⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷⡀⠀⠀
⠀⢀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⠒⠶⢤⣄⣀⢀⣠⡤⠶⠖⠛⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀
⠀⣾⣿⣿⣿⣆⠀⠀⠘⣶⣶⣤⣄⣀⡀⢠⡏⠀⠀⣀⣤⠾⠛⠛⠷⣤⣀⠀⠀⢹⡆⠀⣀⣠⣤⣴⣶⠆⠀⠀⣠⣿⣿⣿⣷⠀
⢸⣿⣿⣿⣿⣿⣦⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣾⣉⠀⠀⠀⠀⠀⠀⣉⣿⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⣴⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⡴⠛⠛⣿⣿⣿⣿⣿⡟⠉⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⠙⢷⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡀⠀⠀⣏⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢹⡇⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠻⣦⣀⣿⠀⠀⠈⠹⣧⣀⠀⠀⣀⣼⡏⠁⠀⠀⣼⢀⣴⠞⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠳⢦⣄⣻⣿⣿⣿⣿⣿⣠⡴⠞⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⢻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢻⣿⣿⣿⣿⡟⠉⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠀
⠀⠈⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣦⠴⠖⠛⣿⣿⣿⣿⠛⠲⠦⣤⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣿⣿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠹⠏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡀⠀⣼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣦⡏⠈⢧⢠⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⣃⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣇⠀⠈⡏⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⣀⠾⠉⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⡀⠀⢹⠀⢸⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣠⠜⠁⠀⣀⠔⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠈⡇⠀⢸⠀⢸⠃⢀⣧⠒⢹⠀⠀⠀⣀⠔⠊⣡⡔⠋⢀⣠⠴⠚⠋⢉⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⠀⢸⠀⡜⠁⡼⠁⢀⠏⣠⠴⠊⠁⠀⠈⠈⠐⠚⠉⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡎⠀⡏⢠⠃⡴⠁⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠓⢒⡲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠁⠰⠁⠘⢀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢖⠦⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠤⠤⠒⢉⡩⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠈⠳⣄⣏⠀⠀⠀⠀⠀⢨⡓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡠⠴⠚⢓⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠶⢶⣛⠉⠉⠉⠁⠀⠀⢸⠉⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⣀⣠⠴⣞⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡤⠴⠒⠺⠦⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠋⢉⣁⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠉⢦⠀⣸⠀⠀⠀⠀⠀⠀⠰⠤⠒⠒⠋⠉⢀⡩⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠶⢏⣁⡀⠀⢀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⣴⣪⡵⣺⣫⢿⡅⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠰⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠉⣁⣠⡴⠿⠛⣿⢁⣦⢛⢦⢈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠠⣯⡧⡼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢒⣋⣉⠁⠀⠀⣀⠀⣿⣀⠈⣯⢼⠊⣠⠞⠛⠒⠲⠒⠒⠒⠋⢉⣡⠖⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⡶⡲⣿⣄⣹⡇⣠⠖⣿⠀⣿⣍⠏⣁⡤⠞⠁⠀⣠⠤⠤⠤⠴⠖⢚⣩⠽⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠷⣄⠀⠀⠀⠀⠀⠀⢀⡠⠞⡅⠀⠀⠀⣛⣘⡧⠉⣻⠻⠧⢊⣲⡥⠖⠋⠁⠀⠀⣠⠾⣉⡙⠒⠒⠒⣋⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⣬⣷⣄⡀⣀⡤⡶⡋⡀⢾⠀⣄⠀⠀⠧⠟⢓⣪⠵⠒⠋⠉⠁⠀⠀⠀⢠⡴⢾⣉⠓⠦⠭⢭⠭⠭⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⣎⠉⠙⣻⡉⢉⡡⠜⡏⢸⡇⢸⠀⢈⠆⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⡤⠞⣯⣑⢦⣈⡙⠒⣶⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠛⠴⠏⢠⡯⣾⠁⢨⠗⣭⠖⣡⠔⠋⠀⢀⣀⣀⣠⡤⠴⠒⠻⣅⠀⠀⠀⠉⠚⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠡⡀⠀⢀⠜⠀⠙⠒⢊⣨⠷⠊⠉⠉⠉⠉⠉⠉⢧⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡶⠤⠬⡭⠥⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⣆⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⠎⠃⠉⠲⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀