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⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠤⠀⠤⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢠⣴⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⢀⠀⠀⠀ ⠀⢀⠜⠁⡔⣀⠬⠲⡒⠀⠀⠤⠤⣀⡠⠤⠄⠀⠐⡶⠢⢀⡑⡄⠱⣄⠀ ⢰⠯⢔⠾⠁⠀⠀⠀⠘⣄⠤⠒⠉⠀⠈⠑⠠⢄⡜⠀⠀⠀⠈⡙⢖⠼⣦ ⠈⢦⣇⠀⣇⡀⠤⠒⠉⠈⠑⢄⠀⠀⠀⠀⠔⠉⠈⠑⠠⢀⣀⠃⣈⣶⠃ ⠀⠀⠙⢍⠛⢔⠂⠠⠤⣂⡀⣀⣙⡒⣊⣀⡀⣀⡣⠤⠐⣂⠉⡫⠝⠁⠀ ⠀⠀⠀⠀⠈⠪⣳⣦⡀⠘⡄⠀⠀⡘⡀⠀⢀⠜⠀⣠⣶⠅⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢌⠢⡘⡄⢠⠃⢃⢀⢊⡠⢊⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡻⣜⠀⢸⠖⡩⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⠴⡶⣟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠖⠁⣠⣊⡀⠠⠵⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀ ⢸⡓⣈⠝⡅⠀⠀⠀⠀⠰⡀⠀⠈⣉⡒⠦⣤⠤⠤⠤⠤⠄⣠⡔⠊⢻⠓⢄⠀⠀ ⠀⢻⣧⡀⡀⢀⣀⠠⠄⠒⡗⢍⠁⠀⠀⠀⠈⠑⠤⡀⡠⠊⠀⠈⠒⠤⣇⠀⢣⡀ ⠀⠀⠱⣌⠫⣑⣤⣀⣀⣠⠁⠈⠣⡀⠀⠀⢀⡠⠔⢪⠑⠤⡀⠀⠀⢀⠎⢗⠢⣷ ⠀⠀⠀⠈⠢⡙⣆⠈⠑⢢⠭⠶⠦⣈⠲⠮⣁⣀⣀⢸⣀⠀⠈⢑⣤⣜⣀⡼⡲⠊ ⠀⠀⠀⠀⠀⠈⢿⡕⢄⠀⢆⠀⠀⢠⠏⠉⠉⠉⢐⠖⠒⠉⢙⡶⠒⣉⠔⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢌⠣⡘⡄⢀⠎⢀⠀⢀⠔⠁⡠⢔⣞⠭⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢷⡌⠀⢸⣠⠫⢒⡩⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣣⢠⣊⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⢶⣾⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⠋⠀⢀⣴⠏⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡾⠋⠀⠀⣠⠞⢁⣀⣠⠤⠤⠿⣶⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣯⠤⠶⣲⠞⡟⠉⠁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠉⠙⠓⠲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⣿⢷⣦⡀⠀⠀⠀⠀ ⠈⣿⡀⢀⡴⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣀⣀⡤⠴⠒⠛⠻⢭⡉⠉⠉⠉⠙⠛⠛⠒⢲⠶⢯⣁⠀⠀⠹⡄⠀⠙⣦⠀⠀⠀ ⠀⠘⣟⢿⣀⠀⠀⣧⠀⠀⠀⠀⢀⣀⣤⠴⠖⡿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⢀⡴⠋⠀⠀⠈⠓⢦⣀⢻⡄⠀⠘⣷⡀⠀ ⠀⠀⠹⣷⠻⢷⣤⢿⣴⠖⠚⠋⠉⠀⠀⠀⢠⠇⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⣴⡋⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠀⠘⣷⡄ ⠀⠀⠀⠈⠳⣄⠉⠳⣌⡙⠦⣄⡀⠀⠀⠀⡼⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠉⡏⠙⠦⣄⠀⠀⠀⠀⠀⠀⣼⠁⢯⠙⠢⣼⣿ ⠀⠀⠀⠀⠀⠘⢧⡄⠘⣯⡉⠉⠙⠿⣍⡉⠙⠲⣄⣀⡀⠀⠙⣦⠀⣀⡤⠞⠉⠀⠀⠀⢰⠃⠀⠀⠈⠛⢦⣀⠀⠀⣸⠃⠀⠈⣧⢀⣨⡿ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⣿⣄⠀⠀⠀⠙⣟⠛⠛⠛⠻⠯⣍⣉⠙⠛⠦⠤⣤⣀⣤⡤⠾⣤⣀⡀⠀⠀⢀⣈⣳⣶⣧⣀⣠⡴⢛⡽⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣏⠳⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀⣹⡏⠉⠉⠉⠉⠓⠲⢤⣤⠤⠾⠛⠛⠻⢭⣤⡤⠖⠛⢉⣩⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠙⢦⡀⠀⢳⡀⠀⠀⠀⣰⠋⡇⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣠⣴⠞⠁⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⠻⣄⠈⣧⠀⠀⢠⠏⠀⡇⠀⠀⠀⣠⠞⠁⠀⢀⣠⠖⣻⣟⣡⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡈⢧⡸⡆⢀⡟⠀⠀⣧⠀⢀⡴⠋⢀⡤⠞⠉⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢿⡞⠀⠀⠀⣿⣠⣏⠴⠚⢁⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⢷⠀⠀⢠⠟⠋⣡⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⣴⣯⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠒⠒⠈⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡶⠋⢉⡼⠉⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢳⡈⠉⠳⣄⠀⠀⠀ ⠀⢀⣴⠏⠀⢀⠞⣀⡤⠔⠒⠉⢻⡍⠉⠉⠛⠒⠒⠒⢒⣠⣤⡐⠒⠒⠒⠛⠋⠉⢉⡽⠉⠓⠢⢤⣀⠹⣄⠀⠙⣷⡄⠀ ⣴⡿⣁⡤⣴⢿⠋⠁⠀⠀⠀⠀⠀⠹⣄⠀⢀⣠⠴⠚⠉⠀⠀⠉⠑⠢⢤⣀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠉⡿⣶⢤⣈⢻⣦ ⢿⡉⠁⡴⠃⠘⡆⠀⠀⠀⠀⠀⣀⡤⢾⡿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⡿⢤⣀⠀⠀⠀⠀⠀⢀⡇⠈⢧⡀⢉⣿ ⠈⢻⡻⢅⡀⠀⢷⢀⣀⠤⠖⠋⠁⠀⢸⠃⠈⠓⢦⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡇⠀⠀⠉⠓⠦⣄⡀⣸⠀⢀⣠⢟⡿⠁ ⠀⠀⠙⢿⡛⠻⢿⡛⠢⢤⣀⠀⣀⣀⣸⣄⠀⠀⠀⠙⠲⣄⣀⠴⠋⠀⠀⠀⣀⣧⣀⣀⠀⣀⡠⠴⢛⣻⠟⢛⡹⠟⠀⠀ ⠀⠀⠀⠀⠙⠲⣄⠉⢻⣏⠉⠉⠛⠢⢤⣨⠭⠿⠿⠿⢭⣉⣉⣭⠿⠿⠿⠭⣅⣠⠴⠛⠋⠉⣙⡷⠋⣀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⢦⡹⣷⣤⡀⠀⠀⢳⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⡼⠁⠀⠀⣠⣾⠏⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣷⡝⢦⡀⠀⠹⡄⠀⠀⠀⡞⢸⡀⠀⠀⢀⡞⠀⢀⡴⢊⣽⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡉⠳⣄⠹⣆⠀⢰⠃⠀⣇⠀⢠⠎⣀⠴⢋⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⠓⢾⣆⡞⠀⠀⢸⣠⣯⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡛⢧⠀⠀⣸⠋⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣧⣴⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠤⠴⠶⠒⠒⠛⠋⠉⠉⠙⠛⠒⠒⠶⠦⠤⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣛⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣭⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠉⢩⡟⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⢿⡉⠉⠙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠏⠀⠀⣰⠏⠀⠀⢀⣠⡼⠿⣷⠒⠒⠶⠦⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠴⠶⠒⠒⣾⠻⢥⣄⡀⠀⠀⠻⣄⠀⠀⠹⣷⡀⠀⠀⠀ ⠀⢀⣴⡿⠃⠀⢀⣼⣇⡤⠖⠛⠉⠁⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢈⣩⡭⠟⠻⢯⣍⡁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠉⠛⠶⣤⣹⣆⠀⠀⠘⢿⣦⡀⠀ ⢰⣯⢟⣀⡤⢶⡿⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢿⠶⣤⣈⠻⣿⡆ ⢿⣟⠉⠁⢠⡞⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢿⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣷⡿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢷⡄⠈⠙⣻⡇ ⠈⢿⣷⣴⡏⠀⠀⠀⣿⠀⠀⠀⢀⣀⡤⠖⠛⠉⠀⣸⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⡇⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⡿⠀⠀⠀⢻⣤⢾⡟⠀ ⠀⠀⠻⣎⣛⣦⣄⣀⣸⣤⡤⠖⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠉⠙⠲⣤⣴⣇⣀⣠⣶⣋⣱⠏⠀⠀ ⠀⠀⠀⠙⢳⣍⠉⠛⢯⣍⠙⠳⠦⣄⣀⣀⣀⣀⣤⣿⣄⡀⠀⠀⠀⠈⠛⢦⣀⣠⡶⠋⠀⠀⠀⠀⣀⣤⣿⣄⣀⣀⣀⣀⣤⠴⠞⠋⣡⡾⠋⢉⣤⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠻⣶⡒⠛⠋⠛⠿⢭⣄⡀⢈⣙⣛⣶⣖⣒⣒⡛⠛⠛⢛⣓⣒⣲⣖⣛⣋⡁⢀⣠⡭⠟⠛⠙⠛⢓⣶⠛⠁⢀⡴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠈⢿⣦⣀⠀⠀⠀⠈⠹⣏⠉⠀⠀⠀⠀⠉⠉⣻⡏⠉⠉⠀⠀⠀⠀⠉⣹⠏⠁⠀⠀⠀⣠⣶⡟⠁⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡹⣟⢷⣄⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢀⡟⣷⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⡿⢋⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⡈⠳⣤⡀⠀⠘⢧⡀⠀⠀⠀⢸⠃⢸⡄⠀⠀⠀⢀⡾⠁⠀⢀⣴⠟⣡⣾⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡈⠛⢦⣀⠈⢷⡀⠀⠀⡾⠀⠈⣧⠀⠀⢀⡾⠁⣀⡴⠋⢁⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠙⢷⣌⣷⡀⢰⡇⠀⠀⢹⡄⢠⡟⣠⠾⠋⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠙⠿⣷⣾⠁⠀⠀⠈⣧⣿⠞⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡊⢻⣄⠀⠀⣰⠏⢁⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣽⡄⣰⣫⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⣶⣾⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠛⠿⢿⣶⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⢀⣴⠟⠁⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⡿⠋⠀⠀⠀⣠⠟⠁⠀⠀⠀⣀⣨⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣾⡿⠋⠀⠀⣀⣤⣾⣥⠶⠒⠚⠋⠉⠉⠁⠀⠘⣧⠈⠉⠛⠒⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣝⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠒⠛⠋⢉⡽⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⢶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠙⣟⠚⠻⢶⣄⠀⠀⠀⠀⠀ ⢻⣷⡀⢀⣴⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣀⣤⣤⠴⠖⠚⠋⠉⠛⢦⣄⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⠿⣥⡀⠀⠀⠀⠹⣆⠀⠀⠹⣧⡀⠀⠀⠀ ⠈⢿⡹⣿⡁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣿⣶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠈⠙⠳⣦⡀⠀⢻⡄⠀⠀⠹⣷⡀⠀⠀ ⠀⠈⣷⣬⣿⣦⣄⠀⣿⠀⣀⣠⣤⡴⠖⠚⠋⠉⠁⠀⠀⡏⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣷⡀⠀⠀⠹⣿⡄⠀ ⠀⠀⠈⠻⣆⠉⠙⣿⡙⠻⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⢦⣄⠀⠹⣿⣆ ⠀⠀⠀⠀⠈⢷⣄⠀⠙⢷⣄⣉⡻⣶⣄⣀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⢸⡇⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⣧⠈⠙⢦⣽⣼ ⠀⠀⠀⠀⠀⠀⠙⢧⡄⠀⠻⣯⡉⠉⠉⠛⢿⣍⡉⠉⠙⠷⣤⣀⠀⠀⠀⠈⠻⣦⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⣼⠃⠀⠀⠘⣦⠀⢀⣬⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⢹⣷⣄⠀⠀⠀⠈⠙⢶⡶⠶⠶⠯⣭⣛⣓⡲⠶⠾⠷⠿⣭⣀⣀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣰⠏⠀⠀⢀⣠⡿⢟⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢻⣟⢷⡄⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠈⠉⠓⢶⣦⠴⠶⠾⠭⣭⣍⣉⣉⠉⠉⠉⠙⠳⢶⣤⣄⣤⡴⠶⠖⠛⠋⣙⣿⠷⠿⠿⣧⣶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣆⠻⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠈⠉⢛⣶⠶⠛⠉⠉⠁⠀⠉⠙⣳⣶⠞⠋⠉⠀⣀⡶⠾⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⠌⢳⣄⠀⠀⢹⣆⠀⠀⠀⠀⠀⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⣧⡀⠀⢻⡄⠀⠀⠀⣸⠇⠀⣿⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢀⣤⠾⣫⡿⢋⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠈⠻⣆⠈⣷⠀⠀⣰⡏⠀⠀⢻⠀⠀⠀⢀⣴⠏⠀⠀⣀⣴⠞⠋⣠⣾⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢷⡼⣇⢀⡟⠀⠀⠀⢸⠀⠀⣠⠟⠁⣠⡴⠞⠉⢀⣠⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠹⣿⡾⠁⠀⠀⠀⢸⣀⣾⣣⠶⠛⠁⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠈⢿⡀⠀⠀⢀⣼⠟⠋⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣜⣧⠀⣠⠟⣁⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠔⠢⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀ ⠀⢀⡴⣺⢛⣤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣤⡛⢗⢦⡀⠀ ⢱⡿⡶⡍⠉⠀⢙⣦⡤⠛⠉⠉⠛⢤⣴⡋⠀⠉⢩⢶⢿⡆ ⠈⠛⢶⢷⣖⣉⣀⣆⠉⠢⢄⡠⠔⠉⣰⣀⣉⣲⡾⡶⠛⠁ ⠀⠀⠀⠙⢷⣮⡉⢨⡉⠉⢻⡟⠉⢉⡕⢉⣥⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠪⡳⢵⡀⡆⢰⢀⡮⢞⠵⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⡅⢨⣫⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡴⢻⡍⠉⠉⠉⠉⢩⠟⠻⡍⠉⠉⠉⠉⢩⠟⢦⠀⠀⠀⠀ ⠀⠀⣠⠎⠀⠀⠙⣆⠀⢀⡴⠁⠀⠀⠈⢦⡀⠀⣠⠋⠀⠀⠱⣄⠀⠀ ⠠⡾⠥⠤⠤⠤⠤⠼⣶⠯⠤⠤⠤⠤⠤⠤⠽⣶⠧⠤⠤⠤⠤⠬⢷⠄ ⠀⠙⢦⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡰⠋⠀ ⠀⠀⠈⠳⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⠞⠁⠀⠀ ⠀⠀⠀⠀⠙⢆⠀⠀⠀⠘⡆⠀⠀⠀⠀⢰⠇⠀⠀⠀⡰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢳⠀⠀⠀⠀⡞⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⡇⠀⠀⢸⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢹⡀⠀⡏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⣇⣸⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⢠⡙⢎⠱⡉⠆⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡙⠤⠈⡀⢂⠡⠈⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣶⣤⡀⠀⠀⠀⠀⠠⠓⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⢂⠁⠀⢂⠀⡁⠀⠠⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⠛⣿⣿⢣⣦⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠩⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⠄⠄⠀⠀⠀⠠⠀⠀⠀⠀⣀⣤⣾⣿⣿⡉⢀⣿⣿⣄⣻⣿⣄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⣀⠠⡀⠄⢤⡀⢀⢀⠄⡄⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰⣦⣾⣿⣿⣿⣯⣥⣀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄ ⠓⡈⠑⠀⠉⢂⠁⠈⠈⠘⢈⠂⠐⠀⠀⠀⠄⠀⠠⠐⠀⠀⢈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢈⠀⠐⠀⠐⠀⠀⡁⠀⠂⠀⠂⠀⠂⠀⢈⠀⠐⠀⠠⠃ ⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣿⣿⣆⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣾⣽⣿⣷⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⢡⣀⣤⣴⣶⣿⣿⣿⣿⣿⣯⣟⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣦⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣷⣯⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣆⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⢸⣿⣿⣿⡿⠟⠋⣹⣷⡀⠈⢿⣿⣿⣿⣿⣶⣤⣀⣀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡾⠃⠀⠀⢀⣠⣾⣿⣿⣷⡀⠀⠻⣿⣟⣾⣽⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⣿⠖⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢧⣄⠀⠀⠠⠿⠛⢹⡟⠈⠻⣦⡀⠘⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⣷⣤⣀⣠⣴⠟⠀⠀⠀⠉⢻⣾⠋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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