⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀大头照⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣱⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⣿⡀⢘⣦⠤⠤⠖⠒⠒⠒⠒⠒⠒⠲⠤⠤⢴⡾⢋⣾⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣳⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣾⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣿⣿⣿⡇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠶⠆⣐⣒⣆⡹⠇⠸⣿⣿⣿⠟⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠀⠀⢒⡈⠥⠀⠂⠐⠂⠉⠁⢀⡞⠀⢀⠀⠀⠈⠉⠁⠜⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⢖⠅⠀⠈⠀⠀⠀⢀⣀⣀⣠⠤⠔⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠔⢲⠟⠉⠉⠉⢩⠋⠀⠄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢐⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠏⠀⠀⠀⡰⠁⢀⠎⠀⠀⠀⠀⡄⠀⠀⠈⢧⡀⠀⠀⠈⡇⠀⢠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠜⠁⡼⠁⠀⢀⡤⡚⢁⡴⠋⠀⠀⠀⢀⠔⠰⣀⠀⠀⠈⢳⡀⠀⠀⠹⢦⠈⡄⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣉⠚⠒⠒⠒⣋⡥⠞⠛⠄⠀⠀⢀⡴⠊⣀⡀⢽⣤⣶⡷⠆⠙⢆⠀⠀⠈⠳⣧⢹⣤⠤⠖⢋⣟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢔⡱⠉⠛⢻⠛⣧⠤⠤⡴⣖⠦⠖⠋⠈⠁⠀⠀⠘⣿⣷⡷⠿⠆⠀⠑⢦⡀⠀⠈⠻⣆⠀⠀⠀⠈⣉⡭⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡜⠁⠀⠀⠈⠀⣿⠀⠈⢹⠀⠀⠀⠀⠐⣶⠤⣤⣀⡈⠣⡇⠀⠀⠀⠀⠀⠈⠳⢦⡀⠈⢷⡒⠚⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠐⠀⢹⡄⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⢹⠋⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢄⢳⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⢶⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢻⠀⠀⡼⠀⡏⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡇⣇⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣄⠀⠀⠸⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⡼⡴⠊⢀⡴⠖⠁⠀⠀⠀⠀⢀⠤⢋⡠⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⠞⠉⠑⠦⣄⠘⠮⡹⢳⠢⢤⣄⣀⣀⣀⣀⣀⣀⣀⣠⢜⡵⢞⡩⠴⠂⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⡴⠒⠠⣀⠁⠂⣠⠇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠽⢱⡯⡲⠉⠐⠀⠀⢀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⢅⠰⢔⣂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠒⠂ 傻不啦叽到此一游

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀全身
照

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣦⡀⠀⢀⡀⠄⠒⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⢂⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡟⠙⢻⣿⣿⣿⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠚⣩⡇⠀⣽⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠰⣶⡿⠷⢦⣿⣿⣿⣷⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠉⠛⣦⠀⠉⠻⢿⣟⣡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⡀⠁⠀⠈⠳⣄⠀⠀⠙⣆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣤⡾⠁⠀⠀⠀⠘⣿⣦⠀⠀⠈⢎⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣰⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠁⠘⠋⠀⠀⢠⠀⠀⠀⠸⡏⢧⡀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠠⢀⣀⣠⣤⠖⠋⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠀⠀⢀⠀⠀⠀⠀⣸⡀⠀⠀⠀⣇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠱⠁⠀⢀⠂⠀⠀⠀⢀⠇⠱⣦⠀⠀⣹⣀⡄⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣶⠿⠋⠁⠀⠀⡠⠁⠀⢠⠎⠀⠀⠀⣠⠂⠀⠀⠈⠲⠞⡟⢁⣠⡀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⢃⠆⣠⠎⢀⡠⠚⠁⢀⠀⡠⠞⠁⠀⣀⣀⣀⡀⢶⡟⠋⠁⠀⠀⠈⠻⢦⡀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠣⢀⢀⣩⠤⣴⣾⡷⠆⠒⠛⠛⠉⠀⠀⠀⢚⣿⣿⠯⠙⢧⡃⠀⡀⠀⠀⠀⠀⠘⡝⢦⡀⠢⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠀⡆⠀⢰⢸⢸⡇⠀⠛⠹⠇⠰⠀⠀⠀⠀⠀⠀⠀⠸⠉⠷⢐⠀⢸⠇⢠⠃⣸⠀⣸⠀⠀⢳⠀⠙⢄⠠⠀⠀
⠀⠀⠀⠀⠀⣣⡞⠁⠀⢀⠀⣿⡀⢸⣸⠘⡏⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡞⢠⣿⣤⣿⠀⠀⠘⡇⠀⠈⣧⢁⠀
⠀⠀⠀⠀⠀⢻⣿⡄⣨⣾⣄⣿⣷⣜⣿⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣇⣾⣿⣿⣇⣤⣼⣠⡅⠀⢠⣿⠇⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠈⠛⢿⣿⣿⣿⣿⣿⣵⣿⠋⠛⠓⢒⠒⠒⠚⠉⢿⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣇⢸⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⠿⠿⢻⣿⣿⡧⢕⢀⡀⣺⢼⣿⣿⡏⠀⠈⠿⠿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠈⢻⣿⣣⣴⣄⣾⣿⣿⣗⣯⣜⣣⣽⣮⣬⢝⢻⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠁⠀⢀⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣾⠿⣄⣤⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⢼⣿⣿⣿⣝⠟⢰⣿⣿⣿⣟⣟⣿⣿⣿⠛⠛⣿⣿⡆⠻⣷⡜⠃⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣛⠋⠠⢿⣿⣿⣽⣯⣿⣽⣾⣯⣏⣽⣿⣿⡿⠀⠙⣟⣦⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠻⠷⠶⠒⠶⠿⠿⠿⠿⠷⠾⠛⠛⠃⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣀⣀⣀⣠⠃⠀⢄⣀⣀⣀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢩⣿⡏⠁⠀⠀⠈⢹⣿⡏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣽⠃⠀⠀⠈⣯⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣉⡃⠀⠀⠀⠀⢘⣉⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀