Beep Emojis & Symbols

⠉⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⠀⣀⣀⣤⡤⠶⠶⠶⠶⣶⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠋⠉⣤⡾⠟⠛⠉⠁⠀⢀⣀⣀⣀⣠⣼⡿⠶⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠀⠀⠀⣤⡶⠶⠞⠳⢶⣶⡦⣤⣄⣀⣀⣀⣴⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⢻⣆⢠⣦⣀⠀⣀⣤⣀⣀⣀⠀⠴⠶⠶⠶⠶⣤⣤⣄⣀⣀⠀⢀⣠⣿⠃⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢸⣿⣦⣿⣄⣼⣿⣿⡷⠶⠿⠿⠋⠉⠛⠓⠶⠶⠿⠛⠁⠀⠉⠉⠙⠉⠉
⠀⠀⠀⠀⣄⠀⠀⣀⣼⣿⣶⠟⣥⣶⠄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⣿⠓⠛⠋⠁⠈⠀⢠⣾⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠒⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢦⣀⠀⢀⣀⣴⡿⢻⠏⢀⣾⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠂⠘⠋⠁⠈⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⢠⣿⣯⣴⣟⠉⣷⣄⠀⣀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⡁⠶⠋⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⡀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⢀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢯⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⡀⢀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠰⠧⡄⠀⠀⠀⠀⠀⠀⠀⠐⡗⠈⠦⡁⠀⠐⠀⠀⠀⢠⡴⣂⠶⣦⠀⠀⠀⠀⠀⠌⡳⠞⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠓⢈⣴⣶⡦⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠰⠞⢃⡱⡾⠛⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⢹⠅⠈⠁⠀⠀⠀⣀⠀⠀⠐⡀⢦⡷⠐⠈⠐⣶⠊⠃⢀⠀⠁⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⡜⠁⠃⢀⠈⠀⠈⢡⠘⠂⠀⠸⣄⠷⠉⠀⠀⠀⠀⠈⠀⡰⠋⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠿⠓⠄⣴⣾⣷⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⢀⠎⠀⠀⡤⠂⠀⠴⠠⠬⣿⣿⣏⠀⠀⠀⠀⠀⠀⣀⣀⠎⠀⠀⢀⠜⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢐⡀
⡀⠀⡠⠁⠀⠀⢐⠇⠀⠀⠚⢰⣾⠉⢿⣿⡄⠀⠀⠀⢀⠈⠙⠁⠀⠀⡠⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢠⣾⣷
⠁⡐⠁⠀⠀⢠⠿⠇⠛⠀⢀⣄⣬⠓⠈⠻⠿⠆⠀⠀⠀⠁⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡞⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠿⠀⢉⣀⠙⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⣰⠈⣿⡿
⡷⠈⠀⢜⣄⢖⣧⡿⠛⠛⠛⠛⠒⠶⠶⠶⠶⢶⡂⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣷⣟⢿⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣿⡇
⡅⢱⠄⠀⠉⠀⠈⠀⠶⠿⠿⣿⣿⣶⣶⡶⠀⠈⠓⠉⠓⠲⠟⠆⠀⠀⠀⠀⠀⠀⠀⣸⣇⢸⣿⠿⢼⣿⠀⠀⠀⠀⠀⠀⠀⠡⠾⡇⢸⣿⡇
⡅⠘⢄⣤⣤⣶⣴⣖⠲⠶⠶⠶⠶⠦⠤⠤⠤⠤⣤⠤⠄⠀⠀⠀⠀⠀⡀⠀⠈⠀⢸⣿⣿⠟⣷⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⡇⠀⠈⠉⠉⠁⠀⢭⣷⣶⣄⣀⣐⠀⠐⠀⠂⣰⣿⡟⠛⠛⠛⠛⠲⠞⣡⠄⠀⠀⢠⣤⣾⣷⠈⠉⣿⣟⠀⠀⠀⠀⠀⣠⣦⠁⠀⠠⣿⡟
⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⡀⢠⡆⠁⣈⡁⠀⣀⠀⢠⡌⠉⠁⠀⠀⣠⣾⢟⣽⣅⠀⠀⢈⣿⣿⣷⣄⣀⣼⣿⣿⣶⠆⠀⠉
⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠇⠈⠷⠀⠹⣿⠀⠻⡆⠘⣿⢀⣀⠀⢀⣿⣿⡞⠋⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠠
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣷⣄⠀⢀⠀⠀⠀⣀⠠⡀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⢧⠀⠀⠙⣤⠻⠄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣀⠀⠐⠘⠃⠐⠂⠀⠀⠈⢻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⡶⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢤⣤⣬⣭⣽⣿⣿⣿⣆⢿⣿⣿⣦⠤⠤⠄
⡇⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣟⣫⣥⣶⣾⣿⣿⡀⢸⡟⢀⣴⣿⣦⡀⢸⣿⣿⣿⣷⣶⣶⣾⠭⠛⠛⠋⠉⠉
⡇⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣴⣿⣿⣿⣿⣷⣌⣿⣿⠿⠛⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡶⡄⢠⠤⢠⠖⢰⣛⡆⠀⠀⠀⠀⠀⠀⠀⢸⡧⣿⢰⡯⠄⣾⡙⢠⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣭⠇⣼⣃⢸⣏⡘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠈⠓⠘⠧⢠⡟⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⢿⣦⡀⠀⠀⠀⠀⠀⢀⡼⣽⢆⡤⠄⣀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠈⠛⠫⣞⡙⣰⠯⠁⣾⣹⠆
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⡶⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠂⠸⠋⠁
⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⣰⢿⣷⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⡀⠴⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢣⠀⠶⠒
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣽⣶⣶⣭⣝⡻⣿⣿⣷⣦⣤⣤⡜⠰⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⠿⢿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢋⡖⠛⠓⢮⢻⣿⣿⣏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⣿⣿⣿⢸⡄⠀⠀⣸⢻⣿⣿⡿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣭⣓⣻⣵⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⣤⣶⣿⣶⣦⢡
⠀⠀⠀⢸⣿⠿⠻⣿⠁⣹⡏⠛⠿⣿⡿⠏
⠀⠀⠀⠸⠋⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⠛⢿⡿⠿⠿⠿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⠀⠀⠀⠀⠀⢀⣾⡇⢸⡇⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣥⣤⣤⣤⣤⣼⣿⣧⣼⣧⣤⣤⣤⣤⣤⣤⣤⣽⣿⣆
⠀⠀⠀⠀⠀⡜⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⠟⠻⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣷⣤⣼⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣦⣴⣿⣿⠏⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋

⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⣶⣶⡄
⠀⠀⠀⣰⡿⠁⠀⠀⣀⠀⠀⠀⣿⣿⣷⣄⡀
⠀⠀⢰⡿⠁⠀⢀⣾⠏⠀⠀⠀⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣿⠇⠀⠀⣾⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣷⡄
⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⡄⠀⠀⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠛⠻⣿⠙⠙⢻⣿⣿⣿⣿⣿⠏
⠀⠀⢹⣧⠀⠀⠘⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠻⣧⡀⠀⠈⠛⠀⠀⠀⣿⣿⣿⠟⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢷⠄⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣴⡶⠿⠋





⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢾⡅⢸⠥⢸⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡳⠘⠒⠘⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⣖⡘⢾⠃
⠀⠀⠀⠀⣮⢇⢹⣆⡘⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠙⠊⠀⠁⠀⠀⠀⠀⠀⠀⢀⣮⡗⣸⡁⢸⡍⢸⡼⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠛⠂⠛⠒⠘⠁⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⢰⣦⡀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡇⠀⠀⠀⠹⣿⣄⠀⠀⠘⣿⡄
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⡄⠀⠀⢹⣷
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢄⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡿⠛⠛⠠⣿⣿⡇⠀⠀⠀⢻⣷⣮⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⠃⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢿⣿⣷⣄⣀⣤⣿⣿⡟⠀⠀⠈⠹⣿⣿⣿⡇⠀⠀⢀⣴⡿⠃⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠘⠋⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣰⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣤⣼⣿⣿⣽⣖⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠶⠛⠉⠉⠁⠀⠉⠉⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣴⡿⠁⠀⠀⣠⣴⣶⡶⢶⣶⣦⡄⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⡿⠃⢸⡇⠀⠉⢻⣿⡆⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣼⣿⡟⠀⠀⣸⡇⠀⠀⠀⢻⣿⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠋⠉⠉⠉⠉⠉⠿⠟⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡇⠀⣀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⢛⣿⣷⣦⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣶⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⢞⣵⡶⠋⠉⠉⠉⢿⣧⠀⠀⣿⣿⣁⣀⣄⠀⠀⣴⣿⢹⣿⣌⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⣈⣿⣿⣦⣠⣤⣤⣤⣤⣿⣿⣿⠁⣀⣀⠀⠀⣾⢿⣶⣾⣿⣿⠿⠿⠿⠷⠀⢿⣿⣤⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣼⡗⠀⣿⣭⠽⠿⠿⠿⠿⠿⠿⣿⣿⡇⠐⠛⠋⢀⣴⣿⠞⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠛⠁⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣤⡶⠟⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⡿⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⣶⣶⠄⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⢠⣴⡆⣀⠀⠀⠀⠀⠀⢠⡖⠚⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢀⣿⣤⣴⣾⣁⠀⣰⣞⣉⠟⢀⣴⣿⠏⠀⠀⣾⣿⠛⠻⣿⣷⡄⠀⠀⢸⣷⣤⣎⠁⢰⠒⠂⢠⣶⠤⠀⢰⣃⡀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣸⣋⣉⢉⣹⡿⢻⣿⣯⣀⣠⣾⣿⣁⣀⠀⢀⣿⡿⠶⠖⠋⠁⠀⠀⠠⣾⣿⢀⡽⢢⣿⡥⢠⣾⣏⡄⣴⡿⠉⠛⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠁⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣍⣼⣭⣤⣬⣽⣮⣼⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠈⢿⡄⠀⠀⠀⠀⣶⡶⢶⣶⣶⣶⣶⠀⠀⠀⢠⡶⠶⠶⢶⣶⠀⠀⣶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠀⠀⠀⢸⣿⠀⠀⠀⠛⠀⠀⣿⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣼⣏⣀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⡄⠀⠀⠀⠀⢸⣿⠛⠿⢶⣶⠀⠀⣿⡇⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠉⠉⠛⢿⣦⡀⠀⠀⠀⣿⠀⠀⠙⠃⠀⠀⠀⠀⢸⡏⠀⠀⠈⠃⠀⠀⣿⣧⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠹⣷⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⣾⠃⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡀⢸⣇⠀⠀⠀⠀⡀⠀⢨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣤⣴⡾⠟⠁⠀⠀⠀⠻⣷⣶⣶⡶⠾⠿⠿⠻⠇⠈⠛⠛⠿⠿⠿⠷⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠠
⠀⠰⠒⡆⠐⢀⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆⠀⢰⣶⠀⠀⠀⢀⠀⠐⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⣠⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠃⡁⢠⡄⠀⠀⠀⢣⣢⠄⠀⠠⠴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⣰⡀⠀⠀⡀⣀⣈⠈⠀⠰⠀⠀⠀⠈⠈⠀⠀⠁⠈⠁
⠀⠀⠯⠟⠿⠂⠀⠿⠍⠒⠂⠀⠀⠀⠀⠀⠀⢠⣤⠤⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠂
⠀⡄⠀⠀⠀⠠⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠓⠁⠀⡀⠀⠀⠀⠻⠂⠒⠒⠐⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑
⠀⢣⠤⡄⢠⠬⡴⢦⡀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠈⠈⠉⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠤⠤⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠠⠄⠀⠄⠈
⠀⢲⠶⠶⠒⠒⠀⡤⠤⠜⠁⠀⠀⢀⠀⠒⠐⣲⠀⠀⠈
⡈⢉⣥⣤⣀⠶⠬⣧⣤⡀⠀⠀⠀⠈⠬⢖⡳⠐⠀⠰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡆
⠀⠀⠚⠀⠃⠀⠀⠉⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠠⠀⠀⢤⣤⠼⣤⠀⡇
⠀⡀⢀⠀⢀⢀⢀⣀⡤⠤⠀⠀⠀⠀⠀⣈⠊⠈⣧⣀⡤⠀⠀⠀⠐⠐⠀⠀⠀⠋⠂⠈⠁
⠀⢠⣀⣀⣠⣠⣀⣸⣇⠀⢰⠀⠀⠀⠀⠛⠁⠈⠙⠁
⠀⠐⠏⠝⠀⠺⠭⠊⠩⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠶⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠄
⠀⠀⠀⠀⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⠤⠀⠠⠀⠀⣤⣤⣤⣤⣤⠀⢠⣤⠄⣠⣤⠄⣠⣤⡤⠄⠀⠠⢤⣤⣄⠀⣤⣄⠠⣤⡀
⠀⠚⣡⢠⡀⠀⠀⠀⠀⠀⠙⢿⠀⡇⠾⠛⢰⣿⠃⣼⡟⢁⣴⣶⠿⣶⠂⠁⠉⢦⠘⣿⡄⢻⠇⠀⠀⠀⠄⠀⠀⠀⠠⡘⣀
⠀⠀⠸⠘⠃⠛⠲⠆⠦⠀⡄⡼⢇⠀⠀⢀⢼⡏⢸⣿⣁⣿⣯⡤⣶⡄⠒⣀⠀⣼⡇⢹⣷⢀⠀⠁⠀⠀⠀⠰⡀⠀⠀⠈⢩⢁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠆⢀⠀⢈⡿⡯⠿⠛⠳⣜⣀⣼⡟⢠⣿⠃⣾⢏⠀⠀⠀⡀⠐⠀⠀⢸⠀⠀⠆⡀⣠
⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣷⣾⣸⠁⠀⣄⠀⠸⡟⢋⣴⣿⠏⣰⡟⡀⠘⢃⠴⠁⠠⠤⠔⢋⠈⡉⣢⠜⠁
⠀⢀⠰⠀⠄⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠷⠈⢿⣿⡀⠀⠁⠀⣰⠿⠟⢋⣠⣾⠏⠀⠀⠀⣀⠄⠀⠀⠀⡀⢰⣴⣿⣷
⠀⣨⠲⣉⣤⡷⠲⠋⠉⠙⠚⢢⣀⡀⠀⠀⠀⠀⠀⢹⠿⠶⠖⠛⠓⠀⡠⠉⠛⡁⠀⠀⠀⡏⠀⠀⠁⠀⠀⠀⠀⣽⣿⣿⠃
⠀⠴⣻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡀⠀⠀⠀⠜⢀⠀⠀⠄⠀⢶⡀⠀⠀⣀⠀⠀⠀⢧⡀⠀⠐⣷⣦⠀⢀⡾⠛⠁
⠀⢾⠅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠦⠠⠀⠀⠸⠃⣀⣤⣄⠀⠁⢃⣴⣿⣦⠶⢶⡶⡶⡆⠈⢹⠉⠀⡞
⠀⣸⠀⠘⠙⠀⢀⠰⡀⠰⠀⢠⠀⠨⠉⠙⠀⢀⠀⠀⢈⣄⣙⢿⠏⠀⠀⠠⣵⡾⢼⣛⣻⣟⣛⡇⠀⠈⠲⠄⠀⣀
⠀⢹⣷⣤⣤⠴⠋⠋⠉⠃⠛⠁⠙⠒⠲⢦⣤⣧⣤⠤⠟⠁⢹⡇⢀⣤⣷⡦⠀⠀⠠⣿⣽⣯⣿⡇⠀⡀⠀⠐⣿⣽
⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢻⠃⠀⠀⢊⠀⢸⣿⠿⠆⠘⠓⠰⢿⣽⣯⣿⡇⠀⡅⠀⢸⢠⣤⣦⣀⡀
⠀⢺⣿⣷⣻⡿⣿⣦⣤⢤⣀⣀⣴⠛⡛⢅⠤⢰⡤⣀⠴⠋⠿⠀⠈⠁⠀⠀⠀⠀⠀⠈⢹⣿⣿⡇⠀⠆⠀⢸⣴⣿⣿⣿⣇⣰⡄
⠀⠈⠉⠉⠉⠹⢨⡍⠙⠊⠉⠉⠀⠃⠀⠈⠀⣬⡙⠲⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠁⠀⠰⢼⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠠⢡⡋⠀⠀⠀⠀⠀⠀⠀⢠⡀⠛⠉⠓⢻⢖⡆⣶⢸⣠⡀⡀⣀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠨⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠘⠃⠊⣱⣠⣶⡄⠀⠀⠀⠤⣈⡙⠃⠁⢀⣫⣞⢁⡼⢧⣕⢕⣝⢵⣫⠴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢯⡀⠀⠀⠀⠠⣤⣯⣝⣒⡥⢋⠜⣌⠧⠛⣿⣿⣛⢾⣟⣪⠭⠇⠀⣀
⠀⠀⠀⠀⠀⡀⠄⠄⠀⠁⠀⢀⡀⠀⢨⣿⡽⠶⠶⡎⣓⠇⠀⠈⢻⣿⣿⣿⠳⠾⠭⠯⠀⠂⢰⠆⣩⡀⠖⢀⡄⢠⠒⣠⠄⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠷⠀⠀⠀⠀⠹⠷⠟⢲⣜⣎⡀⠀⠀⠈⣹⣿⣷⡏⣭⠭⣽⣤⣥⣼⠷⣬⡴⠷⣬⣥⣦⣴⣠⡀⣾⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠛⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠛⠁⢰⣿⣿⡿⠟⠩⠄⠀⡀⠀⠀⠀⠀⠀⠀⠉⢉⣛⣷⠾⠴
⠀⠀⠀⠣⠀⠄⡀⠀⠀⠀⡀⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣏⣀⣀⡀⠀⠀⠀⠀⠂⡀⠀⠂⠀⠀⠒⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠡⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⠀⣀⠰⠉⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⠤⠴⡆⠠⣶⠛⠂⠀⠚⠛⠀⠀⣀⠜⠃⡤⠀⠀⠀⠀⡀⠁⣢⠄⣀⢲⠆⠐
⠀⣠⣤⣤⣤⣼⠁⠀⠉⠀⠈⠁⠀⠀⠈⠀⠀⢱⠀⠀⠀⠀⠀⢰⠁⠀⠈⠀⠃⢼⠈⣉⡁⢈⣩⡀⢋⡰⢀⡀⠀⠀⣥⡄
⠀⢺⣿⣿⡿⠏⠀⠀⠀⠐⠀⠂⠀⡐⢠⠀⣠⣙⣦⢠⠀⠀⠀⢸⡀⠀⢦⣈⣋⣴⣀⣉⣥⣀⣀⣄⡟⢠⠎⠡⠀⢀⡄
⠀⣿⣿⣿⣇⠘⣁⢲⠀⣃⠀⡄⠶⡀⢸⡀⠷⢉⣇⡈⠀⠀⠀⠀⠙⠶⢦⣽⣿⣬⣯⠙⢿⣿⢿⣥⣴⠇⠀⠀⠀⠀⠁
⠀⢸⣿⢿⢿⣦⡴⠞⠛⠉⠉⠙⠁⠉⠁⠙⠒⠻⣽⡀⠀⠀⠀⠀⠀⠀⠀⠳⢉⡙⠁⠀⠀⠁⡀
⠀⠈⣿⡌⠈⠷⠶⡆⠀⢦⣀⣀⡄⠀⣠⠆⣤⠤⠚⣁⠴⠂⠉⠀⠉⠢⠤⣄⠘⢄⠀⠀⠀⠀⠈⢤⠀⢀⠀⠀⣼⣦⣤⣠⣄⠆
⠀⠀⣿⣧⠀⠀⠀⠈⠛⠁⠀⠉⠙⣿⠉⠛⠁⠀⢀⡁⣀⣠⣄⣤⠀⣤⠀⣤⣌⣮⡓⣄⡀⠰⠒⢌⣛⠛⢷⡄
⠀⢼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠸⡟⠿⢿⡇⢿⣄⣯⡸⣧⡿⣻⣿⣾⡉⣶⣼⣾⣿⡜⢿⡍
⠀⣼⣿⣿⣿⣿⣿⡆⠀⣰⣄⠀⢸⣿⡇⠀⠀⠀⠀⠸⢦⡀⠀⠀⠀⠀⠀⠈⠀⣨⣟⣿⣿⢿⣿⢿⣭⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢹⣿⣿⣿⣿⣿⡇⠀⢹⣿⡇⢸⣿⣿⣇⠀⠀⠀⠀⠀⠙⠒⠞⠳⢦⡀⣤⣴⣿⣿⣿⡏⠀⠙⠉⠩⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⢺⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠱⢦⣄⡀⢀⣀⣀⣠⡤⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠒⠒⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣶⣿⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣶⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣆⠀⣀⣀⣀⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⣀⣸⣇⣀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣯⣤⣶⡿⠿⠿⠿⠿⠿⠿⢿⣶⣤⣽⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠋⣴⣾⠿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠻⣷⣦⠙⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠲⠄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⠆⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠓⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣁⡀⠀⠀⠠⠄⠀⠀⢀⣈⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠿⢿⣾⣶⣶⣾⡿⠿⠛⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠘⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠉⠉⠉⠙⢻⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⣷⣄⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠆⠀⠀⣠⣤⣤⣤⣤⡄⠀⠀⠸⣿⠄⠀⠀⢀⣿⡇⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠉⠉⠉⠁⠀⠀⠀⠉⠀⢀⣠⣾⡿⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠿⢋⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠁⠀⢀⣤⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⢸⡿⣡⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣰⣿⢋⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⠀⠀⠀⠁⢿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡿⠋⣰⣿⢃⣾⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⣿⡀⠀⠀⠀⠈⠙⠛⠛⠛⣹⣿⠟⠙⠛⣋⣉⣉⣉⠀⠀⣰⣿⣧⣬⣯⣹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣤⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⣰⣿⢛⣿⡟⠀⠀⠈⠉⢉⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣰⣿⢃⣾⣿⣀⣀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣬⣟⢻⣿⡟⠁⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢙⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⣧⠀⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⢶⡶⢶⡶⢶⡶⢶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⡀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠅⠂⠀⠀⠀⠀⠑⢼⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡤⠾⡀⠀⠀⠀⠀⠀⣀⣈⣷⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣴⡎⠀⠀⣀⣀⣬⣦⠀⠀⠄⣯⡀⠀⠀⠈⠑⠢⡀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣏⢋⣿⡿⣫⡤⡶⢶⣧⣬⣵⣤⣀⡀⢀⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⢟⡻⠙⡉⠉⠀⠰⠉⠉⠻⢿⣿⡟⠉⠛⢍⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡵⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠂⠹⡹⡄⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡎⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠑⣽⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠓⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⠁⠈⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠀⠀⠀⠀⠀⣀⣤⠟⠀⠀⠀⠀⠀⠀⣀⠁⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡼⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⢧⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣬⡼⡃⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⣯⣢⡤⢀⠀⡀⢀⣀⣀⣤⠖⣋⡉⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡾⠋⠁⠉⠛⠻⠿⠿⠯⢭⣭⢄⠈⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡘⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⠋⠉⠁⠀⠀⠀⠈⠉⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢃⣄⠀⣜⡇⠀⠰⠆⠀⠀⠀⠀⠀⠰⡄⠀⣿⡀⠖⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡽⠞⠋⠉⠭⢝⠢⡀⠀⣖⢲⡤⣄⡤⠒⠒⠛⢧⣞⣳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣠⡤⢒⡶⢋⣀⣈⣽⣖⣧⡀⠀⠀⠀⠀⠉⠛⢄⠰⠚
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⢺⢀⡤⣚⣩⠿⠛⠉⠉⠉⠉⠉⠙⠳⢤⣈⢳⣄⡀⠀⠀⢸⡌⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢋⡽⠋⣀⣴⠖⠛⠉⠉⢹⠛⠒⠤⡀⠈⠻⣟⠛⠲⢤⣀⣡⠇⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⠏⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢣⡀⢠⠙⣅⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⢳⠃⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢳⡀⢇⠸⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠇⡇⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⣇⢸⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠂⠀⠀⠀⠀⠸⡊⢂⠀⠀⠀⠀⠀⠀⣀⣧⠀⢹⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡄⡇⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⡼⢸⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡸⡄⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⢇⡏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠱⣜⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣼⢞⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠓⢍⣒⠤⠀⠰⠀⠀⠀⣀⡴⠊⠁⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣲⢤⣈⠉⠛⠒⠛⠋⠉⢁⣀⡤⢞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠙⠛⠛⠋⠉⠉⠀⠱⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⢧⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⠟⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠑⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠋⠀⢀⡴⠟⠉
⠀⠀⠀⠀⠘⠛⠷⠶⢤⣄⠀⢀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠈⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠐⠉⠀⡀⢀⡀⠀⠄⠀⡀⠀⡀⠈⠂⠀⠘⡄⢰⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⡀⠀⢀⠜⠋⠁⠀⠀⠀⠠⠀⠉⠃⢆⠀⠄⢀⠇⡎⠀⡰⠛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡴⠁⠀⠀⠰⠆⠈⠊⠀⠀⠀⠀⠀⠳⣄⣀⡀⠀⠀⠊⠉⠁
⠀⠀⠀⠀⠠⠠⠠⠀⣀⠀⠀⠤⠾⠁⡀⠘⠓⠀⢄⠀⠀⠀⠀⠀⠐⠀⠀⢃⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠢⢄⠀⠂⠈⡆⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠄⠀⠀⠀⠀⠆⠆⢸⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠰⠀⠂⠀⡄⠀⠀⡞⠀⠀⠀⠀⣀⠀⠀⡈⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠡⡀⠀⠀⠠⠀⠀⡀⠀⢠⠀⠀⠀⡰⠁⠀⠀⠀⡤⠒⠡⠤⠶⠆
⠀⠀⠀⠀⠀⠤⠶⢚⡅⢀⠞⠀⠀⠀⠀⢦⡀⠀⠀⠀⠁⠀⠀⢀⡠⠎⠀⠀⠀⠀⠘⢇⠠⣘⠒⠲
⠀⠀⠀⠀⠀⠠⠴⠋⠀⠃⠀⠀⠲⡄⠐⠀⠀⠉⠀⠒⠒⠂⠈⠁⠀⠀⠀⢀⡄⠂⠀⠀⠐⠈⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡆⠃⡀⠈⠙⢦⠀⣠⠀⢒⣉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢲⡄⠀⢸⡇⠀⢸⡇⣸⢡⠀⡄⠀⣳⢛⠀⢉⡁⠀⢰⠀⠀⡄⢀⡀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⡄⠘⠇⣦⠀⢣⠇⠼⡄⠀⠈⠁⢿⡀⠉⢁⠀⢸⠀⠀⡇⢸⠃⢸⠆⣸
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠹⣆⣘⠖⠀⠛⣞⣸⣧⣈⡉⠉⠉⠀⠸⣄⣐⡃⣾⠀⠚⢊⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠓
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢶⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣽⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⣳⠆⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣿⣿⡿⠁⢠⡴⠖⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠠⠶⣄⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⢰⣿⣁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⢠⣿⣿⠃⠀⠈⠙⠛⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⠀⣸⣿⠏⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣬⠋⠀⠿⣯⡀⠀⠘⣧⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠙⠛⠁⠀⠀⠒⢸⣷⠀⠀⠈⠻⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠛⠻⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠷⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣠⡴⠟⠋⠁⠀⠀⠀⠀⣰⡟⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠈⣱⠟⠛⢷⡄
⠀⠀⠀⠀⣠⡶⠟⠉⠉⠉⠉⠀⠀⠀⢀⣠⣶⣦⣴⣟⡀⠀⠀⠙⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠋⣿⠀⠘⢳⣾⠋⠀⣠⡞⠻⣦
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠠⣾⠛⠉⠀⠀⠈⣹⡿⠛⠂⠀⠀⠙⠻⢶⣭⣙⣛⣻⣿⡿⠛⠛⠛⢿⡍⠀⠀⢀⣿⠆⠀⠀⠙⠳⢾⡋⠀⣰⡟
⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡆⠀⠀⣻⣦⣴⠟⠁⠀⠀⢀⣤⣀⣈⣿⠿⠋
⠀⠀⠀⠀⠈⠻⣦⡖⠀⠀⣴⠂⣴⠟⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡾⠃⠉⠁⠀⠀⠀⣠⡾⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡴⠟⠛⠉⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢶⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣴⠾⢶⣄⠀⠀⠀⠀⣿⡷⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⣠⡾⢃⡴⠋⠹⣧⡀⠀⠀⢹⣇⠀⠀⠈⠉⠙⠛⠳⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣠⡾⠋⡠⠋⠀⠀⣰⡟⠻⢦⣄⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⣶⣦⣤⣾⠃
⠀⢀⣴⠏⣠⠞⣡⣜⠳⣾⠋⠀⠀⠀⠙⠷⣿⣍⡛⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⠻⣧
⣰⠟⣡⠞⠉⡞⣡⢘⡶⠻⣦⡀⠀⠀⠀⠀⠀⠈⠛⢦⣬⡿⠛⠻⠶⢶⣤⣤⣤⣿⠁⠀⠀⠀⢹⡇
⠛⢶⣧⣤⣴⠿⠋⠉⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠈⣽⠏⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣦⣀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⡀⠀⠀⠉⡿⠛⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠓⢦⣀⠉⠿⣤⡾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣌⡑⠲⣎⡁⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡙⠢⣼⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣷⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣾⣿⣿⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠛⠻⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣠⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⠟⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠛⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣸⡇⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣧⣾⣿⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄
⠀⠀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣾⣿⡿⠋⣿⣀⠀⠀⠀⠀⠀⢸⡛⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠁⠀⢠⡬⡇⢀⡀
⣼⣿⡟⣴⣿⣿⡿⣿⣶⡄⠰⣿⡿⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⠀⠀⠀⠙⡴⢤⡀⠀⣹⠟⠋⠙⠲⣭⡆⠀⠀⠰⢃⣀
⢸⣿⡀⣿⠃⢸⡇⠈⢻⣿⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⢸⣷⢀⣾⠃⠀⠀⠀⠀⠀⠙⠳⡒⠚⠋⠁
⠀⠹⢷⣜⠃⠈⣿⣀⣾⠏⠀⠀⠀⠀⣴⠆⡜⠀⠀⠀⣴⡧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠐⣿⣉⡼⠃
⠀⠀⠀⠉⠛⠛⢿⡋⠁⠀⠀⣤⣤⡀⠘⠋⠁⣰⣶⡴⠉⡟⠀⠀⠀⠀⣦⠀⠀⠀⠀⡠⠀⠀⢸⡿⠟
⠀⠀⣴⣿⣿⣧⢸⡇⠀⡠⠊⢙⠛⠃⠀⠀⠀⠈⢉⣥⡚⠀⠀⠀⣀⡘⢧⠀⠀⠀⢀⢀⣀⣴⡟
⠀⠀⠙⢿⣿⡧⠞⣠⣞⣛⠛⠋⠀⠀⠀⠀⠀⠀⠹⡟⠁⠀⠀⠘⠿⠃⠌⠀⠀⣄⠈⢻⣿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⡘⢷⠆⠀⢿⡇⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣻⠃⢀⣴⡇⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢰⠲⢄⡖⢦⣰⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠒⠊⠓⠋⠘⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⡇⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠘⠇⠀⠸⠇⠀⠀⠀⠀⠰⠆⠸⡇⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠛⠒⠶⢦⣤⡀⢠⡴⠶⠶⠶⠶⠶⠶⠶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢰⡄⠀⠀⠀⠀⠀⢸⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣿⣹⡇⠀⠀⠀⠀⣤⠀⠀⢸⣇⣈⣀⣀⣀⣀⣀⣀⣸⡷⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣈⣉⣀⣀⣀⣤⡴⠿⣦⣀⡀⢹⡏⢉⡉⢉⡉⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⠉⢉⣉⠉⠉⠀⣀⣀⠀⢹⣧⣼⡇⠘⠁⠘⠇⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⠀⠺⠻⠀⠀⠀⠻⠟⠀⢸⡇⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣿⠀⠀⠀⣀⣄⣀⠀⠀⠀⣸⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠿⣧⡀⠐⠋⠉⠙⠃⢀⣴⠿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⢸⡟⠷⣶⣶⣶⠶⢻⡿⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⢸⣧⡾⣏⠀⣹⡷⣾⡇⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠛⢿⡄⠈⢁⣀⣀⣀⣀⣀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⢸⣏⣉⣉⣉⣽⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣈⣷⣀⣈⣉⣉⣉⣉⣉⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠒⠒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣓⠒⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢠⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢳⡄⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠳⣞⣴⣣⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⣝⣮⣳⠚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡶⡫⠁⠀⠀⠀⠀⠈⣓⡄⠀⠀⠀⠀⠀⠀⣴⣊⠉⠈⠀⠀⠀⠊⠝⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠀⠀⠀⣠⠴⢚⣉⠥⠔⠒⠒⠒⠒⠒⠒⠦⢬⣉⠓⠦⣄⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡴⢋⣱⠖⢉⡄⠒⠈⠁⢠⠀⠀⠀⠀⠁⠐⠤⡙⠲⣎⡙⢦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡴⠋⣠⠊⡠⠊⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠑⢌⠱⣄⠙⢆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡜⢁⠚⠄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⡈⢧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠁⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠂⡠⠄⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠜⠀⠀⠀⠀⠀⠀⠀⢨⡏⢱⠄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢄⠄⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⠄⡀⠀⡀⠀⠀⠀⠀⠒⢐⠀⠀⠀⠀⢑⠄⢊⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢲⣌⡘⠀⠄⠀⠀⡀⠀⠀⠀⠠⠄⢂⣡⡖⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣠⠎⠀⠉⠙⠒⠶⠤⠤⠤⠤⠖⠒⠋⠁⠀⠻⣦⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠇

⠀⢶⣶⣄⠀⠀⠀⠀⣴⡄⢀⠀⣤⡀⡀
⠀⠀⠫⠻⣶⣦⡀⠒⢟⣿⣤⣆⣼⣿⣿⣆⡑⢀⣰⣤⡴⣤⣁⡐⣤⣴⡖⠰⣤
⠀⠀⠘⣷⠞⣿⢗⡛⡌⣹⣿⣿⠿⣯⠈⢹⠞⠿⢻⣴⣟⣿⣿⠐⢿⡿⣻⠃⠘⣣⣰⡆⠶
⠀⢤⡠⢄⡀⢺⠾⣷⣿⢿⣿⣏⢀⡩⡙⢷⠄⠀⠀⠈⠙⠉⠛⠀⢸⡇⢷⣤⡼⢫⡽⢃⠀⣴⠀⣄
⠀⠀⢙⢻⣯⡾⢷⣿⣾⣿⣿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢿⡀⠱
⠀⠀⣄⠱⣾⠃⢺⣿⣿⠋⠁⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢢
⠀⠀⣼⣄⠀⠉⣾⣿⡇⢼⡦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃
⠀⠀⠘⣿⣶⣷⣿⡟⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⢰⣾⡿⣿⣿⣿⡟⡟⢡⣄⣤⣀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠘⣿⣿⣿⣿⢋⡤⠸⣧⠄⠀⠀⠉⠙⠛⣷⣶⠶⠚⠂⠐⠂⠤⢀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣼⣄
⠀⠀⡈⢛⣿⢿⡇⣾⠗⠀⡿⠂⠀⠀⠀⠀⠀⠈⢷⠶⢦⡂⠀⠀⠀⠀⠠⢠⣄⣤⠾⠋⠀⠀⣠⡾⠈⣠
⠀⠀⠀⢈⣱⣾⡇⢿⢀⣾⠓⠀⠀⠀⠀⠀⠘⣀⣈⢠⣿⣦⣈⣿⠟⢣⡰⠿⢟⢻⣶⣦⣀⠈⢤⠛⠀⡿
⠀⠀⢀⠺⡟⢿⣇⡀⢸⣿⡆⢠⣴⠀⠀⠈⠛⢻⣮⠻⢯⠚⣿⢹⣴⣯⠿⠀⣾⢈⡿⠷⠹⣿⢣⡄⡘
⠀⠀⢺⠒⢿⣾⣿⢡⠈⠻⣇⠀⠀⠀⠀⠀⠠⠜⢻⠀⠀⢹⡏⠙⠁⡇⠀⠀⢩⡆⠰⠑⡆⠚⢇
⠀⠀⠙⠀⢨⣽⣿⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠁⠀⠀⣸⡏⢼⡂⠙⢦⠈⢥⠀⠆
⠀⠀⣤⠀⣾⣿⠳⣷⣄⣀⣼⣏⠀⡤⠀⠀⠀⢀⠢⡄⢰⠃⡐⠀⠀⢀⠀⢠⡟⠙⠾⠹⡆⠀⢣⢈⣆
⠀⠀⠈⣻⡉⢿⠀⢹⣿⡏⢙⡿⠀⢼⠀⠀⠀⡻⡄⠀⢸⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⡆⠘⠀⢀⡤⠡⡄
⠀⠀⠸⠿⣷⣿⠐⢈⣿⣿⣀⠀⠀⣼⡀⠀⡸⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠘⣧⠀⢠⠘⢃⡀
⠀⠀⠶⢀⣿⣟⢠⣼⣿⣿⡏⠀⠀⠸⣀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠐⡏⠀⠂⣸⡇⠀⠑⡀⠘⡇⠀⠇
⠀⠠⢰⡇⣿⣧⠋⢹⣿⣿⡇⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⡄⠀⠳
⠀⢀⣾⣿⣿⣿⠆⠈⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠟⠀⠀⢈⡤⠀⠀⠰
⠀⠸⣿⣿⣿⣿⠀⢐⢾⡟⢿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠈
⠀⠀⣿⣿⣿⡿⠀⠠⠛⡁⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⣶⡏⠀⠀⠀⠀⠀⢀
⠀⠀⡿⢻⣿⠗⠰⢷⡄⠐⣀⣤⡅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄⣸⠇⠀⠀⠀⢠⣶⠟⠇
⠀⠀⠛⣼⣏⣤⣤⣤⣼⣶⣿⣿⣟⠦⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⣻⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠈⠀⢨⡄
⠀⠀⠚⠛⣿⡿⢻⡿⣷⠶⠿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡤⠄⠀⠀⠀⠀⠀⠀⠂⠻⣤⣄⡀
⠀⠀⠀⠠⠘⣷⢿⣿⡗⠀⠈⠚⢀⠐⣧⢴⣄⣄⠀⠈⠉⠁⠀⠁⡈⢠⣡⣗⠌⠀⠀⠀⠀⠀⠀⠀⣹⣿⠆
⠀⠀⠀⠀⠂⢸⡾⠟⣏⣀⠠⠀⣈⡀⠀⠀⠈⢿⡻⣎⠊⣡⣅⡘⢰⠈⡳⣿⣄⠀⠀⠀⢀⠀⢀⣾⡟⢳⡶⣤
⠀⠀⠀⠀⠀⠋⠀⠀⠸⢿⣿⠲⠁⠙⠚⣿⠻⢦⡗⠸⡇⠀⣿⡇⢠⣤⢠⡿⢏⠂⣤⣄⠎⠈⡳⡈⠢⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣠⣸⢷⣬⣄⢸⡇⠀⠀⢠⠈⠃⢈⢹⠈⠀⠘⠿⣿⠏⢀⡀⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⢀⠍⠞⠘⢃⣀⣄⣀⣀⡶⢀⣈⣠⢰⣤⢰⡄⠚⠿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⢠⡖⠳⠃⠀⣿⠋⠠⠁⠘⠏⠈⠙⢻⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣶⣾⣶⠐⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠉⠙⢦⣄⠀⠀⠀⠀⣼⣿⣿⣿⣯⣿⣿⣿⡿⡥⣁⣀⣀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣬⣹⣿⣿⣿⣿⣿⣿⣽⣟⠓⠆⠢⠀⠀⠀⠀⢀⠐⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣏⣿⣶⡍⠙⠏⠑⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠿⠿⣿⣯⣕⡉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡏⠀⠀⠈⠈⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠉⢿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠰⠁⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠉⠉⠒⠢⠴⠾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠠⠂⠀⠀⢠⠀⣤⢤⣀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠐⠐⠂⡰⠁⠀⠀⠀⠀⠠⠞⠀⠡⠴⡶⠶⠶⠶⠶⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠢⠤⡾⠃⠀⠀⠀⣠⠃⣀⠴⢂⡂⡉⠉⠈⡀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⢀⣀⣐⣂⠀⠤⢀
⠀⠀⠀⠀⠀⠀⡈⠀⢀⡠⣠⠞⡵⢊⠀⣪⡥⠂⠒⠒⠒⠂⠶⢄⡀⠌⠂⠀⠀⠀⠀⠘⠣⣷⠈⠙⠛⠻⠿⠿⠿⠷⠮⠶⡑
⠀⠀⠀⠀⠀⢰⡇⠎⣩⠞⢡⠊⠐⣡⠎⠁⠀⠀⡁⠀⠠⠀⢀⠀⠉⠣⡔⠌⢢⡀⠄⣈⠁⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠇
⠀⠀⠀⠇⠰⡀⢓⠜⠁⢀⠇⠀⡼⠁⠀⠁⠀⠀⢂⠀⠀⠀⠀⠐⠀⠀⠸⡆⠀⢣⠊⠀⠈⠀⠈⢦⡀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⢠⠇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠄⠀⢻⠀⠘⠀⠀⠀⠀⠀⠀⠑⠤⠌⠁⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⢸⠀⠀⠀⠀⠀⠀⠀⡾⠂⠁⠀⠀⠀⢂⠀⢸⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢇⠀⠀⠀⠀⠀⢻⠿⠀⠀⠀⠀⠀⠀⠀⡜⠐⢰⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠑⣆⠀⠀⠄⠀⠨⠀⠀⠀⠀⠀⠀⢀⡼⡁⢠⣧⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠈⡳⢆⡀⠀⠀⠀⠀⠀⠀⡠⡴⠋⠀⡰⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡲⢌⡀⠈⠙⠻⠯⠼⠾⠾⠚⣩⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠙⠒⡶⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠴⠶⠞⠛⠛⠛⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⡀⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⢰⢂⢄⠀⠤⣤⣄⣀⣴⣉⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠣⢙⡆⠻⢦⡀⠘⡴⠊⠉⢳⡄⠀⠀⠈⠺⢺⡗⡀⠀⢨⠻⠋⠙⡟⢢⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠁⢀⣀⣅⣸⡀⠀⠰⣅⡴⠄⠀⠀⠀⠀⠀⠀⢠⠃⡷⠀⠢⠀⠸⡇⣜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣦⡀⠀⢀⣸⣿⡧⠝⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⢧⠤⡤⣤⣼⣤⣤⢤⣤⠀⠀⠀⣠⠤⠴⠶⢾⠀⠉⢀⡰⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠉⠉⠉⠉⠉⠉⢉⡏⠉⠉⠁⠀⠀⢀⣎⣡⡤⢲⣶⠋⠀⣠⣏⠀⠀⠀⠀⠈⠉⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⣀⣤⣶⣿⡿⠋⢴⣿⣿⣾⡿⢋⣩⣷⡄⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⠋⠀⣠⣔⣊⣀⡿⠿⡏⠀⠀⠀⠈⠙⠁⣰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⡾⠓⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠅⣼⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠁⠀⠀⠀⢠⣾⣿⣿⡿⠋⢹⠉⠙⡄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣾⣿⣟⣫⠤⠤⠔⠒⠚⠉⠉⠀⠀⠀⠀⠀⢀⡠⠾⠟⠛⠛⠒⠈⠉⢇⠀⢩⠑⡄⡜
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣠⣤⣄⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡾⠋⢛⠿⣿⣿⣿⣿⣿⡉⣉⣙⡛⠻⠿⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎⠀⠂⠉⠻⣿⣿⡇⠀⠀⣀⣉⡉⡚⠈⠑⡄⠀⠀⠀⠀⠀⠀⠸⠠⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡴⠁⠀⠀⠦⠤⡔⠁⢹⣗⣒⣂⣁⣭⣉⡇⠀⢀⠯⠽⠀⣒⣒⣒⣐⠁⢰⠤⠄⠬⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢃⠎⠀⠀⠀⠀⢢⠎⠀⣠⠎⠑⠒⠩⠭⣉⡉⡓⠈⠁⠀⢀⣀⡠⠤⠀⠘⠒⠊⠹⢹⢹⠉⠉⠐
⠀⠀⠀⠘⠮⠶⢌⣁⠎⣤⡀⠀⣀⠔⢁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⡏⠒⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣳⣤⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠙⢦⣄⡀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⣼⣿⠛⠳⡄⠀⠀⠀⠀⢱⣘⣤⠀⠀⠀⠀⠀⠀⠀⢹⡛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣿⣿⣿⣆⠀⣿⣿⣿
⠀⠀⠀⢻⡇⠀⠀⣿⡄⠀⠀⣀⠘⢿⠽⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠘⣧⡀⢤⣿⡗⠈⠁⠀⠀⢰⣿⢿⡃⠀⢀⢠⣀⠀⠄⠀⠠⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⡇
⠀⠐⠀⠉⠈⣷⣿⣿⠃⠀⠀⠀⣀⡀⠼⣆⠳⠈⠉⣇⣷⡄⠀⢠⣶⣦⠀⠀⠀⠉⠀⠐⡀⠀⠀⠀⠀⢸⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⡯⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⣏⢧⡠⠘⠛⠉⠀⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⣾⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⠋
⠀⡠⠄⣾⣿⣿⠃⠹⣄⢀⣀⣀⡀⠀⣀⠤⠐⠒⠈⠁⢾⡿⢟⠀⠀⠀⠀⢀⡀⠠⠤⠀⠀⢁⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢄⡀
⠀⠀⢰⣿⣿⠁⠀⣠⣿⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣹⡬⠆⠒⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠆
⠀⠀⣺⣿⡇⠒⢸⣿⠟⠉⢧⡀⠀⠙⣿⣄⡀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠚⠉⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡎⠁
⠀⠉⠹⣿⡇⠀⠘⢿⡄⠀⣈⣷⡄⠒⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣇
⠀⠀⠀⠙⢷⣄⡤⠔⠛⠛⠂⠀⢹⣴⠃⠀⠀⠀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⢹⣿⣿⠉⠻⠀⢻⣿⣿⡄
⠀⠤⠔⠊⠉⠙⠓⠶⠶⠶⠶⠚⠉⣹⣦⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣿⣿⡇⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⢻⣿⣧⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⣀⡤⠔⠒⠉⠀⣠⣾⣿⣶⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠘⣿⣿⡆⠀⠀⠀⠸⣿⣿⠆
⠀⠚⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠏⢱⣾⠿⠛⠃⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⣉⣤⣤⣤⣤⣬⣍⡛⠶⠀⠀⣀⣤⠶⠛⠛⠛⠛⠛⠷⣦⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡤⠶⠶⠶⣦⣬⡁⠀⠀⠘⠉⣠⠴⠞⠛⠛⠛⠻⠶⣦⣅⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢠⡆⣰⠇⢀⠔⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡠⠞⠻⢷⣆⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀⠈⣷
⠀⠀⠀⠀⢠⡟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣷⣄⣠⣠⠿⠒⠛⠶⠶⣤⣀⠀⠀⠈⢷⠀⢸⡇
⠀⠀⠀⠀⢸⠇⣿⠀⡇⠀⠀⠀⠀⣀⣠⡴⠚⠀⠀⠀⠀⣟⣹⣽⣁⣸⣿⣿⣿⣶⣄⠙⢷⡀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⢸⡆⣿⠀⣷⠘⠛⠛⠋⢩⡀⢶⣿⣷⡀⠀⡀⠉⠉⠙⠉⣉⣉⣉⣙⡛⠛⠷⠦⣿⣄⡈⠀⠺⣦⣀
⠀⠀⠀⠀⠈⠃⠹⣦⠘⢷⣄⠀⠀⠀⠻⡌⠻⢟⡥⣊⣤⡴⠾⣻⣿⣿⡿⠿⢿⣿⣿⣿⣶⣶⣭⣙⠷⣦⣀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⡠⠚⠙⠷⢶⣤⡤⠶⢚⣥⣞⣉⡠⠖⠋⠉⠀⢀⡄⢠⣤⡄⠀⠉⠙⠻⣿⣿⣷⣦⡙⢷⣄⠙⢷⡀
⠀⠀⠀⣀⡀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠔⠛⠒⡴⠋⠀⠰⡇⠰⡇⠀⡇⣼⣷⡇⠀⠀⢴⡆⠀⠙⢿⣿⣿⣦⡙⢷⡈⢷⡀
⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⡇⠀⠇⡇⢿⡶⠃⠀⢸⡇⠀⢀⡀⠙⢷⡝⣿⡌⢿⡄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡴⢳⡄⠃⠀⠃⠀⢸⠇⢸⡇⠀⠀⠘⠀⠀⠟⢹⠀⠈⢿⡌⢿⡌⢷⡀
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢸⠀⣇⢀⡇⠀⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⠀⣴⣏⣴⠀⠈⢿⡘⣿⠘⣇
⣿⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡜⠀⠀⠘⠀⠙⠛⠁⠀⠀⠀⠀⢸⠇⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠸⣇⢹⡇⢹
⠿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡇⠀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⢀⡿⠀⣿⠈⣇⢸
⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⣻⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⢈⡽⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠶⠋⠀⡿⠀⡿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠛⠁⢀⣴⣆⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⢀⠇⠀⡇⢸
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢹⣇⠀⠀⢸⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣧⣿⡄⠀⠈⠀⠸⠀⠄
⠀⠀⠀⢻⣄⣀⣀⣀⣀⣀⣀⣀⢻⣧⠀⢻⣆⠀⢸⡁⣿⠀⠀⠲⠶⣶⠂⠀⣠⠆⠀⠀⣠⠛⠁⠀⠀⣿⠀⠀⠀⠀⠁
⠀⠀⢀⡀⢹⣦⣤⣤⣤⣤⣤⣤⡄⠹⣷⡄⠻⣧⡈⠛⠃⠀⠀⠀⢰⠇⠀⢰⣏⡀⠀⠀⠹⣦⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠈⢿⣄⠙⢷⣤⠤⠤⠤⠤⠤⠤⠜⢿⣦⣙⢿⣦⡀⠀⠀⢀⡟⠀⠀⣾⠙⣧⠀⢠⣴⠏⠀⢀⡤⠚⣲⠎⡀
⠀⠀⠀⠀⠙⢦⡀⠙⢷⣶⠶⠶⠛⠛⠻⣶⡟⠻⣷⣽⣿⣷⣤⣀⡀⠀⠀⠘⠛⠃⠀⢀⣀⣤⠖⣋⡴⢞⣡⠊
⠀⠀⠀⠀⠀⠀⠙⢷⡄⠙⠻⠃⠀⠀⠀⠈⢻⣄⣀⡙⠛⠿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠿⠞⢛⣩⠖⠉⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣴⣿⣶⣶⠶⠶⠆⠀⠀⠉⠉⠉⠉⢉⣉⣡⡤⠶⠚⠉⠛⠛⠻⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠖⠋⠁⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⢁⣤⣶⠾⠟⠛⠛⠛⠛⠻⠿⠶⣶⣤⣀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣿⠛⠿⢶⣦⣄⠀⠀⡟⠉⢹⡇⠀⢀⣤⡶⠿⠛⠛⠛⠻⢶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣀⣠⡾⠃⠀⠀⠀⠈⠹⣷⠀⣧⠀⢸⡇⢠⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⡂⣻⣀⣸⡇⣺⡏⠉⠛⠛⠷⢶⣤⣀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠉⠉⠉⠛⢛⣷⣦⣄⡀⠀⠀⠈⠙⠷⣦⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⣁⣤⣴⠶⠾⠛⠛⠛⠛⠛⠛⠻⢷⣤⡀⠀⠀⠈⢻⣆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣤⣴⠶⠿⠛⣋⣥⡶⠟⢋⣁⣤⣴⡶⠶⠶⠶⢶⣦⣤⣀⠀⠙⠻⣷⣄⠀⠀⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢀⣠⡾⠛⢁⣤⠾⠛⠉⠀⠀⣀⣄⡀⠀⠀⠀⠉⠛⠿⣶⣄⠈⠻⣷⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣰⡿⠋⢀⣴⠟⠁⠀⠀⠀⠀⠸⣧⣤⠗⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣾⠟⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣾⠏⢀⣾⠋⠀⠀⢀⣴⠞⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣾⡏⢀⣾⠁⠀⠀⠀⠻⣤⡀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢰⡿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡘⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⡇⠀⣿⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠀⣹⡆⠀⠀⠀⠀⠀⠐⢯⣨⠇⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠸⣿⠀⠿⣬⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣏⠻⣦⡀⠀⠀⠀⠀⠀⠁⠀⢀⣿⠇⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢸⣇⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠳⣄⠀⠀⠀⠀⠀⠀⣼⠏⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⢿⡀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣙⣷⠀⠀⠀⢀⣼⠏⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⢷⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠋⠁⠀⠀⣠⡾⠃⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠙⠄⠈⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠺⣭⡿⠀⠀⠀⠀⢀⣠⡾⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⣄⣀⠀⠀⠉⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⠾⠟⠉⠀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣀⣠⣤⣶⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠿⠷⠶⢶⣶⣦⣤⣤⣴⣶⣶⠶⠶⠿⠛⠻⣍⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠠⠐⠉⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠡⢀⣀⠴⡵⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢐⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢄⣶⠠⡄⣀⣀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣅⣀⠀⡌⠩⢕⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠦⣌⣉⣩⡀⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢱⡀⠀⠀⠀⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⠀⢃⠀⢠⠟⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠈⣄⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠙⢓⡒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠈⠁⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣽⣧⠀⢢⠀⠀⠀⠀⠈⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢂⢀⡾⠘⡷⢤⠗⠀⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠈⠀⠁⣑⠿⠴⠚⠤⣀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢺⠋⠈⢠⣤⠐⠒⠀⠙⠃⡁⠀⠀⠀⠀⢀⠄⠒⠉⠁⠁⠀⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠉⠀⠂⠇⠀⠀⠀⠀⠀⠈⣦⠀⣠⡶⣥⣦⢄⣸⠇⠐⢾⠻⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⢾⣖⠉⡛⡀⠀⠀⠢⢄⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⢄⠙⣧⠀⠀⠀⠀⠀⠣⣙⠢⣀⡀⠙⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠑⢌⠺⡄⠀⠀⠀⠀⠈⠓⢌⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠁⠀⠀⠀⠀⠀⠀⠀⢀⣨⠤⠇⠀⠀⠀⠶⣀⠳⡈⢢⡀⠀⠀⠀⠀⠈⠂⣸⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢞⠉⠉⠉⠉⠉⠉⠉⠐⣷⠛⠉⢛⡻⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠛⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠰⠂⠀⠐⠀⠐⠐⠀⠀⠐⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡄⠀⠀⠀⡼⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⣀⣀⣁⣀⣀⡀⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠈⢧⠀⠀⡤⠊⠉⠁⡄⠈⠉⠙⠛⢔⠄⠈⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⢠⣄⣼⣃⡉⠀⠀⢃⠀⠰⠃⠀⢸⡆⢀⡀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⢀⣴⣿⣿⣿⣿⣶⡱⠀⠫⣯⡶⢪⣷⣾⣿⣿⣏⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠈⠿⣛⣿⣿⣿⣿⣶⣾⣿⣟⣛⢾⣿⣿⣿⣿⣿⢧⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡀⠀⠈⢊⡿⣫⡵⠞⠛⠉⠹⠛⠻⢿⡻⣧⣽⣿⣝⣛⡘⠀⢀⣀⣤⠴⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣰⢫⣾⠋⢀⡀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣯⠻⣿⡄⠈⠁
⠀⠀⠀⠀⠶⠶⠶⠶⠶⠆⠀⢰⢇⣏⠇⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢷⢹⣇⢻⡿⠀⠀⠰⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠈⡖⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠶⠒⠋⠉⠀⢸⡸⡼⡀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢹⠇⡿⢸⣧⠁⠈⠉⠓⠲⠦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢧⢳⡱⡀⠀⠀⠾⠀⠀⠀⠀⠀⠀⢀⡾⣸⢇⣿⠇⠠⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⡈⢳⣵⣌⡢⣀⠀⠀⠀⠀⠀⢀⣠⢞⣴⣫⡿⠃⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⢿⣿⣖⣶⣦⣴⣶⣶⣿⣷⡿⠛⠁⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢉⠉⠛⠛⠋⠉⠁⠘⣳⡀⠈⢆⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⡼⠀⠀⠀⡇⠀⠀⠀⡈⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠇⠀⠀⠀⠁⠀⠀⠀⢳⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠛⠟⣋⣭⣧⣤⣦⣶⣶⣷⣾⣭⣽⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢛⣯⣴⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠻⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠀⠀⠀⠀⠀⢀⡀⢄⡀
⠀⠀⠀⠀⠀⢪⣀⣀⣈⣲⡀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣔⣉⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⢠⠋⠉⣩⠷⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣋⣡⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣷⠀⠸⡇⠀⠀⠀⠺⣍⡉⠙
⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢠⡞⠉⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⣿⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⣘⡧⠀⠀⠀⠀⠀⠀⣾⣁⣀⡈⣷⠀⢸⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⣷⠶⠶⠚⠛⠻⠏⢹⠇⠀⠀⠀⠀⠀⠀⠸⣄⣉⣩⠟⠀⢸⣧⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠙⢦⣀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉⠁⠀⠀⢸⣷⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠻⢿⡿⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠞⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠞⠋⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣬⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⣃⠹⢿⣿⣿⡏⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⢀⡟⠉⣻⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠙⠙⠿⡿⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡶⠛⠓⢲⡇⠀⡸⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣛⡿⠿⢿⣶⣤⢤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣇⠀⠤⣾⢧⣴⠁⢰⠏
⠀⠀⠀⣀⡴⠶⠛⠛⠛⠉⣠⡶⠋⠁⠀⠀⠀⠈⣧⣄⣀⣙⣷⣀⠀⠀⠀⠀⠀⠀⣠⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⢁⣀⠨⠛⠁
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⠀⠙⢛⠿⠶⠶⠾⠟⢹⣄⣽⣧⡄⠀⠀⠠⠄⣠⡴⢋⣤⡾⠃⠠
⠀⠀⠙⣶⠃⠀⡀⠀⢀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠻⣷⣶⣶⣶⣿⣯⠾⠛⠁
⠀⠀⠀⠘⠷⣾⠁⢘⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠖⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣦⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⡾⢋⡔⠙⣧⠀⠀⠀⠀⠀⣿⡯⠛⠛⠻⠶⠶⣤⣤⣀⣀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⢀⣴⠟⣱⠋⢀⣴⢻⣆⠀⠀⢀⣠⡿⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢻⡟
⠀⠀⠀⣠⡾⢃⠜⠁⣼⣿⢷⡎⢻⡄⢀⣿⣏⠀⠙⢷⣄⣀⠀⠀⠀⠀⠐⠶⢦⣴⣟
⠀⢀⣼⠏⡰⣏⠀⢀⡿⠃⠈⢷⡀⠙⢋⣿⠟⢦⡴⠛⠉⠙⠻⢶⣤⣀⣀⣠⣴⣿⣷⣤⣀⡀
⣠⡿⢡⠞⠁⣸⣷⠟⠁⠀⠀⠈⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠙⠻⢦⡌⠙⣷
⠛⠷⠿⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⢲⣾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⠛⢿⠿⠟⠉⠛⢛⣷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣉⣓⡒⠶⠒⠦⠤⣤⣤⣏⣀⣀⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠶⢶⣶⣦⣬⣭⣍⣹⣷

⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣄
⠀⢠⣾⣿⠀⢸⣿⣷⣆⠀⠀⠀⠀⠀⠀⠠⣾⣦⠀⣶⠀⣠⣦⡀⠀⠀⠀⠀⠀⣾⣿⣟⡿⠿⢿⣿⣿⡧⠀⡀⠀⠀⠀⠀⢠⢏⡞⣠⠀⣀⠀⢠⢳⡘⣆
⠀⣿⣿⠛⠀⣌⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣩⣥⣰⠟⠀⠘⣻⣅⡀⠀⠀⠀⠸⣷⣿⣿⡀⠀⢀⣿⡟⣿⢿⣧⡦⡀⠀⠀⢼⢸⡁⡇⢸⣿⡷⢨⡇⡇⣿
⠀⢿⣿⡀⠤⠈⣠⣿⣾⣧⠀⠀⠀⠀⠰⣿⣻⣿⡇⢠⣤⣤⣿⣿⡟⣷⠀⠀⠀⠻⣿⣿⣿⣿⣯⣯⢹⣯⣿⣾⣿⡏⠀⠀⠘⣆⠳⠉⣴⣶⣶⠈⠼⣡⠇
⠀⠈⢿⣿⣶⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⢈⣽⣿⣷⡀⠈⢩⣿⣿⡏⠋⠀⠀⠀⠀⠈⠛⠿⠿⠗⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠁⠀⣿⣿⣿⠀⠀⠁
⠀⠀⣸⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⣼⠟⠉⣿⠃⠀⣿⡟⠻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⣷⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣀
⠀⠀⠀⠘⣷⣛⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠻⠿⠃
⠀⠀⠀⠀⢹⣿⡟⣷⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢰⡟⣿⣿⡆⣀⡰⣦⣰⣿⣷⣶⡀⠀⠀⠀⢸⡏⢉⣉⣉⣉⣉⣉⣉⡉⠙
⠀⠀⠀⠀⣸⣿⣷⡉⠁⠀⠀⠀⠀⠀⠀⣿⣰⣿⡆⠀⠀⠀⣾⣿⣰⡇⠀⠀⠈⢰⣿⣿⡙⠋⠁⠈⢋⣿⣿⡘⠃⠀⠀⠀⢸⡇⢻⣥⣿⣯⣽⣿⣤⡿
⠀⠀⠀⢰⣿⠋⢿⣇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⣠⣿⢟⣿⠀⠀⠀⣾⡟⣿⣅⡀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣴
⠀⠀⠀⠘⠛⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠙⠛⠁⠀⠀⠀⠈⠛⠁⠘⠋⠀⠀⠀⠛⠃⠀⠙⠁⠀⠀⠀⠘⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⢀⡴⢛⣉⣉⡛⢦⡀
⠀⠀⠀⣾⢱⡏⠀⠀⠹⡆⣷⠀⠀⠀⠀⠀⠸⣿⢇⣠⣀⠰⣿⡷
⠀⠀⠀⢻⡘⣇⠀⢰⡇⠁⠿⠀⠀⠀⠀⠀⠀⣴⣾⣭⣹⣵⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⢸⠦
⣠⣄⡀⠀⢳⡄⣾⠋⢰⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠻⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣭⣀⠰⠞
⢒⠶⣝⢷⡀⢻⡈⠳⡼⠃⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣸⣿⣿⡧⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⢰⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⣀⣚⠋⣿⣿⠛⣻⣀
⠉⢻⡜⡇⣷⠀⠳⣤⣠⡴⠃⠀⠀⠀⠀⠀⣾⠟⠁⢿⣿⡇⠘⢿⡦⠀⠀⠀⠀⠸⢿⣿⣿⣿⣤⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⢾⣿⣿⣿⣶⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠘⢷⣄⢿⡿⠀⠀⠀⠀⠸⣿⠇⣰⠟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠰⣮⡻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣭⣅⠀⣤⣤⠀⠀⠀⠀⠻⣶⣶⣤⣀⣀⣠⣴⣶⡾⠋⠀⠀⠀⠀⠀⣠⣠⣾⣿⠀⣄⠳⡜⣧
⠀⠀⠀⠀⢀⣴⣷⣌⠻⠎⠉⠀⠀⠀⠀⣤⣤⠀⣤⣤⠀⣤⣤⠀⣤⣤⠀⠀⠀⠀⠀⠹⣿⣷⡉⠋⢡⣿⡿⠁⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⠀⠘⡇⣷⢸
⠀⠀⠀⣴⢟⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⣤⣤⢀⣤⣤⠀⣤⣤⠀⠀⠀⠀⠀⢠⣿⢿⣷⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⠀⠼⣡⠇⡼
⢤⣀⡼⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⣿⣿⠘⣿⣿⠀⣿⣿⠀⠀⠀⠀⠠⣿⠏⠀⢻⣿⠃⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⣡⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣶⡾⣿⣿⣿⣿⣷⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣯⡿⣶⠋⠋⠈⠁⠻⠣⡟⣿⣿⣿⣿⣿⣿⣿⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠐⣿⠼⣿⣿⣿⣿⡟⠋⡟⠁⠟⠀⠀⠀⠀⣊⣸⡇⡟⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢰⣿⡀⠀⢁⡇⠉⠘⢾⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣁⢀⣨⣸⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡟⠙⠀⠈⠀⠀⠀⠀⠙⠘⣿⡇⠀⠀⠀⠀⠎⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢠⡄⠠⠐⠉⢁⡤⠤⠀⠈⠙⠻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⠀⢠⡀⢀⣠⣄⣀⣤⣄⠀⠀⠄⠀⢠⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢫⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠸⠈⣿⣿⣿⣿⡿⠇⠀⢠⡤⡤⡸⠃⠀⠀⠀⠀⢀⣄⣤⣤⣦⣿⣅⣿⢠⠀⢻⣿⣷
⠀⠀⠀⠀⠀⢸⣿⠦⠰⢠⣿⣿⣿⡋⠀⠀⠀⠘⢻⣷⠇⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⢻⣿⣿⡄⠈⣿⣟
⠀⠀⠀⠀⠀⢸⣿⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⣸⣿⣄⠀⠀⣠⣶⠿⣷⣄⣠⡤⠄⠀⣸⣿⣿⣿⡀⢿⣿
⠀⠀⠀⠀⠀⢸⢇⣴⣿⣿⣿⣿⣿⠉⠀⡀⠀⠀⢻⠃⣁⡀⠀⠾⠋⠈⣽⡿⠟⠀⠀⠀⣿⣿⣿⣿⣷⣿⡿
⠀⠀⠀⢴⣤⣼⣿⣛⣿⣿⣿⣿⣿⣶⣶⡷⠶⠶⠞⠛⢓⣦⣤⣤⣴⣦⣤⣧⣄⣀⣀⠀⠾⣿⣿⣿⣿⢱⡇
⠀⠀⠀⠙⠛⠋⠭⣭⣿⣿⣷⣤⣤⣤⣼⣿⣶⣴⣿⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣷⣽⣶⣾⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠘⣿⢫⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠁⠹⠛⢻⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠿⠻⠿⠛⠉⠹⠋⠉⠉⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⣿⣿⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠉⠁

⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠶⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⣠⣾⠟⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠙⠻⢷⣦⡀
⠀⢀⣾⠟⠁⠀⢀⣴⠞⠉⠀⠀⣤⡤⠴⠶⢿⣿⣿⣶⣤⡀⠀⣤⣤⣶⣶⣆⠀⠀⠀⠀⣀⣤⡶⠚⠋⠁⠒⠠⣴⡆⠀⠉⠓⢦⣀⠀⠀⠙⢿⣆
⠀⢸⠇⠀⠀⣰⠟⠁⠀⠀⠀⡔⠉⠀⠀⢀⣼⣿⣿⣿⡿⠛⠀⠙⠉⣿⠉⠀⠀⠀⠀⠘⠻⣿⣷⣦⣄⣀⠀⠀⠀⠱⣄⠀⠀⠀⠙⣧⡀⠀⠈⢿
⠀⠸⠀⠀⢰⡟⠀⠀⠀⠀⡌⠀⠀⢀⣴⣿⣿⣿⠟⠉⠀⣀⡠⠤⠴⠛⠒⠒⠶⠦⢤⣄⣀⠈⠙⠿⣿⣿⣿⣦⣄⣀⣿⣧⠀⠀⠀⠘⣷⠀⠀⢸
⠀⠀⠀⠀⠸⡇⠀⠀⠀⢰⣇⢀⣴⣿⣿⠿⣫⣤⡠⠖⣋⣥⣶⣾⡿⠿⠿⠿⠿⣿⣿⣶⣯⣿⣦⣄⣬⡙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⣿⣿⡿⠋⠁⠀⡼⢋⣴⣾⠿⠛⠉⠀⠀⠀⣾⡆⠀⢀⠀⢉⠛⠿⣿⣿⣿⣄⠀⠈⠛⢿⣿⡿⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢠⠎⣴⣿⠟⠁⠀⠹⠂⠀⠀⠀⠉⠁⢀⣿⠀⠚⠁⠀⠈⠻⣿⣿⣷⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⡿⠃⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣾⣿⠁⠈⠛⠀⠀⠀⠙⢦⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠉⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣼⠀⢸⣼⣿⡇⣴⣶⡆⠀⠀⠀⠀⠀⠀⠈⣶⣿⡄⠀⠀⠀⠀⠀⠀⠸⢿⠷⠀⣿⣿⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⠀⢸⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡟⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⡄⠘⣾⣿⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢰⣿⣿⠁⢠⠇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠀⠹⣿⣿⣧⡀⠋⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⡡⢣⣿⣿⠇⠠⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⢀⣄⠀⠀⠀⢋⡀⠀⠀⠀⢠⡄⠀⢀⠔⣡⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣄⡈⠁⠀⠀⠀⢸⣿⠀⠀⠀⢀⠡⢂⣡⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣭⣴⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⣾⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⢀⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⠀⢤⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⢰⠟⠀⠀⠈⠋⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡇⠀⠀⠸⠁⠐⠀⠀⠈⠠⣄⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⢀⠀⠀⠀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡁⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡀⠀⣠⠠⠚⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠘⠓⠲⠄⠀⠀⠤⡀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⢲⠃⠀⢀⡀⠄⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠨⠡⠾⢀⡀⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡄⠁⠀⠐⠈⠀⣠⠁⠺⠛⢀⠂
⠀⠀⠀⠀⠀⠀⢀⠴⠇⢠⡄⠀⢣⠐⠆⠀⠉⠀⢂⡴⠶⠀⠀⠐⠘⢿⣿⣿⣿⣿⠀⠀⠀⠆⣨⣿⠆⢀⣄⠀⠀⠁⠐⠁⢎⢠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡣⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠁⣏⢠⡌⢿⣿⣿⣿⠀⠀⠀⠠⢯⣿⠇⠉⢀⡀⠤⠀⠀⠈⠘⠄⠆⠄⠆
⠀⠀⠀⠀⠀⠀⢰⢀⠠⠠⠀⠀⠀⡀⠀⢀⠤⡠⣀⣀⠔⠉⠐⠃⠨⡃⢀⢻⣿⣿⠀⠐⢠⠠⠀⢙⠿⢻⡾⣁⠶⣾⠂⢀⠃⠀⢠⣄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⠅⣰⣯⡞⠙⢸⣿⠀⠀⠤⡠⢹⣇⡮⡙⢿⣿⢀⠀⠘⠘⣳⢮⣰⠞⢟⣷⣵⣯⠆⡍⠧⠀⠰⠌
⠀⠀⠀⠀⠀⢀⡼⡐⠜⠃⠀⢀⠄⠈⣍⢨⠙⣇⣽⡛⠒⢒⡖⠚⢿⠷⡶⣼⡸⣿⠉⢄⣤⠿⣅⠔⠁⣠⠞⠙⡿⠻⣾⢷⢿⠶⠄⠰⠞
⠀⠀⠀⠀⠀⠈⠁⠀⠛⠂⠐⠂⠠⣤⣿⣿⣦⡻⢤⡍⠙⠟⠳⠷⠾⠷⣮⣶⣿⠟⢛⡍⣠⠔⢻⣘⡶⠧⢤⡾⣳⣾⠇⠀⠘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⠛⢧⡜⠳⠤⣈⠉⠑⠚⠓⢦⣴⠟⣻⡿⠶⠺⡏⢁⣤⡿⣯⣀⣴⠋⢽⣿⡁⠀⠀⣀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⡰⣠⠀⠈⠒⠴⣇⠉⠙⠓⣦⡀⠈⠳⠾⢥⣴⢶⠟⠻⢃⣰⢾⠟⣒⣰⡏⠩⠔⠢⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠀⠀⠀⠀⠀⢉⣵⣾⠁⡙⠺⣧⣤⣠⣤⣤⠴⣾⡛⠳⣠⠼⠋⠀⠀⠀⠀⠰⠦⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶⡄⠀⠀⠀⠀⠀⠈⠛⠧⣤⣰⣇⣩⣁⣸⣤⠴⠓⠛⠁⣄⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢽⡇⠀⠘⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠉⠛⠓⣀⣛⡛⠿⢿⣿⣿⡿⠿⢛⣃⣤⣚⣋⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⣶⣿⣿⡿⠿⣒⣤⣤⣐⠻⢿⣿⣿⣿⣿⣿⣿⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠃⢠⣿⣿⠟⣋⡥⢶⣿⣿⣿⣿⣿⣿⣶⣮⣝⡻⢿⣿⡁⠘⠉⣠⣤⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢘⣩⣶⣿⣿⣿⣮⠙⠿⣿⣿⣿⣿⣿⣿⡿⠟⣲⣬⡃⠀⠀⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡴⠋⠸⣿⣿⣿⣿⡿⢋⣾⣿⣶⣬⣭⣭⡉⢴⣶⣿⣿⣿⠇⠈⠳⣄⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣨⣭⡍⣴⡞⡻⠿⢿⣿⣿⡿⣛⡛⢷⣦⢉⣭⣥⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠆⠸⣿⣿⡇⣿⡔⢧⣻⢆⣿⣿⠸⣥⢝⣆⣿⢸⣿⣿⡇⠐⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣿⣿⣶⣶⣿⣿⣿⣷⣶⣿⣿⣿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣧⣤⡄⠀⠘⢿⣷⣿⣶⣵⣾⣷⣤⣾⣿⠃⠀⠀⠀⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠃⠀⠀⠀⠀⠀⣰⣷⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣐⢾⣿⣿⣿⣿⣿⣿⡷⢂⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⢿⡿⠿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣶⣶⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⠟⡛⢋⣥⣬⣵⣷⣦⣴⣦⡙⣋⣛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣍⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢈⠀⠈⠲⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠉⠉⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⢀⡔⠉⠀⢈⡆
⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣴⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⢰⠋⠀⣰⠖⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⢠⡀⠀⠈⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣶⠀⢿⣿⣿⡇⠀⠀⠀⠐⠳⣈⠉⢳
⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⢀⣀⣉⡶⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⣼⣋⡀⠙⣯⡄⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠸⣧⠴⠶⠒⠛⠿⠉⡿⠀⠀⠀⠀⠀⠀⢫⡉⠙⣛⠃⠀⢿⡁⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣧⠀⠀⠀⠀⠹⣄⡀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣦⣾⣃⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠛⠛⠋⠹⡆⠀⠀⠀⠀⠀⠀⣠⣼⡶⠾⣇⡑⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣰⢿⣿⣿⣷⣾⠃⠀⠀⠀⠀⢠⡾⠃⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠧⠤⣝⣿⣿⡏⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣼⡁⣸⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⢀⣴⠟⠀⠀⠀⠀⢸⠁⡀⢈⣿⠀⡸⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣹⠿⢷⡟⠙⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠘⣇⠀⠙⠋⠛⣧⠔⠃
⠀⠀⠀⠀⢀⡄⠀⢤⣀⣀⣀⣰⠃⢰⠃⠀⢠⡟⠛⣾⡟⣿⠶⢦⣤⣀⣠⡤⡶⣿⢷⣄⠀⠀⠀⠀⠀⠀⣰⠋⢀⡤⠀⠊⠁
⠀⠀⠀⠀⡌⠀⡽⠋⡀⠀⠈⠁⠀⠘⠒⠦⣼⡗⢀⣿⠇⡗⠀⠲⣟⣨⡷⠂⠀⢻⣾⣿⣦⣄⣀⣠⣴⣋⡥⠞⠉
⠀⠀⠀⢰⠁⠀⡿⠃⢁⡀⢀⡴⠞⠳⣤⣀⣼⣧⣼⡟⣸⠃⠀⣼⠋⢉⡗⠀⠀⢸⣿⡇⠈⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⢳⡔⠉⣰⠏⠀⠀⠁⠘⠭⣝⣿⠿⠛⠁⠀⣸⠃⠀⠀⣳⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣞⠀⢠⡏⠀⠀⠀⠀⠀⢰⣩⡿⡀⠀⠀⠀⢻⡄⠀⠀⡼⠀⠀⢸⡿⠁
⠀⢠⡄⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⣮⣼⣏⠛⠳⠶⢦⣤⣼⣟⣋⡀⠀⠀⢸⡇
⠀⠐⠀⠈⢡⣦⣀⡀⠀⠀⠀⠀⠀⠀⢰⣵⣿⣤⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢳⡿
⠀⠈⠀⣴⠟⡡⠋⢱⣶⣄⡀⠀⠀⠐⡞⣾⠇⠙⢷⣄⣄⠀⠀⠀⠀⠒⠦⢤⣿⠁
⠀⣰⡾⢋⠼⠅⠀⣸⠟⠀⠹⣇⠂⣶⡿⠟⠶⠖⠋⠈⠙⠻⠶⣤⣄⣠⣴⣾⣿⠦⣤⣀
⣴⡟⡴⠋⢀⣼⠞⠁⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⢳⡆⠉⣿
⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⡾⠃
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣡⣿⣥⣤⣤⣤⣀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣀⣀⣉⠙⠛⠃⠀⠈⡽⠛⠳⣤⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣾⣥⣭⣍⣍⣛⣓⣚⠳⠶⠤⠬⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠛⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⡄⣤⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠋⡼⠁⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⢰⠃⣀⡀⢸⠃⠀⣠⠴⠶⠋⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠎⠳⣄⠀⠀⠀⠁⠀⣴⢤⠀⣴⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣸⣴⣦⠀⠀⠙⠋⠁⠙⠋⣤⣾⠵⢦⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣠⡼⠗⠀⠀⠀⠀⠈⠉⠀⠙⣤⡇⠀⠀⠀⢠⢦⣴⢦⡀⠀⠀⠙⠃⠉⠁⢀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⣠⠔⠚⠉⠛⠲⣌⠁⢀⡴⠖⠚⠀⠀⠀⣉⣙⣦⠀⢀⡴⠛⠉⠉⠉⠙⢦⡀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⣷⠀⠛⠋⢳⠀⠀⢰⡇⠈⠁⠀⢾⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⠧⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠼⠃⠀⠀⢾⠀⠀⠀⢀⣠⡤⠖⠋⠀⠀⣀⣸⠀⠀⣸⣇⣀⣀⣀⡈⢙⡶⠠⣤⣀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠛⢯⠀⠱⣶⠚⠋⠉⠹⣭⠄⣴⣾⣅⣀⠼⠉⢩⠿⠁⢰⣇⡈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡇⢀⣠⠆⠀⣀⣀⡀⠀⠀⠀⠀⣀⢀⣀⣀⡳⠄⠨⠂⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠉⣁⠤⠒⠉⠀⠀⠉⠀⠒⠒⠚⠁⠀⠀⠀⠈⠉⠒⠀⡀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡠⠊⠁⠀⢠⡀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠢⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⡄⠀⠀⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠎⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⡄⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢱⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢀⠇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠔⠻⣙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠲⢄⠀⠀⠀⡀⠀⠀⡜⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⢢⡀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠥⠀⠀⠋⢀⠞⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⠦⣀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠑⠢⣤⣀⡀⠀⠀⠀⡶⠀⠀⠀⠀⢀⣉⠤⠒⠁⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⣤⣀⡤⣄⣀⠈⠉⠙⠓⠒⠒⢒⣒⣈⣭⣤⣄⢀⡀⢴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡞⠀⠀⠀⠀⠉⠉⠛⠓⠚⠛⠋⠉⠉⠀⠀⠀⠈⠉⢳⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡴⢣⠖⠀⠶⠀⠀⠀⠀⢀⡰⠀⠀⣨⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⣤⠷⣞⠀⠳⡄⠀⠀⠃⠘⠉⡏⠑⠀⣀⠀⣠⣄⠀⢸⡇⠀⠀⠀⠘⠀⢀⠀⢀⡼⠀⠀⢀⣀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠜⠛⠏⠁⢀⠘⣆⢀⣀⡀⠀⠀⣠⣶⢋⣼⣿⣿⣷⣾⠁⠀⠀⠀⠀⣀⡀⢀⡞⠀⡀⠀⠚⠟⠂
⠀⠀⠀⢦⡀⠑⣄⢠⣄⢠⠎⠀⢹⣿⣿⠁⠀⠀⠈⠙⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠳⡀⣤⠀⡰⠃⢀⡴
⠀⠰⡦⢸⣷⡀⠈⣿⣿⠃⠀⠀⢘⣿⣿⢧⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⢠⢿⣿⡟⠀⠀⠀⢹⣿⡟⠁⢀⣼⡇
⠀⠀⠀⠀⢹⣿⠀⢸⣿⡆⠀⠀⢸⣿⣿⡎⠇⠀⣆⣠⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⢃⣾⣿⣿⠀⠀⠁⣸⣿⡇⠀⣾⡏⠁
⠀⠀⠀⠀⢸⡏⠀⣿⠻⡇⠀⠀⣾⣿⣿⣿⡌⢙⡟⠧⢰⣿⡿⠉⢿⣿⡆⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⣿⠻⡇⠀⢸⡇
⠀⠀⠀⠀⡼⣇⠀⡿⠀⢿⠀⠀⢹⡏⠉⢹⡇⠀⠀⠀⣾⣿⠁⠀⠀⣿⣷⡀⡀⠀⣿⠉⢉⣿⠁⠀⢠⡏⠀⣷⠀⢸⢳
⠀⠀⠀⠀⠁⠈⠀⠁⠀⠈⠁⠀⠈⡇⠀⠈⣧⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⢠⡇⠀⠸⡇⠀⠀⠈⠁⠀⠉⠀⠉⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣛⣁⣀⣀⣀⣈⣛⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣄
⠀⠀⠀⠀⣀⣤⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠈⣿⡄⠀⠀⠀⠀⠀⣠⡄
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃⠀⠀⢹⣧⠀⠀⠀⣠⣾⠟⠁
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢻⣿⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠸⠟⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠷⠿⠷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠉⠛⠉⠀⠀⠀⣾⡇⠀⠀⠀⠀⣠⣶⠶⣶⣶⢶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣦⡀
⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⣿⣅⠀⣼⡇⢀⣿⠃⠀⠈⠙⠻⣦⡀⠀⠀⣸⡟⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠈⠛⠟⠋⢀⣼⠟⠀⠀⠀⠀⠀⠘⣿⡆⢀⣿⠇⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⡷⠶⠶⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⣀⣀⡽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⣀⡤⠴⣖⣺⣭⠷⠞⠛⢋⠁⠀⠀⣴⠶⢦⣤⠀⠀⠉⠋⣀⣀⣀⣀⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⡧⢖⣺⣭⠶⠞⣿⣽⠷⠖⠛⠛⠛⠛⠛⠛⠛⠛⠶⢶⣿⣀⠀⠀⢿⡝⣏⠉⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠛⠋⣁⣤⠶⠛⠉⠀⢀⣀⡤⠤⠴⠒⠶⠦⠤⢤⣀⠀⠀⠉⠻⢦⣄⠻⣜⢦⠀⠀⠀⠙⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡾⠋⠀⢀⡠⠖⣊⣭⠶⠞⠛⠛⠛⠛⠛⠶⠶⣬⣉⠲⣄⠀⠀⠙⢷⣝⣯⢳⡀⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⣠⢔⣯⠶⠛⢩⡀⠀⠀⠀⠸⠇⠀⢀⡾⠰⢶⡍⠻⣦⡱⣄⠀⠀⠹⣿⣷⡱⣄⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣠⢞⣵⠟⣁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣀⣄⠛⠿⠁⠀⠈⠻⣎⢳⡀⠀⠘⣦⠻⣜⢆⠀⢰⡇⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡰⢣⡾⠁⢿⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⣿⠀⠀⠀⠀⢀⣀⠙⣧⠹⡄⠀⠸⣇⠹⣮⣷⡟⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣰⢡⡟⠀⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡾⠁⠀⠀⠀⠀⠈⠁⠀⠸⣇⢳⠀⠀⢿⡀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⡿⠀⢰⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢸⡇⢀⣀⠀⠀⠀⠀⠀⣠⠞⠛⠓⣶⣟⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⡷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡸⡇⠈⠉⠀⠀⠀⠀⠀⠙⢶⠶⠛⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣼⢃⡇⠀⣸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⢀⡿⠀⠟
⠀⠀⠀⠀⠀⠸⡄⠘⣧⠀⠈⣏⣷⡀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣼⣷⢠⡟⡴⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠁⠀⢹⣆⠀⠘⢎⢷⡄⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠳⠟⣰⢏⡞⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⠀⠈⠳⣝⢦⡀⠀⢸⡿⣮⠁⠀⢠⡄⠀⠀⠰⡆⠀⠀⢀⣠⠞⡡⠋⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⣌⣷⣄⠀⠈⠳⢽⡷⣬⣍⣁⣀⣀⠈⠀⠀⢀⣀⣤⡴⠞⣫⠵⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡴⠟⠁⠈⠻⣦⣀⠀⠉⠓⠮⠭⠭⢭⣍⣛⣛⣉⡭⠴⠒⠉⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡞⠋⠁⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠙⣿⠚⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣰⡟⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠠⠟⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠚⠛⠛⠶⢦⣄⠀⠀⠀⠐⠃⠀⠒⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⣴⠯⠤⣤⣀⠀⣀⠀⢀⡀⣠⠶⠚⢋⣉⣉⣲⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣷⣦⡭⠇⠛⢾⡟⠁⠓⠤⣾⣿⣿⣿⣿⣿⣿⣷⡄⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡏⢠⡏⢰⠃⣿⣿⣿⣿⣿⠟⣋⣤⡤⠶⣾⣳⣶⣶⣶⣤⣍⣻⣿⣿⣿⣿⡧⢻⠀⢿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠁⣾⠀⣿⠀⣿⣿⡿⢻⡷⢚⣭⣶⡿⠿⠛⠛⠛⠻⠿⢿⣿⣿⣷⣌⡙⠻⢇⡼⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠹⣤⠞⠁⡴⢋⣴⡿⢋⡁⠀⠀⢸⣿⠀⠀⠀⠴⠈⠛⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡹⣿⣿⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⢱⣿⠃⠦⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⣷⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⢠⡤⠀⠀⠀⠀⠀⠐⣿⡿⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣿⠇⢰⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣇⠀⢿⣿⣷⡀⡤⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠈⢁⠟⣼⡟⢀⡞⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⣦⠈⢻⣿⣿⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣴⢋⣾⠟⢠⠞⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⢿⣿⣿⣦⣍⣀⠀⠀⠿⠀⣀⣠⠶⣋⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⣿⣿⣿⣯⣽⣶⠿⠛⠻⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠉⠉⠉⠉⠉⠉⣠⠴⠀⠀⠈


⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣼⠛⢆⠀⡼⠉⠳⣄⢀⡾⠙⢦⠀⠀⢀⡴⠚⣆⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠓⠶⠃⠀⠀⠛⠁⠀⠀⠘⠛⠁⠀⠈⠳⣤⠏⠀⠀⠘⣧⠴⠋⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⡟⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⢀⡏⠉⠙⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠛⠉⠁⣿⠀⠀⢠⡿⢄⡀⣴⠋⠳⣄⠀⣰⠟⠳⣄⡿⠀⠈⠙⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠛⠛⠛⠻⠶⠶⠦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠈⠛⠁⠀⠀⠈⠛⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣦⣰⠟⠢⣾⠀⢰⠇
⠀⠀⠀⠀⠀⢀⣾⠃⡐⠁⠀⠀⠀⠈⠀⠐⠒⢤⠀⠀⡀⠀⠤⠄⠤⣈⡟⢠⠶⢤⣠⡟
⠀⠀⠀⠀⠀⣼⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠀⠀⠀⠀⠀⣿⣡⣿⠀⠀⠉
⠀⠀⠀⠀⣸⡏⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢠⡿⠏⢻⡄
⠀⠀⠀⢰⡿⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣷
⠀⠀⢠⣿⠁⠘⠤⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢰⠀⡆⠀⠀⠀⠀⠀⢀⣀⠷⠘⣧⣤⣄⣀⢀⣀⣀⡀
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⣸⠃⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⣉⡉⠙⢶⡀
⠀⢸⡇⢀⣤⣶⣤⡀⠀⠀⠀⠈⠣⠤⠠⠤⠞⠁⠀⠀⠀⠀⠀⢠⡏⠉⢡⠀⠀⠀⠀⠀⠀⢸⡁⠈⡄⠘⣇
⠀⢸⣇⣾⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠑⠒⠁⡰⠊⠉⠉⠉⠐⢄⠙⠋⠀⢀⣿
⠀⠀⣿⡇⡤⠄⠀⡛⠓⢲⡶⢦⣤⣤⣤⣄⣀⣴⣿⠿⠿⣷⠀⠀⠀⠀⠀⠓⠂⠂⠀⠐⠒⠚⠀⠀⠀⣸⡏
⠀⠀⠹⣧⣀⢁⣠⣃⣠⣾⠃⠀⠀⠀⠀⠉⣽⠟⢁⡀⠀⣿⡀⢀⣀⣀⣠⣤⣤⣤⠤⣤⠤⠶⠤⠶⢶⡟
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠱⠃⢀⠁⠉⢹⡟⠉⠉⠀⠘⢿⣄⣼⡀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⡴⠿⠶⠾⠛⠁⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣽⣻⣉⣝⣛⣫⣉⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀
⠀⠀⠀⠀⣯⠻⠿⠶⣶⣶⠦⠖⠐⠒⠒⢒⣒⣒⡒⠒⠒⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢤⣰⣶⡾⡿⢻
⠀⠀⠀⠀⣿⠀⣅⡍⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⡍⠍⠩⢩⠉⠉⠉⣩⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⡇⢺
⠀⠀⠀⠀⣿⠀⡇⡇⣀⣀⡀⡀⠀⢀⣀⣀⡈⠀⠀⠀⠀⠃⠁⠀⠘⠀⠀⠀⠙⠐⠀⢀⠀⢀⡀⠀⠀⠀⣀⢀⠀⢠⠇⡅⢸
⠀⠀⠀⠀⣿⠀⡇⠉⣽⣿⣿⣿⣿⣿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣠⠟⠋⠉⣉⡉⠳⢮⡀⠁⠉⠁⢀⣠⢇⣾
⠀⠀⠀⠀⣿⠀⠇⣼⣿⣿⣿⣿⡟⢠⡶⠛⠉⠛⠲⡌⢻⣿⣿⣿⣿⡆⠀⠀⣼⠃⣠⠖⠉⠉⠙⢷⡀⢻⣆⠀⢀⠞⠀⠼⢸⡇
⠀⠀⠀⠀⣿⠀⣰⣿⣿⣿⣿⣿⡁⣾⠁⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡇⠒⠂⣿⠰⡇⠀⠀⠀⠀⠀⡗⢸⣿⣆⠀⢀⡀⡆⢸⡇
⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣧⡘⢦⣀⣀⣠⡤⠋⣼⣿⣿⣿⣿⠇⠀⠀⠸⣄⠻⣤⣀⣀⣠⡞⢃⣿⠋⢻⣧⠀⠀⡀⢸⡇
⠀⠀⠀⠀⣿⠀⣿⠏⢿⣿⣿⣿⣿⣿⣤⣬⣉⣥⣴⣾⣿⣿⣿⣿⡟⠀⡀⠀⠀⠝⠷⣬⣉⣉⣡⡴⠟⠁⠀⠀⢻⣧⡀⡃⢸⡇
⠀⠀⠀⠀⣿⢠⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡇⢸⡇
⠀⠀⠀⠀⣿⢸⡟⠀⠀⠀⠀⠙⠓⠾⣽⣿⣿⣿⡿⠿⠟⠛⠑⠖⠖⠶⠖⠲⠾⣗⠒⠒⠒⠒⠂⠖⠒⠒⠂⠒⠒⠒⠻⣷⢸⡇
⠀⠀⠀⠀⣿⢸⣃⠀⣀⣀⠀⢰⠄⠀⠀⠀⠀⣀⣀⠤⠤⠒⠒⠋⣔⣶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡤⠤⡄⣽⢉⡇
⠀⠀⠀⠀⣿⠀⠙⣯⣶⣼⢧⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠀⠀⠈⠉⠉⠒⠂⠀⠀⠀⡀⠀⠇⠮⢭⣵⣼⢣⣤⡇
⠀⠀⠀⠀⢿⣿⣀⣈⣙⣻⠷⡾⠶⠶⠄⢀⠦⠴⠴⠶⠶⠴⠐⠒⠒⠒⠶⠶⠆⠰⠒⠒⠒⠒⠂⠐⠓⠒⠒⣸⠛⡉⠅⠹⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠋⢉⣩⣍⡉⠙⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣩⣤⡄⠀⠀⠀⠸⣧⣼⠇⠀⠀⠀⢠⣤⣍⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢿⣤⠟⣀⣤⣴⠶⠶⠶⠶⣤⣤⣀⠻⣤⠿⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣠⡴⠛⠉⣠⣤⣤⣤⣤⣤⣤⣄⠉⠛⢦⣄⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⠀⠀⣼⠏⣾⠛⣷⢀⡾⠋⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠙⢷⡀⣾⠛⣷⠹⣧⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣠⠶⠛⠋⠉⠉⢉⣿⣧⣤⣴⡏⠀⠈⠛⢡⡟⠁⢠⣾⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⡛⣛⣷⡄⠈⢻⡌⠛⠁⠀⢹⣦⣤⣼⣿⡉⠉⠉⠙⠛⠶⣄
⠀⠀⠀⣼⠋⠀⣤⠶⣦⡀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⣀⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢸⡇⢀⣴⠶⣤⠀⠙⣧
⠀⠀⠀⣿⠀⠸⣇⠀⣨⡇⢸⡇⠀⠀⡟⢠⠶⣦⢰⡏⠀⠻⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠟⠀⢹⡆⣴⠶⣄⢻⠀⠀⢸⡇⢸⣅⠀⣸⠇⠀⣿
⠀⠀⠀⠹⣦⠀⠉⠛⠋⠀⢸⡇⠀⠀⣧⠙⠶⠟⢸⣇⠀⣴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣦⠀⣸⡇⠻⠾⠋⣸⠀⠀⢸⡇⠀⠙⠛⠉⠀⣴⠏
⠀⠀⠀⠀⠈⠛⠶⢦⣤⣤⣾⡇⠀⠀⣿⠀⠀⠀⠀⣿⡀⠉⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠉⠀⣿⠀⠀⠀⠀⣿⠀⠀⢸⣧⣤⣤⠴⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⣇⠀⢀⣤⡘⣧⡀⠘⢿⣭⣬⣥⣭⣭⣭⣭⣭⣭⣭⣬⣤⡿⠃⢀⣼⢃⣤⡀⠀⣸⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢿⣤⡿⠈⢷⣄⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⢶⡄⠀⠀⣠⡾⠁⢿⣤⡿⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠙⠳⣤⣀⠙⠛⠛⠛⠛⠛⠛⠋⣀⣤⠞⠋⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣾⠛⣦⠉⠛⠛⠶⠶⠶⠶⠛⠛⠉⣴⠟⣷⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣙⠛⠃⠀⠀⠀⢰⡟⢻⡆⠀⠀⠀⠘⠛⣋⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣙⣋⣁⣠⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠻⣟⠛⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⢧⡀⠀⠀⠉⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠹⣿
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠿⢶⡄⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿
⠀⣰⣾⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠚⠋⠉⠁⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⢰⣿⣿⠋⠉⠉⠻⣿⡟⠓⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠶⠶⠖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿
⣾⣿⡇⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⠁⠀⠀⠀⠀⠀⢀⡏⠀⢀⣴⣿⡟
⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠁⠀⠈⠻⣿⣦⣤⣀⣀⣀⣼⣤⣶⣿⡿⠋
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠋⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉
⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋
⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣴⡿⠋
⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⣿⣾⠟⠉
⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣶⣤⣾⡟
⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣯⣽⣴⣬⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣿⣿⣿⣶⣶⣾⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠄⠠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠀⠀⢰⠂⠀⠀⠂⠀⢀⠀⠀⣀⠠⡈
⠀⠀⠀⠀⠀⠐⠠⠊⣄⡀⠇⠐⠀⠀⠀⢀⡤⠀⠀⡆⠀⠀⢀⠀⣦⡀⠀⡎⠀⠀⢈⠀⠀⢁⣀⠎⠀⡀⢀⡘⡀
⠀⠀⠀⠀⠀⠰⡠⡞⠀⠀⠢⡤⠒⣞⠉⠈⡃⠆⠀⢦⡀⠀⣠⡷⠦⢴⠞⠀⠀⠀⢸⡀⠀⠀⠀⣴⠀⠀⠀⣧⢰⡀
⠀⠀⠀⠀⠀⠰⠎⠢⠤⣵⠞⠀⣤⣀⣀⣰⣧⣊⣀⣪⡴⠛⠁⠀⢒⡉⠀⠀⢀⡠⠃⠈⠓⡲⠋⠐⢀⡠⢷⢒⣲⡇
⠀⠀⠀⠀⠀⠀⠑⢔⣆⡸⠦⠤⣠⠀⣩⢟⡫⣉⡿⣻⡴⢴⣖⡤⠤⠖⠒⠒⢉⣇⣀⣀⣉⡵⣢⡼⠋⢠⢮⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣶⣶⡾⣳⣾⠞⣥⡔⢫⠀⣺⡟⡦⣤⡐⢢⣚⣉⣀⣠⣤⠀⢱⣥⣤⣴⣯⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⣷⠿⣾⣆⣿⢶⠷⠸⣞⣀⣋⣿⣀⣭⣍⣛⣛⣛⣯⣵⣿⣛⣉⣽⣚⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢿⣿⡻⣥⣟⣒⠒⡿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠛⣿⠿⣿⢿⣿⢾⢿⠋⡇⢸⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡟⢠⡧⣼⡇⠘⢸⠀⡇⠈⠘⣿⠉⠿⡿⠿⠀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⢸⡇⠀⠈⠀⠇⠀⠀⣇⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⢐⣤
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢻⡿⢛⣿⠟⣰⡟
⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢠⠋⡄⠀⠀⠀⠀⠘⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⣠⡞⠁⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠘⠀⠁
⡼⢫⣦⣄⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂
⠡⠈⢀⡸⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣣⠇
⠀⣤⠀⠀⠀⠀⠙⠟⠻⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⣊⣉⣉⣍⣡⡾⢋⡀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠐⠄⠀⢩⡥⠤⢤⣶⠦⢼⠰⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⣠⠀⠚⠁⠀⠈⠉⣉⣉⡓⠒⠤⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠒⠀⢸⡿⣧⡄
⠀⠀⠀⠀⠀⠤⠤⠊⢀⣽⡇⢻⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀⣤⠤⠴⠶⠶⠶⠶⠶⠦⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣄⢞⣰⠤⠤⠤⣄⡀⠀⠀⠀⢀⠀⠀⠀⡠⢤⣤⣴⣧⣄⣠⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⡍⠀⠀⠀⠉⠱⠞⣙⡧⠤⠶⠞⠀⢠⣞⡚⠿⣿⣿⡿⠟⠗⠙⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⡁⠀⢀⣠⣴⡾⠟⠉⠀⢀⣀⣀⣀⠀⠙⠻⣿⣶⣬⣉⠀⠀⠀⠀⠨⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣿⡿⢏⣤⣾⡏⣟⠭⢐⣂⣉⣥⣬⣤⣾⣤⣤⣍⣅⣒⠭⣿⣏⣿⣶⣤⡀⢤⣍⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣭⡾⠟⢋⠕⣫⣴⡾⠟⠛⠉⠉⠀⠀⡀⠀⠀⠉⠉⠛⠿⣶⣭⡒⢌⠙⠻⠶⣍⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⢞⣡⡾⠛⠁⠠⠀⠀⠀⠀⠀⡆⠄⠄⠀⠀⠀⠀⠀⠈⠙⢿⣷⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣁⡶⠋⠀⠀⠀⠀⠂⢰⠀⠀⠀⠃⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⢿⣦⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣰⡟⢁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⡟⠀⠈⠀⢲⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠫⠀⠈⠀⢻⣇⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⠁⠀⠀⠀⠈⠀⠊⠙⢶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠈⠁⠀⠀⠀⠈⣿⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠻⢷⣄⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⠟⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐⠀⢰⠿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣱⡀⠐⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢄⣈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡑⣄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡰⢫⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣎⠳⣄⠀⠐⠀⠈⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠈⠀⠀⠀⣠⢞⣵⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣮⣑⠦⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣀⠴⣋⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⡿⠛⠷⢦⣭⣝⣒⠖⠒⠠⠖⠶⠒⣒⣋⣭⣶⠾⢿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠙⠃



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⣻⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣴⠶⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠻⢤⣈⣱⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⡞⠉⢉⣹⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠛⠿⣿⣿⣿⠁⠀⠀⠀⠀⢰⣶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⢹⣿⣿⣿⣿⡟⠀⣠⡴⠶⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠛⠆⠘⠟⠁⠀⠀⠀⠀⠀⠸⣿⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⢸⣿⣿⣿⡿⠁⠀⠈⠛⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⡷⠀⣾⣿⣿⡿⠁⠀⢴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠟⠁⠀⠭⢹⡟⠁⠀⠀⠈⢧⡀⢹⡆
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡼⠃⠀⠀⠀⠀⠀⠀⢰⣤⡾⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣦⣄
⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠋⢁⣀⣈⣻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣥⣈⣉⣹⡿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⢙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠙⢯⡿⣿⣿⡆
⠀⠀⠀⠀⣠⡶⠟⠛⠛⠋⠁⠀⠀⣀⣤⣀⣾⠁⠈⠙⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡟⠀⢦⣴⠟⠀⢠⠿⣧
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⠉⢛⡷⠲⠀⠀⠙⠿⣭⣛⣛⣳⣶⡶⠶⠞⢿⣏⠁⠀⢈⣷⠀⠀⠛⠦⣴⠋⢀⣾⠁
⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠰⡄⠀⣹⣧⣴⠟⠁⠀⢀⣠⣀⣨⡷⠛⠁
⠀⠀⠀⠀⠙⢷⡆⠀⢠⣎⣴⠏⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠋⠀⠁⠀⠀⣠⡾⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⢀⡼⢋⡴⠛⢷⡀⠀⠀⢿⡀⠉⠉⠛⠛⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⢠⡟
⠀⠀⢀⣴⠏⡠⠋⠀⢠⡾⠛⢦⣄⠈⣷⣄⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠶⣶⣤⡾⠁
⠀⣠⠟⣡⡎⡠⣎⢱⡟⠀⠀⠀⠙⠻⠃⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⣾⣁⠞⠁⣉⣧⠼⠋⠙⢦⡀⠀⠀⠀⠀⠀⢀⣴⠏⠉⠙⠛⠲⠶⣦⡄⠀⠀⠀⢸⡇
⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠙⠷⣤⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣯⣀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⠈⠉⢻⠞⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣍⠒⢤⣈⠺⣅⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣌⡓⠮⣁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣑⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣂⣒⣶⢶⣶⣒⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡿⠉⠀⠀⠀⠀⠀⠀⠈⢻⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⣤⠾⣿⣥⣤⣀⠀⠀⠀⠀⢀⣀⣤⣷⠷⣤⣔⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢀⣠⣬⣿⣿⡆⠿⣿⢿⣿⢿⣤⣄⡀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⣿⣿⣾⡟⢯⢀⣼⣋⡀⣠⣿⠀⣙⢦⣸⣿⢛⣷⣦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣽⠟⣿⣿⣿⣶⡿⠗⣂⣀⣤⣤⣀⣀⠺⠿⣧⣾⣿⡉⠙⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡝⢹⢟⡥⠞⠉⠁⠀⠀⣂⠀⠈⠉⡓⢮⡹⠍⠫⡙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡴⠋⠀⠀⠀⢀⠀⢸⣩⠀⢀⣾⠁⠀⠙⢦⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡾⠁⢀⣤⡀⠉⠈⠀⠀⠀⢀⠞⠉⠀⢠⡤⠄⢳⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⠁⠀⠈⠛⠛⢖⣀⠀⠀⢀⡎⠀⠀⠀⠘⠃⠀⡈⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⠀⠆⡿⠀⠀⠀⠀⠉⢯⣼⠀⠀⠀⠀⠀⢘⡆⠇⣹⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⣿⡼⠀⠀⡀⠀⠀⠀⢀⠋⠉⢂⠀⠀⠀⠀⡀⠀⠀⣿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠳⡠⠄⠟⠀⣀⢠⠂⠀⠀⠀⠱⣀⠀⠚⣧⣤⠆⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠁⠘⠦⡀⠨⠀⠀⢰⡇⠀⠀⠿⣤⣾⡿⣃⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⣷⣄⡚⢷⡶⣤⣤⣥⣤⣾⡾⢟⣯⣬⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⡿⣿⣿⣶⣾⣿⣿⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⠻⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⠂⡏⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⣦⣴⣾⣧⣶⣶⢤⣄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠪⢹⣿⢻⣿⣿⣿⣿⣶⣶⣤⣿⣧⡤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⣸⣧⣀⡀⢈⢩⣭⣥⠩⠉⠙⠃⡿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡠⠋⠃⢿⡿⠟⠀⠘⠛⠛⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠏⠀⣾⠄⣓⠐⢤⡀⠴⠯⢇⡐⠁⢨⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢺⠄⠋⣾⣿⢗⡋⠉⣰⣀⠟⠃⠀⡾⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠌⠁⠚⢃⣴⡟⡇⣠⠀⡶⢁⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⢀⣶⣿⣿⢫⣴⣇⠜⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠘⢞⠁⠠⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡏⣘⡈⠥⠄⣺⣿⠉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠷⠶⣿⣿⣯⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⣿⡿⠿⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡇⠀⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⣿⡟⢷⣄⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠐⣤⣿⡷⠀⢿⣿⣾⣉⢉⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠳⠤⡶⠋⠙⡯⠀⠀⠀⡍⢙⠗⠊⠀⠙⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⡀⠲⠄⠴⠀⠀⠠⠲⠁⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠛⠋⠃⠉⠉⠁⠀⠒⠛⠋⠒⠲⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠶⣤⠤⠶⠮⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠶⣤⣤⣠⢥⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠔⠒⡄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠉⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠑⣖⠁⠀⠀⠑⠢⢄⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠤⠖⣍⠤⠔⠒⠈⠉⠁⠀⠀⠀⠉⠉⠒⠂⠤⣉⡶⣤⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡠⠔⠊⢁⠴⠋⠀⣀⣄⡲⠶⠊⠋⠉⠉⠙⠱⠶⢦⡤⣀⠀⠙⠢⡈⠑⠢⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⢔⡯⠊⣁⠀⠀⠀⢀⡀⠻⣀⠀⠀⠀⢈⠑⠵⡢⡀⠈⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⢔⠕⠁⠀⠀⢹⠄⣶⠀⢈⡇⣀⡋⠀⠁⢠⠘⠁⠀⠈⠪⡢⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⢮⠋⣀⠀⠀⠀⠸⠁⠿⠀⠀⠀⠀⠀⡌⠀⠸⠄⠀⢀⡀⠀⠙⡵⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣾⠃⠀⠉⣗⢰⢱⡄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀⠟⠘⠁⠘⣗⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡏⠀⠀⠀⠛⠈⠚⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢹⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠃⢠⡄⢆⣷⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤⣤⣤⣤⣤⣤⠀⣗⢀⡄⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡄⠀⠀⠐⠁⠀⠀⢀⣤⣶⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠋⠀⠁⢰⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⣧⠀⠀⠀⢦⡔⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡼⠅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⢻⢃⠀⠶⠃⠉⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢤⠀⡐⡝⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠫⡧⡀⠀⠀⠀⠀⡄⠀⠀⠀⣠⠀⠀⠀⠸⣭⠀⠀⠀⠀⢀⢜⠝⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠙⢟⣦⡀⠀⠦⠀⠀⠀⠀⠏⠗⠀⠀⠀⠀⣤⠀⢀⢴⡻⠋⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠪⢖⡤⢀⡀⠀⠀⠸⠂⠀⠀⢀⣀⢤⡾⠕⠉⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢉⠶⢄⡀⠈⠑⠚⠻⠂⠒⠒⠒⠿⠓⠊⠁⢀⡠⢖⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡠⠋⠀⠀⠀⠉⠒⠰⠤⠤⠤⠤⠤⠠⠖⠒⠈⠁⠀⠈⠣⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢶⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠛⢶⠃⠀⠸⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇⠀⠀⣷⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣄⠀⢶⣄⣀⡸⠛⢢⣤⣠⣴⣛⡦⣤⣤⣼⢳⣦⣤⠟⠲⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡷⢀⠀⠀⠀⠀⢸⠙⠋⢠⡤⠔⠊⢁⣀⠀⠀⠈⠁⠀⠀⣤⠀⠀⠉⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢸⡉⠭⢦⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠂⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠉⠉⢱⠖⠚⠁⠀⠐⠮⡠⢄⡀⢀⡀⠔⠀⠀⠢⠤⠀⠀⠀⣠⠖⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⡤⣄⡀⠀⠀⠈⠁⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠰⣥⣈⣵⡤⠇⠀⠀⠀⠀⠀⣀⡼⠋⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠁⣄⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣀⡴⠛⣇⠀⠀⠀⣰⣧⠞⠀⠙⠒⠦⢬⣭⣉⣉⣻⠉⠉⠉⠉⣉⣀⣀⣀⣠⡼⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠈⠛⠛⠛⢡⡟⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠐⢰⡖⠋⠉⠉⠇⢚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢧⠀⠀⠀⢸⡼⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⢇⠀⠀⠈⣇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢹⠀⠸⣤⣀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣨⣦⡀⠘⠓⢦⠤⠼⠷⢤⡾⢻⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡤⠚⠉⠀⠀⠀⠙⠛⠛⠋⠙⠛⠒⠚⠁⡞⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠓⠒⠶⠶⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣤⢀⡀
⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡸⠿⠂
⠀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠛⢿⣿⣿⡷⢠⡀
⠘⠿⢳⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠐⠻⠟
⠀⣠⣍⡿⣿⣿⣿⡿⠁⠀⠀⠀⡤⠀⠀⠀⠀⠈⠁⠀⠀⣿
⠀⠙⠋⠀⣿⣿⣿⡇⠀⠀⠀⠀⠠⢄⠀⠀⠀⢰⡘⡀⠀⢹
⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠰⠤⠀⠀⠀⠈⠒⠀⠀⣼
⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⡠⠚⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣸⠃
⠐⣍⠢⡀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠙⠭⠩⠝⠀⢀⣴⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂
⠀⢃⡐⠀⢄⠀⠀⠀⠀⠈⠳⠦⠄⣀⣀⣀⣤⡤⠖⠋⢳⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⣀
⠀⠀⠈⠉⠢⣄⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠒⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⠛⠛⠛⠉⠉⠉⠁⠀⣼⠃⠈⡿⠓⠲⡄⠀⠀⠀⠀⠀⣤⡤⠤⣼⣿⣤⠤⠤⠤⠼⠧⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⠀⢠⣄⣀⣤⡴⠚⠳⠶⢼⡓⢀⠞⠁⠀⠀⠀⠀⠀⣿⣻⢟⣻⣿⢇⣠⣦⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢙⠷⠴⠋⠀⠀⠀⠀⠀⠀⢠⠞⡰⠋⠀⠀⠀⠀⠀⠀⠀⢻⣏⢺⣿⣿⣇⣿⣿⣿⣿⣿⣟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢸⣟⠷⠿⢿⣿⣿⡿⠿⠿⠵⣾⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⡷



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠰⠂⠀⠀⠀⠐⠐⠀⠀⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⡠⠞⠉⡠⠊⢀⣮⠴⠚⠋⠉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠈⠋⠀⢀⠞⠀⣠⠊⢁⡤⠴⠶⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣠⠷⠖⠚⠉⠉⠉⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⢠⠒⠐⠠⡀⠀⠀⣤⣼⠃⢰⡥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⡠⠒⠐⡆
⠀⠀⠀⠀⠀⠈⠑⠒⠒⠛⠀⢰⠏⠀⡵⠋⠀⠀⢀⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⠓⠒⠒⠁
⠀⠀⠀⠀⠀⡔⠋⣹⠖⠀⠀⡿⣄⣴⠀⠀⠀⠀⢈⣋⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡆⠈⣇⠀⠀⠐⢎⡋⢳
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⣏⡠⣿⠀⠀⠀⣰⠋⠁⠀⠀⠙⣦⠀⠀⠀⡀⠀⢀⡤⠶⢤⠀⢹⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣹⡀⠀⠀⣇⢀⣀⣀⣤⡤⢾⠀⠀⠀⡁⠀⢸⠧⠤⢤⠇⢸⡗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⢧⠀⠀⠻⡉⠀⠀⠈⣠⠏⠀⠀⠀⢧⠀⠀⠑⠒⠊⠀⠀⣇⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠿⢦⣈⡄⠀⠀⠉⠓⠒⠛⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⠀⠀⣠⠏⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣠⣾⣿⣟⣲⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⣍⡹⢿⣿⡟⠀⠀⠀⢀⡴⠋⠀⠀⠀⡞⢙⡧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠸⡆⠀⠀⠀⠀⠉⠙⠻⠁⠀⢀⡴⠋⠀⠀⠀⢸⠉⠑⣺⠀⣘⠓⡄
⠀⠀⠀⠀⣀⣤⣄⡤⠚⣋⡭⠖⠛⠛⢻⠖⠒⢷⡀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀⠀⠀⠸⡈⠘⠟⠚⣧⠜⠁
⠀⠀⡴⠋⠁⠀⠀⠀⢾⠁⠀⠀⠀⠀⠈⠛⢻⡟⠝⡶⢤⣤⣤⡤⠶⡟⢳⡄⠀⠀⠀⠀⢀⡴⢁⡤⠂⠈
⠀⠈⢣⡔⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⠁⠀⠀⠀⠀⢘⢿⡶⠿⣦⣤⣤⣶⡭⠖⠋
⠀⠀⠈⠓⣾⡀⡸⠛⠁⠀⠀⠀⠀⠀⠀⣸⠃⠀⡀⠀⣸⠆⢰⡄⠀⢸⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠉⠁⢀⡀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣁⡈⠋⠐⠾⠁⡂⢸⡇
⠀⠀⠀⠀⠀⢀⡼⢋⢿⡄⠀⠀⠀⠀⣿⠶⢤⣤⣈⣉⡙⠛⠛⠛⠀⢸⡇
⠀⠀⠀⠀⣠⠟⡵⠃⣠⢷⡀⠀⠀⣀⣿⡄⠀⠀⠈⠉⠙⠛⠓⠶⠶⡾
⠀⠀⢀⡾⢫⠞⢰⣿⢷⡊⢧⡀⣺⡏⠈⠳⣄⣠⠀⠀⠀⠐⠢⢤⣾⠁
⠀⣰⠟⡴⢧⠀⡼⠋⠀⢳⡈⣋⡽⠛⠶⠚⠁⠉⠛⠶⢤⣤⡴⢾⣿⠶⢤⣀
⣾⣣⣎⣠⡼⠛⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠆⣸⠇
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢅⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠓⠞⢿⢿⠛⠓⢲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⣒⣒⡒⠠⠤⠤⠏⣀⣈⣳⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣙⣛⣛⣛⣷⣶⣾⣶⣿⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠺⢶⣄⠀⠀⠀⠀⠀⠀⣠⡾⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⡟⠀⠀⣈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢷⣽⡄⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣿⠀⠰⠦⣿⡇⠀⠀⠀⠙⠻⠷⣦⣤⣄⣀⣀⡀⢀⣾⠛⠻⡾⠋⠁⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠴⠶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣤⡤⠶⠀⠀⠀⠀⠀⢸⡇⠀⠠⠖⢻⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣿⠀⠀⠀⠀⠀⣀⠀⣶⠀⣶⠀⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣠⣴⡟⠀⠀⣠⣴⠾⠛⠛⠉⠉⠉⠉⠉⠛⠛⢿⣇⣤⣄⢀⡾⢀⡟⢠⡏⢀⡿⠀⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢿⡆⠠⠞⠁⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣼⣁⣿⣁⣸⣧⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠘⢿⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⢀⣤⠄⠀⣀⡤⠀⢀⡤⠀⠀⣠⠄⠀⢀⣤⠀⠀⣀⡀⠀⣀⡄⠀⢀⣤⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠐⠋⠁⠀⠘⠋⠀⠘⠋⠀⠀⠚⠁⠀⠰⠋⠁⠀⠸⠋⠀⠰⠋⠀⠐⠛⠁⠀⠸⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⡀⠀⠀⡠⠔⠒⠋⠉⠉⠛⠒⢤⡀⠀⠀⣠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢀⣁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠉⣀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠛⠉⠀⠀⠐⢢⡄⠀⠀⢈⠄⡠⠐⠀⠀⠈⠙⠛⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣠⣤⠶⠚⠀⢈⡃⠀⠲⢤⣄⣀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⡶⠟⢋⠩⠛⢂⣀⣀⠉⠉⠀⢈⠛⠫⢉⠛⠲⢦⣄⣀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡠⠂⣡⣴⣾⡿⠝⠒⠛⠓⠒⠶⣬⣐⠠⡁⠢⡀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⣫⡯⠋⢀⢄⠀⠀⠇⡇⠀⠀⡠⠈⠻⣮⠢⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠰⣱⡟⢀⠀⠀⠑⠂⢠⠈⠁⠀⠐⠀⠀⣀⡈⢷⡑⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⢢⠟⠀⠀⠉⠂⠀⠀⣼⣷⠆⣀⠔⠁⠚⠁⠀⠘⢧⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢸⡆⢰⣀⣒⠀⠀⠀⠀⢹⡾⠃⠀⠀⠰⠶⢶⠀⢝
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡸⡄⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡹⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢳⡀⠙⡫⠓⢀⡄⠀⠀⠀⠀⠀⠀⠒⠑⠀⣴⢃⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠡⡹⣦⡀⠀⠞⠌⠀⠐⠆⠀⠈⠂⠀⢀⡼⡣⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠪⢑⠦⢄⣀⢀⣀⣀⢀⣠⠬⢞⠩⣪⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡞⠓⠢⢈⡀⠈⠀⠉⠉⠈⢐⣨⡵⠞⠛⠜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠁⠉⠒⠛⠁⠁⠀⠀⠀⠀⠀⠺⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠟⠁⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡟⠋⠉⢹⡏⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠀⠀⠈⠻⢿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣶⣶⣶⣶⡶
⠀⠀⠀⠀⣰⣾⣾⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⣸⠏⠁⢀⡿⠉⠉⣿⠛⠉
⠀⠀⠀⠀⢻⣿⡿⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣶⣿⣠⣤⣼⢁⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡀⠀⠀⠀⠻⠿⠋⢿⣿⠏⣾⣿⡿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢴⣦⢸⣿⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⣶⡀⣿⡇⢠⣶
⠀⠀⠀⠀⠀⣴⣌⣿⣿⣿⣾⡟⢁⡀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣷⣿⣷⣿⣣⣴⡄
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣴⠿⠋⣉⣤⣤⣤⣄⣉⠛⢷⣄⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⠀⠀⠀⠀⢠⡿⢁⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣷⡀⠀⠀⠀⠀⣦⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⢠⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣷⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠈⠿⠿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠿⠟⠀⢀⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠈⠛⠛⠿⠛⠛⠋⠁⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢿⣿⣦⡀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣤⣀⠀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⠿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⠿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⡇⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣀⠀⣧⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣉⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⡿⠙⠃⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣵⣿⣿⣿⠁⢠⠄⠁⡸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣆⠔⠁⡀⣼⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡽⣿⣿⣿⠟⢁⣴⡊⠠⢑⠔⠂⢰⡤⠒⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠂⠉⠢⣞⢿⣇⠀⠖⠶⠈⣹⣘⠋⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠿⡿⠀⠑⠢⠖⠁⠀⠈⠉⠐⠀⠀⠀⠀⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⢺⠀⠀⠁⠀⡀⠀⢄⡀⠀⠀⠀⠐⠃⠀⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠁⠀⢀⠉⠒⢤⣀⠀⠀⠀⠁⠀⠀⠀⠘⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠃⢀⡀⠀⠆⢘⠀⠀⠀⠈⠙⠒⠢⠤⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡤⠒⠒⠐⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣱⠃⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠬⠀⠉⠲⣄⠑⠒⠊⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⠢⢀⣀⣀⣀⣠⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢦⢄⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢀⠇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡌⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⡰⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠈⠀⠀⠈⠒⠪⡍⠀⠒⠀⠀⠀⠠⠤⠤⠠⠄⠄⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⣰⢆⣠⠀⠀⣼⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠡⠤⠄⠨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠏⢩⢴⠚⠳⠎⢰⠀⠟⠀⠀⠙⠋⠃⠀⡠⠔⡡⠋⠢⠤⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣿⢀⡑⣄⠀⢸⠀⠀⢢⠀⣠⠀⠀⢰⠀⠀⢧⢂⠔⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⡇⠑⠽⢬⠢⣼⢀⠀⢸⡉⣀⣀⣀⣸⠤⣀⡀⠉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣒⡒⠁⠀⢀⣈⣱⣏⣴⡖⢒⣏⣙⣦⣶⣞⡩⠍⣱⢀⣀⡱⣦⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠈⠛⠛⠻⠿⠿⡧⢺⠷⠾⠿⣿⣿⣿⣿⣿⣷⠶⠿⠿⠿⠿⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠌