⣹⣿⢝⣿⢽⣦⡀⠀⠀⠀⠀⠀⢠⡟⠋⡀⠀⠀⢀⡀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⣾⣿⠡⠏⣿⠩⣷⣾⢸⡏⢹⣿⡆⠀⠀⠀⠀⠈⢠⣿⣿⣿⣾⢿⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⡏⠈⡯⢀⣿⡀⣧⡇⣻⠾⡇⠀⢆⡀
⠀⠀⢠⣤⣴⣿⣿⠓⢳⡞⡲⡿⠛⣺⠛⣻⣿⣷⠀⠀⠀⠀⡆⣿⣿⢳⣿⣿⣼⣿⣿⣷⣿⣿⣿⣿⡇⠀⠈⢺⡇⠀⢀⠈⡀⢁⠁⠛⠈⢀⠃⠀⣱
⠀⠀⠀⠀⠀⣿⣿⢀⣽⠀⠋⡆⠨⠿⠀⢿⣿⡟⠒⠛⠀⠀⢿⣿⣿⣸⣟⡭⣿⡫⣝⣟⠅⢿⣿⣿⠇⠀⠀⢾⣇⠀⠰⠀⢆⠸⠂⠡⠀⠻⠀⣀⠟
⠀⠀⠀⠀⠀⠙⠛⢾⣿⣿⣿⣿⣶⣿⣶⣾⠟⠃⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡟⠁⠀⠀⠀⠀⠹⢧⡀⠀⠀⠀⠂⠐⠁⠘⣠⣯
⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⢿⡿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣏⣻⡽⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣦⠴⣦⡴⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣤⣴⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣚⣛⣻⣿⣿⣿⣿⡿⣭⣭⣭⣥⡄
⠀⠀⠀⠀⠀⠀⣀⡼⠻⢿⣿⢿⡿⠻⠿⣥⠀⠀⠀⠀⠀⠀⣦⣿⠋⣩⣿⣿⣿⣿⣿⣿⣿⡿⣷⡇⡀⠀⠀⢛⡛⢋⣙⠛⣛⡛⠛⡛⢛⠛⠛⢛⣋
⠀⠀⠀⠀⢰⣶⡿⢀⣁⣚⢿⡘⡇⣿⣷⢸⣧⡀⠀⠀⠀⢸⣿⣿⣆⢉⣽⡧⠎⣿⠰⢙⠟⡁⣿⣟⡀⠀⠰⣇⣈⠿⠴⡹⣀⣠⡼⠳⣼⢢⡿⢏⣀
⠀⠀⠀⠀⢀⣿⣧⣛⣛⣋⣼⡇⣿⣬⣥⣿⣿⡇⠀⠀⠀⠈⣻⣿⣿⣦⡿⢿⣾⣿⣿⣿⣷⣴⣿⡿⡇⠀⠀⠀⣀⢰⡆⢰⠶⡄⡴⢲⢠⡶⡄⣠
⠀⠀⠀⠀⠀⠹⣿⡏⢟⡻⡿⡻⣇⠊⣱⣿⣿⠁⠀⠀⠀⠀⢻⣿⡿⣿⢘⣻⡿⣻⡏⡍⣿⣿⣿⡿⠀⠀⠀⢠⣤⣬⣤⣬⣭⣥⣩⣍⣌⣉⠅
⠀⠀⠀⠀⠀⠀⣿⣇⣜⣣⣇⢟⣿⢃⡁⣿⠏⠁⠀⠀⠀⠀⠀⠛⣻⣿⣝⣿⣧⣭⣿⣾⣿⡿⠟⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠟⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠿⠿⠏⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠰⠦⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠶⣶⣥⣷⣴⢇⣂
⠀⠀⠀⠀⠀⣠⡀⠉⣤⣤⡀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⣐⡾⠛⢉⠭⢠⠀⢨⡝⢿⡤⠀⠀⠀⠀⠀⣰⣾⣷⣤⣾⣿⣤⣿⣾⣿⣷⣇⡀
⠀⠀⠀⠀⢰⣿⠁⠀⣿⣭⢀⡴⠦⢀⡴⣄⠀⣻⣽⡄⠀⠀⢠⡿⢠⢸⢸⠄⠆⣀⢸⣅⣤⡙⣆⡀⠀⠀⢸⣿⡿⣿⣿⠿⣿⢿⡿⣿⣿⣯⣿⣷⡄
⠀⠀⠀⠀⢮⡿⠀⠀⣿⣶⠜⢧⡤⠸⢧⠾⠀⠹⡷⠶⠀⠀⢾⠁⠸⠎⠸⡄⠸⡼⠛⠳⡙⠇⢸⡅⠀⠀⣿⢛⣧⣶⣿⣥⣾⣮⣷⣿⣿⣿⣏⣹⣷
⠀⠀⠀⠀⣷⣶⠀⠰⣦⡖⢦⡴⠲⡴⢶⡆⠀⣤⣗⡆⠀⠀⢾⡀⠀⢖⡂⠐⠙⣦⡎⢧⢙⡇⣼⡉⠀⠀⣽⣿⣿⣗⣪⣾⣩⣧⣻⣼⣹⣟⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣆⠀⠏⠳⠞⠑⠾⠁⠟⠒⢠⣶⡾⠁⠀⠀⠙⢿⣄⠸⠀⠸⡀⡿⢧⡞⢈⡼⢇⠁⠀⠀⠘⠿⣿⣿⣿⣟⣹⣿⣏⣿⡟⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠛⢥⢄⣀⣀⡀⣀⣀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠛⣿⣶⣦⣭⣥⣤⣴⠟⠇⠀⠀⠀⠀⠀⠀⠉⢼⡿⣿⣿⣧⣽⣽⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠺⢠⣾⡁⠀⠀⠴⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⢻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⢰⠄⠐⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢠⠃⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣉⡀⠋⠉⣵⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠷⠄⢒⠲⠖⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⡛⢿⣆⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢰⣷⣛⣨⠿⣿⣿⡋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣀⣀⣸⣿⣭⣷⣦⡈⣩⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣶⣿⣿⣿⣿⣿⣷⣶⣃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣟⣿⣿⣿⣿⣿⣿⣇⣿⣨⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠒⠒⠒⠒⠒⠲⠖⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠲⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⣀⢄⣠⣤⣤⣤⠤⠤⢤⡄⠠⢤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣿⣿⠀⠒⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣭⣿⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠲⢿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⣇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠲⡀⠈⡀⢀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⣀⣀⣠⣔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣤⣴⣿⣿⠃⠀⠀⠀⠈⢰⡇⣄⣀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣠⣤⠴⢿⣈⣿⡟⠉⠻⢿⡄⠀⠀⠠⡆⢸⣷⣿⠉⠈⣿⣿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣯⠑⢛⡁⠂⠈⢻⣿⣷⠀⠀⡀⠀⢀⣤⡀⣷⣿⠿⣛⡆⣸⡿⢿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⢿⣿⣧⢠⣿⠀⠀⡿⠀⢉⡟⠀⠏⣸⣿⣄⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢠⠡⠹⠆⠀⠀⠈⠀⠀⠘⢻⣿⣾⣧⠀⠰⢷⡄⠸⠷⠠⠂⢁⣾⣯⡿⠛⠿⠿⠿⢇⣤⣄
⠀⠀⠀⠀⠀⣀⣸⣤⣤⣄⡀⣠⠂⠀⠘⢿⣭⢿⣿⣷⠀⠀⣿⠀⠀⠀⠀⠀⠘⡿⠛⠁⠀⠀⠂⢀⣿⠹⠙⢷⡀
⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠁⠈⣀⠉⢿⣾⣿⣿⡀⠀⡽⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⢀⡴⠻⠁⠀⠀⠀⠁
⠀⠀⠀⠘⢷⠶⠦⠤⠂⠄⠀⠀⢂⣄⡈⠻⣾⣿⣿⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠪
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⣻⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡈⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠰⣶⣬⣁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣷⢆⠄⠀⠀⠀⠀⠀⡐⢋
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣄⠀⠀⢠⣦⣰⣾⣴⢂⡤⠶⠦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣄⣀⣤⣀⣀⣀⣤⡶⠶⠖⠛⠛⠻⣿⣿⣧⣄⡀⠉⠉⠻⣿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⣾⠙⠛⠻⠿⠿⠿⠿⠛⠉⠀⠐⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⡄⠀⣶⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠀⠀⠀⠤⠐⠂⠀⠀⠀⠀⢀⣤⡴⢊⡿⢳⣼⡟⣹⠟⡀⢹⡄⠀⢼⣁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣦⣤⣠⠤⠄⠀⠀⢀⣍⣸⡿⠋⢀⣬⣿⣷⡿⠟⡃⢸⣷⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠟⠉⠀⠀⣶⠋⠋⠀⣠⡾⠃⢸⡟⣆⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠇⠀⠀⠀⡰⠃⠀⠀⡄⠉⠀⠀⣿⠀⠘⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣼⠁⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠂⢀⡄⢀⠀⠒⢞⣠⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠤⣉⠀⠀⠚⠀⠁⢈⠀⠀⠀⣓⣴⣊⣀⠀⠪⠼⠧⠘⠀⠀⠀⣀⠜⡇⢈⡅
⠀⠀⠀⠶⠴⠆⠀⠀⡀⢄⠀⢀⠈⡆⠁⠀⠈⠃⠀⠚⠇⠐⠄⡖⠀⢫⠔⠂⡔⠲⠀⠀⠘⠀⠀⠁⠀⠀⠀⠋⠉⠀⠁⢁⣀⡒⠀⠒⡄⣰⠀⣾⢤⢌⢠⠀⡝⠀⠁
⠀⠀⠠⠄⢠⡀⠀⢄⣀⣄⠀⠀⠀⠒⠀⠠⠂⠀⠒⠂⡀⠀⠀⢉⠉⡀⠀⠀⠀⠀⢀⢀⠀⠀⣠⠀⠗⠅⠀⠀⠀⢄⠀⣀⠀⢀⠆⠘⢀⢀⠀⠉⠒⠦⠴⠛⠁⠠⠁
⠀⠀⡄⠀⠉⠁⠀⠀⠐⠭⢁⡀⣀⠀⢀⠄⠰⠀⠀⠀⠁⠀⠊⠝⠉⡄⠩⠀⠀⠉⠀⠘⠀⠀⠛⠀⢶⠆⠀⠀⠀⠀⠀⠈⠉⠉⠤⠠⡎⠀⠑⠀⢀⠀⠀⠐⣈⡀
⠀⠀⠀⠀⠁⠀⠀⠈⠀⡐⡩⠔⣱⠂⠀⠢⠀⠌⠁⠈⠐⠀⣀⢀⠁⠀⣠⠚⡗⠀⠀⣀⡠⠂⠠⠀⣀⠀⢀⠀⠠⠤⠤⣀⠒⠘⠄⠀⠎⠈⠄⠈⠹⣷⡄⠀⣳⠓⢆
⠀⠌⠃⢀⡂⢀⠂⡀⠐⡀⠂⠙⠏⠰⡀⠀⠈⢀⣄⡀⠀⠀⣀⠀⠀⠀⠀⢈⡛⠓⢂⡠⠄⠀⠀⠀⠀⠀⠐⠀⣨⣄⣤⣯⣤⣤⡀⠀⢰⣠⡀⢒⠐⠈⠿⠁⠘⠒⠋
⠀⠀⠀⠸⢥⠉⣀⠉⣨⡇⡀⠀⠺⣋⠤⠀⠀⠫⠭⠇⠀⡛⢻⡴⠷⠆⠀⠓⠋⠀⠃⢤⡜⠨⠀⠘⢎⡱⠀⠰⢓⣒⣚⢛⡛⠚⠣⠀⠳⠤⠀⠄⠴⠤⠀⠀⣀⠀⠑
⠀⠀⢘⠀⢢⣼⢑⣬⠀⠀⠀⠀⠈⠀⠀⠐⣯⢰⠄⠀⡀⠙⠬⡥⠞⢀⠰⢄⡄⠀⠇⢘⡇⠀⠁⠠⠀⠀⠀⠈⢈⠉⠉⠉⠉⠁⠈⠀⢀⡔⠒⢀⣄⠀⠄⠁⠁⠀⡀
⠀⢀⠤⢤⡉⠁⡄⠉⠉⠀⢡⠎⠋⠀⠀⠀⢴⣁⠀⢹⠓⢦⠀⡤⠀⠈⣡⢀⡙⠂⢀⠜⠀⠀⠀⠀⠄⠀⡄⢁⠀⣠⡄⢨⣶⡶⣿⠆⡀⠀⣄⠠⢠⡀⠈⠉⣒⠀⠁
⠀⡎⠔⠀⢣⠀⠃⠀⠀⠀⠈⠛⠀⠀⢰⣈⠀⠋⡀⠘⠒⠊⠀⠀⠛⠀⢀⡀⠁⢠⢤⠀⠀⡀⠐⠀⠀⠄⡥⠊⠀⠿⠒⠚⢋⡡⠖⠂⠙⠀⢠⣁⠑⢃⠈⠁⣀⠀⠁
⠀⠳⣈⣡⠎⠀⠀⢀⠀⠱⠀⠀⠀⢀⣈⣉⣀⠀⢏⠄⠀⠈⠁⠀⢴⠄⠁⠀⠀⠰⠶⠀⡀⡟⠃⠰⣶⡄⠈⡔⢾⠀⡴⠚⠉⠀⠖⠂⠀⢈⡹⠁⠀⠙⠗⣀⣠⡀⣀
⠀⠀⢀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠸⠡⠄⠀⠀⠀⠈⠪⠄⠐⡆⠀⢠⡀⠀⢸⠀⠘⠀⠀⡀⠈⠃⢀⠬⢄⡀⠈⢀⡀⣀⠀⠀⠩⠁⣁⣁⣻⡿⣉⡩⠍⠈⠀⠈⡃
⠀⠀⣾⣻⠀⠀⠘⠀⠀⠀⠀⠀⠘⠀⠀⠐⢂⠀⠀⣠⡦⠀⠀⠠⠈⠁⠂⠀⣀⡴⢢⢠⠃⠀⠀⣇⠀⠀⡇⠀⡆⠗⠴⠠⡆⠐⠀⠀⠀⢺⡗⠀⠀⠈⠂⠀⠚⠆⠃
⠀⠀⠘⠉⠀⢠⡀⠈⠈⡁⠀⠀⢀⣀⣄⡀⠀⢀⠴⢀⠃⠈⠀⠀⣀⣦⣤⣄⣠⠄⠀⠀⠂⠀⠠⠈⠙⠛⠆⠈⢀⣪⡐⡑⠃⠀⣰⠆⠀⠘⠃⠀⠀⢀⡛⡄⠀⠀⠄
⠀⣀⠖⡴⡆⣀⠀⠤⠃⠁⠀⠀⠓⢻⠃⠁⢰⢂⡔⠠⠈⠀⠀⠂⠁⠿⠟⠋⠙⠆⠠⠁⢀⣠⠀⠀⠀⠀⠐⢃⢤⡀⢀⠄⠒⠲⠇⠀⠀⠀⢀⠀⠀⠀⠈⢂⠀⢀
⠀⠈⢉⢃⣀⢘⠁⠀⡒⠂⠐⠂⠀⠸⢀⣀⣀⣈⢀⠀⠀⠀⠀⡀⢀⠀⠀⠁⠀⢁⠐⠂⠘⣯⠖⠀⣀⣦⢀⠳⢿⡇⠰⢤⣇⣘⣀⡄⠈⠅⡧⢼⠨⡀⢀⠁⠀⡀
⠀⠊⠳⠌⢀⠃⠀⠀⠐⣈⠀⠀⠀⠂⠀⢀⠉⡉⠀⠀⡲⠀⠀⠽⠿⠀⠢⢀⠀⠀⠀⠀⠀⣇⡀⠎⠀⠀⠀⡇⠠⠄⣤⠀⢨⠅⠤⢀⠈⠂⡓⢚⢐⠁⠀⠈⠗⠃
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠐⠊⠀⠀⠚⠀⠙⠀⠀⠁⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⣻⣤⣤⣼⣍⣀⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⡷⠋⣁⡀⠀⠀⠀⠉⠓⢦⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠟⢀⡎⠁⢳⡀⠀⡤⠴⣄⠀⠙⡦⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣀⣤⢿⣄⣠⠶⠀⠀⠀⠀⠀⠐⠗⢾⠀⠀⠓⠦⠞⠁⠀⠳⠴⠋⠀⢀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣀⡞⠁⠀⣀⠀⠹⣄⣠⡄⠀⠀⠀⠀⣦⠼⢧⡀⠀⠀⠀⣀⣠⠤⡶⠖⠲⣏⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⠀⢸⡉⣳⠀⣇⢈⡁⠀⠀⠀⠀⠀⢀⣴⠛⠒⡖⠋⢹⡤⠐⠿⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⡇⠀⠉⠁⠀⣏⠙⠃⠀⠀⠀⠀⠀⠀⠉⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠾⢧⡏⠀⠀⠀⠀⢹⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠘⢻⡴⠋⠀⢀⣠⣄⠀⠘⡷⠾⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣶⢀⣸⣧⣤⣬⣏⠀⢠⣤
⠀⠀⠀⠀⠀⠙⢳⡏⠀⠀⢰⠋⠀⢸⠃⢀⡧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠛⣧⡴⠛⠉⢀⣀⣀⡀⠈⠙⢯⡀⢀⣀
⠀⠀⠀⠀⠀⢶⠼⢧⡀⠀⠈⠓⠒⠋⣀⠾⣄⡈⠁⠀⠀⠀⠀⠀⠿⢦⡴⠃⠀⠀⠀⢾⠁⠀⠉⡆⠀⠀⢹⡉⠉
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⣶⠒⢲⠋⢹⣄⠘⠁⠀⠀⠀⠀⠀⢰⠦⣼⠁⣠⠖⢦⠀⠈⠙⠛⠋⠁⠀⠀⣸⠧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠺⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⠀⠻⠶⠋⠀⠀⢀⡤⠶⣶⠒⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢘⣆⡀⠀⠀⣠⠖⢙⣦⠀⠛⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢹⡟⠛⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣿⣿⠃⠀⠀⠀⠰⡶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣶⣶⣶⣿⣷⣶⣶⣶⣶⣤⣴⢶⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⢠⡗⣼⠙⢿⡴⣻⡿⣿⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢉⠁⡄⠈⢁⣀⣀⠈⡤⠤⢀⡠⡄⢁⣌⢁⡀⠀⠀⠀⣿⢸⡂⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠈⡇⢻⣧⣿⡿⢿⣿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣶⢻⠉⠸⡟⢃⣴⣤⣄⣬⡌⡟⠉⡈⢢⠀⠀⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⡇⢸⠙⣿⡳⣞⡯⣵⢷⣿⣷⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⡟⢆⠀⡅⠛⠾⠤⣼⡄⢣⡿⠁⢿⡏⠸⢇⠀⣥⠈⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⣿⣿⡄⠀⠀⠀⠀⡗⣿⠀⠹⣇⣨⣹⣟⣻⣿⣿⣿⣦⡀⠀⠀⠀⠙⠿⠋⣳⠙⢶⣤⠙⢠⡀⢾⠙⣤⠛⣤⣶⢈⣘⡆⢸⠗⠟⣡⠀⠠⣿⣿⡀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⠘⠿⣿⢿⣭⢆⠈⢛⠿⣷⡀⠀⠀⠁⣾⠛⣿⣤⡄⡃⠀⠈⠻⢷⣷⢿⠘⢿⡿⢈⣛⣷⣘⡷⢚⣥⠀⠀⣿⣼⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⠘⠂⠱⣎⠹⠿⣷⡄⣲⠈⠻⣄⡀⠰⠋⠲⠉⠝⣛⠷⡒⠰⠃⣰⠃⠾⠴⢤⣤⣿⣛⠿⠿⠆⠈⣆⡄⠀⣿⣹⡃⠀⠀⠀⣿⣿
⣿⣿⡀⠀⠀⠀⠀⡇⣿⠀⠀⢀⣧⠀⠹⣷⡀⢈⡛⢹⣦⣴⣽⣿⠀⣨⡙⠓⢢⠝⠲⡝⣷⣤⣿⣰⣦⣤⣤⡤⣭⣏⠀⠀⠀⠀⣀⣴⠞⡋⢿⣇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⢸⣟⠃⠀⠘⢿⣾⣽⣿⣿⣿⣿⢿⣷⣌⠁⠀⣧⠀⠀⣦⣀⡸⡆⠉⢰⣧⣌⠀⢸⢸⡇⣠⣶⣿⠏⠑⣮⠟⢠⡿⠀⠀⠀⣿⣿
⣿⣿⣧⠀⠀⠀⢰⡷⣿⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⡿⣷⣄⢻⣿⣦⠀⢏⠀⠀⢿⡉⠙⡁⢶⡈⡉⠛⠶⠞⢫⣼⣿⣿⣿⠶⣦⣠⣶⣿⡅⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣩⠹⣿⣿⣷⣿⣿⣷⡈⠠⡁⠺⠃⠀⠻⠈⠉⠁⠀⠀⣴⣿⣿⣿⡿⣿⣶⣹⣿⣿⣿⠃⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⢀⣤⣶⣾⣿⣷⣤⡈⢻⡖⣿⣿⡋⣿⣿⣿⣻⣶⣌⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⠏⣹⣿⣻⣿⠏⣿⢹⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⣰⣿⣿⣿⣏⣿⣿⣿⣿⣮⢿⣿⢞⣿⣿⣿⣿⠿⠿⠿⣦⡀⠀⠀⠀⠀⠀⠀⣼⠿⣡⡾⠂⣩⣿⣿⠏⠀⣿⣸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⣿⣻⣿⣯⡿⢿⣟⣷⣝⣧⠛⡿⣿⣿⣶⣿⣿⠿⢋⣱⣾⢻⣦⡀⢀⡀⣀⣾⣿⠶⣟⠻⡁⠈⣹⠏⠀⠀⣿⢰⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⣻⣿⣭⣻⣾⣧⠛⣴⣿⡿⢿⣶⣿⣹⣿⣍⠀⣤⠋⣼⣿⣧⣼⡾⣿⣿⣟⣴⡟⢀⡄⠀⡄⣰⡟⠀⠀⠀⣿⢸⡆⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⢠⣾⣿⣿⣿⡟⣿⣿⣷⣿⣷⣴⡿⠿⢿⣿⣿⣿⣿⡀⣠⣾⡿⣣⣾⢟⡋⣼⡿⠋⢀⣿⠀⠚⡁⣿⠃⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣷⣿⣾⣷⣫⣿⣉⡼⣻⣯⣿⣿⣿⣿⣾⣧⣿⠉⠉⠉⢿⣾⣿⡏⣠⡿⣱⣿⣿⡟⠀⢀⣾⣏⣠⣿⠆⣿⡀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣏⣿⣿⣿⣿⢁⠋⣴⣛⣿⣿⣷⣿⣻⣿⣟⢿⡄⠀⠄⠀⣿⡇⢰⣿⣷⣿⣿⡏⢙⡀⣰⡟⢻⣿⠭⣷⣿⣇⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⣷⠈⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣯⡹⣷⣟⣷⣶⣿⣿⠀⣻⣿⣿⣿⠛⣰⣎⠡⣿⢷⡈⡏⠀⢀⣿⣿⡄⠀⠀⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⠛⠛⣯⣵⣛⣿⣿⡿⠿⢿⣷⣟⣵⣻⡇⠀⢣⣼⣧⣿⡀⠋⠀⣣⣼⡏⣿⣇⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⡟⢿⣥⣽⣷⣖⣫⡭⠛⣿⣿⣷⣶⣿⣅⣿⣿⡟⠄⠀⠀⠈⢿⣿⣿⠁⣻⣾⡥⠿⠻⠄⣀⠼⣻⡟⢱⣿⣿⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠸⣿⣻⢤⣿⣾⣿⡻⢿⣴⣏⣏⣿⣿⣿⣟⣻⣷⣾⣷⣦⣤⣤⡶⢸⣿⠻⡾⠣⡼⠀⣂⣠⣶⠟⣴⢋⣴⡇⣿⣿⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣵⣾⣛⣿⣿⣿⡿⢿⣏⠹⣯⠀⡈⢉⣿⡟⠓⢸⣿⡄⠀⠂⠐⢚⠋⠙⠁⠰⣷⣋⣽⣧⣿⣾⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡟⣿⠛⣯⢿⣿⡿⠻⠻⠿⣿⣿⣷⣾⣿⣷⣿⣿⣿⠟⣱⠃⣴⠀⠛⣿⣦⣽⣶⣩⣅⣠⠄⠒⣛⣿⠿⣛⣼⣿⣆⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣧⠀⠀⠀⠀⡟⣿⠀⠙⠿⣿⣿⠀⢂⠰⢀⡻⣿⣿⠟⠉⣿⢻⣿⠀⠉⠀⠹⠀⢀⠸⣿⣿⣿⣩⣾⣛⣶⣛⣫⣿⣶⢛⣿⣿⣿⣷⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠙⠻⣴⣿⣲⣞⢣⣿⣟⣿⡇⣻⢁⣿⠆⡀⠀⡀⡇⢨⣷⣎⣻⢟⣹⡿⠛⢿⣟⣿⣧⣼⣿⣿⣿⣿⣛⣿⢾⡆⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⠙⠻⣿⡞⠹⣿⣿⣿⣿⣿⡿⠸⡇⠄⡙⢿⣷⣿⣻⣿⣿⢋⣷⠏⡀⢟⣻⣿⣿⣿⣿⣏⢾⣿⣿⢘⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣽⣿⣿⣟⣿⣇⠀⣷⣄⣈⣿⣿⠇⣿⣿⣤⣿⣿⣤⣿⣾⣿⣿⡿⣿⣿⣽⣦⣿⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠛⠀⢀⡀⠀⣀⣀⠀⠀⣀⡹⢿⣿⣭⣿⣦⣸⣿⣿⣽⣿⢺⡿⢣⣿⢃⣨⣿⣿⣿⣿⣿⣶⠉⣾⣿⣿⣿⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠠⠆⡰⣯⡿⠀⣻⣯⠛⢛⣿⠸⠾⠋⠤⠀⠙⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡝⢻⣿⣽⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣷⣿⠀⣙⣛⣀⠙⣯⣁⠈⣀⡈⣁⣿⣚⡃⠀⠀⠀⠀⠀⠛⣿⣏⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⢻⣇⡸⣿⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠉⠙⣿⣤⣯⣈⡿⣿⠿⠟⣣⣿⠱⠆⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣿⢟⣷⣿⣏⣿⣟⡽⣧⣀⣄⢻⣿⣷⠘⣿⣸⡀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⢀⣿⣿⠀⠀⠘⠋⠀⠈⠉⠀⠘⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣻⣾⣿⣷⣹⣾⢻⣼⢿⣿⡜⣿⣿⣿⣿⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢉⣿⣧⡝⢿⣻⣾⣷⣟⣿⣿⣿⣿⣿⢸⠀⠀⠀⢠⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣿⣾⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣼⣿⣹⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣿⣿⣿⣿⣷⣿⢿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡻⣿⣿⣸⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⣥⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣄⣀⣀⣀⣤⣤⣤⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣭⡿⣿⠀⠀⠀⠸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠿⠶⠿⠤⠶⠿⠷⠶⠶⠿⠿⠿⠿⠶⠶⠶⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠾⠷⠾⠿⠶⠶⠶⠿⠀⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣤⠀⠀⠀⠀⠀⢸⡇⣿⠀⣤⢠⡀⢀⡿⢾⠉⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠘⢷⣾⣿⣽⣯⣽⣭⣿⡏⠀⠀⠀⠀⣨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀⠀⠀⢀⣴⠞⠉⡥⠶⠶⠶⠶⢮⣽⡢⣄⠀⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡳⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣏⣀⡀⠀⡀⠀⠀⠀⡀⠀⡀⠀⣶⣿⣷⣻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⢛⣅⣛⡣⠼⣿⣧⢳⣤⡇⡇⣿⣧⠿⣋⣭⣤⣍⡻⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⢩⡿⡰⠋⠉⠛⠻⢷⣮⣙⢾⣾⣷⡿⣋⣵⠞⠋⠁⠈⠙⠿⣮⣻⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠠⢤⣿⠉⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈⢻⣦⢹⡏⠘⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠙⢻⡄
⠀⠀⠀⠀⠀⠀⠤⣾⠇⠀⠀⢰⡏⠀⣆⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⢹⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠠⢴⡟⠀⠀⠀⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡄⡅⠀⢀⠀⠘⡇⠀⠀⠀⠀⢸⣿⣸⠀⠀⢹⣦
⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⡆⠀⠀⠀⠀⠘⣗⡇⠀⢸⡆⣦⡇⠀⠀⠀⠀⣸⣿⣿⠀⠀⠘⣧
⠀⠀⠀⠐⠋⢽⠁⠀⠀⠀⢀⣿⣷⡇⠀⣿⠀⢧⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⢻⣷⠀⢀⡆⠀⣿⣿⣿⠀⠀⠀⢹⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⡇⠀⢸⡇⢸⡀⠀⡄⠀⡀⢸⡇⡆⠀⡇⢸⡏⡇⢸⣷⡜⢸⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣿⢷⠰⡄⢻⡄⣇⠀⣧⠀⣷⢸⡇⣇⢰⡇⢸⢡⡇⡾⣻⠃⣿⣿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢸⣾⡄⢳⡀⢳⣸⡄⢸⡆⢸⡈⣷⣿⢸⡇⡿⢸⣳⢣⣇⣼⣿⠇⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢻⣷⡀⢳⡈⢷⣷⠈⣷⠘⡇⣿⣿⣸⣷⣇⣿⡏⣞⣾⣿⠏⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠻⣷⣼⣷⡄⢻⣧⠸⣇⢷⣿⣿⣿⣿⣿⣿⣽⣟⣿⠋⠀⠀⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠀⠀⠘⢿⣿⣿⣦⣿⣧⡞⣾⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⢠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠙⠿⣿⣿⣿⣇⣿⣿⣿⣟⣿⡿⠟⠁⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⠀⠀⠀⠀⠈⠙⠛⠛⠓⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠖⣁⢌⡄⡀⡀⣠⣶⡤⣐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠃⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⢻⡍⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢋⠠⢻⠀⠀⠀⠘⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸
⣦⡀⠂⠀⠀⠀⠐⠀⣀⣀⣐⣁⣀⡀⢀⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠁⠌⠁⠀⠀⠀⠆⣼⡟⢉⣉⠙⠿⣟⠋⠀⠈⠹⣈⠄⠀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢠⠙⠛⠛⠛⠻⢷⡁⠐⢈⣧⡀
⠀⡀⠀⠀⠀⠀⣸⠋⢳⢐⠁⠀⢀⠸⢦⣀⣾⣬⡾⣽⣶⡈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⢁⢧⠀⠀⠀⠀⠀⠣⣴⣿⣍⠛⣷⣤⡀
⠀⣦⡶⢦⡢⢂⢻⣄⡘⠠⠄⠀⠀⠀⠀⠁⠈⠉⢉⠡⢸⡇⡀⠀⠀⠀⠀⢸⠀⢀⠔⣄⠀⠀⠐⢌⣾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢨⡇
⠄⢟⠶⠈⠐⠔⠄⠟⢀⠁⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠁⠇⠀⠀⠀⠀⢸⠀⠈⠲⠋⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠚⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠐⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡀⣀⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀
⠀⣼⠋⠁⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠔⠁⠃⠀⠸⠀⠠⢁⠄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠴⠃⣠⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢑⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣴⣿⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣠⣴⡿⠟⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠋⠀⣠⣾⠟⠉⡶⡾⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣿⣷⣾⣿⠿⠢⠞⠁⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀⡼⢋⣙⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣷⣄⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢻⣆⠀⠀⢜⣋⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣶⣯⡻⣇⣶⣾⣷⡀⠀⠀⠀⠀⣀⠴⠟⣫⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⢺⣇⣀⣿⢷⡲⣶⣶⣶⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠈⣷⡌⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢹⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣧⣤⣤⣼⣷⣼⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢿⣟⣻⣶⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠠⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣾⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣷⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣯⣿⣽⣟⣿⣻⣿⣿⣟⣯⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠐⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢤⣀⠀⠀⠀⠀⡴⠋⣇⡿⠞⢩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣹⡀⠉⢳⣄⠀⣸⠁⣼⣋⣀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠭⣷⡀⡾⠘⡇⣿⡼⠋⢉⣩⠟⠁
⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠻⣇⠀⣷⢿⠗⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⢷⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡤
⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠳⠿⣿⠴⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⣏⣈⣯⣽⣟⣯⣻⣹⣽⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⡠⠠⠠⡄⠀⠄⠀⠉⠀⠒⠂⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⡀⡀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠚⠀⠀⡀⠠⡄⠀⠁⠈⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠈⠁⠉⠉⠀⠑⠤⠂⠀⠀⠀⠀⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠀⢹⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡂⠄⠀⠀⠀⠀⢐⣓⣒⣛⣒⣒⣳⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⢄⠀⢀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⡩⠘⠁⠄⡒⠀⠀⠂⠀⠀⠀⠄⠂⠀⠀⠂⠠⠀⠀⠀⠀⠺⠂⠀⠀⠀⠈⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠛⡄⠛⠂
⠀⠀⠀⢠⢅⣠⠀⠀⠀⠀⠛⢠⡶⣆⠀⢶⠆⠀⡴⠶⣦⠀⣴⠀⠀⢀⡴⠲⣦⠀⣠⠖⠶⠄⠐⣆⠀⣴⠀⠀⠈⠢⠤⠚
⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢸⡷⣯⠀⢸⠀⢸⡇⠀⢸⠄⣿⠀⠀⢸⡇⠀⣹⠀⡿⠀⠰⡤⠀⠘⣾⠃⠀⠀⠠⠀⠠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠧⠞⠀⠾⠆⠈⠷⠶⠛⠀⠻⠶⠶⠈⠷⠶⠛⠀⠻⠶⠾⠃⠀⠰⠏⠀⠀⠀⠁⡀⠁⡀⠈⠁
⠀⠀⠀⠀⠐⠠⡁⠀⡀⠈⠀⠠⠂⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠐⢀⢀⡘⠀⠃
⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠀⢼⠒⠂⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠠⢄⠀⠎⠀⠀⠄⠠
⠀⠀⠀⠀⠈⠠⢀⠀⠂⠀⡀⠀⢀⠔⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⢤⠀⠀⠀⠀⠰⠂⠀⠀⠀⡘⠀⠈⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠒⠆⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠦⠀⠀⠀⢶⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠖⠀⠆⢀⡄⠐⡠⠀⡄⠀⣐⠀⠠⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠉⠐⠀⠀⠰⠒⠀⠀⠀⠰⡐⠒⠀⠰⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⣄⠀⠀⠀⠴⠂⠨⢦⡀⠀⠀⠀⠀⠁⠁⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⡤⠒⣆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣴⣿⣿⣿⣦⣤⣤⣤⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⠟⠛⠛⠛⣿⣿⣿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤⣤⣿⣿⣿⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣴⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⣦⣤⣤
⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⠟⠛⠛⠛⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⢠⣄⣠⡀⠂⣴⢄⣺⡫⢛⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡀⠒⢀⣿⡟⠛⠏⣅⠨⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠂⠡⠃⠘⠾⠀⠃⣀⢌⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠓⠄
⠀⠀⠀⠀⠀⠆⠄⠠⠀⡄⡌⠀⠂⠀⢀⡨⠁⠧⠀⠠⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⣠⣘⠻⠀⠀⠠
⠀⠀⠀⠀⠀⢷⢈⠂⠠⠈⠀⠀⣤⠐⠌⠱⠆⠀⠀⠀⠀⢄⠀⠀⠈⡠⠈⠃⡅⢷⢠⠈⡄⢁⠢⠂
⠀⠀⠀⠀⠀⡉⠴⢆⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣄⠈⢷⣄⠀⠘⣅⢎⠛⣿⡠⠖⣖⠂⠜⠁
⠀⠀⠀⠀⢠⠀⠄⡐⢦⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠁⠰⡌⠢⣚⠀⡈⠺⢷⡞⠁⠠⠀⠠⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠂⠬⠀⠀⠀⠀⠈⢶⡤⢀⡀⠀⠀⢀⡈⠠⠉⢤⡈⠀⡄⠛⣐⣈⣘⣐⣆⠴⠚⠁
⠀⠀⠀⠂⠀⠉⠀⠀⠀⠚⠀⠀⠄⠀⠀⠀⠱⠏⠲⠂⠀⠀⠘⠄⠘⡄⠀⠨⢠⣌⠀⣈
⠀⠀⠀⠀⠀⢈⠀⠂⡤⠀⡀⠀⠀⠢⠄⠀⢀⠀⠀⠄⠢⢄⠀⢀⠀⠔⢰⠀⠉⠍⠀⡈⠀⢛⠉⠟⠒⠂
⠀⠀⠀⡀⢀⡄⠐⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠐⠤⡈⣀⠏⠀⡀⠀⠀⠒⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⢂⡐⠙⠀⢁⠀⡀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠁⡋⠀⠄⠄⢀⠀⠠⢠
⠀⠀⠄⠀⢀⠈⠡⠀⢀⡜⢁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠄⠈⠈⠀⠀⡀⠀⠀⠀⢀⡀⠤⠆⠐
⠀⠀⠠⠀⠠⠐⡂⠐⢀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃
⠀⠀⠀⠘⠀⠀⠁⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠆
⠀⠀⠀⠀⠀⡀⠁⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠀⠀⠀⠠⠈⠁
⠀⠀⠀⠀⢀⠀⠰⠂⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠁⠀⡆⠀⠀⠄⠁
⠀⠀⠀⠐⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠐⠀⢈
⠀⠀⠀⠠⠀⠀⠀⢸⠀⢇⢀⡀⠠⠔⠒⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠹⣄⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⢈⠀⠀⠀⠡⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠁⠘⠀⠀⡀⠑⢀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⣶⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿⡇⠀⠛⠃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣷⡀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣷⠋⢻⡾⣿⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣰⣿⡀⣸⠿⠛⢶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠙⣿⠃⢰⣿⡇⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡁⣿⣿⢾⣿⠀⠈⠛⠃⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⣿⠀⠀⠀⠀⢀⣿⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡻⣿⣿⣧⣠⣿⣷⣤⣤⣴⣿⣿⠏⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠁⠈⢙⣟⡛⠿⠿⠿⣛⣛⠉⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⢷⡄⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣻⣿⠶⣄⠀⠀⠛⠢⡀⠀⠀⠀⡄⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣄⣻⠿⢡⠄⣈⢷⣦⡄⢀⠐⢶⣄⢼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠙⣾⡉⢶⣟⣾⣿⣥⣴⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣡⣧⡀⠂⣨⡭⣥⠤⠐⢃⣀⠀⠀⣀⣀⡀⠀⠉⢻⣦⣻⣿⣮⠝⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣷⣿⣿⠁⣼⠋⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⢀⠀⠀⠀⠀⣷⡌⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣩⢿⣿⣿⡆⠀⠀⠉⠁⣤⡄⡀⠀⠀⠴⠦⠘⠛⠁⠀⠀⠐⠚⠻⢧⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣽⠟⢾⡟⣿⠁⠀⠀⠀⠀⠉⠣⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠁⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠾⠀⢻⣶⡰⠶⠦⣄⠠⠀⠠⣦⣄⠀⠤⢶⣐⣛⠠⠖⠀⠀⣬⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣏⠀⠀⠀⠀⠀⠈⠛⢋⡀⠀⠀⠀⠀⠀⠀⠀⠤⢊⣽⡿⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⣶⡄⠀⠚⠂⠐⠦⠠⠙⢮⠀⢛⣀⠀⣴⣶⠖⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠙⣶⣆⡀⠀⠀⣀⡀⠶⠿⠂⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⠉⠀⣀⡠⠛⠻⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠻⣆⡀⠛⠃⢦⡄⠁⠀⠀⠀⠀⠀⠀⢠⣆⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠿⣿⣦⡀⢢⣄⢠⣤⠂⠀⣆⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠢⣄⣲⠀⢀⣠⠆⠰⠒⣏⣤⣭⢯⣙⠠⠉⠑⢾⣿⣡⣴⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⡄⠀⠀⢀⠘⠛⢷⡾⠋⢠⡿⢿⣿⣶⠆⠀⠛⠷⣤⣀⠀⠉⢿⣤⣟⠋⠃⠀⣄⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⡀⠀⠉⣽⣿⣧⣶⠁⠀⠈⠙⠁⠀⢀⡞⠀⠀⠉⣳⠴⠀⢠⡝⠳⣿⣄⢉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⣸⣿⠋⣿⡿⠛⠛⠡⣤⣴⠤⠭⠷⠖⢋⣉⡁⠐⠛⢻⣦⣀⠈⢻⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣧⠋⠀⠀⠀⠀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣷⣼⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⡤⠀⣠⡄⠴⠛⢿⡟⢧⠄⠺⠿⠿⠶⠤⠤⠀⠂⣩⢿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⢻⠇⠀⢀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡀⠀⠤⢠⣾⠋⣸⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⡄⢠⣶⣶⣿⡿⠂⠀⠀⠻⠇⠐⠒⠉⠀⠀⠰⠟⠃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣧⠀⣹⡏⠀⠀⠀⠀⠀⠀⡀⣀⣠⡄⠀⢀⣤⣤⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣿⠉⠀⢦⡄⠄⠀⣠⡄⠴⠿⣬⡛⠚⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡄⠈⠑⣀⣸⠋⠀⡴⠞⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢀⣿⣧⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣟⠁⠀⠻⣴⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⣿⣧⣰⣄⠈⢦⣞⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣇⠀⠀⠀⣠⡃⣀⡀⠋⠛⢹⣧⣀⠀⠉⠃⠈⢰⣦⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠋⠀⠀⢐⡿⢫⣿⣿⠣⣤⠜⠋⠹⠓⠀⣾⠒⣯⡉⠃⣄⠀⠀⠀⠀⠀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢁⠠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⡼⣿⣄⣄⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠶⠀⠤⣴⠟⣰⠋⢉⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⠀⠣⠄⣀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠴⠧⠀⠀⠀⢀⡄⠀⠂⠀⣄⣨⡟⣷⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠋⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⡀⠚⠁⠀⠀⠀⡰⡿⠿⠁⠀⠀⠀⢘⠫⡞⠻⡦⠄⠀⠀⠀⠀⡠⠂⠀⠤⣀⠀⠀⢀⣠⡶⣾⢿⡟⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠻⣾⣷⠃⠸⢇⡀⠀⠀⡰⠋⠀⠀⠀⢀⡬⠇⠙⠟⠛⣷⡟⢘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⣰⡿⢿⠀⣌⠀⠘⢷⡆⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣼⡄⠀⠀⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣜⠀⠈⠱⢦⣄⠀⠈⠑⠺⣤⢀⡀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢩⡦⣄⠴⠾⠛⠛⠀⠀⠀⠀⠙⠳⢧⣄⠀⠀⠈⢳⣆⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠈⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⣧⠀⠀⠱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⡟⢨⠰⠂⠀⣠⠶⠾⠟⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠞⠀⠀⠀⠀⠀⠀⠈⡇⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡌
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠶⠀⡀⡀⠠⠛⠘⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⣠⠄⠀⠈⢀⡀⠀⠀⠀⠀⠠⡀⠀⣧⠀⠀⠀⠀⠀⢠⣡⡄⠉⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⢣⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠄⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⣠⠀⠀⠀⠀⢀⠀⠀⢠⡆⠀⠀⠐⠃⠀⡠⠀⢐⢀⠄⠀⠀⠀⠀⠀⠀⠀⣤⡇⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠞⠂⠀⢠⠀⠀⠀⠀⣄⠻⣏⢀⠔⠁⠀⢀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠠⠒⠀⠀⢀⣴⡇⡘⣟⠃
⠀⠀⠌⠀⠀⠀⠒⠨⠉⠀⠀⠀⠀⠞⠁⠀⠀⡠⠚⢋⠀⠀⢀⠄⠀⠈⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠦⠚⣣⣓⡉⢑
⠀⢰⠂⠀⢰⡆⠀⠀⠀⢀⢈⠀⠀⠀⠠⠀⠀⠇⡰⠋⠠⡄⠈⠀⡀⠀⢀⢞⠑⢂⠀⢀⡀⠀⠁⠀⠀⠁⠀⠐⠛⣿⡾⡀⠎
⠀⢸⠂⠀⠀⠀⠀⠀⠶⠀⠀⠀⠁⠀⠀⣀⠀⣆⠁⠀⣶⠰⣄⠘⠁⠀⡈⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⢮⠂⢀⣀⠈⠉⠁⠀⠠⠤⠀⣇⡀⢸⠂⡱⠧⠂⣾⡇⢠⠿⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠸⠆⠃⡄
⠀⠚⠀⢸⠛⢀⠀⠀⠀⣁⠀⠀⠈⠀⠈⢇⠁⠂⡜⠱⠹⣺⠃⢀⠄⣄⡜⠂⠀⢸⠃⢀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠘⠰
⠀⣴⡦⠛⣶⢤⡀⠀⠀⠐⠤⠀⠀⠀⢀⠈⠣⡾⠀⡄⠆⠁⠀⠈⠡⢻⢻⠵⠀⠀⠀⠈⡀⣀⠀⠉⠒⢒⣁⣸⡤⠆
⠀⠀⠁⠀⠸⡛⠁⠀⠀⡀⢡⠒⢲⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡞⠉⠀⢘⡇
⢤⡀⠀⣠⠇⠁⠀⠂⠉⣩⠖⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠀⣰⠀⠀⠀⠀⣀⣸⣇⣀⡤⠞⠀⡸⡖
⢨⣜⡜⠃⡠⠀⠀⠠⠈⠀⢀⠀⢀⠀⠀⠀⠐⠠⠀⠀⠀⠊⠀⠀⠀⠉⠁⠂⢤⠃⠀⠀⠀⡞⠉⠉⣯⠀⠀⠀⠀⠀⠿
⠘⠯⣥⠋⠁⠀⠀⠀⠉⠀⡀⠀⠀⡀⠀⠀⠀⠀⠤⣀⡠⠒⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⣠⣷⡤⠞⠃⠀⣀⣲⢀⣀
⠀⠀⠁⠀⠀⠀⠂⠀⠠⠁⡀⠈⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⡀⠒⠀⠂⠄⠉⠀⠀⠀⡏⠀⢈⡇⠀⠀⣀⡿⠟⠙⠋⢷⣄
⠀⠀⣶⠀⢠⠀⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⣀⣈⡁⠁⠀⠀⠐⠄⠀⠈⠀⠁⠀⢀⡤⣷⠒⠉⠀⣄⠀⠀⢸⢂⠀⠀⣠⠁
⠀⠀⠏⠀⠀⢣⡀⠀⠀⠮⠂⠐⠊⠋⠉⠁⠀⠀⠀⠀⢀⣀⣴⣶⡾⠿⠖⠀⠀⣸⠴⠋⠀⠀⠒⠿⠀⠀⠀⠙⠧⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣻⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠔⠒⠒⠖⠒⠒⠒⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣀⠀⠠⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠈⢢⡀⠀⠀⢀⡠⠔⠒⠀⠉⠀⠀⢸⠀⠀⠀⠉⠙⠒⠢⣤⡴⠉⠀⠀⠀⠀⡹⠧⡀
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠙⣦⠒⠉⠀⠀⠀⠀⢀⣀⣠⢤⣤⣄⣀⣀⠀⠀⢀⠞⠉⠒⢄⡀⠀⡰⠂⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⡰⠋⠀⠑⣄⣀⠤⠒⠉⠁⢀⣀⣀⣄⣀⡀⠈⠉⠃⡎⠀⠀⠠⠊⡹⢎⡁⠀⠀⠀⠀⠳⡀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⠎⠀⠀⠀⡠⠊⠣⣀⠤⠒⢉⣉⡤⠤⡧⢤⣉⡉⠀⢸⡇⠀⠰⡡⠖⠀⠀⠱⡄⠀⠀⠀⢀⠵⡔⠋⠁
⠀⠀⠀⡎⠀⠀⠀⠀⢠⠃⠀⠀⢀⠞⠀⢠⠔⢙⣶⠊⢁⡠⠤⠄⣶⠤⢄⡈⠑⠮⣽⠛⡉⠀⠀⡄⠀⠀⠘⡤⠔⠊⠁⠀⢡
⠀⠀⢰⠁⠀⠀⠀⢀⡆⠀⠀⢀⠎⠀⡰⠃⡴⠁⡠⣻⣵⣾⢿⣟⣿⣿⣷⣮⣵⢎⠈⢦⡈⢆⢀⣹⡄⠊⠁⠘
⠀⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⡎⠀⢰⠁⡜⠀⡜⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢳⡀⢷⠘⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠒⠒⠆⠀⠤⠤⠤⡧⠤⠤⢠⡅⠀⡎⢠⡇⣸⣰⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣏⡇⠈⡆⢸⠀⣀⡄⠀⠀⢸⠀⠀⠀⠀⢸⠄
⠀⢰⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⢸⠀⢼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡏⢹⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⢧⠀⠀⠀⡇⠀⢱⠈⡇⠘⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠃⢰⠁⡜⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⢳⠀⠀⠀⠀⠸⡀⠀⠀⠱⡀⠈⢆⡸⣖⠙⢌⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠃⣠⠃⡰⠁⢀⡎⠀⠀⠀⠆⠀⠀⠀⠀⡞
⠀⠀⠈⡆⠀⠀⠀⠀⢱⠀⠀⠀⢳⡔⠈⠣⡈⠢⣄⠙⠪⢿⣿⣿⣿⣿⡯⠗⠋⣱⢖⢁⡔⠁⢀⠞⠀⠀⠀⡌⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠹⡄⠀⠀⠀⠀⢳⡄⠂⠁⠙⢦⡀⠈⠢⣌⠑⠒⠤⢼⣀⣀⠤⠤⠖⠊⣁⠔⠋⢀⡰⠋⠀⠀⠀⠜⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠙⢄⠀⠀⠀⠙⠦⣄⠀⠉⠑⠒⠾⠤⠤⠤⠒⠚⠉⠀⣀⠴⠋⠀⠢⠀⡠⠊⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠉⠒⠲⠤⡤⠤⠤⠤⠤⠔⠒⠉⠀⠀⠀⢀⡠⠊⠁⢄⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠉⠀⠀⠀⠀⠑⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⡆⠠⠄⠀⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢄⣀⣀⢀⡀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⢻⣧⣀⣀⣀⢀⣀⣠⣤⣄⢀⣀⣤⣾⠟⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⠿⣿⡟⣻⣏⣿⡟⢻⣿⣩⣿⠿⣿⣋⣿⡿⣿⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣼⡿⢿⣿⢻⣿⠛⠛⠿⠿⠛⠛⠻⢿⣿⢛⣿⣷⣾⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣷⡾⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣤⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣻⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣿⣷⣄
⠀⠀⠀⠀⢀⣠⣰⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣼⣿⣤⣀
⠀⠀⠀⠀⣿⣋⣿⣷⣾⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣧⣼⣿⣉⣿⠆
⠀⠀⠀⢰⣟⢻⣿⣤⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⢿⣧⣼⡟⣻⡇
⠀⠀⠀⠈⠻⢿⣏⣹⣿⣼⡿⢿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣷⣾⣿⣹⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠋⠁⠻⢷⣾⣯⣹⣿⣄⢀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣀⣿⠿⠟⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣉⣿⣿⣿⣶⡿⢿⣷⣴⡾⣿⣏⣽⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣯⣽⡿⢿⣟⢻⣷⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣿⣷⣾⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣼⡿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠚⠀⡀⠀⢀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣎⣥⣶⣶⣮⣿⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⠋⠀⢈⣿⡿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠉⢁⡀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⡔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠊⠀⠈⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢈⠁⠀⠠⠈⠀⣠⣤⣦⣀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣧⠄⠀⠀⠡⠼⣿⣿⣿⣿⣷⣬⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣽⣿⡍⢀⠀⠀⠀⠠⠄⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣀⣻⢤⣀⡐⣻⣿⠋⠀⠀⠐⠈⠐⠀⢀⡀⠀⠙⠻⣿⣿⣿
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡽⢟⡩⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠈⠻⣿
⠀⠲⣴⣤⠀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣤⣿⠿⠿⣾⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠉⠒⠶⠦⢔⢀⣂⣀⠄⠈⢁⡈⠉⠩⠻⠃⠀⡠⠒⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡥⢔⡈⠀⠀⠠⡉⠀⡠⠚
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣻⠷⠚⠋⣰⠻⢅⠎⠀⡤⠄⣦
⠀⠀⠀⣀⣠⣾⡿⠟⠋⠁⠀⠀⢰⣟⣿⡇⠀⠀⠑⣖⠌⡆
⣷⣶⣬⡏⠉⠁⠀⠀⠀⠀⠀⠀⣿⣤⠟⠀⠀⠀⠀⠙⠲⢿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠀⢠⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⡀⢀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠠⡀
⠀⠴⡀⠀⠀⠀⠈⠉⠀⠁⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⣴⠩⢷⣄⠻⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⡋⢸⠊⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣷⣤⣈⠁⣀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣙⠫⢄⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⡟⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠉⠟⡙⠑⠶⡄
⠀⢠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣸⠃⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁
⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠻⠖⠋⡀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢖⣦⡀⠀⠀⠀⠈⠉
⠀⠀⠉⠀⢠⠂⠀⢰⠇⠀⠆⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣤⣄⣀⣃⣀⡒⠀⠀⠀⠀⠀⣾⡇⢠⢺⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⣿⣿⣿⣛⢋⡆⠁⠀⠀⠀⣿⠃⠨⣭⠁⡆⠀⠀⠀⢀⡐⠀⣩⣿⣇
⠀⠀⠐⠧⣆⡖⢂⣀⡀⣠⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠑⢸⡟⡼⠀⠀⠀⡰⠂⠥⢐⢣⣿⡇
⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠙⠛⢿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠙⠏⠉⠈⠁⠀⠀⠸⣗⠔⣁⣼⡼⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⣀⡀⠀⠙⠙⠙⠛⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⣆⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠤⣀⠄
⠀⠀⠀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠂⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀⠞⢠⡖⡌⢻⠡⠤⡴⢰⡀
⠀⠀⠀⠇⢸⡄⢀⡖⢦⠀⠀⠀⠀⠀⠀⠀⠀⢡⠦⢤⡀⡀⠀⠀⠀⠠⢤⣠⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⡽⢧⣼⣛⣾⣯⣽⣾⢹⡲⠿⡄
⠀⡴⠲⢶⣤⣷⣎⣰⠃⠀⠀⠀⠀⠀⠀⠀⢽⡸⡄⣸⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢹⠭⡿⠻⡿⣛⢻⡟⡙⡶⠆⣾⣧
⠀⠻⢤⣬⠿⡟⢫⣼⣉⠓⢦⡀⠀⠀⠀⢸⠉⡇⣳⡏⠀⠀⠀⠀⠀⠀⠐⠒⣖⠂⠀⠀⠀⠶⠀⠀⠈⠀⠁⠁⠀⠀⠈⢃⡥⢡⡿⢿⣿⠟⠱⣦⠙⡯⠁
⠀⠀⠀⠀⠀⠻⣄⣳⢉⣷⣤⡿⠀⠀⠀⠈⣠⣛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣩⠦⠀⢠⠀⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠮⣆⠀⢄⠱⠂⢐⣁⠞⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠛⢧⣽⠀⠀⠀⠀⠀⠁⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⡀⡰⠤⠀⢄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠈⠁⠤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢰⡆⠙⠀⠰⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠘⠒⣀⠐⠄⢀⠄⠀⠐⢦⡤⢘⠢⣀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢳⠀⣄⠄⡸⠀⠄
⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠸⠀⠰⡀⠀⠀⠁⠀⠂⠀⢼⢠⣼⣅⡌⢀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡘⠃⡉⠊
⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠄⠀⠀⡃⢈⡛⠂⠀⡖⠃⣨⠁⠈⢣⠈⠁⠀⠀⠀⠀⠀⢈⠴⠾⡂⢖⣿⡇⠐⠢⣀
⠀⠠⡐⡉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠙⠀⠀⠀⠀⠈⢄⠠⢀⠡⣀⠄⠀⡁⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠏⠉⠏⠀⠀⢈⠁⠈
⠀⠀⠀⠛⠑⠃⡂⠀⠃⠀⠀⠀⡀⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠡⠄⠳⡀⠀⠀⠈⢲⠃⠰⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠙⠁⢖⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢟⠀⡀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠀⠀⡠⠋⠊⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡠⠋
⡰⠋⠀⠀⠠⠔⣒⠒⠐⠄⠀⠀⠀⠀⠀⠀⠰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⢠⠔⣒⠒⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⢀⢾⣿⠶⠋
⠀⠀⠀⠀⠁⠠⣴⠄⠀⠀⠑⢄⠀⠀⠀⠀⠠⡠⢄⡀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠐⠁⠀⣴⠄⠀⠀⠁⠀⠀⠀⠀⠀⠘⡠⢄⡀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠙⢷⣾⡇⠀⠈
⡀⠀⠀⠀⠀⠈⠳⣄⣀⠐⢾⡰⣼⠀⠀⢀⠤⠒⠒⠉⠉⠉⠁⠀⠐⠤⡀⠀⠀⠀⠀⠀⠲⣄⣀⠐⢾⡴⡱⠀⠀⢀⠠⠂⠒⠉⠉⠉⠉⠀⠐
⠈⠢⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠁⠀⠀⢀⡀⠂⠄⠄⠤⢀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⢠⠃⠀⡀⢀⡀⠂⠤⠄⠤⢀
⠦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣯⠉⠁⠀⠀⠀⠀⠘⠢⣀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣯⠁⠁
⠲⡘⡂⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠲⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠳⣄⡀
⣿⠟⠛⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠶⠶⣶⣿⠟⠟⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠷⠶
⢀⣀⢌⣳⠋⠀⠀⠀⢀⠀⠠⠤⣤⣀⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣳⠋⠀⠀⠀⢀⠀⠤⠤⢤⣀⡀⠀⠀⠀⢀
⠭⠞⠋⠁⠀⢀⠔⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠉⠐⠢⠤⠬⠬⠬⠭⠖⠋⠁⠀⢀⠄⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠈⠐⠢⠤⠬⠤
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣹⠏⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢹⠇⠆⠈⡻
⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⡠⠋⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⡠⠫⠊⠀⢰⠏
⠀⠀⠀⠀⠄⢀⢾⣿⠶⠋⠀⠀⢀⡰⠃⠀⠀⡠⠒⠀⠀⠒⢄⡀⠀⠀⠀⠀⠀⢰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⡠⠒⠀⠀⠒⠄⡀
⠀⠀⠀⠰⡴⢄⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⢰⠁⠀⣴⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡰⢌⡀⠁⠀⢀⣀⠴⠊⠀⠀⠀⠀⠁⠀⣴⠆⠀⠀⠐⢄
⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⡄⠀⢠⠀⠈⢂⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠙⣿⣶⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡆
⠀⠀⢀⠄⠐⠚⠉⠁⠀⠉⠁⠒⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢐⣿⡴⡧⠀⠀⢀⠤⠒⠚⠉⠁⠀⠁⠀⠀⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢈⣮⡴
⠀⢠⠃⠀⠀⢀⡂⠒⠠⠄⠄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠓⠉⠀⠀⢀⠃⠀⠀⢀⡐⠒⠢⠄⠤⠀⠀⠈⠒⡀⠀⠀⠀⠀⠀⠉⠙⠓⠉
⠀⡆⠀⠀⠐⣿⠁⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣯⠈⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦
⠀⠠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠰⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠳⣌⢦⠀⣃
⠀⠀⠱⡀⠀⠀⠀⠀⠉⠓⠳⠶⢶⣿⠟⠛⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠛⠳⠶⢶⣿⠟⠓⢀⣸
⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡣⠃⠀⠀⠀⣀⠤⠀⠤⣄⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⡳⠋⠀⠀⠀⣀⠤⠀⠤
⡀⢛⡧⠀⠀⠀⠈⠒⠲⠤⠬⠬⠭⠽⠞⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀⡀⠌⢛⣦⠀⠀⠀⠈⠐⠲⠤⠤⠬⠬⠽⠚⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀
⠃⢈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣹⣇⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⡀⡀
⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢰⠉⢀⡹⠀⠀⢠⠊⠉⠙⢄⠀⠹⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠘⡄⠀⠀⠈⢆⠀⠀⠀⠀⢨
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠘⢦⣀⠠⠊⠀⠀⠸⠄⠂
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠐⠒⠒
⠀⠀⠀⢠⡄⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡠⠄⠀⠈⠠⠠⢢⠄⡄
⠀⠀⠀⠈⠙⠚⠁⠀⠠⠂⠀⠰⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡇⠀⠄⠀⠀⠀⠀⠘
⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠄⠤⠀⠀⠈⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠛⠁⢀⠁
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠄⠢⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠰⠁⠀⠠⡀⠀⠈⠀⠀⠀⡠⠔⠒⠊⡅⠀⣠⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠖⠊⠁⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠶⠀⠀⠈⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣠⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⣄
⣴⡗⠀⠀⠈⠃⠀⡠⡖⠀⠀⡏⠀⠀⠰⢦⠎⢢⠀⠀⠈⣁⠀⠀⠀⡑⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⠇⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠠⠂⠁⢶⠀⠀⠀⣲⣿⠀⡤⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠉⠀⠀⠀⠀⠀⢀⢴⡜⠃⢰⡂⠀⠀⠀⠀⠈⠀⠀⢰⣿⠃⠐⠇⠀⡠⠠⠀⠀⠀⠀⡀⠀⠄
⣆⠀⠀⠀⠀⠈⠛⠶⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠠⠄⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡌⠀⣧⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⢀⠠⢀⡀⠀⠀⠀⠊⠀⠀⠀⠀⢀
⣘⣣⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠠⠀⢐
⠸⣾⠍⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠐⢀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠁⠀⠀⠨⠀⠈
⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⣠⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠈⢠⡀⠀⠨⣀⠀⠒⠀⠀⠀⠀⠀⠀⢀⠀⡀
⡄⠃⠚⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠉⠀⡇⠀⢱⣄⡀⠈⠐⢸⢀⠰⠀⠠⠀⠀⠿⠟⠠⠠
⠐⠘⠀⢀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠇⠀⠈⣡⡠⢀⡀⠀⠈⢄⠸⠠⠙⠢⡀⡼⠀⠀⠀⠀⠄⠰⣅⠀⠀⠈⠃
⠀⠀⠢⣿⣀⣀⡁⠉⠀⢀⠀⠀⠀⠀⠀⠂⠜⠉⠈⠀⠀⠠⠀⠁⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃
⠀⠀⠀⡇⠀⠀⠉⡆⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠠⠄⣀⠀⠀⠀⠓⡀⠀⠐
⠀⡎⠀⠈⠲⠤⣀⣇⣀⣀⠀⠀⠀⢢⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠄⠀⠀⠀⢠⠠⠴⡖
⠘⠀⠀⠀⠀⠀⢸⡁⠀⠈⡄⠀⠀⠀⢤⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢹⠊⠁
⢀⣀⣄⣨⣤⡄⠀⠙⠒⡾⠦⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠜⠃⠀⠈⠛⠧⠂⠀⠘⢇⡀⢸⠀⠀⠀⢀⠐⠀⠀⢀⡄⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢺⡇
⡠⡀⠀⣀⡝⠀⠀⢄⠀⠀⠈⢹⡒⡄⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠠⠄⠀⠄⢀⣀⠀⠀⠀⡀⠀⠂⠀⠀⠈
⠀⠀⠂⠈⠀⠀⠀⠘⠉⠀⠀⢀⠙⠧⠄⠀⠀⠉⠉⠙⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⢐⡂⠀⠀⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⡼⠀⠏⠀⠀⠀⢠⣄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣷⡈⢧⠀⠀⠀⠀⢰⠃⡜⠀⢀⣤⠖⠋⣈⣠⣀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣉⣥⣀⣄⣉⠀⠈⢦⠀⠀⠀⡿⢠⣇⣴⠋⢀⣴⣋⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠳⣄⠀⣦⣠⡼⠋⠈⠁⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⢀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⣽⡟⠉⠀⠀⠀⣀⣤⣶⣶⣤⣄⣀⡤⠿⠶⠚⠋⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡿⠀⠀⠀⣠⡶⠋⠉⠉⠉⠉⠉⠀⠀⠀⣀⡤⠴⠒⠉⢚⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠉⣷⣾⠋⠀⠀⠀⢰⣿⡃⠀⠀⠀⠀⠀⠀⣠⠶⠉⠀⠀⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢹⡟⠀⠀⠀⢀⣿⢩⡗⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⣹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⠾⠃⠀⠀⠀⠀⣿⡅⠀⠀⠀⣀⠁⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⣾⡁⢀⡀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⢰⣇⠀⠀⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣶⣴⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠛⢋⡛⠟⠛⠉⠛⠿⠿⠿⠿⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⣡⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢢⠄⠈⢙⢦⡀⢰⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡷⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⠟⠙⠀⠈⠓⠠⠂⠈⠉⠴⣤⠄⢠⡀⠀⠀⠀⠀⣧⣾⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⠀⠀⠀⠀⠀⢀⣼⣤⣤⣷⠶⠀⠶⠆⠀⠀⠀⣴⢀⣴⣄⣀⣂⡁⠀⠀⠁⢀⣿⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠈⠗⠠⣤⠒⠋⠀⠀⠀⠐⢀⣽⠊⢑⣋⠉⢁⣿⠄⠀⠀⠉⠈⠉⠛⠁⣴⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠉⠉⣃⣀⡀⠀⢀⠈⠀⠀⠀⠀⠀⠙⢁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢠⣄⡀⠰⣶⠁⠀⠀⠀⠀⠀⠐⡲⠋⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⢳⣼⣭⣥⣉⡲⢄⠀⠀⠾⣵⠀⠈⣇⠀⠀⠶⢶⡶⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠉⣙⣳⡷⣄⠐⢽⡇⠀⠘⡆⠀⢀⡏⠀⢠⡿⡄⠀⠀⠀⠤⢚⣉⣭⠽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣑⣮⣇⣀⣀⣱⣀⣨⣀⢀⡇⡇⡇⠀⠀⣨⠞⠋⣡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⣿⣟⡟⠛⠛⣛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⣿⣿⣿⣿⣿⣶⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣿⢠⠞⠉⠀⠀⠀⠉⠉⣭⣥⠉⠀⢉⣴⠟⠻⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣠⡊⣠⡆⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠺⠿⠷⣤⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡶⠋⢹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⢤⣷⠀⣀⠤⠀⣾⠁⠀⠸⠷⡀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡄⠀⠀⠀⡠⢴⠞⠁⠀⠀⢀⡴⣧⠀⠀⠀⠀⠚⣦⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠴⠋⠀⠀⠀⡴⠋⠐⠛⢦⠀⠀⠀⡿⠆⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⡀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣤⡀⠀⠀⠀⢠⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣾⣿⠟⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠄⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⢨⠽⠂⠀⠀⠀⠀⡝⠐⠀⠀⣠⠁
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠈⠂⡀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⡀⠀⠀⠠⠨⠈⠀⠀⠀⠀⠀⡀⠡⠮⠠⠀⡀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠧⠈⠀⠐⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢸⡀⠊⠀⠂⢸⠀⠀⢄⠠⠀⠀⠀⠀⢠
⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠈⠶⠠⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠐⠀⢈⠠⠠⠘⠈⠀⠀⠀⠀⠀⠈⠂⠀⡆
⠀⠰⠰⠀⠀⠴⡆⣠⣄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠯⠭⢭⠭⠭⠭⠀⠀⠀⠀⠚⠁⡈⠑⠂⠀⠀⠀⠠⠁⠄
⠀⠀⠀⠀⠀⢆⣘⡠⠄⠀⠀⠐⠁⠐⠀⠀⠀⠈⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠄⠅⠐⠀⢀
⠀⡰⠒⠢⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⣶⠄⢠⡴⢦⡀⢰⠀⠀⢀⡴⢶⡄⠀⡴⠶⡄⠀⣦⠀⣴⠀⠀⠀⠀⠠⠁⠀⠈⡆⠒
⠀⠀⢀⠀⠆⠆⠸⠆⠃⠀⢸⡷⣇⠀⣿⠀⣿⠀⢸⡇⢸⠀⠀⢸⡇⠀⣿⢸⡇⠀⣦⠄⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠘⠷⠋⠐⠛⠂⠘⠶⠚⠁⠘⠓⠒⠈⠳⠞⠃⠈⠳⠶⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⣼⣃⣘⠿⠃⡋⠀⠀⠀⢀⠁⠀⠂
⠀⠘⠃⠀⠁⠀⠸⠂⠀⠀⠀⠐⠇⠀⠀⠀⢄⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⡀⡄⠀⠀⢀⡠⠔⠀⣠⠀⠀⠀⠁⠀⠀⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠐⠅⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠃⠂⠇⠁⠑⠀⠀⠐⡂⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠨⠀⠀⠀⠀⢀⢀⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠄⡀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⡐⠀⠃⡀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠀⠀⠀⢈⠐⠁⠀⠸⣀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⡀⠀⠂⠀⠄⡐⠀⢂
⠀⠀⠀⠀⠀⡴⠁⠀⠠⠄⠀⠀⠀⠈⠸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠁⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠹⠃⠀⡐⠄⠈⠁⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣦⢄⠈⠠⠟⣹⠯⠫⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠃⠠⠿⠀⠉⠠⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⠈⠃⢈⠀⠆⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠈
⠀⠀⠀⠀⠀⠀⡆⠡⠐⠀⢴⠆⠀⠁⠀⢦⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⡀⠊⢦⡍⠆⠀⠐
⠀⠀⠀⠀⠀⠀⢻⠐⡀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠘⢆⠀⠀⠨⡠⠈⣳⣙⠆⠀⢊⡀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⠆⠈⠿⡆⡀⠱⣊⣴⢛⣦⠁⠒⠀⡁
⠀⠀⠀⠀⠀⢀⠀⠀⠠⠈⠠⠀⠀⠁⠀⢄⡀⠀⠀⠀⠀⠂⠑⠌⠰⠄⠀⢌⠉⣣⣈⠈⣀⡀⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣁⠀⠀⠀⠀⠀⠙⣁⡔⠀⡀⠀⠐⡀⠃⣈⠁⢀⡛⠀⠂⠲⠖⠐⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠉⠄⠀⠀⠈⠒⠲⠀⡰⠡⠳⠆⠰⠄⢤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠠⠀⠃⠀⠂⠠⠀⠉⠀⠀⠐⠄⠈⠀⠁⠀⠀⠀⠄⢠⠂⠀⠀⠀⠆⠄
⠀⠀⠀⠀⠂⠀⠅⠀⢴⠀⠄⠀⠀⠀⠀⠀⢀⠀⠴⠀⠀⠀⠀⠈⠑⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠀⢈⠠⠀⠀⠘⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠤⠄⠀⠂⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠁⠀⠆⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠁⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠠⠈⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠠⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠩⡈⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢡⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣤⣤⣀⣀⣠⣤⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢀⣀⣤⣴⡾⠿⠋⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠷⠿⠿⠟⢛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣉⣙⡛⠛⠿⠿⠿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣠⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⢿⣆⡀⠀⠀⣠⡿⠿⠿⠿⠿⢿⣆⡀⠀⠀⣠⣿⠃⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⢷⣶⣶⣶⠗⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣟⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢿⣦⣿⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⣀⣀⣀⣀⣠⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣇⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠛⠛⠛⠛⠛⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⣈⣿⣆⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠛⠛⠛⢿⡆⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⣟⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⢻⣿⢶⣦⣄⠀⠀⠀⠀⠹⣷⡀⠀⠀⠘⣿⡄⠘⣿
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⢸⣿⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣸⡏⠀⠈⠻⣷⡄⠀⠀⠀⠘⢿⣦⣤⣴⢿⣷⣸⣿
⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠙⠿⣷⣤⣿⣿⡏
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠻⠷⣶⣤⣄⡀⠈⢿⣷⠶⠶⠶⠾⣶⣿⠃⠀⣠⣤⣴⡾⠿⠃⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠇⠀⠈⢻⣦⠀⠀⣰⡿⠁⠀⠘⣿⡉⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣤⡀⠀⢀⣀⣀⣀⣀⣨⣿
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣶⠀⣼⣟⠀⠀⠀⠀⠻⣧⣴⡟⠁⠀⠀⠀⢸⣧⠀⣴⡆⠀⢸⣿⠉⠉⠉⠉⣿⡇⠀⢹⡇⠀⠀⠀⢨⣧
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⣾⠏⠀⠈⠛⢷⣦⡀⠀⠀⢹⣿⠀⠀⢀⣤⣾⠟⠁⠀⠘⣿⡄⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠉⠻⣷⣄⣸⣯⣠⣶⠟⠋⠀⠀⠀⠀⠀⢸⣷⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾⣧⣼⣿⠀⠀⠀⠀⣿⣧⣤⣾⡇⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⣶⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⣿⡏⠉⢻⡇⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠀⠀⠀⠀⠶⣶⠆⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢼⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣿⠇⠀⢸⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠿⣶⣶⠿⠋⠀⠀⠈⠻⢷⣶⣶⠟⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣿⠁⢸⣿⠀⠀⠀⠀⠶⠾⠆⢸⣿⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⢤⣤⣴⣟⣤⣤⣶⣶⣶⣶⣾⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣟⣧⣤
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠂⠠⠈⠈⡄⠀⢤⠀⠀⢀⠀⡀⠀⠀⠐⠀⠀⡈⠀⠀⠀⠀⢀⠨⠶⠥⠄⠈⠂⠑⠀⡀⢀⠄⢈⠀⠴
⠀⠀⢈⠁⠃⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠈⠀⠁⠢⠀⠁⠁⠁⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠐⣀⢀⠂⠂⠰⢑⡁⢐⡴
⠀⠀⠈⠀⠁⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡒⠀⡀⠀⠀⠐⠐⠐⠀⠸⠀⣀⠀⠀⠀⠀⠀⠂⠐⢂⢀⠒⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠂⠀⠂⠢⠀⠲⢦⡀⠐⡥⢄
⠀⠈⠀⡄⢀⠀⡀⠀⠀⠘⢃⢂⠀⠈⢀⣄⠀⠀⣀⠀⠀⠀⢀⣁⠓⠈⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢥⡤⡄⠀⢰⠄⢀⠀⠀⠛⠀⠑⠊
⠀⠀⡀⠓⠀⠄⠠⠼⠀⠀⠈⠀⠀⢀⠐⠀⠁⢨⠙⡞⡛⠀⠈⠈⠀⡂⢠⠁⠂⠀⠊⠁⠀⠛⡏⠏⠭⠉⠁⠀⠁⠀⠀⠐⠐⠀⢀
⠀⠀⠀⠠⠖⠐⠦⠀⠀⠀⠀⠀⠀⢐⠴⠀⢠⠀⠑⠊⠁⠤⠁⢊⡀⠀⡸⠀⠀⠐⠀⠀⠠⠀⠀⠀⢀⣀⢠⡀⠀⠀⠀⠒⠀⠠⠄⡀
⠀⡎⠉⢣⠀⠇⠀⠀⠀⠥⠀⠀⡀⠈⠶⠀⠪⡨⠀⠂⠤⠐⠁⠃⢀⣈⠀⠀⠀⠀⠁⠈⠀⠀⢼⡥⣞⠛⡘⠁⠂⠈⠂⠴⡆⠠⠀⠂
⠀⢄⠂⡴⠀⠀⠀⢀⠀⠀⠀⠀⠘⠃⠀⠆⠀⠀⠀⠀⣤⠀⠀⠀⠠⠌⠀⠸⠂⠀⣤⠀⠂⢴⡀⡠⠔⠊⠤⠄⠀⠐⠍⠀⠐⠄⠀⡀⢀
⠀⠀⣀⠀⠀⠀⠐⠆⠀⠀⠀⠉⠁⠀⠀⠀⠤⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠂⢀⠈⢀⠈⠀⡀⡀⠀⠀⠀⢀⡐⢿⠂⣀⠀⠀⠉⢙
⠀⠀⣏⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠄⠀⠀⠈⠀⠀⠠⠔⠀⠘⠀⠀⢃⠀⠠⠀⠀⢀⠐⠐⠀⠀⠀⠀⢹⠀⠀⠀⠁⠀⠑⠁
⠀⢀⠀⠀⠐⠀⠀⠠⠀⠀⡄⣤⢠⠀⡀⠂⠀⠀⠀⡀⠄⢶⣲⣤⠂⠀⠀⠀⠀⠄⠀⠙⡀⠀⠀⠈⠈⠀⡰⠁⠀⠈⠀⠀⠀⠠
⠐⠪⢬⠐⠲⠀⠀⠀⠀⠀⠀⡆⠀⠐⠠⠂⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠴⣂⠀⠀⡀⢠⣒⡆⢀⠀⠀⠁⠀⠀⠠⠂⠄
⠀⠤⡀⢃⠂⠀⠀⠀⠀⠀⠀⠀⠁⠓⠒⠀⠀⠄⠀⢰⣖⠀⠀⠀⠀⠀⠀⠸⠁⠐⠈⠁⠀⠀⡁⡀⠁⡒⢀⠁⠂⠘⠄⠀⠃⠀⠰⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐⠈⠀⠀⠐

⣀⡆⠾⢠⡆⣠⠀⠀⢰⣤⠐⠚⢣⠀⢊⠣⠰⠬⡑⠕⣽⠦⣀⠀⠐⣯⣹⢆⠀⢤⣀⡴⢫⠞⣀⡜⠁⢠⠊⡘⢰⢰⠑⢆⠀⠀⢀⢔⡅
⠺⣜⢌⣦⡈⡕⢶⠁⣀⠣⢀⠔⠓⣤⠀⠖⢇⠀⠀⠉⠙⢄⣀⠁⠢⡆⠉⠀⢠⣾⡅⢀⣍⠤⠛⣆⡠⢃⠎⠀⠀⢁⣠⡚⢶⡏⢻⠟⠋
⠈⢉⡷⡏⠋⣬⡡⠹⣁⡀⢸⣠⠋⠉⠃⠈⡊⠆⠨⡨⠇⠀⠉⠢⣤⣘⠆⠀⠴⠋⠀⢹⡇⠀⠀⠸⠁⠏⠐⠐⣴⡿⠄⢀⡐⢃⡬⠓⠂
⡀⡀⠠⠟⣔⣍⠡⢣⠧⡀⠀⠉⠓⠒⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠊⠀⣀⠼⠆⠁⠀⣶⠛⢍⠀⠀⣔
⣼⠤⡕⡐⠉⠹⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠉⠉⠀⠀⠁⢐⠊
⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠞⢦
⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⡀⢀⡀⡀⢀⣠⡀⣀⣄⢀⡀⢀⡀⠀⣀⠀⡀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠐⠚⢣⡀⡀
⠁⢠⡼⠓⠀⠀⠀⠀⠀⠀⢺⡀⣿⢸⠻⣼⡇⡇⣿⠀⡀⣿⠂⢸⡇⢸⡇⠀⣿⢀⡇⣿⠀⢠⣯⣷⢸⡷⣟⠀⠀⠀⠀⠀⠀⠀⠁⠘⢃
⢤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠈⠁⠁⠈⠉⠁⠉⠉⠈⠉⠉⠉⠁⠈⠉⠀⠉⠉⠉⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢶⣠⡖⣶⢠⡶⠲⠀⣰⣆⠀⣦⡀⡆⣴⢠⡖⠆⣶⡀⣰⡆⣶⠲⠀⠀⠀⠀⠀⠀⠀⠀⠔⣭⡡
⡴⣉⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡼⠻⡏⢷⠘⢦⡽⠢⠟⠺⡆⠇⠹⠇⠿⠠⣭⠇⠏⠻⠋⠇⢬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠢⡪⠕
⠀⠈⣲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⢉
⠐⠨⠑⠒⢀⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⡈⠙⠚⠙⠚
⠀⠀⠊⠀⠁⠀⢠⡾⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⡱⣪⠕⡳⡣⠀⠀⣷
⢉⣴⠏⠀⢀⡔⣹⠃⢰⢞⣼⣗⠇⠀⣄⣴⣔⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⡀⠀⢸⡿⢇⣺⠀⠄⢣⡻⠣⠃⣗⣄⣀⠈
⠝⡰⣷⡾⠋⣤⠇⠀⢸⢘⠉⠀⢥⣮⠯⠊⡼⠀⡰⠩⠒⠁⡘⠄⡂⠠⠀⡠⠀⠀⠀⠤⡊⣹⣆⠘⢌⣁⡾⠀⢀⠋⠘⠉⢢⢀⣄⣌⢲
⠀⠐⡰⠀⡼⠇⠀⢀⡜⠎⣀⣀⣭⡿⡦⡞⠁⠀⠃⡇⠒⠠⠼⣫⣌⠱⡮⠀⢰⡉⣦⠀⢹⡠⢬⡆⠀⢸⠀⠐⣱⡿⠀⠈⡹⢌⡛⣋⡼
⣤⣶⣧⣤⣤⣤⣤⣯⣮⣿⣥⣤⣤⣤⣤⣥⣤⣼⣼⣤⣤⣭⣽⣬⣥⣶⣭⣥⣤⣭⣥⣤⣼⣤⣴⣧⣤⣼⣧⣤⣬⣭⣵⣤⣤⣼⣽⣥⣷
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢼⠀⡶⠆⠀⠀⠀⠀⠀⠀⣀⡈⢁⣈⢁⠈⠁⣀⠀⠀⠀⠀⠀⡇⠠⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉
⠀⠀⢸⢠⣀⣠⠀⠈⠀⠀⠀⠀⣿⠉⠉⠉⠈⠈⠀⣿⠀⠀⠀⠀⠀⡇⣤⣀⡄⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈⢢
⠀⠀⣼⣀⣉⣁⢰⣶⡆⠀⠀⠀⠿⠒⠂⠒⠂⠐⠂⠿⠀⠀⠀⠀⢀⣇⣈⣉⡀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟


⠀⠀⠀⠀⢠⠶⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠲⠀⠖⡆⠀⠀⠀⠀⠀⠀⡠⠖⡒⠤⡀
⠀⠀⠀⠀⢸⣄⣀⡼⠀⠀⠀⠀⡖⠉⠉⡩⡉⠉⢱⡄⠀⠀⠀⠀⢰⣴⠀⣀⡇⠀⠀⠀⠀⠀⡜⠴⠜⠃⢶⢸
⠀⠀⣠⡶⠋⠀⠁⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠰⣔⠇⠘⢓⠜
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⣶⡎⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢂⣠⣤⢂
⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣀⡽⠀⠀⠀⠀⠀⠀⠈⠀⢻⢿⠃⠘
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠉⠘⠂


⠀⠀⠀⣤⠈⠛⢫⣄⠀⠀⠀⠀⠀⢀⡨⠄⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢙⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡐⠠⠄⠃⠎⠀⠀⠀⠀⠀⠀⢀⣂⣈⡄⠀⠀⠀⠀⠀⠀⠀⣄⣿⡀
⠀⠀⠷⣶⠾⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠋⡒⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣠⣿⣄⡀

⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⢰⠄⡀⠀⠀⠀⠀⣀⢄⡄⠀⣶⠂⠀⠀⠀⢠⡔⣶⠆⠀⠀⡠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⡀⠀⠀⣤⣈⡃⠐⠛⢘⣣⡌⠀⠀⠙⣦⡀⣿⣿⡍⡤⡟⠀⠀⣜⠦⣹⣿
⠀⠀⠀⠀⠀⠀⠀⢿⢘⠻⣷⣄⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠂⠉⠞⠁⢤⣤⣹⣶⣧⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣰⣾⣥⣾⣤⣀⣀⠀⠀⠀⠀⠀⠠⣤⠤⠄⠀⣀⠠⢦⠐⢺⣶⣽⣿⡟⠏⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⢩⣄⠙⢿⣿⣏⣶⣄⠀⠀⠀⠁⠀⠀⠘⢦⣄⣶⣿⡻⠿⠟⡊⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣰⠂⠉⠉⠉⣉⣉⠁⠀⠠⢤⠤⢤⠄⠀⠀⣀⣀⠘⠻⠿⠛⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢧⣴⡔⠁⠀⣴⣶⠀⢻⣦⠽⣦⡀⠀⠀⡀⢀⣴⠿⢹⡟⢐⣿⣦⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣽⣆⠀⢿⣮⡑⢪⣆⢠⣴⡑⢈⣰⣿⠀⢸⡿⣿⣇⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⠿⠟⠀⠰⣇⠄⣀⠹⣿⡗⠀⣤⣸⡆⠀⣸⠗⣿⣿⡀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡀⢾⣉⡀⠠⢘⡀⠀⠙⣶⡟⠀⠉⠀⢼⣦⠋⠀⠀⣿⢠⣿⡿⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠃⠈⠛⢧⡤⣘⠁⢀⡼⠃⠀⠀⣀⠀⠀⠛⢆⠀⠸⠿⠚⠋⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⠸⣿⣧⣄⣀⠀⠁⣰⣦⣄⡀⠀⠀⢀⣤⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣀⣠⣶⣿⣿⡟⠃⠀⠀⠀⠲⠶⢤⡙⣷⠀⢸⣋⢿⣿⣦⣤⣿⣿⣟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⢈⣀⡀⡀⠀⠁⠀⠀⣹⣲⣿⣿⢿⢿⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠟⠙⠃⣿⣿⣿⠇⠀⣶⣦⣄⠀⠀⠀⠀⠀⢀⡀⠀⠸⢿⣿⠇⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⡈⠋⠁⣀⠀⢸⡾⣿⣷⣤⣄⣲⣿⣛⠏⠀⣶⣀⡀⠶⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠾⠛⠋⠀⣼⣿⣧⠈⠙⠻⠋⠿⠩⢿⡿⠇⣀⣼⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢤⡾⠉⠈⣀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣰⡿⢟⡗⣿⠁⢘⠃⠀⠐⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⢰⣍⣻⣿⣷⣦⠀⠀⢠⣾⢟⡹⣾⣻⣯⡏⠠⠎⠈⠀⢐⣄⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⠀⠀⠀⣰⣾⣿⡿⣿⣿⡿⠀⠀⢿⣫⣾⡷⠟⠿⣛⣧⠀⠀⠀⠀⠈⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣶⣶⣾⣿⣿⣿⡙⠳⠄⠀⢀⠀⠤⣤⣤⣤⠄⢈⣉⣿⣿⣯⣳⡶⢦⡤⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⣿⣿⡆⢠⣾⣭⠽⠾⠉⠉⠀⡴⠟⠻⢌⣛⣍⣭⣿⣶⣾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠿⠛⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠀⠉⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣌⡉⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡈⠲⠞⣁⠉⢢⣄⠠⠀⢀⠀⢰⣦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡸⠛⠁⠀⠀⠀⠀⠉⢳⡔⠨⡿⣬⣟⣠⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣴⣠⠀⡤⠋⠄⠤⠃⡄⠀⣀⢀⡀⠀⠙⠦⡝⢧⣉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⣷⣿⡃⠎⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⣦⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡶⣹⣿⡗⠀⠀⠀⠐⢆⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣃⠰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⠀⡏⠸⣇⠀⣀⣀⠀⠀⠑⠈⠁⠀⣀⠀⠆⢀⠀⠀⣐⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡽⠟⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢰⣂⠀⠒⠀⠀⠀⠣⠀⠠⠄⠀⠴⠖⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠹⣆⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡘⠻⠄⠀⠀⢶⣌⠉⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢆⠀⠲⠣⣀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣤⠀⣄⡀⣤⠀⠀⡀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡂⢀⡤⠀⢀⣻⠠⠘⢪⡁⠉⠐⢾⣥⡴⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⠐⠀⠀⠀⢈⣹⡞⠁⠘⠻⢿⠓⠁⠀⠙⠲⠤⠀⠈⠷⠿⣈⠀⠰⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠂⠀⣸⡟⢿⡟⠀⠀⠀⠀⠀⢪⣤⡤⠀⠈⠠⢤⡃⠈⠻⣦⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠟⠁⠀⠀⠈⠛⠀⠀⠀⠘⠉⠀⠀⠀⠉⣳⣄⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣀⠠⡄⠠⠆⢽⠃⡤⠐⠻⠶⠤⠤⠄⠃⣩⢿⡿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠃⠀⣤⡀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠾⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢿⡾⠟⠁⠀⠀⠉⠀⠈⠁⠀⠀⠉⢁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠜⠃⣀⠀⠀⠀⠐⣰⡔⢲⡀⠔⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⡀⠹⠊⢐⠆⠁⡤⠺⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣸⡏⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡉⠀⠁⠆⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠉⠨⢿⡦⡄⠀⠚⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠇⠀⠀⢸⠥⣶⡆⠀⠀⠿⢦⡀⢀⢀⡘⠷⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠟⠋⠈⠁⠀⠀⠀⠈⠒⣹⣖⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠒⠀⠰⠟⠰⠋⠸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠙⠀⠀⣠⣴⠀⠈⠀⢢⡼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡟⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢴⠀⠀⠀⠀⢬⠉⠁⠀⠀⢠⣤⡜⠀⣅⠀⠀⠀⡠⠀⠀⠀⠀⡤⠤⡴⢾⣹⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡿⡇⢀⠁⠐⠤⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣌⠀⠘⠠⣅⠀⠘⠀⠤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠦⣄⠚⠋⠉⠀⠀⠀⠈⠙⢣⠄⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠀⠂⡀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡄⠄⠀⡼⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠸⠄⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⠈
⠀⠀⠀⠠⠀⠐⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹
⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠒⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠆⢱⠀⠀⠀⣀⡴⡄⠠⠀⣀⠤⣀⠀⢀⠀⠀⠀⡀⠀⢀⡀⡀⡀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠃⠈⠀⡘⠀⠀⠀⠀⠉⣤⢺⠁⠀⣸⠁⢨⠥⠀⣠⠃⡇⢸⠈⠩⡍⠀⠀⢹⠀⠀⠀⡆⠀⠞
⠀⠐⠒⠂⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠘⠉⠐⠃⠐⠚⠀⠋⠐⠁⠁⠚⠁⠒⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠂⠀⠈⠙⠋⠀⠿⠧⠽⠟⠟⠿⠉⠿⠯⠤⠤⠷⠾⠾⠿⠀⠈⠁⠀⢖⠀⢆⠀⠲⠀⠠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⢀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠐⣄⣀⣴⣶⣄⡤⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⣿⣿⣿⣿⠖⠘⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠊⠀⠀⠀⢿⣿⣿⡿⢠⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡤⠊⠉⠛⠋⢹⠀⠢⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⢀⠄⠒⠄⠀⠀⢠⠐⠦⣀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⣌⠀⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡠⡄⠀⡠⠤⡉⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡤⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢇⡤⢺⡆
⠀⠀⠀⠀⠀⠀⠐⠠⠤⡄⠀⢠⣿⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠤⢼⣅⢀⣽⡧⠔⢢
⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⠀⢸⡇⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠃⠀⠀⢸⠀⢈⣿⠇⡔⠉⠔⡄
⠀⠀⠀⠀⠡⠐⠀⠠⠂⠑⠒⠛⠁⠐⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠃⢀⠔⠚⠳⠞⠛⡆⠢⠤⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⡠⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠐⠀⠠⢀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄
⠀⠐⠐⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠗⠀⢠⠇
⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢦
⠀⠀⠀⠁⠀⠄⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠈⠁⢀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡎⢱⠀⠀⢀⣠⡄⠀⣀⡠⢀⡀⣀⠀⠀⢀⠀⠀⣀⣀⡀⠘⡂
⠀⠀⠀⢲⠀⠘⠀⠀⠈⠀⠀⠌⠀⠀⠀⠈⣠⠼⢁⣀⡇⠀⠕⠀⣄⢸⠠⢁⡀⢟⠀⠈⡇⠀⠀⠦⠀⠃⠁
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠀⣀⣈⢀⣁⣀⣈⣀⣁⣀⣀⣈⢀⣉⣁⣀⡇⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠈⠉⠈⠉⠉⠉⠈⠉⠉⢉⠉⠉⠉⠁⠀⠀⡀⠃⠈⠀⠘⠀⠈⠈
⠀⠐⠀⠀⠀⠠⠀⠀⠀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠰⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠄⠡⠤⠤⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠄⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⠆⠀⠀⠹⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⢠⠶⡄⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠂⠀⠂⠐⠀⠀⠀⢠⠋⠀⠹⣄⣭⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠹⡄⠀⠀⠈⠀⠁⠄⠁⠄⠀⠀⠀⠀⢻⡀⠴⢃⡟⠀⠈⢳⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⣂⡏⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠉⠛⡙⢤⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢢⡀⢹⠉⠀⣠⠤⣦⠀⠀⠁⣀⣤⢤⣤⣤⣀⠀⠀⠚⠁⠀⣤⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣙⣶⡃⢸⠀⣾⢡⠀⣼⠀⣠⠮⣵⣇⣸⣇⣹⣬⠷⡄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠀⣸⠳⠚⠁⢰⡇⠀⣟⠀⢸⠃⠀⣧⠀⢹⠀⢸⠓⠦⣄⣀⣀⣀⡤⠖⢻⠂
⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⣤⣽⣾⣥⣤⣤⠀⠸⡏⠉⣏⠉⢹⡏⠉⡿⠉⢹⠁⢸⣀⡴⠋⠀⠀⠈⠙⢆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠻⡖⢺⡗⢲⠗⣶⠏⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠋⢩⠍⠩⠉⣧⠀⠀⠈⠓⠻⠾⠷⠟⠋⠁⠀⠐⢷⠦⢤⣈⣀⣀⣀⣠⡤⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠈⠓⠦⣤⣿⣬⣯⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢶⡶⣄⠀⠀⠀⣹⡟⠁⠀⢈⣧⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡵⠚⣧⠞⣇⠀⠀⠀⣇⠀⠀⠉⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣋⣹⠆⠀⠘⢀⡀⠀⠀⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣉⣻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⡀⣀⠈⣾⣺⠀⡴⠃⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⠀⠀⠀⠎⠀⢀⠆⠀⠄⠐⠒⠚⢳⡀⢀⠠⠄⠤
⠀⠀⢯⠾⣨⠌⠀⠁⢀⠀⠀⠀⠀⡀⠀⠁⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⢀⠠⠀⡀⠀⠀⡣⠦⡐⢀⠂
⠀⠀⠀⠁⠉⣠⠄⠈⠣⠟⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠆⡥⠀⠌⠠⠜⠋⠀⢐⠜⣠⡀
⠀⠀⠶⠀⠉⠀⠀⠄⡄⡄⠀⠀⡀⠀⡀⢠⡦⣔⠀⠀⠴⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠂⠁⠚⠒⠀⠈⣶⠓⡤
⠀⠀⠀⠐⠀⠀⠀⣶⣼⡗⠀⠀⠀⠈⠀⡁⠒⠁⣠⠀⠀⠀⠀⠀⣀⢤⣄⠻⠏⠀⡴⠆⡀⠑⠒⠰⣖⢄⠀⠀⡄
⠀⠀⠠⢉⠀⠀⠀⠉⡋⠁⠀⠀⠀⠀⢈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠈⠠⠘⢓⠂⣁⡄⠀⣀⡀⠀⠀⠐
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⢂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠖⣤⡁⠀⠀⠉
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⠀⠀⠈⠈⠁⠀⠠⠄
⠀⠰⢆⠀⣀⠀⠀⢀⣠⠀⢀⠀⠀⣀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠂⠀⠀⠀⠐⢀⠀⡡⠄⠀⠅⠀⠐⠀⡜⣦⡀
⠀⠘⠐⢀⣿⣷⣿⠿⣷⠀⠘⢳⡤⠜⠤⠀⠀⠁⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⢱⣊
⠀⠀⠀⠀⠉⠓⠒⠋⠉⠄⠀⢄⠀⣠⢄⣀⡀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠁⠻⡊
⠀⠀⢠⠴⡀⠀⠀⠁⠨⠂⢀⡦⠀⡁⠘⠒⠁⠋⡇⠀⠁⠀⠀⠊⠀⢠⠊⠙⢦⠀⢀⢀⠀⠀⠄⠐⠛⣋⢐⠀⢾⣕
⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠁⠐⠉⠓⠒⠒⠎⠀⠀⠐⠒⠄⠀⠀⠸⠆⣤⠟⢀⣜⣹⣖⠀⠀⠁⠘⠃⣀⠔⠠⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠘⠋⠅⢀⣀⠀⠀⠰⠂⠀⣤⡄⠀⠈⡁⡈⢀⠀⠀⠀⠀⠀⠀⠂⠒⠂⣈⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠒⢀⣄⡉⢀⠛⠁⠙⠃⠛⠶⣀⠻⠗⠀⣬⠃⠤⣤⠀⠂⡄⠚⢀⠐⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠈⠁⢀⠙⣉⡘⠋⡀⢴⢆⠨⠤⠔⠂⠉⠐⠒⢠⠐⠛⢀⡀⠀⢈⠠⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠚⠉⠢⢀⡼⠢⠁⠁⣤⣡⣜⢩⣶⠆⠺⠇⠘⠇⠀⠻⠂⠰⠊⣁⠰⠿⠀⣔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⠶⠂⢠⣤⡄⠀⠧⣤⡄⠠⣤⣤⡄⠀⠀⣶⠆⠠⠀⠄⣀⢠⡅⠘⠀⠀⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢠⠀⡆⠠⣤⠀⠀⠀⠀⠐⠁⠀⡉⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢰⡄⠀⢲⠆⠀⣵⡆⠠⠀⢀⠀⣠⠈⣀⢀⡄⢒⡀⠘⠈⠁⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠂⢠⡀⠰⡆⣆⠀⠀⡘⠀⢠⠄⠀⠰⣥⠀⡰⣬⠁⠀⠀⠀⠤⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠬⢴⡧⣈⠀⠀⠀⠧⠀⣄⠁⠀⣠⡄⠀⠀⠀⠀⠀⠁⠀⠰⠬⠦⠀⠴⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠚⠀⠴⠀⢠⠀⠀⡄⠀⠐⣒⠂⠀⠀⠀⠀⡁⠀⠀⠢⠀⡄⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⢀⣀⠘⠛⠀⠀⠩⠀⠤⠀⣰⠊⠁⠐⠂⠐⠆⠐⢆⠈⠉⡉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⣀⠀⣤⣈⠉⠅⠤⠀⠀⠀⡀⡁⣶⠁⡄⠉⠀⠉⡀⠒⡛⢨⡇⠀⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠉⢠⡀⠁⠀⠁⠄⢠⠘⠀⠀⠠⠁⠋⠀⠃⠂⠸⡂⡸⠈⠁⠴⠀⣴⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⢙⠡⠀⠛⠀⠚⠠⠀⡺⠏⡀⠿⣃⠀⠀⡉⠁⠈⠉⠣⠀⣀⠐⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠀⠀⠁⠁⠀⠀⠀⠈⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣏⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⠁⠀⠀⠀⢳⣤⣶⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣾⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣯⣽⣾⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣼⣿⣿⣿⣿⡿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠻⣿⣿⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣀⠴⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠂⠀⠀⠤⠚⠁⠀⠉⠐⠉⠀⠀⠀⠀⠐⠂⢙⠉⢥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⠤⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠑⢆⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⠀⢀⠁⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢀⡀⣀⣀⣀⡀⠀⠀⢀⠜⠉⠣⠄⠠⠒⠉⠓⠦⣀⣀⠤⠆⠁⠠⠄⣈⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠖⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⠑⠆
⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠸
⠀⠀⠀⠀⠀⡐⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢃
⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⠁
⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠁⠲⠶⠀⠀⣀⣉⣤⡉⠀⠰⠶⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⡙⠋⠀⠒⠒⢠⡄⠀⠀⠄⣤⠐⠒⠒⠂⠛⡍⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠸⠁⠲⣄⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⣠⠔⢺⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠃⠀⠀⠈⠓⡄⢨⡇⠀⠀⠀⣿⠀⣠⠊⠁⠀⠀⠲⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢠⠉⠀⠀⠀⡠⠎⠀⢸⡇⠀⠀⠀⣽⠀⠈⢢⠀⠀⠀⠀⢡⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡆⠀⠀⠀⠀⠙⢄⠀⠀⡇⠀⠀⠀⠸⠀⠀⡰⠃⠀⠀⠀⠀⠦⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠳⣀⠇⠀⠀⠀⢀⢀⠎⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⢀⠴⠖⣨⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⣶⢀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⠓⠐⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⣥
⠀⠀⣀⡤⠊⠀⠈⠑⠢⢄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠤⠒⠁⠀⠣⢄⡀
⡤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣶⡟⠁⠀⠀⠀⠀⠀⠀⠉⠓
⠉⢰⠆⢀⡀⠀⠀⠀⠀⣀⡴⢄⠀⠀⣠⡞⠋⠉⠉⢛⢻⣶⡦⠤⢤⡤⠤⠴⠦⠤⠀⠀⠀⠀⠀⢸⠀⢀⡿⠀⡄⠀⠀⠀⠀⢀⠀⠰⡆
⠀⠈⠶⣟⠁⣰⠆⢀⣤⡀⣷⢀⣇⢠⡏⠀⠀⠀⠀⠀⠈⢹⡇⠀⠐⠇⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⢨⡏⠀⠇⣀⡀⠠⣄⠈⣷⠶⠃
⠀⠀⠀⠈⠒⠉⠒⠂⠈⢻⡉⠃⢧⡘⣧⡀⠀⡀⠀⠀⠀⣼⡇⠀⠐⡆⠀⠀⡇⠀⠀⠀⡰⠺⣷⣦⠀⣼⠛⡀⢸⠁⠐⠀⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⢸⣦⣬⣷⣶⣤⣤⣤⡾⢁⡦⠀⢠⡇⠀⠀⡇⠀⠀⠘⢤⡀⢘⣿⢠⡏⣭⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⣌⣤⣤⣤⢱⣿⠀⠠⢄⠨⣟⠀⢸⡇⠀⠀⡇⠈⠀⠀⠀⣹⣏⣹⣿⣀⡤⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠱⠆⠠⠄⠴⠋⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠈⠲⠄⠀⠠⠴⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⠸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠐⡇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠺⢿⣭⣭⣤⣤⣬⣽⡋⢸⡏⠘⢯⣭⣭⣭⣭⣽⡟⠿⠃⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠛⠃⠀⠀⠀⠀⠈⠉⠁⣼⠣⠘⠃⠀⠀⠀⠀⠀⠰⠟⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢭⠴⠆⢀⣀⡀⠰⢦⡁⠞⠓⢨⠴⠆⣀⣀⣀⡀⠰⠮⠓

⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠀⠐⢛⠒⠂⠒⠀⢲⠀⡛⠁⠍⠀⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠠⡄⠐⠒⠒⠂
⠐⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡆⠀⡆⠁⣀⠠⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢠⢶⠴⢫⠽⠯⠉⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢀⡀⠙⠈⢀⣀⣀⠘⠁⣠⢀⠀⠀⠀⠀⠀⠠
⣠⡆⠀⠨⢤⡄⠀⠊⠠⠤⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠸⣿⣿⡿⣤⡄⠐⠉⠄⠀⠤⠀⠴⠦⠀⠀⡿⣿⣷
⢬⠏⠀⢀⢉⡉⢁⠶⠆⠤⠀⡤⠬⢛⠀⠂⠀⠤⠟⠀⢤⠈⣀⠶⠀⣼⣿⢻⡟⠁⠀⠛⠂⠐⠀⠈⠂⠀⠀⢶⣴⣤⠿
⠄⢠⠀⢠⢠⣖⢳⡌⠉⠉⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⣁⡈⠠⠀⠀⠾⠀⠘⠂⢀⠀⠀⠀⢀⠄⠄⠀⠀⢀⣘⣿⣿⣿
⠲⠚⠂⡀⠛⣱⠄⡐⠀⠀⠀⠂⠠⠃⠀⡀⠀⠀⢄⠀⠿⠟⠀⠘⠁⠀⠄⠂⠰⠈⠠⠐⠂⠉⠈⠙⠥⠄⠀⠀⠙⠿⠿
⠀⠉⠁⠁⢨⣉⢀⣆⣄⠀⠐⠉⠁⠀⠀⠁⠀⠀⠈⠐⠀⢤⡀⠤⠄⠁⠤⠄⠀⠀⠀⠤⠥⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠐⠚⠀⢘⠋⡿⣴⡧⠀⠀⠀⠐⠀⠀⠃⠀⠀⠉⠀⣶⡖⢀⣚⣋⣀⠂⠀⣃⣐⡂⠐⠂⠀⠙⠛⢛⣋⣈⡁
⠉⢡⡄⠀⢀⠘⣳⣚⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠢⠀⢠⠀⠐⠡⣤⠤⠀⠴⠶⠀⠀⠀⣤⣤⣴⣎⡀⠤⠔⠋⠀⠆⢶
⠉⠘⠁⠀⣉⠉⠉⠉⠁⣀⣀⡀⢀⠀⠀⠀⠁⠀⢀⣀⣘⡁⠄⠘⢙⡉⠈⠈⠀⡀⠀⠒⠛⣺⢏⣁⣀⣀⡄⠀⣀⠀⠈
⠐⠒⠺⣾⣭⡗⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠂⢸⣿⣿⣷⠿⠀⠿⠟⠀⠀⠀⠀⡂⠀⠀⠠⠠⠤⠀⠀⠢⠀⢈⡀
⠀⠀⣰⡟⣱⣗⡀⠈⢘⠈⠁⣀⠀⠀⠀⣀⠀⢀⠄⠉⢁⠀⠤⠄⠃⠐⠂⠉⠀⠊⠀⠐⠒⠀⠈⠂⠀⠀⠀⢠⡩⢉⡆
⢢⠀⠘⠋⠃⠀⠀⠀⠀⠉⣀⣄⠀⡀⠠⠸⠀⢂⣀⠴⠟⠀⡒⠃⠶⠀⠼⠁⠀⠀⠀⠄⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⢀
⣾⠠⢀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠈⢉⣠⠤⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠹
⡞⢀⣀⢡⣉⠀⢀⡀⠀⠀⠀⢙⣉⡀⡆⠀⠀⠒⠒⢳⡀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸
⡇⠐⠊⠈⠟⠀⠏⢀⠘⠂⠀⠼⣿⣿⣷⠄⠰⠡⠈⠡⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⡒⠦⠐⢐⣤⣦⡌⠁⠀⡉⠈⠟⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠁⠀⠀⣠⣤⣄⠀⠂
⠓⠡⠚⠁⠊⠉⠙⠂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⣸⡃⠀⢸⣿⣽⣿⠇⠀⠀⣠⠄⢤⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⡒⠀⠀⢀⣀⣠⠀⠛⠃⠀⠀⠙⠛⠋⠀⠀⠐⣅⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢖⠂⠤⠀⠀⠀⠀⠀⠀⠀⠟⠒⠀⠀⠀⠀⠀⠀⠂⡰⠀⠐⠂⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢁⠈⠢⠀⠐⠀⠀⠀⠀⢘⣻⣇⣾⡿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⡿⠋⠀⠀⠀⠀⣆⠀⢰⡟⢀⡴⠁⠀⠀⠀⠁⠳⣆⡄⠀⠀⠀⠀⠻⢿⣟⢫⣾⡿
⠀⠀⣠⣀⡀⠈⢻⡟⢀⣤⣴⠆⠀⠀⠀⠘⠻⢿⠷⣿⡇⠀⠀⠀⣿⡀⢈⣠⠞⢁⠀⠀⠀⠀⠂⠀⠘⡄⠀⢀⠀⠀⠀⠻⢿⠟⢏⣴⣶⠄
⠀⠀⠘⠿⣿⣷⣄⣧⣿⡿⠋⠀⠀⠀⠸⢿⣷⣾⣶⣿⡆⠀⠀⢦⠘⢧⡍⠀⣰⠏⠀⠀⠀⠀⠀⠀⠓⢧⠀⠀⠀⠀⠀⠀⠿⠿⢿⡛⣩⣄
⠀⠀⢤⣤⣀⡉⠉⡍⢠⣴⣶⠇⠀⠀⣴⣶⣦⣇⣤⣥⡄⠀⠀⢸⣆⠀⣤⠾⠋⡠⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⢾⣿⣷⡿⠟⠋
⠀⠀⠈⠻⢿⣿⣦⣵⡿⠟⠋⠀⠀⠀⢈⣉⡉⡏⠙⠛⠁⠀⠈⣦⠙⢦⠀⢠⡾⢁⠀⠀⠀⠀⠈⠠⢤⣸⠀⠀⢀⠀⠀⠀⢰⣶⣶⣷⣿⠿
⠀⠀⢤⣶⣤⣄⡀⡇⣠⣴⣶⣶⠂⠀⢿⣿⡿⢷⣿⣿⡷⠀⠀⠘⢧⣀⠚⠋⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣠⠀⠀⠀⠀⠀⣤⣦⣤⣧⣶⣷
⠀⠀⠀⠙⠛⠛⠛⠻⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠉⡤⠞⠁⠀⠀⠀⠀⠀⠈⠀⣤⡘⠁⠀⠀⠀⠀⠀⣨⣭⣉⣥⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠛⢻⡍⠉⠁



⠀⠀⠀⠀⠀⠀⢰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢷⢸⡇⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⡰⢩⢪⠀⠀⠀⠀⠀⢸⠁⡰⠛⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢦⢸⣿⣷⣋⣤⠶⠂⠀⠀⠀⣓⣖⢢⢣⣧⣎⣀⠀⠀⢲⠆⠈⡞⢁⣦⠀⠀⠀⠀⡈⢿⣿⠂⣠⣶⠀⠀⠀⠉⠀⠀⠀⢀⠈⠁
⠀⠀⠀⢲⡘⣿⣿⢛⣫⣥⠶⠂⠀⠀⣀⢈⡢⠹⠿⣒⠪⠟⠁⠀⢸⡀⡸⠖⠋⠀⠀⠀⠀⠀⣿⣦⣹⣾⡿⠃⠀⠀⠀⠳⢀⠈⡇⠂⠀⠊
⠀⠀⠐⣦⡻⣟⣮⣽⠿⣷⣚⡀⠀⠀⠹⡗⠮⣷⣖⠩⢗⠆⠀⠀⠀⠱⡇⠀⣰⠟⠀⠀⠀⣤⡈⠻⢿⣠⣴⡾⠀⠀⠀⣄⠀⠈⠟⠀⠀⡤
⠀⠀⠲⣬⡻⣎⠳⢚⣛⣋⣭⠀⠀⢴⢖⡒⢬⣈⡡⠯⣥⣄⠐⢷⠀⢸⠤⠚⠁⠀⠀⠀⠀⠹⣿⣷⡼⠿⣛⣥⠀⠀⠀⠈⠀⠰⣾⠄
⠀⠀⠓⢮⣟⢮⣉⣩⣭⡷⠶⠂⠀⢈⣓⣭⠵⡿⢖⡭⠕⠁⠀⠈⠣⣼⠀⠀⣤⠀⠀⠀⠀⢷⣦⣍⣷⣾⡿⠃⠀⠀⠈⠇⡀⢀⣠⣀⠖⠃
⠀⠀⠙⢶⣽⡳⠤⠴⢶⣟⣛⡁⠀⠹⣓⠬⣳⣷⡫⠭⣿⠇⠘⢇⠀⢸⠤⠚⠁⠀⠀⠀⠀⣌⡛⠛⣧⣴⣶⡿⠁⠀⠀⠀⠀⠄⢛
⠀⠀⠀⠀⠈⠉⠓⠛⠋⠉⠁⠀⠀⠀⠈⠉⠈⡏⠈⠉⠀⠀⠀⠀⠑⢾⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠋⠂⠀⠰⢖⠀⠀⠀⠀⠀⠀⢰⠊⢦⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡆⠀⠀⠀⠚⠝⠇⠁⠀⠀⠀⠢⠀⠀⠀⣁⠘⠊⠻⣯⣿⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣆⠂⠀⠀⠠⢀⠐⠃⠀⠀⠀⠀⠀⠀⠘⢋⡆⠀⠀⠸⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠡⣀⠠⠮⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠹⣄⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⢀⠑⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠈⠞⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠘⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠉⣉⡀⢠⣄
⠀⠀⠀⠀⣀⣀⠃⠀⠀⠀⠉⠀⢤⡀⢀⠀⢤⠀⠄⠀⠀⠄⠀⠀⡠⢹⡴⡼⠂
⠀⠀⠀⠈⢄⡱⠀⠀⠀⠀⠀⠀⠀⠁⢄⠐⠀⠈⢀⠄⠂⠆⠀⠀⠈⣺⣿⢫⡶⡄⠀⠀⠀⢀⢰
⠀⠀⠀⠀⠈⠀⠒⠀⢀⠀⠀⠀⠀⢠⣠⠀⣠⠀⠀⠀⠀⠀⠀⣦⢾⡿⠕⠙⠣⡁⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠐⡀⠏⠃⠻⡆⢹⡇⠀⠀⠀⠀⠂⠉⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⣠⠀⢄⠈⠄⠀⡀⠀⠀⠐⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠄⢠⣄⠤⠆⠀⠀⠘⠄⠀⠈⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠠⡀⠈⠀⠀⠀⠀⠉⠀⡀⠄⠄⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⢂⠀⠀⢀⡀⠀⢀⣠⣤⡔⠐⠉⠚⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⡁⡀⠀⡔⠁⠘⡇
⠀⠀⠀⢠⠊⠁⡦⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠀⠴⢤⣾⡀
⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢇⠀⣠⢤
⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⠀⢰⠒⠀⠀⠠⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠌⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠢⢇⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠈⠀⣤⢠⠀⠀⠀⠀⢠⡴⢄⠀⠺⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠈⠓⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡅⠀⠀⢀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠰⠆⠀⡀⠀⠦⠀⠀⠳⣆⣀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣀⠀⠀⠀⢠⣧⢠⠀⠤⠀⡤⠈⣉⠹⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢻⣷⣤⣤⣾⣡⣴⣶⡶⣦⣴⢶⣤⣶⣿⣦⡀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⡀⠀⠀⢾⢋⣡⣶⣿⢿⣻⠷⠟⠁⠘⠻⠿⢛⣡⣾⣿⣿⡿⢟⠉⡇⠀⣶⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠃⠀⠀⢸⡿⣟⡿⢾⣛⣥⣶⠀⡾⠛⢷⡔⢻⣿⣿⡟⠧⡑⠊⢀⡇⠀⣿⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣸⠗⢫⣵⣾⣿⣿⠇⣾⡆⠀⠘⣧⠘⢋⠓⠉⢀⣴⣾⣿⡇⠀⠈⠻⠶⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠙⠗⠛⠛⠛⠛⠻⠖⠛⠁⠀⠀⠻⠖⠛⠛⠓⠾⠟⠻⠾⠃⠀⠟⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣼⠇⠀⠀⠀⡀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠤⢤⣾⢷⣄⠀⠀⠀⡶⠀⠀⠀⠀⠀⠃⠀⠀⢀⣠⡴⠛⠉⡟⠛⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠉⢳⣶⣤⣤⣤⣤⣤⣤⣤⣤⠶⠖⠋⣿⣄⠀⣠⠇⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠴⠀⠋⠀⠈⠳⠶⡾⢿⡄⠀⢀⣿⡅⠀⢀⣿⣆⠀⣠⡟⢻⡟⠁⠀⠀⠀⠈⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠙⠛⠻⠉⠙⠒⠛⠉⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠈⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⡄⠀⠀⡀⠸⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠁⠀⠀⠀⠀⢤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⡆⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠟⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠈⠀⠈⣷⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠉⠀⠀⠀⠀⠀⠀⣀⠃⠈⢷⣄⢀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀⣠⠇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠄⠈⢳⡶⠋⠀⠀⠀⠈⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢷⣄⣀⣴⠟⠀⠀⠀⠀⠈⠷⣤⣴⠟⠁⠀⠀⢠⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠾⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⡀⠈⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠓⠒⠛⠁⠀⠀⠻⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠸⠇⠀⢡⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠀⠀⣶⠀⠀⠀⠀⠀⠈⢷⣄⣀⣴⠆⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣠⡏⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⡀⠀⢸⣽⣿⠀⠀⢰⡀⠀⠘⠁⠀⢸⣄⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⠞⠋⠀⠀⠀⠛⠀⠀⠀⢀⠀⠀⠈⠁⠀⠘⣿⢾⣇⠀⣸⡇⠀⠀⠀⠀⢸⡛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⠀⠀⠀⠰⠗⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣎⢻⡟⢿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢧⡙⢿⣷⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠸⣦⣤⣴⡿⡹⣦⢻⡌⢿⣦⡀⠀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⣿⡀⠉⠈⠷⠸⣧⡿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣼⣟⠀⠀⠀⠀⠀⡇⠀⣤⠀⠀⠀⣿⠃⠀⠀⣤⠀⠈⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣿⠀⠀⠀⠀⣀⠃⠀⠋⠀⠀⠀⣿⠃⠀⠀⠀⢠⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⣀⣤⣿⠀⠀⠀⠀⠀⢀⣿⠀⠂⠀⣄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⢿⡄⠀⠀⠀⢀⣼⠇⠀⡀⠀⠘⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠞⢿⡏⠀⠈⠃⠀⠀⠠⠀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⠀⡀⠀⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠲⠀⠀⠈⠃⠀⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢠⠀⡀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⠀⠀⠁⢤⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣀⠀⣀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁