⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠉⠉⠉⠉⠉⠙⢢⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢘⡉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠳⡦⣸⣷⣄⡀⢀⣀⡀⠀⠀⠀⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡊⣿⣿⣿⣿⣯⡩⣉⠹⢷⢦⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢻⣿⣿⣿⣿⣿⣿⣶⣶⡞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢀⠉⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⣀⠠⠤⠐⠚⠱⠀⠀⠀⠈⠀⠀⠀⠉⣻⠛⠋⠀⠀⠀⠀
⡇⠀⠀⡊⠠⠐⠁⠀⠀⠀⠀⢰⠀⢀⠆⠿⡀⠀⠀⠀⠀⠀
⡗⠒⠒⠀⠀⠀⠠⠤⢤⡀⠀⢸⠀⠘⠀⠀⢌⠑⢢⠀⠀⠀
⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⠀⠐⠀⠀⠂⠀⠀⠉⠒⠢⣄
⡇⠀⠀⠀⠀⠀⠀⠂⢰⠤⠀⠀⢦⠁⠀⠀⢂⠀⠀⠐⠄⠀⠠⠈⠉⠑⠦⡀
⡇⠀⡀⢀⠐⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠄⠄⠄⠄⠄⠄⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠄⠄⠄⠄⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠄⠄⠄
⣿⣿⣿⠟⠋⠁⣀⣀⡈⠙⣿⣿⣿⣿⡿⠿⠿⠿⠿⢡⣤⣄⡈⠙⢧⠄⠄⠄
⣏⣉⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠶⠶⠤⣉⠙⠷⣼⣇⠄⠄
⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠄⠄⣿⣿⣶⣈⠙⣄⠄
⣿⣷⡶⠶⠶⠶⠒⠂⠄⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣆⠄⣿⣿⣷⡶⠖⠄⣶
⣁⣤⣴⣶⣶⠾⠟⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣓⠂⠄⣤
⠟⢛⣉⣥⣤⣶⡶⠛⢋⣉⡴⢟⣙⠶⣋⣿⣿⣿⠿⠛⠄⠛⠻⢧⡙⠾⢂⣄
⣾⣿⣿⡿⠓⣀⠐⠲⠞⣡⣶⠟⢁⣴⠽⠛⣉⣠⣶⣿⣿⣿⣶⣤⠉⣠⣌⠻
⣿⣿⣫⣶⣾⣿⡟⣠⣤⣤⠄⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⢋⡄⢻⣿⣷

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6900

⣿⣿⣿⣿⣿⣿⣿⠿⣿⣛⣛⣭⡭⣙⣛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢛⣵⣟⣾⣿⣿⠏⣼⣿⣿⣿⣟⣤⡙⠉⠄⠄⠈⠛⠿⣿⣿⣿⣿
⣿⣿⣿⡿⠷⢿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣽⣾⣿⣿⣶⠄⠄⠄⠄⠄⠈⠻⣿⣿
⣿⣛⣑⠺⣉⣭⣍⣛⣛⣛⣛⣿⡿⠿⢿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄⠄⠘⣿
⣷⡬⣣⣞⠺⣮⢿⣿⣿⣿⣿⣿⢟⣛⢷⣶⣍⡛⠿⣿⠄⠄⠄⠄⠄⠄⠄⠄⣹
⡿⣸⣿⠄⢺⡿⣾⣿⣿⣿⣿⡇⠄⣸⡇⣿⣿⣿⣧⠄⠄⠄⠄⠄⠄⠄⠄⢀⣿
⡇⣿⣿⣷⣭⣾⣿⣟⢖⣾⣿⣧⣄⣜⣷⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄⠄⢀⣼⣿
⣧⢿⣧⠄⠄⠄⠄⣶⣶⣮⠉⠉⠙⠛⠿⠿⣿⣿⣿⡇⠄⠄⠄⠄⠄⢀⣼⣿⣿
⣿⣧⠻⣷⠄⠄⠄⠛⠹⠛⠄⠄⠄⠄⠄⠄⣸⣿⡟⠄⠄⠄⠄⠄⢀⣾⣿⣿⣿
⣿⣿⣷⣬⡓⠤⡀⠄⠄⠄⠄⠄⠄⢀⣤⣶⠟⠋⠄⠄⠄⠄⠄⣤⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣥⢷⣲⡥⣤⣐⣐⣒⣒⢩⣭⣖⣅⡀⠄⠄⠄⢀⣾⣿⣿⣿⣿⣿⣿