Futebol Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣡⠊⠉⠉⠉⠉⠙⢦⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣣⣶⣿⣿⣿⣶⣜⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡤⠶⣅⠀⠀⠀⠀⠀⠀⢨⠷⢤⣀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣫⡑⣿⣿⣿⣿⣿⣿⣿⢇⣙⡻⣷⣄
⠀⠀⠀⠀⠀⠀⣰⠛⡞⠁⠀⠀⠈⢦⣀⣤⣤⣀⣴⠃⠀⠀⠈⢳⠞⢧⠀⠀⠀⠀⠀⠀⠀⣰⡍⣴⣿⣿⣿⣮⠻⠿⠿⠿⠟⣵⣿⣿⣿⣦⣩⣤
⠀⠀⠀⠀⠀⢰⡇⢰⡇⠀⠀⠀⣠⠋⠀⠀⠀⠀⠘⢆⠀⠀⠀⢨⡇⠘⡇⠀⠀⠀⠀⠀⢰⣿⣳⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⢰⣿⡆
⠀⠀⠀⠀⠀⢸⠀⢨⠧⠤⢤⣴⠃⠀⠀⠀⠀⠀⠀⠈⣧⡤⠤⠼⡅⠀⡇⠀⠀⠀⠀⠀⢸⣿⢃⣛⣛⣛⢡⣿⣿⣿⣿⣿⣿⣿⡎⢛⣛⣛⡸⣿⡇
⠀⠀⠀⠀⠀⢸⣀⡏⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢹⣀⡇⠀⠀⠀⠀⠀⠸⢇⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣷⢹⠇
⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠈⢳⣄⣀⣀⣤⡴⠁⠀⠀⠀⠀⢸⣻⠁⠀⠀⠀⠀⠀⠀⡎⣿⣿⣿⣿⣿⣧⠻⠿⠿⠿⡛⣵⣿⣿⣿⣿⡿⢰
⠀⠀⠀⠀⠀⠀⠘⢞⢦⡀⠀⠀⢠⠏⠀⠀⠀⠀⠸⡄⠀⠀⠀⣴⡻⠃⠀⠀⠀⠀⠀⠀⠀⠘⢌⢿⣿⣿⣿⢇⣿⣿⣿⣿⣿⡸⣿⣿⣿⡿⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠛⠒⠛⢤⡀⠀⠀⢀⣠⠟⠒⠒⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣭⣭⣜⠿⣿⣿⣿⠿⣣⣭⣭⡵⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣈⣹⣎⣉⣠⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠶⠡⠶⠿⠿⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⡻⠿⠟⠛⠿⢿⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣀⣤⣤⣤⣀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⠞⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢏⣾⣿⣿⣿⣿⣿⣷⡝⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣠⣴⣿⣿⣷⡀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣄⣱⡄⠀⠀⠀⠀⠀⠀⠀⢀⠾⠟⠁⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠈⠛⠷
⠀⠀⠀⠀⠀⠀⡞⠀⣿⣿⣿⣿⣿⡿⠒⠛⠛⠒⢻⣿⣿⣿⣿⣿⡇⢹⡀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⣬⣭⣭⣭⣥⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⢸⠃⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⠀⡼⠉⠉⠉⠻⡄⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⢧⠀⡇⠀⠀⠀⠀⠀⢸⡟⣵⣶⣶⣶⡸⣿⣿⣿⣿⣿⣿⣿⢇⣴⣶⣶⣎⢿⡇
⠀⠀⠀⠀⠀⠸⣶⡇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢸⣶⠇⠀⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⠘⠁
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⣼⣷⣶⣶⣶⣯⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠈⠉⠉⠉⠁⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⠦⣤⣀⣴⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠿⠿⠁⠀⠀⠀⠀⠀⠈⠿⠿⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠙⠻⢿⡿⠿⠋⠁⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⣀⠀⣀⣤⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠠⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣴⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣬⣥⣤⣬⣿⣅⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣴⣾⣷⣤⣤⣤⣄⣀
⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⡀⢁⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠒⢆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠴⠖⢒⡿⣛⡛⣲⡦⠙⢄⠀⠀⠑⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠁⠀⠀⠀⠄⣀⡤⠖⠚⢋⡉⢁⡅⠰⠾⠎⡑⠊⠀⠁⣈⣿⡟⠛⠛⠃⠂⠒⠚⠻⠚⠟⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⣁⠀⠀⠀⣀⣠⠖⠋⠙⣄⠀⠀⠃⡈⠉⠀⠀⠠⠀⠐⠀⠍⠁⡀⠌⠉⡏⣻⠆⠠⠀⠀⠀⠱⡆⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⣀⣤⠾⣛⢯⣥⠧⠑⠂⠁⠐⠀⢄⠀⠀⢣⠊⠠⠤⠀⢑⣠⣠⣤⣷⣯⠾⢣⢀⢠⢳⡀⠀⠀⢡⣠⢐
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠠⠀⢀⣴⠛⣡⠒⠼⠓⠀⠀⠀⢁⠀⠀⠀⢰⠈⠐⠠⠄⢂⢁⡤⠞⢛⡉⠀⡀⠀⣧⡀⠰⣡⣯⢮⣧⠀⠀⠀⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣦⣿⣬⣶⡁⠀⠀⠤⠐⠀⠀⠀⢒⠠⠀⡀⣲⣤⣶⠷⠛⢋⣠⡄⢸⠃⣆⢈⡐⠈⢓⠈⡾⠕⡑⢀⣆⠀⠀⢸⣿
⠀⠀⠀⠀⡰⠁⠀⠀⠀⣮⣾⠗⠋⣡⠖⠁⠀⠄⠀⢈⣴⠶⠞⠟⠋⠙⠉⠹⠐⠖⠀⠹⡥⠡⠀⠸⢹⡹⡈⠀⢈⣷⠢⢪⣼⣴⣿⠀⠀⢸⡟
⠀⠀⢀⡼⢡⡀⠀⣠⠜⠻⡄⠀⣼⣣⡞⣢⣶⡤⠞⠋⠁⠠⠂⠀⠀⠄⠄⠀⠀⢀⡀⢀⣄⠄⠀⣥⡈⣑⡃⠐⠗⢈⣴⣿⣿⣿⣿⡇⠀⡼
⠀⢀⡎⠀⣾⣷⠋⠁⠀⠀⢧⢠⣼⡍⢏⡍⠳⠐⢀⣀⢸⡈⠗⠺⠔⣈⣈⠪⠞⠞⡟⠀⠤⠃⡋⣮⣻⢁⣋⣶⣾⣟⣿⣿⣿⣿⣿⣇⠞
⠀⡜⣠⡟⠋⢸⡀⠀⠀⠀⠘⡖⡍⣥⡸⡴⠐⢇⠘⢫⢇⢣⠀⢖⠇⢙⣐⡄⠄⠀⢁⡀⡈⢗⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠋
⣸⡟⠁⠀⠀⠀⢃⠀⠀⠀⠀⠸⡀⣵⢷⢳⡤⢸⣷⠲⢊⢁⡖⠨⡠⢿⠜⡾⣿⣇⣭⣿⣿⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⠋
⡟⠀⡀⠀⠒⡂⠈⣆⠀⠀⠀⠀⢳⣄⠻⢣⠛⠂⣿⣾⣻⣿⣥⣡⣗⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠋
⢻⣼⣾⣷⣶⣷⣀⣹⡄⠀⠀⠀⠀⢳⣤⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⠿⠉
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠠⠤⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢨⠋⠀⠀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠉⠉⠉⠉⠁⠐⠒⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠠⢀⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠁⠂⠄⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⠿⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⣄⡀⢠⠊⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠐⠒⠀⠀⠀⠤⠀⣀⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠙⢿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⠛⠋⠁⠀⠀⠑⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⣨⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣶⣶⣶⡁⠀⠀⠀⣀⠠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣴⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡻⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⠔⢚⠛⠓⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⢿⣶⣤⠞⢲⣿⣷⠂⠺⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠻⣿⢦⣌⠉⠁⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠃⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠗⠈⠛⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣭⣭⣿⡟⢻⣿⣿⣟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠻⣿⣿⣿⣟⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠁⠀⠀⠙⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠀⠀⣀⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⢠⣾⣿⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣙⠿⢟⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⡇⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣷⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠈⠛⠿⣿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠃⠀⠀⠀⠀⠀⠙⠻⣷⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠻⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠘⠯⠽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣶⣾⣿⣿⣿⣛⣯⣭⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣏⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣷⣄⠳⣦⣭⣛⠿⣿⣿⣿⣿⡄⠀⠀⠀⢿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢹⣿⣿⠗⠈⠻⣿⣿⣾⣿⣿⣿⡇⣠⣴⣶⣿⣿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠟⠙⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣌⣻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣿⡟⠀⠀⠀⠀⢴⣿⣿⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠄⠀⠀⠀⠀⠁⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠀⠀⠀⠘⢿⣄⠀⢘⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⣩⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⠛⠒⠲⠶⢦⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢤⣀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠉⠓⠶⢤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠛⠓⠒⠶⠶⠤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡟⠉⠛⠓⠲⠦⠤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠓⢦⣄⡀⠀⠀⠀⠀⢀⡤⠞⢁⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣠⠖⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣠⣤⠤⠴⠶⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣈⣛⣦⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠋⢉⣩⣭⣽⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⠿⠛⠁⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⣀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢿
⠀⠀⠀⠀⠀⠀⣧⡤⠀⠀⠙⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠿⠟⠃⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⣤⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣢⣤⡤⠴⠖⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣠⣼⣧⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠒⠂⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢟⣿⣖⠖⠀⠤⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠑⢿⢟⣵⣷⢶⢐⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠀⠀⠀⠀⠉⠝⢹⣷⣗⣵⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣿⣿⣿⣿⢟⢄⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⢄⢿⣿⣿⣿⣷⣔⠀⣸⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀⣠⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⣄⣕⢝⢵⣿⣿⣿⣵⡾⢋⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⠕
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠿⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠙⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠢⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢗⣵⣖⠄⡀⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣿⣿⣶⣾⣷⣉⣊⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⡤⠀⠀⠂⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠙⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣠⠔⠋⠉⠀⠀⠉⠉⠙⠛⠻⢿⣿⣿⡿⠟⠛⠉⠁⠀⠈⠐⠢⢄⡈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣌⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣵⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠉⠛⠒⠶⢦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⠶⠖⠛⠋⠉⠀⠈⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧
⠀⠀⠀⣿⠸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠋
⠀⠀⠀⣿⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⢿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⢸⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⣧⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠐
⠀⠀⠀⠀⠸⣆⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⠃
⠀⠀⠀⠀⠀⠹⡄⠀⠈⣷⣦⣤⣀⡀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⣀⣠⣴⣾⡅⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣶⣿⣿⣿⣿⣿⣿⡇⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠟⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠙⠻⢿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠯⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣷⣶⣶⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠻⠿⣿⣿⡿⠟⠛⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣤⡀⠀⠀⣴⣶⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡇⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠙⠻⠿⠿⠟⠁⠀⣠⣴⣿⣦⣄⠀⠈⠙⢿⣿⣿⠇⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⡀⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⠟⠀⣴⣿⣿⣶⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣾⣿⣿⣦⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠉⠀⣾⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⠋⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣄⠀⠈⠛⠋⢉⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⣰⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣄⠀⠙⣿⣿⣿⣿⣿⠟⠀⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆⠀⠈⠉⠉⠉⠁⠀⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⣀⣉⢻⣿⣿⣿⡟⠀⠀⠀⣠⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣾⣿⣿⡟⡄⠀⠀⢠⣝⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣷⣄⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡸⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣛⠻⡿⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣶⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣿⣿⣎⣻⣿⣿⣿⣿⡿⢱⣿⠁⣔⣉⣉⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷⢸⡿⠿⣿⠟⣫⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣿⡶⠄⠀⠀⠈⠡⠚⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠉⠉⠃⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢣⣾⣶⣮⣍⠛⠿⠛⠉⠁⠘⠿⢿⣿⠇⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⢸⡿⠟⠛⠋⠋⠉⠉⠉⠙⠛⠻⢿⠇⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢷⡄⣀⣀⠀⣲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣤⣶⠠⠘⣷⡿⠃⠈⠛⢿⠿⢛⣻⠀⠀⠀⠀⠀⠈⠾⣸⣍⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣾⣿⡧⠑⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⠀⠐⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣟⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡙⠁⠀⠀⢀⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣟⣩⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠒⠛⠛⠛⠛⠛⠛⠳⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⢁⡀⠠⠀⠀⠀⠀⣀⠀⠀⣀⣀⣈⠛⣛⣛⣫⣟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⢀⠴⠊⠁⠀⠀⢤⣤⣽⣶⡿⠿⡏⠁⠀⠀⠀⠈⠻⣿⣿⣧⡀⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣀⠴⠋⢠⣀⣨⣷⣿⠿⠹⡏⠀⠃⣀⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠔⠊⠁⠀⢐⢦⣶⡯⢿⡉⠘⠃⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⠀⠀⠀⢀⡴⠃⠀⠰⠁⠀⠀⣈⣷⣿⠗⠻⠀⢈⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧
⠀⠀⠀⢠⣾⣄⡀⠀⠀⠀⢈⠳⣟⠋⠙⠂⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆
⠀⠀⢠⢿⣿⣿⣿⣦⣀⠔⠁⠀⠙⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢣
⠀⢠⠏⠀⠈⠻⣿⢟⣵⣆⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡎
⢀⠏⠀⠀⠀⡴⠋⢾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡞
⡸⠀⠀⢀⠎⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠇⠀⣠⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡴⠋
⠀⢤⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢋⣠⠞⠁
⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⣀⡴⠛⠁
⠀⠐⢤⡉⠙⠓⠲⠶⠤⣤⣬⣭⣛⣛⣃⣀⣤⣤⣤⡤⠤⠶⠖⠚⠋⠉⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡶⠞⠛⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁⠀⠀⠀⠀⠀⠈⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⣇⠀⡀⠀⠀⠀⠀⢀⣼⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣼⣿⣿⣀⣀⠀⣀⣀⣿⣿⣧⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⢿⣿⣭⣭⣶⣭⣽⣿⡿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣤⣀⣙⡛⢸⣿⣿⣿⣿⣿⣿⣿⠣⢛⣋⣀⣤⣤⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣿⠿⠿⠻⠟⠟⠻⠛⢻⣿⣷⡶⣾⣿⠉⣿⣶⢶⣿⣿⡟⠻⠟⠛⠿⠛⠿⢿⣟⢦
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⠃⡀⠀⠀⠀⠀⠀⠈⠳⡻⢧⣿⣿⢀⣿⡟⡿⣏⠟⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⡄
⠀⠀⠀⠀⠀⠀⠀⣇⢻⣷⠇⣽⣷⣶⣶⣶⣶⡶⠬⠿⠙⠳⣾⣶⣷⠟⠈⠿⠴⢶⡶⠶⣶⣶⣾⣇⢲⣿⡏⣸
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣇⣿⣥⣷⣿⣿⡿⠁⠀⠈⢷⢰⣍⠋⣥⢠⡿⠁⠀⠈⢿⣿⣿⣶⣸⣷⣸⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠳⢼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣳⠏⠈⠻⡞⠁⠀⠀⠀⢈⣿⣿⣿⣿⣿⠵⠚⢇
⠀⠀⠀⠀⠀⢀⣴⡵⠃⠀⠀⠈⢿⣿⣿⣷⣤⠞⢀⢔⣚⣋⠄⠀⠠⣙⣒⠠⡀⢷⣴⣾⣿⣿⡟⠁⠀⠀⠘⢾⣦⡀
⠀⠀⠀⢀⠔⠋⠡⣤⣴⣶⣶⠟⠁⠏⠹⣤⡄⢈⣨⠭⠥⠤⠔⠐⠤⠤⠭⢭⣉⡀⢠⡤⠏⠇⠈⢿⣶⣶⣦⣤⠈⠛⠢⡀
⠀⠀⣰⡿⠆⠀⠀⠀⠉⠛⠃⠀⠀⠀⠦⢼⡷⠐⠲⠶⠟⠒⠀⠀⠀⠚⠳⠾⠒⠂⢿⠥⠆⠀⠀⠀⠙⠋⠁⠀⠀⠀⠰⢷⡄
⠀⠐⣧⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢤⣿⣿⣿⡷⠂⠀⠀⠀⠒⢾⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣼
⠀⠀⠿⠿⢿⣿⣿⣿⡿⠿⣶⡶⠶⠾⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠷⠶⣶⣾⠿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠾⣿⣿⣿⣿⣤⠀⠀⠀⣼⣿⣿⣿⣿⠶⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣶⣾⣿⣿⣿⣦⣀⣾⣿⣿⣿⣷⣶⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠠⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⡜⠛⣀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣏⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡄
⠀⢰⣄⡀⢙⠃⢠⣰⠀⠀⠀⠀⠀⢰⡿⠷⠠⠿⣷⠀⠀⠀⠀⠀⠀⡿⣛⠛⣛⢆⠀⠀⠀⠀⠀⢠⢾⢟⡍⣙⣷⢦
⢰⣿⡏⣀⠻⠇⡈⣽⣷⠀⠀⠀⠀⠀⠱⠐⠓⠰⠁⠀⠀⠀⠀⠀⠀⢨⠡⣶⢉⡄⠀⠀⠀⠀⠀⣿⠀⡄⢴⠆⡄⢸⡇
⠀⠀⡇⠙⠃⠘⠁⡇⠀⠀⠀⠀⠀⢐⣿⣶⣷⣾⣗⠀⠀⠀⠀⢠⣶⠈⠀⠶⠈⢰⣦⠀⠀⠀⠀⠿⢿⣦⠶⢦⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⡄⣤⡰⢎⡶⣤⡄⠠⠀⠀⠀⠀⡠⢊⣡⣴⣠⠷⠂⠀⠀⠀⠀⠀⠀⣠⣅⣦⣆⡤⠀⠀⠀⠀⠀⡀⣠⠿⢧⡀⡀
⠀⠀⣿⠇⢤⡄⢾⡇⠀⠀⠀⠀⢸⢠⠛⣁⡙⠳⠁⠀⠀⠀⠀⠀⢀⣾⢉⣉⢩⠋⠀⠀⠀⠀⠀⡜⠸⡉⠒⠈⡹⠘⡄
⢠⣶⣭⣘⡂⢒⣨⣵⣦⠀⠀⠀⢀⠚⠃⣩⡁⠃⡄⠀⠀⠀⠀⢀⢀⣳⡦⠡⣆⡴⣿⡀⠀⠀⠀⠀⠂⢡⡙⣡⠁
⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⠷⠉⠉⠛⠛⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢭⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⢙⣁⠀⠀⠀⠀⠀⠀⠠⠀⠨⠭⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡈⣀
⠀⠀⠰⠃⣴⡄⠺⠀⠀⠀⠀⠀⠀⠀⡈⢡⣤⠉⡀⠀⠀⠀⠀⠀⠀⠟⢰⣶⠐⠇⠀⠀⠀⠀⠀⠀⠀⠋⣠⡌⠃
⢠⣿⠷⠶⠄⠴⠶⢿⣧⠀⠀⠀⢠⠛⠋⢀⣅⠈⠛⢣⠀⠀⠀⣲⣦⣴⣦⣠⣶⣤⣶⡆⠀⠀⠀⠅⠹⠀⣙⡁⠸⠀⠇
⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⢀⡈⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣀⢁⡀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣂⠀⢄⠀⠀⠀⠀⠀⢀⠔⣠⠄⢤⡐⢄
⠀⠠⢁⡉⣤⡌⢁⠸⠀⠀⠀⠀⠀⠀⡈⢡⣤⠉⡀⠀⠀⠀⠀⠀⠎⡴⢀⣅⠰⡄⠆⠀⠀⠀⠀⠈⢠⡀⢶⠆⣠⠘
⠀⠀⡌⠃⣨⡄⠋⡀⠀⠀⠀⠀⠀⠀⠋⢀⣁⠘⠃⠀⠀⠀⠀⠀⠐⢰⣌⢉⣴⡀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠄⠉
⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠲⠙⠛⠙⠛⠱⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣛⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⢾⣯⣥⣤⠒⠉⠉⠛⢿⡷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣋⠐⠛⠛⣭⣶⣶⣦⣄⢈⡛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⠃⣼⣿⣿⣿⠦⣄⡀⠀⠀⢹⡈⢷⡀⠀⠀⠀⢸⣿⣿⣿⣿⠏⣴⠏⠀⠀⠀⣘⠿⢿⣿⣿⡇⢿⡌⢿⣿⣿⣿
⠀⠀⠀⢸⣧⠞⠈⠙⡏⠁⠀⠀⠉⠓⣾⣿⣷⣬⣇⠀⠀⠀⢸⣿⣿⣿⡿⠸⣡⣿⣶⢠⣾⣿⣿⣷⣮⠉⠀⠀⠻⠘⣿⣿⣿
⠀⠀⠀⢸⣿⠀⠀⠀⢷⠀⠀⠀⠀⢀⡿⣿⣿⠃⡿⠀⠀⠀⢸⣿⣿⣿⣇⠀⣿⣿⣿⡇⣿⣿⣿⣿⡿⢂⡀⠀⣼⠂⣿⣿⣿
⠀⠀⠀⠘⣿⢦⡀⢀⣼⣶⣤⣤⠞⠁⠀⠀⡟⣰⠇⠀⠀⠀⢸⣿⣿⣿⣿⡄⠜⠿⡿⠇⠙⠻⠿⣯⣾⣿⣿⣧⡿⣼⣿⣿⣿
⠀⠀⠀⠀⠘⢧⡉⠻⣿⣿⣿⡇⠀⠀⢀⣴⡷⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡜⠶⣦⠀⠀⠀⠸⣿⣿⣿⠟⢙⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠳⢿⣭⣉⣉⣭⡿⠟⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣮⣁⡲⠿⠷⠶⢋⣠⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠖⠚⠛⠛⠋⠉⠉⠉⠉⠛⠛⠒⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⢁⢤⢀⠴⣀⡰⢆⣀⡔⣆⣀⠖⣀⣠⢂⣀⡴⡄⢠⢄⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣅⣠⠤⠯⢭⢸⠤⡀⠦⢆⡴⠒⢆⡒⠒⣀⠓⢺⣰⠒⡇⠷⠯⠨⠽⠲⠤⣴⠈⠙⠶⣄
⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⡍⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⣴⡯⢾⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢝⣦⡀
⠀⢠⡾⠋⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⢷⡄
⢠⡟⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠻⡄
⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿
⣷⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾
⠘⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣰⠃
⠀⠘⢦⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡴⠃
⠀⠀⠀⠳⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⢀⡴⠊
⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠒⡄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠒⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢠⡇⠀⠂⢢⠀⠀⠀⠈⢳⣤⣤⠞⠀⠀⠀⣰⠒⠲⡀⢿⡀⠀⢀⠇
⠀⢀⠄⠀⢢⡀⢀⡠⣄⠀⠀⠀⢹⡏⠹⡇⠘⡦⢼⠀⠀⠀⠀⣾⡗⢸⡀⠀⠀⠀⠹⠦⠖⠀⣾⡟⡟⠋⠀⠀⠀⣀⡀⠀⠀⡔
⠀⠸⣄⠀⣠⣇⢸⣀⣀⡇⠀⠀⠘⡇⠀⢣⠀⠁⠈⣆⠀⠀⢀⢿⠇⠸⣇⠀⠀⢀⡆⠀⡆⣸⣿⠁⠟⠀⠀⠀⣬⣀⣈⠀⣸⡆⠀⠠⠂
⠀⠀⠈⠙⢏⠺⣦⠉⢣⠈⠢⠀⣀⠇⠀⠀⠳⣄⠀⠘⣆⢀⣾⡏⠀⠀⠙⡆⢀⡞⠀⢀⠟⡱⠁⠀⢰⢁⡴⠋⣠⠋⢀⣴⠟⣰⠋
⠀⠀⠀⠀⠈⢧⠈⠳⢦⣣⣀⡴⢂⠅⠀⡀⠀⠙⢗⣒⣛⣹⠟⠀⡰⢆⠀⠘⣯⣓⣚⣡⠒⠀⢀⡄⠰⣏⠀⣸⣡⡴⠛⢃⣾⠃
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠒⠒⠚⠉⠀⡜⠙⣦⠀⠀⠉⠉⠁⠀⡜⠁⠈⢧⠀⠀⠉⠉⠀⢀⡴⠋⠸⡀⠈⠓⠲⠉⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠘⣄⠀⢸⠃⠀⠀⠀⠀⠀⠱⡄⢀⠎⠀⠀⠀⠀⠀⠘⣇⠀⠀⠃⠀⠀⠀⠀⠀⡴⢻
⠀⠀⠀⠀⠀⠀⣇⠈⡆⠀⠀⠀⠀⠀⠈⢦⠋⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠹⠆⠁⠀⠀⠀⠀⠀⢠⡁⣸
⠀⠀⠀⠀⠀⠀⠈⢦⡁⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣬⣭⣭⣿⡿⠿⠿⠿⠶⠶⠤⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠘⡷⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠷⢒⣛⡉⠭⠭⠅⡖⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣐⣶⣶⣦⣤⣭⣭⣍⣒⣲⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠈⠉⠙⠻⠿⣿⣿⣿⣿⡿⠛⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⣶⣤⣤⣤⣤⣤⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠻⣿⣿⣿⣿⣿⣷⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣀⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⣿⣷⠖⠚⠉⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣄⣀⡼
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠇
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⢀⣀⣠⣤⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠛⠉⠉⠉⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⣻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣀⣈⡿⣅⠉⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠞⠉⠀⠀⠈⢳⠀⠀⠉⡉⠶⠦⠤⠤⠤⣠⡞⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡞⠁⠀⠂⣤⠀⠀⠈⠻⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⣤⣀⠀⠀⠘⢳⣶⠖⡙⠛⢄⣀⠀⠀⢸⡃⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⣀⠀⠠⠂⠈⠙⡚⢉⠉⠙⢷⣅⡀⠀⠙⣷⣰⣇⠈⠀⠀⢄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡠⠞⠁⢑⣦⣤⣤⣤⣶⡒⠒⠒⠺⢿⣷⣤⡀⠀⠉⠙⢦⣄⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠈⠁⠀⠀⢠⣾⣿⣿⣿⣿⡅⣀⠤⠒⣉⠉⠀⠀⢹⡆⠀⠀⠃⠈⢢⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠰⠄⠀⠀⠀⠀⠈⠛⠭⡉⠉⢡⠴⡇⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⢀⠄⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⠉⠑⢀⣤⠿⠁⠀⠀⠀⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣼⣧⡀⠀⠀⣧⠀⠀⢀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠶⠋⠉⢸⡇⠀⢀⡇⠑⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⠀⠀⠀⠀⢸⡇⠀⢸⣷⡾⠟
⠀⠀⠀⠀⢰⠦⣄⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⡁⠤⠤⠾⢚⠏⠀⣰⣏
⠀⠀⠀⠀⠈⢄⠉⠻⢏⣷⠐⠂⠉⠀⠀⠀⣠⠴⠁⠀⠀⠀⢀⡞⢠⠼⡟⢡⠜⡂
⠀⠀⠀⠀⠀⠀⠑⣄⠀⣿⠛⠋⠉⠉⠛⠋⠁⠀⠀⠀⠀⠖⢉⡠⠃⢀⣠⣯⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠃⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⠶⠶⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡽⣫⡴⠛⢉⡤⠀⠒⠀⠐⠊⠛⠓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣩⠟⠉⠠⠴⠀⠀⠀⡀⠀⠂⠐⠛⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠾⣥⠟⠀⠰⠞⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⠞⠁⠀⠞⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣝⡷⠋⡀⠾⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣆⠰⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⢠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡸⠀⢀⠐⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢣⡚⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣧⠀⡦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣻⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠆⡤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡀⠒⠀⠀⡔⠀⠀⠀⠀⠠⠀⣨⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠴⠶⠶⠖⠚⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣦⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⡎⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢠⠟⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇
⠀⠀⢀⠏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣹⠟⠛⠛⠛⠛⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢠
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⣀⣀⣀⣀⣀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢱⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠈⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡀⢀⣀⣀⣀⣀⠀⠄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠉⠁⡸⠃
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣀⣤⣤⣴⠶⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠂⢈⣉⣈⣁⣀⣒⣂⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠑⠠⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠑⠠⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⣠⣤⣤⣤⣤⣤⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣀⠔⠉⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡠⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠉⠀⠂⠀⠀⠀⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠈⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠈⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠉⠉⠉⠉⠉⠁⠀⠀⠱⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢀⣴⣿⣿⣿⣷⣶⣤⣤⣀⣀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠛⠉⣉⣈⠉⠀⠤⠜⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⣼⠿⠶⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡴⠛⠊⠑⢦⠀⠈⠷⠤⣄⡀⢀⣀⠀⣠⠎⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢅⡀⣴⠊⠁⠍⡉⠉⠉⠻⣄⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠙⢧⣤⠤⠾⢇⠀⠀⠀⠙⡇⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠂⠈⠉⠍⠉⠓⠲⠚⠛⠻⣦⡃⠀⠙⢷⣄⣎⠑⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠠⠋⠑⣦⣤⣤⣤⣤⠘⠒⠒⠾⢿⣦⣀⠀⠉⠙⢤⣄⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠈⠁⠀⠀⣴⣿⣿⣿⣿⡇⣀⠴⠒⡉⠁⠀⠈⣷⠀⠀⠀⠈⢢⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠐⠄⠀⠀⠀⠀⠉⠫⠍⠁⣡⠾⡇⣀⡀⠀⠀⣤⡾⠁⠀⠀⣀⠄⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡁⠀⠁⢠⡾⠋⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣠⡾⢷⡄⠀⠘⣧⣀⠠⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠁⠀⢸⡇⠀⢸⢃⣹⡷
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠠⠃⠀⣀⣠⣼⠃⢀⠼⠛⠋⠁
⠀⠀⠀⠀⢏⠙⢦⣤⢤⡀⡠⠄⠐⠉⠀⠀⡠⠐⠈⠉⠉⢡⠁⣠⡿⠓⣠
⠀⠀⠀⠀⠀⠑⡄⠉⢻⡤⠶⠴⠶⠶⠶⠋⠀⠀⠀⣀⠴⢃⠜⠁⢁⣞⠔
⠀⠀⠀⠀⠀⠀⠘⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠉⠀⠘⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠖⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⣀⣤⣶⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡾⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣨⣗⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡛⣿⣻⣿⡻⠃⠀⠀⠀⠀⢹⡇⠀⠀⠀⣗⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣠⣤⣀⡄⣴⢠⣶⣿⣧⣿⢷⣿⢱⣶⣴⡤⣤⣄⣠⣇⡀
⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⣶⣾⣿⠿⠿⠓⠛⢁⠉⠘⠋⢀⡀⣸⠁⣠⠀⣉⠈⠉⠙⠃⠻⠿⣿⣿⣶⣦⣅⣀⠠⢀
⠀⠀⠀⠀⠈⠂⠘⠻⢿⣿⣿⣿⣅⢈⡃⠚⣄⠸⠇⣠⣆⣘⣋⣹⣄⣙⣋⡟⠀⠆⠛⠃⢈⠃⣼⣿⣿⣿⣿⠿⠋⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣯⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⣽⣿⣿⡏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠛⠛⠉⠉⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⠉⠉⠛⠻⠿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠰⣶⣾⣿⣿⡿⢛⣛⢻⡟⡟⠛⠛⣿⣿⣿⣿⣶⠦⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣬⣥⣬⣷⣥⣧⣤⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠶⠶⠖⢲⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⡾⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⢰⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠻⣿⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠹⡇
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠁
⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⣠⣾⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣟⣛⣛⣃⣀⣠⡤⠤⠀⠀⠈⠉


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⠶⠶⢶⣶⠶⣶⣶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣴⣦⣦⣄⣤⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣿⢏⡿⣷⠞⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠉⠙⢋⣁⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⣠⣿⠇⢱⣮⢷⢾⣿⣿⡷⣀⠄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡜⢿⣻⣷⣾⣿⣿⣿⣿⣶⡀⠀⠈⠉⠛⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣷⣤⣀⠠⢀⡠⠂⠀⠠⢋⣹⣿⠿⠿⢿⣿⠿⠋⢹⣿⣿⣷⣦⣄⠀⢀⠜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⡑⢶⠆⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣿⣿⣶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠉⠛⢿⠟⣠⠞⣿⣿⣷⡲⠷⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⠿⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣩⡴⠶⠚⠛⠿⢿⣦⣄⠀⠀⣄⡴⢃⠾⣿⣧⢹⣿⡇⠐⠶⣶⣦⠶⠀⠚⠛⠋⠙⠛⠛⡛⠉⣀⡠
⠀⠀⠀⠀⠀⠀⢀⠏⢠⡞⠡⠀⠈⠉⠉⠙⠲⣌⠙⢿⠆⠁⣼⣿⣷⢹⣿⡼⣏⣷⠄⢄⠈⡃⠀⠀⠀⠀⠡⠀⠑⠄⢈⣀⠈
⠀⠀⠀⠀⠀⠀⡜⠀⡟⠀⠁⠀⡀⠀⣇⣀⣌⠀⠿⠁⢀⣼⣿⣿⣿⡇⣿⣧⡚⣡⠇⣼⣷⣤⣄⠠⡀⠘⡖⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⣧⣼⡇⠆⠀⠀⢸⡏⢀⣴⣴⡋⠀⠰⠋⠹⣿⣿⢿⣿⠛⠹⣧⡹⣲⣿⣿⣇⣽⠃⠐⠂⠘⣶⣆
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠁⠀⠉⢹⣇⠸⣿⣶⡟⡶⠀⠃⠀⢿⡇⠉⣩⢾⣧⢾⡟⢙⣿⣿⠟⢎⢓⠀⠀⠀⠏⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠄⠠⠊⠙⢦⣤⣁⡠⠆⡀⠀⠀⣸⣧⡈⣹⣻⠿⠀⡷⢺⣩⣿⣿⣿⡎⠄⠄⠀⠂⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣌⠠⡀⠘⠀⠀⠡⠀⠀⠀⡅⢀⣿⡇⠥⡷⠟⠛⠚⠓⢫⣌⢋⣿⣿⣿⢐⠈⠁⠀⠀⠀⠀⡀⢴⣶⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣌⡐⠀⠀⠀⠀⠤⠞⣠⣾⠟⠀⠀⡏⣤⣴⡆⢛⣤⣫⡾⣿⣙⣿⠌⠀⠀⠀⢸⣽⣿⣦⠀⠀⠈⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣶⣶⣶⣿⡿⠋⠀⠀⠀⠀⢄⠄⠠⠈⠙⢿⣗⢽⣯⡜⣶⣖⣶⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣀⣹⣳⣿⣿⣻⢿⣩⡛⠏⠉⠅⠉⠙⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣯⣽⠀⠀⢠⣤⢤⡀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⣿⣷⣦⡀⠁⠆⢀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡘⠿⣿⣿⡏⠲⣄⠀⠈⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠜⢻⣷⡁⠠⢐⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠘⠈⢛⠀⠙⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡂⠀⡀⠂⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠁⢀⣴⠞⠁⠀⠀⠀⠉⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⡀⠄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠙⠻⠶⣦⣤⣤⣾⡷⠶⠶⠚⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⣽⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇
⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⣠⣤⣤⣶⠶⣾⡿⠶⠶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⣸⡴⠟⠋⠉⠁⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⣠⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣴⠾⠛⠛⢻⣿⠋⠙⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡇⢀⣼⠏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⣧⣾⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⣠⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣷⣤⣄⠀⠙⣷⡄⠀⠀⠀⠀⣀⡀⢀⢀⣠⣴⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣶⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⠉⠉⠉⠉⠉⠉⠁⠁⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⢀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠄⠀⠀⠁⠀⠀⠀⡈⠙⠢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠀⠈⠁⢤⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠁⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡄⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⢂⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠂
⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⢂⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠋⠀⠀⠀⡤⠀⡠⠀⠀⠀⠀⠀⣄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡲⡄⠐⠀⠀⠀⠀⣀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈⠉⠀⠠⠐⠒⠉⠐⡶⢖⠊⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠈⠀⠀⣀⣠⣤⣾⣦⣄⡀⠈⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠉⠉⠓⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⡀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣛⡒⠒⠸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠿⢿⣿⣿⣿⣿⣿⠟⠁⠊⢿⣿⡿⣿⣞⢥⠄⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⠨⢽⣿⣿⣷⣖⡄⠀⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢩⣿⣿⣿⣿⣕⢔⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢀⣠⣴⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⢕⣿⣿⣿⣿⣿⢕⣴⠇⠉⢣
⠀⠀⠀⠀⠀⠀⠁⠈⣦⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣿⣽⣿⣿⣿⣿⣿⡥⢋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡊⠀⡃
⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠅
⠀⠀⠀⠀⠀⠀⡤⠀⠁⠉⠛⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⡁
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠨⡻⣮⡀⢄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⡄⠉⢢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢿⢿⣿⣶⣕⣷⡶⡡⣢⣆⢁⢄⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡊⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠂⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠛⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠛⠋⠉⠉⠉⠙⠛⠿⠿⠿⠿⠟⠋⠉⠉⠉⠙⠛⠿⠿⠿⠷

⠀⠀⠀⢀⣤⣤⣶⣾⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣿⣿⣿⣷⣶⣤⣤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⠿⠛⠋⣉⣀⣄⣈⡉⠛⠻⠿⠿⠛⠋⣉⣀⣤⣈⣉⠙⠛⠿⠿⠛⠋⣉⣁⣠⣀⣉⠙⠛⠿⠿⠟⠛⢉⣁⣠⣀⣉⠉⠛⠿⠇
⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠁



⡿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⣿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣧⡀
⠀⠀⠀⠀⣠⣿⡿⠋⠉⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⠀⠛⠉⢿⣿⣄
⠀⠀⠀⣰⣿⡟⠀⠀⠈⠛⠛⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡿⠀⠀⠀⠀⢻⣿⣆
⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠐⠶⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢾⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢲⡄⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⣤⠈⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⡉⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⢿⣦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠆⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣶⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢁⣤⣀⠀⢀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠰⣿⣿⣿⠁⠀⠙⠿⢇⠀⠀⠀⢀⣌⠱⡎⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠙⠉⠉⠀⠀⢀⡀⢸⠀⠀⠀⠓⢌⠓⠉⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⡀⠀⠀⠀⢸⣿⠟⠆⠀⠀⠀⠰⢍⣀⡀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠂⠀⠀⠀⠁⠀⠀⠀⣀⣀⡀⠀⠀⠹⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠘⠣⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠐⢀⠆⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⠄⠀⠠⡞⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠊⠀⠠⠀⠀⠀⠀⠠⠄⠳⣁⠀⠈⢳⡄⠰⡇⣀⠀⣀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡦⠄⠀⠰⠄⠂⠠⠄⠀⠠⠄⠀⠲⠄⠀⠀⠄⠀⢀⠀⠑⣄
⢀⠃⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠑⣆⠑⠟⢄⢠⣿⠄⠈⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘
⠈⠀⢸⠀⠀⠀⠀⠀⠀⠄⠀⢀⡐⠌⢢⡀⠀⠈⠳⣄⠨⡅⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠀⠀⠄⠀⠀⠀⠠⠀⠠⠂⡀⠀⠂
⢀⠀⢸⠀⠀⠀⠀⠀⠀⢢⠈⢁⡤⠄⠀⠱⢆⠀⠀⠀⠋⠑⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠠⠄⠀⠀⠤⠀⠀⠤⠀⠀⠤⣄⠀⠠⠀⠀⠀⠀⠀⠀⡄
⠈⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠐⠀⠀⠐⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠰⠀⢸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⢰⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠑⠦⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⡀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡇
⢠⠀⢸⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢨⡇
⠀⠀⢸⠂⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔⠀⠀⠈⠀⢠⡇
⢠⠀⢸⠀⠀⠄⠀⠀⡀⠄⠀⡀⠈⠀⡀⠈⠀⡀⠀⠁⢀⠀⠁⢀⠀⠉⢀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢂⠀⠉⠀⡀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠰⡇
⠈⠀⢸⡄⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠌⠃⡘⠃⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⡇
⢸⠀⢸⠁⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠷⠀⠀⠀⠀⠀⠄⠂⠀⠀⠂⠀⢀⠀⠀⠀⢢⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠠⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠬⠄⠀⠀⠀⢀⠀⠈⠀⡀⠀⠀⠳⡄⠀⠀⠛⠦⠀⠀⠃⠀⠀⠀⠀⠀⡀⠈⡇
⢀⠀⢸⠃⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⡀⠀⠀⢸⠀⠀⠀⠁⢀⠀⠀⠈⢦⡀⢀⡀⠐⠠⣄⠀⡄⠁⠀⠀⠀⠰⡇
⠘⠀⢸⡀⠈⠀⡀⠐⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠉⠁⠀⠑⡄⠐⠀⠀⠐⢀⡇
⠠⠀⢸⡁⠄⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠶⠖⠚⠀⠈⠂⠈⠀⢠⡇
⠸⠀⢸⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠁⠐⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠐⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠈⣀⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⡄⠀⠀⠄⠀⠠⠀⠠⠀⠄⠄⠀⠀⠀⠀⠀⠰⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⠛⠃⠀⠀⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣷⣿⣽⣦⣰⣿⣦⡐⣦⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣧⡀⠀⠀⠀⠠⣤⣤⡽⣿⠻⣿⣿⣿⣟⠧⠿⣷⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⡀⠀⠀⠸⣿⣿⣦⣇⢿⠿⣧⣹⠷⣰⣍⠃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⡎⢹⡀⢠⠴⠍⠰⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠂⠀⢄⣠⠙⣿⣿⣶⣿⡄⠀⠠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⠉⠛⠺⣶⣷⣾⣿⡿⣆⣈⠛⠛⠛⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣯⣭⠐⠉⠉⠁⣠⣤⣾⢷⣦⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⢀⣴⣿⣿⡟⣿⡍⢈⠙⠃⠀⢀⡈⠂⢉⣵⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠙⠀⣀⠀⠀⣴⣿⣿⣿⣿⣿⣮⠙⠋⠀⣰⣾⣋⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⣴⣿⣿⠟⠋⣠⣶⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡦⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣯⣄⣰⣿⡟⢁⣠⣼⣿⠁⠈⠉⢈⡁
⠀⠀⠀⠀⠀⠀⠀⣰⣦⡓⠤⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡾⠁⠘⣭⡍⠁⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠛⠁⣀⡀⣼⠁
⠀⠀⠀⠀⢀⠀⣴⣏⠚⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠐⠒⢂⣀⡀⠉⠑
⠀⠀⠀⠀⡄⣼⣿⡇⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠙⠻⠓⠀⢸⡟⡩⠟⠠
⠀⠀⠀⠀⠇⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠹⣿⣧⠀⠀⠀⠀⠀⠀⢰⡿⠋
⠀⠀⠀⠀⠀⡆⣿⣿⠃⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⢠⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⢸⠘⣿⡄⠀⠀⠀⠀⢀⠏⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠸⠀⢹⣧⠀⠀⠀⠀⢸⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡇⠸⣿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣄⣀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⣶⣶⡶⠶⠶⢶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠻⠯⠍⠉⠠⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢻⣦⠀⣰⣦⡀⠈⡁⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡔⠒⠀⠐⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣦⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⣷⣶⣯⡻⢏⢽⣿⣿⡻⣶⢕⠉⢿⣦⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠸⣿⣿⡿⣾⡜⠟⠻⢧⢾⢋⣼⡷⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣿⣿⣧⠈⣧⠀⢖⠙⠀⠘⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢿⠿⠙⠀⠠⣀⣴⠙⣿⣿⣷⣿⣷⠄⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠆⠀⠀⠀⠀⠉⠛⠓⢿⣿⣶⣿⣿⡿⣆⣌⠻⠛⠟⠋⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣛⣛⠴⠉⠉⠁⢂⣀⣠⣷⣶⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣍⠋⠉⠻⠂⠀⠀⠐⠠⠚⢛⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣎⠻⢶⠆⠀⢠⣴⡟⠊⠀⠐⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠐⠂⠀⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣿⣿⣾⡶⠂⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠐⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠏⠀⢸⣿⣿⡿⠋⢠⣾⣿⠏⣶⠦⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⡄⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⡿⣿⠇⢠⣾⣿⣿⠏⠀⠴⠤⢤⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣍⡓⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡏⠀⠈⠶⡞⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠛⡿⣿⣿⣿⣷⣶⣄⣐⠂⠀⣀⠀⠀⠀⠀⠉⠉⠠⠤⠄⠾⠅⢀⠀⣀⠀⠞
⠀⠀⠀⠀⠀⡔⢠⣾⢋⠋⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠐⠒⢃⣀⣄⠉⠉⠆
⠀⠀⠀⠀⢀⠀⣾⣿⡇⠀⠀⠙⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⣗⠒⠀⢹⣿⣻⠿⠀⠐
⠀⠀⠀⠀⢸⠐⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠘⠊⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⢡⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠈⡌⣿⣿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⣇⠘⣿⡆⠀⠀⠀⠀⠀⢸⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⠅⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠁⣾⡿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠂⣈⣉⠭⠵⠶⢖⡒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠑⠢⢤⣉⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣀⣤⡶⠾⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠈⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠞⢱⣴⡶⠟⠋⠁⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⡰⠃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⡜⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠒⠊⠉⠉⠉⠉⠉⠉⠑⢺⣆⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⡸⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⢠⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠸⠒⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣠⡇
⠀⠀⡇⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠒⠒⠒⠉⠙⣵
⠀⠀⡇⠀⠀⠀⢿⡄⠀⢀⣀⡤⠤⠒⠉⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⠀⠀⠀⠘⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⡄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⢣⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠶⠶⠖⠒⠶⠾⠿⠟⠛⠳⢄⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠱⣄⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⢯⡀⠉⠒⠤⣀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣎⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠑⠒⠲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠽⢷⣄⣀⡀⠠⠤⠴⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣡⠊⠉⠉⠉⠉⠙⢦⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣣⣶⣿⣿⣿⣶⣜⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡤⠶⣅⠀⠀⠀⠀⠀⠀⢨⠷⢤⣀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣫⡑⣿⣿⣿⣿⣿⣿⣿⢇⣙⡻⣷⣄
⠀⠀⠀⠀⠀⠀⣰⠛⡞⠁⠀⠀⠈⢦⣀⣤⣤⣄⣴⠃⠀⠀⠈⢳⡞⢧⠀⠀⠀⠀⠀⠀⠀⣰⡍⣵⣿⣿⣿⣮⠻⠿⠿⠿⠟⣱⣿⣿⣿⣦⣩⣤
⠀⠀⠀⠀⠀⢠⡇⢠⡇⠀⠀⠀⣠⠋⠀⠀⠀⠀⠘⢆⠀⠀⠀⢨⡇⠘⡇⠀⠀⠀⠀⠀⢰⣿⣳⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⢂⣿⡆
⠀⠀⠀⠀⠀⢸⠀⢠⠧⠤⢤⣴⠃⠀⠀⠀⠀⠀⠀⠈⣧⡤⠤⠼⡅⠀⡇⠀⠀⠀⠀⠀⢸⣿⢋⣛⣛⣛⢱⣿⣿⣿⣿⣿⣿⣿⡎⢛⣛⣛⡸⣿⡇
⠀⠀⠀⠀⠀⢸⣀⡏⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢹⣀⡇⠀⠀⠀⠀⠀⠸⢇⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣷⢹⠇
⠀⠀⠀⠀⠀⠈⣟⣆⠀⠀⠀⠀⠈⢳⣄⣀⣀⣤⡴⠁⠀⠀⠀⠀⢸⣻⠁⠀⠀⠀⠀⠀⠐⡌⣿⣿⣿⣿⣿⣧⠻⠿⠿⠿⡛⣵⣿⣿⣿⣿⡿⢰
⠀⠀⠀⠀⠀⠀⠘⢞⢦⡀⠀⠀⢠⠏⠀⠀⠀⠀⠸⡄⠀⠀⠀⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠘⢌⢿⣿⣿⣿⢇⣿⣿⣿⣿⣿⡸⣿⣿⣿⡿⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠛⠒⠛⢤⡀⠀⠀⢀⡠⠟⠒⠒⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣭⣭⣜⠿⣿⣿⣿⠿⣣⣭⣭⡵⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣈⣹⣏⣉⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠶⠠⠶⠿⠿⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⡻⠿⠟⠛⠿⢿⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣀⣤⣤⣤⣀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⠞⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢏⣾⣿⣿⣿⣿⣿⣷⡝⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣠⣴⣿⣿⣷⡀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣄⣱⡄⠀⠀⠀⠀⠀⠀⠀⢀⠾⠟⠁⠀⠈⠻⣿⣿⣿⣿⣿⡟⠁⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⡞⠀⣿⣿⣿⣿⣿⡿⠒⠛⠛⠒⢻⣿⣿⣿⣿⣿⡇⢹⡄⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⣼⣿⢿⣿⡯⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⢸⠃⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⠀⡼⠉⠉⠉⠻⡄⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⢧⠀⡇⠀⠀⠀⠀⠀⢸⡟⣵⣶⣶⣶⡸⣿⣿⣿⣿⣿⣿⣿⢇⣴⣶⣶⣎⢿⡇
⠀⠀⠀⠀⠀⠸⣶⡇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢸⣶⠇⠀⠀⠀⠀⠀⠈⠱⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⠘⠁
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⣸⣷⣶⣶⣶⣯⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠈⠉⠉⠉⠁⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⠦⣤⣀⣴⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠿⠿⠁⠀⠀⠀⠀⠀⠈⠿⠿⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠙⠻⢿⡿⠿⠋⠁⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⣀⠀⣀⣤⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⡀⠀⠋⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣤⣶⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⡔⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⡌⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⢤⡀
⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠓⠒⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠓⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⢉⡁⠀⣠⡀⠀⣤⠀⠀⡠⠄⠀⢠⠄⠀⢀⢤⠀⢀⢄⠀⢀⡉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡏⠁⢀⣠⠒⡏⢐⢚⠃⣟⣹⠀⣋⣉⡇⣨⣉⡇⢸⣉⣟⢸⣋⡋⢸⣒⡇⠐⢲⣄⡀⠈⠏⠓⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠷⠚⠉⠉⠉⢧⠏⠉⠦⠁⠈⠖⠁⠀⠓⠂⠀⠰⠆⠀⠐⠞⠀⠰⠌⠀⠧⠏⠉⠀⠉⠙⠃⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⢀⣴⢿⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⢷⣄
⠀⠀⠀⣠⣿⠗⢻⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠑⢽⣷⡀
⠀⢀⣾⠟⠁⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢿⣆
⢀⡾⠃⠀⠀⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣇
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⢹⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼
⠀⢻⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠃
⠀⠀⠹⣦⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⢠⡾⠁
⠀⠀⠀⠈⠳⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⣠⡴⠋
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠖⠛⠋⠉
⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣦⣶⣶⣴⣧⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣾⠝⠙⢧
⠀⠀⢳⣀⡄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠷⢦⣀
⠀⠀⠀⠹⡷⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⠶⠾⣿⢲⡄⠀⠈⠳⣄
⠀⠀⠀⠀⢷⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⣠⡼⣟⣥⣤⡄⡀⠈⢷
⠀⠀⠀⠀⠸⣧⢰⠀⠈⢷⡄⠀⣀⣀⣀⣀⣀⣠⣴⡖⠛⠛⠓⣀⠀⢠⡾⠋⠀⠀⠀⠈⠙⢾⣀⣸⠃
⠀⠀⠀⠀⠀⢻⣮⡄⠀⣼⡷⠛⠉⠀⠈⠉⢉⠁⠀⠉⠳⣄⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢻⣷⣾⠋⠀⠀⠀⠀⠈⣦⡀⠑⠀⠀⠈⠹⣆⣴⠖⠁
⢀⡴⠊⠁⠀⠀⠲⣏⠁⠀⠀⠀⠀⠀⢀⣽⠷⠶⢶⣤⣤⣴⡿⠁
⡟⠀⠀⠀⠀⣀⡠⠻⢄⠀⠈⣦⡶⠖⠋⠀⠘⡦⠀⣹⣿⣧⣤⣤⣀⢀⣤⠶⠛⠛⠋⠛⠿⠙⠓⣄⡀
⢷⣠⠄⠀⠀⠀⠀⢂⣾⣤⣸⡿⠋⠀⠀⠈⣀⣴⡾⠟⠀⠀⣀⣀⠋⡉⠁⠀⠀⠐⢦⠀⠀⢀⡀⠈⠙⠓⠶⣄
⠀⢻⣆⠐⢀⡀⣀⡼⠋⠙⠁⠁⠀⠀⣀⣴⣟⡿⠶⠤⢤⣤⣭⣤⣤⣈⡀⠀⣀⣀⣀⣤⠴⠋⠹⣤⡀⠀⠀⠹⣧
⠀⣠⡿⠓⣲⠟⡏⠀⠀⠀⠀⢀⣴⡾⠿⠷⠭⣭⣙⡂⠀⠀⠀⡴⠺⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠲⢤⡀⠘⢧⡀
⢠⡏⠀⡞⠁⠀⠡⠀⠀⠀⢠⢿⡏⠀⠀⠀⠀⣀⢈⠉⠓⠮⣄⢀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠆⠈⠛⠦⡀
⠀⢧⣾⡇⠰⡀⠀⠀⠀⠀⠈⠘⣷⡄⠀⡆⠀⠀⠀⠀⠀⠀⠈⢻⣇⡉⠽⠋⠻⠿⠛⢻⡿⠯⠀⠀⠀⠀⠀⠀⠡⡀⣄⠀⢿
⠀⠈⢻⣷⡀⠹⣦⣀⡀⠀⠀⠀⠈⢻⣦⣇⠀⠀⠀⠀⣠⠤⣄⢼⡋⠻⡤⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠂⠎
⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣶⣤⠀⠘⠁⠀⠀⠈⣧⣄
⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣰⣯⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⢀⡼⣿⠀⠀⠀⢀⣴⢿⣿⣷⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠋⠀⣿⠀⠀⠀⠀⣿⡆⠀⠈⠩⠷⢶⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣄⣹⡄⠀⠄⠀⣿⠇⠀⠀⠀⠀⠀⠀⡉⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣧⡀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⢧⣀⡀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡀⠀⠈⢿⡛⠶⢧⣤⣀⣀⣀⡀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡚⠓⢿⣷⣄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⡤⣤⣤⣶⡟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠙⣦⠀⡟⠙⢧⡀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⡀⣀⣀⣀⢀⣀⠀⢹⡷⠶⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢸⣇⠀⡀⠀⠙⣄⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠉⠉⠛⠛⣿⡅⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠋⠀⠀⠈⠙⡳⣰⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠿⠿⠯⠭⢍⣉⣽⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠈⠉⠛⠻⢿⣿⣿⡿⠋⠉⢳⣄
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⣦⣤⣤⣤⣤⣤⣤⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⡀⠀⠀⠀⠘⡇
⠀⠀⠀⢸⣇⠀⠀⠀⢀⣠⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⢀⡴⣿
⠀⠀⠀⠸⣿⣦⡤⠚⠉⠀⠀⠈⠙⢿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠙⠲⠤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⠋⠀⡿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⡇
⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⠁
⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⠇
⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠟⠛⠛⠛⡇⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢻⣝⢦⡀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣟⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣉⠳⢤⣀⣤⣶⣿⣿⣿⣿⣶⣦⣤⣀⣀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠯⠭⠥⠼⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⠴⠋⣠⠄⠀⠀⠀⠀⠀⠀⢀⣠⠖⢁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⢀⡾⠛⠛⠐⠀⠀⠀⠀⠚⣋⡵⠞⠋⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⢤⣄⡀⠀⠑⢶⣤⡀⠀⠀⠀⢻⡄⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠙⠷⢦⣄⡈⠙⠷⣦⣀⠸⡇⠀⠀⠀⠈⢿⣆⠀⠀⢀⣀⡤⠶⠛⡭⠶⠛⠁
⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣌⠙⠻⣿⣄⡀⠀⠀⢈⣿⠆⠚⢋⣡⠄
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠀⣍⡃⠠⠖⠈⣡⠄⠒⠉
⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠋⠁⠠⣶⡛⠻⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⠒⠈⢁⣠⠤⠚⠁⠀⠈⠙⠳⣦⣌⠙⠷⢶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠈⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⢀⡀⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠙⠻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣟⠙⢿⣿⣿⣦⡀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠙⠿⠃⣀⡉⢻⣿⣿⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠛⠿⠃⢀⡈⢻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠛⠻⠇⢀⡀⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡛⠻⠗⢀⡀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠘⢿⣿⣷⣦⡀⠻⣿⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠙⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣄⠀⠈⠻⢿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠐⠒⠒⠒⠒⠂⠀⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢠⠀⠀⠀⠀⠀⠀⢤⠀⡔⢂⣀⠒⣀⡞⢢⣰⢱⣀⡎⣆⡔⢢⣠⢲⢀⠤⠀⠀⠀⠀⠀⠐⡀⠈⠲⣄
⠀⠀⠀⠀⠀⡠⠊⢹⠠⠀⡆⠀⠀⢀⣠⣤⣶⣀⣿⣧⣸⣿⣤⣿⣧⣼⣿⣼⣿⣇⣿⣷⣼⣿⣸⣿⣀⣷⡦⣄⣀⣀⣀⡃⠀⠀⡏⠓⢄
⠀⠀⠀⣠⠊⠀⣰⠃⠀⠀⡿⠟⠋⠉⠉⠉⠛⠿⠏⠛⠟⠉⠛⠁⠙⠋⠈⠛⠁⠙⠉⠙⠋⠙⠟⠛⠿⠋⠀⠀⠉⠉⠛⢷⠀⠀⠸⣦⡀⠱⡄
⠀⠀⠰⠁⣠⣺⣑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡙⠐⠻⢤⡈⡆
⠀⠀⣟⠉⠀⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠙⢁
⠀⠀⠘⣷⣤⣤⣠⢼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡇⣀⣀⣠⣶⠋
⠀⠀⠀⠈⢿⣿⣿⢸⣤⣆⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⣾⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠙⠿⣾⣿⣿⣿⢻⣀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣄⣴⣴⣧⣿⣿⣿⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣏⠿⣿⣿⣿⣧⣷⣶⣴⣰⣠⣤⡄⡀⡄⣄⣀⢀⢠⢠⢀⣠⣦⣦⣷⣾⣿⣿⣿⣿⠿⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣭⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣻⣭⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢻⢶⠾⣭⣭⣝⣛⣛⣛⣛⣛⣛⣛⣛⣩⣭⣭⠶⠶⠛⠻⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠉⠩⠭⠭⠭⠭⠍⠙⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣀⣤⡀⢠⣤⣤⣤⡄⡄⣀⠀⢤⣤⣤⡀⣤⣤⣤⣤⡄⢀⣠⣄⣀⣤⡄⢀⢠⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠛⡛⢱⡄⣿⣿⣿⢳⡇⣿⣴⡾⣟⣿⢠⣯⠾⣹⣿⠇⣹⢷⣿⡿⢿⡆⣾⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⡏⣸⢃⣿⣿⣿⢸⡇⣿⣿⣿⣿⡏⢰⡽⣿⣿⣿⠀⡿⠛⣫⠾⡝⡄⢻⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠏⣸⣿⣿⣿⡎⡇⢿⡿⣿⣿⠁⣿⣹⣿⣕⣺⡀⣠⠕⣚⣽⡷⡐⠘⣰⠿⡿⠿⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠈⢠⣿⣿⣿⣿⣿⡄⠸⡆⣠⣽⠀⣼⢿⣧⣿⣟⡥⠙⢾⠯⠟⣉⡵⢠⡐⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⡇⢸⣿⡿⣿⣿⣟⢿⡄⣿⣿⣿⠇⢹⣿⣿⡟⣟⣿⠂⣈⣥⣾⡿⠆⣼⡇⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⣿⣷⣿⣿⣿⡏⡇⢿⣻⣿⣾⡸⣯⣯⣟⣧⢿⡆⡿⣚⣥⠶⢀⡟⣱⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠘⢯⣾⣽⡽⣾⠃⣸⠿⣿⣿⣇⢻⣿⣿⣎⡓⢐⣻⣭⢶⣫⠀⢘⣉⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⢿⡷⢸⡎⣿⣿⠟⡥⢠⣯⣠⣴⣿⣿⢸⡿⢝⣿⠃⣺⣽⢾⡻⠵⡄⢎⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡶⢸⠇⣿⡟⢸⠇⣾⣿⣭⣶⣼⡇⣸⣿⣿⣿⠨⢝⣊⡵⣞⣟⢿⡘⣧⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⢏⣴⣿⣇⢹⣰⡿⢿⣿⣿⡿⢀⣿⣿⣿⣿⠐⣏⡵⠾⢛⣻⡼⡇⢹⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⣿⠏⣴⣿⠿⡿⣿⣎⠍⣧⣤⣼⣿⡇⣼⡷⣿⣿⣝⡀⣻⡷⠛⠛⢹⣷⡳⠀⣈⣉⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣵⣿⣿⣮⣿⡇⢸⣯⣿⣾⡇⢸⣿⣿⣿⢾⡥⢫⢧⣲⣿⠿⣚⠁⣀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⠸⣿⣮⣻⣿⣻⣿⠃⡿⠉⣻⣿⣇⢿⡿⣻⢷⣏⣾⠀⢊⣭⢶⡻⠍⢀⢇⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⡌⢿⣿⣿⣿⢣⢼⣷⢿⣿⣷⣿⡈⣾⣿⣹⡾⣷⡀⣓⠫⣁⣲⠄⢀⡾⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢿⡆⢻⣿⡇⢸⠘⣷⣿⣿⡿⢽⡇⠛⣿⢛⢷⡝⢱⣞⣿⣭⠷⠂⡐⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡘⣿⠈⣿⣧⠘⡇⢹⡏⠙⢻⣿⡇⣼⢲⣿⣯⠁⡿⠭⢷⣒⣛⠁⢳⡘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠷⠿⣰⣿⣿⣷⣬⡀⢷⡾⣿⡟⠰⣿⣧⢿⡏⢰⣺⡭⣟⣒⣦⡆⡜⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⢰⣿⢫⣶⣶⣜⣷⠘⣿⣿⣥⠀⢿⡇⣾⡇⠸⣿⡎⣙⣻⢽⣷⠃⠐⣛⣛⣋⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣼⣿⡸⣿⣿⡿⡿⢠⡇⢉⣹⣇⢩⡾⣿⣻⡄⢻⢷⣾⣿⡭⠷⠀⡎⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢂⣿⣿⣟⣾⣽⡿⢁⣾⡷⣟⣛⢻⢸⣿⣶⢋⣤⡈⣯⠽⣶⣚⡋⡸⢣⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢾⣿⣿⣿⠟⣵⢃⣾⣷⣿⣿⡏⡟⣽⣿⢣⣿⣿⠃⢺⣿⣿⣿⠁⠵⠯⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣲⢶⡠⡜⣿⣿⡏⣸⡏⣿⡟⠀⣙⣿⡞⡸⣿⣻⡸⣿⣿⡄⣹⣿⣿⣿⠆⡘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠛⠃⠙⠁⠛⠛⠛⠛⠛⠃⠙⠉⠙⠃⠙⠋⠀⠀⠛⠛⠛⠃⠈⠈⠛⠋⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠔⠈⠁⠀⠀⠈⠉⠛⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣛⣛⣛⠛⢛⣲⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⠟⠁⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣷⣶⣶⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣄⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣠⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⡰⣿
⠀⠀⠀⠀⣿⣷⣀⡠⠖⠉⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⠚⠁⣿
⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡟
⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣸⠇
⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⡟
⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠁⠁⠀⠀⠸⡇⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⠳⢄⡀⠀⠀⠀⠀⢀⣠⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠲⢤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣭⣭⣥⣤⡽⠿⠿⠟⠛⠉⠁


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠉⠙⠒⠤⡀⢀⣀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣀⠤⢊⡠⠚⠢⡀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠤⠤⢄⠀⠈⠑⢒⠿⠒⢊⢉⠀⠀⠀⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠤⠈⠁⠈⠉⠁⠀⠀⠋⠀⠀⠃⠈⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢀⠄⠘⢦⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠆⠄⠰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠄⡠⠂⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠨⡋⠙⠀⠀⠀⢤⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⢣⠀⠈⠉⠉⠉⠉⠀⠀⠈⠒⠤⢄⣀⡦⠀⠑
⠀⠔⠀⡠⠀⠈⠀⢀⣀⣀⠠⠒⠒⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠉⢢⡀⡀
⠀⠀⡜⠀⣀⠄⠚⠒⠀⠀⠀⠀⠠⠤⠒⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠘⠄⢀⡇⣀⣀⣀⠤⠁⠒⣤⠞⣀⢄
⠀⠀⠀⠸⣁⡠⠄⡰⠆⠀⡎⠀⠀⠀⠐⠤⠒⠋⠉⠉⠂⠀⠀⠀⠒⠀⠁⠀⠈⢺⠀⠀⠀⠀⣀⢄⡀⢸⡍⠤⠰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠒⠂⠉⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠉⠅⠈⠑⠢⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⣆⠀⠀⠀⢀⣴⣄⡀⠀⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠉⠓⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡟⠀⠀⠀⠻⣿⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠲⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⡹⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⡇⠀⠐⡀⠀⠀⠀⠉⠁⠑⢄⡀⣸
⠀⠀⠀⠀⢀⡤⠊⠁⢀⣠⠇⠀⠀⠀⠀⣑⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⣀⠀⠰⡀⠀⢐⣤⣶⡀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⣠⠏⠀⡀⢰⠁⠀⠐⠢⣈⠙⠉⡁⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⢀⡞⠁⠢⢄⠀⠀⠀⠀⠀⢀⡠⠖⠀⢀⡽⠀⠀⠈⠣⣍⡛⠿⠋⠀⢀⡨⠟⠁
⠀⢠⡞⠁⠔⠀⢀⠔⠢⡀⢀⠎⠉⠚⠊⠁⠄⠀⠀⠀⢀⡴⠛⣆⠀⢀⡴⠛⠠⣄⠀⠈⠇⠠⡀⢀⠔⠁⠐⠀⣸⠟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⡰⠋⠁⢀⠤⠀⠁⠀⠀⠈⠛⠂⠀⠀⠀⠐⠨⡀⠤⠒⠉⠀⠀⠘⠊⠁⠀⠀⠀⠊⠥⣀⠀⢀⠌⢣⠄⠀⢀⡼⠃
⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠐⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡠⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡠⠔⠊⠁⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠐⠈⠁⠀⠀⡀⠐⠁⠀⢀⣰⠿⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠁⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠤⢐⠜⠁⠀⠀⠀⠀⠀⠀⣠⢺⠇⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⡰⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⢀⠔⡙⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⢀⣴⣿⡇
⠀⠀⠀⠀⠀⡰⠁⢠⢁⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⣶⣾⣿⡙⢣
⠀⠀⠀⠀⡐⠀⢀⢃⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣻⣿⠇
⠀⠀⠀⠰⠁⠀⡈⡜⠀⠀⠆⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣯⣿⣿⣿⡿⣿⠉
⠀⠀⢠⠃⠀⠰⢠⠁⠀⠈⠀⠀⠀⠀⠀⣰⣾⣿⡟⣻⣛⡿⣿⣿⣷⣿⣿
⠀⠀⠎⠀⢀⠃⡌⠀⡔⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⡿⣻⣾⣿⣿⡷⠋
⠀⢰⠀⢀⠎⢠⠃⠜⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣿⣿⣿⣿⣿⠞⠁
⠀⡆⢀⠊⠀⡬⠊⠀⠀⠀⠀⠀⠀⠀⣿⠿⣫⣾⣿⣿⡿⢟⡷
⢀⡡⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⣀⣤⣷⣿⡟⠋⠉⠉⠛⠁
⡼⢁⢔⠏⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇
⣏⡴⠁⠀⠀⠀⠀⠀⠀⠀⣠⣲⣻⣞⢿⢟⠇
⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠁

⠀⠀⠀⢀⡠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⡔⠁⢧⠒⠊⠉⠉⠳⡀⠀⠀⣴⣿⣩⣵⣶⣾⣿⣦⠀⠀⢀⠾⣁⢀⡠⠄⠠⢝⢆⠀⢀⣜⠿⡿⢟⣯⣭⣟⢆
⠀⢸⢇⠀⠈⠢⡤⠄⢦⠤⡇⠀⢈⢿⣿⣷⣝⣛⣿⡟⣟⡃⠀⡎⠀⠈⠉⠀⠀⠀⠈⡞⠀⣼⣿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⠘⡄⠑⢄⡼⠀⠀⡆⢠⠇⠀⠘⣷⣝⡿⢧⣿⣿⢷⣿⠃⠀⠱⣀⠤⠤⢤⣀⣀⡴⡹⠀⠸⡿⣛⣛⡿⢿⣿⡿⡹⠁
⠀⠀⠈⠲⢎⣀⣀⡴⠕⠁⠀⠀⠀⠈⠛⢵⣿⣿⠟⠞⠁⠀⠀⠀⠙⠢⢄⣀⣈⠥⠚⠁⠀⠀⠘⠻⢿⣿⣷⡶⠛⠁
⠀⠀⠀⢀⣀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⡀
⠀⠀⠰⠛⢁⣀⡀⠛⠻⠂⠀⠀⠀⣠⣤⡾⣿⢿⣦⣄⣤⠀⠀⠀⠀⠀⠀⠀⢈⡛⢦⡀⠀⠀⠀⣠⣾⣿⡿⢦⣍⠓
⠀⢠⡀⠀⣼⣿⣷⠀⠀⣠⡀⠀⠐⢿⣿⠁⠀⠘⣿⣿⠟⠆⠀⠀⠀⠀⠀⣰⠿⠁⠀⠉⠀⠀⣰⣿⣿⠟⢠⣾⣿⠇
⠀⠘⣿⠀⠀⠉⠀⠀⢸⣿⠇⠀⠀⠰⣿⣿⣶⣿⣿⡇⠀⠀⠀⠰⣦⡀⠾⠋⠀⠀⠀⠀⠀⠀⠻⣿⣃⣴⣿⣿⠏
⠀⠀⠀⠀⢰⣾⣶⠄⠀⠀⠀⠀⠀⠈⠻⠟⠉⠙⡿⠟⠁⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⠀⢷⣌⡛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⢀⡤⠂⠀⠀⠂⣄⠀⠀⠀⢀⢠⣶⣾⣶⣶⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⣿⣿⣿⣷⡀⠀⠠⢡⠇⠀⢀⠖⠉⠉⢁⠀⢠⡟⣼⣿⡿⣣⣶⣿⣧
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠎⠀⠀⣾⠀⠀⠀⠨⠀⠘⣴⣿⣿⠅⣿⣿⣿⣿
⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣿⣿⣿⠟⠀⠀⠈⢄⠀⠀⠸⣄⠀⢀⠆⠀⠈⢿⣿⣿⣇⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⢁⡂⠀⠈⠋⠀⠀⠀⠀⠀⢉⡛⠛⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛
⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢾⠀⠀⠀⠀⠀⠀⠀⠀⣨⡅
⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⡠⢂⡉⠉⠑⢦⠀⠀⢠⣿⣿⣶⢾⣿⣶⣄
⠀⠀⠀⠩⡑⠀⠠⠐⡈⠩⠴⠀⡀⢻⣦⣤⣤⣶⣿⣿⣿⣤⣄⠀⠀⢸⠀⠠⠐⠂⠀⠀⠁⠀⢻⣷⣿⣟⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠑⠀⠀⠀⠉⢠⡀⠄⠃⠀⠹⣿⣿⣿⣷⡿⠿⠿⠛⠀⠘⣘⡀⠀⠀⠀⠀⢀⠆⠀⠘⣿⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⠒⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠉⠉⠉⠉⠙⠓⣲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣧⣄⣀⣀⣤⣤⣤⣤⣄⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠘⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠻⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣼⢀⣿⠛⠉⠁⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⣦⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡏⣸⠇⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⣴⠶⠞⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⣀⣠⣴⣿⣤⣤⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡤⡀⠀⠀⠀⣼⣷⣾⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠙⠟⠹⠀⠀⠀⠀⠀⠿⠋⠀⠀⠈
⠀⠀⠀⠀⢀⣠⠄⠀⠿⣤⣦⡶⢶⡶⠲⠀⢀⠸⠄⠀⠈⠁⠁
⠀⠀⠀⠔⠁⢀⠀⡀⠀⠉⠉⠁⠀⢠⠀⠀⠈⠄⠀⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⣀⡔⠁⢀⠀⠴⠥⠶⠶⢼⡌⠳⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢮⣿⣄⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠉⠉⠁⠒⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡂⠀⠀⠠⢤⠄⣀⠀⠀⠉⠀⠀⠈⠉⠁⠁⠀⠀⣀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡬⡛⢄⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠔⢶⣖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠁⠀⠀⠀⠀⢀⣀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢀⣀⣤⣠⣤⡭⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⡋⠁⠉⠁⠀⠀⠀⠀⠙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⠐⠢⠭⢄⡉⠉⠁⠀⠀⠀⠹⣍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⠀⢠⣤⡈⢉⡀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⡃⠀⠀⠈⠣⣸⠇⠙⠲⢬⡑⠢⠀⠀⠀⠒⣬⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠾⠃⠀⠀⠀⠀⠙⠒⠾⣧⡀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢶⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⣆⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠉⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⡾⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣴⣾⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣼⣿⢦⣴⠀⣀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣉⣭⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣥⠄⠂⠂⢄⡀⠈⢐⠿⡟⠋⠁⠛⠉⠙⡖⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣆⠈⠢⣀⠀⡴⠞⠁⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣫⡵⣿⡽⣆⠀⠀⠍⡀⠀⠴⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡱⣷⡝⣛⢴⣺⡇⠈⠀⠀⠀⠉⠒⠀⣸⡶⣤⠔⠋⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣞⠿⢊⣞⣵⡿⠋⠁⠀⢈⠐⢄⡀⠀⠀⠜⢿⣾⡻⡥⡀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⡛⢣⣷⠛⢻⠀⠀⠀⠀⠀⠑⠀⠙⠂⢀⠀⠀⢹⠙⣾⡜⠷⣄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣽⣅⣿⠃⢀⡼⢦⣤⣄⢔⣿⣽⣶⣦⣌⡊⢳⡤⢯⡀⠘⡿⡘⣳⣦⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣯⢸⣿⣄⠞⠀⠀⠀⢻⣾⣿⣿⡿⠻⣿⣿⣿⣷⠀⠹⣤⣿⡇⣻⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⢸⢿⣿⡇⠀⠀⠀⠀⢹⣿⡟⠀⠀⠙⢿⣿⣿⣇⢠⣿⡯⢇⣽⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⡾⠆⢟⣿⣷⡀⠀⠀⣠⠟⠀⠈⠢⡀⠀⠈⣿⠿⠯⣾⣿⡽⣨⣽⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢾⢿⣈⢞⣿⠉⠙⠚⣏⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡽⡳⢱⣾⡍⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡻⣫⣮⠳⣷⢤⡀⠈⣢⣄⣀⣀⣨⡄⠀⠀⢁⠀⢟⡰⣿⢎⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⢱⣿⣢⣝⠺⠿⣻⡿⣿⣿⠿⣻⡄⠀⢈⣼⣝⠿⡣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣟⠣⣿⢷⣶⡌⠙⠋⠀⢰⡏⢄⠀⢩⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠿⡇⠰⣿⡇⢀⣥⠞⢂⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣤⣿⡿⠀⠀⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⠈⠻⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⢀⣀⡀⢀⡈⡉⠉⡁⣀⣀⡀⣀⣀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠏⠇⠗⠬⠄⠆⠏⠇⠷⠀⠇⠧⠧⠇⠇⠿⠼⠦⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⢰⠲⡐⠂⣧⢰⠐⠀⡆⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⣉⣁⠀⠈⠉⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠉⠉⣉⡭⠿⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢳⡀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢳⣤⣶⣶⡺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⣴⡿⠋⠀⢀⡇⡿⠤⠤⠤⠤⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⣠⠏⢀⣀⠤⠖⠚⠙⡿⣇⣀⡤⢞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢰⡧⠖⠉⠀⠀⠀⠀⠀⡹⠶⠶⠒⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⢹⡄
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⣧
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠱⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠱⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⢤⣤⣀⣀⣀⣠⣤⠤⠴⠖⠚⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⣠⠴⠚⠉⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠃⠂⠤⣀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠉⠉⠛⠒⠶⢦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⡴⠶⠚⠛⠉⠉⠈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷
⠀⠀⠀⢸⡛⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿
⠀⠀⠀⢸⠀⠈⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏
⠀⠀⠀⢸⡆⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠸⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠸⡆⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⡀
⠀⠀⠀⠀⠀⢻⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⣷⣦⣤⣄⣀⡀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣀⣠⣤⣶⣿⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣿⣿⣿⣿⣿⣿⡇⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠦⢤⣤⣤⣤⣤⣤⡤⠴⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⠤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠒⠋⠉

⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⡿⢿⠿⢿⠿⢿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⠿⠋⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⡼⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⢰⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⡎⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿
⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻
⠀⠀⠈⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸
⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠈⠻⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡆
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠴⠒⠀⠀⢰⠘⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⣁⠀⣠⡤⢴⣯⡄⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣈⣿⣆⡀⠀⠙⠿⡛⢉⡇⠀⣰⣿⣯⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⣿⣿⣿⣿⡙⠖⢦⢄⠉⠑⡶⠙⠁⠙⠓⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣹⣿⡿⠛⠟⠱⣙⠆⢉⣗⣠⣽⡤⠶⣄⢠⠈⡈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡿⠛⣳⠇⠀⠀⠁⢸⢯⣉⠉⠘⠀⠀⠀⠉⠀⢸⡀⠙⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢘⣦⡤⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⣄⠀⠀⠀⠀⠈⠍⢦⡀⠈⢂
⠀⠀⠀⢀⣀⠀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠒⠦⣤⡄⠰⣄⡀⠀⠀⠀⠈⢲⡀⣀⡀
⠀⢀⣄⣿⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣫⣥⠜⡃⠀⠀⠀⠀⠀⠙⢦⣉⢲⡄
⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠚

⣶⡶⠶⠶⠶⢶⢶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⡠⠔⠁⠈⠉⠙⠛⠿⢿⡿⠿⠛⠛⠉⠁⠉⠢⢄⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠗⠤⢀⣀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⡠⠄⠚⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠑⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖⠊⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⡿⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⢻
⠀⠀⠀⠀⣇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣸
⠀⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡇
⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠉⠉⠉⠉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡸
⠀⠀⠀⠀⠀⠘⣆⠀⠸⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣠⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠘⢆⣼⣿⣿⣶⣦⣤⣀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣠⣤⣶⣾⣿⣿⣧⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡷⠒⠒⠒⠒⠒⠒⠒⠒⠻⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⠤⣄⣀⣀⣀⣀⣠⠤⠤⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⢀⡠⢴⠋⠁⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀⠀⢀⡀⠀⠈⠙⡖⢤⣀
⠀⠀⠀⠀⣠⡔⠉⠀⠘⠰⢀⡄⡄⠄⠀⠸⠐⠐⠃⠃⡇⠃⠐⠰⠠⠈⠤⠄⣄⠆⢡⠀⠈⢳⢤⡀
⠀⠀⢠⠞⠁⡇⠀⠀⡗⡀⠑⠃⠃⢃⠇⠉⠈⠀⠀⠁⠁⠉⠁⠈⠈⠀⠃⡇⠗⡁⢸⠀⠀⠘⡀⠙⢦⡀
⠀⡴⢁⠀⠚⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⡇⠐⠀⠱⡄
⣼⠕⠁⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻
⡇⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀
⢱⡀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⠀⡠⣸
⠀⠹⣆⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡃⠄⢀⡴⠁
⠀⠀⠈⠫⡀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠸⢀⡴⠋
⠀⠀⠀⠀⠈⠓⢄⡀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⡇⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⡀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠙⠋⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⠀⠀⠀⠀⠀⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣴⣧⠆⠀⠀⠀⠀⠀⠀⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⣿⡿⠧⠀⠀⠀⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⣀⣈⣙⣁⣀⢘⣿⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⡇⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣏⠻⣛⣵⣦⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡴⣿⡿⠟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠛⠿⠁⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⠎⠀⢰⡏⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠎⠀⠀⠸⣗⣀⠛⢤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠐⠁⠀⠀⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠟⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢨⣷⠆⠀⠀⠀⠀⠀⠰⠰⠲⣞⠶⠯⠄⠈⠛⠛⠛⠑⠀⠂
⠀⠀⠀⠤⣤⡶⠾⠜⢿⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡵

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠄
⢛⠻⡕⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡌⠀⢻⣋⣤⣾⡿⠃⣀⡤⠳⢠⣴⠊⣀⣴⢃⣘⠠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⠆⠒⠒⠀⠉⠰⢀⣀⣀⣤⠖⢀⣸⡆
⣧⣶⣾⡝⢋⣉⠙⢶⣻⣷⣿⠶⢏⡀⠘⠪⣟⣯⠗⣤⣀⡀⠀⠐⢤⡐⢄⠀⠐⠐⠄⠀⠀⠀⠀⠠⠉⠀⠀⠀⢈⠀⡠⣤⡾⠂⢋⠘⢿⡟⢁⣤⡴⠄⠍⠀⡀⠘
⢿⣿⣿⠀⡉⠋⠀⢸⡏⣿⡿⣾⣿⣿⡴⡆⣉⣿⠿⣥⢻⡌⢉⠛⣃⣹⣟⡄⢀⡤⠞⠺⢤⢀⢐⡖⠀⠀⠠⡄⣌⠉⠁⢹⡟⣛⣻⣏⣛⣱⡟⠁⠀⠀⠛⣷⢖⠾⠇
⣹⣹⣿⠼⠟⣋⢛⡛⡧⣿⣾⣿⡿⢻⣿⡿⠀⠀⠀⠀⢯⣐⢟⣛⠀⢹⣿⣭⠠⣤⠄⠀⠾⡻⢎⢠⠗⢴⠆⠀⠌⠢⢹⣠⣵⣿⣿⣿⠉⡉⠀⠀⠰⡛⢠⠉
⣿⣿⣭⣶⠞⣿⡗⢀⣽⣿⠛⣿⣿⣿⣿⠗⠟⢷⢀⣷⡼⢻⣄⠈⣿⣎⠷⠸⢁⠀⠀⠈⣷⣥⡈⢏⣤⡜⠳⣤⠔⠀⣾⡟⠉⠙⢿⣿⣷⣀⡾⣡⠟⡆⢀
⣋⡛⡡⢐⢛⡉⠓⡛⠩⣿⡟⢿⣯⣽⣻⣿⠂⡉⣼⣶⣥⢟⣿⣿⣯⣃⡈⠁⡁⢀⣠⣄⣀⣤⡄⢿⡘⠂⠀⠉⠀⢰⡏⠁⣾⣿⣬⠹⢬⠁⠐⠃⠀⡀⢡⡆⢠
⠛⠓⣰⣿⣶⣤⣤⡷⣢⡬⠛⠋⠉⠀⠈⠛⠛⡼⠛⣿⢡⣿⠋⠀⠀⠀⠁⡒⠘⣏⣷⣿⣷⢹⡷⣺⠅⣱⡄⠀⢠⣜⡇⣠⣿⠷⢿⡀⠀⣟⡇⢠⣜⡇⣼⣿⣿⠀⠒
⠐⠚⣿⣿⣿⡇⠠⠆⠀⠀⡀⠀⠀⣴⠖⠛⢯⠾⠱⣿⣾⡇⠄⠀⠀⠀⠀⠀⠸⠋⢽⡏⣠⣁⠰⠃⠀⠀⠀⠀⢉⠿⠿⣿⠀⠀⠀⠉⢠⡿⢃⣾⠿⢁⡀⣸⠁⠐
⠐⢄⣸⣿⣿⡇⢀⡀⠀⠀⢁⠀⢸⡇⢐⣦⡈⠹⠆⢙⣿⣿⣰⡅⢀⡠⠈⣠⣴⠾⢷⣾⢿⡟⠛⠢⡀⢀⡐⠓⣂⡄⠀⠈⠣⣀⡀⠀⢘⣵⡾⠁⠀⠈⠙⢿⡆⠢⣤
⣤⣼⣿⣿⣟⣙⣭⡾⡷⣶⡿⣤⡀⠓⢥⡶⢥⡶⠂⠙⠉⠀⣴⣷⣤⢤⣐⡁⢛⣶⣼⣮⣼⡗⣀⠀⠀⠀⠒⠺⡾⣇⣀⠄⢠⡈⠻⢶⠾⠋⠀⠀⠀⠀⠀⠀⠈⠁⠈
⡿⠻⠉⠁⡸⢿⣿⢟⠋⠭⠙⣄⠐⢿⠿⣇⣜⡁⠀⠀⠀⠀⡃⠈⢀⣛⡰⡛⣿⣷⡿⡇⠀⢽⠛⠃⠙⠁⡄⠀⡀⠨⠉⠂⠾⣿⣶⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⣍⠓
⠻⡿⣹⣶⣿⣾⣿⣏⡤⢀⣌⡁⠀⠈⢡⠸⠧⠙⠤⣀⠀⡸⣇⣰⣇⣫⣾⡏⠉⠁⠀⠄⠀⠐⠀⢀⠀⢀⠠⡀⠈⠢⡀⠰⠖⢈⣿⣤⠀⠀⠀⣠⣦⠊⡔⠀⢰⣷⣼
⣤⣴⡁⢩⡟⣉⢁⡭⠴⣤⠘⢻⣆⠀⣼⣶⣘⠀⠀⠀⠀⠙⢤⡄⢈⠸⠟⢃⡀⢀⢠⠀⡀⠀⡀⠀⠉⠁⣀⠀⣧⡀⣟⠒⠒⣿⣿⣟⣀⣠⣴⠟⠠⠀⠀⣼⣟⣿⠟
⠘⡈⣥⣸⠂⠴⠛⢉⠒⠆⠀⠄⡅⠀⢸⣿⣿⠁⠁⠀⡀⠀⠈⣀⠈⡓⢺⣻⡅⢢⡄⠂⢁⠒⡀⠈⡻⠋⠁⠀⢸⣟⣦⣤⣾⣿⣿⠟⠉⢉⣡⡄⠀⢴⡀⢠⣀⠄
⡄⠐⠹⣿⠀⠀⠀⠘⠈⠧⢀⠄⣀⣶⣼⣿⣿⠈⡀⠁⠘⠖⠡⠵⠆⢀⠁⠀⠱⣠⡤⠔⠀⠤⡇⠀⠀⠀⠂⢠⠠⢟⣝⡯⠈⠬⠛⠷⣤⡘⠇⠹⠀⢼⣏⠙⠁⠴⢾
⠳⣄⠀⠻⡀⠀⠀⠀⠒⢈⣵⠞⠹⠋⣿⡿⠿⡷⢤⣤⢤⣤⣴⣴⣦⠀⠀⡀⠀⠉⠀⠘⠀⠀⡹⠀⠀⢀⠀⠀⠀⠀⡼⣯⡦⠀⡦⠄⣶⠓⠀⠀⠡⡨⢻⠁⡐⠰
⣷⣈⣧⠀⣾⡖⠂⠀⢁⡀⠀⢛⠀⠀⠎⣿⡀⣹⠀⢈⠈⠁⠉⠉⠁⠀⠄⠀⠐⡇⠀⠄⠀⠐⠂⢀⠁⠀⠁⠀⠀⢀⣀⡠⣀⣤⣴⡷⠅⠀⠀⠈⠀⠄⡀⠀⡈⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⣒⣲⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠳⣄
⠀⠀⠀⠀⠀⠀⡠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⠟⠁⠀⠈⠑⡄
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⡞⠀⠀⠀⣠⣤⣤⣤⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⡜⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢠⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣄⠀⠀⠀⢠⣿⡇
⠀⠀⢸⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⡇
⠀⠀⢸⣀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠃
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠰
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⠂
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣐⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⠴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠵⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣿⣿⣿⡇⣿⣿⣿⣿⣷⣶⣆⣴⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠉⢿⣹⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⢷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢫⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣱⣿⣿⣽⣟⡂⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣾⣿⡿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⡿⣿⠟⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣎⢿⣿⣮⣽⣿⣿⣿⣿⡀⠀⠀⠀⠻⣤⣼⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣻⣿⣿⣟⠈⠉⠉⠻⢿⣣⣮⣽⣇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣄⠀⠀⠀⠈⠻⣿⣿⣿⣤⣀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣀⡀⠀⠘⠿⢿⢿⣿⣿⣄⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠁⠀⠀⠀⠀⠈⠛⠿⣿⣅⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠉⠁⠲⣄⠀⠀⠀⠀⢰⡆⠄
⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠇⠀⠈⠑
⠀⠀⠀⠀⣰⣋⠤⠴⠖⠒⠛⠛⠛⠛⠲⣿⠧⣤⣄⣀⡿⠀⠀⠀⢀⡶⠶⢄
⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣻⠛⠶⢦⣤⣿⠁⠀⠈⢧
⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⢠⡟⠀⠀⠀⢸⠟⠣⣄⠀⠈⡆
⠀⠀⡃⠆⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⠆⠀⠀⠓⣄⣹⠄
⠀⢈⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⡆
⠀⢸⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠸⡇
⠀⠈⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢰
⠀⠀⠰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡜
⠀⠀⠀⠡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠉⡄⠄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠞⠁⠀⠀⠀⢀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠄⣠⡟⠀⠀⠀⠀⠀⢀⣀⣤⠤⠞⠋⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣀⣤⣤⡶⠶⠶⠶⠿⠟⠛⠛⠛⠛⠻⠶⠶⠶⠶⢶⣤⣤⣄⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠈⠙⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣀⣀⣬⠦⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠙⠛⠛⠛⠛⠻⢿⠛⠋⠉⠉⠀⠀⠀⠈⠳⠀⠀⠀⠀⠑⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣆⣀⣀⣀⣀⣀⡀⠀⠀⠙⠄⠀⠀⠀⠀⠈⠙⠓⠢⠤⠠⣄⡀⠤⠄⠀⠒⠈⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠤⠦⠚⠛⠛⠉⠉⢻⣿⠉⠉⠉⠍⠉⠙⠛⠳⠤⣤⡀
⠀⠀⠀⠠⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠻⣿⠟⠛⠳⢦⣄⡀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀⡼
⠀⠀⠀⠀⠳⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢈⡃⠁
⠀⠀⠀⠀⠀⢹⡆⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⡀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠚⠋
⣄⣤⣤⣤⣤⣀⣤⣄⣀⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣠⣄⣠⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⡖⠒⠛⢛⣲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠛⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢖⣛⠛⠒⢶⣄⡀
⠀⠀⠀⠀⡴⠋⢠⣿⣿⣿⡅⠀⠀⠈⣟⢦⡀⠀⠀⠀⠀⡰⢫⠁⠀⠀⠀⠀⠀⠀⠀⠏⢢⡀⠀⠀⠀⠀⡴⣭⣄⡀⠀⠈⠑⢄⠀⠙⢟⢦
⠀⠀⠀⣼⡠⠞⠛⢿⡿⠛⠓⠦⣀⢀⣼⡀⢣⠀⠀⠀⣸⠁⠘⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⢳⠀⠀⠀⡜⡴⠁⠀⡨⠳⡄⠀⠈⢣⠀⠘⡼⢧
⠀⠀⠀⣿⠁⠀⠀⢸⠀⠀⠀⠀⢈⣿⣿⣷⢼⠀⠀⠀⡇⠀⠀⠘⢆⠀⠀⠀⠀⢠⠎⠀⠀⢸⡆⠀⠀⣿⠀⢀⠎⠀⠀⣸⢤⣤⡼⠤⠊⠁⢸
⠀⠀⠀⢿⠳⣄⣠⣼⣤⣀⣀⡤⠚⠻⣿⠃⣸⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⣸⠁⠀⠀⣿⠀⣸⠀⠀⣰⠁⠀⠀⠀⠀⣀⠴⡿
⠀⠀⠀⠈⢦⡀⢻⣿⣿⣿⠁⠀⠀⠀⣞⡰⠃⠀⠀⠀⠈⢧⡀⢀⡜⠀⠀⠀⠀⠸⡄⠀⣰⠃⠀⠀⠀⠘⢆⢻⠀⠀⡏⠙⠓⠒⠚⠉⢁⡴⠁
⠀⠀⠀⠀⠀⠑⠶⣍⡉⠉⠓⣢⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠯⣄⡀⠀⠀⢀⣀⡬⠛⠁⠀⠀⠀⠀⠀⠀⠙⠦⣀⣹⡖⠤⢤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⢀⠔⠋⢉⣓⣦⣈⣆⣠⡛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⣉⣹⢟⣿⣷⣄⢸⠀⠀⠀⠀⢀⣴⣏⠀⠀⠀⠀⠀⠀⣩⣶⡄
⠀⠀⠀⢰⣫⠔⠊⠉⠀⢸⠃⢹⠈⣏⠓⢾⣆⠀⠀⠀⠀⠀⣠⠞⢥⣻⡾⠋⠀⠀⠙⢿⣿⣿⠀⠀⠀⢠⠋⠀⢹⣆⠀⠀⠀⠀⢴⡟⠀⠘⡆
⠀⠀⠀⡟⠁⠀⠀⠀⣠⠏⠀⠸⡄⠘⢆⠀⢹⠀⠀⠀⠀⡴⢡⣽⡾⠋⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⡴⠁⠀⠀⠀⡇⠀⠈⡆⢸⠀⠀⠀⢸⣧⣰⠋⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢧⠀⠀⠀⣿⠀⠀⠀⠀⢿⡄⠀⠀⣸
⠀⠀⠀⠹⡄⠀⡼⠀⠀⠀⠀⢀⡇⠀⠀⣿⠏⠀⠀⠀⣿⣿⣱⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⣆⢀⣼⠏⠀⠀⠀⠀⠹⣧⠀⣠⠃
⠀⠀⠀⠀⠙⢦⣇⠀⠀⠀⠀⣸⠀⢀⡴⠋⠀⠀⠀⠀⣇⠙⢿⣿⣷⣤⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⡀⠀⠀⠀⠀⠀⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠓⠊⠁⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉

⠀⠀⠀⠄⣢⣥⠉⠳⢄⠀⠀⠠⠒⠩⡭⣴⠂⡀⠀⠀⠴⠀⠀⠉⠰⠄⠀⠀⢠⡀⠉⠈⠙⠢⠀⠀⠀⠀⡠⣀⡻⢿⣍⡂⠀⠠⢆⠀⠀⢀⡦
⠀⠀⣴⠀⠙⠉⠀⣶⣦⡄⢠⠋⠀⡀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠉⠀⠠⠐⢁⠀⢀⢨⠞⠁⠀⠀⢹⠁⠀⠁⠈⡆⠀⢸
⠀⠀⠈⡐⣾⣶⠀⢉⡡⠀⠀⢀⡀⠀⠀⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠐⠠⠀⢀⠁⠀⠸⣯⣄⠀⠀⠀⠁⠀⠀⢂⡸⠁⠀⠘⣄
⠀⠀⠀⠸⠷⠦⠶⠿⠀⠀⠀⠀⠷⠶⠶⠶⠆⠀⠀⠀⠸⠶⠦⠶⠾⠀⠀⠀⠀⠱⠾⠶⠾⠧⠀⠀⠐⠼⠿⠷⠷⠆⠀⠀⠀⠀⠴⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡻⠿⢟⣵⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡂⢸⣷⣷⣶⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣽⣿⣧⣼⢿⣿⣷⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⣿⣿⣿⡿⠛⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠈⠯⠁⠀⠀⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⣿⡿⡛⣀⢸⣣⣀⣠⣼⣯⣽⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠸⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡈⢦⣀⡈⣹⣿⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠋⠈⢉⣽⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠈⠀⡏⠀⠀⠘⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠛⠃⣀⠀⢀⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣀⡀⠀⠀⠈⣿⣾⣿⡁⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⣿⣿⣿⣦⣀⣸⣿⣿⣿⠙⠷⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣛⢙⣿⣿⣽⣿⣷⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣶⣿⣿⣿⣷⣿⡿⣿⣿⡿⠳⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⣻⣿⣿⣿⣷⣾⡿⠛⠁⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣿⣿⢿⡿⠋⠑⠒⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⠻⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠒⠛⠛⠛⠋⠉⠙⠛⠛⠛⠓⠲⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⢩⠄⢀⢤⣀⡠⢆⣀⣰⢢⣀⡰⢆⣀⡴⣄⣀⠤⠀⡠⡌⠙⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣁⣀⣴⣏⡅⢨⢭⢸⠥⠅⡨⠤⢅⠸⠀⠇⡼⠨⠅⠯⢭⢨⠭⡅⣯⡵⠤⣄⣈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⢘⠉⠀⠀⠀⠘⠃⠀⠋⠀⠈⠁⠀⠈⠁⠀⠈⠁⠀⠉⠀⠈⠉⠀⠘⠁⠀⠀⠀⠨⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⢠⣾⣭⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⣙⣦⡀
⠀⠀⣴⡿⠋⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠙⢷⣄
⢀⣾⠋⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠻⣆
⣼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢳⡄⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⡼⠃
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠻⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠤⠶⠖⠛⠉