I love you text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣠⡴⢶⣦⣄⠠⢤⣴⣶⡖⠀⠠⢤⠄⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⢠⣿⣿⡇⠀⣿⣿⣧⠘⣿⣿⣷⠀⠀⡟⢠⣿⣿⡟⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠘⣿⣿⡇⢸⣿⣿⡇⠀⢸⣿⣿⠀⢹⣿⣿⡆⣰⠃⢸⣿⣿⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠘⢿⣿⣧⠀⢸⣿⠏⠀⠀⢻⣿⣿⠃⠀⠈⢿⣿⣧⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠒⠀⠀⠀⠚⠛⠛⠓⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡆⠀⠰⢤⣄⢀⣴⠶⢶⣦⣄⠀⠠⣤⣤⣄⠠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⡇⢰⣿⣿⠀⠈⣿⣿⡆⢰⣿⣿⡏⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣠⠀⢺⣿⣿⠀⠀⢹⣿⡇⢸⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠀⠘⢿⣿⣇⠀⣼⡿⠁⠸⣿⣿⡇⣠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦⠀⢀⠟⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠈⠙⠋⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠔⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠖⠛⠒⠀⠀⠀⠀⠃⢀⣤⣤⠀⠀⠀⠀⠀⠀⢠⠶⠚⠓⠂
⠀⠀⠀⠀⠀⠁⣴⠞⠛⠉⣉⠉⠉⢡⣿⡿⠁⠀⠀⢀⣀⠀⠀⢀⣴⡾⠋⣰⠀⠆⠀⠀⠀⠀⣠⠖⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠸⣇⡀⢀⣰⡿⠃⠀⣾⣿⠁⠀⠀⠀⠈⠋⠀⢠⣾⠏⠀⡴⠃⠀⠀⠀⢀⠀⠠⡇⡰⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠉⣭⣥⡀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⠏⠠⠊⠀⢀⠀⠀⠀⠁⡀⠀⢠⡇⠃⠀⠀⢀⡀⠀⢤⡀
⠀⠀⠀⠀⠈⠁⠐⠀⢸⣿⠇⠀⣸⣿⠁⠀⣤⠀⠀⠒⢠⣿⡟⠀⠀⢠⣾⡿⢁⡀⠀⣠⣿⡇⠘⡆⠀⢀⣾⠟⢩⡆⢠⠇
⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣿⡿⠁⠀⠁⢠⣿⡟⠀⡰⠙⢢⣾⠏⡤⠊
⠀⠀⠀⠀⠀⢧⡀⠀⢀⣀⣴⠿⢋⠔⠀⢰⣌⢹⡆⠀⠸⣿⢀⠰⠉⢿⡇⠀⠀⠀⣿⡟⠀⡴⠁⠀⣿⡏⠀⢀⡤⠀⠁
⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⣰⠃⠀⢀⣾⡿⠸⠃⢀⣠⣬⠁⠀⠀⠀⠀⠀⡀⠀⠙⠓⠋⠀⠀⠀⠈⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡇⠀⢠⣿⡿⠁⢀⣴⣿⠏⢀⣴⡅⠀⠀⠀⣤⡀⠀⢀⡀⠀⠰⠶⠀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣿⡟⠀⠀⣾⣿⠃⣰⣿⠟⢦⠄⠀⣾⡿⠁⢀⣾⡿⠀⠀⠀⢠⣀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠙⠓⠀⣼⣿⠃⠀⣿⡏⢀⠂⠀⣸⣿⠁⢠⣿⡿⠁⠀⠀⠀⢸⣿⣇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⡀⠤⠤⠀⠀⣰⣿⠃⠀⠀⠙⠓⠁⠰⠀⠙⠗⠀⠘⠿⠁⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡾⢁⡞⠁⠀⠀⠀⢀⣴⡟⠁⢀⠐⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡴⠞⢉⠀⠀⠛⠃⠀⠀⠈⠙⠛⠿⢿⣶⣶⣶⣿⣿⣿⣿⠿⠛⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⢤⠴⠞⠋




⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢸⡟⢀⠀⠀⣠⣤⢰⢑⢀⣶⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣿⠁⢸⡟⢸⠁⣿⢀⠏⣹⡏⢀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⣀⣾⣇⡀⠘⠓⠁⠀⠙⠊⠀⠘⠗⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠊⣸⠏⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣴⠋⠔⢻⡆⠀⠙⠳⢤⣀⣀⣀⠤⠚⠁⣰⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸⠀⢸⡇⠀⣶⠀⣀⠀⢀⡀⣸⡇⠀⣿⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡇⢀⣿⠀⢣⣶⠀⢻⠸⣧⣰⠛⢧⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢚⣿⠄⠹⣿⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⡿⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣸⣿⣎⣟⣿⣞⣿⣿⣷⣦⡀⠀⠀⢀⣴⣾⠿⢿⣿⠿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣯⣿⣿⣿⣹⣯⣽⣿⣟⣿⣿⣿⣿⣄⢀⣿⣛⣿⣿⡏⣟⢛⣻⣻⣻⣟⠛⣛⣂
⠀⠀⠀⠀⠀⠀⣴⣷⣷⣿⣷⣾⣿⣻⣫⣛⣏⣿⣟⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇
⠀⠀⠀⠀⠀⠐⠶⢿⡷⠾⢶⣟⣿⡛⣛⣛⢻⣟⢛⢛⢛⣿⣏⣹⣉⣿⣿⣿⢷⠶⡞⣦⠾⡿⢿⣿⣯⣽⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣿⣿⣿⣿⣛⣟⣖⣾⣻⣓⣛⣿⣷⣷⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠸⣿⡿⣯⣽⣿⣭⣿⣯⣭⣯⣭⣿⣿⣹⣽⣹⣍⣍⣿⣭⣽⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢛⣹⣙⣉⣿⣛⣙⣹⣿⣿⣶⣾⣧⡶⣾⣿⣿⣧⣤⣼⣿⣤⣤⣿⣿⢾⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣓⣾⣟⣻⣿⢻⡟⠛⠿⢿⣿⡟⠛⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⡿⠿⠿⢿⡿⠿⠿⣯⣿⣿⢿⣿⣿⣿⡿⢿⣿⢿⣿⣿⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣹⣾⠷⢶⡶⢾⣧⣶⣷⣿⣿⣿⣼⣧⣿⣷⣧⣾⣿⣷⣯⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣾⣾⡷⢾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣽⣿⣯⣽⣿⣯⣿⣟⣿⣻⣩⣽⣋⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⣿⣿⣽⣏⣭⣩⣹⣉⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣤⣤⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣶⣦⡀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⣤⣤⡄⠀⠀⢀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⢿⡄⠀⠀⣸⡿⣿⠃⠀⠀⢸⣿⣿⣭⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻⣽⡿⣿⣿⡇⠀⠀⠈⣿⣾⣷⠀⢰⣿⣷⡏⠀⠀⠀⢸⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣣⣿⣿⡇⠀⠀⠀⠸⣷⣻⣧⣿⢵⣿⠀⠀⠀⠀⠘⣿⣟⣛⣛⣻
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣀⣀⣀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣷⣻⣏⣿⠇⠀⠀⠀⠀⢸⡿⣻⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⣹⣉⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣟⣙⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣶⡀⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣶⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹⠻⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⢻⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡾⣿⣿⣿⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⢼⣗⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣯⣻⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋

⠀⠀⠀⠀⠀⠐⠛⠛⣿⠛⠛⠋⠁⠀⠀⠀⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠞⠀⠀⣠⣄⡀⢀⣄⠀⠀⡀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣼⢉⠜⣷⠁⣾⠀⠀⣿⢀⡟⠁⣹⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⠉⠀⣿⠀⢻⠀⢰⡏⣸⣧⠶⠋⠀⣀
⠀⠀⠀⠀⠀⠰⠶⠚⠓⠶⠖⠀⠀⠀⠸⣇⣀⡴⠛⣧⣀⣰⡟⠀⠘⣷⠟⠀⠈⢿⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠛⢶⣄⢠⠎⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣿⠀⠀⣴⠀⠀⡠⠿⣦⡀⡔⡆⠀⠀⣰⡀⠀⠀⠀⡇⠀⠀⠀⠹⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡇⠀⢰⡇⠀⣸⡧⠎⢸⡇⠀⣇⠀⢀⣿⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣾⡇⠀⣿⠀⠀⣸⡇⠀⣿⠀⣼⣿⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⢹⡇⠀⠘⠷⠶⠟⠀⠀⠻⠾⠋⠹⠶⠂⠀⠀⠀⠀⠙⢦⡀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡤⠾⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠀⣤⢤⡀⠀⠀⡴⠛⡆⠀⢰⠏⣴⣩⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⡀⠙⣆⠀⠀⢧⠀⢳⠀⢠⡇⢰⠇⠀⢸⠀⣨⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⡇⠀⢻⠀⠀⠈⣧⠈⠓⠚⠁⡞⠀⠀⠸⡄⠱⠤⠤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢷⣀⠀⠀⣀⡀⠀⠀⢸⡆⠙⠞⠁⠀⣼⠀⠀⠀⠘⣦⡀⢀⡼⠁⠀⠀⠀⠙⠦⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠈⢹⠆⠀⠀⠳⢤⣀⣀⡴⠁⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠄⠄⠴⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⣠⡤⠶⢶⣤⠀⠀⠀⣰⠒⣆⠀⢠⡏⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⢠⡏⠙⡆⠀⣿⠀⢸⡄⠀⠀⢰⡏⠀⣀⠀⠙⣇⠀⠀⢹⠀⣿⠀⢸⡇⠀⣧
⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⢶⣄⣀⣴⠟⠁⠀⠀⠙⣿⣆⠀⠀⠈⣧⠀⠛⠐⠋⠀⢸⡇⠀⠀⢿⡇⢸⠁⡷⠀⣿⠀⠀⢸⡇⠘⠦⠞⣰⡄⣿
⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠣⠤⠤⠚⡧⠈⡇⠀⠀⠸⣧⠈⠉⠀⢀⡿⠀⠀⠈⢿⣦⣤⠾⠛⠧⠟
⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⡤⠤⠖⠊⠀⡸⠁⠀⠀⠀⠙⠳⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠛⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⣠⣾⠏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⣠⣾⠿⠟⠁⠀⠈⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⣼⣿⣿⠋⠀⠈⠀⠀⠙⠙⠋⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣄⣠⢠⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡇⠀⠀⢀⡞⢀⠀⠀⠀⠀⡀⢉⠐
⠀⠀⠀⠀⠀⠀⠀⡆⠀⣸⠁⠀⠀⡞⠀⠂⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀
⠀⠀⠀⠀⢠⠀⠀⠘⣰⠃⠀⠀⣸⠀⢠⠔⡄⡴⠐⢆⡔⠂⠀⠀⢀⠄⣠⡠⠠⣠⢀⡄⠀⠈⢆
⠀⠀⠀⠀⠈⠀⢀⠠⠋⢄⠀⠀⠣⠀⠃⠀⠀⠃⠀⠸⠄⠀⠀⠀⠈⣰⠛⠃⠀⠃⠚⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢠⠃⠀⠀⠈⠉⠐⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠰⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⢀⣿⠋⠀⠀⠀⣠⠞⠋⡇⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢠⣾⠃⠀⠀⢠⠞⠁⢀⠜⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⢀⡤⠒⠂⠈⠓⣦⡀⢸⡇⠀⢠⣿⠃⠀⠀⣰⠏⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣼⠇⠈⠻⣤⣿⠁⠀⠀⣰⡟⠂⠀⢀⠤⣤⠀⢀⠄⠀⠀⢀⡠⠄⠀⠀⣠⡟⠁⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⣼⡇⠀⠀⠀⠀⠠⠞⠋⠀⢀⣴⠟⠁⠀⠀⠀⠸⡤⠄⠺⠧⠔⠓⠂⢾⠤⠚⠂⢾⡌⠤⠀⣰⡏⠀⠀⠀⣀⣾⢃⠄⢠⠆⢀⡤⠀⢀⡤⠀⠀⠠⠋
⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⠴⢺⡿⠁⠻⠄⠚⠋⠘⠓⠊⠙⠓⠂⠚⠃
⠀⠀⠀⠈⠓⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠒⠒⠒⣴⠟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠋


⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠋⠁⠀⠀⠀⠀⠛⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⢀⠐⠀⠀⠀⢀⣼⡿⠃⠀⠈⠛⠛⠁⣤⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⣴⣾⠀⠀⢀⣾⡇⢀⠂⠀⠀⣠⡖⠂⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠰⣿⡇⢀⠀⢸⣿⠀⠀⠁⠀⣸⡿⠀⠁⠠⠂
⠀⠀⠀⠀⢠⠖⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠛⠇⠀⠀⢸⣿⠠⠀⠀⠀⠹⢧
⠀⠀⠀⠀⠈⠀⠠⠔⠚⠉⠐⢤⣀⠀⠀⠐⠖⠀⠀⠀⠀⠀⣉⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠳⠶⠶⠋⠀⠀⠀⣼⡇⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⣠⠀⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⣿⣿⡇⠀⠀⠁⠀⠉⠁⢸⡏⠀⢿⠀⠸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠋⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠄⠠⠄⠀⠀⢠⠂⠉⠉⠙⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⡀⡐⠒⢦⠀⠀⠀⠈⠻⣗⠒⠊⣡⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⠁⠀⠀⣇⣰⡏⠀⠀⢹⠀⣾⠁⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣿⠓⠒⢰⠃⢸⡇⠀⠀⡜⢸⣿⠂⠀⠀⠀⠰
⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠻⣧⠴⠃⠀⢸⣇⣀⡔⠁⠀⠻⣦⡀⣠⠐⢁⡤⠤⠴⠦⢤⣄⡀
⠀⢠⡞⠉⠉⠉⠉⣩⡿⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⡭⠒⠉⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠘⠷⠶⠶⠖⠋⠁⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠶⠶⢤⣌⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠉⠛⠳⠶⣤⣀⣠⡒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠉⠉⠛⠛⠒⠒⠒⣲⣒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠁⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⠀⠀⠀⣀⣀⡠⠤⠒⠉⠀⠙⣷⠀⠀⠀⢰⡏⢠⠊⠀⠙⣧⠀⢠⡟⠀⠀⣿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⡠⢻⠇⢹⣏⣀⠀⣹⡄⣾⡇⠀⢐⣿⡀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠔⠁⣿⠀⢸⡏⠉⠉⣹⠃⢿⣇⡠⠊⠙⠻⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠚⠁⠀⣸⠇⠀⠸⣷⣄⣠⠏⠀⢀⣁⠤⠄⠒⠒⠒⠒⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠒⠒⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢉⣡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣰⠏⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⠦⣤⣊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠀⢀⠞⠀⠈⠉⠓⠲⠤⠤⢤⣄⣀⣀⣀⣀⡠⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠶⠖⠚⠛⠋⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠔⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠦⠠⠤⠤⢤⠤⡤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠒⠒⠠⣄⠀⠀⢀⣤⣤⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠈⠓⣶⣿⡟⠉⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⠀⠀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣿⡷⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡗⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠒⠛⠛⠃⠀⠀⠀⠻⠦⠤⠤⡄⠀⠀⠀⠀⠀⠈⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣦⣤⣤⣤⣤⣤⣤⣀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡛⠓⢦⠀⠀⠀⠀⢠⣶⡞⠒⠒⠆⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠣⡀⠀⢠⣿⡟⠀⢀⠞⢀⣴⣾⠿⠋⠉⠋⠑⢄⠀⢀⣠⣾⠟⠓⢲⠀⠀⠀⠀⣠⣤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠱⣄⣾⡟⠀⢀⠎⢰⣿⡟⠁⠀⣀⢴⣦⡄⠀⢳⠈⣿⣿⠂⠀⠈⠀⠀⠀⠀⣿⡿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠘⠛⠀⢀⠋⠀⣿⣿⡇⠀⠀⠁⠀⢻⣿⠀⠀⠀⣿⣯⠀⠀⡇⠀⠀⠀⠀⣿⡧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⢠⠃⠀⠀⣿⡟⠀⠀⡀⠀⠀⣸⣿⠀⠀⢸⣿⡯⠀⠀⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠠⡄⠀⠀⢰⣿⡇⠀⠀⠃⠀⠀⣿⡇⠀⢸⢸⣿⡇⠀⢸⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠀⠀⠇⠀⠀⢸⣿⡇⠀⠀⢡⡀⣴⠟⠀⠀⡾⢸⣿⡃⠀⢸⠀⠀⠀⠀⣾⣿⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠇⠀⠀⢸⣿⣇⠀⠀⠈⠉⠁⠀⠀⢰⠇⣾⣿⠀⠀⢸⠀⠀⠀⣰⣿⡿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣀⣠⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⢀⣴⠟⠀⣿⣯⠀⠀⠘⠦⣤⡾⠿⠟⠁⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠉⠉⠛⠓⠦⣄⡀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⡼⠁⢠⠢⡷⣀⣀⡀⢀⡴⣶⠀⠀⠀⠀⠿⠇⠀⠀⣰⡏⣻⠀⠀⠀⠐⢳⣆⡀⠈⢷⡄
⠀⠀⠀⣸⠁⠀⢈⠝⣿⡟⠈⠀⣾⠀⣿⠀⠀⠀⠀⣠⠀⣿⡇⢿⣶⣋⡸⠓⠀⠃⣠⢀⠙⠀⠈⣿
⠀⠀⠀⡿⠀⠀⡆⠀⣿⡇⠀⢸⣿⢠⡏⢀⡤⣤⡈⣿⡀⣸⠏⠀⠉⠁⠀⣰⡇⠀⣿⢨⡠⡄⠀⢸⡇
⠀⠀⠀⣇⠀⠀⢧⡀⣿⡇⠀⢸⣿⡼⠀⢸⣇⢸⣧⠈⠛⠋⡀⢀⡞⠹⣦⢸⣇⣀⠟⠢⠔⠁⠀⢸⡇
⠀⠀⠀⢿⠀⠀⠀⠙⢿⣇⠀⠘⣿⡁⠀⢰⣭⠼⢁⣤⠀⢸⡇⠈⡿⢄⡿⠃⢈⡕⠢⢤⠀⠀⠀⣸⠃
⠀⠀⠀⠘⣧⠀⠀⣾⡵⡻⠀⠞⢻⣧⣤⠏⠀⠀⢸⡇⠀⢸⣷⢰⠟⠋⠁⠀⠈⠓⠛⢸⠇⠀⢠⡟
⠀⠀⠀⠀⠙⣧⡀⠉⠋⠁⢴⡰⠂⢠⡄⠀⠀⡠⠊⠛⠖⣻⣿⠃⢰⡐⢢⡐⠤⠤⠔⠋⠀⢠⠟
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠣⣤⡤⠖⠋⢀⣤⢒⠍⠀⣿⠄⠤⠍⠟⠋⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⢼⡇⣯⣲⢠⡟⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠈⠻⠶⠴⠊⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⠀⠀⣀⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣐⠤⠤⣤⣔⣀⠀⢀
⠀⠀⠀⠀⠀⢀⢀⠴⠒⠀⢿⡀⡔⠁⠀⠀⠀⠁⠨⡀⠀⠀⠀⠀⠀⠀⢀⡥⠊⠉⠁⠒⢦⡞⠈⠀⠉⠓⢤⡢⡀
⠀⠀⠀⠀⠐⠕⠀⠀⠀⢀⢀⢹⠀⠄⠴⢦⠀⠀⠀⠈⢢⡂⠀⠀⠔⣰⠋⠀⠀⠀⡠⠠⡄⣧⡀⠀⠀⠀⠀⠊⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⡓⠳⡐⢀⡴⡇⠀⠄⠀⠀⠡⢀⡀⠜⢬⠀⠀⠀⠀⢳⢀⠶⡣⡿⠆⠀⠀⠀⡴⠒⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠞⠀⠒⠡⠄⡂⣡⠄⠷⠐⣆⠀⢈⡀⠀⡼⢂⠀⠀⡤⢤⡷⠲⠟⠠⠀⠀⣠⠺⠗⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⡆⠠⣀⠞⢁⣸⠀⠘⠁⢿⠎⠁⠉⢂⢂⠀⡀⠰⠀⠌⡄⠀⡒⠚⠠⠊⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠁⠀⠸⢸⠀⢈⠀⢸⠀⡓⡑⢸⢾⡄⠰⠇⢀⠇⡄⠀⠜⢀⢁⡠⠤⠦⢶⠊⣹⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡎⢁⢀⣉⡷⠐⢰⡀⠈⠉⢙⢆⠈⢀⡼⠹⢃⠀⠀⡾⠀⣀⣀⣀⣺⡋⠀⠀⠀⠀⢱⡈
⠀⠀⠀⠀⠀⢂⣁⣠⠖⠰⠅⡀⡨⠃⠀⠀⣥⣉⠀⠈⢻⠉⡟⠉⠉⣢⡖⠉⠱⡁⠀⢻⢈⠵⠋⠉⠳⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠑⢄⠀⠀⣤⠿⢄⡠⢄⠈⣮⠀⡀⢈⡡⣹⢀⢄⡑⢤⠜⠁⠀⣠⣤⠎⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠈⠃⡂⠀⠀⠀⠀⠈⠁⠈⢆⠈⢁⠜⠐⢁⣀⠈⣾⠀⣿⠸⠀⠃⠀⠀⠀⢠⠤⡎⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢈⠀⢸⣄⠂⠈⠖⢀⣅⡀⠘⠃⠰⠀⠀⡠⠐⡷⠀⣤⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⠀⢀⠰⠄⡼⠁⢉⣦⡤⢞⠻⠳⢤⡤⠓⢲⠏⠀⠰⠃⠀⡘⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⣴⠉⠉⠵⠂⡀⠀⠀⣟⠁⠀⠀⠘⡀⠈⠀⠀⢻⠀⠀⠀⣀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠢⠀⠀⠢⡀⠀⠀⠂⢃⡀⠀⠀⠡⠔⠉⠉⠚⠀⠀⢄⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠀⠀⠀⣸⠋⠀⠈⠐⡀⠈⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡋⠩⠇⠀⠀⠀⠈⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠐⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡂⢀⠀⢐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠛⠚⠿⢛⣓⢰⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃⣌⢢⠟⠛⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢰⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠨⠨⠉⠲⣄⢀⡉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠰⠚⠉


⠀⠀⠀⠀⠠⡍⠉⢷⡀⠀⠀⠀⢀⡴⢀⣡⡄⠀⢀⠤⠒⠊⠁⠀⠀⠠⢄⠀⠀⠀⢀⡐⣒⡆⠀⠀⠀⠀⠀⠒⠳⡆
⠀⠀⠀⠀⠀⠸⣆⠽⡻⡄⠀⢀⡞⠀⢠⠟⠀⡰⠀⢀⣤⡶⠖⠲⢦⣜⠒⠱⡄⠀⢸⡁⢼⡇⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠘⣆⠙⠟⣤⠎⠀⣶⠋⠀⢰⠀⢀⡜⠁⠀⠀⠀⠀⠈⢳⠀⢻⡀⠸⠁⢹⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⡾⠃⠀⠀⡿⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⢸⠀⣸⡇⠀⠀⠀⠀⢰⠦⡑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣤⡄⠀⠀⠀⢹⠀⠺⡀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠁⠸⠢⡈⡇⠀⠀⠀⠀⢸⠁⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⣿⠇⠀⠀⠀⠈⣆⠘⣻⠢⣀⠀⢀⣠⡾⠷⢀⠆⠀⠘⡆⠀⢿⣦⣀⣀⣠⠞⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣿⠀⠀⠀⠀⠀⠈⠢⣄⢀⠈⠋⡛⠁⣀⡴⠋⠀⠀⠀⠙⢦⡀⠙⠛⠙⠋⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⣿⢿⠿⡿⡿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣿⣿⣿⣟⣿⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠲⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠉⢙⣻⣿⣿⣷⡄⠈⠒⡀⠀⠀⢀⠘⠁⠀⢠⣾⣿⣷⣯⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠋⠉⠉⠹⣿⠇⠀⠀⠈⢄⡠⠁⠀⠀⠀⢸⣿⠿⠟⠫⠉⢻⣿⣿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⢷⠃⡈⡄⠀⠀⠀⠙⠀⠀⠀⠀⠘⠃⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢼⣝⣿⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠀⠀⠀⢡⠙⢀⡀⠤⢤⡈⡀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣤⠄⠀⠀⠀⠈⣿⣳⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⣞⠁⠀⠠⡀⠁⠀⠀⠀⠀⠀⡠⠉⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢠⣿⡿⠀⠀⢠⣷⠀⠲⣀⠀⢀⠜⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣆⢲⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠄⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⠀⠀⠘⠓⡉⢉⣁⠲⠚⠁⠙⢄⣀⣀⣠⣤⠶⠃⠀⢀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣟⣭⣭⣿⣿⣿⢿⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⢸⡿⣿⣿⣿⣭⣭⣻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⢿⡇⠀⠀⠀⠀⠀⠀⠑⠤⡀⢀⡤⠊⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣍⠙⠛⠿⢿⣿⡟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣻⣿⡿⠿⠛⠋⣹⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡀⠀⠀⢶⡄⠈⠉⣀⠀⠀⠀⠒⠒⠂⠐⠐⠂⠒⠀⠀⠐⠀⠀⠀⠀⠉⠁⠀⠀⡄⠀⠀⠀⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⣿⠁⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⣸⠰⡇⠀⠀⠀⡀⢀⡀⣧⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠦⠀⠘⣧⣀⣸⡇⢀⠿⣇⠸⢿⡇⠀⠀⠀⡈⢸⡷⡇⠀⡷⣇⢸⠇⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢿⣿⣿⣿⣿⣳⣦⣀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣽⡿⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⠀⣱⠾⣿⣿⣿⣿⣿⣿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⡄⢰⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⠟⠉⠁⠈⠁⠺⢷⣵⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠙⠙⠀⠆⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠹⢧⣟⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠇⠀⠀⠀⠘⣌⣤⠐⠋⠛⠀⢿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⠀⠀⠀⠈⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣹⣷⠀⠀⠘⣆⠘⢿⣿⣿⣿⣿⠟⠀⡶⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡀⢄⣰⣿⡏⠀⠀⠀⠛⠀⠈⠛⢿⡿⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣷⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣄⣠⣤⠄⢀⣀⣤⣿⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣿⣿⣿⣿⣷⣶⣶⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠁
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⠇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠀⡏⠂⢀⠀⢐⢹⠀⣄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢀⢹⠀⡈⡄⠇⠇⢀⠀⠨⠸⢠⠁⠀⡏⡀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡀⡎⢆⢱⢃⡆⡇⠀⠡⢸⢀⡘⡎⡰⢡⢀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠱⡑⠀⡎⠀⠀⠀⠑⠀⠘⠊⠀⠀⠀⢸⠈⢈⠎⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⡄⢡⠑⠁⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠈⠊⡌⢀⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠁⠈⡡⠔⠚⠈⠉⠑⠒⢤⡀⢀⡤⠖⠛⠋⠓⠓⠢⣌⠁⡈⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⠰⣄⢘⢀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⡀⡇⣠⠆
⠀⠀⠀⠀⠀⠀⠀⢎⠹⠄⠑⢄⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⡤⠊⢠⠇⡹
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠙⢮⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡵⠋⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⠋⣗⣺⠃⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⣗⣺⠙⠤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⣠⡾⠛⢄⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⣠⣋⠻⣦⡀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⡋⠀⢀⣾⠃⢂⣤⣀⡀⠈⠑⠢⢄⡠⠖⠉⠀⢀⣀⡄⣴⡞⢾⡟⠷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢿⢧⢠⡿⠉⣿⢸⡏⣹⡏⣼⡷⠎⠉⠹⣧⣼⡏⠹⣧⣬⡿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠿⣾⣋⠸⣷⡟⠀⣿⣗⡂⠀⠀⠈⣿⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠚⠛⠒⠒⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠛⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠓⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⡄⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠘⠒⠋⠙⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢉⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠻⠟⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⢠⢁⠁⠈⠈⠗⡴⡆⡠⠒⢴⢦⢶⠖⢲⡔⠇⠉⠀⠁⢠⢈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⢀⠀⡀⡍⠓⢮⣇⣛⣧⣛⡼⣆⡼⣁⣸⢯⠖⠋⡁⡀⢀⠈⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠒⠣⠠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠮⠠⠓⡊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢈⠣⣀⠆⠀⠘⣿⠀⠀⠁⣰⠋⠐⣆⠀⢹⡇⠀⠀⠈⠀⠀⣆⡠⢃⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠀⡄⠛⠀⠀⠀⠘⣧⠀⢰⡏⠀⠀⢹⡄⢸⡇⠀⠀⠀⠀⠀⠘⠃⡄⠰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠦⠱⠀⣀⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⢸⠇⢸⡁⠀⠀⠀⠀⠀⢀⡀⠰⠑⢆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠆⠁⠀⠀⠀⠀⣿⠀⠀⢷⡀⢀⡟⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢆⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⢠⠀⠀⠀⠈⠉⠁⠀⠀⠉⢉⡀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠀⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠲⢃⠀⠀⠀⠀⠀⠘⠷⠒⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠳⢆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠒⠦⠀⠀⠀⠠⣔⠁⢠⠮⢗⡀⠀⢒⣀⠀⠀⠠⠒⠂⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⢄⡀⠀⠀⠀⠀⠃⢔⠊⠁⠘⠉⠉⠀⣀⠄⠀⣤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⠉⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠙⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢀⣦⡀⢘⡁⠲⠀⠀⠀⠠⠂⣙⠀⣠⣆⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡳⠙⠅⢘⡀⠀⠀⣸⠀⠝⠱⣻⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠈⢀⡁⠀⠀⣁⠌⠀⢰⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠰⠀⢰⠁⠀⠀⢱⠐⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠀⠀⠀⠈⠁⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠿⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⢀⣤⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⣴⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠰⣢⡀⠀⢸⡇⢹⠣⣤⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣴⡟⠉⠉⢻⣣⠙⢷⡄⢸⠇⠀⡟⣅⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⢿⢇⠀⠀⢀⣗⠀⠈⢻⣿⠀⠀⠘⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣇⠀⣀⡈⠻⠷⠶⠿⠋⠀⠀⠀⠀⢀⣤⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿
⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠛⠋⠁⠀⠀⣠⠄⣠⡾⠛⠻⡷⡄⣟⡄⠀⠈⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣿
⣿⡇⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣢⣄⢸⡟⠀⡏⡁⠀⠀⢸⣾⠸⡳⣀⣀⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿
⣿⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣹⠀⠀⠱⣵⣄⣠⣼⠏⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣿
⣿⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣿
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣼⡟
⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠦⠤⠤⠤⠤⠤⠤⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠄⠄⠀⠄⠀⠠⠄⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⢻⡛⠛⠛⠓⠒⠒⠻⠶⠶⠶⠶⠦⠤⢤⣤⣤⣤⣄⣼⣅⣀⣀⣀⣀⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣼⠿⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⠭⣭⡉⠉⠉⠉⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣇⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠓⠚⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠳⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣴⠟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣼⠛⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⢧⣀⣀⣴⠇⠀⢀⡞⠁⠀⠘⣇⠀⢠⡟⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡀⠀⠉⢉⡟⠀⠀⢸⡇⠀⠀⢀⡟⠀⢸⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⢷⣤⣤⠟⠁⠀⠸⣇⣀⣀⡼⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠶⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠲⠶⠶⠶⠶⠤⠤⠤⢤⣤⣤⣤⣤⣤⠤⠶⠶⠚⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡤⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠉⠉⠉⠉⠉⠳⡄⠀⣿⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠶⢖⣒⣛⣓⣒⠒⠲⢦⣄⠀⠀⢸⠀⠀⠀⠀⢀⣴⠃⠀⢹⡆⠀⠐⠞⠋⠀⠀⣠⢔⣫⢖⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢛⣽⣿⠀⠀⢸⣀⣀⣤⠶⠋⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠺⣿⠯⣭⠤⠴⠞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡡⠖⠁⣿⠏⠀⠀⢸⠋⠡⠀⠀⠀⣰⡞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠑⠲⠿⠀⠀⡆⠀⣸⢄
⠀⠀⠀⠀⠀⠰⡀⡠⡄⠉⡉⠀⠀⠀⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⣧⣤⣤⡴⠏⠀⣀⠀⠀⠀⣠⠀⠀⠀⢄⠤⠛⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠉⠙⠤⠼⡏⠀⠀⢀⠀⠓⠀⠀⠘⠠⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠈⠁⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⠆⠠
⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⣴⣿⣿⣿⡿⣿⣿⣿⡿⠛⣉⣤⣤⣤⣍⠻⣿⣿⠹⣿⣿⣿⣿⢁⣿⣿⡿⠋⣠⣴⡆⢹⣿⣿⣿⣿⣿⠆⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣽⣿⣿⠀⣿⣿⡟⢠⣾⣿⡿⢛⡻⢿⣷⡸⣿⠀⣿⣿⣿⡇⣼⣿⡟⠀⣴⣿⣿⠇⣸⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠈⠀⠀⡇⠀⠀⠰⣿⣿⣿⡟⠀⣿⣿⢠⣿⣿⢋⣾⡿⣿⡎⣿⡇⣿⡀⣿⣿⡿⢠⣿⡿⠀⣼⣿⠟⢃⣼⣿⣿⣿⣿⣿⡿⢃⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⢈⣽⣿⡇⢸⣿⣇⢸⣿⣿⢸⣿⡀⠟⣱⡿⢱⣿⡇⢻⣿⠇⣾⣿⡇⢠⣥⣴⣾⣿⡿⢁⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠿⣿⣿⠁⣼⣿⣿⣼⣿⣿⣦⡛⠿⠿⣛⣵⣿⣿⣧⢸⡟⢰⣿⣿⡇⠸⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠰⠶⠿⠖⠀⠀⣠⣾⣟⠀⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢡⣿⣿⣿⣿⣄⠙⠛⣉⣴⣿⣿⣿⣿⣿⣅⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⣤⠈⡷⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⡀⠀⠈⢉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⢹⠛⠁⠀⡀⠈⠁⢀⠀⠀⠃⠀⣼⠃⠘⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⠀⣤⠀⢀⠀⠀⢰⠄⠙⠀⠀⠳⢾⠉⢠⡆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢹⣆⠀⠉⠀⠀⠀⣰⠏⠀⠀⣰⣿⣿⣿⣿⠟⢻⣿⣿⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢰⠏⠀⠀⢰⣿⡿⠀⠘⠃⠀⣼⣿⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠹⣦⠀⢠⡏⠀⠀⠀⢸⣿⣿⡀⠀⢀⣾⣿⣿⡏⠀⠀⣿⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⠀⢸⣿⣿⣷⣤⣾⣿⣿⡿⠁⠀⠀⢻⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢷⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠉⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣀⡤⠤⠤⠤⣀⡞⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⣼⡟⠀⠀⠀⢀⡾⠉⠓⠦⣀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⢻⣿⡄⠀⢠⡞⠀⠀⠀⠀⠈⢙⡿⣤⣀⡀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠙⢿⣶⣏⡀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣴⡿⢁⣴⣾⣷⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠘⣿⢀⣿⣿⠟⠁⠀⠀⣿⣿⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⡀⠀⢰⡏⠀⠀⣀⣤⣤⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⢸⣿⣿⠃⠀⠀⢀⡴⣋⠤⠄⢤⡀⠀⣸⣿⡇⠀⡾⠀⢠⣾⡿⠁⢀⡟⠀⢠⣾⢋⡟⠀⢀⡴
⠀⠀⣀⡀⠀⠀⠀⠀⠹⣇⠀⠀⠀⣼⣿⣿⣀⠤⠚⣡⠞⢡⣴⡆⠀⢹⠀⣿⣿⠀⢰⠇⢠⣿⣿⣃⡴⠋⠀⠀⠘⣿⣾⢁⣠⠞
⠀⢀⣭⡁⠀⠀⠀⠀⠀⠈⠛⠐⠀⣿⣿⡏⠀⠀⢰⠇⢠⣿⣿⠁⠀⢸⡗⣿⣿⡄⣾⠀⢸⣿⡿⠁⠀⠀⠀⠀⢀⡞⠉⠉
⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠸⣄⣸⣿⣟⣠⠔⣻⠀⢹⣿⣧⡇⠀⢸⣿⡇⠀⠀⠀⠀⡴⠋
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣸⠿⣿⡏⠀⢠⠏⠀⠀⢿⣿⠃⠀⠈⢿⣧⠀⢀⡴⠊
⢸⣿⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⣰⠃⠀⠙⠷⠴⠋⠀⠀⠀⠀⠛⠀⠀⠀⠀⠉⠋⠉
⢸⣿⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣤⡾⠃
⠘⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠈⠛⠁⠀⠀⠀⠀⠀⣠⠴⠚⠳⣦⡄⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠈⠙⣆⠀⠀⠀⣠⣴⠄⠀⢀⣾⡟⠀⠀⠀⢀⣶⢶⡄⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⡟⠀⠀⠀⣀⡀⠀⠘⡆⠀⣼⣿⡏⠀⠀⣾⣿⠁⠀⠀⠀⠘⢿⣾⣡⠞
⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⣧⠀⢀⣾⣿⠃⠀⢀⣷⠘⣿⣿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⣠⠊⠉⣿⣆⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣶⡆⠈⠑⣾⣿⡯⠄⠒⠉⡇⠸⣿⡟⠀⢀⡼⣿⡇⠀⠀⠀⠀⡴⠃
⠀⠀⡼⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⠇⠀⠀⠀⡇⠀⢿⣧⢀⡾⠁⠘⢷⡀⠀⣠⠞⠁
⠀⢸⠃⠀⠀⠀⢿⣿⠇⠀⠀⠀⢰⣿⣿⡇⠀⠀⣿⣿⣇⠀⣰⢿⣿⠀⠀⠀⣸⠃⠀⠀⠉⠉⠀⠀⠀⠀⠉
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣴⠃⠈⢿⣆⠀⣰⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣸⠉⣿⣿⡇⠀⠀⠀⠉⠉⠁
⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢠⡏⠀⣻⣿⣿
⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡾⠀⣰⠛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠇⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡴⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣷⣞⣩⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⣰⡋⠉⡱⠊⠉⠁⠀⠢⢐⠄⡀⠀⠀⠀⠀⠀⠀⢀⠠⢂⠤⠖⠯⢁⣀⣹⡍⠓⠒⠢⣄⡠⢀
⠀⠀⠀⠀⠀⠀⢂⠐⠉⠀⠀⠈⠳⡼⠀⠀⢀⠀⠀⠀⠀⠐⢌⠂⠀⠀⠀⠀⠐⣡⠞⠁⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠙⡢⡑⠄
⠀⠀⠀⠀⡐⠐⠁⠀⠀⠀⢠⠒⣤⢧⡐⠡⠊⠑⡄⠀⠀⡀⠄⠷⡑⠀⠀⢊⠐⠇⠀⠀⠀⠀⡜⠀⠇⢸⢢⡈⠠⠀⠀⠀⠠⠈⣂⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢠⡏⡈⢃⠄⢰⠟⡇⠀⠐⠀⠀⠀⠐⢠⠄⠊⠰⠀⠀⠀⠀⠀⠹⡠⠞⢥⡲⠞⠁⠀⠀⢀⡾⠉⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡞⠒⠚⠓⠒⠀⡁⢥⡖⠛⢃⠑⣄⠀⢠⡐⠀⠠⠓⡄⠀⢀⠒⢤⠷⠛⠛⠃⠤⠀⢀⡤⠹⠗⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⢲⠀⢰⢀⠞⠀⣄⡇⠀⠃⠰⢹⠊⠀⠈⢣⠘⡀⢰⠀⠘⠀⡄⣠⠀⣆⠀⠉⡰⠋⠀⠀⠀⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⢨⠀⠀⢸⢀⡇⠀⠀⠀⠻⠰⠒⢒⠈⡴⡇⠀⢶⠁⢀⠆⣥⠀⡤⠇⡈⢀⣀⡤⠤⣴⠆⠉⡂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠁⡐⠚⠀⠘⠐⣖⠡⢀⡅⠀⠑⠒⠻⠀⠑⠁⢰⠆⠿⠀⠀⠀⡾⠠⠁⠀⠂⠐⡶⠋⠀⠀⠀⠈⢣⡌⠁
⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⢀⡙⠀⠀⢲⠊⠁⠀⢚⠗⠀⠒⢲⡗⠒⣶⠖⠓⢄⣀⠱⠢⡨⠂⠀⢼⠛⢂⡸⠓⠲⡄⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠠⠓⢢⠏⠁⠀⠀⠰⠌⠁⠀⠀⠀⢿⡒⡄⡀⠀⢃⡰⠁⠀⠀⠞⠛⡄⠀⠘⢄⠀⢈⡵⠋⠀⠀⠀⡄⠀⠀⠀⠟⠌
⠀⠀⠀⠀⠀⠀⠁⠹⡄⡀⠀⠀⠀⠈⠐⠤⣄⢺⡉⠱⡔⠉⡢⢀⠓⠀⢢⢀⡆⢱⡇⡐⢰⠠⠑⠋⠀⠀⠐⠛⡞⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⡜⠀⠆⢴⢖⠀⡏⡇⠸⣇⠃⠸⠀⠀⠀⠀⠠⠏⠸⠀⠀⢀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⢦⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⣄⡇⠈⠊⠀⣧⡄⠀⠉⠀⡈⠀⢀⠔⠈⣹⠃⠀⣆⡰⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⡠⢀⡀⠀⣀⠀⠠⠧⠠⠋⠀⢙⡦⠤⢚⡘⠉⠢⡤⠚⠙⣻⠃⠀⠀⡇⠀⢀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠠⡔⠉⠉⡵⠆⢠⠂⠀⢠⡏⠀⠀⠀⠘⠆⡐⠀⠀⠀⣿⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢄⠀⠑⠲⡁⠀⠀⠠⠸⠂⠀⠀⠀⠈⣀⠊⠉⠱⠟⠀⠀⡠⠪⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⠈⡀⠀⡴⠂⠉⠑⠠⠀⠀⠂⠀⠀⠐⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⡄⡥⠚⢧⠀⠀⠀⠀⠱⠀⠀⠀⠀⢠⢟⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡃⢀⢉⠀⠀⠀⠀⠀⠠⠀⡠⢔⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢆⠀⠀⠀⠀⡠⢈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⠠⡠⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣉⡍⠻⣷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣰⡟⠀⠀⣻⣷⠀⠐⠀⠄⠀⠂⡄⠀⣼⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡤⠀⣿⠃⠀⠀⣿⡇⠀⣀⡀⣘⠀⢈⣀⣸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢦⠀⣸⡟⠀⠀⣼⡿⠀⣾⠁⣹⡏⢰⡟⢀⣿⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⣠⡿⠁⣠⡾⠟⠀⠈⢿⡴⢿⡴⠻⣧⠾⣿⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⡋⠩⠘⠉⠉⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠌⠀⠀⠀⡀⢰⠟⠋⢩⣭⠅⢭⣭⠉⢭⡍⢭⡭⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⣰⠟⢹⢆⣤⣶⡄⢻⡆⡜⢿⡄⡞⠀⢸⡧⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣰⣿⣴⠟⠀⠙⠟⠁⠈⠿⠁⠘⠿⠀⠀⠼⠧⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣿⠇⠀⣴⢿⣧⢀⣾⠁⣾⢀⡾⣻⠆⡀⡠⠴⠋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣰⡿⠀⠀⣿⣼⠟⠻⣧⣼⣣⠾⣿⣡⠜⠁⠑⢄⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣽⠟⠛⠶⣦⣤⣥⡄⠠⣤⠀⣤⠄⣠⠤⣤⠀⢤⡤⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠉⠉⠀⠀⠙⣷⠁⢸⡇⠀⢸⡇⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠐⠛⠀⠈⠓⠤⠚⠁⠈⠳⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣎⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠟⠁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣢⢄⠒⠀⠀⠀⠀⢟⡀⠀⠀⠀⠀⢼⣶⠂⠀⢀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠭⠀⣠⠄⠀⠀⠈⢇⡀⠀⠀⠀⠈⢻⡆⠀⠘⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠰⢿⣦⣀⣀⡠⠤⢩⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠆⠀⠀⠀⠈⠟⠉⣤⣶⣶⣷⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢷⠀⠀⠀⢀⠀⠀⢹⣧⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠐⣤⣘⣋⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠰⣿⡟⠁⣠⠄⠈⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣤⣀⣿⠀⢀⣿⡄⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⣴⣤⡆⠿⠟⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⣶⢦⡶⣤⢾⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣷⣤⣴⣛⠏⠃⠚⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡢⣱⣛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠌⡀⢟⡱⠋
⠀⠀⠀⠀⠀⠀⠂⢀⢀⡑⠊
⠀⠀⠀⠀⠀⠐




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣠
⠀⠀⠀⠐⠊⠐⠒⠀⠐⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠔⠈⠀⠀⠉⠣⠀⢂⠀⠀⠀⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠐⠈⠐⠂⠁⠂⡀
⠀⠀⠀⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠁⠀⡀⠀⠀⠀⠋⠀⣸⠀⠘⠂⠒⡄⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⡌⠒⠒⠁⢀⠘⠀⠀⢀⠙⠀⠰⠬⠄⠤⠀⠀⠀⠀⠀⠈⠢⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠐⠂⠀⠀⠐⠃⠂⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠄⠀⠀⠈⠁
⠀⠀⡠⠠⡀⠐⠤⢀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠒⡤⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⡀⠀⣄
⠀⡠⠃⠖⠩⠉⢢⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠐⡌⢂⡵⠓⢤⡫⠅⡀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠴⡤⠊⠐⠣⡠⡆
⠀⠐⠒⢂⡀⣂⠴⢠⠂⠀⠀⠀⡀⠀⠤⠄⠠⠄⠀⠀⠀⠀⠀⢸⢒⠺⡀⠀⢨⠃⣘⠀⠀⠀⠀⢀⠈⢰⠒⡎⠀⡀⠀⠀⠀⠀⡤⠆⠁⠀⠠⢅⠄
⠀⠀⠁⠒⢀⠹⠀⠂⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠣⡆⡍⣉⢡⡱⠒⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠉⠐⠄⠀⠀⠁⠰⠁⠉⠄⠔
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠓⠀⠀⠀⠀⠡⡀⠀⠀⠁⠁⠀⢀⠊⠀⠀⠀⠰⠄⠀⠀⠀⠴⠀⠀⠀⠈⢀
⠀⢀⠤⠄⠀⠀⠀⠆⠠⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠄⠐⠀⠀⠀⠀⢠⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠡
⠀⠀⠄⠌⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠐⠤⠄⠂⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠆⠀⠀⠊⠀⠀⠀⠀⢄⣀⠄⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⡰⢆⠀⠀⠀⠀⠳⡀⠀⠀⠠⠂⠂⠀⠀⡙⠀⠀⠐⡓⠒⠒⠒⢖⠒⠒⠒⠒⠶⠒⠒⠒⠒⠖⢒⠒⠒⡲
⠀⠀⠀⠀⠀⠀⠀⠑⢀⠌⠀⠀⠢⠀⠐⠀⠀⠐⢄⠐⠁⠀⠀⢡⠌⠀⠀⠀⠀⠈⢄⡠⠂⠀⠁⡀⠠⠊⠀⠐⠄⠠⠂⠀⠀⢡⠔
⠀⠀⠀⠘⠃⠀⠀⠀⠈⠂⠀⠀⠠⠛⢄⠀⠀⢀⠈⢀⠀⠀⠠⠂⠀⠀⠀⠁⠀⠀⠀⠡⡀⠀⠀⠜⢀⠀⠀⠀⠜⢃⠀⠀⢀⠊⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠁⠀⠈⢂⡔⠁⠀⠀⢡⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠊⠀⠀⠡⡀⠊⠀⠀⠁⡔⠁
⠀⠀⠀⠀⠠⠄⠀⠠⡄⠀⠀⠈⠢⠀⠠⠊⠑⠄⠀⢀⠊⠀⡔⠈⠁⠉⠐⠂⠉⠉⠑⢢⠀⠀⠡⠀⢀⠔⠁⢄⠀⢀⠌⠀⠀⠀⡰⠀⢀⠤
⠀⠀⠠⡀⠨⠄⡚⠠⠀⢠⠀⠀⠀⠐⠀⠀⠀⠈⡶⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⢂⠀⠀⠀⠰⠂⠀⠀⢄⠠⠴⠈⠂⠌⠀⠤
⠀⠀⢀⠄⢃⠨⠠⠀⠮⢁⠀⠀⠀⠀⠈⠂⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠡⡀⡔⠁⠀⠀⠀⡀⠌⡀⠂⠘⠀⠏⡀
⠀⠀⠈⠀⡘⠀⢂⠨⠈⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠠⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠌⠐⠂⢃⠁⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠑⠀⠄⠀⠀⠀⢀⢀⠀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢄⠐⠀⠑⢄
⠀⢠⠀⠑⠖⠉⢠⠀⠀⠀⠀⢂⠀⣀⣘⠀⠀⠀⠈⢄⠀⢁⡐⠀⡠⠁⢀⡀⠈⠚⡈⠱⠈⠁⠀⠂⠀⠀⠀⢀⣀⡀⠀⠊⠀⠀⠀⠐⠀⠰⠆⠉⠢
⠀⠀⢢⠀⠀⢀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠄⠀⠀⡠
⠀⠀⠀⠠⡠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠁⠄⠈⠑⠈⠀⣠⡄⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡐
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣈⣀⣀⣀⣀⣀⣈⣀⣈⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢶⣿⡿⣟⢿⡿⣶⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⡶⢨⡽⣿⣿⡧⢸⡇⢿⣧⣇⠿⣿⣿⣿⣯⣿⣷⢤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⡿⣿⣿⣿⢶⣧⣤⣷⣾⣿⣿⣾⣷⣶⡄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣴⣾⣿⣿⣟⣇⣯⣔⣿⣿⣧⣆⣏⣿⣿⣿⣻⣛⣟⣿⣿⣻⣓⣀
⠀⠀⢀⣤⣪⣯⣩⣿⣿⣿⣿⣷⣾⣿⣿⣇⣿⣿⣿⡟⣛⢿⢿⣟⣟⠻⣿⣿⣧⡄⠀⠈⢹⣏⠉⢹⣿⣿⣿⣿⠈⣿⠀⠛⣿⢻⡟⢻⠛⣿⣿⠛⠛⠻⢻⠛⠃
⠀⢀⣼⣟⣛⣟⡟⣿⣿⣛⣻⣿⣿⣿⢿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⡿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣾⣿⣿⣷⣿⣿⣿⣶⣿⣾⣿⣷⣶⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡘⣯⡺⣺⣎⣾⡀⣿⣿⣷⣸⡰⢇⣇⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣯⣿⣤
⢠⣤⣴⣶⣾⣿⣠⣦⣦⣴⣼⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡛⢛⡟⠛⢻⣿⣿⣿⣿⣏⣇⣉⣉⣁⣿⣩⢈⢙⣿⣿⣿⣻⣛⣻⣿⡟⢛⢛
⠈⠉⠉⢹⣿⡏⠙⠉⠉⢹⣿⣸⣿⣇⣥⣀⣵⣀⣧⣀⣿⣿⡆⣼⣄⣨⣄⣸⣿⣿⣧⣶⣾⣧⣦⣼⡏⣽⣿⢹⡏⣭⣯⠉⣽⢡⣽⣿⡍⢩⣯⡍⡏⡏⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢻⣿⡏⡿⠻⡟⣿⢟⣿⣿⣻⡟⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣻⠷⣿⢿⣶⠶⣶⡿⠶⡿⠶⣾⣿⣷⣾⣷⣶⣷⣶⣿⣿⣿⣤⣮
⣿⣧⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣾⣿⣾⣽⣯⣿⣿⣼⣭⣾⣧⣿⣤⣿⣿⣼⣿⣥⣿⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣧⣭⣬⣽⣏⣠⣌⣿⣿⣇⢈⣀⢸⡏⡀⡁⣿⣿⣿⣏⢸⡇⢸⡇⢾⣇⢙⡇⢨⣿⡇⢩⡁⣿⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣻⣉⣿⣿⣿⣿⡿⣿
⠀⣏⣿⣹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⡟⠟⡿⣿⣿⠻⡟⠻⠿⣿⣿⢻⣿⡏⠟⡟⠛⢻⣿⡟⠛⠛⠛⢻⣿⣟⣿⢿⣿⢿⣿⣿⠿⡿⣿⣿⣹⣿⣇⣟
⠀⠸⡇⢸⣭⠉⣏⠩⣿⣇⢉⡏⢹⡉⢹⣿⣿⣿⣿⣿⣿⣷⣿⡿⣼⡿⣿⣿⣿⣿⣾⣿⣷⣶⣶⣶⣶⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠹⣿⣿⡿⠿⡿⠿⣿⣿⢿⡿⣿⣿⣿⣻⣛⢛⣿⠛⡛⣿⣧⣿⣤⣭⣥⣬⣤⣽⡅⣨⣥⣭⣭⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⣿⣛⣻⣟⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⢿⣿⣿⣿⣻⣿⣿⢰⣿⡏⢿⢠⡼⢟⣿⣽⣽⣿⡏⡩⡃⣤⠟⣉⠉
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⠶⣶⣷⣾⣾⣾⣿⣷⣶⣷⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡙⣿⣟⠛⠛⠛⠻⠛⢿⡟⠛⠛⠻⠛⢻⣿⡏⢹⣿⣿⢙⣿⡟⣿⡟⣏⣿⣻⡏⣯⣿⣿⣟⠿⣿⢻⣟⢿⢻⣏⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣋⠋⢻⣶⣿⣧⣽⣼⣬⣼⣵⣾⣇⣁⣽⣼⣷⣾⣿⣗⣸⣿⣿⣘⣿⣧⣛⣷⣿⣆⣿⣃⣷⣻⣿⣿⣂⣿⣘⣿⣾⣜⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣯⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⠿⣿⣿⡏⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣧⣿⣴⣶⣶⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿⡿⢿⣶⣶⣿⣿⣴⣶⣿⣿⣽⣿⣯⣭⣽⣿⣏⣭⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣯⣽⣿⣿⣿⣧⣿⣯⣿⣿⣯⣼⣿⣿⢹⣿⡇⢿⡡⠆⣷⢡⡇⢼⣿⣿⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡍⠉⣿⣿⣿⣿⡟⣿⡿⠿⠻⠿⠿⠿⢿⡿⠿⠿⠿⠟⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⣿⣿⣿⣧⣿⣧⣵⣤⣌⣤⣯⣼⣇⠑⣱⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⠙⣿⣿⠉⠉⠉⠙⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⡟⣿⣿⣿⡿⠟⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⡈⢁⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⠀⢸⢸⠀⡇⢸⠀⡇⡇⠀⣤⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢩⢳⠀⡝⡆⢸⢸⠀⡇⢸⠀⡇⡇⢠⢣⠀⡾⣙⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⢇⢸⡀⢃⢧⢡⢸⠀⡇⠸⠀⠇⡄⡼⡔⢀⡇⡸⢠⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⢇⢣⢸⠀⡇⠘⠘⠞⠸⣀⠆⢸⣀⠇⠳⠃⢇⢸⠀⡃⡜⡰⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢄⠀⡘⢸⢠⠂⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⡄⡇⢃⠀⡠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⡌⣄⢸⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⡆⢠⢡⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⡁⠈⣉⡤⠖⠚⠊⠉⠛⠒⠦⣄⠀⠀⣠⠴⠖⠛⠛⠓⠒⠲⢤⡉⠁⢈⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠺⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢠⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢨⠰⣄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⣠⠎⡅⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠻⡆⠈⠣⣄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⠜⠁⢰⠟⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠈⠳⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠞⠁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡠⢲⡤⢼⡇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢰⡥⢤⡖⢆⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⢀⣬⣷⠊⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠑⡾⣥⣄⡉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣴⡟⠁⠈⢣⣀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⣠⠾⣷⣌⠙⣿⣄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⣠⡿⠃⢈⣲⣤⡤⣀⣀⠀⠉⠒⢄⡠⠞⠉⠀⣀⣀⠤⣤⣒⣿⠟⢿⣯⠛⠿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣿⢧⡀⣾⠏⢉⣷⢸⡆⢉⣿⠍⣾⣵⠯⠉⠉⢻⣧⣰⡿⠁⢿⣦⣀⣿⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢿⣦⡾⠏⠸⣷⣾⠏⠀⣿⡷⠆⠀⠀⠀⠙⣿⡇⢀⡠⠌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠻⠯⢤⣄⣻⣿⣫⡤⠤⠤⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠋⠀⠀⡇⠀⠀⠀⡠⠒⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⠐⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠁⠀⢀⡼⠁⠀⡀⠀⣈⡀⠀⠑⠖⠒⠀⠁⠀⠀⣀
⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠉⠒⠄⢄⣘⠀⠀⠑⠾⠤⠤⠊⢁⠈⢴⡴⠚⣿⠇⠀⠀⠀⡰⠁⡈⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⣠⣴⡦⣀⠀⠀⣿⠀⠀⠂⠘⡟⠀⠀⠀⡾⠁⠈⠀⠘⠤⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⡄⠀⢀⠔⠊⠉⠉⠻⠿⡴⠋⣠⠾⠀⠈⣧⠀⠿⠤⠀⠀⢿⡇⠀⠀⠀⠣⠀⠀⠀⠀⠄⠐⠒⠂⠠⡀
⠀⠀⠀⠀⠀⠈⠢⣃⣀⣀⣠⠎⠀⢰⠁⢰⣿⡇⠀⠠⡏⠀⠀⠀⡠⠀⠀⢀⠄⠢⠀⡠⡄⠀⢀⠴⠀⠀⠀⢀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⣎⠙⢷⣾⡃⠀⠀⢠⠃⠀⢀⠂⠸⠾⠋⣿⠇⠀⣼⠃⠀⡴⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⠀⠀⢸⡿⢕⠀⣀⣾⠀⠀⡘⠀⠀⠀⢰⡏⠀⣰⡇⠀⠚⢄⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⣿⠁⠀⠙⣿⡟⠀⠀⠙⠦⠂⠀⠺⠧⠔⢿⡀⠀⠀⡼⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⢿⣆⠀⢰⣻⠉⠓⠬⢓⣄⡀⡀⠀⠀⠀⠀⠉⠉⠉⢀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣏⣀⣀⣀⣀⠈⠉⠉⠙⠒⠒⠂⠈⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢊⡙⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠀⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⣀⠰⠖⠊⠀⠉⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢄⠀⠀⠀⡜⠀⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠣⠀⢰⣇⣾⣿⣴⣧⠀⣾⣦⣿⣇⢀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⣿⣶⣧⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣦⣤⠀⣤⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠿⠛⠛⠻⠟⠛⠛⠛⠛⠟⠛⠛⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⡇⠀⣴⠋⣷⠀⣿⠀⣿⠰⣞⠻⠄⠀⣿⠇⣾⠇⣴⠋⣷⡄⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⣿⣀⡀⣿⢀⡿⠀⣿⣠⠋⢴⡋⢁⠀⠀⣿⣠⡿⠐⣿⢀⡿⠁⣿⣀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠉⠀⠈⠉⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠤⠿⠃⠀⠈⠉⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣈⠀⠤⠤⠤⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠤⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⣀⢀⡀⡤⢤⠀⡶⠀⢶⡀⣶⢰⡄⡄⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡤⢄⢠⡄⠀⠠⡤⢠⡄⡤⢠⡲⠀⢰⢚⡇⡟⣼⢀⡇⣟⣸⠡⡇⢼⠀⠇⠘⠸⠇⠇⠸⠰⡇⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⢇⠼⢸⠃⠀⢰⡇⢸⠃⡇⠺⠅⠀⠘⠘⠃⠃⠈⠉⠀⣀⣀⡀⠀⠤⠤⠤⠄⠀⠠⠀⠠⠤⠤⠀⢀⣈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⣀⠀⢀⣀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠇⠉⠶⠠⠼⠀⠸⠶⠰⠣⠸⠄⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣴⣦⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⡀


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

⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣿⣟⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⣿⡿⣿⡟⠛⠛⠷⠶⣤⣄⣀
⣿⡇⠀⠀⠀⠀⣠⡴⠛⣩⣴⠾⣿⠗⠻⠁⠈⠁⠀⠀⠀⠉⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀
⣿⡇⠀⠀⢀⣼⠋⢀⡾⠟⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⢻⢷⣤⡀
⣿⡇⠀⠀⣼⠃⢰⡟⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠾⠋⣡⠔⠀⠈⠀⠀⠀⠀⢀⠀⠀⣀⣀⣹⠞⠉⠻⣦⡀
⣿⣿⠀⢸⡏⠀⢾⠀⠀⠀⠀⢀⡄⠀⠀⠀⣰⡗⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠉⠁⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⣿⣿⠀⢸⡇⠀⠀⠀⠀⠠⠀⢸⡇⠀⠀⣰⣿⠃⠀⣼⠏⠘⣧⢰⡆⠀⣠⠀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⣿⣿⠀⠸⣇⠀⠸⡄⠀⠀⠀⢸⡇⢀⣀⡻⠿⠿⣾⡟⠀⠀⣿⡜⣿⢠⡟⢠⣿⡉⠛⠟⠀⠀⢀⡀⠀⠀⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⣿⣿⠀⠀⢿⣆⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠻⣿⣶⣾⣿⠇⣿⣿⠃⣼⣟⣁⣠⣤⡀⠀⠈⢿⡄⣼⣿⡟⣿⣴⡄⣶⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⣿⣿⠀⠀⠀⠻⣷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠿⠟⠛⠉⠉⠀⣀⠀⢘⣿⢣⡟⠀⣿⣿⠀⢸⣧⠀⠒⠀⢀⣴⣿⣿⣿⠃
⣿⣿⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠛⠷⠶⢿⣿⣶⣾⣿⠀⢀⣴⣾⣿⣿⡿⠃
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⠀⠀⠀⡠⠞⠃⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡟⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣞⠀⠀⠀⠀⠀⠘⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠿⠉
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠀⠀⠠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣿⣿⣿⣿⣦⠀⠀⠀⣿⡀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⣻⠋⠻⣿⣦⡀⣸⠆⣠⣶⣿⣿⣿⣿⠿⠟⠋⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠠⣿⠇⢩⣿⣀⣸⣿⣿⣿⣾⣿⣿⡿⠟⠉
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⣿⡏⠀⠺⠛⢿⣿⡿⠁
⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣶⣿⣿⣿⣦⣴⣶⣾⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⢠⠐⠉⠁⠀⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣰⢏⡟⠀⠀⠀⠀⠀⠀⡟⠻⣶⠋⢹⠇⠀⢠⠃⠀⠀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⢤⣸⠆⠀⠀⢠⣿⠎⠀⠀⠀⠀⠀⠀⠸⡇⠀⠁⡰⠋⠀⠀⢸⡄⠀⠘⠟⢳⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⣠⣤⠶⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣧⡤⠊⠁⠀⠀⠀⠀⠙⢦⣤⣤⠏⠀⠀⠀⣿⠰⡟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢠⠔⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⣿⡘⣳⢻⡀⠀⠀⢠⠠⡖⣆⣰⠀⢀⣤⣰⠖⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠉⠁⠸⣇⠀⠀⡟⠀⢨⠏⣽⣠⠞⢨⡟⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣉⢳⡄⠀⣿⠃⠀⠀⠀⠀⠀⠀⠙⠶⠞⠛⠞⠋⠀⠻⠋⠀⠈⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⠣⠼⠁⢀⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠒⠋⠀⠀⠀⢸⡇⠀⠘⣇⢀⡞⠁⠙⣧⢸⡇⠀⢸⡇⠀⠀⠀⠀⣀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⣄⠈⢷⣤⣤⣿⠀⢧⣀⣠⠏⠈⢧⣀⠸⢧⣀⡠⠔⠉⣰⡖⠲⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⣿⡻⣀⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣀⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡉⠁⠀⠀⠀⡰⠃⠀⠀⣴⠋⠉⠉⠙⢦⠀⣀⡤⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠀⠀⠀⠐⣇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⢉⡉⠉⠉⠓⠒⠦⢄⡀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠿⠏⠃⠀⠀⠀⠀⢀⣈⡲⡀⠈⠻⣦⡀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⡠⠄⠀⠀⠀⠀⠀⢯⣈⣁⡔⠀⠀⠈⢷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠄⠂⠀⠀⠀⠀⠈⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⣶⡇⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠈⠠⠠⠄⡀⡀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⢰⠀⠀⠰⠀⡀⢀
⠀⠀⣤⣤⣿⣷⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣹⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⡠⠀⡀⠀⠀⠀⠀⠠⢀⡄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡘⠀⢰⢀
⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⡄⠁⢈⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀

⢀⣤⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣤⣀⣀
⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡷
⢿⣯⣟⣛⣫⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⠿⠿⠿⠟⠻⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣛⠛⢿⣦⡀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣼⡏⠀⠀⣿⣇⠀⠘⠄⣐⠉⠠⢄⠀⢀⣼⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⢰⣿⠀⠀⠀⣿⡇⠀⠀⠀⠈⠤⠤⠊⠀⣼⡧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣍⠉⠀⣾⡇⠀⠀⣸⣿⠁⣴⠟⢹⡾⠀⣴⠏⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠈⠁⣰⡿⠀⠀⣴⡿⠁⠰⣿⣀⣾⡇⣰⣿⣀⣾⡇⣠⠞⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⡤⠶⠛⣥⠴⠟⠋⠀⠀⠀⠙⠋⠙⠋⠁⠙⠋⠙⠛⠁⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠮⢌⠁⠀⠀⠀⢠⣶⣾⠿⠿⠿⠿⠿⠷⠶⠶⣶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⣫⠄⠀⢀⣤⣄⠘⠉⠀⠐⣿⡁⢘⣿⡁⢈⡖⠀⣶⡏⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⡿⢁⣿⢰⣷⣿⠇⠹⣧⡼⠹⣧⡼⠀⠀⣿⡗⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣿⡷⠞⠁⣀⠈⠋⢀⡀⢛⡁⠀⣛⡁⠀⠐⠛⠓⣲⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡣⠀⢸⡟⠀⢠⡾⢹⡦⢀⡿⠁⣾⠁⣾⢋⡟⢠⢀⠴⠞⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠃⠀⠸⣧⣼⠟⠹⣧⣾⣧⠞⣿⣭⡴⠃⠈⠳⣄⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣭⠿⠛⠻⣶⣤⣤⣤⠄⠤⣤⠀⢤⠄⣠⠤⢤⡀⠠⣤⠄⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠉⠉⠉⠀⠀⠹⣷⠃⢰⣿⠀⠀⣿⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠌⠒⠊⠀⠀⠀⠀⠀⠠⠿⠄⠀⠻⠤⠴⠋⠀⠻⠦⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠪⣄⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢥⡤⢀⡨⢑⡨⠝⢁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠂⠆⠀⠀⢀⡰⢤⡄⡙⢀⠠⠃⠒⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠐⠀⡞⠀⡆⢀⠤⡁⡀⡀⡤⠀⢰⢸⠀⠐⠀⠀⣄⠄⠂⡁⠂⢀⡸⡊⠰⣄⠙⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠤⠇⠳⠁⠯⠀⠈⠉⠀⠀⠀⠀⠀⠑⠀⢓⠂⣥⠀⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⢆⣈⠣⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⣠⠖⡉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢖⣌⡱⢄⠀⠀⢠⠞⠥⠺⢹⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⡱⣠⢇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢠⠔⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠂⠀⠀⠀⠀⠀⠂⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⠄⠀⠀⠀⡄⠐⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠰⡄⠈⢄⠀⠀⠀⠀⠀⠐⠀⢀⡊⠔⠀⠀⠀⠀⠀⠀⡰⠁⢠⠂⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢄⠐⠀⠑⡢⢄⠀⢀⠐⢄⣀⣀⠠⠂⡀⠀⡤⢐⠉⠀⠂⡘⢀⠀⠂⠀⠀⡄⠈⣀⠀⠀⠌⠄⠀⠄⠀⠀⠀⠈⡥⠰⠒⠀⠀⢀⡀
⠀⠀⠈⠂⡀⠘⢤⠚⠀⢀⠀⠀⠀⠀⠀⠀⠇⠀⢃⠔⠃⣀⠀⠀⠀⠀⠀⠐⠀⡇⠀⣿⠀⣾⠙⡆⣧⠈⢹⣏⠁⠀⣧⠀⠐⠂
⠀⠀⠀⢈⠀⠀⣰⠈⠀⡄⠓⣂⢄⣠⢐⣊⠀⠀⡄⡆⠀⢀⠅⠀⠀⠀⠀⠀⠈⠁⠀⠃⠄⠻⠰⠃⠸⠆⠸⠇⠀⠀⠙
⠀⠀⠀⠀⠑⠠⢎⡀⠀⠇⠸⣸⠈⡾⢸⡂⠀⠀⢓⡣⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐