Spiders Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠆⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⢠⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⡤⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠁⠀⡖⠂⠀⢀⠖⡄⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠉⠀⠀⠀⠀⠱⡄⠀⠀⠐⠓⣄⠳⠯⡄⡎⠖⢃⡜⠂⠀⠀⢀⡖⠁⠀⠀⠐⠈⢀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠈⠀⠀⠈⠣⣆⠀⣈⣎⠓⠶⠆⠶⠞⢻⡎⠀⣄⡶⠋⢀⠀⠈⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⣄⡼⢦⡼⠋⠀⠠⣤⡤⠀⠈⢻⣴⠾⡀⣄⣁⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⣴⠇⠀⠉⠀⠀⠀⠈⠁⠀⣧⣤⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣄⣊⢙⡆⠀⠤⠀⠙⠀⠠⠄⢀⣟⢉⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⠀⠠⠀⠠⠠⠤⠄⠐⠈⠁⠀⡩⣏⣙⠦⣀⣀⣀⣀⣀⡠⢎⣙⠯⡀⠀⠉⠐⠀⠤⠤⠀⠀⠤⠌⠠⠆⢀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠉⢁⣾⠿⠋⢻⠛⠻⢷⡄⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠢⣄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡱⣤
⠀⠀⠀⣠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠀⠀⠐⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⡀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣧⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡊⣢⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠢⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠑⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡀⠀⠀⠀⠀⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⣀⠀⠀⠀⢀⣩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣈⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡙⢦⡀⡶⢖⠶⡄⣠⠞⣡⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣧⠙⢡⣾⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣄⣎⡻⢈⠸⢻⣇⡄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠋⠉⠀⢄⡨⠋⡄⢲⠀⡌⢫⣁⠀⠈⠉⠛⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⢀⣀⠄⠀⣅⠂⡡⢬⢄⠁⢈⡂⠀⢄⣀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣠⠟⠁⠀⢸⠄⣸⡄⢛⢠⣧⠁⡆⠀⠀⠙⢧⡀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⣏⠺⢵⢿⣇⠕⢫⠇⠀⠀⠀⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀⠘⢦⡀⠉⢄⡼⠋⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣟⣿⣻⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⣿⣟⣻⣟⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢾⣿⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣻⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡉⣸⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⢦⣥⣾⡇⠠⢀⠾⠟⠋⡤⢁⢴⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⢤⣴⡿⠀⠈⢁⡠⢄⠀⠀⡵⢦⢸⣾⢢⣀⣀⡀⠀⢀⡀⢀⠀⠔⢀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⢹⣏⢀⣚⠿⠗⠂⢰⡍⠀⠺⡃⠀⡇⢈⣿⣻⣿⣿⣿⣶⠃⠈⢀⣀⡠⣠⣾⣿⣿⡀⠀⠀⢀⡔⡋⠙⣿⣿⣀⡿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⡁⠀⠀⠀⠘⣿⠶⢊⡇⠀⣇⣾⣷⣿⣿⡟⣹⣿⣴⣷⣿⣾⣿⣿⣿⣿⣿⠃⣠⡖⣡⢊⣴⠖⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠁⢙⡏⠀⠢⡀⠀⢹⣿⣼⣳⣆⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡁⠈⢿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⢀⠤⠫⢀⣀⠉⣈⣶⢺⣦⣟⡩⢷⣷⣶⣬⣙⣿⣿⣿⣿⣿⣿⣿⡿⣛⠁⢾⣭⣶⣶⠏
⠀⠀⠀⠀⠀⠀⣠⡄⡸⡟⠁⠀⠀⠀⠉⢻⣟⣻⣾⣩⣟⣙⣼⣿⣧⣄⣽⣿⣎⢻⣿⣿⣿⡛⢚⡵⣣⡼⠁
⠀⠀⠀⠀⠀⢐⡁⠀⠟⠀⠀⠀⠀⢀⣠⣴⣿⣿⣏⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣏⡏⣸⣿⣿⣿⣿⣯⢶⣖⡀
⠀⠀⠀⠀⣠⠈⢾⠗⠀⠀⠀⢀⡠⠾⢛⣿⣧⡟⣛⠛⢿⣿⣷⣿⡏⣿⣜⣿⣯⡿⢋⣌⣽⣿⡿⣿⡃⢿⣍⠿⠓⠄
⠀⢀⣤⣄⣈⠘⠃⠀⠀⠀⣴⡉⠀⠔⣲⣿⣿⣿⣿⣿⣶⣤⣈⠻⣧⣼⣿⣿⠿⡓⣼⢿⣿⡯⣥⠿⠓⠈⠛⠆⣾⣿⢷⡄
⠐⠩⠷⠋⠀⠀⠀⠀⣰⠊⠐⢹⡆⠀⠛⠗⣿⣿⣿⣿⣟⣿⣿⣦⢾⡿⠛⠧⢸⣿⣯⠉⠙⠮⢴⣦⠀⠀⠀⠀⠙⣿⡟⠁
⠈⠁⠀⠀⠀⠀⠀⣮⡀⠀⣴⠟⡠⠾⢿⣷⠈⠭⢾⣳⣿⣤⣽⣿⣿⣻⣿⣷⡌⠙⠛⠦⣄⠀⣤⢾⢀⠀⠀⠀⠀⠈⢣⣾⣣
⠀⠀⠀⠀⠀⣰⢧⢠⣽⠆⠁⢾⣷⠄⠈⠀⠀⠀⠀⣁⡙⢛⣿⠏⠁⠉⢿⡿⠁⠀⠀⠀⠀⢈⣷⣼⣄⡀⠀⠀⠀⠀⢸⠿⠟⠆
⠀⠀⠀⠀⣴⡡⠀⣸⠋⢀⢦⡄⠁⠀⠀⠀⠀⠀⠰⠛⠗⢼⣿⢫⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠛⢀⠉⠇⠀⠀⠀⠀⠈⢤⣶⣶⢄
⠀⠀⠀⢠⠃⠁⢸⠃⠀⢈⡛⠀⠀⠀⠀⠀⠀⠀⠱⢴⡆⢨⡟⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⢿⡆⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⡐⢲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠁⢸⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⢸⠃
⠀⠀⢠⠛⠓⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠾⠀⡼⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠺
⠀⠀⣠⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⡿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢱⡄
⠀⢰⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠛⠁
⠀⠰⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡣
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⣻⣉⣝⣛⣟⢋⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠐⢀⣠⡄⠤⠴⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠔⠁⠀⣠⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠈⠀⠂⠂
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣂⢄⡀⡀⠀⢄⡀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣰⣾⣍⣹⣿⣿⣆⣱⡈⣦⠀⢉⣳⣤⠀⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠄⠂⢠⣾⣿⣵⠿⠻⣿⣿⣿⠛⣹⣽⣿⣿⣛⣿⣏⣽⣉⡀⢠⣶⢿⣿⠛⢦⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡴⠟⠉⠁⠀⠀⠀⠀⢰⢏⣽⣿⡿⠹⣿⣍⡀⣀⡀⣸⣟⠉⠁⣸⠂⠀⠀⠈⢣⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣺⣿⠏⠀⠀⠈⠙⠙⠋⠙⢏⢻⣆⠀⠁⠀⠀⠀⠀⠀⠙⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃

⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⡦⢤⣄⡀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⢠⢹⠆⠀⢸⠏⠀⠀⠀⠀⠀⠐⠒⠂⠉⠉⠀⠀⣀⣠⢴⢾⠀⠀⠈⠳⠄⣀⣀⣀⣀⣀⡤⣤⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⣏⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⢠⠏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⠈⠁⠀⠈⠀⠀⣀⡴⠖⠉⠉⠀⢀⣠⢴⠇⠀⠀⠀⠀⠢⢤⣀⣀⣀⡠⠊⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡆⠀⠀⣻⡷⡚⠁⠀⠀⠀⠒⠉⡉⠠⠁⠀⠀⠀⠀⠀⠀⠀⣈⢝⡟⠀⠀⠀⠈
⠀⠀⠈⠛⡓⠦⢤⣤⣇⣀⣈⣷⣼⣿⣄⣴⠏⠀⠈⠾⡉⠉⠉⠉⢀⡄⠀⠀⠀⠐⠦⣄⡠⠔⠉⠀⠘⠁
⠀⠀⠀⠀⠘⣆⠀⣀⣙⣿⣿⣿⣿⣿⣿⣯⡤⢴⠶⠓⠛⢯⣙⣉⠉⣄⠀⢱⣄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠾⢛⣿⣿⣿⣿⣿⣿⣿⠉⠁⠘⣗⠲⡶⢧⣤⣯⣭⣶⣪⣍⣀⣄⠀⠀⠰⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠋⠁⠀⠸⣿⣿⣿⣿⣿⡿⠙⣎⡆⠀⡸⠀⢈⠹⣽⠉⣤⢀⡁⢠⣜⠁⠈⠉⠉⠛⠛⠒⠒⠒⠒⠬⠷⠤⣄⣀⣀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⢸⠃⠀⣸⣷⡀⠀⠀⠈⣷⣁⠄⠈⠋⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⣾⠐⠁⠀⠀⠉⠀⠀⠀⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢀⡼⠁⣀⡤⠒⠉⣿⠉⠢⠀⠀⠀⠀⠘⣦⣠⠄⠀⠀⢈⡾⠁⠀⠀⠀⠀⠀⠀⠠⠤⣾⣇
⠀⠀⠀⠶⠿⠾⠯⠭⣄⠀⠁⡗⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠒⢤⣀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠇⠀⠀⠀⠘⡄⠀⠀⢀⠠⠤⠤⠤⣄⡀⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣌⡓⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠋⣰⠆⠀⠀⠀⠀⠀⠈⠙⢿⠃⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⣞⣡⠀⠀⠀⠀⠀⠀⠀⣀⠈⢧⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠻⡦⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⢱⢡⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡷⡀⠀⠀⠀⢠⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣱⠀⠀⠀⣾⢾⡃⠀⠀⠀⢀⣀⠀⠀⠀⢀⠏⡹⠀⠀⣼⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣤⣀⠘⢦⠳⡀⢠⡾⠋⠉⠙⢦⢀⣞⠜⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣌⢷⣹⣿⣠⣤⠤⠤⠬⠿⣎⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠡⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⠛⠢⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡏⢀⡏⠎⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⠱⡌⣄⠈⢿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡼⠀⢸⢻⡀⠀⢻⣆⠀⠀⠀⠀⠀⢀⡞⠀⠀⢻⠹⠂⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠈⣇⣣⠀⠀⠙⢷⣄⠀⠀⣠⠞⠀⠀⠀⢸⣸⡄⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢯⡣⡀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⡟⡜⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠊⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡻⣧⠀⠀⣤⣠⣠⡄⠀⣠⡿⣣⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣳⣤⡋⠶⠎⢣⣶⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⢿⣯⠠⢘⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠄⠸⢴⡧⠉⡰⡘⠡⣧⠽⠠⠴⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠀⠀⠠⠐⢤⠎⠐⡆⢹⠀⡔⠈⡦⡅⠀⠀⠀⠉⠃⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⣠⣤⠄⠀⠰⢈⢀⠤⢤⢤⠀⢁⣸⠀⠐⢬⣄⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⣧⠀⣭⡄⠛⠣⣽⡀⢸⡆⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⢸⠑⠭⡰⣿⢦⡭⠞⡿⠀⠀⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠀⠀⠀⠀⠀⢳⡀⠉⠒⡉⢄⡾⠁⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡿⠿⠿⠿⡿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⠿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⣦⠀⠀⠀⠀⠀⢠⡆⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⢻⣷⣄⠀⢿⣠⣤⠀⢠⣤⣸⠇⢀⣴⣿⠃⠀⠀⠀⠀⣀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠙⢿⣷⣼⣿⣿⣿⣿⣿⣿⣴⣿⠟⠁⠀⣀⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠛⠛⠉⠉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠈⠉⠙⠛⠿⢿⣶⣦⣄
⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⣤⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⢿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠠⠤⠄⠂⡀⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠆⠄⠀⠀⠀⠀⠀⢀⠀⣠
⠀⠀⠠⠄⡶⢀⡋⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⡸⢆⠀⠀⣀⠠⠊⠁⡜⠁
⠀⠀⢀⡔⠀⠠⢦⡀⠉⠉⠑⠒⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠉⠀⠀⠀⠀⠄⠈⣩⢁⣠⣴⣤⡎⢀⢂⡀⠀⠱⡀
⠀⠀⠀⣀⠈⠱⡄⠀⠑⠦⣄⡀⠀⡀⠀⠀⠀⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠃⠀⠉⠀⣠⠊⠙⠁⢢⡀⢀⠀⠐⠊⠲⣄
⠀⠀⠀⡀⢁⠀⠈⠢⠀⠀⠀⢉⠠⣤⡀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠠⠁⠀⠈⢾⠀⠁⠀⠀⡴⠊⠁⠈⠉⠂
⠀⠀⠀⡇⠀⠅⠀⠀⠁⢄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡔⠀⠢⡱⡅
⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠒⠒⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠣
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⢄⠀⠀⡇⠀⠄⡀⢀⢀⡀
⠀⠀⠀⠀⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢴⠒⠮⠀⠀⢊⣀⡈⢆⣠⠀⠠⡤⠒⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡄⠀⢈⣅⠀⠿⡿⣗⠀⢠⣄⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀⣤⠥⠚⠉⠁⠀⢠⡶⠞⠲⡁⢀⠀⠀⠀⠲⠦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠡⡌⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠅
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡉⢀
⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠈⢆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⡀⠀⠀⠋⠈⠀⢠
⠀⠀⠀⠀⢀⠀⠘⡄⠀⣀⠀⠀⢡⡢⠀⢀⠼⠁⠀⠁⠤⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢤⡀⢳⢠
⠀⠀⠀⠀⠄⠀⠀⢰⠀⠈⠈⠀⢂⠱⢦⠁⠔⠂⠊⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠤⠒⠒⠂⡈⢸⣗⠘
⠀⠀⠀⠀⠀⠤⠄⣀⠀⠤⠄⠀⠀⠈⠀⠙⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡈⠁⠀⠀⠀⠀⣀⠤⠈⠉⡴⢉⠈⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠑⡄⠀⠀⠔⠁⠀⡀⠤⠀⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠈⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⡀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠁⠀⠀⠀⠀⠀⡼⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠠⠠⠎⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⠂⠁⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣄⠀⣤⣆⠀⠀⠀⠀⣤⡄⠀⣠⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣦⠈⠟⢃⠀⠀⠘⠻⠁⣼⣷⠌
⠀⠀⢀⢠⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢈⣁⡇⠸⣟⣀⣀⣻⠇⢨⣌⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠈⠈⠛⠂⠉⠉⠘⠿⢯⣽⣶⣄⡀⢸⣿⣧⣶⣸⣿⣿⣇⣶⣾⣿⠇⢀⣤⣾⣯⠽⠿⠚⠉⠉⠘⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣅⣱⡀⣿⣽⣿⣿⣿⣿⣿⣿⣽⣿⢠⣎⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠰⣶⡍⠿⠛⠸⠿⢷⢿⡿⢟⣡⣘⠻⢿⣿⡽⠿⠇⠛⠿⢹⣶⠦⣄⡀
⠀⠀⠀⠀⠀⡠⢾⡿⠉⠁⠁⠀⠀⠀⠀⢀⣸⣧⣰⣿⣯⣽⣿⣂⣼⣅⠀⠀⠀⠀⠀⠉⠈⠙⢿⡷⢄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠻⠿⡿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣋⢭⣾⡿⠛⠀⠘⢇⠻⠿⣿⣷⡭⣙⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃⣾⣿⣷⡇⠀⣾⡇⠀⠘⣿⣿⣷⠘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡔⠰⣿⣿⠱⠠⠀⠙⣿⠀⠠⠈⣿⣿⠀⢂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⢿⣯⡦⠀⡀⢀⣿⠀⠀⢰⣿⡿⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⢿⣿⣦⡀⠉⠛⢁⣴⣿⡿⠁⠀⠀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠙⠻⢷⣾⣿⡿⠟⠋⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠉⠑⠲⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣻⣿⣇⣨⣿⣶⠀⠀⠀⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⡆⠈⣓⣪⡼⡛⣩⣄⠃⢄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡼⣷⣤⣨⣀⠘⣟⢁⣼⣃⣼⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⣿⣼⣿⣿⣷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣶⣄⡈⠻⣿⣿⣿⣿⣿⠟⠋⢀⣠⣤⣤⡴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣿⣿⣿⣷⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⣿⣾⢿⣿⣿⣿⢿⣿⣿⣶⣶⣾⠿⠿⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⣴⣿⣿⣿⣴⣾⣏⣽⢿⣶⣶⣶⣶⣄⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⢸⣿⠋⣿⡝⠛⢿⣏⣼⠂⠀⠀⠈⠉⠛⣷⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢹⣧⡀⠀⠀⠀⡀⡀⠀⠀⠀⣠⣿⠃⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠙⢿⣦⣀⣾⣷⣿⣆⣠⣾⠟⠁⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⡶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⣩⣽⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠙⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣴⡾⠟⠹⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⣶⣄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⢻⣆⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢿⠀⠀⠀⠀⠀⠙⢷⣦⣭⣭⣿⠟⠁⠀⠀⠀⠀⢸⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠄⠠⠄⠐⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡆⠀⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠛⡺⠀⠂⠠⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠴⠖⠂⠀⠀⠠⠤⠄⠋⠆⠀⠔⠘⠀⠀⡁
⠀⠀⠈⠀⠤⡉⠂⢄⣀⠀⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠀⠚⠐⢻⠿⠷⢐⠐⠂⠀⠀⢄⡀
⠀⠀⠀⠁⠀⠑⢄⠀⠈⠑⠀⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡐⠁⠀⢦⠈⠃⠀⠀⠄⠂⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠐⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⡔⠀⠀⠀⠀⠂⠀⠀⠀⠈⡄⠂⠀⢺
⠀⠀⠀⠀⠈⠆⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠒⠒⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠆
⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠢⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⡂⠀⠀⠤⠄⣡⣶⡀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠤⠖⠀⢙⣋⣧⡀⠓⠂⠀⢐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⡘⠉⠀⠑⢄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠱⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠘⠀⠂⠠
⠀⠀⠀⠀⠀⠈⠀⠠⣄⠀⠀⣼⠀⡀⠊⠀⡈⠔⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡱⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠳⢀⠈⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠐⠀⠘⠁⣉⠄⠨⠿⠈
⠀⠀⠀⠀⠀⠀⠂⢀⠋⠀⢀⡄⠀⠀⠁⢠⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠐⠁⠀⡘⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠂⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⣴⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠓⢀⣄⣀⣠⡤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠠
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⡀⠀⠀⠀⣀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⣜⠛⢿⣿⣟⡌⢣⠑⣄⠀⠙⢶⡀⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⡀⠀⣀⣤⣔⣢⣾⣿⣷⣷⣿⡿⢿⣿⣷⣾⡶⣴⣿⢻⡗⠂⠀⣀⣴⣾⡷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⡿⠛⠛⠉⠀⠈⠛⢻⡿⢲⣾⣿⢿⣿⠷⠋⠉⠛⢱⣶⠶⠛⠉⢯⠇⠀⠉⠻⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⡿⠋⠀⠻⠿⠷⠶⠶⢞⢿⣆⠀⠀⠋⠀⠀⠀⠀⠘⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠤⣄⣴⣶⣶⣄⢺⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡄⢰⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⣀⣸⣿⣿⣿⣿⣏⣾⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣾⣜⡁⠀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⢀⡾⠉⠙⣿⣿⣿⣿⣿⡷⠟⠙⠳⡄⠀⠀⢀⣠⠴⣾⣿⣿⣿⣿⣷⣛⣁⠀⠀⠀⠀⠀⣀⣠⢴⣶⡴⡀⡼⠁⠀⠀⢀⣠⠤⠒⠒⠉⠉
⠀⠈⢀⡶⠟⣿⣿⣿⣿⣿⡷⣦⡀⠀⠙⠤⢀⡾⠀⠀⣿⣿⣿⠟⠹⣆⠀⠈⠓⠦⡀⠀⠸⠁⠀⢃⣴⣷⣿⣿⣦⣴⠾⠭⠤⠴⠂⠀⠠⠄
⠀⢀⡞⠀⠀⣽⠉⡟⠋⠛⣇⠈⢿⡄⠀⠀⠘⠁⠀⠀⠀⣠⠟⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⢳
⠀⡞⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⢹⡆⠀⠳⡀
⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠛⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⣀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢹⡄⠀⠀⢰⠓⡀
⠀⠀⡰⢤⡈⣆⢰⣿⣿⣿⣆⢸⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣧⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⡇⠀⠀⡿⠀⢱⡀
⠀⠀⠁⠀⠹⣼⡸⣿⣿⣿⠏⣜⡼⠁⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⣈⢿⣿⣿⣿⠇⣀⡤⠤⢄⣀⡀⠄⠀⠀⠀⠀⢀⡿⣅⠠⣃⣄⡄⡇⢀⡽⣇
⠀⠀⠀⢀⡴⣾⣿⣿⣿⣿⣾⣿⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣿⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢈⣻⣿⣿⣿⣿⡋⢀⣼⠂
⠀⢀⠔⠁⠀⡇⢉⠟⠋⠙⢏⠀⡇⠈⠳⡀⠀⠀⠀⠀⠀⣠⠞⢋⡽⢿⣿⣿⠿⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠡⣿⣿⣿⡏⢹⠛⠁
⠀⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⣠⠞⠁⠀⣸⠃⠈⠀⠈⠀⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠻⣿⠟⠀⠘⡄
⠀⠁⠀⠀⠀⠹⡀⠀⠀⠀⠀⢀⠁⠀⠀⠸⠀⠀⠈⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⡠⠚⡟⢢⡀⠀⠀⠀⢠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣸⠀⠀⠀⣐⠁⠸⡿⠀⢑⠀⠀⠀⢸⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⢦⡀⠀⠹⣧⢨⣯⢠⡟⠁⠀⣠⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⢦⠀⢿⡘⡇⣸⠃⢠⠞⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣷⣼⣷⢴⣿⣴⣧⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⣀⡸⣿⠛⡉⠩⡙⢻⡿⣀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠾⠙⠛⠙⠉⠀⠙⠉⣹⣿⣟⡶⠰⣍⣿⣿⠋⠙⠁⠈⠉⠙⠛⠹⢆⣶⣄
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡾⣿⢛⡄⠀⣜⣻⡿⣾⠦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⡿⢃⢈⣿⣿⣸⣿⠏⢀⠻⣇⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡴⠂⢀⡾⢡⠃⣾⠉⠻⡿⠋⢺⠆⢣⠹⣆⠀⠢⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠀⠀⠀⢨⣿⠋⠀⠘⠀⠀⠀⠀⠘⠀⠈⢳⣯⠀⠀⠀⠈⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⡀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⡄⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⡀⠀⠀⠀⠀⠀⢸⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⡾⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢷⠀⠀⠀⠀⠀⡞⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣆⠀⠀⠀⠀⠀⣼⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣆⠀⠀⠀⢀⡇⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⡆⠀⠀⠀⠀⣿⢿⣟⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⠟⢠⠇⠀⠀⢀⣾⣄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣤⣀⠀⠀⠹⣆⠙⣆⠀⠀⢀⣶⡿⠟⠛⠛⢦⡄⠀⢀⡾⣠⠋⠀⢀⣠⢞⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⣝⡢⢄⠙⢧⡘⢧⢀⣾⠃⠀⠀⠀⠀⠀⠹⣄⡞⡰⠃⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⡚⢿⣌⣿⣏⣤⣶⠶⠶⠶⠶⠶⠿⢾⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣷⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣄⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⢩⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⡛⠷⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⡶⠁⢀⡞⢰⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⡆⠱⡀⠈⠻⣶⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠃⠀⣼⣃⠃⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠹⣄⣹⣄⠀⠘⣇⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⡏⠀⠀⣿⢻⡄⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢻⠁⢿⠀⠀⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⢹⡄⢧⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢸⡄⣼⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⣷⣼⣦⠀⠀⠀⠈⠻⣿⣦⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⣼⠧⣿⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⣌⢣⡀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⡟⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠴⠟⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣼⣧⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠓⣄⠀⠻⡟⣢⠀⠀⠀⠀⢀⡚⣿⠇⢀⡴⠻⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⣧⠀⠙⠋⢃⠀⠀⢀⠚⠛⠁⢀⣾⣿⡷
⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⣳⠠⣿⡞⠀⠀⠈⣿⡷⠀⡋⣉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠺⠭⢿⣿⡉⠻⠿⢾⢛⣿⣷⡶⣦⣄⣀⠀⠀⠘⣾⣿⣿⢀⡌⢿⣿⣿⣿⡞⣄⠘⣿⣿⡆⠀⠀⠀⣀⣤⡴⢶⣾⣿⣱⠾⠿⠏⣹⣿⡿⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠻⢿⣿⠷⣄⠀⢻⣿⣿⣿⣧⣞⣾⣿⣟⣦⣿⣿⣿⣿⠇⢀⡴⢾⡿⠿⠗⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣼⣆⢀⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣿⠀⣾⣄⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣾⢉⣿⣿⡿⣯⣿⣿⣿⡿⠿⣿⣿⣿⣯⡿⣿⣿⣮⢹⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠒⢶⣿⣄⠻⠛⠙⠒⠻⠿⣏⠻⡯⠿⢛⣀⣗⡘⠻⠿⡿⢇⡿⠿⠗⠚⠙⠻⢃⣼⣷⡖⢲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⡷⠛⠑⠈⠉⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀⢼⣟⣟⣉⣿⣿⠤⢀⣿⡁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠛⠻⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠣⠬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⢿⣿⣟⣍⠘⠛⣿⠛⣿⣿⣿⣯⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣅⠕⣴⣿⣿⠛⠁⠀⡈⠿⡄⠹⡿⢿⣿⣷⡜⢄⣩⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⢰⣿⣹⡧⣇⠀⠈⣼⣿⠈⠀⠈⣿⣿⣿⣿⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⢹⠀⣿⣿⡿⠿⡛⠀⠀⢾⣿⣄⠀⠀⠈⠿⣿⣿⡇⠸⡙⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⠁⠀⣿⣿⣗⠀⠃⠇⠀⠈⢸⣿⠀⠈⠂⢸⣿⣿⡇⠀⢱⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⢻⣿⣷⣶⠄⢀⠀⢀⣸⣇⠠⠁⠀⣾⣿⣿⠃⠀⠈⠿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣁⠄⠀⠀⠀⠻⣿⣿⣤⡀⠀⠉⠹⠟⠀⢠⣼⣿⣿⠃⠀⠀⠀⠄⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⡀⣦⣦⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠉⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠠⢴⣿⣿⠡⢻⣷⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⢔⣛⠿⠟⣲⡞⠿⠟⠦⡀⠀⠀⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣆⠀⣸⡇⠀⠈⣭⣵⢶⢈⣁⣴⣴⣈⠀⢢⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣹⣷⣦⣄⣀⡀⠀⢿⢟⠁⣠⡝⢁⣈⠃⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣧⣯⣇⣠⣿⢙⣿⣿⣿⣯⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠦⣤⣤⢀⣀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣦⣄⠘⠿⣿⣿⣿⣿⣿⣿⣟⠁⢀⣀⣤⣶⣶⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢾⣿⣿⡟⣿⣿⣿⣿⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣷⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣴⣶⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⠔⠉⠉⠉⠉⠛⠋⣩⣿⣿⣿⡟⣃⣿⣿⡿⣿⣟⣛⣛⣉⣉⡉⠉⠉⠉⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣾⣿⡿⡽⣿⣷⣿⣿⣧⣶⡟⠿⠿⢿⣿⣿⣿⣷⣆⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢰⣯⣭⠛⠛⣿⣋⣠⡿⠀⠀⠀⠀⠀⠉⠙⢻⣧⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠙⠃⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠄⠀⠀⠀⠀⠀⠀⢀⡤⠊⣉⠿⣍⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⢀⠞⠀⣻⡷⠀⢻⣇⠀⠱⡄⠀⠀⠀⠀⠀⠰⣾
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⢦⠀⠀⠀⠀⡾⠀⠸⣷⣿⠀⢸⣿⡇⠀⢻⡀⠀⠀⠀⠀⢤⡏⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠘⢴⠄⠀⠀⠀⠀⠀⠀⠈⠣⣽⠤⡀⠀⡇⠀⠰⣏⣥⠄⢁⣚⠿⠀⣸⡇⠀⣀⡄⢒⡼⠁⠀⠀⠀⠀⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡦⡀⠀⠀⠀⠀⠀⠈⠢⡈⠛⣏⡀⢰⣭⡿⠃⠸⢶⡄⢀⣿⠖⢋⡿⠟⠋⠀⠀⠀⠀⠀⢴⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡐⠄⡀⠀⠀⠀⠀⠈⠑⠿⣷⣄⣠⣶⡆⣠⣶⣶⣶⠿⠚⠉⠀⠀⠀⠀⣀⣤⣀⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣬⠁⢤⣤⠖⠀⢲⣶⣲⣿⡟⠛⣿⠿⠙⢿⣍⡯⣭⣏⣉⣿⣏⣏⡭⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⢉⡅⣾⣿⣧⢐⢻⣄⣀⣾⣟⣷⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⢉⣴⢟⡴⣿⢩⡧⣝⢻⣿⣟⣪⡻⣄⢑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣭⠴⢣⠋⡼⠁⡼⠶⣃⣷⠞⡇⠙⣆⠐⢆⠙⠻⣕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⠔⠁⢀⣮⡾⠁⠀⢓⡀⠀⠀⢰⡃⠀⠈⠱⣏⡣⠀⠈⠳⣬⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡜⠁⠀⢠⢆⡜⠁⠀⠀⠀⠃⠀⠀⠚⠀⠀⠀⠀⠈⠳⣜⢄⠀⠀⠙⠦⣕⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠉⠀⠀⠀⢂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡗⡀⠀⠀⠈⠳⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡺⠋⠀⠀⠀⢀⢾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⣄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡴⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⠀⠀⠀⢠⠞⢥⣖⠙⣦⠈⠣⡀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⡄⠀⠀⠀⢀⠃⢠⣾⣯⠀⣼⣷⠀⢹⡄⠀⠀⠀⠀⣈⡏⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠘⢆⣄⠀⠀⠀⠀⠀⠀⠹⣑⣄⡀⠀⢼⠀⢀⡿⣛⡀⢊⣿⡆⠀⡇⠀⠀⠀⡠⢹⠁⠀⠀⠀⠀⠀⢰⡶⠁
⠀⠀⠀⠀⠀⠀⠑⢄⣄⠀⠀⠀⠀⠀⠈⠣⡀⠲⣿⠀⢠⣛⣿⠀⢻⣅⡀⢰⣧⠔⢺⡷⠞⠁⠀⠀⠀⠀⣴⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⡠⠄⠀⠀⠀⠀⠈⠒⠾⣷⣌⢩⣤⠄⣠⣬⣵⣿⠷⠒⠉⠀⠀⠀⢀⣠⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣭⠠⣤⣤⠄⠠⣤⣌⣿⡟⠛⣿⡟⠻⣿⣱⣴⣏⣈⣿⣏⣞⣩⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢈⡭⢺⣿⣧⢐⣻⣄⣰⣿⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢴⠟⡱⣿⠹⡧⡏⣿⣿⡓⢝⠧⣈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢿⠴⢋⠎⡸⠁⡞⠻⠭⠗⢻⠌⠻⣄⢡⡈⠙⢯⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⡶⠁⢀⠾⡾⠁⠀⠩⡄⠀⠀⣬⠁⠀⠈⠻⣍⢀⠀⠙⢦⣰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡼⠋⠀⠀⠎⡜⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢶⠑⡀⠀⠈⠓⢵⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬⠋⠀⠀⠀⣈⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣭⡄⠀⠀⠀⠙⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠈⠙⣾⣿⣿⣧⣏⣤⢤⠀⠀⠀⠀⠀⠐⠚⠉⢇⡇⡜⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠇
⠀⢀⡖⠻⣿⣿⣿⣿⣿⡵⠚⢦⡀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣴⡊⠉⠁⠀⠀⠀⢀⣠⣤⣣⢀⡎⠀⠀⠀⣀⡠⠤⠔⠒⠊⠉⠉
⠀⠈⣠⠶⢻⣿⣿⣿⣿⢦⣄⠀⠹⠄⢠⠏⠀⢿⣿⣿⠟⢯⠉⠉⠲⠄⠀⠀⠎⠁⢊⣼⣿⣾⣦⣤⡶⠯⠡⠤
⠀⢠⠏⠀⣸⠋⡟⠋⢻⡀⠻⣆⠀⠀⠋⠀⠀⢀⡰⠏⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠳⡀
⠀⠇⠀⠀⣿⠀⠇⠀⢸⡇⠀⢻⡀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⡗⠀⠙⡄
⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⢧⠀⠀⢀⡧
⠀⠀⡤⡀⢢⢠⣶⣿⣶⡀⡆⠠⠆⠀⠀⠀⠀⠀⠀⠀⠈⣣⣾⣿⣦⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢸⠀⠀⢸⠁⢡
⠀⠀⠀⠈⢾⡾⣿⣿⡿⢳⡰⠁⠀⠀⠀⠀⠀⠀⠢⠤⣄⡹⣿⣿⣿⢇⣠⠤⠤⠤⠀⠄⠀⠀⠀⢀⡿⢅⢸⣠⣤⢸⢀⡽⡇
⠀⠀⢀⠴⣲⢿⣿⣿⣿⡿⣶⢢⡀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣨⢽⣿⣿⣿⣏⣠⠞
⠀⡰⠁⠀⣇⠀⠋⠀⠈⠀⣿⠀⠙⡄⠀⠀⠀⢀⠴⠋⢰⠋⠟⠻⠟⡇⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢸⣿⣿⡇⢸⠁
⠀⠃⠀⠀⢹⠀⠀⠀⠀⠀⠈⠀⠀⢃⠀⠀⠐⠁⠀⢠⠋⠀⠀⠀⠀⠃⠀⠈⠒⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠙⠋⠀⠀⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⢸⡀⠀⠀⠀⠀⢀⡇⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠀⠀⠀⠈⢿⣷⡄⠸⣷⣶⣄⣠⣶⣾⠇⢠⣾⡿⠁⠀⠀⠀⣀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⣀⡙⢻⣶⣿⣿⣿⣿⣿⣿⣶⡟⢋⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⢷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠁⠀⠀⠀⢀⣴⣾⠟⢿⣿⣿⣿⣿⣿⣿⣟⡻⣷⣦⡀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠻⣷⣄⠀⠀⣠⣆⣦⡀⠀⢀⣴⡿⠃⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⠈⢻⣷⣴⣿⣿⣿⣷⣴⣿⠋⢀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⣠⣴⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣴⡿⠟⠉⢹⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠿⣷⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⠈⢿⣄⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡇⠀⠀⠀⠀⠈⠻⢷⣦⣬⣭⣿⠟⠋⠀⠀⠀⠀⠀⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃

⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢲
⠀⠀⠀⠀⠀⠀⢰⠋⢫⡙⠒⣴⠁⠀⠀⠀⠀⠀⠠⠤⠔⠒⠋⠉⣀⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⠏⠁⠀⠀⠀⠉⠉⠉⠉⣉⢽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠙⠉⠉⠁⢀⣠⠔⠂⠀⠀⣀⠴⠆⠀⠀⠀⠠⢄⣀⣀⡠⠚⠁⠘
⠀⠀⣀⡀⠀⠀⠀⠀⢹⡄⣿⠀⠀⣹⠿⡋⢀⣀⣀⣈⠉⠠⠀⠀⠀⠀⠀⠀⢀⠌⣿⠁
⠀⠀⠈⠩⡓⠒⠾⣦⣤⣿⣿⣷⣴⠇⠀⣈⣣⣀⢀⡤⠔⠀⢀⠀⠈⡲⠖⠊⠀⠀⠁
⠀⠀⠀⠀⣱⣴⣶⣾⣿⣿⣿⡟⠟⠻⡝⣁⣤⢘⣖⣶⡘⠦⠘⡓⠉⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠰⠊⠁⢸⣿⣿⣿⣿⡟⢧⣂⠀⣱⠈⠓⣿⠟⡉⠙⢉⣱⠃⠐⠒⠓⠂⠠⠤⠤⢼⣦⣀⣀⠈⠳⡄
⠀⠀⠀⠀⠀⠈⠛⠛⠋⢹⠃⢀⣷⡄⠀⠀⢱⣍⠀⠑⠉⠀⠀⠀⣠⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⡄⠀⠀⢀⣾⣈⠀⠀⠈⠀⡀⠘⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⣠⣎⡤⠴⠈⠀⡟⠈⠀⠀⠀⠀⢸⡶⠂⠀⠀⢺⠁⠀⠀⠀⠀⠀⠒⢚⠿⠦⣀⠀⠀⠀⡀
⠀⠀⠈⠉⠉⠉⠉⠂⠀⡄⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠲⣄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⠄⠀⠀⠀⠈⠙⢾⡏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠺⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢀⣜⡡⠀⠀⠀⠀⠀⢀⡀⢣⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣬⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢉⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢜⠶⣾⡅⠀⠞⠋⠁⠂⠺⠓⠢
⠀⠀⠀⠀⠀⠀⣤⠒⣦⠀⢹⣿⡅⢀⠐⠉⡆⠀⠏⢷⣿⣵⣶⣆⡄⠐⠀⠂⢁⣤⣶⠀⠀⠀⢀⠄⢴⣶⠀⣦⡏
⠀⠀⠀⠀⠀⠀⠉⠑⠋⠒⠉⠀⠀⠘⡷⠆⡃⢀⡄⣿⣾⣿⢟⣿⣤⣶⣾⣿⣿⣿⣿⠇⣠⢒⢗⡤⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠠⠐⠋⢈⠇⠀⡢⡀⢹⢷⣿⣦⡭⢽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠉⠈⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢻⡦⠔⠉⠀⠤⣴⣿⣹⢿⢵⢻⣿⡛⢺⣿⢿⣿⣿⣿⣿⢇⡀⡳⠛⠛⠁
⠀⠀⠀⠀⠐⠉⠾⠁⠀⠀⠀⢀⣽⣾⣟⣿⣿⣿⣯⣿⣿⣿⣷⠛⣹⣿⣶⣿⣟⣥
⠀⠀⠀⢠⢩⠗⠀⠀⢀⡀⠾⠻⣷⣟⣛⠻⢿⣶⣿⢻⣟⣿⣽⢟⣍⣿⡿⣿⡳⣯⡹⠒⡀
⢀⢴⣦⠄⠊⠀⠀⡀⠪⡀⠊⣾⣿⣿⣿⣿⣷⣬⠹⣾⣿⡟⣻⣽⣿⣿⢒⠚⠁⠈⠓⢾⣿⣧
⠀⠈⠁⠀⠀⢠⠚⠀⣠⠇⣠⣤⡘⣿⣿⣿⣛⣻⣿⣿⣤⣅⠻⠿⣄⠀⢈⣻⠀⠀⠀⠈⠻⣡⣄
⠀⠀⠀⠀⡰⡈⣵⠆⠡⣶⠄⠊⠀⠀⠈⣙⠿⣿⠛⠉⢿⡿⠀⠀⠈⠁⣺⣴⣄⠀⠀⠀⠀⠿⠿
⠀⠀⠀⡼⠄⣠⠋⢠⡶⠀⠀⠀⠀⠀⠐⠙⠸⣿⢽⣷⠃⠀⠀⠀⠀⠀⢘⣀⣉⠀⠀⠀⠀⠑⢶⣶
⠀⠀⢰⣁⡀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠻⠀⠇⠀⠛⠀⠀⠀⠀⠀⠀⢸⡧⢻
⠀⠀⠼⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡇⢨⢶⢦⠀⠀⠀⠀⠀⠀⠀⠞⠻⠜
⠀⢀⣄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡯⡾⠀⠀⠀⠀⠀⠀⠀⣻⢓⡄
⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⣁⣉
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣷⡆⠀⠀⠀⠀⠀⠀⠀⢠⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⣿⣿⠟⠿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣋⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣶⣿⡆⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⢀⣾⣰⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠛⠀⠀⠙⣿⣃⣀⠀⠀⠀⠀⠀⠌⣉⡋⠀⣀⠚⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣌⣧⡄⠀⠘⣏⣈⠠⠀⠀⠀⣘⠁⢛⠁⢰⡇⢠⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠛⣛⡄⠀⠙⣿⣏⠀⠀⠀⢸⣶⣿⣠⣺⡿⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⣾⣷⡽⠀⣤⣶⣆⢷⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠦⣄⠀⠀⠀⣿⣿⡇⠈⣿⣿⣵⣶⣿⣿⣿⣼⣿⡏⣾⣿⣿⠃⠀⢀⡀⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡾⣧⡿⢷⣾⣿⡷⢀⠀⠸⣿⡻⣾⡟⠛⠉⠁⠁⠉⠉⠻⣿⣿⣿⡿⢋⣴⣶⣿⣿⡾⠻⠏⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠨⠿⠋⠀⠀⠉⣭⣥⣾⣧⣀⣻⠿⢋⠈⣠⣴⣾⣿⣿⣷⣦⣄⠈⣿⣧⣼⣿⣿⡿⠋⠀⠀⠀⠘⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣧⡶⢀⣾⣿⣿⣿⣿⣷⣿⣽⡿⣆⠁⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠟⢹⡦⣿⣿⣿⣿⣿⣿⣿⣿⣳⡟⢼⣆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⣈⣷⢘⡀⢻⣿⣻⣾⣿⣿⣿⡟⣿⣇⡋⢼⣧⣚⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⢠⣿⣿⣿⣿⣈⣅⠀⢘⠛⢫⣱⣦⣍⠀⢥⡤⠻⣿⡿⠿⠻⣾⣦⡀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡾⠛⠉⠉⣡⣴⣿⣿⡁⡈⣶⣿⣿⣮⡛⠛⢠⣶⣾⣿⣿⣤⡀⠀⠉⠒⢿⣧⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⣿⠏⠀⠀⢠⣾⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⣿⣧⠹⡄⠀⠀⠀⠉⠛⣿⣧⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⢻⡟⠀⠀⠀⢀⣤⡘⢿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⠿⣿⣧⣆⠀⠀⠀⠀⠈⠙⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠋⠁⠀⠀⢠⡏⠼⡿⠀⠀⣾⣿⣿⣿⣿⡿⠛⠁⠘⣽⢻⣿⣿⣿⣧⠀⢻⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠁⠀⣴⠁⠀⢠⣿⣿⣿⣿⢻⣧⠾⠀⠦⠀⣿⣿⣿⣿⣿⠀⠀⠻⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡴⠁⠀⠀⠀⣿⣿⣿⣿⣾⣧⣄⡄⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢹⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣰⣆⣴⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠜⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣯⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⣷⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⢿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛



⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣝⣭⣭⣥⣭⣽⣯⣍⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣯⣿⣿⣿⣭⣽⣯⣭⣿⣭⣭⣿

⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠐⡀⠂⢀⠀⢀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠄⢁⠀⠀⠀⠀⠂⠂⡀⠀⠂⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠁⠀⠉⠄⠀⡄⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⡀⠈⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠄⠀⣉⣀⣀⣀⠀⠀⠀⠄⠐⠊⠁⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡗⠀⠀⠀⢶⣄⠀⠀⠀⠀⢠⡄⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⡀⠘⠁⠀⠀⠀⠀⡋⢀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣾⡦⣤⣤⢰⣿⣾⣽⡇⠀⠀⠀⠀⣀⡀⠤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⡶⠢⠶⠶⠄⠀⢀⣀⠘⣿⣿⡿⢞⣉⣛⡺⢿⣿⣿⠀⣤⣦⠄⠀⠋⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡙⣌⣿⣿⣷⣿⣿⣮⠙⣇⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⢹⣿⣿⣿⣿⣿⣿⡇⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣲⣲⣶⣾⡷⢿⣿⢿⣿⣿⡿⢳⣿⣿⡿⠅⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠙⠋⠉⠁⠈⠉⠉⠉⣣⣤⣅⣚⢛⣉⣡⣯⡁⠀⠀⠀⠀⠉⠂⠺⢗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢡⣾⣿⣿⠉⠍⠿⣿⣿⣎⢻⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⠁⠀⠀⠀⠀⠈⢻⣿⡄⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠃⢨⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⡇⠀⠀⢿⣿⣧⡀⠀⠀⠀⢠⣾⣿⠁⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠻⣿⣿⣿⣷⣶⣿⠟⠁⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠙⠟⠛⠋⠁⠀⠀⠀⠀⠀⢈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⣼⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡄⠀⠀⠀⠀⠀⠀⠀⢦
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠷⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⣧⡀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠘⡟⠑⠄⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠔⠙⠛
⠀⠀⢣⠀⠈⢢⠀⠀⠀⠀⠸⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠸⠀⠀⠀⠀⢠⠊⠀⢀⠂
⠀⠀⠀⠣⡀⠀⠡⡀⠀⠀⠀⢣⠀⠀⢳⡀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠠⠁⠀⢠⠃⠀⠀⠀⡰⠁⠀⡠⠃
⠀⠀⠀⠀⠙⢄⠀⠑⡀⠀⠀⠀⢂⠀⠀⠷⠀⠀⠀⣚⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡇⠀⠀⠀⠂⠀⢀⠂⠀⠀⠀⡐⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠑⣄⠜⢃⠀⠀⠀⠆⠀⢐⠀⠀⠀⠈⠻⣆⢠⠖⢤⡀⣠⠔⢦⢀⡾⠋⠀⠀⠀⢀⠀⠀⡎⠀⠀⢀⠛⢄⡀⠁
⢲⡀⠀⠀⠀⠀⠀⢡⠀⠈⠄⠀⠀⢸⣤⠿⠳⣄⣠⠴⠲⠾⣿⣀⡀⢸⠁⣀⣨⡿⠶⠲⢦⣀⡴⠻⠧⣴⠀⠀⠀⠈⠀⢠⠁⠀⠀⠀⠀⠀⣰
⠈⢿⣆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⢦⣠⠀⢀⣠⠤⣈⡔⡩⠀⠙⣆⡞⠁⠨⡑⣌⠠⢠⣀⡀⢠⣠⠎⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢀⣾⠏
⠀⠀⢿⢧⡀⠀⠀⠀⠈⢂⣀⣿⠑⠒⠲⠾⠯⠶⠠⢀⠎⠌⠀⠀⠀⣿⡇⠀⠀⠈⠌⢆⠠⠰⠿⠿⠶⠒⠒⢹⣇⣀⠊⠀⠀⠀⠀⢠⣺⠏
⠀⠀⠀⠙⠷⣄⣀⠀⠀⠈⠣⢄⣀⣠⣀⣤⣄⢠⣄⣈⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⠀⢈⣀⣤⣀⣠⣀⣀⣀⣀⠴⠋⠀⠀⢀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠛⢥⣉⡀⠂⠠⠄⠀⣄⣠⡤⠔⠈⠉⣉⣦⣀⣀⣤⣴⣾⣶⣤⣄⣀⣠⣞⡉⠉⠐⠤⢤⣄⡄⠀⠤⠀⠂⣈⣠⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠠⣜⠀⢀⣠⡴⣻⠟⣩⢛⡿⣹⠋⣀⡈⢫⡹⣟⢫⡙⢿⡳⣤⣀⢀⣘⡤⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠴⢉⡾⠁⠄⢧⠸⠀⣇⠰⡁⡱⢀⡇⡸⢀⠇⠄⠹⣎⠱⢌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢠⣿⠁⣰⢆⠘⡄⠱⡘⣆⠁⢡⡎⡰⠁⠘⠀⢶⠀⢹⣧⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠘⣆⠈⣡⠔⣁⠄⣴⠏⣈⡈⠣⡐⢄⠰⢤⡉⢀⠎⢘⡇⠀⠀⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠆⢿⢠⠞⠀⢧⡰⣅⠀⡇⠸⣅⡽⠀⡷⠀⡵⣠⠏⠘⢦⢸⠇⢆⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⢠⠎⠀⠘⣧⠀⣲⡄⢱⠈⢃⠹⡄⠠⠀⡜⢡⠂⢰⠁⢴⡦⢠⡟⠀⠈⢦⠀⠀⡠⢔
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡸⠚⠁⠀⠀⠀⠈⠣⣈⠀⠘⣇⠹⡄⡧⡂⠲⡇⣼⣁⡜⠀⠀⠠⠋⠀⠀⠀⠀⠉⠺⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠭⢷⡀⣴⠿⠍⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶
⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧
⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠄
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⡴⢀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡀⢮⡤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠀⠀⠈⠣⠘⡇⠀⢠⠖⠁⠀⠀⠀⠈⠲⣄⠀⢸⠃⡜⠁⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠢⠡⣴⣇⣀⣀⣴⡒⣦⣀⣀⣸⣦⡌⠔⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣑⢚⠀⠠⣤⠀⠐⠀⡄⠀⠹⣿⣿⡴⡶⠛⢷⢦⣿⣿⠏⠀⢁⠀⠂⠀⣤⠄⠀⢓⣊⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁⠐⠿⠁⡀⢴⡶⠀⠰⠈⣀⣁⠴⠚⢀⠀⠊⠀⠑⠀⡀⠋⠢⣈⣀⠁⠦⠀⢺⡦⢀⠨⡿⠃⠈⠐⠀⢠⡀
⠀⠀⠀⠀⠀⠀⣡⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠇⠀⠀⠉⢀⠈⢉⠀⠐⣶⠒⠀⡍⠁⡀⠉⡀⠀⠸⠂⠀⠁⠀⠂⠀⠀⠀⠀⠀⠘⣌
⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠲⣸⢃⢀⡀⠀⠀⠀⣿⠀⠀⠀⠀⡄⠘⢋⠰⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀
⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⠃⠐⠀⢀⣿⡃⠀⠀⠐⡿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡄⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠁⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠛⠀⠛⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⢸⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠱⡄⠀⢀⠏⡸⠀⢀⣀⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠒⢒⡊⠐⠲⢄⠈⣆⠸⡄⡎⢠⣣⠖⠁⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠓⠒⠒⠋⠉⠉⠉⠉⠱⣄⠑⣼⠀⠷⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⣀⡼⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢂⣀⠤⣈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣀⣀⡀⠀⠄⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠈⠑⢌⡒⢢
⠀⠀⠀⠀⠀⠀⢀⠔⣡⠚⢉⢞⠭⠴⡆⠀⢁⢀⣀⡀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠞⡞⠁⡰⡻⠁⠀⢀⡟⠀⠀⣀⣀⣀⣀⣅⠀⡗⠒⢲⡀⡇
⠀⠀⠀⠀⣔⢃⠜⠀⠘⠊⠀⠀⢀⢎⡼⢀⠎⠀⠀⠈⠀⢹⠀⢣⠀⠀⢇⠸⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡜⣸⡃⣸⠀⠀⠀⠀⠀⠘⡆⠸⡀⠀⠘⣄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠵⢻⠀⡟⠀⠀⠀⠀⠀⠀⢳⠀⢇⠀⠀⠈⠢⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⠇⠀⠀⠀⠀⠀⠀⠈⡆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⢈⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣿⠇⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⣦⡀⠀⢰⣿⠀⢼⢁⣤⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠠⡀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠈⣿⡇⡹⣂⣽⣄⠀⠀⣄⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣶⣦⡤⢄⣀⠀⠀⠉⠻⣦⣸⣿⣿⣻⣿⣿⡗⣘⣛⣀⠞⢁⣴⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠛⠿⣷⣶⣤⣈⢿⣿⣿⣿⣿⣿⣿⣮⣭⡒⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⡶⡶⠿⠿⠿⢿⣿⣿⣿⣿⡟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡄⠸⠛⠋⠉⢩⡾⣟⣄⣀⣼⣿⣷⣾⣿⣿⣿⡛⠛⠿⢶⣶⣆⠤⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣿⣿⣄⠀⠀⠀⠉⠒⠛⠛⠛⠓⠚⠳⠲
⠀⠀⠀⠀⠀⣼⡗⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⣡⡀⠀⠀⠀⡜⣿⣿⣿⣯⢿⣦
⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⡙⡛⣶⣦⠐⣷⣿⣿⣿⢿⡞⣿⣧
⠀⠀⢀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⡙⢣⣤⣬⣴⣿⣿⡿⠃⠸⣿⡸⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢟⠙⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⣾⡗⠀⠀⠙⠿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢯⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⣀⡤⠶⠖⠒⢶⣦⡀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠜⣆⠀⣰⡟⠀⠀⠀⠀⠀⠈⢻⡆⢀⡼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⣤⣿⣿⠂⢾⡄⣿⡀⠀⣀⣬⣷⡄⠀⢠⣿⣾⣿⡟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⣷⣻⣿⣿⣾⣿⣷⣹⣟⣀⣘⣟⡟⠋⠀⢻⣿⣿⡟⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣿⠋⢻⣿⣿⣿⣿⣿⡿⠏⢀⠉⡿⠉⠉⢜⣻⣿⣿⠁⠀⠈⣿⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣤⡌⠉⣽⣿⣿⣿⢁⡔⣡⣖⣟⠢⡘⣆⢙⠛⠉⣷⡶⣺⣭⣿⡿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⣿⠿⣿⣶⢳⣿⣿⣿⣿⣿⣾⣯⣿⣿⣯⣿⣾⣿⣧⠰⣿⡿⢿⣿⢙⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣿⠀⣿⣿⣾⠋⠉⠉⠋⣹⣿⠿⣿⡿⠟⣽⣿⠛⢻⡜⣿⡇⢸⣿⣾⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠃⢀⡿⠿⣏⠀⠀⠀⢰⣿⣿⡰⣾⣇⠀⣿⣿⡆⠀⣿⣿⡇⠈⢿⣿⡿⣷⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠤⠿⣿⡼⡄⠈⣿⣿⣏⠀⠀⠀⠸⡛⣏⠙⠉⠈⢻⣿⣿⠃⢸⣿⡁⡇⠀⠈⢻⣿⢻⠀⠻⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⢿⡇⣯⠀⠀⠀⠀⣿⣯⠀⠀⠀⠘⣿⣧⠀⢸⣿⣷⡇⠀⠀⠈⣿⣿⡃⠀⠰⣮⡻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⡆⢸⣧⣿⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣿⢿⠀⢸⣿⣿⠁⠀⠀⠀⢸⡿⣷⡄⠀⠀⠙⢧⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⠇⠀⣟⣿⣇⠀⠀⠀⣾⢻⠀⠀⠀⠀⢿⡼⠀⢸⣿⢻⡆⠀⠀⠀⠀⠹⣜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⡟⠀⠀⢿⣿⡿⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⠀⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠥⠞⠁⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠁⠉⠙⠲⠦⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠉⠒⠂⠲⠦⢤⣄⣍⡙⠓⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠉⠙⠒⠂⠭⠥⠤⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠄⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡄⠖⣰⡞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⡌⠁⠀⣀⠃⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠦⢤⣤⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠒⡧⠀⠐⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⢻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣷⢰⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⢰⠏⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣦⣶⣶⣦⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⢶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠀⠀⠀⠀⠀⢈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣖⣐⡶⢄⠀⣾⡃⠀⠀⠀⢀⣀⠀⠈⣿⣤⠤⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⢭⣥⠤⠬⣷⡄⢱⣿⠴⢦⠤⠦⣤⣌⠁⣤⡿⢴⠧⣉⠉⠺⣙⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣉⡽⠖⠒⠉⠲⣤⡆⣹⣏⡀⠀⠀⠀⠀⠀⣽⡿⣋⣤⡞⠳⣈⢳⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣖⡽⠗⠋⠁⠀⢀⡴⠚⠋⠉⠉⣻⡷⠒⢶⠖⠲⣦⣠⢽⡻⣃⣴⠿⡄⠈⠻⣌⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢙⡷⠶⣶⡞⠋⣿⡁⠀⢠⠀⠀⣼⣷⡄⠉⠉⠈⢧⢹⡀⠀⠘⢯⡈⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢧⡴⠋⠀⣼⠁⡿⢺⡿⣇⣠⣸⡄⠀⣽⠏⠇⠼⠀⠀⠘⣟⢣⠀⠀⠀⠙⢯⣉⣧
⠀⠀⠀⠀⠀⠀⢀⡴⠻⣤⠴⠋⠀⠀⢀⠿⣾⠁⠘⡧⡇⠋⠀⢹⣋⡟⠀⢟⢀⡄⠀⠀⢹⣤⡆⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣾⣁⡜⠁⠀⠀⠀⠀⢸⣀⡞⠀⠀⡷⡇⠀⠀⢠⣩⠇⠀⢨⠍⠁⠀⠀⠀⢷⠸⡀
⠀⠀⠀⠀⠰⣯⠴⠋⠀⠀⠀⠀⠀⠀⣄⢀⠇⠀⠀⢷⣣⠀⢠⠿⡶⠀⠀⠘⡗⢣⠀⠀⠀⠘⣟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡟⠀⠀⠀⠀⠁⠀⠈⠉⠁⠀⠀⠀⣧⠼⡄⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠃⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣰⡴⠇⣀⡴⠀⠀⠀⢸⣇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡈⠁⠀⠀⠈⡀⠀⠀⠀⠸⡇⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡼⠛⠛⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⢲⣩⣡⠤⢶⣥⡀⠀⠀⠀⠸⣄⣶⣀⠀⠗⠚⠓⠒⠒⠀⠀⠀⠀⣠⡞⢁⣴⠋⣀⡀⠀⠀⠀⠀⠳⣴⣄⠄
⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⡂⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⡙⢷⣦⡀⢠⢹⣟⣛⡂⡀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣴⠿⠛⠛⠋⣿⠧⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⠀⣠⠤⠟⠷⣷⠏⠀⢀⠋⠛⠓⣄⢠⣠⣤⣾⣩⢿⣈⢯⣴⡶⠖⠋⠁⠀⠀⠘⠣⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢀⣀⣤⠔⠛⠛⠒⠊⢀⣷⣦⣤⡏⠀⢠⠃⠀⠀⠀⢠⠟⣿⡖⢚⣷⢀⣼⣃⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠄⠀⢀⣀⣤⠽⠿⠛⠁⠀⠀⠀⠀⣠⡿⠁⠀⠀⠇⠀⢸⠀⠀⠀⣴⡟⠉⢹⡯⠊⠀⠹⠗⠽⣿⣶⣿⣟⠳⠀⠀⠀⠀⠀⠀⠀⠠⠴⠄
⠀⠀⠀⠀⠔⠺⣷⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡟⠁⠀⠀⠀⠀⠀⠘⢧⣀⣾⠋⠙⣶⣾⣷⠛⠑⣶⠃⠀⠀⠀⠙⢎⢷⣄⡀
⢀⡤⠞⡧⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⡟⠁⢿⠀⠀⢁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠚⠀⠀⠸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⢳⡈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢱⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢜⣄⠀⠠⠀⢐⣀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⠀⠀⠀⠀⡀⠝⠂⠀⠠⢟⢛⡀⠀⠀⠀⠘⠷⡄⠚⠋⢄⡀⠀⠀⠀⢀⡀⣀⢀⣀
⠀⠀⠀⣀⡤⠒⡉⠌⠒⠒⠂⠒⠚⠈⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⠂⠀⠀⠂⡀⠀⠀⢈⣲⡎⠉⠒⠂⠒⠒⠚⠌⡑⠢⣄⡀
⠀⣠⠒⡥⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡝⢢⡀
⢜⡡⠋⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡔⠀⠀⠀⣀⠀⠐⢄⠀⠀⢀⠠⠓⢄⣀⣀⠤⠁⠀⠀⠀⠀⠐⣄⢀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠣⣘
⠀⠀⠀⠀⠀⠀⣀⠔⡪⠥⠒⠂⠀⡧⡆⠀⠀⠰⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡇⠀⠒⠂⠥⡒⢄⡀
⠀⠀⠀⠀⢀⠞⡡⠋⠀⠀⠀⠀⢀⡄⣿⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⢸⡅⣄⠀⠀⠀⠀⠈⠣⣉⢦
⠀⠀⠀⠠⢣⠜⠁⠀⠀⢀⡠⢚⠧⠂⠉⢧⣦⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⢠⣦⠏⠁⠂⢟⠢⣀⠀⠀⠀⠙⢤⠣
⠀⠀⢴⣓⡎⠀⠀⠀⢠⢎⠜⠁⠀⠀⠀⠈⠀⢳⣄⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀⣴⠃⠈⠀⠀⠀⠀⠙⢌⢦⠀⠀⠀⠈⣖⣳⠄
⠀⠀⡆⡌⠀⠀⠀⠠⠃⡌⠀⠀⠀⠀⠀⠀⡰⢩⠊⠓⠏⠢⠤⣼⠁⠹⠤⠤⠊⠛⠉⢪⠑⡀⠀⠀⠀⠀⠀⠈⠄⠣⠀⠀⠀⠘⡄⡆
⠀⠀⠈⠀⠀⠀⢀⣃⡎⠀⠀⠀⠀⠀⠀⡴⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠰⡆⠀⠀⠀⠀⠀⠈⣆⣃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⢰⠁⠀⠀⠀⠀⠀⢠⡃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢣⠀⠀⠀⠀⠀⠀⢱⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠼⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢸⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠺⣿⢿⡛⠶⠶⠶⠶⢦⣤⣤⣤⡏⠀⠀⠀⢸⠀⠀⠀⠸⣧⡤⠤⠴⠶⠖⠒⠒⠚⣻⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠙⢦⠉⠓⢦⣄⠀⠀⠀⠀⠀⠹⡄⠀⠀⢸⠀⠀⢀⡼⠁⠀⠀⠀⠀⣀⣤⠖⠋⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⠙⠲⢤⡀⠀⠀⠙⣆⠀⢸⠀⢀⡞⠁⠀⢀⣠⠴⠚⠉⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠉⠓⠦⣄⡘⣦⢸⢠⠟⣀⡤⠖⠋⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣀⣀⣀⣬⣽⣾⠛⣿⣿⣥⣀⣀⣀⣀⣀⣀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣀⡤⠖⣻⢿⢿⡓⢦⣄⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣠⡴⠚⠉⠀⣼⠃⢸⠀⢳⡀⠈⠙⠲⣄⡀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⣠⠖⠋⠁⠀⠀⠀⡼⠁⠀⢸⠀⠀⠻⡄⠀⠀⠀⠉⠳⢤⣀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⣰⣟⡤⠞⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⠀⠀⠹⣄⣀⣀⡀⠀⠀⠈⠛⠦⣌⣳⡄
⠀⠀⠀⠀⠀⠺⠿⠷⠶⠖⠒⠚⠛⠛⠉⠉⠉⢿⡀⠀⠀⢸⠀⠀⠀⢠⠏⠉⠉⠉⠛⠛⠛⠛⠷⠾⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢸⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣰⠶⡀⠀⢸⡓⣀⡰⠁⠈⠛⠶⣆⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡦⠊⠁⠀⢉⠁⠈⢔⡀⣴⣄⣼⡷⣤⣖⡲⠀⠀⠉⠙⠳⠖⠒
⠀⠀⠀⠀⡀⢠⡤⠆⠛⠁⣠⡔⣲⣧⣽⣦⢷⣾⣿⣿⣿⣿⣿⢿⡟⠃⠐⢤⣤⡀
⠀⠀⠀⠀⠁⠈⠉⠉⠀⣼⣿⣿⡟⣻⢿⣾⣮⣿⣿⣏⣟⣿⣏⣤⡿⢧⠀⠀⠈⠛⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣿⣮⣧⣾⡯⣿⠿⠊⠁⠀⠈⢦⠀⠉⠒⠒⠮⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢯⣿⣿⡿⠟⠋⠀⢙⠟⣇⠘⠛⠓⠲⠤⠀⠀⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⠁⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠚⠛⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⠛⠀⠀⠀⠀⠀⢈⣷⡂⠐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣤⡄⠀⠀⢠⡇⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠈⠁⠀⠀⢼⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠄⠀⠛⢁⠹⢥⣄⠀⠀⠀⣧⣀⠀⠀⠀⢀⣁⠘⣷⠀⠀⣤⣀⠀⠀⠀⠢⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠔⠀⠀⠐⠶⣥⢠⠀⠙⢠⡠⠛⠋⠉⠓⠒⢶⠙⣏⠀⡀⠀⠘⠋⠀⢀⡄⠀⠀⠈⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠄⠀⠀⠀⠠⣤⣬⣼⡞⡁⠀⠀⠀⠀⣠⣷⡿⠞⣷⡦⠄⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⢴⣮⠙⣧⠤⣥⠀⠂⡔⠀⢲⠉⢻⣽⡀⡙⠀⠀⣀⠀⢣⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⠀⠀⠀⣠⡀⠀⠘⠓⠷⠄⣟⡠⢰⢀⠞⠂⢠⡼⠄⠈⠀⠀⠘⠋⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⢀⠄⠀⠀⠘⠙⠚⠋⢤⠴⠈⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⠖⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⠀⢀⠈⢀⣠⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠽⠋⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠱⡞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⡾⠢
⠀⠀⠀⠀⠀⠀⠀⣾⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣄⠂⠤⠀⠀⡀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢩⠁⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠙⡽⢅⠀⠄⢀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⣆⠀⡖⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠘⡌⠉⠠⢌⠈⠁⠒⠢⠄⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠈⠈⠉⠒⠰⠤⣤⡈⣒⣣⠔⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠰⢚⠿⡛⢭⡉⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠁⠢⣀⠡⡀⠀⠀⠀⠀⠒⠃⠀⠀⣠⠉⠀⣁⠀⠉⠂⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠤⢠⣈⠐⢈⣄⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠉⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠐⠂⠋⠁⡠⢆⢉⠃⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠴⠉⡤⠁⣼⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢀⠞⠁⠠⠃⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⣠⠋⠀⠀⡸⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡙⠡⡘⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⠤⠐
⠀⠀⠀⠀⣀⣀⡤⠄⠐⠋⠀⢨⠀⠀⢳⠀⠀⠀⠀⠐⠒⠆⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣀⣀⠠⠤⠄⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠣⠀⢀⣴⣾⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⡛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⠄⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠠⡇⠈⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢃⠀⠀⠈⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠠⠤⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣴⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠕⠀⣀⣀⣀⡤⣄⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⣠⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⢠⡀⠠⠐⠠⠀⡀
⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠾⣿⣿⣞⡔⣆⠢⡀⠉⠳⣤⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠂⣄⠀⠀⠀⡀⠀⢀⣠⢤⣺⣿⣿⣶⣾⣿⣿⣷⣿⣦⣿⣦⣴⣾⢿⡧⠄⠈⠀⣀⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⢀⣼⣿⠿⠟⠋⠁⠻⠿⢿⡯⣤⣼⣿⣿⣿⣶⠟⠻⠾⢷⣤⣤⠿⠟⢻⡟⠈⠙⠶⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠟⣴⣿⣿⠏⠘⢿⣶⣦⣤⣤⣼⣿⣅⠀⢀⠾⠁⠀⠀⠀⠙⢦⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣿⡿⠁⠀⠀⠀⠈⠀⠁⠀⠙⡌⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢡⡃
⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠘⠀⢇⠀⠀⠀⢀⡄⢠⡀⠀⠀⠀⡸⠀⠃⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠁⢄⠀⠀⠀⠀⠑⢄⠑⢄⣀⠊⠁⠈⠑⣀⡠⠊⡠⠊⠀⠀⠀⠀⡀⠈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⣀⣀⣀⠀⠀⠁⡤⠉⠀⠀⠀⠀⠉⢠⠄⠀⠀⣀⣀⣀⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⢀⣐⠀⠀⠀⢀⣀⠀⠀⠀⡃⡀⠀⠀⠠⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢘⠔⠈⠁⠀⠀⠀⠁⠢⡇⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⡀⠔⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠠⢀⠁⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠡⠀⠐⠈⠁⠀⠀⠀⡀⠄⠊⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡄⠑⠠⢀⠀⠀⠀⠈⠁⠒⠀⠌
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠔⠈⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡉⠐⠠⢀⠁⠢⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠌⠀⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠘⠀⠡⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠀⡘⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠎⠀⡠⠁⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠣⡀⠀⠀⠀⡎⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠱⡄⠹⡄⠀⡼⠀⡜⢀⡠⠖⠒⠋⠓⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⣛⣁⣀⠭⢤⣀⡍⠳⣄⠸⡄⢸⣸⠁⢰⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⠀⠘⢦⠈⠳⠧⠀⠿⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⢃⣀⠤⢄⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⣀⣀⠀⠀⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠖⠉⠀⠀⠀⠉⠣⣙⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡴⠚⣩⢞⣉⢥⡄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡾⣠⠊⢀⡴⡵⠋⠀⠘⣷⠀⠈⠣⠉⠉⠁⠐⡊⠀⢲⠤⠬⡄⢹⡄
⠀⠀⠀⠀⠀⣠⠎⡰⠁⢀⣎⠞⠀⠀⠀⡜⢡⠆⣠⠞⠑⠒⠒⠚⢷⠀⢻⠀⠀⢹⠀⢧
⠀⠀⠀⠀⠘⠦⠞⠁⠀⠀⠀⠀⠀⠀⡸⢱⡟⢀⠇⠀⠀⠀⠀⠀⢸⡀⠸⡄⠀⠈⣇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣾⠁⢼⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠈⢦⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢸⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⡄⠺⡀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠼⢛⣅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⢂⣠⢺⣼⠃⠀⣣⣴⣀⡴⠀⠀⠀⠀⠀⠀⠀⡐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⣶⣾⣏⢀⠋⡄⢿⠘⡄⠀⠟⠿⠃⠀⠀⣠⣦⣤⣿⠋⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⣿⣿⠟⢧⠘⢼⣆⡙⢄⣴⣰⣆⣄⣴⣿⣿⣿⡿⠟⢯⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠻⣿⣿⣦⣀⠁⠈⢹⣇⢏⣿⣿⣟⣿⣿⡟⠛⣿⣧⡀⠘⢿⣷⣤⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⡀⢀⣀⣼⡆⠀⠀⢻⣿⣿⣿⣆⣄⣾⣷⣾⢻⣯⣾⣿⡿⠀⠀⠈⣿⣿⣶⠇⠀⠀⠿⠃⢀⣴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡞⠛⠛⠬⢬⣿⡟⠈⢷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣤⣴⣶⣿⡿⠋⢀⣠⣀⠀⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠀⠀⠀⢸⡄⠐⣠⣷⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢩⣿⠛⠁⠀⠘⣿⣇⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠆⠁⠀⠀⢀⡀⠀⠼⣷⣄⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠘⣿⡃⠚⠀⠀⠉⠉⠀⠙⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⣰⡷⢀⣦⡘⢹⣿⣻⣿⠛⠛⠙⢉⠉⠠⡯⣭⣿⣿⡟⠙⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⡨⠟⠓⠾⣯⡉⣹⣿⣫⣿⣿⣾⣓⣛⣤⣤⡄⠈⣿⠿⣷⡇⣖⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠏⠴⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡦⠀⠀⠈⢀⡀⠀⣴⣿⠋⠹⡿⣛⣩⣿⣿⡋⣻⣿⣿⣄⣴⣿⣦⡿⢿⡟⠃
⠀⠀⠀⣾⣧⠀⠀⠈⠁⠀⠀⠀⢠⣬⣠⣴⠋⡘⠙⣶⣿⣿⣿⠀⠉⢻⣿⡶⠶⣎⢿⣿⡧⡀⠀⢉⣂
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣤⣶⣾⠟⠁⠠⣧⣀⣾⣿⣿⣿⡀⢀⣀⢿⡀⠀⣿⠛⠻⠟⠉⠸⣿⠿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡟⡽⠋⠀⢠⠞⢿⣿⣿⣿⣿⣿⡿⠛⠛⣾⣷⡄⠃⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠀⠀⠀⣯⠀⠈⠈⢿⣿⣿⣿⠀⠀⢴⢄⣻⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗
⠀⠀⠀⠀⠀⠀⢀⣤⡜⠿⠃⠀⠀⠀⣠⣦⠀⠀⠈⠁⠉⠉⠉⠡⣤⡜⠈⠛⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣈
⠀⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⢀⠞⠉⠛⠀⠀⠀⠀⠀⠀⠀⢰⠿⠣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⡷⠦
⠀⠀⠀⠀⡀⠰⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠐⠄
⠀⠀⠀⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡀
⠀⢠⢞⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⠑
⠀⠰⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠘⣿⣦⡀⠀⠀⢀⡀⣀⠀⠀⠀⣠⣾⡟⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⠻⣿⣦⣠⣿⣿⣿⣧⣀⣼⡿⠋⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⡾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⣻⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣀⣴⣿⠟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣷⣄⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡟⠋⠀⠀⢹⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠛⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⣿⠃⠀⠀⠀⠀⠻⣧⣈⠛⠿⠿⢿⣿⡿⠃⠀⠀⠀⠀⢻⡇⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⡓⠲⠤⣰⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉⠁⣠⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡘⠀⢀⡟⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣠⠴⢺⠻⠀⠀⠀⠑⠒⠶⠶⠶⠶⠒⣲⡏⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡼⣀⣤⣄⣀⠀⠀⠀⠀⢀⣀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡼⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠈⠀⣀⠀⠀⣠⠖⠋⠁⠀⢀⣠⠶⠇⠀⠀⠀⠈⠐⢤⣄⣀⡠⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣤⣔⡀⠀⠀⠀⠀⠀⠈⣧⠀⣷⠀⠀⢹⡿⡛⠁⠀⠀⠒⠉⡉⢠⠂⠀⠀⠀⠀⠀⠀⢀⡤⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠈⠙⢗⠦⢤⣤⣇⡀⠘⣧⣿⣆⣠⡟⠀⠘⢿⠋⠉⠉⠁⡠⠀⠀⠀⠀⠦⣄⡠⠒⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢦⠀⠈⣙⣿⣿⣿⣿⣿⣟⣤⡤⡴⠒⠻⣋⠚⠉⢁⠀⠘⣆⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢀⣸⠞⣿⣿⣿⣿⣿⣿⡏⠉⠒⠯⠤⡴⢃⣨⣭⣷⣖⣛⠉⣅⠀⠀⢰⡀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢀⡴⠋⠀⢠⣿⣿⣿⣿⣿⡟⣇⣂⠀⢸⠀⠑⢻⡻⢋⡉⠚⢁⣩⠋⠉⠒⠚⠓⠒⠦⠤⠤⢤⣷⣄⣀⠀⠈⠳⣄⠀⠀⠀⣿⣿⠃
⠀⠠⠊⠀⠀⠀⠀⠙⠿⠿⠛⣽⠁⠈⣧⡔⠀⠀⠱⡞⠁⠀⠳⠋⠀⠉⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⠩⠖⠃⠀⠀⣿⣿⡁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠄⠊⠉⠓⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢀⠎⠀⢀⡠⠚⡷⢦⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⣀⣰⣯⣴⠚⠓⠒⠠⡇⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⣩⠟⠣⣄⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠉⠉⠀⠉⠉⠉⠑⠄⠀⠁⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⣧⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢳⠀⣀⠐⠊⠉⠉⠓⢦⣤⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣳⣟⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⣠⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢠⣯⠶⠂⠀⠀⠀⠀⠀⠠⢀⣹⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠄⠀⠐⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠒⠀⠂⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠘⡆⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠒⠒⠚⠊⠉⠉
⠀⢀⡀⢀⣀⣠⣤⠾⠑⠢⠽⣤⠤⠔⣚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠉⠉⠉⢀⣀⣀⣀⣀⣀⣤⣀⡚⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣨⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⢾⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⢤⣤⠤⠤⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠐⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡟⢣⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠡⡴⢻⡟⡀⠈⢾⣧⡜⠀⠀⠀⠀⠀⣀⡀⢂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣿⣧⣤⡀⡆⣿⠰⡄⠈⠙⠁⠀⠀⣼⣶⣾⣿⣰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣿⣿⡁⠑⠘⠛⣦⢨⢾⣼⣧⣶⣾⣿⣿⣿⡉⠉⣵⣖⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠂⠀⠀⣄⠀⠀⢻⣿⣿⣶⠀⢀⣿⣎⣾⣿⢫⣿⣿⠃⠀⢻⣷⣄⣨⠛⠛⢿⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢯⡰⢤⣶⠞⢿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⠏⢀⣀⣠⣿⣿⠃⠀⠀⠈⠁⣶⡿⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠉⣟⠀⢌⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⢻⡿⠟⠁⠀⢾⡧⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⢦⡤⠃⠀⠀⠀⠀⠀⣿⣄⢈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⢸⣿⠠⠄⠀⠘⠛⠉⠘⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⣽⡆⢠⡌⠉⣿⡿⣿⠟⠻⠙⠉⠉⢩⣟⣻⣿⡿⠛⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡸⠟⠳⢿⣍⢙⣿⣟⣽⣿⣶⣓⣃⣤⣄⠀⢹⡿⢷⣆⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡾⠋⠴⠄⠂
⠀⠀⠀⠀⠀⠀⠘⣿⡧⠀⠀⠈⢀⠀⢀⣼⠟⠙⢿⢛⣩⡿⣿⡋⣿⡿⢿⣤⣾⣷⠼⠿⡿⠊
⠀⠀⢐⣿⠇⠀⠀⠁⠀⠀⠀⠰⢦⣤⡞⢁⠉⢻⣾⣿⣿⠃⠈⢻⣿⠶⢶⡬⣿⣷⣂⠀⣈⣅⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⢴⣿⡾⠋⠀⢸⣦⣼⣿⣿⣿⣄⣀⣄⣿⡀⢀⡟⠙⠛⠁⠘⢿⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠞⠁⠀⡜⠙⡿⣿⣿⣿⣿⠟⠉⠙⠿⣷⡄⠁⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠃⠀⠀⢠⠃⠀⠀⣈⠿⠿⠿⡄⠀⢹⢰⡵⠞⠃⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢄
⠀⠀⠀⠀⠀⠀⢾⡿⠈⠁⠀⠀⣠⠾⡗⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢆⣤⡀
⠀⠀⠀⠀⠀⣀⣤⠃⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢍
⠀⠀⢀⣴⣦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄
⠀⢀⠤⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠠⡀
⠀⣯⠇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⣀⣤⣤⡄⡦⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠏⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⣠⣼⣿⣿⣿⣷⢟⣷⠀⠀⠀⠀⠀⢀⣤⣾⣼⠀⣀⠤⠆⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡀⠠
⠀⠜⢁⣬⣿⣿⣿⣿⣋⠈⠱⡄⠀⡐⠊⣿⣿⣿⢿⡛⠒⢄⡀⠀⢀⠔⠪⢛⣦⣴⣀⢀⡠⠒⣈⠉
⠀⢠⠋⠀⡟⣿⠟⢿⠙⢷⠀⠀⠘⠁⠀⠉⢹⠇⠀⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢏⠉⠁
⠠⠃⠀⢸⡇⠻⠀⢸⡀⠈⣇⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⡇⠈⢂
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠄⠀⢀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⣀⡀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢰⠃
⠀⠐⠓⢌⣆⣿⣿⣿⢰⢠⠊⠀⠀⠀⠀⠀⡀⠀⠸⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠇⠀⢸⠀⣱
⠀⠀⠀⣨⣿⣽⣿⣯⣾⣁⡀⠀⠀⠀⠀⠀⠈⠙⠓⣿⣿⣿⠴⠋⠉⠉⠁⠀⠀⠀⠀⢸⡉⢢⣶⣿⣾⠜⢙⡆
⠀⡰⠊⢘⠉⠙⠋⠛⠉⡇⠙⠄⠀⠀⠀⢀⡴⠊⡽⢿⠿⡿⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⣿⣿⡏⢹⠋
⠀⠁⠀⠘⡄⠀⠀⠀⠀⠃⠀⠰⠀⠀⠄⠋⠀⡴⠁⠀⠀⠀⠇⠀⠑⠄⠀⠀⠀⠀⠀⠀⢸⠀⠙⠛⠁⠈⠄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⢹⣿⣆⢠⠄⠀⡄⣰⣿⡏⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣄⣀⠀⠀⠈⠻⣿⣦⣿⣿⣾⣷⣾⣷⣿⣿⣴⣿⠟⠁⠀⠀⣀⣠⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠉⠙⠻⢷⣶⣤⣌⡻⣿⣿⣿⣿⣿⣿⣿⡿⢟⣡⣤⣶⡾⠟⠋⠉⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⢰⣶⠿⠿⠛⠛⠋⠉⣼⣿⣿⣿⣿⣿⣿⣧⠉⠙⠛⠛⠿⠿⣷⡆⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠛⣾⠉⢰⡀⠀⠀⠀⢀⠀⠤⠶⠦⠄⢀⠀⠀⠀⠀⣰⠈⢹⡞⠃⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡞⠀⠀⠀⠀⠈⢆⠈⡇⠀⢠⠖⠉⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⡏⢀⠎⠀⠀⠀⠀⠈⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠈⢆⢱⣰⣷⣀⠀⣀⣴⡎⣲⣄⠀⢀⣰⣷⣰⢁⠎⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠴⠖⠀⢠⣀⠀⠠⠄⢀⠈⠀⠹⣿⣿⣏⣴⣴⠾⢶⣬⣀⣿⣿⡿⠁⠀⢀⠀⠤⠀⢀⣠⠀⠐⠲⠴⠂
⠀⠀⠀⠀⠀⡐⠀⡀⠔⠀⢠⣿⠞⠀⠀⣈⢋⠀⢀⡠⠚⠁⠇⢀⡸⠏⠉⠀⡅⠒⠂⡅⠈⠉⠿⣄⠀⠇⠙⠂⣀⠀⢨⢋⡀⠀⠘⢾⣧⠀⠐⠄⡀⠀⡀
⠀⠀⠀⢠⠖⡧⠀⠀⠀⠀⠀⡡⠋⡐⠈⠹⠂⢀⣨⠀⠀⠓⠶⠏⠀⠤⠄⢀⣀⣀⣀⣀⠀⠤⠄⠈⠵⠖⠃⠀⢨⣀⠀⢺⠉⠐⡈⠣⡁⠀⠀⠀⠈⠠⡗⢦
⠀⠀⠠⢂⡼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠠⠀⠙⡀⠀⣠⡀⠀⠀⠀⠶⠀⠀⣿⡏⠀⠰⠆⠀⠀⠀⣤⡀⠀⡘⠁⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣄
⠀⢠⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠂⠀⠀⠘⢧⡜⣡⢀⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡆⢠⡙⣤⠟⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣤
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠈⠿⡇⠀⠀⠀⠀⣿⡇⠀⠐⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⡀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢶⠈⠛⠋⢰⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⢐⠟⠀⠀⠀⣁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠠⠀⠘⠦⠄⠠⠞⠀⠠⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡁⠀⠀⠘⢗
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⢢
⠀⠀⠀⠠⠀⠘⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⠀⠀⠀⠀⢀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠪⠁⠀⠀⠀⣀⣠⡴⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠤⢀⡴⠶⠶⠶⣶⡦⢄⡀⠀⠙⢳⢦⡀⠀⠀⢀⣤⠎⠀⠀⠀⣴⠮⠛⠁
⠀⠀⠀⢀⡤⠔⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠢⢝⠦⣌⢻⣷⡀⠀⣷⡌⢠⣦⣴⣯⣤⣤⣄⣀
⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣳⣭⢷⣰⣿⣼⢿⣿⡿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣬⣾⡿⢟⣿⣿⣿⣿⣞⣋⣽⠍⠱⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢡⣿⣿⣶⣾⣿⣿⣿⣟⠉⢁⠀⠀⠀⠀⠁⠨⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⢤⡤⢿⠞⢹⣯⣼⡇⠈⠉⠘⠁⢶⡆⠀⠀⠀⠀⠀⠀⠉⠙⠲⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢐⡢⠴⠋⢁⠏⠀⠀⠀⠀⠀⠀⠋⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⣠⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢀⣰⡼⠏⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠳⢶⣤⣀⡀⠀⠀⠀⠀⠀⣠⣜⠿⣁⡠⣤⣴⠶⡾⠯⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⢦⡀⠀⠀⡰⣿⢿⣼⡷⠍
⠀⠀⠀⠀⣀⣀⣠⢠⡤⣤⣤⣰⢶⣶⠶⣤⣀⠻⣿⣆⣰⣿⡣⣿⢌⣄⡶⠲⠦⠄
⠀⠉⠉⠈⠉⠉⠉⠀⠀⢀⣤⣶⣶⠿⢿⣷⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣏⣾⣰⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣯⣁⢤⢄⣀⣤⣤⣶⣶⠶⠴⠶⠶⠤⣤
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⡿⣤⣶⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡛⠿⠷⠛⠛⠚⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⣧⣿⣬⣵⣾⣿⡿⣿⠟⢹⣿⡆⠉⠻⢿⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⢛⡻⣯⠷⠋⠀⠐⣿⣿⠀⠀⠀⠉⠛⠻⢷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⠿⠚⠉⠁⠀⠀⠀⠀⠈⢫⣷⡀⠀⠀⠀⠀⠀⠈⠈⠙⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢆⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠠⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢢⡀⠀⠀⠀⠀⠀⠀⠠⢸⡄⠀⠀⠀⢀⡛⣃⡘⢻⡂⠀⠀⠀⠇⢀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠲⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣿⡦⣄⠀⠀⠀⠀⢰⡘⡇⠀⠀⠀⠀⢀⣿⣏⣿⠀⠀⠀⢠⣀⣼⠁⠀⠀⠀⠀⢀⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⣷⡀⠀⠀⠀⡉⢹⡇⠀⠀⠀⠘⣧⠛⡇⠀⠀⠀⠜⣻⡅⠀⠀⠀⣠⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣽⠷⢦⠀⠀⠸⠾⡇⠀⠀⠀⣰⠁⢀⣧⡀⠀⢘⡷⠟⠀⠀⢀⠰⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣷⡀⠀⠀⣷⠀⡀⢠⡇⠀⠈⠀⢹⡀⢠⢠⣿⠀⣠⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⣰⡀⢽⠀⠀⣼⢠⡄⣤⠀⢸⡇⠘⣸⣿⡟⠉⢛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣸⣇⡐⣳⣎⡷⣛⣧⡿⣠⣦⡿⡟⢠⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠞⢷⣻⣌⣷⣯⣽⣿⣿⣿⣷⡶⢾⣽⣣⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⡟⢹⣽⣿⣿⠛⠿⣿⣿⣿⣯⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠑⡲⢯⣽⣿⣿⣶⣶⣽⣿⣿⡥⠴⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⣤⠖⠚⣿⣿⡛⣷⡿⣿⠿⠿⣿⣿⣿⡟⡛⠳⠦⢀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣆⠞⠀⡴⡫⣺⣿⠟⠋⠉⠁⠀⠀⠨⣿⠷⣄⡠⠑⢦⡀⢢⡠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⡟⢀⣬⣀⠜⠉⠀⠀⣼⡷⠀⠀⠀⠈⣿⠀⠈⠻⢧⡀⢹⠀⢿⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠈⠀⠈⠘⡇⠀⠀⠀⠀⣿⣧⠀⠄⣀⣸⣿⠀⠀⠀⠀⢹⡟⢧⠈⠣⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢫⠏⠀⠀⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢃⣸⠂⠀⠘⠝⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠋⠀⠀⢰⠏⡿⠀⠀⠀⠀⠀⠀⠙⣿⠿⣿⠛⠁⠀⠀⠀⠀⠀⣿⢿⡄⠀⠀⢂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⡿⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠚⡇⠀⠀⠀⠁⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢨⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⡔⠀⠀⠀⠐⢄⠸⣀⣀⡇⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠰⡀⠀⠀⣀
⠀⠀⠀⢰⣶⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣽⣏⠀⠀⠀⠀⠀⢀⢙⣿⣿⡋⡀⠀⠀⠀⠀⠀⢡⣤⡆⠀⠂⠀⠀⠀⣲⣶⠃⠀⠀⠀⠀⠀⢹⣿⡏⠁
⠀⠀⠀⠘⠻⠃⠄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠋⢿⡏⠑⠀⠀⠀⠀⠀⠾⣿⣿⠷⡄⠁⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⢿⣿⠷⠀⠀⠀⠀⠀⠛⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⠀⠀⢀⠔⡶⠲⠤⠤⢤⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠐⡆⠀⡴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⡤⢄
⠀⠀⠀⠀⢀⠤⠜⠒⣤⣾⣷⣠⣾⡾⢖⡋⠙⠓⠒⠽⢄⠀⠀⠀⠀⠀⠀⠀⣠⣽⣦⣷⣾⣇⣀⣀⡀⠀⠀⠀⠀⠀⢀⠤⠀⠒⢤⣠⣶⣸⡏⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠾⣿⠛⠉⠉⠙⠁⠀⠙⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠔⠈⠀⠈⠉⠟⠉⠩⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠿⠛⢯⡓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠉⠡⠇⠀⠀⠀⠘

⠀⠀⠠⣠⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣽⣿⡀⠀⠀⠘⣶⣦⠖⠀⠀⠀⠀⢬⣴⣦⠀⠀⠀⠀⠠⣄⢣⣠⡼
⠀⠀⠁⠋⠙⠀⠀⠀⠐⢿⠿⠀⠀⠀⢀⡴⠖⠻⣧⠀⠀⠀⠀⠀⠈⣺⣿⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡗⠀⠀⠀⠀⠉⣹⣿⣯⠑⢄⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⠀⠉⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⢾⣿⢯
⠀⠀⡄⠃⠀⡔⠀⠀⢄⡀⢴⣇⡜⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⣙⣷⡾⠔⠁⠀⠠⠬⢿⣿⣷⣆⡀⠀⠀⢳⣄⣀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄
⠀⠀⠹⡿⢏⠀⠀⠀⠀⠀⠀⠻⠿⠗⠈⠀⠀⢀⠩⢿⣿⡒⠀⠀⠀⠀⠀⠀⠐⣆⣻⣿⣃⡔⣀⣀⣀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠻⠟⠆⠀⠀⡠⢾⠿⢿⣾⣿⣿⣿⣿⣷⠶⣌⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠈⡰⠋⠀⣼⠁⡏⠀⠘⡄⢹⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⡏⠀⠁⠀⠈⠀⠸⡇⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⠀⠀⠀⠀⠙⠒⠒⠊
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡟⠂⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠰⠀⢄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠲⣤⣄⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣿⣿⣿⠷⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⠀⠀⠔⠁⠀⠀⠀⠖⠛⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠔⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠟⠧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⢿⠷⠂⠀⠀⢠⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠀⠁⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢻⠿⠇
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠉⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰
⠀⠀⢐⡿⡆⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠛⡟⠉⠁⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡟⠛
⠀⠀⠀⢰⣾⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣷⠆
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡈⠉⠛⠒⢦⡀⠀⠀⠋⠁⠙
⠞⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠛⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⡠⠂⠀⠄⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣎⠠⢀⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡽⢿⠀⠀⠈⡀⠀⠀⠀⠀⠢⠰
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠠⠴⢿⣿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠂
⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠎⠀⠀⢢⣴⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣷⡃
⠀⠀⠀⠀⠐⠦⠀⠤⠀⠉⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡤⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠳⣄⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣲⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠈⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⢤⣷⠄⠀⠀⠀⠀⠠⠤⠀⠀⠀⠐⠲⢶⣿⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠙
⠀⠀⠠⠐⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢒⠄⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⠆⠀⠀⠀⠀⠀⠠⠆⠁⡈⠈⠢
⠀⢀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⠒⠀⠁⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠠
⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠜⠀⠀⠈⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠁
⣀⣀⣀⣈⣂⣒⣀⣀⣀⣀⣀⣀⣀⣈⣓⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣀⣀⣀⣀⣠⣃⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡄⠀⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠂⠀⠀⠀⠀⢠
⠀⠀⡀⣬⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣾⠃⠀⣇⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣆⡀
⠀⠀⠠⢌⣲⣟⡠⣏⡃⠀⠀⠀⠀⢠⠀⠀⠀⠙⡒⠇⠘⠀⣟⢀⠄⠀⠀⣣⠀⠀⠀⠀⠀⢠⢠⡞⠉⠀⠈
⠀⠀⡀⠲⠀⠙⠑⣘⣶⠧⠂⠀⠀⡸⡀⡇⠁⠀⠑⣄⠎⢹⠖⠋⠀⠀⢀⣫⠆⠀⠀⡀⢰⡖⠚⠁
⠀⠀⠙⠢⣬⠂⠀⡿⠁⠀⠀⠀⠀⠄⡟⢀⠀⠀⠀⠘⠀⠀⠀⠀⠠⣀⢸⠏⠀⠀⠀⠈⣾⣏⡠⠀⠀⠀⢀
⠀⠀⠀⠁⠲⣷⠘⠁⠀⢀⠀⡄⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠁⠀⠀⠰⣄⡿⡠⠀⠀⠀⠱⣰
⠀⠀⠀⠚⠀⠈⠒⠀⠀⠀⡙⢧⠆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⣵⡠⠂⠀⠀⣸⡟⢁⠀⠀⠀⢠⣏⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠸⠋⠀⠀⠀⠀⠹⢿⠟⠀⠀⠀⠐⠌⢏⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⢸⠂⠀⠀⠀⠣⣾⡐⠁⠀⠀⠀⠈⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⡆⠀⠀⠀⠀⠀⠨⣧⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠘⠇


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠉⠒⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⡀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠠⠔⠲⠦⠀⠀⠀⠀⠀⢠⠴⠦⢤⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠼⢤⡙⢦⡀⠀⠀⠀⡜⠀⠀⠀⢀⠤⠐⠀⢄⠀⠀⠀⢀⠤⠀⠀⠄⡀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡴⠊⡗⠢⣀
⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠉⠳⣜⣷⡄⢰⠁⠀⠀⠐⠁⠀⠈⣿⣷⡔⠀⠠⠁⠀⢻⣿⣦⠘⠀⠀⠀⢣⠀⠀⣠⠞⣡⠴⠋⠉⠳⢬⡑⢤⡀
⠀⠀⠀⡴⣫⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⠀⠀⠀⠀⠘⣷⣶⣿⣿⡇⠂⢀⢷⣶⣿⣿⡿⠀⠃⠀⠀⢸⣠⣾⡷⠛⠁⠀⠀⠀⠀⠀⠙⢶⣝⢦⡀
⠀⢠⢮⣾⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠻⡄⠀⠀⠈⠢⢈⠙⢛⡩⠊⠀⠀⠢⢉⠛⢋⡠⠊⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢷⣝⢄
⢠⢃⡿⠁⠀⠀⠀⢀⡴⣩⠤⠭⣭⣭⣿⣶⣦⣤⣵⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣴⣶⣶⣿⣭⡭⠭⠭⡟⢦⠀⠀⠀⠀⢻⣎⢧
⣏⡼⠁⠀⠀⠀⢠⢎⡴⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⣄⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⢀⣜⣋⣉⣉⣀⣀⣀⣀⣀⠀⠀⠈⢦⡱⡄⠀⠀⠀⢻⣈
⠀⠀⠀⠀⠀⡰⢣⡞⠀⠀⠀⣠⢖⠋⠉⣉⣉⣉⣩⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣭⣥⣤⣤⣀⣀⡈⣹⢣⠀⠀⠳⡜⢆
⠀⠀⠀⠀⡼⣱⠏⠀⠀⠀⣰⢃⡞⠚⠉⠉⠉⠀⣀⣴⣾⡿⠛⠉⠙⠒⠲⠤⠤⠤⠴⠒⠊⠉⠉⠛⠿⢿⣶⢤⣀⠀⠀⠀⠀⠉⠙⢆⠳⡀⠀⠹⣎⢣
⠀⠀⠀⡜⣴⠏⠀⠀⠀⣰⢃⡞⠀⠀⠀⢀⠴⣚⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣙⣢⡀⠀⠀⠀⠈⣆⠱⡀⠀⠙⣧⣳⡀
⠀⠀⢰⢹⡟⠀⠀⠀⢠⠃⡾⠀⠀⠀⢰⢓⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠀⠀⠀⠀⠘⣆⢱⡀⠀⠸⣷⢳
⠀⢀⡇⣾⠁⠀⠀⢀⡇⣼⠃⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡆⠀⠀⠀⠀⠹⣆⢣⠀⠀⢹⡆⢇
⠀⠘⠤⠋⠀⠀⠀⡸⣰⡏⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢱⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠣⠼
⠀⠀⠀⠀⠀⠀⢠⢣⣿⠁⠀⠀⠀⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⡄⠀⠀⠀⠀⠘⣿⠸⡀
⠀⠀⠀⠀⠀⠀⢸⢸⡏⠀⠀⠀⢰⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⢻⡀⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⠀⠀⠀⠀⠀⠸⡇⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠⢤⣴⠚⠉⣁⠀⣈⠁⠉⠶⢤⣤⣤⡔⠈⠀⢀⣀⠀⠑⢄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣷⠀⠡⡰⠂⡁⠤⠄⡀⠳⣀⠌⣽⠏⠀⣴⣾⠟⡛⢷⡀⠀⠂⠀⠀⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢨⠄⠑⠄⢀⡤⠀⠤⠶⠾⠛⠿⡿⠏⠀⢰⡇⠌⠀⠀⠀⡈⠆⠘⡀⠈⢄⣼⣛⣿⠄⠿⠿⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢘⠇⠀⠀⠀⠁⠀⠘⢖⢁⠄⠚⠧⡜⠀⠀⢤⠐⢂⠀⠉⣄⠘⣿⣿⠁⠠⠀⠀⠀⠀⠐⠀⠀⠀⠔⡂⡀⠀⠠⡀
⠀⠀⠀⠀⠰⡄⠄⢀⠀⠀⠙⡫⠤⣄⠀⠀⠀⢀⡴⠆⣿⡀⠠⢀⠘⠀⠀⠀⠀⠈⡭⢄⠀⢂⠹⣿⡄⠀⠀⠀⠰⣄⢀⠔⠂⠘⣿⡷⠀⠠⠄⢰
⠀⠀⠀⠀⠀⠐⠀⠀⠌⠁⠀⢧⡀⠈⠓⠀⠀⠋⠀⠠⠋⠉⠁⠀⠀⠈⠈⠳⣄⣤⣷⠆⠐⢊⡡⠉⠀⠀⡲⠶⠀⢡⠀⠠⠀⠂⠉⢄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⡸⠟⠛⠻⢷⡤⠂⠠⠄⠁⢲⠟⠚⠀⢱⠎⠧⡀⠀⠸⡟⣡⠅⡈⠐⢢⡴⣮⢑⡆⠳⠀⠵⠄⠒⠒⠂⠈⠙⢏⣀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠠⠀⠀⠹⣌⢲⣐⢣⡎⣠⠖⠉⠙⢦⠀⠑⡀⠈⢡⠠⠄⠒⢈⡤⠂⠀⠻⠗⡀⠀⢌⣻⠟⠃⠀⠒⢄⠀⠹⣿⣿⣧⠐
⠀⠀⠀⠀⡀⠄⡀⠀⡇⠀⣷⠀⠀⠀⣿⡖⠄⢊⠠⡄⠀⠀⠀⣸⢅⣀⡫⠀⠈⣀⠰⠂⠁⠀⠀⠀⠺⡈⠄⠢⣼⡿⠦⠤⣤⣴⡆⠀⠀⣿⣿⠋
⠀⠀⠀⠀⠀⡔⡀⠂⠐⠀⠠⠂⣠⠠⠿⢧⡀⣻⠇⠄⠀⠓⠊⠁⠀⣠⠇⢀⠴⠥⢤⣄⠃⢜⠂⠠⠀⠆⠈⢂⠉⢤⣶⣦⠈⢿⡗⠀⠀⣿⠇⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠄⢈⠄⠉⠀⡢⠀⠐⠈⠳⣀⠠⠂⠒⠆⠔⠊⠁⠈⡀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠐⠀⠈⢠⠀⠛⣦⣴⡿⠁⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣤⣤⠼⠁⠀⠀⠀⠑⠀⠊⠀⠀⠈⡖⠀⠀⠠⢀⣘⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⢀⣀⣠⣴⣇⡀⠈⠀⣀⡄⠚⠛⠁
⠀⠀⠂⠀⠀⢠⠟⠁⠄⠀⠑⠈⠈⠀⠈⠂⡀⠀⡴⠁⠀⠢⠀⠤⠄⠁⠀⠀⠀⠁⠀⢂⡠⠁⠀⠀⠀⠋⠁⠀⠀⠀⠙⠻⣿⣟⠨⡀⠀⢈
⠀⠀⡑⠂⡤⢠⣧⣦⣤⣴⣀⡀⠀⠐⢐⣨⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢡⡐⢋⡁⠒⠉⣠⢊⡠⠄⣈⠌⣴⣶⡖⠂⠀⠀⣿⡿⣦⣬⡴⠆⣰⠆
⠀⠀⠁⠀⠀⠘⠉⠀⣀⣀⣀⠍⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣴⠆⣿⣻⠟⠁⠀⠌⠰⠉⠛⢧⣉⣀⣴⣫⠞⠋⠀⣀⣴⡿
⠀⠀⠀⠀⠀⠀⣴⡟⠛⢿⣿⠀⠀⠣⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠏⢻⣫⣾⣽⠋⠀⠀⣠⡞⠳⠊⠠⠂⣠⢟⡵⠃⠲⠘⠛⢉⣽⡷
⠀⠀⠀⠀⢀⠀⠈⠷⠆⣸⡇⠀⠀⠀⠐⡀⠘⠀⠀⠆⠀⡤⢤⣴⣎⡙⢿⡿⢀⣿⡿⠛⢦⣠⣾⠿⢞⡀⠀⡠⠂⠽⢋⡅⠀⠀⠰⠖⠛⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣄⡉⠟⣉⠁⠃⢾⠟⠁⢠⠞⠛⠛⠂⠤⡉⢣⡀⠀⠀⠠⠓⣀⢂⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠠⠀⠀⠙⠿⠀⠀⢠⠁⣐⢀⠠⠀⢀⡼⠟⠿⣶⡿⠁⠊⠀⠀⡀⠂⠀⠴⡁⠀⠀⠀⠄⠑⠌⢀⠐⡀⠀⠀⠠⠀⠐⠦⠁⢠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠠⣄⣈⣀⣀⠤⢚⠻⣇⠰⣦⢘⠃⠀⠀⢀⠌⠀⠠⠊⠀⠈⣶⠟⢿⡄⠀⠀⠀⠆⢙⠀⠀⠀⠀⠀⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⣏⠐⣿⡁⠾⠓⠊⠁⠀⠀⠀⠣⣀⡔⠁⠀⠀⢀⣶⣤⣾⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡶⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⢀⠴⣛⠛⠛⠁⠀⠊⢠⡀⠇⡞⠀⠀⠀⠀⠠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠀⠀⠀⠀⠀⢀⡀⠁⠀⠄⠀⠀⠀⠎⠀⠀⢀⣀⡀⠈⢀⠀⠀⠑⡀⠈⢀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⣰⠖⡉⠐⢎⢤⣶⣬⣤⡧⠀⠐⢄⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡧⡇⡀⢀⠂⠆⠀⡈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡁⠠⠤⣀⡀⠀⠀⢀⠌⠀⠀⠀⠈⠂⠐⠈⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣀⣀⣀⣐⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⠒⠖⢖⠲⠒⠒⢒⣲⣶⣶⣶⢒⠒⠖⡖⠲⢒⠖⠒⠀⠀⠀⠀⠀⢰⣶⣶⣒⠒⠒⠒⠒⠒⢲⠒⡖⢲⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠈⠀⣀⣤⠒⡉⡴⢉⡏⢧⢉⠞⢠⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⢺⠳⣌⠁⠒⠤⢄⡀⠈⢰⠀⡇
⠀⠀⠀⠀⠔⠪⠁⠢⠑⣜⢁⠰⡇⢈⢣⡈⡀⢈⡵⠢⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧⠈⠳⣄⠀⠈⡈⢋⠶⢤⡇
⠀⠀⠀⠀⠀⠀⠀⢂⡝⡒⠂⢬⡇⠐⢂⢻⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢎⡠⠐⡳⣔⢠⠂⡔⠁⠀⠀⣀⣤⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠰⡇⠁⠀⠀⠑⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡉⠹⡄⢊⠤⠊⢓⣼⠠⠀⠀⠀⣿⣩⣏⣽⡇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⠠⠀⠒⠲⣂⠔⠈⠀⠀⠄⠀⠀⠀⠈⠛⠛⠉⠈⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠐⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣋⣟⣹⡯⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠠⢚⠠⢀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⡍⠐⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠱⡄⠀⠂⣭⡑⠂⢀⢮⠡⡀
⠀⠀⠀⠀⠀⠘⠣⣀⠀⠀⠐⢉⡏⠐⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠲⢆⣁⠐⡡⠛⣍⠀⠶⠄⢩⡟⢄⠀⢌⡰⡖
⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⠀⢉⡅⠀⢀⣴⠊⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠏⡟⠴⢊⡸⢆⣛⣐⠦⣀⠦⠛⠁⡀⠇
⠀⠀⠀⠀⠄⠀⠄⠀⠀⠘⠢⣈⣅⠑⠇⠈⠄⠈⠄⠐⠀⠀⠀⠀⠀⠀⣠⡂⣌⣴⣡⡆⣬⢹⣯⣷⣟⣇⢡⣠⡄⣤⢡⡌⣤
⠀⠀⠐⠛⠐⠛⠐⢛⠐⢓⢒⠿⡿⡒⠺⠒⡚⠒⠚⠂⠚⠂⠀⠀⠀⠀⠀⠡⠐⡀⡆⣁⠴⢞⡳⠿⠿⣓⠦⣀⠀⠁⠌⡐
⠀⠀⠀⠀⠁⠀⢁⠀⢂⠐⠓⠠⡦⠘⠣⣠⠁⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡛⠏⠑⠾⠓⠿⢊⣷⡖⡭⢛⣲⢦⡇
⠀⠀⠀⠀⠀⢀⢀⡤⢉⠉⠐⠠⡤⠐⠁⡉⠢⡅⠠⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠢⡈⢆⠖⠒⠢⢴⠔⠒⠻⡴⠋⠔⠋⠋⠓
⠀⠀⠀⠀⠀⠼⠃⠠⠀⡈⠀⠠⡆⠂⠁⡀⠄⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⠒⠤⣙⠻⢋⠭⠆⠿⡆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⣏⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢺⣭⣭⣽⡇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂