⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣮⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠀⠉⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⢣⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠄⠀⠈⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣱⣧⠞⢅⡿⢌⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠸⠙⠯⡊⢑⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⣷⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡴⢁⢠⣿⣮⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣄⠀⠀⡇⠈⡌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⠙⢿⣬⠟⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠣⡉⡇⠀⣺⠀⣠⠞⣹⣶⡏⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡿⠂⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⢰⠉⢸⠁⢰⠁⣾⢫⠉⡝⣷⠈⡆⠀⠀⠀⠀⠀⠀⢀⠔⠉⠻⡿⠊⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢰⡔⠀⠀⠀⠈⠁⠒⠒⠤⠤⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡇⠀⠘⡀⠻⣮⡤⣵⠟⢀⠇⠀⠀⠀⠀⢀⣀⣼⣆⡀⠀⠀⣶⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠑⠂⠤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠙⠑⢄⠩⡑⠲⢦⠀⠀⠀⢸⣥⡇⠀⠀⠘⣄⣷⠀⣿⣨⠋⠀⠀⠀⢀⠔⠁⡠⠘⣿⡿⣶⢾⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣉⣒⡢⢤⣀⣀⠀⠀⠈⠂⠥⡈⠢⢸⡆⠀⠀⡸⢟⠡⣕⠶⣶⣮⡿⠿⢿⣴⣶⠴⣀⢐⢍⠳⣮⢠⣤⠏⡠⠃⠸⣢⠏⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣤⡤⡤⣼⡾⢦⡛⣦⠤⠭⠿⠿⠶⢖⠒⢚⣾⣍⠉⠉⣹⣖⣡⣾⡿⠉⠙⢠⠽⠭⠿⡔⠋⠁⢿⣦⡍⡢⢔⠈⠂⠤⠵⣤⠒⠒⠲⠲⠶⢒⡒⣦⠮⠴⣷⡧⣤⢤⣤ ⠀⠀⠀⠀⢧⢦⠧⣼⣇⣀⡁⣿⠈⢀⣒⣢⡀⠀⠑⢽⣿⡿⠉⠉⠷⣮⢻⣿⠀⠀⠀⠀⢠⠤⡄⠀⢀⣀⠈⣯⡣⡇⠠⢱⠀⠀⣀⠼⡠⡠⢒⢒⣒⡎⠁⢿⢃⣸⣸⡧⠴⡤⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠒⠓⠚⠉⠙⢍⢿⣟⢦⣙⣥⣨⢙⠷⠇⢸⣤⡇⠸⠾⡛⣅⣼⣮⠜⠃⢾⣍⠙⠤⠤⠜⠒⠒⠁⠀⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠙⢞⣿⣿⣏⣯⢱⣶⣲⣿⣿⣽⣶⣶⡮⣿⠙⠌⡢⠀⠐⢌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⢊⣁⣘⣈⠢⣀⠀⠀⢀⡴⣿⣻⢷⣿⣾⣿⣿⡿⣻⣟⠇⠀⠀⠈⢪⣑⡬⠛⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠖⠬⠭⠽⠄⠀⠀⢘⢉⣹⣹⢞⡽⣯⢳⣿⠫⠿⠟⣿⡟⡼⢄⠀⠀⠀⠘⢄⠰⣄⠀⠀⡩⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠾⠃⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠟⠀⠀⠀⢸⣇⣠⡳⣧⣶⣶⢶⣼⢟⣄⣸⠆⠀⠀⠀⠀⠛⢦⢻⡞⣦⣳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠤⠂⠉⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠉⠀⣀⣀⣀⣀⡄⡞⠻⣿⣁⠈⢛⣒⠚⡁⣼⣯⢟⢂⢤⠀⠀⠀⠀⠀⠈⠓⢕⢇⣾⣿⣖⠒⠦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⠂⣭⠀⠀⣀⣀⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⢠⠏⢁⠑⡭⠙⣇⢀⠀⠈⠻⣿⡔⠶⢀⣿⠟⠁⠀⡄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⣿⣿⣷⡖⢄⡵⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠴⠠⢊⠔⠚⡼⣦⡀⠀⠉⠸⡏⠀⢻⠇⠉⠀⢀⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⡽⡿⡿⡇⣞⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠂⠐⠁⢰⠞⠧⣿⣻⠀⠀⠘⡇⠀⢸⠃⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⡵⢕⣪⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⣠⠇⠀⠀⠙⡿⠀⠀⠀⡇⠀⢸⡁⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡎⠁⠀⠀⠀⠀⢸⡁⠀⠀⡇⠀⢸⠆⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡬⠋⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⠀⢸⡁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢠⠼⠁⠀⠀⠀⠀⠀⠀⠀⢀⢸⡅⣠⢻⠀⡟⡅⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣃⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠻⣿⢿⣾⣿⣿⠟⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒⢆⡸⣿⣴⡾⠇⡸⢒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢁⢠⠙⡄⡈⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⣹⠀⣏⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⠀⣯⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢚⣤⢸⢴⡇⡤⢓⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⣿⣻⣿⢽⣿⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠣⣎⣞⡫⠈⢝⣱⣱⠜⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠤⠟⠁⠀⠀⠀⠀⠚⠠⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀