Greasy Emojis & Symbols

⠀⠀⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠈⠉⠀⠔⠄⠐⠒⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡉⠀⣉⠀⢁
⠀⠰⠁⠀⠀⠀⠠⠤⠐⣊⠴⠂⠀⠀⠀⠀⢀⡠⠒⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠄⠀⠀⣀⡠
⠀⠀⠂⠀⠀⠀⠀⠉⠁⠄⢚⠀⠀⠀⠀⠀⡎⠀⠐⠀⠔⠉⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠈⠀⡀⢀⡈⢀⢀⣠
⠀⠀⡇⠀⠀⠀⠀⡀⠤⠔⢺⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠈⠅⣀⠊⣰⠀⠀⠀⠀⠀⠡⡁⠉⢚⢏⢊⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⡴⠃⠀⠀⠀⠀⠀⠀⣗⢟⣿⡫⢻
⠀⠀⠐⠀⠈⠀⠀⣀⡀⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡹⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⡄⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠃⠀⠀⠀⠀⠀⢋⠀⢤⢼⠀⠃⠤⢀⠧⠀⠀⠀⠀⠀⡀⠀⠐⠂
⠀⢀⠄⠂⠐⠁⠈⢅⢀⡔⠃⠘⠁⠀⠀⠀⠁⠃⡈⠀⠘⢲⢀⡾⠀⠈⠀⠀⠀⠰⠄⠄
⠰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠸⠚⠛⠁⠀⠀⠀⠀⠀⠀⠯⠬⠤⠅⡈⠘⠀⠐⠀⠀⠘
⠆⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠐⠄⠀⠄⢀⠀⠒⠚
⠀⠀⠀⠀⣀⣜⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⡔⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡠⠤⠄⠄⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠖
⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠳⢠⠒⡆⣀
⠀⡁⠀⠁⠀⠀⠀⠀⢀⠠⠔⡠⢇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠠⠀⢀⠀⠘⠀⠀⠀⠀⠃⠉⠘⢤⣖⣤
⠀⡩⠐⡂⠐⠖⠒⠖⠒⢊⡉⠠⢊⠀⠀⠀⠀⠀⠠⠌⠀⡄⡠⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠐⠠⠄⢀⣀⡀⠀⠀⠅⠠⠂⢡⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⢁⠀⠀⠀⢀⡀⠠⠔⠋⠀⠀⠀⠀⠀⠀⠺⠀⠀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢠⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⡄⢀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠆⢲⡅⠀⣸⠀⠈⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⠑⣀⡰⠞⡇⠀⠄⠀⠐⠶⡄⣉⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠙⢲⣷⢠⡄⠀⠀⢠⣴⢏⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣇⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢈⣳⠈⣿⠁⣎⠀⢸⠀⠀⡂⠀⠀⠀⠀⠀⠈⢛⡋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠐⣿⡀⡠
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠟⠉⠁⠀⠀⡟⠀⢸⠀⠀⡇⠀⠀⠀⢀⢀⣤⣶⣷⣓⣶⣀⣀⢀⡀⠀⠀⠀⠀⠀⠸⣇⠀⠀⡙⠀⠀⠇⢿
⠀⠀⠀⠀⠀⠐⣴⣾⣿⣿⡇⠀⢀⠀⠀⢸⡇⠀⠘⠀⠀⠁⠀⢐⠀⢸⣖⣁⣠⣾⠍⣻⡿⠧⡆⠤⢀⣀⠀⠀⠀⠀⢀⡦⠒⠘⣴⣀⣄⣸
⠀⠀⠀⠀⠀⢠⣿⣿⣏⠘⢃⠦⣄⠀⠀⠈⡁⠠⠀⣶⡄⠈⣧⣼⢃⣾⣙⣏⣹⣿⣾⣧⠀⣄⡼⠣⡄⠻⠆⠀⠠⣧⣠⣥⡀⠀⣰⣿⣿⣿⣆
⠀⠀⠀⠀⢨⣿⣿⣗⡀⠴⣿⠟⡉⠀⠠⡷⢛⢰⠀⢶⡾⣠⣷⣷⣼⣿⣿⣿⣟⠿⠟⠁⠈⠉⢃⣽⣷⠴⣋⡕⠃⢀⡙⢿⣿⣧⣨⣿⣿⣿⣿
⠀⠀⠁⢠⣷⣾⣿⣷⣦⣼⡏⢰⠃⠿⢀⠉⠀⠀⡀⠀⢰⣌⡿⢿⡿⠿⢻⣿⡿⣿⣷⣄⠀⠀⠈⣩⣿⣿⣶⠆⠀⠘⠃⠀⠀⠉⢱⣼⣿⣿⣿⣇
⠀⠀⠀⢸⣿⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠸⠋⠀⠀⠀⣠⣿⣣⣶⣄⢹⣿⠆⢠⣶⣯⣿⠻⣷⣴⡶⠃⠀⠄⠀⠀⢹⡶⠟⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢀⣀⣠⢰⡆⢿⠏⠻⠛⠋⠸⠛⠀⡀⢩⣅⠔⠊⠻⣯⣟⠢⠂⠀⠀⠀⠈⠀⣸⣿⣿⣿⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⡛⠁⠀⠠⡄⠀⠀⢀⣤⡀⣄⠈⠁⠈⠋⠀⠀⠀⠀⠘⡇⠀⢀⡠⠄⢤⢀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠸⣿⣿⣿⣏⣄⣰⣾⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣅⠟⠠⡄⠄⠦⢀⠀⠀⠈⠈⠃⠌⠗⠡⠐⣶⣾⣿⣿⣿⠿⢁⡀
⠀⠀⠀⠀⢰⡉⡉⠛⠀⠘⢿⣟⡉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠛⠁⠉⣄⣓⣀⡲⢶⢾⣀⠒⢒⡀⢙⠁⠀⠀⣲⣿⣿⣿⣿⠇⠀⠘⠁
⠀⠀⠀⠀⠛⠁⠁⠄⠀⠀⠘⠛⠟⢸⡇⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠿⠛⠻⠒⠾⢿⣿⣿⣿⣿⡅⢀⣤⣤⢍⠉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢓⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠈⠙⠁⠟⠛⠙⠛⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠴⠒⠒⠒⠋⠉⠉⠉⠉⠉⠓⠦⣀⡀
⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⡀
⠀⠀⠀⠀⢠⠏⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠜⠀⠀⠀⠳⡀
⠀⠀⠀⢠⠏⠀⠀⠣⡤⠤⠤⠄⠐⠒⠒⠂⠉⠉⢉⠥⡀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣄
⢀⡤⢴⠏⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢥⠊⠙⣤⠀⠀⠀⠀⠀⠀⢹⡀⠈⢦
⡏⠀⢸⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠰⡦⠤⠤⠞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢧
⢳⠀⠈⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⡀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡸⠤⣀
⠸⡄⠀⠹⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠒⠉⠀⠀⠈⢱⡄
⠀⢧⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠤⠤⠖⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⠤⢤⠖⠋
⠀⠘⡄⠀⠀⠓⠒⠒⠂⠉⠉⠉⠁⠀⠀⠀⢀⣀⣀⣀⡠⠤⡤⠄⠒⠒⠒⠚⠉⠉⠁⠀⠀⢸⣧⣤⣀
⠀⠀⠙⠦⢤⠤⠀⠒⠒⠒⡖⠒⠀⡉⠉⠉⢁⠜⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⢀⡐⠘⠃⠀⣹
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⠒⠁⠈⠢⡀⠎⠀⠀⠀⠀⠀⠘⢄⠴⠉⠙⡄⠀⠀⠀⠈⡁⠀⠀⠀⠈⠙⠒⠦⠤⣀
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠱⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠔⠃⠀⠈⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⣏⠁⠀⢀⣀⣀⡤⠤⠖⠒⠚⠋⠉⠉⠉⠙⠦⠤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠶⠀⠲⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀⢠⣖⠚⢁⡄⠀⢸⣷⣿⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠧⠀⡀⠀⢸⠛⠀⣀⣀⣀⣼⣿⡿⢠⣶⣿⣿⣷⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⠃⠈⠀⠀⢸⣧⣿⣿⣟⣿⣷⣿⣇⣿⢿⣿⣿⣿⣇⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠻⣿⣿⣆⣴⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠤⠠⠀⣼⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣨⣿⣿⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠒⢒⠚⢠⠞⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⢀⣠
⠀⠀⣤⡴⣶⡄⠀⣂⠀⣸⡿⣳⠄⣸⡃⣘⠀⠂⠄⣸⣿⡇⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⡀⠀⣀
⠀⠀⠘⣶⡟⠃⠒⠏⠀⡽⠈⡇⠀⠟⠀⠋⠀⠀⠀⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡫⣷⠀⠀⠛⠉⠩⠁⠀⠀⠀⠂
⠀⠀⠀⠳⠷⣀⠀⣶⡿⠟⢻⡗⠀⠘⠛⠃⢁⣴⣾⣿⣿⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣷⠘⣦⠀⢡⠀⡁⢄
⠀⠀⠀⠐⠀⠈⠀⠉⢒⣰⠏⣅⠘⠀⢀⣼⣿⣿⣿⣿⡋⣀⣤⣴⣾⡿⣿⣿⣿⣿⡿⡿⣧⠀⠁⢹⡆⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⣆⠉⠒⣿⣿⣿⣿⣿⣟⣋⢭⣆⠻⣿⣿⡿⢯⠿⡿⢷⣄⠀⠉⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠴⠤⢼⣿⣁⡈⠀⠹⣿⣿⣿⣿⣿⣿⣷⣌⠑⠸⠗⡲⣴⣤⣄⠀⠙⠷⣄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠋⠉⠉⠙⠛⠛⠛⠛⠛⠂⠈⠉⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠖⠒⠚⠉⠉⠉⠉⠉⠁⠀⠈⠉⠓⠤⣄⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⣄
⠀⠀⠀⠀⠀⢠⠏⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠀⠒⠃⠁⠀⠘⢆
⠀⠀⠀⠀⢠⠏⠀⠀⠑⠦⠀⠒⠒⠒⠀⠉⠉⠉⠁⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⣁⠈⢣⡀
⠀⢀⠴⢲⠏⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏⠈⡲⠄⠀⠀⠀⠀⠀⠈⡆⠀⠱⡄
⠀⣯⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢗⠀⠒⠚⠁⠀⡗⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢹⡀
⠀⢸⡀⠀⢇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣤⣤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠷⢤⡀
⠀⠈⡇⠀⠘⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣠⠤⠤⠒⠂⠉⠀⠀⠀⢈⡇
⠀⠀⢹⠀⠀⠸⡀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠄⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⡖⠋
⠀⠀⠈⣇⠀⠀⠙⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⡤⠒⠒⠂⠉⠉⠉⠀⠀⠀⠀⠀⡷⠤⢄
⠀⠀⠀⠘⠲⢶⠒⠒⠒⠒⠀⢻⠉⢁⣈⠉⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⡔⠒⠃⠀⢨⡃
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠉⠁⠀⠱⠤⠎⠀⠀⠀⠀⠀⠀⠢⠴⠉⠈⣆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠉⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠤⠔⠃⠀⠀⠉⠀⠈⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠉⢿⣁⣀⣀⣀⣠⠤⠴⠖⠒⠋⠉⠉⠉⠉⠉⠓⠦⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡛⠛⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⡄⠀⣤⣠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢴⣖⠀⠀⠀⢾⣶⣾⣿⣿⣿⢿⣿⣿⠓⠒⢿⣿⣿⣿⣿⣿⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⣿⡀⠀⠀⠀⠈⢥⣬⣿⣿⠿⠛⠁⠀⠀⠈⠿⠿⣿⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⠁⠀⣤⠀⠀⠀⠈⠉⣀⡴⠆⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣰⣏⣠⣤⣤⣴⣾⣿⠛⣶⣦⣤⣤⣶⣶⣿⣿⣦⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⢸⠿⣏⢽⣿⣿⣿⣄⠀⠈⢹⣿⣿⣿⢯⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⡀⠙⢿⣙⡟⠋⠛⠿⣿⣻⣻⣟⣿⣿⡿⢿⡟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⡀⣹⣿⣿⣿⡀⢘⠘⠁⠀⠀⠀⢀⣈⣉⣠⣺⡯⠀⢸⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣸⣇⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠐⠛⠿⠿⠛⠛⠃⢀⣾⣿⣿⣿⣿⣿⣶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⢶⠦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⠛⠀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣧⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠈⣿⣿⡿⠿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⣿⠿⠛⠿⠻⣿⠟⢿⣿⡿⠟⠻⡿⠿⠿⠿⠻⠿⢿⣿⠿⢿⣿⡟⢿⡟⢻⡿⠛⠻⣿⠻⣿⡿⠛⠛⢻⠛⠛⠻⣿⣿
⠀⠀⣿⡏⢠⣆⢸⡇⢠⠀⣿⠀⢶⣤⡏⠀⢸⡇⠀⢤⣠⡄⠙⠀⣿⣿⠀⠠⣄⣦⡆⢠⣔⠀⠦⠀⣿⠀⠀⣿⠆⠈⡇⢸⠀⣰⡀⣿⠀⣿⣿⠀⠷⣾⠆⠶⠀⣽⣿
⠀⠀⣿⣷⡎⢉⠉⢱⡆⢀⠉⣶⠀⣈⣱⡆⠀⠉⣶⢦⡉⠙⣶⠀⣹⣿⣷⡶⣌⠉⢷⡎⢹⣦⠀⡀⢹⡆⠀⠉⢳⠀⡄⠈⢰⠁⣀⠉⣶⠉⣿⣶⠀⣭⣴⠄⣀⠙⣿
⠀⠀⣿⣿⣧⣈⣁⣸⡇⢸⡀⢻⡀⠈⢙⡁⣴⡄⢠⡈⠁⢰⣿⠀⢸⣿⣿⣄⠈⠀⣾⡇⢸⣿⢀⣧⠈⣇⣰⣆⢘⠀⣶⣄⢸⣄⢈⣀⣿⣀⡈⣠⣀⣀⣹⡆⣻⡀⣽
⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⡤⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠀⠀⣀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠐⠂
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣢⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠀⠁⠀⠀⠀⠀⠀⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠀⠀⣄⣰⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢆⣀⠀⡀⠀⠀⡄
⠀⡇⠀⠀⠠⠄⠠⠠⡤⠀⠤⠀⠀⠀⠉⠠⠁⠀⠀⠈⠀⠀⠀⠀⠀⢤⣤⠀⠀⠂⠀⡀⢴⠟⠀⠀⢀⣃⠀⠀⡁
⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⢠⣾⡿⠟⡿⣮⠀⣶⠤⠛⠡⠂⠀⠃
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⠋⠀⢀⣀⠐⢩⡄⡾⠃⣹⠇
⠀⡇⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⢩⠏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠀⠀⠘⣭⠄⢸⡇⠀⣠⢻⠄⣀⡄
⠀⡇⠠⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠓⠀⠀⠀⠀⠀⢸⠀⠀⠓⠀⠀⠀⢹⣿⡀⠀⠈⠋⠀⣼⣿⣤⣿⣿⠆⠁⠁
⠀⣃⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡈⢀⣘⣀⣀⣀⣀⣀⠀⠀⡀⠀⡀⣀⠈⢻⣿⣦⣤⣤⣾⣿⣿⠟⠋⠓⠒⣂⠆
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⢀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢁⡀⡀⣀⣀⡀⢀
⠀⡰⠈⠁⠀⢀⠀⣤⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢀⠀⠀⠀⠀⠀⢀⠀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡇⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⣰⠛⣹⠛⡇⠸⣶⠀⠀⠈⠀⠀⠀⢿⠊⠀⠀⠀⠀⣀⠂⠀⠀⠀⠐
⠀⣇⣀⠁⠀⠀⡘⠒⠼⢤⡀⠀⢀⣀⡀⠨⠷⠞⠒⢛⡇⢸⠀⠀⡄⠀⠀⠈⡀⠂⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐
⠀⡏⠘⠆⠀⠀⠀⠀⠲⢬⠁⠀⠀⠁⠀⠀⠀⠄⠄⢤⡇⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠂⠀⠀⠀⢠⢺⣄⡀⠀⢠
⠀⡄⡀⠀⢀⡄⠀⠛⠋⠙⠀⠀⢀⠤⠐⢈⠀⠀⠀⠀⡇⢂⠀⠀⠀⠀⠀⠄⠀⠀⡰⠈⠀⣤⡀⠠⣿⠝⣷⣆⣈
⠀⡀⠀⠀⠀⠀⠀⠈⠀⠙⠐⠶⢋⠀⠀⠀⠀⠐⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠄⣸⣷⣾⠅⠘⠿⡥⢁⠀⠻⣿⣿
⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⡤⢷⠸⡇⠐⠒⠒⠒⠄⠀⡇⠈⠀⠀⠐⠂⠀⠀⠐⣿⣿⡟⠀⣶⡌⣡⠟⠁⢀⣬⣽
⠀⠇⠀⠀⠀⠀⠀⡠⠚⠀⠀⢰⠾⢁⣀⡁⡀⣈⣎⠀⡇⠒⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⢆⢳⡆⢀⣴⣿⣿⣿
⠀⠱⡀⠢⠀⢰⠀⠀⢀⣐⣢⣽⡤⣐⣢⡔⠀⠃⠀⡲⠁⢰⠀⠀⠀⠀⡀⠀⠀⢻⣿⣿⣦⣠⣾⣷⣿⣿⣿⣿⣿
⠀⠀⠈⠓⠀⠀⠑⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠚⠉⠀⠀⠐⠀⠀⠒⠀⠐⠂⠂⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣰⠖⠀⠀⠀⠉⠁⠀⠐⠲⠐⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⡍⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠐⠀⠀⠡⠖⠀⢀⡘⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣎⣀⠐⠀⠀⠙⠄⡀⠀⠀⠗⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠉⠂⢁⣄⣀⠢⠕⢦
⠀⠀⠀⠀⠀⠀⠀⢀⠰⠄⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⢀⠎⢇⡀⠠⡄⠀⠦⢄⢀⠀⠀⠁⠚⠛⠄⠀⠦⠈⢡⡄
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠎⢀⡈⠅⠀⠀⠀⠀⠀⠀⠐⢀⣤⢤⣤⡤⠀⣀⠀⢤⠶⡀
⠀⠀⠀⠀⣀⣀⡄⠀⠀⣀⣀⣀⡀⢀⠀⢀⣤⣖⡉⢀⣀⣀⣉⡀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⡤⠃⠀⠀⢠⡀
⠀⡀⠰⢾⣷⡶⢾⣵⡛⠀⠀⢀⣶⣿⣷⣿⣿⣿⣿⣧⣿⣿⣿⣿⠁⠰⣿⣿⠀⢰⣿⣿⣿⡶⣿⣆⠀⣸⣿⠆⢀⣀⢼⣖⣶⣢⣄
⢀⠧⠀⠀⠙⠻⠒⢽⠷⢀⠀⢿⣿⠟⣿⣿⣿⣿⣿⠟⣿⣿⡄⠈⠛⣶⣿⣿⣟⣿⣿⡌⠛⠁⢿⣿⣿⣿⣏⠐⣬⡻⣴⣯⣉⣿⣏⡛
⠀⠑⢄⡀⠀⠀⠀⣾⠀⢻⣦⣾⣿⢤⠀⢼⣿⣿⣿⣠⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣸⣿⣿⣿⢤⣿⣏⠑⢎⡛⢬⡷⢯⠟⠦
⠀⠀⠀⢙⣷⡿⠛⠟⠀⠸⠻⣿⣿⢰⣶⣞⣿⣿⣿⡸⣿⣿⡛⠋⠉⣿⣿⣿⣿⢹⣯⣿⣿⣿⢼⣿⣿⣿⡀⠁⠈⠠⣶⣩⣖⣲⣏⠤⠄
⠀⠀⠀⠀⢉⠀⠀⠂⠠⠀⠀⢿⣿⣄⣿⣿⣿⣿⣿⣷⣽⣿⣷⣤⣶⣿⣿⠹⣿⣿⣿⣷⣽⣿⠌⣿⣿⣽⣿⠄⢺⠀⠛⢹⠻⠾⠃
⠀⠀⠀⠀⠀⣳⡄⠀⠶⠶⠖⠛⢿⣿⢿⣿⣿⡿⠻⣿⣸⡟⢿⣟⠛⢿⠟⣀⡻⠏⠉⠙⠋⠁⠀⠻⠗⠠⠀⠀⠀⠀⠀⠉⠻⣾⡃
⠀⠂⠀⠀⠀⠉⠀⠀⢠⣴⣶⣤⣾⣿⣷⢛⣿⣤⣿⣶⣿⣷⣿⣿⣷⣦⣾⣿⣿⣿⣷⣾⣿⣦⡀⣴⣴⣤⣶⣶⣶⣤⣄⠀⠀⠀⠉⢢⡀
⠀⠀⠒⠀⠀⣤⣴⠦⢸⣿⣿⠿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣶⣶⣸⣿⣯⣍⢻⣿⡻⠷⠈⣹⣿⠛⠛⠃⢠⡀⠀⠀⡑
⠀⠀⠀⣀⢠⡹⡶⠚⢸⣿⣤⣶⣽⣿⣿⣄⢻⣿⣿⣿⣿⣿⣽⣿⣾⣿⢿⣿⠉⠀⣼⡟⠻⠃⢘⢿⣷⡄⢀⣿⠇⠈⠁⡠⠈⠉⠐⠠⠇
⠀⢀⠂⢀⣤⠰⠂⠠⡄⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠻⣿⠘⣿⠛⠋⢸⣿⠀⠀⢽⣿⣷⣾⣿⣴⣿⠂⣼⡿⠀⠐⠂
⠈⠣⡔⠋⠀⠀⠀⠀⢠⠸⣿⣿⣿⡟⠟⣤⣥⣿⣦⣭⣤⣧⣤⣤⣤⣤⣤⣿⣷⣤⣦⣽⣿⣤⣭⣉⠁⠀⠛⠃⠘⠀⠁⠀⡤
⠀⠀⠀⠓⠠⡀⢀⠀⠈⢄⠀⣰⠿⠃⠈⠙⠟⠻⣿⣿⡟⠛⠛⢻⣿⣿⡛⣙⠛⠍⣹⣿⣿⣟⣻⡟⠀⢀⠈⠡⢤⡀⢈⡠⣏
⠀⠀⠀⠘⠛⠁⢈⠀⠠⢶⠀⡷⣤⡀⠐⠂⠀⠀⢸⣿⣿⠄⠀⠨⣿⣿⡇⠀⠠⢀⣿⣿⣿⢥⠄⠀⠀⠀⢣⡀⣊⠀⢜⠓⠫
⠀⠀⠀⠀⠑⠀⡌⢱⡄⠀⠀⢷⣄⡙⠀⠶⠤⣤⣄⣿⣿⣧⣤⣤⣿⣿⣷⣤⢤⣾⣿⣿⣁⣀⠀⠀⠀⠀⠸⢿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠂⠘⣇⠀⠀⠀⠀⠙⠀⠘⢲⣾⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⠃⠀⠐⠋⠁⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡄⠀⠀⠀⠀⠀⠸⣃⡽⢫⣉⡭⠍⠉⠭⢁⡀⠀⠀⣔⠚⢀⣠⠞⠅⠘⠒⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠁⠀⢠⠄⡀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠐⠚⠙⠦⠀⠸⠟⠋⠁⠀⠀⠀⡀⠀⠴⠒
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⠂⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠐⠒⠒⠒⠃⠀⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠖⠒⠒⠛⠉⠉⠉⠉⠉⠙⠢⢄⣀
⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⡀
⠀⠀⠀⠀⣰⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠤⠐⠃⠁⠀⠱⡀
⠀⠀⠀⣰⠃⠀⠈⠢⠤⠤⠐⠒⠒⠂⠈⠉⠉⢁⠤⣤⠀⠀⠀⠀⠀⠀⠀⡀⠘⢆
⣠⠴⢲⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡎⠈⡲⠄⠀⠀⠀⠀⠀⠸⡀⠈⢣
⡇⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢳⠀⠒⠒⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢧
⢹⠀⠈⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠢⢄⡀
⠘⡆⠀⠸⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⡀⠤⠤⠄⠒⠂⠉⠀⠀⠀⠀⡹
⠀⢣⠀⠀⠱⡀⠀⠀⢀⣀⡀⠤⠤⠤⠔⠒⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⠠⠤⠔⠒⢺⠉
⠀⠈⣆⠀⠀⠉⠉⠁⠀⠀⢀⣀⣀⣀⡀⠠⠤⡤⠤⠒⠒⢖⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢘⠒⠲⣄
⠀⠀⠈⠛⢻⠉⠉⠉⠉⠉⣅⡀⠤⡄⠀⢀⠎⠀⠀⠀⠀⠸⠀⠀⡠⢄⠀⠀⠀⠀⢠⠋⠉⠀⠀⢯⣀
⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠑⠊⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦
⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠢⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⢤⠄⠒⠒⠒⠉⠀⠀⢀⣀⣀⡤⠤⠤⠤⣄⠀⠀⢀⣠⠴⠚

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣤⣴⣿⣶⣿⣼⡷⢤⣿⣿⣭⣿⣿⢿⣭⣶⣽⣿⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠻⠛⣼⠻⣉⢛⡟⠛⠛⠳⠛⠉⠿⡹⣿⡿⣼⠿⠝⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⡾⠟⠚⠛⠛⠛⠻⣶⣾⣧⣶⣀⣄⣠⣾⣿⣶⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣩⣴⣿⣿⣶⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⡇⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢸⣿⣠⣤⠄⣙⣿⣿⡏⣴⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⡿⢿⡗⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣻⣽⣷⣿⣿⣿⣿⢋⣷⣎⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡅
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⡇⣿⣿⡿⠁⣿⣸⣿⣿⣉⣿⣧⣿⣿⡇⣿⡿⣿⣭⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡿⢷⣬⣄⣿⣧⣴⣿⣿⡞⣿⡿⣿⢿⣿⣿⠇⣿⣠⡦⢸⣯⣿⣿⣯⢉⣿⣿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠻⢟⣿⣿⠻⢻⣿⠛⡈⢱⡎⢹⠉⣈⣉⡈⢡⡜⠛⣃⠸⡿⠿⠸⠓⠿⠙⠟⠹⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠓⠔⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣠⡤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠖⣀⣴⣶⣿⣿⣶⣦⡀⢤⣀⡀
⣿⠿⠿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠿⢿⡿⠿⠿⢿⣿⣿⣿⠋⠿⢻⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⢏⣾⠟⠁⠀⠀⠀⠙⠻⣿⣆⢿⣿⣿
⠟⢙⣶⠋⢻⣾⠉⠁⠐⠛⠚⢻⣿⠻⣿⠒⠢⠖⢶⠸⢮⠰⠛⢂⡾⢻⣿⠃⠀⠀⠀⣿⣿⣿⠛⠛⠃⢸⠋⢋⡟⠻⣯⣽⢿⣸⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡸⣿⣽
⠀⠸⠽⠀⠈⠁⠠⣄⣰⠀⣰⣧⣧⢰⣧⠀⠛⠀⣞⢰⠈⠋⠀⠷⢣⣿⡟⠀⠠⠀⠀⢹⣿⣿⣆⠀⣖⢸⠀⢧⡇⢸⡿⡇⢸⣻⣧⣦⣤⣀⣠⠀⢀⣼⣿⣿⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⢻⣆⠉⠀⠀⠀⠉⠋⠀⠀⠀⠀⣿⣿⣷⣦⣤⣶⡀⣸⣿⣿⣿⡆⠘⠋⠀⠀⢀⠸⣴⠇⠸⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⢴
⠀⠀⠰⠀⠀⢀⣠⠴⡟⢠⣿⡏⢸⡫⢻⡞⢆⠀⡀⢰⠀⠀⠀⠀⣿⣿⣿⡏⠈⠛⠛⠛⠻⠋⣿⡇⠀⠀⡅⠀⡰⠀⠀⠞⠆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⡄
⠀⢠⡶⠁⠀⢾⣀⣴⠇⣼⣿⢧⢎⠳⠴⠃⢸⠀⡷⠋⠀⠀⠀⠀⢿⡿⣿⣷⣶⣒⡶⢦⣀⣀⣿⠃⠀⠀⠙⣖⠁⠸⠷⠀⠻⠟⣿⣼⠿⢿⣿⡿⠿⣯⣿⠏⠺⠂
⠀⠘⡇⣆⢀⣀⠉⠀⢰⡿⣿⠸⡈⡇⣠⠂⢸⣠⠇⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⢿⣽⣀⠀⠀⠀⣸⠀⠀⠀⠀⣠⡴⣿⠃⠀⣿⣻⣇⠀⢹⣿⣦
⠀⠀⡷⠋⠁⠀⠀⣴⢟⣱⣿⡄⠙⣟⠁⠀⢸⠁⠀⡄⡀⠀⠀⠞⢋⡏⠀⠀⣸⡿⣿⠉⠀⢀⡿⡙⠗⠄⢰⠃⠀⠀⠀⠘⣧⣱⡟⠀⣾⣿⣷⣝⡆⠸⣧⣽⠇
⠀⢰⠃⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⡾⠀⠀⣸⠀⠀⣱⡆⠀⠀⠙⠚⡁⠀⣾⢻⣿⣿⣷⢰⠇⠻⠶⠛⠀⠸⡄⠀⠀⡄⠀⣰⠁⠀⠈⢷⣽⣿⣿⠇⢀⡀
⠀⠘⡆⠀⠀⠀⠀⠀⢨⣏⠁⠀⠀⡇⠀⢠⠇⠀⢠⡏⠀⠀⡆⠀⢸⠁⠀⠘⠛⣿⠛⠃⠘⣇⡴⠋⠀⠀⠀⢹⡆⠀⢷⣠⠇⠀⠀⠀⠀⣸⡁⠁⠀⠀⣷
⠀⠀⠘⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢱⠀⢸⠀⠀⠀⢣⠀⠀⠙⣶⠏⠀⠀⠀⠀⣟⠀⠀⠀⠘⢦⠀⠀⠀⠀⣸⠃⠀⠘⠁⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠈⣷
⣤⣤⣴⣦⠤⣶⣖⣒⣾⣷⣤⣤⣤⠾⢶⣾⣦⣤⣤⣼⣧⣤⣠⣾⣤⣤⣄⣀⣠⣿⣦⣤⣤⣤⡼⢧⣄⣀⣀⣿⣤⣀⣶⣄⣀⣀⣤⣶⣾⣶⣧⣤⣤⡤⠴⣯⣀⣀⣤
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⡀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣀⠉⠉⠉⠉⠉⠁⠀⠀⠈⣉⣉⣉⣁⣈⣉⣉⣀⣀⣀⠈⠉⠉⠉⠉⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣟⡿⣿⢿⣦
⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⢿⣆⠀⠀⠀⠀⠀⠀⣾⢏⣶⣶⣷⣾⣯⡝⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣱⢳⡏⠥⣽⡧⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣻⣏⣿⢞⣿⠀⠀⠀⠀⠀⠀⣿⡇⢿⣷⢼⡿⠻⣿⣶⡝⣿⡆⢀⣤⣶⣶⣦⣤⣤⣄⡀⠻⣷⣤⣇⣺⣻⢫⣾⠟⠁
⠀⠀⠀⠀⠀⠘⢿⣮⣭⣝⢎⢻⣶⣄⠀⠀⠀⠀⠘⣿⡇⣿⡰⣶⡷⣴⣿⣇⢿⣷⣿⢯⣶⡶⣩⣾⣭⡝⣿⣦⣾⣿⡏⢿⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣧⡡⠍⠻⢷⣶⣶⣤⣤⣿⡿⡒⣚⣏⣴⣿⣶⣿⡇⡾⣰⣿⢿⣷⣿⣿⣿⣿⡙⡻⢷⡴⣴⣇⣙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣝⢤⡲⢌⣶⣩⣍⣵⠾⣾⢯⣶⣯⣿⢿⣯⣷⢁⣿⣷⣿⢿⣿⣿⣻⣿⡸⣿⢗⣸⣿⡟⣭⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⡕⣾⣿⡟⣷⣿⣿⣶⣜⢿⣷⣿⣿⣯⡿⢎⣛⣛⣯⣻⣿⣿⡿⣿⣛⣨⣼⣿⡿⣴⣎⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢹⠈⢿⣿⣟⣿⣷⣷⡿⡎⢿⢱⡿⣫⡾⣿⣿⣿⡿⣷⣝⠿⣣⣿⢿⣿⣟⣿⣷⣼⣿⡏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡞⣞⢟⡟⣛⣵⣾⡾⣿⣜⠎⣳⣿⣟⠻⡇⢟⣿⣿⣿⣶⡝⣷⣾⡿⣿⣿⠷⣸⣿⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣶⢘⠧⣼⢿⣿⣿⣾⢿⣿⢸⠿⡷⢩⣥⣾⡸⢯⡿⣿⣾⣿⣸⣿⣿⡿⢋⣸⡿⣣⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⢿⡞⣷⣮⣑⡫⢛⣻⠿⣋⣴⣿⣿⣶⣭⣭⣧⣘⠱⠿⠿⢾⣣⣉⡰⣷⣉⣵⣾⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣷⢻⣿⣿⣿⣷⣾⣤⣍⢿⣿⣿⣿⣿⣿⣿⣿⢀⣛⣛⣭⣭⣶⣦⡿⣿⣿⣿⡿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿⣿⣿⣿⣿⣿⣿⣷⣶⡹⢿⣷⣹⡿⠿⣺⣿⣿⣿⣿⣿⡟⣣⣿⣿⣿⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣿⣌⡿⣿⣿⣶⣯⣽⣿⣿⣟⡃⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣫⣶⡇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣷⣿⡞⣿⣿⣯⣟⣻⠿⠿⢿⣿⡧⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⣯⣷⣿⣿⣿⡇⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠟⢻⡷⢩⣟⣿⣿⣿⣿⣿⣷⣶⣶⢹⣟⣼⣿⣶⣾⣿⣿⣛⣛⣛⣿⣭⣿⣟⢱⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⣿⣿⣿⣷⣯⣽⣿⣿⣿⢼⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⡷⢹⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡇⣾⣿⣿⣿⣿⣿⢿⣿⣟⣻⣿⣧⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⣟⣛⣛⣛⣻⣟⢱⣷⣶⣿⣿⣿⣿⣿⣿⣯⡅⣿⡇⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡱⣾⣿⣿⣿⣿⣿⣿⣿⣧⣝⡿⢿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣥⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⡶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣭⣭⣭⣽⣁⣿⣇⣛⣻⠛⣭⣭⣭⣽⣶⡶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣜⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢙⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣭⣭⣭⣿⣿⣷⣾⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡤⠤⠄⢀⣀⠀⡸⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠈⡉⠉⠉⠁⠀⠀⠒⠂⠐⠈⠉⠉⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⠤⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠘⠉⠭⠽⠟⠛⠛⠛⠋⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠻⠛⠛⠓⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⠤⣄
⠀⠀⠀⠀⠀⢀⡴⢚⠁⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢦⡀⠀⢀⣠⡤⠖⠛⣉⠥⠄⠠⠜⠻⣦⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠁⠀⠔⠊⠉⠴⠊⠩⡝⢳⣄⡀
⠠⢶⠤⣰⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⢣⡺⡤⣿⣌⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣠⢼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡲⠤⣄⣀
⡠⢀⠙⠺⠻⣷⣶⡤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣩⡾⡃⣀⣚⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣤⣽⣦⣀⠤⢶⢺
⠀⠐⠣⡅⣙⢄⣋⣭⣛⣓⣶⠶⢶⣤⡤⣤⡴⠶⠶⠶⠶⠚⡟⠛⠶⠿⢱⣚⡏⠩⠈⠓⢄⡀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢿⢿⠿⠿⠟⠛⠉⠉⢀⣀⣼⠿
⠀⠀⣾⣷⡔⠀⢨⠃⠂⠘⠑⠷⢶⣧⣲⡖⠃⢂⡵⠷⠒⠛⣓⣲⡒⠄⡽⣿⡀⠀⠀⠀⠀⠙⠢⣀⣴⡟⠛⢿⡟⠀⣠⣲⣷⣲⠶⢶⣒⠚⠿⢍⡳⢤⣤
⠀⠀⡟⠬⡙⠗⠦⣤⣀⠀⠀⣀⣀⠀⠀⣙⡉⠀⢀⠭⠒⣈⠡⠖⠴⠼⢂⣿⡁⢠⢠⡔⠀⠀⢠⣾⡇⠘⡳⡖⠀⡴⣱⡁⢸⡌⠉⢳⢦⣍⡒⠤⣉⣲⠖
⠀⢀⠛⣦⡘⠀⢀⡈⠉⠛⠖⠀⣀⣀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣠⠎⢱⠙⢦⡸⢃⠄⠀⣾⣿⡇⠀⣷⡉⢙⡴⣝⢧⡀⣷⠀⠈⣶⣄⣹⣲⣇⡰
⠀⠐⡀⠈⠀⠩⠴⠿⠧⠤⠤⢤⣁⣉⣥⣌⡱⣶⡴⠭⢄⣒⣂⠭⠔⠋⠀⡸⠀⠀⠙⢼⠃⢠⡟⣿⣿⠀⠸⣿⡋⠵⢾⣭⣏⣻⡖⠐⡧⣄⣈⣉⣏⣹
⠀⠀⠑⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠙⢮⡇⠈⢻⠇⠀⢳⡉⠲⣤⣄⠤⣞⠛⢟⠿⣓⠊
⠀⠀⠀⠀⠈⠉⠒⠛⠛⠉⠁⠲⠶⠶⠶⠦⠤⠤⠄⠀⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢿⠭⡛⡘⣤⡉⢉⠇⠈⠑⢤⣙⡚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣈⣆⠱⣸⣌⣄⠉⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣃⢸⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⡏⠀⠀⠀⠀⢀⡠⢄⢴⠊⠉⢱⡀⡏⠉⠀⣁⢀⠖⠤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠰⡁⠀⠈⢎⡆⠀⠀⢣⠡⠀⠀⢠⡌⠀⠀⡰⡰⠁⠉⢢
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣼⠀⣧⣤⣤⣤⣀⣱⡀⢺⠁⠘⡀⠀⠀⣾⠀⠀⢸⠁⠀⢠⠛⠳⡄⢀⠎
⠀⠀⠀⢰⡉⢖⠉⠉⠀⠀⠀⠘⠤⠃⠀⠀⠀⠉⢁⡣⢉⣇⠀⢇⠀⠀⢹⠀⠀⡍⠀⠀⠸⠀⡸⠀⡎
⠀⠀⠀⢸⠪⠭⢉⣛⣒⣛⠛⠚⠶⠚⠛⣛⣚⣛⡉⠭⠑⡟⡀⢸⠀⠀⢸⠀⠀⠇⠀⠀⡇⠀⠇⣼
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠧⣀⡇⠀⠸⠀⢸⠀⠀⠀⣃⡴⠊⠸
⠀⠀⠀⠀⡇⠀⠀⠀⣼⢷⡀⠀⠀⠀⢠⡾⣦⠀⠀⠀⢸⡀⠀⠈⠉⠒⠓⠒⠚⠒⠒⠉⠁⠀⠀⡇
⠀⠀⠀⠀⢡⠀⠀⠈⠁⠀⢁⣴⣶⣦⡉⠀⠈⠁⠀⠀⡏⡇⠀⠞⠋⠳⠀⠀⠀⠀⠞⠉⠳⠀⢰
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣿⡟⣻⠁⠀⠀⠀⠀⢠⠄⢻⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠁⢀⣀⠀⣀⠀⢼⢀⣸⡀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⡝⡤⠖⢀⣉⣛⠫⠽⠿⣓⠒⠶⣶⣶⣶⣶⣤⣬⡿⣍⡓⠛⣉⣐⡶⣚⠭⠭⠓⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⡴⠛⢒⡒⢛⡒⠢⠤⠤⠒⢬⠲⣦⣄⣢⣶⠖⠥⠦⠶⠶⠛⠛⠛⠚⠲⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠉⢲⠋⠀⠀⠰⠃⠈⠁⠺⡄⠘⣀⠘⢣⡄⠰⠂⣰⠂⡤⢸⡇⣨⡃⠘⠁⠀⠀⠀⠱⡖⠁
⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠆⠤⠤⠤⢀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⡀⠤⠤⠄⠒⠒⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠦⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠾⠃⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡀⢀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⢀⢤⠴⠆⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠃⠈⠂⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⢀⠁⠄⠀⠀⠒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⢀⠀⢀⣀⡠⠀⠀⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠐⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢩⠀⢀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢘⠀⠀⢨⠁⠀⢀⠀⣀⡠⠄⡄⠤⠈⠡
⠀⠀⠃⣀⡁⠀⠂⠈⠅⠀⠀⡰⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢂⠘⠈⠀⠐⢈⠀⠀⠸⠀⠀⠈⣉⠀⠈⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠈⠁⠀⢠⠘⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⢀⠀⠀⠀⠀⡄⢀⣡⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡍⠅⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⢀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠊⠀⠁⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠇⠢⠠⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣄⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢰⡄⠀⡴⠂⠀⡄⡄⠀⢰⠀⠀⠀⠀⠀⠀⠾⠁⢈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠠⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⡄⠉⡁⠘⠒⢒⡓⢊⠉⠙⡆⠀⠀⠀⠀⠀⡀⢀⠀⠤⣁⡀⠀⠀⠂⠀⠀⠀⠀⠠⠒⠉⠀⠄⠠⠈⠉⠒⢄
⠀⠀⠀⠀⢀⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⠌⠥⠢⠳⠈⠁⠭⠄⢤⠄⠀⠀⠀⠀⠀⠁⠃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠤⠤⠀⠤⠠⠔⠆⢸
⠀⢠⠀⠀⢈⠑⠀⠀⠀⠄⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠈⣀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠍⠁⠂⠀⡀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠘
⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⡀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠱⡀⠀⢀⣀⠀⡖⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⣰⠀⠀⠀⠀⠠⢉⣠⣁⠀⠀⢠⣠⡄⣀⣠⣠⡠⠀⠀⠀⢰⡆⠀⠅⠀⠀⠉⠁⠀⠀⠀⢷⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠓⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠁⠈⠈⠈⠀⠀⠀⠀⠁⠈⠀⠀⣠⢄⡛⠉⠄⠀⠀⠀⠠
⠤⠀⠆⠀⠀⢠⠀⠀⠆⠀⠔⠊⢀⣠⡤⣦⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⣏⠠⢉⡀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠟⠉⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠴⠀⠰⠀⠀⠄⠀⠀⠀⠈⡁
⠀⠀⠀⠰⣄⣢⣼⣀⠄⠀⠀⢠⡀⡀⠀⠀⠐⠂⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠄⠀⠀⠀⠀⠀⠀⡀⠠⣤⢀⡀⠀⢀⡁
⠀⠀⠐⠲⠼⢿⣿⠷⠦⠆⠀⠈⠻⡀⠀⠀⣹⡿⠁⠀⠠⢢⢤⢄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠤⢕⠘⣯⠀⠀⡉
⠀⠀⠀⠚⠒⠃⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠑⠚⠋⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠉⠀⠀⠀⣠⠤⠀⠀⠐⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠒⠤⡄⠴⡴⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠞⠣⠒⠗⠒⠀⠀⠀⢄⢠⠤⠄⠤⣤⠲⠈⠀⡠⠶⠈⠑⠀⠤⣥⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣁⣂⣀⠁⠀⠈⠀⠀⠀⠀⠀⢂⠤⣎⣁⠠⠄
⠀⠣⠀⠐⠠⠄⠀⠀⠀⠤⠀⠀⠀⢠⠞⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠐⠁⠀⢠⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠄⠊⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠓⠦⢀⡀⠀⡠⠖⡩⠄⠀⠀⠀⢸⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⠈⠀⠈⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠭⠔⠉⠀⠀⠀⠀⠀⠘⡇⡞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠄⢠⡄⠀⠒⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠀⠄⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠈⠀⢠⠘⣠⠀⠅⠤⠀⠃
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⢀⡌⠀⠈⠀⠸⠁⠐⠀⠀⢀⠁⠉⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠠⠴⠄⠊⠀⢀⠘⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡜⠚⠀⠁⠂⠀⠀⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⣴⠄⢀⡀⠙⠂⡀⢀⡀⠀⠀⠐⠧⡄⠣⡀⠀⠀⠀⠀⠀⠛⡠⠄⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⢠⣄⣀⠀⠀⠀⢀⠀⠐⠠⠤⠀⠉⠈⠒⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠠⢌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠈⠀⢀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⢆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀
⠰⢦⡀⠴⠄⠦⠔⠃⠀⠀⣀⠤⢠⡄⡶⠠⢄⠀⡆⠀⠀⠀⡀⠀⡝⠤⢀⡀⢠⡄⢤⣤⠀⣀⡠⠄⠀⡢⠄⠠⠄⠀⠀⣀⠤⠀⢨⣅⡰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⡥⠀⣶⠀⠀⠀⠀⠀⠀⠀⠁⢀⢈⣛⡀⠀⢠⠀⠀⠘⠡⡤⠀⠁⠀⠕⠀⢀⡀⣤⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠐⠈⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢩⠁⠀⣠⡀⠑⠓⠐⠆⠀⠀⠀⠀⠈⠉⠀⠉⠀⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⣀⣀⣈⡀⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⠀⠈⠁⠉⠀⠦⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠷⠀⠀⠐⡶⠀⡀⠀⠀⣀⡀⠀⠁⠀⠄⠀⠺⢷⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠔⠀⠀⠠⠤⠀⡀⠠
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠌⠓⠀⠀⠁⠀⠒⠀⠀⠀⠑⠠⠌⠂⠉⠐⠂⠉⠀⠀⠀⠀⠔⠀⠑⠒⠂⢀⣁⡀⠀⠈⠁⡠⠀⠀⠀⠄
⠀⣤⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠆⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⡀⠀⠀⠀⢈⠄⠠⠐
⡇⠀⠀⠁⢄⠘⠦⣄⢠⡄⠔⠀⠘⣰⠀⠀⠀⣀⣦⠄⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠡⠀⠀⣤⠀⠀⠀⢠⠁⠀⢠⡏⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠄⡀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡀⠘⢇⣀⠀⣀⠀⠔⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢋⡤⠀⠀⠀⠀⠐⢀⠁⠀⠀⠠⠒⠈⠉⠉⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠇⠀⠀⠀⠀⢀⠄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠤⡀⠀⢀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⢰⠀⠀⠃⢄⣀⡀⢀⣀⡰⠞⠀⡈⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠊⠔⣈⠉⠋⣀⠲⠀⠀⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣊⠤⠖⠶⠤⡑⠀⠀⠡⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⣀⡀⣀⣀⠈⠁⠈⠣⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡧⠼⣀⠀⠀⠀⠀⠀⠆⠀⠴⠀⠀⢀⠤
⠀⠀⠀⠀⠓⠈⠜⢉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣰⠁⠀⠀⠀⠀⢠⠈⠁⠜⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠃
⠀⠀⠀⠀⣀⠤⠒⢠⠉⠉⠉⠉⠐⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠚⣆⠒⠄⡖⢲⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠀⣿⣀
⠀⢀⡴⢈⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⡙⢦⠀⠀⠀⠀⢀⣶⡦⣀⡭⣶⠀⣿⢸⢉⣇⣽⠉⣯⠉⣹⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⢸⡀⣠⠏⠉⠉⠲⣄
⢀⡮⠄⠄⠀⠀⡄⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⢡⠀⣧⠀⠀⠀⠘⢦⠑⣿⠊⢹⠀⡾⢼⡌⡍⢹⢠⡿⣄⡏⢹⠖⣆⠀⠀⠀⣧⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⠆
⠸⡇⠒⠀⠙⠀⢀⠀⠤⠀⠀⠠⠁⠀⠀⠤⠀⠀⠂⣾⡀⠀⠀⠀⠈⢣⠘⡇⢸⡆⡇⢀⡇⡇⢸⢸⠉⢸⡇⣯⡴⠁⠀⠀⠀⠳⡍⣓⠒⠶⠶⠶⠶⠶⠖⠒⢋⡹
⠀⠙⠦⣅⡘⠁⠀⠠⠀⠴⠀⠀⠄⠐⠂⠀⢀⣩⠞⠁⢈⡆⠀⠀⠀⢰⡷⣧⣤⣧⡥⣬⣇⡥⣼⣼⣦⣯⣧⣿⡄⠀⠀⠀⠀⠀⣇⠀⠉⠁⠒⠒⡲⠒⠞⠉⢈⠇
⢣⠔⠖⠄⠉⡉⠓⣒⡒⠒⠒⠒⠒⣒⣊⡉⢩⣤⣤⢿⡉⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠸⡀⠸⡀⠀⢸
⠈⢦⡳⡶⠮⠗⠊⠙⠙⢒⠞⠢⠴⠣⣈⢋⡩⣞⡡⢊⡼⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠑⠄⠙⢄⡜
⠀⡚⠿⣒⠶⠬⠭⠤⠔⠊⠀⠀⠀⠉⢉⣉⣉⠥⠔⢻⡠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣀⠴⠃⢠⠎⡇
⠀⠱⣄⣀⠈⣉⠕⠛⠀⠀⠈⠉⠉⠉⠉⠀⠈⣓⡦⢬⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡜⠉⠀⠀⠀⣇⢰⠇
⠀⠀⠀⠙⠚⠓⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠒⠒⠒⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠤⠤⠤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠄⠐⠀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠒⠒⠒⠒⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⣀⡀⠸
⠀⠀⠀⢀⡠⠔⢚⣉⡥⡴⠒⢺⣏⣩⠯⠤⠔⠒⠤⡉⠈⢆⠀⠀⠀⠠⠐⠁⠀⠀⠀⠄⠒⠒⠒⠤⠀⠀⠀⠈⠱⢦⡀⠀⠀⠀⠀⠀⠀⢂⡠⠢⣀⡠⠤⣀⡇
⠀⢠⣊⠥⣶⠋⣹⠤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠖⠃⠀⠀⡀⠀⠀⢀⠀⠀⠐⠂⠬⠭⠉⠒⠁⠀⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⢀⣇⡤⠀⠀⠤⢨
⢠⠛⠓⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣢⠞⠀⠀⠀⠀⣇⣁⡀⡀⠀⠁⠀⠁⠀⠀⡀⠀⠄⠀⠀⣂⡈⠀⣠⡇⠀⠀⠀⠀⠀⡜⠘⠑⠀⠀⠀⠚⢣
⠘⠢⠄⢇⠀⠀⠀⠀⠀⠀⠀⢀⣒⣀⡭⠤⠖⠊⠁⠀⠀⠀⠀⠀⠈⢄⠀⠐⠤⠗⠉⠲⣄⣀⠴⠊⠢⣤⠜⠁⠈⢊⡵⠁⠀⠀⠀⠀⡼⠱⠁⠀⠀⠀⠀⠄⠠⠱⡀
⠀⠀⠀⠀⠈⠁⠐⠒⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⢀⣀⣀⣀⣀⡠⠤⠔⠚⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠐⠀⠀⠈⠁⠀⠀⢠⠃
⠀⠀⠀⠀⣀⠀⠤⠀⠐⠒⠒⠂⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢠⠠⢠⠃
⠀⢠⠂⡡⠔⠒⡂⠨⠍⢈⣉⠉⠀⣒⠒⠪⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠸⢀⠀⠇⠸⠈⢸
⠀⢸⡛⠤⠄⣀⣀⣐⠂⣀⣀⣈⣂⠠⠥⠴⣛⣯⢩⣳⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠉⠒⠢⢀⠀⠀⠀⠀⠀⠀⢀⠏⠄⠀⠀⠀⠀⠘⠈⢆
⠀⠀⡟⠓⠶⠤⠤⠤⠤⠤⠤⠤⢰⠒⠲⠟⠋⣇⡠⢻⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⠀⠀⠀⡞⠀⠀⠴⠀⠀⠀⠂⠀⠘⣆
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠔⠃⠀⠀⢨⣉⣀⣠⢠⣀⡄⣀⢀⡀⡄⠠⠤⠤⣤⣤⡤⣖⣲⣶⣶⣶⣾⠀⠀⢰⡇⠀⠀⠀⠀⠀⠐⠀⢠⠀⠸
⠀⠀⠄⠓⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠯⢐⠒⠤⡀⠀⠀⠐⡛⡯⢜⣛⣭⣴⡟⢉⣤⣢⡀⢂⣠⣌⣯⣥⣩⡭⠍⣋⣉⣩⠀⠀⠘⡇⢃
⠀⡁⠀⠀⠀⠈⠉⠛⠧⠒⠛⠫⠍⠃⠀⠀⠀⣈⠇⢈⡇⠀⠀⢉⢉⠉⠛⣦⣀⡠⣠⢚⣁⣀⣉⣀⣠⡒⢄⢀⡠⣲⣉⣁⣸⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢁⡴
⠀⠈⠒⠂⠥⠤⠄⢀⣀⣀⣒⣒⣀⣀⣀⡩⠭⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠁

⢀⡀⠀⠠⠅⠀⠀⡠⠂⠈⠢⡈⠁⠠⠄⠄⠀⠂⠀⢀⠴⠀⠐⠛⠻⠀⠸⠇⠄⠄⢄⠀⠀⠊⠅⠀⠀⡠⠊⠉⠠⢀⠇⠘⡄⢀⠀⠀⠀⢀⠴⠀⠐⠛⠳⠁⠸⠔⠠
⠀⠀⠈⠀⠐⠀⠂⠁⠀⠀⢀⠜⠀⠀⠖⠀⠨⠀⠠⡀⠀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠑⠄⠀⢀⠘⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀
⠺⠂⠳⣀⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠠⠀⠠⠃⠀⠈⠠⠈⠀⡔⠓⡜⢂⠀⣾⠃⠺⢆⠽⣠⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠂⠔⢂⠀⣺
⠀⠘⠂⠁⠀⠀⡠⠐⠀⠁⠐⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠈⠲⢪⡖⡛⠀⢙⠒⠂⠛⠛⠏⠀⠀⠠⠐⠀⠀⠐⠢⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠈⠶⢢⠔⡛⠀⢛
⠀⠀⠀⠀⠀⠀⡶⠤⣂⢴⡤⢴⡆⠀⡏⠀⠄⢩⠂⠀⠀⠆⠐⠈⡧⢾⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠄⣂⢠⡆⢶⡆⠀⡍⠀⠈⢩⠂⢰⠀⠀⠀⠈⡳⢮⠃⠀⠈
⠀⠀⠉⠀⠀⠀⠉⠉⠷⠘⣣⠍⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠆⠀⠐⠂⣀⢀⡀⠁⠀⠀⠉⠀⠀⠀⠉⠉⠳⡜⣫⠝⠁⠀⢠⠀⠀⡀⠀⠀⠑⠀⠆⠀⠐⠂⢀⢀⡀
⠀⢀⠊⠀⠈⢢⠀⠀⠀⠈⠁⠀⠀⠀⠸⠄⠀⠄⠀⠀⢀⣲⠦⠀⠀⡁⠀⠀⡀⣥⠀⠠⠈⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⣶⠦⡀⠰⡉⠀⢀⡀
⠀⢨⠀⠀⡠⠂⢀⢀⣑⠄⢀⣴⠤⠂⠀⠀⠀⣦⣡⡾⠟⠁⠀⡀⠀⠀⠂⠀⠀⡀⠀⢀⡀⠀⡀⠂⠀⢂⡐⠄⢀⡕⠴⠠⠀⠀⠀⣤⣱⡾⠟⠋⠀⠀⠀⠁
⡄⢢⠘⠈⠀⠀⢈⠠⡔⠲⠵⠷⣄⠒⠀⠀⠈⢜⠁⠀⠀⠠⠊⠀⠀⠀⠒⠐⠀⠀⠄⠡⠚⠈⠀⠀⠄⠀⡴⠲⠾⠶⣄⠂⠀⠀⠀⢎⠀⠀⠀⠠⠊⠀⠀⠈⠂
⢀⡁⠀⣀⠀⠀⠈⢐⠂⠠⠄⢂⠄⢀⠀⢠⣂⠀⠀⠀⠀⠀⠘⠀⠇⡈⣄⠀⠀⠀⢀⡀⠀⣀⠀⠀⠐⢐⠂⠠⠄⢂⠄⠀⠀⣘⣀⢀⠀⠀⠀⠀⠸⠁⠇⡘⡀
⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡯⠇⠀⠀⢀⠀⡰⠂⠺⠀⠀⠠⠀⠌⠢⠰⠁⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⣠⡿⠇⠀⠀⢀⠀⡯⠒⠲⡀
⠀⠃⢀⠀⠀⠀⣠⠄⠒⠀⠲⠀⠐⠂⠁⠂⠈⠁⠐⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⢀⠀⠃⠀⢠⢄⡒⣀⢶⣄⠐⠂⠑⠐⠈⠁⠐
⠀⠂⠁⠐⠊⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⡀⡀⡀⠀⠄⢀⡀⠀⠀⢀⠀⠀⠀⠒⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⡆⣀⠠⠀⠒⣀⠁⠀⠦⢷⠀⠘⡉⠁⡙⠀⠀⠀⠉⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⣂⣀⠠⠀⠒⡀⠁⠀⢨⠷⠄⠘⠃⠉⠛⠀⠀⠀⠉⠀⠀⠉
⠉⠀⠉⢉⡄⠀⠀⠀⠀⢀⠨⠀⠁⢀⣀⡀⠄⠀⠠⠀⠀⡀⠴⣀⢦⠀⢀⡁⠉⠀⠉⠀⠋⢉⡆⠀⠀⠀⠀⠀⡤⠀⡃⠀⢌⡄⣄⠀⠃⠀⠂⠠⠴⣐⢦⠀⢀⡀⠉
⢉⣑⠈⢛⠄⠀⠀⡠⠊⠈⠐⡈⠃⠀⠖⠀⢀⠂⠀⣀⠖⠐⠒⠋⠺⠀⠰⡃⣀⣄⢢⣄⠨⢋⠖⠀⠀⡀⠊⠈⠀⢀⠃⠐⡔⠀⠀⠀⠀⠀⠔⠐⠒⠉⡳⠁⠘⡏⣑
⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⢀⠘⠀⠀⠔⠀⠰⠀⠨⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢋⠐⠀⠀⢀⠜⠀⠀⠆⠂⢀⠀⠈⡀⠀⠀⡠⠈
⠿⣆⡵⣠⠀⠀⠈⠃⠈⠃⠀⠀⠀⠀⠂⠀⠀⠃⠀⠈⠂⠊⠀⡐⡁⣜⢂⠀⣷⢃⡿⢂⠵⣠⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈⠂⠂⢀⡜⡁⣄⢂⠀⣾
⠒⠛⠈⠁⠀⠀⡀⠂⠁⠀⠁⠢⠀⠀⢀⣀⣃⣀⠀⠀⠤⠀⡀⠒⠢⢔⡚⠁⠙⠐⠓⠛⠋⠇⠀⠀⠀⠀⠉⠉⠁⠢⠀⠀⢀⣀⣂⣀⠀⠀⠤⠄⡈⠖⠢⢔⡺⠀⢋
⠀⠀⢀⠀⠀⠀⡷⢒⣒⢒⡒⢶⡇⠐⡅⠀⠀⢨⠂⢀⠀⠆⠀⠈⡗⠺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⢒⣂⢒⡒⢶⡆⠐⠍⠀⠀⢨⠂⢰⠀⠀⢐⠈⡷⢮⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠌⠶⡜⣣⠍⠀⠀⢀⠀⠀⠈⠀⠀⠁⠒⠒⠀⠐⢂⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠙⠌⠷⠜⣯⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⠒⠂⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠆⠀⠀⣐⣶⠶⡄⢠⣁⡀⣀⡀⡤⠀⠠⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣶⠶⡀⠰⣁⠀⣀⣀
⠀⢠⠀⠀⡀⠂⢀⢀⡠⠄⠠⡔⠴⠂⠀⠀⠀⣤⣦⡿⠟⠁⠀⠈⠀⠀⠂⠀⠀⡀⠀⢠⠀⠀⡠⠂⠀⢀⡈⠄⠨⡔⢤⠢⠀⠀⢠⣔⣤⡿⠟⠁⠀⠄⠀⠁
⡔⢢⠊⠀⠀⠀⠀⠀⠌⠒⣋⠶⡴⠒⠀⠀⠈⢊⠀⠀⢀⠄⠊⢀⡀⢈⠁⠂⠉⠀⣔⠠⠈⠁⠀⠀⠁⠀⡌⠒⣟⠧⢴⠒⠀⠀⠀⢎⠀⠀⠀⠠⠊⣀⡀⢈⠁⠂⠉
⢀⡁⠀⣀⠀⠀⠈⠜⠂⠰⠄⢀⠄⠀⠀⢠⡇⠀⠉⠁⠀⠀⠘⠒⠃⡌⣄⠀⠀⠀⢀⡁⠀⣀⠀⠀⠀⠈⠊⠡⠤⢈⠄⠀⠀⢘⡄⠀⠉⠉⠀⠀⠘⠒⠂⡬⣄
⠁⠈⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣨⠯⠇⠀⠀⢀⠀⡸⠂⠸⠀⠀⠠⠁⡀⠃⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⡀⠀⠀⣨⡿⠅⠀⠀⢠⠀⡯⠂⠒
⠀⠁⠀⠀⠀⠄⣠⢀⡔⠭⣳⠄⠘⠄⣉⣀⢈⡁⠜⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⠃⠄⣠⢆⡔⢭⣳⢄⠘⠆⣉⣀⣈⡁⠜⠀⠀⠀⠁
⠀⠂⠀⠐⠀⠀⠁⠂⠀⠀⠀⠐⠇⠀⠀⡀⠂⠀⣀⣀⡀⠀⠄⢠⡀⠀⠀⢰⠀⠀⠀⠂⠀⠑⠀⠀⠡⠀⠀⠀⠀⠈⡆⠀⠀⠠⠂⠀⣀⣀⣀⠀⢀⢠⡀
⠀⣀⠀⠀⠀⠀⣎⠀⠄⠀⠀⢈⠀⠀⠲⢿⠀⠘⠅⠀⠜⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⣀⠀⠀⠀⠀⣂⠀⠄⠐⠀⣀⠀⠀⢰⡷⠀⠸⠁⠀⠘⠀⠀⠀⠀⠀⠈⢀
⣁⣀⣉⣈⡀⠀⠀⠀⠀⠀⡈⣀⣁⢀⣀⣀⣄⠀⠠⠠⠀⣀⡒⣑⢢⡀⢀⣀⣁⣀⣉⣀⣃⣀⡂⠀⠀⠀⠀⢀⡤⣀⣃⢀⣌⣄⣀⠀⠃⠀⠂⣀⠐⣑⣦⡀⢀⣀⣁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⡆⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠠⢄⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠈⠙⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⣔⠃⠋⠓⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠠⠀⠂⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀⢈⠉⠈⠀⠀⠀⠀⡌⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⡀⠀⠀⠀⠀⠈⠂⡀⠀⠂⡀⠈⠁⠁⠄⠀⡁⠀⢀⠠⡄⢀⠈⠀⠀⠠⠄⡀⣀⢀⠀⣼⣇⢄⠀⠀⠀⠈⠀⠀⢀⡀⠠⠲⠀⢀⡀⢀⠀⠀⠐⠁⢁
⠀⢰⡀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠀⠀⠁⠐⢁⡄⠀⡀⠈⠑⡽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⣤⡠⡤⣤⡴⡀⠈⢤⡀⠔⢀⠠
⠀⠀⣦⣄⡠⠆⠀⠒⠁⠉⠀⠀⠀⠀⠡⠄⠠⡁⠀⠀⠁⠀⠀⠀⢀⠌⠀⠀⢨⡕⠀⠀⡀⢠⠀⠀⠀⠠⠀⠀⠠⠀⠦⠄⠘⣄⢋⠀⠤⠂⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠂⠀⠀⢀⡀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠐⠀⠄⠀⠀⢀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠠⠄⡀⠀⠀⢘⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌⠡⠒⢈⠀⠂⠀⠀⠀⠀⠐⠀⢀⣀⠈⠀⠀⠣⠊⠁⠆⠀⠀⠀⡀⠀⠀⠀⠔⠁⠀⠀⠀⠰⠀⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠂⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣄⣄⣀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⠊⢀⡐⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢠⣶⣿⣿⣿⠛⢛⡛⡻⡟⣿⣿⣿⣶⡄⠀⠁⠀⠉⠀⠠⠸⡈⣈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⡐⠂⠠⠁⠀⠀⠀⠀⠀⠑⠄
⠀⠘⡒⠐⠈⠀⠀⢀⠀⢀⣿⢛⡟⣿⢻⡛⢛⣿⢛⡛⠻⠟⠟⢻⣿⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⢀⠀⣂⢀⣀⣀⣀⠀⠀⡀⡂
⠀⠀⢡⠀⡄⠀⠀⠀⠀⠘⣿⢨⠁⢹⡜⣿⢸⣿⢈⡁⡇⠀⠀⡆⣿⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⡂⠀⠀⡁⠀⠁⠀⠀⠇⠀⠍⠛⠋⠀⠛⠀⠐⠈⠁
⠀⠀⠀⠆⠃⠀⠀⢀⠀⠀⠹⣼⣼⣮⣭⣿⣼⣿⣼⣧⣡⣬⣤⣴⠏⠀⠀⠀⠀⠰⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠠⠀⠐⠀⠀⠀⠉⠛⠛⠛⠻⠛⠛⠛⠛⠛⠉⠀⠀⠀⠂⠀⠀⡀⠀⠠⠄⠁⠀⠀⠀⠀⠈⠀⠀⠀⢐
⠀⠀⢅⠀⠀⠀⠂⠀⠒⠠⠀⠀⢠⠐⢀⠀⠀⠠⢀⠀⠠⡀⠀⠀⠀⠀⠄⠀⠀⠠⡈⠀⡀⠔⠀⠄⠀⠀⣀⣀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢉⠀⠸⠀⣕⠐⠘⠂⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⢀⠗⠁⠀⠀⠉⠄⠀⠀⠂⠈⠂⠀⣈⠀⠀⠀⠀⢙
⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⡀⠀⠐⢀⠀⠀⠘⠕⠀⡀⠀⠀⢘⡂⠀⠀⠆⠀⠀⣀⠀⠀⠀⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠑⠂⠀⠘⠀⠰⣀⣀⠬⠃⢈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠐⠬⠄⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡄⠀⠀⠀⠀⠀⠀⢀⠰⠸⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠁⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠖⠃⢀⠄⢀⠀⠒⠑⢀⠀⠀⠠⠀⠀⠀⠃⠁⠦⠀⠐⠀⠅⠀⢸⠀⠁⠈⠀⠂⠀⠐⠀⢴⣊⠖⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠠⠤⠆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⢀⠀⠀⠨⠂⠀⠀⠠⠊⠀⠀⢄⠀⠀⢀⡈⠀⠂⢰⣀⡠⡰⠱⢡⠄⠀⠀⠀⠀⡆⠀⠠⠀⠠⠀⠁⠒⠈⠀⠤⠀⠀⠀⠀⣠⠀⢀⠠
⠀⠈⠀⠀⠀⠄⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠠⢇⡀⠀⢸⢆⡀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠐
⠀⠢⠀⠠⠄⠂⠁⠀⠀⡀⠀⠀⡠⠔⠊⠁⠁⠀⠀⠈⠍⠀⡄⠀⠀⠈⠚⠚⠁⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⡄⠀⠀⡀⠀⠀⡄⠀⠄
⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠑⠂⢀⠉⠀⠐⠀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠁⠀⠠⠤⠄⠀⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠓⠀⠁⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠁⠀⠀⢀⠠⠤⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠤⡀⢤⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠦⠤⠐⠀⠈⠀⠠⠀⡀⣤⠀⠤⢤⡌⠛⠂⠀⠤⠆⠉⠉⠁⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⣀⣡⡒⠦⠤
⠀⠂⠀⠀⠢⠄⠀⠀⠀⠄⠀⠀⠀⡀⠞⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠁⠒⠦⢀⡀⢀⡤⢊⠡⠀⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠔⠈⠀⠀⠀⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠥⠖⠁⠀⠀⠀⠀⠀⠸⡄⠃⠀⠄⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠄⠤⠀⢤⠄⠀⢂⠀⡰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡆⠀⠀⠄⠂⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⠄⠃⡤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⢀⠀⠘⠀⠐⠄⠀⠀⠁⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⠀⠀⠀⡐⠁⢠⡕⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠇
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀⠂⢀⠀⠙⠂⠀⡀⠀⠀⠀⠑⢧⠘⠀⠀⠀⠀⠀⠀⠐⢁⠤⠀⠀⠘⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⣀⠀⠈⠀⠀⠀⠀⠢⠤⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠈⠠⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠁⠀⡄⠀⠊⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠦⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠘⠲⡀⠶⠄⠦⠐⠃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠁⠤⠄⠀⠀⠀⠤⠄⠀⢀⡀⠀⢀⠠⠐⠠⠀⠀⠀⠠⠄⠀⠀⢀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣁⡀⠠⠄⠄⠀⠈⠠⠄⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠠⢤⠄⠙⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠠⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⠀⠀⠨⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠉⠉⠀⠦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠖⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠐⠈⠁⠀⠂⠀⠀⠀⠀⠐⠒⠈⣀⣁⠀⠀⠀⡁⠀⠀⠀⠀⠃
⢀⠤⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⢀⠀⠀⢀⠀⠀⠐⠢⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠈⢂⠘⠢⠄⠀⠠⠒⠀⠈⡠⠀⠀⢀⡄⠆⠆⠀⠙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠰⠀⠂⠀⠀⠀⠀⠁⠂
⠀⢀⠀⠀⠀⠱⡀⠀⠄⠒⠀⠀⢰⠁⠀⢰⠑⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠊
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⢆⣀⣀⡀⠀⠂⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⡀⠀⠀⠀⠄⠐⠈⠉⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⢀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⢠⠄⠀⠀⣤⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠢⠄⡈⠣⡙⠃⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⡐⠒⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⣤
⠀⠂⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡀⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠶⠾⡄⠀⠁⠀⢂⠐⠃⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠑⠀⠈⣉⠲⠀⠀⠀⠀⠀⠀⢀⡉⠀⠭⠭⣝⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣑⣤⣤⡤⠖

⠀⠀⠀⠆⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⡠⠐⡠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⣄⡆⣦⡤⠼⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠟⠁⠀⠠⢂⡘⡄⠀⡘⠀⠀⠀⢠⡖⠒⠒⠛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠘⠁⠀⠚⠀⠀⠀⠀⠈⠙⠖⠀⠀⠃⠀⠀⠀⠁⠀⠀⠂⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠐⡤⠀⠀⠸⠃⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠸⠀⠀⠀⠀⠀⠀⢀⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⠀⠀⠀⠀⡀⢤⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠸
⠀⠀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⢎⡩⣄⠀⠀⠑⢌⠀⢡⠀⠀⠠⠈⠂⠀⠀⠀⢀⠀⠘⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠨⠗⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉

⢀⠄⠀⠋⠀⠁⠐⠀⠀⠀⠠⣴⡄⠐⡤⣧⠄⠀⠀⠀⠀⠀⣄
⠀⠀⠔⠋⠽⣟⠐⠀⠀⠀⠀⠍⠉⢰⠛⠧⠀⠀⠀⢀⠄⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⢀
⠀⠀⠀⠈⢰⠁⠀⠀⠀⠀⠀⢰⠀⠰⢀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠠⡐⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠈⠚⢻⠋
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢂⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡀⠀⠀⠀⢀⢖⠃⠒⠒⢤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣄
⠀⠈⠀⡀⣠⠤⠤⣀⡄⠀⠀⠀⠄⠠⡂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢣⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠠⠁⢠⠀⢰⠀⠠
⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠣⢀⡐⠀⠂⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠐⠈⠀⠀⠀⠈⠂

⢀⣀
⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⣴⣦⡄
⠀⠀⡀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡿⠟⠁⠀⠀⢀
⠀⠀⡇⠀⡆⠀⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢳⡄
⠀⠀⠃⠀⡇⠀⠁⠀⢠⠦⠤⠤⠤⠤⠤⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⡀⠀⠀⠀⠀⠂⠀⠠⢉⠁
⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⣎⣉⣳⡀⠀⠀⠀⠀⡤⡤⠒⡶⣠⠒⡦⡀
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⢠⠮⠭⠭⠭⠽⠄⠀⠀⠀⣸⠥⠄⠬⠦⠨⣆⠀⠀⠀⣜⠁⣼⡙⣧⢎⢫⣾
⠀⠀⠀⢠⡗⡒⡒⢖⠠⣒⡲⣶⠾⡀⠀⠀⠀⠘⡎⠉⠉⠉⢹⠁⠀⠀⠀⠙⣟⢻⡭⡛⢹⠁⠀⠀⠀⢹⠙⠓⠓⠚⠚⢉⡇
⠀⠀⠀⠀⢹⠒⠾⡉⣘⢿⠓⠞⡟⠀⠀⠀⠀⠀⢣⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⡟⢤⣺⠃⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠉⠁⠘⠳⣰⠞⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡁⡝⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡤⢒⣂⡉⣐⠲⡄⣠⢤⠀⠀⠀⠀⠀⣀⠤⢤⠒⠢⡄⠤⡀⠀⠀⢀⡠⠔⠒⠒⠠⢄⠀⠀⠀⠀⠀⢀⠤⠒⠢⢄
⠀⠀⠀⢠⢋⠖⠧⠎⢀⡠⡫⠞⠹⡆⠇⠀⠀⢠⠞⠁⠀⠀⠣⡀⢣⣀⣈⠆⠀⣎⣀⣀⣀⣀⣀⣠⡕⠀⠀⠀⢠⠋⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠈⠆⠏⠋⠻⠒⡿⢭⢅⠙⠂⠀⠀⡜⠣⡀⠀⠀⢀⡝⠁⠀⠀⠀⠀⠈⡄⢠⠈⡄⠰⢠⠁⠀⠀⠀⠸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⢆⠳⢖⢐⢢⣀⡰⢋⡞⠀⠀⠀⠀⡗⢄⣈⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⢡⣘⠀⢃⣃⠎⠀⠀⠀⠀⡼⢑⣤⠴⠊
⠀⠀⠀⠀⠀⠑⠢⠤⠭⠤⠒⠋⠀⠀⠀⠀⠀⢇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⢭⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⣔⣒⣢⢠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⢖⣂⠴⡒⣒⣄⠀⠀⠀⠀⠀⡤⠤⠤⠧⠧⠤⣄⣀⡀⠀⠀⠀⢸⠀⣇⠾⠼⠄⠀⠀⠀⢀⡔⡢⣄⡠⢚⠦⡀
⠀⠀⠀⠀⡎⡡⠒⠉⠒⠒⠒⢝⢦⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⣯⣗⠅⠀⠀⠀⡸⠀⡧⠋⠈⠣⡄⠀⢠⠊⠀⢱⠈⢳⠸⡄⠈⠆
⠀⠀⠀⢸⡴⠁⠀⠀⠀⠀⠀⠈⢿⠂⠀⠠⡆⠀⠷⠤⠄⠖⠋⠃⡲⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠸⡀⢀⠇⠀⢸⠀⡇⠀⡄
⠀⠀⠀⠸⠤⠤⠤⠀⠒⠀⠀⠤⠊⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠉⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠀⠑⢤⣃⠴⠛⢄⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠤⠤⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠀⣞⣵⣵⠗⠺⡄⠀⠀⠀⢠⠃⠘⡀⠀⠀⠀⠀⠀⠀⣠⠊⠱⢼⢌⢷⠀⠀⠀⣠⣀⡠⠤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⢰⣊⠭⣔⡺⣽⠝⠁⠀⠀⡇⠀⠀⠀⡞⣚⠓⠙⡆⠀⠀⠀⠀⣴⠥⠔⠚⠉⢉⡏⠀⠀⢸⠀⠘⠀⣀⠈⠀⠀⠋⠀⢹
⠀⠀⠀⢎⣪⠛⠊⠉⠀⠀⠀⣠⠎⠀⠀⠀⠀⠹⠀⡇⢰⠃⠀⠀⡠⠊⠀⠀⠀⠀⡠⠋⠀⠀⠀⣞⡋⢛⡓⠒⡞⠉⣖⡛⢳⣋⡢
⠀⠀⠀⠈⠡⡀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠸⠋⠁⠸⡄⠀⠀⠣⢄⡀⠀⠀⡔⠁⠀⠀⠀⠀⠘⠬⠅⠈⠫⠬⠍⠤⠬⠥⠜
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡄⠠⠃⠀⠀⠀⠀⠈⠢⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣤⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠝⢱⠀⠼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠍⠱⠀⠼⢉⡀
⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡀⠀⠀⠀⠀⡴⠋⡏⡩⠦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡴⠫⡎
⠙⢣⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠆⠅⠜⢃⡶⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠐⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠰⠤⠒
⡄⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠖⡼⣿⡆⢊⠀⠀⠀⠌⠄⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣖⣾⣻⡆⠊⠀⠀⠀⠌⠆⢙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠀⠀⠀⠀⠶⢋⠘⠃⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠶⠛⠘⠇⢦⡴⠂
⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠨⣁⠀⡤⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣀⠂⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⡠⠦⡴⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡠⠢⡤⠀⠀⠀⠀⠆
⠀⠀⠈⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃
⠀⠀⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⢀⠉⡰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡰⠉⠆
⠀⠀⠀⠀⡶⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠃⠠⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠜⠹⠀⠼⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠱⠀⠍⠹⠀⠨⢡⡀
⠦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠐⠀⠀⠀⣴⠁⡏⠩⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡰⠉⡏
⠙⡃⡶⠀⠀⠔⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⠜⠃⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠒
⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆
⣗⠺⣻⡆⢂⠀⠀⠀⠌⠂⢉⠿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡷⣊⣖⢾⣹⡖⠊⠀⠀⠀⠈⠂⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠖⢋⠘⠃⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡴⠀⠀⠀⠀⠷⢛⠘⠃⢢⠴
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣁⠐⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣁⠂⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡰⠦⠶⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡤⠲⡴⠐⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠉⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃⠀⠀⢀
⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠈⠉⠰⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠃⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠂⠐⠀⠀⠀⠐⠈⠒⠒⠀⠁⠁⠘⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠄⠄⠀⡐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠰⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠉⠙⠓⠒⠒⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠛⠉⠙⠒⠲⢤⡀⠀⠀⠀⢀⣸⠤⠔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠖⠋⠁⠀⠠⠖⠡⠟⡷⣄⡀
⠀⠀⠀⠀⠀⠐⡒⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⡈⠹⠿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢟⣹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⣲⣄⣀⢤⠄
⠀⠀⠀⠀⠀⠀⢁⣮⠆⢽⡍⢿⣖⢶⠶⢶⠒⣒⣚⣹⠉⠞⣳⡽⠉⠈⠢⣀⠀⣀⣤⣴⡶⢛⣟⢛⡛⣉⣁⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠸⢛⠦⢄⣀⠀⠈⠉⠙⡓⠀⣉⠀⠘⠋⡥⢎⡟⢠⢀⠀⠀⣽⠉⢤⡏⠀⡎⢻⠛⢯⣄⡈⢙⣭⠗
⠀⠀⠀⠀⠀⠀⠘⠦⢀⣠⡌⠛⠁⠤⢄⢠⣈⣁⡀⠀⡀⣠⠎⠁⠣⣌⠄⢸⣿⡄⢸⣬⣖⡽⠄⣇⢀⠦⠽⢾⡜
⠀⠀⠀⠀⠀⠀⠐⢄⢀⠈⠉⠁⠈⠀⠈⠁⠉⠉⠉⠁⠈⢀⠄⠁⠀⠈⠢⣥⠙⣧⠈⣟⠬⣉⣁⡟⢴⣟⠓⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠐⠒⠒⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠙⡓⡁⢶⠨⠇⠈⠂⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠘⠏⠇

⣿⣿⠻⢿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⡘⠀⠤⢤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠀⠀⠈⠘⠛⠛⠿⠿⠯⠂⠀⠁⠀⣤
⠀⠀⠀⢦⠀⠀⠀⡀⡀⠀⠀⡄⠀⠀⠘⠆⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣚⠓⠒⠀⠐⠂⠒⠂⠀⠖⠒⠶⠒⠚⠋
⠀⠀⠀⠈⠃⠀⠀⠀⠣⠀⠀⠑⠀⠂⠀⠸⠇⠀⠀⠇⠀⠀⠀⠀⠀⢠
⠂⠀⠀⠀⠀⠀⣺⡀⠀⢀⠀⢠⠄⠘⠀⠀⣜⠁⠄⠀⠀⠀⠀⠀⠀⠀⡀
⢨⠆⠀⠀⡀⢁⣈⠃⣀⣰⠀⠀⠘⠃⢀⣀⡉⣀⠀⠄⠄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢰⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠐⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣷
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣸
⠀⠳⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌⠒⠒⠒⠒⠛⠓⠒⠂⠀⠀⠴⠶⠶⠒⠒⠠⠶⠶⠶⣦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⡠⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠⣤⡄⠀⢀⡀⠀⠠⢈⠁⠀⠐⠂⠂⠀⠤⠀⠀⠐⡀⠀⠀⠀⠀⢀⡇
⠀⠀⢋⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠐⡇
⠀⠀⠈⢠⣄⣀⣀⣀⡀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⣀⡼⠉⡆
⠀⠀⠀⣠⢿⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣀⡠⢼⣃⣰⣇⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⡠⠖⠒⡄
⠀⡰⢦⣉⣹⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⣼⡸⢀⣖⣛⣦⣝⡞⣇⠀⠀⠀⠀⠀⣎⠀⠀⢀⣡⠤⣄⠀⢳⡀
⠚⠓⡏⠀⠈⠳⢤⣀⠀⠀⠉⢑⣞⠀⠀⠀⡿⠷⠽⣭⣤⣵⠎⠀⠸⡄⠀⠀⠀⠀⠈⣳⠀⡏⠀⠀⠈⡇⠀⠙⢦
⠀⠀⠙⢄⠀⠀⠀⠉⠛⠛⠻⣅⣬⠀⠀⠀⠸⡄⠀⠂⣠⠋⠐⠀⠀⢳⠀⠀⠀⢠⠞⠁⠀⠳⢤⣠⠴⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠒⠦⠤⠤⠤⠴⢧⡞⠀⠀⠀⠀⠙⣄⣰⠃⠀⠀⠃⠀⠈⣇⠀⠀⢸⡀⠀⢀⣠⠤⠤⣤⣀⡀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡄⠀⡀⢸⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠂⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⢺⠻⠛⠀⠀⠀⠀⠀⠀⠸⣙⡆⠀⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⣀⠖⢤
⠀⠀⠀⠀⠀⠀⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠳⡀⠀⠀⢠⢂⡀⠀⠀⠀⣠⡀⠀⠀⠘⢧⡼⠿⣼⢷⡛⣶⢦
⠀⣠⠶⠒⣒⣚⣛⣒⣒⣒⣲⡄⠀⠀⠀⠀⣞⣓⣒⣛⡇⠀⠸⡘⢄⡤⣄⣴⠟⠁⠀⢰⣟⣚⠣⣜⣹⢸⢷⠈⢧
⠀⠉⣏⠉⠉⠉⠉⠉⠉⢉⡇⠀⠀⠀⠀⡔⠉⠀⠀⠀⠙⢦⠐⣁⣼⣆⡀⣻⠀⠀⠀⠀⢠⣼⣧⣈⣳⣜⣸⡧⠴⡗
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣸⣅⠀⣹⠉⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠈⡇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⡏⠉⢻⡝⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡴⠋⠙⢻⡗⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⠤⠤⠤⠤⠼
⠀⠀⠀⠈⠓⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠳⠶⢦⣾⠦⣦⠴⠁
⠀⠀⠀⣀⣤⡤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠓⠒⠦⣄⡀
⠀⠀⡰⠛⠩⠉⠓⠦⡛⢺⠷⡶⢤⡀⠀⠀⠀⠀⣠⠖⣋⠉⡉⠏⣓⠦⡀⠀⠀⠀⠀⠀⢸⡚⠦⢤⣞⠀⠀⠉⠳⣄
⠀⢸⠀⠀⠀⠀⠃⢀⠈⢮⡑⡿⣢⢹⡀⠀⠀⢰⡁⠆⠈⠀⢁⡄⠁⠴⠙⡆⠀⠀⠀⠀⢸⡙⣦⠀⠬⠙⠻⣄⡠⠈⢳
⠀⠈⢦⡁⠐⠂⠀⡀⠀⠆⢳⠉⣿⣾⠇⠀⠀⠀⣟⣓⣒⡒⢚⣒⣶⣒⣲⣟⠀⠀⠀⠀⣼⠕⠃⣔⣭⣽⣿⣢⡵⠖⠚
⠀⠀⠀⠈⠓⠦⣀⠁⠀⠄⠈⣷⠷⡟⠀⠀⠀⠈⢯⠥⠤⠾⠿⣶⡶⠿⠷⡾⠀⠀⠀⠀⡷⢤⣈⣯⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣷⠞⠀⠀⠀⠀⠀⠈⠳⠤⣤⣀⣀⡽⠦⠞⠁⠀⠀⠀⠀⠷⠚⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡩⢣⠀⣤⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠓⣀⢦⠠⠤⡏⠇⠰⠰⡅⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⢆⡰⢌⡄⠹⡤⠿⠲⠁⣎⡹⠆⠡⠀⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣄⢀⡸⠒⠎⠘⡀⡠⠞⢢⠀⠨⠁⠈⡀⢂⠈⠎⠖⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢹⠇⣤⠋⢄⠀⠑⢻⠲⠉⢇⠀⠁⠡⠐⠀⣃⣸⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣶⠀⠀⠀⠀⠀⣀⡇⠀⠈⢆⠈⡆⠀⠈⠓⠋⢇⢃⠘⡆⠀⠀⣣⡶⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣰⠃⠀⠀⠀⠀⢸⡗⠶⠦⢤⣬⣤⣽⣄⣦⣤⣥⣸⣬⣤⡴⣶⠞⠉⠀⠀⠀⠀⠀⡇
⠀⠀⣠⡤⠔⠒⠂⠀⣈⡧⡤⠓⠒⠤⢤⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⣤⣤⣤⣤⣧⣤⣀⣀
⠀⣼⣏⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⣀⢟⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠁⢀⠀⠀⠉⠉⠉⠛⠻⢷⣦⣤⡀
⠀⡷⠬⣍⣛⣒⠚⠛⠒⠒⠒⣒⣚⡉⠥⠚⡇⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⢉⡁⡄⠀⠀⠠⠀⠂⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⡏⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠈⠀⡇⠀⠸⡆⠀⠀⣀⣴⠾⠋⠁⡠⢰⠄⠉⠀⠂⢂⣠⠤⠖⠒⡈⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢿⣷
⢠⡇⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⡀⠀⠀⢀⡇⠀⠀⣇⣠⡾⠋⠁⠀⠀⢀⣈⣀⣤⠤⣤⠴⠿⠤⠤⣤⣉⣀⠀⢴⡴⠀⠉⠉⠠⡠⠆⠀⠀⠀⠈⣿
⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⢀⠀⠐⠊⠉⠁⣠⠔⠋⠀⠀⡄⠀⣀⠀⠈⠉⠛⠲⣄⠀⣆⠜⠀⠀⠀⠀⠀⠀⣸⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⢸⣷⠟⠁⠀⠀⠺⠈⢀⡠⠂⣤⠞⠁⠀⢀⡀⠉⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠄⡆⠀⣠⠞⠁⠐⠁⠐⠒⠁⢠⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣰⡟⠀⠀⠀⠀⠀⠀⠋⠀⡴⠃⠀⠀⠸⠥⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⢀⣤⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⣀⣤⠞⠋⣠⡇
⢸⡇⠀⠀⠁⠀⠀⠀⠀⡜⠀⠀⢨⣿⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠉⣀⣤⠶⠛⠉⢀⣤⠞⠉⡷⢤⡀
⣿⡇⠀⠀⠀⠀⠀⢠⠎⢀⡀⠔⠉⠳⣍⡛⠿⢿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠿⠟⠛⢉⣁⣤⠴⠞⠋⠉⠀⣀⣤⠾⠋⠁⣀⡼⠃⠀⣿
⣿⠇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣇⠙⠓⠦⢤⣈⣉⡉⠉⠉⠉⠉⠉⢉⣉⣁⣠⣤⠴⠖⠚⠋⠁⠀⢀⣠⣤⠶⠛⠉⠀⣀⣴⠞⠋⠀⠀⢠⣿
⣿⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⢦⣄⣀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⢀⣀⣤⠶⠛⠉⠀⠀⠀⢀⣴⡿⠁
⣿⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦⣌⠉⠙⠛⠓⠒⠲⠶⠶⠶⠖⠒⠛⠛⠋⠉⠁⢀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡿⠋
⣿⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠲⠶⠤⢤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁
⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⢛⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⢿⣝⡛⠻⠷⠶⠿⠿⠟⢛⣋⣩⡴⠖⠛⠁⠀⠉⠛⠷⠶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣴⠶⠶⠟⠛⠋⠁
⣤⣤⣬⣭⣿⣿⣷⣾⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣏⣼⣉⣯⣩⣿⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣀⣀⣏⣁⡀⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⠀⠀⢀⣠⠤⣤⣿⣯⣕⢦
⠀⠀⠀⡜⠁⠈⠀⠁⠈⠀⢹⡄⠀⠀⠀⣴⠓⠒⠒⠚⢳⠀⠀⠀⠀⠀⡾⠤⢧⠀⠀⠀⠀⡰⢫⠖⠋⡇⣯⣶⠾⡛⠁
⠀⠀⠀⣿⠭⢭⡩⠭⣩⠭⢽⡇⠀⠀⠀⠈⡏⠉⠉⠉⡏⠀⠀⠀⠀⢸⠓⢦⢸⡆⠀⠀⢰⡇⡟⢯⠗⣇⠭⡒⢻⢹
⠀⠀⠀⢹⡒⣖⠚⠛⢒⡶⣺⠁⠀⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⠀⠘⡗⠋⢸⠁⠀⠀⠈⣇⢧⡺⡧⣀⡛⢋⠞⡼
⠀⠀⠀⠀⠉⠉⠑⠶⠋⠉⠁⠀⠀⠀⠀⠀⢸⣀⣀⣼⠀⠀⠀⠀⠀⢰⣃⣀⣸⡄⠀⠀⠀⠈⠳⢝⣚⣓⣛⡥⠞
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⣤⢻⠹⡇⡟⡽⣦⡀⠀⠀⠀⠀⠀⠀⣯⣯⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠦⢤⡀⠀⠀⠀⠀⠀⢀⡴⠫⠙⣝⣧
⠀⠀⠀⣏⠉⠛⠛⠛⠉⢹⠇⠀⠀⠀⠀⢰⠒⠒⠒⠒⣦⢤⠀⠀⠀⢾⣁⣀⣀⣀⣀⣈⡳⠀⠀⠀⠀⡞⠐⠀⠀⢂⡟
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⡧⠞⠀⠀⠀⠈⢧⠸⡇⢀⡇⣸⠁⠀⠀⢀⡴⢳⣬⡤⠖⠉
⠀⠀⠀⠘⣇⣀⣀⣀⣠⡇⠀⠀⠀⠸⣏⣉⣉⣉⣉⣉⣉⡹⠃⠀⠀⠀⠸⣄⣧⣸⣠⠇⠀⠀⠘⢯⡵⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣞⣙⣦
⠀⠀⠀⠀⣀⠤⠔⠛⢆⠀⠀⠀⠀⢀⣠⠤⣄⡤⢤⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢳⡄⠀⠀⣸⢥⣤⣿⣤⣷
⠀⠀⠀⢰⠛⠒⠒⠒⠚⢣⠀⠀⠀⣞⣀⣀⣈⣀⣀⣁⣀⣀⣹⡀⠀⠀⠀⠀⢀⡴⢇⡈⠉⡧⠀⠀⠈⣏⣩⠽⢛⡏
⠀⠀⠀⢸⡉⢻⠉⣻⠉⡟⠀⠀⠘⣿⡳⢾⣷⠞⠳⣞⡷⢞⣿⡇⠀⠀⢀⡤⠾⣄⠀⠙⢲⡇⠀⠀⠀⢹⡴⢚⡽
⠀⠀⠀⠀⣧⢸⡀⡟⢰⠃⠀⠀⠀⠓⠻⠯⠭⠭⠭⠭⠽⠿⠚⠀⠀⠸⣍⣳⡀⢈⣧⡤⠚⠀⠀⠀⠀⠀⢿⢩⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⣤⣄⠀⠀⠀⢀⡤⣄⠀⣠⢄⠀⠀⠀⠀⣤⣤⣤⡄⡸⢧⡀⠀⠀⠀⠀⠀⠀⢠⢾⢶⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠙⡶⢳⣶⣳⠄⠀⢠⠎⢠⡈⢾⠁⣌⢳⡀⠀⠀⢸⠁⢹⢘⡗⢺⡃⠀⠀⠀⠀⢀⡴⣳⣫⠏⠀⢹⡆
⠀⠀⠀⣠⠞⠁⠀⢠⠏⢙⡷⠃⠀⠀⢸⡀⣞⠀⣸⢰⠃⢠⠇⠀⠀⡼⠀⠸⡏⠀⠀⢹⠀⠀⢠⣞⣽⣺⠖⠁⠀⢀⡞
⠀⠀⠐⢧⡀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠳⣄⡔⠙⢦⡰⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⠘⢷⡋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠙⢯⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠧⠤⠤⠼⠀⠀⠀⠀⠑⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⡄⠀⠀⣀⠀⠀⣤⣀⡄⠀⠀⠀⢀⡂⠀⠀⢀⠐⠲⠂⠀⠀⠀⠀⠀⠀⣦⡦
⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣀⣛⢦⣀⣬⠶⣴⠚⠛⢯⡁⣈⠀⠀⠀⡀⠘⣆⠀⣉⣻⣿⣿⣿⣿⣿⡖
⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠉⠉⠉⠙⢿⣍⣢⣤⠬⠷⢶⡛⠉⠃⠀⠀⠀⠀⠀⠙⠀⣒⣶⠿⢿⠿⠛⠉⠁
⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠘⢿⣁⣈⣳⣤⡴⠛⠞⠀⡀⠀⠉⠀⠀⠀⠀⣭⡀⠀⠀⣀⡀⣀⠤
⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢈⠁⠈⠁⠀⠀⠀⠀⢀⣿⠉⠉⠀⠀⠀⠑⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣷⠀⢀⣿⢳⡟⢁⣰⣶⣧⣄⢀
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠈⠋⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡤⢿⠇⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⣸⠃⣿⣿⣿⣿⣿⡆⣷⡀
⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠹⣿⣧⡙⢿⣿⣿⡿⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢯⣻⣤⣤⠄⠀⠙⠛⠲⠟⠻⠇⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠤⠔⠀⣠⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠐⠂⠀⠂⠀⠀⣹⣷⣀⣠⣤⣶⡶⠶⠶⠶⠾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡄⢀⠐⠁⠔⢸⡄⠀⠀⠀⠀⠀⠀⠁⠀⣵
⠀⠀⠀⢀⡠⠈⠋⠆⢰⠆⣝⠀⠀⠀⠐⠐⠶⠚⠙⠿⠿⣖⡂⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡼⠎⠀⠀⡀
⠀⠀⠈⠐⠂⠀⡧⠐⠒⡠⠡⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠚⣿⡷⠀⣤⢠⠌⣍⢀⣀⣈⣉⡀⢀⡀⠀⠀⠈⠙⠒⠒
⠀⠀⠀⠤⡀⢶⠸⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⣿⡇⠀⠈⠻⠴⣧⣰⣄⣤⣠⡷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠃⠀⢰⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣷⣄⣤⣾⣿⣿⡿⠀⠀⢀⡀⠡⠔⠤⠀⠀⠀⡇⠀⠀⠀⠐⠒⠀⠡⡀
⠀⠀⠀⠀⠀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠁⠀⠀⠀⢀⣀⠀⢐⠇⠀⢠⠃⠀⣄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠸⠀⠀⠹⡇⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⣀⣴⠋⠀⠀⠘⢄⣀⢀⣠⣠⣶⡞
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠻⣷⣶⣾⣿⢃⡖⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠨⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠖⠋⠀⠀⠀⠔⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⢂⣿
⠀⠀⠀⠀⠀⠑⠀⡾⠀⠀⠐⢦⣀⣧⣀⣴⡷⠃⠠⢂⣱⣯⢧⠷⠾⣷⣄⠀⢐⠀⣏⠀⠀⠈⠻⣤⣀⣀⣀⣰⣦⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠃⠁⠈⠉⠆⠀⠀⠈⢻⡆⠀⠀⢹⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠡⠀⠀⠀⢴⡇⠀⠈⠒⢤⣄⣠⣼⣶⠿⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣤⣀⣠⡶⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣾⣎⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣄⠀⠀⠏⠀⠀⠀⠀⠠⠟⠃⠙⠁⡧⠠⠄
⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣟⠓⠀⠈⠳⣦⣄⣀⣀⣀⣀⣀⣴⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡏⠓⠒⠯⠝⢻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠆⠀⠀⠹⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢉⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣥⣤⡀⡥⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⠞⡃⠠⡠⢹⣦⣾⣟⣽⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣻⣿⣿⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⠙⢋⡿⠣⣮⣉⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣏⡉⠙⠁⠀⠀⠒⠦⠈⠉⠉⠉⠿⣿⣿⣿⣿⡟⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠻⠛⠲⠶⠶⣄⣲⣀⡀⡒⠒⠺⠽⠛⠛⢋⣼⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣛⣉⣤⣶⣶⣮⠙⠉⠉⠉⠉⠉⠉⢉⣭⣶⣶⣤⣀⣾⣿⣿⠏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡿⣭⣙⡻⣿⣿⣿⣷⡄⠀⠀⢀⣴⣿⢿⡟⣛⣹⣿⣿⣿⣿⢾⣾⡏⠎⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠆⣈⡴⣋⠿⡝⢁⣙⠳⢶⡟⡇⠈⠀⢽⠋⡛⠞⢻⠁⢀⣰⡗⣵⠐⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡔⢡⠗⡂⣨⣍⠳⢮⠀⣀⣚⠋⠘⠀⠀⠀⢡⣴⣿⣉⣸⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣏⡟⠳⠓⠜⠉⠉⠐⠚⠛⠿⢆⠍⣀⣎⣹⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⠤⠄⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣀⠤⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⠀⠀⠀⠀⣠⣂⣒⡄⠀⠀⠀⠀⢰⣲⠒⣶⣤⢒⣆⣀
⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠜⠁⠉⠘⠒⡆⠀⠀⢸⣥⣤⣷⣸⡆⠀⠀⠀⢮⣁⡸⡌⢣⣮⠽⢾
⠀⠀⠀⠀⣯⠍⠢⣄⣢⡴⠫⢍⠇⠀⠀⠀⠀⠗⠁⠀⠈⡞⠁⠀⠀⠀⢫⠖⣮⣽⠀⠀⠀⠀⠈⢆⠉⠉⠉⠀⢀⠎
⠀⠀⠀⠀⠘⢍⡉⠙⢷⠘⣟⠏⠀⠀⠀⠀⠀⢈⠀⠀⢠⠁⠀⠀⠀⠀⠈⢟⣠⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣆⠤⠼⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠰⠴⠀⠀⠚
⠀⠀⠀⠀⠀⢀⡀⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡠⠤⣤⣄⡀
⠀⠀⠀⠀⡔⣡⢒⠖⠒⣢⣼⡶⡉⢆⠀⠀⠀⡔⠁⢀⠀⠑⡀⠀⢠⡃⢛⡀⠆⢘⢙⠄⠀⢀⣀⣴⣒⠤⣀⡠⢄⣤⣀
⠀⠀⠀⢸⠸⠠⠲⠦⠮⢹⣭⣤⠷⠬⠀⠀⠀⠇⠀⠀⢀⢠⠃⠀⠀⢩⢡⠉⡏⢡⠙⠀⠀⠘⢴⠉⠙⠫⠝⠹⠛⠙⡬
⠀⠀⠀⠈⡞⢤⡀⡐⡄⢊⠔⢰⠀⠀⠀⠀⠀⠀⢆⡠⣄⠎⠀⠀⠀⠘⠄⡀⣢⢥⠃⠀⠀⠀⠸⣀⠂⠀⢀⠀⢀⡠⠃
⠀⠀⠀⠀⠈⠢⠍⢉⣋⠩⠔⠁⠀⠀⠀⠀⠀⠀⠀⣳⢬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠸⡭⢭⢊⢇
⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣆⠀⠀⠀⠀⠀⠀⢰⠸⣯⠭⡇⠀⠀⠀⠀⡤⣀⣀⠔⠢⡀
⠀⠀⠀⠀⣠⠟⡱⠶⢝⣚⣳⣄⠀⠀⠀⠀⢘⠉⠉⠉⠉⠉⣷⢲⡀⠀⢠⠜⢰⠉⠀⠈⠑⡀⠀⡜⠑⡌⠑⠄⡇⠈⢢
⠀⠀⠀⠠⣃⡎⠀⠀⠀⠀⠈⢣⡇⠀⠀⠀⡬⠄⠀⠤⠤⠾⠿⡍⠀⠀⢸⠀⠀⡀⠀⠀⠀⡇⠀⢄⡐⢄⠀⡐⠸⣀⠜
⠀⠀⠀⠀⣃⢀⣀⡀⠠⠬⠤⠤⠇⠀⠀⠀⠑⠒⠒⠒⠒⠒⠈⠁⠀⠀⠘⠤⠤⡇⣀⣀⠀⡃⠀⠀⠈⠑⠎⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁
⠀⠀⠀⠀⠀⢀⠤⠤⡒⢢⡤⣀⠀⠀⠀⠀⠀⣿⢿⠃⠀⠀⠀⠀⠀⣖⢺⣻⣗⡀
⠀⠀⠀⠀⣔⠁⠀⠀⠱⣀⣧⣈⡣⠀⠀⠀⢀⣿⣆⢇⡀⠀⠀⠀⠀⡏⠝⡿⠁⢸⠀⠀⠀⠴⠐⡶⠊⢙⠂⠙⠖⠲⠆
⠀⠀⠀⢰⡉⠢⣀⠀⡠⠜⠀⠈⠀⠀⠀⠀⠸⡤⢤⠀⡝⠀⠀⠀⠀⢎⡞⠀⠀⠸⠀⠀⢀⢶⣀⠴⠒⢂⣐⠲⠶⢦⠛⡄
⠀⠀⠀⠘⡍⠲⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠜⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⡆⠀⠈⢛⣒⡁⠒⢉⡒⠭⠭⠯⠋
⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⣀⣀⡳⠀⠀⠀⠀⢰⣀⠤⠤⠤⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡠⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠠⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠰⠀⠀⠈⡠⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠠⠠⠂⠀⠀⠀⠀⡀⠠⢰⢁⠄⠀⠁
⠀⠀⠀⠀⠈⠂⠀⠔⠂⠀⠠⠊⠀⠀⠀⠀⠁⠂⠀⠀⡆⠀⠀⠀⠁⢀⠀⠄⠰⠀⣀⠀⠀⠀⡀⠄⠀⠤⠀⠀⡀⢠⡅⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠐⠁⠠⡀⢀⠀⠀⠘⣦⡇⠀⠠⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠓⠈⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⡠⠂⠀⠀⠂⠖⠀⠀⠀⠢⡀⠀⠀⠀⠀⡠⠠⠐⠀⠊⠀⠈⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠔⡀⠀⠀⡀⡀⢀⠀⠀⠀⠢
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠢⠀⠐⢊⠀⠀⠀⠐⠂⠀⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠂⠐⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣗⠓⢢⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠰⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⡊⡀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠑⠀⠀⠀⢰⠃
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠄⠄⠠⠀⠀⠀⠀⠀⠠⠂⠀⠡⠼⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠁⠀⠀⠤⠊

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠁⠀⠀⠀⠀⠉⠈⣆⠈⠁⡎⠀⠂⠀⠑⡄⠀⠀⠠⠁⡠⠖⢄⠠⠕⠌⠀⠀⠀⠀⠀⠃⠠⠀⡠⠂⠀⠂⠁⠀⢅⢜⠀⢀⠄⠒⣄⢤
⠀⠀⠀⡀⠀⠤⠀⢐⠊⢮⡀⠀⠳⡀⠈⠆⢄⠀⡆⠀⢇⣀⡠⢀⠔⠀⠀⠀⠠⠀⠀⢀⠀⡀⢀⠊⠀⠀⠈⡰⠁⢠⣤⡉⠀⠓⠒⠂⠌⠉
⠀⠀⠐⡲⠤⠁⠀⡀⢈⠠⠃⠀⠀⠑⠢⣈⠠⡑⠘⠀⡀⢒⢝⣱⠀⠀⠀⢠⢁⣄⡀⡈⠀⠃⠂⠀⠀⢀⠜⢡⠀⠀⠀⠀⠄
⠀⢰⡀⠐⢒⠂⠀⠀⣠⠄⡒⢢⢂⠒⠠⣀⠀⠁⢀⣾⠅⠘⡮⡞⠀⠀⢢⡐⠁⠀⠰⠀⠀⢈⠐⢄⠔⠁⠀⠀⠏⠑⠒⠂⠀⠀⠀⠈⠁⢄
⠀⠀⠁⠀⠘⠀⠠⠊⠄⠄⢀⢁⠂⣬⠤⣂⡗⠀⠈⠁⢀⠀⢹⠃⠀⠈⠙⠥⢀⣀⢾⡢⠄⠈⠀⠁⠠⢁⠂⠀⠑⠒⠊⠀⡄⡘⠂⡄⠀⠈
⠀⠀⡏⠙⡆⠀⢡⠬⢉⠭⠆⠤⠔⠊⣉⡴⠀⢸⠉⠉⠑⢢⠈⠁⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠁⠐⠗⠀⠐⠀⠀⠀⠀⠐⡀⠠
⠀⠀⡷⢀⠘⢄⠀⠐⠒⠒⠒⠒⠋⠉⠀⠀⠀⡌⠀⠀⠀⡷⠀⢀⠠⠀⠠⡊⠘⠀⠀⢠⣾⣿⣻⣟⣙⣷⠀⢠⠀⠀⢠⡀⠀⣰⠃⢀⠋
⠀⠀⢧⠐⠂⡸⠀⠀⠀⢖⠒⠂⠠⠤⠐⠲⠂⠙⠀⠒⠊⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⡀⢀⠿⠁⠀⠀⠀⢃⠐⢀⡀⠐⠀⠀⠈⠉⠁
⠀⠀⠈⠉⠉⢁⠔⣄⡀⣄⠉⠀⠒⠒⠈⠁⠀⠀⣀⢒⣂⠀⠀⡠⢀⡀⠀⠒⡲⢲⠀⢡⠀⠀⠀⡙⠅⠨⠀⢀⡀⢇⠀⠀⣠⠈⠣⠈⠀⡆
⠀⢌⡀⠅⠀⠂⠀⠈⠀⠈⠀⠀⠀⠊⠖⣂⡎⠧⠓⢃⠜⣠⡄⢰⠀⣀⣀⡀⠁⠁⠀⠀⠐⠂⠀⠐⠀⠁⠰⠀⠀⠉⠀⢐⠁⠀⡠⠋⠑⠕
⠀⠀⠀⠀⠌⠀⠀⠄⠠⠀⢸⠆⠈⢉⡀⢁⠀⠄⠂⢁⠬⠐⡁⢀⡮⠞⠁⠀⠀⠀⠈⡄⠀⠋⠀⢠⠦⠄⠰⠢⠄⣤⠀⢇⡀⠼⡀
⠀⠀⠀⡈⠠⢄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠄⠰⠗⠚⠓⠉⠀⣠⠾⠆⠀⠀⠠⡠⠁⠀⠀⠃⠌⠀⠁⠉⠀⠃⠀⠱⠀⠐⠊⢁⠔⠂
⠀⢰⡀⠁⠀⠠⠒⠀⠀⠀⣐⣥⡌⠁⠄⠀⣀⣀⣤⡄⣸⣆⠀⠀⠲⠉⢀⠳⠒⠀⠠⠲⠀⢀⠠⠀⠁⠀⠠⠀⠀⠀⠴⠀⠀⠀⡄⢀
⠀⠀⠉⢀⡄⢢⠞⠁⠀⠀⠀⠘⢄⠁⠀⠜⠉⠀⠀⠠⠀⠚⠛⠂⠠⢒⠁⡀⠀⠀⡀⠀⡀⠸⠂⠀⢀⣀⣀⣀⣀⠤⠶⡀⠀⢀⠁⠀⠘⡆
⠀⢐⠁⠖⠀⠠⠀⢈⠀⣀⢀⣀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠠⠀⠒⠄⠀⠑⠁⠅⡀⠤⠊⠁⠀⢀⢀⠀⠀⠀⠀⠀⠂⠈⠐⢂⠈⢤⣀⠠
⠀⠈⡄⠀⢀⠤⠂⠀⡊⡴⠀⡄⠡⡀⠐⠀⠀⠐⠒⠛⠠⠁⠀⠀⢰⠀⠠⠀⠤⠃⠔⠐⠄⠰⠯⢀⡀⠀⠀⣀⠔⠆⠀⠙⠗⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢱⠈⠈⣀⠀⠄⢰⠁⠂⠒⠀⠐⠀⠀⠀⠄⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠒⠺⡀⡀⢀⠱⠀⠀⠀⠀⡀
⠀⢠⠄⠅⠋⢇⢸⡄⠈⠒⣊⡀⠀⠠⣁⢠⢔⠁⠐⠀⠀⠙⠀⠀⠱⠀⠐⠈⣉⠀⠀⠠⠒⠉⠀⠀⢀⠔⠂⠁⢁⡟⠁⠀⠀⢺⣿⡤⠐
⠀⠀⢀⠀⣂⢀⠠⠄⠀⠈⡤⠌⠂⠀⠀⠈⠈⡄⠀⠢⠁⢀⡠⠴⠁⠀⠀⡀⠀⢠⠂⠣⣀⡀⢐⣢⠄⣀⣀⡠⠎⡐⠇
⠀⠀⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⡀⠔⠀⠀⠀⢀⡠⢤⣄⠀⠠⢀⠀⢀⠊⠐⠠⠑⠂⠀⠀⠀⠑⠊⠈⠁⠒⠉⠀⠰⠅⠀⠀⠈⠀⠰⡀
⠀⠀⠀⠁⠀⠀⠀⠄⠀⡀⢆⠀⠀⠁⠀⢔⠒⡂⢹⠀⠀⡜⠂⠀⠌⠀⢀⠀⠀⢀⠄⠀⠀⢰⢩⠇⠔⢉⠆⠆⠙⠄⠀⠀⠀⢠⡠⡀⡀
⠀⠘⠜⠀⠀⣀⠀⠀⠀⠈⣉⠀⠀⡀⢀⠀⠋⠀⠘⠤⠤⠧⠀⠠⠀⣠⡀⠁⠈⠋⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢰⠉⠀⠒⠀⠀⠐⣺
⠀⠀⡴⡝⠃⣴⠓⠀⡠⡈⢂⠄⠂⠀⠀⡅⠀⢀⠄⠂⣀⣂⡄⠀⠀⢀⠠⠠⠆⠀⠀⠀⠠⠀⠐⢢⠴⣶⣖⠀⠐⠀⠀⢣⠄⣀⣀⣀⡐⠃
⠀⠀⣧⠤⠙⠀⠀⡄⠀⠀⢀⠀⠀⣀⠔⣁⠀⡂⡰⠋⠀⠤⠈⠂⠤⠤⠄⠊⠀⠠⠂⠀⠀⡀⡀⠜⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠐⠒⠶⠖⠲⠆⠀⠀⠰⠒⠦⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⡍⣷⠀⠀⢀⡄⣶⣤⣠⣴⠀⣶⣄⡰⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣇⠀⠀⣽⠀⠀⠘⠃⠁⡉⡉⠀⢀⡀⠁⠀⠀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠋⢀⡇⠸⠀⡖⠀⠏⡖⡸⠂⣾⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠛⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛
⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠒⡰⠄⢢⣎⣁⠀⠐⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠶⠶⠒⣒⡒⠲⢤⡀⠀⡤⠀⠀⠀⠀⠀⠀⢀⣠⠖⠻⡄
⡟⠓⠺⣄⠀⢀⣇⣀⣹⡄⠀⢸⣄⠀⠀⠂⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⢀⠀⠈⢑⡦⢷⡀⣌⠐⢣⡄⢀⣀⡰⠟⢫⣾⠟⠁
⠇⠀⠀⠀⠉⠉⠀⠀⠀⣹⢿⣧⡎⠀⠀⠀⠀⠀⠀⠀⢸⡂⡈⠀⠀⡐⢀⡀⣈⢀⣀⣤⣾⠁⠉⠀⠛⠓⢀⣤⠶⠛⠉
⢰⠀⠀⠀⠄⠀⠀⠀⡐⠉⠀⢧⠀⠀⢐⠀⠀⠀⠀⢴⠉⠻⠽⠿⣭⠿⣯⠽⠛⣛⡻⢟⡟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⠸⠀⠀⠀⠀⠀⠀⠐⢀⣠⠴⠚⠀⠀⠀⠉⠉⠁⠀⠈⠲⢍⣀⣒⣐⣒⣀⡨⠭⠄⠒⠉⠀⠀⠰⠀⠀⠀⠀⠈⠀⠈⠁⡆⠀⠀⡀⠀⠀⠨⢆
⠀⠉⠙⠛⠛⠒⠚⠞⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢀⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠀⠀⠱⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡨⠓⠀⠀⠀⡈⠓⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⣼⠃⠀⠀⠀⣤⣶⠶⣤⣤
⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠰⢄⣨⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠢⡀⠙⢆⠀⠀⠁⣆⠀⠀⠀⡇⠀⠀⠀⠀⠁⢀⠠⠐⡄
⠀⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠤⠀⠀⠀⢀⠎⠀⠀⠐⠦⠀⠀⡀⢀⣨⡦⠠⠇⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠀⡁⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠀⢀⠀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⢂⣤⠾⠛⠁⠐⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠄⢙⣣⡄⠀⠀⠈⠀⠉⠀⠀⠀⠀⢸⣀⣴⠟⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠘
⠀⢀⠄⠒⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡤⠒⠛⠛⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⡤⢀⢄⡀
⠀⡀⢰⠀⠀⢧⠀⠀⠀⠀⣠⣄⣴⣄⠐⢃⣀⡀⠀⠀⠀⢠⠏⠀⠀⠈⠀⠀⠀⠀⢀⣠⢼⠀⠀⠤⣜⠷⠻⣇⢱⠈⡁⠀⠀⠀⠐⠀⠀⠈⠠
⠀⠄⣸⠀⠀⢸⠀⠀⢠⣾⠏⡠⠊⠀⠀⠀⠀⠉⢶⠀⠀⡟⠀⠤⠀⠀⠀⣠⣤⣶⠿⢳⣻⡀⠀⠀⣿⠄⠀⠟⣸⣄⡿⠃
⠀⡇⣇⠀⠀⣼⠀⠀⢼⡫⠜⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⣤⡤⠶⠊⣙⢋⠽⣷⢦⣎⡥⢴⠋⠀⡋⠘⠚⠷⠛⢛⡇⠀⠀⠀⠀⠀⡀⠠⠤
⠀⢶⢸⠀⠀⡇⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠀⠠⠃⠀⠀⠈⣼⣄⣸⣭⣴⡶⠿⠋⠃⣱⠎⠀⠀⢸⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠃⠀⠄
⠀⢸⡌⠀⢰⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢀⣀⣈⣉⣀⠤⠒⠊⠁⠀⠀⠀⠀⠃⠀⠀⠠⠓⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠳⣤⠟⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠂⠐⠚⠀⠀⠀⢀⠀⠐⡀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣠⡌⠢⡀
⠀⠀⠀⢸⠀⠀⠀⠐⠂⠀⠀⠐⠖⠒⠲⡤⠠⢤⡶⠀⠀⢀⠤⣠⠶⠶⠚⠋⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡆⢀⣬⡦
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠂⠀⠀⠁⢨⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘⠦⠂⣀⣒⠀⠉⠝⠃⠚⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⠤⣽⣋⣛⣛⣛⣛⣋⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢻⡆⠀⠀⠀⢀⡴⠂⠁⠀⢀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣀⣄⠁⣦⢀⡄⡄⠀⠐⠂⣤⠤⠄⠒⠀⠀⠀⠀⢸⡀⢸⣇⠈⠻⡄⠀⠠⠉⠖⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⡹⣶⠜⠀⠀⠀⠀⠀⠀⢠⣤⠶⣄
⠀⠀⠉⠉⠈⠀⠸⠬⠁⠗⠀⠀⠲⠲⠖⠺⠛⠁⠀⠀⠀⢘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠜⠒⠙⠦⡀⠀⠀⠚⢵⢏⣻⡿⠋⠀⠀⠀⠀⠀⠂⠀⢺⣟⣶⠟
⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠰⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠰⣦⠘⠃⢰⠀⠀⠈⠛⠿⢿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠂⢤⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⡀⢚⡁⣻⠆⠉⢀⠀⠀⠀⠛⠇⠀⢀⡴⠃⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣶⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠇
⠀⠀⠀⠀⡆⠻⠀⠀⠀⠀⠀⠇⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣤⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢠⠀⠀⠀⠀⠀⠀⢦⡤⠤⡀⠀⠀⠀⠀⠹⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢸⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡈⠀⠀⠈⠀⣀⠀⠐⢶⡀⠒⠙⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠷⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠊⠀⠀⠀⠀⢰⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠛⢷⠜⠃⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣶⡄⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣄⡴⠆⠀⡀⠀⠀⠄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣦⣤⣄⡀
⠀⠀⡀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠤⣈⣅⣨⡴⠚⠋⠀⠀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠉⠀⢀⡰⠶⠋
⠀⠀⠇⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠈⠀⢹⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⣡⡀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡟⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢤⠄⢸⠀⡀⠚⠁⠀⠀⢠⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠘⠀⡉⠛⠀⠀⠀⠃⣀⡰⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⢀⡀
⠀⠈⠀⠀⠀⡀⠀⠈⠀⡀⠀⠀⣠⡟⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡠⠞⠁⠀⠀⠀⠀⠐⠘⢣⠀⠈⠐⠂⠀⠀⠀⠀⠀⢠⡎⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⠈⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠞⠃
⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⡀⠀⠄⠀⠀⠁⠆⠀⡀⠀⢠⣶⢶⡿⢿⣿⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡴⣶⠀⠀⢠⠶⡄⠀⠀⠀⣠⠀⢙⢃⠀⠀⠀⠀⠀⢀⣤⣶⣠⡄⠰⠶
⠀⠱⣦⣤⣤⣤⣤⣴⠆⠀⠀⠙⠿⣦⣿⣶⡿⠇⠀⠀⡀⠀⠋⠈⠃⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⢰⠀⠀⠸⠁⡴⣿⡞⢴⡏⠓⣤⠀⢿⠿⣁⡼⠃
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠋⠀⠀⠀⠀⠀⡄⠀⠁⠀⠈⠀⠀⠀⠀⢰⣏⣤⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠸⡷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣴⡄⠀⠀⠀⠀⠘⠻⣿⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠋⣆⠀⠀⠀⠀⠀⠐⠀⡌⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠄⣰⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢳⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠛⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⠛⠁
⠀⠀⠀⠀⢀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠄⠀⢑⠀⠀⠀⠀⠀⡀⠀⣀⠠⠄⠀⠀⠀⢠⣬⡑⠣⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠄⠠⡄
⠀⠀⠀⠘⠃⣀⠶⢟⡀⠀⠐⠚⠶⠑⠶⠉⠄⠀⠀⠀⢴⣬⣻⣷⣤⡈⠀⠀⠀⠀⠀⢰⡀⠊⣹⠀⠀⠀⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠰⡶⠚⠟⠒⠿⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡼⠏⣽⠇⠶⡷⠀⠀⠀⠀⠂⠙⠁⣟⠁⠀⠀⠀⠘⠛⢁⣰⡄⢶⡆⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀
⠀⠀⠐⠖⠂⢐⠀⠀⠀⠀⠀⠂⠀⠁⢡⡄⠀⠀⠀⠀⣀⣤⣶⠿⠟⠂⢀⠀⠀⡄⠈⠁⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠒⠀⠆⡀⠀⠀⢈⠙⡀⠀⠰⣺⢉⣦
⠀⠀⠀⠶⠿⠿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⣾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡖⠀⠀⠀⢀⣤⣀⣀⣘⣀⡶⠀⠁⠀⠀⠀⢁⡀⠀⠘⠁⠈⠁
⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠐⠉⠀⠀⠀⠀⠼⠿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠳⠀⢀

⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡛⠏⠙⢻⡏⠉⡟⠙⢻⡝⠏⣹⡿⢛⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠀⠀⠀⠀⠀⡠⠔⠒⢤⡀
⠀⠀⢀⠔⠋⠉⡉⠑⢄⠀⠀⠀⠀⣀⣀⣠⣏⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⡇
⠀⠀⢸⠈⠠⡁⡨⠀⢸⠀⠀⠀⠀⢸⠉⠉⠉⡉⡟⠀⠀⠀⠀⠀⠱⡞⠞⠃⡿⠁⠀⠀⠀⠀⠈⢣⠀⠀⢠⠃
⠀⠀⠈⠣⣄⣈⣐⡰⠋⠀⠀⠀⠀⠈⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢳⠀⢪⠃⠀⠀⠀⠀⠀⠀⠀⠳⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠞⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣖⠉⢁⡀⣠⠈⢱⠄⠀⠀⠀⠀⣠⠾⠹⢦⡀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠲⡄⠀⠀⠀⠀⢰⣿⣿⣿⡿⣶
⠀⠀⠘⡎⢫⠅⠇⢡⠎⠀⠀⠀⠀⢀⠗⠀⠂⠘⡇⠀⠀⠀⠀⢸⣆⠲⢶⡶⠶⡾⠀⠀⠀⠀⢸⣿⣿⣼⣿⡏
⠀⠀⠀⠙⡖⢂⣻⠋⠀⠀⠀⠀⠀⠈⢯⣐⣉⡾⠃⠀⠀⠀⠀⠼⡏⠟⠟⠻⠟⡿⠀⠀⠀⠀⠈⡇⠀⠀⢸
⠀⠀⠀⠀⠘⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠓⠶⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠃⠀⠀⠀⠀⡎⣽⣠⢿⠈⡆⠀⠀⠀⢰⡛⣿⣗⣆
⠀⢀⡶⠋⠉⠀⠉⠙⢷⣄⠀⠀⠀⣀⣀⣿⣇⣀⣀⠀⠀⠀⠀⢰⠀⢨⢙⣾⠀⡇⠀⠀⠀⢸⠘⢜⣿⣿⣆
⠀⣼⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡏⠁⠀⠀⠀⡟⠀⠀⠀⠀⠸⠂⢸⢯⣴⠀⡇⠀⠀⠀⢸⠀⠀⠪⢿⣿⣆
⠀⠈⠉⠉⠉⠉⠐⠒⠉⠉⠀⠀⠀⢻⠻⠿⠶⠿⡇⠀⠀⠀⠀⠀⢇⢸⡴⢻⣀⠇⠀⠀⠀⠸⣀⣀⣀⣑⣹⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠈⠱⠋⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣐⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⡃
⠀⠀⠀⡖⠂⠀⠂⠐⡆⠀⠀⠀⡰⠊⠀⠀⠁⠀⠙⢆⠀⠀⠀⣠⡾⠉⠙⠉⠛⣦⠀⠀⠀⠀⠀⢸⠅⠀⡅
⠀⠀⠀⡇⠀⠀⠀⢀⠇⠀⠀⢤⡇⠀⠀⠀⠀⠀⠀⢸⣀⠀⢸⠇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⠂⠀⡇
⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠈⠛⠶⡤⠤⠤⣤⠶⠟⠁⠀⠘⠦⠤⠤⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠓⡖⠁
⠀⠀⠀⠘⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠈⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡄⠀⠀⠀⡀⢸⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣭⣥⣶⣶⠶⠂⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠠⡄⠠⠄⠀⡂⠀⠀⡀⣀⠀⢀⠀⠀⠈⡇⢻⣿⣿⣯⡁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⡀⢀⡄⡀⣀⠀⢸⣇⠋⢰⠟⣿⠁⠎⠀⠀⠀⣿⢸⣿⣿⣟⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⡇⠸⣇⢱⠸⠀⠸⣿⠀⢠⣀⡿⠀⠁⠀⠀⠀⢹⡘⣿⣿⣿⡦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⣿⢴⣿⣼⣇⢠⡄⡟⠀⣸⣿⠃⢰⡆⣀⠀⡄⢸⣇⣻⣿⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣽⠾⠟⠛⢿⣿⣷⡇⢀⣿⣿⣤⣾⣿⣯⡄⢉⠠⣠⣌⠉⠿⠇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠙⠿⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣶⣿⣷⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠉⠉⠀⠀⠀⠀⠈⠉⠙⠿⡟⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠠⡈⠫⡤⠴⢒⣋⣉⣹⣿⣿⣍⣉⣁⡀⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠆⢶⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢷⠀⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠑⢢⣬⣶⣾⣿⣿⣿⣷⣦⣥⣶⣿⣿⣷⣶⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⡈⠿⠯⠍⡁⠀⠠⠀⠀⠀⢀⣈⣉⠉⠁⣴⣤⡤⠏
⠀⠀⠀⠀⠲⠛⠿⠿⢿⣶⣶⣶⣶⣾⣧⡶⠶⠶⣾⣛⣛⣉⣿⣥⣭⣭⣯⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠛⠗⠊⠀⠀⠀⡯⠥⠠⠄⠢⠴⠇⠀⢀⠂⠁⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⡌⠀⠀⠀⠐⠁⠀⠀⠀⠀⡀⠀⡤⢀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠁
⠀⠀⠀⠐⠄⠀⠚⠀⠀⠤⠀⠀⡰⠆⡅⠠⠃⢡⠀⢀⡞⠉⠀⢀⠀⠙⠄⠀⢠⡤⠀⠀⠄⠠⠤⡀⠀⠰⠭⠜⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈
⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠮⠀⢰⡂⠰⢀⡀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡕⠀⠐⠀⠀⠘⠀⠂⡀⠀⠺⠀⠐⠈⠣⠐⠂⠀⠀⠀⠀⠠
⠠⠒⠂⠀⠀⠀⠀⢤⢢⣤⡀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠱⠆⣀⣀⡀⠔⠃⠀⠀⠈⠠⠄⢃⠀⠁⠲⠀⠀⠓⠀⠀⠁⠀⠀⠁⠂⠀⠀⠄⠈⠁⢀⡄⠀⠰
⠀⠊⠁⠀⠀⡪⡿⠑⣯⢹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠠⠀⠰⠀⠀⠀⠀⠘⠒⢂⠉⠀⠀⠠⡄⠀⠀⠀⠀⠠⡮⠁⠀⠐
⠀⠀⠂⠀⠀⠀⠖⠴⠛⠁⠀⡄⠀⠀⠀⠰⡖⠀⣀⠀⠰⣃⠂⠠⠀⠐⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠊⠀⠀⣄⡐⠀⣚
⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠄⠁⡤⠁⠠⠀⣤⠇⠀⠤⠀⠀⠀⡔⠁⣀⢄⡀⠀⠄⠀⢠⠀⠴⠘⠀⠀⡄⢀⡁⠦⡀⠀⠈⠚⠁⠐⠊⡀
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⠠⠒⠀⠀⠠⠠⡀⣠⡀⠀⡠⠀⡄⠀⠀⠀⠐⡅⠌⠃⡐⠁⠠⠆⠀⠀⠀⠀⣀⠀⠀⠆⣠⠄⠖⢛⠀⠀⠀⠀⠀⠀⠁
⠀⣀⠀⠀⠀⠀⠀⠀⠠⠂⢉⠀⠢⠀⠀⠀⠙⢺⢃⢹⡏⡀⠇⡏⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⣻⡯⠎⠃⠀⠩⣄⡠⠌⠚⠀⠀⣀⠀⠀⠀⢀
⠁⠀⠉⠀⠡⠀⠀⢠⠂⠄⠒⠀⠀⡃⠀⠀⠀⠀⠐⠀⠀⠊⠀⠙⠈⠀⠀⢀⣀⣀⡀⠀⠀⠀⣴⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⠨⣜⡿⣃⠀⠁⢇
⠀⠒⠀⠈⠀⠀⢠⠀⢰⡀⣀⣀⣸⠀⠀⠀⠀⠀⠤⠄⠠⡀⠀⠀⠀⢀⠞⠁⢀⠀⠈⠑⠀⠀⠑⠛⠒⠂⠀⠀⠀⠀⠀⢀⡀⠀⠈⣇⢀⡹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠉⠉⡍⠀⠀⠀⣐⢢⢤⣌⢁⠀⠐⠀⠀⢰⡀⠰⣀⠠⠀⠀⡆⠀⠀⣀⠦⣀⠀⢀⡄⡠⢄⠀⣨⢆⠀⠀⠀⢀⠠⠐⠀⠀⢶
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠹⢮⣄⣞⣯⢋⡿⠀⠀⠀⠳⠆⣀⣀⢀⠔⠁⠀⠀⠰⠂⠂⠀⠨⣧⣤⣝⣤⢤⡜⠀⠀⠀⠀⡠⠤
⠀⠠⠄⠀⠀⡀⠈⢠⠀⠀⠀⠀⡆⢐⠀⠀⠘⣿⡎⢟⣽⠉⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⣰⡄⠀⡀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠐⡛⠂
⠀⠀⠉⠀⠀⠄⢀⠀⠀⠀⠀⠠⡁⢈⠀⠀⢰⡞⢞⡽⠀⠀⠰⠀⠀⠀⠒⠀⠀⢰⡚⠓⢀⠤⣀⣹⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄⠀⠧⠀⠰⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠰⣟⡌⠀⠀⠀⠄⠐⠂⠤⢀⡅⠀⠈⠥⠨⠀⠀⠀⠘⠀⠀⠀⠀⠆⣉⠡⠘⢑⠀⠈⢢⠄⠀⠤⢼⠁
⠀⠀⠀⢀⠄⠀⠀⠀⡾⠀⠀⠠⠤⠤⠄⠀⠈⠊⠀⠀⠀⠒⠂⠐⠐⠀⠂⠘⠀⠀⠀⠀⣀⠀⠀⠀⢠⡀⠀⢰⡆⠀⢀⡈⢹⠀⠀⢸⣒⡚⠛⡟
⠈⠀⠀⠈⠀⣠⠀⠘⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠐⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⣀⠁⠸⠀⠈⠃⠀⠀⠀⠊⠀⠀⠀⠂⠀⠀⠁
⠀⠸⢄⠀⠀⠉⡏⡉⠉⢹⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠄⣀⢑⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠂⠑⠀⠀⢠
⡀⠂⡘⡂⠀⠀⢠⠀⢀⡞⠀⠀⢀⠈⠀⠒⣈⠀⠘⠄⠀⠄⠀⠀⠠⠀⠃⠀⠃⠙⠀⠛⠀⠀⢴⣉⡤⣉⠂⡧⠀⠀⠀⠓⠠⠓⡀⠀⠀⠀⠒⠂⠀⠀⣎
⡶⡶⢺⠃⠀⠀⠈⠋⠉⠁⠀⠀⠈⠄⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⢏⠝⣬⠀⠀⠀⢘⠀⠀⠁⡁⠀⠀⠀⠀⠘⢀⠀⢙
⠊⢶⡍⠀⠀⢀⣠⠤⢦⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⢐⣀⠀⠀⢰⡁⠀⠰⠄⠀⠀⠀⠱⣍⣫⡖⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⢘
⠓⠊⠁⠠⣞⠿⠖⠓⠋⠈⠈⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠂⠀⢰⣀⣪⠐⠜⢓⠀⠀⠀⠀⠀⠀⢀⠤⣀⡀⠀⡀⠇⠁⠀⠀⠈⠀⠀⠁
⣀⠀⠀⠀⠈⠃⠠⠄⠀⠀⠀⠀⢀⠰⠁⠐⠄⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠈⠡⣀⡤⠐⠋⠠⠄⠀⠀⢐⣦⠃⢶⢱⡥⠀⠀⠀⠀⢪⠰⡄⠀⠀⠀⡤
⠛⠂⠀⠀⣀⠀⠀⠀⣠⠀⠀⢰⠢⣔⠈⣉⡃⠀⠙⠿⠟⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠪⠤⠴⠚⠁⠃⠀⠀⠀⢨⡀⠼⡀⠀⠀⠃⢀
⠉⠀⠀⠀⠙⠁⠀⠤⠀⠀⠀⠸⠤⣄⠈⣸⠃⠀⣀⠠⢀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠈⠃⠀⡃⠈⢤⠀⠈⠠⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠈⡀⠀⠑⠒
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠁⠀⠠⡅⠁⠈⠷⠀⠀⠀⠀⠀⠰⠗⠂⣀⡀⠀⠀⡉⢄⠰⠖⠂⠀⠀⠀⣰⠶⠂⠑⠀⠀⠑⠒⠀⠁
⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠂⠈⠀⠉⠆⠠⠀⠀⠀⠹⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠈⠢⠊⢀⠀⡀⠀⠀⠀⠀⠀⢏⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠃⣾⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠂⠀⠀⠶⠈⠁⠀⠠⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡤⠄⢀⠀⢤⠀⠎⠀⠀⠀⠀⠐⠴⡈⠁⠀⠀⠑⢤⠆
⠀⠀⠀⠰⠀⠀⡌⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠆⡀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠀⠀⠀⠉
⠀⠀⠀⠸⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠉⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹⣣⠀⠀⠀⡠⠂⠀⠀⠊⠀⠀⠀⠀⠀⠼⠒⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠒⠚⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠤⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⢄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⠀⠀⢀⠔⠊⠉⠁⠈⠁⠂⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠄⢡⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢀⡹⠀⠀⠳⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⣈⡈⡄⠀⠀⠐⠀⡇⠀⡄⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠆
⠀⠀⠀⠺⢤⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠀⠀⠠⣇⠀⡠⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠢⠅⠀⠉⠤⠔⠁
⠀⠀⠀⠀⠀⠈⣉⡋⠉⠉⠉⠉⠉⠀⠀⢠⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢰⠂⢄⠀⠀⠄
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠊⠁⠀⠁⢄⠈⡨⠀⠱⡀
⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠃⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢱⣲⢄⡀⠤⣀⣀⠤⠤⠔⠁
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠃⠐⠀⠁⠀⢡⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠑⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠢⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢸⡟⢠⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠧⢸⣀⣁⣰⠔
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠁⢀⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡰⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠘⠶⣤⣀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣀⡀⠀⠀⠉⠂⡀⠀⠀⢄⡤⠀⠀⠁⠂⠼⢉⣀⠀⠀⡀⠀⣀⣀⣀
⠀⠀⠀⢴⢬⡜⠧⠉⠉⠱⠄⢈⠉⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠤⠤⠈⠃⢀⠀⠪⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢄⠀⠠
⠀⠀⠀⠸⡀⠈⠀⠀⠀⠚⠑⠒⠤⠀⠀⠀⠘⣦⣀⠀⢰⠀⠀⠀⡇⠐⢀⠘⠀⠀⠨⠠⠬⢡⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠃
⠀⠀⠀⠀⠈⠂⠠⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠬⣀⡃⠘⠑⢂⡀⠧⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⡀⠀⠀⠀⣀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⢄⡀⠛⠛⠛⠓⠃⠀⠀⠃⠑⠒⠒⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠸⠤⣧⠀⠀⡆⠘⢵⠶⠟⠸⠿⠆⠗⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠟⢠⠀⡇⢀⠄⣤⡀⣰⢠⡄⡀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠀⠃⠃⠇⠸⠣⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠾⠁
⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣀
⠀⠔⢂⠶⠘⣆⣁⡀⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠶⠖⣒⡒⠒⠤⡀⠀⠤⠒⠀⠀⠀⠀⠀⣠⠖⢻⡀
⡏⠙⠳⣄⣀⣭⠤⣽⣄⣀⡼⡄⠀⠂⠀⠀⠀⠀⣯⠀⡀⠀⠀⠀⠀⠀⠈⢶⠼⡄⢌⢑⣦⠄⠀⠠⠟⣩⠾⠛⠁
⠇⠀⠀⠀⠀⠀⠀⠀⡜⢻⠾⠃⠀⠀⠀⢀⠀⢀⣧⣠⣀⣀⣌⣠⣄⣦⣤⣴⣾⠇⠀⠄⡉⣁⠴⠚⠉
⢰⢰⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⠀⠄⠀⠜⠀⢧⡈⢙⣛⣚⣛⡓⠋⠍⢝⡪⠟⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠋⠢⡀
⠘⠤⢤⣤⣤⣠⣦⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠚⠃⠉⠁⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠆⠀⠀⠁⠰⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠯⠄⠉⠙⠲⣄⠀⠀⠀⢹⡀⠀⠀⠀⢠⠏⠀⠀⠁⢀⣤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⣀⡒⠁⠀⠂⠀⠀⠀⠀⡠⠁⠂⠀⠀⠀⠢⡀⠑⢄⠀⠀⠃⡀⠀⠀⠘⠀⠀⠀⠈⠍⠉⡉⣝
⠀⠀⠀⠀⠲⠅⠀⠀⠀⠀⠀⠉⠁⠀⠀⢄⠀⠀⠀⣰⠁⠀⠀⠆⠀⠀⠀⣈⣦⠄⠆⠀⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠐⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⠀⢀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠃⠀⣠⡴⠚⠉⠀⠘⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⠀⡆⠀⠀⠀⠀⢰⣼
⠀⠀⠀⠀⠀⠠⠠⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠛⠁⢀⣠⣤⡦⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠔⢉⠉⢳⠀⠀⠀⠀⠀⢀⡀⢀⡀⡀⠀⠀⠀⠀⣠⠞⠙⠠⠁⠉⠉⠀⠉⢱⡀⠀⣀⣠⣁⣉⣡⡀⡀⠀⠀⠸⣽⣋⣦⣄
⠀⠀⢆⠀⢸⡄⠀⠀⣴⠟⢪⠟⠈⠐⠒⠣⣄⠀⢠⠏⠀⠀⠀⠀⠀⣀⣥⣾⣽⠀⠀⢉⣏⠉⠹⡟⡇⣧⠄⠀⠀⠈⠉⠀⠈
⠀⢰⡃⠀⢸⠃⠀⣺⣛⠔⠁⠀⠀⠀⠀⠀⠈⡀⠸⣄⣀⣤⠔⢲⠟⣿⣥⡴⣚⣡⡆⠀⡇⠢⢴⡽⠿⣏⠀⠀⠀⠀⠀⠀⢀
⠀⡇⡅⠀⢸⠀⠀⠈⠓⠢⠤⠤⠀⣀⠀⠀⠤⠁⠀⠈⣭⣄⣀⣋⣭⣾⡟⠋⢱⡜⠀⠀⢇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠁⡠
⠀⢹⠁⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅⣀⣉⣉⡠⠴⠒⠉⠀⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠉
⠀⠈⠣⡜⠁⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠂⡀
⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⣀⣤⣴⠟⠛⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⢶⠈⠢⡀
⠀⠀⠀⡁⠀⠀⠈⠁⠀⠀⡙⠉⠉⠛⠉⠑⡉⠀⠠⠐⠗⠛⠉⠉⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⡿⣼⢄⣶⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠆⣀⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠠⠐⢀⣀⠤⣤⠄⡀⠀⠀⣤⣄⠀⠀⠀⡆⠀⢀⣀⣼⣁⣀⢀⠀⠀⠀⢀⢀⠀⠀⣨⣯
⠀⠀⠀⢀⣔⠥⠠⣀⡀⡀⠀⠱⠀⠈⠻⡇⠀⠀⢴⣧⢤⣜⣿⡖⣾⠎⠀⠀⠀⢹⠆⣵⣄⠈⢉
⠀⠀⢐⠃⠀⠀⠀⠀⠒⠚⠃⠭⣣⠀⠂⠀⠀⠀⠀⢸⠀⢸⡇⠀⡆⠀⠀⠀⠀⢸⡇⠨⣌⣢⡈
⠀⠀⠀⠹⢝⣛⣛⣛⠙⢚⠉⡲⠞⠀⠀⣶⡶⣤⠀⢸⠖⣻⣇⣦⡆⠀⠀⠀⠈⠈⣟⣃⠛⠉⢉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠀⠈⠉⠁⠀⢰⢎⡏⣰⡭⢃⠀⢀⡀⠀⠀⢹⠤⢾⣓⡯⠟
⠀⠀⣠⠢⠢⠀⡠⢴⡸⠽⣒⣄⠀⠀⠀⠀⠀⠀⠁⠀⢉⣈⣉⡁⠁⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠠
⠀⠀⠂⠀⠊⣸⠒⣾⠑⣢⢯⡔⣳⡄⠀⠀⡶⠀⢀⠖⠁⠀⠀⠀⠑⢄⠀⢀⠖⠤⠀⢀⣽⣿⣼⣣⡀
⠀⠀⠀⠀⠀⡽⢩⠉⠋⠏⠛⢋⠁⠀⠀⠀⠀⢀⠖⠀⠀⠂⠒⠒⠒⠚⡢⠈⠉⠳⢀⢼⣿⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠇⣜⠀⠀⠀⢰⠘⠀⠀⠀⣙⠂⠈⡛⣗⢾⢭⡀⡁⣉⣝⣷⠀⠀⠀⠈⠉⠉⠉⠉⠉⠿
⠀⠀⠐⠶⠀⠀⣸⠀⢰⠀⢸⠀⠀⡀⠀⠉⠁⠘⢖⠩⡭⠭⠭⠛⠑⢒⠖⠁⠀⢀⠀⠆⡐⢢⠒⠀⡇
⠀⠀⠀⠀⢀⠐⠾⢄⣈⣠⢘⡰⠋⠀⠀⠀⠀⠀⠀⠑⠐⠄⠤⠀⠒⠁⠀⠀⠀⠀⠀⢰⣀⣀⣀⣠⠁
⠀⠀⠀⠀⠀⣡⡀⠀⠀⠈⠉⠀⢠⠀⠀⠀⢠⠀⠀⠀⣀⣶⣤⠄⠀⠂⢆⠂⣄⡠⠲⠀⠀⠀⠀⠐
⠀⠀⠀⠆⠀⠉⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠀⢋⠤⡄⡀⠸⠇⠋⠛⠤⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⢀⣀⣀⣰⡏⠀⠀⠆⠀⠀⠀⠀⠀⡀⠛⠀⡠⠋⠈⢧⠀⢁⠀⠐⠀⠀⣀⣠⣄⡀⠹⠁
⠀⠀⠀⠀⠀⠙⠓⠒⠛⠿⠊⡃⠀⠄⠀⡀⠀⠳⠵⢀⠔⠑⠀⠀⢠⠀⠎⠀⠀⠐⣿⣿⣿⣿⣧⡉⠐⠂⡄
⠀⠀⠀⠀⡔⣁⠠⠭⠍⠉⠀⢨⡐⠀⠀⠻⠀⠀⢠⣛⣀⣤⡶⡒⠉⠌⠀⠀⠀⠀⢹⣮⣻⢿⠿⣷⠀⣴⠁
⠀⠀⠀⢠⠀⠀⠁⠀⠉⠀⠁⠀⠠⠀⠀⡤⠔⡄⠘⣿⣿⣿⡙⣄⠎⠀⠀⢠⣤⠀⠀⢿⢿⣿⣧⠽⠾⠃
⠀⠀⠀⠀⠢⠕⣂⠰⠠⠄⠐⠢⠕⠀⠀⠈⠊⠁⠀⠘⠋⠿⠛⠋⠀⠀⠀⠀⠉⠀⠀⠈⠋⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⡀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢄⠀⠀⢀⡀⠢⢨⣄⠄⠠⠄⡠⠤⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⡾⠂⠂⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⠈⠀⠆⣰⠁⠀⠀⠀⠁⠈⢀⠨⠀⠌⠁⠒⠡⠅
⢀⠀⠀⠑⠤⠐⠁⠀⢠⡆⠀⠀⠀⠐⠀⣄⠀⢀⠤⠦⠀⠀⠔⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣡⣀⡀⠰
⠈⠆⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠰⡠⠅⠈⡀⡀⠵⣠⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠙⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⣞⠀⢈⠔⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⠀⣀⡀⠀⡀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠉⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⣸⡇⠸⡏⠓⠉⡏⢸⡏⠁⣼⢹⡇⣿⢹⡆⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⣿⣿⢀⡙⣆⠀⡇⢸⡟⠁⣽⢸⡇⣿⢸⡇⡇⣸
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠂⢠⠀⠀⠀⠠⠀⢀⡤⠃⠀⠀⠀⠀⠈⠃⠀⠃⠘⠈⠛⠃⠀⠃⠘⠃⠀⠘⠛⠁⠙⠛⠀⠛⠋
⠀⠀⡀⢶⠀⠀⠀⢀⠀⠉⠁⠀⠀⠐
⠀⡚⠁⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣲⣀⣤⠚⠉⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠊⠇⠉⠈⠒⠢⣠⡀⠀⠀⠀⠀⢠⣶⣶⣄⡀⣄⣦⠀⡠⢤⠴⡚⠊
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠀⠀⠀⠀⠈⡠⠈⠓⣄⠀⠀⠀⠀⠁⠀⠀⠈⠙⠩⠾⢶⣌⣭⣬⡶
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣊⠠⡢⠀⠀⠀⠀⠀⠀⠀⡀⢐⣠⣶⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠭⠿⠋
⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠁⠐⠀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠒⠀⠀⠄⠴⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠸
⠀⠀⢸⠖⢤⠀⠀⠀⡤⠤⣤⣀⠐⣞⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⢾⡀⠙⠓⠂⠀⠲⠌⠀⡀⠔⠋⢱⠀⠀⠀⠀⠀⠀⠀⡀⣈⡅⠒⣬⢁⠒⠆⠀⢀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⡠⠚
⠀⠀⠈⠤⣄⠀⡀⠐⠂⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀⠜⠄⠀⠄⠀⠈⡈⢀⣙⡢⠊⠵⢲⣀⡰⠆⠀⠀⠈⠡⠀⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠂⠬⠁⠐⠀⠉⠄⠛⠁⠀⠀⠀⠀⠀⠉⠒⠒⠾⠤⣤⠈⠁⡔⠉⣀⣒⣀⣀⣐⣂⣀⡷

⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠠⢤⡈⣷⡀⠀⣀
⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠑⢄⠀⠀⢀⢀⣴⡞⢹⣧⣿⣱⡡⣥⢾⡼⡆⠀⠀⠀⠀⠀⣠⠀⢤⢀⣆
⠀⢰⠁⠀⠀⠠⠀⠀⠄⠀⠀⠈⡆⠀⠈⠢⣇⣧⡞⣼⡟⣸⣸⡕⡯⢁⡯⠃⠀⠀⢀⠈⠀⢱⣶⣿⣷⣀
⠀⢳⣂⡂⠀⠀⠀⠀⠀⣀⣀⣈⢗⡄⠀⠀⢹⠙⠃⠷⠴⠿⠧⠶⠜⢊⠁⠀⢠⠔⠉⠁⠈⢁⣉⣉⣀⠀⠩⠶⢤
⠀⣶⣦⣽⣭⣭⣿⣹⣷⡤⣼⢵⡞⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠖⠢⠖⣄⠖⣤⠒⠤⠲⡔⠶⣾
⠀⢫⣽⡯⠹⢖⣛⣻⣷⣾⣿⢿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡻⠶⠶⠶⠶⠖⣖⣒⣒⣲⣟⡇
⠀⠀⠑⠂⠀⠀⠀⠀⠐⠒⠚⠁⠀⠀⠀⠀⠀⠀⢆⣀⣀⣀⣀⣀⡜⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠤⢄⣀⢀⣀⠤⠔⠒⠉⠒⢄
⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⡠⠤⡴⠁⠘⠉⠀⠀⠔⠠⠕⠀⠐⠁⢁⡈⠀⡼⢒⡶
⠀⠀⣀⣔⣊⣁⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠬⠵⠦⠀⠀⠑⢢⣘⣌⣀⣉⣀⢀⣀⣐⣒⣒⣂⣈⣡⣴⡊⣤⠋
⠀⠀⢒⣒⣶⣶⣶⣶⣶⣀⣈⣏⣉⣻⡿⠯⣿⠏⡹⡄⠀⠀⠓⣖⠪⡭⢿⡶⢲⣲⣒⣶⣿⣿⣿⡿⢔⣵⡿⠂
⠀⠀⠁⠐⠚⠒⠚⠒⠒⠂⠀⠀⠉⠀⠈⠈⠁⠀⠉⠁⠀⠀⠀⠈⠁⠒⠀⠉⠉⠓⠂⠐⠒⠓⠒⠉⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⣀⠔⣹⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡔⢣⠃⠀⠀⠀⠀⠀⢰⣍⡠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡃⢸
⠀⢸⠁⠘⠎⣓⡦⠀⠀⠀⠀⢠⠒⢶⡀⠲⢥⠇⠀⠀⣠⠤⠀⠐⢆⡹⠲⠶⢦⣀⠀⢀⢔⢒⣄⢠⠚⡟⣿⠛⠛
⡀⠮⡝⣉⣉⣩⠖⠳⡀⢠⠋⡀⢁⠉⣈⢢⠜⡄⠀⠀⢿⡓⠒⠒⠒⠒⠒⢒⣚⠏⠀⠰⠧⠄⢉⠎⣣⠿⠉⠘⠂
⠑⠶⠤⣤⢤⠾⣶⡚⠀⠘⣍⠙⠈⢉⡠⢯⠴⢸⠀⠀⠈⣦⣒⣙⣭⣋⡑⠠⡼⠀⠀⢀⠀⣰⣯⣾⡋⣦
⠀⠘⣮⡱⢪⠼⣱⠃⠀⠀⠡⢍⡉⠉⠉⣀⠔⠁⠀⠀⠀⢰⠄⣰⢀⢀⠀⢰⠃⠀⠀⡗⠀⠨⠝⠉⠀⣺⡗⠉⡄
⠀⠀⠘⡾⠿⠾⡾⠀⠀⠀⠀⠀⢀⢙⣉⣀⠀⠀⠀⠀⠀⠀⠄⢽⠈⠤⠀⡏⠀⠀⠀⠹⡉⠛⠛⠓⢈⡽⠧⠕⠁
⠀⠀⠀⠐⡄⢠⠃⠀⠀⠀⠀⢈⡀⠀⠀⢀⡹⠀⠀⠀⠀⠀⢠⣞⡘⢚⣾⠃⠀⠀⢠⡖⠚⠒⠂⠒⠋⠙⢱⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠶⠤⠤⠤⡆⢠⣀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣀⣀⣀⣠⡄⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⣀⣸⠀⠀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⣸⠀⢉⠉⠉⠙⡋⠉⠉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠆⢀⠠⠀⢠⠃⠀⠀⠀⣀⢰⡇⠀⠲⠌
⠀⠀⠀⠀⡀⠈⠀⡇⠀⠀⠃⠐⠀⡀⢀⠀⠀⢀⡡⠷⠓⠚⠉⠉⠉⠉
⠀⠀⠀⡞⢲⡺⣄⢡⠀⢀⠆⢠⡇⠁⠈⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⡀
⠀⠀⠀⣇⢸⡍⠳⣆⣰⠆⣠⠋⣰⡠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢫⡢
⠀⠀⠀⢻⠘⡇⠀⠈⠉⠛⠛⠛⠉⠀⣾⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⡹⢿⣿⣿⣷⣾⣶⣤⣀⣳⣄⣦⣄⣠⡴⡊⢁⣀⣤⣖⣁⣤⠾⠁
⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⢃⠠⠉⡛⡛⠛⠿⣿⠿⢿⡿⢿⣿⣿⡿⠿⢿⣿⠛⠙⠻⡤
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⡈⢀⣌⣉⡒⢒⢫⣀⡴⠶⡾⠵⠶⢥⠤⠤⠤⢤⡤⣮⣭⣵⡿⠃
⠀⠀⠀⠀⠀⢹⣇⠀⢀⣀⣀⣀⣀⣈⣍⠙⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⢈⠀⢀⣴⣿⣿⡟⢁⠇
⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉⠉⠉⠉⠓⢤⣀⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠋⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠦⠤⠤⠀⣀⣀⡤⠴⠒⠋⠁

⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣄⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⢸⣀⣨⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠔⠊⠉⢣⠀⠞⠉⠉⠈⡆⠀⡤⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡔⠋⠁⠘⡌⠆⠀⠀⠈⡇⢸⠀⠀⠀⠃⡸⠀⠀⠀⡹⡰⠋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠋⠉⠄⠀⠀⠀⠐⠀⠠⠌⠉⠓⠲⡄⠀⣀⠼⠚⡄⠀⠀⠸⣀⡄⠀⠀⢸⠃⠀⠀⢠⣡⠃⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠁⠤⠀⠒⢀⠀⠁⡀⠀⢀⠀⠀⠈⠀⠴⡀⠘⡄⠀⢱⠀⠀⠀⢻⡇⠀⠀⡜⠀⠀⠀⡇⠀⢩⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠁⠀⠀⠀⡀⠒⠀⠀⠀⠀⣀⠁⠀⠐⠀⢱⡀⠰⠀⠀⡆⠀⠀⠸⡇⠀⢀⠃⠀⠀⢸⠃⠀⡎⠀⡎
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡆⠀⠀⠀⣾⣯⡷⠀⠀⠀⠀⣧⠀⠇⠀⢣⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⢰⠁⣴⠁
⠀⠀⠀⣀⣀⠠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣾⣿⣶⠈⠉⠁⠀⠀⠀⠀⢡⠑⢼⡀⢸⠀⠀⢠⠁⠀⣸⠀⠀⠀⡇⠀⡬⠊⠹
⠀⠀⠀⠑⢄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣹⡟⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠚⠦⠤⠼⣀⣀⣿⡀⠤⠴⠓⠉⠀⠀⡇
⠀⠀⠀⠀⠀⡽⢦⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⢰
⠀⠀⠀⠀⢸⡀⠀⠙⠢⡉⠑⠒⠠⠤⠤⠄⠀⢀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠖⠒⠛⢳⠀⠀⠁⠀⠈⠀⠀⣀⠀⠀⠁⠀⠀⠁⠀⡜
⠀⠀⠀⢀⡤⢟⠑⠢⠤⠜⠦⡀⠀⠀⠀⣀⠠⠤⠒⣲⠪⣉⠁⠀⠀⠀⢀⣀⡀⠠⢼⠄⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⡞⠹⡋⠛⠋⠋⠉⠛⠋⠉⠙⠙⠉⠋⠁⠑⠚⠛⠒⠚⠋⠁⠒⠒⠒⠘⡇⠀⠀⠀⠀⠀⠘⢿⠏⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠙⢢⠍⣂⣀⣀⣀⣀⣀⣀⠠⠤⠶⠶⠄⣀⠐⠂⠐⠂⠀⠐⠀⠂⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⢀⣀⡠⠽⠦⠤⠔⠚⠋⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠤⠤⠤⠴⠒⠉




⡿⠿⠿⠿⡿⠻⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠒⠀⠧⠄⠁⠀⠆⠀⠃⠈⠈⠀⡀⠀⠰⠥⠝⡠⢠⠀⠀⠀⠈⡗⠀⠀⠀⠘⠄⠃⠸⠂⠀⠀⠀⠀⠀⡀⠄⡀⠈
⠀⠐⡀⠀⠠⡈⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣆⣦⠅⠋⠈⢀⠀⢀
⠀⠀⠀⠀⠁⢀⠠⠄⠀⠀⠠⢀⠀⠀⠀⠌⠀⠀⠀⠄⠀⠀⠀⡀⡄⠀⠀⠣⠘⢠⣖⡲⠀⠀⠀⠀⠐⠀⠀⠑⠄⠀⠀⠀⠀⠼⠁⠉⠀⠀⠀⠘⠃
⠀⠀⠀⠐⠄⠀⠀⡠⠐⠁⠠⠚⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠁⠣⠘⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡀⠀⢤⡀⠀⠀⠀⠄⠀⠀⣔⣒⡆⠠
⠀⠀⠀⠄⠀⠀⠈⠣⠂⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡀⠀⠠⠀⠀⡀⠀⠀⠁⠀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠄⣱⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⢀⠀⢐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠉⠀⢀⡀⠀⠠⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⢤⡀⠀⢀⠀⠀⠄⠀⠀⢈⠀⠀⠐⠁⡃⠀⠀⠀⠐⠄⡀⢀
⠀⡄⡀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠒⠈⠀⠸⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⡅⠊⡀⢠⡀⠀⠀⠀⠠⢳⠤⢤⣀⡀⠠⠀⣀⠀⠀⠀⠀⠀⠀⡀⡀⠙
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠄⠀⠀⠀⡰⠀⠀⠁⠀⠠⠓⠂⢯⠌⠀⡀⡀⠀⠀⠑⠀⠀⠄⠀⣀⡙⠃⠀⠀⢀⠀⠙⢨⠀⠈⠂
⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠀⠀⠀⠀⠀⢀⠀⠐⠛⠀⢰⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠀⠀⠁⠀⠀⡀
⠀⡖⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⣰⠀⡠⡀⠀⠓⠀⠁⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉