⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⡏⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⣿⡄⠀⠀⠀⠀
⠀⠀⠀⢀⣴⡏⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⣿⣄⠀⠀⠀
⠀⠀⢀⡾⠁⣇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡇⠹⣆⠀⠀
⠀⠀⢸⡁⠀⣿⠑⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢩⡇⠀⢹⠀⠀
⠀⠀⢸⣧⡀⣿⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⣼⠇⢠⣾⠀⠀
⠀⢠⠾⡇⠁⠘⣿⡉⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀𝔦 𝔠𝔞𝔫´𝔱 𝔩𝔧 ⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣹⡿⠀⠀⡿⢦⠀
⠀⡿⠀⢿⣆⠀⠱⣿⡆⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣾⣿⠁⢀⣼⠃⠘⡆
⠀⣿⡀⢈⢷⡀⠀⠱⡿⣦⣀⡀⢰⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠀⢀⣠⣾⡿⠁⠀⣠⠏⠀⢰⡇
⣴⢿⡄⠈⢯⢿⡖⠀⣿⢿⢷⣍⣈⣷⡈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣰⡟⢀⣹⢿⣿⡇⠐⣺⣯⠇⠀⣸⢧
⣏⠈⢷⣄⠀⠳⣿⣦⣌⣻⣿⡏⠙⠻⣟⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⢸⡿⠛⠉⢿⡿⢋⣠⣾⡿⠋⢀⣴⠏⠈
⠹⡄⠈⣿⣅⠀⠘⣿⣷⣍⢻⣇⣷⠄⠈⠳⣤⡀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⣀⣴⠋⠀⢠⡇⣾⢋⣤⣿⡿⠁⢀⣽⠋⠀⡴
⠀⢻⠦⠹⣝⣷⡂⠈⣿⣿⠛⠻⣮⡃⠀⠀⣿⣿⡶⣄⣀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⢀⣀⡴⣾⣽⡿⠀⠀⣾⡿⠛⠻⣿⡟⠀⣲⣿⡽⠡⢾⠃
⠀⠈⣷⣄⠈⠳⣝⣧⡀⢿⣷⣀⠈⠙⠶⣄⡚⠽⣿⣿⡉⠙⠂⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠘⠋⣝⣿⣻⠕⣂⣴⠞⠉⠀⣠⣿⠇⣠⢾⡿⠋⢀⣰⡏⠀
⠀⠀⢸⠙⢯⣅⠀⢽⡯⣿⢷⣽⣂⠀⠀⣓⡯⣗⣾⣷⣄⡀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣽⣿⣖⡿⣟⡋⠀⢀⣺⣷⢿⣻⣿⠉⢀⣩⠟⢹⠃⠀
⠀⠀⠈⢧⡀⠙⣿⣇⣉⠻⣿⡋⠉⠓⠶⡤⢭⣽⣿⡅⠀⠀⠀⠀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⣽⣿⣭⠥⠴⠖⠋⠉⣻⡿⢋⣁⣽⡟⠁⣠⠟⠀⠀
⠀⠀⠀⠘⣿⡂⠈⠓⢯⣷⣿⣿⣾⠤⠀⠩⠭⢽⣿⣦⡴⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠰⣦⣾⣿⠭⠭⠁⢀⣬⣾⣿⣷⣿⠟⠋⠀⣺⡿⠀⠀⠀
⠀⠀⠀⠀⠈⠛⢶⣤⠀⠈⠻⣿⣿⣿⠶⠶⠶⣒⣿⣿⡶⠀⡀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⣄⠠⣼⣿⣖⡒⠲⠶⢾⣿⣿⡿⠉⠀⢠⣴⠾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⣼⣟⡁⠀⠀⢀⣀⡭⣟⣿⣾⠁⠀⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⢀⢹⣿⣿⣿⣅⣀⠀⠀⠀⠘⣿⡔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣃⣴⠞⠋⠁⠈⣛⣽⣿⣶⣾⠃⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡼⠋⠀⢀⢀⢹⣾⣿⣿⢯⡋⠁⠉⠙⢶⣄⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⡀⢠⠞⠁⠉⣵⣿⣿⣦⣼⡀⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠀⣸⣾⣾⢿⢷⣍⠀⠙⢦⣀⣰⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢶⡏⠀⠀⡼⠁⢉⡿⠋⡽⠉⠉⠉⠓⠚⠉⠀⠀⠙⠒⠋⠉⠉⠹⡍⠿⣇⠁⠹⡆⠀⣈⢿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠭⠿⣧⣖⣼⡧⢦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠢⢻⣔⣲⡿⢿⡽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀