Pickaxe Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⣝⡛⠻⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣍⠒⢭⣛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡈⠙⠮⣝⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠈⠛⢮⣻⣷⢶⣶⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣴⠟⡡⠀⠙⢷⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠡⠚⠁⠀⠀⢀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣦⡀⠀⢀⠔⣡⣾⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣴⠟⠈⢻⣦⣠⣾⣏⠀⠹⣮⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣣⠞⠁⣀⣴⠟⠉⠉⠀⠙⢷⣄⠈⢷⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠻⣧⡀⢳⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠱⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡁⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡌⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣫⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⡾⣫⠞⠁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣌⠁⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣼⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠾⠿⠿⠷⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣋⣁⣀⣀⡀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠿⠛⠛⠛⠛⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⢙⣿⡿⢿⣦⡀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⣴⡿⠋⠀⠀⠙⠿⠟⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⢰⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢠⣾⢿⣦⡀⣠⣾⠟⠁⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢀⣴⡟⠁⠀⠙⠿⠿⣷⡄⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⡿
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⠇
⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⠋
⠀⠀⣼⡟⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁
⠀⠀⢻⣧⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠙⠿⣶⣶⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣕⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠷⣄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⣯⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣮⡟⡅⠈⠳⡀
⠀⠀⠀⠀⠀⠀⡴⢧⣴⠊⠈⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⢶⣤⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⠒⠢⠭⢄⡩⣄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠱⢾⣏⣿⣌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢵⠋⠢⣀⠀⠀⠀⠀⢀⡴⠃⢀⡴⠚⠁⠀⠙⢷⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⢄⠀⣠⠎⠀⣠⠊⠀⠀⠀⠀⠀⠀⠳⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣴⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡴⠋⠈⠑⢦⣈⣗⣤⡀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠀⠀⠀⠀⠈⠣⣝⢮⡻⢶⣶⡿⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠉⠂⠙⢧⡀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠳⠄⠀⠙⠆⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣖⡛⠙⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣀⠈⠉⠛⠲⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠉⠛⠲⣤⣀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡉⠓⢤⡉⣿⠣⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡆⠁⠘⠷⣤⣼⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⠀⢐⣶⣾⢟⠦⣌⡙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠂⠀⢠⣿⣿⡿⢿⣥⣀⠉⠓⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣴⣿⣿⠟⠀⠀⠀⠉⠙⠳⢦⣄⡀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣬⣪⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢨⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣾⣷⣶⣿⣶⣶⣶⣾⠆⣠⣆⠸⣷⣾⣷⣶⣶⣶⣶⣿⠂⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠘⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⠃⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠘⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⠃⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠧⠸⠟⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠻⠇⠼⠿⠿⠿⠿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣦⡀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⢀⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆⢻⣿⣿⣿⣿⡟⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠈⣿⣿⣿⣿⠁⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠸⣿⣿⠇⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢿⡿⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠉⠉⠉⠉⠉⠉⠉⠉⣹⠟⠻⣏⠉⠉⠉⠉⠉⠉⠉⠉⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠸⣧⡀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠈⢷⡄⠀⠀⠀⠀⢀⣼⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣧⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⣼⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⢙⣧⣠⡟⢁⣀⣀⣀⣀⣀⣀⣀⣀⡀⢻⣆⣼⡋⡀⣀⣀⡀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢿⡆⠀⠀⠀⠀⢰⡿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⣿⠀⠀⠀⠀⣿⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⣇⠀⠀⣸⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⡄⢠⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡋⣻⣛⡛⣛⣙⣟⣛⣦⢙⣛⣻⡛⡋⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣯⣨⣯⣭⣭⣭⣭⣭⣿⣯⣭⣍⣩⣭⣍⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣾⣿⣿⡷⣦⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣻⣿⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣽⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⣟⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠀⠀⠀⣼⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣂⠀⠀⠀⠀⣰⣟⣽⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⢶⡄⠀⢀⣰⣶⣷⡻⣿⣿⢻⣿⣿⢣⣿⣶⣀⠉⠱⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣝⣾⡟⢠⣿⣿⣿⣿⣿⣿⡋⣷⣻⣿⣿⣿⣿⣿⣷⣀⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢹⣿⢹⣿⣷⣿⡟⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⢻⡇⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣻⣜⣿⣿⣿⣸⡇⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⢽⣿⣿⣿⡇⠘⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣛⣯⣭⡍⠉⣽⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⠷⠶⢾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢨⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⣿⣟⣻⣂⣀⣿⣿⣿⣿⡆⠀⠀⢀⣴⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⠉⠁⠉⠉⢩⠝⢿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⠋⠀⠀⠴⠒⠒⠒⢶⠂⣠⡶⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠢⡈⢻⣿⠀⠀⠀⠴⠞⠋⠑⠀⠰⡿⠛⠴⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⣇⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠳⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⡄⠀⠀⠀⠀⠰⠠⠤⠤⠤⠤⠂⣶⡂⢠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠙⠦⠀⠀⠀⠀⠀⠀⠀⣀⢀⡨⠋⠁⡝⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⢿⡷⢹⣆⠀⠀⠀⠀⠀⢀⠀⠀⣀⣼⠛⠿⠛⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⣾⣿⡿⠛⠋⣉⣁⠈⣠⣿⣿⣦⠀⠀⠀⢀⠈⠿⠿⡿⠃⢀⣿⣿⣿⣿⡿⡿⠷⣆
⠀⠀⠀⠀⠀⣠⣿⣿⣷⣆⠉⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⢴⣬⣥⣶⣦⣶⣿⣿⣿⣿⣿⣿⣶⣴⣌⢷⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠤⠐⠒⣦⠈⢿⠿⠟⠋⠙⠛⢻⣿⡿⣿⣿⣿⣿⣿⣧⢻⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡿⠟⠛⠛⢱⠈⠀⠀⠀⠈⠂⠰⠀⠒⡄⠐⠀⠘⣿⣿⣿⣭⣻⣿⣿⣿⣿⢻⡀
⠀⠀⡼⢹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧
⠀⢰⠃⣿⠏⣿⣿⣿⣿⣿⣿⢰⣿⡿⠟⠊⠀⠀⢀⢠⣵⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⡄
⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣿⢸⣿⣷⡄⢇⠀⠀⠀⢀⡘⣇⠀⠀⠄⠀⢸⣇⠀⢠⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡌⣿⣿⣿⣦⡀⢠⡀⠀⠁⣹⡄⣤⠀⠀⠀⣿⠀⢸⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡇⢻⣿⣿⣿⠋⠀⢠⡴⠊⠀⣠⢿⡔⢤⡄⢻⡀⢸⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⢿⡇⢸⣿⣿⣇⠀⠘⡟⠀⢀⣾⠟⠁⣠⠏⣡⣈⣁⣾⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣾⣿⣿⣿⣷⡄⠃⠀⡾⠃⠀⡴⠃⣰⣿⣿⣿⣿⣿⣿⣿⠿⠆⠘⠋⣿⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠋⢉⣧⣀⠀⠀⠀⡜⠀⣸⠇⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣄⡀⠀⠈⠃⠀⠟⠛⠿⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠆⠆⠀⠀⠀⠀⠀⠀⡄⡆⠰⢀⠆⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⢶⣖⣒⣭⢿⣽⣿⠭⢽⣛⡛⢧⣀⣠⣖⣒⡲⢶⣶⣶⣤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢁⡈⣎⢩⣙⠒⣫⣵⡯⢷⣘⣛⣒⣿⣇⡴⣿⡻⣝⣹⣒⣉⢘⣊⣻⣌⠤⠔⣺⣏⢢⡀⠀⠀⠀⠈⠡⠆
⠀⠀⠤⠈⠁⠀⠀⠀⣠⠖⢹⠀⢛⣃⢼⣾⣺⡩⢁⡲⢣⣠⠴⠚⠉⠣⣯⣢⣫⠷⠊⢙⠯⣀⠀⢂⠔⠉⣷⢤⣼⣨⢃⡜⣦⠀⠀⠀⠀⠉
⠀⠒⠄⠀⠀⠀⢠⠚⣁⠤⠚⠟⡽⣛⡟⠀⠙⢮⣊⠕⢛⡱⣄⠀⣀⡦⠼⡿⢥⣀⠀⠦⣱⠬⢳⠧⠤⢤⣥⣪⡹⡌⢹⠢⣕⣵⣄
⠐⠒⠀⠀⠀⣶⣓⠉⠀⣤⣀⢸⠮⡞⠀⢀⠵⠊⢣⠀⣾⡪⡼⢫⠀⠀⣸⡠⠓⡢⠛⠫⡀⠘⠘⣼⠃⡜⢀⠙⢶⡱⣼⠀⠠⣉⡻⢷⡄⠀⠀⠀⠠⠄
⠉⠉⠀⠀⠀⠘⢆⠉⠙⠒⠬⣀⣿⡤⠚⠁⣠⣤⠈⣆⣛⠞⡸⡃⢧⠀⠗⡽⠊⠀⣠⣕⡝⢦⠀⡏⡜⠀⢣⢺⢷⣙⣿⡤⠬⠤⠒⢒⡟⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⢙⡆⢿⡉⠒⠒⢢⣥⡥⢼⡧⡤⠮⠎⣘⣿⢎⣀⣀⣴⣊⣛⣕⣤⣱⡿⠄⠒⠚⢉⢅⣴⠃⠀⡀⠀⡰⠋⠀⠀⠀⠀⠒
⠈⠁⣀⠀⠀⠀⠀⠀⠘⢦⠀⢓⠘⡑⡄⠀⠀⠿⠿⢸⢇⠀⠀⠨⢡⢳⠀⠀⠀⠀⢀⠠⡀⢠⢞⠃⠀⣠⠰⣨⢪⠏⢀⠞⡠⠊⠀⠀⠀⠀⠠⡈⠁
⠀⠉⠀⡠⠀⠀⠀⠀⠀⠀⠑⢔⠂⢻⢚⢄⠀⢘⡃⢸⡸⡆⠀⠈⡸⠘⡄⠀⢀⢮⡲⢁⠔⡉⡆⣀⡖⢉⢞⢱⠊⡺⢁⠜⠁⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⡄⢪⢦⠀⡂⡈⠨⣸⡄⢀⠃⡇⣣⠀⠪⢃⡴⠁⡶⠰⠡⢉⡴⢁⣎⠏⢈⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⢡⢳⡀⡇⠈⣆⢧⡜⠀⡮⢸⠀⡠⠊⠀⠜⢀⣇⠴⠫⠸⢦⣼⠔⠁⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡅⢋⢧⡀⠐⢽⡇⠀⠙⡎⡏⠀⠀⡌⠎⡼⢋⣐⠒⣰⠞⠁⠀⠀⣄⢦⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠀⠀⠀⠀⠈⠢⡁⢳⣄⠠⢻⡀⠀⠏⡇⢀⢞⢈⡜⢡⡜⣫⠞⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠪⡜⢦⠑⣧⠀⢀⠇⠨⢣⠎⠀⡫⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣣⡸⡆⠈⡇⢡⢋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣽⡀⣷⣵⣯⣤⠤⣄⣤⣶⣶⣖⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢌⣭⣭⣭⣭⣽⣿⣯⣀⣭⣍⣑⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⣈⣭⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⡒⠦⢤⣴⣶⠒⠶⠶⠒⢶⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣚⣮⢢⡀⠀⠀⠀⠀⠀⢸⡏⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠈⠘⠁⠀⠀⠀⠀⠀⠀⠠⢀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⠀⠀⠀⠀⠀⠀⢀⡴⢾⣧⠀⠉⢷⣦⡀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀⡠⢉⣱⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⢹⣦⣠⡄⠀⠀⣀⠀⢈⠁⣿⣿⣆⠀⢸⣿⣷⠰⠶⣆⣲⣶⣤⣦⣦⣶⣾⠏⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣾⣯⣿⣿⣶⡾⠛⢸⣿⣿⣿⣿⣿⣷⣼⣿⣿⣷⣾⣿⠏⠈⠉⠉⠉⢉⣿⣠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⠻⣿⡿⠁⠀⠀⣿⣿⠇⣿⣿⣿⣿⣿⣿⠙⠻⠟⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣩⣿⣿⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣧⣽⡇⠀⠀⠀⣿⣿⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⣼⣿⣾⣿⣿⣧⣼⢻⣾⡄⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣿⣿⣆⠀⠀⠀⠀⡀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⣿⣼⣿⢻⣿⣷⠀⠀⢫⠉⣿⣿⣿⣿⣿⣿⣿⣿⡐⢒⣲⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⣿⣿⡿⢿⡹⣿⣿⣟⣿⣿⡇⡉⠿⠻⢿⠋⠉⣹⡿⠉⠉⣿⡇⣿⣿⡄⠀⠠⠀⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⠷⠠⠠⠀⠄⢨⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⣿⣟⢳⣎⢹⣿⣧⣿⣿⣿⣏⢠⣙⣳⣿⡇⠀⢸⣧⠀⠀⣿⣣⢸⡟⢹⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣾⣟⣿⢼⣿⣿⣿⣿⣧⠀⠈⠉⠀⢻⠀⡽⠿⠀⠀⣿⠉⠈⣿⠈⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠠⠤⠘⠀⢩
⠀⠀⠀⠉⠉⠁⠘⠿⡆⠙⢿⣿⣿⢻⣿⣺⠿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠘⠃⠁⡠⠊⣿⠀⠀⣼⠀⠀⠀⢀⠀⢩⠀⣿⣿⡟⢻⣿⣧⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⢈⡟⢿⣿⢿⣿⣿⣿⣿⠟⠀⠀⢀⠴⠃⢴⣴⠈⣀⣀⣘⣧⡀⣸⠀⠀⢀⣽⡿⠁⢸⣿⣿⡇⠘⣿⣿⡆⠆⠒
⠀⠀⠀⠀⠀⠀⠰⠛⢡⡆⢀⣿⡟⣿⣿⣾⣿⣿⣿⣿⠒⠒⠛⣧⡀⠴⠢⢿⠁⠉⠉⠉⣿⠋⣷⡴⠚⠛⠛⠁⠀⣼⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⣸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣆⣤⣤⠼⣾⣆⣎⣡⠤⠝⠛⢻⣯⠅⠒⠀⠀⠀⠀⠀⣠⣿⣿⡇⢀⡤⣿⣿⡗⣒⡢⠴⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠛⢿⣿⡿⣿⣿⣿⣼⣿⡿⠏⠉⠀⠀⠈⠋⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⣠⢿⣿⡏⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣚⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠒⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⢄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠄⠀⠆⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠈⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠈⠁⠆⠀⠀⠀⠀⢂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⢆⠀⠀⠐
⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣀⠄
⠀⠀⠛⠀⢦⡀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⢀⢈⠛
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⡶⠶⠶⠶⢶⢶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⡤⡤⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⢀⢠⣤⣤⣤⡀
⠀⠀⠀⢀⠔⠁⠸⠀⠀⡜⠁⠙⣄⠀⢸⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣿⣿⣫⣿⣯⣻⣿⣯⣿⣦⡀
⠀⠀⣰⣋⣀⣀⣀⣦⣌⣀⣀⣀⣈⣦⣇⣀⣀⣀⣳⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⠜⢵⣿⣿⣿⣷⠝⢼⣿⣿⣿⣦
⠀⠀⠹⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⡘⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⢿⣿⣿⣿⣿⢷⣿⣿⣿⣿⠋
⠀⠀⠀⠈⠢⡀⠀⠀⢣⠀⠀⠀⢠⠃⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡞⣿⣿⣿⡟⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠘⢆⠀⠈⡆⠀⠀⡎⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⢻⣿⣿⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠑⣄⢸⠀⢰⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⣿⣏⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣧⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠭⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠔⠒⠻⠿⣷⣶⣤⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⣯⠉⠉⠐⣒⣛⡿⠿⣿⠶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣵⠀⠀⠀⠀⠀⢭⣿⣿⣿⣮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⣀⡀⠀⠀⠀⠾⠟⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⠞⠀⢀⡠⠔⡿⠀⠀⠀⠀⠠⢂⣿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠊⠉⠀⢈⠕⠀⠀⠀⠲⠒⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣀⣀⡀⠀⠀⠀⣠⢴⣯⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⡛⠉⠙⠛⢦⠞⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⢙⠛⡳⠀⢀⡾⢆⠛⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢩⡟⠘⠧⠀⣸⣧⣿⣗⡫⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⢸⡶⢧⢻⣶⣿⣿⣿⣿⣂⠀⠀⢹⢹⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠀⠀⠙⢿⣿⣿⣿⡿⠒⠚⢷⠾⣷⣿⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣴⡞⣟⡂⠀⠈⢳⣬⡿⠁⠀⠀⠀⠀⠀⠉⠻⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢉⣯⣽⡽⢀⡴⢊⡾⠁⠀⣸⣷⣿⡒⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⢃⡵⠋⠀⣾⡇⠀⠀⠙⣻⣙⣭⡇⠀⠀⢀⡏⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣴⠋⠀⠀⠀⢹⣇⠁⠀⠀⠉⠏⠃⠀⠀⢠⡞⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣀⣽⢷⣍⣀⣀⣀⣀⡤⠾⢧⣤⣀⠀⠀⠀⠀⢰⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡼⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠙⠻⢶⣦⣤⢿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⠳⣄⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡼⠛⠶⠋


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣉⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡀⠰⠏⠁⠈⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⡤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠂⠠⣀⣄⡀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⠙⠣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠤⠆⠉⠀⢡⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⢠⡀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠑⣶⠀⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠸⡅⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⡨⣠⠤⢠⢃⠀⠑⢺⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠊⠁⠀⢄⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠁⢰⡇⠀⠃⡀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡆⠀⡔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠌⠀⠉⠑⠉⠁
⠀⠀⠀⠐⠲⡌⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠑⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⡠⡈⠀⠀⠀⢠⠈⠀⠯⠶⠀⠀⠀⠀⠀⠈⠒⠂⠙⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠂⠐⠁⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⡀
⠀⠈⠙⡦⠤⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠄⣀⡀⡀⠀⢀⡀⣤⠔⠀⠀⠀⠀⠀⠡⠀⠀⡠⠀⠀⠀⠀⠠⢢⠔⠉⠈⠀⣄⣀
⠀⠀⠈⡠⠰⣀⣴⡀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠐⡀⠀⠀⠀⠀⠀⠀⢃⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣔⠉⠀⠈⠱
⠀⠀⠀⠐⢂⠠⢋⣷⣂⡂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣶⣶⣶⣶⡞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⠔⠀⠁
⠀⠀⠀⣀⠀⠀⠈⠛⣁⡿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠒⠕⠓⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢉⣀⣀⡁⠀⠙⠂⠉⢀⠀⠀⡀⠀⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠘⠄⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠉⠢⠴⡀⡠⣁⠈⡀⠀⠀⠀⠢⠤⣀⢀
⠀⠀⠀⠀⠀⢠⣥⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠄⠀⠑⠀⠸⠤⠄⣀⠀⢀⢀⠚⠄⠼⠀⠙⣠⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⡴⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠳⣀⡄⠀⠠⠴⠴⣠⠤⠁⠘⢲⡄⡠⠀⠀⢰⠂⠁⠈⠱⢄
⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠔⠁⠈⠊⢐⡀⠤⠐⠳⠄⠋⣨⠖⠄⣀⣠⡝⠂⠀⠀⠀⣺⠀⠀⠐⠰⣲⡎⠀⠈⠉⡛⠳⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠉⠀⢻⡤⣀⠀⣠⡿⠀⠀⠀⢼⡆⡐⠁⠀⠀⣙⣿⠟⠁⠀⠑⡄⣁⣀⠀⠀⣄⣾⠑⠀⢒⠈⢣⡤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢀⣈⠃⢛⠃⠀⠈⡵⠀⠁⠃⠠⣻⣦⣀⡠⠋⠘⠳⠄⢀⡌⠊⠁⠀⢈⢠⠀⠽⣀⣀⡀⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠿⢢⣠⠦⠀⠈⠡⡤⣶⠖⠁⠁⢺⣑⡀⠀⠀⠄⠔⠛⠀⢀⠀⠀⡤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⡰⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠉⠉⠀⠤⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣐⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠸⣍⡇⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠸⠂⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⢀⠠⠀⠀⢠⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⢤⡴⡦⠴⠶⠒⡖⠓⠀⠘⠛⠉⠁⠀⠂⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢰⠀⠂⠀⠀⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠔⠀⣸⡄⠠⠆⠨⠀⠀⠀⠀⠀⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠀⢠⣔⠉⠻⠖⠀⠀⠀⠀⠀⠀⡄⡀⣠⡾⠁⠐⢠⠀⠀⠀⠀⠀⢸⡄⣀⡀⢀⢀⢀⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⠀⠚⣷⡄⣿⠁⠒⠂⣠⠀⠀⠀⠀⠀⠐⠘⠓⠓⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⡞⣧⠕⠋⠁⠀⠀⠀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣼⣿⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⣿⣷⡀⠈⡄⠁⠈⠀⡀

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠒⠠⢑⠢⣀⣀⡠⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠀⠀⡸⠁⠀⠑⠠⢆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⡀⠀⠀⠀⠀⡱⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠈⡖⢤⣀⣐⠁⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⠎⡐⠁⠀⠀⠉⠒⢄⡀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⢊⡜⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠉⠉⠉⠉⠉⢩⡟⠒⠦⠤⣀⡀⠀⠀⠑⢌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠈⠉⢳⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠤⣀⣀⡀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢈⠷⡀⠀⠀⠀⢥⣤⣭⠑⠂⠠⠤⢀⠄⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⢃⡬⠘⣦⡀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⣰⡗⠉⠀⠀⠘⠿⢦⠀⢹⡏⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠄⠀⠀⠑⢂⠀⠀⠀⠀⠑⠂⠃⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠓⡀⠀⠀⠀⠀⠀⠀⠀⠜⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠆
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠐⡀⠀⠀⠀⠀⠀⠌⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢰⢖⠄⠡⠒⢎⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡼⣀⠀⠀⠀⠀⠄⡃⠀⠀⠀⡂⠀⠀⠀⠀⢀⠴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢱
⠀⠀⠀⠀⠙⡦⣁⠒⠠⠄⣰⣕⠠⠤⢒⣔⠠⠤⠒⢊⠥⠞
⠀⠀⠀⠀⠀⠈⠢⢉⠒⠠⠀⠤⠤⠤⠤⠠⠀⠒⣉⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠠⠄⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢛⡽⠟⠉⠉⠉⣹⡿⠉⠉⠉⠉⠉⠉⢻⣏⠉⠉⠉⠛⢿⡙⢳⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠟⣽⡇⢄⠀⠀⠀⠀⣴⠟⠱⡄⠀⠀⠀⠀⣰⠃⠹⣧⡀⠀⠀⠀⢠⠸⣿⠙⢦⡀
⠀⠀⠀⣠⡴⠋⠀⣸⡟⠀⠘⡆⠀⢀⣾⠋⠀⠀⠹⡄⠀⠀⣰⠃⠀⠀⠘⢷⡄⠀⢠⠇⠀⢻⣧⠀⠙⢷⣄
⠀⣠⠞⠉⠀⠀⠀⠏⠀⠀⠀⢹⣤⡿⠁⠀⠀⠀⠀⠹⠄⠰⠃⠀⠀⠀⠀⠈⢻⣤⡟⠀⠀⠀⠹⠄⠀⠀⠈⠳⣄
⠻⣇⠲⣶⣶⣶⡆⢲⣶⣶⣶⣶⡿⣷⣶⣶⣶⣶⣶⣶⡆⢲⣶⣶⣶⣶⣶⣶⣶⢿⣷⣶⣶⣶⡶⢰⣶⣶⣶⠖⣸
⠀⠈⠳⣌⢿⣿⣷⡀⢻⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⡟⢀⣾⣿⡟⣡⠞⠁
⠀⠀⠀⠈⢷⡝⣿⣧⠀⢻⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⡟⠀⣼⡿⣫⡞⠁
⠀⠀⠀⠀⠀⠙⢮⣻⣧⠀⢻⣿⣿⡆⠈⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⠁⣸⣿⣿⡟⠀⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⢻⣿⣿⡀⠸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⠃⢠⣿⣿⡟⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⣿⣧⠀⢹⣿⣿⡇⠀⠀⢸⣿⣿⠏⠀⣾⣿⠟⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠹⣿⡆⠀⢿⣿⠁⠀⠀⠸⣿⡟⠀⣸⣿⢏⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⡀⠈⣿⠀⠀⠀⢀⡿⠀⢠⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠸⣇⠀⠀⣼⠃⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢻⡀⢠⡏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣾⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣀⠄⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⢧⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀⠞⠁⠀⣸
⠀⠀⠀⠀⡀⡀⠤⢤⠀⠀⠀⠀⡠⠊⠘⢳⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡞⠁⠀⠀⠈⢠⡀⠀⠀⠀⢀⠜⠒⠒⠺⡀⠀⢠⠃
⠀⡠⠒⠉⠀⠀⢻⠆⡆⠀⠀⣜⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠱⡆⣰⠇⣀⠤⢽⣦⡀⠀⠣⢄⣤⠴⠚⠤⠔⠧⢄⡀
⠀⢁⢳⠄⢀⠠⠐⠁⠁⠀⠈⠻⣙⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠎⠀⠀⠀⠙⠈⠋⠀⡀⠀⠻⢿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠸⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⣀⣀⡀⠴⠐⣇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠛⣠⠀⢰⣲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⣀⡄⠀⠀⢀⡤⢚⠥⠀⠀⠀⠐⠀⡿⡄⢂⠀⠀⠀⠀⠀⠀⠑⠒⠊⢸⠀⡌⠇⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⢈⠠⡆⠉⠉⠉⠠⣆⢠⠀⠀⣮⠞⡡⠔⣀⠔⠊⢩⠟⠀⢸⠘⡔⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢟⠁⠀⠀⠈⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠸⣈⣃⣀⣀⣀⠠⠍⠘⠀⠸⣥⠊⡠⠞⠁⠀⠀⠸⠾⣴⠋⢣⠐⡵⠀⠀⠀⠀⠀⠀⠀⡌⢸⢹⠀⠀⠀⢰⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⢀⣠⠂
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠋⠈⢆⠘⢆⠱⢃⠀⣀⡀⠀⠀⢠⠃⣼⡾⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⢆⠈⠀⠇⡬⠳⣀⡞⠀⣿⡇⠑⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠢⣤⠋⢢⣠⠎⠀⠀⡛⡷⡄⢰⠁⡠⡄⣀⡠⣶⣲⣒⠖⣂⣲⠂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡀⢠⠉⡆⠈⢣⡀⠀⠀⠉⠀⡱⠗⣢⣒⣹⠤⢷⠤⡽⠍⣃⠬⡄⢻⢢⠍⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⡎⠀⣣⠀⠀⠙⢦⡀⡠⢾⣤⢚⡯⢿⠁⡟⢛⣫⣙⡜⠉⠛⣹⠗⠕⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠲⠊⠃⠀⠀⢠⣁⡀⡿⣄⡤⠒⠙⢉⠗⡎⢹⡯⣥⡽⠦⡧⠈⠁⠸⢀⠤⠚⠁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡃⠀⠀⡠⠳⢊⡜⣰⣁⢁⣘⣐⣋⣧⠠⠔⠋⠀⠀⠀⢀⠟⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢸⡠⠊⢀⡶⢻⠊⣿⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⣤⡤⠊⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢄⡈⠈⣧⡄⠅⠂⠁⠀⢳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣠⠎
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⡏⣠⠞⢁⡔⡏⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠉⠐⢺⢻⠎⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠖
⠀⠀⠀⠀⠀⠔⠁⢀⣠⠔⢹⡁⠀⡌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠤⠄⠠⠖⢉⠈⠀⠀⠀⠀⠀⠀⢀⣼⣀⣀⠀⠀⠀⠀⠀⢠⢆⣀⡠⠃
⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠑⢄⡁⠀⠀⠀⢀⣀⡠⠤⠐⠚⠛⠑⠻⢄⠀⠀⠀⠀⠈⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡆⠔⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⢀⣀⣀⣀⣀⠤⠴⠲⣿⢆⠀⠀⢀⡠⠤⠚⠁⠉⠂⢶⡀⠀⠀⠀⠀⠀⠀⢀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⣀⡤⠤⠒⠉⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣀⣤⣞⠊⠉⢉⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠂⠈⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⢀⣀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠙⠋⠉⠐⠉⠉⠁⠂⠉⠉⠐⠂⠉⠉⠐⠉⠉⠀⠀⠍⠀⠈⠩⠚⠛⠓⠋⠒⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⠀⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠐⣄⣤⣀⡜⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⣏⠀⢈⡇⠀⣀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠗⠨⠍⢉⡛⣋⠡⠅⠚⢭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⡇⠀⠀⠙⠀⠀⠀⠘⠀⠀⠐⣗⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠁⠐⠀⢙⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡿⠉⠁⠁⠀⠈⡹⢩⠁⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⢞⠁⠘⠀⠀⠀⠠⠁⡄⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠋⠉⠉⠉⠃⠀⠙⠀⢄⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠊⠉⠑⢆⠀⣦⠄⠀⠀⠀⠀⠠⡄⠀⠀⠈⢆⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⣷⡀⢀⣠⠄⡸⢣⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢿⣧⡉⠀⢀⡁⢼⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⣤⣤⣍⣳⣴⠉⠀⢸⣯⣀⣄⣤⣤⣀⣠⣇⣠⣄⣠⠇⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠤⠼⠤⠾⠤⠤⠤⠤⠤⢤⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠧⠤⢴⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢽⠀⠀⠀⡠⠐⠂⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠡⡈⠑⠤⡀⢴⠁⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠭⠟⠦⠄⢿⡼⣿⣿⢵⣏⣉⣉⣉⣉⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⣤⡀⠙⡤⠐⢁⠆⠀⠀⠀⠀⠀⡠⠶⠏⠚⢿⡦⠵⠶⠶⠯⣾⡙⣉⣉⣙⣉⣷⣲⣛⣲⣿⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⠛⢄⡠⢎⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⢰⡿⠭⡭⠭⠭⣿⢿⣒⣛⣓⠫⣟⣲⣒⣾⣿⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠁⡔⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⠽⠭⠽⠯⣿⡿⣷⣺⣷⢬⣷⢶⣶⠯⣿⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠭⠭⠭⠭⣿⣯⠯⠿⠯⣽⡋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠶⢦⠩⠽⠉⣙⣍⣒⣋⣭⣅⣨⣭⣙⣒⣩⣋⠉⠭⠍⣴⠶⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⡜⠀⡲⠁⢀⣤⠂⢹⠑⢤⡀⠀⠘⠃⠄⢀⡠⠊⡏⠐⣤⡀⠈⢖⠀⢣⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠋⡄⢸⠀⣷⠅⠊⠁⡊⣣⠘⠀⢀⠟⠢⣘⣃⠔⠻⡀⠀⠃⡜⢱⠀⠑⠪⣾⠀⡇⢠⠙⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡡⠁⠀⡇⡇⠜⡟⢄⠀⠀⡇⠈⢦⣀⠎⣀⠔⡚⢓⠢⣄⠱⣀⡴⠁⢸⠀⠀⡠⢻⠣⠸⠸⠄⠈⢌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡤⣄⣾⣏⠠⢷⠊⢣⡀⠇⢀⡨⠿⡉⠀⠰⠁⠈⠆⠀⢉⠿⢅⡀⠘⢀⠜⠑⡾⠤⣑⣷⣠⢤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢯⡉⠙⠓⠒⡻⡶⠥⠤⠤⠬⠦⠧⢤⡤⠼⠴⠥⠤⠤⠬⢶⠿⡒⠚⠛⢉⡽⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣝⢦⡀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⢠⠋⠀⠀⢀⡴⣫⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⢦⠀⠀⠘⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠃⠀⢀⡰⣫⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣵⣄⠀⠉⢦⠀⠀⠀⢸⡇⠀⠀⠀⡴⠉⠀⣠⣮⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⢧⠀⠀⢸⡇⠀⠀⡼⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠳⡐⢸⡇⢂⠞⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣵⣼⣧⣮⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣾⣄⣀⡀⠀⠀⢀⣀⣀⣀⣠⣿⣧⠀⠀⠀⠀⠠⠾⣿⠧
⠀⠀⠀⠘⢿⣿⣿⣏⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣤⡄⠀⠀⣺⣿⠆
⠀⠀⠀⠀⠘⠟⠉⠙⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠛⠻⣿⣿⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠋⠉⠁⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣿⣦⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣶⣶⡤⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣿⠃⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠿⢿⣿⣿⣿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣧⡀
⠀⠹⢿⡏⠀⠀⠀⠨⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠶⣾⣿⣿⣿⡿⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡀⣠⣾⣿⣷⠀⠀⠀⠀⠀⢸⣿⠿⣿⣇⠀⠀⠰⣶⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠾⠿⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡿⠉⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠛⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⢸⣿⣿⣦⣠⣤⣤⡄⠀⠀⠀⣤⣤⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣦⣶⣶⣶⠆
⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀
⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢲⣶⣿⣤⡀
⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣠⡄⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⡀⠀⠸⠛⢿⠁
⠀⠀⠀⠀⡿⠋⠁⠀⠀⠀⠈⠀⢀⣴⡀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠘⠟⠃⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣿⣧⣀⡀⠀⠈⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣷⣶⡶⠀⠀⠼⣿⠇
⠀⠀⠀⠀⠰⣾⣿⡶⠄⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⠉⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡷⠆⠀⠀⠀⢀⣿⠟⠛⠻⠿⠀⠀⣠⣤⣿⣦⣀⡀
⠀⠀⠀⠀⢀⣰⣆⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⢈⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣠⢶⡒⠲⠖⠒⠲⠖⣂⡴⢤⡀⠀⠀⠀⠀⠀⢀⣴⡊⣡⠛⣄⢠⡄⠀⠀⠀⠀⠀⠀⣠⡶⣶⠶⠖⠒⠒⠒⢒⡶⣦⡀
⠀⠀⢸⠛⠆⠡⠀⠐⠒⠂⢀⠌⠀⣏⣇⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⢀⠀⡄⠀⠀⠀⠀⢀⣿⢆⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⢸⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⣟⡵⠛⠀⠀⠃⠀⠠⠧⢸⡀⠀⠀⠀⢰⡏⠀⠙⠦⣀⡀⣀⠤⠊⠁⠸⣿
⠀⠀⢸⣦⢠⠃⠀⠀⠀⠀⠀⠈⡀⢠⣿⠀⠀⠀⢸⣯⡀⠀⡰⠂⠀⠻⡀⣇⣸⡇⠀⠀⠀⢸⡅⠀⠀⠀⢸⣤⠼⠀⠀⠀⢀⡿
⠀⠀⢸⣽⣿⡖⢀⡠⡄⢀⠀⢤⣿⡏⡏⠀⠀⠀⠘⣿⣿⣿⣄⢲⣴⢢⣼⣿⣽⠃⠀⠀⠀⢸⣷⣤⠖⡠⠊⠀⠀⠢⡀⠤⣼⡇
⠀⠀⠈⠿⣿⣿⣯⣤⣆⣨⣽⢿⣿⡿⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⣷⣶⣤⣤⣀⣀⣤⣼⣶⣿⠇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣀⣀⠀⠀⠃⠖⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡄⠀⠠⠠⣄⣀
⠀⠀⠀⠀⠁⠀⡈⠀⠀⠈⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠅⠀⠀⠀⠐⠀⠀⡉⠀⠑⡄
⠀⠀⢠⠐⠈⡄⠀⠀⠀⠀⠈⢆⠀⠀⡄⠀⠀⠀⢠⡾⠒⢰⠓⠰⠖⠀⢲⠀⢲⠀⠀⠀⠀⢸⣇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠈⢷⣦⠴⡄⠀⠀⠀⣠⠽⣖⡿⠁⠀⠀⠀⡼⢹⠀⡄⡆⡘⢃⢠⠀⡆⡌⠇⠀⠀⠀⠸⣿⡷⢠⡀⠀⠀⠀⠀⣀⣁⣴⡟
⠀⠀⠀⠈⢿⣤⣼⣞⠋⣳⢷⣴⡿⠁⠀⠀⠀⠀⠧⠤⠿⠶⠽⠦⠼⠯⠤⠷⠥⠬⠀⠀⠀⠀⠹⣷⣾⣷⣾⣟⣿⣾⣿⣽⡿⠃
⠀⠀⠀⠀⠀⠈⠉⠛⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣠⠔⠀⠀⠀⠀⠤⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠚⠉⠟⠳⠀⠂
⠀⠀⢸⠡⣀⠀⡙⠀⢀⠀⠐⠞⠋⣽⡆⠀⠀⠀⠀⠐⠦⡐⠠⢀⡀⠀⢒⡼⠂⠀⠀⠀⠀⠀⣰⢹⠀⢀⣁⠤⠤⣁⠀⢡⡇
⠀⠀⢸⠀⠉⢠⠀⠀⠀⠀⠀⣷⣾⣿⡁⠀⠀⠀⡀⡬⠁⠨⠶⣘⠁⡶⠋⠠⠀⠂⠀⠀⠀⢠⣁⡭⢷⡟⠀⠀⠀⠈⣷⠞⣴⣄
⠀⠀⢸⢄⢀⣾⠀⠀⠀⠀⠀⢽⠟⢘⣷⠀⠀⠀⠛⡒⡲⡟⢲⣾⣿⡒⢾⢷⣒⣾⠀⠀⠀⢸⣿⣅⣸⡄⠀⠀⠀⠀⣾⢀⣨⡿
⠀⠀⢸⣼⠟⢻⣶⣤⢤⣤⣴⠿⣷⣅⡛⠀⠀⠀⠠⣏⢽⣿⣤⣇⣿⣽⣿⡚⣿⡏⠀⠀⠀⠈⣿⣿⡟⢳⣤⣀⣠⣼⠛⢿⣏⠃
⠀⠀⠈⠿⣶⣾⣯⡀⠀⣈⡽⣷⣼⡿⠃⠀⠀⠀⠙⢷⣶⡏⡍⣷⡟⣯⣿⣿⠿⠀⠀⠀⠀⠀⠘⢿⡾⣿⣏⠀⣽⣷⣶⡾⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠋⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⠿⠿⠋

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠚⢛⠛⠛⠛⢃⡀⢀⠀⢂⡂⠒⠛⠓⠆⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠛⠗⠆⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⣸⢀
⠌⠀⠀⠐⠀⠀⠈⠂⠀⠀⠠⣤⢀⡄⠈⠀⠀⢀⣉⠠⡤⠅⠦⢤⢴⡅⡈⣞⠛⣣⣔⡐⢀⡛⢁⡋⠘⠀⠂⠋⠛⠠⠞⠠⠁⠋⠀⢸⣶⠂⢰⡿⠈
⠇⠀⠄⠠⠨⠄⢄⣀⡀⢀⡙⠈⠋⢉⡉⢈⣂⣀⣂⠐⠒⠀⠆⠒⠐⠀⠶⠂⠴⡀⠠⠁⣤⠄⠈⢁⣁⠁⠋⠐⠀⠒⠖⢲⣴⠀⠀⢸⠉⠀⣿⠃⠀⠀⢀
⠀⠰⠀⠷⠂⠛⠙⠳⠂⠒⠖⠂⠐⠢⠨⡄⠠⠁⠬⠄⡁⣋⠁⣀⢘⠀⠂⠐⠰⠤⠄⢀⠀⢠⡄⣈⠁⢈⡚⠀⠘⠁⠞⡔⠈⣧⠀⠀⠀⣘⣿⠀⠀⢰⠇
⠄⠰⠀⠏⠀⠖⠚⠋⠙⠁⠉⠃⠉⠃⠘⠉⠂⠐⠂⠶⠀⠆⠆⡤⢠⢈⢉⣄⢂⣐⣂⠆⠤⠬⠀⡃⣘⢘⣹⡀⠉⢀⡤⢘⡇⠀⠀⠀⠀⣿⠏⠀⢀⡟
⠀⠆⠰⠟⠀⠞⠘⠃⠀⠂⠞⠉⠙⠇⠀⠸⠃⠻⠆⠶⠚⠂⠰⠖⠰⠆⠬⢩⡀⣀⠈⠂⠘⠃⠐⠀⠯⠨⠝⠛⢻⣅⠁⠾⠀⠀⡠⠂⣸⠏⠀⠀⣼⠁
⠀⢰⡴⢶⡀⢲⠀⠸⠀⠺⠀⠐⣿⠧⠐⠀⡆⣰⡆⡰⠂⠀⡖⢰⠆⢴⠆⢠⢀⠁⢀⠙⠀⠂⠣⠂⠆⣠⣄⠘⠛⠋⠀⠀⢀⡾⠁⠀⡟⠀⠀⠀⣽
⠁⠀⣁⠀⡁⡀⡄⢠⣁⠀⢀⠀⣤⠀⢀⣀⠀⢀⡁⠀⡀⠀⢁⠀⠀⠈⠀⡁⠁⠀⠋⠘⠜⠑⠛⠂⠀⠀⠀⠀⠀⠀⣠⣴⣾⡁⠀⣰⠇⠀⠀⠀⣧⢰
⣤⠀⠹⠆⠁⠀⠣⠀⠘⠀⠛⠀⠉⠀⠀⠙⠀⠸⠁⠀⠿⠀⠏⠰⠀⠀⠘⠃⡇⠀⡾⠁⡀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠚⠻⠟⠻⠶⠿⣤⣀⣈⣘⡇
⠀⠀⠀⢠⠄⠀⠀⠀⠐⠀⣠⠀⢰⡄⠀⢠⢤⣠⡄⠀⣤⡄⣠⠀⢀⣀⠀⠀⢀⡀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠤⠀⠀⡀⠉⠓⠒⠶
⡶⠈⢀⠰⡆⠀⡘⠈⠇⠀⠸⠇⠀⠁⠀⠛⠀⠀⠀⠰⠇⠁⠋⠀⠈⠁⠀⠀⡞⠀⡿⠀⢀⡴⠀⠀⠀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠛⠓⠀⠀⠀⠀⠒⠂⠀⠀⠰⠶⠦⠄⠀⠀⠀⠀⣰⠃⠀⡼⠁⠀⠀⠀⣀⣇⠀⠀⣤⠀⠀⠀⠀⠀⠢
⠀⠀⠀⡀⢠⡀⠀⣄⠀⠀⣠⠄⠀⣄⠀⠀⢠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⢰⠇⠀⠀⠀⡐⠏⠅⠀⡀⠁⠀⠀⠀⠀⠀⠙⠃
⠘⠇⠀⢀⠀⠁⠁⣬⣄⣀⠀⠴⣦⠀⠀⠀⠀⢀⣈⣤⡁⠀⠙⢳⡄⠀⠀⠀⠠⢀⣼⠋⠀⡼⠀⠀⢵⠰⠂⡀⣀⠀⠀⠀⠀⠶
⡃⠐⠻⠿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⣈⠀⠿⠴⠄⢀⠈⠁⣠⡼⠃⠀⠀⡀⠀⠂⠀⠈
⠷⠀⠀⠀⠠⣶⠶⣾⣦⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠈⢉⠶⢖⠒⠀⠀⠀⠀⠩⣦⠀⢠⡈⠁⠀⠀⠀⠀⢤
⣤⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⡀⣄⠀⠀⠉⠋⠱⠄⠠⠄⠸⣷⡙⠂⠈⠰⠆⠉⠀⠃⠀⠀⠒⠈⠁
⠀⠘⠓⠀⠀⠀⠀⠀⠽⠀⠀⠈⠠⠀⠈⠓⠀⢀⡀⠤⠄⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⢀⠀⢀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⢀⠄⠀⡀⠈⠀⠠⠀⠁⢁⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣭⠀⠀⠀⠀⠀⠢⣤⣥⡤⠂
⠀⠉⠠⠀⠀⠀⠀⠀⠁⠀⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠈⣻⣿⣾⠟⠁⢠⡀⠀⠂⠐⠆
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⣤⢿⡤⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠚⠀⠠⠟⠋⠛⢇⠀⠙⠛⠀⠠
⠀⠀⠈⠀⣄⠀⠀⠁⠀⣣⢬⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠞⠙⠇⠀⠀⠀⠀⠀⣀⣀⣠⠃⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠠⣤⠞⠘⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠉⠲⡔⠀⠀⣠⠊⠀⠀⠴⠆⢠⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⢨⣃⣤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠈⠀⠀⢸⣥⠖⠦⣸⡀⠀⠀⣤⣤⣾⣧⣤⡤
⠀⠀⢈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⢇⠀⠀⠐⠐⠀⠐⠀⠀⠀⠈⠀⠀⠀⠈⠡⠀⠀⠀⣹⣿⣿⡏
⠀⠀⠈⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⣤⣾⣿⣏⣤⣤⣄⡄⠀⠀⢶⣶⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠋⠁⠈⠓⠀⠀⠈⣇
⠀⠀⠀⠐⠀⢀⡾⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠠⣄⠀⠋⠀⠐⠦⡤⠀⠀⠀⠀⠈⠛⠻⣦⣯⣤⠔⠂
⠀⠀⠲⢶⠶⢋⡴⠟⣻⣶⣦⠶⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⢸⣿⡿⠿⣿⣷⠀⠀⢀⣀⣼⣧⣀⡀⠈⠁⠀⠀⢠⡀⠀⠀⢤⣦⡤⠀⢀⡿⠁⢷⡀
⠀⠀⡀⠈⢶⡿⢁⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠛⠁⠀⠀⠈⠙⠂⠀⠀⢹⣿⢿⡏⠀⠀⠖⠉⠀⠐⠇⠀⠀⠘⠉⠃⠀⠈⠀⠀⠀⠉
⠀⠘⠋⠀⢨⢶⠿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠂⢀⣀⡰⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⡆⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠂
⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠠⣤⠤⠶⠞⢀⠈⠳⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠸⠛⠉⠛⠇⠠⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⢀⡄
⠀⠲⣶⣶⣿⣿⣷⣶⠖⠀⠀⠄⠀⠈⠳⡄⠘⣿⣿⠂⡴⠊⠀⠀⣤⠀⠀⠰⣶⣶⡿⠧⢀⡄⠀⠀⠀⣀⣴⣆⣀⠀⠀⠁⠀⠀⠀⠀⣀⡤⠞⠙⠤⢀⡀
⠀⠀⠈⣿⣿⣿⣿⠁⠀⠂⠀⠀⠐⠂⠀⡇⠀⣁⣉⠀⢧⠀⠐⣾⣿⡶⠂⠀⠈⣹⣮⣶⡏⠀⡀⠀⠀⢙⣿⣿⡁⠀⠀⠀⠀⠀⠐⠀⠈⢲⠀⠀⢰⠋
⠀⠀⠸⠛⠁⠈⠛⠇⠀⠀⠂⠀⠃⠀⠸⠗⠉⠀⠈⠙⠻⠀⠀⠋⠉⠓⠀⠀⠀⠉⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠟⠊⠙⠺⠄

⠀⣀⡜⣆⣀⠀⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⢠⡆
⠙⣤⠁⠡⡜⠁⠀⠀⠈⠳⠀⠀⣩⠋⠀⠀⠀⠉⢛⡽⡻⠋⠀⠀⠀⠀⢩⠰⠆⠅⠁⠀⠀⠀⠑⠀⠀⡈⠉⠀⠀⠀⠘⢻⡭⠶⠉⠁⠀⠀⠈⠻⡭⠀⠈
⠀⠷⠊⠑⠇⠀⠀⠀⠀⠸⠊⠁⠺⠀⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠀⠀⠀⠀⠀⠛⠁⠙⠂⠀⠀⠀⠀⠘⠃⠈⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠠⢢
⠀⢖⢣⢗⠆⠀⠀⠀⠀⠛⣟⠙⡴⠂⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⠘⣭⠁⠈⣭⠃⠀⠀⠀⠒⠆⠉⠲⠂⠀⠀⠀⠐⠖⠈⠐⠛⠂⠀⠀⠘⢭⠁⠀⢩
⠀⠘⠁⠑⠀⠀⠀⠀⠀⠸⠃⠛⠆⠀⠀⠀⠀⠀⠶⠀⠸⠀⠀⠀⠀⠀⠻⠖⠲⠟⠀⠀⠀⠀⠀⠟⠈⠳⠀⠀⠀⠀⠀⠴⠃⠸⠇⠀⠀⠀⠀⠠⠕⠒⠭

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⢖⣚⣓⠖⠀⠀⠀⠀⢶⣾⣿⣶⠆⠀⠀⠀⢈⠉⠀⠈⡡⠀⠀⠀⠠⣄⠁⠀⠒⠂⠀⠀⠀⠠⣤⠻⡤⠀⠀⠀⠀⠰⣖⠋⢓⡶⠀⠀⠀⠰⢦⠈⠀⠒
⠀⠘⠛⠛⠀⠀⠀⠀⠀⠰⠿⠻⠧⠀⠀⠀⠀⠀⠡⠤⠄⠃⠀⠀⠀⠀⢀⠤⠀⢣⠀⠀⠀⠀⠀⠛⠛⢃⠀⠀⠀⠀⠀⠺⠖⠾⠆⠀⠀⠀⠀⢠⠔⠀⢷

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣄⠊⠂⣤⠄⠀⠀⠠⡆⠀⠈⠀⡦⠀⠀⠀⢤⠐⠁⠓⣠⠀⠀⠀⢰⣟⠃⠘⢻⡆⠀⠀⠀⢤⡀⠃⢤⠄⠀⠀⠀⠤⠀⠀⣀⠠⠄⠀⠀⠠⣤⠘⠑⢤
⠀⣸⠴⢮⡅⠀⠀⠀⠀⢰⡀⠀⣀⠀⠀⠀⠀⠀⣇⠤⣘⡅⠀⠀⠀⠘⢿⣤⣤⡿⠃⠀⠀⠀⠀⡤⠀⢦⠀⠀⠀⠀⠀⡁⢲⣿⡗⠀⠀⠀⠀⢨⡤⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⣀⡀⡀⠀⠀⠀⠀⣀⡠⠧⣀⡀⠀⠀⠀⣀⠴⠋⠢⢀⠀⠀⠀⢀⣀⣰⣀⠀⠀⠀⠀⢀⡠⠞⠀⠳⢆⠀⠀⠀⣀⠠⠇⠤⢤⠀⠀⠀⠀⠚⠁⠁⠙
⠀⠠⠛⢏⠀⠀⠀⠀⠀⠈⡧⢠⡍⠀⠀⠀⠀⠀⢆⣀⣰⠃⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⢹⠀⣀⠐⡏⠀⠀⠀⠈⠓⣠⠐⡆⠀⠀⠀⠘⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉

⣀⠤⠎⠣⠤⡀⠀⠀⠀⣀⣰⢧⣀⡀⠀⠀⠀⢀⣀⣾⣄⣀⠀⠀⠀⠀⠤⠎⠱⠤⠀⠀⠀⠀⣀⠀⡗⢀⡀⠀⠀⠀⣀⠠⠏⠡⢀⡀⠀⠀⠀⡀⢠⢇⣀
⠘⡆⠀⠀⡖⠁⠀⠀⠀⠙⣆⡀⣞⠁⠀⠀⠀⠈⣿⣥⣿⠋⠀⠀⠀⠈⡢⠀⠀⢔⠁⠀⠀⠀⠉⣃⠀⣍⠁⠀⠀⠀⠉⣷⢀⡀⡞⠁⠀⠀⠀⠙⢊⡺⡍
⠀⠓⠉⠑⠂⠀⠀⠀⠀⠘⠉⠈⠉⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠀⠙⠋⠉⠊⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⠀⠛⠉⠙⠃⠀⠀⠀⠀⠘⠉⠀⠉

⠀⠀⡀⣀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡰⢳⣀
⠀⠨⠀⠈⡄⠀⠀⠀⢠⠀⣻⢿⠃⡠⠀⠀⠀⠑⠄⠀⠀⠌⠀⠀⠀⠈⢫⠀⢈⡝⠁⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠈⢣⠰⠷⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠺⢦⣄⣀⡆⠀⠀⠀⠀⠀⠀⠠⠂⡀⠔⠀⠀⢀⡤⣴⣞⡷
⠀⠀⠀⠀⠀⠀⢀⠤⠢⠈⠁⠀⢰⣮⣛⠒⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠠⠀⠛⡉⠁⠀⠰⣯⣯⣷⡆
⠀⠀⠀⠀⠀⠘⠔⠀⠀⢰⠀⠀⠛⢻⣿⠆⠀⠀⠀⠀⠀⠀⢀⠈⢠⠀⠂⠀⡤⠀⠃⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠁⠀⠐⠂⡨⠋⠀⠀⠀⠀⠀⠀⠀⠞⠀⣶⣿⣇⡎⠀⣀⠀⢀⣰⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠧⠤⠤⣄⠀⢀⣤⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠸⣿⣿⡇⠀⠹⢿⡿⠏⠀⢀⠕
⠀⠀⠀⠀⠀⠆⠉⠆⢠⢧⠾⢛⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⢀⣦⣿⣿⡁⠈⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⡇⢀⣠⠬⠿⣿⠏⢴⣸⣷⣶⣶⡆
⠀⠀⢀⠖⢠⣶⠀⠙⣛⡿⠁⠐⡶⣿⣿⣉⠁⠀⠀⠀⠀⠀⣸⡇⠁⠀⠀⠀⠈⠀⠀⢹⣿⣿⢿⣿⣦⡀
⠀⠀⢸⠀⠘⠛⠁⢠⡏⠀⣴⣶⡀⠈⢋⠉⠀⠀⠀⠀⠀⠀⠉⠅⠐⢲⠀⡀⠔⠚⠛⠦⢻⣿⡄⠻⠻⠁
⠀⠀⠈⢑⠖⠀⠀⠸⣆⠀⠘⠚⠁⢀⠌⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠛⢇⣄⣀
⠀⠢⡄⠁⠀⢀⡴⠚⠉⠓⠀⠀⠐⠳⢤⡀⠀⡑⠄⠀⠀⠀⠀⠀⠈⠩⠤⠐⣇⠀⢀⡠⢠⣔⣫⣶⡁
⠀⠀⠰⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠀⠀⠀⠀⠒⠃⠀⠀⠢⠀⠈⠉⠁⠀⠺⠼⠛⠋
⠀⠀⠀⡀⠀⢀⠒⠐⠀⠀⡀⠀⠀⠀⠀⠀⢠⣂⣐⣖⠶⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠈⠳⠆⣀⣀⠠⠖⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣵⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⢠⠉⠠⠀⢈⡀⠀⠀⠀⠀⣤⠞⠁⢀⣤⣄⠀⠈⠑⢤⡀⠀⠀⠀⠂⠀⠀⠀⠀⠎⠀⠅
⠀⠀⡀⢈⡦⠈⠃⠁⠀⠀⠀⠀⠀⣾⡋⠀⠀⠛⢳⣳⡶⠀⠀⠀⠗⡄⠀⠀⠀⠰⣆⠀⡂
⠀⠀⢧⡘⠃⢀⣠⢀⠠⣀⠀⠀⠀⢿⣶⡢⠀⠀⠉⠃⠁⡀⠀⠀⡠⠃⠀⠈⠆⠂⣁⡀⠑⠠⡀⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠉⠛⠛⠶⠶⠚⠉⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⣀⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠉⠈⠀⠈⠡⡀⠈⠈⠨⠈⠉⠩⠡⠀⠀⠀⠀⠂⠀⠀⡠⠀⣠⣀⠀⡀⠀⢠⠄⡍⠉⢉⠩⢤⠀⣠⢠⢠⠄⢠⣆⡀⢠⡇⠆
⠅⠀⠀⠀⡀⡀⠀⠀⠀⠈⠶⠃⠄⠤⠄⠀⠉⡯⢀⠉⡋⡉⢀⡙⡐⠚⠚⢀⠂⠐⠆⠆⠠⠄⠄⡈⡥⣄⡀⠀⢸⠟⠀⣿⠁
⠁⠠⢠⡤⠱⠘⠯⠠⠭⠤⠠⢈⢃⠈⠙⣙⡂⠒⠖⠂⠀⠄⠤⠠⢡⢀⠁⡈⢁⡀⠘⠃⠢⠂⠰⠂⡤⡈⢣⠀⠈⠀⢸⡏⠀⠀⡔
⠀⠶⠰⠂⠐⠔⠃⠒⠀⠒⠐⠂⠒⠒⠀⠆⠤⠁⠍⠬⠅⡍⠀⣀⢀⣀⠤⠡⠌⠁⠃⡊⢛⡇⠘⢀⡄⢰⠊⠀⠀⠀⣿⠃⠀⣼⠁
⠐⠄⠾⠃⠘⠈⠀⠀⠀⠉⠙⠃⠀⠛⠈⠃⠐⠚⠀⠲⠂⠆⠠⠩⢤⡄⢙⠀⠃⠐⠐⠇⠍⠛⣛⣏⠁⠏⠀⡀⠀⢸⠃⠀⢠⡇
⡀⢰⠚⠆⠘⠀⠛⡀⠃⠀⠻⠓⠈⠰⠤⠿⠰⠃⠀⠇⠗⠰⠖⠠⡠⢀⡄⡃⡃⡓⠐⠠⠾⠄⠉⠁⠀⠀⣼⠁⠀⡟⠀⠀⢸⠁
⠀⠀⣦⢠⠀⡆⠲⣦⢀⡆⠴⠀⠠⡶⠀⡆⠀⣆⢀⡄⡀⠀⠀⠄⡀⠀⣨⠉⠁⠉⠀⠀⠠⠀⡀⣀⣲⣿⣧⣄⣼⠃⠀⠀⣸
⠋⠀⠉⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⠀⠁⠀⡉⡈⠀⠁⠀⠀⠀⠃⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠉⠉⠑⠒⠲⠾⣀⣀
⡄⠀⠀⣅⠀⠠⠰⠄⠀⡧⠀⠇⠀⠞⠉⠋⠀⡏⠃⠇⠀⠛⠀⠂⡼⢠⡇⠀⣠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠
⠁⠀⠀⠈⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠤⠀⠀⠠⢤⠄⠀⠀⠀⠁⡼⠃⢠⠃⠀⠀⢀⣹⠀⠀⣠⠀⠀⠀⠀⠠
⠀⠀⢀⠀⡄⠄⡄⠀⠀⠤⠀⢤⠀⠀⠠⠀⡀⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⡟⠀⠀⠀⡘⠉⠀⠀⠁⠀⠀⠀⠀⠉⠃
⠈⠀⣀⠀⠈⠀⠼⢤⠀⠐⠶⠀⠀⠀⠀⠤⢤⡄⠀⠉⠳⢀⡀⠀⠐⣠⠟⠀⡰⠁⠀⠖⠂⠀⢀⠀⠀⠀⠐⠂
⡅⠈⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢤⢄⢙⣛⠃⠀⠀⢰⡾⠁⠀⠠⠀⠈
⠉⠀⠀⠀⠙⠋⠛⠃⠀⠀⠀⠀⠀⢴⠶⡀⠀⠀⢠⡀⣌⠉⢄⡀⠄⠠⠀⠙⣀⠐⠆⠀⠀⠀⠀⠉
⠉⠴⠄⠁⢀⠀⠐⣆⠀⠐⢘⡂⠰⠄⠀⠁⠀⡀⠌⠛⠀⠀⠈⠉⠀⠀⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣐⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⣶⣿⣿⡛⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣽⣷⣿⣤⣼⣿⣿⠶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡉⠹⣧⠀⠀⣾⠃⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⣿⠛⣶⣶⣤⣤⣀⡀⠀⠙⢷⣄⢻⣆⢠⡟⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⣦⣬⣿⣾⠋⠉⢿⣄⣽⠿⣦⠀⠀⠙⢷⣿⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⣿⠉⠛⠛⢿⣿⣿⣤⣽⣷⡀⠀⠀⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠀⠀⢀⣾⠃⠀⣀⣽⠟⠁⠀⠀⣀⣤⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡀⢠⡿⢁⣠⡾⠋⠁⢀⣠⣶⠟⠋⠀⣿⡀⠈⠉⣙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣴⠟⠉⣀⣤⠾⢻⡟⠛⠻⠶⣤⣼⣧⣴⠾⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠋⠁⢀⣾⣯⡁⠀⣼⠇⠀⣀⣤⡾⠟⣿⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⠻⣦⣿⣴⠾⠛⠁⠀⠀⢹⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⣤⡶⠟⠻⢷⣄⠀⠀⠀⠀⠘⣷⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⠁⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢻⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⣀⠀⠀⠙⢷⣄⠀⠘⣧⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣙⠻⣦⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⡿⠃

⠀⡴⡶⠦⠤⠀⠀⠀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⡤⠀⠀⠀⠀⠀⠀⡀⠀⢠
⡄⠀⠀⠀⠈⠀⠀⠀⣅⣀⣀⡠⢀⠤⡤⠵⢤⠶⠄⢶⢒⡴⡄⣐⢂⡂⡂⡀⠐⠀⠆⠀⠋⠀⣧⠂⣾⠈
⠃⡀⣀⢐⡴⣦⢂⣂⠈⣐⠆⠘⠬⠄⠩⠬⠈⠈⢈⢁⣂⠐⠐⠒⠀⠰⠤⡥⢁⡌⡉⠻⡀⠘⠁⢸⠇⠀⣠
⠀⡄⠔⠠⠴⠒⠆⠐⠐⠂⠘⠂⠠⠡⠅⠥⢴⢀⠒⣀⢀⣤⠌⢈⠁⠃⠒⣒⠐⢀⡈⡶⠁⠀⢀⣿⠁⢰⠇
⠐⠐⠛⠐⠈⢃⢀⠈⢉⡃⢀⠃⠙⠐⡛⠀⠒⠰⠐⠫⢤⠈⢁⢈⡐⠘⠉⠋⣹⡯⠘⠃⣠⠂⣼⠃⠀⣾
⠄⠛⠙⠀⠃⢁⠈⠁⢘⠉⠀⠘⠚⠀⠁⠘⠘⠁⠋⠐⠀⠰⢠⡄⠬⠌⠘⠃⠀⠀⣀⣴⠇⢀⡇⠀⠀⡇⡄
⡤⠘⠇⠃⠳⠉⠃⠸⠈⠁⠈⠃⠸⠀⠻⠰⠱⠀⠀⠃⠆⡰⠂⠀⠀⠀⠀⠀⠒⠒⠛⠿⠳⠾⢥⣀⣐⡇
⡀⠀⢐⠀⢀⢠⠁⢰⠀⠆⠀⡖⠶⠀⡖⠦⠆⠰⠆⠄⡤⢸⠁⢀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠐⠀⠠⠀⡉⠙
⠁⠀⠈⠃⠀⠀⠀⠤⠴⠄⠀⠀⠠⠀⠁⠠⣤⠀⠀⠀⠁⡞⢀⡎⠀⠀⣈⡇⠀⣀⠀⠀⠀⠠
⢀⠀⠠⢤⠀⠄⠀⠰⠂⠢⠀⠀⠄⠄⠀⢀⣀⠀⠀⠐⠀⢀⡸⠁⡀⢠⠛⠀⠀⠀⠀⠀⠀⢈⠁
⠌⣠⣴⠄⠀⠚⠒⠀⠙⠂⠀⠀⠐⠒⠂⠀⠈⢣⣤⡀⠑⠞⢁⡜⠀⠈⠋⠀⠐⠂⠀⠀⠉
⠇⠀⠀⠠⠶⣶⠄⠀⠀⠀⠀⣀⡁⠀⠀⢀⢛⠶⡖⠃⡀⠀⠻⠄⢠⡈⠀⠀⠀⠤
⠂⣠⠐⠀⠀⠠⡄⠀⠔⠀⢨⡉⠘⠀⠀⠘⠮⠁⠀⠃⠀⠀⠄⠈⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠂⠀⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠁
⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⡀⠀⠂⠀⣠⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠽⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠿
⠀⠀⠀⢰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠈⠁⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿
⡀⠀⠀⠀⠠⠀⠀⠀⢹⡿⣿⡁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⢻⡿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣶⠀⠀⠀⢴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⢴⡦⠀⠀⠠⣼⣷⠄
⠀⠀⠀⠤⣽⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⢀⠀⠀⠀⠰⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠃
⠃⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠟⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⢀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠠⣦⠄⠀⠀⢸⣿⡷⠄⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⣻⣿⡶
⠿⡗⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⢿⠂⠀⠀⠨⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡦
⠀⠿⠆⠀⠀⠀⠀⠂⠀⠀⠛⠙⠂⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠠⣼⣧⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀
⡦⠀⠀⠀⠀⠈⠛⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⢲⣿⠄⠀⠀⠀⠀⠘⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⣶
⠁⠀⠀⢀⣠⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠻⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⢀⣄⠀⠀⠀⢀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠀⠀⢠⣄⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⢰⣀⡀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⡿⠿⠄
⡦⠀⠀⠈⠝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⣴⣄
⣴⡄⠀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠚⠛⠏⠀⠀⠀⢠⣴⡀⠀⠀⠰⣿⣗⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠛⠻⠇
⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⣀⣶⣄⣀⣀⣀⣀⣀⣀⣈⣿⣿⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣦⣀⣀⣀⣀⣀⣀⣀⣈⣿⣯⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖
⠀⠀⠀⠙⠻⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⢀⣠⣾⣷⣄⡀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣠⣴⣿⣿⠟⠻⣿⣿⣦⣄⠀⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢀⣴⣾⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⡸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣋⣭⠽⠟⠛⠉⠻⢭⡉⠉⠉⣉⣩⡭⠟⠛⠉⠉⠙⠻⠯⣭⣉⡉⠉⠉⣩⠝⠋⠙⠛⠯⢭⣍⣳⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⠛⠉⠁⠀⠀⠀⠀⠀⢀⣠⣽⢾⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⢾⣥⣀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣦⣀
⠀⠀⠀⠀⣀⣴⠟⠁⢸⠀⠀⠀⠀⢀⣠⠴⠚⠉⢠⡏⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠘⣇⠈⠛⠶⣤⡀⠀⠀⠀⠀⣸⠀⠹⣷⣄
⠀⢀⣠⢞⡽⠋⠀⠀⢸⡆⣀⡴⠞⠋⠁⠀⠀⢀⣞⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⣠⠶⠋⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠉⠓⠦⣄⡀⣿⠀⠀⠈⠻⣝⢦⡀
⠀⠸⣟⠿⣿⠛⠛⠛⠿⢿⡿⠛⠛⠓⠛⠛⠿⠿⣿⠿⠛⠛⠛⠛⠛⠛⠿⠿⡽⠿⠟⠛⠛⠛⠛⠛⠿⢿⡽⠿⠟⠛⠚⠛⠛⢻⣿⠿⠟⠛⠛⢻⡿⢛⡿
⠀⠀⠈⠓⢮⡳⣄⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣤⡟⠁⠀⠀⣀⡴⣫⠖⠋
⠀⠀⠀⠀⠀⠙⢮⡑⢦⡀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣸⢻⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣾⠋⠀⠀⣠⢞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⢦⡀⠀⠙⣟⢦⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣠⢞⡟⠁⠀⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡲⣄⠈⢷⡙⢦⡀⠀⠀⢳⡀⠀⠀⠀⢰⡇⠀⣧⠀⠀⠀⠀⣸⠃⠀⠀⣠⠞⣱⠋⢀⡴⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⣄⠹⣆⠙⢦⡀⠀⢷⠀⠀⠀⣸⠁⠀⢻⠀⠀⠀⣰⠃⠀⣠⠞⢁⡞⢁⡴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣷⢬⣣⡀⠙⢦⡈⢧⠀⠀⡿⠀⠀⢸⡇⠀⢰⠇⣠⠞⠁⣰⣫⢖⡽⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣿⣄⠀⠙⢮⣧⢠⡇⠀⠀⠀⣇⢠⣯⠞⠁⢀⣾⣿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠻⣾⠁⠀⠀⠀⢻⡟⠁⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠘⣆⠀⠀⢀⡞⠀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡸⡆⢀⡞⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⠶⠶⢶⣤⣤⣶⠾⠿⢿⣿⠆⣀⣤⣤⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⠥⠤⡶⠶⣶⣶⣶⣦⠀⠀⣴⣛⣓⠋⠉⠀⠀⣀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⠀⢺⣿⣁⣠⣽⣶⡾⠛⣻⠟⠛⠚⠛⢛⡿⠋
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠻⣯⡉⠉⠀⠀⣰⠃⠀⠀⢀⡴⢋⣀⣤⣤⠴⢶⣤⡄
⠀⠀⢰⡟⣿⣿⡿⠿⠛⠛⠋⠛⣉⠉⠀⠀⠀⠀⠀⢀⣠⣝⣻⠶⣬⣿⣄⣀⣀⣁⣤⣤⢴⣿⣿⣯⣥⣴⣶⡶⠿⠛⠁
⢀⣤⣾⣿⡟⠁⠀⠀⠀⠀⠀⢰⣾⣷⡄⠀⣀⣤⣾⠟⠉⠈⠉⠛⠛⠛⠻⠿⠿⠿⠾⠟⠋⠳⣦⣄
⣿⢋⣁⠀⠀⠀⢠⣤⠀⠀⠀⢠⣤⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⢻⣾⣿⣦⠀⠐⠿⠃⣀⠀⠀⢈⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⡀
⠀⠙⣿⣿⡁⠀⠀⠀⡴⠋⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠲⡄
⠀⠰⡇⠒⠷⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠜⣷
⠀⠀⠙⠷⠶⠾⣇⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢻⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⢛⣽⣇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⣶⠿⢿⡛⠛⠻⢿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣿
⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢠⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣀⣈⣧⣤⣴⣾⣷⣶⣶⣶⣤⣀
⠀⠀⠀⣤⢎⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠿⡿⠛⠛⠻⣿⡇
⠀⠀⣸⠃⠈⣛⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡀⠀⠀⢻⡀⠀⣠⡿⠁
⠀⠀⢿⡄⠀⣛⡻⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⡀⠘⣇⣀⣀⣬⣷⡾⠛⠁
⠀⠀⠈⠳⣤⡩⠭⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢻⡟⠛⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣭⡏⡛⢻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⢿⣛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣼⠿⣿⣯⣟⣿⣳⣿⠏⠀⠈⠉⠙⢿⣧⣭⠿⣽⢾⣻⣾⣻⣽⣾⢷⡀⢀⡴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢯⣝⢣⣟⣳⢦⣾⣽⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⡿⣿⣾⣻⣽⠛⢹⣷⠟⠁⢀⡗
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣾⣳⠾⣽⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣿⣿⣿⣿⣿⡿⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠋⣽⣿⠾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠃⢹⣿⣿⣏⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣽⣦⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡘⢿⣏⢁⡿

⠀⠀⠀⠀⠀⢀⡴⡟⠛⠓⣳⠲⣟⠛⠛⡳⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢾⣛⠛⠛⢛⡷⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠖⠒⠒⠒⠒⠲⠶⢤⡀
⠀⠀⠀⢀⡴⠋⠀⢻⣠⠞⠁⠀⠈⢦⣰⠃⠀⠳⣄⠀⠀⠀⠀⠀⣰⠃⡇⠀⣨⠽⠺⣅⡀⢸⡏⢧⠀⠀⠀⠀⠀⢀⡴⢻⡓⠒⠶⠤⣤⣤⠤⠶⠒⢚⡟⢦⡀
⠀⠀⠀⠘⢯⡉⠉⠉⢯⠉⠉⠉⠉⢉⡟⠉⠉⢉⠟⠀⠀⠀⠀⡴⢃⡤⡟⠋⠁⠀⠀⠀⠉⢻⣧⣀⢳⡀⠀⠀⠀⠙⢶⣄⣹⡄⢀⡴⠋⠘⢦⡀⢠⣞⣠⡶⠋
⠀⠀⠀⠀⠀⠹⣄⠀⠘⡆⠀⠀⠀⡼⠀⢀⡴⠋⠀⠀⠀⠀⢼⣟⠉⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠈⢙⣷⠀⠀⠀⠀⠈⠳⣍⠻⡿⠶⠶⠶⠶⢿⠟⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠹⡄⠀⣸⠃⡰⠋⠀⠀⠀⠀⠀⠀⠈⢫⡙⠲⣇⡀⠀⠀⠀⠀⠀⣸⡷⠚⣹⠃⠀⠀⠀⠀⠀⠀⠈⠳⡹⡄⠀⠀⢠⢏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣷⢠⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡇⠉⠓⢦⣤⠖⠋⢹⡇⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣴⣚⣉⣈⣙⣦⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⢀⢠⣤⣤⠄⣀⢤⣤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣄⡓⢶⡶⢚⣠⡆⡀
⠀⠀⠀⠀⢀⣴⣿⡎⠿⣣⣾⣿⣦⡙⠟⣸⣷⣄⠀⠀⠀⠀⠀⢀⡄⢛⣛⣛⠿⠿⠿⠿⢟⣛⣛⢀⣄⠀⠀⠀⠀⠀⠀⢠⣿⢸⠟⣋⣴⣦⣙⠻⡇⣿⡄
⠀⠀⠀⠀⠨⣭⣭⣥⡠⣭⣭⣭⣭⣥⢠⣭⣭⡭⠀⠀⠀⠀⠀⠛⠿⣌⢿⣿⠟⣡⣦⡻⣿⣿⢋⡾⠟⠁⠀⠀⠀⠀⠰⢟⣭⢰⣿⣿⣿⣿⣿⣿⡆⣭⡻⠆
⠀⠀⠀⠀⠀⠈⢻⣿⣧⢻⣿⣿⣿⢇⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠱⣮⣈⢁⣚⣛⣛⣛⡊⢃⣬⠖⠁⠀⠀⠀⠀⠀⠚⢿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⢿⣿⡏⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⢿⣿⣿⣿⢣⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⢘⠿⣿⣿⣿⣿⠿⡃⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠜⡿⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢻⡿⠣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢸⣿⡶⢉⡋⢶⣿⡇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠛⠛⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠿⠀⠙⠉⠻⠶⠟⢳⣤⡀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠟⠀⢀⠀⠀⠀⠀⣠⣦⠀⠸⢧⣤⠶⠟⣻⢄⣴⡄⣠⠾⣆⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⡟⠙⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⢼⠿⠞⠁⠛⠃⠀⠙⠉⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣁⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠶⠶⠂⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠤⢤⢤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠤⠤⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢳⣤⣷⣤⣤⣴⠋⢀⣤⣀⠙⣧⣤⣤⣤⣤⡾⠉⣠⣤⡈⢻⣦⣤⣤⣾⣴⠞⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣀⣀⣠⣿⠀⢿⣤⡿⠀⣿⠀⣀⣀⣸⡇⠸⣧⣼⠇⢠⡟⠀⣀⣀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠁⠉⠙⢷⣤⣀⣤⡾⠋⠀⠀⠁⠉⠻⢦⣄⣀⣤⠞⠁⠀⠈⠁⠉⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⡤⢤⠀⢠⡀⡇⠀⡿⡄⡰⡇⣤⢠⠤⡀⡅⡤⢤⢠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠂⠳⠚⠘⠝⠃⠃⠀⠃⠙⠃⠃⠛⠘⠀⠃⠃⠃⠘⢸⢛⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠀⠀⠉⠁⠀⠂⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠐⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠙
⠀⢀⢀⠠⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠄⠀⠠⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⡊⢉⣹⣿⠛⢉⣉⡁⠈⢉⡉⠉⠉⣡⣿⠟⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣉⣷⠟⠉⠀⠀⠈⠙⢿⣄⠈⢈⣱⡾⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠏⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⣉⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣋⠵⡀⠀⠀⠀⠀⠀⠢⡀⠀⠀⡰⢆⣉⡱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⣰⠦⣾⣽⡤⣶⠀⠀⠀⠀⠀⠀⠈⢄⢐⡦⣼⣽⡦⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⢀⣏⠉⠛⡦⢤⣶⠤⡞⠃⠀⠀⠀⠀⠀⠀⠀⢻⡧⢤⣧⠤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⢻⣸⠶⡶⢿⣖⡒⣾⣤⣤⣄⣠⣄⣀⣀⠀⠀⠀⣫⡖⡒⣎⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠰⡀⡸⠁⣠⠠⠄⠤⢳⠨⡠⢋⠛⠉⢉⣁⣀⣷⠋⠄⠠⢡⡀⠘
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠄⠇⠠⠧⠴⠀⠀⠀⠀⠀⠹⠀⡔⢰⠐⠒⠒⢺⡀⠁⠆⠀⠀⠀⢿⠇⢿⡆⠒⠒⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣨⣤⣀⣀⣼⠀⠂⠀⠀⠀⠀⢸⡇⣸⣇⣠⣠⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣾⠉⠁⠉⠉⠉⡀⠀⠀⠀⠀⠀⣼⡖⡍⠈⠉⠉⠉⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⢆⠀⠠⠀⠀⢰⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡜⠀⠀⠀⠀⠀⣀⠼⡆⡈⡀⠀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠼⣈⠂⢠⠀⠀⠀⠀⢀⠈⢀⡇⢊⡹⠜⣁⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣮⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣥⣌⡉⠙⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⠿⠷⠒⠾⠿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣠⣶⣴⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⣄⣀⣤⣶⡒⠒⠄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡛⣿⠂⠘⠻⢟⠙⠛⠓⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠴⠂⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣇⠀⣀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢷⣾⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠚⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⠦⠾⡿⢿⠭⠥⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣸⣿⣦⣬⣤⣌⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢶⣦⣤⠔⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢠⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠛⠂
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣿⣿⣿⣿⡟⠀⠻⣍⠤⠤⠀⠀⢀⣠⠔⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⡴⡾⢋⣭⣭⣽⣿⣿⣿⣿⣿⣾⣽⣶⣼⣷⣶⣶⣶⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡆
⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⢀⣾⣿⣿⣿⡿⣿⠟⠁⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠈⠓⢄⣀⠔⠊⠁⠈⠑⠢⣄⡴⠋⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠞⢿⡟⠀⣠⣾⣷⣄⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⣽⣷⠤⡀
⠀⠀⠀⠀⠀⢠⣖⣁⣴⣁⣀⣈⣧⣞⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣷⣤⣼⣿⣿⣷⣌⣢⡄
⠀⠀⠀⠀⠀⠀⠙⢦⣹⠻⣧⢀⠏⢳⣤⡀⠀⠀⡠⠊⠙⢢⡀⠀⠀⢀⠔⣿⣇⠀⡠⢺⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⡀⠀⢻⣿⣦⡞⠁⠀⠀⠀⠙⢦⠚⠁⣼⣿⡿⠊⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⢄⠀⢻⣿⣇⠀⠀⠀⠀⠀⠇⢀⣾⣿⠟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡡⡀⢻⣿⡄⠀⠀⠀⡜⢀⣾⡟⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣆⠻⣷⠀⠀⠰⢠⣿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣇⢀⣳⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⠀⠀⠀⣠⣿⣿⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⡀⠀⠀⠀⢀⡀⠄⡁⠛⠉⠀⠉⠢⡀
⠀⠀⠀⠀⠀⣰⠃⡠⠄⣉⠉⠀⠐⠀⢀⠀⠈⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢠⠄⠀⠀⠀⢨⡁⠈⡁⠀⠘⢿⠂⢠⡇
⠀⠀⠀⠀⠀⠑⠀⠒⡾⠁⠀⠀⣀⠄⠘⠓⠂⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠸⠋⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠸⡀⢦⣴⡾⠁⠀⢀⠌
⠀⠀⠀⠀⠀⢠⠏⠀⠠⠂⠀⠀⠀⢟⠀⠠⠀⠄⣠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠄⡀⠉⣢⡄⡀⠀⣼⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⣠⠛⠀⠀⢀⠠⠀⢀⠄⢚⠤⠀⠂⡀⠀⠀⠀⠄⠲⠀⠀⠃⠄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠂⣄⢸⣶⣿⣿⣷⣤⣾⣿⣿⡿⠻⣿⣿⣿
⠀⠀⠀⣰⠃⠀⢠⡼⠋⠘⠀⠄⠀⠈⠃⠀⠌⠄⠈⠀⢀⡤⠴⠒⠀⠈⠃⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣿⣿⣿⣿⣿⣿⠏⢉⠒⢾⣿⡿⠃
⠀⠀⢠⠏⠀⢀⡝⠀⡀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠁⢁⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠀⠚⠉⠉⠙⠿⣇⣩⣮⣴⡄
⠀⠀⡎⡀⢠⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⢉⠵⠷⠶⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⠉⡑
⠀⣴⠟⠁⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠛⠛⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⠃⠀⠀⡀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡀⢀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠋⣁⣵⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣶⠿⢛⠉⠐⣨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⡴⠃⢠⣤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡬⢔⣮⣵⡄⠀⠁⢠⠈⢆⠀⢀⡀⠀⠀⠀⠀⠀⢈⠇⠀⠨⠣⣀
⠀⠀⠀⠀⠀⠘⢷⣀⠀⠛⠁⠀⠀⠂⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠛⠻⠃⠀⠀⠀⠀⠀⠎⢠⠷⠀⠀⠀⠀⡀⠉⠀⠉⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠈⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⢳⡙⠤⠁⠀⠀⠀⠐⠂⠀⡂⠈⠑⢌⠀⡰⠂⠄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣀⠀⠀⡀⠐⣁⡀⠀⠀⢨⡇⣶⣤⣤⡆⠀⠀⠔⠀⣀⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡷⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣼⣦⡀⠘⠀⠁⠀⠀⣼⠀⠈⠀⢠⢀⣨⠄⢀⣾⣭⣭⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⠩⣭⠅⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢻⡀⢨⣤⠈⠁⠀⠀⠀⢤⠴⠞⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⣌⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢄⠀⠠⠤⠀⣽⠁⣾⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠛⠉⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⢰⡙⠛⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠁⢊⠀⠀⠀⠁⠀⠀⢀⣿⢹⡏⣹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⠇⠘⣦⠀⡀⠶⠷⣥⣾⠖⠛⠁⠀⠀⠀⠀⠀⠀⢀⣸⣥⡤⠂⠹⣤⠴⠤⠀⠀⠀⠀⠀⠀⠀⢠⡴⡴⠂⠀⠀⠱⠴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠃⠉⠁⢈⣦⢔⠂⠁⠀⠀⠉⠐⢢⣴⡁⠈⠉⠙⠛⢦⣄
⠀⠀⠀⠀⠀⣠⣖⣫⣋⣰⣀⣤⣒⣉⣠⣂⣀⣁⣢⣀⣀⣄⣊⣁⣈⣄⣉⣒⣤⣀⣇⣙⣝⣲⣄
⠀⠀⠀⠀⠀⠙⠧⣍⠢⡈⠳⣄⠀⠀⠈⠅⠀⠀⠀⢈⡁⠀⠀⠀⢠⠋⠀⠀⣠⠟⢁⠔⣩⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢦⡙⠷⡄⠀⠘⡄⠀⠀⡈⢁⠀⠀⢀⠂⠀⣠⡾⢋⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⢪⠢⡀⠘⡀⠀⡇⢸⠀⢀⠎⢀⠔⡕⣡⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⡈⠢⡱⠀⠄⠀⠀⣌⠔⢁⣾⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡈⢷⠀⠀⡾⢁⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⣸⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠓⠄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠿⠃
⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⢀⣠⣶⡞⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣥⡀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠴⠛⠃⠀⠀⠀⣠⣴⣿⣿⣿⢁⡄⠀⠀⠀⠀⠀⠀⢀⣴⠀⠸⣿⣦⣄⠀⠀⠀⠸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣧⠹⣿⠃⣾⣿⡄⠀⠀⠀⢀⣴⣿⣿⠀⠀⢻⣿⡿⠃⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠁⠘⠋⠩⠄⠀⠀⠴⠿⣿⡿⠿⠄⠀⠀⠃⠀⠀⠀⠀⠀⠘⠛
⠀⠺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣦⠀⠠⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂
⠀⠀⠘⢷⡄⠀⠀⠱⡄⠀⢀⣠⡆⢀⠀⠀⠀⢻⣶⣦⡅⠀⠀⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠻⣆⠀⠀⠹⣾⣿⡿⢠⣿⡆⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠘⢧⠀⠀⢻⣿⢣⣿⣿⣿⡀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⣾⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢣⣿⣿⣿⣿⣧⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⢿⣿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⡟⠁⠀⢨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⢦⣦⡀
⠀⠀⠀⠀⠀⠀⣾⢫⣷⠟⠋⠉⠳⣮⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣫⣥⠀⣬⣙⣷
⠀⠀⠀⠀⠀⠸⣷⡏⠰⠾⡠⡻⠇⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠁⢧⣷⠰⣽⡮⠸⠦⡀
⠀⠀⠀⠀⠀⡞⣝⠁⠀⠙⠀⠉⠀⠈⣙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣬⠠⡀⣐⠀⣌⢠⢀⣯⠇
⠀⠀⠀⠀⠀⠑⠒⢷⡀⠀⢌⠁⢠⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠳⡱⣀⠁⡠⢢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡱⢤⠤⢴⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⠀⣖⣁
⠀⠀⠀⠀⠀⣀⣤⣾⠳⡘⠤⠃⡸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡈⣆⢠⣿⣷⣄
⠀⠀⡠⠐⣿⣿⣿⣿⣄⡚⠀⣈⣵⣿⣿⣿⣿⣷⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠸⢿⠇⣿⣿⣿⡆
⠀⢰⣷⣾⣿⡟⢻⣿⣿⣿⣿⠇⡜⣿⣿⡟⢻⣿⣷⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢰⣿⣧⣿⣿⣿⣷
⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⡟⢀⣇⣿⣿⡇⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣧
⠀⠸⢿⡿⠿⢄⢻⣿⣿⣿⣦⣾⣿⣿⣿⡇⡠⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⡜⢉⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡉⠇
⠀⠀⢸⠀⠚⠚⣘⠻⣿⣿⣿⣿⣿⣿⠟⠃⢃⠗⠀⡇⠀⠀⠀⠀⠀⠀⠀⣐⣿⣃⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣃
⠀⠀⠀⠁⠊⠉⠢⣴⣿⣿⣿⣿⣿⣿⣮⠐⠈⡑⠈⠀⠀⠀⠀⠀⢀⠒⠾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠷⠒⡄
⠀⠀⠀⠀⢠⣀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠀⠀⠀⠀⠀⠀⠈⣶⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣶⠁
⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠒⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣀⠃⣼
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⢙⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣋⣶⠇
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⡇⢿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠿⠋⣥⣶⣿⣿⣿⠿⣿⣿⣿⣶⣬⠙⠿⠧⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⢸⠉⠈⢹⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠠⠅⢒⠚⠢⠆⠚⢒⠂⠵⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠀⠰⠄⠀⠀⠀⠆⠀⠀⢸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡤⠤⠤⠤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⠀⠀⠀⠀⡴⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⢀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⢰⠂⠀⠀⠀⠀⢣⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡴⠋⠀⢸⣷⡀⣠⠴⠂⡈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠁⠀⣀⠚⢿⣧⡀⠀⢠⠄⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠛⠦⣤⣤⢬⣷⡴⠀⠀⢠⡿⠄⡄⠠⠄⢠⡀⠠⠀⠠⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠬⠤⠤⠥⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠁⠀⡠⠐⠀⠀⠴⠁⠀⠀⠀⣀⡀⣀⠀⡐⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢀⣄⠘⠢⠄⠀⠀⠀⢰⡁⠀⠀⠀⢰⠁⠀⠁⠛⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⢁⠂⠸⢦⠤⢤⡇⣀⠀⠀⢀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠈⠂⠌⠀⠂⠀⠀⠀⠀⣂⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿

⠀⠀⢼⡿⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠃
⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠻⠂⠀⠀⠀⠀⣲⣿⡥⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠁⠀⠀⠀⣄⣠⠀⠀⠐⠀⠠⣴⣄⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⢻⠟⠂⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢿⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟
⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡧⠀⠀⠀⠀⠀⣺⣷⡥⠀⠀⠀⠀⢀⣠⡄
⣶⡇⠀⠀⠀⠀⠀⠀⠄⢠⣷⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠄⠀⠀⠘⠻⠋
⠛⠉⠀⠀⠀⠀⠀⠃⠀⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⣽⣯⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠄⠀⠀⠀⠀⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠜⡿⠏⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⢀⠀⠐⠂⠀⠁⠀⢀⣄⠀⠀⠀⠀⠀⠚⠟⠃⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⢠⣀⠄

⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠈⠉⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣠⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁
⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠠
⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠽⡗⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠲⠆⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⣀⠀⠀⢰⡄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣷⠇⠀⠠⠀⠀⡀⠀⢠⠀⠀⠀⠀⣤⣀
⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁
⠄⠀⠀⠰⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⢺⣷⠀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠸⠗⠀⠀⠀⠂⠀⠀⠀⠐
⠀⣤⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠸⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐
⢰⠄⠀⠀⠂⠀⠀⢀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠀⠠⠄⠀⠁⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⢠⡄
⢠⠄⠀⠁⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢷⡧⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⢰⣴⡄
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠶⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠈
⢀⠀⠀⠈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⣠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⣰⣦⠄⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠃⠀⠀⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠆⠀⠀⠛⠀⠀⠀⠰⠀⠀⠀⠀⠆
⠀⠘⠿⠅⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠂⠀⠀⠛⠀⠀⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠘⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠃⠀⠀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠂⠀⠄⠀⠀⠰⠆
⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⡀⠀⠰⠆⠀⠀⢀⡀
⠙⠃⠀⠠⠀⠀⠁⠀⠀⠀⠛⠃⠀⠀⠠⡄⠀⠀⠀⣠⡤⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠀⠉⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠄⣀⠤⠔⢐⡄⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠶⠚⠉⠀⠀⠘⠛⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⡀⠘⢀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠘⠃⡐⣘⠀⠀⠀⠀⠀⠘⠠⣄
⠀⠀⡠⠄⢀⠄⠀⠀⠀⠀⠀⠀⠞⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀
⢠⠢⠂⠀⠋⠀⢲⢌⡴⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢘⠀⠀⠰⡌⢴⠂⠈⡇⠀⢨⢢
⠘⠇⠂⠰⡆⢀⠦⣊⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢤⠀⠀⠀⠀⠀⠀⡘⠀⠘⠠⣉⣂⢄⠀⡷⠄⠐⡊
⠒⠈⢏⣀⠜⠁⠀⠈⡄⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡌⠀⠀⠙⢁⢈⠏⠂
⠀⠀⠀⡡⠀⢾⢤⡀⠣⠄⢀⠀⠀⠑⠄⡀⠀⠒⠆⢀⠀⠀⠀⠀⠈⠃⠁⠀⡀⠔⠁⠀⢀⠀⠠⠃⣠⢶⠄⢨⠁
⠀⠀⠴⠉⠀⡉⠀⡌⣙⠖⠐⠨⠅⡀⠂⠨⣰⠂⠠⠤⠄⠀⠀⠀⠀⠒⠲⡅⠐⢐⠀⠭⠐⠰⣚⠁⡄⠏⡁⠈⠢⡀
⠀⠀⠀⠁⠂⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢄⡀⠁⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠊
⠀⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠈⠓⠦⢀⡀⠀⠀⢀⡀⠤⠊⠁⠐⠀⠤⣀⠤⡀⠀⠂⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠠⠖⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣡⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣻⣉⣛⣿⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣄⠀⠀⠀⠀⢠⣤
⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⣤⣦⣀
⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣧⣀⠀⠀⠀⠀⢠⣠
⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠐⠿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠟⠛⠉⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠋⠁⠐⠈⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠉⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠋⠁⠀⠀⣀⣠⣤⣶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⢉⡀⠀⣀⣤⣴⡶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠸⣿⣄⣀⣀⣠⣴⡾⠟⠋⠁⢀⣀⣤⣵⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡟⠿⠻⣿⡋⣁⣠⣤⣶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣷⡀⢠⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡷⢾⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣌⢿⣆⢀⣠⣶⠾⣿⠿⠿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣦⣿⣿⣋⣀⡴⠃⠰⠆⣀⣿⣷⣶⡿⠟⣿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣼⡿⡛⠻⠟⢻⡿⣾⣶⣾⠛⠉⠀⣩⡴⣾⠋⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⣸⠏⠙⢧⠀⢿⣌⠳⣤⣉⠋⢀⣀⣴⣋⣀⣿⠀⠀⠁⠸⣿
⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⢻⡟⠃⣿⡶⠀⠈⠃⠠⢶⡆⢈⣿⠿⠛⠛⠋⠙⠛⠻⣧⣆⣄⣠⣿⡄
⠀⠀⠀⠀⠀⣼⣟⣿⣼⣿⣤⣽⣶⣇⢶⣤⡀⡀⠀⣴⡶⠿⢿⣦⣤⡀⠀⠀⠀⠀⠉⢻⡏⡀⠙⠻⣷⣶⣆
⠀⠀⠀⠀⠀⠈⠿⢷⣾⣿⡙⢻⣭⣿⣦⣬⣴⣷⣾⣿⣧⣀⣸⠟⢹⣿⣶⣆⢺⣂⣀⣸⣇⠛⠂⣀⣿⣾⠟⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠘⠓⠆⠹⡻⣿⣿⣠⣤⣬⣿⢉⡷⠛⠛⠻⢦⡞⠋⠁⢸⣿⢿⡿⠛⠙⢿⣿⣶⡿⠁⣠⡾⠷⣦⡙
⠀⠀⠀⠀⠀⠀⢠⣴⡿⢷⣄⠈⠉⣩⣭⣉⣿⣾⣇⣀⠻⠷⣾⠀⣤⣾⣼⡿⠸⠷⢶⣶⠿⢋⡀⠀⠀⠻⣷⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠾⠟⠀⡀⢿⣿⣙⣿⠟⡛⢻⠿⠿⠿⠛⢛⡉⣁⠀⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠘⠛⠋⠀⠁⠉⠙⠁⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠉⢀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠠⠐⠉⠑⣄⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠘⢄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⡀
⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠠
⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢃
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠀⠀⠘⡀⠛⢀⡀
⠈⢄⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⢆⠀⠀⢱⠂⢩⠁
⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠦⠀⠙⠢⡴⠀⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢋⡗⠀⠀⠀⠀⠀⠀⠀⢴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠃⠰⠏⠀⠲⢢⠀⡠⣄⢠⠤⠤⠵⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠁⠸⠎⠀⠈⠓⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⣡⠀⢀⡀⠀⢀⠄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠦⢾⣥⢧⣤⣤⣤⡔⠁⠀⠈⠢⠠⡠⠊⠁⡤⠊⠉⣠⣮⣄⡸⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣶⣶⣯⣭⣭⣽⣭⣭⣥⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠄⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠂⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣮⡾⠟⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⢀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡴⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠑⠶⠀⠂
⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠂⠤
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣴⣿⣿⣧⣦⣤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⣼⣧
⠀⣟⣿⣿⣿⣿⣽⠿⣿⣿⣿⠇⢸⣿⣿⣿⣿⡿⣡⡞⢁⣴⣿⣶⣶⣦⣤⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⠟⠃⠀⠀⠀⠀⠀⣗
⠀⣿⣿⣿⡿⠟⠁⠀⣿⠿⠿⠀⢸⣿⣿⣿⣿⣶⠋⣠⣾⣿⣿⣿⣿⣿⡿⢡⡏⠑⠢⣄⡀⠀⠀⠀⠀⠀⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠄
⠀⠸⣿⠋⢀⣠⣴⣾⣶⣾⣿⣿⣿⣿⣿⣿⡿⣻⣾⣿⠿⠛⠿⢿⣿⡿⣡⣿⠁⠀⠀⣿⣿⠀⣀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠙⢿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⠀⠀⠀⢸⣿⣳⣿⣯⡤⠶⠖⠛⠉⠀⣿⡀⠀⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠪⣳⢤⣿⣿⠿⠟⠛⠉⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢸⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠑⢝⡷⣦⣀⡀⠀⠙⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣙⢿⣷⣶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⡼⠇⢀⣀⡤⠖⡊⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⢿⣿⣿⣷⢶⣶⣶⣶⣤⣤⣤⣜⣛⣙⢁⣙⣛⣛⣤⡤⠄⠀⠀⠀⠀⡀⠘⠋⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣝⣿⣿⣿⣿⣟⣫⣉⠉⠘⠋⠉⠁⠀⠀⠀⣀⣀⠒⢪⠅⠔⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⣛⣿⢸⡿⢾⣿⣿⣵⡾⠁⠀⣠⣠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣄⢾⣿⡿⢬⠀⠀⡬⠉⠈⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣍⠻⣷⣽⣙⠀⡞⠜⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡙⡿⣯⠤⢊⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡔⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣤⣄⣐⣶⣲⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠊⠉⠀⢰⡟⠘⣹⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡠⠁⠀⠐⡂⠀⠁⠚⠛⠛⠛⣳⢀⡀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣧⠀⡄⠀⠂⣿⢇⣀⢨⡯⢽⣿⣩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠘⠉⠀⠃⠠⠊⡽⢼⢿⡛⢷⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⣀⣤⣌⣀⣼⣷⣦⠴⣿⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣒⢾⡛⠋⢩⡾⡋⢁⣨⣿⠋⢣⣤⡿⠿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠁⠜⠇⢐⠿⠉⠀⣰⣿⣟⡩⠿⠿⣅⠀⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢴⣶⣾⠂⠀⣠⣶⣿⠟⠻⠇⢙⣋⣈⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣭⣿⣿⣷⠿⠿⠷⠾⠞⠛⠛⠋⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣼⣧⣀⠀⠀⠀⠀⠀⠀⣀⣣⡀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣀
⠀⠀⠈⠉⢻⡟⠉⠁⠀⠀⠀⠀⠀⢑⡠⠫⡀⠀⠀⠀⠀⠑⠆⣀⣀⠚⠁⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠁⢱⢿⡏⠁
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠃⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠐⠋⠀⠑⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⠄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣦⠀⢠⠆⠩⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⣤⡀⢛⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠢⣤⡀
⠀⠀⠀⠀⠐⠐⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄
⠀⠀⠁⠘⢃⠂⡈⠀⠀⠀⠀⠄⠀⠀⠑⡒⠀⠀⠀⠀⠀⠤⢠⠟⢲⡶⠀⠀⠀⠲⣿⣿⣿⣤⡤⠞⠁⠀⠀⠐⢀⠈⡠⠂
⠀⠀⢠⡄⠈⠚⢠⠶⠀⠀⠀⠀⠀⠀⢈⠉⠉⠀⠀⠀⠀⠀⣙⠶⢭⡆⠀⠀⠀⠸⠋⠉⠃⠀⠀⠀⠀⠀⠀⢠⠄⠁⠰
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠀⠐⠀⡀⠀⡀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⡄
⠀⠠⢴⣿⡶⠂⠀⠀⠀⠀⠀⠀⠉⠈⠀⢉⠐⠁⠀⠀⠀⠒⠿⣭⢭⡉⠀⠀⠀⠠⢤⣥⡤⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡍
⠀⠀⠞⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⠀⠈⠑⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠟⠁⠉⠓
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⡁⠀⠀⠀⠀⣀⡀⣿⢄⣠⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡟⣿⡉⠁⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀
⠀⠀⠀⢠⠀⠤⠀⠀⠐⠀⠀⠀⢄⡄⠀⡷⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠒⠀⠀⠀⠀⢺⠋⠀⠰⠛
⠀⠠⠁⡐⠀⠰⠖⠀⠀⠀⠀⠀⠀⣑⡤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡀⠀⠀⠀⠐⠿⠈⠈⠳⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠺⡿⠋⠻⣿⠗⠲⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣀⣰⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠽⢶⣻⡿⠿⠛⠛⠛⠛⠛⠶⣄⡀
⠀⠀⠀⠀⠀⣀⣴⣿⡇⠢⡀⠀⠀⠀⠀⠀⠀⢀⣁⠠⠤⠒⠊⠉⠀⠐⠒⠉⠁⠀⠀⠀⠀⠀⢀⣠⡾⣿⡝⣦⣄
⠀⠀⠀⣠⠾⠛⠙⢿⠁⠀⠈⠳⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⡅⠈⢸⠙⠧⡛⣷⣄
⢀⡠⠊⠁⠀⠀⠀⣾⠀⠀⠀⠀⠘⢿⣆⠀⠐⠂⠤⠤⢤⣤⣀⣠⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣷⣦⣤⣙⡀⠀⠀⠘⢎⠳⣄
⡞⠠⠀⢀⠠⠀⠘⢫⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⣬⠒⢸⣿⠛⠡⠓⠋⠑⠸⢹⠇⠀⠀⢀⠘⢦⠸
⣧⠖⠃⠁⠀⡐⠀⢸⠀⠀⠀⠀⠀⠀⠀⣨⣵⣞⠉⠉⣿⣿⣿⣿⡿⠿⣿⣿⣷⣯⡁⠀⠀⠁⠀⠀⠀⠈⠀⠱⡀⠀⢉⠟⣷
⠙⢦⡂⢀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠴⠊⠁⠁⠈⠀⠀⠉⠁⠠⢴⠅⢀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢐⠀⠀⢵⡄⡣⣤⠟
⠀⠀⠙⢼⡗⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡂⠀⠂⡿⢨⣿⣿⣿⣿⣿⣿⣩⢿⣿⣦⣄⠀⡀⠀⢶⣄⣽⠟⠁
⠀⠀⠀⠀⠙⢿⣿⣶⣶⣦⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢻⣆⣀⣷⣿⡟⠃⠄⠚⠛⢏⣛⣳⣭⣻⣽⣿⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⡛⠻⣿⣿⢿⣶⣶⣧⣯⣤⣤⣤⣤⣽⣷⣿⣿⣭⣼⣿⣯⣵⣽⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⢌⠻⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡱⡌⠪⣶⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡄⠈⠀⠛⢶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⣿⣿⣿⣿⣿⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠟⠁
⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣐⡠⠔⠒⠉⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠘⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⢀⣴⠎⠁⠀⠲⣋⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢆⠡⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠀⠀⡀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠈⢇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⡄⠣⠄⠐⠄⠒⣀⠀⢀⠀⠀⠀⠀⠈⢧⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⠀⠀⢼⡏⢸⢳⡀⠘⢧⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠤⠟⠀⢻⠁⠈⡎⠑⡄⢘⣆⠥⠈⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠃⢀⡀⠦⠄⠠⠈⠁⠀⡡⠚⡋⠀⠐⡤⡗⡀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⠀⠴⠞⠁⡠⠏⠀⠀⠀⡤⢎⠀⠀⠂⠀⠐⠀⡴⠳⠀⡀⡀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠐⠉⠀⠀⠀⠀⣐⠀⠀⠉⠇⠀⠀⠀⠛⠣⢄⢇⠠⠈⠢⣄⠀⠀⠀⠀⠀⠈⠾⠤⠂
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠁⢠⠄⠀⠀⢣⠀⢀⡄⠀⠀⠀⠀⠀⠼⡃⠀⠙⡄⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡃⠀⠠⠀⠁⠀⠀⠀⠀⠀⢸⠄⢸⠀⠀⠠⢀⡀⢔⠀⠀⠀⠀⠡⠀⠈⢠⡑⠄⡀
⠀⠀⠀⠈⢩⡀⠈⠁⡅⠇⠀⠀⡄⠀⠀⢃⠀⠀⠀⠀⡧⢠⠀⠀⠀⠀⢹⠈⡆⠀⠘⠀⠘⣮⡊⡀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⠀⠈⠒⢤⣡⡀⠀⠄⠀⠀⠀⠀⢀⡀⠄⠂⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠳⡈⢦⡀⠀⠀⡀⠇⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠄⡀⠀⠀⠀⠨⡄⣀⣀⠀⡠⠤⣅⣀⣀⣘⣤⣥⣤⣇⠤⠤⠤⠿⢛⡈⠉⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠒⠊⠁⠀⠀⠀⠨⠴⠀⡀⠀⠱⠄⠘⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠿⢿⣷⣦⣄⡀⠀⢀⣠⣴⣶⣶⣤⣀⠀⠀⣀⣤⣶⣿⠿⠟⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠈⠛⠿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⠿⠟⠋⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡗⠋⠓⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢻⣿⢦⣈⣠⢾⣿⢻⣿⡏⡀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⢠⣶⣿⡿⢿⣿⣿⣛⣻⣿⣿⠿⣿⣿⣧⢀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣲⣶⡿⠓⠙⠛⠻⠷⠶⠶⠶⠶⠶⠶⠿⠛⠛⠑⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠉⠀⠀⠐⠠⠐⠒⠋⠉⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⡁⠀⠤⠒⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢇⡄⠀⠠⠌⡆⡴⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠈⡰⠂⠀⢠⠐⠦⠀⠀⠌⢀⠀⠀⠈⡀
⠀⣠⠀⠤⠶⡈⠓⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠅⠒⠈⠀⠀⠀⠎⠌⠀⡂⠠⠀⡸⠄⠀⢀⠁
⠑⠀⡠⠟⠆⠠⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠈⠐⠊⠉⠀⠀⠁
⠀⠀⠈⠆⠀⠠⠏⠉⠢⣀⢀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠤⠰⠊⠀⠀⠀⠀⠀⠀⠀⢠⠂⡩
⠀⠀⠀⠰⠀⠐⢆⠀⡠⠈⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⠀⠐⠄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠐⠀⠀⢩⡁⣰⢀⡂⠈⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⢑⢄⠀⢳⡀
⠀⠀⠀⠀⠀⠌⣠⡈⠿⠈⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠄⠀⢃⠀⠀⠉⠰⠤⠄⠉⠚⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠃⠆⠠⠦⠔⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠛⠤⠀⠤⠀⠒⡄⠀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⣀⢐⡄⢠⣶⢳⣾⣽⢧⣴⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠐⠆⢸⡅⡟⣁⡛⢨⠥⢏⠰⠣⠆⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢀⠰⣋⠁⠀⠀⠀⠂⠀⣀⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⡀⣯⡄⢀⣀⣠⠂⢠⣻⢡⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠁⠀⠂⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢂⡀⣀⢂⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⠁⠀⠉⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⢀⢜⣻⣃⡴⢏⠋⢹⠶⢸⣀⠀⣀⡀⠀⠀⠀⠜⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠚⠛⢀⠼⠛⠐⠠⢀⣼⡏⢋⠈⡘⠁⣠⠐⠦⡄⠀⠈⠦⠀⣀⠀⣀⣀⢠⠖⣥⣭⠻⢶⠣⣤⡖⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠉⠉⢚⣛⠐⠻⠼⠷⠶⢿⣶⣶⡮⢿⣦⣴⣯⣿⣶⠿⠻⠦⠀⠀⠙⠆⡽⠆⠨⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠶⠶⠶⢶⣶⠀⠀⠀⠀⠀⣀⣤⣾⣶⣤⡀⠀⠀⠀⠀⠀⢰⣛⡄⠀⠉⠳⣤
⠀⢀⣴⣴⣿⣿⣷⣴⣄⠀⠀⠀⠀⢸⡇⢸⢛⠛⢻⠁⣿⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⢦⡠⠋⠈⠳
⢠⣾⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⢸⡇⣸⠆⠀⢸⡀⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⠊⣹⣾⣷⡄
⠀⠀⠀⠘⡆⠑⠲⠄⣄⡀⠀⠀⠀⠘⠟⠁⠀⠐⠀⠙⠛⠀⠀⠀⠀⠀⠘⠛⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⣀⣯⣹⢀⠛⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠉⢹⣿⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⢠⣶⣶⣠⣤⣶⠄
⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⡖⡖⢖⣀⣿⣇⡀⠀⠀⠀⠀⢀⣯⣽⣻⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠉⣾⣀
⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣛⣻⠧⠀⠀⠀⠀⠸⣿⣿⠏⠉⢿⣿⡿⠀⠀⠀⠀⠈⢻⣯⣯⣯⣯⣷⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⠀⠴⠦⣟⠀⠀⣾⣿⠀⠀⠀⠀⢠⡾⣅⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡃
⠁⠀⠀⠀⣹⡆⠀⣿⣿⠀⠀⠀⠀⢸⣧⠈⠉⠀⣬⣤⡀⠀⠀⠀⠀⢀⡾⣷⠉⠃⢠⣤⣤⡀⠀⠀⠀⠀⣻⣿⠉⠃⢼⣥⣾⣷⡄
⠀⠀⠀⠴⠣⠇⠠⠿⠿⠀⠀⠀⠰⠋⠘⠃⠀⠛⠻⠿⠛⠂⠀⠀⠀⠋⠀⠛⠀⠀⠛⠻⠟⠛⠂⠀⠀⠰⠃⠸⠀⠀⠘⠿⠛⠟⠁


⠀⠀⠀⠀⡇⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠋⣽⣿⡍⠻⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃
⠈⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣷⣶⡄⣀⡀
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⡅
⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠛⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠁⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠑⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠁⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣨⡟⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣦⣤⣤⣄⠀⠀⣀⣴⣶⣶⣾⣯⡀⠀⠀⠀⢀⡇
⠀⠀⠀⣰⣿⣶⠖⠀⠺⣿⣿⣦⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⠛⠻⣿⣿⣆⠀⠀⢀⡇
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣤⡀⢤⣤⣤⣤⠤⢀⣀⣤⣄⣀⠠⢤⣤⣤⣤⠄⣠⣄⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⣿⠆⠉⢡⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⠉⠡⢾⣿⣿⣿⣿⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⣿⣿⡿⢟⣡⣾⢸⣷⣍⠻⣿⣿⣿⣿⣿⡿⢋⣵⣿⢸⣦⣙⠿⣿⣿⡇⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠿⣋⣴⣿⣿⣿⢸⣿⣿⣷⣬⡻⣿⡿⣫⣴⣿⣿⣿⢸⣿⣿⣷⣌⡻⠇⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠨⣭⣭⣭⣄⠠⣭⣭⣭⣭⣥⠠⣭⣭⣭⣭⣥⡄⣤⣭⣭⣭⣭⡥⢠⣭⣭⣭⣭⡥⢀⣬⣭⣭⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠘⢿⣿⣿⣿⡆⢿⣿⣿⣿⣿⢁⢹⣿⣿⣿⣿⠇⣾⣿⣿⣿⠟⢀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢦⠻⣿⣿⣿⡘⣿⣿⣿⡟⢸⠸⣿⣿⣿⡟⣸⣿⣿⡿⢣⢆⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡌⢷⡜⢿⣿⣧⢹⣿⣿⡇⣾⡆⣿⣿⣿⢡⣿⣿⠟⣴⠏⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡌⢿⣦⠻⣿⡆⣿⣿⢁⣿⣇⢹⣿⠇⣾⡿⢣⣾⠏⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢿⣷⣜⢿⡘⣿⢸⣿⣿⢸⡿⣸⠟⣴⣿⠏⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠁⠃⣼⣿⣿⡄⠃⣡⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⣿⣿⣿⡇⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠸⣿⡿⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢿⢇⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿