⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⡶⢶⡞⣟⡻⢻⡝⣫⡝⢮⣱⢋⣖⢳⣼⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⢶⡞⢿⡹⢭⡓⢧⠳⣍⡳⡜⢶⡩⢗⠮⣕⡺⡱⣎⠽⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣀⣤⢶⡻⢏⣝⡲⢭⡓⢮⢧⡹⢖⡹⣍⡳⣍⢶⡙⣧⢹⢎⡽⢲⣍⣳⣼⣿⣡⣤⣤⣶⢶⡶⣻⢻⣛⢟⣻⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⣀⣴⡾⡻⡝⣎⠧⣝⠺⡴⢭⡣⢏⡳⢎⡵⢫⠵⣎⢵⠺⣌⡗⣎⡳⣚⡜⢧⣚⡬⡝⣭⢛⡜⣣⢎⡳⢼⣡⠗⣎⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣾⣥⣴⣿⡛⢧⣓⢳⡹⣌⡻⣌⠟⣜⣣⢝⣣⡝⣣⢞⡹⣚⡜⢮⡝⣲⡙⣦⠳⣍⠾⡱⢎⡶⣙⠦⣏⠞⣥⡛⣜⠧⣎⣽⡾⠃⢀⣠⣶⡇⠀ ⠀⠀⠀⠀⠀⢀⣴⣟⢣⣾⣿⡟⣗⡲⢭⣓⢎⡧⢳⢥⢳⣯⣞⡱⢎⡞⡴⡹⡜⢮⡱⢧⡹⢎⡼⢥⡛⡴⣛⣬⢳⡙⣧⢚⣥⠻⣌⡻⢴⣙⢎⣳⣾⣟⣤⡶⢿⣙⢾⡇⠀ ⠀⠀⠀⠀⢠⣾⠯⣜⡣⢟⣱⡹⢦⡝⣣⢎⠷⣜⣯⣾⣿⣿⣧⣏⠳⢮⡕⡻⣜⢣⡝⢶⡩⢏⡼⢣⣝⡱⣣⢎⠧⣝⢲⣋⢖⡻⣌⡳⣍⠞⣼⠿⣟⢯⠳⣍⡳⢎⣿⡇⠀ ⠀⠀⠀⣰⣿⢣⣛⡴⡹⣍⠶⣙⢦⣝⣮⣿⣿⡿⠟⠋⠁⠀⠸⣯⣏⡳⣜⠳⣜⣣⢞⡣⡽⣩⢞⡱⣎⠵⣓⢮⡛⣬⡓⢮⣙⠶⣱⣓⢎⡻⣌⠟⣜⠮⣝⠼⣱⣋⣾⡇⠀ ⠀⠀⣰⡿⢎⡳⣜⢲⡝⡬⢏⣵⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠹⣷⡳⣜⢫⢖⡱⢮⣱⢳⡱⢎⡳⡼⡹⣜⡲⣙⢦⡝⣣⡝⢮⢽⣿⢪⠵⣎⢻⢬⣓⠮⡝⢦⣣⣿⠀⠀ ⠀⢠⣿⡝⣣⠽⣌⡗⢮⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡭⢞⢮⣙⡖⣣⢧⡹⢭⢖⣷⡝⡦⣝⡱⡞⡼⡱⢎⣏⠾⣿⣏⢾⡘⡧⢞⡬⣳⡙⢧⢖⣿⠀⠀ ⠀⣾⢷⡹⢬⣓⠞⡼⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡞⡜⡦⣝⢲⡣⣝⠺⣜⣻⣿⡵⣎⡵⣙⠶⣙⠧⢮⡹⣿⣿⣧⣛⣜⣣⠳⣥⢫⡝⣺⡇⠀⠀ ⢸⣟⢧⡹⢖⡭⢞⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣝⢶⡩⢶⡹⢬⣛⠴⣻⣯⢿⣶⡱⣋⡞⡭⢞⣣⠳⣽⣿⢻⣷⣎⢖⡻⢴⢣⡝⣽⣧⠀⠀ ⣼⣟⢮⣱⢫⡜⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣹⠖⣭⡓⢮⣹⢹⣿⣌⣿⣷⢥⡛⣜⡳⣜⡹⣜⣿⡆⢹⣿⢎⡵⣋⡞⡼⣿⠿⠀⠀ ⣿⢏⣖⢣⢧⣻⣿⡟⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡦⣝⠳⣬⢓⣿⡏⠛⠿⣷⣝⢮⡱⢎⡵⢎⣿⣷⠀⢻⣯⢖⡭⣚⣵⣿⡆⠀⣤ ⣿⣏⡜⣣⢾⣿⣿⠁⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⣠⣾⠟⠁⠙⠻⣮⣟⡴⣋⢾⣷⠀⠀⠈⢻⣧⣟⡼⣱⢫⡜⣿⡄⠈⣿⡞⣴⢋⣾⣯⣷⣾⡏ ⣿⠞⡼⣡⣿⣿⡇⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢰⣿⠃⠀⠀⠀⠀⠈⠛⢷⣯⣞⣿⡀⠀⠀⠈⣿⡿⣾⣥⢳⣚⣿⣧⠀⢹⣟⢦⡛⡿⢻⡱⣿⣿ ⢻⡯⣕⣣⣿⣿⢀⣤⣤⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣷⣾⠿⢿⣶⣹⣿⠀⢸⣿⢲⣍⡳⣝⣲⡿⠇ ⠘⣷⢣⢞⣿⡿⠀⠀⠈⣿⡏⠉⢉⣽⣿⣿⣿⣿⣿⣍⠉⠉⠉⡀⢹⣿⣿⠡⠀⠄⢠⣾⣿⣿⣿⣷⣄⠠⠀⠄⠠⢀⠀⣿⡇⠀⠀⠀⠙⠻⣿⠀⢸⣿⢣⣎⠵⢮⣿⡟⠀ ⠀⠹⣏⠾⣿⡇⠀⠀⠀⣿⡇⠠⢸⣿⣿⣿⣿⣿⣿⡿⢀⠂⢁⠀⣾⣿⣿⡘⠀⠌⠘⣿⣿⣿⣿⣿⣿⠠⠈⠐⡀⠂⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠳⣬⢫⣿⡷⠁⠀ ⠀⠀⠹⣟⣿⡇⠀⠀⠀⠹⣿⡀⠄⠙⠿⠿⠿⠿⠋⢁⠠⠐⠀⣼⣿⠻⣿⡇⢈⠀⠂⠌⠛⠛⠟⠋⡁⠄⡈⠐⢀⢢⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⢳⣱⣿⡟⠁⠀⠀ ⠀⠀⠀⠙⢿⣷⠀⠀⠀⠀⠙⣿⣦⣈⠀⠄⢂⠐⠈⡀⠄⢂⣽⡿⠃⠀⠙⢿⣆⡈⠄⠂⠄⠡⠐⠠⠐⡀⠄⣁⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢧⣿⡟⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠙⠿⢿⣶⣤⣤⣥⣴⣾⠟⠋⠀⠀⠀⠀⠀⠙⠿⣶⣬⣤⣡⣌⣤⣡⣴⣾⠿⠋⣡⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢀⣀⡌⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⢰⣿⡏⠉⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠘⠛⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⣠⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠁⠀⠀⠀⠀⣠⣾⠟⢡⣿⠹⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠋⠁⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⣼⣿⠀⢻⣇⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠛⠁⠀⠀⢀⠀⣿⡇⠀⠸⣿⡀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡾⠿⠛⢹⣿⠁⠀⠀⠄⠈⠀⢰⣿⡇⠀⠀⢿⡇⠀⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢻⣿⡟⠛⠛⠛⠛⠛⣿⡏⠉⠀⠀⠀⣠⣾⠋⠀⠀⣄⣄⠀⠂⢸⣿⠁⠀⠠⢸⣷⠀⠘⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠸⣶⣤⡀⠀⠙⠻⠶⣶⣶⠿⠛⠁⠀⣴⣿⣿⡋⠀⠀⣹⣿⠀⠀⠄⠀⣿⡆⠀⢹⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⠄⠀⠀⣽⡏⠀⠀⡀⠀⢻⣇⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣿⣿⠀⠀⢀⠀⠁⠀⠐⠈⠀⠀⠠⠀⣿⣿⠂⠀⡀⣿⡇⠀⢀⠀⠀⠘⣿⡀⢸⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠂⣿⣿⠀⠀⡀⢀⣀⣁⣄⣀⣐⠀⠀⠄⣿⣿⠀⠀⠀⣿⡇⠀⠀⢀⠈⠀⣿⡇⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠠⠀⣿⣿⠀⠀⣴⣋⢾⣿⣿⢉⣽⣯⠳⡄⣿⣽⠃⠀⠀⣿⡇⠀⠈⠀⠀⠀⢹⣧⣼⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠄⠀⣿⣿⠀⢼⡿⢿⣿⣋⣯⡌⡫⢓⣟⡟⣿⢼⡇⠀⠀⣿⡇⠀⠐⠀⠈⠀⠘⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢀⠠⠀⣿⣿⠀⠀⠻⡌⠿⣲⠯⡿⣯⣿⠟⡇⣿⢺⡇⠀⠀⣿⡇⠀⠀⠂⠀⠁⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⡀⠀⠀⣿⣿⠀⠀⡀⠈⠛⠭⣛⣋⣛⣳⣴⠇⣿⢺⡇⠀⢨⣿⡇⠀⠐⠀⡀⠈⠀⢻⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⠀⠠⠀⣿⣿⡄⠀⣴⣶⣶⣴⣶⣯⣭⣽⣴⡦⣿⢸⡇⠀⢸⣿⡇⠀⠀⠄⠀⠀⠐⢸⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢀⠀⠀⠈⠛⠀⠀⠾⠎⠉⠉⠁⠉⠉⠉⠉⠁⠙⠻⠃⠀⢸⣿⡇⠀⠀⠠⠀⠁⠀⠘⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⢀⠈⠀⠀⠈⠀⢀⠠⠀⠀⠀⠀⡀⠀⠄⠀⠠⠀⢀⠀⠀⠠⠀⢸⣿⡅⠀⠐⠀⠀⠐⠈⠀⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢀⡀⡀⢄⣈⢀⣠⢀⣀⣀⣀⣁⣀⣀⣀⣠⣐⣀⣀⣀⣀⠈⠀⢀⢸⣿⠀⠀⠄⠐⠈⠀⢀⠀⢸⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⡝⠙⠋⠙⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡆⢸⣿⠀⠀⠠⠀⠀⠄⠀⠀⠈⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣸⡿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⢻⣷⢸⡿⠀⠀⠄⠀⠂⠀⡀⠁⠀⢸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣿⠇⠀⢀⠈⢀⠀⣀⠈⣀⢀⠁⣀⠈⣀⢀⠀⣈⠀⣀⠀⡀⢀⠘⣿⢸⡏⠀⢀⠀⠄⠐⡀⢀⠀⡈⢀⣿⣿⠀