Pride dragon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠐⣲⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠺⣿⡿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣄⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⣿⢸⣿⡁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣾⣯⣸⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣁⣠⣴⡶⠛⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣉⠛⠉⠉⠉⠋⠹⣿⣿⣿⣿⠿⠋⠁⠀⠀⣗⣦⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣾⣿⣷⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣴⠂⠀⠀⠀⠀⢦⢀⠀⠀⠀⠀⢲⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣻⣿⣿⡿⠛⠛⠛⢀⣼⣿⣿⣿⣬⡆⠀⠀⠘⠛⠛⠻⣿⣿⣿⣻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⠟⣿⣿⣷⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣟⡳⣄
⠀⠀⠀⠀⠀⢀⡴⣫⡾⣿⣿⣿⣾⣿⡿⣻⣿⣿⡄⠀⠀⠀⠘⣿⣿⣄⠘⢿⡙⣷⠀⠀⠀⠀⠀⣼⣿⣿⡻⣿⣿⣾⣿⣿⡿⣮⣳⣄
⠀⠀⠀⠀⢀⣾⠟⣡⣾⣿⣿⣾⢟⣫⣾⣿⣿⣿⣧⠀⠀⠀⠀⠹⣿⣿⣦⣄⠙⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣮⣛⢿⣾⣿⣿⣦⡙⢿⣆
⠀⠀⠀⣠⢎⣴⣿⣿⣿⣿⣿⣶⣿⣿⡿⣩⣿⣿⣿⣧⡀⠀⠀⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⣠⣿⣿⣿⣧⡹⣿⣿⣷⣾⣿⣿⣿⣿⣷⣌⢦⡀
⠀⠀⡴⣣⣿⡿⠋⣩⣿⣿⣿⣿⡿⢋⣼⡿⣿⣿⣿⣿⣿⣤⣾⣿⠿⣿⡿⣿⣿⡟⣿⣦⣼⣿⣿⣿⣿⡿⣿⣌⠻⣿⣿⣿⣿⣯⡉⠻⣿⣧⡳⡄
⠀⠜⣵⡿⠋⣠⠾⠋⠉⣹⣿⠋⢀⣾⠋⣰⡿⣽⣿⣿⣿⠿⠁⠀⢀⡼⣿⣿⣿⡇⠀⠹⢿⣿⣿⣿⡽⣷⡈⢻⣆⠈⢻⣿⡉⠉⠻⢦⡈⠻⣷⡝⠄
⠀⣼⡟⢁⡜⠁⠀⣀⡴⠛⠁⠀⣼⠟⠀⢿⡇⢿⠁⠙⠟⠀⣰⠹⠋⣳⣿⣿⣿⣇⠀⠀⠘⠟⠁⢹⠇⣿⠃⠘⢿⡄⠀⠙⠳⣄⡀⠀⠙⣄⠙⣿⡄
⢰⡟⠀⣠⣤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⠟⠹⣿⣷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣤⡀⠘⣷
⣿⠁⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⢹
⡿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢻⡄⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸
⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣈⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣳⣿⣤⠔

⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⣀⣀⣙⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣋⣀⣀
⠀⠈⠙⠿⣿⣿⣿⣿⣿⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠋⠙⠛⠛⠉⠙⠿⢻⣿⣿⡟⠿⠋⠉⠛⠛⠋⠙⠛⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣧⣆⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⡟⣿⣋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡦⣾⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣿⣿⡉⣽⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣳⢠⣿⣿⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠿⠶⠷⢿⣿⣿⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠁⠹⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣇⣴⣿⠏⠀⠀⢀⣀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⣸⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠒⠒⣒⣤⣤⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢓⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⡀⠐⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⠴⠿⢿⣷⣆⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⠄⠀⢧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠐⠁⠀⠀⠀⢹⣿⣧⠀⠀⢻⣿⢻⣾⣿⣿⣿⣿
⠀⢾⣮⣷⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠈⠻⢿⣿⣿⣿⣿⣿⣟⣻⣷⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠋⠑⢻⣟⠭⡻⣷⣧⣄⣀⠀⠀⠀⣠⢖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡆⠀⢰⣿⣷⣦⡤⠈⣻⠿⠿⠀⠀⣼⢷⣋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⠀⢻⣿⣟⣿⣷⠀⠀⠀⠉⠁⠀⠀⠀⠻⠛⠀⠀⣸⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢧⢸⡌⢿⣿⣟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡾⠸⣅⠀⠀⢘⡟⠋⠁⠀⠀⠀⠘⣿⣦⣤⣤⣠⡟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣾⣿⣶⡄⠀⠀⠀⠀⣩⡙⠟⠻⠇⡰⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⡋⣉⣊⠴⠀⠀⠀⠐⡏
⠀⠀⠀⠀⣰⣾⣿⣿⣿⠿⣛⣭⣥⣶⣶⣶⣶⣿⣾⣿⣭⣿⣟⣿⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢀⣿⡗⣿⡟⠀⠀⠀⠀⠀⡇
⠀⠀⣤⣾⣿⣿⣿⢏⣵⣿⣿⣿⣿⣽⡿⠛⡛⠉⢉⠛⠛⠿⢿⣿⣿⣶⣭⣟⡿⠷⣶⣶⣿⣿⣿⣿⣶⣤⣤⣴⣿⡟⣸⣿⠟⠀⠀⠀⠀⢸⠇
⠀⢴⣿⣿⣿⢿⣷⣿⡿⠿⠻⠟⠋⠀⠀⠐⠀⠀⠀⠈⠁⠀⢀⠉⠙⠻⠋⢿⡿⣿⣷⣾⣭⣭⣛⣛⣛⣛⣋⣩⣭⣾⣿⡿⠀⠀⠀⠀⢠⠎
⠀⣿⣿⣿⢣⣾⡿⢩⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠻⠛⠿⠿⢻⣿⢿⣽⠟⠿⠛⠀⠀⠀⠀⠀⣄⠊
⠀⣹⣿⡏⣼⣿⠂⣀⣠⣴⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⣿⡿⣸⣿⣟⠿⠟⡋⢼⣿⡏⢱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⣀
⢀⣿⡇⣿⣿⣿⡇⢹⢃⣿⡟⠸⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠙⠛⠙⠓⢻⣶⣦⡀
⠈⣿⣿⣿⣿⣏⠐⠈⢼⣿⠀⠀⢨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢉⠀⠁⠀⠀⠀⠀⠀⠐⠈⠿⣦⡀
⠀⢻⣿⣹⣿⠟⠀⠀⣾⣿⣆⠀⢸⣞⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣏⠀⠀⠀⣀⣤⣤⣶⣤⣤⣤⣄⡘⣧
⠀⠨⣿⣾⡿⣷⠀⠀⠘⣿⣿⣧⡀⠙⠍⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⠀⠀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣼⠆
⠀⠀⢿⣧⣻⣿⡄⠀⠀⠈⠛⠻⠓⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣿⠁⠀⢠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢻⡞⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⣿⠀⠀⠀⡏⠿⠉⠀⠀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⢨⣿⢫⣿⣌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⡇⠀⠀⠀⣨⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⢿⣧⣿⣿⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⠀⠀⠀⠀⠘⢧⣀⢀⣀⣀⣤⠾⣿⣿⠇
⠀⠀⠀⠀⠀⠻⣷⣻⣿⣧⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢠⣿⠏⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠘⠻⢿⡻⣯⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣹⣷⢶⡔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢷⣶⣄⣄⡀⣀⠀⠄⠀⠀⣀⣀⡀⠠⠠⢀⣀⣀⣴⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⢷⡷⣶⣾⣶⣾⡶⣾⣿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣄⢠⣄⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢨⣇⣴⠿⠛⡛⠛⠟⢻⣷⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⣼⣿⠿⡑⠧⠎⠐⠏⠘⣁⣉⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣉⣻⣿⠏⢣⠟⠀⠀⠀⠀⠠⡤⠈⠠⣿⡷
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠲⠾⣿⣿⠠⠝⠁⠀⠀⠀⠀⠀⡙⢦⣴⠙⠀⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣾⣿⣿⡒⣾⠀⠀⠀⠳⣄⡤⣳⠞⠛⢳⠄⢠⣤⡶⠉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣼⡿⡿⠗⢠⣷⡄⠀⠀⠈⠀⠀⠀⠀⠁⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡠⠴⢿⠟⠛⠉⠉⢉⠀⠀⢀⣼⣏⠓⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⡀⠁⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣬⣦⢤⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣾⣇⠈⣡⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣿⢿⣯⣀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡄⠀⢈⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣷⡴⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠊⠉⣻⢿⣿⣡⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⣒⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢠⣿⢿⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣾⣿⢈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣻⣿⣯⣽⣿⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⣀⡶⠀⢠⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠾⣿⣿⠠⠋⠚⣽⢻⠁⢀
⠀⠀⠀⠀⠀⢦⡄⢳⣸⣧⣧⣿⣧⣾⣿⣦⣥⣸⣇⣾⡴⣂⠄⠐⡄⠀⠒⠒⢦⡐⣮⣿⣿⣿⡗⠀⣤⠣⣆⣰⢾⣦⣀
⠀⠀⠀⠀⠳⣬⣿⡿⣟⠩⣿⣛⣿⣿⡯⣭⣻⡟⣻⢿⣿⣏⣰⣇⣿⣰⣆⣹⣾⢿⣿⣽⣧⣽⣿⣿⣯⠷⠞⠛⢻⣿⣿⡷⡀
⠀⠀⠒⠒⢲⣿⣯⠾⣷⠟⠋⠙⠛⠛⠳⠿⣤⣃⡽⢏⠴⠟⣻⠟⠻⠛⢫⡟⣿⣿⢻⣦⣿⣡⣾⠟⠋⠀⠀⠀⠀⢀⠹⠂
⠀⠀⢀⣉⣼⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⣜⡛⢵⣆⣆⣜⠠⣋⣻⣉⡯⡿⠞⠋
⠀⠀⠉⠀⠸⢿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡶⢦⣤⣄⣤⣤⣦⣶⣶⣶⣿⣿⣿⡿⣷⣴⣞⣡⡤
⠀⠀⠀⠀⠀⠚⠛⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠗⠟⣸⡟⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠱⠋⠙⢩⡿⠋⠋⠙⠁⠀⠀⠀⠀⠀⠙⣣⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣴⡾⠿⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⣿⣿⣿⣿⣿⣷⣾⡷⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣿⣾⣷⣾⣷⣶⣶⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣶
⣿⣭⣭⣭⣭⣭⣭⣥⣭⣭⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣷⣶⣶⣾⣿⣷⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠾⣿⣷⣷⣶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⠀⠀⠀⡀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⡇⢀⣾⠃⠠⠆⣠⣶⣿⣯⡿⠿⠀⠀⢀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⢿⣿⣿⣿⣿⣿⣰⠉⣿⣿⣿⣿⢀⣠⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢾⣶⣿⣿⣿⡟⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢻⡆⠈⡀⣿⣿⣿⣿⣿⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⠟⣸⣿⣭⣿⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠷⣤⠯⡄⣸⠟⣿⣿⣿⣿⣿⠶⠷⠿⠋⣿⣿⢿⣿⣿⣿⣾⣯⡽⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠰⢾⡧⠒⠿⠁⠀⠿⠿⠿⠟⠁⠀⠀⠀⠀⠁⣵⠟⣿⣿⣿⢿⠈⢀⣦⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⢢⡔⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠁⡀⠸⣿⣷⡟⠀⢸⣿⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣱⠋⠀⠀⠀⠀⣾⣾⠀⠀⠿⣷⣴⣦⠤⠋⠀⢠⢀⣾⣷⠚⣿⣿⠇⠀⢸⣿⠸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⡼⠁⠀⠀⠀⠀⠀⢻⠁⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠛⢹⡿⢈⣿⡟⠀⠀⣼⣿⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣫⡟⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⣼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣶⠀⠀⢠⣿⡟⠀⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣶⣍⠁⠀⠀⠀⠀⠀⠀⠀⡄⠨⠇⠀⠀⣼⣿⠁⠀⠈⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣷⣷⣦⣤⣄⣠⣤⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⢽⣿⣿⣿⣿⣇
⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⢀⠀⠀⠰⠿⢿⣿⣿⡿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠙⠛⠋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡘⠁⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠒⠤⠀⡀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣟⣉⣉⣀⣥⣾⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⠃⢸⣿⣿⣿⠿⣿
⠀⠹⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠘⣿⣿⣿⡇⢻
⠀⠀⠙⢿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣦⣄⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣄⣀⠀⠀⠀⣿⣿⣿⡇⠸
⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣃⣀⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣶⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣆⠀⢹⣿⡿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⡄⠀⣼⡄⢿⣿⡟
⠀⠀⠀⠀⠀⠈⢸⠏⠙⠓⠛⠻⠚⠻⢹⣿⠛⠛⠛⠋⣿⣹⣷⠿⠀⠀⠘⠻⠇⠀⠘⣿⣿⠉⣿⣿⠛⠻⠿⠿⡿⢯⡉⠉⣉⠹⠥⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⣸⣄⠿⠧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠛⠘⠓⠂
⠘⠀⠂⠀⠀⠰
⠀⢻⡇⠀⠲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠊⠛⣹⢟⣿⣿⣷⣶⠶⠶⠆
⠀⠀⠁⠆⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡄⠀⡏⠙⠛⠛⠓⠶⠂
⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠙⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⡞⠛⠛⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠴⠒⠀⠀⣀⣀⠤⠄⠊⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢠⠄
⠀⠀⡠⠞⠀⢠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⣰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠤⠖⠂
⠀⠀⡇⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠤⠖⠐⠚⠁⠈⠉⠁⠤⠄
⠀⠀⠀⠘⡇⢤⠀⡀⠀⠀⠀⠀⡀⢀⣤⣤⠴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠁⠈⠂⠐⠢⠐⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⢛⡛⢋⠁⠀⠀⢉⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠁⠐⢚⣈⣡⣤⣤⣤⣤⣤⣤⣌⡀⠂⠠⠙⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣒⣿⡿⠛⠛⣻⣿⣿⡿⣫⣉⣉⣱⣾⣦⠀⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠭⣴⡾⢛⡹⣞⣻⣏⣩⣭⣿⣹⣿⢻⣿⣙⣛⡄⣨⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣥⢉⣔⢻⣌⣿⣭⣿⣷⣟⣾⣮⣧⣿⢩⢶⣟⢿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣉⣩⣼⣿⡄⠻⣍⣿⣿⠟⣛⣿⣻⡿⣏⢿⡴⣸⢿⣦⡙⠛⣣⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠏⣴⣿⡿⢿⡿⢶⣛⣿⣿⣟⣾⢻⣟⡛⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣠⣿⣿⡟⠋⣴⣼⣿⢸⡾⣏⡿⣼⣯⣵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⣋⣺⣿⣾⣿⣿⣿⣿⡭⣿⣧⡟⣷⣎⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⣿⣯⣿⡿⢿⡿⣗⡞⣿⢻⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣋⣡⢮⢹⣿⣿⣾⣮⣷⣷⢾⢻⡿⢨⣿⣯⣾⠏⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡶⢼⣟⣩⠲⣞⣯⣷⣿⠟⣭⡁⠙⣛⡄⣔⡿⢻⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣿⣿⣩⣿⣵⣿⣏⣠⣶⣾⣿⣀⡹⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡉⢻⣷⣿⣻⣿⡿⣿⣿⣟⣻⣥⣶⣞⣁⣀⣈⣥⣤⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⣿⡽⣿⣿⣿⣿⣿⣿⢻⣿⣿⣟⠛⠉⠉⠉⣿⠟⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢈⠻⣿⣍⡈⠿⣿⣿⡿⣣⣿⣿⣆⢠⣴⣶⣾⠀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠆⠉⠛⠷⠶⠶⠾⠿⠛⢉⡡⠀⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣈⡈⠀⠂⠈⠸⠀⠒⠚⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠀⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣶⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⡿⠿⢿⣿⣿⣿⡇⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢾⣿⣿⣷⠄⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⢹⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⣋⣡⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣴⠟⣋⡴⠚⠋⠁⠀⢸⣶⣷⣤⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⢀
⠀⠀⠀⢀⡶⠋⣡⠚⠁⠀⠀⠀⠀⠀⢸⣿⣿⣞⣁⣀⠀⠀⠀⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣠⣤⡾
⠀⠀⢀⡞⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠉⠁⠀⠀⠀⠀⢶⣤⣤⣿⠿⠿⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⢠⡟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⣸⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠇
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁
⠀⠸⢿⣦⣄⡀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠛⠁
⠀⠀⠀⠙⠛⠓⠿⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⡩⠿⠧⣂⠲
⠀⠀⠀⠀⠀⠀⢀⢔⡡⠔⠉⠀⠂⠀⢌⠑⣄⠂⠄⢀⠀⠀⡜⠫⣍⢁⠭⠋
⠀⠀⠀⠀⠀⠀⠌⠀⣉⡱⣦⠀⣀⣀⠀⢣⠈⠢⡀⠈⠐⡾⠘⠄⠔⠈
⠀⠀⠀⠀⠀⢸⠀⣸⣿⣿⣿⣏⣀⠀⠉⠦⠐⠒⠈⠀⠀⢳⡒⡉
⠀⠀⠀⠀⠀⡎⠀⣿⣿⣿⣿⣿⣿⣴⣶⣤⣀⣠⡀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄⢉⣀⢠⡀⠀⡦⡀
⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠒⡄⣟⠒⠱⣀⠁⢢⡀
⠀⠀⠀⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⢿⣿⣿⣅⠸⡅⠘⣆⠀⠘⢇⠀⢡
⠀⠀⠀⠀⠀⢹⠸⣿⣿⣿⣿⡿⣿⣿⣯⣀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠙⡀⠘⣆⣀⣼⠶⠿⠋⠓⢢⡀
⠀⠀⠀⠀⠀⠘⡄⢿⣿⣿⣿⡇⣿⣿⣿⣿⣦⠀⢸⣿⣿⡏⢿⣿⣿⣆⠙⠲⠟⠋⠉⣷⣰⣨⣥⣬⡗
⠀⠀⠀⠀⠀⠀⣧⠸⣿⣿⣿⣧⠘⢿⣿⣿⣿⠀⠈⣿⣿⣇⠈⠻⣿⣿⣿⣶⣶⣿⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠻⣿⣿⣿⡄⠀⠙⠛⠋⠀⠀⢻⣿⣿⣶⣦⠈⠙⠻⠿⣿⣿⣿⣿⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠛⢿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣉⠛⠻⢿⣿⣿⣿⠿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠶⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄⢠⣀⣀⡀
⠀⠀⠀⠀⠠⣤⣤⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠙⠻⣿⣿⣾⣷⣠⡤⠄⣀
⠀⠀⠀⠀⠊⠀⠉⠙⠛⠻⠿⢿⣿⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⠿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣾⣽⠛⡿⢹⢶⡀⠀⠀⠀⠀⣀⣠⡤⣴⣾⣿⢷⡈⠙⢦⣉⠓⢬⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣯⣶⢳⠼⠞⠞⢶⡒⢶⣿⣵⠶⠋⠙⢻⡿⠶⡝⢦⠀⠙⢦⣃⡹⡍⣷⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢤⣿⣵⣟⠟⢁⢠⡶⠀⠶⠙⣿⣏⣀⠲⠀⠀⡜⠀⢤⢄⠗⠱⣄⡀⠳⣄⠟⣿⢯⠱⢦⡀
⠀⠀⠀⠀⠀⠀⠰⡀⣀⣦⢾⣳⠇⡿⠊⣀⠀⣪⣴⣿⡜⠀⠻⣿⡷⢶⣅⡾⣃⠉⠀⠘⡰⠀⢈⣾⡻⣭⣍⢉⣯⢧⣈⠛⢢⡀
⠀⠀⠀⠀⠀⠀⡌⣼⣿⣿⢸⡝⣢⡇⣸⣿⣽⣽⠟⣉⣷⣄⣰⢯⠸⣄⣿⣿⡻⡍⠛⠦⣣⣡⣿⡿⢧⡹⢿⣿⠸⣷⣣⠽⠥⠘⢆
⠀⠀⠀⠀⠀⠀⢰⡿⣻⢓⣠⣏⠵⣤⣿⣿⣅⠘⣄⣤⠶⣷⡽⣼⣇⣿⠂⢷⠹⣵⠂⠀⢸⡿⣿⡉⠻⣟⣿⡿⠁⠋⠳⢣⠒⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⣿⠀⣧⣚⡿⣿⢻⢹⢁⡾⣻⣶⣿⣿⣷⠿⣆⣦⣿⣿⣆⣼⠀⠹⣍⠀⠀⡆⣽⡇⠀⠀⠀⠀⠀⠀⠀⠈⢣⠎⠀⠀⠙
⠀⠀⠀⠀⠀⠠⣏⡹⣝⣿⣹⠏⢀⣾⣼⠟⣹⠠⣿⣿⣿⣛⣿⢿⣿⡻⣿⠛⢄⡀⠙⠺⠿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⣶⠃⠀⠘⣿⣿⡟⠁⠀⡮⣞⡙⠀⠘⢬⣽⡧⢽⣿⣿⠄⠹⣷⢿⡖⠤⢍⣲⣶⠴⠖⠁
⠀⡴⣻⢧⢾⣿⡼⣫⠍⡶⠀⢀⠛⢿⡟⠁⠀⢀⣀⣤⣾⣽⣷⣶⣴⣽⡿⣿⣷⡄
⠀⡹⢿⣉⣯⣿⣿⡿⣻⠗⠀⠀⢦⣿⣷⡶⢠⠾⠳⣿⢿⠿⠋⣹⢯⠁⠀⠈⢫⡉⠑⠖⠐⠀⠓
⠀⢳⣿⠚⣿⣿⣩⠭⣗⡴⠀⠀⠘⠻⠛⢁⡻⣀⢀⠀⠘⠀⠈⠸⠃
⠀⢠⡟⣨⡿⠛⡶⠛⠝⠀⠀⠀⠀⣴⠉⠉⠀⠈⠑⠐⠂⠠⠤⠔⠢
⢠⣏⣿⣥⣺⣛⠇⣴⠋⠀⡄⠀⠈⠙⠶⠦
⠸⣍⣝⣿⣥⣴⠳⣿⣿⠾⠁
⠀⠫⡶⠟⠃⠈⠓⠛⠋

⠀⠀⠀⠀⠀⠀⠹⠎⠷⠹⠥⠆⠀⢸⠸⠊⢯⠹⠂⠀⢸⠆⠿⠛⠷⠀⠀⡟⠙⠳⠾⢰⠀⠀⡼⠿⠻⡇⠾⢰⠀⠀⡟⢻⠸⢿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠤⡤⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⣥⣤⣤⠈⠉⡄⠀⠹⣧⠀⠀⣀⣤⣴⡶⠶⠶⠶⠶⠚⠛⠛⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢏⣉⣉⣀⡠⠆⠀⠀⡯⣀⣾⡿⠥⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠈⠀⡘⠨⠀⠀⢸⢇⢻⡿⢍⠓⠲⢄⣀⠀⠀⠉⠉⠑⠶⠾⠆⠀⠀⠊⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⠃⠀⠀⠀⢀⠂⠠⠁⠀⠀⡾⡜⣿⣅⠈⠣⡀⠀⠈⠑⠲⢄⠀⡂⠀⢀⠊⠁⢄⡉⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡄⠈⠀⢀⠆⠀⠅⠀⠀⢀⣻⡾⡅⠸⡀⠀⠹⣆⠀⡴⠤⠭⠍⣓⠀⠈⢄⡈⡀⠗⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡇⠡⢸⢀⣨⡅⡰⠊⡉⠁⠃⢁⠀⣧⠔⠒⠛⠿⠀⠀⠀⠀⠀⠈⠁⠂⠀⠂⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇⠀⠻⠄⠐⢣⡑⠈⠁⠌⠣⠁⠈⠛⡠⠤⠠⠰⠂⠤⢄⡀⠀⠀⠀⠠⡀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠠⡇⠀⠀⠀⢠⠚⠉⢁⢀⡠⡴⠂⠦⣄⡄⠘⠲⠄⡀⠀⠩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠄⠛⢲⡇⠀⠀⠀⢸⠤⠒⠈⠙⢆⡘⡂⠀⠈⢍⠁⠦⠤⣡⢂⠀⠈⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠁⢀⠖⠢⠄⠀⠀⠀⠀⠀⡘⠀⠀⠴⢠⠀⠀⠀⠀⠈⠀⠀⠚⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣇⠀⠀⡠⠁⠀⠀⠀⠀⢀⠾⣐⢀⡠⠎⠀⠔⠁⠀⠀⠀⠀⢤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠄⡈⠀⠀⠃⢀⡄⠀⢨⡖⠒⠠⠀⠄⠈⠥⠿⠀⠀⠀⠐⢣⠩⠈⣁⠀⠀⡂⢂⡄
⠀⠀⠀⠀⠀⣀⣠⠶⠶⠶⠖⠤⣈⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠰⣧⠉⠀⠀⠀⠀⠒⢠⠇
⠀⠀⠀⠀⠀⠈⠑⠓⠛⠛⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢱⠀⢇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢧⢸⢀⣠⠈⠎⢦⡆⢘⡤⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢄⠘⠈⣿⠀⠀⠸⠃⠈⢰⣛⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣈⢀⡀⠀⢀⠀⠀⠀⠀⠘⣻⣯⣽⣯⣿⣷⣦⣀⠀⠀⠀⣠⣶⠾⠿⠿⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡘⣇⣼⡆⣧⡄⡀⠀⠀⢡⣾⣯⣿⢷⣿⠛⠿⣿⣿⣷⣿⣥⣴⣶⣶⣄⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⡰⢀⠉⠈⠉⠙⢧⢇⠀⠠⢼⣿⣾⡿⣿⣿⣶⣤⣀⣠⣔⣫⣥⣤⣤⡌⠻⣷⣄⡙⠻
⠀⠐⠄⠀⠀⠀⠀⠀⠁⢊⡔⢳⡆⠁⠀⠀⠀⠀⢸⣫⠀⠀⢩⣿⣿⢿⣿⣧⣈⣉⣉⢟⣉⣥⣄⣀⡉⢿⣦⣈⠙⠻⠿
⠀⠀⠀⠠⠰⡂⠀⠀⠀⠛⠛⠋⠀⢠⣄⠀⠀⠀⡸⠒⠀⡠⠺⠾⣟⣿⣁⠙⠛⣻⣛⣩⣭⣉⣉⠙⣿⣦⡙⠛⠿⢿⠖
⠀⠀⠀⠂⢁⣁⣀⠤⡀⠀⠀⣀⣴⣶⠝⠀⠀⢸⣍⢀⣚⠻⠿⣶⣬⡙⠻⠿⢿⣋⣉⣉⣉⠛⢿⣧⡈⠙⠻⠿⠻⠂
⠀⠀⠀⠀⠸⢏⢰⡆⣽⣿⠛⠋⣿⠁⠀⢀⣠⣿⠂⣈⡹⠶⠶⣦⡙⠿⠶⠶⠋⢉⣈⣉⠙⢻⣦⡛⠿⣷⣶⡖⠁
⠀⠀⠀⠀⢀⠼⠻⠍⠈⠛⠀⠠⣧⠀⠀⡿⣟⠉⠤⣾⣿⣷⣶⣄⠛⠷⠶⡆⠀⠀⠀⠉⠹⠧⣈⠻⠶⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⢀⣿⣾⠉⠀⠚⠛⠛⠈⠙⠻⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣒⣒⣒⡀
⠀⠀⠀⠀⠀⠀⠀⣄⣠⣀⣴⣦⠾⣿⣿⣿⣿⣿⣿⣿⣷⣭⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⠿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣟⠢⠀⠀⢠⢆⣴⣧⣶⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣿⢿⣫⣾⣿⣿⣿⣿⣿⣷⠙⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠑
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⢻⡇⠟⠀⣼⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⠀⠀⢠⢆⣴⣾⣴⣶⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⢀⣿⣿⣿⣿⣿⡇⣼⣿⣿⡿⠋⢠⣧⣿⣿⣿⣿⠿⢿⡛⠻⣿⡦
⠀⠀⠀⣴⣶⠶⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢯⢹⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⠂
⠀⠀⠀⠁⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⡏⠸⡇⢸⡇⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢀⣀⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠒⠀⠁⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠛⠛⠉⠻⣷⠶⡄⠀⠀⠀⣱⠄⠀⠳⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⢀⠀⢀⠦⢠⠒⢳⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⣀⣀⡤⠴⠒⠉⢠⠴⠋⠀⡆⣠⠀⠷⠘⣴⣿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡰⡟⠀⢠⡷⠋⠀⢘⡴⢡⠉⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠺⢦⠾⡀⠀⠀⠀⢀⢻⠇⠀⢸⡂⠤⠂⠁⠀⠈⢰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⢃⣬⡂⣤⡠⠊⡝⠀⠀⢸⡇⠈⠱⠄⠤⡀⡜⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠉⠀⠀⠀⠈⣲⠁⠀⠀⢻⠁⠀⠀⠀⠀⣇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠫⠤⠤⣀⡀⠀⠀⠀⣀⠴⠋⠁⠀⠀⡄⢸⡀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠉⠑⡦⠚⠁⠀⠀⢀⡴⠊⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⡀⠀⠀⠈⡄⡌
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣀⣀⣀⣀⠀⢠⠞⠀⠀⠀⠀⠀⠘⠣⠤⢞⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠘⡇⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⡼⠁⠁⠁⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣇
⠀⠀⢀⡠⠖⢲⠇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸
⠀⢀⠊⠀⠀⢸⠀⠀⡀⡄⣀⠀⠀⣀⣼⠁⠀⠀⠀⣠⠖⠋⠉⠉⠉⠁⠀⠀⠀⠘⠲⣄⠤⠒⠒⠲⣄⣀⢀⢀⡄⠀⠀⠀⠀⠀⠘⡄⠀⡆
⠀⢸⠀⠀⠀⢸⠂⠉⠀⠈⠉⠀⠀⠀⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠐⠀⠠⠴⠁⠀⡇
⠀⠈⢧⣀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠠⣖⣖⣹⠋⣏⢙⣦⣀⠀⠀⠀⢀⡤⠤⠷⠄⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠒⠒⠒⠒⠒⠋⠉⠉
⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠛⠒⠻⠠⢦⣆⣀⣀⡠⠴⠊⠉⠚⠀⠀⠈⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠲⠠⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⡀⠁⡀⠀⠀⠀⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠀⠐⠀⠂⡀⠀⠘⠂⠀⠀⠀⠀⠀⢀⠘⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠣⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠠⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠘⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⡀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢈⠉⠀⠤⠄⠀⠀⠀⠀⢤⡒⣠⠴⢖⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⣦⡀⠀⠉⡆⡄⢀⠉⠀⠀⠀⠉⠥⠀⠀⠂⠀⠀⠀⠀⡴⢀⡐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠖⢀⠀⠤⠀⠓⡀⠄⠈⠅⠀⠀⠁⢅⢂⢠⠄⠈⠄⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣉⡀⠤⠠⠀⠂⠩⢀⠀⠂⠀⢰⠦⠀⠲⠗⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⠓⠁⠂⠀⠠⠄⠉⣀⢰⢠⡄⢈⠡⠀⣈⠖⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⡆⠐⠂⠀⡇⠀⠀⠁⢠⠑⠀⢩⡶⣤⡇⢀⠀⠀⠀⢄⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⠐⠀⠐⢀⠀⠉⠀⠀⡀⠘⡀⠀⠀⠐⠀⠀⠀⠉⠀⡀⠀⠀⠀⠂⠀⠀⠀⡤⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠌⠁⢠⢀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⡏⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠆⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠲⠂⠀⠆
⠀⠀⠀⠀⠀⢁⢀⠘⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠣⠄⡀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠠⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠓⠲⢶⠧⠖⠀⢀⠀⠀⠀⠀⠁⠀⠐⠶⠿⠇⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠴⠾⠟⣂⠀⠀⠀⠀⠾⠋⠐⢘⠒⠋⠉⠀⠀⠀⠀⠀⠀⣌⠻⣾⡟⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⠏⣴⢠⡀⠀⢀⣴⡶⠈⢷⢦⡄⠀⠀⠀⠀⢠⣶⣜⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠼⡿⢨⣧⡯⠈⣸⠁⠈⠈⠁⠁⠀⠀⠀⢠⡘⣿⠟⠂⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠘⠻⡇⠀⡇⠀⠀⠀⠘⡀⠀⠀⣴⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢯⠀⠈⠠⠄⠀⠀⠐⢿⡏⠃⠀⠀⠀⠀⠈⠁⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⠀⠀⠈⡂⠸⡄⠠⠀⠀⠉⠀⠻⣦⡁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠐⠀⢳⡀⠘⠢⠀⠀⠀⢈⠓⠀⠀⠀⠀⢤⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⢀⠀⠈⣇⠀⢰⡀⠀⠀⠘⠻⠄⠀⠀⠀⠛⢀⣆⠀⠀⢅⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠹⣄⠀⠉⠃⠀⠀⠘⠄⠀⠀⢀⠆⠀⠃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⡆⠀⢠⠀⠐⣤⢸⠀⠀⠀⡀⠀⠁⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠠⣤⠀⠀⠀⠀⠁⠀⠄⠀⠀⠁⠀⠀⢀⠀⡧⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠄⣸⡧⠀⠀⠘⠁⠐⠀⠀⠀⠂⠈⠀⢀⣰⠁⡄⠀⠌
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠂⠘⠧⠑⠋⠀⠁⠀⡠⠀⡀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠰⡀⢰⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠈⠁⠓⠀⠀⠀⠀⠉⢧⡈⠻⠄⢀⡟⠶⠿⣠⣯⣡⡶⠒⠀⠀⢠⠀⢀⠈⠃⠉
⠀⠀⠀⠊⢠⠊⠑⠦⠄⠀⠀⠀⠄⠀⠈⠋⡀⠀⠖⠈⠀⠀⢅⠀⠀⠀⠀⡀⠐⢫⠴⠠⢈⣤⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠉⠀⠀⠂⠀⠀⠚⠓⠂⠀⠀⠀⠂⠘⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣉⣉⡉⠝⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⡾⣁⠀⠀⠀⠀⠀⢀⡤⠀⢀⠀⠀⡀⠁⠚⠛⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢀⠆⢀⣠⡴⢟⣡⡞⣁⠹⡁⠀⠐⢉⠰⠖⠒⠓⠒⢍⣠⠌⠸⢓⠢⢤⣄⡀
⠀⠀⠀⠀⠀⠰⣡⠤⢓⣉⣬⡭⠿⢯⠍⠃⣵⠆⢜⢁⣶⡿⠿⠿⢷⣬⡈⠀⡢⠀⠀⠘⠛⢭⣳⣄⡀
⠀⠀⠀⠀⣌⢓⣉⢹⣙⣽⡦⠙⢇⣄⢀⡐⣡⢎⣴⡿⢉⠔⠀⠀⠐⢌⠻⣧⡀⠤⠀⠀⠀⠀⠉⡸⣷⡀
⠀⠀⠀⠀⠦⣴⣶⡿⡟⢀⢒⡼⠛⢁⠆⣄⠁⣼⡟⠰⠁⠀⠀⠀⠀⠀⠡⡘⣿⡌⠗⡀⠀⠀⢀⡑⣡⡇
⠀⠀⠀⠀⠀⠰⢥⠔⢡⢡⡟⠀⢰⢈⡜⠈⢰⡿⠃⢅⠀⠀⠀⠀⠀⠀⠀⢐⠜⢿⡄⢷⠆⠀⢠⣶⣿⠃
⠀⠀⢠⠼⣶⣦⣤⠠⢲⠘⣷⣠⡠⠀⠲⠔⣫⣶⠒⡆⣁⡀⠀⠀⠀⠀⠀⠀⣢⡮⡿⠶⣶⡷⣸⠟⠁
⠀⠀⠐⠚⠝⠁⢻⡟⠉⠁⠌⠛⢣⣴⣶⡿⣊⢿⡿⠶⠌⠛⠃⠰⣿⣷⢶⢾⡾⢀⡤⣤⣤⡳⠧⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠎⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠚⠟⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣭⣭⣭⣽⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠄⠤⠖⠫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠁⣀⠠⠤⠒⠒⠒⠂⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡏⠀⢀⠞⠁⠀⠀⢰⣴⣖⠀⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⢱⣀⠈⣇⡀⢀⠀⢜⡎⠀⠀⠀⠲⠐⢆
⠀⠀⠀⠀⠀⠀⢀⡀⢠⣶⠀⠀⠻⡑⢬⠣⣦⣠⢦⢳⡀⠀⣰⣶⣤⣀⣲⣀
⠀⠀⠀⠀⠀⠀⢀⠠⣦⡹⡄⠀⠀⠈⠳⣍⡘⠿⠦⠂⢳⡀⠈⠛⣄⠀⠉⠁⠑⠂
⠀⠀⠀⠀⠀⠐⠁⢊⠐⡜⠙⢆⡀⠀⠀⠀⠉⠛⠒⠒⠛⠁⠀⠀⠘⣢⠀⠀⠈⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⡀⠀⠄⠀⠀⠀⠀⠀⢸⣄⣀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢅⡀⠠⠄⣀⣔⢀⣀⠭⠛⠤⠉⢌⠲⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠀⠛⢝⢀⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢺⠈⠢⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠒⠂⡲⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠂
⠀⠘⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⠗⣀⠀⠀⠀⠀⠠⠖⠫⠀⠄⠰⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⣈⠛⢶⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠇⣀⠀⠀⠀⠀⠀⢀⣀⡀⠱⡆⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡘⣷⣦⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⣰⡿⠘⣧⢠⡄⠰⠟⡕⠀⡄⠹⠉⠇⠀⠀⠀⠀⠀⠀⣸⣿⠷⢌⠏⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⡀⠉⡇⢠⣿⣾⠃⠀⢸⠂⠀⠀⠀⢀⠀⠀⠀⠀⠁⣠⣦⠘⡏⠁⠀⠀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⠋⠛⠡⠀⡏⠈⠀⠀⠀⠘⢀⠀⠀⠀⣶⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⠀⠢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣛⠀⠀⢀⠄⠀⠀⠀⠀⠤⢼⣯⠙⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠⠀⠸⡂⠀⡀⠀⠀⠐⠁⠀⣦⣌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠂⠀⢳⠀⠀⣀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠈⢧⡀⠉⠙⠃⠀⠀⠀⢰⣄⠁⠀⠀⠀⠀⠀⣞⠀⠠⠀⠀⢠⡁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⢹⡄⠀⠰⡄⠀⠀⠀⠈⠙⠗⠀⠀⠀⠀⠀⠁⢠⣇⠀⠂⠒⢄⠀⡌⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢣⠀⠀⠈⠘⠆⠀⠀⠀⢃⠀⠀⠀⠀⠰⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⢀⡂⠀⠀⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠃⠀⠐⠀⠠⠂⠀⠀⠁⠀⠀⠿⠀⠧⠈⠀⠀⢱⢠⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠲⢶⠀⡀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⡀⠀⠀⠀⢰⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡆⢠⡼⡦⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠂⠀⠀⠠⣀⣠⠃⢠⠀⠀⠎⢀⠄
⠀⠀⠀⠀⠀⠠⠀⠈⠒⠀⠂⠀⠀⠀⠀⠀⠀⠻⡀⠁⠚⡀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠄⠸⡀⠀⡆⠀⠀⠊
⠀⠀⠀⠀⠀⠀⡄⠈⠒⠤⠤⠀⠀⠀⠀⠀⠐⠶⡀⠲⢴⡀⠀⠰⡇⣥⣾⡞⢀⡆⠐⣠⣤⠄⠀⠀⠀⠈⠀⠀⠀⠇⠀⠃
⠀⠀⠀⠀⡠⠂⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⠀⠀⢀⣘⠧⠀⠈⠐⠚⠛⠊⠉⠁⠀⠀⢀⡠⠉⢀⠐⢀⠂⠀⠐⡀
⠀⠀⠀⠀⠁⠐⠁⠀⠈⠑⠒⠐⠀⠀⠈⠐⠀⠄⠀⠀⢄⠀⠘⠂⠀⣀⠀⠈⠦⠀⠀⠀⠀⢀⠄⠀⠁⠊⠉⠈⠀⢶⡆⠀⢤⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛⠓⠂⠀⠀⠀⠀⠉⠀⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣇⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡇⢸⣼⡿⡉⢀⣠⣂⢌⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣸⣇⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣯⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⢉⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡯⣿⣿⣿⣿⣿⣿⣟⠭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡙⢽⡿⣿⣿⣿⣿⣷⡿⣻⣿
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠻⡿⢣⣿⣿⣿⣿⣾⣿⠟⠁⠀⠙⣿⣗⣈⣯⣽⣿⣿⣿⣯⣥⡵⢿
⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢐⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣰⣿⡿⠥⡝⠟⣼⢿⢿⣿⣳⣳⣟
⠀⢸⣿⣿⣿⣿⣿⡏⠙⠉⠁⠀⠀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣴⣿⡟⠓⢲⣁⣧⣟⣞⣿⣿⣧⡼⠸
⠀⠈⠻⢿⣿⡿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⣟⠋⢹⣿⣧⡦⡷⡷⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣫⣽⣿⣿⣿⡿⠁⠀⠀⢀⣴⣿⣧⡈⠉⠛⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⠋⠀⠀⠀⣴⣿⣿⣭⡉⠛⠻⣶⣾⣟⣯⡯⣿⣿⣿⣿⣿⢿⣾⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣤⣾⡗⡇⣷⣿⣿⣿⣿⣿⣿⢿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣿⣉⡇⣿⣹⣿⣿⣿⣿⣿⣿⣿⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣾⣿⣵⠾⣿⣿⣃⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣰⣿⠿⠛⠉⠄⠐⢂⠐⠀⠆⢙⢻⣿⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⣰⣿⠟⠁⠤⠈⡤⠒⠉⠈⠉⠉⠘⠤⣐⢘⠻⣿⣉⣀⠀⠀⠀⣠⡔⣰⣾⣏⣾⣿⠇
⠀⠀⠀⠀⢀⣿⠏⠀⠀⣨⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣈⠻⣯⣭⣤⢀⣿⣿⣿⣿⣿⣯⣵⠄
⠀⠀⠀⠀⣿⡇⠀⠄⠀⠥⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠾⠿⠛⠻⣿⣿⣯⡟⠛⠁
⠀⠀⠀⠀⢹⠄⠀⠀⡀⢃⠫⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⢀⠀⢸⣧⡁⠂⢌⠀⠀⣻⣧⠀⠂⢀⢀
⠀⠀⠠⡀⠠⣳⣿⡄⢻⡀⠀⠸⢾⢆⢉⢁
⠀⠀⠀⣾⡿⠐⣟⣿⡀⢱⣑⡆⠀⢦⠈⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⢰⡿⢇⠀⣟⣻⠇⢸⠨⠀⠀⠀⠀⠀⠀⣽⣾⣶⣄⠀⠒⠀⠀⢐⠀⠀⠀⠀⠁
⡀⠀⡘⢯⠵⣲⢻⡿⢀⡶⠃⠀⠀⠀⠀⠀⢄⣢⣀⣉⣁⣀⡀⢠⢀⡈⠁⢀⡄⡂⠠
⠁⠀⡆⠀⡴⠋⣾⣇⡞⠁⠀⠀⠀⠀⢈⣲⣶⣴⣾⣿⣿⣥⣄⠀⠀⣄⢂⠌⠀⠠⠀⠀⠀⠀⠠⠀⠀⠂
⠀⢀⠀⢠⢅⠢⢿⣟⡀⠀⠀⠀⠀⣰⣾⡿⣻⡿⣹⣟⡽⣻⢿⣷⣴⡦⢌⠠⡈⢰⠊⠀⡀
⠀⠀⠀⣘⡀⠠⠀⢻⣧⡆⠀⠀⠀⣻⡟⠬⣭⣧⣿⣾⡵⣯⣿⣟⠉⠀⠀⠒⢌⡠⠤⠘
⠀⠀⠀⠈⣀⠅⠁⠈⣿⣱⡄⠀⢸⣿⡁⢅⡏⠋⣙⡄⠚⡩⠟⠿
⠀⠀⠀⢀⠀⠨⠁⡄⠘⢿⣷⢄⠀⢸⣷⠡⢺⢫⣠⠜⠓⣢
⠀⠀⠀⠀⢨⠹⠉⢑⠧⢬⢻⣾⣇⡈⠛⢣⣌⢸⢘⡑⣎⢀⠽⡀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⣧⢘⠔⡂⠂⠁⠙⠿⣿⣦⡘⣿⣧⢠⠒⢾⣁⡤⢾⠡⠤⡴⣾⠃
⠀⠀⠀⠀⠀⠐⣖⢪⡧⣌⢐⠠⡀⠄⡉⠋⡛⡍⢒⣨⠧⠤⢤⡼⡆⡬⠖⠁⡀⡀
⠀⠀⠀⠀⠀⠀⠈⢾⠷⠠⠙⠋⢑⠚⡦⢦⡤⠶⡚⠙⢢⡤⠴⠛⠁
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⡰⢀⠈⠉⠑⠀⠳⠔⠚⠒⠋⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣠⣴⣿⣿⣩⣴⣾⣿⣿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⢟⠛⠫⢉⡘⢠⡈⢉⡉⠿⢿⣿⡿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡿⠛⠡⠠⡄⣈⢁⣌⠀⠆⠈⣆⣠⠸⡄⠛⢿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠂⢐⡷⠋⠁⠀⠀⠀⠀⠀⠈⠑⠧⣉⠨⠹⢿⣧⣤⣤⣀⠀⠀⠀⣰⣾⣡⣾⣿⣏⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣸⣿⠋⢂⠈⡀⣸⠋⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣇⡹⠿⣧⣭⣤⡤⠀⣿⣿⣿⣿⣿⣿⣿⣯⣴⠆
⠀⠀⠀⠀⠀⣾⣿⠃⠂⠈⠄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠦⣯⣿⣿⡿⣿⣿⣿⣿⡟⠿⠿⠿⠃
⠀⠀⠀⢀⠃⢻⡟⠀⡌⡁⠄⢸⠈⡤⣾⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠸⣗⢀⠀⢐⢠⣂⠤⡙⣗⡇⠢⡀
⠀⠀⠀⢄⠀⠀⣯⣦⠀⢁⠀⡀⢀⠠⢸⣜⡆⢀⠑⠀⣄⢠
⠀⠀⠀⠂⠀⢄⠹⣯⣷⡀⠜⣧⢠⠄⣸⣷⣷⡄⠉⠐
⠀⠀⠀⢀⣵⣶⡟⢹⡽⣿⡐⠚⡇⠢⣼⠀⢁⠚⠐⠒⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⣠⠃
⠀⠀⠀⢨⣿⡿⠀⠀⣷⣾⡧⢈⢽⠶⠎⠀⠀⠙⠂⠈⠀⠀⣤⢀⣓⡀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠈
⠀⠀⠀⣿⣟⣓⡄⢀⣧⣹⡗⡉⡾⣰⠀⠀⠀⠀⠀⠀⠠⡀⠾⣷⣿⣷⣦⠀⠀⠀⠀⠀⠁⣧⠀⢀⣆⠈⠀⠀⡇
⠀⠠⣉⠸⣯⣷⢆⡾⣿⣿⠡⣸⡳⠃⠀⠀⠀⠀⠀⠀⠀⣈⣂⣀⣈⠀⡀⠀⣀⠀⡤⢒⢸⡉⠀⠀⡠⢒⠂⡰
⠇⠀⢠⠀⠘⣈⡼⢳⣼⡇⣡⠟⠁⠀⠀⠀⠀⠀⠐⠶⣤⣴⣪⡴⣿⣿⣿⣉⣁⠀⠈⠈⠃⠠⠀⠡⠁⣀⣀⠠⠐⠉⠀⠈⠆⠀⠀⡠⠤
⠀⠀⠘⠀⠀⠿⣈⠱⣿⣷⠏⠀⠀⠀⠀⠀⠀⢀⣙⣿⣽⣿⣿⡞⣿⣿⢿⣿⣿⣮⢄⠀⣜⠒⢢⡁⠀⠀⣀⡦⠀⡀⠀⠀⠈⠉⠁
⠀⠀⠆⠀⢸⠃⠌⣉⠛⣿⡴⠀⠀⠀⠀⠀⢠⣿⣿⡿⣫⣼⣞⢱⡟⣵⡏⣵⣻⣿⣿⣿⠿⠚⢢⠘⣦⣈⡏⠀⢀⠇
⠀⠀⠀⠀⣸⡑⠐⠤⠥⢹⣧⣼⠀⠀⠀⠀⢘⣽⡿⠤⢦⣭⣷⣿⣿⣿⠼⣯⣿⣿⡏⠀⠀⠀⠀⠙⢆⣤⠤⠄⠃
⠀⠀⠀⠐⠈⠥⡉⠒⠁⠀⣿⣟⢠⡀⠀⠀⣾⣿⠓⣙⢬⠎⠟⠉⣏⠀⠞⢛⡻⠎⡟
⠀⠀⠀⠀⠀⠈⠆⠤⠀⠀⡈⢿⣾⣧⠀⠀⠋⣹⣇⠔⢯⢷⡖⠒⠉⣲⣄⣉
⠀⠀⠀⠈⠠⠀⡬⣭⣉⣅⡨⢉⢿⣿⣸⣦⠀⢻⣿⣌⠇⡧⠼⠳⣯⣁⣠⠜⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠨⣆⢃⡂⠨⡕⠻⢖⡹⣿⣿⢤⣀⠙⠘⣷⣇⢚⣈⠥⡽⣆⣠⠴⠫⢀⠀⠀⠀⠀⠀⢀⠀⠄⠱⠄
⠀⠀⠀⠀⠀⠀⢹⡣⢚⡕⠇⢈⡂⠡⢌⢻⢷⣿⣦⡰⠛⣿⣷⠘⡔⠢⢾⣀⣀⣤⣞⣁⣤⣤⠶⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢧⠭⣔⣻⣀⠘⢠⠬⡸⠘⡭⠟⢻⠻⡟⠫⢫⠅⢳⡏⠁⠀⢀⣻⣆⢐⢢⠝⠋⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣳⣷⡈⠓⢶⡤⠼⣈⣱⠚⢀⠑⠬⠗⢘⡴⣏⠈⠉⠉⣽⣩⠗⠚⠁⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠈⡂⠹⠚⠉⠉⠈⠉⠀⢤⣈⣋⠉⢶⠂⠙⢧⡀⠈⣩⠟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⢄⠉⠁⠉⠉⠀⣸⢂⠀⠂⡀⠙⠒⠚⠳⠒⠊⠉⠋⠁⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠚⠁⠘⠁⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡇⠀⠀⣴⢃⡔⠀⠀⠀⠀⠀⠀⢢⡘⣦⠀⠀⢸⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣸⣷⣿⣾⣿⢸⣷⣆⢸⡀⢀⡇⣰⣾⣇⣿⣷⣿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠐⢤⡀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⡿⣿⣿⣷⣄⡙⢿⣿⣿⡿⢋⣠⣾⣿⣿⢿⣿⣿⣿⠇⣾
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠻⣿⣿⣿⣿⣿⣿⡻⢿⣦⣹⣏⣰⡿⢟⣿⣿⣿⣿⣿⣿⠟⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠏⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣋⠉⠉⣙⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠗⠤⣤⠤⠖⠛⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠟⠶⠦⣤⡤⠺⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢿⣿⣀⣀⣿⡿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢟⣽⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣶⣶⣶⡄⣦⣰⣄⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣯⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣷⡙⠏⣻⣿⣿⣆⠀⢀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⢾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠙⠿⣿⣶⣌⠻⢬⡉⢠⣾⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣈⢻⣿⣷⣤⣵⣿⠿⢿⣿⠃⠁⢹⠀⠀⢸⣿⠿⢃⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⣰⣿⡿⡿⣿⣿⢱⡿⢿⣿⠿⠋⠙⠋⠘⠏⠁⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⣿⢿⣿⠻⣿⡇
⠀⠀⠀⣰⣿⢯⣿⣿⣻⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⠏⠸⡿⠀⠀⠃
⠀⠀⢰⡿⣵⠟⠋⢻⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⠀⠀⠙
⠀⢀⡿⣽⠋⠀⠀⠘⠁⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠀⠉⠉⢻⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡾⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⣙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠉⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠙⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣵⣶⣤⣶⣴⣿⣽⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⣠⡾⠋⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⣴⠞⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⣰⡾⠋⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⣀⣒⡒⠛⠛⠋⠀⠀⠠⠤⠄⠺⢥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢠⣾⠏⠀⠀⢀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠴⠖⠀⠀⠀⠛⠀⣀⠀⠉⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⣠⠀⣰⡿⠁⠀⣠⠞⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠁⣰⠋⠀⠘⢦⣤⠶⠶⣭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⡔⢁⣾⠟⠀⢀⡴⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠸⠓⢢⠀⠀⠐⢂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣰⠏⢠⣾⠋⠀⣰⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⠄⢀⡠⠆⠀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢠⡾⠁⢠⡿⠁⢀⡼⠁⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠰⡃⠀⠀⠀⢿⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣴⠏⠀⢠⣿⠁⠀⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠈⢇⠀⠙⠃⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢠⡾⠃⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠑⣄⠀⢤⣀⠀⠀⠀⢀⣀⡙⠠⠄⠘⡆⠀⢤⠆
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣰⡟⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠁⠲⠦⣤⣀⠁⠀⠈⠳⣄⠈⠉⠓⠀⠀⠀⠙⠳⣄⠐⢸⡄⢀⣀⡀⠀⠦
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣼⠏⠀⠀⠀⣼⡏⠀⠀⣀⣠⣤⣤⣤⡤⠤⠄⣀⠉⠑⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠀⡈⠛⠀⠀⢠⡀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠶⠦⣀⡀⠀⠀⢀⣀⠀⢠⡀⢀⠀⢠⠀⠀⠀⠀⡀⠀⠈⠶⠂⠀⠀⠉
⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠏⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢀⣉⠉⠒⠀⠀⠀⠀⠐⠒⢤⡀⠙⣼⠁⡏⠀⣼⢤⠀⠀⠙⡾⣀⠰⠄⠀⠀⢀⡷
⠀⠀⠀⣾⠁⠀⠀⠀⣼⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⡀⠉⣉⡽⠋⢁⠀⢰⠀⠀⠙⢆⢳⡀⠈⢀⠁⠀⢻⡀⡇⠀⠇⢹⠀⡤⠀⢀⡰
⠀⠀⣼⠃⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣀⣀⠄⣠⡾⠋⠀⢀⠈⢧⣀⠆⠀⡀⠀⠀⠱⠀⠉⠙⠢⠄⢣⠁⠀⠂⡟⢀⣀⡴⠈⠁
⠀⢰⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠐⢀⡾⠋⠀⠠⣄⠈⠛⠀⠀⠈⠀⠀⠂⠀⠀⠀⠛⠀⠀⠀⢸⠀⠀⢰⠁⠀⠈⠀⠀⠐⠀⢀⠀⠱⠄
⠀⡿⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢠⡟⠁⣀⠙⢂⡤⠒⠉⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⠇⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢰⠃⡸⠃⢀⠉⡴⠋⠀⠀⠀⠀⠀⠀⢦⡀⡀⣁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀
⡎⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠂⠀⠰⢆⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⢹⡟⠃⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠁
⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠀⠐⢉⠠⣀⢤⣀⠀⠀⡀⠀⠀⠛⠀⡈⢁⣀⠀⠀⠀⠀⠀⠀⠣⣀⠔⠤⠐⠂⠀⠀⠀⠀⠀⠻⠀⠀⢰⠟⠃
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡠⠖⠀⢄⠠⠀⠀⠛⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠻⢄⡰⢷⠘⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠈⠁⠀⠓⠈⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣤⣤⣀⣀⣈⡀⠒⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣛⣫⡥⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣟⣽⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⡾⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡾⢋⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣿⡿⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣷⣦⣄
⠀⠀⠀⠀⠀⢀⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠿⣷⡄
⠀⠀⠀⠀⠀⢼⣿⣿⣿⠿⡟⠛⠉⣽⣿⣿⣿⠿⠶⠖⠂⠀⢹⣿⣿⣿⣿⣿⣿⢻⣿⣷⡄⠙
⠀⠀⠀⠀⠀⠀⠻⣏⠋⠀⠀⠀⢀⡿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⡟⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠊⢀⣿⣯⣀⡠⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣾⡿⠿⠉⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣩⣴⣾⣿⠟⣋⣥⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⠟⣛⣩⣥⣶⣾⣿⣿⣟⣫⣭⣶⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⢛⣩⣴⣶⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣋⡤⠾⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⢀⣼⠿⠃
⠀⠀⠀⠎⠀⠀⠀⠀⣄⣢⣠⣀⣐⣿⣩⢿⣿⣿⣿⣿⠿⢿⣶⣶⣦⠤
⠀⠀⠀⠀⢀⠤⠒⠈⠹⠹⠿⢟⠛⣋⣙⣏⣿⣿⣿⣿⠇⠛⣉⡿⣿⣋⡥⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⡜⣿⣿⣽⣿⣿⣿⣷⠚⡆⢛⣹⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠈⠉⠉⠙⠓⠀⠀⠀⣼⡯⣷⣿⣷⠀⠀⠀⢀⣀⡶⠾⢷⣾⡷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⡘⠉⠀⠛⣿⡃⠁⠀⠀⡞⣡⣶⣿⣿⠿⣿⣻⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠃⢌⡀⢉⢼⠇⠈⠀⠀⡌⠀⣿⣿⡿⢙⣀⣉⠩⢿⢿⣿⡆
⠀⠀⠀⠀⠀⠠⠶⠶⢖⡀⠀⠀⠀⠀⠀⠀⠀⡃⠠⠀⣀⠠⠖⠋⠀⠀⠀⠀⠀⠀⣾⡿⢾⠇⠈⠛⢯⣿⠀⢠⢿⡇
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣷⣟⢖⡾⠛⢛⣨⣴⣀⢀⡀⠀⠀⠀⡈⢠⣿⣿⡟⠀⠀⠀⢀⡤⢸⣾⣿⡇
⠀⠀⠀⠀⢀⣬⢿⣟⠀⠀⠀⠀⠐⣿⣻⡟⣣⡴⡿⣟⣿⣹⡽⡻⠶⣂⣀⠼⣡⣯⣿⣿⠂⠀⢀⣠⣿⣶⠏⣿⢿
⠀⠀⠀⠀⠀⠀⢠⣿⣰⠄⠀⠀⢼⣷⠻⠿⣽⢻⡑⣿⢿⣻⢓⣝⣯⢔⡴⣿⣽⣯⣿⠇⣴⣼⢿⡿⠛⣡⡾⡇
⠀⠀⠀⠀⠀⣄⣈⣫⡭⠶⣾⣄⠙⢼⣿⣟⣻⠿⠃⠁⠉⢿⣿⠷⡟⠻⢾⣶⣯⡽⢟⣁⣠⣀⣤⣤⣾⡿⠏
⠀⠀⠀⠀⠈⣻⠷⣏⠀⠀⢸⡿⣯⣬⡥⠌⠀⠀⠀⠀⠀⣸⣳⡾⣧⣶⣦⢭⣽⠶⠏⠉⠛⠻⠛⠛⠋
⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠵⣿⣿⡟⣷⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠅⠈⠋⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢛⣋⣥⣤⣾⣿⣾⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣯⡶⠾⠟⠛⠫⠽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣴⣿⣿⡭⠶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣭⣟⣛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣬⣼⣾⣿⣿⣿⣿⣷⣶⣾⣯⣽⣻⢿⣿⣿⣿⠟⠋⠉⠉⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠄
⠀⠀⠀⠀⢀⣠⣢⣦⣾⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶⣿⠿⠿⠿⠿⠓⠒⠒⠂
⠀⠀⠀⢀⣾⣿⣿⠿⢿⣿⣷⣆⡠⢔⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⠛⠉⠉⠉⠉
⠀⠀⠀⠺⠛⠉⠀⢀⣠⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠛⠓⠒⠂⠀⠀⠀⢀⡤⠴⠖⠚⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠟⣿⣿⣿⣿⣿⣿⡿⠟⠛⣻⣿⣿⣿⣿⣯⡻⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡏⠀⠀⢀⣿⣿⠟⢿⣿⣿⣿⣷⣭⣛⠿⣤⣶⣀⢀⡀⣀⢀⡀⣀⣀⣠⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠙⣧⠀⠀⠈⠻⣿⡀⠀⠈⠉⣹⣿⠉⠛⠻⠷⠶⠿⠿⠿⠿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠞⠋⠠⠶⠾⠟⠀⠴⠶⠾⠛⠁⠀⠀⠴⡾⠿

⠀⠀⠀⠀⠀⠀⠀⢠⠤⣀⠀⡠⡎⠑⠢⠄⠀⡀⠠⠀⡠⠄⠠⡀⠀⠀⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠉⠀⠀⠐⠀⠀⠐⢤⡱⠎⢀⡀⠀⠀⣤⠀⠁⠀⠀⠀⣀⡀⠠⠤⠦⠀⠒⠒⠒⠒⠲⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⣁⣤⣤⣄⠀⠀⠠⠀⢀⡀⠀⠀⠀⢠⡷⠄⢁⡄⠀⠠⠰⠊⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠃⠀⣀⠀⠀⠀⠒⢀⡶⠠⠄⠠⠤⣤⣤⠄⡤⠤⠤⠤⠠⠄⠐⠒⠐⠒⠒⠒⠒⠐⠂⠄⣀⠀⠠⠒⠆⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠚⠁⡀⠀⠀⠀⠔⠉⡀⠐⠀⠀⣀⠀⠀⠤⣤⡤⣀⣀⢀⣀⡴⠄⠢⡄⠈⢣⡤⢘⠂⠀⢸⠧
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⢄⣤⣤⠴⠶⠒⠛⠉⠓⠘⠁⠷⠊⠉⠉⠉⠉⠀⠁⠀⣀⡠⣤⣝⣋⣀⡀⠃⠀⣠⣤⣔⣀⣿⡈⠀⢀⡘⡀⠀⡀
⠀⠀⠀⠀⠀⢀⡴⢉⣤⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢈⡩⠒⢤⠀⠀⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⠈⠉⠉⠁⠈⢁⣌⣤⠂
⠀⠀⠀⠀⠀⢸⠀⢨⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡰⣤⢴⢒⠤⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠶⠛⠛⠚⠉⠉⠙⠛⣶⡄⠙⣴⠃
⠀⠀⠀⠀⠀⠀⢢⣾⠃⠀⠀⠀⠀⠀⢠⣖⣩⣤⠶⠶⠶⠐⠳⢬⣤⡀⠀⢀⣀⠴⠶⠾⢻⣧⣤⣤⣀⣠⣀⡀⠂⠀⠐⠀⠀⡌⣡⡄⠃⣀⣀
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⣴⡟⠉⠀⠉⠲⡄⡤⠲⡄⠀⠈⣉⣀⣤⣤⡤⠶⠶⠶⠖⠺⠿⠿⢯⣽⣟⡛⠳⠞⠶⠺⡇⠫⣶⣀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⢸⣏⡨⠟⠀⢀⣀⠄⢐⣀⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠙⠷⢦⣄⠀⢀⢃⡈⠉⠀⢉⣂⠞
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠶⣤⣬⣡⡽⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡉⠒⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠤⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⢉⣉⣀⠠⣄⣀⣀⡈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⢀⡀⠀⠀⡴⠈⢙⠷⠶⣤⠖⠙⠎⣤⣤⣴⣤⣎⣹⠥⠤⠶⠚⠋⠉⠉⠉⠀⠀⠀⠉⠈⠛⠶⢤⡙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⢀⠐⠂⢠⡰⠏⠠⠄⠀⠀⠀⠈⠀⠁⢈⣁⣤⣤⣤⠤⢤⣤⣤⣤⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⢲⡉⢦⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢨⡏⠑⢺⡃⠀⢇⠀⠀⠀⠀⣀⣴⠚⠉⠛⠀⠀⡄⠀⠀⡄⠀⠈⠑⠆⠁⠐⠦⠀⠠⡄⠀⢀⠀⠀⠀⢀⠀⠙⡄⠇⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠁⠀⡀⡰⠦⠜⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠊⡧⠈⠀⢀⠒⣠⠀⠀⠂⠀⠀⠁⠂⠀⠔⠠⠃⠄⠀⡌⠀⠀⢰⢸⡇⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠳⠄⠀⢀⡼⠋⠀⠀⡀⠰⠆⠀⠋⠀⠈⠳⣄⠀⢁⡀⢦⣉⡀⠉⠳⠀⠀⠀⠀⠀⠀⠑⠚⣷⢤⡀⠘⢠⠇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢀⠔⠈⠀⠀⠀⡀⢠⣀⣄⣠⠬⠷⣦⣄⣀⠛⠐⠋⠓⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⢹⡄⢠⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡤⠉⠀⠀⠀⡰⢂⡽⠛⠉⠉⠀⠀⠀⠀⡼⣩⠛⠀⠰⠦⠀⠤⡀⢀⣦⠶⠐⠛⠙⠛⠛⠻⢾⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢠⡟⠀⡸⠁⠀⠀⢠⠎⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠰⠙⠶⣾⣂⠀⠀⠀⢈⢿⠛⠀⢀⠀⠀⢀⡀⠀⣨⡇⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⠀⠀⢠⡎⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡁⢲⡆⠀⠹⣆⣁⢢⣾⡗⠢⢾⣿⣾⠏⠂⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⣶⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠄⣒⠈⣿⣿⠀⠻⢖⣾⡤⣙⡆⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣿⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠟⢛⠁⠈⠻⠤⠟⠋⠁⠸⠃⠀⠀⠀⠀⢀⡟⠀⣀⣠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠿⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣂⣠⡞⠢⠚⠃⠀⠀⠀⠀⠀⣼⡴⠫⢊⣠⠦⢤⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⡤⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣾⣭⣀⣄⡀⣀⣀⠖⠨⠥⢤⡟⠏⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣩⡼⠋⠁⠀⠠⠄⠤⣤⡄⠀⢉⢀⠀⣐⢲⡿⢷⣄⡀⠀⣀⠴⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠈⠢⣆⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⡞⠉⠛⠀⠀⠀⠀⠈⠉⠙⠛⠂⠛⠁⠀⠀⠀⠐⢂⡀⢀⠜⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣄⠀⠈⠑⠋⠤⣀⠀⠀⠀⠀⠀⠄⠀⠸⣇⠀⠳⠤⠀⠒⡀⠀⠀⠀⠀⢀⡀⠤⠤⢄⠀⠀⠈⠠⠞⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⢀⣀⠀⠀⠈⠉⠓⠢⠤⠂⠤⣄⣉⣤⣇⠈⠘⠀⣁⣠⡶⠾⠋⡉⠠⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠀⣤⠤⣤⣤⣤⢀⣀⣄⠀⠀⣙⢻⡽⠷⠶⣄⡀⠀⠀⡠⠈⠀⡧⠀⢸⠀⢀⡀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡒⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡦⠄⠐⠀⠒⠚⠉⡠⠂⠐⠀⠈⠉⠲⠍⠁⠀⣰⠁⠀⠘⢛⣉⡤⢄⡴⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠊⠉⢦⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢧⠀⢀⡀⠀⠤⠀⡇⠠⢂⡠⠆⢀⠄⢠⡤⠚⠁⠀⠀⠐⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣀⣠⡞⠻⠶⣤⡀⠧⠀⠀⠀⣠⠾⠁⠀⠀⢀⣌⡷⠿⠸⠃⠀⡈⠀⢠⠁⠀⠒⡷⠚⠀⡠⠒⠘⠀⠀⡀⢸⣥⠶⠶⣦⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⢸⣁⣀⡤⠀⢤⠉⠺⠓⠒⠊⠁⢀⣤⠴⠋⠀⠈⠁⣄⡠⠈⠠⠃⠀⠀⠀⣠⠊⡡⠀⠈⡀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢠⠀⠀⠠⣞⠉⠀⠀⠀⠐⠓⠲⠀⠀⠀⠀⠀⠀⠀⠀⢁⡾⠛⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣤⠇⠺⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡄⠀⠀⠓⠢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢶⣠⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⠾⣦⣤⠰⠜⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠰⣬⣢⣀⣀⠴⠦⡆⠐⣶⠖⠁⠈⢀⠀⢀⠀⣠⣦⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡀⠀⠀⢀⣀⣠⣦⡤⡤⠠⢶⡶⠚⠉⠀⢀⣀⣀⣀⣧⡞⣡⠖⠀⣀⣨⣶⣶⡶⠾⠞⠓⠿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⢐⣒⣮⠉⠁⠀⠈⠉⡷⠀⢛⣿⢿⣧⣼⣏⠄⠀⢀⣠⣾⣹⣿⡿⢿⠐
⠀⠀⠀⠀⣀⣤⠤⠂⠐⠖⠒⠒⠚⠳⢶⣶⣦⣤⣤⣴⡶⢎⣡⡇⠘⠁⠂⣠⡮⠁⣴⠛⣯⣿⣿⣿⠉
⠀⠀⠔⡟⠉⠀⢀⣀⣰⡂⠙⠛⢻⣿⣿⠟⢩⣞⠁⠀⠀⢾⣁⡄⠀⠀⡀⠀⣴⣺⣿⣷⣿⣿⣏⠈⠁
⠀⠀⢸⣇⠀⠐⠁⠀⢀⡐⠀⠀⡾⡫⠀⠀⠈⠉⠀⣠⠒⠻⠁⣀⠄⠛⠑⠇⠀⠈⠀⠨⢝⣯⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠈⢙⣒⣂⣀⣀⣤⣤⡴⠋⠉⠒⠤⠀⠀⢀⡄⠀⠀⣚⣉⠀⢠⡄⣷⠖⠀⠀⠀⠀⠙⣔⢶⣶⣾⡋⢴⠀⠀⠀⠀⠀⢀⡤⠤⠤⠄
⠀⠀⡔⣰⠿⠉⠉⠙⠛⠿⣿⣇⣸⠒⠀⠀⠀⠀⠉⣐⣦⠀⠀⠀⠁⠀⠡⣿⣿⣿⣿⣿⣶⡌⠀⠓⠉⠉⠙⠲⠶⠀⠒⠀⠈
⠀⢸⠘⢧⣀⠀⠀⠐⠒⠚⠋⠉⠲⢢⣴⣦⣤⣀⠀⡈⠙⠂⠰⠦⣀⠀⠀⢙⣏⢻⣿⣿⣿⣧⡄⠀⠀⢀⣀⠠⡀
⠀⠀⠑⠄⠉⠀⠀⣀⣐⣒⠶⠤⡀⠙⠿⣦⣼⣧⣀⣀⣈⣁⠐⠀⢜⡳⢄⢨⠫⠘⣽⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⣀⣤⣤⡖⠒⠒⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠧⣄⡀⠉⠉⠉⠲⡆⢠⣶⣿⠉⠉⠁⠈⢢⣈⠈⠑⠯⡟⣿⣇⣀⣀⣀⣤⠖⠋⣁⠀⠀⠈⢠⡤⠀⠀⠀⠀⠲⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⡛⠒⠊⠉⠛⠛⠓⠄⢠⣕⠿⣼⠛⠛⠛⠧⠤⡤⠦⠤⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿⢀⣠⡤⠶⢖⡒⣠⣖⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣼⡇⡔⢿⣏⢸⣧⡈⠉⣱⡏⢾⣽⣻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠔⣚⣉⣥⣽⣌⢿⣷⣿⣷⣔⢿⠀⠀⠈⠛⢿⣮⡻⣮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣛⣥⣶⣿⣯⣭⣉⡁⠬⢇⣿⣿⣿⣿⣷⡀⠀⠀⠐⢦⡉⢿⣮⣻⣟⣿⣆⢠
⠀⠀⠀⠀⠀⠀⢀⣤⣴⠦⠀⠋⢈⣩⣤⣤⣉⠉⠀⠈⢹⣿⣿⣿⣿⣿⣇⡹⣷⡀⠀⠀⠀⠙⣎⢻⣷⣻⣎⣿⡆⢷⣄⢠
⠀⠀⠀⠀⠀⠀⠈⠅⠙⡠⢀⣴⣿⡟⠻⢦⣈⠓⢦⡐⠾⡿⣿⣿⡿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠸⡎⣿⣿⢿⣾⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⣿⠟⢋⠉⠓⠂⠈⢉⡀⠈⠁⠀⣻⣿⡀⠀⠈⠻⣿⣿⣿⣷⣤⡀⠀⣿⢸⣿⢸⣷⣿⣇⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣿⡀⠘⠀⠀⠀⠼⠋⠀⠠⣤⣴⣿⣿⠅⠀⠀⠀⠀⠟⠛⠛⠛⠉⢀⡟⣼⣿⡇⣿⢻⣿⣿⣇⣿⡆
⠀⠀⠀⠀⠀⢀⡤⢸⣻⠷⣬⣭⣭⡄⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣅⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣱⣿⣿⢠⣿⣿⣿⣿⢸⣿⣷
⠀⠀⠀⠀⢠⣾⣏⢸⡏⠀⡎⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣖⣯⣾⣿⣿⡏⣼⣿⣿⣿⣿⡆⠻⢹⡀
⠀⠀⠀⠀⠀⠀⣿⠈⡱⠘⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣽⣿⣿⣿⢿⣮⣿⣿⢟⣴⣿⢻⣿⢹⣿⣿⣶⣾⠁
⠀⠀⠀⠀⠀⠀⣿⡀⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣵⣾⡿⢁⣾⠇⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⢀⡴⢟⣩⣥⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣟⣥⣴⣾⠟⢰⢇⣿⣿⣿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡴⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡭⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣌⣹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠘⣿⢿⣄⠀⠀⠀⠀⠀⠈⣰⣿⡿⠿⠛⠿⢻⣿⣿⣿⣿⣇⠀⢀⣤⣬⣿⣿⡿⢻⣿⣿⣟⡻⣶⠙⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢱⣼⣿⡀⠀⠀⠀⠀⢠⣿⣿⣶⣌⠀⠀⠢⢍⠿⣿⣿⣷⠈⢸⣿⣿⣿⣷⣶⣿⣿⠿⠿⠿⠟⠀⣿⢣⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⠀⠀⠑⠍⠙⠣⠂⠈⢉⣛⣿⣝⠷⣮⡍⠛⠳⠚⠋⣰⡟⡈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⣿⡀⣄⠀⠀⢦⢻⣿⣿⣿⣿⣿⣧⠈⢷⡄⠀⠀⠀⠀⠸⢿⣿⣿⣷⣦⣶⣦⣠⣤⣾⡿⠹⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠹⣦⣀⠈⢷⣽⣿⣿⣿⣿⣿⣧⡀⠁⠀⠀⢠⡞⣿⣶⣮⣍⣈⣛⣻⡽⠟⣩⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣌⡻⣿⣿⣿⣿⣿⣿⠙⣦⠀⢀⡀⠱⣌⢰⡿⣻⣿⣍⡁⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣽⣻⣿⣿⣿⣿⠏⣰⣿⣷⡀⣿⡄⣸⡆⡿⣳⣌⣛⣛⣭⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⣻⠏⠘⠻⠿⠿⡇⠿⣿⠉⠛⠃⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠐⢂⠂⠀⠐⠀⠤⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠐⢦⡀⠀⠁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡴⠒⠋⠁⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⢀⡂⡰⢀⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠊⠁
⠀⠀⠀⠀⠀⠀⢈⠸⡇⣿⣿⠀⠀⠀⠀⣰⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠒⠂⠈⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠸⠴⠉⠛⠛⠀⠀⠀⢠⣿⢻⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠀⠲⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠄⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠤⢀⣀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣄⠀⠀⠀⠀⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠙⠦⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⡄⠀⠀⠈⠑⠦
⠘⢉⠁⠀⠀⠀⠋⠉⠉⠉⠉⠉⢁⠀⠠⠀⠂⠀⠠⠤⠄⠀⡄⠉⠁⠀⠀⠀⠘⢦⡠
⠀⠀⠀⠀⡀⠀⠀⠈⠀⠄⠠⠄⠀⠢⠀⠀⢘⠀⠀⠄⠀⠀⡅⠀⠐⠂⠀⠀⠂⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠠⢄⣀
⠀⠀⠊⠛⠀⠀⠀⠀⢀⠀⠐⠀⠀⠁⠀⢀⠀⠀⠈⠀⠀⠀⠳⠀⠀⠀⠁⠀⠀⠁⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠡⢀⠀⠈⠀⠀⢀⠀⡀⠀⢀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⡐⣀⠀⠐⠀⠉⠡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⠘⠀⠂⠠⠋⠐⠀⠀⠄⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠁⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠠⠰⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠀⠀⢀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠴⠺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⣀⡼⠊
⠀⠀⠀⠀⠀⠀⠀⡐⢁⠞⠁⠄
⠀⠀⠀⠀⠀⠀⢸⡧⠋⢀⣠⠖⠋
⠀⠀⠀⠀⠀⡆⡘⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⡶⠶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⢭⣶⣦⡀⠀⠀⠀⠀⢉⣙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⠀⠀⠙⢿⣷⣀⠀⠀⠀⠈⠛⠶⣬⡙⠶⣄
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡷⠀⣀⣤⣠⣀⣿⡿⠂⠀⠀⠀⠀⠀⠀⠙⠳⣌⠳⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠝⡁⠛⠟⠋⠉⠉⣿⢷⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⢧⡀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢰⣀⠀⠀⠀⠸⣆⠈⢳⡝⡂⠀⠀⠀⠀⠀⠀⠀⠙⣆⢻⡄
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣶⡟⢧⣈⡣⠀⣈⠁⠀⠹⡍⠂⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⡀
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠫⠄⢀⠝⠁⠀⢿⡃⠀⠀⢿⠳⠀⢀⣤⠶⣦⡄⠀⣦⠸⡆⠱
⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⠆⠁⡔⠋⠁⠀⢸⡦⣰⠏⠀⠀⠀⢻⡀⣿⡀⢿
⠀⠀⠀⠀⠀⠀⠘⣯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠐⢲⡆⢸⣧⠘⡀⠀⠀⠀⠈⡇⠙⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠸⠁⡼⠾⠆⠸⠀⠀⠀⠀⣧⠀⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⣰⠷⠀⠸⠀⠁⠀⠀⠀⢸⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣌⣑⠒⠤⠤⢤⣤⣤⡤⠴⠂⣁⣠⡶⠟⠁⢠⠌⠀⠀⠀⠀⠀⠀⠀⢁⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⣶⠀⠀⠀⠀⠀⠀⢛⠀⠀⢒⠁⢄⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢀⣠⠴⡶⠋⠁⠀⠀⠀⢠⡴⢀⣋⡤⣤⠈⠑⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠂⠈⠉⠀⠜⠀⠀⢙⠀⠀⠀⠀⠙⠉⠀⠀⠈⡅⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠁⠀⠀⠀⠀⠀⢀⠎⠀⡠⠁⢘⡀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢀⠀⠀⢲⡀
⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡰⠁⠀⡌⢳⡀⠤⠀⠀⠀⠀⠮⠀⢈⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢤⣀⣂⠀⠀⠃⢠⡀⠀⢀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⠜⣁⠁⠀⠀⠀⡄⠀⣀⠀⣀⠙⢎⡂
⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠂⢨⢀⡀⠀⢀⠀⠀⢀⠃⠀⣠⡼⡏⠁⠐⠡⡜⠀⠀⠀⢀⡰⠅⠠⢿⠂⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡄⠀⠀⠈⢀⡼⠋⠉⠁⠀⠈⠉⠁⠀⠀⠠⢈⡀⡲⡃⠀⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢼⠔⠁⠀⠀⠀⠀⠑⡇⠀⠀⣾⡗⡊⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠵⠃⠀⠀⠐⠀⠀⢀⠂⣿⠀⠠⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⡀⢠⠄⠀⢀⣠⣾⣿⡟⠀⠰⠀⢋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⢸⡶⢾⡟⠷⠻⠾⢿⡀⠀⠒⠣⠀⠰⡄⡀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠁
⠀⠀⠀⠀⠰⠄⠀⠀⠀⠐⠂⠀⡲⠂⠀⢀⡴⠖⣃⢠⢀⡦⢰⠀⠀⠀⠄⠀⠉⠸⠓⠚⠙⠋⠈⠈⠁⢤⠀⠀⠀⠀⠐⠀⠈⠁
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⡀⠈⠙⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠐⣄⣰⡀⠀⠹⠅⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⢢⢄⠂⠀⠀⠉⠁⠘⢀⡑⠠⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠒⠀⣈⠉⠉⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⢉⠉⠒⠂⠁⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠤⠤⠤⠭⠦⠄⣄⡀⣀⠶⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠁⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⠤⠐⠂⠉⠉⠉⠉⠉⠁⠖⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠞⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠋⠔⠤⠀⠐⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠤⠤⠀⠐⢂⠈⠠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠑⣬⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠐⡀⠀⠀⠀⠀⠀⠀⢠⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⠂⠆⠀⠀⠀⠀⠀⢰⣠⣶⣶⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡆⠀⠉⠀⠀⠀⠀⢀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠂⠀⠀⠀⠀⠀⠸⣿⣤⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣀⠀⠙⠀⠀⠀⠀⠀⠀⢿⣿⣧⠾⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣆⠀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠑⠤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠉⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢀⠠⠀⢐⠒⠂⠀⠬⠍⠥⠥⠤⠤⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠂⠀⡀⠀⠂⠁⡄⠀⠀⠀⠀⠀⠀⣅⢠⢁⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢀⣀⣤⣴⣶⠿⠛⡁⡤⠂⠁⠀⠀⠀⠀⣁⡀⠄⢀⣔⠅⠀⠀⢂⢂⠈⠊⠔⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢍⠉⠀⠂⠁⡐⠋⠉⠓⢄⠀⠀⠀⠀⠈⠙⠊⡀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠈⠲⠠⠀⠀⠀⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠉⠠⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣀⠅⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣲⡖⠚⠀⠀⠀⠀⠀⠀⠀⡤⠄⢁⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠒⠒⠪⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⠤⠤⠤⠤⠤⠤⠄⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣐⢀⠠⠄⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⣀⡠⠈⠁⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⠠⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣤⠀⠀⠈⠁⣰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⠵⠐⠊⠁⠀⢠⠴⠒⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠻⠃⡤⠊

⣷⣶⣶⣶⣷⡿⣷⣾⣿⡿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣿⣿⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⠿⡾⠷⠿⠿⣿⣿⠿⠷⡿⠿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣧⣑⢄⡀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⢷⣮⣕⡲⠤⣀⠀⠀⡈⠛⢦⣔⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢬⡛⠿⣷⣦⣝⡳⢬⣷⣄⠙⣿⣿⣦⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⣿⣿⣿⣿⣦⡌⠻⣿⣿⣶⣝⢿⣷⡘⣿⣿⣿⣆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣛⣿⣿⣿⣿⣿⣿⣿⣆⢘⣿⣿⣽⣿⣿⣭⣟⢿⡌⢿⣧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡌⣿⣮⣟⢻⣿⣶⣿⣿⣷⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⡌⣝⢿⣿⣿⢿⣎⣛⢿⣿⣿⣮⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣌⠛⠿⢿⣮⣿⣿⣿⢷⣍⣉⡙⠻⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⢿⣿⣿⣿⣿⡻⣿⡷⣤⣖⣲⡶⣦⡀⣀⠻⣦⣙⣦⣈⣉⣿⣿⣥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣰⣿⣿⣿⣿⣿⣷⡌⠙⠃⠉⣉⣉⣀⣛⣿⣿⣿⣛⣛⠻⣿⣷⣝⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠷⠄⠀⠈⠻⣿⣿⠿⠿⢿⣯⣟⢿⣌⢣⣬⣉⠙⢿⢟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣲⣄⣄⠘⢿⣧⠸⣿⣿⣿⠳⣽⣳⣿⣿⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⡇⢿⣿⣿⡗⠙⡹⡟⡿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠸⣿⠛⣿⣿⣿⣿⠿⣿⣿⣟⣉⡿⣷⠘⣿⢸⣿⣿⡷⠈⠁⠀⠱⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⢻⣿⣿⡄⠙⠇⠹⠛⣿⣾⣄⠸⡎⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠁⠘⢿⣧⠹⣎⣹⣻⠿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠄⠀⠀⠀⠀⠹⣷⣌⣉⣉⢉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡹⡿⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⢏⡏⠀⢀⣀⣠⣤⠾⣷⣶⣿⣤⣤⡄⠀⠀⠀⠀⢸⣷⡹⣎⡳⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡽⣁⡿⣸⣇⠀⢀⣿⣻⣿⣿⠿⠿⢿⣿⣿⣷⡦⠀⠀⠀⢸⣿⢿⣹⣷⡝⣖⢟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡫⡼⣱⢹⢳⢸⣿⡰⡿⡛⢹⡿⠋⠀⠀⠀⠑⢻⣿⣷⣄⠀⠀⢸⢿⢸⣇⢷⢻⣞⣎⢿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⡴⣱⣳⢣⡏⣾⢸⡞⣿⡷⡘⠀⢻⣅⣤⣀⠀⠀⡐⣹⣿⡏⠀⠀⢠⠇⣿⢸⣿⡸⡏⣿⡞⣎⢿⣽⣆
⠀⠀⠀⠀⠀⠀⣼⣱⣇⡏⣾⡇⣿⢸⣧⢻⣯⢉⠳⡦⣿⣿⣋⣤⠮⣶⣿⣿⢀⣠⡴⣣⡆⣿⢸⣿⡇⣧⢉⣍⢹⡜⣿⣟⣆
⠀⠀⠀⠀⠀⣸⢣⣿⣸⠃⣋⠃⣿⠘⣛⣃⢻⣎⢳⡘⣿⣿⣿⠓⢒⣿⣿⣿⣿⠋⢾⣿⢹⡏⣨⣤⣤⣹⡟⠙⢷⣷⢉⣉⠘⣆
⠀⠀⠀⠀⢰⡏⠾⠇⣿⣾⠛⣷⣿⡾⠟⠛⠻⢿⣆⢻⣿⣿⣿⠥⠀⢺⣿⡿⠉⠻⣧⠛⣼⡿⠁⠀⠀⠹⡇⠀⠈⢿⠋⠙⠻⣾⡄
⠀⠀⠀⠀⣾⣰⡿⢶⣿⠃⠀⢸⡏⠀⠀⠀⠀⠀⠹⡆⣿⡟⠘⣏⡩⠼⣿⣷⣿⣦⠙⣇⢿⠇⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠘⣷
⠀⠀⠀⢰⣿⠟⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢷⡟⢸⣿⣿⣦⠒⢉⣿⣿⣿⣦⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⡆
⠀⠀⠀⢸⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⣯⣛⣿⡻⣅⠔⢻⡿⣿⡇⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠛⠙⣯⠋⠀⠑⣏⡜⢻⣁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣴⣾⡿⠟⠻⡥⢿⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⡯⢼⠂⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣤⡾⢍⠟⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠑⠘⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣾⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣴⠀⣿⣼⠟⠁⠀⢀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡇⢾⠀⣿⣿⣿⣣⣆⣠⣤⣿⣴⣹⣾⣦⣤⢄⡄⣴⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣨⣿⣧⢸⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣽⣽⣿⣿⢿⣵⠆⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣿⣻⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣿⢿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣾⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⣧⣽⣿⣿⣗⣭⣻⢛⣻⣿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣽⣿⣷⡺⣞⢯⢭⣽⡿⣿⣿⣿⣯⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⡿⠷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣟⣳⣻⡿⣽⠻⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷⣱⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡻⣝⢯⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣿⣷⣿⣅⢈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⢿⣿⣟⡿⣟⣟⣿⣿⣿⣿⣿⣽⣯⡿⠟⢟⢧⢻⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣯⣿⢿⣿⣟⣿⣿⣿⣿⣿⣌⣝⣎⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣦⠌⠳⡽⣹⣟⡻⣿⣿⣷⣹⣿⡹⡌⢿⡿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⠿⢡⣿⣿⣿⣿⣿⣗⣿⣿⡿⠁⠀⠀⠈⢻⣿⣟⡀⣹⣤⣸⢿⢻⣿⣿⣷⣽⣱⡹⡜⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡠⢾⣶⣿⣿⣯⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣋⠙⣿⣼⣟⡏⣿⣿⣿⡿⣇⣧⢦⢿
⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠋⠑⠀⠀⢈⣤⣶⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣉⣉⡹⢢⡇⣏⣏⣿⣹⣿⣷⠾⠾⡜⡶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠀⠈⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠉⠉⣭⡆⡧⣯⢹⡸⡷⣿⣿⢺⡆⡃⢳
⠀⠀⠙⠿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢟⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠛⠉⢹⣟⣾⣧⡧⣯⣼⣵⣷⣿⣿⢞⡟⡟⢻
⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠀⠀⣀⣠⣴⡿⢟⣯⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣴⣿⣿⠉⠛⠿⢿⣷⣦⡼⢿⣽⢽⡇⣿⢼⢾⣿⡿⣿⣻⠿⡗⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣴⣾⣿⢿⣿⣷⣤⣤⡀⠀⢸⣟⣿⢾⢾⡿⣿⣾⣾⡿⡟⣿⢻⠏⡿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⡄⠈⠉⠛⢻⡿⢯⣏⣷⢾⢼⣿⣷⣿⣿⣿⣿⡟⡿⣾⢵⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣤⣼⢿⢶⡧⢾⡼⡞⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⣭⣍⢉⣿⠛⢿⠼⣷⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡞⣹⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡃⣿⡀⢿⡜⣿⣿⣿⣿⣿⣿⣿⣷⣏⣿⣧⡏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣿⣟⣛⣿⣿⣷⣯⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣰⠁⠘⣄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠰⢾⡛⠶⢦⡀⠀⢸⠀⠀⠀⠀⠠⠀⢀⡤⠶⠚⠋⠁⠉⠓⠚⠁⠉⠛⠲⠦⣄⠀⠸⠀⠀⠀⠀⢸⡀⠀⣠⠴⠆⢋⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠳⣼⠀⠀⠀⠀⠀⢟⡁⠀⠀⠀⠀⠀⠀⠜⢣⠀⠀⠀⠀⠀⠈⢙⠇⠀⠀⠀⠀⢨⡴⠋⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢸⡀⢀⠇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠁⠀⣀⣠⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠉⠑⠦⣥⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣩⡉⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⣧⠴⠋⠉⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡦⠦⢤⣄⣈⡷⢤⣠⠖⠁⠀⠀⠀⠀⠀⠀⢰⡁⠙⡄⠀⠀⠀⠀⠀⠀⠙⠲⢄⡠⢿⠁⠀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡛⠛⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠶⠶⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⣸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⡄⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡇⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠦⣤⠤⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠲⠤⠴⠂⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠘⠲⢄⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠶⠋⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⢀⡤⠖⠛⠚⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡠⣋⠴⢶⠋⠁⠢⣄⠙⢦⣀⠀⠀⡟⠉⠒⠢⢤⣤⢄⣀⣀⣀⣀⣀⣀⢤⡤⠒⠚⠋⠀⠀⣠⠞⠁⣠⠖⠉⢻⠶⣌⠳⡄
⠀⠀⠀⠀⠀⢠⣾⠟⠁⢠⠇⠀⠀⣴⠉⠳⢦⡉⠣⣴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠸⡠⠚⢁⡴⠋⢹⠀⠀⠀⢳⠈⠳⣌⢦
⠀⠀⠀⠀⢠⡟⠁⠀⢠⠏⠀⠀⢀⡏⠀⠀⠀⠙⢲⠇⠀⠀⠀⢠⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⡇⠀⠀⠀⢡⠖⠉⠀⠀⠘⡇⠀⠀⠈⢧⠀⠈⠻⣷⡀
⠀⠀⠀⢀⣏⣀⡀⠀⡎⠀⡀⠀⢸⠃⢀⣀⡀⢀⡜⠀⠀⠀⠀⢸⣄⠔⠊⠉⠁⠈⠉⠐⢦⣠⠃⠀⠀⠀⠀⡆⠀⣀⡀⠀⢷⠀⠀⠀⠀⢣⠀⢀⣘⣧
⠀⠀⠀⠀⠀⠀⠉⢿⠖⠉⠈⠙⣶⠟⠁⠀⠈⣻⠁⡆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡌⢰⡏⠀⠈⠙⢾⡶⠋⠉⠙⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⣆⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠠⣏⡀⠀⠀⠀⡴⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠳⢦⡴⠛⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡴⠋⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡝⠲
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠧⣤⠁⣠⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠤⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡠⠄⠀⠀⠀⡆⠀⠈⠛⢦⣀⠈⡆
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠉⠙⢻⠒⠒⠂⢺⡋⠉⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠈⠙⠳⠴⣎⣉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡜⠁⠉⠓⠲⠤⠤⣀⣀⡀⠀⠀⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣼⠁⠀⠀⠀⠀⠸⣦⣀⣄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⢶⠆⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠵⣶⠶⠶⠤⠭⣌⡭⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣲⢇⣤⡀⠀⠀⢀⡠⢀⠄⠒⠀⠀⢄⣀⠠⣆⠢⣀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣠⣔⣼⢚⣡⣾⣃⣀⠻⡁⠀⠠⠋⠁⠒⠚⠁⢍⠝⡲⢄⣰⠄⠁⠯⠍⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢊⡔⠕⠚⢉⣌⣭⠭⠭⣍⡉⠇⣵⡆⢠⡣⣣⣶⣿⡿⠿⠿⣶⣕⠨⡈⣢⡄⠀⠀⠙⠓⢨⡝⣶⣄
⠀⠀⠀⠀⠀⠜⢦⠚⢓⡚⢟⣹⣤⠙⣶⢡⠠⠀⠸⠹⡬⢐⣼⡿⠋⡠⠐⠒⠐⠤⡙⢿⣦⡈⠐⡄⠀⠀⠀⠀⠉⠁⣿⣦
⠀⠀⠀⠀⢀⡁⣘⣉⣭⣾⡏⠑⡥⢴⡷⠡⠀⡜⠡⠻⢠⣾⡏⢠⠊⠀⠀⠀⠀⠀⠀⢄⠻⣷⡄⢶⠄⠀⠀⠀⠀⠈⡔⣿⡇
⠀⠀⠀⠀⠀⠉⣟⠿⠚⡱⢁⠚⣰⠋⢀⠄⠗⡰⡷⠀⣼⣿⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⠹⣷⡆⠹⡃⡀⠀⠀⢚⢲⣯⡇
⠀⠀⠀⠀⣀⠀⠈⠒⠚⠁⠂⢸⡇⢐⠠⢂⠐⠀⠁⣰⠟⠉⡘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡘⢿⡁⠻⠒⡁⠈⣷⣿⡿
⠀⠀⠀⠾⢓⣿⣷⣦⡄⢚⣧⠘⣷⣤⣥⠒⠘⠓⢚⣡⣾⡋⢙⠀⣇⣄⠀⠀⠀⠀⠀⠀⠀⡱⣺⠪⠿⠿⠿⣿⢠⠏⠊
⠀⠀⠀⠂⠉⠝⠁⢺⡿⠉⠀⠑⠌⣙⠛⣤⣶⣾⡿⣪⠽⣿⡷⠦⠈⠉⠓⠀⣾⡿⡷⣶⠿⣿⠇⣀⡤⣤⣤⣋⠺⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠉⠽⠃⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠉⠉⠈⠨⠾⠟⠙⠁⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⣤⣤⣀⣀⣙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡟⢿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣼⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠹⣿⣿⣦⣽⣿⣄
⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣶⣿⣿⡿⢿⣿⣿⣷⡄⣦
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣿⣿⣿⣀⠉⠿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣈⣹⣷⠆⠀⠼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⣿⣯⣽⣛⡿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⡿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡼⣿⣿⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣵⣿⣿⣿⣿⣷⣯⣟⡿⣶⣄⣀⣀⣀⣴⡿⣳⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⡟⠁⠀⠀⠈⠙⠿⣾⣽⣟⣿⣟⣯⣾⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠩⣿⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠿⠟⠁⣿⠏⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⣿⣷⣽⣿⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡟⠻⠾⢿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠉⠀⠀⠈⠉⠛⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣤⣤⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣄⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠀⠀⠀⡀⢀⠀⡀⢤⠁⣘⠀⠀⠀⠀⠀⠂⠀⠐⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠄⠀⠀⠀⠀⡜⠀⡿⠂⠁⠀⠀⢹⢳⠀⠀⢀⠀⠀⠀⠀⣨⠄⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠒⣼⡃⠈⠀⠀⠀⠀⢁⢠⠀⠀⠂⠀⣁⣠⠀⡰⠀⠀⠀⠀⡀⠁⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠻⠀⡈⠀⠀⠀⠀⠘⠂⠀⠀⢀⠀⠙⠀⠀⠀⠀⠀⠀⠢⠈⢙⣋⡀⠤⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡛⠀⠠⠀⣀⣀⠑⠂⠀⠀⠀⠀⠀⡰⠀⠀⠀⠐⢀⣀⣀⣠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠲⡦⢀⣾⡿⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⣿⣧⢄⡚⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢸⣿⢧⣀⣠⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⣠⠾⣿⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠑⣠⢿⠸⣿⣾⣿⣿⠄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⢰⢧⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠳⣝⠹⢶⡿⠀⠀⠀⠀⠀⠀⠘⣷⠾⢏⡡⠏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣌⡀⠀⠀⠠⠀⠀⠀⠀⣤⡀⠀⠀⠀⢠⣦⠈⢀⡀⠠⠔⠁⢀⣡⣔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⡟⢦⡀⠀⠀⠀⠘⠦⡉⠁⠀⠀⠀⠈⣁⢚⠁⠀⠀⠀⡴⢛⠅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡤⠀⢘⠃⠀⠀⠀⠈⠁⠀⣀⠤⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠉⠓⢄⢀⡠⠤⣀⢠⠴⠶⣄⣸⠃⠀⠈⠀⠀⠀⠀⠀⡀⠀⠹⣄⡴⠰⢄⠀⡠⠤⣄⢀⠖⠉⠉⠓⢆⣀
⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠋⠀⠀⠘⠃⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⠀⠀⠀⠛⠀⠀⠀⠋⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣀⡀⠀⠀⠀⠂⠀⠀⣦⠀⠀⠀⠠⠆⠀⠀⠀⠀⠄⠀⠀⠀⠧⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⡛⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠠⡄⠉⠀⠀⠀⠀⠂⠐⠒⠾⣆⠀⠀⠘⡀⠀⠀⠀⢧⠀⠀⠀⢠⠇⠀⠀⠀⠆⠀⡠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠂⠨⠅⠙⠂⠀⠠⣷⠀⠀⠀⠘⣦⣄⣠⡾⠀⠀⠀⠸⢄⡚⠁⡠
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠐⠐⠆⠀⠆⡧⠰⠷⠆⠀⠀⠀⠫⢍⡩⠃⠀⠀⠀⠢⠼⠷⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠋⠂⠀⠀⠈⠁⠐⠀⠁⡠⠈⠀⠀⠆⠀⣀⠀⠀⠀⠉⣸⡄⠁⠀⠀⠀⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠁⠈⠀⠈⠁⠀⠉⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⣿⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣫⡾⠛⣡⡿⠁⠀⠀⣀⣤⡴⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⡿⢋⢀⣼⡿⢁⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣱⡿⢋⣴⠃⣾⣿⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⣾⡟⣱⣿⡿⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⣰⡟⣵⣿⣏⣀⣭⣴⣶⣾⣿⣿⣿⣿⡃⠁
⠀⠀⠀⠀⣠⢴⣿⣿⣿⡿⣿⣷⣶⣛⣁⣀⠀⠀⣰⢟⣾⣿⣿⣿⢟⣯⠷⣻⣿⣿⣿⣿⣿⣧
⠀⠀⣠⣶⣷⡭⢿⣿⣿⣿⢿⣿⣿⣿⣯⣅⡀⣼⢯⣾⣿⠿⣫⡾⣫⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠤
⠀⠘⢾⡏⠁⡄⢺⣿⠋⠁⠀⠈⣿⣿⣿⣍⣹⣯⣿⢟⣥⣾⡏⢾⣇⢸⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⡠⠂⠡⣾⠇⠀⠀⠀⣨⣿⣿⣿⣹⣿⡿⣡⣾⣿⣿⣿⣶⣦⣤⣭⡿⢿⣿⣿⣤⣄⡀⠀⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⡈⡿⠫⠾⣛⣯⣭⣷⡶⢛⣻⡭⢉⣥⣶⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡻⡎⢻⣃⠴⠛⠻⣿⣭⣛⠷⣬⣻⠀⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠶⢤⡀
⠀⣀⠰⣄⠀⠀⠀⣼⣿⣿⣿⡿⠃⠀⠚⠁⠀⠀⠀⢸⣿⣿⣿⣮⣝⡳⣽⣿⣿⣿⣷⣤⡀
⡶⣭⣿⣿⡗⠀⣂⣿⣿⣿⣿⣻⣄⡀⠀⠀⠀⠀⢀⣾⣿⣅⡲⠶⠶⢭⡑⠯⣛⡿⣿⠿⠿⣷⣦⣄⡀
⠀⠈⢻⣿⡀⠀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠿⠿⠛⠛⠒⠶⠶⠿⣿⣿⣶⣤⣀⠉⠙⠳⠄
⠀⢠⣿⠛⣷⣤⣿⣧⣚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣦⣄
⠀⠀⠀⢀⣾⣟⠁⠀⠉⢐⣿⣿⣋⢋⠛⡛⠻⠿⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡀
⠀⠀⠀⣼⣿⣿⠿⣿⣿⡟⠛⠋⢀⣸⣾⠑⢷⣦⣎⣼⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⢺⣽⣿⣷⣤⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⣩⣿⣿⠛⠿⣿⣦⡉⢌⣹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣷⣶⣟⡛⠉⠀⢲⣻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠛⠉⠈⣹⡟⠀⠀⠀⠦⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀⠈⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠈⠙⢿⣿⣆⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣶⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠯⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣶⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡕⣟⠳⡤⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⡿⠶⠅⣻⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣱⣭⣯⣟⢶⣤
⠀⠀⠀⠀⠀⢀⣾⣿⠹⣿⣟⢣⢸⠈⢾⣿⡦
⠀⠀⠀⢠⡀⠀⠀⣀⡼⢟⣷⡇⣿⠀⠀⢓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⡐⠂
⠀⠀⠀⠰⣙⠛⠻⣍⢿⣼⣇⢠⡽⡄⠀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠈⠛⠢⡈⣿⠿⠻⣾⣷⡙⣸⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⠁

⠀⠀⠀⠐⠀⢀⡠⠐⠀⠀⠠⢀⣴⣶⣾⡦⣶⠆⣴⣶⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠒⠻⣿⣿⢟⡻⠛⠂⠰⣿⣟⠛⠙⣿⠳⠐⣦⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡿⠏⠉⢹⣤⣄⠉⣙⢿⣷⠀⠉⠀⠐⢌⠁⢀⣸⢆⡘⢦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢿⣿⣧⣤⣴⣦⣬⣥⠀⠈⣿⣯⡀⠄⡤⠀⡎⣧⠘⣷⢎⣷⡈⢰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠞⣽⣿⣧⣿⡿⠛⡙⣦⡀⠤⠿⢧⣔⠶⣦⠠⠜⣦⡈⠻⢿⣷⠈⡇⠚⡄⠀⠀⠀⢀⠴⠒⠂⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⢀⣀⣠⣿⡟⠁⣽⢾⣿⣟⠛⠅⠠⠉⠉⢳⡷⠀⠉⠒⣋⣀⣈⢾⡉⠁⠒⡬⠄⠛⠖⣃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣽⣟⣋⠄⠀⣽⣿⣿⣉⠶⣈⣍⢰⣂⣈⡁⠀⠀⠾⢧⣄⡴⢊⡁⠸⡋⢣⡴⠐⠦⣿⠆⠀⠀⠀⠀⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⢀⣿⣟⣡⡶⠀⣷⣾⣽⣷⣈⢀⣿⡄⠠⠊⠩⡿⣄⣸⡦⠀⣁⠚⣍⡠⡠⠼⠖⢤⣆⠬⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠠⢊⡉⠀⠁⣴⣦⢹⡿⣿⡿⢿⡉⠳⢷⡀⠀⠴⠒⠈⣿⠓⣶⡗⢡⡈⠻⢿⣿⣿⡀⠙⠀⠻⠄⣤⠈⣱⡆⠀⠀⠀⠀⡼
⠀⠀⠀⠀⡄⠘⠄⠐⠀⣹⣟⠀⢿⡜⡇⢄⠙⢦⡀⠋⢠⠀⠀⢠⢻⡞⣿⣥⣤⣽⣦⣈⡿⠿⣿⣿⣷⣶⣦⡄⣾⡟⠣⣄⣀⣠⠜⠁
⠀⠀⠀⠀⠑⠠⠘⠂⠘⣯⡅⢸⡾⠁⣿⣌⠳⣎⢿⣦⡀⢿⠂⠀⣹⢂⡿⠛⠁⠀⠉⢹⠙⣧⡰⢆⣓⣘⠀⣁⠜⠁
⠀⠀⠀⠀⠀⠁⠀⡀⣀⡽⠇⠋⣴⡾⣹⣿⣆⠛⠘⢹⣿⣾⠆⠀⠃⠀⠁⠀⠀⠀⠀⣸⠀⢼⢟⣹⡋⣯⣈⡉
⠀⠀⠀⠀⠀⢠⠖⣉⠀⣴⣦⣴⢶⣾⠿⠋⣿⠄⠀⠈⠟⠛⠓⠀⠀⣄⣀⢀⣀⣠⡼⠃⠀⠶⡿⠛⠿⡧⠞⠁
⠀⠀⠀⠀⢠⠋⣾⡿⠧⣤⡄⢠⡿⠋⡀⢂⣾⠀⣠⡶⣀⢂⠄⠠⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢨⠀⣍⠁⢺⠏⢰⣿⢇⠐⣠⣿⡇⢸⡿⠃⡟⠉⠀⠀⠀⢀⠀⠄
⠀⠀⠀⢠⣾⠦⠀⠤⣀⠀⠛⣑⣡⣾⣟⣮⣷⣈⢁⣤⣷⢤⠄⠀⠀⠀⠐⠀⠀⢀⣶⡀
⠀⢀⡴⣿⠁⡀⣛⡀⠉⣤⢶⣟⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠀⢠⣤⢴⣤⡶⠶⠏⣩⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠘⠿⢿⣿⡿⠭⠤⣰⣯⣿⢯⣿⣾⣿⣿⠿⣿⣿⡀⢈⣴⣦⣌⣩⣞⣉⠉⢃⢾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠀⠈⠀⠀⠈
⠀⠀⠀⣾⣿⣶⣤⣸⣟⣿⢷⣻⣟⣿⡛⢿⠀⢿⠃⢡⢁⣯⣤⣶⣿⣿⡴⢢⣟⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⣴⢋⣥⠤⢴⣛⣞⡿⡳⢿⡟⣹⠇⡈⠀⣼⣷⣶⠀⣋⢺⣿⠛⠁⣠⣿⣽⣻⣄⠐⠍⠱⠀⠀⠀⠀⠀⠀⣀⣄⣤⣄⠀⢀⡅⠋
⠀⠀⠟⠺⣷⠐⣿⣿⣻⣿⣟⢿⡇⠀⠘⠃⣼⡏⢀⡀⠌⢠⣷⣦⡤⠀⢸⣶⣿⣿⡏⠁⢈⠁⢀⣤⠴⠟⠛⠉⢉⣉⠉⠙⠻⢿⣬⡅⡀
⢀⠀⠀⠀⣿⣤⣿⡿⣻⡿⣿⣄⡀⠀⠀⠀⣀⣴⣿⣇⠡⢰⣏⣥⡴⠆⢸⣿⣿⠁⠀⠛⢻⠂⠉⠀⠀⢀⡔⠐⠁⠈⡳⠀⠀⠀⢹⣟⡉
⠈⠤⠤⠀⡋⠀⢸⡷⠸⠇⠘⠿⠃⣠⠀⢀⡿⣿⡛⠁⠀⣼⣿⡿⡠⢂⡘⣿⣿⡷⠆⠀⠀⢸⠀⡀⣢⣶⡧⠀⠀⣶⠉⣆⠀⠀⠀⣿⠛
⠀⠀⠀⣰⡿⠗⠈⠀⠀⢀⠠⠀⡨⠉⠴⠉⢀⣿⣛⡃⠀⣿⣟⣿⣧⣿⣠⡞⠁⠀⠈⠑⠊⣹⠉⠈⠃⠀⠀⠀⠈⣿⡇⠎⠀⠀⠀⣿⠿⣄
⠀⠀⣠⡟⠀⡠⠖⢈⡠⠂⠀⠁⢀⣴⡶⢶⣿⣿⣿⣥⡄⢹⡿⣿⣿⣿⠋⠀⠀⠀⠀⣀⣴⠟⠳⠂⠀⠀⠀⢈⣿⡿⠃⠀⠀⠀⢰⣿⣧⡀
⠀⠀⢻⡇⡂⠀⢠⠂⠀⠀⠀⠀⠈⠉⢀⣴⣿⣿⡏⣩⠀⢀⢿⣿⠟⠁⠀⠀⠀⢀⡼⢛⣿⡀⣀⣤⣤⣶⣶⡾⠛⠀⠀⠀⠀⢠⣿⠛
⠀⢰⣸⣿⠀⠀⢺⠀⠀⠀⠀⠂⣒⠻⣿⣿⣿⣿⣿⣿⣦⣼⠛⠁⠀⠀⠠⢀⣴⠟⠙⠠⠀⣯⠙⠉⠛⠋⠡⠒⠄⠐⠆⣀⣶⣿⣯⡤
⠀⠀⠻⣿⡄⠀⠈⠳⣿⣿⡿⢻⣷⣆⣨⠟⠛⢿⡿⠟⠋⠀⠀⠀⠐⣀⠴⠿⡿⠓⠶⠲⠞⠉⠈⠦⢠⠉⠁⠀⠀⠀⠙⠉⠉⠁
⠀⠀⠀⢬⣿⣄⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⣴⣾⡇⠀⡒⢁⠤⠤⠀⠀⠀⠐⡟⠉⢀⠀⠐⠁⠈⠤⠀⢀⣀⡶⠤⠄
⠀⠀⠀⠀⠈⠉⠙⠂⠠⠀⢀⠀⡀⠀⠀⠀⣀⣀⡠⠤⠖⠛⠛⠋⠙⠛⠾⠀⠙⠀⠀⠐⠂⠐⠐⠛⠓⠊⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠶⣶⡲⠦⠤⣤⣀⡀⠀⠀⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠈⠉⠓⠦⣄⡀⠀⠘⣎⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠈⠙⢦⡀⠘⡆⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢖⡲⢽⣦⠀⠀⠀⠙⣷⠿⡀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠿⠶⠈⢧⠀⠀⠀⡸⠑⢬⡳⣄⣻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠤⠤⠤⢤⣄⣸⡆⠀⠀⠀⠀⠀⠙⢮⣻⡈⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠐⠛⢋⣹⠷⠲⢤⣀⠀⠀⠀⠉⠁⠀⠲⣄⠀⠀⠀⠻⣝⡃⣸⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠴⢯⡤⠤⣤⣄⣙⡷⠄⠀⠀⠀⠀⠀⢌⢫⠳⣦⣀⣀⡿⠚⢦⠇
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⢠⠟⠙⢿⡧⢀⡶⠋⢉⠀⠀⠉⠛⠋⠉⠋⠁⠀⠀⠙⡲⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠠⢻⠇⠀⢠⡏⠀⠀⠲⢤⡞⠀⠀⠙⠲⢶⣤⣤⣀⠀⠀⠀⠀⠸⢷⡄⠈⠉⢹
⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⣾⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⣿⣿⣎⣿⣦⡀⠀⠀⠈⠁⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⣸⣼⡄⠀⣿⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠘⢿⢿⣿⠀⢉⠝⠛⠛⠙⡳⠶⠃
⠀⠀⠀⠀⠀⠀⢸⠀⢧⠀⢿⠀⠀⠀⠀⠀⣠⠖⠋⠉⠓⠦⣄⠈⠳⡹⣷⡀⢠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠈⢧⡘⣧⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠳⡄⠙⢮⣹⣿⢄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⣷⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀⠈⢉⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣽⣦⣀⡀⠀⠀⠀⠀⠀⠁⢷⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠄⠀⠀⠀⠀⢶⣿⠟⡿⠁⠀⠃⠀⠀⠈⠀⠀⠀⠴⠆⣀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠘⢡⡞⠀⠀⣀⠀⠀⠀⠒⣠⡀⣠⡴⠂⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣷⣶⠶⠦⠒⠋⢀⣠⣾⠁⢈⣤⡔⣺⡿⠛⠁⠀⡤⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⣺⣿⡿⠟⠛⠉⢡⡄⣠⣦⣴⡿⠿⠛⠛⠿⠿⠿⠛⠉⡁⢠⠄⠃⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣋⠁⣴⣦⣰⣿⣶⣿⡿⣿⣿⡟⠀⣿⣆⠘⣷⡀⢰⡇⢸⡇⠈⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⢰⣄⣿⣼⣿⣿⣿⣿⣿⡁⠠⠀⠠⠛⣦⠘⢿⡄⢻⠂⢨⡇⣴⡁⠀⠀⣴⠶⠋⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⣤⣽⡿⣿⣿⣿⢿⡿⣿⣿⣿⣷⣶⣤⣀⠈⢸⣇⣸⠀⣼⠀⣾⣿⣿⣛⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⠽⢀⣉⢁⡀⠀⣀⡀⢿⣉⣻⣿⣿⣿⡆⢸⣿⡟⢰⣯⣾⣿⣿⠋⠁⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣶⢋⣵⣯⣥⣤⡌⠱⠟⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⡀⠀⠀⠆
⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠹⠟⢿⣿⣿⡟⠋⣰⡟⣠⠂⣰⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠙⢓⠀⡀⠀⠀⢀⣀⡤
⠀⠐⢤⣴⣚⣫⠿⠛⠁⠀⣄⣴⣾⣿⣿⠆⠰⣿⢁⣟⣴⣿⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣟⠛⠛⠁⠉⠁
⠀⠀⢸⣿⣟⢁⣤⣶⣾⣿⠿⢿⠻⣿⣿⣷⣿⣿⢈⣿⠿⣠⣿⣿⣿⣿⣿⣿⡟⣿⣿⠋⣛⣿⣿⣟⠁⠄⠈⠉⢷⡄⠀⠀⠀⠀⠒
⠀⠀⣠⣿⣿⣿⢿⣟⠋⠙⠀⠀⠠⢸⣿⣿⣿⠇⣿⠧⣴⣿⣿⣿⣿⣿⣿⣿⣟⠁⢉⣿⠟⠉⢯⣹⣷⣶⣦⣀⡂⠀⠀⠀⠀⠘⠁
⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢸⡿⣼⣿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣦⣤⠞⢿⡦⣬⠙⣿⣿⡓⠳⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠡⣾⣷⣿⠁⠀⠀⠀⠈⢿⣿⣿⠾⣷⠒⠙⢻⡀⢀⣾⡛⣿⣧⡈⠉⢳⠀⠀⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡇⣠⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣯⠀⣾⡧⢤⡞⠋⠋⢻⣧⠀⠘⣿⣦⡀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣽⡀⡴⢟⠿⠟⠉⠀⠀⠀⣰⣿⣿⣄⣀⣶⣀⣤⣦⢆⣤⠼⣿⣦⣶⣿⣿⣷⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠁⠀⠀⠀⠀⠀⠀⣠⣼⣿⡟⠋⠉⣉⠛⢿⡟⠀⠈⣿⣿⣿⠛⣿⣿⣿⡿⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣯⣉⡉⠑⢶⠷⡴⠿⠟⠘⡆⢻⣿⣿⣤⢻⡿⣧⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⣷⣆⡈⠉⠙⢶⣿⣴⣿⠀⣰⣾⣿⡿⢿⣿⡏⠞⠃⠈⢿⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⣿⣥⠒⠈⠙⠛⢳⣦⣶⣶⣿⠋⢿⣿⠛⠻⣿⡁⠸⢿⣧⠀⠀⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡷⠖⡟⠋⡁⠙⠿⢶⣾⣷⣿⣿⣿⣦⣈⣿⣟⠀⢻⣷⣴⢾⠛⢆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠛⠛⠻⠛⠑⢿⣧⣾⣿⣿⣿⣿⣿⢩⣿⡿⠋⣿⢿⡄⢻⠟⢷⠈⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⣸⣷⣶⡀⠈⠳⠀⠙⠀⠀⠀⠐⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠈⠛⠉⠉⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠂⠀⢀⠀⠀⠀⡶⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣹⣿⣿⣷⣶⣦⣶⣴⣷⣾⣿⣿⣿⣿⣿⣿⡿⣿⣭⢿⡑⣆⠰⠈⠀⣈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⣿⣿⣯⣈⣱⣤⣼⣿⣿⣿⠋⠄⠈⢻⡿⣷⣿⣿⣷⣿⡅⢺⣟⡛⢡⣤⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢴⣿⣗⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣽⣿⣿⣿⣿⣿⣿⠁⠠⠀⡷⠄⢹⡋⢸⣿⣿⣿⣿⣿⣿⣿⠘⠻⠿⣦⠉⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣿⣿⣿⣿⣿⠛⠏⠰⣤⠀⠀⢂⣾⠁⠈⠛⠋⠻⣿⣿⣿⣿⣷⣄⠀⣁⠀⠀⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠹⣿⡏⠠⠀⠲⠈⣉⠋⠠⠀⢀⠀⣐⠀⠀⠈⠋⠹⡿⠙⢿⡄⠈⠂⠈⠟⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠛⠀⠀⠠⢀⡈⠁⠀⠀⠁⠀⠀⠀⣠⠀⠔⠀⠀⠈⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠁⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⢉⣾⣠⡾⠡⣐⣿⠲⠂⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠆⣩⣷⣿⠿⢷⣗⣒⢻⡿⠟⠛⣲⠒⠅⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡂⠁⠂⠀⢙⠃⠀⠀⠈⠋⠀⠉⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⡀⠛⠀⠀⢺⠀⢠⠀⠀⠀⠀⠖⠀⢢⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠁⠄⠀⠀⠎⠁⠚⠟⠀⠀⠤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠔⠛⠒⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⡀⠀⠀⠀⠀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢶⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢍⠀⠀⠦⡐⠉⠀⣈⠂⡀⠀⢳⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣦⡀⠀⠾⡿⣿⡗⠿⣧⡴⣷⣠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⢰⡶⠿⣿⣿⣦⣄⠈⠈⠈⠫⠉⢀⠈⠛⠀⠷
⠀⠀⠀⠀⠀⢀⠄⠀⢠⡼⠋⠀⠐⣾⣷⣆⣈⠁⠀⢀⡀⠀⠈⠑⠄⠁⠻⠺⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠒⠾⣿⣛⠛⢹⡇⠄⡘⢿⣿⡶⣦⣀⠀⠀⣶⠙⢃⢠
⠀⠀⠀⠀⠚⠂⠀⣼⠀⠀⠀⢀⣀⣿⣿⡷⠄⡙⢶⠀⠀⣅⣵⣧⣿⣶⣤⣴⡊⠚⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⣾⡝⢻⣯⠘⠄⠈⠁⠂⠀⠊⠀⠥⠀⠤⠂⡓⠂⠀⢤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠘⢿⣿⠍⢵⠀⠀⠘⢇⣶⣦⣤⣀⣀⠀⠀⠀⠙⢶⣮⠸⢩⡉⠒⢂⡂
⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⣼⣷⡶⣮⣦⡀⠘⠂⠘⢻⣿⣿⣿⣿⣦⡀⠀⠀⠉⠀⠈⠛⢀
⠀⠀⠀⠀⠈⠃⠀⠰⡀⠀⠀⠀⠉⣿⡇⡙⠿⠿⣄⣂⡀⠠⢻⡟⣌⠻⢿⡟⠑⠲⠠⣦⣤⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠈⠺⢣⡀⢄⠀⠨⠷⣄⠀⠘⢽⣆⠀⢿⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠚⠳⣆⠀⡻⢦⣾⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠈⢂⠰⣯⢿⡿⣖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⠫⢰⡻⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⠳⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠑⠄⠀⢠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀
⠀⠀⠀⠀⣀⣤⣶⣿⣩⠁⠠⣀⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣁⠀⢩⡹⣿⣶⣄⡀
⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⣶⣿⠹⡟⠛⢠⠀⠀⠀⠀⠀⠀⠀⢐⡀⠾⠛⣁⣹⡇⠀⣿⣿⣿⣿⣿⣦⡀
⠀⡰⠋⣱⣿⣳⣟⣿⠿⠿⢻⣿⣷⣤⡴⠏⠀⣆⡀⠀⠤⢤⣀⡄⠙⢦⣼⣿⣿⣧⣴⣿⣿⣷⣻⣧⡙⢷⡄
⠀⠀⢀⡟⢡⡿⢹⡏⠀⠀⠀⢀⣻⣿⡇⠁⠜⠙⠑⢄⠀⠈⠟⠂⠀⢾⣿⣷⡄⠀⠉⠻⣿⠹⣧⠹⣧⠀⠁
⠀⠀⠘⠁⢸⠁⠈⠁⠀⢀⣠⣼⣿⡿⠁⢈⠀⡠⠔⠁⠈⡘⠀⠀⡇⠸⠿⣿⣿⣤⠀⠀⠹⠀⢹⠀⢹
⠀⠀⠀⠀⠘⠀⠀⠀⣀⣴⠟⠋⠀⠀⠐⠚⡟⠀⠈⡄⠒⠒⠒⠻⠧⠀⠀⠀⠈⠙⢿⣄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠂⠠⣴⣄⡤⠔⠀⠀⠀⠀⠀⠀⠀⣠⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⣀⣶⣾⣧⣤⣤⣞⡅⡀⠀⠀⠀⠀⠀⠰⡄⣄⠠⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡁⢀⣴⣶⣇⣤⣤⡄⠀⠀⠀⠀⠀⢠⢆⣼⣤⠾⠟⠻⠉⡉⠉⠉⠛⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⣛⠻⡟⣦⣲⣤
⠀⠀⠀⠀⠀⠄⡀⡀⠠⠀⠈⣉⠙⠟⣩⡥⣶⣶⣧⡄⠀⠀⣦⣿⠟⠉⠀⠀⡰⢤⣦⠵⠄⡄⠀⢸⣿⡟⢡⡾⣦⡤⠈⠀⠀⠈⠳⣼⣿⣿⣽⣷⣶⡄
⠀⠀⠀⢀⣀⣀⡨⠀⢜⠂⡡⠀⠀⡂⠐⠒⣼⠟⠁⠀⢀⣿⠋⠀⠀⡠⢢⠀⠀⡟⣨⡓⠀⠁⢀⣼⡿⠁⠘⢀⠟⠀⡀⠀⠀⠀⢻⣿⠞⢻⡦⣌⠻⣷⡁
⠀⡐⠋⠀⡠⠒⡄⠀⠉⣁⣄⣠⡖⠙⢐⡀⣻⠀⠐⣼⡟⠁⠀⣠⡂⠃⠀⠀⠀⠃⢀⡕⠀⣠⡾⡿⠓⠀⠀⠘⠀⠃⢐⣧⣴⣤⣤⠀⠉⠹⠟⣹⣆⠈⠇
⠀⢇⠀⢠⠀⠀⠀⢈⣉⣡⣬⠿⠁⠶⠋⣤⣠⢀⣷⡟⠀⡴⠛⠁⠀⠀⠀⠀⢀⠀⢉⡤⠾⣿⠟⠁⠀⠀⣀⣤⣶⠟⠛⠉⠛⠋⣻⡇⡀⠀⠀⠀⠻⠄
⠀⠀⠉⠁⠀⠀⠀⣿⠒⠁⠁⠀⠇⢀⢔⡽⠃⣿⠟⠀⣸⠏⠀⠀⠀⠀⢠⣴⣀⣶⣿⠓⠀⠀⠀⢠⣴⡞⠁⠀⠀⠀⠀⠀⣠⡴⢾⠃
⠀⠀⠀⠀⠀⠀⠂⣁⢠⣀⠀⠀⢠⢀⣞⣱⣿⣿⡆⣸⢗⠀⠀⠀⠀⢠⡿⠋⠈⠝⠁⠀⠀⠀⣄⣿⡟⠀⠀⠀⠀⠀⠄⠞⠃
⠀⠀⠀⠀⠀⠠⢇⠉⠉⠉⠀⠀⠈⠻⠿⠿⣿⢿⢍⡱⢉⣀⣄⠀⢄⣿⠃⠐⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⡈⢉⣁⡌⢉⣩⠏⡀⢩⣿⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠊⠁⡀⠠⠸⣿⣶⣄⣀⣀⣠⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠋⠙⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⣶⢶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣴⣷⡟
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣷⡄⠀⠀⠀⣀⣴⣶⣾⣷⣿⣶⣢⣤⣀⡀
⠀⠀⠀⠀⣠⣹⣿⣿⡟⠉⣿⣿⡗⠀⣠⣾⢟⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠘⠛⢿⡿⠈⢀⣾⣿⡏⣀⣶⣿⣤⣟⣫⣷⠄⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣆⣀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢹⣿⠃⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣈⣿⣿⣿⢿⣽⣿⣿⣾⠛⠁
⠀⠀⠀⠀⢐⣶⣄⣀⣤⣤⣽⣿⡿⠛⢻⣶⣾⡇⠀⠀⠀⠀⢠⣿⣀⣹⣿⢿⣽⡍⠳⣿⣿⣾⣿⠿⠟⠹⡿
⠀⠀⠀⠀⠀⠞⠛⠏⠉⠉⠉⠛⠛⠛⠀⠈⠁⠀⠀⠀⠀⠀⠒⠻⠋⠉⠉⠉⠉⠀⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢠
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⡆
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠻⣷⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠙⠻⢷⣦⣄⣀⢙⣷⣌⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠻⣇⢷⣸⡄
⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣧⡀⠙⠻⣦⣄⠀⠀⠀⠀⠀⢹⣯⢻⣇
⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⠿⣦⣄⠀⠀⠈⢻⣧⣿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠿⠿⠿⠿⢿⣿⣿⣷⡄⠀⠈⠛⢿⡆⠀⣶⣻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡶⠀⠀⠠⣤⠾⢿⣿⣿⡇⠀⠀⠀⠀⢹⡄⣿⣿⣯⣿⣿⣆
⠀⠀⠀⠀⠀⣴⠏⠁⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠈⢿⣿⠙⣿⣿⣿⣿⣄⣦
⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⡿⠃⠀⠀⣠⣴⡶⠿⣂⣤⣶⡦⣰⣦⠀⠀⠀⠀⢾⣿⣷⣾⣿⣝⡿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣾⣿⡿⡛⠁⠀⡴⠟⠵⢛⢁⣾⣿⣿⣴⣿⠿⠿⠄⠀⠀⣶⣾⣯⡙⢿⣷⣌⢻⣝⣿⡷
⠀⠀⠀⠀⠀⣾⣿⠋⣾⠁⠀⠼⠁⠀⣰⠃⣾⣿⣟⣿⣷⣄⢿⣷⣀⡀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⠃⢸⣿⠀⠀⠀⠀⢀⡟⢸⣿⠻⣿⣮⡻⠏⠀⠙⣿⠇⠀⢨⣧⣙⣿⡿⢿⣿⣯⣿⣿⣻⣆
⠀⠀⠀⠀⠀⣿⠀⢸⠏⠀⠀⠀⠀⢸⡇⢸⣿⣷⣜⠿⣿⠀⠀⠀⠁⠀⠴⠿⣿⣶⣬⣱⢎⡻⢿⣿⣿⣿⣛⣧⣰⡆
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⣌⡿⣿⣮⡀⠀⠀⠀⠀⠀⠀⢸⠟⣿⢿⣿⣿⣧⣙⠻⣿⣿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⣿⡀⣿⣿⢿⣮⣝⣃⠀⠀⠀⠀⠀⠀⡟⠀⠁⢸⣿⣿⠿⣿⣿⣌⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠹⣷⡘⢿⣶⣭⡻⠿⣧⠀⠀⠀⠀⠀⠃⠀⠀⢸⠃⠉⢀⡟⢿⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⡹⣷⣌⠻⣿⠻⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡿⠁⠘⢿⣷⣌⠳⣶⣭⣛⡻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡙⠿⣷⣦⣙⠻⢿⣿⡟⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣈⠙⠻⣿⣶⣬⣍⡛⠲⢄⡀⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠀⠉⠙⠻⢿⣷⣶⣤⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣄⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢠⠄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠲⠾⢤⡤⢶⣉⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠏⠀⠐⠒⠢⠀⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡠⢄⣀⣀⠀⠸⢀⠀⠆⠁⠀⠂⠀⠀⠀⠀⠀⠹⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠴⠋⠁⠀⠊⣤⣄⠙⢦⣵⢽⠀⡰⠆⠀⡃⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⠔⠀⠀⠀⠀⠈⠛⠃⠜⠙⢷⠶⠦⣤⠔⠁⠀⣀⣀⣀⣀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠊⠁⠀⠀⠉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣠⣴⠶⠦⢤⣀⡀⠀⠀⠀⠀⠀⣀⡴⠓⠀⠀⢀⡜⠁⠰⡖⠈⢉⢭⡶⢖⣢⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠚⠁⠘⢦⡀⠀⠀⠉⠉⠓⠒⠂⠉⠀⠁⠀⢀⣴⠫⡒⢒⡖⠛⡆⣎⢓⢳⢦⠈⠉⠳⢽⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡙⠒⠦⠤⣄⣀⣀⢀⡤⠤⠲⢎⠁⢫⠂⠘⡿⣅⠑⡶⡎⣮⡀⠑⡱⡀⠀⠀⠑⠕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠉⡇⠀⠀⠀⠀⠀⠀⡷⠤⠀⠘⢇⠀⠳⣴⡏⢸⣠⢃⠇⣽⡇⠀⠸⡄⠀⠀⠀⠈⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠓⡝⠂⡷⠊⠉⡿⠀⠀⣠⠟⠄⣀⣀⣼⠀⠀⠈⡿⠞⡡⠊⢀⣿⠀⠀⠀⠇⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢄⣈⡀⢜⠋⣠⢶⠞⢣⡀⠀⠀⠀⡾⡠⠀⠀⠈⠺⣗⢀⢸⠃⠀⠀⠀⢸⠀⢀⠄⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢛⡵⡷⢚⡉⠉⠓⢤⡞⢹⡀⠀⠈⡆⠀⢹⠸⠃⠒⠀⠠⢄⣬⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⢣⣏⠀⠀⣀⣠⡉⠉⠑⠀⣠⠃⠀⢸⠇⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠡⠀⠀⠙⠲⠾⠍⡇⠈⠓⠒⠒⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡏⠀⠀⠁⠢⠄⣀⣀⣈⣇⡤⠶⠶⠶⢤⣀⠀⠈⡧⠀⠀⠀⠀⠀⠀⡤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣧⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠈⢆⠀⠻⣄⢀⠀⢀⣠⠞⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣯⠑⠤⡀⠀⠀⢰⠃⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠛⠉⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢹⡄⠀⠀⠉⠁⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⣦⣀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⢶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡖⠈⠧⣌⣉⣉⣀⡽⠦⠤⠤⠀⢹⡦⢤⣤⣠⣤⢤⠖⣻⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣼⣄⣸⠁⡤⠒⠂⠀⢀⣀⣀⣠⣇⣤⠴⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⡾⣇⠀⠀⣾⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙

⢀⡀⠀⠐⠀⠄⠀⠠⢀⠀⢀⠱⣧⣾⢻⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠃
⢸⣿⣷⣦⣤⣄⡴⠧⠆⠑⣼⡷⠾⢿⣿⣿⣭⠿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡄
⢸⣿⣏⡆⡏⡿⢫⢳⢴⣏⣁⣤⣰⡶⠛⠿⣿⣇⠈⠻⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡇⠀⢀
⠈⣿⣼⡿⣧⣄⢨⢸⠇⣯⠏⢿⣿⣿⣧⣀⣤⠝⠛⠓⠟⣿⠳⠈⠂⠘⢳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡠⠁
⢠⡿⠛⠄⠌⠛⢿⣿⣦⡇⠸⣞⢿⣿⣯⢍⣷⣷⠀⠄⢀⣀⢠⣄⠀⠀⠀⠉⢙⠃⠻⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡟⠀⣠
⠈⠀⠀⠀⠀⠀⠘⣿⡿⢿⢆⠹⡞⠚⣽⣿⠟⣧⠾⠷⠾⢿⡿⢿⣷⣶⣄⠀⠀⠙⠦⣄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⣧⠞⠀⢠⠃
⢀⠛⢶⣖⠤⠤⠄⠛⠳⠦⣧⣱⡄⠓⠶⣍⣙⠶⢽⣥⡶⡶⣶⢮⣁⣉⣉⡻⣷⠀⠀⠈⠳⡈⠢⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⣸⠇⠀⣰⠃
⠀⠀⠀⠝⣟⣶⣦⣦⣠⣤⠀⠌⠡⣤⣶⣌⡉⠒⠺⠶⠖⠒⣲⣄⠹⣧⣤⡽⠦⣤⠀⢀⡖⠨⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠁⠀⢰⡏
⠀⠀⠀⠀⡩⠟⠛⠉⠉⠀⠀⡀⣰⡇⣿⢭⣟⣿⣄⠉⣠⠤⠿⣝⠷⠄⠀⣀⢀⠀⢠⠈⠋⡛⣢⠀⡇⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠪⠟⠀⢀⡟
⠀⠀⣉⣉⣐⠻⠿⢷⣶⣶⡆⣱⡼⣟⠿⣮⡛⡿⠛⢏⢇⡄⠀⢈⢧⠀⠙⣿⣮⣆⣈⣥⣤⣶⣌⣀⣀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣞
⠈⣿⠁⠀⠀⠀⠀⠀⠟⢻⣗⣈⢻⢚⢻⣭⣻⣿⣾⣮⡄⠁⠀⣸⠀⠈⠀⠙⠴⣿⠟⡧⠏⡟⣸⢾⣹⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡾⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢬⣤⣿⣿⣖⣄⢹⡆⠀⠀⡟⢆⠐⠀⠀⠀⠀⠀⠀⠘⠀⡙⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⣾⠁
⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠙⢧⠀⠀⡇⡀⢱⡌⡄⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⢀⡾⠁
⠠⣄⣠⡷⠖⠠⢄⠀⣿⡀⢀⡀⠀⠀⠀⠀⠀⠁⠀⢀⠘⠀⢢⠝⣰⠌⡇⢠⠀⢍⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⢄⠞⢻⣄⢆⠨⣥⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⢄⠀⡤⠒⢦⣀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⣄⢨⠆⢫⡿⣦⡁⡈⠲⣥⡦⠠
⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣳⠟⣿⡮⣳⣶⣦⣿⣷
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⢬⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠘⣧⠟⠛⠋⠉⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⡴⠃⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⠶⣦⣶⠶⡿⢇⠐
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠋⠀⠀⠀⢸
⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⠶⠶⠶⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠈⠉⠛⠷⢦⣄⡀⠀⠀⠀⠀⠳⡌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠹⣆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠻⣦⡀⠀⢿⡄⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢶⡶⠦⣬⣻⣦⠀⠀⠀⠀⠈⠹⣶⢾⣇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡉⠙⣷⡀⠀⠀⠀⠀⢸⡦⣍⠳⢤⡀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠟⠛⠋⠉⠀⠘⣷⠀⠀⠀⠀⡸⠁⠈⠳⣤⡙⢦⣸⡏⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠤⠤⠤⠤⣤⣤⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣹⣆⢸⡟⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⠶⢶⣶⣤⣄⡀⠀⠀⠀⠈⠉⠙⠛⠦⠀⠀⢤⡀⠀⠀⠀⠀⠈⢿⡛⠶⠇⢸⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣄⡀⠀⠀⠙⠲⣄⢸⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣶⠶⠶⠶⠤⣤⣄⣘⡛⠦⠀⠀⠀⠀⠀⠀⠀⠲⣌⢳⡈⢿⣶⣄⣀⣀⡟⠉⠙⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⣠⡟⠉⠻⣿⣯⠁⢀⣴⠞⠋⠉⠀⠀⠈⠙⠛⠚⠛⠙⠻⠍⠁⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡟⠀⠀⠀⣰⡟⠀⠀⠀⡈⠓⢠⡾⠁⠀⠰⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⠄⠙⢶⠚⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⢠⡿⠀⠀⠀⠈⠉⠻⣿⠇⠀⠀⠀⠀⠈⠙⣿⣿⣷⡶⣤⣀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⢀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⢀⣽⣷⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⢹⡟⣿⣿⣿⡏⠉⠝⠲⣶⠴⣶⠶⠶⢤⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠛⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡶⣤⣀⡀⠀⠀⠙⢿⡻⣿⣧⠀⠰⠉⠀⠀⠀⢱⡤⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉⠛⠶⣄⡀⠈⠳⣜⢿⣷⣀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠻⣄⠀⢿⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢦⣙⢻⣿⣧⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢷⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠉⠓⠿⠷⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⣷⣄⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⡆⠀⢀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣦⣬⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣧⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⢷⣄⣈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣴⣿⣿⡿⠻⡦⠀⠀⠀⢤⣀⣉⣻⣿⣿⣿⣷⣤⣠⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣋⢹⠁⠀⠀⠀⠑⠶⣤⣌⣽⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣯⣿⠄⠀⠀⠀⠀⠀⠀⡀⠹⣿⣽⣻⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⠂⡤⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⢸⣦⣶⣿⣶⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣟⣻⣿⢆⡽⠀⢀⣤⣿⣿⣿⣿⠟⡿⢿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢰⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠉⣩⣿⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣷
⠀⠀⠀⠀⠈⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣿⣿⡥⡆⠀⠾⠁⣻⣿⣏⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣄⠀⠰⠏⠙⣿⣷⣌⢉⠓⠲⠦⣤⣀⠀⠀⠀⠀⠀⣠⣇⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣤⣀⡘⠡⠟⠻⣿⣷⣶⣄⡀⠈⢙⠶⣄⣠⣼⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⣶⣟⣛⠻⠿⠿⢿⣦⣀⠤⠚⠻⣿⣿⣿⠿⠛⢿⣿⣿⣿⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠛⠻⠿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⡬⠒⠩⢻⣆⠂⠉⠉⣻⠏⠀⠀⠈⢿⣿⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣍⣳⣯⣿⣿⠛⠋⢙⡆⠀⠀⠀⢸⡿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢉⡇⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠚⢻⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⣨⣥⣾⣻⣟⢿⣿⣿⣿⢋⣿⡥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣾⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⠀⠀⠀⠀⠙⢻⣿⠁⠀⠀⠀⠟⠀⢬⣿⣿⣿⣿⣿⣿⣯⠛⢤⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡖⠀⠀⠀⣀⣾⠟⠀⠀⠀⠀⠠⣄⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣆⢀⠙⠋⡁⠀⠀⠀⠰⣧⣤⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣶⣿⣦⣷⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡿⣿⣿⣿⠿⡿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⠀⢰⣦⣿⣷⣿⣿⣿⣷⣦⣄⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⡀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⢿⠋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⠁⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⠿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢠⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠁⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⡿⢿⡗⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠃⠈