⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡢⡀⠀⣀⢀⣤⡲⠤⢒⠆⠀⠀ ⢸⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣄⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢳⠁⠈⣾⢽⣶⡕⣉⢤⡲⠗⠁⠀⠀ ⢸⡇⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠉⠉⣯⠉⠙⣿⠿⣿⣶⣄⠀⠀⠀⢀⣴⣿⢿⣾⣿⠁⢹⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⢨⠚⠡⠤⠤⠄⠀⠀ ⢸⣧⠀⠀⠀⠘⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠘⠆⠐⠻⠈⠈⠻⣿⣷⣄⣴⣿⠋⠁⠨⠿⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⣞⠶⠀⡰⡷⠳⠕⡂⠈⠉⠉⢐⡄⠀ ⠀⣿⣆⠀⠀⠀⠀⠀⠘⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⡀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⠀⠀⢀⣰⣿⠁⠀⠀⠀⠀⠀⢸⠈⠀⣔⠟⠀⣴⡞⠁⠀⣀⢴⠏⠀⠀ ⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠨⢻⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣴⣄⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠈⣖⢼⡎⠀⣼⣦⠃⠀⠀⢁⣯⢿⠀⠀ ⠀⠀⠈⠛⠿⣿⣶⣶⣶⡶⣶⣎⠀⠘⣿⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⢨⣾⣝⢄⠿⣇⣇⠦⣫⣸⢾⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣀⣴⣾⣿⠛⠛⠛⠛⠛⠿⣿⣶⣦⣴⠿⠛⠛⠿⣿⠀⠀⠀⠀⠀⠀⠢⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⢖⡂⠡⣓⢿⢾⢌⢶⡣⣎⠀⢀⠏⠄⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣷⣿⡟⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠏⠃⠀⠀⠀⣰⣿⠀⡀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⢸⡗⠉⢩⡺⠑⢪⢉⠃⠩⡸⠆⠀⠀ ⠀⠀⠀⣠⣾⠿⠛⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⢀⣴⣿⡟⠀⠘⠦⣠⣶⣦⡀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠣⣳⣤⣪⢧⣲⢕⣓⡄⠘⡼⣤⡤⡋⠃⠆⠀ ⠀⢠⣿⡿⠋⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢀⣾⠛⠻⣧⣄⠀⠀⠀⠘⣷⠈⢿⣦⠸⣿⣇⠀⠀⠀⠀⠀⣀⡀⣮⠖⠉⢳⢵⢀⡜⡅⠀⡡⡅⢈⡫⡆⠀⠀ ⠀⣿⣿⠀⠀⠀⢀⣬⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢂⣠⣾⠋⠀⠀⠀⠻⣧⡀⠀⠀⠻⣧⠀⢻⣧⣿⣿⠀⠀⠀⠠⡹⣑⠙⠮⠆⠀⡿⡙⠻⣞⢦⢀⡼⣪⠽⣼⢥⠀⠀ ⠘⢿⣿⣄⠀⠀⠘⣿⣏⢿⣧⡀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢹⣧⣀⣹⣿⠋⠀⠀⠀⠀⠈⢳⡶⠂⠀⣴⢳⠃⠀⢈⢿⠸⡸⡀⠀⠀⠋⠃⠀ ⠀⣸⡿⠋⠀⠀⢠⣿⣿⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⢉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⣦⣤⣾⠉⠻⣿⣥⣀⣀⡀⠀⠀⠀⠘⠽⣒⠯⠛⢞⡢⠤⣊⠎⠀⠑⠬⣒⣀⠁⠀⠀ ⠀⣿⠃⠀⣠⡀⠈⣯⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢸⠻⣆⠀⠈⠙⠛⢻⣿⡆⣀⣀⣀⢀⠀⡀⢀⡀⠉⡉⠁⡀⣀⣀⣀⡂⠀⢀⣀⡀ ⠀⣿⡦⣞⢿⣿⠀⠈⢩⡶⠦⣄⣀⣀⠀⠀⠀⠀⠀⢻⡀⢿⣇⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⣽⣦⣿⡷⣾⣶⣾⡿⠟⠁⣽⣛⣚⢹⣺⡇⡧⣿⢸⡇⣾⣇⢷⣵⢳⣿⣟⡶⢯⡝ ⠀⠙⣷⡌⠙⠃⠀⠀⠸⠦⣤⣄⡉⠉⠛⠶⣦⣀⠀⢸⡇⢸⣿⡀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠉⢹⣿⣦⠀⠀⠀⠀⠀⢀⣈⡽⢿⡼⠇⣯⠫⠏⠇⣿⠘⢫⣿⣫⡟⢿⣵⣟⡵ ⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⣦⣤⣙⣳⣆⣿⡌⣿⠇⠀⢠⣴⣿⠟⢿⣷⣤⣀⠀⣀⡀⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠉⠀ ⠀⠀⠀⠀⠙⠿⣦⣄⣀⣀⣀⣦⣄⡀⠀⠀⠀⠉⠹⠋⠈⠛⠋⢀⣴⣿⣯⣤⡄⠀⠉⠛⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⣽⣷⠆⠀⠀⠀⠀⣀⣠⣴⣿⠿⣻⣿⣿⣥⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⢈⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⠈⠛⠛⢻⣛⣿⣛⣻⣽⢟⠽⣾⣿⠟⠋⢁⡀⠀⡀⠀⢈⡽⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢀⣤⠟⠙⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⡀⠀⠀⠀⢠⣾⣿⣿⠛⠛⠋⢹⣾⣓⣿⣄⣴⡿⠛⠛⠋⢀⡞⠀⠒⣼⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠈⠁⣠⣤⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⢀⣟⣾⠉⢻⣄⠀⠀⠘⣿⣿⣷⣾⢿⠁⠀⠀⠀⢸⡇⠀⢀⡧⠤⠸⣿⣿⣄⠀⠀⡀⢀⣴⣿⠟⠋⠀⠀⠀⠈⠉⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣼⣿⣿⣀⢸⣷⠳⢦⣤⣹⣷⠋⣿⢸⡇⠀⠀⠀⢸⡱⢴⡛⠓⠶⠖⣻⣿⡿⢻⢶⣶⠿⠛⠉⢿⡀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⣿⡘⣿⣶⣤⣍⣿⣥⢸⣌⢧⠀⠀⠀⠘⣇⠃⠙⠢⠤⢴⣿⣿⠀⠘⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠙⢻⣿⣿⡿⣿⣿⣮⢧⣀⠀⠀⠈⠢⣤⣀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢉⣻⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⠀⠀⠀⢐⣿⡏⠀⠘⠻⣿⣿⣿⣿⣶⣶⣶⣾⣿⡟⠛⠁⣶⣦⣤⠀⠀⠀⠀⠀⠀⣲⣷⣶⣤⣀⡈⠉⠉⠻⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠁⠀⠻⣷⣤⣴⣿⢻⣿⣦⣀⣠⣴⣿⡟⢸⣿⣯⣤⣤⡈⢙⡻⠶⣿⡁⠾⣿⣤⣤⡄⠀⠉⢻⣟⠛⠻⢿⣿⣶⣤⣤⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠙⠛⠛⣿⣿⡿⠀⠀⠉⠉⠙⣿⣿⣿⡙⠛⢹⣿⣄⣹⣿⣆⢷⣄⣀⣪⣿⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⠀⣠⣾⡟⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠙⠿⠷⠿⠿⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢹⣿⣷⡠⡀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣤⣤⣤⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀