⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⢦⠤⡄⠀⠀⠀⠀⠀⠀⠀⢻⠺⣆⠈⢆⠘⣷⡀⠘⣆⠀⠀⠀⠀⠈⠑⠰⠀⣿⠀⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⢦⠈⢦⠈⠿⠀⠻⢦⡀⠀⠀⠀⠀⠀⣦⣿⠀⣶⢰⠀⠀
⠀⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡞⠲⣧⠀⠀⠀⠀⠀⠀⠀⠠⠼⢿⠙⣧⡈⢳⡀⠀⢶⣄⠈⠓⠦⠤⠤⠼⠟⠁⠸⠇⣼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠥⠳⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢀⣀⣀⣤⠤⠤⠤⠘⠃⢸⣿⢦⡈⠲⣄⠙⠻⠶⠀⠀⢠⣤⣶⠟⢀⡴⠁⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡤⠖⢚⣏⣩⣥⣴⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣦⣄⣙⠲⢤⣄⣀⣀⣀⣠⡴⣯⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠏⠙⠛⠀⠀⠀⢀⣠⠖⢋⣁⡤⠞⠋⢀⣠⠴⢚⣩⣤⣴⣿⣿⡿⢿⣭⣥⠤⠒⠒⠂⠀⠂⠀⠀⠈⠛⢿⣿⡏⠙⢛⢿⣿⣿⣯⡈⢳⡉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠴⠿⠒⠊⠉⣀⡤⢴⣺⢿⣷⣿⣛⣯⡭⠭⠴⠚⠛⠻⢶⣾⣿⣗⠦⣄⡀⠀⠀⠀⠀⠀⠀⢻⣧⠏⠉⢻⠷⣌⡙⢿⣆⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⢀⣀⣤⣖⣫⣵⠞⠋⠀⣼⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠙⣟⠻⢿⣶⠭⣷⣦⣄⣀⠀⠀⢨⡟⠀⠀⢸⠀⠀⠙⢮⣿⣧⣧⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⢀⣤⠶⣏⡭⠗⠛⣧⠟⠁⠀⠀⣼⣻⠏⠻⣿⣿⣷⣾⣿⣿⣿⣿⣶⡶⢾⣧⣀⣩⣷⣾⣿⣷⢾⣿⣷⡿⠃⠀⠀⣸⣆⣀⣀⣈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠴⢚⣩⠶⡻⠋⠀⠀⢠⠏⠀⠀⢀⣾⣿⠃⠀⠀⠀⢉⣽⠍⣽⣿⡏⢛⣿⣿⠛⠿⣿⣟⠹⣿⡯⠴⠚⠉⠉⠀⠀⢀⣴⣿⣿⡿⣿⣿⣿⡇⠿
⠀⠀⠀⠀⠀⠀⣠⣴⣞⣉⡴⠚⡽⢡⠞⠁⠀⠀⡰⠃⠀⠀⣠⣾⠟⠁⠀⢦⡀⠀⠀⠸⣿⣿⡀⠻⠛⢰⣾⡀⠀⡈⢿⢄⣻⣽⡄⠀⠀⠀⢠⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀
⠀⠀⣀⡤⣶⡯⢻⢟⡿⠃⣰⣾⣷⠋⠀⠀⢀⠞⠁⠀⣠⣾⠟⠁⠀⠀⢰⡿⢿⡄⠀⠀⠀⠙⠹⡟⠛⠉⣍⣭⣴⣛⣴⣾⠟⠋⠁⠀⠀⠀⢸⡟⢿⢋⡿⢀⣼⣿⣿⣿⠇
⠀⠈⢰⠞⠁⣴⠿⠋⢀⣾⠟⡱⠃⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠈⠙⣿⣿⠅⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣷⣾⠟⢋⡽⠋⠀⡴⠃
⠀⡰⢋⡠⠞⠁⠀⡴⡻⢋⡜⠁⠀⢀⠀⢀⡴⣿⢏⡇⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣘⣿⣿⣿⣿⡿⠟⠉⣿⠖⠋⢀⡤⠚⠀⠀
⡾⠗⠉⠀⠀⠀⠀⡼⢁⠎⠀⠀⢠⠞⣠⢻⡟⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣿⣿⣿⡐⠀⢸⣃⠤⠖⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⢃⣼⠁⡼⠀⠀⢀⡟⣼⠁⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠃⠃⠀⠀⠹⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠠⠶⢛⣷⣿⠃⢰⡇⠀⠀⣸⢠⣿⡀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣴⠟⢩⡟⠀⡿⡇⠀⠀⡇⣾⣿⣷⣀⣧⠀⠘⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠟⠁⢠⣿⠇⡼⠁⣷⠀⢰⣷⣿⣿⣿⣿⠻⢧⡀⠹⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣅⢀⣠⠤⠖⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣿⣿⣰⠃⠀⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⣽⣦⠘⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡞⡿⣿⠇⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⡾⠛⠁⠀⣠⠜⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡖⠒⠛⠛⠲⢬⣥⣴⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⢉⠁⡇⠀⣠⣼⣿⠀⢸⡿⠿⠛⢻⣿⣿⣿⣤⢖⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠻⠿⣿⣿⣯⣿⣿⣶⣾⠟⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⡏⢸⢸⠁⢀⣾⠉⣿⡀⠀⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⠈⠉⠉⠉⠉⢱⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢾⣸⢸⡞⠀⢰⣿⣧⡀⢻⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⣀⣀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠿⣦⡀⢰⡟⠉⠙⢮⣿⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠿⣏⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠿⣿⡥⣤⣴⠞⠉⠉⠁⣠⢿⣿⣿⣿⣿⣿⣿⣛⣿⡿⠻⡿⣿⣶⣄⣧⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⠀⣠⡶⠛⠁⠀⣻⡿⠟⠋⠀⠀⣿⡛⠀⣠⢧⠸⡿⣏⡟⠷⣄⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣵⣶⣤⣶⣿⣯⠀⠰⠃⠀⠀⠈⢧⢠⠏⠨⢿⡱⠘⣿⡀⠈⠙⠓⠶⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣥⣿⣷⣦⡴⠒⠛⢏⠀⠀⠀⠙⠲⢬⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠛⢿⣿⣖⠦⣄⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢁⣿⣀⣠⠀⣾⡧⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⣠⡤⠤⢤⣄⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠙⢮⡳⣄⠙⠢⣀⠀⠀⠙⠿⣿⣿⣿⢹⡟⠃⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠉⠛⠀⠛⠋⠀⠀
⠉⠑⠒⠿⣶⣦⣀⠈⢳⣌⠳⣄⠈⠳⣄⠀⠀⠘⢿⣿⡾⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠙⢿⣾⣿⣆⡈⠳⣤⡉⣦⡀⠀⠈⢿⠇⠀⠀⠸⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀