Sanemi Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣀⣲⠄⢳⡀⠑⢄⠄⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡦⢿⡀⠈⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⠞⠉⠚⠛⠑⠂⠴⠂⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠘⣄⠀⡀⣀⣀⣀⡠⠔⠊⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢚⣿⠓⢢⡀⠀⠀⠐⠀⠀⠀⠘⡆⠀⢶⠀⠀⠀⢠⠀⠀⠀⠀⠘⣆⠀⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢫⡇⠀⠠⢯⠀⠐⠓⠤⣀⡀⠀⣽⡀⠘⡄⠀⠀⠀⢇⠀⠀⠠⡀⠈⢆⡷⠤⣠⠒⠒⠤⠤⠖⠒⠉⠁⠀⢸⠑⡄⠀⠀⠀⠀ ⠀⠀⣀⡴⣱⢻⡿⢄⡄⠘⣆⠠⡀⠀⠀⢬⡉⠤⢥⠀⢱⡀⠀⠀⠈⢆⠀⠀⠙⢄⠘⢷⠤⣀⡀⠠⢄⡐⠂⠀⠀⠀⠀⢾⡄⠘⢆⠀⠀⠀ ⠀⠀⡏⡴⠁⢸⣇⠈⢧⣀⢸⣦⣌⡦⠈⢁⡊⠀⠀⢢⠀⢣⠀⠆⠀⠈⢆⠠⡀⠀⠣⠈⢆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⡇⠀⢀⠀⠀⠀ ⠀⠀⣿⣴⡟⣇⣿⠀⢸⣿⠛⠛⠿⣿⣶⣄⢹⡀⠀⠸⣇⠀⢃⢸⠀⠰⡈⢆⠑⣄⠀⠑⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⠀⠘⣆⠀⠀ ⠀⠀⢹⣿⡷⢩⢘⡆⠸⣿⠀⠀⠀⢀⡉⠻⢿⣿⣄⠀⠘⡄⠀⠀⡆⠀⢳⡈⢦⠘⢧⡀⠈⠢⠳⡀⠀⣀⣤⣤⣶⣠⣾⠉⠀⢣⡀⠉⠀⠀ ⠀⠀⠈⣿⠀⢸⣸⡇⠀⢿⡀⠀⢠⣿⣿⣷⣦⡙⢿⣧⠀⢹⡄⠀⢸⠀⠀⢿⣄⠁⠈⢿⢦⠀⠀⠹⡟⠛⠉⠉⠉⠉⠙⠛⠻⠶⣧⠀⠀⠀ ⠀⠀⠀⠈⢧⣸⣄⢸⣀⣈⣇⠀⠀⢿⣿⣿⣿⣧⠀⢻⣧⠘⠹⡈⢄⠇⠀⠘⡇⠹⠦⣈⢿⠓⢄⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⡼⢹⡟⢜⣯⡈⠉⢢⣄⠀⠈⠙⠛⠁⠀⠀⢻⡆⠀⠘⡌⢾⡀⠀⢱⡀⢀⡞⠙⠓⢾⣿⣦⡈⢿⣿⡏⠀⠀⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⣸⢡⠃⢱⡀⢣⠈⠢⡀⠙⠧⣄⣀⣀⣀⢀⣀⡸⣇⠀⠀⠘⡌⢣⠀⢆⢣⢼⠀⠀⠀⠈⠛⠿⠷⢌⣯⠀⠀⡠⠚⠓⠒⠀⠀⠀⠀ ⠀⠀⠀⡧⡴⠀⣿⠷⣼⣆⠀⠈⠚⠓⢤⡉⠉⠉⠀⠀⠉⠁⢰⡀⠀⠘⣆⠑⠌⢿⠛⠳⢄⣀⣀⣀⣀⣀⣀⠽⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡧⠧⣼⡃⢠⢋⣿⠑⣄⠀⣀⠀⠈⠓⠤⠒⠚⠀⠀⠘⡋⠉⠉⠙⠣⡀⠀⢣⣄⠀⠀⠀⠉⠀⠀⠁⢠⠤⠬⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡹⠁⠈⡸⢹⡆⠀⠓⠀⠉⠑⠢⠤⠒⠠⡄⠀⠀⠈⠐⠈⠙⠖⠛⠢⢄⠑⢤⡄⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠅⠴⣥⠔⢺⠁⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⢰⠃⠀⠚⠉⢠⣿⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⢀⠇⠀⡇⠀⢀⣾⣷⣿⢷⡀⠀⠀⠀⠘⠻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⠁⠀⣾⣿⣿⣿⡄⢳⡄⠀⠀⠀⠀⠀⠙⣿⡢⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈ ⠁⠀⠀⠃⠀⠀⢠⣼⣿⣿⣿⣿⡇⠘⡉⢦⡀⠀⠀⠀⠀⠈⠛⢒⠦⣥⣤⡤⠤⣔⡶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣄⢃⠀⢹⣦⡀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠏⠀⢠⠎⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠂⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢺⠏⢀⠌⢀⡔⠁⠀⠀⣠⣾ ⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⠿⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠈⠋⣀⡨⠖⠋⠀⠀⣠⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠢⠈⠹⣿⣷⠦⣤⣀⡤⠤⠔⠒⠉⠁⠀⠀⠀⢀⣴⠖⢊⡁⠀⠀⣀⣠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⣤⠔⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠤⢊⢆⠁⡂⠀⠁ ⠀⠀⠀⢀⡝⠐⠒⠂⠂⠘⡀⠀⠀⠀⠀⠀⠐⡀⢩⢁⠠⠤⠤⠒⠈⠘⡄⠀⠀⠀ ⠀⠀⢀⣾⠉⢐⠀⠬⣀⠀⣃⠘⡀⠀⢂⠀⢀⠐⣸⢀⡠⠄⠀⠤⠐⠈⡷⡀⠀⠀ ⠀⡦⡒⣽⠠⠈⢆⢀⠠⠢⠒⢂⠡⠀⠀⢂⠀⠡⡘⡆⠄⠐⠀⠀⠀⢈⢇⠐⠀⠀ ⠀⢳⣔⠻⡄⣿⠚⠻⢶⣜⡀⠘⠆⠂⠆⢠⢊⢂⠀⢜⠄⠀⠀⠀⠀⢀⡸⠀⣆⠀ ⠀⠸⡏⡇⡇⢹⠀⢠⣶⣬⡻⣦⠘⡀⠠⠀⢧⡂⠳⣄⠉⢦⠖⠛⠓⠳⠦⢵⠀⠀ ⠀⠀⢙⢷⣰⡬⢇⠈⠻⢿⠇⠘⣆⠒⡡⡂⠘⡈⢂⢽⣠⣄⢻⣷⡆⠀⢀⠎⠀⠀ ⠀⠀⠦⢉⡌⡕⠠⣑⠤⣀⡀⠀⣸⠀⠘⡜⡀⣥⣎⠀⠈⠛⠷⢹⡀⠀⠓⠂⠀⠀ ⠀⢰⡉⣼⢩⢳⢄⠀⡁⠢⠄⠤⠀⠸⠀⠘⢎⠚⢍⠀⠒⠒⠒⢀⡁⠠⠀⠀⠀⠀ ⠀⠸⢀⢋⣠⠛⡄⠁⠀⠁⠒⠐⢄⠀⠈⠀⠉⠁⠨⢲⡄⠀⠀⠀⠄⠁⠀⠀⠀⠀ ⠀⠈⢠⢃⠘⢈⣷⡀⠀⠀⢀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠘⠀⣾⣿⡝⣄⠀⠀⠑⢦⡄⠀⢀⡀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⣾⣿⢸⣇⢁⠢⡀⠀⠀⠉⠴⠒⠒⠆⠚⠉⠀⠀⠀⠀⠀⡠⠎⢀⠌⠀ ⠀⣀⣴⣿⣿⣿⣾⣿⣧⡂⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣰⠋⠌⡠⠁⢀⣴ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠨⠛⣦⣄⣀⣀⡠⠄⠒⠈⠀⣠⠅⠂⠁⣀⣴⣿⣿

⣿⣟⣿⣿⣄⠈⠈⠹⡈⠈⠁⠰⠀⠃⡔⢎⠨⢉⡉⠫⡑⢄⠀⠀⠀⠀⠀⠀⠊⢛ ⣿⣿⣷⣬⡉⣉⠀⡇⠁⠀⠀⠇⠐⢀⢃⣠⠈⠔⢌⢂⢸⠄⠑⠰⡒⠂⠀⠀⠀⠄ ⠹⣻⣟⢛⡡⠐⠈⢿⠀⠁⠀⠀⢀⠸⠁⠀⠀⣙⠃⢧⡀⡌⢀⠀⢸⢀⠀⠀⠀⠀ ⠀⢷⣤⣀⡠⠐⢠⢫⡆⢰⠀⡃⢀⠠⢐⡲⠋⠀⠀⠀⠡⠇⠀⠀⡎⢄⡡⠄⠀⠀ ⠀⢸⣟⣉⡀⠐⡇⣝⢠⢆⠄⢠⢸⢼⠀⠀⡠⠤⣀⠈⠤⠃⡀⠀⡯⠂⠀⠀⠀⠀ ⠀⢸⣿⠃⡠⢺⢀⢤⡪⢺⢄⠀⠀⡌⢧⡔⣪⣭⣄⠀⡜⢡⠁⡔⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠈⠠⢺⠵⠓⠲⠥⡈⢂⠈⣴⣼⠀⠻⠿⠃⠘⠡⣌⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⣴⣶⣏⡘⣦⡘⢿⡿⢘⣤⠽⡐⡭⣀⢀⣀⠀⠀⠰⠃⢸⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⠿⢻⣥⡶⢸⣋⠭⢓⠣⢏⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⠏⣰⢹⣷⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣦⣙⡄⠀⠀⠀⠠⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠽⠄⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠈⠱⢦⣄⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣛⣦⡀⠀⠀⠀⠀⠀⡠⢐⡁⠧⠀⠒⠒⠂⠉⠉⠈⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢳⠦⢔⠶⡑⠬⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡛⡽⡇⢄⠆⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠀

⠀⠀⠀⠀⠀⢀⢋⠔⣔⡏⣩⣸⠀⡇⠰⢀⠀⡇⢠⢸⢱⠀⡏⣚⣒⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠒⠁⠈⢼⠹⢤⢸⠀⠻⡄⠘⠀⢀⢸⠈⡾⠸⠙⠀⠉⠈⠀⠀⠀⠀ ⠀⠀⠉⠁⠐⠒⡶⠊⢼⡯⢂⠻⣰⠀⣱⡄⢃⠈⠀⡄⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠌⠀⠊⠘⢷⣿⠓⢳⣎⠭⢜⢄⢢⠀⢁⠘⣾⡒⠐⠢⢀⠀⠀⠀⠀ ⠀⠀⠤⠴⠮⠤⠄⡖⡅⣿⣿⡆⠀⠑⠈⠉⠈⢺⠀⣮⠀⠷⠏⠀⠺⠁⠉⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠚⠈⠇⠛⡿⠀⠀⠀⠀⡠⠒⠒⠧⡸⠧⣠⠀⠀⠀⡀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢬⠕⠓⠂⣠⠀⠀⣀⡬⡝⠛⠻⢷⣾⣷⣷⢓⠀⠄⡀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⠁⠀⠑⠢⠠⡀⠀⠀⠉⠂⢄⡀⠺⣿⣿⢋⠷⠶⢶⠗⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡡⡀⠀⠀⠓⠨⠈⡂⠆⢀⡀⠀⠉⠉⠓⢄⢀⢤⠃⠌⡠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢃⡁⠀⠀⠀⠀⠀⠈⠐⠢⠤⢧⠠⠀⡀⠔⠕⠁⡠⠖⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠢⢄⡀⠀⠀⠀⠀⠀⠀⠤⠴⠭⠐⢒⠛⡀⠤⢢⠃⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⡪⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠁⠘⣁ ⠀⠀⠀⠀⢀⠄⠂⠁⢀⢔⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢰⠊⠁ ⠀⠀⠀⠐⠁⡀⠄⡺⠡⢢⣎⣦⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠌⠀⠀ ⢈⠉⢀⠄⠊⢀⣰⠁⠁⣿⠻⠘⢿⠱⡿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠘⢿⡘⡄⠀⠀⠀⠈⣿⣾⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠘⣷⣱⡀⠀⠀⠀⠘⠿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠹⣧⠱⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣇⣀⣠⣤⣿⣷⣶⣶⣤⣤⣀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣟⡽⠋⠁⠀⠀⠘⠄⠘⣷⠈⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⣸⣿⣁⠀⠀⠀⠀⠀⣠⠾⢃⡼⠋⠙⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣏⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠙⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⢿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⠳⡄⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣷⢶⣄⢰⡄⠀⠀⠀⠀⠈⠋⠁⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡽⣄⡇⠀⠀⠀⠀⠀⠀⢀⣤⠔⠂⢠⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠹⣿⣿⣿⣿⣿⣿⠹⡀⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣋⣴⠶⣶⣦⣅⣀⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⡇⠀⠉⠛⠛⢻⠃⠀⠀⠀⢀⡾⠟⠁⠀⢠⣯⣽⡿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠰⠾⠟⠋⢉⣠⣾⣿⠟⢻⠟⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠒⠶⠤⠄⠀⠿⠋⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣀⣠⣤⣾⣿⡿⠟⠁⢠⡿⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⢶⣶⣿⣿⠿⠛⠛⠉⣁⣠⣤⠄⣿⢇⠀⣿⡆⠀⠀⠈⣆⠀⠤⠒⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣈⠛⠻⠿⠿⠿⠿⠛⢉⣀⣤⣿⢸⠀⢷⣿⡄⠀⢀⣄⣀⣀⡀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣜⣂⣴⣾⣿⡄⢸⣟⣛⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠀⢸⡏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⢸⡿⠁⡟⠀⣼⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⠉⣿⠃⢸⠃⢰⠁⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠀⢸⣿⠀⢸⠀⢸⠀⠀⠇⠀⠸⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠏⠀⢠⣿⣿⠀⢸⠀⢸⠀⠀⠇⠀⠀⢻⣿⣿⣿⡿⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣼⣿⣿⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠛⠉⡸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⢸⡁⠀⠀⡀⠈⠳⠤⢄⣀⣀⣀⣀⠤⠴⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣷⠀⠀⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⢦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⠇⠀⠘⠓⠢⠤⠠⠶⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡄⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⢰⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⡁⠀⠀⠸⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣟⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣙⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠈⣿⣿⣿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠈⠙⠿⢿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠉⢻⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠳⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢹⠉⠉⠉⢷⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣸⠃⠀⠀⢸⣇⣠⠴⠛⣇⣠⠴⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⡏⠛⠛⠛⢶⡤⠴⠞⠳⣄⣀⣤⠾⣥⣀⡀⠀⠀⠀⠀⢈⠓⠶⣦⣤ ⠀⠀⠀⢀⡼⠁⠀⣠⡾⠋⠳⣤⣀⣠⢧⣀⣹⡄⠀⠉⠉⠛⠛⠛⠋⣩⡴⠛⠉⠀ ⢀⣠⠴⠋⠀⣠⠞⠁⠀⠀⠀⠘⣯⢳⣄⠉⢩⣷⠾⠛⠛⠷⣦⣀⡾⠋⠀⠀⠀⠀ ⠀⢳⠀⢀⡞⠁⠀⠀⣠⡴⣾⠋⠉⠁⠙⢷⡌⠀⠳⣄⡀⠀⠈⠛⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠊⠀⠀⠀⣼⠋⠼⠛⠲⣦⡀⠀⠀⠙⣦⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⠶⠟⠛⠓⢾⡇⠀⠀⠀⠀⠈⢿⠀⠀⠀⠈⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠒⠒⠲⢮⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⢴⠒⡖⣒⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⣔⣉⡸⠊⠀⢇⡙⣷⠀⠀⠀ ⠀⢀⡠⠮⢂⡔⡡⣏⡉⣰⠸⣝⡇⠀⠀ ⣠⠻⣉⡠⠟⢮⠗⠒⡼⣦⢟⡉⢻⣄⠀ ⠡⣷⡊⠩⢍⢉⣩⣉⣉⠭⠒⠋⠵⣻⣡ ⠀⠀⠉⠓⠓⣟⠆⢠⢸⣴⣦⣧⣴⠿⠋ ⠀⠀⠀⠀⠰⢽⡖⣿⠼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠈⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠀⠈⠊⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⣀⣀⣀⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠤⠤⠀⠤⠄⠄⠄⠀⠠⠴⠂⠄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣿⣿⠯⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⡾⠤⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⠖⡚⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⡶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡈⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢃⠀⠀ ⠀⡀⣄⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠇⠀⠈⡄⠀⠀ ⢔⣼⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠹⠁⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⣿⣿⣿⡏⠉⠛⠋⠁⠀⠀⠀⣿⠋⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⣀⠀⢀⡾⠧⢀⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣿⠟⠗⣂⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠭⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠚⠉⠑⣀⠔⠐⠢⠀⠈⡹⠶⣄⠀⠀⠀ ⠀⠀⡰⠋⠀⠀⠀⠀⡏⢄⣀⡰⢠⠊⠀⠀⠈⠳⡄⠀ ⠀⣸⣅⡀⠀⠀⣀⠔⠀⢀⡀⠀⠸⡀⠀⠀⠀⠀⢸⡄ ⢀⣿⣿⣾⡭⡭⠐⢢⠊⠁⠈⢣⠀⠙⠢⢄⣠⣴⣿⣷ ⢸⠁⠀⠈⠹⣿⣶⣼⣆⣀⣀⣼⣠⣤⣾⣿⠟⠉⠙⢿ ⠈⢧⡀⠀⣠⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡀⠀⣀⠞ ⠀⠀⠈⠉⢩⠃⠀⢀⣤⠀⠀⢠⣦⠀⠀⢸⠉⠉⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠉⡀⠀⢈⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠂⠁⠀⠀⢀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠸⣏⠁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⠹⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡟⠁⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⡾⠀⠀⠀⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣠⠎⠁⠀⠀⣠⣞ ⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⠞⠁⠀⠀⣠⣾⠟⠁ ⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⢀⡴⠒⣖⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣭⡙⠲⢤⠀⠀⠀⠀⢻⠀⣰⠋⠀⠀⢀⣾⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⢀⡴⠁⠀⢰⣿⠀⠀⠳⡄⠀⠀⠀⠀⠀⢠⠎⠀⠀⢠⣿⡇⠀⠈⢳⡀⠀⠀⠘⡶⠁⠀⠀⣴⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⡼⠀⠀⠀⢸⣿⡀⠀⠀⢹⡄⠀⠀⠀⠀⡞⠀⠀⠀⢸⣿⣿⠀⠀⠀⢳⠀⠀⠀⣧⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⢸⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⡇⠀⠀⢹⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⠀⠀⢸⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣇⡇⠀⢸⣾⣿⠁⠀⠀⠀⠀⢀⣠⠞ ⠀⣠⠟⠀⠀⠀⠀⠸⣆⠀⠀⠀⢸⣿⡇⠀⠀⢀⡿⠀⠀⠀⠈⢧⠀⠀⠀⢸⣿⡇⠀⠀⠀⣰⡟⠁⠀⠘⡷⣇⣤⣤⣤⠴⠚⠉⠀⠀ ⣴⡇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠸⣿⠁⠀⣠⠞⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⣿⠁⠀⣀⡴⠋⠀⠀⠀⠀⣧⠴⠋⠉⠀⠀⠀⠀⠀⣀ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣲⣯⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⡒⠒⠋⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢀⡠⠔⠋⠀ ⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢹⣄⡤⠴⠚⠉⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠉⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⢹⠳⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡶⠾⢟⣿⠛⠁⠀⠀⣾⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠈⢳⣤⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⡴⠋⠀⠀⣠⠂⢠⡟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠘⣆⠀⠀⠙⢿⣳⠶⣤⣀⣀⣀⣀⣀⣀⣠⣄⣤⡤⠟⠁⠀⠀⢀⠞⠁⣠⠟⠁⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠈⠛⠲⠤⠤⠠⠬⠔⢛⡩⠗⠋⠀⠀⠀⢀⡴⠃⠀⣴⠋⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⠷⣦⣄⣀⡀⣀⣠⠴⠚⠉⠀⠀⠀⠀⢀⡴⠋⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⡾⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠙⠦⣄⣀⣠⡶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⠉⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢘⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀ ⣀⡤⢰⣴⠁⠀⠀⢀⠀⠀⠀⠀⢸⠂⡐⣄⠀ ⠻⡇⠚⣟⠀⢀⡀⠿⡿⠇⢀⣀⢸⣴⢣⡽⠃ ⠀⠈⢹⠞⣉⠠⣄⠶⠶⢖⣠⠴⢌⢻⢏⠀⠀ ⠀⠀⣿⠋⢱⢹⣿⡇⠀⢸⣿⡏⠄⠙⡼⠀⠀ ⠀⠀⠈⠂⣤⠷⣍⠠⠹⣠⣀⠌⠄⠚⠁⠀⠀ ⠀⠀⠀⠀⣳⣶⢂⠈⠉⢁⡔⠕⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⣀⠉⠀⠉⢀⣸⢆⢑⡀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⣠⡝⢻⠀⢈⠉⢣⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠻⣿⠛⢷⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⣀⣤⣤⣤⣀⠀⢨⣿⣇⠀⠙⢀⣾⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣋⣉⢻⣿⣶⣤⣼⡿⢛⣉⡙⣿⣧⠀⢻⣿⣤⣴⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠻⣿⡈⠿⠿⢁⣿⡏⠙⣿⣇⠘⠿⢃⣾⣿⡀⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠹⢿⣶⣶⣿⠟⠀⠀⠙⢿⣷⣶⣿⠿⠻⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀ ⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀ ⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀ ⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀ ⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀ ⠀⠘⢿⣷⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠏⠛⠻⠭⣽⣒⣲⣤⣤⣤⣤⣼⣿⣷⣶⣶⡯⠿⠟⠋⠉⢹⣿⡄⠀⠀⠀⠀⠀⠀ ⢀⣤⠶⢾⣿⡏⠀⠀⣀⡤⢶⣿⡟⠉⠁⠀⠀⢉⣿⣿⣄⡀⣀⠀⠀⠀⣠⡾⢿⠛⢦⡄⠀⠀⠀⠀ ⠀⢻⣦⣟⠈⣿⠂⠉⠻⣄⣾⠉⣿⠁⠀⠀⢠⡟⠉⣧⢈⡛⠃⠈⠉⠙⠛⠦⠞⠒⠒⠓⢲⣤⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠓⠒⠚⠛⠛⠛⠒⠒⠀⠂⠙⠓⠛⠙⠀⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣡⣴⣶⣿⠛⢫⣯⣤⢟⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡄⠀⣠⣶⠟⠺⢟⡕⠋⣿⣯⣤⠌⠉⣩⢿⡝⠛⠯⣽⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⣧⡼⠛⠁⣿⢸⡟⠀⣼⢡⡏⠀⠀⣼⢣⣼⠁⠀⠀⠀⠉⠓⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢃⢿⢧⡀⠀⠻⣾⣧⡠⠿⠟⠙⠉⠋⠻⣯⢾⣤⡴⢶⣶⡒⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⢰⡏⠘⣿⢇⣹⠟⠉⣹⠏⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠛⢶⣕⢦⣄⠀⢿⡳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⢷⣿⣷⠶⣾⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠣⣌⣳⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠁⣟⡛⡿⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣸⠛⠯⠷⠂⠚⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡓⢶⣍⣸⠃⠀⣠⣄⡀⠀⠀⠀⡿⣶⢀⣀⡀⠀⠀⠀⣸⣷⠦⣤⣠⣧⠒⡓⢦⠀⠰⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣧⣀⣤⡽⠠⠞⢁⣠⡯⠽⠷⣶⣾⠋⠈⠻⡝⠶⣾⣿⣛⣿⣄⣀⠉⢻⣦⡙⠻⡗⠰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⡛⠻⡇⠀⣞⡽⠞⣿⣍⣽⠟⠀⣷⠀⠀⠀⠲⠿⠳⠾⢿⠶⠗⠀⠀⣿⠸⣷⡿⢦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⣴⣻⠀⠉⠛⠃⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣿⡞⣙⣿⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣽⢿⡆⠀⠀⠀⠀⠀⠀⠀⠠⣏⢀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢰⣿⢱⡟⢹⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣝⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⣟⣿⣷⣾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣮⢿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠶⠶⠶⠶⠶⠖⠋⠁⠀⠀⣻⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠙⠋⠀⣀⣀⣤⣤⣄⣀⡤⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡽⣏⢿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣹⡿⡇⣿⢸⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⢻⣯⢧⡿⣴⢧⣿⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣻⣿⣿⡟⣿⣧⣏⣾⣾⣿⣷⣫⢿⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⠿⣾⣾⢋⡿⣼⣽⡿⣻⣿⣿⡽⣵⣃⠀⠀⢻⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠺⠃⡷⣻⢣⣿⣟⣿⣿⡿⡁⠀⠀⣠⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⠃⢇⡿⢯⡾⠻⠏⠘⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣠⠖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⢀⡴⠞⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢀⡤⠞⢋⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⣰⣿⣿⣋⠀⠀⢠⠞⠁⢀⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢟⣻⣭⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⣰⣿⣿⠋⠀⢙⡷⠁⡀⣤⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⡇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠈⠑⢆⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢲⡀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⣤⡀⠀⢳⣄⠀⢠⡀⠀⠱⡀⠀⠀⠀⠀⢳⠈⠳⢄⠁⣤⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣝⣦⡀⢹⡦⡀⠙⢦⡀⢱⠀⠀⠀⠀⠘⣇⠀⠀⠻⣿⣉⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠠⠀⡆⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢻⡏⠻⡗⡄⢳⠈⢦⡈⢟⠢⣇⠀⠀⠀⠀⢹⡄⠀⠰⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠇⠀⣇⢰⠀⠀⠀⠀⠀⢠⡟⠀⠳⠦⢼⣧⣄⣱⡼⡤⡧⠜⠿⣶⢷⠾⡤⠠⠀⠀⠈⡷⡄⠀⠹⣇⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⡄⢸⣇⠀⣸⡆⠇⢀⣴⠃⢀⡞⠀⠀⡄⠀⢸⠀⠀⠀⢣⡸⡇⠀⠀⠈⢿⠀⠃⠀⠀⢸⠀⢸⠈⢂⠀⢿⡀⠀⠀⠀⠀ ⠀⠀⢧⠀⢇⢸⠙⡆⠸⣿⣾⠟⠁⠀⡜⠀⠀⡸⠀⣰⣼⠀⠀⣀⣤⣤⣵⣶⣶⠶⢾⣷⡀⠀⠀⡎⠀⠘⡀⠐⢆⠸⡄⠀⠀⠀⠀ ⠀⠀⢸⡆⠸⣼⠀⢸⡴⠟⢿⢣⡀⠀⠀⠀⢠⠃⢰⡿⣿⠀⠸⠛⢉⣿⠭⠷⠚⠁⠀⠀⡇⢸⢀⠃⠀⠀⡇⡄⠈⢳⣇⠀⠀⠀⠀ ⠀⠀⠈⣷⡄⢹⡖⠉⣧⠆⠈⢇⢙⣬⣠⠀⡌⢀⣞⠁⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⢇⡼⠂⢀⠄⢸⡗⣮⣦⡀⢫⠀⠀⠀⠀ ⠀⠀⠀⢻⣟⠀⢳⡀⢛⣠⣴⣿⡛⠛⠈⢻⡥⠯⢤⣉⡳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠋⡇⢀⣾⠃⢸⡆⡇⢹⢻⣌⡇⠀⠀⠀ ⠀⠀⢆⠈⡎⠀⣠⣿⠿⢛⣩⠝⠛⠙⠀⡟⠁⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠀⢰⢃⣾⡏⠀⣾⡟⠀⣾⡀⠉⢿⠀⠀⠀ ⡀⠀⠈⢢⠘⣄⡿⢁⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢿⠁⢰⡷⣧⡴⢩⠃⡀⡜⡀⠀⠀ ⠱⡄⠀⠀⠱⣜⣅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⢠⢋⠇⣼⠓⢼⣇⠈⣧⡄⠀⠀ ⠀⠙⣆⠀⠀⠈⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣸⠟⢸⡄⠀⠉⢦⠀⠀⠀⠀ ⠀⠀⢸⣦⠀⠀⠐⠢⢬⣓⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⢀⡟⠀⢸⢇⠀⠀⠀⠑⠀⠀⠀ ⠀⠀⣸⡙⠳⣜⣦⣄⡀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠛⠈⠉⣀⠹⣷⠀⠀⠀⠀⠀⢀⡎⢱⠀⣸⠘⣴⠀⠀⠈⠀⠀⠀ ⠀⠀⢿⡌⣦⣈⠻⡟⢌⢷⣒⠪⠓⠒⠄⠀⠀⠀⠀⢸⡟⠃⠠⠤⠔⠊⠁⠀⡟⠀⠀⠀⠀⢀⠞⠀⢸⠀⣟⣀⣻⣤⠖⠂⠀⠀⠀ ⠀⠘⣮⠈⠎⢆⠑⠻⠬⣿⣏⣳⣄⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⣀⡠⠴⠊⠀⠀⠀⠀⣠⠋⠀⠀⠈⡄⢹⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢆⠀⢸⠀⠀⠀⣠⡿⢆⡀⠉⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣦⣀⡠⠔⠋⠁⠀⢸⣷⡀⠀⣧⡉⠓⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠃⠀⠀⠀⠀⠀⢹⡇⠙⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠓⠒⠒⠂⠒⠋⠛⠛⣇⢰⢿⣷⣄⠀⠈⠻⣿⣷⣶⣤⣤⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠘⣎⡆⢿⡌⢦⠀⠀⠈⠙⠻⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠛⠫⠤⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢸⡇⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⣾⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠘⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣙⣧⡀⢬⣉⣙⠓⠿⣦⣌⡙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡀⣶⣦⣤⣥⣌⣿⣿⣿⣶⣤⣸⣿⣷⣦⣄⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢛⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠠⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠧⣼⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣿⣿⡿⠋⠉⠉⠉⠛⠉⠀⠈⠁⠈⠛⠿⢿⡿⢿⠟⠉⠘⠁⠀⠉⠙⠋⠉⠉⠙⢿⣿⣿⡇⢹⠂⠀⠀⠀⠀⠀ ⠀⣴⠞⠛⠲⣿⠀⣿⡿⠁⠀⠀⣀⣀⡀⠀⠀⠀⠐⢄⠐⡄⠀⠁⢀⠆⢀⠔⠀⠀⢀⣀⣀⣀⡀⠀⠀⢻⣿⠇⣾⠖⠒⠲⣦⠀⠀ ⢰⡏⡴⠶⢤⣸⡆⢹⣷⠀⠀⠀⣾⣿⠿⣶⣄⡀⠀⠀⢣⣼⣠⣆⣼⡴⠁⠀⠀⣨⣴⠿⣿⣷⠄⠀⠀⣸⣿⠀⡟⣠⠶⢦⣸⡇⠀ ⠘⣧⠀⡴⠋⢻⣧⠘⣿⣷⣄⠀⠈⠻⣷⣿⣿⣿⣶⣦⣾⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣶⡿⠋⠀⢀⣾⣿⡇⢸⡿⠛⢢⡀⢸⡇⠀ ⠀⠹⡆⠁⣠⠜⠃⣼⣿⠁⠈⠐⠂⠀⠀⠀⠀⢀⡶⢛⠻⠿⠿⠿⠿⠿⠛⢶⡄⠈⠁⠀⠀⠤⠒⠋⠈⢿⣷⡈⠳⣄⡀⢀⡿⠀⠀ ⠀⠀⣹⣞⠁⣶⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠰⣾⠰⢩⣿⣦⠀⠀⣠⣾⣏⠏⢳⡴⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣶⡌⣿⣿⡁⠀⠀ ⠀⢀⡽⢁⣼⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⡀⠀⠈⠑⠦⠈⠙⢇⣠⠟⠉⠠⠚⠉⠀⢰⡂⣩⣽⣶⣿⣿⣿⣿⠻⣿⣷⣌⢿⣍⠀⠀ ⢀⡾⢡⣾⣿⣿⠋⠀⠋⡿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣟⠿⡙⠆⠁⠀⢹⣿⣿⣦⢻⣆⠀ ⣾⡟⢡⣿⣿⣇⠀⠀⠀⠀⢁⣾⣿⡿⠋⠁⠀⢀⣀⣀⣀⣀⡉⠉⠒⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⣼⣿⣿⣧⠸⣿⡆ ⢹⡇⢸⣿⣿⣿⢰⠀⠀⠀⣾⣿⣿⠁⣴⡏⠉⠉⠀⠀⣅⢀⣩⣏⣉⣙⣶⣦⣤⣀⠉⠑⠿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⢀⡇⠁ ⠀⣷⢸⣿⣿⣿⣾⣶⠀⣠⣿⣿⠇⠀⢿⣿⣴⣿⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠑⠢⢼⣿⣿⣇⡄⣰⣿⣿⣿⣿⣿⣸⠇⠀ ⠀⠸⣧⣿⣿⣿⣿⣿⣦⣿⣿⣿⠀⠀⠚⠋⠁⠀⠀⠀⢠⣴⣶⣿⡿⡿⢿⠂⠀⠀⠰⠤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀ ⠀⠀⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡴⠚⠁⠀⠀⠊⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣴⣦⣄⡀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠐⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡏⠻⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠈⠙⠻⢿⠛⠛⠛⠉⠹⠟⠋⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠛⠉⠠⠀⢀⣠⠟⠋⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠹⣿⢷⣦⣤⣠⣾⣿⡿⠿⠁⠀ ⣁⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣓⢾⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠙⠛⠛⠛⠓⠒⠒⠒⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⡻⣿⣷⣮⡙⠛⠛⠛⠓⠒⠛⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠈⠀⣠⡴⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⢀⡴⢊⣥⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀ ⠀⠀⠀⠀⡰⢋⣴⣿⣿⣿⣿⣿⣿⣿⠋⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠁ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢔ ⠀⠀⠀⠀⢸⡟⢰⣿⣿⣿⣿⣿⡿⢁⡔⠙⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠜ ⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⠁⠙⢿⣴⡾⠁⠀⠀⠀⣦⣤⣴⣿⣾⣲⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠈⠀⠀⢿⣏⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡨⠿⣿⣿⣤⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⢀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡸⠀⠀⠀⢻⣿⡦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠐⢚⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⣀⠀⢀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⡀⠀⠀ ⠀⠀⠸⣿⣿⠟⢠⠏⡜⢃⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⣀ ⠀⠀⠀⠹⣿⡄⢸⠀⠁⠸⡀⠀⠘⠞⠈⠓⠤⠄⠀⠀⠀⠀⠀⠀⠐⠛⣉⡽⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⣿⣿⣿⡿⡄⠘⣿⣽⡇ ⠀⠀⠀⠀⡠⠟⡎⠱⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡥⣾⣿⣿⣿⣿⡿⠟⠉⠀⠀⢀⣿⣿⣿⣿⣿⣿⢃⢹⡎⡉⢢⠉ ⠀⠀⢠⢚⡶⢺⣆⠀⠘⣄⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣲⣾⣿⣿⣿⣿⣿⡿⠋⠀⢀⣀⣤⣶⣿⣿⣿⡿⠟⣹⢿⡀⠀⣇⣸⣴⠤ ⠀⠀⡼⠁⢀⠾⠚⢉⡗⡻⠀⠀⠉⠁⠒⠒⠒⠶⡒⠲⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠃⢶⣾⣿⣿⣿⠿⠿⠿⡉⠀⠀⣇⣼⡇⣀⠜⠋⠀⠀ ⠀⡜⢀⠔⠁⣠⣴⢎⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⡿⠟⣿⠃⠀⠀⠀⣈⣹⠧⠈⠉⠋⣿⢶⣷⣤⣀⠘⣾⠟⠁⠀⠀⠀⠀ ⡞⡠⠃⢀⣼⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⠋⢀⡴⡏⠉⠙⠅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠃⠀⠀⠀⠀⠀⠀ ⢱⠁⠀⣾⠊⠁⠒⡾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⠀⡇⡠⠋⠀⠏⢀⡠⠴⠛⠓⠀⠉⠉⠉⠉⠒⠒⠂⠤⢤⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢠⠊⠀⣠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠾⢤⡀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠁⠀⠜⠊⠠⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⡹⠋⠀⠀⢀⠀⡤⠒⠒⠈⠉⠉⠉⠑⡖⠢⠤⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⡞⢀⡠⠊⢀⣠⠔⠉⠀⣀⠁⠀⠀⠀⠀⢀⡤⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠳⣌⢢⣀⣀⣀⣣⣀⣠⠤⡆⠀⠐⢚⣏⡩⢴⠋⢈⠟⣫⠟⠁ ⠀⠀⠉⠛⠛⠻⢮⣮⠙⠛⢻⣛⠭⢿⠒⢊⠏⢉⣯⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢱⡎⢹⣀⠤⡖⠒⣸⣵⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠉⢀⣠⣧⣾⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢺⣡⣾⣿⠿⡛⠛⣉⣩⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⣼⢯⡡⠔⠊⢩⠁⠀⠀⡎⢹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢃⠎⠱⡀⢀⡨⡦⠀⢒⠳⣄⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠿⢻⢇⣀⣤⣾⣇⡀⢹⠀⣸⡴⢾⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⢀⠇⣰⠏⠁⠀⠈⠻⣶⣓⣿⠁⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⡑⣿⠀⠀⠀⠀⣴⠏⢨⠙⢧⣠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⢧⣿⣆⣠⣴⢿⠛⠒⢼⠔⢹⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣘⠛⢫⡴⠁⢀⣀⣎⡤⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠐⠒⠊⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠈⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢣⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⠋⠀⠀⠀⢸⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⡺⠁⢀⡴⠋⠀⠀⠀⠀⠀⠘⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⡴⠋⡰⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⢀⣠⣴⠀⠀ ⠀⣰⢃⠎⠀⠀⣧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠔⠒⠉⠉⠁⢈⡌⠀⠀ ⢀⡟⡘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠜⢀⠀⠀ ⠸⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⠔⡛⠀⡠ ⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠀⡔⡡⢾⠃ ⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢉⠔⠁⠀ ⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⢀⣴⡿⣽⣷⣾⣝⣷⣦⣤⣀⠀⠀⠀⠩⡝⠦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣝⣯⡿⣼⣿⣿⣿⣿⣶⠌⠉⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠁⠈⠻⣮⣭⣭⣾⠟⠁⠈⠙⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢂⠆⠉⡇⢐⡠⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠜⠋⠉⠉⠉⠉⠉⠛⠂⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⢦⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⣷⣦⣀⣀⣀⣤⣾⣿⣿⡀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡸⢨⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⢇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠒⢒⣉⣉⠡⠔⠊⠀⠹⣉⣛⣛⡟⣏⣉⣉⣠⠘⡀⠱⠤⠤⠖⠂⢄⠀⠀⠀⠀ ⠑⠒⠊⠀⠀⠀⠀⠀⠰⠿⠿⠿⠟⠃⠿⣿⡿⠟⠀⠈⠢⠤⠄⠒⠘⠊⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⠉⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⢿⡇⢠⠴⠋⠉⠑⣦⡀⠀⠀⠀⠀⠀ ⠀⣴⠟⠓⠲⣄⡀⠀⠀⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⠁⠀⠀⡠⠂⠈⣷⠀⠀⠀⠀⠀ ⣰⡏⢤⡀⠀⠈⠛⣦⣄⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣇⠀⢠⠎⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⣿⠁⠀⠙⢦⣄⠀⠀⠹⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⣰⢿⡆⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⢻⡆⠀⠀⠀⣿⠇⠀⠀⡇⠀⢠⣿⣟⢻⡟⠛⢻⠟⢻⡿⣿⠄⠀⠀⠀⣿⣿⣻⣋⣉⣋⣠⣧⣴⣿⣦⣸⠃⢸⣿⢀⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠻⣆⠀⠀⢿⡀⠀⠀⡇⢀⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⣉⣷⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠈⢻⣶⣴⣧⣬⣁⣉⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣯⣀⠀⣹⣿⣿⡋⠁⠀⡠⠔⠊⠉⠉⠉⠉⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡿⠛⠉⣀⡀⠀⠀⠀⠉⠉⠒⠀⠀⢸⣿⣿⣿⣿⣿⠋⠁⢀⣼⣿⣿⣇⡀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⢠⣾⣿⣿⡇⠀⠀⣀⣠⣤⣤⠴⢾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠛⠉⠻⢷⣶⣦⣤⣿⣿⣿⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡄⢾⣿⣿⣿⣷⣶⣿⣿⠟⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣀⣤⣽⣿⣿⣿⣿⣿⠿⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣇⠈⠛⢿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀⡘⢿⣿⣿⣠⡤⢒⣢⣴⣾⣿⣿⣿⡿⢿⣯⣿⣿⡇⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡆⠀⠘⣿⣿⣟⠉⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣾⣿⣿⠛⠛⣿⠋⠉⡇⢘⣿⡟⢸⠇⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⠀⠹⣿⠻⣦⣸⡀⡇⠀⢰⠀⠀⡆⠀⠈⢿⣿⠉⠀⢸⡇⠀⢠⣇⠀⢸⣷⣸⡿⠁⡸⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⠀⠙⣿⣿⣿⡀⣼⡄⢰⣷⣤⣦⣼⠿⢤⡴⠛⣷⡤⠻⡟⣦⣾⣿⣿⠃⠀⠀⣰⠇⠀⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡀⠇⠀⠘⢿⣿⣿⣿⣝⣶⣿⡄⠀⢻⠀⢠⡇⠀⣏⣀⣴⣷⣿⣿⣿⠃⠀⡄⢠⣿⣶⢶⣾⣿⣿⣿⡿⠿⣷⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠀⢸⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⣿⡾⠃⠀⣰⣿⣿⣿⡿⠃⠀⠘⡇ ⠀⠀⠀⠀⢀⣠⣿⣿⣤⣸⣿⣷⠘⣦⠀⠀⠛⢿⣭⣍⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⠿⠛⢠⣦⣴⣿⡿⠁⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⡧ ⠀⠀⢀⣼⠛⠁⠈⠉⠛⠿⣿⣿⣆⢹⣷⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡿⠛⠉⠁⠀⢀⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡛⠛⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⢀⣠⣤⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣼ ⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡄⠀⠀⠙⠷⢤⣀⠀⠐⠛⢿⣿⣷⡿⠋⠀⠀⣀⣴⣿⣿⣿⠟⠋⠉⠁⠀⡶⢿⣶⣤⡤⠾⠛⠋ ⠀⠀⠀⠈⢿⡄⠀⠀⢀⣀⠀⠀⠻⢿⣿⣿⣦⣤⣀⡀⠀⠀⠉⠙⠛⢉⣡⣴⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠶⠾⠛⢻⡄⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣤⣄⡀⠀⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠉⠉⠛⢛⣛⠻⣿⣿⣿⠿⠟⠛⣫⣽⡾⠟⠋⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣴⠶⠟⠛⠛⠳⠤⣀⣀⣀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡟⠉⡉⠻⣿⣷⣮⣿⣿⣿⣿⣿⣿⡿⠿⢷⣦⠀ ⠀⢠⣾⣿⣿⣿⣷⡀⣿⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣧ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⣿⣿⣿⣿⣿⣿⣍⠉⠿⠋⠹⠟⠛⢿⡿⢿⣿⠿⢿⡿⠻⠟⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⠁⠀⡿⠀⠘⠁⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣠⡄⠀⠀⠀ ⠀⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀ ⠀⠘⣿⣿⣿⣿⣶⣶⣦⣤⣶⣶⣶⣆⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠊⠉⠉⠉⠉⠙⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠈⠱⣄⠀⠀⠀ ⠀⠀⡴⠁⡠⣴⠟⠁⢀⠤⠂⡠⠊⡰⠁⠇⢃⠁⠊⠑⠠⡀⠀⢹⣶⢤⡈⢣⡀⠀ ⠀⡼⢡⣾⢓⡵⠃⡐⠁⠀⡜⠀⠐⠃⣖⣲⡄⠀⠀⠱⠀⠈⠢⠈⢮⣃⣷⢄⢳⠀ ⢰⠃⣿⡹⣫⠃⡌⠀⠄⠈⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠣⠀⠀⠱⠈⣯⡻⣼⠈⡇ ⡞⢈⢿⡾⡃⠰⠀⠀⠀⠀⠀⠀⠀⠀⣘⣋⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⢿⣿⢠⢸ ⡇⢸⡜⣴⠃⠀⠀⠀⠀⠀⣀⣀⣤⡎⠹⡏⢹⣦⣀⣀⠀⠀⠀⠀⢈⠘⣧⢣⡟⢸ ⢧⢊⢳⡏⣤⠸⠀⠀⠀⢸⣿⣿⣿⡇⢰⡇⢠⣿⣿⣿⣷⠀⠀⠀⡆⢸⢹⡼⣱⢸ ⢸⡘⢷⣅⣿⢂⢃⠐⠂⣿⣿⣿⣿⣿⣼⣇⣾⣿⣿⣿⣿⠁⠂⡰⡠⣿⢨⡾⠃⡇ ⠀⢳⡱⣝⠻⡼⣆⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⣰⣇⠿⣋⠝⡼⠀ ⠀⠀⢳⡈⢻⠶⣿⣞⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣿⡶⠟⢉⡼⠁⠀ ⠀⠀⠀⠙⢦⡑⠲⠶⠾⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠷⠶⠶⠊⡡⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣝⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣋⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠿⣿⣿⣿⣿⣿⣿⠿⠧⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀

⢰⠁⠀⠀⢔⣼⣽⢟⠘⢄⠀⢸⣿⡌⡷⣾⡿⢺⣿⣿⡻⣷⣂⠈⢂⠀⠀⠀⠀⠀ ⢻⡀⢀⣾⣯⣾⠋⣼⠀⣼⡀⠈⣿⢿⡑⠛⠂⠐⠉⣉⣵⢤⣷⣧⠀⠢⠀⠀⠀⠀ ⣀⣷⣞⣵⡿⢹⡆⢺⡆⢸⣷⠄⣿⠌⠀⠀⢤⢢⣾⣿⣷⣿⣿⣿⣧⠀⠱⡀⠀⠀ ⣯⣛⣻⣿⡀⢸⣿⢸⢿⡜⡏⠇⠛⠀⢀⠺⣴⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠐⠀⠀ ⢿⡼⠛⡅⠸⠈⣿⢻⠈⠁⠃⢘⢰⠀⠈⠄⠻⠻⣽⣿⣿⣿⠿⠿⠇⢣⠰⠀⠀⠀ ⡿⡷⣄⣷⠀⠀⢿⠃⠀⠠⢕⣢⣨⠀⠀⠀⠐⠢⠬⠉⠁⠀⠀⠀⠀⢠⢆⢡⠀⠀ ⣧⡇⠀⢹⢠⡗⣽⣾⣿⣿⣿⣶⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠸⡀⢃⠀ ⡏⡧⡀⢸⢉⣾⣿⣿⣿⣿⣿⢿⡸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠐⡇⠀⠄ ⣷⣀⠀⠀⡏⠿⣿⣿⡿⠭⠊⠋⠃⡇⠀⠀⠀⠀⠀⠀⣀⡤⢞⣿⠟⡤⢂⢣⢳⠸ ⣯⠹⠤⢄⠉⠀⠏⠇⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣠⡾⠋⠈⠻⠏⢈⠀⣸⠆⢻⡄ ⣿⣷⡀⠀⠈⡧⠀⢵⠠⢀⠀⠀⠀⠁⣠⡴⣟⡫⠄⠈⠀⠀⠀⣭⢕⢻⣿⡘⠈⡇ ⡏⡏⠉⠂⠈⢠⠀⡾⣦⣄⠈⠛⠻⣿⢷⣿⡁⠂⡀⢀⠤⢐⡸⠽⣿⣾⣿⣿⡡⠀ ⡇⠁⠀⠀⠀⠞⠀⠁⣿⣿⢿⣶⣦⣿⣐⣬⡆⢠⠍⠵⡾⠟⠂⠀⣼⣿⣿⡿⣧⠆ ⡇⠀⠀⠀⠀⠀⡇⢸⢹⣿⣸⣿⡏⢻⣿⣿⣰⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣧⠻⡞ ⠳⠀⠀⠀⠀⠀⢹⠀⡌⣯⣿⢹⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⢻⠓⢱ ⠀⠀⠀⠀⡀⠀⠘⡀⠁⠛⠋⡩⢿⢸⣿⡾⠛⠉⠛⢿⣿⣿⣿⣿⠏⠀⡌⡞⠆⠈ ⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⢸⡃⠀⠃⢐⠃⠀⠀⠀⠀⠉⠙⡓⠁⠀⡀⢀⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠉⠉⠉⠉⠛⠷⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⢤⣤⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠈⣹⣷⣄⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣦⣀⠀⠀⠀⣠⡾⠋⠀⠙⢷⡄⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣼⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⢻⣄⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣤⣤⠶⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣃⣀⣀⣠⡟⠀⠀⠀⠀⠘⢷⣄⠀⢀⣠⡴⢿⡄⢸⣇⠀⠀⠀⢴⣤⣄⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠏⠉⠉⠉⠻⣇⠀⠀⠀⠀⠀⠀⣩⣿⠟⠁⠀⠀⢿⣸⡏⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣿⡄⠀⠀⠀⠀⠹⣆⠀⠀⠀⣠⡾⠋⣿⠀⠀⢀⣤⠾⠛⣷⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣧⠀⠙⢶⣄⠀⠀⢠⡿⠛⠛⠉⠉⠀⢀⣯⣤⠶⠛⠁⣀⡾⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠿⠋⣿⠻⣦⣀⠉⠛⠶⠿⢦⣤⣤⠴⠶⠞⠛⠉⠀⣀⣤⠾⠋⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠺⣿⠀⠀⠉⠛⠶⢦⣤⣤⣀⣀⣀⣀⣤⡤⠶⠞⠋⠁⠀⣾⠋⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣦⣤⣀⣈⣉⣉⣀⣀⣠⣀⠀⠀⠀⠀⣿⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⢷⣤⣤⣤⣼⣷⣬⠟⠉⠉⠉⠉⠉⠀⠉⠻⢶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⢀⡴⠖⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣹⠖⠋⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢹⠏⠀⠀⠀⠘⠁⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢠⠏⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⣤⣄⣀⠀⠀⢠⡇⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠳⣄⡀⠉⠑⠚⠳⠤⣇⡀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⠻⣍⠓⠲⠤⣄⣀⡀⠙⢦⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣷⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣤⡄⠀⠀ ⠀⠘⣧⠀⠀⠀⠈⠓⠤⣄⣀⣀⣉⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣠⠞⢩⡾⠛⢁⣴⠿⣷⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⣠⠞⢁⣴⢿⡄ ⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢁⡼⠁ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢈⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⡾⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⡴⠛⣻⣠⠴⣄⣀⡴⠚⠙⣧⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠴⠛⠀⣰⠟⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣏⠉⠉⠉⠉⠉⠉⠉⣿⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠾⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠽⣿⣿⠀⣀⣤⠟⠀⠀⠀⠀⠀⢀⣀⡗⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠉⠉⠀⠀⠀⠀⠀⣐⣶⣟⣁⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞⠛⠯⡉⢻⡇⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠉⠙⠢⡈⢦⣿⡀⠀⠀⢾⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⣄⡀⣤⣄⡀⠀⠀⠀⣰⡯⠴⣒⣛⣓⣒⣦⢄⣼⠛⠉⠳⡀⠀⠈⢷⣷⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⠿⣄⠙⢦⣀⡾⠗⠋⠉⠉⠀⠀⠀⢉⡟⡁⠀⠀⠀⠁⠀⠀⠸⢿⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣈⡳⣄⠀⠈⠁⣈⢿⡗⠀⠀⢀⣀⣤⣤⣀⡞⠀⠈⠓⠶⠤⢤⡄⠀⠀⣸⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠉⠙⠳⢄⣸⡏⠙⣧⠀⢰⠏⣧⠆⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⣼⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⠀⣹⣿⣆⠘⣧⣼⠀⢸⣆⠀⠀⢀⣥⣠⣤⣰⣤⣤⢴⡞⣿⠁⠀⣰⠃⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠚⢧⡈⠑⠎⡻⡄⠈⢻⣽⡇⠀⠈⠻⠷⣶⠿⠟⠉⢰⠇⠀⣰⠃⢀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣶⣶⣶⣦⣭⢷⣦⣴⢻⣆⣹⣇⡠⠆⣤⠀⠀⠀⢀⣠⢄⡟⠀⣰⠃⢠⠎⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢲⢿⣽⣶⣤⣿⠙⡟⠉⣩⣽⠟⠛⢳⡶⠒⠛⠉⠀⢸⠇⢀⡇⢠⠏⢠⠏⣠⣄⡀⠀ ⠀⠀⠀⠀⢀⣠⣴⠶⠚⠛⠛⠛⠲⠦⣄⣇⠈⣯⣤⣶⣯⠁⠈⣿⠁⣀⡻⠟⢀⣠⠿⠀⠀⠀⠀⠀⢸⡀⢸⡇⣾⠀⡞⣾⡽⡌⢹⣦ ⠀⠀⣠⣴⠟⠉⠀⠀⠀⢀⣠⡤⣤⣤⣤⣻⡄⢘⠾⣏⢫⣤⣤⠟⠊⢀⣿⠛⠛⠁⠀⠘⠓⠲⢤⣄⠘⣧⠀⢇⠸⡄⠳⠾⠟⢁⣼⣿ ⠀⣴⡟⠁⠀⠀⠀⣠⠞⢉⡴⠋⢉⣽⡟⠛⠃⠈⠛⠉⠉⠻⣼⣆⣀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣧⣌⡳⢌⣓⣒⣲⢝⣵⠟ ⢰⣿⠀⠀⠀⠀⣰⠃⡴⢹⡇⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⣀⡤⠤⣍⡙⢷⡷⣄⣀⣀⣤⣴⣮⣤⠤⠴⠿⠋⠉⠙⠳⠶⠶⠿⠛⠁⠀ ⢸⣿⠀⠀⠀⠐⡇⠰⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠛⠓⢦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣯⣇⠀⠀⠀⢷⡀⠙⢄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣀⡴⠋⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣆⠀⠀⠀⠑⢤⣀⠙⠲⠤⣉⣓⠶⣤⣤⣤⣤⣤⣤⠿⠿⠿⠗⠚⠛⣉⣽⠿⢿⣿⢽⣓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣎⡳⢤⣀⡀⠀⠈⠙⣒⣲⣤⣶⠿⠛⣁⡤⠖⠋⠁⢀⣀⡤⠶⠛⠉⠁⠀⠀⠈⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣦⣌⣉⣉⣉⣩⣥⣖⣋⠥⠖⠊⠁⢀⣀⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠿⠾⠯⢭⣤⠤⠤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣰⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⠱⣌⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⠄⠀⠘⡇⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠈⢢⠀⠈⠳⣶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠶⠋⠀⡰⠃⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠑⣄⠀⠸⡇⠈⣳⣤⠤⠶⠶⠶⠤⣼⡋⠀⡿⠀⢀⠜⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⢀⣨⠷⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢧⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⣧⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠸⡇⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀ ⠀⠀⠀⢰⠧⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠓⠀⠀⠀⠀⠈⠋⠀⢀⣀⡀⠀⠀⠀⣀⠀⠀⢷⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⡞⡿⠀⣴⡞⣇⣄⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⣼⢹⠇⡼⣻⢁⡟⡿⠀⠀ ⠛⠒⠺⡇⠀⠀⠀⠀⢀⡀⢐⡦⠀⠀⢰⠀⠀⢠⣇⠀⠀⣶⠀⠀⠀⣖⣘⣇⢺⣴⠇⡏⣼⢡⠟⠒⠃ ⢠⡤⠴⢷⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠓⢶⠛⠙⢳⠖⠋⠀⠀⠀⠀⠉⠙⠷⣤⣌⣻⣵⠾⠤⣤⠀ ⠀⠀⣤⠼⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⣧⠟⠻⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⣽⠋⠙⠛⢻⠟⣿⡻⡏⠉⠉⡏⠉⢸⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⠞⠁⠀⣠⠏⠘⠛⠉⠻⢃⣠⣤⣷⡴⢾⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⡴⠯⣤⡤⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⢳⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣯⠞⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠿⣧⣤⠼⡇⠀⠀⠀⠀⠀⣀⣰⡬⠶⠻⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢧⣀⣀⣀⣀⣿⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢳⣄⢀⣴⠏⣰⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢦⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠣⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⠴⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠁⠃⠛⠛⠃⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⢹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⠶⠛⠛⠛⠛⠳⢶⣦⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⠉⠛⣷⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣿⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣀⣤⣴⠟⠀⠀⠸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⢷⣦⡀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⢀⣠⣴⠶⠾⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀ ⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠈⢿⣦⣄⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠈⠉⠛⠛⠛⢻⣟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠷⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠖⠊⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡟⢀⠎⠀⠀⡠⠒⠉⠙⠓⢬⣳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠚⠛⠳⢧⣀⡀⡎⠀⠀⡸⠁⠀⠀⠀⠀⠀⠑⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠓⠒⠒⠒⣒⣺⣿⣧⡀⢠⠗⠒⠻⣍⠉⠉⠓⢄⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⢰⣁⣀⣀⠬⣛⠾⠛⠛⠓⠃⠈⠙⠢⡀⠈⢳⣄⡀⠀⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡧⢤⡴⢪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠑⢽⢦⡀⠀⠀⠈⣄⡀⠀⠀ ⠀⠀⢰⣡⠏⡰⡹⢀⣤⣤⣤⣤⠄⠀⠀⠤⠤⠶⠾⠿⢍⣇⠙⢦⣀⣀⣩⠇⠀⠀ ⠀⠀⢸⡏⡸⢀⣿⣿⣷⣶⣤⠀⢃⠀⠀⠀⢠⣶⣿⠻⣷⢼⣆⠀⠈⡏⠁⠀⠀⠀ ⠀⠀⠘⡀⣧⡞⡟⢏⠸⣿⡟⢡⠸⠀⠀⠀⠌⢻⣟⡡⠜⠀⡏⢳⡄⠸⡀⠀⠀⠀ ⠀⠀⠀⢳⠃⡇⡇⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⣯⣢⣹⠖⠀⠀ ⠀⠀⠀⠀⠻⡧⣡⠀⠀⠀⠀⠀⠦⠄⠠⠴⠀⠀⠀⠀⠀⢸⠋⡠⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⡼⢧⠀⠀⠀⢀⣤⡴⢶⠶⡤⠀⠀⠀⣠⢏⡉⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠈⠳⣄⠀⠀⠀⠉⠉⠁⠀⠀⣀⡔⠁⠀⠈⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⢀⠜⠛⡲⠤⠤⠤⠤⠔⠊⡟⣩⠷⣤⡀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡇⠀⠀⠀⠀⠀⣴⡿⠒⠒⡄⠈⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠀⠀⢰⣟⣀⣀⠴⢧⠀⢸⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣹⠀⠀⠀⠀⠀⡼⠁⠀⢸⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡤⠖⠚⠉⢀⡏⠀⠀⠀⠀⢰⠃⢀⡠⠋⢢⠀⡜⠲⢤⣄⣀⠀⠀⠀ ⢀⡴⢛⣛⣥⡀⠀⠀⠀⣸⠀⠀⠀⠀⢠⣿⠊⠁⡗⠀⠀⡷⠑⣺⣋⠤⢬⢟⣳⣆ ⡎⠑⠼⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⢿⠇⢀⠞⢳⠀⡸⠁⠀⠀⠀⠀⠋⡹⡝⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⠤⠤⡞⢘⠖⢧⠀⠈⡖⠁⠀⠀⠀⠀⠀⠜⡟⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠿⠋⠁⣰⠃ ⠀⢸⠉⢿⡒⠒⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣡⠚⠁⠀⠀⣰⠇⠀ ⠀⠘⣇⠀⠙⠢⢄⣀⠀⠀⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢠⠞⠀⠀⠀⢀⣴⠃⠀⠀ ⠀⠀⠘⣄⠀⠀⠀⠀⠉⠑⢦⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡰⠃⠀⢀⡠⢶⡟⠁⠀⠀⠀ ⠀⠀⠀⠘⢦⣄⣀⠀⠀⠀⠀⢳⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠞⣀⠤⠚⢁⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠲⢬⣉⡉⠉⠙⠳⣄⡀⣧⠴⠒⠊⠙⠛⠉⠧⢤⡎⢀⣴⠟⠋⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⢤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠙⡆⠀⠀⠀⣠⠖⠋⠑⠢⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣻⣦⠀⢹⠀⠀⡴⢁⣾⣿⣆⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⣿⣿⣿⠀⢸⠀⠀⡇⢸⣿⣿⣿⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠙⠿⠋⠀⣾⣖⣲⡇⠀⠛⠿⠃⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠐⣇⠀⠈⢻⠋⠁⢀⡷⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⣦⡀⠀⠀⠀⠈⠑⡎⢹⠑⡶⠋⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠋⠈⠋⢩⠟⠁⠈⠙⠒⢢⣤⣆⠈⠙⠋⠀⣠⣤⠤⠖⠒⢺⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠈⠑⠒⠒⠋⢹⡄⠀⠀⠀⠀⢧⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠷⠒⠒⠦⢄⡞⠀⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠒⠋⠉⠀⠈⠹⡆⠀⠀⠀⠀⠀ ⢰⠋⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⢷⡀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢧⠀⠀⠀⢀⡞⠀⠀⠀⣰⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⠦⢄⣀⡀⠀⠀⣀⣙⣦⠀⠀⠘⣦⡀⠀⡼⠀⠀⠀⢸⡅⢀⣀⡤⠶⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠈⡇⠀⠀⢀⠹⣾⠁⡄⢀⠀⣸⠏⠉⠀⠀⠀⢄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣰⠃⣠⠆⠀⡰⠷⣀⣹⣨⡶⠛⠶⠧⠼⠞⠧⣄⣀⠀⠙⣆⣸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⠤⠚⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢠⣿⠀⠙⣦⣤⠀⠀⠠⠀⡄⠀⠀⣸⣧⠀⢤⡀⠀⠸⠳⡤⡀⠀⡀⣄⠈⠀⠀⠒⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⢘⣿⡤⠔⢠⠀⠀⠠⠀⠤⣄⠀⡴⡉⠉⠱⠼⠀⡆⣠⠀⠀⠀⠠⠐⠿⠰⡶⠤⠆⢰⠶⠘⢤⠄⠀⢀

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⡿⠷⡶⢦⣤⣀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⡐⠂⠒⠏⠙⠷⢦⡀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡄⢰⠀⠀⠘⣇⠀⠀⠀⠀⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣛⣿⣿⣿⣿⣶⣤⣘⣇⣘⣺⡹⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣆⣧⠀⠀⠸⡆⠀⠀⠀⠀⣾⠀⣿⠀⠀⠀⠀⢀⣠⣴⣾⣿⣭⡿⠿⠛⠛⠛⠛⣋⣛⡛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⠀⠀⠀⢱⠀⠀⠀⢀⡏⢠⠇⠀⣀⣤⣾⣟⠩⠿⠛⠉⠀⠀⠀⠀⢠⡤⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⢨⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⡀⣿⡇⢳⡀⠈⣇⠀⠀⢸⠀⢸⠶⠚⠉⠀⠈⠙⢿⣗⠶⠖⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢿⣦⣍⠛⠿⣿⣆⠀⠀⠀⠀⠀⠀ ⢻⡱⢸⣽⡇⠀⢧⡀⠸⡆⠀⡞⠀⡟⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣻⠂⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠈⢻⣧⡀⠀⠀⠀⠀ ⠀⢧⡀⢻⣇⠀⠈⠳⢄⣸⣼⠇⢰⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⠞⠁⠀⠀⢀⣠⠞⢉⣴⠟⠀⠀⠀⠀⠀⠀⠀⣿⢿⡻⣧⠀⠀⠹⡅⠀⠀⠀⢀ ⡄⠈⢣⠀⢿⣦⣤⣀⣠⠼⡿⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⢀⣠⠾⠋⣓⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣧⢻⣇⠀⠀⠹⡄⠀⠀⢸ ⣻⡀⠈⢧⠘⣟⣿⣹⣿⣾⡇⢠⡇⠀⢀⡾⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠘⢉⣠⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⣤⠄⠀⢰⣟⡇⢸⡀⢻⡄⠀⠀⢻⡄⠀⢸ ⠀⢣⠀⠈⣆⢹⣿⣿⠙⢾⠁⢸⠀⢠⡾⠀⠀⣠⣤⣤⣶⣚⣭⣤⣤⡤⠴⠒⣚⣭⢿⣿⠟⠁⠀⠀⠀⠀⠀⣠⡞⠁⠀⢠⣿⢹⠃⠀⣧⠘⣷⠀⠠⡄⢳⠀⣾ ⠦⣌⣷⠋⠙⣿⣿⡟⠀⡼⢀⣏⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣀⣡⡴⠋⠁⠀⠀⠀⢀⣠⣶⣿⠏⠀⠀⣰⣿⡇⢸⠀⠀⢻⠀⢹⡀⠀⢻⣜⡇⣹ ⣴⠛⠻⣶⡆⠙⣧⣷⣸⡇⢸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡿⠟⠋⠁⠀⣀⣠⡤⠶⠚⢋⣡⠟⠁⠀⣠⣾⢣⡟⠀⣼⠀⠀⢸⡆⠈⡇⠀⢸⡟⣿⣿ ⠛⢦⡀⡈⠛⠆⠈⣿⡿⠀⡾⠃⣀⡴⠀⠀⡇⠀⠀⠀⠀⢠⠙⢛⣿⠟⣿⣿⠟⠋⠁⠀⠀⣀⣤⢟⣁⣠⠴⠚⣱⣣⠟⠀⢰⢿⠀⠀⠘⠃⠀⡇⠀⠘⡇⠘⣿ ⣤⠾⠿⠥⠀⠀⠀⢨⡇⢠⡗⠚⣹⠀⠀⠀⣇⠀⠀⠀⠀⡾⠀⣾⢯⣾⠟⠁⠀⠀⣠⠴⠚⠉⠉⢹⠉⠀⠀⣴⣿⠋⠀⢠⡇⠈⡆⠀⠀⠀⠀⡇⠀⠀⢳⠀⣼ ⣯⣤⣤⣄⠀⠀⠀⣸⠀⢸⠀⢠⢿⠀⠀⢠⣿⠀⠀⠀⠀⡁⢠⣿⠟⠁⢀⣠⡖⠋⠁⠀⠀⠀⠀⡇⠀⢀⣼⠟⠁⠀⢠⡿⠀⠀⢧⠀⢀⠀⠀⡇⠀⠀⣿⢷⣿ ⠀⣿⣿⣿⣷⡖⠢⡟⢀⡏⣠⡾⡿⡄⠀⣸⣿⣆⠀⠀⠀⠀⢸⣁⡴⠖⠉⠈⠉⠙⠛⠶⢦⣀⣼⠀⠰⠋⠀⠀⠀⣰⠏⠀⠀⠀⢸⡄⣸⠀⠀⠀⠀⣸⣿⣮⣿ ⣌⢸⢿⣿⡀⠀⢸⡇⢸⠟⢻⣇⠁⣇⠀⡟⢻⡸⣆⡀⠀⠄⡟⠿⣶⠿⢶⣤⣤⣤⣀⣀⡤⢬⣧⠀⠀⠀⠀⢀⡼⡷⠛⠛⠋⠉⠉⢇⡏⠀⠀⠀⢀⢿⡁⠈⢿ ⡝⢿⣿⣿⣦⣀⡿⠀⡞⠀⣿⢻⠀⠸⣄⡇⠀⢧⣸⡿⣆⢰⣇⠀⠈⠛⠧⢼⣫⡯⠥⠽⠛⡼⠁⣠⠖⠀⣰⠏⢠⣿⣿⣤⣤⣤⣤⣽⠁⠀⠀⢀⣞⡏⠳⡀⢾ ⠐⣾⣿⣿⣿⣿⡇⢠⡇⠀⣿⠸⡄⠀⠹⡇⠀⠈⢷⣧⡈⠻⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠚⣡⣤⠞⢹⠀⠈⠛⠛⠿⠯⠿⢻⡇⠀⠀⢀⣾⡿⠀⠀⠹⣿ ⠀⣿⣿⣿⣿⣿⠁⢸⠀⢠⣿⡄⡇⠀⠀⠀⠀⠀⣽⡝⢷⣆⢸⡀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣠⣾⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣴⣿⡽⠀⣾⠓⠲⣿ ⠀⢸⡽⣿⣿⡟⢀⡏⠀⠀⢹⡇⠁⠀⠀⠀⠀⢠⣇⠉⠑⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⣼⢄⡴⢿⠁⡟⠃⠀⡇⠀⠀⣿ ⠀⠀⢣⢻⣿⠁⢸⠇⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗⠀⠀⠀⠀⠿⢷⡿⠁⠈⠣⣧⢸⣼⠁⠀⠀⢻ ⠀⠀⠈⠀⡿⠀⡞⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⢸⠏⢸⣿⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠸⠁⠀⠀⠀⢺ ⠀⠀⠀⢀⡇⢠⡇⠀⠀⠀⠀⠈⣧⠀⠀⢱⡀⢸⡀⢸⣿⡏⠙⣿⣄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣄⠀⢠⣸⠁⣼⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⣷⡘⡇⡼⠃⣷⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⡉⠀⠀⠀⢀⣴⣻⣿⣻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢻⣦⣸⡟⢀⡟⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⡞⢾⡀⠀⣿⡇⠀⠀⠻⣽⣦⡀⠀⠀⣠⡴⠻⠥⡄⠀⠛⢦⣤⣶⣿⣿⣿⡾⢷⣦⣤⣴⢶⠶⠿⠿⠛⠒⢻⣿ ⢸⡿⢿⣧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠸⣄⢹⡾⢿⣿⡀⠀⠀⠀⠻⣿⣷⣿⠁⣠⡴⠞⠛⣦⣠⣼⣿⠿⢿⣿⣿⣿⣟⢹⣢⣌⠳⣳⡄⠀⠀⠀⠀⡟ ⠟⡇⣸⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣘⢿⡀⠈⣇⠙⢦⠀⢆⠀⠻⣿⣿⡀⢿⣤⣴⣶⡿⠛⠋⠉⠙⠻⣿⣿⣿⣿⡀⠹⡿⣕⢹⣽⡀⠀⠀⠀⢸ ⢰⣳⣧⠏⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡿⠛⢒⣿⡀⠈⠳⢮⣧⠀⠙⣿⣷⣿⣿⠟⠁⠀⣤⡾⠤⢤⣄⠘⣿⣷⡏⢷⡀⠹⣎⠳⣕⡻⣤⣤⣄⣼ ⠟⠛⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡃⠀⠐⣿⣧⠀⠀⠀⠈⠓⠦⣤⣶⡾⠃⢀⣠⠞⠁⠀⠀⠀⠘⢷⡌⣿⣿⣄⠹⣆⢙⣦⡀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⠛⠭⠏⠐⠻⣿⡄⠀⠀⠀⠀⠀⠀⣼⢧⣠⠟⠁⠀⣠⡾⣠⣤⣀⡀⣻⡟⣿⣿⡄⠘⣟⣼⡿⠦⢤⡀⢼⣿ ⠀⠀⠓⢦⣞⠁⠀⠀⠀⠀⠀⠀⣠⡴⠋⢀⢏⡇⠀⡀⠉⠀⠀⣿⣿⡀⠀⠀⠀⣀⣼⣃⡼⣃⠀⣠⡾⠋⠀⠀⠀⠙⣿⣦⡀⢻⠘⣿⣦⣹⡯⠀⠀⠀⢹⠈⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠉⠉⠓⠒⠢⢤⣄⣀⠀⠀⢀⣴⣩⣴⡾⠛⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠹⢦⣤⣤⣴⣶⣿⣿⣿⣿⣶⣾⣿⣟⣿⣿⣿⣿⡿⠶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣻⣆⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⡶⣭⣛⢿⣿⣷⠀⣀⣴⣾⡿⠟⠛⠃⠀⠀⠀⠀⠀ ⣶⠶⣾⣿⣿⣷⣿⡿⠓⢲⣾⠟⣩⣾⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠿⠛⠛⠒⠂⠀⠀⠀⠀ ⢠⣾⣷⣾⣿⣿⣿⠀⣠⣾⣷⡞⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡀⢘⣿⣿⣷⣶⣦⣤⣾⠀⠀⠀⠀ ⣿⡟⢉⣾⣿⠟⠛⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⡿⠿⢿⣿⣿⣿⡉⠉⠛⣦⠀⠀⠀ ⣏⣠⡿⣿⣟⢠⣴⣼⣿⣿⣿⣾⣧⣿⠏⠀⠀⠙⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣦⠀⠘⡆⠀⠀ ⠁⠀⣰⡟⠉⣲⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⡇⠀⠀⠹⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣩⣤⣿⡈⣿⢿⣿⠇⠐⠁⠀⠀ ⠀⠰⠏⠀⣴⢟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⢻⣿⣿⠀⢻⣿⣿⣍⢙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⠀⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⠂⠀⠀⠀⠀ ⠀⠀⢰⡟⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⣸⠀⠸⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠁⠀⢀⣹⣧⠄⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⡏⠈⠉⠓⢒⣒⠂⠉⠀⠀⠀⠈⠉⣉⡉⠁⠈⢻⡄⠀⡿⢿⣿⣿⣿⣿⡿⠛⣉⠻⡅⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢿⢿⣿⡇⠀⠒⠒⠲⣶⡄⠈⠆⠀⠀⠀⠐⠛⠉⠻⠿⠋⠙⠒⣧⢸⣿⣿⣿⠋⣵⡯⠼⢧⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠎⢸⡿⢷⡀⣀⠀⠀⠈⣀⠴⢸⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⣀⠀⣿⣿⡿⠁⠀⣻⢙⡆⠀⣾⣦⣀⡀⠀⠀⠀⠀⠀⠀ ⠰⠂⠀⠀⠀⠀⠀⠀⠘⠃⠈⢷⡀⠉⠉⠉⠀⢀⠇⠀⠀⠀⠀⠀⠀⣩⣍⣙⣍⠤⠀⠿⠏⠀⢀⡴⠗⠉⠀⡔⠉⣽⣶⣿⡷⢦⣤⡀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⢠⣄⡀⠈⠁⣀⢴⠊⠀⠀⠙⠯⠧⠀⠀⠈⠻⠦⣄ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡆⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⣿⣿⣋⣑⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠰⠀⠀⠀⠀⠀⠀⣠⠞⢁⡔⠊⠑⣄⠀⠘⢻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠀⠘⣿⣏⣉⡙⢿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢆⠀⠀⠀⢀⠜⣹⡿⣿⠁⠀⠀⠈⠳⢄⡀⠙⠂⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠋⠇⠠⡀⠈⣿⣿⣿⣦⣿⣿⣿⣶⡔⢎⠂⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⢀⠏⡜⠜⠁⠉⠀⠀⠀⠀⣴⡗⠉⠒⢄⣀⢀⣀⣴⣾⣿⣿⡿⣷⠏⣼⠄⠀⢳⠀⠘⠏⣿⣟⣿⣿⠿⣿⡏⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠳⣗⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣻⡀⠀⠀⢁⡠⠊⢹⣿⣿⣿⣷⣼⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⣀⠀⠀⠀⠀⠀⣴⡟⡰⠀⣼⣿⣷⣿⠻⣿⣿⣿⣿⣿⣿⣧⢿⢻⠁⣠⡖⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣝⠦⣀⠀ ⠀⠀⠀⢸⠀⠀⣼⡇⡄⠀⠀⠀⡞⠘⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠹⡿⣿⢣⣧⡿⠋⠀⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡓ ⠀⠀⠀⡇⠀⠀⡿⠇⠁⣀⣤⠼⠖⣒⣲⣿⣿⣿⣿⣿⣿⣿⣿⠋⢷⢤⣤⣿⡽⠋⠀⠀⢠⡇⠀⣠⠎⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⠀ ⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢳⡧ ⣜⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣡⡾⣥ ⠙⣧⡈⠛⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣫⡵⠟⣉⣤⠏ ⠘⢷⣉⠓⠶⣤⣼⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣇⣤⠶⠚⢋⡵⠃ ⠀⠐⢭⣛⡳⠶⢼⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠯⠴⢖⣛⣽⠆⠀ ⠀⠀⠀⢯⣍⠛⠒⠚⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠓⠒⢛⣫⡽⠂⠀⠀ ⠀⠀⠀⠀⠩⣽⣛⡛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠋⠉⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣛⣯⠍⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠭⠭⠭⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⠭⠭⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣛⣻⣭⠉⡽⠟⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣼⡿⣧⡥⢸⡧⢉⣵⣿⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡻⢯⠉⣭⣟⣛⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣫⡶⢟⣴⠾⣛⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⢰⣿⣧⣭⡄⠶⣂⣙⣋⣿⣇⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣏⣛⠷⣦⡻⢿⣝⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⣴⠟⢡⡾⢛⣹⣿⣿⣿⣿⡠⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠆⣼⣿⣿⣿⣏⡛⢷⡌⠻⣦⣹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⣼⠟⣴⢟⣹⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣍⡻⣧⠹⣧⢹⣷⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⣼⡇⣻⣩⡿⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡏⢿⢸⣧⢹⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣏⢸⡏⣼⠔⡟⢸⡏⢻⣿⣰⡆⠀⣶⡎⢹⣿⡍⢹⣿⠉⣶⡆⢰⣶⡆⢰⣶⢸⡿⠹⣇⢻⠿⣧⢸⡇⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣇⣿⢸⡏⣼⢀⡘⠿⣿⡇⠀⣿⡇⢸⣿⡇⢸⣿⠀⣿⡇⢸⣿⡇⢸⣿⠸⢣⡄⣧⢸⣇⣿⢸⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠞⣧⣹⣿⣿⡀⣿⡇⢀⣿⡇⢸⣿⡇⢸⣿⠀⣿⡇⢸⣿⡇⢸⣿⢀⣾⢳⡟⣼⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠃⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⠀⣿⡇⢸⣿⡇⢸⣿⢸⠛⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣿⣿⣷⡶⠀⢀⣄⣿⡇⠘⣿⡇⢸⣿⡇⢸⣿⠀⣿⡇⢸⣿⡇⢸⣿⢸⣦⠀⢰⣶⡆⠀⠀⠀⠀⡀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠀⠀⢸⣿⢿⡇⠀⣿⡇⢸⣿⡇⢸⣿⠀⣿⡇⢸⣿⡇⢸⣿⢠⣿⠀⠀⠙⣿⡀⠠⣴⡶⡝⠌⠧⠓⢿⢸⣶⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠘⠁⠀⠀⠀⠀⠀⣻⣌⣓⡂⠛⣧⠼⣿⡇⢸⣿⢀⣿⠇⢼⠛⠃⢛⣉⣾⠃⠀⠀⠀⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈⢘⡵⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⡲⢿⠿⣟⠛⠻⠿⠟⠀⠀⠉⠹⠟⠀⠀⠀⠻⠷⠾⠛⣻⡿⠷⠖⠀⠀⠼⢿⣷⣤⠀⠀⠀⣠⣾⣿⣷⣶⡖⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠿⠿⠿⢿⡿⠸⣿⢸⣿⡿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⣿⡏⣧⣾⠇⢽⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠀⣰⣿⣇⡏⣾⢸⢹⡿⡇⣷⢻⣽⣿⣆⠀⠈⠁⠁⠈⠀⠼⢛⠛⢻⣿⠀⠀⠀⠙⠿⠿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣷⡇⣿⢸⡇⣿⢸⡼⣿⣿⣿⣆⠀⠀⠀⠀⢀⣪⠅⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣷⣿⣾⣧⣿⣼⣿⣿⣿⡿⠛⠀⠀⠀⢀⣯⠖⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠠⠶⠚⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⡀⠈⠹⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⠈⠓⣄⠈⢷⢀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠳⣄⢧⢣⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡼⠃⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠐⠬⢿⡎⣇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⢰⠇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⢧⠐⠢⣄⠀⢻⢹⡀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡟⠀⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠳⣼⡏⣇⠀⠀⠀⢀⣼⡿⢿⡀⠀⠀⠀⠀⠀⠀ ⠤⡄⠀⠀⠀⠀⠀⠀⢀⡟⣸⠀⠀⠀⢸⢁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣏⢳⣤⠄⠀⠀⠀⠀⠀⠀⢹⠐⠦⡀⠹⣇⢹⡀⢀⣴⡿⠋⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⡊⠁⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀⠀⠀⡎⢸⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⡇⢳⡄⠀⣀⣠⣾⠋⢇⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠈⠳⢿⢸⡇⣾⠉⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⣦⠀⠀⠀⠀⣿⠀⡏⠀⠀⠀⡇⢸⡷⢤⣀⣿⢸⡄⠀⠀⠀⠀⠀⠈⣇⣀⠹⣎⠉⠀⢸⠄⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⡈⠳⣄⢸⣼⡇⢻⣷⣤⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀ ⠙⠓⢦⡈⣧⠀⠀⢀⢾⠀⡇⠀⠀⠀⡇⠈⣧⠀⠈⢿⠛⢷⡒⠂⠀⠀⠈⠙⡏⠀⠀⢈⣷⣶⠟⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⣇⣇⠀⠈⣻⡿⣧⡀⠙⠻⣿⣛⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⢧⡀⠀⢸⢀⡇⠀⠀⢰⣇⠀⢹⣆⣤⣿⣤⣌⣳⡄⠀⠀⠀⢀⢳⠠⠾⠋⣵⠂⠛⢷⡄⠸⡏⣿⠏⠀⠀⠀⣀⣿⠉⣿⠚⠁⢀⡀⠙⣆⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢾⠰⣿⠀⠀⠈⢼⡀⢸⣿⡿⢅⡶⠸⣍⠙⢷⣄⠀⠨⢿⡄⠀⠀⣇⣠⣤⣨⣿⠀⣷⠟⠀⠀⠀⢸⡏⡇⠀⡿⠀⢠⢞⣇⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⠀⠸⡄⣿⡀⠀⠀⠘⣇⠸⣿⣇⢸⠁⣤⣽⡆⠀⠉⠳⣄⠋⡇⠀⠀⢿⣄⢉⣸⡿⠀⢹⠀⠀⠀⠀⣺⢿⢃⡼⠁⢠⡟⢫⡅⢠⠞⠁⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⣧⣇⣷⣀⠀⠀⠸⣆⠹⡈⠸⣦⠉⣼⠇⠀⠀⠀⠈⠛⢺⠆⠀⠀⠙⠛⠋⠀⠀⠘⡇⠀⠀⢰⣿⡟⠀⠀⠀⣈⣷⡟⢀⡞⠀⠀⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣶⣿⣿⣇⠀⠀⠹⣿⠘⣾⣆⠀⠀⠙⣦⣻⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣿⡇⠁⠐⠋⠉⠉⠁⢀⡸⠁⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠟⠋⠀⣿⡏⠉⠁⠀⠀⠀⠹⡄⠙⣞⢆⠀⠠⣿⣟⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡞⠘⠀⠀⣦⣀⣠⣤⣶⣏⠉⠀⠀⠀⢸⡇⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠿⠀⢀⡀⠀⠀⠀⠀⠛⠀⠘⢿⡷⣄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⠋⠀⠀⠀⣰⠃⣸⣿⣿⣿⢸⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠋⣡⣴⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠙⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠀⠀⢀⡼⠁⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⣿⣜⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠋⢀⣿⣥⣤⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⣿⣿⣿⣇⢸⢀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠸⡿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠑⢦⣀⠀⣀⣤⣶⣤⠴⠶⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷⢸⣼⡄⠀⠀⠀⢸⣾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡤⢜⡛⣽⠯⣏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⡏⢇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠤⣤⣜⣁⡧⠔⠛⣉⡥⠖⠛⡇⠘⡄⠈⣿⣦⣤⣀⣀⣤⣴⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣷⣸⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡵⠋⠉⠉⠉⣉⣩⠷⢶⡏⠀⠀⠀⠀⢹⢰⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠈⠉⠓⢷⡀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢶⡟⠁⣰⠞⠋⢉⣁⠤⠔⣻⠟⠀⠀⠀⠀⠸⡄⣧⣇⠘⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠠⡄⠀⠀⠀⠙⢦⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⠏⠠⠞⠁⡠⠒⠉⣀⠔⠊⠁⠀⢀⣠⡤⠴⠒⠛⢻⣿⣦⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠈⢧⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢰⠋⣹⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣻⠀⠀⢀⡠⠞⡱⠋⠀⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⢇⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⢠⡇⠀⠀⡾⠀⠀⠀⠀⠀⡄⠀⠛⣆⡴⠋⢠⠞⠀⢀⣀⡼⠀⠀⠀⠀⣀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠸⡆⠀⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⣼⡁⠀⣸⠁⠳⢄⠀⠀⢠⡇⠀⣠⠏⠀⡰⠃⠀⠀⠀⢿⡁⢠⠖⠊⠉⠁⢸⠀⠀⠀⠀⠀⢀⣠⠶⠒⠊⠓⠦⣄⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣸⡟⣇⢠⡏⠀⠀⠈⠳⣄⢸⢧⠞⠁⢀⡼⢧⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠤⣿⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠸⡇⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⡇⠀⠀⠰⢋⡿⢿⣾⠁⠀⠀⠀⠀⠈⣿⠋⠀⢠⠎⠀⠈⠳⣤⣄⣀⣀⣤⠔⠚⠉⠀⠀⣿⢠⠔⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣇⠀⡀⠘⡆⠀ ⠀⠀⠀⠀⠀⣼⣷⣷⡇⠀⠀⣀⠞⣡⣾⡇⡇⠀⠀⠀⢀⡞⠁⠀⣰⠋⠀⠀⠀⠀⠀⠉⣉⠁⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢸⠀⢹⠀⢳⠀ ⠀⠀⠀⠀⠀⣏⠙⠻⢧⣠⠞⢁⡼⢃⣿⠁⣇⠀⠀⣠⠏⠀⠀⡴⠃⠀⠀⠀⡀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢸⠀⠈⡆⢸⡇ ⠀⠀⠀⠀⢀⣯⠙⠦⡄⠀⠠⠚⠀⠀⠙⡆⢻⢀⡾⠡⠐⠒⠺⠧⢤⣤⣄⣀⣃⣋⣀⣀⣀⣤⣤⣤⣤⣤⣤⠃⣿⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⣼⠀⠀⣷⠀⡇ ⠀⠀⠀⢠⠛⠻⣄⣀⡀⠀⠀⣀⡤⠀⢸⠁⠘⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⢱⣿⢀⠀⣿⠀⢰ ⠀⠀⠀⠀⣷⣀⣀⣀⡴⠒⢋⠁⠀⠀⢈⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡞⢸⢸⠀⣿⢠⠈

⠈⠉⠒⠒⡲⠂⠀⠀⣠⠶⢲⡶⢋⠀⡠⠀⢫⢂⠲⡄⠠⡀⠐⡄⢀⠀⠠⡄⠀⡐⣄⢀⠤⣀⠈⠳⠦⣄⣀⡀⠀⠀ ⠀⠀⢀⡜⣡⣴⣶⠎⠀⣴⠋⡠⢃⡔⠁⠀⠀⢻⠄⠹⣤⡈⢢⡈⠂⠳⡄⠈⢢⡀⠈⠺⡦⡈⠑⠢⣀⡈⠐⠀⠠⠄ ⠀⠐⠉⠁⣰⠟⠁⣠⡞⢁⡼⢡⡟⣰⢠⠀⡤⠀⠀⠀⠈⠙⡄⠑⢄⠀⠈⠢⠀⠈⢢⠀⠸⡮⢲⣄⠒⣤⡤⠤⠖⠁ ⠀⠀⠀⠞⢋⠴⢿⡿⢣⠃⢃⡎⣵⣿⢸⣰⡇⢠⡀⢷⣲⣄⢹⡄⠣⡈⣦⠀⢧⡀⠀⡳⣄⠱⣄⢹⣇⠘⡝⠂⠀⠀ ⠀⠀⢀⠞⠁⠀⣾⠕⢩⢃⣾⢠⣿⣿⣜⣿⣿⡀⣷⠸⣿⣿⣧⣹⣄⢻⣮⢧⠈⢷⢄⠽⣾⣷⢿⣦⣻⡷⣜⣆⠀⠀ ⠀⠀⠈⠀⠀⣸⠋⣠⢏⣾⡇⢸⡏⢹⣿⣶⡿⣷⢸⣧⣿⣽⣿⣿⣿⡶⣿⣿⣷⡈⢺⣾⣻⣮⢻⠈⣿⡓⠄⠈⠂⠀ ⠀⠀⠀⠀⠀⠃⠀⡏⢸⢸⢹⣗⠹⣄⠻⠿⠇⠹⠻⡇⠛⠉⢿⣿⠿⠁⣠⠋⢸⣿⣶⢙⣟⡳⡸⢀⡿⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠘⢸⢸⢻⡄⠈⡓⠒⢀⠄⠀⠁⠀⢘⣶⣤⡔⠚⠁⢀⠠⣷⣿⣶⢤⣾⡶⣏⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢷⡴⠀⠀⢯⠀⠀⠀⠀⠐⢿⠋⠁⠀⠀⠀⣥⢾⣀⣠⣾⠋⠁⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⢤⣄⡀⠀⠀⠈⡇⠰⣠⠔⣹⣿⣿⣿⡸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠈⠀⠀⢀⣼⡷⣋⣤⣾⣿⣿⡏⠁⠧⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠈⢓⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⢰⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀⠔⠁⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢠⣿⣿⣿⣿⣿⣿⠟⠋⠀⣠⣤⠔⢀⡔⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡝⠁⣾⣿⣿⣿⡿⠋⠁⠀⠀⠛⠋⠀⡀⣩⠤⠀⠀⠀⢀⠠⠐⠒⠻⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡜⢀⡄⣿⣿⡟⠉⠀⢠⣤⠄⠀⠀⠀⠛⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡝⠀⢸⡇⠙⠋⠀⠀⠀⠀⠁⠀⠈⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀

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⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⡇⠀⢰⢰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢏⠉⠁⠀⠀⠀⠀ ⠀⠀⢰⠀⡇⢀⠀⠡⣧⡀⠀⣧⠀⠀⡀⠇⠀⠀⠀⡆⠀⢀⠀⠀⠀ ⠀⠀⠘⠐⣷⢸⡀⠀⠀⡉⠀⣇⡱⠁⡀⢻⠀⠀⠀⢱⠈⠁⠀⠀⠀ ⠀⠀⡌⡰⠊⢋⣧⡀⠀⢧⠀⡇⢀⠈⠢⣸⠀⠀⠀⢸⠀⠀⣀⠄⠀ ⠀⠀⡗⣡⣶⣼⡟⠕⢄⣘⣂⡽⣿⣿⣿⣮⣤⡀⢠⢸⠀⠉⢸⠀⠀ ⠀⠸⡿⠍⠷⠿⡵⠀⠀⠀⠀⠀⢸⡙⣭⣛⠋⠀⡀⢸⢣⠀⢸⠀⠀ ⠀⠀⡏⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⢼⠀⢠⠃⢸⡸⠀⠂⠀⠀ ⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⡟⠁⢠⠀⡄⠀ ⠀⠀⢃⠀⡅⠂⠄⡀⠀⠀⠀⢀⠀⠀⢐⠇⠈⠀⢀⠃⢠⠀⣴⣇⠂ ⠀⠀⢸⠀⣇⠀⠀⠀⡩⢙⡏⠀⠀⣀⣌⠀⠀⡰⣘⣰⠏⠷⠿⡁⠀ ⠘⠄⠀⢇⠏⠴⢊⢋⡔⠁⡀⠀⠀⣠⡂⠄⠊⢘⠡⢊⠂⢄⠐⠀⠑ ⠀⠈⡲⢤⠵⠥⠁⡮⠐⠠⢈⢢⡍⡲⡀⠀⡀⠀⠴⠁⠀⠀⠡⠀⠀ ⠀⠈⠀⠈⡢⠀⢠⠀⠀⠀⠀⠙⠃⠀⠈⠪⠠⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠚⣿⠉⢫⡉⠉⠙⢯⠳⡶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢖⡾⣻⠋⠀⠀⣰⠋⢧⠀⣷⡀⠀⠈⢧⠹⣤⡀⠉⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠞⢁⡴⠋⢠⠇⠀⠀⣰⠋⠀⠈⣦⡇⠹⡀⠀⢹⣷⣧⠳⡄⠀⢸⡎⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠴⢋⣽⡏⢠⠞⠀⠀⣼⠀⢀⠞⠁⠀⠀⢀⡿⠁⠀⡇⠀⣼⢸⡟⠀⠘⡄⢰⢃⡇⠈⣦⢄⡀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⣠⠏⢸⣦⣏⣀⣤⣤⣽⣤⠏⠀⠀⠀⢀⡼⠁⠀⢠⣇⡴⠃⢘⣀⣀⣀⣷⠏⢸⠁⣀⣿⠂⠉⠂⠀⠀⠀⠀ ⠀⢾⡇⣸⠃⠀⣸⣿⠛⠉⠉⠀⠉⠿⠀⠀⠀⠀⠘⠁⠀⠀⣾⡟⠀⠀⠛⠉⠉⠙⡿⢆⣰⣼⢩⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⡇⠀⠀⠁⠘⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⣀⠀⠀⠈⠙⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⠇⠀⠀⠀⣠⢴⣿⣿⡻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣇⡀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢘⠆⠀⠀⡞⠁⡼⢿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣻⢿⣿⣷⡽⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⢀⡞⠃⠀⠰⢾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⣿⡿⠁⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣟⣺⣿⠀⠀⠀⠉⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⣅⡀⠀⣰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣹⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣷⠟⣆⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⠀⠈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡴⠚⠂⠒⠒⠢⠤⣀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⡿⢶⣦⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣬⠉⠛⠓⠲⠤⢭⡑⠒⢒⣩⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠶⠤⣄⣀⠀⠀⠘⣦⠞⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⡀⠀⠀⠈⠉⠉⠉⠉⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣾⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢆⠀⠀⠀⠀⠀⣀⠤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢢⡀⢀⠔⠊⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠒⠤⠼⠀⠀⠀⠙⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣤⣚⣉⣉⡉⠛⠲⣄⠀⠓⠂⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠃⣼⣛⠉⠉⠙⠻⢷⣦⡈⢳⡀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣠⡞⠉⠉⠙⣆⡀⠐⠢⢭⡁⠀⡇⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⣆⡀⢠⣤⢿⡁⠀⠀⠀⡿⠀⡿⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⠛⠛⢫⢇⡄⣙⡺⢶⡖⠁⢰⠁⢠⠄⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⠀⠘⠋⠀⠀⠉⠉⠀⠀⣮⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡯⠑⠲⠤⠤⢴⣲⡆⠀⣼⠟⠁⡖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⣀⡀⠀⢀⢀⣴⣹⠉⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⡿⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢉⣽⡋⢡⠀⡄⣄⣿⣶⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢈⠔⠁ ⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⢴⠿⢿⣭⣼⣴⣷⡿⠛⠉⠀⠐⠚⡿⠻⠏⠓⣦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⢀⡠⠤⠬⠶⠆ ⠀⠀⠀⠀⠀⡠⠊⢀⡴⠁⠀⠳⣾⣿⣿⣿⠋⠀⠀⡄⠀⠀⠘⡄⠀⠀⠀⣸⣧⠀⠀⢀⣠⠖⠋⢁⣀⠤⠐⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡜⢁⡴⠋⠀⠀⣠⣾⣿⣿⣿⠇⠀⠀⣰⡷⡖⠲⢄⠈⢲⠐⠚⠁⠘⡟⠛⢿⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢎⡴⠋⠀⠀⣀⣼⠟⠁⣸⣿⣿⠀⠀⠘⡟⠀⠀⠀⠈⣧⠀⠽⠃⣠⡄⢹⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡿⠋⠀⠀⣠⠞⢹⠁⠀⠀⣿⣿⣿⡀⠀⠀⠘⢄⣀⣀⡴⠃⠀⣤⣾⠟⠁⣸⠋⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⣠⠞⠁⠀⢸⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⢠⠏⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠖⠋⠁⠀⠀⠀⡌⠀⠀⠀⢹⠹⣿⠿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣸⠀⠈⠛⢦⡖⠶⠤⠤⣤⡴⠚⠉⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡇⠀⠀⢠⠎⠀⠀⣰⣶⣃⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣠⣏⣀⣀⣴⣿⣿⣿⣷⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣇⣀⣀⡟⠉⣿⠋⠁⠀⢘⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⡏⠀⣸⣿⣦⣀⡀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⢘⣿⣿⡿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡿⠿⠛⠋⠛⠙⠿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠞⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠀⠀⠀⠐⠒⠤⢤⣀⠀⠀⠘⡆⠀⠀⡇⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣘⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣀⡀⠈⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠈⠁⠒⠉⠙⠷⡤⠤⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣧⠞⠉⠈⡟⠙⠒⠢⢄⣀⠀⠀⣀⠀⣷⡖⠉⢁⣀⣀⣀⡀⠀⠈⠉⠓⠤⡀⠈⠣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⢠⡇⠀⢀⡞⠁⠀⠀⠀⠀⠈⠉⠉⢁⡼⠀⠛⠋⠁⠀⠀⢀⠈⠙⠦⡄⠀⠀⠈⠀⠀⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣼⡇⠀⠀⠻⠒⠶⠤⠤⣤⡤⠤⠒⠉⠀⠀⠀⢀⠀⠀⠀⠈⠀⢠⠃⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡷⢄⠀⢀⣠⡤⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠀⠀⢀⡞⠀⠀⢸⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⣴⠟⠃⠀⠀⠉⣷⡀⠀⠀⠀⠀⢠⣴⡞⢻⣧⠀⢀⡞⠀⠀⠀⡄⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠠⠹⡀⠀⠀⠀⠀⠀⠀⢰⣦⣬⣿⡿⠛⣷⣄⠀⠀⠀⢺⡇⠀⠀⠀⢠⣿⡅⠀⠘⣿⣶⣮⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⡄⢳⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣤⣿⣟⣧⠀⠀⢸⠇⠀⠀⠀⣞⣽⣿⡆⣐⣾⣿⠛⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⢰⠐⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡇⠚⠹⢿⣿⣻⠀⠀⡞⠀⠀⠀⣰⣿⣿⠿⠁⠺⠟⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⢱⠀⠳⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢃⠀⢣⡀⠘⢆⠀⠀⠀⠀⠀⠘⡟⠦⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢸⡀⠀⢣⠀⠈⢦⠀⠀⠀⠀⠀⡇⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠠⠴⠋⠀⣀⠔⠋⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢸⡇⠀⠀⢧⠀⠀⢧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠻⡍⢿⣛⠒⢤⣠⠔⠋⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⢹⠀⠀⠘⡆⠀⠈⢇⠀⠀⠀⢸⡈⠓⣄⠀⠀⠀⠱⡀⢙⠢⠀⠙⡄⠀⣠⠎⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠀⢀⡇⢸⠀⠀⠀⢱⠀⠀⠸⡀⠀⠀⢸⠳⡀⠘⡆⢀⠀⠀⠱⢌⠀⠡⠀⠹⡴⠃⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠸⠀⢸⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⢸⠀⢷⠀⢹⠈⣇⠀⠁⠀⠁⠀⠣⣄⣧⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠘⡆⠈⡇⠈⠑⠂⢄⠈⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⡤⠎⠀⠀⢀⡞⠀⠀⠀⢰⠃⠀⢰⠁⡆⠀⠳⠀⡇⠙⠀⠒⠒⠻⢦⡀⢀⡀⠘⠀⠀⠀⠀⡴⠻⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢀⡎⠀⢠⠇⠀⡅⠀⠃⢸⡇⠀⠀⠀⠀⠀⠀⢷⡖⠃⠀⠀⠀⢠⠞⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣄⣀⡠⠖⠁⠀⠀⠀⢀⠞⢀⡴⠋⠀⠠⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣗⠒⠲⠦⠴⠮⠥⠖⠉⠀⠀⠀⠀⠀⢀⡤⠟⠲⢤⣀⣀⣀⡀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢿⡿⡟⡹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡧⢀⣰⣧⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠙⠛⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⣾⣿⣿⣿⡿⠿⣿⡇⠰⠊⠉⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⢻⣿⣿⣿⠷⣶⠈⠇⢀⠀⠀⠀⠀⠲⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⢸⣿⣿⡟⠘⣿⣇⢰⠀⠙⣾⠳⢶⣤⣀⡈⢿⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⢎⡉⠉⠑⠢⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⣀⣼⣿⣿⡇⢼⠁⣿⢾⠀⠀⠈⠓⠤⠛⣛⣻⣄⡙⢧⠀⠀⠀⢰⣾⠿⣋⣡⣤⣄⣀⣀⣠⣤⡤⠄⢠⠟⣡⣤⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⠙⣿⣿⣿⣜⢦⣹⣮⠀⠀⡀⠀⣴⠀⠀⠈⠉⠁⢸⡆⠀⠀⠈⠀⠻⢿⡭⠽⠿⠉⣤⠶⠋⠀⠀⣾⣾⡿⠎⣸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣆⠹⢾⡇⠀⢹⣿⣿⣦⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣸⡿⠀⣧⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣹⣷⠀⠼⠛⢻⡇⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⢠⠟⣡⠖⣡⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡇⠀⢠⣿⠞⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢠⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣆⠀⠀⢆⠀⠀⠀⠀⠳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡇⠈⢷⡄⠀⢙⡒⠲⠶⠦⠴⠤⠤⠤⠤⠤⠚⠁⠀⣠⠞⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⠘⣧⠀⠈⣿⣆⠀⠙⢦⡤⢤⣄⣀⣠⠴⠂⠀⢀⣤⡞⠁⢠⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⣿⣿⣿⣿⣿⡟⠁⠀⡾⣿⡄⠙⣷⣄⠸⣿⣦⠀⠀⠉⠙⠛⠋⠁⠀⢀⣴⠟⡿⠁⣠⡿⠋⢠⣿⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠟⠛⠉⠉⢀⡤⠋⠀⠀⢰⣧⠘⢿⣦⠈⣿⣿⣷⣿⣧⠀⠀⠀⠀⠀⢀⡴⠋⢠⣾⣶⡿⠋⣀⣴⡟⣸⠃⠀⠈⢿⣝⠛⠿⠿⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣾⣿⣆⠀⠛⢷⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣿⣷⣿⣿⣿⣿⣧⣿⡿⠛⣠⣿⡄⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣄⣸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠁⣠⣰⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠊⠻⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣷⣶⡿⠟⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⡠⣤⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡟⢋⠁⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣟⣣⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⡀⠐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣭⣉⣛⠛⠿⠛⢳⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠀⠀⠈⠉⠲⣄⠀⠀⠀⣠⠴⠒⠒⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⢣⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠚⣭⡄⠀⠀⠀⢀⣤⣤⡞⡟⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⣷⠀⠀⠀⠛⠙⣿⣸⠁⢶⣄⠀⠀⠀⠀⠈⠓⠒⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠋⠀⠀⢀⡴⢚⠟⢸⠀⡍⡿⠃⠀⠀⣀⣀⣀⣀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠰⠿⠿⠥⠖⠁⠀⡼⢇⠈⠣⣀⠀⠀⠉⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠓⠤⣀⣀⣀⣠⠴⠚⣀⣀⣳⠤⠤⣉⠉⠁⢀⡠⠞⠉⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠞⠋⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠘⢦⡀⠀⠀⠀⠀⠈⠳⣼⣿⣭⣭⣶⢞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠊⠁⠉⢲⣄⠀⠀⠘⣆⠀⠀⠈⠑⠂⠤⢄⠀⠀⠘⣿⠍⠉⠀⠀⠉⢦⡀⠀⠀⠀⣀⠤⠄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠈⢆⠑⣄⠀⢸⠓⠦⢄⣀⠀⠀⠀⢧⠀⠀⠈⢷⠦⣄⠀⠀⢀⣧⠴⠒⠉⠀⠀⠀⠀⠀⢀⣘⣄⠀⠀⠀⠀⠀⠀ ⢼⠀⠀⠀⠀⠀⠈⡇⠈⢢⡜⠀⠀⠀⢩⠉⠐⠒⠸⢷⡄⣤⣼⣷⠏⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠈⢱⣦⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢡⠀⢀⠇⠀⠀⠱⣼⠀⠀⠀⠀⠀⢻⣿⠿⡿⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⢷⡄⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⣏⡹⣦⣤⣄⣀⠀⠀⣇⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠈⡆⠀⠀⠀⠀⠀⢸⠀⠈⣆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⠉⠳⣦⣼⡀⠀⠀⠀⠀⠀⢸⡘⡄ ⠀⢡⠀⠀⠀⠀⠀⢸⠀⠀⠈⢆⠀⠀⠀⢸⠀⠀⠀⣀⣀⠀⢀⣧⠤⠤⠤⣿⣆⠀⠀⠀⠀⠀⠀⠈⠳⣧⠀⠀⠀⠀⠀⠀⢧⡁ ⠀⠈⡆⠀⠀⠀⠀⢸⠀⠀⠀⠈⢆⠀⠀⠈⡇⠀⠀⢀⡴⠋⠈⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⢰⠀⠀⠀⠀⢸⢦⡀⠀⠀⠈⡷⠀⠀⣣⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠙⢄⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠇ ⠀⠀⣠⠇⠀⠀⠀⢸⠀⠉⠲⠤⣼⡥⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠸ ⣠⠚⠁⠀⣀⡤⠔⠚⠉⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⣘⡄⠀⠀⠀⠀ ⠉⠉⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀ ⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠈⠁⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣣⠞⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⡿⠟⠒⠂ ⠀⠉⠙⠻⢿⣟⠛⠛⠿⠯⢭⣍⣉⠉⠙⠛⠒⠦⢤⣀⡀⣠⣿⣽⣟⣁⣼⣁⣀⠀⠀⠀⣀⣀⣤⠶⠞⠛⣩⡽⠟⠉⢁⡴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠓⠦⣄⡀⣠⣾⣿⣿⣿⣏⠁⠀⢹⣿⣿⣿⣿⣿⣯⣀⠀⢀⡴⠛⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢲⡀⠀⠀⠀⢈⡿⣫⣿⣿⠿⠛⠁⠀⠀⠀⠉⠛⠿⣿⣯⡁⠙⣶⠏⠀⠀⡖⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⠲⠤⣴⠋⢰⡿⢋⣥⢶⡖⠀⠀⠀⠀⢠⣤⣄⠈⠻⣧⠀⠈⣧⠀⣰⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣀⣠⡏⠀⠉⢠⠟⠁⠀⢳⠀⠀⠀⠀⡾⠁⠈⠳⡄⠙⠀⠀⢸⣛⣡⣴⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠟⠃⠀⠀⠀⠀⠙⠛⢶⣶⣶⣾⣷⠀⠀⢼⣷⣶⡶⠖⣿⠶⠚⠛⠉⠉⢉⣹⡿⣿⡖⠒⠊⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠲⢦⣄⣀⡀⠀⠀⠀⠀⠙⢧⡀⣿⢀⣀⣸⡇⠀⣠⠞⠁⣀⣤⠴⠚⣋⣩⣥⣤⣤⡿⢷⡤⠶⠒⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣼⣧⣤⣶⡶⠊⣹⣯⣉⣛⠒⠶⠤⣄⣀⣻⢿⣯⣽⡿⢿⣾⣵⣾⡯⠿⠒⠛⢉⣩⠴⠲⡟⠻⡛⣿⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⢻⠏⢸⠀⡼⠁⠀⣹⠛⠿⠭⠽⠷⠿⡿⠀⠉⡏⠀⠀⠹⡯⠤⠤⠤⠒⠛⠉⠿⢄⠀⢸⠀⡇⢸⠻⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⠸⣤⣬⣷⣧⣀⣀⣉⣧⠤⠄⠀⠀⢸⡁⠀⠀⢧⠀⠀⢸⠁⠠⣀⣀⢀⣀⣀⡤⠤⣶⣿⣤⠧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡄⠈⠁⠀⢹⣠⣄⠀⠀⠀⢧⠀⢖⠚⠒⠀⣏⡴⡄⠀⠀⠀⡟⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢸⠇⠸⣾⠛⣶⠾⣦⣀⣉⣀⣠⡟⠀⢹⡶⣦⣼⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⠀⠀⠿⠀⠛⠀⠹⣮⣉⡭⢿⡇⠀⠘⠃⢿⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣸⠃⠀⠀⠀⠀⠘⣷⣄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠇⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠹⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠠⠤⠤⠤⠤⢤⠤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⠀⠀⢀⡠⠖⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠈⠉⠓⠒⠒⠒⠒⠒⠒⠚⠋⢉⠄⠒⠁⠀⣀⠀⡄⠂⠀⠁⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠁⠀⠀⠀⠀⠀⠀⠈⠓⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⢸⢇⡴⡆⠀⠀⠀⠀⢸⠗⠞⠛⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢺⣍⡀⠀⠀⠙⢢⡀⠀ ⠀⠀⠀⢀⡠⠖⠋⠀⠀⠰⠗⠉⠀⢹⡀⡴⠛⠳⣼⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣠⠴⠚⠉⠀⠀⠀⠈⢳⣀⣴⠶⠞⠃⠀ ⢀⡤⠖⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⣄⣨⣽⣦⣤⣶⠛⡆⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀ ⠈⠀⠀⣴⡟⠙⣧⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⡿⠿⠿⡝⣮⡟⠻⠿⢿⣖⣶⢤⣄⡀⠀⠀⠀⠀⠀ ⠀⢀⡟⢻⡇⠀⠙⠁⠙⢷⣄⠀⠀⠀⠀⡴⢶⣦⣤⢖⡿⠟⠋⠉⠀⠀⠀⠀⣇⠁⣧⠀⠀⠀⠀⠉⠙⠲⣍⢳⣶⣤⡄⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠻⣾⢿⡇⢻⠀⠀⣀⣠⡤⠴⠒⠛⡿⣿⠿⢿⣻⡲⠦⣄⣀⠀⢸⠈⣿⣶⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢷⣀⣰⣿⡟⣧⠼⠛⠉⠁⠀⠀⠀⠀⣾⣿⡇⣷⠀⣷⣷⠀⠀⠈⠙⠛⢦⣹⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢸⡷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⣝⣺⣞⠵⡿⠀⠀⠀⠀⠀⠀⢾⣷⡦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⡇⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣴⣚⣁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⢠⣿⠹⣀⡤⠞⠀⢸⠀⣀⣤⣀⠀⠀⠀⠀⣼⠉⠉⠉⠉⠉⠉⢱⡀⠀⠀⠀⢠⣤⣷⡀⠀ ⠀⠀⠀⢀⣠⡴⠛⣿⠤⠖⢚⣉⣿⠀⠀⠀⠀⠀⣼⣟⣛⣿⢸⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣭⣿⠀ ⢀⣤⠖⣯⣤⣷⣶⣿⢸⣡⣿⣿⣿⠀⠀⠀⠀⠀⢹⡿⠟⢛⣁⣀⣀⣀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇⢀⡤⠤⠴⠾⣿⠋⠀ ⠈⡏⠀⡿⣏⣗⣿⢿⡬⠥⠽⠶⢾⣀⣠⡤⠴⠒⢻⡏⠉⠉⠁⠀⠀⠈⠑⢞⣆⠀⠀⠀⠀⠀⣸⡷⠃⠀⠀⠀⠀⢸⡄⠀ ⢴⣷⣆⣧⣀⡇⠀⢸⡿⠿⠷⠄⢺⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡷⡀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢸⡇⠀ ⠐⠳⠿⣟⡛⠿⣿⣞⡷⠤⢭⣁⣸⣇⣀⣀⣀⣀⠀⣇⣀⣀⣠⣤⡤⠤⠤⠤⢤⠽⣷⣤⣴⣿⣥⡤⠴⠶⠴⠶⠶⢼⡇⠀ ⠀⠀⠀⠀⠉⠳⢄⡉⠙⠳⢦⣄⡈⠹⡟⣟⣿⣯⣿⡏⠁⠀⣶⣶⣶⣶⣴⣾⠉⠉⠉⠉⠉⠉⠉⣻⣶⣶⣶⣶⣶⠚⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢓⠦⣄⡈⠛⠷⣿⣻⣟⣿⣾⣇⠀⠀⠘⠛⠛⠛⠛⢻⠛⠛⢻⡟⣿⣟⠛⢻⡏⠉⠉⠉⠉⠀⣿⠀ ⠀⠀⠷⠗⠀⣠⣤⣾⠙⠲⡄⠉⠢⣄⡈⠙⠿⣿⢻⡟⣦⣀⣀⣀⣀⣀⣀⣸⣆⣀⣸⣷⣿⣿⣀⣸⣧⣤⣤⠤⠴⠖⡿⠀ ⠀⠀⠀⢀⡞⣿⠁⢸⣹⣤⠿⠀⠀⠀⠉⢦⠀⠈⠙⢧⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⣾⠵⠿⣤⣿⢻⡏⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀ ⠀⠀⠀⠉⠀⣠⡿⢽⠿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⠀⢀⣀⣀⣾⡀⠀⠀ ⠀⠀⠀⠀⣠⠋⠀⠀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⣶⣶⣶⣶⣶⣶⣶⢾⢿⠿⠿⣿⣿⣿⣿⣿⣿⣫⣄⠀ ⠀⠀⠀⡟⠉⠀⠀⣤⣟⢸⡇⢰⣦⣤⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⣿⣿⣿⣿⣭⠭⠭⠭⠭⠿⠶⠶⠖⠚⠛⢦⡹⣽⣟⠁ ⠀⣷⣄⣳⣀⣀⡀⣀⣼⣆⣳⡆⠈⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢼⣒⣺⣿⣿⣒⣒⣀⣀⣀⣉⣉⣉⣁⣈⣭⢵⡘⢾⠂ ⠀⠈⠛⠒⠚⠛⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⠭⠭⣿⣿⡏⠁⠉⠉⠡⠀⠀⠀⠀⠒⠒⠒⠻⡌⠁ ⠀⠀⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⣾⣿⣿⡇⡗⠒⢒⣒⣒⣀⣉⣛⠛⠛⠛⠛⠛⣻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢼⣭⣭⣼⣿⠃⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣼⠆

⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠁⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣙⠒⠲⠦⠤⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣗⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠥⢀⣈⣑⣒⣂⠀⠉⠙⠛⠿⠿⢷⣶⠶⠖⠲⠶⠶⠤⠤⠤⢤⣄⡀ ⠀⠀⠈⠛⠦⠬⣙⣒⠶⠤⢤⣀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠰⢶⡤⠤⠉⣑⣒⠒⠒⠒⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣨⣿ ⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣟⣒⣶⣽⢷⣖⣲⣼⠿⣶⣼⣷⣒⡒⢤⣌⣓⣤⣤⣴⣿⣭⡐⠒⠒⠉⠉⠁⠀⠀⠀⢀⣤⣾⡽⠋ ⠀⠀⠀⠀⠀⢰⡏⢱⠗⡌⢫⢻⡁⠉⠓⠛⠋⠉⠉⠉⠑⠚⠻⠿⠭⣍⣙⣛⠓⠲⠦⠤⠤⠤⠤⠤⢤⡶⣖⣶⣿⣿⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⡈⠏⠁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⣿⢶⣾⡛⠛⣛⢿⣿⣀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡤⡄⠙⣿⡟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⢻⠃⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠠⠒⠂⠈⠉⠉⠉⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀ ⠀⠀⠀⢀⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀ ⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠀⠀⠀⠙⠲⢄⣀⣠⠋ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡆⠀⣸⣤⣤⣄⣸⠁⠀ ⠀⠘⢧⡀⠀⠀⢀⣀⠀⣰⣿⠋⢀⡤⣍⣻⣾⡏⠀⢈⡙⣿⠀⠀ ⠀⣠⡼⠻⢶⠚⠉⠀⠀⠘⣿⠀⠸⣿⠞⣸⠁⣧⠀⢿⠇⣼⡀⠀ ⠘⠗⢾⣿⡎⣼⠀⠀⣤⠄⠹⣿⣶⣤⣴⡟⠀⣿⢿⣾⣾⡏⠀⠀ ⠀⠀⢘⡏⣧⠉⠀⠀⣧⠀⠀⠈⠉⠟⠋⢁⠇⣹⠀⠀⠉⡇⠀⠀ ⠀⠀⠀⠉⢹⡀⠀⠀⠙⣗⠂⠀⠀⢤⣞⠉⠀⠘⢦⣀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠱⢄⣠⠀⠈⠁⠀⣀⡞⠘⠒⢦⣄⣈⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢠⣾⣷⣄⠀⠨⡼⢇⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⢠⡀⢸⣙⣿⣿⡿⣿⣿⣾⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡇⠀⠀⠸⡀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⡀⠀⠀⠳⡄⠀⠀⢹⠃⠀⠉⣻⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⢀⡀⠀⠀⠀⠈⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⣀⠴⠳⠤⠾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⣉⣷⠤⣶⡒⠦⣤⡴⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠴⠚⠉⠉⠓⢦⡀⢠⠞⠁⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠘⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⠀⠀⠀⢀⣀⡀⢹⡏⢀⣀⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢧⠀⠀⠀⠻⣿⠏⡿⣇⠻⠿⠇⠀⠀⠀⠀⡞⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⣰⠋⠀⠈⣿⠶⠤⠤⠔⠋⠁⠘⢦⡀⠀⠀⠀⣠⣾⡁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣀⠀⠀ ⠀⣼⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⣿⡇⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀ ⢰⠇⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣀⠀⣿⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⢸⡄⠀⠀⢀⡏⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⡏⢷⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀ ⠀⠙⠢⢶⣞⠁⠀⢳⡀⠀⠦⣄⣀⢀⣀⣠⠀⠀⢀⡿⠀⠈⠓⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⢨⡗⠀⠀⠑⢤⡀⠀⢹⠉⠁⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠉⠙⠚⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡏⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⠤⠤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠤⠴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡾⠉⣽⡀⠀⠀⠀⣰⡄⠀⠀⠀⢀⣶⡀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣰⢫⠟⣲⠖⠚⠁⠙⠲⠤⠔⠋⠀⣟⠓⡞⣏⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⢠⣇⣼⢠⣯⣀⣤⣤⣤⣤⣤⣤⣄⣀⣼⡀⣧⣸⡀⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⢸⣿⡀⠀⠀ ⠀⢀⣾⡿⠁⠀⠀⠈⢿⣷⡀⠀ ⢀⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⡀ ⢸⣿⣥⣤⣤⣤⣤⣤⣤⣬⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⡿⠟⠛⠉⠀⣹⣿⣿⡇ ⢸⣿⣿⣧⣀⣤⣶⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇ ⠸⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⠇ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠈⠙⠷⣄⡀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣶⡿⠋⠀⢀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠈⠻⣶⣿⣿⣩⣭⣭⣷⣶⣿⣿⣿⡿⠁⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣾⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⣿⣷⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⡷⢀⣿⠿⠻⣷⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⣿⠏⠙⣩⣧⠈⠻⣿⣿⣿⣿⣿⠟⢁⣼⡝⣷⠀⠸⣿⡈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡏⠀⢸⡇⠸⠷⣄⠈⢻⣿⣿⠋⢠⣿⣋⣵⠟⠀⠀⣿⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣷⠀⠀⠙⠓⠒⠛⣷⣄⠈⠁⠀⣿⣧⠀⠀⠀⠀⢀⣿⣿⣾⠿⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣴⣿⣷⡄⠀⠀⠀⠀⢛⣫⣤⣤⣦⣤⣀⣀⠀⠀⠀⠙⢻⣿⡄⠀⢀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⣩⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣏⠀⢨⣿⣿⡟⠀⠀⠀⢀⣶⣿⣿⣦⣾⣿⣷⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⣾⠏⣾⣿⣿⣴⣶⣄⠀⠀⠀⠈⠛⣿⣦⣾⣿⣯⣀⣠⡴⢾⣿⣿⣿⣿⣿⣿⢏⡀⠉⣹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⣿⠀⣿⣿⣿⣿⣿⣿⣷⡶⠶⣶⣾⣿⠿⠿⢿⣿⣿⣯⣴⣿⣿⣱⣿⣿⣿⡏⣾⠁⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣸⡏⠀⣿⣿⣿⣿⠟⠿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠛⠋⠁⠸⣿⣿⣿⣿⠃⣿⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣴⣿⣿⠇⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣇⠈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⢡⣿⣿⣿⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⢹⣿⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣿⣿⠀⣼⣿⣿⣿⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣦⣄⣰⡏⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⢠⣿⣿⣿⡿⢧⣤⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣉⣴⣿⣿⣿⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣼⣿⣿⣿⣿⣾⣤⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣿⣿⡏⠘⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⡟⠛⠻⠿⠿⠈⠀⠀⠘⣿⣇⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⣿⡇⠀⠙⠋⠁⠀⠈⠛⠃⠙⢿⣿⣿⣿⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣴⣾⣧⠀⠀⠀⠀⠈⣿⡀⠀⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⡇⠀⣿⣿⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⢿⣿⣆⠀⢠⣄⠀⢸⣿⣿⣷⣄⠀⠀⢠⣦⢀⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⠀⣿⣷⠀⣿⡟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣟⠻⣦⠀⠀⠀⠀⠈⠻⣿⣧⡈⣿⣿⣾⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⠀⣴⣿⣿⢀⣿⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠹⣇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠻⣿⣿⢠⣿⣿⣿⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠹⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⡿⠃⠀⣀⣤⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣇⠙⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⣿⣿⣦⠀⠀⣿⣷⣭⣉⡉⠛⠛⠛⠻⠿⠿⠶⣶⣤⣀⡀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠘⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣤⠀⠀⢸⣿⣿⣷⣶⣿⣿⣿⣿⣿⢷⣼⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣶⣤⡀⠉⠛⠿⣿⣄⠀ ⢠⣏⠙⠳⢦⣀⠀⠀⠀⠀⠀⠈⢿⡄⢹⣇⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⡄⠀⠈⣿⣿⣿⣿⡿⠿⠛⠿⣿⣼⣿⣿⡿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⢸⣿⡇ ⣨⣿⣿⣦⣀⠈⠛⢦⣄⠀⠀⠀⠘⣿⡀⢻⡄⠀⠀⠀⠀⣸⡆⠀⢸⣿⣷⡶⢶⣿⣿⡟⢁⣤⣶⣿⣿⣿⣿⣶⣤⣤⣶⣶⣶⣶⣤⣭⣛⣛⠛⠛⠻⢿⣿⣿⣿⣿⡟⠀ ⢷⣦⣍⡛⢿⣷⣦⡀⠈⠻⢶⣶⣶⣿⣷⡸⣷⡀⠀⣠⣾⣿⡇⠀⢀⣿⣿⣷⣸⣿⣫⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠛⠻⠶⣦⣬⣻⣿⣿⡇⠀ ⠀⠈⠙⠻⣦⣝⠻⣿⣷⣄⡀⠉⠙⠛⠛⠃⠻⠿⠿⣻⣿⣿⣿⣿⣍⣛⣿⣿⣿⣿⠟⠋⠻⢧⡈⠻⣿⣿⣿⣿⡏⣿⣿⣿⣷⡙⢿⣿⣷⣿⠀⠀⠀⠀⠙⠛⠿⠟⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣌⠻⣿⣿⣶⣶⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⢉⣾⠟⠁⠀⠀⠀⠀⠻⣆⠙⣿⣿⣿⣷⢹⣿⣿⣿⣷⡌⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⣋⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣿⣿⣿⣸⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣶⣶⣶⣶⣶⡶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⢿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⠀⡜⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⡠⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⢀⡜⠁⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⣆⠀⠀⠀⠀⠀⣠⠾⢒⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀⠈⠉⠁⠒⢒⣾⡽⡖⠉⠀⠀⠀⢠⠂⠀⠀⠀⣠⠞⠧⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢉⣀⠀⠀⠀⣠⠞⠉⠀⠀⠘⢄⠀⠀⠀⡈⠀⠀⣠⠞⠁⠀⠀⠀⠉⠳⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⡤⠊⠁⠀⡠⠚⡿⠁⠀⣀⡾⣥⠄⠀⠀⠀⠀⠀⠉⠢⣞⣁⣀⣴⡃⠀⠀⠀⠀⠀⠀⣀⡠⠽⠒⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠋⠀⠀⢠⠞⠀⠀⠓⠒⠉⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣁⣀⠤⠴⠒⠚⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⢠⠇⠀⢀⠀⢀⡠⠔⠋⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⢠⠎⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⣿⠒⠀⠀⠳⣄⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡎⠀⠀⠀⣠⣶⣾⡿⣿⢠⠃⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⡆⠀⠀⠈⢇⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠇⠀⠀⣰⣿⣇⣳⣧⠟⠃⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢰⠇⠀⠀⠀⠘⢄⡠⠔⠪⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠐⠉⠉⢩⠟⠁⠀⠀⢠⠶⠒⡖⢲⠏⠀⠀⠀⠀⠀⢸⠤⠔⢆⠀⠀⢨⠇⠀⠀⠙⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⢹⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⣟⢢⠀⢸⠎⠀⠀⠀⠀⠀⠀⡎⠀⣀⡬⠗⠶⣋⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀ ⠀⣠⠚⡇⣀⡼⠁⠀⠀⠀⠀⠀⣠⠤⠀⠀⠘⠀⠀⠀⣠⠏⠀⡄⢳⡞⠀⠀⠀⠀⠀⠀⢰⡇⡘⠁⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠱⡄⠀⠀ ⢠⠇⠀⠈⠀⠀⣠⠆⠀⠀⢀⠞⢁⣤⣤⣤⠤⠤⠖⠚⠻⢶⣄⠰⣰⠃⠀⠀⠀⠀⠀⠀⢸⠁⠇⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠘⡄⠀ ⠸⡄⠀⠀⠀⠐⠁⠀⠀⠀⣠⣶⢿⣍⡿⣏⣀⡤⠤⠒⠒⠒⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⢘⣿⠤⠤⠔⠒⠒⠒⠒⠤⢼⠄⠀⠀⠀⠀⠸⡀ ⠀⠙⢦⣄⣀⣀⣀⣀⣤⣾⠛⢟⠺⠆⣰⠞⠁⠀⠀⠀⠀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠘⣿⣿⣿⣽⣧⣿⠢⡘⡄⢰⠃⠀⠀⠀⢀⡤⠤⠤⠄⢼⣇⠀⠀⠀⠀⢀⠞⠁⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠈⡇⠀⠀⠀⡿⡅⠀⠀⢀⣸⣿⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣴⣷⣷⠀⠀⣸⣍⡏⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⣋⡡⠔⠋⠀⢈⣿⠀⢀⣛⣼⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⣺⠭⠔⠒⠊⣉⡇⠀⠀⣄⣠⣾⣿⠄⣀⢫⡽⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣏⠻⣀⣀⣀⣤⡾⠋⡀⠀⠀⠙⣏⡿⣬⣦⣀⡽⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⠤⠤⠭⠽⠟⠋⠁⠀⠀⠀⠹⢍⡉⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠖⠒⠒⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⢀⣠⣴⠶⠟⠀⣀⣉⣉⣉⡉⠉⠉⠉⠙⠛⠓⠒⠲⠶⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⣤⡾⢛⣩⠴⠒⢋⣉⣭⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠂⠀⠩⣙⣁⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⣘⣡⠖⢋⡤⠶⠚⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠶⠿⠿⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣀⣀⣤⣶⡾⢿⣿⡿⢿⣶⣦⠀⠀⠀⠀⠈⢷⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣶⣶⣶⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠻⢿⣿⣿⣷⣶⣿⣿⣿⣶⠿⠛⠀⠀⠀⠀⠀⠈⢧⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⢀⡄⠀⢠⣶⣿⠇⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⣰⠏⠀⠀⢸⣿⣇⣴⣶⣶⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⢀⡟ ⠀⠈⢷⡀⠀⠀⠀⣠⣴⣶⣾⣿⡿⠛⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠟⠉⠛⠉⠀⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⣼⠀ ⠀⠀⠈⢷⡆⠀⢰⣿⡿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣬⣟⣛⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡄⣰⠃⠀ ⠀⠀⠀⠈⢷⡀⠸⣿⣧⣿⡿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⠿⣿⣷⡏⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⡀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⠶⠤⢤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠦⠤⠤⢤⣤⣤⣤⣤⣤⣤⠤⠞⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣻⣿⣿⣿⣿⣯⣍⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⣾⠟⠋⣁⣀⣤⡉⠻⣷⡀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⢸⣿⠀⠼⢋⣉⣈⡳⢀⣿⠃⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠿⣷⡀⠀⠀⠀⣼⣿⠃⠀⠀⣀⣤⡿⠟⠛⠋⠉⠉⠙⢛⣻⠶⣦⣄⡀⠀⠘⣿⣷⡀⠀⠀⠀ ⢠⣾⠟⠳⣦⣄⢸⡇⠀⠈⣷⡀⠀⣼⣿⡏⢀⣤⡾⢋⣵⠿⠻⢿⠋⠉⠉⢻⠟⠛⠻⣦⣝⠻⣷⣄⠸⣿⣿⠀⠀⠀ ⠘⣧⠀⠀⠀⠙⢿⣿⠀⠀⢸⣷⠀⣿⣿⣧⣾⣏⡴⠛⢡⠖⢛⣲⣅⠀⠀⣴⣋⡉⠳⡄⠈⠳⢬⣿⣿⣿⡿⠀⠀⠀ ⠀⠘⠷⣤⣀⣀⣀⣽⡶⠛⠛⠛⢷⣿⣿⣿⣿⣏⠀⠀⡏⢰⡿⢿⣿⠀⠀⣿⠻⣿⠀⡷⠀⣠⣾⣿⡿⠛⠷⣦⠀⠀ ⠀⠀⢀⣾⠟⠉⠙⣿⣤⣄⠀⢀⣾⠉⠀⢹⣿⣿⣷⠀⠹⡘⣷⠾⠛⠋⠉⠛⠻⢿⡴⢃⣄⣻⣿⣿⣷⠀⠀⢹⡇⠀ ⠀⠀⢸⡇⠈⠉⠛⢦⣿⡏⠀⢸⣧⠀⠈⠻⣿⡿⢣⣾⣦⣽⠃⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⡇⠉⢿⡇⠀⢀⣼⠇⠀ ⠀⠀⠘⣷⡠⣄⣀⣼⠇⠀⠀⠀⠻⣷⣤⣀⣸⡇⠀⠹⣿⣿⣦⣀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⢸⣷⣾⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⢦⣍⣀⣀⣀⡄⠀⣰⣿⡿⠿⢿⣇⠀⠀⠉⠛⠻⣿⣿⡷⠾⣿⣿⡿⠉⠁⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⢿⣿⣇⠀⠀⠈⢿⣧⣄⠀⠀⠀⢹⣷⣶⣶⣾⣿⡇⠀⠀⣀⣴⡿⣧⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠙⢿⣿⣶⣤⡀⠻⢤⣀⡤⠞⢀⣴⣿⣿⠟⢷⡀⠙⠻⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢠⡟⠁⠙⢻⣿⠷⠶⣶⠶⠾⠛⠙⣿⠇⠀⠀⢻⡄⠀⠀⠙⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⣿⠁⣤⣤⡄⢻⡶⠶⠛⠛⠛⠛⠛⣿⢠⣾⣷⣆⢻⡀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⡈⢿⡀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⢸⡇⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⣴⣶⣶⠲⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠈⢫⣈⣦⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣻⣇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠇⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣟⣆⡠⠤⠤⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⢀⡀⠘⣆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠉⢀⡀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠙⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣹⠾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⣡⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢀⡠⠞⡏⠀⠀⠸⠁⠀⢀⠤⠀⢠⡀⠀⠀⠀⢀⢸⣿⣿⡿⠛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠴⠋⠀⠀⠳⡀⠀⠀⠀⢠⢃⣤⣶⢶⣿⡄⠀⠀⠈⢮⠓⠂⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⢹⡄⠀⣠⣤⡀⢹⠀⠀⠀⠈⠙⠛⠛⠉⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠚⠉⠳⣼⡿⢿⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣠⣤⣼⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠙⡄⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⠻⣰⠞⠓⠈⢡⣭⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⡵⢤⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠬⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠻⡀⠀⠈⠁⠀⠀⠀⠀⣴⣿⣿⣡⠤⠤⠖⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠙⢀⠀⠀⠀⠀⠀⠀⠀⠛⠤⣀⣀⣀⡠⠞⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠉⠉⠒⠒⠦⠤⣤⣤⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⢣⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠱⡀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⢱⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠒⠢⢄⡀⠀⠀⠘⢦⡀⠈⠳⣄⠀⠀⠀⠀⢿⠀⢰⣿⡀⢇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⢤⠑⢤⡀⠈⠳⣄⠀⠀⠘⡀⢸⠀⢇⠘⡄⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠑⣄⠙⢦⣀⠀⠑⢦⣀⡀⠈⠀⢸⠀⠇⠀⠀⠀⢻⣒⣲⣿⣛⣓⣲⣂⣲⣒⣲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣉⣓⣛⠻⠾⠷⠻⡇⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠟⢁⡀⠀⠹⡆⠀⠀⠱⢄⡠⠴⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⢤⣔⠛⠳⠄⠀⠙⠠⠤⡗⠀⠀⠀⠀⠀⠀⠐⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣰⠴⠶⢤⡀⠀⡀⠀⢀⣀⣠⠤⠴⠿⠧⠤⠤⠤⢤⣀⡀⠀⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⢤⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⢶⣾⡁⠀⠀⠀⢻⠉⢻⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣇⣀⠈⠓⢦⡀⠀⠀⠀⠀⢄ ⠀⠀⠀⠀⠀⠀⠀⡄⣠⠟⠁⠀⠀⠀⣼⡇⠹⡀⠀⠀⠸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⣾⡆⠀⠉⠓⢦⣀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠟⠦⣄⡠⠴⠚⠁⡆⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢰⣶⠄⠀⣨⣾⡟⠋⢻⣶⣤⡵⠀⠀⠀⠀⠹⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢰⡷⠁⠀⠀⣼⡦⢰⡏⠀⠀⠀⠀⢀⣀⠀⣰⠫⣾⣷⠀⠸⣿⡿⢷⡀⠀⠀⠀⠀⢹⣆⢀⣠⠤⢶ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢤⢀⡿⣄⣀⣠⠾⠛⣱⠏⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣛⣁⣠⣶⡿⢷⠛⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿ ⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⣏⠀⠀⣹⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠠⠤⠶⠂⠈⢧⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠂⢻⣤⣀⣀⠴⠋⢻⡀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⣸⣇⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠷⠞⠛⠋⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠠⠴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⠀⠀⠀⠀⠀⠀⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠛⣿⠿⠛⠿ ⠀⠀⠀⠀⠀⢀⡤⢤⣤⣴⠒⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡏⣀⡴⣿⡿⣄⡀⡴ ⠠⠀⠀⠠⢀⡟⠀⣰⠃⠈⠀⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⡞⢸⠀⠀⠀⢰⡟⣡⠞⠉⠳⠦⣤⣉ ⠀⠀⠀⠀⢸⡓⠋⠁⠀⠠⡀⠀⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣇⠀⠀⠀⢰⠇⣸⡇⠀⠀⣸⡿⣅⣀⠀⠀⠀⠀⠀ ⢀⡶⠚⠛⠛⠯⣍⠀⠈⠓⢧⢀⣽⢦⣹⣆⠀⠀⠀⣠⠄⠀⠀⠀⠘⠳⢤⣀⠀⠀⠀⢸⣄⠀⣀⣼⣿⣿⣿⡒⠚⣿⠓⠶⠤⣭⣍⣉⡀⠀ ⣾⡁⠀⠀⠀⠀⠀⢳⠀⢀⣼⣯⣥⣬⣤⣬⣿⣶⣾⣀⡀⠀⠀⠀⢀⡾⢿⣽⣷⣦⣶⣾⣿⠛⣭⣿⣷⣾⣿⣧⣾⣿⡀⠀⠀⠀⠀⠀⠈⠁ ⠉⠻⠦⣤⣀⣀⣤⠾⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⠾⠷⠶⠾⠿⠿⠁⠈⠙⢷⣿⠏⠈⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣶⣤⣄⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣨⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡿⣿⣿⣿⣷⣄⣴⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⢻⣿⣿⡇⠙⣿⡟⣿⣿⣿⣿⣿⠿⣿⣿⣋⡙⢦⡀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣸⣿⣿⣿⡇⠀⢼⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣷⣶⣌⣙⠛⢶⠿⣦ ⣠⠶⠟⢋⣽⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⢹⣿⣿⣿⠀⠀⠀⢿⣿⡇⠠⠤⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣾⣆⠈ ⠀⢀⡰⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣞⣀⡀⣸⠇⢸⣿⣿⡟⠀⠀⠀⢸⣿⣀⣀⣀⣀⣻⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣴⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠟⣿⡿⠁⠉⢻⡟⠀⣼⣿⡿⠁⠀⠀⠀⠞⢋⠄⠀⠀⠀⠙⠛⢿⣿⡟⠻⣿⣿⣿⡟⠀⢻⡛ ⠟⠋⠁⠀⣸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣧⣾⣿⣅⣠⣀⡜⠀⢀⣿⠟⠀⠀⠀⠀⠀⠠⣄⣦⣀⣀⣤⣂⠴⢿⣿⣇⠀⠹⣿⣿⡇⠀⠸⣿ ⠀⠀⡎⠉⢿⣿⣿⣿⡇⣿⣿⣯⣿⣿⣿⣿⣿⠁⠀⠀⠈⠁⠀⣼⠏⠀⣀⡠⠂⠀⠀⠈⠀⠀⠀⢀⡤⠚⠉⢸⣿⣿⡆⠀⠸⣿⡇⠀⠀⣿ ⣄⠀⢙⡄⠈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠚⠅⢊⡥⠒⢹⣿⣿⣿⡄⠀⢿⡇⠀⠀⣿ ⠈⠳⣼⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣀⣀⡠⢤⣤⡤⠤⣀⠀⠀⡀⠀⠀⠀⡂⠀⠀⣼⣿⣿⣿⡇⠀⠸⡇⠀⠀⡻ ⠄⠀⠈⢻⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣿⡟⠋⠉⠁⠀⠈⠉⠑⠲⣾⡇⠀⠀⠀⠿⠀⢀⣿⣿⣿⣿⡇⠀⠀⠃⠀⠀⣿ ⢀⣦⠀⠀⠙⠿⠄⠀⣹⠷⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢇⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣦⣄⣀⡰⠋⠀⠀⠈⠛⢿⣿⣿⣿⣦⣄⠈⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣀⣴⣿⣴⣿⣿⠏⠀⠀⠀⢉⠇⠀⠀⠀ ⢿⡏⠀⠀⠀⠈⠣⣤⠚⠳⣤⡀⠀⢹⣿⣿⣿⣿⣷⣦⣀⠀⠀⠙⠂⠀⠀⠀⠐⠊⠁⠀⣀⣴⣾⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⣿⠉⠉⠉⠙⢦⡀⠈⢲⠀⠁⠀⠀⢸⣷⡛⢿⣿⣿⡿⣏⠙⢶⣤⣀⠀⠀⠀⣀⣤⣶⠟⠙⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣆⠀⠳⡄⢠⠝⠢⣴⠁⠀⠀⠀⢸⣿⠿⠾⣿⣿⡀⠈⠢⣀⠈⠛⠿⠿⠿⠿⠟⠁⢀⠴⠀⠙⢴⡋⢹⣿⠉⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣦⡀⠉⠁⠀⠀⠈⢦⡀⣀⠀⢾⣿⠀⠀⢹⣿⣧⠀⠀⠀⠉⠑⠒⡄⠀⠀⢖⠉⠀⠀⠀⠀⠀⡇⢸⡏⠀⠀⡌⠀⡇⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⡦⢄⡀⠀⢠⠜⠋⠁⠀⠘⣿⡄⠀⣾⢿⣿⠀⠀⠀⠀⠀⢰⣷⣶⣶⣿⡄⠀⠀⠀⠀⡰⠁⢸⠁⠀⢰⡆⠀⡇⠀⠀⠀⠀⠀⠀ ⣿⡟⣿⣿⠃⠀⢙⡆⠀⠀⠀⠀⠀⠀⢹⣧⠀⠈⠀⢻⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⡄⠀⠀⡰⠁⠀⠈⠀⠀⣸⠃⢸⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⣿⡏⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠈⡟⢆⠸⠤⠀⠙⢄⠀⠀⡜⢹⣿⣿⣿⡟⠀⢣⠀⡰⠁⠀⠀⠀⠀⠀⡟⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⣿⣧⠀⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⠳⢄⡇⠀⢿⣿⣿⠃⠀⠈⠶⠁⠀⠀⠀⠀⠀⠀⢸⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡏⠀⠀⢀⡀⢼⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠐⠊⠉⠒⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠆⢾⡛⠙⢿⣶⣿⡄⠉⠻⡛⢷⣆⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣾⠿⣹⠶⣤⣼⣏⣀⡀⠙⢋⣰⡚⢾⡟⠺⠛⢉⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣾⠇⠸⢥⡄⠈⠈⠩⠩⠾⣄⠉⠀⠁⠙⣁⠀⠀⠀⠛⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⠀⢯⣀⣄⠀⠀⠀⢸⡧⠀⠀⠀⠈⠋⠛⣦⠀⠸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⣤⣴⣿⣿⣷⣦⡎⣜⡶⡄⠀⠀⠀⣀⢀⡀⠀⠈⢻⡆⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⢀⠔⠋⠉⠻⣿⠺⣿⣫⢞⣛⣆⣀⠀⠉⢻⣷⠀⢀⢈⣿⠓⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠻⠈⠂⠀⠀⣠⠴⡏⠳⡀⠀⠀⠀⠳⣽⠟⠋⠁⠐⢿⣥⡄⠰⡷⣦⣴⠾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡏⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠈⠀⠀⡀⠀⠘⡇⠀⠀⠀⠀⠀⠛⠒⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠈⠀⠀⢀⡠⠚⠙⠄⠀⠀⠀⠀⠀⠀⠀⠙⣄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⢀⠴⣏⠀⠀⠀⠀⠀⠀⠀⠐⢎⢢⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⢀⠀⠀⠀⠈⢦⣀⡤⠚⠂⠈⠓⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠟⢻⣦⠀⣀⣷⠤⠴⢛⣿⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠶⠚⠉⠉⠁⠀⢀⡴⠟⠉⠳⠀⠀⠀⠀⠀⠘⢎⣦⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠿⢄⠀⠀⠀⠀⡄⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⡤⢀⣼⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⠀⢤⣲⡾⠟⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣀⡤⠒⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠶⣶⣶⣤⣀⠀⠀⠀⠀⢇⢀⡠⠞⢁⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠈⠻⣾⠑⣦⣀⣠⣼⣿⡶⣾⣿⡷⢶⡚⠛⠒⠒⠲⣤⣄⡀⠀⣠⣾⡿⠋⠀⠀⠈⠀⠈⢷⡄⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢷⣜⣿⡿⣫⠞⠛⠉⠉⠉⣳⣽⣒⣒⠲⢞⡯⠽⠿⢯⣿⣻⣄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠿⠛⣿⡿⢿⣄⣀⣀⣤⣾⡿⠋⠀⠈⣧⡻⣤⣀⡀⠀⣀⣽⣿⢙⡇⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⡟⠉⠓⠒⣷⡶⠟⠻⠦⠀⠀⠀⠀⠙⢲⣭⣭⣭⡽⣾⢉⡟⠇⠀⠀⠀⠀⢰⡏⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⠀⢸⠃⠀⢰⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⣿⠏⠀⠀⠀⠀⠀⠐⡾⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⢸⡄⠀⢈⣇⠀⠀⠀⠀⢀⣤⢶⣶⠆⠀⠀⠀⠀⢠⣴⣶⣾⠁⢸⠇⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⠀⠀⢸⡇⠀⠀⢿⣀⣀⣀⣤⣿⡿⣿⣏⢹⣤⣤⣴⣤⣼⣿⣿⣿⣦⣿⣇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠸⡇⠀⠀⠺⡏⠉⠉⠉⣉⣉⣙⣻⣛⠀⠉⠻⡿⢋⣸⣿⣟⣛⣻⣿⣉⣉⡭⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢶⣷⡀⠀⠀⠻⣟⠉⠩⠭⠽⠛⠋⠙⠦⢤⠴⠷⠒⠋⣹⠗⠀⣨⠟⠉⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣠⠞⠁⠀⠀⠀⠀⠀⢰⣦⡭⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠹⣶⠶⣤⣤⣤⣤⣤⠴⣾⣿⠿⠛⠛⠦⣄⡀⠀⠀⠀⣠⡏⢿⣇⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⣿⣶⣨⠛⠉⠙⡄⢰⠏⠉⠳⢦⡀⠀⠀⠙⢦⡀⢠⠏⡄⠸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠻⡿⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⠓⠦⣀⠀⠈⠻⢤⡃⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⣚⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⣺⠟⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣀⣸⠿⠤⢄⣲⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⣧⡤⠴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢉⡴⠁⠀⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠾⠿⣇⠀⠀⣼⠋⠃⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⢀⡾⠁⢠⣾⣤⣴⣄⡀⠀⠀⠀⠀⠀ ⠀⣀⣠⠾⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⢹⣦⡐⣿⢰⡀⠀⠀⠀⠀⠳⡄⢀⣠⢶⡾⣿⠀⣠⠟⠉⢾⣿⠋⠙⠛⠶⢦⣤⠀ ⠈⠛⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⢬⣷⣄⠀⠀⠀⠀⢹⠏⠀⠀⣸⢏⣼⣇⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣭⣀⣠⣾⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡴⢋⡽⡞⣡⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⢀⡴⠋⡸⠋⠀⢈⣿⣅⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠞⣁⡀⢀⡞⠁⠈⡙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⠉⠳⡄⠀⢀⡜⢁⣴⠃⠀⠀⣼⡿⣀⡀⢠⠷⢰⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡆⠀⢹⣴⠏⢠⣾⠋⠀⠀⣼⠋⠀⠀⢹⠏⠀⣼⢀⡞⠀⠀⠀⠀⣠⠶⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⢠⣾⠁⠀⢸⠁⠀⢠⣾⠋⠀⠀⢀⡞⠀⢰⡿⠋⠀⠀⠀⠀⠉⣁⣀⡤⠒⠉⣳⡦⣤⡀ ⠀⠀⢸⠁⠀⣿⠋⠁⠀⠸⢄⠀⠸⠃⠀⠀⣀⣾⠇⠀⣾⣀⣀⡠⠤⠴⡖⠉⢁⣀⣼⢴⡏⠁⠀⣠⠇ ⠀⠀⠈⡇⢠⡉⠀⠀⠀⠀⠀⠀⠈⠒⠆⠀⢸⠃⠀⢰⠇⠀⣌⠀⣀⣤⡷⠞⠋⠁⠀⢀⣡⠤⢾⠁⠀ ⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣼⠀⠀⠸⣏⠉⠀⠀⢀⣠⠤⠒⠏⠀⢠⠞⠀⠀ ⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⣧⣀⠀⠻⡶⠒⠒⢻⠀⠀⣀⣴⣶⠋⠀⠀⠀ ⢀⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡿⠉⠀⠀⡆⠀⠀⣿⣴⠟⠉⣠⡿⠀⠀⠀⠀ ⠀⠋⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⡟⠀⠚⠓⠲⠦⠀⣿⠞⠛⠉⠉⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠋⠀⠀⠀⠀⠀⠀⠳⣦⣄⠐⢋⣼⠋⠠⢤⣤⣤⡾⢶⢆⣠⡿⠛⢉⣠⠶⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠛⠉⠒⠒⠒⠒⠒⠒⠛⠋⠁⠀⠈⠭⠤⠶⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠐⠀⠠⠀⣀⢀⣀⣤⣠⣄⣤⣤⣤⠀⠀⠀⠀⠀⠁ ⠀⠀⣼⣴⣼⣷⣿⣿⣿⣿⣿⢿⡗⡿⠿⠿⠄⠀⠀⠀⠀⠀ ⠀⠀⣿⢿⢻⢋⠟⡏⠁⠁⠀⠄⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⡵⠅⠐⡷⡂⠀⠀⢠⣇⢸⣀⠀⠇⠀⠀⠀⠀⠀ ⠀⣽⠁⠆⣥⢤⣤⣠⢃⢰⠀⡈⠈⣜⠳⣆⠆⡀⠀⠀⠀⠀ ⢀⣿⠀⣶⠀⢸⠿⠷⠀⢻⡆⡁⢠⣼⣶⡿⣦⡀⡄⠁⠀⠀ ⢸⣿⠀⣯⠀⠀⠉⠁⠀⠀⠈⠃⠀⠯⠩⠁⠋⢀⢀⠀⠀⠀ ⣿⣿⡆⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⢀ ⣿⣮⢀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠇⠀⡄⠈ ⠻⣷⢨⡀⢹⢿⣦⡀⠀⠀⠀⢀⡀⠔⢪⣿⠀⢺⢹⠀⣧⠀ ⠀⡄⢸⢱⢸⣽⣿⣿⣷⠐⠊⠁⠀⣀⢼⣏⢈⣿⣸⡀⢿⡆ ⡸⡀⠮⠘⢆⠛⠻⠛⠻⣄⡠⠔⠊⠀⢰⠃⣼⣿⣿⣇⢸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠟⠋⠉⠙⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣄⣀⣀⣠⣤⣤⣤⣤⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡏⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠀⢰⣿⢻⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀ ⠀⣼⠏⠀⣾⣿⢸⣧⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀ ⢠⡿⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⠿⣶⡄ ⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣧ ⣿⡇⠀⢸⣿⣿⣿⣿⣿⠟⣿⣿⣿⣧⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣴⡿ ⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡄⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃ ⢿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠛⠛⠁⠀ ⠸⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⠋⠛⠻⠷⣶⣤⡀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣷⣌⠛⠿⢿⣿⣿⣿⣿⣿⠏⠀⣼⡿⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⢿⣷⣶⣄⣉⣉⠛⠛⠁⣀⣾⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⣿⣶⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠋⠁⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⡿⢁⡾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣤⣀⣤⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠛⠛⠻⢽⣍⣋⠝⣹⣷⠶⠶⠾⠻⠿⠷⢍⣹⣷⣻⣶⢿⣻⣉⣧⣿⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡈⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡗⢐⠃⣴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣷⢣⠀⠀⠀⠀⠀⠀⢀⣿⡗⢺⢳⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣻⣿⣼⣇⣀⠀⠀⣀⣤⢿⡞⣩⣻⢿⢧⡉⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡟⢏⣀⣾⣿⣿⣿⣿⣿⣿⡿⢏⡽⠣⡼⢩⣿⣾⣦⣌⠲⡄⠈⣹⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⠛⠻⣿⣁⠞⢂⡜⢠⣾⣿⣿⣿⣿⣧⠙⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⢹⣹⣿⣿⠇⠀⣶⣇⡞⢢⣾⣤⢚⠟⠈⠙⠿⣿⣿⣷⣼⣅⡉⠉⠉⢻⣿⠛⠓⢲⡀⠀⠀⢀⣠⣄⡀⠀ ⠀⠀⣼⣿⡟⣿⣿⡟⠁⣼⣿⣿⠏⠀⣸⣟⡼⢂⣾⡟⣱⡿⣄⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠃⢸⡏⠀⠀⠀⠀⠀⢠⣿⡿⢿⣿⣧ ⢀⡼⠛⢻⣷⡈⣁⣴⣾⣿⠿⠃⠀⣼⣿⣎⢽⡟⣾⡇⣼⡿⣯⡓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⠆⠀⠘⣯⣿⣿⢦⣾ ⢸⠀⠀⢠⣿⣿⣿⠿⠛⠁⠀⣠⠞⣿⠛⢁⡜⣴⣿⢡⣯⣧⣌⣻⣦⡀⠉⠒⠢⠤⢤⣀⣀⡠⠤⠴⠚⢉⣥⣤⣶⡯⢿⣾⣫⡞⠁ ⣼⠀⠀⠸⡇⠀⠀⠀⣀⠴⠊⠁⢀⡿⠞⡹⢲⡿⢃⣎⣉⣿⣿⣿⣿⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⢇⡱⣞⣳⡾⠋⠀⠀ ⠈⠒⠢⠴⠒⠒⠈⠉⠀⠀⠀⠀⣾⠓⢰⠧⣟⣴⣿⡷⣄⣻⣟⢿⣷⣾⠙⢻⣆⠀⠀⠀⢀⣤⣾⣿⣿⡿⣷⣮⣷⣺⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠤⢼⠄⠙⣿⡟⠂⠘⣄⣴⣾⣦⣸⠑⢤⢹⣦⣴⣾⣿⣿⣿⣿⡿⢣⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⡤⢤⡾⠳⣀⠴⣿⣿⣿⣿⣟⣤⠎⣱⠽⠛⠛⡿⣿⣿⣯⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠱⣜⠳⢄⣟⣦⡿⣿⡁⢳⢸⣷⣄⣧⡤⠒⢉⢀⡧⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢭⣶⠤⣽⢻⣄⠳⡈⣭⣯⡇⢘⠤⢤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⢸⠏⠙⣿⣿⠉⢻⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣄⡴⠛⠛⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣖⣡⣧⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠶⠶⠶⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠂⠀⠲⠶⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠞⠉⠉⠛⠓⠲⠶⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠖⠒⠋⠉⠙⠓⢶⡀ ⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⣤⣼⡿⣷⣾⣿⣷⣤⣾⣿⣷⣤⣿⣿⣷⣾⡿⢷⡤⠴⠖⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢠⣼⣧⡈⠻⣁⡈⠻⠟⠉⠙⠿⢋⣀⠙⢯⣵⣦⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏ ⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠻⠻⣷⣾⣿⣿⣶⣾⣿⣷⣶⣿⣿⣷⣾⠟⠛⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃ ⠀⠸⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠋⠁⠈⠛⠏⠀⠉⠻⠁⢠⠙⠃⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣴⣿⠏⠀ ⠀⠀⠘⢿⣷⣿⣷⡤⣤⠀⠀⠀⠀⠀⠀⢤⣄⡈⠳⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠙⢿⣟⣿⣶⣤⣿⣶⡄⠀⢀⣀⡈⠉⠓⠺⠿⠓⠒⠦⣤⣄⢢⠦⠤⠤⣤⣄⠠⢤⠀⠐⠿⠉⠀⠀⢀⣀⣀⣀⣤⣴⣿⣽⣾⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⢽⣽⣿⠿⣿⣶⣿⣿⣯⣽⣶⣶⣶⣦⣠⣤⣤⣤⣄⡤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠶⠿⢿⣭⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣦⣀⣠⣶⣄⣀⣀⣀⣰⣄⣀⣀⣶⡄⢀⣀⣀⣀⣀⡀⣀⡠⣤⠴⣦⢴⣴⣦⣦⣴⣦⣤⣤⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡛⡟⡟⠛⣛⣋⡛⠛⣛⣛⣟⢛⢛⣛⡓⡚⢚⢛⢻⡋⡃⢉⢐⣟⠒⡓⡟⣛⢚⢛⡓⡃⡚⣛⢛⢛⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠖⠒⠒⠲⠶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠽⠠⠴⠶⢶⠒⠈⠉⠉⠉⠉⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠶⠒⠒⠛⡓⢦⣀⣧⡤⠖⠛⠉⠉⠙⠓⠲⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⣰⠃⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣯⣀⣀⣠⣤⣤⢔⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣧⠀⠀⠀⠀⠀⠈⢦⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠹⠦⠤⠴⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣠⣤⣀⡀⠀⠀⠀⢀⣠⢴⡾⢛⡿⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠊⡝⣾⢉⠻⣄⡠⠖⠋⠀⣾⠀⣸⠁⣤⣬⣟⣏⢳⡄⠀⠀⠀⣠⠞⠁⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⣿⢸⣶⣯⠀⠀⠀⠀⢹⠀⣏⠀⣿⡧⡏⣹⠀⣷⠀⠀⣰⠃⠀⢀⣤⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⢹⣿⣼⣿⡏⠀⠀⠀⠀⢸⠀⢹⠀⢿⡇⣧⡏⠀⢸⠀⢠⠏⠀⢠⠟⣯⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⢳⣳⣸⡞⡿⣜⡇⠀⠀⠀⠀⠈⠧⣘⣧⣀⣼⠟⠀⠀⢸⠀⣸⠀⢀⣎⣠⡿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⠿⣻⡿⠙⢷⠤⢤⣈⣻⣽⠁⠈⠛⠅⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡼⠀⢠⠀⠘⣿⣛⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⣥⡾⠛⠁⠀⢸⡇⠀⠉⠛⢿⣧⡀⠀⠀⠀⠤⣤⣤⠤⠖⠀⠀⠀⠀⠀⠀⣼⠃⠀⢘⣦⣤⣬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠻⡷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⣴⠋⠀⣀⡬⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⠉⢓⣶⠶⠦⠤⠤⠶⠞⠻⢿⣍⡉⣠⣯⣠⠼⣥⡀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠞⠋⡼⠀⠀⠀⠀⢀⡀⠀⠀⢨⡟⣧⣿⠁⠀⠀⠻⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣼⣁⣀⡀⠀⢀⣀⣿⣦⢠⡟⣿⠁⠈⢳⡀⠀⠀⠙⠆⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⡴⢿⡇⠀⠉⠉⠉⠉⠉⣹⡎⠻⣿⠉⢣⡀⠀⠙⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠳⢦⣤⣀⣀⠀⠀⣀⣤⠾⠋⢀⡞⢣⡀⠀⠀⢀⡴⠖⠺⢷⡀⠘⣦⠀⠙⠂⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣼⠁⠀⠙⠶⣴⡏⠀⠀⠀⠀⠱⣄⠈⠳⢦⣀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⢦⡀⢰⡇⢻⡄⠀⢀⣠⠤⠼⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠙⢻⡄⠀⢷⡀⡜⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋⠉⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⠤⠤⣤⣤⠤⠴⠾⠛⠁⣀⣀⣀⡀⠀⢀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠈⢿⡯⠂⡟⠝⢻⣿⠸⠀⠀⢀⣃

⠀⠀⠀⠀⣀⠠⠄⢦⡀⠰⣼⡀⢠⠈⠆⠀⡏⠀⠙⡆⠀⠣⡆⢢⠀⢀⠀⠀ ⢠⠔⠊⠁⢀⣞⡀⠘⠃⠈⡟⡇⠘⠃⠈⡀⡇⢠⡀⠀⢰⡻⠀⠐⠂⢁⣨⠆ ⠸⣶⣶⠀⠙⠙⢃⠀⢧⠀⢁⡇⣰⡟⣀⣰⣇⣸⢣⠀⣾⠁⢰⠂⠘⠉⠀⠀ ⠀⠀⠘⣣⣈⡄⢣⣶⣿⠿⠋⢻⢃⠜⠙⠻⠛⢫⠛⠻⣿⡶⣋⣀⠀⡇⠀⠀ ⠀⠀⠀⠉⠉⠰⣿⣦⡈⠀⠀⣦⠃⢰⡷⡄⢱⡉⠀⢰⡇⠀⡙⣻⠷⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⢠⡇⠀⠃⠗⠀⠈⡇⠀⠿⠀⢠⡱⠁⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⡸⢿⣄⣀⣀⣠⣿⣆⠀⠀⣠⢷⠿⢶⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠁⠀⠙⠛⠋⠁⠘⠻⠿⠛⢹⣿⣄⡨⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣄⡀⠀⠀⠀⣠⡾⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠙⠿⣶⣤⠞⢉⣴⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠁⣴⡿⠋⣿⣻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠉⠉⠉⠉⠉⠁⠀⢠⣄⠰⣤⠾⠿⠃⠀⠟⠉⠉⠉⢿⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⣤⠀⠀⠙⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠀⠠⣤⡈⢿⣄⠀⠀⠀ ⠛⠻⠿⢭⣄⣤⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣿⠀⢻⣏⠙⢻⣏⠛⠻⠃⠀⠀ ⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢸⣿⡄⢠⣿⠀⠈⢿⡄⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⡠⠋⠈⢿⣾⣿⣿⣼⡟⠀⠀⠘⣿⡄⣿⠁⠀⠀⠀⠀ ⠀⠀⣿⡿⠿⣷⠄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠀⠈⠃⠘⠿⠃⠀⠀⣾⣿⣿⠿⢤⣤⣤⣀⡀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⡏⢴⣶⣶⠄⠀⠀⢀⣀⠠⠄⠀⠀⠈⣿⡇⠀⢀⣠⡾⠟ ⠀⠀⠀⣼⡇⢀⣷⡀⠀⠀⠀⠀⠀⣼⣿⣧⢸⡷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢿⣿⣿⠟⠉⠀⠀ ⠀⠀⠀⠛⢷⣼⣿⣧⣠⣴⣆⠀⢀⣿⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⣸⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣽⡿⠋⠈⠻⣷⣾⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⡟⠋⠀⢘⣛⣁⣈⣁⣀⣀⡀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠛⠛⣻⣿⠟⠛⠛⠻⠿⣿⣛⠛⢻⣿⡿⠿⠿⠿⣿⡟⢛⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢀⣠⡶⠟⢋⣿⠟⠉⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣤⣼⡇⠀⣠⣾⠟⠉⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢙⣿⠷⠀⣽⣿⠋⠀⠀⠀⣸⡟⠁⠀⠀⠀⢠⣤⠀⢀⡀⢹⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⢀⣾⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⣄⣾⠇⣼⡇⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⣼⣿⠃⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⣯⠀⠀⢸⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⣿⣿⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⠀⠀⠀⣿⣆⠀⠘⣿⡄⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀ ⠀⢀⣠⣄⣸⠿⣤⠙⢧⣉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡞⢉⣿⣼⡇⠀ ⠀⠘⠛⢲⠈⣇⣜⢀⣮⠝⠀⡟⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢥⣿⠿⣇⡸⠿⣅⡀ ⠀⠀⣠⢏⣉⣁⡨⠯⢕⣠⠞⠁⠀⠀⣠⠞⠋⠉⠀⠈⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣴⡷⠘⠿⢤⣾⣿⠗ ⠀⢸⠁⠀⢀⠤⢽⣮⢉⠉⡆⠀⠀⡼⠁⠀⠀⣠⣤⣄⠀⠀⠀⠹⡄⠀⠀⠀⠀⢰⠎⢀⣩⣽⣧⡤⠄⠘⢆⠀⠀ ⢠⣿⠓⠢⣅⠀⠀⠙⢀⡼⠀⠀⣠⡇⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⡗⠢⣄⠀⠀⠘⣆⠀⠋⠁⠈⠇⣀⣀⣸⡀⠀ ⣸⡛⣇⠀⠈⠙⣻⠋⠁⠀⢠⠞⠁⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠳⡄⠀⠈⠓⢤⡤⠤⠒⠁⢉⣷⡇⠀ ⣿⠇⠀⠀⠀⠀⣧⡆⠀⢀⣏⣀⠀⠀⠙⠳⣤⣄⣀⣀⣤⠴⠛⠁⠀⠀⠀⠤⣵⠀⠀⠀⣼⠇⠀⠀⠀⠘⣹⡅⠀ ⢱⠀⠀⠀⠀⠀⠹⢷⣆⡾⠋⣠⣤⣤⣀⠀⠀⠒⠙⠓⠒⠂⠀⢀⣤⣶⣶⣄⠈⢧⢀⣶⠟⠀⠀⠀⠀⠰⠛⡇⠀ ⠘⣇⠀⠀⠀⠀⠀⠘⢻⡇⠀⢿⣿⣿⣬⣷⣦⣄⣀⠀⣀⣠⣴⣯⣼⡟⣻⠏⠀⢸⠟⠃⠀⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠘⢆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠛⢿⣛⣿⣧⣀⣿⣿⣿⠿⣏⣹⠿⠛⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀ ⠀⠀⠘⢷⠄⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⡀⢀⡴⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⣷⠄⠀⠀⠀⠀⠙⣿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡡⠋⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠙⠲⣦⣄⡀⣀⠀⢀⣤⣤⣞⠁⠚⠀⠀⠀⡀⠀⠀⣴⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣄⠀⠀⠀⠀⠉⠉⠙⠲⠻⠛⡽⠁⠀⠀⠀⠀⡼⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⣿⢄⡠⣄⠀⠀⠀⠀⠀⠘⠀⢀⠀⣀⣴⡟⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠀⠈⠃⠙⠏⠓⢤⡀⠀⣄⣀⡴⡿⠞⠋⠋⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡀⠀⠀⡟⠳⠤⢀⣀⣀⣀⣀⣀⠤⠤⠒⢦⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠖⠒⠒⢄⡘⠳⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠀⣀⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠒⠒⠒⣒⡲⣿⣶⣼⢲⡬⢧⡀⠀⠀⠀⠀⠀⠀⢰⣿⠽⢶⠊⢉⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣦⡶⠟⢻⡓⢢⡙⣷⣷⣄⡈⢧⠀⠀⠀⠀⠀⠀⠈⠻⣽⡏⣯⡭⠗⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠷⠬⢤⣌⣉⣉⣠⣼⠟⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡘⠾⠤⢀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠤⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣴⣸⣇⣷⣌⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣥⣴⠾⠉⠻⢸⣧⣤⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣀⠀⠀⠀⠁⠻⠺⠆⣠⣤⣄⠀ ⠘⢿⣿⠭⠭⠿⠿⠿⠿⠿⠿⣿⣿⣿⠋⠟⠛⠛⠛⠛⢛⡛⠿⠿⠟⠀ ⠀⡶⠒⠒⠒⣶⠖⠒⢲⣦⡴⠞⠛⠛⠓⠦⣴⡖⠒⠒⣿⡗⠒⠒⢲⡆ ⠀⢻⡆⠀⣼⣿⡆⠀⣾⣿⡀⠀⠺⠷⣤⣤⣿⣿⠀⠀⠈⢿⠀⠀⣿⠁ ⠀⢸⡇⠀⢹⣿⠇⠀⣿⣿⠿⠷⣶⣤⠀⠈⣿⣿⠀⠀⣦⠈⠀⠀⣿⠀ ⠀⠘⢷⣀⣈⣉⣀⣴⣿⣿⣤⣀⣈⣁⣀⣴⣿⣇⣀⣀⣻⣧⣀⣀⣿⠀ ⠀⠀⢠⣬⣉⠉⠉⠉⢉⣿⠿⠏⢹⣿⡏⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⠀ ⠀⠀⢸⣿⣷⣭⢦⣼⣿⠏⠀⠀⣸⡟⣧⠀⠀⠀⠀⠴⢾⣿⣿⣿⢿⠀ ⠀⠀⠸⣿⠿⣿⡼⣷⢢⣄⣀⣴⣿⡇⣿⣧⣄⣀⣠⣴⣿⠿⠋⢯⡜⠀ ⠀⠀⠀⠉⠀⠀⣿⣯⠙⠻⣿⣿⠿⠀⠻⢟⣫⢿⣛⡉⠁⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠘⢻⣿⣄⡀⠉⠻⢶⠞⣉⣴⡾⠯⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢶⡶⠶⠟⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⣩⣿⣿⣷⣾⣿⣿⣿⠿⠋⠉⢯⠻⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⣺⠃⢐⣿⣿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠘⡆⠙⣿⣿⣾⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⣸⠃⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⠘⣿⡻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⢀⡏⢀⡞⢹⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢆⠘⣷⡹⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢄⠀ ⢸⢁⡞⢀⡇⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠆⠘⣷⣼⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁ ⢸⡾⠀⢸⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡨⠖⠚⣿⣽⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⢸⡇⠀⢸⣇⢹⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡟⠁⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⠃⣸⣿⣿⣿⣿⣿⠁⠀⠀ ⢸⡇⠀⠘⣿⣼⣧⢿⡄⠠⡔⣖⢒⣲⡄⠀⠀⢰⠁⠀⢹⣟⣙⣿⡿⢿⣿⠘⣿⣿⣿⣿⣿⣿⣿⡟⢀⣜⣰⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⢸⣷⡀⠀⠹⣿⣽⣾⣿⣴⣿⣿⣿⣿⣿⡆⢀⠇⠀⠀⠀⠀⠉⠉⢣⠀⢹⠷⣿⣿⣿⢹⣿⣿⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣅⠁⠀⠀ ⠀⡇⢳⠀⠀⠹⡿⣿⣿⣿⠿⣧⠿⠋⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠀⢹⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠁⠱⠄⠀⠀ ⠀⢷⡀⠳⡀⠀⡿⢿⣿⣿⣧⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⢤⣿⣿⢻⣿⣿⠁⣽⣿⣿⣿⣿⣿⣿⡏⡅⠀⠀⠀⢰ ⠀⠈⢧⠀⠙⢄⢡⠀⠻⣿⣿⣧⠀⠀⠁⢺⣤⡄⠒⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣾⡏⠸⠀⠸⡿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘ ⠀⠀⠈⢣⠀⠀⡻⢄⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⡞⠀⡸⠁⠀⢰⣟⣿⡿⠁⠀⠀⠀⢣⣈⡿⠿⠿⠿⠣⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠑⣄⡇⠀⠣⠀⠹⡿⣿⣷⡀⠀⠀⢿⣿⣿⣿⠿⠋⠀⠀⠁⠀⠀⣾⣿⡏⠥⠤⠐⢒⣈⣁⣀⣀⣤⣤⣤⣤⣀⣈⠑⠀⠀ ⠀⠀⠀⠀⠀⣸⠓⢄⡀⠙⢦⣳⡜⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢋⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣓ ⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢹⠆⢿⡏⢻⣿⣦⡀⠀⠀⠀⢀⠴⢊⣡⣴⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢸⠃⠀⢹⡙⠏⠓⠄⢈⣡⣶⣿⠿⣛⣭⣶⠿⠟⢛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⢀⣠⡴⠟⠛⣉⡴⠞⠛⠉⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⣀⠴⠞⠋⠁⠀⠀⠉⠁⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣯⣿⣿⡿⢛⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠒⠲⢤⣀⡀⠀⠚⣫⣿⣿⣿⣿⡿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣤⠴⠒⠛⠒⠯⠥⣄⣀⠀⠀⠀⠉⠉⠙⠛⢿⢶⣴⡋⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠈⢇⠹⡆⠀⢀⣀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣀⣀⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢸⡀⡇⠀⠘⠛⠁⣀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⢀⣴⣋⠥⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠱⡀⠀⠀⣸⢃⡇⠀⠀⠀⢾⣿⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣧⡴⠚⠋⠙⠃⠀⠀⠀⠀⠁⢀⣠⠷⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠏⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠙⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡈⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠇⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⣩⠴⠛⠋⠛⠲⢦⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠏⣠⣿⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢏⡟⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⢠⡏⠀⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣀⣀⣠⣤⠶⣿⣿⣿⣿⡆⠀⠇⠀⠘⣿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⣀⣀⣠⣤⣤⣴⣶⠚⠁⠀⠀⠀⠈⠉⢹⣿⣷⠾⠛⠋⠙⡿⢿⣄⡴⠀⠀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡟⣿⣿⡿⠿⠷⠶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⣇⣼⡿⣶⣶⠂⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣧⣿⠃⠀⠀⠀⢸⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢻⣿⣷⡾⠿⢩⠻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣽⣟⡛⠂⠸⢠⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⠖⢋⣁⡆⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠸⣿⣿⠿⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⢸⠀⠀⢰⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⠴⠗⠒⠶⠄⠀⢀⣠⣾⠏⠀⡜⠀⠀⡼⠀⣼⣇⣀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⣿⣿⣿⣿⣶⣄⣀⣤⢤⣘⣁⣀⠀⠀⠀⢤⡶⠟⠊⠁⠀⢀⡇⠀⠀⡇⠀⣿⡏⠉⠙⠛⠓⠲ ⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠶⣄⠀⢀⣀⣀⣰⡏⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢸⣿⢷⣄⠀⠀⠀⠀ ⣅⣀⡀⠀⠈⣿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⣷⣿⣿⣿⠟⣧⠀⠈⠉⡉⠀⠀⢹⠃⠀⠀⠀⠀⠀⡇⠀⠀⡎⠀⡿⢿⠀⠙⣦⠀⠀⣚ ⠀⠀⠉⠙⠓⠿⣿⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠙⣏⡸⠃⣰⣿⡷⢦⣄⣑⡄⣠⣿⠀⠀⠀⠀⠀⢰⠃⠀⢰⠃⢰⠇⠈⠳⣄⡇⢐⠋⠉ ⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⣿⡇⢰⡿⠹⣧⠀⠈⠉⠣⡀⢹⠀⠀⠀⠀⠀⡸⠀⠀⣸⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠈⡆⠀⠀⠀⠀⠀⡇⠻⡇⢸⡇⠀⣿⣆⠀⠀⢠⠟⣿⠀⠀⠀⠀⠀⡇⠀⠠⡇⠀⢿⡇⠀⠀⡼⠷⠀⠀⠀

⠀⢀⣾⣿⣿⣟⡿⠛⣩⠟⣉⠽⠛⡂⣀⠀⠀⠀⡀⠬⣍⣓⠦⣈⢢⡻⣯⠳⣄⢺⡦⠙⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢋⣵⠏⢠⠀⣠⣯⠞⠁⢠⣾⠿⡿⡄⣾⣯⡙⣷⡌⠻⣷⡜⢳⣵⡈⢷⡈⢦⠙⣿⣦⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣵⣻⠇⡰⣁⡼⢉⠏⠀⢠⢣⡟⠀⠸⢀⡿⣿⡿⣯⠙⣖⡜⢿⣶⡟⢿⡄⢳⡘⣧⠈⢟⢷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⡳⢰⢁⣽⠁⡎⠀⢠⠇⣸⠀⠀⡿⠘⠀⢻⠁⢹⡆⢻⡾⡌⢻⣿⣌⢧⠀⢳⢸⣧⠈⢧⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣇⢇⣿⡇⢰⠀⠀⣸⠀⡏⠀⠀⠀⢠⠀⠸⡀⠀⣷⠀⢿⣿⣄⠛⢿⣇⣧⠀⢧⣿⡳⣎⣧⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡾⡼⣿⠀⣼⠀⢸⡇⢠⡇⠀⠀⠀⢸⠀⡆⡷⡆⠹⡆⢸⣿⣿⡆⠈⢿⣷⠀⠘⣿⣇⢸⣿⣧⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢷⣷⡇⠀⡿⠀⣿⡇⢸⡇⢰⠀⠀⢺⠀⡀⡗⡁⢸⡗⠀⣿⡈⣿⡄⠈⣿⡇⠀⠉⣿⣮⣿⣷⣈⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⣾⣿⡇⢰⠁⠀⣻⡇⢸⡇⢸⡇⠀⣿⠀⡇⣿⡇⠸⢯⠀⣿⡇⠸⡇⠀⣿⣿⡀⠀⢹⣷⡟⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣾⣿⣿⡅⡈⠀⢸⣿⠃⢸⡇⣾⡇⢀⣿⡀⢿⣿⡇⠀⡄⠀⣿⡇⠀⢿⡆⣸⣿⣿⣼⠈⣿⡇⣿⣋⠹⡇⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠃⡇⢠⢸⣿⠇⢸⡇⣿⣿⣸⣿⣷⣶⣿⣿⠀⠇⣽⢿⠃⢀⣰⣿⣿⣿⢻⡿⡄⢿⣷⣍⣉⢋⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⡇⡇⢸⡜⢿⢰⣾⣷⣿⠻⣿⣿⣿⣿⠉⣟⠀⣆⣿⣾⡾⢟⣯⣴⣿⣿⣾⣿⡇⢸⡇⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣽⡇⡇⢸⡇⢸⣿⣿⠻⣿⣠⣿⣿⣿⣿⠀⢿⣼⣿⣿⠏⢰⣿⣿⣿⣿⡿⣹⣿⢱⡾⣇⡟⢹⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⢛⡇⣷⢈⣿⣾⣿⣿⣆⣿⣿⣿⣿⣬⣿⠀⣸⣻⠿⠋⠀⠘⠉⠽⠿⠿⡾⠟⢹⣸⠀⣿⡷⣻⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣷⣿⣸⣿⣿⣿⣿⠿⣿⣿⣿⣿⢧⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡏⢹⡟⠋⠙⢶⠌⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣻⠿⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡃⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢀⡇⠀⠉⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣿⣤⠃⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⢹⠋⠉⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢀⣷⢸⣿⢁⣀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⢀⡿⣷⠘⢸⡇⠀⡀⣏⠳⣄⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⠋⡀⠀⠀⢀⣿⠏⣼⠁⠈⠈⠉⠙⠲⢤⣠⡄⢸⠄ ⠀⠀⠀⡰⠋⠀⢻⡀⢿⡇⠀⢡⢿⠀⠀⠑⢦⣄⠀⠀⠀⠀⠠⠤⠤⠴⠊⠀⠀⣠⣿⣿⢠⡿⠄⠀⠀⠀⠀⠀⢠⠿⢉⣿⠀ ⠀⢠⠞⠀⠀⠀⢆⢇⢸⣷⠀⢺⣌⡇⠀⠀⠘⢿⣿⢷⡦⠤⣄⡀⠀⠀⠀⣀⢼⡏⣽⣇⣿⠂⠁⠀⠀⠀⠀⠀⠘⠀⣸⣏⠀ ⢀⡇⠀⠀⠀⠀⠈⣞⡄⣿⡶⡈⠙⣿⠀⠀⠀⠈⢿⡳⣄⠀⠀⠈⠉⠉⠉⠁⡸⢹⣿⣿⡏⡖⠀⠀⠀⠀⠀⠀⢀⣼⠏⠘⠄ ⢸⠁⠀⠀⠀⠀⠀⠘⢷⣼⣷⠹⣄⠘⢷⢄⡀⠀⠀⠙⠾⣆⠀⡀⠀⠀⠀⣴⡷⢿⡟⣿⠆⡇⠀⠀⠀⠀⢀⠆⣾⣿⡴⡴⠁ ⢸⡀⠀⠀⠀⠀⣠⡤⠈⢻⣿⣆⠈⢳⠘⢧⠉⠲⣄⡀⠀⠈⠙⠻⢆⣀⡜⠉⠀⠋⡰⠋⠀⣇⠀⠀⠀⠀⠸⠀⣿⣽⣾⡗⠀ ⢸⣇⠀⠀⣠⠈⠉⠀⠀⠀⠹⣟⢆⣀⣧⠀⢷⡀⢀⠉⠓⠦⢤⠀⣠⣿⣿⢿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⢸⣷⠎⠀⠀ ⠀⢫⠳⣞⡁⠀⠀⠀⠀⠀⠀⠈⢣⠱⠜⣧⠘⣟⣄⠑⠢⠤⠄⣠⣿⣟⠉⠀⢹⡟⠲⢤⣀⠀⠀⠀⠀⠀⠓⠀⠘⣿⡀⠀⠀

⠀⠀⠗⢝⠦⣠⣊⣽⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⠀⠈⠓⢄⠀⠀⠀⠀⠀ ⠀⢀⣤⡴⠾⠋⣩⣿⣿⣿⣿⣿⣿⠟⠉⢹⣿⢾⣿⣷⣦⣄⡐⢄⠀⠀⠀ ⡠⠛⢃⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⣿⠈⣿⣿⣿⣿⣿⣦⡑⡀⠀ ⠀⠀⢈⣾⢿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠦⣿⣤⣸⣇⣸⣿⢻⣿⣏⢪⡂ ⠀⠀⠜⠉⢺⣿⣿⣿⠀⢀⣠⣀⠀⠀⠀⠋⢹⢧⠀⠀⠈⠻⠛⣿⣿⣦⣷ ⠀⠀⠀⠀⣾⠏⣿⢹⠀⠁⢀⡈⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⢰⡿⣿⣿⡟ ⠀⠀⠀⠀⠘⠀⢿⢈⠀⠀⠀⠤⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠈⢰⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠄⠘⠀⠀⠟⡩⠂⠂ ⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⡐⠀ ⠀⠀⠀⠀⠀⠀⢠⣘⣂⠀⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⣨⢶⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠉⠀⠇⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⢤⣄⢀⣀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣧⠀⠀ ⢀⣾⣾⣿⡿⠃⢸⣿⣿⣿⣯⣿⣿⡟⢿⣦⡄ ⠘⢿⣿⡟⡀⢢⣄⠛⠉⠉⢃⣭⡙⠎⣿⣯⠃ ⠀⠨⣿⡇⠀⠙⠛⠁⠀⠀⠘⠛⠃⠀⢸⡟⡄ ⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠗⠀ ⠀⠀⣸⣿⣷⣤⣀⠀⠀⠀⢀⣀⣴⣿⠁⠀⠀ ⠀⠀⣥⡏⣟⣿⣿⣿⠀⢸⢿⣿⣿⣯⡿⠀⠀ ⠀⠀⣿⣿⠛⠋⠋⡀⣆⡎⡈⠋⠙⢻⣷⠇⠀ ⠀⢰⣿⣿⡄⠀⣿⣿⡿⣿⣿⡏⠀⠌⢹⣿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠶⠛⠓⣶⠚⠛⢻⣿⣷⣦⡾⣥⣈⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣯⠿⣧⠀⣀⣴⡟⣶⠾⠟⢛⣉⣉⣉⣉⣿⣿⣤⠤⣿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣭⡴⣶⣋⣉⣤⣼⣟⣛⣩⣍⣿⡞⠉⠙⢿⡉⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣭⣛⠿⠥⣾⣿⡇⠀⠀⣠⣌⣷⣶⣿⣛⣛⠲⢦⣽⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠶⠶⣿⡶⣎⠁⠀⠀⣹⠇⠈⠉⣻⢿⡒⢿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡑⢦⡶⣧⣀⣴⣾⠗⠛⢳⡦⢿⣄⡀⢸⣇⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠻⣿⣅⡉⠓⠦⣼⣧⡈⣿⣿⣻⣿⣦⡀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣎⣫⡙⠲⣶⣿⣽⣷⠿⠟⢻⣿⣿⡇⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⢾⣿⡿⡟⠳⣶⣞⠛⣿⡿⣿⠀ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣥⣭⡗⣿⣿⣿⢿⣥⣿⡇ ⠀⠙⠓⠦⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⣥⣼⣿⠑⣦⣼⢿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠻⣿⣿⠞⢻⣶⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣏⣴⣯⢽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠈⣧⢻⣧⣼⣿⣻⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⠶⠤⣤⣘⣿⣿⣥⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⠤⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠿⠶⣤⣀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠙⢷⣄⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡽⠷⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢷⠄⠀⠀⠀⠀⣷⠀⠀⠀⢀⣤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⢀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠳⠤⠞⠀⠀⢀⠀⠀⠀⠦⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠐⢒⡲⠆⠀⢿⠗⠀⡶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠞⠷⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⢀⡞⠹⠗⠚⠋⠉⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⡤⠶⠞⠁⠀⠀⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⠈⢷⣄⡀⠀⠀⠀⠀⣀⣀⣤⣟⣀⣀⣀⡴⠞⠋⠉⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀ ⠀⠀⠉⠉⠙⠛⠋⠉⠉⠁⠉⠉⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠶⠶⠶⠶⠶⠖⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣾⣟⠳⢾⣷⡤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣆⢙⢤⢺⠻⣿⣾⡖⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣿⣿⣯⣾⣿⣿⣾⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡟⠟⣿⣿⢏⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣤⣴⢾⠁⢜⣿⣷⣦⠹⡉⠓⠁⠈⡡⣻⣷⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢪⣇⣼⣿⣎⣱⡦⠔⠉⠑⡆⠀⠁⣀⢥⣿⣿⣿⡿⠷⣄⠀⠀ ⠀⡀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⡠⠀⣴⢊⣡⢿⢟⣿⣾⣷⣀⠹⣦⠀ ⡌⡄⠀⠀⠀⠀⠈⣻⣿⣱⡇⢀⠠⠀⠀⢸⣿⣿⣿⣽⣿⣝⢿⣖⢺⡠⣿⡄ ⣷⡀⠀⠀⠀⠀⠐⣪⣿⣷⣌⢃⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⣿⣿⣿⣻⡿⣿ ⠸⣧⡀⠀⠀⠠⢮⣿⣿⣶⡿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿ ⠀⠈⠻⠶⣤⣤⠾⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⣈⢻⣃⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣉⡉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠉⠉⠙⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⣿⢿⡇⠀⠀⠀⠀⠀⠀⢹⡿⣿⢳⣄⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠹⣆⠀⠀⠀ ⠀⠀⢠⡟⠀⢸⡇⠀⠻⣦⣀⠀⠀⣀⣴⠟⠀⢸⡇⠀⢻⡄⠀⠀ ⠀⠀⢸⡇⠀⠀⢻⣄⠀⠀⠉⠙⠋⠉⠀⠀⣠⡟⠀⠀⢸⡇⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠙⠷⣤⣀⣀⣀⣀⣤⠾⠋⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⢰⠶⠾⠷⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠾⠷⠶⡆ ⢸⡷⠒⠒⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠒⠒⢾⡇ ⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇ ⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇ ⢸⣷⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣾⡇ ⠀⢷⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⡾⠀ ⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣾⡉⣩⣲⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠘⠂⠂⣒⡒⣒⢒⣖⠚⠯⠭⠽⣛⣒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⢀⠄⠀⠀⠁⠕⡘⠛⠿⠷⠦⢤⣉⡑⠢⢍⡛⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠚⣹⡏⠉⠑⠒⢒⠟⠫⠭⠷⣾⣯⡥⣀⣨⠉⠑⠲⢬⣑⠢⠍⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣴⣖⣲⡖⣿⠭⡭⠉⠿⠷⢒⣒⣦⡾⣄⣀⠀⠀⠀⠈⠉⠙⣛⡶⢤⣀⣀⠉⠓⠠⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⢿⡭⢾⢓⡺⢏⣉⣭⡩⠭⠯⢅⣭⣉⣉⣛⡣⠶⣿⣙⡲⠧⣄⣀⠀⢀⠀⠈⠙⠯⣀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢮⣆⡀⠐⡊⠂⠉⣶⠛⠚⠋⠉⠛⠓⠚⠓⠣⠭⢝⣒⠯⠵⣒⣌⣙⠒⠤⣀⡀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠦⣍⡂⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠭⣟⡷⢦⣤⡉⢒⡤⣼⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣤⣯⣿⣄⡀⠀⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢬⡑⠻⢷⡯⡲⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢿⡷⣿⣥⣿⣽⣿⣦⣀⣼⠿⠶⢶⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣤⣠⣬⣷⠀⠙⢎⠑⣝⢢⡄⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠘⣬⠋⠹⣵⡏⢻⣇⠀⠐⢻⣿⣛⢽⣷⡤⣶⡶⠖⠚⠛⡿⠋⠉⠉⠉⢹⣧⡀⢨⡇⣗⠀⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣀⣰⣿⠀⠀⢻⣆⠀⢌⠉⠀⠀⣿⡈⠉⠀⠀⠀⠀⠀⠀⠰⡇⠀⣼⡿⠦⠬⠶⠿⠶⠿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⠆⠀⠀⠀⠹⡷⠦⠤⠤⠾⠃⠁⠀⠀⠀⠀⠀⠀⠀⡇⣨⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣄⣀⡴⠶⠦⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠺⠋⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⡀⢠⠀⡀⠀⠀⠸⡄⠀⠰⠀⠀⠀⠀⠀⠀⣸⡁⠀⡰⢻⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⢿⣛⣯⣵⣦⣄⡀⢳⠀⠀⠀⠀⡀⠀⢀⣬⠃⡑⠊⠁⢸⡿⡌⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠉⠀⠀⠀⣀⡈⠳⡀⠀⢀⠇⣀⡾⠃⠀⠇⠀⢀⠜⠀⢧⠀⠙⢦⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⣠⠿⠊⠀⠀⠀⠠⠀⡰⠃⠀⠀⣼⠀⠀⠀⠈⢯⠙⠦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠳⢄⣀⣀⠀⠀⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢠⠇⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⡼⠋⡉⠫⣉⠉⠲⢄⡀⠀⠠⡀⠀⢀⡴⠋⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠉⠳⠮⣕⢄⡀⠙⣆⣀⡴⠞⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢰⡇⢀⣀⡀⠀⢉⡿⣿⠿⠓⠒⠉⠉⠉⢳⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠨⢿⠀⠈⠩⠭⠽⣀⣿⣒⡒⠒⠉⠁⠀⢸⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀ ⠈⡇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢸⡄⠀⠀⢀⣴⠏⠈⠑⢌⠑⢦⣀⠀⢨⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⠀⠀⢸⠧⢴⠞⣽⡞⠀⠀⠀⢠⠳⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⢸⠄⠀⠀⢿⡇⠀⠀⠀⠞⠀⠈⠓⢚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢑⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⡔⠵⠠⠊⠈⠉⠠⣀⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡞⠃⢈⢈⣿⠔⣀⣄⠂⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢋⡐⣿⡧⡴⠚⠙⢿⠿⠭⠠⠂⢀⣬⣈⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⢷⣷⠄⠠⢂⠃⠀⢀⠀⠀⠘⠻⢑⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁⠘⡉⠛⠁⢡⠀⠀⠑⣤⠴⠣⣭⠂⠱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣽⠗⣦⠎⡢⢴⠊⡄⠀⠀⠀⠫⡉⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠸⠋⣵⣶⣁⣀⣱⡀⢀⠄⠊⢣⠜⠀⠀⠀ ⠀⠀⣀⡴⢂⡖⢢⣄⠀⠀⠀⢳⣀⣁⠀⢀⠏⠀⠈⣿⠀⡧⢎⠀⠀⠀⠗⡄⠀⠀ ⠀⣎⣙⡧⠘⠓⢻⣟⣑⡀⠀⢸⠛⢓⡓⡖⠤⢀⣠⡃⠠⠃⠉⠢⡀⠀⠘⠚⠒⡄ ⢸⣿⣿⠀⠀⠀⢠⣧⣭⠁⠀⡸⢷⣤⣏⠰⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⠄⡤⡔⠁ ⠈⠛⠃⠀⠀⠀⣎⠛⡏⠀⢰⣇⠀⡾⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠀⣘⣉⡻⠁⣠⡇⠉⡻⠦⠀⢀⠊⠑⠦⣀⠀⠀⠀⠀⣣⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⢿⢟⡷⠺⣎⠻⢦⡉⠀⠠⣺⡀⠀⠀⠐⢌⠉⠉⠉⠙⡣⡀⠀⠀⠃ ⠀⠀⠀⠀⠀⢈⡟⢿⣆⠘⡆⠘⣀⠔⠰⠟⣉⡆⠀⠀⠀⠑⢄⠀⠀⠐⡌⡂⠀⠀ ⠀⠀⠀⠀⠀⣸⡻⢦⣍⠁⡡⠒⢣⠈⠖⣚⣫⠃⠀⠀⠀⠀⠀⠈⢒⠀⠜⠁⠀⠀ ⠀⠀⠀⡔⠉⠀⠉⠁⡠⠊⠀⠀⢎⠈⠓⠊⠁⢹⠀⠀⠀⠀⠀⠀⠈⠂⠚⠂⠀⠁ ⠀⠀⠀⠣⢄⣀⠤⠂⠀⠀⠀⠀⠀⠉⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠂⠀⡁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣶⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢉⣥⡤⢬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠃⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠄⠀⠀⣼⡇⣼⡟⠀⣴⡗⠀⣴⡿⠋⣷⠀⣰⡾⠋⣷⠀⣼⣟⠔⣿⠇⠀⠀ ⣼⠿⢤⡄⢠⡿⢱⣿⠁⣰⣿⠁⣸⣿⣁⡾⠃⣸⡿⣠⡾⠃⣰⣿⠏⣼⡏⢀⠞⠀ ⠹⣄⣸⣷⡿⠃⢼⣇⡼⣿⣇⠜⠹⣯⣁⣀⠼⠹⣯⣁⣠⠞⣿⠏⢠⣿⣡⠎⠀⠀ ⠀⠈⠉⠙⠷⢂⣬⣿⣶⡾⢅⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠈⣠⣄⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⠋⣰⡿⠁⢠⡇⠀⣀⣀⡀⠀⠀⢀⣀⡀⠀⢀⠁⠀⠁⢀⣐⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣧⡶⠟⢁⣼⠟⢡⡷⢀⣼⠟⢁⡗⠀⠈⠂⡠⡀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡏⠀⢹⡄⣸⣟⣤⠟⢁⣾⣏⣴⠟⢁⡜⠀⡪⡪⠚⡀⠀⣀⣡ ⠀⠀⠀⠀⠀⠸⢿⢤⣤⡾⠃⠸⢧⣄⡤⠎⠙⢧⣄⡤⠏⠀⠀⠀⠀⠀⠐⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠒⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡸⠥⣄⣀⠀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⠶⠯⠽⣗⣾⠽⣧⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠉⠹⣗⠺⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠋⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⣰⡄⢹⣠⠖⠉⠉⠉⠙⢢⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢠⠿⣿⠀⠀⢸⠆⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡶⢶⡏⢠⠛⣄⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡞⢀⡞⠀⠈⠉⠒⠒⠚⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⣧⡞⠀⣀⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢦⣀⣀⡴⠟⠇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡧⡀⠀⠀⠀⠀⣴⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⡋⢹⠙⠿⣄⣾⣣⣞⣣⡴⠿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⣭⡦⢿⣧⡿⠀⠀⠀⠀⠉⠁⠘⣧⡀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⢿⠸⣎⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⡟⢾⣿⣉⠙⢤⡀⠀⠀⠀⠀⠀ ⠘⢦⠈⠢⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⡄⠹⡄⠀⠀⠀⠀ ⠀⠀⠑⣄⠈⢢⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡠⠔⢋⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢲⣋⣉⡬⠓⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⢳⠤⣄⣀⣀⣀⣀⣀⣀⡯⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠠⣤⣤⣬⣍⣉⠉⠉⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠃⠀⢠⠏⠀⠀⠀⠘⢦⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⡴⠃⠀⠀⠀⠀⠀⠀⠑⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⢦⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⡠⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣄⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣖⠉⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡉⣹⣄⠀⠀⠀⠀ ⠀⠀⢀⡔⠋⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠉⠁⠀⠙⢢⡀⠀ ⠀⠰⠯⠤⠤⠤⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠤⠤⠽⠆ ⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠖⠚⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⣴⡿⠃⠀⣴⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣠⠆⢀⣾⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⡴⠃⢀⣿⠏⠀⠀⣸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⡽⣱⢃⡞⠁⢀⣾⠋⠀⠀⡴⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡜⠁⡼⣳⢣⠞⠀⢠⠾⠃⠀⢀⡾⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠟⠀⣰⣿⢣⠏⠀⢠⠏⠀⠀⠀⡼⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⢀⣿⢧⠏⠀⢠⠏⢀⠄⠀⢠⠇⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠁⠀⢸⣟⡏⠀⠀⡞⢠⡞⠀⢀⣾⠀⢰⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠇⢀⡶⢹⡿⣠⠀⣸⠃⡼⠁⠀⣼⡇⠀⣸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢸⠁⣿⠁⡇⠀⡇⢰⠃⠀⣼⢹⠀⢀⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠓⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⡞⠀⡏⢸⠁⢸⢁⡞⠀⣸⠁⢸⠀⣸⢻⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⣀⣠⠄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢸⡇⡄⢹⢸⡀⢸⢸⠃⢰⡇⣀⣸⠀⣇⠈⣇⢹⣿⣿⣿⣿⢿⣿⣷⣿⢷⣻⣏⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢸⢸⠁⣸⠀⡇⢸⡟⠀⡞⠛⠛⢻⢻⠛⠛⢼⣿⣿⣿⣿⡿⠀⢿⡋⠀⠘⠿⣼⣠⠴⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢸⢸⡇⣿⠀⢷⣸⡇⢰⢡⣤⣶⣾⣿⣶⣤⡄⢻⣿⡟⠈⢷⠀⠈⠉⠛⠉⠉⠉⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢫⣧⢸⣿⣿⣿⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣼⣷⡿⢠⡾⣿⣧⣼⡋⠉⠁⠀⠹⣿⣏⡭⣦⡟⠃⠀⠈⠛⠶⣤⣄⣔⣠⡴⠚⠉⠀⢸⣿⡇⢸⣿⣿⣿⣿⡟⣰⠟⢣⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⢿⢹⣿⡾⡇⢻⣿⣧⠙⠶⠦⠴⠖⠚⠉⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢻⣿⠀⠛⢉⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡁⢸⣼⡟⣿⡆⠀⠀⢀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⢋⣠⣴⣿⣿⣿⣿⣿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢠⠤⡀⠁⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⣿⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣧⠀⠀⠉⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⣶⣶⣶⣾⣿⠿⢿⠿⣼⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢹⣎⣯⡀⠀⠀⠀⠀⠘⣿⣶⣶⡿⠟⠀⠀⠀⠀⢖⣠⢤⠄⠘⣿⣿⣿⡿⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣯⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡉⣿⣿⣿⣯⣿⣿⣟⣿⣛⣿⣿⣿⠿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣵⡿⢻⡇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣴⣶⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⢟⣽⠟⠀⢸⡇⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣆⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣷⡙⣀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣛⣭⠉⠁⠉⠹⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣽⣿⠛⡏⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⡿⠿⡁⢀⡀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⢸⠛⣿⣿⠇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⣴⣾⡿⠯⢁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⣀⣴⣿⡿⠋⡙⣿⣿⣿⣿⣿⠁⠈⠹⡆⢸⣿⣺⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣿⣿⣿⣿⡿⠀⢀⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⣏⠰⣆⢷⡸⣿⣿⣿⣿⣞⠉⠀⢧⠸⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣴⣿⣿⣿⣿⣿⠟⠀⠀⠈⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣳⡆⠹⡆⢹⡎⢷⣿⣿⣿⣿⣇⠀⠀⠘⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⢶⠇⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⠀⠒⠒⠒⠂ ⠙⠉⠀⣰⠎⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠙⣆⣀⠀⠀⠀⠀ ⠀⠀⡰⠉⠒⠂⠤⠤⡾⠤⠤⠤⣤⣤⠄⣠⠂⣶⠶⢽⡕⢲⠈⢣⠈⢯⠀⠀⠀⠀ ⣴⣼⡷⢖⡒⢲⠂⣹⠉⠉⢉⡏⣰⡇⣰⡟⣸⣿⠀⣿⣿⡄⣧⠀⢷⡘⡆⠀⠀⠀ ⠉⢉⠷⣤⣝⡏⢲⡇⢰⡀⣾⣶⣿⣰⣿⣧⣿⡟⣸⣿⡿⣷⣿⣿⡘⡷⣷⠀⠀⠀ ⠀⢰⣶⣭⣽⣯⣿⣷⢾⣾⣿⣿⣻⣿⣿⡿⣿⣷⣿⢻⠛⣿⢻⣿⣧⣿⣿⠀⠀⠀ ⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⠯⣿⠃⣿⡿⠣⢓⣽⣿⠹⢿⣿⡇⠃⠀⠀⠀ ⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⡻⡿⠒⠽⠃⠁⠀⠈⠁⣀⣿⣿⣀⣀⣀⣀⣀ ⣤⣤⣤⣽⣿⣿⣿⣚⡌⢻⡇⠈⠒⠂⠀⠀⠀⠀⠀⠀⣤⠘⠙⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⣝⢊⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿ ⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡦⢄⡀⠀⠀⠒⠴⠖⠛⠟⠁⣰⣿⡇⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⡷⠀⠹⢶⣤⣀⡀⠀⠀⣠⣾⣿⣿⠁⣿⣿⣿⣿⣿⣇ ⣿⣿⣿⣿⣇⢻⣿⣿⡿⠸⣧⡀⠀⠀⠉⠻⢿⣿⡿⣿⣿⣿⡟⡇⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣾⣿⣿⠁⠀⠡⡈⠢⢄⠀⠀⠀⠀⣗⡌⠻⣿⢳⡇⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠐⢄⠀⠈⠁⠐⠈⠩⣻⡄⠙⣷⣦⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠶⠦⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠉⠉⠙⠒⠶⣤⡤⠤⠴⢶⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠞⠀⠀⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡆⠀⠀⠀⠀⠈⠉⣻⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠃⢠⠎⠀⠀⠀⠀⠀⡴⠞⠛⢉⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣦⣄⠀⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⣈⡙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣙⣶⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⢾⣷⣿⢿⣿⣿⣷⣌⠛⢷⣤⣄⣀⣀⣀⣰⣿⣫⣴⣦⣴⣾⡛⠉⢀⣠⠞⠋⠀⠀⡠⠆⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⢻⡀⠀⠀⠀⠀⣠⠞⢁⣾⠟⠁⣼⣿⣿⣿⡿⣧⠀⠀⠀⠉⠉⠉⢉⣿⣿⣿⣿⣿⣯⠹⡆⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢃⣀⣺⣤⣤⠿⠶⢶⡇⠀⢻⠀⠸⠃⠀⢠⣿⣿⣿⣿⡇⠘⠂⠀⠀⠀⠀⠀⡿⠉⣿⣿⣿⣿⠹⠀⡇⢹⠷⢤⣄⠀⠀⠀⠊⠀⠀ ⠀⠀⡟⠸⠻⣅⠀⠉⣳⠶⣼⠀⠀⠘⡆⠀⢀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⡇⢸⡀⣰⠏⠀⠀⠀⣀⠀⠀ ⠀⢸⠃⠀⠀⠈⠳⣄⠻⢤⡎⠀⠀⠀⢷⣀⠘⢦⣀⠈⠛⠛⣫⠜⠁⠀⠀⠀⠀⠀⠀⠀⢦⣘⢿⣿⡵⠃⠀⡇⢸⡷⠃⠀⠀⠀⢀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠙⢦⣠⡇⠀⠀⠀⢸⠉⠳⣷⣌⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠉⠉⠁⠐⠞⢲⠇⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣼⢸⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣸⠃⠀⠀⠀⠘⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣰⣇⠘⠞⠁⠀⠀⠀⠀⢠⣤⣤⣤⢤⣤⣤⣤⣤⡄⠀⠀⠀⣠⣶⠋⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠉⠻⠦⣄⡀⠀⠀⠀⠈⣿⣻⣿⡀⡈⢿⣿⡟⠀⣀⡴⠟⠁⠘⢷⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⡤⣆⠉⡟⠒⠦⠤⠼⠿⠿⢴⣷⠾⠿⢾⠟⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠀⣠⡿⠾⣇⠀⠀⠀⠀⠀⠀⢀⣿⣶⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⢳⣄⠀⠀⠀⠀⠈⠙⣦⠙⡛⢦⣄⡀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣯⡀⠀⠀⠀⠀⠀⠀⠙⣏⠉⠉⠉⠉⠉⠙⣧⣀⢘⠋⠛⡷⠀⠈⢧⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠏⠙⢦⡀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡾⠛⠁⠀⢀⣾⡇⠀⠀⠈⢧⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⢠⡟⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠹⣄⣠⠞⠀⠀⠀⠀⣼⠁⢿⠀⠀⡄⠈⢷⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠤⠚⠋⠁⠀⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠹⡄⠈⢷⡀⠀⠘⣆⠀⠀⠀⠀⢀ ⡴⠒⠉⠀⠀⠀⠀⠀⠀⡤⣸⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢻⡄⠀⢻⡄⠈⢷⡄⠀⠈⢧⡀⠀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠒⠒⠦⣄⣰⠯⣐⣒⢙⢆ ⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠐⠀⠁⠀⠀⠀⠀⣀⡼⣯⠎⠁⠈⡇⢻ ⠀⠀⢀⡠⢖⠫⠐⠈⠀⠀⠀⠀⠀⠀⣀⣠⠴⢚⡡⢴⣿⠀⠀⡰⢃⡞ ⣠⠲⠑⠈⠀⠀⠀⠀⣀⣀⣤⢴⣶⢫⠟⡓⢧⠇⠴⣆⣿⡰⣮⠞⠉⠀ ⢹⣝⣒⣒⣒⣚⣫⣉⡉⡖⢩⣵⡹⢴⡺⠃⠀⠙⠋⣩⣽⢿⡇⡤⡄⠀ ⠀⢳⡀⠀⠀⠀⠀⣬⣹⣸⠈⠛⠁⠀⠀⠀⠀⠀⠌⣶⣿⠮⣝⣫⠏⠀ ⠀⠀⢳⡀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⢐⠯⣲⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⣷⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⡽⢿⣥⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣖⠚⣉⡡⠴⠚⢉⡴⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⠉⠉⠁⢀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣄⣤⣤⣴⣾⣧⣄⣒⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣲⠾⠋⠁⠀⠀⠀⢠⠀⠀⠀⠀⢺⣿⢿⣿⣽⣿⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣯⠖⠋⠁⠀⢀⡴⠋⠀⢀⡜⡠⠞⠀⠈⢆⠙⠫⠿⢿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⢀⠀⢻⠀⠀⠘⠋⠉⢀⠰⠀⢧⠈⢦⡀⡀⠒⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⣠⡷⢋⠞⣡⡮⢷⢾⣿⠇⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣎⣻⠀⠀⢸⡰⡀⢉⠸⡧⠗⢛⣩⣴⣿⠿⢻⠇⠀⣿⣿⡆⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⡏⠀⠀⣿⣇⢢⣤⣦⣤⣤⣄⠀⠉⠉⠁⣀⣤⣤⣭⣟⣷⣄⡐⣾⠛⣿⣝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡏⢧⠀⢰⣿⣿⠟⢉⣠⣤⣤⣄⡁⠀⠀⠀⠉⣠⣤⣤⣌⠉⠛⢻⣿⡆⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠘⢧⣰⣿⠃⠀⠻⣟⢿⣿⠷⠘⠂⠀⠠⠴⢿⣿⡏⣹⠟⠁⢸⣰⣿⣿⠽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣆⠀⠙⣧⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣼⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡷⢤⣹⡄⠀⠀⠀⠀⠀⠀⣴⡋⠁⠀⢠⠀⠀⠀⠀⠀⣸⠃⢸⣇⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⣿⡆⠀⠀⠀⠀⠀⠻⣷⣤⠾⠛⠀⠀⠀⠀⢰⣿⣠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⣩⣷⡀⠀⠀⢠⡤⠤⠤⠤⠤⠤⣀⡄⠀⠀⣸⢿⣟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⢷⣄⠀⠀⠀⠓⠒⠒⠂⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣏⠳⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⠲⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⣿⠀⠀⠉⠒⠒⠶⠒⠚⠛⠉⠀⣿⣷⣄⠚⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣳⡟⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⠀⠒⠢⠌⠙⠓⠒⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡶⠛⢉⣵⢃⣿⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⣀⠤⠋⠛⢀⣿⣧⡀⠀⠀⠀⠀⠀⠐⢀⣴⣇⣀⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⠋⠀⠀⠘⡟⢘⣿⡗⢤⡀⠀⠈⠙⣲⣤⠤⣴⣉⠁⠀⠀⠀⣼⣿⣿⣿⣯⡦⢄⡀⠀⡴⠋⠁⠀⠀⠙⠿⠒⠀⠤ ⠀⠀⠻⢦⣀⣀⠀⠀⠈⠀⢻⣳⠀⠙⠦⢴⣿⣏⣹⣶⣆⣉⣷⣦⣀⣴⣿⣿⠿⠋⠘⣯⠸⣄⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠔⠋⠈⠹⣶⣤⣄⢠⡏⠻⡇⠀⠀⠀⠈⠉⠉⡿⣿⢹⡛⠛⢻⠉⣌⠃⢀⣀⡀⢸⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⢹⣿⠉⡗⠀⣿⡀⠀⠀⠀⠀⢰⢱⠏⠻⣇⠀⢸⣦⣿⠿⠋⣿⠖⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢧⢸⣿⣿⠲⢶⣦⣤⣼⣯⣀⣀⣉⣧⣤⣬⣵⣶⡟⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⣿⣦⡝⣿⣿⣏⣫⢉⣉⠀⢹⣿⣿⡟⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠉⠀⠉⠙⠻⠿⠶⡶⠿⠿⢿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀