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