⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⠀⠈⠉⠙⠻⣷⣄⠀
⠀⠀⠀⠀⢀⣿⠇⠀⢀⣴⣶⡾⠿⠿⠿⢿⣿⣦⡀
⠀⠀⣀⣀⣸⡿⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀
⠀⣾⡟⠛⣿⡇⠀⠀⢸⣿⣿⣷⣤⣤⣤⣤⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀
⢀⣿⠀⢀⣿⡇⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣆
⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⡇⣀⣠⣴⣾⣮⣝⠿⠿⠿⣻⡟
⢸⣿⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀
⠸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀
⠀⠻⣷⣶⣿⣇⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⠉⠁⠀⠀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⢸⣿⣀⣀⣀⣼⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠙⠻⠿⠟⠋⠑⠛⠋⠀

⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⢤⣍⡳⣤⠤⠤⣤⡶⢛⣩⢶⡦⢸⠀⠀⠀⢀⣀⣀⡀⠀
⢸⡐⣿⣫⠁⣰⠀⠀⢦⠀⠉⢹⡿⢂⣾⠀⢠⡾⠋⠀⠀⠙⠂
⠈⣷⢇⡧⣤⣧⣠⣄⣼⢷⣀⡀⠇⡘⢿⡄⡾⠀⠀⡀⠀⠀⠀
⢀⡏⣏⠀⢿⡇⢹⣏⠀⢸⣿⠹⡆⡇⢨⣻⣷⠀⠀⣇⠀⠀⠀
⢸⣧⣿⣷⡚⣷⣋⡙⠳⠼⢫⣾⡅⣷⠬⢿⡻⣷⡀⠹⡄⠀⠀
⠀⠉⢹⡿⣍⡙⠒⠿⠗⠒⠛⣩⡿⠋⠀⠀⠹⣿⣷⡄⢹⠀⠀
⠀⠀⢸⡇⠈⠙⠂⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⢹⣿⡼⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀
⠀⠀⠀⠘⠀⠐⣤⠀⠀⠀⢀⡚⠀⠀⠀⡇⠀⣼⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣆⣀⣈⣳⡄⠀⣸⠀⠀⢀⡄⣿⣾⣿⣿⣿⠟⠀⠀
⠀⠀⠰⣴⡟⠛⠛⠛⢿⣷⣾⡷⠾⠛⠿⣿⣷⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠛⠓⠒⠒⠚⠓⠛⠓⠦⠴⠶⣾⣿⠯⠟⠀⠀

⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⢤⣍⡳⣤⠤⠤⣤⡶⢛⣩⢶⡦⢸⠀⠀⠀⢀⣀⣀⡀⠀
⢸⡐⣿⣫⠁⣰⠀⠀⢦⠀⠉⢹⡿⢂⣾⠀⢠⡾⠋⠀⠀⠙⠂
⠈⣷⢇⡧⣤⣧⣠⣄⣼⢷⣀⡀⠇⡘⢿⡄⡾⠀⠀⡀⠀⠀⠀
⢀⡏⣏⠀⢿⡇⢹⣏⠀⢸⣿⠹⡆⡇⢨⣻⣷⠀⠀⣇⠀⠀⠀
⢸⣧⣿⣷⡚⣷⣋⡙⠳⠼⢫⣾⡅⣷⠬⢿⡻⣷⡀⠹⡄⠀⠀
⠀⠉⢹⡿⣍⡙⠒⠿⠗⠒⠛⣩⡿⠋⠀⠀⠹⣿⣷⡄⢹⠀⠀
⠀⠀⢸⡇⠈⠙⠂⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⢹⣿⡼⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀
⠀⠀⠀⠘⠀⠐⣤⠀⠀⠀⢀⡚⠀⠀⠀⡇⠀⣼⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣆⣀⣈⣳⡄⠀⣸⠀⠀⢀⡄⣿⣾⣿⣿⣿⠟⠀⠀
⠀⠀⠰⣴⡟⠛⠛⠛⢿⣷⣾⡷⠾⠛⠿⣿⣷⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠛⠓⠒⠒⠚⠓⠛⠓⠦⠴⠶⣾⣿⠯⠟⠀⠀

⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⢤⣍⡳⣤⠤⠤⣤⡶⢛⣩⢶⡦⢸⠀⠀⠀⢀⣀⣀⡀⠀
⢸⡐⣿⣫⠁⣰⠀⠀⢦⠀⠉⢹⡿⢂⣾⠀⢠⡾⠋⠀⠀⠙⠂
⠈⣷⢇⡧⣤⣧⣠⣄⣼⢷⣀⡀⠇⡘⢿⡄⡾⠀⠀⡀⠀⠀⠀
⢀⡏⣏⠀⢿⡇⢹⣏⠀⢸⣿⠹⡆⡇⢨⣻⣷⠀⠀⣇⠀⠀⠀
⢸⣧⣿⣷⡚⣷⣋⡙⠳⠼⢫⣾⡅⣷⠬⢿⡻⣷⡀⠹⡄⠀⠀
⠀⠉⢹⡿⣍⡙⠒⠿⠗⠒⠛⣩⡿⠋⠀⠀⠹⣿⣷⡄⢹⠀⠀
⠀⠀⢸⡇⠈⠙⠂⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⢹⣿⡼⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀
⠀⠀⠀⠘⠀⠐⣤⠀⠀⠀⢀⡚⠀⠀⠀⡇⠀⣼⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣆⣀⣈⣳⡄⠀⣸⠀⠀⢀⡄⣿⣾⣿⣿⣿⠟⠀⠀
⠀⠀⠰⣴⡟⠛⠛⠛⢿⣷⣾⡷⠾⠛⠿⣿⣷⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠛⠓⠒⠒⠚⠓⠛⠓⠦⠴⠶⣾⣿⠯⠟⠀⠀

⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⢤⣍⡳⣤⠤⠤⣤⡶⢛⣩⢶⡦⢸⠀⠀⠀⢀⣀⣀⡀⠀
⢸⡐⣿⣫⠁⣰⠀⠀⢦⠀⠉⢹⡿⢂⣾⠀⢠⡾⠋⠀⠀⠙⠂
⠈⣷⢇⡧⣤⣧⣠⣄⣼⢷⣀⡀⠇⡘⢿⡄⡾⠀⠀⡀⠀⠀⠀
⢀⡏⣏⠀⢿⡇⢹⣏⠀⢸⣿⠹⡆⡇⢨⣻⣷⠀⠀⣇⠀⠀⠀
⢸⣧⣿⣷⡚⣷⣋⡙⠳⠼⢫⣾⡅⣷⠬⢿⡻⣷⡀⠹⡄⠀⠀
⠀⠉⢹⡿⣍⡙⠒⠿⠗⠒⠛⣩⡿⠋⠀⠀⠹⣿⣷⡄⢹⠀⠀
⠀⠀⢸⡇⠈⠙⠂⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⢹⣿⡼⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀
⠀⠀⠀⠘⠀⠐⣤⠀⠀⠀⢀⡚⠀⠀⠀⡇⠀⣼⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣆⣀⣈⣳⡄⠀⣸⠀⠀⢀⡄⣿⣾⣿⣿⣿⠟⠀⠀
⠀⠀⠰⣴⡟⠛⠛⠛⢿⣷⣾⡷⠾⠛⠿⣿⣷⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠛⠓⠒⠒⠚⠓⠛⠓⠦⠴⠶⣾⣿⠯⠟⠀⠀

⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⢤⣍⡳⣤⠤⠤⣤⡶⢛⣩⢶⡦⢸⠀⠀⠀⢀⣀⣀⡀⠀
⢸⡐⣿⣫⠁⣰⠀⠀⢦⠀⠉⢹⡿⢂⣾⠀⢠⡾⠋⠀⠀⠙⠂
⠈⣷⢇⡧⣤⣧⣠⣄⣼⢷⣀⡀⠇⡘⢿⡄⡾⠀⠀⡀⠀⠀⠀
⢀⡏⣏⠀⢿⡇⢹⣏⠀⢸⣿⠹⡆⡇⢨⣻⣷⠀⠀⣇⠀⠀⠀
⢸⣧⣿⣷⡚⣷⣋⡙⠳⠼⢫⣾⡅⣷⠬⢿⡻⣷⡀⠹⡄⠀⠀
⠀⠉⢹⡿⣍⡙⠒⠿⠗⠒⠛⣩⡿⠋⠀⠀⠹⣿⣷⡄⢹⠀⠀
⠀⠀⢸⡇⠈⠙⠂⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⢹⣿⡼⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀
⠀⠀⠀⠘⠀⠐⣤⠀⠀⠀⢀⡚⠀⠀⠀⡇⠀⣼⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣆⣀⣈⣳⡄⠀⣸⠀⠀⢀⡄⣿⣾⣿⣿⣿⠟⠀⠀
⠀⠀⠰⣴⡟⠛⠛⠛⢿⣷⣾⡷⠾⠛⠿⣿⣷⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠛⠓⠒⠒⠚⠓⠛⠓⠦⠴⠶⣾⣿⠯⠟⠀⠀