⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⣦⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⢀⣼⣿⣟⣿⣻⣽⣟⡿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠊⠀⠀⣾⣿⡷⠛⠉⠉⠉⢻⣿⣽⣻⣧⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⢰⣿⡟⠀⣰⣾⡄⢁⣹⣿⣿⣟⣿⡽⣯⣿⡽⣿⣿⣦⣄⠀⠀ ⠀⡀⠀⢠⢹⣿⠁⣰⣿⡿⣵⣿⣿⠟⠓⠛⠉⠛⠛⢷⣿⣻⣞⡿⣿⣆⠀ ⠀⣱⠴⠶⠾⣏⠀⠙⢻⣿⡿⠋⢁⣠⣼⣶⣾⡄⢂⠠⣹⣿⡽⣿⣽⢿⡆ ⡼⠁⣀⡀⢀⠈⣷⣸⡿⠋⢀⠀⡿⠿⠿⠽⠋⢁⠠⠶⣿⣯⡿⣟⣾⢿⡇ ⢧⡘⠁⠹⠀⣠⣿⡟⠁⡐⠀⠂⠄⣐⣀⣦⣐⣀⠂⡐⠈⢻⣽⡿⣯⣿⠇ ⠀⠙⠲⡶⠗⠛⢿⡁⠠⢀⠡⠈⡀⠻⠟⠿⠟⠛⡀⠄⢂⣴⣿⢿⣽⠏⠀ ⠀⠀⠐⣟⡀⠠⠀⣷⣄⢀⠂⢁⠐⣤⣤⣆⠠⢁⠐⢻⣿⡿⣯⡟⠋⠀⠀ ⠀⠀⠉⢸⢹⠓⢾⢙⡾⣟⠶⠦⣤⣍⣛⣛⣁⣄⣦⣿⣿⣟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠂⠘⣯⠰⡼⠳⣦⡀⢤⣤⣐⠠⠀⠄⡈⢻⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁⢀⡼⢛⢾⣟⠻⠿⠇⠠⠐⣸⣿⣻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠮⢼⡇⠐⢈⠈⣿⣿⣟⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠞⠛⠛⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠄⠐⠠⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢂⠐⠠⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢢⠁⢊⠐⠠⠀⠌⡁⠒⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠂⠌⠄⡡⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⡌⠠⢁⠊⡐⠠⠁⠤⢁⠂⠄⡉⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⣢⠬⢔⣈⠄⠡⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢔⠂⡐⠠⠁⣌⡰⠖⠚⠢⢄⣁⠊⠄⢂⠑⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡐⡎⠀⠀⠀⠈⢦⠁⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠨⠐⠠⢁⢲⠊⠀⠀⠀⠀⠀⠈⠳⣌⠠⠘⡀⢂⠉⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠐⢠⢹⠀⠀⠀⠀⠀⢰⠈⠄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠡⠈⢼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡂⠄⡁⢂⠐⠠⢁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡐⢈⠐⡠⢈⣇⠀⠀⠀⠀⢨⠈⠤⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠨⢀⠂⠡⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢈⠐⠠⢁⠊⠄⠂⠄⡑⢄⠀⠀⠀⠀⠀⠀⠅⢂⠐⠄⢂⠐⠠⠸⡆⠀⠀⢀⠎⡐⠠⢁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠑⠠⢈⠡⠈⠄⠓⠤⡀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠔⢂⡜⠠⢅⠌⡐⠠⠑⢄⠀⠀⠀⠜⠈⠄⡨⢐⡈⠄⢃⠐⢳⠀⢠⠎⡐⠠⢁⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⠁⠤⢁⠂⠄⠃⠌⡠⠁⠌⡉⠔⠢⠄⣀⠀⠀⢸⡐⠈⠄⢧⠀⠀⠉⠢⣡⠈⠄⡑⢄⡐⠄⡁⠎⡎⠉⠈⢪⡄⠘⢸⡴⠉⠠⠄⡁⠂⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠜⠠⢁⠂⠤⢈⠂⡁⠆⠠⢁⢂⠐⡈⡐⠈⠄⠡⠑⠢⠇⠌⡐⠈⢧⠀⠀⠀⠈⠳⣄⠐⡈⢣⡔⡈⢼⡀⠀⠀⠀⡣⠈⢄⠠⢁⠟⢱⠀⡉⢐⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⡈⡐⠠⠌⣰⠤⠶⠤⠬⠔⡂⠄⠒⠠⣀⠉⠄⡡⠘⠠⢁⠂⠄⡉⠌⢳⠀⠀⠀⠀⠈⢦⡁⢂⠹⣆⠀⠳⡄⠀⢠⠃⠌⣀⠂⠭⠀⠀⢧⠐⡈⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡐⠠⢁⣾⠁⠀⠀⠀⠀⠀⠈⠑⢬⠐⠠⢈⠐⠠⢁⠒⠠⢈⡐⠠⠌⠠⢳⡀⠀⠀⠀⠀⠙⣄⠂⠜⣧⠁⡙⠦⠃⠌⡐⠠⠌⡇⠀⠀⢸⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠀⠅⢂⠘⣄⡀⠀⠀⠀⠀⠀⣀⣀⠻⢀⠂⠡⠌⠠⢈⠄⠡⢀⠡⠈⠔⡀⠳⡄⠀⠀⠀⠀⠈⢧⠂⠌⢧⡐⢈⠐⠂⠄⡡⢸⠀⠀⠀⢸⢁⠐⠇⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢎⠐⠠⠂⠄⠨⠑⠒⠒⡈⠉⠄⢠⠈⠄⡘⠠⠈⠔⡍⠉⠉⠉⠉⠁⠒⠤⢡⠸⣄⠀⠀⠀⠀⠀⢻⡀⠊⣧⠞⠁⠺⡄⡀⡇⠀⠀⠀⢸⠀⢺⠀⠘⣐⢸⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠈⠰⢡⡈⠐⠡⠈⡄⠡⣀⠉⠰⠀⠌⡐⠠⢁⠡⢂⢳⡀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣄⠀⠀⠀⠀⠀⢳⢁⠘⡄⠀⠀⢱⢠⠃⠀⠀⠀⡇⠌⣰⠀⠀⠀⠁⠐⠀⠀⠀⠀⠠⡠⢑⡄ ⠀⠀⡔⠁⠄⠉⠄⠡⠀⠡⠀⠌⠄⠡⠒⠠⠁⠂⠰⠀⠂⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢧⠈⢱⠀⠀⢸⠌⠀⠀⠀⠀⠣⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀ ⠀⠀⡅⠂⢄⠡⠐⢢⠵⠒⠚⠒⠤⡂⡐⠠⢈⠐⠂⠌⡐⠠⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡉⡆⠀⢸⠆⠀⠀⠀⢘⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠱⡈⠄⢂⠉⢧⠀⠀⠀⠀⠀⡹⢀⢁⠂⠌⡐⢂⡤⠇⠚⠀⠭⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⢱⠀⠘⠀⠀⠀⠀⡘⣈⠆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠘⠤⡊⠐⡠⠑⠒⠒⢒⠊⡁⠂⠤⢈⠐⠠⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⡆⠀⠀⠀⠀⠠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀ ⠀⠀⠀⠀⠀⠈⠑⠠⢅⡌⠒⡀⢂⠐⡁⢂⠰⠈⠄⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡜⡈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢂⠈⡉⠓⠲⢌⣔⡀⠢⢀⠅⠒⡀⢂⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⢀⡰⡘⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢁⡐⢀⠒⠠⢁⠂⢄⠠⠘⡙⠒⠪⠔⣤⣁⡌⠐⡠⢀⠐⡉⠒⡐⠠⠤⣀⡀⣀⠀⠀⠀⠀⠀⠀⢠⠃⢼⠒⢒⣉⡜⠀⡀⠂⠁⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢁⠂⡐⠠⣬⠖⠂⠉⠒⢢⡡⢀⠡⠌⡐⠠⠀⠌⡙⠒⠒⡊⠤⢥⣠⣁⣂⣄⠐⠠⢈⠩⢁⠒⠒⢊⠡⢨⣾⣠⠟⠠⠌⢫⡈⠙⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢂⠐⠠⢁⠣⢄⣀⣀⡠⠔⡁⢂⠰⠀⣤⡱⠜⠒⠐⠓⠂⠀⠁⠀⠀⠐⠒⠒⠉⠙⠛⢕⡒⠚⣲⠟⠋⠉⠀⠹⡌⢂⡑⢂⡇⠀⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠌⡐⠂⠌⢠⠀⠄⡐⠠⠐⠂⠄⡡⠃⠤⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠃⠀⠀⠀⠀⠀⠹⣤⣒⠜⠁⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⢀⠂⣄⣡⡌⠤⠬⠴⠤⢅⣘⡠⠁⠄⣁⣢⠔⠒⠊⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣒⣬⠿⡻⠁⠀⠀⠀⠀⠀⠀⠀⡡⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⢁⠐⣠⠞⠉⠀⠀⠀⠀⠀⣀⠴⠁⠄⡱⠚⠁⠀⠀⠀⠀⠀⢀⡠⠠⠒⣉⡡⢒⠞⠋⢱⠀⠀⢸⠀⠀⣄⢴⡄⢿⡦⠜⠩⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⡐⢀⠊⢼⠀⠀⠀⠀⣀⠴⢊⠁⢂⢁⠺⣁⣀⣀⡠⠄⠄⡒⣉⡡⠔⠑⡉⠐⢁⠀⠀⠀⠈⢄⠀⠀⢃⢤⡿⣬⠟⢙⠝⢄⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣀⠡⠈⠄⡉⢉⠉⠌⡐⠠⠂⠌⣀⠂⡐⣀⢂⡤⠔⠂⠓⠉⠀⢀⢐⠀⠀⠀⠀⡄⠀⠀⠀⠀⡨⢒⡴⠋⣐⢯⠀⠈⡆⠈⢣⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠒⠈⠔⠀⠊⠐⠤⠑⠘⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⢀⠐⠀⠘⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠾⠀⢀⡅⡼⠀⠀⠇⠀⢨⠇⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠑⢄⡀⠀⢀⠀⠀⠀⠀⠀⠘⢆⠀⢙⠧⡀⢸⠇⠀⡎⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢆⠀⠀⠀⠀⢀⠕⠁⠀⠀⠀⠀⠀⠀⢸⡄⢲⠀⢸⠀⠻⠀⡃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠁⡀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠈⠀⠘⠆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀