Me Without U Emojis & Text

Copy & Paste Me Without U Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣡⠑⡀⠀⠀⡑

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⣡⠑⡀⠀⠀⡑⠨⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⣴⢕⣕⣢⣽⣴⣬⣭⣄⣠⢤⢱⡀⠀⠀⠀⣀⣔⡚⠒⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀ ⠀⠀⠀⡜⢁⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⡯⡝⡇⠀⠀⡴⢗⣤⣤⣶⣶⣶⣤⣬⣇⣀⠀⠈⠣⡀ ⠀⠀⠀⢇⢼⢿⣿⣇⣹⣿⣿⣿⣿⣿⣿⣸⡟⢨⡇⠀⠸⡷⣿⡟⣹⣿⣿⡿⠛⣿⣿⣿⣿⣮⣄⢳ ⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⠓⣼⠁⠀⣇⢫⣿⣇⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⢀⠏⣀⠀⡏⠘⣤⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣟⣾⠏ ⠀⠀⠀⠀⠀⠫⢝⡛⠟⠛⠟⡋⢉⡡⠊⣀⠞⠰⢈⢷⡧⡀⠁⢅⡙⠿⣿⣿⣿⣿⣿⣿⡿⡻⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⠣⠭⣙⠐⡢⣔⠚⠃⠀⠀⠀⠁⠻⢬⡢⢌⡣⠤⣀⠋⠛⠛⣛⠽⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⡘⢆⠈⣇⡀⠀⠒⠑⠀⠀⠀⠀⠀⠀⠙⠮⠥⢰⣖⡞⣍⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⢣⠶⠀⠀⠀⠀⠠⣀⡀⠀⢄⠀⠀⠀⠀⠀⢀⠈⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡔⠁⠀⠀⡀⠀⠀⡈⢄⣑⠨⡖⠄⢀⠀⠁⢀⠌⠈⡱⣐⠠⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⣰⡀⠣⣞⣤⣵⣽⣶⣾⣶⣤⠀⠢⠑⠡⠂⠀⠀⠀⠁⢡⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠀⠈⠀⠐⠀⠢⡀⠑⡗⣟⡭⠚⠋⠉⠃⡪⠀⠐⠄⡀⠄⠀⢀⠀⠂⡀⡆⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠀⠀⠃⢠⠕⢆⢤⣎⢭⠈⠀⠀⠀⠀⠁⠀⠐⡉⠀⠈⠄⢀⠀⠀⠀⠄⢰⠀⠀ ⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⡀⠁⢩⠟⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⡇⠀⠀⠀⠀⠘⡠⠀⠀⠉⠢⢡⡄⡡⢎⠀⡁⠀⠀⠀⠄⠠⠄⠠⡀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀ ⢸⠀⠀⠀⠀⠀⠐⠁⡀⠀⡐⠠⢓⣄⠀⡬⠦⡁⠀⠀⠘⠂⠀⠀⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⡇⠀ ⡆⠀⠀⠀⠀⠀⠀⢠⠁⠐⠀⠀⢠⡁⢠⠀⠁⠠⠀⢀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⣔⣀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠐⠀⠠⡈⠀⠁⠀⠀⠀⠠⠀⠅⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠁⠔⠑⠀⡠⢄⠠⠔⠠⠂⠄⢁⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠐⡕⡀⠠⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⡔⠀⠀⠀ ⠀⠀⠐⢍⠑⠒⠒⠒⠒⠒⠒⠓⠒⠂⠂⠔⠒⠒⠒⠓⠒⠒⠒⠈⠀⠉⠩⠀⢀⢦⡣⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣲⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣠⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⡷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣎⢣⡀⠀⠀⠀ ⠀⠀⢰⣿⢿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣧⣿⣿⣿⣦⡳⠀⠀⠀ ⠀⠀⡿⣿⣿⡭⡻⠟⣛⠓⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣃⠀⠀ ⠀⠀⡇⢿⡯⡉⠀⠀⠻⡿⡁⠂⢹⣿⣿⣿⢕⠍⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⡀⠀ ⠀⠀⢹⡈⢎⢻⡆⠀⠀⠹⠇⠀⢸⣿⣿⣿⡄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀ ⣀⠀⠀⢣⣺⣷⠇⠀⠀⠀⠀⠀⢸⡟⣿⣿⣇⣼⣿⣽⢻⢻⣿⣿⣿⣿⣿⣿⣷⠀ ⣿⣯⣅⠀⠷⣿⣦⢀⡀⡀⠀⠀⢸⡇⣿⣿⡇⢻⣿⠇⣸⢸⣿⣿⣿⣿⣿⣿⣏⠀ ⣿⡿⢿⡇⢠⠟⠿⡑⠕⠃⠀⠀⣸⣧⣿⣿⡐⢳⣿⠀⢻⠀⢿⣿⣿⣿⣿⣿⣿⡇ ⣏⠙⠆⠑⠑⣒⢒⡗⠈⢂⣲⣿⣿⠁⢸⡏⡎⠘⣿⣿⣞⡇⡸⣹⣿⣿⣿⣿⣿⡇ ⢿⡆⠀⡇⠀⠠⢠⣶⣾⣿⠟⠋⠹⡤⣸⡇⣇⣴⣿⣿⣿⣾⣿⣯⡻⣿⣿⣿⠈⡇ ⠘⠁⣾⡇⠀⠒⣪⣿⣿⣿⣁⠒⠁⢓⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡆⢇ ⠀⢸⣿⡇⠀⢀⠞⣿⢿⠙⠛⡻⠿⢿⣿⡿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬜🐸🐸🐸🐸🐸🐸⬜🐸🐸⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🐸✅✅✅✅✅✅🐸✅✅🐸⬜⬜⬜ ⬜⬜⬜⬜🐸✅✅🐸🐸🐸🐸🐸🐸✅🐸🐸🐸⬜⬜ ⬜⬜⬜🐸✅✅🐸✅✅✅✅✅✅🐸✅✅✅🐸⬜ ⬜⬜⬜🐸✅✅✅🐸🐸🐸🐸🐸🐸✅🐸🐸🐸🐸🐸 ⬜⬜🐸✅✅✅🐸🐸⬜⬛⬛⬜🐸🐸⬜⬛⬛⬜🐸 ⬜🐸🐸✅✅✅🐸⬜⬛⬛⬛⬜🐸⬜⬛⬛⬛⬜🐸 🐸✅🐸✅✅✅✅🐸🐸🐸🐸🐸✅🐸🐸🐸🐸🐸⬜ 🐸✅🐸✅✅✅✅✅🐸🐸🐸✅✅✅🐸🐸🐸⬜⬜ 🐸✅✅✅✅✅✅✅✅✅✅🐸✅🐸✅✅✅🐸⬜ ✅✅✅✅✅✅✅✅✅🐸🐸✅✅✅🐸🐸✅🐸⬜ ✅✅✅✅✅✅✅✅✅🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥 ✅✅✅✅✅✅✅🟥🟥🧰🧰🧰🧰🧰🧰🧰🧰🟥⬜ 🐸✅✅✅✅✅🟥🧰🧰🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥 🐸✅✅✅✅🐸🟥🟥🟥🟥✅✅✅✅✅✅✅🐸⬜ ⬜🐸✅✅✅✅🐸🐸✅✅✅✅✅✅✅✅🐸⬜⬜ ⬜⬜🐸✅✅✅✅✅✅✅✅✅✅✅✅🐸⬜⬜⬜ ⬜⬜⬜🐸🐸✅✅✅✅✅✅✅✅🐸🐸⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🐸🐸🐸🐸🐸🐸🐸🐸⬜⬜⬜⬜⬜⬜
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣀⣀⣄⣀⣤⣀⣄⣠⣀⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣄⣀⣄⣀⣠⣀⣀⣄⣠⣠⣄⣄⡀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⢹⣿⣿⡟⠋⠙⠉⠋⠙⠉⠋⠙⠉⣋⡙⠉⠋⠙⠉⠋⠙⠉⠋⠹⣿⣿⣿⣿⡟⠛⠙⠋⠛⠙⠋⠛⠉⠋⣙⡉⠋⠙⠉⠋⠙⠉⠋⠙⠙⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⠂⠈⢠⠐⣥⢋⡴⣻⣿⡗⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠠⠀⠈⢰⣟⣧⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⢠⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⡀⠀⠆⠀⠠⠸⠀⢼⣮⣿⢿⡽⣧⠀⢡⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⠀⡁⠐⠐⢸⡎⣽⣧⢀⠀⠀⠀⠁⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⢰⣁⣬⡟⣿⢞⣯⣿⡷⣐⢦⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢦⣕⡷⣭⣿⣾⡔⡌⠠⣄⠘⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠈⢛⡶⣽⢯⣿⣯⣿⣿⣽⠞⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣜⠷⢡⠊⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠙⠫⢿⡿⣿⠿⠟⠁⠀⠀⣠⣾⣿⣿⡟⢣⠚⡽⣿⣿⣿⣆⡀⠀⠈⠹⢿⣿⣿⣿⠯⠛⠁⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⣿⣿⠟⠈⠀⠐⠈⠹⢿⣿⣿⣷⣦⣄⣀⣀⣠⣀⣀⣀⣀⣠⣤⣶⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡤⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⡉⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⠀⠀⠀⠐⣝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢢⠀⠀⠸⠜⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠖⠰⠀⠆⠰⠀⠆⠄⠲⠴⣶⣤⡀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⢀⠠⠀⡀⠀⠄⡀⢀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢅⢂⠰⣀⠂⢄⠡⠈⠄⡐⠠⠐⣀⢂⡐⢠⢁⣒⡰⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣈⠗⣦⢯⣴⣌⣱⣌⣰⣡⣣⣔⣦⡼⣖⠫⠔⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠉⠄⠓⠌⠫⢙⠋⠟⠹⢩⠟⠌⠱⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢀⢀⠠⠤⠌⢶⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⢮⢿⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢣⢨⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⢡⡈⠀⢀⢴⠀⠀⣠⣴⣖⣖⡶⢃⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠆⠀⢀⣾⣍⢻⣢⢄⠃⠀⣼⠈⠀⢼⣟⣽⣶⣶⣍⠻⣇⠀⠀⠇⠀ ⠀⠀⠀⢀⡍⠀⣠⣾⣿⣿⡇⠃⡈⠀⡘⡅⠀⠀⠘⢸⣿⢿⡿⣿⠀⣳⠀⠀⠐⠀ ⠀⠀⠀⡴⠀⡰⡕⠿⠿⠟⠁⠄⠁⣰⡲⢸⠀⠀⠠⡀⠛⠿⠟⠃⣠⣧⠀⠀⠀⠀ ⠀⠀⢰⠃⡰⢠⠾⠒⠒⠚⢙⠄⣰⣯⠁⠀⣆⠀⠀⠙⠉⠒⠒⠋⣿⡏⠀⠀⠀⠀ ⠀⠀⡼⢠⠃⡼⠀⠀⠀⣀⠏⡰⢫⠃⠀⠀⠘⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⣰⡆⠀⢀⡾⠁⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠝⢠⠀⠀⠀⠀ ⠀⠀⠀⡆⠘⣷⣤⡟⠐⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡑⡀⣼⠀⠀⠀⠀ ⠀⠠⠂⢷⢀⢏⣾⡟⣟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⡿⢰⠁⡇⠀⠀⠸⠀ ⣴⡄⢛⡀⠢⣾⣿⢱⣿⣷⡈⠑⠦⣄⡀⢀⣠⡴⠚⣡⣾⣿⠃⣧⣇⠘⣆⠀⠀⠀ ⢭⣽⠆⢉⠂⢤⣴⣎⣿⣯⣿⣶⣄⠉⠛⠋⢁⣴⠟⣿⣿⣿⠀⠮⡛⠷⡈⠂⢠⠀ ⡍⣲⣾⣿⠀⢪⣷⣽⣾⣿⣧⡙⢿⣿⣶⣾⠟⢁⣴⣿⣿⣯⡳⣦⡇⠐⢟⣛⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
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⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to _ノヽ ノ\_ me or my son `/ `/ ⌒Y⌒ Y ヽ ever again. (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ ノ ヽ___>、__/ |( 王 ノ〈 (\__/) /ミ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⡈⠀⢀⣴⣦⢶⣴⣴⣦⢶⣴⢦⣶⡴⣦⡶⣴⣦⢶⣴⣤⡀⠀⠠⡀ ⠀⠀⣿⣟⣾⠗⢀⢸⣾⢿⣽⣻⣾⠻⠝⠛⢉⡈⠛⠻⢾⣿⠀⠀⠀ ⠀⠀⣿⣾⠷⠞⣹⡿⣯⢿⡞⠋⣡⣴⣾⢿⣟⡿⣟⣷⣄⠹⠀⠀⠀ ⠀⠀⣿⣯⣤⣼⡿⣽⡛⢁⣴⣿⣻⣽⡾⣯⡿⣽⣟⣷⣻⡆⠀⠀⠀ ⠀⠀⣿⣽⣻⢯⡟⠃⣴⣿⣻⢾⣽⣳⡿⣽⣻⣽⡾⣯⣷⢿⠀⠀⠀ ⠀⠀⣿⣳⡿⠏⣠⣿⣟⣷⣻⣯⣟⣷⣿⣻⣽⣷⣻⢷⣯⣿⠀⠀⠀ ⠀⠀⣿⣽⠃⣴⣿⣳⢿⣞⡿⣿⠆⠀⠀⢠⣿⣞⣯⣿⣳⡏⠀⠀⠀ ⠀⠀⣿⠃⣼⣻⢾⣽⣯⣿⠟⠁⠀⣠⣄⣸⣿⢾⣽⣞⣯⠅⠀⠀⠀ ⠀⠀⡇⣸⣷⣻⣯⣷⣻⣿⡀⣠⠞⠹⣿⣿⢯⣿⣞⣯⠏⢸⠀⠀⠀ ⠀⠀⢁⣿⣽⣯⢿⣽⡟⢿⠗⠉⠀⢠⣿⣽⢾⣯⣟⡿⢀⣾⠀⠀⠀ ⠀⠀⢸⣟⣾⡽⣯⣿⠀⠀⠀⣠⣶⣿⣻⢾⣟⣾⡽⢀⣾⣻⠀⠀⠀ ⠀⠀⣿⣟⡷⣿⣻⣿⣤⣤⣤⣬⣿⣷⣻⣯⢿⠞⢠⣾⢯⣿⠀⠀⠀ ⠀⠀⣿⣽⣻⢷⣟⣿⣻⣟⣿⣻⣟⡾⣷⡻⠋⣰⣿⢯⣿⣽⠀⠀⠀ ⠀⠀⢻⣷⣻⢿⣾⣳⡿⣾⡽⣷⣻⡽⠛⣠⣾⢿⡽⠿⢾⣽⠀⠀⠀ ⠀⠐⡌⢳⣿⣻⡾⣽⣻⢷⣟⠏⢃⣤⣾⢿⡽⡟⣁⣤⣾⣿⠀⠀⠀ ⠀⠀⣿⢦⣈⣑⠛⠛⣋⣁⣤⡾⣿⡽⣾⣻⡏⠛⣡⣾⣟⣾⠀⠀⠀ ⠃⠀⠙⢿⣯⣟⣿⣻⣯⣿⣽⣻⣷⣟⣯⣷⣷⣶⣿⣳⡯⠋⠀⠀⠀
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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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