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