Baby Duck Emojis & Text

Copy & Paste Baby Duck Emojis & Symbols 🐣🐥🦆🐤

Related Text & Emojis

╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⣟⡿⠿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡟⢛⣽⣶⠿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠈⣿⣿⠲⣿⢨⣿⠤⢤⠀⠀⠀⠀⠀ ⠀⠸⣏⡾⠉⣽⡀⣦⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠀⠀⠘⢿⠠⡏⣼⠃⠀⣸⡤⣤⠀⠀⠀ ⢀⣴⠿⣧⡄⠙⠁⢸⡇⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢇⡀⠀⠀⠀⠀⢰⠏⠀⣰⠋⢠⡿⣶⡄⠀ ⠸⠟⢻⡇⠹⣦⣠⡿⠃⠀⠀⠀⠀⠀⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠷⠚⠋⠀⠀⠀⡤⣾⡟⠀⠘⠁⢀⣿⣧⡟⢧⠀ ⠀⠀⠸⣇⡀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⢷⢿⣦⣙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⣴⣶⡿⠏⢡⣿⣷ ⠀⠀⠀⠈⠉⣹⠁⠀⡄⠀⡀⠀⡀⠀⠰⡈⠋⢿⢿⡷⠽⣦⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⡼⡁⣀⣴⣧⣀⡏ ⠀⠀⠀⠀⢀⡿⠀⢰⢻⡀⣷⣠⣷⣤⠀⠹⡄⠀⠀⠁⢠⣬⣷⠶⠒⠒⠒⣲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣽⣷⣿⠹⣤ ⠀⠀⠀⠀⢸⡇⠀⠘⡎⣧⠛⣇⠹⣿⣀⣠⣤⠴⠚⠉⠀⠀⠀⣀⡤⠔⠈⠉⠙⠒⠲⢤⣤⣀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢶⡄⠀⠀⠀⠉⣹⣷⠏ ⠀⠀⠀⠀⣿⡇⡀⠀⣷⣿⠀⡼⠚⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠰⠚⣽⠄⠀⣠⣾⡥⠀⠀⠀⠘⡏⠁⠀ ⠀⠀⠀⠀⢿⡇⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠙⠆⣦⡀⠘⠋⠉⠀⠀⠀⠀⢰⠇⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣼⣀⣀⣀⣀⣀⣠⣿⣄⠀⢀⣰⣌⣻⠆⣀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⢴⡇⠀⣀⣀⣠⠤⠤⣴⠟⠀⠀⢡⠽⠁⣠⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣄⡀⠀⠀⠠⡶⣫⠀⢀⡤⠋⠀⣈⣭⡥⠤⠖⠋⠹⠦⣤⣤⣀⣠⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠳⢤⣆⠉⠽⠋⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣦⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡴⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⢀⣀⣀⣠⡤⠉⠉⠉⠉⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠘⣻⡭⢥⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡆⢀⡀⠀⠀⠀⠀⠀⠀⣴⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⣥⣳⣿⣷⣴⣖⣀⣐⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣦⡽⣿⣻⣭⡽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⢛⣫⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢶⡤⢤⣦⠤⠾⠋⠻⣟⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡜⠁⠀⠀⠀⠀⠸⣾⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡿⠁⠀⠀⠀⠀⠀⠀⢻⣹⡀⢠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣀⣠⣿⢹⡀⠀⠀⠀⢀⣀⣀⣠⣤⣷⣙⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⠯⠿⢷⣛⣫⡤⠬⢭⣷⡄⠀⢿⣯⠤⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⢠⣷⣇⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠁⣶⠀⢸⣿⡿⠋⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠿⡾⢻⡆⠀⠈⠁⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠤⠗⠈⣿⣤⠀⠀⢀⣸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠞⠁⠀⢀⣠⣶⣽⣿⣶⠾⠛⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠋⠀⢀⣠⣶⡿⠞⠁⣸⡇⠀⠀⠀⠀⠀⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠛⠉⠁⠀⠀⠀⢀⣿⠃⠁⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠸⣿⣴⣶⣿⡿⠿⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠶⠶⠶⠶⣶⣦⣤⣄⠀⠀⠈⠙⠛⠷⣦⣀⣠⣤⣶⣄⣠⣴⡄⠀⠀ ⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠉⠁⣀⠈⡏⢹⣟⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⣠⡞⠁⠀⠀⠸⠿⣭⣼⠇ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠖⠛⠀⠀⠀⠀⠀⣾⣿⣯⠀ ⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⡶⠿⠛⠉⠀⠀ ⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⢉⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠉⣁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⣛⡶⢾⣭⣤⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⢿⠿⠿⠶⠖⠋⢹⠁⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣏⠀⢸⡀⠀⠀⠀⠀⢸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⠉⣛⣻⣶⣿⡧⣰⡷⠷⠀⠀⠀⢠⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⢿⣏⣅⣤⣶⢿⣧⣀⣀⣀⣠⣾⣃⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣾⣃⣤⣼⠿⡿⢛⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠻⠿⠦⡴⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⣄⢀⢀⣀⣄⣀⣀⣀⣠⣀⣀⣀⣀⡀⠀⣀⣀⢀⣀⡀⠀⠀⢤⢀⡀⢀⠀⡄⣀⠀⡄⣤⠠⠄⠀⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠋⡛⠛⡓⢃⠻⠛⠘⡛⠛⢛⠛⠛⠓⠘⠚⠓⠛⠃⠃⠀⠀⠒⠚⠚⠚⠚⠚⠓⠋⠃⠚⠛⠂⠐⠘⠋⠀⠀⠀⠀⠀⠀
<( ˶• ◊ •˶ )>
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡶⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡌⠳⣄⠉⠳⢤⠴⠒⠛⠛⠛⠛⠒⠦⢤⡤⠚⣡⠞⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡷⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠙⠓⠦⢤⣀⡀⢸⠁⠀⠀⠀⣰⠟⠛⢦⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢳⡆⠀⠀⠀⠸⣇⣀⣠⠤⠶⠛⠁ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⣿⠒⠦⢄⠀⠻⣴⣳⠾⠁⠀⠰⣿⣿⠂⠀⠘⢿⣿⡽⠋⠀⣤⢖⠚⣏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢻⣍⣽⠿⠀⠀⠀⠀⠀⠀⠸⣦⣼⣷⣼⠆⠀⠀⠀⠀⠀⠐⠿⣍⣹⡏⠉⠉⠉⠉⠙⠁ ⠀⠀⠀⠀⠀⣀⣠⠤⠶⠚⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠓⠲⠤⣄⣀⠀ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⢀⡴⠖⠲⢄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⢠⠏⠀⠀⠀⠈⢧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢸⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠘⡇⠸⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⢧⡀⠀⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⣧⠀⢻⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣠⠀⣠⠀⠀⠀⠀⠀⢈⣟⠀⠀⠀⠀⢠⡏⠈⢳⡀⠀⠀ ⠀⢻⡄⠀⠀⠀⠀⢹⡄⠀⡳⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣟⠀⠀⠈⣇⠀⠀ ⠀⠀⢳⡄⠀⠀⠀⠀⠳⡄⠀⠙⢦⡀⠀⢹⡀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⢀⡴⠋⣿⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠱⣄⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⠮⣧⠀⠀⢀⠀⡾⠀⢹⡀⢀⠀⠀⣸⣇⡤⠞⠉⢀⣴⠃⠀⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠈⠳⣿⣸⡾⠛⠛⠚⢷⣟⣸⡴⠋⠀⠀⣀⡴⠚⠁⠀⠀⠀⣼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⠤⠤⣤⣤⣤⣤⠼⠵⠶⠖⠚⠉⠁⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⣤⡀⠀⠀⠀⠀ ⠀⠀⣠⠖⠚⠙⠁⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣤⠤⠤⠖⠛⢦⡸⢷⡀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢴⡶⣶⣦⣤⣤⣤⣀⣠⠤⣴⣖⣿⣍⣿⣧⡙⢦⡀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⠛⢛⣉⡉⠉⠉⠛⠓⠒⠶⠟⠛⠋⠁⠀⣠⣤⣽⣆⢻⡀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣏⠉⠉⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣘⣀⣿⣼⠃ ⠀⠀⢳⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣰⠞⠁⠈⠉⠙⠚⠃⠙⢦⡀⠀⠀⠀⠀⡼⠁⠈⠀⢠⣷⠃⠀ ⢀⡴⠚⠉⠀⠉⠙⠓⠦⣄⡀⠀⠀⢰⠃⠀⠠⡏⠀⠀⢀⣠⢶⣶⣦⣄⠀⢳⡀⠀⠀⢸⣟⡭⠿⠷⣼⠉⣷⠀ ⢸⡇⠀⠀⣤⠤⢤⣀⠀⠈⠙⠦⣄⢸⡀⠀⠀⠀⠀⢰⠟⠋⠉⠉⠈⠋⣧⡀⢻⡀⠀⢸⡆⠀⠀⠀⢹⠀⡿⠀ ⠀⢻⡄⠘⣇⠀⠀⠀⠉⠓⠤⣀⡈⢦⣷⡄⠀⠀⠀⢿⡀⠀⠀⠀⢸⡗⢺⡆⠀⠁⠀⠀⠻⡄⢰⣻⣾⣿⠃⠀ ⠀⠀⠙⢦⠘⢦⣀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⢈⡷⠞⠋⠙⠳⣽⡏⠀⠀⠀⠀⠀⠀⠙⠳⢿⣏⡘⣦⠀ ⠀⠀⠀⠀⠱⢦⡈⠓⠦⣄⣀⣈⡷⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣹⡖⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠙⣾⡆ ⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⣿⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣱⣬⠉⠉⠉⠉⠀⠙⠲⣄⣀⢀⣠⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠋⠙⠲⠤⠤⠤⠤⠤⠖⠋⣉⠽⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⣧⠀⠀⣿⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⢠⣿⡦⣴⢿⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⣠⡶⠋⢸⣷⡏⣿⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣤⢞⡋⠀⠀⢸⡇⣹⣿⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟧🟧⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟧🟧🟧🟧🟧⬛⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛🟨⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛🟨⬛ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛🟨🟨⬛ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
:¨ ·.· ¨: `· . 🐣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣣⠞⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣾⣿⡿⠿⠓⠂ ⠀⠉⠙⠻⢿⣛⠛⠛⠻⠿⢭⣍⣉⠉⠉⠛⠒⠶⢤⣄⡀⢠⣞⣹⣟⣁⣰⣃⣠⠀⠀⠀⣀⣀⣤⠶⠖⠛⣉⡽⠟⠋⢁⣴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠓⢦⣄⠀⢠⣾⣿⣿⣿⣯⠉⠀⢹⣿⣿⣿⣿⣿⣯⡀⠀⢀⣴⠞⠉⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢰⡀⠀⠀⠀⢈⡿⣫⣿⣿⠿⠛⠉⠀⠀⠀⠉⠛⠿⣿⣿⡉⠙⢶⡞⠁⠀⣸⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⠲⠤⣴⠏⢰⡿⢛⣡⢶⡞⠀⠀⠀⠀⠀⣤⣄⠈⠻⣷⠀⠈⣧⠀⣠⠇⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣀⣀⡏⠀⠙⢀⡞⠁⠀⢻⡄⠀⠀⠀⣼⠃⠈⠳⣄⠙⠀⠀⢸⣖⣁⣤⠞⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠃⠈⠉⠀⠈⠙⠻⢶⣶⣶⣾⣧⠄⠀⢸⣧⣴⣶⠶⣿⡴⠖⠛⠉⠉⠉⣙⣿⣿⡶⠒⠚⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣩⡟⠛⠲⢤⣄⣀⠀⠀⠀⠀⠀⠙⢧⡁⢸⢀⣀⡘⣇⠀⣠⠞⠁⣀⣠⠤⠖⢚⣉⣁⣠⣤⣽⣶⡤⠤⠤⠶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣏⣠⣴⣲⢚⣹⣏⣉⠛⠒⠦⣤⣀⡀⣳⢿⣭⣭⣿⠿⣾⣥⣖⣫⠵⠶⠚⠉⣉⡥⠾⡟⠻⡟⢶⠿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⢶⡟⣸⠁⡸⠁⠀⣹⠛⠯⠽⣶⣾⠿⡿⠀⠙⡏⠀⠀⠹⣯⠥⠤⠤⠴⠒⠋⠹⣄⠀⠘⡄⢣⢸⠿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⢸⣄⣨⣶⣧⡀⠀⣉⣣⠤⠄⠀⠀⢸⠁⠀⠀⢣⠀⠀⢠⠃⢀⡀⠀⠀⢀⣀⣠⣤⣤⣞⣡⡾⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⠉⠉⠁⢸⣀⣄⠀⠀⠈⢧⠀⢤⠘⠦⠀⣘⡤⡄⠀⠉⠉⡽⠁⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢸⠇⠘⣶⠛⣦⠾⣧⡀⠙⠀⣀⣿⠁⢹⡴⣦⣴⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣼⠀⠀⢿⠀⠸⠀⠻⣏⣉⣉⢽⡇⠀⠘⠃⠿⢹⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⠇⠀⠀⠀⠀⠘⣷⣀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠹⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢋⣻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⣸⣧⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣠⠞⠉⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⣠⡴⠞⠛⠉⠉⠀⠀⠀⠈⠉⠙⠛⢶⣤⡀⠀⣰⡟⢀⡞⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡞⠀⠀⠀⠀⠀⠀⣀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡴⠏⠀⠀⠀⠀⠀⢸⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣷⣄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣷⣘⡷⠶⣬⣭⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣛⠁⠀⠉⠓⠶⠄⢀⡤⠞⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠿⢿⣄⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠿⠿⢿⣐⡟⢳⡀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡄⠀⠀⠀⠀⢸⣍⡙⣷⡦⣄⣠⣭⡀⠘⢷⡀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⡟⠈⢧⡀⠀⠀⠀⢀⡼⠗⢷⠽⠀⠳⠶⠛⠶⢬⣧⠀⠀⠀⠀⢸⠃⠀⠀⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⣠⣄⠙⢶⣄⣀⣸⣇⡀⠀⠀⠀⢰⣟⣗⣤⣿⠙⣗⠀⠀⠀⢸⠀⠀⠀⢰⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠁⠙⠷⣦⣀⣀⣀⣉⣉⣽⡏⠙⠓⠺⣯⣀⠀⠀⠙⠶⢦⣤⠟⠀⠀⢀⡿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣿⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣤⣀⣠⣤⣴⠟⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢈⡟⠉⠛⠛⠛⢻⣟⠛⠛⢻⡛⠉⢻⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⠇⠀⠀⠀⠀⠀⠹⣧⠀⠈⣿⠀⠀⠹⣆⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣾⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⠀⠀⠀⠙⢧⡈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠙⠳⣤⣈⠛⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣉⣙⠓⠶⢤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠞⠛⠛⠋⠉⠙⣀⣸⡆⠀⠀⠀⠀⠀⢸⡇⠀⠹⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢦⣌⠳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠒⠒⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣀⠈⠉⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⢋⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⣚⣋⣩⡭⠴⠖⠚⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⢰⣞⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣭⣍⣉⣉⣛⣒⣒⣶⡄⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⠉⠉⠙⠛⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⣠⣾⣿⣿⣿⢿⣿⣿⠃⡀⠀⠘⣿⡝⣿⣿⣿⣿⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢟⣻⣿⡟⠀⣷⡀⠀⠸⣿⡼⣿⡻⣿⣦⣙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣩⠟⠋⣿⡟⠉⣿⣿⣷⡀⢹⣿⠀⠀⣿⣇⣿⡗⠸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⣴⣧⣿⢣⡶⢿⣿⣏⣿⠈⣿⡆⠀⣛⣿⣾⡇⣿⡄⠈⢹⣿⣿⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣾⣃⢸⣿⣿⡏⠿⣿⣷⠀⢿⣿⣿⠃⠉⣿⣄⣀⢸⣿⠀⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣙⣿⣿⡿⢻⣿⡆⣿⣿⡇⢀⣿⣿⡆⢸⣿⡟⠀⡀⣿⡇⠨⢸⣿⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣿⣿⣿⡷⣿⣿⣷⣼⣿⣇⣿⣿⢿⣿⡸⣿⡇⠀⠁⢹⣧⠠⢼⡿⢀⣼⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⡿⠀⠼⣿⡼⣿⣿⣿⣼⣿⠀⠻⣿⣿⣿⠀⡀⣸⣿⣧⣼⣧⣾⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⡇⢀⣀⠻⣇⠹⣿⣿⣿⣿⢀⣀⣹⣿⣿⣦⣄⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣻⣿⡿⣿⣿⣿⡿⠛⠉⠉⠛⠀⠘⢿⡿⣿⡏⠁⠀⠈⣿⣿⣿⣿⡟⢻⣿⣿⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠀⢧⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⠎⠃⠀⠀⢠⣿⣿⡿⣿⠇⠛⣿⢻⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡞⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠸⣼⡟⠀⣿⣷⡿⠃⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⢿⣄⠀⠀⠀⠘⣿⣯⣼⠇⠀⠀⠀⠀⠛⣡⠞⠛⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⢤⣀⣀⡤⠴⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⡠⢀⡆⠀⣇⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠲⣤⠞⢡⠒⠊⠀⣼⣡⠶⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⢢⠀⠈⠑⠮⣄⣠⡴⠛⠁⠀⢀⡤⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠈⠳⢍⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣡⣾⣿ ⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⢤⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣙⣦⠀⠀⠀⠀⠀⢀⣼⣿⣿⣵⣿⣿⣿ ⠀⠀⠀⠀⠀⣰⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢧⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⡇⠀⢰⡏⣿⣯⣾⣿⣿⡟⣿⢹ ⠀⠀⠀⠀⢰⣧⠀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⡞⠁⠀⠀⠀⡀⠀⢧⠀⢸⣿⣿⣿⣿⣿⡟⢸⡇⣾ ⠀⠀⠀⠀⣸⢹⠀⠃⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⡿⠀⠀⠀⠀⢠⠇⠀⠸⣆⣸⣿⣿⣿⢿⡿⠷⣜⠃⣏ ⠀⠀⠀⢰⠇⢸⢰⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡟⠁⠀⠀⠀⠀⣾⠀⠀⠀⢹⣿⣿⣿⣿⡘⠇⠀⠀⠀⠘ ⠀⠀⢀⡏⠀⢸⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢰⠃⠀⠀⡇⠸⣿⣿⡿⣟⠓⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠀⢸⣼⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⢠⡏⠀⠀⢠⡇⠀⠹⣿⡀⢻⡀⠀⠀⢠⣤⣀ ⠀⢰⠃⠀⠀⢸⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠀⠀⢀⡞⠀⠀⠀⠸⡇⠀⠀⢳⡁⠈⢻⡀⠀⠸⠏⠁ ⠀⡏⠀⠀⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡇⠀⢀⡾⠀⠀⠀⠈⠀⠇⠀⠀⠀⢧⠀⣀⡽⣄⠀⠀⠀ ⣼⠁⠀⠀⠀⠀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⣓⣦⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠝⠁⠈⣛⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠉⠁⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⣤⣶⣚⡋⠉⠉⠉⠓⠲⠶⣤⣀⠀⠀⠀⠀⣠⣴⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣋⣾⡿⠷⠇⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣠⠞⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⣦⠀⠀⠀⡀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⠀⠘⣆⣀⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠋⠀⣸⣍⣽⣒⠶⡀⠀⠀⣾⣦⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣶⡶⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠈⠻⠓⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣟⣇⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠉⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⡆⠀⠀⠀⠀⠰⣿⠶⣤⣀⣀⣀⣀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠶⢤⣿⣄⠀⠀⠀⠀⣎⢦⣶⠿⣍⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⢤⡀⠈⠙⢷⡀⠀⠀⠘⠶⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣋⣀⣠⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⡤⠶⠋⠀⠀⠁⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠖⠋⢉⣉⠀⠀⠀⢠⣅⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠉⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠈⠙⣦⣀⣠⠴⠶⠋⠉⠀⠐⠒⠉⣉⡥⠶⠶⠶⠶⠷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠻⡇⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠐⠦⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣶⡒⢦⠀⠀⠀ ⢀⡴⠋⠀⠀⢳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠠⠤⢄⣈⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠉⠙⢿⣄⠀⠀ ⣼⡇⠀⠀⠀⢀⣹⣶⣋⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⣰⠟⡀⠀⠀⠀⠀⠀⠙⢷⡄ ⢸⡇⠀⠀⠀⠸⣏⠀⣴⠃⠀⠀⠀⠉⠉⠑⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⢵⣤⣀⠀⠀⢸⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻ ⠸⢷⡄⠀⠀⠀⠙⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠘⢷⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣀⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⣼⠳⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀ ⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣀⣶⡏⠁⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢠⠶⢻⡇⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠁⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⣴⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠓⣦⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠙⠳⠶⣄⣀⣀⡀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠈⠉⠙⣯⠉⠉⠉⠉⠀⠺⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡠⠤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠙⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠀⠀⣠⠖⠋⠹⣆⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠚⠷⠦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⢠⠞⠁⠀⠀⠀⣸⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢰⠋⠀⠀⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⣀⣀⣠⠖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠁⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢇⠀⠳⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠘⣧⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⣷⣶⣤⡀⣿⡇⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣿⣿⣿⣿⣿⣯⣦⣼⠋⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠛⠋⠉⠉⠙⠛⠛⠛⠉⢉⣁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣰⠋⠀⣠⣶⠟⠙⢿⣿⣿⠿⠛⠛⠛⠛⠛⣉⣀⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠁⠀⣰⡏⠁⠀⠀⠈⠉⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⢸⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣼⡟⢘⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠅⠀⠀⠀⢀⡾⠋⠀⣼⣧⠤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡁⣱⠀⠀⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡆⠀⠀ ⠀⠀⢀⡟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠙⢿⡋⠉⠉⠀⠀⢸⣿⢟⠃⠀⠀⠀⠀⣶⠛⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣇⠀⠀ ⠀⠀⡸⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠙⠓⠒⠒⠶⠞⠛⠃⠀⠀⠀⠀⠀⠙⠷⠖⠒⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢸⡄⠀ ⠀⢠⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⢻⣄⡴⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢧⠀ ⠀⣾⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣸⠇ ⢀⠇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣄ ⢸⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣶⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠛⠋⠉⠉ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠙⣆⠀⠀⠀⠀⠀⣴⢟⢭⢛⡅⠀⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠶⣤⣘⢧⡀⠀⠀⠀⠙⠚⠛⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⣀⣀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠓⠷⣤⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠉⠉⠉ ⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠳⠶⠤⣤⣤⣤⠤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⣾⠁⠀⢹⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠉⠙⠓⠒⠒⠼⠲⠴⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢩⡟⠉⠉⢩⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠛⢻⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠁⡾⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠰⠖⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⢳⠀⠀⠀⠀⠙⢿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⢠⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⣿⣿⣿⣿⠃⠀⠀⢸⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜ ⠀⠀⠀⠈⠛⢿⡇⠀⠀⠀⢸⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠸⡇⠀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⣠⠇⠀⠉⠳⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠉⠛⠒⠦⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠶⠒⠋⠉⠘⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⣀⣀⡤⠤⠖⠒⠒⠲⢤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⢀⣀⡠⠬⠥⠤⠤⣄⣀⠈⠓⠋⠀⠀⠙⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⣄⣰⠖⢳⠀⠀ ⠀⠀⣸⠧⠔⠂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⠀⠠⡇⠀⠀⢠⣃⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠀⠀⣇⠀⠀⣼⣿⣿⣿⣿⡆⠀⠚⣻⣿⣿⣟⣷⡄⠀⢳⡀⠀⠀⠀⠀⠙⠂⠚⡇ ⢀⡼⠋⠀⠀⣸⢿⣿⣿⣿⠃⠀⠀⢻⣿⣿⡿⠃⠀⠀⠈⣧⡀⣀⠀⠀⠀⠀⢸⠃ ⠈⢷⠀⠀⠀⡏⠀⠈⠉⡍⠀⠀⣀⡈⠉⠉⠀⠀⠀⠀⢀⠇⠉⠁⠀⠀⠀⢠⠞⠀ ⠀⢸⠀⢠⡀⡇⠀⠀⢰⣅⣀⡠⠤⠽⢆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠈⢧⠀⠈⢷⠀⠀⢞⡀⡈⣧⠀⠀⡀⠗⠀⠀⠀⠀⠘⣄⣠⣤⠾⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⠒⠾⡄⠀⠀⠙⠯⠉⠍⠉⠉⠀⠀⠀⠀⠀⢠⢃⡴⠁⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠒⠂⠀⠀⠀⠀⣀⡠⣶⠟⠁⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠉⠀⢹⣷⠢⠤⠤⠤⠔⠚⢉⣡⠞⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⠀⠀⢈⣧⣽⣦⠤⠤⠒⢚⡭⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀ ⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⡗ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣿⣇⢠⡶⣿⣴⢲⣦⣶⢷⡾⡦⣿⡂⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⢸⣀⣀⣀⣀⣀⣘⣁⣙⣈⣛⣙⣈⣛⣋⣉⣙⣃⣛⣛⣁⣀⣀⣀⣀⣀⣿ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠿⠋⠁⣰⠃ ⠀⢸⠉⢿⡒⠒⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣡⠚⠁⠀⠀⣰⠇⠀ ⠀⠘⣇⠀⠙⠢⢄⣀⠀⠀⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢠⠞⠀⠀⠀⢀⣴⠃⠀⠀ ⠀⠀⠘⣄⠀⠀⠀⠀⠉⠑⢦⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡰⠃⠀⢀⡠⢶⡟⠁⠀⠀⠀ ⠀⠀⠀⠘⢦⣄⣀⠀⠀⠀⠀⢳⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠞⣀⠤⠚⢁⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠲⢬⣉⡉⠉⠙⠳⣄⡀⣧⠴⠒⠊⠙⠛⠉⠧⢤⡎⢀⣴⠟⠋⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⢤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠙⡆⠀⠀⠀⣠⠖⠋⠑⠢⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣻⣦⠀⢹⠀⠀⡴⢁⣾⣿⣆⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⣿⣿⣿⠀⢸⠀⠀⡇⢸⣿⣿⣿⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠙⠿⠋⠀⣾⣖⣲⡇⠀⠛⠿⠃⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠐⣇⠀⠈⢻⠋⠁⢀⡷⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⣦⡀⠀⠀⠀⠈⠑⡎⢹⠑⡶⠋⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠋⠈⠋⢩⠟⠁⠈⠙⠒⢢⣤⣆⠈⠙⠋⠀⣠⣤⠤⠖⠒⢺⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠈⠑⠒⠒⠋⢹⡄⠀⠀⠀⠀⢧⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠷⠒⠒⠦⢄⡞⠀⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠒⠋⠉⠀⠈⠹⡆⠀⠀⠀⠀⠀ ⢰⠋⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⢷⡀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢧⠀⠀⠀⢀⡞⠀⠀⠀⣰⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⠦⢄⣀⡀⠀⠀⣀⣙⣦⠀⠀⠘⣦⡀⠀⡼⠀⠀⠀⢸⡅⢀⣀⡤⠶⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠈⡇⠀⠀⢀⠹⣾⠁⡄⢀⠀⣸⠏⠉⠀⠀⠀⢄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣰⠃⣠⠆⠀⡰⠷⣀⣹⣨⡶⠛⠶⠧⠼⠞⠧⣄⣀⠀⠙⣆⣸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⠤⠚⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢠⣿⠀⠙⣦⣤⠀⠀⠠⠀⡄⠀⠀⣸⣧⠀⢤⡀⠀⠸⠳⡤⡀⠀⡀⣄⠈⠀⠀⠒⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⢘⣿⡤⠔⢠⠀⠀⠠⠀⠤⣄⠀⡴⡉⠉⠱⠼⠀⡆⣠⠀⠀⠀⠠⠐⠿⠰⡶⠤⠆⢰⠶⠘⢤⠄⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠈⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⡽⠿⡍⠉⠙⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⣠⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡏⢀⣀⠀⢹⡀⢰⠃⣀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⡿⠟⠋⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⡇⢼⣿⠀⠀⡇⢸⢸⣿⠆⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⢠⠾⠋⠀⠀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠘⣇⠈⠉⠀⢀⣇⠸⡀⠉⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡏⠀⢴⣶⣄⠀⠙⣄⠀⢀⡼⠀⠀⠳⡀⠀⢀⡾⣿⣿⠀⠀⣤⣤⣀⠀⠀⠀⠀⣾⣿⠋⢻⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⢈⣿⣿⣷⡀⣸⢈⣧⠀⠀⠛⠛⠋⠀⠀⠀⣀⣈⣛⣟⣂⣀⠙⣧⠀⠘⢦⠈⠙⠲⣤⡀⠛⠁⠀⢸⣿⠏⠀⠀ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⠏⣿⠃⣻⢯⡈⣱⢦⡀⠀⠀⢰⣾⣉⠉⢠⣤⣤⣤⣭⣭⣿⣧⣀⠈⣧⠀⠀⠀⠙⢦⠀⣰⠟⠁⠀⠀⠀ ⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠘⠏⣠⡟⠀⢸⣾⣿⣧⣴⡁⠀⡍⢀⡻⢿⣿⣷⣶⣿⣿⣿⡿⠋⠀⠉⢷⣿⡄⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀ ⠀⠸⣿⡟⠀⠀⠀⠀⢀⣤⣴⢞⣩⠄⠀⠀⢻⣿⣿⠿⠓⣦⣀⣀⣀⣀⠽⢿⣿⡿⠿⢯⣀⣀⣀⣠⠾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⣿⣍⣻⡿⣿⠀⠀⠀⠀⠙⠿⢷⡤⠀⠀⠀⠀⠀⠀⣞⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤ ⠀⠀⢀⠀⠀⢀⡴⣆⠉⠛⢿⠀⢹⣷⡀⠀⠀⠀⠠⣀⣀⣀⠆⠀⠀⠀⢸⣯⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠳⢤⣾⠀⠘⣦⣀⣾⣤⣿⣿⡷⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⣤⣄⣀⣤⣤⣶⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣽⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠂⠀⠐⠒⠒⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠔⠋⠉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠙⠓⢶⣄⡀⠀⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⠇⠀⣇⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⣀⣀⣀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠚⢹⠀⢀⠘⢦⡀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢹⡀⠀⠀ ⠀⠀⠀⢀⠞⠀⠀⠘⣆⣺⣄⡀⠉⡳⠏⠀⠀⢀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⣇⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⠁⠀⡾⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠙⣦⣠⣤⣾⠿⠃⠀⡆⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠃⠀⠀⠀⠀⡇⠉⠛⠛⠛⠉⠉⡆⠀⠀⠀⠀⢹⠩⠁⠀⠀⠀⠀⢧⣀⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠀⢸⠀⠀⠀⠀⢸⠉⠓⠲⠤⠤⠤⠖⢧⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⠀⠉⣿⠈⠣⣀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠀⠀⢀⠀⠀⠀⠀⠰⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⢰⠉⠀⢠⡟⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠚⠁⠀⢀⡞⠁⠀⢀⣀⣠⠞⠒⢦⡀ ⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇⠀⠀⣸⠉⠉⠉⠉⠉⠒⠒⠒⠦⠤⠤⣄⣀⣀⣀⠀⠀⣰⠋⠀⠀⢠⢞⡟⠁⠀⠀⠀⢧ ⠀⠀⠀⠀⣸⠀⠀⠀⣸⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠁⠀⠀⣠⢿⡞⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⡇⠀⠀⠀⣧⣤⣀⣸⠄⠒⠒⠒⠒⠒⠒⠠⠤⢄⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⢸⠀⠀⠀⢀⡿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⢠⠇⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡇⠀⠀⣠⠋⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⢠⠇⠀⢀⠃⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠀⠘⠿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀ ⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⠇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀ ⠀⢰⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀ ⢀⠗⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠐⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠙⠛⠛⠛⠻⠷⢶⣤⣀⠀⠀⠀⠀⠀⠘⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⡸⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠤⣀⣂⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠠⡐⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⠾⠋⡐⠨⢄⠱⡈⠜⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣋⠅⡨⢐⢂⠰⢠⠡⢇⢣⡙⣌⠱⢌⠹⢻⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⢉⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡜⣧⢱⠩⢎⣌⠣⠞⣌⠦⢱⡈⢎⢬⡑⢎⡜⢢⣛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣮⣳⠹⣆⢬⡓⢭⡒⡍⢦⡙⣌⠦⣙⠦⣜⣳⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣼⣙⣦⣛⣼⣒⣟⣦⣻⣬⣯⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣾⣯⣤⣶⢶⣶⣶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠻⣯⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣦⣤⣀⣀⠀⠀⢀⣀⣠⣤⡶⠾⠛⠛⠉⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀ ⢰⡁⠃⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡠⢤⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⢣⠀⠁⢨⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡔⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠑⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡎⠑⡄⠀⠀⠀⠙⣷⡌⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣶⠟⠋⠀⠀⠀⠀⠀⢠⠐⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠇⠀⠀⠀⠀⠈⢿⣦⡁⠢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠛⠷⢶⣤⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡶⠟⠛⠉⠀⠀⠀⠄⠠⠑⠀⡐⢈⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣧⡐⠄⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠟⠿⠻⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⠘⠄⠀⠀⠀⣄⣵⠿⠉⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣂⢀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡐⢈⠀⠄⠂⣀⠀⣤⣶⠟⠉⠀⠀⠀⠀⠀⠘⡄⠀⣁⡵⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣔⡁⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠁⠀⠄⠂⠀⢂⣰⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⣂⡀⠠⠀⡀⠠⠀⡀⠂⠀⠂⠀⠠⠀⠀⠂⠀⠄⠂⠄⠂⢈⠀⠄⣀⠃⠠⠄⣁⣠⣤⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣶⣤⣤⣀⣀⣀⠂⡀⠄⠀⠂⠁⠀⢂⠐⡀⣁⣂⣈⣤⣤⣾⡶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠉⠻⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠿⠛⠛⠛⠿⣶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢿⣄⠙⢯⡻⢶⣄⠀⠀⠀⠀⠀⠀⣠⣾⢿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢀⣀⣀⣀⣀⣀⣄⣿⣦⣀⣙⣦⠙⢧⡀⠀⠀⢠⣾⠟⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⢧⠈⢷⡀⣰⠟⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣛⣉⣥⣴⣶⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠛⠋⠉⢉⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⣃⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⣠⢾⡟⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⢷⡄⠀⠀⠀⠀⣰⠿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠉⣡⠞⠁⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⢸⣷⠀⠀⠀⣰⠏⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡘⣿⣇⠀⠀⡟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⣿⣿⠀⠀⣧⠀⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡿⠋⣘⣦⠿⠷⠤⢿⣀⣨⣿⠟⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣦⣿⣶⣶⡶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣿⣏⣙⣿⣿⠂⠉⢱⠀⠐⣭⣽⣯⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠊⠉⢹⡏⢉⡽⣿⠏⠙⣾⠁⠀⢀⡶⠳⠦⢽⣆⠉⠉⢑⣀⣀⠀⠀⠀⢀⣠⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⢿⣤⣬⣝⣒⣛⣷⣞⠉⠀⠀⠀⣀⣿⣷⠶⠟⠋⠛⣷⣶⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⣠⡾⢋⣩⡿⠛⢛⡿⠓⠒⠚⣹⡿⠋⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣴⠟⠁⢀⡾⠋⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣼⠋⠀⠀⠋⣠⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣄⢀⣠⡴⠶⠛⠉⢀⣴⠋⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠋⠀⠈⠻⢿⣯⡀⠀⠀⢠⡿⠁⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡇⢠⡾⠋⠳⣄⠙⢿⣆⣠⡟⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡶⢞⣿⠃⠘⣇⠀⠀⣸⠀⢻⡙⣿⣅⡼⠏⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠛⠁⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⠉⠁⠀⠀⢈⣙⡿⠓⠒⠒⠓⠛⠉⠀⠀⠀⠀⣀⣴⠶⠟⠋⠉⠀⢿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣟⣀⡹⠀⠀⠀⠰⡏⠈⠳⣦⣴⠖⠃⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⣍⡴⠒⠒⠶⣄⠳⣄⣴⡏⢁⣠⡴⠃⢀⠀⡄⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣷⣄⠀⠀⠈⢧⠀⠈⠛⠋⣟⠀⣠⠟⣾⠃⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⢀⡼⠃⠀⣀⣈⠙⠛⣿⣾⣇⣼⢋⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣥⠀⠀⠧⠼⢂⡴⣿⣛⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢹⣿⢦⣀⡀⠀⠀⠀⣠⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⡴⣯⣼⡿⣿⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠶⣭⣙⡛⠚⠛⣩⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠁⠀⢻⡆⠈⠛⠶⠤⣀⣀⣀⣤⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣿⠋⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠙⣷⣀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠈⠻⣶⣀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⢻⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣉⣩⠙⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠈⠉⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠟⠉⣠⠶⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⣆⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⣴⣇⣀⣀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣤⣤⣴⣿⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡿⠿⣦⡠⠗⢤⣽⣬⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡶⠟⠀⠀⢸⣷⠄⢻⡟⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⣀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠹⣧⠏⠀⠀⢀⣠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣤⣤⣀⣀⠀⠀⠀⠀⣻⣦⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠽⠿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢤⣴⣾⣃⠀⠀⠀⢰⣾⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⠀⠀⠀⢠⡟⠉⠁⢩⣛⣾⠉⣄⠀⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡏⠀⠀⠀⣿⠀⠀⠀⠸⠟⠈⡿⠟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⣠⠚⣧⣼⠁⠀⠀⠀⠙⣦⡀⠀⠀⢀⣴⣇⡀⢀⣠⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠤⠤⠄⠠⠀⠀⠀⠀⠀⠤⣤⣼⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⢹⡟⠉⠀⠀⢭⠩⠁⠀⢻⣿⣟⣳⣶⣶⣶⣤⣄⣀⣀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣽⣿⣿⣿⠷⣤⣀⡀⠀⠀⠀⠀⠀⠻⣦⣐⡴⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁⠀⠘⢿⣦⡉⠻⡷⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡴⠟⢻⡏⠈⢿⡛⠿⢿⣿⣿⣿⠀⠀ ⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⠸⢷⡄⠀⠙⢿⣿⣦⣄⢢⠛⠀⠉⠉⠉⠉⠉⠁⠉⠁⠀⠀⣾⠃⠀⠀⢻⡄⠀⠈⠙⠻⢤⣀ ⣿⣿⣿⣿⣿⣿⣟⣛⣿⠟⠁⠀⣀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠈⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙ ⣿⣿⣿⣿⣭⣽⣿⡟⠁⠀⢠⠞⠁⠀⠀⡤⠚⢉⣿⠀⠀⠀⠀⠀⠀⠈⠁⢻⠙⠶⣤⣀⠀⠀⠀⠀⣰⢿⡇⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣰⡿⠔⠒⠦⣄⠀⠰⣄⠀⠹⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠛⠶⣴⣾⠃⠰⣧⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠉⠉⠉⠋⢹⣿⠁⠀⠀⠀⠈⣳⣀⣼⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣷⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⢿⡄⢤⣄⠀ ⣀⡀⠀⠀⢸⣿⣀⣀⣠⣴⣾⣿⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣇⣀⣀⣀⣸⣄⣤⣼⠀⠀⠀⠀⠀⠀⢸⡇⠐⠊⠉ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢙⣿⠛⠉⠉⠉⠙⣯⣀⣹⠀⠀⠀⠀⢀⣠⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣾⣿⡟⠉⠀⠀⠀⠀⠀⠙⣿⣿⣶⣾⣿⣿⣿⣿⠓⠒⠒⠒⠚ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⣇⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠉⠉⠁⠀⠈⢻⣿⣿⣿⡿⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⣋⡉⠉⠉⠉⠉⠉⣡⡟⠁⠀⠀⠀⠀⢳⣀⠀⠀⠀⢀⣴⡏⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣀⡤⠒⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠶⣶⣶⣤⣀⠀⠀⠀⠀⢇⢀⡠⠞⢁⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠈⠻⣾⠑⣦⣀⣠⣼⣿⡶⣾⣿⡷⢶⡚⠛⠒⠒⠲⣤⣄⡀⠀⣠⣾⡿⠋⠀⠀⠈⠀⠈⢷⡄⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢷⣜⣿⡿⣫⠞⠛⠉⠉⠉⣳⣽⣒⣒⠲⢞⡯⠽⠿⢯⣿⣻⣄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠿⠛⣿⡿⢿⣄⣀⣀⣤⣾⡿⠋⠀⠈⣧⡻⣤⣀⡀⠀⣀⣽⣿⢙⡇⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⡟⠉⠓⠒⣷⡶⠟⠻⠦⠀⠀⠀⠀⠙⢲⣭⣭⣭⡽⣾⢉⡟⠇⠀⠀⠀⠀⢰⡏⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⠀⢸⠃⠀⢰⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⣿⠏⠀⠀⠀⠀⠀⠐⡾⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⢸⡄⠀⢈⣇⠀⠀⠀⠀⢀⣤⢶⣶⠆⠀⠀⠀⠀⢠⣴⣶⣾⠁⢸⠇⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⠀⠀⢸⡇⠀⠀⢿⣀⣀⣀⣤⣿⡿⣿⣏⢹⣤⣤⣴⣤⣼⣿⣿⣿⣦⣿⣇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠸⡇⠀⠀⠺⡏⠉⠉⠉⣉⣉⣙⣻⣛⠀⠉⠻⡿⢋⣸⣿⣟⣛⣻⣿⣉⣉⡭⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢶⣷⡀⠀⠀⠻⣟⠉⠩⠭⠽⠛⠋⠙⠦⢤⠴⠷⠒⠋⣹⠗⠀⣨⠟⠉⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣠⠞⠁⠀⠀⠀⠀⠀⢰⣦⡭⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠹⣶⠶⣤⣤⣤⣤⣤⠴⣾⣿⠿⠛⠛⠦⣄⡀⠀⠀⠀⣠⡏⢿⣇⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⣿⣶⣨⠛⠉⠙⡄⢰⠏⠉⠳⢦⡀⠀⠀⠙⢦⡀⢠⠏⡄⠸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠻⡿⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⠓⠦⣀⠀⠈⠻⢤⡃⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⣚⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⣺⠟⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣀⣸⠿⠤⢄⣲⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⣧⡤⠴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢉⡴⠁⠀⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠾⠿⣇⠀⠀⣼⠋⠃⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⢀⡾⠁⢠⣾⣤⣴⣄⡀⠀⠀⠀⠀⠀ ⠀⣀⣠⠾⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⢹⣦⡐⣿⢰⡀⠀⠀⠀⠀⠳⡄⢀⣠⢶⡾⣿⠀⣠⠟⠉⢾⣿⠋⠙⠛⠶⢦⣤⠀ ⠈⠛⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⢬⣷⣄⠀⠀⠀⠀⢹⠏⠀⠀⣸⢏⣼⣇⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣭⣀⣠⣾⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠖⠛⠉⠉⠉⢧⣉⠉⠙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠛⠁⠀⠀⠀⠀⣀⠤⠤⢿⠉⠳⡄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠔⠠⠾⠀⠀⠀⢸⠆⠀⠈⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀ ⠀⠀⣠⡿⠃⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠰⡇⠰⠄⠀⢀⠀⠀⣀⠤⢄⣻⡆⠀⠀⠀ ⠀⢠⠟⠁⠀⠐⢆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢻⡆⠀⠀ ⢰⡏⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠢⠤⣠⡤⢿⠀⠀ ⢸⠁⠀⣀⡀⠀⠀⢨⣇⡄⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⢰⡉⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⢸⡆⠀⠃⠘⣆⠀⠈⠳⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⡥⠆⠀⠁⠀⠀⢀⠀⠀⠀⠀⢻⡄ ⠈⢻⡄⠀⠀⠀⠀⡰⠃⣠⣴⣶⣶⣿⣿⣿⣿⣶⣦⡄⠀⠀⡠⠊⢉⣤⣶⣿⣿⠗⣾⠇ ⠀⠀⢿⡄⣀⠀⢠⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⣿⣿⣿⣿⣰⡏⠀ ⠀⠀⠘⣧⠼⠀⢸⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡄⠀⣿⣿⣿⣿⣿⣟⣿⠁⠀ ⠀⠀⠀⢿⠀⠀⢸⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⢿⡍⠀⠁⠀⢻⣿⣿⣿⡿⢿⣇⠀⠀ ⠀⠀⠀⠸⣧⡀⠘⡄⠑⠄⠂⠀⠉⠉⠉⠉⢉⣤⠜⠁⠀⢀⣴⣶⢃⡀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⢠⡾⠋⠛⣇⠀⣀⣠⣤⡶⠒⠂⠀⠀⠀⠀⠀⣴⣿⢟⡏⢸⡿⠛⠛⠋⠁⠀⠀ ⠀⠀⠀⠘⢷⡄⢉⢈⣿⠋⠁⠈⢿⠀⢰⡀⠀⠀⠀⠸⠿⠻⠚⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠘⢿⡀⠀⠀⢸⡄⠀⡇⠀⡄⠀⡇⠀⠀⠀⡇⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⠙⠀⠹⣦⡀⣸⡿⢤⡤⢄⣁⣠⣅⣀⣑⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⡈⠃⠙⢿⣿⣷⠾⢇⣠⣿⠀⣸⣀⣽⡶⡿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠈⠙⠒⠚⢇⣈⣻⣉⡹⠧⠔⢻⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠁⠀⠂⠀⠀⠀⠉⠄⢸⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⢤⣄⣀⠀⢀⣀⣼⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠓⠛⠓⠛⠙⠃⠉⠓⠟⠛⠟⠃⠚⠻⠛⠛⠂⠀⠂⠰⠘⠡⠛⠛⠂⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡜⠁⠀⠙⣜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡞⠀⠀⠀⠀⠘⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠞⠀⠀⠀⠀⠀⠀⠈⢎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠏⠀⠀⡀⣀⡠⢴⠞⠓⠒⠒⠚⠛⠒⠢⢤⣤⣀⠀⠀⠹⡽⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⣠⢴⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⠉⠒⢤⣽⣝⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣟⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⣀⠀⠈⠛⣽⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠾⠯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠚⠉⠀⠀⠉⠓⣤⠉⠙⢆⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⢀⡠⠤⠬⢝⡒⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣸⢀⣀⣀⣀⣰⣄⣀⠈⡇⠀⠀⢱⣤⣄ ⠀⠀⠀⣼⠁⡔⠁⠀⡀⠀⠀⠙⡆⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠉⠉⠉⢉⡇⠀⠀⢸⣏⡿ ⠀⠀⢰⠃⢸⢀⡠⠴⠓⠊⠉⠉⡿⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠑⢦⣀⣀⣀⣀⠔⠋⠀⠀⠀⣰⠃⠀ ⢀⣰⡏⠀⠈⢧⡀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀ ⢸⣿⣰⠀⠀⠀⠉⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠉⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⡯⠏⠀⠀⠀⠀⠀⢀⡤⢚⢏⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡤⣄⣀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣀⣤⡤⠲⢯⣁⡤⣞⡺⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣱⣀⣉⡽⠛⣿⣿⠉⠉⠉⢁⣿⠃⠀⢀⡞⠑⢿⣖⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣿⡇⠀⠈⢻⣳⣄⣤⣾⡏⠀⢀⣾⣀⣀⣀⣳⣷⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣿⣅⣹⢆⠀⠀⢙⠿⠛⠚⢤⠀⡼⠀⠀⠀⠀⠉⠉⢲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋⠁⠀⠀⠑⢄⡏⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠙⠦⣀⣠⡴⠃⠀⠀⠀⣀⣤⠄⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣶⠢⠤⢄⣀⠀⠀⠀⠀⣀⡤⠒⠉⠁⢸⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠉⢲⡦⠺⡅⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⣰⠿⣹⠧⣀⣀⣀⡤⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠉⠋⠉⠀⠀⠘⡄⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⡤⢞⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⠀⠀⠀ ⠀⣠⠒⠉⠁⠀⠀⢠⣤⠤⠐⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⠚⣢⣼⣆⠀⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⣀⢼⠿⠿⠶⢶⣒⣒⣲⡾⠿⠛⠛⠢⡑⡄ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠒⠲⣄⠀⠀⠀⠀⠀⠀⢰⡛⢏⣳⡽ ⠀⢸⣀⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⡴⠋⠉⠁⠒⠋⠑⣄⠀⠀⠀⣰⣉⠉⠉⣿⠁ ⣼⠋⠀⠀⠈⠉⠒⠤⡀⠀⡆⠀⠘⠁⠀⣤⡶⠿⠷⣦⠈⢆⠀⠀⡟⠛⠛⢲⠏⡇ ⠹⡄⢰⡏⠉⠑⠢⢄⡈⠢⣵⡀⠀⠀⢸⠁⠀⠀⢠⠬⣧⠘⠂⠀⠹⡀⣤⣬⣷⠃ ⠀⠙⢄⠳⢄⠀⠀⠀⢉⠀⠈⠁⠀⠀⣈⠷⠒⠛⠲⣽⠁⠀⠀⠀⠀⠙⠺⢿⡙⡆ ⠀⠀⠀⠑⠤⣉⠒⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠑⠀⠀⠀⠀⠀⠀⠈⡿ ⠀⠀⠀⠀⠀⠀⠉⠑⠒⢶⡒⠂⠀⠀⠀⠒⠤⠴⢚⡛⠂⠀⠒⠒⢄⡀⠀⠀⣰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠋⠓⠦⠤⠤⠤⠔⢋⡩⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⣇⠀⣸⠓⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⣀⠔⢻⡿⢿⠀⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣖⠁⠀⢸⢓⣾⠀⠀⠈⢣⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡴⢶⠶⠶⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠟⠀⠞⠀⠰⠆⠀⠻⠄⠘⠄⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣤⣤⡦⣀⠀⢀⣠⣤⡤⣄⡀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠧⠤⣤⣤⣾⡿⢻⣟⠛⢾⣷⣯⠾⣿⣟⠶⣽⣄⣨⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣀⣀⣀⣿⣿⡀⢻⣿⠇⢠⣿⣇⠘⢿⡿⠂⣹⡇⠀⣠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⠀⠀⠀⠉⠻⣝⡿⢶⣾⣿⠟⢯⡷⢖⣲⣾⡿⠉⠉⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣨⡀⠀⠀⠀⠀⠀⠉⣍⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠉⠲⢄⠀⠀⠀⠀⠀⠉⠒⠢⠤⠔⠂⠀⠀⠀⢀⡴⠋⣹⠄⠀⠀⠀ ⠀⠀⠀⣀⠤⠛⡗⠦⣀⠙⠢⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠚⠁⡠⠚⠃⢤⡀⠀⠀ ⠀⠀⡜⠁⠀⣠⠁⠀⠈⠐⠢⠃⠀⢠⠤⠤⠤⠤⠤⡄⠀⠳⠦⣏⠀⣦⡀⠀⠙⡄⠀ ⠀⣸⠁⢀⣼⠛⠒⢒⠾⠒⠆⠀⠀⠰⣀⣀⠀⢀⣰⠇⠀⠀⡴⣟⠒⢷⣽⣆⢀⣸⡄ ⢰⡋⠉⠉⢹⣇⠉⠁⠤⠤⠼⠦⠤⠤⠤⠬⠭⠥⠤⠤⠤⠾⠤⠀⠉⡹⣧⠀⠀⠈⣽ ⠀⣳⠀⠀⠈⢿⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠏⠀⠀⠘⣇ ⢠⡃⠀⠀⠀⠀⢧⠀⠉⢀⡒⠒⠒⢖⡒⠒⠒⣲⠖⠒⣶⡒⠉⠀⠀⡎⠀⠀⠀⠀⢸ ⠀⢧⠀⢀⣀⡠⠜⠀⣰⣁⣀⣀⣀⣀⣙⣤⠋⠀⠀⠀⠀⠈⡆⠀⠀⠓⠤⠤⢄⣀⡞ ⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡻⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⡏⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡇⢹⣿⣿⣿⡿⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠸⣿⡿⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⣿⣧⣄⣰⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡻⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠋⠙⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⠶⠾⠛⠛⠛⠛⠿⠿⣿⠷⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠐⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⡷⠂ ⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⢸⡇⠤⠤⠤⠶⠿⠟⠛⠁⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠒⠺⠟⠓⠲⠶⠶⠶⠾⠟⠛⠃⠀⠀⠀⡇⠀⢀⡀⠀⠀⠀⠀⠀⣾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠋⠀⠀⠀⠀⣰⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⡉⠓⠶⠶⣶⣶⣶⣶⣶⣶⣶⠶⠃⠀⠀⠀⠀⢦⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣦⣤⠤⠤⢤⣤⣭⣭⠽⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠙⢿⡉⠛⠳⣦⣻⣹⣆⣀⡄⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠍⠙⠛⠉⠁⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⡉⠉⠛⠓⠶⠶⠶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠏⠀⢰⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣹⣷⡦⢤⡤⢤⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡟⠀⠀⣾⣿⣿⣿⡇⠀⠀⠈⢿⢻⡿⢿⣍⡇⠀⣧⣈⣇⢻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠀⢀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠘⣏⢳⠀⠉⢻⠞⣡⣦⡼⡖⢻⣏⠛⠻⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠟⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⡏⢷⠀⠀⣧⠹⢿⣷⡇⠀⠙⣷⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⡘⣧⠀⠈⠛⠚⠋⠀⠀⠀⠈⠻⣦⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠃⢷⣸⣆⣀⣀⣀⣠⡤⠤⠤⠴⠒⠚⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠳⢦⣀⠙⢿⣿⣿⣿⣿⣿⣄⣀⡀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡄⠹⣿⣿⣿⣿⡀⠀⠉⠙⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡏⢰⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠛⠛⠛⠛⠛⠛⠓⠶⠶⢶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⣷⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⣿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣼⠏⣀⣀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠉⠳⣄⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⢻⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇ ⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣰⠇⠀⠀⠀⠀⡀⡀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠷⠶⠟⠁⣀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣄⡀⠀⣠⠞⢻⠾⣆⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣰⡿⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠙⠳⣆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⡾⠋⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠾⢿⣦⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣀⣠⠶⠞⠋⠁⠀⠈⢿⣆⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡏⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣶⠿⣆⡴⢷⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠁⠀⠉⠀⠘⠋⠀⢿⡴⢺⡇⢀⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢻⣤⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⢲⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣴⠤⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠃⠀⠀⠀⢠⡿⢼⣆⡀⠀⠀⠀⠀⣤⠀⠀⢀⡀⠀⠀⠀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣻⠂⠀⠀⠀⢸⠀⠘⠛⠈⠙⠲⢄⡀⢸⡧⠄⠈⠳⣄⢀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢷⠩⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠉⣿⢧⣄⠀⠀⠈⢷⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠋⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⣠⠴⢎⡁⠈⠋⠙⠲⢄⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡆⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⠀⠀⠘⠛⢯⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣤⢟⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⡋⠻⣄⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⡋⠁⠀⠀⠉⢳⡄⠈⠓⠦⣄⣀⠀⠀⣠⡤⠬⠿⠲⢤⣀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⠛⠙⢶⡀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⣿⠦⣄⠀⠀⠀⠉⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢻⡄⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⢀⡤⠊⠀⠀⠀⠀⠀⣠⠶⣏⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠚⠋⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣉⠛⠋⠀⠀⠀⠀⢀⣴⡾⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠞⠉⠠⠤⠒⠀⢀⡴⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠦⠞⣻⠀⣀⠀⢠⠏⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣄⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠾⢻⣇⣏⠀⠀⠈⢻⡓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⡀⠀⢀⠀⠈⢓⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠉⠀⠀⠈⠙⠛⠒⠶⠶⠤⠤⠤⠤⠶⠶⠶⣿⠋⠀⠀⠀⢹⠀⠈⣦⠀⠘⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠚⠙⣆⠀⠀⠀⢘⡇⣠⡀⢳⠦⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⠀⠀⠀⠀⠀⠀⠀⢻⢲⠒⠚⠁⠀⠀⠀⢀⣸⠆⠀⠀⠸⠶⠙⣧⠾⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡗⠒⠢⢦⡶⠒⠃⠘⠒⠒⢲⡖⠒⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣿⡀⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣌⣉⠉⠉⢉⣿⠀⠀⠀⠀⢀⡿⣄⣉⣉⣁⡤⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠈⠉⠉⠉⠈⠳⡀⠀⠀⡾⠀⡞⠹⡄⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢰⡧⠤⣝⣚⣁⣀⣀⣀⠤⠔⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣈⡉⠒⠒⠒⠒⠒⠒⠚⡃⠀⠙⠒⠢⢤⠤⠤⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⡊⠉⠉⠉⠉⠁⠒⠂⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠖⠒⢒⡶⠒⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊ ⠀⠀⠀⠀⡠⠋⠀⠀⠀⠈⠀⠀⠀⠀⣠⠤⡀⠑⢄⠀⠀⠀⠀⠀⠀⡸⠁⢀⡴⠒⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠹⣄⠈⢣⡀⠀⠀⠀⢰⣷⢶⣞⣀⠀⠀⠀⣰⠋⣸⠋⠉⠑⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠘⣄⠀⢣⢀⣠⠔⠛⠉⠀⠙⠋⠱⡄⣰⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢧⡀⠀⠀⠸⣆⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠷⡄⠳⣄⣀⡤⠾⠁⠀⠀⠀⠀⠀⠀⠀⣀⠾⣏⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⠞⠀⢰⠃⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⢀⣾⣋⡉⠲⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⣀⣀⣀⠔⠁⠀⠀⡞⠀⠀⠀⢀⣴⡿⢷⣦⠙⢦⠀⠀⠀⠀⣸⣿⢉⣿⣆⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡇⠀⠀⢀⠏⣿⣤⡼⣿⡆⠈⣇⠀⠀⠰⡇⢿⣯⣾⣿⠀⠘⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣾⠀⠸⣿⣿⡿⠁⠀⢸⡄⠀⠀⢳⡈⠛⠛⠋⠀⣀⡿⠎⠓⠒⠒⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣐⣷⣀⣀⠈⠉⣠⠤⠖⠚⢻⡛⠋⠉⠉⣹⣿⠯⠉⠉⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢶⠒⠚⠁⠀⠀⠀⠀⠀⠈⠉⠙⢉⣁⡀⠀⢆⡀⠙⠒⢤⠞⠁⠨⣤⠥⠄⠀⠀⠀⠀⠀⠛⠛⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠴⣯⣉⣀⣀⣀⣈⣀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⣠⠴⠦⡤⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⢰⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠻⠭⣩⡥⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡎⠉⠙⣆⣀⠇⢈⡧ ⠀⣠⠶⡞⠛⣲⠶⠦⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠒⠒⢛⡁⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⢸⠀⢸⣿⣽⡟⢶⣆⠀ ⡤⢇⠀⠃⣤⣻⣤⡀⢹⡌⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠉⠀⠀⢀⣠⠤⠒⠊⠁⠀⠀⣠⠏⠀⣼⠋⠀⢙⡌⢓⡟ ⢣⣀⣸⣽⡿⠧⢿⡃⠀⠳⡀⠀⠉⠒⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣀⣀⣀⣀⣀⡠⠞⠁⠀⠀⠳⣄⣀⠜⣠⠎⠀ ⠀⠻⣕⠹⡇⠀⠀⢱⠀⠀⠈⠒⠤⢄⣀⡠⠤⠟⠛⠉⠑⠒⠦⡄⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀ ⠀⠀⠈⠲⣝⡢⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠲⢤⡀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠙⠋⣹⡄⠀⠀⠀⢀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣄⣀⣀⣀⣀⣀⣀⠤⠂⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢛⡟⣗⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡹⠻⡝⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠓⠴⣇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢿⢀⡤⠔⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠑⢄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠞⠉⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⡀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠛⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠛⠒⠒⠲⠤⣄⠀⠀ ⠀⠀⠀⠀⠀⡞⢁⡴⠆⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⢀⡧⠤⠤⠤⠤⠼⡆⠀⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⠀⠀⠀⠐⠦⣀⠱⡀ ⠀⠀⠀⠀⢸⡷⠋⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠉⢢⠃ ⠀⠀⠀⠀⠘⣇⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣸⠀ ⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠀⠀⠀⠀⣰⠏⠁⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣽⣶⣶⣶⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣷⣶⣶⣾⣥⣤⣤⣤ ⣿⣿⣿⠉⠹⠉⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿ ⣿⣿⣿⣶⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣿⣿⣿⣷⣄⢀⡜⢠⣄⣹⣆⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣍⣴⣿⡃⠀⠈⢻⣧⢀⠤⣽⣿⣿⢛⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠻⠟⠋⠀⠁⠀⠀⠻⣿⣏⢀⡼⠋⠀⠀⠀⠀⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣶⣦⣤⣄⣀⣀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⠁⠀⠀⠀⣠⣴⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣴⡶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠰⣶⣾⣿⣋⡀⠀⠀⠀⠀⢘⣛⣿⣿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣿⡗⠀⠀⠀⠀⢠⡿⠛⠉⠉⢉⠛⣶⡛⢉⡁⠉⠉⠻⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣶⡋⢻⣸⣷⠆⠀⠀⣹⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠟⢡⡿⠀⠀⠀⠀⢼⣿⢸⠀⠀⠀⠈⠉⠀⣸⡇⠉⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣤⣠⡞⢹⣧⣾⡇⠀⠀⠀⠀⠀⠙⢧⣅⡀⠀⠀⢀⣴⠿⣄⣀⣀⣠⡼⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠤⠤⠤⠤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣿⣿⣿⠿⣿⣿⣿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡍⡭⠉⠁⠀⠀⢤⢈⡭⠀⠀⠹⣿⣿⣟⣟⣶⣶⣶⣶⣤⣄⣀⣀⣀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣤⣴⣶⣿⣛⣿⣯⢩⣧⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠤⣠⡿⠃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢿⣆⡙⠿⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠙⠳⠟⠋⠀⠀⠀⠀⢀⣠⣼⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⢦⣀⠀⠀⠀⣙⢿⣧⡄⠈⠽⠹⠛⣿⡶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⡿⠟⠋⠉⣿⡇⠀⠘⢷⡉⠙⠻⢿⣿⣿⣿⡇⠀⠀ ⣿⠋⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⡀⠰⠿⣦⠀⠀⠈⠳⣿⡿⣶⣄⠙⣩⠉⠁⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠈⢿⣄⠀⠀⠈⠉⠻⢧⣤⣀ ⠿⣿⣿⣿⣿⠿⠿⢟⡻⠿⣿⣿⠿⠋⠀⠀⠀⠀⠐⠉⠁⠀⣸⣿⡆⠀⠀⠀⠀⠙⠮⣝⡿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠈⠛ ⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠟⠁⠀⠀⢀⡴⠋⠀⠀⠀⢀⣠⠞⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⢻⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣯⠘⠀⠀⠀⠀⠀⠊⣿⡀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠻⠿⠷⠿⢿⣿⠟⠀⠀⠀⠰⠏⠀⠀⠀⠀⠸⡏⠀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⠻⢶⣄⣀⠀⠀⠀⣠⡿⢋⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣠⣾⡿⠊⠙⠛⠳⣦⡀⠀⠻⣦⠀⠀⢹⡶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠉⠙⠻⠷⠿⢿⠁⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⠉⠉⠙⠙⠛⠛⣿⡿⠀⠀⠀⠀⠀⠀⠹⣆⢀⣼⣤⡾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄⠀⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⣿⣿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⢸⠁⠀⠀⠀⠀⢻⠀⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠠⠭⠕⠒ ⠛⠓⠂⠀⠀⠙⠛⠻⢷⠶⠾⠿⠟⠛⠛⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣾⣶⣶⣶⣶⣾⣿⡿⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣠⣾⡇⠀⠀⠀⠀⠀⢸⣯⣤⣤⡇⠀⠀⠀⣀⣀⣠⣤⣶⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣙⣛⣻⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠉ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠹⣇⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠾⠿⠿⠛⠋⠛⢿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣿⣿⡿⢿⡿⠟⠀⢀⡀⠘⠻⣿⠛⠿⠿⠿⠿⠿⠿⠛⢛⣿⡿⠭⠄⠀⠠⠠⠤⠤⠤⠀ ⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢛⣓⣀⠉⠉⠉⠉⠉⠁⠀⣠⣞⠉⠁⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣾⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⠟⠉⠉⢦⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠋⠀⠀⠀⠀⢳⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣰⠃⠀⠀⠀⠀⠀⠀⠻⡜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡼⠃⠀⠀⠀⠀⢀⣠⡤⣶⠟⠛⠛⠛⠛⠛⠛⠛⠒⠦⢤⣤⣀⡀⠀⠀⠈⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡽⠃⠀⣠⡶⠟⠊⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠲⢦⣀⡀⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣇⠴⠊⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠈⠙⠿⣿⡽⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⣤⣤⣄⣀⠀⠈⢻⣽⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⢿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣫⠞⠋⠀⠀⠀⠀⠈⠓⢦⠀⠀⠛⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⣀⣙⡓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⢹⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈⢷⠀⠀⠈⠳⣄⣀⠀ ⠀⠀⠀⠀⣠⠏⢁⡴⠚⠉⠉⠉⠉⠱⢦⡁⠀⠀⠀⠀⠀⠀⣦⡿⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠾⠿⠶⠶⠦⢼⠀⠀⠀⠀⣿⡿⣷ ⠀⠀⠀⣸⠏⢀⡟⠀⠀⢠⡄⠀⠀⣀⣈⣷⠀⠀⠀⠀⠀⢰⣿⣀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⢾⣦⡿ ⠀⠀⢀⡟⠀⢸⠀⣀⣤⠞⠛⠋⠉⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⡀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢀⡿⠁⠀ ⠀⢠⣾⠀⠀⠸⣏⠁⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀ ⣼⣿⠏⡀⠀⠀⠙⠷⣄⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠺⠷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠹⠾⠼⣇⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠾⣿⣛⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⢫⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⣀⣯⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⡶⠦⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⣤⣴⡗⠏⠉⠙⣦⣰⣎⡿⠿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣹⣄⣀⣠⡟⠉⢿⣿⣿⠉⠉⠁⠀⠀⣿⠏⠀⠀⠀⡸⠋⠙⢿⣟⡃⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⣹⡆⠀⠈⠻⣿⢦⡀⠀⣀⣿⡿⠀⠀⠀⣸⡇⠀⠀⠈⢻⣽⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣸⡿⠛⢧⡀⠀⠀⠈⠻⣿⣟⣿⣿⠃⠀⠀⢸⠟⠛⠛⠛⠛⠛⠫⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⠤⠾⠳⣄⠀⠀⣠⠟⠉⠀⠈⠙⣆⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⠀⠀⠈⠳⣄⣿⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣀⡄⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⢀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣠⡤⠞⠋⢹⠃⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⡈⠙⠛⠶⠤⣄⣀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⢿⠶⠘⣧⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⣼⣿⣙⣿⣄⠀⠀⠀⠀⣠⠞⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠛⠲⠤⠤⠤⠚⠉⠀⠹⡄⠈⠉⠛⠛⠉⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣄⣠⠴⠞⡳⠦⠤⠴⠖⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣴⣦⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⡝⠃⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠋⠀⠉⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣥⣤⣤⡀⠀⠹⣿⣿⣿⡿⠋⠀⠈⠻⢿⡟⠛⠻⠿⠟⠋⣁⣤⣴⣶⣿⣿⣷⣶⣤⣀⢀⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣳⣿⣿⣿⣿⣿⣷⣀⣀⣈⣹⠟⠁⠀⠀⠀⠀⠀⠙⠲⢤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⣝⠻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠒⠒⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡍⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣀⣀⣀⡄⠀⠈⣿⡟⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠻⣿⣿⣿⣿⣿⣶⠶⠦⣽⣶⣄⡀⠀⠀⠢⣀⣀⣠⣴⠿⠗⠛⣿⡯⠉⡿⠁⠀⠀⡿⣴⠆⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣟⡟⢆⣀⣙⣛⣁⠽⢦⡀⠀⠈⠃⠉⠙⠶⠤⠤⠤⠤⠾⠋⠀⠀⠘⠣⢷⣴⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠓⠲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠲⢶⣞⣻⣿⡿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠦⠤⠤⠖⠋⠁⠀⠀⠀⠀⣿⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠛⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡽⠟⠁⠀⠀⠀⢀⣿⡟⠙⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢸⣿⣽⡉⠉⠉⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠛⡟⠛⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣿⣭⣧⣤⠤⠤⠤⠤⣄⡸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⡈⠙⠲⣄⠀⠀⠀⢀⣀⣀⣀⣀⣤⣿⠀⠀⡾⠀⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣆⠀⠙⠓⠚⠋⠛⠒⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣴ ⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿ ⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⢰⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡏⣀⡤⠴⠒⠒⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠴⠚⠃⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠎⣁⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠟⠉⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢀⡤⠤⣄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⢷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡘⡆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⣿⡿⣷⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⡟⠀⢀⡖⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠁⠈⠉⣡⡾⠀⡈⠳⣄⡀⢠⠖⠲⣄ ⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡞⠉⠉⠀⠀⠉⠂⠀⠉⢻⢤⠀⣼ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣀⣀⣀⣠⠤⠖⠋⠁⠀⠀ ⠀⠀⣰⡀⠀⠀⠀⠀⠈⠙⠲⠶⠤⣤⣄⣀⣠⠤⠤⠤⠤⠤⠤⢤⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠇⠙⢦⡀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀⠀⠀⠓⠦⣀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⠉⣳⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣧⠀⠀⢿⡀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⣠⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡷⣄⠀⠙⠒⠒⣞⠉⠀⠀⢀⣠⠴⠚⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⠈⠉⠒⠀⠀⠈⠓⠚⠉⠁⠹⠤⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣀⣀⣀⣀⣀⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢀⡀⡀⠀⣀⣀⢀⠀⠀⡀⠀ ⠸⡟⠻⠀⢛⢍⢜⢟⠃⢕⢃⠻⣛⢛⠃⠘⢘⣻⡟⠛⠀⠁⢰⠊⠛⡫⠒⠁⠰⠐⠙⡘⡓⠂⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣦⡀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢙⡧⠠⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠏⠀⢠⠏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢷⢦⠀⠀⣠⣾⣿⡆⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢰⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡽⠲⡀⠀⠀⢀⣼⣾⣀⠔⢭⣿⡿⢳⣼⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣷⣄⡀⠀⢷⣄⠀⠀⠀⢀⡞⠁⠀⡼⣀⠴⣫⠶⠛⢧⡀⣸⣿⡔⢺⡇⢀⠇⠀⠀⠀⠀⠀⣰⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠓⠾⠏⠳⣄⣀⡜⠀⠀⠚⠋⢡⠞⢁⡤⣶⣾⡟⣿⣟⠀⢸⠄⢸⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡗⠒⠢⣄⡀⠀⠉⠀⠀⠀⠀⣠⡿⠚⠙⣷⡿⠟⢸⣿⠙⠀⣸⠀⡇⠀⠀⠀⢀⣾⠟⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡿⣋⣹⣟⣷⣄⠀⠀⠀⠀⠀⠛⠒⠒⠉⠁⠀⠀⡾⣿⣇⡴⠁⠀⡇⠀⠀⢀⣾⡟⡔⠁⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⡄⣀⣼⠁⠀⣿⠁⠉⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠁⠀⠀⢸⠀⠀⠀⣼⡿⡰⠁⠀⠀⠀⠀ ⡟⠀⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⡟⢦⠀⠀⠀⠀⠺⠄⠀⠀⠀⣠⡞⠀⠀⠀⠀⢠⡇⡇⠀⠀⠀⢸⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣠ ⣿⣇⡀⠀⠀⠀⠀⠈⠉⢸⣿⠏⠀⠀⣸⠀⡏⠑⢦⡀⠀⠀⠐⣾⣿⣿⡿⠁⠀⠀⣀⠴⠉⡇⢹⠀⠀⠀⢸⠀⠀⣸⣿⠘⠀⠀⠀⠀⠀⡀ ⠿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣯⡤⠄⢴⠇⣸⣀⡀⠀⠉⠓⠦⣀⡉⠉⠉⠀⢀⡤⡾⠁⠀⣰⡇⢸⣷⣦⠤⠞⠒⠒⠺⣧⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡎⢠⠃⠀⠉⠙⠒⠂⠤⠤⣽⠓⠒⠊⠉⠀⣧⣀⣼⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢀⡞⢠⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡇⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⡼⠀⠀⠀⡞⢠⠏⠀⠀⠈⠑⠦⡀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠁⢠⠇⠀⠀⡸⣰⣯⠏⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⢀⡼⠧⠶⠦⠾⠦⠤⠤⠷⠿⠥⠤⠤⠶⠿⠋⣸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⡜⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀ ⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣤⣤⣴⣾⣿⣦⣈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠼⣟⠁⠀⠀⠀⠀⠀⢠⠟⢏⠻⠷⣦⣀⣀ ⠞⡏⠳⣄⡀⠀⠀⠀⠀⠘⡆⢹⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⡞⠀⠈⢆⠀⠀⠀⠀ ⠀⡇⠀⠀⠈⡏⠹⡟⣆⠀⢃⢸⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⠆⠀⠀⠀⡼⠁⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠹⢶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⡰⠋⢁⣠⢤⣤⣤⡴⠚⠁⠀⡼⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠈⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⣴⣾⣿⡟⠀⠀⠀⠀⡇⠀⠀⢀⠟⡇⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⠇⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠘⡆⠀⣣⢸⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⠀⠀⣰⠁⠀⠈⣇⠀⠀⠀⠀⠀⠈⡄

Warning: This item may contain sensitive themes such as nudity.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣃⢤⡟⣗⢸⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⡇⠈⠳⠏⢯⢸⡇⢻⡉⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠐⠠⠀⣸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠐⠛⠛⠽⢹⣿⣿⣿⣿⣿⡄ ⠠⠀⠒⣊⠩⠿⡟⣿⣿⣿⣿⠈⢄⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⣿⠃ ⠂⠈⠀⢀⡠⢴⠳⠘⣿⣿⣿⡧⡀⠑⠉⠢⠄⠀⢀⠴⠟⢺⣿⣿⢳⣿⠟⡀ ⢀⡠⠐⠁⠀⠀⠲⢑⠈⠚⡿⡇⠰⠤⠤⠄⢐⠎⠇⣈⡠⣿⡟⠏⠀⢿⢉⡃ ⡦⠀⠀⠀⠀⢀⠁⣴⢁⠀⠈⡈⠀⠀⠐⢀⠈⡀⡸⠀⠐⠋⠈⡰⡱⠈⢸⠃ ⠐⠡⡀⠀⢃⢸⠀⣿⠀⠁⠒⠃⢆⠀⠀⡌⠧⢊⠃⠀⠀⣄⣇⡳⠀⠀⡸⠀ ⠀⠀⠩⠢⡈⣼⠀⡄⢂⠀⠀⠀⣂⢑⡂⠐⠀⡬⡀⠀⠀⠛⡟⠀⡀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⢿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⡿⠿⠿⠿⢿⣷⣦⣄⣀⡀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢀⣀⣠⣴⣶⣶⣶⣤⣀⡀⠀⠀ ⢀⣾⡿⠋⠀⠀⢀⡴⠛⠉⠉⢉⡙⢻⣷⣶⣶⣤⣈⣻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣭⣶⠶⠿⠿⠿⠿⠷⣤⡀⠈⠉⠻⢿⣦⠀ ⢸⡿⠀⠀⠀⠀⠈⢷⡀⠀⣶⠛⠉⠉⠉⠀⠀⠉⠉⠙⠛⠻⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠿⠛⠉⠉⠻⠶⠶⠶⣦⡀⠀⢸⡇⠀⠀⠀⠈⢿⡇ ⢸⣷⡀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⣰⠏⠁⠀⠀⠀⠀⣸⡇ ⠈⢻⣷⡀⠀⢀⣴⠶⠟⠁⣀⣘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠻⠶⣦⣄⠀⠀⢰⣿⠇ ⠀⠀⠹⣿⣶⣏⠁⠀⣰⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣦⡀⠀⠙⣧⣴⡿⠏⠀ ⠀⠀⠀⠈⠙⠻⠿⣶⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠀⠀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣧⣴⣶⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⢿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠿⠟⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠄⣿⠋⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠂⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⣾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠛⣿⡄⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠙⠛⠳⠟⠛⢙⡟⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢰⡶⣦⣤⣀⣴⡿⠋⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠁⠸⣷⣤⣤⣤⣾⣶⠀⣾⡇⠀⠀⣀⣤⣴⣾⠟⠁⠀⠀⠀⠀⠉⠻⣿⣄⠀⠀⠀⠀⠘⣷⠀⢈⠛⠉⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠛⠛⠛⠋⣩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡛⠻⣶⣤⣴⡿⠀⣾⡟⠶⣦⣤⣴⡿⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣠⣴⡶⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣷⣤⣄⣠⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣤⣤⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣶⣶⣶⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢠⣾⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠒⠲⢤⡀⠀⠀⠀⢈⣽⠟⠁⠀⠀⢠⡞⠁⠀⣼⠿⢯⡑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⢀⣴⠏⠀⠀⠀⠀⠀⣾⡇⠀⠘⠁⢀⡈⠻⡯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡟⠙⣧⢹⣷⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⠤⠤⠤⣄⣀⢳⠀⠀⢸⣦⡀⢸⠄⣧⣻⣿⢀⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠙⣻⣇⠀⢸⣿⣿⡾⠀⢻⣿⣿⣿⣇⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⣼⣹⡇⠀⠀⠀⠀⡶⢶⡶⠭⠉⠀⠀⠙⠟⠁⣠⠼⠋⠉⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⢿⡛⠶⣤⣤⣤⡤⠖⠛⠈⢻⡇⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠀⠀⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⢀⣤⡞⠛⠦⣄⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀ ⠀⠀⠀⢀⣼⠃⠀⢀⡴⠖⠛⢯⡙⢶⠶⠶⠦⠤⢤⣀⣈⣳⣄⣀⣶⡀⣇⢹⣎⡳⢤⣀⠀⠀⠀⠀⣀⣠⣶⡭⠤⠴⠶⠖⠒⠋⠉⠱⡆⠀⠈⡄⠀⠀⠀⠀⢳⣜⠷⣄⠀ ⠀⠀⢠⣾⡟⠀⢠⠏⠀⠀⠀⠘⡇⠘⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢷⣜⠶⠽⢷⣾⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠇⢀⣼⠁⠀⠀⠀⠀⢸⡟⠳⡌⣦ ⠀⣴⢋⣼⡇⠀⠀⠀⠀⠀⠀⣰⠃⣠⣧⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⠒⠚⠛⠉⠉⠀⠀⠈⠉⠁⠉⠛⠲⢤⣄⠐⠋⠙⢤⠙⣾ ⣸⣣⠏⠀⣹⡦⠀⠀⢀⡤⠞⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠳⣄⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠬⢝⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⢸⡧⠿ ⢹⠏⠀⣼⠋⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡴⠞⠉⠁⠀⠀⣠⠶⡄⠀⠈⣙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀ ⠸⣄⣸⡁⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⣴⠏⠀⢹⡄⠈⡏⠹⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠙⣦⠀⣸⠃⠀⢳⣤⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡆⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⢀⣀⣤⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡼⠓⠚⠋⠉⣽⠟⠲⢤⣰⡟⠚⡿⠛⠛⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⣠⠞⠁⠀⠀⢠⡞⣁⣀⣤⠴⠛⠀⠰⢧⣀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⢀⡴⠉⠀⠀⢀⡴⠋⠉⠉⠁⠀⠀⠀⠀⢀⡾⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢀⣀⣤⠖⠛⠁⠀⠀⠀⣠⠏⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠀⠀⢠⣏⠀⠀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⢀⣴⠻⣟⠁⠀⠀⣠⠟⡗⠀⠀⠀⠀⠀⠀⠀⣼⠃⢻⣀⣀⣠⡏⢸⡟⠉⠁⠀⠀⠀⠀⠈⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣄⣈⡉⠉⠉⣀⠴⣇⡀⠀⠀⠀⠀⢀⡞⠛⠦⣄⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠉⠉⠀⠈⠁⠀⠀⠉⠳⢤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠤⠤⠤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⢻⣿⣿⣖⣲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⢀⣠⡴⠚⠉⠁⠈⠻⣄⠉⠉⠛⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠛⠓⣶⢶⣏⡁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣿⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡾⠁⠀⠀⠉⠳⢦⡀⠀⠀⠀⣠⠾⡷⢦⣄⢸⡇⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢠⡟⣴⡄⠀⠀⠀⠀⠀⠙⣦⣶⠛⠁⠀⢿⡀⠈⢹⣧⣴⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⢿⢶⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣆⠀⣀⣼⣷⣤⣼⣿⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡋⠀⣿⣀⣿⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⡏⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣾⣯⢿⣿⣶⣤⣤⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⠷⣾⠻⣿⣦⣄⡀⠀⢀⣠⣴⡾⠿⢧⣿⡤⠶⠿⣏⠈⢻⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⡷⣄⠉⠙⠻⠻⣿⣿⡉⠀⠀⢰⠇⠀⠀⠀⠹⣦⡞⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⢷⡀⣠⡼⠋⠀⠉⠳⢶⣿⣤⠴⠶⠒⠒⢻⡅⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡟⠿⢤⣀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠙⠳⣤⣉⠳⣄⣰⣇⣀⣤⡤⠤⠶⠒⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠓⣷⠼⠿⢿⣿⣯⣁⣀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⣿⠀⠀⠀⢸⠁⠀⢹⡏⢙⣿⣿⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⣏⠻⣿⠦⠤⣤⣼⡦⠤⠶⡟⠉⣸⢧⡀⠀⠀⠀⣈⣽⠶⠦⢤⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣏⠁⠀⣠⡾⠋⠀⡇⠀⠀⠀⡿⠀⠀⠀⣿⠀⠏⠈⠳⣄⣤⠞⠉⠀⢀⣠⠴⠛⠁⠀⠀⠀⣈⣉ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢶⣋⡁⠀⠈⣳⣾⡋⠀⠀⢠⡇⠀⠀⢰⡇⠀⠀⠀⢻⠀⣀⣤⣾⣻⣷⣤⡖⠚⠉⠀⠀⠀⣀⣤⠖⠛⠉⠀ ⠀⠀⣀⡤⠖⠛⠛⠷⣄⡀⠀⠀⠉⠙⣻⠟⠿⠶⠿⠷⣦⣾⣥⣤⡀⣼⢁⣠⣶⣶⢿⡟⠉⠉⠉⠀⠀⠈⠳⣄⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠈⠈⠙⢦⣄⣴⠞⠁⠀⠀⠀⠀⣸⠋⠈⠙⢦⣝⣿⡿⠛⠉⠀⠈⣧⠀⠀⠀⠀⣀⣠⡤⠾⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⠓⠶⢤⣀⣴⠇⠀⢀⣤⢄⢸⡏⠠⣄⠀⠀⠀⢻⣀⣠⠶⠛⠉⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⣿⠤⣤⣀⡀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢈⡟⠛⢻⡿⣷⣿⣼⣅⣴⡾⣷⡖⠚⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡀⠠⠀⠐⠂ ⢹⡀⠀⠈⠉⠳⢦⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⣱⣿⣼⣿⣿⣼⣿⡾⠷⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⢻⡅⠀⠀⠀⠀ ⠈⠇⠀⠀⠀⠀⠀⣹⠟⠓⠶⢤⣀⡀⠀⠀⠀⣿⠀⢈⣧⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⢸⡆⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢹⣦⣤⣶⣶ ⠀⠈⠀⣀⣤⣶⣿⣿⣷⣤⣀⠀⠀⠉⠓⢦⣄⣿⠀⠘⡇⢹⠁⣿⣿⣿⢀⡟⠀⣿⠃⣀⣨⣷⠶⠋⠁⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠉⠉⠉⢀⣿⣿⣿⣿⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⢿⣿⠛⢍⡭⠿⣛⡿⠋⠉⠉⠿⠿⣿⣿⠟⠛⠻⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⡿⠿⡣⣀⡽⡻⠋⠀⢀⢤⠬⠽⠋⡛⢧⡀⠘⣇⠀⠀⠀⠙⣿ ⣿⣿⣿⡿⠟⠀⠀⠀⠀⡰⠋⠌⠀⠀⣠⠃⠑⢃⠓⢄⡈⢂⠹⣆⠘⠓⣶⣤⣶⣿ ⣿⣿⡏⠀⠉⠉⠀⠀⡜⠀⡘⠀⡔⠁⠀⢡⠀⡘⠀⠀⠈⡆⢃⢹⣦⣀⣿⣿⣿⠟ ⣿⡏⠀⠀⠀⠀⠀⣼⣀⠠⢁⣘⠀⠀⢀⣈⡄⢡⣀⣀⣠⣤⣎⠁⠀⠈⢹⣿⣿⡀ ⣿⠇⠀⠀⠀⢠⠎⠁⠀⠀⠀⠙⠛⠛⠹⣻⣠⣬⡭⠋⠀⠀⠀⡀⠀⠀⠀⡟⠙⠋ ⡘⠀⠀⠀⠀⣏⠀⠀⠀⠄⠀⠀⠀⠠⠤⠅⠣⡤⢣⠒⠒⠀⠁⠀⠀⢀⡼⠃⠀⠀ ⠁⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⡄⠀⠀⠀⣀⠤⡶⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠈⠐⠂⡤⢤⢄⣀⡠⠤⠭⢥⡄⢒⠃⡙⠀⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⡰⠁⠀⠙⣄⠀⠳⣼⣸⢠⠁⢀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡄⠈⠑⠠⠃⢻⡈⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡠⠁⠀⠀⢡⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⢐⣿⠏⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠀⣤⡿⠉⠀⠀⢀⠠⠒⠊⠉⠉⠉⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠶⣤⣀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠤⣄⣀⡀⠙⠶⢦⣀⠀⠉⠻⣦⣀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠳⣄⠀⠀⠙⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡇⠀⠀⠀⠀⠀⠀⠈⠗ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠒⠒⠚⠓⠒⠒⠒⠋⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠄⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⠒⠒⠒⠒⠒⠲⢤⡄⠀⠘⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠈⢹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣶⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠉⠐⢠⣤⣤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣴⠟⠹⣇⠀⠀⠀⠠⣸⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣦⣴⣶⣶⠶⢤⣀⡄⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠁⠀⠀⠻⣦⣠⡶⠟⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⡾⢿⣿⣿⣼⣿⣧⡴⠋⠀⠀⠀⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣷⡌⠀⠀⠙⠿⣿⣿⣇⠀⠀⠀⠀⠘⢧⣀⠀⠀⠘⢧⡀⠀⠀⣀⣤⠽⣦⡀⠀⠀⠀⠀⠀⠀⠳⣽⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡀⠀⠀⠠⠈⢿⣿⣦⡀⠀⠀⠀⠀⠉⠓⠒⠒⠀⠙⣶⣶⡿⣾⣿⣿⡟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⠇⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣤⣠⣤⣤⣀⠀⠀⠀⠙⣦⣽⣿⣿⣿⣦⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⡆⠐⠀⠀⠀⠀⠐⣿⣴⣿⣿⣿⣿⣿⠀⠀⠙⢧⠀⠀⠀⣇⠀⠉⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⣿⣦⣤⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢳⡀⠀⢸⡄⠀⠀⠀⠀⠸⣧⡀⣸⡿⠇⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⡇⠀⡟⠉⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠇⢷⠀⠈⢧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⣴⠾⢛⡇⠀⠀⠀⠀⠀⣰⠃⠀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡁⠀⡇⠀⡇⠀⡇⠀⢠⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⢸⡇⠀⠈⢷⡀⠀⠀⠀⠀⢠⣤⡾⠛⠋⠁⣠⣾⠃⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⠀⢀⣸⣿⣿⠟⡇⠀⡇⠀⡇⠀⡇⠀⠸⣆⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠙⢦⣀⠀⠀⠀⠙⠻⢶⣶⡾⠟⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⣦⣤⣼⣿⣿⣿⣤⣿⣿⣿⠀⣇⠀⣿⠀⠇⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⢿⡛⠛⠦⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠴⠦⢤⣀⠀⠀⠀⠈⠙⠓⠦⢤⣀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠈⣳⣠⣤⡤⠴⠚⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠉⠙⠲⢦⣀⣀⣠⠤⠾⠷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠚⠢⣄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡆⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⢠⠟⢄⠙⠳⢤⡀⠀⠀⠀⠀⢠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⢤⡎⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⣼⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡜⡌⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⣰⠁⢿⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡟⠀⢀⠟⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣼⠁⢰⠃⠀⠘⣧⣇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⢸⡗⡇⠀⣼⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⣼⡏⢀⡏⠀⠀⠀⢻⣿⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⣼⢀⠁⢰⡏⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⣸⠃⣰⣿⠃⣼⣦⣤⣀⡀⠈⣿⡄⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣦⣺⠇⢸⡀⣿⣧⠀⠀⢸⣿⠀⣤⠀⠀⠀⠀⢰⡿⢠⣿⣿⢰⡇⠀⠀⠉⠉⠓⠾⣧⠀⠀⠀⠇⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡆⠀⣾⣿⡀⣧⡀⠀⠀⠀⣿⣧⣾⣿⣿⣾⣿⣾⣿⣿⣷⣆⠀⢻⡆⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢁⣿⣿⠿⣿⣿⣄⡿⢹⣿⣿⣷⣄⡀⢸⡟⣽⣿⣿⣿⡟⠛⢻⣿⣿⣿⣟⣿⣾⣷⠀⠀⢸⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⣸⣿⣿⣶⠿⣿⣿⡇⠀⢿⠛⢿⣿⣿⡿⠀⢹⣿⠟⠉⠃⠀⣨⣭⣿⣿⣿⣿⣿⣿⡆⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⣿⣿⣿⠿⠚⠁⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠻⣦⣄⣀⣀⢿⡟⠉⠙⣻⣿⣞⣻⣿⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣿ ⣿⣿⣿⣿⡟⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣼⠟ ⣿⣿⣿⣿⣷⣸⡟⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⠋⠁⢀ ⣿⣿⣿⣿⣿⡍⢳⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡠⠔⠁ ⣿⣿⣿⣿⣿⣷⣴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⡌⠀ ⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⡇⠀ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⠖⠛⠉⠁⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⡟⣋⣹⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⡟⢫⠉⠋⠭⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⡧⠃⠀⠠⠐⠴⠹⢤⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⠈⠀⠈⠀⠆⢐⡉⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⣀⣄⣈⣿⡿⠛⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠉⠀⠆⠁⣆⠀⠀⠀⠀ ⠀⠀⠀⠛⢿⠟⣟⠉⣉⠙⠻⣿⡀⠀⠀⠀⠀⠀⠈⡆⠀⢀⣤ ⠘⡏⠲⣠⢴⠤⠉⠉⠁⠀⠀⠈⣧⢀⣀⠤⠒⣻⠒⠋⠢⣎⡸ ⠀⠈⠢⡴⡪⠓⢳⠀⠀⠀⠀⠀⢸⣿⡀⠀⠰⡉⠬⡣⢳⠊⠀ ⠀⠀⠀⢣⡘⢀⡋⠀⠀⠀⠀⢠⣿⣿⢷⣄⠀⠙⣤⣥⡊⠀⠀ ⠀⠀⠀⢀⣼⣻⣿⣦⣀⣀⣴⣿⢸⣿⠈⢻⣷⣄⣿⣿⣿⣦⠀
⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡠⢒⡊⠭⠽⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡦⠿⠀⠀⢣⠀⢰⠀⠀⠀⣠⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠰⠇⠀⡉⠁⠀⠈⣦⣼⣶⣾⣿⡿⡏⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⣿⡿⠁⣿⣯⡄⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡇⢀⡠⠛⠛⠓⠀⡁⠈⠙⠨⠓⡈⢍⠕ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⡈⠑⠢⢀⣀⣀⡠⢔⠙⠍⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠸⣷⣶⠖⠂⠉⠑⠀⠓⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢃⣶⣶⣧⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣀⣤⠤⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠒⠊⠭⠀⠀⠤⢺⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠒⠙⠁⠅⠈⠈⠓⠂⢀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⣀⣠⡶⡾⢷⣤⣾⡿⢦⣀⣃⠀⠀⠀ ⠀⠀⠀⠢⠤⠤⢿⣜⣛⣠⣿⣌⣛⣨⡧⠤⠃⠀⠀ ⠀⠀⠀⣠⠀⠀⠀⠙⠛⠋⠀⠙⠙⠋⠀⢠⠀⠀⠀ ⠀⠀⠀⠷⡀⡂⠀⡀⠀⠁⠐⠀⢀⠀⠀⡡⠄⠀⠀ ⠀⢠⠀⣠⣀⣘⡐⠀⠀⠀⠀⠀⡀⠒⣃⢰⢄⠀⠀ ⠠⠗⠒⣇⠐⠁⠀⠄⠈⠐⠒⠈⠀⠎⠑⢺⠏⠀⣳ ⠀⡅⠀⠙⡂⠄⢀⢀⣀⣀⣀⡀⢀⡀⠔⢡⠀⠀⢡ ⠀⠃⠀⠀⠃⢰⣤⣤⣤⣤⡀⠀⣀⣠⠀⠘⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠈⠉⠉⠉⠉⠉⠐⠒⠒⠀⠤⠤⠤⠄⠐⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠉⠉⣩⡿⠋⠉⠉⠉⠉⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁ ⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⣀⡶⠶⠶⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⢳⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣼⣧⣤⣼⠋⠀⠀⠀⠀⠀⣠⠟⠉⣿⠓⠒⠲⠤⠤⠤⣤⣤⡤⠤⠄⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⠀⠀⠀⠀⢳⡄⠀⠘⣆⠀⠀⠀⠀⣠⡿⠏⠙⢿⣷⠶⣄⠀⠀⣰⠏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠹⡄⠀⠹⣆⣤⠖⠋⠁⠀⠀⠀⠈⠁⠀⠘⣆⢠⡏⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⡄⠀⠀⠀⠀⢹⡄⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡜⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡄⠹⣦⡀⠀⢀⣠⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠙⣆⢈⣿⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠈⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠛⢦⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀⣠⣾⣯⡍⠉⠷⡄⠀⠀⠀⠀⠀⠀⣾⣿⠛⢿⣦⡀⠙⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⣠⣾⡿⠋⠹⣿⣷⠀⠹⣄⠀⠀⠀⠀⢳⣿⣿⡤⠾⣿⣷⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⠏⢸⣿⣶⡞⣻⣿⠀⠀⢹⡀⠀⠀⠀⢸⡏⢿⣿⣾⣿⣿⠀⠀⠹⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣾⠀⠀⢿⣿⣿⣿⡿⠀⠀⠈⣇⠀⠀⠀⠘⣇⠈⠛⠿⠟⠁⠀⠀⣀⣿⠮⠙⠛⠿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣏⠀⠀⠀⠙⠛⠋⠀⣀⣤⡴⢿⣶⡶⠶⠒⠛⠓⠒⣶⣶⣒⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠃⠀⠀⠀⠐⠛⠛⠲⠶⠦⣤⠤⠶⠋⠉⠀⢀⠀⠻⢦⣀⠀⠀⣠⡾⠛⠯⠡⠤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⢀⣐⡤⠀⠀⠈⠛⡞⠁⠀⠀⢲⡾⠓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣯⣉⠀⠀⠀⠀⠀⠁⣀⣤⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣀⡤⠶⢶⣶⠦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⠿⢿⣛⡉⢉⣡⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢳⠞⠉⠻⢧⠀⠀⢸⠀⢻⣇ ⠀⠀⠀⣀⣠⣤⣤⣄⢀⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣉⣙⣻⣥⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⡜⠀⢀⣤⡾⣶⣶⣤⣄⠘⠁ ⠀⣰⠋⢹⡏⠀⢠⡿⠉⠉⢻⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⠉⢉⣡⠆⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⢠⡇⠀⠈⣿⡿⠿⣏⠓⣿⣶⣠ ⡴⠿⡄⠈⠁⣤⣜⢷⣤⡀⠀⢿⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣠⠴⠞⠋⠁⠀⠀⠀⠀⣠⠟⠁⠀⣼⠁⠀⠀⢘⡇⠉⣫⡏ ⢧⠀⠀⣸⣽⡗⣿⣤⣷⠃⠀⠈⢷⡀⠀⠈⠉⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⢿⡀⠀⢀⡼⢁⡴⠋⠀ ⠈⢳⡿⠿⠏⡏⠀⠀⠈⢳⡀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠈⢉⣛⡿⠶⠶⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠋⠉⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡠⠞⠀⠀⠀ ⠀⠀⠙⢧⣀⢧⡀⠀⠀⢠⡇⠀⠀⠀⠀⠈⠙⠓⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣍⠓⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠊⠓⠦⣄⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠛⠉⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡶⠴⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠶⣶⡶⢶⡶⠚⠉⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡇⠙⡟⠁⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠛⠳⢾⣇⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣧⢀⣠⠶⠒⠚⠙⠒⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⢤⣤⣄⣠⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠋⠉⠉⠉⠉⠉⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠊⠉⠉⠉⠉⠉⠓⠲⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠟⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠤⠤⠤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠐⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠈⣦⠀ ⠀⠀⠀⠀⠀⠀⣾⣰⠊⠁⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠀⠙⢣⣸⠇ ⠀⠀⠀⠀⠀⠀⣿⠇⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠹⢧⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣷⣤⣤⣶⣾⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣻⣶⣤⣤⣴⣟⣁⣀⣀⣀⣀ ⣿⣿⣿⣿⠿⠟⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣟⠀⠀⠂⠀⠆⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⣷⣾⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠟⠛⠛⠛⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⢿⣿⣿⣿⡇⠀⠀⠉⠉⢻⣿⠛⠋⢹⣿⣧⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⣸⣿⠀⠀⠘⢿⣧⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾ ⠀⠀⠀⠀⢀⣤⣶⣾⡇⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠀⢀⣴⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣄⣀⣀⣤⣤⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢠⣿⠟⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣤⣤⣤⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⢠⡟⠁⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠉⠛⢿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠘⣏⠛⠻⠿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣶⣶⡿⠿⠛⠋⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠉⠉⢻⡟⠛⠛⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠛⠛⠛⣿⠉⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠶⠦⣽⣦⣤⣀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣸⣇⣀⣠⣤⣤⠴⠾⠷⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⣿⠉⠉⠉⠉⠉⠙⢻⣿⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠋⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣠⣼⣿⣾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣀⣀⣀⣀⡀⢸⣇⢀⣀⣀⣀⣀⣠⣤⣾⣶⣾⣿⠿⠿⠛⠋⠉⠁⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢹⠛⡛⠦⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣾⠇⠀⢀⣠⣴⣶⣶⠿⠿⠛⠛⠛⠛⠛⠛⠿⠿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⣡⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⡇⢀⣾⣏⣴⡾⠟⠋⢉⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠈⠉⠻⢿⣶⣦⡀⢀⣤⣾⡿⠋⣁⣴⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⣋⣴⡿⠁⣼⡿⢟⣩⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⣧⡀⠀⠈⠛⢿⣿⣛⣡⣴⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⢒⣲⣾⠿⢋⣥⣾⣿⡿⢁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠛⢿⣿⣶⣶⣤⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⣡⣴⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⠀⠰⣿⡟⠋⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⣿⣿⠿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣿⡄⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠳⣦⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⡄⠀⣿⡟⠓⠒⠒ ⠀⢠⣾⡿⠋⠉⠉⣁⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⢰⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣿⡇⠀⢸⡏⠛⢿⣿⣿⣿⡇⠀⢿⣿⡇⠀⠀ ⠰⠿⢿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⡇⠀⠀⠉⠛⣿⣿⡀⢸⣿⠁⠀⠀ ⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠻⣿⠄⠀⠀⠉⠉⣿⡏⠉⠉⠙⣏⠹⠿⠿⢋⡉⠉⢻⡿⠁⢸⣿⡏⠈⣍⡻⠿⣁⡀⠀⠈⢳⢸⣿⠿⢿⡿⠶⠶⠶⠶⠾⠿⠿⣿⣿⠶⠶⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⢞⣉⡙⢦⡀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⣼⠃⠀⢸⠿⣇⠀⠈⠉⠉⠉⠀⠀⣀⡾⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⡏⠈⠁⣨⠇⡀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣀⣀⡤⠚⠁⠀⠀⢸⣆⣈⣛⠲⠦⠤⠤⠶⠚⡋⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠓⠚⢁⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⡇⠀⣸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡴⠶⠋⠀⠀⣸⠁⣰⡿⢻⣇⣸⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠉⠀⠀⠀⠀⣼⠃⣴⣟⣠⡾⠟⠉⠁⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠈⠙⠻⢿⣿⣿⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣥⡿⠟⠋⢀⣀⡤⠶⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠉⠀⢀⣠⡤⠖⠚⠋⠙⣠⠀⠉⠛⢷⣌⣻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠊⢁⣠⠤⠖⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡷⠖⠋⠁⠀⢀⣤⠶⠛⠉⡀⠀⠀⠀⠈⠙⠷⣿⣙⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣀⣤⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⡀⢀⣠⠞⠉⠀⠀⣀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠿⠿⣿⣶⣶⣴⣾⣛⣿⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣠⠞⠉⠀⢀⣾⠀⠀⠀⠀⠀⠀⣀⣸⣧⠶⢾⣻⣽⣾⣿⣿⣿⣿⣇⠀⢸⣇⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠈⠙⣷⣤⠟⠁⠀⢀⣴⣿⣿⣿⣷⠶⠶⠶⢛⣋⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣷⣤⣤⣤⣶⣾⣿⣿⣿⣏⠁⢹⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣴⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀ ⠀⠀⡏⠀⠀⠀⣀⡠⢀⣀⠴⠒⠒⠒⠒⠒⠠⠬⠵⢤⣀⠀ ⠀⢸⠀⢆⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇ ⠀⢸⢰⠃⠀⠀⣀⡤⠤⠖⡔⠒⠒⠲⣲⠒⠒⠒⢦⠐⢴⠃ ⠀⢸⠸⢤⡴⡚⡁⠸⠀⠸⣀⡀⢿⡿⡹⢾⡿⠀⢠⠃⢨⠃ ⠀⢸⡀⠀⡇⢅⠄⠱⠀⠘⢽⣯⠗⠊⠈⠖⢂⠉⠬⠃⣏⠀ ⠀⡎⠉⠉⢻⡆⢠⠤⡆⠀⢸⠀⠉⠉⠴⢂⠿⠉⠄⠤⡇⠀ ⠈⠣⣀⣀⡜⢹⢌⠒⢂⡄⢜⢖⡲⠒⢄⣜⠀⢀⡢⠔⡇⠀ ⠀⠀⠀⠀⠀⣎⣈⣦⣬⢵⣊⣵⣖⣋⣓⡮⣤⣴⣦⣴⠇⠀ ⠀⠀⠀⠀⠀⠀⣾⠉⢻⠉⠛⠛⠛⢻⣿⡟⠀⠈⠁⣷⠀⠀ ⠀⠀⠀⠀⠀⢠⣋⣟⢚⡒⣒⠖⠒⠚⢻⣓⡲⢒⣾⡟⡄⠀ ⠀⠀⠀⠀⠀⠘⠓⠃⠀⣤⠀⠀⠀⠀⠀⣿⠀⠈⠛⠚⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣀⠀⠀⠀⠠⠿⠄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣀⡨⠂⠀⠙⠒⠲⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠶⠶⠶⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠑⠁⠀⠀⠀⣀⣀⣀⠀⣀⣰⡋⠀⠉⢶⡲⠶⢽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠸⡇⠀⠈⠹⣍⡈⠙⣆⡀⣀⣷⠤⠤⠭⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢀⣠⠞⠻⣄⠀⠀⣨⠷⢚⡉⠉⠉⠁⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠞⠁⠀⢀⣽⠷⠶⠋⠀⣠⠟⠲⠶⠶⠶⠒⠒⢶⣦⡀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⠋⠀⣠⠴⠋⠀⠀⠀⣀⡶⠋⠀⠀⠀⠀⠀⣀⡤⣠⢷⠛⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡏⣠⠞⠁⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣸⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⣷⠀⠀⣸⣴⠋⠀⠀⢀⣴⠟⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⢀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠈⠇⠀⢸⠃⠀⠀⣴⠏⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⠈⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠻⠀⠀⣰⡿⠀⢰⠋⣰⣶⣶⣶⣤⣀⠀⠀⠀⠀⠉⠉⠉⠀⠈⡇⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠛⣷⠀⠀⠀⠀⠀⠀⠻⢻⡀⠀⢸⣿⣿⣿⣿⣇⠿⠀⠀⠀⠀⠠⣄⠀⠀⢀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣛⣤⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⠃⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣻⣿⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠉⢿⠶⠶⠦⠀⠀⠀⣸⣴⣿⢷⡀⠀⠀⠀⠉⠛⠿⠿⠷⣻⣫⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠰⣿⣿⣿⠳⢷⠐⠲⠶⠤⣦⠤⠶⠞⠉⣿⠉⣸⣋⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣿⡟⣞⣷⡈⠳⣄⠀⠀⠿⠉⠓⠶⣄⣿⡀⠉⠉⠉⠓⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⢳⣿⠙⣟⠦⣈⠙⠶⣄⡀⠀⠀⠀⠙⣟⢦⡀⢀⣀⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠷⠶⠶⠶⠶⣏⣉⣉⠉⠛⢶⣿⣄⠀⠀⢿⣆⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⣆⠻⡄⢹⡉⠑⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⠚⠋⠉⠻⢷⣄⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢹⡄⢹⡄⢷⣤⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣤⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠉⠲⣄⡀⠀⠀⢸⠀⠀⠀⣸⠃⠀⢿⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢹⠃⠀⠀⣶⠀⠀⠘⡗⠾⣷⣀⠀⠀⠀⣿⠉⠀⠀⢸⡀⣀⡴⠋⠀⠀⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⠀⠀⣰⠋⢧⠀⠀⣷⠀⢹⣭⠲⠦⢤⣿⠀⠀⠀⠘⡏⢻⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣏⣩⡿⠀⣴⠃⠀⠈⣧⠀⢿⠀⠀⣸⢷⠀⢀⡏⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠻⣄⣀⣀⡿⠀⠈⠉⠉⠉⣼⡀⡾⠀⠀⠀⠀⢸⠁⠀⡿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠤⣌⣁⠀⠀⠀⣀⣠⣾⣁⡿⠁⠀⠀⠀⠀⣾⠀⢠⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣿⣉⣉⣉⣉⣉⡭⠖⢹⠟⠀⠀⠀⠀⠀⠀⡿⠀⡾⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠉⠉⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣼⠃⣰⠁⠀⢠⡏⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠⠟⢠⠏⠀⠀⣾⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⣀⡠⣾⣿⣿⣂⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠀⠀⠀⠀⣠⠟⢀⡟⠀⠀⠀⡟⠲⢤⣀⡀⠀⠀⠉⠉⠈⠉⠁⠀⠉⢈⠹⣟⡭⠿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⡀⠀⠀⠀⣰⠏⠀⡾⠀⠀⠀⠀⣧⡀⠀⠈⠉⠓⠶⠦⣄⡀⠀⠀⣀⣠⣴⣞⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡏⠈⠉⠓⠒⠚⠁⠀⣼⠁⠀⠀⠀⣠⠟⠳⢤⡀⠀⠀⠀⠀⠀⠉⠒⠶⠶⠚⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣹⡶⣄⡀⠀⠀⠀⢠⠃⠀⣀⣤⠞⠙⠲⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣴⡽⠃⠀⠉⠒⠶⣀⣾⡤⠖⠉⢯⢳⡀⠀⠈⠳⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣰⠋⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢷⡁⠀⠀⠀⠙⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⢻⡛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⡖⠀⠀⠈⠉⠉⠠⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠜⠀⠀⠀⢀⠀⠑⠤⡧⢸⣆⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠤⠤⣀⡼⠂⠀⣆⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠋⠀⠸⣄⡀⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣆⢀⠀⠀⡀⠀⠉⣭⣽⣿⡷⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⠶⣾⣾⣿⠿⢟⠙⢆⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⠀⠘⠆⠈⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⠟⠋⠉⠉⠛⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡆⠀⠀⠀⠀⠀⠀ ⢀⣄⡀⠀⠀⠈⢻⡇⢠⣿⣦⣤⡤⠆⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⣧⡀⠀⢀⡼⢻⡆ ⠺⣇⠙⢶⣄⡤⣼⡧⢼⡏⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢀⣀⣤⠶⠟⢩⣿⠉⢹⠏⠙⣦⡞⢁⡼⠁ ⠀⠙⣦⡌⠙⣀⡜⢧⡠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠋⠁⠀⠀⢠⡟⢯⡑⠂⣴⢒⣇⣼⠟⠁⠀ ⠀⠀⠀⠛⣿⢧⣝⣁⡴⢋⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠈⢷⠒⠋⠙⡗⠋⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠸⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠳⣤⣀⣁⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢲⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣿⡟⣿⣿⡇⢻⣿⣦⡀⠀⢠⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⣀⣀⣠⣾⣿⡟⠁⣿⣿⣇⠀⠹⣿⣿⣦⣼⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⠿⠟⠿⠿⠿⠛⠿⠿⢿⣿⣿⣿⣷⣽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣿⣿⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣭⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣶⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡆⠈⠙⠛⢿⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣯⣉⣉⣹⢿⢿⣯⣼⣧⠀⠻⣿⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣸⡎⢿⣿⣿⣆⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡡⢴⣿⣿⣿⡆⠀⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣴⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠈⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⠓⢶⢶⣶⠒⢲⠰⠶⠶⠖⠠⢶⠶⣶⠂⠀⢸⢹⣸⠿⢟⣷⡿⠇⡿⠟⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀ ⠀⡐⠁⠀⠀⠐⠄⠈⠉⠀⣤⣶⣒⡂⢠⣍⡪⡢⡀ ⠀⠃⠀⠀⠀⠀⠀⠁⠀⣠⣓⢢⡀⠉⠁⢀⣖⣸⡄ ⢀⡜⠒⠒⠠⣀⠀⠄⠜⠀⣠⠤⣌⠂⠀⠶⠶⡼⠆ ⠈⢇⢈⠉⠐⠠⠑⠅⠀⢸⢀⣀⢖⠆⠀⠡⣐⡶⡃ ⠀⠀⠑⢕⡢⠤⠆⠀⠀⠊⠀⠀⡽⠂⠀⠀⠀⠁⠇ ⠀⠀⠀⠀⠀⠉⠙⢅⠀⠈⠀⠨⢏⠀⠈⣂⠤⡤⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣣⣰⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⣠⠊⢸⢯⠀⠡⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⡆⠻⣿⡿⢿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢄⠀⠈⢧⢀⠀⠸⡄⠈⠁⠀⣆⠀⠀⠀⢧⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⠀⠀⠀⢸⢷⡀⠀⠀⢸⡦⠀⠚⢿⡖⠒⢳⠀⠀⠀⢸⡀⠀⠀⠸⡆⠙⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⡎⠀⠀⠀⢠⠀⠀⡇⠀⠀⢸⠀⢧⢰⡀⠀⢳⠀⠀⠘⣷⡀⠈⢷⡀⠀⠀⣇⠀⠀⠀⣷⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⡇⣼⠀⠀⠘⡆⢀⣷⠒⠁⢸⡀⠈⢧⣷⡀⢠⣿⣉⣩⣽⣷⣤⣴⣧⡀⠀⢹⠈⠱⣤⣿⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⡇⡀⠀⠀⣷⡏⠀⠀⢀⡷⠋⢸⡴⢒⣉⡇⠀⠈⢿⣷⡀⢳⠘⠋⣿⣿⣿⣿⣯⠀⠀⢸⠀⠀⢹⡇⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠈⣷⠃⡀⠀⢸⣧⠀⠀⠈⢹⣰⣿⣿⣿⣿⣿⡅⠀⠈⠟⠉⠉⠀⠀⢙⣿⣿⣿⢻⡆⠀⠸⡀⢠⣿⡇⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠸⣾⠀⠀⣀⣿⠀⠀⠀⠸⣿⠏⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⣟⣿⡇⠀⠀⢿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⢻⣧⡜⠁⢸⡇⠀⠀⠀⢿⡆⣀⡈⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢁⣷⠀⡆⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣧⡀⠀⢷⠀⠀⠀⢸⣿⡟⣷⣾⣿⠛⠁⠀⠀⢀⣀⠤⠀⠀⠀⠀⢀⣾⣿⠀⡇⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣶⣼⡄⠀⠀⠈⣿⡉⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣴⣿⣿⣿⡀⡇⠈⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⠀⠀⢻⣿⣦⣤⣄⣀⣀⡀⢀⣀⣤⣴⣾⠋⢩⣿⣿⣿⣿⡇⣿⣠⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⠟⠋⠀⠀⠀⢉⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢻⡀⢸⡿⠿⢿⣿⣛⣯⣿⡏⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣿⣿⣛⢿⣿⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⢷⡀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢧⣿⣷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⡇⢧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⠿⠋⡀⠛⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⠿⠃⠖⠋⣉⣴⣶⣾⢿⡟⠁⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⠿⣄⠁⠉⠉⠉⠀⢠⠄⠀⢾⣿⣿⣿⣿⠁⣼⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢉⣉⣩⣤⣴⣶⣶⣟⠀⠀⠀⠀⢸⠀⠀⠈⢯⣭⡾⠟⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢧⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣄⠀⠻⢧⣭⣴⠯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⣠⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⣾⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣇⠘⠱⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣦⣄⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⢉⠿⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠛⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠛⠿⣿⣿⣶⣦⣤⣀⣀⣀⡴⠋⠀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⡿⠋⠀⢀⣴⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠐⠒⠋⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠟⠟⣛⡻⢿⣝⠛⠿⠿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⡿⣧⣀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠂⢉⣷⣄⠀⠐⠋⠳⡍⠳⡀⢹⣿⣿⣿⡈⠳⡍⠋⠙⢲⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⣀⣀⣀⠀⠙⣿⣧⣀⣀⣀⣀⠀⠙⣦⣹⣿⣿⣧⣄⣀⣀⣠⣞⣀⣇⣀⣏⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣾⣏⣀⣏⢀⣀⣀⣈⣻⣿
⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⠉⠀⠀⣿⣿⣿⣿⣿⣿⡏⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡷⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣐⣶⣿⡿⠿⠛⢛⣿⠿⠛⠛⠷⣦⣤⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡟⠋⠁⠀⣠⣴⡟⠁⠀⠀⠀⠀⠈⠻⠿⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⠋⠉⠻⣿⡿⠟⠛⠛⢿⠏⠉⠉⠀⢀⠘⣲⡟⢡⣷⣴⠶⢿⡿⠉⠛⢶⣤⣀⠀⠀⠀⣀⣠⣬⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠴⢿⡇⠀⢀⣾⠁⠀⠀⠀⢈⣹⣿⢾⡛⠉⠁⠀⠀⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡁⠀⢹⡇⢀⣼⡇⠀⠀⣠⣶⠟⠉⠀⠘⣧⡀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣼⣿⢛⡿⠙⣷⣾⠋⠀⠀⠀⠀⢠⣾⣿⣦⣄⣀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠙⠿⣿⣿⣼⡇⣼⣯⣼⣷⣶⣶⣶⣾⣿⣿⢿⡟⠉⠉⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣄⡀⣸⣿⣿⣿⣿⡿⠛⠉⠉⠉⢉⣵⣿⡟⣿⠀⠀⠀⣼⡟⠃⠀⠀⠀⢠⣾⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠋⣿⠻⣷⣦⣤⣤⣶⣿⠿⠋⢉⣿⣄⠀⣰⡟⠀⠀⠀⠀⠀⢸⣿⣈⣿⣆⢰⡿⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠈⢻⣿⣀⣹⣤⣬⠿⢿⣟⠉⠁⠀⣴⠟⠉⠙⣿⡿⠠⠀⢀⣤⣤⣤⣄⢻⣯⡤⣿⣿⠓⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⣾⠉⠉⠹⣏⠀⠀⠀⠙⢷⡀⣼⠃⠀⠀⣰⡟⠐⠂⣤⣿⢧⣸⣏⣿⣾⣿⣤⣿⣿⣍⣙⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡆⢸⡇⠀⠀⠀⢿⡀⠀⠀⠀⠈⣻⣏⠀⢀⣴⣿⡇⢀⣼⢿⣼⡿⢿⡿⠵⣿⡿⠰⣿⣿⣥⣼⡏⢀⣶⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢻⣿⠀⠀⠀⠀⠸⣇⠀⢀⣤⠾⠋⠹⣦⡾⢿⢻⣧⣾⡋⣸⡏⠀⣿⣷⣾⣿⣝⣶⣿⠧⣤⣾⠇⣾⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣼⡟⠛⠛⠛⠳⠶⣿⡴⠛⠁⠀⢀⣼⣿⠀⣸⣿⣿⠤⣽⣿⠁⣸⣏⡿⢹⠏⣿⠛⣿⣶⣶⣿⢟⠻⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠘⣷⣀⣤⣾⠿⠵⣿⠛⢻⣿⣯⣤⡴⢿⣶⣏⣼⢃⡿⣸⣏⣼⡿⣯⢿⣇⣸⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠶⠶⣶⡶⠟⠋⢹⡇⠀⠀⣿⠀⣘⣿⣷⣠⡴⢟⣽⢿⣿⣼⢳⣿⣿⠻⣇⠘⢷⣭⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡿⣦⣄⣻⣀⣀⣀⣸⣤⡶⠶⢿⡇⠉⢿⡘⣷⣴⠟⢃⡿⠈⣿⣿⣿⡸⣧⡉⠛⠓⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣟⣩⡿⠁⣿⠃⠀⢈⡿⠁⠈⠉⣿⠁⠀⠀⠈⣷⣀⣼⢿⡛⢷⣴⠟⠁⣰⣿⣿⣌⠻⣮⣙⢛⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⣻⣿⠿⢫⠁⣠⡾⠛⠲⣼⣏⣀⡀⢸⡇⢀⣀⣀⢻⣦⣤⠶⠶⢿⡏⠀⠈⠻⣄⣽⣿⢾⣿⣬⣿⣿⣷⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⠟⢉⣽⣶⡞⠋⠀⠀⣨⣷⣟⠁⠀⢰⡟⠀⠉⠙⣿⠛⠛⠉⠙⢻⡏⠀⠀⠀⠘⣷⠀⣠⣴⠿⢿⣽⡆⣦⡀⠈⣯⣩⣭⣤⢸⡟⠶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⣡⡶⠟⠉⠈⣷⡀⢀⣾⠟⠁⠉⠳⣤⡟⠀⠀⠀⢠⡿⠀⠀⠀⠀⢸⡇⠀⠀⣀⣠⣿⡟⠉⠀⠀⠀⠹⣿⢹⡄⠀⢻⡆⠀⠀⠀⢻⣶⣮⡻⣷⣄⠀⠀ ⠀⠀⠀⣠⡾⡩⠟⣍⡀⠀⠀⠀⢹⣷⠟⠁⠀⠀⠀⢠⡿⠙⠻⢶⣤⣼⣇⣀⣄⣀⣀⣸⣷⠶⠛⠉⡉⣀⣿⡄⠀⠀⠀⠀⣿⣎⣷⡤⠾⣷⠶⠶⠶⠎⢻⣅⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⡟⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣿⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢠⠏⡼⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢸⡟⣿⡇⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⡼⣰⠃⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡟⠀⢀⡏⠀⢻⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⢀⡷⠟⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⣿⠀⢀⡾⠁⠀⠈⣧⣴⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⢸⡟⣼⠀⠀⣸⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣾⡇⠀⣼⠃⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⡀⠀⠀⠀⣼⠁⡇⠀⢰⡿⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣼⣿⠀⢠⠇⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⡟⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣇⠀⠀⣰⡏⢠⡇⢀⣿⡇⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣰⣿⡟⢀⡿⠷⢶⣦⣄⣀⠀⠘⣿⡄⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⣒⣿⠁⢸⡇⢸⣿⣇⠀⠀⠀⣼⣿⡇⢀⡆⠀⠀⠀⠀⠀⢠⣿⡇⢠⣿⣿⠇⣸⠃⠀⠀⠀⠈⠉⠛⠲⢿⣷⠀⠀⠀⠀⢿⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣾⣿⣿⡄⠀⠀⣿⣿⡄⢸⡇⠀⠀⠀⠀⠀⣼⣿⢀⣾⣿⣿⣦⣿⣶⣭⣭⣶⣒⡤⣄⠀⠈⣿⡆⠀⠀⠀⢸⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣇⣾⡷⣄⠀⠀⠀⢀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢷⣶⣤⣘⣧⠀⠀⠀⢸⡇⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠇⢸⣿⡿⠿⠿⣿⣿⣧⣸⡏⢸⣿⣿⣿⣿⣶⣄⡀⣼⡿⢴⣿⣿⣿⣿⣿⠉⠉⢩⣿⣿⣿⣾⣯⡹⣿⡿⣿⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⡟⠹⣿⣿⣿⣿⣿⠁⠘⣿⣿⠟⠁⠻⠀⠀⣀⣀⣨⣿⣿⣿⣿⣿⠻⣿⣿⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⠴⠃⠈⠛⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠹⣿⣄⠀⠀⠀⠀⢿⣿⠿⠛⠻⠿⣿⣿⣴⠏⣿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⣼⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠹⣶⠖⢶⣼⡿⠤⠤⠤⣴⣿⠿⠶⠚⠛⣿⣆⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⣿⣿⣿⣿⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⡿⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⡯ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⢹⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣧⣾⠟⠁ ⣿⣿⣿⣿⣿⣿⣦⣿⡯⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠛⠉⠁⠀⢀ ⣿⣿⣿⣿⣿⣿⣏⠹⣧⡀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣠⠔⠋ ⣿⣿⣿⣿⣿⣿⣿⡄⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠊⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⡠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢰⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⢸⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠋⠙⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⣶⠾⠿⠛⠋⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣶⣞⣛⣛⣟⣿⣿⣿⣿⢉⣥⣤⣭⣷⣷⣿⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠛⠲⣿⣷⣭⣿⣯⣿⣿⣯⡼⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⡏⠋⠛⠾⢞⣒⣤⠿⠟⠋⣉⣠⣴⠾⠋⠀⠀⠀⠀⠀⠉⠿⠿⠿⢿⣿⣿⣿⣿⡿⠋⠉⠀⠉⠹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⠿⡧⣰⣦⣶⡿⠋⠁⠀⠀⠛⠛⠛⠛⠻⢶⣶⣶⣤⣶⣤⣤⡀⠀⠀⠀⠙⢻⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣟⣀⣴⠀⣠⣴⠟⢫⡞⠉⠀⠀⠀⠀⠀⠀⢶⣤⠶⠶⠤⡽⠏⠙⢦⡙⠻⣿⡆⠀⠀⠀⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠋⠁⠋⠀⠉⠀⠉⠉⢁⣷⠟⠁⣴⠋⠀⠀⠀⠀⠀⠀⡝⠳⣄⠙⣧⠀⣄⠀⠀⠀⠈⠻⣆⠈⠻⣿⣦⠀⠀⠻⣷⣤⣀⣀⠀⠀⠀⠀⠀⢀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⡟⠁⠀⡼⠁⠀⠀⠀⠀⠀⣠⣶⠟⠀⠈⠛⠾⢆⡟⠷⣦⣀⠀⠀⠘⢦⠀⠘⢿⣷⠀⠀⠈⠹⡿⣿⣷⣶⣶⣴⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣸⠃⠀⠀⠀⣀⣴⠞⠛⢷⡄⠀⠀⠀⠀⣸⠁⠀⠀⠙⠷⣤⡀⠈⢧⠀⠈⢿⣷⠀⠀⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢠⠇⠀⠀⢰⡞⠉⠀⠀⠀⠀⢻⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢻⡉⠉⢧⠀⠘⣿⣇⣀⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⠟ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡞⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣧⣀⣹⡿⣿⣦⣶⣘⣿⣿⣿⣿⣿⡿⠃⠀ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⣸⠃⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣽⣤⠖⠋⠁⠀⠀⠀⠀⠀⠉⣝⣻⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣠⠤⠶⠶⠟⠶⠦⣼⣇⣀⡀⠀⠀⣀⣀⣤⣤⣾⠷⠀⠐⡷⣶⣶⣶⣶⢶⣾⠿⠿⠷⣖⣂⠀⠀⠀⠀⠀⠀⠀⢠⡹⣿⣻⣿⣿⣶⡄ ⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠐⢖⣚⡲⠿⠿⢿⣍⣛⡭⠞⣽⠀⠀⠀⢹⡙⠓⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠿⣿⠿⠛ ⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣴⣣⣴⣖⣺⠿⣝⡚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀ ⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⣶⡋⠀⠀⠀⣼⢃⣀⣀⣀⣀⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⡓⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⠤⠤⠤⠤⠤⠤⠒⠒⠋⣟⠂⠀⠉⠓⢲⠊⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢄⣀⡤⠏⠑⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠤⠴⠚⠁⠀⠀⢀⡴⣂⣠⢴⡶⠋⠁⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⠙⠒⢶⡦⠤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣠⣤⣤⡴⠖⠚⠋⡟⠉⠀⣼⠁⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⣠⠟⠛⠻⢿⣯⠉⠉⠁⠀⠀⢠⡟⠳⡄⠀⢰⠇⠀⢠⠇⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡿⠁⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠛⢷⣄⢹⡄⢸⠀⠀⡼⠀⠀⠀⢠⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠈⣏⢳⣷⢸⠀⢠⠇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠁⠀⠀⠀⠈⣇⠀⠀⠈⠈⠳⢤⣄⣠⡟⠀⠙⣾⠀⣿⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠇⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⣸⠏⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⡴⠋⠄⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⢠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⢀⡶⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠠⡇⡀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⣧⢹⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⣿⢸⢳⡀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡞⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀ ⠀⠸⡞⡄⢳⡄⠀⠙⢷⡀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣸⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠀⠀⣧⢳⠀⠙⣦⠀⠀⠙⢦⡀⠀⠀⠀⣿⠀⠀⢀⡇⠀⢸⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠸⡎⣇⠀⠈⠳⣄⠀⠈⢳⡄⠀⠀⣿⠀⠀⣸⠁⠀⡾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠹⣌⠳⣀⠀⠙⢦⡀⠀⠹⡄⠀⢸⠀⠀⡟⢀⡼⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣌⡳⣄⡀⠻⣄⠀⢹⣄⣸⣤⡶⡧⢟⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡓⠾⠆⣸⣿⣿⣿⣧⣠⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣾⣟⠉⠛⠀⠟⡻⣯⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⡟⣿⣄⠀⠀⣸⣿⢾⡀⠈⢳⡄⠀⡤⣤⢤⣄⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢰⣿⡟⢧⠀⢾⠛⠁⢳⠀⠀⢙⣦⣧⣹⡀⡬⢷⡄⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣟⠁⠈⣇⠸⣆⠀⢸⡶⠞⠉⠀⠀⠙⠻⣧⡀⠹⡄⢰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠶⠶⠼⢦⣀⣼⣤⣼⣷⢋⠤⠔⠚⠉⠉⠀⠀⣿⠱⠀⢻⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠢⠤⠐⠒⣂⣀⣴⡯⠛⣋⣹⣷⣒⠒⠒⠉⠉⠉⣱⠛⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡤⠴⠚⠉⣡⣴⣿⣯⠉⢣⠠⣿⠋⠁⠀⠀⣠⠾⡇⢠⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢦⡀⠀⠈⠁⠉⣿⣿⣧⣼⣦⠏⠀⣠⡴⠛⠁⠐⣇⢸⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢮⣝⣛⣩⠥⠔⠋⣼⡗⠶⣄⠀⢹⣾⣀⡤⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠧⡀⠀⠀⡏⠻⣆⠘⢧⡈⢳⠒⠚⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢣⠀⠀⠀⠀⠈⢧⡀⢻⣼⡆⠀⠈⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⡄⠙⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢹⠀⠸⡆⠀⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⠀⣀⠀⢿⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣴⣯⣿⡌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠉⠀⢀⣠⡾⢃⣾⣷⡙⢦⣄⡈⠉⠉⠙⠛⠛⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⣀⣠⣤⡶⠾⠛⠁⣠⡾⠁⠈⠻⣦⣉⠙⠳⠶⢤⣤⣀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⢀⣀⣠⣴⠟⠋⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠈⠉⠙⠻⢾⣿⡀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣠⣶⠾⠛⠋⠙⠛⠻⢶⣦⡀⠀⠀⠀⠀⢀⣤⡾⠿⠟⠳⣦⣄⠀⢻⣇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠿⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠙⣿⣼⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢱⣷⠶⠿⠷⠶⣶⣶⣶⣤⣤⣄⣘⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣷⣤⣿⠟⢿⣧⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⣧⠀⠀⠀⠀⠈⠻⣏⣀⣈⣉⣉⠿⠛⠂⠀⠰⢾⣿⠛⠉⣉⣭⠟⠁⣿⡀⠘⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣦⣤⣴⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠐⠛⣻⠇⠈⠉⠉⠁⠀⠀⠀⣿⠃⠀⢻⣷⠀⠈⠙⠻⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠘⡟⣮⣝⡻⠷⣖⡲⠦⣤⣤⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣦⣄⡀⠀⠹⣌⡙⢿⣷⠾⠛⠉⠉⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⢠⣤⣀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⠇⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡿⠿⠿⡟⢻⠛⠁⠀⠀⠀⠈⠛⢿⢻⡿⠿⠿⢿⣿⣿⣿⣿⠃⠀⠀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⠋⠀⠀⠀⢻⡄⢷⡀⠀⠀⠀⠀⠀⠘⣇⠹⣄⠀⠀⠈⢻⣿⡏⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⠇⠀⠀⠀⠀⢼⣧⠈⠷⠤⠤⠤⠤⠤⠤⠾⠆⠹⠷⣤⣄⠀⠙⣷⡀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠸⣿⣿⣿⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⠏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠰⣞⠛⠋⢻⡶⠾⢿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣷⠾⠛⠛⣛⣿⡿⠿⢧⡀⠈⢷⣴⠶⠿⢷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⡷⠾⠛⠉⠀⠀⠀⠈⣻⣦⠞⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⠀⠀⢀⣀⣀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⠝⢾⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢀⠖⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣉⣉⡉⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⣠⠴⠛⠥⠐⣉⠤⠤⣌⡀⠀⠀⠙⢷⡄⠀⠀⠀⠀⡇⠀⠀⠀⣠⠔⠉⠀⣇⣀⣀⠤⠤⠤⠴⠶⠦⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠋⠉⠉⢲⠞⠁⠀⠀⠀⠙⢦⠀⠀⠀⠹⣆⠀⠀⠀⠁⠀⣠⢞⡡⠴⠒⠉⠉⢀⣀⡠⠤⠤⠀⠒⢲⣶⣿⠤⣄⡀⠀ ⠀⢀⡾⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡄⠀⠀⣠⡾⢟⣩⣖⡥⠖⠊⢉⡀⠤⠔⠂⢀⡤⠚⠁⠀⢸⠀⠀⣹⠀ ⠀⡜⠀⠀⣴⣶⣦⣸⠀⠀⢠⣶⣶⣤⠀⠀⠘⡇⠀⠀⠀⣧⣠⣾⣫⣶⠟⢋⡠⠔⠊⣉⡀⠤⠄⣠⠞⠁⠀⢀⡔⠀⣿⠴⠚⠁⠀ ⠀⡇⠀⠀⠻⠿⠿⢻⡀⠀⠸⣝⣻⡽⠀⠀⠀⡿⠀⠀⠀⢹⠁⠉⠙⠳⣮⡥⠔⠊⠁⠀⢀⡴⠊⠁⠀⢀⡴⡟⠀⣸⠛⠲⣄⠀⠀ ⠀⢳⡀⠀⠀⠀⣀⡾⢧⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢸⠀⠀⠀⠀⠈⢷⠤⠤⢴⡶⠋⠀⠀⣠⣴⠋⣸⠁⢀⠏⡇⠀⠘⣧⠀ ⢠⡏⠙⠓⠒⠛⠁⠀⠈⠳⣤⣀⣀⣀⣠⠴⠃⣀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⡇⣠⠏⠀⠀⣠⣾⠟⠈⣧⠇⠀⡼⠀⢸⠀⠀⣿⠀ ⢸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⠀⠙⠂⠀⢠⡏⠀⠀⠀⠀⠀⢀⡿⠃⢀⣠⣾⠟⠁⠀⠀⡿⠀⢰⠃⢀⠏⢀⡼⠃⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠃⠀⠀⢀⣾⠁⠀⠀⠀⠀⣀⣼⣧⠿⠛⠋⡸⠀⠀⠀⣰⡷⢀⠇⣠⣮⡴⠛⠁⠀⠀ ⠈⢷⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡠⣿⠀⠀⢀⣾⣷⣛⡲⣄⢀⣰⣿⣤⣌⠳⣄⡴⠁⢀⣀⣴⣿⠇⡼⠞⠋⠁⠀⠀⠀⠀⠀ ⠀⠈⠳⣤⡀⠀⠀⠀⠙⠒⠒⠒⠚⠭⠚⠁⣀⣴⢿⠛⠛⣻⣿⢸⣿⣇⠀⠉⠉⡇⣿⠉⠉⠉⠉⠉⣸⢰⠧⠤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⣀⣀⣤⡤⢶⠚⠉⠙⠚⢳⠀⣷⠺⠞⠉⠙⠳⣄⡴⠣⠋⠉⠓⢦⠀⣞⣉⣀⣀⣀⡀⠀⠉⠓⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠙⠦⢤⣤⣤⠤⠋⠙⠲⠤⠤⠤⠚⠀⠉⠀⠀⠀⠉⠉⠉⠉⠛⠚⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠙⢯⠓⠦⣄⡀⠀⠉⠲⢤⡀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣶⣶⣶⣶⣶⣶⣾⣿⣋⠋⠈⢻⣿⡇⠀⠀⠀⠈⠻⡄⠈⠙⢳⣄⡀⠀⠈⠳⣄⣰⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠿⠿⠿⣿⣛⣋⣭⣤⠴⠟⢹⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⠛⢦⠀⠀⢨⣿⣆⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⢀⣀⣠⣿⡦⠤⠤⠤⣤⣷⣄⣸⠀⢻⣧⢸⡇⠀⠀⢀⣀⣤⢶⣾⣿⠿⠛⠋⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢺⡇⢀⣴⣾⣿⣿⡿⠇⠀⠀⣀⣤⣴⣾⡿⠟⠲⢬⣿⣿⣇⡤⣶⣿⣭⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡇⠀⠀⠀⠘⣷⣿⠟⣯⠁⠀⠀⠀⠀⢸⠏⠉⢿⣹⣷⠀⠀⠀⠿⠛⢃⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢺⡇⠀⠀⠀⣼⡏⣡⠞⢻⡇⠀⠀⢀⣤⠿⣆⠀⠈⠷⠙⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼ ⠀⠀⠀⠀⠐⠀⠀⠠⠤⣀⣸⣇⠀⠀⣈⣿⣴⣯⣄⣼⠇⠀⣲⡟⠁⢀⣽⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⡤⠞⠀⠀⠀⠀⣀⡴⠋⣀ ⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣘⣏⣩⣿⣿⣿⣼⣿⣩⣿⣤⣼⣿⣿⠿⠶⣼⣧⣤⡄⠀⠀⠀⠀⢀⡽⠛⠋⠉⠀⠀⠀⠀⠀⣠⣾⡯⠖⠉⠀ ⠀⠀⠀⠙⠛⠒⠤⢤⣀⠀⠀⢿⠈⠻⣿⡯⠿⢿⣇⢻⠛⠋⠹⣷⣴⣾⡿⠴⠦⠴⠶⠤⠤⢤⣾⣧⣀⣀⣀⣀⣠⣴⡶⢿⣋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⡆⠀⠈⠻⣦⡀⢿⡙⠒⠚⠉⢁⣽⠛⠿⠿⠓⠶⢤⣄⣀⣴⣿⠿⠿⠛⠋⠉⠉⠉⠛⠀⣨⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⡤⠦⠤⠤⠿⠿⠿⠶⣶⣶⣋⣀⡀⠀⢀⣀⣠⡴⠞⠋⠙⠓⠶⠤⣄⣀⠀⢀⣀⣤⠾⠯⠤⠂⠀⠀⠀ ⠶⠦⠤⠤⠤⠤⠤⠤⠖⠊⠉⢁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠦⢤⣄⣀⠀⢀⣴⣂⡤⠼⠛⠛⠧⠄⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⣀⣀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠤⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠒⠦⢄⣈⡉⠉⠙⠓⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⡀⠀⠀⠀⠉⠙⠒⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠈⠛⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⠀⠀⠀⠙⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⡄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⣠⡞⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⣠⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢸⣟⣁⠀⢾⣿⣿⠻⣿⣿⣿⠏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣇⠀⠀⠀⠀⠀ ⢸⡟⠛⠀⣾⣿⢿⣷⣌⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠘⠀⠀⢠⣿⣿⣆⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡘⣿⣿⣿⡂⢻⣿⣬⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣿⢻⣿⣇⠈⢿⣿⣷⠉⢻⣧⠀⠻⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⣀⣀⡀⠀⡇⢿⡇⢻⣿⣵⡀⠻⣷⠀⣀⣿⡤⣀⣹⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⡿⠂⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠴⠛⠉⠀⠀⠀⣧⢸⡇⠀⠹⣿⠳⠀⢸⣿⣫⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠹⣿⡏⣇⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣭⣼⡇⠀⠀⠘⠇⠀⠈⠛⠋⣽⡾⠟⠛⠛⠉⠉⣿⣿⣿⣿⣿⣦⢹⣿⢹⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⡿⠃⠀⠀⢀⣤⡆⠀⠀⣠⠔⠁⠀⠀⢀⣠⠄⠸⣹⣿⣿⣿⣼⢸⣿⡼⠀⠀⠀⠀⠀⠀ ⢸⠒⠲⢾⣿⣿⣿⣿⣿⠀⣠⣾⡿⣟⣿⣷⣿⠿⠛⠀⠀⠠⠶⣯⣅⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⠏⣸⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⡿⠿⣷⠟⢁⣼⠟⠋⠁⠀⠀⠐⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⢳⡶⣿⣧⣨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣒⣿⣭⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣤⡗⣿⢻⢷⡄⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣾⣭⠵⠚⠛⠉⠁⢹⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣧⡙⠿⣽⣷⡄⠀⠀⠀⠀⠀⠘⣿⠙⣿⡀⠀⠀⠀⠀⣀⣴⢾⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣅⣹⣦⠀⠀⠀⠀⠀⠈⠳⢬⣻⣶⣶⣞⡯⠽⠚⠉⠀⠀⢀⣴⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⡆⣻⣿⣿⣿⣿⣿⣿⠟⠿⣽⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢃⣿⣿⣿⣿⣿⣏⣀⣼⢺⣝⣙⣷⣶⠤⢤⣀⣀⣀⡀⠀⠀⣀⣴⠟⠉⢰⣿⣿⣧⠀⣿⣿⣿⣿⡏⣿⡄⠀⠈⢳⡍⢳⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⣿⠁⠀⡎⢸⠈⠻⡏⠙⣧⡀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣼⢹⣧⣿⠀⣿⣿⣿⣿⣿⠈⣧⠀⠀⠀⢿⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣿⠀⣿⡇⠀⡇⢸⡄⢰⡇⠀⠈⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢻⣿⠀⣿⣿⣿⣿⣿⡄⣿⠀⠀⢠⣾⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣸⠁⠈⡇⣸⣧⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⡼⠁⠀⣀⣾⡏⠀⣿⣿⣿⣿⣿⣇⣿⠀⢠⡞⣹⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣧⣿⠀⠀⢳⣿⡟⢦⣄⡀⠀⠙⣦⠀⠀⠀⢀⣼⣁⣤⠞⠉⢸⠇⠀⣿⣿⣿⣿⣿⣿⣿⢀⡞⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣇⢸⣿⣿⣿⣿⣿⠃⠀⣀⣘⣿⣇⣈⣉⣙⣷⣶⣶⣤⣀⣀⣸⣛⣉⣀⣀⣀⣸⢀⡀⣿⣿⡇⣿⣿⣿⣿⡾⣁⣸⣁⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣦⣤⣄⣀⣠⣄⠀⣰⡆⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠹⠛⠛⢽⠟⠁⠸⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⠚⠛⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣸⣶⣇⠀⢰⣿⣿⣷⣤⠤⠴⠖⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⣇⠀⢰⣾⣿⣄⣼⡿⠿⢿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠖⠚⠛⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢾⣿⠽⢼⡛⠋⠉⠉⠁⢸⠀⠀⠈⢻⣄⣀⣠⠤⠤⣶⠒⠚⠋⢉⣉⣠⣤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠀⠀⣾⠃⠀⠈⢻⣀⣠⠤⢤⣿⠀⠀⠀⠀⢿⡇⠀⢀⣤⡿⠗⠒⢚⣏⠉⠱⡄⠀⠀⠀⢸⠈⠙⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣀⣀⡤⠤⠶⡿⠀⠀⠀⠀⣿⠀⠀⠀⢿⠀⠀⠀⠀⠘⣇⣴⠃⠀⠻⢤⡸⣿⡿⠏⢀⡿⠀⠀⢠⣏⡀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⡆⠀⠀⢸⡁⠀⠀⠀⠀⢹⡏⠀⠀⠀⣰⣿⣗⠓⠒⠛⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢳⠒⠒⢙⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⢿⣧⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠛⠛⠀⣠⠞⡉⠉⠳⣄⠀⠀⠀⠀⠀⢳⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢠⠇⣴⣿⣷⠀⠸⡆⠀⠀⠀⠀⢸⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⡄⠉⠋⠉⠀⠀⢷⠀⠀⠀⠀⣸⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠃⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⠇⠀⠀⠀⠀⠀⠀⣸⠀⣠⠞⠁⠀⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣄⣀⡀⢀⣀⣀⡠⠷⠚⠁⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣠⠞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠤⠤⠦⠶⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣴⣆⠀⠤⠄⠐⠂⠀⠉⣀⠠⠀ ⠀⠀⠀⠀⣀⢰⡿⡆⠛⢻⠉⢫⡀⠀⡤⠄⢐⡂⠀⢁⡀⠀⠀⠀ ⠀⠀⠀⡀⠀⠜⠀⠘⡂⢸⠀⠀⢇⠂⠋⣽⡆⡀⠀⢄⠈⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠀⠀⠘⠀⠐⣏⠁⠀⠀⠀⠈⢂⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠠⠷⠀⡆⠀⠈⠀⡆ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⠌⠰⠀ ⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠂⢁⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡀⠘⣧⠀⠀⣹⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠠⣽⣄⠙⢦⣤⠋⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡉⠳⣼⠀⠀⠀⠀⠻⣤⡾⠀⠀⠀⣾⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣈⣷⠀⢈⣧⡀⠀⠀⠀⠀⣇⠀⢀⣼⢻⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡉⠉⠁⠈⠉⠁⠉⠲⠦⢄⣀⣽⣶⡯⠔⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠁⠀⠀⠘⢧⠀⢀⣤⠶⠶⠚⠷⠶⠦⣤⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⡀⠀⠀⠀⢀⣠⡴⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⠀⠀⠀⠀⠀⢰⡄⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠉⠉⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠆⠀⠀⠀⠀⠀⠀⠀⢈⣇⣿⣦⣤⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡆⠀⠀⢠⡴⠿⠛⠉⣻⣿⣿⣿⣿⣷⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠛⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡇⠀⣿⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⣛⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢰⡟⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠛⠦⣤⣄⣀⣀⣤⠾⠃⠀⢠⣟⡄⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⠦⣄⡀⠀⠀⠀⠀⠈⠉⠉⣸⠇⠀⣰⠟⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⡄⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⠉⠳⢤⣀⠀⠀⢀⡼⠃⢠⡾⠁⠀⠀⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠧⠴⠛⠛⠉⠉⠙⠛⠛⠒⠶⢤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣧⡀⣠⡞⠁⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠘⠒⣒⠦⠤⣌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡇⠀⠀⠀⠀⠐⠋⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠛⠉⠁⠀⠀⠀⠀⠀⠈⠓⠦⣄⣙⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⢙⡗⠒⠒⠋⠁⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⠟⠋⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣈⣧⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⡼⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⢰⡄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠹⣆⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠎⠁⠙⣦⠀⠀⠀⠀⠀⠀⠈⠳⣿⡆⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠈⢳⣄⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠙⠓⠒⠒⠛⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠤⢤⣀⣹⣆⢸⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣾⣹⠶⢤⣀⣀⠀⠀⠀⠀⠀⣠⡼⠿⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠉⠁⠀⠀⠀⠈⠉⠉⠓⠒⠒⠋⠻⣧⡀⢻⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⢀⣤⠞⠛⠛⠛⠲⣤⠀⠀⠀⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣀⡤⣶⠤⠾⢤⡴⠶⠦⣄⠀⠘⣷⠀⠀⠀⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⠀⠈⢷⡀⠀⠈⠳⣄⠈⡇⠀⠀⠀ ⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢹⡄⡇⠀⠀⠀ ⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⠁⠀⠀⠀ ⠀⠀⠀⠈⢷⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢶⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢠⠏⠀⠀⣴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⣀⡴⠋⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢁⣤⡴⠛⠁⠀⠀⠀⠈⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⣙⠓⠦⢤⣴⣶⣿⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⢉⠉⡉⠉⢉⠉⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠛⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣿⢀⣀⡤⠶⠖⠛⠉⠉⠉⠉⠉⠉⠛⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠏⠀⢀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠞⠉⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢥⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣾⣡⠴⠖⠒⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠉⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠋⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠈⢻⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⣀⣀⠌⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⣿⠿⣿⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣿⣻⣿⠟⠀⠀⣰⡶⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠿⠋⠙⠛⠶⠦⣠⡟⠀⠈⢷⡀⠀⠀⢀⣀⣤⣀⡀ ⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⣀⣠⠶⠟⠀⠀⣦⣀⠙⠷⢦⣼⠁⠀⠉⢷ ⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠗⠆⢠⡾ ⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁ ⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠖⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠓⠒⠒⠒⠛⠋⢉⣍⠉⠉⠉⠉⠙⠒⠾⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠃⠈⠳⣄⡀⠀⠀⠀⠀⢀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠉⣳⡶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣾⣇⠀⠀⠐⣾⠉⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣆⠀⠀⠹⢶⣄⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⢀⣠⠾⠉⠀⠀⠀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢿⠳⣤⣀⠀⠀⠉⠉⣧⣀⠀⣀⣀⣀⢴⣶⠉⠀⠀⠀⠀⣀⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠷⠤⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣤⣀⢀⣤⢴⢄⣀⣀⡀⡀⣤⣀⣀⣀⣤⣄⠀⣀⢀⣀⣀⣀⣀⠀⢀⠀⢴⢤⣖⣦⣖⠀⢢⠠⡆⠐⣶⡖⣄⢠⠀⠄⠀⡆⠀ ⢿⡟⠻⢛⠚⡛⣜⣘⢿⡛⢀⢋⠛⡙⠚⣛⠚⡛⠀⢙⠚⡓⣟⠃⠚⠀⠈⠀⢺⠂⠚⠁⠲⠑⠂⠀⠓⠘⠀⢓⢋⠙⠁⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⣤⠞⠉⠀⠀⣀⣠⠴⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢻⠿⣿⣷⢦⣄⡀⠀⠀⠀⠀⢸⠀⣠⡴⠋⢀⣠⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠻⣉⠻⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⠋⠀⠀⠀⠀⠀⠙⣦⡬⡻⣦⣀⠀⣀⣨⣾⣯⣴⢾⣿⠽⢦⣶⡛⠛⠛⠲⠶⠤⠤⣄⣀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠈⠀⠃⠙⣧⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢈⢿⣟⣿⡿⣛⣽⡶⠖⠓⠒⠲⣮⡹⣦⣤⣤⣄⣠⡴⠟⢛⣛⣖⡖⠿⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣾⣿⣧⡾⡋⠀⠀⠀⠀⠀⣠⣾⣷⠷⠶⠶⣬⢉⡾⠋⠉⠉⠉⠙⠛⢾⡝⣷⣤⣄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠯⠉⢙⣿⣿⢶⣧⣤⣤⣤⣴⢾⣫⡷⠋⠀⠀⠀⢿⣎⠻⢦⣄⣀⡀⢀⣠⣼⠟⣾⣀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⣼⡇⠙⠛⠶⠶⣶⣶⡿⠟⠷⢤⠀⠀⠀⠀⠀⠈⠛⢶⣬⣭⣭⣭⣥⣴⡟⢨⡿⠇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣼⠏⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠧⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⡄⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠋⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠘⣿⠀⡀⠆⣿⡀⠀⠀⠀⠀⠀⣠⡶⢞⣿⣹⢋⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡗⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⣿⠀⡇⠀⢸⣇⠀⠀⠀⢠⣤⣿⣿⣿⣿⡉⠙⣦⣀⣤⣴⣦⣴⣿⣿⣿⡿⣲⣦⣿⡏⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⣿⠀⠇⠀⠘⣿⡛⠛⠛⠛⠛⠛⠛⠶⠾⣿⠿⠍⠈⠻⣿⣿⣿⠋⢻⣿⡿⠿⠿⢿⣿⡷⠓⠒⣚⣻⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣄⡀⢿⡀⠀⠀⠀⢹⣧⣤⣤⠤⠶⠶⠶⢶⣶⡿⣷⡖⠀⠀⠈⡿⠁⣲⣾⣿⣿⡓⠛⠛⣿⡿⠶⠾⢯⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢻⣿⣧⠀⠀⠀⠀⠻⣧⡀⠀⠒⠒⠚⠋⠁⠀⠀⠙⠓⠶⠚⠛⠋⠉⢀⣼⠏⠉⠀⣰⠟⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣠⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣹⣿⣭⣽⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣶⠿⠿⢦⣉⠀⠀⠀⠀⠀⠀⠀⣰⡏⣼⣾⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠸⣷⡀⠸⢯⡽⠿⢿⡛⠋⢉⣿⠿⢯⣁⠠⠀⢀⠉⠛⢦⣄⠀⠀⠀⢰⠏⡆⢸⡇⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣦⠀⠀⠀⠀⢸⣿⣿⣷⠏⠁⠀⠀⠹⡈⣼⠃⠀⠀⠉⠳⢦⣄⠀⠀⠀⠉⠳⣦⣠⡟⢀⡇⠀⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠘⠿⣿⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠓⢶⣄⠀⠀⠀⠙⢧⣼⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠈⠀⠴⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⣀⡤⣾⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠈⢀⣾⠋⠲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⣠⡿⠳⠤⣤⣌⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⢳⢀⣀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⣡⡞⠀⠀⠀⠀⠀⠉⠉⠙⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡆⠈⠀⠀⢠⡿⢋⠁⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⣰⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠶⠶⠒⠛⠛⠛⠉⠹⣷⡀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢀⣀⣰⠟⠀⢀⣼⣿⢻⣟⣿⡧⣤⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⡽⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣜⢓⣿⢰⡇⠀⠀⠀⠀⠀⠀⠻⣆⠀⣀⡴⢞⣯⠿⣿⠀⢠⡾⠡⠈⠛⣽⡿⠁⠈⠉⠛⠻⢶⣤⣤ ⠐⠀⠀⠉⠻⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⢿⣥⣈⣻⣦⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠐⣾⠏⣰⡟⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢦⣄⡀⠀⢀⢰⡃⠀⠀⣠⡾⠃⡼⠋⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢿⣲⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠲⠶⠦⠾⠿⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠪⠿⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠷⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⣠⠶⠞⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣤⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣰⠟⠁⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⣀⣴⡾⠿⠋⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠿⣶⣄⡀⠀⠀⣰⡿⠁⢀⡾⠃⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣰⡿⠁⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⢠⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⢀⣀⣤⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣦⡀⢀⣤⠤⠶⢶⣦⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠾⢶⣦⡄⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⡿⠟⠃⠀⠉⠛⠷⣦⣄⠀⠀⣠⡾⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠻⠿⣶⣦⣤⣤⣤⣤⣥⣶⣛⠉⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣾⣁⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠶⠿⠛⠛⠛⣿⣨⡿⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠂⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠻⣷⣤⣄⣀⣨⣍⡀⠀⠻⣶⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣸⡏⠹⣿⡀⠀⠀⠀⠀⠀⠈⠉⣿⢼⣏⣷⠉⠻⣍⣉⣷⣤⣀⠘⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣶⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⠛⠁⠀⠙⢷⣆⡀⠀⠀⠀⢰⡟⠁⠈⠙⠉⠀⠀⢈⣭⣀⠀⢉⣽⣿⣆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣦⣀⣀⣴⣶⣄⠙⠻⣶⣤⣤⣼⣷⣄⣀⣀⣀⣀⠀⠻⣭⣿⣴⢾⡿⠈⣿⡅⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⡏⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠁⠈⠻⢷⣦⣀⣀⣀⣀⣈⣉⣉⣿⠋⠉⠛⠓⠺⣿⣅⡀⠀⠀⠈⠿⠶⢶⣤⣾⠟⠀⠀⠀⣠⡿⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠈⠉⠻⠷⣶⣄⣀⣀⣀⠀⠀⢀⣀⣀⣴⠿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠻⠷⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⡿⣿⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠁⠈⠉⠉⠙⠛⠛⣿⡛⠛⠛⠻⣯⠁⠀⠙⣷⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣿⡇⠀⠀⠘⣿⡀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⡇⠀⠀⠀⠈⢿⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⢷⣄⡈⠛⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣄⠈⠛⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣤⣄⣈⠙⠛⠳⢦⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⠿⠿⠛⠛⠻⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⣦⣄⡙⠻⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣃⣀⣠⣤⣤⣤⣤⣤⣶⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠙⠛⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⠙⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢷⣦⣤⣄⣀⡀⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠾⢋⣁⡼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠶⠛⣋⣉⣩⣤⠶⠶⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⣡⣤⠶⠶⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠘⠿⢤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⢦⣤⣤⣈⣉⣉⣉⣉⣙⣓⣶⡦⢀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⢿⡇⠀⠀⠀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣽⣿⣿⣤⣄⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠶⢶⣤⣀⣀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠸⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡍⠙⠒⢶⡤⠀⢻⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠘⢧⠀⠸⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⣼⢆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢧⡀⣇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⡀⠀⠀⠀⠀⠀⠘⡇⠀⡇⢸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇⣠⠴⠟⠛⠳⣤⡘⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⢰⡇⣾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠻⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⢻⡅⠁⠀⠀⠀⠀⠀⠙⠶⠮⠭⠤⠖⣶⡶⠂⠀⠀⠀⠸⣾⡃⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢳⠀⠀⢀⡇⠀⠀⠀⠀⣤⣤⣶⣖⠉⠋⠀⢠⣀⣀⣤⣖⣶⣤⣠⣤⣤⡤⠶⠚⠻⠉⠀⠀⠀⠀⠀⠀⢹⡇⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⡄⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⣻⢋⡽⢋⣰⠏⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣷⠀⠀⠻⣆⠀⠀⠀⠀⠀⣠⣎⠀⡠⠀⠊⠀⠋⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⠀⠀⠀⠘⣶⢶⠀⣠⠞⢡⣧⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⣸⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⠀⠀⣰⠃⣼⡾⠁⢠⣯⠏⢀⡏⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢻⠉⢿⠉⢫⡙⣆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣹⠀⢰⠇⢸⣿⠀⢠⠟⡼⠀⣸⣻⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡄⠈⣧⠀⢳⠙⣇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡆⢸⠀⢺⡇⠀⣸⣠⠃⠀⣧⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⣳⡀⠈⢆⠀⣇⠹⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⡇⢸⡄⠸⠁⠀⡿⠃⠀⢸⣻⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣧⠀⠸⣄⠈⠀⢳⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣷⠘⣇⠀⠀⠀⠀⠀⠀⠈⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡀⠀⠁⠀⠀⢸⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠙⠀⠀⠀⠀⡼⠙⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢰⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠁⠀⠀⠀⠀⢀⣞⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⢤⣤⣽⣀⣀⣀⣀⣬⡆⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣄⣤⣤⣤⣤⣤⣶⡒⠚⢿⣿⣥⣿⡇⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠹⣿⠉⠀⠈⢻⠀⠀⠀⠀⠀⢀⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⡿⠃⢧⠀⠀⠀⠀⠀⢸⠀⠀⠈⢳⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⡿⠀⠀⠀⠀⠀⢸⣇⣾⣿⣿⣿⣿⣿⢹⡿⣿⣿⣿⣿⣾⣿⡀⠀⣸⡆⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⡼⠁⠀⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⡇⢸⡇⣿⣿⣿⣿⡿⠛⢻⡄⡏⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⢠⢫⣿⡿⣿⣿⣿⣿⡇⢸⡇⢹⣿⠛⢁⣀⢰⡟⠀⠇⣇⠀⠀⠀⠀⠀⢣⠀⠀⢸⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⡟⢿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠛⠛⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⣠⠞⡽⢟⠦⣍⡙⠛⠛⠻⣷⠀⠀⠀⠀⠀⢼⣿ ⣿⣿⣿⣿⣿⣿⣿⠥⠖⠒⢋⢉⡤⠞⠁⠈⠙⠦⣍⣙⠒⠢⣼⡆⠀⠀⢀⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⣠⢴⡞⠋⠉⠉⠓⠦⠀⠀⠠⠖⠛⠙⠲⣄⣷⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠋⡷⠼⠗⢶⣤⠤⣄⣣⡀⠀⢀⣀⣀⣬⣦⣽⠻⡆⢾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⢳⣀⡄⠀⠉⣒⠒⠈⠀⠤⡍⠛⠒⠊⠁⣿⠀⢷⠈⠻⢿⣿⣿ ⣿⣿⣿⣿⣿⠀⢀⣿⣿⣇⠀⠀⢗⢯⣟⣡⠶⠖⠀⠀⠀⣠⠇⠀⢸⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠈⠑⠉⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠘⣶⣤⣴⣾⣿⣿⣏⡿⠀⠀⣸⠇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⢰⡟⠀⠀⠀⠀⠀ ⣿⣿⣽⣿⣿⡄⣸⠋⠀⠘⡜⣄⠀⠀⠀⠱⡱⡄⠉⠻⡟⠀⢠⡟⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⣷⠈⠉⠉⠉⠉⠁⠉⠑⢦⠹⣴⣿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⢹⣿⣿⣿⣿⣷⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣇⢀⣀⣀⣰⡒⠲⡶⠯⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢘⡭⠵⠚⠉⠙⣄⠟⠉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣴⣷⡖⠲⢆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠠⠊⠁⡑⠂⠤⣬⡀⡌⠹⣵⡀⠘⡵⡋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣒⠀⠈⠀⠎⠉⠀⢐⠤⠒⣓⠣⠇⠀⣡⣧⠞⢻⣃⡾⣗⠀⠤⠤⠤⠄⠀⠀⠀ ⢉⡼⡠⠉⠑⠨⠆⠠⠀⠀⢠⡾⠚⢚⠒⠛⠻⡔⢯⣶⡂⠈⠣⠄⠒⠤⢠⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⠛⠀⠀⠸⠰⠠⣄⠱⠶⢈⣀⡀⠏⡇⠀⠘⢀⢌⠄⢀⠑⢠⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⠀⠛⠙⣀⣀⠘⠺⠌⠀⡇⠀⠀⠇⠁⠀⠀⠂⠱⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠘⡀⡔⠁⠀⠀⠈⠄⠀⠀⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠵⠐⠂⣄⠀⠀⠈⡀⢠⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠐⠁⠀⡈⡄⡰⢄⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢸⢲⡗⣅⡨⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⣀⡮⢤⡤⠤⠐⠊⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⠸⠀⣐⠍⠉⠉⠉⠉⠉⢐⠆⢀⡨⠀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠥⣀⣰⣵⡀⠠⠀⠀
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⡆⢸⣟⠁⢠⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⠖⠻⣷⡀⠀ ⠀⠀⠀⠀⣧⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠴⠖⠛⠛⠛⠻⠿⠷⠀⠀⠘⠋⠀⠀⠀⠀⠘⣷⠀ ⠀⠀⠀⠀⢿⠀⢿⣿⣿⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⢠⣿⣆ ⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣇⣀⣀⣠⣤⠴⠟⢹⡇ ⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣧⠀⠴⠿⠶⠶⠶⠶⠶⠟⠋⠀⠀⢁⣀⣀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢠⡟⠀ ⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⠤⣄⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⢀⡿⠀⠀ ⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢦⣤⣄⣩⣩⣩⡭⠏⠁⠀⠀⠀⢀⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⣍⣛⣶⣾⣽⣤⡄⠀⠀⣰⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⣠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡓⠒⠶⠤⠤⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⢰⣿⣿⣿⠿⢿⣿⣿⣿⣿⠶⢤⠤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⣼⣿⣿⣿⠀⠀⠸⡟⡟⠻⣦⡠⠷⠿⣼⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⢠⣾⣿⣿⣿⡏⠀⠀⠀⢹⡿⡄⠈⡅⢿⣷⡇⠘⢧⡀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⢳⣹⡀⠈⠓⠛⠁⠀⠈⠻⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣄⡷⠷⠤⠤⠤⠖⠒⠒⠋⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⡀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠲⣤⡙⢿⣿⣿⣿⡧⠤⣀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡈⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣦⡾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠀⠉⠀⠻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢀⡶⣶⠀⠀⠀⠀⢯⣷⣽⡇⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠛⠞⠏⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢤⣿⣿⡆⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠲⣶⠞⠛⠻⣶⡴⠖⠶⣄⠈⠃⠉⠁⠀⠀⠀⠈⠻⣄⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⢠⡶⣤⣀⣶⠟⠉⠛⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠟⠒⢿⣄⠀⢀⣀⠀⠀⠹⣧⠀⠀ ⠀⢀⡿⣡⢾⡆⢸⡇⢾⣝⠿⣦⣀⣀⣤⠴⠶⠖⢻⡟⣿⠛⠶⠶⢦⣤⣀⢀⣠⣿⣿⡛⣿⠀⢀⣄⠘⣧⠀ ⠀⣾⠁⠻⣾⡷⢾⣇⣼⡿⠃⠈⠉⠉⠀⠀⠀⠀⣸⠉⣿⠀⠀⠀⠀⠈⠉⠋⠽⢿⣿⢡⣿⣀⠘⢿⠇⢹⡆ ⢸⡇⠀⣸⡏⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⠃⠈⢳⡄⠀⠀⢿ ⣾⠁⢀⡿⠗⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢹⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠻⣦⠀⠸⣧⡀⠀⢸ ⢻⡀⣿⠀⠀⡿⠀⠀⠀⠀⠰⣶⣶⠆⠀⢀⣼⠃⠀⠀⠀⢿⣤⠁⠀⣾⣶⡦⠐⠀⠀⠀⠹⣇⠀⠀⣻⠀⣼ ⠸⣧⣼⠗⢸⡇⠀⣠⣤⣤⣤⣤⣤⣤⣤⡞⠁⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣀⣀⣀⡀⠀⠀⣿⠀⠸⣿⣠⡏ ⠀⠹⣇⠀⢸⣇⣸⡟⢹⣿⣿⣿⣿⣿⠏⣿⠀⠀⠀⠀⠀⠀⡟⢹⣿⣿⣿⣿⣿⠏⣿⣀⣀⣿⠀⠀⢸⠏⠀ ⠀⠀⠙⣷⠺⡏⠉⠻⢮⣝⣛⣟⣛⣥⠾⠃⠀⠀⢠⣶⠀⠀⠻⢮⣝⣛⣻⣛⣭⠞⠉⠀⠀⡟⠀⢴⡛⠀⠀ ⠀⠀⠀⢿⣄⣻⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣸⠃⠀⢨⠇⠀⠀ ⠀⠀⠀⠀⠉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠶⠒⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣉⠓⠶⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠋⣡⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠻⢿⣶⣤⣤⣀⣨⣭⠟⣿⠛⢯⣭⣁⣀⣀⣤⣴⠞⠋⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⢏⣴⣦⡄⠀⠀⠈⠁⠀⣼⠃⣰⠟⢧⡈⢿⡈⠉⠉⠀⠀⣠⣶⡄⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⠸⠿⠛⠁⠀⠀⠀⠀⠀⠛⠟⠉⣀⠈⠛⠛⠁⠀⠀⠀⠀⢳⡿⠇⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⢸⣻⡇⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⢠⣤⠀⢸⣄⣀⣀⣀⣀⣀⣠⣿⠈⠫⠼⣿⢀⣀⣀⣀⣀⣀⠀⣟⢀⣄⠀⢻⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠸⠀⣱⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⢸⣆⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣷⣤⣿⣄⢠⠿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⣋⣠⣴⣾⣿⣿⣿⣿⣿⣇⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⡰⠃⢀⡴⠋⠙⣿⠿⠛⠋⠉⢛⣉⣠⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡞⠁⢠⣿⣤⣤⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣰⡟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠯⠀⠀⠀⠼⠋⢠⡧⠄⠺⢿⣿⣿⣿⣿⣿⣿⣦⠘⡆⠀⠀ ⠀⠀⢀⠎⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀ ⠀⢀⡞⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠓⢾⡖⠒⠂⠙⣿⣷⠆⠀⠀⠀⣤⠴⠒⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⠀ ⠀⡜⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠑⠒⠒⠒⠛⠛⠀⠀⠀⠀⠙⠶⠒⠚⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢇⠀ ⢰⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣙⡴⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⡄ ⡎⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢘⡁ ⠃⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢳⡀⠀⠀⠀⠀⢀⣴⠶⡤⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠒⠛⠉ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⣄⡀⠳⡄⠀⠀⠀⢾⣯⡩⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠓⠿⣆⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠒⠒ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠉⣳⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠒⡶⠶⣶⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠲⠤⠄⢀⣧⣠⠞⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⠟⠉⢉⣁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣉⠛⠛⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⠟⠁⡎⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠉⠉⠉⠀⠀⠀⠀⠈⡆⠀⠀⠈⢻⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠋⠀⢰⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢻⡋⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠈⠛⢿⡏⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠈⡇⢰⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠀⠀⠀⠀⣇⠀⠀⠀⠀⡔⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⢳⠋⠀⠀⠉⠓⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢺⡀⠀⠀⠀⠀⢸⠀⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀
⠀⠈⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⢁⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠖⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⡤⠞⠋⣠⠴⠒⠋⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢿⡇⠀⠀⠀⠈⣇⠀⠀⣷⠀⠀⠀⠀⠀⠀⣧⢀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠁⢺⠥⢦⠀⠀⠀⢹⡄⠀⢸⣆⣀⣤⣶⣶⣾⣯⣭⠭⠭⠭⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢸⠠⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⢈⣻⣿⡟⣁⠀⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠘⣿⠋⠣⣟⡰⠳⢤⠀⢀⣀⣀⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⢀⡴⠚⠉⠀⠈⠉⠒⠊⢡⡆⠀⠀⠉⠱⠞⠋⣁⠤⠔⣠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠹⣄⠰⠊⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⣏⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣤⣀⠀⠈⠙⠒⠒⣲⣶⣖⠋⠉⠢⡄⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⡾⣿⣿⣿⡞⠋⠉⠉⠉⠈⠓⠲⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⢀⣀⣀⣠⡃⠈⢙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣾⣿⣿⣿⣿⣷⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⠤⠶⠛⠛⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠋⠉⣁⠀⠐⠂⠀⠀⠀⢤⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⠶⠶⠶⠶⠶⢶⣶⣤⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣴⣶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠀⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⠀⠀⠀⠀⡎⠘⣿⡏⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣅⣀⣽⣿⡄⠀⠉⠻⣿⣦⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⢀⣴⡿⢋⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠀⠀⠀⠀⠈⠻⣿⣍⠉⠉⠉ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀ ⠀⢠⣿⣿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷ ⠀⣼⡟⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢀⣿⠇⢀⣦⡉⠳⢦⣄⡀⠀⠀⠀⠈⠻⢷⡦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⢸⣿⠀⣼⣿⣿⣷⣤⡈⠙⠳⠦⣤⣀⡀⠀⠙⠲⣄⡈⠉⠙⠓⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠛⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿ ⠸⣿⠀⠛⡇⠈⠙⠻⣿⣷⣦⣀⠀⠈⠉⠙⠓⠒⠒⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⡟ ⠀⣿⡆⠀⣇⠀⠀⠀⠀⣿⣿⣿⣷⣦⣀⠀⢠⠀⠀⡄⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⡟⠀ ⠀⢻⣷⠀⠘⢦⡀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣾⡄⢸⣧⣶⣾⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠉⠉⣹⠛⠷⠀⣿⣿⠟⠚⠲⣄⠀⠀⣼⣿⠁⠀ ⠀⠈⣿⣧⡀⠈⠛⢦⣀⠀⠀⠈⠉⢉⣠⠞⠛⠃⠛⠻⣏⠉⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⢀⣴⠋⠀⠀⢰⡿⠁⠀⠀⢀⡟⠀⣼⣿⠃⠀⠀ ⠀⠀⠘⢿⣧⡀⠀⠀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁⠀⠀⠀⠈⠁⠀⢀⣠⠟⢁⣼⣿⠃⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⣀⣀⠀⠀⠀⠀⠀⠠⣖⠋⠁⣠⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠙⢦⡀⠀⠀⠀⣈⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠶⣤⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⣁⣤⣶⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⢸⠟⠋⠉⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣠⣴⠚⠉⢹⡍⢿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣄⣀⣀⣀⠄⠀⠀⠀⠀⢠⡞⢹⠋⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⡼⠁⠀⠀⠀⣷⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡇⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠇⠀⣾⠀⠀⠀⢐⣞⣛⣂⣀⠈⢀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡞⠀⣠⣇⡴⠞⠛⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢈⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀⠀⠑⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢞⠀⡠⠊⠀⠀⠀⠀⠀⢠⡀⠀⠈⢹⠠⡀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢐⢡⠃⠀⡁⠀⠀⠀⢲⢄⠀⠀⣫⢆⢔⣿⢇⡇⡆⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠈⠚⣷⣄⣱⢄⠀⠰⠁⡰⠕⠞⢊⣱⣼⡗⢸⢀⠁⠀⠀⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣢⣄⠉⠁⠀⢀⠎⢊⡿⠟⣾⠁⡸⠘⠀⠀⣴⢯⠀⠀ ⠀⠀⠀⠀⣠⣤⡀⣰⠈⡗⠚⠚⠃⡀⠀⠀⠀⠀⠀⢰⢹⠊⠀⡆⠀⣸⢏⠃⠀⠀ ⣅⠁⠀⠀⠹⢿⣿⠃⢀⢓⢄⠀⠈⢃⣀⢤⡎⠀⢀⣼⢰⠀⠀⡇⠀⡿⡀⠀⠀⠐ ⠿⠇⠀⠀⠀⢀⡧⠄⡜⡬⢀⡉⠢⠄⡉⠉⡀⢴⠁⣸⠘⣶⠤⠓⠚⢇⠀⠀⠀⠐ ⠀⠀⠀⠀⣠⠋⠀⡐⡐⢀⠀⠀⠉⠁⠁⠀⠀⢘⣶⣿⠀⡿⠀⠀⠀⠀⠡⠀⠀⠀ ⠀⠀⢠⠊⡌⠀⡰⣐⠄⠀⠁⠂⢀⣀⣤⣶⣾⣿⣿⣿⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⡴⠁⠀⠃⠤⠿⠧⠤⠶⢊⡏⢿⣿⣿⣿⣿⣿⣿⣿⠀⣣⠁⠀⠀⠀⣆⣀⠀⠀ ⢼⢣⡀⠀⠀⠀⡐⠘⣿⣿⣿⣿⣦⣬⣍⠉⠉⠉⠉⠉⠉⠣⠀⠀⠀⡜⠘⡌⠑⠒ ⠘⠀⠈⡍⢏⣀⣧⣤⣿⣿⣿⣿⣿⣟⡡⢂⠄⠀⠀⣀⠴⢀⠃⠀⢰⠁⠀⠘⡀⠀ ⠀⠀⠀⢧⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣷⣧⣮⣽⡿⠁⠀⢸⠀⢀⠳⠀⠀⠀⠰⠀ ⠀⠀⠀⠈⡄⢸⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠀⡌⠀⡆⠀⠀⠀⠀

Warning: This item may contain sensitive themes such as nudity.

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣆⡀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣼⣿⣿⣿⣿⡟⠛⠳⡆⣦⣼⠿⠟⢋⣩⡽⠏⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⠟⠋⠉⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠙⣷⣶⣶⠟⠉⠀⠀⠈⠉⠉⠛⠶⣶⣶⠶⣶⣆⡀⠀⠈⢹⣿⠃⠀⠀⠀⠀⠘⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠛⠟⠛⠶⠺⣴⡿⢋⠞⠁⠀⠀⠀⠠⣄⠙⣏⠉⠉⠃⠈⠱⣌⠙⢷⣤⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⡾⠋⢠⠋⠀⠀⠀⠀⣠⡾⠀⠑⠾⠆⡷⢦⣀⠀⠈⢧⠀⠻⣷⠄⠈⠛⡿⣶⣦⣤⣤⣴⣿⣿ ⣿⣿⣿⣿⣿⠏⠠⠤⠤⠤⠀⠀⠀⠀⣰⠏⠀⢀⠏⠀⠀⣠⠴⠚⠙⢦⠀⠀⠀⣸⠁⠀⠉⠓⢦⣀⣳⡀⠹⣷⡀⠀⠁⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡜⠀⢀⡞⠁⠀⠀⠀⠈⡆⠀⢀⡇⠀⠀⠀⠀⠀⢇⠀⢣⠀⢹⣧⣆⣀⢹⣿⣿⣿⣿⡿⠋ ⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠁⠀⡼⠀⠀⠀⠀⠀⠀⢳⠀⠘⡇⠀⠀⠀⠀⠀⢸⣠⠜⠓⠉⠉⠉⠉⠛⣿⣿⣿⣿⡀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠤⠒⠒⠛⠒⠲⣧⣤⣀⣀⣠⣤⣶⣾⠃⠀⣿⣶⣶⣶⣶⠿⠛⠳⠦⠄⠀⠀⠀⠀⠀⢨⣻⣿⣿⣷⣆ ⣿⣿⠇⠀⠀⠀⠀⠀⠀⣴⣫⠁⠀⠀⠀⠀⠀⠀⠈⠒⠛⠉⠙⠳⢞⣋⡏⣀⣠⣼⢦⡽⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠃⠙⠋⠁ ⠹⡟⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢽⠋⠉⠁⡹⢀⣀⣀⣀⡠⠤⠒⠈⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀ ⣰⠁⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠒⠒⠒⠈⠹⡃⠀⠉⢰⣎⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠋⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠤⠔⠋⠀⢀⣠⣀⣠⡤⠒⠉⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⢲⠦⠤⣤⢤⣄⣀⣀⡤⠤⠤⠤⠤⣤⡖⠒⠉⡏⠀⢰⠁⠀⠀⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣧⠞⠉⠉⠙⣷⡀⠀⠀⠰⣯⠙⡆⠀⠁⠀⡇⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡾⠀⢰⡇⠀⠀⠀⠀⠈⢿⣄⠀⠀⠘⡷⢿⣼⠀⣸⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸⡃⠀⠀⠀⢇⠀⠀⠈⠑⠦⠤⠇⠈⢻⣀⠇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡴⠃⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠋⠉⠉⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡷⠶⠖⠒⠛⠋⠉⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣠⣶⣟⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠆⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⣩⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢀⡈⣿⡾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣴⡟⢹⣿⣷⢿⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⢸⣿⢿⣏⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢠⠿⢹ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢹⠏⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣴⠏ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡼⠋⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠻⣦⠀⠀⠀⠀⠀⠀⢸⣇⣼⣻⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣴⣿⡉⠘⣧⡀⠀⣸⣷⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣹⣤⣤⣄⣀⣿⡆⠀⠀⠀⠀⠀⢸⠏⠈⠳⣄⠘⢷⡄⣏⣿⣿⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⣀⠀⠀⠀⣀⣴⣏⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠉⠝⢿⣦⡀⠀⠀⠀⢸⡄⠀⠀⠈⠳⣤⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⣽⡿⠛⠛⠉⠉⠀⠀⠀⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠈⠛⠀⠀⠀⠀⠈⢻⡾⠽⠛⠟⢀⣤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡏⢻⣦⡠⣄⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠿⢶⣶⡶⢞⣫⣿⠖⠋⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠙⠳⠿⠻⠶⠶⠶⠞⠻⣇⡀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⣀⣀⡤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢺⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠲⠶⠶⢺⡟⠀⢀⣴⡛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣧⡀⠀⠐⣷⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⢀⣤⣾⡍⠃⠐⠋⠈⠻⣄⠀⢀⡼⠿⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠷⠦⠼⠷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡚⠁⠻⣄⣠⢟⡿⠋⡴⠀⠀⣄⡀⠀⢘⡷⠛⢠⣄⣐⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠟⠓⠲⣆⠀⠛⣾⠀⢸⡇⠀⠀⢨⡿⠲⢮⣥⣴⠿⣷⣬⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⠴⠒⠛⠛⠉⠁⠀⠀⠀⠀⠈⠛⠛⣿⠀⠘⠃⠀⠀⢸⡇⠀⠀⠀⣠⡾⢋⡿⠀⠀⠉⠙⠛⠓⠲⠦⢤⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠛⠓⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⢸⣧⠀⠀⡴⣫⣄⡼⠃⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣀⣀⣭⣍⣓⠶⢦⣄⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡽⠟⠁⠀⠀⠀⠀⠀⣀⡶⠛⠁⢠⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⡯⡅⠀⠀⠈⠙⣶⣄⠈⠉⠛⠿⣤⡀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⡇⠀⠀⠀⢿⣤⣿⢤⡀⢠⡞⠉⢹⠇⠀⠀⠀⠀⠉⠛⠦⣤⣀⠀⠀⣼⠃⠀⠀⠀⢠⡴⣿⣧⠤⠤⠤⠾⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⣞⣋⣉⣀⠀⢀⡇⠀⠀⠀⠈⠿⠿⣿⢷⣸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣅⣀⠀⣠⠾⠋⢰⠟⣻⡆⣀⢀⡐⢚⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠙⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⣰⢯⣴⣿⣷⣿⣿⣧⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣰⠃⣸⠃⠀⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣰⠇⢰⠇⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢠⡏⠀⡞⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼⠁⢸⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⣤⣿⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠀⠀⠀⠀⢀⡾⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⢸⣣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠛⠛⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣀⢀⣾⣿⣿⣿⣿⣿⡿⠛⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣀⣤⣤⣤⣶⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠐⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⣀⣀⣀⣀⣤⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⣀⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀ ⠀⣴⣿⠛⣹⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣇⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⡏⢹⣿⠀⠀⠀⢻⣿⡿⠿⠿⠛⠋⠙⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣧⠀⢿⡄⠀⠀⠀⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠟⠛⠛⠛⠋⢀⠀⠃⣄⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⠖⢲⣶⣶⠒⠛⠛⠛⠛⠛⠒⠒⠒⠦⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⣠⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠈⠓⠦⣄⡀⠀⠀⠈⣿⠀⠹⡆⠀⢀⣤⣞⣡⡤⠶⠲⢾⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣿⡶⣤⣤⡿⠀⠀⠙⠶⣿⠋⠉⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣴⡿⠟⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣀⡤⠴⣶⣿⣿⣷⣶⣾⣿⠟⠀⣸⡇⠀⠀⠀⠀⠀⠘⢧⣀⣠⡤⠴⠖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠟⠁⠀⠀⠘⣿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢈⣛⣿⠿⠿⠟⠛⠋⠉⡽⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⡋⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠛⠉⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⠤⢤⣤⣀⠀⠀⣾⣿⣿⣷⠀ ⢹⣿⡿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠏⠀⠀⠀⠀⠈⠉⢳⣿⠿⣿⣿⠀ ⢸⣿⠃⠀⠉⣹⣿⣿⣿⣿⣷⣄⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠉⠳⣄⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⢤⣤⠤⠤⠤⠔⠒⠋⢉⣾⠏⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠈⡿⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠟⢻⣿⣿⣿⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡏⠀⠀⢻⣿⡟⠀⠈⠻⢿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠹⣿⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⡿⠟⠛⣿⣅⣀⣸⣷⠶⠶⠶⠾⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡟⠛⠛⠻⣿⣉⡽⠋⢯⣁⣤⠏⠙⠶⠶⠏⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢸⡿⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣠⠾⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⡞⠁⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣦⣤⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠁⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⣇⡀⠀⠀⣠⠏⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠚⠉⠉⠉⠉⠉⠉⠁⠀⢠⣿⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠤⢄⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⢀⣀⡤⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣠⣴⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⣿⡄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿ ⠘⠛⠿⠿⠿⠿⣿⣿⣦⣄⣀⣀⣀⣀⣠⠤⠤⠶⢾⠃⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠏⠀⠘⣦⡀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠋⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⢠⣿⡉⣹⡆⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⣷⢠⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⢁⣤⣤⣤⡾⠂⠀⠀⢸⡀⠀⠀⢸⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣠⣬⣍⠁⠀⠀⠙⠲⣖⣫⠶⢟⣷⠧⠶⠶⠶⠮⣷⣄⣀⡿⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠛⢻⡟⠀⠀⠈⣧⠀⠀⠀⠀⠙⣇⢀⣼⣿⣿⣂⠀⠀⠀⠀⠙⢿⡁⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠳⣄⠀⠀⣼⠀⠀⠀⠀⠀⠈⠻⢿⣷⡛⠿⠷⠄⠀⠀⠀⠀⢻⣀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠀⠀⠀⠈⠳⢾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠉⠀⠀⠀⠀⠀⠀⠀⣠⢾⣦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡤⠖⠛⠛⠲⣤⡼⠻⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠴⠋⠀⠀⠀⠀⣠⡎⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠳⢤⣄⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡉⡉⠛⠛⠛⠛⠻⡛⣻⢟⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠛⠛⠛⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⠶⠿⠛⠛⠉⠉⠀⠀⠀⠉⠉⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣠⣴⠿⣧⣀⣨⣧⣤⣴⣶⣶⣿⣭⣭⣍⣉⣁⡀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⢀⣴⣿⡣⠹⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⡿⣋⣥⣶⠟⠛⠉⠉⠀⠀⠀⠀⠉⠙⠻⢿⣶⡲⢬⡉⠀⠀⢸⡇⠀⠀⠀⠀⣴⡟⠹⠟⠁⠀⠈⢿⣦⠀ ⠀⠀⠀⠀⣠⣴⠞⡏⠀⠀⢀⣴⡟⣣⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⢿⣦⠉⠀⣠⡿⠁⠀⠀⠀⠀⠙⢿⣆⣠⡶⢠⠀⣀⣽⡗ ⠀⠀⢠⣾⠟⠁⠀⡇⠀⣠⣾⣥⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠹⣧⡾⠟⠁⠀⠀⠀⠀⠀⠀⣠⡿⣋⣴⠋⣠⡿⠃⠀ ⠀⣰⡟⠁⠀⠀⠀⠙⣰⣟⣽⡟⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣠⡾⢋⡼⠋⠙⠿⠋⠀⠀⠀ ⢠⡿⠀⠀⠀⠀⠀⢰⡟⣽⡟⠀⣰⠏⣠⠶⠛⠛⠛⠻⠷⢦⣤⡀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠘⣿⡀⢀⣠⣤⡤⠴⣿⣶⣿⣥⣤⣀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⣿⢱⡿⠀⢀⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⣻⣶⣦⡀⠀⢹⡿⠛⠁⠀⠀⠀⠀⠙⣷⡀⠉⠙⢷⣦⡀⠀⠀ ⠀⢿⣆⠀⠀⠀⠀⣿⣿⠇⠀⠸⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⡏⠛⠋⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠙⢿⡄⠀ ⠀⠀⠙⢷⣦⣀⠀⢻⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠉⠙⠓⠚⠉⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠈⠙⠛⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠙⢲⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢦⠀⠀⠀⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣚⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠈⢧⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠓⠀⠀⠀⠀⢰⣏⢠⠟⠉⠀⠉⠙⠛⠓⠦⠤⠤⠤⠤⠞⢷⣄⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠸⣇⣼⠏⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠳⡖⠶⢤⡀⠀⠀⣈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡀⠀⠘⠒⠦⠽⠆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠶⠛⠁⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⢶⣶⣶⣶⣶⡶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣾⠟⠛⠁⣿⠀ ⠀⠀⢰⡶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣩⠖⠋⠀⠀⢀⣾⠁⠀ ⠀⠀⢸⡇⠘⢮⡉⠉⠓⠲⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⣠⠞⠁⠀⠀⠀⢀⡼⠃⠀⠀ ⠀⠀⠸⣧⠀⠀⠙⠲⣄⡀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⠀⠀⠉⠛⠒⠦⢄⡀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⡰⠋⠀⠀⠀⢀⡴⣺⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⡞⠁⠀⣀⣠⠞⢉⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⣤⣄⣀⣀⣀⣀⡀⢹⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⠋⣠⡴⠚⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀⠀⠈⠙⠻⣄⡀⠀⣿⡤⠴⠚⠛⠉⠛⠋⠉⠻⢤⣰⡏⠀⣠⡾⠗⠋⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣄⣀⣉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠚⠉⠀⣀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⣀⠀⠀⠸⡇⠀⠀⠀⢀⡴⠋⣀⡀⠀⠙⠧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⣞⣩⣷⡀⠀⣧⠀⠀⢀⡟⢀⣾⣹⣿⣆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣾⢸⣿⣿⡗⠀⢸⠀⠀⢸⠀⢸⣿⣿⣿⣿⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠁⠀⠀⢹⣜⣿⣿⠁⠀⣏⠀⠀⢸⠀⠘⣟⢻⢿⡏⠀⠀⠀⠀⠨⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠉⠉⣁⠀⠸⣿⣯⣭⣿⠇⠀⣈⠉⠉⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠚⢧⠀⠀⠈⢹⡟⠁⠀⢀⡼⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠓⢶⠚⢻⠛⠲⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⡟⠋⠳⠖⠒⣶⠞⠉⠳⠶⢤⣀⣀⠀⣀⠈⠳⢼⠥⠞⠁⢀⡀⠀⢀⣀⣀⣠⡴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡏⠀⠁⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢹⡟⠻⢦⡀⠀⠀⢀⣤⣾⡷⠋⠉⠉⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠛⠛⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢘⣷⠖⠒⠶⠦⣄⣀⡏⠀⣤⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⠖⠛⠉⠁⠀⠈⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠁⠀⠀⠀⠀⠈⠙⠳⣤⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠹⣆⠀⠀⠀⢀⡿⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠶⠤⣄⣀⣀⣀⣀⣠⡴⠿⣆⠀⠀⠀⠻⣦⡀⠀⡾⠁⠀⠀⠀⠀⣿⣀⣀⣤⠴⠞⠛⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⡀⢹⣾⠇⢠⠀⢀⡀⠀⣿⠉⠁⠀⠀⠀⠐⢦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⣠⠟⠀⣠⠀⠀⢀⣿⣄⠀⢻⡀⢻⣰⠿⣧⣼⣀⣸⣵⢾⣁⡀⠀⠀⠈⠳⡄⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢯⣀⣾⠁⠀⣴⠟⠀⠉⠓⠾⠗⠛⠁⠀⠈⠉⠉⠁⠀⠀⠈⠙⠳⠶⠶⠶⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢲⣶⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⢰⡷⢀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣀⡀⠀⠀⠀⣠⡖⠂⠀⠀⠀ ⠀⠀⠀⡀⠀⢾⣿⠀⠀⢸⢻⠚⠀⠈⠀⢘⠀⠻⠀⠀⠀⣰⣧⣷⡄⠘⡶⠉⠁⠐⡆⠛⠋⡖⠒⠀⠎⣳⠀⠀⠀⠐⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⣸⣿⠤⠔⠁⠼⠀⠀⠠⠤⠠⠤⣯⡄⢀⠴⣇⠀⠀⠸⠆⠃⢰⡇⠠⠇⠀⠀⡆⠠⠖⠩⠽⠄⢿⡗⣦⠚⠀⠾⠟⠈⣷⡤⠄⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⢿⣇⠹⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠉⠉⠋⠉⠒⠛⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣠⣿⢻⣿⠻⣦⡈⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⢀⣠⣾⠟⠀⣾⠿⣧⡙⠿⣦⣄⣀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⣀⣠⣤⣴⡾⠟⠋⠀⣠⣾⠏⠀⠙⢷⣦⣌⠙⠛⠷⢶⣤⣤⣀⣀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡶⠾⠛⠛⠛⠉⠉⠀⠀⣀⣴⡿⠟⠁⠀⠀⠀⠀⠙⠛⢷⣦⣄⡀⠈⠉⠙⠛⠿⢶⣦⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣟⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀⠀⠈⠙⢿⣿⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣠⣴⣾⠿⠟⠋⠉⠀⠀⠉⠙⠻⠿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠟⠋⠙⠻⣷⣤⡀⠘⣿⣇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣾⡿⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠀⠙⣿⣦⣻⣿⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢱⣤⣄⣼⣿⣄⣤⣤⣤⣄⣀⣀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢹⡟⢿⣿⣧⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⡏⠉⠉⠉⠁⠉⢻⣿⣿⣿⠟⠛⠿⢶⣶⣼⣷⣄⠀⠀⠀⢀⣠⣤⣤⣶⣶⠶⠶⢶⣿⠟⣿⡏⠈⢻⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠙⠻⠷⢤⣀⣀⣠⠤⠶⠋⠉⠁⠀⠀⡙⠿⣿⣋⣀⣀⣠⡶⠟⠁⠀⣿⣇⠀⠈⣿⣧⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣦⣀⣤⡦⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⠀⠀⠘⠛⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢹⣿⡆⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⢿⣿⣿⣿⠀⠀⠀⠀⢸⡿⣯⡻⠿⣗⣶⡤⢤⣤⣄⣘⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣾⡿⣿⣿⡀⠀⠀⠀⠀⢷⡘⢯⣗⡦⣭⣙⣲⣶⣭⡽⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠈⠳⣤⡈⢙⣷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣷⣦⣤⣤⣤⣶⣿⣿⣿⣿⣧⣶⣿⡆⠛⣿⡇⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣷⣶⣿⠃⠀⠀⠀⠀⣦⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠈⠿⢿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢰⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣟⣻⠿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⡿⠋⠁⠀⠈⣷⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⢷⡄⠀⠀⠉⠻⣿⣿⣿⣿⠇⠀⠀⠀⣸⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⠏⠀⠀⠀⠀⠀⢹⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⢻⣆⠀⠀⠀⠀⠻⣿⣏⠀⠀⠀⢘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⡿⠀⠀⠀⠀⠀⠀⢶⣿⡀⠘⢷⡶⠶⢶⠶⣶⠶⠶⠶⠾⣧⠀⠻⣷⣤⣤⣀⠀⠘⣿⣦⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠘⣿⣾⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠸⣿⣿⣿⣾⣿⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣾⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠒⠛⠛⣷⣴⣶⣿⣯⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣤⣶⣶⣶⣦⣤⣬⣿⣆⠀⠀⠸⣧⢀⣠⣙⣿⣦⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡍⠀⣀⣠⣴⡾⠟⠛⠁⠹⣧⡀⠀⠹⡿⠛⠛⠛⠛⠛⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣼⡷⠿⠛⠉⠀⠀⠀⠀⠀⠀⢈⣿⡶⠞⡃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⢶⣤⡀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡶⢶⡶⣶⣦⡀⠀⠀⠀⠀⠙⣦⡈⠉⠻⢶⣄⠀⠀⠀⠉⠳⢦⣀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣭⡌⠁⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠉⣻⣦⣀⠀⠀⠀⠙⢷⣄⡾⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⠿⠿⠽⠿⣿⣟⣛⣛⣉⣤⣤⣤⡾⢋⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⠀⠀⠛⠝⢷⡄⠀⠀⠀⣹⢷⣄⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⠁⠀⠀⠈⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⠀⠹⣦⠀⠀⡿⠘⣿⣆⠀⢻⡆⠀⠀⠀⠀⠀⠀⣀⣤⣴⢶⣾⣯⣿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣿⠂⠀⠀⠀⣠⣴⣶⣶⣿⡿⠋⠉⠉⠉⠋⠙⡛⣿⣷⣴⣇⠀⠘⣿⣧⣿⡇⠀⠀⣀⣴⡶⠿⣯⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢿⡄⢀⣴⣿⣿⡿⠿⠿⠸⠁⠀⠀⢀⣀⣰⣾⣿⣽⠿⠒⠉⠟⠶⣿⣿⣿⣧⡶⢿⣝⣳⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣷⣿⡿⠟⣯⠒⠀⠀⠀⠀⠀⠀⣿⠉⠈⠻⣧⣹⣿⡀⠀⠀⠀⣼⠟⠟⠇⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠢⢤⣿⠀⠀⠀⠀⠀⣼⡟⠋⣤⡶⢿⡇⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⢹⣇⠻⠇⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⣿⢁⣼⠏⠀⢸⡇⠀⢀⡀⣶⠟⠁⠈⣷⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠢⠤⣤⣿⣄⡀⠀⣀⣼⣿⢿⣷⣶⣦⣿⠇⠀⣈⣽⣋⡀⠀⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⢀⣴⡾⠋⣀⡤ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⣿⣈⣩⣿⡿⡿⣷⣼⣿⣉⣸⣿⣦⣬⣻⣿⣿⣿⠿⢶⣼⣇⣄⣤⣄⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⡭⠖⠋⠁⠀ ⠀⠀⠀⠒⠺⠯⠥⢤⣀⡀⠀⠀⠀⠈⢹⡏⠙⢿⣟⣟⣛⣿⣿⣿⠙⣿⡾⠿⠛⣟⣦⣄⣤⣞⣯⣍⣤⣀⣠⣤⣀⣀⣀⣀⢤⣿⡀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⢤⡀⠈⣧⠀⠀⠙⢿⣍⠉⠉⣿⣧⣿⣀⣀⣠⠬⠟⠻⣿⣷⣤⣤⣄⣀⣀⠀⠉⠉⠉⠙⣿⣿⣿⣿⣶⣶⣶⠶⠿⠿⣯⣏⠙⠳⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣽⣆⠀⠀⠀⠙⠷⣦⣈⢷⣄⠀⠀⠀⠀⣀⡼⠋⠉⠉⠉⠉⠉⠙⠛⠶⣦⣤⣾⡿⠓⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣤⣥⣦⠤⠴⠾⠿⡷⣿⣿⣶⣶⣟⣉⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠉⠙⠻⠶⢶⣤⣀⠀⠀⠀⣀⣀⣴⣾⠯⠴⠶⠒⠂⠀⠈⠉ ⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⢯⣭⣁⣀⠀⠀⠀⠀⠀⢀⣤⠶⢀⣉⣽⠷⠾⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠒⠛⠛⠛⠒⠒⠒⠲⠦⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠦⢴⣿⣵⡞⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠲⠦⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡓⠲⠦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣀⣀⠈⠉⠉⠛⠓⠶⠶⠶⠶⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣀⠀⠀⠀⠀⠉⠙⠳⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠙⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⢠⣴⣷⣆⣀⣠⡤⠤⣤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠿⠿⣿⣿⣾⣏⠀⠈⠛⠻⣧⡀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠓⠤⣀⡀⠀⠀⠀⠀⢷⠀⠀⠀⡼⠋⢻⣿⠹⡄⠀⠀⠘⢯⡛⢦⣴⠏⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⣀⠀⠀⠉⠙⠓⢲⣶⣾⣧⡀⢸⠁⠀⠈⣿⣇⣷⡀⠀⠀⠀⢳⣶⣏⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⢀⡖⠉⢀⡴⠒⠒⠒⠋⠉⠉⢳⡀⠀⢀⣀⣸⣿⣙⣿⡙⣿⠀⠀⠀⠘⣿⠉⣳⢀⣤⣾⣿⣿⣿⠀⢀⣾⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠋⣉⣙⠒⠚⠋⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠀⣻⠿⠍⠉⠉⢀⣀⠈⠙⢿⡀⠀⠀⠀⣘⣧⣷⢿⡿⠋⠉⣻⣏⣠⣿⣿⣽⣿⠉⠙⠒⠦⠤⠤⠔⠺⠟⠶⡄⠀⠀⠀⠀⠀⠀⠀ ⠋⠒⠋⣰⡳⠀⣠⠴⠒⠦⣄⠀⢷⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⢉⣾⣛⣦⠀⢱⡀⠀⣺⣿⣿⣿⡿⠀⢀⣴⠟⠋⣀⣄⠀⠀⠺⠿⣖⠀⠀⠀⢀⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⡷⢁⡴⠋⠀⠀⠀⠈⠑⠦⠼⠆⠀⣰⢋⠀⠀⠀⠀⠀⢮⣿⡛⠋⠙⠋⢉⡟⠉⠁⠁⠉⠉⢳⡞⠋⠳⣶⣯⣿⡞⠁⠀⠀⠀⠘⢦⡤⠚⠁⠈⣳⠤⣄⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠸⠿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡏⠀⠀⠀⠀⢀⡾⠸⡄⠀⠀⠀⠘⢧⣀⡀⠀⣀⣠⠞⠁⠀⠀⠙⢾⡿⢿⠉⠀⠀⠀⢲⣾⡆⠀⠀⡼⠁⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡼⠀⠀⠀⠀⠀⢸⡇⠀⢹⠒⠤⣤⣤⣤⠬⠟⠻⢤⣀⠀⠀⠀⢀⣠⡾⠁⠘⡆⠀⠀⠀⠀⢱⡀⢀⡴⠁⣠⠖⠒⢦⠀⠈⠉⠲⡶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡄⠀⠸⡆⢠⠿⣬⠇⠀⠀⠀⠀⠈⣿⢹⡏⠉⣸⠁⠀⠀⡇⠀⠀⠀⠀⠀⣇⠾⠴⠚⠁⠀⠀⠈⢇⠀⠹⣄⠙⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠚⠀⠉⠀⠀⠀⠀⠀⠀⠿⠟⣽⡴⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢷⢤⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣠⠔⠚⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠬⠷⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⣇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣸⡾⠔⠛⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢠⠃⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠞⠁⠀⠀⠀⢀⡤⠞⠓⠦⣄⡀⠀⠀⠀⢀⡇⠀⠀⡞⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠹⡄⠀⢀⡾⢤⡀⢰⣇⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡄⠈⣇⢀⣼⡇⠀⢹⣸⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡴⠛⣆⡽⠻⣼⠇⠀⢈⡿⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⠤⠼⠧⠤⠿⠤⠖⠛⠁⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣀⣀⣀⣀⣀⣀⡠⠴⠚⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠲⠤⢄⣀⣀⡤⠴⣯⣉⣉⣉⠭⠿⢛⢋⠁⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢾⡉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⢦⡀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠍⠉⠓⠚⠁⠀⣀⡤⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣤⣤⡚⠁⢀⣀⣀⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡏⠀⠀⣀⡠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠲⠶⠤⠤⣌⣉⠉⠀⠐⠒⠢⣄⣙⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣸⣷⣼⡧⡤⠄⠐⠛⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠋⠙⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⢰⡶⠾⠿⠿⠛⠛⠻⣿⠋⠀⠀⢸⡟⠉⠉⣭⣍⢹⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⣿⡀⠀⠀⠰⠿⠆⣠⡿⠀⠀⠀⠈⢷⣤⣀⣼⡿⠟⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠘⠿⣶⣤⣤⣶⠾⠟⠁⠀⠀⠀⠀⠀⠈⠉⣁⣀⣀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡶⠶⠶⠶⠶⠖⠛⠛⠛⠛⣿⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⣺⡇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⡇⠀⠀⠀⣤⡄⠀ ⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢠⡿⠁⠀⣠⣾⠏⠀⠀⠀⢀⣿⣇⠀ ⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠟⠁⣠⣾⠟⠁⠀⠀⠀⠀⣿⠉⣽⠂ ⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣹⣿⣴⡿⠋⠀⠀⢀⣠⣤⣶⣿⡽⠞⠁⠀ ⠀⠀⠀⠀⠀⣸⡿⠻⠿⢶⣶⣶⣶⣶⣶⠶⣛⣷⡾⠛⠉⣿⣁⣠⠴⢞⣫⡵⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⢀⣤⡴⠟⣋⣥⡶⠚⠋⠁⠀⠀⠀⣿⣋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⠀⠀⠐⣋⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Warning: This item may contain sensitive themes such as nudity.

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠎⠀⡘⠈⣁⠤⠒⠒⢲⡤⢄⠀⠀⠀⠀⠱⡀ ⠀⠀⠀⠀⠀⢸⠀⡾⠁⢩⠒⣆⠁⠙⠿⠷⠂⢠⡧⣿⡶⠵⣆⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⢨⡾⠁⡐⠘⢄⠈⠀⠈⠀⠀⠁⠘⣕⠠⠐⢠⠙⠃⠀⠀⢸ ⠀⠀⠀⠀⢰⠃⢐⠊⠀⠀⠀⠱⡀⠀⠀⠀⣠⡬⣄⠀⠀⡜⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠀⠀⠑⣄⠀⠞⠓⡈⡻⢀⠜⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⡇⠁⠒⠒⠒⠊⠁⠀⠀⠀⢀⣴⠮⠄ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡊⠀⢼⣀⣠⡴⠒⠉⠉⠆⠀⢀⣴⠟⢹⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⡐⠁⢀⠏⠀⠀⠀⠀⡠⠄⠀⡇⢼⠛⠓⠀⢸⠉⠀ ⠀⠀⣽⣧⣀⡧⡀⡜⠀⠠⡃⠀⠀⠀⠀⢰⠀⠀⢠⡷⢾⡿⡷⠀⢸⠀⠀ ⠀⠀⠷⢝⢮⣻⢞⠀⠀⠈⠉⠒⠤⢀⣀⡆⢀⠔⡕⠑⣫⠊⠉⠉⢹⠀⠀ ⠀⠀⠘⢖⣃⡀⢃⠑⠖⠠⠤⠀⠀⢀⠀⠈⠠⡬⠠⠜⢲⠃⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⢚⡛⠛⠒⣒⣠⣤⡤⠤⠤⢤⣴⠗⡒⠒⠚⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠳⡦⢄⡀⠐⠤⡀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⢷⣶⣶⡿⠯⠁⣹⢿⠀⠀⠈⢂⠈⠱⢄⠈⠑⣜⠐⡄⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠉⠉⠏⠀⣸⠀⢀⣀⣬⠦⠤⠤⢵⣄⡋⣧⣰⠀⢀⣠⣴⡶⠟⠛⠉ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣴⢿⠋⠋⠀⢰⠺⣿⡏⠈⠹⠿⡪⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠉⢸⠀⠀⣞⡵⢉⠆⣀⠔⠻⡀⠙⠁⠀⢀⠎⠀⠀⢀⠄⠀⠀⢀⠜ ⠀⢀⣀⠀⠀⠈⢹⣰⣾⣯⣿⢽⣤⣾⠶⣪⠧⠤⠀⠀⢈⡗⠒⠉⠀⠀⣠⡾⠑⠈ ⠀⠀⠀⠈⠁⠂⢌⡄⠙⢭⡹⡾⠤⠜⢻⠿⠭⠭⣉⣉⣾⠷⠶⠒⠚⠯⢓⡄⠀⠀ ⣀⣀⣀⣀⣀⡀⠤⠝⠒⠒⠚⠛⠓⠺⠥⠤⢤⡔⠚⠉⠉⣒⠢⣤⣤⠔⠛⠂⠀⠀ ⠀⠀⠠⠤⠄⠒⠂⠉⠉⠉⠉⠀⠐⠒⠂⠤⢀⣀⠈⠉⠚⠛⠁⠤⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠅⣒⠂⠠⠤⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠢⢄⡀⠈⠁⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠈⢆⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣟⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⡆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀ ⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠇⠀⠀ ⣿⣿⡿⠍⡀⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⣿⣿⣷⠀⠡⣠⠘⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⣤⡀⠀⠀⢸⢰⡂⠀⠀ ⣿⣿⣿⣇⠀⠹⡀⠱⠀⠀⠀⠀⣻⠿⠂⠁⠁⠪⠿⣥⡤⠀⠈⣆⠃⠀⠀ ⣿⣿⣿⣿⡆⠀⢃⠰⡀⠀⠉⢉⠖⠾⠪⢋⠁⠁⠁⠀⠀⠀⠀⢼⡄⠀⠀ ⣿⣿⣿⣿⣿⠀⠈⠀⢸⢂⠔⣽⢢⡀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢬⠇⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⡇⡆⡏⣘⠇⡾⡁⠀⠀⠀⠀⠀⠀⠀⡷⡆⢃⢋⡄⠀ ⣿⣿⣿⣿⣿⡇⠀⢠⠃⠁⠋⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠠⠙⡀⠂⢸⡄ ⣿⣿⣿⣿⣿⣇⠀⠘⠈⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡌⠀ ⣿⣿⣿⣿⣿⣿⠀⢸⠀⠐⡀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣤⡜⠀⠀⡸⡀⠀ ⣿⣿⣿⣿⠟⠁⠀⠈⢫⠉⡇⠀⠀⡈⣽⣿⡿⣿⣷⣌⡟⢁⠀⠀⠃⠈⡆ ⣿⣿⣿⣿⠀⠀⠀⠀⠈⡦⠁⠀⢀⣻⣿⣿⡇⣿⡿⠛⡱⢸⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠘⢷⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣾⣿⡟⠀⠈⠉⢹⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⠷⣾⣿⠁⢸⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣿⣿⡅⠀⠀⠀⠀⠀⢹⣿⣿⡟⠻⠿⠿⣿⣿⣿⣿⣿⣿⡄⣀⡄⠀⣾⠛⡆ ⠀⠀⠀⠀⠈⣿⠀⢸⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡷⣦⡟⠉⠁ ⠀⠀⠀⠀⠸⣿⠀⠀⢧⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⢡⠃⠀⠀⠀⠀⢸⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣖⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⠳⣄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⡞⠀⠀⠀⠀⠀⢾⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠟⠁⢠⡏⠀⢿⡞⢻⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⣀⣠⠴⢚⡟⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⣼⠇⠀⣼⢣⣼⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⠲⢤⣀⣀⣀⣀⣀⠤⠚⣹⡟⠀⡠⠃⣼⠋⠀⠀ ⢀⡀⠀⠀⠀⣿⣿⣿⣷⡄⠉⠐⠒⠂⠤⠀⠒⠊⠁⠀⠀⣀⣤⣶⡒⢢⣄⠀⠀⠀⠑⢄⡀⠀⠈⠉⠁⠀⠀⣰⣿⠀⠾⢧⡾⠃⠀⠀⠀ ⠈⢿⣦⡀⠀⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠈⠑⠒⠀⠄⣶⣾⠟⠛⠁⣴⡟⠁⠀⠀⠀⠀ ⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠛⠶⣶⣛⣛⢛⢿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣀⣤⣶⡾⢋⣯⣴⣶⡿⠑⢲⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⠛⠛⠛⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣷⡟⢽⣟⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⠒⠂⠤⠼⢿⡙⠛⡿⢿⣿⣿⣿⣿⣿⡿⠋⠙⠋⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣿⠀⠀⠀⢀⣄⡳⣾⠁⠀⠀⠉⢹⣿⣿⠇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠉⠉⠉⠉⣿⠀⠸⠛⢩⡿⠃⠈⣿⡀⠀⠀⠈⠯⢿⣿⣦⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠀⠀⠀⠀⣿⠀⠀⣠⡿⠃⠀⣼⣿⣿⡷⠶⠦⠤⠬⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⢶⡶⠟⠉⠁⠉⠙⠛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣫⡶⠋⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡠⠞⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣠⠤⠤⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣞⡵⠋⠀⢀⣴⣾⡿⠛⢆⠀⢸⡇⠀⢀⣠⠤⠶⠶⠦⢽⣷⠀⠀⠀⢠⠿⣆⠀⢶⡄⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠁⠀⣴⣿⣿⣿⣇⠀⣸⡀⢸⠁⠀⣀⣤⣶⣶⣶⣶⣤⣌⠳⣄⠀⡏⠀⠹⣇⠀⠉⠉⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⢸⢀⡾⠋⠘⣿⣿⣿⣿⣿⣿⣷⡀⢰⠇⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⢸⢻⣧⣄⠀⠉⠛⠻⣿⣿⣿⡿⣿⡾⠀⡔⠻⣦⢸⡈⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⠘⣆⠀⠀⠹⣿⣿⣿⣿⠿⠋⣠⠏⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣹⠇⣸⣀⣰⣿⡄⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⢠⡀⠀⠈⢦⣀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠙⢿⣇⠀⠀⠀⢀⣴⣿⡿⢠⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⢸⡇⠀⢀⣠⡬⠽⠶⠶⠿⠽⠯⠤⠤⠤⠤⠤⠤⣄⣉⣻⠶⠞⠛⠉⠀⡇⠸⣿⣿⣿⣿⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⣴⠃⠀⠀⣸⢳⣜⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠓⠦⣄⠀⢷⡀⠙⠿⠟⠁⢰⠃⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⢠⡏⠀⠻⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠤⠀⠀⠈⠙⠾⣿⣦⣀⣀⣴⡏⠀⠀⠀⠀⠀ ⠀⠀⣼⠀⠀⢠⡟⠁⠀⠀⠙⢦⠙⣟⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⡞⠀⠀⠀⠀⠀⠈⠳⣿⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠞⠛⡄⠀⠀⠀⠀⠀ ⠀⠀⡇⢀⡼⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣻⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣩⣿⡿⠛⠉⠀⠀⢳⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⣠⡶⠛⠁⢀⣿⡟⠀⠀⢶⣎⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⢷⢸⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⡼⣿⡇⠀⠀⢾⣧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⡞⠀⠀⠀⠀⠛⠛⠺⢧⡀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢻⡄⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⣸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠙⢦⡘⣇⠀⠀ ⠀⠀⠀⠈⢿⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢻⣙⣦⣀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢻⣿⡀⠀ ⠀⠀⠀⠀⠈⢦⠀⠹⣧⠀⠀⠀⠀⠀⠀⠰⠚⢢⣀⣽⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡄⠀ ⠀⠀⠀⠀⠀⠈⠳⡀⠹⣄⠀⠀⠀⠀⠀⠀⣀⣿⣿⣇⢠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠷⣦⡀⢠⡀⢀⣽⡟⢨⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⠿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠛⠛⠛⠿⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⡆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠻⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣅⣀⠀⢱⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡆⠀⠸⡅⠀⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣡⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⠘⢆⣣⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣀⠀⠀⣴⣶⣦⡄⠀⠀⠀⠀⢸⡁⠋⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠈⢿⡀⠀⢣⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡧⠖⠉⠉⠑⢦⣙⠿⠟⢁⣀⣀⠀⠀⠈⣷⡇⡗⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠇⠀⠀⡇⠀⠀⠀⣀⣠⣤⠰⠋⠁⠀⢀⣀⣀⣀⣀⡈⣉⠭⠽⠛⠁⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⠀⠰⡁⠀⠀⠀⠀⠀⢉⡽⢒⢟⠝⣩⠟⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠇⠀⠙⢆⣀⠀⠀⡠⣾⣀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡸⢹⣠⠊⣰⡟⢙⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠶⡖⢾⢷⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⢠⠃⣾⠁⢠⢻⠁⣸⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡀⠱⡀⢊⢳⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡇⢸⠀⡏⠀⣶⠎⢀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⣷⠀⢱⠈⠌⢧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠸⡄⠀⠀⠋⠀⠘⠟⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡇⠀⠃⠀⠘⣦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⠂⠀⠀⢰⠋⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠈⢆⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢠⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢀⡎⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⢀⢸⣄⣀⣀⣸⡄⠀⠀⠀⠀⢸⣤⣀⣀⣀⣀⣀⣤⣤⠔⢶⣾⣹⣿⠀⠀⠀⠀⢸⠙⢦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣧⠀⠈⡇⠀⠀⠀⠀⡜⢨⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⠏⢸⠀⠀⠀⠀⢸⠀⠀⢱⡀ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣆⢸⡇⠀⠀⠀⢸⠀⠀⢸⠁ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⣿⢸⡿⠛⣉⢠⠏⠘⣇⠀⠀⠀⠀⡇⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⣶⣶⣄⠤⢤⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⢸⠀⠈⢻⣿⣿⣿⠀⠀⠩⣵⣦⠀⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠉⠑⠢⠤⣤⣼⡄⠀⡎⠀⢻⣇⣧⠀⠀⠈⣦⣽⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⢀⠔⠉⡠⠒⠒⠒⠀⠙⢦⡀⣀⣀⣿⣿⣿⢻⠀⠀⠈⢻⠋⡇⣠⣼⣿⣿⡇⢀⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣉⠤⡍⠉⠁⠀⠈⠙⡄⠀⠀⠀⠀⣠⠟⠃⠀⠠⣤⣀⠙⢆⠀⠀⣠⣷⣿⡟⠉⢨⣿⠴⠿⠓⢿⣅⡉⠑⠒⠒⠚⠛⠻⡄⠀⠀⠀⠀⠀ ⠁⢀⣼⠇⡠⠋⠉⠙⠦⣈⣢⠀⢀⠜⠁⠀⠀⠀⣴⣿⠾⠷⠺⡶⠖⠛⠛⠻⣅⡴⢏⣡⣶⡦⠀⠈⠉⢣⣀⡠⠖⢢⣀⠀⢇⠀⠀⠀⠀⠀ ⠀⢾⠯⠚⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⢠⠟⣇⠀⠀⠀⢧⡀⠀⢀⡠⠏⠀⠈⠹⣿⣗⠀⠀⠀⢤⡏⠀⠀⡞⠀⠁⠸⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡾⠀⠸⠓⢢⣤⡤⠘⠛⠣⣄⣀⣀⣠⢴⠃⢸⠀⠀⠀⠈⠇⢀⠜⣠⠖⠀⢆⠀⢉⠲⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢿⠀⠀⢧⡞⠳⠃⠀⠀⠀⠀⣧⢧⢠⠃⠀⢸⡆⠀⠀⠀⢸⠈⠉⠁⠀⠀⠈⣄⠈⢦⡙⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⢀⡠⠤⠒⠢⠤⣀⠁⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠢⠄⠻⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡇⠀⡰⠋⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢸⠀⠀⠀⢀⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠸⣴⢁⣀⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡎⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⠔⠋⠁⠀⢈⣳⣄⡀⠀⠀⠀⠀⡇⠀⢰⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠔⠉⠀⠀⠈⢳⡀⠀⣰⣅⠀⣦⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡴⢂⠀⣇⡰⡇⠈⢧⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⢳⡏⢳⣇⣀⡼⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⠇⠉⠉⠉⠁⠀⣀⡠⠔⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠤⢤⣀⣠⡴⣮⣉⣉⣭⣟⣛⡉⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣰⡏⠀⠀⢸⣍⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⢓⡆⠀⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⠁⠀⠀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠅⢀⣀⣛⡓⠤⠖⠒⠪⣉⠒⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⣀⣿⣽⡯⠤⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣐⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣠⣴⣶⣾⡿⠿⠟⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⢀⣨⣴⣿⡿⠟⠛⠉⣻⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀⡟⢿⣿⡿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⡀⠀⠀⠀⠀⢸⠁⠈⣿⣿⡈⠙⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣤⣄⣘⣀⣀⣸⣿⣷⠀⠀⠈⠛⢿⣿⣦⡀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⡿⠿⠛⠀⠀⠀⠀⠀⠙⢿⣿⣿⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⣠⣾⣿⣋⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀ ⠀⢠⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧ ⢀⣾⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⣸⣿⠏⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⣶⡀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⠀⣸⣿⣿⣷⣤⣀⠉⠛⠷⣦⣤⣀⠀⠀⠀⠀⠙⠳⣤⣈⠉⠛⠛⠳⠶⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⣿⣿⠀⣿⣿⠛⠿⣿⣿⣿⣦⣄⠀⠉⠙⠛⠲⢶⣤⣤⣄⣈⣙⠳⣦⣄⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿ ⣿⣿⠀⠁⣯⠀⠀⠈⠙⠻⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣶⡆⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁ ⣿⣿⠀⠀⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⢠⡄⠀⢀⡄⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀ ⢸⣿⣧⠀⠘⣷⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣦⣸⡇⠀⣸⣅⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⢛⡿⢻⣷⠀⢸⣿⣿⣿⠦⠶⣤⡀⠀⠀⠀⣸⣿⡟⠀⠀ ⠈⢿⣿⣆⠀⠈⠻⣦⡀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠛⣿⣿⡇⢠⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠉⢀⢸⣿⠋⠀⠀⠀⠈⣿⠀⠀⣠⣿⡿⠁⠀⠀ ⠀⠘⣿⣿⡄⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⢀⣠⣴⠞⠁⠈⠁⠈⠁⠘⣧⡀⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⣼⡟⠀⣰⣿⣿⠁⠀⠀⠀ ⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣰⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠛⠁⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠷⠶⢦⣄⠀⠀⠀⠀⠀⠙⠷⣤⣠⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⢀⣠⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⠳⢦⣄⡀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣃⣤⣶⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⣽⡿⠟⠋⠉⠉⠈⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣀⣰⠾⠉⠙⣿⡙⣿⣿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠈ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡿⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠾⢛⣿⠏⠀⠀⠀⢸⣇⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣤⣤⣴⠞⠀⠀⠀⠀⠀⠀⢸⡿⠁⣸⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢿⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⠀⠀⠀⠈⠑⠂⠈⢃⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠀⠀⠘⢄⢠⣴⠾⠳⢄⠀⠀⠂⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣾⠃⠀⢠⡏⢀⣀⣤⡴⠶⠿⠗⠒⠛⠓⠲⠶⢾⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⠏⠀⣠⣿⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⣀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
If you'd like to report a bug or suggest a feature, you can provide feedback here. Here's our privacy policy. Thanks!
AI Story Generator - AI Chat - AI Image Generator Free