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