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