⡚⣬⠇⣿⣿⣿⣿⣿⣽⣿⣿⣿⢧⡿⢿⠛⠪⠑⠉⠀⠄⠀⠀⠀⠀⠀⠀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⣿⣿⣸⠸⠀⠀⠀⠁⠞⡠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣌⢢⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⡟⣭⡿⣿⣿⣿⣿⣿⣿⣿⢿⢛⠿⣿⣿⣿⢿⡻⣙⣉⢤⡦⡳⠛⠉⠈⠀⡀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⣱⡆⢀⠀⠀⠟⣼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢂⠫⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⢯⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣶⢿⠻⠙⣉⣤⣶⣶⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢰⠀⠀⠇⣿⢀⠀⠀⠀⠁⠉⠉⠋⠖⠐⠖⠐⠂⠀⠈⠀⡀⠤⠐⠀⡄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣾⣶⣤⣴⣦⣿⣽⣿⣿⡈⠀⣄⣤⣶⣿⠻⡀⢠⢀⡃⣷⠶⡀⣀⢭⡤⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠉⠀⣾⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⡀⣧⣿⣿⠺⠂⠙⠈⠀⣠⡳⣾⢰⠀⠀⠀⠀⡀⡉⠙⠉⠫⣿⣿⣿⠺⠐⠊⣀⢿⠿⠻⡛⣭⣤⣿⣿⣿⣿⣿⣿⢿⢌⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠢⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠰⠀⠀⠀⠀⣀⣄⠀⠀⣄⣿⢿⠻⣘⠀⠀⠿⣿⣿⣿⣿⣿⣿⣶⣶⣠⢤⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀⠃⣿⠸⡀⣀⣭⣶⣷⣿⡿⠈⠀⠀⠀⠀⠀⠄⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣦⣷⣶⣤⠐⠀⡀⣀⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠘⠀⠀⠀⠁⡽⣍⢁⠉⠉⠋⣏⠞⡶⣄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠁⠚⠂⠒⠒⠓⠑⠚⠐⠀⠀⠀⠁⠯⠛⠝⡭⣉⠉⠉⠉⠋⠛⡿⣿⣿⣀⠠⣀⣀⡀⢀⢄⣂⣀⡎⣿⣴⣡⢏⠿⠿⠿⠜⠶⠶⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣤⣤⣀⣤⣦⣽⣤⣶⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⡢⠴⠟⠿⡴⣤⡤⠤⠤⡤⠤⣤⣠⣃⢚⣷⣷⣿⣾⠀⠀⠀⠀⠀⠀⠄⠀⡀⠼⣄⢿⠈⣿⣿⣿⣰⠀⠁⠻⡞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⠿⠭⡤⢦⣿⣿⣿⠿⠛⣻⣿⣤⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠍⠿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠞⢰⡀⠀⢀⠃⣿⢠⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠋⡿⣿⣿⣶⢠⠀⠀⡏⣿⢸⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠻⠈⡀⣅⣿⣿⣿⣿⣿⣿⢿⠻ ⠒⠐⠉⠉⠛⠛⠟⡽⣭⠻⠈⠀⠀⠀⠀⠀⠀⡓⣴⠀⠀⠀⠀⠃⡾⣠⠀⠀⠘⠀⠀⠀⠁⠔⢀⠋⡿⣿⣿⣿⣿⢽⢓⠈⠇⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⠿⣿⣠⣀⣄⣷⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⣀⣀⣀⠄⠴⠤⠤⡤⠤⠦⠠⠆⣷⣷⢚⠒⠒⠒⡖⠐⠀⠾⣱⠟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣙⡽⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⣀⣶⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⡀⢄⠦⠑⢈⠀⠦⠀⠀⡀⣀⢤⠶⠓⠊⡀⢀⡤⣄⣳⣙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠻⠛⠛⠻⠛⠛⠟⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣾⣼⢴⠤⡦⢤⠢⠒⠒⡒ ⠶⠿⠿⠛⠒⠒⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⠀⠀⠀⡀⣄⠾⠒⠉⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠆⣸⡀⣤⣶⣿⣶⣦⣶⣶⢿⠿⠟⠼⠀⠀⠀⠀⡄⣿⣿⣿⣾⣎⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠀⣄⣼⢽⠤⠵⠤⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⣇⠼⠢⠑⠉⠀⢷⠀⠀⣀⠤⠒⠑⡎⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢱⠀⠀⠀⠀⢀⠀⠀⢄⠒⠄⡠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢸⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⢤⠀⠀⠀⠀⠀⡁⠀⡈⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⡀⠱⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠫⠒⠴⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡅⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⡀⠠⠢⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆⠙⠒⠝⡇⢎⠀⠀⠀⠀⠃⣾⣠⣄⢤⠤⠶⠒⠙⠉⠇⣦⡇⢿⣸⣄⠱⠨⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⡉⣯⣯⢡⢀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠈⠀⠀⠀⠀⢁⠾⠴⣤⣠⣀⣀⣀⣺⣀⣀⣯⢼⠤⠤⠠⠂⠒⠒⠐⠀⠀⠀ ⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⠶⠻⠒⠙⠉⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡳⣼⢥⡿⣩⠌⠤⡏⢺⠀⠁⠒⠬⠶⠒⠈⠀⠀⣀⢿⠀⠀⠀⠋⣴⠀⠀⠀⠀⠀⠀⡎⠸⠉⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀⠀⠒⠒⠒⠒⠒⠒⣒⢒⠒⡀⠁⣉⣉⣉⣉⣉⣉⣉⣄⣤⣤⢤⠤⣻⡿⠸⣦⡿⣿⣿⠿⠛⣿⣸⠀⠀⡈⣀⠠⠀⠒⠫⠙⠀⣿⠸⠀⠏⣰⠀⠀⠀⠀⠀⠀⠟⢁⣴⠀⡀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣇⡧⡘⠯⠅⣘⣽⡘⣄⣤⣶⣷⠻⠛⡍⢝⠪⠙⡛⠿⡽⠎⡎⢸⠏⣱⠐⡭⠋⠒⠉⠈⡟⣿⡾⣿⠿⠾⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡾⢂⡇⡈⡂⢿⣸⠈⠀⠀⠀⠢⡀⣀⣁⣤⣤⣤⣶⣶⢲⢶⣶⣷⠛⡟⣿⢿⡿⡻⡟⣿⣻⡛⠟⣿⣿⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⢫⢺⣡⡁⣤⠜⠆⠀⠀⠀⠀⡀⡀⣀⣤⣤⣤⣤⣀⣀⠀⢀⠤⠶⠶⢛⠛⠛⠟⣿⣿⣿⣹⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣼⣿⣧⢡⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣾⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠷⣿⣯⣼⣃⢴⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣾⡟⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣹⣰⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠅⠟⣿⣽⣿⣾⢇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⣿⣷⣞⠐⠇⠛⠉⠁⠉⠉⠀⠀⠀⠀⠁⠉⠉⠃⠟⠿⣿⡿⣻⣵⡟⣾⢋⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡲⣟⣬⠴⡩⢄⢶⠍⠤⠈⡐⠔⠛⢛⢟⣿⣿⣿⣿⣿⣿⣿⡿⣴⠐⡿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⢻⡈⢅⠫⠓⣙⣩⠀⠍⠀⣝⣵⣿⣷⣿⣿⣿⣿⣿⣻⡾⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⡲⡄⢺⢯⠋⢉⣓⢛⢿⣻⣟⠿⡿⣷⣿⣍⣿⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⣄⠴⡀⣄⣦⣶⣶⠶⣲⣒⣒⣒⢶⠤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀