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

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