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