Cooker Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⠶⠞⠓⠒⠒⠒⠛⠲⠶⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⣴⠛⠛⠛⡛⣻⠋⠓⠶⠦⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠴⠶⠶⠒⠚⠛⣻⠛⠛⢛⣛⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠙⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢶⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠛⠛⠓⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠖⠒⠚⠋⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⣠⠤⠶⠦⣄⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢧⣀⣀⣠⡾⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⡴⠖⠒⠲⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠷⣄⣀⣠⡼⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⠲⢤⣀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢀⣀⡤⠞⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡲⣤⣈⠙⠒⠲⠤⢼⡀⢀⣿⣉⣩⣭⣭⣍⣻⡆⢸⡗⠒⠒⠋⠉⣀⣤⣞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠶⠦⣼⣧⣈⣓⣒⣒⣒⣒⣛⣛⣃⣼⡦⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣈⣿⣿⣉⣉⣹⣿⣉⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢠⣶⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣷⣄
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⣧
⢀⣴⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣤
⣾⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⠿⠿⠛⠛⠉⠉⠁⠀⢈⣿
⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣧⣠⣤⣤⣶⣾⡿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⡿⠟
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⡟⠋⠉⠁⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⡿⠿⠟⠛⠋⠉⠉
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣇⣤⣤⣶⣶⣾⠿⠿⠛⠛⠋⠉⠁
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠋⠉⠉
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠈⠻⢿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠐⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠐⠐⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⢆⣀⠰⡀⠀⠀⠀⠀⠀⢨⠿⠖⠁⠀⡀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⠀⠱⠀⠀⠀⠀⠀⠈⠳⡆⠀⠋⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠋⢻⡆⠸⡄⠀⠀⡰⢷⣀⠀⠀⠀⠀⠀⠈⠐⢦
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠈⢢⡀⠈⠀⠁⠀⠀⢀⠄⠀⠀⠘⠈⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠱⣄⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠳⣤⡾⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⣀⣀⠀⢤⡤⣄⠐⠶⣶⣶⣶⡦⠴⠶⠂⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⢏⡏
⠀⠀⠀⠀⠿⢿⣿⣦⣼⣗⣚⠂⠀⠩⣭⢴⡄⠻⣝⠾⡀⠂⢠⡇⣿⣦⡀⠀⠈⠀⠀⠀⢀⣤⡾⠋⣼
⠀⠀⠀⠀⠈⢌⢻⣿⣿⣿⣿⠄⠙⢰⣿⠀⠀⠀⠈⢻⣿⢀⣸⠁⠀⣿⣷⣄⠀⢀⣠⣴⣿⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠙⠺⠛⠛⠛⠘⠁⠀⠀⠀⠀⠀⠀⣼⢧⣿⡿⠀⠀⠈⠙⠿⣿⣿⡿⠋⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢤⣉⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠠⠀⠄⠒⢛⣳⣿⣿⣿⣶⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠉⠉⠉⠉⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⢀⡠⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢠⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣶⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣥⣿⣿⣿⡄⠀⠀⣤⡖⠛⠛⠛⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⠸⣿⣷⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡟⠁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠿⠃⠀⠀⠒⠈⠁⠐⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⡄⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⡀⠀⠀⠀⠤⢀⡠⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣧⠑⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠿⣷⣿⣿⣷⣄⠀⠠⣤⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣎⠀⠙⠲⣝⠿⣿⣿⣿⣿⣶⣤⣽⡿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠹⣆⠀⠈⠳⡄⠉⠉⠛⠙⣿⣿⣷⡌⡎⢣
⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⣆⠀⠀⠸⣿⣿⣿⣿⣷⡀⡆⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠘⣇⠀⠀⢹⣿⣿⣿⣿⣿⡾⡀⠀⠀⠀⠀⠀⡰⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠘⠷⠔⠚⢿⣿⣇⠻⣿⡇⢷⠀⠀⠀⠀⢀⣵⠇
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠈⠃⠘⣇⠀⠀⢠⠆⠁⠀⣠⣄⡀⠀⠀⠠
⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠀⢠⡏⠀⠀⠀⠈⢿⣇⠀⠀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⣞⠀⠀⢡⠀⠀⢾⣿⠉⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠚⠉⣁⡈⠀⠸⠷⠶⢶⠃⠀⠈
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠂⢁⣹⣶⠟⢀⣀⣀⠤⠤⠔⠒⠚⠛⠀⠀⠀⠀⠀⢠⡇⣤⡆⠀⠐⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠞⡡⢊⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡧⣿⡤⠒⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠈⡆⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣶⠖⠚⠉⠀⣇⠰⡄⣚⣛⣛⣋⣙⡛⠛⣛⣛⣋⠀⡄
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠀⠀⠀⠀⠀⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣀⣀⣀⣀⣠⡤⢤⠄⠀⠀⢰⡖⢲⡈⠀⣀⣂⣲⠀⠀⣀⢻⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡹⠉⠉⠋⠻⠉⠩⠇⠀⠂⠆⠐⠃⢰⡗⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠊⠁⠯⠽⠭⠇⠤⠀⠿⠿⠼⠵⠸⠥⠁⠸⠿⠫⠼⠯⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠁⠀⠀⠀⠀⠈⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠂⠀⠀⠀⠢⣤⣀⣠⣴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠅⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠒⠂⠀⣀⠄⠀⠀⣀⡄⣀⡤⠞⣹⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠈⠉⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⣉⠙⠛⠛⠉⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢅⣀⠤⣤⢤⣤⢤⡤⠼⢑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⡄⠀⠜⣀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠼⡇⠂⠀⠒⠒⠒⠒⠂⠀⠐⡁⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠜⠉⡤⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠢⣀⡠⠆⠀⠀⠀⠀⠀⠀⡠⢶⠁
⠀⠀⡀⠀⠠⠀⠀⠀⠀⠇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⢀⣀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⣀⣀⣤⣤⡲⠯⠖⠋
⡀⢀⡍⠀⠐⠒⠒⠂⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢀⠀⣤⢯⡑⢢⣀⠀⢀⡔⠙⣏⡙⠉⢹⠏⠀⠀⠙⣄⠀⠀⡀
⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⢀⢀⡀⠀⠀⡀⠀⣀⠠⠤⠌⠀⠠⠀⠘⢯⣻⠄⠈⠒⠚⠳⠆⠀⠀⠉⢹⠀⠀⠀⠀⡇
⡇⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠠⠀⢀⠀⢀⡀⠀⢀⠤⢄⠀⠀⢀⡤⠴⠖⠊⠷⠀⠚⠀⠘⠒⠲⠤⢄⣸⠒⠤⣀⡴⠁
⡇⠀⠈⠦⠤⢤⠤⠤⠴⠏⣄⠀⠀⢩⠀⠀⠀⠁⠀⡯⠉⠐⠅⢤⣀⠀⠀⠘⡄⠀⠈⠁⠠⠠⠠⠄⠀⠀⣀⡤⠞⠋⠀⢠⣧⡴⢲
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣟⠀⠀⠀⠐⡬⠤⣈⡤⠼⡆⠁⡀⠀⠀⠀⣺⠌⠉⠀⠀⢀⣠⠔⠉⢹⣤⠶⠥⠤⠤⠤⠤⠤
⡇⠁⠈⠁⠀⠉⠁⠉⠉⠉⠉⠁⠈⠈⠉⠁⠁⠁⠁⠉⠐⡀⠀⡌⠁⠉⠉⠁⠉⠁⠐⠠⠄⢀⣀⠳⣊⣤⠤⠚⠉⠀⠀⠀⠸⡎⡅⠉⠁⠉⠉⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖
⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⢹⠃⠀⠒⠂⠒⠁⢧
⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠧⠤⠤⠤⠤⡌⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡔⠉⠑⠲⠤⢤⡼⠀⠀⠀⠀⠀⠀⠀⢣⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⢀⠷⠤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠐⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣄⠀⠀⠀⠉⠉⠐⣒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠉⠁
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠳⢤⣄⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⢀⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠈⠻⡄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡰⠛⠁⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠞⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣴⠶⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣆⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠶⢦⣄⣀⣀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣾⣏⣉⣀⣀⣀⣤⣤⣤⣤⣭⣩⣭⣷⣦⣤⣶⡿⠂
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⢭⡭⠥⢤⣼⡟
⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠐⠿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣾⣋⣀⣀⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣯⣉⣉⣉⣉⣉⣭⣽⣿⡿⠿⢛⣻⣋⣉⣉⣝⣿⠿⠛⠁
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⣿⡏⠀⠀⠀⠀⠈⠛⢷⣶⣶⡶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⣿⡟⠋⠉⠀⠰⠾⠛⢛⣛⣉⣭⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣀⣤⣤⣤⣤⣬⣿⡄⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣼⠏⠀⠀⠀⣀⣀⣤⣤⡬⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣉⡀⠀⠀⠀⠀⣹⣷⣾⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⢰⣿⠁⣸⡏⠀⠀⢀⣾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣦⣄⠛⠻⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣿⠇⢠⣿⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⠙⠛⠿⣿⣦⣤⣀⣿⠏⢀⣾⠇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣏⠀⣼⡟⠀⠀⠀⣾⡇⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠀⠀⢰⣿⠃
⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣾⡟
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢻⣿⣦⣀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠋⠀⠀⠀⣠⡿⠋⠉⠻⣷⣄⣠⣾⠟⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⣼⡟⠁⠀⠀⠀⠀⠙⠿⠏⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣿⠿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⢀⠀⠕⠀⠀⢄⠀⢀⣾⠛⠿⢿⣶⣦⣄⣀⠈⢻⣿⣆⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠠⠈⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠈⠙⠻⢿⣿⣶⣿⣿⡄⠀⠀⠀⠈⠙⠻⠿⣷⣦⣄⣠⣿⡿⠋⢀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⠋
⠀⠀⠄⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠘⢀⡀⠀⠀⢿⣿⠀⠀⠀⣀⣤⡶⠾⣛⣩⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣶⣿⣿⡿⠶⠛⠋⢡⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠉⠙⣿⡄⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣤⣆⢀⡆⣠⠀⡀⢰⠀⡇⢰⠀⢰⠀⠀⣤⡄⣤⡤⢤⣤⢀⣄⣄⣠⣄⣤⠀⣦⢀⣴⠆⠀⡄⠀⣠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠋⠉⠉⠉⠉⠁⠀⠉⢉⡉⠉⠉⠙⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠛⠉⠉⠛⠛⠛⠳⠶⠦⣤⣀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢀⡞⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠿⡄⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣤⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⡤⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠛⣦
⠀⠀⠀⠀⠀⠀⢿⡶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⢉⡿⠀⢸⡇
⠀⠀⠀⢠⣤⠶⢾⡷⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⢻⣟⣉⣻⡇
⠀⠀⠀⠸⣧⠤⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣽⠁
⠀⠀⠀⠀⠛⠶⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣚⣛⣛⣒⣶⡶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡞⠉⠁⠀⠀⣀⡀⠉⠉⠉⠓⡌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⠀⠀⠠⣞⠉⢹⡇⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠙⠓⠛⠁⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣶⠛⢳⡆⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠻⠶⠾⠃⠀⠀⠀⡧⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⡴⠶⠶⠶⠶⠶⠶⣦⣠⣷⣇⣀⣀⣀⣀⣀⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣀⣀⣂⣀⣐⣂⣀⣸⣿⢸⡏⠉⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠶⠶⠶⠶⠶⠶⠶⣾⣿⣾⠃⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠶⠶⢦⣤⣤⣤⣼⣿⣝⣷⣶⣶⣶⣶⣖⣛⣋⣼⣿⣤⣤⣤⣤⠶⠶⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⣶⡶⠶⠶⠶⠶⠶⠶⠬⠭⠭⠭⠽⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⣶⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠈⠻⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⠿⠋
⠀⠀⣀⣤⣶⠟⠁⠀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⡆
⢠⣾⣿⡟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠿⠿⠃
⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀
⠻⣿⣿⣧⠀⠀⠀⠸⠿⠷⠶⠶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠈⠛⠻⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⡧

⠀⠀⣾⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣾
⠀⠀⠙⠻⠿⢿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠛⠛⠛⠛⠛⠛⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡖⠛⠉⣿⣟⣾⠉⠉⠉⠉⠉⠉⠹⣏⣿⣿⠲⢦⣀⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣩⡴⠋⠉⠉⠙⠳⣤⡀
⠀⠀⠀⢀⣤⢖⣿⣦⣄⡀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠘⢯⣤⣛⢿⡟⠻⠿⣷⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠴⣺⡿⢿⠗⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠯⠿⠽⠯⣭⣭⣭⡭⠭⢷⣶⣚⣋⣁⡀⢸⣛⡿⢛⣡⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣄⣀⣉⡉⣛⡭⠞⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣄⣀⣀⣀⣀⣀⣠⣤⡤⠶⠚⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⢀⡀⠴⢾⣿⣿⣿⠿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣼⣿⣿⣷⣤⣤⣴⣶⡽⠷⠒⠊⠉⢉⣡⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡚⠉⠀⠀⠀⠘⢿⣿⣃⣀⠀⠀⠈⠱⡢⣴⣶⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⡎⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠁⠂⠠⢼⣝⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠘⡇⠀⠠⣤⣤⣴⣾⣿⣿⣷⣦⣤⣤⡤⠀⢰⠇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠈⠀⠀⠀⣈⣉⡉⠛⠛⠋⠉⠉⠀⠀⠀⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣦⣀⠀⠀⠈⠉⠙⠛⣛⣂⣀⣀⡤⠄⠀⠀⠀⣠⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡻⡏⠁⠀⠀⠀⠀⠀⠾⠿⠯⠄⠀⠀⠀⠀⢀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢀⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢰⠁⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢰⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⡇⠎⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣄⠀⠀⠀⠈⣿⣿⣿⠃⡇⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⠀⠿⠿⠿⠀⡃⠤⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠛⠉⣡⠔⠂⠒⠢⢍⠉⠛⠛⠳⠶⠶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠘⠢⠤⢀⣠⠴⠃⠀⠀⠀⠀⣀⣀⣀⠉⠉⠛⠻⠷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣤⡶⠖⠛⠋⠉⠁⠀⠀⠀⠀⡖⠂⠒⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣃⠀⠀⠀⠉⢢⡀⠀⠀⠀⠈⠉⠛⠛⠶⣤⣄
⠀⠀⠀⠀⠀⣿⠋⠈⠁⠀⠀⠀⠒⠂⠤⠤⣀⣀⡈⠂⠀⠤⠤⠤⠟⠀⠀⠀⠀⡠⠒⠂⠀⠒⠢⡌⠁⠐⠂⠒⠊⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⢿⠇
⠀⠀⠀⠀⠀⠙⠳⣶⠒⢦⠤⠤⣄⣀⡀⠀⠀⠀⠈⠉⠉⠒⠂⠀⠀⠀⠀⠀⣀⠈⠒⠤⠀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⣀⡀⠈⠉⠁⠐⠂⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⢤⣀⣀⣀⡤⠀⠀⢀⣀⡠⠤⠀⠒⠋⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠓⠃⠀⠘⠟⠀⣰⣆⠀⣀⡀⠀⠈⠉⠒⠒⠂⠠⢀⡀⠀⠀⢀⣟⡉⠅⠐⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠠⠄⠠⣤⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡗⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡁⠀⠀⠀⠀⠀⣠⣀⡉⠐⠒⠢⠤⠄⣀⣀⠀⠀⠀⠀⠀⠘⠀⡇⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡇⢀⠀⠀⠀⠀⠑⠒⠤⠍⣛⡓⣲⠀⠀⠀⠉⠉⠙⡇⠀⡄⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⢸⠀⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣍⣹⣤⣀⣀⡀⠉⠙⠒⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠛⠛⠶⠶⣤⣤⣀⣀⠀⠀⠀⠀⠤⢀⣀⡸⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣤⣤⣀⡈⠁⠀⣀⠀⢠⢀⣸⡀⣀⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢶⣏⣉⣻⣋⣤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⠿⠿⠿⠿⠿⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⣴⡿⠛⠿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣴⠿⠛⢿
⢿⣧⡀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠁⠀⢀⣼
⠀⠙⠻⣷⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⣾⠟⠋
⠀⠀⠀⠀⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⣶⣶⣶⣶⣶⣶⡶⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣀⣀⣀⣀⣀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠛⠛⠛⠛⠛⠛⠛⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣤⣤⣤⣤⣤⣤⣤⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⠃⠈⠐⠠⠀⠊⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢱⠀⡐⠂⠠⠤⠄⠀⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠤⠀⠀⠠⠀⠀⠒⢂⢺⠁
⠀⠠⡤⠤⠤⠄⠐⡄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⡔⠠⠤⠤⠄⡤
⠀⠀⠀⠉⠑⠢⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡠⠒⠉⠉
⠀⠀⠀⠀⡠⠂⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠢⡀
⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠐⠒⠀⠤⠤⠤⠤⠤⠀⠀⠀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⠤⠄⠐⠒⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠐⠇⠁⠀⠀⠀⠠⠤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠀⠀⠀⠀⠁⠗
⢷⣒⡚⠛⠋⢹⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠛⠛⣒⣲
⠀⠀⠉⠙⠢⡘⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠚⠉⠁
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡤⠂⠉⠁⠢⡄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠘⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠘⡄⠀⠀⠀⢀⡜⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠁⠒⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⠆⠀⠀⠀⠀⠀⠱⡀⠀⠄⠀⣀⣀⣀⣀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠒⢲⡤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⣴⠒⠊⣽
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣴⣯⣥⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣭⣷⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⡐⠓⠒⠓⠒⠓⠒⠒⠒⠢⢤⣶⡄⠀⠀⠀⢀⣤⡴⢲⠖⢢⣄
⠀⠀⠀⢀⣴⠞⠋⢉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠒⠚⠒⠚⠛⠓⠉⠁⠀⠀⠀⠀⠀⢀⡾⣠⣤⣼⣄⣤⣼⢳⠀⠀⠀⠀⠀⢰⠨⠤⠤⢼⡀
⠀⠀⠀⣾⠁⠀⠀⣀⡀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡞⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠟⠀⠒⡒⠚⣣⡀
⠀⠀⠀⣟⠁⠀⢰⠋⠙⠂⠂⣸⠃⠀⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⢀⢄⡀⣸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠘⢦⣀⡉⡄⣀⣠⡴⠋⠀⠀⢠⣀⡆⠀⣿⡅⠀⣾⠙⡶⠻⠼⠋⢹⣿⡃⣠⡏⢰⡟⡇⣾⣹⡀⠀⠀⠀⠰⠄⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣤⠞⣿⡀⠀⠘⠳⠔⠛⠚⠁⠀⠀⠀⠈⠁⠉⠉⠛⠉⠀⠉⢉⢽⠇⠀⠀⣠⠶⣦⡀⠀⠀⠘⠛⠋⢥⢈⡭⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠀⠄⠊⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠒⠀⢀⠀⠈⠋⠀⢀⡾⢥⣬⣏⣝⣷⡄⠀⣀⣴⠟⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣐⡡⢀⠁⡆⣿⡄⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⢐⠒⠤⣀⠀⠀⠄⠀⠀⣿⠄⣺⢲⠓⡇⢁⡟⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣠⠶⠛⠛⠛⠛⠓⢦⠀⠘⠿⢻⣄⢀⠢⢀⡇⠀⢀⡤⠚⠉⠀⠀⠴⠀⠀⠀⠉⣢⡈⠡⠀⠐⠢⡀⠙⠶⣍⣹⢙⣳⠟
⠀⠀⡯⢏⠉⠉⣢⠀⠀⢸⠀⠀⠀⠀⠙⠳⠾⠛⠀⡴⠉⠀⠀⠀⠀⠀⠀⡐⣈⠀⠂⠀⢌⠀⠀⠀⠀⠈⠢⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠈⠓⠚⠛⢶⠖⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡦⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣲⣶⣾⣷⣰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣼⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠀⠻⠀⠀⠀⠀⠀⠹⡛⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠨⡇⠆
⠀⠀⠀⠀⠀⠀⠳⠛⠾⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⠤⡤⢤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⢈⡶⠤⢴⡄⢰⠋⠁⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠼⠂
⠀⠀⠀⠀⢀⠎⠁⢰⢏⠤⠂⠑⠀⢸⠆⠀⠀⡆⠀⠀⠀⠉⠢⠤⠄⢀⣀⡜⠙⠀⠸⡁⢙⠀⠀⢀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠘⣄⠐⠬⢀⡀⠠⠊⣠⠞⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⡼⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⢠⣤⢴⠶⣀⣲⠶⣤⣼⣄⠀⠀⠀⡧⠀⠀⡠⠇⠀⠀⠀⡴⠁⠀⠀⠀⠀⢿⠀⠀⠆⠀⢀⡿⢶⡆
⠀⠀⠀⠀⠀⣤⠤⢤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠈⠓⢧⠤⠭⠥⢴⣎⡓⢋⠁⠀⠀⣤⠤⠚⠀⠀⠀⢀⠜⠁⠀⠀⢲⠀⠀⠸⡄⠀⠂⠀⢠⣧⠟⠁
⠀⠀⠀⠀⠀⢷⠋⠉⠉⠙⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢩⠀⡀⠀⠀⠤⠀⠀⢀⡀⠞⠁⠀⠀⠀⣴⠀⠀⠀⠀⢇⠀⠥⠀⢸
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⡇⠀⠀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠒⠒⠒⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣤⣤⣤
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⢰⠃⠀⢺⣯⣭⣭⣝⣳⠀⠀⠀⠀⠰⣽⣿⣿⣯⡿⠀⠀⠀⢠⢻⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⠉⠉
⠀⠀⠀⠀⠀⠈⠲⠶⠦⠤⠞⠁⠀⠀⠀⠈⠈⠉⠉⠀⠀⢠⠇⠀⠀⠀⣇⣠⣤⣄⠀⠀⠘⢼⣿⡿⠀⠀⠀⠀⠘⠾⠟⠀⠀⠀⠀⠀⠀⢠⠴⠚⡚⠒⢄
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⣀⡀⣹⣇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣫⠄⠠⢑⡊⡇
⠀⠀⠀⣔⣒⣒⣚⣛⣒⣒⣒⣆⣀⣀⣀⣠⡤⣤⡄⠀⢸⣇⠀⠀⠀⠀⢨⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡔⣊⣉⣀⣀⣀⣉⣑⣦⡀⠀⠘⠰⠷⠶⠶⠶⠥⠗
⠀⠀⠀⣇⣭⣄⣬⣡⣤⣄⣤⡟⠉⠁⠓⠛⠉⠉⠁⠀⠀⠛⢷⣦⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣭⣭⣥⣭⣭⣭⣭⣭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣧⣶⣦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠁⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡾⠁⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠖⢶⡀⠰⢖⡓⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠉⠉⠀⠀⠈⠁⠁⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣀⠙⠃⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢄⠀⠈⠙⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣾⠐⣤⣀⣀⡠⠀⢸⡧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠤⠞⢿⣟⠢⡐⠉⠉⠀⠀⠈⠀⠀⠀⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠀⠈⠛⠂⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠒⠉⠻⣇⢰⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣖⣈⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣻⡿⢿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢿⣂⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⠟⠋⠁⠑⢆⢻⣷⡂
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⢻⡆⠀⠀⠀⠘⠁⠀⠀⠀⠀⢈⣠⡏⠉⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⡄⢀⣀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠉⠉⠉⠛⠶⣄⠄⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⣱⠞⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⣼⡏⠀⠀⠀⠀⠀⠀⢀⡠⠰⠿⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠄⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⣄⢀⡀⢀⠄⣤⡀⣀⡀⣀⢀⠀⣤⣀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠚⠑⠊⠚⠛⠛⠐⠃⠙⠒⠀⠛⠋⠒⠉⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠉⠉⠳⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠄⠀⠀⢄⣀⣠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠣⢀⡞⠙⢆⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣎⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢅⠀⠘⠧⠒⢦⠉⢙⠎⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡀⠉⠐⠒⠒⠒⠉⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠑⠢⠤⣤⣬⠶⠻⡄
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢰⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢸⣠⡠⠀⠀⡇⠈⠑⠒⢤⡘⠄⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣀⠴⠖⠁⢸⠀⠀⠠⢀⠂⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠹⡙⡆⢀⠁⠀⠀⠀⠀⠈⠉⠉⢒⠒⠋⠀⠀⠀⠀⠀⠀⠀⢐⠅⢒⡊⠉⠉⠀⠀⠂⠀⠈⠦⠤⠖⠾⣀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣌⠊⠀⠀⠐⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⡄⠀⠀⠀⢀⠀⠀⠀⠀⣠⠊⠀⠞⠳⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢵⣆⢄⣀⣈⢒⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠷⠄⣀⠐⠃⠀⡀⠄⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡁⣈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⡍⠒⠊⠁⠀⢹⠄
⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠄⠚⠀⠀⠈⡗⢄⡀⠀⠴⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⣚⠠⠁⠀⠀⠀⠐⠻⠀⠀⠀⠀⡼⠠⣰⠇
⠀⠀⠀⠀⠀⠀⢀⠴⣶⠀⣤⠀⠘⠀⠀⠁⠀⠁⠀⠀⠤⠀⠀⣧⡍⠲⣤⣤⣤⠄⢡⣀⣈⣀⠀⠀⠀⡤⠤⠁⠀⠀⠀⠤⠚⣆⢀
⠀⢀⠀⠀⠈⠀⠘⢦⣼⠖⠁⠀⠒⠒⠀⢰⠀⠀⣶⣈⠁⠀⡬⠃⠐⠃⠀⢀⡁⠀⠃⢈⡿⠉⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢧
⡀⢠⠀⠀⠀⠀⠐⠠⡉⠀⠀⠀⣠⠀⠀⠀⡄⠀⢱⡈⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠄⣤⠂⠀⢠⣀⠀⠀⠀⢀⣄⣤⣤⣺⣀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠍⠠⠄⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣀⠉⠉⠉⠉⣗⠀⠤⠤⠤⠀⣂
⣇⠀⠀⠀⠀⠀⠐⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⣄⣀⡀⠀⢀⣀⣀⡤⢶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠋
⡟⠶⠦⠤⣤⣄⣀⡀⠀⡐⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡤⠛⠛⠲⠶⠭⠭⠭⠵⠖⠒⠋⠀⠀⠀⠀⠀⠀⠰⠦⠤⠤⠶⠩⡀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠉⠓⠚⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⡇
⡇
⠃
⡿⠿⢿⠿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡐⠉⠁⠀⠀⠀⠀⠀⠱⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢀⠄⠒⠀⠚⡆⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⠄⠀⠀⢀⡄⢠⠤⠄⠒⠀⠘⠛⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠀⠀⡰⢋⡄⠃⠀⡐⠀⠀⢠⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡀⠐⠈⠔⢣⡘⡀⠀⠸⠇⠀⠀⠘⢞⠃⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠀⠀⡇⠉⠀⢀⠀⠀⠀⠀⠀⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠀⠀⠈⠲⣆⠀⠐⠂⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠄⡀⠀⠐⠡⠅⠠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠑⠤⡀⠀⣠⢔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠈⠀⠀⠀⢠⣄⠀⠐⠤⢌⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⢀⠀⠀⡟⠀⡴⣇⣀⠘⡄⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⣀⠤⠒⠂⠉⠉⠀⠀⠉⠉⠙⠒⠠⢄⡃⠀⠀⠀⠃⠀⠈⠑⠢⡀⠀⠀⠀⠘⠀⠀⡐⠊⠀⡠⠚⡀
⠀⠀⠀⠀⠀⡠⠐⠂⢒⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⡾⠀⠀⠀⠐⠉⢀⣄⠠⠀⠀⠀⢐⠒⠈⣀⠤⢑
⠀⠀⠀⢀⠌⡀⠈⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡇⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡊⣉⡀⠄⠊⠄
⠀⠀⠀⢀⠈⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣤⠀⠄⠊
⠀⠀⢀⡼⠞⢉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠚⢆⠀⠀⠀⠀⠁
⠀⠀⢎⠀⠀⢪⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠤⠐⠂⠀⡀⠔⣸⠃⠀⢠⠃
⠀⠀⠈⠳⢤⣀⠑⠢⠤⣀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⣐⣠⠥⠖⠋⣁⠤⠚⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠭⢭⣽⣿⣟⣛⣛⣛⣛⣻⣿⡭⠭⠭⠐⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠠⠤⠤⠆⡒⠚⠛⠁⠤⠤⠤⠄⠀⠠⠤⠤⣄⣀
⠀⠀⠀⠀⠤⢀⠠⣄⠀⠀⢠⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉
⠀⢀⠠⠒⠂⢠⠄⠄⠀⣰⡟⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⣀⡀⠊⢀⡘⠈⠢
⠀⠈⣀⠀⣤⠄⢈⡑⢊⣀⡀⢡⣤⡀⠀⠠⠀⢀⠄⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠐⠤⡞⣀⣌⡉⠉⠑⠀⠀⠀⠀⠐
⠀⠀⢋⢳⡆⠀⠈⠉⠉⠁⠠⠄⡁⢀⠠⢒⢀⠦⣨⠀⠀⠁⠀⠀⠀⠠⠀⡄⠀⠀⢀⡀⠌⡆⠂⠀⠀⠀⠈⠉⠑⢒⢚⡀⠀⡾⡁⠀⣤
⠀⠀⠀⣑⣌⠱⠂⢰⡂⢀⠈⣰⠀⠕⣤⠥⢮⣖⠆⠀⠀⠀⣤⠖⠂⠀⡸⠤⠀⠁⠣⣹⢶⡶⠤⠄⠀⠀⠀⠀⠀⢀⠞⠐⡰⠐⡇⠀⠠⠁
⠀⠀⠀⠈⠙⠷⢾⡤⡤⠄⠰⢩⠿⡛⠛⠋⠉⠀⠀⠀⠀⠀⡎⢀⡴⠡⡇⠚⠹⠤⠄⢤⠼⠁⠀⠀⠤⠀⠀⠀⣠⠎⣠⠖⠁⣸⠃⠀⠰⠂
⠀⠀⠀⠀⠆⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⡄⢸⡀⢲⠀⠀⠀⠀⠠⠀⠈⠀⠀⠡⠄⠀⣤⡞⢁⡴⠀⢀⡴⠃⠀⢀⠒
⠀⠀⠀⠀⠀⠤⠖⢴⣞⣁⣄⣚⣂⡠⠀⠀⠀⠀⠀⠀⠀⠂⠈⢺⠙⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠞⠁⠔⣻⣥⠔⠋⠀⣀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠉⠛⢶⠖⠈⣛⢅⢀⠀⠈⠀⠀⠘⣀⠘⡔⠋⠁⡐⠒⠛⠛⢋⠍⡩⠇⠊⠤⢀⠀⠤⠄⠒⠒⠚⠁⡸
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⢠⡀⠹⡤⠤⣴⣎⠀⠀⠀⠀⠀⠻⠉⣇⠀⠘⠤⣤⠤⠒⠁⠀⣀⣴⣊⠀⠀⠀⠀⠤⠀⡀⠠⠊⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢥⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠦⢤⣤⠖⢞⠁⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢤⡀⠀⠀⣠⠈⣆⢉⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠑⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠀⠘⠌⠦⣼⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠳⢆⣀⣄⣀⠞
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⢀⡍⠑⢖⠓⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠜⠁
⠐⠄⡈⠒⠀⠐⠂⡁⠀⠀⠀⠀⠀⠀⠁⠉⢀⡙⢌⡁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠆
⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠄⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⡖
⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢠⡾⣞⣷⢠⠃⠀⠀⠀⠀⠁⡉⢀⠀⠐⠀⡎⠉⢲⠀⠈⡓
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⡽⠐⠑⠡⠋⢈⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠓⠒⠚⠁⢀⠁
⠀⡀⠐⢠⠀⠀⢀⡂⣀⠤⠂⠀⠀⠈⡀⠀⠀⠀⡘⢸⠀⠀⠀⠠⡴⠀⠀⠀⢀⣤⣄⠀⣀⡤⠖⠁⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠆⠀⢀⢠⠟⠁⠂⠀⣁⡀⠀⠀⠀⠀⠀⠀⢀⠑⠂⠀⠁⠀⠑
⠀⠀⡄⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠔⢬⡀⠤⠂⠉⠀⢀⣀⣀⡀⠀⠀⠀⠙⠀⠻⡄⠀⢀⡄
⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⢣⡐⠉
⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡀⠢⠀⢀⠀⠀⠠⠄⠀⡀⠁⡀⠌⠀⠀⠀⠀⠀⠈⠂⡀⠐⠀⠀⠪⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠈⠑⠀⠀⠄⠀⠀⠀⠀⠘⢀⠀⠀⠐⠀⡈⠐⠀⠀⠄⠀⠈⡄⠰⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠐⣤⠀⠀⠆⠀⠀⠈⢢⠈⡇⠀⠀⠀⡅⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⡅⠀⠀⠀⠨⠃
⠀⠀⠀⠐⠋⠀⠀⠀⠂⠈⠁⠄⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⡓⠂⠀⠀⠀⠀⠁⠀⠀⠐⠀⢰⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠓⢄⢀⡇⠀⠀⠁⠨⢆⠐⢀⠀⠐⠀⠠⠀⠀⠀⠄⠀⠤⠁⠀⠀⠠
⠀⠀⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄⠀⠀⠱⠤⡈⠀⠀⠀⠂⢀⣀⠴⠊
⠁⣀⡀⣠⣶⣿⣧⣴⣾⡟⠀⠀⠀⠀⢀⡀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠠
⣈⣿⣿⣍⣟⣿⣿⣿⣯⣷⣤⠤⠄⠒⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡲
⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣛⠆⠀⠀⠀⠄⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠟⠛⢻⢿⣿⣿⠂⠃⠀⠙⠋⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠘
⠀⠀⠀⠛⡙⠉⠀⠀⠀⠀⠀⠀⠠⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣀⡤⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠚⠛⠛⠛⠒⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠉⠉⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠠⠤⠒⠊⠉⠀⠀⠉⠉⠓⠒⠒⠒⠒⠘⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠉⠁⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠤⠤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠄⠒⠒⠶⠦⢤⣄⣀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⣂⡀⠀⠀⠀⢀⠤⠈⠉⠑⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡡⠀⠀⡞⠁⠙⡀⠀⠀⠐⢋⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣍⠤⡃⠀⠀⢣⡔⡄⠀⠀⠀⠀⠋⠂⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢀⢀⡇⠀⢀⠞⠁⠀⠀⠀⠉⠀⠀⠀⠀⠠⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⡇⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢣⠀⠀⣀⣀⠀⣀⡠⠀⠈⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠲⡀⢠⠓⠤⣀⠀⠣⡀⠣⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⣧⠱⡼⣄⠀⠈⠳⡄⠙⠦⡀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⠒⠓⠢⡈⢳⡀⢀⠋⠀⢀⡜⡖⠀⣀⡴⠊⢣⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⢀⣠⡤⠚⢦⡴⢀⡌⠀⠀⠈⢧⠘⢾⡉⢀⡠⠃⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⡠⠴⢮⠠⡜⠀⠀⠀⠀⠀⠉⠀⠉⢟⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠤⠤⢤⠴⠚⣄⢣⠀⠀⠀⠀⠀⢀⣀⣠⠦⢖⠴⠂⣸⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⣸⠋⡆⢣⣀⡤⠖⠚⠉⢁⡠⠖⠉⠀⠀⢻⣇⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠞⡄⠁⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⢸⡟⢦⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢁⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⡴⠒⣬⣇⡼⠋⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠎⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠋⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠇⠀⠈⠳⡄⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠚⠋⠉⠀⠀⠀⠀⣠⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡈⠙⠒⠶⠦⠤⠴⠿⠶⢶⣶⠶⢒⣀⣠⠄⣠⠞⠉⠉⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⠀⠀⠀⠀⠀⠉⠉⣉⣉⡳⠿⠓⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣷⣶⣶⣾⣶⡿⢿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣾⣿⣿⣿⣾⣷⣿⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⡾⢿⠿⠿⠿⠾⣷⡶⠶⠶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠲⠶⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢁⡀⢻⣦⣀⢰⣦⣀⣀⣀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠍⠉⠉⠉⠉⠉⠉⠉⢸⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠓⢒⡖⠀⢲⣒⠛⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⠀⠙⢻⠀⡟⠋⠁⣻⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⣤⣬⣤⣥⣤⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠢⡀⠀⠤⠀⢀⠔⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⢤⣀⢀⡗⠀⢺⡅⣀⡤⠓⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡞⠁⠀⠀⠀⠀⡀⠉⢃⡶⡘⠉⠳⠤⡀⠀⠀⠉⢳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠡⠀⠀⠀⠀⠐⠖⢒⣉⠀⠈⠒⠲⠂⡼⠀⠀⠀⠆⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠐⡺⠁⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⣀⠤⠔⠁⠀⠈⡙⣆⣱⠁⠀⠀⣠⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⣠⠔⠊⠉⠀⠀⠀⠀⣀⣀⠀⠀⡾⠧⣤⣴⠚⠃⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡖⠀⡞⠁⠀⠀⠀⠀⠀⢀⡔⠉⠉⠓⠊⠀⠀⠀⠈⠳⣄⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡇⠀⠀⠀⠀⢀⡠⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢘⣦⣤⡶⠓⠉⠀⠀⠀⠉⠓⠦⠤⣄⣀⣀⣰⠦⠤⠤⠷⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠒⠂⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⡾⢺⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢈⠒⠀⠀⠀⠀⠀⠀⠀⠙⢄⢠⣟⡾⣿⡀⠀⠀⠀⠀⠀⣠⡾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑
⠀⠀⠀⠀⠀⣀⠄⠒⠈⠁⠀⠀⠀⠈⠁⠀⠠⢀⠀⠀⠀⠀⠈⢺⣯⠈⠌⠛⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢂
⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠄⠀⡀⠀⠀⠀⠀⠐⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡤
⠀⠛⠤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠒⠉⠱⠀⠀⠀⠀⠉⠀⠀⣤⢺⠈⠲⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠐⠀⠀⠀⠰⠐⠋
⠀⠀⠀⠀⠈⠈⠙⢛⠲⣴⠢⣄⡤⢀⡀⠀⣀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠐⠀⠐⠘⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠄⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⠓⠈⡍⢀⠐⠟⡙⠛⠛⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢬⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠓⠀⢿⠗⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢳⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠈⠄⠀⠀⢀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⠁⠀⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⣓⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠄⠀⠀⠐⠉⣇⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢹⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⡐⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠊
⣿⣿⡟⠻⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡶⠒⠒⠒⠒⠒⢲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⣒⡒⠒⠒⠒⠒⠒⠚⠃⣠⠗⠒⠒⠒⠒⠒⠚⢧⡀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⡽⣛⡛⢦⡀⠀⠀⣞⢓⣒⣒⣒⠒⣒⣒⡒⣒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠞⠹⡟⠁⠉⢻⠇⠀⠀⠉⠉⠉⠉⠉⣩⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡶⢶⣏⣀⠀⠀⠀⠀⠀⢯⠀⢸⠆⢸⡄⠀⠀⠒⠒⠲⡖⠒⢲⡖⠒⢶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠉⠀⠈⣷⠀⠀⠀⠀⢘⣀⣤⣄⣘⠁⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠀⠀⡶⢳⢄⣿⡀⠀⣀⣰⠯⠥⠤⠤⠭⢷⣀⡀⠀⠀⠀⡇⠀⣸⣇⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣅⠀⠘⠳⢦⣠⣟⡏⢠⠈⠓⠶⠯⣿⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡞⢹⣆⡏⢹⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡶⠴⣇⣹⠇⢺⠶⠶⠶⠶⢾⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠙⠚⠙⠓⠚⠈⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠳⠶⠶⠶⠶⠞⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣶⠶⠶⣶⣶⡶⠶⢶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣿⠸⠭⠇⠸⠭⠭⠿⠀⠯⠟⢸⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢛⣛⣛⣛⣛⣛⣛⣛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣈⣉⣉⣉⣉⣉⣉⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠐⢀⠠⣄⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠈⠁⠈⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠠⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⢶⣤⠙⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣶⣬⣿⠟⠦⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣼⠋⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣤⠁⠀⠀⠀⠀⠀⠀⠀⢿⣆⠆⣠⡅⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠐⣋⣽⡇⠀⢾⣭⡉⢸⡿⢤⠖⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡷⠀⠀⠀⠉⠀⠀⠀⠀⠸⠿⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀⠀⠓⠒⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠙⢓⠂⠛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⢀⣴⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⢿⣿⣿⣿⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣍⡋⠁⠀⣠⠎⠀⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⣌⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⣤⠴⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣢⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⡰⡁⠀⠀⠀⡀⠐⠀⠀⢸⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠁⢀⡸⠇⢀⠀⠀⠀⠸⡆
⠀⠀⡼⠁⠈⠀⠀⡌⠀⠀⠀⡀⣼⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣤⣾⣿⣿⡟⢻⡗⣦⠙⢷⣌⠀⡀⠀⠀⣿
⠀⢠⡇⠤⠒⠘⣼⡃⠀⠀⠀⢥⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠋⣾⣿⣿⣿⣧⣸⣧⠀⠂⠀⠻⣷⡘⣆⠀⢸⡀
⠀⢸⡇⠀⠀⠀⠹⣁⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠃⠠⣿⣿⣿⣿⣿⣷⠟⠂⠀⠀⠀⠻⣖⠘⡆⢸⡇
⠀⣜⠁⠀⠀⠀⢀⣻⣴⣶⡞⠁⣇⠀⠀⠀⠀⠀⠀⢸⡇⢰⣴⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⢹⡇⣷⢸⡇
⠀⠘⣦⡀⠀⠀⠸⣴⣿⡟⠀⠀⠏⠀⠀⠀⠀⠀⠀⠘⠣⣾⣿⣿⣿⣿⣿⣿⣿⡉⢻⠀⠀⠀⢔⣀⢴⠂⠀⠸
⠀⠀⠈⠻⣄⣀⣀⣻⠟⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠳⠦⠶⣄⡐⠀⠒⠀⢁⡾⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⠲⠾⣽⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢸⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⢿⡿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⠳⡖⢋⠕⢊⣾⠟⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣿⠃⠀⠉⠉⢠⣿⠇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢧⠀⠀⠀⣾⣿⣀⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣧⣀⣼⡇⢀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣄⠀⣀⣠⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣟⢶⡀⠀⠀⠀⡼⠁⠀⣰⠋⠉⠁⢸⡇⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⢫⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⠿⠀⢹⡆⠀⡰⠁⢀⡜⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣇⢀⣠⠗⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡿⣄⢀⣀⡼⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⢷⡿⡆⣤⠀⢁⠀⡀⢰⠃⠀⠀⠀⠀⠀⣰⠃⣬⣿⡿⠟⠋⠉⠀⠀⣀⣤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡿⣔⣿⡻⠛⢡⡀⠀⠀⠀⠀⡴⢁⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠀⠈⠁⠙⠉⠳⠤⠏⢹⣄⣀⢀⣜⡡⢟⣫⣥⣾⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠀⢀⣺⣷⣤⣦⡀⠀⢀⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣏⠀⠉⣷⢀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠢⠤⠂⠢⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⢠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣘⡍⠀⠀⠀⠀⠀⠀⠀⡦⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠤⠤⠄⠀⠤⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⠀⢐⠦⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠘⠁⠑⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠶⣄⡠⠏⣀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠃⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⠴⢉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠀⠀⠘⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠄⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠈⠒⡤⠀⢀⡉⠄⠂⠛⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢁⠀⠀⡆⠀⣀⡠⡚⠉⡉⠑⢆⡀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠊⠀⠀⠀⡸⠀⢃⠀⠀⠀⠀⣆⢸⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠁⠀⠙⡆⠣⠤⠔⠁⢉⠋⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠳⢅⠀⠈⠁⠒⠒⠂⠁⠀⣷⠀⠀⠈⡆⠰⠲⠶⠶⠶⢌⠉⠉⠉⠉⠀⡸⠀⠀⢠⡀⠀⠀⠀⡘⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⠀⠱⠤⡀⠀⠀⣀⡀⢤⠞⣧⡀⠀⠸⠀⠀⠀⣠⡶⠚⠛⠛⠛⠋⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡀⠀⢦⣧⢔⡩⢄⠖⠃⣠⠟⠁⠀⢰⠀⠀⢘⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢹⢋⣼⠿⠓⠁⢀⡠⠋⠀⠀⡴⠃⠀⣭⠾⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠓⠤⣄⡀⠿⠁⠀⢀⡤⠊⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠀⠀⠀⠀⠈⠀⠐⠂⠉⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠇⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⢀⠏⠈⠈⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠈⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⡇⠀⠀⠀⠀⢳⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⡀⠀⠀⢀⣀⣠⠇⠀⠀⠀⠀⠸⠤⣤⣀⣀⠤⠤⠜⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⡿⢿⠙⠶⠖⠀⠀⠈⢛⡄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣌⣀⠠⠀⠀⠀⠀⠈⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠀⠠⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⠆⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⢷⣶⠾⠛⣉⡤⠞⣡⣿⡿⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢡⣾⡟⠁⠀⠿⢤⡼⠥⢤⣴⣿⡿⠁⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⣾⣿⠁⠄⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⡀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠈⢷⡀⠀⠀⠀⣸⡿⠛⢿⣶⣤⣤⣤⣤⣤⣼⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⡀⠀⣠⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣀⣀⣿
⢀⠀⠀⠀⠀⠀⠀⣾⣆⢠⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠞⠿⠷⠛⠉⣿⠃⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣷⣴⠞⠋⠉⠉⠉⠙⣿
⣼⡄⠀⠀⠀⠀⠀⢻⡜⠛⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣻⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⡿⠹⡆⠀⠀⠀⠀⠀⢿
⣿⣧⠀⠀⠀⠀⢠⡜⡇⠀⠸⣷⡇⠀⠀⠀⡼⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡧⠚⠁⠀⠀⠀⠀⠀⣸
⣿⣿⣆⠀⢰⡄⠸⠀⠀⠀⠀⣸⠇⠀⢀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢹⡟⢿⣆⣺⢷⡜⢦⣀⢀⣠⠟⢀⡴⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠈⣧⣈⣿⣯⣠⣿⡆⠈⢉⠁⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠛⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠘⣿⣇⠙⢿⠙⢿⣀⣿⡀⢀⠘⡴⢀⣴⢆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡏
⠀⠀⠈⣿⡄⠀⠀⠘⣿⡿⣇⢸⣷⡙⡟⠼⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣾⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡀
⠀⣧⠀⢹⣷⡀⠀⠀⢻⡇⠹⣾⡏⢿⡆⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⢀⡾⠁⣤⣿⡿⠿⠛⢉⡝⠀⡔⣠⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢳⣾⣿⡇⠀⠀⠀⠀⡀⠈⠀⠀⠙⠳⠛⠋⠀⢹⣧⣀⣀⡀⢠⣞⣡⠶⠋⣁⣤⣶⣿⣿⣤⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡀⠈⠋⠋⠀⠀⠀⢦⣿⣦⡀⢠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠘⣧⠀⠀⠀⠀⠀⣷⣾⣿⡯⠻⢿⣿⣦⠀⠀⠀⢸⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠘⣧⡀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠈⣿⣿⣀⣤⢿⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⣤⣤⣀⠹⠿⠿⠶⣖⣒⣭⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⢻⡉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠜⠁⠁⠀⠀⠀⠀⠆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⣃⠠
⠀⠀⠀⢀⠀⠀⠀⠌⠀⢀⠔⠱⠋⠅⠀⠀⠀⠈⡁
⠀⠀⠀⠈⠢⢀⠀⠄⠠⢀⠘⠀⠰⠇⠀⠀⠰⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠈⠧⠠⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠤⡀⠁⠁⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠀⢢⠑⠀⠀⢀⡀⠁⢈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡔⠀⠸⠤⡄⠄⠀⠀⠈⢄⠀⠀⢀⣤⠄⠀⠐⠀⠢⣞⠆⠀⠀⡠⡄
⠀⡀⠀⠀⠀⠀⡀⠀⠀⣆⠄⢨⣣⠀⠈⡄⠀⠀⠀⢀⠈⠀⠨⣄⠈⡁⠀⠄⠐⠀⢀⡀⡄⠀⠀⠈⠡⣄⠀⡆⠈
⡌⡀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⢸⠂⢀⠃⠀⠐⠀⠾⣄⠀⠛⢁⠓⠀⠂⠀⠀⢀⡀⣄⠀⠂⡄⣊⠀⠐⠋⢁⣠
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠊⠁⠀⠀⠀⠀⠀⠾⡙⡶⡤⢤⣈⣉⣉⣉⡀⠉⣉⣉⣉⣀⣠⣤⣴⠾⠛⠉
⠘⠤⠀⠠⠀⣄⠀⠀⠀⠀⢀⢠⠉⠉⠉⠉⠉⠉⠈⠉⠀⠈⠉⠉⠉⠉⠉⠋⠙⠛⠻⠛⠟⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣉⣢⣤⣤⣔⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠙⠶⠦⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⢀⣰⡩⠂⠀⠀⠀⠀⢠⣞⣠⣴⡂⠀⠀⢸⣄⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⢧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⣇⡀⠀⠀⠐⠒⣞⠉⠁⠀⠀⠀⠀⢀⣠⠤⠐⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⢹⠁⠀⠀⠀⠊⢈⢦⡀⠀⠀⣠⠖⢋⠀⠀⠀⣂⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠸⣄⠀⠀⠀⠀⠁⣠⣷⣄⣼⣅⠀⠀⠶⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠈⣷⣶⣦⣴⣶⣿⣿⣿⠟⠿⠂⠀⠀⠀⠄⠚⠀⣤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣌⠓⠀⠀⠸⢆⡀⠨⠄⠺⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣛⣛⣟⣿⣛⣿⣿⣛⣦⣤⣤⡀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠀⣾⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠾⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠟
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠙⠲⠶⠶⠚⣹⣤⠼⠷⠛⢻⠈⠉⠙⠛⠿⣿⣿⣿⣶⣶⣶⡀⠐⠶⠶⢶⡶⠶⠒⠒⢒⡶⠒⠊
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠐⢧⣀⡀⠀⠀⣠⠶⢿⣁⠤⠀⣠⠟⣄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠠⣴⣾⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠉⠉⢹⠉⠶⣄⣹⠆⠉⣀⠴⠊⠀⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⡏⠛⠷⣦⣤⣤⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠑⠒⠲⢶⠶⣶⠺⡘⢆⢸⢹⠀⠀⠈⠢⡀⠀⠀⠀⣈⡆⠀⠀⢱⡀⠙⣿⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⠙⣆⠰⡑⢷⡀⡸⣺⠀⠀⠀⢀⡜⠀⠀⠀⠘⢷⡆⠀⠀⠇⢠⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡄⠀⡜⠠⡿⢤⣀⠈⠛⣥⠇⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠸⣿⣿⣿⣿⡿⢁⡴⠀⠀⠀⠈⡿⠚⠧⠰⠧⡀⠈⠉⠒⣾⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⢿⣿⣿⡿⣡⠏⢀⣤⠤⢶⡞⠉⠀⠀⠦⢀⢹⠀⠀⠀⣿⠊⣀⡤⠤⠀⠀⠀⣤⣄⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏
⠀⠈⢿⣿⣷⠃⠀⠁⠀⣠⠾⠀⠁⠀⠠⢀⢈⡇⠀⠀⠀⡸⢿⡁⠰⡶⠀⠀⠀⠈⠡⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⡿
⠀⠀⠈⢿⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠢⢤⠟⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⣷⠀⠀⠀⠘⡇⠀⠢⣼⣷⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣴⡄⠀⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠱⣄⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⣬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣶⡆⠀⠀⠈⠋⠀⠀⠀⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣻⣿⣷⣶⣶⣶⣾⣶⣶⣿⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡤⠔⠀⠉⠉⠉⠉⠉⠁⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⢀⣀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⠀⠀⠀⠠⣄⡀⠀⠀⠤⠄⠒⣩⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢻⠀⠀⠀⠀⠀⢀⠶⢆⡀⣀⠰⠚⠁⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠖⠓⠀⠤⠤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢌⡦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠻⣦⠈⠡⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⠶⠶⠶⠆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠔⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢋⡆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠏⠦⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠰⠀⠳⣄⠀⠀⠀⣀⢠⠔⠒⡝⠁⠈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠈⠷⠐⠊⠁⠀⢀⡠⠟⠲⠦⣤⣀⡀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠱⣤⡜⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⡠⠛⠻⠉⠉⠉⠁⠀⠀⠈⠒⢄⡀⠀⢀⠞⠀⠈⠙⠃⠤⠤⠌⠿⠿⣧⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠙⠓⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⡨⠛⢷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⣳⣤⡚⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠒⣒⣖⡚⠛⣻⣿⡛⢻⣿⣖⠒⠒⠖⠲⠚⠷⠲⣶⣶⡶⠶⣶⣶⡿⢵⣶⣤⢶⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠘⠋⠉⠃⠈⢉⠉⠃⢹⣏⣹⠃⠀⠀⠀⠀⠀⠰⣿⣽⣿⢺⣿⣹⡿⢺⣯⣽⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡦⠤⠴⣦⠤⠤⠤⣤⡤⣥⣤⣤⣤⠤⠤⣤⣤⣤⣬⢭⣥⣤⣭⣭⣥⣬⣭⣉⣠⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢠⣀⣀⣠⣘⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣻⣯⢸⡇
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠐⠒⠚⢦⠔⡄⠤⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⠀⠀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣆⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠍⢹⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⢘⣄⠀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠬⠤⠤⠤⠤⠤⠤⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠓⢤⣤⣇⠀⠱⢦⣄⠀⠠⣄⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠓⠒⠚⠛⠛⠛⠒⠛⠓⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢿⠈⣧⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⢞⣵⣺⢦⠀⠀⠀⠀⠀⠁
⠀⠠⠶⠶⠆⢱⢰⢄⡆⠀⢁⣒⣂⣂⡤⠀⠀⠀⢸⡄⠸⠂⠈⡦⠀⠈⠈⣁⡀⠀⠀⠀⠀⡴⣩⢟⣾⡽⠃⠀⠀⠀⠀⠀⣰⡞⢹⡆
⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⢧⣄⣥⠔⠃⠀⠀⠉⠁⢀⣨⠀⠀⠀⠈⠉⠺⠋⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣄⠓⢀⡄⠀⠐⠳⢿⣾⠟⠃⠀⠀⠰⢀⡁⠂⢀⡄⠀⠀⠀⣾⣶⣶⡿⠆
⠀⠀⠀⠈⢀⡀⠀⠀⠀⢀⢰⡁⣼⠂⠁⠀⠀⠀⠙⠇⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⣰⡾⠁⡤⠀⠙⠀⠀⠀⠀⠨⠙⠂
⠀⠀⠀⣀⡘⠁⠀⠀⠀⠘⠀⠀⠤⠖⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠡⠤⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠸⠉⠃⠀⠀⠀⢀⣈⠁⠚⡆⢀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⡐⠀⠀⠙⣷⡀
⠀⠀⠀⠀⢠⣆⣠⡀⠀⢰⡁⠂⠀⠀⠀⠸⠀⠀⠉⠂⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠨⠽⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠉
⠀⠀⠀⠀⠰⢷⡽⠂⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠋⠁⠀⠀⠀⠀⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠰⠆⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠙⣡⠀⠀⢀⠀⠆⠀⣢⠴⠁⢀⠀⠀⠠⠀⠰⠀⠀⠠⠶⣶⣶⠶⠢⣤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⢠⡄⠀⠠⣀⡝⠀⠐⠶⠀⠶⠋⠁⠀⠀⠰⠠⠆⠀⣤⠄⠀⠀⠀⠃⢄⠀⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠀⡀⠛⠀⠀⢀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠉⠻⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢀⣾⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠤⠊⠀⠀⠀⠀⠀⠚⡄⠈⠒⠀⠀⠀⠀⠀⢠⡄⣤⡈⡷
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠓⠃
⠀⠀⠀⠐⠗⠀⢀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⣄⠀⠀⠀⢀⠀⡀⠀⠠⣿⡟⣭⡛⣷⠀⠀⠀⠀⡴⢤⠀⠀⠀⠀⠛⠃⠀⠀⠛⢃⠀⠀⣬⠃⣠⣥⣀⡤⣀⠀⣠⣾⠿⢶⠃⠉⠁
⠀⠈⠻⠿⠾⠿⠟⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠰⣤⣀⣀⡤⠂⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⡁⠘⣹⠃⣸⣇⡼⠃⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢺⡆
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣶⠆⠀⠀⠀⠘⢻⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢐⣠⣖⡀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⢠⠐⡂⠈⢤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠹⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⠀⠀⠀⠦⠀⣠⡖⠀⠀⠠⠤⠤⠈⠛⠀⠀⠀⢠⣘⣿⣦⡈⠂⠀⠀⠀⠀⣄⠀⢳⡄⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⣤⠤⡤⠤⠆
⠀⠀⠀⠄⠙⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠏⣹⠙⣽⠆⠀⠀⠀⠂⠛⢰⠊⠀⠀⠀⠸⠛⣀⡀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠢⣤⣤⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⣶⠄⠀⠀⣀⡀
⠀⠀⢉⣡⣤⡄⠀⠀⠀⢠⠀⠀⠘⠆⠀⠀⢀⣤⠶⠟⠋⠉⠀⠀⠀⠂⠀⢰⣌⡉⠀⠀⠀⠀⠉⢉⡁⣀⢃⠀⠀⠀⠀⠄⠀⠩⠃⠼⠂
⠀⠀⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠟⠀⠀⠀⣱⣷⠶⠶⠷⠊⠀⠀⠀⠀⢠⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⡙⢻⡏⢉⡟⢛⣏⠋⣹⡿⣻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣀⠀⡴⠋⢳
⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣈⣹⠇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⢀⠀⠾⣥⠟⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠖⠚⣉⣻⠲⣾⣟⣦⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠙⠒⠶⠖⠋⠁⠀⢸⡆
⠀⣰⠛⣧⠤⢼⣄⠀⠀⠈⠓⠦⣄⣀⠀⠀⡀⠀⠀⠀⢰⣇⡞⣠⣾⣥⣬⡷⢦⡼⠙⣇⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢀⡴⠶⠲⢦⡀⠀⢧⣀
⠚⠓⢺⠁⠀⠀⠙⠳⣄⡀⠀⠀⠀⠉⠉⣿⢻⠀⠀⠀⢸⡛⠿⢵⣏⣄⣀⣽⠞⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⡧⠀⣿⠀⠀⠀⠀⢻⠀⠀⠉⢳⡀
⠀⠀⠈⢧⡀⠀⠀⠀⠈⠙⠛⠷⠶⣾⡋⣉⡛⠀⠀⠀⠈⣇⠀⠀⠦⠀⣠⠏⠠⠀⠀⠀⢷⠀⠀⠀⠀⠀⣠⠞⠁⠀⠻⣄⠀⠀⣀⠞⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⢀⣽⢹⡇⠀⠀⠀⠀⠘⢧⠀⠀⣰⠋⠀⠀⢠⠀⠀⠘⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠙⢿⠁⠀⠀⠀⠀⠀⠈⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠧⣄⣀⡤⠶⠚⠛⠛⠓⠲⠤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠴⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠃⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠖⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⡶⠲⡄⠀⠙⠶⣤⣬⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣆⡖⠲⡇⢀⣏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠘⢧⣀⠀⠀⢰⡏⣴⠀⠀⠀⠀⢀⡴⡆⠀⠀⢀⣀⠙⣶⠋⢛⣶⠟⣯⠈⢯⣹
⠀⢀⠖⠒⠒⠒⢒⣛⣛⣛⣛⣛⣛⣻⡄⠀⠀⠀⠀⠀⢼⣉⣉⣉⣉⣹⠀⠀⠘⡇⢹⢀⡴⣤⣤⣿⠟⠁⠀⠀⢸⣭⣉⠛⠦⣏⣸⢠⡿⣧⠀⢳⡀
⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠳⣄⠀⠏⢀⢸⣄⠀⠈⣧⠀⠀⠀⠀⠀⢠⣸⣿⡄⠈⢻⣸⠃⣼⣆⣠⣷⠆
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠉⠙⢿⡳⠾⠃⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠛⠛⠋⠉⠉⠀⡞
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⢤⣿⣦⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⢸⣇⢀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣴⠋⠍⠛⢿⡟⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⡤⠤⠤⣤⣼
⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣄⣽⣆⡰⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠤⢤⣄⣀⡀
⠀⠀⠀⢀⣴⣒⣾⣓⡶⠶⣦⠴⢶⡄⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⢈⠉⠓⠶⣤⡀
⠀⠀⢠⠞⠉⠉⠆⠉⠙⠳⣝⠛⣻⠿⣟⠲⢤⠀⠀⠀⠀⠀⠀⣠⠞⢫⣁⠀⡀⠒⠍⡙⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣛⠛⠲⢤⣞⡀⠀⠀⠀⠙⢶⣄
⠀⢠⡏⠀⠀⠀⠀⠘⠂⠀⠈⠳⣍⠳⣾⢶⣌⢷⠀⠀⠀⠀⢸⠃⠴⠀⠉⠀⠃⣀⠈⢁⡤⠌⢷⡀⠀⠀⠀⠀⠀⣸⠩⢳⡄⠀⣤⠉⠻⢧⡀⣠⡄⠙⢦
⠀⠀⢧⡐⠂⠀⡤⠀⠀⠀⠁⢠⡙⣆⠛⣿⣳⢸⠀⠀⠀⠀⠈⣷⠦⣤⣤⣤⣬⣥⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⣾⣋⡼⠃⣤⢖⡚⣓⠦⣝⢳⣄⣤⠼
⠀⠀⠀⠙⠦⣄⡀⠀⠀⠦⠀⠀⠀⠸⡄⡾⢹⡾⠀⠀⠀⠀⢠⡷⠶⠒⠒⠦⡴⠖⠛⠓⠶⠶⢋⡷⠀⠀⠀⠀⠀⣿⠁⠀⢸⠳⣏⣇⣯⠿⠚⠋⠁
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠐⠀⠀⣿⠟⣹⠃⠀⠀⠀⠀⠀⢻⡗⠚⠛⠛⠛⠿⣿⣛⠛⠛⣹⠇⠀⠀⠀⠀⠀⡟⠓⣆⣼⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣼⡾⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣄⣀⣤⡽⠷⠶⠋⠀⠀⠀⠀⠀⠀⠷⠚⠉
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠀⡰⠚⠉⠉⠩⢭⣉⡙⢦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠁⠈⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢰⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠑⠆⠀⠀⠰⠚⠉⠉⠁⠀⠀⠀⠀⠀⡎⠀⠠⠴⠋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⢰⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣇⠀⠐⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠐⠚⠉⠉⠁⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⡤⠶⠒⠛⠛⠉⠙⠛⠛⢻⡇⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠁⢀⡤⠤⠀⠀⠠⠖⠲⠄⠘⡇⠀⠀⠀⠘⢦⠀⠀⠀⢰⠑⢮⠱⢄⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀⠀⠀⠈⠁⣠⣤⣤⣷⡌⡦⢀⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡄⢹⡀⣠⣴⣾⣿⣶⣿⣿⣿⣶⣾⣧⣴⡗⠀⠀⠀⣴⣋⣀⣄⠈⢡⠃⢰⠟⠀⣱
⠀⠀⠀⠀⠀⢰⠀⠀⠀⣾⠀⠀⠘⢷⣾⣿⣿⡿⠟⢉⣉⣉⠉⠙⠛⣿⠛⠋⠀⠀⠀⢰⠛⡇⠀⢸⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢸⡄⠀⠀⢿⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠁⠀⣀⡼⠃⠠⡄⠀⠀⠀⢸⡀⠙⠤⠎⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⡆⠀⠀⠀⠀⡎⠀⠈⠙⠓⠶⠚⠛⠉⣀⠀⢀⡇⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢳⡀⠀⠀⠀⣹⠖⢋⣩⣤⣷⠀⢸⣧⠤⠈⠻⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠱⡄⠀⢰⠇⠀⠈⣈⠅⠛⠒⠋⠑⠢⢄⣀⣈⡷⢰⠚⢲⣀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠈⠢⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡶⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣤⣄⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣻⣉⣟⣻⣋⣿⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⡤⠤⢤⡀⠀⠀⠀⠙⠆⣰⠿⠃⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢱⠀⠀⢀⡀⠀⠀⢠⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢸⣧⠀⢰⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢧⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠚⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠲⠤⠞⠋⠛⠿⠿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⢀⣤⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⡂⠀⠀⢸⣧⣤⣤⣤⣄⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠛⠻⠛⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⣽⣿⣿⣿⡇⠀⣀⣀⣀⢀⣀⣀⠀⠨⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡿⠁⠀⢨⡟⣱⣿⡇⠀⢿⣿⣿⣿⣿⣿⠁⠈⣿⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠙⢿⡇⠀⠀⠛⠻⠿⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⡇⠀⢀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⢈⠀⢁⠀⠆⠀⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⢠⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠙⠛⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠆⣀⠄⡆⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢦
⠀⠀⠀⢘⡀⡘⠠⡴⡀⡀⡛⠀⡄⠀⠀⠀⠀⡀⣀⣀⣠⢿⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠
⠀⠀⠀⣀⠤⠆⠀⡀⠹⢠⠓⢰⠇⠀⠀⡀⠀⠀⠙⠋⠁⠈⠙⠋⢛⣾⣅⡀⠀⠀⠒⠄⣀⣀⡀⣀⢀⣀⡀⠔⠛⠀⠀⠈⠤⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠅⠐⡳⠀⠉⢡⠖⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⢶⣀⠆⢠⠤⢤⠤⣤⠤⣤⠀⣤⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠠⠄⡘⢷⠸⠝⠖⡁⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠙⠷⢾⣤⣴⣄⣤⣄⡼⠶⠛
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠁⠁⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣹⣦⡀⣠⣠⣿⣿⣿⡟⠀⠀⠀⡀⠙⣀⢤⣈⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠄⠐⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣿⣿⠿⠿⠁⠀⠀⠀⠃⠀⠀⠁⢠⡎⠀⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⡰⠊⠉⠿⣦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠦⠔⠁⠀⣰⠁⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣹
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠰⢾⡇⠀⠀⠀⠈⠲⣶⣤⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⡇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠾⣠⡿⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⠀⠀⠇⠀⣼⡿⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢸⡃⠀⠀⢀⠀⠀⠀⠀⠀⢀⢨⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠧⠀⣸⠀⠀⠈⢤⣆⠀⢸⠀⢀⣼⣼⠃⢀⠄⠰⣼⣻⣸⣧⣴⣦⣄⠀⠀⠄⢠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠄⠀⣤⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⡔⠒⠉⠒⢣⠋⠁⠀⠹⢻⣇⠀⠀⠈⢷⠀⠀⠀⠀⠈⠛⠻⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡀⣀⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⡿⠀⠀⠀⠉⠲⠦⣤⣴⡾⠿⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⡄⣠⡾⢇⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣶⣶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣷⣦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣨⡛⠓⠉⠇⢸⠅⡀⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣢⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠁⠀⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠖⠚⠛⠉⠁⠉⠉⠉⠑⠒⠠⠄⣀⣀⣀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣇⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢹⣿⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣄⡈⣿⣇⠐⣄⠀⡀⠀⠀⠈⠀⢀⠀⢀⠀⠀⢰⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣝⠿⣿⣿⣦⡈⠳⡌⢄⠀⠀⠀⠀⡇⠘⡀⠀⢧⠤⠤⠿⠦⠄⠀⠀⠀⠀⢀⡀⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣿⣆⠸⠈⢠⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⢀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⢆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⡴⠞⢋⠁⠀⠤⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⡔⢠⠿⠿⣷⣦⡀⠀⡀⠀⠀⠀⣠⣴⣶⡶⣦⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⠐⠋⠀⠀⠀⠈⠙⠛⣤⠓⠀⠁⠾⠟⠁⣀⠀⠈⠀⠀⣿⠛⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡙⢿⡿⢿⠃⠀⠀⢀⣄⠀⠀⣼⡆⠀⠘⠀⡄⣡⡈⢳⣄⠂⠀⠈⢴⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣸⣧⡄⣩⠄⠀⢌⣉⠅⠈⣿⡁⠀⠀⠀⠤⠉⠉⠄⠈⠁⠀⢤⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠀⠀⠀⠀⠀⠀⠀⠸⣧⢋⢻⣿⣿⣤⠰⠀⠀⣀⢀⡞⣿⠋⠀⠁⠀⠀⣀⣠⠀⠀⠀⠀⠻⠀⡸
⠀⠀⠀⠀⠀⠀⠀⡴⠳⠄⠞⠉⠁⣼⠆⢀⣀⡀⠀⠀⠀⠀⢻⠈⢸⣿⢿⣿⠖⢾⡿⢯⣌⣿⣿⠷⠆⠘⠈⢹⣿⣿⡇⠀⣆⠀⠈⠟⠁⠲⣄
⠀⠀⠀⠀⠀⡠⠊⠀⣸⠀⠀⡺⠉⢀⣀⣈⡨⠃⠀⠀⠀⠀⣸⣦⣼⡇⠈⡟⠀⠈⠧⠠⣬⣉⠻⠶⢰⣾⣛⣧⠄⠋⠁⠀⢸⠀⠀⢰⠀⠀⠘⢷⣤⣄
⠀⠀⠀⠀⢰⠁⠀⠞⠁⣠⡞⠀⢀⡘⠉⠀⠀⡔⠳⣀⣠⣾⣿⡿⢿⣇⠀⢿⠀⠀⠀⠀⠈⠻⣶⣤⣤⣴⠞⠁⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⠀⠀⠀⡟⢦
⣠⣄⡀⠀⡌⠀⢀⡄⠀⠁⢸⠀⣩⣅⣠⣤⣶⡀⠀⠙⡏⢸⣿⠁⠸⣿⣆⠘⢧⡀⠀⠀⠀⠳⣤⣉⣁⡅⠀⠀⠀⠀⠀⡰⠁⠀⢠⠎⠀⠀⠀⠀⠘
⢣⡀⠘⢾⡇⠉⠉⢱⣄⡠⠀⠉⠁⠸⢿⣿⡿⡿⠦⠀⣧⠸⣿⡆⠀⠻⣿⣄⠀⠙⢦⣀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣠⠞⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢫⡀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⢄⡀⠟⠀⠻⢧⠀⠀⠈⠻⣶⣦⡀⠉⠳⢦⣀⠀⠀⠀⣀⠔⠋⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠈⢳⡄⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⡆⢠⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⣤⣙⢛⡛⢛⣁⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠃⢀⠎
⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠾⠿⠷⠶⠦⡤⢀⠀⠈⢫⡉⣉⠅⠈⠀⠀⠀⠀⠀⢀⡀⠀⢀⠔⠁⡴⠃
⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣌⣀⣀⣉⢀⣀⣀⣤⣤⣴⠶⠞⢋⣠⠖⢃⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⠛⠿⠶⢶⣶⣤⣤⠶⠶⠖⣿⡟⠙⠻⠿⣯⣭⣭⣤⣴⡶⣛⣩⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢠⣤⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⡰⢉⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡘⠇⢷⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢹⣞⢳⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠆⣎⣱⠟⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠸⣾⠟⠀⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡍⡉⠀⠀⣼⡰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢰⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⢿⣁⠀⣀⠠⠛⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⠇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠫⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡴⠃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣠⠞⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠞⠁⠀⢰⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⣧⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⠤⠴⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠤⡀⠀⠒⠒⠒⠒⠢⢄⡀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⢹⡆⠠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠭⠍⠉⢩⠭⠑⢦⣸⡧⠯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠀⠀⠘⠃⠀⠸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣟⣀⡀⠀⠀⠀⠀⠀⡇⢜⣁⣀⠒⠄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⢗⢦⡀⠀⠀⢣⠈⠻⠛⠋⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡝⡄⠀⢠⡗⠢⠄⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢗⡦⣟⠣⣄⣀⠤⠖⠋⢡⠷⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠙⠦⢭⣙⣒⣒⡒⠒⣲⣶⣶⣾⣿⡿⠟⠃⠘⢦⡈⡇⢀⣠⠔⠁⠀⠀⠀⠈⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⡏⢿⡉⣹⢹⠃⠀⠀⢰⠃⣬⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠁⠘⢦⣄⠀⡞⢀⠁⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⣄⠤⠞⠉⠳⣅⠘⠃⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢷⠃⡆⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠘⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⡀⠈⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⣸⣿⡿
⠀⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⣿⢀⡀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠰⣶⡆⠀⠀⠀⢹⡟⠁
⠀⢹⡄⠀⠀⢥⣀⠀⠀⢰⠆⠐⠰⣿⡇⠀⣿⣿⠸⡧⠀⠀⠘⠛⢿⠀⠀⠙⠛⡟⠾⠆⣺⠂⠀⠛⠇⠀⠀⢀⣿
⠀⠈⣇⠀⠀⠘⣇⠀⠀⠘⡄⠀⠀⢸⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⠀⠀⣼⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠶⠀⠒⠈⠉⠐⠲⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡊⢠⠄⠠⣄⠀⢰⡄⡄⢠⠂⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠣⣜⢀⢀⡙⠧⠀⢁⣷⣃⠀⠀⠴⣾⡧⡠⠶⠆⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡇⢀⠜⠋⠀⠀⠀⠀⠀⠀⠁⠘⠃⠾⠋⣨⣔⣥⣤⡄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠯⢷⣶⣦⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣬⣤⣻⠶⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⠴⠒⢛⣛⠩⠉⠉⠉⠛⠒⢦⣄⠀⠀⠀⠀⣼⣀⣒⣋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⠛⣡⠶⠶⢦⠀⠀⠀⠀⣿⣿⣦⣀⣰⣏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⣽⠛⣛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠶⠄⠀⠀⡀⠠⢒⠤⠀⠐⠂⠀⠀⠀⠀⣷⢈⡇⠹⢻⡄
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣇⠀⠒⡧⠀⠓⠐⠁⠂⠀⠈⠁⠀⠀⠀⠀⠸⡌⠰⣡⡏
⢀⡀⠀⡎⠠⠄⠄⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠸⠞⢻⠃⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡶⣿
⢀⠹⡀⡇⠀⣠⠀⠐⣋⡔⠒⠶⢄⡀⠀⠀⠀⡜⠀⢸⣄⡰⣶⣬⣜⠩⠉⠀⡇⠀⠀⠀⠀⠀⣸⠁⣯⡀
⠈⠄⠡⣡⡀⠙⣆⡀⠛⠀⣰⠂⠀⣉⠀⠀⠀⢧⠠⡇⢾⠡⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⢃⠔⣵⠟⠉⢹⡆
⠀⠐⣄⠘⠓⠂⠀⠀⠁⠀⠘⡆⠀⣯⠀⢧⠀⠘⣆⠉⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠑⢱⠞⣩⡤⠀⠈⣿⠲⠖
⠀⠀⠀⠢⡀⠙⠄⡀⠉⠀⠀⠁⠀⣼⠀⡼⠀⠀⠈⢢⠸⡇⠀⠀⠀⡠⠈⠀⠀⣠⠎⢂⠄⠈⠀⠀⠀⠀⠰⠾⠿
⠀⠀⠀⠀⢧⠀⠀⠈⢦⠀⠀⠀⠀⠘⢦⠃⠀⠀⠀⠀⠑⣌⠐⠒⠈⠀⢀⣠⡞⡡⠂⠄⢒⡁
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⡀⠀⣠⡧⢄⡀⠀⠀⠀⠀⢘⣶⣤⣴⠚⣉⢂⣪⠔⠒⠚⠉
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡠⠚⠓⠒⠓⢌⠒⠃⠉⢩⡶⢚⠿⡠⣞⠻⠛⠄
⠀⠀⠀⡔⢿⠁⠀⠀⢀⠀⡌⠀⠀⠀⠀⠀⠀⠑⠦⠤⠗⠋⠁⠀⠀⠈
⠀⠀⢰⠀⠈⠀⠀⠈⠀⠾⠁

⠀⠀⠀⠀⠀⠀⢀⠤⠔⠢⢤⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⣤⢤⠀⡠⢠⣄⢀⣄⢀⣀⠀⢠⣤⡀⣠⠄⡤
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠁⠉⠉⠉⠉⠈⠁⠁⠈⠉⠀⠉⠉⠁
⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠒⠒⠊⢳
⠀⠀⠈⠓⠒⢷⠒⠂⠸⠤⠖⠉⠛⣄⢀⡮⣀⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠉⠓⢤⡀
⠀⠀⠀⢀⠎⠈⠙⠒⠒⠒⠒⠋⠁⢀⠀⠀⠀⠀⠀⠀⠘⢉⡆
⠀⠀⠀⡜⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠄⠀⠐⠠⠀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⢳⠤⣀⣈⡠⢄⣀⠈⣀⣤⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠈⡄⢀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠀⠈⠉⠁⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠠⠤⣌⠢⡀
⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠉⠉⠉⢨⠀⡠⡖⠁⠀⠀⠀⠀⠀⠈⡖⢄
⠀⠀⠀⡇⢠⠀⠀⡆⠀⠀⡇⠀⠀⢀⡀⢀⡠⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡌⠉⠭⠭⠭⠭⠍⠋⠥⠎
⠀⠀⢴⠃⠠⠀⠀⠀⠀⢀⣇⣀⣀⠀⠈⣉⣠⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡀⠀⠀⠉⠳⣄⣠⣄⡀⢸⠉⠙⢏⠙⠛⢡⡟⢦⡀⠀⣀⠄⢢⢧⠄⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⣤⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠘⡏⠉⠀⠰⠚⠂⠀⠀⢴⠋⠂⠄⡀⠀⠀⠐⠂⠤⠔⠒⣁⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠶⣼⣄⣀⠤⢞⡥⠒⡂⠉⠁⠙⠁⠀⠊⠓⠲⠦⣅⠀⠀⠁⠀⠀⠀⠈⠀⠈⠗⠀⣤⠀⠀⣸⡀⠀⠀⠀⠀⠀⢸⠗
⠇⠀⠀⠀⠀⠀⠈⠂⡤⠏⠡⡀⠈⠑⠨⠑⣒⠀⠀⠀⠀⠒⠒⠂⢁⠅⠀⠀⢠⣀⣀⣀⣠⠀⠰⡀⠀⠇⠀⡀⠩⣷⣦⣤⣤⣤⣶⡧
⡆⠀⠀⠀⠀⠀⠀⡔⢸⠁⠀⠘⠢⠄⡀⠀⠀⠰⢁⠀⠀⠀⢀⡠⠂
⠁⠀⠀⠀⠀⠀⠀⣗⠃⣀⠀⠀⠀⠀⠈⠐⠒⠚⡳⣶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡬⠤⠭⢭⡭⠄⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠙⢄⠀⢀⡾⠄⡀⢥
⠁⠀⠀⠀⠀⢀⠞⠁⠉⢦⠤⠉⣽⠂⠠⠐⠚⡦⡀
⠁⠀⠀⠀⠀⠘⡀⠀⠀⠘⢄⣀⠼⡄⠀⠉⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡳⠄⣀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠚⠁
⣶⡶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⢶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠁⠀⠂⠁⠀⡄⣀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠇⠀⠀⠀⠀⠠⠀⣀⡄⠀⢀⡇⢸
⠀⠀⠀⠐⠌⡀⠀⡂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠐⠀⠀⠀⢤⠈⡀⠁⢘⣋⠀⠋
⠀⠰⠂⠀⠄⢀⡰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉⠁⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⠃⠈⠓⡢⠭⢮⣄⡈⠉⠤⠈
⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡔⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣵⠀⠀⠁⠀⠀⣀⠀⠀⠐⠲⡀
⠀⠀⠀⠈⠠⣀⠀⠀⠢⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡇⠀⢀⡀⠀⠠⡁⠄⠀⠁
⠑⢄⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠠⠔⡀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⢢⡀⣌⣉⣠⠄⠂⢁⡤
⠀⠀⠉⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⠁⠀⠀⠀⠈⠢⡀⠀⠐⠀⠀⠈⠲⣌⡀⠀⠀⠐⠁
⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠢⢄
⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠈⠆⢰⣿⣦⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⣀⡀⣀⡀⠈⠛⢿⣿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠄⠀⠀⠀⠀⠀⠂
⠀⠀⣰⠋⣡⢦⣼⣌⣤⠀⠀⠀⠀⠀⠀⢀⠀⠈⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠄⠺⣆⡢⣨⡔⢢⡀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠄⠙⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠹⣅⠧⢏⢱⣁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢰⠁⠐⠈⠻⣔⠣⠤⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠈⠑⠚⠑⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠸⡀⠀⠀⠚⠉⢀⣰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⡠⠆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠂⠀⠀⠀⠀⠀⣀⠐⠈⠈⠀⣀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠚⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣓⣈⡀⠀⠬⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠀⠀⠀⠀⠐⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⡀⢀⡆⢀⠀⣀⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠧⠈⠃⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⡏⠀⠀⢀⣀⣤⠀⢀⡄⠉
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠢⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣴⣿⣿⠟⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠇⠀⠐⠀⠁⠠⠀⠀⠀⠀⠀⢀⡀⠄⠀⠠⠄⠛⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡈⠐⠒⠛⠀⠀⠘⠛⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠤⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⠒⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⣰⠋⠉⠉⠉⣗⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣧⣄⠀⢀⣀⡈⠲⣀⣤⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢘⡷⡆⠀⢠⣄⠁⠀⠋⠀⣹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⢸⠀⣄⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⢰⡬⢤⡤⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⣆⠓⠊⠀⠀⣠⠔⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠒⠉⠀⠀⠹⣷⣄⣀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢧⡀⠀⠀⢀⡏⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠓⠢⠞⠀⠀⠀⠀⠀⠘⢆
⣠⠶⠿⣽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠦⣤⣀⣤⠖⣫⡥⢭⣑⣶⠚⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠔⠋⠀⠀⠀⢯⠙⢷⡄⠀⢧⡀⠀⠀⠀⠀⠀⠀⣸⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠻⣦⡀⠱⣄⠀⠀⠀⠀⠀⡇⠀⠘⢾⣷⢄⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠻⡓⠾⢦⣄⣀⣀⠀⣷⣄⠀⠀⠻⣮⠳⡄⠀⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠈⠓⠒⢶⡙⠲⣝⢷⠈⠓⠦⣄⣹⡷⡈⠢⣼⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⡀⠀⠹⢤⣈⣻⡆⠀⢀⣀⣩⢃⣷⣄⣈⣳⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠛⠛⠛⢻⠿⠆⠀⠀⠉⡿⠯⢭⣉⣽⣟⣋⣉⣉⣉⣉⣉⣉⣉⣩⠭⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠒⢾⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠙⠲⢤⣄⡀⠀⠀⠉⠳⣶⣦⣤⣤⣤⡤⢤⣤⣤⡶⢶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠒⠤⢄⣉⠉⠉⠁⠀⠀⢀⣤⣤⣭⣭⣥⣤⡴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣤⡤⠶⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣼⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠉⠓⠲⢤⣉⡙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⣰⡄⣄⢠⡀⣼⡇⢸⡇⢢⣰⢠⢠⣠⠋⡿⡶⣤⣬⣙⡶⡦⣶⣀⣠⠂⣼⣦⣾⣾⢦⠀⠀⡀⠀⠀⢉⠧⡎⡦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠈⠀⠁⢹⠉⢹⡏⠉⠈⠈⠈⠈⠀⠁⠁⠋⠉⠉⠛⠧⢬⣉⠉⠛⠻⠇⢿⢹⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣦⣄⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠈⠀⠀⠈⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠠⠂⠀⠀⠀⢀⣀⡀⠈⠳⣦⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠤⠤⠀⠘⢁⠴⠶⠀⠀⠸⣇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠴⠶⠈⠋⠉⠀⠀⢀⡜⣧⡀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⣠⠎⠀⡈⠑⡀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡎⠓⢄⠠⠄⠊⡏⠀⠀⠀⠀⠈⠃⠀⡷⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠛⠀⠀⠀⠀⠠⠀⠐⠂⠳⠀⠐⠂⠖⠞⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠡⠀⠃⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⢈⠀⠐⢄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⡖⠀⠀⠀⠢⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⠃⠀⠀⠀⠀⠘⠤⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⣀⣀⣠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠡
⠀⡀⠔⠂⢉⣠⣴⡶⠄⡉⠁⠀⠀⠀⠈⠀⠁⠈⠉⢁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⢇⠘⠄⠈⠙⠛⠀⢨⠓⣶⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣙⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠁⠂⠤⢀⠺⠀⠃⠾⢃⣠⣼⣿⡏⠀⠠⠀⠀⠀⠀⠈⠉⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠰⠆⢤⣬⠉⢉⣈⣋⣀⡀⣀⣀⣀⣠⡤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠓⠀⠀⠀⠀⠀⡌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⣠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢺⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠅⠀⠀⠀⠀⠉⠉⢢⠀⠉⢰⠁⡠⠀⠈⢢⡀⠀⠀⡰⠁⡠⠆⠄⠀⡝⠌⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠐⠈⠆⠸⡠⠁⠀⣀⠤⠄⡤⢤
⠀⠀⠀⡀⠀⠀⠠⠄⠲⢥⡁⠀⠐⣄⠀⠁⠤⡀⠰⡀⠀⡅⢀⡀⢀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⡐⠀⠀⠀⠁⡜⠀⢠⣈⠁⠘⠗⠤⠤⠍⡏
⠀⠀⠀⢰⣐⠀⠀⠀⠀⢂⠽⠀⠀⠈⠢⢄⠀⠌⠢⠇⠀⠀⢎⣕⡲⠀⠀⠀⢀⠂⡀⡀⢸⠀⠀⡐⠀⠀⠀⣡⠊⡔⠀⠀⠈⠢⠀⡄⠀⠀⠀⡇
⠀⢠⠀⠀⠄⠀⠐⠈⠁⣠⠤⠤⡠⠠⠀⣄⠉⠐⠀⢠⣞⡃⢨⣊⠼⠀⠀⢄⡠⠃⠀⢱⠄⠈⢠⠠⠄⢀⠔⠁⠀⠸⠓⠤⠴⠄⠀⠁⠐⠒⠁⡀
⠀⠈⠃⠀⠨⠇⠀⠴⡃⠠⠀⠐⠡⢁⣂⡠⢕⡄⠀⠘⠋⠀⠀⢷⠇⠀⠀⠲⢇⠀⠀⢰⠦⣐⠈⠂⠐⠁⡐⡠⠀⠐⠦⠤⠀⠀⡀⠴⠈⡀⠀⠈
⠀⠀⡔⠲⡄⠀⡔⣀⡒⢒⣢⢁⣁⠼⠃⢊⡍⠀⣔⠒⠓⠼⢄⠘⠀⠀⠀⠀⢐⠀⡍⠀⠉⠀⠀⠀⠀⠀⠐⠁⢴⠄⠀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣷⠀⠘⠄⠀⠢⠄⠄⠤⠤⠴⠒⠚⠉⠀⢄⡇⠀⠀⠀⡇⠀⠌⢀⠁⢀⠼⠰⠁⠀⠀⡠⣶⠿⣿⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠚⠐⠆
⠀⠀⣇⠨⡁⢸⠀⠀⠀⢤⠤⢄⠀⠀⢀⣀⣤⠈⢧⠠⢄⡘⠁⠀⠈⠨⠆⠀⠀⠀⠂⠀⠈⠉⢻⡒⠛⠛⠛⠳⠀⠁⠀⠀⡍⠀⠈⠓⠒⠊
⠀⠀⠘⠦⠴⠊⢀⠄⠀⠈⠂⠤⠀⠤⠄⠔⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠑⠒⠁⠐⠠⢖⠒⠒⠁⠀⢹⠉⠀⠀⢀⠤⠄⠠⠄⡀
⠀⡠⠀⢠⠀⡰⠁⠙⠀⠘⡀⠀⠀⢀⢀⣄⢠⢤⢰⡿⠞⢱⠀⡠⠩⠐⠒⠐⠒⠪⠔⠁⠀⠠⠄⠀⠈⠀⠠⠀⣀⠒⠀⠐⠀⠰⠃⠀⢈⠤⢤⢃
⠀⠙⠣⠁⠠⠁⠀⠀⠀⠐⢀⢤⠀⠠⠀⠐⠚⠈⢉⠠⠒⡱⠘⠏⠙⡠⣲⠖⠁⠀⠀⠀⠄⠀⠴⠀⠀⣀⠀⠀⣁⠀⠀⠀⢠⠃⠀⡔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠈⠐⠂⠀⡈⠀⢀⣊⡭⡴⠦⠒⠋⣡⡀⠀⠀⠀⠀⡜⠀⠀⣠⠐⠇⠩⠠⠅⠩⠈⠣⡀⠑⣀⠽⠆⢀⡀
⠀⢀⠀⠂⠐⠙⢄⠀⠀⠀⠀⡲⠁⠤⠄⠀⠀⠊⠀⠈⠀⣠⡀⠀⠀⡺⠭⠃⣄⢀⠨⠊⣀⠀⠀⡀⠀⠄⠈⠉⠉⠀⠈⡀⠁⠀⠀⠀⡜⠀⠈
⠀⠘⠤⠀⠀⠈⢀⡄⠀⠀⠐⠚⡞⠠⠀⠀⣰⠶⠞⠛⠀⢛⡧⣤⡀⠉⢀⠔⠈⠀⠀⠀⠈⠀⠀⡆⠁⠀⠀⠀⠁⠈⠀⠈⡇⠀⠀⠠⢃⠐⢀⡁
⠀⢀⡀⠐⢊⠔⠃⠠⡀⠀⠂⠁⠉⠀⠀⠜⠁⠀⠀⠀⠐⠌⠈⢁⡀⠈⠀⢄⠆⠀⠀⠒⢀⠣⠈⠑⠀⠀⠐⠒⠒⠒⠊⡊⠝⢀⠀⠀⠀⠀⢀⠁
⠀⠰⠀⠉⠀⠘⠀⠠⢂⠄⣀⠐⠠⠀⠀⡀⠀⠀⠀⣀⣄⠀⠌⠀⠀⢂⠀⠀⠀⠀⠐⠀⢁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡮⡆⠀⡒⠒⠊
⠀⠀⠣⠬⠄⠂⠁⠀⢇⢸⣁⡐⠀⠢⠀⣁⡀⠀⠉⠉⠀⢌⠀⠀⠀⢸⠀⠘⠀⠀⠁⠊⡀⠁⠀⠁⠠⠐⢒⠂⠠⡎⠈⠂⢀⠈⠁⠀⠧
⠀⠀⠄⡠⡀⡠⢆⡀⠀⡆⢀⠤⠄⠊⢀⠇⠈⢁⠁⠠⠁⠀⣄⠀⠀⡾⠀⠰⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠂⠀⢉⢱⠤⣀⠤⠊⠀⣀⢀⠀⠆
⠀⠠⠂⠂⠃⠓⠀⠖⠀⢈⠥⠤⡀⠀⠢⠄⡶⡇⠀⢀⠀⠐⠈⠀⠀⡜⠀⠈⠀⢤⠀⠀⡰⠋⠁⠀⠀⠀⡔⠁⠀⠀⡴⢁⠀⠀⢀⠹⠗⠎⠈
⠀⠀⠀⠀⠰⠀⠄⠒⠀⠀⠐⠒⠊⠀⠀⠀⠀⠠⠀⠀⠑⠄⠠⠔⠚⠀⠀⠀⢄⡀⠠⡘⠄⠦⠄⠠⢭⠒⠤⣤⠤⢚⡀⠝⢀⠀⢈⠀⢀
⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠘⣠⠠⠁⠀⠁⠀⡠⠤⠴⢆⠀⠀⢄⠀⠠⠉⠈⠑⢊⠉⠐⠒⢒⡀⠉⢀⡀⠈⢁⡀⠀⠐⠀⠀⠁⠀⠀⠜⠔
⠀⢀⢀⠐⣀⢀⡀⠄⠀⢠⠁⡠⠤⠀⠁⠀⢎⣉⠆⠱⠀⠀⠚⠀⠀⠊⠀⢠⡀⠀⣀⠀⠀⠀⠐⣃⠟⢰⢁⠘⠐⢁⡑⠀⢀⣀⠄⠤⠤⢀⠄
⠀⠈⠚⢀⡀⠄⣀⠀⠀⠀⢨⠀⠀⡠⠤⢄⠈⠀⠀⠐⠒⠒⠂⠀⠐⠀⣤⠄⠀⠈⠉⠀⠠⡄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠨⠉⡀⠀⠀⠀⠈⡹
⠀⠀⡔⢽⢃⢴⠋⠂⢠⠦⠈⡠⠂⠀⠀⢨⠅⠀⡠⠂⢁⣈⡰⡄⠀⠀⠀⠠⠰⡆⠀⠀⢀⠠⠐⠀⠐⡴⢶⠖⡂⠀⠀⠀⠈⢢⠄⠀⠀⢀⠔⠁
⠀⠀⢯⠴⠐⠁⠀⡄⠀⠀⠈⡀⠀⣀⡠⢊⡀⢰⢀⠜⠁⠀⢄⠈⠂⠤⠤⠔⠊⠀⠀⠂⢁⠀⡀⠀⠔⠁⠀⠐⢄⠀⠀⠀⠠⠄⠁⠀⠀⠀⡠⡲
⠀⠀⠀⠁⠒⠒⠒⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠳⠶⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⣀⡮⠕⠀⠀⠀⠀⢀⣴⣁⣤⡂⠀⠀⠀⣧⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠻⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⢸⣄⠄⠀⠀⠉⣻⡉⠉⠀⠀⠀⠀⠀⣀⠤⠄⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣀⣀⡴⢦⡀
⠀⠀⡟⠀⠀⠀⠐⠁⡽⣄⠀⠀⢀⠴⢋⠀⠀⠀⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⠦⢤⡴⠋⠁⣀
⠀⠀⠳⡀⠀⠀⠀⠀⢀⣾⣦⣴⣧⡀⠀⠶⠂⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣠⢾⠆⠀⢉⣢⡴⣣⠷
⠀⠀⢀⣿⣷⣶⣶⣶⣿⣿⣿⡟⡛⠇⠀⠀⠀⠐⠘⣁⢶⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠠⡏⢰⠋⠀⡼⠉⠀⢀⡇
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠂⠀⠘⠣⡄⠭⠀⠸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠓⠈⠀⠀⠁⠀⠀⣸⠇
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣸⡄⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠭⠥⠬⠙⠳⠶⠦⠶⠮⠛⠿⠥⠤⠉⢹
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣧⠀⠈⠓⠒⠒⠊⢹⣥⠖⠓⠋⢹⠀⠈⠉⠛⠿⣿⣿⣿⣿⣶⣶⣒⣒⡒⠲⢶⠒⠒⠒⢚⡠⠛⠋⠉
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠇⠻⢤⣀⣀⢀⣠⠖⠻⣤⠤⢂⣠⠟⢦⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢰⣶⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠀⠀⠀⠀⠉⢹⠉⡙⢦⣸⠏⠉⢠⠒⠋⠀⠀⠀⢠⠀⠀⠀⠉⢿⣿⣿⠏⠙⠷⢶⣶⣾⡿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠙⠒⢒⡶⢶⡚⣆⠳⠈⣽⠀⠀⠀⠳⢄⠀⠀⠀⢈⣇⠀⠀⢱⠀⠙⡟⠀⠀⠀⠀⠀⠀⢀⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡏⢳⠀⠎⠻⣆⡸⣹⠀⠀⠀⢀⠜⠁⠀⠀⠈⢿⡇⠀⠀⠇⣸⠇⠀⠀⠀⠀⠀⠀⣸⣿⡇
⢹⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣠⠀⣸⠀⢾⠲⢤⣀⠉⢣⡏⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⠘⣿⣿⣿⣿⣿⠃⡰⠋⠀⠀⠀⣹⠋⠙⠀⠓⢤⠀⠈⠉⢻⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠈⠀⠀⠀⠀⠀⢠⣿⣿⡿
⠀⢹⣿⣿⣿⣇⡞⠁⡤⠖⠒⣾⠁⠀⠀⠑⠢⣨⠇⠀⠀⢸⡊⡠⠔⠒⠀⠀⠀⢴⡦⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⢻⣿⣿⡟⠀⠀⠀⢠⠞⠃⠉⠀⠀⠂⢄⡾⠀⠀⠀⠀⠻⡄⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣀⣀⠀⢀⣠⣾⣿⣿⠏
⠀⠀⠀⠻⣿⡁⠀⠀⠀⣾⠀⠀⠀⣀⠉⢲⠞⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣇⠀⠀⠀⢹⠀⠀⢺⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠾⠆⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢳⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠲⣦⣶⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠾⠇⠀⠀⠀⠁⠀⠀⢠⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣤⣤⣀⣀⠀⠀⠀⢸⠀⠀⣀⣠⣤⠶⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡀⠙⣦⡠⠄⠒⠒⠒⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢰⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁⣀⠰⡟⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢠⣼⠀⠀⠀⠀⠀⠙⠋⣀⠀⠉⠉⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠉⠲⠄⠒⠉⠀⠀⠀⠀⡄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡰⠋⠁⠐⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠤⡱⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠹⣦⡈⠋⠴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⣤⣤⣤⠤⠤⠐⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⢷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠠⠄⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠸⢡⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⠢⠄⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠂⠘⢆⠀⠀⠀⠀⠀⢀⡀⡤⢸⠇⠀⠂⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⣤⠠⠔⠒⠈⠁⠀⣸⢤⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡴⠁⠀⠀⢀⡠⠔⠋⠀⠀⠈⠉⠛⠲⠦⠴⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢟⡤⠤⠤⠤⠴⠀⠉⠳⢄⠀⠀⠀⠀⢀⡜⠛⠦⢤⡄⠉⠀⠀⢦⣤⣄
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⣠⠊⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠉⠑⠒⠒⠒⠀⠐⠒⠒⠢⣤⠔⠁⠈⠻⣦⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠾⠅⠴⠂⠀⠀⠀⠐⠀⠒⢾⣶⣦⣠⡄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠋⢉⣉⣉⡙⢛⣛⣛⡛⢛⣛⣋⡉⠉⠉⠉⠀⠉⠛⠛⣛⣛⣛⠛⣛⣛⣛⠁⣀⣦⣀⢰⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠿⠉⠉⠁⠘⢋⣉⡟⠸⣏⡉⠟⠀⠀⠀⠀⠀⠀⠸⣿⣩⣿⠺⣿⣭⣿⠺⣿⣭⣿⢿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠦⠤⠴⠦⠤⠬⣭⠤⢤⣤⢤⣤⠤⡤⢤⣤⣤⣤⣤⣬⣭⣥⣤⣬⣭⣥⣤⣈⣉⣅⣸⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡧⠀⠀⣴⣀⣀⣂⣆⣀⣀⣀⣠⣀⣀⣒⣲⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣿⠍⢹⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⡤⠤⠄⣠⡀⣀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠂⢰⠒⠒⠒⠒⡖⠲⠒⠒⠒⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠧⢤⡤⢤⣤⣤⡤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠙⠲⠤⢧⡀⠘⠒⡤⢄⡀⠠⢄⡀⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠛⠛⠋⠛⠓⠛⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠋⠁⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠷⠧⠦⠧⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠄⣀⣀⣀⠠⠄⢂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠂⠤⠤⠤⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢀⠉⠄⢀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠁⢀⠄⠠⠀⠐⡒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⠖⠁⠀⣤⡌⠣⡀⠀⠀⠀⠀⠈⠀⠐⣊⡅⠀⠀⠀⠐⢈⡑⠤⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡰⠐⠋⢁⠀⠀⠀⢀⣠⡄⠀⠀⢀⠀⠀⠀⢀⡀⠀⠑⣀⠀⠀⠀⠀⢀⠉⠈⠗⠁⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⢀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠁⠑⠀⠀⠛⠀⡠⠀⠀⠛⠁⠀⠠⠒⠀⠀⠀⠀⠐⡀
⠀⡐⠐⠤⡈⠒⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⣄⣀⣠⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⣠⣬⣆⣤⣤⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⣹⡜⣸⣆⣂⡼⠦⠀⠀⠀⠀⠀⠀⠀⢀⢁⡒⠀⢂⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⡐⠠⠠⠄⣀⣡⡄⠀⠒⠀⢀⡀⠀⠀⠀⠀⠀⢸⡀
⠂⠠⣤⣤⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠉⠀⠀⠈⠀⠀⠀⠒⠀⠀⣒⠠⡀⠀⠁⠈⠰⠀⡄⠂⢰⠀⠀⡀⠀⠀⠀⠀⣧⠇
⠀⠀⠈⠉⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠐⠉⠛⠀⠈⠁⠀⠚⠀⢶⠓⠋⠐⠀⠁⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠠⠄⠠⠈⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠡⢀⡀⠀⠀⠀⠀⠀⠀⢰⠈⣅⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⣉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⢊⣁⠀⠀⠀⠀⠀⠀⠰⡄⠠⠤⠦⠀⠋⠑⠉⠑⠉⠉⠁⠁⠀⠀⠀⡠⡆⠀⠀⠀⠀⠠⠀⠃
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠳⠤⠔⠃⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈

⣠⣄⠛⠀⠀⠐⠤⠀⠀⡀⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣖⠀⢰⠁
⠛⠉⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⢀⣚⡐⠀⠀⡱⠓⠀⠀⠀⠀⠀⠠⠀⠐⡀⠘⡆⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠁⡬⡉⠀⠀⠔⠀⠀⠀⡔⠀⠀⠀⠀⠐⠒⠆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣠⣄⠀⠀⠠⠡⡠⠤⠤⠬⠄⠀⠁⡂⠀⡀⠀⠀⠾⠃⢤⣀⠀⠀⠀⠣
⠒⠂⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠞⣄⠚⡙⣨⠀⠀⡀⠀⠀⠠⡀⠀⠛⠀⠀⠀⢀⠀⠁⠑⠃⠈⠛
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠅⠀⠀⠈⠛⠻⠯⠋⠀⢀⠄⠐⠲⠾⠆⠀⠀⠠⠀⢄⠠⣧⠀⠠⠃⠀⠀⢀⠀⠀⡀⡴⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⣔⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠄⢀⣄⡀⢤⡈⠃⠡⣀⠀⠀⠾⠀⠈⠈⠀⠀⠀⡀
⠀⠐⠀⠀⢁⣄⠀⠀⠄⠀⠀⠌⠀⠈⠫⡃⠀⢀⠂⠀⠀⠀⠀⡌⠁⠀⠂⠀⣤⣌⠈⠐⠄⠀⠀⠁⠀⠀⠙⠀⣀⠀⠀⠈⣄⠁
⠂⡰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⣤⣤⣦⠀⠁⠀⠀⠀⠀⠒⠀⢀⠀⠈⠁⠉⢫⡒⠀⠀⠄⣄⠀⠀⠐⠉⠀⠀⠈⢀⢤
⠊⠀⠀⠀⠀⠀⠐⡼⢠⡀⠀⠀⠀⠀⠀⠙⠻⠀⢠⠤⠈⠷⠀⠀⠀⠆⠀⠀⠀⠤⠄⡀⠀⢄⡀⠈⠑⠇⠀⢀⠀⠀⠐⠀⠀⡀
⠤⢀⠐⠋⠁⠀⢀⣰⡜⢡⠆⠀⠈⠀⠄⠃⠀⠊⠠⡑⠝⠀⠔⠉⡢⠄⠀⠠⠈⠀⡀⠃⠀⠾⠉⠀⠀⢀⠴⠉⠀⡀⠀⣠⣾⠏
⠀⠀⡀⠂⠄⠀⠀⠙⠜⠁⠀⠀⠂⠉⠀⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉
⢀⡀⠿⠀⠁⠠⣀⠀⠀⠀⣤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠀⢠⠃
⠿⠛⠀⠀⠀⠐⠂⠀⠌⠁⠀⠀⠀⠴⠤⠀⠀⠲⠤⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠈⠂
⠀⠀⠀⠀⠂⠀⠀⢀⡁⠀⠀⠀⠈⠉⢁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠴⠁⣐⠒⠁⠀⡡⠄⠀⠀⡠⠀⠀⠀⠀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⢀⣂⢀⣀⣁⣐⡀⠀⠃⠅⠀⠀⠀⠀⣴⠆⣁⠀⠀⠀⠀⢆
⠤⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡴⡀⠽⠻⢐⠀⠀⠀⠁⠀⢀⠀⠀⠶⠀⡀⠀⠁⠀⠂⠢⠆⠘⠿
⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡘⡂⠀⠀⠐⠿⢲⣗⠟⠀⠀⡁⠠⢤⣴⡅⠀⠀⢀⠀⡀⢈⣆⠀⢀⠆⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⢠⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⣀⠘⠆⠋⠀⠀⠀⣴⠀⠘⠐⠀⠁⠁⠀⠈
⠀⠠⠀⠀⠂⡀⠀⠀⡀⠀⠀⡐⠀⠐⢟⠇⠀⠀⠄⠀⠈⠀⠈⡑⠃⠀⠄⠀⣈⡙⢑⠨⡁⠀⠀⠋⠀⠀⠲⠀⠀⠀⠀⠒⡀⠃
⠄⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣄⠈⠂⠀⠀⠀⠀⠥⠀⠀⠀⠒⠋⠛⢖⡄⠀⠀⡀⣀⠀⠀⠠⠒⠉⠀⠐⠀⣉
⠔⠁⠀⠁⠀⠀⠠⣸⢀⠀⠀⠀⠙⠀⠉⠻⢿⠀⠀⣀⠐⣦⠀⠀⠀⡈⠀⠀⠀⣀⡈⠁⠀⡀⠐⠙⠢⡆⠀⠀⠀⠀⠠⠘⠈
⣀⠀⠠⠖⠂⠀⠀⢡⡸⢃⡄⠀⠐⠀⡀⠆⠀⠄⢀⠢⡲⠀⡠⠒⢄⡀⠀⢀⠐⠀⢈⠇⠀⣼⠛⠀⠀⠀⣠⠘⠁⠀⠀⢀⣴⡗
⠀⠈⠀⣄⡀⠀⠈⠻⡱⠊⠀⠀⠄⠒⠀⠀⠀⠢⠡⠁⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⠉⠳⠀⠈⠉⠉⠁⠈⣇⠀⠀⠀⠀⢠⡇⢸⠇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⢀⡏⠀⠀⠀⠀⢾⠁⠘⠀⣟
⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⡠⠀⣠⠤⠖⠒⠉⠀⠀⣿⣠⠞⠀⠀⠀⠀⠀⢀⣠⣼⡧⢤⣄⡀
⠀⠀⠀⠀⠀⠘⢦⣀⡀⢸⣇⠈⠁⠀⠀⠀⢀⣠⠀⢻⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣇⠀⠀⠀⣀⣀⣤⣤⣼⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠞⠋⠉⠀⠀⣀⡀⠀⠀⠀⠙⠶⢤⣤⣤⣤⣄⣀⣤⣤⣬⣭⡵⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠲⠆⠀⠀⠉⠀⢰⠀⢀⡄⠀⠀⠀⠙⣧⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⣴⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⡟⠲⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⠿⠃⠈⠉⠏⠁⠀⠀⠀⠀⠀⡼⠁⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠎⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠓⠒⠀⠀⣀⠔⠀⠀⠀⢠⠷⣦⣄⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣄⠀⠀⠀⠰⡎⠁⣀⠀⠀⠀⡇⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠘⣆⠀⠀⠀⠹⡄⠉⠀⠀⠀⠁⠀⡏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⣿⠀⠀⠀⠀⢱⡐⠗⠀⠀⢀⡤⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⢈⠟⠀⠠⢜⡧⠗⣨⠴⠚⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠎⢀⠀⠀⢈⡲⢻⠠⡤⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢗⡠⠜⠁⠸⢀⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠄⠄