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