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