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