Shrub Emojis & Text

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

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