Smiling Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠤⠖⠛⠛⠛⠶⠖⠛⠛⠓⠲⠤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣛⣭⣥⣶⣤⣍⣩⣴⣶⣬⣝⣻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠲⣶⠒⠶⠶⣶⣦⣤⣤⣤⣤⣴⣶⠶⠖⠒⡶⠂⠀⠀⠀⢸⣿⣿⣿⣯⠉⣭⣍⣉⠉⠛⠛⠛⠛⠛⠛⠉⣉⣩⣭⢉⣽⣿⣿⣿
⠀⠀⠀⠐⡌⠻⢤⡀⠀⠈⠀⠈⠁⠀⠁⠀⢀⡤⠛⡠⠀⠀⠀⠀⢸⣿⣿⣿⣿⢷⣬⡛⣿⣿⣷⣿⣷⣾⣿⣾⣿⡿⢛⣴⢟⣿⣿⣿⣿
⠀⠀⠀⠀⠘⢦⡀⠙⠲⠬⣄⣐⣂⣠⠥⠗⠉⢀⡴⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡻⣿⣶⣍⣛⠻⠯⠿⢟⣛⣭⣶⡿⢫⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢛⣊⣙⠻⢿⣿⣿⣿⣿⡿⢟⣫⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣽⣿⣧⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠄⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣉⣀⡀⠀⠀⠀⠰⣄⢹⡄
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⠛⠻⠶⣥⡀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣀⡹⣆⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⢻⡆⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣛⣧⣴⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣄⣿⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠠⠴⡞⠁⣼⡟⠁⠀⠀⠹⡆⠀⠀⠀⠀⢰⢋⡀⠈⠙⡾⡇⠀⡀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣴⢛⠓⢆⠀⡇⠀⢻⡀⠐⠧⠆⢠⠇⠀⠀⠀⠀⠈⣿⠷⠀⢠⠇⢻⡟⢻⡌⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⠋⠳⡌⠣⣇⠀⠀⠙⠦⠤⠤⠋⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠀⠈⣯⣼⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣆⠀⠃⠀⠀⢠⡶⠒⠀⠀⠀⠀⠀⢠⣄⠀⠀⣀⡆⠀⠀⠀⠠⣄⢹⡅⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⠶⡆⠀⠘⠀⢼⣿⣄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⣦⡀⠏⣼⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢻⣿⣝⠓⠶⠤⠤⢤⣤⠤⠴⣺⣿⠋⠀⢰⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠙⠮⣍⡓⠒⠀⠀⠀⢒⣪⠟⠁⠀⣠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢰⠀⠀⠈⣻⣦⣄⠀⠀⠀⠀⠉⣉⣛⣛⣋⠉⠀⠀⢀⣴⠏⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡿⡇⠀⣰⠏⠀⠙⠻⢦⣄⠀⠀⠀⠉⠉⠁⠀⢀⣴⢿⣇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡾⠁⢿⣰⠏⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣴⠟⠁⠀⠙⣦⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠟⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠓⢤⣘⣧
⠀⠀⠀⠀⠀⠀⠀⢿⣴⠏⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⣲⠟⡿⠁⠀⠀⠐⠀⠉⣳⣦⣄
⠀⠀⠀⠀⡰⢁⣥⠞⢁⡄⢈⣄⡨⠀⠉⠓⠲⢌⡉⠻⢷⣄
⠀⠀⠠⢀⡴⢋⡴⠞⣉⡤⠊⠈⠛⠻⠶⢦⣄⢀⠨⡳⣄⠉⢦⡀
⠀⠀⢡⠏⣰⢋⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⢎⢎⢧⠀⢳
⠀⢀⡏⢀⣧⠋⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⢾⠈⡆⢸⡆
⠀⠘⢇⢸⡇⠈⣠⣤⣌⡙⠃⠀⠀⠀⠒⢛⣉⡉⠑⡇⢸⢀⡇⡼
⠀⠀⠸⡇⠇⠀⠙⠶⠿⠉⠀⠀⠀⠀⠘⣽⣏⠿⠂⣿⢟⣎⣼⠁
⠀⠀⠀⢱⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡼⣿⠹⣆
⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠇⣿⠀⡹
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠙⣧⢣
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⣉⣓⣋⡀⠀⠀⠀⣴⣿⣟⢦⣄⢘⣮⡃
⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⣠⡾⡿⡏⢈⡇⠙⢷⡹⣧⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⠠⠐⠉⠀⣣⠻⣷⣼⠀⠸⢸⠃⢸⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠈⡿⡀⢡⠏⠂⠘⠀⠀⢠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢱⠁⠱⣿⡄⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈
⣀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢸⠀⡼⠁⢳⡐⡀⠀⠀⠀⠀⠀⠁
⢹⡟⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏⣧⢠⡄⠓⡿⠷⠶⠤⣄⡀
⢸⡇⠀⠀⠀⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠓⠛⠛⠉⢉⣼⣾⢣⡎⠀⠀⠀⠀⠀⢳⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠛⠛⠿⠿⠿⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⢿⣿⡿⠟⠋⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣴⣦⡰⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡌⢯⣛⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⢀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣀⣀⣠⣤⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣭⣛⣛⣓⣒⣒⣚⣛⣉⣭⣥⣾⣿⠃⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠛⠛⠛⠛⠛⣿⡿⠟⠁⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣀⣀⣀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⣠⣤⣤⣤⣶⣶⡾⠿⢿⣿⣿⣿⣿⡏⠋⠉⠉⠙⠒⣶⡖⠛⠛⠉⠉⢉⢻⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠸⣿⢿⣿⣿⠟⠛⢛⠛⢛⠿⠿⠿⠿⢷⣶⣷⣶⣶⣶⣿⣶⣿⣿⣿⡿⠿⠿⢿⠛⠛⣟⡿⡻⠿⣿⣿⣿⣷
⠀⠀⠉⢳⡽⣿⡀⠃⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠁⠉⣤⠀⠀⠸⠞⠀⠘⠀⠃⠿⣿⣿⡽⠋
⠀⠀⠀⠀⢻⣼⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣀⡶⣿⣿⠁
⠀⠀⠀⠀⠀⠻⣟⠻⠿⣂⠛⠀⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠦⠀⠰⢓⡾⠫⡜⡿⠃
⠀⠀⠀⠀⠀⠀⠳⣦⡀⠈⠹⣶⡤⢄⣈⣉⣁⠀⠂⠀⠀⠂⠀⠀⠒⠒⠂⢀⠀⠴⢶⠄⠠⢀⣔⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣆⠀⠀⠀⠀⠉⠉⠁⠙⠛⠒⠛⠉⠛⠉⠉⠨⠗⠘⢈⠀⣀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢰⣀⣀⣠⣴⣿⣰⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠿⣿⣴⣾⣾⣶⣾⣿⣿⣿⣿⣯⣽⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠉⠉⠉⠉

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡎⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⢀⣀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⢱
⠀⠀⠀⢇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⠎⠁⠈⠑⣄⠀⢠⠔⠒⠲⢄⠀⠑⢄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡸
⠀⠀⠀⠀⠓⣄⠀⠈⠢⢄⡀⠀⠀⡜⠁⠀⠀⡇⢠⣴⣶⡄⠘⡆⠃⢠⣶⣆⠈⠇⠀⠈⢧⠀⠀⠀⡠⠔⠃⠀⢠⠞⠁
⠀⠀⠀⣀⠤⠚⠀⠀⠀⠀⠉⢆⢰⠁⠀⠀⠀⢇⠈⠛⠛⠁⢠⠇⠄⠈⠉⠁⠀⡆⠀⠀⠈⡆⠠⠊⠀⠀⠀⠀⠧⢄⡀
⠀⠀⠎⠀⠀⠐⠈⠑⡄⠀⠀⢸⡞⠠⢶⡀⠀⠀⠑⠂⠄⠒⠁⠀⠀⠐⠒⠒⢊⣠⠜⠳⠀⢷⡇⠀⠀⢠⠂⠀⠂⠀⠈⢣
⠀⠀⠱⣄⡀⠀⣀⡠⠓⡄⠀⠸⢱⠀⠀⠉⠳⡖⠤⢤⣀⣀⣀⣀⣤⡤⠶⠚⣩⠏⠀⠀⠀⡏⠇⠀⢀⠜⢄⡀⠀⠀⣀⠌
⠀⠀⠀⠣⣈⠉⠁⣀⡴⢹⣄⡀⠘⡄⠀⠀⠀⠈⢷⣶⣤⣤⡤⠤⢤⣤⣴⣿⠏⠀⠀⠀⢠⠃⢀⣠⡟⢆⡀⠉⠉⢉⡜
⠀⠀⠀⠀⠫⣉⣉⣀⠤⢊⡜⠀⠀⠹⡄⠀⠀⠀⠀⠹⣅⡀⠀⠀⠀⣀⣩⠏⠀⠀⠀⢠⠏⠀⠀⢇⠑⢄⣈⠉⢉⡹
⠀⠀⠀⠀⠀⠈⠙⠒⠒⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⠓⠤⣤⠤⠞⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠉⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⠀⠀⠀⠀⣀⣠⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠚⠛⠉⠉⠉⠀⠉⠙⠲⠶⠖⠛⠉⠉⠉⠉⠉⠙⠓⠒⠤⠤⣀⣀
⠀⠀⠀⠀⢠⣴⣶⣭⣭⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠴⠶⠖⣾⣿⡿
⠀⠀⠀⠀⠀⠹⣟⢧⣀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡽⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡈⠛⠶⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⠖⠋⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠉⠛⠷⢶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣾⣶⠶⠟⠋⠉⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠶⠶⠴⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠓⠒⠲⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡾⠉⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⣿
⠀⠀⠀⠀⣶⣶⣿⣿⠷⠄⠀⠀⠀⠀⣧⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢿⠓⠦⣤⣀⡀⠀⠀⣀⣠⣴⡾⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠙⠛⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⢤⣀⠈⠉⠉⢉⣩⡵⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣤⣤⣤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⠴⠛⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⠀⠉⠂⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⣠⢞⡥⣞⣫⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡈⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠘⠀⢀⡼⣋⠵⣚⣽⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⠀⠀⢄⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡼⢋⣵⣾⠟⠛⣁⡴⠚⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢳⡀⠈⢧⣹⣷
⠀⠀⠀⠀⠀⠀⢀⡷⠿⢋⡴⡫⢞⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⡄⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⢸⡇⣴⠏⣨⣴⣿⠗⢡⡿⣿⣿⣿⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠈⠒⠻⢿⣿⣿⣿⣿⣿⣿⣿⠘⣷⡘⡌⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣯⣼⣿⡿⠁⢀⡟⢸⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⡌⣇⢸⡘⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⡼⠁⡇⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣽⣿⣿⣿⡇⠰⢹⡄⢧⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣸⠁⣸⢱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠊⣧⠸⡄⣿⣿
⠀⠀⠀⠀⠀⢀⡟⢙⢻⠇⠀⢠⠃⢀⡏⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠸⣆⡇⢿⣿⡇
⠀⠀⠀⠀⢀⣾⠃⣼⣿⢠⡇⠀⠀⣼⣹⣿⣁⣀⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣿⣿⣿⣿⠀⠀⡄⣿⣷⢸⣿⣿
⠀⠀⠀⠀⣼⣣⢠⢸⡇⣼⠀⠐⢰⣿⣿⡿⠋⠉⠉⠉⠛⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠟⠛⠋⢉⣀⡀⠸⣿⣿⣿⡄⣆⠀⢸⣿⡘⣿⣿
⠀⠀⠀⣰⣿⡏⠆⢸⢠⡏⠀⠆⣾⣽⣷⡇⠀⣰⡶⢾⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⡿⣏⠱⣤⣿⣿⣿⡇⢹⡄⠀⢻⣧⣿⣿
⠀⠀⢀⣿⣿⠐⠀⡇⣼⠇⠘⢰⣿⣿⡿⠁⠀⠈⠓⠘⠈⠙⠁⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠉⠃⠐⠉⠈⣿⣿⣿⠘⣿⡄⠈⢿⣿⣿
⠀⠀⣼⣿⣏⠀⢠⢀⣿⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⢻⣿⡄⢸⣿⣿
⠀⠀⡿⡏⣿⠀⡿⢸⡿⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠘⣿⣷⡀⠻⣿
⠀⢸⣷⡇⣿⠀⡗⣿⡇⠀⣸⣿⠋⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣧⣿⣿⣷⡀⢿
⠀⢸⣴⣤⠃⢸⣿⣿⡇⠀⣿⣿⣤⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣿⣿⣧⡸
⠀⠈⣿⠃⡀⢸⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢰⠇⠀⡇⢸⡿⢹⣿⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣀⣀⣀⠀⢠⣤⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⠀⠀⠀⣾⠃⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣀⡀⠤⠚⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡆⠀⢰⠇⣸⣿⢻⠀⠀⢹⣿⣿⣿⣿⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢳⣀⠎⢠⣿⡟⢸⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⠏⠀⣼⢸⠇⢸⠀⠰⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣼⣀⣁⣏⣘⣁⣘⣃⣀⣃⣂⣻⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣙⣓⣶⣶⣶⣶⣚⣋⣁⣀⣀⣐⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡴⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠀⣀⣀⡠⠊⠀⠀⠉⠰⠊⠀⠀⠀⠀⠈⠢⠘⡋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠳⣄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⠀⠀⢠⠀⠈⠛⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠆⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⣄⠀⢀⡀⠤⠤⣀⠀⠀⠉⣀⡠⠤⣀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢁⡠⠔⠃⠐⠒⠒⠒⠀⠠⠤⠎⠀⠀⠈⠁⠈⠀⠀⠀⠈⠓⠒⠊⠁⠀⠀⠈⠀⠒⢤⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡌⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣆⠈⡄
⠀⠀⠀⠀⠀⠀⢀⠃⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢃
⠀⠀⠀⠀⠀⢠⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⣧
⠀⠀⠀⠀⠀⠘⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠝
⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠤⢀⣀⣀⠀⠀⠀⠤⠀⠤⠄⢀⣀⡀⢠⡤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣴⠄⢀⣈⡁⠀⠀⠒⠒⠛⠓⠀⢀⣉⣁⢠⣤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣴⠀⠀⠀⠉⠀⢹⡇⠀⠀⠀⢺⠁⠉⠀⠁⠀⣘⣦⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣀⠃⠈⠑⢤⡀⠀⢸⡇⠀⠀⠀⢸⠀⠀⢀⣠⠞⠉⠱⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢠⠁⠀⠀⠀⠀⡹⠂⢸⡇⠀⠀⠀⢸⠀⠰⡈⠀⠀⠀⠀⢣⡀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⠆⠀⠀⠀⢠⡖⠁⠀⢸⡇⠀⠀⠀⢸⠀⠀⠙⢆⠀⠀⠀⠀⢴⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠑⣄⠀⢸⠇⠀⠀⠀⢸⠀⠀⡠⠊⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠣⣸⠀⠀⠀⠀⢨⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠶⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⣠⠶⠆⣩⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢠⡍⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠙⠦⠔⢛⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢩⡄
⠀⠀⠀⢀⠴⠉⠀⠙⠶⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠴⠊⠁⠑⢄⡀
⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠙⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢤⣶⠋⠀⠀⠀⠀⠀⠀⠈⠳⢦
⠳⢄⡤⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⢀⣠⠶⠛⠛⠻⠶⣦⣤⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠸⣀⣴⠗⠀⣀⠀⠀⠐⠛⡇⠙⡄⠀⣾⠃⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⠀⡷⠀⠀⠀⣀⠀⢰⣄⣈⠇
⠀⠀⠀⠙⢀⠰⢏⣀⠘⠻⣤⢷⠔⡟⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⣀⣶⣠⡀⠀⢸⣿⡀⠰⡖⢃⡀⣹⢆⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⠂⠻⣆⣀⡀⠀⠀⢀⣴⠏⡇⠀⢸⡇⠀⠀⣇⠀⠀⠀⣴⠁⠘⢿⣷⠀⡿⠤⣶⢀⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⣖⠸⠟⠛⠛⠿⢿⡶⠚⠿⠃⢤⡇⠀⢸⡇⠀⠀⣿⠀⠀⠀⠈⠢⣤⣼⣷⣼⠃⠺⠇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡿⠦⠾⠿⠿⠖⠛⣇⠀⠓⠤⠚⡇⠀⢸⡇⠀⠀⣏⠀⠀⠀⠀⢠⠾⠤⠼⠿⠦⠛⠲⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡏⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⢀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠑⠒⠒⠂⠒⠊⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠒⠂⠒⠂⠒⠊⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⠶⠶⠶⠶⠖⠶⠶⠶⠶⠶⠖⠲⠶⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢤⣶⣞⣛⣋⣉⣉⡛⢻⠗⢰⡷⠙⣿⣛⣛⣛⣛⣛⣻⢷⡶⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠰⠎⠉⠛⠉⠉⠛⠛⠻⠂⣸⡇⠰⠎⠛⠉⠉⠙⢉⣉⣠⡦⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠠⢀⣀⠀⠀⠀⠀⣀⡀⠄⡹⢎⠰⢀⣀⠀⠀⠀⠀⠀⣀⠠⣞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠽⣿⠑
⠠⢶⢶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠋⣹⠀⡿
⠀⢸⠀⢸⡉⠙⡖⠲⢤⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⢴⡖⠋⠉⢸⠀⣸⠞⠁⠀⡇
⠀⢸⡀⠀⠙⠲⢧⡀⢸⠀⠀⠀⡇⠉⠉⠉⡏⠉⠉⠉⡏⠉⠉⠀⣷⠀⠀⢸⡇⠀⢀⡼⠛⠁⠀⠀⢠⡇
⠀⠘⡇⠀⠀⠀⠀⠉⠙⠦⢤⣀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⣀⣀⣸⠗⠋⠁⠀⠀⠀⠀⠀⣸
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠓⠒⠳⣤⠤⠴⠓⡖⠚⠋⠉⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠣⠤⠴⠁⠀⠀⢀⣀⣠⠿⠤⠤⠤⠤⢤⣄⣰⡃
⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡠⠞⠁⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠙⣲⠎⢀⣴⣋⣠⣤⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣰⠒⠒⢲⠋⠉⠉⢹⡉⠀⠸⡏⠉⠉⡏⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢤⣀⡘⡇⠀⠀⠘⡇⠀⠀⡇⢀⣀⡧⠴⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠓⠚⠛⠉⠉⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣦⣤⣤⣤⣤⣴⣖⣚⣉⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⠀⡀⢠⣠⡄⡀⢰⡄⣤⡄⠀⠠⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡤⠒⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠘⠂⠙⠈⠸⠆⠑⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⣄⠸⣵⠤⠚⡀⠀⠀⣠⠊⠑⣤⠀⡾⠁⠈⢀⠌⠀⠀⣸⠀⢠⢶⣄
⠀⠀⠘⢇⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⡼⠾⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢅⡀⣀⣨⠴⠃⠀⡏⣸⠁⠀⠀⠀⣠
⠀⠀⡀⠘⣆⠇⠀⠀⠀⣰⢆⣠⠊⠀⠀⠰⠛⢧⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠒⡉⠋⠉⠛⠻⣏⠉⠁⠀⠀⠀⠀⢇⠸⣀⣀⠴⠻⣮
⠀⠀⠙⢦⢹⡃⠀⠀⣶⠁⠀⠙⠷⠀⠀⠀⠀⠀⠀⣠⠝⠒⠒⠒⠠⠖⠷⠆⠾⠃⠀⠀⢘⠠⠁⠀⢅⠀⠈⡀⠈⡇⠀⠀⠀⠀⠀⠘⢦⣀⣀⠤⠚⠁
⠀⠀⠀⠀⢻⡅⠀⢀⡼⢦⣀⣠⡷⠀⠀⢠⣲⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⢇⠂⠁⠂⠌⡀⢀⡴⠃⡠⣲⠶⠄⣠⡀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⣀⣾⠞⢀⡴⠖⠒⠒⠚⡓⢖⠚⠒⠚⠉⠀⡎⡞⠀⠀⡴⢱⢃⢞⡆⢀⣀⡀
⠀⠀⠀⢀⠀⢱⡸⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⢹⠀⠀⠁⠀⠀⠂⠈⣳⠀⠀⠀⠀⢇⣉⡽⢾⢁⡈⠉⡼⠀⢸⣿⣟
⠀⠀⠀⠉⢣⢸⡇⠀⢠⠒⠒⠒⣦⢞⡉⠂⡇⠀⡀⢀⣠⡴⠖⠲⠒⠶⠖⠤⣬⣯⣀⣀⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠛⠁⢟⡴⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢿⠀⠀⠘⣦⠀⣴⢃⣄⠉⢲⣇⠀⠁⠉⠑⠀⠀⢀⠀⠁⠀⠐⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⠉⡇
⠀⠀⠀⠀⠀⢸⠁⠀⢀⠈⡻⣅⠀⠉⢠⠟⠈⢣⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣠⠴⠋⠀⠀⠀⠀⠐⡿⠷⠀⡿⢻⠀⠐⡾⡖⠀⠀⢸⢸⢀⡇⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠉⢀⡇⠀⣉⡶⠧⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⣿⣾⠀⠀⡇⡇⠀⠀⢸⠰⢨
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⡶⡄⠀⠀⢀⡔⠢⡀⠀⠀⣿⡇⠀⣿⣿⠀⠀⣧⡇⠀⠀⢸⠈⢸
⠀⠀⠀⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠤⠃⡇⠀⠀⢸⡘⢳⢣⠀⠀⢿⠇⠀⠿⠿⠀⠀⢿⠇⠀⠀⢸⡀⢸⠀⡀
⠀⠀⠀⠀⠉⠀⡇⠄⠘⠂⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⢸⠀⡤⠦⡀⡇⢀⡀⢸⡐⠞⡜⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠘⡇⠀⠀⠀⣇⠇⠀⠱⠇⢠⡇⠀⠑⠊⠀⠀⠀⢀⡜⠁⠀⠀⢀⣠⣶⣄⠀⣠⠚⠛⢤⡀
⠀⠀⠀⠀⠀⠀⣹⡃⠀⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠲⢖⡖⠉⠀⠀⠈⠿⠁⢀⡀⠀⠙⠇
⠀⠀⠀⠀⢀⣔⣁⠳⡀⠀⠀⠀⠀⠀⠀⡮⠀⣰⠀⠀⢳⠀⠀⠀⠸⠇⢶⠀⠀⠉⢉⡉⢹⡀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⡞⠑⠸⠟⢧⠀⠀⠀⠀⠀⣸⣷⣶⣾⣷⣶⣾⣇⠀⠀⠀⠀⢽⠀⠀⠀⢸⡇⠀⣉⠉⠉⣭⠉⠉⠙⣄⣀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⣇⠀⠀⠀⡸⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⠠⢼⠀⠀⠀⢸⡇⠀⢸⠀⠀⣾⠀⢀⣄⠀⠀⠈⣭⡍⠉⢹⡅⠀⠀⠉
⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⡀⠐⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⢸⠀⠀⠀⢸⠁⠠⢸⠀⠀⣿⠀⢸⣾⠀⠀⠀⡏⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⢈⣿⣆⣀⣠⢿⣦⡤⠤⠄⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⢸⢰⠀⡏⠀⠀⣿⠀⢸⡏⠀⠀⠀⡇⡇⠀⢸⣧⠀⠀⢤⡀
⠀⠀⠀⢀⣤⣤⠴⠛⢻⡿⠁⠀⠾⠎⠀⠐⠗⠁⠀⠀⠀⠀⢠⣀⠠⠤⣼⠤⠤⠤⠾⠼⠼⠷⠦⠤⠿⠤⠴⠧⠧⠤⢤⡷⠷⠶⠾⠷⢼⡆⠚⠁
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠃⠁⠀⠉⠉⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠠⠤⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠤⠄⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⠀⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠄⢀⡀
⠀⠀⢀⡤⢂⡈⣀⣀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠁⡀⢤⡀
⠀⠀⠘⡂⢜⠀⠀⠘⠀⠀⢸⠌⠉⠉⠫⠀⠂⠶⠤⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠤⠴⠀⠂⠜⠉⠉⠡⡅⠀⠀⠃⠀⠀⢃⡴⠃
⠀⠀⠀⠐⡀⠑⢄⡀⠀⠀⠘⠀⠀⠀⠀⡖⠀⠀⠀⠀⠡⢀⠐⠉⠉⠉⠫⡉⢉⠝⠉⠉⠉⠂⡀⠈⠀⠀⠀⠀⢲⠀⠀⠀⠀⠃⠀⠀⢠⣀⠔⡡⠁
⠀⠀⠀⠀⠐⡀⠀⠑⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠘⠁⡔
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠣⢀⡀⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠄⢀⣀⠜⠉⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠑⠠⡀⠄⠀⢀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣀⠀⡀⠀⠠⢀⠄⠊⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠩⠀⠀⣉⣁⣀⡉⠀⠨⠉⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠂⠈



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠠⠀⢀⡀⠀⠀⠀⣤
⠀⠀⠀⡠⠂⠉⢉⡰⠶⡒⠏⠉⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⡇
⠀⠀⢰⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀
⠀⠀⠘⡄⠀⠀⢣⠀⠀⠀⠀⠰⠁⠀⢀⢠⠄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡆⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⡤⠤⠒⠉⠀⣸
⠀⠀⠀⠈⠢⡀⠈⡆⠀⠀⠀⠀⠑⠀⢀⡀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠚⠱
⠀⠀⠀⠀⠀⠘⢄⢹⡀⠀⠀⠀⠀⠀⠀⠀⢂⡃⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠲⠆⠐⠶⡆⠀⠀⠀⠒⠋⠙⠃⠀⠀⡠⣇
⠀⠀⠀⠀⠀⠀⠀⡂⢇⠀⠀⠀⠀⠀⠃⠀⠀⢀⣀⡤⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠴⠖⠒⠲⠛⠉⠹⠉⠂⣀⠀⠀⣀⣀⠀⡀⠀⠀⠤⠀⠂⠩⠀⣸
⠀⠀⠀⠀⠀⢆⠈⠀⠈⠓⠢⠴⠦⠖⠒⢊⣉⣉⣁⡤⢤⠤⠖⢲⠒⠋⢉⠋⠉⢀⠃⠀⢀⠂⠀⢀⠂⠀⢀⠃⠀⠀⠃⠀⢀⠃⣀⣀⣇⣀⣠⡧⠤⠤⠦⠚⠁
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⡴⠛⠋⠉⠉⠌⠀⠀⠌⠀⠀⠌⠀⠀⠌⠀⠀⡌⢀⣀⣌⣀⣠⡬⠤⠤⠶⠖⠒⠚⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣐⣀⣀⣠⣀⣤⡤⠤⠤⠴⠖⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢦⠀⠈⠉⠁
⠀⠀⠀⢠⠀⠀⠠⣀⡬⠐⠁⠈⠷⠲⠶⠶⢤⣤⣤⠴⠶⠚⠛⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⢀⣤⠶⠖⠚⠓⠲⠶⠶⢤⣤⣤⠴⠶⠚⠛⠛⠛⠶⢦⣄⠀⠄
⠀⠀⠀⠉⡉⠉⠁⢀⠔⠀⠀⠀⠊⠀⠀⠀⠤⠤⠶⠒⠁⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠠⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢻⡀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠰⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⠴⠤⠤⠤⣀⠀⠀⠀⢀⠤⠄⠀⠤⢦⡀⠀⠀⠀⢸⠃⢹⡄⠀⠀⠀⣈⠤⠤⠤⢤⡀⠀⠀⠀⢀⠠⠤⠤⠤⣀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠈⣧⠀⢀⠜⠁⠀⠀⠀⠀⠀⠑⣄⡔⠁⠀⠀⠀⠀⠀⠙⢄⠀⠀⣿⠀⠘⣇⠀⢠⠊⠁⠀⠀⠀⠀⠈⠣⣀⠜⠁⠀⠀⠀⠀⠈⠱⡄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢹⡄⡈⠀⠀⠀⠀⢠⣶⣤⡄⢸⠀⠀⠀⠀⢠⣦⣤⡀⠘⠀⢸⡇⠀⠀⢻⡀⠇⠀⣶⣆⡀⠀⠀⠀⠀⡿⢠⣶⣆⠀⠀⠀⠀⠀⠙⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠈⣧⢠⠀⠀⠀⠀⠀⠛⠛⠁⡼⡀⠀⠀⠀⠈⠛⠋⠀⡸⠀⣿⠀⠀⠀⠘⣇⢂⠀⠙⠛⠁⠀⠀⠀⠀⢿⠈⠛⠋⠀⠀⠀⠀⠀⡔⠀⡿
⠀⠀⠂⠀⠀⠀⠀⢹⡄⠱⣄⡀⠀⠀⢀⣠⠞⠀⠙⣦⣀⠀⠀⢀⣀⡔⠁⣸⠇⠀⠀⠀⠀⢻⡄⠳⣄⡀⠀⠀⢀⡠⠊⠀⠑⢄⡀⠀⠀⠀⣠⠜⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠉⠉⠉⠉⠀⠈⠳⠋⠀⠉⠉⠉⠉⠁⠀⢠⡟⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠉⠉⠁⠀⠈⠛⠁⠀⠉⠉⠉⠉⠁⠀⢠⡏⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣰⡶⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣴⡟⠁⠀⠀⣠⡴⣤⡀⠀⠀⠀⠀⠀⢸⣇⣀⣼⠏⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⣠⡴⣤⡀⠀⠀⠀⠀⠀⢸⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⠀⣼⠋⠀⠈⢳⡄⠀⠀⠀⠀⢸⡿⠟⠁⠀⠀⢀⣴⡿⠋⣿⠀⠀⠀⠀⠀⣼⠃⠀⠈⢷⡀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⡿⠋⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⣷⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣿⣿⣀⣸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⢠⣶⣿⣿⣿⣿⣿⣽⣿⠿⢿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣟⠀⣻⣿⡿⢿⣿⣿⡿⠃⠀⠀⣀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠛⠀⠘⠻⣿⣶⣴⣶⣾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢋⣀⠀⠀⠀⣀⣀⣀⡈⠙⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣉⣉⠁⠀⠈⠉⠡⡄⠀⠀⢀⣿⣿⠌⢙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠛⣷⣮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⢲⣀⣀⣠⡶⠃⠀⠀⢀⣾⣿⣿⡟⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢲⣾⣿⣿⣿⣿⣆⠈⠉⠁⠀⠀⣠⠔⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⣿⣿⣿⣿⣿⣿⣦⣤⣤⠔⠋⠀⠀⠸⡏⢻⡟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣼⣶⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡼⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢛⣉⣉⣉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡴⠚⠉⠀⠀⠈⠉⠳⣄⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠱⣄⠀⠀⠀⠀⠀⠀⢀⡴⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡙⠲⠦⠤⠶⠒⢋⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡖⠒⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢵⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⡀⢠⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠉⠙⠲⠶⣶⣚⡉⠀⠈⠑⣄⠀⠀⢠⠞⠁⠀⠉⠑⠲⠶⣶⣚⡉⠀⠈⠳⣄⠀⢠⠞⠁⠀⢉⣑⣶⠶⠖⠚⠉⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠤⠀⠀⠀⠤⠄⠀⠀⠀⠘⡆⢀⡏⠀⠀⠀⠀⠤⠀⠀⠀⠤⠄⠀⠀⠀⠸⣤⠇⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⣀⣤⢻⡁⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⣼⠁⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣉⣤⣄⣠⣉⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⡼⣱⠃⠘⣇⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⢠⢿⡟⡇⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢠⠟⣦⣤⣤⣤⣼⣿⣩⣿⣏⣿⣷⣤⣤⣤⣤⢻
⠀⠀⠀⡠⢷⠁⠀⠀⣸⢆⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⣠⠎⢸⡇⠙⢆⠀⠀⠀⠀⠘⠒⠋⠀⠀⠀⠀⣠⢺⡄⡟⣄⠀⠀⠹⣿⣶⣿⣶⣿⠏⠀⠀⣠⠋⢸
⠀⠀⠀⡧⠟⠁⠀⣰⠃⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⣷⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⣿⡁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣼
⠀⢀⡞⠀⠀⠀⣰⠃⠀⠀⠀⡇⠀⠀⣠⠤⢤⠀⠀⢸⡇⠀⠀⠸⣤⠇⠀⠀⡇⠀⠀⣠⠤⢄⠀⠀⢸⠀⠀⠸⣤⠇⠀⠀⡇⠀⠀⣠⠤⣄⠀⠀⢸⠀⠀⠹⣥
⢀⡞⠀⠀⠀⣰⠃⠀⠀⠀⠀⡇⠀⠀⡇⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⢸⡆⠀⠈⡇⠀⠀⠀⠀⠀⢰⡇⠀⢰⡇⠀⢸⡄⠀⢸⡇
⣎⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠈⣇⠀⢸⡇⠀⢸⡀⠀⢸⠃
⣈⣓⣦⣴⣁⣀⣀⣀⣀⣀⣀⣈⣢⣴⣃⣀⣀⣳⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣈⣦⣼⣁⣀⣀⣣⣴⣃⣀⣀⣀⣀⣀⣀⣀⣘⣦⣼⣁⣀⣈⣧⣴⣃⣀⣀⣀⣀
⣿⣿⡏⠙⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠔⠐⠂⠀⠈⠉⠉⠉⠉⠀⠒⠤⢄⡀⠀⠀⠀⠀⣀⠤⠐⠒⠈⠉⠉⠉⠁⠀⠒⠀⠄⠠⢄⣀
⠀⠀⡀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⡀
⢴⠋⠀⠐⠒⣶⠒⠒⢦⠠⠤⢤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⠄⠀⢲⡆⠒⢰⠌⣳
⠘⡎⠣⡀⠀⡅⠀⠀⢸⠁⠀⠀⠱⡠⠊⠉⠉⠳⡒⠂⣠⡤⢤⣤⡀⡀⠀⣠⣤⠤⢤⡀⠒⡲⠋⠉⠉⢢⡰⠁⠀⠀⢹⠀⠀⠀⡁⠀⣠⢖⠋
⠀⠈⢄⠈⠲⢇⠀⠀⡄⠀⠀⠀⢀⠃⠀⠀⠀⠀⢢⠌⠀⠀⠀⠀⠑⠄⡔⠀⠀⠀⠀⠘⢤⠁⠀⠀⠀⠀⢃⠀⠀⠀⠈⡄⠀⠀⡷⠘⡡⠃
⠀⠀⠈⢆⠀⠀⠑⢤⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢸⡀⠀⠀⠀⣧⡤⠊⠀⡰⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠉⠲⣆⠉⢁⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢠⠉⠑⡢⠒⠁⠀⢀⠜
⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠑⠪⠑⠒⠠⠤⠸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠿⠠⠤⠐⢒⠩⠒⠉⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡑⠠⠄⠀⣀⣀⡠⠞⠦⣀⣀⡀⠀⠤⢐⡡⠄⠂⠈⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠒⠒⠒⠒⠂⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠠⠤⠤⠄⠤⠤⠀⠀⠒⠈⠁

⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠂⠉⠉⠉⠁⠀⠉⠁⠒⠠⢄⣀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠁⠈⠉⠉⠁⠒⠒⠠⠄⢀⣀
⠀⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢀⡀
⢶⡓⢲⡒⠒⣶⠒⠒⢖⡢⠤⢤⡄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⠤⠤⣤⠔⠒⢲⡖⠒⣲⠚⣳
⠈⡌⠻⡓⠟⣦⠄⣀⢸⠁⠀⠀⠱⡠⠊⠉⠉⠳⡐⠒⣠⠤⠤⣤⡀⠀⠀⣠⡤⠤⢤⡐⠒⡴⠋⠉⠉⢢⡰⠁⠀⠀⢹⢀⡀⢤⡞⠗⡫⢒⠃
⠀⠈⠀⠈⠳⢏⠉⠚⣷⡒⠢⢦⣀⠃⠀⠀⠀⠀⢡⠎⠀⠀⠀⠀⠑⣄⡔⠀⠀⠀⠀⠈⢦⠁⠀⠀⠀⠀⢃⡀⠤⠒⣾⡛⠊⠉⡷⠊⡠⠃
⠀⠀⠈⢆⠀⠀⠑⢤⡇⠁⠉⠋⡘⢳⣉⠒⢲⡀⣎⠀⣤⡀⠀⣀⠀⢸⠀⢀⡀⠀⣠⡄⢈⡄⣰⠒⢊⣱⠻⡀⠋⠉⠁⣧⠄⠊⠀⡰⠁
⠀⠀⠀⠈⠣⡀⠀⠀⠈⠲⢔⠈⢁⠀⠀⠈⠋⠀⡌⢹⣀⢀⣉⢀⠖⢺⠂⠇⢈⡁⢀⣸⠉⡆⠈⠋⠀⠀⢠⠉⠐⡲⠒⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⠢⢑⠒⠂⠀⠺⡃⠀⠀⠀⠀⠉⠀⢸⠀⠈⠁⠀⠀⠀⠀⠿⠂⠀⠒⢒⠡⠒⠁⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⠒⠀⠄⣑⠀⠤⠄⠀⠀⠠⠎⠦⠀⠀⠀⠤⠄⡐⠡⠄⠒⠉⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠀⠀⠂⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠐⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣐⣢⣤⣤⣤⣤⣤⣤⣤⣔⣂⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠀⠀⣐⡜⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⡴⠋⠉⠁⠀⢤⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⡀⠙⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡯⠔⣒⡀⠀⠠⡔⠂⠹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠁⠈⠁⠀⠀⠀⠀⠀⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠠⠤⠞⠁⠀⠀⠀⠀⠀⡁⠠⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠐⢥⣤⠀⠀⠀⠒⠲⣶⣞⠀⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠹⡆⠑⠦⢤⣀⣉⣠⠞⠁⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠹⡄⠀⠀⠀⢸⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠀⠀⠀⡀⠀⠀⢹⡀⠀⠀⢸⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠁⢠⠔⠚⠋⢳⣤⠼⠇⠀⠀⠀⠘⣦⠙⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⣧⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠘⣇⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⡼⠃⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢘⠈⡰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉⠂⠊⢐⠟⠉⠁⠢⡀⣀⡀⠀⠈⠂⠄⠺⣄
⠀⠀⠀⠀⠀⠀⢠⡎⠉⢳⣴⠋⠉⣦⠀⣼⣷⣿⣶⣤⠇⠛⠃⠐⠒⠂⠀⠀⠙⢷⠄⣶⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠰⠗⠶⠋⠈⠓⠖⠧⠀⢻⣿⣿⣿⡇⠀⠀⠀⠈⠒⢦⡀⠰⠆⠆⠶⠠⠈⢀⣀⠴⠷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣖⠒⡸⠀⠀⠀⠀⠀⠈⠿⠿⠷⠼⠤⠛⠠⠼⠀⠙⣦⠀⠀⠀⠀⠀⠈⠁⢀⣠⡬⠭⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠀⠰⠆⠀⠘⣿⡆⠀⠀⠀⠀⢀⣤⣞⠀⠈⣧⢀⣤⠀⢀⡴⠞⣩⡅
⠀⠀⠀⠀⠀⣀⡀⠘⢎⣉⡀⠁⢾⣿⣿⣿⡗⢿⣿⠀⠀⠀⠀⠺⣿⡿⠀⠀⢹⡄⠉⣴⠋⠀⠀⠻⠃⠴⣒⠁⠀⡀
⠀⠀⠀⠀⠀⠉⠀⢰⠃⠤⠹⡄⠰⣿⣿⣿⣿⠻⣿⠇⠘⠟⠀⠀⠰⠀⠂⠀⢸⡇⣼⡇⢰⣶⡆⠀⠀⠀⠋⠁⠈⠛
⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠒⠲⢤⣀⠈⢀⠀⡀⠁⣾⢣⣿⠀⢸⣿⡇⢀⡛⠀⠀⠀⠀⠀⠘
⠀⠾⠶⣤⠈⢁⠐⠀⠀⠊⡠⠀⠀⣷⠀⠰⠀⠀⠀⠀⠀⠀⠈⢷⡌⠀⠀⢰⡿⣸⡇⠀⠀⣬⣶⣼⣇⠀⡦⠀⠠⡆
⠀⠀⡼⠁⠐⠒⠀⠀⠀⠀⠒⠀⠀⣿⢰⣿⣿⣇⠀⠀⠐⠀⠀⠀⣿⡆⣠⣿⢣⣿⢁⡄⠀⠛⠛⠋⢛⣀⣤⣤⣤⣤⡀
⠀⠀⣀⡀⠀⠁⠀⣀⣀⠀⠨⢦⠀⣿⠀⣉⣩⣥⣤⣀⠀⠀⠀⠀⣼⣿⣿⣷⣿⠏⠺⠛⣫⢁⠀⠘⠛⠛⠛⠛⢋⠁⠂
⠀⠾⠋⠀⢶⣶⠀⠙⠟⠀⠀⠋⠀⣿⠈⠙⣿⣿⣿⡟⠛⠀⠀⢠⣿⣿⣿⡿⠃⠀⢲⣶⡁⠷⣤⠀⠀⠀⠈
⠀⠠⣶⣤⠈⠏⠀⠀⠀⣸⣧⡴⡀⢻⣆⠀⠀⠉⣩⣴⠀⠀⢠⣿⣿⠟⣁⡤⠀⠀⠈⢉⠁⠐⠁⠀⠄⢐⠀⠀⠀⡌
⠀⠀⠀⠀⠀⢀⣄⣀⠀⣀⣠⠏⠀⠀⠛⢿⣶⣤⣙⠋⠀⣰⣿⠟⢁⠀⠀⠀⢀⠀⢸⣿⠀⠀⠀⠀⢂⠉⠐
⠀⠀⠀⠀⠀⢰⣿⣿⠀⠸⠷⠄⠀⠀⠀⠀⠉⠻⣿⣿⣾⣿⡏⡰⠀⡐⠁⡤⠁⢰⡄⠀⠀⠆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⢠⣼⣍⠀⠀⢡⠀⠀⣸⣿⣿⣿⣷⡀⠀⣿⠀⠀⠀⣼⠇⡤⠘⠛⢠⡄⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠈⣠⣾⣿⣿⣿⣿⣿⠿⠷⠦⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⣼⣿⣿⣿⣿⣿⡟⢁⣠⠤⠖⠒⠚⠛⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡼⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⢀⣾⠴⠒⠋⠉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠓⠲⢤⣸⡇⢀⣠⠤⠖⢒⣛⣋⣉⣉⣉⣉⣉⣛⣒⣲⣦⣼⣆
⠀⠀⢀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠲⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡄
⠀⣠⣺⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⣶⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀
⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣷⣬⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣷⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣷⣆⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⡏⠀⢀⡀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀⠀⠀⠈⠁⠀⠀⡇⣼⣿⣧⣴⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣈⡙⢦⡀⠀⠀⠀⢳⠻⣿⣿⠿⠁⠀⠀⣸
⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠚⠛⠿⢿⡄⠀⠀⠈⢧⡀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠾⠟⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⣷⢽⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡿⢤⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡃⠉⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠉⠉⠉⠛⠉⠉⠉⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠙⠒⠒⠒⠒⠛⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠋⠁

⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠿⣿⣿⣿⣦⣀
⠀⠘⣿⣿⡟⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣤⣟⠿⣿⣿⣷⠀⠀⠀⣠⣶⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠛⠠⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠘⠻⣿⣿⣷⣾⣙⢿⣷⣦⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡠⢦⣴⣶⢦⡤⠔⣶⣶⣿⣿⣿⣿⠏⠉⠉⢻⣿⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿⢻⣿⣟⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⠧⣼⣿⣿⣿⣿⣿⣿⣷⣀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠘⠛⣻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡉⢁⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠓⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠈⠋⠋⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⢠⡀⠀⠈⠛⠋⢀⣠⠄⠀⠀⢘⣛⠀⠀⢀⣸⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⣽⣶⡀⠀⠀⢾⡷⠀⠀⠀⣿⣿⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠲⣿⠟⠁⢰⡄⠀⠀⠺⠇⠀⠻⠇⠀⠀⠀⢾⣿⣿⣿⣿⡆⠀⠀⠈⠿⢿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠀⠀⠀⠀⠀⣀⣾⣦⠄⠀⠀⣠⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⢸⡆⠀⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⣤⠀⠀⠀⠐⠛⠛⠀⠀⠀⠈⣿⣿⣿⣿⣖⣤⣾⡎⢀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠦⢾⣿⣶⣤⣤⠼⠷⠶⠛⠓⠂⠒⠻⠶⠀⢀⣿⣿⣿⣿⣿⠿⡿⠃⢸⡆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣴⣾⣿⠋⠉⠉⠁⠀⠀⣴⠟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡀⠀⢀⡄⠠⣾⣿⣿⣿⡿⠿⠛⠉⢀⣴⡆⠀⠀⠘⠋⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡋⠉⠀⠀⠈⠙⢿⣿⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙

⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣶⣄⠀⠀⠀⠀⣸⣛⢛⣓⣀⠀⠀⠀⠀⣴⣶⠶⣆⠀⠀⠀⢀⣶⣾⣶⣦⠀⠀⠀⠀⠠⢒⣆
⠀⠀⠀⠀⠀⢻⠿⠿⠿⣿⠀⠀⠀⠛⠋⠀⣀⠈⠛⠃⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⣾⡧⠀⠠⢿⡇⠀⠀⠀⡖⠋⠋⢲
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄⠀⠀⠀⠀⢀⣠⣄⣀⣦⡄⠀⠀⠹⣷⡄⠀⣾⠃⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠐⠄⠀⠀⠀⠄⠀⠀⠂⠀⠀⢀⠀⠀⠈⠗⠻⡛⡗⠃⠀⠀⠀⣀⠁⠀⢁
⠀⠀⠀⠀⠀⡀⠀⡀⠁⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⣷⠹⠄⠀⠀⠀⠈⠂⠔⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠁⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣶⣶⣶⡄⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⡿⡿⠟⢿⠀⠀⠀⠀⣾⠋⠈⢿⠀⠀⠀⠀⣾⠛⠛⢻⠀⠀⠀⠀⠸⡇⠀⠉⡓⠀⠀⠀⠀⡿⠛⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣄⠀⠀⠀⠰⣤⣤⡼⠁⠀⠀⠀⠀⠁⡀⢠⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⡟⠀⠀⠀⢀⠉⠉⠁⡀⠀⠀⠀⠀⠴⢠⣀⠦⠀⠀⠀⠀⣄⠈⠀⠡⠆
⠀⠀⠀⠀⢠⣾⣿⣷⣷⣿⣷⡄⠀⠈⠀⠂⠀⠂⠈⠃⠀⠀⡙⠄⠀⠼⡃⠀⠀⠀⠀⠳⠀⠠⠇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠠⠶⠀⠀⠰⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⡄

⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⡟⠛⠛⢿⠀⠀⠀⢠⣿⡿⠋⣿⡆⠀⠀⠀⢐⣋⣉⣙⣓⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⣴⣿⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠌⠉⠉⠡⠀⠀⠀⢸⣇⠁⠀⢠⡇⠀⠀⠀⠘⠁⠀⠀⠋⠀⠀⠀⠐⡟⢛⠛⣿⠀⠀⠀⢸⣿⠃⠐⢉⣧
⠀⠀⠀⠀⠀⠀⢀⠂⠐⡀⠀⠀⠀⢸⣿⠇⠀⢿⡇⠀⠀⠀⠀⠴⢀⠴⠄⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠘⢿⡦⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠁⠐⠃⠁⠀⠀⠀⠀⠋⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⣤⡐⠀⠐⢁⣴⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⡮⢵⣿⣿⡇⠀⠀⠀⠘⡿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠛⠛⠃⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠐⠀⠉⠉⠀⠀⠀⠀⠈⠁⠒⠠⠄⡀⠀⠀⣀⠠⠀⠂⠈⠀⠀⠀⠀⠉⠉⠐⠂⠀⠠⠄⣀
⠀⠀⠀⢀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡀
⠀⠀⠘⣯⣉⠋⠉⠹⠋⠉⢫⡔⠒⠲⡀⠤⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠤⡴⠒⠒⢶⠂⠉⠻⠉⠉⢛⣉⡟
⠀⠀⠀⠐⡈⠢⣀⠀⠀⠀⠸⠀⠀⠀⢰⠌⠁⠀⠈⠡⠈⡩⠒⠒⠲⢖⠒⢒⠶⠒⠒⠪⡉⠡⠉⠀⠀⠈⢴⠀⠀⠀⠸⠀⠀⠀⠀⢠⢜⠏
⠀⠀⠀⠀⠐⡀⠈⠓⢄⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢡⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆⠀⡠⠛⢀⠊
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠙⢇⡀⢀⠠⠇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠧⢀⠀⢀⠗⠋⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⠃⢄⠡⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⠠⢃⠤⠊⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠒⠬⣉⠁⠰⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡰⠀⢉⠩⠐⠈⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠤⠀⠀⢈⣀⡈⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠀⠤⠄⠀⠀⠀⠠⠤⠀⠀⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠒⠂⠀⠈⠉⠁⠐⠂⠄⢀⡀⠀⠀⠀⠀⣀⠠⠄⠒⠀⠉⠉⠀⠒⠒⠠⠤⠀⢀⡀
⠀⠀⠀⠀⢀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠄⣀
⠀⠀⠰⣞⠒⡒⠒⢲⠒⠒⢖⡢⠤⢤⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⣠⠤⠤⣀⠔⠒⢲⠒⢒⡖⢛⡶
⠀⠀⠀⠠⠙⢏⠛⢧⡄⣀⡸⠁⠀⠀⢡⡔⠉⠉⠙⢃⠐⣒⠦⠤⠤⡤⠤⠤⡤⠤⠤⢖⠒⢀⠛⠉⠉⠑⣠⠁⠀⠀⠹⣀⠠⢤⠟⢊⠝⡟⠁
⠀⠀⠀⠀⠡⡀⠙⠯⡀⠉⡽⣃⠒⢢⣸⢀⡀⠀⠀⢀⡖⠁⠀⠀⠀⠈⢂⠊⠀⠀⠀⠀⠑⣆⠀⠀⠀⣀⢸⣠⠒⣊⡻⡍⠁⢁⠖⠉⠌
⠀⠀⠀⠀⠀⠱⡀⠀⠈⠲⣇⠀⠈⣁⡎⠏⠉⣉⠷⢤⣁⡴⢄⣀⡠⠀⢸⠀⠠⣀⣀⠴⣄⣥⠰⣏⡈⠌⠋⣆⠉⠀⠀⡷⠖⠁⢀⠊
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠙⠪⡀⢃⠀⠀⠈⠀⣸⠀⠥⠂⠠⣀⠃⢹⠀⢃⡤⠀⠠⠅⢸⡀⠈⠀⠀⢀⠂⡈⠔⠋⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠈⠐⠨⣀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠨⠑⠈⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⠐⠀⠡⠒⣀⡀⠀⠐⠀⠀⠀⢀⡀⠀⠂⠁⠐⠈⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⢀⠀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠤⠐⠊⠁

⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣿⣟⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⣒⠒⠲⣒⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⣯⣶⣻⣽⣿⣿⡿⣯⣾⣷⡂⠤⢈⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣾⢷⣿⣟⣩⢙⣷⣷⣶⣿⡗⠲⠞⡛⢿⣿⡖⠪⣾⣆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣵⢿⣯⣿⡿⣷⣾⠿⢟⣛⠻⢿⠿⣟⡶⢤⡑⢿⢙⠻⡢⡙⣜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⣶⠋⡫⢺⣿⣿⡾⢿⣿⣶⣦⠤⠀⡉⠘⠿⣾⡇⢇⠐⢦⡾⢟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⣿⣿⠟⣹⡟⡹⠁⠈⣟⡿⣶⠍⣙⠲⢤⣈⠐⠼⡟⠢⡃⠜⣧⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⣿⣧⣴⡟⣰⠁⠀⠀⠈⢻⣮⡻⣮⣗⡂⠉⠻⡄⠈⢧⢿⢀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣷⢿⡵⠁⠀⠀⠀⠀⠀⠉⠻⢮⠪⡙⠢⢅⣈⣃⠬⣨⣤⢿⣇⢺⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣿⣿⣟⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠷⣄⣙⠻⣦⡑⢟⣸⣿⣸⣟⢲⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠁⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠞⢿⣿⣿⣿⣿⡮⣿⣳⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⣼⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡇⠻⣽⠯⢝
⠀⠀⠀⠀⠀⠀⠀⠐⢓⣻⣭⡀⢸⣿⣿⡆⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⣠⣿⡏⣿⣇⣾⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⢾⣧⡇⢿⠃⢻⡦⡠⢀⠀⠀⠉⠉⠙⠛⠛⠉⠉⠀⣀⠤⠊⢭⣿⢠⣟⡸⣟⠶⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣜⣿⣽⣿⣿⡿⢻⣿⠀⠑⡄⠁⠒⠀⠀⠀⠀⠐⠂⡏⠁⢀⠊⠿⡿⣾⣧⠶⢮⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠸⣷⣞⣿⡇⠀⠴⠐⠒⠂⠀⠀⠂⠒⠂⠄⠀⣶⡷⣶⡷⣟⠻⢷⣯⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡰⠠⠁⠀⢿⣍⣻⠁⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⡴⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣷⡀
⠀⣠⣶⣶⣤⣤⣦⣄⢺⣿⣿⣿⣿⣷⣄⠠⣴⣾⣿⡷
⠀⢿⣿⣿⣿⣿⣿⣿⣦⢻⣿⡿⢿⣿⡿⢹⣿⠃⠈⠁
⠀⣼⣿⣿⣿⡅⠈⠻⣿⣿⣿⠁⣸⣿⢣⠟⢉⣡⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠻⣿⣿⣿⣿⣶⣄⢹⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣶⣄⡀
⠀⣀⣤⣤⣭⣭⣽⡿⠇⢴⡿⢟⣛⣉⡉⠉⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣤⡀
⣾⣿⣿⣿⡟⠁⠀⢀⣴⣦⡘⢻⣟⡻⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⡀
⢘⣿⣿⣿⣧⣤⣶⣿⡿⣿⣿⠀⠙⣿⣶⡙⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⣾⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⠈⠻⠛⢹⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⠿⠏⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⢠⣿⣿⠏⠀⠀⢿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷
⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿
⠀⢹⣿⣷⠀⠀⠀⠀⠠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣤⣤⣤⣤⣤⣤⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠛⠈⠋⠴⠓⠋⠉⠉⠉⠉⠉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠈⠉⠀⠹⠓⠀⠀⠀⠀⠀⠄⢀⡀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠐⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢠⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⣮⠆⠀⠀⢠⠻⡀⠀⠀⠀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠈⢧⢳⡀⢱
⠀⠀⠀⠀⠀⠀⣸⠀⠠⡎⠀⠀⢀⠎⠀⠱⡄⠀⠀⠈⣄⠀⠀⠀⠀⠑⡀⠀⠀⠈⠀⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠇⠀⢱⠀⠀⡠⣫⠔⠚⠛⠛⠦⣄⡀⠈⣗⠤⣀⡀⠀⢹⣆⡀⠀⠀⡇⠀⠸
⠀⠀⠀⠀⠀⢸⠀⠀⢀⡷⡞⠁⠀⣄⠤⠤⡀⡄⠀⠉⠙⠁⢠⢀⠬⠭⣡⠈⠙⢢⢾⡀⠀⠀⡇
⠀⠀⠀⠀⠀⣸⠀⠀⣾⠐⡇⠀⠺⠇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⠗⠀⢸⠂⡳⠀⠀⣇
⠀⠀⠀⠀⠀⡏⢀⠀⠘⠦⣿⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠃⠀⠀⢸
⠀⠀⠀⠀⠀⣇⢈⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠃⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢀⡠⠋⠀⢈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡈⡆⠀⠀⠸⡄⠀⠙⠒⠦⢤⣀⣀⣀⣀⣀⣀⡤⠴⠒⠋⠀⠀⠀⠸⡄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠳⡈⠀⠠⡄⠱⡕⡀⠀⠀⠀⢠⠇⠀⠀⠸⡄⠀⠀⢀⢎⠃⠀⢠⠴⠃⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠢⠤⠽⢢⣤⡴⠋⠀⠀⠀⠀⠙⢦⣤⡔⠯⠤⠔⠛⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠰⢍⣒⠦⠤⠤⠴⣒⡉⠚⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠉⠉⠁⠈⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠘⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣜⣀⣀⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣀⣀⣣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠑⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢂⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⢀⣎⠀⣀⣀⣀⣀⣀⣂⠁⠀⠀⢠⠤⠤⠤⠤⠒⠁
⠀⠀⢀⡀⠄⠀⠀⠄⢀⠀⢸⠀⢀⣤⣾⠿⠇⠀⠀⠀⠀⠀⠀⠨⣷⣶⣤⡀
⠀⠀⠀⠉⢢⠀⠀⣀⣀⣨⣼⣮⣥⣬⣅⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣥⣬⣷⣤⣤⣤⣤
⠀⠀⠀⠀⢸⠀⠀⢷⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾⣿⣿⣷⠟⠤⣀⠀⣀
⠀⠀⠀⠀⠘⡆⠀⢠⢿⣿⣿⣿⠟⣡⣾⣿⣿⣿⡏⠀⠈⣿⣿⣿⡿⠉⣴⣿⣿⣿⣿⠟⡄⠀⠀⠉⠁
⠀⠀⡠⠀⠁⠀⢀⡏⠘⢿⡿⢃⣼⣿⣿⣿⣿⠟⠁⠀⠀⠘⢿⡏⣠⣾⣿⣿⣿⣿⠏⠀⢱⠀⡠⠂
⠀⠘⠐⠢⡀⠀⢸⠀⠀⠀⠙⡛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠈⡏⠑⢦⡀
⠀⠀⠀⠀⠀⢂⣼⠀⠀⠈⠙⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⡇⠀⠀⠑⢄⣀⣀
⠀⠀⠀⡠⠒⠁⢸⠀⠀⠀⠀⠀⢱⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⠈
⠀⢀⠎⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢣⡜⠉⠉⠐⠒⠒⠂⢸⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠤⠄⠊
⠀⣌⠤⠤⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠱⣖⠶⠐⠂⠖⠀⠘⢲⠒⠒⠑⡆⠀⠀⠀⠀⢠⠃⢱
⠀⠁⠀⠀⠀⠈⠁⡲⠘⢆⠀⠀⠀⠀⠀⠀⠙⠢⠄⣸⣀⣀⣠⡤⠤⠀⠁⠀⠀⠀⡴⠁⠀⠀⠓⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠅⢀⣀⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠃⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠉⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠝⢟⠛⠛⠋⣩⠛⢄⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠀⠈⠢⡀⢰⠁⠀⠀⠑⠢⠤⢘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⣄⣀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠩⠩⣵⣾⣿⣺⠭⠥⠅⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⣤⠤⢀⣩⣽⣿⣿⠿⠿⠭⠍⣙⠒⠶⢤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⡾⠋⢠⠖⢉⣥⣶⣾⣿⡶⣿⣿⣦⡀⠀⠀⠀⠈⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⢀⣴⣿⠿⠟⠛⠛⡟⠛⠷⠿⣧⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣙⢆⡀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⡏⠀⠔⠚⠛⠻⠶⠶⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠻⣶⣤⣀⠘⣆
⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⣿⠁⠀⠀⢠⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⢿⠏⢳⠆⠀⠀⣯⠈⢿⠙⢺⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⣟⢿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡀⣾⠀⠘⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⡇⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣧⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⠁⠀⠀⣇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⣿⣿⣯⠻⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢇⢹⠀⠀⡀⠀⠀⠀⢱
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⡇⠀⠑⠦⡀⠀⠀⠀⠀⠀⡠⠊⠀⣿⣿⣾⠀⡄⠀⣷⣂⠀⠀⠀⢇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⠀⣿⡿⣿⠀⡇⢸⣿⣿⡄⠀⠀⡸
⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⡃⢁⣾⣿⣿⡇⠀⢀⣷⠁
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣇⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⢿⣿⣿⠂⠀⡸⠛
⠀⠀⠀⠀⠰⠤⢠⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢃⡤⠞⠁
⠀⠀⠀⠀⢀⣶⠥⢰⠇⢀⣆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⢸⢃⡰⢋⣠⣾⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠉⠁⠉⠘⠉⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⠀⠀⠀⠀⠀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢤⡀⣀⣀⠀⠀⣠⣔⠒⠉⠁⠀⠨⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠓⠦⡀⠀⢠⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠋⡀⢢⣀⣀⣀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢘⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⢸⠗⢤⣀⡜⢸⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡊
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢇⠀⠉⠐⠊⠓⠒⠠⠤⠤⠴⢒⠒⠲⠖⠉
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠤⠀⠀⠀⠀⣀⠬⠤⠶⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣠⡄⠀⢰⡎⠘⡇⢀⣀⠀⠀⠀⣇⣤⡶⠛⠉⠉⠉⡿⢻⡅⠀⠤⠀⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠃⠘⠁⠑⢼⢰⡉⠳⠼⠁⠀⠻⡀⠀⠃⣠⠇⠀⢙⠦⠤⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠥⡀⠀⠀⠀⠀⠉⠙⠉⠁⠉⠚⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠤⣤⣄⢀⣀⣀⢤⠤⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠐⠢⢧⡐⣰⣇⣀⠇⡅⠀⠠⡒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠙⠳⡃⠀⣿⣉⣆⡴⢓⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠘⠋⠁⠀⢸⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠓⣤⣀⠀⠀⠀⠀⠀⠸⣤⡴⠚⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢠⠈⠉⠒⠒⠒⠒⣿⠁⠀⠀⠀⢱⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠄⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡟⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠘⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⢳⠤⠤⠔⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⢀⡇⢀⢀⣀⣠⠤⠒⠋⠀⠀⠨⡍⠁⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⢟⠁⠉⢉⢉⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢡⠀⠀⠀⢀⠔⢡⠀⠀⠓⠤⢤⡞⠉⠒⠒⣹⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠂⠀⢰⠁⠀⠀⠈⡖⠶⠶⢶⡉⠐⢆⡉⢀⡟⠢⡀⠀⡠⠊⠀⠀⠈⠒⡄⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠰⠀⢸⡀⠀⠀⠀⠱⢤⡠⠜⢡⠀⠀⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠣⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⢀⣠⠜⠁⠀⢆⠀⠀⠀⠀⠀⡜⠀⡄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠓⠒⠒⠒⠂⠁⠀⠀⠓⢤⣀⣀⣀⣀⡤⠊⠀⠉⠉⠀⠀⠀⠀⠀⠀⠑⠠⠦⠐⠋⠀⠀⠁

⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠤⠀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣠⠒⠁⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢁⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢘⡤⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠢⢄⡀⠀⠀⠀⠀⠀⡂⠑⢤⡀⢀⠀⢀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⢀⠀⠀⠀⠈⢻⠀⡀
⠀⢀⠔⠒⡻⠆⠀⠀⠀⢀⢞⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⠀⣘⡴⠁
⠀⡊⠀⠀⢇⣇⠀⠀⠀⡌⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⢡⠀⡄⠀⠀⠀⠋
⠀⡇⠀⠀⠀⢹⢆⠀⠀⠇⠀⠀⠀⠔⠋⠁⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⡘⠀⣧⣀
⠀⢳⡀⠀⠀⠀⠀⠃⠀⠘⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⣤⡀⠀⠉⠊⠀⢀⠇
⠀⠀⠑⢄⡀⠰⠀⢠⣀⠀⣘⠆⠀⠈⠀⢠⣆⠀⠀⠀⠀⠀⡆⠙⣁⠇⠀⠀⠀⢡⠀⠀⡠⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠈⠒⠧⠠⡁⠀⠉⠀⠀⠀⣀⠈⠉⠄⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⢸⢠⠊⢠⠁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀⡐⠀⠀⣀⠀⠈⠂⠀⠕⠊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠐⠲⡒⠀⠁⡅⠀⠀⠤⠒⠉⠙⢅⡀⢈⠉⠀⠀⠀⠀⠘⠂⠈⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢄⣀⠀⠀⣀⡀⢈⡠⠬⠰⠋⠠⡀⠀⠀⠀⠀⠀⢸⠣⢀⣀⠀⠀⡐⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⢰⡀⠤⡈⠉⠀⠀⡈⠀⠀⠀⠀⡠⠃⠀⠀⠀⠶⢀⠏⠀⠀⠈⠑⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠲⢄⡎⠀⠀⠇⡀⠀⠀⠈⠐⠂⠀⡠⠂⠐⠄⠀⢀⠀⡏⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢎⠀⠑⠒⠈⠶⠀⠁⠀⠈⢶⠑⢄⠀⠀⢠⠂⠀⠁⠀⢀⠆⠀⠀⠣⡕⠀⠂⠁
⠀⠀⠀⠀⠀⡀⠉⢐⠀⠄⠀⠀⠀⠀⢀⠜⠀⠸⡀⠀⠈⠢⠀⠀⠠⠃⠀⠀⠀⢀⡜⠲⠠⡀
⠀⠀⠀⠀⢺⡀⠀⣀⣀⢀⡀⠀⠀⠀⡸⠀⠀⠀⣕⠢⢀⡀⠀⠀⠀⠀⣀⠠⠐⢉⠔⠁⠀⠈⠢⠤⢐⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠂⣉⠔⠚⠀⠈⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⢲⡎
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⠀⠀⣠⠎⠀⠀⠀⢐⣄⠀⡤⠐⠊⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⠈⠉⠉⢹⠀⠀⠀⠘⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠊⠀⠀⠀⠀⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠀⠀⠀⠀⢠⠒⠄⢁⢐⠆⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠎⢁⠜⢁⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠘⠂⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠑⣼⡇⢀⡴⠋⠀⠀⠀⠀⠀⠀⡤⠀⠀⣸⢹⠇⢀⣴⣯⡤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣿⣧⠞⠁⠀⠀⠀⠀⠀⢀⠌⠀⣠⠾⠃⢸⡶⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠁⠒⠲⠤⣿⣦⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣠⠞⣡⠴⠋⠁⠀⢀⣼⣡⠤⢤⡴⠒⠦⠤
⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢻⣷⣠⣿⠏⠀⠀⣀⡤⠖⢋⡵⠚⠁⠀⢀⣤⣾⣋⠁⠀⠀⠀⠀⣀⡤⠀⠒
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⣿⣿⠁⢄⣠⡾⠁⠀⢠⠟⠀⠀⣠⡾⠋⠀⠀⠉⢣⡠⠀⡰⠋
⠐⠠⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⠀⠀⣿⡇⠀⣰⠟⣦⠈⢠⡏⠀⣠⠞⠁⠀⢀⡠⠄⠀⠀⣱⠏⠀⠀⠈
⠐⠒⠈⠉⠉⠛⠟⠲⢦⣄⠀⠀⠀⠀⠈⢳⠀⢀⣿⣇⡼⠋⠀⣸⠀⣾⣡⡿⠁⢀⡤⠖⠉⢀⣠⡶⠚⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠈⡇⢀⣿⣿⠀⠀⢀⣇⣴⣿⠋⣠⠞⠁⠀⢀⣴⠛⠁⠀⠀⠀⠀⠈⠀⠀⡀
⠒⠖⠦⣄⡀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣹⣿⡁⢻⣧⣀⣼⡿⢫⣿⠟⠁⠈⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠲⠶⠦⢤⡀⠀⠀⣿⡆⠀⣰⡏⠈⢷⣼⣿⣿⢋⣴⡿⠋⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⠛⠛⠒⠿⢿⣦⣘⣿⣿⣿⡿⢋⣠⣤⡴⠶⠿⢯⡤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠟⢋⠁⠀⠠⠀⠀⡀⠙⡀⠀⠀⠉⠓⠠⢀⠀⠀⠤
⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠐⠋⠈⠁⠀⠀⠀⠀⠀⠑⢤⠄⠁⠀⠂⠂⠈⢢⡀⠀⠐⢄⠁
⠀⠀⠐⣧⣀⣤⠄⣀⣀⠠⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠢⠀⠀⠀⠑⠦⣀
⠀⠤⠧⠼⢿⢵⣺⣻⣷⣂⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠦⠀⠤⢍⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠟⠛⠛⠋⠉⠉⣀⣤⣿⣿⣷⣾⠥⠆⠠⢤⣄⠦⣙⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣶⠶⠞⠛⠛⣉⣩⠽⢂⣠⣿⣿⣿⣿⠖⠀⠀⠀⠀⠚⠢⠌⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⣀⡀⢀⣴⣋⠁⠀⣉⣿⣿⣿⣿⣟⣛⠉⠀⠀⠀⠀⠠⡀⠀⠙⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⣴⣶⣿⠟⠉⣠⣾⣿⠂⠀⣨⣿⣿⡿⣿⣿⡿⠁⠀⠀⠉⢻⣿⡒⠄⠈⢦⡘⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠁⠀⢀⣽⡿⣋⠴⠋⣩⣿⣿⡇⣿⣿⣥⣶⣶⣤⣀⣀⢀⡉⠲⡄⠈⢿⣌⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⢀⠀⢀⠞⣡⠞⣡⣶⣿⣿⣿⡿⠁⠿⣿⣿⣿⣿⣿⣿⣿⣷⣎⢳⣌⠀⠈⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣴⠏⠀⢋⡾⣷⡿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣧⠹⣧⠀⢿⣿⣿⡇⣧⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢀⣾⡏⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⢹⡇⢸⣿⣿⣷⢹⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢡⣿⡿⠀⣼⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⣿⣾⢹⣿⣿⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇⣼⡿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢸⡿⠸⣿⣿⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣸⣿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⠈⡇⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣷⣿⣏⡄⢸⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⠀⡇⠀⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠸⣿⣿⣿⣿⣿⡇⣸⠛⠉⠉⠛⠛⠿⠿⣿⠄⠀⠀⠀⠀⠀⠀⠾⠿⠟⠛⠉⠁⠀⠀⢹⡆⡇⠀⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢻⣿⣿⣿⣿⠇⢸⠀⢀⣤⢤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣶⣾⡿⣿⢧⣄⠈⡇⡇⠀⣿⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣿⣿⣿⣿⠀⢸⠀⠙⠇⠸⠘⠋⠏⠱⠀⠀⠀⠀⠀⠀⡇⠀⠏⠸⠙⠃⠏⠸⠋⠁⣿⡇⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢹⣿⣿⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⡏⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⣿⣿⣿⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠃⢀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⢹⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣸⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⣷⠀⡇⢸⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⡏⢸⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⢰⡇⢸⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠂⠞⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣸⠃⣾⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⢸⡇⢸⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⠃⢀⡿⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣼⣿⣿⡿⠀⣿⠀⠀⠀⠀⠀⠘⠒⠐⠂⠀⠀⠀⠈⢉⣙⣿⠋⠁⠀⠀⠀⢰⣿⣿⠀⣸⡇⢸⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⢰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣰⣿⠁⣼⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠄⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢸⣿⢸⣿⣿⠃⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⡇⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⢸⣿⣾⣿⡿⠀⠀⢸⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣻⣀⣻⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣃⣀⣀⣀⣀⣀⣈⣙⣛⣓⣒⣛⣛⣉⣀⣀⣀⣀⣄⣈⣿⣛⣛⣇⣀⣀⣀⣻⣇⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠐⠣⠼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠑⠟⠀⠀⠀⣿⣦⡀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⣿⠙⢿⣶⣄⣈⣀⣀⣴⣇⠀⠀⢀⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠈⠙⠛⠛⠋⠉⠛⠻⠟⠛⣿⡏⠀⣤⠤⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣷⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⠖⠻⠦⣄⣻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⢸⣧⠀⠀⠀⣀⣀⠀⠀⢀⡏⠹⣞⠁⣠⣤⣤⣄⣼⣻⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⡶⠛⠋⠉⠓⠾⣿⡟⢦⡀⢸⠀⠀⢹⣾⠃⢾⠉⠉⠀⢸⣷⣀⣹⠂
⠀⠀⡖⠒⠀⠀⠀⠀⢈⣿⡄⣠⡶⠶⣤⠀⠘⣧⠀⠙⠞⠀⣀⠀⢻⡳⠾⠟⠃⢀⡞⣹⠁⣘⡶⠦⠤
⠀⠀⠉⠘⠀⠀⠀⢀⣼⣿⣿⡏⠀⠀⠈⡇⠀⢹⣿⣄⠀⠀⡿⡄⠈⣷⣤⣤⠶⢛⡞⠙⠛⠉⠁
⠀⠀⠀⢀⣠⣴⣾⠿⢿⣿⣿⡷⢤⣤⠴⠁⢀⣾⣿⡟⢷⣼⠃⠛⠛⠉⠀⢀⣀⣀⣣⡀⠀⠀⠠⠂⣂
⠀⠀⠀⠀⠀⠀⢀⡠⠊⡹⠿⣿⣄⣀⣀⣤⣾⣟⠋⠁⠀⠀⠀⠀⠀⠀⠜⢣⡙⢄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠋⢠⠞⠀⠀⠘⠉⠉⠉⠀⠀⠙⣆⠀⢀⡴⠋⢉⡉⠒⠅⠀⠙⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⢹⢠⠏⢠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣀⣠⠁⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠘⣧⠀⠀⢸⡇⠀⠀⣼⠃⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⢻⡇⠀⢻⡇⠀⣸⡟⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠻⣧⠀⠀⠛⠀⠘⠁⠀⠋⠀⠀⣼⠏⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⢷⣦⠈⠃⣠⡾⠟⠛⠛⠻⢦⡀⠈⢁⣴⠾⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠈⠙⠳⣶⣤⡀⠁⣼⠋⠀⠀⠀⠀⠀⠀⠹⡄⠈⢀⣤⡶⠞⠋⠁⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠙⠻⢷⣤⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⠿⠛⠉⢿
⣾⠛⠒⠶⠶⠶⠤⣤⣏⣀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡴⠟⠉⠀⠀⠀⢀⣈⣧⡤⠴⠶⠶⠒⠒⢻
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⡀⠀⠈⠻⣆⠀⠙⠳⠤⣤⡤⠴⠊⠁⢀⡾⠋⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⠷⠶⠾⠿⠿⠿⠿⠿⠶⠶⠶⣦⣤⣄⣀⠀⠈⠒⢄⠈⢆⠀⠀⠀⠀⠎⢀⠔⠋⠀⢀⣀⣤⣤⡴⠶⠶⠾⠿⠿⠿⠿⠿⠿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠤⡀⠁⠀⠀⠀⠀⠀⠀⠁⡠⠴⠚⠉⠁
⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡤⠶⠒⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠶⢦⣄⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠲⠶⣤⡀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠶⢦⣄
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢸⡇⠀⠐⠟⠀⠐⠟⠀⠀⢹⡄⠀⠀⣿⠀⠀⠻⠃⠀⠺⠃⠀⠈⡇⠀⠀⢸⡇⠀⠘⠟⠀⠘⠟⠀⠀⢹⠀⠀⠀⣿⠀⠀⠻⠃⠀⠻⠃⠀⠘⡇
⠀⠀⠸⣇⠀⣤⡀⠀⠀⢀⡄⠀⣼⠁⠀⠀⢿⡀⢠⣤⣤⣤⣤⣤⠀⢠⡇⠀⠀⠸⣇⠀⠀⢀⣀⣀⡀⠀⠀⣼⠀⠀⠀⢿⠀⢀⡴⠖⠒⠶⣄⠀⢰⡇
⠀⠀⠀⠙⢦⣈⠙⠓⠚⠋⣠⡼⠃⠀⠀⠀⠈⠳⣄⠉⠛⠛⠛⢁⣤⠟⠀⠀⠀⠀⠙⢦⡀⠈⠉⠉⠀⣠⡾⠃⠀⠀⠀⠈⠷⣌⠀⠀⠀⠀⢈⣴⠟
⠀⠀⠀⠀⠀⠉⠛⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠉

⠀⠀⠀⠀⣤⠖⠛⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⣤⠞⠛⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⠙⠳⢦⡀
⠀⠀⢀⡾⠁⢀⣀⠀⠀⣀⠀⠘⣧⠀⠀⠀⣰⠏⠀⣀⡄⠀⣀⡀⠀⢻⡄⠀⠀⢀⡞⠁⣠⣠⡀⣠⣤⡄⠘⣧⠀⠀⠀⣰⠋⣴⢋⡉⠛⣉⢳⡄⢻⡄
⠀⠀⢸⡇⠀⠉⠉⠁⠈⠋⠀⠀⢸⡆⠀⠀⣿⠀⠀⠉⠀⠀⠈⠉⠀⠀⡇⠀⠀⢸⡇⠀⠙⠋⠁⠈⠛⠁⠀⢸⠄⠀⠀⣟⠀⠹⢦⣥⢦⣥⠼⠃⠈⡇
⠀⠀⠘⣧⠀⢶⣄⡀⢀⣠⠆⢀⡾⠀⠀⠀⢻⡄⢠⠞⠋⠉⠛⢦⠀⣰⠇⠀⠀⠘⣧⠀⢶⣄⡀⢀⣠⠆⢀⡾⠀⠀⠀⢻⡀⠀⢀⣶⣶⣦⠀⠀⣸⠇
⠀⠀⠀⠈⠳⣤⣈⣉⣉⣁⡤⠞⠁⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⠈⠳⣄⣈⣉⣉⣁⡴⠟⠁⠀⠀⠀⠀⠙⢦⣈⣙⢛⣋⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⡶⠋⠉⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠈⠙⠳⣄⠀⠀⠀⠀⢠⡶⠋⠉⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠈⠙⠳⣄
⠀⠀⢠⡟⠀⢰⣴⠆⢰⣶⠆⠀⢷⠀⠀⠀⣼⠁⠠⣴⡤⠀⣴⣦⠀⠹⡆⠀⠀⢠⡏⠀⣠⢤⡀⣠⣤⡀⠈⢷⠀⠀⠀⣼⠁⠀⣤⡄⠀⣤⡄⠀⠹⡆
⠀⠀⢸⡇⠀⠈⠉⠁⠈⠉⠁⠀⢸⠇⠀⠀⣿⠀⠀⠉⠁⠀⠈⠉⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⣿⠀⠀⠈⠀⠀⠈⠀⠀⢀⡇
⠀⠀⠈⢷⡀⠀⠰⠶⠶⠂⠀⣠⡟⠀⠀⠀⠹⣆⠘⠷⣤⣀⣤⠞⢀⣼⠃⠀⠀⠈⢷⡀⠻⢦⣤⣤⡤⠁⣠⡟⠀⠀⠀⢻⣆⠀⠰⠿⠛⠛⠁⢀⣾⠃
⠀⠀⠀⠀⠙⠶⣤⣤⣤⡤⠞⠋⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⠴⠛⠁⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⡤⠾⠃⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⠶⠛⠁

⠀⠀⠀⠀⠀⣠⡤⠴⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⢤⣄⡀
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⢀⡾⠿⠿⠿⠿⠿⠿⠿⣦⠀⠀⠀⠀⣰⠟⢁⠀⠀⠀⢀⠉⢳⡄⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠈⠙⣦
⠀⠀⢰⡟⢻⣿⣿⡟⢻⣿⣿⠛⢻⡀⠀⠀⣾⠁⠀⠶⠆⠀⠴⠆⠀⠘⡇⠀⠀⢰⡇⠀⢾⡷⠀⠰⣿⠆⠀⢻⠀⠀⠀⣾⠀⠐⠦⠖⠐⠦⠶⠀⠘⡇
⠀⠀⢸⡇⠀⣉⠉⠀⠀⠉⣁⠀⣸⠃⠀⠀⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⣿⠀⢀⡀⠀⠀⠀⢀⠀⢠⡇
⠀⠀⠀⠻⣄⠙⠳⠶⠶⠞⢁⣴⠏⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠻⣄⠀⠘⠛⠛⠁⢀⣴⠋⠀⠀⠀⠘⢧⡈⠛⠶⠶⠖⠋⣠⡞⠁
⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠐⠁⠀⠀⠀⣀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠀⠦⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠒⠁⠀⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⢀⠸⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⣯⣶⣤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⠄⠠⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠄⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣭⣤⣤⣤⣤⣴⡾⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡉⠉⠙⠻⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⠿⠋⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⠂⠁⠀⠀⠈⢿⣷⣄⠀⡉⠒⠀⡄
⠀⠀⠀⠀⠀⠀⠺⣁⡁⣼⢀⣴⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡾⢷⣾⣎⡀
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣻⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⢹⢿⣿⣿⣿⣦
⠀⠀⠀⠐⠿⣿⣿⠿⢟⠇⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠇⠈⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠈⠲⢊⠤⠤⢄⠀⢀⠴⠒⠒⢦⡀⠆⣀⣀⡀⠀⠈⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠜⠀⡔⠁⠀⢄⠀⠑⠃⠀⢠⠀⠀⠷⠊⠀⠀⠈⡆⠰⣍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠑⠲⠁⠰⣒⡼⠀⠀⠀⠠⠔⠁⠀⠀⠀⢇⣐⠆⠷⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠸⣭⠆⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢤⡀⠀⠀⠀⠀⢀⣀⡄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢇⠈⠢⠀⠀⢠⠂⠀⠀⠀⠀⠁⢀⠤⠀⢹⠀⠀⠀⠀⠀⠁⠀⢚⡤⣾⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠃⡼⠂⠀⡀⠀⠀⠑⠂⠀⢀⡀⠀⠈⠒⠔⠊⠀⠀⠉⠀⠀⠀⠙⣔⢊⠥⢳⡈⢣
⠀⠀⠀⠀⠠⣄⣄⠀⠸⡀⠐⠤⢝⠀⢠⠦⠤⠴⠊⠱⣄⠀⠀⠀⢀⣤⠀⢰⠋⡉⠀⠀⠈⢧⢚⠥⡳⡄⠳⡀
⠀⠀⠀⠰⡛⠈⠘⡦⠀⠑⢢⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠘⢄⠈⠀⢁⠀⠀⠀⠘⢷⠋⠀⠘⢄⡱⣄
⠀⠀⠀⠀⠘⢦⠐⣇⠀⠀⡎⠀⠀⠀⠀⠀⠀⡀⣠⢀⠀⠀⠀⡀⣀⢀⠀⠉⠉⠉⠑⠢⠤⠖⠁⠀⠀⣀⠼⢿⣴⣇
⠀⠀⠀⠀⠀⠈⢆⠈⠢⣰⠀⠀⠀⠀⠀⠀⠀⠏⠀⠹⠀⠀⠀⠎⠀⠙⠀⠀⠀⠀⠀⠀⠀⢸⠠⠔⠉⢀⠴⠋⢆⠈⢆
⠀⠀⠀⠀⠀⠀⠈⢆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡤⠚⠁⠀⠀⠈⣆⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⠀⠀⠀⠀⠀⠀⠘⢆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠔⠒⢄⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣠⠃⠀⠀⠈⢇⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠖⠁⠀⠀⠀⠀⠈⠣⠤⠤⠞⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡟
⠀⠀⠛⣲⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠓⠞⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⡻⠗⠛⠚⠳⠒⠛⠛⠛⠚⠒⠚⠒⠒⠒⡋⢹⠛
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⠂⠀⠐⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘
⢠⠶⣸⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⢈⡄⠀⠀⠀⢠⠚⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠱⣖⢩⡇⠀⠀⠀⢸⠒⢤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡁⢸⡆⠀⠠⡏⠑⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢼⢃⡀⣴⡀⣤⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢛⢨⠀⠀⠀⠉⠀⢹⠀⣞⣷⣔⢷⣶⠄⢀⣤⣤⢀⣤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠜⠀⠀⠀⠀⠀⠀⢸⡀⠋⠁⠈⠀⢉⡆⢨⡿⠛⠚⠓⢿⠀⠈⣿⠿⣼⣽⣿⠀⣴⣶⣖⣶⣦⡄⠀⢀⣤⣤⣤⣄⡀⠀⢸
⠀⡿⠛⠒⠀⠠⠤⠤⠼⠦⡄⣀⣀⣀⣨⡇⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠈⠀⡼⠋⠉⠉⠉⡇⠀⢸⠿⠛⠚⠻⠏⠀⢸
⠀⢥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠛⠛⠒⠚⠂⠾⠦⠤⠀⢀⣠⣀⣥⣀⠀⠀⠀⣟⠀⢈⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠒⠦⠶⠦⠀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠀⠒⠶⠶⠾⠄⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠉⡘⠀⠀⠀⠀⠉⠉⣛⠉⠑⣶⠒⠲⠖⠒⠠⣤⣤⣤⡤⡀⠀⢀⣀⣀⠀⣸⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡜⢠⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢸⠀⠀⠸⢠⡄⠀⠀⠀⠈⠉⠉⠁⠉⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⢡⠌⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢿⡀⠀⠀⡇⠀⠀⠏⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢠⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠸⠂⠀⠸⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⢲⠀⠀⠸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡜⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⣠⢁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢰⠆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠇⠀⠀⠟⢰
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⣨⠁⠀⠀⡘⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢰⠄
⠀⠀⠀⠀⠀⢠⠁⠀⠀⣠⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠇⢰
⠀⠀⠀⠀⠀⠆⠀⠀⢰⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⠀⡆
⠀⠀⠀⠀⠚⠒⠒⠒⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢶⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⡆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⢸⣰⠆

⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠶⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠄⢀
⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠄⢀⡀⠀⢀⡀⠠⠀⠀⠀⠀⠈⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠆⠈⠛⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠋⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠛⠁⠰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠠⠂⠀⠀⠀⠀⠀⠀⠢⡀⢀⠔⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣐⣒⣢⢤⡉⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠳⣌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣹⣿⣧⣼⣿⣿⣿⣿⣿⣿⢿⣿⣆⢰⣝⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⣿⣿⣿⣿⣿⣿⠯⣿⢷⣽⣫⣿⣿⢨⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡄⢸⡏⠉⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⡾⠘⣼⢳⣇
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡴⢁⣷⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠿⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠇⠈⣇⣀⡀⠀⠀⠀⣤⣶⣾⣛⠓⠤⠀⢻⣿⣿⣛⡶⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⣯⡉⠀⠀⠀⠉⠘⠉⠙⠻⠆⠀⠀⢿⣿⣯⣉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡳⣤⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣮⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠒⠃⠀⠀⠈⠙⠋⠀⠀⠀⠀⣿⣿⣿⡟⠥⡟⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠇⡇⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⣿⣿⣿⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢿⡒⠦⠤⠤⠔⠊⠁⠀⠀⢸⣿⣿⣿⣿⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⡇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⢡⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⠐⡀⠣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣅⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠀⢀⣑⠦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢁⢈⠻⢷⣤⣀⡀
⠀⠀⠀⣠⢔⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⠎⠉⠁⠱⡄⠀⠀⠀⠀⢀⣿⣿⣿⣷⡀⠁⠁⠈⠻⣷⡄
⠀⠀⠈⠐⠒⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠑⠂⠀⠹⡄⠀⠀⠀⠞⣿⣿⠉⢻⣷⡀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⡈⢯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠌⢀⡿⣁⣤⠄⠻⡇⠲⠛⠉⠈⠋⠓
⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡞⠀⠀⠈⠀⡿⠉⠙⠋⠀⠁⠈⠂
⡜⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢀⠀⡤⠀⢠⠃⠀⠀⠀⢀⣀⣀⣀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠻⢿⠟⡿⠿⠿⠿⣿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⢛⣿⣿⣯⣽⣿⠿⠿⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣵⣾⣿⣿⣉⡒⠒⣶⣿⣦⡉⢉⣻⣿⣿⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠋⠛⠋⢹⣿⣿⣿⡀⠉⠻⢿⣿⣌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠻⠟⢻⣿⣿⣿⣤⣀⠀⠀⣠⣿⣿⣿⣇⠚⢻⣷⣬⣿⣧⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⡡⣠⡴⣼⣿⣿⣿⣿⣿⣦⣾⣿⣿⠟⠈⠻⠶⠿⠛⠿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⡤⠶⠶⢶⣤⣄⠀⠀⠀⠀⣀⣤⣤⣤⣸⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⢙⣿⣿⠁⠀⠀⠘⠶⠶⣿⡷⢦⡅⢢⠀⠀⢠⣼⣷⣶⣾⣿⣿⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡈⠛⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⠈⠁⠀⠀⣿⡏⠀⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢣⣿⣿⣷⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⢠⣰⣌⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⣸⣿⢿⣿⣿⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⢰⣿⣿⠿⣿⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣱⣿⠏⣸⣿⣿⡇⠘⣇⠀⠀⠀⠘⢿⣟⠶⠾⠷⠶⠶⣶⠆⠀⣰⣿⣾⣿⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠁⢀⣿⣿⣿⡁⠀⠹⣆⠀⠀⠀⠀⠛⢷⣦⣤⣴⡾⠃⠀⣼⣿⣿⡏⣿⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⣠⣴⢺⣿⣿⣿⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣾⠟⠱⣿⣧⡻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⡿⢸⣿⣿⣿⣧⠀⠀⠀⠀⠙⢶⣄⣀⠀⠀⠀⣀⣼⣿⣡⣶⣾⠟⣻⠷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣾⣿⢇⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⢻⣿⡿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣟⣻⣿⣿⣿⡿⠃⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢦⣽⣿⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣟⣽⣿⠿⠋⠁⠀⠀⠀⠛⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢻⣿⢋⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢟⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⣶⣿⣧⣾⣿⣿⠋⠁
⠀⠀⠀⠀⠀⢀⣾⣿⠟⢛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⠿⣥⣾⣿⣿⣯⣠⡿⠟⠁
⠀⠀⠀⢀⣴⡿⢛⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⣿⣿⣿⡿⠋⠹⣿⣿
⠀⠀⠀⣾⣛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻⣿⣿⢿⣶⠶⠀⠈⠛⠃
⠀⠀⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛
⠰⣶⣶⣿⣾⡿
⠀⠙⠿⠿⠛⠁




⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠄⠲⠀⠇⠈⠐⠉⠂⠀⠀⠅⠀⠒⠀⠓⠀⠐⠀⠀⠆⠐⠀⠀⠀⠀⠶⠀⠁⠀⠂⠀⠀⠀⠛⠠⠀⠀⠃⠠

⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⣿⣿⣄⠀⠀⠀⠀⢷⣄⠹⡿⢿⣿⣿⣿⣶⣄⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣦⡀⠀⠀⠸⢿⣷⠐⡀⠀⠀⠈⠙⣿⣿⣷⣦⣙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠻⣿⣶⣄⣀⠀⠙⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣠⡴⠶⠶⢤⣄⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡤⢼⣏⢿⣿⡀⠀⠀⠀⠀⠀⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡠⢚⡏⢀⡖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠹⠀⠙⠇⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⢤⣈⣇⠈⠁⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣴⠿⢿⣿⣿⠃⠀⠉⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠉⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣴⣾⣿⣿⠟⠋⠉⠙⠄⠀⠘⣿⣿⡆⠀⠀⠀⠈⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣾⣿⣿⣿⠿⣿⡟⢹⠁⣠⣶⡟⠉⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡻⡶⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⠄⠐⢛⣻⣿⣿⣿⣿⠟⠋⠁⠀⠀⠘⢧⠃⢰⣿⠉⠉⠂⠀⠀⠀⣤⣘⣿⣷⣄⠀⠀⠀⢠⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⠀⠀⠀⠸⠟⠉⠉⠉⠉⢉⡽⢋⣡⠶⢻⡍⠠⠄⢸⡇⡙⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣆⠀⠠⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⣸⡆⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢤⣤⣤⣀⣥⣾⣯⣀⣀⡀⠙⠶⠖⢋⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡿⠋⡠⠁⣤⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠯⢍⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⢀⡴⢡⣤⣿⣷⣄⢿⣿⢿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣶⢿⡿⠋⠻⡇⠈⢃⠀⢻⠀⣿⣿⣿⣿⡿⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⣸⣿⠟⠻⡄⠀⢱⡀⠀⠡⠀⠀⡄⠈⠄⢻⣿⣿⡿⠃⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣶⠉⠙⣆⠀⢡⠀⢸⡇⠀⠀⢇⠀⠘⢆⠀⠈⢿⡟⠁⣀⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⣀⣴⡏⠁⢹⡄⠀⣿⠀⢸⠀⠀⢷⣄⠀⠘⠂⠀⠀⠀⠠⠂⣠⡀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⠀⠀⠀⡇⠀⡇⠀⣾⣄⡀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠤⠀⡿⠀⠀⠀⠀⢠⡾⢻⡏⠀⢿⡀⠀⠀⡇⠀⡇⢀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⣿⡏⠀⠙⢿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣿⠃⢸⡇⠀⢸⡇⠀⢰⡇⠀⣹⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⣿⣧⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⠙⢿⣯⡻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⢸⣿⠀⢿⠀⠈⡇⠀⠘⡇⠀⠸⣇⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡸⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⠂⣸⠿⠷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢹⡇⠀⢹⡄⢸⡇⠀⣧⠀⠀⡇⠀⢀⣿⣿⣿⡇⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠱⣻⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣼⠃⠀⡜⠀⠀⠉⢙⡿⠟⠛⠉⠁⠀⣸⠁⠀⡇⠀⠘⣧⠘⣧⠀⢣⠀⠀⡇⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠉⠑⠢⠤⢀⣀⣀⣀⠠⠤⠄⠀⠀⠠⠄⡀⠀⡀⠄⠀⠐⠒⠒⠂⠀⠀⠀⠀⠤⠔⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⣠⣤⡦⣶⣶⣦⠀⢤⣶⣤⡀⢤⣤⣤⡤⠤⣶⣶⣤⠤⢤⣿⣤⢤⣤⣆⣀⣤⣔
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⡟⠛⠀⢿⣿⠏⠀⠘⣿⠙⠁⠘⣿⡿⠁⠀⢹⣿⡟⠀⠸⣿⠁⠓⠿⡏⡟⣥⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣏⡇⠀⠀⠸⡟⠀⠀⠀⣿⠀⠀⠀⢹⡇⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⣧⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣷⣦⣤⣤⣬⣤⣤⣤⣬⣤⣤⣤⣤⣼⣧⣤⣴⣾⣷⣴⣾⣿⣿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡏⣿⢺⡟⣿⠋⠉⢻⠉⠉⢹⠉⠉⠉⡏⠉⠉⣿⠉⠉⢹⠉⠉⢿⢻⡋⣿⣸⡠⢿
⠀⠀⠀⠀⠀⠀⠀⢸⣝⡓⣻⣤⣧⢸⡀⠀⣿⡀⠀⣼⡆⠀⢀⣇⠀⠀⣿⠀⠀⣾⠀⢀⣇⣼⣷⣟⣫⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠉⠻⢧⣸⠿⠇⢀⣿⣷⡀⣸⣿⣀⣠⣿⡇⢰⠿⠄⠜⠛⠉⠙⠛⠉⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠛⠁⢸⠁⠀⠉⠁⠀⠂⠀⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠀⠁⠀⡀⠀⠤⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⠴⠁⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣈⣀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⢀⡀⠀⠰⠈⠑⠲⣔⠀⠠⣄⠀⠀⠂⠌⠤⢀⡈⢉⣀⢈⣀⣍⣉⠉⠶⠦⣭⣡⣶⡦⠤⠤⠟⣟
⠀⢀⠴⣦⣤⠀⠀⠠⠄⠀⠀⠀⠒⠡⡤⠀⣀⠉⡄⠀⠀⠀⠀⠑⠦⣀⠠⠊⠁⠀⠀⣌⢫⠈⡠⢬⣭⣀⡉⠁⠦⠶⣤⠥⠤⠶⠒⣛⡯⠉
⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢌⣉⠓⠲⠄⠤⠤⠔⠂⠋⣉⠅
⠀⠀⠀⠀⠂⠄⠀⠀⢀⣀⡀⠔⠠⠒⠀⠀⠀⠈⠐⠦⠉⠁⡠⠖⠆⣖⠒⢐⠀⠀⠀⠀⠀⠀⡀⢂⠀⡀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠛⠒⠤⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠤⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠠⠤⠀⢀⣤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠸⠶⢤⡄
⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢛⣧⣖⡯⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⡅⠀⠀⠀⣻⡇
⠀⠀⠘⠇⠠⠀⡀⠀⠀⠀⢠⣠⣴⡶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠈⠉⠲⡆⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣴⣿⠇
⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣷⠀⠒⠲⠎⢹⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⢈⠒⠶⣤⣤⣤⣀⣀⣀⣠⣴⣾⠿⣛⣫⡽⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠈⠙⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣈⠓⠦⠀⠉⣑⢲⣚⠩⠕⢚⣩⠵⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠉⠢⢄⣐⣄⡭⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⣶⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠘⠗⣱⡄⠀⠀⠀⠀⠨⣥⣟⠀⠠
⠀⠀⠀⠀⢔⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢨⣔⣀⣀⣠⣤⡴⠞⠛⠉⠀⠀⣀⠄⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡆⠸⣷⢰⡆⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠃⡳⢚⣷⣌⠐⣄⣀⠄⠊⠀⠀⣀
⠀⠀⠀⣿⣠⣿⣾⠀⢄⡄⠀⠀⠀⠄⠀⠀⢀⣾⡄⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⣠⢴⣾⠋⠀⠀⣠⠀⠀⠀⠂⠀⣤⣠⣤⣠⠤⢀⠀⠢
⠀⠀⠀⠸⡏⢻⣿⡗⣼⠀⠀⠀⠀⠻⢇⣀⢸⡆⣉⠛⠶⣶⣤⡄⣀⡀⣀⡠⠔⣚⡭⠊⠀⠐⣪⢽⠁⠀⠀⠒⠡⠤⠊⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠢⣽⣼⣇⣄⠀⠰⣇⡈⠻⠷⣤⡐⠈⡁⠦⣬⡥⠔⠋⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠳⠶⠶⠦⠿⠷⠚⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⣦⡀
⠀⠀⠀⠀⢸⡄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠈⠛⢤
⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⡀⠀⠀⠀⠀⠉⣉⣉⣀⣀⢀⣀⣀⢀⢈⡉⡉⠉⠉⠁⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⣣⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠐⠒⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢳
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⢄⠀⠀⠀⠀⠀⠀⡠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⡆⠀⠀⠀⠀⠀⠀⢀⠁⠈⣿⠋⠸
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣠⣔⡉⢸⣵⢄⠀⠀⢠⣈⣠⠠⠄⡀⠑⠄⠀⢰⣖⡀⠀⠀⢀⣧⠀⠠⣳⣄⠀⠀⠀⠀⠀⠇⢀⣼⠇⢠⠓
⠀⠀⠀⠈⠂⠀⠀⠀⠰⠊⢤⣀⣷⢟⠁⢀⠰⠀⠞⠁⠀⠀⠀⠀⠐⠋⠀⠈⢁⠠⠀⡠⠀⢀⠀⠀⠈⣻⡳⣦⣠⣤⢶⠶⡞⢁⢀⠐⠁
⠀⠀⠀⠀⠀⠁⢼⡁⠐⣤⡾⠋⠄⠠⠂⠀⠀⠀⠀⠀⠠⣄⠀⠀⣀⠀⠀⠀⢭⠩⡉⡏⡍⢽⠀⠀⠀⠉⠛⠿⢿⣽⡷⠦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢾⡋⢰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⡿⠃⠀⠀⡺⣐⢓⠅⠂⣢⠀⠀⠀⠀⠀⠀⠐⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠊⠉⠀⠀⠀⠀⠨⠠⠠⠥⠀⠜⠀⠀⠀⠈⠙⠀⠄⠤⠠⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣷⣶⣴⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣴⣶⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣿⢿⡟⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠈⢿⣿⣿⣋⣀⠀⠀⠀⠀⠀⢀⣈⡀⠛⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⢇⣬⣭⡃⠀⠀⠛⣭⣥⣄⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣭⣭⡃⠀⠀⠋⣭⣥⡀⠀⠘⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⢿⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⢹⣿⣿⡿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⢨⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣧⡀⠀⠀⠄⠀⠀⠀⠀⠸⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠒⠒⠦⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⢠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⡄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⢀⡀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⣀⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠉⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠉⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⢿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⡿⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⢍⡉⠛⠛⠛⠛⠛⠛⠛⠟⠉⡩⠋⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣤⣤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠶⠶⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠸⢹⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣮⠹⣧⠹⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣿⣿⠟⣻⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡈⠇⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡟⠁⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠘⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⢧⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⠀⢀⡿⢀⣠⣤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣤⡀⢹⣧⠈⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢀⠀⠀⢸⡇⢈⣭⣽⣿⣟⡛⠃⠀⠀⠘⠛⣻⣿⣿⣭⣍⠘⣿⣆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣠⣿⣼⢄⣿⠉⠻⣿⣧⡭⠟⠓⠀⠀⠀⠀⠘⠛⠧⣭⣿⠟⠋⢻⣿⣆⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣵⣿⣿⣟⣾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⣿⣦⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡋⣻⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⣟⠉⣹⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⡉⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡀⠀⠀⠠⢶⣾⡿⠿⠿⢿⣷⡦⠀⠀⠀⢀⣾⣿⣿⡙⣿⡙⢿⣮⡙⢿⣯⡛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⣿⠏⣿⠿⣿⡇⠀⣿⣿⣷⡀⠀⠀⠀⠙⠿⢿⡿⠟⠋⠀⠀⠀⢀⣾⣿⣿⣿⠃⠘⢿⡄⠻⣷⡄⠙⣷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⠀⣿⠀⡿⢁⠀⢻⡟⠿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⠀⠀⠻⣆⠈⢿⡄⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠿⠀⠁⠘⠀⠸⣷⡀⠀⠹⣿⣦⣄⣀⣀⣀⣀⣠⣴⣾⣿⣿⣿⣧⠙⢿⣿⣷⡀⡀⠈⠁⠈⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⡄⣿⡟⠿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⡄⠙⢿⣿⣷⡐⣦⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠀⡀⠀⠀⣀⠀⠀⠀⢿⣿⣶⣿⡇⠀⠀⠈⠁⠀⠀⣿⣿⣿⢻⣿⣿⠳⣄⠀⠀⠻⣿⣷⢹⣷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⡇⣴⠀⣿⡀⠀⢀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣏⠈⣿⡝⠧⠈⢧⠀⡄⢻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⣿⡆⣿⡇⢰⣿⣶⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠸⣿⣆⠀⠈⠇⢿⣼⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣙⣿⣆⠀⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⣽⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠋⠴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠖⠚⠛⠛⠛⠒⢢⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⢀⡴⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠇⠀⠀⢀⣎⠄⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⡿⠿⡇⠀⠀⠀⠙⢔⠃⠈⠢⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢐⠾⠁⠀⢰⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⡧⠆⡇⠀⠀⠀⠀⠀⠑⣄⣠⣾⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠲⠄⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠁⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⣥⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠳⣄⡉⢀⣠⠞⠀⠀⠀⠀⠘⣇⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠋⠀⠀⠀⠀⢸⡋⡉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠚⠁⣂⣄⣃⠙⠆⠀⠀⠀⣠⡾⠶⢿⣤⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣞⡄⠀⠀⠀⢰⠋⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⠇⠀⠄
⠀⠀⢴⠈⢼⢡⣶⢹⠌⢑⠄⠀⠀⢼⣇⣛⣸⣷⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⠇⠀⠀⠀⠸⣖⠤⠀⣠⡿⠀⠀⠀⠀⠀⠈⣠⣤⣬⢏⣤⣀⡈
⠀⠀⠀⣈⠁⡓⠖⣋⢈⡅⠀⠀⠀⠀⠙⠉⠋⢰⣯⣷⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠈⠙⠛⠉⢿⣦⡀⠀⠀⠀⠈⢙⢿⠏⠈⣿⢟⠈
⠀⠀⠀⠈⠀⠑⠖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⠀⢀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠝⡻⣦⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠴⢶⣾⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⠛⢠⣾⣿⣿⣷⡖⢒⡶⠀⠀⠀⠀⢠⡶⣿⣿⠾⠟⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⡆⠀⠀⠸⠟⠛⠛⠿⠟⠛⠉⠉⠀⠀⢸⠀⢸⠀⠀⢀⣤⠚⢹⣿⣿⣟⣫⠟⡉⠀⠀⠀⠀⣴⢶⣿⣶⠿⠁⠀⠀⠀⠀⣾⡏⠀⠀⣿⣿⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⠀⠀⠀⠉⠉⠁⠈⠉⠉⠁⠘⠛⠀⠀⠀⣀⣿⣕⣪⣷⠀⠀⠀⠀⠀⠀⢿⣧⣠⣤⣥⡅
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⠉⠁⠀⠀⠀⠀⠀⠀⠼⠿⠷⠬⠍⡥⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⢀⣸⣿⡇⢠⠀⠀⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠙⠿⢿⣷⣶⣴⣶⣿⣿⣿⣿⣧⣀⣠⣾⣭⣿⣤⣤⣀⡀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠻⣿⣿⡏⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠿⣿⡿⠿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣶⣿⡟⠁⠀⠀⠀⣾⡟⠹⣿⣿⣿⣿⣿⣿⡀⠀⢋⣴⣤⠀⣉⡉⢹⡟⣿⣿⣿⡟⣉⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⠿⠿⠿⢷⡄⠀⠉⠀⠀⠻⣿⣿⣿⣿⣿⣧⠀⣌⣛⣋⡘⠿⠿⢘⠁⢿⡿⠙⣧⣉⣤⡉
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣶⣋⣠⡄⠠⣶⣶⣷⣾⣿⣿⡿⠂⠈⠀⠀⠉⠉⠙⠀⢹⣿⣭⣿⣶⣶⣿⣿⣿⣷⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⣀⣢⣽⣿⡛⠛⢁⣤⡀⢀⠸⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⣿⡿⠉⠛⠿⢿⣇⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⡿⠛⢹⠀⢶⣿⣶⣿⠏⠀⠀⠀⠀⠀⠀⠤⠀⠀⣤⠀⣀⣸⣶⣤⣤⣴⣶⡅⠘⠃⠀⢲⣼⣿⠟⠛⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⠾⠿⣣⣾⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡿⣀⠀⠀⡀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣣⣿⡿⠟⠉⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠀⠈⣿⣿⢀⣤⣤⣤⣀⣿⣷⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⢀⣀⣀⠀⠀⠀⢣⡀⠀⠒⠀⢼⢿⡿⢿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠹⢿⣿⠏⠀⠀⣀⣠⣿⣿⣧⠀⠀⣴⣿⡿⠿⢷⣀⣀⠀⠀⠀⡀⠀⠈⣼⢠⡀⠀⣀⢸⡟⣧⣀⣀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⠘⢿⠀⢠⣿⣿⣿⡿⠛⠉⠶⣤⣿⠁⠀⠀⠀⢹⣿⣧⣾⣿⣿⣿⣷⣾⣀⡤⣤⢉⡼⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠀⠀⠀⠠⢶⣿⣿⣿⠇⠐⠀⠓⠶⠆⠒⠀⠀⠒⠀⣿⡏⠉⠉⣻⣿⣿⣿⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠛⠛⠛⣶⣟⣷⣶⡾⣿⣇⠀⠀⠋⣿⣿⠟⠃⠀⠀⠹⠀⠀⠀⠀⠀⠶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⢘⠛⠛⠛⣛⠛⠛⠋⣾⣿⣿⣷⣤⠄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣶⣿⣏⠉⠉⠀⠐⣶⠂⠈⠉⣉⣿⣿⣦⣤⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣾⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⢰⣿⠉⠉⠹⠉⠉⢉⡹⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢋⡉⠉⠉⠍⠉⠉⣿⠆
⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢈⠁⠀⠀⠀⡔⠀⠀⠈⠩⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠍⠁⠀⠀⢠⠀⠀⠀⠈⡃⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⢿⣷⣦⡀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⣸⣾⠏
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣇⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⢸⣦⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣧⣀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⣼⣿⣿⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⢰⣿⣉⠉⢩⠉⠉⢙⡙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⢛⡛⠉⠉⡍⠉⣉⣿⠆
⠀⠀⠀⠘⣷⣍⠛⢳⣤⣤⣈⠁⠀⠀⠀⡄⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⢀⠄⠀⠀⠈⣃⣤⣤⡞⠛⢉⡝
⠀⠀⠀⠀⠈⢿⣷⣄⠀⠉⠹⣿⣶⣶⢰⢀⡀⠀⠀⠀⡖⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢲⠀⠀⠀⢀⡀⡆⣶⡶⣿⠏⠉⠀⣘⣴⠟
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡃⠀⠀⣁⡌⠹⠿⢿⡷⠠⠅⣰⣦⣀⣠⡄⠈⠁⢠⣄⣀⣴⣆⠨⠄⢾⡿⠿⠏⢠⣈⠀⠀⢸⣦⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⣿⣧⡀⠀⠀⠀⢸⠀⠻⠛⠛⠿⠏⠈⠉⠹⡿⠛⠛⠟⠀⡇⠀⠀⠀⢀⣼⣿⣿⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠢⡄⠐⠒⠒⠊⠥⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠰⠊⢀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠑⢄⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠰⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⢨⠉⠢⠔⠸⡑⠤⡀⢀⡀⠀⠀⠀⢀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⣼⠀⠀⠀⠀⢣⠀⠀⠁⣀⠉⠉⠈⢁⣂⣸⣄
⠀⠀⠀⠀⠀⠀⣇⡄⠀⣄⠈⡄⣀⠀⠀⢸⣀⣤⠖⠒⠒⢶⢺⠁⢠⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠁⠐⢆⡎⠑⠊⠀⠘⣄⣈⣠⢏⢀⠑⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⠀⢉⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠍⣟⠈⣜⢙⣝⠀⠀⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠛⢏⠈⣯⢡⡤⢳⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠢⣀⠀⠀⠀⠁⠀⠀⡄⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡗⠢⠤⢀⡀⣤⠿⠋⠀⠣⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠐⢃⠀⠀⠀⠀⠘⡂⠀⠀⢸⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠀⠀⢀⠃⠀⠀⠈⢸⠀⠀⠀⠀⠀⢹⡖⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠢⢤⡀⠤⠴⢦⠄⠐⡖⠉⠁⠀⠀⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡠⢔⠁⠣⢄⣀⠞⠠⠤⣃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⡌⠀⠀⢰⠒⠀⢾⠁⠲⡈⡉⠓⠄⠀⠔⠁⠀⠈⠢
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⡀⢃⠀⠀⠀⠓⠀⠊⢆⠀⠀⠀⠀⡸⠰⠀⠀⠀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠀⠈⠢⡀⠀⠀⠀⢀⠜⠂⠀⠐⠈⠀⠀⠂⢄⣀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡿⠿⠛⠛⠛⠉⠉⠛⠛⠒⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠄⡁⠄⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⡿⣿⣿⣿⣆
⠀⠀⠀⠀⠁⠀⠀⠂⠐⠀⠀⠀⠀⢸⣿⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠻⠿⠛⠛⠃⠛⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠻⣿⠀⠀⠀⠀⠀⠀⢸⣶⡄⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠛⠛⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠛⣛⠙⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⢸⠀⡇⠐⠀⠀⠀⠀⠀⠀⠒⡆⠐⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣤⡄⠄⡊⠀⡏⣀⠀⠀⠀⠀⠀⠀⡐⡃⠀⠂⡄⡍⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⡄⠀⠂⠈⠁⠀⠀⠀⠐⠀⠀⠔⠀⠙⢺⣠⢁⠆⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣟⣽⣿⣿⣿⡇⣈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠉⠈⠒⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣇⠂⠀⠁⢀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢉⠀⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠻⢶⣦⡀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠾⠿⢶⣦⣄⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠙⠳⣄⠀⣠⣾⠟⠉⠀⠀⠀⠈⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡆⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠈⠳⣄⡀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟
⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠛⠋⣿⡟⠀⠀⠀⡀⠈⠙⠓⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣤⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠐⣻⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢤⡤⠀⠄⠤⠤⠤⠤⠄⠤⠄⠠⠄⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⡿⠿⢛⣫⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⢿⣿⣿⠿⢛⣋⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣶⣤⣍⣙⠛⠿⢿⡿⠿⠛⣋⣩⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡃⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣿⡇⢉⣛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣛⣉⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣉⠸⣿⡇⢸⣿⣿⣿⣶⣬⣉⠻⢿⡿⠟⣉⣥⣶⣿⣿⣿⣿⠿⠛⠉⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⣶⣶⣦⣤⣉⡙⠛⠿⢿⣿⣦⣴⣿⣿⣿⡿⠟⠋⠁⢀⣠⣴⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⣤⣉⡙⠻⠿⢿⣿⣶⣶⣬⣍⡙⠛⠉⠁⣀⣤⡶⠾⠛⠉⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣉⠛⠻⠿⣿⣿⣶⣦⣬⣉⡛⠻⠿⣿⣤⡶⠟⠋⣥⣶⣿⣦⠶⠟⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣷⣶⣤⣌⣉⠛⠻⠿⣿⣿⣶⣦⠀⣀⣠⣶⠶⠛⣿⣿⣧⣠⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣶⣦⣬⣉⡛⠛⠋⠁⢀⣠⣴⠽⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣤⡶⠟⠋⠁⠀⠀⠈

⠀⠀⠀⡠⠴⠒⠒⠒⠒⠒⠒⠒⠶⠦⠤⢤⣀⣀
⠀⠀⠐⢧⣤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⢶⣬⡭⣽⣓⣒⡶⠤⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠀⡏⢽⠉⣟⡙⠛⠻⣍⢱⡎⠛⢼⣀⣠⣬⣭⣐⡒⠋⠭⠽⢗⣒⣒⠶⠯⠭⠭⢭⣭⣽⣛⣛⣛⣛⣛⣋⣉⣭⣭⠥⠴⣾
⠀⡰⠈⠸⡀⢀⠏⠉⠀⠀⠀⣿⠀⠁⠤⢼⡅⠀⠀⠀⠀⠙⠲⡄⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠒⠶⠤⠤⠤⢤⣤⣀⣀⣀⡤⠔⠃
⠀⣧⡀⠀⠀⣿⡀⠀⢹⡀⠀⠈⠁⠘⣆⣸⠁⠀⠀⠀⠀⠀⠀⠹⡆
⠀⡟⠛⠶⠖⠋⠓⠤⠔⠋⠃⠀⠠⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡿
⠀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠐⠁⠈⠁⠀⠀⠀⠀⣰⠃
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠙⣆⠀⠀⠀⠀⠀⠈⠒⠤⠤⡤⠤⠔⠊⠁⠀⠀⢠⠞⠁
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠞⠁⠙⡆⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠁⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸
⠀⠀⣾⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣸
⠀⠀⢸⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⠏
⠀⠀⠈⠳⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠋