Encanto Dot Art

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