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