Bicycle Text Art

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

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