⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠻⢯⣽⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣤⣤⠤⠖⠚⠛⢿⡟⠣⢄⡀⠙⢶⡒⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣽⣟⠉⠀⠹⣻⣆⠀⢀⡀⢠⡝⣆⠀⠙⢦⢤⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢟⡏⠈⠓⠦⠤⡈⢩⠭⠟⢓⣽⢃⡏⠙⠢⠬⠷⣽⣷⣏⡱⢾⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠛⣱⡏⢻⣄⠀⠀⠀⠀⠀⣀⣴⠿⢃⡼⠁⠀⣀⣤⠾⣻⡋⠀⣠⣿⠃⢀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⢀⡞⠎⠀⢸⣿⣿⣭⣬⣟⣛⣋⣥⣶⣿⣛⣛⡩⠭⢖⣉⣈⠛⡮⣤⣿⣯⣽⢿⣿⣲⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⢷⡄⠀⢸⣿⣿⠐⢺⣿⣿⣿⣿⣿⣿⣿⡝⣶⣤⣤⣖⣚⣋⣉⢠⣴⠊⠉⣹⡇⠙⠻⢿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⣇⠈⢧⠀⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⠏⣿⠀⣀⣿⡄⢐⡿⠃⠀⠀⠀⠙⢿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢉⣹⠿⠾⠆⠘⡆⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⡟⢀⣿⢰⣧⣿⣟⠝⠁⠀⠀⠀⠀⠀⠈⢻⣿⡄ ⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠉⠳⠦⣤⣖⣹⣿⣿⣿⣿⣄⣹⣿⠟⠛⠛⠛⠛⠻⣿⣿⡿⠁⢸⣇⡾⣫⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷ ⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⡼⠓⠼⣿⠿⡿⠟⣋⣡⣤⣶⣶⣶⣿⣿⡷⠿⠇⢲⠟⠉⠙⣲⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠀⠀⣴⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣟⠓⠻⣄⠙⠻⠿⠾⣿⡿⠿⠿⠛⠁⢀⣬⣴⣭⣖⣲⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟ ⠀⣸⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢚⣿⣲⣦⠤⣤⣤⣄⣀⣤⣴⠚⠙⠳⠄⣈⠉⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁ ⠀⣿⡀⢸⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡼⠋⢠⣤⠀⠀⢀⣈⣿⣿⠟⢻⣧⠄⠀⠋⣭⠀⠀⣽⠆⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀ ⠀⣷⣷⣿⣿⡌⡈⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠆⠘⠃⠀⣠⣼⣿⣿⣿⣤⣿⠄⠀⠙⠀⠛⠀⢶⡿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀ ⠀⢿⡟⢿⣼⡇⡇⢱⢇⠀⠀⠀⠀⠀⠀⠀⠘⢻⡶⢀⡤⠖⠀⣽⢻⡏⢉⣿⣏⠁⠀⠀⠀⠀⠀⢀⡶⠋⢹⡆⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀ ⠀⢸⡇⠘⣿⡇⢱⠘⣿⡀⠀⠀⠀⠀⠀⠀⠠⣾⣁⠈⣲⡀⠀⠘⣿⣧⡿⠁⢀⡖⣀⡀⢀⣀⣶⣾⠁⠀⠈⣿⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣷⣿⣧⠘⡆⢛⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⠀⣸⡟⠀⠀⢀⣀⡀⣩⣡⡶⣻⣿⠇⠀⠀⠀⠸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠉⣿⣿⡀⢳⠸⡘⡆⠀⠀⠀⠀⠀⠀⢸⢯⡿⠚⠷⣿⠋⠉⠛⠩⠉⠀⠈⠉⠀⢰⣿⡏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⣿⡄⠹⣿⢷⣞⣗⣷⣿⡀⠀⠀⠀⠀⠀⡟⢸⣇⠁⢠⣏⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣧⢹⡇⠀⢻⣏⣁⣀⣤⠞⠁⠀⠀⠀⠀⢸⡇⢸⠉⠀⢸⢛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⡟⢳⠀⠀⢀⣼⡿⡛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠉⠀⢸⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⡦⠰⠛⠙⠀⠀⢈⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣀⣠⣼⣷⣤⣼⣷⡶⢶⣶⠤⢤⣄⣀⡀⣸⠁⠀⡼⠀⠀⢀⣠⠴⠚⠉⠁⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣆⢷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠍⠁⠀⢀⡟⢸⣿⡇⠂⢸⣿⠀⠀⠀⠈⣿⠁⠀⠀⠙⣦⢶⠏⠁⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣜⡆⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⢀⡾⠛⠓⢿⣿⠶⠾⠿⠤⠤⠤⠴⠿⢧⣄⠀⠀⢿⡈⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠘⣷⠶⢲⣶⣾⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⢿⣅⣠⠤⠤⠶⠒⠒⠲⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⢰⡳⠀⣾⣿⡗⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡏⡇⢰⡿⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠛⢿⣟⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣤⣤⡤⠶⠾⠿⢿⡛⠷⣄⡀⠙⢷⣒⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢞⣽⣟⠉⠉⢿⣽⣇⣀⣀⡀⣸⡟⣦⡀⠙⢿⣾⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣯⢿⡟⠙⠳⠦⣤⣈⣩⠭⠿⢓⣿⢃⡏⠙⠶⠬⠷⣽⣿⣯⣷⢾⣇⣀⣀⠀⠀ ⠀⠀⢈⣿⠛⣱⡟⢿⣄⠀⠀⠀⠀⢀⣠⣴⡿⢃⡼⠁⢀⣀⣤⢾⣻⡏⠀⣠⢿⠇⣸⡿⠁⠀ ⠀⢰⡿⢡⣞⡞⠀⣼⣿⣿⣷⣶⣿⣛⣋⣥⣴⣿⣛⣛⣯⠭⣗⣋⣊⣻⣯⣵⣿⣮⣥⣤⡀⠀ ⠀⠀⢷⠈⢿⡆⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠙⣶⣶⣶⣒⣚⣋⣩⣤⣶⡋⠉⣹⣃⠀ ⠀⣤⣼⣇⠈⣷⠀⣟⠻⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣶⠇⣿⢀⣸⣿⡇⢰⣿⠃⠀ ⢀⣙⣿⣿⠆⠘⣆⣿⣷⣮⢑⡿⢿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⡟⢀⣿⢸⣿⣿⣿⡟⠁⠀⠀ ⠀⠉⠻⠦⣤⣖⣻⣿⡿⢡⣿⣿⣶⣬⠟⠛⠛⠛⠛⠿⣿⣿⣿⠁⣸⣯⣿⣿⣿⠿⠀⠀⠀⠀ ⠀⠀⠀⣶⢤⡼⠻⣿⡿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣲⢿⠉⣼⣿⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⣄⣤⡿⢿⣦⡀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠈⣹⣞⡵⢋⣄⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠒⣷⣶⢀⣿⣻⣷⣶⣤⣤⣬⣀⣀⣤⣴⣿⣿⣿⣟⣫⡿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⠗⠻⣿⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢄⣾⣾⠟⠋⣡⣾⣿⣿⣤⡾⠁⠀⠹⣿⡿⠁⠘⠿⣶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣆⣾⢻⡏⢉⣿⣯⣤⣶⣿⣿⢟⡿⠀⣀⣀⣹⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣷⣼⣧⣿⣿⣿⠻⠛⠛⢡⢿⠣⡾⠛⠉⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠻⣿⡿⠉⠀⠀⠀⠀⠀⣟⡟⠁⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣠⣤⣰⢿⣃⣀⠀⠀⠀⠀⠀⢿⠇⠀⠀⢀⣤⠄⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢹⣽⣏⣿⣾⡽⣾⡷⠀⠀⠀⠀⠘⣇⠀⣰⡿⠅⣐⣐⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⢸⣨⣿⣿⣯⣿⣻⡷⠀⠀⠀⠀⠀⣿⣴⠟⡿⠛⠉⣴⣭⣿⠖⠀ ⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣾⣿⡯⣿⣿⣿⣿⠇⠀⠀⠀⢀⡾⠉⣹⡿⠋⠀⢀⣀⣬⣼⣧⠀ ⠀⠀⠀⠀⠀⢙⡿⢤⣬⣿⠏⣟⣯⣿⣷⣿⣻⠧⠶⠒⠛⣿⡟⠀⠘⢷⣶⣾⣏⣑⣐⣻⣿⠀ ⠀⠀⠀⠀⠀⣾⡀⠀⡼⠃⠀⠈⠙⣿⣏⡉⠙⠀⠀⠀⠀⠁⣧⠀⠀⠀⢸⠙⠲⠀⠀⣾⣿⡀ ⠀⠀⠀⠀⢀⣏⣍⡽⠧⣄⣀⣀⣰⣿⡇⠙⠲⣀⣀⣀⣀⡤⠼⡄⠀⠀⠈⢳⣖⣒⣶⢭⡇⠀ ⠀⠀⠀⠀⡼⢱⣾⣁⠀⠀⠀⠀⢹⣿⠉⠉⠉⠉⠁⠀⠀⢀⣀⣷⠀⠀⠀⢸⣯⠀⢸⠀⣧⠀ ⠀⠀⠀⢰⣗⣿⣯⣿⣿⠻⣶⠶⣾⣷⣶⡶⣶⠶⠶⣾⣟⣻⣿⣽⣧⡀⠀⢰⣿⠤⢾⠴⣼⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡦⢸⡟⠀⢸⠀⣸⠀