⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠾⠟⠛⠛⠛⠛⠷⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⣁⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠷⢬⣙⡛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢉⣠⠴⠚⠉⠁⣀⡀⠠⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣍⡻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢋⡤⠞⢉⣠⡤⠖⢚⣉⣁⣤⣤⣴⣦⣤⣤⣄⣀⣀⠀⠀⠘⠲⢤⡀⠀⠈⠙⠲⣌⡛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣡⠞⣋⠴⠚⣉⣥⡴⠾⠟⠛⢉⣉⣀⣠⣤⣤⣭⣍⣉⣛⡻⠶⣦⣤⣀⠉⠓⠦⣄⠀⠀⠙⢦⡉⠻⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣴⠟⢁⣴⣫⠷⢛⣡⣴⠟⠋⣁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⣿⣶⣬⣝⡻⢶⣤⡀⠙⠂⢀⠀⠘⠢⡈⠻⣶⣄⠀⠀⠀
⠀⠀⠀⠀⣠⡾⠛⠁⢠⡿⠛⣡⣶⠟⢋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⠀⠻⣿⣿⣿⣷⣮⣟⠷⣦⣜⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀
⠀⢀⣰⡾⠋⠀⠀⠀⢋⣴⠿⢋⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠈⣿⢿⣿⣿⣿⣿⣾⣝⡻⣦⣄⠀⠀⠀⠀⠀⠙⠷
⣰⡿⠋⠀⠀⠀⣠⡾⢛⣡⣶⡿⠛⣿⣿⣿⣿⠻⣿⠸⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⣿⠈⢻⣿⢿⣿⢿⣿⣿⣷⣭⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣾⣯⣴⡿⠛⠋⠀⠀⢹⡼⣿⣿⠀⢿⡀⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡇⢀⡿⠀⣸⡏⢸⡟⢘⣿⠁⠙⠛⣻⣷⠀⢸⡆⠀⠀
⠀⠀⠀⠘⣯⣾⡟⢷⡄⠀⠀⠀⠀⠀⠀⠙⢿⣆⠘⣷⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡾⢀⡼⠁⣰⡟⠀⠞⠁⢸⡏⠀⢀⣴⣿⠁⠀⣸⠇⠀⠀
⠀⠀⣰⣿⢛⣿⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣈⠃⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠴⠋⣠⠞⢀⣼⠏⠀⠀⠀⠀⡞⢀⣴⣿⣿⠏⠀⠀⠁⠀⠀⠀
⠀⠀⠙⠛⠛⠛⠿⠿⣷⣦⣄⡐⢦⣀⠀⠀⠀⠀⠈⠛⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣡⣴⠟⠁⠀⠀⠀⢀⣠⣾⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣭⣟⡦⣤⣀⡀⠀⠀⠉⠛⠻⠿⠶⣶⣤⣤⣤⣶⣶⠿⠟⠋⠀⠀⠀⢀⣠⣶⣿⣿⡿⠋⣠⣾⠇⣠⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠻⢷⣦⣀⠀⠀⠀⠈⠉⠛⠷⢮⣽⣓⡲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠛⠉⢁⣴⠟⢡⡾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣄⡈⠛⠿⣶⣤⣄⡀⠀⠀⠀⠀⠉⠙⠛⠿⠷⣶⣦⣤⣤⣤⣤⣴⣶⣶⡿⠿⠿⠟⠛⠋⠁⢀⣠⡾⠛⢁⡴⠋⣠⠆⢀⡴⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣌⡛⠶⣤⣀⠈⠙⠛⠿⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⣠⡶⢋⡠⠞⠁⠠⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠷⣍⡛⠳⢶⣭⠅⠀⠀⠀⠀⠀⠈⠉⢛⠛⠿⠷⢶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⡾⠟⠛⠉⠀⠀⠚⠡⠖⣋⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠦⠤⠤⠤⠤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣓⣒⡒⠒⠶⠦⠀⢲⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀