Fancy symbols Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤
⠀⠀⣤⣤⣤⣤⣤⠶⢶⣿⡿⠿⠿⠿⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣤⣤⣤⣄
⠀⠀⢸⡇⢀⡀⢀⡰⠋⣡⠄⣰⣷⢀⣴⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⢟⡷⣝⢦⠀⠀⠀⠀⠀⠀⠀⠸⣿⡋⠉⣀⣀⣀⣀⣀⠈⢻⠏
⠀⠀⠸⣷⢸⣧⣾⠁⣼⣿⡾⠟⠁⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⢱⢏⡾⣡⡌⢿⢳⡄⠀⠀⠀⠀⠀⠀⠹⣷⡈⢻⠏⠉⠉⣿⡟
⠀⠀⠀⠹⣷⣿⠟⠀⣠⣶⠾⣿⣿⠛⣿⣯⢨⣿⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⣧⣿⢃⠈⣇⢷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢠⣾⡋
⠀⠀⠀⠀⠈⠛⠀⣴⠟⠋⠀⣿⡿⢀⣿⠏⢸⡏⠀⠀⠀⠀⠀⠀⠀⣧⢹⡀⢋⣿⢻⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠰⠏⠀⡼⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⣧⡻⠞⡼⢣⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⢾⣡⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠃⡄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠛⠿⣾⣷⣤⢠⣤⠄⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠄
⠀⠀⠀⢀⠀⢸⡆⢸⣇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢤⣤⡀⠀⣙⣿⣟⠁⠀⠀⠀⠀⠀⣸⣿⡟⣠⡄⠀⠀⢰⡄⢻⡿⣯
⠀⠀⠀⠀⢳⡾⠁⣛⣛⠊⢻⡾⠁⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⣾⡿⠟⣋⣵⠞⠋⢸⣿⡇⠀⠀⠀⠀⣰⠏⢸⡀⢿⣷⣦⣴⣿⡇⢸⡇⠸⣷
⠀⠀⠀⠀⠘⢃⣼⣿⣿⣿⣌⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⣀⣬⡶⠟⣩⣴⣾⠀⠈⠉⠁⠀⠀⠀⠀⠻⣷⡜⢷⣄⠙⠛⠛⠋⣠⡾⣡⣼⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⡶⠿⣿⣯⡁⠀⠻⠿⠉⣉⣴⣤⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠙⣿⡇⢸⡟⠉⣼⠟⠁
⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠷⢶⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠰⠟⠀⠈⠳⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢛⠛⢛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠙⠁⠋⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢾⣧⣤⣿⡿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠉⠀⠀⠀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣷⣤⡀
⠀⢠⣴⣾⣿⣦⣶⣾⡿⠋⢿⣿⣿⣿⣷⣤⣴⠖⠀⠀⠀⠀⠈⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢻⣇⠀⠈⠛⠄
⠀⠀⠙⠛⠉⠙⠟⢿⣶⣀⣴⣿⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⣶⣦⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢸⣿⡄⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣴⣾⣿⣇⣿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢾⣿⣿⠙⢿⡟⢹⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⠹⣿⣿⣿⣷⣶⡶⠂⠀⠀⠀⠈⠳⣤⡀⠀⢀⣿⢀⡀⣿⡀⠀⢀⣴⠞
⠀⠀⠀⣠⣿⡉⠁⢠⣬⣤⠈⢉⣹⣧⡀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠘⠠⣿⣿⡟⠛⠋⠀⠀⠀⠀⠰⠶⢴⡿⠻⣷⡟⢁⣾⣷⡘⢷⣾⠛⣷⡤⠶
⠀⠀⠘⢿⣿⠟⠃⠸⠿⢿⠀⠛⢿⣿⠟⠀⠀⠀⠀⠸⣿⣦⣄⣠⣤⣤⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢠⣿⣿⣿⣿⡈⣿⠀⣸⡀
⠀⠀⠀⠀⣻⣷⣶⠀⣴⡄⢰⣶⣿⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠿⢿⣿⠦⠄⠀⠀⠀⠀⠉⠙⣿⡾⠏⢸⣿⣿⣿⣿⠇⠻⣶⣿⠋⠉
⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⢻⡆⢰⠏⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣰⡟⢀⣤⠄
⠀⠀⠀⠀⣰⠞⣿⠛⠲⡄⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⢠⣄⣀⣀⣤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⡟⡁⠞⠥⣐⠺⠛⠛
⠀⠀⠀⢰⡇⣀⣿⣄⡀⢹⠀⠀⠀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡡⢎⡁⠐⢶⣄⣙⠛⠂
⠀⠀⠀⠀⠻⣍⣸⣀⣹⠏⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⣀⡆⠀⣀⣸⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠻⠷⠴⠄⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠛⠋⠀⠛⠛⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠄⠀⠀⠀⣠⣤⣄⢀⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⠀⠀⣤⣾⡟⣟⢿⡿⠯⣏⠿⣷⣤⠄
⠀⠀⠀⢠⠮⠅⠡⠄⡉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⣹⠏⡠⠊⣰⣯⣤⠖⠋
⠀⠀⠀⢰⡂⣀⠐⢀⣒⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠐⠁⡀⠜⠉
⠀⠀⠀⠈⠉⢹⣟⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡐
⠀⠀⠀⠀⠀⡿⠛⡟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠤⠴⠚⠻⢿⠧⠄⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠊
⠀⠀⠀⠀⠀⡇⠀⢱⠀⠀⠀⠀⠀⠀⣈⡉⢐⡀⠀⢀⣐⠠⠤⢔⣂⡀⠂⠀⡐⢒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣠
⠀⠀⠀⠀⠀⢣⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣾⣿⣯⣿⠽⢷⣆
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⡱⠀⠀⠀⠀⠀⣠⠔⠲⠀⠀⠀⠀⠙⢤⣇⣙⣷⣆⡠⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣤⠒⠉⠀⠀⢀⠠⠀⠀⠀⢀⡴⠊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠋⢠⢯⠄⢁⡠⠤⣰⠁⢠⣯⠈⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠃⡌⢀⠀⠀⠀⠀⠀⠀⠢⡐⠋⣀⠂⠀⠀⠘⢄⡐⠃⠠⠀⠀⠀⠀⠀⠀⡗⠚⠓⠇⠀⠀⠀⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠀⠀⠔⠖⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠃
⠀⠀⠀⠀⠀⡊⠤⠀⠠⣶⣶⠆⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠇⠠⣶⡶⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠐⢤⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠀⠞⠁
⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⣠⣶⡆⢀⣴⢾⡇⢀⣤⠶⢶⡆⠀⠀⠀⢀⠚⠀⠸⠁⠌⢢⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠠⠤⠴⠵⢋⠠⠄
⠀⠀⠀⠀⢰⡟⠉⠀⠹⣶⠟⠹⠷⠟⠁⠘⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⡈⠃⠚⠐⠂⣺⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠄⠤⢴⣅⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠶⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀⠷⠷⠿⠶⠶⠖⠁⠻⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣧⣤⡀⠀⠘⣷⣦⣀⣾⣧⠀⢀⣿⣆⣠⣶⡞⠀⠀⣀⣤⣿⣇⠁
⠀⠀⠀⠀⠀⠀⢀⠖⠿⠀⠀⢀⣀⠀⣾⠁⢶⣿⠇⠀⠀⠙⣿⣿⣿⣿⡄⣼⣿⣿⣿⡟⠁⠀⠀⢿⣷⠆⢹⡇⢀⣀⠀⠀⠸⠗⢆
⠀⠀⠀⡀⠀⢸⡟⠀⠀⠀⠀⠈⣻⣿⣿⡀⠀⠀⠀⠀⠀⠸⠟⠛⢿⣟⠀⢘⣿⡟⠛⠷⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⠘⣿⠀⠀⡀
⠀⠀⠈⣿⣷⣼⣷⠀⣴⡶⢄⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⢀⠴⣶⡄⢰⣿⣴⣿⡟
⠀⠀⠀⠈⠻⣿⣿⣆⠉⠁⡼⡗⠲⣌⠉⣿⣿⣿⣶⣤⣀⠀⠀⢠⣿⡿⠀⠸⣿⣧⠀⠀⠀⣠⣴⣾⣿⣿⡏⢉⡴⠲⡾⡄⠉⢁⣾⣿⡿⠋
⠀⠀⠀⠀⢀⣴⣿⣿⣷⣼⣅⣿⣈⡛⠀⠛⠉⠉⠉⠉⠛⢷⣶⣿⠿⠁⠀⠀⠹⢿⣷⣶⠟⠋⠉⠉⠉⠙⠃⠘⣋⣸⣇⣿⣴⣿⣿⣿⣄
⠀⠀⠀⠀⠘⣿⡿⠛⠛⡿⢿⣾⣧⣭⣓⣦⣀⣀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⢀⣀⣠⣖⣫⣥⣿⣾⠿⡟⠛⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⡌⠛⠻⠿⠿⠿⠿⠿⠿⢶⣦⣄⠀⢻⡄⠀⠀⣼⠃⢀⣤⣶⠾⠿⠿⠿⠿⠿⠿⠛⠋⣴⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣴⣶⣶⣶⣶⣶⣶⣤⣄⠙⢷⡄⢣⠀⢠⠇⣴⠟⢁⣠⣴⣶⣶⣶⣶⣶⣶⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⣾⣿⡏⠁⠀⠀⣾⡿⠿⠿⠿⣿⣦⣿⣸⡄⡼⣸⣣⣾⡿⠿⠿⠿⣿⡆⠀⠀⠉⣿⣿⣆⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠛⠿⠶⠀⠀⠙⠃⠀⠀⠀⠈⢿⣿⣿⠇⣿⣿⡿⠋⠀⠀⠀⠀⠛⠁⠀⠰⠾⠟⠋⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⣿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣿⠿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⡀
⠀⠀⠀⢀⣀⠤⠄⠜⠀⠘⠧⠠⠤⣤⠀⠀⠀⠀⠀⠀⣠⣤⢀⠕⢓⡦⢀⣄⣀⣀⡀⠀⠀⠀⠠⣤⣤⢤⣼⠧⠼⣷⣤⣤⣤
⠀⠀⠀⠈⠙⠢⢀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠠⠠⢔⠭⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠂⣴⡇⠀⠀⣸⣿⠋⠁
⠀⠀⠀⠀⠀⢀⡏⣠⠄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡡⠬⣥⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⡶⢿⡉⢿⡄
⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠁⠸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⢥⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠉⠀⠀⠉⠻⣧


⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢢⡀
⠀⠀⠀⠶⠶⠖⠒⣾⠷⠒⢾⡖⠀⠀⠀⠀⠀⠀⠀⢶⣴⣾⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠘⢫⡉⠁⠀⠀⠀⠀⠀⠉⡩⠃
⠀⠀⠀⠀⠀⠢⣴⡇⠀⠀⢀⣽⠂⠁⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⢠⠏⠀⡲⢶⣁⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠙⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⠤⡀⠈
⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠈⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⣿⣫⣦⣀⣀⣀
⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠈⠉⢉⡴⠋⠀⠀⠀⠀⠻⢧⣉⠉⠁⠀⠈⠉⢉⠭⠛⠁⠀⠀⠀⠀⠲⢿⠉⣫⣾⣿⣿⢷⡿⠋⠁
⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⣟⣵⣿
⠀⠀⠀⠀⠀⢸⠀⡠⠀⠑⠄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⠐⠲⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠙⠁⠉⠻⢟⡀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⡀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣼⠀⠆⡀⠄⣰⠜⠉⠙⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⡆⠂⠀⠑⠀⠁⢀⣼⠁
⠀⠀⠀⠀⠆⠀⠀⠀⢃⠀⠁⠄⠀⠀⠀⠀⠠⠀⣀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠻⠤⠤⠤⠔⠚⠦⠬⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠀⠒⠒⠻⣤⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠒⣄⠀⠀⠀⠀⢐⠀⡲⠶⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠤
⠀⠀⡎⢁⠀⡀⡀⢀⠀⠀⢣⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢁⣄⣠⡄⡀⠀⠀⢰⠂⠀⠆⠀⠰⣀⣀⣂
⠀⠈⡁⠘⠖⠋⠉⠘⠀⠀⡸⠀⠀⠁⠀⠀⠀⠰⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠛⠀⢀⠀⠀⠁⣄⠀⠀⢀⠂⣀⠀⢀⡀⠑⡤
⠀⠀⠈⠂⠄⢀⠀⠀⣠⠞⠁⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠃⠈⠀⢀⠀⠁⡀⠀⠀⠀⠅⠒⠺⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀
⠀⠀⣀⡇⢠⡘⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠉⠀⠀⡀
⠀⠀⢥⡀⢀⠘⢨⠀⢉⠤⠀⠀⠀⠀⡈⠄⠰⠂⠤⠂⠁⢤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁
⠀⠀⢸⠃⢸⠀⢘⡀⡇⠀⠀⠀⠀⢀⡅⠀⠠⠀⠒⢁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⢠⠂
⠀⠀⠀⠂⠀⠀⠈⠑⠃⠀⠀⠀⠀⠈⠇⠄⠀⠀⠀⠈⡀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⢀⡅⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡄⠀⡐⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⣄⠁⠀⠈⠃
⠀⠘⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠀⠒⠃
⠀⢤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇⠀⠄⠀⠀⢀⣀
⠀⠈⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠘⡐⠃⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⢀⠔⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⢀⡔⠁⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠤
⠀⠋⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣘⣠⣈⠀⠀⠀⠀⠀⠀⢁⡀⠠⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠐⢺⠀⡉⠉⠉⠀⢺⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⠠⠂⠘⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠐⡖⠊⢤⠄⠀⠠⡀⠁⠊⢄⠀⠀⢀⡀⠀⠀⣼⣗⣧⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣤⣾⣧⣀
⠀⠐⠀⠀⠀⠠⠀⠀⠀⡐⠂⠀⠐⠁⠲⠁⠀⠀⠰⠁⠀⡠⠊⠀⢀⡾⣧⠀⠀⠀⠈⠀⠀⠀⠌⠈⠀⢁⠀⠀⠀⠀⣀⣠⣴⣿⣷⠶⠒⠀⠀⠟⠻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠈⣆⠠⠀⠀⠠⠀⠀⠀⢠⣤⣤⣠⣾⣁⣽⣄⣀⣀⣀⠀⠀⠈⠀⢁⠐⠀⠆⠀⠀⠀⠀⠀⠈⡿⠻⡇
⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⣤⠀⠀⠄⢀⡩⠀⠀⠀⠀⠀⠐⢠⡾⠁⠀⠈⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢾⠀⠀⠘⠃⠄⠘⠀⠀⣠⠎⠱⠄⡀
⠀⠀⣷⣿⣀⠈⠂⢄⡒⠀⠀⠀⢀⡐⢍⠀⠀⠀⠀⠀⠀⠀⡜⢉⣶⣶⠞⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡝⣺⡷⠆⠀⠀⠀⠄⠀⠈⢠⠀⡀⠰⠁
⠀⠈⠉⠛⠁⠀⠀⠀⠃⣀⠀⡭⣀⠀⣬⢣⠀⢠⣄⠀⠀⣼⠷⠋⠁⠀⠙⢾⣧⠀⠈⠓⢶⠃⠂⠠⡀⠀⠈⠉⠈⠻⠄⠀⠀⠘⠃⠠⠀⡀⠈⠚⠊⠁
⠀⠀⢀⡤⣀⡀⠀⠀⠠⠔⠈⠀⠀⠈⠀⠂⠀⣸⣿⣦⣤⣤⠆⠀⣀⡀⠀⢀⡈⠀⠀⡀⠔⠃⠌⠀⠀⠀⠘⠃⠲⠆⠀⠀⠀⠀⠀⣠⣴⡇⠀⠀⠀⢠⡄
⠀⢀⢸⠈⣿⣰⢳⢆⡄⢀⠀⠀⠀⠀⠀⠶⢾⣿⣏⣽⣿⣇⠀⢀⣸⣿⣛⣿⣤⡀⠀⠀⠀⠈⠁⠀⠸⣿⠆⠠⣀⢀⣤⣤⠄⣤⣮⣿⠿⠇⠀⠰⠷⠀⠁
⠀⠙⠛⠸⢡⢧⢇⡾⣧⢇⡏⠁⠀⠀⠀⠀⠀⢹⣿⠟⠛⠛⠃⠀⠀⠘⠟⠀⠀⠀⢠⡳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢂⡻⠟⣩⣶⣺⡽⢦⣄⠀⠘
⠀⠐⣠⢂⠀⠈⠘⠸⠇⣞⠉⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⡀⠉⠖⢲⠖⠀⣀⠠⠀⠀⠀⢱⣥⠴⣻⣿⣿⣷⣚⣭⣴⣿⣶⣤
⠀⠀⠀⡁⠀⠂⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡆⢀⡈⠠⣏⠀⠀⠼⠦⡞⠀⢠⣯⣴⣿⣿⣿⠿⣛⣭⡞⠋⠉⠁
⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣄⠀⠀⠀⠀⠀⠀⢰⣤⣶⡀⠀⠀⣧⠞⠉⠳⢿⠀⠀⠀⠀⠀⣠⠟⠛⠩⠟⠛⢶⣾⣿⣿⠀⠀⠴
⠀⠁⠀⠀⠀⡀⠀⠐⣄⠀⣀⡄⠀⠀⠺⡒⠁⠘⠦⣄⠀⠀⠰⠞⠛⢿⣿⠛⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠻⣿⢻⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡅⠀⠀⢰⠣⢤⣠⠎⠁⠀⠀⠀⠀⠀⠈⡏⠀⢀⡀⣤⢺⣢⠀⠀⠐⠂⠂⠀⠀⠀⠀⠳⢀⡀⡤⠀⠀⠘⢿⢀⠀⢠⡰
⠀⠀⠀⠀⠠⠀⠉⠉⢻⣿⠋⠛⠃⠀⠀⠀⠀⠙⠀⠀⠀⣇⠀⠀⠀⠀⠀⣔⠏⢂⠘⡦⠹⠂⠀⠀⠀⠀⠀⠀⠀⡠⠈⡬⣽⠣⡀⠀⠀⢠⣏
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠱⣡⡟⠉⠀⠀⠈⣷⠄⠃⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⠚⠭⠒⠛⠾⠁
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡆⠳⠐⠠⠆⠀⠀⠀⠀⣀⣠⣦
⠀⢲⡄⠠⠊⣇⠀⠀⠀⡀⠂⠰⠟⠀⠕⠀⠠⣄⡀⠀⠀⠀⢀⡀⠀⢤⣶⣦⡀⠀⠀⠠⠀⡁⠀⢀⣀⠀⢀⠞⠤⠀⠀⠀⣹⣿⣿⠛
⠀⠀⡹⠀⠀⡀⠉⠓⠀⠀⠐⠆⠀⠈⠀⠀⠀⠆⠙⠲⡄⠐⣸⠃⠀⠀⢽⡛⢷⠀⠀⢐⠋⠜⠀⠘⠉⠁⢀⠈⠂⠠⠀⠀⠁⠀⠙
⠀⠐⠀⠀⠢⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⠀⠧⣀⠀⠀⠀⠙⣿⠀⠀⠁⢀⡄⢀⡌⠂⠀⠁⠷⠈⠀⠀⠀⠓⣄
⠀⠀⠀⠀⣄⠈⢀⠀⠀⠇⡸⠃⡀⠀⠀⢠⣞⡥⢀⡀⢀⡀⠀⠈⠳⠄⠀⠀⠈⠀⣶⠀⠀⠀⠈⠁⠰⠈⠈⠀⠀⠀⣀⢰⡦⠘⢷⡀⠀⠀⠀⡼⢤⣀
⠀⠀⠛⢦⡹⠆⣸⣧⡀⠀⠱⠚⠋⠀⠀⠀⠀⠀⠀⢇⣼⠀⠀⠀⠀⠀⠀⠙⢻⣿⠟⡓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢼⡄⣀⡐⠃⡀⠀⠛⣵⡷⢿⡀
⠀⠘⠓⠒⠊⣀⣿⣿⣿⣶⣶⡞⠁⢀⡀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠾⠋⠑⠑⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⢸⠀⠈⠉⠁⠘⠀⠀⠉
⠀⠀⠀⠘⠧⢻⣿⣿⣟⣿⡏⠐⠯⣭⣄⠀⠀⠀⣀⠀⠂⠐⠀⡀⠀⠀⠀⠀⡠⠀⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⢰⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡤⠶⣂⠈⣿⡿⠋⠘⠿⠀⠳⠆⠀⠀⠀⠀⠁⠀⠀⠈⠀⠰⠀⠀⠀⠘⣅⢈⠃⣶⣆⢹⡄⠀⠀⢉⡴⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢲⠶⢻⣤⡀
⠀⠀⠀⠾⠃⠀⠋⠀⡆⢳⡄⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢠⣈⠇⠆⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠛⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠇⢣⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠢⢀⡀⠈⢿⣄⠀⡜⠀⡀⠀⣼⠇⠀⠈⠁⡠⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠒⠄⠀⠀⣼⣿⡆⠁⠀⣰⣿⡏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣈⡄⠀⠙⢿⡿⠆⠒⠛⠿⠇⠀⠀⠀⠀⢁⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣦⡬⠃⠀⠀⠀⠀⠀⠈⠲⣿⣿⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠁⠐⠂⠙⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠐⠠⠠⠐⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠑⣢⣤⣴⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡉⠙⠒⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⠿⠛⠏⠀⠓⣄⡀⠀⠀⣀⠤⠙⢍⠻⢿⣷⣶⣆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢿⣿⠇⠈⢸⣿⣦⡤⡀⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⣀⠠⠁⣼⡿⠈⢂⠀⠟⢿⣷⠈⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠸⠊⠀⠀⠀⠀⡿⠁⠀⠸⠀⡀⠘⣿⠀⠈⠢⠧⠄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠌⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠟⠋⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠈⠁⢠⣾⠟⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠙⢿⣆⣴⡿⠃⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠟⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⡿⠃⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⣰⡿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⢀⣾⠟⠁⢠⣿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⢠⣿⠋⠀⣴⡿⠁⢀⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣾⠟⠀⣠⣿⠋⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢠⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠉⠀⣰⡿⠋⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠉⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣄⣀⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠻⠶⢶⣤⡀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠛⠛⠛⠶⣄
⠀⠀⢀⣤⣏⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⣰⠟⠉⠉⠉⠙⢷⡀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⣄
⠀⢰⡇⠀⠳⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⣷
⢀⡴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⣄
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠘⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠚
⠀⠰⡅⠀⡴⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠲⡄⠀⡿
⠀⠀⠉⠒⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠹⣦⣀⠀⢀⣠⡼⠃⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡗⠊⠁
⠀⠀⠀⠀⠈⠳⢤⣤⣤⣤⣤⡶⠶⠛⠉⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠙⠳⠶⣦⣤⣤⣤⣤⠴⠋
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠰⣶⢃⡞⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⣀⠀⡀⠍⠙⠁⠀⠀⠄⠀⠀⠀⠁⣶⣀⠀⠄⠀⠀⠀⢀⡤⡀⠀⠈⣀⣛⠀⠃⡀⠀⠲⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⠀⣿⠀⠉⠒⠐⠂⠀⠀⠀⠀⠀⢠⣆⡄⢹⢀⡀⢻⣄⠀⠉⠻⠋⠀⠀⠹⠌⠀⠀⢱⡆⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣐⡇⠀⢀⡐⠋⠀⠀⠀⡄⢀⡹⣆⠀⠀⠀⠀⠑⠀⢩⣶⠀⠀⠀⠀⠀⠈⠔⣀⠀⠀⢃⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠊⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢠⠀⠁⠈⠓⢠⡀⣄⠀⠀⠀⠀⠀⠀⠦⢄⡈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠉⠀⠓⠀⡀⠃⠀⠀⡇⢀⠁⠈⢳⡏⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡀⠀⣴⠀⠀⢀⠇⠀⠀⠀⠀⠉⣤⠀⢁⠞⣠⠀⣠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡭⠂⠀⠒⠄⠀⢉⡀⠁⠀⡝⠀⠀⠈⣴⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⠀⠾⠡⣀⢀⢠⠐⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠀⠤⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⠀⠀⠸⢓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠰⠀⠚⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢛⡅⠀⢠⠀⠀⡀⠀⡔⠀⠀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠦⠀⠀⢰⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣸⡆⠀⠀⠀⠀⠀⠤⠆⠀⠀⢁⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⢤⣀⠀⠀⠀⡤⠿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠂⡀⠀⠀⡄⠀⠀⠀⠀⣠⡐⠀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠓⠤⣀⠴⠬⠆⣌⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢈⠀⠀⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀⡀⠀⠀⢰⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢀⡤⠒⠃⠟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠃⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠑⠀⠀⠀⠀⠄⠂⠀⠀⠀⣀⠀⣀⠤⠂⠀⠁⠀⠀⠀⠘⣇⣀⠐⠀⠒⡄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⡄⠃⢠⠐⠁⠀⠀⠀⠈⠀⠂⠀⠀⠄⠀⠖⠀⠀⠀⠀⠀⠀⠈⠁⠣
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⣄⠀⠀⣀⢀⠀⠢⣀⠴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠐⠀⠲⠄⠢⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢀⠂⠀⣠⠉⠘⠷⣆⠀⠈⠇⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠈⠂⣀⠕⣠⠀⠀⠀⠀⢀⡴⠖⢀⡠⠊⠀⠈⣫⡄⣀⡀⠩⠄⠀⠀⢑⢦⣀⠩⣷⠄⠀⠀⠀⣠⠀⢄⣠⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡎⢠⣆⠀⠀⠀⣿⠃⢀⠱⣇⠀⠠⡀⠀⠀⠀⠁⠀⠀⠀⠰⢣⡖⠛⠂⢽⡆⠀⠀⠠⠵⠛⠉⠀⠉⡌
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⠆⠀⠀⢺⡅⠀⠃⢀⣹⡶⠀⠂⠀⠀⠀⠀⠀⠀⡀⠹⣤⠤⠀⣸⠇⢀⣤⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡽⣦⠀⠈⠳⠀⣀⣉⡫⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠔⠀⢁⡴⠛⠉⠰⠄⠀⠀⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠺⠀⠁⠂⠠⣀⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦⠉⠀⣰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀⠄⠐⠉⠁⠙⡁⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⡠⠃⠀⠃⠀⠀⠀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠤⠀⢀⢤⠀⠀⠈⠀⠐⢂⠡⠆⡈⢀⡐⠀⠀⠀⢀⡱⡃⠀⢀⠤⠒⠠⢄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠊⠀⠀⠂⠀⠀⠀⠀⠀⡀⠜⠣⠐⠈⠤⠈⡀⠀⠀⡍⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠎⠉⠀⠀⠀⡄⠀⠐⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣸⣇⣠⡆
⠀⠀⠀⠀⡰⠊⠁⠀⢀⣷⣴⣧⣴⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠻⠁
⠀⠀⢀⡞⠁⠀⢀⣶⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣶⣻⠶⢄⣀
⠀⠀⣼⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⢷⠀⠀⠀⢀⡀⠀⠐⠀⠀⢸⣿⣯⣻⠿⠎⢿⡆⠀⠀⠀⠀⢀⡀
⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢸⠀⠀⠀⢀⣹⣿⠀⠀⠀⣾⣿⡃⠛⠣⡄⢠⣷⠀⠀⠀⣿⣏⡁
⠀⠀⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢸⠀⠀⠈⠉⣻⣿⠀⠀⠀⢻⣿⣿⣥⠉⣈⢻⣿⠀⠀⠀⣿⣟⠉⠁
⠀⠀⠸⡆⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠏⠀⠀⠀⠘⠉⠉⢂⠀⠀⠈⠉⠀⣿⣿⡿⣾⠷⠄⠀⠀⠉⠉⠃
⠀⠀⠀⠙⢆⠀⠀⠀⠀⢀⣿⣿⣿⣻⢯⠛⠁⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠈⠑⢦⣀⣠⣿⣿⣿⣿⡏⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠿⠿⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣶⣆⠿⠿⢾⣰⣷⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣾⠶⠋⠁⣄⠀⢀⣆⠀⠈⡙⠢⣿⣶⣀
⠀⠀⠀⠀⠀⠀⣤⠞⠋⡅⠀⣴⠀⢉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡽⠁⠀⠀⠀⢻⣦⣾⣿⣤⣾⠁⠀⠈⢫⣡⡄
⠀⠀⠀⠀⢀⡞⠁⠀⠀⢻⡾⣿⣶⡏⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢽⡿⠀⠀⠀⠀⢶⣼⡿⣽⣝⢿⣧⠀⠀⠀⠀⢻⣿⠅
⠀⠀⠀⠀⣼⠁⠀⠀⢸⣿⣿⡷⠻⣷⠀⠀⠀⢸⡄⠀⠀⠀⠀⣐⣶⡃⠀⠀⠀⠀⣸⣿⡟⣾⠉⠌⢻⡅⠀⠀⠀⢸⣶⣂
⠀⠀⠀⠀⢿⠀⠀⠀⣾⣿⡈⢁⢧⣾⡆⠀⠀⢸⡇⠀⠀⠀⠀⠨⠿⡇⠀⠀⠀⠘⣿⣿⣤⠀⡌⠢⣾⣏⠀⠀⠀⢸⠿⠇
⠀⠀⠀⠀⠸⣆⠀⠀⠘⠛⢻⣦⣶⣿⡀⠀⢀⡾⠀⠀⠀⠀⠀⠀⣻⣿⡀⠀⠀⠀⠻⠿⠛⣷⣠⣶⣿⡇⠀⠀⢀⢼⣿⡁
⠀⠀⠀⠀⠀⠘⢦⣀⠀⢀⣼⣿⣿⠇⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢋⣵⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⠈⠀⣀⣮⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠿⠿⠿⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⢷⣤⣀⣠⣿⣿⣿⣿⣯⣤⡚⢾⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠻⠋⡿⣿⢿⠙⠟⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣭⣯⣭⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⣤⣄⠰⣿⣿⣿⡷⢀⣤⣄⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡆⣾⠀⣼⠃⡀⠈⡧⠉⢻⠋⠡⡏⠀⡄⢻⡄⢸⡆⣦⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠓⠘⠆⠹⣄⣙⣉⣁⡴⠋⠣⣄⣉⢉⣁⡼⠁⠜⠐⠃⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠏⠙⠦⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡠⠞⠉⠿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⡅⣴⢚⡋⠙⠒⠮⣾⠁⣈⡇⠀⣀⠄⢄⡀⠀⣏⡀⢹⡮⠖⠚⠉⣛⢲⡄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠦⠞⠀⠀⠀⠈⠓⠾⠖⠚⠁⠀⠀⠙⠒⠾⠖⠋⠀⠀⠀⠘⠦⠞⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡴⠚⠛⠢⣄⡴⠒⢦⠀⡴⣋⣅⡀⠈⠑⢄⠔⠉⠀⣀⣍⡳⡄⢠⠖⠲⣄⡤⠚⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠳⠼⠂⠀⠈⢧⣈⣋⠼⣇⠁⠀⣳⠀⠀⠀⠀⠀⢰⡃⠀⢁⡿⢌⣋⣠⠏⠀⠀⠺⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢾⡭⢾⡩⣍⢲⠋⠭⡉⢢⡴⣛⡉⠛⠢⡀⡠⠚⠉⣙⡳⣤⠊⡩⠍⢳⢊⡭⣹⠮⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠳⠴⠃⠘⢧⣁⡽⠀⠀⠙⠁⠀⠸⣅⣡⠟⠀⠳⠴⠋⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠠⠵⠀⠀⠀⣒⡇⠀⠀⠀⡠⢀⠀⠀⠀⡣⢄⡁⠀⠀⠠⠀⠆⠀⠀⠈⣟⠃⠀⠀⠐⠷⠄⠀⠀⠀⣿⡼⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡀⠀⠀⢀⡤⠄⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⢄
⠀⠀⠀⠊⠀⠀⠀⠐⠲⠒⠀⠀⠈⠘⠁⠀⠀⠀⡫⠩⠀⠀⠀⠑⠆⡦⠀⠀⠀⠀⢱⠀⠀⠀⡖⢚⠂⠀⠀⠢⠉⠵

⠀⠀⣒⠶⠒⠀⠀⠀⢈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠓⡞⠀⠀⠀⠀⠦⠄⠀⠀⠀⠐⡊⠀⠀⠀⢀⠀⠀⠀⠠⠄⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠒⠺⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣩⣂⡍⠀⠀⢐⠄⣟⠀⠀⠀⢤⡄⠀⠀⠀⠒⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠈
⠀⠀⠀⠉
⠀⠀⢠⣤⡀⠀⠀⢠⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢆⠀⠀⠀⡠⠀⠀⠀⠀⣤⡄⠀⠀⠀⠠⠆
⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠐⠐⠀⠀⠀⠀⠷⠂⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢠⡀⠀⠀⠀⢀⣁⣁⠀⠀⢠⡬⣅⡤
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⠆⠀⠀⠀⠐⠿⠑⠀⠀⠀⢆⠠⠀⠀⠀⡄⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉

⠀⠀⠀⢠⡄⠀⠀⠀⠂⠀⠀⠀⠠⡰⠂⠄⠀⠀⠀⠛⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠀⠐⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠱⠀⠀⠀⠘⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈

⠀⠀⢄⣠⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠒⡀⠀⠀⢦⡴⠀⠀⢆⡐⠀⠀⢶⡆⠀⠀⠀⢀⠄⡀⠀⠀⢺⣟
⠀⠀⠀⠰⠆⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠟⠀⠀⠀⠀⠃⠀⠀⠊⠐⠀⠀⠉⠑⠚⠀⠀⠁⠀⠀⠀⠀⠘⠿
⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⢤⠆⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴
⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠈⠀⠀⠀⠀⠓⠂⠀⠀⠨⠁⠀⠀⠀⠆⠀⠀⠂⠀⠁⠀⠀⠁⠐⠀⠀⠀⣾⣻
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡀⠀⠀⢠⡄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠰⣀⠜⠀⠀⠚⠓⠀⠀⠀⡆⠀⠀⢈⡈⠀⠀⠀⠀⠹⠀⠀⢐⡊⠀⠀⠈⡍⠀⠀⠠⢀⡀⠂⠀⠨⠉⠛
⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣉⣹⣸⠀⠀⢈⠁⠀⠀⠀⡁⠀⠀⠀⣓⠀⠀⠀⢦⠴⠀⠀⠤⠤⠀⠀⢀⠀⠁⢀⠒⡆⠉⠒⡆⠀⣖⣱
⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁
⠀⠀⣤⣠⣀⠀⠀⢠⡦⠀⠀⠀⢠⡄⠀⠐⠀⠐⠀⠀⠀⣤⡀⠀⢠⡄⠀⠀⠰⠤⠀⠀⠀⢀⠆⠀⠀⠀⣶⢰
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠁⠁⠀⠀⠛⠀⠀⠀⠊⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠠⠄⠀⠀⠀⡤⢤⠀⠀⢀⡄⠀⠀⠀⣤⠀⠀⠀⡤⠤⠀⠀⠀⢀⠀⠀⣤⣦⡄⠀⠀⢠⣦⡀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠂⠀⠸⠹⠆⠀⠀⠀⠐⠀⠠⠔⠌⠁⠀⠻⠿⠃⠀⠀⠀⠹⠃⠀⠀⢸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⠲⢄⠀⠀⢀⢀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠴⠂⠀⠀⠀⢀⠀⢀⠀⠀⠀⠠⢴⣿⡦⠄⠀⠀⢀⡤⣀⠀⠄⠀⠀⠀⢤⡈⡣
⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠁⠼⠧⠐⠀⠀⠀⡠⠊⠦⡀⠀⠀⠀⢬⣉⡤⡄⠀⠀⠀⠨⠀⡍⠀⠀⠀⠀⠸⠭⠁⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠚⢽⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠈⡤⠆⠀⠀⠀⢠⡀⣀⣐⡠⠀⠀⠘⠀⡼⠛⠋⠀⠀⠀⡤⡻⠣⠀⠀⠀⠐⢇⢐⢀⡀⠀⠀⠈⠀⠀⠦⡀⠀⠀⠠⠀⣀⣹⡄⠀⠀⠀⡁⠠⠗⢄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠃⠀⠀⠀⠀⠈⠉⠚⠃⠀⠀⠀⠁⠀⠐⠇⠀⠀⠀⠘⠀⠐⠀⠀⠀⠘⠊⠁⠈⠉

⠀⠀⠀⢀⣤⠤⠐⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠓⣶⠖⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⡠⠾⠀⠀⠀⠀⠖⠀⠒⠀⠀⠀⢀⡀⣰⡄
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠄⠐⠠⡄⠀⠀⠀⢀⠐⠉⡁⠀⠀⠀⣀⣯⣄⡀⠀⠀⠀⠀⡐⠈⠂⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢀⣁⠂⠀⠀⠀⠈⣀⣡⣬⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⡁⠀⢘⠀⠀⠀⠀⢦⠀⡵⠂⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⡴⠷⢶⠄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠒⡔⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠋⠚⠊⠁⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⢤⡤⣄⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠒⣤⠂⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⣤⠒⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢠⢤⠄⠀⠀⠀⠀⠠⠷⡄
⠀⠀⠀⢀⡀⠋⠄⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⢈⠋⠁⠀⠀⠀⠀⠸⠀⠆⠀⠀⠀⠀⢀⣵⡤⠀⠀⠀⠀⠈⠁⢄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠚⣒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡦⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣤⡰⠤⡁⠤
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⡀⠂⠀⠀⠀⠐⢀⡂⡀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠠⢺⠠⠀⠀⠀⠐⠹⠯⠌⠃⠀⠀⠀⠸⠄⠔⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠠⣀⠔⠁⠀⠀⠈⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠒⠖⠀⠀⠀⠀⠀⠊⠀⠆⠀⠀⠐⢠⡉⡅⠋⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠰⠈⠈⢁⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠂⠉⠲⠀⠀⠀⠀⠈⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣤⠐⠂⠀⠀⣄⠤⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠈⠟⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠒⠴⠀⠀⠀⣀⠀⣒⣄⠀⠠⣤⣄⣀⠀⠀⠀⣭⣬⡀⠀⠀⣴⠀⢠⡀⠀⠀⣔⣶⠀⠀⠀⠀⣀⡄⠀⠀⠀⢀⣠⠄⠀⠀⠀⣠⣤⠀⠀⠀⢠⣤⣤
⠀⠀⠐⠀⠸⠂⠀⠈⠛⠛⠛⠛⠀⠀⠀⠉⠀⠀⠀⠀⣯⣿⠃⠀⠀⠈⠀⠋⠀⠀⠀⠛⠛⠁⠀⠀⠀⠈⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠋⠛

⠀⠀⠀⣠⡶⠀⠀⠀⣄⣠⣤⡄⠀⠀⠚⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⣶⣶⠀⠀⠀⣤⣦⣤⠀⠀⠀⠀⠄
⠀⠀⠀⠉⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⠁⠉⠀⠀⠀⠛⠛⠛

⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⡶⡆⠀⠀⠀⠀⡔⠀⠀⠀⠀⠠⠞⠀⠀⠀⢤⠤⠂⠀⠀⣠⣤⣤⣤⠀⠀⢠⣶⡄⠀⠀⠀⡀⢀⡄⠀⠀⢀⣦
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠈⠁⠀⠀⠈⠛⠃
⠀⠀⠀⠀⡀
⠀⠀⠀⢸⢽⠃⠀⠀⢠⣤⣶⡄⠀⠀⢜⠉⣳⠀⠀⠀⡐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⡇⠀⠀⢠⣿⣷⡀⠀⣀⣃⣐⣠⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠛⠈⠁⠀⠀⠀⣿⣇⠀⠀⠀⠀⣿⠄⠀⠀⠠⣤⣤⠄⠀⠀⠀⢴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⣤⡴⠀⠀⠀⢰⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠔⠛⠂⠀⠀⠀⣀⡀⠀⠀⠀⣠⣰⣶⠀⠀⠀⢸⡿⠀⠀⠀⠘⠶⠣⠀⠀⠀⢨⠹⠃⠀⠀⠀⠺⠇⠀⠀⠀⠺⢷⣶⣤⠀⠛⠃⠰⠅⠀⠀⠸⠏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⡄⠀⠀⠀⣤⡤⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤
⠀⠀⠀⠿⠿⠗⠀⠀⢰⣿⣿⠀⠀⠀⢹⡴⠇⠀⠀⠀⡿⣟⠀⠀⠀⠐⢿⣆⠀⠀⠀⠾⠿⠆⠀⠐⠟⠟⠛⠻⠀⠠⠖⠴⠷⠀⠀⠼⠿⠷⠶⠂⠀⢸⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡸⣆⠀⠀⢸⠶⠿⠿⠆⠀⡷⠾⠿⠷⠀⢸⠶⠿⠿⠧⠀⣟⣻⣃⣻⡇⠀⠀⣾⣷⠀⢴⣷⡆⣴⣶⠀⣿⠀⠀⠀⠀⢀⣾⣫⣯⣫⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠙⠋⠀⠙⠙⠁⠉⠉⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡄⡀⠀⢠⣤⠀⢤⣤
⠀⠀⠸⠿⠇⠿⠇⠠⠿⠀⠸⠷⠄⠸⠆⠶⠰⠇⠀⠀⠀⠀⠀⠀⠀⠺⠂⠾⠂⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠂⠺⠆⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠻⢦⡄⠀⠀⠀⠀⠀⠠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠘⡏⢸⡁⠀⢀⣣
⠀⠀⠀⠀⠀⠀⢠⣾⡆⢀⡖⠠⠄⠀⡀⠀⠀⠁⠀⠀⣀⠘⢳⠀⠀⣄⠀⠠⠶⡴⠀⠀⢲⠂⠀⠐⡀⠨⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⠃⠀⠀⠴⠀⠀⠀⠀⠀⢦⠹⠁⠈⠚⠣⠈⣃⣄⠀⠀⠀⠀⠘⠀⠀⠀⠱⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⠁⠀⠀⠀⠀⡀⣏⠈⠁⠀⢀⠀⠂⠐⠍⣉⢀⠀⠀⠀⠀⠀⠁⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⠀⠉⠀⠂⠀⠒⠀⠀⡂⡄⠀⠙⣼⠀⠀⠃⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡄⠠⡆⠀⠀⠼⠀⢀⠀⡀⢁⡄⠀⠘⣡⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠎⠀⠀⠒⡀⠀⡄⠀⠐⠀⠀⠀⢰⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠈⠐⠠⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢦⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢲⠂⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠶⠀⠀⠀⠀⠀⠀⡠⠀⠀⢨⠀⠠⠈⢀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⠀⠂⢀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣸⠀⠀⠀⠀⠀⡈⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⣀⡀⠀⠀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠁⢠⡤⠦⠆⠨⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢤⠀⠀⠐⠏⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠐⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠄⠈⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⠀⠀⡀⠄⠀⠀⠀⠂⠠⠈⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⠛⢄
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢄⡁⠀⠐⠀⠀⢄⡀⠔⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠁
⠀⠀⠀⢀⠀⠰⠄⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠈⠘⠳⣄⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⣤⢁⡄⠀⠀⠀⣠⡶⠂⢠⡄⠁⠀⠩⠄⢠⡀⠀⠀⠀⠀⠲⣀⠨⣷⠀⠀⠀⢀⢄⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠐⡅⢴⠄⠀⠀⢸⡃⠄⠹⢤⡀⠢⠀⠀⠀⠀⠀⠀⠀⠂⡜⠉⠁⢸⠆⠀⠀⣒⠋⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄⠀⠨⣇⠀⠀⢤⠟⣡⠀⠀⠀⠀⠀⠀⠀⠜⠛⠂⠀⠜⢀⣴⠾⠁⠀⠀⠀⢠⠀⡀
⠀⡃⠀⠀⠀⢀⠈⠀⠀⠀⠀⡔⠹⢃⠀⠈⠠⠤⠔⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢉⠴⠈⢠⡄⠁
⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⢁⠀⢀⠠⠔⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠭⠐⠀⠋⠒⠀⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠠⡀⠉⠈⢉⡀⠀⢀⠁⠀⠀⠄⠠⠀⡄⠀⠁⠀⠀⠀⠀⠀⠔⠀⠀⠀⠄⢀⠀⠀⠐
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠠⠢⠀⠊⡠⠂⠀⠀⢁⠈⠀⠀⠴⠀⠀⠁
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠰⠉⠀⠀⠀⠄⠀⠐⠀⠀⠈
⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⢉⠄⠠⡋⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠙⠀⣴⠖⠒⠶⣼⡄⠀⠀⠀⠀⠀⠀⢠⣧⠶⠖⠲⣦⠀⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣱⠀⣛⠚⠀⠀⠈⢿⣆⠀⠀⠀⠀⣰⡿⠁⠀⠀⠓⡛⠀⣎⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡚⣿⣯⣁⡀⠀⠀⠈⢿⣧⠀⠀⣼⣿⠃⠀⠀⢀⣈⣽⣿⢓⡋
⠀⠀⠀⠀⠀⠀⢀⠔⠒⢄⠀⠈⠙⢻⡿⠛⠻⠷⢦⣤⡈⠛⢧⡼⠛⢁⣠⡴⠾⠟⠛⠻⡟⠋⠁⠀⡠⠒⠢⡀
⠀⠀⠀⢠⠤⢄⡇⠀⢐⠮⡄⠀⠀⠈⠓⠁⣀⠀⠀⠀⢿⣷⡜⢃⣾⡿⠀⠀⠀⡀⠈⠛⠁⠀⠀⢀⠵⡂⠀⢸⡠⠤⡀
⠀⠀⠀⠈⠁⠀⠙⠢⣧⣐⣠⣤⣴⠶⠿⣛⣛⣛⣛⠦⡀⢹⡇⠸⡏⢀⠴⣛⣛⣛⣛⠿⠶⣦⣤⣌⣂⣼⠴⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠾⠛⠋⠉⠁⠉⠉⢡⣤⣤⣤⣤⡌⠉⠁⠈⠉⠙⠛⠷⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣰⣿⣿⣆⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⢶⢞⡻⠛⠛⢟⠳⡶⢶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢹⡏⠀⣡⠋⠀⠀⠀⠀⠙⡌⠀⢹⡏⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠶⣿⡄⠈⠃⠀⡏⠀⢀⠀⠀⡀⠀⢸⠀⠘⠃⢠⣿⠾⠿⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢀⣐⣒⣒⣦⣽⣦⣄⠀⠻⡀⣿⠀⠀⣿⢀⠟⠀⣠⣴⣿⣶⣒⣒⣂⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣠⡾⠋⠉⠉⠉⠛⢿⡏⠀⠈⠀⠁⢻⠀⠀⡟⠈⠀⠁⠀⢹⡿⠛⠉⠉⠉⠙⢷⣄⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡇⠀⠀⠀⠒⣒⣶⡧⢀⣤⣶⣶⣦⡀⢀⣴⣶⣶⣤⡀⢼⣶⣒⠒⠀⠀⠀⢸⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡄⢀⣴⡿⢟⠉⣴⣿⣿⣿⣿⣿⠁⠈⢿⣿⣿⣿⣿⣦⠉⡻⢿⣦⡀⢠⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣩⣤⣮⣴⡶⠋⣸⣿⡿⣟⢠⣿⣿⣆⣰⣿⣿⣄⣻⣿⣿⣇⠙⢶⣦⣵⣤⣍⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⠗⣫⣿⣿⣿⣯⡄⠀⣿⡍⢽⡭⢻⣡⣾⣿⣿⣷⣌⡟⢥⡫⢩⣿⠀⢠⣽⣿⣿⣿⣝⠺⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⣿⠿⠿⣻⣿⣿⡏⠀⢿⣿⣿⣿⣎⡿⣿⣿⣿⣿⠿⣱⣿⣿⣿⡿⠀⢹⣿⣿⣟⠻⠿⣿⣟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⠕⣪⣽⡿⢟⣋⠀⣷⡄⠙⢿⣿⣏⣰⣿⣿⣿⣿⣆⣹⣿⡿⠋⢠⣶⠀⣉⡛⢿⣯⣕⠪⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢁⣾⣿⣵⣾⣿⡿⠀⠹⣿⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣴⣿⠏⠀⢿⣿⣷⣮⣿⣷⡈⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡿⢋⣽⣿⣟⣁⣤⣄⡈⢻⣿⣿⣿⣌⣉⠉⠉⣁⣩⣿⣿⣿⡟⢁⣠⣤⣈⣻⣿⣯⡙⢿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⣰⠟⣱⣿⣿⣿⣿⠟⠃⠀⢻⣺⣯⣿⣿⡇⢸⣿⣿⣿⣗⡟⠀⠸⠛⣿⣿⣿⣿⣎⠻⣆⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠃⣰⡿⠛⣩⣿⣯⣤⣾⣿⡌⠻⠿⢿⣟⡁⢈⣻⡿⠿⠟⢡⣿⣷⣦⣽⣿⣍⠛⢿⣆⠸⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⡟⠀⠀⠉⠉⢰⣿⣿⠟⠀⠰⣶⣿⣿⣦⣴⣿⣿⣶⠆⠀⠻⣿⣿⡆⠉⠉⠀⠀⢻⡀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⢠⡄⠀⠀⠀⢿⡏⠀⠀⠀⠹⣿⣿⠛⠛⡿⣿⠏⠀⠀⠀⢸⡿⠀⠀⠀⢠⡄⠘⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢾⡇⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⢸⡷⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣧⠀⢸⡇⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⢸⡧⠀⣼⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡘⣿⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⣾⢃⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⠿⣦⣀⠀⠀⠈⠻⣆⠀⠀⣰⠟⠁⠀⠀⣠⣴⠿⡷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣽⣦⣴⣯⣤⣴⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠶⠶⠶⣤⣀⣴⡇⢸⣶⣀⣤⠶⠶⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠶⢭⣷⣆⠰⢦⣍⣸⡃⢸⣇⣩⡴⠆⣰⣾⡭⠶⠶⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢦⣄⠒⡍⠉⠒⠒⢦⡉⠃⢸⡇⠙⣇⣸⠋⢸⡇⠘⢉⡤⠒⠒⠉⢡⠒⣠⡴⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠀⠹⡆⠘⠀⠀⢀⡏⠀⢀⣘⣓⣦⡌⢡⣴⣚⣃⡀⠀⢹⡀⠀⠀⠃⢰⠏⠀⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⢧⣸⠇⠠⠀⠀⠸⠗⢋⣩⡭⠭⢭⣭⣭⡭⠭⢭⣍⡙⠺⠇⠀⠀⠄⠸⣇⡼⠃⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣈⠀⢀⡀⠁⠀⠀⠀⢀⣀⣰⣯⠀⠀⢀⡾⠁⠈⢷⡀⠀⠀⣽⣆⣀⡀⠀⠀⠀⠈⢀⡀⠀⣁⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣡⠞⣻⠁⢀⣠⠶⣚⣩⣭⠄⠀⠀⠀⠺⡅⠀⠀⢨⠗⠀⠀⠀⠠⣭⣍⣓⠶⣄⡀⠈⣟⠳⣌⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣡⣆⢸⡴⢋⡴⠚⢩⠟⠁⠀⠀⠀⠀⠀⢹⡀⢀⡏⠀⠀⠀⠀⠀⠈⠻⡍⠛⢦⡙⢦⡏⣰⣎⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣼⠃⢹⡌⢡⡟⠁⠀⡏⠀⢠⣤⣤⣄⡀⠀⢈⡇⢸⡁⠀⢀⣠⣤⣤⡄⠀⢹⠀⠈⢻⡌⢡⡏⠘⣧⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠻⡟⠀⠀⠀⢿⠀⠀⠷⣌⠻⣷⣄⠈⠃⠘⠁⣠⣾⠟⣡⠾⠀⠀⣿⠀⠀⠀⢻⠟⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣀⠤⠤⣤⠀⠀⠀⡀⠘⢧⠀⠉⠒⠲⡌⣿⠇⠀⠀⠰⣿⢡⠖⠒⠉⠀⡼⠃⢀⠀⠀⠀⣤⠤⠄⣀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣥⢶⠀⡟⢰⡤⠤⠟⠀⢸⡆⠀⠀⠀⢱⠏⠀⠀⠀⠀⠹⡆⠀⠀⠀⢰⡇⠀⠻⠤⢤⡆⢹⠀⡶⣬⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡆⣇⠈⣇⠀⠀⠀⠘⢧⡀⢧⠀⣹⣠⣠⣄⣠⣤⣀⣇⠀⡜⢀⡼⠃⠀⠀⠀⣸⠁⣸⢰⡇⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡌⣧⠸⡀⠈⠢⣄⣀⡀⠈⠳⣤⠇⢣⡁⠹⣄⣰⠏⢈⡜⠸⣤⠞⠁⢀⣀⣠⠔⠁⢀⠇⣼⢡⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣾⣆⠳⣀⠤⢤⠀⠀⠀⠀⣿⠪⣐⠀⠀⢸⡇⠀⠀⣂⠑⣿⠀⠀⠀⠀⡤⢤⣀⠞⣰⣷⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⣠⣥⠀⠘⣆⢠⠀⠀⠘⢶⣶⣶⠶⠋⠙⠶⣶⣶⡶⠋⠀⠀⡀⣰⠃⠀⡬⣄⡉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡰⢋⣤⢸⡇⠀⠘⢶⡀⠀⠀⢸⣷⠂⠀⠀⠀⠀⠐⣾⡇⠀⠀⠀⡶⠃⠀⢰⡇⣤⡙⢆⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡏⢸⢸⡇⠀⠀⠀⠀⠠⡄⠈⢿⣶⣄⣠⣀⣠⣶⡿⠁⢠⠄⠀⠀⠀⠀⢸⡇⡇⢹⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⡞⣼⠁⣠⡴⢶⡆⢸⣁⣀⠀⠟⠻⣿⣿⠟⠻⠀⣀⣈⡇⢰⡶⢦⣄⠘⣧⢳⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣏⢸⡏⠀⢸⡇⣨⡄⢸⠀⠀⠀⠘⠃⠀⠀⠀⡇⢨⣅⢸⡇⠀⢹⡇⣹⠎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣝⢿⡇⠀⠘⣿⠁⣿⠘⡆⠀⠀⠀⠀⠀⠀⢰⠃⣿⠈⣿⠃⠀⢸⡿⣫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠹⠀⠸⣆⠙⠇⠀⠀⠀⠀⠸⠋⣰⠇⠀⠟⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⣆⠀⡴⠋⠙⢦⠀⣰⠟⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⠀⠀⣼⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⣀⣄⣄⢀⡀⠀⠀⣲⡀⠀⠀⠀⠲⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠉⠀⠀⢠⣄⠀⠙⠂⢀⠈⠀⠁⣉⠋⣷⡆⠀⠀⣬⠖⠠⣇⠀⠈⡲⠄⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣄⠀⠀⣀⠀⠀⠄⣆⢬⡼⠓⠀⢠⣰⡧⣀⣀⣻⣇⡀⠀⠀⠀⢀⠉⢀⠙⣄⠈⠉⡒⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⠀⣧⡄⡈⣥⢾⣜⡓⢉⣁⡀⠀⡀⠈⠁⠀⠀⠀⠈⢛⣁⠐⠤⠤⢀⡉⠁⠳⢽⡄⠀⡇⠀⠀⣷⣼
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⣶⣿⣦⣿⠿⢋⠁⡠⢈⣨⠍⣁⠐⠦⠀⠀⠀⠀⠀⠈⢥⡆⢀⠀⠨⡇⠢⣀⠀⣿⠢⣅⠀⠀⠹⣿⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠎⠀⣠⣿⡏⢱⢋⣴⠥⠐⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⡆⣷⢀⠈⠀⢹⠆⢺⣷⡀⢣⢹⣦⠞⢹⡆
⠀⠀⠀⢸⡄⠀⡄⠀⣸⠿⣸⠷⣿⠁⣀⢂⡂⣔⣬⣰⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⠓⠾⢬⣤⡈⢧⡑⣼⢠⣿⣦⣿⠁
⠀⠀⠈⡀⢧⣠⠓⣤⣿⢟⡟⣸⡿⠬⠋⠣⠑⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⠌⢳⣄⠸⡋⠙⢫⣷⣼⠁⢸⣿⠁⢰
⠀⢢⠀⢧⠸⣧⠑⣾⢧⡾⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠙⣿⡗⢾⣿⣊⣋⠄
⠀⠈⣧⢨⠃⠸⣿⣣⡾⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⣄⣿⣧⠸⣿⠈⣯⠆
⠀⠀⠘⣷⣀⠀⢻⣿⡡⣺⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⢻⣿⠀⣿⣇⡳⠂
⢦⡀⢰⡛⣿⣦⣾⣯⣠⣿⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠹⣿⠳⣿⣧⣟⠁
⠈⢷⡌⡾⠰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣱⣿⣧⣿⣿⠃
⠀⠈⢷⡸⡇⢸⣿⣿⠁⣀⡀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⣿⠇
⠀⠀⠘⣿⠷⣸⣿⣿⠘⡿⠛⡸⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⠀⠈⠣⣼⣿⣿⣿⣆
⠠⣼⡇⣹⣯⢸⣿⣿⡏⠀⠐⣮⣿⢅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢷⣫⣴⣶⣼⣿⣿⡇⢸
⠀⢨⣟⡵⢻⣿⣿⣿⣇⠀⢐⡫⢷⢝⡂⠀⢄⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣷⡋⠡⣼⣿⣿⡇⢸
⠀⠀⢻⣫⠌⢻⣿⣿⣿⡆⠀⢩⠽⣝⣃⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⡂⢀⣿⣿⣿⡃⣾⠀⢸⠁
⠀⠀⠈⠧⣞⢄⢹⣿⣿⣿⣄⠈⠬⣯⢲⣵⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢽⣿⠒⣾⣿⣿⣿⣶⠃⠀⠅
⠀⠀⠀⠀⠻⢎⢔⣿⣿⣿⣿⣦⠨⣧⣾⣿⢓⣂⣤⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣯⣄⠀⡄⠀⢀⣦⣄⢺⣿⣃⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢏⣿⣿⣿⣿⣿⣷⣾⣿⠻⠛⢻⣟⣿⣿⣤⣤⠀⠀⠀⢀⠀⠀⠐⡩⣻⣽⠇⡇⣇⡼⣻⠏⡽⢷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣿⣿⣷⣬⣧⣼⣽⣽⣿⣿⣀⠀⣈⣄⣄⣀⣈⡴⠖⠓⣚⡛⠛⣿⣾⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣤⣀⡀⢹⣿⣟⠁⠀⠀⠀⡀⢀⠌⠋⠙⠻⣧⡊⠁⢀⣅⠚⢻⣛⣠⣿⣿⣿⣿⣿⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⢿⣯⣭⣭⠾⢿⣤⣀⢀⠠⠊⢀⣱⡤⢶⣿⠖⡛⠛⠋⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣿⣿⣧⣼⣾⣾⠾⠷⣦⠾⡉⠐⢣⡏⠀⠀⠀⣈⡥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣙⣇⣀⣜⣁⣀⣈⣠⣎⣈⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠰⠆⣀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡁
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠛
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⣠⣿⣆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢶⣾⠀⠀⠀⠀⠀⠀⢀⣜⠻⣦⡉
⠀⠀⠀⠀⠀⠀⠀⢇⠇⠀⠀⠀⠛⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠟⠃⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⢠⢻⣄⠀⠀⠀⠀⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠤⠜⠀⠀⠀⠀⠀⠀⠀⢠⡜⢦⡰⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠙⠶⠛⠗⠀⠀⠘⢧⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⣧⡃⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⢇⡈⡄⠀⠀⠰⡅⠙⢈⠇⠀⠀⡀⠀⠀⠀⠀⣔⢣⣸⠂
⠀⠀⠀⠀⠀⠀⠈⠓⠙⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠄⠀⠀⠀⣠⣄⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢠⠾⣏⡄⠀⠀⣠⠃⣨⠀⠀⢀⡾⢿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⡰⠀⠀⠀⣞⣳⡖⠂⠀⢀⣷⡡
⠀⠀⠀⠀⠀⠀⠈⠓⠛⠃⠀⠀⠉⠐⠁⠀⠀⠀⠓⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠋⠁⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠻⢣⠀⠀⠀⠀⠀⠄⠀⠀⣼⡟⣷⠀⠀⠀⢀⠱⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⠀⠀⠈⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⢀⡜⣷⣾⠀⠀⠀⢠⠀⠀⠀⠀⢠⡞⢁⡀⠀⠀⢀⠀⠀⠠⠄⠀⢞⡵⣋⠀⠀⠀⠈⠁⠀⠀⠀⠠⡎⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠆⠘⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣇⠀⠀⣿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣀⣠⣦⡀⠀⢀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠙⢉⡟⠁⠀⠀⠀⠀⢤⠀⠀⠀⣷⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⢰⣤⣠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡄⠀⢰⣿⡇⠀⠀⢠⠀⠀⠀⣀⣂
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢰⠛⡚⣅⠀⠀⠀⠀⢸⣿⡯⠀⠀⡞⠃⠀⠀⣿⣧⠀⠀⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠻⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⢶⣀⠀⠀⠀⠀⠹⡿⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠄⠈⢆⡀⠀⠀⠐⢍⣣⡀⠀⠻⠿⠿⢷⣿⣽⠄⠀⠘⠀⠶⠀⠀⠀⠄⡠⠀⠀⠢⣄⣠⡆⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠁⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠖⠛⠇⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠀⢈⣴⠛⣹⣤⠀⠀⠀⣠⠖⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡩⠘⠁
⠀⠀⢠⠀⠀⠀⠀⠀⢼⣦⡄⠀⠀⠀⠀⠈⢹⡿⣿⡇⠀⠀⢀⣒⣀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠀⠀⢰⠶⠶⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠶⠦⠄⠀⠀⠀⣅
⠀⠀⠀⠀⠰⣛⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠛⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⣞⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠈⠁⠀⠛⣀⣠⡤
⠀⠀⠀⠀⠀⠉⠍⠀⠄⡀⠀⢀⡀⠀⠀⠀⠠⠌⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣉⠆⠀⠀⢉⣤⠖⠉⠛⠛
⠀⠀⠀⠀⠀⠒⣂⠛⣦⣮⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⢀⠀⠢⠐⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠻⢛⣾⣿⣯⣠⣫⡕⠂⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⢣⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠠⠞⢡⡄⠀⢄⣀⡀⣀⠑
⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⡾⠛⢻⣏⠠⡀⠀⠔⠀⠀⠀⠀⠀⠐⢀⢀⡀⠀⠀⠀⠀⠁⡴⣦⠀⠀⠀⠀⠀⠀⠀⣀⡶⠉⡟⠧⠎⠙⠉
⠀⠀⠀⠀⠀⠀⠈⠁⣿⣠⣘⣟⡳⠏⠰⠄⠀⠔⣣⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠷⡄⣀⠀⢤
⠀⠀⠀⠀⠀⠠⠀⠀⢈⣹⣦⣤⣿⡤⠀⠀⠄⠸⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠘⠀⠀⠀⠀⠀⠀⢂⣠⣴⡆⠀⠴⠷⠖⠒⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⢟⣳⣘⠻⠎⠀⠲⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠉⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠈⠛⣛⣙⣃⠀⠰⢿⡎⠦⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢣⠀⠀⠀⠀⠀⠐⣉⠛⡉⠹⠂⠀⣸⣈⣀⡄⢠⠀⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠙⣯⣽⠀⠀⡿⣷⡀⢂⠀⠀⠀⡀⠀⠀⠀⠿⠐⠧⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡼⠃⠐
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⢹⡆⠀⠐⠋⠁⠈⠀⠀⠘⡅⠀⠀⠀⡀⠀⡀⠀⡄⠀⢀⡀⢀⣀⠠⠤⠄⠒⣀⠀⡌⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠙⢦⣤⣤⠤⠤⠤⠒⠀⠀⠀⠠⠀⠓⣈⡁⠴⡿⠀⠈⠉⠫⡉⠁⠂⠠⣤⡴⠶⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠘⠲⠆⠀⠀⢀⣀⠀⠊⢀⡜⠋⢠⠙⠋⠀⠦⡄⢀⡀⠉⠀⢀⠀⡀⡀⠤⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⢈⠀⠢⢉⡙⠏⡯⢉⣐⢀⠘⠄⠙⠒⢤⡀⠈⠁⢀⡀⠄⠂⠀⠀⢀⠀⠀⠁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠄⠤⠊⠀⠀⠀⠀⠀⢀⠀⠀⢰⡏⣳⣆⣸⣿⠄⠀⠐⠄⠀⠀⠉⠀⠛⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣉⣩⣠⣿⢀⠀⢀⠄⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠈⢀⡤⠀⠀⠀⠀⠐⢻⡿⠥⢄⣈⠛⠭⠉⠥⠀⢰⠎⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠾⣷⢶⠶⠤⠛⡦⠰⠖⠀⠘⠂⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠦⠀⢀⡀⠐⢁⣠⠶⡄⠀⠐⠒⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠠⠞⠉⠉⠉⠁⠀⡔⣴⡄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⣿⠉⣷⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢠⡄⠀⠀⠀⠀⠀⠛⢠⣼⠋⢲⣄⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡼⠀⠀⠀⢀⡀⠀⠀⢘⡃⠀⠀⢿⣧⢈⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢈⠁⠀⠀⢸⣏⠀⠀⢀⠀⠈⢣⠀⠀⠀⠂⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣾⠀⠀⠀⢨⡻⠄⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠈⠀⠀⡿⠀⠀⠀⠘⣵⠆⠀⠀⣿⠀⠘⠠⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⠤⠆⠀⠦⠆⠴⠒⠠⠿⠀⡜⠀⠀⠀⠀⣇⠀⠀⠀⠀⢹⠆⠀⠀⢹⠄⠀⠴⠆⠛⠷⠀⠤⠀⠐⠠⠂⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠇⠀⠂⠀⢀⣬⠀⠀⠀⡀⣿⠇⠀⠀⠘⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠋⠀⠀⠉⢁⠙⠋⠹⠀⠀⠀⢁⠀⢠⡀⠉⠁⠀⠀⠀⠀⢠⠀⠂⠀⠀⢆
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠘⠀⠾⠀⡀⢀⡆⠘⠆⢨⠧⠀⢀⠀⠀⠰⢜⡧
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡠⠀⠀⠠⠂⠁⠠⢀⠁⠜⠁⠀⢀⡁⠀⠈⠃
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣄⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠇⠀⠄⠀⠀⠆⠀⠋⠀⠈⠡⠀⠘⠉⠀⠀⠀⠀⠠⠀⠄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠠⠀⠈⠠⠊⠀⠀⠀⠀⠀⠀⠀⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢈⡷⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠒⠛⠊⢠⡀⠲⠶⢄⠀⠁⠲⠊⠑⢀⡀⠀⣀⠴⠾⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠆⠀⠀⠸⡅
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⡺⠃⠀⣼⡟⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠔⠂⠘⠈⡄⠉⠡⢅⠀⠄⠈⢁⣀⡀⠀⠀⢸⣧⡀⠀⠛⠄
⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣠⣤⠘⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠃⢤⣄⡀⠘
⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⢸⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⠃

⠀⣀⢀⡀⠀⠀⡐⢉⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠹⠀⠀⠀⠀⠙⢌⡣⠊⠁⠀⠀⠀⡎⠢⠐⠀⠀⢀⡀
⣶⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠐⠀⢃⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠑
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⢀⡀⠀⠀⢀⡴⣚⡂⣄⠀⠀⠀⢤⡀⠀⠀⢰⣄⠀⠀⣠⠦⢤⡀⠀⠀⠀⠀⠠⠄⠀⣠⠷⠀⠀⣀⡀
⠀⠰⠋⠀⠀⠀⠙⠮⠚⠁⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠈⢢⠀⠁⠈⠘⠀⠀⠠⢤⠀⡦⠀⠀⠀⠴⠋
⠐⠪⠅⠀⠀⠆⠀⠠⠆⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠣⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠺⡒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣤⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⡴⢦⣀
⠀⠀⢠⣤⣤⣤⣄⣄⣤⠀⠀⠀⢠⢳⢀⠚⣀⠞⡄⠉⢁⠉⠀⠀⣮⣠⣤⣤⠥⣵⡀⠀⢀⣀⡀⣀⣀⣀⢀
⠀⠀⠈⠀⠀⠀⢠⣥⣤⠀⠀⠀⠛⠒⠛⠐⠛⠒⠃⠀⠀⠀⠀⠀⠄⠀⠄⠴⠠⠠⠀⠀⠀⠉⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⣀⣀⡀⠀⠀⢀⢀⡀⡀
⢄⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⣾⣷⡇⠀⠀⠀⠀⢆⣦⡆⠀⠀⠀⠀⠀⠀⣀⡠
⠒⠋⠀⠀⠐⠩⠀⠬⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠱⠃
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠊⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢚⡱⡇⡓⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠊⡇⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⠈⠑⠊⠃⠀⠀⠌⢱⠆⢡⠀⠀⠉⠙⠙⠋⠉⠀⠀⢠⣏⣧⠀⠀⠀⠛⢣
⠵⠇⠀⠐⠀⠁⠂⠒⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠒⠐⡁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠓⠒⢒⠃⠀⠀⠰⠢
⠀⠀⠀⠀⠀⣈⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠄
⣉⡉⠉⠀⠀⠀⠀⠀⣠⠀⠀⠘⣀⡛⣤⠃⠀⠀⣶⣛⣶⠀⠀⢀⣀⢘⡓⣄⡀⠀⢀⡼⣻⠛⠀⠀⠀⠉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠠⠁⣀⣠⣂⠀⡤⠃⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⢀⠈⢸⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠃⠄⠀⠁⠀⠁⠏⠀⠀⡤⠂⣠⠾⠅⠀⠀⠊⠭⠋⠀⣈⠉⠛⢤⡀⣧⡀⠀⠘⣿⢃
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡟⠀⢁⠞⠁⠀⣢⠎⠀⣂⣴⡤⠊⠁⠀⠈⠈⠁⠀⠀⠀⣸⣿⣿⡧⠀⠙⢿⡄⠑⢀⣿⡈⣞
⠀⠀⠀⠀⠀⠀⡰⠃⡿⠀⢸⠃⣠⡶⢋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡄⠘⠀⠉⣷⣾⣿⣧⡿⡄
⠀⠀⠀⠀⠀⣰⠁⢰⡇⠀⣿⣟⠁⣰⣿⠡⠄⠀⠀⠀⠀⠀⠀⠒⠠⠤⣭⡽⠦⠤⡿⣿⣿⣿⣧⠀⠀⠀⣌⣿⣿⣿⡇⠘⡄⠀⡀
⠀⠀⠀⠀⢠⣿⠀⢸⣧⣰⡿⠈⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢦⡀⠀⠀⣿⣿⣿⡇⠀⢸⣠⠃
⠀⠀⠀⠀⠘⣿⠀⠀⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⣼⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⠃⠀⡊⣉⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣧⠀⢀⠀⠀⠀⠀⠀⢈⣽⡇⠀⣿⠀⠀⣄⡟⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠻⠿⡿⠶⡷⠶⠶⣤⣬⣾⣿⣸⣿⣶⡶⠿⡿⣿⠟⠋⠉⢙⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣧⣤⣤⣴⣷⣤⣧⣦⣀⠠⠬⣿⣿⠛⡲⣗⡂⢠⢠⣿⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣨⣿⣾⣿⠁⠀⠀⠴⠿⠿⢭⣭⡭⠀⠼⠿⠷⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠶⠒⠾⠖⠛

⣀⣠⣖⠀⢀⣆⠀⠀⣠⣴⠂⠀⠀⣠⣷⢠⣀⣀⠄⠀⣀⣌⠀⢠⣾⣷⣆⢠⡦⢿⡆⠠⡾⢣⡄⠀⠀⠆⠀⣦⠘⣧⠀⣼⢶
⠉⠁⠉⠀⠀⠋⠑⠀⠿⠇⠀⠀⠀⠛⠃⠀⠋⠙⠀⠈⠹⠅⠀⠀⠻⠟⠋⠘⠛⠛⠃⠙⠒⠛⠀⠀⠀⠀⠀⠛⠲⠋⠀⠙⠟
⣶⣀⣤⠀⢤⣄⠀⠀⢀⡀⡆⢠⣆⣤⡄⠀⠀⡴⠀⠀⢀⡴⠂⠀⣤⠶⣄⢠⡶⢶⡀⢠⣶⣦⠀⣠⡶⢤⡀⣀⣴⣄⠀⣰⡶
⠈⠋⠉⠀⠚⠉⠛⠀⠛⠿⠓⠘⠛⠛⠂⠀⠜⠁⠀⠀⠘⠁⠀⠀⠻⠺⠃⠘⠛⠿⠁⠈⠛⠛⠀⠸⠔⠟⠀⠻⠷⠿⠀⠻⠷
⢴⣶⣦⠀⢶⣤⡶⢠⣤⣀⣤⢠⣄⣀⡄⢠⣄⣠⡄⢤⣀⣤⠆⠀⡀⣂⢀⢠⣴⢶⡀⢠⣤⢶⡀⠀⢦⣴⠀⠐⣦⠆⠀⠲⣤
⠀⠩⠿⠀⠛⠉⠛⠀⠿⠻⠗⠀⠛⠹⠃⠈⠟⠻⠃⠺⠋⠻⠀⠀⠊⠚⠁⠸⠧⡾⠃⠸⠷⠾⠁⠀⠼⠿⠀⠠⠿⡄⠀⠲⠿
⢠⣄⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢠⣄⠀⠀⢠⡄⠀⠀⣠⣀⠀⠀⢠⣤⡄⠀⢤⣤⠄⠀⣄⡤⠀⠠⣤⡤⠀⢤⣤⡤⠀⡀⣀
⠘⠿⠟⠃⠘⠛⠀⠠⠘⣫⠀⠀⠹⡏⠁⠈⢽⠏⠁⠈⢹⠍⠀⠰⣺⣿⡇⠰⣾⣿⠀⠠⣼⡇⠀⠢⣿⣷⠀⢾⣿⡇⠈⠉⠏
⠀⢀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⢀⡀⠀⢀⢀⣀⡀⠀⣀⣄⠀⢠⣀⣀⠀⡠⠄⢀⠀⣀⠀⠀⠀⣀⣄
⠐⢺⡗⠀⢸⣾⣾⠀⣿⣿⣿⠀⡏⠦⣹⢀⣟⣽⣇⢸⣯⢝⡇⠸⢿⣿⠟⠰⢿⡿⠆⠸⣝⣮⠆⠙⠾⡯⠀⠙⠿⢦⠈⣹⣿
⠀⠈⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠈⠋⠀⠀⠉⠉⠀⢀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢰⡿⣿⡆⢿⣿⣿⠇⢿⣷⡿⠐⣏⠉⡽⠀⠀⢀⡷⢈⠉⠉⡗⠸⣧⣄⡀⠸⣿⡟⠁⠾⢶⡼⠁⢶⡶⠤⠄⢾⣿⣟⢰⣿⡿
⠀⠙⠉⠀⠀⠙⠁⠀⠀⠉⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⠀⢀⠀⠈⢁⡈
⢴⣷⣾⡆⢠⣼⣤⠀⠤⠐⠠⠀⣰⣶⡆⠀⡔⠒⡄⢠⣶⣶⡄⢰⠿⠟⠆⠀⠲⡦⡄⠘⢺⠿⡆⢴⠶⡿⠀⡶⣿⠉⠈⠷⢶
⠀⠙⠉⠀⠀⠋⠓⠀⠐⠀⠂⠀⠈⠉⠁⠀⠈⠋⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠄⠀⠦⠰⠄
⣀⣂⣀⣀⣙⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣿⣽⣽⣯⣿

⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢄⡀⠀⠀⠀⠀⢀⡀⣠⣤⣠⣀⡀⠀⠀⠀⢀⣤⠤⢄⠀⠀⠀⠀⠒⠢
⠀⠀⠀⠀⢁⣘⡀⠰⠀⠠⠀⡰⢋⠂⠀⠀⠀⢆⡀⠀⠀⠸⠑⠀⠀⢠⡆⠁⠀⠀⠀⢠⢠⢉⣳⠀⠀⠂⠄⠀⢂⠁⠀⠊⠄⡄⢨⠰⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠈⠓⠦⠤⣤⣤⠤⠤⠤⠊⠀⠀⠈⠑⠀⠐⠀⠀⠀⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⣶⡛⠄⠒⠂⠀⠐⠢⡐⠀⣴⡟⠉⢀⡀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢠⣧⡄⠀⠀⠀⣠⠏
⠀⠀⠀⠼⠑⠤⠈⠳⠀⠀⠀⠀⢀⡞⠃⠌⠀⠀⠻⡄⠀⠀⠀⢐⢌⣂⣐⡑⡁⠀⢠⡄⠀⠠⢀⠊⠦⢰⠀⠀⠀⠈⢋⠟⠀⠀⠚⣹⢁⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠭⠉⠍⠃⠀⠘⠀⠀⠐⡶⣷⠷⠟⠀⠀⠀⠠⠮⡤⠀⠀⢠⢿⡏⠀⢀⣾⡷
⠀⠀⠀⠀⠀⠀⣄⠀⡀⠀⠀⠀⠠⡄⠤⣤⢕⡴⢂⠴⠀⠀⠀⠀⡄⢠⢀⠀⠀⠀⠂⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡼⠀⠀⠀⡾⠁
⠀⠀⠀⠃⠵⠂⠄⠱⠌⠀⠀⠀⠀⡘⠗⢮⣩⠔⠟⢆⠀⠀⠀⡗⠈⠩⢯⠀⠘⣤⠀⢠⠊⠅⠦⠒⠚⠒⠴⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⠑⠀⠀⠓⠀⠀⠈⠀⢰⠠⠤⢐⣴⠀⠉⠀⠀⠀⠛⠀⢠⠀⡀⡤⠀⠀⢀⣠⠄⠀⢀⠄⠀⠀⣠⠂
⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⣉⠀⠀⠀⠀⠀⠀⠀⠈⢫⠞⠁⠀⢀⣾⣇⠀⢠⣮⡤⠀⠐⣻⠃
⠀⠀⠘⠿⠁⠀⠘⡶⠁⠀⢩⡏⠀⠀⢈⡥⠒⢢⡇⠀⠀⣄⣴⣠⠀⠀⣤⠀⠈⠈⠀⠘⠀⠀⠰⣤⣦⡄⠀⠀⠀⢰⠇⠀⠀⢘⣿⡇⠀⢀⣾⡅⠀⠰⣻⠟
⠀⠀⠶⠶⠆⠀⠰⠷⠀⠀⠚⠓⠀⠀⢌⡓⢚⣫⠏⠀⠀⠰⠿⠇⠀⢠⡀⡴⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠸⠇⠀⠀⢉⡟⠁⠀⠈⡟⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠀⢀⡄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢮⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⢀⠀⠈⠁⠠⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⣀⡴⡼⠁⠀⡠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⢀⠊⢹⣷⠻⡆⠸⣴⠏⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⡄⠰⠏⠀⠀⡀⠀⠀⠀⢀⠀⠀⣿⢷⣿⣿⣱⢿⣾⢷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠆⠀⠀⠀⠂⠀⠀⠁⠀⠀⢀⠈⠀⠀⡹⣾⣿⡿⠁⣾⢃⠌⣰⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⢀⡀
⠀⢸⣀⡆⠀⡀⠀⠀⠀⢀⠤⡀⠀⠑⠀⠀⠁⢿⣿⡇⢠⠛⡏⣴⠿⠒⠀⣴⠁⠀⠄⢠⠈⠀⠀⠈⠙
⠀⠐⠀⠀⠈⠇⠀⢀⠔⣋⡀⠄⠁⠷⠛⢷⡉⠷⣼⣷⡶⢻⣠⡿⣢⠴⠆⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠖⠈⣩⠖⠈⠀⠀⠀⠀⠀⠀⠚⠳⣦⣴⡬⠛⠛⠿⣵⠄⠀⠀⠛⠓⠚⣁⡴⠆⠰⢤⠤⠄
⠀⠰⡄⢰⠀⡔⠁⠀⠐⣦⡠⡄⠀⠀⠀⠀⠐⠉⣙⡕⠊⠉⠑⣖⠓⣞⡤⡶⠐⣊⠁
⠀⠀⠄⡌⡀⠀⠀⠀⠀⠈⠻⣶⣃⡀⠀⠀⠀⠀⡿⠀⠴⠀⠛⠹⡆⣉⢷⡄⢀⢈⠙⠢⣀⠀⠀⠀⣠⠄⠶⠀⡄⠀⠀⠀⠄
⠀⠰⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⢀⡝⠳⡄⠰⠟⠀⢿⣸⠎⠷⠆⢘⣋⡄⢹⠗⠂⠉⠐⠖⠒⠈⠀⢠⠾⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠀⠉⠒⣰⣷⡶⠟⠊⣠⣔⣻⣧⢈⣁⣙⣧⠳⣄⢦⣄⠠⠀⠉⣸⢇⣀⡀
⠀⢰⠆⡄⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⣼⠆⣠⣤⡀⢠⠞⢢⣴⢇⣼⠿⠿⡄⣉⡻⣹⡆⠈⠴⣉⣦⡰⠞⠁⠀⠈⢉⠆
⠀⢨⡂⡇⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⡧⠴⠇⠀⠳⢶⣢⣶⣶⣿⣷⠄⣀⠿⢿⠙⢦⣛⡶⡘⠗⣤⠸⣄⠀⠰⠆⠈
⠀⢠⠍⠀⠀⠈⠷⢀⠀⠀⠀⠀⠀⠈⢉⠅⡲⣓⢛⠶⠹⠃⠌⢹⡄⣀⠙⠶⡫⠄⠰⢇⠠⡏⢳⠚⣤⠀⠙⢿⡓⠳⣄
⠀⢠⠀⣆⠐⠀⣄⠀⠙⠙⠢⠄⣠⣖⣁⡴⢉⠋⡽⢛⢄⣼⢳⣷⡾⠙⠥⠀⡿⣤⡚⠁⠀⠿⠀⠃⢻⡉⠩⣈⠣⢤⣁
⠀⠈⠀⠉⠠⡀⠈⠀⠀⢀⠀⠉⠉⣠⠞⣴⠋⣼⠳⠟⣘⡣⠙⠁⢀⡐⠂⠤⠭⢙⣡⡴⠂⠀⠀⠙⢮⣹⠶⠺⢿⠂⣉⠓⡀
⠀⠀⢀⠀⠰⠁⠀⠀⠴⣿⠀⠀⠀⠀⠘⠀⠢⠙⠒⠎⠁⠴⠣⠾⣦⡀⠀⠀⠀⠈⠳⠶⢞⡉⣤⡄⡀⠈⢷⡒⠦⠀⢉⡜
⠀⠀⠈⠂⠀⠀⠀⠀⢠⣄⠙⠆⣰⡆⠀⠂⠀⠀⠈⠀⠀⠀⢰⡞⢻⣿⡧⠀⠀⠀⠀⠀⠈⡡⠟⠐⣻⣿⡀⠘⢦⠁⠈⠓
⠀⠈⠀⢀⠄⢰⡆⠀⠰⣿⠀⠘⠉⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠⡿⢇⣈⣿⣀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠏⠿⣄⠈⠼
⠀⠀⠀⠈⢀⣈⠹⠀⡀⠁⣾⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⢷⣄⣤⠙⣟⠻⡶⣦⣤⣄⣰⡁⠀⢸⣿⣿⠛⡇⢠⠀⠀⠀⡀
⠀⠀⡄⠀⠈⠟⠀⢠⡁⠢⠘⠄⠀⠀⠐⣦⠠⡀⠀⢀⠀⠀⠀⠀⢠⡁⣘⣇⠠⡏⡹⢏⡿⢻⢦⡏⠀⠀⠀⡀
⠀⠀⠁⢀⡈⠀⣀⣾⠑⠊⠀⠀⠀⠀⠈⠈⡠⡏⠀⠘⠀⠀⠀⠀⠀⣉⣹⠟⢻⡷⠇⠈⠱⡟⢬⣿⣶⠟⣿⣀
⠀⠀⠀⠸⠓⠁⠙⢉⠀⠀⠠⢦⠀⢠⡀⠄⠡⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⣼⢁⢦⡀⠆⢻⡆⣿⠻⣿⣽⣯⣶⡖⠀⠠
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⣇⠄⠻⢠⠀⢈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠤⠜⣡⡜⠀⠈⠀⡌⢛⣦⡁⠈⠉⢻⡎⣠⠀⠇
⠀⠀⠀⠀⢳⡤⠤⣄⡈⠀⠀⠈⠀⡀⣦⠈⢀⣊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠁⠻⡄⠀⠀⠸⡇⠙⠻⣦⣡⣤⢹⡗⠀⡀
⠀⠠⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠞⠉⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠙⠄⠀⠀⣷⢀⡀⠟⣀⠀⠀⠀⠀⠁
⠀⢰⣤⠐⠒⣋⠟⣚⣡⡾⠲⣟⣵⠞⣍⣓⣶⣤⣼⡵⠦⠠⠀⢠⠀⠠⠄⠠⠤⠆⠤⠤⠔⠉⣉⣠⣾⠷⢦⠟⠷⣦⡄
⠀⢸⡟⠛⠛⠟⠛⠉⠏⠑⠛⠋⠉⠀⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠙⠋⠴⠁
⠀⠸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀⡀⢘⡀⢀⠐⠀⡀
⠀⢠⡀⡀⢀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠁⠁⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣬⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣋⣴⣿⣿⣿⣿⣿⢟⣿⣯⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣽⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣒⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣟⠋⡽⠋⠉⢻⣿⡿⠿⣿⡿⠛⣿⣿⣿⣿⣿⡟⣭⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣓⣽⣿⣿⣿⣿⣇⠀⠀⣼⡿⠁⠀⢈⡇⢀⣼⡷⠿⢿⣿⣿⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠋⠈⠙⣿⣷⣾⣿⣷⣿⣿⠿⠿⠿⠋⢀⡴⢊⣽⣿⣿⡿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⣠⠴⠚⠙⠻⣿⣿⣿⣿⣿⣷⣶⡶⠋⠉⠉⠁⢿⣿⣿⣆⣣⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣦⡭⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⢀⠾⠒⠑⠀⠙⠳⣦⡀
⣿⣿⣿⣿⢟⣏⣴⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣴⡟⠃⠀⠀⠀⠀⠀⠙⣏⡠
⣿⣿⣿⡿⣻⣽⢿⡿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⠼⣠⠀⡀⠀⠀⠀⠀⢠⣿⢰
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⠟⣻⣿⣿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠁⡂⢘⣔⢀⡀⠀⢀⣤⠊⢜⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠌⠘⠈⠀⡯⠥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠥⢌
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠂⠐⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⢀⠀⠐⠀⠀⢠⢀⠀⠀⠀⠀⠁
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⡆⢀⠀⠀⠀⠀⠀⢠⡄⠠⣄⠀⠀⠠⠐⡆⠀⠀⢀⠄⠀⢰⠄⠀⠀⠀⠀⠀⠠⡆⠈⢦⡀⠀⠀⠀⣷⠀⠀⠀⠀⡠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡗⠁⠀⠀⠀⠀⠀⠠⡆⢀⡞⠀⠀⡇⠠⠁⠀⢠⡏⠀⠐⠈⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢱⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠂⢸⡇⢀⠀⠀⠀⠀⠀⠐⡗⠊⠉⣷⠀⡟⠀⡀⠀⢸⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⠀⢸⠇⠀⠀⡏⠀⠀⡤⠊⠙⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡇⣎⠀⣴⡄⠀⠀⠈⡇⠀⣠⠟⠀⣇⠀⡅⠀⠸⣧⡀⠀⡼⢲⡇⢀⠀⠸⣧⢸⡇⠀⣠⡞⢣⠀⠰⣇⠀⠈⢷⡀⠀⡰⠞⣇
⠀⠀⠀⠀⢰⡆⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⠹⠄⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠉⠀⢘⡇⠀⢀⡿⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⣀⠀⠀⠀⡾⠀⠀⡇⠀⢿⡌⠀⠀⠀⠀⣾⠁⠀⠈⣿⠀⠀⠀⠀⢠⠎⠀⣿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⣀⠀⠀⢰⡇⠀⠀⢰⡇⠀⠀⠀⠀⢻⠀⠀⡿⠀⠐⡗⠁⣾⠀⡄⠀⠀⠀⢻⡄⠀⠀⣿⠀⡄⠀⣰⠇⠀⠀⣏⠀⠠⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠩⡆⠀⢸⣆⠀⠀⣾⡃⡀⢀⡀⡰⠃⠀⠀⡇⠀⠀⡇⠀⣿⠀⣿⠀⠀⠀⠀⠛⠦⣰⠇⢰⠂⠀⢿⡀⠔⢠⡟⠀⣶⠀⠠⠋
⠀⠀⠀⠀⢀⣤⠀⠀⣼⠃⠀⢸⢰⡇⠀⠀⠉⠃⣠⡿⠀⠃⣼⠋⠀⠀⠀⠀⠃⠀⠀⡇⠀⠙⠀⣿⠀⠀⠐⠀⠀⠘⠁⠀⢸⠀⠀⠀⢀⠖⢹⠇⡀⣾⠁
⠀⠀⠀⠀⠘⠳⠀⠚⠁⠀⠀⠸⠞⠁⠀⠀⠀⠘⠟⠃⠀⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠳⠛⠀⠿⠘
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢻⡇⣰⠁⠅⢸⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⠀⠐⠁⠀⠀⠀⢠⠃⡇⠀⡤⣀⠀⠀⠀⠀⠀⠀⣽⠀⠐⣆⠀⠀⠀⠀⠀⡐⠀⠀⠶⣶
⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⣾⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⠀⡇⢸⡀⣿⠀⠀⠀⠀⠀⠀⣽⠀⠀⣿⠀⠀⠀⠀⢰⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡏⠐⡆⠀⢻⠺⡄⠀⠀⠀⠀⣸⡄⠀⠀⢸⡇⠀⠀⠀⠀⣻⠀⢿⡀⠃⡟⠀⡄⢲⡤⠀⠀⣿⠀⠀⣿⠀⡄⠀⡄⢸⡄⠀⠀⠀⢸⡇⠀⢠⡄
⠀⠀⠀⠀⠀⢸⠇⢀⡇⠀⢸⠀⣿⠀⠀⣧⡀⠘⠓⠦⡀⠸⣇⠀⠀⠀⠀⢸⡄⠀⠀⠐⡇⠀⡇⠸⢀⡇⠀⢿⠀⠀⣿⠀⠇⠀⡇⠀⠳⣄⡀⠀⠎⠙⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠄⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⡾⠀⠀⠀⠀⠻⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⠀⠀⠀⡧

⠀⠀⠀⠀⠀⠀⢴⠂⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠀⢰⠄⠀⠀⢀⡤⠀⠲⠀⠀⠀⠀⠀⢀⠠⠤⠀⣄⠠⠄⢰⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢈⠀⠀⢨⡇⣠⠀⣾⠀⠀⠀⢿⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⡇⠐⠂
⠀⠀⠀⠀⠀⠰⣯⡀⢀⡴⠋⡀⢀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠤⣬⡄⢠⡞⠀⠓⠈⣇⠀⠀⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⢸⡁⢸⡇⠀⢠⡄⠠⢄⣠⠃⠀⡆⢠⡄⠀⠀⢸⠀⠀⢹⠀⠀⠀⣯⠀⢺⡅⠀⠀⠀⣼⠃⠀⠐⠡⡀⠀⠀⠀⠀⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠋⠉⠀⠀⠀⠉⠁⠈⠉⠉⠀⠉⢹⡇⠀⠀⠈⠀⠀⣻⠀⠀⠀⢿⡀⠀⠉⠉⠀⠉⠀⣀⠀⠀⠀⣽⠂⣄⠀⠀⡏⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠉⠂⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢴⠁⡸⠁⠘⢷⡀⠀⠀⠀⠀⠀⣴⠁⣼⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⣷⠀⠀⢀⡄⡦⠀⠀⡿⠀⠀⢸⡇⠀⠈⣷⠀⠀⠀⠀⢠⠴⠄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⢀⠀⠀⠸⣇⠀⠀⠀⣿⠀⡆⠘⡇⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⡿⠀⡖⠀⣄⢸⡆⠀⠀⠀⠀⠀⡼⣇⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠈⠳⠀⠚⢧⠐⠆⠛⠀⠀⠀⠙⠦⠀⠘⠁⠀⠳⠄⠃⠀⠀⠀⠙⠆⠀⠚⠛⠤⠞⠁⠀⠻⠔⠻⠜⠃⠀⣀⠀⠀⣴⠃⠹⣄⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠁⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⠁⣾⠀⢠⡆⠀⠀⠀⠀⢶⡀⠀⠀⠀⣸⠇⠀⠀⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠀⡀⠀⠀⢸⠇⠀⠀⣰⡋⠀⠀⠀⢀⡀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⡇⠀⣅⣰⡶⠋⠀⠀⠴⠃⣹⠇⠀⠀⣼⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡎⡽⠁⢠⡎⣹⠀⠀⠀⠀⢠⣞⡟⠀⠀⣞⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⣤⣤⠀⠀⣠⠖⣉⠀⠀⢀⡶⠀⣴⠃⠀⢀⣾⣄⢀⣠
⠀⠀⠀⠀⠀⠀⡀⡰⠀⠀⣿⡇⣉⡃⠀⢀⡏⠀⣻⡁⠀⢸⣇⠀⠘⠀⠀⠈⢳⣿⠘⠁⠀⠀⠄⢀
⠀⠀⠀⠀⢀⡸⠀⠉⠀⠀⣿⡇⡟⠀⠀⠈⣧⠀⠞⠀⠀⢸⢟⠀⣧⣀⠀⠀⢸⣿⢀⠀⠀⠀⠈⠈⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠙⠓⠀⠀⠀⠘⠛⠋⠛⠃⠀⠀⠘⠛⠃
⠀⠀⡄⠀⢠⠢⠀⡠⠠⠀⡄⡀⠀⡆⡄⠀⠢⠄⠠⢠⠀⠀⠆⠀⢰⠀⠀⢀⠂⢰⠠⠀⢰⠀⠀⡄⠂⠀⡆⠆
⠀⠐⠎⠦⠸⠬⠀⠙⠄⠀⠷⠂⠀⠳⠄⠀⠆⠀⠰⠌⠀⠲⠹⠀⠸⠀⠀⠮⠀⠘⠒⠂⠘⠆⠀⠇⠳⠀⠗⠂
⠀⢀⠀⠀⠀⢀⠀⠀⡀⡀⠀⣀⡀⠀⠀⢀⠀⢀⡀⠀⠀⢀⡀⠀⡀⡀⠀⠀⣀⠀⢀⢀⠀⠀⡀⠀⠀⢀⡀
⠀⢨⠸⠀⠀⡆⠀⠀⡄⠁⠀⣇⢤⠀⢈⣂⠀⠀⣇⠀⠈⣜⠃⠀⢣⠁⠀⢣⣉⠀⢸⢣⠀⢀⡇⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⢠⠠⠀⢸⣐⠀⣄⠆⢠⣨⡀⢀⠴⠀⣏⠇⢰⠀⠀⢈⡀⢀⡇⢸⠄⢸⢀⠀⣨⠀⠀⣆⣄⣄⠀⠀⠀⢀⠆
⠀⠀⠁⠁⠀⠁⠀⠈⠀⠀⠈⠁⠈⠁⠀⠉⠀⠈⠀⠀⠈⠁⠀⠁⠈⠀⠈⠉⠀⠈⠀⠀⠉⠉⠁⠀⠈⠀⠀⠁
⠀⢠⣄⣄⢠⡰⠀⢸⡠⠀⠐⣆⠀⣃⠂⠀⡦⠀⠐⣆⠂⢆⢂⠀⢡⡂⠀⡆⡀⠀⡎⠀⢘⠂⠀⢰⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⡀
⠀⢀⠇⠀⢳⠀⣖⡀⢸⠂⠸⣤⠀⣟⠁⢄⠆⢸⡃⠠⡃⠀⡵⠀⢠⣀⠀⣄⡀⢦⠀⢸⡄⠀⡇⠠⢄⠀⡙⡁

⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⡄⢸⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠂⠑⠈
⠀⠀⠀⠀⠱⢵⣰⣄⣀⡀⢐⣁⣹⠀⢀⣀⣴⣰⠵⠅⠀⠀⠀⠀⠀⠀⠁⠘⠀⡔⠁⠀⠈⡆⠀⠀⢀⠄⢸⠀⠀⡄⡠⡀
⠀⠀⠐⠀⠀⡐⠥⡝⢹⠃⠆⢀⠀⠦⢻⠝⡥⠕⡀⠀⠐⠀⠀⠀⡀⠁⠀⠐⠎⡢⠀⠀⡰⠀⠀⠀⠸⠺⠂⠸⠇⠀⡀⠄
⠀⠀⠀⠀⡧⠀⠀⠈⠒⢻⠀⠼⡀⢸⠓⠊⠀⠀⠂⡅⠀⠀⠀⠘⢀⠀⠀⠀⣯⣆⢡⠎⠀⠀⣀⠀⣰⠺⠀⠀⠁⠀⡃⢄⣀⣀
⠀⠀⠀⠀⠈⢶⠮⢒⡤⠊⢂⠛⢃⠈⠣⡔⠢⢶⠎⠀⠀⠀⠀⠀⠀⠀⠰⠀⣉⡁⠰⠀⠀⠀⠡⡀⠉⠀⠀⢀⢀⠀⠑⠉⢀⠌
⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠐⠂⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⠈⢄⠘⠀⢠⠍⡡⠃⠀⠀⠀⠀⠱⡀⢠⠚⢳⡖⣛⠆⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠉⠀⠁⢠⠊
⠀⠀⠀⠀⣠⠥⠺⢤⡐⣀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣴⠀⣀⠀⠀⠀⠀⠑⠂⠐⠊
⠀⠀⠀⣻⠁⣒⡥⠒⠛⢠⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⢀⠺⣤⠚⢵⣼⡆
⠀⠀⠀⠋⠍⠁⠈⠀⠐⢸⠀⠀⠀⠰⠄⠀⠀⣀⣀⡀⠀⠀⠶⠀⠀⠀⡄⠘⣜⠀⡜⣀⠅⡂⠀⠀⡐⠄⢡⠤⢤⣊⡠
⠀⠀⠀⠀⠚⠀⠀⠀⠃⡘⠀⠀⠀⠦⠀⡔⢉⠄⠂⢌⠑⡄⠠⠆⠀⠀⢃⠀⠈⠉⠉⠁⡐⠀⠀⠀⠀⠀⢠⣘⣣⠀⠃
⠀⠀⠀⠈⠢⠄⢉⠠⠊⠀⠀⠀⠀⠀⠚⠂⠒⠀⠀⠐⠂⠚⠒⠀⠀⠀⠀⠑⠤⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣇⡀⠀⠠⣤⣀⠀⣴⠀⠀⣤⠀⣀⣤⠄⠀⢀⣸⡟⠇
⠀⠀⠀⠀⠀⢀⠴⠆⠀⢀⡀⢰⡟⢭⣿⠂⠀⠸⣿⣿⣿⡇⢸⣿⣿⣿⠇⠀⠐⣿⡯⢻⡆⢀⡀⠀⠠⠦⡀
⠀⠀⣀⠀⢰⡏⠀⠀⠀⢈⣻⣿⣇⠀⠀⠀⠀⠀⠟⠛⣿⡃⢘⣿⠟⠻⠀⠀⠀⠀⠀⣸⣿⣟⡁⠀⠀⠀⢹⡆⠀⡀
⠀⠀⠹⣿⣾⣧⢰⡿⢲⡈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⢁⡔⢿⡆⣼⣷⣿⠏
⠀⠀⠀⠈⣻⣿⣧⡀⡞⢏⢹⡆⢾⠿⠿⠿⢶⣄⣀⣼⡿⠁⠈⢿⣧⣀⣠⡶⠿⠿⠿⡷⢰⡏⡹⢳⢀⣼⣿⣟⠁
⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣗⣲⣄⠀⠀⠀⠀⠈⠻⣯⠀⠀⠀⠀⣽⠟⠁⠀⠀⠀⠀⣠⣖⣺⣿⣿⡿⠿⢿⣿
⠀⠀⠀⠀⠈⠀⠀⢳⣠⡝⠛⠿⠿⠿⠿⠷⠶⣦⣀⠘⢧⠀⠀⡼⠃⣀⣤⠶⠾⠿⠿⠿⠿⠛⢫⣄⡜⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⢿⣶⣶⣤⣙⢳⡘⡄⢠⢃⡾⣋⣤⣶⣶⡾⠿⠷⣶⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣴⡿⣿⣀⡀⠀⢿⠛⠉⠛⠻⣷⣷⣧⣼⣾⣾⠟⠛⠉⠛⡿⠀⢀⣀⣿⢿⣦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣿⣿⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠃⠁
⠀⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡀⠀⠄⠀⠀⠀⠀⠐⠿⠿⠀⠀⢸⣯⡀
⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⣄⢀⣄⢀⣤⢀⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈
⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠀⠀⠀⠀⢮⠇⠀⠀⠐⠁⣰
⠀⠀⠀⠀⠀⠉⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠠⠀⠔⢢⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠛⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠸⠤⠼⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠄⡄⡀

⠀⢠⡄⠀⣤⠀⠀⠀⠀⣠⣤⡄⠰⠶⠀⢀⠀⢀⠀⢀⠀⢀⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠹⠹⠀⠈⠀⠀⠄⠁⠰⠁⠰⠖⠁⠀⠀⠀⠀⠸⠿⠀⠞⠀⠿⠀⠐⠀⠐⠂⠀⠂⠀⠠⠀⠂⠀⠞⠀⠲⠖⠐⠶⠂⠀⠂⠀⠀⠐⠀⠀⠐
⠀⠀⠀⢠⣤⠀⢀⣀⠀⡄⠀⠀⠀⡄⠀⣤⠀⣄⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⢀⠀⢠⣤⠀⣀⠀⣤⠀⠀⠀⠀⠀⡤⡄⠠⠀⠀⡀⢀⡀⢀⡄⠀⣠⠀⡠⠀⣤
⠀⠈⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠈⠀⠐⠀⠲⠀⠀⠀⠇⠰⠁⠘⠀⠀⠀⠘⠀⠪⠀⠀⠠⠀⠸⠇⠀⠚⠀⠐⠂⠀⠐⠂⠀⠐⠀⠨⠒⠀⠐⠂⠀⠐⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⠒⠒
⠀⢀⠀⢀⣄⢀⣤⠀⡠⡀⢀⡄⠀⣀⠀⡀⠀⡀⢠⡄⢀⡀⠀⠀⢀⣄⠀⣀⡀⢀⢀⢀⣤⡀⣠⡀⢀⣄⠀⠀⠀⠀⠀⠀⡤⡄⠀⡀⠀⢀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠈⠀⠀⠁⠀⠈
⠀⠰⠆⠀⠨⠆⠐⠖⠐⠿⠀⠐⠀⠐⠂⠀⠲⠀⠐⠂⠐⠗⠀⠾⠂⠸⠇⠀⠷⠀⠐⠂⠐⠂⠐⠗⠀⠿⠀⠺⠆⠰⠿⠀⠿⠇⠰⠇⠀⠖⠀⠺⠂⠐⠗⠀⠒
⠀⣠⡄⢀⡀⠀⣄⠀⣠⠀⣀⡀⢀⡀⢠⡄⢤⠄⠀⠀⠀⠀⠀⢠⠀⢀⣠⠀⢀⠀⠀⢠⠄⢄⠠⠀⠄⠀⢀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠄
⠀⠈⠁⠈⠁⠈⠉⠀⠉⠀⠈⠁⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠁⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⢶⡆⠀⣸⡇⠀⣸⡂⠀⢿⡆⠀⣼⡀⠀⠀⠀⠰⣿⡇⠰⠆⠼⠆⠰⠀⠻⠂⠻⠟⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⡀⡀⠀⣀⡀⣀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⠀⠀⠀⠀⣠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢋⣄⣠⣷⠤⠞⠒⠛⠋⠥⠤⠬⠤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠁⠀⠀⠰⠆⠀⢀⠛⡀⠄⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣩⠔⠀⠠⣴⠀⡀⢠⡶⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⣠⣾⠝⠀⠀⢀⠀⠐⡴⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢡⡖⠀⠀⠀⠀⣄⠉⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡁⢠⡌⠀⠺⠧⠀⠀⢸⣀⡓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣀⠀⢧⠀⡀⠠⣾⠦⣬⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢺⢁⡏⠃⠈⡄⠁⠄⢠⠀⢻⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠲⢸⡇⠈⠁⡀⠀⠹⠀⠀⣀⠀⢸⢠⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⢸⠇⠶⠁⠁⣀⠀⢀⠀⠋⠀⢀⢠⡟⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢾⢘⣦⠠⡆⠙⠀⠀⠀⣤⠀⣨⡘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣾⡈⣁⠶⠆⠛⠀⢀⠀⠀⠸⠝⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡉⠣⣴⠰⠶⢌⠡⢀⠀⢪⡸⡄⠈⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠡⠘⠔⢦⡓⠲⢤⢤⣛⣃⣤⣽⢿⣄⢲⣬⡅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⢀⠀⢸⡀⢫⡐⣦⠠⡤⡄⣠⡍⣹⣿⣆⠻⣧⠀⠑⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄⢠⣴⡇⠚⣠⣤⣤⡍⢺⠧⠠⣭⣷⣌⠳⠾⠷⠂⠀⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠙⠦⠁⡄⣸⢋⣥⢬⡛⣏⠡⠐⠦⠄⠀⠰⢦⠉⠛⠷⠤⡹⣆⠠⠤⣀⠑⠦⢄⢰⡿⣡⠴⢚⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢾⢰⡄⣾⣯⡟⠀⢈⣅⢰⣿⠀⠀⡘⢣⡖⣲⢽⠮⣶⣖⠀⣀⣀⣴⢋⣾⣿⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠠⣀⠲⣯⡀⢀⡀⠿⠋⠀⣠⠀⣠⡀⠈⢰⠡⡗⠀⠸⠆⢀⠑⢺⢃⠚⣯⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⢰⠎⣱⡮⢝⠳⣤⢂⣀⣈⠀⠀⠉⡁⢀⠈⠁⠠⡆⢴⠆⠀⣴⠏⠆⢙⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠽⢦⡦⠽⠓⠭⣌⣣⡼⠃⢢⡜⣦⣤⣲⣐⠙⠻⢛⣫⢉⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⠀⠀⣠⠜⣋⡉⠃⠲⣶⢚⠓⠚⠯⠙⠉⢀⣴⡄⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠙⠨⢁⠃⠀⠙⠈⠀⠀⠀⠀⠀⠴⠛⡿





⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣏⣻⣧⣤⣤⣴⣤⣬⣤⣭⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠀⣴⣶⣶⣶⡄⠉⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣰⡀⠻⠿⠿⠟⠃⠸⠂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠘⢿⠟⠀⠀⠀⠰⠆⠀⠀⠘⠁⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⣿⠟⠀⠃⠀⠈⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠻⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⢰⠄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠺⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡟⠀⠀⠀⠀⣠⡀⠘⠋⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠺⣿⠗⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣥⣤⣶⠾⠃⠀⠀⠀⠈⠻⠿⠋⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⢀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⢋⣡⣶⠿⠟⠛⠋⠉⠉⠉⠛⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠻⠋⢡⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡉⠻⣿⣿⡿⢉⡀⢤⣥⣤⣤⡄⢀⠈⠋⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡿⢡⣾⣿⣄⠙⠿⢋⣴⣿⣧⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣆⠀⣤⣤⣤⣤⠀⣤⣤⣤⡤⠀⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣷⡌⠻⣿⣿⠀⣿⣿⠟⠀⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣴⡿⠁⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠉⠀⠀⠀⠀⠀⣠⣾⣿⡷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣩⣭⣭⣭⣭⣭⣤⣤⡀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⡛⠛⠛⠛⠛⠛⣃⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠃⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋

⠀⠀⠀⢀⣶⡆⠀⠀⠀⢰⡶⠶⣦⠀⠀⠀⣠⠶⠶⣦⠀⠀⠀⣶⠶⣦⡀⠀⠀⢰⡶⠶⠖⠀⠀⠀⢰⡶⠶⠆⠀⠀⠀⣴⠶⢶⡄⠀⠀⢰⡆⠀⣴⡆
⠀⠀⠀⣼⣧⣽⡆⠀⠀⢠⡿⠛⣿⠀⠀⠀⣼⡇⠀⣀⠀⠀⠀⣽⠂⣨⡗⠀⠀⢀⣿⠛⠛⠀⠀⠀⢨⡿⠛⠃⠀⠀⠀⣿⠀⢶⡶⠀⠀⢨⡟⠛⢿⠇
⠀⠀⠘⠋⠀⠈⠃⠀⠀⠘⠛⠛⠋⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠘⠃⠀⠙⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⠀⣠⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⡀⠀⣠⣄⠀⠀⣤⡀⠀⣤⠀⠀⠀⣠⣤⣄⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣻⠄⠀⠀⢻⣾⣏⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣻⢳⣄⡿⣿⠀⠀⢻⡿⣦⣻⠄⠀⠀⣿⠀⠘⣧⠀⠀⠘⣧⣤⣿⠄
⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠶⠶⠟⠀⠀⠀⠿⠁⠻⠆⠀⠀⠀⠿⠶⠶⠀⠀⠀⠿⠘⠿⠰⠿⠀⠀⠿⠀⠹⠿⠀⠀⠈⠻⠶⠾⠃⠀⠀⠸⠇
⠀⠀⠀⢀⣠⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⡀⠀⣀⠀⠀⠀⣀⠀⠀⣀⠀⠀⣀⠀⢀⠀⢀⠀⠀⢀⡀⠀⢀
⠀⠀⠰⣿⠁⠹⣇⠀⠀⠸⣏⠙⣷⠀⠀⠀⠸⣏⣙⠃⠀⠀⠈⠉⢿⡋⠁⠀⠀⠸⣇⠀⢿⡀⠀⠀⠻⣆⢰⡟⠀⠀⢻⡄⣿⣆⢾⡁⠀⠈⠻⣴⡏
⠀⠀⠀⠿⣤⣴⠋⠀⠀⢰⡏⠻⣏⠀⠀⠀⢤⣌⣹⡿⠀⠀⠀⠀⣾⠃⠀⠀⠀⠰⣯⣀⡾⠁⠀⠀⠀⢿⡾⠁⠀⠀⢰⣿⠋⣿⡟⠁⠀⢀⣴⠻⣇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠛⢿⣧⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠛⠻⣿⡟⠛⠛⠀⢀⣾⡿⠛⠿⣷⡄⠀⠀⢸⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢻⣷⡄⠀⣀⣀⣀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⢻⣧⠀⠀⠀⠘⣿⡆⠀⠀⠈⠁⠀⠀⠘⣿⣦⣤⣤⣿⣿⡄
⠀⠀⠀⠀⠀⣾⣿⠀⠀⢹⣿⡏⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⣾⡏⠁⠀⠀⠀⠐⣿⡏⠀⠀⠀⢰⣿⡁⠀⠀⣤⡄⠀⠀⣰⣿⠉⠉⠉⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⠹⠿⠀⠀⠀⠿⠿

⠀⠀⠀⣄⠀⢠⡄⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠙⣧⡿⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣼⣧⣤⠀⠀⠀⢻⡄⢹⡆⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⢿⠁⠀⠀⠀⠠⣾⣧⣤⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠻⣦⠿⠁⠀⠀⠀⠀⢸⠇

⠀⠀⠀⠺⠋⣿⡀⠀⠀⠀⠛⢙⣷⠀⠀⠀⠀⣴⢿⡀⠀⠀⠀⢸⣏⣉⠀⠀⠀⠀⣾⣋⣀⠀⠀⠀⠘⠋⢻⡃⠀⠀⠀⢾⣋⣿⠀⠀⠀⠀⣿⠙⣷
⠀⠀⠀⣠⣶⣋⠀⠀⠀⠀⣄⣉⣿⠀⠀⠀⠰⠿⣾⡇⠀⠀⠀⣤⣁⣼⠃⠀⠀⠠⣿⣁⡿⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⣶⣋⣿⠆⠀⠀⠀⢘⣻⡟⠁
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠴⢶⣆⠀⠀⠀⢠⡾⢷⡄⠀⠀⠀⢀⣴⠶⠀⠀⠀⠰⣿⣉⡓⠀⠀⠀⡖⣦⣠⠀⠀⠀⣠⠞⣩⣉⢳⡀⠀⠀⣠⣆⣆
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⠙⢶⡆⠀⠀⠀⢩⡿⠅⠀⠀⠀⠀⣿⣍⣽⠂⠀⠀⠉⣡⣿⣤⠀⠀⣽⢨⣇⣽⢈⠇⠀⢠⣽⣯⣯
⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠈⠛⠛⠀⠀⠀⠰⢦⣬⠿⠀⠀⠀⠈⠁⠙⠚⠀⠀⠙⠮⣭⡍⠉⠀⠀⠀⠋⠘

⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⡥⠒⠉⠀⢀⡤⢲⠎⢀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣟⠀⠀⠙⣆⠠⡇⡇⢀⡔⠁
⠀⠀⠀⠀⡀⠀⣸⠃⢀⠀⢰⠁⢀⣀⣰⣋⣠⣤⡴⠧⠒⠀⠀⢀⡠⠤⠒⣀⠀⠀⠐⠂⢀⡂⠄⠀⡀⠀⠀⣿⠀⠀⠀⠘⣿⣷⢷⣞⡀⠀⢀
⠀⢘⡐⢰⠃⡰⠃⢀⠈⡠⠃⠀⠘⠁⡝⠁⠀⢀⣄⠤⠀⢀⡴⣋⠀⠀⠀⠰⠋⣩⠟⠉⠉⠉⠉⠛⠧⣄⠀⢸⡇⠀⠀⠀⠸⣿⡾⡁⠀⣠⠋
⠀⢸⡇⣿⠞⠁⠶⢉⡼⠀⠀⣈⠀⡼⠁⣄⠐⣠⠃⣀⡶⠫⠤⠅⡦⠤⠖⢊⡉⠀⠀⠀⣰⣷⣶⣶⡊⠈⠳⣌⣇⠓⠠⣄⠈⣿⡇⢧⡴⠁
⢠⡞⣸⡏⠀⣀⡰⠋⠀⠀⣀⡵⠊⠁⣀⣭⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠃⠀⠀⡈⠻⣦⣀⠉⢠⣿⣧⠘⡇
⠏⢰⡿⠀⠀⣽⠁⢀⣴⠟⢉⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠈⠉⠐⠀⣹⣷⣿⣿⣿⣆⡿⣄
⠀⢸⡇⠀⢰⣿⡾⠋⠀⣰⣿⢋⣤⡁⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣉⣉⣉⣙⣳⣤⣀⣘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡈⢹⣿⣿⣿⣿⠇⠙⣆
⠀⢸⡇⠀⣼⣿⠱⠆⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣤⠤⠤⠤⠞⠋⠉⠁⠈⠉⠉⠛⠻⣿⣿⣿⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⠀⠀⠸
⠀⢸⣿⣰⣿⡏⢀⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠙⢶⣄⠀⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣿⣿⣿⡆⠀⣸
⠀⢸⣿⣿⣿⣿⡏⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⣰⡟
⠀⠈⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⢷⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠍⢸⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣃⡤⠾⡟⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧⠀⢰⣯⠄⠀⠀⡞⣼⠃⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⣤⣦⣤⣀⣀⠀⢀⢒⣻⣷⡒⣶⣻⣧⣤⣤⣿⣿⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⠟⠉⢹⣿⡏⣿⣿⡃⠀⠈⠉⠉⡿⡉⠉⡏⢹⠛⠛⠻⠷⠭⣽⣯⣷⣿⠿⣿⠟⠛⠛⡛⢻⡿⠁⠀⠀⠀⣠⣿⣿⠿⠛⠛⠛⠻⠿⠿
⠛⠉⠀⠀⠀⠀⢿⣷⣜⢿⣷⣦⣤⣤⣴⣷⣷⣶⣷⣾⣤⣀⠀⠶⠶⣿⣿⡛⢛⡛⣟⣋⡁⢰⡇⣼⣇⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣿⣷⣾⣿⡏⠀⠈⠉⣉⣽⣿⣿⣝⣋⣛⣏⡁⢀⣼⣷⢿⣿⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⣆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡿⡿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠚⡿⢰⡤⣦⠸⡓⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠈⠀⠀⠀⣀⣀⡐⢾⠦⢴⣅⠀⣄⠙⢿⠰⣸⠞⢁⡀⢠⣷⠴⣿⠖⣀⣀⠀⠤⠀⠁⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠣⢠⡤⠐⠚⠐⠊⣕⣤⣔⡀⠈⠁⠻⡄⢻⡷⣹⠃⡼⠋⡁⠀⢲⣤⣔⡍⠂⠐⠒⢠⣤⠼⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠂⠶⠄⠀⠈⠑⠂⠛⣮⠿⢷⣾⣿⠈⣹⣿⣶⠿⣭⠟⠂⠒⠉⠀⠠⠶⠂⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠨⠖⣺⡿⣿⡄⣿⢿⣯⡒⢄⠀⠀⠀⠀⡀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡘⢀⣴⠂⠀⠀⠀⠀⡽⢠⢹⣷⡿⠥⠹⡄⠀⠀⠀⠀⣾⣀⠘⣤⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢈⡻⠁⠁⠄⠀⠀⠀⠁⠀⡾⢻⢻⠆⠀⠃⠀⠀⢀⠌⠁⠹⡇⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣧⣠⠤⢀⠀⡀⠘⡇⠀⡀⠀⠀⠙⣠⠘⠀⠁⠀⡀⠨⠃⠀⡀⢠⠠⣤⣠⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡻⡧⠘⣾⡣⠒⠄⣀⠐⠀⠉⢲⣀⢤⡭⡥⢆⣴⠉⠁⠰⠀⠀⠕⢦⡻⠊⠰⣿⣙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣗⠡⠈⠈⣡⠀⣀⠂⠐⠀⠀⠀⢠⡎⢻⠛⡄⠀⠀⢀⠐⠐⢃⠀⢀⡉⠈⡰⢱⡷⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡈⢹⣶⠳⠄⠨⢦⠙⣇⣰⢠⠌⡑⢳⢤⠟⢦⡔⢀⡀⣤⢰⣀⡎⣴⢮⠠⠞⣳⡟⢁⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⠶⣌⡓⢼⣦⡀⠀⢿⡻⣾⠓⠙⠋⠀⠀⠀⠈⠻⠗⢻⡾⣻⠆⢀⣀⣦⠘⣣⡴⠿⠧⠞
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠈⠩⡈⢁⠙⠳⣌⣛⠻⠆⢃⡤⣾⣋⣲⠦⣀⠋⠟⢙⣡⠴⠛⠁⠉⡄⠁⠐⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠂⠀⠌⢀⡀⠠⢙⣧⠴⣿⣷⣾⣷⣿⣾⣿⡶⣴⣟⠁⠀⠀⠀⠀⠐⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠐⠀⠚⠓⠒⠀⣀⣀⣦⣶⡿⠞⠛⢻⣿⣿⡀⣿⣿⣿⠛⠓⢿⣷⣴⣀⣀⣀⡒⠘⠓⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣴⠾⠛⠛⠛⠛⠛⠛⡻⠛⢷⣄⡀⠀⢍⢻⣿⣽⢻⠀⢀⣠⣴⠟⠛⠛⠛⠛⠛⠛⠛⠻⣶⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠉⠁⠀⠐⠂⠀⠂⡸⠁⠈⠅⣸⡿⢯⣴⡿⣿⡻⣦⣽⢿⣯⡠⠍⠀⢳⡐⠀⠀⠂⠀⠉⠉⠙⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡀⡤⠀⠠⠘⠛⠆⠛⢁⠜⣡⣾⠋⣀⡞⠳⠾⣿⡷⠶⢹⣎⠈⢻⣦⡁⢀⠙⠢⠚⠃⠠⠀⠠⡄⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠄⣠⠂⢀⠀⢰⡟⠮⠀⠸⠁⠀⠞⠛⢛⠂⠊⠙⠀⢹⠞⣷⠘⣤⠀⢦⡀⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⣿⡄⢃⣠⠀⠀⠀⠀⣲⡁⠀⠀⠀⢠⣜⠃⣿⡀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⣤⣭⠭⢤⠀⠆⣿⠃⠀⣤⠼⢭⣥⣾⠟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠟⠛⠛⠀⠀⠀⠁⠀⠘⠛⠛⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⣿⣿⢟⠛⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣞⣩⣷⣶⣦⣴⣶⣶⣦⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣤⣤⣀⠀⠀⠀⣠⣤⡀⠀⢀⣤⣤⡀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⣼⠻⣇⠀⠀⢸⣏⣹⠀⠀⠀⣾⠟⠉⠁⠁⠀⠀⣿⡟⢿⣷⠀⠀⣿⣋⠁⠀⢸⣿⠉⠀⠀⢠⡿⠋⠉⠉
⠀⠀⠀⠀⢠⣷⢶⣿⠀⠀⢸⡟⠛⣦⠀⠘⣿⡀⠀⠀⠀⠀⠀⣿⣇⣼⡿⠀⠀⣿⠟⠃⠀⢸⣿⠿⠀⠀⢹⣇⠀⠀⢴⣀
⠀⠀⠀⠀⠼⠟⠘⠿⠇⠀⠸⠷⠴⠋⠀⠀⠘⠿⣶⣶⠦⠀⠀⠿⠿⠛⠁⠀⠀⠿⠿⠂⠀⠸⠿⠀⠀⠀⠀⠙⠷⠶⠞⠁

⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠈⣿⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⣿⡄⠀⣿⣧⣴⠟⠁⠀⠈⣿⠀⠀⠀⠀⣿⣿⡄⢰⣿⣷⠀⠀⣿⣧⠀⣿⡆
⠀⠀⠀⠀⠀⣿⣷⣾⣿⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⣿⣿⣯⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡟⣷⡿⢻⣿⠀⠈⣿⠻⣷⣿⡅
⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⠀⣤⣼⡿⠀⠀⣿⡏⠻⣧⠀⠀⠀⣿⣶⣤⠀⠀⣿⠃⠘⠁⢸⡟⠀⠀⣿⠀⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⡾⠿⠿⣷⡄⠀⠀⣿⡏⠛⣦⠀⠀⣰⡾⠟⠻⢿⣆⠀⠀⣿⡏⠙⣷⠀⠀⢠⣾⠛⠃⠀⠐⠻⢿⣿⠟⠂
⠀⠀⠀⠀⢸⣏⠀⠀⠀⢸⣿⠀⠀⣿⡷⠾⠋⠀⠀⣿⠁⠀⠀⢈⣿⠀⠀⣿⣷⡾⠛⠀⠀⠀⠛⢶⣄⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⢿⣦⣤⣤⣾⠇⠀⠀⣿⠀⠀⠀⠀⠀⠻⣷⣤⣾⣾⡋⠀⠀⣻⡟⢿⡆⠀⠀⢠⣤⣴⡿⠀⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠉⠁⠈⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉

⠀⠀⠀⢸⣷⠀⠀⢸⣦⠀⠀⣶⡆⣰⡦⠀⠀⣶⡄⠀⢀⠀⠀⢠⡖⠀⠀⢰⣦⠀⣼⡏⠀⠀⢺⣦⢠⣶⠂⠀⠰⠶⠿⣿⣷
⠀⠀⠀⢸⣿⠀⠀⣼⡏⠀⠀⢿⣧⣿⠇⠀⠀⢹⣷⢠⣿⣧⢀⣿⠇⠀⠀⠈⣿⣿⣿⠀⠀⠀⠈⢿⣿⠏⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠘⣿⣆⣀⣿⡇⠀⠀⠸⣿⣿⠀⠀⠀⠈⣿⣿⠃⢿⣿⡟⠀⠀⠀⢰⣿⠉⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⢀⣾⣿⣁⡀
⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠚⠁⠀⠘⠓⠀⠀⠀⠘⠛⠀⠀⠀⠘⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⢀⣴⣝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠃⠀⣰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣯⡵⣀⣤⠞⣰⢺⠟⣐⣦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⣤⣌⡄⠀⠞⢁⢘⡟⠀⡘⠛⢛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣿⠿⡟⣀⣀⡀⢸⡜⠠⣾⠃⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣃⡤⠂⠋⠜⣿⣿⢿⡆⣸⣧⣴⠇⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⣰⡿⣠⠀⠀⢠⠿⣿⣦⣶⣿⡟⠻⣀⣿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠒⠛⠛⢿⠙⣃⣤⣥⣤⡈⢙⡳⢤⡁⢤⣹⡼⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣴⢯⡾⣫⣤⣤⡈⢻⡎⣿⣦⠑⢸⣿⠷⢸⣯⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠋⢠⠏⢸⣿⡏⠙⠏⡼⢃⣿⣿⡆⠈⣽⡷⢈⡙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠁⠀⠀⠀⠸⣿⣧⡀⠲⠶⠿⣿⣿⠇⠚⢋⡃⣶⡹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣘⠻⣿⣶⣶⣿⣿⣿⠿⣷⣄⠙⣿⢁⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⠁⠀⠈⣿⡇⠘⠼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠶⣶⠿⢁⣷⣄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠐⢿⡋⢻⡌⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟⠋⠙⢷⣄⢻⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⡀⠀⠀⠘⣿⣿⣿⡇⠀⢠⡀⠀⢻⣇⠇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣇⠀⠀⠀⣿⣿⣿⣷⣄⣸⣿⣄⠘⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⢿⣦⣤⣼⣿⣿⣿⣿⡿⢿⣿⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠸⣿⡙⠛⠁⢸⣿⡏⠀⠀⠘⣿⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠹⣿⣄⠀⢸⣿⡇⠀⠀⠀⣿⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠘⢿⣷⣄⢿⣧⠀⠀⠀⡟⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠙⢿⣿⣿⣧⠀⠈⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣏⣀⡀⠀⠀⢶⣦⣄⠀⣴⣶⠀⠀⣶⣆⠀⣀⣤⡶⠀⠀⠀⣀⣹⡟⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⠀⠀⣰⠟⢫⣿⣿⠀⠀⠀⢿⣿⣷⣿⣿⡄⢠⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⡝⢻⣆⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠘⢿⣦⣿⡀⠀⠉⠁⠀⠀⠀⢰⣿⢿⣿⣿⠇⠸⣿⣿⡿⣿⡆⠀⠀⠀⠈⠉⠀⢀⣿⣴⡿⠃⠀⠀⠀⠀⠹⣤
⠀⠀⠀⣶⣤⡀⣿⡀⠀⣀⣀⠀⠰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⡄⢠⣿⡏⠀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⠄⠀⣀⣀⠀⢐⣿⢀⣤⣶
⠀⠀⠀⠹⣿⣿⣿⣧⠸⠿⠏⢳⣀⣈⠻⠿⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣸⣿⡇⢸⣿⣇⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠿⠟⢁⣀⡞⠹⠿⠇⣸⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠛⣿⣿⣧⡀⢠⠞⡏⢩⣷⡄⣾⣿⠿⠿⠿⣷⣤⡀⢀⣴⣿⡿⠀⠀⢿⣿⣦⡀⢀⣤⣾⠿⠿⠿⣿⣷⢠⣾⡍⣹⠳⡄⢀⣼⣿⣿⠛⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣦⢿⡶⢭⣀⠈⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⣀⡭⢴⡷⣴⣷⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠹⠿⠋⠉⢹⠛⠻⣿⣿⣶⣮⣷⣦⣤⣤⣀⣀⠀⠀⠈⠻⣆⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣀⣠⣤⣴⣾⣵⣶⣿⣿⠟⠛⡏⠉⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⠆⠉⠙⠛⠛⠿⠛⠛⠛⠻⠿⣶⣤⡀⠹⡇⠀⠀⢰⠏⢀⣤⡶⠿⠟⠛⠛⠛⠿⠛⠛⠋⠉⠰⣷⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠿⠿⣿⣷⣶⣦⣄⡉⠿⣄⢹⠀⠀⡟⣠⡞⢉⣠⣴⣶⣾⣿⠿⠿⢿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣠⣾⣿⡏⠁⠀⠀⢰⣿⠿⠿⠿⠿⣿⣦⣹⡌⡇⢸⢣⣏⣴⣿⠿⠿⠿⠿⣿⡆⠀⠀⠀⢹⣿⣷⣄⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋⠻⠿⠶⠂⠀⠈⠛⠀⠀⠀⠀⠈⢿⣿⣿⡇⢸⣿⣿⡿⠁⠀⠀⠀⠀⠛⠁⠀⠐⠶⠿⠟⠙⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣠⣿⣿⣿⣿⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⠉⠉⠒⢄⣠⠖⠉⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⡜⠀⢀⠀⠀⡀⠀⢣⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠓⠚⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⣀⣀⣀⠠⠤⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠤⠤⠔⠊⢁⡄⠀⠉⠑⠒⠠⠤⠄⠒⠉⠀⠀⢀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆⠀⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠀⡰⠁⡀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⢠⠃⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡟⠀⠀⠀⢰⠁⠀⡆⠀⠀⠀⠀⠀⠣⠤⠃⠀⠀⠀⠀⠎⠀⡇⠀⠀⠀⠈⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠈⠓⠊⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠖⠁⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⢀⠎⠀⡇⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⢠⠎⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⠀⠀⠀⠀⠀⠈⠢⠞⠀⠀⠀⡔⠁⢸⠀⠀⠀⠀⠀⠸⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⠞

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣿⣻⣟⣙⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠤⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠠⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠎⠶⠂⠈⣠⢢⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣆⡄⢟⣁⢠⡱⠄⠀⠀⡀⠀⠀⠀⠴⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠁⠰⠀⡈⠠⠀⣄⠀⡙⢉⡄⢚⠁⠈⠀⠊⠈⡄⢀⠌⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢀⠀⠀⠀⠂⠁⠈⢀⠀⢩⡈⠓⣘⠣⠤⠂⠸⠀⠐⠂⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠧⠢⠁⠀⠸⠧⡃⠀⠠⠀⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⢠⡖⠰⠶⠀⠁⠶⠁⠀⠐⠀⠀⠀⠠⠄⠁⠀⡂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⢄⠀⡀⠰⠄⣀⠄⠒⠓⢤⣵⢶⠉⠁⠀⠴⠀⢢⡤⡴⠋⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢤⣀⠀⣆⠃⠀⠘⣫⠀⣠⠔⠚⠃⠸⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⢲⠀⠀⠀⠀⠀⠘⡆⠉⠀⠉⠀⠻⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⡘⢄⡇⠀⠀⠀⠀⠀⠸⠀⡠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣈⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠡⡤⠀⣠⡔⠰⡼⠂⠀⠀⠀⠀⠀⠀⠀⢤⠈⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⣄⠄⠛⠏⠀⡁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⠀⡴⡋⠀⠀⠐⢠⠇⠀⠃⠅⠠⡃⠶⡄⠀⠀⠀⠈⠻⡄⠀⠀⣿⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠱⢌⠁⠀⠀⠀⠄⠀⠠⠀⠀⠀⠁⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣽⠧⣤⢆⣶⢶⡄⣻⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⡇⢀⡃⠀⠈⠠⣯⢈⡇⢰⠀⠐⠀⠀⠀⠀⠠⣤⣀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⢰⡇⢹⣧⡀⠀⠀⢽⡆⣄⢘⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠚⠆⠀⢳⡀⠀⠀⣿⡗⢘⠁⠀⠀⠀⠐⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢺⡄⢠⡍⠀⠀⡏⡻⢸⡇⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠂⠀⠂⠀⠀⣽⡾⠀⡹⠁⠀⣼⠃⣳⣾⠀⠀⣤⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠐⠁⢀⡤⠶⡠⢚⡡⠂⣸⠁⢀⠌⠉⢴⠿⡟⡀⢄⠳⢄⠀⣴⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠐⡀⠢⠟⢢⡄⠀⠄⠀⠊⠀⣠⣇⠀⠘⡆⠀⢺⡀⣟⡳⠀⠀⠀⠀⠰⣆⠐⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣃⡀⠀⢤⣈⠶⠀⠁⡑⠲⡆⠰⠖⠎⠁⠙⠀⣴⠿⠄⠀⠑⠾⠥⠑⠂⢀⡮⠕⠘⠧⠀⢀⡂⠀⠀⠀⢀⡀
⠀⢁⠀⠀⠀⢀⣤⠀⠀⠉⠁⠐⠊⢡⠖⢻⠀⠁⠈⠳⠀⢢⡀⠈⠠⡇⠸⢿⣮⡀⢤⣤⠤⠶⢾⡉⠀⠀⠒⢦⠘⠚⢁⠁⡄⠒⠊
⠀⠠⠀⠀⠀⠀⠀⣀⠀⠊⠀⠀⠀⠀⠋⣸⠃⠸⠄⠀⢲⣤⣈⡀⣀⡤⢰⠀⢾⠁⢀⡈⠀⠀⠄⠈⠏⠀⠃⠀⣄⠀⠉⠴⣁⠀⠐⠂
⠀⢠⠀⠀⠀⠀⠀⠤⠀⠀⠠⠆⡀⢀⠋⠀⠀⠁⣰⡞⠈⠉⠈⠁⠋⠀⠉⠀⠘⢴⢻⡁⠀⡀⠃⠀⢰⠄⠅⠲⢄⣦⡀⠀⠉⠉⠶⠓
⠀⣼⠀⠀⠀⠀⠦⣐⣇⡠⠄⠀⢀⠌⠈⢓⠜⠲⠉⡴⠂⢀⠀⠒⠄⠑⠐⠚⢰⠀⠀⢆⠸⠧⡀⢃⡄⠐⠂⠴⣬⠈⠥⠤⠀⠀⡀⢠⣤
⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠴⠉⣁⠀⠈⢠⡄⠀⠀⣄⢀⠌⠈⠔⢃⠀⢰⡊⠠⡾⠄⠫⠀⠈⠧⠀⣁⠀⠀⠀⠐⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉
⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣹⣷⠀⠀⠸⡦⠀⢿⣿⡷⠆⠀⠀⠀⢻⣧⠀⠀⠀⢀⠐⢻⣷⠄⢠⡀⠛⢀⣤⡆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⢯⠀⠀⢸⠛⠍⠀⠀⠀⠀⠀⢀⡈⠀⠁⠀⠀⠞⣷⡈⠁⣠⣤⡄⢉⡀⠛⠋⣠⣿⡄⠀⠸⠻⠄
⠀⠀⠀⠀⣦⠀⠀⢹⣷⠆⢠⡀⢀⠀⠀⢀⡀⠀⠐⠠⢼⡏⠄⠰⠟⣿⠂⠈⠁⣤⡘⢷⡡⠄⠀⠈⣄⠚⠉⠀⣠⡇⢹⡇⠀⠀⠀⢀⣴⡇⠀⠰⠃
⠀⠀⠀⠀⠁⠀⠀⠛⠙⢣⠀⠁⠈⠃⠀⣿⡻⠀⠀⢰⣶⡿⠀⠀⠀⠐⢷⡇⠀⣿⣷⣌⢣⠀⣀⣤⣾⣦⣤⣼⡿⢷⣼⣷⠀⢠⡖⣀⣿⠇⢀⣀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣶⠀⠐⠀⠀⠉⠁⠀⠢⡜⠋⠀⠀⠀⠐⣀⠀⡀⠀⢱⣏⢽⣧⣶⠋⠉⠋⢻⣿⣟⣷⠀⣿⣿⡴⢋⣶⣿⡿⢶⣾⡿
⠀⠀⠀⠀⠀⣿⡏⠁⠘⠇⠈⠒⠂⠒⠻⢄⠰⡂⠘⠛⠆⠈⡧⠤⣄⡀⠁⠙⠲⡤⣿⠀⣻⠋⠘⢦⡶⢸⣿⣿⡇⠀⣿⣿⠁⣼⣿⣿⡇⠀⠁
⠀⠀⠀⡄⠀⠙⠓⠀⣀⡀⠀⢠⡄⠀⣰⡾⢎⠁⠀⠀⠀⢷⠄⣴⣿⣧⣀⢰⣾⡛⣹⣶⡏⠀⠀⠂⠀⢸⣿⣿⣇⣠⣿⣿⣰⣿⡿⠟⣻⣿
⠀⠀⠀⠀⠀⠀⣀⠙⠋⠃⠹⣦⠉⠀⠙⠋⢀⠀⠸⣦⣤⣿⠀⢻⣿⣿⣿⡟⠋⠉⣿⣿⠁⢀⡄⠀⢠⣾⠛⠉⢉⣿⣿⡿⢻⣿⡦⢀⣿⣿⢀⣴⡇
⠀⠀⠀⠀⠀⣼⡟⠃⠀⠀⡈⢻⡆⠀⠀⠀⢨⡄⢰⡌⠛⣿⣧⠀⠿⢻⣿⡇⠀⢠⣿⣿⣷⣾⠅⢠⠋⣽⣆⢠⣾⣿⣿⠀⢀⡿⢴⠞⣿⠏⠙⣭⡄
⠀⠀⢀⡀⠀⠘⠃⡀⠸⠒⠃⠀⢃⢰⣾⣿⣦⠑⢼⣷⣴⡾⢿⣧⣶⣾⣿⡀⠀⠀⡿⠋⢹⣿⣷⡏⢠⣿⣿⣿⣿⣾⣯⠀⠊⠀⣠⣿⣿⣶⡄⠉
⠀⠀⠀⠉⢀⠀⣿⡟⠀⠀⠀⠀⠈⠺⡗⡨⠀⠁⢀⠈⢻⡆⠈⢿⣿⡟⣿⣧⠀⣶⠀⠀⠈⣿⣿⡆⠈⣿⣿⣿⣿⣿⡷⢤⣤⣸⣿⣿⣴⣿⣿⡆
⠀⠀⢠⡶⠟⠁⠀⠀⠀⢢⡀⠀⠀⠐⠋⢀⡀⠀⠈⠀⠘⣿⣦⡟⠻⣿⣿⣿⣷⠿⣏⠀⠈⣿⣧⠄⢰⣿⡿⠟⠀⠀⠀⠰⣿⣿⣏⠈⣿⣿⣿⡇⣀
⠀⠀⠉⠀⠀⠀⣠⣤⠀⠀⢱⡀⠀⠀⠐⠞⠓⠂⢶⣀⠾⠋⠙⠳⣤⣾⣿⣿⣿⢀⣼⠛⠹⣿⣿⢣⠜⠋⠀⠀⠙⣦⣶⣿⡿⠿⣧⣶⣿⣿⣿⠛⠋
⠀⠀⠀⣤⣶⡄⠙⠁⠀⠀⡌⠛⠶⣤⠤⠀⠀⠀⠀⡏⣰⡏⠙⠷⠿⣡⢙⡿⣿⠛⠉⠛⡷⢿⣿⣁⠔⠀⠀⣠⣾⣿⣿⣋⣤⣾⡿⢿⣝⠋⠉⢳⡶
⠀⠀⠘⡙⠀⣁⠀⢀⣀⡙⠆⠒⢀⠃⠀⠀⠀⡻⠎⠸⣿⣤⣶⣶⡄⠀⢨⣄⠀⢠⡀⠀⠀⠶⠈⢷⠤⠴⠋⣿⣿⡿⠛⠛⠀⠉⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠁⠀⠀⣀⠀⣭⡙⠓⠂⡀⢀⣤⡄⠀⣽⠇⢰⣿⣿⣿⣿⠇⠀⠈⠛⢠⣟⡿⢀⣾⣿⠀⠐⢠⡆⣰⡞⢿⠉⢷⠊⠹⡝⠛⠛⠛⠏⠉⢻⡄
⠀⠀⠀⠀⣿⡟⠁⠀⠀⠑⠀⠀⠛⢾⢿⣶⠞⣡⣶⣴⣏⣉⠉⠁⣰⣶⠀⠀⠨⣯⣿⣿⣿⣿⣶⡶⢈⣀⠉⠈⣶⡄⠈⠻⣄⠀⠘⣶⣦⢠⡀⠸⣷
⠀⠀⠰⢦⠈⠃⣶⡷⢀⡀⠱⣄⡖⠠⠘⣣⣿⣿⣿⣿⣿⣿⣧⣨⡿⢿⡶⠆⣀⣈⣈⣋⣉⣍⠛⣴⡟⠻⠧⣀⠀⠉⠂⠀⠻⡷⠀⣿⣿⣿⣭⡀⢸⡆
⠀⠀⠀⠠⣦⣤⡴⠁⣨⠃⡷⢌⡑⠂⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡙⠋⣡⣼⣿⣿⣿⣿⣿⣿⣄⠘⠓⢀⣤⠄⠀⣂⠀⠈⠁⠀⠊⠙⠛⡟⠛⢀⠈⡇
⠀⠀⠀⢀⣈⠙⠀⠀⠀⠈⠁⠀⠉⢩⣿⡁⠙⠻⠿⣿⣿⣉⠀⠐⠈⠎⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⣨⣴⠖⠸⣿⣄⣀⡀⢠⡀⠀⠀⠁⠀⠉⠠⠁
⠀⠀⠀⢸⣯⡤⠖⠀⠀⣀⡀⠀⢲⣾⠀⡀⠘⡷⢰⣿⣿⣿⣦⠈⣤⠓⠻⣿⣿⣷⣿⣿⣿⣿⣿⠟⠀⢿⡷⠖⣻⣷⣿⣿⣤⣘⣛⡂⠀⠀⠋⠀⣾
⠀⠀⠀⣾⡟⠃⢀⣤⠐⠈⠙⠉⣹⣧⣶⠀⠀⣴⣿⣿⣿⣿⣿⠸⣿⣤⡄⢉⢉⣉⡛⠻⠿⠛⢁⡰⠀⣸⣿⣿⠿⠛⠛⠛⠛⠛⣿⣿⣿⠂⠀⢀⡎
⠀⠀⠀⠙⠧⠀⠘⠇⠀⠈⡁⢠⣿⣿⠟⣀⢈⠛⠙⢿⣿⣿⡿⣞⢻⣽⣦⣜⠉⣹⢃⣄⡀⡄⢀⣤⠶⢿⣿⣷⡶⢶⣿⣿⡿⠟⡛⠉⠉⠰⠆⢸⡇
⠀⠀⠀⠳⠆⠀⢠⠈⠐⣤⡈⠀⣿⠿⢿⣯⣮⣤⣴⣂⡟⠲⠞⠈⠀⣿⠹⢿⣿⣿⣿⣿⡗⡘⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢠⣴⣤
⠀⠀⠀⠀⣶⣴⣗⣀⠠⠏⢙⠹⣇⣆⡘⢁⠟⡸⠟⣿⣴⡗⠂⡌⢰⠏⡄⢺⣯⡽⠛⣿⡏⠛⠃⠀⠛⢻⣿⣧⣉⣿⣿⣿⣃⠀⣚⡤⠒⠀⠉⣟
⠀⠀⠀⣾⣈⠿⠋⠁⣤⣦⠀⠰⠞⣿⣿⣿⣶⣿⣴⠃⡼⢻⡟⣠⣧⣸⢁⠛⡏⣀⣾⣿⣶⣋⠁⠞⣃⣉⣉⠻⣿⣿⡟⣿⡯⠙⡿⢷⡗⠀⡰⠟⠛
⠀⠀⠀⠉⠉⣤⡶⠖⠛⢭⢤⣴⣞⡏⢹⣿⢿⣿⡏⢾⣧⣞⣠⠏⢹⡟⢿⣤⣇⣯⣿⣿⣿⣿⢿⣿⡿⢋⡍⣷⣿⣿⣧⣿⣿⣷⣤⡏⢁⣾⠇⣠⣷
⠀⠀⠀⢀⠀⠘⢛⡄⠀⢀⠀⠀⢹⠉⣂⠈⢾⣟⠛⠛⣿⢿⣿⣶⢛⣴⣦⣸⣯⣇⣿⣿⣿⡇⠀⣤⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡟⠀⠛⠁
⠀⠀⠀⠀⢴⣶⣾⠃⠐⢾⡖⠀⢸⠀⢻⠀⠀⣬⠀⠸⠿⣶⣿⣝⠋⢹⣿⣟⣿⣿⣿⣿⣿⢁⡾⢁⣶⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⡉⠀⢙⡿
⠀⠀⠀⠀⠈⠉⠁⣤⡈⠀⢸⠖⠘⢒⡈⠑⡒⠧⠀⢃⡀⢀⢀⣼⠀⣾⡋⠛⠋⣿⣿⠛⢇⡾⣠⡎⠁⠀⠀⠈⠙⠋⠉⡉⠉⠀⠀⠰⠎⠉⢷⢀⣦
⠀⠀⠀⠻⠆⠀⠀⢿⣧⠀⠸⢦⠰⠾⣧⡶⠿⣤⢀⠀⠑⣌⠉⢯⡤⢿⡿⣤⡼⢿⣿⡟⠸⣱⠿⠇⠀⠐⠀⠀⡀⠀⠀⠘⠢⠀⠀⠀⠀⣾⠇⠘⠋
⠀⠀⠀⠀⠺⢿⣆⠀⠀⢠⢴⡾⢁⠀⢀⣤⠄⣿⠘⣿⠀⠛⣶⢈⡔⠻⠖⠾⠶⢞⡾⠁⢀⡏⢠⣤⢱⠆⠁⠈⡏⠀⢰⣆⣠⣧⠄⠀⠀⠁⢀⣴⡆
⠀⠀⠀⠀⠀⠸⢻⠀⣠⠃⣸⣇⠙⢃⠈⢁⡄⢤⡴⡇⠹⠶⢩⡏⠁⠀⠘⡓⠀⠈⠐⠆⠈⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣤⡄⠀⠀⠚⠛⠁
⠀⠀⠀⢾⣤⣦⢀⣨⠷⠂⠀⠙⣶⡿⢶⣦⣄⠈⢻⢃⢄⡀⠙⢁⡉⠀⠈⢀⣴⠾⠀⢀⣧⡀⠈⠉⢐⠀⠀⠠⠀⣷⡄⢀⣀⣰⡿⠛⠃⠘⣷⡆
⠀⠀⠀⠀⠉⢀⣤⠤⣤⠄⢶⠞⢩⢅⡀⢁⡄⠛⠋⠙⠃⠀⡄⠙⠻⠶⠿⡮⢥⢴⠖⠛⠏⠙⠀⢀⡆⠀⠰⠂⠿⡄⠀⣌⠁⠀⠿⢁⣄⠠⡾⠃
⠀⠀⠀⠀⢠⣦⡔⠈⠛⢢⡄⠠⠅⠊⠀⣤⣶⢀⡀⣼⣇⠘⠀⠀⣤⣀⣤⡀⠀⠾⠟⢢⡶⠋⠀⢸⣿⣿⣧⡄⠀⢀⣤⣾⠀⠀⠠⣤⡿
⠀⠀⠀⠀⠀⠻⡶⠂⠀⢿⡄⠀⠀⠀⠀⠈⠛⠛⠁⠘⠛⠃⠀⠀⠛⠁⠚⠁⠀⠀⠀⠘⠛⠁⠀⠀⠉⠛⠛⠁⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⢿⣴⣼⢧⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣄⣀⣀⣀⣀⡾⢻⢿⠟⡷⢋⢉⠉⠳⡛⣻⢿⠻⣆⣀⣀⣀⣀⣤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⣾⠭⠭⠭⡉⢹⢫⠙⢷⠘⠎⠆⢸⠛⢩⢻⠉⡩⠭⠭⢽⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠋⣨⢏⢙⣾⣷⠲⢺⣿⣞⣩⢯⡈⠛⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠈⠈⠋⠘⠈⠋⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠆⠱⢱⠀⠲⢸⠀⠘⠔⠄⠀⠘⠦⠰⢀

⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⢀⣀⣀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡀⢷⠀⠀⣿⠠⡇⠠⡏⠀⠈⠀⣾⠀⢹⠄⢸⣴⠈⠀⢸⣥⠙⢰⡏⠀⠈⡀⠀⠀⡀⠀⠀⡆⢀⠀⡄⠤⢀⠀⣲⠀⡀⣄⠀⡏⢠⠀⡤
⠀⠀⠀⠤⠉⠨⠷⠀⠻⠴⠟⠀⠳⠤⠖⠠⠻⠄⠛⠀⠼⠀⠴⠀⠸⠄⠀⠀⠓⠠⠾⠀⠀⠀⠂⠳⠀⠃⠘⠀⠑⠄⠈⠀⠻⠀⠱⠖⠀⠇⠀⠤⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⣶⠀⢰⠀⠀⠆⠀⠠⡆⠀⣔⣠⠖⠀⢠⠆⠀⠀⠶⣆⠀⢶⡆⠀⠶⡀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠆⢠⠀⡀⠀⠆⠀⣀⡀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⣿⠉⢸⡀⢰⡇⢠⢸⡇⠀⣟⠙⢦⡀⢨⡀⢠⠄⣀⠘⠆⢈⡇⠀⠀⠸⡇⠀⠀⠀⠀⢁⠀⠇⠀⡇⢸⠚⡀⠀⡇⢀⡃⢸⠀⡇⠀⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈
⠀⠀⠀⢀⡠⠀⣀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⠀⢀⠀⣄⠀⠀⡤⢤⠀⡀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⡇⠀⢸⠆⢨⠄⠋⠰⡇⠀⢸⠇⠈⠃⢾⠁⠀⠑⢤⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣂⠀⡎⢳⠀⠎⢐⠀⢰⠒⠂⢊⡂⢨⠃⢠⠀⡄
⠀⠀⠀⠀⠁⠀⠁⠀⠘⠂⠀⠀⠀⠠⣎⠀⠀⠃⠈⠃⠘⠒⠊⠀⠀⠓⠀⠀⠘⠒⠃⠀⠀⠀⠀⠃⢀⡗⠚⠀⠑⢺⡀⠘⠂⠈⠒⠁⠘⠃⠈⠓⠓

⠀⠀⠀⠀⠀⠀⠈⡅⠐⠁⠀⢻⣀⡿⣀⠏⠀⠘⡄⠁⠀⠘⣀⠌⠀⠀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⡀⢤⠠⠀⢠⡄⠀⢤⢠⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠋⠀⠟⠀⠠⠌⠈⢦⠀⠀⠽⡀⠀⠰⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠙⠈⠏⠀⠌⢣⠀⢸⠇⠀⠮⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠂⠀⠀⠀⢠⠃⠀⠀⠠⡇⠀⠀⠀⣆⠀⠀⠐⢤⡀⠀⡼⢠⡄⠀⠀⢠⠃⠀⠀⠢⡇⠀⠘⡄⣹⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠶⠄⠀⠐⠳⠆⠀⠠⠤⠃⠀⠀⠉⠟⠀⠀⠤⠜⠁⠀⠙⠴⠃⠀⠀⠎⠀⠀⠸⠤⠏⠀⠠⠜⠁⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠁⠟⠀⢰⠃⠠⢤⡧⡄⠀⣀⠀⠀⠘⣞⢡⠄⠀⡎⢠⢠⡄⢡⠀⠹⣧⡁⠀⠳⠇⡔⠁⡀⠀⠸⠿⠁⠀⢷
⠀⠀⠀⠀⠀⢧⠀⠰⠆⠠⡆⠀⠰⠀⠀⠰⠂⠀⠀⠃⠀⠈⠉⠁⠈⠶⠼⠿⠆⠀⢇⠻⠺⠶⡣⠀⠦⡿⠃⠀⠀⠎⠀⠳⠟⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⠀⠀⠈⠙⠳⣄
⠀⢀⡾⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⢠⠟⠀⠀⠀⢀⡀⡀⣀⠀⠀⠀⠻⡄⠀⠀⠀⡼⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢸⠃⠀⠀⠀⢋⡔⢰⣿⣷⠀⠀⠀⠸⡇⠀⠀⡟⠀⠀⢰⣌⠲⠥⠿⠈⠣⠀⠀⠀⢻⠀⠀⢸⠇⠀⠀⠀⠀⠀⠈⣒⡠⣀⠀⠀⠘⡇
⠀⢸⠀⠀⠀⠀⢸⡄⠈⢛⠅⠀⠀⠀⢀⡇⠀⠀⣇⠀⠀⠀⢻⣷⣶⣶⣿⣶⠀⠀⠀⣸⠀⠀⢸⡄⠀⠀⠀⢳⣤⡳⣦⣴⣿⡄⠀⠀⡏
⠀⠘⣧⠀⠀⠀⠓⠙⠛⠑⠿⠀⠀⠀⣼⠁⠀⠀⢻⡄⠀⠀⠀⠙⠻⢿⡿⠟⠀⠀⢠⡟⠀⠀⠈⣧⠀⠀⠀⠀⠀⠴⠿⠛⠛⠁⠀⣸⠃
⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠈⠛⠲⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠓⢦⣄
⠀⠀⣴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⢳⡄⠀⠀⠀⣰⠋⠀⠀⣀⣀⣀⣀⣀⠀⠀⠙⣦
⠀⢸⠃⠀⠀⠀⡆⠾⢃⢰⡏⠁⠀⠀⢸⡆⠀⠀⡿⠀⠀⠀⣠⡀⠟⡡⠤⣄⡀⠀⠀⢿⠀⠀⢰⡇⠀⠀⠰⡌⠻⣿⡟⣩⡄⠀⠀⠘⡇
⠀⢸⠀⠀⠀⠰⣝⣛⣡⣿⢣⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⢰⡇⠿⢆⡴⠒⠀⠀⠀⠀⢸⠀⠀⢸⡁⠀⠀⠀⠁⡇⠿⠸⢋⠁⠀⠀⠀⡟
⠀⠸⣇⠀⠀⠀⠈⠉⢭⡴⠋⠀⠀⠀⣸⠃⠀⠀⢻⡀⠀⠈⠣⠰⠎⠀⠚⠂⠀⠀⢀⡿⠀⠀⠘⣇⠀⠀⠀⠼⠇⠀⠀⠹⠆⠀⠀⣰⠇
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⠴⠞⠋

⠀⠀⠀⠀⣠⡴⠶⠚⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠒⠶⢤⣀
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⣀⡀⠀⠈⠙⣦⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢰⡏⠀⠀⠀⠐⢤⠀⢀⡤⠀⠀⠀⢻⡄⠀⠀⣼⠁⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠈⣧⠀⠀⢠⡟⠀⠀⠀⠀⢀⣀⠀⣬⠀⠀⠀⢹⡆
⠀⢸⠀⠀⠀⠀⣠⢼⠤⣾⣠⠄⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠤⠄⠈⢥⣶⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀⢠⣤⢹⡇⣿⠀⠀⠀⠀⣧
⠀⢸⡄⠀⠀⠀⠀⠈⠠⠌⠂⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⠀⠀⢺⣷⡄⠀⠀⠀⠀⣼⠀⠀⠸⡇⠀⠀⠀⠀⣔⣫⣼⣿⠀⠀⠀⢠⡇
⠀⠀⢳⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠟⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠛⠃⠀⠀⢀⡼⠃⠀⠀⠀⠻⣄⠀⠀⠀⠉⠉⠉⠁⠀⠀⢠⡞
⠀⠀⠀⠙⠳⣤⣀⣀⠀⣀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⡀⢀⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⠀⣀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣰⠀⢰⠀⠀⠀⢀⠀⠶⢀⡀⠀⠀⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⢰⡀⠀⠀⢠⡀⠀⢠
⠀⠀⡅⠉⡄⠈⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠃⢠⠞⠉⠂⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢉⠀⠠⡐⠋⠘⠃⠈⠀⠏⠀⠈⠒⢀⠀⢨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠾⠒⠲⣄⠈⠳⡀⠀⣠⡄⠀⠀⠀⠀⠀⣄⠀⠀⠉⣤⣀⡂⠐⢤⣄⠀⠀⠘⠋⠁⠘
⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⡾⠃⠀⣤⢀⠁⠀⠀⢿⡆⠘⠀⠀⠀⠀⠠⠒⠉⠀⢠⠻⠋⣉⣹⣶⠀⠙⣷⠀⠀⠋⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠐⣏⠀⠀⠀⢱⠀⠀⠀⠀⠈⢡⠃⠀⠀⠰⠃⣠⠜⠀⠀⠚⠀⠷⠀⢷⡀⠀⢠⠀⠰⠛⢐⠤⠀⠀⠀⠀⠉⠀⢸⣧⠀⢸⡇⠀⠖⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⡤⠂⡲⣘⠛⣗⣤⠘⠣⠀⠙⠀⢀⣄⠙⠃⠀⠠⡀⠀⣠⡄⣠⡏⠀⣸⠃⠀⢤⡄⣩
⠀⠀⡇⢠⠆⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⠀⠘⣠⠂⣠⠟⠁⠈⢁⣈⠁⠐⢀⡆⠀⠀⠛⢁⠑⡶⠀⠀⣿⡛⠿⠿⠋⢀⣰⠏⠀⠀⣀⡸⢿
⠀⠀⡇⠉⡆⠀⠀⠀⠰⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣥⠀⠐⠃⢰⣯⠀⠀⠀⠀⠀⢀⣶⡄⣥⠀⠀⠀⠈⠣⡀⣀⠀⠀⠑⠒⠲⠚⠛⠁⠀⠤⡀⠸⣀⣈
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠦⠀⡄⠀⠀⠀⢀⠀⣀⣾⠇⠀⠛⠇⠀⠐⠿⣿⡇⢸⣇⠀⣿⢆⣠⠀⠉⣀⠴⡂⢀⠂⡄⠀⣷⠀⡜⠋⠛⠉⡸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡖⠁⠀⠀⠀⠀⣰⣧⡟⢰⠄⠀⠀⡀⠄⠠⣿⢠⡇⣿⠀⠑⠈⠉⠂⡀⠋⣤⠈⣸⡇⣧⡜⠀⠐⠶⣠⣶⣾⢷
⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⠀⢀⡀⠀⠀⢀⡶⠀⠘⠀⠀⢠⡟⠁⢃⣼⡀⠀⠀⠀⠀⣸⣷⡌⢃⠘⡆⢻⣏⣀⣀⡀⠚⠛⣦⠀⣤⡈⠁⣦⣽⣦⠟⢻⡇⢘
⠀⠀⡅⠀⠀⠈⠃⠀⠀⠀⠘⠄⠀⣠⣶⡏⠀⠀⠀⠰⡄⠁⣰⣶⠚⢅⠱⢦⣀⣤⣴⡉⠏⣛⠉⠴⣣⠀⢉⠉⠀⣄⢹⠀⠘⢦⠛⡧⠘⠃⠙⠃⢴⣬⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡶⠀⢻⣿⡌⠛⠂⠀⡀⢾⠀⣀⠀⠘⠋⢼⣿⠀⣉⣤⢷⡆⢸⡍⠛⣀⠙⢆⡀⠁⠀⢿⣥⡄⠀⡀⠀⠇⠘⠀⠀⢀⠾⢋⡀⢸
⠀⠀⣯⠀⠀⠀⠀⢈⡷⠀⡴⠀⠀⣀⣤⠐⠒⠋⢤⡈⠀⡀⠉⠀⠀⠀⢻⡇⠀⣨⡼⣷⣾⠕⠊⡙⠰⠚⠉⢂⡀⠀⠀⠰⣶⡅⡀⠀⠀⠀⠀⠈⢰⡾⠃⢸
⠀⠀⠉⠀⠀⠀⠀⠈⠁⠸⢧⠄⠒⠂⢠⠀⠳⢄⠀⠹⣆⠀⠀⠀⠈⠂⢸⣇⠀⢈⠀⢻⡃⠀⣹⡍⠂⢀⡤⠚⠡⣄⠀⠘⣶⣴⡍⠆⠀⠀⠀⠀⢩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡼⠖⠀⠀⠀⢋⣶⡄⠓⡀⠉⠳⢦⡁⢀⠀⢸⡟⠀⠈⠀⣸⠁⡂⢹⣇⡀⠂⣠⡈⣰⠛⣀⠀⠿⣤⠀⢄⠀⠀⠀⣠⠞⠁⡄⣠
⠀⠀⡄⠀⠀⠀⠀⡾⢠⣾⠃⢲⣶⣟⠀⠈⠁⣿⠀⠀⣠⣤⣄⠙⢦⡀⢨⡗⠂⠔⠸⢷⣈⣱⡞⢋⠀⣤⠼⠈⢉⡴⢇⠀⠂⠀⠀⢸⠁⠀⣐⠁⠀⠈⠓⠹
⠀⠀⡧⠤⠔⠀⠤⢇⣼⠟⠀⣿⢿⣿⠚⣤⠀⠙⣧⡀⢀⠋⠀⠛⠲⠷⣌⡛⠛⠛⠛⠂⡉⢡⡀⣹⣶⠏⠠⢠⡾⡇⠀⢣⡾⠦⣀⠈⣦⠀⡉⠠⠤⠤⠄⣸
⠀⠀⠃⠀⠀⠀⣴⣾⠇⠀⠀⣹⢿⣿⠐⢸⡄⠀⠈⢷⡀⠻⣷⣄⡀⠀⠈⠙⠛⠧⠼⠶⠷⠾⠿⠿⠟⠓⣐⠿⡄⠈⠒⡋⠀⠞⠛⠛⡤⠟⠀⠀⠀⠀⠀⢿
⠀⠀⡆⠀⠀⠈⢻⠋⠀⣤⠀⠇⢸⣿⠀⠈⠀⠀⠀⠈⠳⣄⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠚⠟⣇⠈⡖⠀⠀⣾⠀⠘⣾⠤⠀⠦⠀⠀⠀⠀⣸
⠀⠀⡇⢠⠀⠀⠇⢀⡴⠉⠀⠃⣼⠇⠀⠀⢸⡀⠀⡀⠀⠻⣆⣀⠈⠛⢿⣶⣄⡀⠀⠀⠤⠄⢀⣀⣀⡀⠀⡈⠓⠀⡀⢸⣿⣧⣀⡀⠀⠋⠀⠀⠀⢀⠀⢨
⠀⠀⡁⠘⠆⠀⣀⡌⠁⠀⠁⠀⣿⠀⠀⠄⠀⣷⠀⠹⡀⠀⠙⢾⡦⠀⠈⠻⣿⣿⣷⣤⣤⣤⣴⡾⠋⣡⡞⠃⣠⡾⠃⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⢼
⠀⠀⠟⠃⠘⠃⢸⠀⢀⣿⣠⡄⢩⣷⡄⠀⠀⠘⣧⠀⠀⡀⠀⠈⠷⡼⢆⡀⠈⠙⠷⠾⠟⠉⠁⢀⣼⡟⠀⣠⠁⠘⠃⠸⣿⣿⠏⠠⠖⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠎⠀⠈⠁⠀⠶⠾⢻⣿⢀⡄⢻⣷⠀⠀⠀⢹⣄⠀⠘⠀⠀⠀⠈⠺⢏⠂⡀⠀⠀⠀⡀⠀⢠⡿⠀⡄⢙⡂⠀⠀⠁⠈⢡⣤⡀⢀⠀⠀⠀⠞⠁⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣹⣿⣆⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠈⠀⠉⠀⠈⠀⣈⣡⠏⠱⠀⠀⠀⣠⣌⠟⠻⢮⣧⣆⣰⠇⠀⢀⣿
⠀⠀⠇⠀⠀⠀⠠⠀⠀⣰⠊⠙⢿⣿⣿⡟⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⡏⠀⢠⠀⢠⡎⠁⢈⣅⢠⣼⠋⠙⢿⡎⢉⠉⢻
⠀⠀⠄⠀⠀⢠⠆⣠⠎⡉⠁⠀⠀⠙⢿⡇⠀⢆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠒⠋⣠⣼⠟⠀⢠⡞⠂⠺⣁⠀⠸⢧⣸⣧⡀⢀⠸⢅⣸⣇⣤
⠀⠀⠆⠀⢸⡅⠀⠹⡄⠁⠤⠀⠘⠇⣠⠀⠀⠘⢄⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠠⡾⢂⠀⠛⣷⣤⣤⣠⡄⠀⠀⠀⢤⡄⠀⠆⢸
⠀⠀⠂⠀⠃⠰⣦⡄⠈⢑⣆⣠⣤⡄⢸⠀⠀⠀⠀⢂⠀⠀⠀⠄⡀⠀⠀⠀⠀⠈⠉⠿⠿⠛⠉⠀⠀⣠⠀⣷⠈⡆⠀⠸⠁⢘⡁⢀⠀⠄⠀⠀⠉⡀⠀⢘
⠀⠀⠁⠐⠂⠄⠘⢷⠟⠛⠋⠉⠀⠀⢸⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢱⡄⠀⣦⠎⠁⠐⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⢾⣧⣀⡀⣀⣄⠀⠀⠸⢂⡀⠀⠀⢮⠀⣤⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⢀⡜⠀⠀⢸⠖⢲⠆⠀⠐⠛⠁⠀⠀⠀⣦⡀⠀⡤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠉⠁⠀⢠⡆⠈⠷⠀⠀⠆⠀⡏⠑⣄⣀⢀⠀⠀⠀⠢⠀⠀⠀⣠⡞⠀⠀⠀⡞⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠂⢀⡄⠀⠀⠸⠁⠀⠀⢆⠀⠐⠀⡇⠸⠟⠉⠉⠻⠷⣤⣀⠀⠀⠈⠀⠀⠀⢀⡰⢿⠄⠀⡅⠀⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡄⠀⠀⠀⠐⡀⠀⠀⣀⣴⡄⠀⡇⠀⣿⡟⠳⠦⣤⣤⡾⠛⠙⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⣁⣀⣀⠀⠠⠤⠤⠤⠀⠀⠀⢰⣿⣟⠀⢱⡄⣠⠀⠀⢹⣿⠀⢀⠀⠀⠿⣿⠀⠀⠘⠁⡇⠀⢸⡆⠘⣷⠀⠀⡀⠤⠛⠀⠓⠀⠀⠤⠤⠤⢀⡀⠀⢨
⠀⠀⣙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠁⠈⠁⠀⠦⠀⠀⠛⠀⠸⠀⠀⠂⣿⠀⠀⠀⠀⢱⠀⢸⡇⠀⢻⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠄⠀⠀⠀⢳⣄⠀⠀⠄⡇⠀⠀⢹⡀⠀⠀⠀⢸⡀⠈⣷⠀⠀⢻⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠒⣰⣤⡀⠀⠀⢸⣿⠟⠉⠀⣷⠀⠰⣿⣧⠀⠀⠀⢸⠃⠀⣹⣦⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠞⠛⠁⠙⠁⠶⠚⠛⠦⠤⠴⠿⠀⠀⠿⠗⠀⠀⠐⠚⠓⠘⠛⠹⠶⢶⡴⠆⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠚⠻⣿⡍⠻⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇
⠀⠀⣠⣄⢀⣠⣿⠷⣄⡙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡀⠀⠀⠀⣠⣿⣿⣦⡀⠀⠀⠀⡀
⠀⠀⢹⠟⠛⢻⡏⡀⢈⠻⣿⡿⣆⠀⠀⠀⠀⠀⠀⢦⡌⢳⣄⠀⠀⢀⣴⡇⠀⣠⡞⢁⣠⠀⠀⠀⠀⣿⣾⣷⣾⣿⠋⠉⢿⣿⣶⣷⣾⡇
⠀⠀⠀⠀⣰⣾⣾⣿⣾⢷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡀⠀⢀⣾⠀⢀⡿⠀⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⠄⠀⠀⠀⣽⣿⣿⣿⠁
⠀⠀⣀⣠⢿⠟⢹⣿⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠿⢀⣸⣿⠀⠿⠀⠶⠋⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣾⣷⣶⣶⣿⣿⡿
⠀⠀⣿⣯⠀⠀⠛⢿⠀⢼⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢻⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠙⠋⠙⢹⣿⠙⠉⠛⠙⠇
⠀⠀⠈⠻⢷⣤⣀⣀⣀⣀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠃⡞⠰⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣤
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⣴⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠟⠛⠁
⠀⠀⠀⠀⢰⡿⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠀⠀⣿⣿⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠈⢀⣴⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⢸⡿⢿⡇⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠈⠁⠈⠁⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⣰⠁
⠀⠀⠀⣦⡀⣀⣿⣿⣦⣀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡆⢰⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢁⣾⠏
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢛⠋⢴⣿⠏⢠⠆
⠀⠀⠀⠀⠀⠈⠻⠀⠉⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠋⣿⠈⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣛⠛⠋⠼⠛⣁⣴
⠀⠀⠀⠀⢰⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣆⠻⠏
⠀⠀⢠⡀⢸⣿⣦⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣷⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏
⠀⠀⢸⣿⣤⣿⠈⢻⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣀⣿⣿⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⢸⣷⡈⠻⣧⣄⣿⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡟⡏⠹⣿⢸⡏⢩⡇
⠀⠀⠈⠛⢷⣦⣿⣿⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⠀⣧⣼⠛⠘⢳⣂⡇
⠀⠀⠀⠀⣀⣽⡿⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⠟⠙⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣷⢶⣿⠛⣿⠛⠛⡇
⠀⠀⠀⠀⠉⠛⠷⠶⠶⢶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⠘⢿⠄⣉⢹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡟⠛⠛⢀⣿⣸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⡄⢸⡇⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠
⠀⠀⠀⠀⣠⣿⣧⣾⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣴⣟⠀⠀⣀
⠀⠀⠀⣰⡟⠉⢹⣿⠀⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡿⠿⠿⠛⠁
⠀⠀⢠⠏⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⣶⣖⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢀⣴
⠀⠀⠞⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠙⠉⢠⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⢻⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⠀⣿⢸⡿⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⣴⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠙⢀⡿⠈⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣇⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠶⠷⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⡠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⣆⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠊⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠀⠌⣉⠇⠈⠈⠉⠐⠀⠀⢀⡀⠀⠀⠂⠀⢫⠀⠀⠀⠀⠒⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢲⢄⠰⠘⠂⠀⠠⠄⠈⠁⠄⠁⢀⠬⠋⠀⠀⠀⠀⡒⠀⠧⡄⠀⠀⠀⠀⠄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠐⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⢀⠃⠰⠀⣰⠂⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢖⠲⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⠀⠀⡀⠠⠀⠻⠀⠀⡄⠓⠁⠀⠀⠂⠁⢀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠊⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⠀⡖⠀⠀⠄⠀⢡⡨⠀⠀⠀⢀⠀⡮⠑⠋⠀⠀⠁⠀⡀⠀⡀⢊⠍⠒⠚⠒⠠⠌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⠇⠀⠀⠀⠀⠀⠤⡀⢀⠄⣸⠀⡆⠀⠁⠈⠀⠀⠀⢠⠄⠠⠃⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⡌⠀⠀⠀⠀⠄⡇⠈⠃⣼⡄⠀⢠⠀⠙⠐⠀⠀⠀⠆⠁⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡘⢆⠀⢠⠀⠂⠳⢄⡊⢀⠃⠀⡼⠀⠠⢀⡄⠁⠈⠀⣤⢶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠒⠤⠀⠀⢷⠋⠀⠀⡧⠐⠂⣀⠄⠒⠀⣸⠃⠀⣯⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡟⠀⣸⠃⠀⠀⡀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢆⢀⠀⠀⠀⠀⣁⣀⣀⣀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣼⠃⠐⣯⡀⠀⠀⡁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠂⢒⠀⠱⠄⣠⠆⠐⠛⠋⠉⠙⠛⠻⢶⣤⣤⣄⣠⡴⠛⠁⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠃⠄⠘⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠊⢉⠓⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⠁⠀⠘⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⣠⣴⠶⠞⠛⢛⡇⠀⠀⠀⠀⠀⠀⠐⠂⠃⠀⠁⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⡤⠤⢀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠊⡇⠀⠈⡀⠂⠀⠀⠀⠀⠀⢤⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢩⣀⠠⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠰⠞⢀⠁⠀⠄⠀⠀⠈⠁⠀⠀⠐⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂
⠀⠀⠀⠀⠀⠰⠁⠈⠀⠀⡴⠃⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡤⠴⢦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢘⠛⠋⠀⠉⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢄⠀⠀⠐⡀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⣠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢣⡈⠳⡀⣀⠐⠀⠐⡡⠐⠀⠀⠀⠀⡀⠀⠀⠦⠤⠔⠀⠀⢀⠀⢀⡀⠠⠀⠀⠀⣀⣀
⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠘⠖⠉⠛⠤⠀⠐⠁⢛⠀⠀⠀⠀⠀⠌⠠⢀⣠⠀⠀⠀⡁⠀⠀⠀⠐⠂⠀⠘⠁⠀⢁⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠁⠚⠁⠰⠖⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠁⠔⠂⠀⡄⠀⢠⠇⠒⠀⠈⠰⠀⢀⡀
⠀⢠⠀⠀⠀⠀⠠⠄⠀⠒⠁⠔⢁⠠⢦⠀⠀⠖⠀⠆⠈⠀⠀⡥⠀⠀⠑⠠⠀⠁⠀⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠶⠀⠀⠀⠀⠀⠀⠀⠁⠠⠊⠀⠀⠀⠀⠀⠀⠀⠤⢄⠑⠂⠀⠐⡁⢈⠠⠀⠒⠚⠶⠈⠁⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠌
⠀⣶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠈⠀⢀⠐⠈⠀⠁⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢲⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿
⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⣴⣿⣿⣷⣾⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣼⠟⢒⡆⠀⠀⠀⠀⣀⣀⣄⣀⣤⣾⡷⢿⣿⣿⡿⠟⠉⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣄
⡟⠀⣿⣵⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣄⣨⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⢿⡿⣷⡀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣟⠛⠛⠛⢙⡃⠀⠀⢁⣿⣿⣿⣶⣶⠶⠆
⠀⢠⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣟⠁
⣴⡾⡗⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀
⣽⠟⢿⣶⡆⠀⠀⠀⠀⠀⠀⢸⣟⣹⣿⣟⠁⠛⣿⡏⠉⠻⣿⣿⣿⣧⣀⡴⢾⣿⣷⣴⣾⢿⡿⣿⣿⣿⡿⠛⠹⢿⣟⢾⣿⣿⡇⠀⠀⠀⠀⠀⢦⡻⠄
⡟⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣾⣽⣶⣤⣭⣳⣠⣼⠺⣿⡟⣹⣿⡦⣴⣿⣴⠿⠇⣯⣿⣿⣫⣯⣤⠠⣤⣶⣛⡮⣿⡻⠀⠀⠀⠀⠀⠀⢾⣷⡀
⠤⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⢠⣽⣿⣿⡿⣏⣾⡟⢿⣧⣿⣻⣾⡀⢈⣛⢿⣿⣿⣿⣿⠿⢫⣙⢿⣿⡿⢛⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄
⡿⠂⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣟⣺⡿⢧⣌⢁⡀⠀⢿⢿⣿⣿⣶⣾⣿⣿⣟⡍⣤⣴⣿⣿⢛⣅⣀⣿⣧⣆⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠓⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡽⠧⢥⠡⣟⢢⣙⣿⣿⣿⣿⡿⣿⣿⣿⠿⠯⢽⣿⣿⣿⣿⣿⣈⣮⣿⠵⠼⣿⠵⠶⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣌⣸⣶⣠⣿⡶⠿⣿⠿⠛⢛⣉⡉⢰⣿⣿⣿⣿⣿⡷⠀⠀⠙⠻⠿⠷⣷⣿⣾⣮⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣿⣿⡿⢀⣴⣇⠀⠀⠀⠀⢙⣿⣿⣋⣉⣁⣸⣟⡏⠀⠘⣛⡏⠀⢀⣉⣭⣿⣿⣿⣿⣿⣶⣄⢠⣀⣈⣿⣿⣻⣿⡿⣿⣾⣿⣿⠓
⢸⣿⣿⠇⣾⣿⡿⠀⠀⠀⠀⠀⠉⠛⢿⣟⠻⣿⣷⣶⡶⣶⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠋⠀⣭⡉⠉⠉⢁⣘⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀
⣾⣿⣿⣸⣿⣿⠇⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⢿⣿⣷⣗⣷⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⢀⣤⣤⣤⣤⣤⡿⣿⣿⠋⠟⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⣿⢿⣯⢹⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⡿⠿⣿⡟⣹⣶⣿⠟⠁⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠀⠰⠆⠀⠀⣿⠀⡙⢾⣿⠟⣿⣿⠁⡘⣿⢿⠋⣼⣯⣴⣷⡟⠩⣿⣿⣿⠀⠐⠋⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢶⡦⠀⠀⣠⠀⣿⠀⣀⣼⣿⣿⣿⣿⣾⡇⢹⠘⡀⣸⣽⣿⣿⣿⡿⠋⢹⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠤⠀⠻⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣱⣿⣿⣿⣿⣿⠄⠀⢸⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⣶⣿⡄⠈⢹⣿⣿⣿⡿⣿⣿⣿⠀⢿⣿⣿⠟⠉⠃⠀⠀⣸⣿⠈⠛⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿
⣿⣿⣿⣿⡇⢀⣴⣦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠻⡿⠃⠀⠘⣿⣿⣿⡇⠘⣿⣿⣶⣾⡿⠁⠀⠀⢀⠀⠀⣻⡿⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟
⣿⣿⣿⣿⣧⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⣿⣿⣿⡇⠀⣿⢿⣿⠏⣹⣷⣷⡞⠁⠀⠀⠿⠁⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⣿⡇⠀⣿⡇⠁⠀⠹⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠉⠉⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢂⠖⠐⠢⡀⠀⠀⠀⠀⠀⠀⢠⢔⠉⡏⠉⡳⣄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠑⡀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢀⠊⠀⠐⠀⠘⡆⠀⠀⠀⠀⠀⡧⠤⢵⣷⡮⠤⠼
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠀⠀⠜⠀⡅⠀⠀⠀⠀⠀⠃⡴⠋⣬⠑⢤⡜
⠀⠀⠀⠀⢀⡞⢐⠙⠻⠛⢑⠘⡄⠀⠀⠀⠀⠀⠈⢧⡈⠃⠀⠊⢀⠝⠁⠀⠀⠀⠀⠀⠀⠈⠑⠙⠚⠁
⠀⠀⠀⢀⠎⠀⠀⠉⠀⠈⠁⠀⠈⢄⡀⠀⠀⠀⠀⠀⠈⠉⠁⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣷⣦⣄
⠀⠀⠠⠊⠔⠢⠢⠄⠔⠄⠢⠂⠔⠜⠃⠀⠀⠀⠀⠀⡀⢠⠀⡴⢀⠂⠀⠀⠀⠀⠀⠀⡈⠘⣿⣯⣽⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣆⣹⠞⠒⠓⠺⣤⡄⠀⠀⠀⠀⠀⡀⠀⠈⠻⠟⠛⠉⠉⠹⣿
⠀⠀⠀⠀⠀⢀⣤⡶⠋⠉⠉⠀⠀⠀⠀⠀⠀⣈⠓⡿⠑⠖⠁⠘⠷⠊⣿⣁⢀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠰⠇⢀⡟
⠀⠀⠀⠀⢠⢃⣎⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠹⣷⠀⠀⢀⠀⠀⢀⣿⡍⠀⡀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠐
⠀⠀⠀⠀⡏⢸⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⢧⣄⣙⣁⡤⠾⠁⠀⠄
⠀⠀⠀⠀⠹⡄⠻⣄⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠐⠁⠼⠈⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣆⣤⡄⣀⡀
⠀⠀⠀⠀⠀⠙⠦⣈⡓⠒⢤⣤⠶⠋⠀⠀⢀⢤⡀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠠⣔⡪⠋⢯⠿⠄⠸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⣅⠀⠸⣄⠃⢊⣷⣂
⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⣤⡀⠀⠀⣀⢀⣸⠺⣀⢠⡄⠀⢀⢀⣴⠋⠀⠈⠰⡄⠀⠀⠀⠐⣘⢦⣧⢉⣁⠽⣵⠂
⠀⠀⢠⣾⣯⣥⡖⠋⣟⡏⢲⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣿⣄⡀⢀⣼⡟⠀⠀⠀⠀⠀⠃⠾⠙⠘⠆⠀⠑
⠀⠀⠀⢠⠤⠀⢉⣱⣿⣿⠉⠀⠀⠀⠀⠀⢘⢱⠀⠀⠀⠀⠀⠐⠈⢙⠛⠋⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⠻⡷⠒⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡠⢤⠤⢄⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠘⠀⠘⠀⢸⠀⠀⠀⠀⠀⠠⠐⠉⠉⠀⠂⣀
⠀⠀⠀⠀⢰⠁⠀⢸⠀⠀⠱⠀⠀⠀⠀⠀⠸⣾⣤⠁⠀⠀⠀⢀⡇⠀⠀⠀⢀⣦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠠⠀⣠⢂⢂⠀⠘⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠙⠙⠀⢸⠀⠈⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠘⢃⣼⣀⡟⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⠀⣠⣤⡀⠀⠀⠀⠀⢀⣤⡀⢠⣦⠀⢰⣶⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣄⠀⠀⠀⠀⠀⡶⣦
⠀⠀⠀⣸⠁⠈⠿⠁⢀⡇⠀⠀⠀⠀⠈⠷⣿⡼⠿⠤⡿⠃⠀⠀⠀⠀⠀⣿⣏⠿⣹⠂⣞⣯⢳⡄⠀⠀⠀⠀⠈⡽⠃⣸⠀⠀⠀⠀⠀⣧⡏
⠀⠀⠀⠘⢦⣀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⣸⣤⣤⡀⢿⠀⠀⠀⠀⠀⠀⠘⠿⣏⡁⠀⣨⠵⠛⠀⠀⠀⠀⠀⢸⡷⠋⠁⠀⠀⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠁⠀⠀⠀⠀⠀⠀⠀⢈⣅⠀⠀⠀⠀⠀⠀⠀⣼⣻
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠻⠞⠀⠀⠀⢀⢀⡀⠀⠈⠉
⠀⠀⠀⢸⡉⠉⠉⠉⠀⢹⠀⠀⠀⠀⠀⢀⣴⠚⠾⠹⠖⣦⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⠿⠿⣌⣷⠀⠀⠀⠀⠀⢀⣀⡷⣤⠟⠚⠧⢴⡆
⠀⠀⠀⢸⣇⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⣇⠤⠤⠤⠤⠟⣻⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⢹⠟
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠓⢶⠀⣠⣤⣼⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠛⠛⠋⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⠦⣄⡤⣄⡴⠋⠁
⠀⠀⠀⢀⣀⣀⣼⣭⣷⣤⡀⠀⠀⠀⠀⠀⢀⡀⠀⢠⢤⡄⠀⠀⠀⠀⠀⠀⢠⡏⠀⡴⢳⣄⣶⠀⣤⣠⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⣠⡄
⠀⠀⠀⠈⢧⣼⠃⠀⢈⣿⠃⠀⠀⠀⠀⠀⢿⡙⢦⡏⣸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠠⣇⡼⢿⡾⢸⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⢻⠂
⠀⠀⠀⠀⣴⣩⠿⠻⢯⣽⠀⠀⠀⠀⠀⠀⠀⣹⢂⣀⢷⡀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠻⠴⠚⠓⠛⠓⠋⠓⠂⠀⠀⠀⢀⡴⠋⣁⣤⠄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⡾⠉⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠛⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠗⠒⠒⠛⠉
⠀⠀⠀⢀⣴⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠘⣦⢟⣿⣿⣦⣤⣀⡄⠀⠀⠀⠀⠾⠀⠀⢀⣤⣴⠾⣆
⠀⠀⠀⠈⢠⡷⢻⣷⣿⣶⠀⠀⠀⠀⠀⠀⢸⡛⠒⢲⡿⠋⠀⠀⠀⠀⠀⠀⠠⠞⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⢉⡷
⠀⠀⠀⠀⠈⠁⠈⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣄⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣖⣫⡥⢤⣤⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⣄⠀⣰⠋⣳⠀⠀⠀⠀⠀⠀⢀⡞⢀⡤⠀⡀⠀⠀⠀⠀⠀⠀⣠⠖⣫⠗⢋⣡⠴⣶⡴⠃⠀⠀⠀⠚⠉⠉⠳⣤⠴⢻⡄⠀⣀⣤⠄
⠀⠀⠀⠀⣼⠿⢞⡵⠚⠁⠀⠀⠀⠀⠀⢠⠞⣠⠞⣠⠞⣡⢆⡀⠀⠀⠀⢾⣁⣀⣙⣫⡭⠶⠛⠁⠀⠀⠀⠀⠀⠠⠖⠛⢳⣀⣀⠀⠉⠉⢉⡀
⠀⠀⠀⠸⠧⠤⢿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠘⠁⠘⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠘⢋⠈⠳⠖⠛⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠉⠳⠶⠖⠛⠉
⠀⠀⠀⢀⡞⣩⣭⣽⡀⠀⠀⠀⠀⠀⠀⢠⣦⠀⣀⡀⣀⡀⣤⡄⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢸⠰⣟⢋⡿⢻⠀⠀⠀⠀⠀⠀⢸⣟⠀⣇⡿⣯⡟⣷⡏⠀⠀⠀⠀⠀⣿⣿⣟⠁⠀⠀⠀⣹⡿⠀⠀⠀⠀⠀⠀⣴⠞⠳⡄⢠⡞⠉⢳⡀
⠀⠀⠀⠘⢦⣍⣉⣤⠞⠀⠀⠀⠀⠀⠠⠞⠙⠛⠛⠓⠋⠉⠁⠉⠁⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⡿⠟⠁⠀⠀⠀⠀⢀⡼⠁⠀⠀⠹⡞⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⣰⢦⣼⠁⢳⡏⢸⣦⣤⠀⠀⠀⠀⠀⠐⠂⠒⠀⠒⠐⠀⠃⡀⠀⠀⠀⠰⠶⣶⢶⣶⡶⣶⣾⣿⡶⠶
⠀⠀⠀⠀⣠⠞⠀⠀⢻⡄⠀⠀⠀⠀⠀⠹⡄⠉⠀⠈⠁⠈⠁⣯⠀⠀⠀⠀⠀⢉⡁⢉⡁⢉⡅⢩⠀⣩⠀⠀⠀⠘⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠈⠛⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⡀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣠⣄⣤⣤⣠⣀⠀⠀⠀⣿⡀⣿⢀⣷⢠⣷⠀⣿⡀
⠀⠀⠀⠀⣿⡿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⢷⠿⣷⢿⠿⠷⠶⠶⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⠳⣿⢸⣿⠸⡿⠰⣿
⠀⠀⠀⠀⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠾⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠁⠀⠀⠀⠔⢂⣈⡭⠥⠤⢤⣀⡐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡷⠋⠀⠀⣀⣤⠴⠄⠒⠋⠉⠁⠀⠀⡄⠀⠀⢉⠛⠆⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡛⡴⠖⠒⠉⣁⣀⣀⣤⣴⣦⣾⣴⣿⣿⣿⣷⣷⠟⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠯⢱⣤⠐⢠⡉⢹⣿⠟⠉⠉⠀⠉⠉⠋⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣷⠂⠀⠀⡜⠁⠀⣀⠤⠴⠤⢄⠀⠀⠒⢓⣛⣒⣒⣚⣛⡒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣒⣸⡆⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠛⠋⡩⡭⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣨⢿⠞⢫⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠰⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⡿⠀⢀⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⡄⠀⠀⠀⠀⢀⡾⠀⢰⣧⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⡿⠟⠿⠷⠷⠼⢼⠟⠁⠈⢨⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠂⠀⠀⠀⠀⠀⠘⠀⠈⠀⠁⠁

⠀⠀⡤⠤⢄⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢄
⠀⠠⡦⠋⣴⠄⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠾⢿⣷⡄⠀⠀⢼⣷⠶⠶⠀⠀⠀⠤⠦⠶⠶⠂⠀⠀⠙⢿⡿⣶⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠓⠛⠚⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⠛

⠀⢸⣛⣖⣒⡀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⢠⣾⡿⣶⡀⠀⠀⢴⣲⣶⣶⠀⠀⠀⠘⢾⣇⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⢀⢼⢧⡀
⠀⠈⢿⣿⣿⡇⠀⠀⢸⣟⣏⣻⡆⠀⠀⠀⢈⣡⡇⠀⠀⠀⠘⢿⣷⠿⠁⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢻⡟⠆⠀⠀⠀⠛⠓⠚⠛⠀⠀⠀⠸⣼⡦⠃

⠀⠀⣀⣠⣀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣤⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⠂⠀⠀⠐⠾⢿⠷⠂⠀⠀⠾⠿⠿⠷⠂⠀⠀⠰⣿⣿⡟⠀⠀⠀⠈⠉⢹⣿⠀⠀⠀⢿⡿⠿⡷⠀⠀⠀⠀⣼⣿
⠀⠀⠈⠛⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣾⣿⡇⠀⠀⢀⣠⣷⢀⠀⠀⠀⠀⣤⠿⣄⠀⠀⠀⢠⣤⣤⣆⠀⠀⠀⢸⡗⡿⣤⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠘⢭⣦⡀
⠀⠘⠷⣿⡟⠇⠀⠀⠘⠃⠿⠙⠁⠀⠀⠀⠿⠽⠿⠀⠀⠀⠘⠋⠙⠿⠃⠀⠀⠠⠥⠥⠤⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⡭⢯⠃⠀⠀⠀⠳⠎⠑⠊

⠀⢀⡆⢀⣤⡀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣄⠀⠀⠀⢠⢴⠦⠄
⠀⢸⠉⠚⠙⠁⠀⠀⠈⣿⠾⡿⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⢼⣳⣷⠀⠀⠀⢿⡁⢁⣹⠃⠀⠀⠰⠶⠶⠷⠀⠀⠀⢀⢁⡈⣟⠀⠀⠀⠈⠷⠶
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⡿⣀⠀⠀⠀⢀⣰⡜⡧⡃⠀⠀⣠⣧⣼⣧⠄⠀⠀⠠⠏⠤⢀⠀⠀⠀⠀⠎⠵⡂⠀⠀⠀⢀⡝⢫⡀⠀⠀⠀⢀⣼⣦⡀
⠀⠰⠾⠿⠿⠇⠀⠀⠀⠀⠘⠿⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠿⠀⠻⠿⠀⠀⠀⠘⠓⠒⠛⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠈⠷⠾⠁⠀⠀⠀⠁⠸⠄

⠀⠀⠀⠐⠒⠂⠀⠀⠀⣴⢶⢤⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⢰⣦⣀⡄⠀⠀⠀⠀⠀⣰⣆
⠀⢰⣷⣷⣾⡄⠀⠀⢸⣿⣿⣿⡀⠀⠀⠸⠟⠿⠿⠀⠀⠀⣤⣤⣤⣤⡆⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠘⡿⠃⢠⠀⠀⠀⠈⠿⠿⡋
⠀⠀⠁⠉⠈⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣠⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣶⣿⣶⠀⠀⠀⠈⠰⣿⠇⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⣾⣟⣻⣤⡀⠀⠀⣾⣶⣳⣻⠂⠀⠀⠐⠒⠃⠀⠀⠀⠀⣆⠿⠿⣳⠀⠀⠀⢰⣶⣶
⠀⠀⠛⠿⠛⠀⠀⠀⠀⠿⠿⠻⠇⠀⠀⠀⠿⠙⠟⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠸⠋⠀⠀⠀⠘⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢐⢠⠄⠀⠀⠀⠀⠀⠆⣰⠂⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠅⠀⠀⢈⠈⢠⡀⠶⠿⠂⢠⡄⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠘⠀⠀⠂⠀⠀⠂⠀⠀⡀⢀⠹⠇⠀⠀⠈⣆⣨⣤⠴⠶⢤⣤⡄⠋⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⢀⢀⡃⠀⠀⠀⠒⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠈⠉⠁⢀⠀⠀⠀⠈⠉⠉⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⢀⠀⠀⠀⠐⡠⡶⠀⠀⢀⡀⠀⠠⠀⢠⡤⣤⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⢱⣴⠆⠈⠁⠀⣀⠸⠡⠀⠀⠀⠛⣰⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠁⠀⠈⠀⠀⠀⠀⡔⠈⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠃⠈⡴⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⡀⠀⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⣀⣷⡀⠀⠐⠢⠀⠀⠀⠀⠀⡴⣦⡀⠄⠀⠀⠀⠘⠀⢛⡑⢄⠀⠀⠀⠠⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠉⠓⠀⣀⠀⠀⠀⡀⠀⢰⡿⡁⠀⠀⣠⠀⠀⠤⠛⠱⢀⠑⢄⡀⠄⠈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡐⢋⠁⠃⠀⠀⣤⠂⠀⢀⠀⢳⠈⠳⣀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠄⠀⠃⠀⠀⠧⠀⠀⠀⢄⠀⠠⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠀⠒⠒⠚⠁⠀⠀⠎⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠐⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⠂⠀⠠⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡏⠀⠀⢀⠁⠀⠱⣈⠓⢁⣠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⣀⡀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⠀⠈⠃⠠⡤⠀⡞⠁⠀⠀⠀⡿⠀⠀⠀⣽⠆⠙⠇⠀⠀⢠⡀⢀⣄⡀⠀⠀⠀⣀⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠀⠀⠇⠀⠷⠁⠀⠀⠀⠀⠀⢶⠀⠀⣠⠇⠀⠀⠀⡄⠀⢸⠟⠉⠃⠀⠀⠀⠀⠀⠀⠤⠄⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠰⠀⢠⠁⠀⠀⠀⣀⢿⠀⢐⣆⣶⣤⣤⡶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠏⢉⡿⠂⠀⠀⠀⠀⠇⠀⠀⠀⣠⠤⢾⠆⠉⠀⠀⢀⣀⣁⠀⠀⠀⣀⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠠⠀⢠⠴⠋⠀⣼⠃⠀⠀⠀⠀⢰⠀⠀⢀⠀⠥⠂⡠⠟⠋⠀⠀⠊⠀⠉⠀⠀⠀⠁⠀⢀⡄⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡀⠀⠚⣁⠴⡔⠿⠋⠀⠀⠀⠀⠀⡌⢀⠀⠄⠀⠀⣽⠆⣩⡟⠛⠇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⣐⠁⠀⠉⠀⠀⠠⠄⠐⠁⠀⠀⢀⠀⢲⠀⢠⡥⢤⠤⠤⣶⣞⣋⣀⡗⢡⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⣤⡀⢀⡄⠀⢴⡀⠁⠀⠀⠀⡀⢀⡆⡙⠀⣴⡀⠀⣤⣈⠉⢨⣿⠉⠁⠘⡄⠈⠄⠡⡀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠄
⠀⠀⠀⠀⠈⠀⠉⠀⠤⠐⠃⠈⠁⠂⠀⠀⡀⢡⡌⠀⠁⣠⠿⠁⠀⣍⡙⠷⣼⣇⣴⡶⠂⢙⡤⠐⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠙⡄⢠
⠀⠀⠀⠀⠀⠀⢤⠀⠢⠐⠈⠰⠴⣤⣄⣠⠄⠙⠳⠀⡉⠁⠀⠐⠓⠀⠈⠂⠀⠉⠹⡆⠀⠢⠄⠀⠀⠀⠦⠀⣀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠰⢀⡒⠀⠀⠀⠄⠀⢠⠀⠀⠀⠀⠔⠛⡓⠆⠀⠀⣠⣴⡣⠖⠁⠀⣥⡀⠀⠘⠀⢲⠄⠀⠀⠃⡀⠀⠀⠀⠀⠰⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠄⠈⡀⠀⠈⡜⢀⣠⠀⠀⣉⣴⠔⠊⠸⣿⠶⠶⢷⣦⡀⠉⠰⠀⠀⠞⣿⡀⠄⠀⠑⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⢠⡞⠉⠀⠀⠀⠀⠀⠂⠀⠈⣻⣿⣦⣄⡀⠀⡀⠈⠻⡄⡀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⡞⠁⠀⠐⠂⠀⠀⠀⠉⠀⠀⢡⣄⠺⣿⣯⣻⠁⠀⠀⠈⠁⠒⠂⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠠⠄⠀⢀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠦⠠⠀⣄⣀⣀⡀⣀⣀⣀⠸⠷⣾⠛⣻⠀⠀⠀⠀⠀⠀⡀⠀⡄⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⡀⠂⣤⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣰⠋⠀⡏⠀⠀⠀⠀⠀⠀⡄⢓⡀⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⢘⡧⢤⣀⠀⡄⠀⢦⡀⣠⠀⠀⠀⠀⠀⠀⣠⣿⣤⡧⢠⡾⠀⣀⢀⡀⣄⠾⡁⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠝⠦⠀⠠⠆⠙⠤⠀⣀⠀⠀⠀⡠⢉⣰⠟⠴⠃⠰⠠⠀⠴⠋⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀⠀⠤⠈⠑⠒⠒⠦⢆⡀⠘⢂⡀⣤⠈⠫⡒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣰⣆⠀⢀⠀⢈⣡⣴⡴⠂⢀⣠⡅⣈⣳⣀⠉⠀⠈⠐⠐⢆⠀⠲⠿⢦
⠀⠀⠀⠀⠀⠈⢧⡃⣿⢂⣡⣶⠾⢁⡥⣄⠀⠈⠀⠀⠀⠈⢥⠀⠒⠠⡄⠈⠺⣆⠐⠀⠨⣷⡇
⠀⠀⠀⠀⠀⡸⠂⢻⡿⢻⢋⣀⡠⠁⠒⠐⠆⠉⠀⠀⠀⠀⠈⢣⡆⣀⣧⠐⠂⢼⠙⣦⠀⡼⣇⡰⣆
⠀⠀⢸⡀⢠⠀⡸⢟⡷⣟⢩⣀⣀⣠⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠴⢼⣄⢹⡁⡄⣿⣧⡟
⠀⠀⡄⢧⣊⢲⡟⡿⣼⠟⠉⠑⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠊⠦⣘⡁⠻⢷⣿⣸⣿⢠⠄
⠀⢣⠰⠞⣧⣟⡽⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢤⡀⣿⠹⣿⢲⡂
⠀⠈⣷⡀⢸⣿⡡⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣙⣿⡇⣿⣔⠇
⢶⡀⣏⢿⣾⣿⣼⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⢹⡟⣿⣿⠅
⠀⢻⣸⡎⣿⣿⠋⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⢾⣿⣿⠏
⠀⠈⣿⣧⣿⣿⢸⠟⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠈⠫⣼⣿⣿⡄
⠠⣿⡼⣧⣿⣿⡅⠀⣻⣟⡆⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡶⠷⣾⣿⡇⣷
⠀⢺⣿⡹⣿⣿⣧⠀⢊⣿⣷⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡿⢈⣿⣿⡇⡇⠀⠄
⠀⠀⠩⣾⠘⣿⣿⣧⠘⣿⡏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣽⡗⣾⣿⣿⣷⠁⠈
⠀⠀⠀⠙⣧⣿⣿⣿⣷⣜⣾⣿⣭⣶⣼⡆⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⣰⣶⢽⡟⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣯⣄⣻⣺⣿⣿⣦⠀⠀⠀⠀⠈⣻⠻⠾⠷⢧⣧⣯⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠙⢻⠿⢄⣀⢹⣿⣋⡉⠉⢉⠉⠙⠛⠻⣥⠋⢁⡔⢺⣓⣰⣿⣿⣿⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢿⣶⡞⣛⣶⣤⡔⣀⡤⣷⡺⠛⠉⠉⢉⣉⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠻⡟⠉⠝⠉⠂⠨⠃⠀⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⢠⠄⠒⠄⠀⠀⠠⠐⠢⡄⠀⠀⠀⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⢠⢒⠓⢄⠀⠊⠀⠀⠑⠀⡠⠚⠒⡄⠀⠈⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡿⢷⡄⠈⠒⠠⠬⢦⣆⢈⠀⠀⠀⠀⠀⠀⢀⣠⡴⠥⠔⠒⠁⢠⣾⢿⡆⠀⠀⠀⣀
⠀⠀⠀⢠⣶⡄⠀⢿⡆⢰⣿⠂⡀⠈⣿⣀⡴⠶⢶⣄⠙⣦⡙⢢⠀⠀⡴⢉⣴⠋⣠⡴⠶⢦⣀⣿⠁⢀⠐⣿⡆⢰⡿⠀⢀⣶⡄
⠀⠀⠀⠈⠛⠷⠤⠤⠙⣘⡇⣾⠟⠀⢻⡟⠀⠀⠴⠟⠀⠘⡑⡀⠃⠘⢀⢊⠃⠀⠻⠦⠀⠀⢻⡟⠀⠻⣷⢸⣃⠋⠤⠤⠾⠛⠁
⠀⠀⠀⠀⠀⠺⠿⢷⡄⣿⡗⣣⡀⠀⠈⢷⣴⣿⠃⠀⠀⠀⠀⣀⠀⠠⣀⠎⠀⠀⠀⠘⣿⣦⡾⠁⠀⢀⣝⢻⣿⢠⡾⠿⠗
⠀⠀⠀⠀⠀⠸⠟⠃⣴⡞⠧⠻⣅⠞⠳⣤⠉⠛⢳⡖⢒⣶⣄⣋⡀⢀⣙⣠⣶⡒⢶⡞⠛⠉⣠⠞⠳⣨⠟⠼⢳⣦⠘⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⠾⣭⣅⡘⢇⣾⣛⠈⠶⡁⠹⣿⠀⠀⣿⡏⢈⡴⠁⣛⣷⡼⢃⣨⡭⠷⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⡃⠀⢀⣠⣥⣭⣿⣛⠷⣿⣿⡇⢰⣿⣿⠿⣛⣿⣯⣬⣄⡀⠀⢘⡂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⣾⣿⣿⣿⡿⠿⠿⣾⣷⡽⢯⣾⣵⠿⠿⢿⣿⣿⣿⣿⣦⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠉⠛⠃⠈⠁⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠈⠁⠐⠛⠉⠻⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣿⣿⡁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⣄⣠⣴⠶⣶⣤⣄⠀⠀⢀⡄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠰⠂⣶⠐⠆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⢤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⣤⣾⣤⣶⣷⣦⡀
⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣧⠀⠀⢰⣶⣦⠀⠀⠁⠉⠁⠙⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠖⠂⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣄⢀⡀⡤⣽⣿⢻⣿⠀⠀⠀⠀⠀⠀⢉⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢀⡀⠀⠀⠈⣧⣶⡿⣿⣿⢿⣿⣦⣤⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠊⠉⠉⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣥⣤⣭⠄⠀⠀⢠⡾⢷⣿⣿⣿⣸⣿⣯⡽⠃
⠀⠀⠀⠀⢀⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⣄
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡆⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠴⠘⠃
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⣒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⡾⠄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠰⠆⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠚⠛⠿⠟⠛⠀⠀⠀⠀⠀⠀⠠⠒⠁⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠠⠄⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠁⠀⠘⠓⡄⠀⠀⠀⠋⠒⠀⠀⠛⠁
⠀⠀⠀⠂⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠂
⠀⠀⠀⠀⠀⢸⣏⣹⠄⠁⠦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠂⠀⠲⠒⠒⠶⠶⢶⡄
⠀⠀⠀⠀⢠⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠐⠢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣠⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠐⠆⣀
⠀⠀⠀⢀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⣀⣀⣴⣿⣿⣿⣿⣦⣤⣄⣀⡀⠀⠀⠀⠀⠐⠦⠶⠶⠶⠶⠦⠖⠀⠀⠀⠀⢶⡿⠿⠏⠉⠿⠻⠶⠤⠤⠀⠀⠀⠀⠀⢰⣦⡤⠤⠄⠤⠄⢤⣥⡄

⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠘⡄⢠⢃⡨⠛⠧⣽⡤⠃⠠⠿⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣧⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⠯⠤⠤⠔⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣄⠫⠑⠀⡀⠀⠀⠀⠠⠀⠀⠈⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠐⠐⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠉
⠀⠀⠄⠀⠀⠀⠀⠾⠆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⢀⣴⣿⠟⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠁⠤⢘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠘⠀⡒⠈⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⣾⡇⠀⠀⢠⡶⣆⠀⠀⠀⠛⠛⠛
⠀⠐⠂⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠈⠀⠀⠀⢸⣽⣿⡇⠀⢀⢀
⠀⠀⠀⠀⠀⣀⡀⠳⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⣠⣶⡧⠀⠀⠀⠀⠀⠻⠓⠀⠙⠛
⠠⠀⠀⠀⠀⢙⡃⠀⠀⠀⠐⠂⠀⢠⣤⡄⠀⠻⡟⠀⠀⠘⠁⠀⠀⡀⠀⢀⡴⡶⢢⠀⢀⣦⡀⠀⠀⠀⠀⢴⡷
⠀⠐⠢⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣤⣤⡄⠀⣾⠿⠀⠘⢷⣏⡿⠁⠈⠰
⠀⢈⠡⠀⠹⣾⡿⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠑⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⠮⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⢰⠀⠀⠆⠀⠀⠈⠀⢀⡤⠒⡻⣏⠑⠢⣄⠀⠀⠀⠀⢒⠀⠗⠀⣀
⣐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣏⣤⣤⡧⠼⣦⠤⢬⣇⠀⠀⠠⠈⠀⠀⠀⠐⠀⠀⢀⠠
⠀⠅⠀⠂⠀⢲⡶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠉⠲⣾⣀⠀⣹⡖⠉⢸⠀⠀⠙⠀⠀⠀⠁⣰⣰⡀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⣶⡆⠈⠁⠀⣠⣰⠀⠀⡄⠀⠀⠀⣀⡀⡀⡀⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠠⣤⣈⠉⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄
⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⡄⠀⠀⠀⠨⠁⠐⠀⠀⠀⠂⠄⠂⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠤⠖⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠘⠛⠃⠀⣴⢀⣿⣿⣷⣷⡄⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⠀⠀⢈⣿⣤⣶⡀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡿⠃
⠀⢠⠀⠀⠀⠀⢻⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⡀⠀⠀⠸⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠳⠀⠀⠀⠘⢿⣿⣿⡏⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠰⣿⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⠿⣿⡿⠃⠀⠀⠀⠗⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢤⣤⡤⠀⡆⢤⣤⡤⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠈⠀⠠⠄
⠀⠀⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣼⣿⣆⡀⠀⠀⢸⢻⣄⣀⣀⣰⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣿⣶⣴
⠀⠈⢻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸⡟⢿⣯⣽⠿⡿⠀⠀⠀⠀⢴⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⣿⠀⣧⢀⡆⠀⠀⢿⣿⣟⣿⣿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⢸⡇⣤⠀⠀⠙⠿⠛⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠹⠏⠃⠉
⠀⠀⠀⢠⣀⣀⡀⠀⠀⣇⠇⠀⢤⣀⠀⠀⢠⣄⠀⣿⣧⣿⣼⣅⡟⠀⠠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⢹⣿⠋⠀⢀⠀⠀⠀⠀⢻⣷⠀⠀⣿⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣒⡞⠛⣒⣦⠀⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣧⣿⡇
⠀⠀⠀⣠⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠛⠿⠇⠛⠼⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣿⣿⣿⣿⣦⠀⠲⢶⣶⣾⠿⠋⠀⠀⠀⠙⣿⣿⣿⣿⡟⠀⠀⣄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠚⠛⠛⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠁

⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⢺⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⣆
⠀⠀⠀⠈⢹⣯⠘⣿⡇⣿⠘⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠉
⠀⠀⠀⠀⠈⡿⠀⣿⠋⣿⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⡆⠀⠀⠀⠀⢰⡿⣿⣿⡀⢠⣤⣶⡶⢶⣦⠸⣿⣿⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣤⠀⢰⣶⠶⠀⠀⠀⠀⡈⢻⣿⠁⠀⠁⠀⠀⠀⠀⣼⣧⣼⣿⣇⠀⠉⣿⣷⣼⣏⡀⢻⣿⣇⣠⡟
⠀⠀⠀⠀⠀⣠⣴⡶⢶⡄⣿⣿⠀⢸⣿⢰⣶⣿⣿⡿⠟⢸⣿⡶⠆⠀⠀⠀⠀⢰⡿⠁⠈⣿⣿⡀⠀⣿⣿⠀⣿⣿⠀⠈⠉⠁
⠀⠀⠀⠀⣼⣿⡟⠀⠘⠃⣿⣿⠀⢸⣿⠀⠀⢻⣿⡇⠀⢸⣿⡇⠀⣄⠀⠀⢀⣾⠇⠀⠀⠸⠿⠿⠂⢿⠿⠴⠟⠃⠀⠀⢀⠀⡀⠤⠀⠂
⠀⠀⠀⠀⣿⣿⡇⠀⠀⣀⠸⣿⣤⣿⠃⠀⠀⢸⣿⡇⠰⠾⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠀⠐⠂⠁⠈
⠀⠀⠀⠀⢻⣿⣇⠀⢠⡟⠀⠈⠉⠀⠀⠀⠀⠸⡿⠅⠀⠀⠀⠀⢀⡀⠠⠀⠄⠐⠀⠁⠈
⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⡀⠀⡄⠠⠄⠀⠂⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣄⢠⣀⣀⡄⢀⣤⡄
⠀⠀⠀⠀⠀⠠⠄⠂⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⡄⠀⢠⠴⣶⣤⣀⣤⢹⣿⠀⢹⣿⣼⠀⣿⢿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠆⣀⣀⢀⣾⠉⠇⢸⣿⣸⡧⣶⣀⡀⡿⢸⡟⣦⠀⣿⣰⠜⠁⠉⠀⠛⠈⠁⠉
⠀⠀⠀⠀⠀⠀⢲⣿⠂⣀⡤⣄⢠⡶⠲⢠⡶⣦⢸⡗⠈⢿⡥⢸⣿⠠⣤⠸⠏⠸⠇⠿⠛⠞⠃⠘⠀⠙⠁⠉⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡿⢿⡇⠘⡟⣷⢸⣇⢠⠄⣧⠟⠚⠓⠃⠸⠁⠀⠙⠓⠁⠀⠀⠀⠀⠀⣤⡄⣴⡆⣶⢂⡀⢀⣈⢻⣴⡏⡴⣶⠆
⠀⠀⠀⠀⠀⠸⠁⠘⠓⠀⠋⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠀⠀⠀⢺⣇⢠⡏⠙⣷⡟⣷⡇⠙⣷⣿⠁⢈⣿⠀⣼⡏⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⡤⣄⢀⣤⡜⢿⡏⣿⠀⣖⡀⣿⠐⣿⢸⡏⠈⣿⣼⠀⠀⠉⠁⠉⠀⢸⠏⢿⠄⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⢸⣧⠟⢸⣴⣇⣸⣷⡅⣰⠿⠇⠿⠀⣿⡼⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢠⡟⠘⠁⠀⠀⠀⠀⠘⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠉⠈⠓⠁⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡈⢥⠀⠀⢰⠀⠀⠀⠁⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⡕⠀⠠⠌⡓⠀⠈⠣⠀⠀⡠⣀⠁⠍⠐⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠦⠀⢉⠤⢀⡀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠉⠙⣆⠈⢦⡀⣄⠀⡉⠀⠈⡸⠁⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢘⠔⠀⠀⠀⠀⠜⠢⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠐⠂⠈⠳⡀⣙⠊⠙⠀⠂⠙⠳⠊⣉⡡⡠⠐⠀⠀⠘⡀
⠀⠀⡀⠀⠀⠀⡀⠠⢠⠂⠠⠦⠠⠆⠦⠠⠶⠀⣓⠀⠄⠀⠀⠀⠀⠄⠀⠀⣘⠠⠀⡀⢤⡀⢀⠴⠇⠆⠀⠃⠘⠁⠄⣩⠤⣀⢀⠠⠀⠠⢈⠒
⠀⠀⠁⠀⠀⠀⠀⠀⠈⠆⠸⡀⠀⢀⠀⠀⡸⠀⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠈⠀⠈⣱⡄⠀⠀⠀⠀⢰⠃⠒⡄⣀⠀⠀⠠⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢠⠈⡀⠀⠀⢊⠀⣚⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠉⠉⠁⢐⠑⠘⡆⣶⠰⣆⠈⢆⣀⡀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠡⡌⠚⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠔⠂⢥⠰⡎⠀⠈⠂⠈⢁⠀⠀⠉⠄⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⠀⠀⢠⠃⠀⢠⠃⠀⠘⠀⠀⠀⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠘⠃⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠁⠀⠀⠀⢀⡅⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠐⡀⠀⠀⠈⠀⠀⠀⡄⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀
⠀⠀⠀⠀⠀⠈⠰⠀⠄⠄⠠⠄⢠⢐⠀⠄⠠⠀⠠⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⢄⠁⠠⠘⠀⠐⠈⠠⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠐⣀⢂⣛⡰⠏⠴⢆⣣⢈⡐⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢀⢉⡈⢀⣠⡶⠐⠂⠢⣤⡀⠀⠀⠁⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠆⣡⢼⡜⠁⠐⠒⠐⠀⠙⢦⠦⣅⠰⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠄⢠⠞⠁⠀⠂⡐⠂⠀⠑⣄⠀⠄
⠀⠀⠀⠑⠀⠀⠀⢒⡸⡆⢠⣀⣠⡆⢠⣆⣄⡔⡷⢲⡂⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣺⠰⠶⡷⠆⠀⠲⠶⠶⢸⠀⢀⠈⡀
⠀⠀⠀⢀⠈⠀⠈⠌⣳⢾⣀⠀⠀⠀⠀⠀⠀⣠⠷⡈⠄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⡀⢀⠀⠀⠀⠀⠀⠀⣼⠁⠤⠁
⠀⠀⠀⠈⠀⠠⠀⠠⠝⣛⢳⣆⠀⠐⠓⢀⣸⢛⡂⣁⠒⠠⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠛⠦⣀⠈⠉⢁⡠⠞⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠦⠹⢇⡺⠣⠍⢩⠱⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠉⢏⠈⠋⠀⠄⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠐⠁⠘⠠⠄⠁⠘⠀⠊⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⡿⠉⢻⡟⡿⠿⠿⠟⢿⡛⠿⠻⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⠿⣿⣿⠿⠿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑
⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠰⢶⠱⣾⡄⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢸⣆⠀⠠⡄⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⣦⡈⡵⡞⣧⠀⠀⠀⠌⠉⠉⠀⠀⠀⠀⠀⢸⠛⠀⠘⠃⠸⠛⣧⠀⠐⠀⠀⠀⠀⠀⢀⣆⠀⠐⣇⠀⠀⠀⠀⡆⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⢈⢶⠀⠀⢠⣏⠀⢡⠞⣷⣿⡆⠀⠐⣢⣤⣴⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⠛⠀⠀⠈⣄⢀⣀⣠⢼⣿⣆⠠⠀⠀⣷⣇⠀⢃⣷⣿⣿⣿
⠀⠀⠀⠀⢘⡷⠰⠁⡁⠀⢸⠏⣷⣌⣘⠻⠂⢙⠀⡀⣹⣷⣯⡼⣦⠀⠀⠀⢸⠀⠀⠀⠀⠘⡯⠄⠀⣷⢦⣿⡏⠏⡌⠉⣿⠉⠟⠚⠈⢉⣵⠀⠈⠙⢻⣿⣿
⠀⠀⠀⠀⠉⠱⠀⢀⣿⠀⣿⣀⠫⠹⡿⣏⣼⣿⠀⣶⣿⣟⢁⡀⣻⣅⠀⠀⢸⠀⠀⠒⠒⢀⣭⣦⡴⠁⣴⡶⡀⠀⠁⠈⠀⠀⠀⣀⡠⣾⣿⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⢍⡀⠈⠀⠡⠿⣽⢻⠀⠿⣿⠛⡏⠻⠿⣿⣷⠀⢸⠀⣴⡂⢰⡏⠉⣾⣋⡁⣿⣿⡇⠀⢸⣆⠀⠀⠀⠀⢠⣿⢿⠀⠀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠉⠃⢀⠀⠉⠆⠀⠠⢠⠤⢥⢰⠀⠀⠀⠛⠙⠀⢸⡀⠛⢁⠈⠃⣴⠅⢸⣽⣿⣿⡿⠀⠀⠈⢷⡀⢀⣺⠖⣏⣿⡇⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⠇⠀⡀⠋⠀⢀⣶⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣼⡤⠆⠀⠠⠙⣯⣾⣿⡄⠀⠀⠀⣸⣿⡆⠀⠀⢸⣿⠅⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⢸⡇⠈⠀⣤⣄⣴⣶⣾⣿⣿⣿⣀⢀⣤⣾⠿⠋⠀⠀⠀⠈⠁⠀⠰⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⣘⣷⣛⡂⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⢀⡴⡒⢦⡀⠀⠀⢐⣻⣿⡂⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡿⠃⠀⠀⠀⢻⣮⡻⣆⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣸⣻⣿⣻⡀⠀⠀⢸⡐⠧⠼⠃⠀⢠⣯⡛⢛⣽⡆⠀⢀⣤⣿⣿⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠻⣿⣾⡿⠃⠀⠀⠈⠓⠶⠶⠋⠀⠀⠿⢿⣿⠿⠁⠀⠈⠁⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣴⣾⣷⡄⠀⠀⠀⢀⠤⣤⡞⠁⠀⠀⠈⠳⡄⡀⠀⠀⠀⠀⣰⣷⣴⣧⠀⠀⠀⠀⠀⢀⣿⡀⠀⠠⢾⣟⣟⡷⠄⠀⢠⢴⣤⡾⠷⡄⠀⢰⣖⣟⣟⣗⡆
⠀⠀⠀⠹⠷⠿⠛⠂⠀⠀⢻⣜⣺⠇⠀⠀⠀⠀⠀⢚⣙⡶⠀⠀⠘⠿⢿⣿⠟⠀⠀⠐⢶⣼⣷⡿⠀⠀⠀⢾⣿⣿⡧⠀⠀⠈⣾⡿⠿⣿⠇⠀⠀⠻⠛⠛⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⣴⣷⣾⣶⣧⠀⠀⠀⠰⠶⠀⠰⠶⠀⠀⠶⠀⠶⠀⡆⠀⠐⢷⣾⣷⣄⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠙⠛⠿⠿⠄⠀⠀⣸⣟⣻⣇⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠹⠿⠿⠟⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⢠⣤⣠⣤
⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⢠⣄⣀⣠⣤⠀⠀⢀⢀⣀⣀⣀⠀⠀⢘⣶⣇⠀⠀⠀⠀⠠⢴⣶⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠸⣿⣦⣾⡟⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠠⢾⣿⠷⠆⠀⠀⠘⠛⠛⠛⠛⠀⠀⠘⠉⠛⠛⠋⠀⠀⠈⠽⡷⢶⡶⠀⠀⠀⠺⣿⣿⠿⠀⠀⠀⠀⠻⣿⢟⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠶⢻⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠟⠙⠇

⠀⠀⠀⠀⢀⣶⣠⣄⠀⠀⢀⡴⣶⣦⡀⠀⠀⠀⣠⡀⡠⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡤⠀⠀⢠⣤⡄⢠⣤⡀⠀⠀⣿⡆⢰⣿⠀⠀⠀⡀⠀⠄⠀⡀
⠀⠀⠀⠀⢼⣿⠿⠃⠀⠀⣸⣿⣻⣾⣇⠀⠀⢸⡿⣹⣷⡆⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⣀⡠⠊⠀⠀⠀⢈⣟⣿⣟⣿⠀⠀⠀⣻⣷⣾⣟⠀⠀⠀⣄⣠⣦⣀⡄
⠀⠀⠀⠒⡿⠛⠃⠀⠀⠀⠈⠙⠿⣿⠉⠀⠀⠸⠷⠛⠋⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠻⠾⠾⠋⠀⠀⠀⢷⣿⣻⣾⠃⠀⠀⠹⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡀
⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠙⢦⣠⣄⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢠⣦⣠⣦⠀⠀⠀⢠⣖⠀⠀⠀⠀⠀⠀⠀⡠⠺⣄⠀⠀⢀⣼⣥⣠⣤⡀⠀⢀⡤⠿⠿⢤⡄
⠀⠀⠀⠰⠺⢿⣽⠟⠀⠀⠀⢸⡓⢪⡇⠀⠀⢠⡌⢻⠀⠀⠀⠀⠸⣿⣿⢿⠷⠀⠀⠸⣯⣶⣠⡴⠀⠀⢀⣼⣿⡶⠃⠀⠀⠘⣖⣳⣛⣳⡃⠀⢸⣇⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠙⠉⠉⠻⠁

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⣧⡉⠙⣀
⠀⠀⠀⢸⠃⠁⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠠⣽⠁⠰⡅⣄
⠀⠀⠀⠸⡃⠐⢶⠄⠶⠐⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢀⣸⡅⠈⠀⠀⠀⠀⠠⡴⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣧⠦⠀⠀⢤⣦⡀⣼
⠀⠀⠄⠀⠘⠆⠰⣦⠀⠀⢄⠀⠀⠀⠀⠀⠀⠻⡀⠀⣾⣟⠁⣀⠂⢀⣀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡁⣰⣾⣿⣷⡟⠈
⠤⠤⢍⠀⠘⡇⠀⠛⠀⠀⡎⠒⠀⠀⠀⠀⠀⠀⠱⡀⠹⡿⢠⣄⡈⢋⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣴⢷⠿⠟⠀⠈⡀⢠
⠀⠠⣴⣆⡄⠇⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⣀⣤⣴⣄⠀⢈⢋⡅⠙⡿⢷⠒⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⢸⡟⠍⠀⠀⠀⠀⠘⠂⠙
⠙⣷⢬⢽⣿⡀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠙⠢⣹⣿⣀⠴⣷⠞⣷⣤⠀⠀⠀⠀⠀⠘⠁⢀⣠⡌⢷⠢⢂⠀⠀⠀⣠⣤
⣀⣾⣿⠈⠄⠁⠀⢀⡸⠃⠀⠀⣠⡾⢇⣠⠈⢋⡀⠀⠲⠀⡟⣷⡍⠁⠀⠀⢘⣦⠀⠀⠀⡆⢠⣠⣶⣿⠟⢁⢈⡀⣸⠀⢀⠀⠹⠟⢰
⢨⣿⡿⠀⠈⠀⠀⠋⠰⠃⠀⠀⣿⣿⣾⣿⠀⠏⢀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠠⢿⠀⠀⠀⢃⣾⣷⣭⣤⣤⡴⣻⡆⢸⣶⡘⠆⠁⠀⠴
⣻⣿⣷⠖⠖⠃⠀⠀⡘⠀⢴⣾⣿⣿⡟⣿⠀⣶⣿⡀⠀⣼⡇⣿⠀⠀⢰⠀⠀⣾⠀⠀⢀⣿⣿⣿⣿⡇⣭⠀⠈⣷⣆⠹⠿⢿⣧⣄⣐
⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⣴⣿⡟⠉⠁⢹⠀⣻⡿⠻⠾⠿⠗⠛⠀⠀⠀⠀⠀⠿⠀⠀⣿⡏⢻⠟⡏⠃⢹⡇⠀⠶⣿⡇⠀⠀⡈⠙⢻
⣿⣿⠿⠃⠀⠀⠀⠃⠀⠸⢻⣿⡗⡞⠀⢸⠀⠂⢀⠀⠀⣰⡄⢲⣄⠀⠀⠀⠀⢆⠀⠀⣿⠥⠄⠀⠁⠀⠈⠀⠀⢰⠈⢻⡆⠀⠁⠀⣸
⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠉⢼⡇⠀⢀⣾⠀⠁⠀⢠⣸⣿⠀⠸⣏⣶⡀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠺⠂⠘⠷⠸⢷⡀⣀⠀⣻
⣀⠀⣀⣀⠀⠀⠀⢀⠀⣀⠀⢰⡗⠀⠰⠸⠀⠀⣦⠈⢹⣿⡀⣶⣿⡇⢱⡆⠀⠸⣷⠀⠃⠀⠀⠀⠀⣰⡃⠙⠢⡄⢠⣄⣤⣿⠟⠋⣭
⣿⠀⣿⠀⣀⠋⠉⠄⠀⠛⠘⢋⠀⠀⠀⢠⠀⡀⠘⠆⢠⣿⠁⣦⢹⡇⠈⠀⠀⠀⢻⠀⣠⣠⣤⡤⢰⣿⠏⠀⠀⠀⣬⡖⠙⣷⣶⣂⠙
⣽⠰⢩⠀⠂⠀⠀⠀⠀⠀⠀⠈⣷⣀⡄⢸⢘⣿⢓⣄⢨⡿⡄⢹⣿⠁⢀⡀⠰⡔⢆⠀⠀⣥⡤⠄⣾⡏⢀⣾⠁⠀⠸⠃⠀⠀⣄⢿⠠
⣿⠉⢺⡬⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠈⣿⠺⣿⡾⣧⢣⡾⠃⠀⡀⢿⣆⠙⢄⠁⠀⢸⡇⢸⡟⠀⣸⣟⠀⠀⠀⡄⠀⠀⢀⠈⠐
⢿⢀⣸⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⢀⠈⠀⡈⣁⣿⣿⣜⡾⠃⠀⢧⢧⢧⠻⣄⠀⠀⠀⠀⣿⠸⠀⠀⣿⡏⠀⠀⣶⡇⠀⠄⠛⠃⠈
⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁⠈⠸⣧⢹⣿⣸⣿⡇⠀⣄⠀⠘⣯⠃⠙⢦⡀⠁⣁⣤⠀⠀⣴⣾⣷⣾⣿⣿⣤⣀⣤⠘⠷⢒
⡀⠘⣿⡇⠀⠀⠀⠀⢷⡀⠀⠀⠈⠃⠀⠀⢰⣿⡆⢻⣿⣿⡇⠀⠹⣆⠀⠘⣧⠀⠀⠉⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠘⠏⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠈⣿⣿⣄⠹⣿⠇⣴⡀⠹⣦⠀⠈⢷⣄⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢻⣿⠋⠀⣠
⣦⠀⠀⠀⠀⠀⠀⠀⣠⠘⠀⠚⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠸⣿⣷⡆⠘⢷⣄⠀⠙⢦⡅⠀⠀⣤⠀⢻⣿⣿⣿⣿⣿⠁⠀⢹⣧⠀⠟
⢻⣆⠀⠀⠀⠀⠀⢠⡷⡀⠄⠁⠀⠀⠀⠀⠀⢻⣿⣻⣿⠀⣆⠈⠛⠀⠀⠈⢻⣦⡀⠀⠁⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⢻⣶⣀
⠀⢻⡄⠀⠀⠀⠀⠸⡅⠟⠁⢰⠇⠀⠀⠀⠀⠀⠹⣿⣿⠸⣿⣷⣄⠀⠀⠙⢦⡙⣿⣶⡆⠀⠀⠰⠃⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿
⠀⠀⢻⡆⠀⠀⠀⠀⠙⢮⡷⠋⠀⠀⠀⠀⠐⣇⠀⣹⢛⣿⣛⢿⣿⣷⠀⢲⣤⡈⠨⡛⠇⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠈⣿⣶⡏⢸⣿⣿⣷⣏⠈⢶⣄⠉⠙⢂⡈⡅⠀⠀⠀⣴⡀⢽⣿⣿⣿⡇