Barbarian Emojis & Symbols

⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠁
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⡿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠋⠀⠀⠀⠀⠠⢤⡴⠾⣿⣯⡯⣹⠿⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⢾⣿⣿⣿⣷⡶⠶⡆⠀⠀⠀⠀⠀⢠⣄⣿⡄⢀⢀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⣴⣹⣿⣟⣻⣷⣿⣶⢧⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⡀⠀⣠⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠻⣿⣧⡀⣀⣤⣾⣿⣿⣿⣿⠁⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⣀⣠⠽⠿⠟⠉⡼⠁⣾⣿⣿⣧⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣾⡿⠛⠛⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⢀⣿⠶⢛⣿⡏⣝⣿⣿⣿⣾⣶⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣶⣶⠶⠚⠋⠉⣁⣶⣿⣿⣿⣿⣿⣯⡙⠛⠻⠃⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠠⠉⠀⠀⣿⣿⣿⣿⡇⠳⢄⣰⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡰⠁⠀⡠⠔⠛⠛⠙⠉⢳⡀⠀⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣄⡀⠀⠀⢿⣀⢸⣤⣄⠀⠀⠀⠀⢀⣷⠀⢹⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣴⣟⣠⣦⣄⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣀⣠⣲⣾⣿⣿⣿⣿⣿⣿⣷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣦
⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⡷⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠒⣿⣶⠦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠏⠀⠉⠉⢹⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡾⢃⠼⠟⠛⢉⣼⣿⣿⣿⣿⣿⣿⣷⣾⡀⠀⠀⠀⠀⠈⠛⢿⡿⠷⣦⣄⣀
⠀⢸⡶⣄⣀⣠⡞⡱⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠘⠁⠀⠈⠛⢿⣷⣶⣤⣀
⠀⠀⢵⠈⠙⠛⠃⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⠿⠶⠄
⠀⠀⠀⠀⠐⠦⠶⠄⠀⠀⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⠿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠟⠉⠉⠉⠉⠀⠀⢿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠾⣧⠈⠙⣇⢡⣿⠚⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⡾⣾⣧⣽⣼⡞⢱⣶⣤⢾⣯⣷⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣿⣷⣿⣾⣲⣿⠀⠀⠈⠙⠟⠁⠠⠄⣸⣿⣷⣾⣾⣿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⡛⢿⠇⠀⠀⠀⠀⡀⠤⠀⠀⠸⣿⠟⣻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⢻⣾⢰⣶⣄⡀⠑⡞⠁⣀⣴⡦⢸⣿⠹⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⣯⡀⠉⢚⡛⠋⠙⢛⡛⠋⠁⣸⣯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢻⣿⣿⣿⢿⡉⠙⢷⡴⠛⠘⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⠿⣿⡏⢺⠿⠛⠛⠻⢿⠸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⠏⠠⢻⡷⣾⡶⠋⠙⠳⣾⠾⣿⢿⣿⣿⣿⢾⣆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠈⣿⣿⣆⣶⢰⢖⡫⡆⠘⡆⢠⡾⠓⣨⣾⣿⣿⣿⣧⣌⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡞⠇⢸⣮⣴⣿⣸⢆⣾⡅⣦⣿⢿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣼⣿⣿⣽⢻⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠅⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣾⣷⡿⢻⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⣿⣿⣿⣾⣿⡟⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠋⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⣒⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣠⠾⢛⣫⣿⣿⡿⠷⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⢻⣿⣇⢸⡏⢠⣿⣿⣿⠗⣉⣤⣤⣤⡤⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣟⣿⣿⣿⣾⡀⣿⣿⣿⣵⣿⣿⣿⣿⣯⣶⣦⣌⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⡿⠛⠛⠛⠛⠷⡿⠟⠛⠉⠉⠉⠛⢿⣿⣿⣿⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣾⣿⠤⣀⠐⠴⠀⢀⣀⠀⠦⠔⣀⠤⠦⡘⣿⣿⣯⡓⠌⢿⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡼⣼⡟⢁⣀⠈⠙⠲⢄⡄⢄⡤⠖⠋⠁⣀⣄⠈⢪⢻⣿⣿⣿⣶⡾⠟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⣷⠟⣻⣿⣦⣄⣸⣳⡹⣀⣤⣶⣿⡿⡛⠓⠋⣾⣿⣿⣶⢶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⣿⠇⢷⡛⠉⣿⠟⡏⢹⠛⢿⣏⠙⢛⡰⡲⠀⢻⣿⣿⣿⢷⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠀⠀⠉⠛⡹⡆⠀⠀⠴⢏⠉⠻⠉⠀⢴⣄⢰⣿⢹⣇⣸⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣿⣿⣷⣤⠀⣾⣠⣄⠤⢄⣤⣬⣷⡄⠀⠠⣼⠃⣾⢿⠙⢻⣿⣿⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣥⣾⣿⡟⢻⣏⡔⣡⣶⣿⣿⢿⣻⣷⣦⣍⠢⡀⢻⣟⣻⣿⣦⣾⣿⣿⣿⣮⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣽⡿⣹⣿⣿⡟⣰⣿⡿⠛⠛⠛⠛⠻⢿⣿⣦⠙⣾⣿⢿⣿⣸⣿⣿⣷⣍⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣿⣿⣿⣧⣉⣴⣿⡟⠚⢻⣿⣿⡟⠓⠈⠻⣿⣷⣌⣁⣾⣿⣻⣿⣿⣏⢻⣷⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣟⢻⣿⢿⣿⡇⣠⣾⣿⣿⣷⡀⣤⣴⣿⣿⡿⣿⢛⣿⣿⣿⠛⣿⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣾⡿⠋⢱⡟⢿⣷⡈⠙⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣧⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣴⣧⢸⣇⣾⣿⣧⣷⣿⣼⣿⡿⠛⠻⠿⠿⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣎⣿⣯⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠿⠿⢿⡿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣶⠇⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠛⠁⣠⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡠⢤⣠⣄⡙⠓⠃⠀⠀⠈⠦⠀⣀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣀⢈⡿⢿⣿⡇⠀⠀⠀⠀⢀⣽⣿⣿⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⡀⣰⣷⠈⠁⡘⠃⣸⢟⣿⡄⠀⠀⡰⡒⣿⡿⠋⠀⠀⠀⠀⠀⠄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⣠⣿⣿⡄⠀⠀⢐⣴⣾⣙⡿⣥⣾⠟⠚⠛⠀⡀⠀⠀⠀⠁⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠤⠺⢥⣾⣿⣿⣿⠿⡞⢹⡿⣿⢃⡟⠉⠀⠀⠈⠳⠁⡄⠀⠀⠀⠀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠈⠉⠀⠀⠀⡟⢻⠛⢀⣶⠀⢸⢧⡿⠋⠀⠁⢠⣀⡀⠀⢸⣷⣦⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⡿⢿⢅⡨⠛⠀⠀⠀⢠⡆⠉⢿⣶⣿⡿⠡⣆⠀⡀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠀⠀⠐⡀⠀⠀⠀⠀⠀⢘⡯⠞⠀⢀⣀⣀⣴⣿⣿⣀⣼⣯⣴⣶⡶⡿⠻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⢄⡀⠀⠀⠸⣾⡏⠀⠀⣠⣾⣀⣀⡀⠀⠀⢨⣿⣿⡿⠈⢁⠀⠙⢿⡏⠀⢏⣲⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠀⠄⠀⠈⠳⡆⠙⠃⡀⠘⠻⣿⠟⠛⠛⣷⣾⣿⣿⠟⠀⢠⡾⠿⠲⡆⠀⠀⠀⢿⡛⣧
⠀⠀⠀⠀⠀⣰⣿⡗⠀⠀⠀⠀⡤⠀⠀⣠⣾⢒⠶⠒⠿⠐⡠⣠⣽⣿⠿⠟⠃⠀⠀⠀⠀⠀⣀⠐⡀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢸⡿⠇⢀⣴⣿⠟⢈⡁⠀⠀⠁⠀⠹⠿⣁⢠⣈⣂⠁⠀⠀⠀⠀⠈⢲⣽⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠠⣿⣿⡆⠀⠀⢿⡏⣠⣾⡟⢡⣾⡿⢿⣿⣦⣥⣴⣿⣿⣏⠘⣿⡿⠄⠑⠀⠀⠀⠀⠀⢡⠀⣶⣿⣤⡅⠄
⠀⠀⢀⣀⣀⣿⣄⣹⠠⠖⢀⣾⡿⠋⣴⣿⡍⠀⠈⣿⣿⣿⣷⣿⠟⣿⡓⡘⠻⠶⡴⠒⠀⠀⠀⢀⠐⠀⡟⢿⣿⡟
⠀⠀⢰⠟⠿⣿⣿⣟⠓⠁⢊⠀⢀⣴⣿⣿⣦⢀⣴⡿⠻⢿⣿⣰⡁⠹⠷⠠⠀⠈⠳⠀⠀⠀⠀⡀⢠⡀⣤⠈⠁⣳
⠀⠀⠻⠀⠀⠙⢥⡉⠓⠀⠀⠀⠈⠹⢿⣿⣟⣿⣿⣿⣴⣿⣿⣿⣿⣦⣶⣴⣶⣤⣤⡤⠀⠐⠄⢷⣾⣷⣼⠌⣻⡿
⠀⠀⢲⠃⠀⠀⠘⣡⡀⢀⠓⠄⠐⠀⠀⣿⡿⣋⠉⠀⠐⣡⡟⢱⣿⣾⣿⣹⢎⠹⡓⠁⣤⡀⠀⣾⢿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠠⠤⠃⠀⠀⣸⣿⣿⣟⣠⣼⡿⣿⣷⣿⢿⣿⡿⠁⠈⢡⠈⠀⢈⡀⠀⣏⡾⠀⠀⠙⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠀⠀⠈⢻⡿⣽⣿⣷⣶⣾⡏⠀⣼⣟⣡⡀⠀⠐⢻⡖⠉⠁⢀⣿⣤⢤⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣼⣷⡄⠀⠀⠁⠘⢻⢯⣵⣾⡷⣾⣿⡟⠉⠙⠛⣷⣦⡔⠀⠀⠸⠛⡄⠤⠋⢠⠉
⠀⠀⠀⠀⠀⠀⣶⡀⠀⠘⠛⠻⠙⢻⣦⠀⠀⠀⠈⢶⣾⣽⡇⠘⢻⣷⣤⠀⠀⠸⡋⠉⠢⣀⠠⠀⣠⣤⣦⠰⠄
⠀⠀⠀⠀⠀⠀⢸⣇⣀⢸⣶⣴⠀⠀⣿⡄⠀⡀⠀⠀⠙⠻⠁⠀⠀⠙⣿⣶⣶⣿⣧⣀⣴⣿⢫⢼⡦⠴⡽⠃
⠀⠀⠀⠀⠀⠀⠂⣽⢯⣼⣿⣿⣀⣠⣿⣿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡿⣏⠙⣯⡑⠀⠖
⠀⠀⠀⠀⠀⠘⠈⢣⢀⢸⠻⠋⢁⡃⠉⣸⠁⠀⠀⠀⠃⢀⠀⠀⠀⠀⣿⣿⣿⡟⠟⠁⠀⢡⡾⢙⠃
⠀⠀⠀⠀⠀⠀⠘⠋⢿⣿⣷⣶⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠛⣯⣹⣷⠀⣄⣰⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⣄⠙⢻⡷⢯⣉⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣴⣤⣳⣄⠈⣝⣫⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡘⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢀⣀⡘⠳⣬⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣾⣿⣿⣷⡀
⠀⠀⠀⢀⠀⠙⣿⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⢉⣿⣿⣷⡀
⠀⠀⠀⠀⢱⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠉⢽⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⢀⣤⣴⣿⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣖⠀⠀⠀⠀⠄⠈⠉⠛⠉⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢼⣿⡏⠀⠀⣀⣰⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⠛⠿⠀⠀⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣽⡄⢀⠀⢸⣿⡟⢻⢛⣿⣿⣧⠀⠤
⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⡾⠳⢿⣿⠷⠛⣤⣿⣿⣿⢙⣦⣀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣧⠀⠈⠀⠀⠀⣺⡿⡇⠀⠘⢻⣿⣍⣁⠀⠀⠁
⠀⠀⠀⠀⢿⣷⣼⣿⣿⣿⣿⡟⠉⣠⣿⣿⣿⣿⡟⠇⠁⢀⣤⣿⠃⠈⠉⣋⡼⣤⡾
⠀⠀⠀⠀⠈⠛⡿⣿⣿⠛⣫⢠⣴⣿⣿⡿⠿⢿⣷⣦⣤⣶⣿⣿⣦⠄⠀⢁⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣀⣿⣿⢿⣿⣿⠀⣿⣷⣿⣿⣿⣿⣴⣄⠀⢀⣾⡟⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⢻⣿⣿⣿⣿⡿⠿⠿⣶⠿⠋⠀⠀⠀⠀⠀⠀⠈⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡤⠴⣾⣿⣿⣿⠀⣸⣿⣿⣿⠟⠐⠛⠶⠏⡰⠁⠀⠀⠀⣺⣃⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣾⣿⣿⠀⣿⣿⣿⢇⣾⣥⠀⠀⠀⠀⠢⠀⢀⠀⠉⠹⠗⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⡟⣡⠀⣿⣿⣿⣼⣿⣿⣇⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢢⣄⠛⠂⠀⠧⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣼⣿⡟⠛⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡌⢻⣛⠦⡶⠄⢀
⠀⠀⠀⠀⠀⠀⠀⣤⠿⣿⣿⣿⣿⣥⣤⡆⠀⣺⣿⣿⣿⣿⣿⣿⣯⣽⣿⣧⡀⢹⣷⣄⡰
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⣉⡯⢉⣵⡶⡇⠀⠙⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⠞⣿⣿⣅⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡡⠶⠋⠁⢠⠆⠀⠀⠀⠀⠉⠹⠿⣞⣯⠉⣿⣿⣿⠃⠘⠿⠟⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠈⠉⢁⣤⠛⣿⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⡿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠒⠚⠛⢛⣶⡶⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠹⡇⠀⠀⠀⠀⠈⣷⣦⠀⠐⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣿⠿⢿⣿⣿⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⣺⣿⡿⣿⣶⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢠⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⣿⣷⢺⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⡈⠁⠾⣿⡀⢿⢻⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⣿⣿⠃⣼⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⠶⢴⣶⣶⣿⠏⣰⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠄⠈⠠⠛⠛⡶⠚⠟⣽⣿⣿⣿⣿⣟⡿⠉⣥⡀⠻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⣤⡄⢀⠀⠀⠀⠘⠀⢘⡇⠂⢠⠾⠹⡿⡉⠻⣿⠄⠀⠸⠇⠀⢹⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣋⣿⠀⢿⣄⡤⠀⠀⠀⠀⢣⡴⠻⠀⠀⠑⠈⣤⣽⣄⠀⠀⠀⠀⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⡇⠉⠙⣇⠀⠀⠀⠐⣿⡏⠀⠀⠀⠀⠈⠉⣩⡿⢧⣀⣀⣴⠾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⣿⣆⡀⠀⠀⠋⠀⠀⠀⢀⣀⣀⣴⠏⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⢀⣸⡏⠛⠛⠛⠀⠀⠀⠾⢿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⢸⣿⣟⢻⣿⡾⣽⣷⣶⣶⣶⣶⣤⣤⣀⡀⠀⠘⣷⣄⠀⠀⠀⠀⣀⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠾⣿⣿⠛⣻⣋⣽⣿⣿⣿⣿⣏⡉⢉⣭⣿⣿⠿⠋⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣽⡗⠀⡾⣥⣽⣿⣿⣿⠛⠩⣬⠉⡻⣤⣠⣾⠟⠁⣀⣤⣶⠏⣘⣡⣏⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠈⣽⣿⣿⣿⣿⣷⡄⢠⣬⣵⣿⣿⡟⢁⣀⣠⠤⢎⣥⣿⣹⣿⣿⣿⡅⢀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠁⠈⣿⣷⣿⣿⢿⣥⣹⣿⣯⣭⣶⣿⣿⣿⣿⡿⠛⣥⣼⣾⣿⣿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣃⣰⣦⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣽⣿⣟⣍⣷⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⣿⣿⣿⣧⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⠉⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠋⣼⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⣿⠃⠁⠀⢀⣼⣻⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡾⠋⠁⠈⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠘⣿⣽⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⠟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣤⠟⠀⠀⠀⠀⠀⠀⠀⣀⡴⣄⡀⠀⠀⠀⠀⠀⠀⠐⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠄⣰⠟⠁⠀⠀⠀⠀⠀⣀⣤⣞⠹⠀⠈⢹⡦⣄⡀⠀⠀⠀⠀⠀⠈⠳⣄⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣾⠃⠀⠀⠀⠀⣠⠴⣻⠏⠡⡇⠀⠀⠀⠀⠇⠈⢻⠷⢤⡀⠀⠀⠀⠀⠹⣧⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠀⢠⠞⣡⢲⡟⠀⢰⡇⠀⠀⠀⠀⡆⠀⠀⢢⡀⠙⢦⡀⠀⠀⠀⢹⡆⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣇⠀⠀⣰⢋⣾⢧⡟⠀⠀⢰⠄⠀⠀⠀⠀⡇⠀⠀⠘⢃⠀⠈⢳⡄⠀⠀⣼⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡐⠀⠈⢑⠶⣽⣿⡟⣾⠁⠀⠀⢸⠀⡐⢀⠀⠀⠃⠀⠀⠀⠘⣡⡄⣸⠹⣦⠋⠙⢦⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⡎⣀⢀⠀⣿⣿⢱⣿⡇⢀⢀⣼⠈⠀⢀⠀⢀⡄⠀⠀⠀⢸⡏⣿⣿⣷⠐⣣⠀⠈⣇⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣟⣾⣿⣿⣏⠺⠟⠛⢛⠉⠩⣤⡀⢠⠀⠈⠁⠀⠉⠛⠛⠳⠘⢿⣿⣶⣿⣤⣾⣿⡏
⠀⠀⠀⠀⢀⠀⠀⠀⡼⠁⠙⠻⢿⣯⣶⣞⣉⣰⠀⠀⠀⠀⡌⣴⠄⠀⢀⡀⠀⠀⠀⠈⣧⠀⣀⣮⣽⡿⠿⠋⠉⢧
⠀⠀⠀⠀⠀⠐⠈⠖⠀⠀⠀⠀⢸⣷⣟⣋⣩⣤⣤⣤⣤⣭⡅⠉⠀⡀⢸⣉⣤⣤⣤⣤⣤⣬⣙⡻⣾⡇⠀⠀⠀⠀⢱⠂⠀⢛
⠀⠀⠀⠀⠀⠀⣄⡴⠀⠀⠀⠀⣬⣽⡟⠻⠉⠏⣀⣦⣤⣬⣽⣄⢀⣠⣾⣭⣤⣴⣤⣂⠀⠉⠛⢻⠟⣥⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢾⣽⡇⠀⠀⠘⠋⠀⠁⠐⣿⡟⠉⠉⣿⣿⠇⠈⠀⠉⠁⠀⠈⠘⣧⢸⡆⠀⠀⠀⠀⠀⠈⠧⠀⣠
⠀⠀⠀⠀⠨⠈⠀⠀⠀⠀⠀⠀⢰⠹⡇⣷⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣾⠃⠀⠠⠀⠀⠀⠀⠀⡾⠃
⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⢀⣀⡔⣿⡇⢣⡙⠳⣄⠀⠀⢀⠖⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⡠⡁⠚⣾⣿⡗⠦⠀⠠⠐⡄⠀⠀⢠
⠀⣄⠀⣤⠀⠀⠀⠀⠀⠀⢀⠈⣰⣿⠇⠠⣌⠂⠙⠄⢀⣁⡾⠷⢦⡴⠿⢇⠙⡀⠀⠀⠊⡼⠁⠀⣿⣿⣞⢳⣤⣄⠀⠘⠀⠀⠀⠀⣠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⢠⠞⣽⣿⠀⠀⠾⣷⢀⡴⠋⠁⠀⢀⠸⠇⣀⠀⠁⠘⢆⠀⢾⠧⠀⠀⢻⣯⢉⡓⢆⠉⠣⡀⠀⠀⠀⠀⠹
⠀⡆⠀⠂⠀⠀⠀⠀⣔⠔⠁⢸⢟⣿⡆⠂⠀⠛⠛⠀⢀⣴⡞⠋⠁⠈⠉⡳⣦⣤⠀⠻⡾⠀⢀⠈⣿⠉⡀⠹⠀⢆⠀⢸⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠁⡾⠀⣿⡇⠸⠇⠀⣠⠀⢸⣿⣠⠊⢙⡛⠁⢀⣻⣯⣀⣤⡀⠀⠘⠀⡿⠀⡷⢰⣿⣭⠷⠀⠀⠀⠨⠰⠆
⠀⠀⠀⠐⡀⠀⠀⠸⠀⢸⢘⡇⠀⠘⣿⡄⠠⠘⣿⣿⣿⣿⠇⠀⠈⣿⠂⠘⣿⣿⢹⣾⡗⢠⣆⣿⠇⢀⡟⣸⠋⣀⡤⠭⣖⣒⣿⣭⣭
⠀⠈⠃⠀⠁⠀⠀⠀⡤⣾⣎⢳⡀⠀⢿⣷⡀⢶⣿⡟⢿⠃⠀⠀⠀⠈⠀⠀⠘⣿⡿⣧⡟⠀⣸⡇⠀⢸⠁⣿⣿⣿⣶⣿⣿⠿⢟⡛⠛
⠀⠀⠀⠀⠀⠀⡠⠊⡰⣻⠟⡆⢳⡀⢸⣿⣿⣄⠸⣧⠀⠘⠀⢰⡆⢰⡷⠆⠰⠁⠀⣉⣥⣿⣿⠀⠀⢸⡃⣿⡿⣻⡽⣻⠁⠈⢠⣀⡄
⠀⠀⠀⡀⢤⣤⠁⣸⡿⠃⠀⠘⣷⡇⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⣿⣽⠃⣇⠀⢸⠇⣿⢞⣽⣿⡏⠀⢑⠀⠛
⠀⠂⣱⢿⡠⢋⣠⠟⠃⠀⠀⠁⢸⡇⢸⣿⣿⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣱⣿⡀⢻⢀⣿⣞⣵⣿⠟⢢⠁⠲⡀⡡⠈⠠
⢀⣼⡿⢋⣴⡿⢋⠂⠀⠀⠀⠀⠀⣷⣿⣿⡏⢹⣧⠙⣿⣦⣄⣀⠀⠀⣀⣤⣾⣿⣿⣶⠏⣾⠃⠈⣼⢫⡿⢉⠁⠀⠀⢀⠀⠈⡔⢀⠒
⢸⠟⢀⣾⣿⡇⠀⡀⠔⣡⠎⢠⣾⣿⣿⣿⣷⣈⣿⡆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣵⣷⡿⠀⣿⠀⣰⠣⡿⠁⠈⠀⠀⠀⠃⡀⢈⡁⠛⠁
⠈⠀⣼⢻⣏⠴⠊⣠⠞⢡⠘⠘⣿⣿⣿⣿⣯⣿⠿⣿⡀⠈⢻⣿⣿⠿⣛⣽⣾⣿⡝⣧⠀⢿⣧⢇⡗⢹⠞⡏⠀⠀⠂⠈⣠⣌⡀
⠀⣼⠇⡱⠁⠀⣴⡗⠀⠁⣰⣾⣿⠷⣬⣛⠿⣿⣿⣮⣽⠿⠛⢉⣠⡾⠛⠉⢀⣿⠁⠻⣄⢨⡟⡌⢧⡁⠀⠄⠀⣀⣤⠞⡋⠄⢱⠂⣠
⠐⠃⠀⠀⠀⣸⣿⡇⢠⣾⣾⣿⣿⣅⢈⡙⢿⣦⡀⠀⢀⣴⠆⠛⠁⣐⣤⣶⣿⡇⣡⠀⢹⠿⡇⡷⡆⣼⢶⡆⠸⢉⡀⠊⠉⠞⠁⠘⢁
⠰⠾⢰⣂⣴⣿⠛⡇⠀⣿⣿⠣⡀⠉⠻⣦⡀⠈⠻⠞⠋⠈⣦⣿⠾⠛⢉⣵⠟⢻⡘⠃⣼⡇⣧⠹⢷⡷⠂⣿⢰⡿⣈⠤⠒⢑⠂⠘⠠
⠀⢾⡿⢃⣿⠃⠈⠽⢆⢻⠻⣀⡶⢄⡀⠎⠻⣦⢀⣠⢀⡾⠋⠀⣊⣴⠋⠀⠲⠟⣧⠀⢸⣷⡟⢳⣄⡙⠡⢼⣧⠆⠥⢀⠷⠂⡄⢛⣴
⠀⠏⠐⠛⠁⣀⣠⣴⣾⣼⣿⢿⡁⡈⠳⣦⡁⡿⠳⡥⣿⣥⣨⡾⠋⠀⠠⡄⠀⠀⣿⠀⢀⣿⣷⢿⣿⣿⣶⣤⣀⠀⠀⠀⣈⣤⣾⣿⠟
⢀⣤⣶⣾⣿⣿⣿⡿⠟⠛⣿⠀⠉⠀⠰⠎⢿⡇⠂⡄⣹⠿⠻⡄⣤⠀⣀⠄⡱⡇⣸⡆⣿⠟⠿⣀⣹⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣏⠘
⠘⠉⣹⠏⠀⣽⣿⡄⠀⠀⠈⠸⣧⢠⡇⠀⠈⢧⣑⣠⠎⠀⠀⣷⣤⡔⠁⢀⠈⡁⣹⣧⡻⠏⢀⣞⣵⡿⠛⠀⠀⠰⠋⠀⠉⠛⠀⠉
⠀⠀⠅⠀⢠⡟⢿⢻⣆⡀⠺⠄⠉⢿⣿⡀⠄⠀⠀⠁⠀⠀⣰⣿⡟⠤⠘⢋⢀⣼⡟⠁⠈⢙⣿⣿⢿⠁
⠀⠈⠀⠀⠛⠀⠀⠀⠈⠓⠀⠀⠀⠀⠙⠿⣶⡀⠀⢀⣤⡾⣿⣿⣧⣠⣴⡷⠿⠟⠙⠋⠀⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠰⠞⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠂⠀⠀⠀⠀⠀⠀⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⢠⣾⣿⠆⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠅⠈⠉⠀⠐⢪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⣤⡤⣤⣧⠀⡀⢸⢆⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠘⠀⢀⣀⠓⢍⠁⠔⠀⠊⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠓⠠⠤⢄⣥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠈⠁⠆⠀⠀⠀⠀⠀⠂⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⣀⡈⣧⣀⠜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠚⠁⠀⠀⢡⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠐⠲⠂⠁⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢰⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠀⡇⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠛⠀⠀⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠇⣈⠷⢄⣀⣀⣉⣁⣘⣀⣀⣀⣀⡤⠔⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢝⠉⢉⠉⣉⠀⠀⠤⠀⠋⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠠⠈⠁⠎⠀⠀⠀⡀⠀⡘⠠⠚⠒⠒⠒⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠐⠈⠆⠠⢠⠀⢐⠉⢁⠀⡀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠍⠉⠈⠤⠀⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣀⢱⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡀⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢢⠊⡆⠀⠀⠀⠀⠀⠀⠀⠖⠉⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡠⠚⠛⠓⠧⡀⠀⠀⠀⢠⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠘⠀⠀⡔⠉⠉⠀⠁⠢⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢀⣀⣀⣀⣀⡠⢾⠀⠀⠀⢀⠀⠀⠀⠀⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠁⠀⠀⠀⠀⠈⠉⠉⠛⠉
⣟⣿⣻⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣿⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠛⠋⠒⢦⠀⠀⠀⢨⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡿⠀⠀⠀⠀⠀⣀⣀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠑⠲⠄⠚⠋⠁⢹⠀⢀⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⢸⣷⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢸⣷⡀⠀⠀⠀⢀⣼⣧⠀⠀⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣤⢇⣿⣷⣦⣤⡶⡟⣿⣧⡘⢧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣯⣹⠈⠹⣿⠂⠀⣳⡟⠿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⣤⡶⡟⠹⣅⢉⣷⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⢿⠌⡟⠀⠛⣿⠄⠀⠁⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢴⡇⠀⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠀⠀⠀⠀⡐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠤⡀⢈⡁⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣜⠶⣤⣤⣤⣤⣤⣄⣁⣨⣥⠀⣀⣀⣀⠀⡀⢀⡀⠀⠈⢓⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⢌⠅⠀⠙⠳⣾⠉⠁⠀⠉⠉⠀⠸⣦⠉⠉⣉⣭⣭⣿⡿⣆⠀⢸⣦⡤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣱⡏⢠⣴⣿⣤⣤⡗⠒⠲⠤⢤⣄⠀⠸⠆⢠⡿⢋⣁⡤⠀⠙⣦⣸⡗⠀⠈⠉⡙
⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⡏⠀⢀⣾⣿⣯⠉⠙⠀⠀⠀⠀⢀⣿⠀⣹⠿⠀⡛⠊⣤⡆⣤⢶⣻⣽⡟⠷⠤⢤⠆
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣟⠀⣠⣿⣯⠏⠙⣶⣤⡀⠀⠈⠛⠻⣿⡾⠛⣋⣵⠂⠀⣹⣿⣿⣿⠿⠉⢷⣆⣀⡲⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢫⣾⣿⠁⡿⠀⢀⡇⡖⠀⠙⠲⠄⠀⠀⠀⢀⣹⡟⣥⡴⢿⣭⣆⢠⠀⢀⠘⠁⠠⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠺⣿⡟⠀⠃⠀⠈⠁⡇⠀⠀⠀⠀⠐⠁⢈⠀⣿⣐⣿⣷⣼⣿⣿⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⡿⢷⡜⣿⣧⠀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠰⠸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡆⠈⢿⡶⠙⠀⠰⡄⠀⠶⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠇⠀⠀⠀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢹⣿⣷⣄⣤⣼⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣯⣍⣭⣭⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢷⣾⣿⣻⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠋⠻⠇
⠀⠀⠀⠸⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢄⣤
⠀⠀⠀⠀⠅⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠘⠁⠘⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀⡀⠀⢤⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣷⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠚⠉⣻⣿⣿⣷⣄⡀⠀⠀⢹⣿⣿⣿⣟⠀⢙⣏⠷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣹⣿⣷⣶⣶⣾⣿⣿⣿⣷⣦⡽⠀⡄⠀⢀⡀⢀⣾⣿⣿⡿⠛⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣷⣦⣀⡴⣿⣿⣞⣿⣿⣿⣤⣠⣜⣯⣿⣷⣙⣿⣿⣿⣿⣿⣿⣿⣧⣤⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⡀⠀⠉⠉⢻⣿⣿⣿⣿⡟⣿⣿⣯⣽⣿⡿⣟⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⣿⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠛⠙⠏⠸⣿⣿⣷⣿⣤⡍⠻⢿⣿⣿⣿⣿⣿⠿⢉⣿⣿⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣷⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠉⢉⣴⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⣴⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣿⣭⣿⣿⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠛⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠀⠈⠘⣧⣤⠀⠀⢠⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⠛⠃⣴⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠛⠠⠄⠀⠀⣣⣤⡿⣷⡗⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⣀⣠⣴⣾⣿⣿⡿⣿⣿⣡⣄⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠋⠙⠋⠀⠙⣿⣿⡿⢿⣿⣿⣮⠑⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠸⣷⡀⠀⠀⣀⣠⣶⣿⠟⢿⣟⣀⣈⡑⠀⠀⢿⣿⣿⣾⣿⣿⣿⣾⣿⠳⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠹⣿⣆⢻⣿⡆⢠⣴⣿⣽⣇⢠⠀⣿⠋⠁⠀⡀⢀⣙⣿⡟⠙⠿⣿⣿⣿⣿⡣⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠙⠛⠀⠉⢸⣇⠈⠉⠹⣿⣿⠿⣿⠀⠀⠀⠘⢿⣿⣾⣿⣀⣀⠨⣿⡏⠈⠳⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⡾⠟⠃⣶⣼⣏⢠⡼⠂⠙⢿⡾⣿⣴⣷⡀⣦⢸⣿⡿⠏⠈⠛⠧⢿⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣤⡿⠛⣹⡟⢸⡷⠀⠀⠈⠀⠈⠙⠻⣿⡿⣿⣿⣧⠀⠀⠀⠀⢀⡈⢷⡀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⡛⠁⠀⢀⣴⣿⠁⠀⣷⣄⠀⠀⠀⠀⠀⢠⡿⠃⠉⢹⣿⠀⠀⠀⠀⣸⣧⣤⣙⠛⢿⣿⡀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣤⣄⠠⢾⣿⡥⡿⢷⣶⡦⢿⣷⣶⣤⣤⡄⢾⡷⠖⠈⠛⠋⠁⠀⠰⠾⣿⣿⣿⣿⣿⡟⠛⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠛⠻⠟⠠⢯⣶⣶⢺⠿⣦⡀⠉⠻⣭⣍⣁⣨⣅⡀⠀⠀⣴⡦⠀⠀⣰⣿⡧⠙⢻⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢸⣿⠛⢿⣦⡈⠑⣄⠀⠀⠹⠿⣿⡏⠀⠀⠀⢸⣄⠀⠀⣽⣿⣷⡀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣶⡀⣿⠃⠀⠀⠈⠹⢿⠋⠶⠀⠀⠀⢻⣿⡆⠀⠀⠸⠟⠀⢰⣿⣿⣷⣿⢶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠛⠰⣾⣿⡿⠋⠀⠀⠀⠀⠀⠘⠏⠀⣬⠀⠀⠠⠤⠐⢂⣤⣌⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠐⠃⠀⣿⣿⣷⠆⠙⠃⢠⡀⠀⠀⠀⠀⠀⣰⣷⣴⠀⠀⠀⠀⣰⣶⣟⣩⣿⣿⣿⣇⣼⣿⣿⠏⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢾⡷⠀⠀⠀⢠⣾⣿⣿⣿⢶⡤⠀⠰⠛⢻⣿⣤⣉⡉⠀⣈⣀⣿⣿⣦⠀⠈⠁⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣴⠟⠁⠀⠀⠄⠙⣿⣿⣧⠔⠚⠻⠿⣤⣤⣤⣿⣧⠙⠁⡼⠻⠟⣟⣈⠛⣆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣼⡟⠁⠀⠀⠀⠈⢀⣶⡿⠷⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢺⠂⠀⠸⡿⠛⡇⠈⢷⡀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⡀⠀⠰⣿⠃⠀⣾⡏⠀⡴⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⣄⣿⡏⠀⣿⠀⠀⠀⠀⠀⢋⡀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣿⠇⣤⣿⡆⠀⣾⣿⠃⠀⠀⠀⠀⢸⣷⠀⠀⣠⠀⠀⢸⡟⠉⠀⠼⣋⠀⠀⠀⢿⠀⢸⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⣠⣻⣷⡆⢸⣿⡏⠀⠀⠀⠀⠀⣸⣿⣤⡀⠛⣄⠀⠘⣇⠀⠀⠀⠉⠀⠀⠀⠈⠀⠈⠱⡀⣹⡄⠀⠀⠀⠀⠀⠀⠀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢿⣿⡿⠇⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⣿⣷⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣾⣤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠉⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠿⣿⠻⡿⠁⠀⠀⠀⣿⡟⣩⡅⠉⠂⠀⠀⠀⠀⠀⠛⠂⢰⣿⣌⡉⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣤⠀⠀⠀⣤⡜⡛⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⣴⡾⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡟⠿⣦⡄⠀⢠⡿
⠀⠀⠀⠰⣯⡀⠀⠛⣿⡏⠁⠀⠀⠀⠀⠀⢸⠃⠆⠀⣀⣀⣠⣰⡿⠋⠀⠀⠀⢰⣦⣤⣼⠛⠁⢿⣧⠀⠀⠀⠀⠀⠀⢀⣀⠋⠀⠀⠀⠀⠈⠻⣿⡟⠡
⠀⠀⠀⠀⠁⣹⣿⣾⠋⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠔⠋⢻⣿⡟⠁⠀⠀⠀⠀⢸⣿⠿⣟⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢁⡀⣴⣿⣿⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣼⣿⡀⠀⢀⣄⠀⣀⣿⡇⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠘⠃⠀⠈⠩⠄⠀⣠⣤⣴⡿⠁⠀⣬⣥⣬⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢴⣶⣿⣿⣯⡁⠀⠀⠉⠉⠹⠟⠁⠀⣀⡄⠐⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣇⣴⣤⣼⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠉⢸⠿⠛⢿⣶⣶⢶⡀⠀⠀⠀⠀⠛⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⢻⣿⠛⣙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠈⠀⠀⠞⠛⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠆⠴⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠠⠀⣠⣶⣿⡾⠁⠀⠀⠠⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢣⣸⡷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⡍
⠀⠀⠀⠀⢀⣤⢾⣷⣤⡀⠀⠸⠋⠁⠼⠏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢶⠆
⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⢠⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠘⣿⣆⢀⣠⣴⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣘⣿⢛⣭⣠⢠⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣫⣯⣧⣾⣿⣷⣯⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠿⠟⡓⣿⣿⣿⣯⡟⠙⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢟⣿⢿⣟⠉⠉⠃
⠀⠀⠀⠉⢲⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣿⣸⠀⠀⠀⠀⠀⢸⠺⣿⣟⣟⡿⠽⢻⣻⣿⢞⣟⡶⣅⡆
⠀⠀⠀⠀⠀⢻⣻⣿⡀⠀⠀⢀⡀⠀⢠⡾⣗⢠⠀⠀⠀⠀⠀⣬⣿⣜⣛⢽⣗⣦⣉⣯⣿⠻⣎⡵⠶⢆
⠀⠀⠀⠀⠈⠈⠱⣏⡳⢤⡀⡀⠻⣿⣧⡅⠈⢏⠃⠀⠀⠀⢰⣽⡿⠿⣿⠿⣯⣿⣛⣿⣿⡄⠷⢶⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣶⣛⡸⡿⢻⢻⣷⢦⣣⡘⣀⢴⡄⣎⣿⡎⢀⡨⠳⡌⢿⣿⣷⣿⣷⡖⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠽⠽⣏⡇⠀⠉⢙⣧⣳⡗⡝⣯⣯⣹⢷⢇⢡⡼⢻⠿⣯⣦⣭⣇⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠻⢿⢾⠵⣿⣿⣛⠾⣿⣷⣶⣿⣶⣿⠃⡾⣟⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣟⣷⣿⣤⡙⣋⣿⠿⣧⣤⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⣥⣿⣾⣿⣟⢹⠟⡟⣭⣧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣲⣾⣿⣿⣿⣿⣏⣻⣿⣶⣶⣾⣟⣤⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠞⠋⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀
⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄
⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⣼⠃⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⢀⣀⣤⠔⠒⠉⢩⠋⠀⠀⠀⠀⠙⡍⠉⠒⠦⣤⣀⡀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠸⠏⠻⢦⣄⣀⡤⠞⠋⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠙⠳⢤⣀⣠⡴⠛⢹⠇
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢀⣀⣼⡤⠤⣤⠤⠤⣤⠤⢤⣧⣀⡀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⡤⠖⢶⡏⠉⠀⠀⠀⠀⣇⡀⢀⣽⠀⠀⠀⠀⠉⢹⡶⠲⢤⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠘⢷⡀⠀⠀⠀⠀⣰⠏⠀⢀⣤⠞⠻⣅⢀⣠⣇⣠⣤⣄⣤⣤⣬⠛⢛⢡⣤⣤⣤⣤⣄⣹⣄⡀⣨⠛⠳⣤⡀⠀⠹⣆⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠙⢦⣄⠀⢰⣏⠤⡴⠋⠀⢀⣠⢤⣛⠭⠍⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠒⠫⠬⣛⡤⣄⡀⠀⠙⢦⠤⣸⣆⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠉⢻⡟⠁⣠⠇⣠⢖⡽⠚⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠉⠓⢭⡲⣄⠸⣄⠈⢻⡟⠉
⠀⠀⠀⠀⠀⠀⢸⡿⢛⡵⣪⠞⡡⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠀⠀⠌⢳⡝⢮⡛⢿⡇
⠀⠀⠀⠀⠀⠀⡿⣡⢎⣴⡏⠈⠀⠐⠒⠂⣤⣀⠀⠈⠑⠒⠒⠢⠤⠁⠊⠠⠔⠒⠒⠂⠁⠀⣀⣤⠐⠒⠂⠀⠁⢹⣦⡹⣌⣿
⠀⠀⠀⠀⢠⠞⣻⢃⡾⢻⠅⠆⠀⣄⡴⠋⠀⠉⢉⣢⢄⡀⠀⢀⣰⣠⣄⣆⡀⠀⢀⡠⣔⣉⠉⠈⠙⢦⣠⠀⠰⠨⡟⢷⡘⣿⠳⡀
⠀⠀⠀⠀⢸⢀⡏⣸⠃⠀⡜⠀⠀⠚⠃⠦⣴⣧⣼⣿⠈⣹⣏⣹⠋⠉⠉⠙⣏⣹⣏⠐⣿⣧⣼⣦⠴⠚⠛⠀⠀⢣⠀⠸⣇⢸⠀⡇
⠀⠀⠀⠀⡴⠉⠉⢿⠀⢠⠁⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⢩⠂⠀⠀⠐⡉⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠈⡄⠀⡿⠉⠉⢄
⠀⠀⠀⠀⠃⢠⢢⢸⡄⢸⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠀⠀⠞⠀⠀⠀⠀⠳⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢠⡇⠖⡄⠘
⠀⠀⠀⠀⡆⠀⠀⣿⠀⠐⡟⢆⠀⠀⠀⠀⠀⣠⣋⣤⠷⠾⠿⣆⠀⠀⠀⢀⣰⠿⠷⠾⣤⣙⣄⠀⠀⠀⠀⠀⡴⢻⠃⠀⣿⠀⠀⢰
⠀⠀⠀⠀⠱⡀⠀⢻⠀⠀⢿⢘⣠⠁⡀⣠⠜⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠙⠣⣄⢀⠈⣆⠃⣟⠀⠀⡟⠀⢀⠎
⠀⠀⠀⠀⠀⢱⡄⠹⠆⠀⠇⢸⡿⢛⡾⠁⠀⠀⠀⠀⠀⣀⠀⢀⣀⢀⡀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠘⢷⡛⢿⠃⠸⠀⠐⠏⢠⡎
⠀⣤⡤⠤⠞⠋⢈⠟⠀⠀⠀⡜⢀⣿⠁⠀⠀⣠⠖⠛⣛⣿⣶⠿⣿⣁⣈⣿⠿⢶⣟⣛⠛⠲⣄⠀⠀⠈⣿⡀⢇⠀⠀⠀⢘⡁⠙⠓⠦⢤⣤
⠀⠀⠑⠢⠤⣠⠎⠀⠀⠀⠀⡇⠈⣿⠀⠀⢠⢳⡴⠋⠀⠀⢀⣀⣀⠀⠀⢀⣀⣀⠀⠈⠙⢦⡞⡄⠀⠀⣿⠀⢸⠀⠀⠀⠀⠱⣄⡠⠔⠋
⠀⢲⡖⠒⠞⠉⠀⠀⠀⢸⠀⠃⠀⢹⡀⠀⢸⠸⠁⠚⠛⣿⣍⡉⣩⠟⠿⣍⢉⣹⡿⠛⠓⠘⠇⡇⠀⢀⡏⠀⠘⠀⡇⠀⠀⠈⠙⠳⠒⢲⡖
⠀⠀⠙⠦⣤⣄⣠⡤⠀⣼⠀⠀⠀⠈⡇⠀⢸⣄⠀⢀⠀⠙⠈⠻⠃⠀⠀⠘⠟⠁⠃⠀⡀⠀⣠⡇⠀⢸⠁⠀⠀⠀⣧⠀⢤⣀⣠⣤⠶⠋
⠀⠀⠀⠠⣴⠚⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀⡜⠹⣤⠘⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⠁⣤⠏⢇⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⠓⣦⠄
⠀⠀⠀⠀⠀⠙⠓⠖⡶⠎⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⢦⠈⠀⠀⠀⠀⠀⠀⠱⣶⠒⠚⠋
⠀⠀⠀⠀⠀⣠⡄⠊⠀⢀⣠⡄⢀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠁⠀⠀⠀⡀⢠⣄⠀⠀⠑⢠⣄
⠀⠀⠀⠀⠀⠈⠉⠉⢻⣟⠛⠓⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡀⢀⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠚⠛⢻⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣕⠆⠀⠀⠀⠀⣤⣶⣉⣤⣤⠶⠀⠚⠉⠁⠈⠉⠓⠐⠦⣤⣤⣉⢲⣤⠀⠀⠀⠀⠐⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠴⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣣⣤⣤⣤⣤⣴⣒⣋⣛⣒⣦⣤⣤⣤⣤⣌⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿