Neptune Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔⣖⣒⣶⠶⢤⣄⣰⣄⡀⠀⡀⠀⠀⠈⠀⢀⣤⠒⢌⠄⠉⠳⣶⣄⠀⠀⡀⠀⠀⠀⢀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⣠⣴⣟⣿⣿⣿⣿⣿⣷⣾⣿⣉⠹⣿⡄⠃⢀⠀⠀⢀⡛⠉⠳⣌⠁⢄⠀⠀⠙⢳⡀⠀⠀⠀⢰⠛⠁⠠⠚⢉⣿⣦
⠀⠀⠀⠀⢰⡟⠛⢟⣯⡙⢿⣿⣿⣽⣿⠿⠿⠟⣹⣿⡀⢈⠖⠀⠀⠈⠢⡀⠈⠓⢦⡙⠲⢤⣐⡇⠀⠀⠀⠤⠖⠁⠀⢐⣿⣿⣿
⠀⠀⠀⠀⣰⣏⣴⣿⣿⣧⣌⣭⠙⣿⡛⢉⣿⣶⣿⣿⣷⡛⠀⠀⠁⠀⠀⠈⠢⡀⠀⠈⠑⠢⣬⡇⠀⠀⠀⠀⢦⣤⣶⡩⢐⡽⠃
⠀⠀⠠⣤⠺⠁⣹⣟⣭⣿⣿⡿⣿⣿⣷⠟⢻⢿⣿⣽⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⢶⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒
⠀⠠⣾⡋⢤⣴⣼⣿⣗⢈⣥⠄⠈⡉⢠⡄⠀⢸⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠶⠚⠁⠀⠐
⠀⠀⠀⠉⠙⠻⢅⠈⣻⣿⣷⣾⣼⣧⣿⡻⣻⠿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢈⣹⣿⣿⣿⠞⠋⠑⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡂⠂⠐⢀⢐⣦⣄⡀⠀⠀⠠⣤⣀⣰⣧⡀⣿
⠀⠀⣀⣤⢶⣶⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠓⠂⠀⠀⠀⠄⠀⠂⠛⢛⣦⡀⠀⠱⢼⣃⣀⠴⠃⠄
⠀⠠⡿⠛⠻⠛⠛⠁⠀⠀⠀⢀⣴⡂⡀⢠⣿⣶⣄⠀⠀⠀⠀⠛⠛⠻⣾⠙⠂⠚⠛⠋⠶⢉⠻⠟⣷
⠀⠀⠉⠻⣷⣦⠞⠀⠀⠀⢠⣍⣭⣿⠻⣴⠗⢾⣿⣷⠀⠀⣀⣀⡀⠀⢀⡀⣀⡀⠀⠀⠀⠈⡁⣀⣿⡀⠀⠀⢀⣤⣶⣒⣒⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡏⣽⡃⣤⣶⠋⠉⣿⠇⠀⢹⣿⣿⣿⣟⣽⣿⣻⣷⣬⣽⠷⠯⢿⣿⠁⠀⢰⡿⠋⠉⣩⣭⣍⣻⣧
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠹⢿⣿⣾⢿⣿⣿⣤⣴⡟⠀⠀⠀⢀⢨⣭⣽⣛⣉⣄⣤⣄⣠⣀⣡⣬⠏⠀⠀⢸⡶⠊⠉⠁⠉⠙⠛⣿
⠀⠀⠀⠀⢰⣿⣯⢳⠀⠀⠀⠀⠀⠠⣼⣿⡿⠿⠋⠀⠀⠀⠀⠀⠹⢤⣤⣉⣉⣉⣉⣩⣭⣿⡿⠋⠀⠀⠀⡘⢿⣿⣿⣿⣿⣭⣿⠟
⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠚⠛⠛⠛⠛⠓⠒⠲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣭⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠈⠉⠙⠛⠿⣝⠒⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀⠀⠀⠀⠀⠻⣍⣉⣭⠤⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⢙⣛⣛⣛⣛⣛⣋⣉⣭⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢣⡈⠉⠙⠓⠲⠤⢤⣤⡤⠴⠚⠁⠀⠀⢀⣀⡤⠴⠒⠛⠉⠉⠉⠀⠀⠀⣴⠶⠶⠶⠶⠚⢳⡀
⠀⠀⠀⠀⠀⣠⣏⣀⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀⠀⣠⣤⠤⠤⠤⠤⠴⠏⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠷⠦⣬⣉⣉⣀⣀⣀⣠⣤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠦⠤⠤⣄⡀⠀⠀⠀⠀⢀⣠⠤⠼⣆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠛⠛⠉⠉⠉⠉⠉⠛⠛⠒⠦⢤⣀⡀⠀⠳⢤⣀⣀⡴⠋⠀⠀⠀⠸⡆
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠓⠶⠤⣤⣤⣀⣀⣀⣠⣤⠴⢿
⠀⠀⢸⠧⠤⠤⣤⡤⠤⠴⠖⠚⠉⠀⣠⠞⠉⣷⠀⠀⠀⢀⣠⡤⠖⠚⠋⠉⠉⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡇
⠀⠀⣾⠀⠀⠀⢀⡤⠴⠶⠶⠶⠖⠋⠁⠀⣰⠃⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠓⠶⠤⠤⠤⠶⠒⠒⠛⠉⠉⣠⣷
⠀⠀⣿⣀⠀⠀⠈⢧⣄⣀⠀⠀⠀⠀⣀⡴⠃⣠⠜⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠀⠉⠙⠦⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⣿
⠀⠀⢿⠈⠉⠓⠦⢤⣄⣉⣉⣉⣉⣭⠥⠖⠋⠁⠀⠀⢀⡤⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠀⠀⠀⢀⡿
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣀⡀⢀⣀⣠⠴⠚⢩⡇
⠀⠀⠀⣧⠀⣀⣠⠤⠖⣒⣛⣛⣉⣙⣛⡓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⣼⠁
⠀⠀⠀⠸⡏⠁⣠⠖⠋⠉⠁⠀⠀⠀⠉⠉⠙⠲⠦⣍⡓⠦⣄⡀⠀⠀⠘⠶⠤⣤⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⢩⠇
⠀⠀⠀⠀⠹⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠉⠛⠲⠦⠤⣤⣤⣄⣀⣠⣄⣤⣤⠤⠶⠖⠛⠉⠀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠹⣤⠶⠚⠋⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣖⠛⠉⠉⣩⠏
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠈⠳⢤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠉⠛⠒⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠉⠙⢲⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⣠⠞⠋⠛⠲⣄⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⡤⠟⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣄⣀⠀⠀⠈⠙⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⣤⣤⣄⣠⣤⣤⡤⠤⠶⠚⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠷⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠤⣄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈⢣⢀⠔⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⢀⡀⠀⡏⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⢇⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⢸⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠓⠒⠒⠚⠦⣄⣀⣠⡴⠧⠼⢦⣀⣀⡴⠏⠤⠤⠤⠽⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠘⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠇⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠒⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠒⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢀⣠⠴⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⢤⣀
⠀⠀⠀⢠⠖⠉⢀⡤⠖⢿⡖⠢⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠔⠒⠒⣺⠗⠦⣄⠈⠓⢦
⠀⠀⢰⠋⠀⡰⠋⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⢳⡀⠈⢳
⠀⢀⡏⠀⢸⡇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣷⠀⠈⣇
⠀⢈⡁⠀⠸⣇⡀⠀⠀⠀⠀⠀⠻⣯⡐⠒⠒⠒⠢⠤⠤⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⣀⡿⠀⠀⣻
⠀⡴⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠳⡄
⣸⠁⠀⣠⣤⡀⠈⠉⡧⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠙⠛⠛⣚⣳⡾⠛⠁⠀⠀⠀⠀⠀⠀⠰⡏⠉⠀⣀⣤⡀⠀⢹
⡏⠀⢰⡏⢧⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣦⣤⣤⣤⣤⣶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⠏⣷⠀⠈
⠳⣤⡼⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠿⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠛⠛⠛⠓⠲⠦⣼⡇⢸⡇⣿⠀⣿⡤⠶⠒⠛⠛⠛⠛⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⣹⠟⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⠷⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⡤⠴⠞⠋⠁⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣄
⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠛⠉⠁⠘⣧
⠀⠀⠀⠀⠀⣰⣏⣀⣠⣤⡤⠶⠚⠋⠉⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆
⠀⠀⠀⠀⣾⣀⣀⣀⣀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⠒⠛⠛⠋⠉⠁⣷
⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠛⠉⠉⠉⠉⠛⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⠤⡿
⠀⠀⠀⠀⣯⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠖⠛⠋⠉⠉⠙⠛⠓⠶⠦⢤⣤⣀⣀⣀⣀⣀⣠⣤⢴⡞
⠀⠀⠀⠀⠀⠀⠻⣟⠓⠒⠶⠶⠶⠖⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣉⣿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠯⣤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡿⢿⠿⠿⣶⣶⡦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠿⠿⠿⠿⠧⠞⠠⠀⠀⠉⠈⠈⠹⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⣯⣥⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⣈⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠫⡿⠿⢿⠿⢿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣤⣦⣤⣶⣦⡀⠀⠀⠀⢽⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡆⠀⠀⠀⠀⠀⢀⣀⣀⠤⠿⢿⣿⣏⡿⣿⣿⣿⣿⣿⣿⣦⣤⠴⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⡀⢀⡀⣠⢼⢉⠉⠩⠭⠛⠄⠈⠁⠘⠿⡿⠛⢛⣿⣿⣟⠻⠛⢿⣿⣯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⡾⠟⠋⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠙⠣⣄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣆⣤⣤⡔⣂⣀⣀⣀⣀⣄⣤⣤⣀⢄⣀⣀⡀⣀⢀⡀⠀⠀⢀⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⣙⣽⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠹⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⣩⣄⣤⣤⣤⣴⣶⣶⣦⣤⣶⣄⣀⣀⡀⠀⣹⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡛⠉⣀⡐⢛⡶⡭⠀⣥⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣶⣶⣬⣴⣾⣾⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣻⡟⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠛⠿⠿⠋⠀⠀⠀⠀⣼⣏⡿⠿⠛⠁
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⠀⡀⣀⡀

⠀⠀⠀⢠⣴⣾⣿⣷⣦⡄⠀⠀⠀⣠⣤⡀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⠠
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡏⠐⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠓⡔⠁
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⣧⡀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢣⣠⠾⠃
⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠙⠻⢿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣴⣿⣿⣿⣿⣷⣄
⠀⠀⠐⠇⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣾⣿⣿⠟⠘⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣼⣿⣿⣿⡏⠀⠀⠈⣉⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⣿⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠻⠛⠛⠙⠿⡿⠿⠟⣻⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣰⣿⢿⠿⣛⣛⡻⠟⠋⠉⠉⠉⠙⠻⢿⡟⣷⣶⣤⣀⠀⠙⠆⢀⣬⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢿⣿⣦⣴⣾⣿⣷⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⡿⠘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⡆⣈⠈⣏⣛⢄⠀⢄
⠀⠀⠀⠀⠀⠀⣠⠎⣰⠟⣵⣾⣷⣬⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡙⡦⢹⣿⣿⠱⣄⠠⡀
⠀⠀⠀⠀⢀⠞⣡⣾⣯⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢹⣿⣧⠷⠠⣿⣿⡇⣿⣦⡈⢢
⠀⠀⢀⡴⢋⣼⣟⠻⢿⣌⠛⢿⣿⣿⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢠⣿⣿⠃⣾⣿⣿⣆⠑⢄
⠀⠀⠘⣄⠻⣿⣿⣳⣌⠛⠿⣶⣾⣿⠀⠀⠈⠃⢰⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣾⣿⡟⢠⣿⣿⣿⡿⠃⡴⠃
⠀⠀⠀⠈⠳⡈⢻⣷⣬⣿⣶⣤⣽⣿⠀⠀⠀⠀⠀⢰⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣸⣿⡟⡿⠟⢋⣴⣿⣿⣿⠟⡠⠊
⠀⠀⠀⠀⠀⠘⢦⡙⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣶⣿⣿⣴⣶⣾⣿⣿⣿⡿⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠑⣌⠻⣿⣿⣿⣿⣯⡻⣅⢀⡀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⡀⢀⣽⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⡿⠋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢿⣿⣿⣿⡆⠘⢷⣶⣷⣴⣀⣀⠀⡈⠻⣍⣿⣽⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⢿⣿⣿⣷⣷⣌⡻⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⢟⣩⣾⡿⠏⠿⣿⡟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠻⣿⣿⣿⣿⣿⣶⣶⣬⣭⣙⣋⣛⣻⣭⣿⣿⢺⣿⣿⣿⣶⣄⡿⢋⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡩⠀⠛⠿⢿⣿⠟⡠⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⣠⣶⠟⠁⠞⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠴⠄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠻⣿⣿⣿⣿⠟⣫⣭⢀⣭⣝⣿⣦⡿⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢿⣿⠃⣼⣿⡇⢾⣿⣿⣼⠏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⣿⣿⣿⣶⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣭⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣔⣠⡄⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢟⢿⡿⡿⡫⡪⢂⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠊⠫⠪⣪⠖⣁⡴⢀⢕⢔⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠵⡷⡳⢕⣕⢕⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠊⢔⠕⣵⡧⢑⢕
⠀⠀⠀⠀⠀⡜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢔⠵⠈⢂⡴⢃⠕⢁⠄⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠐⠅⢐⠕⢑⢄⠀⠀⡀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢕⠔⢁⢜⢕⠅⠀⠂⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁⢔⢕⣥⣡⣴⡁⡀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣀⠠⡀⠀⢀⡠⡠⠔⠔⠊⠀⠀⠀⠀⠠⡪⢟⣵⣿⣻⣽⣯⡾⠂⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣾⣶⡷⠕⠊⠀⠀⠀⠀⠀⠀⠀⢀⢈⣾⣾⣿⣿⣿⡿⡣⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⣿⣿⣿⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠎⠚⠛⠛⢻⣿⣿⣿⣿⣿⣾⣾⡢⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣯⣭⣽⣭⣭⣭⣩⣍⢉⠉⠉⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠠⡰⠝⢨⣶⣿⣿⣿⣿⣿⡿⠓⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠰⢪⡐⢭⣲⣔⣤⣾⣿⣿⣿⣿⣿⣿⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣤⣖⣒⢒⣈⡀⠌⣒⢪⣝⢦⢟⠫⢷⡻⣿⣿⡿⣟⢿⠫⠁⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⢍⠀⠀⠈⠀⠀⠀⠀⢀⡤⠐⠉⠛⠋⠑⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠂⠉⠉⠉⠉⠓⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⣀⣽⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⣤⣄⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣭⡵⠖⠋⠉⠀⠀⢈⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠉⠀⠀⠀⠒⠒⠒⠉⠉⠁⠀⠀⠀⢀⡠⠄⠊⡡⠔⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣉⠁⠒⠤⠤⡤⢀⣀⣀⠀⠀⢀⠀⠤⠄⠒⢊⣉⠡⠄⠂⠉⠀⢀⡠⠞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠉⠑⠒⠒⠂⠀⠀⠀⠀⠀⠐⠒⠒⠈⠉⠀⠀⢀⠀⠀⠀⠈⣀⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⠉⠀⠒⠒⠒⠠⠤⠤⠤⠤⠤⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠰⠭⠔⠋⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢖⣈⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠤⠬⠃⡀⣀⡀⠤⠐⣀⣉⠤⢀⣠⠄⢒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠠⠤⢀⡀⠉⠉⠀⠀⠒⠒⠂⠈⠉⠉⠁⢀⣀⣤⠒⠉⠀⠀⠀⣀⠟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⠀⠀⠈⣩⢉⡘⠛⠛⠛⠛⠀⠈⠉⠀⠀⠀⠑⠒⠒⠂⡉⢀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠉⠉⠒⠒⠂⠀⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠂⠉⠉⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡠⠤⠤⢀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠤⠄⢀⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠐⠀⠐⠂⠀⠀⢀⣠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡆⠀⣀⡀⢀⣀⠀⣰⡄⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢷⠁⡟⠒⠁⡌⢈⠆⡜⡀⢸⢠⡇⢸⠁⡇⢴⠒⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠋⠁⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠉


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

⢀⡄⣰⠀⡄⠀⠀⣠⣠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⡀⠀⠀⢀⢀⡄⣀
⣼⠃⢿⠃⢻⡄⣼⣻⣟⠛⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢿⠆⢿⡄⣴⣿⠿⠛⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢿⠀⢸⠀⢸⡟⣿⣧⣙⢟⣸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⢛⣣⣤⡴⠄⠀⠀⠀⠀⢿⠀⢸⠀⢰⠿⣷⣯⡙⠷⣺⠁⠁⠀⠀⠀⠀⠀⠀⠀⣀⡰⠟⣯⣠⣤
⠈⠳⢾⡶⠋⠀⠈⣯⡈⠀⢀⢙⡖⠛⡂⠒⠲⢤⠞⣡⣤⣾⠞⠛⠉⠀⠀⠀⠀⠀⠀⠈⠳⣼⡦⠞⠀⠈⣏⠘⠁⠉⢛⡶⠒⠀⠐⠦⣤⠔⣉⣠⣶⠾⠛⠋
⠀⣴⡏⢱⠄⣀⣴⣿⣷⣤⡿⠟⢰⣾⣧⣤⣴⣶⡶⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⢱⠄⢀⣴⣿⣷⣤⣾⠟⢠⣾⣄⣀⣤⣤⣤⣼⠿⠋
⢠⣿⡿⣏⣾⣏⠀⠈⠻⠟⠀⠀⣾⣿⡟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡏⣤⣏⠉⠉⠻⠟⠁⠀⣾⣿⡿⠛⠛⠋
⣾⣿⠻⢹⣿⣿⡄⣠⣼⡷⢿⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢻⢻⣿⣿⡄⢀⣴⡶⢶⣾⢿⡿⠁
⠸⠧⠼⣼⠟⠛⣿⡋⢹⢀⣿⠣⠋⠀⠀⠀⣀⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⣼⠟⠛⣟⠋⢩⠀⣾⢃⠊⠀⠀⠀⢀⠀⠤⠤⣄
⠀⠀⠀⢿⢢⡀⣿⣿⡙⣴⡟⢀⡀⢀⡤⡊⢁⠄⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⡀⢟⣿⠀⣠⡟⢀⠀⢀⡠⠖⢅⠀⠀⠠⡀⠑
⠀⠀⠀⢸⣼⣷⣼⡿⠿⢋⣴⣏⢻⣕⠮⣊⣵⠥⠒⠉⠉⠉⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣧⣌⠻⡿⢟⣴⡂⢒⠍⠢⢕⣅⡬⠔⠚⠉⠑⠣⣄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣆⠳⣮⠋⢀⠔⡠⢄⠠⠐⠌⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣾⣿⣿⣶⣿⣿⣯⣄⠳⡎⠛⢅⠠⡂⠀⠀⠀⠀⠈⡆
⠀⣰⡿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⡦⠼⠓⠓⠺⢤⡉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⢧⡿⡾⠿⠿⠿⠿⢧⣼⣿⣀⠼⠷⠧⠾⢤⡋⠀⠀⠀⠀⡇
⣼⣿⢋⣥⣠⠄⠀⢀⣀⣤⡤⠄⠀⠐⠀⠀⠀⠀⡀⠌⢢⣠⠤⠞⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢁⣀⠤⠀⠀⣀⣀⣤⠄⠉⠄⠂⠀⠀⠀⠂⠙⢦⢀⣠⠜
⣿⢣⣿⡾⢉⣤⠾⠿⠛⡉⠔⡈⠀⡁⠀⣀⠄⠒⠈⡈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⣮⡖⠉⣀⣴⠿⠟⢋⠡⢊⠄⡈⠀⢀⡀⠦⢀⡀⠀⡆
⢸⣿⠓⣠⡿⠒⠒⣊⡡⠔⠊⠐⢁⣤⣾⠃⠠⠐⠠⢁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠓⢁⡾⠥⠖⠒⡈⠤⠂⠁⠀⣀⣶⠁⠀⠒⠀⢃⠀⡇
⢸⣻⣶⡇⢫⡍⠉⠁⠂⣀⡠⠖⣻⣿⣿⡷⣤⣀⣀⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⣴⡇⢻⠉⠉⠉⠐⠀⡀⠴⢾⣿⣿⡧⣄⣀⣀⡠⠞
⠀⠳⡻⣿⣦⣉⠒⡚⢛⣉⣤⣾⣿⡿⢋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡻⣷⣤⣐⠒⠒⢚⢋⣤⣼⠿⠿⢟⡔⠁
⠀⠀⠉⠺⢝⣛⠿⠿⠿⠿⣛⣫⠭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣟⡿⠿⠿⠿⠿⠿⣛⠫⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠛⠛⠛⠛⠒⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢭⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠈⠉⠙⠓⠻⣽⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀⠀⠀⠀⠀⠻⣍⣉⣭⠤⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣭⣭⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢳⡈⠉⠉⠓⠲⠦⠤⠤⠤⠴⠚⠁⠀⠀⢀⣠⡤⠶⠒⠛⠉⠉⠁⠀⠀⠀⣴⠖⠲⠶⠖⠚⢳⡀
⠀⠀⠀⠀⠀⣠⢯⣀⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⠴⠏⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠓⠦⣬⣉⣉⣀⣀⣀⣤⡤⠤⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⠶⠦⠤⣤⡀⠀⠀⠀⠀⢀⣠⠤⠼⣆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠛⠒⠶⢤⣀⡀⠀⠱⢤⣀⣀⡴⠉⠀⠀⠀⠸⡆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠉⠛⠲⠤⢤⣤⣄⣀⣀⣤⡤⠴⢿
⠀⠀⢸⠧⠤⠤⠤⠤⠤⠴⠒⠛⠉⢀⡠⠞⠉⣷⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⠉⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⣼⠀⠀⠀⢀⡤⠶⠶⠶⠶⠖⠋⠀⠀⣰⠃⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠓⠶⠤⠤⠶⠶⠒⠚⠋⠉⠁⣠⣧
⠀⠀⣿⣀⡀⠀⠈⠧⣄⣀⡀⠀⠀⣀⣀⡴⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⣰⠞⠉⠉⠁⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⣿
⠀⠀⢻⠀⠉⠓⠲⠤⣄⣈⣉⣉⣉⡭⠵⠖⠋⠁⠀⠀⢠⠤⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠚⠋⠉⠀⠀⠀⣀⡟
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣀⣀⣀⣀⣠⠴⠚⢩⡇
⠀⠀⠀⣧⢀⣀⣤⠴⢖⣚⣋⣉⣉⣉⣙⣛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⣀⣼
⠀⠀⠀⠘⡏⠁⡤⠞⠉⠁⠀⠀⠀⠀⠈⠉⠙⠓⠦⣌⡙⠲⢤⣀⠀⠀⠘⠲⠦⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⢱⠇
⠀⠀⠀⠀⠹⡞⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⠙⠒⠶⠤⠤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠚⠋⠉⢀⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠙⣦⠖⠛⠉⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠤⠶⠶⠶⠦⢤⡀⠀⠀⠀⠀⠀⣞⠉⠉⠉⣡⠏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠈⠓⢦⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠙⠛⠒⠶⠤⣤⣀⠀⠀⠀⠀⠀⠈⠙⢓⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⡴⠚⠉⠙⠲⢤⡀⠀⢀⡤⠤⠤⠤⢤⣤⣤⠴⠚⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⡀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⣤⣤⣤⣤⠤⠤⠶⠒⠚⠉⠁

⠀⠀⠀⢀⠔⠚⠙⢩⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠽⡿⣶⣤⡀⠀⠀⠀⠀⠀⣠⣆⣹⠉⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣶⣤⡀
⠀⠀⢀⡀⠀⠀⠀⠀⢘⢸⣿⣆⠀⠀⠀⠀⠀⠀⣀⡂⣋⠋⣿⣷⡀⠀⠀⠀⡞⠁⡉⠉⠢⣀⣬⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⡄
⠀⠀⠻⠀⢠⡄⠈⠤⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠰⠆⣏⡨⣾⣿⡇⠀⠀⠘⣧⣤⣀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠠⠶⢤⣷⣴⡼⣿⣿⡇
⠀⠀⠱⢀⠀⠀⠀⠐⠘⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⢰⣼⣷⣿⣿⠃⠀⠀⠀⠉⣻⣿⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠔⠃⢦⣿⠗⣿⡿⠃
⠀⠀⠀⠈⠢⢀⢱⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⣘⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢿⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠉⢠⣤⣦⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣤⣄⣀⣠⣤⣄⠀⠀⠀⠀⠀⠄⠀⢠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠲⠿⣷⡀⠀⠀⠀⠀⠀⠁⡠⢈⠝⢻⣿⣇⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠐⠒⠶⠖⠛⠻⢻⣷⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡿⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠺⣿⡇
⠀⠀⠀⠐⠲⠶⣶⣶⢶⣾⢿⡿⠀⠀⢠⠀⠀⠀⠀⡀⠾⢋⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠟⠁⠀⢀⠀⢀⡀⠀⣠⣤⣴⣿⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⢀⣸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠉⠁⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⢀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⡴⣔⡁⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢃⠀⠀⠄⠀⢀⠠⠀⠀⠀⠀⠀⠀⠔⠖⠚⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⡀⠂⠃⠀⠀⠁⢢⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐
⢀⠑⠚⠰⠦⠖⠁⠲⡤⢮⡆⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢀⠰⣠⠃
⠘⠈⠰⠐⠠⢀⠠⢶⠄⠄⠋⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡉⠰⠂⠂⠈⠒⠀⡈
⠸⡷⠄⠄⠀⠀⢲⣦⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠀⡄⠊⠠⠔⠁
⠀⠘⢤⡠⠔⠂⠀⢤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡄⠒⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠖⠀⠀⠀⠂⡀⢀⠱⡄⠒⠄⠤⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠁⠀⡠⠏⠀⠒⠀⠈⡠⣜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠔⠀⠡
⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠁⣐⢠⠀⠠⣅⣉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⢀⠀⠀⠄⠀⠀⠀⠉⠉⠉⠀⠃⠀⠀⠀⠀⠉⠔⠆⠀⠘⠄⠀⠈⣁⠋⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠔⠃
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠓⢲⣄⣠⠖⢛⣹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⡿⣿⠿⠿⢿⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠉⢀⣠⡾⠛⠁⣱⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⣀⠈⠭⠤⠐⠀⠈⠁⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⣀⣠⣴⡞⠛⠉⣀⡴⢞⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠋⠉⠀⣠⠴⢚⣥⠖⢋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⢰⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣵⣶⣯⠵⠞⢉⣠⣾⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠘⢦⡍⣄⢠⠤⠤⠤⠄⢒⣲⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠀⠀⠑⠒⠺⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣖⡲⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⡀⢀⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⣸⣫⡿⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠦⠐⠃⠈⠀⠉⠁⢅⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣇⣤⠀⢀⣴⣟⢕⣷⡆⠈⣆⠀⡀⠀⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠐⠀⡀⢀⠀⣈⠠⠀⢔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣣⠈⠚⢱⣿⣿⣿⠀⢸⠁⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠀⠀⠌⠠⠀⡱⠈⠆⠀⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠙⠤⡄⠀⠈⢹⢛⠿⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⡀⠘⠤⣉⡀⠜⠀⠀⢈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢷⡁⢠⣿⣦⣰⢋⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⠌⠂⠄⠀⠠⠄⢂⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠘⠛⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢱⢠⠢⠔⠖⠢⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠔⠂⢉⠟⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣤⠖⠀⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠠⠀⢂⠀⢬⣿⡄⠀⣠⠊⢀⢀⣀⠅⠀⠀⠤⢈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⢃⠀⡟⢦
⠀⠀⠀⠀⠠⠒⢉⠄⠀⠀⠀⠀⠀⠏⣀⠁⠀⠀⢀⡠⠀⠀⢎⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡏⠀⢠⠀⠸⣀⠤⡠⠀⠎⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠅⢪⠀⠀⠀⠀⠀⣀⢤⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠁⠀⣀⢄⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠬⠇⠀⠀⠀⢀⠑⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣉⠀⠀⠁⢲⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⣠⠀⠀⠾⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠴⢋⠁⣤⣤⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⣠⡖⢋⡧⢸⠁⠈⠙⠲⡄⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⢈⡠⢋⠝⢦⡀
⠀⠀⠀⠀⠀⢰⠏⢂⡈⠀⢨⠁⡀⠘⠃⡈⣧⠀⠀⠀⠀⢰⠇⠀⠂⠠⣄⠉⡉⢉⣉⡹⡆⠀⠀⠀⠀⡼⢃⠄⠂⡀⠤⠤⠊⡠⠊⢹⡄
⠀⠀⠀⠀⠀⢾⠀⢅⡨⠀⢀⠤⡄⠻⠃⠀⢸⠀⠀⠀⠀⣿⠤⠤⠄⠒⠃⠘⠋⠘⠒⠂⣻⠀⠀⠀⠀⣟⣁⠄⢊⡀⠄⢂⡡⠔⢊⢵⡇
⠀⠀⠀⠀⠀⠸⡆⡀⡄⠀⠘⠶⠋⠀⠤⢀⡞⠀⠀⠀⠀⠸⡦⠴⠀⠚⠀⠫⠭⠥⠤⢠⡏⠀⠀⠀⠀⢳⡦⢊⠅⠂⠉⠐⠒⡈⠐⣹⠇
⠀⠀⠀⠀⠀⠀⠙⢮⡁⠀⠁⠀⠤⢀⣠⠞⠀⠀⠀⠀⠀⠀⠙⢮⣭⠭⠥⠤⠶⢐⡶⠋⠀⠀⠀⠀⠀⠀⠻⢵⣨⠔⡂⠉⠍⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⢞⡉⠒⠀⠤⠤⠬⠓⢦⠀⠰⠁⠄⡐⢉⣻⣟⣉⠁⠀⠂⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⡴⠋⣡⠀⠄⣒⡢⠉⠳⣄
⠀⠀⠀⠀⠀⢰⡇⠀⠉⠒⠤⢀⣀⣐⠍⣈⣧⠈⢄⠡⠑⢄⠑⢬⣉⣉⣉⣉⣉⣉⠉⠼⣇⠀⠀⠀⠀⡼⢱⠄⠀⢀⠂⠁⠑⠈⠛⠹⡆
⠀⠀⠀⠀⠀⢸⠉⣑⡒⠀⠤⠤⠤⠤⠤⠀⢾⠀⠀⠑⢄⠙⠟⠢⣄⠀⠲⠄⡀⠰⠐⠒⣿⣷⣄⠀⠀⡇⠀⠠⡠⠌⠀⠀⠂⠘⢃⠀⡇
⠀⠀⠀⠀⠀⠘⣆⠓⡁⠄⠀⠀⠀⢀⡀⢰⡏⠀⠀⠀⠀⠹⡶⢌⡁⠸⠃⡀⠠⠉⡉⠀⠛⢀⠙⠱⡄⢱⡀⡑⠉⠂⠀⠰⣂⢠⠈⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠣⣄⠐⠀⠀⠐⣢⡵⠋⠀⠀⠀⠀⠀⠀⠈⠶⣌⡳⠶⣤⣁⣀⠀⠛⠁⠀⠈⢀⠄⠀⠙⢦⣀⠐⠀⠈⢀⣨⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⢤⣤⣀
⠀⠀⠀⠀⠀⠀⣰⠊⠀⠈⠉⡝⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⡰⠛⠡⠡⠈⢈⡤⠸⢛⢦⠀⠀⠀⠀⠀⢀⡴⠯⠥⠬⠥⠤⠔⢋⠷⣄
⠀⠀⠀⠀⠀⢰⢣⠀⢤⠐⠁⠀⢀⡬⠛⠼⣷⠀⠀⠀⠀⢸⠃⡀⠰⡅⠴⢀⣀⢣⠱⠬⣇⠀⠀⠀⠀⡾⠬⣉⣑⠒⠀⠒⢊⣁⣠⢼⡆
⠀⠀⠀⠀⠀⢸⠀⠁⢰⠉⠉⠲⡌⠒⢦⠀⢸⠀⠀⠀⠀⢟⠢⡍⠀⡊⠉⠁⢎⠘⠲⢒⡿⠀⠀⠀⠀⡯⢑⣒⠂⢀⣩⡽⠴⢒⡪⠭⡟
⠀⠀⠀⠀⠀⠘⣆⠀⠀⢡⠀⡰⠁⠀⠘⣠⠏⠀⠀⠀⠀⠸⣆⠃⠈⢀⠆⢀⠀⠉⠉⣴⠃⠀⠀⠀⠀⠹⣆⢀⠀⠉⠁⣒⡒⠉⠀⣺⠃
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣘⡘⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠣⣤⣀⡠⣈⣳⡽⠞⠁⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⣠⡬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠛⢲⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣠⡞⠁⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⠃⢀⣼⠏⠀⠀⢀⣠⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣜⣦⡔⡵⠃⠀⣠⡾⠋⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠈⠁⠀⠙⢷⣤⣾⠋⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⡀⠀⡤⠤⢄⣄⣈⢑⠆⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡡⠤⠀⢠⠄⠈⠀⢘⡃⡼⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⢶⡇⠀⠀⠪⠄⠪⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣪⡤⠾⠉⣄⠀⢀⠀⠀⢈⣩⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠋⠌⠀⠀⠂⠰⠎⠙⠢⠿⢚⡿⠋⢙⡴⠛⠳⡄⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⠖⠁⡐⢄⡙⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⠋⠀⠀⠀⢳⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠇⣀⠀⢈⢶⡓⠀⠀⠀⠀⡄⠀⣰⠏⠀⠀⢀⠃⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⡰⢋⡾⡷⠊⢘⣷⣄⣀⠀⠀⢻⡾⠃⠀⠀⠀⡂⣠⣄⠀⠀⠀⠀⢳⡀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢞⡵⠋⠀⣧⠀⢀⡿⣍⠉⠁⢀⡞⠁⡐⠀⠀⢰⠋⢸⡆⠁⠀⠀⠀⠀⢳⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⡟⠀⠀⠀⢸⣀⡼⠃⢹⣄⣠⠟⢀⡞⢠⠀⠀⣸⠠⠿⣿⣄⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⡇⡀⠀⠀⣸⠏⠁⢀⠆⠛⢁⣴⠏⣰⠃⢠⠀⡏⠀⣰⣿⠙⣦⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⠴⠛⠲⢤⣼⣀⠒⠛⢁⡴⠃⢀⡏⠀⣷⣾⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠒⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡀⠈⠈⠙⠂⠀⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠘⠳⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⣠⠀⠈⠏⠀⠀⠀⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠄⠀⠄⠒⢁⠀⠀⠀⠐⠊⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⠀⠀⠀⠀⠐⠔⠀⠤⠋⠀⠀⠊⠙⡇⠀⠐⠰⣦⠸⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠠⡄⣀⠀⠈⠃⠀⠜⠒⠃⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠱⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⣁⠙⠃⠀⠀⠀⡠⠀⠀⠀⢤⡆⠀⠀⠀⡀⠒⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘
⠀⠀⠀⠀⠀⠘⣦⠀⠐⠁⠈⢧⠀⠀⠀⢰⠇⠀⠀⠈⠁⢿⡄⠀⠀⠀⣀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⡇⠀⢻⣀⡀⠀⠀⢀⡴⢚⠁⠀⠔⠋⠀⠈⠉⠻⣻⣄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡑⠂⡊⠀⠢⠟⠫⠉⠁⠊⠐⠻⠁⠀⠀⠀⠀⠀⠁⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⢀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡀⠆⠀⠀⠉⠛⠃⠠⣤⡐⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⣁⠀⠈⣀⠀⠠⣀⠈⠂⠀⠀⠀⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢸⡉⠙⢿⢥⡀⠀⢀⣀⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⠀⠀⢙⠟⠀⠐⠠⠉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠈⠉

⠈⠓⠂⠀⠀⠛⡯⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⢠⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⣀⣀⡀⢠⡤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢢⠀⠀⠐⠂⠄
⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀
⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠂⠀⠒⠀⠀⡀
⠀⡀⠀⣀⡀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⡡⣤⡀⠈⠉⠉⢠⠉⠳⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⢟
⣥⣰⣀⣉⣁⣀⣞⣋⣲⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣿⣲⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⡄⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠑⠛⠃⠀⠀⠀⣀⠄⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⡠⠔⠚⠭⢭⡉⠓⠦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠁⠀⠀⠀⢀⠾⢷⣴⡤⣀⠐⠈⢑⠢⣌⢢⠀⠀⢳⡤⠚⢲⡀⠒⢄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡀⠰⠁⠀⠁⠄⠀⣶⣦⣼⣿⣿⠂⢀⡵⠬⠍⠱⡀⢨⣀⠀⠀⠉⠓⠿⠷⣄⡁⠢⠙⡇⠀⠌⠀⠀⠀⠙⢦⢀⡣⠀⠰⠁⠀⢠⣭⣳⡀⢠⣏⣀⣋⣽⡄
⠀⠀⠤⠾⠁⡇⠴⢄⠀⡘⠀⣿⣿⣏⣽⣿⠇⠸⣄⠀⠀⡀⠀⢸⠿⣿⢿⣷⣶⣤⣀⠈⠙⠦⣌⡇⠀⢃⠀⠀⠀⠀⠈⡟⡞⠀⠸⣀⠀⣿⣿⣿⠃⠐⠈⠓⠊⣉⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠙⠛⠛⠉⠀⠀⠈⢡⡌⠀⠀⠈⢆⠀⠀⠛⠻⢿⣿⣷⣦⣀⡜⠀⠀⠀⠳⠄⣢⣀⣾⡛⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣦⣀⣀⣈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠯
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⠿⢿⢟⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣻⣛⣿⣟⣛⣿⣟⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢤⡀⠀⠀⠀⠄⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣽⣿⠂⠀⠀⠀⣰⡄⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⡤⠀⢀⢠⡜
⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠁⠀⠀⠘⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠃⠓⠋⠁
⠀⠀⢀⢀⡀⠀⠁⠀⠀⠀⠀⣀⢘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠒⠲⠖⠊
⠀⠀⠼⣿⠷⠀⠀⠀⠀⠀⢨⡀⢰⠹⡄⠀⠀⠀⠃⢐⡄⠀⠀⢤⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢻⣖⠚⠖⠓⠉⠀⠀⠀⠸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠈⠁⠄⠀⠀⢀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢽⡿⠄
⠀⠨⠄⠀⠀⠀⠀⠆⠀⠈⠛⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⢤⠀⠁⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄⡐⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⢹⠀⠀⠀⠀⠘⣄⠀⠀⠀⡀⠀⢀⣄⠀⠀⣿⡟⠡⣾⣿⣷
⠀⠀⠀⣼⣿⣅⠀⢀⠄⠀⠀⠀⠀⣀⡖⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈⠙⠁⠀⠱⣦⣄⠀⡉⠁
⠀⠀⡜⠘⠁⠀⢰⠁⠐⣄⣀⡤⠚⡡⠀⠀⣤⡤⠀⠀⠀⠀⠀⡄⠀⢸⠉⠐⢢⣤⡀⠀⠀⠈⠀⠀⡀
⠀⠀⡂⠀⢂⠀⠈⠓⠒⠋⠉⠈⠁⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢸⣠⠖⡋⢀⠙⢄⠀⠀⠀⠿⠃
⠀⠀⠠⠀⡂⠀⠀⠀⠀⠀⡔⠉⠈⡁⣐⡀⠀⠀⠀⠈⠀⠀⠀⣠⣀⠈⠣⡀⠀⠊⠀⡈⠢⣀⣀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠐⠀⡀⡀⠀⠀⠀⠰⠆⠀⠀⠛⠇⠀⠀⠙⢆⠈⠢⢃⣔⠁⠈⢢⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⡨⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠚⠹⡀⠙⣄⡠⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢶⣾⣄⠀⠀⢰⠉⠢⡀⢈⠦⠜⡆
⠀⠀⠀⠐⠦⣠⡠⠔⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠑⠢⢬⣣

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠐⠚⢻⣯⠀⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⣤⣄⣹⡾⠛⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⣀⠀⠀⢼⣿⠖⠀⠀⣐⠻⣮⣿⢹⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣿⠴⠁⠰⣿⣶⠀⠿⠗⠉⠀⠻⠁⠛⠯⠹⢿⣿⡿⣷⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣝⣯⣟⣏⣔⣠⢦⣼⡿⡄⠀⠀⠀⠀⠀⠆⠀⢀⠀⠉⣉⠂⣽⣷⣤⣤⣆
⠀⠀⠀⠀⠀⠀⢰⡿⣼⡿⢾⣿⣿⣿⣿⣿⣿⡯⠎⠈⢠⣶⢊⠜⠀⠀⠀⢈⠅⠀⢸⣧⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠒⠁⡯⣀⣼⣿⣿⣹⣿⣿⡿⠀⡀⠀⠈⠁⠈⠀⠀⠠⠈⠁⠀⠀⣴⠎⠙⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⢢⡈⣹⣿⣿⣿⣿⣧⡀⠀⠀⢀⣶⣄⣠⡴⡆⠀⣤⠒⠂⠀⠘⠀⠁⣤⣿⠁
⠀⠀⠀⠀⠀⠀⢷⡞⠻⣿⢟⡺⣿⠿⣿⣷⣧⣴⢲⣬⣽⣿⣿⠁⢁⡚⠀⠀⠀⠀⠁⠀⢀⣽⡏
⠀⠀⠀⠀⠀⠀⠸⣟⠆⠺⣮⢱⣊⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⢂⣶⣿⣆⡀⠀⢐⣧⣄⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠁⠛⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⡿⣭⠟⠉⠀⠀⠀⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣁⠀⠀⠁⣜⡛⢿⡿⠐⠀⠀⠀⠘⣿⡷⠁⠆⠰⠀⠤⠀⣀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡃⠈⠙⠑⠻⠿⣄⡀⠀⢐⣶⣿⣤⣐⣤⢀⣂⣤⣿⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣒⣦⠠⣰⣦⣥⢉⣼⣿⣟⢻⣿⣿⣯⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠺⠯⠍⢟⣶⣿⡫⠴⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡣⣽⠆⣏⠊⠀⠀⠀⠀⠀⢀⡄⠒⠐⢲⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠥⠤⠇⠙⠀⠋⡈⠀⠀⠀⠀⠀⠘⣿⣶⣾⣩⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⢀⣀⣤⠤⢤⣤⡴⢋⠉⢉⠟⢢⡒⢲⠸⡇⠀⠀⠀⠀⠀⠀⠠⠉⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⡴⠚⠁⠀⠀⠀⠀⠰⣧⣇⠀⠻⡄⡠⠤⠰⡄⡎⠀⠀⠀⠀⠀⡰⠡⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠉⢿⣰⣶⠊⠤⡬⠡⢤⡏⠓⢤⡀⢀⡼⡱⡟⡜⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⢷⡀⠀⠀⣰⠁⠀⠀⠀⠀⠙⢻⠃⠀⠀⠀⠀⠃⠀⠀⠹⠛⠶⣕⡱⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠙⠦⣴⣳⠤⢄⣀⣀⠀⠀⠀⢀⠄⠀⠀⡴⢣⠀⠀⠀⠀⣀⣈⢳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢉⣙⡲⠦⣤⣄⣹⠆⠸⠀⠉⠛⣦⡞⠀⠙⠗⠉⣠⣿⣤⢾⣇⣰⠋⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡜⠉⠋⣿⠀⠉⠀⠀⠀⠀⢀⣯⣉⣛⠲⠦⣾⣭⡀⠀⠀⢙⣧⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠸⣄⠀⢀⣀⡤⠶⠛⠛⢛⡉⠙⠓⠲⠦⣭⣙⡚⠷⢯⠁⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⣀⠀⠀⣠⣴⣛⣙⣒⣒⣌⠭⠭⠒⢂⣈⡤⠖⠊⠁⠀⠉⢹⣛⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣨⣽⣟⣉⣉⣁⡀⠤⠤⠴⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠶⠦⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣁⡀⣀⠹⢤⣅⣿⣦⣴⣴⢶⣤⣶⣅⣥⠸⢁⡀⣄⡠⠀⢀
⠀⠀⠀⠀⠀⠑⠀⠑⣆⣀⠀⠩⠻⠐⢢⡟⠙⢦⠀⡿⠗⢴⠖⢻⣧⡐⠼⠩⠁⢀⣄⡶⠁⠐⠃
⠀⠀⠀⠀⠀⠀⣆⣀⠬⡻⠃⣀⢀⣽⢟⣁⠀⠀⠀⠀⠀⠀⠀⠀⣙⢿⣅⢀⡀⠛⡨⢄⣀⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣼⣿⠹⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣤⡀
⠀⠀⠀⠀⠀⠛⠓⣖⡀⠌⣿⣷⠀⠀⠀⠀⠒⣶⣤⠊⢠⣴⡶⠂⠀⠀⠐⢷⣽⣏⠄⣑⡖⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⡿⢤⠆⠀⠀⠀⠉⠀⠀⠂⠈⠁⠀⠀⠐⣤⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠹⡿⠛⠉⠀⠀⢠⡀⠀⠂⢀⠒⠀⠀⡀⠀⠀⠈⠱⣮⣿⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢽⣧⡀⠃⣠⢀⢊⠁⢠⠮⠉⠵⠄⠺⡇⡄⢠⢀⣴⣿⣿⠗⠈
⠀⠀⠀⠀⠀⠀⠰⠲⢶⣿⣿⣿⡟⡃⠀⠀⢢⣧⡀⠀⠀⠘⣀⠈⠀⠀⠚⢿⣿⣿⣷⡶⠲⠂
⠀⠀⠀⠀⠀⠈⣋⣠⠞⠋⠋⢩⣿⢿⡄⠉⠘⠈⠶⡂⡸⡈⠁⠀⣠⡶⢠⣾⡿⡯⠛⢦⣈⣋⢀
⠀⠀⠀⠀⠀⣉⢉⠁⠀⠀⠴⣿⠷⠚⠁⢀⣀⣲⣶⡿⢰⢁⢰⣞⡉⠻⠎⢻⡷⠄⠀⠀⢉⣉⡡
⠀⠀⠀⠙⢦⣈⣿⠉⡑⢰⣾⣿⠷⣄⣸⣿⣿⠋⣿⠤⠈⠓⢹⣿⡏⢁⣴⢾⣿⣶⠀⡉⢹⣏⣤⠞⠁
⠀⠀⠀⠀⠀⠘⢛⡼⡛⠉⣸⢡⣴⣌⠛⠙⠁⠉⢸⡆⢚⡌⣿⣿⠓⡫⣽⣦⢻⠻⠻⡻⣜⠛
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣸⣏⡙⣇⡀⣀⣤⣭⡁⢀⡇⡿⠋⠀⠊⣉⣿⣸⡇⠀⠀⠈⠁
⠀⠀⠀⠀⣀⡀⠀⠀⣀⣠⢠⡁⣄⢢⠘⠃⣸⣟⠛⠚⠿⠋⣡⡄⠛⣠⢂⣄⣩⢠⣀⣀⠀⠀⣀⡄
⠀⠀⠀⠤⠬⠟⢁⡉⠀⣀⣼⠟⠘⠁⠁⠈⠁⠈⠀⠀⠀⠀⠈⠋⠀⢁⡟⠩⢿⣄⡀⠈⣁⢙⠯⠤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃

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

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣤⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠿⠛⣛⠫⠭⠉⡀⢶⠀⠀⠀⠀⣼⣏⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠶⠶⡿⢀
⠀⠀⠀⠀⢠⡖⣶⣿⣿⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⢿⣟⢻⠀⡀⠀⠆⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡞⠄⠀⠀⠀⠀⠀⠀⠹⢞⡖⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠰⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠄⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠉⠐⠠
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⠀⠀⠐⡄⠀⠀⠀⠀⠀⢸⣿⣭⡴⠶⠒⠛⢻⡆⠀⠀⠀⠀⢸⣿⣿⠀⣀⡤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣀⣠⡾⠀⠀⠀⠀⠀⠸⣿⡛⢉⡀⠀⠀⠈⡇⠀⠀⠀⠀⣴⢿⣿⣟⡀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠘⢿⣿⣦⡀⢰⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠷⣿⣷⣦⡤⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡤⠀⠀⠀⠀⠀⠀⢀⣄⣠⠄⢠⣤⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⣻⢿⣿⠀⠀⠀⠀⢀⣤⣶⣖⡒⠄
⠀⠀⠀⠀⠀⠀⠸⠿⢾⣶⣋⠐⠚⠀⠀⠀⠀⠀⠂⣠⡝⠀⠘⠛⣃⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⣴⠎⢻⡶⠃⠀⠀⠀⠀⣾⣿⡿⠖⠈⠂⢠
⠀⠀⠀⠀⠀⠀⠻⣿⣟⣳⣦⠶⠒⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⠀⠛⢿⣦⠀⠀⠀⠀⠀⠀⠁⢠⢻⣧⠶⢛⡕⠀⠀⠀⠀⠀⢻⣿⣷⣬⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠶⠖⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠁⠰⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⢎⠓⡚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠈⠑⢦⡄⠂⠀⠀⠀⠀⠀⠀⣴⠊⢉⡠⠊⠉⠳⣄
⠀⠀⠀⠀⠀⢀⠔⡁⠀⡴⣀⠾⠉⠠⣀⠾⢹⠂⠀⠀⠀⠀⠀⢸⠃⠂⠁⠐⠀⠠⠠⢼⡖⠦⠄
⠀⠀⠀⠀⠀⡌⠀⠐⠃⠋⠁⢀⣨⣖⡵⢁⣿⠀⠀⠀⠀⠠⠔⢻⡤⠖⣀⡔⠀⠀⠑⠄⠓⢀⡀
⠀⠀⠀⠠⠄⢲⠀⠑⠴⠒⣺⣉⡴⠊⢀⡿⢁⡀⠀⠀⠀⠠⠤⠘⠣⣤⡤⠄⠰⢀⣠⠏
⠀⠀⠀⠀⢨⠁⠙⠺⠮⣵⡿⠋⠀⡠⢋⠺⣶⠀⠀⠀⠀⠀⠐⠈⠀⠨⢉⠛⠋⠍
⠀⠀⠀⠀⠸⠀⠳⠀⠐⠀⠀⢀⠔⠀⠈⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠃⠲⠷⡔⠀⠄⠹⡄
⠀⠀⠀⠀⠀⢀⢠⢠⡇⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⠀⡀⠁⢀⠈⠀⣁
⠀⠀⠀⠀⠠⠠⢿⢿⠏⠀⠀⢊⣉⡀⢗⠃⠀⠀⠀⠀⠀⠀⠸⡄⠏⠵⢾⡏⠙⣀⣴⣾⠇
⠀⠀⠀⠀⢠⠄⠛⢉⠑⠛⡍⠀⢉⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡃⠘⠃⠂⢀⡼⠋
⠀⠀⠀⠀⠀⠲⣀⠀⠀⠐⠡⠄⠀⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠇⠦⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣀
⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⡀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠓⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠐⠊
⠀⠀⠀⠀⢰⠀⠄⠌⢤⡁⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⢠⡄⠇⠀⠀⣀⢴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠜⠀⢸⠃⠳⠀⠐⠠⠆⠃⠀⠀⠀⠀⠈⠳⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠐⢄⣀⡸⠀⠀⠆⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⡄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠂⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠁⠐⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⠀⢀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡇⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢴⡀⠀⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢨⠀⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠚⠀⢰⠶⠂⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⡠⢔⢢⠉⢤⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⠰⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠠⣀
⠀⠀⠀⠀⠀⡣⠗⠁⠀⠀⠀⠀⠱⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⡇⡅⠀⠀⠀⠀⠀⠀⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣇⠀⠀⠀⠠⠀⠀⣍⠹
⠀⠀⠀⠀⠀⠰⡙⢄⠠⠀⠀⣰⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠰⠎⠒⠥⠤⠍⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠯⠇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐⠞⠁⠀⠀⠈⢱⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠃⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠁⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⣀⠼⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣄⠤⠛⠛⠄⣀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠒⠒⠂⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢞⠅

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⠃⠀⠀⠀⠈⠑⡴⠂
⠀⠀⠀⠀⠀⠞⣿⣤⡄⢀⡠⠀⣤⣼⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢽⢄⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠓⢢⡴⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠛⠻⠿⢶⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣔⣋⡀⠀⠀⠐⢾⣓⣫⢤⡀⠉⠉⠉⠓⠒⠒⠒⣒⣒⣒⣒⣒⣒⣻⠦⡀
⠀⠀⠀⠀⠀⡴⠋⠹⡄⠉⠉⠓⠲⠦⠴⠒⠋⠀⢀⣠⠤⠖⠚⠉⠉⠁⠀⠀⠀⡖⠒⠒⠒⠛⢦
⠀⠀⠀⢀⣞⠓⠤⠤⠋⠀⠀⠀⢀⣀⣠⠤⠒⠋⠉⠀⠀⠀⠀⢴⣒⣒⡒⠒⠊⠁⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⡞⠀⠉⠙⠒⠒⠚⠋⠉⠉⢀⣀⡤⠤⠤⠖⠒⠒⠒⠶⠤⠤⣈⡉⠉⠙⢆⣀⣀⡠⠚⠉⠉⢳
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⠴⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠙⠒⠦⢭⣍⣀⣀⣀⡤⠴⣇
⠀⠀⡟⠒⠶⠶⠖⠒⠚⠉⢀⡴⠋⢹⠆⠀⢀⡠⠴⠒⠉⠉⠉⠈⠉⠙⠢⢄⡀⠀⠀⠀⠀⢀⣀⣀⡤⢼
⠀⢰⡇⠀⠀⢰⠋⠉⠉⠉⠁⠀⢠⠎⢀⡴⠉⠀⠀⠀⠀⢀⡤⠤⠶⠲⠤⣀⠉⠉⠛⠉⠉⠉⠁⢀⡤⢺⡄
⠀⠸⡟⠒⠤⣄⣉⡓⠒⢒⣒⣚⡥⠖⠁⠀⢀⣠⠤⠤⠖⠃⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠤⠖⠚⠁⠀⢸⠇
⠀⠀⣇⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠻⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⣀⣀⣠⠤⠚⣹
⠀⠀⢸⣄⠤⠖⣒⡭⠭⠭⠭⠭⣍⣓⠲⢤⣀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⡏
⠀⠀⠀⢣⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢮⡙⠲⢤⣀⣈⠉⠛⠋⠉⠀⠀⠀⣀⣀⡤⠴⠚⠉⠁⡜
⠀⠀⠀⠈⢣⣠⠤⠖⠒⠒⠲⠤⡀⠀⠀⠀⠀⠈⠲⢤⣀⣈⣩⣭⣭⣉⡉⠉⠉⠁⠀⣤⠖⠒⢒⡟⠁
⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠈⠲⣤⠎
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣀⣀⣀⠉⠉⠉⠉⠉⠉⠉⠓⠒⠦⡄⠀⠀⠀⠀⠈⣹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣞⡁⠀⠈⠓⠤⣀⡞⠉⠉⠛⠒⠒⠋⠁⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⠀⠀⢻⡍⠉⠉⠙⡧⠀⠈⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⠀⡞⠹⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠶⣦⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⣐⠰⣟⠀⠀⠀⢰⠉⢻⠇⢠⠀⢀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣰⠋⠙⣿⠀⠀⠀⠀⠐⠪⠃⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠠⡀⠳⡴⠛⠀⢀⡈⢁⣀⡪⢊⣠⠾⠛⠟⣻⣿⡷⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣖⣫⣿⣶⣮⣝⢿⢜⣋⣠⢦⣿⠁⠀⠀⠀⢱⣿⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡆⢿⡘⣿⣧⠻⢆⡀⣀⣠⣬⠁⠃⠂⠀⠀⠀⢀⣴⢿⣿⣦⠀⠀⠀⠀⣀⠁⠈⡇
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣇⣛⣽⣿⣿⣿⣿⣿⣿⣏⡚⠋⡁⡘⠉⠁⠁⢀⡀⠀⠀⣼⠀⠀⠘⡿⢃⠀⡄⠀⠘⢆⠀⡄⠰⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣷⡔⠜⠆⣤⠝⠳⠟⠀⠀⠈⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣀⢄⣀⣠⣤⣴⣄⣤⡤⡄⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠙⢿⣿⣿⣿⣿⣿⣿⣅⠹⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠰⠆⠀⢠⠉⢸⠟⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡄⠀⠛⠁⠀⣀⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣒⡔⣄⣶⣶⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣆⠹⠛⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣛⣉⣩⣭⣽⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠒⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠶⠈⠁⠀⠀⠈⠉⠰⣏⣠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⠠⠌⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⡇⠀⢀⡤⠲⠀⠀⠀⢠⡿⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣀⠤⠊⠀⠔⠂⠁⠀⠈⢿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠀⠀⣼⠁⣈⠔⠀⠀⡠⢀⠔⣫⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠠⠢⠕⠂⠘⢸⡟⠈⠉⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠨⠄⠚⠀⠁⠀⠀⣠⢔⣣⡾⠃⣰⣿⠀⠀⠀⠀⠀⠀⢀⠤⠂⢻⣇⣀⠶⠂⣀⡴⠂⠁⠂⠉⣀⠀⠟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢲⣀⣀⣀⣤⡴⠶⠟⢛⣭⠏⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠈⠉⠁⠂⢀⡀⠠⠤⢀⡶⠠⠁⠈⠃
⠀⠀⠀⠀⠀⠅⢠⣀⠷⣀⡈⢈⠙⣉⣤⡷⣴⣶⠟⠁⠀⣴⠟⠁⠰⠆⠀⠀⠀⠀⠀⠈⠉⠐⠀⠀⠘⢶⣏⣓⣁⣈⣁⣤⡴⠋
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠉⠻⠼⣫⣵⣾⣿⠟⠁⠀⢀⠞⠰⠛⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠒⡀⢀⠀⠠⠀⡉⠉⠉⠩⠀⠘⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⠀⠀⡀⠄⠉⠀⠀⠀⡠⠊⠀⠑⢄⣸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡈⠑⠀⠘⠐⠈⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⠦⣤⣠⣤⠰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠰⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⢆⡸⣦⡀⠀⡀⡰⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⣤⡀⠀⠀⠀⠀⠥⠀⠀⠱⠅⠈⢥
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡆⣺⡅⠀⠀⠀⠀⣽⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠡⣄⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⣟⡋⣗⠀⠠⠀⠔⠀⠂⠁⢀⡂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⡔⠀⣶⣤⢛⠃⠘⠃⠀⣀⢦⢚⡿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡴⣦⣷⣄⣤⣤⣶⠀⠂⠒⠊⠠⠁⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⠁⢠⠄⠀⢸⠂⢀⠐⠋⡇⢾⡟⠁
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⣠⠄⠀⠈⠠⡇⠀⠴⠤⠂⠀⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠁⠈⢁⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠐⣤⠁⠠⠀⠀⠀⠒⣡⡀⠤⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣄⡦⡀⠀⠤⠀⣠⡴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠈⢉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⡠⠆⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠂⡌⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⠀⠀⠀⠀⡰⠇
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠤⡐⠀⠀⠘⠂⠂⠀⠀⡨⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠊⠀⠙⠂⠀⠀⠆⠀⠐⠊⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⢁⠄⠀⠙⡆⡀⠀⠂⠀⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⣚⠄⠰⡄⠀⠀⡠⢴⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢊⠢⢀⠠⡇⠀⢫⠁⠀⠈⠐⠶⢂⡉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢐⡇⠀⠀⡀⠀⠀⢠⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢶⣉⠀⠈⠀⢙⣤⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡂
⠀⠀⠀⠀⠀⠐⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠈
⠀⠀⠈⠀⠀⢠⡀⣠⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠁⠠⠖⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⡀⠐⠐⢲⢤⡀⠀⠀⠀⠀⠀⠔⠀⠀⠤⠒⠖⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠚⠶⠆⠚⠛⠷⠛⡀⠀⠀⠀⢁⠄⠈⠀⠀⣠⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢿⣶⣾⠷⠹⠞⢻⠁⠀⠀⡠⠁⣀⡤⡲⠋⠁⡘
⠀⠈⠀⠈⢀⠄⠁⠈⠀⠀⠈⠫⠭⠭⠭⠟⠃⠀⠠⠊⠀⡢⠕⠂⠒⠐⠈⠀⠀⠀⠈⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡀⢴⣒⣶⣤⣄⠀⠀⣀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⡤⠖⠒⠂⢄
⠀⠀⠀⠀⢀⠉⠉⠉⢐⣓⣏⣉⡤⠂⠄⠀⠀⠀⠀⠀⠀⡀⠰⠓⠰⠂⠀⠀⠀⢀
⠀⣀⠤⢦⢂⣴⣾⣾⠭⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⡞⠉⠈⠈⠂⡀⠂
⠨⠗⠒⠛⠻⡏⠁⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠲⠀⢀⠀⠈

⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⡀⡀⢀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⣿⣿⡿⠟⠛⠻⢿⣿⣿⡿⠛⠉⠉⠉⠙⢿⣿⣿⣿⠿⠛⠻⠯⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⣿⠁⠠⠄⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⣶⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠦⡀⠀⣏⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠔⠄⣬⣄⠀⠀⠀⠀⠀⠻⡆⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⢀⠀⣤⣴⢆⣤⡀⣠⣤⡄
⠀⡠⣤⣠⣾⣿⣿⣿⣦⣤⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠆⠰⣿⡿⣡⣌⣻⣿⣿⡇
⠀⠷⠹⢿⠿⣿⣿⠿⠇⠘⣿⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⢃⣻⣅⣟⣥⠎⠛⠙⡇
⠀⠛⠛⠛⠋⠙⠿⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⢲⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣍⠟⣷⣷⠄⠀⣿⡀
⠀⠄⢀⣦⢴⣶⣶⣶⣶⣴⣦⣟⢰⣾⣯⣿⡥⢦⡀⣿⣷⠞⣷⢦⣄⣰⣾⣤⢀⠂⠀⣃⣶⠧⣿⣮⣿⣯⣏⣾⣿⣅⣴⣯⡇
⠀⠄⣰⣥⣰⣿⣿⣧⣻⢏⣿⣿⠿⢻⣿⣽⣿⣦⣥⣟⣿⢷⠙⡳⣿⣿⣿⣿⣏⡯⢬⣷⣿⠗⠘⠋⢻⣵⣽⣿⣿⣼⣥⣿⡇
⠀⣷⣿⣿⣿⣯⣿⣿⣭⣡⣤⣘⠿⢿⣿⣿⣿⠿⣈⣙⡋⠙⠙⠻⣿⠛⣹⣿⣿⠀⢀⠿⢿⣆⡀⠐⡉⢸⣯⣽⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣼⣿⡟⡛⣩⣿⣛⣿⣻⣉⣾⣿⣏⣿⡻⠴⢬⣿⣿⣾⣿⣿⢿⣿⣿⣷⣴⣾⣿⣗⢺⢿⣿⣏⣭⣵⣾⡇
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣾⣷⣿⣿⣿⡿⣜⣫⣽⣵⣿⣿⣿⣿⣿⣻⣧⣾⠟⢁⣾⣿⣿⣿⢿⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⠿⠿⣿⡿⠿⠿⣿⠿⢽⣿⢿⣿⠿⣿⢿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠯⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⢻⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⣧⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠒⣇⣠⢐⣀⣐⡒⠲⢶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣠⡝⢹⡄⠰⠆⣷⠀⠀⠁⠲⠨⡉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠁⢀⠔⠊⢘⡀⣸⣫⣧⠒⠅⠀⠃⠀⠀⣢⣐⡠⠀⠈⠙⠷⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠟⠛⠛⠋⣇⣿⠃⠀⠁⠀⠢⠀⠐⣄⢨⣈⡀⠄⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠜⠁⠀⠀⠀⢀⣸⡼⣁⠠⡈⠦⢤⠐⢤⡲⢿⠆⠘⣆⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠙⠲⢤⣤⣀⣀⣠⣤⡶⠾⣿⢷⣧⢻⢄⠑⣦⣀⠹⡣⢽⠙⠀⡄⠺⣄⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢻⡧⠈⡎⡌⠂⠠⡌⢱⣬⠈⠀⣸⡇⠀⢨⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠻⡆⢹⣸⠂⠀⠐⠉⡀⠀⠉⠀⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣦⣇⢇⢠⠀⠊⣈⠁⢠⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣜⣼⠀⠘⣡⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠉

⠀⠀⡠⠒⠈⠉⠉⠀⠐⠄⡀⠀⠀⠀⠀⠀⢀⠄⠂⠊⠉⠉⠐⠒⢄⠀⠀⠀⠀⠀⠀⡠⠔⠀⠈⠉⠁⠀⠠⢀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠉⠉⠁⠐⠤⡀
⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣠⠃⠀⠀⠐⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢐⠜⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠐⠂⠤⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠤⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠤⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠤⠐⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠦⣔⡬⠔⠒⢳⢀⠀⠀⠀⠠⠀⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⢀
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠠⠁⠀⠀⡠⣐⠵⠋⠁⠓⡀⣠⠯⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡐⠊⠀⠀⠀⠀⠀⠀⠈⠢
⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠁⢀⢔⡡⠚⠁⠀⠀⠀⠀⢸⠕⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣖⡵⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⡡⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠂⠄⣀⡀⣀⠠⠔⠊⠀⠀⠈⡞⠁⠀⣰⠦⣀⡀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⢄⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠤⠉⠠⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡁⠀⠀⠀⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣶⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠙⠀⠀⠸⠆⠰⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠐⠀⢠⣶
⠀⠀⣴⣶⣲⣦⠀⠀⠀⠂⠀⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠓⠂
⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠴⠒⠒⠀⠀⠀⢰⠛⠋⢲⠄
⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠂⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢿⠀⠀⠛
⠀⠀⢰⣦⣙⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀
⠀⠀⠳⠭⣭⣭⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠽⠃
⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⡇⠀⠀⢀⠴⣿⣛⣹⣬⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠉⠉⠁⠈⠉⠉
⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⡿⢶⣄
⠀⠀⠙⠉⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣡⣴⠿⢻⡇
⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣥⣼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⣌⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⢀⠀⠀⠹⢧⡆⢮⡉⠉⠀⠀⡀⠄⣰⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⢀⠀⠊⠈⣤⢁⡞⠂⠰⣄⣠⣍⡛⠟⠀⠀⠀⢲⠈⠁⠾⠽⢷⣄
⠀⠀⠀⠀⢠⣆⢀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⠨⡞⠃⠀⠀⠀⠚⣹⠇⠀⠀⣼⣸⣋⣳⡄⠀⠀⠄⠈⡌⠀⢴⣖⠀⠉⠐
⠀⠀⠀⠠⢀⣣⠖⠉⠉⠛⢤⡤⠞⡀⠀⠀⠘⠀⠰⠄⠀⠒⣍⣶⠷⢮⠦⣶⡟⢆⡐⠀⢹⠏⡙⢭⠿⣇⡀⠈⠱⢷⢐⣿⡛⠛⢾⡇⡀
⠀⠀⢀⣀⣰⡙⠀⠀⠀⠀⠀⠙⠧⡀⢲⣄⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠠⠄⠹⣮⡻⣥⡠⡐⢁⠈⠁⢳⣆⠠⡀⢈⣦⠈⣲⡄⠾⠃⠈
⠀⢀⡴⠿⠛⠧⡄⠀⠴⠀⠀⠀⢀⠸⠊⡁⠀⠀⠀⠀⢸⡏⠀⠀⠀⡛⠀⣄⣀⠙⣿⣿⠟⣡⣴⣟⣃⣠⡟⣿⣬⠽⢻⠑⣣⣰⣎⡴⣧⣄
⠀⢺⡏⠀⠀⠀⡸⢦⡄⢀⡠⠀⠀⢀⠀⠉⠀⠀⠀⢂⠎⡀⠀⠀⠀⠉⣋⣻⠿⠞⠹⣻⣾⣿⢿⣿⡿⠋⢥⣿⣶⣋⢉⣏⣹⢫⡇⣉⣹⡿
⠀⢿⠃⠀⠀⣆⠀⠈⠀⠀⡀⠀⠠⣤⣁⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠈⠀⠀⠨⣰⡿⣿⣟⡿⡋⠀⢠⣿⣿⣿⡯⡄⢤⠙⢿⣧⣼⣿⡥
⠀⠀⢴⡦⡜⠿⢷⠸⡿⠂⠋⢷⣴⠟⣫⣴⣶⣄⣀⡁⢠⠠⣁⠤⠐⣟⠿⣃⣄⡀⢽⣧⠘⢿⡏⠀⢀⣿⣟⢹⣿⣀⣄⣈⠃⠀⠉⣼⢩⡄
⠀⠀⠉⣃⡐⠌⠈⣤⣔⡛⢃⣮⡛⢀⣵⣧⣈⣭⡙⠰⣿⡘⠏⢀⣩⣯⡭⢹⠛⣿⣷⣿⣿⣯⡆⢀⣾⡭⠖⢋⣙⣻⡿⢷⣌⣿⡄⠈⢛⠂
⠀⠀⠰⠟⠘⣦⠀⢿⣿⠟⠛⣿⣿⣧⣉⣉⣿⣿⠿⣷⡙⢻⠻⡿⢛⣋⡅⣈⣁⢨⣍⣾⣿⣿⡇⣸⣿⢧⣴⡍⣩⡛⠳⣆⣀⣤⣾⣶⠟⠃
⠀⠀⠀⠀⠀⠘⠿⠏⡛⠒⠀⠉⣿⣿⣿⣿⡿⠁⠀⠀⠟⢒⣺⣷⣾⣟⣉⣅⣿⣿⣿⡿⠛⣿⣾⣭⡿⠆⠀⠻⠃⠉⠒⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠑⠂⠀⠀⠒⠀⠈⠉⠁⠀⠈⠁⠀⠂⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⣭⣖⣒⣒⡨⠽⠖⠋⠀⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⠒⣂⡀⠀⠀⠀⠀⠀⠀⣠⣤⣭⡓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠰⣿⣿⠿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠈⠁⣿⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣴⠾⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⠛⠷⣄⠀⠀⠀⠘⠿⣷⡝⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠘⠧⠤⠤⢖⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⠶⠒⠋⠀⠀⠀⠀⠀⠈⠙⠻
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣀⠀⠉⠉⠁⠀⠀⠀⢠⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⡸⠀⢀⡶⠋⣹⡆⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⡞⠛⢗⢆⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⡇⠀⠈⢓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡦⠀⣆⢣⠀⠈⢯⣇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢁⣄⡀⣿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡜⢎⠣⡀⢸⡿⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢸⣻⡎⣷⠀⠀⠀⠀⢠⢯⠇⠈⠑⣌⢣⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠁⠈⠉⠁⠀⣠⢶⣄⠇
⠀⠀⠀⠀⠀⠀⡇⠙⠁⠀⠀⠀⠀⠀⢇⢧⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢿⣸⢿
⠀⠀⠀⠀⠀⠀⢱⠀⠀⣀⠀⠀⠀⠀⠀⠑⠷⠶⠊⠀⠁⠀⠀⠀⠀⠀⣊⠤⠖⠒⢤⡀⣠⣾⣿⣿⠆⠀⠁⡎
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠁⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣀⣴⠇⠈⠛⠋⠙⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠛⠛⠟⠛⠀⠀⠀⠀⠀⠀⠀⠙⠭⠍⠭⠕⠋⠀⠀⠀⠀⠀⢠⣶⡖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡻⢕⣺⣦⠀⠀⠀⠀⢠⣏⣉⣩⡽⠂⠀⠀⡀⠀⠀⣀⡀⢀⡠⠀⢸⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠮⣽⢦⣀⠀⠀⠀⠈⠉⠁⠀⠀⣴⣛⣻⡆⣀⡭⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠢⠤⠤⠔⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢠⡿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢻⣿⠀⠀⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⢸⡇⢹
⣿⣿⣿⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘
⢿⣿⡟⣠⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠸⣿⣇⠹⣃⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢻⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠈⣿⡆⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠸⠇⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⢹⣿⣆⣴⠾⠛⠿⣦⠀⠀⠀⠀⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⠙⢻⣿⣿⠁⠀⢀⣤⣿⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⡀⠀⠀⠀⠀⠘⢿⣦⡄⠀⠀⣿⣿⡀⠀⠈⠉⠁⠀⢀⡴⢋⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣽⣗⣤⣄⠀⠀⠀⠉⠀⠀⢀⣿⣿⣷⣤⣤⣤⣤⠞⢋⣴⡿⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣛⠛⠶⢶⣶⠶⠟⠛⣿⣿⠀⠉⠁⠀⣰⡿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⣿⣿⡆⠀⢠⣾⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠻⣷⣤⡀⢻⣿⣇⣠⣿⠋⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠃⣠⣴⣦⡀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⢀⣴⣾⣶⣤⡙⣿⣿⡇⣼⡟⠋⣿⡿⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⢿⡧⠀⠙⣿⣿⣿⣿⣿⡀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦⣄⡀⠀⣽⣿⣿⣿⡿⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠿⠟⠁⢿⣿⡇⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⢸⣿⣷⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠘⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢻⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢸⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣿⣿⣸⣿⡀⠀⠀⠀⣰⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⣇⣿⣿⣿⣿⡇⠀⠀⠀⠻⠏⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⣾⡟⢻⣿⣿⣿⡝⢿⣦⣄⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⢀⣀⣼⡿⠁⣼⢿⣿⡟⢷⣄⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠋⠀⣸⡇⠘⣿⣷⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⣿⣿⡆⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢸⣿⡇⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠸⣿⣷⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣿⡄⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠈⣿⣿⠀⠀⠀⢸⣿⠀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠸⣿⡆⠀⠀⠀⢻⣿⠀⠀⠀⣸⣿⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⢹⣿⡄⠀⠀⠸⣿⡇⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⣿⣷⠀⢠⣿⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢹⣿⠀⣸⣿⠀⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠗⠀⠘⢿⣧⡈⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⣿⡇⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⢰⡄⠀⣰⡄⠀⣤⠀⠀⢀⢠⢰⣠⣆⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠾⢻⠀⢻⠃⢾⡷⠀⢪⣿⣟⣿⠿⠛⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠨⣤⣉⣀⡿⠀⠀⠀⣿⣿⠙⠟⠃⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⠏⠁⠀⠀⠐⢿⣿⣿⡐⣿⣿⣿⡀⢀⠔⣚⣛⠓⠩⣍⣉⡉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠐⣿⡿⣧⣼⢹⣿⣿⣷⣯⣭⣉⣙⠳⢦⡈⠉⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠸⢰⣿⢇⠀⠀⠀⠀⠀⢹⡷⠈⠻⣿⡿⢿⡯⠉⠛⠻⣿⣦⠀⠻⣦⡀⠀⠀⠈⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠐⡘⣯⠊⠀⠀⣀⡤⠒⠛⣀⠀⠀⡾⢀⡟⠀⠀⠀⠀⢸⣿⠀⠀⠈⢷⡀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠿⠀⠀⢈⠇⠀⢠⠀⠀⣀⣀⠞⠁⠀⢰⣶⣶⠇⢘⣿⠀⠀⠀⠀⠙⣦⡀⠀⣠⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣈⠠⠆⠀⠶⠀⠀⠒⠚⠋⢉⠉⠉⠀⣀⣶⠟⠉⠀⠀⣸⣿⠀⠀⢠⡦⠁⠀⣝⡆⡾⣰⡇
⠀⠀⠀⠀⠀⢴⠗⡢⣀⣠⠶⠶⣦⣤⣤⣤⣤⣤⡶⠖⠋⢭⡤⠤⢀⡀⠘⣿⣿⠀⢰⡿⠋⠒⢦⣤⣴⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇⠀⣀⠼⢄⠀⠘⢦⠀⠈⠳⡀⠀⢁⣀⣠⠔⡞⠉⢻⡆⢿⠁⠀⠠⠄⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠁⠀⠀⠑⣤⡀⢷⡀⠀⡟⡉⠀⠛⠁⠀⠃⣀⠰⣿⡈⠀⠘⠛⠀⠒⠠⠜⠪⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡐⠠⠽⢦⠧⠼⠩⠭⠁⠒⢄⡀⢀⡟⠀⠈⢷⠀⠉⠉⠙⠉⠉⠒⠠⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⢠⡎⠠⠤⠚⢁⠐⠊⢉⣀⠀⢌⠀⣿⡾⠁⢦⠀⠘⣧⠀⠀⠀⠀⢂⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡀⠖⠊⡠⣪⠶⠋⠉⠉⠳⣦⠀⠀⠀⡀⠔⠁⠀⢻⡀⠀⠈⢀⡏⠀⢈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠒⠚⠋⠁⢀⠀⠀⠀⠀⠈⣦⣄⡀⢱⡄⠀⠀⢸⡇⠀⠀⠀⠛⠾⠥⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣠⡀⢸⠀⠀⠀⠀⢰⡏⠑⣤⠆⢀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡰⡶⠝⠅⠃⢸⠀⠀⠀⠀⣾⠁⢠⠇⠐⢌⠀⠀⠀⢿⠙⡷⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡠⢮⣇⠐⠁⢀⠀⠀⠘⣧⠀⠀⣼⠃⠀⡜⠀⠀⡤⢦⠀⠀⡸⣰⠟⠺⣯⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⡠⢇⠀⢎⠀⠀⠘⡄⠀⠀⣿⠀⢘⡟⠀⠀⠇⢠⠃⠀⠀⢀⡜⢡⠏⢀⡴⠃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⡇⠩⡄⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠘⠀⡌⠀⠀⣠⠞⠠⠋⣠⠟⠁⠊⠹⣷⢆
⠀⠀⠀⠀⠀⢀⡔⠃⡀⠈⠂⠀⠀⠀⢡⠀⠀⠀⡇⠀⡘⢘⡇⠀⠀⠰⠀⢀⡾⢁⠔⢁⠜⠁⠐⠁⣠⡾⠻⡌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⣄⠀⠀⠡⠀⠀⠃⠀⡇⣸⠃⢀⠔⠀⣰⠋⠐⠁⠀⠀⠀⢀⣠⠾⠋⠀⠂⣧⡀
⠀⠀⠀⠀⠀⠘⢀⢸⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢤⡀⢸⠀⠀⠀⠀⠀⠐⢉⠀⠀⠖⠴⠲⠋
⠀⠀⠀⠀⠀⠀⠸⣖⠀⠀⠀⡀⠉⠂⠀⠀⢀⣤⣀⠀⠀⡇⢀⡀⢀⣐⣐⠈⢂⠀⣀⠀⠈⢁⢀⣀⢤⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠃⠠⡄⠁⠀⠀⡀⠀⣱⠀⢠⡏⡉⢩⢉⡉⠈⠈⠛⢍⣭⠕⠔⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠋⠈⠁⠈⠏⠉⠘⠛⠷⠴⣀⡀⠘⠗⠋⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈