Pita Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⡤⣀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡴⠛⠺⠇⠀⠸⠞⠓⣦⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣠⠿⠄⠀⠀⠀⠀⠀⠠⠿⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠘⣇⠀⠈⣟⣁⣀⣤⣤⣤⣤⣬⣿⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⢀⣠⡼⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡁⠀⠀⠀⢠⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠙⠓⠲⢤⣰⠏⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠁⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋
⠀⠀⠀⢀⡴⠋⢀⣠⢤⣴⠞⠲⣄⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋
⠀⠀⠀⡾⠀⠀⣸⡅⠀⠉⠀⠀⠋⢉⡏⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢼⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⢸⡇⠀⣞⠁⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠘⡇⠀⢈⡿⠂⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢳⡄⠈⠷⠤⣶⠀⠀⣤⣀⡇⠀⠀⠀⠘⠃⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⠚⠁⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠴⠖⢻⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉

⣏⠉⣹⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣻⣻⣟⣛⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠛⠛⠛⠛⠋⠉⠉⠉⠛⠛⠛⠛⣒⠒⠶⠶⠤⠤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⡤⠖⡋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⢀⣠⠞⠁⠔⡠⠒⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠳⣄
⠀⢀⡴⠋⠁⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣕⢌⠳⣄
⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠈⠳⣄
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣟⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣠⠟
⢹⡆⠈⠳⢤⡀⠈⠐⠠⢄⡀⠂⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡩⠐⠉⢀⡤⠞⠁⢰
⡞⠻⡄⠀⠀⠉⠓⠦⣄⡀⠈⠉⠒⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠒⠉⢁⣠⣴⡾⢋⠀⠀⢠⠿
⢹⡄⠙⠦⣄⠀⠀⠠⢄⡉⠛⠖⠦⢤⣀⣀⡈⠉⠉⠙⠛⢒⣒⣒⠶⠆⠤⠤⠤⠀⠶⠖⠒⠒⠒⠛⠛⠉⠉⢉⣀⣠⡤⠴⠒⠛⠍⣂⠥⠂⠁⣠⠶⠋⢠
⣼⢳⡀⠀⠈⠓⠦⣄⡀⠈⠙⠒⠤⢤⣀⡈⠉⠛⠛⠓⠲⠖⠶⠶⠶⠤⠤⠤⠤⠤⠤⠶⠶⠶⠖⠒⠚⠛⠉⠉⠁⣀⣀⡤⠴⠒⠉⢀⣠⡴⠞⠁⠀⢀⣿
⢳⡀⠙⢦⡀⠀⠐⠤⠉⠛⠲⠦⣤⣀⡀⠈⠉⠛⠒⠒⠶⠦⠤⠤⠤⠤⣤⣤⣤⡤⠤⠤⠤⠤⠴⠶⠒⠒⠚⠋⠉⢁⣀⣤⠴⠖⠛⢛⡩⠐⠁⢀⡴⠋⢀
⣸⢧⠀⠀⠉⠳⢦⣀⠀⠉⠒⠢⠤⣈⣉⠙⠛⠒⠶⠶⠤⠤⢭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠖⠒⠛⠉⢉⣁⣠⠤⠒⠊⠀⣀⡴⠞⠋⠀⠀⣼
⢯⠈⠳⣄⠀⠀⠀⡈⠙⠓⠦⣤⣀⣀⠈⠉⠙⡒⠲⠶⠤⠤⢤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⠤⠤⠤⠶⠖⠒⠚⠉⠉⣀⣀⣤⠴⢚⠫⢑⡠⠂⠀⣠⠞⠉
⠈⡇⠀⠈⠳⢦⣀⠀⠁⠒⠤⣄⣈⠉⠉⠛⠒⠲⠦⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠶⠒⠒⠛⠉⠉⠀⣀⡠⠔⠊⠁⣀⣤⠞⠁⠀⣸
⠀⠘⢦⡀⠀⠀⠈⠙⠲⢤⣄⣀⠈⠉⠓⠒⠦⠤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠖⠒⠊⠉⣁⣠⡤⢖⠫⢋⠄⠀⢀⡴⠃
⠀⠀⠀⠙⢦⣀⠀⠁⠂⠤⣀⡉⠛⠓⠲⠦⡤⣤⣀⣀⣂⡈⠉⠉⠭⠭⠍⠉⠉⠉⠉⠉⠉⠉⣁⣀⣀⣠⣤⠤⠴⠖⠚⠋⠉⢀⡨⠄⠊⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠉⠙⠒⠦⠤⣄⣀⣀⠈⠉⠉⠉⠉⠙⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⣀⣀⣀⡤⠤⠖⠒⠋⢁⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣄⣀⣀⠉⠉⠭⠙⠛⢒⣒⣒⠒⠒⠒⠒⠒⠒⠛⠛⠋⠉⠉⢉⣁⣀⣠⡤⠴⠖⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠛⠛⠛⢛⣛⣛⡛⠲⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⣀⣠⣤⠶⠟⠋⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣦⣤⣀
⣰⠞⠋⠉⢀⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦
⣿⣦⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣠⣿
⠹⣏⠙⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⢁⣠⣴⠶⠟⠋⣩⡟
⠀⠙⠷⣦⣄⡀⠈⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⢤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠋⠉⠀⣀⣤⠾⠿⣦⣄⡀
⠀⠀⢰⡟⠉⠙⠳⠶⢦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⠶⠞⠛⠁⠀⠀⠀⠀⠉⢻
⠀⠀⢸⡷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠳⠶⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿
⢀⣤⠾⢷⣄⠉⠙⠻⠶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⠶⠛⠋⠉⣰⡟
⣿⡁⠀⠀⠙⠻⢶⣤⣀⡀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⢀⣀⣤⢶⣿⠃
⢻⡟⠶⣦⣤⣀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⢛⣫⣭⠶⢟⣿
⠈⠻⣤⣀⠈⠙⠛⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁⢀⣤⣾⡁
⠀⣴⠟⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠋⠁⠉⠛⣧
⠀⣿⣦⣀⡀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⣴⣿
⠀⠸⣄⠉⠙⠳⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠛⠉⣰⠏
⠀⠀⠙⠻⢶⣤⣀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⠶⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠾⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⢤⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡄⠀⠀⠀⣸⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠛⠉⠀⠀⣄⠀⠈⠹⡄⠀⠀⢾⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠘⠀⠀⠀⠙⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠶⠶⠶⠖⠒⠒⠶⠶⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠀⢀⡔⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⠤⠄⠀⠀⠈⠛⠊⠁⠀⠀⡠⢄⠀⠀⠀⠀⠀⡀⠀⢰⣆⡀⠀⠀⠈⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠀⠀⠀⠐⠯⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠠⣎⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣆⠀⠀⠀⠀⠀⠀⠒⠒⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠅⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠸⠶⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠶⠄⠤⠀⠶⠐⠲⠲⠲⠒⠶⠴⢷
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠾⣄⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⢶⠶⠖⠒⠈⠰⠆⠀⠢⠴⠀⠀⠀⠀⣀⠀⠄⠀⠀⣴⠋
⠀⠀⠀⠀⢀⡞⠀⢀⢀⠀⠀⠀⠀⠀⠀⢠⣤⠠⠀⠀⠀⢀⣠⡤⠤⣒⣎⠉⠀⠀⠁⠀⠈⢀⣦⡀⠀⢠⠀⠘⢄⢠⡐⡄⢀⠋⠁⠀⠀⠈⣼⠁
⠀⠀⠀⠀⢸⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢩⠜⣎⡂⣢⣝⣦⣄⣁⡀⢁⣠⣞⠀⢀⠀⠀⠀⡀⠀⡰⠀⢌⣉⣀⣀⠈⠀⠶⣁⠄
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢃⢊⠄⡥⠀⠈⡴⠙⠿⣼⡁⠆⠀⢀⠀⠈⣑⠤⣤⣤⣤⢴⠾⠁⠃⠈⢫⠍⡀⢄⠠⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠀⠀⢀⠔⠉⠘⠁⠁⠦⣽⠁⠠⠀⢀⠀⠀⠋⢱⠀⠠⠄⠀⠀⠀⢀⡟⠀⠉⡀⠀⢠⡶⠦⠆⠀⠔⠊⠉⠁
⠀⠀⠀⠀⢸⠀⠀⠀⣎⡾⠁⢀⡴⠃⡀⠠⣠⠀⢠⡘⣇⠠⠀⠀⠀⠀⢠⠀⠘⠳⠾⡤⢀⡠⠔⣻⠈⠀⣀⣠⠀⡎⠀⠋
⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⡠⠋⠀⠀⠀⢈⣧⣉⢀⠀⠘⢦⣀⡀⠃⠀⢀⡠⠃⠀⠰⠃⠀⠀⠀⢐⣉⠄⠚⠁⠁
⠀⠀⠀⠀⢸⡀⡀⠀⠀⠔⠁⡄⠀⠀⠀⠨⣜⡛⠃⠐⢰⡌⡠⠉⠉⠉⢉⠁⠈⡑⡆⣈⠤⠖⠛⠉
⠀⠀⠀⠀⠀⡟⠀⢠⡾⢄⡀⠀⠀⠀⢁⡠⢚⣅⡠⢀⣴⡶⠺⣶⣮⡴⠿⠛⠢⢏⠈⠃
⠀⠀⠀⠀⠀⢱⣀⠏⠀⠰⠉⠛⠲⠋⡡⠙⢄⠡⡘⣿⠦⠐⠊⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣴⣆⣡⠥⠌⠚⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡠⣤⡄⢾⣬⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⡀
⠀⠀⠀⠄⠀⢤⡾⠃⡀⠀⠙⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠨⡤⠊⠉⠉⠓⢠⡀⠟⡒⠀⠀⠀⣤⠀⠁⠀⠀⠀⠀⢉⠄⠀⠀⠀⠹⢛⡁⣹⣧⠮⠴⠂
⠀⠀⠀⠀⠀⠐⠀⠱⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⢏⠛⠒⠒⠀⢈⡩⠚⡃⠀⠰⡞⠂⠚⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠋⠁⠀⠀⠱⡄⠀⠀⠀⠀⢀⠈⠐⡸⠀⠀⠁⠂⠀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠙⠁⢉⣉⢀⠂⠀⠀⠀⠈⠀⠀⠈⣀⠀⠀⠊⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡚
⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⠀⠨⠿⢊⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⢉⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⠠⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠂⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⡎⠀⠀⠈⣿⡼⠎⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠟⠳⢦⣤⣴⡿⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠶⠶⠶⠶⠤⠤⠤⠤⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⣄
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄
⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁
⠀⠀⠀⠈⣆⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠚⢠⠇
⠀⠀⠀⠰⡙⢆⠀⠈⠑⠲⢤⣀⡁⠒⠀⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠤⠔⠒⣈⣠⠴⠖⠋⠀⣠⠞⡆
⠀⠀⠀⠀⣷⡀⠙⠦⣀⠀⠀⠨⠉⣙⠒⠒⠤⠤⢤⣌⣉⣉⣉⣉⣉⣉⣉⣉⣡⡤⠤⠤⠔⠒⠋⢉⡁⠄⠀⣀⡤⠚⠁⣴⠁
⠀⠀⠀⠘⡄⠑⢄⡀⠀⠉⠒⠦⢤⣀⣉⠁⠒⠒⠦⠤⠤⠤⢤⣤⡤⠤⠤⠤⠤⠤⠖⠒⠒⢉⣁⡤⠤⠖⠛⠉⠀⣠⠞⢉⡇
⠀⠀⠀⢠⠻⣄⠀⠉⠒⠤⣀⡀⠐⠂⠬⢉⣉⣛⡓⠒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⣛⣉⣉⡡⠤⠐⠂⣁⡤⠔⠋⠁⢀⡾⡀
⠀⠀⠀⠀⢇⠈⠳⢄⡀⠀⠀⢉⡙⠒⠢⠤⠤⣄⣉⣉⣉⣉⢉⠛⠉⢉⣉⣉⣉⣉⣩⡤⠤⠔⠒⠚⢉⡁⠀⠀⣀⡴⠋⢠⠃
⠀⠀⠀⠀⠈⢦⡀⠀⠉⠓⠦⢄⣈⡁⠒⠒⠠⠤⢄⣀⣀⣈⣀⣉⣉⣀⣀⣀⣀⡠⠤⠤⠔⠒⢒⣉⣠⠤⠒⠋⠁⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠀⠌⢉⡉⠓⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠚⠉⣉⡁⠠⠐⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⠤⣀⣉⣁⠒⠒⠒⠶⠦⠤⠤⠤⠤⠴⠒⠒⠒⠒⢂⣉⣉⠤⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠤⣤⣤⡤⢤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⠖⢚⡭⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⣀⡠⠴⡟
⠀⠀⠀⠀⠀⠈⣳⠦⣌⣉⣛⣛⣛⣛⡓⠒⠒⠒⠶⠶⠶⠒⠒⠒⢚⣛⣛⣛⣋⣉⡥⠔⠚⠳⢄
⠀⠀⠀⠀⠀⢀⣻⠲⢤⣀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⡤⠴⡾
⠀⠀⠀⠀⠀⣯⣀⠙⠲⢤⣍⣉⣉⣉⣉⣉⣛⠒⠒⠒⠒⠒⠒⠒⢛⣉⣉⣉⣉⣉⣉⣥⣴⡾⠁
⠀⠀⠀⠀⠀⢙⣬⣉⠓⠶⠤⠤⠤⠤⠤⠬⢭⣍⣉⣉⣉⣩⠭⠭⠭⠥⠤⠤⠤⠖⢚⣩⠴⣇
⠀⠀⠀⠀⠀⢸⡦⣀⡉⠙⠒⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⠴⠖⠒⠒⠒⠒⠒⠒⠋⠉⢀⣠⢼⠇
⠀⠀⠀⠀⠀⠀⠓⠦⣍⣑⠒⠒⠒⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠒⠒⠒⣋⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⣂⡒⠫⣙⠃⣀⣑⣢⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⢎⠕⡄⢈⠕⡮⠋⠀⢀⠀⠹⣁⣀⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠮⡜⠘⠦⠼⣈⣶⢁⣀⣀⣀⡀⠀⡗⠋⠁⠻⢕⡤⡄
⠀⠀⠀⠀⠀⠀⡠⠒⠚⠀⠀⢑⣎⣩⡮⢖⡩⠒⠒⢒⡒⠬⡙⢤⠔⠊⠉⢻⣱⢐⣄⡀
⠀⠀⠀⠀⠀⠀⠱⣄⡴⠊⣁⣀⡈⠉⠢⢄⣫⠽⠤⡃⢈⠇⠈⡎⠯⠛⠽⣞⢎⠀⡀⠠⢱
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠑⠒⠤⣀⠉⠒⠭⢷⣒⣂⣀⢀⣀⡠⠬⠯⡇⢀⠀⠸⢤
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠠⠀⠉⠉⠓⠢⠤⣀⣘⣀⣠⣃⠜
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠙⢆⠰⠥⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡇⢶⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡍
⠀⠀⠀⠀⠀⠀⠘⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡄⠒⠒⠒⠒⠒⠒⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢
⠀⠀⠀⠀⠀⠀⢡⠀⠢⡀⠉⠑⠢⢤⠀⢀⠈⡙⠻⣗⠦⣀⠀⠀⠀⠀⢸⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡀
⠀⠀⠀⠀⡀⠀⠀⠳⡄⠱⠀⠐⠃⠂⠐⠆⠀⢀⠀⢂⠑⢌⠳⣄⠀⠀⢲⣀⠉⠓⠦⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠤⠒⠉⢀⡆
⠀⠀⠐⡩⡂⠀⡄⠀⣈⠀⠁⠒⠆⡀⠂⠒⠤⠀⢈⠕⠀⢠⢣⣸⠀⠀⢧⣈⡉⠓⠒⠦⠬⣉⣉⣉⣉⡉⠀⠀⢀⣀⣀⣠⡤⠖⢋⠔
⠀⠀⠈⠢⡘⢀⠀⠐⢇⣐⣀⠀⠀⠈⠁⠐⠦⢄⣀⣀⣀⣀⠴⠋⠀⠀⢺⣄⡉⠉⠓⠒⠦⠤⠤⠤⢉⣉⣉⣉⣉⣉⣁⠠⠔⠊⡡⠞⠁
⠀⠀⠀⠀⠰⢢⡀⢄⠰⠀⠀⢀⡁⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠙⠤⣉⣉⣒⠦⠤⡤⢤⣄⣀⡀⠤⠤⠤⠴⠶⣒⣨⠥⠒⠁
⠀⠀⠀⠀⠀⠢⠀⠂⠤⣀⠩⡏⠄⡳⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⣀⣤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠉⠓⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠉⠙⠒⢲⡐⢶⠀⠉⠉⠉⠉⠛⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⡇⠁⠐⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣸⠈⢷⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢈⡆⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡼⠁⡰⠋⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⡸⠀⠀⠀⠀⢸⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠖⠁⣠⠞⠁⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡾⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⣀⠜⣁⡤⠚⢁⣀⡤⠴⠖⠚⠉⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⡤⠚⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣠⣤⠴⠚⠓⠋⠉⠀⠁⠈⠀⣀⡀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠳⢭⣛⡋⠉⠉⠁⢀⣀⣀⣀⣠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢉⢸⠾⢮⠁⠉⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠘⠛⠒⠛⠓⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡄⠀⢀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣶⣈⡠⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⡀⠠⠀⠀⠈⠉⢢⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠜⠋⠈⠉⠦⠟
⠀⠀⠀⠀⠀⢀⡴⢻⢨⡟⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠓⠀⢈⡀⠀⠀⡈⠒
⠀⠀⠀⢠⢴⣻⣧⣾⡀⠀⠀⣀⢀⠈⢀⡁⣀⣀⠈⠓⡄⢄⠀⠀⠀⠀⠁⠈⠓⠐⠀⠀⠟⠀⠀⠀⠀⠓
⠀⢀⠐⢋⡆⢈⣼⠉⠀⠀⠀⢉⠁⠀⠊⠁⠀⠀⠉⡄⣟⡄
⠀⢄⢡⣾⠣⠁⠀⠀⠀⠀⠀⠈⠀⠿⢀⠀⠀⡠⢆⠉⠉
⠰⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢀⠄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣄⣀⢤⡄
⠀⠀⠀⠀⢀⣾⠊⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢽⠆⠀⢸⢿⣉⡴⣉⣻⢷⠂⣠⠟⠚⠮⡑⢀⡀
⠀⠀⢨⠖⠩⣇⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠓⠃⠘⠀⠋
⠀⢠⣼⣶⡧⡴⠃
⠀⣀⢛⢈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⢀⣿⡬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⡁⢀⡀⠀⠦⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⣀⡀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⣤⣤⡞⠉⠙⣦⣤⣤⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠰⣇⠀⠈⠁⠀⠀⠉⠀⢀⡷⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⢠⠞⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⣦⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠸⡇⠀⠘⢦⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⢿⡀⠀⢰⣏⣠⣤⣤⠤⠤⠤⠤⠬⣷⣤⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠀⠀⣀⡼⠷⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⢿⣤⣀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠘⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⢀⣀⡀⠀⠉⠛⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⡴⠋⠀⢠⠖⠓⢶⠏⠀⢹⣦⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⣸⠃⠀⣀⣼⡆⠀⠀⠀⠀⠈⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠐⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⣿⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⣿⠀⠀⢙⡿⠂⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠘⣇⠀⠘⢧⣀⣴⠀⠀⢠⡀⠀⡇⠀⠀⠀⠀⠷⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠘⠧⡤⠞⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢸⡄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣤⢠⢀⡄⣀⢠⣤⡀⣤⡄⢠⡤⠀⣤⣄⠀⠀⢠⣤⢠⢤⡀⣤⠤⢀⡤⣤⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⡏⢸⢼⡇⣿⢸⣤⠇⣧⡿⢸⠶⠀⡇⢸⠀⠀⣿⠈⢸⣼⠃⣿⠆⢸⣧⣼⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠃⢸⠘⠇⠿⠸⡇⠀⠯⠀⠸⠤⠄⣧⠞⠀⠀⢻⡴⠸⠘⠆⠿⠤⠸⠇⠸⠸⠇⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠆⠀⡆⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠘⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⡻⠀⠀⠀⠁⠀⢰⠀⠀⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⢀⡔⠁⠀⢀⠌⠀⠀⠀⠀⠀⢸⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠚⠁⠀⢀⠠⠋⠀⠀⠀⠠⠀⢀⠌⢠⠃⠌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢀⠔⠁⠀⠀⠄⡀⠔⠁⡠⠂⡴⠃⢠⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠑⠀⠀⠀⢀⠠⠔⠊⣀⠄⠊⣠⠀⠀⠀⢠⠀⢰⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢀⠂⠀⠈⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠊⠀⢀⠠⠐⣈⣉⣀⡠⠤⠔⠊⠁⠀⠀⠀⡀⠔⠁⠀⡠⠀⢀⣼⡅⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡥⠚⠉⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠀⢀⡠⠊⡠⠞⠁⢸⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠉⠀⠀⠠⠒⠀⠒⠒⠒⠀⠉⠀⠀⠀⠠⠔⠊⡁⠀⠈⠀⠀⠀⡸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠄⠐⢒⡀⠀⡈⢉⣉⠥⠄⠒⠒⠒⠀⠁⠀⢀⠔⠀⢀⡴⠁⠀⠀⠀⣾⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠃⢀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠴⠋⠀⠀⠀⢀⡜⠁⢇⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠈⠀⠀⢀⠤⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠖⢹⠀⠀⡸⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠀⡀⠀⢠⠞⠉⠉⠓⠒⠢⠤⠤⠤⠔⠂⠁⠒⠁⠀⠀⢀⠀⠀⠁⠀⠀⠀⣠⠃⠀⣠⠃⢀⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠐⠈⢙⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠁⠀⠀⢀⠤⠊⠀⠀⠀⠀⣀⡤⠚⠁⢀⠔⠁⡐⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠁⢀⣠⠴⠒⠋⠉⠀⠀⣠⠆⠀⠀⠈⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⡠⠒⠉⠉⠉⠉⠁⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣠⡤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣔⣋⡠⠴⢾⡉⠙⠂⠀⠛⠉⠀⠀⠀⠀⣠⣴⣒⣋⣉⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣄⣀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢠⣿⣧⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣌⣿⣿⡿⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣶⠿⣸⣿⣿⣯⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢌⣱⡞⢿⠛⠟⢻⣿⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠐⡚⠛⣋⠩⣴⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠛⢷⣶⣴⣾⠖⢠⣼⢹⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠐⢴⠃⢌⣭⡾⠷⢺⣛⣱⡿⠈⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡕⠊⠉⠀⠀⢘⣠⡞⢁⣀⣤⡾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠉⠉⠙⠲⠖⠒⠉⠙⠛⠿⠛⠉⢶⣶⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠐⠐⠄⢠⠀⢀⡀⠀⡀⠀⡠⣦⡔⢾⢙⣧⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣠⠀⣆⢔⣀⣀⡆⠀⡇⣰⡆⠹⠳⡿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢇⢻⡀⣄⠙⣿⣀⡿⢁⡗⣾⢦⣷⣼⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢼⡾⡏⣭⠓⢿⣀⣧⣾⡧⣼⣾⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣧⣷⢻⣧⣼⡍⣿⣸⣏⣿⣹⣿⣿⡗⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢼⣧⣹⣟⣿⣻⣿⣿⣿⣿⡿⠽⣋⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⡗⠻⢭⠄⠊⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡮⣤⠀⢠⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⢒⣒⠲⣄
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠤⣿⡝⠀⢸⡇⣿⠖⠀⠀⠀⠀⢀⠤⠐⠒⠠⠀⠀⠈⠘⢿⣾⣿⣵⣎⢳
⠀⠀⠀⠢⢀⣀⣀⠠⠄⠂⠉⠀⠀⢿⢇⢤⡿⠋⠙⢇⠀⡀⠄⠊⠁⠘⢿⡛⡧⠙⠛⠛⠛⠛⣿⠿⢿⣿⢸⠇
⠀⠀⠀⣤⣤⣤⣤⣀⣤⣤⣤⡄⢀⣤⣬⣏⢡⣤⣤⣤⣤⢠⣤⡄⣠⣤⡌⠻⣆⢶⣶⡶⢢⡾⠁⠀⠀⠉⠞
⠀⠀⠀⠛⢛⣿⣿⠋⣿⣏⣉⠁⣾⣿⣙⠛⠉⠛⣿⣿⠋⠈⢿⣷⣿⡟⠀⠀⠘⢷⣝⣵⠋
⠀⠀⠀⣠⣿⡿⠁⠀⣿⡿⠿⠃⠈⠻⢿⣷⡄⠀⣿⣿⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⣿⣿⣶⣶⡆⣿⣷⣶⡦⢾⣷⣾⣿⠃⠀⣿⣿⠀⠀⠀⣿⡿⠀⠀⠀⢀⣀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠛⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠉⠁⠀⠀⠹⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⣤⣄⣄⠀⢠⠀⣀⡼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣄⣀⡀⡀⢀⢠⢀⣼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠙⠛⠚⠛⠋⠀⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠓⠶⠶⠴⠤⣤⣦⣦⡤⠼⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⠷⢶⣴⣴⣴⣠⣀⣆⣄⣶⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢸⣸⣠⢀⢀⡃⣀⡰⠈⠉⠉⠩⠅⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠯⠍⠉⠉⠛⠛⠛⠳⠶⡖⣴⣴⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⣯⡝⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⠏
⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⢀⡀⠀⠀⠀⠀⠸⣅⣸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠍⠀⢀⣀⠀⠀⠀⠀⢸⣇⣿⠀⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣉⡽⢿⡚⠳⢿⡵⣦⣤⣄⣒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠛⠻⠿⠿⠿⣶⣶⣯⣁⣀⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢙⣄⡤⠷⡖⠛⠻⣅⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⢀⠤⠄⠀⠢⠈⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢉⣧⡤⠞⢾⠉⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⢀⠀⠐⠔⠀⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⡉⢀⣳⣤⠴⠷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢀⡀⠀⢤⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠛⢯⠁⣘⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠒⠀⠁⠀⣐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡖⠚⠻⣅⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠢⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣦⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⣰⠖⠰⠖⠚⣽⡖⢶⣦⣤⣀
⠀⠀⠀⠀⠘⣙⣿⣿⡻⢭⣍⣛⡻⡷⣦⣄⡀⠀⠀⠀⢸⣍⠓⠢⣤⣉⣶⠀⢙⣖⣋⠁⣀⣠⡜⣳⡀
⠀⠀⢀⣀⡀⣙⣞⣿⡿⡷⣾⣿⣷⢬⣙⣿⣯⣢⡀⠀⣷⣝⡓⠶⣤⣈⣀⣛⣉⣩⣭⣭⠭⠵⠚⢋⡇
⠀⠀⢝⢇⣰⠁⡽⢯⡍⠓⢯⣭⣛⡉⢿⢳⡻⢷⠇⠀⣳⠮⢭⣛⣓⡺⠿⠯⠤⢤⣤⣤⡶⠶⣚⡭⣫
⠀⠀⠀⠡⢄⣸⣷⡊⠛⣦⡀⠀⠉⢹⠛⠋⠉⠁⠀⠀⢺⣷⠶⢤⣍⣉⣛⣉⣛⣓⣚⣛⣿⣭⣵⡾⠃
⠀⠀⠀⠀⢿⠛⣦⣖⣿⠭⣷⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠮⢭⣭⣭⠤⠶⠒⠋⠉⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⣡⠴⠀⠉⣿⠹⡶⢤⡘⠳⠈⡏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡛⢄⢺⠛⠀⡼⠃⣰⣇⣠⡈⢁⡀⠃⣸⠳⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣬⣅⢺⣥⣦⠀⢀⡼⢗⣾⠉⢙⡉⠁⠋⣀⡼⠷⡸⡿⢓⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠄⠈⠷⠀⠿⠐⠂⢀⣤⠞⣡⠏⠙⠗⠉⢁⣤⠾⠿⢄⠜⣱⣃⡩⠉⢹⣧⠑⣆
⠀⠀⠀⠀⠀⡸⠀⠀⣘⡗⡀⠀⡰⢋⣥⠞⣁⣠⣤⠶⠾⠏⠀⠀⠀⣀⡴⣣⡌⠛⣠⣾⠘⠓⣼
⠀⠀⠀⠀⠀⠳⣤⣬⣭⠾⠖⠛⠋⠉⠈⠉⠩⢌⣁⣘⣛⣡⣤⣶⣚⣋⣈⣡⣴⡾⠙⠁⠫⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠭⠭⠥⠤⠶⠶⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⠇⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠢⠤⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢰⣤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣿⡏⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠉⢲⠇⣼⢸⠿⡂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡩⢷⡰⠀⠂⢐⣿⢸⡆⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣼⠁⠀⡹⠁⠀⢾⣿⠈⡆⠀⠠⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢐⢺⡇⠀⠀⡇⠀⠀⠘⣿⠀⢿⣄⠀⠊⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠄⠐⣄⠀⠳⣄⠀⠙⠹⣧⡈⢿⣼⣄⣀⡼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⢠⣶⠶⢈⡉⠒⠺⣟⣶⣶⠶⢷⣆⡈⠃⠒⠒⠺⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠿⣼⠁⠀⠀⢀⢀⡀⠈⠉⠛⠁⠠⠤⢀⡀⠀⠀⠒⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⢧⣄⠈⠢⠤⡔⠋⠀⠙⠲⢄⡀⠀⠀⠀⠀⠉⠲⣏⣿⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⠤⢤⣤⣀⣈⢙⡛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣀⣀⠙⠓⠾⣦⣠⡆⡀⠈⢉⠑⡒⠂⠢⠤⠈⠉⢉⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⣿⡦⠤⣤⣭⣭⣿⣷⣦⣤⣤⣤⡴⠶⠞⣮⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⡇⠀⡇⠀⣿⠀⣾⠉⢹⠇⠀⡿⠀⢸⡇⣼⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠀⢁⠀⣿⠀⣿⠀⢸⠀⢸⡇⢀⣿⢠⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡇⠘⠀⢹⠀⡿⠀⡼⠀⣼⡅⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⢧⠀⠀⢸⠀⣷⢠⣧⣰⣿⢡⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⡆⠓⢺⣶⡿⢸⡟⣿⣿⣿⡿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠋⠓⠚⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣶⣿⣿⣿⣿⣿⣶⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣆⠀⠀⣰⣿⣿⡿⠁
⠀⠀⠉⠉⠉⢉⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⠉⠉⠉⠉⠀⠀⣿⣿⣿⠋⠉⠙⠿⠿⠷⠀⠈⠉⠉⣿⣿⣿⠉⠉⠉⠀⠀⢻⣿⣿⣦⣼⣿⣿⠟
⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⢀
⠀⠀⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠃⠀⠀⠀⠈⠉⠛⠛⠻⢿⣿⣿⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⢠⣿⣿⣿⣷⣶⣶⣶⣶⠀⠀⣿⣿⣿⣶⣶⣶⣶⡄⠀⢿⣿⣿⣦⣤⣴⣾⣿⣿⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠙⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠘⠛⠂⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠓⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣫⢔⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⢞⠕⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣠⢋⡞⡵⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⢌⢳⡀
⠀⠀⠀⠀⠀⠀⣰⢣⢏⠞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⢆⢳⡀
⠀⠀⠀⠀⠀⢰⢃⠏⡎⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠆⢳
⠀⠀⠀⠀⠀⡏⡼⠸⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡈
⠀⠀⠀⠀⢸⠁⡇⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠇
⠀⠀⠀⠀⢸⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠘⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡄⡇⠇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠇
⠀⠀⠀⠀⠀⢧⢹⡸⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⢠
⠀⠀⠀⠀⠀⠘⣆⢧⢣⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢡⢃⡎
⠀⠀⠀⠀⠀⠀⠘⣎⢧⡳⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡱⣝⢎⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠣⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡘⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢣⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠷⠶⠶⠶⠿⠟⠛⠛⠛⠛⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠿⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠿⠛⠚⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⠷⠶⠶⠶⠶⠶⠷⠒⠛⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣾⣿⣿⠿⠶⠤⠤⠤⠴⠶⠶⠶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢶⣿⣿⣿⣶⣦⣤⣤⣤⣤⡤⠤⣶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⣿⣿⠳⠤⠤⠔⠒⠒⠒⢋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⣶⣾⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⡂⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠘⠿⠚⠚⠛⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⠿⠿⢿⣶⢶⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡼⠃⠀⠥⡼⠀⠙⠲⣆⡝⣿⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡠⠂⠀⣰⠇⢀⡃⠀⠀⣟⠳⣅⠈⢿⣌⡃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢡⠎⠀⠀⡴⠃⠀⣨⠅⠀⠀⢽⡄⠻⣦⡀⠙⢮⡀⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⠀⠀⢀⡾⠁⠀⢰⡿⠁⠀⠀⠨⣷⠀⠹⣧⡀⠀⠛⣄⠀⠙⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠜⠁⠀⣴⠋⠀⠀⠀⣼⡃⠀⠀⠀⢈⣿⡄⠀⠘⣷⡀⠀⠈⠶⣤⠄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠆⠀⠀⣸⡃⠀⠀⠀⠨⡯⠁⠀⠀⠀⠀⠈⠇⠀⠀⠸⣿⡆⠀⠀⠙⢂⣐⠀⢱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠊⠀⠀⣸⠯⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠸⣿⠀⠀⠂⢹⣿⡄⠀⠁⠈⣿⣦⢈⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⠊⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⢈⣻⡇⠀⠀⠈⢻⣿⡀⠀⠀⠈⢿⣇⠈⣟⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠄⣠⠏⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠠⣝⠇⠀⠀⠀⠈⠿⣷⡀⠀⠠⡀⢻⣆⠘⣖⣻⡄
⠀⠀⠀⠀⠀⠀⡆⢠⡟⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠭⠃⠀⠀⠀⢀⠸⣿⣷⠀⠀⠁⠀⢿⣆⣿⡵⣷
⠀⠀⠀⠀⠀⢠⡄⣾⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⢼⡷⠀⠀⠀⠀⠀⠀⠀⢸⡶⠀⠀⠀⠈⠀⢹⣿⡇⠀⠀⢀⡀⣿⡼⣿⣹⣇
⠀⠀⠀⠀⠀⢸⢀⡟⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠘⣧⢿⣧⣿
⠀⠀⠀⠀⠀⢸⣾⡃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣺⡇⡀⠀⠀⠀⠀⠀⠀⢀⢻⡧⠀⠀⠀⡂⠀⢘⣿⡇⠀⠀⠀⠀⢩⡈⣗⣿
⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⣋⠀⠀⠀⠀⠀⠀⣯⠚⠁⠀⠀⠀⠀⠀⠀⠀⢼⡗⠀⠀⠀⢡⠀⠛⣿⣿⠂⠀⠐⠀⠘⣇⢴⣿
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣧⠄⠀⠀⠀⠀⠀⣿⣏⡀⠠⠀⠀⠀⠀⠀⠐⢸⣿⠐⠀⠀⢈⠀⠀⢸⣿⡄⠀⢀⡁⢀⣏⢸⣾
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⡀⠀⠀⢠⠀⠀⢹⣿⣼⡀⠀⢈⡇⠀⢴⣿⣅⠀⠈⠁⣼⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡄⠀⠈⣯⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⡀⠀⠀⢸⡄⠀⠠⣿⡿⡇⠀⠀⡇⠀⠠⣿⡧⠀⠀⣰⣿⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡸⣿⣇⠀⠀⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⡇⠀⠀⢿⡇⡀⠀⠀⡗⠀⢀⣿⡇⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠈⢹⣿⠀⠀⣀⠀⠀⢿⠀⠐⢺⡇⠁⠀⣴⡇⠐⢸⣿⣇⣤⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠰⣤⣀⠀⢛⣿⣯⠀⠑⡀⠔⢿⠀⠀⣽⣯⠀⢀⣿⡃⢀⣾⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣇⣰⣯⣧⣼⣿⣿⣾⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠉⠉⠁
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠁⠀⠀⠈⠀⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⣷⣿⣾⣷⣿⣵⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⣠⡶⠟⠛⠛⠛⢶⣄⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣮⣿⡿⢋⣡⣤⣤⣤⣍⠻⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡉⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⣧⠀⢉⡠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢷⣿⡏⣰⣿⣿⣿⣿⣿⣿⣷⡌⢿⣷⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠤⠀⢰⡇⠀⠀⢤⡀⠀⡤⠀⠀⢸⡇⠀⠤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⠀⣿⣿⣟⢿⣿⢟⣻⣿⡷⢸⣿⣛⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠂⠀⢿⡀⠀⠀⡀⠀⠀⠀⢀⡾⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣆⢻⣿⣿⣿⣿⣽⣿⣿⠃⣼⣿⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠋⡀⠈⢻⡄⠀⡇⢸⠀⢠⡞⠁⢀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣵⡿⣿⣆⠹⣿⡿⣿⣿⣿⢃⣾⣿⢷⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⢿⠀⣵⣾⠀⣿⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢾⢿⣿⡆⢻⡗⠉⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡿⠿⢿⡿⠷⠘⠃⠀⣛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣒⡦⠀⠐⣂⡀⠀⠒
⠀⠀⠀⠀⢴⣼⠀⣀⡠⢁⠀⠀⢆⣀⡀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡤⡄⠀⠤⠀⠠⢀
⠀⠀⠀⠀⠀⠀⢚⠈⠦⠄⠀⠂⠄⠁⠠⣈⠁⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠐⠂⠄⢀⠘⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠾⠃⢀⠄⠐⠆⠀⢈⡂⠉⠀⠑⢶⡒⠹⠀⡇⠀⠀⡀⢲⡷⠆⠠⠀⡎⠻⠶
⠀⠀⠀⠀⠀⠊⢰⣦⠈⠁⠈⣑⣍⢙⠁⠀⢀⢄⣠⣠⠄⠀⠿⠶⠄⠛⠓⠁⠛⠀⣀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠁⢀⡆⠀⢀⡀⠈⠉⠳⢶⡃⠀⠉⢝⠋⢁⡀⠢⠤⢠⠎⠀⠀⣏⡈⠙
⠀⠀⠀⠀⠀⠀⠂⠀⢀⠶⠴⠶⠣⠄⠒⠿⢣⠀⠠⣌⢂⢰⠀⡠⠀⣵⠀⠀⣡⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⡀⠠⢆⣀⠀⠀⠀⠀⠀⠈⢛⡻⣏⣤⡤⠈⠂⠈⣿⠄⠂⠀⢀
⠀⠀⠀⠀⡘⠄⠐⠀⠀⠈⠁⡠⠀⠀⠀⡀⠀⠀⠀⠀⡼⠀⠀⠫⠃⢰⠀⠉⢚⡀⠀⣴⣤⣤⣄
⠀⠀⠀⣟⡀⠋⠠⠆⡤⠠⣄⠀⠈⢠⡆⡓⠶⠄⢀⡞⠁⠀⠀⠀⠀⠘⢧⣴⠃⠹⣆⠀⠀⠀⠀⠈
⠀⠀⠀⣶⠐⡄⢰⠻⠁⠠⠙⠆⠂⡀⠳⢠⡄⠰⠋⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⢻⣷⡌⠁⠰⡀
⠀⠀⠀⠈⠉⠅⢸⡔⠈⠳⢈⣴⠀⠀⠀⣮⠗⠞⢀⣀⠀⠀⢴⡀⠠⡄⠀⠁⠀⠀⠈⠘⢿⡄⠐
⠀⠀⠀⠀⠀⠛⠚⢤⣤⣇⡠⠚⠉⠁⠀⡃⠘⣧⣮⠉⣍⡄⣼⣽⠒⠰⣦⡄⣀⣠⠆⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡖⠙⢶⡉⢥⣼⡛⢉⣈⡆⠀⢀⢈⢹⠀⠙⠓⠀⠀⢄⡌⠀⢀⡠⠖⠾⠁
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠸⣅⠀⠉⢱⡈⢙⡟⠶⠾⡟⢠⡔⠀⠀⠀⢊⠀⢳⡄⣤⠀⠸⣤⠄⡠⠂
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⡀⠀⠑⣿⣷⣄⠀⠀⠈⠙⢺⡀⠀⠸⠟⠈⠻⠀⠁⠀⣠⠊
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣿⡿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡰⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⣂
⠀⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⠀⠈⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⡔⠛⠓⠦
⠀⠀⠀⠒⢄⠀⡿⡰⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⣟⠆⠔⠆⢃⢠
⠀⠀⠀⠛⠈⢻⣹⠥⠈⠀⠀⠀⠀⠀⠀⣠⡔⠂⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣻⡀⠀⡆⢀⡉⠘⡄
⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣸⠀⠀⣄⠀⢀⠄⠀⠉⢿⣻⣿⡇⣉⡩⡦⠈⠙⣶⡁
⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⡙⠉⠁⠀⠀⠹⢦⡼⠀⠀⠀⢸⣿⣿⣿⡟⠁⠈⡒⠋⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢻⣿⣿⡿⢤⣎⠼⠻⠏
⠀⠀⠀⠀⠀⠀⠈⠲⣶⣾⣿⠟⠀⠀⠀⠀⠀⠂⠀⠀⢸⡟⡀⠀⠀⡀⠀⠀⠀⠘⠿⠿⠞⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠆⠈⠑⠄⠀⠈⠿⣷⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠃⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢾⣄
⠀⠀⠀⠀⠀⠀⠀⣰⢻⠻⡐⠀⠀⠀⢠⡟⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠰⣟⣲⠿⣋⣩⡝
⠀⠀⠀⠀⠀⠀⠀⠉⣥⣀⣤⡀⣤⣤⣠⠁⠀⣠⡮⣭⡁⠀⠘⡆⠀⢸⣿⣿⣫⣭⣽⡿⣻⡆
⠀⠀⡠⠒⠚⠓⠶⣄⠉⣿⣏⠉⣉⣿⠟⢠⠞⠉⠀⣠⠼⠶⠴⢧⡀⠐⣿⣷⣶⣶⣶⣿⣉⠀⠀⣸⢷⣤⡀
⠀⢸⡁⠀⠀⠀⠀⣽⡆⢻⣿⠿⣿⣿⠀⣮⠁⠀⣴⠃⠀⠀⠀⠀⠨⡀⢻⣞⣽⣟⣩⣿⠇⠀⢸⡼⣊⡿⢽⣄
⠀⠀⠇⠀⠀⠀⠖⢾⡀⢸⣿⡟⣿⡟⠀⠀⡏⣶⠻⡄⠀⠀⠀⠀⢸⡇⠀⣿⣯⣭⣿⡏⠀⢲⡟⣓⢻⡆⣽⣷⡆
⠀⠀⢰⣠⢀⣶⣤⡞⠁⠈⣷⡟⣿⠇⠀⠈⠳⣿⣤⢈⣖⠒⢘⣿⡿⠀⠀⢸⣟⠟⣿⡇⠀⠙⣷⣷⣦⣭⣽⣶⠃
⠀⠀⠘⣭⢻⣽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠋⠀⠀⠀⠘⣯⡿⣿⠀⠀⠀⢻⣿⡿⣷⠺⡟
⠀⠀⠀⢆⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡏⠀⠀⠀⠀⠀⢿⠿⣿⠀⠀⠀⠸⣾⡷⢿⢿⠇
⠀⠀⠀⢸⠷⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣶⢛⠃⠀⠀⠀⠀⠀⢸⣶⡏⠀⠀⠀⠀⢹⣿⢾⡟
⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣺⣿⡿⠦⢹⣷⡒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⢻⣿⢸⠻⠉⠆⠈⣿⣿⡄⢾⣯⠓⡄
⠀⠀⠀⠀⡄⢀⣠⣴⣿⡶⠞⠋⣰⣿⡿⢿⣀⠀⠀⠘⣿⣿⣿⣿⣶⣦⡜
⠀⠀⠀⠀⢀⣿⡿⠋⠀⠀⣠⣾⡿⠋⢀⠀⠛⠁⣴⣄⢈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⠟⡩⠐⠈⠀⠀⣠⣼⣿⣿⣞⢿⣿⣿⣿⣇
⠀⠀⠀⠀⢸⣿⠇⠀⢰⠁⠀⠀⠀⣀⣴⡾⠿⠟⠛⠛⠛⠃⣹⣿⣿⣿
⠀⠀⠀⠀⢸⣿⠀⢀⡏⠀⠀⡠⠾⠋⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠘⠿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠉⠛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠰⢋⣵⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⢽⣥⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⢠⡆⠀⠀⠀⢸⣧⠀⠀⠀⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠟⠃⠀⠀⠰⣄⠐⢋⠀⡾⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣿⣿⡉⠀⠀⠀⠀⠀⢰⣆⡉⠛⠓⠊⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⣀⡤⠞⠛⠉⠉⢻⡆
⠀⠀⠀⢠⣿⠏⠙⢷⣄⠀⠀⠀⠀⣿⡟⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⣼⡿⠀⠀⠈⢿⣦⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⣼⣿⣿⣿⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⢰⣿⡇⠀⠀⠀⠘⣿⣷⡀⣿⣿⣿⣋⠀⠀⠀⣀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣛⣡⣶⣿⣯⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣟⠛⣭⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠛⠛⠿⠶⠶⠶⠿⠿⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⢀⣀⢤⣄⢄⡠⣄⢤⡰⣄⢠⡀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⣉⡡⣄⣶⣽⣷⣯⣿⣾⣿⣿⣾⣷⣿⣮⣷⣼⣦⣳⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣩⣶⣿⣿⣾⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣷⣾⣿⠿⠿⠛⢋⣭⣤⣶⣶⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣿⠟⠷⣄⠀⠀⣶⢿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣷⣾⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⣷⣰⣏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠉⠛⠿⣧⣀⡀⠀⠀⢀⣿⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠐⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢱⣦⣀⠀⠙⠛⢿⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠚⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢯⡳⣄⠀⢾⢿⡟⠁
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣝⢿⣿⣦⠀⢀⠃
⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠄⠀⠀⢼⡫⣷⣿⣿⡆⢸
⠀⠀⠀⣾⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣝⢮⡻⣿⡇⢸
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢮⣻⣷⣿⣿⡇⣸
⠀⢀⡟⢠⡇⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⢠⣨⡳⣿⣿⣿⣿⡇⣿
⠀⢸⠇⣼⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡳⣽⢿⣾⣿⣿⣿⢣⡇
⠀⢸⠀⣿⣿⣿⣇⡇⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⢀⢤⣳⡳⣝⢾⠿⣽⣿⣿⡟⣼⠁
⠀⣼⠀⣿⣿⣿⣿⢿⢻⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⣯⢷⡳⣽⣮⣶⣵⣮⣿⡿⢱⠇
⢠⡟⠀⢿⣿⣿⣿⡾⣟⣏⣯⣷⢷⢲⣰⣴⡰⣆⣦⢶⢶⣳⡽⣞⣷⡻⣽⣮⣷⡿⣾⣿⣿⣿⣿⡿⣡⠏
⣾⢀⡀⣼⣿⣿⣿⣿⣻⣿⡾⣞⣿⣯⢷⣻⣳⡹⣞⣯⢯⢷⣻⣝⣯⣿⣝⣮⣿⣝⣾⣿⣿⣿⠟⣵⠏
⠻⣮⣛⠻⠿⢿⣿⣿⣿⣿⣿⡽⣿⣾⣯⢿⣷⣿⡽⣾⣯⣿⣻⣿⣾⣿⣟⣿⣿⣿⣿⣿⠟⣡⠞⠁
⠀⠈⠉⠛⠛⠶⣬⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣮⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣯⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣬⣭⣭⣭⣩⣭⣭⣭⣽⠶⠾⠛⠋⠁
⣿⣷⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿

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

⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⣀⡀⠄⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⠛⡃⠀⠀⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢾⣿⣿⣿⣿⣿⣿⣧⣁⣺⣦⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣾⣿⣿⣟⠉⠁⠙⠿⣿⠿⠿⠿⠟⢹⣿⣌⠻⣿⣿⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⣿⡟⣠⣿⣿⠟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⣿⣿⢷⣿⣿⣷⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢸⣺⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⢿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⢸⣿⣯⣵⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⣿⡿⠇⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⢨⣀⣀⣀⡀⠀⢀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡀⣿⣿⣽⢠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⡏⢿⡇⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣉⣿⣿⣿⣿⡏⠙⠘⣿⣿⣿⣙⣻⣿⣿⡿⢻⠀⣿⣇⢺⣧⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠿⠟⠛⢩⡇⢸⠀⠈⠙⠛⠋⠙⢻⣟⠀⢸⠇⣿⣿⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣯⠀⠀⠀⠀⠀⣀⣀⠁⢸⠀⠀⠀⠀⠀⠀⢸⣿⠄⣸⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⠀⠀⠀⣟⣁⠀⣿⠀⠀⠀⠀⠀⠀⢸⡏⢠⠋⢺⠿⢿⣿⣿⡅⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⣻⣿⣿⣿⣿⣿⣇⣀⡇⠀⠀⢠⣿⣿⣿⣿⣶⣶⠆⠀⠀⠀⣾⠀⣿⡀⣼⣿⣾⣿⣿⠗⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣸⣿⣿⡿⣿⠉⠁⠀⠀⠀⢀⡏⣸⡇⢸⣿⣿⣿⣿⣿⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡶⠦⠤⢤⢀⣼⣡⣿⡇⢸⣿⣿⣿⣿⣿⣯⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣠⣾⣿⣿⣿⣇⡆⢹⣿⣿⣿⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠋⠉⠉⣸⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣻⣧⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠀⠀⠀⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⣹⣿⠀⢻⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠟⠛⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣹⣿⡇⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠀⡏⡇⠈⠙⣒⠤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡇⠑⠖⠋⠉⡷⠀⠀⠉⣉⡒⠲⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠣⣤⠴⠋⠀⠱⣀⡠⠔⠒⢦⠉⠉⠙⣒⣶⠦⠤⠤⣄⣑⣄
⠀⠀⠀⠀⠀⠀⢧⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠑⠒⠉⠀⠀⠙⠒⠶⠤⠖⠛⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⢾⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠒⣈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠏⢸⠀⠀⢱⢄⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⠀⡟⠀⢸⠀⠀⠈⠚⠝⡲⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣆⣇⣂⡇⠀⠸⠁⠀⠉⠑⠄⠘⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣇⣆⣲⣿⡿⠉⠀⠀⠀⠀⠀⡀⢠⠀⠀⡇⢸⣶⠀⢀⠀⢀⠀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⡶⠒⡟⣷⣿⡟⠀⠀⣀⠤⠀⠀⠀⡠⠋⠀⠜⠀⡿⣒⣾⠒⢀⣰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣿⣷⣶⣿⣿⡇⣠⠞⠁⣀⣠⠔⠊⠁⠐⠋⠐⠚⡇⢻⣿⣶⣸⠘⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠛⣿⣧⣄⣿⡉⠉⠉⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⡰⠁⢀⣿⣿⣿⣺⡛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡧⢄⣿⣟⣀⣀⣠⣤⡴⠖⣋⠠⠀⠀⣠⠞⠁⢠⢿⠹⣾⣾⠻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠍⠟⢿⡁⠀⠀⠀⠉⠀⠀⠀⠀⢀⣠⠞⠁⢀⡴⠃⣸⠀⣹⠻⢿⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣥⣿⣃⠀⠀⠀⠀⢀⣀⠤⠖⠋⣀⣤⠖⠋⢀⡴⠋⢀⣿⣦⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡌⠉⠙⠛⠛⠻⠶⠶⠒⠚⠋⠉⣀⡤⠖⠋⠀⢀⡞⠀⡏⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢽⣇⠀⣀⠀⠀⢀⣀⣀⡤⠖⠋⠉⡁⠀⠀⢀⡠⠋⢀⡼⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣿⠻⢭⣝⣲⠶⠖⠒⠚⠈⣀⣠⣄⣒⡯⠶⠚⠁⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡄⠀⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣓⠶⠤⠤⠤⠤⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠁⡀⠒⠂⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠂⣀⠐⢀⡀⠐⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠀⣀⠐⢂⣀⠐⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⢁⣀⠒⢂⣀⠉⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣁⠤⠒⢂⠤⡉⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣁⣉⣉⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⠿⢿⠿⢿⣿⠿⠿⡿⠿⠿⢿

⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⣿⡄⠀⠀⣿⣿⡀
⠀⠀⠀⢸⣿⣇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⣿⡀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⢸⣿⣇⠀⠀⢻⣿⡆⠀⠀⣠⣴⣾⣿⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣿⣿⡀⠀⠸⣿⣧⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠈⣿⣿⠀⣼⣿⠟⠁⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⢈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⣠⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣄
⠀⠀⢠⣾⣿⠟⠁⣿⣿⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⠈⠻⣿⣷⡄
⠀⠀⣿⣿⠁⠀⠀⠈⠁⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⣿
⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟
⠀⠀⠀⢿⣿⡿⣿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟
⠀⠀⠀⠸⣿⣷⠈⠻⣿⣷⣄⡀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⢀⣠⣾⣿⠟⢡⣿⡿⠁
⠀⠀⠀⠀⢻⣿⡆⠀⠈⠛⠿⣿⣿⣿⣿⠿⠿⠛⠿⢿⣿⣶⣤⣀⣀⣤⣶⣿⡿⠿⠛⠿⠿⣿⣿⣿⣿⠿⠛⠁⠀⣾⣿⠃
⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡰⢦⡶⠀⠐⢶⣶⠆⠀⠀⠐⣰⡖⠀⠀⠀⣤⠀⠀⠄⠀⣀⣤⡤⠔⠒⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣻⡑⢿⡇⠀⠀⠀⣷⡀⠀⢠⣴⠠⢿⡠⢶⠀⢿⠀⠀⠴⠊⣹⠁⠀⠀⢘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠄⢉⣤⡀⢸⣿⡼⡶⢮⣻⠀⠁⠘⢻⠀⠞⠁⢠⡤⣖⢹⡆⠀⢀⡴⠇
⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⢿⣾⠃⠀⠙⠀⠀⠂⠀⣀⠀⠀⠀⣡⠝⠻⢦⣌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⣰⣙⢧⡶⣚⡻⣦⣄⢢⡷⠀⠀⣷⢵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⣏⠀⠁⡟⠉⢙⡿⠿⠆⠰⣡⡈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠾⣿⠟⠁⠀⠀⠀⠀⠀⠘⠤⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢃⠁⠀⡀⠀⢀⡆⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣾⠑⠛⠻⠓⠂⠀⠘⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⠐⠋⠛⠃⠚⢘⠂⠂⠊⠘⠛⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠂⢤⠀⠀⠀⠀⠀⠀⢀⢮⡳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠘⣛⣓⠲⢦⡰⢎⢳⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆⠀⣠⣐⠒⠮⣝⢦⡙⢦⡛⠀⠂⡖⠂⠤⠤⠀⠀⠀⢈⡭⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠶⣽⡢⣌⢳⣹⡮⠓⠀⠂⠒⠀⠒⠲⠄⠀⠠⠾⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⣛⣋⣽⣭⣭⣽⣿⣿⣭⣿⠀⣘⢦⡹⣎⠦⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣇⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇⡟⣷⠈⠂⠀⠄⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡘⢿⣿⣿⣿⣿⣿⣿⣮⡹⣿⣿⣿⣿⣿⣿⣿⠁⢺⣵⣳⡟⢎⠷⠁⢀⠐⠁⠴⠆⡐⠖⠀⡀⠀⠈⠰⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡞⢧⡞⣀⠉⠻⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⡇⢸⣛⠽⠗⠬⠀⡔⠇⠄⠠⠔⠆⠀⠢⠚⢁⠀⠰⠐⠿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⡞⠳⠦⠀⠹⣏⠉⢨⣥⠄⡈⠻⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣷⡀⢒⡃⢸⠀⢀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆
⠀⠀⢰⡞⢠⠐⣯⣝⡠⣄⣼⢷⣄⠂⢰⣞⣡⠖⣤⣀⣷⢆⡈⠛⣿⣿⣿⣿⣿⣾⡿⠋⠉⠈⣡⠈⠶⠊⠲⡄⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⢻⣄⡘⢿⣌⠟⣡⠿⣧⡞⢿⠎⠿⣬⠟⣤⡽⣼⣋⣾⣁⡄⠈⠻⣿⣿⡿⠋⠀⠀⣠⠞⠋⠂⠀⠀⠀⠘⠟⠁⠀⠒⠠⠓⠆⠲⣶⠀⠠⠥⠼⢲⠶
⠀⠀⢻⠉⢝⠦⣍⣿⣭⠡⠯⣷⠄⠒⠛⣻⣶⠛⠵⣀⠟⢣⣼⠟⠂⠀⠙⠟⠐⢁⠀⠀⠉⠒⠶⠒⠄⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠖⠂⠸⢣⠸
⠀⠀⢸⢤⠤⣤⡿⠧⣀⠰⠶⣄⢠⡤⠌⣿⠛⣤⣂⣀⣀⣽⣋⠠⡼⠀⣀⠀⠀⣁⠔⠀⠀⠀⠓⢁⣨⡄⢹⠛⣟⣡⡀⠈⠐⢢⠄⠢⣄⠀⠀⠠
⠀⠀⠘⡦⠒⠿⢹⠷⣞⢲⡞⠻⣁⡴⢧⣹⠾⡉⣿⣭⣏⣸⠻⢶⡄⠐⢮⠀⠀⠉⡴⢁⣴⣿⣿⣿⣟⠇⠈⢻⣿⣷⣳⠀⠀⠀⠄⠀⠈⢃⠀⠨⡤⢄⡀
⠀⠀⢿⡋⠸⠷⠟⣶⠜⡂⠛⠞⣉⣵⠈⣩⣾⠛⠋⣩⠙⠋⠖⣈⡠⠐⡏⠡⠻⢄⠐⣿⣿⣿⣿⠟⢫⣅⡀⢘⡶⣌⡟⠀⠀⠴⢊⠁⠀⡣⠀⠀⡀⠠⠏
⠀⠀⠠⣀⢴⡆⢸⡟⠀⠹⠃⠼⢿⡌⠤⢀⡴⢷⣆⠀⠁⠀⠀⠉⣀⠘⣁⠠⠤⠄⣆⠘⢿⡟⠁⠀⠄⡻⢁⣬⣾⣏⣴⡤⣀⠀⣉⠀⠜⠁⠠⠀⠀⠀⠢
⠀⠀⣸⣁⠄⣰⣤⣦⠴⣘⣿⣴⠚⢿⠚⣮⡱⠇⣡⠴⡄⠂⣠⠢⠍⠦⠼⢧⣤⣼⣟⣦⡈⠓⠛⠣⠀⠀⠘⠃⠙⠷⣿⣷⣧⡔⠥⠂⠀⠀⠀⠀⠀⡠⢸
⠀⠀⢨⣍⣤⣭⣥⣵⡞⠫⢁⢼⣧⣜⠡⢈⣡⣦⠜⠃⠀⢀⡤⣆⠀⠀⠘⣧⣳⣽⣶⡿⠃⠀⠀⣘⠢⠀⠀⠀⣀⣜⡻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠴⠄⣠
⠀⠀⣨⡍⠧⢁⢳⡜⠻⠄⣠⡼⠿⠉⠠⢮⠟⢀⡴⠮⢄⣹⢷⣭⣡⣄⡀⢈⡉⠂⠹⠄⢤⠴⠆⠁⠀⠀⣽⠧⠭⠤⠞⠋⢀⣀⡀⠐⠀⢀⡠⠘⢀⡄⠃
⠀⠀⣠⠹⠀⣫⢛⣃⣡⣀⣽⠗⠀⠖⠛⠀⠀⠓⠈⠲⢤⠆⠀⠁⠸⠗⣀⠁⠁⠈⠀⠂⠚⠂⠀⠠⠠⠰⠿⣯⠝⠀⠀⠀⠀⠀⢀⠀⠀⢬⣥⢶⠻⣤⠇
⠀⠀⣟⣳⣤⣹⣯⠹⡆⠉⢁⣴⠔⠁⣄⡛⡻⠛⠟⢳⣆⢀⡀⠀⡘⠿⠴⠃⠄⠀⠀⠀⠀⠀⠀⠠⠄⡉⠀⠀⠀⠀⣴⡶⠣⣈⠉⢶⡰⡀⠑⢎⣧⡹⡇
⠀⠀⢿⡭⡇⢤⣚⡷⠃⣠⡿⠈⣠⡄⣌⣡⡅⠀⠀⢀⣍⣉⠁⠿⠛⣓⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⢀⠜⠛⢀⡍⠀⠀⠀⠁⢚⣣⡅⠀⠈⠋⠁⡄
⠀⠀⢈⠀⢱⣬⡿⠁⠾⠇⢁⢾⡁⠈⠁⣻⡶⠤⠄⣰⣆⣀⣨⡟⣯⠃⢺⡟⢶⣄⣄⣐⡀⡤⢰⠐⠀⢀⠻⡆⣔⣬⢆⠙⣊⢶⣀⠀⠀⢠⡄⠀⠙⠁
⠀⠀⢿⠖⣷⡜⢀⡜⠂⣠⠴⠃⠀⡁⢀⣀⣉⠐⠚⠁⠈⠁⢻⣇⣎⢢⠻⣼⣶⣿⡞⠛⠃⠛⡾⢄⠀⠈⢵⡟⢀⡙⢀⡤⠃⣄⡉⢷⣶⢫⡀
⠀⠀⠘⠀⡌⢠⠟⢠⠎⠀⣠⠚⠛⠃⡈⠙⠩⠥⣀⣀⠀⠀⣾⡛⢪⢗⡤⠒⠉⠈⣓⢀⡦⣴⠆⠰⠆⡀⠀⠀⡀⢁⡼⢃⡀⠈⢁⣬⠙⣤⠀⠀⠀⠁⢘
⠀⠀⢰⡄⠀⠀⢰⠃⠀⣴⡾⣠⢁⣬⠃⠀⠀⢀⠷⠠⠍⡙⠃⠐⠋⢻⣅⣀⠀⣨⢁⡉⣈⡑⠀⠀⠒⣍⠂⠒⡜⢪⣨⠏⡀⡠⣮⠘⡆⣩⠀⡐⢂⠀⠶
⠀⠀⠘⠃⠀⠀⠉⠀⠈⠋⠀⠁⠉⠈⠁⠀⠀⠘⠃⠐⠀⠙⠀⠀⠀⠚⠚⠁⠘⠛⠘⠃⠀⠀⠀⠀⠀⠀⠐⠃⠀⠃⠈⠃⠙⠉⠉⠘⠃⠋⠀⠃⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡏⣽⡦⡾⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢼⡏⠘⠷⠧⠿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⠀⠀⠀⠀⠀⠁⠉⠘⠛⠛⠒⠒⠶⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠤⠤⠴⠶⠦⠤⣤⣤⣤⣄⣀⣐⣇⠈⠙⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠖⠋⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⣠⢤⣀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣶⣤⣤⣌⣉⠓⠲⠶⠶⠖⠒⠛⠉⠉⠉⠉⠀⠀⠀⣀⡤⠞⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⠛⢠⠈⠁⣀⠈⠛⠓⠶⠢⡑⢢⠀⢀⡈⠉⠳⢭⡳⢯⣍⠉⠒⠒⠒⠲⠶⠶⠶⠶⠒⠚⠛⠉⣁⠤⠊⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⡄⢣⡄⣀⢈⠽⠠⡄⣑⣤⡍⠐⡄⠉⠂⠀⡄⠙⢦⡈⠻⣏⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⣉⠠⠤⢚⡕
⠀⠀⠀⠀⠀⣀⣤⢖⣊⠉⠉⠀⠊⠷⡄⠠⣄⠀⠀⠃⠀⡨⠄⠘⠁⠰⠁⣡⢧⣄⣀⠁⢄⠙⢦⠈⢳⡤⠴⠒⠒⠒⠚⢉⣩⣭⠤⠖⠛⠁
⠀⠀⠀⠀⠸⡁⣰⡋⠁⠈⡠⠂⠀⢀⡀⠀⠀⠉⠛⠋⣀⠄⠊⠉⠋⠄⠤⠉⠂⡠⠪⡓⠤⢱⡄⢣⠈⣧⡤⠶⠖⠚⠛⠉
⠀⠀⠀⠀⠀⠿⣄⠙⠦⠂⠉⠐⢲⡞⠈⢲⠀⠀⠀⠀⠀⠙⠓⠦⢤⣌⣀⠄⠀⠙⠆⠀⠀⠠⠁⢨⡿⠁
⠀⠀⠀⠀⠀⠀⠈⡦⠀⢒⠀⠉⡉⠙⠶⠲⠃⢴⠀⢄⠀⠀⠀⠀⠀⠀⠉⠓⣶⠶⠶⠶⠖⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠟⢣⣀⣀⡍⠀⠎⡴⠁⠀⢡⣀⢁⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⣏⣀⠐⠤⠔⢋⡟⠉⢁⢧⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡁⠀⠀⡡⠝⢦⣤⣘⠂⠉⣀⣞⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠞⠑⠚⠋⠀⠉⠛⠛⠉⠉

⠀⢀⡀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠒⠀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠿⠿⠛⠻⠿⠿⠿⠿⠛⠻⠿⠗⠀⠀⠀⠠⠀⠀⠠
⠰⣿⣿⡇⠰⣿⣿⡇⢰⣿⣿⡇⣉⢈⡁⣈⠀⡁⢈⠀⡁⢈⡁⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠠⠀⠀⠀⠀⠀⡀
⡀⠈⠉⢀⡀⠉⠉⢀⡀⠉⠉⠀⠤⠠⠄⠠⠀⠄⠠⠀⠄⠠⠄⣤⣤⣀⣀⣤⣤⣤⣤⣀⣠⣤⣤⠀⠈⠂⠀⠀⠀⠀⠢
⠁⣀⣀⠀⠁⣀⣀⠈⠁⣀⣀⠀⠐⠀⠆⠰⠀⠆⠐⠀⠆⠰⠀⠛⠛⠉⠙⠛⠛⠛⠛⠉⠙⠛⠋⠀⠀⠀⠈⠂⡀
⠀⠉⠩⠁⠀⠉⠩⠁⠀⠉⠭⠁⠀⠀⠃⠘⠀⠃⠘⠀⠃⠘⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⣀⡀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⡟⠀⣿⣿⠛⠃⢰⣿⠟⠻⠧⠘⢻⣿⡟⠃⠹⣿⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣿⡿⠛⠃⢈⣛⠛⢿⣶⠀⠘⣿⡇⠀⠀⠘⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠃⠻⠿⠿⠟⠈⠻⠿⠿⠋⠀⠀⠿⠃⠀⠀⠀⠿⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠢⠀⢂⠘⡄⠐⠀⠣⠀⠂⠐⡄⠒⠐⠂⠐⠀⠂⠐⠀⠂⠐⠀⠈⡠⢄⠉⣡⠤⡈⢁⠤⢄⠉⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠎⢠⠃⠐⠁⡜⠀⠊⢠⠁⡔⠁⣉⢈⡁⢈⠀⡁⢈⠀⡁⢈⡁⣀⠑⠊⣀⡙⠒⢁⡈⠒⠊⣀⠁⠐⠄
⠡⠀⢂⠘⡄⠑⠀⢣⠈⠂⠐⡄⠀⠀⡄⢠⠀⡄⠠⠀⡄⢨⠀⠠⠃⠘⠤⠜⠀⠣⠜⠀⠘⠤⠃⠀⠀⠐⠄
⠊⢠⠁⠐⠁⡌⠀⠊⢠⠁⡔⠀⠤⠀⠄⠰⠀⠄⠠⠀⠆⠰⠀⠀⢎⡱⠀⢴⣉⠆⠰⣉⡡⠀⠆⠄⠀⠀⠀⠐
⠁⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢉⠀⠳⣄⡀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢢⡀⠀⠈⢳⣦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢀⢤⠀⠤⢀⣀⡁⢐⢿⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠁⠛⠁⠉⠙⢒⠉⣠⠞⠉⠀⠑⣄⣀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡞⠀⡇⠀⠀⠀⠀⡟⢻⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⠴⢃⣀⣠⠴⠚⠀⣘⡇⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡖⠒⠴⠒⠒⠂⠀⣀⡤⠖⠋⠉⠉⠀⣀⣤⣴⣿⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠲⢤⣤⣤⣴⣿⣅⣀⣀⣤⣶⠶⡿⠛⠝⣃⢈⣨⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢤⣀⡀⢀⠀⠀⠈⠀⠈⠈⠎⠁⡡⠀⣀⣢⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⡌⡏⢹⡗⢺⠓⡟⠛⡟⢻⠿⣿⠛⡏⢹⣡⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠑⢹⡈⣇⠨⡇⢳⠠⡇⢸⠀⡇⢰⡇⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣾⡇⣿⠀⣧⣸⢰⣇⣸⣀⣧⣼⣹⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡇⣿⣿⣝⡟⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡝⣦⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⣷⣿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⡼⣽⣿⣿⣿⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠈⠑⢢⣄⣤⣴⡞⡕⣾⣿⣿⠇⠀⣼⡃⠀⠀⢀⣀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠱⣴⣿⠋⢴⣶⣿⠟⠁⢸⣿⣿⡄⠀⢹⣧⣶⣿⣿⡏⣿⣷⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣷⡄
⠀⠀⠒⡒⣀⠀⠀⢸⢀⠀⠀⠘⣧⣼⢋⠥⣴⣦⡄⠀⢿⣿⣧⠀⣸⡿⠛⠻⣿⢇⣸⠟⡻⢿⣯⣤⠤⠤⠤⠤⠤⠶⠟⠛⠁
⠀⠰⠟⠉⠟⠄⠀⢸⠀⣠⣶⣦⠈⠛⠉⠐⡿⡿⣿⠀⠘⣿⣿⣶⠋⣴⡿⠃⠜⠏⠑⠈⠿⡦⢹⣿⣷⡄
⠀⠠⢴⠆⢲⠠⠀⠸⡀⠽⠋⣱⢠⠞⠁⠀⠀⠀⠐⡄⠀⣼⣿⣿⣷⣤⠊⠁⠀⠀⠀⠀⠁⠶⣾⣿⣿⠇
⠀⠀⠞⠠⠏⠀⠀⢠⡙⠀⣶⠁⡚⠀⠀⠈⢾⠀⠀⣷⣎⢻⣿⡿⠟⡇⡄⢀⣰⠼⠄⠴⣄⣆⠹⡀⢸⢠⣄⣀⡀
⠀⠀⡯⡀⡀⠀⠀⠀⣏⡉⠉⠰⠞⠀⠀⠸⡾⠀⡀⠀⢈⡇⠀⠀⠀⠉⢋⠈⠉⠀⠀⠀⠉⠨⠛⢀⡎⠀⠲⡜⠁
⠀⠞⠁⠓⠃⠀⠀⠀⠀⢧⣀⡀⠂⠠⣤⡤⠔⠊⠀⣀⠾⢦⣤⠀⠀⠀⠘⠤⣀⣀⡤⠶⠂⢀⡤⠜⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢲⣬⠗⡶⠋⠽⠷⢾⠏⢹⣦⠱⣖⠲⢶⡘⡏⣤⠞⠉⠉⠁⠀⠀⠒⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠥⢁⠀⢧⠀⢀⠀⢠⡆⣿⡄⠰⠟⠢⠉⠀⠀⠉⢧⡀⠀⠀⠀⠀⢾⠧⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⡍⠂⢀⣙⣾⠿⠾⣵⠏⠀⢿⠁⡆⠖⡷⣤⠒⡢⣓⢐⣿⡄⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⡴⠚⠙⠉⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠛⠓⠼⣤⣾⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠴⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡿⠏⠁⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡞⠻⠷⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠒⢀⣤⣈⣴⣴⣶⣦⣴⡿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠉⢿⣿⣿⣿⣿⣷⣄⣴⣶⣶⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡦
⠀⠀⠀⢰⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠈⠀⠀⠈⠉⠱⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠆
⠀⠀⢀⣠⣿⣴⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣿⣿⣟⣉⣻⣿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⡠
⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⠼⠉⠙⠀⣹⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠈⠙⣿⡿⢻⣿⣿⣿⣽⣿⣿⣮⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣾⣷⣶⣶⣴⣦⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠛⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢵⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢀⣀⣤⣥⣴⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⠱⣾⣿⡿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠛⠋⠿⠛⢿⣿⣿⣿⣿⣧⣤⡎⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⠙⠛⠛⢀⠀⠀⢴⡆⠈⠙⠛⠛⠉⠁⠀⠀⠛⠋⠻⠿⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣄⣰⢟⡃⠀⠀⠀⢀⣤⣴⣶⣤⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠁⠀⣀⡀⠿⣿⡿⠿⣽⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⠶⢾⡉⣉⡉⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⣶⢀⡀
⠀⠀⠀⠀⢠⣾⣿⣻⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⠛⣶⣿⣿⣿⣿⣷⣤⠀⠒⠂⠀⠀⠁
⠀⠀⠀⠺⣿⣿⣿⡿⠿⠉⣀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣷⣦⡀⠰⣶⣄⡀⡀⢀⣀⣄⣤⣠⣄⣸⣟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠟⠛⢩⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣹⠿⠿⠟⠉⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠦⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣀⣀⣤⣶⣿⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡶⣛⣹⣯⣹⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠊⠑⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠋⣁⡠⠶⠖⠳⣄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠒⠊⠉⠀⠀⠀⠀⠀⠣⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠄⠉⠀⠀⠈⠳⡖⠒⢦⣄⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⣠⠞⠋⠙⠳⣄⣧⣴⠤⢤⣀⠀⠀⠀⡇⠀⠀⣨⣅⡀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⠀⠀⣸⢁⣀⣤⠤⠤⠤⣄⠀⠀⠀⠈⠉⠛⠳⣇⡴⠛⠁⠀⠙⢦⣤⣬⣇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠠⣿⣤⡀⣠⠟⠋⠁⠀⠀⠀⠀⠈⠳⣤⣤⠴⠶⣏⢉⡽⠛⠋⠉⠉⠛⠳⢦⡀⠸⡇
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⣷⠒⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠇
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⡾⢧⣄⣀⣀⣀⣀⣀⣈⣹⣆⣀⣏⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘
⠀⣠⠞⠉⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣦⣤⣴⠚⢉⠉⢻⡄
⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠇⠀⠀⠀⢰
⣠⠟⠀⠀⠀⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⣾⡁⢠⡄⠀⠀⢀⣤⠀⠀⠀⢠⣄⠀⠀⠀⢀⣤⠀⠀⢠⣿⠀⠀⠀⠀⣼
⣏⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠈⢷⢾⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣆⠀⠀⠀⢹
⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⡇⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⠀⠀⢸⡷⠈⢳⡄⠀⠘
⠀⠈⢹⡶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⢺⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⣠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠄⠀⠀⢠⡆⢹⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠳⣄⣠⠾⠁⠀⠹⣶⠶⠶⠓⢦⣀⣤⣄⠀⠀⣠⣤⡶⠋⣧⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡜⢸⠀⢠
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠢⡀⢀⡠⠌⠃⢾⠀⣾⠋⣼⠁⠀⣿⠘⣧⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡇⢸⣤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⢢⡀⠀⠒⠉⠃⠄⠀⢠⡟⢠⡇⣼⠃⠀⠀⢸⡆⢻⡀⠈⣷⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣼⠃⢸⠁⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⢂⣀⡀⠠⠈⠉⣹⠃⢸⣷⠏⠀⠀⠀⠈⣷⠘⣧⠀⢻⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⢀⡟⢠⡏⢸⡟
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠉⠢⠀⠀⣰⠏⢀⣼⡏⠀⠀⠀⠀⠀⠸⣇⠸⣇⠈⢣⠀⠀⠸⡆⠀⠀⢸⠇⠀⠀⠀⡈⠁⠀⡘⢀⡾⢠⡿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠐⢤⡀⠀⠶⠈⠉⠙⠓⢛⡿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣦⠈⢣⠀⠀⠙⡀⠀⠀⠀⠀⠀⠰⠁⠀⡜⢁⡾⢡⡿⠁
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠑⠠⡀⡀⠄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡘⢷⡄⠑⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠊⣠⠏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠘⠢⠀⠈⠉⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢁⣴⠏
⠀⠀⠀⠀⠀⠀⢸⡆⠐⢀⠘⠓⠂⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣈⠉⠓⠒⠶⠖⠚⠛⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠑⠶⠆⠈⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠦⠤⠀⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠢⢤⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢠⠀⠀⢀⡀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⣴⠋⠀⠀⠈⢧⠀⠀⠀⠀⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠣⠀⠀⠀⢀⣀⣤⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣳⣦⣤⣶⣤⣤⣶⣶⣶⣚⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣿⣆⣠⣴⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠠⠠⠒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⠸⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣴⠛⢏⡞⠠⣻⡿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⡿⠃⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⢩⠉⣟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡍⠀⡟⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣬⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡕⠋⢢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⢿⡥⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡷⢾⣻⣭⢵⣿⣿⣿⣿⣷⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⢿⣿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣼⣿⣿⣿⣷⠉⢹⠉⠉⡏⠉⢹⠋⠉⢻⠉⠉⡏⠉⢹⠉⠉⡛⠉⢡⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣴⣶⣶⣶⣶⣶
⠹⣿⣿⣿⠟⠀⢺⠀⠀⡷⠀⢸⠆⠀⢾⠀⠐⡇⠀⢸⠆⠀⠶⠀⠺⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠿⠿⠿⠿
⠀⠀⠉⠀⠀⣀⣸⣀⣀⣧⣀⣸⣄⣀⣼⣀⣀⣇⣀⣸⣀⣀⣥⣀⣠⣤⣤⣤⣀⣀⢀⣤⣤⣤⣤⣤⣤⡄⣀⡀⣤
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠸⠀⠀⠂⠀⢸⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿
⠀⣀⣤⣀⠀⠉⢹⠉⠉⡏⠉⢹⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠘⠟⡛⠛⡓⠒⢺⠒⠒⡗⠒⠚⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠉⠻⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿
⢀⠠⠈⠋⠀⠀⢸⠀⠀⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠋⠈⠉⠙⠛⠛⠛⠛⠛
⠁⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⣠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢶⣶⣶⣶⣆⣤⣄⣶
⡀⠔⠊⠉⠂⠉⢹⠉⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠿⠿⠿⠟⠻⠛⠿
⠁⠀⠄⡀⠀⠒⢺⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⣤⣤⣤
⡀⠀⠀⠀⠀⠤⢼⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠿⠿⢿⣿⣿⣿
⠈⠑⢠⣤⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠰⠿⠿⠿⢿⣿⠷⠨⣽⣿⣿⣿⣿⠀⠀⠈⠳⠶⠋⠀⠀⠘
⠄⠊⠀⠀⠀⠉⢹⠁⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⣸⣿⣿⣿⠇⠀⠀⢲⣀⣀⣰⠋⠙⣆
⠀⠀⡠⢄⡀⠉⢹⠉⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠤⠞⠀⡀⠘⠦⠴⠃
⠆⡉⠀⠀⠀⠒⢺⠒⠒⡶⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡄⠀⢰⠋⠉⢳⠀⠀⣼
⢢⡀⠀⢦⡀⣀⣸⣀⣀⣇⣀⣠⡀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠐⠊⠀⠀⠀⠓⠒⠋⠀⠀⠈
⠀⣱⠀⠀⡇⠀⢸⠀⠀⡇⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣄⣀⣠⠎⠉⢳⣀⣀⣰⠋⠙⣦
⡴⠃⠀⡴⠁⠉⢹⠉⠉⡏⠉⢹⠉⠉⢹⠉⠉⡇⠀⢠⠀⠀⡄⠀⠀⠀⠙⠦⠞⠁⠀⠀⠳⠴⠊⠀⠀⠘⠢⠔⠃
⢇⠀⠀⣇⠀⠒⢺⠒⠒⡗⠒⢺⠒⠒⢺⠒⠒⡗⠒⢺⠒⠒⠖⠒⠚⠓⣆⣀⣀⡔⠛⠲⣄⣀⣠⠞⠛⢦⣀⣀⡰
⠈⢧⠀⠈⣧⠄⢼⠤⠤⣧⠠⢸⡄⠄⣼⠄⠤⡧⠤⢼⡤⠀⣤⠠⠤⠴⠋⠀⠀⠳⠤⠜⠁⠀⠈⠦⠤⠞⠀⠀⠙
⢠⠏⠀⣠⠇⠀⢸⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⡂⠀⠀⠀⡰⠒⠲⡀⠀⢀⡔⠒⢦⠀⠀⢠⠖⠲⡄

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣾⠿⢻⣶⣤⡀⠀⠀⠤⡤⠤⡐⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⠛⠛⠁⠈⠀⠆⠀⠀⠀⠀⠀⠉⠴⠂⠂⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣸⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠒⠄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠿⣷⣶⡶⡛⠋⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⣀⠔⠀⣀⡀⠀⠈⠀⠀⣴⣦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣄⡀⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡁⠐⠀⠀⠀⠀⠈⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠐⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢀⣂⣄⠀⠀⠠⠠⠀⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣻⣿⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠠⢤⡚⢂⣀⠡⣀⠀⢀⠄⠀⠆⠀⠀⠀⠈
⠀⠀⢰⡄⠀⠀⠃⠀⠀⠈⠀⠀⠂⠀⠱⠀⠀⠀⠀⠀⡀⠀⢀⣠⣤⣤⡶⠀⠀⠀⠀⢐⠁⠀⠀⠀⠁⠀⠙⡇⠘⢠⠀⠀⠀⠀⠀⠐⠿⠿⠦
⠀⢸⣿⠀⠀⠀⠌⠀⠰⡄⠐⠀⠀⠂⠀⠀⠀⠀⠀⠈⠤⡴⢿⣿⣶⠟⠁⠀⠀⠀⠀⠈⠣⢀⠀⣀⣴⡄⢰⡗
⠀⠘⠿⣄⠀⠀⠃⠂⠀⠈⠑⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠋⠀⠉
⠀⠀⠀⠉⠉⠀⣧⠀⠀⠀⠀⠀⠀⠀⣀⠸⠒⢀⡰⠶⠄⠀⠂⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⢦⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢈⡀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⢺⢿⠁⠀⢠⠞⠓⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠁⠀⠀⠀⠀⠠⡀⠑⠀⠂⠈⢀⠀⠀⠀⠀⣠⠔⠉⠟⠀⠀⢘⠀⠀⠀⠀⠀⠉⢹⠀⠀⢀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⡠⠋⠓⠒⠒⠊⠁⠀⣠⣼⣗⠉⣆⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⣠⠎⠀⠀⠀⠁⠀⠀⣼⣿
⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⣰⣿⡷⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⡂⠀⠀⠀⠀⠀⣻⡾
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢦⠉⠙⠛⠚⠉⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⠴⠀⡤⠈⠛⠳⣄⠁
⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠄⠀⠠⠀⢠⡀⠀⠀⣑⠀⠀⠀⠀⠀⢰⠁⠀⠠⠄⠠⡆⠀⠀⠀⠀⠘⠁⠀⠀⠀⢡⡄⣿
⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠈⠣⠔⠃⠀⠀⠀⠀⠈⢼⣇⠀⠀⠐⠂⠃⠀⠀⢧⠀⠃⣀⠀⢀⠀⠁⠀⠀⠀⠀⠘⢄⣀⡀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠆⢀⣀⠚⣳⠴⡀⠀⠀⠀⠈⠻⠧⣤⡤⠒⢢⡀⠀⠈⠳⢄⣀⣀⣀⡀⠐⠀⠀⠀⡀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡞⠉⠀⠀⠀⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⢼⣆⡀⠀⠀⢀⠼⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⢳⡬⠁⠉⠀⢠⠚⠂⡀⠀⠀⠀⠀⠀⠈⠀⣅⢠⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⠀⠱⠄⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣐⣁⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢠⡤⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣼⠿⠿⠿⠟⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣄⡀
⠀⠀⠀⣨⣿⢿⠿⡿⣿⡫⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡿⠭⣳⡄
⠀⠀⣼⠏⠁⠈⡀⣇⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⢺⣵⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢺⠭⢽⠗⠩⢄
⠀⢰⡏⠀⢀⢺⣿⡇⡇⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠎⠀⣠⡀⢘⣀⠀⠀⠱⡀⠈⠁
⠀⠀⣇⠀⠘⠊⠊⠑⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢘⠀⠀⣹⢯⡿⢫⡆⠀⠀⡇⠀⠠⠄
⠀⠀⠙⠷⢤⣀⣀⣤⠞⠋⠠⡀⠀⠀⠀⠂⠀⣸⠃⢠⣷⡎⠁⠀⠙⣇⠀⠀⠀⠀⠁⠘⡄⠀⠘⠃⠁⠀⠀⠀⡰⠁
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠆⠈⠢⢀⣀⣀⠀⠄⠊⠀⡀
⠀⠀⠀⠈⠀⠸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠠⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠄⠀⠀⠀⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡐⠐⠂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣤⣠⣀⣄⣀⡀⡄⣤⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡐⠀⠀⠈⠁
⢀⠄⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈
⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠀⠀⠀⠀⠈⠱⠶⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠳⣄⠀⢀⠠⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠰⠃⠉⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⢀⡀⠤⠈⠁⠰⠀⠀⠀⠀⠀⡀⠙⠓⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠏⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠂⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⡠⢀⣠⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣮⣵⣦⣴⣧⣼⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠘⠻⣷⡀⠘⠀⠀⠘⠈⡽⠃⠀⠉⠁⠂⠀⠀⠀⠀⠜⠀⠠⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠈⠆
⡀⠁⠉⠐⠰⠦⡀⠀⠀⠀⠀⢠⣎⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⡤⠀⠘
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣼⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠛⠒⠀⠠⠀⠀⠉⠁⠀⠀⠂⠐⠂⠀⠀⠀⠀⠤⠀⢷⡀⠄
⠠⠀⠀⢀⣠⠟⠑⠑⠞⠚⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠃⡸⣇
⣴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣀⡀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⣌⡀⡖⣢⠄⠀⠀⠀⠈⠳
⡀⠀⡀⠀⠀⠄⠀⠀⠀⠠⠜⠁⠀⠀⠀⠉⣿⣄⣀⡀⠀⠀⠀⠜⠳⣥⡄⠀⢀⡰⢃⡄⠀⠀⠀⠀⠛⠐⠬⡗⠻⣖⣺⣇
⡴⣒⠟⠳⠶⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⠀⠀⠀⠀⠐⠶⠝⠳⠏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⣿⡧
⡾⡃⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠙⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣤⠀⠀⢀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⣦⣠⣤⠶⠂⠁⠀⠠⣰⣤⣟⠒⡀⠒⠋⠀⠀⠀⠀⠡⢠⡟⠈⠁⠀⠀⢠⡀⠑⢤⠀⠀⠀⠀⠀⢃⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠠⠃⠀⢈⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⢻⡆⠀⡤
⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠃⠀⠸⠂⠀⠀⠀⠀⠀⠈⠲⢦⣤⠤⠶⠖⠛⠡⣈⠀⠀⠀⣱⣶⠊⠧⠄⠀⢸⠀⢀⣀⠁⠐⠂
⠈⠀⠀⠀⠀⠀⠛⠥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢾⡿⠉⠃⠀⠀⠀⢸⡆⠀⠈⠉⠀⠐
⣀⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⠐
⠟⢠⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠀⠀⠠⠠⠒⠦⣄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⣀⣀⡤
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⠀⢰⣡⢌⣠⣿⣷⡖⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⣤⡀
⠀⠀⠄⠠⣤⠇⢤⡰⠂⠀⠀⠈⢿⣂⠀⢡⡴⡷⣶⠋⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡖⠊⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠽⡃⢀⡀⠀⠀⠀⠀⠹⠿⣿⡶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦⠴⠋⠋⠀⠀⠀⠀⠀⠉⠁⣼⢆⡀
⣀⢀⡀⡤⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠃⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡝⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⠈⠁⠲⠉⠀⠀⠀⠀⠘⠃⣰⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⣀⣀⣐⣀⣀⣀⣀⣀⣀⣠⣄⣠⣀⣒⣀⣉⣛⣷⣠⣬⣃⣀⣁⣀⣀⣀⣀⣀⣀⣸⣋⣀⣃⣀⣂⣐⣃⣀⣀⣀⣀⣂⣸⣋⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠄⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠘⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⢰⢀⠃⠀⠀⠀⠀⠀⠀⡐⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠂⡄
⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠐⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡒⠁⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠁
⢌⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠣⢐⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠞⡠⠂⠁
⠀⠑⠠⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⣔⠁⠊
⠀⠀⠀⠈⠒⢄⠑⢄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠐⠢⢤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠢⠱⡀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⣀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣄⡈⠑⢦⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡰⠋⠀⠀⣠⣾⠿⠿⠿⠧⠀⠀⠀⠈⠉⠉⠛⠻⣷⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣼⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠃⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠁⠠⠊⠀⠀⠀⠉⠢⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⡀⠀⠀⢩⠀⠀⠀⣀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⠴⠶⠶⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢯⡿⠀⠀⢸⠀⠀⠸⣽⠇⠀⠀⡅⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡇⠀⠀⠀⠘⡖⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⣠⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠠⠁⢀⣀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡄⠀⢄⠀⠀⡇⠀⠀⡃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠋⢁⡀⠀⠈⠢⣀⡀⢀⡠⠈⠀⠑⠤⣀⣀⡀⠔⠁⠀⠀⠙⠛⠀⠀⠀⣸⠀⠀⠀⠀⢧⠀⠀⠙⠉⠑⠤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡱⢀⠁⠀⠀⠀⢈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠃⠀⢀⣶⡾⠀⠀⠀⢰⠇⠀⠀⠀⢀⠜⢠⠋⠉⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢿⣶⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⠃⠀⠀⢠⣯⠄⠤⠤⠚⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢹⣦⠀⠈⢿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⢿⣿⣄⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⣀⠼⠋⠳⣄⠈⠻⠟⠉⠀⠀⠀⠉⠁⠀⠀⠀⠉⠛⢿⣿⡿⠃⠀⣠⠞⠁
⠀⠀⢀⡀⠠⠤⢀⡴⠁⣠⠚⠁⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠟⠁⠀⡼⠁
⠀⡐⠁⣀⡀⠀⠀⠀⠼⠁⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠌⠀⠀⠀⣠⣶⠀⢢⠀⠀⢆⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠘⠦⡤⠼⡏⠼⠀⠘⢆⡀⢀⡁⠀⠀⠀⠀⠀⡗⠈⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣇⢀⠀⠤⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⠠⠤⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣍⠀⠤⠤⠄⠐⠒⠂⠈⠉⠉⣀⣀⡀⠠⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⠠⠤⠤⠐⠒⠒⠈⠉⠉⣀⣀⠀⠀⢤⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⣤⡀⠒⠒⠀⠉⠉⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢶⣶⣤⣤⣴⣶⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣹⢣⢎⣿⣝⢯⣝⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⡌⠀⢛⡠⡿⠋⢻⠘⣯⠈⣷⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⣧⣦⡿⣤⣤⠴⢋⣰⣟⣠⡿⠀⡿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠋⢛⣡⠤⡶⠖⠓⠺⠯⠉⣀⡀⠡⠚⠗⣠⣿⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠤⠊⠁⠀⣀⣤⣤⣶⣶⠿⠷⠶⢦⣶⠶⣾⠟⣿⣿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣤⠶⠛⠋⠉⣟⢡⠤⠤⠒⢻⣋⡡⠾⡟⢆⣿⣿⡇⣿⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⡼⠋⠁⣠⠖⠋⠉⣀⡤⠖⠚⠉⠁⠀⣀⣘⣠⠾⣻⣿⢃⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢇⣿⠀⣰⠋⠀⢀⡴⠊⠁⢀⡠⠴⠒⠈⠉⣁⣠⡴⠞⣉⠴⠞⠛⣾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⢿⡄⣧⠀⠀⡎⠀⢀⡖⠉⢀⣠⡴⠚⠋⢉⣠⡖⠃⠀⣀⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠦⣄⣀⠈⠚⠳⣤⣇⣀⣿⢁⣴⣿⣃⣀⣤⣴⠿⣿⣏⣻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠈⠉⠑⠒⠲⠬⣬⣭⣭⣯⣹⣯⣿⣷⣿⡶⣿⢿⢻⡏⡿⢹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠈⠄⠇⠸⠄⢸⠠⡇⢸⡇⣿⡞⢸⢡⣇⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆⢸⠸⡇⢸⢠⡇⣇⣿⣾⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠐⡈⠂⠀⠀⠀⠀⠀⣧⢸⢠⠀⡟⢸⠰⢼⣇⡏⣿⣿⣟⣿⣷⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣦⣯⢪⢺⠈⠀⢢⠁⢸⢸⣸⢰⣇⣿⣿⣿⢸⣿⣿⣿⣿⣯⣿⢿⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⣏⣏⣿⣧⢱⣸⢸⣼⣿⣿⣼⣿⣷⣿⣟⣿⣿⣿⣿⣿⢿⡿⢯⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠹⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡷⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⣛⠭⠕⠒⠛⣋⠉⠈⠈⠈⠈⠁⠉⠉⠉⠋⠛⠶⠮⣭⣛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠁⠀⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⢀⠄⠀⣄⠀⠀⠀⠙⠻⣶⣌⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠹⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⠃⠀⠀⠀⠂⠀⠀⠀⠀⠻⣧⠘⣧
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣿⡆⢻⢧
⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢄⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⠇⣿⠸⣧
⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠴⠛⠁⠀⠀⠀⡠⣖⣾⡟⢀⣿⠇⣿
⢀⣾⠁⠀⠀⣤⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡫⣗⣿⠁⣼⣿⠀⣿
⣸⠇⠀⠀⠀⢈⣤⣤⡄⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣿⣿⠃⣰⣿⡿⠀⣿
⣿⢀⡂⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡺⢝⣿⡿⠃⣴⣿⣿⠇⢸⣿
⣿⣼⣆⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⢀⡀⢄⡪⣕⣮⣷⠟⢁⣾⣿⣿⡟⢀⣿⡟
⢹⣷⣿⣮⣀⠀⢀⠔⡠⣖⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠨⣒⢭⣳⡿⢃⣴⣿⣿⣿⡟⢀⣾⡿⠁
⠈⢿⡘⣿⣿⣔⡵⡫⣾⢕⡵⡠⢀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠁⠰⠋⢁⠤⣀⠀⠀⠀⢀⠬⣓⢭⣲⣽⡟⢡⣾⣿⣿⣿⠏⣠⣾⡿⠁
⠀⠈⢷⣌⢿⣿⣿⣾⣕⠷⡫⣒⠁⠀⠀⠀⡀⠀⠀⠀⠀⢄⡠⢐⠉⠓⠽⠲⢑⡦⣀⢅⣽⣺⣽⡿⠋⣠⣿⣿⣿⠟⢁⣴⣿⠟
⠀⠀⠀⠙⣦⡙⠻⣿⣷⣯⡮⠁⠀⡀⠰⣔⢌⢢⡀⠀⠀⠀⠀⡲⢑⢦⡈⣪⣗⣿⣾⣷⡿⠟⢉⣤⣾⣿⣿⠟⣡⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢷⣌⡙⠻⢿⣧⣷⣵⣌⣪⡳⣵⣝⢆⢤⡀⣢⣪⣷⣿⣿⠿⠟⢛⣉⣤⣴⣾⣿⣿⠿⢋⣥⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣉⡙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⣉⣤⣴⣾⣿⣿⡿⠿⣛⣩⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣟⣛⣫⣭⣷⣶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡋⠻⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⣻⣿⣷⠏⠁⢶⡷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣸⡂⢀⣤⣾⣷⢠⣤⢤⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⣿⣾⣿⣿⣿⡷⣌⣁⣉⣼⠟⠛⢩⢛⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠁⠈⠻⠏⠀⠀⠀⢠⣜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠟⠻⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⣄⡀⠀⠠⠀⠀⠀⣄⣠⣴⣾⠿⠟⠉⠉⠁⠀⠀⢤⣄⠀⢰⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠙⠛⠚⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⠆⠚⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡟⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠉⠁⠐⠒⠐⠦⠤⢦⡤⣤⣤⣤⢶⠶⠶⠞⠛⣋⠉⠳⣤⣧⢉⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣄⡀⢀⡀⠀⢀⠀⠀⢀⡀⠄⠉⣤⢸⣷⣦⣄⢇⡉⣰⣖⣼⣿⣶⠻⢿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡯⠵⠛⣯⣫⠾⠛⢦⣤⢶⠄⣰⠟⣿⢿⠋⠛⢾⣿⣿⡀⠙⠻⣿⠆⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠁⠀⡞⠚⠁⣼⠒⠁⠀⠈⠛⣶⠀⠀⠉⣿⡇⠀⣰⣿⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣷⠀⢰⡆⠀⠀⠀⠀⠀⣿⠀⣤⡀⠀⢰⣿⠐⠀⢸⣿⡧⠀⣿⡏⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠸⣷⠀⠀⣷⠀⠀⣿⣸⣷⣵⠀⢸⣿⣣⠀⣾⣿⠇⣀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⡆⢡⣼⣀⢠⣿⣿⣿⡿⠀⣿⣿⡏⢀⣿⣿⡇⢸⡿⣿⣿⣷⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣾⣇⣸⣿⣿⡸⣿⢮⣿⣧⢈⣿⣿⡃⢰⣿⣿⡆⣿⣻⣿⣿⡧⣞⣶⣾⠭⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣿⣿⢰⣿⣿⡆⢿⣿⣿⣿⣾⣿⣿⡇⢹⣿⣿⡁⣷⣿⣿⣿⣷⣶⣴⢶⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠤⠿⣿⣅⣍⣽⣷⣏⣘⣿⣾⣧⣽⣿⠽⣿⣿⣿⡿⣿⣷⡿⣿⣷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⢿⠿⠿⢿⡿⠿⠷⠛⠒⠛⠛⠁⠤




⣿⣿⡿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠔⠒⣿⠆⣾⠋⠉⢁⠤⠤⠤⣄⣹⠀⡏⠙⠓⡒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠤⡆⢰⠉⠀⣬⣥⡌⠳⠟⠘⢿⡀⠀⠈⠒⠒⠲⣤⡈⠀⣷⠀⢨⠗⢴⡳⣆⣱⢠⣤⡀
⠀⠀⠀⠀⢀⡤⠚⡥⢠⡁⢸⠀⠀⢨⣥⣻⢀⣤⠀⣀⠉⠒⠤⣀⠀⠀⠀⠱⠀⠀⠴⠀⠀⠈⢷⡈⠋⢸⡇⠈⡆
⠀⠀⢀⣴⡡⠴⠊⣴⠟⢁⢀⡄⠀⠨⢤⠵⠞⣽⡇⣧⠉⠒⠂⠀⠀⠀⠀⢀⡀⢸⠀⠀⠀⠀⠀⢻⡄⠀⢇⠀⠇⢸⡄
⠀⠀⠘⠁⡖⠂⠻⢁⡴⢺⠈⣇⣴⣼⣤⠤⠴⠛⠃⠚⠒⠒⠒⠒⠒⠒⠒⠉⠀⠸⢤⣄⣀⣀⢀⠀⣧⠀⣌⠲⠬⢧⣽
⠀⠀⠀⠀⠈⠐⠒⠉⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠿⠠⡏⠑⠒⠂⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢈⡑⢦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡝⡿⢺⣦⡙⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠂⡿⣿⠸⣿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠖⠀⠀⠆⠀⢋⠶⢧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡤⢶⠀⢠⠶⠒⠒⠲⠢⠤⢄⠀⢀⣄⠀⠈⠈⠓⠀⢠⠁⠀⠘⢻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢾⡿⣍⢙⣿⠀⡇⢸⠀⣸⠀⠀⠀⠙⢄⣀⣀⡀⠸⠈⢹⠀⡗⢶⡀⣀⠀⠘⠈
⠀⠀⠀⠀⠀⣠⠴⢠⡀⣧⢸⣄⡷⣽⠟⠀⡇⢸⠀⢺⠀⠀⠀⢠⣤⣤⢄⡀⢸⠀⢸⠀⡗⠈⢻⣿⢻⡇
⠀⠀⠀⢠⢛⠁⡆⢸⠁⣳⢸⡟⢳⠚⣻⠀⡗⠈⡄⡈⠀⠀⣄⣀⠀⠀⠀⡇⠈⡁⢸⠀⡇⠰⠌⠳⠚⡇⡆⠙⢦
⠀⠀⠀⢘⠉⣀⠇⡸⠠⣝⡼⠇⠈⠲⠛⠛⠓⠛⠁⠘⠛⠛⠻⠿⠷⢶⣶⡇⢠⡇⢸⠀⣇⠀⣀⠄⠀⣧⢱⡀⡤⣷
⠀⠀⠀⠀⠠⠐⠊⢀⣀⠀⠀⡀⠀⠠⠀⠄⡀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠈⠈⠓⠾⠂⣿⣸⣿⣏⡅⡏⣤⠹⣷⡘⠆
⠀⠀⠀⠀⢠⣾⣿⣽⠷⠌⠀⠤⠠⠀⠀⡀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢻⣄⣷⢸⣧⡉⠱⡀
⠀⠀⠀⠀⠈⠛⠋⠛⠒⠒⠀⠐⠂⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⢧⡁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠓⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢲⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠠⠄⢀⢴⡦⠴⠈⠀⠀⠀⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡌
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠊⢿⠒⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡞⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠤⠾⠤⠤⠤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⠉⢹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⢀⡴⠧⠤⠼⣄⡀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠲⠦⠤⢬⣤⣤⣤⣤⡤⠤⠴⠶⠒⠋⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠲⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠦⠤⣄⣀⣀⣒⣒⣒⣀⡀⢤⠤⠤⠶⠲⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣐⠂⠀⠠⠤⠤⠤⠄⠀⠀⠀⣀⣀⢤⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠈⠉⢉⣋⠉⠙⠊⠉⠛⢋⡉⠉⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠐⠒⠒⠒⠠⠤⠤⠤⠐⠒⠒⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣤⣀⣀⣀⣀⣠⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢀⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠆⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡴⢶⣀⡴⠖⠳⡤⠞⠉⠓⣠⠆⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⡞⠁⠈⠉⠀⠀⠀⠀⠀⠀⡼⠁⣼⠁⠀⠉⠀⠀⠳⠶⠒⠶⡤⠤⣤⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⡞⠀⠀⠀⣀⡤⠤⢤⡀⠀⢸⠃⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠃⢠⡴⠊⠁⠀⠀⠀⠻⠀⢸⡄⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⢷⠀⠀⢘⡇⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⢶⣿⣿⣿⣿⣿⡚⠓⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⢷⡄⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⡄⢹⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⢦⣤⣄⡀⠀⠀⠀⠀⣼⠁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣹⢦⣿⡙⢿⣿⣿⠀⣈⣿⠟⠛⠉⠁⠀⠈⠙⠻⣿⣿⣿⡆⢸⣿⣿⣿⣿⣶⣤⣤⡟⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢽⠀⠉⠃⠀⠙⠛⠚⠉⢙⣣⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣟⣩⡷⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⢸⡁⠀⠀⠀⢲⡌⢿⣿⠀⢿⣿⣿⡿⣿⠟⣩⠟⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠳⠈⠻⠤⠞⠋⢡⣴⠷⢾⡇⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣽⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠘⠁⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⡄⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⠳⠆⠀⠀⠀⣰⣃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢧⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠏⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠘⣆⠀⠀⠈⠙⠳⢶⡶⣺⠏⠙⠶⣄⣀⠀⠀⣀⡴⠃⠀⠀⠀⣰⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⢀⡀⠀⠘⣆⠀⠀⠀⠀⠸⣟⣋⣀⠀⠀⠀⠉⡉⠉⠉⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠻⡄⠀⠈⠳⣄⠀⠀⠀⠘⠧⣍⣋⣉⣙⡶⠁⠀⠀⠀⢀⣤⠞⠀⠀⠀⠀⢀⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣠⠞⣿⠛⠦⠀⠀⠀⠀⠉⠉⠁⣀⣀⣀⣤⠴⠋⠁⠀⠀⠀⠀⢠⡞⢧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⣥⠚⠻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣤⡀⠀⠀⠀⢀⡶⣠⠋⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠙⣦⣄⠀⡞⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⢀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠛⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⣴⠟⡛⣛⢷⣄⢰⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣍⠁⠀⠀⠀⠀⠰⣿⢸⡷⣻⣇⣿⢸⡇⠀⠙⠢⣤⣀⣀⣀⣀⣀⣀⣤⠴⠋⠀⡇⠀⠀⠀⠀⠀⠀⣀⣠⠽⠷⢦⣀
⠀⠀⠀⣀⡴⠞⠉⠀⠈⠓⢦⡀⠀⠀⠀⠻⢾⡿⣿⠿⠁⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠴⠚⠉⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⡾⠉⠀⣆⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⢸⠃⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠉⠶⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣀⡀⠀⠀⢿⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀
⠀⡟⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⡀⠀⠀⠀⢸⡇⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣸⡆⠀⢸⡇⠀⢀⡾⠁⠀⠀⠀⠀⠀⣸⠁⠀⠈⣧
⢸⠃⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⣀⡀⠈⣿⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠶⣿⡷⢦⣾⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣾⠀⠀⣞⣛⣉⣻⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢧⠀⠻⠿⠿⠟⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⠀⠟⠀⣿⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠛⠛⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢀⡏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣼⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢡⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠢⡀⠀⠀⢸⠀⢀⠂⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠸⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡀⢸⡀⢀⣸⠖⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢳⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢈⠁⠀⠀⢂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠝⠢⡀⠀⠈⠄⠀⠀⠀⠀⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠑⠀⠐⠋⠀⠀⠈⠢⡀⠈⢆⠀⠀⠀⢰⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠣⡀⠀⠀⢃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⢢⠀⠘⢄⠀⠀⠂⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⢂⠀⠀⠑⣄⡴⢚⠝⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⣆⡴⢚⡡⠊⡡⠊⠁⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠚⠡⠂⡡⠐⠁⠀⠀⡠⠊⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠒⠁⡀⠔⢈⡠⠊⡠⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠉⠀⠂⡡⠔⣉⡴⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⡥⠴⠾⠥⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣟⡏⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡄⢠⣶⣦⣾⣻⡄⢿⣃⣦⡙⠛⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⡤⠭⠉⠈⠈⠁⣸⠯⠛⠁⢸⣿⣧⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠁⠀⠀⣀⣀⠤⠓⠃⠀⢀⣠⣿⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠴⠶⠶⠿⠅⠀⣰⡶⠟⠛⠙⣥⣴⣾⣿⣿⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣷⣤⡴⣶⠞⠁⠀⢠⣈⣷⣿⣿⢿⣿⣿⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡴⠞⠛⠿⣿⡿⠟⠁⠀⢀⣀⡠⢦⡿⢛⣴⡿⢛⣿⣋⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣴⡚⢿⣿⣇⣾⠗⠉⢁⡴⣃⣴⣿⣿⠶⠟⠛⣻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⣺⣿⣿⣿⡟⠃⠈⢀⣶⠏⣴⡿⣿⣿⣷⣴⣶⣾⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡟⠻⣿⣿⣇⣀⣀⣠⣿⣁⣾⣷⣤⣾⣿⣿⣿⣿⣿⣿⣻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣻⣿⡎⠃⠠⢨⠻⣿⠻⠏⠉⣉⣥⣭⣤⢨⡿⣫⣍⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⢹⡿⣷⣾⢧⣌⣁⣈⠃⣄⠀⣿⡿⣏⣩⣙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠛⣿⣆⣾⣿⣿⣠⠀⢤⣼⣄⣾⣿⣿⢿⣿⣿⣿⣿⡋⢾⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡀⢹⣿⠟⢿⣿⡋⣤⣾⣿⣿⣿⣿⣿⡇⠹⣿⣿⡟⠁⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣧⠈⣿⡇⡉⠁⣿⣿⠈⢙⣿⡏⠀⣼⣿⡇⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢸⣿⡆⣿⡇⣧⠀⣿⡏⠀⢸⣿⠁⢠⣿⣿⢁⣿⣿⣆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢻⣧⢸⡿⣿⢠⣿⡇⠀⣾⣿⠄⣾⣿⣇⣼⣿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠈⢳⢻⢸⣿⣧⠀⣿⡿⢰⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⣛⣘⣿⠟⠀⣿⣯⣾⣿⣿⣿⣿⣿⣿⣗⣲⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠁⠠⠭⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠃⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢄⡀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠻⡀⠀⠀⠘⠀⠁⣄⠀⠀⠀⢠⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠹⣆⠀⠀⠀⠀⢻⠀⠀⠀⢁⡀⠀⢰⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠤⢄⡀⠀⠀⢸⠀⠀⠘⣦⠀⣀⡀⠀⣤⠌⣠⠛⠁⠀⡆⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⠅⠀⠀⠈⣿⠏⠹⢦⠍⢰⠇⠀⠀⢰⠁⢀⡾⢁⠀⠀⠀⠀⣀⠤⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠈⠳⣶⠀⠀⢀⡌⠀⠆⠈⢻⡇⠀⡆⠀⣎⣰⠏⠀⠌⠀⢠⠄⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠉⠳⢤⣽⠀⠀⣼⠁⠀⠀⠀⠀⢱⡀⠇⢠⡿⠁⠀⣾⡄⠈⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠰⢶⣶⣦⣄⢀⡀⠈⠳⣄⠀⠈⠳⢦⡟⠀⠀⢀⡀⠀⠈⣷⣶⠎⠀⢀⡾⠋⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢌⡋⢤⡉⠠⠙⣦⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⠃⠀⣰⣏⣀⣀⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⢦⣀⠙⢷⡀⠀⠀⠀⠻⣤⡁⠀⣰⡦⠚⠃⠉⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⡀⠀⠙⢀⠹⣶⠘⠛⠂⣤⣄⡀⠘⣧⠞⠁⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠙⠦⡀⠳⣄⠀⠀⠈⠉⠲⣦⡀⠀⠀⠀⢀⠀⣤⣼⠀⠒⠒⠀⠀⠉⡡⠿⠟⠁
⠀⠀⠀⠀⠀⠈⠓⢂⡀⠶⠄⠘⠂⠀⠛⠶⢶⠀⠹⠆⠀⠀⠀⠀⠀⠻⡄⣀⡴⠞⠋⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⡖⠒⢀⠤⢄⣀⠳⠀⠸⠦⢄⠀⣀⠀⠤⠾⣁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠖⡄⠐⠀⠉⠛⠻⣦⣀⠀⠛⠁⠀⠀⠀⠈⠳⡆⠁⠀⢀⡄⢀⣀⣀⠠⠐⠒⠚
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⠦⡄⢠⣄⠢⡔⢄⠀⠀⠙⠲⣤⡀⢀⣤⠄⠒⠚⠒⠂⠰⢿⣦⠈⠉⠉⠐⠒⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠼⣿⣦⣤⣄⠀⠀⠈⠃⣀⡀⠆⠀⠀⠀⢀⣹⣧⠀⠀⠀⠀⡀⣤⣥⡴⠶⠖⠈⢉⠉⠉⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠛⠷⢶⣋⡉⠿⠶⣉⣀⠀⠀⠀⢀⣀⠴⠟⣤⠤⠞⠋⠀⣀⡀⠀⠠⢤⡤⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡒⠂⢠⠈⠳⠖⠠⢀⠈⠛⠷⡁⠀⠀⣀⣀⡈⠁⣤⠶⠋⢉⡄⠐⠀⠉⠁⠀⢠⡄⠀⠙
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣶⣶⠞⠿⠓⠚⠓⠨⢷⣄⠀⠹⠒⠀⠀⠈⠙⠛⢠⣤⢀⡈⠀⠈⠁⢴⣀⠤⠌⠃
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢈⣧⣤⣤⢠⡶⠒⠂⢠⡈⠣⣄⠘⣀⠀⠀⠀⢠⡴⠒⠻⡷⠖⠂⢠⣄⡉⠀⠀⠱⠃⡀
⠀⠀⠀⣀⠀⠀⡌⠁⠲⡀⠸⡇⠀⡤⠁⠤⠀⠀⠀⠘⠆⠙⣄⢉⡷⠉⠹⢦⣤⠈⠀⠈⠀⠁⠄⠘⡉⠀⠂⢲⠀⠑
⠀⠀⠀⠈⠓⢰⡿⠀⠀⣾⣶⠷⠦⣤⠄⣰⡆⠀⢰⡷⡤⠚⢻⡶⢀⣤⣀⠁⠀⠈⢠⡌⢱⣣⣄⠘⠗⠀⠈⠀⠶⡈
⠀⠀⠀⠀⣠⡋⠀⠀⡰⠋⠃⡀⠀⠀⠀⠙⡛⠃⠀⠛⠆⠀⠀⢳⣀⡄⢩⣐⡦⠈⠛⠀⢀⠍⠛⢳⡆⠀⠀⠀⣀⠙⠀⠀⠰⡆
⠀⠀⠀⡐⠿⠃⠀⠰⠁⠀⠀⠑⠀⠀⣀⠊⠀⣀⡤⢴⣤⣴⣞⠉⠁⡧⠈⠁⠐⣦⠄⠛⢫⡤⠀⡀⠘⣂⡀⠀⠁⠀⠀⢠⠄⠃
⠀⢰⡤⠃⢀⢀⡼⢤⡀⠀⢀⣤⠲⡖⠙⠓⢾⡋⠀⣸⡆⠀⠙⢇⠁⠀⠀⠀⡌⠁⠀⠀⢸⠀⠀⢹⡞⠉⠉⠖⠂⠀⢠⡦⠀⣤⠰
⠀⢸⠇⢀⡼⠁⠄⠀⢹⡟⠉⢀⡴⠃⠀⠀⢀⠉⠈⠉⠳⠀⠀⠺⣷⠶⠶⢤⡿⠀⠀⠀⠊⠀⠁⠰⡇⠀⠀⠋⣀⣼⡏
⡀⠘⢀⡌⠳⠖⠀⠀⠀⠛⠰⠂⢡⠀⠀⠀⠸⠂⠀⠀⠀⠀⣠⠞⠁⠀⡀⠀⠘⢣⡀⠀⠀⠀⠀⠀⢧⡀⠀⡀⠀⢸⡇⠀⠀⠰⡆
⠈⣄⡿⠁⠀⠀⠣⠄⢀⣀⠀⠀⠀⠀⢀⡼⠟⠛⡟⠓⠦⣠⡏⠀⠀⠀⠁⠀⠀⠀⣿⣠⠤⠴⣶⠴⢎⡁⠀⠀⠀⠸⣇⠠⠎⠠⡇
⠀⠉⠰⣧⠈⠳⣄⢀⡜⠋⠘⠓⣄⣠⡟⠀⠀⠀⠁⠀⠀⠹⠇⠀⠐⠀⠀⠀⠒⠂⣼⠃⠀⠀⠀⠀⠀⠙⢦⡤⡖⠢⡀⠀⠀⣠
⠀⢠⣾⣹⠆⠀⠘⣿⡀⢀⠀⠀⠈⠿⠀⣤⡴⠀⣆⠀⠀⠀⡃⠀⣀⣤⣤⣤⣄⢀⣿⠀⠀⠀⡀⢠⡤⣴⠟⠀⢀⡄⠀⣦⠐⢠⡦
⠀⢮⡄⠉⠀⢄⠀⠛⠑⠞⠀⠄⠀⠘⣇⠀⠀⠀⠈⠁⠀⠈⣡⠞⠁⠀⢄⠀⠈⠛⣏⠉⠀⠉⠁⠀⢠⡏⠀⠀⡞⠐⡿⠁⠘
⠀⠾⢫⣴⠶⢄⡀⠰⣄⣤⣄⣀⠀⠀⢙⠶⠉⠙⠋⠁⠶⣤⡏⠀⠀⠀⠈⠀⠀⠀⠈⣣⠶⠆⠀⢶⡜⠃⠀⢉⡀⠼⠇⣀⠀⡟
⠀⢠⠸⡇⠐⠀⠙⣶⠋⠀⠉⠈⠛⢶⡎⠀⠀⠀⠃⠀⠀⠈⢷⠀⠙⠛⠁⠀⠙⢠⠟⠁⠀⠀⢰⠆⢱⣆⣰⠋⢥⡀⣀⣥⣴⠇
⠀⢸⣧⠀⠛⡀⠀⠘⣷⠴⢀⡀⠀⠀⢻⡀⠢⣤⠀⠠⠄⠀⠠⣧⣠⣤⣤⣄⣰⠇⠀⠀⠀⡰⠃⠤⠋⢨⠋⠠⠜⢁⠙⠁⢼⠆
⠀⠸⠙⣧⡀⠑⢤⡀⢡⠀⠈⠑⠂⠀⢀⣧⠀⠀⠀⠀⠀⣠⡴⠋⠁⢠⠇⠈⠳⣆⠈⠁⢈⣤⠒⠶⢦⡀⠀⠀⠀⡮⠠⠂⣠
⠀⠀⣠⠀⠑⣄⠀⣨⡽⠶⣤⡀⣠⠖⠉⠉⠉⠉⠱⢦⠾⠁⠀⠀⣠⠘⡀⠀⠀⢸⣤⠖⠉⠀⠀⣷⠀⣴⣶⠶⢢⡀⢀⠾⠋
⠀⠀⠙⣶⡆⠀⢻⡁⢰⡄⠀⠹⣧⢀⣀⢀⡀⠀⠀⠈⣦⠀⠈⠉⠀⠀⢉⠁⠀⢀⣏⣀⣀⣀⡴⠛⠻⠃⠈⡇⢀⡼⣾⠃
⠀⠀⠀⠘⢷⠄⠈⠁⠙⢠⠀⠀⠙⡄⠀⠀⠑⠠⠄⠠⠛⢀⡠⠤⠛⠋⠁⠀⠙⠧⡀⠀⠀⠀⠀⠀⠇⢀⡀⠁⢨⠟⡀
⠀⠀⠀⠀⠀⠂⣰⣧⣀⡀⢑⡀⠠⣧⡤⠒⠒⠲⠒⠢⣴⠏⠀⡀⠀⠀⠀⣠⠀⣀⡿⠒⠒⠛⢶⣞⠓⠀⢀⡘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠙⣯⠙⣇⠉⠁⠺⠏⠀⠀⠀⠀⠀⠀⠈⢣⠈⠉⠐⠀⠁⠉⠸⠋⠀⠀⠀⠀⠀⠛⠓⠫⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠂⠀⠀⠐⠄⠁⠂⠀⠶⠐⠂⠐⢷⣀⠀⠀⠀⢀⣇⠀⢀⠀⠒⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢌⣀⣸⣆⠀⠀⠀⠀⣠⠆⠉⠉⠛⠀⠈⢙⡟⠉⣀⠤⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣾⣿⣶⣶⣦⣤⣤⣤⣯⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠦⠤⣄⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢹⠀⠀⠀⠀⢹⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠚⠉⠀⠀⡄⠀⠉⢹⡅⠀⠀⢴⣛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠹⠀⠀⠀⠛⠂⠀⠈⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⡠⠝⠛⠛⠒⠲⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠉⠀⢠⡖⢉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣔⣒⠀⠀⠀⠀⠉⠙⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⡀⠀⠀⠈⠉⠉⠀⠀⠀⣴⠀⡄⠀⠀⠀⣴⣒⡦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⣠⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠛⠒⠁⠀⠀⠀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣠⠤⠦⠀⠔⠒⠋⠉⠋⠉⢉⠉⠉⢉⡿
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠄⠂⣡⠀⠀⠀⢴⠀⠀⢀⢀⡤⡀⠐⠠⠀⡟⠁
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠐⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢲⠎⠉⠏⢘⡀⠀⠀⠀⠀⢲⡀⢠⡄⡄⣐⡉⠠⠀⠀⠀⡸
⠀⠀⠀⠀⢰⠀⠀⠀⠳⠖⠊⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⠤⢖⣻⡈⠀⢀⠀⠀⡀⠀⡸⠓⠀⠀⠈⠀⠀⠀⢡⠄⣀⣀⣀⡀⠄⠀⠉⣱⠔
⠀⠀⠀⢀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢀⣠⠖⣩⢧⣑⢐⣖⣿⢶⡤⠤⠤⠤⠖⠳⣄⡐⠀⠀⣀⣡⡴⡇⠒⠀⢉⡍⠱⠰⣤⣺
⠀⠀⠀⢸⡆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠇⡔⡁⠀⠉⡨⠙⠳⢾⡀⠆⠀⠠⠆⠀⠒⠉⢹⠟⠙⠃⠁⠀⢠⣦⠴⠀⠣⠛⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠂⠄⡒⣴⠃⠠⠀⢀⠀⠀⠙⠘⡄⠠⠂⠀⠀⠒⣠⡎⠄⠈⠘⠀⢀⡛⠐⠚
⠀⠀⠀⢸⠀⠀⠀⠀⣠⢞⡖⠀⢀⡔⠃⠠⠘⠀⠀⠁⣿⢀⡀⠀⠀⠀⠀⠄⠀⠛⠒⢿⠂⠴⠘⠀⠛⠤⠀⡷⠛⠂⠀⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⣆⠀⠀⠀⣁⡏⠀⢠⠞⠁⠄⠐⣼⠥⠸⠐⢙⢦⡀⠀⠐⠀⠀⢀⠼⠀⠀⠈⢁⠄⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⣫⢿⡀
⠀⠀⠀⠀⢻⠀⠀⠀⠈⠀⠰⠃⠀⡄⠀⢠⠾⣶⡖⠂⠄⣀⠛⣙⠛⠛⠋⢉⠀⠈⡁⢂⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⢠⣔⡒⢾⡏⢹⣎⢞⣴⠁
⠀⠀⠀⠀⠸⡀⢀⠀⠀⡠⠁⢤⠀⠀⢀⠀⠺⣥⠀⠀⠀⢝⣬⣧⣴⣂⣠⠿⠟⠢⢍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢹⣿⢞⡵⠹⢿⣼⠸⣷⢤⡀
⠀⠀⠀⠀⠀⢷⠃⠀⣴⠧⣀⠀⠀⠀⣀⣠⡞⠱⡶⣭⣺⡛⣃⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢣⠹⣟⠳⠺⠃⡀⢈⣀⡿⢨⣤
⠀⠀⠀⠀⠀⠈⡄⢰⠃⠀⠤⠉⠉⠋⠁⡑⢈⢢⣙⣦⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠈⠳⠬⠩⠵⠿⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⣴⣧⡤⠕⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠱⡀⠀⠀⣏⠀⡇⠀⠀⠀⢀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⢄⠀⠀⠘⡆⣇⠀⠀⠈⠉⠀⠀⢀⡔⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⢣⠀⠀⠳⠏⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠺⣉⠑⣄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢣⠀⠀⠀⢀⡤⡀⠀⢠⠎⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠃⠀⠀⠀⡔⠒⢦⡘⢆⠀⠀⠑⢄⣀⠎⠀⢸⢀⠇⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡠⠃⣀⠴⠃
⠀⠀⠀⠀⢀⠤⠄⠤⠤⣀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠠⠊⢀⡤⠒⢑⠀⠀⠸⠑⠊
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⡠⠤⠊⠀⠀⠀⣤⠊⢳
⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠤⠤⢄⠉⠁
⠀⠀⠀⡠⠤⢄⠀⠈⠉⠉⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⡠⢄⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣄⠀⢀⡠⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⠆⠀⠀⡠⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆⢸⠀⠀⠈⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡠⠊⠀⠀⡞⢠⢲⠀⠀⠀⠀⡴⡄⠀⢣⠀⠁⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⡹⠀⠈⠒⡩⠆⠀⠀⠀⠓⠃⢸⠀⠀⣤⠀⠡⠘⠤⠠⠂⠀⠀⠀⠀⠈⠢⢄⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠰⡁⣠⠞⠁⠀⠀⠀⠧⠄⠀⠀⠀⠀⠀⡆⠀⠀⡄⠉⠁⠀⠀⠀⠀⠀⡴⢄⠀⠀⠀⠀⠙⠂⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠱⢬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⢰⡔⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⣗⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣿⠾⠛
⠈⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣷⠉⣷⠀⢠
⠀⠢⡀⠀⠄⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⡰⢻⢁⣦
⠀⠀⠐⡞⠀⠀⠀⠑⢦⡀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⢀⣿⢷
⠀⠀⠀⠑⠀⠀⠀⠀⠈⣇⠀⣀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣬⣿⡾⣫⣾
⠣⠀⠀⠀⠈⠀⣇⠀⠀⠀⠀⠀⢀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⣷⣿
⠀⠁⠀⠀⠀⠱⣝⠆⠈⠀⠀⠐⠁⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢠⠾⠁⣜⠅⠀⠂⠉⠳
⠀⡖⠀⠀⠀⠀⠘⠋⠘⠓⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠁⠀⣸⠐⠀⠀⠀⠀⠦
⠀⡄⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣟⠀⠀⠀⠀⠀⢠
⠀⠃⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⣾
⠀⢽⢸⠀⠀⠠⠀⠀⠀⢀⠄⠀⠘⡆⠀⠰⠀⠃⠆⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⠌⠠⡆
⠀⠸⠀⠆⠀⠘⠄⠀⠂⠀⡃⠐⢆⡀⠀⠣⠄⠠⠊⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠁
⠀⠈⠇⢠⠀⠀⠀⠀⣀⠒⠂⣶⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣏⠀⠀⠀⠀⡏
⢦⡀⠐⠈⡇⠀⠈⠀⠘⠗⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠴⠻⠀⠀⠀⡸⠇
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢾⣿⣿⣿⣿⢿⣿⣿⣷⣾⣿⣿⡳⣍⠷⢀⡀
⠀⠀⠀⠀⠀⠀⡄⣀⢿⢿⣷⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣶⣿⣾⢭⡙⢦⢠⡀
⠀⠀⠀⢀⡔⣫⢰⡟⣜⠎⡳⣽⣟⢿⣿⣿⣿⣿⣽⣿⣿⣿⠏⠿⠿⣿⣿⣿⢻⠞⡇⣼⡣⣤
⠀⠀⣤⢶⣶⣶⠸⣿⣿⣷⢦⡙⡻⠿⣿⣿⣶⣮⡵⢟⣩⢶⣿⢿⣿⣶⣶⣶⣶⣬⣥⣝⣛⠂⢓⡀
⠀⠀⠿⣎⢿⡉⡀⡻⢮⣿⡿⣿⣮⣽⣒⠦⣠⢏⡶⣫⣶⣿⣶⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣅
⠀⠀⣃⢻⣎⢣⣿⣌⠳⣮⣕⣺⠶⠿⣟⣛⡂⣼⣽⣿⣴⣾⣿⣯⣽⣿⣿⣿⣿⣿⣿⣹⣿⣷⣾⣿⣧
⠀⠀⠙⣣⡻⣆⠻⠧⢿⣮⣝⢛⡿⠷⠿⠿⠱⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠘⢱⡮⣁⠻⠿⢒⣉⣚⠿⣿⣞⣭⣥⢹⣧⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⢜⡇⣷⡄
⠀⠀⠀⠀⠀⠀⠛⢱⣶⣤⢹⣿⣿⣶⡭⣭⣭⡜⢿⣿⣿⣿⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠇⢟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⡜⢿⣿⣶⣍⡻⢿⣶⣌⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣭⣿⡿⣨⣭⣶⣺⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣠⡽⣿⣿⣿⣶⣭⣛⠿⣿⣟⠿⠿⣛⣛⣛⣚⣫⠽⠛⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⣿⣎⢿⣿⣿⣿⣿⠿⣶⣦⢭⣭⠭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡾⠿⠿⢟⣛⡯⢅⣲⠍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣛⣯⣭⡭⠷⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⠷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⣁⣠⣤⣴⣶⣶⣶⣶⣦⣤⣄⣈⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣤⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣤⡈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⡾⠋⢻⣿⣿⡿⠋⢁⣤⡴⠖⠲⠦⣤⡈⠙⢿⣿⣿⡟⠙⢷⣄⠙⢿⣦⡀
⠀⠀⠀⠀⢠⣾⠏⢀⣾⡟⠀⠄⠘⣿⡟⢀⣴⣿⠃⣠⣶⣶⣄⠘⣿⣦⡀⢻⣿⠁⠠⠀⠻⣷⡀⠹⣿⡄
⠀⠀⠀⢠⣿⠃⣠⣿⣿⣷⣶⣤⣤⡿⠀⣼⠟⢁⣠⣿⣿⣉⣻⣄⡈⠻⣧⠀⣿⣤⣤⣶⣾⣿⣿⣄⠘⣿⡄
⠀⠀⢀⣿⠇⢠⣿⣿⠿⠋⢁⣠⣤⣤⣄⣀⠀⠻⣿⣤⣼⠛⢿⣿⠟⠀⣀⣠⣤⣤⣄⡈⠙⢿⣿⣿⡄⠸⣿⡀
⠀⠀⣸⡟⠀⣾⡿⠋⣠⠾⠛⠋⢠⣄⠈⠛⠷⣆⠈⠛⢿⡶⠛⠁⣰⠾⠛⠁⣠⡄⠙⠛⠷⣄⠙⢿⣷⠀⢻⣇
⠀⠀⣿⡇⢰⣿⠃⢰⠃⣠⣶⢶⣿⠛⢲⣶⣦⠈⣧⠀⢈⣁⠀⣼⠁⣴⡶⣶⣿⠛⣶⣶⣄⠘⡆⠘⣿⡆⢸⣿
⠀⠀⣿⡇⢸⣿⠀⣿⠀⢻⣧⣴⡿⢷⣿⣿⡿⠀⣾⠀⢈⡁⠀⣷⠀⢿⣧⣼⡿⢶⣿⣿⠟⢀⣿⠀⣿⡇⢸⣿
⠀⠀⣿⡇⠸⣿⡄⠸⣷⣄⠈⢿⣧⣼⣿⠁⣠⣾⡟⠀⢈⡁⠀⢻⣷⣄⠈⣿⣧⣼⡿⠁⣠⣾⠇⢠⣿⠇⢸⣿
⠀⠀⢹⣧⠀⢿⣷⡄⠙⢿⣦⡈⠛⠛⢁⣠⡿⠏⢀⣤⣾⠷⣤⡀⠹⢿⣄⠈⠛⠛⢁⣴⡿⠋⣠⣾⡿⠀⣼⡏
⠀⠀⠈⣿⡆⠘⣿⣿⣶⣄⡈⠙⠛⠛⠋⠉⠀⣴⣏⣹⣿⣤⣾⣿⣦⠀⠉⠙⠛⠛⠋⢁⣠⣾⣿⣿⠃⢰⣿⠁
⠀⠀⠀⠘⣿⡄⠙⣿⣿⡿⠿⠛⠛⣿⠀⢻⣦⡈⠙⣿⣏⣹⣿⠋⢁⣴⡟⠀⣿⠛⠛⠿⢿⣿⣿⠋⢠⣿⠃
⠀⠀⠀⠀⠘⢿⣆⠈⢿⣦⠀⠂⢀⣿⣧⠈⠻⣿⡄⠙⠿⠿⠋⢠⣿⠟⠁⣼⣿⡀⠐⠀⣴⡿⠁⣰⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢷⣄⣼⣿⣿⣷⣄⡈⠛⠳⠶⠴⠞⠛⢁⣠⣾⣿⣿⣧⣠⡾⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡈⠛⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠛⢁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⡉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⢉⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢶⣶⣶⣶⣶⣶⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⣿⣿⠀⣿⣿⠉⠉⠉⠰⣾⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣧⠀⣿⣿⠛⠛⠀⠀⢰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠿⠋⠀⠿⠿⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠓⠶⠶⠶⣶⡶⠛⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡤⠖⡳⠀⢀⡼⠋⠀⠀⠀⢀⣤⡤⠤⣿⠤⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣤⠞⠁⢠⡞⠁⢀⡴⢛⡇⢸⣞⠁⢰⡏⢀⡾⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⠏⠀⠀⢸⡟⠉⣠⠊⣻⡴⣿⠃⣸⣇⡴⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣥⣤⣄⣀⠈⢙⡋⠙⣛⠋⠀⠘⠋⠈⣩⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⢠⠤⠭⢽⣛⡛⠁⢇⠀⠉⠑⢆⢀⡞⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠉⠓⠢⢕⣂⣃⣈⠿⣧⡴⠋