Cuite Emojis & Text

Copy & Paste Cuite Emojis & Symbols ⣿⡻⣗⠿⣘⠿⣹⠞⡛⢜⡫⢓⠌⢃⠰⡁⠠⢈⠐⡈⠑⠠⡉⠐⡠⠂⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⡀⠣⢀⠒⠠⠐⠡⢀⠒⠀⠄⢂⠠⠐

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

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

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