Chook Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣷⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣯⡙⠻⣿⣿⣦
⢀⣀⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠉⠉⠿⠿⠙⡿⢀
⠈⠻⠥⣼⣿⣿⣿⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠠⣶⣦⣰⣿⡋⠉
⢺⣛⣺⣿⣿⣿⡻⣿⣷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷
⢠⠟⢿⣿⣿⣿⣿⠦⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⡄⠀⠀⠀⠀⢠⠀⢿⣿⣿⠟
⣨⠽⣿⣿⣿⣿⠶⠾⠛⠦⠁⠹⣦⡀⠀⣀⣤⣤⣤⣤⣤⠤⠶⠶⠟⣿⣿⣤⡔⠀⠀⣠⢿⡄⠈⢿
⣙⡾⠟⢛⣿⠷⠚⠉⣀⣀⠈⠛⢿⡿⠟⠛⠙⠋⠀⠁⠀⠀⠀⠀⠀⠉⠛⠘⣷⣷⣴⡟⠸⣧⠀⢸
⠙⢶⣵⣿⣿⡶⣞⣿⠏⠉⢠⠖⠀⢀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⠏⠁⠀⣿⣷⡿
⣟⠿⣿⣿⣿⣿⣿⣵⣦⣠⡏⠀⢰⠃⠀⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁
⠈⢙⣛⣻⣿⣻⣽⣿⡟⣼⠀⡴⣿⠀⠀⢸⠁⠀⡏⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠈⠿⣽⣿⣿⣿⣿⡼⡟⣼⡇⣼⣢⣼⣿⡤⠀⣇⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠟⢻⣶⣦⣿⣴⣿⡤⢀⡀⠀⠀⠀⠀⢀⣠⠆⢀⣴⠇
⠀⠀⠀⠀⠀⣰⢻⣿⣽⡿⢿⣿⣿⣶⣟⣭⣥⢶⣻⣿⣛⠛⠋⢓⣦⠤⠶⣶⣿⣿⢿⣿⠏
⠀⠀⠀⠀⠀⢸⣼⣿⣩⠻⠿⠏⠉⠉⣹⣥⡤⠸⠿⠟⣿⣿⣿⣿⣿⣺⣿⣋⣽⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣧⣤⣄⣀⣨⣿⠀⠀⠀⠰⢛⡁⠈⡽⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡻⣶⣤⣾⡶⣏⢀⣰⣄⣩⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣷⣶⣄⣭⣻⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠉⠉⠀⠉⠉⠻⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢿⡄⠀⠀⠀⠀⠀⠀⠈⢯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠞⠁⠈⢹⣤⣿⣿⣿⣿⣶⣂⣤⢴⠶⠿⠾⣿⣿⣟⠛⠻⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡒⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢼⣿⣤⣾⡅⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢛⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⡛⣿⣿⣿⣤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣦⡼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣿⡏⣳⣿⣿⣾⣬⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣇⠹⠻
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣮⣝⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣿⣻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⣤⣿⣟⣿⢟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠞⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢷⣦⣶⡹⣧
⠀⠀⠀⠀⢲⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⢿⣏⣻⣯⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⡏⠻⠆⢹⡄
⠀⠀⠀⠀⠘⢿⡿⠻⢿⣿⣿⣿⣿⡿⢷⣾⣿⣿⢿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣱⣬⡀⠀⠀⠙⢂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⢷⣾⣿⣯⣿⣾⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣻⣽⠟⡿⢿⣷⣿⠟⠃⢀⠐⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠷⣾⣿⣿⣿⣿⣿⣾⣿⡇⢀⣀⣀⣤⠂⣠⡆⣰⡿⠻⣿⠿⠾⠿⢷⣦⣿⣤⣤⡼⣄⠐⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣿⣿⣿⣿⣯⢿⣧⣽⣿⣿⠛⣽⢟⣼⡿⣶⣿⣦⣾⠟⠁⠀⠄⠀⢀⠙⢿⣿⡿⣿⠀⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣿⣿⣿⣯⡙⣷⣿⣿⣿⣿⣾⣇⣿⣿⣤⣯⣄⠉⠀⠀⠀⠀⠀⡀⠈⡁⠀⢿⡟⠀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣇⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⢀⠀⠀⠀⠰⠀⠋⠰⠇⠀⣸⡷⠈⠿⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠆⡴⠀⠋⡀⠸⠃⡄⢰⡇⢀⠀⣰⣟⡼⠟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣏⠙⣠⠀⣾⠇⢠⡀⠃⠀⠀⣨⣾⡟⢻⣷⠿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣇⣈⣀⣿⣧⣴⡾⣿⣿⣯⣾⣛⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠿⣿⡆⠀⠩⣙⣟⢿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣟⣿⣿⣿⣽⣆⣾⠟⢂⣴⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣧⣼⢋⣴⣿⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⢠⠈⠻⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠈⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⢀⠀⢀⣀⢠⣶⣤⣤⣤⣤⡥⠘⠷⠊⠓⣄⡠⣤⣤⣀⣶⣄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠑⠋⠑⠖⢠⣬⡿⢻⣷⣤⢠⣌⣙⠛⠛⢿⣶⣭⣿⣿⣿⢿⣷⡟⠉⠣⠦⠘⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠐⠒⠛⢿⣦⠟⢿⡿⠻⠿⣛⡛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⠉⢦⠀⠁⢢⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⢬⠹⠟⠸⠷⠦⠆⠀⠀⠀⠀⠀⠀⢰⠀⣔⣠⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⡉⢠⣤⡄⢲⡆⠀⠀⠀⠀⠀⠀⠀⣻⣹⡿⡌⢉⢸⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡓⠀⣎⣛⢻⣄⣴⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⣷⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠺⣿⣹⣤⠙⠯⢷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⣿⣛⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢢⣤⣾⣿⡅⡼⣾⣷⣶⢶⡶⣤⣤⣤⣾⣿⣿⣷⣿⣿⣾⣿⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢟⢺⣤⡟⠃⠁⢠⣾⣿⣗⠺⠆⠘⢙⠯⣹⠧⢮⠫⣿⣭⣿⣥⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡑⢿⣟⣷⣠⣍⣟⠼⣻⣧⠷⠲⠅⢈⡁⠬⠨⣚⡃⢌⣽⣾⡿⣟⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣽⡎⠻⠯⢬⡞⠀⢙⣣⡼⣇⢴⣆⡹⣏⠣⢈⠘⣏⢵⠊⣭⣮⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣵⠌⣰⣛⡺⡎⣦⢒⡰⢃⡝⠤⡚⣈⢠⣩⢤⡞⣹⣧⣾⣵⣾⡟⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡟⣽⣣⣧⠡⢳⡄⣒⣹⠈⡂⠁⣄⢻⣶⣻⣾⣿⣹⣿⠿⠢⠍⠿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣵⡿⠰⢊⣀⠱⡖⣎⠉⠩⠽⢧⣾⣿⣿⣿⣾⠿⠛⠁⠀⠀⡌⠀⡻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠈⣐⡒⠜⡘⢿⣶⡈⡋⠙⢍⠀⢠⠀⠀⠀⠐⠁⢀⣰⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⢤⣤⣋⣠⡈⠥⠃⠀⠠⠔⠚⡗⢈⣭⣐⡘⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣾⣷⣦⣦⠨⣿⠻⢤⡤⠀⠘⠂⣐⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⠿⢿⣿⣶⣔⣣⣴⡶⢦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣀⡌⠀⠀⠉⠻⢿⣿⣵⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠈⠀⠀⠀⠀⠀⠀⠨⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡀⡠⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣅⡤⣀⣴⠟⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢉⡙⢶⢏⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣪⡵⣿⣺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢗⣈⣰⣿⣿⣷⣥⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠉⠀⢈⠓⣮⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠛⣈⣁⠀⡤⢼⣍⣌⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⢠⢂⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢿⢠⠀⡤⢀⠈⠀⢉⠾⠉⢿⠁
⠀⠀⠀⠀⠀⠀⡠⠌⡢⣠⡥⢟⠎⢊⡱⠰⠎⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⢋⣰⠂⠒⣀⣦⡝⡣⡂⡤⠞⡀
⠀⠀⠀⠀⠀⣒⣊⣱⡶⢛⡊⣠⠴⡟⢔⡂⠡⠊⠁⠙⢉⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⡱⢯⣍⠁⣈⠀⠤⠿⡎⠀⡥⡔⢧⡇
⠀⠀⠀⠀⠀⣍⢤⣿⠥⠐⡾⢓⢍⠞⠃⠀⠠⠀⠀⠀⢀⠁⠡⠿⠛⢷⠲⠶⣦⣤⢤⣦⢾⡿⢿⢳⣾⡑⠒⢌⡁⠤⢠⠶⠀⢘⣀⣂⣴
⠀⠀⠀⠀⠀⢠⠘⡗⢂⣹⣋⣅⡤⢉⠄⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣤⠀⣌⡁⢁⣘⣩⢟⢻⡿⢘⡉⠆⠡⢞⡁⢉⣨⠿⡏⢁⣸
⠀⠀⠀⠀⠀⠀⠆⠘⢉⣻⡄⣤⡠⠀⠀⠀⠀⠄⠂⠀⠀⠠⢀⡀⠈⠀⠀⢈⡷⠋⠅⠠⠁⣭⠢⡀⢈⡀⠀⡀⠒⢀⡁⢞⢳⠺⠛⢯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⡝⢳⣖⢀⡀⠐⠀⠀⠀⢠⣀⡈⠀⠘⠁⣈⡟⠁⠐⠀⠄⠀⠀⠁⠄⠈⡈⠓⠀⢁⢢⡐⢌⣡⣿⡀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣞⡼⣿⣡⠊⠀⠀⠦⣀⡀⠄⢀⠀⢼⣿⠾⡃⠁⣔⢂⠃⡀⠀⠀⠀⠠⣘⣷⣿⠀⢙⣠⠦⡌⢶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⣋⠐⠒⠀⠀⠂⢄⠸⠰⠠⡾⠁⣿⢠⢋⠜⠑⠧⢖⣂⣀⣲⡶⣟⡣⠴⠆⠘⣧⢔⢁⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢸⡧⡍⢠⡤⠀⣷⣂⡶⢬⡳⣬⡻⣷⣾⣿⣷⣾⠿⢻⠯⢅⣮⠔⠣⢀⠀⡀⢀⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⣶⠟⢷⡶⠿⠙⢧⡜⠛⠋⣹⣭⠉⢡⠟⡤⡳⢫⣔⠼⣧⣠⡉⠊⢔⣄⣈⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢶⡆⠄⢓⢁⠘⠐⠆⠀⡁⠈⡁⢀⡘⢆⢹⡲⠚⢱⡙⢎⠃⣼⣫⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣤⡈⠠⠚⠀⢤⠝⠀⠀⢚⠡⠄⠘⠚⣴⢯⣾⣶⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣯⣀⠒⠑⢎⡱⠄⠆⠺⡽⣶⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣯⠐⠛⠶⢏⢄⠳⣐⣶⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣓⠘⣋⢒⣳⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠟⠉⠀⢻⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣀⣀⡀⠀⠀⠀⠀⠰⠋⠹⠲⠿⠷⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⣿⠿⠖⣶⠶⠄⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡶⠿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⡛⢏⣤⣎⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠒⠱⣿⣦⣿⣴⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠁⠉⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡛⡛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⠁⠀⠀⠠⣴⣿⣷⣤⣀⣀⣀⣀⣠⣤⣤⣴⣶⣾⠿⢿⡏⠙⡷⢾⡿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠂⠀⢠⣼⣿⡿⠯⣽⣛⣲⡯⣽⣿⣛⣿⣿⣿⣭⣙⠛⣿⠚⢓⣿⢾
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⢠⣾⣿⣟⡛⣷⡿⠷⢞⣛⡾⢋⣉⠁⠀⡬⠛⠻⣿⣝⢛⣿⢃⣾
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⣿⡿⠃⠈⣹⣏⣛⣶⣯⠟⣹⣧⣶⣾⡛⢛⠛⢻⢿⣿⣏⣬⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣰⣿⣷⡶⣶⣿⡶⢿⣫⣿⣽⣟⠟⢿⡈⢙⣮⠤⠼⠃⠀⠘⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠈⠀⠀⠀⠈⠛⠛⣻⠿⡿⠯⠉⠀⠉⠁⠠⢄⡀⠈⠁⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⡠⡀⣀⣠⣄⡤⣤⣦⣄⡀⠀⢀⡀⢠⢦⡄⢿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣷⣷⣯⣬⣝⢹⣿⣇⠀⠈⣷⣠⡄⠈⠻⣿⣷⡧⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣼⣿⣿⣿⣿⣿⣿⡿⣿⣆⠀⡘⣿⣿⡁⠀⢻⡿⠿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠙⣷⣿⠆⠙⠒⠇⠷⠊⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⡽⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡷⣄⣸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⢁⢵⢱⠿⡀
⠀⠀⠀⠀⠀⢀⣎⡿⠷⡷⠦⣄⡀⢝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡻⢻⣶⡄⠈⣦⣇
⠀⠀⠀⠀⠀⠬⣔⣛⣯⡽⢛⣉⣉⣶⣄⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠟⢻⣿⣿⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⢻⠋⣄⣿⡿⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⢨⢶⣿⣿⣿⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠸⣠⣿⣽⣶⣺⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣠⡴⣟⠳⡗⢿⣿⣿⣿⡿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⢿⣎⢙⣻⠿⣷⣤⡤⠤⢾⢫⣽⣧⢱⣷⡛⣾⣿⣿⠛⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢋⣾⣭⣶⠿⣿⣾⣾⠋⠦⠈⠈⠀⠐⠻⢿⢾⢧⡺⣿⠋⢀⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣺⣟⣿⣿⣯⢾⣾⣿⣶⡆⠀⢀⡀⠀⠄⠈⣻⣶⣿⡟⠁⠐⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡟⠁⡢⠛⣿⣿⣿⣷⣟⣿⣿⣿⣾⣿⡿⠝⠁⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⢻⣾⡾⣠⣴⣿⣿⣿⣾⣿⣿⡿⢿⡟⠫⡀⢠⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠰⣰⢦⡔⢂⣄⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⢐⣡⣺⣷⢾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣇⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⢸⣟⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢪⡧⠒⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢩⣤⠊⠉⠟⠯⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡶⣤⠉⠛⢖⢺⠿⣶⡌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠙⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠁⣺⣆⡸⠀⢈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠛⠳⠏⠁⠀⠁⠉⡔⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠠⠘⠂⢀⠀⡄⠀⡠⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢚⡲⢦⣤⠁⠂⢠⡁⠀⠀⠿⡄⢠⠀⢤⠀⠀⠀⠀⠀⢠⣀⢀⠀⡃⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠠⢉⡤⠋⣀⠔⠀⠂⠐⢀⠔⡹⡊⠠⠔⠀⠀⠀⠆⠀⠙⠛⠓⢿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠠⠤⢄⠹⠄⣘⣳⠀⡄⢁⠈⡠⢁⠚⡠⠈⡁⠀⠀⠠⠀⠀⠀⠀⠘⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢈⡀⣉⣈⡃⠊⠄⠹⠐⡡⠀⠂⡖⢠⠃⠚⡀⠁⡠⡆⣤⠌⣢⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⢋⢯⠔⣊⣡⠐⢣⠄⠼⢡⠀⠨⠐⠀⠐⠋⣛⣖⣀⠀⣲⣯⣥⠴⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢙⣛⣃⣩⣍⡠⠠⠄⢀⠀⠀⠂⠀⠀⠐⠉⢿⣿⣣⣿⢱⢿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡗⠐⢂⣿⣥⡈⠤⢶⢧⣈⠐⠁⠀⠀⠀⠀⢀⠀⠙⢂⠛⢉⡍⢀⢼⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡓⠺⠭⠭⣢⠁⣀⠄⠐⠀⠀⡀⠀⠀⢀⠀⡅⠀⢚⠖⣩⢃⡴⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣴⡟⠃⣈⣠⢄⠀⠀⠀⠀⠀⠀⠌⠀⠰⠀⠡⠋⠡⣁⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣧⣴⣭⣴⣄⡀⣠⣛⣨⣌⣂⣥⠋⣠⣦⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⢿⡭⠟⢉⣱⣲⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠛⠛⣧⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣀⡤⡆⣰⢟⠩⠀⠖⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠀⠁⠀⢴⣩⠴⠶⡀⠀⣸⣧⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠣⠤⠖⢛⠛⡛⢠⠏⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣻⣛⣿⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠁⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠈⣿⣾⡊⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠆⠀⢤⣨⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠄⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡃⠄⢐⠁⠀⠀⡐⣿
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⢄⠁⠈⠈⠀⠀⠀⠄⣿
⠀⠀⠀⠀⠀⠈⣙⠯⣝⣷⠀⠹⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⠁⠤⠀⠀⠂⠀⠀⠀⠀⠚⢺⡀
⠀⠀⠀⠀⠀⠀⢟⢿⡇⠀⡀⠒⠀⢻⡶⠦⢖⣂⠂⠛⠛⢘⠛⢎⡣⠩⠇⠀⠀⢐⠀⠀⠀⢀⡀⠀⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠄⠖⡈⢋⡄⣀⠀⡀⢚⠁⡄⡀⠂⠑⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠂⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⣛⡟⠄⠉⠠⠃⠀⠐⠂⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⡹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⣹⠅⡂⡀⠀⠀⠀⠀⠙⠂⡈⠁⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠈⣷⡶⢦⠤⠚⢀⡆⠒⣠⢠⠄⠀⠁⠀⠉⠀⠀⠠⠀⠠⠀⠀⠂⡠⢀⡄⠀⠄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠣⣴⡂⢠⡴⠛⣉⣰⣥⣶⣾⣴⢶⣦⣿⡟⠿⡀⠀⠀⠀⠀⢊⢀⠨⡹⠓⢦⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⡻⣷⣾⠿⠿⠁⠡⠄⣉⣃⢺⠉⠓⣼⠂⠀⠀⠀⠀⠀⠈⣬⠁⢐⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣧⣿⡄⠀⠀⠀⠀⢀⠀⢄⡀⠀⠠⠠⠄⠂⠀⠀⡠⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⠀⠀⡀⠠⠀⠀⠁⠀⠁⢆⠀⠄⠀⢀⠁⣂⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠀⠄⠀⠶⠚⠐⠄⠋⠠⢤⠄⠀⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣆⡀⢀⣀⢄⢀⢐⢁⣸⣥⣕⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⢷⠟⠙⠛⢀⡝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢤⣾⣭⣓⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠿⠿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⢠⡶⡄⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⣠⢞⣉⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡙⢷⣿⡇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣿⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣦⣿⣷⡀⠹⣿⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⣿⣿⡿⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣌⠻⣿⣷⡀⠹⣿⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⠀⠀⠀⡀⠀⠈⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡙⠻⢿⣿⣦⡈⠻⣿⣄⠹⣷⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⡀⠈⠠⢄⡀⠁⠶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠛⣿⣿⣆⠙⢿⣧⣙⣿⡞⠶⠄⠀⠄⠀⠠⠄⠀⠈⠁⠀⠐⠂⠀⠀⣡⣤⠀⣸⢿⣿⣾⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣙⣿⡿⣦⡀⠻⢿⣷⣮⣿⡏⠉⠓⠀⣀⠀⠀⠀⢤⡀⠀⠘⠓⠀⢀⣸⣶⠞⠙⣿⣿⣧⣟⣸⢋⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣦⡉⠙⠿⢿⣿⣶⣌⡻⣯⠈⠙⢲⡶⠄⠙⠒⠀⠀⣴⠀⠀⠈⣳⠞⠋⣻⡿⣴⡞⢁⡼⠛⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣳⣤⣀⠉⠙⢿⣿⡟⠳⢤⣀⣙⣦⣄⣀⣀⠒⢺⡿⠛⣛⣻⣷⡞⠁⣈⡼⡻⣿⣧⣞⣠⡟⡽⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⣿⣿⣶⣤⣈⠻⢦⡀⠽⣧⣀⠈⠉⠉⣙⣻⣦⣤⡤⠖⢛⣿⣿⡏⢀⡴⠋⣻⠿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣍⡙⠛⢿⢿⣿⣷⣿⣿⣿⡛⠛⠓⠶⠶⠶⠾⢯⣀⣠⡤⠞⡻⢿⣿⣤⣾⢁⣴⢋⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣦⣤⣭⣉⣛⣻⣿⣷⣦⣤⣌⣉⣙⣻⣿⣯⣀⣤⡖⠋⢘⡿⣿⣿⣿⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣷⣴⣏⣘⣹⣃⣋⣿⣥⣾⠋⢙⣽⢶⣶⣏⣠⡞⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣧⣼⣏⣩⡟⠹⣿⠁⣩⣿⢶⣿⣁⣨⡟⢛⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣟⣻⡟⢻⡟⠛⣿⣁⣠⡿⠛⣿⣷⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣛⣿⣁⣼⣷⡾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠿⠿⠿⠻⣯⠾⣿⠷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠙⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠠⠴⢦⣤⠀⠘⢷⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡏⣩⣤⣄⡍⡍⠨⡿⡅⠀⠈⡷⠂⠀⢤⢴⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠚⠁⠀⠐⠒⠒⠐⣿⢞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢉⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢅⠓⢀⡘⢀⠄
⠀⡰⠁⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠒⠁⢁⠈⠁
⢀⠷⠄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣈
⡜⠒⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⢸⡀
⠱⡠⠀⠀⢀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠘⣆⠂⠀⠀⠀⠀⢄⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠈⠩⠋⠀⠐⠂⠀⣁⡀⣄⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡇
⠀⠀⠀⠀⠀⡂⠀⠀⣸⡅⠤⠄⠈⠑⠤⠀⣀⠤⠤⠤⡤⠤⠤⡤⠲⠅⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢀⠸
⠀⠀⠀⠀⠀⢨⠋⢠⠁⢀⡠⠰⠒⡀⠀⠰⢮⠁⠈⢈⡤⢴⠙⠶⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠘
⠀⠀⠀⠀⠀⠀⡁⠀⢉⠡⠀⡀⢎⠀⡠⠐⡠⠜⡡⠁⠰⠠⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠠⠎⠀⠀⠉⡐⠈⠀⠚⠃⠈⠀⠀⠂⢀⠄⢠⡐⠠⠆⣀⠀⠀⠀⠀⠀⠄⠰⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⢠⢀⠐⠀⠪⠐⠐⠀⢀⠀⢆⠐⠙⠒⠠⠅⠀⢠⠄⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠁⠀⠂⠁⠀⠀⠐⢁⣈⠀⡆⠙⠀⠙⠄⠀⠠⠁⠀⠁⠀⠀⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢄⣀⡠⠀⡠⠈⠁⡀⠁⠀⠀⠀⠐⠀⠄⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠀⠆⣀⡁⠀⠐⠅⢠⠀⠀⠀⠀⠀⡀⠀⠀⠄⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⠓⠇⠀⢀⠀⠀⠀⠱⠀⠈⠁⠂⠈⣠⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠠⠀⠢⢤⠠⠤⠀⠐⠋⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠑⢄⠀⠁⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠀⠀⠙⠦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠰⣇⣽⣭⡭⠆
⠀⠀⠀⠀⠀⠀⠀⢐⢁⡐⡈⢳⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⢷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⣔⠀⡕⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠁⠰⣄⡜⠂⢞⠒⢛⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⢬⣀⢄⣀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣈⢻⡣⠾⢖⢱⣤⠍⣤⠀⢄⣀⢀⡀⢠⡌⣻⠙⣒⠲⡖⢥⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠸⢛⣲⠖⡑⡾⠓⡴⢒⡟⢩⢳⠂⡸⣅⠻⣶⠽⣯⠇⣕⠚⠕⡶⢂⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣌⠓⢯⡩⡇⣈⣩⠉⠧⠎⣷⢒⣷⠏⣠⡟⣷⠲⣧⣉⠛⠶⠚⢚⣫⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⣶⡉⣋⢦⡝⡚⡒⠶⡤⣾⡠⢿⠥⠘⠳⡼⣩⢂⠚⢮⠿⢧⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⢭⣢⣻⠼⡟⣷⣷⣤⣍⡽⢶⣚⠯⡖⣧⠉⢷⢎⢓⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣟⡻⠛⠿⢿⠻⣫⣐⣫⣑⣞⣹⣽⣷⣉⣿⣤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⣟⣿⣒⡿⣂⣯⡭⣗⣺⣻⣟⣿⣿⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣷⣿⣴⣯⣾⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⠿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠉⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣷⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠋⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠙⠹⢶⣗⣌⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡚⠂⢋⣠⣌⠱
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⡿⢷⣦⣹⣞⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠀⠀⠀⠑⠦⣼⡿⢿
⠀⠀⠀⠀⠀⣿⢟⡁⠐⢚⠉⠘⠻⢿⣟⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠄⠀⠀⠀⠀⠀⠙⢡⠈
⠀⠀⠀⠀⢀⣗⢋⣴⢾⡯⣤⣴⣦⡀⠉⠈⣳⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⣾⣿⢟⣤⣾⡿⣿⣿⣿⣿⣄⣄⣹⣀⠀⠀⢀⣀⠄⠐⠅⡁⠉⡄⠐⡄⠀⠀⢠⠀⠈⢀⠰⡀
⠀⠀⠀⢠⣿⡇⣼⣿⣿⡾⠛⡉⠡⣬⣯⡶⠗⠺⠿⣿⣏⣿⠲⠆⡠⣻⠞⠇⢉⢈⠀⢳⡠⠢⠀⠀⠠⡇
⠀⠀⠀⠘⣿⣠⣿⡿⠁⣰⢿⣟⡖⣿⢃⣴⠖⢀⣼⡏⣠⠘⣓⣋⠔⢻⠊⠀⠃⡾⠀⢀⠃⠁⠂⠠⢀⠇
⠀⠀⠀⠀⠹⣧⢿⡇⢸⣇⣿⡘⣡⣿⡞⠁⣠⢾⡏⠀⢺⡓⣬⠬⠇⢎⣒⣆⡨⢾⢿⠏⡾⠨⠀⢀⠎
⠀⠀⠀⠀⠀⠈⠈⡇⢹⣿⣿⣿⢻⣿⡜⣠⠋⢘⡌⢳⡐⠦⠤⢭⣛⡸⢍⣛⣾⠟⣫⡾⠃⢰⣤⠋
⠀⠀⠀⠀⠀⠀⠀⢇⡞⣿⣿⣿⣿⣿⣵⣿⣾⠿⠟⢶⣦⣟⣷⣼⣷⣷⣶⣷⣾⣿⣿⢷⢳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⡿⣿⣿⣿⣿⢃⠀⠄⢀⠄⠈⢁⢺⣹⣿⣿⣿⣿⣿⣿⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣥⠟⢿⣿⡿⢿⣟⡲⣈⣑⠒⣛⣾⣿⣿⣿⠿⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⠁⠀⠙⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡭⠟⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣄⡀⢀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣞⢮⣉⠛⢈⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠿⢰⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠂⢠⡑⠎⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠉⠀⠀⠐⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡆⠀⠀⠀⠀⠀⠀⣀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⣉⣿⡃⠀⢴⣶⣶⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⡇⢈⣁⡄⠀⢿⡀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠟⠀⢻⣿⣿⣇⠈⣿⠆
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡏⢶⠖⢻⣿⠛⣿⡟⢻
⠀⠀⢀⣀⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠾⠧⣁⢀⡐⠃⢿⡧⣄⠐⢉⣶
⠀⠀⠣⢈⡁⠠⠄⠀⠀⠀⡀⠀⠰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠰⠆⠉⠘⡷⠗⡶⢀⠙⠛⠈⣋⠃
⠀⠀⠀⢰⠇⠀⠠⠶⠄⠀⣭⣀⡀⠙⠶⢅⣛⠂⣐⠰⠂⠀⣤⣤⣀⣀⢀⣠⣄⠀⠀⠰⠀⠀⠀⠇⠀⠣⠀⢀⠁⠘⠧⡤⡤⠀⢠⣄
⠀⠀⠀⠈⠀⠀⠲⠒⠀⠲⣀⡀⠈⠁⣄⠀⡀⠀⠈⢘⢂⡈⢹⣤⣛⢛⣦⠛⠡⣤⢀⠀⣰⠈⠄⢠⠀⡼⠀⠈⠳⠄⠠⠂⠁⠐⣾⡇
⠀⠀⠀⠀⠀⠀⢰⣤⠄⠊⠨⣑⡉⣄⠀⠂⢁⡠⣷⣶⢞⡡⣤⠄⠃⠘⠅⠟⠠⠂⢙⢠⠏⠠⡆⢸⡖⢰⠁⠀⠀⡄⠀⠐⠰⡾⠟⡹⡀
⠀⠀⠀⠀⠀⠀⠳⠃⠀⠐⠒⡎⠱⢤⣧⠔⣯⠁⠮⢠⡏⣘⡿⢶⡀⠈⠚⣹⠃⢉⣉⣁⡸⠀⠿⠾⠠⠈⠄⢐⠈⢡⡴⠀⠰⠙⠂⡃⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣯⡽⠞⣡⡄⣸⣿⣸⡦⢾⠷⢉⣽⠾⡝⠩⣼⠋⡙⠃⠀⢁⡀⠀⢀⠀⠀⠈⡀⣡⠼⠀⢠⡘⢇⣠⣂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠉⠤⠁⠚⣷⣾⠿⣿⠟⢀⡴⢛⣓⠿⢀⡄⠡⠄⣉⠈⠁⠛⢀⣀⡠⡀⣀⠄⠉⠀⠀⠘⠏⣤⠸⡇⠱⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠫⣤⣴⢓⣷⠛⣇⣿⡍⣁⣤⣤⣆⣈⠩⡖⢫⣧⣤⡉⢄⣤⠾⢤⡖⢀⠲⠁⠚⠁⢒⣸⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⣀⣿⡶⠚⠋⠈⠠⠾⡛⠻⢿⣿⣾⣿⡟⣋⠙⠳⣤⣰⢭⣿⡿⢿⠙⠁⠰⠗⢸⠇⣤⣄⣸⢎⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠹⢿⡟⠂⠀⢀⡌⢀⠉⠂⠀⠉⠉⠉⠙⠉⠑⠛⡍⠙⠂⢤⢀⡉⠳⠀⠐⠠⡖⢂⠇⠨⢭⡟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠂⠀⠀⣽⠉⠁⠤⠕⠀⠔⠃⢐⡀⠁⠀⠀⢀⣠⣤⣤⣁⣠⣉⣀⡀⣀⣁⣸⣀⣀⣸⣼⣧⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣀⠉⠀⠙⢁⡄⠀⠈⠅⠂⠘⠦⠶⠉⠁⠀⠁⣉⣉⣉⠉⣍⣹⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠙⢋⣭⣤⡎⠀⠀⠀⡠⠀⠈⠶⡦⢘⣛⡋⣀⣟⡉⡛⢛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠤⣫⣄⠚⠃⣮⢤⣌⣸⠊⢛⣿⠿⠻⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢀⡿⣿⣵⢋⠸⣿⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⣿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⣲⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⣿⣡⠇⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⠉⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⠚⢻⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣀⡞⠀⠀⠀⢀⠀⡺⠁⠀⢄⣀⡀⣀⠀⡀⠀⠀⠀⠀⠀⢀⠠⠊⡠⠘⠂
⠀⠀⠀⠀⠀⠀⣀⡄⢈⡀⠀⢀⠀⡠⠤⠼⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢀⠤⡀⠀⢀⠠⠊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⡡⠄⠂⠁⠀⠄⢀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⡀⠀⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠦⢀⡀⠀⠀⠠⠀⠀⠀⣀⡠⠖⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡲⣶⡵⠞⠣⢀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⠭⡿⡏⠱⣿⣿⡷⠼⠻⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠲⠓⢚⡩⠶⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢣⠔⠋⠑⢆
⠀⠀⠀⠀⠀⢀⠤⠤⢄⣸⠀⡠⠀⢀⠀⠀⠀⠀⢸⡀⣀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⠀⠁⠀⠀⢦⠊⠑⠀⢀⠀⠈⡆
⠀⠀⠀⠀⠀⢧⠀⠀⠐⠀⠢⡄⠀⠀⠈⠀⠀⠋⠀⠐⣰⠁
⠀⠀⠀⠀⠀⠘⢆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣀⠑⡄⠀⠀⠀⠀⠀⠀⠔⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣂⡤⠒⠈⠉⠙⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠀⡤⡀⢨⡀⠀⢀⠤⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣴⡄⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠳⣼⢠⠀⢠⠘⡇⡴⠋⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⠗⢠⠐⠒⠒⠄⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⡈⢰⠀⠈⠰⠏⠔⠀⡈⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣦⠀⢰⢦⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠀⠈⠆⠀⠀⡧⠊⠀⡐⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠉⠁⢀⠟⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡥⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠤⢤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠴⠚⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⠖⠋⢩⣀⣠⠤⠢⣄⠀⠀⠀⡔⠢⣄⠠⠋⠀⣠⠞⡕⠈⠉⠓⠲⠤⠤⠤⠤⠤⠶⠖⢛⠀⠀⠀⠀⠒⠂⢸
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⠒⠊⠀⠀⠀⠀⠀⡔⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠘⡄⠐⠠⠂⠀⡀⢸
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡆⠀⠄⠄⠀⠀⠠⠔⠀⠀⠀⠀⡞⠀⠃⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢃⠀⠀⠀⠈⠀⡘
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠢⠔⠀⠀⠀⠒⠂⠀⡆⠀⠑⠒⠀⡁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⢲⠄⠀⠀⠀⢣⠐⠤⠂⠀⠀⠐⠤⠀⠀⠄⠀⠘⠢⠤⠔⠊⡇⠸⠀⠀⠀⢀⠜⠢⡀⠀⠠⠀⡎⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⠴⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠢⢀⠠⠂⡴⢄⠀⠉⢀⡜⠁⠀⢀⡄⠀⡆
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠠⠀⠀⠀⠘⠦⣀⣀⡤⠞⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠉⠃⠂⢹⠀⠀⠀⠹⡄⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⢀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢈⣦⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠉⡟⠀⠀⠒⠒⡏⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠇⠀⠀⠀⠀⡇⢰⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣄⠀⠀⠀⣠⠅⢜
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡮⠞⣲⠞⠷⠰⠿⠚⡇⡶⣵⠄
⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣼⣶⣷⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣯⡉⠬⢉⡁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠝⣱⣦⣴⣌⣳⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠀⠰⣿⣿⣿⣶⣿⠋
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠀⠀⠀⠀⠀⠀⠹⣎⣩⠞
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣤⣙⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠂
⣼⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡎⠀⠁
⢻⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣥⣶⢶⣣⣿⣹⣿⢋⣭⡃⢀⡀⠀⠀⠀⡀⠠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠸⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢅⣽⣿⣟⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⠻⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡿⣿⣿⡏⠀⠐⠈⠠⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠾⠢⢄⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⡞⢀⣴⠀⠀⠀⢠⣾⠀⢀⠀⣤⠒⡞⡠⣠⡄⠀⠀⢠⡀⠆⠉⠞⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⠿⣇⣸⣽⣿⣿⣤⠸⣏⣻⠸⣿⣟⣸⣥⠾⡷⢫⣥⠘⣺⡇
⠀⠀⠀⠀⠀⠹⣿⠛⠙⢻⠛⠁⢻⣿⣿⣿⣿⣿⡿⢧⢀⣴⣾⣾⡿⠿⠈⣷⡄⠻⣿⣿⣿⣿⣡⣘⠣⠚⠋⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⢧⠀⠸⠋⠁⢿⣿⣿⣣⣏⣼⣿⣿⣿⣏⠅⠠⠀⡟⠻⣷⣬⣟⣉⣉⡁⣤⠐⣋⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠙⡿⣿⣿⣿⣿⣿⠟⢂⣴⢞⣡⠤⠀⣈⣿⢻⡋⢁⡈⣥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢿⣟⠭⠶⣛⣥⣵⣾⣿⣿⣿⣿⢣⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⠓⠉⣻⣦⠳⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡄⠀⠓⢶⡃⢀⠀⢏⣿⣾⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣠⣴⣿⠥⣤⣂⣀⣽⡃⠀⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣼⢀⣺⠒⢭⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡀⠼⢆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡀⠀⠙⠻⣟⣫⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠶⡌⣆⢨⢧⡀⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠐⣌⠀⢢⠁⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣦⢐⡜⠆⣬⠧⠶⠺⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⣈⠁⢀⢀⢀⣜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠖⠈⠻⢧⡮⠠⢭⣄⢋⡃⠔⠧⢀⡀⠀⠀⠀⠀⠀⠀⢀⠰⢾⡗⡤⣉⣉⢀⡝⠋⢮⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡇⠈⣆⣉⣭⡗⢒⣊⢭⠤⢿⡇⢈⠲⢶⡔⢶⡄⠹⠦⣞⣥⢸⡶⢈⠴⡀⢛⡆⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢃⣩⡽⠋⣄⢩⠏⢹⣖⣋⣽⠋⣱⠼⡇⢀⡻⣦⠈⢛⣷⢚⠷⠞⠄⣋⠉⠆⠙⡞⢀⡋⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠹⠸⠧⣉⡩⠀⣉⣩⡉⠔⣴⢊⣿⠒⢚⣲⡿⣁⣬⠋⣷⠞⣾⣨⠉⠋⢲⡶⠓⠢⢃⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣾⢈⣡⠞⠚⠏⣹⢰⠦⠶⢴⣤⣄⣉⡽⢔⣩⢟⡋⠩⢧⣌⡝⢋⠅⡢⢶⣸⣞⣯⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣟⢛⣴⢶⡎⢻⠜⣤⣧⣈⣹⡉⠛⢯⠴⢿⢉⣠⣤⣋⢡⡟⠲⣧⢈⡟⣌⣉⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⡟⣾⣭⢦⣽⣹⣖⣾⣾⣿⠗⣣⣶⠛⣯⣤⡇⣻⠀⣿⡀⡋⢟⣔⣩⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣽⣋⣭⠙⠛⢿⢿⡓⢏⣇⣉⣩⣅⣭⣉⣭⣷⣿⣞⣩⣿⣧⡭⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣟⣿⣷⡷⣺⡧⠴⣿⡂⠹⣏⣙⡣⢒⡚⢛⡿⣿⣿⣿⣿⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣻⣷⣞⣩⣞⣠⠿⣫⣿⣯⣿⣯⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠿⣿⣿⣿⣿⣯⣿⣾⣷⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢮⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⣿⣿⣿⣗⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠈⠉⠉⠉

⣀⣠⡅⠀⠀⠂⢀⡀
⡟⠛⢡⣼⡄⣼⡏
⢦⡜⠓⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢸⣿⡆
⠘⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣿⣧⡀⠀⠀⢠⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⠿⠷⠀⠀⠈⠿⠃⠀⠀⠀⣨⣿⠀⠀⠀⢀⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢠⣾⣿⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠋⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⡀⠀⠀⠀⠠⠄⠋⠉⠀⠀⠐⠲⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⠗⠀⠀⠘⠀⠀⠀⠀⠄⠈⠂⠂⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠂⣀⣀⡿⣶⣦⠹⣶⢀⠀⠀⠀⠀⠀⢄⡀⠀⢀⠀⠆⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠠⠄⠀⠈⢿⣀⡘⡤⡦⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡄⠆⢠⡄⠀⠉⠻⠇⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⣟⣻⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣶⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⣄⠀⢸⣿⣿⣿⠸⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡟⣿⣾⣿⣿⣿⡿⠀⠙⠻⢿⣿⣷⣾⣿⣻⣿⣿⣿⣿⣬⣉⣼⣿⣿⣿⠟⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣿⣿⣿⢻⣷⠸⣿⣿⣿⡟⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⡿⢿⣿⣿⣽⣿⡟⣩⣵⣿⠀⢸⣯⡿
⠀⠀⠀⢀⣤⣾⣿⣿⠿⢋⣿⣿⡏⣸⣿⡆⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣍⠛⣋⣭⣵⣶⣿⣧⣤⣿⢿⣯⣿⣭⣧⣾⡟⠁
⠀⢀⣴⣿⣿⣿⠟⢀⠴⣻⣿⣿⣇⠹⢿⠟⠀⣿⣿⣿⣿⣿⣧⡿⠿⠿⢿⣿⣷⣿⣼⣏⠉⠛⠯⣍⠀⠈⠉⠈⣿⣿
⣴⣿⣿⣿⡿⠏⢀⠓⢈⣿⣿⣿⣿⣿⣶⣄⠀⣼⣿⣿⣿⡿⣉⣤⣾⣿⣷⣿⠿⣡⣦⣿⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⣿⣿⣻⠟⠁⠄⠃⣰⡟⣱⢟⣿⢿⣿⣿⣿⡄⣿⣿⠟⣉⣴⠋⣼⣿⣿⣿⣿⣄⣼⣿⠛⣿⣷⣶⣄⡀⠀⠀⠀⠀⢿⡇
⣿⢷⡟⠁⠀⢠⡾⢫⠘⣁⠋⠀⢈⣿⣿⣿⣿⡟⢡⣿⣿⢁⠈⣿⣿⣿⡾⠁⠛⢿⣿⣆⢹⣿⣿⣿⣿⠑⠒⠦⢄⣘⡇
⠻⠆⠀⢀⡼⢋⡔⠃⠀⢀⡞⠀⢸⡇⢸⣿⡿⢡⣿⣿⣯⣾⢠⣿⣿⣿⣷⣈⣧⡾⣿⡿⠂⣿⣿⣿⣿⣿⣦⡄
⠁⢀⠀⠉⢠⠊⠠⠀⣠⣿⠂⠀⠏⡇⣸⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡇⣼⠟⢻⡗⠛⣿⣿⣇
⠀⠀⠀⠀⠁⠠⠀⣴⠛⠏⠀⢠⢰⡇⣿⣿⠀⠹⣿⣿⣿⣟⡿⠉⠈⣿⣿⣿⣿⣹⡿⣱⣿⣿⡟⠁⠀⠙⠿⠸⡀
⠀⠀⠀⠀⠀⠀⠸⠃⢺⠀⠀⠀⢈⢀⣿⣿⣷⣀⠛⠿⣿⡟⠁⠀⠀⠀⣿⣿⣿⢹⣷⣿⣿⡿⣟⡀⠀⠀⠘⢶⡇
⢠⡎⠀⠈⠀⠂⠀⠀⠘⠀⠀⠀⠀⡼⢯⢹⣿⣿⣷⣤⡘⡌⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣷⣿⣧⠀⠀⠀⡼
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣿⢱⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠸⣿⣿⣿⠧⢼⣿⣿⣿⣿⣿⠀⠀⢐⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣤⣸⣿⡿⣎⣃⣼⢿⣿⣿⠟⢡⠂⣠⠎
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣇⣀⣿⣿⣿⡿⣿⣇⢡⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣫⣟⣚⠿⠄⣃⣠⡟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡟⢹⣿⣯⣿⣿⣿⣧⣾⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⡡⢴⣵⠟
⠀⡀⠀⠀⠀⢠⣿⠀⣿⣻⣷⣿⣧⢿⣿⣿⣿⡿⣠⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣩⣴⠟⠁
⠀⠁⡄⢰⢀⡿⣿⠀⣷⣾⣧⣿⣿⣾⣿⣿⣿⣟⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⢀⡄⣵⣾⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⡗⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠀⣿⢿⣿⣿⣿⣟⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄
⠈⠠⣿⣼⣯⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣸⣿⠇⣻⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⣤⠒⠁⠲⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⡇⢀⠄⠠⡀⠀⠀⠀⠀⣇⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⠁⠈⠀⠀⢱⡠⠊⠆⠀⠉⠈⢱
⠀⠀⠀⠀⠀⢇⠀⠀⢠⠒⠤⡀⠀⠀⠀⠃⠀⠰⠂⠉⡆⡸
⠀⠀⠀⠀⠀⠈⢆⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡰⠁
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠐⡄⠀⠀⠀⠀⠀⠀⢀⠔⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡈⠠⢀⡠⠄⠒⠒⠦⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡀⠀⠃⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠢⡀⡇⠘⠈⡀⢸⠀⡠⠎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣤⡄⢀⣀⡀⣌⠛⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠇⡇⠀⠇⢸⠔⡡⠐⠂⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠀⢧⠀⠀⣨⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠇⠑⢄⠁⠀⢠⢈⠌⠀⢠⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡜⠳⠤⠏⠑⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡠⠀⠈⠀⠀⠘⠁⠀⠠⢂⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠣⠤⠤⠤⠚⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣡⠀⠀⠀⠀⠀⡠⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠉⠉⢀⠞⡲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠦⠔⠒⠉⠑⢄⠀⠀⡼⠉⠑⠂⠚⠁⢀⠔⠡⠊⠀⠀⠀⠉⠁⠒⠒⠒⠂⠉⢋⠈⡄⠀⠀⠀⠈⠉⠀⡇
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢠⠋⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢱⠀⠁⠊⠀⡠⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢃⠀⠒⠐⠀⠀⠀⠐⠁⠀⠀⡀⢀⠃⠀⡁⠀⢀⡀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⠘⡄⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠒⠁⠀⠀⠀⠉⠀⠈⡄⠀⠈⠉⢀⡀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢩⠆⠀⠀⠀⠈⡄⠑⠊⠀⠀⠀⠑⠊⠀⠐⠔⠀⠈⠒⠒⠊⠁⡇⠸⠀⠀⠀⢀⠎⠑⠄⣀⡠⠃⡸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢱⠀⠀⠐⠀⠂⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⠤⠔⠁⡜⠢⣀⠀⣀⠴⠁⠀⠄⡠⠀⡸
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡀⢀⠀⠀⠄⠄⠀⠂⠐⠀⠀⠀⠈⠢⠄⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⡇⠀⠀⠈⢣⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⢀⡱⣄⠀⠀⠀⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⡇⠀⠒⠒⠒⡏⠉⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠸⡀⠀⠀⠀⢀⡇⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠵⣴⠮⣲⢠⡚⠵⡆⡮⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠀⠀⠀⠀⠀⠛⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣰⣷⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡴⣿⣽⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠃⢀⠉⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⠴⣥⠇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠳⠀⠀⡀⠀⣠⠬⡎⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣇⣻⡷⡖⣆⢿
⠀⠀⠀⠀⠀⠀⠀⢘⡅⡓⠀⠀⣤⠁⠁⣰⠀⠙⠏⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢭⣿⣽⣿⠁⡛⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⣇⢀⡀⡁⠀⠀⠒⠀⠀⣰⠶⢤⣁⣀⠒⠒⠂⠒⠉⢗⣋⣼⡿⣨⡄⣠⠁⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣤⠉⡰⡀⡈⠑⡲⠀⢉⡵⠂⠰⠎⠉⢉⡀⠠⠴⣸⣿⣋⣾⣟⡽⠋⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣝⣛⣀⢠⠃⢨⣤⠶⠚⢀⠀⠀⣠⠆⠉⠁⠀⡠⠃⠋⠛⢻⣏⠈⠁⢀⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣾⣦⠘⡃⠀⣄⠀⢋⠈⠀⡁⠐⣏⠀⠀⠄⢀⠐⡷⢣⡇⡰⠀⢀⡰⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣏⣿⣿⢣⣦⡛⣺⣿⣦⡁⠀⣤⡖⢚⣋⡴⢉⡄⢠⣧⢋⣥⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⣿⠶⠟⢫⣿⣞⡭⠟⣿⣬⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣌⣡⣿⡀⠀⢠⣍⣙⢗⣢⣿⣽⣿⣗⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣯⣼⣿⣿⣶⣴⣦⣽⡿⢻⣿⣷⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠌⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢺⡆⡥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣤⣢⠚⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣥⠆⠘⠿⢀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠘⣧⡀⣈⣰⠁⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡉⠵⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⠰⢈⠖⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⡡⠤⠀⣤⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠀⠲⠀⠀⠀⠀⠀⠀⠢⠄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢿⠶⢎⣀⡔⠀⠧⠒⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⡃⠑⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠂⠐⠒⠒⠒⠈⠁⠀⠀⠀⡀⠀⠩⢶⡆⢐⣀⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡑⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⣌⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠄⠃⠀⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠘⡂⠀⠀⠀⠀⠀⢀⠀⢠⢹⠀⠀⢀⣀⡀⠀⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢧⢬⣬⡷⢽⡦⠬⠶⢿⠿⠾⠑⣬⡀⢸⣖⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⠀⠉⠴⢦⣴⣠⣄⢀⣽⠍⠀⢽⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⡀⠀⠐⠀⠀⠰⠒⠂⠙⠸⡦⠳⠄⠘⠦⠄⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠴⣤⣀⡀⠈⡄⠐⡀⠠⠄⢀⡂⣄⢠⠔⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢳⣶⡆⠀⠠⠀⠠⡅⢬⣧⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠞⠉⠛⠒⠒⡾⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣴⠏⢠⠃⠀⠀⠀⠀⢸⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠮⠽⠯⠉⡥⢞⠀⠘⢦⣀⢀⡀⢀⠓⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢠⣈⡭⠩⠭⢕⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡤⢲⡸⠄⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣧⠉⠀⠀⠀⠀⠀⠀⡀⣀⢈⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠄⣀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠎⠄⠀⠀⠄⠠⠄⠌⠠⠟⠂⠀⠀⠀⠰⠤⠄⠤⠄⠀⠀⠢⠄⠠⠤⠠⠄
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⢠⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠚⣥⡴⠊⠹⠿⢏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠀⢸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⢦⡙⠚⢷⡔⣺⢿⣦⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠙⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠠⣿⡅⡏⠀⠙⣗⠐⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠃⠀⠀⠄⠘⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⠲⠾⡿⠟⠀⠔⠈⠋⡆⠐⡀⠀⠀⠀⠀⠠⠘⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡖⣃⣁⠶⠀⡀⢤⠃⠀⣁⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⡀⢀⠰⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠶⣤⣀⡰⠀⠒⢪⠃⠈⠀⣷⡀⢀⠀⣀⠈⠂⠀⠀⠀⢀⡀⢀⠀⠰⢠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⣝⠳⡹⠟⢀⡤⠜⠄⠠⢀⡠⢧⠜⢀⡨⠀⠀⠀⣄⠀⠚⠿⢶⣶⣾⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⣀⣉⠁⣎⠉⠴⣞⠀⡰⠊⠐⢀⠃⠴⢀⠀⠂⡄⠀⠄⡀⠄⠘⠠⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠁⠀⠈⠣⠨⠚⢻⡇⠔⡁⢾⡠⢃⠘⠀⣡⢂⡬⢰⠀⠀⢁⣠⢡⢀⢦⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⢿⣒⣩⠿⢂⣰⠅⡀⣠⢇⠈⢴⠹⡈⠠⠴⠶⣤⠜⠉⠸⡿⢾⣁⣾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠉⣯⠴⠾⢿⠄⣋⠉⠁⠘⠀⠨⡄⠠⠀⠀⠞⢿⣿⣶⢰⡿⣟⡧⡾⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡈⣠⢫⡿⡓⠒⣛⣛⠇⠙⠠⠖⠀⠇⠀⠆⠀⠀⠠⡌⣿⡿⢻⠃⣋⣿⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡄⡾⠿⠗⣩⠁⠍⡉⢂⠀⠀⠐⢀⠀⢀⠀⡆⠄⢱⣦⠶⢿⢀⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣫⣭⣽⡏⠜⠋⠅⡀⠠⠀⠂⠀⠀⡰⠆⠛⡆⡜⣭⠾⡶⡛⣱⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⣴⡚⣚⠵⢀⡀⠀⣀⣤⠠⠥⡎⠔⢡⠈⠠⢎⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⡿⣷⣶⣾⡶⣾⡷⠖⣻⣣⣾⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⠛⢯⣭⣤⣾⢗⡻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣇⠀⠀⠀⢉⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⡀⢀⣼⡿⠗⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡀⠢⠶⢻⠃⡾⠳⠙⡀⠋⢸⡧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣀⠀⢀⡂⠻⠖⣛⣋⣤⠀⣼⠗⠂⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠙⠛⠋⠩⠉⠉⡰⠃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠉⠉⠉⠉⠉⠉⠒⠠⠖⠛⠀⣀⣼⣧⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢲⡄⢀⠀⠲⠄⠛⢦⣴⠀⢀⣾⠏⢠⡖⣿⣧⣴⣿⢯⠋⣿⣯⢱
⠀⠀⠀⠀⠀⢸⣷⣶⣖⣺⣙⢛⡙⢳⣦⣀⢀⣀⣰⡞⠉⠉⠉⠀⠀⠈⠛⠿⠿⠿⠋⠀⡻⣿⣞⠔
⠀⠀⠀⠀⠀⠀⠹⢿⣫⣽⣿⣷⣶⣾⣾⠻⣿⣾⠋⣠⠔⡶⠛⠙⠛⠛⠛⠓⠒⠦⠤⣄⣀⣠⠤⠒⠒⣿⣆
⠀⠀⠀⠀⠄⠀⠀⠀⠙⠿⣿⣿⣏⢹⣷⣀⡿⠁⣼⠁⣾⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⢜⣿
⠀⠀⠀⠠⠀⠁⠀⢀⠐⠀⠈⣙⠻⠷⠾⠋⠀⢸⣿⣧⣵⣽⡆⠀⠀⠀⠀⠀⠀⣠⣰⣴⠾⠿⠿⠷⠶⠞⠛
⠀⠀⠀⠀⠀⠀⣴⠁⠠⠐⠠⠀⠄⠐⠀⠂⠀⠈⡿⣿⣿⣏⣛⣦⣤⣤⣶⣴⡟⠋⠁⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣶⣴⠂⠀⢰⠒⠒⢲⡖⠀⠀⠙⡿⢾⣗⣪⣻⣽⣭⡵⡾⠉⠀⠀⣀⡈⠭⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠉⠁⠀⠀⠀⠻⠷⠛⠉⠉⠁⠀⠀⠀⢀⠉⠉⠀⠁⢀


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

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⣾⡲⠾⠲⣄⣀⡀
⠀⠀⠀⠀⣠⠖⠋⠋⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠃⠀⠀⠀⠀⠉⠁⠙⡆
⠀⠀⠀⣼⠉⠐⣄⠀⠀⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠽⠂⢀⠌⡁⠒⠄⢀⣼⠃
⠀⠀⡾⠉⠱⡄⠘⡆⠀⠰⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠐⠀⣉⠀⠴⢿⣿⡧
⠀⠀⡷⡀⠀⠘⠄⠘⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠸⡄
⠀⠘⡇⠈⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢢⡤⠞⠚⠁
⠀⢀⡟⢦⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠘⣇⠀⠃⠀⠀⠀⠀⠀⢄⡈⠉⠛⠒⢦⣤⡤⠖⠒⠒⠒⠚⢁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠣⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠐⠒⡒⢙⣃⣀⣠⠄⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡀⠀⠠⠶⣶⠚⠓⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢠⡖⠻⢤⡀⠰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⡀⠀⠹⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣄⠀⣷⠀⠈⠓⠒⢒⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠙⠋⢐⣲⣄⡐⣦⢭⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⠖⠦⣄⡠⡤⢭⣉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⢆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠃⠀⠀⡆
⠀⠀⠀⠀⡜⠁⠈⠙⠁⠀⠀⢡⡀⠂⠀⠉⠙⡆
⠀⠀⠀⠀⢃⠀⠀⠀⠠⠀⠀⠀⠁⠀⠂⠉⢠⠃
⠀⠀⠀⠀⠈⢆⠀⢀⠀⠀⠀⠀⠀⠀⢀⢠⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⡀⠄⢤⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠁⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠃⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣤⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⢄⡇⠀⠀⠰⢠⠊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⡔⠒⠲⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢈⠁⠀⠀⠸⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡵⢄⡜⠢⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠑⠀⠐⠂⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠦⠤⠤⠊⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠄⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⢀⠔⠊⠘⣄⠤⠒⠢⡀⠀⣠⠒⠦⠠⠃⢀⠔⠁⠀⠈⠑⠂⠠⠤⠀⠐⠂⢻⠀⠀⠀⠐
⠀⠀⠀⡔⠁⠀⠀⠀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠈⠀⠄⠗
⠀⠀⠸⡂⠀⠀⠀⠀⠃⠀⠈⠀⣀⠀⠀⠀⠠⠀⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠑⢠⠀⠀⠀⢘⠀⠠⠀⠀⠀⠀⠀⢀⠀⠱⢤⠄⠄⡆⠀⠀⠀⠀⠰⢀⠀⠀⠄⡄⠀⠀⠀⢠
⠀⠀⠀⢀⠂⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠠⠊⡰⢄⠈⢁⠔⠀⠀⠀⠀⠆
⠀⠀⠀⠘⢄⣀⣀⡀⠀⠘⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠊⠳⢄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢹⠀⠀⠀⢸⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠀⠀⠀⠸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⣸⣦⣀⣤⣮⢈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠃⠈⠀⠁⠘⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢈⣰⡟⠛⣷⣦
⠀⠀⠀⠀⠀⠀⣀⢁⣤⡁⣶⢓⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣿⡟⠛⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⣬⣧⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠳⣆⣼⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠄⠀⢀⣼⣿⣿⣛⡿⢭⣟⣿⣿⠿⣿⣿⣟⡓⠶⣷⠴⠧⣾⣵
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⢠⣾⣿⡛⢶⣾⠯⢿⢓⡶⢛⡙⠋⢈⡹⠛⣧⣝⠒⣾⢋⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⣿⡟⠋⢙⣟⣛⣶⣮⠽⣱⣯⣶⣖⠒⡺⠻⣿⣿⣏⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣴⢿⠷⠶⣾⣷⣻⣯⣿⣿⣟⠛⢧⡈⣱⡥⠬⠃⡀⠘⠟⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠉⠛⠹⠟⠿⠏⠁⠀⠁⠀⠠⡄⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡔⢄⣤⠶⠴⣶⣿⣶⡄⠀⢠⡀⠒⠲⡸⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⢿⣿⣿⣷⣶⣬⣿⣷⡀⠘⢷⣰⣀⠈⢻⣿⣷⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⢿⣟⣯⡛⢷⣀⢞⣿⢷⣄⣤⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠀⠈⠁⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠋⠈⠂⠀⠀⠀⠀⠀⠀⠀⠠⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣦⣄⡀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢡⣿⣿⣻⣿⣿⣿⣿⣿⣿⠏⣾⣿⡟⠋⠀⣠⣦⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢣⣿⣿⣿⡿⣿⣿⣿⣿⡟⠁⣼⡿⠛⠀⢀⣄⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⢹⣯⡙⠛⠁⣈⡀⠀⣉⣠⣤⠟⠀⠀⡀⣎⣽⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⢫⣄⠐⠏⡉⢐⠶⠀⠌⠁⢨⣬⡝⠁⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠟⠋⠐⠀⣤⡶⣤⠀⣌⡉⠰⢋⡠⠶⢶⠋⠀⠀⠴⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠓⠀⠀⢛⡟⠀⠉⠉⠉⢹⣾⡻⠀⣀⢰⣄⣶⣦⣀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⡀⠀⠹⣿⠀⠀⠀⠀⠀⢸⣿⠃⣰⣿⣷⣿⠛⢀⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣛⣉⠁⠴⢶⡇⠀⠀⠀⠀⠀⢳⣶⣾⣿⣤⣍⣠⣴⠏⣸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡋⠂⢀⢸⡆⠀⠀⠀⠀⠀⠀⠋⠙⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠿⠛⠃⠉⠈⠀⣸⠄⠀⠀⠀⠀⠀⠀⠐⠾⠾⠿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⡷⢛⠋⠠⠔⢻⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠃⠘⣯⠀⠀⠀⢻⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡇⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⠀⠀⠀⢹⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢁⣩⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠻⠋⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣣⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣙⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⠀⠀⠠⣤⣤⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡞⢿⣽⣟⢛⡛⢛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠋⠉⠻⣷⣶⣶⠖⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠰⢀⣿⣧⠘⢿⣿⣿⣤⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢰⣏⠩⣿⠀⠘⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡃⠀⠃⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⠀⠀⠀⠀⠀⠀⣿⣦⣸⡄⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡅⠀⡄⠀⠀⠀⠀⠠⢹⣿⡿⣿⣿⣿⣿⣿⣿⡿⠱⣄⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠂⠀⠀⠀⠀⠀⣿⣿⣷⢛⣿⣿⣿⣿⣿⠃⠀⠍⢢⠐⢦⡐⢦⣤⣜⣿⡿⢂⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡾⠿⠿⠿⠟⠃⡀⠀⡤⠘⢣⡀⠙⢾⣯⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣙⣋⣀⣤⣤⠆⠀⠉⠀⠀⠀⠀⢘⠍⢳⣶⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢸⣻⣿⣯⣉⣀⣤⣄⣛⠁⠀⠀⠐⢤⠖⣹⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⢿⣻⣿⣿⣿⣿⣷⣾⠿⠏⠀⣰⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠉⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⠚⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣼⠷⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠆⠤⠡⠈⢆⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠨⠰⡀⠐⡄⢠⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⢠⠙⣾⣈⢈⣍⣭⠟⣠⠀⠀⠀⠀⠀⠀⠀⣠⣧⣈⠦⠖⠲⢞⣧
⠀⠀⠀⠀⠀⠀⠀⢤⣀⠆⣧⣘⣽⠐⣟⣥⢼⡇⡐⢶⠴⣦⠸⢦⢧⡰⣏⡩⡁⢒⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠁⢴⣋⠥⢼⠁⠿⠵⡏⡰⣞⣂⣜⣧⠈⣿⣌⣋⠡⢥⣌⣙⣁⣬⠥
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡌⢓⡢⠴⢲⢢⣨⣇⣛⡐⣻⠁⡾⡕⢻⣙⡳⢆⠈⣭⢤⣥⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣣⡴⣎⢳⢢⣦⢭⣍⡙⠮⢽⣉⢤⢜⣡⡃⢦⣈⢯⣉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠷⣷⣧⣯⣿⠿⠫⠿⠯⠵⢾⣸⣡⢧⡬⢹⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢴⣈⢽⡇⢾⣻⠏⢽⢷⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣯⣽⣫⣿⣽⣿⣿⡽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠋⣇⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠠⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠀⠀⠒⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡞⣹⣆⠀⣴⣤⣖⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⢀⣁⢄⠀⢧⣈⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⢃⣈⣿⣿⣧⣰⣿
⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡜⠉⠉⢉⢿⣏⠙⢋⠟⡀
⠀⠠⡒⠚⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠈⡌⠓⢰⣤⢸⡉⢳⢶⠸⠧
⠀⠀⠀⣴⠈⠁⣤⡀⢐⣂⣀⠻⣭⡂⢦⠀⠄⠄⠀⣀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠖⠀⡌⠀⠘⠘⢇⣀⡄⠁⣄
⠀⠀⠀⠃⠀⠲⠂⠀⢤⣁⢉⠒⣄⢀⡀⠈⠑⢂⡈⢹⣜⡛⣳⠟⠩⡄⠀⢀⡄⠀⢠⠀⠖⠀⠑⠆⠠⠂⠄⢰⢯
⠀⠀⠀⠀⠀⡰⡤⠀⠁⢤⣌⢡⡀⠂⣄⠼⡷⢾⡕⡴⠈⠀⡁⡛⠐⣀⣁⡼⡀⢮⢸⠆⠈⠀⠀⡰⠀⠒⠘⡟⠩⠅
⠀⠀⠀⠀⠀⠘⢁⢄⣉⣽⣈⡳⠷⢘⡇⡘⢐⣏⡬⣏⢧⣀⣈⣸⣡⡤⠬⠔⠃⠘⠓⠐⠀⠂⠄⡀⠚⢀⠑⠉⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠞⠉⢲⣆⣾⣷⣽⡙⢋⣰⣟⡽⠂⠺⠂⠮⠡⠠⠄⠀⠐⠀⠀⠰⠴⠊⢠⡰⠈⢠⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠅⠀⢟⣛⣹⢧⡴⡏⣴⡒⠀⣊⣀⠁⢖⣤⣾⢀⡐⠊⢂⢾⣀⠤⢀⡀⠠⠃⡘⣦⡉
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⣰⣦⠴⠏⠉⣨⠖⠿⣿⣷⣽⡿⠟⠻⢧⣄⣈⣿⣿⣶⠻⠂⡹⠄⡇⣠⡤⣲⡟⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠂⠀⢠⠁⠈⠐⠀⠙⠉⠙⠋⠑⠾⡍⠓⠀⡄⡉⠳⠀⠃⢤⠒⡝⢘⢻⣗⠏
⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⡸⢉⡀⠒⣂⠐⠋⢰⡀⠀⠀⠀⣀⠀⠄⡀⣄⡁⣀⣠⣀⣅⣄⣸⡷⣷⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢤⣀⠄⢠⠶⠀⠀⠂⠁⠑⠊⢀⣀⣀⠀⣤⣤⣀⣬⣼⡷⠯⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢈⡐⠺⠟⢀⡄⡠⠂⢀⡈⢭⣠⣖⣦⡷⡞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠟⠃⢴⣿⣽⠗⣷⠶⣿⣭⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡉⡷⠆⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠾⠟⠛⠛⠻⠿⢶⣦⣄⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⢀⣠⣤⣶⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⠀⣀⣴⣿⡿⠛⠁⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢠⣿⣿⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠰⠿⢟⢹⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠃⢠⡄⢀⣀⣶⣾⣿⣋⣃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠙⢛⣿⣿⡿⣿⣿⣏⢙⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠸⢿⣿⡇⠻⣿⣿⣯⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡄⠄⢀⣴⣤⣬⡀⠀⢿⠟⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢹⡇⠀⣽⣿⣿⣿⡧⠀⢸⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣷⠘⠿⢟⠿⠿⡇⡀⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣄⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢭⣶⣿⣿⣿⣷⣶⣿⣿⣟⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠈⢿⣿⣿⣿⣟⣫⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣽⣿⣿⣿⣿⣿⠟⠁⠀⠁⠈⠈⠻⢧⠄⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠻⢶⣬⣙⠿⣿⣿⣫⡭⢲⣾⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠙⠛⠫⠾⢫⠴⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣷⡀⣄
⠀⠀⢰⡿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠹⢹⡟⣿⡿⡆
⠀⣠⣼⣷⣀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠿⣦⣤⣀⠛⣱⠇
⣾⡉⠓⢦⡈⠙⢦⣀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⣴⣏⢡⣶⡝⣂⣼⡆
⠈⣷⣄⡀⠹⣄⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⣯⠁⡀⠈⢻⢭⣅⡘
⠀⣻⣦⣉⣀⠉⠉⠉⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠘⠧⣇⠀⢀⣼⠉⠻
⠀⢹⣦⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⠀⠀⠀⣀⣀⣤⣴⣶⣶⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠁
⠀⣨⡿⠶⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⡛⠛⠛⠛⠛⠉⠁⠀⠳⢶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⣹⣷⢤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⢿⣇⠀⠀⢀⠀⠀⠀⠀⠀⢀⡾⠋⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⢹⣿⠛⠁⠀⠀⠀⠀⠀⠸⢷⠶⢋⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢾⣏⣠⡆⠀⣀⠀⢀⣰⡟
⠀⠀⠈⢿⣦⡴⠚⠀⠀⠀⠀⠀⠓⠺⣿⣥⣤⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠹⠾⠹⣶⣿⡿⠁
⠀⠀⠀⠀⢿⣧⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⣀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠈⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠈⠛⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⢰⣾⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠛⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣠⣾⠟⢿⣤⣀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣀⡀⣠⡞⠉⠁⠀⠀⠉⠻⣟⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠉⣯⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢑⣄⠈⢣⣠⠶⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠇⠀⠳⠶⣶⣶⣄⠀⠀⢀⣞⠥⠶⣦⡀⢁⣘⡛⠪⠥⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠾⣦⡀⢬⣟⣒⠛⠠⢤⡀⠛⠀⠀⠈⠻⢦⣹⠉⠙⠛⠲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠙⢣⣿⠉⠉⠙⠛⠇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣏⢉⣿⠅⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢄⠂⢦⠈⣇⣀⠉⡹⣿⠆⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣄⢦⠤⢶⡼⠟⠛⠫⠛⢻⡭⠀⠀⢀⣴⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⢧⡀⠐⢳⣜⡀⡾⠛⠃⠨⠆⠀⢃⣿⠇⠀⢀⡀⠈⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢃⣒⣲⣄⠀⠁⢦⣸⢼⡿⠻⠛⠉⠻⠶⣄⡃⣠⠀⢤⣿⣿⠟⣪⠁⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠠⢀⢙⠭⣾⣧⡜⠞⢗⣶⢄⡀⠀⠀⣠⢰⢝⣿⠟⡁⠈⡇⠀⢠⢅⡴⢣⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⡆⠨⠴⠚⠉⠁⠀⠀⠀⠙⠿⣧⣴⡾⢹⣀⣺⡄⠀⠉⣀⠇⠀⠸⠋⢀⣿⠂⢀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⠒⠶⢧⣴⣴⣴⣦⣴⣦⢤⡀⠻⣏⠀⠀⠃⢺⠇⠀⠘⠋⠀⠀⠀⠀⡾⠗⠈⠁
⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠑⠲⣦⡈⣿⡇⢊⢭⠍⣙⢿⠟⠁⠈⠑⠦⣌⣧⠀⢺⠏
⠀⠀⠀⠀⠀⠀⠻⣧⣤⣄⣀⣴⡾⣁⡮⢀⢠⡟⠷⠿⡆⢁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⣽⣷⡌⢉⠋⠚⠀⢋⠟⠒⠒⠶⢦⡴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠋⠀⠀⠉⠒⠩⠜⠂⠁⢐⡭⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠔⠂⠁

⠀⠀⠀⢠⣦⢰⣇⣴⣦⣤⡀
⠀⣀⣿⢾⠏⠉⠠⣥⢿⣿⣿⡆
⢸⠏⠉⠀⣴⡶⠶⠿⢿⣿⣟
⠾⠃⣶⣿⣿⣿⣿⣗⡦⢈⠉⠙⢦⣀
⠘⣶⣿⣯⡍⠛⣿⣿⡾⣿⡦⠄⠀⠈⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣾⠮⢽⡿⣿⣶⣿⢿⢏⡾⠃⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣿⡀
⠀⠀⠘⣿⢿⣟⣷⣶⠛⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⣿⣶⣿⣿⣷
⠀⠀⠀⠘⢮⣛⣿⠁⠀⠀⠀⠀⠀⢀⠰⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣁⣭⣥⣶⠞⢟⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⠃⠀⠁⠄⠀⠀⠀⠄⠀⠀⠈⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠙⠿⠵⠗⣒⣠⣈⣶⠿⣻⣿⣿⠏
⠀⠀⠀⠀⢸⣷⠤⠀⠠⡄⠚⠈⣰⠆⣄⡞⠤⠓⡠⠂⠀⠉⠓⠦⢤⣀⣀⣀⣀⣠⡤⠴⠒⠒⠒⠒⠒⠒⠒⠚⡯⠅⠀⠀⠀⠀⢀⣭⠍⠛⢉⣴⣿⣿⣿⣷⡤
⠀⠀⠀⠀⢸⣽⡄⠂⠀⠀⠈⢠⡉⠦⢈⠙⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣼⠟⠛⢉⣿⣿⡄
⠀⠀⠀⠀⢸⡟⠁⠀⠀⠐⠀⢊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⠀⠠⠦⢄⣀⠀⠈⠉⠀⠶⠶⣖⣀⠙⢻⣏⣭⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⣿⡗⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⢻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠠⣬⡄⠀⡴⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠹⣦⡄⠀⠀⠠⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠈⠙⠳⠦⣄⠉⠓⠶⣄⣉⣉⠁⠙⢋⡸⣿⠋
⠀⠀⠀⠀⠀⠀⢻⣗⣄⡀⢠⠀⠆⠀⠀⠀⡀⢆⠠⢄⡐⠠⣄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⢤⠀⢄⠈⠁⢐⡈⢐⣮⡉⠲⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷⣄⠀⠂⢀⠀⠀⠀⠀⠀⠀⠘⠶⠿⠷⣦⡀⢶⠈⢳⣌⠂⠀⠀⢀⢀⣀⣀⣄⣠⣀⣈⣀⣀⡈⣽⣆⡉⠻⢿⣶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣈⠙⠀⠢⠀⠀⠀⠀⠀⢤⡀⠀⠌⠙⠂⠀⠀⠀⠀⢰⡍⠄⠸⠶⣿⡿⠿⠯⢬⣍⣉⣉⣉⣙⣛⣋⠻⣷⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣗⢂⠁⢀⠀⠢⠈⠀⠀⢀⠀⠠⡖⠀⠉⠐⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠆⠀⠈⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⡁⠐⢦⡀⠄⣀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⡷⣌⠦⡙⡂⠠⣁⠀⠐⠀⠀⠀⠁⠀⠀⠠⠄⠐⠀⠄⠀⠀⠀⡌⠰⠶⠄⢤⢤⣔⣀⣠⣴⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡈⠂⠨⣃⠀⠠⡀⠢⠀⠑⠀⠀⠀⢀⠀⠦⠀⠤⠄⠠⠄⠳⢎⠹⢷⡴⣯⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄⣬⣁⠀⠃⠀⠂⢄⠈⠉⣀⡀⠀⡀⠐⠀⠄⠐⡦⠀⠀⠀⡐⠿⡓⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣿⡷⣶⣦⣶⣶⡄⣀⠘⢯⠀⠀⡀⠀⠐⠂⣁⠀⠀⠖⣈⣠⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⢻⠻⣷⣾⣿⣿⣿⣗⠪⠓⠀⢅⣤⣘⣷⣄⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⢀⣀⣹⣾⡿⠟⠛⠿⠿⣶⣿⣆⠩⡿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⡄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⠘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣶⣲⣿⠟⣤⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣼⣓⠃⡾⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠈⢀⠀⢀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠄⣤⠨⠙⠓⠺⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⢢⣤⣤⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⢉⠟⠖⠖⢂⠀⢲⡌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡐⠈⠙⠐⠊⠓
⠀⠀⠀⠀⠀⠀⠀⡼⢛⡘⢀⠂⠀⢀⠀⢁⠀⠀⠀⠠⠥⠀⠀⢀⡀⠀⡀⡴⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⢻⡋⣯⠀⢐⣀⡛⢀⠈⢡⠀⢡⡎⠁⠀⠍⠑⠂⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠗⢀⡈⠉⡉⠲⣿⣶⣾⡇⠀⡄⠀⡇⠀⠀⠘⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠸⠛⢬⣽⣏⡀⡐⠇⡠⠀⢀⢴⠄⡆⠀⠃⠀⢀⡈⠀⠀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠉⣹⡅⢉⣤⡅⣰⠫⠀⣀⠘⢂⠉⠀⠋⠄⠐⠂⢀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⣿⣿⣿⡧⣶⣿⣎⠉⠁⠀⠀⠉⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⡖⠙⢻⣿⡏⣍⣦⡔⠉⢦⣦⡄⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡾⢋⠻⣷⣾⣇⢀⡌⠉⡠⠁⠀⠀⠀⠀⠀⣁⠀⠀⣤⠤⠀⠂⠤⠀⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⢈⠷⣁⠀⡔⠉⠉⠋⠳⠾⣶⣦⣶⣦⣭⣥⣾⠿⠶⠟⠁⠀⡀⠁⠐⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠘⢀⣀⡤⠀⠀⠀⠀⠀⠠⠆⣰⠃⢰⡎⠋⡠⠒⠀⠀⡸⠟⠡⠉⣠⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡼⠟⣡⠆⠀⠀⢀⠄⣠⡔⠈⢀⠈⠞⡄⣹⠀⣐⠚⢑⣀⣀⡾⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠀⠠⠟⠃⢁⣀⠀⠁⢰⠋⣀⡴⢐⢿⣍⠑⣚⣥⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡧⢲⣧⣀⣉⣤⣀⣩⣿⣿⢿⣿⡥⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⠛⢿⡿⠟⠑⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡚⣄⣉⣶⡀⠰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠘⠻⣧⣀⣤⣌⠉⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠂⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠺⠀⠷⠁⣧⢺⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⣆⠀⠀⠀⠁⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⠀⠀⠈⠳⣤⡀⠀⠀⢠
⠀⠀⠀⠀⠀⡎⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⢻⣯⠀⠈⠰⣶⠆⢉⡷⠒⢇
⠀⠀⠀⢀⣀⣱⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢉⣧⠀⠀⠠⠠⣀⡼⠧⣤⢤
⠀⢀⣄⢸⠀⠙⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠚⠹⣧⡄⠀⣰⠁⠀⠀⣿
⠀⢸⡌⠳⣇⠀⠈⢣⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠋⣴⣠⣟⠓⠶⠞⠁
⠀⠀⢣⠀⠙⠂⠀⠀⢳⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢹
⢸⠁⠈⠁⠀⠀⠀⠀⠀⠻⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣇⣸⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⢆⠀⠀⠀⠠⠀⠀⠀⠀⠹⡖⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠀⠀⠿⠁⣧⠋⡇⠀⣠⠀⠀⠀⠀⢸
⡤⣌⣆⠀⠀⠀⠀⠀⠀⠀⣖⡛⢦⣘⠢⠤⠤⠤⢶⣔⡒⠂⠴⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠚⢹⣀⣤⡀⠀⡆
⠱⡀⠙⢧⡀⠀⠀⠀⠀⠰⣂⠛⠶⢬⠓⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢘⡇⠀⣆
⠀⠙⣄⠀⠳⣄⠀⠀⠀⠀⢠⡛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢨⠷⣆⡾
⣄⠴⠾⢦⡀⠈⠀⠀⠀⠀⠀⡬⣟⣛⣛⣥⠀⠀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⣩⠽⠶⠷⢦⡀⠀⠀⠀⠀⠀⠙⠉⠉⠈⠉⠁⠉⠀⠀⠀⠀⢀⣠⠤⠔⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠙⠒⠂⠀⠀⠈⠓⠤⣄⡀⡀⠀⠀⣀⣀⣀⠠⠤⠄⠀⠀⡀⠈⠀⢀⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸
⠀⠀⠀⠀⢆⣀⣀⣀⡤⠴⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡽⠛⠋⠉⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠀⠀⠀⣀⣀⠤⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡥⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣲⠖⠒⠊⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣀⡀⠀⠀⢀⠫⠤⠤⠤⢤⣀⣀⣀⣀⠠⠤⠤⠔⠒⠒⠛⠉⠁⠀⠀⠀⢰⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡈⠉⠑⠚⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣄⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠤⣀⠤⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢰⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠀⠈⠳⣤⠤⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡄⠀⠀⠀⠀⠘⢆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠄⠘⢶⠲⠿⢿⣦⣬⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠉⠓⠢⠽⣻⣅⠀⠀⠈⢧⠀⠳⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⣤⢷⡀⠙⠿⢟⣉⡭⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠒⠒⠛⠺⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⢨⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣾⠀⠀⠀⡜⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠠⡄
⠀⠃⠀⠀⢀⡘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠶⠶⠏
⠀⠀⠀⠀⠄⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠦⠂
⠀⠀⠄⢀⡂⠘⣽⡀⣄⡀⡀⢠⡄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠆
⠀⢈⡀⠈⠇⠀⣿⠁⠀⠀⠀⠀⠁⠄⠀⡀⠇⠀⠀⠤⠄⠐⠀⠀⠀⠀⠀⢀⣈⡀⢀⡇⣀⣀
⠀⠀⠳⡄⠢⠀⣿⠀⢠⠤⢀⡐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⠳⠚⡉⠉⠈⠉⠈⠉⠁⠀⡀⡀
⠀⠀⠀⢀⡀⠀⣏⡀⢸⠃⠀⠃⡇⠀⠀⠘⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥
⠀⠀⠀⢐⠀⠀⢿⠁⢸⡄⠀⠀⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢻⠇⠀⠀⣀⡧⠈⢁⡀⠀⣴
⠀⠀⣶⣶⠰⠀⠘⢰⢸⡆⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⡷⠂⠩⡋⠀⠀⣸⣂⢺⡏
⠀⠀⠁⣿⠐⠀⢸⠂⢸⡅⢀⣀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡠⣯⠃⢀⡶⠶⠒⠋⠛⠋⣹⣽⣿⠇
⠀⠀⠰⢳⠀⠀⢸⠀⣸⡃⣸⡇⠒⢄⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⢸⣿⡍⠀⠐⣷⠀⠀⣤⣴⣾⣿⡿⠃
⠀⠀⠀⠚⢱⡶⠞⠛⠫⡩⠉⡌⠀⠀⠀⢀⠠⠒⡈⠀⠀⠁⢀⣀⡤⠀⠈⣟⠁⠀⣦⣿⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣔⣀⣘⡐⢒⣃⠊⠁⡖⠶⠿⠁⠀⢀⠀⣟⣭⣷⣿⣿⣿⣿⡿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⣉⡉⢛⠟⠛⠿⣶⣶⣶⣶⣦⣴⣟⣛⣿⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⠀⠀⠀⠔⠂⠀⠀⠚⠋⠈⣩⡌⠉⠉⠩⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠊⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠋⢠⡼⠀⠙⠯⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⣤⣤⣤⡀⢰⡾⠀⠻⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠈⢫⣿⠞⡓⠀⠀⠁⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡏⠀⢀⠃⣬⠀⠘⠷⠽⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠴⢺⡅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠐⡂⡄⠉⠀⠀⣠⠀⠘⡛⠻⢶⣦⣤⣄⣀⣀⠠⠶⠶⠦⢀⡀⡌⠀⡆⢠⡴⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡓⠊⠉⠁⠀⠀⠀⠴⠆⠔⠁⡀⠀⠈⡁⡀⠈⠁⠀⠀⠄⠈⣄⠀⣠⠀⣄⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⠠⠬⠁⠒⠃⠀⢀⡄⡀⠀⠀⣀⠆⠀⣁⠘⠀⣆⠀⠂⠐⠀⡩⠀⠉⢠⡀⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠀⠒⠈⠁⠀⠀⠀⠀⠀⢨⠄⠀⠀⣠⠠⠁⠀⡄⠉⠀⢠⡄⢠⠁⠀⠀⢠⠇⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠲⠆⢀⠀⠐⠂⠀⢰⠀⠘⠂⠠⠈⠁⠀⠀⠄⠀⠁⢰⡯⠂⠾⠀⠀⡆⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣆⠈⣉⠀⠀⠈⠁⠜⠳⡀⠀⠐⠟⠂⠀⢈⠄⠀⠐⠋⠒⠂⠀⠀⠀⠸⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣛⠠⢀⣀⠈⠉⣡⠀⠀⠁⠰⠀⣀⢀⡚⠃⠈⠉⠀⠀⠀⠀⠀⠸⢶⠀⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠲⠤⡤⠀⠉⠠⠖⠠⠞⠀⠟⡋⠘⠃⠀⠀⠆⢠⠀⢀⠀⠀⠄⠏⡀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣐⠾⠿⢛⣁⡄⢀⡰⠔⢁⣆⠀⣆⡀⣰⠀⠊⡨⠀⠇⣴⠄⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢉⣤⡀⠈⠋⠁⢰⣶⠘⣀⡈⠁⢁⠄⡊⠀⠃⡀⠀⢺⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣢⣴⡇⢀⡉⠀⠂⢀⠘⠑⢃⣼⢤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⢾⣷⣌⣷⣤⢥⡿⣿⡾⠿⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⣇⠀⢇⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠛⣩⠿⠏⢫⡤⠑⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢸⡏⣹⠅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠋⠛⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⡄
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⣀⡇⠀⠀⠀⠀⠠⣴⠄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⢁⡠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠚⠀⠀⢀⠀⣰⠔⠊⠀⠀⠈⠒⠚⠺⠶⠵⠀⠀⢀⠀⠀⠀⠂⢁⠄⠋
⠀⠀⠀⠀⠀⠀⠓⠛⠄⠒⠤⠄⠓⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⡀⠔⠉⠸⠀⠐⠊⢁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠉⡤⠔⠊⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠡⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡄⠔⠂⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⢀⣀⠀⠂⠀⣔⠒⠒⠛⠉⠒⣒⠆
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠭⠡⢉⡡⡌⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠠⠀⡠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣯⡟⠋⠑⢠⣤⠄⠒⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠭⢭⢿⠯⢑⣿⣿⡗⠺⢙⣴⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠒⠛⢋⠥⠖⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠦⠤⣤⣤⣀⡀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⢀⣠⣤⣴⡶⠶⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⢀⣠⣶⣿⠟⠉⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⣰⣿⢿⣿⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⢀⡿⠁⣀⠀⠈⣭⣴⣴⠟⠄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠛⣿⣿⡿⣿⣿⣏⢝⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠻⠿⡇⠙⣿⣿⣯⡃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⣷⣷⣆⠀⢹⢉⣯⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢿⡄⢸⡿⢿⣿⣟⠀⢺⣿⢿⡉⠛⢿⣿⣿⣿⣿⣿⣿⣟⡈⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣥⣶⣿⣿⣶⣦⣴⣾⢟⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠛
⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣭⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⡿⠋⠙⠓⠟⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣥⣙⠻⣿⣿⡿⣟⡻⣥⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠈⠉⠛⠛⠫⠾⡫⠾⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢠⡄⣾⣠⡄
⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⢠⣿⣿⡟⠉⠁⠀⠈⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⠶⠲⣤⡴⠟⢻⡷
⠀⢀⣾⣿⣿⠀⠀⢰⡆⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡾⠁⢀⡾⠋⠀⣴⣿⣤⡤
⣼⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⣠⠟⠀⠀⠀⣠⡾⠋⢀
⠀⠀⠀⠘⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡏⠀⠀⢠⡾⣫⠖⢋⡽
⠀⠀⠀⠀⠙⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠞⠀⠀⠰⡫⠚⢁⣠⠞⠁
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣤⣀⣀⣠⣯⣭⣤⡄
⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠛⠉⠉⠁⣀⡀⠀⣾⠃
⠀⠀⠀⣼⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣠⣤⣤⣤⡤⠖⠋⠀⠀⠀⣿
⠀⠀⢰⣿⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣤⡀⠈⠛⠶⣤⣤⣀⣀⣀⣀⣤⣤⣴⠶⠟⢋⡁⠀⠀⠀⠀⠀⠀⠠⢤⣀⠈⠳⢦⡸⣆
⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⢹⣷⡀⢰⣄⠀⢀⡈⠉⠉⠙⠛⠿⢷⣶⣤⣀⠈⠓⢦⡀⠙⠲⣤⡀⠀⠙⠷⣄⠈⢳⣽
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠹⣷⡄⠹⣧⡈⠻⣶⣄⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⠳⣄⠀⠀⠉⠳⢦⡀⠈⢳⣌⠇
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣌⠻⣦⣌⠻⢦⣀⠙⢿⣦⡀⠀⠀⠀⣤⣀⠈⠻⣷⣌⠳⢦⣀⠀⠀⠉⠂⣀⡿
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⢶⣽⣷⣦⣉⠳⢦⣝⡻⢶⣤⣀⠈⠛⢿⣦⣈⠻⣷⡀⠉⠳⣦⡀⢈⡅
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠈⠙⠻⣯⡻⣶⣌⡻⢷⣮⣝⡛⠶⣦⣬⣙⣷⣽⣿⡄⠀⠈⠙⢻⡁
⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⠀⠈⢻⣾⡟⠛⠦⣙⣿⠻⣷⣦⣿⡍⠙⠻⠟⠷⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠘⢿⠆⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⡛⠶⢦⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠙⠛⠶⣤⡀⠻⣶⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠙⠂⠀⠈⠉⢛⡒⠀⠈⠉⠙⠛⠲⠶⠶⠶⠛⠋⢉⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⣀⣠⡽⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣶⡾⠟⠋⠁⠀⠀⠉⠛⠶⣤⣀⣀⣀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⠿⠛⠉⠉⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⢰⡿⠃

⠀⠀⠀⢠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⣤⠱⡴⣓⠦⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠂⠀⢀⡀⠀⠈⠛⢄
⠀⠀⢸⣫⡑⠲⡄⡉⣛⡖⠹⢄⠄⠠⠤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠱⠀⠠⣆⡸⣧⣗⠀⠉⡚⠁
⠀⠀⢸⢿⣿⣄⠤⣠⠜⣛⠵⡖⠙⠋⢈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⣹⣿⠟⢻⠏⠈
⠀⠀⠘⢋⣿⣿⡟⠛⠤⢴⠎⠟⡿⠂⠀⢀⢂⠄⠀⢀⣠⡀⠀⢀⣀⢶⢪⡟⠁
⠀⠀⠀⠈⢲⣿⣿⣷⠂⢿⣶⣏⡓⢺⡏⠀⢀⡀⢢⣴⠏⠨⡙⠀⠠⢮⡿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⢉⡕⢲⠾⠂⡀⢨⣁⣰⢆⠀⢐⣒⣽⣷⡄
⠀⠀⠀⠀⠈⢿⣿⡿⣶⣟⣿⢋⣦⣾⣟⣓⣭⡐⠚⡲⠿⡦⢐⣺⣽⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⣿⣿⣿⣷⠖⣿⢠⣗⢈⡟⡈⢰⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢚⠹⡾⠴⢉⣏⣿⣏⡀⠯⡜⢦⡬⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⣽⢢⣛⠃⣑⠵⣿⣷⠾⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⢶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⠁⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⢃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠋⠉⢻⣿⠂⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠚⠡
⠠⠀⠈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣷⠀⠀⠀⠀⡘⣿⣟⣉⣉⣉⣩⣕⡖⢂⣤⡀⣚⠢⠀⠀⠉⠠
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢻⣿⣿⣿⣿⣿⣧⡀⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣄⡠⠈⠁
⠸⠀⠀⡸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢪⣥⣼⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⣀⣷⣇⠀⠠⠀⠀⠀⠀⠀⠀⣶⣶⣬⣥⣶⣾⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⡟⢉⣩⡉⣻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁
⢨⠀⢘⣿⣿⡟⠐⠦⣀⠀⠀⢀⣀⣹⠿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠈⣯⣿⣿⣿⡆⠈⠿⠛⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠁⠛⠿⢯⣀⠄⠀⠀⠉⠙⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣧⠀⣶⣷⠈⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣀⣈⣁⣠⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠙⠓⠀⠑⠦⣄⠀⠀⠀⢈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠇⠰⡌⠉⠲⢤⡌⢐⡨⢉⠛⠉⠉⠡⠶⢚⡡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠘⠀⠀⠀⡀⢄⠉⠈⠃⠀⠀⠀⠐⠉⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠐⢤⣤⠀⣼⠀⠀⠀⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⡏⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠐⠂⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠐⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣰⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠤⡀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠖⠉⠉⠉⠲⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠠⠤⠤⠤⠄⣀⡀⠀⠀⠀⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣉⠤⠤⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢉⡤⠊⢁⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎
⠀⢀⡠⠤⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠠⠞⠁⣀⠤⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸
⢰⠁⢀⣐⠒⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠒
⢈⠦⣀⠀⠁⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠈⠲⢄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⢻⠉
⡎⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣈
⢳⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡴⠀⠀⠀⠀⠀⢀⠔⠉⠣⠼⠓⠁
⢠⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠳⡀⠀⠀⠀⡰⠁
⠅⢉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠜⡆
⠘⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⡁⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢧⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠄⠀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠉⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⡸⠀⡌
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠜⡴⠁⡜
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⠄⠀⠀⢠⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⡠⢔⡥⠊⠀⠸
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⠒⠐⠲⣁⣀⣀⡴⠃⠀⢀⣠⡃⠀⣠⡎⠀⣀⣀⠠⠤⠐⠊⠉⠀⠀⠀⠀⠖⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡢⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠒⠁

⠀⠀⢤⣴⣶⡦
⠀⣼⣿⣿⣿⣷⣶⣶⣤⣀
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡆
⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣶⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⣼⣿⣿⣿⣿⡆⢀⣠⣤⣤⣄⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠛⠛⠛⠛⢻⡏⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⣸⡅⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠃⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣾⡿⠿⠦⠀⣠⡤⣶⣿⠷⠄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠈⠻⢿⣿⠿⠛⠁⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⣀⠀⢀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣶⣶⣧⣾⣿⣄⠠⡖⢀⣹⣷⣾⣓⠁⡀⣫⣶⣶⣶⡤
⠀⠀⠀⠀⢀⣠⣿⠚⢟⠿⣟⣻⣿⣿⣿⣿⣷⡇⡼⣿⡿⢷⣿⣿⡽⠛⣿⣿⣽⣶⡭⠂
⠀⠀⠀⡀⣈⢿⣿⣴⣶⣦⣽⣿⣿⣿⣿⣿⣯⣿⣿⣾⣾⣿⣿⣿⣿⠌⣿⣫⣟⠁
⠀⢐⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣼⣿⣿⡟⠐⠻⣿⣿⡿⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀
⠀⢈⣿⣿⣿⡿⢿⣿⣿⠟⢋⣭⡽⠿⣿⣿⣿⣷⡀⢿⣽⣻⣯⡁⠀⢸⣿⡭⣥⠀⠀⢠⡄⣿⠀⣇⠀⡀⠀⠀⢠⣦⣿⠒⣠⣞⣻⣇
⠀⢸⣿⣿⣿⣤⣴⣶⡶⣶⣾⠃⠹⠆⢹⣿⣿⡛⠁⠀⣼⣿⣿⡟⠀⠀⣿⡟⠀⠀⣠⣿⣷⣿⣧⣿⣿⣿⣵⣶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⢼⢛⣿⣿⣴⣷⠍⣷⣖⣿⣐⣟⠀⣸⣿⣟⣅⣉⣌⣻⣿⣏⠀⡀⠈⣿⠟⠉⠉⠛⠻⣿⣿⣿⣿⣛⣛⣿⣛⣿⣿⣟⣛⣛⡟⢿⡿⠿⠿
⠆⢞⠐⣾⠬⣛⣽⣀⢶⡾⠻⠷⢿⣯⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⣶⣦⣀⠀⠀⢀⣀⣉⣉⣉⣹⣹⣿⣿⣿⣯⣿⣙⣛⣀
⢰⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣭⣬⣿⣛⣛⣛⣛⡿⣿⡿⢛⣛⣛⣿⣿⣋⣛⡛⠿⠣⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡥
⠀⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠉⠉⠀⠀⠀⠉⠙⠉⠉⠉⠉⡋⢉⡉⢛⡙⣉⢉⣁⣀⠀⣀
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣘⣦⣷⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣟⠉⣈⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⢫⣍⣀⣈⠻⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⢠⣿⣿⣿⣫⣿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣲⣿⣷⣶⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠘⢿⡻⠿⢟⠆
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠋
⠀⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠠
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣤⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢧⠀⠀⠂
⣾⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⣉⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⡧
⢹⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣶⡿⢿⣵⣞⣨⣿⢏⣴⣬⡀⠤⠀⠀⠀⠠⠄⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠘⣿⣿⡏⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⣴⣟⣿⡉⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠈⠛⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⢿⣿⢻⣿⣻⠁⠀⠁⠉⠐⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠾⠢⢄⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣵⠃⢠⡄⠀⠀⠀⢠⣾⠀⠀⠀⣤⠰⣐⠦⢄⣤⠀⠀⠀⢠⠀⠆⠉⡼⡛
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢠⡿⢿⡄⣿⣹⣿⣿⣀⢀⣟⢹⡦⣿⣿⠧⣟⣱⢾⡶⢏⣡⠴⢾⡇⠁
⠀⠀⠀⠀⠀⠙⣿⡿⠟⠻⣿⠿⠁⢿⣿⣿⣿⣿⣿⣿⡿⡀⢀⣤⣥⣿⡿⡿⠉⣯⡀⢟⣿⣶⣾⣿⣟⡉⠱⡂⠶⠋⠡⢾⡛⠁
⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⢹⡄⠀⢾⠿⠋⣿⣿⣿⣧⣰⢃⣿⣿⣿⣿⠓⠁⢀⠨⠷⢶⣾⣝⡻⡛⠛⠛⠁⡀⠤⠂⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠉⠿⣽⣿⣿⣿⣿⣿⣿⣯⠄⣈⡴⠇⢀⠉⠙⢻⣿⡿⠛⠀⠟⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⣻⣿⣿⣿⣯⣴⢞⣫⡴⠟⣃⣤⣴⣾⣷⣷⣤⠛⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣭⣟⣢⣭⣥⣶⣻⣿⣿⢻⣿⣿⣿⣧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣦⡀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡏⠉⠁⢸⢻⣆⣃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠆⠀⠉⢻⡇⠀⡀⠘⣼⣿⠻⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠶⢤⣤⣤⣴⣟⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣾⣧⣶⢧⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠬⠷⠞⠻⢿⣿⣷⡀
⠀⠀⣠⠔⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⣠⣤⣄⠘⢿⣿
⠀⠀⣇⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢰⣶⡄⠉⠁⠀⢀⣈⠳⡀
⠸⢯⠈⡀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⢿⣷⣶⣿⣿⣿⠏⠛⠃
⠐⢾⣀⡀⢀⡀⠁⠂⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⢻⠁
⠀⠠⣾⣿⣿⣷⣤⠄⠀⢤⡄⠰⡆⠀⠈⠿⢷⡶⢤⡤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢢⡀⠉⠙⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣧
⠀⠀⠙⢲⣄⣀⠈⠙⠲⣄⠈⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⢰⣧⣈⠙⠙⠻⠶⣦⠀⠈⢻⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡇
⠀⠀⠀⠉⠻⣿⣷⣶⣤⣄⡀⠀⠘⣏⠀⠀⢠⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⢰⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⠄⠠⣯⠋⠀⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⢠⡟
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡔⠙⠁⠀⢯⡀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣂⡿
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⠉⠀⠈⠹⠖⠒⠀⣠⠔⠂⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠶⠖⠚⢻⣖⣉⢀⣀⣀⡀⠀⢀⣂⠀⠀⢀⡀⢀⣠⠠⠂⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣂⡀⠄⠀⠀⣉⠉⠁⣀⠈⠁⠁⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢡⣩⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡀⢀⠖⠀⠃⠈⠂⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣇⣀⠌⠁⠀⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣀⣠⡰⢤⡶⡟⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣏⣠⣾⠃⠀⣄⠀⣀⠀⠂⠀⠀⢌⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣷⣾⣇⣘⣟⣴⠀⡀⠀⡀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠿⣷⣾⡿⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⢀⣀⠁⠀⠀⠀⢀⣠⣤⣿⣿⣷⣤⣿⣿⣳⠤⣤⣤⠀⠀⠰⠂⣠⠀⠀⠀⢰⡏⠀⣠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⣀⣀⣕⣢⡠⠛⢿⣦⣴⣦⣄⣉⣉⣀⣠⢠⠾⠿⠛⠛⠻⠿⣽⣶⣿⠶⠶⠾⠵⠶⠀⠲⢿⣷⡰⡥⠀⡀⢀⢴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠀⠼⠿⠛⠻⠼⠻⣿⣿⡷⠄⡀⠀⢸⣷⠄⠀⠀⣍⠉⠁⣀⣀⠀⣆⣄⣶⣾⡤⢷⣷⣶⣏⡽⣇⣴

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢦⡀
⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠈⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⡎⠀⠁⠐⠚⠛⠯⡉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡇
⠀⠀⠀⠀⡇⡔⠀⠀⣰⡄⠀⢸⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡼⢻
⠀⠀⠀⠀⠘⠲⠄⠀⠙⠁⠀⡘⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠊⠁⠀⠀⠀⠀⢸⡀
⠀⠀⢀⠀⠀⠀⠴⠀⠀⢆⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠈⠉⠉⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⡐⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⣧
⠀⠀⠀⠰⣄⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠆⠀⠀⢹
⠀⠀⠀⠀⠈⠀⢒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠋⠀⢠⡏
⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠢⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠋⠶⡆⠀⠀⢀⡘⠀⠀⠀⠀⠀⠘⠢⣀⠀⡤⢀⣀⣀⣀⣀⡠⠤⠒⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⡦⢤⠤⠤⠤⠤⠒⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠁⠀⢀⣉⣁⣆⠀⠟⠀⠈⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠩⠐⢊⠃⠀⠁⢐⠶⣂⠤⠤⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠊⠀⠀⡥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⣠⢴⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠈⠀⠀⠀⠉⠀⠀⢀⡰⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡓⠠⠀⠀⠠⠀⠀⠀⠀⢐⡏⠀⢀⠔⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⣿⢠⣤⣶⣤⣤⡡⠤⠀⢚⣃⠰⠟⠂⢆⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠶⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠖⠪⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢱⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡸⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢂⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠉⠙⠀⠀⢀⣀⡠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠨⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠧⠀⠚⠉⠁⠀⠀⣴⣷⣶⣄⠀⠀⠀⡀⠀⣰⣟⠋⠀⡴⠂
⠀⠀⠀⠀⠀⠀⣀⠐⠦⣤⢂⣀⠉⢀⠀⣀⣀⣀⣤⡤⠴⠿⠿⠿⠿⠿⣶⣾⣷⡿⠶⠾⠧⠀⠺⡍⠁
⠀⠀⠀⠀⠀⠘⠀⠚⠉⠉⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠲⢋⠉⠻⣦⣤⡀
⠀⠀⠀⠀⢀⣼⢉⣡⠴⠾⠿⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠀⠀⢶⡓⠘⣿⢸⡷⠶⣄
⠀⠀⠀⠀⠸⣅⠊⢡⣤⠀⣦⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡏⠀⠀⠈⠁⠀⢁⡾⠀⢀⡿⠴⡄
⠀⠀⠀⢀⣞⣛⡦⠀⠁⠀⣏⠃⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣁⠀⠀⠀⠀⠀⣼⠃⠀⠜⠀⡼⠛⡆
⠀⠀⠀⠈⠉⢸⠁⠙⣦⠀⠋⠀⠀⠀⠀⠀⠀⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠐⡆⠃⠀⠀⠀⠀⣰⠞⠙⡆
⠀⠀⠀⠀⠀⠘⢧⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠘⠶⣶⣦⣙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⢴⠿⠋⠀⠸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠈⠉⠛⠀⠹⣆⠀⠀⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡀⠀⣤⡰⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⢻⠀⣧⠸⡷⠄⠀⠁⠀⠀⠀⠀⠐⠚⠋⠉⠉⠉⢹⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠄⢙⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠈⣀⣠⡖⠒⠂⠚⠁⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠈⠉⠛⠓⠦⢤⣀⡀⠀⠀⠀⣺⠀⠀⠀⠀⡰⠀⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠟⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢬⠀⠂⠀⠀⣨⠗⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⡟⠰⠖⠒⠒⠒⠒⣛⡆⠀⠠⠎⢴⠈⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⡀⠀⠀⠀⠀⣀⠼⠃⠀⢀⡸⠀⠀⠒⢒⣋⣉⠽⠋⣀⠀⠀⠀⠉⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣦⣀⠀⠰⠋⡞⠀⠀⠈⣀⡤⠶⠛⠋⠉⠀⠀⠈⠉⠛⣷⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢤⣀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠶⡆⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠈⣁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣀⣡⣄⣄⣀⠀⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣙⡛⢛⣊⣽⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠚⣛⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⣤⣤⣤⣠⠴⠋⠙⠟⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡴⠋⠀⠀⠀⠀⠘⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠁⠀⠀⠀⠀⠀⠀⢹⣹⡄⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⠃⡇⠀⠀⠀⢀⣠⣤⠤⠤⢷⣉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⠭⠶⣒⣛⣫⠥⠤⠼⠷⠆⠀⠘⣯⠴⠖⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣾⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⢦⡘⣆⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠻⣌⣧⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠄⠀⠁⣠⡤⠶⠓⠒⠲⠶⢤⣤⠞⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⠉⠙⠛⠋⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣠⣤⣤⣤⣀⡾⠁⠀⠀⠀⢠⠴⠶⣦⡀⠀⠀⠀⠘⣧⣤⢤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠈⠢⢈⡿⠀⠀⠀⠀⢹⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⢀⣤⠴⠒⠛⠉⠉⠉⠉⠉⠛⠲⠦⣄⡀⠀⠙⣦⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠈⢷⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢰⠏⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠈⠳⣌⢷⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⡟⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠈⢻⣇⠀⠀⢹⠀⠀⠀⠀⢀⣀⣀⣀⣤⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⡙⢦⡀⠀⠀⠙⠀⠀⣸⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⢻⡴⠃⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠦⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠶⠶⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠁⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠦⢤⣄⡀⠀⣿⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢿⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⢸⠃⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢀⣠⢾⡆⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡆⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡴⠋⠁⠀⢷⡀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠻⣤⠞⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣧⡀⠀⠀⠀⢀⣼⣥⡤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡶⠶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣟⠦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⠀⠀⠉⣟⣒⣒⣲⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠛⠛⠲⢦⣝⢳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⡙⠻⡀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠺⡷⣤⡄⢁⡀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡽⣸⡄⠛⠁⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣀⠤⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠈⣁⠀⢰⣴⡆⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⡿⠄⠀⠀⢸⢅⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⢤⢘⠚⣧⣀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⣲⢤⣤⣆⣴⣿⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠰⣶⠋⣆⠈⢹⣍⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣻⣟⣿⣏⡼⠛⠟⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡇⠀⠉⣙⣿⠓⠀⢠⣈⣷⣄⣀⣀⣀⣀⢀⡀⠀⣤⣼⣿⡿⣩⠤⣟⢀⣶⣯⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣦⠠⠙⢾⢛⢀⠀⠂⢡⣿⣿⡏⢰⡋⢹⡉⠙⡿⢟⡅⠳⠘⠧⣛⡥⠈⡍⠲⣜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢈⣳⣶⠂⠀⡀⢸⢎⣾⣿⠄⠃⠁⠀⠀⠐⠂⠠⠐⠒⠄⠐⣧⣤⢼⡕⢤⢥⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠐⠮⡇⡉⡇⣀⣀⢞⠰⢌⡻⡖⠀⠀⠄⠀⣀⠀⠀⠠⠍⠆⠀⢠⠽⠏⢐⠳⡐⡗⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣴⡆⠹⠿⠅⣌⠜⠀⠈⠁⠀⣲⠃⣠⣲⠈⠢⡅⠢⠀⡀⢫⠁⢡⠊⢠⡠⢱⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡙⣠⡙⠁⠐⠆⣴⡘⣀⠠⠀⠀⠈⠱⣀⠠⠍⠛⡀⠑⢀⠀⠂⠼⣀⣜⠂⣤⣟⡺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣉⠀⠦⡄⢙⠸⠈⣃⠋⢈⠒⠄⠐⠀⠤⠁⢠⣆⣀⣴⢈⣦⡴⢸⢾⣯⡉⠊⢁⣲⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠂⣱⠆⡛⡆⠀⠰⠃⠠⠥⠤⠐⢦⡀⠂⣀⢞⢩⣼⢹⣮⣶⣾⠛⠉⠈⠁⠈⢉⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⣯⡐⡉⠀⣄⠘⠇⠳⡄⠀⠀⠘⢳⣿⠿⣿⡷⠾⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢿⣀⠀⣀⢒⠂⠁⠻⣏⣀⠀⠈⠀⠠⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⢴⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣦⢤⣀⠘⣀⠀⠀⢤⠁⠀⠀⠠⠀⠲⠦⠀⢀⣁⠀⠀⢒⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣷⣮⣽⣥⠀⣀⡀⠒⣴⢆⠀⠀⠀⠀⠀⠀⠡⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣭⣤⣽⡇⡀⢈⠉⢀⣀⡀⡀⣾⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⠉⠙⠻⣿⡿⢦⠔⠾⠛⠉⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⣤⠀⠀⠀⠀⠈⠙⠿⢿⣶⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢪⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⠂⠁⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠶⡶⠾⠷⠶⣠⣴⡟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⢉⢋⡼⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣷⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣿⣿⣿⣧⣾
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠻⣿⣿⣿⣿⣿
⠀⠀⢀⡔⣽⢿⣿⣿⠿⠷⢤⣦⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠡⢰⠆⠲⠆⢿⣿⣿⣿
⠀⢀⣾⣹⡇⠀⣈⣤⡤⠤⠤⣤⣉⢻⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠈⣧⣀⣠⡞⠛⢛⡉
⠀⣿⣸⠏⢀⣾⡏⠀⠀⢀⡀⠈⠙⢷⣿⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢿⣿⣿
⢸⣿⡇⠀⣾⠏⠀⣐⣶⣿⣿⣦⣤⣄⠙⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢺⣿⣿⣇
⣿⡿⡇⢠⡟⢠⣾⢿⣿⡿⠿⠿⠿⣿⣷⡸⣿⣧⣸⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁
⣿⡇⠀⢸⣧⢾⡇⣼⠁⠀⠀⣀⣀⣈⣿⣿⣟⢿⢿⡀⠀⣀⣤⣶⠚⠉⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⢹⡇⠀⠈⣼⠸⢁⡏⣀⡴⠟⣫⣽⡏⣩⠛⣿⡷⡾⠛⠋⠛⠋⠚⠋⠈⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠇⠀⠀⡏⠀⢸⣿⠏⣠⣾⣿⣛⢛⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⢸⠁⣴⡟⠉⣰⡟⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣰⣾⠿⡟⢠⣿⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⢋⠄⠀⣀⠔⠃⠀⣾⣿⣿⣿⣰⣯⡾⠛
⠀⠀⣴⣿⠃⠀⣵⣾⡇⣼⡿⣿⡟⠀⡆⠀⠀⠀⢠⠆⠉⠐⠁⠀⠈⠁⠀⣠⣾⣿⣿⣿⣿⡿⠋
⠀⣸⠏⠀⠀⠀⢸⣿⡇⢸⡇⢿⠃⠀⠀⡀⢇⣠⣤⣊⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⠟⠁
⠀⢻⠀⠀⠀⠀⢸⡿⡇⢈⡇⢸⡇⠀⠸⠁⠐⠉⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠈⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠻⡆⠀⠀⠀⠀⢸⣦⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣹⠿⡧⢠⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣧⣄⠀⠀⢠⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⡁⡟⠻⣶⣿⣖⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠛⢿⣿⠀⠀⢠⣼⣿⣿⣿⡿⢷⡄
⠀⠀⠀⠀⠀⣰⣟⣿⣿⡿⡿⣥⣶⠏⡇⣿⠏⠡⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠀⠸⣷⣤⣿⣿⣿⣿⣿⣿⣾⣿⣦
⠀⠀⠀⠀⣼⣯⡿⣜⣿⣷⣵⣿⣯⣿⣱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⢀⣆⣠⣤⠀⣠⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣸⣿⣿⣴⣾⣿⣿⣿⣿⣏⣿⣥⢂⠀⣀⣠⣀⣠⣄⣠⣤⣾⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢰⣿⣿⣿⣿⡿⡄⢻⠉⣿⣿⡏⢷⣏⢊⣽⡿⣿⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣿⣿⣿⣿⣻⣤⡀⠀⠲⣿⣿⣿⢿⣦⣬⡻⣵⣿⣿⣿⣶⡾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⣸⣿⣿⣿⣿⡟⢹⠏⠀⠀⣻⣿⣿⣟⣿⣾⣱⣽⣿⣿⣿⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣷⣿⣦⣷⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠛⠶⡴⠛⠿⣿⣿⣿⣿⣿⣿⠛⢫⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠌⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡙⣯⣥⣤⡟⣿⣧⣀⠀⠀⠀⣠⠀⠠⠝⠋⣉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠰⣿⢿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣻⠿⠿⣿⠁⢸⣿⣿⣶⠖⠚⢿⡧⠤⣶⣶⣶⣿⣿⣿⣷⣷⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⡿⢿⡇
⠀⣿⣿⡛⣋⠿⣿⣍⣿⣶⠶⠾⠿⠿⠿⠷⢶⠋⠀⣾⣶⡿⠧⣀⢀⣴⠋⣠⠞⣟⣿⣿⣿⣟⣋⣛⣙⡿⢸⣿⣿⠀⠀⠈⣇⣽⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⢹⡄⣿⣿⠷⠙⠶⣄⣤⣶⣶⣶⣶⣶⣶⡞⠀⣰⣷⣿⣧⣦⡿⠳⠶⣿⣯⠀⢾⠻⠿⠿⠿⠿⠿⠿⣧⠀⢿⣿⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣇⠈⠉⠀⠀⠀⠘⠿⣾⣿⣿⣟⠻⠥⠰⠾⠛⢛⣛⣻⣿⣿⡆⠀⠀⠉⠀⠈⣤⣽⣿⣶⢶⣶⣦⣿⠀⠀⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣶⣾⣯⣿⣿⣿⣿⣿⡇⢰⡷⠀⠀⠈⣾⣿⣻⣿⣛⣿⣿⡄⠀⠸⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠻⣄⠀⣀⠀⠀⠀⠀⠀⢈⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣤⣬⣭⣭⣽⣯⣼⣿⣧⡀⠀⠻⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠹⣆⠃⠐⠂⢀⡀⣀⡐⠒⠂⠭⢛⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⢧⡹⠶⠶⣴⡦⠠⠤⣤⠤⡀⠓⠿⣿⡿⣭⣝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣾⡛⢋⣿⣿⣿⣿⣷⣷⡆⠘⠛⡛⠛⣿⡿⣿⠟⠓⠛⣛⣽⣭⣽⣯⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣰⣍⡁⠀⠀⠀⠉⡀⠀⢠⡶⢾⢿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣷⣾⣴⣦⣼⣻⣿⣶⣷⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣍⠠⠄⣀⠀⠀⠀⠀⠑⠆⠀⠀⠈⠉⠉⠉⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⢋⣋⣽⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣥⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣿⣿⡿⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡾⡟⠙⢻⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡙⢁⣤⡮⢼⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⢶⡟⣦⣾⣵⣿⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠉⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠻⠛⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠫⠀⠀⠀⠀⣠⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢾⣿⣿⠟⢶⣍⣤⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⡀⠀⠀⠀⣸⣿⣿⣿⠿⣿⢛⣓⠶⢷⣾⢿⣿⣿⣿⣿⡻⠥⣤⣽⣆⣠⣋⣥⢟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣥⡁⠀⠀⣾⣿⣿⣟⣉⣻⡷⠦⣛⣛⣛⣻⡧⣼⠛⠛⠿⣷⣶⡤⠼⣗⣀⣠⡿⢏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⠁⣠⣾⣿⡿⣏⣈⣻⣟⠛⢛⣭⣬⡟⣁⠤⠄⠀⠐⠴⢉⣀⣻⣗⣄⣠⢿⣁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⣿⣿⢏⠁⠤⣽⣯⣉⣿⢿⡥⠞⣡⣯⣴⣾⣟⠋⢙⡛⠻⣻⡿⣿⣦⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢠⣿⣿⣾⣶⣶⣿⡶⢿⣗⡫⣞⣷⣟⠷⠻⣇⠉⠛⣮⣁⣈⡟⠀⠄⠜⠟⠫⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠁⠀⠀⠀⠉⠙⠻⠿⠻⣿⣿⣿⣛⠒⠀⠉⠓⠈⠉⡀⠀⠀⠒⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⣈⠉⠈⠉⠉⠀⠀⠀⡀⡀⠀⣽⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣒⠁⢤⣚⠊⠳⠠⢽⣾⣿⣷⠆⠀⠀⣶⡀⠙⠘⢦⢙⣿⣿⣹⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⢿⣿⣿⣿⣶⣧⣤⣿⣿⣧⡀⠀⢸⣧⣹⣄⡀⠈⢻⣿⣿⡇⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣧⡀⠤⠻⢿⣮⣄⠀⢉⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⢻⣾⣗⠆⠉⠓⠪⠸⠓⠂⠛⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢺⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠟⡩⠋⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠟⠿⢷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠚⣦⠽⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠲⣼⡏⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⣼⣤⣶⡾⠆
⠀⠀⠀⠀⠀⠀⠀⢾⡷⢿⣧⡘⢿⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠘⢿⣿⠟⠁
⠀⠀⠀⠀⠀⢠⡦⢼⣿⣌⠻⣷⡘⣷⡸⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⢠⣼⣇
⠀⠀⠀⠀⠀⠈⢿⣦⡘⢿⣷⣜⢿⣮⣿⡗⠄⠀⠀⠀⠀⠀⠁⠀⢂⠀⣨⣤⢀⢿⢶⣿⣿
⠀⠀⠀⠀⠀⣶⠾⢿⣿⣦⣙⢿⡷⠿⣄⡁⠰⣀⠀⢐⠀⠀⣅⡠⢼⣟⣩⠟⣿⣾⣾⣽⡿
⠀⠀⠀⠀⠀⠙⢷⣦⣈⠙⠻⣷⡿⢦⣈⣣⣄⣀⡀⢼⡶⠖⣾⣴⠞⣩⢿⣾⣥⣋⣟⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⠿⣿⣶⣤⣝⣦⣘⣧⣄⣉⡉⠽⣶⡶⠚⢻⣿⣇⡴⢉⠟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣭⣉⣛⣿⠿⣿⣤⣉⣉⠩⠽⣷⣖⢉⣨⠟⣿⣿⣾⣵⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣯⣿⣙⣿⣙⡿⣽⠋⣹⢧⣶⣡⡟⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣼⣭⣿⣤⡾⢛⣯⣴⣏⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣷⢾⣟⣻⣧⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⠛⠛⠻⠺⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⣀⣀⠘⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠭⠤⠀⠀⠿⠄⢈⡗⠀⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠭⠤⠤⠤⠭⠽⠯

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠴⢤⣀⡀
⠀⠀⠀⢀⡖⢊⣭⠽⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡏⠀⢴⠀⣿⢹⡦⣄
⠀⠀⠀⢸⡔⠁⡦⠰⡄⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠈⠀⢁⡏⠀⡼⢲⡄
⠀⠀⠠⠯⡼⠡⡀⠸⠇⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠤⠀⠀⠀⣀⠾⠀⠈⠀⢊⡹⡄
⠀⠀⠀⠀⠣⣀⣽⠀⠀⠀⠀⠀⠀⢲⣤⣌⡳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠘⢆⠀⢀⡶⠟⠀⠷⡄
⠀⠀⠀⠀⠀⠀⡟⠀⢀⠀⡀⢀⠀⢠⠀⠉⠛⠈⢦⣀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣤⠖⣰⠁
⠀⠀⠀⠀⠀⢰⠇⠀⠚⡆⠧⠚⠂⠀⣀⡠⠀⠀⠉⠉⣀⠀⠘⠣⠤⣄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⣨⠇
⠀⠀⠀⠀⠀⢸⠀⠀⣦⠇⠰⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⠊⠄⠀⢠⠆⠀⠀⠀⠛
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⠀⢠⠃
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⣴⠂⠀⡜⠀⢀⣉⡉⢩⡽⠂⠀⢁⠆⢀⠞
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢧⡀⠀⢀⠞⡅⠀⠔⢁⣠⠥⠖⠒⠉⠐⢶⣄⣠⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢠⣈⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠠⠠⠔⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣀⣂⣀⡀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣛⣩⠽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⢀⠀⣀⡴⣯⣭⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⡹⠋⠁⠀⠀⢾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡼⠀⠀⠀⠀⠀⠸⣱⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣄⣤⠴⠃⣃⣀⠀⢠⡶⣒⣚⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠖⠒⠀⠉⠁⠈⠉⠀⠀⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠿⣿⣿⣿⣿⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣾⡿⠧⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⢛⣿⠟⠃⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣀⣀⣀⣀⣱⣶⣿⣿⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣛⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠐⠑⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢈⠀⠈⠁⠀⠘⠀⠀⢤⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⢀⣀⡤⠤⠤⢤⣀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣁⠀⢠⢲⣾⣿⠑⢆⣀⠶
⠀⠀⠀⠀⠀⠀⠤⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠙⠁⠀⠀⠀⠀⢸⠶⢋⠀⠀⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⣄⠀⠀⠀⢰⠃⠀⠈
⠀⠀⠀⢀⡠⠤⠤⠄⣀⠀⢠⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣰⡗⠀⡄⢈⠁⠒⠚⣧⡀⠀⡰
⠀⠀⠐⠛⠀⠐⠀⠤⡀⠁⠠⡇⠀⡜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡿⣇⡷⠙⠧⡀⠀⣷⡌⠋
⠀⠀⠀⠀⢀⣠⠄⠀⠠⡀⢲⠨⣄⢠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⣁⢚⢄⣦⣷⣸⣰⣄⣌⣄
⠀⠀⠀⠰⠂⣠⣄⡩⡤⣀⡈⠳⣿⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠌⣡⢾⡟⢣⣛⣻⣈⠌⡏⢦
⠀⠀⢠⢇⣵⡉⠀⢄⣀⠀⠙⠷⣌⢣⡀⠀⠈⡄⠀⠀⠀⠀⠀⢀⣧⣀⡀⢊⡥⠊⠠⢴⡍⠹⡈⢷⠐⡼⣧
⠀⠀⠀⠟⠁⣀⠠⠤⢤⠵⢦⣀⠉⢦⡀⢳⠀⡃⠀⠀⠀⠀⢀⣼⡿⢞⠺⠛⢉⡘⠓⣺⠧⠤⣵⣼⠚⡇⣸⢷
⠀⠀⠀⠀⢊⠄⠶⠒⢉⣑⡦⣈⠛⢆⢻⠈⠀⠇⠀⠀⠀⣠⢊⠉⢀⡌⠀⠈⠁⢆⡾⢁⡔⣋⡉⠙⢶⡘⠉⢿⡇
⠀⠀⠀⠎⠀⢀⡘⠛⢉⣋⡙⠀⠙⢌⣳⠀⣴⠀⠀⢀⡼⠁⢸⡠⠋⠀⠀⢀⡜⣾⡷⠋⠀⠀⠈⠀⢸⠃⠀⠈⣿
⠀⠀⠀⠀⢠⣧⠞⢋⣭⠾⠛⠛⠓⢢⣕⣃⣸⣦⡴⠋⠀⠀⠘⢁⡀⠄⢀⡁⠚⠉⡠⠔⠀⠀⠠⢀⡟⠀⠀⠀⡏
⠀⠀⠀⠀⢾⠁⡜⢡⠃⢀⡤⠒⣩⢟⢿⡟⡻⡟⠀⠀⣀⣴⣁⠠⠄⠀⡀⠀⠀⠉⠀⠀⠀⡠⢡⡞⠀⠲⡄⢠
⠀⠀⠀⠀⠨⢸⠀⢸⣤⠋⠀⣴⠁⢡⠎⡔⡇⢱⠀⢸⡣⠞⠃⢀⠊⠁⢉⠀⠀⠀⠀⡠⢒⣴⠏⠀⠀⠀⣵⠄
⠀⠀⠀⠀⠀⠹⣄⠈⣿⠆⢸⡿⢠⡟⠀⡃⣇⠈⢷⡉⠀⣠⠔⢋⠀⠨⢤⡤⠤⠖⣋⠴⢋⡜⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠈⢺⣌⣷⠸⣇⠀⣧⣜⢶⣌⢻⡿⣦⣬⣭⣿⣷⣶⣖⣾⣽⢁⣠⣞⢁⣠⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣿⠀⣺⡇⠀⠉⠛⠿⠶⠀⠀⠈⠈⠉⠉⠁⠁⠉⠁⠼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢢⡀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣠⠞⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡄⠀⠀⢀⣤⠛⣤⠴⠋⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡶⣿⠁⢸⣏⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣴⡿⠃⠀⠀⠈⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣀⡠⠄⣀⣼⡀⢉⣿⡿⢅⣔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠡⣀⠀⣟⣿⣶⡿⣶⢤⣝⡙⠤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠉⠙⠽⢤⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠐⣲⣶⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣌⣹⣿⣿⣿⡿⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣲⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣼⣇⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠟⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠰⣿⣿⣿⡻⢿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣿⢿⣿⣶⣿⣿⠛⠀⠈⠙⠁⠀⠀⠀⢶⣿⣿⣿⣟⡛⠅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⣀⣙⡋⠉⣿⣿⠁⣤⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣲⡄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⣠⣤⣿⣿⣿⣿⣷⣦⣿⣧⣤⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣄⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⡀⣄⠀⠐⠿⣿⣿⣿⣿⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡁
⠀⠀⠀⠀⣤⢶⣶⣀⣜⣿⣿⣿⣿⣿⣶⣍⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣷⣆⠐⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⢀⣡⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣯⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣷⣬⣤⣄
⠀⠀⠀⢨⣳⡿⣿⣿⣿⣻⣿⣷⣿⣷⣿⣧⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣏⣿⣽⣿⣿⠁
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣬⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⢿⣿⣿⣿⣿⣿⣷⣼⡁⣿⣷⣾⣿⣿⣟⣿⣿⣦⡅
⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠜⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⣷⣿⣿⣿⡿⢿⣿⣯⡀
⠀⠀⠀⠤⣾⣿⣿⣿⡿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣽⣶⣉⣸⣿⣿⣿⣾⣿⣿⠁
⠀⠀⠀⠐⢿⣷⣾⣿⣿⢾⣿⢿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⡟⠊⠉⠀⠋⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣸⢟⡿⣿⣻⠧⣆⠙⠋⠀⢨⣰⢆⣀⠀⠀⠀⠀⠈⠀⢀⠀⡉⠟⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠾⢡⣟⣻⡿⣿⡟⠄
⠀⠀⠀⠀⣿⢿⣻⣿⣿⣞⣿⣦⣀⡀⣈⣙⣋⣉⣀⣀⣀⣀⣀⣠⣄⣠⣤⣁⣦⣤⡀⠀⠠⠀⠉⠉⣛⣭⣿⡿⢿⣿⣿⣉⣐⡃⣀⣠⠀⢔⡡⢀⡀
⠀⠀⠀⢠⣿⣿⣿⣿⡟⡟⢻⡟⣻⡋⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣷⣻⣿⠿⣿⡿⠛⣭⣏⡛⠛⢄⣴⢧⡔⢢⡄
⠀⠀⠀⠀⣩⠉⣬⣽⡛⠃⠈⡛⡃⠴⠰⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣦⣴⣶⡄⠀⠀⠀⠀⠰⠄⠀⢉
⠀⠀⠀⠀⠀⢴⡷⣮⠤⠤⠈⠛⡃⣤⣀⣠⢶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡉⢫⡄⢂⠶⠒⢤⣄⢀
⠀⠀⠀⠀⠀⠀⠒⠀⢸⠿⢏⠈⠉⠀⢀⣀⣀⣀⣀⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⢷⣄⣿⣿⣿⣯⣟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠐⠛⠛⠛⠉⠉⣩⣭⣽⣿⣿⣿⣿⣿⣿⠿⡿⠟⠛⠉⠁⠺⣿⣿⣿⣿⣿⣷⣎⣷⣜⢿⠿⣛⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠄⠀⡀⠀⣀⠶⢾⣟⣛⣿⣛⣻⣯⣀⣤⠶⠾⢿⣶⣤⣤⣉⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣀⢦⠴⢨⠿⢟⣛⠛⢛⣟⡛⣛⣛⡻⠛⠉⣓⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠐⣇⠈⣼⡗⣿⣿⣿⡃⣶⡄⣿⣏⣤⣟⣩⡿⠉⢭⣉⣩⣍⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣷⣟⣴⠛⣴⠄⠻⠟⠺⠷⠀⠀⠀⠀⠂⠀⠀⣚⣿⣟⣻⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⣿⣿⣿⣿⠷⣿⣆⢛⣿⣾⣀⠀⠒⠀⠐⠚⢙⣛⠛⣣⣤⡤⡄⠉⠉⠀⠀⣍⢉⠉⢻⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣅⡡⠋⠋⠛⠛⠿⠷⢿⣍⢿⣿⣿⣿⣴⣿⣻⣾⣿⡿⣿⣿⡿⠋⠠⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⠟⠉⠛⠁⠙⠁⠈⠁

⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⢴⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⡶
⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠐⠶⡞⠁⠀⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⡆⠀⠀⠀⠀⠀⠀⢰⣦⣤⠆⠀⠒⠀⢀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⢠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡠⠀⢀⣤
⠀⠀⠀⠀⠀⠀⣀⡀⢐⠄⠀⠀⠀⠀⠀⠀⢠⠣⣄⣀⢀⣀⣂⡴⠕⡄⠀⠀⠀⠠⠰⠀⠀⠀⠀⠠⠬⠄⢠
⠀⠀⠀⠀⠈⠛⠏⠀⠈⠿⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣈⣀⣅⠤⠞⠀⠀⠀⠀⠀⠐⢄⢖⠃⠀⠒⠂⠄⠒⠖⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠹⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⡲⢆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⣤⠀⢀⣠⠄⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠏⣉⡀⠀⣇⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢞⣀⣿⣾⣤⢸⡇
⠀⠀⠀⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠈⠡⢻⣥⡉⠰⣱
⠀⠐⠉⡁⠤⠀⠀⢀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠈⠉⠳⢲⢀⡙⠃⠙
⠀⠀⠸⠃⢀⡚⠂⡐⠒⢌⠘⠂⠁⠤⢈⠀⠶⢢⡴⣤⡶⠀⠀⠀⠀⠀⠁⢈⠀⢈⠀⢱⢒⠀⣲⠄
⠀⠀⠀⠀⠠⣄⠀⢘⢂⢂⠉⠄⡂⣠⣤⠞⣈⠓⠐⠊⠆⠈⠒⢰⠁⡅⢢⠈⠀⠀⠁⠀⠄⣤⠟⡄
⠀⠀⠀⠀⠐⠇⡀⠐⡞⢃⣴⢔⡏⡨⢴⣃⣞⢒⣀⠚⣐⡈⢉⡡⠆⠲⠊⢄⠀⠂⠡⠔⢀⠜⢈⡀
⠀⠀⠀⠀⠀⠀⠙⠿⠛⠑⣦⣸⣧⣿⠛⣣⢞⡿⠀⢾⠠⠅⠀⠀⠀⠀⠀⠀⠤⠆⢀⣴⠉⡴⢌⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠄⠘⣉⡼⣥⢾⣱⡟⢂⣈⣌⠐⡢⢴⣠⡔⠈⡠⢇⠤⠢⠄⠘⠡⣱⢌
⠀⠀⠀⠀⠀⠀⠘⠀⣠⣷⡒⠋⠀⠞⠘⠻⢿⣿⣟⣉⡙⣦⣤⠽⠿⢟⡉⠀⠃⠓⡰⢦⣗⢉
⠀⠀⠀⠀⠀⠀⠁⡀⠈⠛⡥⠀⣘⡀⣠⣄⡀⢄⣀⠀⣈⣁⡀⢠⠇⡀⣁⢨⡘⢁⣧⣄⣸⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠂⠐⠆⠁⠈⠁⠀⠁⠀⠁⠉⠀⠉⠈⠡⣿⣿⣿⢻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠡⢴⡗⠀⠐⠐⢂⡒⢒⣹⣾⣲⣾⠿⠞⠋⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⠟⠩⣼⢟⠗⣧⠸⣿⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢪⢽⠒⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⣾⠿⠛⠃⠐⠀⠀⠀⠀⠀⠀⠣⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣀⣤⠀⠀⠀⠀⠀⠀⡀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠻⢿⣄⣀⣤⣠⣤⡺⣂⢠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠿⣿⣷⢿⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⠀⠀⠀⢸⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⣸⣭⡄⠐⠁⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⡆⠘⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠄⢠⣿⣿⢿⣿⣅⣿⣹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⡇⠉⠉⠹⠃⢹⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⣠⡿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠹⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠼⠛⠀⣾⠋⠉⠀⠀⠀⠀⠀⢀⢀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⢀⠇⠀⠀⢀⣀⣀⣀⣀⣼⣿⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢘⣀⡌⢠⠀⠐⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠰⠆⢀⡴⠋⢠⠠⡆⠀⠤⢨⡝⠁⠀⢀⣤⡼⢿⢻⣏⠀⢴⣿⢃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠙⢩⣿⠀⠀⠘⠈⠛⠁⢙⣄⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⣚⣷⠐⣂⣤⣤⡴⣤⣴⣦⣤⣬⡀⠀⠚⢻⣄⣤⣤⣆⠀⠀⢬⣮⣧⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢻⣿⣿⣿⣿⡆⢀⡏⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢉⠍⠉⠉⠙⠉⠡⣀⢀⣶⣛⣋⣉⣉⣁⣉⣉⣹⡏⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠤⠉⣉⣏⢭⠉⣩⠉⠁⠁⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠸⠀⠀⠀⣤⣤⣦⣴⣶⣶⣷⠶⣿⣿⣿⣿⣿⣿⣷⡿⠄⠷⠖⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⢩⣷⡆⣹⡃⠘⠻⣿⣿⣿⣯⡽⠛⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢉⠁⠀⠁⠤⢼⡿⢏⣉⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠑⢦⣠⠔⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡤⠒⠉⣉⠶⠛⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡞⠀⠀⠀⢡⢖⠒⣄⡴⡛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⣾⠁⠀⠀⠀⢻⣛⣁⢜⣹⠥⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠉⠁⡎⠀⠉⠛⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠐⣏⠈⣉⡡⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣰⠉⠋⠻⢄⡀
⢰⠋⠙⠦⡖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⡀⢠⠀⠈⢄⡀⠀⠀⡱
⠸⡕⠤⡀⠘⢆⠀⠈⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠢⣅⠀⢂⡰⠈⢿⠛⠋⠁
⠀⢟⠢⣈⠑⠦⠑⠀⠀⠁⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠈⡇⠈⠀⠠⠜⣧
⠀⠀⠑⠮⣅⡀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠛⠲⠶⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠉⠙⢲⠀⠀⠀⠀⣾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣏⢦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠘⡦⣍⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠉⠒⠭⢍⣀⣀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠻⠭⠤⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣍⠛⢲⡶⠤⠤⠤⠤⢤⠤⠔⠒⣾⣉⡁
⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠛⠓⢀⣀⠀⠀⠀⠈⢷⣄⠀⢀⡴⢧⣀⣤⣞⡁⠉⠭⠃⣢⣄
⠀⠀⠀⠀⣠⠖⠈⢁⡤⠖⠊⠁⠀⠀⠈⠀⠀⠀⠀⠈⡏⡏⢀⣀⠿⡀⣀⣀⣀⣀⡀⠤⠬⠽⠦⣄
⠀⠀⠀⣰⣋⠠⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡃⠓⢹⠗⠂⣠⢬⣉⠞⠲⢀⠓⣤⠉⠉⠩⠵⢦⡀
⠀⢀⣼⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠉⠙⢦⡻⢯⣒⡦⣬⠬⣉⣿⠓⠚⠁⠀⠀⠀⠀⢙
⠶⢯⠥⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⢻⡢⣝⣲⡄⠀⠀⠀⠀⠀⠀⢸⠊
⠀⠲⣄⢒⣀⠀⠀⠀⠉⠑⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠿⠀⠈⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠈⠙⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⠞
⠀⠀⠀⠀⠀⠀⠙⠮⢦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⢠⠤⠖⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣚⣓⣦⣤⣤⣶⣶⣶⣚⣳⣤⣤⣴⣒⣉⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠁⠀⠈⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡁⠐⠀⠀⠁⠢⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠁⠀⠒⣶⡦⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈⠀⠀⠀⠠⠀⠀⠀⣀⠀⡠⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠀⠀⠘⠌⢠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠂⡀⠀⠀⠀⠀⠲⠎⠁⣰⠁
⠀⠀⠀⠀⠀⢈⠀⢀⠀⠀⢀⠀⡀⠈⣄⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠆⠀⠁⠀⠀⠀⣤⠲⠼⠁
⠀⠀⠀⠀⠀⠈⠀⠁⠁⠐⠈⢀⡀⠀⠘⠀⢴⠥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⠀⠆⠀⠁⢀⠀⠱⡄⠐⠠⠆⠀⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠁⠀⠤⠀⠤⡀⠈⠑⠄⠌⠄⠰⡇⡁⠀⢉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⢂⠀⠀⠁⠀⠆⠐⠂⠀⡇
⠀⠀⢠⠑⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠆⠀⠀⠀⠀⠡⠛⠒⠢⠤⠤⠤⠒⠖⢊⠁⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡃
⠀⠀⠀⡇⠀⠐⠈⠀⠐⠀⠠⠀⠈⠁⠀⠀⠠⡀⠀⠁⠀⠈⠀⠂⠀⢀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠁
⠀⠀⠀⡐⡀⠤⠌⠀⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣠⠀⠀⡠⠀⠀⠀⡄⠀⠀⠃⠠⠀⠂⢀
⠀⠀⠀⠉⠧⠆⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠀⠀⠉⠒⠀⠀⠀⠀⠀⡀⠀⠐⡀⠀⠀⠀⡀⠀⠈⠀⠀⠠⠀⠁⠀⡀⠉⠀⢈
⠀⠀⠀⠀⠀⠓⢂⠈⡄⠀⠁⠣⠂⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⠀⠀⠀⠐⠀⠀⡄⠀⠄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣋⣱⡤⢂⠤⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⣀⡀⠀⠈⠗⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡁⠀⠀⠀⠐⠀⡀⠠⣀⣤⣨⡀⢂⠈⡰⠞⢣⣼⠂⠈⡅⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠢⢥⠶⠛⠉⠉⠉⠉⠙⢿⢒⣒⣧⠴⠿⡶⠋⠀⠉⠁⠈⠉⠑⢯⡀⠀⡈⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠷⠁⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡭⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠐⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢉⡲⠦⠤⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠣⠄⠁⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠒⠦⣄⣁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⠀⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠈⢢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠠⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⣠⠶⠛⠋⠉⠉⠁⠀⢤⢽⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠞⠁⠀⠀⠀⣀⣤⠤⠄⠀⠀⠘⠳⠦⠶⠚⠁⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠤⠄⠐⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⠂⠀⠀⠀⢀⠣⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠚⠳⣄⠀⠀⠀⠀⡠⠊⣀⠀⠀⠀⠀⠘⠁⠀⢠⠇⠀⠌⢀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣈⠭⠟⠁⠀⠀⠀⠀⠀⠀⣠⠏⠀⠁⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⣤⣂⡀⠀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣀⠄⠀⣠⠾⣃⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠒⠲⠬⣝⠶⣤⣀⣀⠐⠠⠒⠒⠒⠒⢉⣉⡤⠖⢋⣁⣨⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⠩⠭⠭⠥⠬⠭⠽⠖⠚⠋⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⣴⡏⡏⡱⠶⡄⢀⢀⡀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠞⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣹⡭⠿⠷⠷⣴⠖⡇⡴⢻⠉⢷⡏⢹⠋⠉⠉⡿⢉⡉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡤⣰⣀⢀⡄
⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⢸⡇⢰⣋⠽⠀⣿⠀⣠⡇⣼⢀⡈⠃⠸⣶⠀⣾⠟⠉⡈⣱⠦⡀⣠⡤⢀⠀⠀⠀⣠⣾⠽⣛⣭⡛⡟⠉⠹⠳⣄
⠀⠀⠀⣿⣿⡿⣿⠟⣏⡽⣿⢸⡇⢀⣡⠤⢞⣿⡀⠈⢀⣏⣸⣷⣤⣞⠿⢊⢠⢶⣾⣟⢅⡀⠘⢻⣶⣿⣶⣿⣷⣿⣿⣾⣶⡏⠛⠂⢠⠆⢠⠹⠇
⠀⠀⠀⣿⣟⢧⣿⠖⠉⠀⠉⢸⠁⢸⠁⣀⠤⠚⠛⢒⡉⡍⠁⠀⣴⣄⡠⠏⡄⣿⡟⢹⠉⡷⠀⠀⢻⣿⣿⠏⠉⠿⠾⠿⣼⣿⡿⠖⢾⠜⠛⠒
⠀⠀⠀⠈⠙⠍⢻⠀⠀⠀⠀⢸⣤⡞⠋⢀⡀⢀⠆⠁⡡⠂⠀⢀⠜⠛⠁⣸⠃⠈⡶⠶⠀⠃⠀⠀⠈⢹⠟⣄⣹⠶⣲⣿⣿⣧⣶⣾⡿⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠰⢬⠤⠜⠂⠁⠀⠀⠈⠀⢀⡴⠁⠀⠀⠠⡟⢀⣠⣞⠈⠉⠿⡒⠲⠶⠟⠀⠉⡹⠋⠁⠀⠈⠙⣻⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡤⠁⠀⢈⠇⠀⠠⠀⠀⠀⣠⣾⣶⠀⠀⡴⢀⣷⣿⣿⡟⣿⢦⣀⠘⢦⣀⠀⢀⡼⠃⠀⠀⠀⣠⡾⢋⠄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡼⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠹⠃⠀⣰⠁⠘⣏⠁⠊⠜⣹⣇⢸⢝⣦⠈⢻⠛⠀⠀⠀⣠⡞⠫⠄⠈⠀⢀⠄⠑⢄
⠀⠀⠀⠀⠀⢀⠚⠋⡰⠁⠀⡄⡘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⡧⠀⠀⠘⡁⣿⠿⢛⠠⣀⡌⠀⢀⡠⠟⠁⠈⢀⠀⠀⠀⠀⠐⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⡇⡇⠀⠳⡄⠀⢀⠖⠀⠀⠀⠀⠘⡃⠀⡸⠀⠀⠀⡼⠟⠉⠀⠀⠀⣤⣴⠗⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠨⢰⠛⠀⢀⡴⠿⣇⡃⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠉⠩⠛⠀⣠⡴⠿⠖⠀⣀⣠⠴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⡦⠈⠁⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢁
⠀⠀⠀⠀⠀⢚⣄⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠤⠤⠤⠤⣉⠑⡄
⠀⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⣀⡀⠀⠀⠀⠙⢣⡀
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠱
⠀⢀⡀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⣶⠤⡑⡄⠀⠀⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢒⣶⠤⠤⣀⡀
⠀⠀⠀⠈⠳⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⡠⠚⠉⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⣴⡁
⠀⠀⠀⠀⠀⠀⠈⠱⡖⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡰⠋⠀⠀⠀⠀⣀⠤⠒⠋⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⣄⡜⠀⠀⣀⠤⠒⠉⠀⠀⠀⢀⣀⠤⡊
⠀⠀⠀⠀⠀⠀⢠⡜⠀⣀⢀⠀⠀⢠⠐⠀⠒⠒⠁⠀⠈⠒⠒⠤⠤⠤⣤⣤⣀⣀⣈⡳⡄⠊⢀⣀⡤⠔⠒⠋⠉⠁⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠙⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⢱⢚⣉⣀⣀⣀⣀⣤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠔⠒⠚⠉⢩⠂⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢩⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠐⠒⠒⠈⠉⠁⣀⠴⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠤⠤⠴⠒⠋⠁⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⢀⡽⠓⠒⠒⢄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠲⠎⠀⠀⠀⠀⠘⠺⡉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠃⡈⠀⠀⠀⠀⠀⠀⢀⣱⠈⠦⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣓⣭⢄⡠⠭⣵⠄⠀⠀⢠⡮⡵⣪⢖⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠷⠻⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣴⠟⠛⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⡧⠾⠟⠂⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⣦⣠⣾⣖⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢿⣻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣠⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣿⣟⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⡾⢤⣿⢦⡴⡾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠟⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠿⡖⢶⡾⢼⠶⣇⠛⠟⠿⢳⠆⣤⡄⣄⣀⣠⡖⠛⠉⡰⠶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡉⡆⡑⢦⠷⡌⢢⡈⢹⣄⢬⣈⣲⡀⢯⡭⣈⠛⠿⠂⠀⠜⢒⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠩⡏⡕⣾⢳⠓⣺⡍⢛⠓⠂⢼⠉⣉⣻⣖⡨⠅⠋⠄⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⡿⠓⢛⡿⠾⢠⢿⡌⠠⠄⣀⡈⠳⠦⠽⠂⠀⠠⣀⠢⢤⡶⢈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣟⣬⡌⢧⠶⡸⣰⣿⠁⢲⣬⣙⡋⠲⢤⠆⠑⣳⠤⣙⡾⢇⠢⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣏⣈⣡⡘⢆⣅⠹⠸⣷⠺⢄⠈⢹⡂⠘⢦⣄⢙⠲⢾⡙⡖⢦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡹⣇⢀⡀⣌⣻⣳⢽⡗⠠⠉⢻⡉⠓⠆⠻⢀⢀⣦⢝⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡾⣾⣻⣍⣳⡌⣶⣳⡄⠢⡀⠻⣟⡛⠲⠄⠃⡻⣝⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣯⣿⣿⣹⣇⠀⠙⢦⣘⣄⡀⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⡿⣻⣷⡾⣼⠋⣧⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣹⡶⢼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠃⠈⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠏⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⡿⠷⣤⣤⣤⣶⣶⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠸⠏⠀⢴⠾⠿⠟⠛⠹⠿