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