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⣿⣿⣿⣿⣿⡇⠤⠄⠳⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣶⡄⠀⠀⠀⢀⣠⡤⠶⠚⢿⡦ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣋⢙⠉⣀⠀⢀⡴⢛⡥⠀⠀⠀⠀⢳ ⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⠿⣿⡿⡿⢿⣿⣿⣿⣿⠇⣻⡾⣫⡕⠋⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⣿⡙⠉⢸⡾⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠛⠛⠛⠛⠻⠿⠿⢻⠿⢿⣿⡶⢾⣶⣤⣤⣾⣈⣥⠀⢨⣽⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⡧⠘⠿⢤⠀⠀⠀⠀⢠⠀⠀⡄⡄⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⣆⡴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣶⣿⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⡟⠀⠀ ⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣌⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⡟⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣏⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣄⡀⠀⢀⣾⣷⠄⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠥⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⣿⣿⣿⣿⠙⡟⠛⢿⣿⣿⣿⣿⣯⡽⠿⠟⠛⠉ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠰⢤⡀⠀⠀⠙⠟⠉⠻⠿⠿⠿⠾⠃⢠⡿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠤⡀⠀⠀⠀⠀⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠟⢹⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠅⠀⠀⢠⣮⣭⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠌⠙⠂⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠛⣿⣿⠁⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣉⠀⠀⠀⠀⡀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠶⠶⠶⢶⣤⣤⣤⣤⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣠⣤⠤⠤⠤⣴⡶⠤⠤⠢⠤⠤⢤⡤⠴⠒⠒⠛⠉⠉⠉⠛⠒⠲⠦⢤⡀ ⠈⠳⡤⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⢴⡒⠉⠉⠁⠀⡩⢙⡥⠞⠋⠉ ⠀⠀⠙⣎⢗⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⡠⢊⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⢼⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢡⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠑⠢⡀⠈⠖⠀⠀⠀⠀⢀⡠⠔⠂⠉⠉⠒⣼⣿⣵⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡦⡤⣈⢱⠂⣆⡐⠒⠉⠁⠀⠀⠀⠀⠀⠀⢸⠸⡄⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡇⢣⢷⣾⣹⠀⡇⠁⢸⠙⣿⣉⣩⣿⠏⡹⠉⡝⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⡀⠉⡫⠓⡶⣻⢄⠀⠳⣌⣙⣛⡡⠜⣁⠜⠀⣠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣍⣀⣀⠕⡉⠀⠉⠒⠂⠤⠤⠒⢈⣡⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡓⢒⡒⠒⠒⠚⢛⣉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⡞⠀⢰⠀⡴⠁⣀⡝⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣙⣳⢫⢙⢦⣾⣲⣵⣶⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⡺⣛⠍⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠟⣁⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜ ⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬛⬛🏽⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🏽⬛⬛ ⬛⬛🏽🏽⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🏽🏽⬛⬛ ⬛⬛🏽🟧🏽⬛⬛⬜🏻🏻🏻🏻🏻🏻🏻⬜⬛⬛🏽🟧🏽⬛⬛ ⬛⬛🏽🟧🟧🏻🏻🏻🏻🏻🏻🏽🏻🏻🏻🏻🏻🏻🟧🟧🏽⬛⬛ ⬜⬛⬛🏻🏻🏻🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏽🏻🏻🏻⬛⬛⬛ ⬜⬛⬛🏻🏽⬛⬛⬛⬛⬛🏽⬜🏽⬛⬛⬛⬛⬛🏻🏻⬛⬛⬛ ⬜⬛🏻🏻⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛🏻🏻⬛⬜ ⬜⬜🏻🏽⬛⬛🟦⬛🟦⬛⬜⬜⬜⬛🟦⬛🟦⬛⬛🏽🏻⬜⬜ ⬜⬜🏻🏽⬛⬛🟦🟦🟦⬛⬜⬜⬜⬛🟦🟦🟦⬛⬛🏽🏻⬜⬜ ⬜⬜🏻🏽⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛🏽🏻⬜⬜ ⬜⬜🏻🏽🏽⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛🏽🏽🏻⬜⬜ ⬜⬜🏻🟧🏽🏽⬛⬛🏽⬜🟪🟪🟪⬜🏽⬛⬛🏽🏽🟧🏻⬜⬜ ⬜⬜🏻🏻🟧🏽🏽🏽⬜⬜⬜🟪⬜⬜⬜🏽🏽🏽🟧🏻🏻⬜⬜ ⬜⬜⬜🏻🏻🟧🏽⬜⬜⬜⬛⬛⬛⬜⬜⬜🏽🟧🏻🏻⬜⬜⬜ ⬜⬜⬜🏻🏻🏻🟧⬜⬜⬛⬜⬜⬜⬛⬜⬜🟧🏻🏻🏻⬜⬜⬜ ⬜⬜⬜⬜⬜🏻🏻🏻⬜⬜⬜⬜⬜⬜⬜🏻🏻🏻⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🏻🏻🏻🏻🏻🏻🏻⬜⬜⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡼⢿⣆⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣷⡟⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠻⠷⠶⠶⠶⢦⣾⡁⠙⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡍⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣀⣀⡀⣸⡇⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠉⠉⠉⠉⠙⠇⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠀⠀⢴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⢘⡿⠫⣩⣹⣷ ⠀⠀⠀⠘⣆⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⢠⣿⠈⠀⠀⠀⠀⣀⣀⣠⣤⡶⠷⠿⠛⠉⠁ ⠀⣀⣶⢟⠉⠳⢤⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣾⣿⣅⣴⣶⠾⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⣀⣴⡶⠶⠟⠛⠉⠉⠉⠛⣿⣿⠛⢛⣹⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣠⢿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠙⣆⠀ ⠀⠀⠀⠀⡦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⣧⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⢻⡄⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠙⣿⣧⣀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⡴⠋⢀⠔⡀⠀⠀⠀⠀⠀⢰⡏ ⠀⠀⠀⠀⠀⢹⣆⠀⠐⢆⠘⢌⣻⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣿⣦⣴⣧⡊⢀⠤⠂⠀⠀⠀⡞⡇ ⠀⠀⠀⠀⠀⠀⢻⠣⡄⠀⢷⣞⣿⣿⡿⠏⠋⠀⠀⠀⠀⠀⠀⢩⣿⣿⣷⣏⠳⣄⠀⠀⠀⡼⢰⠃ ⠀⠀⠀⠀⠀⠀⠘⡆⠘⠦⠋⠘⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⢹⠿⢿⣆⠀⠀⡞⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠂⢀⣀⣀⠀⠈⢳⠀⠀⠀⠀⠀⢀⡴⣶⣎⠙⣾⣉⣀⣀⡀⠀⠸⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡀⣾⡟⣶⡾⠀⠀⠀⠀⢀⢼⣆⠻⣿⣆⡿⠁⠀⠀⠑⡄⠀⠀⢸⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⣉⠽⠋⠹⢁⣀⣀⠀⠀⠋⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢷⡀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡗⠲⣼⡇⠀⠀⢰⠋⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣣⣀⣘⡇⠀⠀⠘⢷⡀⡿⠛⠁⠀⠀⢀⡀⠤⠤⢀⡀⠀⠀⡀⠀⠀⠀⢸⠀⠀ ⠀⠀⠤⠒⠊⣉⠡⠼⣖⣺⣷⠄⠀⢀⣀⣹⣥⣀⠀⠀⠈⠉⠩⣹⡒⠤⣌⡤⠚⠁⠀⠀⠀⢸⡀⠀ ⠀⣀⠤⠒⠉⡀⠔⠊⢻⠀⠈⠓⢤⡽⠦⣀⣀⡴⠏⠑⠢⠔⠚⠁⠙⠢⡀⠉⠒⢄⡀⠀⠀⠘⡇⠀ ⠈⠀⢀⠴⠊⠀⣀⡠⠊⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠂⠀⢀⣷⠀ ⠀⠘⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣂⣠⣴⠶⠟⠋⡅⢀⡇ ⢠⡤⠖⠚⠛⠛⠛⠛⠛⠓⠶⠤⢤⣀⣀⣀⣤⡤⠶⠞⢻⡛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠚⠛⠉⠉⠁⠀⠀⢀⣤⠞⠁⣼⠃ ⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠐⢒⣾⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣴⣾⠯⠀⢀⣼⠏⠀ ⠀⠀⠈⠓⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣳⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣹⡿⢃⣴⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠠⠿⢷⠇⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡴⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡆⡾⠀⠀⢀⣀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡼⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠃⢀⣼⣿⣿⣮⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣸⣿⠟⣿⣿⡄⠀⠀⠀⠀⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣹⣿⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⢿⣿⣿⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣿⣿⡿⢃⣀⠈⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠾⣇⠀⠀⠀⠉⠉⠉⠁⢀⣠⠴⠶⠻⣿⡛⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢻⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠺⣿⠀⠀⢰⡿⢿⡿⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠠⢻⣿⣀⡾⠁⠀⠀⠀⠀⠀⠀⠰⠦⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣀⣠⠴⢲⣄⠘⠙⠋⠁⠀⠀⠀⠀⠀⢀⠀⠢⣤⠀⣠⠾⠉⠙⠒⠶⢤⣀⠀⣰⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠙⢦⣤⠊⢳⣜⣧⡶⢶⣤⡀⠀⠀⢠⣌⡳⣄⣤⠟⠳⣤⡀⠀⠀⠀⣰⣄⡽⠓⠦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠖⠉⠀⠀⢀⠴⠋⢙⣶⣯⡈⠛⣷⡀⣿⣿⣷⣦⡤⠈⠉⠙⣆⠀⠀⠀⠈⠓⢦⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⡰⠋⠀⠙⠹⣦⣿⡟⠉⢹⠏⢠⠇⠀⠀⠀⠈⢧⡀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢹⡇⠰⠟⣴⠋⡴⠃⠀⠀⣀⡤⠿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⢾⣷⣾⣥⡤⠖⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡤⢦⠀⢈⣿⣌⣽⣷⣶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⣁⣴⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⣶⠚⣩⡾⠋⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⠾⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡚⡝⣇⣀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣴⣶⣾⣻⠿⢯⣍⡀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣽⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⣾⣿⡿⠛⢿⣿⣷⣦⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⢙⣳⣶⠶⣶⣤⣤⣄⣀⠀⠀⢻⡅⠀⢰⡇⠀⠀⢀⣤⡄⣀⣤⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣷⣤⣾⣿⡿⣿⣧⠀⠘⣧⠀⠀⠀⢀⣤⣾⣿⣿⣶⣦⣄⡈⠉⢻⣭⡉⠀⠀⢿⡀⢸⠃⠀⠀⢸⡏⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡟⡾⣿⣿⣿⣿⣿⣿⡿⠟⠀⢸⣿⠀⠀⣿⠀⢀⣴⣿⣿⣿⠟⠛⣿⣿⣿⣿⣦⡀⠙⣷⠀⠀⠘⣧⡟⠀⠀⠀⠘⣷⣜⣽⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⡇⠸⣿⣿⣇⠀⠀⠀⣀⣴⡿⠋⠀⣰⡏⢀⡾⠁⣿⣿⣿⣶⣴⣿⣿⠿⠁⠹⣿⡀⢸⣧⠀⠀⢹⠇⠀⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⢸⠃⠀⢷⠀⠈⠻⠿⠿⠿⠛⠋⠉⠀⠀⣰⡟⠁⣼⠇⠘⣿⣿⡿⠛⠿⠛⠁⠀⠀⣰⣿⠁⠀⣿⡄⠀⢸⡀⠀⠀⠀⠀⣀⣁⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⢦⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⢹⡇⠀⢻⣿⣿⣄⣀⣀⣀⣤⣾⡿⠃⠀⠀⢹⡇⠀⢸⡇⠀⠀⢠⠞⠋⣉⡽⠃⠀⠀⠀ ⠀⢀⣀⣠⠤⣼⣄⠙⠒⠛⠛⠶⣤⡤⢤⠤⠴⠚⠋⠀⠀⠀⠀⠈⣷⡀⠀⠙⠿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⣾⡇⠀⢸⡇⠀⢰⡇⠀⢰⠋⠀⠀⠀⠀⠀ ⠈⠉⢁⡠⠔⢻⣇⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢀⣀⣀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀⣸⠁⠀⠘⢧⠀⠈⢧⡀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⢿⡆⠀⠀⠀⠀⢠⠾⠃⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠙⢳⣦⣤⣀⣀⣤⣤⣤⡴⠞⠉⠀⣀⡤⢤⣿⣀⠀⠀⠈⠳⣄⠀⠱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢻⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠻⢧⣐⠊⠁⠀⣼⠇⠀⠀⠀⠀⠀⠙⣆⠀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠈⠓⠒⠒⠋⠳⢤⣀⠀⠀⢀⣼⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⣿⠿⣤⡀⠀⠀⠀⠀⠀⠘⢧⠀⠈⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢦⡀⠉⠳⠄⠀⠀⠀⠀⠈⡇⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠛⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠶⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠻⣯⣛⡿⠿⠿⣿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⣿⠀⠀⠀⠘⣷⠒⠒⠓⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡶⢦⡤⠖⣯⣀⣀⣀⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣸⡇⠀⠈⠉⠉⠁⠀⠈⠛⢷⣦⣤⣀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣤⣀⠀⣿⡄⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⣇⣀⣀⣴⠶⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠉⠁⠀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡾⢿⡟⠲⣄⡀⠀⠀⠀⣠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⠈⣷⠀⠈⠙⣦⣤⣞⣁⣠⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⠀⢀⡏⠀⠀⠀⠈⠀⠛⠛⠛⠛⠛⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⠠⣲⣿⣄⠀⠀⠀⠀⠀⠀⢠⠞⠻⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⣠⡼⠡⡦⢈⡧⠀⠀⠀⠀⠀⠹⣤⣀⣤⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠈⠙⠲⠶⠚⠁⠀⠀⠘⣻⡤⠶⠶⠷⢦⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢭⣿⠁⣴⠞⠛⣷⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢰⡏⠁⠀⢠⡏⡏⠀⠀⢠⡆⠀⠀⣤⡤⣤⠀⣶⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡇⠀⠀⢸⠀⡇⠀⠀⢸⡇⠀⠸⣏⠀⣸⡇⣿⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇⡞⠀⠀⠀⢸⠀⡇⠀⠀⠘⠿⠾⠆⠙⠿⠛⠀⠻⠶⠇ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣿⠀⣇⠀⠀⢀⡾⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣍⣛⣛⣭⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀ ⢸⣿⣿⡿⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⡿⠛⠛⠛⠻⢿⣿⡇ ⢸⣿⣿⣷⣤⣤⣄⠉⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⡟ ⠸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠙⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃ ⠀⠹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣴⡏⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣿⣿⣿⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⣿⣿⣷⣦⡀⠀⠀⠀⣠⣿⠇⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠃⠀⢰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⣾⣧⡀⠀⠀⠀⠀⠀⢠⣀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢠⣤⣿⣿⣿⣷⣄⠀⣤⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⠛⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡆⠀⠀⢸⡿⠀⠀⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠟⠛⣿⡛⠉⠉⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣄⡀⠀⠀⠀⣀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⢿⠇⠀⠀⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣤⣀⣀⣀⣠⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⠛⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠿⣤⣄⠀⠀⠀⠀⣀⣴⠏⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣤⣠⠞⠁⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠋⠉⠉⠙⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⠀⠀⠀⠉⠛⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⣿⣿⣿⣦⠀⠀⢸⣿⠀⠀⠀⠀⣠⣶⣿⠋⠉⠙⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢿⣿⣿⣷⣄⢸⣿⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣿⣿⣿⣾⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⣸⣿⣿⠏⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⠿⠶⠀⠀⠀⠀⠀⠙⠿⠿⠀⠀⠀⠀⠈⠛⠿⠧⡤⠴⠿⠟⠁⠀⠀⠀⠹⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⠳⣄⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⡠⡞⠀⠀ ⠀⠀⠀⠑⢕⢄⠀⠀⠁⠢⠤⠒⠒⠒⠒⠒⠒⠒⠒⠠⠔⠊⠀⠀⡠⠪⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡧⠐⡾⠉⠀⠀⠀⡰⡴⢄⢦⠀⠀⠀⠀⠀⠀⢴⠕⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠉⣏⠀⢤⣀⡀⠀⠀⠀⡀⢀⠀⠀⠀⢀⣀⣠⠀⢹⠏⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⢄⠈⠢⠙⠩⠆⢀⠇⠈⡄⠰⠬⠙⠔⠁⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠈⠒⠤⣀⣀⠔⢪⣤⢤⣈⠢⢄⢀⠠⠐⠁⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠀⢀⡠⠄⠒⣺⡻⠆⣀⠬⠯⣁⠀⠝⣓⠒⠠⠄⡀⠀⠱⡀⠀⠀⠀ ⠀⠀⡠⠃⠀⠐⠁⢀⠔⠉⠈⠢⠬⢀⣉⣈⣁⠵⠔⠁⠈⠢⡀⠈⠑⠀⠈⢆⠀⠀ ⠀⡰⠁⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⢢⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢰⣷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢶⣆ ⢺⣿⣶⡎⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠠⡟ ⠈⣿⣿⣷⣄⠄⠈⢻⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣼⠁ ⠀⢸⣿⣿⣿⣠⣤⣤⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣄⠀⠀⣰⠇⠀ ⠀⠀⢻⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣃⢰⠏⠀⠀ ⠀⠀⣼⣿⠇⠀⢠⡀⠀⠀⠀⣀⣴⡇⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀ ⠀⠀⠉⠀⣀⣠⣾⣿⣷⣴⣿⣿⣿⡿⠀⠀⢿⣿⣿⣷⣶⣤⡀⠀⠀⠈⠃⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣏⠉⢹⠛⢿⣿⣿⠁⠀⠀⢸⣿⡿⢿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣿⣿⠇⠀⠀⠀⠸⣿⣄⣘⣀⣸⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⡿⠿⣿⠟⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠓⠦⣀⠔⠊⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠾⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⢤⣤⣄⠀⠠⢤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣧⡀⠀⡇⠀⢀⣤⠴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⣿⣦⡇⠀⣿⣿⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠧⠀⠀⠘⢿⡇⠀⠙⢿⣀⣸⠟⠁⠰⣿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠛⠉⠉⠉⠉⠙⠛⠛⠻⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⠶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡷⢶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠶⠛⠉⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠈⠉⠻⢶⣤⡀⠀⠀ ⢰⣾⣯⣅⣀⡀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣀⣀⣬⣽⣷⡄ ⠈⠻⢦⣀⠀⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠁⠀⣠⡴⠋⠀ ⠀⠀⠀⠙⢷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠃⢀⣤⠶⠒⠲⠦⢤⣄⣀⡀⠀⠀⠀⠀⠉⠻⠋⠉⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⠒⠦⣄⠀⢸⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⡟⠀⠀⠀⣤⣤⣤⣤⣬⣭⣍⣉⡛⢻⠀⠀⠀⠀⢸⠟⢛⣹⣿⣭⣥⣤⣤⣤⣄⠀⠀⠈⢳⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⣧⠀⠀⠀⣿⣅⣀⢀⣀⣽⣿⡿⠃⢸⠀⠀⠀⠀⢸⠀⠹⣿⣿⣇⠀⠀⠀⣹⣷⠀⠀⠀⡼⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⠹⣆⠀⠀⢻⣏⣈⣿⣿⡿⠛⠁⠀⢸⠀⢠⣄⡀⠸⡄⠀⠈⠻⢍⣹⣿⣿⣿⠏⠀⠀⣼⢃⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⡟⢧⡀⠀⠈⠉⠉⠁⠀⠀⠀⠀⡾⠈⢻⠷⡌⠀⣧⠀⠀⠀⠀⠈⠉⠉⠁⠀⣠⠞⣡⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣝⠳⠦⣄⣀⣀⡀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠘⠧⣄⣀⢀⣀⣀⣤⠴⢚⣡⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣿⠷⠶⢶⣶⣶⣶⣶⣶⡶⠶⠿⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣿⣀⣄⣀⣠⠀⠀⠀⡀⠀⠀⠀⣆⣀⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⢸⣏⠀⠈⢻⣆⠀⠀⣷⠀⠀⣸⠟⠁⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢠⡾⠻⢷⣄⡀⣿⣄⣠⣿⣄⣰⣟⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢀⣴⡟⠁⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡿⠙⢷⣄⣀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠶⠶⠾⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠒⠘⠅⠠⠔⠡⠤⠤⠀⢀⡀⠀⠀⢉⢡⢵⠊⠀⠀⢡⠀ ⠀⠀⠑⠠⠤⡜⠀⡠⡠⠐⠈⢉⢀⠎⠀⠀⠀⠀⠀⡀⠁⠊⡔⠁⠀⠁⡰⠀⠀⠀ ⠀⠀⠀⠀⢠⣇⠔⡕⠁⡠⡐⣡⠋⠀⠀⠀⠀⠀⠊⡰⠀⠀⢈⠢⡀⠈⢃⠀⠀⠁ ⠀⠀⠀⢀⠜⢁⢎⠀⢠⠁⡐⢱⠀⠀⠀⠀⠀⢀⠔⠁⡅⠀⠀⡆⠈⠔⢟⠀⠀⠀ ⠀⠀⣠⢃⠖⡍⡌⡠⢹⢰⣁⠼⠀⠀⠀⠀⢐⠟⠠⢰⣧⠀⠆⢹⠀⠀⠘⡆⠀⠀ ⠀⣼⢪⡏⢠⡰⢠⠓⠈⠣⠀⠀⢧⠀⠀⣸⠆⠀⠄⠈⣏⡆⢰⢸⡇⠀⠀⠁⠀⠀ ⠀⠃⢘⠅⠘⢧⠦⣠⠤⠤⠤⢦⠀⠑⠠⢽⠀⣒⣆⣤⡘⡘⣸⠀⠇⠀⠀⠀⠀⣴ ⠀⠀⡈⠀⢠⡈⠛⠹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠴⢔⢻⡿⣏⡀⠀⠂⠀⠀⠀⣿ ⠀⠀⠁⠀⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢡⠁⠌⠀⢠⠀⠀⣿ ⠀⢠⠀⢸⡟⡇⠀⠀⠀⠀⢀⠤⣒⣂⠄⡀⠀⠀⠀⠀⠀⢀⠇⠌⠀⠀⠈⠀⠀⣿ ⠀⣿⣀⣼⢳⠇⠀⠀⠀⠀⢸⣤⣿⣿⣿⣾⠆⠀⠀⠀⡠⢢⢊⠀⠀⠀⣀⠇⡀⠟ ⠸⢸⡏⣻⢾⠈⣄⢠⠒⢐⠘⡟⠉⠉⢉⠏⠀⠀⢀⢔⠁⠁⢁⠅⣐⠙⠁⢰⠁⠀ ⠀⠀⢧⢸⢸⡦⠛⠢⡁⠈⠀⠈⠛⣏⠉⠀⢀⢔⣵⣃⢠⡄⠊⡸⡱⠀⢨⣇⠀⣀ ⠀⠀⠚⣧⡿⢅⡀⣀⣸⣦⢀⠀⠀⠸⣠⢪⣑⢡⡞⠀⣟⠁⣰⣗⢀⡶⣻⣩⣆⠀ ⠁⠀⠀⠈⠉⠁⠈⠛⣿⣿⣧⣩⣀⣤⣭⣀⣠⡜⠀⠀⢉⣾⡿⢣⠾⠓⠉⠁⠀⠀
⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤⠂ ⠨⡻⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣫⣻⠎⠀⠀ ⠀⠐⡇⠘⡓⢿⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⡿⢃⠏⠀⠀⠀ ⠀⠠⣧⠂⠀⢧⢧⠀⠙⣷⣶⣶⣶⠿⠿⠟⠻⣿⢿⢿⣿⣿⣿⠁⢸⠀⠀⠀⠀ ⠀⠀⠹⣯⠁⠈⢻⡧⣘⣿⣿⣿⠏⠀⠀⠀⠀⠇⠈⠀⠈⠉⠻⣷⣼⢃⠀⠀⠀ ⠀⠀⠰⣿⡗⣤⣾⣟⣉⠉⠉⠉⠠⢠⡀⠀⠀⠀⡔⠀⢀⣴⢾⠛⢿⣿⠀⠀⠀ ⠀⠀⠀⣇⣾⡿⠀⠻⣾⡷⡄⠀⠀⠀⠘⠄⠀⠸⠄⠀⠸⣿⠃⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⡟⠹⠁⢄⡀⡈⠉⠻⠂⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡠⣺⡇⠀⠀⠀ ⠀⠀⠜⡇⠀⠀⠀⠈⠻⣦⣄⠀⠀⠄⣀⠀⣀⠀⢘⡀⠤⠤⡬⠞⣹⡀⠀⠀⠀ ⠀⠀⠈⡇⠀⠠⠄⠂⠈⠀⣀⠕⣎⠍⠀⠁⠘⠛⡛⠤⡴⢲⠤⣁⢿⠄⠀⠀⠀ ⠀⠀⢘⡇⠀⠀⠀⠀⠐⠁⠀⡠⠘⡢⢤⡐⠒⠭⡭⠓⣨⠗⠨⡒⣽⠠⡈⠂⠀ ⠀⠀⢹⡅⡀⠀⠔⠀⠀⠠⠊⢀⠔⠀⠀⠉⠒⠒⠒⠈⠁⠀⠀⠈⢣⡑⡀⠀⠀ ⠀⢀⡟⢀⢔⡑⠀⢀⠀⢀⣀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣐⣷⡘⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢁⠠⢘⣖⠤⠤⣀⡀⠀⠀⣀⡤⠊⢁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣨⠔⠊⠁⡀⠀⢀⠀⠀⠉⠳⣏⢀⡀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣞⣥⣖⡶⢏⠀⠀⠘⠤⣀⠀⠀⠈⢫⡕⠸⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣧⣾⠿⡆⢣⠀⣠⣶⣿⣭⡙⢧⠀⢃⡀⠀⢸⣾⠏⠀ ⠀⢀⠇⡙⢿⣭⡥⠜⢁⡎⡜⣿⣷⡾⠟⢹⡆⢇⠘⠃⠀⠘⠋⠀⠀ ⢈⣹⡢⠱⢄⣀⣀⠠⠊⠀⣇⠹⣷⣤⡴⠚⠀⢸⠀⡆⠰⢋⠝⠀⠀ ⠐⠈⣇⠀⠀⡱⠀⠠⡤⠀⠈⠢⣀⣀⣀⣠⠔⢁⣰⡀⠐⠌⢂⠀⠀ ⠀⠀⠘⢆⠀⠂⠤⠠⢀⡀⡰⠀⠁⠀⠀⠈⠚⢤⠎⡀⠀⠈⢆⠡⠀ ⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠑⠈⠀⠀⠜⢀⠇ ⠀⠀⠀⠀⠀⠀⢀⠜⠓⣖⠶⢖⣒⣊⣉⣀⣳⠀⠀⠀⡔⠁⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢢⡄⠪⠤⠼⣄⡀⠀⠀⠈⡇⠀⠀⢠⠀⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠉⠑⠲⠤⢳⠀⣀⠜⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡀⠄⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⣄⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⣿⣯⣲⡀⠀⠀⠀⣀⣀⣀⡀⠀⢀⡔⢡⣾⣿⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⠏⠓⠉⠁⠀⠀⠀⠈⠉⠉⠰⠿⣿⣿⣿⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⡌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⡟⢷⣾⠀⣧⣶⡶⢛⠛⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣋⠷⡷⣾⠫⡄⠸⣿⣷⣼⣶⠟⠁⡠⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⣺⣛⣷⠎⢉⠶⢅⠀⠙⠦⡤⠀⠒⠉⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀ ⠀⠀⢒⣿⣶⠧⢄⠁⠀⠀⠑⢰⣴⣷⣭⢍⡐⠢⢄⠀⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠐⢻⠀⠀⠈⠣⠄⠀⠴⠃⠙⡎⠻⡢⠈⢦⠀⠑⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⡄⠀⠓⠀⠀⠀⠀⢇⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄ ⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠤⢤⣼⠏⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡴⠛⠛⠲⣤⡴⠒⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢼⠀⠀⠓⠀⣽⡘⠀⢀⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠁⠀⠈⠳⠤⠤⢞⣻⡋⠉⢉⣠⡤⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠸⣥⣴⢷⡄⠈⠹⢦⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⡷⠄⠀⠀⠙⢿⣘⣆⠀⠀⢹⡎⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠈⠁⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠶⠛⠛⠳⣄⠀⠀⠀⠀⢲⠀⠀⠀⠀⣠⣟⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢀⡿⠀⢠⠀⠀⠸⡇⠀⣠⡾⣻⠇⠀⠀⠀⣀⣀⣤⠤⠤⠤⠴⠦⠤⢤⣄⡀⠀ ⢰⡟⠁⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⣠⡾⠧⢤⡘⡇⠀⠀⠹⣟⠁⣿⣿⡆⠀⠀⣼⡛⠛⠓⠒⠒⠒⠒⠒⠒⠋⢽⣧⠀ ⠈⠳⠦⢤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣶⡶⢿⣦⣤⣤⣆⢰⣾⣿⣿⣿⠀⠀⡀⢺⣟⡿⠿⠟⢀⣼⣯⣅⣀⡀⠀⢀⣀⣀⣀⣀⡤⠾⠟⠂ ⠀⠀⠀⠀⠀⠀⠘⠋⠋⠙⠉⠈⠁⠁⠉⠀⠈⠉⠙⠃⠈⠉⠉⠁⠉⠙⠳⠚⠛⠚⠉⠀⠀⠀⠈⠙⠑⠋⠙⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⣀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠊⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡍⠒⠦⣄⠀ ⠸⣗⠒⠢⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠒⢒⡿ ⠀⠀⠙⢾⠁⢀⣀⡀⠀⠀⠀⠀⠠⢀⠠⠄⠀⠀⠀⠀⢀⣀⡀⠀⢹⡖⠁⠀ ⠀⠀⠀⢾⠐⠁⠠⣤⠭⠭⣶⣒⢲⠀⠀⢰⢒⣲⡦⠭⢥⡄⠀⠑⢸⡇⠀⠀ ⠀⠀⠀⢸⡼⡀⠀⣗⣲⣶⠽⠃⢸⢀⡀⢸⠈⠻⣗⣦⣴⡗⠀⡸⣼⠀⠀⠀ ⠀⠀⠀⠀⠹⣝⠦⣀⠉⠀⠀⢀⠆⠘⠓⠈⢆⠀⠀⠈⢁⡠⢞⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⢭⣍⣉⣁⠀⠀⠀⠀⢀⣉⣉⣭⠵⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠉⠉⠉⠉⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢀⢀⠀⠀⠀⠀⢀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠚⠉⠀⣸⣅⠙⣇⠀⡇⢀⡟⢁⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣋⣴⠂⠀⠀⣇⠈⠉⠈⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠈⠓⠢⠤⠬⠽⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⣤⡾⠿⠿⠿⠛⠛⠻⠿⠶⠶⣿⣥⣄⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣆⠀⠀⠀⠀⠀⠀⢰⣶⣶⡀⠀⠀⠀⠀⠙⣷⣄⠀⠀ ⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⡀⠀⠀⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣼⠇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⠀⠀⣨⣿⣷⣄⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠁⠀⢹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢙⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⢉⣿⡿⠶⣶⣤⣤⣄⣀⣀⣠⣤⣤⣴⡶⠾⣿⣏⠁⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣸⣇⢠⣿⣿⣷⣤⣿⣀⣀⣀⣀⣉⣉⣀⣀⣸⣧⣼⣟⣻⣧⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⢁⣠⣤⣤⣤⣀⣈⠉⠉⠛⠲⢦⠀⠀⠀⠀⠀⠀ ⠀⡰⢇⠀⠀⠸⠀⡏⢠⠾⡄⠀⠀⠉⠉⠛⠲⡄⠀⢧⠀⠀⠀⣀⡀ ⠀⡇⣸⣠⣤⣤⣤⣤⣇⠀⢱⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀⡞⠁⢹ ⢠⠃⠉⠀⠀⠀⠀⠈⠉⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⢸⠴⠞⠀⢀⡎ ⡎⢤⠀⣀⢀⠀⠀⠀⣀⠀⠈⠆⠀⠀⠀⠀⠀⡼⠀⡼⣤⣤⠶⠋⠀ ⢇⡀⠀⠛⠛⠀⠀⠀⠈⢀⣼⣳⠦⠤⠤⠤⢞⡁⣰⠁⠀⠀⠀⠀⠀ ⠀⠙⠒⠶⣶⠴⣶⣶⣚⣉⡞⢉⣇⣀⣀⣸⡍⠙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣥⠶⠛⠉⢩⣋⡴⠋⠉⠙⣏⢹⠙⢦⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠛⠀⠀⠙⠃⠀⠀⠀⠀⠀
⠀⠀⠀⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠀⠀⠀⢸⡈⠓⢄⠀⠀⣠⠄⠒⠊⠉⠉⠉⠉⠉⠒⠢⠤⣀⠀⠀⣠⠔⠊⡽⠁⠀ ⠀⠀⠀⠀⢇⠀⠀⣩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⡀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠸⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠃⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⠺⠽⠷⠂⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠀⡔⠭⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⠈⢄⠀ ⠀⡘⠐⠒⠒⠒⠀⠀⠨⠂⢰⣶⡶⠀⠀⠀⠐⢉⡉⠤⠤⠤⠤⠀⠀⠀⠤⠀⠈⡆ ⠀⡇⠐⠈⡉⠄⠤⠤⠁⠀⠀⠀⠀⠀⠀⠈⠡⠀⣂⣒⠒⠂⠀⠐⠒⠠⠄⠀⠀⡇ ⠀⢳⠀⠈⠠⠂⠉⢀⣀⣤⠶⠶⠾⠶⠿⢶⣦⣅⠀⠀⠀⠉⠉⠀⠂⠄⠀⠀⠀⠇ ⠀⠈⣦⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠲⡀⠀ ⠀⠀⢀⡤⠒⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠘⢄ ⠔⠊⠁⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
ฅ(•̯́•̀)ა
⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⣦⣤⣀⡀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣤⣴⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠐⠫⠻⢿⣟⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡹⡍⠀⣀⣴⣶⣿⣿⣿⣿⣶⣦⣀⠀⢫⢏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡍⣠⣾⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣷⣄⢫⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣰⣿⣧⣙⣫⣿⠟⠀⠀⠻⣿⣌⣋⣽⣿⡆⢸⠀⠀⠀ ⠀⠀⠀⠈⠉⠁⡗⢛⣿⣿⣿⠏⢁⢔⡟⣫⢄⠈⠹⣿⣿⣿⣛⢺⠃⠉⠁ ⠀⠀⠀⠀⠉⠁⠙⣄⡡⡝⠻⣷⡇⠀⠀⠁⢞⣦⡾⠟⢫⢌⣠⠋⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⡱⠁⠈⠒⢄⢀⠎⠡⣔⡊⠤⠊⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠄⡀⠀⢠⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣋⡁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡿⠋⠁⠀⠉⢳⡄⠀⠈⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡼⠁⠀⣰⣦⠀⠀⣧⣤⠴⠲⠤⣄⠉⠉⠛⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢷⡀⠀⠈⠁⠀⣰⡟⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠈⠳⣄⡀⠀⠀⣿⠐⢺⣿⡶⠀⠀⠀⢹⡀⢦⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⣴⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⠇⣸⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⠟⣛⣿⡿⠷⠾⠛⠛⠛⠛⠛⠛⠛⠓⠶⢤⣄⡀⠀⠀⠀⢀⣤⠾⣧⡀⠙⠳⣤⣀⣀⣠⡴⠋⠰⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣶⡟⣧⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠈⠷⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣻⡟⣧⣘⡤⠖⠛⠉⠉⠉⠉⠉⠉⠙⠒⠶⣤⣀⠀⢸⡏⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⡇⠈⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣔⠇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣇⠀⠀⠀⠉⠻⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣼⠟⢻⡏⠈⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⣭⡽⢯⣿⠀⠀⢻⣾⠇⠀⠀⠀⠀⠀⣀⣼⠗⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢶⣤⣤⣄⣀⣀⣤⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡏⠻⠿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠿⢦⣄⡀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠙⢿⠆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⠀⠀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⠇⠀⠀⠀⠀⠙⣶⣤⡀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠾⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠉⢻⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣠⣶⡿⣯⣍⡙⠶⣦⣀⣀⣀⣿⡋⣠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣾⠃⢹⣧⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣄⡙⠶⣝⡻⢶⣤⣈⣭⣭⣿⣿⡇⢠⠆⠀⠀⠀⠀⠀⠀⣀⣠⣶⠟⠁⢀⣾⠇⠀⠀⠀⠀⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠈⠛⠃⠉⣿⠁⠀⠀⠉⠛⢿⣶⣤⣤⣤⣴⣾⣛⣋⣁⣠⣤⡾⠟⠁⠀⠀⠀⠀⢀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣽⡿⠿⠿⡿⠿⢿⡿⢛⣥⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⣿⠛⠟⠃⠀⢀⠀⠀⠀⠀⢱⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣟⠁⣠⣶⣷⣿⣿⣿⣿⣶⣌⡙⠻⢷⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣦⢻⡜⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠏⠘⣿⣿⣿⠹⠿⣿⣟⠀⢸⣿⣿⡿⣿⣿⣷⣷⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠘⣿⣷⣶⣿⣿⣿⡟⢻⣿⣿⡅⠘⣿⣿⣿ ⣿⣿⣏⠀⠀⠀⠘⠿⣿⡿⠋⠁⠓⣦⠂⠙⢿⣿⣿⣿⡿⠀⢸⣿⠿⠁⠀⠉⠛⢿ ⣿⣿⣋⠀⠀⠀⠀⠀⠘⣧⣄⡐⠉⠀⠀⠀⣠⣿⠟⠁⠀⠀⢿⣿⠀⠀⠀⠀⠀⣼ ⣿⣿⡅⠀⠀⠀⠀⠀⠀⠈⠉⠐⠶⠶⠒⠛⠋⠁⠀⠀⠀⠀⣨⣿⣧⠀⠀⠀⢸⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿
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