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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⢀⠀⢠⣹⢨⣶⣤⡴⣻⣦⡀⠀⠘⣾⣭⣽⠀⠈⠑⢦⠙⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠤⠼⠿⠿⠿⠷⠦⠤⠤⠤⢄⣀⣀⣻⣷⣼⣿⡇⡌⠓⠚⠉⢻⣷⡀⠀⣿⠏⢻⣣⡀⠺⡶⣄⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠿⠚⠛⠉⠀⠀⢾⡛⠛⠉⠛⠛⠛⠻⠽⠿⢷⣒⣦⠤⣤⣍⣛⡻⠧⣧⡀⢀⡴⠚⠁⡉⠳⣟⠀⠀⠳⣝⢦⡙⢦⡛ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⠛⠉⣀⣠⡤⢖⣶⣶⣶⠞⣉⣽⣷⠶⠶⢶⣤⣤⣄⣀⠀⠀⠉⠙⠓⠮⣭⣝⠓⠦⣼⣋⠀⠀⠾⠿⢦⠘⣧⡀⠀⠈⠳⣄⠈⠣ ⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⢀⡴⠞⠋⣁⣤⡶⣾⣿⣿⣭⡾⢟⣫⢕⣺⡭⠿⠒⠑⠀⣠⠶⠟⣉⡟⠛⠛⠿⣶⣶⣤⣄⡀⠈⠉⠛⠶⣮⣍⡓⠦⣤⣼⣦⣼⣗⢦⡀⠀⣿⠑⠦ ⠀⠀⠀⠀⠀⠀⢸⢿⣆⠀⡠⠞⢁⣴⣾⣿⡿⣫⣾⡿⠞⠋⢁⣠⠽⠞⠉⣠⠦⠀⢀⡰⠟⢁⡤⠞⣏⣿⢆⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣄⡀⠉⠻⠷⣶⣍⣓⢿⣿⠀⣹⢻⣇⣀⡀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⠊⢀⣠⣿⠿⢋⣥⡾⠋⠁⠀⠠⠖⣋⡤⢖⣫⠟⠁⣠⡶⢋⣠⣶⠋⠀⠀⠘⢿⣮⣷⣤⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣤⣈⠙⠻⣿⣿⣿⣥⣻⡟⣦⡀ ⠀⠀⠀⠀⠀⠀⣨⡿⣫⣵⣞⣩⣴⣾⠟⠉⠀⠀⠀⣠⡴⣻⣭⣶⡟⠁⣠⣾⣫⣴⡟⢿⢿⣶⣦⣀⠀⠀⠙⣿⣿⣷⣶⣄⡀⠀⠀⠀⢀⡞⠁⣹⣿⣿⣿⣷⣤⣤⠉⠛⢿⣿⣶⣿⡁ ⠀⠀⠀⢀⣤⣾⣽⢟⣿⣿⣿⡿⠋⠀⠀⣠⣤⡶⣟⡵⢞⣫⡿⠋⢠⣾⠿⠛⠁⢿⣿⣿⡷⣿⣷⣽⣱⣶⣄⡈⣛⠿⣿⣿⣿⣦⠀⣠⠟⠁⠐⠁⠹⣿⣾⡿⣻⣿⣿⣶⣄⠈⠙⠻⣿ ⠀⢀⣴⡿⣟⣯⣾⢿⣿⢟⡷⠊⠀⣠⣿⢟⣯⡞⠁⠚⣩⠞⢁⡴⠋⠁⠀⠀⠀⠸⢷⣝⣿⣿⣿⣿⡿⠿⣷⣝⢿⣿⣽⣿⣿⣿⠝⠁⠀⢀⣤⣶⠾⠛⢋⣩⣿⣿⠻⣿⣿⣿⣧⣄⣀ ⣴⣿⣵⣿⠿⠋⣡⢟⣵⠋⣀⣴⣾⣯⡿⠯⣭⣥⣤⡶⠁⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣍⠉⠛⠲⢿⣿⣷⡽⣏⡝⡝⢁⣠⡤⠖⠋⠉⣠⡤⠓⢻⠉⢠⣺⠀⢼⣿⣿⣿⣿⣿ ⠟⣩⠞⣡⣮⠞⣡⢏⣠⣾⣿⣿⣿⠏⠀⠀⣿⢟⡽⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠈⠹⡷⡶⣦⠉⣵⠫⠊⢈⣉⣀⡤⢶⡶⠛⠁⢀⣠⣾⣷⣦⡾⠀⣿⡿⢅⠀⠙⣿ ⡞⣡⣾⡿⠁⣾⣷⡿⠟⡿⢁⢸⣿⡄⠀⢰⡷⡟⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⢀⢿⣃⣸⠶⢖⣺⠟⠙⣉⡤⠚⠉⢀⣴⣿⣿⣿⠿⢛⡿⢻⠀⡿⠁⠘⡆⣮⠹ ⢞⡽⠋⣠⣾⢿⠋⠰⣾⠷⠤⡌⠓⠙⣦⠈⡞⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⣛⢉⠜⣢⣶⣫⠤⠖⠋⠁⠀⠀⢠⣾⣿⣿⣟⣶⣦⡤⣔⣸⡄⡇⠀⠀⠹⣿⣿ ⠞⢀⣾⡟⣵⣿⠀⠀⠘⢧⣀⠈⢳⡆⠋⡾⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⢀⣤⣴⣮⠗⣭⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⣾⣏⠛⣿⣿⣿⣿⣿⣯⣷⣷⣇⢸⣆⠀⠻⣿ ⣾⡽⣫⣾⠟⣹⣆⡀⠀⠀⠈⠙⣾⣧⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⣶⠟⠋⡱⣫⡾⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡏⠀⠹⣮⣙⢶⣿⣿⢿⣯⣹⣟⡿⡇⠀⢻ ⢩⣾⢟⣡⣾⣿⣿⣿⣦⣀⣀⣀⣿⣿⣫⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠋⠀⢀⣾⠟⠋⢀⣶⠤⠄⠀⠀⠀⢸⡇⠀⠀⠀⣿⡀⠀⠀⠹⣏⣷⣿⢳⣸⣯⣼⣿⣆⢳⠀⠈ ⣟⣥⣾⣿⡿⣻⣿⣾⣿⣻⣿⣿⣿⢯⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⣰⠟⠁⠀⠀⠈⠳⣴⠶⣾⠟⠃⠀⢙⣶⣤⣶⣿⠀⠀⠀⠀⣿⢸⣿⣾⣿⡿⠟⠻⠹⣾⡄⠀ ⡿⣹⡿⣫⣾⣿⣿⣿⠋⣿⣯⣿⡟⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⣠⣶⣿⣿⣾⣽⣿⠀⠀⠀⠀⣹⡼⠛⢁⣀⢤⢤⣀⣦⣽⣷⠀ ⣾⢏⣼⣿⠟⣱⣿⠃⠀⣿⢿⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠀⣿⣯⣿⣿⣿⡿⠏⠀⠀⣠⠞⣋⣴⣾⣿⣿⣿⣿⢻⣿⡇⣿⢰ ⢃⣾⠟⢁⣼⠏⣿⠀⢸⡟⠈⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠖⢒⣲⣊⣭⣻⣥⡀⣝⣧⡈⢿⡿⠿⠋⠀⠀⠀⣰⢃⡴⠛⠉⣸⣿⣿⣫⡟⣸⢿⠀⣿⠸ ⣼⢏⣴⡿⠋⢰⡇⠀⢸⠃⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠷⣶⣒⠛⠯⢭⣉⡉⠉⢻⣦⢳⣿⣶⣷⡄⠀⠀⠀⢠⣷⠋⠀⠀⣰⣿⣿⣿⡿⠛⡁⠁⣴⣿⡄ ⣿⣿⣟⡵⠊⢹⠃⠀⣾⠀⠀⠀⠀⠀⢱⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡀⠀⠀⠉⠉⠓⠦⣄⡉⠐⢿⣿⣿⣿⣿⠇⠀⠀⢀⣼⠁⢀⣠⠾⣟⠛⠉⠁⠀⠐⣡⠾⢫⣟⠇ ⣿⠟⠋⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡆⠀⠀⠀⠀⠀⠀⠉⠻⢤⣹⣿⡟⠁⠀⠀⠀⢸⣯⡾⠟⠛⢉⣀⣀⡤⠼⠛⢋⣥⣴⣿⠁⡼ ⠋⠀⠀⠀⣀⣼⠀⠀⢹⡀⠀⠀⠀⠀⢠⡇⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣹⣿⠇⠀⠀⣠⣾⣿⣥⣶⣶⣭⣭⣥⣤⣶⡶⢚⣾⢋⣾⢇⡾⠉ ⠀⢀⡰⠞⠁⠈⣆⠀⠸⣇⠀⠀⠀⢀⡾⡇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⡀⠀⣾⣿⣿⠀⢀⠴⣟⡿⣢⣿⣾⣿⣿⣿⠿⠟⢡⣴⣿⣳⣾⣫⠏⠀⠀ ⡴⠋⠀⠀⠀⠀⢻⠀⠀⢻⡄⠀⠀⡜⢳⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣿⣿⡇⡀⡿⣀⣿⡿⠯⣿⣛⡿⣥⣖⠦⠝⠋⢀⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠶⠃⠀⠈⣧⠀⣰⢿⣾⠙⢦⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣿⣿⣆⣻⣿⠽⠒⠒⠒⠒⠚⠉⠉⠀⠀⠠⠖⣻⡽⠋⠀⠀⠀⠀⠀ ⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠘⣆⡟⠘⠞⠀⠀⠳⣦⣥⣾⠿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠹⣣⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀ ⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⠀⠈⠙⠻⣷⣀⡸⢿⣏⣿⢿⣿⣶⣤⣄⣀⣠⣤⣤⣾⢿⠁⢀⠟⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣿⣿⡦⢶⣶⣟⣛⣿⣿⣿⣿⣏⣘⣠⠏⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠘⢇⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣿⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠹⠧⡄⠀⠙⢦⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣭⣴⡿⠛⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⠒⠯⣕⢷⡝⢆⠀⠀⠀⠀⠘⠰⠀⢸⣼⠀⣠⣴⣿⣿⣿⣿⣿⣿⣼⣀⠉⠉⢻⡦⠀⠀⠀⠀⠀⠀ ⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠃⢸⣿⠛⢻⠟⠉⣭⣿⣿⡿⠋⠀⢈⡿⠀⣸⣁⣠⣤⡖⠋⠀⣠ ⣦⡁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⢸⣄⣾⣿⣿⣿⡦⠀⣴⡟⢁⡴⣻⣿⣿⡟⢁⠴⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠄⢠⠀⢰⡄⢀⠀⢈⣿⣟⡽⠋⠀⢀⣾⠋⣰⢫⣾⣿⢿⣿⣿⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡠⠔⠉⢀⢜⣠⡿⠇⣸⣄⣼⣿⣿⠁⠀⢀⡾⢁⡼⠃⠀⠀⣠⣾⡷⣾⣫⣶⠀⠀ ⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⣴⠶⢖⣶⠏⢁⠀⠀⢰⡟⣼⣿⣴⣿⣿⣿⣿⣿⠿⣷⣌⠾⠓⠋⢁⣤⠒⠚⠉⡟⣿⣿⢋⣼⠀⣠ ⠂⠀⡀⠄⠀⢀⠠⠀⠀⠀⠀⠤⠒⠉⢀⣀⣬⠴⣖⡏⣀⠔⢩⣯⣏⠑⣿⣿⣿⣿⣿⣿⢏⢻⣧⡀⠀⠀⠨⠿⢗⡀⠀⣿⣷⣷⡾⠡⠞⠁ ⠞⠉⠀⣀⡀⠤⠄⠒⢂⡲⠤⠶⠤⣤⣬⣭⣭⣭⠷⢿⣷⣦⡈⣷⠉⠀⢀⣉⣙⣿⣯⣿⠀⣈⣿⣿⣿⣷⠶⣤⣴⡇⠀⢹⣿⠟⢀⣠⠆⠀ ⡤⠖⠉⣁⡠⢴⡒⠍⠁⢀⣠⣴⠊⣰⡟⠙⢷⣄⡀⠀⠛⢿⣿⣿⣧⣿⣈⣿⣿⣿⣿⡻⣆⠘⢈⡉⣻⢷⣖⣡⣾⠁⢀⣾⣿⣀⡀⠀⢀⣴ ⣤⠖⠉⠁⠈⠁⠀⠠⠞⠩⣾⡟⠛⠋⠀⠀⠈⢻⣿⣿⣰⣶⣯⣝⣻⣿⣿⣿⣿⣿⣿⡶⢻⣟⠻⠶⢖⡶⠋⣩⣵⣶⡿⣿⠏⣿⣥⡾⠯⠓ ⣷⡾⢭⣄⡠⣴⢶⣯⢔⠂⣿⠁⠀⠀⠀⠀⠀⠀⠻⣆⠈⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣦⢻⡇⠈⣉⣴⣾⣿⣿⣭⣿⠏⡤⠾⣛⣛⠿⠭ ⡿⢰⡟⠀⣹⣿⠛⠿⢉⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢿⣿⣟⣀⣹⣿⣧⢽⣿⣿⣿⡇⡇⣸⣿⣿⣿⣿⠏⣰⢣⡾⠛⠛⠋⠓⠂⠀ ⣿⡄⢇⢸⢃⠟⠁⠰⢇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠿⠦⣑⣮⢻⣀⣞⡉⠿⣿⡿⠟⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣎⢘⠘⠄⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠳⡞⣿⣿⡿⠉⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣌⠓⠒⠚⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⡟⢇⠀⠀⠀⠀⠀⡆⢹⠇⠀⠀⠐⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⣸⣿⠓⣦⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣷⠛⡆⣀⡤⠄⢠⡇⠈⡇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣾⡏⠹⠀⠇⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣵⣶⣤⣀⣷⣄⡁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⡆⠀⢰⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣌⣩⡿⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⡇⠀⢸⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣈⡽⠭⣍⣉⣁⣤⣤⠤⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⠀⡇⠀⠈⡆⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣏⠙⠃⠀⠀⣶⡶⢿⣿⡝⠉⣼⣠⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀ ⣾⣿⠀⡇⠀⠀⢳⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠗⠶⠬⠿⠥⠒⠒⢿⠀⣸⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛ ⣿⡇⠀⡇⠀⠀⠸⡇⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠔⠉⠸⠿⡇⠨⣶⣤⣤⣤⣤⣤⡊⢠⣿⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⢸⠀⠀⠀⡇⠀⠀⢘⣿⣿⣿⣿⣷⣦⣄⡀⠈⠀⠀⠀⣼⡇⠀⠈⣿⣿⠁⠀⠉⠀⣼⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣶⣿⢿ ⡿⣿⣦⣸⣧⡀⠀⢻⠀⠀⣼⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢹⠁⠀⠀⠻⢿⣄⠀⠀⣴⠿⣫⣴⣿⣿⣿⣿⣿⣷⣾⣿⡟⢋⣿⣿⣿⣿ ⡿⠿⣿⣛⣿⣿⣶⣾⣤⠀⠈⡆⠈⠿⣿⣿⣿⣿⣿⣭⣶⣿⣿⣦⣷⣄⣀⣀⣀⣈⣠⣾⣿⣿⣿⣿⣿⣿⣮⣴⣾⡿⠟⣛⣃⣾⣛⣿⣷⣺

⠓⠋⠁⠶⢀⡄⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣼⣊⡀⠀ ⠀⠀⠀⠀⠀⡗⠀⣣⠘⡟⠀⠀⢰⠉⠤⡁⠆⢯⢉⢀⠤⣲⠙⠛⠋⠁⠀⠀⢷⠀ ⠀⠀⠀⡀⠀⣿⣶⠁⠀⡰⠀⠀⠀⣃⠆⡁⡀⢸⢪⠔⢍⠥⠐⠤⠀⠀⠀⠀⠀⠐ ⠠⡀⠀⠀⠀⢳⠝⣀⣰⣾⠗⠚⢏⢯⠤⠊⠴⡿⣮⣂⠃⠊⢸⠇⠂⠀⠀⠀⠀⢀ ⢓⢤⡑⠠⠀⡀⢤⣾⣿⣇⠀⣠⢬⣔⢂⡀⠀⣿⠉⠉⠢⠭⠕⠊⠀⠀⠀⠀⡘⠀ ⠀⠀⣨⢕⡧⣅⡊⠍⡁⠘⢟⣇⠁⣁⠊⡰⢾⡄⠐⡄⠀⠀⠀⠀⠀⠀⢀⡼⡡⠐ ⣠⣿⠖⣩⣴⢲⣿⠑⡦⢍⣐⠸⠦⢤⡴⠿⠶⠤⢍⡙⠂⠦⠄⣀⡠⣺⠟⠙⡰⠁ ⠏⣥⢞⡣⠿⢾⣿⢿⡤⡀⣈⢋⢲⡦⠤⢀⣀⣁⣠⠤⠬⠶⢖⠂⡠⡁⠀⠀⣀⠀ ⣼⡘⣾⠁⠀⠀⣰⣿⣦⢱⣭⢣⣯⣴⡶⠟⠒⣤⢷⠀⢆⠴⠟⠛⠚⠂⠉⠉⠁⠐ ⠸⢇⣿⠀⣀⡼⠟⡿⡇⡿⣧⡟⢿⣽⡷⣶⠖⠁⡜⣜⡾⠁⠖⣧⠆⠶⣶⠤⠀⠠ ⣀⣴⣿⡀⣿⡁⠀⠐⣠⠁⠁⠀⠀⠉⠉⢁⢶⣞⣼⡟⠠⣰⠖⠋⢓⣶⡂⠴⣀⠀ ⠟⠻⣿⣷⣿⣯⠝⠒⠁⠀⠀⠀⠀⠀⠐⠋⢉⠵⣏⠟⠉⠀⠀⡠⢎⡀⠙⡄⢘⡇ ⠀⣰⣿⡏⠺⣍⠛⢦⠀⠀⠀⠀⠀⠀⣠⡶⠵⠍⠁⠀⡠⢔⠉⠐⠒⠀⠀⡀⠎⢠ ⣰⣿⠟⠛⠢⠉⣉⣁⡀⠤⠤⣶⣖⣻⢿⣶⣷⣿⣖⠉⣿⠝⠀⠀⠠⠂⠀⠀⠐⠈ ⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⡿⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠒⠲⠦⣭⡳⣵⣌⠳⡄⠀⠀⠀⠀⠀⠈⠆⢇⠀⢸⡇⡞⠀⢀⣣⣾⣿⣿⣿⣿⣿⣿⣿⣆⡛⠈⠉⡉⠙⢿⣦⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⣄⠀⠀⠉⠈⠉⠂⠘⣆⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⣧⣶⡽⣯⡿⠿⠓⣲⣿⣿⢟⡷⠛⠉⠛⣶⡆⠀⣾⠋⠀⠀⠀⣠⡴⠊⠀⠀ ⠀⢷⠢⣀⡈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⠀⠀⠀⠀⠀⠀⠘⡿⡇⠀⠀⡇⠀⢠⣷⣿⣿⣵⠏⠀⠀⠀⣴⡟⠁⢀⡿⣰⣾⣿⣿⡅⠀⢀⣤⠾ ⠗⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⣧⢠⣿⣿⣫⡾⣷⠧⠀⢐⣾⠋⢀⡾⢋⣼⣿⣿⣽⠃⣠⠶⠋⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡾⠋⠀⠀⠀⠀⠀⢀⡄⢠⡀⠀⣰⡄⠀⠀⠀⠀⣿⣿⡗⣵⠟⠁⠁⠀⣴⡿⠁⣴⠟⣵⣿⣿⠵⣺⣷⣾⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠋⠁⠀⠀⠀⠀⢀⡤⠞⠀⢀⡇⢠⣯⣷⠀⣆⠀⢰⡿⣿⣽⠋⡄⠀⠀⣰⠟⠀⣼⠋⠈⠉⠙⠁⣰⣿⣭⣽⠟⣄⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠀⢀⣴⡏⣶⣿⠋⣡⣴⣿⣦⣞⣿⣿⣷⡄⠱⡄⣸⡏⣠⡾⠁⠀⠀⢀⣴⢿⣿⣯⣴⣷⣾⢛⡇⠀⠀ ⠲⠦⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⡒⠂⠐⢒⣒⡽⠟⣋⣭⠷⠃⢀⠄⠀⢀⣼⡿⣸⣿⢻⣾⣿⣿⣿⣿⣿⣿⣿⢙⣿⣦⡼⠛⠛⠉⠀⣴⣶⡋⠉⠁⢸⡏⣿⣿⡿⢁⣼⠇⢀⣰ ⠒⠀⠁⣀⠤⠀⠀⢀⡠⠤⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⣀⣀⡤⠶⣟⡥⢀⡠⠚⢹⣇⣻⠁⣸⣿⣿⣿⣾⣿⣿⣿⡿⡎⢿⢿⣀⡀⠀⠀⠀⣽⡮⣟⡀⠀⠈⡇⣿⣼⣧⣿⢋⡴⠛⠀ ⣠⠖⠋⠁⠀⠀⠂⢁⣀⣀⣀⡤⠤⠤⢤⣤⡀⠀⠐⠿⠛⠒⣒⣊⣭⣶⣯⣄⡀⢸⣿⠙⠃⠈⠈⠏⠛⣿⣿⣷⢹⡇⠉⠘⣾⣿⣷⣶⣶⣤⣄⠀⢈⣿⡆⠀⣧⣿⣿⡿⡁⠈⣠⠀⠀ ⠁⠀⢀⣤⠴⠒⠊⠉⢉⣠⡤⠖⠚⠉⠉⢉⣩⠟⣿⣿⣿⠟⠛⠋⠉⠻⣿⣿⣿⣦⣿⣇⢠⡄⢹⣰⣶⣮⢻⣿⢸⣿⠀⢲⠸⠿⢿⣿⣟⠋⣙⡿⢛⡿⠀⠀⡼⣿⡏⠀⠴⠞⠃⠀⠀ ⠶⠋⠁⣀⣠⠴⢒⣩⠕⠒⠈⠀⣀⡤⣶⣟⠀⣼⡿⠁⠈⢿⣶⣤⣀⠀⠈⠻⣿⣿⣿⣿⣶⣷⡠⣽⣿⣿⣿⣿⡇⢻⣆⣈⣁⠤⠠⠬⠿⢿⣥⣴⣿⠇⢀⣠⣿⣿⣇⣄⡀⠀⣀⣠⡾ ⣀⡾⠽⠄⢀⡈⠁⠀⠀⢐⣻⠏⣠⢾⣿⠿⠾⠃⠀⠀⠀⠀⠹⣿⣾⣍⣛⡻⠶⣌⣙⡛⣿⣿⣿⣿⣿⣿⣟⣻⡷⠶⢿⣟⠻⡿⠿⠿⣴⡾⠋⣁⣤⣶⣿⡿⣿⡟⢘⡿⣡⣾⣋⠭⠶ ⣋⣤⠴⣒⡂⠀⢀⣩⡤⣴⣒⡤⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠛⠻⢿⣿⣾⣽⣿⣿⠿⣿⣿⣿⣿⣿⣷⣤⡈⢿⡖⠀⠴⠟⣁⣤⣾⣿⣿⠿⢻⣶⡟⠀⣨⣿⡿⠶⠶⠶⣒ ⣿⡞⢩⣿⠟⠲⣽⣯⣹⣿⣫⠖⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⢸⡟⣿⡏⣿⠻⣷⣝⣯⠹⣿⣿⣿⣿⣷⡈⣧⠀⢠⣾⣿⣿⣿⢿⣿⡝⢻⡏⣠⢞⣩⣥⣶⣖⣉⡉⠉ ⣿⠀⣿⠇⠀⣴⢞⣧⠉⠙⢃⡴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠯⠼⣯⣥⣤⣘⣿⣿⡗⢮⡻⢿⣿⡿⠇⡿⣠⣿⣿⣿⣾⣿⣿⠏⢰⡟⣼⠿⠉⠁⠀⠀⠀⠈⠉⠀ ⣿⣆⠸⣇⢸⠏⣼⠋⠁⢀⡿⡀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⠷⢦⣙⡶⡝⢾⡀⣶⣋⠹⠿⣿⣻⡿⠿⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⠙⠘⡆⣇⠀⠀⢀⢿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠙⢦⡼⣿⣿⣿⣿⠟⠉⠀⠀⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣻⣿⣷⠰⣄⣈⣁⣴⡵⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣬⣫⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⢻⡞⡟⠉⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀ ⣿⣿⡟⣿⣦⡀⠉⠉⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣩⣿⡈⢺⡄⠀⠀⠀⠀⠀⠀⠇⠈⣇⠃⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠁⠀⣿⢸⠛⠳⣶⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢥⣼⣷⠋⣳⠀⣠⣤⡤⠀⢰⡇⠀⢹⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀ ⣴⣤⣿⡟⢸⠀⢸⡇⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠁⠈⡘⢳⣤⣄⠀⠈⣧⡀⠘⡆⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠘⠀⠘⡇⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⠛⢿⠟⢿⣿⠟⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂ ⣿⢿⣿⠃⡇⠀⠀⡇⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣤⡴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣏⣾⠀⡇⠀⠀⢷⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣬⡯⠭⣤⣉⢁⣠⣤⣤⡶⢄⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣾⡟⠀⡇⠀⠀⢸⡀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠻⠭⠀⠠⢤⣴⣶⣿⣿⣿⣹⠋⠁⡞⢀⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⡇⠀⠀⠀⡇⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⢦⣅⣄⠲⢤⡶⠊⣉⣁⣙⣾⠁⠀⡼⣷⣛⣿⣯⣭⣭⣭⣿⣿⣿⣛⣛⣿⣿⣷⣶⣶⣦⣤ ⣿⣿⠇⠀⡇⠀⠀⠀⢹⡄⠀⠸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢿⡟⣿⠛⣌⠙⠛⠓⠚⠋⠉⠀⠈⡧⠀⣸⣥⠟⣻⣿⣻⢿⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣋⣉⣨ ⣿⣿⠀⠀⣇⠀⠀⠀⠘⡇⠀⠀⠘⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢸⠛⣿⠀⢪⣓⣶⣶⣶⣶⣶⣶⣴⠁⢀⣿⡧⢜⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣽ ⣿⣯⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠸⠀⠀⠀⢠⣠⢿⠀⠀⠉⣿⣿⡏⠁⠀⠉⠉⠀⣼⣿⣷⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣥⣮⣿⣷ ⣿⣿⣆⠀⢸⣧⠀⠀⠀⢹⡀⠀⠀⢰⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⢧⡏⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⢰⣿⡿⠟⣡⣶⣿⣿⣿⣿⡿⣿⣋⣵⣿⣿⣿⠿⣿⣻⣽⣿⣾ ⣏⣽⣾⣿⣶⣿⣦⣀⠀⠸⡇⠀⠀⢾⡇⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢳⢦⣀⠀⣇⠀⠀⠀⠈⠙⠛⢦⡀⠀⣰⢟⣋⣴⣿⣿⣿⣿⠟⣿⠶⠿⣟⣛⣯⣥⣶⢀⠴⣿⣿⣿⠿⠿ ⣿⠿⠛⣛⣛⣓⣒⣯⢿⣿⣷⡆⠀⠀⢹⠀⠈⠭⢿⣿⣿⣿⣿⣿⣯⣤⣾⣿⣿⣿⣷⡾⣶⣄⣀⣀⣀⣀⣠⣤⡾⣿⣽⣿⣿⣿⣿⣿⣷⣻⣵⣾⣿⣿⠿⠛⣛⣩⣼⣛⣛⣿⣶⣚⣻

⣛⣥⣶⠟⢛⠋⢁⣦⠆⠀⠀⢠⣃⠄⠀⠀⠀⠀⠀⠀⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠙⢷⠀⠀⠀⠀ ⠉⠁⠀⠀⠈⡲⡼⠿⠒⠀⣐⣿⠁⠀⠀⠀⠀⠀⡀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠖⣛⣉⣤⣬⠤⠀⠀⠀ ⢀⠂⠀⠉⠀⠀⠀⠄⠀⠀⢸⣯⡄⠀⣠⢞⠴⡨⠞⣿⢿⡇⠀⠀⠀⠀⢀⣠⠶⠚⠉⠉⠓⠶⣄⠀⠀⣴⠶⠶⠦⣄⠀⠀⠀⠀⣀⣠⣴⡶⣾⣛⡯⠷⠖⠋⠉⠅⠀⡀⢻⡿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⢀⠔⢃⡨⣖⡁⣻⡿⠁⠀⠀⠀⠀⠸⣷⡄⠀⣴⢶⣦⡀⠈⢇⠀⣿⣦⠀⣀⣸⢀⣠⡴⠟⣫⠤⠚⠋⠙⠛⠛⠁⠀⠀⠀⠀⠀⠁⠀⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣖⢀⠠⡿⠛⠁⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢷⡀⣷⠀⠙⣿⠀⢸⠀⠈⣿⠀⡧⠴⠛⣡⣴⠿⠗⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢪⢾⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢸⡇⠘⡆⠀⡽⠀⣸⠀⠀⡿⠀⣇⡴⠛⠳⣄⢀⣤⡴⠒⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸ ⠤⠤⠶⠶⠶⠶⠶⠶⠦⠤⠼⣟⠻⣿⣖⡇⠀⠀⠀⠘⢧⡽⣆⠀⢀⣀⣀⡠⢴⣿⠀⢧⠞⠁⣰⠇⢀⣠⣷⠀⣏⡀⠀⢀⡴⠋⢁⡠⢤⣧⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀ ⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡼⠃⠀⠀⢰⣿⢾⣻⡽⢿⣭⠶⣞⠉⢹⣏⠀⣀⣸⠞⢁⣠⣾⣷⣴⣦⣤⡗⠀⡾⠀⢠⠋⠀⠀⢻⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀ ⡄⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⡰⠾⣛⣭⣬⣽⠏⠀⠀⠀⠀⠀⢹⠬⠿⠍⠑⠐⠚⠋⠙⠻⣿⣐⣚⣓⣒⣺⡇⠀⢸⡀⠀⣠⠟⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠤ ⢿⣦⣄⠀⠉⠓⢤⡀⠀⠀⠀⠀⠸⢇⣀⣴⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⡞⠀⠰⢤⣤⣀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⢻⣄⡀⠙⠋⣁⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⣨⠝⢿⣦⣄⠀⠈⠂⠀⢀⡤⠞⠙⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣴⢿⡙⣿⣷⣶⡀⢀⣶⠁⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠈⠀⠀⠀⠈⠛⠛⣡⣴⣚⠉⠙⠢⣄⡛⠛⠛⠉⠉⠀⠙⣿⣶⣿⣿⠀⠳⠈⠛⠋⢠⡾⠋⢀⣀⣴⢞⠍⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⡴ ⠌⠀⠀⠀⣀⣴⠾⠋⣉⡻⠷⣶⣄⣀⠉⠓⠦⣄⡀⠀⠀⠘⢿⣈⣿⡄⠀⠀⢤⣰⠉⠀⢀⣾⠿⢿⣿⣟⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⢃⣤⠞⠉⡌ ⠊⠀⣠⣾⠟⣁⣴⠿⠋⠁⣀⣸⣝⣿⣿⢶⣤⣀⡉⠛⠲⢤⣀⡀⠸⣷⡀⠀⠀⠀⠀⠀⣿⣿⣄⡀⠀⠈⠙⠓⠿⣾⣿⣦⠀⣠⠀⠀⠀⠤⠀⠀⠀⠀⢀⣴⣾⣿⡿⠃⡾⠁⢠⡼⠀ ⠂⣴⡿⣡⣾⠟⠁⣠⣶⣮⣿⠛⣿⢾⣿⡄⠉⢻⡿⢶⣦⣄⡈⠉⠒⠛⠻⢶⣶⡒⠶⢾⣿⣿⠿⠿⠷⠶⢶⣤⣀⠀⠉⠉⠒⠻⠿⢦⣤⣤⣀⣀⣀⣤⣈⣿⡿⠋⠀⠞⠁⢠⡟⠁⠀ ⣾⣿⣿⠟⠁⣠⣾⡟⢻⣿⣿⣰⣍⣿⣿⣷⡀⡞⠁⠀⠈⠙⠛⢷⣦⣤⣀⠀⠀⠉⠉⠒⠂⠀⠀⠀⠠⠴⠔⠒⠛⠛⠒⠲⢤⣄⣀⡀⠀⠀⠉⠉⢉⣁⣴⠛⠁⠀⠈⠀⠔⠋⠀⠀⠀ ⡿⠁⢀⣴⣿⠟⣿⠁⣾⣯⢿⣧⣻⠿⠾⠿⣿⢡⠆⠆⡴⠀⢀⡐⠂⢨⠍⢻⣷⣶⣤⣄⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣶⠾⠿⢿⠋⠉⠉⣠⠔⢀⡠⠂⠐⠁⠀⠀⣠⠀⠀ ⠃⢰⡟⣡⡟⣰⣿⠎⠁⠈⠈⠙⠟⠛⠷⢢⣿⡏⡘⢸⡟⢠⡞⡴⣠⠃⣠⣿⠟⠁⠀⠈⣩⣙⣛⠛⠛⠛⠻⣟⠛⡉⠉⠀⡇⠀⠀⢀⣴⡇⣠⡴⢋⣥⠊⠁⢀⣀⣀⣠⣤⣾⡛⠀⠔ ⢠⢿⠃⡿⣧⣿⡿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣹⢁⡎⢀⡟⡐⣴⠇⣰⣿⣁⣤⣤⣶⣿⣿⣿⠿⠿⠦⣤⣠⣿⣆⡇⠀⢠⠇⡀⠀⣾⡫⠿⠿⠿⢿⠑⠚⠋⠉⠉⠀⠈⠁⠀⠀⠀⠚ ⢸⢼⢸⠁⢻⣎⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣾⠀⣸⣴⣱⡟⣸⣿⣿⣿⠻⣿⣿⠋⠉⠀⠀⠀⠀⣼⠏⠉⣹⠁⠀⡞⣰⣿⡼⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⣿⣾⠀⠘⢿⡇⠀⠀⠀⠀⣰⣿⣿⡟⢹⣿⣟⡟⢰⣷⡿⡻⢠⡟⢿⣟⢯⣙⣾⣽⣷⡦⢤⣤⣤⠾⠁⠀⢀⡟⠀⣼⣠⣿⡿⠁⢀⣤⣶⣯⡁⣠⢇⣴⣶⣶⣤⣤⡀⠀⠀⠀⢀⠠ ⠀⠳⡙⣆⢸⣾⡇⠀⢀⣤⣼⡷⠻⠋⠀⠸⡿⢹⡇⢸⣿⠃⡇⣿⣧⡀⠹⣿⣿⣿⣦⠿⢋⣿⣶⠶⠀⠀⠀⣼⠁⣼⣱⣿⠟⠁⠀⢸⠛⢰⣿⣿⠛⠒⠒⠪⠽⠭⣉⣉⠁⠀⠁⠈⠁ ⠀⠀⠀⢀⣿⣿⣇⠀⢸⣿⣿⠁⠀⠀⠀⠀⣧⢸⠁⡾⠙⠀⠹⠁⠀⠉⠀⠈⠛⠿⢿⠿⠋⠉⠀⣄⣤⣴⡾⠁⣼⣿⣿⠋⠀⠀⣀⣼⣀⣾⣿⠻⣧⣄⣀⣀⣀⣤⠤⢤⡄⠀⠀⠀⠀ ⣤⣤⣴⣿⣿⣿⣿⡀⠸⣿⣿⣆⠀⠀⠀⠀⡘⢸⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣛⡟⣡⡾⣟⣿⡁⠠⠔⢛⣩⡟⠋⠉⠉⠃⠀⢉⣽⢟⣯⡉⠛⠒⢽⣄⡀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⣦⣽⢿⣟⠷⠶⣦⣬⣠⠴⠟⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⣠⣾⣿⡿⢽⡿⠼⢉⣼⡿⢯⣵⣤⠞⠋⠁⠀⠀⠀⠀⠀⣠⠟⠁⠈⠳⣵⣄⠀⠀⠙⣷⡇⠀ ⡿⠛⠉⠹⣿⣿⣿⣷⠸⣿⣎⠻⣶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⠀⠀⠈⣠⡾⠟⣽⠇⡴⠁⠀⠀⠀⠀⠀⠀⠀⣠⡼⠧⣄⣀⣀⡀⠘⢾⢆⠀⠀⢸⡗⠀ ⠀⠀⠀⠀⣸⣿⣿⡿⣆⠹⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣠⠾⡫⠟⠀⠀⠀⠀⠀⠀⢀⣠⣞⣉⣀⣐⣊⣉⠁⠀⠀⠈⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⣰⣿⣿⣿⡇⠈⠻⣦⡀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡥⣖⣫⡅⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠜⠛⠛⠃⠀⠀⠀⠀⠀⣴⠟⠕⠀⢠ ⠀⠀⣴⣿⣿⣿⣯⢿⡄⠀⠸⣿⣦⣤⣄⣀⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠿⡿⣃⣈⣅⠀⣤⣤⠤⠂⣀⣴⣾⣋⣤⣶⡏⠍⠀⠁⠀⠀⠀⠀⠀⣀⣀⠄⠚⠁⠀⠀⡰⢯ ⠀⣼⣷⣿⣿⣿⡿⠗⠙⢦⣄⠈⠉⠋⠉⠁⠀⠀⠀⠀⠀⣀⣤⣴⣦⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡿⠋⠁⠀⢳⣾⣉⣿⠋⠀⠀⠀⠀⠀⢠⡖⠉⠁⠀⠀⠀⠀⠐⠂⠀⠀ ⣼⣿⣿⡶⠋⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠶⠶⠖⠒⠋⠉⠁⠀⠀⢸⣧⠾⢷⣖⣛⣛⣻⣿⡿⣿⣿⣿⣿⣯⣵⡦⠀⣀⣬⣿⡟⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣁⣬⣿⣒⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣉⣱⣿⣿⠿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣠⡮⣷⣄⠀⢀⢳⣟⣦⡤⢛⣶⣄⠀⠀⢳⡤⣽⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣦⣤⡤⠤⠭⠍⠉⠁⠒⠠⠤⠤⠤⣤⣈⣛⠷⡌⠟⣼⡍⠒⠉⠈⢾⡇⠀⢸⠇⠑⣗⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⠀⠀⣍⡉⠉⠉⠉⠙⠛⠷⠶⠮⢖⣒⡶⠦⣌⣙⡒⠮⣅⣀⣠⠞⢉⡉⡙⢮⡀⠀⠈⢧⡀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⣉⣠⣤⠤⣒⣶⣿⡿⣟⣻⠽⣿⠟⠻⠿⣶⣦⣤⣤⣀⡀⠀⠉⠛⠲⠤⣝⣓⠢⢿⣀⡀⠼⠿⠃⡄⢳⡄⠀⠀⠙⣄⡀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠴⢛⣩⣶⣶⢿⣿⣿⣭⠾⠟⠫⣕⣫⠵⢚⡟⠁⠀⣠⠞⠛⣩⣿⠉⠛⠻⠿⣶⣤⣄⣀⠀⠉⠛⠻⢦⣭⣛⠦⣤⣿⢼⣿⠓⣄⡀⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⢀⡤⠚⣡⣶⣿⣿⣟⣯⠼⠛⠉⢀⣠⠔⢊⡉⡠⠖⠉⢀⡴⠋⢁⡴⠊⣯⣿⢷⡀⠀⠀⠀⠉⠙⠻⢿⣶⣦⣤⣀⡈⠛⢿⣶⣽⣿⣧⣀⡼⢉⣤⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⣡⣴⣾⣿⢟⣫⡾⠋⠁⠀⠀⠀⣉⣴⣶⣫⠄⠀⣰⠞⢉⣠⣾⠉⠀⠀⠈⠻⣷⣿⣦⡀⠀⠀⠀⠀⠀⠉⢻⠿⢿⣿⣷⣦⡈⠉⠻⢿⣿⣶⣍⠍⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣿⣿⣿⣾⠟⠁⠀⠀⠀⣀⣴⣾⣿⡿⠏⢀⡰⢟⣡⠶⣏⣹⣏⣝⣷⢤⡀⠀⠙⢾⣿⣿⣿⣦⣄⠀⠀⣀⡼⠀⣸⢿⣿⣿⣿⣷⣦⣄⠉⠻⢿⣿⣦⣄ ⠀⠀⠀⠀⠀⢀⣤⣾⢿⣻⣿⣿⡿⠋⠁⠀⢀⣄⡴⣻⡿⠛⠫⠛⠁⣠⡾⠟⠋⠀⠰⣎⢿⣏⣿⣿⣿⣼⣿⡢⣄⡙⠻⢿⣿⣿⣧⠘⠟⠱⠋⠁⢠⣹⣾⡿⢻⣿⣿⣷⣦⣀⡈⠙⠿ ⠀⠀⠀⣠⣴⣟⣯⣶⠿⢻⡿⡯⠀⠀⣠⣶⣿⣯⠶⠟⠋⢁⠄⠀⡶⠋⠀⠀⠀⠀⠀⠙⠦⣛⡿⠿⢷⣟⡛⣿⣮⡻⣶⡦⠽⠟⠇⠀⠀⣠⣤⠟⠛⣋⣡⠴⢿⢸⢻⡻⣿⣿⣿⣶⣄ ⠀⣠⣶⡿⠞⡿⢋⣵⡶⣫⠆⣠⣾⢟⣫⡷⠛⠳⣶⣶⡶⠋⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⠀⣤⡉⠙⠋⠛⠿⠃⢀⣠⠶⠒⠉⢁⣠⡴⠚⠉⠀⣷⠞⢸⢀⣭⣿⡿⠻⣿⣿ ⠾⠋⠁⣤⢮⣷⡿⠋⡴⣃⣾⣿⠿⢛⣿⠁⠀⠀⣿⡽⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⢯⢏⡷⠴⣖⣉⡥⠤⠶⠶⣺⠿⠋⢤⣀⣠⣾⣿⣿⣶⠀⣿⡏⠀⡀⠈⣿ ⢀⡴⠞⣴⣿⠟⢀⣼⡿⠟⢡⡏⠘⠙⣿⣦⡀⠸⡿⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⣶⡿⠷⠚⠋⠁⠂⣀⡤⠴⠋⠁⢀⣴⣿⣿⣯⣟⡉⠉⣸⡆⣿⠀⠀⢳⣦⡈ ⠋⠀⣠⡿⠁⣰⡿⣻⡇⠀⢺⣏⠛⠲⣿⡆⡿⣰⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⢁⣠⡀⢒⣀⡤⠶⠚⠋⠁⠀⠀⠀⠀⣜⠿⣿⣾⣿⣿⣷⣶⢻⣇⣿⢠⣄⠀⢻⡟ ⡞⣰⠋⡤⠾⢋⣴⡟⡇⠀⠀⠈⠳⣤⣸⡇⢠⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⢀⣤⣤⠟⣫⣥⡿⠋⣀⡤⠀⠀⠀⠀⠀⠀⢸⣿⠄⠸⣟⠻⣿⣻⣿⣿⣿⢿⡘⣿⡄⠈⣿ ⣴⣣⡾⢀⣴⠟⢋⣴⣿⣦⣀⠀⠀⠐⢾⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠉⢀⣼⠟⠉⣠⠊⠁⠀⠀⠀⢰⠀⠀⠀⢸⡏⠀⠀⠹⣷⢼⣿⣻⠹⣿⣦⣷⡁⣇⠀⠸ ⢙⣩⣴⡿⣁⣶⣿⣿⢿⣿⣿⡶⣦⣴⣿⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⡰⠋⠀⠀⠐⢿⣉⣀⣤⣤⠄⠘⠦⣄⣀⡾⡇⠀⠀⠀⢹⡌⡿⡏⠇⣿⣿⢿⠻⣼⡀⠀ ⣿⣻⡯⠞⣿⡿⣫⣾⣿⣿⡿⣸⠋⣹⠷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠙⠁⠋⠁⠀⣠⣾⣟⣟⣤⡇⠀⠀⠀⢸⣇⡷⠃⢀⣉⡀⢠⣒⢻⣇⠀ ⣿⠋⠀⣼⢏⣾⡿⢋⣾⡟⠁⣏⣼⠋⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣾⣿⣿⣿⡿⠃⠀⠀⣠⠞⢁⣤⣞⣻⣿⠿⣿⣿⡏⣿⠀ ⡷⢀⡼⢁⡾⠋⢠⡿⢻⠀⢰⣯⡟⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢤⢀⡤⠒⠒⢶⣤⡙⢆⠉⣿⣿⡿⠏⠀⠀⠀⡜⢁⡾⠛⢹⣿⣿⣿⣶⢹⡿⠃⢸⠀ ⡇⡞⢁⡿⢁⣾⡟⠁⡾⠀⢸⡏⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⡶⠶⢶⣒⠒⠛⠛⢷⡅⡤⣤⢭⣅⠀⠀⠀⠀⣰⡷⠋⠀⢀⣾⣿⣿⣿⡿⢋⠀⢠⣾⠀ ⢰⠇⣸⣡⡿⡋⠴⠘⡇⠀⣸⠁⠀⠀⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠒⠶⣌⣉⠀⠠⣿⢶⣽⣿⣿⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣛⠯⠥⣠⢎⣴⢟⣿⢆ ⣿⢰⣿⠿⠉⠁⠀⢰⠇⠀⢻⠀⠀⠀⠀⠀⢨⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣳⢹⣄⠀⠀⠀⠀⠀⠈⠛⠶⣌⣻⣿⡟⠁⠀⠀⠀⢰⣧⡴⠛⠁⠀⢀⡀⠠⠴⠁⣩⣤⢾⠟⡼ ⣏⣿⠋⠀⠀⠀⠀⣸⡄⠀⢸⡄⠀⠀⠀⠀⢠⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣧⣀⣀⠀⠀⠀⠀⠀⠀⣹⣿⠃⠀⠀⢠⣾⣻⣭⣴⣶⣾⣭⣭⣤⣴⠲⣿⠏⣵⢏⡜⠁ ⢹⠃⠀⠀⢀⡤⠊⠉⣇⠀⠘⣧⠀⠀⠀⠀⡘⡇⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⡀⢀⣴⢿⡇⠀⢀⣴⡟⢉⣻⣽⣿⣿⣿⣿⠛⠛⣩⣼⢏⣴⣫⠏⠀⠀ ⡟⠀⢀⠴⠋⠀⠀⠀⢹⡄⠀⢹⡄⠀⠀⣸⠻⣇⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣾⡿⢀⣴⡏⢋⣵⡿⠿⣿⣿⣭⣍⣽⠵⠚⠁⣸⢿⡿⠋⠀⠀⠀ ⣧⠔⠁⠀⠀⠀⠀⣀⠴⠃⠀⠀⣷⠀⢰⢻⠀⠘⢇⠀⢀⣀⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡿⣷⣺⣿⡯⠿⠶⠆⠀⠚⠋⠉⠀⠀⣠⠴⢺⡿⠛⠁⠀⠀⠀⠀ ⡏⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠘⣦⣏⠸⠀⠀⠈⢷⡙⣷⣶⣼⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢁⣧⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠉⠛⠻⣿⣼⣿⣽⣟⣻⣯⣷⣲⣤⣄⣰⣤⣶⣶⣶⢀⣧⡾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡴⠉⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣽⡳⠀⠓⠿⠍⠛⠿⣽⡛⣷⢞⣥⠋⣸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⡿⠉⢠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢘⣦⠀⠘⠶⣄⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⠏⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠈⠳⠆⠀⠘⠧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣥⣶⠿⠛⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣯⠷⠟⠛⠁⣰⡆⠀⢀⣦⠀⠀⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡌⠳⠀⠀⠀ ⠀⠀⠠⠀⠉⠋⠁⠀⣿⠁⠀⢀⢄⠀⣴⣿⡇⠀⠀⠀⠀⢀⣠⠤⠤⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣺⡿⠽⠓⠐⢾⣅⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠕⣑⡥⠚⣿⠃⠀⠀⠀⢸⣇⠀⣠⣤⡀⠙⡄⢸⣆⠀⠈⠀⣀⡴⢞⡫⠝⠛⠻⠟⠀⠀⠀⠀⠈⠈⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⣸⠋⠁⠀⠹⡄⠀⠀⠀⠀⠙⡆⢇⠈⢻⠀⡇⠀⣿⣠⠕⢛⡥⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠ ⠀⠀⣀⣀⠀⣀⠀⠀⢹⣿⣷⣿⠀⠀⠀⣀⢳⠀⠀⠀⠀⠀⣿⠸⣄⡜⢀⡇⠀⣿⢹⡖⠁⠙⣢⠴⠊⢉⡙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠁⠀⠀⠀⠀⠀⠀⠁⠸⣦⣉⡿⠀⠀⣠⣮⣿⡷⣶⣾⡟⠛⣿⠀⣉⡦⠊⣠⣾⣭⣌⣱⠀⡼⠁⡔⠉⠙⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀ ⡄⠉⠢⣀⠀⠀⠀⠀⠀⢹⠉⠠⠖⣪⣭⣽⠏⠀⠀⠀⠈⡷⠽⠉⠓⠀⠉⠙⢿⣓⣾⣷⣲⡇⠀⢇⣀⡴⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄ ⠙⢶⣤⡀⠑⠢⠀⠀⠀⣈⢥⣶⣿⣿⣿⣏⠀⠀⢀⣠⢴⣧⣀⠒⢒⡆⠀⠀⢸⣧⠀⠀⠀⠙⠦⠤⠥⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀ ⠀⠁⠈⠛⠷⢄⣠⠔⠚⢄⡘⠿⠿⠛⠛⠛⣧⣤⣾⡝⠆⠻⠟⢁⡾⠃⠀⣠⡞⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠ ⠀⠀⢀⣠⡴⢛⣹⠿⠶⣤⣈⠑⠢⢤⣀⠀⠘⠯⢽⡇⠀⠠⠤⠉⠀⣴⠟⢿⣷⣀⠀⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢏⡴⠊⡅ ⠁⢠⡿⣩⣶⠋⢁⣠⣴⣿⣿⡟⠶⣦⣄⡉⠒⠦⣄⣿⣄⣀⣀⣀⣠⣿⣶⣤⣀⣈⠉⠛⠿⢷⣠⣤⡀⠐⠀⠀⠀⠀⣶⣿⡿⢁⡞⢀⡞⠀ ⣴⣿⡿⠋⣡⣾⢿⣿⡇⣿⣿⣷⡀⡼⠋⠙⠳⠶⣤⣀⠉⠙⠛⠫⠍⠉⠉⠉⢉⡉⠽⠶⠤⠤⣀⡉⠉⠙⠒⠒⠒⢓⡾⠋⠀⠈⠀⠊⠀⠀ ⡟⢁⡤⣾⢻⡇⣼⣿⢷⣽⡿⠿⢿⢣⠂⣠⠀⢀⠒⠩⠙⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠾⠿⠿⠛⠉⢉⡥⢂⠤⠀⠀⠀⢀⡄⠀ ⢁⣾⢱⣇⣾⡏⠀⠀⠀⠉⠉⢁⣿⣏⢀⠟⣰⠫⣢⢃⣼⠟⠁⣀⣠⣮⣭⣉⠉⠙⣯⢁⠀⢀⠇⠀⣠⣾⣤⣾⣥⣎⡠⠤⠤⠴⠶⠟⠁⢠ ⢼⣧⡏⣿⣹⠁⠀⠀⠀⠀⣰⣿⣿⣿⡜⢠⣧⣷⢇⣾⣿⣾⣿⡿⠟⠛⠉⠉⢙⡿⠛⡟⠀⡘⣰⣢⠟⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠸⣿⡅⠸⣿⠀⠀⠀⢀⣾⣿⠟⣿⣿⡇⣾⡿⡟⣼⠿⣟⣟⣿⣿⣶⣤⣤⡤⠎⠀⢠⠇⣰⣱⣿⠏⢀⣤⣶⣀⡸⢠⣤⣦⣤⣄⡀⠀⠀⣀ ⠀⠛⠳⣼⣿⠀⢠⣶⣿⠋⠁⠀⠟⠸⠀⣿⠃⣧⠿⠄⠙⢿⣿⣷⣋⡿⠟⠃⠀⣀⡞⣰⣿⡿⠃⠀⢸⠁⣾⣿⡉⠈⠉⠛⠓⠤⠀⠀⠀⠀ ⣀⣀⣴⣿⣿⡆⢸⣿⣇⠀⠀⠀⠘⢀⡸⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣠⠷⣿⠟⣴⣿⡟⢀⡠⢴⡿⠞⠻⠏⠛⢒⣶⣶⠧⠭⣧⡀⠀⠀ ⣿⣿⣿⣿⣿⣧⣤⣿⣿⠶⢤⣤⣅⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⠯⢋⣽⠿⣷⣤⠖⠋⠁⠀⠀⠀⣰⠋⠉⠻⣦⠀⠈⠻⣶⠀ ⠟⠁⠈⢿⣿⣿⡞⣿⣜⣿⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠔⢋⣿⡰⠁⠀⠀⠀⠀⠀⣠⠞⠳⡤⠤⠀⠙⠗⠀⢀⡿⠀ ⠀⠀⢀⣿⣿⣏⠳⣬⡙⠛⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡡⣖⠋⠈⠀⠀⠀⠀⣠⡴⠛⠀⠠⠤⠴⠂⠀⠀⠀⢀⡼⠁⠀ ⠀⢀⣾⣿⣿⣿⡄⠈⢿⣦⣀⣈⡙⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡏⢉⡉⣉⣠⡄⢀⣠⣴⢎⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢾ ⢠⣿⣿⣿⠿⠛⠙⠢⣄⡉⠉⠁⠀⠀⣀⣀⡤⠴⢶⡶⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢱⣯⡽⠃⠀⠀⠀⢀⠴⠉⠀⠀⠀⠀⠈⠀⠀ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢈⡟⣩⣿⣿⣷⣿⣿⣿⣿⣿⡛⠾⣧⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢺⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🧛🏼‍♂️🎭🌍

⠀⠀⠀⣦⣤⣾⠾⡧⢟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢶⣬⢭⣟⣳⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣾⠅⢸⠓⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠺⢽⡏⣟⠻⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⣴⡌⣶⣷⠤⠔⢤⣐⣯⡑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡍⠑⠢⣈⠻⣦⣤⣤⣤ ⠀⠀⢀⣿⣿⣿⣦⣷⣀⣀⣴⣆⣿⣙⡣⠼⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢀⣈⠑⣿⣿⣻⣿ ⢰⠋⢹⣿⣿⣿⣿⠙⠛⢻⣫⢡⣿⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⡏⠉⠉⠉⠉⠉⠉⢻ ⠸⣷⣿⣿⣿⣿⣿⡄⠀⢠⡟⢂⣹⣤⡈⠑⠂⠠⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⣿⣿⣿⣿⣿⣿⣦⠄⣧⠀⣿⡀⠀⠀⢀⣀⡈⠉⠉⠉⠉⠙⠒⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡇⣦⡄⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣿⣿⣿⣿⡿⠃⣠⣴⠛⢀⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⢶⣿⢿⡞⢲⠶⣶⣤⢤⣬⣍⣙⣻⣿⣿⡇⠀⠀⡀⠀⠀⠀⠘ ⠀⠀⣿⡿⢿⣟⣡⣾⡿⡧⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢾⣿⠙⣷⣾⣄⠹⣿⣷⣆⠈⢻⣿⡏⣿⡿⠀⣈⣉⣁⡀⠀⢸ ⠀⠀⠘⣿⠀⢨⠭⠀⢀⣄⣴⠏⠀⠀⠀⠀⢀⣤⣾⣿⠛⠋⠉⠀⢀⣼⠟⠀⠙⣿⣿⣦⣌⠻⣯⡇⠀⣿⡇⡟⢧⠀⠉⠉⠉⠁⠀⢸ ⠀⠀⠀⠈⠓⢶⣶⡿⣿⡋⠁⠀⠀⣤⣶⢚⣉⣿⣿⣿⣷⣶⣶⣿⣹⡇⠀⠀⠀⢹⣿⣿⣿⣷⣌⠑⠲⢿⡇⡿⢿⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠉⠛⠓⠻⢷⣄⠀⠈⠉⠟⠿⠿⠿⣿⣿⣏⣤⣿⠟⠁⠀⠀⠀⠈⢿⣿⠁⠀⠉⠻⢶⣢⣷⡇⣸⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⡇⠀⠀⠀⠀⠀⠐⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⠯⠅⠀⠀⠀⠀⢻⡇⡷⢿⡒⠲⣶⣲⡶⣶⡺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⢸⢿⣷⡼⣯⣷⡸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⡇⢱⣿⣿⣷⣝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠘⡄⡇⣸⠟⠁⠈⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣨⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣰⢳⣿⠃⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣴⣾⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⡟⠁⢠⠊⢀⡞⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣠⣴⣶⣶⣶⣶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠀⡰⠁⣠⡟⠀⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡟⠛⠋⠁⢀⣠⡾⢉⡿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⠀⡜⠁⣼⣿⠁⣰⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⣠⣾⡿⠟⡻⣿⣇⡜⠀⠾⢣⠇⣰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢇⠀⠀⠀⠀⠀⢀⣠⣾⣟⣿⠴⠋⠀⣿⣿⠃⠀⠀⡼⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠈⠢⢤⣀⣠⣴⣟⣻⠟⠋⠁⠀⢀⣴⣿⡏⠀⠀⢰⣷⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠙⣿⣏⣁⣤⢤⣴⣾⡿⠛⡹⣷⣄⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢢⣄⣀⣴⣿⠟⠻⣄⠀⠹⢷⡜⠉⢧⣿⠋⣼⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⢀⢌⣳⡀⠀⠉⠉⣿⣿⣴⠋⠀⠀⠀⣼⠇⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣦⣷⡀⠀⡙⣦⣠⣴⢿⡟⠁⠀⠀⢀⣼⠃⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⡿⠁⠀⠙⠻⠿⠁⣼⣁⣀⣠⣴⡿⢁⣰⠏⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠲⣦⣤⣀⣀⣼⡏⢹⣿⢿⡟⣠⢾⢃⡤⠂

⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⣀⡀⢠⣤⣄⡀⢀⣀⣄⣶⡳⠞⢦⠈⡿⣆⢤⡁ ⠀⠀⠀⢰⠁⠀⠀⣠⠤⣐⡊⣭⡤⣜⡤⠤⣍⣉⡙⠛⠷⣫⠥⣀⠠⢎⢆⠈⢃⠩ ⠀⠀⠀⣿⠀⢔⣭⢶⡿⠟⡋⢿⡻⠉⡠⣊⢵⣧⡉⠛⠲⢦⣌⣑⠮⣜⣿⣑⢺⠈ ⠀⠀⢀⣿⣴⣯⠗⠉⣀⣴⣾⢏⣴⢯⣺⣦⢀⠙⢿⣦⣀⠀⡸⠹⣿⣶⣍⡻⢯⣇ ⣠⣾⡿⣿⡿⢃⣴⡿⠋⡻⡡⠊⠀⠘⢿⡿⢿⣿⣶⡿⢿⠖⣁⠴⢚⡩⠟⢿⣶⣬ ⡫⣿⢦⣯⡾⢿⠃⣸⢍⠔⠀⠀⠀⠀⠀⠘⡈⡶⣏⣚⠥⢭⠖⣊⣤⣷⡇⡼⢋⡹ ⠟⡱⡟⠑⡗⢈⡱⣍⠊⠀⠀⠀⠀⢀⠤⢒⣢⣽⠴⠑⠈⠀⣰⢿⣷⣾⣼⡇⡈⢷ ⢾⢟⣽⣄⡈⢹⣶⠃⠀⠀⠀⠀⠈⡠⠚⡩⠖⡁⠀⠀⡄⠀⡟⠈⢯⣾⣻⣹⡷⠘ ⣷⢟⣽⡿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠑⢛⢁⣼⣖⡇⠀⢸⠿⣛⣉⣹⡆ ⢫⢏⣾⠁⡟⠀⠄⠀⠀⠀⠀⠀⠀⢀⠠⢤⣠⣤⣐⠜⡿⠟⠁⣐⠵⢻⣿⣟⠏⡇ ⣿⡫⢺⢠⠁⠀⠸⠄⠀⠀⠀⠀⠀⣩⠉⠚⠡⢀⡹⣿⡿⠀⢠⢃⣠⠟⠋⣁⢔⡗ ⠃⢀⢬⠈⡄⠀⢨⠈⢄⠀⠀⠀⠀⠙⠷⣄⣀⠀⢈⣿⠀⣠⢾⣵⣤⣬⢽⣞⣟⠌ ⠆⠁⠈⡄⢣⠀⣾⡀⠀⢂⠀⠀⠀⠀⠀⠀⠈⠙⣾⡏⣼⢾⣿⣿⠽⠔⣩⡿⠃⠀ ⢀⠔⠁⠀⠈⣼⠙⠈⠢⣶⠷⣦⣤⣀⠀⠀⣀⡜⢻⣿⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀ ⠁⠀⠀⠄⠀⠘⠄⠀⠀⠀⢳⣾⣷⣿⣭⣿⣿⡥⢱⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠴⡌⠢⣀⣠⣾⣿⣿⡿⣟⡯⠟⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠂⠀⠞⢷⣄⠀⣱⣷⣤⣾⣶⡄⠀⢳⠦⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠶⠛⠛⢒⠶⠿⠦⠔⢶⣆⣉⣍⣰⣒⡛⠷⣝⣺⠀⠀⡨⠿⠤⡜⠀⠙⣄⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣀⣤⠴⢚⣉⣡⢤⣴⣶⣶⣾⣿⡶⠶⢦⣤⣄⣀⡈⠉⠓⠫⢍⣒⠮⣵⡋⠀⣾⠧⡘⣆⠀⠈⢣⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠴⣚⣭⣷⡾⣿⡿⠟⠛⣹⡯⠟⡻⠋⢀⡴⠚⣩⣿⡉⠙⠻⠶⣦⣤⣀⠉⠛⠻⢿⣗⣶⣷⣾⠓⢦⡀⠉⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡤⢚⣡⣾⣿⣿⠷⠚⠉⠀⠔⣊⡵⠀⠊⣠⠔⢉⡴⠊⠘⣿⣷⣄⠀⠀⠀⠉⠛⢿⣶⣶⣤⣉⠛⢿⣿⣦⣎⠴⢆⠀ ⠀⠀⠀⠀⠀⠀⢀⣯⣼⣿⣿⡿⠛⠁⠀⢀⣠⣴⣿⡟⢋⡤⢊⢵⡞⣿⣲⣤⣀⠈⠻⣿⣷⣦⣄⠀⠀⣀⡏⢹⣿⣿⣷⣦⣌⠙⠿⣷⣮⣁ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠀⢀⣤⢾⣿⠛⠝⠃⣠⠾⠛⠁⢰⡝⣿⣿⣿⣿⣿⡢⣌⠛⢿⣿⣷⠐⠋⠚⢁⣨⣿⠿⣿⣿⣷⣦⣀⡙⠻ ⠀⢀⣴⣿⣿⢿⣋⣿⠛⢀⣤⣾⣿⣿⣋⣁⡴⠀⡜⠁⠀⠀⠀⠀⠙⠚⢿⡛⠛⠽⢿⣾⣿⡗⠋⢉⣀⠤⠒⢋⡩⠔⣞⡿⡏⠻⣿⣿⣿⣶ ⡴⠛⢉⣴⣵⡾⣫⢋⣼⡿⢿⡟⠀⠈⣿⠏⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢷⠖⣆⡨⣔⣊⣁⢤⢴⠞⢉⣀⣠⣿⣥⡅⢹⡟⠁⠈⢿ ⣠⠔⢹⡿⠋⣠⡿⠋⣸⡁⢸⡷⣄⠰⠏⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠴⠾⠟⠚⠉⣉⡠⠔⠊⠁⣠⣾⣿⣿⣉⠉⣡⢸⠁⠈⢶⣌ ⣡⢠⠟⣠⡾⣻⡇⠀⠻⣍⠙⣯⠘⣼⡜⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⣤⠦⣠⡴⠚⠉⠁⠀⠀⠀⢰⡏⢻⣿⣿⣿⣯⣽⣼⢰⣦⠘⣿ ⣱⣧⠎⣡⠾⣋⣷⣄⠀⠈⠹⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣵⠟⢋⠔⠊⠀⠀⠀⠀⠀⢸⠏⠀⢻⣍⣿⣿⢿⣏⣧⠻⡀⢹ ⢛⣥⡾⣡⣾⣿⣿⣿⡷⣤⣴⡏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢠⠎⠁⠀⢿⣩⣤⣤⠄⠳⢤⣀⢾⠀⠀⠈⣇⢿⡿⢸⣿⢿⢷⡇⠀ ⣿⠿⢛⡿⣿⣿⣿⡿⢳⢃⡝⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠉⠀⠀⣠⣾⣿⣯⣾⠀⠀⠀⡴⠞⣁⣤⣤⣴⣮⣿⠀ ⡏⢀⠞⣼⠛⣱⣟⠁⢸⡻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠤⣄⡀⡄⠻⣿⣿⡟⠁⠀⢠⢋⡴⠿⣿⣿⣯⣿⣿⢹⠀ ⠇⡎⡼⢡⡾⠋⡼⠀⡿⠁⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⣤⡴⠿⠒⡒⠛⣧⡨⣤⣯⡁⠀⠀⢀⡷⠋⠀⣰⣿⣿⡿⢟⠀⣼⠀ ⣼⢰⣷⡿⠐⠊⡇⠀⡇⠀⠀⠀⠸⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡄⠀⠈⠉⠒⠤⣀⠺⣷⣾⣿⠇⠀⠀⢸⠀⣠⠾⠻⠝⠓⡰⠫⠞⣿⢆ ⣇⡾⠋⠀⠀⠀⡇⠀⡇⠀⠀⠀⢈⡆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣦⡀⠀⠀⠀⠀⠙⢺⣿⠁⠀⢀⣤⣿⣋⣤⣤⣄⣀⣨⣥⡶⣻⢋⠎ ⡿⠁⠀⢀⠴⠊⢇⠀⢱⠀⠀⠀⣘⡇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀⣠⣾⡇⠀⣠⡞⢙⣿⣿⣿⣿⡿⠛⡡⡟⣵⣿⠃⠀ ⡇⣠⠖⠁⠀⠀⢸⡀⠈⣇⠀⢰⡟⢧⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣿⢠⣾⣭⡵⠟⢻⣿⡿⠽⠛⠋⣠⣿⡟⠁⠀⠀ ⡟⠁⠀⠀⣠⠔⠉⠀⠀⠸⣤⠿⠇⠈⢣⡰⣖⣚⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⢛⣻⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⠜⠁⠀⠀⠀⠀ ⡇⠀⡠⠊⠁⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣷⣶⣤⣀⣠⣤⣤⣤⢉⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠊⠀⠀⠀⠀⢀⠔⠂⠀⠀⢳⡀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣂⡙⠛⣉⣿⣯⣻⣿⡿⢡⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⠀⠹⣄⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⣀⠔⠈⠓⠄⠈⠳⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣽⡾⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⡈⠀⢊⣣⡨⢷⠞⢳⡀⡗⠇⠠⠀ ⠀⠀⠀⠀⠰⠁⠀⢀⡤⣐⣢⣭⣤⣴⣷⠖⢤⣭⣍⡙⠋⠼⢃⣆⣱⠎⢢⡈⢢⡀ ⠀⠀⠀⠀⣧⠠⣪⡷⡿⠝⠋⢅⡚⢝⡡⢒⠕⢾⣄⠉⠙⠲⢦⣬⣙⠿⣿⣬⠢⡀ ⠀⠀⠀⣠⣷⣿⠟⠋⢀⣤⠾⠟⣱⠜⡪⣧⣶⣄⡙⢿⣦⡄⡴⠨⢻⣿⣦⣝⠳⢧ ⢀⣴⠾⣟⢝⣃⣴⡾⣗⡡⢀⠊⠀⠀⠙⠻⡟⡫⠿⠷⠛⡃⠤⣚⠭⢓⢿⣻⡿⣶ ⡉⢴⡟⣱⠕⡏⢹⡀⡼⡑⠁⠀⠀⠀⠀⠀⣰⡼⠯⠚⢂⠨⠋⣱⣶⡟⢳⠘⠰⣜ ⢤⡪⢾⢿⠈⠫⢽⣨⡗⠀⠀⠀⠀⠀⢂⡡⢔⡶⡂⠉⠀⠀⢸⠝⣿⣻⣿⣆⣇⢹ ⣫⣗⣵⣿⣷⠤⣼⡛⠀⠀⠀⠀⠀⠔⠉⡐⠉⠸⡤⡤⠘⣤⢼⠀⠸⢿⠏⠟⢻⡀ ⡏⡑⡽⣻⠋⣷⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⡀⡐⢾⣿⠛⢀⢔⢵⣾⣾⡿⡇ ⡛⣜⡞⢱⠀⠃⠀⢡⡀⠀⠀⠀⠀⠀⡒⠲⠛⡈⢙⣔⣾⡄⠀⡜⢁⣼⣿⣛⣠⡇ ⣷⠋⠀⣸⠈⠀⠀⢰⠐⡀⠀⠀⠀⠘⠾⣄⣀⠀⠁⢺⠏⠀⣤⣳⣥⣀⣠⣵⣺⠙ ⡇⡠⠊⠈⡄⢃⠀⡾⡀⠐⡄⠀⠀⠀⠀⠀⠈⠙⣲⡿⣠⣚⠴⣿⡛⠯⢂⣷⠏⠀ ⡏⢀⠄⠊⠀⠘⣾⠃⠐⢴⣬⣦⣤⣄⡀⠀⢀⣀⠟⣩⡏⠁⠀⠀⠀⠈⠘⠁⠀⠀ ⡗⠁⠀⢀⠄⠀⠐⠄⠀⠀⠈⢿⣿⣏⣛⣹⣿⣿⠎⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠁⠀⡠⠰⠌⠢⣀⣴⣾⣿⣿⣿⣻⠝⣡⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣰⣀⣀⣰⣷⢿⣀⣿⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠶⢦⣤⡬⣉⣙⣻⠷⢷⣤⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⢋⣼⣋⠀⣶⡥⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠮⣽⣓⢿⡟⣿⠷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⠀⡀⢷⠀⣿⠀⠀⠀⠀⠀⣀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⢻⢦⣈⠉⠿⣦⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⣽⣿⣿⣼⡷⢨⣵⠿⠒⠒⠋⠳⣤⣝⣲⡌⠻⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠙⠦⣌⡻⣿⡶⣶⣶⣦ ⠀⠀⠀⣿⣸⣿⣿⣷⣤⣷⡀⣀⣀⣾⣄⣿⣅⣙⡥⠴⠖⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣀⠌⠛⢾⣷⡙⢻⣿ ⣴⠖⢛⣿⣿⣿⣿⣿⡿⠻⠿⠿⡿⡋⢡⢺⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⣿ ⣿⣦⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⢹⣿⠸⢸⣇⠈⠙⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠘⢿⣿⣹⣿⣿⣿⣿⣿⣦⠀⠀⢿⡏⠱⢸⡿⠷⠦⠄⠀⠄⠉⠷⠶⠦⠤⠶⣶⣦⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢸⣿⠀⣼⣇⢀⣀⣀⣀⣐⣦⣀⣀⣀⣀⣀⣀⡀⠉⠉⠉⠠⣤⡀⠀⡐⠀⠀⠀⠀⠠⣤⣤⣤⣄⣀⣠⡇⢸⣶⡇⠀⠀⠀⢀⠀⠀⠀⠀⢸ ⠀⠀⣿⡏⣿⣿⣿⣿⡿⠃⢀⣤⡾⠛⠀⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⡻⢿⣿⠿⣷⠶⠷⠦⢤⣤⣤⣤⣀⣈⣉⠙⠛⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⣿⣷⣿⣿⣿⠏⣠⣼⣟⣿⡁⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡷⢿⣧⡸⡽⠀⢾⡶⢶⡮⡉⠉⢻⣿⣷⡟⣹⢷⡇⠀⠀⠾⠗⠷⠀⠀⠀⢠ ⠀⠀⢹⣟⣌⠙⠛⠶⠟⠛⠋⡜⠁⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⡶⠖⠛⠉⢁⣿⡷⠀⢯⣻⣿⢷⡈⠻⣧⣽⡻⣄⠀⢹⣷⡇⢸⢿⡇⠀⠶⣾⡷⠷⢶⠀⠀⢨ ⠀⠀⠀⠹⣮⡃⠰⠖⠒⣀⣠⣴⣴⠟⠁⠀⠀⠀⠀⢀⣀⢤⣾⣿⣿⣯⠁⠀⠀⠀⣀⣠⡾⠟⠀⠀⠀⢳⣽⣿⣷⡳⣌⠻⢿⡍⠀⢸⣿⡇⢸⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠈⠙⠿⣿⣿⠿⣿⣏⠉⠀⠀⠀⢠⣼⣻⠙⣁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣯⣵⡾⠂⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣄⠉⠒⠾⢿⡇⢸⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠷⢬⣽⣦⡀⠀⠀⠉⠙⡻⢛⣿⢿⣿⣿⣿⣿⡏⢁⣴⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⠋⠀⠈⠛⠿⣶⡤⣤⣿⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠭⠽⠇⠀⠀⠀⠀⠀⠹⣶⡟⢽⣐⣇⣀⣀⣀⣀⣀⣀⣀⣀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍⠀⠀⠀⠀⠀⠀⠹⡇⢸⠉⣿⣦⣄⠙⣿⡞⣿⠙⣿⣍ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡟⠛⣏⢷⡸⣿⣜⣦⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢳⠀⢻⠀⣇⣹⣮⣻⣧⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⠀⢸⡀⢸⠀⣼⣿⠟⠉⠻⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⠀⢸⡇⡿⣴⠟⠁⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣤⣤⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣠⡎⣼⡿⠋⠀⢀⠄⠀⣼⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣾⣿⡿⠿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣰⡿⠁⠀⡴⠃⠀⣾⠋⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣠⡴⢶⣶⣶⣒⣲⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢸⣿⠟⠁⢀⠞⠁⢀⣿⠃⠀⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣽⣿⡾⣿⠿⠛⠉⠉⠀⣠⣶⠒⣶⡶⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⠏⠀⣠⠏⢀⢰⣿⡏⠀⣠⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣤⣴⣾⣿⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣾⡿⣿⢻⠀⣰⠃⢀⣾⠏⡾⠁⣰⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢚⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⣡⠞⣿⢸⢰⠇⠀⠙⠏⣸⠃⣰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⡛⣥⡶⠋⠀⠀⣿⢸⡟⠀⠀⠀⢠⡏⣰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠘⢦⣀⡀⠀⣀⣠⢴⡿⢿⣷⠿⠛⠁⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⣾⢱⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠈⠉⠛⠿⣷⣷⠶⠚⠁⠀⠀⣀⣠⣴⣿⡿⢿⢸⡀⢀⠄⣰⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⢹⣿⣤⣴⠞⠛⢿⣿⣿⠻⣍⣠⣾⢸⣿⡴⢀⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣹⣦⣀⣠⣶⣿⣿⠋⠙⢦⡀⠀⠘⢿⣧⣁⠀⣿⣸⡟⢁⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣽⢻⢿⠁⠀⠀⣠⠝⣦⠀⠀⠉⠉⠉⣿⣿⣇⣼⠋⠀⠀⠀⠀⣰⣿⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⣤⣴⣫⠔⠉⢁⢻⣄⠀⢀⣠⣿⣿⠟⠁⠀⠀⠀⠀⣸⡿⠀⢴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣏⣻⡶⠀⠘⢶⣽⣿⣿⠛⢹⢸⠀⠀⠀⠀⣠⣾⠏⠀⣠⠿⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣬⣛⡛⠁⠀⠀⠀⠈⠛⠃⢠⣿⢸⣤⣤⣖⣿⣿⠋⢠⣼⠗⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣏⠙⢷⣶⣦⣄⣀⣠⣿⣿⢸⣿⡿⢫⡿⢁⡼⢻⢉⣤⠏⠁

⠀⠀⣖⡞⣗⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠺⢯⣷⢿⣤⡀⠀⠀⠀ ⠀⠀⣿⣴⢣⠧⠤⣄⣔⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⢝⣦⣤⣤ ⠠⢤⣿⣿⡾⠴⠞⣺⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠐⠈⠛⢻ ⠘⣾⣿⣿⣧⠀⡟⢽⠦⠁⠀⠤⠄⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸ ⠀⢸⣿⣿⠟⣩⠟⣸⠖⠒⠒⠒⠒⠒⠲⢤⣷⠤⡤⣤⣐⣒⢲⣾⠇⠀⡀⠀⠘ ⠀⠸⣝⠯⠾⠻⢠⠏⠀⠀⠀⣀⣤⠤⠖⢺⡏⢿⣦⡻⣷⡄⢻⣹⡇⠠⠿⠄⢐ ⠀⠀⠑⠺⣶⣟⠃⠀⢴⣒⣽⣿⣷⡶⣶⡏⠀⠈⣿⣿⢮⡃⠼⣸⠆⠀⠀⠀⢘ ⠀⠀⠀⠀⠀⠩⠽⢆⠀⠀⠉⠹⣿⡶⠋⠀⠀⠀⢙⡇⠀⠉⢻⢿⣠⠀⡀⣀⡰ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠘⠓⣽⣷⣻ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠸⡸⠋⠻ ⠀⠀⠀⠀⠀⠀⠀⠨⣀⣠⣤⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⡞⠁⠀⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠨⣥⣄⣶⠶⠖⣋⣀⠀⠀⠀⠀⣴⣿⠏⡠⢁⡞⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣤⣴⠾⠵⠃⠀⠀⣠⣾⢿⣿⠐⢡⢻⢡⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⠀⠀⣠⣾⡯⠒⢁⣿⠃⠀⢦⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠉⢻⣗⣁⢤⣴⠟⡻⣄⣸⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⣤⣾⠋⠓⡄⠛⠥⣽⢡⠏⠀⢠⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡇⢩⣦⡴⡿⠁⠀⣰⠋⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠥⣄⣈⣡⡗⡶⡿⣡⢞⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⣼⡶⣦⠴⣻⣦⡀⠈⣿⢯⡇⠈⠑⠌⠂ ⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠒⢲⠶⠿⠿⠿⣷⣶⣦⣄⣒⣒⣻⠿⢿⣷⡆⠉⢀⠽⠷⢤⡿⠈⢻⣦⡙⣗⢤ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⣁⣠⣤⣤⣴⢞⣲⣦⠤⣤⣄⣀⡀⠉⠙⠛⠯⢝⣒⠾⢭⣖⠁⠀⠶⣆⠱⡄⠀⠙⢧⡈⢧ ⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⠴⢛⣩⣤⢶⣿⣿⡿⢿⣿⣿⠾⠟⠋⠁⣠⠶⢋⣽⠛⠛⠷⣶⣤⣄⣈⠉⠓⠾⣭⣒⠦⣼⣦⣿⠢⢄⣸⠟⠢ ⠀⠀⠀⠀⠀⣿⣷⡠⠊⣠⣾⡿⣻⡿⠟⠋⢁⠤⢚⣩⡠⠊⢀⡠⢊⡡⠞⠙⣿⣷⣄⠀⠀⠈⠙⠛⠿⣶⣦⣤⡉⠛⠷⣿⣿⣆⡼⣽⡖⠀ ⠀⠀⠀⠀⠀⣿⢯⣠⣾⣫⣵⠞⠋⠀⠀⣠⣴⣺⣵⠚⣁⣴⣫⡴⣿⣧⣀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⢈⠟⢻⣿⣷⣦⣈⡙⠿⣿⣿⣽⠇ ⠀⠀⢀⣤⣾⣿⣿⣿⣿⠋⠁⣀⣤⣴⡿⣿⣿⡟⢁⣶⠟⠋⢹⣷⣿⣿⣿⣿⣶⣦⣈⣻⣿⣿⣷⡄⣠⠏⠀⠉⢹⣿⣿⣿⣿⣶⣄⡉⠻⢿ ⢀⣴⣿⣿⡿⢻⣿⡿⠋⣀⣼⣿⡿⠏⠈⡡⠋⡴⠋⠀⠀⠀⠈⠻⢿⣿⠿⣿⣟⣿⣿⣿⡿⠿⣿⠟⠁⣀⡴⠟⢋⣉⡴⠿⡏⠻⣿⣿⣶⣤ ⡿⢛⢟⣥⡴⡫⢊⣴⣾⣿⡟⠉⢻⣿⡟⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠰⣬⣍⡛⠛⡿⠟⠥⠒⣉⣡⡤⠖⠉⢠⣧⣌⡇⢸⣿⠟⠻⣿ ⢞⣵⡿⢋⣾⡿⠿⡟⠩⣿⡄⠀⣾⠟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣸⣓⣽⠔⣲⠖⢛⡩⠟⠉⣠⣶⣿⠿⠟⡿⡇⣼⠃⢠⢰⠹ ⣻⠋⣠⢞⡟⠀⢾⡓⠦⡉⢹⡆⣌⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⣉⣉⢚⣵⠯⠖⠊⠁⠀⠀⣰⣿⣿⣿⣶⣖⣧⣾⣇⢀⠀⢻⣿ ⣡⣾⣿⡾⣧⠀⠀⠑⠦⣼⡇⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠊⢁⣠⡶⢟⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣿⠆⢹⡿⢿⣿⣿⣿⢿⣼⣧⠀⢻ ⢫⡿⣫⣴⣿⣷⣄⣀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⣰⠟⠋⣠⡀⠀⠀⠀⢰⠀⠀⠀⣟⠀⠀⢻⣷⣿⣯⣽⣡⣿⡝⡄⠘ ⣯⣾⣿⢟⣿⣿⣿⣿⣿⣿⣳⠇⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⢀⡾⠁⠀⠀⠙⢶⠞⠿⠃⠈⣱⣶⣾⡇⠀⠀⠀⣇⣿⡾⠿⠟⠛⠻⣧⠀ ⣻⣿⣿⡿⣿⡿⠁⣿⡿⠋⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣾⡇⠀⠀⡠⢟⣩⣴⣶⣾⣶⣿⣿⠀ ⢋⣾⢋⣰⢻⠃⢰⡟⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣤⣒⣲⣆⡀⣳⡈⣿⡿⠿⠉⠀⢀⢎⡴⠟⢻⣿⣿⣿⢻⡟⢸⠀ ⣾⣧⡾⢃⣼⠀⢸⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣚⡿⠏⠉⠉⠻⣯⣿⣾⣧⠀⠀⠀⣼⠊⠀⢠⣾⣿⡿⠟⠁⢠⣾⡤ ⣿⣿⠟⠁⣽⠀⣾⠀⠀⠀⠀⡛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠉⠐⠦⣌⠻⣿⣿⠟⠀⠀⢰⣇⣤⡶⠟⠋⠀⣀⡤⠔⣫⡿⢣ ⠏⠀⠀⢀⣇⠀⢻⠀⠀⠀⠀⣹⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⣀⠀⠀⠀⠀⠈⠙⣿⡇⠀⠀⣠⣾⣋⣥⣖⣒⣊⣩⡥⣦⡟⣿⢣⠛ ⠀⡠⠔⠉⢹⠀⠸⡆⠀⠀⢠⣿⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⣄⠀⣾⣿⠀⣠⢾⣿⣿⣿⣿⣿⠿⢟⣫⣷⣿⣾⡿⠁⠀ ⠎⠀⠀⠀⠈⡇⠀⢳⠀⢀⣎⣿⡀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣇⣰⣿⢾⣛⣛⣻⣿⠾⠛⠊⢁⡼⣿⠟⠁⠀⠀ ⠀⠀⣀⠔⠋⠁⠀⠈⣆⡾⠹⡇⠙⢄⣠⣤⣼⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⢿⣿⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢡⠟⠁⠀⠀⠀⠀ ⣠⠊⠁⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠙⠻⢧⡉⠿⣿⡿⢶⣶⣤⣄⣀⣤⣤⣾⡇⢨⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⠀⠀⠙⣄⠀⠀⠀⠀⠀⠈⢷⣶⣯⣿⣒⣿⣯⣽⣿⣿⣿⣬⣴⠃⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠘⢦⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠖⠹⣦⠀⠑⢤⣀⣤⣾⣿⣿⣿⣿⣿⡿⢟⣯⣶⠟⠁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠤⠀⠛⠓⠑⡀⠀⠈⠠⢸⣧⢴⠿⢿⡿⡿⠣⡍⢹⠂⢀⡠⠀ ⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠘⠃⢠⣴⣿⠿⢀⡾⡡⣺⣿⢏⠔⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡀⠔⡰⣰⠇⡆⣸⣿⢁⢠⢏⠜⠘⣋⡿⣿⣥⠀ ⠂⠀⠀⠀⠀⠀⠀⡀⠖⠒⢞⡠⠀⢼⡹⢷⣿⣿⣿⡿⡦⠋⠉⣴⡌⠹⣹⣏⢞⡠ ⠐⣁⠠⠤⣀⠰⠴⢠⢴⣭⠥⠷⣧⣜⡏⡈⣋⣻⣿⡄⣻⢷⡶⢦⢽⠀⣿⠋⠠⠀ ⡩⠔⠊⠃⢁⢔⣼⠷⠋⠈⢳⣦⣬⣟⣿⣷⣿⣿⣷⢷⢶⠤⡽⢒⣣⣴⡿⣖⣴⠺ ⡶⡷⠠⣖⣿⢄⡏⠀⠀⠀⠀⠳⢌⢿⣟⠻⣿⣻⣿⣦⢃⣨⣶⣿⡝⣟⣔⠯⠍⠛ ⣧⢃⣎⠃⢰⡹⠂⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠯⠫⡻⣴⣹⡿⠟⣸⠋⠀⠀⠀⠀ ⣿⣷⡢⠤⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠇⠀⠀⠈⢸⠏⠀⢤⠃⠀⠀⠀⠀⠀ ⣋⡼⡏⡶⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⢠⣒⠰⡀⡄⠀⡌⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⡆⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡫⠛⠁⡜⠀⠀⠀⠀⠀⠀⠀ ⣿⢷⠀⢡⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣶⠲⠂⢩⣴⣶⠟⣝⣄⣀⣀⣀⣀⣀⠀⠀ ⣿⠸⠀⠈⡄⠹⣿⣆⠀⠀⠀⠀⡠⢰⡿⢛⣚⣓⣈⠨⢰⢿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⠀⡆⠀⠇⠀⣻⣿⣿⣦⣄⡀⠀⠀⡂⠈⣿⡏⠉⢁⣿⢾⣿⣿⣿⢿⣿⣿⣽⣿ ⡿⢿⣿⣦⣼⡀⢣⠘⣿⣿⣿⣟⣷⣦⣣⣀⣈⣑⣠⣮⣵⣿⣿⣻⣯⠽⣗⣼⣿⣿