⠀⣠⣄⣀⢀⡞⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠁⠀⠈⢻⡄⢠⣄⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢺⡄⢰⣤⡀⢳⠈⣿⡃⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢷⡌⢯⡅⠘⡧⠘⠅⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢳⡄⠁⠀⠈⠀⢀⣀⣨⠿⠓⠒⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠞⠁⠀⡴⠶⠀⢡⠟⠁⠀⠀⠀⠀⠈⢻⣗⣤⣤⣤⣄⠀⠀⠀
⢠⡿⠀⠀⠀⠁⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⢿⣄⣀⣀⣠⠄⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣙⡛⡟⠋⠀⠘⠉⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣠⠛⠀⣿⠁⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⣿⡀⠀⢛⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀
⠘⠻⢦⠬⠿⢦⣤⣤⣴⣤⣦⡟⣦⣤⣤⣤⣤⡴⠟⠁

⠀⠀⠀⠀⠀ ⠀⢀⡤⢤⡄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⢻⢀⡾⠋⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀
⢠⢤⣠⢄⡀⢸⡇⠀⠀⣼⡟⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀
⠳⣄⢁⡴⠃⠘⣧⠀⢀⡿⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⣠⡴⠞⠋⠘⠃⠀⠀⠺⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡾⠁⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⢀⠀⠀
⠀⠀⣾⠁⠀⠸⠇⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⢻⡗⠹⣷⡄
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⣿⡗
⠀⠀⠀⠙⢳⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠛⠃⠀
⠀⠀⠀⠀⠘⢧⠾⠷⠴⠏⠛⠛⠛⠛⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣤⡀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀
⠀⠀⠀⢀⣤⡄⠀⣿⡏⠀⡀⢹⡇⠀⠀⢸⡿⠁⠀⠀⠙⣇⠀
⢸⡟⠢⡏⢸⡇⢸⡏⠀⢸⠃⣽⢀⣀⣸⣿⢀⡶⠃⢠⡟⠀⠀
⠀⠙⢦⡴⠋⠀⣸⡇⠀⠈⠀⠛⠉⠉⠉⠉⠘⠁⢠⡿⠁⠀⠀
⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀
⠀⠀⠀⣴⠏⠀⠀⢙⡷⠀⠀⣀⠀⠀⠺⣿⡁⠀⠀⠀⠘⣧⠀
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣄⡀⠀⠀⣸⠇
⠀⠀⠀⣾⠻⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⠛⣦⣿⠃⠀
⠀⠀⠀⠹⣦⡀⠈⠩⠆⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⢻⣆

⠀⠀⠀⠀⠀⣰⠛⠉⠹⡆⠀⢀⣤⠶⢦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⡇⣠⠟⠀⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⢰⡇⠀⠀⠀⣰⠟⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀
⠀⣠⠶⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀
⣴⠃⠀⠀⠐⠇⢀⣤⠀⢠⡆⠀⠀⠀⠈⢷⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀
⠀⡿⠂⣰⠟⠛⣦⠞⠛⢦⠀⠀⠀⠤⣾⡁⠀⠀⠀⠀
⠘⡇⠀⠻⢦⡀⠀⢀⣤⠼⠆⠀⠀⠀⠈⢻⡄⠀⠀⠀
⠀⡟⠓⠖⠚⠧⣤⠼⠧⢤⠀⠀⠀⠀⠀⠀⣷⠴⣄⠀
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠂
⣴⡋⢀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⣠⡞⠛⠉⠀
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡀⠀⢀⡴⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⠟⠉⠙⢷⣾⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⣀⡀⢹⡄⠀⡖⢄⢘⣷⠀⠀⠀⠀⠀⠀⠀⣾⠫⣽⣴⠟⣿⡆⠀⠀
⠹⣧⠀⡀⠑⡈⢿⡄⢃⢸⡿⠛⣧⣀⣤⠶⣄⠀⠻⣦⠈⢁⣴⡿⠁⠀⠀⠀
⠀⠹⣦⠱⣄⡅⠈⢿⠌⠺⣧⠀⢘⡏⠁⢀⡿⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠈⠁⠀⠀⠀⠀⠉⠛⠉⠻⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⢿⣄⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠁⠀⠀⠀⢀⡿⠃⠀⠀⠉⠛⠀⠀⢸⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⣻⡶⠞⠶⣤⡀⠀⠀⠀⠀⠀⠀⡀⣰⡾⣁⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⢀⣸⡧⠤⠤⠖⠒⠒⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠛⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣤⣶⣤⡀⠀⢰⡟⠉⠙⠻⣶⡀⠀⠀⠀⠀⠀
⠀⠀⣾⠋⠀⠀⠈⠻⣦⠸⣇⠀⠠⣆⠈⣷⡀⠀⠀⠀⠀
⠀⠀⢻⡆⠀⠸⣆⠀⠹⣧⣿⠄⠀⠿⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⣻⡆⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀
⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡇
⠰⣏⠀⠀⠀⠀⠿⠃⠀⢰⣧⠀⠀⠛⠁⠀⠀⠀⠀⢸⡇
⠀⢻⣆⠀⠀⢀⣀⣀⢀⣤⣴⣦⣤⡀⠀⠀⠀⢀⣰⡿⠁
⠀⠀⠙⢷⣾⠛⠉⠉⠛⠁⠀⠀⢸⣷⠶⠀⢸⡟⠉⠀⠀
⠀⠀⠀⣿⣽⣧⡀⠀⠀⠀⠀⣠⣼⠿⠶⠆⢸⣇⠀⠀⠀
⠀⠀⠀⠈⠉⢹⡿⠷⣤⣤⡾⠛⠁⠀⠀⠀⢠⣿⣀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣹⡷⠀
⠀⠀⠀⠀⠀⠘⣷⣤⡾⠛⠛⠛⠛⢻⣆⣴⡿⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀