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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡵⢁⡾⠛⠁⣨⣿⡷⠊⣁⠀⣀⣴⠟⠉⠀⣀⠤⠔⠲⠶⠛⠃⠀⠀⠋⠥⠒⠟⠋⣠⠞⢉⡠⠀⣀⠀⢀⣤⠶⠛⠉⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⢀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠁⢀⠔⠁⡰⠢⠊⠴⠟⠚⣩⡷⠛⠁⠠⠖⠊⠉⣀⠤⠀⢀⣤⣶⣾⣿⠟⠋⢀⣠⠴⠊⠀⠀⣡⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣠⣴⠶⠟⠋⠁⠀⠀⠀⣀⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠃⢈⠋⡀⠏⠀⣀⢈⡴⢋⠴⢋⢴⠿⣿⡿⣾⠋⠞⠉⠁⠚⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⠀⠀⣀⠤⢀⣠⠔⠊⣉⣤⠔⠀⠀⣀⠤⠄⠀⠀⠀⠐⠒⠚⠓⢒⣲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⠂⠔⠁⣠⠐⡽⠈⠀⢀⡔⠁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢠⢞⡁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠁⠀⠀⣀⣾⣿⣿⠟⠁⢀⠾⠫⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣿⣽⣿⣟⣋⡉⠉⠛⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢀⢀⣧⡇⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⡜⢿⣿⣿⣦⠀⠀⡆⢰⣱⣫⣮⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⣫⠿⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣉⣩⣽⣿⠿⠿⠟⠛⠛⠉⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠤⢾⣾⣿⣷⣾⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣿⣿⣿⠀⢀⠇⣼⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⣂⠭⠒⡩⠔⢊⡀⠀⠀⠀⢀⣤⡶⣞⣥⣶⠿⠟⠛⠛⣒⣚⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⣴⣶⣶⡽⣿⡿⣿⣾⣷⡅⠀⠀⢀⡄⠀⠀⠀⢠⠀⠹⣿⣷⣤⣤⣼⣿⣿⠟⢀⡜⣰⠿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠔⢊⣡⠔⠋⣠⣶⣿⣾⣟⣥⣾⣿⣿⣿⡿⠿⠟⠛⢛⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠾⣿⣿⣿⣶⣶⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣂⠛⢙⣾⣿⣽⣿⠗⣲⣋⠄⠁⠡⠠⣀⠑⠠⢈⠛⠿⠿⠿⠛⢁⡠⠞⣈⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⠖⠋⢁⣴⡿⣿⣿⣿⣿⠿⠟⠻⠛⣉⣡⣴⣶⠾⠛⠁⠐⠒⠲⢿⣿⣿⡿⠿⠿⠛⠛⠷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⡯⣅⠨⣾⣿⣿⣿⣯⣭⣟⣔⠄⠀⠈⡩⡙⠓⠢⠬⠉⠀⠈⠉⠁⠀⣬⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠠⠖⠛⢉⡨⣵⣾⠿⣂⣠⣴⣶⣿⣿⣿⣥⡤⠤⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠠⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡹⣿⣿⣟⠁⠀⠈⠙⠢⣽⣷⣿⡿⢿⣷⣾⣽⣿⣫⣴⣎⣴⣭⣀⣀⡀⠀⢀⣀⡠⠶⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⣠⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⣛⠛⠶⠦⢤⣄⡀⠀⠙⠷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢀⣿⢿⣿⡄⠀⠀⠀⢄⣲⣟⡵⠪⠏⠞⠟⠉⠋⠛⠻⠿⠿⣿⣿⣿⡿⠾⠶⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠁⠀⠀⢄⣺⠿⠛⣉⡩⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⣛⣀⣤⣴⣶⣾⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠁⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠈⢿⣿⣟⠿⣦⣤⣽⣿⣿⡥⠂⠀⠀⠀⣠⣴⣶⠿⠟⣛⣫⠭⠵⠒⠒⠒⣋⣉⣩⣥⣤⣄⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⣀⡤⠤⢶⣾⣿⡿⠿⠿⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠤⣾⣿⣿⣿⢿⣿⣟⡻⠿⣭⣭⣉⣙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⡿⠁⠀⠀⠈⠻⠊⡻⠶⣬⣭⣭⣵⣶⠶⠶⣚⣛⣭⠴⠖⠛⠉⢁⣀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣂⣉⣉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⣀⠤⠶⣿⣿⣷⣶⣶⣦⣤⣄⣀⠉⠛⠛⠛⠻⠿⠷⠦⠌⠉⠑⢂⠈⢙⡛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣷⣾⠿⠋⠟⠉⠀⣀⣤⠶⠟⠉⠽⠶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠿⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢀⣤⣶⢶⣽⣦⡉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣶⠟⠋⠉⠀⢀⣠⣤⣤⣉⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣶⠶⢶⠶⢭⣿⣿⣟⠿⢿⣷⣬⡉⢭⣭⣥⣀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣦⡀⠉⠛⢿⣧⡀⠀⠀⠀⠀⠀⢄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠈⠛⠍⠫⢛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⡉⠉⠉⠁⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣈⡙⠛⠿⠦⣄⠀⠈⠀⣽⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠻⣍⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⢤⣻⣿⣮⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠿⢟⠅⡀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⣠⣌⣿⣿⣷⣤⣀⡠⢤⣀⣩⣶⣯⣉⠛⠛⠷⠄⠀⠀⠀⠈⠢⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡈⢷⣹⡻⣿⣿⣿⢿⣿⣿⡿⣯⣛⠙⢿⣿⣿⡷⣤⠑⡠⡀⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⢿⣿⣷⣌⠙⢿⣿⣿⣷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠟⢿⣌⢾⣿⣿⣿⣷⣄⢌⣿⣮⣿⣷⣝⣆⠁⠘⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡙⠿⣧⡈⠓⠙⢷⣄⠙⣿⣯⠛⢧⡀⢌⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠹⠊⠟⣿⢿⣻⡿⣿⣿⣿⣿⣿⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣄⠁⠀⠀⠀⠙⢧⠈⠻⣇⠀⠁⠀⠑⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣴⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣷⣸⠀⠀⠀⠀⠀⠀⠸⠈⢷⠁⡿⡟⡏⢇⢻⡇⠏⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⢲⣄⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢹⣷⣠⡀⢾⣿⠀⠀⠀⠠⠀⢀⠀⣀⣈⣤⣥⢁⣷⡜⡄⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⣆⢢⣧⠀⠡⡀⠀⠸⣿⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣝⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⣭⣻⡿⣿⢙⣛⠿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⠻⠀⣼⠀⣡⣾⣿⣿⣿⣿⢟⡅⠈⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⣾⡞⣿⡇⡄⠘⡄⠀⢹⢿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⢿⣷⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣶⣄⢻⣿⣮⡙⠟⣿⣏⣿⣿⣿⣷⣻⣧⢸⣏⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⡀⠸⡄⢦⣷⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠙⢧⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣣⣶⣶⣬⣍⡻⣿⣿⢙⣿⣿⣿⣆⠈⢿⢹⣿⣿⣿⢁⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⠀⢰⠀⢀⠀⢰⢰⢸⣿⣿⢿⢹⣿⣿⣿⡇⡆⣿⣼⣿⣿⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢿⣧⠀⠀⠀⢠⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣢⣶⣶⣶⣄⢣⣿⣿⣿⣿⡿⣛⣎⠉⣼⣿⣿⣶⣝⢧⠘⣿⣿⣿⣫⣌⠻⡿⢸⣿⣿⣿⣿⣿⠿⣋⠀⠀⠀⠀⠀⣴⠀⣰⡾⠀⣸⡆⠀⣸⣿⣿⣿⠈⢢⣿⣿⠹⡇⡇⣿⣿⣿⣿⢿⣿⣹⠇⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⡙⠨⡕⢪⠢⠀⣿⣿⣿⣿⣾⣄⠀⢻⣿⣿⣿⣿⣷⠁⠸⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⠇⠀⡟⢡⣷⣿⣿⢠⣿⣿⣧⢹⡄⣾⣿⣿⡇⠃⠁⣿⣇⢻⣯⢣⢿⡏⠀⠀⠀⠀⢷⣄⢳⣄⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⣿⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣿⠿⠀⡯⠿⢅⣶⣾⣤⡀⣿⣿⣿⣿⣿⣿⣷⡌⠿⡟⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠎⠁⠀⠀⠀⢸⣿⣿⡟⣾⣿⣿⣿⠈⣷⣿⣿⣿⡇⠀⠀⣿⣿⠈⣿⠈⠘⣿⠀⠀⠀⢸⡜⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣶⣴⣶⣶⣶⣦⣤⣀⡈⠻⣟⢉⣛⡛⠧⠈⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠇⣿⣿⢸⡇⣸⣿⠿⣛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡟⣼⢿⣿⣿⣿⠀⢿⣿⣿⣿⠀⠀⠀⣿⡿⠀⢿⠀⠀⢹⠀⠀⠀⠈⣿⡜⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣻⢿⣿⣿⣿⣿⣿⠛⢽⡷⡌⢸⣿⡿⠗⠆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠸⠀⠀⣿⠇⣩⣶⣶⣭⣾⣿⣆⠹⠋⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡼⣹⠏⣾⣿⣿⣿⡀⢸⣿⡿⠁⠀⠀⠀⢸⠇⠀⠈⠀⣄⠈⠀⠀⠀⠀⢹⣷⢹⣿⣿⣿⡇⣄⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣧⠻⣿⡄⢈⣵⣯⣷⡢⡀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⣿⣿⠂⣾⢦⠀⠙⢸⣿⠿⣿⣿⣿⣿⣿⠀⠀⢀⣀⠀⠀⢠⢃⣾⡤⠀⠀⢃⡟⠀⣿⣿⣿⣿⠁⢸⡿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⣿⠀⢿⣿⣿⡷⢿⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢙⡻⠿⠿⣿⣿⣿⣿⣧⢻⣿⡈⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣝⣗⠁⠀⣿⡿⠀⠛⠈⢀⣠⣌⣿⣿⣿⣿⣿⣿⣿⢀⣶⠏⠀⠀⠀⡠⢿⣿⡴⠁⠀⣼⠁⠀⣿⣿⣿⣿⠀⠈⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⠀⠈⣿⣿⡇⢸⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⡩⡝⢿⣿⣷⣝⠣⠹⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⡌⠀⠀⠘⢁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⠀⠀⠀⢀⠜⢠⣿⡿⣡⢣⣷⡟⠀⠀⣿⢟⣿⡿⠀⠀⠀⣴⠃⠀⠀⣷⠀⠀⠀⠀⠀⢸⣿⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⡇⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⣝⢷⣬⣛⡻⢷⣦⣙⠿⠿⠟⠿⡷⠌⠊⠛⠻⠌⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠏⠀⠀⠀⠀⢠⠏⠀⡾⠙⠁⢡⣿⣿⢃⡄⠀⠏⣼⣿⠇⢀⡆⣸⠏⠀⠀⣰⣿⠀⠀⠀⠀⠀⠘⡇⠀⢰⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡹⢿⡟⣣⣤⣤⣝⣻⣿⣿⠿⣿⣿⣶⣤⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠞⢁⡄⠀⠀⠀⠀⠎⠀⢸⠁⠀⣰⣿⡿⣿⣾⡇⠀⣸⣿⡟⢀⣾⢷⠏⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣝⡞⠻⣿⣿⣿⣿⣿⣿⣶⣭⣉⣛⠛⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠠⢴⣿⣅⠀⠀⠀⠀⠀⠀⡏⠀⠠⢋⡿⠁⣿⣿⡇⢀⣿⣿⠁⣾⠟⠈⠀⠀⠀⣾⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⡿⠿⠟⠋⠀⠈⠛⠿⠿⠿⠿⠛⠛⠋⢀⣠⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠁⠀⣿⣿⠇⣾⣿⠃⠀⣿⠀⠀⠀⠀⢠⣿⣵⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⣀⣀⠤⣀⣤⣴⣶⡶⣿⣿⣛⣉⡥⠀⣠⡴⠊⠀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⣿⠿⢸⣿⠃⠀⠀⡇⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣴⠇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⠾⢋⣠⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⢠⠎⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠸⠀⣾⠃⠀⠀⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣯⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡌⠙⠿⠿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠻⠟⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢏⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⠟⡡⠊⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠱⣿⣻⣟⣿⠿⠋⠁⠨⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠂⠀⠀⠀⠈⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠠⢾⣶⣿⢂⣀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢀⣠⣤⠔⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⣠⠯⠟⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

`);