Addictive Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠙⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠻⣿⣿⡿⠟⠉⠉⠀⢠⠄⠀⠀⠶⢿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⣀⣤⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠴⠶⠆⠀⠀⠀⢰⣿⣿⣿⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⢀⣀⠀⠀⠀⣿⡿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢰⡟⣼⣿⣿⣿⣿⣿⣷⡄⠸⡿⠁⠈⠿⠇⠈⢿⡀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣸⣿⡏⠉⠉⠉⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡼⠋⢙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⢳
⠀⠀⢠⣾⡿⢟⣩⣷⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⠀⠀⣠⠎
⠀⠀⠘⣿⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢿⣿⢣⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢟⣷⣾⣤⡄
⠀⠀⠀⠀⠁⠀⠤⠴⠶⠾⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⢧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡷⠋⠀⢿⣷⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠐⣆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⡟⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠤⠤⠤⠤⠤⠤⠽
⠀⠀⠀⢸⡇⢠⠞⠁⠀⠀⠲⣿⠇⠀⠀⠀⠀⠀⠀⣾⠉⠉⣿⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣴⣶⣾⣶⣶⠄
⠀⠀⠀⠀⠙⢈⡄⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⣶⣶⠀⠀⠀⠀⠀⠀⠀⠰⡆⠒⠂⠐⠀⠀⠀⡲
⠀⠀⠀⠀⠀⠙⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣶⣿⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈

⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢿⡷⢿⣗⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚
⠀⠀⠀⠀⢠⣽⣙⣯⠾⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⡖⠨⠉⠀⠍⢹⣶⠀⠀⠀⠀⠀⢠⣾⣿⣦⣼⣥⣾⢿⣧⡀
⠀⠀⠀⠀⠈⢶⣮⣣⡿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠒⠒⢳⣧⡰⠟⠓⠄⣼⣿⡀⠀⠀⠀⢰⣿⣉⢈⣿⣿⣿⣽⢿⣽⣷
⠀⠀⠀⠀⠀⠘⣿⣁⣤⠴⢟⡂⠀⠀⠀⠀⠀⡄⠸⠗⢸⣿⠐⠶⡾⠃⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠩⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠁⠉⠉⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠙⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣭⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⢀⣴⣶⣾⠀⠀⠀⠀⠀⣀⠀⣶⡀⣉⡀⠀⠀⠀⠀⠀⣠⣴⡾⣿⣳⡄⠀⠀⢸⣿⣿⡆⢠⡤⣤⠀⠀⠀⠀⢸⡶⠶⡶⣿⡆⠀⠀⠀⠀⠂⠉⢣⠜⠁⠂⠄
⠀⢀⣴⠋⠻⣿⡿⠃⠀⠀⠀⠀⢻⠄⢻⡇⠠⣅⠀⠀⠀⠀⠀⢿⣵⠿⠟⠛⠀⠀⠀⠀⠉⢉⣀⡹⠿⠿⠁⠀⠀⠀⣸⣦⣤⣤⣿⠁⠀⠀⠀⠘⣠⢶⡀⠶⠇⠠⠁
⠀⠈⠻⣷⡤⠋⠀⠀⠀⠀⠀⠀⢠⡀⢻⡝⠀⡄⠀⠀⠀⢀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣶⣾⣟⠁⠀⠀⠀⠀⠧⡤⠇⠃⠬⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡆⠀⠀⠀⠀⣠⡐⠾⠖⠀⠒⠒⠀⠀⠀⠀⢀⠀⣼⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⠉⢉⣉⠉⠙⡄
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⠃⠀⠀⠀⠀⠿⣧⣶⡆⠀⠀⠀⠀⠀⠀⢀⣈⢷⣽⣴⢏⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⠛⠀⢀⠏
⠀⠀⣛⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠁⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠨⠽⠛⠻⠭⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠛⠉⠉⠉⠁⠴⠁
⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⡴⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠖⢀⡀⢶⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢠⡌⠙⠛⢡⡄
⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠸⣁⠰⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠷⠆⠀⠀⠀⠀⠼⠿⠿⠛⠿⠿⠿⠄⠀⠀⠀⢤⡈⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⢰⡎⠁⠀⠀⠀⠀⠰⣶⣶⠆⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣴⣶⣷⣶⣄⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⣤⠤⠴⠶⣤⣤⡀
⠀⢘⣿⣿⣿⠻⣟⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀⣏⠀⠀⠠⢹⡇⠀⠀⠀⠀⡿⣿⠀⢨⡿⡇⠀⠀⠀⠀⢀⡘⠿⠷⢁⡀⠀⠀⠀⢸⡇⡄⣦⢠⢸⣿⡇
⠀⠰⣿⣿⣿⡿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣶⣾⣿⠁⠀⠀⠀⠀⠁⠄⠈⠀⡀⠀⠀⠀⠀⠀⢈⣭⠶⢶⣭⠀⠀⠀⠀⠈⢧⣤⣤⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⢸⠛⠛⠛⢻⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⡇⠀⠀⠀⠀⡴⣏⠙⠋⣽⢆⠀⠀⠀⠀⠀⢿⣭⣭⡟⠀⠀⠀⠀⠀⡀
⠀⢠⠊⠙⢿⡿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⣤⣀⣀⣤⡇⠀⠀⠀⢸⡶⠀⡅⢊⠀⢾⠀⠀⠀⠀⠀⡏⠀⠀⢹⠀⠀⠀⠀⠈⠇⢀⣀⣤⡤⠖⠂
⠀⠈⠢⠔⠋⠢⡈⠁⠀⠀⠀⠀⢸⡶⣶⡶⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠲⣗⣠⡄⡿⠎⠀⠀⠀⠀⠀⣗⣭⠀⣾⠀⠀⠀⠀⠀⠺⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⡄⢢⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⣛⣛⠛⢓⠀⠀⠀⠈⢳⣤⣠⣤⣤⣄⠀⠀⠀⠀⠀⡏⠉⠉⢉⠀⠀⠀⠀⠀⡆
⠀⢠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠀⠀⠀⣿⢾⡿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⣤⡦⠀⠀⠀⣀
⠀⠘⢿⣧⣾⠟⠂⠁⠀⠀⠀⠀⢸⣿⠀⠲⠀⠀⠀⠀⠀⣼⣿⣿⡛⢿⣿⣿⡄⠀⠀⠀⠰⣤⠤⠠⡤⠀⠀⠀⠀⠀⠀⣇⠀⢀⣈⠀⠀⠀⠀⠀⣬⣷⠶⠛⠋⠁
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⣀⣴⢾⣷⠀⠀⠀⠀⠀⠘⠉⢆⠀⠀⠀⠀⠀⠀⣐⠉⠇⠀⠀⠀⠀⢠⠒⡶⡄⠀⠀⠀⠀⢤⣰⣆⡠
⠀⠙⠟⢋⣁⣀⡀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠘⠾⠤⠃⠀⠀⠀⠀⠚⠿⢿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢤⣀⠀⠢⠀⠀⠀⠀⢸⠿⠿⡇⠀⠀⠀⠀⠀⡅⢨⠀⠀⠀⠀⠀⣠⡴⣮⠕⡀⠀⠀⠀⣼⣧
⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⢸⣄⣠⡇⠀⠀⠀⠀⠀⡃⢘⠀⠀⠀⠀⠈⢔⡻⠞⠋⠀⠀⠀⠀⣇⢘⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⣀⢀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⢴⣿⣿⣏⠀⠀⠀⠀⢀⣤⣄⠠⠀⠀⠀⠀⠾⠿⣟⣷⠀⠀⠀⢀⣤⣀⣂⣥⠀⠀⠀⠀⠀⠙⣏⡀
⠀⠀⣾⣛⣻⠃⠀⠀⠀⠀⣼⣯⣽⠟⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⣾⣥⠿⠿⣿⣷⠀⠀⠀⣄⣀⣀⣠
⠀⠀⠉⠉⠋⠀⠀⠀⠀⠈⠉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⣠⡀⠀⡀⠀⠀⠀⢸⠛⠛⠛⡇⡄⠀⠀⠠⠐⠂⠐⢲⡄⠀⠀⠠⠐⠂⠐⢲⡄⠀⠀⠀⠀⡹⢻⠃
⠀⠀⠈⠀⠈⠁⠀⠀⠀⢸⣿⠿⣿⣧⡇⠀⠀⠀⠀⠄⠄⣾⡇⠀⠀⠀⠠⠄⠀⣾⡇⠀⠀⠀⠼⣷⡾⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠑⠀⠒⠀⠛⠃⠀⠀⠐⠀⠒⠀⠛⠃⠀⠀⠀⠀⠈⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡩⠐⠒⠒⠠⣅⣂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢊⡠⡈⠀⠁⠈⠑⠺⢦⣠⡿⠮⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢐⡱⠊⠀⡀⣀⡀⠀⠀⠀⠉⠛⠶⣬⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡴⡡⠊⣠⠖⠉⣴⡠⢀⠈⠑⢦⠀⠀⠀⢀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⢊⠎⠀⡜⠁⠀⢀⡄⡁⠛⠀⠀⠰⠀⣀⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡔⡁⠁⠀⠘⠀⢠⣄⠈⠛⠰⠂⢀⠔⣡⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⢎⠞⠀⣀⠠⠜⠀⣀⠉⣘⢃⡤⠐⣡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠠⠃⠀⠀⠀⠉⠁⠉⠀⠁⠀⠈⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢉⠭⠤⡔⠒⡖⢤⢴⡟⠁⠀⠀⢀⠎⠁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣀⣘⣂⣐⣁⣐⣌⣠⠋⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠤⠅⠠⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠩⠍⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⣰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣀⣀⠠⠄⠊⠀⡐⠂⣰⠧⡐⠀⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⡀⠀⠀⢀⣠⠞⣑⣂⠂⢀⣾⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠘⠀⠉⠁⠈⠀⠀⠀⠁⢠⣟⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⢊⣉⣀⣫⠀⢈⣉⣉⡆⢠⠏⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⡠⣔⠎⠓⢙⣙⣩⡇⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⡉⠄⡴⠋⠉⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⡜⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⠔⣠⢎⡔⠀⠀⠀⠀⠘⡀⠀⡀⢄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⣲⣲⣰⣼⣦⣮⣭⣭⣭⣥⣄⠀⠀⣀⣒⣐⠒⠀⢀⠀⣠⠄⠀⠀⠐⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠳⢟⣋⠩⠉⠈⠉⠀⠀⠀⠐⡰⡀⠀⡠⢠⡀⠀⠀⢉⠱⠎⠉⠉⠛⠋⠛⠋⠃⠠⠓⠨⠐⠀⠚⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠚⠒⠒⠓⠓⠒⠓⠓⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⢀⣀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⣦⣄⣈⠒⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠆
⠀⠀⠀⠀⢈⣰⣦⣀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⠆
⠀⠀⠀⡠⠚⠋⡙⠛⠓⠤⣤⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧
⠀⠀⠀⠀⠀⠀⠑⠠⠄⢀⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⢠
⠀⣷⠀⣶⣤⣤⡀⠠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⡇⠀⠀⠀⠀⠸
⠀⠸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣽⣿⣿⣄⠀⠀⠀⡄
⠀⠀⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡾⠋⠀⠈⠉⠁⠀⠀⡇
⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣱⡿⠁
⠘⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣱⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⢀⣁⢠⣽⣿⣦⣀⠀⠀⠀⠀⣠⢟⡴⠋⠀⠀⠉⠁⠀⠀⠀⣠⣐⢾⡏
⠀⠀⠀⢀⡔⢛⡵⠋⠱⡙⣿⣿⣷⣦⣀⠀⣩⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢀⡊⣠⠏⠀⠀⠀⠘⢮⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⣀⣤⠴⠶⠒⠒⠀⠸⣧
⠀⡾⠛⣇⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣤⣴⣶⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠹⣧⡀
⢰⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡞⠓⠒
⠘⣶⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠂⣔
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡷⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⣸⠟
⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠸⡿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠙⣿⣿⣿⡗⠁⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡄
⠀⠙⣄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⣹⣿⠙⠇⠡⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠈⢿⣦
⠀⠀⢈⡿⠋⠀⠂⠤⣤⡀⠒⠀⠀⠀⠀⠀⠀⣿⠿⡇⠀⠀⠱⠀⠀⠘⠷⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠙⠒⠤⠄⣠⣭⣵⣆⣀⣀⣀⣀⡀⠀⠛⠄⠹⠄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣾⣾⣿⡿⢦⣄⣀⢀⠀⣀⣀⣢⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⣷⣿⣷⡿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣿⣶⣾⣷⣾
⣿⣿⣿⣀⣀⣠⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠶⠰⠆⠠⠄⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⢀⡀⣠⠀⠤⠠⣄⢀⡀⠀⠉⠐⠆⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢠⠔⠚⠈⠀⢀⣀⣀⣀⡀⠀⠀⠙⠂⠀⢀⠔⠁⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡀⠚⠀⣀⠴⠚⠉⠉⠁⠀⣈⣁⣀⢀⡤⠖⢲⠁⠠⠀⠣⠼
⠀⠀⠀⠀⠀⠀⡘⠁⢀⡌⠁⢠⠞⠁⠀⠀⠀⠀⣠⢾⠉⢣⡈⠻⣄⣠⠏⠀⠀⠘⣂⠀⠉⡄
⠀⠀⠀⠀⠀⣈⠁⠀⠖⠀⣰⠃⠀⠀⠀⠀⣠⢾⡙⣆⠳⣄⠙⢦⡀⢳⠀⠀⣆⠀⠈⣄⠀⢡
⠀⠀⠀⠀⠀⡅⠀⠸⠀⢰⠇⠀⠀⠀⣠⢾⠙⣆⠳⣌⠑⠀⠀⠀⢈⠟⠀⠀⠸⡄⠀⢨⡀⠀⠆
⠀⠀⠀⠀⢠⡄⠀⡋⠀⠈⠀⠀⢠⠔⠙⣄⠳⢌⠓⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡇⠀⠀⡆⠀⠲
⠀⠀⠀⠀⠰⠆⠀⣃⠀⠀⠘⣞⠉⢦⡀⢌⠓⠀⠀⠀⢀⠔⣁⡤⠤⠶⠤⢄⡀⠃⠀⠀⠆⠀⠛
⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⣸⢦⡀⠑⢦⡱⣄⢠⠔⢁⡜⢁⡴⠚⠛⠒⢤⠙⢦⠀⠐⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⠞⣡⠞⢙⠦⣀⣉⠟⠁⠀⣸⠀⡞⠀⡀⠀⡀⠈⡇⠘⡆⠀⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡈⢧⡘⢁⠔⠁⠀⠀⠙⠂⠀⠀⢸⡀⢹⠿⠽⣛⠭⢿⡇⢰⠇⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⢳⠀⠈⠙⠢⢤⣄⣀⣀⣀⠳⣌⠉⠧⠤⠞⢉⡤⠋⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠛⠉⢀⡤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠄⣀⠀⠈⠁⠘⠃⠛⠁⠉⠀⢀⡀⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠒⠂⠒⠐⠒⠐⠃⠉

⠀⠀⠀⠀⠀⢀⠄⠀⠠⠂⢀⡀
⠀⠀⠀⠀⠀⠘⠀⢀⠆⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠯⡪⠊⠁
⠀⠀⠀⠀⡀⠀⡀⠚⢄
⠀⠀⠠⠉⠀⠀⠀⠀⠰⠀⢀⡰⠂⠒⠒
⠀⠀⠀⠆⠄⠀⠀⠀⠘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠏⠀⠉⢁⡆⠄
⠀⠀⠀⠋⠒⢲⡇⠐⢄⠀⣰⠧⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⢸⡀⠂
⠀⠀⢠⠂⢀⠚⠃⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠒⠒⠀⠁⠈⡀⠐⠒⠈⠨⠁⠒⠂
⠀⠀⠀⡈⢀⠄⠁⠀⠀⠐⠦⢄⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢁⣀⠀⠀⠀⠀⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠀⣀⡀⠀⡀⠀⢸⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⠠⠄⠀⠶⣁⣠⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄
⠀⠀⠈⠁⠀⣠⠊⠀⠀⠀⠄⠀⡀⡀⡠⠃⡠⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠉⠁⠀⠀⠈
⠀⠀⢀⠁⠹⠁⠀⠀⠀⡀⢠⠄⠀⢅⠀⠀⠀⣉⣠⡂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠒⠁
⠀⠀⡈⠔⠁⠈⠁⠙⡿⡁⠀⢐⣢⠀⠂⡆⠈⡡⠄⢽⠀⡠⠀⢠⠤⠺⣀⣀⠀⠀⢠⣁⣠⠄⠀⠀⠘⠃
⠀⠀⠀⠐⠀⠐⠠⢤⠰⠀⠈⠤⠢⡅⣤⠋⠉⠪⣀⢀⣥⠔⠂⣀⠀⠀⠀⠀⠉⠀⠞⢩⠂⡶⠤⣖⠤⡀⢐⡆
⠀⠀⢀⠗⠀⣀⡀⠀⠀⠀⠀⠀⠴⠆⠈⠢⣔⠮⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠴⠁
⠀⠀⠈⠂⠀⠀⠀⢀⡁⠀⠀⠠⢠⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠻⠁⠀⠀⠘⠀⠄

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠐⠀⠤⠀⢀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠠⠄⠒⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠂⠀⠠⠤⠄⢹⣿⣿⣿⣿⢉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠤⠤⠀⠀⠂⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠤⠠⠤⢼⣿⣿⣿⣿⠘⢃⡄⠀⢀⡀⠀⠀⢠⡀⠀⠀⣿⡦⠤⠠⠄⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⣀⣸⣿⣿⣿⣿⠀⠈⠛⠠⡼⣇⠀⠀⢸⣷⠀⠀⣿⣅⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠀⠼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠂⠛⠛⣿⣆⢠⣿⠤⢀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠒⠉⠀⠀⡀⠄⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣼⣿⠄⡀⠀⠈⠐⠂⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣴⣶⣶⣶⣶⣶⣿⡿⠿⠛⢿⣏⡁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠉⠉⠀⠈⠛⢿⠟⠋⠀⠀⠀⢠⣿⣿⣿⣶⣦⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣾⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⢤⢻⣿⣿⠧⠔⠀⣸⣿⣿⡿⢻⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⠀⠀⠀⣿⡇⠀⠀⢠⡿⣿⣷⣾⣿⣿⣿⣿⣇⠀⢸⡇
⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣇⠀⢰⣿⣿⠀⠀⣾⣿⣯⣻⣿⣿⣿⣿⣿⣿⡄⢸⡇
⠀⠀⠀⢸⡇⠘⠛⠛⠛⠛⠛⠛⠛⠛⠓⠙⠛⠛⠀⠚⠛⠛⠃⠘⠛⠛⠑⠛⠛⠛⠛⠛⠛⠛⠓⣸⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠥⣏⣳⢾⣹⢶⣏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⣀⡀⣈⠀⣀⣁⣀⣉⡀⢀⣀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠸⠼⠻⠧⠇⠼⠸⠤⠄⠏⠠⠇⠧⠼⠸⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡏⣷⣴⣿⡮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢄⠀⢹⣏⠁⢀⠿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⡐⠊⠁⣱⡄⠁⣼⢸⡄⠁⣔⠁⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣥⣠⡾⠛⠋⠉⠋⠙⠋⠉⠋⠀⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢏⠈⢀⣤⣶⢶⡦⡀⠀⠀⠀⠦⣀⣴⣲⣀⠔⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣾⣿⣫⣿⢞⣿⠀⠀⢀⣔⣓⣒⡒⠒⠓⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠽⣫⣽⣶⣷⠝⠀⠀⢸⡧⠄⠦⠤⠢⢽⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⣀⣀⣀⣀⣈⣉⣉⡳⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠿⠷⢤⡾⢦⠿⢿⡇⡀⠀⡠⢺⣟⠒⠒⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣉⣉⣉⣉⣉⣉⣉⡹⠙⠞⠁⠸⣜⣭⣭⣭⣭⣟⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⣿⠿⣿⣿⣿⣿⢿⣿⣿⣷⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣨⣿⣿⣽⣙⣱⣽⣿⣿⣿⣍⣉⣱⣿⣿⣦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣤⣤⣤⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⠿⡿⠛⢻⣿⡟⢉⣡⠔⢀⣀⣤⣀⠀⢀⣤⠄⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⠤⣤⣬⣿⡛⠛⠛⢶⣶⣿⣅⠀⠀⣴⣿⠁⣠⣴⣿⣿⢀⣾⠏⢠⣿⢏⣴⣿⠟⠛⣏⢀⣾⣿⠀⣼⡏
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⣨⣿⠛⣿⣦⢀⣾⡟⠩⣿⡷⢸⣿⠃⣴⡿⡫⠿⠃⣾⠏⠀⣾⠏⣾⣿⠋⠀⣰⠟⣼⢿⣿⣰⡟
⠀⠀⠀⠀⠀⢀⡾⣿⡏⠀⣰⡿⠁⣠⡿⢫⣿⠏⣠⣾⠟⢡⡿⢁⣾⠟⠀⣀⠀⣼⠟⠀⣼⠏⢠⣿⣇⣀⣼⡟⣸⡏⠀⣿⣿⠃
⠀⠀⢀⣀⣠⣿⣷⣿⠗⣴⣟⣥⠾⠋⣰⣿⣧⡾⠋⠁⢠⡿⢁⣾⢏⣠⠞⠀⣼⠏⠀⣸⠏⠀⠀⠻⠿⠟⠉⢠⠏⠀⠀⠹⠁
⠀⠀⠉⣸⠏⠀⢸⢇⣼⡿⠛⢁⣠⣴⠿⠛⠁⠀⠀⢠⠞⠁⠸⠿⠟⠁⠀⡰⠏⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡜⠁⠀⠠⠟⡽⠁⠀⠀⠋⡹⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣷⣶⣶⣶⠶⠶⠖⠚⠀⠀⠀⠀⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⠴⠿⣿⡿⠟⠛⣿⣿⠋⠁⢀⣴⣿⣿⡆⠀⢠⣶⡗⢠⣿⣿⠁
⠀⠀⠀⠀⠀⣠⢠⡶⠒⠀⠀⠀⣴⠃⠉⠛⠉⣛⣿⡿⠉⢉⣿⣿⢇⣾⣿⠃⠀⣼⣿⠃⢀⣴⣿⠟⣹⣿⠃⢠⣿⡟⠀⣼⡿⠃
⠀⠀⠀⠀⣰⠃⠘⣧⠀⢀⣀⣾⡿⠀⠀⠀⢠⣿⣿⣃⣴⣿⠟⠋⣼⣿⠃⠀⣸⡿⠁⣠⣿⡟⠁⠐⢋⢤⣴⣿⣿⣷⣿⣿⠓
⠀⠀⠀⢠⠃⠰⠒⠋⠀⠀⠋⠐⠃⠀⠀⣠⣾⣿⣿⣿⣏⡁⠀⢠⣿⠃⠀⣰⣿⠇⢠⣿⡟⠀⠀⣀⡴⢢⣿⠏⠉⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠏⠈⣹⣿⣿⢠⣿⠃⠀⢰⡿⠁⢠⣿⣿⣀⣤⣾⠏⠀⣾⡏⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣴⣿⡿⠛⢁⣿⠋⠀⢠⡿⠁⠀⠘⢿⣿⡿⠛⠁⠀⣸⠏⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠟⠛⠋⠁⠀⢀⡞⠁⠀⢠⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⡤⠞⠙⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣩⣿⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⡧
⠀⠀⣠⠴⠚⢉⣤⡴⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠁⠀⠀⠜⠁
⠀⠀⢿⠀⠿⠟⠉⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⡻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⢑⢀⣴⡁
⠀⠀⠈⠳⠦⠖⠋⣁⣀⡤⠴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⢘⡵⣿⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠀⠈⠛⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⢲
⠀⠀⠀⢻⣷⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡀⠤⠒⡠⢄⡀
⠀⠀⠀⢠⣿⠇⠀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣥⣤⣤⣤⣤⣥⣬⠽
⠀⠀⠀⢸⠸⠠⢚⠕⠋⣠⡴⠚⠉⠢⠀⠀⠀⠀⠀⠀⢸⣷⠂⠐⣸⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣭⣭⠽⠛⠛⠛⠛⢓⡄
⠀⠀⠀⠈⠲⠀⣡⠴⠋⠁⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⡇⣿⠦⠄⣿⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠉⠉⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⢾⡙⣧⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠚⠁⠘⢦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⠀⠀⠠⠤⠧


⠀⠀⠀⠐⣏⣽⡷⠄⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⢻⣼⣿⡾⡿⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣃⣀⣐⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣴⠾⢛⣁
⠀⠀⠀⠀⣸⣙⣟⠛⣽⣷⣶⡟⠂⠀⠀⠀⠀⠀⠀⠀⣴⠶⡄⠊⠹⠍⠉⠯⢹⠋⠁⠀⠀⠀⠀⢀⡴⠋⡀⠈⠛⠛⠊⢡⣄⠑
⠀⠀⠀⠀⠉⢿⠙⢿⣟⡀⢀⢹⠀⠀⠀⠀⠀⠀⢀⡾⣟⠻⣿⢢⣟⣠⣤⣷⣸⠀⢀⠀⠀⠀⠀⡾⠀⠾⣤⡖⢠⣤⠘⢇⡙⠗
⠀⠀⠀⠀⠀⠸⡄⠿⠥⣔⣊⣀⣀⠀⠀⠀⠀⠀⢸⡗⣿⠗⣇⢸⠿⣭⣨⠾⣽⠀⢸⠀⠀⠀⠀⣧⠀⠀⢉⡴⠒⠒⠲⣌⠉
⠀⠀⠀⠀⠀⠀⢹⣿⣯⠭⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠈⠲⠖⠋⠀⠀⠀⠀⠈⠑⠢⠖

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣰⣾⠿⢛⣫⣭⡗⠀⠀⠀⠀⠀⢦⡀⢸⡇⢀⡴⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇
⠀⠀⠀⠀⢹⣶⣿⠿⠛⠋⠁⠀⠀⠀⠀⢀⣈⢿⣼⣧⡟⣁⡀⠀⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⢿⠟⠁
⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠩⠽⠟⠻⠯⠅⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⢨⣬⡇⠀⠀⠀⠀⠀⣠⠟⠷⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⣰⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⠙⠉⠬⠦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣠⣤⠘⠛⠓⠒⠒⠒⠂
⠀⠀⢀⣴⠋⠙⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣾⡷⠊⡄⠀⠀⠀⠀⠀⢿⣿⣴⣶⡀
⠀⠀⠘⢿⣷⣄⡠⠋⠀⠀⠀⠀⠀⠀⠀⣶⣦⣴⠆⢰⣿⣿⡆⠀⠀⠀⠀⠀⢈⣓⣦⢴⣚⡋⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⠤⠷⠄⠀⠀⠀⠀⠀⠀⠀⠸⣧⣬⣤⡼⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠘⣿⣶⠒⠛⠆⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⣡⣤
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠘⣏⡷⢁⠼⠀⠀⠀⠀⠀⠀⢸⠀⠃⢀⣸⠀⠀⠀⠀⠀⠀⠈⢻⣯⣠⣤⡶⠒⠋⠁
⠀⠀⠐⠚⠛⠓⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠱⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠧⠤⠾⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠶⠤⠤⠤⠤⢴⡂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⡴⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣀⣠⡄
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⣨⠟⡕⡰⢄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣤⡄⠀⠀⠀⠀⠀⠀⢨⣴⣶⠿⠛⠉⠁
⠀⠀⠸⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⠡⠂⣉⠁⠐⢢⣬⣑⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⠔⡁⠚⠁⠈⠙⠲⢯⣄⣨⣷⡦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢁⢔⡵⠊⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢥⣌⢷⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⢔⡴⠋⢀⡴⠊⡉⢉⠉⠁⠲⢤⡀⠀⠀⠀⠈⢛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡔⡡⠊⢀⠔⠁⠀⠘⠉⠇⣴⠄⠀⠀⠃⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⢊⠔⠀⢀⠎⠀⠀⠀⣰⣄⠂⡀⠀⠀⢀⠇⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡰⠡⠊⠀⠀⢸⠀⠀⣶⣄⢀⠈⠘⠃⢀⠔⢁⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡔⡐⠁⢀⣀⠠⠔⠀⢀⡀⣈⣙⣁⠤⠐⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⢍⡌⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡱⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⠁⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠓⠒⠀⠠⠤⣄⠀⢀⣀⣀⡀⠀⣴⣿⠃⠀⠀⠀⢀⡤⠞⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠀⠀⠀⠀⡞⠁⢙⠃⠀⡍⢭⢻⡟⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠤⠤⠥⠤⠥⠤⠴⠌⠦⠋⠀⠀⠀⠀⠀⢡⡀⠀⣀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠛⠃⠀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢈⣀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠂⠀⠀⠀⠀⠻⡈⢂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠉⠀⠀⡇⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠀⠀⣠⠃⠠⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⡐⠀⠰⠃⠂⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠤⠠⠒⠈⠀⠀⠀⠀⠀⡰⠛⠒⠂⠀⢰⡅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠠⠐⣋⡀⣤⡚⠁⠠⠭⠁⠀⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⡈⠭⠉⠀⠠⠄⡒⠂⠈⠀⢠⣙⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠐⢂⡡⡐⢾⠀⠐⠢⠄⠉⠀⢠⠋⠈⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⠰⣌⠢⡑⠙⠆⢻⡀⠐⣈⠡⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠺⡆⠁⢀⡤⠖⠒⠛⠉⠇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⡑⠈⢠⠎⠀⠀⠀⠀⠀⠸⠀⠀⠄⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠂⠀⠠⠑⠀⠀⠎⢀⠀⡀⠀⠀⠀⠀⢃⠀⠈⠤⢐⠀⢣⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠠⠊⠠⢊⠔⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢣⡀⠠⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠊⠤⢂⡀⢤
⠀⠀⠀⠀⣠⣤⠴⠒⣖⣲⣲⣲⣒⣦⣠⣄⣄⣀⣀⣐⣂⣒⣒⣒⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠉⠐⠀⣠⣄
⠀⠀⠀⠸⣵⡿⠻⠋⠛⠉⠍⢍⠍⠌⠡⢉⠊⠌⠈⠁⢠⠀⠉⠉⠉⠙⠓⢤⠟⠀⠛⠰⠶⠶⠶⠦⠒⠁⠌⠑⠀⠁⠢⡴⠂⠐
⠀⠀⠀⠀⠈⠙⠓⠳⠶⠤⠬⠈⣈⣠⣀⣆⣈⣰⣠⣠⣄⠼⠦⠼⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠔⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⣤⣀⠀⠀⡀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢉⠱⡀⠀⠀⠀⠀⠀⢀⠛⢀⣰⠆⠀⡀⡀
⠀⠀⠀⠳⣅⡢⡌⢉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠈⠺⡖⠁⠀⠀⠀⠀⠀⠀⠁⢀⠠⢰⠊⣰⡿
⠀⠀⠀⠀⠈⠁⠙⠏⣗⡤⡈⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⢅⣶⠳⠏⠸⠁
⠀⠀⠀⠀⠀⠀⢄⠠⠻⡙⡇⠀⡀⣸⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣆⠕⠁⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠑⡀⠄⠆⢀⢠⡇⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠠⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠆⠈⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⢁⠠⠂⠀⠀⠀⠀⠐⠀⠀⠀⡀⠓⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣸⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⢀⠃⠇⢰⠀⠀⠈⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⡄⣎⠄⢈⣆⠀⣸⢤⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡇⣯⠀⠀⠉⠈⠀⡘⠀⠀⠀⢀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠄⢸⠜⠀⠀⠀⠀⢀⠃⠀⡀⠀⢾⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠤⠤⠜⠀⠀⠀⠀⠀⠘⠦⠤⢄⣤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⡒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠
⣆⠀⢀⠀⠀⢀⣀⠌⠀⠀⠀⠀⠀⠀⠈⠳⠄⠄⠔⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠄
⠈⠉⠉⠉⠉⠁⠀⠀⢀⣀⣀⣀⡀⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⢀⣀⠀⠤⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡆⠀⠀⠀⠀⢇⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠐⠀⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣀⠤⠂⠀⠁⠀⠀⠀⠀⠀⢀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠦⡀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠰⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠝⠀⠀⠀⠀⠀⣀⠔⠈⠁⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⣀⠤⠤⠒⠂⠋⠉⠁⠀⠀⠀⠀⠄⢀⠖⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠊⠀⠀⠀⠈⡄
⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⠂⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⢀⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠤⠒⠒⢲⣄⡀⠀⠀⠀⠀⢸⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠈⠂⠤⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠴⠊⡅⠀⠈⢁⠀⠐⢀
⢄⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠈⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⡀⠀⠀⠀⠀⢀⡀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠤⠣⡀⠀⠐⢄⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠡⡀⠀⠀⠑⢄⠠⠖⠉⠀⠀⠀⠀⠀⢂⠀⠀⢀⡏⠄⠄⠈⠀⡀⠢⠀⠀⠀⠀⡠⠂⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢷⠂⠉
⠀⠀⠀⢡⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠢⣀⠀⠀⢀⠠⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢆⠀⢀⣀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠒⠤⢤⡀
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂
⠀⠁⠀⠀⠁⠀⠀⡠⡞⠙⠢⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠦⠤⢤⡈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡠⠃⠠⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⡗⠀⠀⠐⠒⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠃⠀⠀⠀⠀⠀⠐⠀⠤⠁⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡠⠃
⠤⠀⠀⠀⠀⠈⠢⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡰⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡃⠀⠀⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡌⢠
⠀⢀⠔⠋⠀⠀⠁⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡇⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐
⣆⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⡀⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣒⣈⣁⣀⣀⣀⣀⣀⣐⣈⣀⣀⣈⣁⣘⣃⣀⣀⣀⣀⣀⣐⣁⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⡏⠁⠀⢩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⠛⠛⠟⠛⠛⠛⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⡀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠉⠉⠉⠉⠁⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣄⣀⣀⣠⣄⣠⣤⣤⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠒⠛⠛⠉⠉⠙⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⢀⣼⠃
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘
⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⣀⣀⠀⠀⠀⢀⠔⠋
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡏⠀⢈⡱⡄⠀⣯⠀⣰⠋⠀⡄
⠀⠀⣿⠀⠀⠀⠀⠀⣀⠞⡡⠖⠂⠂⠀⢣⡀⠀⠳⣷⡀⠘⠿⣥⡤⠞⠁
⠀⠀⡇⠀⠀⠀⢀⡼⠃⢸⡁⢀⡜⠁⢀⠀⠁⠀⠀⠉⢃⠀⠀⠀⠀⠀⡠⠖⠲⢦⡀
⠀⠀⢹⠀⠀⣴⠋⠀⠀⠀⠻⢯⣤⠴⠋⣠⠄⢦⣀⡠⠎⠀⠀⠀⠀⠛⠀⠀⡀⢨⠇
⠀⠀⠈⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣠⠆⠀⠀⠀⢀⣞⣀⠀⢀⣴⣫⠖⠋
⠀⠀⣰⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡄
⠀⣰⠇
⠀⡏
⢸
⣾
⣿
⢿
⢸⡆
⠀⢿⡀
⠀⠘⣧
⠀⠀⠘⢷⡀
⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣶⣾⣦⣾⣿⣿⣿⣿⣽⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⠛⣿⣞⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢰⣿⠟⠹⣷⡆⠀⠀⠀⠀⠀⠠⣄⠀⢸⣿⠀⢀⡤⠀⠀⠀⠀⠀⣠⣭⣭⣤
⠀⠀⠀⠀⢸⣷⣶⣶⣿⠂⠀⠀⠀⠀⠀⠀⠙⢿⣮⣿⣴⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⢿⡿⠿⣿⠟⠓⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⡾⢿⠿⠿⠿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠀⠀⢿⣿⣷⣶⣶⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣞⡧⣒⠾⢧⣙⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢞⣷⣴⠻⢰⣟⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁
⠀⠀⠀⠀⢨⣷⣹⣼⣿⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⢛⣿⡿⠋⣿⡏⠻⣿⣟⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠀⢀⣾⠏⠀⠀⣿⡇⠀⠈⢿⣆⠀⠈⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣀⣀⣀⣼⣏⣀⣀⣀⣿⣇⣀⣀⣈⣿⣄⣀⣀⣀⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⣿⡟⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⡇⠀⠀⢻⣶⣦⣤⣀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣷⣶⣶⡈⣿⣿⣿⣿⣿⣷⣶⣬⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⢹⣧⠀⠀⠀⣿⡇⠀⠀⢠⠸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣦⣀⠀⢻⣧⡀⠀⣿⡇⠀⣠⣿⠃⢻⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⣿⣦⣿⣧⣶⣿⣷⡾⠄⢿⣿⡿⠉⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠘⠟⠀⠀⠀⠀⠙⢿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⠟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠖⢀⠀⠀⠀⠀⠀⠈⠁⠀⠻⣾⣿⣦⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣷⣿⠀⠀⠀⠀⠈⠁⣤⡀⠰⢷⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⠀⠀⠀⠀⠀⠀⠀⠉⣲⣤⡤⠶⠾⠇⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠆⠘⠟⠋⠁⠀⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠷⡄⠀⠠⠄⢀⣤⡀⠀⠀⠀⠘⠃⠈⠀⠀⡄⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣾⠶⣃⠀⠀⠀⣈⠋⠀⠰⠆⠀⠀⠀⢀⣄⠀⢀⡀⠀⠀⠀⢀⠴⣶⣄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠋⠘⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⢿⡟⠀⠀⠀⠻⣶⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⢨⡕⠶⢌⡁⢀⠀⣴⡄⢠⣾⡟⠓⡀⠀⠀⠀⠀⠐⠰⠆⠘⠦⠌⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠀⢶⠀⠀⢀⠀⡅⠙⠁⠦⢀⠀⠡⠼⢶⣥⠀⠀⠀⠀⠐⠆⠘⠲⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠿⠛⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣤⡈⠅⣤⡐⠊⠀⣤⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠣⡀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⠀⠀⠉⠀⠤⠀⢠⡄⠀⠀⠠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠦⣤⣤⡶⠚⠛⢦⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣷⣬⣿⡶⠆⠁⢀⡀⢀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠘⢿⣷⡄⠀⠀⠙⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡏⣀⠿⡆⠛⠁⠀⠆⠀⠴
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠈⠳⣄⠙⢄⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣟⣀⡁⠀⠘
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠳⣄⠑⢄⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣍⠋⠄⠀⠁
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠈⢷⣄⠳⣄⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⡛⠃⡀
⠀⠀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠙⢷⣌⠳⣄⣤⠶⠛⢉⣿⣿⣿⡇⣶⠄⢀⠈
⠀⠀⣧⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠹⣷⡇⠀⠀⠀⢸⣿⣿⣿⡆⠻⠀⠉⠁
⠀⠀⠹⣄⠀⠈⠓⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⡆⠀⢀⣠⠬⠟⠀⠀⢀⣼⣿⡿⢡⠀⠀⠀⠁
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠁⠀⠸⠟⠋⠉⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣒⣶⡟⠀⠘⠒⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠶⠷⠒⢶⣶⠀⠀⠀⠨⢿⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠰⠖⠘⢉⡷⣃⣴⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠂⠠⣤⠐⣿⠋⠶⢎⣓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠠⣞⠏⠀⢸⡧⠙⠿⡏⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠰⠷⠐⠿⣿⠀⠀⠚⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠘⢦⣀⣸⡷⠆⡸⠁⡀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠀⠐⠿⣿⢿⠀⠀⠨⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠉⠀⠀⡠⠁⡄⠈⠻⠿⠶⢒⠒⠒⠒⠒⠒⠚⠛⠛⠛⡏⠀⠀⠠⣽⡈⠳⣤⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢰⠶⣿⣄⣀⣨⣀⣀⣀⣁⣘⡁⠀⠁⠀⢙⣁⣀⣀⣀⣀⣀⣀⣀⣬⣧⡀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⢠⣦⣶⣇⡀⠀⠀⣰⣄⠉⠛⠋⠋⠙⠛⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⣹⠂⠀⠀⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠿⠟⢿⠛⢦⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⢀⣾⠿⠿⠿⠿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠿⣦⣄⣀⣀⣸⡇⠈⠛⠓⠾⠿⠟⠛⠿⠟⠉⠳⢶⡶⠶⠶⠿⠒⠿⠟⠉⠙⠛⠙⢩⣆⣠⣤⣤⣷
⠀⠦⣤⣀⠀⠀⢠⣝⡛⠶⣬⣭⣭⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣬⣥⣴⠶⣾
⠀⠀⠈⢻⠃⠀⠀⠈⠙⠳⠶⣤⣤⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠖⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⢼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠠⠄⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⠶⠚⠁
⠀⠀⠀⠸⡉⢡⣤⡤⣀⠀⣀⣀⣀⣴⠂⠉⠀⣠⣖⣲⡄⢤⡀⠈⡉⠒⠠⠄⠀⢀⡒⠄⣀⢠⡀⡶⠒⣦⠀⠙⣿⣟⠋⠩⢿⡞⠁⣠⡿⠃⠀⠁
⠀⠀⠀⠀⠈⠙⣿⡁⠀⣿⡇⠈⢿⣷⠂⠀⠀⠙⠓⡚⠃⠈⠷⠊⢀⣽⢻⠇⢀⣻⡄⣧⠛⠚⠁⠃⠀⠙⠂⢼⣻⣧⠀⠤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⠤⠾⠿⠧⠖⠊⠉⠀⠉⠉⠉⠓⠲⠤⣌⣀⣉⣉⣈⣀⠠⠐⠉⠁⠈⠓⠲⠶⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⡶⠒⠓⢶⡶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣰⠏⠀⠀⠀⠀⠹⣆⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠶⢤⣴⣏⣀⠀⠀⠀⠀⣀⣹⣤⡤⠶⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⣧⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⡷⠶⠶⠶⠶⠶⠶⠶⠶⢿⠶⠶⠶⠶⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⣻⣀⣠⣤⣤⣤⡄⠰⡶⢤⣀⣀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠚⠋⠙⣇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠉⠙⢓⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠹⣆⠀⠀⠀⠀⣀⠘⣧⠀⣀⠘⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠷⠤⠴⠾⠷⠂⠸⣶⠏⠳⣄⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⡶⠶⠶⠲⠶⠶⢶⡶⠛⠀⢀⣤⠀⠀⠀⠀⣤⡞⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠾⠇⠀⠶⠶⠶⠶⠾⠷⢶⣄⣾⠙⣧⠀⠀⣼⠋⠙⢦⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠸⡆⠀⢹⡄⠀⠀⠙⠆⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡟⠀⣤⠀⢿⠀⠀⠙⠦⣤⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠁⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡙⠛⠳⠦⣤⡀⢸⡇⠀⣿⠀⢸⡇⣀⣤⠶⠞⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠙⢿⣇⠀⣿⠀⣼⡟⠋⣠⣤⡀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⠀⠛⠀⠉⠀⣴⠋⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⠄⠀⣤⠀⠀⣼⠃⠀⡇⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⡏⢀⡾⠁⠀⠀⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠃⣸⠃⠀⢀⣴⠟⢀⡾⠁⠀⠀⠀⡁⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⣀⣀⣀⣀⢀⣿⣤⠶⠛⠁⠀⣿⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠣⠘⠀⠀⠂⠀⠀⠀⠀⠐⠁⠀⠐⠂⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢈⡇⠀⠀⠀⠀⠀⢀⣀⡤⠶⣄⠀⠀⠀⠀⢸⠖⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠼⠀⢀⣀⡤⠖⠚⠉⢳⣀⣠⠟⠀⢀⡴⠀⢸⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠚⠉⠀⣀⣠⠤⠒⠋⠉⠀⠀⣠⠋⠀⠀⡟⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣦⠤⠖⠋⠉⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⡜⠁⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⢴⡋⠀⠀⠀⢸⠀⠀⣀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠳⣎⠀⠀⠀⠀⢸⠀⡏⠉⠉⠉⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⠀⢠⠞⠁⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠃⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠁⠁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣦⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠧⢤⣤⠤⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⣀⣀⣀⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠃⠂⠂⠁⠐⠀⠀⠘⠀⠘⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠒⠒⠖⠒⠶⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣷⣶⢶⣆⣴⣶⢿⣻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣶⡶⠿⣶⢶⡴⠚⢷⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠄⣀⠀⠁⠀⠀⢀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠂⠀⡄⠚⠢⣦⠀⠤⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢸⣧⠰⢤⣄⡀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣸⡀⡤⠀⠸⢹⡰⠏⠈⡉⠓⠉⠁⢴⠶⣤⣠⡀⠀⠀⠀⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢭⡙⠳⠚⢤⠈⢀⣠⡖⠀⠀⣴⣾⣿⡿⠻⠙⠷⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡿⠓⠲⠄⢈⣉⣻⢀⠀⠦⠄⠉⢻⣽⣿⣷⣶⣶⢤⡄⠀⠰⣾⣻⠇⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣤⣴⣦⣒⢤⡤⢤⢥⣀⣵⣶⡆⢉⡽⢾⣄⡀⠀⢳⠄⠙⠉⣿⣿⣿⣤⡚⢃⠄⢉⡹⣿⡄⠀⠈
⠀⠀⠀⠀⠫⣛⣛⢛⠛⣒⢒⠒⣀⣉⣥⠂⠉⠛⢿⡼⣿⢳⣖⠛⠂⠄⠈⢻⡿⢎⡹⣴⣏⣲⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠙⠿⣿⠿⠿⠿⢛⡛⠻⠃⠀⠀⠀⠀⠱⠌⠶⣟⡀⣠⣤⢘⠋⡥⠊⢑⣤⣞⣽⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢴⠮⢌⡉⠀⠘⠵⠛⠂⠴⠻⢺⣯⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢀⠌⠷⢰⠃⣀⣖⠶⠊⢠⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠏⣀⠠⣾⠟⣁⢠⣾⣿⣿⣭⡿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠖⠟⠊⣡⠾⡿⠗⢻⣿⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡏⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣅⡩⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣶⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⢿⣿⣿⣷⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⢄⠀⠀⠀⠀⠈⠛⣻⣿⣿⠃⠀⣠⣤⣀⠀⠀⠀⣀⢣
⠀⠀⠀⠀⠀⠸⡘⢿⣷⣷⣀⣶⣾⣿⡿⠋⢰⣿⣿⣿⡿⠛⡳⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣧⡙⡻⣿⣿⣿⡿⠃⠀⢯⡻⠟⠛⠁⠀⣱⡮⠟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠳⣗⣎⠹⣋⣉⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠇⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⡈⠿⢿⣭⣻⣶⣤⠀⠀⠁⠁⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⠀⠸⠿⢸⡟⠉⠄⠤⠀⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⢟⡿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⢿⡆⠀⢺⣌⢛⠁⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣟⣾⡞⣫⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣬⣿⣷⣤⣤⣁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣿⣧⣿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣧⡘⢻⣿⣿⣿⡏⢶⡦⣤⣀⣀⣀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢫⡧⢼⠁
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣿⡌⠻⠿⠿⣿⣄⠀⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⢲⠃
⠀⠀⡠⢶⣿⣿⣿⣿⣿⡿⣿⣷⡀⠀⢰⣿⣿⡧⠘⣿⣿⣿⣖⡲⣄⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⠙⠳⣄
⠀⠀⠀⠛⠻⢿⣿⣿⣿⡇⣿⣿⣷⡀⠉⠊⣿⣷⡄⢻⣿⣿⣿⣿⣎⢧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣄⠀⠂
⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣼⣿⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣜⣿⠿⣿⣷⡄⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⢇⠀⠀⣸⣿⣿⣿⣿⣿⣄⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢟⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠟⠻⡿⠟⠛⠋⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⠿⠿⠃⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⢷⠝⠏⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣞⣿⣽⣿⣍⣗⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⠟⠋⠉⠁⢀⢀⡀⠀⠈⠙⠻⣿⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⢀⣤⣶⣯⠿⠿⠿⠿⣷⣦⣄⠀⠻⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⢀⣴⣿⠿⠿⣿⣲⣄⠀⠀⠙⠀⠀⢀⡴⢋⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠙⠿⠂⠀⠀⠀⠀⠙⢾⣠⠐⢉⣦⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣔⠫⠁⣬⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠟⣠⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢁⡘⢿⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣄⠘⠛⣴⣿⢟⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣋⢿⣮⠛⣠⣼⠤⢄⡀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠸⣅⠀⠈⠻⡟⠞⠙⢧⡚⢀⠚⢑⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣅⠱⡬⠖⠁⠉⡝⠁⢀⡼⠃⠀⠀⠀⣠⡶⠋⠁⣀⡀⠀⠸⣿⣿⣿⣶⣄⠀⠀⢠⣽⢷⣄⢀⡇⠀⠀⠀⠈⠳⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠳⠴⠋⠻⠂⠀⠀⣼⣿⣇⠀⠘⠿⣟⣷⡄⠙⢿⣿⣷⠛⣧⠀⠀⠁⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡵⠃⢰⢦⠀⠙⠿⠇⠀⣠⣿⣧⣾⡟⣇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢧⣠⣼⣾⡀⠀⠀⢠⣾⢿⣿⣟⣞⣼⣿⠀⠀⠀⠀⠀⣀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣞⣿⣯⠇⠀⠀⠈⠛⠛⠁⠹⣿⣼⡿⠀⠀⠀⠀⠈⠻⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣤⠀⠀⠀⠘⣟⣉⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⡄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠈⢻⣿⠀⣠⣄⣀⣴⣾⣽⣷⣶⣤⠞⠁⠀⠀⠀⢠⣾⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⣤⣤⡄⠀⠀⠀⠈⠛⠿⢷⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⣧⢸⡟⢹⡏⢩⡖⠒⣾⣳⠀⣷⠀⡇⢀⣷⠘⠙⡟⢩⡇⣠⣄⢀⣷⠀⡇⢀⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠙⣾⠀⢸⡇⢸⠛⠁⡿⢧⣸⡇⢿⡇⡾⠺⡆⠀⡇⢸⡿⣇⡼⢻⡏⢿⡇⡾⢺⣄⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠈⠀⠈⠁⠈⠉⠉⠃⠀⠙⠃⠈⠁⠃⠀⠁⠀⠁⠈⠁⠀⠀⠘⠃⠈⠑⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⣤⠤⣶⠶⣆⣠⢀⣤⡀⢠⡄⢠⢀⣀⣤⠤⣶⠶⠆⢀⣀⠀⠀⣤⠀⣄⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⣧⡟⠀⣿⠀⣿⠤⢸⣶⠃⣾⢷⣼⢸⡧⠄⠀⣿⠀⠀⢠⡏⣷⢰⣿⡄⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡇⠘⠇⠀⠿⠀⠷⠤⠼⠉⠳⣿⠈⠿⠘⠧⠤⠀⠿⠀⠀⠈⠟⠁⡟⠈⠇⣾

⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⠀⣽⣇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠈⠛⠛⠈⣠
⠀⠀⠀⠀⣠⣌⠁⡆⠈⣉⠓⠀⠀⠀⠀⠀⢸⡷⠾⠈⢡⡤⠀⢀⣃⠀⠀⠀⠀⠘⠚⠿⠴⠂⠀⠀⠀⠈
⠀⠀⠀⠐⠛⠛⠓⠀⠛⠿⠗⠀⠀⠀⠀⠀⠏⠁⠀⣿⡇⠀⠀⠸⠛⠀⠀⠀⠀⠀⠈⠷⠾⠧⠀⠀⠏⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢠⣴⣞⣟⣷⠀⠀⠀⠀⣶⣷⡀⠀⠀⠀⠀⠀⢀⡇⢸⠀⡆⠀⠀⠀⠀⠀⢿⣾⠇⠀⠀⠀⠀⢰⣤⣀⣾⣇⡀⠀⠀⠀⠀⢾⣿⣷
⠀⠀⢨⣿⣟⠉⠀⠀⠀⠀⠀⣤⣤⢘⣛⠀⠀⠀⠀⣿⣿⣿⣿⣿⡃⠀⠀⠀⣤⣶⣴⣦⡄⠀⠀⠀⠸⣿⣿⣶⣿⡇⠀⠀⠀⠀⠘⠿⠋⠀⠃
⠀⠐⠛⠛⠛⠃⠀⠀⠀⠀⠀⠻⠟⠘⠟⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠋⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⣀⣀⡀⠀⠀⠀⠀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠀⠀⠀⣀⡄
⠀⠀⣠⣼⡿⠋⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠈⢉⣀⠿⠿⠃⠀⠀⠀⢠⡻⠿⢃⡀⠀⠀⠀⠞⢀⣤⠞⠋⠀⠀⠀⠀⠏⣠⣴⠿⠉⠁
⠀⠠⠎⠋⠀⠀⠀⠀⠀⠀⠀⠿⠇⠘⠀⠀⠀⠀⠀⠘⢿⡿⠂⠀⠀⠀⠀⠀⠠⠝⠚⠧⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀
⠀⠀⣠⠾⣿⣿⡄⠀⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⠘⠃⠀⠐⠃⠀⠀⠀⠀⢠⠋⠉⢣⠀⠀⠀⠀⢠⡟⢉⡉⢻⠀⠀⠀⢰⣖⣨⡁
⠀⠘⢷⣄⡼⠋⠀⠀⠀⠀⠀⢰⣦⣶⡄⠀⠀⠀⠀⣦⣤⠆⣴⣶⡀⠀⠀⠀⢸⢔⡀⣼⠀⠀⠀⠀⠘⣷⣬⣵⣾⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠠⣤⠐⢂⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠰⠇
⠀⠀⣿⢻⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠘⠦⠘⣷⡄⢡⠀⠀⠀⠀⣘⣉⣏⣁⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠐⢾⡇⣀⣤⠤
⠀⠀⠿⠿⠇⠻⠃⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠛⠛⠛⠿⠀⠀⠀⠀⠘⠛⠛⠛⠟⠀⠀⠀⠀⠚⠛⠉

⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠦⠶⠶⠶⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⢀⢐⡠⡆⠀⠀⠀⠀⢀⡄⢀⣀⡀
⠀⠀⠈⠱⣆⢈⣄⠀⠀⠀⠀⣤⣄⣀⣤⠀⠀⠀⠀⢀⣳⣿⣴⡁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⡿⢿⡛⠀⠀⠀⠀⢈⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠠⠿⠿⠿⠿⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⢾⣄⣀⣿⠀⠀⠀⠀⠈⠿⠿⠟⠱⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⢠⠀⢀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣤⠖⠀⠀⠀⠀⡖⠀⠀⠀⣀⡀
⠀⠀⠶⠛⠁⠀⠀⠀⠀⠀⠸⢿⣹⡿⠗⠀⠀⠀⠀⢇⣀⠜⢁⠐⠀⠀⠀⠀⢾⣭⣽⠟⠁⠀⠀⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⢰⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠛⢻⣿⠛⠂⣿⡟⠛⠃⢠⣾⠟⠛⠆⢸⣿⠀⢸⣿⠀⣾⣷⣄⢸⡧⢀⣶⠟⠛⣷⡄⢸⣷⠀⠀⢀⣶⠟⠛⢷⡄⢠⣶⠟⠛⠷⠈⢿⣆⣰
⠀⠀⠀⢸⣿⠀⠀⣿⡟⠛⠃⢸⣧⠀⠀⠀⢸⣿⠛⢻⣿⠀⣿⡏⢻⣾⣟⠸⣿⡀⠀⣼⡗⢸⣿⠀⠀⠸⣿⡀⠀⣸⡇⢸⣿⠐⢿⣷⠀⠈⢻⡟
⠀⠀⠀⠘⠛⠀⠀⠛⠛⠛⠃⠀⠙⠛⠛⠃⠘⠛⠀⠘⠛⠀⠛⠃⠀⠛⠋⠀⠙⠛⠛⠋⠀⠘⠛⠛⠛⠀⠙⠛⠛⠋⠀⠀⠙⠛⠛⠛⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⣾⡿⠻⣶⡄⠀⣿⠟⠷⣦⡀⠺⣿⠟⠀⣴⡾⠛⠷⠘⠿⣿⡟⠓⠘⣿⡟⠀⣰⡾⠛⢷⣄⠀⣾⣷⡀⣾⡆
⠀⠀⠀⠀⠀⠀⣾⣧⣽⣧⠀⣿⡇⠀⣸⡿⠀⣿⠀⢀⣿⠇⠀⣿⠀⠸⣿⡀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⣿⠙⢷⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠀⠈⠛⠂⠛⠛⠛⠋⠁⠀⠛⠛⠛⠋⠀⠚⠛⠛⠀⠙⠛⠶⠛⠀⠀⠛⠃⠀⠘⠛⠛⠂⠈⠛⠶⠛⠁⠀⠛⠀⠈⠛⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣰⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣥⣭⣭⣭⣭⣭⣥⣭⠿⠛⠉⠉⠉⠛⠿⣬⣥⣭⣬⣭⣭⣭⣭⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡄⠀⠀⠀⢠⡄⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣠⣤⠀⠀⣧⣸⡇⠀⣤⠀⢸⣇⣸⠇⢤⣤⣄⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡋⠁⠀⠀⠀⠈⢹⡇⠀⣿⠀⢸⡏⠁⠀⠀⠀⠈⠙⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⣿⠀⠀⠈⠛⠲⠶⢤⣤⣤⣀⣀⣀⣀⣀⣈⣠⣤⣤⣤⠶⠾⠛⠁⠀⠀⣿⠠⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀
⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⢀⡴⠛⠛⠛⠛⢿⡟⣻⡿⠛⠛⠛⠻⣦⠀⠀⠀⠀⠀⠘⠛⠻⠛⠛⠟⠻⠟⠛⠛⠃⠀⠀⢀⣤⡴⠶⠶⠛⠛⠛⠶⠶⢦⣤⡘⠃
⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⣿⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠧⠶⠞⠛⠛⠛⠛⠛⠳⠶⠼⠷⣄⡀
⠀⠀⣸⡇⠀⡄⠀⣦⠀⣿⠀⠀⠀⢠⣄⠀⠙⢀⡼⢛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣁⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⣻⣄
⠀⠀⢸⡇⠀⡇⠀⣿⠀⣿⠀⠀⠀⣠⡿⣷⣶⢋⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠀⠀⠀⠀⢀⡴⠀⠀⠀⠉⠉⠉⠉⢹⡆
⠀⠀⢸⡇⠀⡃⠀⣅⠀⠤⠀⣠⣾⠙⢿⣏⣽⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠁⠀⠀⠀⣠⠞⠁⠈⠳⣄⠙⣷⡾⠛⠗⠀⠀⠀⠀⠀⠀⣾⢻⡆⠀⣰⠿⣦⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿
⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠰⣦⣹⡿⠋⣤⡀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠇⠀⢸⡷⢿⡆⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶
⠀⠀⢸⡇⠀⣠⠞⠁⠀⠀⠀⠺⣦⡾⠋⠀⣶⠈⠻⣄⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢸⣇⣨⣷⣀⣀⣈⣅⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣼⣇⣠
⠀⠀⢸⡇⢸⡏⠀⢀⡀⠘⣷⡾⠋⠀⠀⠀⣿⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⢿⡀⠀⢻⣯⠁⢻⡍⣿⠁⠹⣧⠀⠀⠀⠀⠀⢸⡏⠈⣿⢉⡿⠈⣩
⠀⠀⠀⢁⡼⠻⣦⣈⣻⡾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠘⣷⠀⠘⣯⠀⠸⣇⢸⡇⠀⣿⡀⠀⠀⠀⠀⣿⠁⢠⡏⢸⡇⠀⢸
⠀⠀⢀⣼⠿⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠘⣧⣴⣿⡀⠀⢿⠀⣷⠀⢸⡇⠀⠀⠀⢰⡏⠀⣼⠁⣿⠀⢀⣿
⢀⣴⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡸⣇⠸⣿⠁⠸⡇⢹⡆⠈⣿⠀⠀⠀⣼⠃⢀⡟⢰⡇⠀⣻⠇
⠛⠁⢸⡇⠀⠀⠀⠀⠰⠶⠶⠶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠟⠁⠹⣦⣽⣇⠀⣿⣘⣧⣀⣿⠀⠀⠀⣿⣄⣼⡇⣾⠁⣰⡟
⣀⣀⣈⣻⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣙⣷⣞⣋⣉⣉⣀⣀⣀⣀⣀⣈⣉⣙⣻⣶⣋⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⢳⡄⠀⠀⢀⡀⠀⠀⠀⢠⠖⣾⣷⣦⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣄⣨⡗⠀⣰⠟⠉⢳⡀⠀⣏⠀⠈⠛⢿⡇⠀⠀⠀⣰⢿⣻⣟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠟⠁⠀⠙⠶⡶⠞⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⢿⣾⠿⢋⣷⡿
⠀⠀⠀⠀⣀⣐⣒⡒⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶⡶⣦⡀⢀⣾⡟⢿⡷⣦⠀⠈⠙⠿⠿⠋⠁
⠀⠀⠀⢸⣿⣿⣿⣧⣿⣿⡀⠀⣴⠋⠉⠻⣆⠀⣿⣻⢭⣲⡇⢸⡟⠃⠀⠀⣻⠆⠀⠀⢀⣀⡀
⠀⠀⠀⠸⣿⣿⣿⡿⣿⡿⠁⠀⢿⣤⢠⣴⠏⠀⠈⠛⠟⠋⠀⠈⠿⣦⣶⡿⠟⠀⠀⣴⡟⠙⠛⣦
⠀⠀⠀⠀⠙⠻⠿⠟⠛⠁⠀⠀⠀⠁⠈⠉⠀⣠⣶⣾⣿⣶⣦⡀⠀⠀⣴⢶⣶⣤⠀⢿⣆⣄⣸⡿
⠀⠀⣴⡂⠀⣄⠀⠀⢠⡾⢿⠿⣿⣦⡀⠀⣼⣿⢫⠶⠶⣬⢻⣿⡄⠸⣿⣿⣿⣽⠃⠀⠉⠉⠉
⠀⠘⣿⣇⣼⡿⠁⠀⣟⢀⣛⣋⣀⣹⡇⠀⣿⣧⢿⣘⣃⣙⣼⣿⡇⠀⠙⠛⢛⡁⠀⠀⠀⣠⣶⡶⣶⣄
⠀⠀⠈⠉⣉⣀⣀⡀⠘⢿⣿⣿⣿⠟⠁⠀⠘⢿⣷⣭⣭⣼⣿⠟⠁⢠⣜⡾⠾⢳⣷⡄⢸⣿⣯⣽⢿⢭⠄
⠀⠀⣰⣾⢿⣿⠛⣽⣷⡀⠀⠁⠀⣴⠞⠛⠷⣆⠉⠙⠛⣋⣁⣀⠀⢸⣿⡀⠶⠘⣯⡿⠈⠻⢿⣿⡶⠊
⠀⠀⣿⣿⣎⢿⣿⣋⣼⡷⠀⠀⠸⣏⠸⠿⠇⣿⠀⠀⣾⡿⡿⠟⣷⠀⠻⢿⣿⣿⠿⠁⠀⠀⡀
⠀⠀⠻⣿⣿⣷⣍⣿⣿⠇⣠⣤⣤⡙⠷⠶⠾⠋⠀⠀⢿⣧⣶⣶⡿⠀⢀⡀⠀⠀⠀⠀⡾⠛⠋⠻⡆
⠀⠀⠀⠈⠛⠿⠟⠛⠁⢸⡏⠁⠈⣿⡀⢀⣴⣿⣿⣷⣦⠉⠉⠉⢀⣾⣿⣿⡟⢰⣆⠈⢧⡀⠀⢰⡏
⠀⠀⠀⠀⢀⣤⣶⣤⡀⠘⠿⣿⡿⠟⠀⢹⡉⠉⠁⠀⣿⡇⠀⠀⢸⣿⡿⢛⣶⣿⣿⠀⠈
⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠧⣤⣤⡤⠟⠀⣀⠀⠈⠻⠁⠭⢿⠿⠃
⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⢠⣾⡿⢟⣀⠀⠀⠀⢰⡟⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⠟⠀⠀⠀⠸⣿⣦⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⡰⠒⢤⠀⠀⠀⠀⠀⠀⠰⣶⠿⣦⠀⠀⠀⠀⠀⢠⣶⢏⠛⣦⡄⠀⠀⠀⠀⠀⣒⣦⠀⠀⣀⣀⠀⠀⠀⠀⠀⣶⡆⣤⡄
⠀⠀⢀⣴⣆⡵⠗⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠉⣽⣯⠉⠁⠀⠀⠀⠀⣠⣟⠃⠀⣤⣿⠋⠀⠀⠀⠀⢰⣾⡶⣾⣶
⠀⠀⣿⡿⠿⠁⣈⡴⠄⠀⠀⠀⠀⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⠀⠀⠀⠀⠀⣿⡿⠶⣼⢿⡿⠀⠀⠀⠀⠀⢸⣿⣧⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⣠⡀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⣀⡤⢎⣨⠄⠀⢠⠀⠀⠀⠀⣠⣽⡟⢣⣄⠀⠀⠀⠀⠀⢠⡤⣈⣛⣋⡀⠀⠀⠀⠀⢀⣻⣋⣘⣿⣀⠀⠀⠀⠀⠀⠨⣭⣭⢉⣤⡆
⠀⠘⠌⡒⠀⡈⠅⠂⠁⠀⠀⠀⢸⣿⣻⣷⣳⣞⠀⠀⠀⠀⠀⠛⠀⣯⣿⣿⡷⠀⠀⠀⠀⢸⣿⡟⠉⣿⣿⠀⠀⠀⠀⠰⠶⣍⠙⣾⠏
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢸⣆⣐⡿⣂⣤⣤⠀⠀⠀⠀⠠⣼⣿⣿⣇⡠⡀⠀⠀⠀⠀⠸⢿⡿⢿⠿⠅⠀⠀⠀⠀⠐⠂⣶⣷⡆⠒⠀⠀⠀⠀⢸⣿⣾⢿⣶⡄
⠀⠀⢩⣿⠻⠯⢹⣿⣷⠀⠀⠀⠀⠙⠿⣻⣾⠟⠀⠀⠀⠀⠀⠀⠈⠻⠘⠒⠀⠀⠀⠀⠀⠉⠆⢻⣿⠃⡆⠁⠀⠀⠀⠈⠉⠱⠛⢸⣟⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⣠⣄⠺⣀⣸⠀⠀⠀⠀⢀⣤⣶⣦⣄⢀⡀⠀⠀⠀⠀⡆⡀⠐⣄⣠⣀⠀⠀⠀⠀⠀⠈⠀⠨⡁⠢⠀⠀⠀⠀⠘⣷⣄⣶⣷⠄
⠀⠀⢀⣹⣿⡾⠋⠀⠀⠀⠀⠀⢀⣛⣿⣯⣿⣽⡟⠀⠀⠀⠀⣶⢿⣾⣿⣿⣿⠀⠀⠀⠀⠐⢀⢌⡁⠄⡔⠂⠀⠀⠀⠀⠈⢻⣾⣿⣶⡄
⠀⠀⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⠀⣴⣶⣶⣴⣶⢦⠀⠀⠀⠀⠀⢰⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⣠⡄⠺⣇
⠀⠀⠀⣿⣷⣷⢀⡀⠀⠀⠀⠀⠀⠰⣿⡿⣿⠋⠀⠀⠀⠀⠀⢻⡿⠇⠈⣡⡾⠀⠀⠀⠀⠀⠘⢺⠿⠟⠁⠀⠀⠀⠀⢠⣿⣏⠰⣾⣻⣧
⠀⠀⠀⠀⠀⣶⠞⠋⠀⠀⠀⠀⠀⠾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⠖⠀⠀⠀⠀⠳⠿⠟⠀⠟⠺⠷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⡍⠁⠀⠀⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢀⡀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠙⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⠠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣤⡀⣀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⢦⠴⡦



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣯⣽⣽⣿⣶⣯⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣾⣿⣿⣾⣷⣶

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠞⠓⠤⡄⠀⠀⠀⠀⠘⡀⠩⠤⢒⡊⠀⠈⢆⠤⠞⢣⠀⠀⢠⡇⠀⠙⠁⠀⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⡇⡇
⠒⢢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠩⠄⠒⠀⠀⣀⣀⠤⠞⠀⠀⠈⠟⠤⠤⠤⠚⠀⠀⠀⠘⡹⣄⠀⠤⠤⠒⣠⢷⠀⠀⠀⡀⢀⣤
⠛⠅⢀⡹⢧⠀⠀⠀⢀⡠⠔⢒⣒⣒⠒⠤⣀⠀⠀⠀⠘⢄⡠⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣖⣒⡒⠮⠟⠒⠉⠀⠀⡐⡜⠁⡃
⠖⠘⡅⠀⡇⠀⢀⠔⡡⢖⡩⠥⠄⠬⢌⡑⠢⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠶⠤⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⣃
⠜⠆⡏⡸⠁⠀⠑⢊⠔⡡⠖⣋⣉⣉⡒⢌⢳⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⣠⡀⠀⣤⠀⠈⡆⠀⠀⠀⠠⠀⠀⠀⠀⣀⠤⢰⣶⠀⠀⢶⠀⠉
⣥⡾⠋⠁⠀⠀⠀⠀⠛⡰⢋⠔⠐⠢⢌⢢⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣈⠂⠀⠼⠀⢠⠥⠤⠤⠅⠀⠀⠀⠀⠀⠐⠮⡉⢀⢴⠏⢸⠀⠀⠀⠱⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡔⠉⢳⠀⠁⠀⠀⢄⠤⠒⠊⠉⠒⠀⠀⢢⠂⠀⠀⠉⠀⠉⠁⠀⠘⠄⠠⠤⠀⠀⠀⠀⠀⡀⠀⠄⢸⡡⢎⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⡆⠀⠀⢀⠀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉
⢄⡒⠒⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠊⠈⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢲⢮⠹⣱⡄⠀⠀⠀⠀⠀⣀⡠
⢀⠀⠀⠠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠤⠄⠐⢒⣂⠀⠥⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⣁⡠⠤⠒⠊⡥⠑⢢⠡⠀⠀⢠⠠⠉
⠡⠀⠀⠀⡼⠀⠀⠀⡤⠠⢄⡐⡆⠀⠀⠀⠀⠀⠀⠀⠈⣭⣧⣐⠺⠤⠆⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠇⠩⠐⢒⡉⠥⠀⢣⠀⠀⣻⡀⠀⠈⣼⠀⠀⠐
⣀⡀⠠⠄⢋⠇⠀⠀⠧⢀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡔⢊⢫⢢⣤⠁⠑⢤⡀⠀⠀⢸⠀⠭⠴⢒⣪⠄⠈⠃⠉⢀⡇⠀⠀⢣
⠐⢲⡀⡉⠀⠀⠀⠀⢀⣠⣴⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⠤⠾⠊⢣⡈⢶⠂⠉⠰⠀⠀⠀⢇⠈⠉⢀⣀⠤⠴⠒⠈⠁⠀⠀⠀⠘⠌⠍⠤
⠒⠂⠉⠁⠀⠀⠀⡜⠁⣸⠀⠱⣆⠀⠀⠀⢀⡀⣀⠀⠄⣄⠀⠀⠀⠀⠈⢱⡀⠔⢏⠉⣧⠨⠦⠴⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠛⠀⢰⠁⠀⠀⣯⠔⠂⠉⠉⠙⣜⣵⠀⠀⠀⠀⠀⠑⢄⡔⠛⢌⣶⠔⠁⠀⠀⠀⠀⣀⠤⠒⣂⣀⣀⠒⠢⢄
⣤⠄⠠⡀⠀⠀⠙⠲⠤⢄⠠⠂⠀⠀⠀⢻⠀⠀⡀⡠⠀⢸⢹⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⡠⢊⡤⣊⠭⠐⠒⠢⠌⡑⠢⡙⢆⠀⠀⠀⠀⣀⡠
⠀⢀⠀⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⠘⠀⠈⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⠊⡡⢚⡉⠭⢉⡒⢌⣳⠈⠁⠀⠀⠀⡝⠉⢀
⠀⣍⢀⣀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠀⠀⠀⠀⡷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡔⣡⠖⠒⠲⢌⡢⠀⠀⠀⠀⠀⢈⠢⠀⢨
⠀⠅⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠢⠀⠒⢒⡉⠠⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡎⠉⢱⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠙⠒⠊⠉⠀⠀⠀⢰⠠⠄⠬⠭⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢂⣉⠉⢉⣉⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠐⠃⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡔⢕⠈⢉⠵⡦⢄
⠤⠤⠤⢤⢢⠀⠀⢠⠊⡴⣊⠅⠒⣀⠐⠢⢌⡑⢌⣳⠀⠀⠀⠀⠀⠀⠀⠣⠠⠤⠤⠤⠄⠀⠀⣃⠀⠀⠀⠀⠀⢠⢁⠀⡘⠓⡾⢼⠤⠴⠀⠀⠀⠀⡂⠀⠄
⠂⠀⠀⠀⢸⠀⠀⠈⠉⡎⡠⢊⠭⠄⠬⢍⠢⣙⠆⠀⠀⠀⠀⠀⠀⠀⠔⠹⠻⠻⢛⡋⣛⣛⣓⠈⢂⠀⠀⠀⠀⢀⠀⢨⠁⠲⠂⣬⢀⣀⢣⠀⠀⠀⡇
⠀⠀⠀⠠⢸⠀⠀⠀⠀⠈⢰⣡⠖⣈⡐⠢⡱⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣀⣰⣃⣀⣀⠒⡀⠀⠀⠠⠇⠀⠀⠀⠻⣍⠹⠉⢓⠴⡁⢀⠬⠂⠀⠀⠀⡇⡀
⡆⠯⠷⠦⠈⢂⠀⠀⠀⠀⠀⠀⢈⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠁⠐⠋⠁⠀⠀⠀⠀⡠⢣⠦⠦
⠁⢸⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⣨⠂⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣴⣀⣀⣁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡤⡀⠀⠀⠀⠀⢆⣀⠀⠤⡀⠀⠀⠠⢖⡨⠅⠘⠒⠢⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢊⡽⢻⠀⠀⠀⠀⢀⠠⠔⠒⠈⠉⣙⠪⠇⣓⢳⠀⠀⠀⠀⠀⣀⣴⢊⡀⠀⠀⠀⣧⠀⠀⠀⡀⠀⢣⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⢦⠔⡹⠁⠸⠀⠀⠀⠀⢧⠤⠔⣒⠩⠅⠀⢊⠉⠀⢇⡆⠀⠀⠀⡜⠁⣼⡀⠙⡧⠀⠀⢻⠀⠀⡹⠳⠀⠸⡼⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⠒⠒⠒⠒⠒⠒⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠧⠿⠤⢤⡀⢀⡤⠤⠧⠼⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣶⣶⣶⣶⠞⠁⠀⣀⣀⣀⡼⠁⣸⣄⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⢸⡇⣿⠀⠀⠸⣇⣀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⡇⣿⠀⠀⠀⢸⡉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⡇⣿⠀⠀⠀⠀⣽⠋⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠿⣿⣿⠿⠒⠒⢺⡇⠈⠉⠉⢩⡍⠉⠓⠒⣲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⠀⠀⠀⠀⠙⠒⣶⢶⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣳⣀⡀⠀⠀⣠⢿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣞⣒⡧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠛⠈⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠄⣀⠀⠄⠀⠀⠌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⢂⢤⣈⢂⢰⡄⡀⠂⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠤⠖⠋⠀⠙⠮⠟⠒⠟⠒⠤⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄⠀⠈⠵⠂⠀⠀⢲⠖⠀⠀⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠘⣄⠀⢠⢂⡐⠂⠠⠀⢀⠞⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡀⠈⠓⢾⠀⠀⠀⠰⠗⠋⠀⢀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠂⠤⣸⠇⠀⡠⢾⠀⠀⠀⢠⣄⡀⠀⠘⡧⠤⠔⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣀⠼⠴⠞⠀⠈⣬⣷⡤⡌⠁⠙⠒⠲⠧⡄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠⠴⠲⠮⡛⡿⠖⠒⠒⢤⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡤⢔⡞⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⢻⡦⢤⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡟⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡦⠘⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡇⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣿⠀⠀⠀⠀⡼⡇⠀⠀⠀⢰⣃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⠤⠤⠤⡿⡇⠤⠤⠤⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢶⠶⢶⠢⣇⡷⡚⠛⢻⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢽⠛⢦⠁⢻⠀⢾⠛⢷⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠈⠸⡀⢸⠀⡨⠀⠈⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⣸⡁⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣒⣠⣐⣪⠟⢿⣒⣤⣖⡺⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⠟⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⡿⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⡀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣶⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⣠⣴⡀⢿⡿⠿⣿⣿⡿⠿⣿⠏⢠⣦⡀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⣠⡄⠹⣿⣷⡀⠀⠀⣿⣿⡇⠀⠀⢠⣿⣿⠃⣤⡀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⣰⣿⡿⠀⢻⣿⣷⡀⠀⣿⣿⡇⠀⢠⣿⣿⠃⠰⣿⣿⡄⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢠⣿⣿⠃⠀⢸⣿⣿⣧⠀⣿⣿⡇⢠⣿⣿⣿⡇⠀⢹⣿⣷⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢸⣿⡏⠀⠀⣿⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢸⣿⣇⠀⠀⣿⣿⡇⢻⠀⣿⣿⡇⢸⠏⢸⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠘⣿⣿⡄⢀⣿⣿⠀⠈⠀⣿⣿⡇⠈⠀⢸⣿⣿⠀⣸⣿⡿⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠹⣿⡇⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⣿⡿⠃⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠘⠇⢸⣿⡿⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡀⠛⠁⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠘⠻⠇⢸⣷⣶⣿⣿⣷⣶⣿⠀⠿⠟⠁⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⣀⣤⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢰⡏⠀⣿⠀⢹⠇⢸⡇⠈⡿⠀⣿⠀⢹⠅⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⢶⡶⠶⠶⣶⠶⠞⠃⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢶⡀⠀⢀⣤⡴⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡾⠃⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⠶⠶⣮⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⠉⠉⡏⠉⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⠶⠶⠚⠛⠺⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡴⠶⠚⠛⠶⢦⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠇⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠴⠶⠀⠀⢀⡧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⡴⠾⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡶⠶⠶⣶⠾⠃⠀⠀⠀⢻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⡿⠀⠀⠀⠀⠀⢿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⠤⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⡴⠋⣭⠤⢬⡉⠳⣄
⠀⠀⢠⡏⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡇⠀⠀⠀⠀⣞⢁⠎⠀⠀⠀⠈⢆⢹⡆
⠀⠀⠀⠣⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢢⡀⠀⠀⠀⣠⠋⠀⠀⡇⠀⠀⠀⠀⢻⡌⢆⠀⠀⠀⢀⠏⡼⠁
⠀⠀⠀⠀⠈⠙⠋⠁⢱⣶⣄⠀⠀⠀⠀⠀⠀⡇⢀⠔⠁⠈⠢⠤⠊⠀⠲⢄⠀⡇⠀⠀⠀⠀⠀⢻⡄⠉⠒⠊⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠀⠀⠀⠀⠀⠳⣋⣀⣀⣀⣀⣀⣀⣀⣀⣈⡣⠃⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠙⠲⣄
⠀⠀⠀⣀⣀⣀⡴⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡠⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⢄
⠀⠀⠀⣯⡼⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡠⠾⠤⠤⠤⠤⠤⠤⠾⠦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠐⡿⠒⠒⠲⠒⠒⠒⢺⡗⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣯⠀⠀⣤⢤⡄⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⢠⠇⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡿⠀⠀⡇⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⠀⢣⠀⠀⠀⢸⠀⠀⠀⠫⡉⠉⠉⠉⠉⠩⠍⠉⠉⠉⠉⢉⠝
⠀⠀⠀⠛⠒⠒⠃⠀⠓⠒⠚⠁⠀⠀⠀⠀⠀⠘⢄⣀⣀⣀⣉⣉⣁⣀⣀⡠⠞⠀⠀⠀⠀⠈⠉⠉⢉⡽⠿⠿⢯⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠚⠋
⠀⠀⠀⠀⡀⣀⣤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡶⡶⡦⣄
⠀⢠⡴⠏⠁⠀⣀⣀⣀⡀⠀⠉⠷⣤⠀⠀⠀⠀⡴⠊⠀⡞⠀⡇⢸⡆⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠲⣄
⠀⠀⠀⣠⠾⠋⠉⠀⠀⠉⠙⠦⡀⠀⠀⠀⠀⡘⠉⠉⡹⠉⠉⡏⠉⠻⡉⠉⠱⡀⠀⠀⠀⠀⣤⠖⠃⠀⠀⠀⠘⠲⠦⣄
⠀⠀⠀⠀⠀⠔⠋⠉⠉⠛⠦⠀⠀⠀⠀⠀⢸⣤⣤⣤⣧⣤⣤⣧⣤⣬⣧⣤⣤⣵⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⢠⠒⠉⠑⢢⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢇⠀⠀⡇⠀⢰⠇⠀⠀⠌⠀⠀⠀⠈⠣⢄⣀⠀⡇⢸⠀⣀⣠⠜
⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠘⣖⠒⠚⡶⠒⡗⢲⡟⠒⢒⠎⠀⠀⠀⠀⠀⠀⠀⠲⣆⠃⠘⡰⠆
⠀⠀⠀⠀⠀⠀⠑⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣑⢄⣇⢜⡥⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣿⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣟⣿⣿⣛⣛⣿⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⡶⠟⠛⠉⡏⠙⠛⢷⡶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⡴⠋⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⡀⠉⠓⢦⡀
⠀⠀⠀⢀⡴⠋⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⣄⠀⠀⠉⠢⡀
⠀⠀⢠⠞⠀⠀⠀⢀⣞⣤⠤⠶⠒⠒⠒⠚⡟⠒⠒⠒⠲⢆⣠⣬⠶⠶⠶⢶⣭⣀
⠀⢰⠋⠀⣠⠴⠚⣽⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦
⢠⣏⡴⠋⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷
⣼⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⣟⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣏⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⢻⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁
⠘⡏⠣⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠳⢶⣤⣤⣤⣤⠶⢿⡿⢟⣥⡄
⠀⠹⡄⠈⠓⠦⣄⣳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⣀⡤⠖⠉⠀⠰⣿⣿⣿⣦⡀
⠀⠀⠘⣄⠀⠀⠀⠉⣟⠒⠦⠤⢤⣤⣀⣠⣇⣀⣠⣤⠤⠴⠖⢺⠏⠁⠀⠀⢀⠞⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠈⠳⣄⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡴⠋⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠳⢤⡀⠈⠳⣄⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠋⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠬⣷⣤⣀⣀⣇⣀⣠⣴⠯⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⠒⠒⠒⠒⠒⠒⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠧⠿⠤⢤⡀⢀⡤⠤⠧⠼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣶⣶⣶⣶⠞⠁⠀⣀⣀⣀⡼⠁⣸⣄⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⢸⡇⣿⠀⠀⠸⣇⣀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⡇⣿⠀⠀⠀⢸⡉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⡇⣿⠀⠀⠀⠀⣽⠋⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠿⣿⣿⠿⠒⠒⢺⡇⠈⠉⠉⢩⡍⠉⠓⠒⣲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⠀⠀⠀⠀⠙⠒⣶⢶⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣳⣀⡀⠀⠀⣠⢿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣞⣛⡧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⣶⣶⡀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⢦⡀⠀⠀⠀⠀⠀⣴⣶⣶⡄
⠀⠀⢠⣶⣿⠋⡴⣄⠀⠀⠀⠀⠀⢸⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⡛⠁⠀⠀⠀⠀⠀⢰⣿⡇⣰⣾⠁⠀⠀⠀⠀⠐⠀⠠⠀⢀
⠀⠀⣿⣿⢿⣯⣿⡅⠀⠀⠀⠀⠀⠘⠛⣻⣴⠷⠀⠀⠀⠀⠀⠸⣿⣿⣟⠁⠀⠀⠀⠀⠀⠚⢣⡭⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⣠⡖⣗⠶⠀⠀⠀⠀⠀⠀⠱⣮⣵⣄⠀⠀⠀⠀⠀⠀⢰⣟⡙⢫⣻⡆⠀⠀⠀⠀⠘⠻⣿⠻⡟⠇⠀⠀⠀⠀⠀⠀⠈⠻⣟⣀
⠀⠀⢼⣿⠿⠇⣒⣤⠄⠀⠀⠀⠀⠀⠈⠻⠿⢇⠀⠀⠀⠀⠀⠈⢹⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠈⡡⣈⠀⠀⠀⠀⠀⠀⢄⣀⣸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠁

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢤⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⢸⣏⣰⣷⢀⡀⠀⠀⠀⠀⠀⠘⠷⣦⡿⠟⠀⠀⠀⠀⠀⠀⢀⣨⣶⡄⠀⠀⠀⠀⠀⠀⢄⠸⢟⣛⠋⠀⠀⠀⠀⠀⠀⣻⣿⣧⡀
⠀⠀⠀⢹⣷⣿⣽⣟⠀⠀⠀⠀⠀⢀⣸⢿⢗⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣘⠯⠀⡀⠀⠀⠀⠀⢸⣿⣥⣿⣿
⠀⠀⠀⠈⠉⠙⠛⠛⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠙⠛⠋⠛

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⣾⣷⠀⠸⣧⡄⠀⠀⠀⠀⢀⠻⠇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠀⠀⠀⠀⠀⠀⢾⢧⣶⣶⣤⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡷
⠀⠀⢀⣭⣯⣴⡾⠋⠀⠀⠀⠀⠀⠀⢰⡂⣤⠀⠀⠀⠀⠀⠀⠀⡤⠉⡀⠀⠄⠀⠀⠀⠀⠛⠛⣵⠏⣿⡷⠶⠀⠀⠀⠀⠀⢩⣭⢍⡁
⠀⠀⠹⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠈⠡⡿⠃

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⣏⣈⡗⠀⠀⠀⠀⠀⠀⠀⢘⣿⣬⠟⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡅⠀⠀⠀⠀⠀⠀⣤⡐⢿⣀⠀⠀⠀⠀⠀⠀⣠⣤⠿⡿
⠀⠀⢠⡄⢨⣯⢀⡤⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠀⠀⠀⠀⠀⣸⣿⡍⢴⣟⣿⡆⠀⠀⠀⠀⢺⣼⣯⣿⣿⡇
⠀⠀⠀⠙⣾⣷⡟⠁⠀⠀⠀⠀⠀⠢⣽⣿⠆⠀⠀⠀⠀⠀⠀⠴⠿⠟⠋⠀⠀⠀⠀⠀⠈⠾⠿⠃⠘⠃⠿⠶⠀⠀⠀⠀⠨⠻⠏⠿⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣤⣴⣶⣿⡿⠿⠿⣿⣦⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢰⣿⠿⠿⠿⣿⣿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠘⣿⣇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⣿⣿⠀⠀⣿⣿⣿⣿⡷⠀⠀⢾⣿⣿⣿⣿⠀⠀⣿⣿⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣶⣿⡿⢿⣿⣶⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠺⠟⠉⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠿⠿⣿⣿⣿⡿⠿⠿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣿⠋⠀⠈⠛⢿⣷⣄⣠⣾⡿⠟⠁⠀⠙⣿⣧⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠿⠟⠛⠛⠛⢿⣷⣤⡀⠀⣀⣽⣿⣿⣯⣄⠀⢀⣠⣾⡿⠛⠛⠛⠛⠿⠿⣿⣶⣦⣄⡀
⠀⠀⠀⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠿⠋⠁⠈⠙⠿⣿⣿⠟⠋⠀⠀⠀⠀⢀⣀⣀⡀⠈⠙⠻⢿⣷⣄
⠀⣠⣾⡿⠋⠀⠀⠀⢀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⣿⣦⡀⠀⠙⢿⣷⣄
⢠⣿⡟⠀⠀⠀⠀⣰⣿⠟⠉⠉⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⢀⣠⣾⡿⣿⣧⠀⠀⠀⢹⣿
⣾⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀⠀⢸⣿⣤⣴⣿⠟⠋⠀⣼⣿⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⣠⣴⣿⢿⣷⣄⠀⠀⠀⢰⣿⠟⠉⠀⢈⣽⣿⣿⡄⠈⢿⣿⣿⣁⣀⣠⣼⡿⠃⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣾⡿⠋⠁⠀⠻⣿⣦⡀⠀⣿⣿⠀⣠⣾⡿⠟⠉⣿⣷⠀⠀⠉⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠈⣿⣧⠀⢻⣿⣿⡿⠋⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⣠⣿⡏⠀⠀⠙⠿⣿⣶⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⣿⣿⣿⣿⡿⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⣿⢟⡭⠋⣰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠉⠁⠀⠀⣾⠟⣩⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢠⣸⡿⠁⠀⠀⢀⣠⣶⣯⣴⣿⣿⣿⣿⣒⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣼⡋⠁⠀⠀⠠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⠀⠀⠀⠀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⣾⣿⣿⣿⠿⢋⣽⠿⣻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠿⠛⠋⠁⠈⣁⣴⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠴⠛⣩⣭⣬⣍⡙⠳⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑
⠀⠀⠀⠀⠉⢡⡴⠦⣤⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⢛⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣾⣇⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢐⣶⣷⣖⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢈⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣲⣾⣶⡂⠠⠀⣶⠀⠀⢀⣦⣷⣖
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⣀⣀⡀⣒⣒⣒⡒
⠀⠀⠀⠒⡶⠚⣙⠳⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠭⡅⠀⠚⠀⣸⠭⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣤⣤⡤⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⡜⣤⣬⠂
⠀⠀⠀⠒⠛⠲⠶⢾⠓⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙



⠀⠀⠀⣴⣄⡴⢿⡿⢆⣰⣆⠀⠀⠀⠀⢀⣀⣴⣦⣄⣀⠀⢀⣠⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣤⣬⢷⣿⣷⡿⣤⡄⠀⠀⠀⠰⢿⠿⢿⡿⠿⠿⠇⠺⠿⠿⣿⡿⠿⠿⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣷⣀⣀⡀
⠀⠀⠀⠈⢁⣈⣙⣋⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⢰⣧⡛⠛⢛⣰⡆⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠐⠚⠚⠚⠚⠚⠒⠀⠀⠀⠀⠀⠀⠀⠚⢚⡀⠀⠀⠀⠀⠐⠓⣓⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣘⣧⣀⡀⠈⢻⡁
⠀⠀⠀⠀⠘⠙⠋⠙⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠒⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⡳⠮⠀⣩⣼⢦⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠖⢰⡠⠤
⠀⠀⠀⠀⠀⢠⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⡏⢸⡿⣇⣀⡁⠀⠀⠀⠀⠀⠨⠉⠬⠕⠰⠶⠀⠍⠡⠅⠁⠀⠀⠀⠀⠀⡏⠀⠈⢴
⠀⠀⠀⣶⣷⠸⣿⣿⣿⢷⣾⣦⠀⠀⠀⠀⠀⠀⠐⢹⢭⡘⣄⢸⡿⠃⠀⠀⠀⠀⠀⠠⠥⡵⠓⠉⠁⠀⠤⢨⠗⠂⠀⠀⠀⠀⢰⠿⠤⡾⠛
⠀⠀⠀⠉⠉⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⡿⡟⣻⣿⣿⡾⠃⠀⢰⣯⠀⢂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉
⣼⣿⣿⣿⣟⡷⠈⠋⠙⠉⠁⣁⠉⢁⡀⢀⣰⡇
⣿⣿⣽⣿⣿⡇⠀⠀⣶⣶⣷⣿⡇⢼⣷⣿⣿⠁
⣽⡟⢻⣿⣿⡟⠀⠈⣼⠢⡏⠝⡇⢾⡘⠫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⠇⢻⣿⣟⡃⠀⠀⠁⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠙⠻⡇⠀⠀⠀⠠
⡿⠀⠸⣿⣿⡇⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⠀⢰⡃⠀⠀⠀⠀⣷⡖
⠁⠀⠀⠘⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡙⠤⠄⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⢿⡏⠃⠔⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⡀⣀⣀⣀⠀⠤⠴⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠰⣿⠸⡗⠂⠁⠀⠀⠀⠀⡀⠀⠀⢴⣷⡦⢾⠦⠤⣶⠾⣟⡚⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠝⠠
⠀⠀⢠⢿⡀⢰⣶⠀⠀⣼⣷⣤⣧⠀⠀⠀⣰⣶⡀⠀⠀⠀⠀⢀⣀⠀⠠⠧⣷⠀⠀⢠⣷⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⢀⡆
⠀⠀⣿⣎⠡⣾⠛⡇⢠⠟⢿⣷⠙⠀⠀⠀⢘⣻⠀⢠⡤⢰⡆⢠⢿⡄⢠⣿⢿⡄⠀⢸⡿⠀⠀⣶⠆⢀⠋⠀⣴⡂⠀⡸
⠀⠈⠋⠉⠀⡏⠀⢀⠀⣴⣾⣿⣤⠀⠀⠀⠛⢹⣷⠀⠀⢸⣵⣿⣎⣉⢠⣿⣿⡀⣠⣿⣷⣶⣿⣦⣐⡺⠇⠘⠋⣿⢀⠁
⠀⠀⠂⠀⢰⡗⢀⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⣇⠀⠀⠸⠏⣻⣿⡟⢋⣼⣿⣿⣿⣿⠁⠀⠀⠀⣈⡀⠀⢀⡀⠁⠸⣰⠇
⠀⠀⠀⠀⠸⠇⢿⣿⣿⣿⣿⣤⣤⣶⣄⠘⢿⠠⠟⠀⠀⠘⠇⠉⢹⡇⣯⠀⠀⠀⢸⡿⠁⠀⠀⠀⠉⠀⠀⡈⠀⠀⣾⣿⣿⡦⠊
⠀⠀⣶⠆⠀⠀⠀⠉⠀⣸⣿⣿⣿⣿⡏⠀⢠⣤⠠⣀⡘⠒⢾⠀⢀⡑⣿⢀⠀⢀⢘⡷⢆⢀⠈⣉⣙⣷⢻⣷⣶⡆⢻⣿⣿⣛
⠀⠀⠀⠀⠀⠀⢀⠀⠰⠿⠋⠉⠉⠉⠀⠀⣼⣿⡠⣭⡄⠀⠼⠂⣨⣿⣿⣀⣀⣠⣴⡟⢉⣽⣾⣿⣿⡿⣸⣿⣿⣿⡘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣟⣶⣶⡆⠀⠀⠀⢸⣿⣿⣧⣿⣿⡇⠻⢃⠀⡻⠽⠿⠟⠛⣻⣶⣿⢿⠻⠟⣫⣾⣿⣿⣿⣿⣷⠘⣿⡿⠇
⣤⣤⣤⣤⣤⣴⣭⣭⣭⣼⣭⣥⣤⣤⣬⣤⣭⣭⣿⣭⣯⣧⣤⣤⣤⣤⣤⣤⣤⣬⣽⣯⣥⣤⣤⣾⣯⣭⣽⣿⣿⣿⣿⣥⣬⣥⣤
⣿⣿⣥⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿