Zoology Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠸⣆⠀⠸⣷⣄⡀⠀⢰⡟⣿⠀⢠⣰⣾⠟⠁⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢻⣤⢀⠐⠿⣿⣧⣸⣿⣿⣤⣾⣿⠋⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⠉⠓⠶⣤⡀⠀⠈⢿⣯⣆⠀⠙⣿⣟⣿⣿⣿⠟⠁⢀⣰⡟⠁⢀⣠⠤⠖⠒⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠈⠓⠦⣝⣷⣄⡀⠹⢿⣤⣠⠈⢿⣿⣿⣿⠁⣀⣣⢟⡤⠞⠉⠁⠀⠀⠀⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⣦⣄⡠⠤⠈⠙⠻⣶⣤⣙⢷⣿⣿⣿⣿⣿⣾⣿⠿⠋⡀⠁⠀⣀⣠⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣦⣤⣀⠀⠊⠛⢿⣿⣿⡻⣿⣿⡿⣟⣚⣋⡬⠖⠛⠋⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⣚⣿⣿⣷⣿⣿⣭⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⢻⣿⣿⣿⣿⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣻⡿⠋⠈⣰⣿⣿⣿⣿⣿⡀⠈⠛⣿⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⣼⣿⠿⣿⣿⣾⣿⡅⣼⣧⠀⠀⡿⣧⡑⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡇⠀⢀⣿⡟⢈⣿⣿⣾⣿⠂⢸⡗⡄⠀⠀⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠋⠉⠀⠀⣸⣿⠃⠘⣿⣿⣿⣿⠀⢸⡆⡇⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⣽⠟⠀⠀⢸⢿⡾⠋⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠉⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠐⠈⠁⠀⠘⠊⢷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣶⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⡶⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⣀⡀⡾⠉
⠘⠁⠀⠀⠛⠄⠀⣀⡤⠀⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣈⡃⣀⣴⢶⠳⣓⣄⠀⠄⠐⠋⣳⠙⠀⠀⠞⠀⢸⣧⡤
⠀⠀⠀⠀⢀⣤⣾⣯⣴⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠉⠛⠁⠀⠐⠢⠢⢤⠀⡀⢀⠁⡀⠀⣸⠄⠀⣿⡟⠄
⠀⠀⣠⣶⣿⣿⢻⡷⣼⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠙⠀⢿⣀⢠⣿⠁
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠉⠁⢀⣴⣦⣿⣿⣷⣿⣿⣿⣿⣧⣤⣤⣤⣤⣄⠀⢤⡀⠀⠀⠀⠈⠖⢿⠷⢦⣍⢺⣿⣄
⠀⢸⣿⣿⣿⡿⢏⣿⣿⣩⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠘⢻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣾⠿⣦⡀⠀⢀⡠⡄⠀⠈⠉⠉⣿⣀⠀⠄
⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⠙⠛⠋⢹⣿⣿⣿⣿⣿⡯⢿⣿⣿⣦⣹⣿⡄⠀⠀⠀⣀⡀⠀⠀⣻⠉⢷⣦
⡎⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⣼⣿⣿⡿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣆⠀⠘⢻⡇⠀⢠⣿⡄⠀⠙⢤⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣤⣴⣾⣏⣻⡓⠞⢿⣿⣿⣦⣼⣿⠟⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠒⠈⠁⠀⢸⣿⠂⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠨⠝⠋⠉⠉⣿⣿⣿⣯⣉⣽⣿⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠨⢝⠢⠤⠬⠛⠁⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⡟
⠐⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇⣀⠀⠀⠃⢀⠀⠘⠋⠿⠿⠟⠛⣻⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⣠⣿⣿⠃⠀⠀⠀⢀⡀
⠉⠀⠀⢿⣿⡇⠀⠉⢙⠻⠿⣿⣿⣏⣀⠀⠀⠉⠲⠿⢷⣾⣟⠾⡈⣁⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣃⣠⣴⣄⡀
⠀⠀⠀⠘⣿⣷⡀⠀⡀⠀⢀⠈⠻⣿⣿⣷⣄⠀⠀⠀⢀⣿⣿⢀⡁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣙⣛⣟⠿⠛⠃
⣤⠀⢀⡀⠘⣿⣿⣦⣁⠀⠈⠁⠀⠈⣙⣻⣿⣷⣶⣶⣿⣿⣿⣴⣮⣤⣶⣶⣿⣿⣿⣻⣯⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠀⠈⠿⠶
⣿⣇⣈⡅⠀⢨⡽⢿⣿⣿⣶⣤⣄⣀⣨⣹⣦⣴⣿⣿⡿⢟⣿⣿⣿⡿⠿⡿⠟⠛⠛⢛⣻⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣤⣀⡀⠂⠀⠀⠐⢠
⠻⡿⣿⢽⡿⣿⣷⣼⣿⣯⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⠛⣛⣻⡿⠞⠛⠆⡀⠉⠀⠊⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣀⣬⣍⡿⣿⣿⣿⣌⠙⢀⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣀⣉⣉⣉⣀⣈⣉⣉⣉⣉⣉⣉⣉⣁⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡋⢱⣾⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠷⠶⠄⠀⠀⠀⠰⠶⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡁
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⡄
⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿
⠀⠈⠛⠛⠛⠛⢋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⡿⠿⠟⢿⣿⣿⠏
⠀⠀⠀⠀⣴⣿⠿⣇⠰⣿⣿⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣮⣓⣀⡀⠀⣸⣾⠟⠁
⠀⠀⠀⠠⣟⣱⣾⣿⣿⣿⠿⠛⠚⠛⠛⠿⢿⣿⡿⢯⣽⣿⣿⣿⣿⣿⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠙⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣾⣯⡾⠟⠉⠉⢉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⣄⣾⠃⣀⣀⣤⣴⣦⣴⣶⣶⣦⣸⣧⣀⣀⣀⣠⣾⣿⣷⣶⡄
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⡉⢀⠀⠀⡀⠀⢀⣠⣌⠁
⠀⠀⠀⠀⢿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⢿⡿⢿⢿⣷⣾⣁⣿⣿⣷⣿⠉
⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠿⠿⠟⠙⠋⠉⠙⠁⠐⠁⠙⠿⣷⡄⠂⠈⣫⣝⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⢀⣾⣿⣿⣿⠟⠛⠈⠙⠛⢿⣿⡿⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣶⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠈⠉⠙⠿⠿⣧⠀⠀⠀⠀⠸⣟⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠐⠂⢠⣄⣀⣀⠀⠙⢦⢀⡀⠙⠛⠀⢀⣀⣤⣤⣤⣶⣶⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⡿⣿⡯⠍⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢃⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠻⣧⡈⠟⠛⠋⠐⠮⠙⠻⠿⢷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣀⠀⠀⠈⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠿⠗
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡐⣀⣀⣀⣀⡞⠁⠀⠈⠃⠀⠀⠀⠀⠶⠸⠽⠺⡷
⠀⠈⠀⣠⣴⣿⣿⣿⣦⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⢀⣠⠶⢀
⠀⠀⢸⡿⠋⠀⢀⡈⢻⡖⢳⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡋⠀⠀⠀⠀⠈⠇⢠⣀⣠⣤⡄⢠⡄
⠀⣴⠾⣧⡀⠆⠈⠃⠘⠻⣏⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠻⠈⣿⠚⠁⠀⠀⠀⠀⣿⠀⢸⠇⠈⠩⠷⠟⠃
⠀⠙⠛⣿⠀⠠⣤⣶⠟⢀⣽⡇⠀⢢⠀⠀⠄⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢁⡀⠀⠀⣤⠀⠠⢄
⠀⠀⠀⠹⢷⣤⣤⠶⠖⠛⠉⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⡀⠀⠃⠀⠀⢸⠇⠀⠸⡆⠀⠀⠸
⠀⠀⢀⠔⠠⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⣴⠒⣖⢲
⠀⠀⠈⠀⠀⢈⠆⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠏⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⠞⠁⢀⣀⡀⡴⠛⣳⢰⠋⢓⡆⣧⢾⡉⡳⢴⢫⣷⠈⣧⣿⠀⠀⣀⠈⠋⢁⣀⡌⠂
⠀⢀⣴⣆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠙⠚⠁⠈⠙⠋⠀⠉⠀⠉⠁⠈⣩⣾⠒⢠⢾⠋⠀⡟⠁⠀⠉⠉⠀⢀⠁
⠀⠀⠋⠀⣀⠀⠀⠀⠀⠀⢾⠆⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⢤⣤⣄⡀⠀⠷⠃⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘
⠀⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠠⠈⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠁⢆⠀⠀⠀⣄⠀⠀⠀⠀⠈⠘⠀⠀⡀⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁⢠⡀⠄⠀⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡀⠀⠲⠀⠀⠀⣠⡤⡐⠦⠛⠀⠀⠀⣶⢶⣶⣄⡂⠀⠀⠀⠀⠀⠐⠂
⢀⠀⠀⠁⠀⢠⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠁⠀⠀⠖⠀⠀⠈⠙⠛⠚⠃
⠀⠀⠈⠁⠀⠌⠉⠘⢿⠂⠈⣿⠀⠀⠀⠀⠀⠀⠀⠋⠞⠁⠀⠁⠀⠀⡀⣐⣁
⠀⢠⠀⢠⠄⣄⠀⠀⡄⠀⠀⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠜⠀⠀⠀⠀⠈
⠀⠈⠀⠷⡀⠆⠈⢒⡠⢀⠀⠀⠀⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠁⢈⢀⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⡏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣦⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢠⣾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⠀⠘⠲⢖⡭⢭⡷⣤⡴⠶⣶⣶⣶⣶⡶⠞⢛⠖⣹⢟⣿⠓⠒⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠤⣄⣀⠀⣀⣀⣰⠟⢋⣁⣀⠖⢀⣴⣿⣿⣏⣀⣀⣀⣀⡠⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣾⡭⣭⣯⣽⣯⣿⣽⣇⣴⣿⣿⣿⣿⣯⣼⣾⣾⠷⠶⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠚⠉⠀⠉⠘⠻⢮⠉⠉⠀⠀⠀⠯⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣤⣤⣤⣾⣿⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⢛⢃⣀⣀⣈⣉⣟⠁
⠀⠀⠀⠀⠀⠀⢠⠀⣤⠀⠁⣠⣜⣦⣤⢰⣸⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⣠⡖⢿⠟⣿⡀⠄⠘⠃
⠀⠀⠀⠀⠀⠠⢿⣴⣍⣼⡀⣩⣼⣿⣷⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠘⠿⠓⠛⠀⠄⣃⣿⠀⠂⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣾⣛⣫⣽⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⡄⢐⢡⡀⡂⣧⠀⢠⠒⡀⠐⠠
⠀⠀⠀⠀⠀⠀⢉⡝⣱⣧⣿⣿⣿⣿⣿⣞⣏⣛⠑⡈⠀⠀⠀⠀⠀⠀⠈⢀⢈⠓⠒⠈⣿⠊⠭⠂⢄⡤
⠀⠀⠀⠀⠀⠉⠻⣿⡻⣿⣿⣿⢻⣿⣿⣿⢿⡎⠈⠀⢀⠀⠀⠀⠀⠀⠤⠋⠠⠵⢷⢤⣿⣄⣠⣀⠈⠙
⠀⠀⠀⠀⠀⠀⠸⠛⡗⢿⠻⣿⣧⠿⠙⡿⠁⡉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢴⣿⡿⠋⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣬⠈⡄⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠀⠠⠙⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣶⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⣤⣀⣤⣥⠟⡒⡠⢤
⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⢿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⣯⣛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⣹⣿⣿⣷⢮⣄⣤⡀⠀⠄⠀⠀⣤⣼⠇⡄⠀⣨⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢿⣿⡿⠓⠚⠿⠿⠞⠚⠓⠛⠛⠛⠛⠁⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠦⠞⠿⠴⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⢤⣾⣥⢤⠄⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢢⠀⡄⢹⣧⡀
⠀⠀⠀⠀⠀⠀⢠⡗⡄⠀⠀⠀⣿⣆⢀⡠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣸⡄⣧⠀⠈⠀⠀⣀⠠⣄
⠀⠀⠀⠀⠀⠀⠸⠻⡇⠀⠀⢞⣿⣿⣿⣠⠅⡀⠀⠀⠀⠀⠀⠐⣴⣤⠀⠀⠀⣸⡿⠷⠙⠀⢤⡀⠉⠃⠄⠀⠧
⠀⠀⠀⠀⠀⠀⠃⢘⡁⠤⠘⢹⣿⣿⠟⠻⢾⣷⣥⣄⣀⣤⣠⣴⣾⣿⢐⠀⢰⡟⠀⠀⠀⠀⠀⠉⠑⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⣼⢓⠀⠀⢰⣿⣿⠀⠀⠀⠀⠈⠉⠁⠁⠁⠀⠀⠀⠈⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⠀⠀⠀⠀⠭⠿⠦⠀⠀⠀⠀⠠⠀⠀⠀⠸⠃⠄⠻⠿⠧

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣶⠶⣤⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣟⠀⠩⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⢿⡟⠋⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠛⠋⠀⠀⠉⠻⣿⡟⠀⠀⠙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡏⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢰⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣻⣿⣷⣶⣤⡄⠀⠀⠀⠀⣀⣀⣰⠏⢹⣿⣿⣿⣿⣿⣶⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠁⠠⠟⠛⢿⣿⣿⣿⣿⣿⣷⣦⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠠⠔⠒⠲⢄⡀⠠⠂⠀⠐⣊⣩⣥⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣉⣉⣹⣿⣿⣾⣤⣶⣿⣿⣿⣿⣿⣿⠿⠛⠟⠃⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⣐⣲⣤⣴⣾⣿⣿⡿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣐⣒⣛⡽⣛⡽⠣⠤⠀⠤⣤⡀⠀⠀⠀⠀⠀⠀⠈⣟⣥⣿⣿⢿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣩⠟⠉⣿⣯⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠁⢀⠞⡹⠁
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡾⠁
⠀⠀⠀⣤⣶⣿⠀⢻⣷⣤⡀⠀⠀⢀⡤⠀⣏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠻⣿⣿⣀⣼⣿⠟⠁⠀⣀⣾⣠⢀⠬⢳⣭⣱⣿⣴⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠙⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠙⠿⠋⠁
⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢉⣩⣶⣛⡿⠟⠛⠭⠽⠛⠂
⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⢠⠾⠋⠹⡄⠘⢧⣀⣀⡠⠤⠄
⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢠⣿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠘⠸⣹⠆⣇⠇⠃⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⠶⠶⠆
⠀⠀⠀⠀⠀⣇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⢛⠛⠛⠛⠛⠻⠿⣿⠢
⠀⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠒⠶⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⣠⠀⠀⠀⢉⡁⠒⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⡰⠀⠀⡼⠁⠀⢀⠔⠉⣠⠖⡣⣄⡬⠭⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡐⠁⠀⢠⠋⢀⠊⡠⣪⠞⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⡈⠀⢀⠅⠀⢠⠃⡠⠃⣨⣾⣱⣄⣀⣰⡀⠀⡀⣀⠇⠀⢀⣀⠀⠀⠀⣀⡀⣾⣿⠇
⠀⠀⠀⢠⠞⠁⠀⠀⡄⠰⡀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⢠⠃⠰⠁⣴⠋⠠⢀⠠⢈⠉⠉⠉⠉⠛⠢⣠⠏⣽⣠⠔⠊⣽⡿⣿⢇⣀⡀
⠀⠀⢠⠏⠀⠀⡀⠀⠈⢄⠐⡀⠄⠀⠀⢁⠀⠀⡇⠀⠀⠀⡎⠀⢀⣾⠃⠀⠀⠀⠁⠈⢳⣄⣀⠀⣠⢶⣧⡾⠟⢥⢰⣤⢞⣱⣟⣿⣿⣿⡷⠂
⠀⢠⠿⢀⠀⢑⡀⠤⠒⠚⠲⠖⠴⣤⣀⠀⡄⠀⠇⠀⡀⢀⠀⠀⣼⣁⣀⣤⣔⠒⠒⠈⠁⠀⠀⠀⣸⣶⣿⠷⣯⠶⡿⢿⡿⠟⠉⠉⠀⠙⠁
⠀⡝⢀⡤⠚⠁⠀⠀⠀⠀⢠⠂⠀⢈⡙⠳⣦⠀⠀⠀⡇⠈⠀⢰⣟⡿⣧⡈⣿⣻⣷⢶⠶⣤⣶⣿⠟⢛⣳⢶⣿⣿⠈⣆⣹⣄⣀⣀
⢸⠃⠎⣠⠔⠒⠒⢦⡄⠠⠃⠀⢀⠎⠀⠠⢈⢷⣘⠀⠁⠀⢀⣿⣿⣧⢹⡿⢅⠉⠀⠙⢦⡀⠈⠑⠿⣒⠒⠚⠚⠿⢿⢿⣷⡄⢹⠹⢿⡦⣤⡀
⡎⠘⠘⠠⠢⡄⠀⠀⢻⡆⠀⠠⠋⠀⢀⠄⠀⠉⢻⡤⠀⡇⢸⣯⣼⣍⣸⠃⣸⣦⠀⠀⠀⣻⡀⠀⠂⠘⣦⠀⠀⢀⠁⡀⣬⡷⡤⣿⣔⣧⣬⢻⣦
⡇⡆⡼⠃⡿⣿⠀⠠⣿⣿⠀⠀⢀⠔⢁⠤⠊⣀⡾⢿⡇⠃⠸⡻⣧⡎⠀⣸⣿⣿⡷⢤⠞⠈⠳⠦⣠⡏⠈⣇⠀⠀⠂⠐⣿⡄⢠⠩⣙⣽⣿⠚⠻⣷⡀
⡇⡇⠙⠢⠞⠁⠀⠀⢸⣿⠀⠀⠁⠀⢁⡠⠀⢁⠥⣻⣇⠃⣼⠃⡡⠀⢀⡻⣿⣿⠁⡄⠀⠀⣶⠀⢠⡇⠀⢸⡗⠲⠶⠶⠾⣻⡈⠁⠌⠠⠹⣿⣧⡙⢷
⡇⠹⡄⠀⠀⣀⠠⡤⣤⠇⠀⠀⠀⠀⠁⠀⠀⠡⠚⠛⣟⢴⠇⠀⠀⣠⠞⢁⣿⡇⠀⠇⠀⠠⡿⠀⠠⠃⠀⢘⡇⠀⠀⠀⠀⢿⠡⡁⢀⠘⠿⠛⢧⡹⣾
⢹⠀⠙⢲⣄⣬⡷⠛⠁⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⢀⠄⠂⢀⠔⢚⠵⡣⣾⡿⣯⠀⡋⢃⢰⠇⠀⠀⡏⠁⢾⡁⠀⠀⠀⠀⠘⢷⢤⡿⠧⠐⣶⣯⣿⡛
⠈⣧⢀⠀⠱⣄⠀⠉⠁⠀⠈⠉⠀⠀⢀⡀⠤⠄⠊⠁⠀⡈⠠⠚⠁⣈⣻⣿⣿⡇⠀⠃⠀⢹⠀⠀⠤⢸⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⡗⠶⢮⠱⣆⢹⡇
⠀⠘⢆⠂⠀⠈⠓⠤⣀⡀⠀⠀⠀⠉⠀⢀⣀⠤⠔⠊⠉⠀⠀⢂⣴⢞⣽⣿⡟⠀⠀⡀⠀⢘⠀⠊⡠⠊⡇⠐⣯⠀⠀⠀⠀⠀⢀⠏⣷⠛⠖⢸⣿⣿⡇
⠀⠀⠈⠣⡑⢄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⠤⠒⠊⠁⢴⢭⡿⠋⠀⠀⢀⡇⠀⢸⡠⠊⠀⠀⣷⢲⠏⠀⠀⠀⠀⠀⢸⢰⠛⡆⠀⠦⣿⣿
⠀⠀⠀⠀⠙⢦⣙⠢⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠂⠀⡨⣒⠕⠋⠀⠀⢀⠤⡸⠗⣲⠟⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⠇⠎⠀⠱⣄⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠓⠦⢌⣁⣂⠀⠀⠀⢀⣀⡀⠠⠄⠶⠓⠉⠀⠀⠀⠀⠊⠁⠀⣀⠞⠁⠀⠀⠀⠀⢀⢣⡏⠀⠀⠀⠀⠀⢸⠎⠀⠀⠀⠈⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠠⠚⠁⠀⠀⠀⠀⠀⠀⡘⣾⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣨⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⢹⣷⣆⣀⣀⣀⣀⡤⡀⡀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⣏⢻⣴⣎⣿⡟⠩⡝⠛⠋⣾⣿⡎⣷⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬⣽⣽⡿⣿⡟⡟⢹⠏⡶⠀⠀⠀⠀⠈⠩⠀⠀⠛⡁⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣷⣷⣾⣿⣿⣝⡷⢏⡚⠃⠋⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣶⣠⡾⠉⠙⠟⣉⣿⣻⠿⣷⣧⣽⣹⢤⣡⡝⢾⡱⡬⢻⡀⢇⡀⡠⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⢖⠄⣍⣻⡁⠀⠾⠿⡇⠹⡷⣿⡘⣧⠹⢤⣧⣻⣌⢏⣱⠻⣻⡷⣶⣃⠀⠀⠈⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣨⣴⠶⠞⢃⣈⠑⢶⡍⠀⠀⣶⣄⢈⡓⢳⣌⠻⠛⠷⣶⡚⠳⣬⣷⣿⣽⣿⣿⣿⣿⠿⠷⠖⠒⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⣡⠄⢁⡤⢈⣈⣼⠋⣛⠚⠀⠀⢰⡇⠣⡀⠳⢄⠘⡈⠶⣤⣼⣙⢻⡾⣧⣼⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣡⡤⢼⣅⣀⣼⣻⠟⠉⠋⠀⢠⣿⡁⠀⠰⡀⢦⡉⠑⠲⠴⣌⠉⠶⣽⣿⣾⣧⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣛⢻⢦⡾⢃⠀⣣⠉⠙⣿⣠⠄⠄⠀⣠⠟⠀⠻⠄⠀⠙⠂⠱⠂⠳⡶⢾⣿⢿⣏⢿⣯⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣉⣼⠁⠸⡶⠛⣿⢞⡿⠁⠀⠀⠜⠃⠀⠉⣆⠀⠲⣆⠘⢆⣁⠲⣦⣾⣿⣷⣿⣿⣾⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣰⢿⡈⠙⣦⣤⣄⣀⣻⠞⠁⢀⠀⢠⠀⠀⠄⠀⠈⠳⠄⠀⠀⠹⣿⣷⢲⣵⡿⣶⠿⣿⣟⣻⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⣶⣟⠥⠚⡹⠜⢿⣷⡿⠏⠁⠀⡠⠞⠀⠀⠦⣀⠀⠙⠀⠠⠀⢙⢶⣀⣁⠘⠻⢾⣵⣙⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣰⣿⡀⠂⣎⡀⣠⣼⢞⢛⣏⣥⠎⢁⠀⠀⠀⠀⠉⡄⠀⣄⡻⢶⣤⠀⡄⢡⡝⢾⣯⡄⣿⣶⣾⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡾⢫⡿⢫⣟⣽⣫⣁⡾⣼⡿⠋⠉⠀⠀⠐⠀⢀⠀⠀⠀⢀⠈⠙⠒⠠⡄⢠⣄⣈⣉⠛⣿⡿⡼⢏⡜
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⣰⠟⣵⡞⡤⣡⣯⣏⡾⠟⠀⠀⠀⠀⠀⠢⡀⠁⠙⢦⣤⣀⠁⠁⣦⢀⣳⢦⡀⠉⢰⠶⣷⣿⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢼⣫⣾⡷⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⣀⠜⡙⣦⣴⣦⡿⠃⣌⡘⢳⣾⣶⠟⠉
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠙⠛⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠔⠀⡄⠐⢤⣀⣨⠿⣛⣽⣿⣷⣤⣬⣿⣿⡾⠃
⠀⠀⠀⠀⠀⣀⣾⠟⢶⣄⣀⠀⠀⠀⠀⠙⠲⣄⣀⣀⠀⠀⠀⠃⢀⣀⣼⠿⢯⡭⠡⢶⣿⣿⡛⠿⣯⣿⠟⠋
⠀⠀⠀⠀⡾⣋⣷⣶⣿⣿⣿⡶⣤⡀⠀⠀⠀⠈⢹⡏⣷⢤⣶⣾⡿⠟⠲⢴⠤⠴⡶⣤⣿⣿⣟⣿⠟⠁
⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⡟⣇⠀⠉⣐⡄⠀⡀⣼⣡⣿⢣⠥⣀⠐⡂⠤⠈⠓⢦⣆⣸⣿⠟⠋
⠀⠀⠀⣻⣿⣿⣿⣿⣿⡿⠀⢨⡦⠘⡽⣻⠾⣡⣯⡷⠟⠉⠀⠈⠻⢍⢙⣾⣿⣿⣿⣿⠁
⠀⠀⢠⣿⣿⡿⣿⣿⣿⠹⡄⣀⡄⠀⢀⠉⠀⣨⠟⠀⠐⠦⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⣼⣿⡟⣱⣿⣿⡟⠀⡠⢩⡜⠤⠚⢧⣼⠋⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠉⠻⢿⣿⣦⣄
⠀⣼⣻⠏⢠⣷⣿⣿⠹⢲⠇⢻⠃⣀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠉⠛⠿⣽⡳⠦⣄
⢰⡿⠃⠀⣾⣿⣿⣿⣌⠠⡀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠈⢘⣖⡼⠇⠠⠀⡀
⡞⠁⠀⣸⣿⣿⣿⣿⣾⣷⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡠⣄⠀⡾⢁⡟⡙⠀⠀⠀⠐⢠
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⡿⠿⠞⢁⠀⠀⠀⠀⠈⠳⠄
⠀⠀⢸⣿⡷⣡⣾⣿⣿⣿⡿⣡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣟⣷⡏⣿⢿⠋⣠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡛⠉⠉⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡰⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠔⣿⣿⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡿⠟⠁⣺⠀⠘⠈⣿⣿⣿⣿⣶⣿⣿⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⢀⣿⣷⡁⠀⢹⣿⣿⡟⠛⠛⠁⠀⠀⡘⢀⡞⠁
⠀⠀⠀⠀⢀⣾⣿⣿⠏⢀⢀⢀⣾⣿⣿⣷⣄⠈⣿⡇⣹⣆⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣷⣬⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣮⣿⣴⣾⣿⣿⠋⠀⠀⢀⣠⡔⡊⣉⣽⠿⠟
⠀⠀⠀⠀⣽⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣁⠹⣿⣿⣿⣿⣿⣿⣿⣏⣀⡠⠔⠊⠁⣿⠓⠹⠋
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣷⣾⣿⣿⣟⠻⣿⠟⢋⣁⣀⣠⣶⣿⡯⠄
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣟⢁⠂⠙⣿⣿⣿⣿⣿⣟⠙⢣⡀⠈⠉⠋⠉⠉⠉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢂⣄⣶⣿⣿⣿⡿⢿⣿⣷⡾⣷⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⣀⠀⠙⠿⣿⣾⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠈⠉⠙⠻⢶⣿⣿⠻⢆
⠀⠀⠀⢸⣿⣿⡏⠉⢉⣉⣉⢉⡉⠉⠙⠛⠊⠐⠃⠀⠀⠈⠙⠳⣦⡱⢤⣄
⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⠀⠀⠀⢀⣀⣤⣤⣤⣬⣀⣀⣀⣀⣀
⠀⠀⠛⠛⢻⣿⣿⣏⠀⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⢦⡀⠙⠉⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠧⠶
⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣷⣦⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣦⣶⣶⣶⣶⣿⡿⠿⠛⠉⢡⣬⡉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠛⠋⠛⠒⠒⠒⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⣀⣭⢤⣄⣀⠀⠈⢇⠐
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⠄⠠⡀⠀⠀⣴⠻⣿⣿⢿⢾⣽⣳⣲⢄⣖⡀
⠀⠀⠀⠀⠀⢷⣿⠙⢸⠁⠀⠀⠀⠀⡜⠾⢩⢿⠷⠦⢴⡯⣛⠿⣿⡿⠛⢷⣿⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⣷⡴⢩⣵⠛⡷⢾⢦⡏⣹⣏⢫⣶⣾⣿⣿⣷⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠲⠧⠀⠀⠀⠀⠘⡟⠞⠋⢠⠒⡇⢺⠉⢠⣶⡼⢹⣟⣿⣿⣷⡿⣿⢿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠁⡞⠐⡇⣯⠀⢶⢀⣜⢻⡦⣽⣟⣿⣿⡿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠬⢀⡿⡗⠀⣤⠈⠁⡻⠿⢷⣬⠛⣿⣿⣿⣿⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡂⢸⡇⢰⠄⢍⠁⢨⣉⣟⢠⡜⠓⢻⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣂⣸⣁⣼⣿⣮⣤⣹⡗⢿⠈⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣋⢪⡿⣿⣏⠉⠃⢸⡇⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⢢⠀⠀⠀⠀⠀⠺⣿⠋⠙⢻⣿⣿⣾⣾⣷⣤⣼⣧⣼⢿⡿⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⡰⠃⠈⢢⣀⣘⣀⡀⣤⡀⠀⠀⣿⡀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣆⢷⡹⣧⡘⣿⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠡⠄⠀⠀⠛⢉⣿⡗⠈⠁⠈⠉⠉⠁⠀⠀⠀⡟⠈⠻⣿⣿⣿⣿⣿⣾⣎⢳⣜⢿⣿⣇
⠀⠀⠀⠀⡔⠉⠀⠀⠀⡀⠂⣀⡴⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠠⣸⠃⠀⣼⣿⠻⣝⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⢤⣄⣀⠀⣀⠘⢦⣴⠁⠀⠀⣘⣇⠀⠀⠈⣿⠋⠻⣿⢿⣿⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⣶⣶⣾⣾⣿⣿⣿⣤⣾⣿⣿⡇⡀⡤⢿⣤⣶⣤⣿⡀⠀⠘⢷⡈⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⡛⠉⠙⠛⡛⢛⠿⢿⣿⣿⣷⣷⣧⢸⣿⣿⣿⣿⡇⠀⠀⠈⢹⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠏⠳⠦⠤⠀⠀⠴⣿⣿⣿⣿⣿⠘⢿⣿⢁⣿⠁⠀⠀⠀⠀⠗⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠀⢘⣿⢀⡿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠌⠈⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠊⠉⠉⠉⠉⠉⠉⠓⠒⠲⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⣀⣠⣶⢀⡴⣛⣥⠾⠋⠉⠉⢻⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⢻⣾⣿⣏⣡⢼⡟⠉⠳⡄⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡃⠀⠀⠘⠛⠻⢿⣿⡧⣟⠀⢰⠇⠀⠀⢀⡾⠀⠀⠀⠀⠀⢠⡶⠶⠶⢤⡴⠋⠙⠓⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⡟⠀⠀⠀⢀⡴⠛⢉⢿⣰⠋⠀⡏⠀⡴⠞⠋⣤⣤⠀⠀⠀⠀⣸⠃⣴⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡾⠀⠀⠀⠀⢾⡀⣴⠋⠦⡧⠀⠈⠧⠞⠀⠀⠀⠉⠉⠀⠀⠀⢿⣁⠐⡏⢳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣼⠁⠀⠀⠀⠀⠀⣿⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⢉⣙⣧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢀⡴⠒⢦⡀⠀⠀⢠⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠠⢶⡞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢯⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡴⠶⢦
⡞⠀⠀⠀⢹⡄⠀⣼⠀⢸⠃⠀⠀⠀⠀⠀⠀⣠⠴⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠀⠀⣀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢠⡏
⡇⠀⠀⠀⠀⣇⠀⡇⠀⢸⣆⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠎⣁⡈⢿⠷⣮⠓⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸
⡇⠀⠀⠀⠀⢸⠀⡇⠀⠘⣿⠀⡴⠒⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠛⠉⠁⠙⢦⣠⠶⠲⠖⣁⠀⢰⡛⣦⡴⢦⠀⣾⣿⠀⡇
⡇⠀⠀⠀⠀⢸⡀⡇⠀⠀⠸⣆⣧⣤⢶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⢇⠀⠉⢩⠇⠸⣿⣿⣿⠀⡇
⡇⠀⠀⠀⠀⠈⡇⢳⠀⠀⠀⠈⠳⣼⡆⠙⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡀⣠⠞⠀⠀⣿⢹⡏⢸⠁
⡇⠀⠀⠀⠀⠀⡇⠘⡀⢠⠔⠢⣄⠈⠻⣄⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣇⣠⠖⢦⣄⣼⠁⢸
⡇⠀⠀⠀⠀⠀⢳⠀⢻⡏⠀⠀⠈⢣⠀⣸⠇⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⢹⡟⠀⡾
⡇⠀⠀⠀⠀⠀⢸⠀⠸⡇⠀⠀⠀⠈⡆⢧⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⢀⡞⣻⠀⠀⠀⠀⢸⠇⠀⡇
⢳⠀⠀⠀⠀⠀⢸⠀⠀⢷⠀⠀⠀⠀⠸⡌⢧⡀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣡⠇⠀⠀⠀⠀⡿⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠘⡆⠀⠘⡇⠀⠀⠀⠀⠹⣆⠙⢦⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡜⣿⠏⠀⠀⠀⠀⣸⠃⠀⢰⠃
⢸⠀⠀⠀⠀⠀⠀⢧⡀⠀⢻⡀⠀⠀⠀⠀⠙⢦⡈⢇⠀⠀⠀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡴⢋⡼⠃⠀⠀⠀⠀⠀⡟⠀⢀⡼⠀⠀⠀⠀⠀⢀
⠈⡇⠀⠀⠀⠀⠀⠀⠉⠲⣜⣇⠀⠀⠀⠀⠀⠀⠙⢾⣆⢀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢋⡴⠋⠀⠀⠀⠀⠀⠀⣸⣣⠖⠉⠀⠀⠀⠀⠀⠀⢸
⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠤⣤⣤⣄⣀⣀⣠⣤⣤⠤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⠈⣉⣁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⢾⣽⣿⣿⣿⣿⣯⡗⠀⠀⠀⠀⢀⣤⠴⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠇⣀⠁⣀⣀
⠀⠀⢿⣿⡿⠁⠎⢻⣿⡿⠀⠀⠀⠀⣾⣿⣷⠰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠉⠘⠃⠨⠄⠉⠁
⠀⠀⢫⢿⣿⠀⠀⢸⣿⣍⠁⠀⠀⢸⣏⠉⠀⠁⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⣿⣤⣤⣼⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡖⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣀⣈⣉⣩⡅⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠀⠀⡀⢀⡀⢀⡀⣀⢀⢀⠀⢀⢀⢀⠀⣀⢀⠀⢀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀
⠀⠀⠀⠀⠀⣔⣆⠆⠀⠀⢶⣌⠉⠀⠀⠀⣱⢸⠀⠺⡇⣿⢾⢸⠇⢿⢸⢹⠀⢿⠈⡇⢸⠀⢻⡇⡟⡇⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢹⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⠄
⠀⠀⠀⣀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣿⡎
⠀⠀⠀⠙⠁⠙⠛⠈⠋⠀⠀⢠⣤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢶⣦⠿⠚⠿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⠶⣿⡇
⠀⠀⠀⢠⣤⡀⢀⣀⡄⠀⠀⠈⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⣷⣶⠇⠀⠐⠀⠘⣷⣶⠀⠀⠀⠀⠀⢿⣿⡤⡀⠀⠁⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⢐⣂⣀⣉⣭⡅⠀⠀⠀⠘⠇⠀⠀⠀⠿⠁⠀⠀⠀⣶⣾⡀⠀⠀⠀⢀⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⠀⠀⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢰⣿⢲⣶⣾⢿⡧⠉⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣶⡇
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣉⡛⠈⠀⠀⠀⠀⣴⣶⡖⠀⣨⣭⣅⠀⠐⣶⣶⠆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⢿⣄⠄⠀⢤⡤⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠸⣽⣷⣦⣀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢂⣶⣿⣷⣾⣿⣷⣦⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠁⢀⢤⣽⣿⣿⣷⡄⠀⠀⠀⡇⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⡟⠻⣷⣒⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡿⣏⠋⢹⡇⠀⠀⠀⡇⠀⢸⠀⠀⢸⠋⣿⣪⡟⢸⡇⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⣃⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠉⠁⠉⠉⠐⠟⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡃⠀⢘⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣴⣆⣴⣤⣄⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠄⢀⡀⠴⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⢿⡏⢛⡻⣿⣗⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣠⣯⣥⣬⠆⠀⠀⠀⠀⡇
⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⣍⣃⡈⢠⣿⣿⣦⠄⠀⡇⠀⢸⠀⠀⢀⣀⢂⣩⣟⣻⣝⡁⠁⠀⠀⠀⡇
⠀⢀⣻⠁⠀⠛⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⣶⣾⣿⣿⡟⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠁⢿⢹⡯⡟⠐⠓⠁⠀⠀⡇
⣾⡿⠋⠤⠠⠀⢤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢿⢺⡿⠿⠋⠁⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⣷⣶⠄⠀⠀⠀⠀⠀⡇
⠉⠃⠈⣶⣿⣤⡷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⡇
⣧⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣶⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠂⠀⠀⠀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡰⠀⠈⠈⠀⠀⠀⢀⣀⠀⠢⠈⠀⠀⠀⠠⠄⠉⠑⠀⠁⠈⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠠⠊⡐⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠂⠐⠳⡄⠀⡀⠘⡀
⠀⠀⠀⠀⠠⠁⠌⠠⠂⠀⠀⠀⠊⠀⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠱⠀⠀⢙⣈⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢹⣃⠀⠸
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠁⠀⠀⡤⠂⠀⠀⠀⠀⠈⠀⠀⢀⣤⠦⣬⠀⠀⠀⢸⡆⠐⡈⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠁⠀⠀⠀⢠⠣⠀⠀⠈⠂⠂⠀⠁⠀⠀⠈⠑⠈⡑⢫⠋⠩⠂⠈⠙⣗⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠁⠈⠈⠙⠉⡊⠈⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠉⢪
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡠⡀⣀⠂⠀⡁⠀⠀⠁⡀⠀⠁⠉⠡⡞
⠀⠀⠀⠀⡂⠀⠀⠀⠈⠀⠀⠂⡀⠂⠀⠀⠐⠀⠀⠀⠀⠎⠁⠉⠈⠉⠉⠠⠀⠀⠈⠑⡦⠂⠀⢠⡁
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠐⢠⠐⠈⠳⠤⠜⠱⢃⢑⣦⡌⢀⠐⠀⠱⠰⠄⠖⠄⠤⡤⠄⠀⠀⠘⣠⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢀⠀⠀⠉⢏⠀⠈⡛⠋⠋⢻⣀⠀⠠⠂⠐⢂⠀⠐⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⡜⠃⠠⠔⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⢀⠀⢀⢀⠄⠀⠀⠠⠄⡀⢡⡄⠀⡀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⠀⠀⠀⠀⡄⠀⠂⠀⠂⠀⡄⠆⡬⢡⢀⣶⠄⠀⠀⠀⠀⠈⠀⠀⣀⠙⠦⡀⠸⠘⠀⠠⡀⠂⡦⡤⢀⠀⢠⡀
⠀⠀⠀⠀⡇⠀⠀⠳⠖⢂⡤⠤⠄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣀⣁⣀⡀⠠⠤⣤⡰⠶⠾⢊⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⡄⠈⡧
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⡧⠀⡠⢀⠄
⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⢁⠌⡀⠀⠂⠀⡀⠁⠀⠀⠄⠀⠀⠀⡠⠊⠐⡁⠐⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣤⢄⣀⡀⠀⠀⠀⠀⠄⠡⠊⠔⠁⠈⠀⠡⠂⠈⠀⢀⣀⡄⡤⡶⢚⠁⢂⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠲⠒⠐⠒⠒⠒⠃⠙⠩⠀⠉⠀⠈⠀⠁

⢸⠃⢀⠃⠀⠀⢹⡆⢹⡇⠀⠀⠀⠀⣧⢷⠀⢰⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠝⠻⡀⠀⠀⠀⠀⢀⢹⠇⠀⠀⣿⠛⢿⣿⢷⡶
⠀⠾⠀⠀⠀⠀⠚⠃⠀⠃⠀⠀⠀⠀⢸⣾⠀⠀⡏⣧⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⠀⢰⣞⡇⠠⣠⡀⣼⣿⡆⠀⠀⣿⠀⢀⣿⣿⣷
⠀⢀⠀⠀⠀⢀⣾⡆⢰⣶⡀⠀⠀⠀⠈⠙⠀⠀⠇⠸⠂⠀⠹⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣷⢀⣿⣷⠘⠉⠁⢿⢿⡇⠀⠀⢸⣿⣿⣿⣿⠟
⢰⡏⠀⠀⠀⣸⣇⡷⠟⢻⡗⠀⠀⠀⢠⢠⡄⠀⠀⠀⠠⡄⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡚⣿⢹⠿⡀⢰⣶⢄⣈⣋⡅⠀⠀⠀⠛⣿⠻⠝
⣿⠀⠀⠀⠀⠉⠀⣠⣴⠈⡏⠀⠀⠀⢈⢸⡇⠀⡇⠀⠀⢣⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿⣿⢙⠀⣸⠇⠰⠇⣼⡿⣽⠃⠀⠀⢀⡇⠀⠀⡀
⠋⠀⠀⠀⢰⠆⢸⠇⠘⡀⣷⠀⠀⠀⠸⢠⣆⠀⡇⠀⠀⢘⡄⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣸⣷⠀⠀⢡⠀⠁⡴⠁⢁⣿⡄⠀⠀⠘⢧⣶⣶⠁
⠀⢀⠤⠐⡤⠀⠒⠀⢈⡁⣿⠀⠀⠀⠀⢀⡉⠀⠇⠀⠀⢸⣇⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠁⠀⣇⠹⡄⠀⢀⣝⠀⢼⢰⡿⣻⠇⠀⠀⢠⡀⠈⠛
⠀⠀⠀⢀⡀⢀⡀⠀⢠⡄⢸⠀⠀⠀⠠⢀⡉⠐⠂⠀⠀⢸⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡀⠒⣸⠁⠘⡇⢿⡁⠁⢀⣾⡟⠀⠘⠺⡁⣸⠀⢀⣤⣶⣿
⠀⠀⠀⠹⣇⣼⡧⢀⡟⣿⢸⠀⠀⠀⢹⣾⣿⠀⡆⠀⠀⡎⠀⢸⣿⣿⣿⠓⠒⢒⠂⠀⠉⠀⠀⠋⣠⢠⡷⠀⣷⠀⣼⣼⣁⢰⣶⣴⣧⡏⠀⠘⠿⠋⣷⣿⠆⠀⣤
⠀⣴⠀⠀⠛⠐⡇⣼⠁⡍⢻⠀⠀⠀⣸⣿⢹⠀⢃⠀⢠⠀⠀⢨⣿⠿⠿⠰⠒⢋⣈⠱⡂⡄⢸⣆⣧⣾⠶⢛⡏⠸⠶⠠⠾⠁⢓⢿⠸⣣⠀⠀⠀⠀⣯⡉⠀⠀⠘
⠀⠀⠀⠄⠀⠀⡇⣿⠀⡇⠨⠀⠀⠀⢸⡧⢸⡇⠀⠀⠀⠀⣤⣾⣯⡢⠖⡀⠆⠇⠀⢀⡙⡴⢩⠧⠘⠛⣛⠠⣴⢈⠙⡷⢽⣡⠛⠞⡱⠢⡌⠳⣄⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠇⢻⢸⣧⣰⠀⠀⠀⣩⣧⢸⡇⠸⡿⢣⠋⣼⡜⣫⣱⠞⣉⠀⠠⢠⠒⢊⠓⢤⡠⢄⠡⠈⣀⠙⠲⠚⣰⠲⢄⠻⠶⠁⡚⠳⢆⠋⡵⢀⢽
⢠⠀⠀⠀⠀⠀⠀⠈⢻⢹⡯⠀⠀⢀⢻⡟⣼⣿⠀⡅⣷⣴⣄⣤⣆⠉⠀⣧⢸⡄⡅⢛⣀⣨⣗⡐⠢⡜⣻⠭⢡⣴⡴⠀⠈⡙⠶⠚⡎⠻⠑⠞⢾⣤⣼⣀⠀⠀⣤
⠸⡆⠿⣦⠀⠀⠀⠀⠀⢐⡇⠀⠀⠈⠘⠿⠃⣿⡆⠳⡅⠄⠉⠹⠉⣙⣁⣸⠞⣓⡠⠋⠆⠠⡜⠹⠏⠐⣉⡖⢻⡄⠐⠗⠀⠩⠆⣀⢀⡀⠙⠀⠀⠙⠬⡱⠓⢏⠙
⠀⠛⢰⡝⢆⣠⡀⠀⠀⠘⠷⠀⠀⡆⣷⣾⠀⣿⣷⠀⢫⡲⣶⠖⣴⣿⣯⣴⣋⠝⣯⡀⢀⠘⢱⠧⢾⣆⠻⠇⠿⠐⠛⠀⠰⣗⡉⢙⠸⠋⠓⢄
⡀⠀⠀⠉⠘⢿⣿⣦⡀⠀⠀⠀⢸⣷⣎⡿⢶⣿⠿⣧⡀⣩⠍⠁⣹⣿⣿⣿⡟⠣⣔⣥⡉⣘⢂⠀⠀⠀⠁⠃⠀⠀⣶⠀⠀⢹⣏⠾⠀⠁⠀⠈⠳⣄
⡟⣻⡗⢦⡀⠘⣿⣯⣵⣦⠀⠀⠀⠱⣮⡢⣿⢑⣤⣠⣌⢿⣷⡄⢸⣿⢻⣿⣧⠀⠈⠄⡶⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣧⡶⠺⠀⠀⠀⠈⢳⡀
⠿⠏⢿⣬⣍⣷⣦⣙⠿⠿⠧⠀⠀⠀⠈⢿⣧⣍⡙⣍⡻⣾⣿⡇⣘⡯⣰⣿⣹⣆⡀⡀⢅⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡜⡁⠃⠀⠀⠀⠀⠀⠹⣶⡄
⠀⢶⣶⠇⢿⣿⣟⠛⢻⡷⠀⢠⣗⣄⠀⠈⢋⣸⣷⣿⣿⣜⣿⣟⢜⠣⠛⢺⠹⣽⣧⠁⠀⢠⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣤⣾⠇⠛⢢⡄⠈⠃⣼⡷⠀⢸⣿⡿⢷⣤⡈⢻⣿⣅⣽⣿⣿⣿⣿⣷⣾⢧⣷⡏⠁⢀⣽⣽⣿⣿⣤⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠙⠃⠈⢉⠈⣷⣀⢀⣟⠀⠀⠘⠛⠃⢈⡙⠙⠆⠙⠛⠉⠈⢿⣿⣿⣿⣧⠈⢉⣿⣿⣧⣭⣍⣿⡿⠀⠀⢀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠾⠻⣿⣿⡏⠀⠀⠰⣶⣤⣈⠹⠠⣧⠀⣂⣸⠇⠈⣧⠿⣷⣦⡿⢿⣄⠛⢡⣤⠉⣉⣤⠀⣺⣿⣿⡟⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⣳⠀⠀⠀⠀⠘⠿⣿⠤⠀⣰⠈⠏⢁⣿⣷⣤⣷⣾⡿⣿⣅⣀⣤⣤⣤⢠⡶⣴⢦⡴⠋⢠⣾⣿⣷⣿⣿⣿⣿⡷⠿⢷⣿⣀⡀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠰⢠⣆⡀⠀⠀⠙⠃⠀⣿⣧⡜⣿⣿⣿⣿⣿⣿⣱⣿⣧⡈⠁⠀⠀⢸⣧⠄⠀⢱⡿⣿⣿⣿⣿⣿⣿⣯⣕⡂⠤⠬⠉⠉⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⢠⣿⣿⣿⣷⣄⠀⠀⠀⢺⣿⣿⣿⣠⣹⣿⣿⣿⣿⣿⠟⠁⠀⠘⠀⠘⠀⠀⠃⢰⣇⣿⣿⣿⣿⣿⠟⢋⡁⠀⢶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⣾⣾⣿⣿⡍⢹⡃⠀⠀⢀⣀⠉⠻⣿⣿⣻⣿⣿⣿⡿⠁⠀⠀⠁⠀⠀⠀⠠⠃⠀⠈⠙⣷⣿⡿⢫⠀⠀⠹⠃⠀⠈⡿⠃⠀⠀⠒⠀⠀⠄⠀⠀⠀⠈⠳⢄⡀
⣿⣿⣏⠈⣷⠘⠃⠀⠀⠈⣿⢷⣶⣬⣝⣻⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣿⣿⣝⠂⠀⠀⠀⠀⢀⡀⠀⠺⣿⠉⠛⠿⠿⠿⣿⠇⠀⠀⠱⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠟⠃⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣿⣟⣿⣦⠀⠀⠀⠀⠸⠀⢀⣤⣻⣷⠀⠁⠀⠀⢸⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆
⣿⣿⣿⣷⣾⣴⢆⡞⡴⢦⠠⣬⣍⠹⣿⣶⡈⠀⠸⡧⠀⠠⠀⣴⡞⠀⠒⠂⢠⣴⣶⡦⢶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄

⠀⡤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠀⠠⠤⠄⡄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⢤
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣘⡤⠄⠀⠀⡀⠸⠠⠀⠀⠀⠀⠂⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠁⠀⠀⠀⠀⠀⠳⠑⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⢀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸
⠀⡇⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⢀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⡀⠀⠀⠈⠐⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⡇⢀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠈⠁⠀⠀⠀⠤⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⢸
⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⢸
⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠂⠀⠉⢼
⠀⡇⠀⡀⡤⠖⠒⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠋⠉⠀⠐⠀⠀⠀⠠⢼
⠀⣧⡊⡁⠀⠀⠀⠀⡤⠶⠶⠴⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡔⠀⠄⠀⠀⠀⠠⠂⠀⢦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣁⣀⠀⡀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠁⠀⠀⠀⠀⠀⠁⣀⠈⠉⠀⠉⠈⠀⠀⠈⠀⠁⠀⠉
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⡇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⣿⡃
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣄
⠀⢢⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠘⣧⠀⠀⡄⠀⠁⠀⠀⠀⠈⠀⠂⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⡀⠀⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁⠠⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠒⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠠⠤⡄⠀⠂⠢⡰⠲⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡄⠀⠀⠀⠀⠀⠀⠀⠠⠟⠷⡀⠀⠀⠀⠀⠀⢀⢸⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣑⠀⢄⠀⠀⠀⠌⡠⠀⠀⠀⢀⡁⠁⠙⢀⠄⠾⠟⠠⢿⢛⣿⣦⡄
⠂⢀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡲⣤⠸⠯⣆⠀⠀⠠⠈⠀⠀⠠⠀⠤⠊⠀⡀⠀⠂⠸⠈⠀⠀⢀⠂
⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠲⠴⠠⠈⠄⠀⠀⢰⠇⠀⠀⠠⠉⠀⢀⣰⠦⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢋⠉⠀⠀⠤⠁⠠⠴⠁⠈⠦⠀⠀⢂⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣷⣶⣾⣷⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠤⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠁⠒⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠠⣈⡠⠂⠀⠀⠀⠀⠀⠀⢀⠤⠤⠂⠀⠀⣀⣀⠀⡠⢀⡀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⢀⠠⠃⠀⠀⠀⠀⠀⣀⠤⠔⠈⠐⠁⠀⠀⠀⠀⠊⠀⠈⡀⠀⠅⣂⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠔⢁⠖⠁⠀⢀⠄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⣈⣗⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠃⠀⠀⢠⠆⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠈⣥⣂⠡⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⡈⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⡀⠀⠠⠂⠀⠀⠀⠄⠔⢀⡆⠀⠀⠈⢏⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠁⠀⠀⢲⠂⠀⠀⠀⠀⠀⢈⠀⢀⣠⣴⢢⢤⠁⢊⡂⣈⠇⠈⡭⣅⠮⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠜⠢⡈⡀⢀⡐⢁⣀⠀⠀⠀⠀⢉⠐⠉⠩⠉⠁⠒⠈⠉⣳⠭⡂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠈⠀⠁⠩⠍⡉⣁⡂⡠⠀⠀⢀⡀⠀⠀⠂⠁⠀⠀⠀⣈⠻⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣌⡤⣨⣌⠀⣀⡀⠀⠀⠁⡀⠀⠒⠉⠁⢾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠐⢄⠐⢂⠁⠠⠊⠀⠐⠀⠀⠌⠊⠁⠈⠉⠉⠄⢄⠀⡄⠑⢦⠐⠐⠠⡎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡕⠊⢛⠦⡴⠋⠛⣘⣹⣭⡁⢨⠂⠀⠖⡲⢀⠖⠔⠤⣤⠄⠠⠊⠚⢀⢗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠍⠊⠀⠈⠳⣅⠀⢉⠚⠉⠩⣒⣀⠁⠨⠊⠐⢂⡈⠀⠊⠈⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⢐⠛⠂⠈⠓⠐⠀⠀⠁⠀⠀⠐⠂⡀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠐⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠒⣻⣿⣶⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⣣⠀⠀⠀⠀⡋⠀⠀⠀⠐⠛⠛⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠆⠀⠀⠄⣄⣲⢠⢟⡀⢣⣄⠐⠁⠀⠀⠈⢒⠀⠁⠈⠻⣍⠙⢻⠻⠛⢁⠃⡆⣶⢡⡉⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠤⣀⡤⠀⠀⣈⣈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠉⠀⠃⠃⣂⣁⡀⠉⢠⣄⣡⡤⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠚⠛⠋⠉⠉⠁⠀⠨⠭⠭⠍⠉⠉⠉⠐⠒⠒⠂⠈⠉⠉⡁⠀⢠⢁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⢆⢀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⡐⢁⠈⡐⡠⢂⠈⡐⠀⠠⠁⢀⠀⠊⡡⢋⡠⢊⠄⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⡀⠀⠀⠀⠠⠐⠀⠈⠀⡠⢊⠔⡠⠊⠐⠡⢂⠔⡠⠁⠌⠐⠐⢀⣁⡤⠖⡈⠐⡁⢀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠒⠦⠦⠤⣤⣬⣄⠁⣈⡀⢈⣤⢤⣤⠄⡠⠶⠂⠜⠛⠉⠊⠔⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣾⣿⠁⠀⠀⠀⢰⣷⡄⠀⠀⠐⠦⢄⠴⠖⠀⠀⣀⣶⣷⡆⡀⠀⢀⡀⠘⠿⠀⠀⠠⠚⠁⠈⠁⡆
⠀⠀⠘⠸⠟⠀⠀⠀⡀⣈⢛⡁⡀⠀⠀⠀⢸⠀⠀⠀⠀⠨⠻⡿⠣⠀⠀⠸⠋⠠⣴⡤⠀⠀⠈⠉⢩⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢀⣴⠙⢁⣦⠀⠀⣿⣿⡇⠀⠀⠀⠀⣠⡞⢶⡆⠀⠀⣀⣀⢀⢀⡀⠀⠀⠀⣤⡅⠂⠀⢠⣤⣤
⠀⠘⡩⡄⠘⣏⠃⠀⣻⣿⣻⣿⡇⠀⠈⣿⠀⢀⡟⠀⠰⣏⣿⣸⣮⡇⠀⠈⠈⣿⡃⠌⠀⠀⣾⣿⠟⠻⠆
⠀⠀⠈⠑⠀⠁⠀⠀⠛⠀⠛⠛⠃⠀⠀⠛⠉⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠃
⠀⠀⠀⡐⢂⡀⠀⠀⠀⢀⡗⢠⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡴⢰⣀⠀⠀⠀⡤⠀⢄⡀⠀⠀⢀
⠀⠀⢀⡁⣉⠀⠀⠀⠀⣾⡉⠛⠀⠀⢀⣴⣧⣀⠡⠀⠀⢹⢐⡍⠔⠂⠀⠘⠌⣮⢚⠃⠀⢠⣾⡂⢐⣿⠂
⠀⠀⠈⠻⠟⠀⠀⠀⠰⠃⠃⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠻⠛⠛⠉
⠀⠀⡀⠀⠀⣀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡀
⠀⠘⠿⣀⣘⠿⠃⠀⢰⣿⠟⠈⠀⠀⠀⣤⣿⣿⡇⠀⠀⣔⡀⠰⣄⠀⠀⣶⠒⢲⡄⠀⠀⠀⣿⢰⡆⣤
⠀⠀⠀⠧⠟⠀⠀⠀⠸⠏⠀⠁⠃⠀⠀⠸⠦⠤⠃⠀⠀⠻⠛⠛⠿⠃⠀⠻⠗⠚⠛⠿⠂⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣄⣤⣠
⠀⠀⢠⢖⡢⡄⠀⠀⠀⢸⡆⢹⠀⠀⠈⠃⠸⠀⠛⠀⠀⠒⣿⠷⠄⠀⠀⠀⢠⡾⠅⠀⠀⠀⠈⣿⢁⣀
⠀⠀⠣⣘⣃⠎⠀⠀⠀⢼⡧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⣶⠂⠀⠀⠀⠙⠀⠀⠀⠀⢰⢻⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡴⢣⡐⢦⠀⠀⣴⣧⢀⣿⡆⠀⠀⢰⣶⡇⠀⠀⠀⡔⢉⣥⠛⡄⠀⠀⣠⣼⣶⡄⠀⢀⣾⡏⢹⣷⡄
⠀⠀⢣⡉⢃⠞⠀⠀⢣⣨⣶⣀⠇⠀⠀⠲⠌⠶⠃⠀⠀⢧⡘⢛⣠⠃⠀⠀⠟⠁⡼⠃⠀⠈⢿⣿⣺⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢟⣭⣭⡉⢙⣛⣉⠉⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣟⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠛⠛⣿⣿⣷⣿⣾⡄⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡀⣀⢼⣿⣿⣭⣴⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄⢈⣿⣿⣿⣿⣷⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠍⠡⣨⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣇⢸⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣶⣾⣶⣾⡀⠙⣿⣼⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⢪⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠦⢹⣏⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠏⠀⠉⠠⠈
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⢀⡠
⠀⠀⠀⠤⢄⠃⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⣉⣗⣶⣷⣯⣠⡤
⠀⢀⣀⣠⠙⢶⠺⠃⡰⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡄⠀⠐⠒⠐⡆⣜⣈⠍⠉⣿⠟⠟⠁⠀⢤⡆⠀⣀⡄
⠀⠀⠒⠚⠐⠎⢐⠺⣆⣪⠤⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⢠⠀⠀⢰⠀⠀⠀⠀⢸⣆⣤⠀⠋⠀⠀⡀⡿⢠⢠⠖⣳⠺⡿⢟⣡⣄
⠀⠐⠛⠉⠉⡠⢦⠄⠘⠉⢒⡀⠀⠁⠀⢐⠢⠆⡜⠈⣥⠁⣖⡀⠀⠀⠀⠈⠉⠳⢋⢏⡀⡧⠤⢤⠈⣷⠘⢲⣾⣡⠦⡿⡲⠀⠁
⠀⠀⠀⠀⠀⠀⠨⡆⡴⠠⡿⠀⠀⠀⠀⠠⠒⠒⢀⢄⠀⠛⠁⠀⠀⠂⠀⠶⠉⠀⢠⠏⠀⠁⣉⣉⣈⠻⢠⠓⢣⣥⠖⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠈⡟⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠊⠉⠀⠀⠜⢸⠂⠈⠀⠩⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢐⣇⠀⠀⠀⠙⡆
⠀⠀⠀⠰⢄⣲⠂⣥⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠋⠀⠀⠀⠀⠃
⠀⠀⠐⢷⣾⣿⠿⠿⡖⠊⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⡀
⣠⡳⠀⣤⣧⠿⠀⠀⠁⠀⠃⣰⠄⠂⠒⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠲
⡿⡿⣿⣿⣶⣴⣿⠿⢳⠾⢧⣑⡐⢊⠹⠘⠹⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⠑⢲⣦
⣙⡗⣁⣠⠙⡦⢼⣷⡧⠠⢮⣌⠀⢨⡖⢂⡠⡟⡅⡌⡠⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠂⠀⠀⠀⠀⠙
⠉⣄⠮⢊⣹⣥⡞⠟⠠⣾⠞⢲⡾⢻⠀⣈⠿⠁⣹⠋⢡⢀⠠⠹⡇⢀⠀⠀⠀⢀⠐⠁⡀
⠳⠶⣆⡁⠉⠙⣷⢲⣜⢧⠴⣟⣇⣞⠿⠦⠒⠈⠌⠂⠹⡂⠀⠀⠀⠊⠀⠀⣛⠎⢀⣉⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠀⠠⢀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠆⢀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⢀⠐⠈⠂⠄⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⠡⠄⠤⠬⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠐
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⢀⠠⠤⠀⠀⠀⠄⢀⠀⠀⠀⡠⠀⠀⠀⠀⠈⢦
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠑⢀⠐⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠁⡀⠀⠀⡈⠁⠀⠄⠁⠀⠀⠀⢀⠀⠀⠀⠑⠀⠠⡄⠀⠀⠀⠀⠀⢀⠶⡆⠀⠀⠀⠀⠀⠆
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠀⠈⠀⢀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣃⠀⠀⠀⠀⠀⢀⠇⢀⡆⠉⠁⠀⠀⠀⠉⢐⡂⠀⠀⠐⢄⠀⠀⠀⠠⠂⠀⢇⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠘⠢⢤⠤⠤⠤⠊⠀⠀⠁⠄⠠⡠⢀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⡙⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠂⠀⠀⠀⠀⠀⠀⡀
⠀⣔⠉⢱⡄⠀⠀⢀⡞⠉⢳⠀⠠⠎⠃⠀⠀⠤⠀⠁⠈⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⡄⠁⠀⠀⠈⠁
⠀⢈⠉⠁⠈⠂⠀⠀⠈⠉⣉⠀⣈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠂⠀⠖⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⢸⠟⠀⠀⠀⠀⠈
⠀⠈⠀⡀⠀⠂⠀⠀⢀⠐⠁⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠁⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡂⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⠀⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠰⠶⠀⢱⠈⠉⠦⠀⡀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⡀⠀⠀⠴⠄⠀⠠⠄
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠃⠚⠂⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠰⠆⠀⠀⠀⠀⠀⡀⢀⣠⡄⠠⠀⠉⢀⠀⢈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠉⠁⡈⠒⠉⠒⢂⠐⠉⠈⠀⠁⡀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣣⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠰⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠠⠺⡷⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠠⠐⡄⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠓⠀⠈⠀⠀⠐⠁⡇⠈⠁⠐⠑⠈⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⢭⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠐⠘⠘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢰⠀⠄⠀⠀⠖⠀⠂⠱⠤⢤⠔⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠉⠊⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠐
⠀⠀⡼⠛⣷⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⣷⣷⣟⣾⢻⣿⣷⡇⢸⣿⣿⣿⣾⣷⣿⡿⣿
⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢫⣙⣋⣍⣉⡉⠋⣌⣋⡍⠉⣙⣩⡩⠈⠛
⠀⠀⠙⡋⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠻⠿⠓⠈⠛⠛⠷⠀⠿⠛⠗

⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⡉⠀⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠸⡿⠋⠀⠀⢠⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠄⠀⠀⣿⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠃⠐⡀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⢀⠀⠀⠀⠀⣤⡿⠈⢈⡤⢃
⠀⠀⠀⠀⠀⠈⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠆⠈⢠⠸⠀⠀⡘⣴⣟
⠀⠀⠀⠀⠀⠀⠈⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠞⢹⡇
⠈⠁⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⡎
⠀⠀⠀⠀⠀⠀⠀⢠⣽⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠄⢠⡾⠀⠀⠀⢾⡁⠀⠀⣿⡄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡄⠀⠀⡀⢘⢀⡀
⠠⡄⠁⠛⠃⠀⠀⠻⠎⠆⠀⡿⠷⠿⠙⠁⠌⠡⠀⠐⠂⠀⠀⠀⠐⠲⠶⠀⢰⡄⠀⠂⠀⠀⠀⠀⢨⠿⠿⠦⠤⠣⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠠⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠒⠈⠁⠉⠉⠉⠉⡋⠀⠂⠠⢀⡀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠑⠄⠀⠠⠀⠀⠐⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⢀⠔⠁⠑⠤⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡰⠁⠀⠀⠀⢀⡤⢀⠀⠀⠀⠀⣰⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀⠀⠡⡀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡠⠟⢅⠀⢃⠀⠀⠀⠓⠀⠙⠂
⠀⠢⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠔⠉⠉⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⡀
⠀⠀⠀⠀⠂⠄⡀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠌⣑⠂⠬⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⠄⣀⠉⠑⠂⠒⠀⠐⠒⠂⠂⠀⢂⢀⠁⠀⠄⡓⣄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠒⠒⠠⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠁⠀⠀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠈⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠿⠒⣴⠞⣴⠛⣱⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⣿⡏⣀⠁⡐⢃⡴⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠔⠚⠘⣿⠿⢆⣿⣴⢳⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣴⣿⣦⠀⣘⠙⠿⣟⠻⠈⣾⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣤⣤⢾⣴⣫⣍⡻⡎⣶⡕⢸⡿⢼⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠋⣾⣏⠙⢓⣣⣿⣷⢈⣽⠀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢿⣦⣭⣭⣿⣧⣤⡰⣾⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣮⣽⣿⡟⠁⠘⣷⠘⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠛⣋⡾⣮⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠉⠙⣿⣿⣿⣿⠟⠳⣬⢳⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠸⣿⣿⡇⠀⡄⠘⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣇⠀⣠⣿⣿⣿⣶⣿⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢻⡟⠛⠉⣿⠏⠉⠙⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢻⣦⡀⣿⡆⠀⠀⡿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢿⣾⣷⡀⠐⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢰⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠰⠶⠶⣶⡾⠿⠿⣿⡶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠴⠂⠐⠤⡉
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢇⣄⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⣿⣷⣶⣿⢡⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⠸⡟⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠉⠉⢱⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠾⠀⠄⠾⠸⠲

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣳⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠙⠟⡇⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠐⡂⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡷⣄⣿⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⣌⡃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⠀⠀⠀⢀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⠀⢸⡿⠛⠁
⠀⠀⠀⠀⠀⠀⡀⣠⢠⠄⡀⢀⠄⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡉⢀⠈⠁⣀
⠀⠀⠀⠀⠀⠀⠇⠧⠸⠜⠧⠸⠄⠿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠄⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠓⠀⠛⠛⠀⠒⠛⠚⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠶⡄⣴⠄⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠒⠖⣡⣾⢟⠕⢮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠶⠦⠴⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠾⢿⠗⢡⢀⢠⠘⢮⠻⠷⠀⠀⠀⠀⠀⢀⡴⠚⢻⣿⡑⠤⡀⢀⢃⣽⡞⠛⢶⡄⠀⠀⠀⠀⠀⣿⣿⣿⣏⠈⠙⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡠⠄⠚⠀⠀⡀⠀⠀⠀⠀⢸⡅⠀⠋⢀⡗⠀⠈⠛⢺⡗⠛⠂⠀⣿⠀⠀⠀⠀⠀⣿⣿⠏⢹⣿⡶⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠁⠶⢀⠀⣀⢈⠀⢀⣤⢄⠲⠈⠀⠀⠀⠀⠈⠻⠶⠶⠟⠁⠀⠀⠀⠀⠛⠶⠶⠞⠁⠀⠀⠀⠀⠀⣿⣿⣦⣤⣿⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠠⠄⠁⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢆⠘⠁⠋
⠀⠀⠀⢰⢆⠀⡀⠀⠀⢹⠓⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠐⡾⢉⢦⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠂
⠸⣶⢡⠆⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡐⠛⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⡠⠆⣧⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠤⠀⠀⠀⠀⠒⠁⠀⢀⠀⠀⠀⢠⠀⠀⣠
⢀⡂⠀⣴⢿⠇⡿⢀⡐⣆⣾⢧⡳⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⣖⣦⣶⣤⢴⣞⠟⣀⣤⡌⢷
⠞⣤⣶⣮⢣⣌⢣⣯⢿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠻⢫⡷⣶⡷⢿⢾⣨
⠛⠛⠛⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⣴⠀⠝⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⡤⠀⠴⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⣠⠀⠀⠈⠃⣴⠃⣴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡿⣿⠏⠀⠀⠀⣄
⠀⠀⠀⠀⠈⣷⠀⠀⣤⠃⣰⡇⠀⠀⢠⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⣿⣄⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣀⠀⣠⠆⠃
⠀⠀⠀⠀⠀⠸⣆⠀⢁⣠⢿⠁⠀⠀⠀⠀⠀⠀⠙⠙⠗⠀⠀⠠⠆⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻
⠀⠀⠀⠀⡄⣰⠹⣶⡈⣧⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠂
⠀⠀⠀⠀⢱⡏⠐⠋⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠈⠁⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣆⣠⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠄⠀⠀⠀⢀⠤⢴⠲⠶⠶⠛⠉⠃⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⡿⢦⠄⠤⠼⠛⢻⠀⠇⣠⠀⠀⠀⡈⣠⢆⠀⠈⠇⠀⠤⠆⢠⡖⠀⠀⠀⢸⡇⣠⠛⠢⠀⠐⠁⢀
⠀⠀⢠⠃⣰⡇⠀⠀⠀⠀⠀⠀⣇⣼⠇⠀⢀⣴⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢰⠃⠀⠀⠀⠀⠀⣸
⠀⠀⢸⣾⡁⠧⠶⠄⠀⠀⠀⠀⠸⠿⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠤⠿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠷⠶⢖⣒⣛⣫⣭⠭⠭⠶⠶⠖⠚⠛⢻⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢧⣤⠤⠤⠶⢖⣒⣛⣩⣭⠭⠴⢶⠆⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠰⣞⠛⠉⠉⠉⠀⠀⣀⣀⣴⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⠶⢒⣚⣋⣭⣭⠅⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡻⢦⡴⢞⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢟⣠⣄⡻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠋⠁⠈⠙⠲⣍⡳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡶⠦⣭⣛⡲⠦⢤⣀⡈⠙⢦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣴⠋⠀⠀⠀⠈⠉⠛⠲⠮⣭⣛⡲⠷⠌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠃⠀⢔⣽⣷⠄⠀⠀⣾⣿⣦⠈⠉⠛⢶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⠀⠀⠈⠋⠋⢠⡠⣤⠈⠉⠁⠒⠀⠀⡾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢙⣒⠶⠤⣤⣀⡜⠗⡂⠀⠀⠀⠀⢀⡼⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢯⡙⠓⠲⠦⢵⣜⣓⠲⠦⣤⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⢦⡀⠀⠀⠀⣉⡽⢓⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⠲⠶⢛⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣫⠴⢦⣝⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⣋⣁⣠⣤⠬⠷⠆⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣬⡭⠭⠶⠖⠒⠚⠛⠉⠉⠳⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⠀⠀⠀⣀⣀⣀⣤⣤⠤⠴⠶⢚⣃⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣛⣛⣯⣭⠭⠷⠶⠒⠒⠛⠋⠉⠉⠉⠹⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡈⠙⠲⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣶⣶⣶⣒⣴⣧⡀⠀⠙⣿⣷⡄⢹⡎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣮⣿⣿⣿⢷⣄⠀⠈⣿⣧⡀⠁⠂⠹⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣾⠁⣿⣷⣶⣦⣾⣿⠍⠀⠠⠄⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣤⡛⠿⣿⣿⡟⠛⠀⠀⠀⢀⣴⠀⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⢀⠀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⢻⣿⠛⠻⣤⠉⠛⢠⠈⠁⠈⠉⠁⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣿⣿⣿⣷⣾⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⡿⠋⢉⣿⡿⣷⣀⣀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⣾⡿⠃⠸⠛⠛⠋⢻⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠁⠉⠛⠛⠛⠉⠉⠀⡀⠀⠀⠀⠘⢿⠀⠀⠘⣦⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡤⠄⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⡔⠃⠀⠀⠈⠉⣉⣱⡦⠶⠆⠀⢀⣴⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢀⡀⢁⡠⢔⣰⣿⣿⣏⣴⣶⣶⡾⠟⠛⠁⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⣬⣶⣼⣿⣿⣿⣿⠟⠛⠁⠀⠰⣤⣄⠂⠀⠀⠀⠄⠀⠀⠀⠀⢀⣷⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⢠⣰⠂⠀⠀⠀⢂⣤⣿⣿⣿⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣾⣯⣧⣿⣿⢻⠛⣿⠁⡉

⠀⢠⠀⣼⢹⠏⠈⠻⠋⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧⠈⠉⡀⣹⢻⣠⡞⠀⠂⢺⣶⠟⠉⣻⢄⢒⡶⢀⡐⡄
⠀⠀⠀⡏⠸⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣘⢧⠀⢭⠆⠈⡩⠃⠀⠀⠀⣙⡄⠀⠀⢬⠃⠙⠸⠇⠼⣦⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⡄⢀⣄⠄⠛⠋⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⡂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⣧⣤⠈⠁⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⢀⠻⢷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⠀⠀⠈⣿⣷⣼
⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⢜⣦⡀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⣠⣿
⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡈⠀⢠⠀⠗⠀⠲⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠂⠀⠀⠀⠀⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠠⣄⠁⣸⣿⠀⠗⠛⢉⠄⣠⠉⠀⢠⣐⠇⠀⠀⢀⣠⡉⠀⠀⠁⢠⢠⣴⣧
⡃⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡔⠀⠀⢀⣓⣾⣿⣆⣠⠀⢁⢰⠃⠀⠀⠀⣻⢄⠀⠊⠉⠉⠉⠂⠀⣴⣿⠘⢿⣟
⣷⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣰⠊⡸⠀⠀⣴⣿⠿⣩⣿⣿⣿⣇⠘⣂⣼⠇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠓⠀⢸⠀⠻⠏
⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠠⠾⠃⠀⠃⠀⠨⠟⠉⢠⣿⣿⣿⣿⣿⠓⠙⡿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣄⣤
⣿⣿⠀⡀⢠⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣿⠘⢿⡇⠀⢡⠠⠀⠀⡅⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⠀⣿⣝
⣿⠏⣠⡇⢸⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠁⠀⠀⠀⢘⠙⠀⠐⡄⠂⠀⡇⠀⠀⠀⠀⠀⢠⣏⣦⡠⣼⡀⢏⣽
⣇⢸⣿⣧⣿⣿⢸⣿⣿⡇⠀⠤⢦⢾⢳⣤⠀⠃⠀⠀⠀⠀⠀⢀⡆⠀⠞⡚⠆⠀⡄⠀⠀⣬⠀⠀⠀⠀⠀⢾⡿⠫⠶⣼⠀⠘⠛
⣿⢾⡿⣽⣿⣿⢸⣿⣿⣷⣄⠀⢀⡀⠣⠋⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⡇⠀⠃⠀⢠⣿⡆⠀⠀⠀⡀⢘⡇⢠⢂⠼⠀⣈⠛
⡿⢟⣼⣿⣿⣿⢸⣿⣿⣿⣟⣣⡬⢥⡀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⢆⠘⡆⢀⣷⠀⠀⢸⡷⠀⠀⢀⣡⡪⠤⠣⠶⠶⠘⢻⠆
⣴⣿⡟⡿⣿⣿⡝⣷⣹⣿⣿⣿⣿⠄⠀⠀⢠⠈⢀⡀⠀⠀⠀⡀⠀⠀⠸⣰⡀⢸⣟⠰⠄⠟⠤⠈⠀⢀⠁⣁⠂⠻⡫⣀⢈⠈⠃
⣟⠟⣄⠻⣿⣿⡂⣿⡆⠻⣋⣭⣭⡄⠀⠀⠀⢂⢸⡇⠸⣃⡀⠃⠰⣆⡀⠨⠅⣈⣫⡎⢍⣛⣦⡿⡄⠩⣠⣤⠮⠂⡀⠤⠀⠉⠒
⠉⠀⠀⣿⣿⡟⣦⢸⣧⠀⢻⣿⣿⣿⡀⠀⣰⡘⣿⣧⡄⠙⠛⢷⣦⣄⠻⣦⠀⠻⣿⢯⣼⡼⣿⡏⠳⠔⠀⠀⠘⠀⢹⠄⠀⠢⡀
⠁⠀⣾⣿⣿⣱⣿⠀⢿⡇⠀⠃⠿⣏⠓⠀⢹⣮⣻⣾⠧⠀⠀⣀⣱⠟⠟⣻⢰⣤⡩⣿⣿⣯⣭⣿⠃⣴⣆⠀⠀⠀⠈⠀⠀⠀⠘
⠀⢠⣿⡟⣻⣿⣿⠂⠈⠛⢁⢀⡀⠀⠀⠀⠀⠙⣿⡐⠲⢆⣄⠀⠉⠀⢷⡇⢨⣅⡣⣈⡌⠻⠧⣾⡻⢚⣡⣶⣶⡆
⡀⠈⣿⡇⣿⡿⣿⣄⠀⢠⣼⣿⢿⡀⠀⠀⠀⠀⠹⣭⢦⣀⠻⣧⢀⣦⡈⠁⣷⣾⣿⣿⡿⠉⠸⠋⣱⣿⣿⠟⢩⡍
⣷⢸⡏⠓⠿⢻⣿⣾⣷⣸⡿⠙⠋⠀⠂⠀⠀⣀⣼⡿⣆⣬⢢⠿⣿⡻⠃⠀⢮⣽⣿⣟⠀⠀⠀⠀⠈⣟⠁⠀⡈⠁⠀⠀⠀⠈
⣽⣮⣿⣦⠀⣼⣁⣽⣿⣫⣟⣧⣀⠀⠀⢠⣤⡿⣠⣤⣸⢽⡿⣿⣿⣦⣀⡀⢸⢦⡀⢁⠀⣀⠀⢀⣀⡀

⠀⠀⠀⠀⢀⣀⠀⡖⣦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠙⢬⠦⠟⠧⢼⡴⠃⠀⠀⠀⠀⠀⠀⠀⣠⡤⢴⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⢤⣤⠀⠀⠀⠀⠀⠀⠀⠠⣄⣹⣶⣮⣀⣄
⠀⠀⠀⢏⡹⡎⠰⢀⣀⡀⣳⢏⠵⠀⠀⠀⠀⢠⣈⡟⠀⠀⢹⡂⠀⠀⠀⠀⠀⠀⢤⡼⠁⠈⢨⣆⠀⠀⠀⠀⠀⢦⣘⣴⣿⣿⣿⢤⡀
⠀⠀⠀⢠⠖⡧⣄⠘⠶⡧⢗⠲⡄⠀⠀⠀⣴⠋⠁⢆⠀⣠⠟⠀⠀⠀⠀⠀⢰⡞⠁⠀⠀⣤⡞⠀⠀⠀⠀⠐⠒⣾⡽⢦⣿⡿⠳⡄
⠀⠀⠀⠈⠉⢠⢋⡏⢹⢳⠈⠉⠀⠀⠀⠀⠹⣦⣘⣤⠾⠋⠁⠀⠀⠀⠀⠀⠰⠣⢴⡤⠲⠁⠁⠀⠀⠀⠀⠀⠰⠊⢻⠛⣧⠘⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣦⠲⢤⡀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣩⣍⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⣉⠉⢉⡳⢤⠀⠀⠀⠀⢀⡴⠋⢉⢩⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠹⡄⠈⠷⠀⠀⠀⠀⠀⣼⢁⣶⠀⠛⠛⠀⡀⢹⡀⠀⠀⠀⡟⠀⣾⠟⠁⠈⠁⠊⣧⠀⠀⢠⡏⠚⢋⠿⠁⠩⠠⠌⣇
⠀⠀⠀⠀⠀⠀⢰⡷⣤⢷⠀⠀⠀⠀⠀⢿⠈⢋⠤⢄⠀⠀⠗⢸⠇⠀⠀⠘⡇⠀⣀⠀⢀⣠⣤⠀⡿⠀⠀⠸⡇⠁⠈⣛⠀⠻⢶⡆⡿
⠀⠀⠀⠀⠀⠀⠀⡇⡃⠃⠀⠀⠀⠀⠀⠈⢧⣘⠢⠞⠰⢂⣠⠏⠀⠀⠀⠀⠙⢦⡈⠀⠛⠛⣁⡼⠁⠀⠀⠀⠹⣜⡳⠎⢠⡶⣈⡼⠁
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⠀⠀⠀⠀⠀⢠⣄⠀⢻⠃⡴⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢘⡄⠀⠀⠀⣠⣀⣸⣿⣿⣿⣷⣚⣣⡀⠀⠀⠀⠀⠻⢿⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⡄
⠀⠀⠀⠀⢠⠋⢀⡤⡄⠀⢸⠀⠀⠀⠀⠈⣈⣽⣿⣿⣽⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⣠⠔⢊⣠⡤⢰⠃
⠀⠀⠀⠀⠘⣄⠈⠛⢁⡠⠃⠀⠀⠀⠀⠀⠁⣤⠛⣻⢺⣅⠙⠛⠀⠀⠀⠀⠀⠠⠴⠚⢦⣀⣽⠇⠀⠀⠀⠀⠀⢇⠀⠈⣊⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⠓⠳⢔⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣀⠇⠀⠀⠀⠀⠀⠀⠀⣀⡆⡀⢀⢀⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠳⢤⠎⣗⠀⠀⠀⠀⠀⠲⠶⣼⣿⣿⣶⠚⠉⠀⠀⠀⠀⠐⠉⠄⣴⡌⣹⠿⢇⠀⠀⠀⠀⠀⠺⢿⣝⢗⣦⠙⡇
⠀⠀⠀⠀⠀⢀⣀⡴⠊⢰⠇⠀⠀⠀⠀⠺⢹⣶⡿⠿⣻⡿⠖⠀⠀⠀⠀⠀⢰⣦⣠⢞⢤⣡⣢⠀⠀⠀⠀⠀⠀⠮⢿⣅⣨⢿⡀⠟
⠀⠀⠀⠀⠈⣏⣁⣸⠷⠋⠀⠀⠀⠀⠀⠰⣟⠿⣧⡴⠯⠖⠂⠀⠀⠀⠀⠀⠀⢀⣱⠽⢽⡀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣿⣧⡞
⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠘⠚⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣠⡄⠂⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣰⣿⢀⡆⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣼⠋⠀⠘⠄⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⠀⠀⠀⡼⠛⠿⠟⠋⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡄⠀⠀⣀⣠⣤⣾⣿⣯⣷⣞⡿⣿⠀⠀⠐⣡⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⣴⣏⠀⣴⣾⣷⣾⡿⣿⠛⠻⣿⡿⣁⣿⣆⠀⣎⠀⠀⠀⠀⠘⠀⠀⣼⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣿⢿⣼⣿⣿⣿⣿⠋⠋⠒⠶⠿⠟⠛⠋⢹⠀⠹⡄⠐⣄⢳⢁⣼⠏⠙⢿⣜⡇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⠟⣾⣿⣿⣿⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠸⡆⢸⡎⢈⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣴⠟⠻⣿⣉⣿⣿⣿⣿⣷⣿⡿⢻⡟⢻⣿⣭⠿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠉⠀⡀⢀⡀⣿
⠀⠀⠀⢸⣿⠀⠀⢹⣿⣿⡿⠿⠟⡛⣋⣀⠟⢁⣸⣿⣿⠀⠘⣦⢻⡿⠓⠿⢳⡶⠆⠀⠀⡆⠀⠘⢆⡀⢠⠁⠀⠀⣿
⠀⠀⠀⠸⣿⣦⣶⣿⣿⣿⣷⣤⣤⡿⠯⡉⣀⣾⠈⠻⣿⣔⣛⡁⠈⠐⢦⣆⣈⣧⠀⠀⢤⣷⠐⠂⢨⣿⣿⠂⠆⢰⣿
⠀⠀⠀⠀⣸⣹⣹⣿⠿⠥⠾⠷⠦⠶⣾⣿⣌⡙⠛⠚⠚⠛⠛⠓⠒⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠂⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠤⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠤⠤⢤⡼⣅⡀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠹⡱⡀⠀⠀⢠⣤⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⠤⠄⠀⠀⠀⡴⠁⠱⡀⠀⡾⠈⠃⠀⠀⠀⢱⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⡠⠀⣀⠀⢞⠀⠀⠀⠱⣀⠇⠀⠈⠀⠀⠀⠀⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠢⢶⣷⣠⡄⠁⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠬⢿⠀⣀⠈⡀⠉⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢉⡖⠀⠀⠀⠀⠄⠈⡆⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠣⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠦⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠐⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠉⣰⠔⠀⠀⠀⠀⠑⡄⠀⠀⠀⠲⠏⠀⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⢎⣠⡤⠤⢠⣤⡄⢀⠐⠀⢀⠀⠀⢀⡜⠹⣇⣉⣀⣁⣀⣀⣈⣂⣤⠴⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⢮⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠠⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡀⠀⠀⡀⠀⠄⠀⢠⠀⠀⠀⠈⢳⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡤⠀⠀⠀⠀⠀⠀⣢⠄⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠉⠲⠀⠐⠚⠀⠀⠈⠀⣄⠀⠀⠀⠙⢄⠀⣿⣀⣀⡀⣤⠤⠖⣋⣵⢊⢿⣶⠀⠀⢀⠄⡑⢉⣄⣰⣈⠱
⣘⠀⠐⣈⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡤⠀⠈⠢⢀⠀⠀⠀⠳⡇⠀⠀⠀⢨⠄⢚⣿⣿⡷⣔⣊⢉⠒⠀⠚⡋⢟⣿⣿⡥⠄
⠙⠐⠂⠪⠛⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠁⠀⠀⠈⠉⠂⠂⠈⠀⠀⠀⠀⠀⠓⠥⣨⡀⠤⠋⠀⠈⠄⠀⠀⠙⢬⣌⣁⣩⠞
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀
⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠐⢨
⠀⢸⠒⠀⠀⠀⠑⢀⠆⠀⠀⠀⠀⠀⠰⠌⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰
⠀⢸⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠸
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⠀⠀⢸
⠀⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⠠⠀⠀⠀⠸
⠀⢠⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢐
⠀⠘⠀⠀⢁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⢰
⠀⠰⠀⠀⠈⠤⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢐⠀⠀⠀⠀⠉⠎⠁⠀⠐⠀⠄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢘
⠀⠸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡦⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠐⠀⢸
⠀⢸⠂⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠋⠓⠀⢸
⠀⢘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢸
⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰
⠀⢘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐
⠀⠀⠁⠉⠀⠈⠀⠈⠀⠉⠀⠁⠈⠉⠁⠉⠁⠉⠈⠀⠀⠉⠁⠈⠁⠀⠈⠀⠉⠀⠀⠀⠉⠁⠁⠈⠈⠁⠁⠁⠈⠉⠁⠈⠉⠈
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠛⠛⠛⠓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⣮⡟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣿⢉⣤⣤⡀⠀⠀⠀⠀⠀⠀⢘⣻⡆⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠙⠋⣴⢮⣷⠀⠀⠀⠀⠀⢠⣾⣏⣤⣀⣀⣀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣉⠉⢹⡇⠀⠀⠹⡆
⠀⢀⡶⠛⢷⠀⠀⢸⣇⢰⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠉⠉⠻⣎⠛⣷⣠⣄⣿⠀⠀⢰⠟⠳⣆
⠀⣼⠁⠀⢸⡇⠀⣾⠻⣮⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣤⡈⠀⠈⢹⡆⠀⣿⠀⠀⢹⡆
⠀⡟⠀⠀⢸⡇⠀⢹⡄⠀⠈⢻⡏⠛⠛⢦⡄⠀⠀⠀⠈⠛⠶⠟⣦⠀⠀⠀⣠⡞⠁⠀⠀⣸⠁⠀⣿⠀⠀⠘⡇
⢸⡇⠀⢀⡸⠇⠀⠘⣇⠀⠀⠸⣇⠀⠀⠀⠙⠛⣻⠄⠀⠀⠀⠀⢸⡇⠀⢀⡿⠀⠀⠀⢀⡟⠀⠀⠟⣀⠀⠀⣿
⢸⡇⢠⡟⠙⢷⡀⠀⢹⣆⠀⠀⠙⠳⣆⠀⠀⣀⡿⠀⠀⠀⠀⠀⢸⠀⢠⡟⠁⠀⠀⢀⣾⠁⠀⣰⠟⠙⣧⠀⣿
⣼⠀⠈⣧⠀⠀⠻⣆⠀⠹⣦⠀⠀⠀⠹⣦⣸⠋⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⢠⡾⠁⢀⡾⠋⠀⢠⡏⠀⢸
⣿⠀⠀⠘⣦⠀⠀⠈⠳⣄⡈⠳⣄⡀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣀⡴⠋⠀⠀⢠⡟⠀⠀⢸
⢿⡀⠀⠀⠈⢷⣄⠀⠀⠈⠻⣦⡈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⣠⡾⠋⠀⠀⢀⣴⠏⠀⠀⠀⣸
⠈⠻⣦⡀⠀⠀⠙⣷⠀⠀⠀⠈⠻⣆⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⢀⡾⠋⠀⠀⠀⢰⡟⠁⠀⠀⣠⡾⠋
⠀⠀⠈⠻⣆⠀⠀⠘⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠙⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠻⠀⠀⣀⣀⣀⣀⣠⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⣀⣀⣀⣀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⢸⡛⠛⠋⠉⠉⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠉⠉⠛⠛⢻
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣀⣤⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣄⣀⣀⣀⣀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⣄⠀⠀⢃⠀⠀⠀⠈⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠲⣶⣾⣿⣿⣿⣿⣧⠀⠀⠀⠉⠀⠀⠐⠲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣴⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠐⠋⠀⢸⡖⡄⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣴⣦⡀⠀⠀⠀⠘⣿⣷⣦⡄
⠴⠖⠀⠀⠀⠀⠘⠛⢠⠀⢀⣠⣤⣄⡀⣱⣿⣯⣶⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣶⣔⡄⠀⠈⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣁⡉⠉⠙⠛⠛⠻⢿⣿⠿⠿⠿⠷⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣿⡛⠂⠀⠀⠀⠀⠀⢀⣶⡀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣶⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠏⠉⠉⠉⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠛⢿⣿⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠉⠻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠽⠞⠋⠀⠀⠀⠀⠀⠂

⡀⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⠦⢀⣴⠘⣁⣬⠥⠀⣤⠀⠀⢀⣁⠀⠀⠀⢠⠀⠀⠄⠀⠀⢸⣿
⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⡀⠀⠓⢄⣺⣿⡈⠁⠠⢊⡰⠀⠀⠐⣾⠁⠀⠠⠶⠦⠄⠀⢀⣴⢸⣿⡿
⣇⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢠⠄⡎⠀⢀⣴⣶⢿⣿⣿⣿⠀⢾⢃⡄⠀⠠⢿⠓⠀⠀⠀⠀⠀⢠⠘⢻⠈⣿⠶
⣿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣴⠃⠸⠁⠀⣾⠟⢁⣿⣿⣿⣿⡷⠴⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠉⣁
⣿⣶⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⡏⠻⣿⠀⠘⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⣟⣫
⣿⠟⢰⡄⣿⣹⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠀⠅⠀⠏⠂⠀⡆⠢⠀⡇⠀⠀⠀⠀⠀⣾⣧⢀⣸⠀⣟⣿
⣏⢸⣿⣷⣿⡇⣿⣿⡇⠀⠠⢤⢾⢦⡄⠚⠀⠀⠀⠀⠀⢀⡂⠠⢓⠓⠀⠄⠀⠀⣥⠀⠀⠀⠀⢸⣿⢻⠤⣼⠀⠙⠋
⣿⣿⣿⣿⣿⣇⣿⣿⣿⣦⡀⢀⡈⠏⠃⠀⠄⠠⠀⠀⠀⠈⠀⠀⠁⠸⠀⠀⠀⠠⣿⡀⠀⠀⢠⢀⡷⢠⠀⠾⠀⣈⠃
⠟⣫⣾⣿⣿⣇⣿⢿⣿⣟⣥⣖⢦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠇⡱⠀⣿⠀⠀⣸⠧⠀⢀⢠⡴⠗⣚⣒⡟⠈⢹
⣾⣿⠋⣿⣿⣷⢹⡮⢿⣿⡿⡿⠀⠀⠀⠀⠀⡆⢀⣀⠀⡄⠀⠀⠐⡷⠀⣯⡔⣆⣋⠢⡄⠌⣆⢠⢄⡐⠱⠤⠬⣞
⣿⠓⠢⣽⣿⣿⢸⣿⠈⣵⣶⣿⡆⠀⠀⠈⣤⡇⠈⣥⣤⣁⠛⢢⣄⠑⢠⣧⣧⢱⢶⣷⢿⡀⠐⠚⠋⡀⢦⠀⠀⡀
⠖⠀⣴⣿⣿⣹⡏⢿⣆⠘⣿⣿⣿⡀⠰⣗⢿⣟⣯⠀⠈⠙⣻⣦⣿⡇⡈⠻⣷⣾⣾⢿⣧⠈⣀⠀⠀⠀⠸⠋⠀⠀⢄
⠀⢀⣿⡿⣷⣿⡇⠘⢷⠆⠀⠉⠓⠀⠀⠛⣷⢟⣭⡅⠀⠓⠛⢹⣰⠃⡟⢶⠻⡻⣿⣟⣳⡾⡿⢀⣀⡀⠀⠀⠀⠀⠈
⠀⠸⣿⢠⣿⣿⣇⠀⠀⣸⣶⣦⠀⠀⠀⠀⠙⣕⣢⡘⢿⡆⢂⡀⠛⢰⣩⣷⣿⣷⠖⢹⠓⣵⣿⣿⠟⡓⠀⠀⠀⠀⠐
⣧⢰⡟⢿⡿⣾⣯⣷⣸⣿⠻⠟⠃⠄⠀⠀⣠⣿⣯⣝⢄⣷⣾⣿⠀⢨⣻⣿⣿⠁⠀⠀⠀⢻⡛⠉⢀⠃⠀⠀⠀⠐⠄
⣻⣬⣷⣄⢠⣟⣹⣿⣟⣿⣦⣀⠀⠀⣠⣼⢏⣩⣸⣿⡾⣿⣿⣀⣀⣀⣧⡉⢉⠀⣀⠀⣀⣈⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢉⡆⠀⠀⣎⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡷⠀⠀⢾⢷⢦
⠀⠀⠀⠀⠀⠀⠀⠸⠓⢒⣁⡀⠀⠀⡠⠔⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢛⣁⡀⠀⠀⢠⣤⣶⣇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⢇⡀⠉⢦⠀⠘⢶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⣿⣿⣧⠀⠈⠻⣿⡟
⠀⠀⠀⠀⢸⠹⡀⠈⢆⠀⢹⡰⠃⠀⠀⢀⡷⠁⢰⢉⡆⠀⠀⠀⠀⠀⣷⠀⠈⢦⡀⢸⣿⠃⠀⠀⠀⡹⠁⠀⣾⠇
⠀⠀⠀⠀⠘⡄⢡⠤⡀⠑⠢⠤⠤⠤⠒⠉⣠⠤⡌⢸⠀⠀⠀⠀⠀⠀⣿⣦⣤⡀⠉⠂⠤⠤⠤⠔⠊⢀⣠⣤⣿
⠀⠀⠀⠀⠀⢣⠀⠱⡌⠓⢄⠀⠀⠀⡴⠊⢡⠊⢀⠎⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⠀⠀⠀⢠⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠢⡄⠀⢸⡀⠀⢀⠁⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠀⠀⠀⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⣉⡱⠀⢏⣉⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡶⠀⢴⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⠤⠒⠂⠈⠉⠉⠉⠑⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠉⠉⠉⠉⠒⠦⣀
⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠒⢄⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡯⠉⢳⡀⣱⣄⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⡌⠀⠀⠀⠀⠀⠀⠀⢰⠉⠹⣶⡄⠀⢸⡏⠀⠸⣿⣿⣿⣧⣶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢹⣾⣿⣇⠀⢹⣿⠛⣿⣿⣿⣿⣷⣤
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⣿⣿⣿⣦⣘⣿⡄⢿⣿⢋⣶⣿⠿⣷⣶⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣷⣿⢩⢻⡿⣿⣿⡧⠌⣟⣿⡟⢁⣤⠾⢻⣿⣦⣤
⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣿⡏⣧⢸⠏⣷⡌⢹⢇⣶⡿⢸⡼⣿⣋⣴⣿⣿⠿⣿⣧⣄
⠈⡄⠀⠀⠀⠀⠀⠀⣠⢿⣿⡟⢸⡇⠇⠟⡦⡿⣸⣦⠸⢹⢳⡿⢰⣿⢹⣿⠋⢠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠘⡄⠀⠀⠀⠀⣼⢃⣵⣾⠘⣼⣷⣶⣮⠁⣵⠛⡾⡇⡞⢸⢃⣿⠃⣸⡏⢹⣿⣿⠿⢛⣹⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠙⡄⠀⢀⡼⠡⣪⢟⢕⠟⢉⠛⢛⣣⣴⡇⢸⡇⡇⠁⣿⢸⡟⣰⡿⠁⣸⡟⢳⣤⣿⣿⠿⠛⢿⣷⣄⠀⠀⠀⢀⠄
⠀⠀⠀⠘⢄⢞⡵⠉⠑⢁⡵⠾⠛⠛⢋⡽⢹⣧⢸⡇⠃⠀⡇⣿⢱⡿⠁⣴⣿⠇⣼⣿⣟⠁⢀⣤⣶⣿⣿⡿⠂⢀⠎
⠀⠀⠀⣠⣿⣫⣀⣠⣞⣥⣶⣶⣶⠿⠋⠀⣾⣿⡄⣷⠀⣸⢃⣿⣿⠄⣼⣟⡞⢸⣿⠇⢘⣿⣿⣿⣿⠟⠋⠀⡰⠃
⠀⠀⣼⣿⣿⣿⣿⣫⠥⠤⣀⡉⠛⣿⡧⠀⣿⡇⢣⣹⠀⣿⣿⣿⠏⣼⠏⠊⣰⣿⢣⠀⣨⣿⣿⠟⠁⠀⠀⠔⠁
⢀⡼⣼⣿⣿⣿⣿⣿⡿⠟⢾⣿⡆⢸⡇⠀⣿⣇⣆⣿⣰⢏⣾⠏⣼⣳⠃⣰⣿⣿⡆⢰⣿⣿⠏⠀⠀⠀⠊
⣾⣿⣿⣻⣿⣿⣿⠿⢶⣶⣤⢸⡇⡼⡰⢠⣿⣿⣿⣿⢃⡾⠃⣼⣿⠃⡰⣿⣿⡟⢀⣿⡟⡏⠀⢀⠔⠁
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡼⠑⠋⠁⠀⠀⠹⣿⠟⠁⣼⣿⠃⡔⣼⣿⡟⢀⣾⣿⢱⠁⡠⠃
⠀⠙⠿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠘⢄⠀⠀⠀⠀⠀⣿⠀⣸⣿⠃⣘⣾⣿⡟⠁⣼⣿⣏⡯⠊
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠘⣶⡟⢁⣴⣿⠫⠋⢀⣾⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠀⠉⠉⠛⠓⠒⠛⢛⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠔⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣱⣔⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣯⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣿⣯⣽⣯⣭⣭⣭

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡶⣒⠶⠶⠶⠶⣶⣶⣶⣶⢒⡒⢲⡖⡒⠒⣖⣶⠀⠀⠀⣇⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⡉⠷⣖⣯⣭⣭⣿⣿⣿⡛⠉⠎⢢⢘⣦⠟⢉⠀⠀⠀⣿⣇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⡄⠉⢷⡒⣟⣻⣯⣾⡷⢚⣦⣾⣿⡿⠶⢌⠀⠀⠀⣿⣿⣿⡇⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢾⣷⣧⣄⢱⡴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠜⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣓⢋⠽⣿⣿⣶⣿⠻⠹⣿⣿⢫⢰⣿⣿⠿⡿⢻⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢏⠛⢮⡽⡿⣿⣿⣧⠰⣼⠋⠆⣾⠽⣶⣥⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢿⣿⣾⢣⡟⣿⣿⣷⣿⣾⣰⣧⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣟⣷⢿⣧⡿⣼⠟⣿⣿⣾⣿⣿⣿⠟⠻⡏⠉⣿⠅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣨⡏⢿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣇⠒⢞⠒⠶⠤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠁⣰⠆⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣇⣽⣟⣿⡿⢿⣿⣿⣷⣿⣿⠿⠿⠿⠿⢿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⡀⠀⠫⠙⠁⠰⠏⣿⣿⡗⠀⣄⡿⠦⢀⣤⠠⣽⣶⡖⣿⡟⠙⠘⢷⡦⠀⢠⢇⣦⡄⠀⠀⢴⣄
⠻⣷⡀⢠⠀⣠⣐⣹⠇⠈⣿⣸⣯⠇⠀⠀⢀⠀⠨⣽⣱⠋⠀⠀⠀⡮⠑⣄⠈⠸⢧⡅⢴⣦⠤⢿⡄⠀⢀⡀
⡀⠹⣷⠐⠂⣉⣬⣱⠄⠒⢈⡡⣞⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠁⠀⠀⠐⡌⠳⠂⠈⠇⢼⣧⡳⣄⣿⣦⠀⠙⢦
⢿⣦⡘⠆⠁⠀⠛⠁⠀⠆⠘⠁⠀⠀⠀⠀⠀⣠⢠⡤⣱⠍⠀⠀⠀⠀⠈⣽⠀⠁⠀⠀⠀⠀⠀⠀⢸⣟⣗⠀⠄
⠀⠉⢻⣦⣂⠀⠒⠀⠀⡀⣠⣤⠀⣨⣅⡰⠤⠉⠓⠋⠁⠀⠀⠄⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡝⠇⠦
⠀⠀⡶⠈⠻⠝⣯⡈⢁⡇⠓⠀⢠⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡆⢦
⠀⠀⢀⣀⠠⠔⠶⣶⢈⣫⠷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠧⠀⠀⠀⠀⠀⠀⣀⣁⠹⠿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠘⠓⢸⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢫⠀⠀⠀⠀⠀⠀⢚⣲⣿⣶⡆⣿⣿
⠀⠈⠃⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢡⡐⠀⠀⠀⠀⠈⣿⣿⠟⢴⣿⡟
⠀⠈⠀⠀⠱⠄⣀⡀⢹⣶⣀⢀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡀⠀⠐⠀⠉⢀⠀⠀⠀⠀⠈⠙⠁⣼⣿⣷
⠀⢘⢆⠀⢀⡀⠀⠙⠪⡗⣿⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠲⠀⠀⠀⢶⣼⣿⣿
⠀⢸⠜⠓⠀⠛⠚⠶⠀⠀⠁⠀⠀⠀⣀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢻⣿⣽
⠀⠀⣦⣤⣶⡶⠖⠛⣉⠍⡺⠲⠆⠀⠀⠀⢠⣤⡄⣤⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠚⠁⠀⢱⠀⠀⢀⣼⡏⢿
⡇⠀⠛⠉⠀⠀⣠⠞⠁⣸⠁⠀⠀⠀⣀⣶⣤⣝⠃⠀⠀⠀⠀⣀⣀⣠⣇⠀⠀⠀⠄⠀⠀⠀⣼⠀⢶⣿⣿⠱⣿
⣥⡄⠂⡀⠀⠚⠁⢠⣦⡏⠀⠀⠀⠀⠀⠐⢧⣍⡀⠀⠀⠴⠚⡉⠉⠋⠉⠛⠢⠀⠀⠀⣠⣴⣿⠀⢸⣿⣏⡾⡛
⣷⣾⣷⣏⠀⠀⣾⢸⢷⠀⣀⠀⠀⠀⠀⢐⣿⣟⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡿⠻⣿⠀⠘⣡⣾⣦⣆
⣿⣿⣿⣿⣃⠀⠻⢺⢸⣰⣿⠀⠀⠀⠀⠉⠹⡇⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠩⠢⠀⠀⣹⠀⠠⡟⣿⠙⠉
⣿⣿⣿⡿⣿⣧⡀⣾⢸⣿⡯⡄⠀⠀⠀⠀⡀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠉
⣿⡻⣿⣿⣾⡏⠓⠜⢸⣽⠂⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣦⣠⣾⣂⣀⣦⣧
⣿⡇⠹⣿⣿⣷⠀⠀⢈⠟⡀⢠⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⡇⠉⣿⠿⠳⣤
⢹⠁⠀⠈⢻⢿⡄⠀⠀⢹⢱⠸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹⡅⠀⣿⣷⣤⢛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⢀⡀⣤⠀⠀⠀⠀⢸⣤⣄⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠆⠀⠀⠀⠀⢰⡏⢿⣀⣶⣶⣄⣼⣻⡇⠀⠀⠀⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠀⠀⠀⣹⡿⠿⢿⣗⣛⡺⢿⡀⠀⠀⠀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡄⠀⣠⠞⠁⠀⠋⠉⠉⠉⠙⠛⢮⡳⣄⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣮⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⠟⠿⢖⣠⣶⡄⣆⣰⣠⣸⣆⣸⠿⢛⣛⠻⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⠟⢻⡟⡴⠛⠻⢶⣮⣝⠳⣯⣿⣿⡾⣋⡵⠟⠋⠙⠻⣦⡻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣀⣿⠋⠁⢀⡿⠈⠀⠀⠀⠀⠀⠙⢿⡌⣿⠁⠚⠉⠀⠀⠀⠀⠀⠈⢻⣿⡝⠻⡇
⠀⠀⠀⠀⠀⠠⢴⡏⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠈⣿⢻⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⣿⡇⠀⢿⡀
⠀⠀⠀⠀⠀⢤⡿⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⡀⠀⡇⠀⠀⠀⠀⣿⣧⡇⠀⢸⡦
⠀⠀⠀⢀⣠⣾⠁⠀⠀⠀⣿⡀⠀⢻⡀⢰⠀⠀⠀⠀⢸⣿⠀⠀⣇⢴⣧⠀⠀⠀⠀⣿⣿⡇⠀⠈⢧⡀
⠀⠀⠀⠉⠘⠃⠀⠀⠀⢠⣿⣿⠀⠸⡇⢸⡀⠀⠀⠀⠈⣿⠀⠀⣿⢸⡿⡀⢠⡇⢸⣿⣿⡇⠀⠀⠸⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⡿⡀⠀⢿⡈⡇⠀⡇⠀⡄⣿⢸⠀⣿⢸⡇⡇⣼⣽⢆⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣷⣃⢱⡈⢷⢹⠀⢻⠀⣧⢹⣾⡆⣿⢸⢡⣇⣏⡏⣸⣿⠃⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠸⣿⡄⢳⡈⣯⣇⠘⡇⢸⢸⣿⣇⡟⣾⣼⡿⣼⣽⣿⡏⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠹⣿⣄⣷⡈⢿⣆⢻⡘⣿⣿⣿⣿⣿⣿⢷⣿⣿⠏⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠈⢿⣿⣿⣄⣿⣮⣷⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣬⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠈⠙⠛⠛⠓⠛⠉⠉⠀⠀⠀⠀⠀⠀⢻⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢠⡿⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⣠⣴⢶⣤⣤⣤⣄⣀⠀⠀⠀⡾⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⢫⣾⡿⢣⣶⡙⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⣱⣿⣿⢡⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⣼⣿⣿⣿⡜⢿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣭⣙⡛⠟⠼⢿⡿⠛⠿⣿⣶⢠⣾⣿⠟⠛⣿⡟⡛⠿⢛⣻⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢰⣿⣶⡆⢹⣷⣦⡙⠘⣫⣶⣿⡇⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⡘⢿⣿⣿⠰⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣶⣭⣥⢠⣬⣥⣾⣿⣿⣿⣿⣿⣟⡻⠟⣛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣥⣤⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠏⠹⣿⣿⣿⠟⡹⣿⣿⣿⠟⡙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⢠⣶⣿⣿⣶⣬⣴⣾⣿⣶⣤⣴⣾⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠸⠿⠟⣛⣛⣛⣉⣉⢸⣿⠟⢿⣿⣿⡿⠻⣿⣿⣿⠟⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣩⣥⣶⣦⠹⣿⣿⣿⣿⣿⣿⢈⣵⣾⣦⣭⣭⣶⣷⣬⣭⣵⣾⣦⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣌⢿⣿⣿⣿⢘⣋⣵⣦⣙⣛⣫⣴⣬⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⡙⢿⣿⢸⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠘⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣟⠳⣦⣀⠀⠀⠀⡠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡀⠀⠀⢶⠀⠀⠀⠀⠐⣼⠀⠀⠀⡠⠔⠙⢛⣿⣄⠀⠀⢈⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠁⠀⢰⠉⢃⠀⠰⠎⣸⠏⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⠄⢹⣿⣷⣖⢾⢺⣿⣛⡆⠀⠀⠀⠀⡀⠀⢀⠈⡆⠈⢤⠄⡀⣇⡃⠾⠹⠂
⠀⠀⠀⠀⠀⠁⣠⣤⣿⣿⣯⣮⣿⠿⢟⡿⢠⡿⡄⠀⢸⣧⠀⣌⣀⠱⣀⣘⡀⣻⢻⣇⠀⣠⡤⠖
⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⠜⠟⠉⠠⠏⠁⣼⠁⠣⠀⠎⢿⠀⠙⠛⣧⣤⣭⣴⢏⡼⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠁⠀⢹⣤⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢍⣀⣀⠆
⠀⠀⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⡄⠐⠄⠀⠀⠀⠀⠙⠇⢠⠏⠁⠀⢠
⠀⠀⠀⠠⠀⠀⠈⠢⠄⠀⢀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣡⠀⠴⠴⣏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⢡⠃⠀⠀⠈⠁⠀⠳⠒⠲⠀⢵⠞⠉⠂⠚⠃⠀⠀⢐⠀⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠼⠀⢰⡀⠠⠗⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⡀⠠⠄⠀⠀⠀⠉⠘⠈⠱⠤⡴⠶⠶⠚⠿⢹⠗⠄⠀⠀⠀⠀⠀⠐⡄⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠻⠴⣄⠀⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⣰⡀⠘⡄⣸⡄⠀⠘⠛⠏⢃⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⣀⣀⢠⡀⠀⠄⠀⠀⠀⢠⡀⢀⠀⠇
⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠈⠑⠀⠂⠀⠀⠀⠀⢙⠘⠻
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠺⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⢈⡏⠈⢻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⠇⣌⣴⡶⠀⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠘⢿⣿⠀⠀⣸⡿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢯⡙⢄⡹⣿⠀⠐⠇⢀⠞⠋⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⢿⣦⢻⡀⡁⠀⠀⣀⣴⡏⠀⣠⣿⢋⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⢹⢸⡇⣿⢸⡇⣟⣧⠀⣾⢻⠁⣿⠟⠙⢻⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢨⣰⠃⡿⢸⡇⠿⢸⣇⣯⠟⣰⡌⢸⢰⣿⠀⣴⠏⢉⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣚⡽⣡⡾⠃⣼⣿⣶⣦⣨⢎⡼⢋⡇⣿⢸⡇⢸⣿⠰⠏⠈⣽⣿⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣋⡾⠋⣁⣈⡙⠻⠾⢫⠌⠈⣇⢾⢰⡟⢸⡇⣼⡿⢰⣦⡾⠛⢻⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣩⡶⠟⠋⠉⠙⠷⣦⡄⠘⡆⢻⠀⡿⢰⢸⣀⡿⢁⣾⡏⡀⣠⡿⢻⣿⣗⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣯⣿⡿⠗⠛⠛⠿⣿⣦⡀⠀⢻⡄⣧⢸⡄⢁⠈⢸⡿⢡⣾⡿⠁⣿⡏⠀⣻⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣿⡿⣵⠾⠿⣷⣦⣄⠀⠹⣷⡄⠸⡇⢸⠈⣧⡘⠆⣾⢣⣿⡟⠁⣼⣿⡇⡞⠉⢼⣿⠁⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⣥⣦⣄⠀⠉⠛⢷⡄⢈⡿⠀⡇⢸⡆⡎⣧⢸⠏⣾⡟⠀⣼⣿⡿⠁⣷⡤⢿⡇⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⣿⣧⠉⠛⠻⠿⣶⣤⠈⠇⣼⠃⣸⠇⣸⠀⣷⢨⠞⣼⣿⠁⣼⣿⡿⠁⣸⣿⣷⣿⡃⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣾⡇⢹⣿⠳⢒⠲⢤⣄⠸⠀⣼⣣⢴⡟⢠⡟⢠⡏⠀⣰⣿⠃⣸⣿⣿⠃⣸⣿⡇⢸⠿⣇⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⣿⣛⣠⣿⣿⣿⣿⣷⣇⣿⣼⣸⡷⠿⠏⢰⡋⠶⠟⣠⣼⡟⠁⣰⣿⣿⠏⢀⣿⣿⡇⣾⢸⡏⣷⣀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⢀⠻⣶⠿⠟⠋⢠⣾⢟⣿⠇⢀⣾⣿⣿⠁⣿⣾⣷⡿⣧⢹⣦⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⣉⣴⡿⠃⢀⣼⣿⣿⡇⢰⣿⣿⠃⣿⠸⡆⢯⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⢰⣾⣿⠟⠀⢀⣾⣿⣿⠟⠀⣼⣿⡇⢰⣿⠀⢿⢸⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠁⠀⢠⣿⣿⡿⠋⠀⣴⣿⣿⠇⣾⣿⠀⢸⡆⣿⣿⡏⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢠⣿⣿⠟⠁⢀⣾⣿⣿⡏⢰⣿⣿⠀⢸⣧⢹⣿⡇⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⣆⠀⠀⠀⣿⣿⠋⠀⣴⣿⣿⣿⡿⠀⣼⣿⣿⠀⠀⣿⠀⣿⡷⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⢿⣶⣾⡟⠁⣠⣾⣿⠟⠋⠀⢀⣴⣿⣿⣿⠀⠀⣿⡀⣿⡗⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣄⠉⠉⠀⠠⠛⠉⠀⣀⣤⣴⣿⣿⣿⣿⡟⠀⢸⣿⡇⣿⡷⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠉⠉⠛⢦⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾⣿⠀⣿⣧⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠉⠙⠛⠛⠋⠉⠀⠀⢀⣼⣿⡏⢠⣿⡇⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⣾⣿⡧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠟⠁⢀⣼⠿⣿⡇⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⢻⣷⢦⣤⣤⣤⣤⣴⣾⣿⡿⠟⠛⠁⠀⣠⡾⠋⠀⣿⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⢦⣽⠿⠛⠋⠉⠉⠉⠀⣀⣀⣀⡾⠋⠀⢀⣴⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠉⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠂⠀⣰⢷⠀⢹⣯⡹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣢⣶⠜⠋⠁⠀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡏⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠉⠀⠒⢦⣴⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⣠⣆⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣇⣧⣴⣿⣷⣽⡟⢦⡐⠓⠀⠚⠘⡛
⣂⣀⠤⠆⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀⢀⣤⣶⡶⠖⠈⠉⠉⠀⠸⠛⠛⠛⠛⢛⣿⣿⣿⣿⡿⣿⣧⣸⣿⠷⢿⣿⣷⣾⡷⢄⠰⣬⡼⣽
⣿⣿⣿⣿⣶⣿⣿⣿⣾⣷⣥⣭⣤⣸⣿⣿⣿⣶⣂⣤⣄⣀⣀⢀⣠⣤⣴⣴⣿⣿⣿⣿⣞⣏⡀⣹⣿⣿⣷⣿⣿⣿⣿⣿⣷⣽⣛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⡶⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣴⠋⠀⠀⣷⠀⠈⠹⣄⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠳⣤⣼⠁⠀⠀⠀⣿⠀⠀⠀⠘⣦⡤⠞⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⢸⠋⠛⠒⠶⠶⣿⠴⠶⠒⠋⠹⡆⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠺⡟⠒⠒⠒⠒⠚⣿⠒⠒⠒⠒⠒⢻⠓⠒⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⣸⣷⠖⠛⠉⠉⣍⠉⠉⠛⠲⣾⣅⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣏⠁⠸⣆⠀⠀⠀⣿⠀⠀⠀⣴⠃⠈⣻⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⣷⣄⡀⣿⢀⣠⣾⣥⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠢⠀⢀⠀⢀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠒⠒⠒⠠⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢠⠴⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣱⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⠤⠤⠤⠤⠤⠤⠔⠀⠒⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠁⢒⣠⠖⡊⠀⠘⠈⠁⠀⢾⣶⠀⠀⠀⢀⡞⠂⠀⠀⡴⠀⠀⠚⠀⠀⠀⠐⠃⢀⡉⠀⠘⠑⣶⠀⠀⠀⠀⠛⠠⢀⠀⣤⠄
⠖⠒⠛⠉⠀⠘⠛⢀⠀⠀⠀⠰⣖⡨⠚⠁⠀⠘⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠐⠹
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⣀⠀⠀⡦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠾⠁⠀⢀⡀⠀⠀⠀⠐⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡄⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠐⠀⠸⣉⡷⠀⠀⠀⠀⢀⠀⢀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠆⠀⠀⠀⠀⡨⠛⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢋⠉⠁⠀⠀⠛⠀⠤⠄⠀⠀⠦⠄⠀⠃⠀⠀⠀⠀⠀⢈⠠⢃⠁⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠀⠀⠴⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠉⠁⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⡇⣸⢻⡇⡞⢰⡆⡇⣼⠁⠀⠀⠀⠀⠉⠐⠛⠀⢦⠄⠀⠀⠀⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠁⠉⠈⠈⠁⠈⢸⠧⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠒⠰⠆
⠀⠀⢀⣀⡀⠀⠘⠿⠂⠀⠀⠀⠰⠀⠀⠀⠉⠀⠀⠀⠐⠀⠐⠀⠐⠀⠁⠀⠀⠒⠒⠒⠛⠋⢀⡀⠀⠀⠀⠀⠠⣄⡀
⠀⠸⡿⠛⠻⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⢰⣞⣷⣆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠊⠂⠀⠉⠉⠙⠒⠄
⠀⢸⡇⢠⣦⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠱⠁⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠄⠐
⠀⠈⠻⢮⡉⠀⠀⢀⠀⠃⠶⠀⡀⠚⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⢀⠈⠁⠀⠀⠀⡈⠓⠀⠰⠀⡀⠀⣰⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠈⢿⣿⣀⣠⣄⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⡀⠀⠀⠀⠰⣂⠁⠠⢡⡁⠠⢬⣿⣿⣟⡀⢸⡣⡀⠀⠠⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⢈⠉⢉⠉⠀⠀⣤⣀
⠀⠛⠀⠀⠛⠀⠀⠀⠏⠙⠀⠸⠋⠃⠘⢻⣿⠿⠿⠃⠈⢿⠅⠀⠀⠈⠀⠀⠀⠉⠛⠛⠋⠉⠀⠈⠉⠀⠈⠉⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⣠⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠛⠷⠀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠠⡿⣱⡿⠃⠀⠈⢷⡝⠷⠀⠀⠀⠀⠀⣼⣿⣿⡇⠈⢻⣿⣆⠀⠀⠀⠀⠀⢸⠀⣘⠀⣁⠀⡃⢈
⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⢤⣤⣤⠀⡐⠀⠀⠀⠀⠀⢸⡟⠙⢿⠁⠀⣸⣿⣿⠀⠀⠀⠀⠀⠠⠠⠤⠠⠤⠠⠤⠠⠄
⠀⠀⠘⠿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠘⠦⣈⣙⣻⠔⠁⠀⠀⠀⠀⠀⠀⢻⣦⣬⢧⡾⢋⣼⠏⠀⠀⠀⠀⠀⢈⠬⠭⠬⠏⢈⡉⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠋


⠀⠀⠀⣄⡞⣉⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠒⢦⡄
⠀⠀⠠⠠⠄⢤⠀⠤⢰⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠙⢆⠂⠁⠔⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⠿⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⠀⣠⣶⠶⠹⡆
⠀⠀⢀⣔⡆⣰⣠⣶⣆⣀⡀⠀⠀⠀⠀⠀⢡⣄⣀⠀⡈⣧⠴⡞⡃⠀⠀⠀⠀⠀⠈⠻⠷⠀⢠⡶⠆⠀⠀⠀⠀⠀⠀⢻⡀⠉⠁⠉⠁⠀⢠⡇
⠀⠀⠀⠙⠻⠿⠿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠉⢿⡜⠛⣻⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣶⣶⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀
⠀⠀⢠⣾⠏⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⢀⣀⡴⠉⠉⠉⠉⢳⣀⡀
⠀⠀⢸⠫⠠⣤⣤⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⢬⣿⣻⣖⢄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣽⣛⣿⣿⣻⣿⣛⣻⠁
⠀⠀⠰⣦⣤⣽⣿⣷⣷⣦⣄⠀⠀⠀⠀⠀⠀⡆⠞⠁⠆⠰⠠⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠹⠿⠋⠉⠏⠉⠻⠟
⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⢿⠀⠀⠀⠀⠀⠀⠐⢿⣀⣃⡜⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠂


⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⡀⢈⣤⠶⣦⣌⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠾⢿⣿⣭⡇
⠀⠀⠀⠁⢾⡁⣾⠍⣹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⣤⣾⣇⡸⡿⢠⡿⠟
⠀⠀⠀⠁⢈⠻⠷⠾⢋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠖⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡟⠀⣶⡾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⡇⠀⠉⢁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⣿⣄⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⣿⠁⢹⣟⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣴⣿⣦⡼⢋⣭⡻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⣯⢀⣿⠁⢸⣿⡇⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣼⡟⠛⣿⠀⠀⠁⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⣼⣆⠀⠀⢀⣼⣿⡟⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠮⠛⠿⣿⣾⣿⣿⣿⣿⡿⠿⠋⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⢰⣿⠆⠀⠁⠀⠺⣷⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠹⣷⡀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠻⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⣸⠇⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠠⠖⠛⠉⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⢴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⢿⣿⡗⠀⠀⠀⠀⢤⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠄⠀⠀⠀⣸⢹⣷⣾⠀⠘⢿⣶⡧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠸⣾⣿⡏⣀⡀⢸⣿⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⠀⢰⣄⣆⣠⣿⣿⣧⠻⠇⠠⣽⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣶⣢⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⡿⠟⠛⠻⣟⣽⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⣿⣿⣯⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠚⠈⠀⠀⠀⠀⣫⣽⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⢫⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠈⠏⠻⠏⠙⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁