⠤⠔⠒⠚⢷⣤⣰⡟⠁⠀⠀⠀⠈⡇⢀⡴⢣⠞⠁⠀⡰⠋⣀⣴⣚⣹⣯⣥⣤⣀⠀⢀⣠⠤⠖⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣟⠻⢶⣤⣈⢻⣆⣀⣤⡾⠤⢄ ⠀⠀⠀⠀⢀⣼⠟⠷⣦⣄⠤⠤⠔⢳⠏⡴⣃⣤⣴⡾⣿⡿⠟⠋⠉⠀⠀⠀⢀⡀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣈⣹⡷⣿⣯⠁⠀⠀⠀ ⣄⣠⠤⠤⢺⠁⠀⠀⠀⢇⠀⠀⣠⣯⡾⣿⡫⣥⡠⣟⠽⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⢀⡀⠀⠙⠢⡄⠀⠀⣀⠀⠠⢤⣄⠀⠘⢿⣦⣀⠙⣷⣄⣀⠀ ⡲⣄⠀⠀⠀⡇⠀⠀⠀⢸⣠⣾⠟⡟⣜⣏⡴⣫⠞⠁⣠⠖⠀⠀⠀⣠⠀⠘⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠠⢝⣦⡀⠀⠀⠀⠀⢬⣷⡿⣦⡙⢷⣦⣀⠙⣿⡳⣍⣳⡀⢉ ⠙⢦⡱⢄⠀⢸⡤⠤⣴⡿⠋⡏⢸⣹⣿⡿⡻⢋⡴⠋⠀⠀⠀⢀⣼⠅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣆⢣⡀⠀⠀⠱⣄⠳⡄⢻⣿⢦⡀⠀⠀⠀⢳⣯⡳⡕⣄⠈⢪⡑⢾⣿⣎⠻⣷⣋ ⠀⠀⠙⢦⡳⣄⢀⣾⠋⠉⢹⠃⣷⣿⣯⢞⠕⠁⢀⣀⡔⣠⢖⣹⡇⠀⠀⡄⠀⢲⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠘⣯⡷⡀⠀⠀⠈⢦⠹⣆⢫⠣⠱⣔⣦⡀⠱⣿⣷⡙⠈⢻⣦⣱⡄⠈⠻⠂⠀⠩ ⠀⠀⠀⠀⠹⣌⢿⡃⠀⠀⣞⣾⢟⣿⡿⠁⣠⣶⣿⣯⠞⠁⣾⣾⡇⠀⠀⡇⠀⠀⢻⡀⠀⢧⠀⠀⢠⠀⠀⠀⠀⠀⢻⢿⡹⡄⠀⠀⠀⢳⣹⣯⣧⠀⠈⢮⣟⢞⣞⣷⠱⡄⠀⠙⢿⣿⠆⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢾⡳⡀⣠⠟⣡⣿⢏⣤⣾⠟⣱⣿⠏⢀⣼⡿⢻⢧⢰⡆⡇⠀⢀⠈⢧⠀⠸⡄⠀⠸⣆⠀⠀⠀⠀⠈⡎⢇⠹⡸⡄⠀⢳⣱⣣⢻⡆⠀⠀⠹⡆⠻⣿⣧⠙⡄⠀⠈⠞⢧⢌⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢯⡿⣣⡾⣽⣵⢟⡕⢁⣼⣿⣷⣾⡿⣿⠁⠀⡿⣸⡇⡇⠀⢸⡀⠘⡆⠀⢧⠀⠀⡿⡄⠀⠀⡀⡀⢱⠈⠀⢱⣻⡄⢈⣷⡿⡆⢹⡀⠀⠀⠹⡀⠈⠹⡄⠘⡄⠀⠀⠈⠉⠣⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣞⣼⢇⣾⣻⣣⠏⢀⢞⣽⣿⣿⠋⠀⣿⡄⠆⢣⣿⢹⣷⠀⠀⡇⡎⣿⠀⠘⡇⢠⣇⢱⢄⠀⣧⣷⢸⡆⠀⠀⢻⡽⡜⣾⢻⠹⡀⢧⠀⠀⠀⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⢠⣯⠟⣞⠎⡱⣱⠋⢠⠏⣺⣫⠟⠁⠀⠀⠸⣧⠀⠸⣸⡜⡿⣇⣆⢧⣿⡏⣇⠀⢱⢸⣿⠈⢿⣆⢻⡇⢧⡷⠀⠀⠀⣏⣵⡿⡆⡇⠱⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⢰⣿⠃⢸⠏⣰⠁⠃⢠⠃⣴⡟⠁⠀⠀⠀⠀⠀⢻⣧⠀⣧⣇⢳⡿⣟⡼⡟⡇⠘⣼⣼⣇⣿⡆⠈⡟⣼⠙⠈⣇⠀⠀⠀⠈⢱⠓⠀⠃⠀⠱⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⢠⠏⣰⠃⠀⢀⢏⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡘⡞⡄⢸⠹⠘⣧⢃⠀⢹⡾⡟⡇⠹⡀⠀⠙⠀⠀⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⢃⣠⡞⣰⡏⠀⢀⢎⡿⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣽⡄⣇⠀⠘⡾⡄⠀⢇⠁⠹⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀ ⠤⠶⢾⡟⡩⢸⢡⢳⠀⡆⣜⣾⣳⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⡀⠀⠹⣣⠀⠀⠀⡀⢳⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡙⣄⠀⠀ ⡆⠀⢸⠳⢁⡇⣾⡞⢰⠉⣏⣿⢧⡀⠹⣠⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣄⡘⣯⢿⠶⣤⣻⡄⠀⠀⢱⠀⢣⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠈⢢⡀ ⠸⡀⣸⡅⢸⢸⢹⠁⡘⡾⣸⣾⡟⣿⣦⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣣⡀⠈⢻⠲⠦⣌⡄⠀⢳⡈⢆⠀⠀⠀⠀⠀⢀⠀⠀⢇⠈⡆⠀⠀⠀⡆⢠⠀⠀⠀⠀⠀⠀⠃⠀⣷⠲⣄⡙ ⠀⢳⡇⠙⣾⡇⣿⠀⣷⠁⡇⡿⡇⡈⣿⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠲⢄⡀⠘⢿⡷⡄⠈⡀⠀⠀⢫⠑⠢⢷⡈⢧⠀⠀⠀⠀⢸⠀⠀⢸⠀⢹⡀⠀⠀⠃⠀⢇⠀⠀⠀⠀⠀⢸⠀⣹⠀⡇⠈ ⠀⢰⣷⡀⣇⢻⣿⠀⣿⠀⣿⠁⢻⡈⣞⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡞⣀⠀⠀⠉⠒⢌⣿⣜⢆⠸⡀⠀⢸⠀⡀⠘⣟⣕⢳⣄⡀⠀⠘⡀⠀⢸⡀⠈⣇⢸⠀⠀⠀⡜⡆⠀⡆⠀⠀⢸⠀⡿⢠⡇⠀ ⠳⣼⡿⠯⣿⢸⢻⡄⣿⡀⡽⠀⠀⠙⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠽⣟⣷⡶⣄⣀⠈⠻⣮⠳⣇⠀⠀⡇⡇⠀⢸⠈⣦⠱⡍⠢⡄⡇⠀⠀⣧⠀⠘⡄⡆⢰⠀⢱⢹⠀⢸⠀⠀⢸⠀⡇⣸⡇⢀ ⠀⣸⣧⠀⣿⢿⣾⢱⢹⣇⡇⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⠀⢜⣻⣻⠉⠛⠛⠛⣧⡹⡀⠀⠇⡇⠀⢸⠀⡧⡳⣜⣄⠘⢸⠀⠀⢮⡇⢰⢣⢣⢸⡀⢸⠈⡇⠸⠀⢸⢸⠀⣦⣿⡇⣼ ⠞⠁⢘⣿⣹⣏⣼⣾⣿⡿⡇⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣻⣃⣀⣠⡴⠾⢋⠳⣧⠀⢰⡇⠀⢸⠀⢠⠙⢮⡫⡳⡈⡆⠀⣿⢸⡘⠸⣸⣾⢁⢸⠀⢳⠀⠀⢸⢸⡄⣯⣾⣾⠽ ⢀⡴⢋⠞⣡⣿⣸⡏⠘⣷⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢣⠘⡷⡀⠇⠀⡘⠀⠘⠀⠀⠙⡟⢿⣶⡀⡼⣾⡇⠇⣿⡟⣼⢸⠀⣼⢀⠀⡼⠟⢳⣯⠱⡄⠀ ⣫⠖⣁⠞⠁⣧⢹⣇⣀⡼⢿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⠀⠀⡇⠀⠀⠀⠀⠘⠸⡈⠙⣿⣾⣙⡇⣸⣿⢷⣿⣯⡾⢻⢸⢠⠃⠀⣴⠻⡄⢻⡀ ⡥⠚⣁⡠⠴⠻⣍⣿⠷⢴⣒⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⢀⠘⢇⡆⠀⠀⡇⡇⠀⢱⡀⢹⠈⢹⠳⣯⣿⡾⠛⠉⢢⢸⣸⢯⡆⠀⢸⣇⠈⢺⣧ ⠒⣉⡠⢴⣒⠭⠟⠺⣏⡡⠞⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣇⠀⠈⣇⠀⠀⡇⡇⠀⡈⡷⡀⢧⣜⡼⠟⠁⡌⠙⡄⠘⣾⠇⠀⣷⠀⠀⢻⠀⠀⢩ ⠭⠓⠋⠁⠀⢀⣠⠶⡟⢷⡀⠀⢹⡀⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣸⠀⠀⠀⡏⡆⢰⣧⠁⢰⠁⣇⣷⡜⣟⡁⠀⠀⠱⡄⠙⠀⢸⡄⠀⠘⡆⠀⠈⠂⠀⠘ ⠀⠀⣀⡤⠖⠋⠀⠀⢹⠀⠙⢦⡀⢃⠀⠈⠺⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⢋⡆⠀⢠⠇⠀⣼⡿⢀⡏⢠⡻⡡⣜⢾⣞⠀⠀⠀⠁⠀⢀⡇⠘⡄⠀⠘⡄⠀⠀⠀⠀ ⠖⠋⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⢼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣷⣿⡇⠀⡸⡀⢠⢿⢇⣾⠁⣼⣟⠁⠘⣦⣝⢢⣀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣉⣤⡾⢟⠭⣺⣿⢠⣼⢁⣯⣿⠮⣏⡾⠋⠈⢆⠀⠸⡌⠛⢯⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⣈⣤⣴⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⡀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⡻⠝⠋⠀⠀⠉⢂⣟⣿⣏⡾⠯⣁⣾⠟⠉⢦⠀⠈⢣⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⠽⠞⠛⡛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠉⠛⠛⢟⢋⠉⠉⠉⠉⠀⢉⣭⠟⢛⣿⣯⣁⠀⠀⠀⠀⠀⠀⣀⣼⢟⠿⠫⣄⡀⠉⠀⠱⣤⣀⠀⠢⡀⠁⠀⠀⠳⠄⠀⣀⣤⣴⣖⣮⠥⠔⠒⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠳⡁⠀⠀⠀⣸⡛⡾⣴⠋⡞⠈⡝⢷⣦⡀⠀⣀⠴⠯⢄⣀⠀⠀⠀⠉⠢⠄⠀⠈⠻⣅⠀⠈⠂⣀⣠⣴⠶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠙⣆⡴⠛⣟⠓⡇⡇⣸⠀⣰⣃⡤⣻⡿⠚⠓⢤⡀⠀⠈⠉⠢⢄⡀⠀⠀⠐⠢⢄⣨⢷⣲⠝⠛⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⢖⢺⡿⢳⢻⢠⣧⣞⣯⡶⠟⠉⠲⠤⣀⡀⠈⠑⠢⢄⣀⠀⠈⢉⣒⢴⡻⠝⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡀⠀⠀⠀⠀⠀⠀⠈⢿⣟⡾⢞⣻⡽⠺⠫⢄⡀⠈⠢⣄⡀⠈⠉⠒⠢⠤⣄⣥⡲⣝⡮⠷⠤⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⡀⠀⠀⠀