SpongeBob SquarePants Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠠⣀⢠⡀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⠈⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢐⡭⠄⡷⢑⠄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡒⠈⠤⠚⠂⠢⡀⡄⠈⡤⡌⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡱⣍⠀⠠⡀⡈⠃⠀⠄⠜⣠⠅⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⠀⠱⣌⠰⣤⣤⣥⠀⣶⣭⡀⠰⠆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢝⠠⣬⡢⡈⠻⣿⠿⠿⠛⠇⠘⠿⠘
⠀⠀⠀⠀⠀⠀⠶⠖⠀⠶⠆⠶⠆⠰⠆⠶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⠑⠈⢄⠡⡾⢂⠁⢒⣚⣥⢶⣾⣥⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠈⠁⠀⠛⠠⠘⠐⣚⣻⣷⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢀⣀⠻⢿⣿⣿⠟⠋⣉⡀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⢼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⢆⡨⠏⠉⠀⢸⡏⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠻⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣴⣶⣶⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣉⠛⢉⡉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⡛⣠⣌⣵⣿⣿⠀⠀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⣾⠁
⠀⠀⠀⠀⠀⣘⣶⣧⡀⠀⢿⣿⣿⣿⣿⡿⢿⢻⣿⣿⠡⠴⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡽⠋
⠀⠀⠀⠀⠀⠘⠋⠉⠉⠳⠎⢻⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⠛⣛⣻⣿⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠻⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⡏⠁⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡀⠀⠶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢰⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠀⠤⠒⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠙⠂⠐⠂⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢸⠀⠀⠀⠀⣀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠣⡀⠀⠸⠁⠀⠀⠘⠂⠀⠀⢀⡀⠀⠀⢰⣶⠀⢀⣀⠀⠀⢀⣤⠀⠀⠀⣿⡆⠀⣠⣄⠀⡇⠀⠙⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠙⠀⠐⢄⣀⣀⡴⠀⠀⠀⢻⡿⠄⠒⠚⠛⠂⠾⣿⠁⠀⠈⡿⠗⠒⠈⠉⠉⠚⠻⣇⠀⠘⠀⠚⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡠⠆⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠎⠀⠀⢀⠇⠘⠀⠀⣰⠊⠉⠂⠀⢰⠁⠀⠀⡀⠀⡀⠀⠀⠀⠀⢠⠁⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⢱⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢄⣀⡠⠎⠀⠀⢃⠀⠹⠄⠠⠃⠀⠀⠀⠠⡎⣴⣶⣌⢣⠀⠀⠀⢸⠀⠀⡜⣵⣾⣷⡜⠀⠀⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠀⢐⣏⠿⠿⢛⡜⠀⠀⠀⠈⡄⠀⠱⡙⠿⢛⡱⠀⡀⠀⠀⠀⡜⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⡔⠋⠑⠀⠀⢀⠀⠀⠀⢀⠴⣂⠉⠴⠉⠙⡀⠒⠉⠀⠀⠀⠀⣠⠞⠢⡀⠈⢉⡩⠔⠊⠁⠀⢱⡞⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠑⠤⠚⠀⠀⠈⢣⠀⠀⡎⠀⠁⠘⣀⡀⢠⠇⣀⡀⢀⡀⠰⠊⠁⠀⠀⠙⠉⠁⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⠤⠤⡀⢸⠀⠀⠘⠄⠀⠋⡍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠤⠄⢶⡉⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠃⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠳⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠢⠤⠔⠁⢠⠀⢀⠊⠑⢆⠀⠸⠀⠀⠀⠀⠀⠀⠈⣿⠀⠐⠶⠂⠲⠀⠉⢹⠉⠁⠀⣠⠖⠢⡀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡄⢳⡘⣄⣀⡼⠀⠀⢶⠀⠀⠀⠀⠀⠀⠿⠀⠀⠇⠀⠠⣀⣀⡸⠀⠀⠀⢧⣀⣀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠨⡄⢀⠆⠀⠱⠀⣀⠴⢄⠀⠈⢣⣀⠄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⢀⢀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠰⡇⠀⡃⠀⠀⢱⠀⠀⠣⣀⠀⠀⠈⠛⠁⠀⠈⠑⡄⠀⣉⠀⠀⢀⠎⠁⠀⢱⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠔⠃⠘⡀⠀⢠⠀⢣⡀⠀⠸⠂⠀⠀⣈⠓⠦⠄⣀⣀⣀⣀⠤⠾⠒⣁⠀⠀⣇⠀⠀⢠⠌⠀⠃⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡇⠀⢸⠀⠀⠉⠀⠁⠀⠀⠀⠀⠉⠑⠒⠀⠀⠠⠀⠐⠒⠉⠀⠀⠀⠈⠒⠂⡁⠀⠀⠇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⣀⡀⠀⠀⣧⣀⣠⣀⣀⠠⠔⠂⠤⢄⠀⢤⠤⠀⠀⢴⡦⠤⠤⣤⠐⠒⢒⠶⠀⠀⠒⠁⠉⠐⢻⣀⣀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠁⣜⠁⠠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠞⠀⡰⠲⡏⠀⠑⠖⠁⠀⠀⠀⣀⣀⢀⣀⣯⠁⢨⡤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⡟⢉⣀⣀⡀⠐⡗⠀⢀⣀⣒⣒⡒⠒⠒⣒⣒⣒⣺⠁⠀⢹⡀⠀⢀⡀⢀⡉⠉⠉⢭⠉⢙⢣⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡈⡇⠘⠠⠀⠇⠀⠀⠀⠲⠤⠀⠤⠋⠀⠘⠤⠀⠘⢧⡀⠀⡠⠃⠀⠘⠁⠘⠁⠀⠃⠉⠀⠸⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⢇⣀⣀⣀⣀⠀⢰⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡙⢊⡀⠀⠀⠀⠀⢀⠠⠄⠤⠤⠤⠆⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢾⠀⠀⠀⠈⠁⠀⠀⠈⢘⠃⠀⠀⠀⠀⠈⡍⠉⠈⠁⠀⠀⢸⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠺⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⡄⢶⠊⠁⠀⠀⠀⠀⠀⠈⠁⠖⢲⠒⠂⠉⠀⠀⠀⢀⡔⠊⠁⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⣈⡁⠀⠀⠀⠀⠈⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⢠⡒⠒⠊⣀⠀⠀⠀⠀⠡⢄⡀
⠀⠀⠀⠀⠀⠀⣉⠴⢃⣄⡀⢠⡎⠱⣄⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠⣆⣄⠀⠀⠀⠀⠙⠈⠁⢸⠃⢀⡀⢠⡶⢤⡬⠂
⠀⠀⠀⠀⠀⠘⣄⣠⠏⢰⠁⠸⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⡇⠀⠀⠀⠀⠀⠀⠀⢐⡇⢺⠀⠀⠀⠀⠀⠀⠀⣌⠀⢸⠘⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠃⠀⠀⠀⠀⠀⠀⠀⣨⠁⢹⠀⠀⠀⠀⠀⠀⠀⠙⠴⠊⠀⠑⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡸⠒⠢⡀⠀⠀⡴⠈⢇⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠔⠁⠀⠀⢡⠀⣈⠁⠀⠀⠑⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠉⠀⠀⠀⠀⠀⡜⠀⠻⡄⢀⠀⠀⠀⣈⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠘⠚⠁⠀⠀⠉⠚⠀⠀⠀⠈⠙⡁⠀⠀⠓⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⢀⡀⠞⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⡠⠞

⠀⠀⠀⠀⢴⡖⢰⢲⣤⠖⣆⣴⣠⢠⠖⡀⣶⠂⣶⡆⡴⢲⣠⣶⡄⠀⣶⡦⡄⠀⣰⡆⣴⠒⢤⡴⠀⢀⣦⠀⣆⣤⣴⢢⡄⠰⣠⣆⡦⣆⣤⣤⢲⡆⣴⡆
⠀⠀⠀⠀⠐⠛⠘⠉⠈⠓⠋⠉⠙⠈⠓⠃⠛⠀⠓⠋⠙⠚⠙⠛⠃⠀⠓⠋⠛⠒⠋⠙⠙⠂⠉⠙⠀⠘⠉⠃⠁⠋⠙⠚⠁⠀⠋⠙⠀⠃⠉⠉⠘⠁⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠀⠲⠀⠐⠂⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢋⡙⠟⣁⡈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⡘⠛⣠⣙⣵⣿⣿⠃⠀⢶⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣠⣿⠁
⠀⠀⠀⠀⠀⢶⣴⡇⠀⠈⣿⣿⣿⣿⣿⣾⡿⡿⢿⣿⣿⡇⣠⠾⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⡿⠛
⠀⠀⠀⠀⠈⠿⠟⠛⠳⢦⡜⢿⣿⣿⣿⣿⣷⣿⣾⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⠿⠟⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣭⣴⣶⣶⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠏⠉⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠹⣿⡿⠟⠛⠻⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⡄⠀⢸⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⡄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠨⠄⠻⢃⢄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⡉⠠⠚⠀⠂⠀⠤⠀⠔⡄⠐⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣈⠢⣀⠀⡄⠄⠉⠀⠀⠄⣰⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⠈⠲⡈⢶⣦⣤⣄⣾⣶⡄⠀⡂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢅⢶⡞⢄⢙⠿⡛⠛⢉⡃⠈⢛⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠂⠘⠓⠐⠃⠐⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢤⡆⠁⢢⡄⠺⠣⢀⣉⡭⢶⣻⣯⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢂⠌⠀⠀⠀⠀⠈⣀⣀⣀⣩⣽⣿⣿⠿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⠜⠛⣿⣿⠏⠁⣴⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠛⠴⠂⠀⠀⠘⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠲⠶⠖⠚⠛⠛⠒⠶⠆⠀⠚⠛⠛⠲⠶⠤⠄⠰⠖⠲⠶⠦⠤⠤⠶⠶⠶⠤⠤⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⡤⠖⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⡀⢹⡀
⠀⠀⠀⢀⣤⠞⠁⣀⡀⢸⡀⠀⠀⢈⠀⠀⢀⡼⠀⣤⡀⠀⢸⡇⠀⣰⠆⠀⠀⠀⠰⣆⠀⢀⣿⠀⠀⣤⠀⠸⠤⠔⠁⣸
⠀⠀⠀⡸⠁⠀⠌⠀⠁⠀⠳⡀⠀⠀⠁⣀⠁⠀⢀⡼⠛⠉⠉⠉⠉⠉⠳⢄⠀⣀⠔⠋⠉⠈⠉⠁⠺⢏⠀⠀⠀⠀⠀⡟
⠀⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠐⠁⢠⠋⠀⠀⠀⠀⠀⠀⣀⠀⠈⢳⠁⠀⠀⠀⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢲
⠀⢿⡀⠀⠀⠀⠑⠜⠀⠀⠀⢰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣡⣶⣭⠆⠘⠀⠰⢩⣴⣍⠳⠀⠀⠀⠀⡆⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⡴⠋
⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡙⠻⠋⠃⡸⠀⠰⣜⣻⣋⡴⠀⠀⠀⢀⡁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⡤⢠⡿⠒⣻⣄
⠀⠀⠀⣿⠀⠀⠀⠀⠐⠀⠀⠀⡃⠀⠀⠀⠀⠰⠉⠃⠉⠳⢦⡀⠀⠉⣀⠔⠙⢦⡀⠀⠉⢁⡠⠤⠂⠀⠈⢑⡄⠀⠀⣇⠀⠀⠀⠀⠀⢰⡏⠠⣀⣽⠋⠉⢉
⠀⠀⠀⠹⣦⠀⢀⡀⣠⠂⠀⠀⠁⠀⠀⠀⠀⠈⠀⠠⡤⠀⠀⠟⠒⠉⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⣀⣠⠴⠊⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⢧⡀⠀⠑⠖⣠⠎
⠀⠀⠀⠀⠈⢣⠀⠉⠁⡰⠋⠑⡬⡀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢋⣉⠉⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡟⢠⠖⠚⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠇⢱⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠒⠒⠒⣶⣶⠒⠊⢹⡏⠉⠁⠀⢀⡀⣀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡾⢠⠏
⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⠦⠊⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⡤⠤⠴⠃⠀⠀⢰⠁⠀⢈⠀⠈⡀⠀⠀⠀⠀⢀⡼⢁⡟
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣀⢄⠘⡄⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⣼⠶⠒⢢⣀⣠⠞⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢈⡷⠲⣤⡁⠌⠀⢱⠀⠰⠛⠀⠀⠘⢦⣀⡀⠉⠉⠉⠉⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠂⣦⠀⢠⠃⠀⢘⣉⣭⡥⠴⠋
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠸⠁⠀⠀⢸⠀⢀⠊⠈⡱⠀⠢⣈⣉⣛⣛⣛⠛⠛⠉⣁⠀⠀⠀⠀⠀⠀⠑⠘⠁⠀⢸⣤⣤⣬⠜⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣧⣀⠀⣀⣀⣈⣒⣈⣀⡀⠀⣈⣀⣉⣁⣈⠉⠉⠉⢁⣀⣀⣀⣀⠀⣀⣀⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠉⢶⠲⡖⠁⠀⠀⠀⠉⠉⠀⠁⠉⠙⠛⠭⣀⡀⡠⠝⠻⣉⣩⠋⠣⢄⡨⠟⠉⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⢽⣤⣶⠒⠶⠀⢀⠀⠀⠀⡀⠀⢀⣈⣀⣒⣶⠃⠘⣖⣒⣀⣀⠐⣒⣒⣒⣒⡒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣧⠀⠀⠉⠀⠀⠀⠘⠛⠛⠛⠛⠀⠘⠛⠛⠛⠳⡀⣠⠟⠋⠉⠉⠀⠙⠋⠙⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠙⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⣇⠈⣏⠉⠉⠉⠉⠉⠉⣻⠉⠉⠉⠉⠉⠉⠻⣍⣉⣉⣉⣉⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡇⡄⢰⠆⠘⠀⠈⠙⢶⠶⡶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠤⠇⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣦⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠈⠄⣠⣶⣿⣿⡿⠿⠿⣿⡿⠛⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠷⠛⠛⠛⠛⠉⠉⠉⠛⠛⠛⠉⠉⠒⠦⠤⣠⣴⣒⠓
⠈⠢⣴⣿⣿⣿⣿⡟⠀⢰⣦⣤⠀⠰⣦⣄⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢸⠁⡠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⢀⢷
⠀⢰⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣧⣀⣹⣿⣧⣘⣿⠄⢰⠀⣄⣥⣄⣀⣴⠋⠀⣸⡿⠀⠑⠋⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⠤⣤⠝⢀⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⠁⠀⠁⢈⠁⠀⣴⣿⠁⠀⠛⠀⠀⣠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠋⠀⠲⠄⠀⠀⢰⣿⡏⠀⠀⠀⠀⢰⣿⡤⠀⠀⠀⢠⣿⣤⠀⠀⠀⠀⠀⠀⠔⣠⡄⠛
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠄⡀⠸⣿⠇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠿⠃⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⣀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⠁⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⡘⠀⣠⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⢐⣤⣀⠀⠀⠌⢠⣶⡌⣼⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣇⠀⠀⢰⣶⠀⠀⣀⣿⠇⠀⠀⠀⠸⠟⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠓⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⣀⠀⠀⠄⣀⣀⣿⣿⣿
⣿⣿⣿⣿⣿⢟⣩⣽⣶⣭⣛⢿⡋⠉⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣖⣲⠆⠀⠀⠙⠻⠿⠿⠿⠛⠁⠸⡥⠇⠘⡀⢿⣿⣿⣿⣿
⣿⣿⣿⠿⣷⣿⠿⡿⠟⣈⠛⢢⠷⣄⡀⠈⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢾⣿⣶⣤⣤⣤⣴⣶⣿⡆⠀⠀⠀⢀⡁⠜⢿⣿⣿⣿
⣿⣿⣧⡔⢂⣄⠀⠀⠄⠈⡀⣂⣥⣘⣇⣴⣿⣦⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠉⣠⣴⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠿⣟⢦⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⣮⣧⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠀⠉⠁⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⢹⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⡤⠒⠚⠉⠛⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠃⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡌⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡽⠀⠄⢀⡠⠞⠁⠀⢠⡄⠁⠀⠉⠓⠒⠆⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢘⠁⠀⠀⠀⠀⡴⠀⠀⠀⣀⡀⠀⠀⣄⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠀⢹⠀⢳⠄⠒⢲⠲⡿⣋⠈⠉⠉⠉⢍⠛⢫⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡞⠁⠘⠢⣀⠀⠑⠈⠉⣆⠀⠀⠀⠀⢈⡔⠀⠀⠀⡜⠀⠀⠀⠀⠉⡀⢠⠏
⠀⠀⠀⠀⢠⠔⠉⠉⠓⢤⡀⠀⠀⠀⣳⣄⡀⠀⠀⠁⠒⠤⠊⠀⠑⠒⠒⠒⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⡔⠁⠀⠀⠀⠉⠐⠈⠲⡄⠀⢻⠈⠙⠓⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⢀⣠⣇⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠸⠀⠀⠀⣠⡤⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠸
⠀⣯⠤⢼⠀⠀⠰⠨⡀⣀⡴⠁⠀⡖⠒⠀⠀⡀⠦⠐⠀⢡⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠐⣧⠄⢺⠀⠀⢀⠀⠈⠩⠇⠀⠀⢡⠀⡄⠀⠀⠈⠀⠀⠘⢳⠀⠀⠈⠉⠀⠀⣀⡤⠒⠉⠉⠆⠀⠀⠀⢰⠃
⠀⠙⢾⠉⠀⢰⠀⠀⠀⠘⡀⠀⠀⢰⠐⠼⣠⡤⢶⠀⠀⠀⠻⢤⡀⠀⠀⠀⢸⢁⡀⠀⠀⢀⡆⠀⠀⠀⣿
⠀⠀⣀⠀⠀⠄⠳⣄⡀⢀⡅⠀⠀⠻⢦⠞⠁⠀⠈⠓⠲⣄⠐⢄⠈⠀⠀⣀⠼⢋⡼⠆⣠⠎⠀⢀⠀⢠⡏
⠀⠀⢻⠀⠀⠀⠀⠀⠉⢩⣍⠢⠔⣃⠈⡗⠒⠲⢶⡒⡳⠆⣷⣤⡙⠫⠛⣁⠔⠉⠑⠚⠉⠉⠋⠉⠉⢻
⠀⠀⠈⠓⢤⡀⠀⠀⠀⢰⠀⠙⠊⠉⠉⡗⣒⣀⠀⠈⢠⠈⢱⡈⡙⠢⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⢺
⠀⠀⠀⠀⠀⠉⠲⣄⡴⠋⠀⠀⠀⠀⠀⡇⠉⠉⠁⠙⠛⢆⢠⠛⠒⠀⠰⠶⠦⠄⠀⠉⠀⠘⠛⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠖⠶⠶⠶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⡤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⠀⠀⢰⠃⠀⠀⠀⡜⠉⠉⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⡼⠥⠎⠀⠀⠀⠀⢱⠎⣱⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡠⣆⠀⠀⠀⠀⠀⠀⠊⢰⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠠⣄⠀⠀⠀⠀⠐⣮⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣾⣷⣾⣿⡇⠀⢀⣀⣀⣸⣦⣼⣶⡀
⠀⠀⠀⠐⢀⣀⣂⣑⣼⣥⣄⠀⠀⠀⠀⠀⢿⣿⣾⡿⠛⠹⠟⠁⠠⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣯⡽⠾⠾⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⢀⡞⡭⠷⡀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠘⢭⡗⢡⠃⠀⠀⠀⠀⠀⡰⠱⠆⠈⠉⠉⠢⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠎⡄⠀⠀⠀⠀⠎⢂⠔⠚⠓⠫⡤⠀⢀⠀⠈⠀⠉⠓⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠘⡼⡀⠀⢀⠜⢀⡃⠀⢠⣶⣆⡜⠊⢉⠙⠣⡤⠀⢰⣶⠄⢀⠭⢽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣣⠀⢸⠀⢪⠉⠳⡈⠛⢻⠀⠸⣿⡷⠀⢱⠀⠀⢀⠴⢡⣶⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠓⡇⠀⠶⡓⠤⣈⠒⠙⢄⠀⡠⠤⣠⠃⠀⡠⠃⢀⠀⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠃⠀⠀⢼⣑⣦⠤⢤⠤⠭⢷⠆⢈⠆⡸⡀⠀⠈⡠⠊⠀⠀⠀⠀⢀⡤⣴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡆⠀⣜⢉⡬⢿⠯⢤⡴⠁⡀⠀⡞⠀⠛⣠⣊⠀⠀⢀⣀⠠⠤⣊⢸⡼⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡑⠬⠝⣒⢒⡒⠁⠀⠘⠋⡰⢁⡔⠊⠁⣶⡯⠭⠒⠂⠉⠁⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣈⣫⢶⣤⣅⣀⡀⠀⠂⠀⡇⠓⢉⡲⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣋⡙⢿⠉⣾⣯⣭⣍⣑⢺⣓⣊⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⡍⢉⠟⠓⠳⠬⢬⣛⣛⢹⣝⣋⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⡕⠛⠓⠁⠀⠀⠀⠀⠀⠀⠈⠻⣍⡥⢟⡢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⠋⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠓⠒⠒⠋⠉⠉⠓⠦⠤⠖⠋⠉⠉⠲⠤⠤⠶⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠃⠀⢠⡆⠀⠀⠀⢰⠄⠀⠘⠃⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣀⠤⠾⠤⣀⣀⠑⠳⠶⣷⠒⣴⠁⠙⡖⢒⣓⣒⡓⢋⡹⠷⠶⠦⣄⡀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡎⠀⠀⣠⠤⠀⠀⣱⠀⠀⠀⠀⣯⠀⢸⠀⠀⠀⠀⠠⡏⠀⠀⢴⠤⠀⠈⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⠤⠀⠀⠢⣀⠐⠁⠀⠀⠀⠀⠸⠀⠂⠀⠀⠀⠀⠀⠙⠂⣠⠎⠀⠠⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠤⠖⠋⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠩⠉⠀⠈⡇⡀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠺⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢧⣀⣀⣀⣤⣀⣀⣀⣤⠤⠤⣄⡀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⡇⠀⠀⠀⠀⠉⠀⠉⠓⠦⣠⠿⣉⡽⢄⡬⠟⠛⠛⠉⠉⠉⠉⠛⡯⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠒⣒⣒⣒⡒⢒⣒⣒⣒⡒⡾⠀⢹⣀⣶⣶⣶⠶⢶⣖⣒⣒⢲⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⠀⠉⠉⠉⠀⠈⠉⠉⠛⠁⠣⣀⠞⠉⠉⠉⠉⠀⠈⠉⠉⠉⢸⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠒⢒⠒⠶⢤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⣸⠀⠀⠈⠉⢻⠛⡏⠁⠀⠀⠀⠀⠈⡛⢹⠋⠉⠀⠀⣆⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠢⡣⡅⠀⠀⠀⠀⣆⣰⠀⠀⠀⠀⠀⢰⣀⡆⠀⠀⠀⢸⠕⠞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⡏⠈⡆⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠘⠚⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣠⣇⡀⡇⠀⠀⠀⠀⣧⣀⣧⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⡿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠙⠉⠁⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣀⣤⠴⠶⢦⣄⣀⣀⣤⡤⠶⠦⣤⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠈⠙⠲⠶⠚⠉⠀⠈⠙⠲⠖⠚⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⣭⠑⡄⠀⠂⠀⡔⢋⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣀⢤⣤⡀⠀⠀⠀⠀⠣⣈⣛⡠⠃⡠⠤⡀⢇⠘⠛⣠⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠞⠀⢀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠊⠈⠉⠱⡄⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢀⠌⠁⠰⠃⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⡤⢤⠤⠤⢰⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠠⠃⠐⠦⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢲⠤⠤⠶⠲⠦⠤⠴⢶⣚⠛⠲⢤⣄⣠⡴⠶⢤⣄⣀⣀⣠⠤⠤⣄⣀⣠⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠊⡳⢴⡟⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⣼⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⡏⢉⣭⣭⣭⠉⠉⣭⣭⣭⣭⢹⠃⠀⢯⣹⣿⣿⣿⠛⣻⣿⣭⣭⠙⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⠀⠉⠉⠉⠀⠀⠉⠉⠉⠁⠙⢦⡴⠋⠀⠀⠈⠀⠀⠈⠉⠉⠉⢸⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⢙⣟⠓⠲⢶⠶⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠞⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢻⣿⠀⠀⠈⠉⢻⡏⢿⠉⠀⠀⠀⠀⠀⢹⠋⣹⠛⠉⠀⠀⣇⠂⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⢾⢻⡗⠀⠀⠀⠀⣇⢘⡆⠀⠀⠀⠀⠀⣯⣠⡇⠀⠀⠀⢼⡑⡶⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠛⠁⠀⠀⠀⠀⡏⠁⢷⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⠀⠘⠾⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣇⠀⢸⠀⠀⠀⠀⢠⡇⣸⣧⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠻⠿⠛⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡇⠀⠀⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⢂⣈⠭⢄⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠄⠔⠀⡠⢂⠔⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⢀⠎⠀⠀⠀⢀⣠⣤⣤⣌⣀⣤⣤⡀⠀⠀⠀⠊⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⣠⡤⠦⣤⣤⡴⠞⠛⠉⡛⠛⠉⠙⠉⣀⠦⠆⠈⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢴⡁⠈⠉⢁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠈⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⡏⠈⠐⠢⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡰⠦⠀⠀⠀⠊⠢⠀⠀⠘⡄⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠂⠈⢄⠀⠈⠀⠀⢐⠒⠠⢄⠀⠀⠁⠀⢀⠀⠀⡠⠀⠀⢠⠃⠀⠀⠀⠀⢠⠀⠀⣰⠋
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠁⠀⠑⠢⢀⠀⠀⠀⠀⣨⠄⠀⠀⠀⠀⠀⠁⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⣧⠜⠁
⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠉⡉⠁⠀⠀⠤⠤⠤⠤⠆⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢀⣀⣀⠀⠌⠉⠦⠀⣀⡀⣠⡄⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢠⠋⠁⠀⠀⠀⢀⡤⠂⢈⠀⠀⠀⠀⢀⠈⠂⠀⠱⣦⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⢸⠀⠀⠀⠄⡀⠈⢀⡐⠄⠀⠀⠀⠀⠈⠁⠀⠄⠀⠘⢿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠆⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠈⢦⡀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠄⠀⠀⠀⠘⠆⠀⠠⠀⠀⠢⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠉⠒⢒⣁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⡌⠑⠂⢠⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠂⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢂⠉⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠂⠉⠁⠀⠀⠀⠉⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠙⠢⢀⠀⠀⠀⠀⢀⡀⠠⠀⠐⠀⠈⢀⣀⠤⠔⠒⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠒⠈⠁⢀⣀⡤⠤⠒⢂⠉⠁⢄⠀⠀⣀⡐
⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣶⣶⠀⢀⠄⠀⠙⠲⠒⠒⠉⠁⠀⠀⣠⣾⡿⠇⠀⡠⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠟⠋⠈⠉⠋⠀⠀⠡⢄⡀⠀⡠⠀⠀⠀⠀⢸⣿⠀⠘⣶⣦⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢠⡞⠋⠉⠛⠛⠛⠋⠉⠈⠉⢿⣟⠛⠛⠋⢉⡿⠃⠀⠀⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⢀⣠⣭⣭⣉⠉⠉⠉⠙⣧
⠀⠀⠀⢸⡄⠀⠀⣤⠶⠶⠶⣦⡀⠀⠀⠙⠛⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠉⢳⡄⠀⢀⡟
⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⣨⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⠀⣾⠃
⠀⠀⠀⠀⣹⠀⠀⠈⠛⠛⠛⠉⠀⠰⣆⠀⠀⠀⣿⠀⠀⢠⡗⠀⠀⠀⠀⢰⡆⠀⠀⢸⡇⠀⠀⣰⠇⠈⠻⢶⣤⣤⠾⠃⠸⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠶⠾⠛⠶⠶⣾⡁⠀⠀⠀⠀⠀⣻⡴⠶⠟⠳⠶⠶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⣠⡶⠛⣿
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣴⠶⠶⢶⣄⠀⠈⢿⣼⠃⠀⠀⣠⡴⠶⠶⢦⡀⠀⠀⠈⢷⡀⠀⢰⡏⠀⢰⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⢠⣶⣷⣦⠘⣧⠀⢸⣿⠀⠀⢸⡏⣰⣶⣶⡄⢻⡄⠀⠀⢸⡇⠀⠘⣧⠀⣾
⠀⠀⠀⠀⠀⣾⣤⣀⠀⠀⠀⣿⠀⠀⠀⠈⣧⡘⢿⣿⠟⣠⡟⣠⣼⣿⣤⡀⠸⣇⠻⣿⡿⠃⣼⠃⠀⠀⣸⠇⠀⠀⠈⢻⡇
⠀⠀⠀⠀⢰⡏⠀⠉⢳⣄⠀⠘⣧⡀⠀⠀⠈⠛⠶⠶⠞⠋⣰⠏⠀⠀⠈⣿⠀⠙⠳⠶⠶⠟⠁⠀⠀⣠⠟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠀⣿⠀⣀⣌⠳⣦⣀⡀⠀⠀⠀⣀⣠⣿⠀⠀⠀⢀⣿⣦⣀⠀⠀⠀⠀⣀⣠⡾⠋⢠⣄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢹⡆⢀⣴⠏⣼⠿⣤⡀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠾⠃⠀⠉⠛⠛⠛⠛⠉⠁⠀⢀⡼⠻⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⡋⠁⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣏
⠀⠀⠀⠀⣴⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⠛⠳⣶⣶⠖⠚⠛⣿⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⡏⠙⣦⡀
⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⣿⣀⣀⣀⣿⠀⠀⠀⠀⠀⣰⠟⠉⠈⠉⢳⡄⠸⣇⠀⠈⣷
⠀⠀⠀⣿⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣌⣉⢉⣉⣁⣌⣉⡉⢉⣁⡴⠟⠁⠀⠀⢿⡀⠀⠀⠀⢠⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠈⣿⢙⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠋⠀⠀⣿⡟⢻⡏⠁
⠀⠀⠀⠀⡇⢸⡟⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀⡀⢀⣼⠃⣿⠸⡇
⠀⠀⠀⢰⡇⢸⡇⠈⣿⠛⠛⠛⠶⠶⠚⠋⠉⠙⢿⣍⡉⠉⣻⣿⣅⢀⣴⠿⣄⠉⠛⣻⡿⠟⠋⠛⠛⠉⠉⠉⠉⣿⠁⠀⣿⠀⡇
⠀⠀⠀⢸⡇⢸⡇⠀⢸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣾⣋⣀⣿⠛⣷⣀⣙⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡟⠀⠀⣿⠀⣷
⠀⠀⠀⣸⠇⠘⣧⡀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠇⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⣰⡟⠀⣿⡀
⠀⠀⢠⣏⠀⣰⢿⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⢷⡀⢈⣧
⠀⠀⣾⢻⣇⣸⣾⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣾⣀⡿⢻
⠀⠀⠸⣦⡙⡏⣿⡗⠀⠸⠷⠶⠶⣶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠾⠃⠀⠸⣿⣿⡟⣡⡟
⠀⠀⠀⠈⠙⠻⠟⠁⠀⠀⠀⠀⠀⠻⣦⣤⣀⣀⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣄⣀⣀⣤⡴⠇⠀⠀⠀⠀⠀⠀⠙⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠏⠙⠛⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠙⠞⠋⠻⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣤⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣄⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⡴⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠳⣤⣀⣠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡤⠀⢀⣀⡤⠤⠄⡤⠤⠀⠠⠴⠒⠢⠒⢤
⠀⠀⠀⠀⠀⠀⢀⠔⠉⡁⠀⠀⠀⠀⠀⠀⠀⡀⢰⡄⣄⠀⠰⠄⠓⠸⠀⠐⠸⡇
⠀⠀⠀⢀⠄⠐⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠐⡄
⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢃⠀⠗⠈⢢
⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⡂⠀⠀⠀⠘⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠠⡀⠀⢀⣦⡵⣶⡄⠂⠀⣀⠔⢻⠀⠀⠀⠀⠀⠀⡠⠄⠤⠀⡔⢀⠁
⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⢀⡀⠐⠤⠠⠟⠀⠉⠠⠐⠚⠁⣀⠸⠀⠀⠀⡠⠀⠈⠁⠈⠢⠀⠃⢎
⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣶⣤⣤⣤⠤⢤⡴⠖⠚⠉⠀⠀⢣⠀⠜⠀⠐⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣀⣸⣷⣤⠜⠀⠀⠀⠸⠀⠯⠀⠠⠀⠠⠀⠀⠒⠋⠀⡹
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡀⠣⡤⠤⠐⠀⠠⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠿⠿⠿⠿⢿⣷⡀⠀⠂⢸⠤⢤⠑⠂⡤⢤⠔⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡄⠢⡀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢀⣿⠇⠀⠁⢀⢰⠒⠒⣋⠡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠸⠀⠀⢰⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⢀⣰⢯⠅⠠⠂⠁⢱⠤⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡇⠀⠀⠈⡤⠤⢥⡀⠤⠴⢆⡀⠊⢁⠜⡀⡈⠑⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢲⢲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣁⡐⠀⢰⡶⠖⠟⠛⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠿⢸⣦⣤⠀⠐⢀⣤⣴⠶⠐⠛⠋⠁⠀⠀⣀⣠⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣸⠸⠀⠀⠀⠀⠈⠁⠀⣀⣀⠤⠴⡖⠋⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⣗⠒⠲⠒⠚⠙⠁⠀⠀⠀⠙⡖⠲⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣹⠢⠤⢤⠐⠊⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣠⣸⠀⠀⡇⠨⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⢀⣴⣤⣧⣄⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣠⡀⢀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣿⡆⠀⠀⠉⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣠⠤⠴⠞⣛⡓⡶⠶⠒⠲⠶⠒⠿⠔⠶⠖⠒⠒⠒⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠠⠄⠀⠀⠈⠀⡄⢀⠀⠀⠀⠀⡀⢰⠀⡄⠀⠀⠀⠀⠀⢠⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⡸⠖⠓⠻⢄⠀⢀⡤⠃⠉⠙⠣⡀⠀⠀⠂⠀⠋⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠁⠀⠎⠀⠀⠀⡀⠀⠱⡎⠀⠀⣀⣀⠀⠘⡄⠀⠀⠀⡄⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⠀⠀⡰⢉⣌⠱⠀⠀⠀⠊⣤⣄⠡⠀⡇⠀⠀⢰⠁⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡴⠒⠦⡤⠦⠾⠿⠗⢢⠗⢒⣚⠛⡿⠫⠉⡑⠀⠀⠀⠀⠂⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⢇⡀⠀⠈⠑⠤⣀⡴⠋⠑⢄⡀⠰⡅⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠉⠓⠲⣤⠤⠤⠀⠀⠀⠀⠉⢉⡩⠓⠒⠂⠀⠀⡇⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠯⣤⣤⣤⣤⡤⠤⡔⠂⠁⠀⠀⡆⠀⠀⠀⡇⣰⣆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣧⣀⡿⢸⣄⣠⡇⠀⠀⠀⢀⡇⠀⠀⠀⡇⡿⠯⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣻⢿⢢⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠄⢸⠁⡄⠀⠘⢇⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣞⡀⠌⠉⢸⠇⢀⠁⠀⢳⠀⢀⡤⠒⠖⠛⢉⠇⠀⠀⠀⠀⠀⢣⠀⠀⢈⠆⠀⠀⠀⡃⠥⠠⠒⣈⠇
⠀⠀⠀⠀⠀⠀⢰⣧⡘⣮⠴⣤⣤⣤⠟⠐⠀⠀⠀⠀⠳⡞⠀⠀⠀⣠⠋⠀⠀⠀⡀⢀⠄⠈⠳⣶⡙⡄⠀⠀⢸⠀⠀⠀⡛⣉⠬
⠀⠀⠀⠀⣀⠔⠋⣀⡿⢓⡴⢁⡤⢾⠀⠀⠀⠀⢀⠤⢄⡨⣥⣤⣭⡤⠤⠤⠀⠀⠀⠀⡀⣀⡠⠶⡷⡈⢆⡠⢀⠔⠒⠢⠍⠱
⠀⠀⢠⣮⢁⡤⠞⠉⡃⠋⠀⣋⡄⠘⣦⠶⠒⠂⠺⡀⠀⢩⠀⢐⠨⠄⠀⣴⠖⠒⠲⠖⡏⠉⠀⠀⣧⠙⢄⠔⠁
⠀⠀⠘⠛⠁⠀⠀⠀⡇⢀⠔⣡⣞⣠⢿⡀⣀⠀⠀⠳⡶⠚⠓⠚⠑⠦⠤⠞⠀⠀⠀⠀⢠⢀⣠⡶⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠞⠁⠈⠁⠈⡇⠺⠶⠶⠶⠀⠶⠶⠶⠶⠶⠀⠀⠶⠶⠶⠦⠀⠈⠉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⢤⡤⠤⠤⡤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣄⣀⣠⡗⠀⠀⠀⠀⠀⠠⣇⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣤⣷⣿⠄⠀⠀⠀⠀⠀⠀⠀⢈⣌⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠻⠟⠀⠀⠀⠀⠀⠀⣾⣵⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⢈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠿⠀⣀⢈⡖⠠⣀⠀⠀⠀⠀⠀⢎⠛⠉⣬⢔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⠀⢀⠠⢦⠈⢷⠀⠀⠀⠀⠘⡔⣃⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠰⣎⠀⠀⡸⠤⠼⠄⡀⠀⠀⢰⢳⠇⢠⠒⠲⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣄⣉⣉⣀⣀⣤⡾⠃⠀⠀⡀⡞⡴⢋⠠⠚⠰⢆⡄⢉⡍⢑⠒⠒⠦⠤⠤⣄⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣿⣿⣿⡿⠷⢤⡴⢣⢀⣳⡖⡐⠁⢀⣤⡄⡠⠓⠉⠉⠙⢶⠀⢰⣉⠅⡠⠔⣷⠀⠀⠀⠀⡸⠸⢔⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠙⠤⣄⣤⠤⠊⠀⢸⣎⡽⢸⡉⠂⡈⠛⠛⠀⢼⣿⡆⠀⡘⠀⢀⡴⠂⢰⢓⠌⡆⢀⠀⢐⣁⠔⠀⢤⠼
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠞⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⣕⠦⠌⠈⠱⣀⢀⠉⠀⢞⠁⡠⠎⢴⠄⢈⡠⠀⠩⠄⠈⠀⠀⠀⠀⠐
⢀⠤⠐⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡏⠇⢸⣉⣷⠲⣦⣤⣥⡾⠃⢊⠎⠀⡠⢺⢚⣅⠂⠔
⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⣾⣿⣿⣿⣿⣿⠏⠀⠰⣉⡀⣎⣀⣈⡥⠃
⠀⠀⠉⠉⠒⠒⠶⢦⡤⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢜⠻⠇⠤⠤⠚⠡⠒⣠⠃⠧⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠲⠐⢦⠬⣍⣉⣀⣈⢀⡇⠀⠁⠰
⠀⠀⠀⠀⠀⠀⣠⣤⢇⡈⠀⠐⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠗⣈⠙⠶⠏⣧⣄⠠⣤⡀⣍⢁⣈⣴⠇
⠀⠀⡀⠀⣀⣠⡇⠀⠢⡄⠀⠀⠀⠁⠨⠂⠀⢀⡀⠀⢀⣀⡀⢄⣠⡴⠴⠙⡏⠐⠓⣤⢤⣤⣈⣁⣇⣈⡥⠼
⠀⠸⡀⠀⠀⠀⠁⡀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣀⠒⠒⠈⠁⢤⠀⣨⡞⠙⠦⣔⢇⠀⢠⣿⣄⣀⣠⠃⠀⣠⣤⡀
⠀⠀⠙⠦⣄⡀⠀⠑⢄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠦⠤⠀⣀⣴⠾⠋⠀⠀⠀⠈⠮⣱⡿⣿⣿⡟⢾⠦⣜⣽⣿⣇
⠀⠀⠀⠀⠀⠉⠙⠓⠒⠛⠃⠉⣉⠜⠋⠒⠒⢦⣀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠙⠉⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⣈⡽⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠤⠒⠢⢄⡠⠄⠒⠒⠤⣀⠤⠒⠉⠑⠤⠔⠉⠀⠀⠉⠉⠀⢨⠹⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡴⢉⠇⠀⠀⢠⠋⠀⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⢸⢀⡀⠀⢰⠂⠀⠀⡀⠀⢀⣠⣧⣄⣀⣠⠂⠀⠑⠉⠀⠀⠀⡏⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠰⠁⠹⠤⠃⣠⢷⠶⠿⢯⡓⠚⡥⢊⡕⠊⠉⠉⠒⣍⠳⣄⡠⠀⠀⠀⠀⢱⠀⡞⢃⠀⠈⠓⠢
⠀⠀⠀⠀⠀⠀⢃⢠⠋⣆⡞⠁⡇⣴⣶⡄⢹⡞⠀⢸⠀⣶⣿⡿⠀⡸⠀⠈⢆⠀⠀⠀⢠⠃⡸⠀⡌⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⡘⠘⠔⢹⠀⠀⠙⠿⠭⠖⢹⠀⠀⠈⠳⠬⣉⡤⠞⠁⠀⠀⢸⠀⠀⢀⠇⠀⠧⠔⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⣄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠘⡄⠀⠀⠀⡰⢦⠀⢸
⠀⠀⠀⠀⠀⢸⠄⠀⠐⡇⠀⠈⠑⠦⣀⠀⠀⠙⣄⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠢⠀⢀⠇⠀⠀⠀⠣⠼⢀⠜
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠙⢄⡀⠀⠀⠀⠉⠛⠛⠈⠑⠢⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡠⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢰⠁⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠎⣠⠃⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⠀⡠⠉⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠉⢁⣀⠀⢰⠁
⠀⠀⠀⠀⠀⢈⠆⢈⠀⠐⠀⠌⠀⠀⠀⠀⡈⠈⠉⠁⠀⠀⠀⠀⠀⡴⠋⢣⠀⢸⠀⠀⠀⢎⡠⠃⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡎⠀⡸⠀⠀⠀⣀⣀⡜
⠀⠀⠀⠀⢀⡸⡆⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⢰⠁⠀⢀⠞⠁⠈⢆
⠀⠀⢠⠚⠁⠀⡄⠀⠁⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡇⠀⢸⠀⢀⠎⠀⠀⠀⠈⡆
⠀⢠⠃⠘⠓⢄⡧⠈⢀⣀⣀⡀⠀⢀⣀⠤⣀⣀⠀⠀⣀⣀⡀⠀⠙⣋⡀⠀⢠⠂⢸⠀⠀⠀⠀⠀⡇
⠀⠈⠃⠀⠀⠈⠀⡴⠁⠤⠤⠬⠉⠉⠀⡲⢶⠦⠭⠭⠤⠤⠬⠽⠉⠀⠨⠥⢭⡥⢽⣦⣔⠀⢰⠞
⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⠞⠁⠉⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠤⠜⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢺⣍⣭⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡼⣿⣯⠀⠘⢄⣀⣤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠀⠀⠈⠓⠦⢤⠤⠤⠚⠁⡠⠄⢽⢣⠁⡀⠀⢴⢸⢀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠤⡖⠒⢠⡨⡍⡷⢁⠠⠀⡆⢏⠛⣺⠀⠈⠢⠀⠸⡘⡀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡍⠡⢇⠈⠈⠃⠄⣣⣀⣀⣀⣁⣠⣤⠶⢷⠶⣶⡶⣶⢟⢿⣠⠋
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢰⡶⢾⣟⢿⢻⢻⣏⢻⢉⡏⢉⡇⢜⡏⢸⣆⠙⡇⢾⡮⢹⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⡯⠽⡾⢾⡜⢸⡔⢸⣸⣿⣍⣧⣿⣷⡾⣿⢗⠛⠺⠓⠛⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠳⠚⠛⢻⡿⠿⢿⣋⠉⠁⠀⡠⠚⠉⠁⠀⠈⠉⠉⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠁⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⠰⠜⠀⠃⠀⠀⠀⠀⠀⠢⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⠃⠀⣤⡁⠐⠿⠀⠐⣀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⡠⠀⠀⠉⠀⠂⠄⠀⢴⡁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡒⠀⠀⠈⠀⠆⠀⠀⠀⠰⣌⣀⣀⠀⢤⠒⠋⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠘⢿⣿⣦⣾⣿⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠈⠃⠀⠙⠛⢛⣋⠅⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣖⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣧⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⢷⠈⣿⣿⡿⠿⠛⠛⠉⠉⠁⠈⠻⠟⠃⠤⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿

⠀⢀⡠⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣀⣀⣀⣀
⠀⡎⠑⡎⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠄⠠⠤⢤⣀
⠀⠣⢬⡋⠀⡎⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡰⠦⢠⡆⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠲⠤⢤⡀
⠀⠀⠀⠈⢳⡰⡀⠀⠀⠀⠀⠀⠸⠀⠀⠔⠁⠀⠀⠀⠈⠛⡀⠀⠘⠂⠼⠃⣠⠀⠀⠀⠀⠀⠀⢀⠄⠊⠻
⠀⠀⠀⠀⠀⢳⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⡇⠀⠀⠋⠀⠠⡀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⠀⠢⣄⠀⠈⠀⠀⠄⢆⠀⠀⠀⡀⢀⣀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠶⠋⠀⠀⠀⠀⠀⠀⣀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⢺⠀⠀⠀⠣⣄⡉⠓⠒⠀⠀⠀⠙⠒⠘⢀⣀⠀⢡⠀⢀⡇⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢠⣋⠉⠖⡖⠒⡲⠒⠈⠉⡠⠃⠀⠈⢀⠜⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⡀⠀⠐⠀⣀⢸⣋⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⡜⠉⠀⢁⢀⣁⡠⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀⡸⠅⣒⡦⠠⠐⣀⠤⠔⠂⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣔⣁⣀⣡⠔⠊⠀⠀⠀⠀⢠⠂⠀⡖⠁⠀⠀⠷⣶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠑⠲⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⠻⠹⢶⠤⣤⡤⢄⣀⠀⢀⠀⠀⠀⣀⣀⠴⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠶⠦⠉⢥⣴⡉⢳⣑⡉⠀⠉⠉⣉⡀⣟⣁⠤⠒⡊⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠄⠀⢄⢀⠀⡠⠉⠉⠁⠐⠲⠶⠀⢹⠀⠶⠛⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⢄⠀⢀⡞⠉⠉⠉⠑⠒⠒⠒⠒⠦⣤⠷⠒⢈⡟⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠴⡯⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠈⠉⠐⠲⠭⣅⣒⢶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⣠⡶⠶⠤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣰⠟⣇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠲⣤⣀⣀⣀⣀
⠀⠀⠀⢀⣰⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠉⠉⠓⠶⠤⠤⠤⢤⣀⡀
⠀⠀⢠⡟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠙⠓⠦⣇⠀⠀⠀⢰⡀⣾⠀⢈⠙⠛⠓⠒⠲⣄
⠀⢠⠟⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⢢⠀⡔⠊⠁⠈⠁⠻⡀⠀⠀⠀⠀⠈⣇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡄⠀⠀⢂⣤⣍⢢⠀⠀⠛⠀⢀⠀⠀⣄⠀⠈⠆⠀⠀⠀⢠⡇
⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣃⠀⠠⡘⠿⠟⠠⠀⠀⢸⠀⡎⢰⣶⡎⠃⠀⠈⡀⠀⠀⠀⢳
⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡠⠪⠅⡀⠝⣦⠉⠒⠂⠀⠀⠀⣘⠀⠡⡈⠛⡡⢁⣠⠖⠓⢲⡄⠀⢸⡇
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡁⠀⠠⣥⠀⢦⡀⠀⠀⠀⠀⡰⠉⢄⠀⠀⣀⠴⠋⠀⠀⠀⣸⠧⡀⢸⠃
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠈⠓⠂⠀⢸⡲⣄⠈⠑⠒⠒⠉⠀⠀⠠⠗⠊⠁⠀⢀⣀⣴⠞⠁⡀⡈⢾⡄
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢇⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠐⠒⠛⠉⠁⢀⣠⡟⠂⢀⠇⣷
⠀⠀⠀⠀⢻⠀⡖⠓⠶⣤⡀⠀⠳⠀⣠⣴⠒⢻⣄⠀⠀⠀⠈⣿⠓⠶⢦⣤⣤⣤⢤⡶⠞⠋⢁⠃⠀⠁⢠⡏
⠀⠀⠀⠀⠸⡇⢃⠀⠀⠀⠙⢦⢀⠀⣇⠊⠀⠈⢉⣧⣀⣀⣀⠿⢤⣀⣸⠀⣗⠀⠀⡇⠀⠀⡘⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢻⠈⡆⢠⡞⢧⣸⢿⠀⠈⣳⠀⢀⣀⣴⣿⣿⣿⠀⢠⣶⣮⠀⠉⠙⠛⠃⠀⢰⠃⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢈⡇⠙⠦⠽⣄⠻⣌⣧⠞⢁⡴⠋⠁⠈⢿⣿⣿⣦⣼⣿⣿⡇⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠢⣈⣡⠔⠋⠀⠀⠀⠀⠈⢿⡛⠻⢿⡿⠿⣅⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠈⠙⣆⡴⠋⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡠⠞⠛⠲⠒⠒⠶⣤⣄⣀⣀⣀⡀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⣇⣠⠶⠊⠀⠀⢀⠀⠀⠀⠀⠀⠉⠻⣤⡀⢙⣿⣶⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢀⠤⠂⠋⠈⣀⣉⡐⠒⠀⠤⠀⣙⡋⠀⢹⡦⣤⠞⠳⣭⣽⠿⠿⠷⣤⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠤⢊⣥⣶⠇⠀⠀⠙⠛⠛⠿⠷⠀⣶⣦⣤⣭⠟⠀⢸⡦⠤⠀⣀⡀⠀⠀⠈⠉⢹
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠟⠋⢀⣠⠶⠠⠤⣀⣀⡀⠀⠀⠀⠀⠉⢳⡄⠀⣠⠿⠿⣶⣠⣤⣭⣍⣒⠶⠾⠦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠢⠤⠽⣞⣁⣀⡴⠛⢱⡴⢛⣩⠴⠒⣶⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⠾⢉⡧⢤⣀⡿⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⢀⡞⠛⠲⠶⠦⣤⣤⣀⣀⣀⠀⠀⠀⢤⠤⠶⠞⣋⡤⠞⢩⡇⡸⠀⣠⣤⣤
⠀⠀⠀⠀⠀⣰⣶⣶⠀⠀⢻⣦⣀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠲⠶⠴⠚⠉⠀⠀⣜⣠⡃⢰⣿⣥⢿
⠀⠀⣠⣶⣿⣿⠛⠿⠀⣰⠋⡴⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⢀⡼
⠀⠀⣿⣧⡟⢐⡦⡷⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢟⣦⠔⠋
⠀⠀⠈⠉⠀⠀⢆⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠄⠀⡠⠤⠠⠤⠤⠔⠒⠂⠐⠒⠈⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⠉⠁⠀⡀⢀⣄⢀⡀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⡰⠁⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⠀⡠⠋⠁⠀⠈⠑⢤⠖⠉⠀⠀⠉⠢⡀⠀⠀⠀⡃⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⢀⢠⡄⠀⡇⠀⠀⢠⡄⠀⠀⢱⠀⠀⢰⠃⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠒⠢⣄⠀⠀⠀⢇⠀⠈⠂⠀⠀⠀⠼⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⢄⡀⠙⠢⠔⠉⠑⠤⠀⠀⢄⣠⠄⠰⠀⡼⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠮⣬⣉⣉⣁⣀⣀⣤⠴⠒⠉⠂⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⢀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢧⠀⠀⠀⠀⠰⠤⠤⠿⠄⠀⠄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡜
⠀⠀⡂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠁⢒⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⢸⠀⠀⠠⠀⠈⠁⣠⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠃⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠀⣀⠀⠠⠠⠄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⠢⠤⠒⢢⡤⠤⡤⠤⢄⣀⣀⣀⠄⣀⣰⠠⠤⠤⢒⡎⠄⢉⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣠⣄⣀⠀⣈⣀⠔⠢⡄⠂⠀⠀⠀⠀⠀⠀⣀⠀⢠⠊⠀⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠉⠉⠡⠀⠉⠙⠁⠀⠛⠛⠂⠀⠀⠘⠛⠀⣀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠃⠀⠒⠒⠲⠒⠀⠤⠆⠲⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠈⠀⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠷⣦⣾⣶⣷⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠿⠛⠀⠀⠀⣾⡛⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠋⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠤⠄⠤⠔⠒⠤⠤⠒⠒⠒⠒⠒⠉⠉⢳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⠀⢀⠀⢠⡀⢀⠀⠀⢀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⠎⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⠜⠋⠉⠈⠉⠲⣄⠔⠉⠉⠈⠉⠢⡀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⡎⠀⠀⠀⣂⡂⢀⠇⠀⠠⢂⡐⠄⠀⠸⡀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⠧⠤⣀⠐⠍⠅⠈⡆⠀⠐⠬⠡⠂⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢦⣀⠈⠑⠦⣀⡠⠛⢦⣀⠀⠀⡈⢀⡀⠁⡄⢀⡇⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣨⠛⠒⠢⠤⠄⠀⠀⠈⣉⡭⠔⠛⠁⠈⠀⢸⠀⠀⠀⠀⠀⡎
⢀⠤⠂⠄⠈⠐⠀⠤⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠉⡏⠉⢱⢲⠂⠉⠋⠀⠀⠠⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄
⢈⢂⢦⠀⠌⠁⠈⠀⠀⠂⠀⠬⣉⠂⠀⠙⡆⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⡁⣀⡠⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀⣸⠁⡀
⠡⢀⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠰⡁⠀⠀⠀⠀⠀⢢⠐⠁⠐⠁⡀⠔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠘⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠑⠒⡤⠤⡬⠘⢉⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠉⠙⠫⢉⠝⡒⠲⢖⠒⡲⠤⠤⠴⠒⠲⠴⠗⠒⠒⡪⠙⠒⣁⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠶⠤⠄⢠⣤⣴⠃⠱⣒⣁⡀⠀⣀⣀⡀⠀⠤⠀⣀⡎⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⣀⣀⣀⣀⣀⠁⠀⠉⠉⠁⠀⠉⠉⠉⠀⠀⠀⠉⠑⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠉⢉⠉⠉⠉⠁⢐⠒⠒⠒⠒⠒⠎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡁⠀⠀⠀⠀⠀⠀⠁⠲⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣶⣼⣦⠀⠀⠀⠀⠀⠀⠀⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡿⠿⣿⠿⠀⠀⠀⣴⡶⣦⣾⣷⣾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠸⠆⠐⠃⠀⣠⠄⠀⣤⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠁⠀⠀⠀⠀⠀⠁⢀⠀⠘⠁⠈⠁⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠘⠛⠃⠀⠀⠀⢹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣇
⠀⠀⢀⠀⠔⠂⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠈⠀⢀⡀⠔⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⡠
⠀⠀⠶⢊⠅⠀⠀⠀⢀⢑⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠦⣄⣀⡈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠃⠒⠉⠉⠉⠀⠀⠈⠁⠂⠈⠀⠂⢄⠀⠀⣀⠀⠀⠀⠀⠈⠓⠦⣤⣀⡀⠁⠁⠀⠀⠀⢀⣀⣤⣾⡟⠂⠀⠀⠀⠀⠀⠀⠛⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⠃⠀⠁⠀⠀⠀⠀⠀⠀⣇⠀⢸⣿⠉⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠄⠀⠀⠀⠀⠀⢨⣿⣿⣿⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⢿⡋⠀⠀⠉⠉⠉⣉⠟⠀⠀⠀⠀⠀⠀⠸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⣭⣥⡔⠀⣀⣀⡜⠹⣀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⡇⢀⣀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠉⠛⡀⢀⠵⠾⢧⠀⣠⣀⣀⠀⣤⣀⣀⠑⢸⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⠓⠲⠶⡬⢥⣀⣀⢀⠀⠀⠉⠉⠁⣿⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢲⠖⠁⠀⠀⠀⢉⡏⠙⠛⠒⢾⠿⠿⠿⠿⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠒⠠⠲⠊⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢃⠀⠀⠁⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⠂⠈⠃⠠⡘⢁⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⣠⠖⠛⠋⠓⠦⠤⠒⠚⠙⡷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠤⣤⣤⠴⠖⠉⠁⠉⠙⠲⠖⠚⠉⠁⠀⠈⠓⠒⠚⠉⠀⠀⠀⠈⠙⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⢠⠇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣸⠀⠀⠀⠀⣰⠋⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡞⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠀⠈⠧⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⡼⠀⢻⠀⣀⣀⣯⣀⣀⣀⣠⠏⢀⡤⠖⣚⣩⢭⣝⣓⠲⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡀⠀⠀⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠓⠚⠁⣠⠞⣫⠟⠛⠓⠲⣄⠉⢙⡶⠋⣰⠋⠁⠀⠀⠀⠈⠳⡄⠈⠳⣤⠞⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⣧⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⠎⢹⣄⡞⠁⢸⠁⣠⣤⣶⡄⢘⣦⠏⠀⠰⡇⢀⣴⣿⣿⣿⠀⠀⡟⠀⠀⠹⡄⠀⠀⠀⠀⠀⡼⠁⢰⠇⠀⡟⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⡼⣿⠀⠀⠘⢦⣿⠿⠛⣡⠞⡟⠀⠀⠀⠳⣌⠛⠛⠛⠁⢀⡼⠁⠀⠀⠀⢻⠀⠀⠀⠀⣼⠁⠀⡟⢀⡴⠃⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠉⠀⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⡇⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠈⠓⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠲⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠤⠄⣾⠁⠀⠉⠙⠲⣄⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠈⠑⠤⠀⠀⠀⣿⠀⠀⠀⠀⠐⣇⣀⠇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠙⠲⠤⣄⣠⣴⠛⢦⣀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠈⠉⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢠⠖⣦⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠛⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡄⠀⡟⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡇⣸⠃⢀⡏⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀⠀⠀⢀⠠⢤⣀⠀⣀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠞⠁⣏⣠⠞⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡀⠀⠀⢀⠊⢁⠔⠉⠀⠀⣨⡀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡤⡄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠈⡶⠁⠠⠃⠀⠀⡠⠊⠀⢈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⡄⠀⢸⡄⠀⠀⠀⠠⡏⢀⡏⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠑⢄⠀⠀⠀⠀⠀⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠙⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡼⠀⠀⡼⠀⠀⠀⠀⣠⠤⢤⡼⠁
⠀⠀⠀⠀⠀⠀⢀⣨⢷⠀⠨⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⢸⠁⠀⠀⢀⡾⠁⠀⠀⢳⡀
⠀⠀⠀⠀⡤⠞⠉⠀⢸⠇⠀⢣⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⡆⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢀⡞⠀⣤⣀⠀⢸⠀⡠⠃⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠀⢸⡆⠀⣼⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣼⢀⠔⠁⠈⢣⡼⠊⠀⢀⣬⡤⠤⣄⣀⠀⢀⣠⠴⠶⠤⣤⣀⣀⢀⣀⣠⠤⣄⣀⠀⢀⣀⣤⣄⡀⠀⣸⠃⠀⡏⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠸⠃⠀⠀⡠⠊⠀⢀⡴⠁⢠⣀⣀⡤⠬⠉⠉⠀⠀⢶⢦⡤⠤⠭⢭⣥⣄⣀⣀⣉⡭⠍⠁⠀⠀⣍⣛⣉⣙⣋⣻⣄⣐⠋⠉⢱⡤⠋
⠀⠰⠁⠀⠀⠀⠀⡠⠂⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠶⠸⡀⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠙⠻⠀⠀⢀⠁
⠀⠠⠀⠀⠠⠐⠈⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠰⠋⢠⢡⡅⢡⢁⠐⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠢⡰⠡⠊⠀⢸⢡⡑⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠁⢐⢇⠀⠀⠀⠀⠀⡠⠄⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡄⠀⢈⣼⡆⠀⠀⠀⠀⠁⠁⢐⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠗⠀⠀⠀⠀⠐⢡⠀⠀⠀⠄⢁⠑⠀⢄⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠐⠀⠀⠀⠀⠀⡀⠆⢠⡤⠟⣿⠞⢠⡆⠀⠀⠀⢀⠞⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⠀⠀⠀⠀⠀⠀⡜⡎⠀⢀⠍⠀⠀⠐⠋⡌⠋⠉⠀⠀⠠
⠀⠂⠢⢄⠀⠀⠀⠀⠀⡄⠀⠀⢠⡄⠰⠆⠀⠀⠀⠀⠀⠀⠐⠁⠹⠀⠀⠋⠈⡽⢏⠠⠟⠂⣇⣀⠎⡙⠰⠒⠒⠊⠁⠀⣀
⠀⢢⠀⠀⠈⠀⢀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠀⠀⠁⠉⠁⠀⠀⣠⢀⡤⢠⡀⠀⠀⠀⠀⢈⣬⡧⠈
⠀⠀⠡⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⢢⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠖⢰⠛⡙⠛⠔⠁⢠⡄⠀⠰⠄⠩⠙⠀⡠
⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠣⡀⠁⠀⠀⠀⠀⠂⠐⠀⠃⠀⠀⠀⣋⠘⢘⠁⠀⠀⠓⠳⠝⠢⣀⣈⣉⡙⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠸⡿⢄⠀⣶⡆⠀⠀⠀⠀⠙⠆⠀⠀⠀⠰⠂⠂⠖⠀⠀⠀⢰⡄⠡⡌⠀⠀⠀⣃⠠⠊⢁⡵⠬⡭⠹⠫⠉⠥⠱⠄⣄⡀
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠠⠀⠣⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⠄⠀⢸⠿⠀⣅⡀⠀⡞⠀⣠⣆⣁⡷⠰⠅⠀⠀⠀⠠⣀⡀⠀⢈⠤⠄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢚⡎⢞⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠇⠈⠉⢱⢤⠛⠋⢉⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠇⢀⠀⠈⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⢘⠀⡀⠀⡀⠤⢺⣑⡀⠀⠀⠈⠈⠃⠀⠀⠀⢀⡇⡔⠀⢸⠓⠀⡟⠁⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠁⠘⠀⠉⠀⠀⠀⢀⡐⡇⠠⠀⠠⠜⠢⠠⠠⠤⢼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢁⡆⠀⣤⢤⠄⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⡤⢲⢶⡈⢀⣀⠤⠐⠁⠻⠓⠒⠒⠒⠒⠒⠒⠒⠒⠊⠀⣀⠀⠀⡷⠀⡀⠀⢀⣀⠀⠼⠌⠉⣉⣏⡁⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡤⠉⠠⠀⡀⠻⢍⠳⠐⠒⠚⠀⠀⡌⠀⠀⠀⠀⠀⠈⡅⠀⢸⣠⣵⠠⠇⠄⠧⣤⠤⣧⣀⣀⣀⡎⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⢐⡉⠈⠫⡤⠀⠀⠀⠄⠠⠤⠜⠛⣱⡖⠤⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠉⠀⠀⠀⠀⠀⠈⢡⡇⠈⠉⡵⠚⠛⠛⠋
⠀⠀⢠⠈⡉⠙⢆⠎⠁⠀⠀⠀⠀⢀⡀⠀⠀⠈⣧⣀⡸⠨⠭⠈⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠤
⠐⠁⠹⠭⡜⠃⠀⡁⠀⠨⢁⠃⠀⠀⠐⡏⢙⡥⠐⢃⣼⡒⡅⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡘
⠐⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⢨⠀⢀⠞⠙⠇⠁⠄⠐⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇
⠀⠈⠐⠐⠐⠈⠀⠁⠠⡄⠀⠀⡀⠀⣀⠈⠊⡔⠁⠀⡁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠀⠀⠀⠄⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠖⠁⠀⠉⢆⡚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠄⠀⠀⠤⠄⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠤⠤⠀⠀⣤⡤⠶⠀⠀⢤⡤⠶⠖⠀⠂⠠⠶⠶⠒⠒⠀⠴⠶⠖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠐⠦⡀⠀⠀⡄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠒⠀⠰⣆⡀⠿⠀⢰⡇⠀⠀⠈⡷⠀⠼⠄⣠⡖⠈⠠⠀⠀⠂⠀⢀⠃⠠⠄⠉⢲⡄
⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠁⡴⠉⠀⠀⠀⠀⠀⠑⠄⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠈⠢⡌⢳⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⠀⠀⠀⡔⣭⣅⠆⠀⠀⣴⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⠀⣸⠆
⠀⠀⠀⠀⢠⡟⢐⡧⠐⢄⠀⠀⠀⠀⠈⠇⠀⠀⢀⠀⠀⠀⠂⠻⠯⠂⠀⡀⠉⠛⠃⠀⠀⡀⡀⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⢁⡀⢈⠷⠆⢘⠀⠀⠀⠀⢀⡄⠀⠀⣄⠀⠀⠀⠠⢀⣀⣤⠊⠉⠂⢀⢀⡔⠋⠁⠀⠙⠂⠀⠀⠀⠅⠀⢈⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠳⠌⣀⠠⠋⠀⠀⠀⠀⠈⣧⠀⠀⠈⠙⠓⠤⢤⠤⠤⠀⠀⠀⠀⠀⠀⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⠤⡈⠢⠂⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢣⠀⠀⠀⠀⠀⠹⠀⢀⣀⠀⠀⠚⢳⠖⠀⣤⣤⠀⠀⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠌⠇⠀⡅⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀⠀⢀⠀⢆⠀⠐⠀⠀⠘⠀⠠⣿⣿⣤⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⠐⠀⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠳⠤⠾⡉⠻⠆⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⡿⠟⠛⡟⠀⢀⡀⠀⠀⠀⠂⡀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⢶⠃⠀⣈⠀⠀⠀⠆⠀⠀⠀⠀⠘⠿⢥⣤⡤⠤⠶⠊⠁⡠⠀⠁⠀⠀⠀⠀⠖⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣄⢀⠀⠀⠀⠀⠀⡀⠐⠒⠂⠒⠒⡒⠚⠉⠀⠀⠀⠂⠀⠀⠀⣀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠉⠀⠉⠉⠫⠉⠉⠛⣉⡸⠋⠍⣉⠩⠝⠋⠉⠉⠉⠙⠁⠀⠈⢲⠐⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⠀⣤⣤⣼⠃⠘⣦⣤⣤⠀⢠⣤⣤⣤⠀⠚⠠⡶⠿⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣛⠛⠛⠛⢳⠖⠒⠐⠒⠒⢶⠖⠲⠖⠲⠖⢾⠋⡝⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⠉⠁⠀⠀⠀⠀⠀⠈⠑⠀⣶⠴⠖⠉⠀⠥⡆⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠘⠀⠀⠀⠀⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣴⣧⠀⠀⠀⠀⠀⠀⠀⢀⣆⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠉⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠘⠑⠄⢰⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⣀⣤⣤⣬⣽⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠐⠊
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠌⠁⠖⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠠⠄⠂⢀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⢠⠀⠀⠀⢀⠀⢀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⢂
⠀⠀⠀⠀⢀⠀⠋⢀⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⡘⠀⠀⠀⠀⠐⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠈⠀⠁⠀⠀⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠲⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠈
⣀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠠⠀⠀⠀⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠛⠄⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠀⠼⠆⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠉⠀⠈⠩⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⡆⠈⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠈⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠇⠀⠀⠰⣄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠳⣄⠔⠒⢮⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡒⠒⢤⡟⠒⠢⢌⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⡞⠃⠀⢠⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠑⠒⠊⠙⠦⠴⠋⠀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠑⠲⠤⠤⠤⠤⠒⠉⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣌⠢⢄⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⢱⠉⠢⣍⡒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢚⢧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡠⢧⠸⣄⣈⡉⠒⠢⠬⠭⢉⣉⣉⣉⡉⠭⠭⠔⡲⠮⡀⡜⠣⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠠⡏⠀⠀⠐⡗⠲⠔⠃⠀⠀⠀⢀⡜⠁⠀⠓⠁⡰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠒⠲⠚⠁⠀⠀⠀⠀⠀⠀⠈⠳⢲⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢄⣀⠀⠀⠀⠲⡆⠤⠤⡀⠀⠀⠀⠀⢰⡃⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⣁⠖⠚⠁⠀⠀⠙⢤⣄⣠⡤⠤⠝⠛⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡤⠞⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⢰⣄⣈⣉⣳⡇⠀⠀⢰⣶⣯⣥⣀⣰⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡴⠋⠁⠀⠙⣆⠀⣠⠋⠁⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠁⠀⢰⠋⣷⣸⢀⡇⠀⠠⡎⣽⡆⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⣄⠀⠀⠙⣡⠃⠀⢧⡀⠀⠙⠋⢀⡞⠀⠀⠀⠀⠰⠀⢰⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⣞⡻⠥⠤⠤⠤⠟⣒⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠀⢠⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⣿⡿⠿⡿⠿⠿⣿⠟⠀⠀⠀⠀⠀⠀⡈⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠦⣼⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⢰⡇
⠀⠀⠀⢀⠞⢻⣤⣿⣇⡠⠴⠚⠉⡏⠉⠉⠁⠒⠲⡏⣉⣲⡖⠒⠒⣦⣀⣀⡀⠀⠀⠀⢠⡁⢠⡟⠀⠀⣼⠀⣠⣤⣄⡀
⠀⠀⠀⢸⡟⠉⣰⣿⡀⢣⡤⠴⢶⡇⠀⠀⠀⠀⠈⢥⡤⣾⡌⠢⣀⡇⠀⠀⠈⠉⠉⠓⣺⠉⠛⠷⣤⣰⡏⢸⣿⣦⣾⡛⣣
⠀⠀⠀⠀⠻⣏⣡⠾⠿⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⡔⣼⣿⡏⢦⡼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀⠉⠓⠞⣿⣧⣀⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠛⢍⠉⠉⢙⡻⢛⢿⣷⠒⠲⠦⢤⣀⣀⠀⠀⢰⣿⣿⣿⠃⠈⠉⠛⠦⣿⣦⣈⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠤⠆⠀⠀⢸⣧⣉⣼⡿⠀⢰⠉⠀⠑⡆⠉⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠚⠒⠒⠒⠒⠒⠚⠍⠛⠛⠥⠀⠀⠙⠒⠚⠁⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡠⢴⠺⣍⠉⠉⠉⣉⣉⣉⠀⠒⠒⠒⠒⠒⠤⠼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠳⣌⢿⡉⠉⠁⠀⠀⠉⠉⠓⠲⢄⡀⠀⢀⡴⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠒⠛⣆⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡷⣄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⣄⡨⠆
⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠄⠒⠒⣺⣿⡿⢿⣫⡵⠛⠋⠀⠀⠀⠁⠈⠉⠉⠉⠉⠙⣧⣤⣼⡏⠉⠑⠒⠒⠠⠤⠤⣀
⡤⠒⠚⠉⠉⠀⠀⡀⠄⠐⠀⠐⠒⠈⠛⠶⠾⠿⠟⠿⠗⢁⢀⠂⢈⣀⣀⣀⣡⣀⣠⡀⣿⣿⣿⣿⣦⣀⠀⠒⣀⣀⠀⣀⢈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠉⠀⠀⠁⠀⠀⠀⠈⠈⠛⠛⠻⠯⠿⠛⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⢀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢀⣂
⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡤⢈⠄⠀⠀⢀⠀⡄⠀⢀⠀⢠⣀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⡠⠃⠀⢸⠀⠴⡆⠸⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡤⠤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⣈⠑⠨
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠊⠐⡌⠉⡆⠰⠈⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⡎⠀⡄⠀⠀⠀⠀⠀⠀⡠⣬⠀⠻⣴⣉⣼⡉⠀⡆⠀⠀⠀⠀⠀⠀⠀⠆⡐⠂⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠘⣇⠸⢇⢀⡀⠀⠀⠀⣀⣤⠉⣄⠀⠈⠹⠞⠣⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠜⠐⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢻⣠⠼⠷⢃⠀⠀⠀⠀⠙⠔⠹⡖⠶⠂⠘⠛⠂⠙⠆⠀⠀⠀⠈⠀⠀⠀⡀⠉⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠶⠦⠂⠠⢴⠂⠀⠀⡀⠙⠀⠀⠀⠀⡀⠀⠐⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⣘⡀⠀⠠⠄⠀⡀⠀⠀⠀⠼⠠⠄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⠶⢤⡀⠀⠤⣀⡀⢀⣀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠀⣆⠰⡆⣠⠀⠀⡀⠀⡄⠀⠈⠉⠁⠀⠀⠌⠁⠀⠀⢹⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠁⣀⠄⠋⠈⠁⣴⠂⠀⠀⠂⠀⠀⠀⠀⢀⠌⠀⠈⠓⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠠⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠠⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠀⠀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⡄⢠⠄⠀⠴⠒⢄⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⡀⠀⠐⢠⣿⡦⣴⣦⢠⠀⠀⠐⠲⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⣰⠄⠀⢠⠜⠓⠈⠁⡀⠀⠀⠀⠀⠀⠇⠀⡀⠙⠂⠄⠀⠉⠀⠙⢃⣄⡀⠆⠀⠠⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⢰⠁⠀⠁⠀⠀⠀⠀⠀⠄⠀⠱⠄⠀⡘⠀⠈⠑⠲⠤⢤⣀⣀⣀⠀⠀⢀⣀⣤⣾⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⡗⠂⢂⣤⡀⠀⠀⠀⣁⠀⠀⠰⣆⠀⡇⠀⠀⠀⢠⣀⠀⣼⡏⠈⢙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠈⠉⢁⠀⠉⠀⠀⣹⠀⡅⠀⠀⠀⠀⢸⣿⣿⣷⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⠤⣀⡀⠀⠐⠀⠀⠀⠐⢂⡾⠀⠰⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⡀⢲⠈⠉⠀⠂⠒⠇⢈⠁⠀⣼⣿⠟⠛⠛⠻⠟⠛⠛⡟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠉⠋⠒⠄⣀⠀⠃⠀⢿⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⣠⡏⠀⠐⢄⠠⠝⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠁⠒⢀⠈⢏⠈⠓⠀⠀⣤⣄⣀⠀⢀⣇⣀⣸⠀⠀⠀⠀⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠶⣶⣄⣠⣀⠎⠈⡄⠑⠂⠈⠁⠀⠀⠀⠀⠉⠀⠀⠠⢄⣤⣤⠔⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⠛⠀⠀⢰⣶⣦⣄⢀⣀⠀⠀⠀⣀⠀⠀⠀⢀⡇⢸⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⠤⢌⣀⠁⠀⠀⠁⠈⠛⠻⠷⠆⠀⠀⠐⠟⠛⡇⡘⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢹⠋⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⡀⠁⢻⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢻⠁⠀⠀⠀⠀⠈⠁⠉⠓⠒⠚⢻⠙⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠓⠤⠤⢀⡤⢜⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⡀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣸⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⢰⡇⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠿⠟⠻⠿⠿⠁⠀⣠⣴⢦⣤⣴⣶⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠈⠛⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢡⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⠐⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢇⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠆⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠁⠀⠀⠀⡠⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠐⠁⢠⡄⠰⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢤⣉⡼⠃⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣠⣤⠤⠤⠤⣤⠽⠶⠤⠤⠤⠤⠴⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣄⢀⣶⢀⡰⠀⠀⣦⡠⠷⠤⣟⠀⠀⠁⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠉⠁⣠⠊⠀⠀⠀⠉⢣⡼⠁⠀⠀⠀⠈⠳⡀⠀⠀⣾⠀⠀⠀⠀⢀⡴⢊⡗
⠀⠀⠀⠸⡗⠢⢤⡀⠀⠀⠀⠀⣧⠀⠀⡀⠜⠀⣅⠀⠀⠂⢰⡇⠀⠀⠀⢀⣀⠀⠃⠀⠀⣤⠀⠀⠀⡇⠀⢀⡏⠀⠀⣠⠴⠋⢁⡾⠁
⠀⠀⠀⠀⢻⣆⠀⠀⠉⠉⠐⠒⠺⡆⠀⠀⢀⡀⢹⠀⠀⠀⠸⣇⠀⠀⠀⠈⠛⠀⣤⠀⠀⠀⠀⠀⣠⠃⠀⠀⡷⠚⠋⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠹⡆⢀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⣣⣀⣀⣀⣠⠞⠀⣑⡶⠤⠐⠋⠉⢳⡄⢠⡇⠀⠀⢀⡴⣳
⠀⠀⠀⠀⠀⠀⠙⢆⠑⢄⠀⠀⠀⢹⡀⠀⠀⠀⠸⡆⠀⠒⠒⠚⠋⢀⠀⠀⠀⠀⠐⠶⠶⠶⣶⡶⠖⠋⠀⢸⡇⠀⡴⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡙⠢⢄⣘⡇⢀⢀⠔⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⢤⡶⠒⢺⠉⠀⠀⠀⠀⢀⣷⠚⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠽⣿⣷⣦⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠛⠶⠚⠀⠀⠑⠐⠃⣸⡗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢸⡏⠐⢾⠤⣀⣀⠀⠀⠀⠀⠒⠴⠞⠛⠉⠉⠉⠁⣀⡠⠤⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⠀⡼⠁⠀⢸⠀⠀⠀⣉⡩⠓⠒⠂⣤⣠⣴⣶⡶⠖⠉⠀⠀⠒⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⡇⢰⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠀⠀⠀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⢸⡇⢸⠖⠶⣧⣤⣤⠤⠴⠶⠶⠶⠶⠒⠒⠖⠒⠒⢛⣿⠏⠉⣉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡟⡇⢸⠓⠲⠷⠦⣾⣧⣀⡀⠀⠐⠀⠀⠀⠀⠀⡄⢀⡤⠖⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⡟⡇⠸⣀⢀⡀⠀⢀⣀⣉⣙⣦⡈⠁⠀⠀⠀⣠⣿⣥⣴⣶⠶⠖⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣸⢿⠁⠀⠙⢏⡙⠋⣿⢩⠏⠉⠉⠙⠷⠶⠶⠞⠋⢸⢀⡟⠧⣾⣤⣧⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⠀⣿⢸⠠⢀⠀⡗⠃⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢸⡇⠀⠘⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡹⠀⡏⠘⠶⠖⠂⠀⡠⢼⡃⣻⠄⠀⠀⠀⠀⠀⠀⣸⠉⠧⠼⠇⢀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠐⠁⠀⣇⠀⠀⠀⠀⢀⡇⠈⠉⠁⠀⡆⠀⠀⠀⠀⠀⡏⠀⠀⢠⣤⡿⠀⠀⠀⢸⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠂⠀⠀⠀⣿⠀⠀⠀⠀⢸⠃⠀⠀⠉⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⣠⣀⡇⠀⠀⠀⢸⠈⣆
⠀⠀⠀⠀⠀⠀⣠⡏⠀⠠⠆⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠛⠁⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢸⠀⠘⣆
⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⠀⠀⠀⠀⢸⡶⣄⠀⠀⣾⠀⠀⠀⠰⠆⡟⠘⢦⣠⠟⢹⡇⠀⠀⠘⠉⡿⣤⣤⠶⢾⠀⢰⠹⡆
⠀⠀⠀⠀⢰⠃⠀⢠⢂⠈⠣⠀⠀⠀⠈⢃⠈⠶⠎⢻⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠘⡇⢀⠀⠀⠀⣳⠀⠀⠀⡿⠀⠀⢹⡇
⠀⠀⠀⠀⠸⡀⠈⠀⠒⠈⠀⠀⠀⠀⠀⠈⡄⠀⠀⠸⠀⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠻⠞⠓⠦⡀⠈⡆⠀⠈⠳⠶⠖⠋
⠀⠀⠀⠀⠀⠙⠲⢤⣄⣠⡤⠤⠤⠤⣄⡀⠘⣄⠀⠀⠑⠛⠋⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡼⠂

⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣠⠴⠤⠒⠐⠂⠚⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿
⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠂⠐⠀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠀⢀⡀⠀⠰⣿⣿⣿
⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠂⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢌⠀⢀⡀⠀⣱⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠁⠀⠀⠀⢀⢀⡠⢔⣪⠕⠊⠉⠈⠁⠈⠉⠁⠀⢠⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣀⠂⠀⠤⠤⠄⠰⠒⠆⠀⠛⠃⠐⠒⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣀⣠⠄⠀⠀⡤⠤⠤⠄⢶⠀⠀⣲⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢧⡀⠀⢲⢰⠒⠁⠀⠀⠀⠈⠃⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⣀⡤⠖⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡤⠒⠐⠢⠔⠊⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡤⢄⠀⡀
⠀⠀⠀⠀⠀⣠⡤⠤⠤⠔⠋⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡄⠀⠣⣀⠇⢇
⠀⠀⠀⠀⢀⠇⠸⣄⠀⢰⠂⠲⡄⠀⠀⠀⠀⢠⡀⣀⣠⠂⠀⠈⡢⠖⠉⠉⠉⠑⠢⡀⠀⡶⡌⢧
⠀⠀⠀⡎⠁⣀⠄⡈⢱⠈⠢⠴⠃⠀⠀⢳⠔⠋⠁⠀⠈⠉⠲⣜⠁⠀⢠⢔⡢⣄⠀⠘⡆⠈⠁⢸
⠀⠀⡜⠁⢎⠀⠀⣸⠀⡆⠀⠀⠀⠀⢠⠃⠀⠀⡠⢒⡲⣄⠀⠈⠆⠀⢇⠫⠼⣸⠀⠀⣁⣀⠀⡎
⠀⠀⠣⢤⠈⠓⠚⠁⠀⠘⢄⠀⠀⠀⢸⠀⠀⠀⡄⠧⠜⡸⠀⠀⠸⠀⠀⠑⠊⠁⣠⠞⠁⠀⡇⠘⡄
⠀⠀⠀⠘⡄⠀⢠⠊⠢⠀⠀⡇⠀⠀⠈⢆⣀⣀⠈⠙⠉⠀⠀⣠⠋⠢⣄⣀⠤⠚⠁⠀⢠⠞⠀⠀⢱
⠀⠀⠀⠀⠙⠢⡈⠒⠃⠀⠀⠱⡀⠀⢀⠎⠁⢀⠙⣄⣀⠤⠖⠁⠀⠀⢀⣀⠀⠤⠤⠚⣡⠄⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢹⠀⠀⡎⠉⢆⠙⢆⠀⢦⡈⢹⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠁⣀⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠱⠄⠜⠀⢸⠀⠀⠀⠀⢧⠀⠀⠉⠉⡟⠉⠙⡏⢻⠀⠈⢣⠀⠸⡀⠈⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡠⢄⠀⠘⢆⠀⢠⢄⠈⢆⠀⠀⠀⠱⠴⠄⠃⠘⠒⠙⡏⠀⠀⠑⠒⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⠊⠀⠀⠀⡇⠘⠚⠀⠈⠣⡤⠄⠠⢤⡖⠒⠢⢄⡀⣱⠀⢠⠒⡄⠀⢸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⣀⠀⠀⡇⠀⡞⠙⡆⠀⠈⠲⢄⣀⣁⣀⣀⣠⠝⢁⡤⠀⠑⠁⠀⢸⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⠁⠈⢆⠀⠘⡄⠱⢄⠆⠀⠀⠀⠤⠤⡤⠤⠤⠴⢒⣉⢠⡤⠔⠒⠊⢻⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠸⡀⠀⠇⠀⠀⠀⢀⣀⣀⣤⢤⠖⢶⣊⡹⠉⠑⣊⡀⠤⠔⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⢤⠔⠋⠁⢓⠈⠉⠉⠁⣀⣀⡈⠥⠄⡺⠀⠘⡭⠅⡆⠸⠩⠬⠃⣇
⠋⠁⠒⠒⠉⠉⠒⠒⠈⠉⢹⢹⢸⠯⢔⠒⠺⠒⡢⠭⠅⢰⠀⠐⠭⠥⠗⢤⣔⣉⠭⠤⡔⠒⡎⠉⡈⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢸⠭⣘⣀⠀⡇⠓⢈⣉⡁⢤⠔⠒⠒⠘⣍⡀⠀⠀⣀⡇⢠⢣⢠⢣⡸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠓⡄⠈⠉⢻⣉⠁⠀⠀⣸⠀⠀⠀⠀⠀⡏⠉⠃⠀⠀⠈⢧⠼⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⢠⢌⣢⠀⠀⢸⠁⣉⠀⠀⠀⠀⠀⠀⠀⠗⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣳⣸⡄⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⡖⠙⠦⠎⠑⡤⢔⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢻⣀⠟⠱⡤⠤⠤⡀⢇⠀⠀⣀⠀⠀⠧⠝⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⠰⣋⠆⡄⠀⠉⠈⠉⠓⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠲⣖⣒⡒⠖⠒⢒⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠾⠟⠈⠁⠙⠚⠳⢌⣛⣃⠠⣤⣍⠓⢒⣓⡶⣤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢭⣉⡀⠀⠸⠶⠖⣂⠀⠀⠀⠈⢉⣉⠛⠤⢤⠭⠞⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠑⢤⣾⣱⡉⠩⠋⣒⡖⠒⠖⠒⠂⠀⠘⢿⡷⠀⢏⢠⣿⣿⣦⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠶⠭⣦⣀⣲⡈⠛⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⢸⠘⢿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢂⢩⣭⠄⠀⠀⠀⣤⠄⣉⠓⢆⠉⠅⡂⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⢡⣤⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠄⠘⠇⠀⠀⠀⠤⠫⠀⠀⠅⠦⡑⢄⠁⣠⣀⠀⠀⠀⠀⢀⡇⡞⠉⠒⠿⣟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣒⣶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⣨⠆⠙⠋⠀⠀⠀⠀⠘⢆⠈⠀⠐⠒⠬⡙⠢⣀
⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⠤⠒⣉⠤⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣷⠀⠀⢸⠓⠦⣑⠤⡀
⠀⢰⠯⢒⡲⠀⣀⣈⡉⠠⡞⠉⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⣠⣤⣄⠀⠹⡄⠀⠀⢀⣀⠘⡆⠀⠈⠑⠬⡳⢄
⠀⠈⢘⡡⠔⠉⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀⠀⢨⢟⡒⠒⢒⣲⣾⣥⣤⡤⢤⣀⣀⣀⣙⣛⣋⣀⣰⣃⣀⣀⡨⠯⠤⡇⠀⠀⠀⡠⠚⣃⠑⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⡻⢤⣄⠸⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣩⣍⠉⠹⡍⢠⣤⠀⠀⠀⣧⠀⠀⢸⣠⠋⠀⠙⢄⢠⡑⢜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣚⠥⠒⠉⠀⠉⣿⣿⣿⣿⣿⡟⠓⠦⠤⠤⠴⠬⢥⣀⣼⡥⡤⢤⡴⠚⠓⠋⠀⠀⠀⠀⠀⠀⠀⢸⠈⡙⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠉⠉⢁⣀⡸⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⠀⠈⠑⠒⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠴⠏

⠄⠀⠀⠄⣠⣶⣿⣿⡿⠿⠿⣿⠿⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠷⠛⠛⠛⠛⠉⠉⠉⠛⠛⠛⠋⠉⠒⠦⠤⣤⣔⣒⠓
⠈⠢⣴⣿⣿⣿⣿⡏⠀⢰⣦⣤⠀⠰⣦⣄⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢸⠁⡠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⢀⢷
⠀⢰⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣧⣀⣹⣿⣧⣘⣿⠄⢰⠀⣄⣥⣴⣴⡴⠋⠀⣸⡿⠀⠑⠉⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠱⠤⣤⠝⠀⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⠁⠀⠁⢈⠁⠀⣰⣿⠁⠀⠛⠀⠀⣠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠂⠄⠀⠀⢰⣿⡏⠀⠀⠀⠀⢰⣿⡤⠀⠀⠀⢠⣿⣠⠀⠀⠀⠀⠀⠀⡔⣠⡄⠛
⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⡀⠸⣿⠇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠿⠃⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⣀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⡘⠀⣠⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢐⣤⣀⠀⠀⠜⢠⣶⡌⣼⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣁⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣇⠀⠀⢰⣶⠀⠀⣀⣿⠇⠀⠀⠀⠸⠟⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠓⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⠋⣀⠀⠀⠄⣀⣀⣿⣿⣿
⣿⣿⣿⣿⣿⢟⣩⣽⣦⣭⣛⢿⡋⠉⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣖⣲⠆⠀⠀⠙⠻⠿⠿⠿⠛⠁⠸⡥⠇⠈⡀⢿⣿⣿⣿⣿
⣿⣿⣿⠿⢷⣟⠿⡿⠏⣀⠛⢢⠷⣄⡀⠈⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢾⣿⣶⣤⣤⣤⣴⣶⣿⡆⠀⠀⠀⢀⡁⠜⢿⣿⣿⣿
⣿⣿⣧⡔⢂⣄⠀⠀⠀⠈⡀⣈⣤⣘⣇⣴⣿⣦⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠉⣠⣴⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣷⣶⣾⣶⣿⣿⣿⣻⣿⣿⣿⡟⣿⣿⣿⠿⣿⢦⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣯⣧⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠀⠉⠁⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠰⡄⠏⠿⠋⠉⠉⠀⠀⠠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠂⠀⣀⠀⠒⠀⠀⠀⠀⠠⢀⣀⡀⠠⢀⡀⠀⣀⡀⠀⠀⢠⠉⠂⠐⣯⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢼⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠋⣒⠀⠾⠤⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⢀⢀
⠀⠀⠀⠀⡀⢠⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⣼⣿⡧⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠁⠀⠀⠠⠐⠶⠂⠀⠀⠒⠒⠲⠖⠄⢀⠀⠀⠀⠀⠘⠛⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⢨⠀⠀⠀⠾⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠄⢀⣠⠄⠀⠀⠀⠸⠰⣶⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇
⠀⠀⠀⠀⠘⢀⠊⠀⢀⣀⣀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸
⠀⠀⠀⠀⠁⣇⠈⠁⢾⠿⠿⠿⠿⠿⠿⠿⠀⣶⣄⠈⠀⠀⠐⠀⢀⠀⠃⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡄⠬⠣⡀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠠⠄⠀⠃⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠄⢠⣶⣌⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⡆⠀⠀⠀⠂⠀⢀⣄⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠂⠀⡌
⠀⠀⠀⠀⠄⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⣾⠟⠀⠉⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣡⡼⠟⠛⠛⣷⣶⣀⣤⠶⠶⠰⢧⣀⡀⣆⠀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠋⢰⣾⣿⣷⣻⣿⢋⣴⣶⣾⡄⠀⣿⣧⠈⠆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠑⢿⣿⣿⣿⣿⠇⢸⣿⣿⣿⡿⠀⣾⣿⠀⠃⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⠗⣬⣭⣽⣿⣿⣧⣤⡯⠛⠉⣠⣼⢿⡟⠀⠃⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣳⡾⣵⣯⡿⡿⠉⢻⣿⣿⣿⣏⠀⣀⠀⢀⠀⢀⢾⣿⡿⣅⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠊⣉⣛⣭⣷⣿⠃⠐⠃⢰⣿⣺⣿⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣴⣦⠨⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⢻⣈⣇⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢸⡟⠃⠸⣿⣶⣻⢿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣴⣶⠀⢺⣿⣿⡿⣿⠿⢋⣩⠟⠁⣀⣤⡀⠀⢀⣿⣿⠿⣈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠋⢠⣤⡉⠛⠿⠿⠟⠛⠁⠀⢰⣿⣿⠣⣠⣾⣿⠏⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⡿⢾⣶⣮⣿⣿⣶⣶⣶⣖⠀⠀⠀⢹⠁⠀⢸⣿⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣾⣽⣯⣉⣿⣿⠟⠯⣽⠿⠶⠾⠿⠦⣤⣼⣿⣿⣄⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠻⣿⢺⡿⣿⣿⣿⣿⣶⡖⠲⣤⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡿⣿⠾⣧⣬⣿⣟⣣⠁⠀⠀⠉⠉⠻⠛⠀⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠉⠀⢻⠿⠁⠹⢿⣿⡿⢷⣦⣴⣤⣀⣘⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠈⠇⢠⣄⠹⢆⠘⡟⡋⠙⣟⠉⠛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠠⡇⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠂⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣁⣤⣿⡿⠟⢿⠿⣷⣶⣆⣀⣀⣰⣦⣶⢦⣾⣤⡄⡀⠀⡆⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣿⡛⣤⣴⣶⣷⣾⣿⣿⣿⠿⢛⣉⣤⣴⡀⠈⢽⣿⣷⡀⠻⡄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠥⣼⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⡀⠐⣿⣿⣧⠀⡁⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⡗⠛⡿⢿⣿⣿⣿⡿⣻⡟⠀⢿⣿⣿⣿⣻⣿⠃⢠⣿⣿⣿⢠⡋⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢹⡶⣴⣻⣻⣏⣿⣿⣿⣷⣄⣴⣿⢻⠟⠛⠁⣤⣾⣿⣿⡏⠀⠿⠀⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣠⡿⣹⡿⣿⣿⡿⠟⣿⣿⣿⣿⣷⣴⣤⠚⠋⠙⠉⠛⡀⠀⠀⢠⣿⣿⣿⣗⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣋⡽⠿⠳⣿⠴⣿⠺⠇⠀⠼⣿⣿⣿⣿⣿⣷⢀⣠⡄⠀⢀⡄⠀⣠⡾⣿⣿⣿⢹⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠛⢌⠉⠛⣉⣥⣶⣿⡟⠀⠰⠋⠀⣼⣧⣟⣿⣿⣃⣸⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⠐⣢⣤⠀⠐⣿⣿⣷⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣻⡍⢿⠞⠛⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣇⠚⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⠇⣠⣤⡀⠀⣰⣿⡴⠳⣾⡿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠻⠿⡿⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠋⠃⠈⢻⣿⣿⣯⣿⢿⣇⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣠⣶⡄⠡⢾⣿⣿⣿⣿⢿⣿⡿⠿⢋⣻⡿⠋⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⢟⣻⠈⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⣸⣿⣿⠏⠀⠀⡿⢿⣿⣷⣿⣿⣴⣷⡾⠋⠀⠀⢠⣿⣿⣿⡆⠀⣠⣿⣿⣿⠃⠀⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⣇⣀⣼⣟⢁⡀⠹⢿⣦⣄⣈⡉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡿⡋⠓⢼⣿⣿⣿⡇⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠙⢟⠿⢿⣿⡿⢶⣾⣿⣿⣿⣟⡿⢶⠖⠒⠀⠀⠀⠀⢻⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣉⣼⣏⡹⡿⠻⠻⣿⣿⣿⠿⣏⠙⣿⣷⣦⣤⣾⣿⣦⣀⡀⣸⣿⣿⣿⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣧⣤⣌⣉⣋⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣏⢉⣿⠏⢸⡟⠻⣿⣿⣿⣿⢿⣿⣿⠉⢛⣿⣿⣷⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⢿⡷⣾⣧⣤⣹⣿⣿⠛⣮⠀⠀⠀⠀⠉⠉⠛⠻⠟⠇⠐⣿⣿⣽⣿⣿⣿⣿⣿⣿⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡇⠘⢻⢸⠃⢐⠿⣿⣟⠭⠿⣿⣷⣶⣶⣴⣄⣀⠀⡤⠁⠀⠀⢾⣿⢹⣿⣭⣿⣿⣿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⠇⢩⡀⠀⢋⣿⣿⠛⠉⠛⣿⣻⠛⢿⣷⣶⡶⢿⣾⣿⣿⢿⣿⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⡇⠐⣦⣄⠀⠟⣴⠉⢹⢁⠇⠘⣻⣏⠀⠚⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⢀⣿⠀⠀⠀⠹⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠠⠤⣀⠆⠐⠤⡀⣀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣉⠛⠀⣐⣀⣀⣈⣠⣤⣤⣥⣤⣬⣦⣤⣵⣬⣼⣉⣰⣊⣑⡇⠀⠯⡱⡄
⠀⠀⠀⠀⠀⠀⢀⡶⠚⠛⠉⠉⠉⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠙⠿⠟⠺⠦⣄
⠀⠀⠀⠀⠀⠀⢸⡅⠰⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠠⡦⠀⣸
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠸⣿⡿⠃⠀⠀⠠⣾⣶⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡟⠀⠀⠁
⠀⠀⠀⠀⠂⠐⠀⣿⠀⢀⡀⠀⠀⣀⡀⢀⣤⡉⠁⠀⠀⠀⠈⠀⢀⣀⠀⣠⡀⠀⠀⠻⠟⠀⠀⢸⠇⠀⠀⠀⠂
⠀⠀⠀⠀⠄⠁⡀⢿⠀⠈⠁⠀⠀⣻⣷⠼⠿⣧⣀⠀⠀⠀⠀⢀⣸⡿⠤⢿⣇⡀⠀⠀⠀⠀⠀⣼⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣤⣤⠞⠁⠀⠀⠀⠀⠉⢳⡄⠀⣰⠟⠁⠀⠀⠀⠀⠙⢦⣠⣄⠀⠀⡏⠀⠐⠀⠂
⠀⠀⠀⠀⠀⡴⠋⠙⣧⡀⢙⡏⠀⣰⣾⡟⠛⢢⠀⠀⢿⢸⡇⢀⣴⣿⠛⠒⡄⠀⠈⣟⠁⠀⢰⡗⠒⢦
⠀⠀⠀⠀⠀⢧⡑⢤⣿⠃⠘⣇⠀⣿⣿⣿⣶⣾⠃⠀⣾⢸⡆⢸⣿⣿⣷⣶⡇⠀⢀⡟⠀⠀⣾⡥⢂⡼
⠀⠀⠀⠀⠀⠀⠉⠓⣿⠀⠀⠙⣦⡈⠲⠿⠟⠋⣀⡼⠃⠀⠻⣄⠑⠾⠿⠋⠀⣠⡾⠁⠀⠀⡿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠓⠒⠒⠛⠉⢀⣀⢀⣀⡌⠙⠒⠶⠒⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠠⠄⢸⡏⠀⢰⣶⠀⠀⠀⠀⠀⢀⣈⠁⠀⢈⣀⣀⠀⠀⠀⠀⢰⣿⣿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠈⣇⠀⠀⠀⠀⠀⡄⠀⠀⢹⣯⣉⣉⣩⣿⡇⠀⠀⠀⠀⠀⠉⣁⠀⣾
⠀⠀⠀⠀⠀⠀⣠⠴⠚⢻⠀⠀⢠⣶⡄⠀⠀⠀⢸⣿⣿⣛⣛⣿⡇⠀⢀⠀⠀⣀⠀⠈⢀⡏⠙⠲⢤⡀
⠀⠀⠀⠀⠀⡼⢁⠄⡤⠺⡆⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠈⠉⢉⣛⡂⠙⠃⠀⠉⠀⠀⢸⠋⠓⢦⠀⠙⢦
⠀⠀⠀⠀⠀⢧⣮⡼⠁⠀⢹⡟⠖⡶⠶⣶⠶⠤⣤⢤⣤⣤⢤⡤⣤⠤⠤⡤⠤⣶⡶⢶⠋⠀⠀⠈⢧⣧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣧⣤⣼⣄⣀⣇⣀⣡⣤⣁⣀⣧⣀⣀⣧⣄⣆⣄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠋⠉⣻⠉⠉⠉⠉⢹⠉⠙⠛⠛⠛⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⣀⡀⣀⡀⠤⠤⢀⣀⣀⡠⠤⠄⠀⠠⠤⠠⠄⠒⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⡀
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠤⠤⠤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠈⠀⠀⢤⣌⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠆⠉⠈⠉⠒⠒⠒⠒⠒⠒⠈⠉⠉⠉⠉⠁⠒⠊⠉⠀⠀⠈⠁⠒⠂⠉⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠈⠉⠒⠂⠀⠐⠒⠉⠉⠀⠀⠙
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⡌⠀⠀⡀⠀⠀⠀⡐⠀⠀⣾⣿⣿⣿⠿⣿⠿⠿⠿⠿⠍⣉⠉⠉⠉⠀⠀⠀⠀⠉⣉⡉⠉⠉⢛⡛⠻⠿⣿⣿⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠃⠀⠠⣀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⢒⣒⠢⡀⠀⠀⠀⢣⠀⡞⠀⠀⢀⢒⣤⡲⠄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢸⢿⣿⠇⡄⠀⠀⠀⠈⣶⠀⠀⠀⠻⡘⠿⢃⡄⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠑⠒⠊⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠘⠃⠂⠲⢄⡀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⠔⠞⠒⠐⠒⠀⣠⡀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠞
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⡀⢀⡸⡄⠀⠀⣠⣁⣀⠤⠒⠉⠀⠀⠀⠀⠀⢰⠤⠄⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⢇⠀⠆⢁⠀⠀⠀⠴⢎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡆⢀⠏
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⡀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⢀⠞⢠⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠱⡀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠰⠖⠒⠒⠒⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⠀⠀⡰⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢁⡎⡹⠀⢠⠁⣈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠚⠁⠀⠀⠀⠈⠀⡀⣠⢺⠁⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠀⢀⣉⠒⠀⠒⠉⠁⠒⠂⠤⠤⠤⠄⠀⠤⠤⠤⠤⠐⠒⠀⠉⣁⢔⠒⣖⠈⠉⢉⣀⠀⡟⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⠆⠀⠀⠀⠁⠀⢠⣛⠀⠐⠒⠠⡄⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠲⠦⣈⠙⣡⠄⠀⣈⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⠘⡍⠃⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠓⠀⣴⠊⠑⢂⡀⠀⠀⠉⠁⠀⣤⠉⢠⠺⠁⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡠⣀⠀⠀⠀⠀⠀⣀⣈⠀⣀⠁⠁⢀⡀⠀⠀⠀⠀⠀⠀⢹⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⡄⣬⠴⠘⠛⠲⢋⠋⠈⠲⠞⠁⠀⠀⠙⠈⠉⠒⠊⠀⠈⠋⠀⠉⠒⠁⠈⠦⣀⡐⠉⢢⡔⢹⠖⠁⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠀⠀⠈⡀⠃⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠵⠀⠀⢣⡦⠄⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⠀⠀⢘⡇⡱⢄⠀⠈⠟⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠁⣀⣀⣠⠞⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡳⡟⠀⠀⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠚⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⠪⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡀⠒⡝⢫⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠰⠉⠀⢀⡄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⠼⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠂⠰⠀⠀⠖⠛⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⢀⡶⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⢸⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⣰⠀⠀⠀⣠⠦⠀⠃⠀⢰⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡷⠂⠀⠉⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠈⠲⠎⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠐⣥⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠉⠀⢀⠤⠀⡰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⠀⣿
⠀⠀⠑⣄⠀⠀⠀⠈⢂⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⣀⠖⢀⡀⠀⠂⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠁⠉⢀
⠀⠀⠀⣿⠀⠀⠀⠀⢠⠀⢀⠉⠀⣤⠀⠃⠀⠐⠈⠉⠀⠀⠈⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⡇⠐⠀⠀⠀⠀⢁⠀⠀⠁⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⡇⠈⢦⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢍⠀⠈⠁⠈⣀⡀⠇⠀⠀⠀⠀⠀⢀⡀⠀⠠⠐⠈⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠸⠄⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⢡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⢠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠀⣡⠀⠀⠒⠀⠀⠀⠀⣀⡀⠀⣀⡀⢀⣀⡠⢀⡀⠄⠀⠄⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠿⡄⠐⠊⠉⠀⠀⠀⠀⠁⠂⠁⠰⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⡄⢳⡀⠀⣥⠀⢀⣀⣀⣀⡀⠀⣠⣤⣤⡄⠀⢰⣶⣶⠆⢰⣦⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠼⠶⠖⠰⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⡀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠠⠁⠀⠁⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⢠⠀⠀⠀⠂⠠⠌⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⣀⠐⠃⠀⠀⠀⠀⠀⠀⡃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⢻⣿⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⡿⢿⡗⣶⣦⣤⣶⣿⣷⣾⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠛⠉⠉⠉⠙⠛⠛⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⠙⡏⢉⠲⡖⢉⠑⡖⢺⡏⡷⢋⡙⠎⢉⣹⠉⡉⢲⠊⡉⢾⠉⡉⢶⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣌⠳⡇⠸⢀⡀⢸⠀⡀⠈⠁⠅⢘⠓⠃⠈⣹⠀⡁⠲⠀⡇⢨⠀⡁⢾⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡤⢥⡈⢀⠆⣰⡭⣧⡈⠠⣇⣸⠄⢶⠈⢁⣄⠈⢙⡀⢋⢴⡄⠁⢼⡀⠉⣼⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠰⣄⡉⢰⠀⠃⢸⠀⡟⠀⢸⡇⢠⠈⠁⢴⣦⢠⡌⠛⠀⢸⡇⠸⠀⣶⠀⣶⠀⢦⣹⠀⣾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢣⠈⠁⢸⠀⡀⠸⠀⡇⠘⠈⡇⠀⢸⡇⢰⣿⠈⣡⡆⠘⠈⡇⣆⠀⣿⠀⣿⠳⡄⢹⠀⢿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠔⠛⠦⣄⡿⠦⠞⠓⠛⠦⠗⠚⠦⠶⠤⠖⠚⠁⠓⠛⠦⠗⠛⠶⠛⠶⠛⠲⠤⠛⠀⣻
⠀⠀⠀⠷⢤⠤⠤⠤⠤⢤⠤⠤⠤⡤⠤⡤⠤⠤⡤⠤⡤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾
⠀⠀⠀⠈⠉⠈⠉⠀⠀⠉⠁⠉⠀⠉⠈⠉⠈⠀⠁⠈⠁⠀⠉⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⡀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡁⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡆⠲⠄⣝⣀⣴⢄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠈⠁⣹⡟⣄⠀⠂⠀⠀⠀⠀⢸
⠀⠁⠀⠀⢘⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠌⢑⣤⡴⢴⣦⢉⡁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡎⠀⣼⠓⡄⠱⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠀⠤⣼⡙⡀⠰⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠉⠀⠀⠠⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠴⠒⠂⠤⠤⠤⠤⣀⡤⢄⡀⠀⣀⠈⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⣠⠤⠞⠀⠄⠀⠀⠀⠀⠀⣄⠀⣆⢀⡤⠈⠉⡀⠉⠁⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⡤⠶⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⠀⠀⠈⠱⣬⠂⠁⠺⡀⠘⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⢹⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢠⢮⡿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣷⠄⠀⢇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠠⢀⡀⠼⠋⠦⠤⠼⠛⠓⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠤⠼⠦⠄⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠉⠛⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⣳⠀⠀⣠⠞⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡼⠉⠳⢴⡎⠁⠀⠀⢸⠁⠀⠀⠀⠀⠀⠓⠢⠐⣱⢰⡉⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡞⠀⠀⠀⢸⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠲⠲⢂⣀⣀⡠⡀⠀⢀⣧⣬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀⠊⠘⠄⠀⠀⢠⠓⠢⠄⣀⠀⠀⠀⠀⠀⣀⣀⠀⠶⡫⠭⢍⡙⠢⢍⣒⠻⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠝⡶⡞⠑⠚⠀⠋⣐⠒⠤⠀⡈⠀⠀⠀⠀⠀⠀⢀⡀⠈⣡⡌⢠⣤⢄⡏⠉⠉⠁

⣿⡿⠟⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤⣀⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠇⠀⠀⠉⠛⠛⢻⣼⣟⣩⣶⢶⣄⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣟⠋⢻⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣷⠀⢤⣀⣀⣀⣀⠀⠀⠀⠈⠛⠋⠀⣾⣷⣌⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠖⠁⠀⠴⠛⠛⠀⡅⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢷⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⣷⣾⣿⣿⣿⣶⣶⣦⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠉⠉⠉⠋⠉⠉⠉⠉⠓⠂⡠⠰⠆⠀⠀⠀⠀⢨⠘⠉⠙⠻⠆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠰⡯⠻⢷⠶⣤⣁⠀⠀⠀⠀⠀⡏⢩⢰⡟
⠀⠠⠤⠴⠀⠀⢒⡹⠞⠉⠀⠀⠠⠤⣤⣄⣤⣴⣏⡀⠀⠀⠀⠀⠸⡿⠂⠀⢠⢀⣐⣿⢾⡃⠀⠈⠙⠲⢤⡁⠲⠧⢀⣼⠃
⠀⠀⠀⠀⠈⢐⠀⠀⠀⠀⠀⠀⠀⠉⣁⠀⠀⣈⡌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠈⢰⡚⡇⠀⠀⠀⠀⠀⢳⣀⠀⡀⢹⡄
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡶⣶⠗⠀⣬⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⣛⠤⠴⠋⠁⠀⠀⠀⠀⠀⠈⠏⠀⢱⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠞⠁⠀⠀⠱⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣆⠀⠀⠀⠀⠀⠀⠀⠁⢨⡁⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠣⠀⠀⠀⠀⠀⠀⠀⠺⠓⢸⠇
⠀⠀⠀⠀⠀⢀⡠⠔⢁⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⢠⡀⢱⣴⠦⠀⠠⣀⡄⠀⣤⠋⠀⠀⣀⢤⡀
⠀⠀⣴⠂⠉⠀⠀⢀⣴⠀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⠛⠶⢦⣼⣏⣠⣌⢁⣀⣠⣶⣿⡾⠁
⠀⠀⠙⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⣄⡀⣈⠿⠁⠙⠉⣿⣫⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠰⢶⠾⠷⠾⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⠛⠟⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⠤⠠⡔⠲⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢉⡉⠓⠒⠯⡠⢄⣨⣉⠳⠒⣲⢖⡤⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠈⢒⡄⢤⣀⠀⠀⠀⠀⠀⠀⠁⠄⠙⢒⠖⠉⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⡐⠙⠃⡌⠰⠷⠀⠈⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⣒⡶⠬⠭⠭⢭⣉⡑⠲⣖⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣘⠓⠲⠦⠶⠶⠶⠒⠒⠚⠓⠎⢣⡀⡀⠀⠀⠀⠀⠀⢸⠐⠑⠒⠦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢟⣹⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠒⢭⡒⢄⡀
⠀⣴⠶⠒⠒⣒⡒⠲⡭⠓⠋⠁⠀⠣⣀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢀⠀⠀⠸⡀⠀⠐⠁⡀⢣⠈⠑⠫⣶⣄
⠈⠳⠬⠚⠉⠁⠈⠑⣘⠀⠀⠀⠀⠀⠀⣹⠒⠒⡒⠲⠊⠁⠄⠀⠀⠀⠀⠠⠄⢀⢀⡇⠀⠀⠀⠜⢼⠀⠀⠀⡠⢓⣉⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣼⡷⠦⣁⣤⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡇⢄⡀⠀⣀⡨⠂⠀⠘⠞⠁⠀⠙⡾⡦⣯
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠔⠒⡭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠚⠉⠻⣝⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣂⠉⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⣀⡠⠤⠤⢤⣀⣀⢀⣀⠠⠤⠤⣄⣀⣀⣀⠠⠤⢤⣄⣀⣀⣀⠤⠤⠤⣄⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⢨⣧⠀⠀⣠⠆⠀⠀⠀⠰⣆⠀⠀⣿⡀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠜⠋⠉⠀⠀⠈⠉⠛⢄⠀⠀⢀⠔⠋⠁⠀⠀⠈⠁⠛⢄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢀⠊⠀⠀⠠⠒⠀⠒⠠⡀⠀⠓⡀⠂⠀⢀⠄⠒⠒⠠⣀⠀⠈⢢⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠀⢀⣂⢀⣾⣿⣷⡄⠐⠀⠀⡇⠀⢠⠁⣰⣾⣷⣦⠈⢂⠀⠈⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⡠⠾⠿⠿⠧⣍⠉⠙⠋⠉⠉⠛⣹⠿⣄⠙⠋⠉⠉⠉⠉⣩⠽⠖⠛⠻⠦⣀⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢠⡎⠀⠀⢠⠤⠀⠀⠀⣷⠀⠀⠀⠀⣸⠁⠀⠈⡇⠀⠀⠀⠀⣾⠁⠀⠀⠤⠄⠀⠀⢹⡄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠓⠤⠀⠀⠢⣄⠀⠚⠥⠤⠤⠐⠈⠐⠀⠀⠠⠋⠐⠢⠤⠤⠜⠢⠀⢀⠜⠀⠀⠤⠚⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠁⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠰⠶⡖⠒⠒⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠀⣨⣿⣇⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠀⠀⠀⠈⡏⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⡈⣷⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡟⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣦⡤⠤⠤⠤⢤⣠⠤⣤⣀⣀⣠⠤⢤⣀⢠⠤⡤⠄⣀⣀⡤⢤⡤⣤⡤⠤⠴⢤⣤⡼⠁⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡠⠂⢡⣄⡰⠉⠢⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⣿⠀⠀⠀⠀⠀⠂⠐⠀⠒⠀⠂⠀⠒⠦⠀⠑⡖⠂⠀⠐⠐⠐⠒⠐⠂⠂⠐⠒⢾⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢠⠀⠀⣿⠀⠀⠿⠿⠿⠿⠇⠀⠀⠿⠿⠿⢿⠁⠀⠀⣹⠿⠿⠇⠀⠀⠿⠿⠿⠿⠗⠀⢸⠀⠀⢀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢇⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠇⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠸⣡⠄⠠⠀⠖⠠⠄⠘⠓⠒⠒⠲⠖⠛⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⠲⡖⠒⠒⠒⠒⠲⡖⠒⠒⠒⠋⠰⣁⠠⠀⣀⠀⡉⢢
⠀⠀⠀⠀⠀⠀⠘⠂⠸⢤⠇⠀⠀⠀⠀⠀⠀⠘⠶⠤⣤⢤⡤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠷⢤⣤⣤⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⣄⡁⠂⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⣼⣧⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣾⣷⣶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⣿⣿⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⢿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠿⣭⣭⣽⣟⣒⠶⠶⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠁⠀⠀⠀⠀⠉⠙⠳⠶⠶⠾⣭⣭⠟⠶⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠷⢶⣍⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣠⠋⣠⣄⠈⢳⣀⡤⠤⠤⣄⠀⠀⠀⠀⢠⣿⡤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⡇⠸⣿⣿⡇⠀⠀⢠⣤⣄⠈⢧⠀⠀⠀⣿⣹⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡙⢦⡈⢉⡠⠔⡄⠻⣿⡿⠃⣸⠀⠀⢀⣿⣞⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣆⠉⠉⠀⠀⠙⣤⣀⣠⠞⠁⠀⠀⣾⢳⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⠦⣤⣤⣀⣀⣠⣤⣦⠀⠀⢀⣿⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠹⣿⣿⣦⣾⣅⣹⣿⣿⡿⠁⠀⠀⣾⣃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⡀⠀⠙⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⡿⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠛⠲⢦⣤⣉⣉⠉⠀⠀⠀⠀⢀⣾⢇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣦⣤⣀⣸⣿⡟⠉⠛⠲⠶⢤⣄⣸⣧⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⢀⣟⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⣿⠿⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⠀⠀⠀⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⣿⣿⣿⢽⡷⣛⠓⠀⠔⠈⠥⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠌
⣿⣿⣿⡏⣿⠋⡡⡈⠂⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠄⠀⠀⠀⠁⠂
⠋⣟⡇⠃⠁⠠⠟⠁⠈⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⢤⡦⠴⢒⡚⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠀⠀⠀⠂
⠀⣃⡄⠩⠄⠀⠀⠠⠞⠛⠓⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⡀⡀⡀⠀⠂⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡒⠿⡉⠻⠀⠈⠘⢤⣶⣆⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠐⠛⢛⡋⣠⡀
⠀⠀⠀⠀⢀⣀⡤⣄⠤⢄⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢐⠟⢻⡍⠁⠄⠀⠁
⠀⠀⠀⠀⢘⣥⡠⠃⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⣀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠣
⣀⡀⠶⠯⠂⠀⢤⣼⡿⠹⠛⠻⢠⣰⣄⠀⠀⠀⠀⠈⠡⣄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠹⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠈⢺⣦⠀⠀⠀⠀⠀⠈⠒⢋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡂⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⣀⣮⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⡄⠁⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠠
⡀⠀⠀⠀⠀⢠⠆⠀⠀⡀⡀⠒⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⡒⣐⣒⣐⢃⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣹⠁⢻⡇⠀⠼⡏⠯⠿⠟⠿⠯⠸⠿⡇⠀⡀⠀⠀⠈⠀⢠⠂⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠈⠀⣱
⢀⠔⢀⠐⠟⢴⣼⡀⠂⢸⣾⣶⣶⣿⣾⡷⠿⢿⠇⠀⠰⠀⠀⠀⠀⢈⣠⣀⢀⣰⢂⢀⣀⠀⢀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠁⠀⠀⠀⠀⡠
⢁⡔⠁⡐⢰⣶⣿⠊⠀⠠⠈⠀⣀⣼⣒⢃⣠⡄⢤⣤⣶⣶⣾⣿⣿⡾⢿⢿⣿⡹⠏⠙⠛⠒⠚⠃⠉⠚⡅⢀⣀⠔⠂⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⣥⣶⡞⠁⢡⣤⣿⣧⡀⠀⢇⠐⣿⣿⣿⣟⣛⣃⡨⠿⠞⠋⠁⠀⠀⠀⠀⢨⣿⡇⠈⢈⣧⡀⠀⠀⠀⢀⡑⣤⡀⠀⢀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣆
⣿⣿⣧⣤⣤⣀⣿⡿⣯⣷⡜⢀⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⢸⡿⣧⡴⠒⠉⠉⣿⣿⣿⣾⣿⣾⣦⣤⣤⣤⣼⣯⣿⣿⣅⢀⡮⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡀⠂⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠠⠈⢁⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⣼⠃⠀⠀⠀⠀⣀⠤⠒⠉⣀⣀⣤⣤⣤⣀⣈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⠞⢁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠈⣦⠤⠤⣄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢰⠏⠀⠀⢀⡞⢁⣴⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣦⠈⢧
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠐⢠⡟⠀⠀⠀⡞⢀⣾⣿⣿⣿⣿⡟⣀⠀⣀⡀⢹⣿⣿⣿⣿⠇⣸⣿⣿⡇⢸⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟⠀⠀⠀⠀⣇⢸⣿⣿⣟⣋⡹⢧⡛⣥⡛⢁⢞⣁⣿⣿⠏⣰⣿⣿⣿⡇⡘
⠀⠀⠀⠀⠀⠃⠀⠀⢀⡟⠀⠀⢀⡄⠢⣜⢆⠻⣿⣿⣿⣿⣿⢇⠉⣀⣿⣿⣿⣿⣟⢰⣿⣿⡿⢛⣭⠙⣆⣀
⠀⠀⡤⡤⠤⣀⠀⠀⡞⠀⠀⠀⢨⢸⣿⣮⣁⠓⠈⢻⣿⣩⣱⣾⣿⣿⣷⣀⣾⣿⣿⣦⣭⣥⣾⣿⠏⣼⣿⣿⢹⠆⠀⠀⠀⠀⣊⠰⠒⠆
⠀⢰⢁⠀⠀⠀⣼⠘⠃⢀⠀⠀⠈⢣⣙⣿⣿⠿⠿⠿⠿⠿⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠉⠓⠿⠿⢿⣃⠞⠀⠀⠀⠠⠐⣮⠋⢛⠉
⠀⠈⢳⣊⡑⠂⠢⠐⠄⡜⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠠⠤⠀⠀⠀⠀⢸⠃⠀⠀⠉⠉⣳⠀⠀⠈⠂⡁⠀⠀⡄
⠀⠀⠸⠀⠺⣤⠀⠓⠛⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⡠⠊⠉⠀⠉⠑⢶⠤⠂⣁⠀⠀⠀⠡⠀⠀⠀⠆⠀⠠⠀⠰⠃⠀⠀⠀⠀⠀⢰⠋
⠀⠀⢸⠒⠂⣿⠈⠢⢄⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⠀⠀⠠⣶⣶⠀⢆⠀⣮⡶⠔⠒⠒⣨⠧⢀⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⠇⡌
⠀⠀⠘⠿⡴⠃⠀⠐⠢⢍⠂⠄⡀⠀⠀⢹⠀⠀⠀⢄⡠⠐⠯⢙⠀⠸⣦⡀⠀⠀⠀⣎⠀⣀⠀⠀⣀⠀⠀⠀⠀⡃⡀⠀⡠⠊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢌⡓⠄⢹⠀⠀⠀⠘⢧⣀⠀⠈⠉⠙⠀⠈⠉⠈⠋⣡⣾⣿⡄⠀⢛⠀⠀⢀⠔⢣⠴⣋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⡓⠀⠳⠀⠀⠀⠀⠀⠾⣉⣀⣀⣀⣤⠤⠲⣿⣿⣿⣿⣇⠀⢸⠀⢀⠂⠀⠈⢚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⡄⠀⠀⠀⠀⠀⠀⢸⣀⣀⣿⣤⣴⡿⠛⠛⠛⠛⠀⠀⢀⠀⠃⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠤⠔⢀⠁⠀⠀⠀⠂⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢆⣀⣄⣰⢃⠄⠀⠀⠀⢀⠀⢁⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣀⡤⣤⣄⣀⠤⢤⣤⠤⣤⠈⠩⠶⠖⠚⠓⠒⠋⠉⠀⠀⢸⡄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⠰⠀⣶⠞⠋⢧⣴⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠫⣍⠒⠶⠟⠀⠘⠛⠃⠀⠘⠛⠛⠀⠙⠛⠛⠙⠀⠄⠀⣀⣤⢾⡈⡇⡉⠻⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⡐⠲⠀⣀⠐⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠲⣶⠋⠉⠀⡠⠣⠇⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠃⠂⠙⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠻⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⣈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣀⡀⠀⠠⠴⠒⣦⢀⡤⣄⠀⠀⠀⡄⠀⡤⠀⠀⠀⢰⠖⠒⠀⠒⣋⡽⠃⢀⡤⢤⠐⣦⠀⡼⠁
⠀⠀⡞⠀⣀⡀⠀⣷⠴⢋⡎⠁⣿⢸⣷⡀⡇⢸⠁⣤⡔⠒⢺⣤⠤⠀⠀⡏⠉⣳⠾⣄⡞⠀⠈⣻⠁
⠀⠀⠙⠉⠉⣹⠀⢹⠀⠸⣇⣠⠏⠸⠇⠻⡇⠸⣄⣠⡝⠀⠈⣇⣠⡄⠀⢷⡶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠶⠞⠁⠀⠘⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⢤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⣤⣤⣤⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠒⠚⠛⠛⠋⠉⠉⠉⠁⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣝⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣼⣿⠟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠐⠤⠔⠒⠂⢤⠤⣿⠿⠿⠿⣉⣢⠤⠤⢬⣀⢤⠤
⠀⠀⠀⠀⠀⠀⣠⠊⠀⢠⡀⠀⠀⠀⠀⠀⣀⠴⠂⠓⠤⡌⣠⣶⣶⣦⠀⡄
⠀⠀⠀⠀⠀⠔⠁⢀⣴⡄⡏⠀⠀⠈⢀⠔⠁⠀⣠⣶⣦⡘⠿⣿⣿⠟⡠
⠀⠀⠀⠀⢨⡚⠀⣾⠏⠀⢧⠀⢀⣀⡨⣀⡀⣼⣯⣶⡿⠃⣀⡰⠚⠋⡠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢽⠀⠀⠰⠆⡿⠀⠁⠀⠀⠀⠈⠫⡙⢉⡠⡼⠃⠀⢀⡠⠁⠒⠐⠒⢄
⠀⠀⠀⠀⠀⠘⣦⠀⠀⠘⠀⠀⠀⢀⢶⡇⡀⠀⠉⠉⠀⢦⣤⠔⢯⠀⠀⠠⣄⡄⠀⢳
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠘⠂⡤⠄⢤⣤⣤⣤⠵⠊⠁⠸⠛⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⣟⠛⠀⠡⠄⡀⠀⠀⣀⡠⠖⠀⡗⣦⠴⣟⢶⠀⠀⢀⡀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢿⢰⣷⣦⡉⢘⠀⠀⠀⠀⠀⡀⠈⠁⠀⢈⠉⠀⠀⠀⠉⠉⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠴⠇⠀⢀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⢸⣤⣤⣤⣤⣤⣄⣀⣀⣠⣀⣀⣀⠀⣀⡀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⠿⠟⠛⠛⠛⡛⠻⢿⣿⣿⠿⣿⠶⣶⣶⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣽⣿⣿⠉⠉⠈⠉⠉⠠⠿⠋⢹⠀⠘⠛⠃⠐⠒⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠼⢏⣹⣧⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⡤⠓⢎⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⢾⠢⠶⣉⠻⣿⣿⣿⣿⡏⠉⠙⣿⣿⢿⣿⣿⠟⠿⡗⣦⠘⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠈⠀⠈⠉⣸⡉⠀⠀⠀⠀⢐⣇⠀⠀⠀⠘⠖⢁⣨⣺⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣷⣧⠀⠀⢀⣴⣯⣿⣦⣤⣤⣤⣶⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣷⣶⣿⠿⠟⠻⠿⠇⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠸⠀⣠⠞⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠴⠒⠒⠒⠒⠒⠙⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠐⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠲⣄⣠⣀⡠⠤⠤⠀⠀⠀⠀⠤⠤⠤⣀⣴⣠⠆⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠐⠀⠀⠀⢀⡤⠒⠉⠉⠉⠒⢄⡠⠔⠒⠒⠒⠢⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⣰⠃⠀⠀⠀⢀⣀⣀⠀⠱⡀⠀⠀⠀⠀⠈⢢⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢰⣿⣿⠋⢙⡄⣇⣴⣿⡟⠓⡄⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠸⣿⣿⣿⣿⢇⠏⢿⣿⣿⣿⠇⣸⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠘⢄⠀⠀⠀⠈⠙⠋⣡⠞⠀⣀⠉⠉⢁⡴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠉⠒⠒⠒⠒⠊⠀⢄⠀⠀⠉⡋⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡆⠉⠑⠊⠁⠀⠀⢀⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢨⡇⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⢸⢇⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡎⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⣾⡉⠑⠒⠒⠲⠀⠤⠤⠄⠄⠄⠖⠒⠒⠂⢉⠇⡞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜⠀⠱⢦⡤⢠⣀⣀⣀⣀⣀⣀⣀⡀⣀⠠⡤⠊⠀⠹⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠡⠗⠒⠲⢖⠒⢲⠖⠒⠘⠭⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⣀⡠⠔⠋⠀⠈⠓⠤⢄⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⡀⣀⠀⣀⠀⢀⡀⢠⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⣀⢀⠀⠀⢀⠀⡀⠀⢀⡀⣀⡀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠙⠀⠉⠀⠁⠀⠀⠈⠁⠈⠉⠁⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠉⠀⠀⡈⡁⡁⠉⠁⠈⠀⠉⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠂⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠐⠀⠀⠀⠐⠒⠂⠀⠀⠀⠒⠂⠐⠒⠒⠐
⠀⠀⢈⠀⠀⠀⠁
⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⡀⡄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣄⠀⡀⢠⣀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⡀⣀⠀⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⢀⣈⡀⡀⢀⡀⢀⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢠⠀⠄⠀⢄⠀⠀⠀⠠⠄⠀⠀⠠⣤
⠀⠤⠀⡤⠄⠤⠀⠤⠄⠀⠤⠤⠤⠄⠄
⠀⠀⠤⠠⠀⠤⠤⠄
⠀⠀⠀⠠⠄⠤⠄⠠⠤⠀⠠⠤⠤⠤⠄
⠀⠀⠀⠄⠐⠠⠀⠀⠠⠄⠀⠤⠠⠤
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂
⠀⠒⠐⠒⠂⠀⠐⠒⠂⠀⠒⠀⠒⠂
⠀⠐⠒⠒⠂⠐⠒⠒⠐⠒⠂⠐⠀⠐⠂⠂
⣀⣀⡘⠐⣀⡀⢀⡐⢒⣂⣂⣐⡐⢂⣀⢀⣀⣀⣀⠀⢀⡀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⣿⣿⠿⠿⡿⢿⢿⣿⢿⣿⣿⡿⣿⢿⣿⠿⡿⢿⣿⣿⣿⡿⠿⣿⡿⢿⡿⠿⣿⠻⠿⢿⣿⡿⡿⠿⠿⠿⢿