Suns Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠰⠃⠀⢠⡎⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠁⠀⠀⣤⠀⠀⠀⣠⣿⠁⠀⠈⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢳⣄⠀⢀⣴⠿⣤⣤⠞⠁⠹⣦⣤⣤⠀⠀⠠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠈⣏⠛⠛⠁⢀⣀⣀⣀⠀⠀⠀⠸⣇⡀⠀⠀⣀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢶⠖⠃⣠⡴⠚⠉⠉⠉⠉⠙⠳⢤⡀⠈⠉⠉⠉⣹⠟⠁⠀⡠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⠶⠟⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢿⡀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣽⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣄⠀⠉⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⣾⣁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣀⣙⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⣾⠁⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠖⠛⠁⠀⠀⠐⠳⣄⠀⠀⠈⠙⠶⢦⣤⣤⣤⠴⠞⠋⠀⠀⠀⣼⠉⠉⠂⠀⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⡟⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢻⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠁⠀⠀⢸⠶⢦⡀⢠⠞⠛⠳⠞⠉⠙⠳⣼⣇⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⢠⡀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⡟⠀⠀⣰⠀⠀⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⡿⠀⢠⠀⠀⠀⠀⠀⠀⣠⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢦⡀⠀⠀⠀⢹⡆⠀⠀⠀⠸⠇⢠⡿⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣠⡴⠶⠛⠛⠛⠛⠛⠻⠶⣤⡀⠀⠈⠁⠀⠀⣠⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠈⠛⠲⢤⡀⠀⠀⣠⡾⢋⠔⠊⠁⠀⠀⠀⠀⠀⠲⣌⠻⣦⠀⠀⠐⠛⠉⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⡀⠀⠀⣼⡟⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣧⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⡿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⣿⠃⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠶⠶⠶⠄⠀⠀⠹⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣠⡿⠃⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣐⠒⠶⠖⠒⢋⣁⣤⡾⠋⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠘⠳⢦⣄⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⢠⡀⠘⣧⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢠⡟⠀⣾⠃⠀⠀⠀⠀⢷⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣼⠃⢀⡟⠀⠀⠀⠀⠀⠈⠁⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢰⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻⣿⡏⣿⣿⢟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠻⣿⡎⢻⡇⣹⠟⢸⡿⣋⣽⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡈⣧⠾⠚⠓⠾⣥⠴⠀⠀⠀⠀⠀⠀⣿⣿⣿⡻⠿⠷⣄⣿⠾⠛⠛⠾⣯⣤⠿⢟⣛⣿⣿
⠀⠀⠀⠀⠀⣄⣹⠃⠀⠀⠀⠀⠘⣗⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢦⣽⠃⠀⠀⠀⠀⠘⣷⠶⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠤⢽⡄⠀⠀⠀⠀⢠⣏⠙⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⠶⢿⡄⠀⠀⠀⠀⢠⣟⠳⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠖⢛⡶⢤⡤⡶⢻⡀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣭⣵⣶⠛⣻⡶⣤⣤⡶⣿⠙⢶⣶⣮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣩⣾⡇⣴⣏⢸⣧⡸⣿⣧⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣸⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⡄⠀⢷⣄⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡆⢸⣿⣷⢠⣿⣿⡇⠀⢀⡆⠀⠀⠀⣠⣴⡶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣦⣻⣿⣿⣧⣿⣿⣿⣿⣿⡿⣠⣴⣿⡇⠀⢠⣾⣿⡏
⠀⠀⠀⠀⠘⢶⣤⣤⣤⣤⣤⣀⠀⠈⢿⣿⣿⣿⡿⣟⣿⣯⣽⣿⣻⢿⣿⣿⣿⣴⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣶⣬⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⡿⠛⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣙⣿⣿⢧⣿⣿⣭⣭⣻⣿⣿⡿⠿⠿⣿⣿⡽⣿⣶⣶⣴⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣾⣿⣟⣶⣿⣷⣿⣿⣟⣋⣁⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠂
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⢿⣿⣞⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣻⣿⣯⣍⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣤⣶⣿⡿⠿⠋⠁⢠⣾⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣷⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠉⢉⣼⣿⣿⣷⣯⣿⣿⣿⣯⣽⣾⡟⠿⣿⣿⣏⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣾⣿⣿⢏⣿⣿⡿⣿⣿⣿⢿⣿⣷⠀⠙⢿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠸⣿⡟⠁⣽⣿⣿⠀⠻⢿⣤⡀⠀⠙⠛⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⢹⡇⠀⢹⣿⣿⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⠀⠀⣸⣿⠀⠀⡀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢿⣤⡄⣿⣿⠀⢰⣇⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢳⣔⣦⣿⣿⣦⣼⣿⣿⣿⣿⣦⣿⣿⣧⣿⡿⠁⢀⡄⠀⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣻⣿⣿⡿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣇⣴⢟⡆⢀⣤⣶⡿⠟⠁
⠀⠀⠀⠠⣤⣤⣀⣀⡀⠀⠀⠐⢦⣔⡶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⣤⣀⡈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⣤⡶⠚⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣀⣤⣤⣤⣶⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣶⡶⠦
⠀⠠⠴⠶⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣽⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⢿⣿⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⢶⣤⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⢛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⡉
⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠉⠀⠀⣨⡿⠛⢹⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣯⡉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠮⠻⢦⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢻⡟⠀⣿⣿⢿⣿⡟⠻⣿⣿⢿⣻⣆⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠚⠀⢠⣿⡟⠈⢻⡇⠀⢻⣿⠀⠁⠹⠄⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠃⠀⢸⣿⡆⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠖⠛⠛⠛⠛⠓⠒⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢹⡄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠹⣌⠙⠲⠦⣤⣀⣀⣀⣠⣤⣶⡿⠃⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⠳⢤⣀⡀⠀⢀⣉⣤⡴⠛⠁⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠈⠉⠋⠉⠉⠁⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣄⣀⣀⣠⣤⡤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃



⣀⣀⣀⠀⡀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠻⣄⠘⡄⠻⣧⡀⠀⠱⡄⠀⠀⠈⣧⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣿⣴⢀⠷⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢠⡄
⠀⠀⠀⠀⢀⠈⢧⠘⢆⠹⣷⡄⠀⠙⡄⠀⠀⡇⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣠⣿⣿⠘⠇⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢠⡄⠄⠁⠀⢠⡾⠁⣰⡏⠀⠀⠀⢀
⢀⡀⠀⠀⠈⠳⡀⢃⢸⡇⢻⣿⡡⠄⠀⠀⠀⠹⣆⠀⠀⠀⠀⣾⠏⠀⠀⠀⢻⠉⡿⢆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡀⢀⠏⣰⠏⠀⡴⢋⠄⠀⢀⡴⣿
⠀⠁⠀⠀⠀⠀⠙⠄⡸⢣⢸⡯⠻⢶⣄⠀⠀⠀⠈⠷⠀⠀⠀⢻⣦⠀⠀⠀⢘⠸⣷⡎⠠⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⠟⠈⢀⣿⠀⡌⢣⠈⠀⣴⣿⠟⢃
⠀⠀⠁⢀⡀⠀⠀⠈⢱⡄⠛⣷⡄⠠⡿⣦⠄⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠈⢸⠙⡟⢀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣼⠃⢰⠀⠆⠀⣼⠟⠁⣠⣾
⠀⢀⠐⠉⠁⢦⡀⠀⢠⡷⠀⠘⣷⠀⡄⠙⣿⡀⠀⠀⠀⠀⠀⠙⣷⡄⢀⠀⠀⣸⠀⡵⢩⡄⣿⡀⠀⠀⠄⠀⠀⢰⠁⠄⢁⣼⡟⠀⣸⡗⠀⢰⠏⣰⠟⣹⡏
⠀⠈⠳⢀⠀⣀⠙⠲⠛⠿⣄⠀⡈⢣⠒⡀⠈⢷⠀⠀⠀⠀⠀⠀⣿⡁⠈⠀⠘⡋⢾⡇⡤⢿⡟⠁⠄⠛⠀⡀⢀⡆⠀⠀⣾⡿⠁⠠⡿⠃⢠⠟⣠⢣⣾⠏
⠀⠀⠀⢀⠀⠈⠉⠁⠚⢥⢸⣇⠘⠀⠂⣷⡀⠁⠀⠠⠀⠀⠀⢀⣼⠟⠈⠀⠀⡇⢸⡇⢼⡟⠁⢸⠊⠀⢀⡽⠋⠠⠀⡼⣿⠁⣠⡾⢃⠄⢡⠞⣷⠟⠁⢀
⡀⠀⠀⠈⠳⣄⠐⠄⠀⠘⡄⢿⣦⣄⠸⣟⠑⡄⠁⠀⠀⠀⠀⠘⢿⣄⡸⣇⠰⢡⡞⠀⣸⣷⠀⣸⡄⠀⣸⡇⣠⠗⠀⡰⠃⡜⣿⠴⡋⠀⠃⠀⠀⢀⠀⠁⢀
⠘⢦⡄⢠⡄⢩⡄⠘⠧⠀⠈⠳⢄⣿⡇⠘⠦⢇⠀⡀⢀⠂⠀⢀⣴⣿⡟⠈⢀⣻⣥⡾⠛⠁⡾⠛⢀⡾⠋⢘⡇⡠⠚⣡⣴⠟⠁⠀⢡⡶⠈⠀⠀⠊⣠⣷⡟
⠀⠀⢡⡀⠐⠀⠛⢦⡀⠡⣄⠀⠈⣿⠁⠀⠐⢄⠘⣤⡀⠀⠀⠸⣿⣿⣧⣄⠈⠺⣿⣇⠀⢸⠃⣠⣾⠇⢸⠋⠀⢀⣼⡟⠁⠀⠀⢀⡏⠀⠠⢫⡴⠞⣡⠆⠰
⠀⢀⠀⠈⢣⡁⠀⠀⠉⠄⠉⢷⡄⣿⣇⠀⠀⠀⠚⠵⣭⡆⢁⠀⠀⠙⣿⣿⣷⡀⠈⣿⣇⢸⣶⣿⠃⢠⡄⠀⣿⡿⠋⠁⠀⢀⣴⢞⣤⠆⣠⣏⣠⢾⣽⠟⠊
⠀⠀⢱⣄⣀⣧⣀⠀⠀⠘⣆⠸⣇⠈⠛⢿⣶⣦⣤⡐⢬⣧⣀⢀⠀⢀⣾⣿⣿⡇⠀⣿⡟⡸⣿⡇⠀⢊⣠⣴⡿⢁⠀⠀⢀⠜⢡⣾⡷⠞⣻⣏⣴⠟⣁⠔⠚
⠀⠀⠀⢿⡉⠉⠻⢯⣄⠀⠈⣃⠙⠓⢤⣄⠈⠙⢿⣿⣦⠉⣿⣾⢢⣾⣿⣿⡟⢠⣾⣫⣖⣴⣿⠇⠈⢸⡏⠁⠐⠀⠀⡔⢁⣴⣾⣟⣤⡾⠟⠉⣠⡂⣁⣶⣟
⠀⠶⠤⣄⡙⠛⢷⡀⠝⢳⡄⠙⠦⣄⠀⢸⡇⠀⠀⣿⣿⠁⣿⠙⢿⣿⡏⣿⢡⣿⣿⣿⣿⣟⣥⣴⣧⣼⠇⡀⠀⡀⢂⣤⣾⣿⡿⢯⠉⢠⡤⠚⣠⣷⣾⠗⠉
⣄⠀⠀⠈⠉⠶⠶⢿⡻⣏⠙⢳⣆⢹⣄⢀⣙⣦⣄⣿⡏⢰⣿⡜⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣉⣰⡿⠋⣰⣿⠍⣱⡿⠁⠰⠏⣠⣼⣿⡿⢉⠀⡀
⠄⠉⠳⢄⠀⠀⠀⠀⢳⣌⣿⣿⣿⣦⣬⣁⠈⢹⣿⣿⣷⡀⢿⣿⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣿⣤⣾⣭⣡⡾⢋⣀⣴⡿⢿⡟⣿⡷⠟⠛⠁⠀⠠
⣤⣈⠀⠐⠃⠀⠀⢀⠀⠈⠉⠉⠻⠿⠿⣿⣧⢸⣿⣿⣿⣿⣿⣿⡿⠛⢫⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣡⣤⣥⡾⢋⣤⣥⡾⠃⠀⣀⡤⠐⣾⣶
⠈⠉⠁⠈⠁⠂⠙⠻⣧⣤⣤⣤⣴⣤⡀⠻⣿⣌⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣉⣀⣶⣾⡿⢿⣾⣻⣛⣿
⠿⠒⠂⠤⠰⠦⢄⣀⣀⣉⣀⠀⣀⣉⣿⣶⣬⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣻⣛⣻⣭⣵⠿⠻⠛⠉⠩⠄
⢖⣲⣤⣤⠤⠀⣀⣈⠉⢉⣛⡛⠋⠉⢙⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠿⠿⣟⠛⢋⣩⠧⣤⣤⣴⠛⠛⠃⣀⣤
⠀⠈⠉⠉⠉⠉⠈⠙⠛⠋⠉⠛⣿⡿⠿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣶⣶⣿⣿⡿⣿⣶⣴⡾⠿⠿⣿⣿⣷⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠛⠉⠳⣤⣤⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣮⣥⣯⣥⣶⣶⣤⣴⡿⣿⣤⣴⣦⣬⣭⡥⠴⠶
⠀⠀⢡⠈⣤⣶⡶⠶⣤⠶⠟⠛⠻⢶⡬⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢿⣍⣉⠛⢦⣄⣿⣉⣛⣟⣉⣽⡶⢶⡶⠒⠒⠒
⠤⠚⠃⠈⣀⣈⣀⣵⣄⢀⣾⠟⢦⣄⣤⣿⠟⣿⣏⣿⣿⣿⣿⣦⣀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣄⣿⢿⣏⣉⠳⣤⣌⣉⡉⠉⠉⠉⠉⠉⠉⠉⠑
⣤⣤⡶⠛⠟⠋⠙⠋⠀⠛⢛⠖⠀⠉⠛⣿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⣶⣉⠛⢷⣤⣄⡉⠑⠲⠂⠤⠤⢀⣀⣀⣀
⠉⠀⠀⠀⢀⣀⠠⠀⠀⠀⢀⣀⣠⡿⠛⠛⠐⣾⠟⢻⡿⣸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣄⠈⢻⣿⣿⡿⢦⡌⠹⣿⣦⣤⣤⡀⠀⠈⠙⠛⣉⠱⣟
⠀⠀⠀⠜⠁⠀⠀⢀⣤⠤⡾⠃⢈⡡⠚⣶⢶⣿⣷⡿⣡⣿⠹⣿⡝⣿⠃⢸⣷⢻⣿⣏⠻⣞⢿⣿⣿⣦⣀⠀⠙⠻⠶⡿⠿⣦⠹⣿⣄⠰⢄⠀⠀⣀⡀⠈
⠀⠀⠀⠀⢀⣤⠶⠾⠃⠀⠀⠊⠉⠰⠏⣁⣼⡟⢁⣸⡿⠀⣠⣿⣡⡿⠀⢻⣧⢨⣿⢫⠘⢏⢹⣿⣍⡛⢿⣷⣤⡀⠀⠈⠁⠉⠒⠌⣿⣧⣄⠈⠉⠢⠀⡄⠐
⠀⣤⡳⠽⠛⠁⠀⠀⠀⠀⣠⣰⠗⣉⣾⣿⠛⠀⣿⠁⠀⢸⡏⢿⡟⠁⠀⢺⣇⠹⣿⡈⠷⡈⢛⡹⡿⢿⣿⣿⣿⣿⣌⠲⣦⡀⠁⠒⣌⠛⣿⠷⣶⣦⣀⡀
⠞⠋⠁⠀⠀⠀⠀⠀⠀⢈⣀⢁⣾⣿⠟⠉⠂⡠⠋⠀⠀⣠⣿⣼⣷⠀⠀⢸⡿⡇⠈⢻⣦⢱⠈⣇⠁⠀⠹⣿⣿⠙⣿⣷⣘⢷⣄⠀⠘⣧⡀⠳⠙⢿⡛⢳⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢛⠿⢿⠋⢀⠀⣀⠇⠈⠀⠀⣿⣿⡏⠁⠀⠀⠈⣿⡧⠀⣸⡏⠘⡀⠈⠀⠀⠘⣿⡙⢧⣈⠙⢿⢷⣉⠻⣦⡈⠙⢷⡄⠘⠛⣦⡙
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢴⠋⠄⡻⠃⠀⣰⡃⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠘⢿⣄⠛⣏⣿⡀⢷⡀⠀⠀⠖⠫⠛⠷⣄⠙⣆⠀⠩⣆⠘⣷⣄⠀⢻⣄⠀⠠⠙
⠀⠀⢀⡀⣈⣴⡟⢡⡾⢋⣷⡞⠋⠀⣴⡿⠁⠀⣠⣀⣬⣿⣿⡇⠀⠀⠀⠀⠈⣿⡷⠃⢈⡧⠈⢻⣦⡀⠀⠀⠑⠀⠙⡄⠈⠑⡀⠈⠙⢷⣉⠛⠶⣌⠙⢷⣄
⠀⠀⣼⡟⠉⠙⠁⢂⣿⠿⠇⠀⠀⡾⢸⡇⠀⢾⡟⠋⠉⢹⣇⠀⠀⠀⠀⠀⠀⢿⣇⡂⠘⢧⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢈⠻⣦⠘⠀⠈⢿
⢀⣴⡿⠁⠀⠀⣀⠿⠃⠀⠀⢀⠜⠁⢞⠃⢸⠈⢧⠀⠀⣿⠁⠀⠀⠀⢀⡀⠤⣿⣿⣷⠣⠀⠉⡄⠀⢬⣿⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠢⠙⢳⣦⣄
⠎⠁⠀⠀⠀⠀⣿⠊⠀⡘⡀⠉⢀⣼⠃⠀⠈⣀⣼⡇⢸⡇⠀⠀⢀⡴⠋⠁⠀⣽⣇⠙⣶⠀⠘⢷⡄⠀⢃⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡝⢷
⠀⢠⠀⠀⣤⠘⠁⠀⢠⡷⠁⣰⢋⡽⢠⡶⠛⠋⠁⠀⣼⠀⠀⠀⡸⠇⠀⠀⠀⢷⡙⠆⠁⡄⠀⠛⢻⣆⠈⣝⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⢀⠀⠈⠀⠀⢸⠇⠀⡆⣸⡏⠀⢸⡇⠀⠀⠀⠀⠋⠀⢀⠈⠀⠰⡆⠀⠀⢸⡃⠘⣄⠐⣷⡀⠀⣿⠰⡀⠂⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠈
⡰⠂⠁⠀⠰⠀⠀⠃⠀⣠⠷⡿⠀⠀⢿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠻⢦⠸⡆⠀⠘⡞⣿⡄⡇⠀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⡀⠀⠀⠀⠀⣠⠾⢁⡾⢁⡰⠃⡌⠀⠀⣠⠀⠀⠀⢠⡇⠀⢀⡿⣇⠀⠀⠀⢀⣦⠀⠐⠄⠀⠣⣈⢏⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠸⠁⠒⠟⠀⠈⠀⠊⠀⠀⠀⠃⠀⠀⣠⠈⣙⠀⡌⢳⠈⡇⠀⠀⠘⣇⠀⠀⠀⣆⠀⣿⡀⣷⢨⡆⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢠⡽⢆⠀⣶⠀⣿⠀⠀⠀⠉⠀⡀⠀⠸⠀⠻⢷⡬⡁⠡⡀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠸⢠⡇⠀⠙⡄⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠹⣿⡀⠻⡀⠀⠀⠀⠀⠀⢈⠀⠖⠒⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⠀⠀⠀⡇⠀⢀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⡀⠙⢄⠀⠈⢆⠀⠀⡇⠀⡞⠀⢀⡜⠁⠀⡀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠈⠢⡈⠢⠐⡈⠄⠆⡇⠱⠱⢡⢊⠀⡠⠊⢁⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠈⠂⠐⠀⠀⠀⠇⠀⡐⠁⠀⢊⠤⠂⠁⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠉⠓⠢⠄⠀⠀⠄⠠⠂⠀⠀⠀⢈⠀⠂⠁⠂⠀⠒⠉⠁⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣀⣀⣈⣉⡉⠁⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢪⠟⠛⠉⠉⠁
⠐⠋⠉⠉⠉⠀⠀⠀⠀⠈⠑⠤⢄⡀⠀⠀⣄⠠⠄⠀⠤⠐⠂⠉⠉⣡⠋⣁⠄⠀⠀⠀⠀⢀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠠⠀⠈⠉⢦⣤⠀⠤⠤⠤⢤⡴⠒⠊⠁⠌⠁⢤⡀⣔⢊⠁⡀
⠀⠐⠂⠐⠂⠂⠀⠂⠐⠒⠀⠈⠁⠒⠒⠚⠋⠉⠀⢀⡴⢚⣤⣠⣰⣂⠀⠀⠐⠁⠓⠀⠑⠮⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠠⠤⡤⠶⢚⠚⠁⠀⠡⠤⠀⠭⠩⠝⠋⠉⠉⠛⠉⠉⠉⠛
⠀⠀⠀⠒⠋⠉⠉⠉⠉⠉⠻⠤⠀⠀⠀⠒⠒⠡⠤⠈⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⢹⠱
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⠀⠀⠀⠀⣠⠃⡼⢠⠁⢀⡴⠖⠀⠀⠀⠀⠀⣴⠛⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣉⣛⡛⠙⠩⡑⠆⠀⠛⠀⡄⠀⠠⠊⠄⠈⣰⢁⡠⠈⡀⠜⠀⠀⠀⠀⠀⡿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⡄⢱⢘⠀⠀⠀⢷⠄⠀⠁⠀⣌⣟⠁⠀⣸⢃⠀⠀⠤⠄⠠⠞⠁⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢷⡅⢀⡠⢖⣚⡩⠭⠭⠭⣑⣒⠦⣌⠀⠀⠁⠀⢀⢀⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⣰⠞⡡⠚⠉⠀⠀⠀⠀⠀⠀⠈⠙⠢⣝⢶⣨⠾⠥⠄⠀⢠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠡⢤⣀⢂⡰⢡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡱⡄⢀⣤⠄⠤⠄
⠀⠀⠀⠀⠀⢀⣀⠄⣀⠀⢠⡀⠈⢸⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢹⡀⠀⠀⡀
⠀⠀⠀⠀⣴⠗⠒⠒⠢⡑⠲⡷⠴⡏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠈⠢⣀⢀⣀⡾⢋⣹⠷
⠀⢠⣤⡚⣡⡶⠛⠛⠂⡀⠀⠈⠉⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢤⣦⡀⠢⣈⠉⣉⣴⠟⠁
⠀⠀⠉⠛⠉⠀⠀⠀⠀⠈⠀⠁⡀⢳⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢱⠃⠀⠳⡀⠐⠢⠭⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⡤⠗⠈⢣⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠏⠀⠴⠦⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠀⠀⠤⢄⣤⣳⣝⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣵⠋⠐⠀⠀⠀⠑⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡐⠋⠁⠀⠈⡱⢮⣝⡒⠦⠤⠤⠤⠶⣒⡩⠖⠛⣮⡂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠞⢁⡤⠠⠀⠀⠁⠀⢄⠄⠈⠙⡟⠋⠉⠉⠁⢐⡄⠀⠇⢡⠀⡀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠀⠀⠀⠀⠀⠤⠊⠀⠐⢩⠇⠀⠀⡠⠀⠀⡁⢀⡀⠘⢄⠣⣀⣉⡛⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣰⡇⠀⠀⠀⠀⢀⣠⠖⠀⡰⢡⠖⣡⠊⠀⠀⠀⠁⢠⠇⠀⠀⠉⠘⠋⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢰⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣻⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⡠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢄⠀⠀⡀⠁⠀⠀⠀⠀⠁⢀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠌⠀⠀⠩⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠉⠀⠀⠩⠤⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⡀⠀⠀⠀⠀⢀⠘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⡆⠀⣿⡃⣠⣾⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠄⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣙⣿⡦⠿⠷⢿⣇⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠈⢲⣦⣤⣽⠟⠁⠀⠀⠀⠀⠈⢻⣵⡾⠷⠒⠁
⠀⠀⠀⣀⠀⠀⠀⠒⠀⢄⡈⠀⠀⠉⡠⠀⠰⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣉⣽⡏⠀⠠⠄⠀⠀⠤⠄⠀⣿⣥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣫⣇⠀⠀⠀⣀⣀⠀⠀⠀⣿⣭⣈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠒⢀⠀⠀⠀⠀⢀⠀⠁⠈⠀⠠⠀⠀⠀⠀⠀⠠⠶⠿⠟⢻⣦⣀⠈⠙⠋⠀⣠⣾⣍⡉⠛⠦
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠃⠘⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠿⠃⣿⡟⢿⣟⠻⣷⡍⠻⣇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⢸⡟⠀⢹⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠠⠀⠀⠀⠀⠀⢠⠞⣷⡀⠀⠀⠀⠐⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⢲⡄⠀⠀⠀⠀⡘⠀⡻⣧⠀⠀⠀⢀⡖⡟⣷⠀⠁⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢈⡇⢣⢹⢶⡀⠀⣶⠁⠀⡇⣿⡄⠀⣰⠃⣰⡱⣧⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⢶⡦⣄⣀⠀⠀⠠⡇⠀⢣⠈⡻⣤⡏⣀⣠⣧⣿⣷⡜⠁⢠⣷⠻⣧⠀⠀⢀⢀⠔⣢⣿⠡
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⢮⡫⡳⡶⣤⣽⢀⣨⠷⠛⠛⠉⠉⠉⠀⠀⠉⠉⠑⠻⢮⣽⣇⡤⠖⠉⣠⢞⡿⠋⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠪⣪⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⣀⢞⢕⡿⠁⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢁⣠⢀⡤⠤⠴⣤⣴⠆
⠀⠀⠙⢿⡿⢽⣛⣫⣟⡻⣞⡿⠃⠀⠀⡤⠴⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣤⣄⠀⠀⠈⢧⠀⢀⠠⢔⢢⡵⠛⠁
⠀⠀⠀⠀⠉⠳⣄⡉⠙⠻⢾⠃⠀⠀⠀⣠⠴⣶⣶⣶⢿⣹⣆⠀⠀⢠⣞⢣⣤⣤⣴⣤⢄⡀⠀⠀⠀⢿⣙⣤⡶⠛⠁
⠀⠐⠒⠀⠀⠀⠀⠙⠢⣤⠏⠀⠀⠀⠀⠀⠀⠽⠿⠿⠶⠿⢿⠀⠀⣿⠋⠉⠉⠻⠿⠯⡼⠅⠀⠀⠀⠘⡿⢅⣀⡀
⠀⠀⠀⣀⣀⣤⠤⢶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣇⠀⠀⢈⣉⣒⠲⣀⣀
⠀⠶⣾⡛⠋⠀⠘⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡿⠛⠛⠋⠁
⠀⠀⠀⠀⠈⠛⠀⠠⠤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠼⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⢏⡉
⠀⠀⠀⠀⠂⠀⠀⣠⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⠀⠙⠤⡀
⠀⠀⠀⠀⢀⣤⢞⡱⠞⠛⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠂⠬⠤⠞⠛⠲⠴⠀⠂⠀⠀⠀⠀⠀⣼⣿⣷⣟⣶⣆⣨⢷⣄
⠀⠀⠀⣴⣿⣫⠥⠤⠄⠶⠒⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⠐⢡⠔⡀⠀⠀⠀⠀⠀⣠⠎⠙⣄⠁⠀⠉⠀⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡯⠨⡻⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⢀⣠⡾⢿⡢⡀⠈⢦⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠁⠀⢠⡯⣠⠞⠁⣠⢼⡿⣶⣤⣀⣀⠀⠀⠀⠂⠀⠀⣀⣄⣤⡖⠋⠻⠙⠶⢯⣮⡂⢈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢞⡡⠔⠋⠀⢨⡗⢈⠏⠀⣩⠿⡿⣟⠛⠉⠉⡿⣿⡇⡐⠀⢸⠆⠀⠀⠉⠙⠶⠶⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠉⠀⠀⠀⠀⢸⡗⡌⢀⡔⠃⠀⢷⠹⠀⠀⡘⠀⠈⠹⣾⡡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣸⡳⢡⠈⠀⠀⠀⠸⣧⠀⠀⠏⠀⠀⠀⠈⢳⣀⠙⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠁⠀⠀⠀⠀⠀⢻⣴⡸⠀⠀⠀⠀⡀⡀⠙⠷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠃⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢷⠀⢸⠃⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⢘⡦⠶⠒⠺⢄⠊⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡄⠀⠀⠀⣀⣠⠄⠾⠀⠀⠀⠀⠈⠇⢡⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣀⡿⠀⠀⠀⣀⠀⢀⢀⣶⠀⣀⠀⢀⢀⣤
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠁⠀⠀⣷⢰⣿⠀⣾⡾⢸⠌⣿⢠⣿⡟⣾⢔⡿⢀⣶⠷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⠛⠶⣌⠙⠃⠘⠛⠉⢁⠀⠀⠙⠋⠈⠀⠀⠘⠷⠻⣇⣠⡾⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⡿⠀⠀⣆⢰⡇⣴⠀⣿⣽⠀⣾⡒⢠⡞⠦⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢻⣼⠀⣿⠀⣿⢸⢷⡇⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠙⠂⠛⠋⠈⠓⠂⠘⠾⠃


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢸⠀⢰⠇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⢀⡵⠒⠋⠓⠢⡉⡠⠤⠖
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢶⡄⠀⠀⠠⠴⠖⠘⠁⠀⠀⠀⠀⠛⠐⠶⠆
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠠⠼⠃⢀⡀⣠⡀⢠⣆⣾⣇⣤⠀⢠⣤⢾⢂⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⡀⠼⣧⠿⣇⡼⣿⠘⠋⢾⣰⠿⠏⠻⢫⡏⣰⠟⠋⣠⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠉⢻⡆⠀⠀⠈⣀⠀⠆⣠⢤⡀⣀⣀⠀⣈⡉⠙⠲⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠴⠁⠀⢸⣤⡇⢸⡇⣿⠛⡄⡿⠀⠸⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⡇⢿⡴⠃⣷⣀⢠⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⣆⠀⠀⢀
⠀⠀⠀⠀⠀⢤⠀⡀⠷⠀⠀⠾⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣰⡸⣿⠼⠸⣿⣴⣠⡾
⠀⠀⠀⣀⠀⠈⢁⣠⣴⣶⣶⣦⣤⡈⠡⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠤⢤⣄⣢⠟⣫⣴⣶⣶⣶⣶⣤⡙⠷⣣⣴⠆
⠀⠀⠀⠈⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⢵⡂⣀
⠀⠀⠒⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠋⠁⠀⠀⠀⠀⠀⠒⠛⠿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⠉
⠀⢀⣀⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣭⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣦⣤
⠀⠀⠀⠐⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⢶⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣟⠂
⠀⠀⠀⠊⠁⠀⡈⠙⠛⠿⠿⠟⠛⢁⡀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⡳⢦⣝⠻⠿⠿⠿⠿⢛⣡⣜⠯⠙⠓⠂
⠀⠀⠀⠀⠀⠘⠁⠈⢰⠆⠀⢰⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⠏⣿⠶⡖⣿⠙⠌⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡏⠐⢁⢀⣰⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣠⠀⢀⣰⣇⣴⣽⣦⣌⡖
⠀⠀⠀⠀⠀⠀⠀⣀⠙⢠⠻⠿⠋⣿⠀⢰⡇⠀⠀⠀⠀⣀⣰⣇⠱⡀⢀⡖⣯⣸⣷⣄⡠⢻⡄⠀⠀⠀⠀⠹⢄⡹⣧⣾⠏⢿⢋⢹⡁⡙⠁
⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⢠⠤⣖⢤⣠⢾⠁⠀⠀⠀⠘⠉⠀⠙⢆⠓⡏⠃⣹⠁⢹⡉⠃⡸⢁⠒⠖⠁⠀⠀⠀⠓⠀⣥⠘⣏⢾⢀⡜⣧
⠀⠀⠀⠀⠀⠀⠀⣿⢯⢸⡌⢳⡘⡏⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠆⠈⣦⠙⠛⠾⠀⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⢰⡄⡆⣆⠰⢠⡆⠀⠀⠀⠀⠀⠀⠀⢁⠶⠙⢒⠸⠚⠆⠁⡀⠀⠀⠀⠀⢠⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⢠⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⢐⢸⠀⠀⢱⡇⡈⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⢀⠰⡄⡈⠀⠀⠀⠀⠀⠀⢣⢨⢸⢸⢰⠀⢡⠐⢰⠀⠈⣦⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠄⣤⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⠀⡀⠮⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⢀⡀⢀⡁⣀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡿⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠅⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠂⠘⡅⡷⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠚⠃⠁⠙⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠃⣘⠀⢰⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠋⠁⠓⠁⠃⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣿⠄⢈⡀⠀⠀⠀⠀⠀⢀⡴⢢⡄⠀⠀⣈⣉⣉⣉⣉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣦⣤⢦⠂⡀⢀⠀⠀⠀⠀⠸⣧⡜⠁⣀⢀⣤⣤⣠⣤⣤⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠯⢅⣿⣴⣟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⡠⡀⡀⠀⠁⣡⣌⠀⠁⣸⠀⠀⠀⠀⠀⠀⠙⣷⠯⠻⠿⠘⠙⠋⠘⠹⠛⠄⢿⡹⠃⠀⠀⠀⠀⠛⠋⠈⠃⠈⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠃⣿⠁⡜⠧⠻⡌⠟⠿⢯⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣒⣒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⢻⠀⣯⠁⣯⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠓⠀⠛⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⣾⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠀⣸⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡳⢦⡀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⢀⣤⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣦⡀⠀⠀⢀⣠⣤⠤⣤⣤⣀⠘⠁⠀⠀⠀⢀⣤⠾⣋⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⡾⢋⡥⠶⠶⠶⢦⣍⡛⢦⡀⢀⣴⣿⡷⠛⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡴⢋⡴⢖⣚⣒⠶⣬⡻⣆⠻⣆⠉
⠀⠀⠀⠀⠀⠀⠿⣭⣉⣉⣉⡛⠛⠶⠶⢤⣀⠀⠀⡟⣸⢡⡏⡼⣫⠥⣭⡙⣮⢳⡜⣇⢻⡄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋⣠⡀⣇⢻⠸⡞⣟⢧⢾⡆⣷⢸⡆⡇⣿⢸⡇⠶⢿⣿⣿⣯⣭⣭⣭⣭⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⡽⣎⢷⣙⢮⣽⣭⠾⢃⡾⣱⢇⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠻⣌⠳⣭⣓⠲⠖⢚⣋⡴⢋⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣦⠀⠈⠳⣌⡛⠦⣭⣍⣉⣩⡥⠞⣋⡴⠋⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⣥⠞⠁⠀⠀⠀⠀⠉⠓⠶⠦⠤⠶⠖⠛⠉⠀⠀⠀⠈⠻⣍⡳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠠⡶⡄⠀⠀⠀⠀⠈⠙⢦⣉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡟⠀⠀⠀⠀⠀⠀⢷⠹⣄⠀⠀⠀⠀⠀⠀⠉⠳⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣸⠇⠀⠀⠀⠀⠀⠀⠘⣇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠈⣿⠿⠈⠃⠁⠀⠃⠋⡿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠙⠌⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠟⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣴⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣟⢀⡄⣠⣠⢀⡀⡆⡀⡀⢰⣄⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠉⢷
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣱⣄⣤⣤⣤
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⣤⠀⠀⣀⠀⢀⡄⠀⢀⢴⡄⠀⢀⣴⠶⣆⠀⠀⡇⠀⣰⡟
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⣤⡄⠀⠀⣤⠀⠀⣼⡇⡴⢹⣇⠔⢡⡟⠀⢰⡏⡰⣹⢇⡜⢡⡿⠀⢰⡟⢁⠠⠃⠀⡴⠁⣼⠏
⠀⠀⠀⠀⠀⠙⣷⡄⢀⠔⢉⣿⠁⣠⢺⡏⠀⠀⣾⡟⠀⣿⠏⢠⡿⠀⠀⣼⡟⠀⠿⠋⢀⣾⠁⠀⣿⡇⠀⠀⣠⠎⠀⣸⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢸⣿⣴⢃⣿⠀⠌⠀⠛⠁⠀⠋⢀⣾⠁⡔⠀⠿⠁⠀⠀⠀⣸⠇⢀⠂⠹⣧⡴⠚⠁⠀⠀⠹⢧⠤⠚⠁
⠀⠀⠀⠀⠀⢀⠎⠘⣿⠀⠈⠛⠁⢸⡇⡸⠀⠀⠀⠀⠀⠀⣸⢇⡜⠀⠀⠀⠀⢀⣀⠀⣟⡠⠃
⠀⠀⠀⠀⢠⠃⠀⠀⣿⠇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣼⠋⢹⠀⠉⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⡇⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠴⠀⢀⣾⠃⢠⠋⠀⢀⣠⡤⣄⢀⣾⠋⣀⠟
⠀⠀⠀⠀⢧⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢏⣸⠁⢰⡖⠀⣼⣇⠔⠁⠀⢠⡿⠁⢀⠜⢸⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⢀⣿⠁⢰⡿⢁⠖⢄⢀⣿⠃⠉⠁⣠⠃⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⡞⠀⣸⡇⠀⣼⡇⠀⠓⣺⠁⢿⣄⣀⡴⢁⣀⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡟⠀⠀⢹⣇⡴⢻⡇⠀⣠⠃⠀⠀⠉⠁⠀⡎⠀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠳⠤⠞⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢹⣿⣿⣿⡇⠙⣿⢸⠃⠇⠈⢸⡏⣻⡏⣿⢿⣿⣿⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢟⢿⣿⣷⠀⢹⣿⠻⡅⠀⢹⠘⠀⠀⠀⠸⠀⢃⠀⡿⠣⡾⠁⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣎⠳⡀⠂⠫⠃⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠜⡰⠱⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⡉⠻⣯⡂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⣹⠿⣿⢿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠻⣤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⡕⠋⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣍⠻⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢋⢴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣪⠛⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢉⣿⣿⣿⣿⣿
⣿⣿⣾⣍⡋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣟⣿⣿⣿⣿
⡷⠷⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣞⣿⣿⣿
⣿⣯⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠏⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢛⣻⣿⣿
⣾⣯⢤⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠀⠈⠹⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣠⣿⣿
⣿⡿⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⢠⡀⠀⢹⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣭
⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠘⠀⠈⢳⡄⠀⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢬⣭
⡿⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠿⣿
⣿⣖⣛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⡶⢶⣮
⣿⣿⡻⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⣷⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣙⠿⣿
⣿⣮⣡⣀⣄⣤⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣶⣷⣿⣿⣿
⣿⣿⣿⣿⡟⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣽⣻⣿⣿⣿
⣿⣿⣿⣿⣾⣛⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣉⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢟⣡⣾⡣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⢢⣀⢵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⢀⣠⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⣰⠇⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠐⡀⣄⣆⢰⣄⠰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⡿⡕⠀⣼⠀⣴⣧⢎⡄⢸⢠⡄⣇⠀⡀⡈⠀⠀⣿⡄⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣹⣾⣿⣿⡄⣾⣼⣧⣿⡆⣷⣾⣇⡰⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⣄⠀⠀⢠⣶⠂⠀⢲⣦⠀⠀⢀⣤⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣖⠀⠉⣧⠀⠈⡟⢧⣀⡿⢹⠀⠀⢸⠻⣇⣠⠟⡿⠀⠀⣿⠛⢻⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣙⣃⡀⢻⡄⠀⢸⠆⢀⣿⡄⠻⠁⠼⠷⠠⠾⠄⠹⠋⣰⣇⠀⣰⠏⠻⠁⠀⢠⡟⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⢈⡷⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢀⡔⣹⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠃⣠⡿⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⣀⡤⣴⣯⡿⠱⢿⣷⠶⢢⡄⣂⣁⠀⠠⣤⣄⡀⠈⠁⠸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⢶⠋⣽⢣⡇⣼⢡⡾⢰⠇⣸⠿⢤⠍⠱⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⢠⣾⣿⡇⠀⠀⢰⢀⡡⠻⢈⢡⣬⣴⣿⠦⠔⢚⣒⣮⣅⣤⣄⣀⣹⣿⣿⣆⠀⣀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⢀⣾⣿⣿⣠⣤⣤⣤⣤⣤⡀⠀⠀⠈⠉⠀⠀⠘⠋⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠋⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⠃⡨⠋⠉⠱⠦⢀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠄⠀⡀⠇⠈⠀⢀⠀⡆⠀⠀⠀⢈⣡⣿⣿⡿⠛⣿⡿⠙⢻⡿⣿⣿⣷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⣿⣿⠟⠹⠃⠘⢿⠋⠙⠛⠿⡷⣄⠀⠙⠊⠐⠊⠁⠀⠐⠐⠃⠀⠛⠉⠁⠀⠀⠀⠛⠀⠀⢡⠀⠈⠋⠻⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠐⠂⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡟⠛⠻⠿⠿⢿⣿⣿⣿⣿⡿⠿⢶⣶⠶⠂⠀⠉⠁⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠂⡆⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠣⠤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠧⠤⠚⠒⠒⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠸⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢤⣄⢣⠀⣰⢷⢸⢀⡴⢃⡤⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⢇⡖⡆⢰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢱⢀⡄⠀⠰⡰⠃
⠀⠀⠀⠰⠦⠭⠓⣰⠃⠈⣇⣙⣚⠁⡀⠀⠀⠀⠀⠠⣄⠀⣈⣓⣀⡼⠀⠸⣄⣁⣊⠀⣀⡤⠀⠀⠀⠑⠂⠈⠳⢌⡞⢹⡀⠜⠁⠀⢀⠤
⠀⠀⠀⣀⡛⠯⣉⠁⠀⠀⠈⠀⣠⠞⡥⠄⠀⠀⠀⠀⠀⢈⠣⢄⡀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠛⢉⡿⠛⠛⢿⣛⠿⠃⢀⣀
⠀⠀⣠⣤⠴⠆⣼⠀⢀⣀⠀⢸⢑⡒⠶⠤⠀⠀⠀⣀⠨⠍⢐⠂⡏⠀⣀⡀⠹⡄⡊⠭⠁⠀⠀⠀⠀⠲⠶⠓⢨⠛⣠⣴⠚⣇⠴⢤⣄
⠀⠀⠈⠀⡴⢁⣧⠖⣋⡈⣑⢦⡇⠻⡆⠀⠀⠀⠀⠁⠀⠘⠉⠸⡤⠞⠡⢨⠲⠿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⠊⠁⡀⠁⠺⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⢰⢹⡇⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠛⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢤⡹⡄⢠⡿⣆⠀⣴⢢⡶⠀⠀⠀⠀⠀⠀⠘⢦⡘⣧⠀⣠⠀⠀⡟⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣦⠀⡀
⠀⠀⠀⠘⠓⠶⠕⢀⣞⠁⠽⡄⠋⠭⠖⠂⠀⠀⠀⠀⠰⠶⣬⡳⠙⣰⣿⡆⠘⠐⣫⣤⡆⠀⠀⠀⠀⠀⢀⣀⡴⣣⠏⠈⢧⠹⠦⠤
⠀⠀⠀⠐⠻⣟⠋⡉⠱⠄⠀⠟⠉⣻⠖⠀⠀⠀⠀⠀⠀⠀⣤⢤⣶⣿⣿⣿⣦⣤⣤⠄⠀⠀⠀⠀⠀⠀⢶⡚⠋⠁⠀⠀⠈⠉⠉⣲⠆
⠀⠀⢈⣛⣳⠎⢳⠋⠀⣀⢉⡂⣾⢁⠮⣥⣄⠀⠀⢀⣀⣀⡈⠹⣿⣿⣿⣿⣿⠟⢡⣤⣤⠀⠀⠀⠀⠀⠤⣍⢲⡀⠀⠀⠀⢠⣞⡵⠂
⠀⠀⠉⢉⡴⠃⣾⣠⠟⢛⢶⣄⣿⠈⠳⠀⠀⠀⠀⠈⣁⣴⠂⢠⣿⠟⠋⠻⣿⠀⢬⠳⣶⠄⠀⠀⠀⠀⠀⠻⢸⢀⡴⣛⢦⣸⡏⠇
⠀⠀⠀⠀⠀⠀⠟⢁⡞⣿⠸⠙⠻⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⣴⢹⡆⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠚⠉⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⣤⠐⠣⠉⠄⠋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠦⡑⢠⠃⠸⡌⢠⢊⡄⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⡤⠀⢃⠔
⠀⠀⠀⠂⢀⠀⠨⠥⠃⣀⠘⠬⠥⢈⡁⣀⠀⠀⠀⠀⠀⢠⡤⠥⠒⠋⠀⠀⠓⠶⠦⣤⠄⠀⠀⠀⠀⠠⠦⡀⠱⠈⠑⠀⣀⢈⠔
⠀⠀⠀⠤⠈⢂⡀⠀⢻⠟⠃⠀⢀⠜⠅⡀⠀⠀⠀⠀⠀⠐⡈⠓⡄⠀⠀⠀⠀⡠⠚⠡⠄⠀⠀⠀⠀⠀⢄⣘⠆⣀⣹⣶⣇⡀⢜⣡⣆
⠀⠀⠀⠀⠶⢃⠃⠀⢀⠌⡁⠀⢁⠻⠇⠀⠀⠀⠀⠀⠉⠩⠔⢸⠁⣠⠔⢦⡀⢹⡀⢝⠲⠀⠀⠀⠀⠈⠉⠒⠀⠈⠀⠿⠀⠁⠠⣒
⠀⠀⠀⠀⠞⠸⠤⡂⢱⣆⠈⡂⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⡠⢰⢠⡈⠲⠇⠀⠀⠀⠀⠀⠀⠀⠠⠆⠙⡃⠁⢰⠀⡙⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠙⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠘⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢡⡾⠋⠛⣷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣠⣄⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡄⠻⠧⠛⢁⣾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣛⣉⣉⣁⣀⣀⣀⣉⣉⣉⣙⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⢻⡏⠛⠷⢦⣤⣀⡀⠀⠈⣿⢋⡭⠥⢄⠀⡀⠈⠉⠉⣉⣉⡉⣿⣁⣀⣤⣤⠴⠶⠞⠛⠋⢉⡿⠀⠀⠀⢀⣤⣦
⠀⠀⠀⢀⣀⣤⣤⣿⠀⠀⠀⠀⠉⠛⠻⢾⡏⡆⠀⠀⠘⠈⡇⠉⡇⠈⠀⠀⠈⡿⡏⠉⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠰⣿⣷⣿
⣠⣾⣆⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠇⠀⠀⠀⠁⡇⠀⡇⠀⠀⠀⠀⢇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣄⡀
⠉⠛⠛⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠈⠀⡇⠀⠃⡆⠀⠀⠀⠘⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠃
⠀⠀⢀⣤⡴⠾⠛⠀⠀⠀⠀⠀⠀⠀⢰⠇⡂⠀⠀⠀⠀⠀⡇⠀⡆⡇⠀⠀⠀⠀⠇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠠⠀⠀⠀⠀⠀⡇⡇⠀⡇⡇⠀⠀⠀⠀⠸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⢀⣹⡧⠀⠀⠀⠀⠀⠀⢰⠇⡆⠀⠀⠀⠀⢠⠇⡄⠀⡇⡇⠀⠀⠀⠀⠀⡇⢻⡄⠀⠀⠀⠀⠀⠀⠰⣿⣀
⠀⠀⢠⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⡞⡸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠰⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡦
⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⣸⢣⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⢿⡆⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⣹⡷⠀⠀⠀⢠⠏⡎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⣠⣶⠛⠁⠀⠀⠀⠀⣾⢠⣁⠀⠀⠀⠀⠀⠀⡂⡸⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⢸⠄⣿⠄⠀⠀⠈⠻⣦⡄
⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⠹⡄⢀⣉⠉⠑⠒⠀⠒⠀⠓⠠⠤⠃⠘⠦⠤⠴⠒⠚⣉⣁⠀⡿⠀⠀⠀⣀⡴⠟⠁
⣀⣠⣤⣤⡄⠀⠀⠙⣷⠄⠀⠀⠹⡼⡄⠀⠉⠉⠉⡆⠀⡖⠒⠒⡆⡰⠒⠉⠉⠀⠀⢀⡌⡼⠁⠀⠀⠺⣯⡀⠀⠀⢾⣿⣿⡆
⢻⣏⣼⠏⠀⢀⣤⠞⠁⠀⠀⠀⠀⢻⡱⡀⠀⠀⠀⢰⠀⡇⠀⠀⠃⡇⠀⠀⠀⠀⢀⠎⡼⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⠁
⠈⠋⠁⠀⠀⠛⠛⠛⠛⢿⡆⠀⠀⠀⣷⠱⣀⣀⠀⢸⠀⣇⠀⡘⢰⣀⣀⠀⠀⡠⢂⡼⠁⠀⠀⠀⢠⣶⠶⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⠶⠛⠻⣷⣤⠬⠭⠍⠀⢈⣉⣀⣀⣀⣀⣀⣀⣀⣾⣁⠀⠀⠀⣠⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣅⣀⣀⡀⠀⠀⢀⣀⣀⣀⣬⣿⠏⠁⠈⠛⠶⣤⡏⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⣉⣉⣉⣉⣉⣥⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⢀⣀⠸⡄⠀⣰⡆⢸⠀⣴⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡆⡴⡄⢀⡖⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⢀⠀⡔⡴⠁
⠀⠀⠀⠀⣤⣙⡳⠅⣰⠃⠸⡄⠾⠵⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⠑⠄⠂⣸⠁⠸⡈⠖⠰⠂⠀⢀⡀⠀⠀⠀⠢⠀⠘⢶⡌⣡⠻⡄⢠⠞⠀⠀⠀⡀
⠀⠀⠀⠀⠠⣶⠖⠒⠁⠀⠀⠛⠛⢛⣰⢆⡀⡀⠀⠀⠀⠈⠁⠰⣏⠉⠉⠁⠀⠀⠉⠉⣉⠗⠈⠉⠀⠀⠀⠀⠀⠀⠤⠤⢴⠿⠶⢷⠶⢶⡶⠄⠉
⠀⠀⠀⠚⣒⣀⠉⡆⠀⠀⠀⠀⢰⠋⣄⣉⣁⠀⠀⠀⠀⠀⠶⠒⢨⠕⡆⠀⠀⠀⢰⡋⠅⠒⠆⠀⠀⠀⠀⢀⣀⣤⣤⠑⡾⡀⠀⣨⣷⠁⣀⠀⠒⠒
⠀⠀⠘⠛⠉⡴⢸⢃⣠⠖⠳⣄⠸⡔⢦⡈⠉⠁⠀⠀⠰⠂⠉⢤⠖⢰⠁⣠⠞⠢⣄⢳⠰⡌⠁⠐⠀⠀⠀⠀⠈⠡⠀⣼⣡⠞⠛⠠⢘⡆⠩⣙⠛
⠀⠀⠀⠀⠘⠁⠛⠋⢠⢰⠀⢦⡙⠇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠋⣧⠈⠈⠆⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣆⠠⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⡀⠐⣎⢳⠀⣴⠻⣆⠀⣾⣡⠞⠁⠀⠀⠀⠀⠀⠀⠙⢧⡘⣧⠀⣴⠀⠀⡞⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡶⣄⢠⡀
⠀⠀⠀⠈⠙⠛⠊⢁⣰⡏⠁⠿⣄⠁⠵⠞⠃⠀⠀⠀⠀⠀⠻⠶⢬⡗⠉⣸⣿⣇⠀⠁⠫⠤⠶⠂⠀⠀⠀⠀⠀⠠⠤⠴⣣⠏⠀⠹⣌⠳⠶⠂
⠀⠀⠀⠀⠛⢯⡛⢉⠉⠶⠀⠀⠏⠉⣛⠟⠃⠀⠀⠀⠀⠀⠀⢠⣦⢰⣶⣿⣿⣿⣷⣤⣤⡤⠀⠀⠀⠀⠀⠀⠐⢶⡛⠉⠁⠀⠀⠀⠉⠉⢙⡷
⠀⠀⠈⣛⣛⡶⠙⡶⠁⢀⡀⢁⡂⣾⢁⢾⣭⣄⡀⠀⠀⣀⣀⣀⠙⢸⣿⣿⣿⣿⣿⡿⠋⣀⣤⣄⠀⠀⠀⠀⠀⢤⣙⢳⡄⠀⠀⠀⠀⣴⢫⠔
⠀⠀⠉⠉⣡⡾⢸⣗⣰⠞⠳⣤⡄⣿⠈⠳⠀⠈⠀⠀⠀⠉⣉⡴⠂⢸⣿⡿⠛⠟⣿⠆⢤⡳⢶⣤⠀⠀⠀⠀⠀⠀⠹⢸⠇⣠⠞⢦⣀⣿⢹⠄
⠀⠀⠀⠀⠁⠀⢸⠟⢡⡆⣷⢮⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⠁⣰⢲⡄⠙⠂⠈⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠟⠵⠛⠳⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⢄⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡐⡄⢀⡞⢳⠀⠇⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢀⠀⢠⠀⡀
⠀⠀⠀⣀⠀⠀⠘⣷⢠⠇⠈⢇⢰⡯⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⢂⡼⠀⠀⢧⡐⠁⠚⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⡠⠄⡌⠁⠂⠎⣐
⠀⠀⠀⠀⠠⡖⠒⠒⠋⣤⣆⡈⠒⠒⢒⠄⠲⠀⠀⠀⠀⠀⠀⠲⢏⡉⠉⠀⠀⠀⠈⠉⢉⡽⠃⠀⠀⠀⠀⠀⠉⠓⢂⡘⠁⢤⣀⣰⠀⠚⣡⠄
⠀⠀⠀⠘⠂⣩⢢⠀⠈⠟⠁⡀⠀⡴⣋⡐⠂⠀⠀⠀⠀⣀⣀⡥⠄⢉⠆⠀⠀⠀⠀⢰⠋⢄⡓⠀⠀⠀⠀⠀⣈⡡⠤⠑⢢⠴⢿⠿⠦⠂⠶⠾⠆
⠀⠀⠀⠀⠘⡃⡌⠀⢀⠔⠢⣀⠀⠆⣙⠃⠀⠀⠀⠀⠀⠀⠀⠐⠃⡞⣀⠴⠊⠓⢤⡈⡇⠰⠍⠃⠀⠀⠀⠀⠀⢐⠉⣀⡌⠀⠘⠣⠀⡀⠢⢍
⠀⠀⠀⠀⠚⠁⠃⣺⠁⢺⡆⠠⡑⠊⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠔⢸⠀⡄⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠘⡡⣀⢰⠂⣈⡑⡈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠙⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠠⣄⠰⡄⢠⠒⢠⡇⡸⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠈⡐⠪⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⢈⡄⠀⠀⠈⠆⠀⢀⡀
⠀⠀⠀⠀⠀⣀⠙⠀⢈⠂⠹⡸⠄⡸⠀⠅⢁⣠⠆⠀⠀⡀⠀⠀⠀⠒⠈⠀⣈⠙⠆⠢⠀⠀⢸⠀⠀⠂⠄⠀⠀⠀⠠⢄⠀⠈⠋⢁⣀⣀⠂⢀⠴⠁⢡
⠀⠀⠀⠀⠀⠀⠙⠓⢦⣅⡨⠊⠉⠙⠢⡶⠋⢀⠤⠾⠛⠁⠀⠀⠀⢀⣀⣀⠀⠠⠂⠀⠁⠂⠁⡠⠀⡀⡄⠀⠀⠀⠇⠀⠉⠂⡔⠁⠀⠀⠈⢣⠊⠁⠀⠄
⠀⠀⠀⠀⠒⠀⢒⣀⣀⣼⠁⠀⠀⠀⠀⢱⠠⠤⠤⠤⠄⠀⠀⠀⡪⠊⠀⠤⠀⡀⠀⠀⠀⠀⠀⠤⠄⠈⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⢨⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⣠⡔⠌⠣⣀⡀⣀⡠⡳⠤⣀⠀⠀⠀⠀⠀⠘⠁⠀⠆⣀⠄⠑⢄⢀⡀⠔⠐⠂⠀⠀⠡⠀⠀⢢⡀⠈⡧⠀⠉⠦⠄⡠⠔⠃⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠈⣩⠀⢠⡼⠁⣇⠉⢀⠑⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣄⠠⡀⠀⢀⠑⠒⠐⠊⠀⠀⠀⠀⠳⠈⠀⠀⠊⢠⠀⣄⣸⡀⠀⠄⡐
⠀⠀⠀⠀⠀⠈⠀⠀⣩⠀⢸⠃⢸⠀⠇⠀⠙⢆⠈⠂⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠑⢆⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡆⠀⠈⠉⠁⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠻⠀⠀⢀⣈⣁⡀⠀⠀⠸⠏⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢀⣠⣴⠾⠛⠛⠛⠛⠛⠛⠷⣦⣄⡀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⡄⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⣤⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠿⠃⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠈⠛⠷⣦⣤⣄⣀⣀⣠⣤⣴⠾⠛⠁⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢠⣤⠀⠈⠉⢉⡉⠉⠁⠀⣤⡀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡞⢹⠧⣄⠀⠀⠀⢀⡤⠼⡎⢳⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠗⠀⠀⠀⠺⣍⠀⣠⣄⠈⡽⠗⠀⠀⠀⠲⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢺⢃⡞⢳⡹⡟⣸⠁⠘⡞⣻⢋⡞⢳⡘⡗⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⣇⠸⡇⢰⠀⣿⠃⡼⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣤⡴⣄⣤⣄⣠⡶⢻⣄⣧⣸⣠⠟⢶⣧⣄⣠⡴⠦⣴⢖⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡁⢺⣧⣾⠀⣿⣧⢸⠙⢠⠀⠋⠀⡟⠛⣄⠘⠃⢸⡇⢐⣓⣸⣮⢁⡍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢲⡌⢻⡀⣿⡇⣼⠀⣾⡆⣸⠀⣷⠀⣿⢀⣿⢸⡇⠸⡿⢻⣿⣼⡇⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠛⢳⡬⢶⣻⡇⣿⣿⠟⠀⠿⣴⡿⠛⠿⣼⠟⣓⢶⡏⠀⠈⠳⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⢹⡇⣾⡂⣿⠇⣿⠀⣻⣥⣇⠘⢯⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢁⣿⡇⡿⠁⣤⡘⣿⡀⠿⢏⣿⡟⠶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠓⠚⠷⠶⠞⠋⠙⠛⠋⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⢠⡄⠀⠀⠀⢠⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠿⠀⠀⣀⣀⣀⣀⣀⠀⠈⠃⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠙⠃⣀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠳⢦⣄⠀⠰⠞⠋
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠻⠆⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠈⠙⠻⠷⣦⣄⣀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢀⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠲⠶⠶⠶⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⢠⠶⠶⠞⠛⠛⠉⠉⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠁⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠈⠛⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠈⡉⠛⠒⠶⠶⠶⠶⠖⠛⠋⠁⠠⣦⡀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠢⡄⠀⠘⡅⠉⠑⢦⡀⠀⠀⠀⢰⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠈⣦⢠⠃⠀⠀⠀⢱⠀⠀⣠⠋⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠊⠃⠒⠢⣄⠀⡞⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⡷⠚⠁⠀⠀⠀⠀⠃⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠈⠻⡄⠀⠀⢀⣀⣀⣤⡧⠀⠀⣤⣠⣎⡀⠀⠀⠀⠀⠀⠀⣇⡠⠔⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡖⠙⠉⠉⠉⠙⠲⢤⡇⠀⠀⠀⠀⢀⡽⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀⠀⡼⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠙⢄⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣀⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡴⠚⠉⠉⠉⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⠙⢒⠶⣐⡻⠭⠝⠛⠙⠋⠩⠿⢶⣢⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣖⡶⠿⠋⠙⠋⠙⠋⠽⢜⣣⢄⡀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⢀⠞⠀⠀⢀⣀⡰⡩⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⣄⠤⠤⠤⣤⢞⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡝⢦⣒⣫⢄⣀⡀⡄
⠀⠀⠀⠀⠘⠒⠒⢴⡃⢸⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢻⡠⠤⢤⡆⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡅⠘⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣀⡼⠧⣄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣬⠀⠀⠀⠇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠴⠀⣠⠞
⠀⠀⠀⠀⢠⠎⠁⠀⠀⠘⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠃⠀⠀⠀⠸⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⠓⠒⢏⡀
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⢮⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡵⠃⠀⠀⠀⠀⠀⠙⢞⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⠃⠀⠀⠀⠉⠑⠒⠒⡆
⠀⠀⠀⠘⠒⠂⠁⠒⠢⣄⡀⠀⣻⠪⢗⣤⠤⠄⡠⢤⣤⣒⠾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣲⣤⠤⡤⠀⠤⣔⡪⠕⣻⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠉⠙⡆⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢀⠧⠤⣄⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣀⣠⠔⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⣄⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠳⠊⠁⢀⠜⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠙⡶⠤⠤⠤⠤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢇⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣄⣀⣴⠋⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠉⠀⠀⠈⢳⢤⣀⠀⠀⢀⣈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡠⠚⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠈⠉⠙⠛⠀⠲⠂⠚⠋⠉⠉⢇⠀⠀⠀⠀⠀⢀⡎⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣠⢼⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⡞⠀⢸⠀⠀⠀⠀⠀⢀⠜⢆⠀⠀⠀⠀⡇⠈⠢⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢦⠀⠀⠀⢠⠋⠀⠈⠓⢤⣀⣀⣣⠀⠀⠀⠉⠑⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋

⣶⣾⣿⣾⣶⣿⢶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⠾⣶⠷⡶⢶⢶⣶⣿⠷⠶⠾⠷⡾⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣸⡼⠁⠀⠐⠂⠀⠀⠀⢀⣔⠯⠭⠭⢭⣑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢰⢋⡜⠠⠀⠀⢻⡇⠀⠀⠀⠀⡾⠃⡰⠋⠀⣀⣀⣀⠀⠈⠑⠾
⠀⠀⠀⠀⠀⠀⠀⠟⢸⡁⠀⠀⠃⠈⠻⠄⢀⡠⠤⠤⠤⣄⡀⠀⠁⠈⠉⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⡈⢧⠀⠀⢶⡀⠀⡴⠉⠀⠀⠀⠀⠀⠙⢆⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢤⣀⣀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣀⡀⠈⠙⠮⡑⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⠉⠉⠉⠘⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠉⠚⠀⠀⠀⠙⡌⡆
⠀⠀⠀⠀⠀⠀⢀⣌⠃⠀⠈⠀⠲⠞⠁⠙⢤⡀⠀⠀⠀⣀⡴⠃⠠⣄⡀⠀⠲⡄⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠘⢎⡳⣄⡀⠀⠀⢀⣠⠄⠀⠈⠉⠉⠉⠁⠀⠘⠂⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠯⠽⠟⠋⠁⢀⡤⠀⠰⠀⣼⠀⠀⡄⠀⠀⠈⡏⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⢾⠇⠀⠈⠃⠀⠀⢀⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⣙⣋⠭⠖⠁⠀⠀⠀⢀⡩⠴⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠘⡷⠀⠀⠀⢰⠇⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣷⢀⣠⠤⠒⠂⠈⠉⠁⠒⠲⢤⡀⠰⠋⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢲⠄⠀⠀⠀⠘⠀⠀⠀⠀⢀⣤⡀⣠⣄⠀⢀⠀⢀⡀⢀⣤⡀⠀⠀⢀⡀⠻⢼⢤⣄
⠀⠀⠀⠀⠀⡀⠀⢀⠽⣿⣇⣠⠞⣿⠀⢠⣶⠀⠀⣷⠎⢸⣷⢣⡿⠀⣿⡠⠋⣷⠎⣸⡇⠀⣼⣯⠇⢠⠏⣼⡟
⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⣿⡇⠀⣿⣀⠎⣿⠀⡘⣿⠀⢸⡇⣸⡇⡼⣿⠃⠀⠟⠀⣿⠃⣰⣿⠁⣠⠋⢸⣿⠀⣰⠂
⠀⠀⠀⠑⠀⠀⠀⢀⡾⢁⣿⡇⠀⠈⠋⠀⣿⡸⠀⠀⠀⠀⠀⣿⡿⠁⠈⠀⠀⠀⠀⢿⡴⠋⠙⠋⠁⠀⠘⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢧⠾⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠃⠀⣾⠀⡟⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢰⠗⢺⡇⢀⣧⣾⢤⣄⣴⣾⠹⠆⣰⣿⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡼⠀⢸⡇⣸⡿⢁⣴⡏⢺⡇⠀⣠⠇⡼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠈⠛⠋⠀⣎⠼⠁⠈⠛⠚⠁⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⣿⠀⠀⣿⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠱⣱⠀⢸⡇⠀⠋⣰⠀⢀⣾⠁⢀⢴⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠙⠆⠘⠀⢸⢹⠀⠀⣿⢀⢿⠇⢠⡿⠃⠀⠀⠞⠉
⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠈⠻⢶⣄⡀⠘⠦⠘⡏⣇⠀⢁⠎⡞⠀⢈⡴⠃⠀⢀⣀⣤⠖⠂
⠀⠀⠀⠀⠀⠀⠈⠓⠬⣝⣲⣄⡀⠀⠙⢯⡲⣤⠖⠋⠉⠉⠙⠺⣅⠀⣉⡠⢔⡺⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢿⡭⠚⠉⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠶⠶⢾⣾⣛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡤⢤⣌⣙⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣞⠲⢬⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⠭⠚⢡⠟⣦⣤⣀⣀⣠⡴⢫⣌⠉⠓⠺⠽⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⢏⠞⠁⠀⠀⠸⡄⢷⠀⠳⡕⢄⠀⠀⢀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⣴⡷⠃⠀⡴⡇⠀⡀⠹⡼⡆⠀⠈⠪⣧⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⢠⡾⠋⠀⠀⢰⠟⠀⠀⣷⠀⢻⣷⠀⠀⢦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⡀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⢠⣴⣦⡀⢠⣶⡄⣠⣦⠀⢠⣴⣦⠄⣴⡶⣦⡀⢀⣤⡶⣄⠀⣴⣶⣄⠀⣦⡄⠀⣤⡄⣰⡄⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠈⢿⣦⣄⠀⣿⡇⢸⣷⢸⣯⣿⣟⣿⠀⣿⣿⠿⠂⢻⡷⣟⠃⢰⣷⠀⣿⡄⣿⡃⣼⡇⠈⢿⣿⠋⠀⠛⠁⠻⣷⣄⡀
⠀⠀⠀⠀⠀⢰⣷⣿⣿⡇⢿⣿⣿⡿⣸⣿⣇⢸⣿⣇⢿⣿⣳⣦⣰⣇⣼⣷⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⣾⣿⡄⠀⠀⠰⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠈⠛⠛⠁⠙⠛⠃⠘⠛⠋⠈⠛⠓⠋⠛⠛⠛⠋⠀⠙⠛⠋⠈⠛⠛⠋⠀⠀⠛⠛⠃⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⠀⠀⢠⣴⣤⡀⠀⢠⣦⡀⢠⣶⡄⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⢀⣤⣶⣦⠀⠀⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣤⣿⠇⢀⣿⡃⢸⣿⡆⢼⣟⣷⣿⢻⡗⠀⣿⣧⣿⠇⠀⠀⠀⠀⢀⣿⣈⣿⡀⠀⢻⣿⣄⠀⠀⠸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⣷⣦⡸⣿⣷⣾⣿⡇⣾⣿⡟⢋⣿⣷⠀⣿⡟⢻⣶⡄⠀⠀⠀⣼⣿⠛⣿⣧⢀⣤⣝⣿⣿⣆⣠⣬⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠻⣿⣿⡿⠁⣿⣿⡿⢸⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⢰⣿⣿⡇⣿⣿⡏⢿⣿⣿⣿⡟⠻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠈⠁⠀⠈⠁⠉⠁⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⣿⣿⣷⣄⠀⠀⣿⡇⠀⢰⣿⣧⠀⢸⣿⢧⠀⢀⣶⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣀⣿⣿⠀⠀⣸⣿⣿⠀⠘⣿⣿⡆⠀⣿⣿⢿⣿⣷⣐⣿⣟⠀⢸⣿⣿⠀⢨⣿⣷⠀⢸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣅⠀⠀⣿⣿⣿⡀⢀⣿⣿⣷⠀⣿⣿⡄⠹⣿⣿⣿⣷⠀⣼⣿⣿⡀⣸⣿⣿⠀⠀⠙⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⣿⣿⣷⡄⢿⣿⣿⣿⣿⣿⣿⡷⢘⣿⣿⣷⠀⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣇⣶⣿⣦⣹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿⡷⠘⢿⣿⣻⣟⣿⣿⠁⣼⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠛⠀⠀⠀⠻⠿⠿⠟⠁⠀⠙⠿⠿⠿⠃⠘⠿⠿⠿⠃⠈⠻⠿⠿⠿⠿⠋⠀⠈⠛⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⠀⠀⠀⢀⣴⣶⣤⡀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⢀⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⡿⢿⣿⣿⣷⡀⠀⠀⢀⣿⣿⣿⣿⣧⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣆⣾⣿⡿⢿⣿⣿⠀⠀⠀⣾⣿⣿⡟⠀⠀⢻⣿⣿⣿⡀⠀⢸⣿⣿⠿⣿⣿⣇⣼⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⢹⣿⣿⣿⣿⠃⣾⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣇⠀⢸⣿⣿⣇⢹⣿⣿⣿⣿⠇⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⢻⣿⣿⠏⣸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣧⡀⠀⣸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣆⢻⣿⣿⡟⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆⠉⠉⢀⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣆⠉⠉⢀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠻⣿⣿⣿⣿⣿⠟⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡠⠤⡀⠀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⡼⠀⡈⢢⢀⠎⠀⠀⠀⠈⢢⠀⣀⡀⠀⠀⠀⡤⠒⠦⡀⢰⠁⠀⠹⡄⠀⠑⠉⠁⠀⢨⡀⢠⠤⠤⠄⢀⡀
⠀⠀⠀⠀⡜⠉⠁⠀⠇⠀⠿⡀⠀⠀⠀⢀⠍⡜⠁⠈⠉⠐⢺⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠶⢅
⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠈⠒⢤⣰⠋⢚⠀⠀⠀⣴⠤⠏⠉⠉⠓⡦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣁⣀
⠀⠀⠀⠈⡙⠀⠀⠃⠀⠀⠀⠑⠀⠀⣹⣀⡂⠁⡐⠠⡇⠀⠀⠐⠀⠠⣇⢀⡴⠚⠙⠒⢅⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⢀⠇
⠀⠀⠀⠀⢣⡀⠀⠀⢀⢄⡀⠀⠀⠀⢹⠁⠐⠀⠉⢰⠁⢀⠀⠀⠀⡤⢨⣟⠂⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⢻⣇⠀⠒⠀⠀⠀⠘⡆
⠀⠀⠀⠀⡎⠁⠀⢈⠥⣤⡁⠀⠈⢻⠶⠗⠒⡲⠂⢸⢰⡯⢦⡀⠀⠩⢿⡃⠀⠀⠀⠀⢠⢷⣀⠆⠀⠀⠀⠢⠀⢣⠀⠀⠀⢰⠴⠃
⠀⠀⠀⠀⣇⠀⠀⡆⠀⠀⠉⠢⣄⡼⠀⣠⣞⠃⠀⢸⡾⠁⠀⠀⡰⠃⡿⡟⠒⠢⠤⣴⠣⣻⡎⠀⠀⠀⠀⢀⢀⡽⠀⠀⠀⠈⠑⡄
⠀⠀⣄⣀⡈⣒⠖⡹⢆⠀⠀⠀⠨⠷⢆⠁⠘⡧⠄⠘⠃⢄⢀⡜⠁⠀⢈⠞⣆⠀⠀⢀⣠⡟⠓⠜⠀⢀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠽
⠀⠀⡼⠃⠀⠀⠉⠚⠈⠳⡄⠀⠀⠀⢀⠆⠀⢃⠀⠀⠀⡄⠊⠀⠀⠀⠊⡜⢨⡖⠈⣌⠀⣼⡀⠤⢱⠉⠐⠄⣀⢅⠀⠀⠀⠀⡤⠃
⠀⠀⠱⣄⠀⠀⠀⣐⠦⠀⠈⠢⣀⠤⡙⢄⠀⢸⠀⠀⢠⡁⠀⠙⠄⠰⢱⠀⡈⠁⡞⠔⢀⣽⠛⠢⣄⠓⠛⠒⢅⠀⠀⠀⠀⢴⠁
⠀⠀⡖⠒⠛⠀⠀⠈⠀⠀⠠⠀⠀⠀⠈⠊⠀⠘⠢⠤⠞⠀⠈⠀⢠⠘⣾⠮⠉⣴⡽⠀⠈⠀⠀⠀⠀⣣⢀⠈⠀⢳⠀⠀⠀⠀⢱
⠀⠀⠈⣢⡴⠆⠀⠀⠀⣀⠀⠀⠀⡰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⢠⣟⠀⠊⠀⡠⠀⠀⠴⠁⠀⠀⠈⡀⠇⠐⠠⣔⠁
⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡠⠒⠉⠁⠐⢦⣰⠉⠉⠁⠛⠀⢰⢄⠀⠀⣠⠊⠀⡀⠀⠀⠀⢀⡏⠀⠀⠀⠱
⠀⠀⠀⠳⡀⠈⡀⠀⠄⠀⠀⢬⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣸⠔⡡⠊⠉⠉⠄⠑⠦⣀⣀⣀⡠⠎⢡⢀⠀⠀⠈⠆
⠀⠀⠀⠀⢨⡖⠛⠁⠀⠀⠀⡀⢇⣀⢀⠠⢤⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡧⠔⠁⠀⠀⠀⠀⠀⠘⠠⠀⠀⠐⠄⢩⠀⡀⠀⡠⠃
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⢘⡤⡄⠀⢀⣀⣀⢴⠋⠀⠀⣸⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⡈⠀⠘⢣⡀
⠀⠀⠀⢼⡄⠀⠄⠀⠀⢀⡘⠙⠦⣀⡠⢶⣯⣞⠏⠂⠁⠀⠀⠸⢤⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠑⠀⠈⠠⣀⠀⠑⡀
⠀⠀⠈⠓⣅⣐⡀⣀⣀⠜⠀⠀⠀⠀⢠⠟⢉⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠴⢄⡀⠀⠀⠐⣲⣄⡴⣤⠐⠺⡀⠁⠀⣀⣅⠢⠕
⠀⠀⠀⠀⠀⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠑⠒⠊⠀⠁⠀⠁⠀⠀⠉⠑⠀⠉⠘⠀⠙⠚⠀⠀⠉⠉⠉

⠀⠀⠀⠀⡀
⠀⠀⣘⣶⣷⣖⡀⠀⠀⣴⣶⣦⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⣴⣶⣦⠀⠀⠀⢰⣶⣷⡄
⠀⠀⠨⠿⡿⠯⠀⠀⠀⠙⠿⠋⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠙⠿⠟⠁
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⣾⣿⣿⣿⡆⠀⠠⣿⣿⣿⡆⠀⠀⣲⣿⣿⡆⠀⠀⠀⣶⣶⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢰⣿⡆⠁
⠀⠀⠙⠿⡿⠟⠁⠀⠀⠻⠿⠟⠁⠀⠀⠈⠛⠛⠁⠀⠀⠀⠉⠋⠀⠀⠀⠘⠿⢿⠿⠃⠀⠀⠂⠄⠄⠂
⠀⠀⠀⣀⣄⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⡀
⠀⠀⢼⣿⣿⣿⠄⠀⠨⣿⣿⣿⠅⠀⠠⢽⣿⣿⡧⠀⠀⣹⡋⠉⣷⠂⠀⠀⢰⣿⡆⠀⠀⠀⢼⣿⣿⡆
⠀⠀⠈⠛⠟⠋⠀⠀⠈⠙⠛⠋⠁⠀⠀⠁⠹⠙⠁⠀⠀⠐⠛⠿⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠊⠙⠩⠂
⠀⠀⢀⠄⠢⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⣠⣠
⠀⠀⡃⢾⣿⠈⠂⠀⠰⣏⠀⣹⠇⠀⠰⣿⠀⢈⣿⠀⠀⠀⢾⣿⠀⠀⠀⢺⣿⣿⣿⡗⠀⠀⢺⣿⣿⡇
⠀⠀⠈⠂⠒⠉⠀⠀⠀⠈⠋⠁⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠜⠈⠢⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⣄⠀⠀⠀⢹⠃⠀⠀⠀⠰⠆⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⢸⡏⢿⡄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⠇⠈⢿⣄
⠀⠀⠀⠰⢤⠐⠋⠈⠦⣀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠙⠳⠶⣦⣤⣤⣤⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠱⡄⡔⠋⠉⢀⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⢿⠢⠤⠤⢺⠏
⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠉⠛⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡤⠤⠤⢬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣷⢀⣾⠁⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠑⠤⣤⠄⠀⠀⠀⠀⢀⡾⠀⠙⢦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢄⢠⠊⠀⠀⠀⢠⣴⣚⡉⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠈⢢⠀⠀⠀⡖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠡⠀⡠⠃⠀⠁⡀⠀⠀⠀⠀⠀⠀⡠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠂⢄⣸⠁⢀⣀⣀⣠⣤⣤⣀⣋⣀⠀⠀⠀⠰⠴⠒⠒⠒⠒⠋⠁⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⡇⠀⠀⣠⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠛⠢⡄⠀⠀⠀⠀⠉⠒⠤⣇⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣜⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠉⠲⠤⠴⠋
⠀⠀⠀⠀⠀⠀⣇⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡠⠁
⠀⠀⠀⡠⠐⠈⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡠⠚
⠀⠀⠮⠤⣀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠑⠦⡀
⠀⠀⠀⠀⠈⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣈⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠒⢒⠏
⠀⠀⠀⢀⡴⠊⠁⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⠔⠁
⠀⠀⢠⠊⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡠⠤⠄⠒⠊⠁
⠀⢠⡇⣀⣀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⡄
⠀⠸⠋⠀⠀⠉⠑⠠⢤⣀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠻⣤⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⡤⠄⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⢀⠇⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⣩⠿⡛⠛⠛⠛⠉⣩⠓⣄⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣀⠴⠒⠚⠉⠀⠀⠱⡀⠀⠀⡼⠁⠀⠈⠑⠤⣀⣀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢧⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣶⠀⠀⠀⠀⡞⠳⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⡄⠀⠀⣿⠀⠀⠀⣸⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⣄⠀⠀⠀⠹⡄⠀⢹⠀⠀⢀⡾⢷⣶⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⢃⣄⠀⠀⠘⣄⢸⠀⠀⡸⠀⣠⠋⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢼⣸⠁⠑⡤⠖⠉⠉⠉⠉⠓⢶⡁⠀⠀⣀⡴⠚⠁⠈⣇
⠀⠀⠀⠀⠀⠀⢸⠓⠲⠤⣄⣀⠀⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣶⠊⠁⢀⣀⣀⣠⡼⠦
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⢉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠉⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⢙⣦⡀⠀⠀⠀⠀⠀⣠⠞⠳⣄⠀⣠⡿⠋⠙⠒⠒⣦
⠀⠀⠀⠀⠀⠀⠀⢶⠊⠉⠀⠀⢀⡴⠋⠀⣹⠛⢲⠒⠲⡏⠳⡄⠀⠀⠑⢿⡁⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡠⠊⠀⠀⢰⠇⠀⡿⠀⠀⢧⠀⠘⢆⠀⠀⠀⠙⠢⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⢠⣯⣤⡤⠇⠀⠀⢸⡄⠀⠈⢣⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠚⠋⠉⠉⡇⠀⠀⠀⣇⠀⢀⣤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⡀⠀⡇⠀⠀⠀⢻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠈⢳⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⡟⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣄⠀⠀⣿⣿⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⡆⠀⢸⣺⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⢿⡀⢠⠏⢀⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠻⢦⠈⠇⢠⠟⠉⠉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠄⡀⠙⠀⠀⠋⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠁⠀⠀⠀⠁⠐⠂⠺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⢀⣤⠄⠀⠀⠀⠀⢈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⡋⠀⢀⡄⢀⡠⠀⡀⠀⠲⣦⢀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠸⠁⠀⠰⣦⠈⢷⣌⢳⣶⣶⣾⣿⣿⣿⠛⢿⣿⣿⣿⡏⣰⡟⠁⣼⣧⡄⠀⢉⢸⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣆⠀⢰⡇⣿⡄⠘⣿⣬⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣷⣿⠃⣰⣿⡟⣧⡀⢸⡸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣿⣴⣿⡇⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣴⣿⣿⡇⣿⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢨⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⣸⡇⠀⠀⠀⣿⠃⠀⣤⠀⠀⢠⡾⠋⣿⡄⠀⣼⡏⣠⡿⠀⢀⣠⡶⠶⠆
⠀⠀⠀⠀⠀⠀⣼⠏⠀⢻⣿⠇⠀⠀⣼⡏⠀⠀⢉⡀⠀⠸⣧⡀⠿⠁⢀⣿⡿⠛⠁⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠻⠀⠀⢸⣿⠀⣀⣼⠏⠀⠀⠀⣿⣧⠀⠀⣈⡻⣦⣤⡿⠻⣧⣀⣠⡿⠁⠀⣀⢠⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⠟⢿⡄⠀⠀⢸⡟⣿⡀⢠⡿⠁⣼⠟⣷⡀⠈⠉⣉⠀⢶⣄⠸⡀⢷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠘⣷⡀⠀⣾⠃⠙⠷⠟⠁⢸⡏⠀⢸⣧⠀⠀⢿⢣⠈⡏⠳⣇⠸⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠹⣧⣼⠏⠀⠀⠀⠀⠀⢻⣇⣀⣸⡟⠀⠀⢸⡊⢳⠘⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠈⠁⠀⣀⣀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠈⠁⠀⢠⡾⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠏⢹⣧⠀⠀⠀⠀⢠⣦⠀⠀⠀⢀⡀⢠⡿⠁⠀⣾⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⢻⣆⠀⠀⣿⠀⢸⡿⠀⠀⠀⠀⠈⠉⠀⠀⠀⣾⣇⣼⠇⠀⢠⣿⠀⠀⣴⠟⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣿⠀⠀⢿⡄⣼⡇⠀⣀⡀⠀⠀⢸⣷⠀⠀⣿⣿⣿⠀⠀⣾⠇⠀⣼⣏⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡿⠀⠀⠸⣷⡿⠀⣾⠋⢻⡆⠀⢸⣿⡄⢀⣿⢿⣿⠀⣸⡏⠀⣼⣿⡛⠋⠉⠀⠀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠛⠁⠀⠀⣰⣿⣧⠀⣿⠀⢸⣷⠀⣸⣿⡇⢸⡏⠸⠟⠀⣿⢁⣼⠏⠙⢷⣦⣤⡶⠟⠋⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⢶⣾⡏⠀⠹⣧⣿⡆⠀⣿⠀⣿⠀⠿⠿⠁⠀⠀⠀⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⢿⡄⠀⠈⠉⠁⠀⠹⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠈⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⡼⡄⠀⣤⡝⠦⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⠀⠒⠾⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⠁⡧⡀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠌⠀⠀⢀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠘⠋⠓⠒⠀⠂⢄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢴⣒⡒⠛⠛⣓⠲⣤⢶⡖⣦⣀⣰⢶⠋⠉⠙⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠀⢀⣀⣀⠀⠀⣿⠀⠀⢸⣿⡏⢸⠀⠰⣶⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠐⠿⠿⠛⠀⠀⣿⡆⠀⠀⠁⠀⢸⠀⠀⣤⣴⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⣶⣶⣶⡆⠀⣿⣿⠀⠀⡀⠀⣸⡀⠀⠀⠉⠉⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠦⠾⠿⢿⣿⣿⣾⣿⣿⣷⡾⡻⢶⣿⣿⠛⣿⠛⠿⠗⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢶⣶⣶⣿⠉⠈⣁⣀⡀⠘⡏⠀⠈⠻⠁⠀⣿⠀⢴⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠢⠀⠀⠀⣿⠀⠘⠿⠛⠋⠀⡇⠀⠀⣀⣠⠀⢹⠀⠰⠶⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣠⡴⠛⠶⠶⡶⣢⣶⣿⣧⣤⣴⡟⣵⡧⠼⢤⠤⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣸⣿⡇⡽⣽⣻⡿⢰⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣳⣼⣿⢃⢇⠿⣱⣇⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠷⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⡟⣧⠀⠀⠀⠀⠀⠀⣸⢿⣿⡄⠀⠀⠀⠀⠀⣀⣤⠞⡻⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⡿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣄⡀⠀⠀⠀⠀⢻⡄⠳⣄⠙⠳⢦⣄⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡀⣧⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⡈⠙⢲⣄⠈⢿⣾⠃⢸⡇⠀⢿⡀⢀⣸⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡑⢌⠙⠳⢤⡀⠀⠙⣦⠀⢻⡄⣸⣿⣤⣼⣧⣄⣸⣷⡟⠉⣠⠟⢀⣾⣁⣤⠞⢋⡖⣿⠋
⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⢠⡴⢋⡼⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣶
⠾⠛⠳⣦⡉⣷⣄⠀⠀⠀⠀⠀⣀⢹⣄⠀⠻⣦⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣾⠋⢠⡞⠁⠀⢀⣤⠶⢛⣋⣉⣉⡛⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⠛⠷⠿⠛⠋⠉⠙⠻⢧⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣟⣀⣀⣴⠟⣡⠞⢉⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣮⣙⡓⠒⠛⠛⠛⠲⣤⣼⠏⠀⣠⠶⠞⠛⠻⠿⢷⣴⣶⠀⠀⣾⣆⣤⣶⣞⣾⠳⠶⣤⣀⠹⣏⠉⠉⣁⡴⠃⢠⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⣦⣸⠏⠀⣀⠁⢠⣴⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣛⡽⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⡿⠷⠶⠃⠈⣿⠿⠿⣯⣄⣀⡀
⢀⣀⣠⣤⡶⠶⠚⢛⣉⣁⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣀⣉⣉⣙⣛⣷⣶⣦⣤⣄
⠈⠛⠛⠛⠿⠿⢭⣤⣄⣀⡈⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢡⣟⠀⠀⠈⣿⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣀⣀⣠⣤⠤⠶⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⠿⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⠷⠶⠾⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢠⡴⠖⠚⠛⣷⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣤⣤⣤⣤⣤⣀⣠⣄⠀⠀⠀⠀⠀⢀⣿⡀⠀⠳⣤⣄⣠⣤⣀⣀
⠀⠀⠀⣀⣀⣀⣀⣼⠇⣰⠏⣠⣤⢤⣾⠟⢳⡄⠀⠀⠀⠀⠟⠛⠛⢿⡷⠾⠷⠞⢻⡟⠛⠛⠀⠀⠀⠀⢠⣾⡀⠙⠳⢦⡤⠴⠶⠦⢬⡙⢷⡄
⠀⣴⢟⡭⠍⢩⣭⠤⠞⢃⡼⠋⠀⣰⠏⠀⢀⣽⢦⡀⠀⠀⠀⠀⠀⠀⠙⢶⣶⡶⠞⠃⠀⠀⠀⠀⣠⣴⡋⠈⢷⣦⣄⣀⣤⡤⠶⠶⢶⣌⢦⣹⡄
⢰⣧⡶⠶⠛⠲⠶⠶⠞⠋⠀⠀⢰⠏⠀⣰⠟⠁⢀⣽⠷⣤⣀⠀⣀⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣉⠈⠙⢦⡀⠻⣆⠁⠀⠀⠀⠀⠀⠙⣦⣹⡿⢶⣶
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠞⢁⣠⢾⡟⠀⢠⡟⠉⢙⣿⡿⠷⣶⡶⠶⢶⠟⢻⡏⠀⡟⠙⠳⣦⡀⠙⢦⠙⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣴⣡⠶⠋⠁⠘⣷⠀⣾⠀⣰⠏⠈⣷⠀⢻⠀⠀⣾⡄⠈⣧⠀⢷⣀⠀⠈⠙⠳⣦⣁⢬⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡄⢸⠀⢰⡟⢷⣄⠈⠳⢤⡙⢷⡄⠀⠀⠀⠉⠻⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⠇⡼⢀⣿⠀⠀⠘⣧⢸⠀⣾⠃⠀⠙⠓⠶⣆⢹⡄⢿⠀⠀⠀⠀⠀⠀⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⡔⢁⡼⠃⠀⠀⠀⢻⣸⢠⡇⠀⠀⠀⠀⠀⢹⡆⠇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡶⠛⠁⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣡⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⡗⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠋⠁⠀⣾⡆⢻⠏⣹⣶⣆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠶⠀⠀⣤⣤⣾⠛⣁⣄⢰⡄
⠂⠀⠀⡔⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠸⢿⡏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡖⠛⡻⣿⣷⡟⠤⢛⣻⣿⣿⠻⠛⡉⢉⡄
⠀⠀⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠁⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⢧⣿⣿⠋⠀⠀⢸⣿⣿⠂⢻⠿⠻⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣆⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣉⣿⣿⣿⠖⠉⠀⣰⣿⣿⣷⢰⣿⢷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡿⠉⠀⢀⢾⣯⣼⣯⡏⢠⣄⣤⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠂⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣠⢠⡟⠀⠀⢠⡟⢸⣿⣿⣿⠿⠛⠻⢿⠁
⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡄⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⢠⡞⣡⠟⠀⠀⠀⢈⠁⣾⣿⣿⣷⣦⣄⣶⣾⣇⣸⠂
⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⢀⣮⠁⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣿⡟⠏⠀⢀⣝⠛⢿
⠀⢀⠀⠀⠄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⣠⣾⣿⣿⠟⠁⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠸⣧⡈⣿⣿⣿⣿⡿⢃⠀⢽⣿⣮
⠀⠀⠀⠁⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⡴⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠘⠃⢸⣿⡀⠀⠀⠀⠀⠀⠀⠻⣬⣟⠻⢿⣾⣿⣿⣾⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⡀⠀⠀⠻⠟⠛⠻⠷⢦⠀⠀⠀⠀⢻⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⢮⡙⢩⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠿⠿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠙⣯⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⠀⠀⢀⠀⢰⡀⡀⡋⠀⠀⠘⢻⣗⠀⠀⠀⣠⣶⣾⣿⣿⣶⡄⢨⠆⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣦⣈⡛⠛⢿⡷⠀⠀⠠⢤⣿⡏⠐⢶⣿⣿⣿⣯⣽⣿⣿⡇⢰⠄⢿⡿
⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣧⣦⣀⣴⣀⠈⠰⠿⠏⠀⠀⢰⣿⣿⣿⣿⣿⡿⠛⢠⡾⢰⣿⣿
⠀⠀⠀⠘⠞⠉⠀⠋⢉⣄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⠓⣿⣥⣾⣿⣿⠿
⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⢿⣟⠓⠛⠁
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠄⠀⣠⡴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠰⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠈⣿⣷⡽⣧⡀
⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠃⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⢀⣼⣿⣿⣷⣾⣧⡆
⢀⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣿⡛⣿⠿⣿⣿⣿⣿⣿⣿⣦
⣼⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡜⢇⠀⠀⠀⠀⠹⣷⡀⠀⠀⣼⣿⣏⣷⣾⣿⣿⣿⣿⣿⣯⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠀⠀⢀⡀⢹⡾⠃⠀⠀⠀⠀⠘⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣾⣣⡘⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⢻⣿⣿⡿⠋⢉⣽⣿⣿⣿⣿⣿
⡿⠟⠲⢺⡅⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢰⠀⣤⠀⠀⣀⠛⣁⢡⡀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠋⣀⢀⣿⣿⣟⠻
⡷⢺⣦⢤⡇⠀⠀⠀⠀⠀⡄⠐⣿⣇⠀⠀⠀⠀⠘⣷⣄⡤⠀⠛⢱⡏⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⣀⣴⢿⣏⠉⠻⢿⣿
⣿⣿⣄⣶⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⣈⢥⠄⠲⢶⠞⣣⠀⠀⠀⠀⠀⣼⡏⠛⠛⠉⠉⠹⣿⣿⠧⠔⠈⣻
⣿⣿⣿⣿⠟⠗⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠑⢀⠛⢃⡶⠦⡀⠀⢡⣴⣶⣆⠀⠀⠈⣡⡄⠀⠀⠀⠀⣶⠀⠀⠀⠐⠻
⣌⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡈⠻⠟⣡⣦⡀⠀⠛⠀⠀⠹⠃⠀⠀⢙⣥⣤⠀⠀⢸⠋⠀⠀⠀⠀⠆
⡏⢹⣟⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠋⠀⡅⠀⠀⠀⠿⠀⠀⠀⠀⠈⣻⠁⠀⠀⠺⣤⣶⣦⣄⣀
⠏⠸⣧⣻⣿⡿⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⠻⣦⡄⠀⠀⠘⢿⣿⣿⣿⡏
⣆⠀⠀⠙⠟⠀⣠⠶⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠈⡜⠂⠀⣄⡀⠉⠁⠉⠻
⠉⠂⢀⡀⠀⠂⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣆⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠁
⠀⠀⠈⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠀⠀⠀⣹⣿⣿⣷
⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣶⣶⣄⠀⠀⠐⣭⣻⣿⣭⣅⠀⢸⡆⠀⣀⠀⠀⣠
⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⠀⠀⠀⠀⠻⠿⠿⠆⠉⠀⠉⠛⠁⠀⠈⠁⣼⠷⠾⠛⠁⣈⠙
⣯⡛⣷⡄⠀⠀⠀⠀⠀⠘⣿⠛⠉⠉⠁⠀⠀⣨⣿⣿⣿⠃⠀⠀⠀⠈⣷⣶⡷⣠⣤⡀⠀⠀⠀⠀⢠⣶⣤⡄⠀⣾⣿⣤⣴⣶⣶⣿⡇
⡙⢻⡼⣿⠀⠀⠀⠀⢶⣾⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⡟⠉⣵⣿⡾⣿⣷⡄⠀⠀⠘⠛⠁⠀⠀⠀⠻⠛⠃⠸⣿⣿⣷
⠇⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣤⣤⣷⡀⠈⠻⠷⠛⠁⠀⠈⢣⣶⣦⣴⣶⣶⣾⣿⣿⣿⣶⡟⠿⠿
⡄⢰⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠘⢿⠏⢙⡃⠀⠀⢀⡀⠀⠘⠀⠸⠛⠻⠿⣿⡟⠉⢻⣿⣿⡿⣇
⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣴⡦⢿⣿⣟⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡅⠻⣿⡇⡀
⢸⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠛⠋⠀⢻⣿⣿⣷⡄⠘⠷⠀⠀⣤⣤⣤⣤⣮⣉⠀⠀⣀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢷⠀⠀⢿⠀⠀⡿⠀⢀⡎⠀⢠⠆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠐⣄⠀⠈⢧⠀⠘⣇⠀⠸⠄⠠⠧⠀⣼⡀⣠⠏⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⢣⡠⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢎⠀⠀⠀⠀⠀⣀⣤⣤⡄⠙⣿⡿⢛⣿⠟
⠀⠀⠀⠀⣴⡟⠁⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣤⣀⣴⣶⣦⠀⣴⣟⣽⠟⢀⣼⠟⢀⣾⠏
⠀⠀⠀⢸⣿⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⢀⣤⣤⡀⣴⠾⣿⡆⢀⣿⣿⡟⠀⣿⣿⠃⣿⡇⢰⣿⡿⠋⢠⣾⠋⠀⣾⡏⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢰⣶⠆⠀⣼⣿⣷⡟⠁⣿⣿⠏⢸⣿⠀⣼⣿⡟⠀⢰⣿⠇⢰⣿⣁⣾⣿⣤⡴⠟⠁⠀⠀⣿⣇⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⢀⣴⣿⣿⠀⢠⣿⣿⠀⣼⣿⣿⡟⠀⢸⣿⡏⠀⣿⣏⣼⣿⣿⠀⠀⠺⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣶⠛⠁⣿⡇⢀⣾⣿⣟⣰⡟⢹⣿⠀⠀⠸⠟⠀⠀⠈⠉⠁⣠⡤⣤⡄⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣿⣇⠀⠻⠷⠾⠋⠈⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢡⣿⠇⠀⠀⠀⠀⣾⡟⣽⡟
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣟⣰⡿⠋⠀⠀⠀⠀⠀⢘⣿⣿⣅⡀
⠀⠀⠀⢰⣿⠁⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣾⡟⣿⡆⠈⠛⠀⢠⣿⣿⣋⠀⠀⣴⡟⣿⡇⢠⣾⠏⠀⠙⣷⡄
⠀⠀⠀⠈⢿⣦⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣶⣿⠷⣿⡟⠀⣾⣿⢿⣽⣷⣼⣿⠟⠋⣰⣿⣷⡶⠷⢄⣿⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣿⡏⠀⣿⡇⣸⣿⡇⢀⣿⡏⠸⣿⣤⣾⠟⠘⠿⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣾⡟⠀⠀⣿⣷⡟⠙⠻⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠾⠋








⣿⠛⠛⣿⢿⠿⢿⠿⠿⣿⡿⠿⠿⡿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⣿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⣶⡆⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡺⠂⢒⡆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠐⢋⣀⣏⠀⠀⣀⠀⠀⠀⠀⠀⠘⠓⢆⡠⠗⠀⠀⠀⠈⠻⠃
⠀⠀⠀⠀⠀⠀⣰⢀⡠⠃⠐⢅⠵⠀⠀⠀⠀⠈⠀⡀⢄⠀⠈⠀⠀⠀⠸⠥⠇⠀⠀⠀⠔⠊⠀⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠤⠒⠀⠀⠀⣀⡀⠤⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠒⠢⠄⡀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠐⠀⢀⠎⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠤⢤
⠀⠀⠀⠀⠀⠀⢰⣛⠆⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠑⠀⠀⠰⠀⢠⠃⠄⠀⢀⠤⠒⠁⠀⡤⢦⠀⠀⠰⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⠉⠀⠀⠎⠆⠀⠀⠁⠢⢀⠀⢀⠀⢀⠆⠀⡠⠂⠀⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⢄⢀⠀⠀⠊⠐⣀⠠⠤⠒⠂⠉⢡⣄⠀⠀⠉⠉⠀⠀⠀⢀⣃⡀⢈⠝
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⢄⠀⠀⢠⠀⠈⠉⠡⠉⠀⠀⠐⠂⡀⠀⠀⠂⢈⣀⣐⡀⠀⠀⠀⠈⠋⠀⠀⡄⠀⠰⣉⡇⠀⠀⠈⠛
⠀⠀⠀⠀⢰⠒⠋⢦⡄⠀⠃⠚⠀⢀⡀⠤⠄⠒⠂⠁⠉⠉⠁⠀⡀⠀⡀⠀⢀⠐⠀⠀⠈⠉⠉⠑⠒⠠⠤⣀
⠀⠀⠀⠀⠰⠥⠦⠇⠀⠀⠐⠊⠉⠀⠀⠀⡀⠁⢀⠠⠒⢉⠀⡘⠀⠃⠐⡄⠂⠁⠀⡈⠀⠀⠀⠀⡤⢄⠀⠀⠉⠒⢄⡀⠀⠀⠀⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠄⠊⠉⠀⢀⠥⣄⠀⠀⡔⠀⠀⡄⠀⠐⡄⠀⣀⡀⠑⢄⠀⠀⠑⠋⠀⠀⠀⠰⠆⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⡠⢐⠁⠀⠈⠓⠋⢀⠎⠀⠇⠀⡇⠀⠀⠠⠸⠤⠏⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡀⠀⠀⠻⠇⠀⠀⠀⡰⠁⠀⡜⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠛⠀⠀⠀⠀⠀⢾⣉⡆⠀⠀⠀⠘⡦⣀⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠤⠜⢂⠉⠀⠤⠀⣠⠆⠀⡠⠊⠀⠀⠐⠁⠀⠀⢠⣶⡄⠀⢠⠀⠀⡴⠒⡄⠀⠀⠣⠀⠀⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠨⠤⢐⠉⠀⠄⠊⠀⡠⠊⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⢀⠀⢸⠀⠀⠈⠋⠁⠀⠀⣀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠑⠼⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⢀⡀⠀⠀⠀⠀⣱⣀⣠⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡤⠁⢠⠄⠀⠀⠀⠈⠀⠻⠿⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠒⠋⠀⠂

⣿⣿⡿⠛⠋⠉⠁⠈⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠿⠛⢉⡽⠛⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋⠁⣠⠞⠉⠀⢀⣤⣤⣶⣤⡀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣀⣠⠞⠁⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣭⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠞⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢯⡾⣰⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡏⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠏⢼⠃⣿⣿⣿⣿⣿
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣠⣴⣫⠭⠍⠉⠈⠰⠿⠋⠠⠏⢸⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣶⣶⣶⣶⡆⢶⡀⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠻⡆⠀⣴⣿⣿⣿⣿⣿⣷⣶⠀⢸⣿⣿⣛
⠈⢿⣿⣿⣿⣿⣿⣿⣧⢸⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠤⠖⠖⠚⠇⠀⠀⠀⠀⠀⢀⡄⠘⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿
⡀⠘⣿⣿⣿⣿⠿⣿⣿⡌⢿⡌⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢁⣠⣤⣶⡆⠀⠀⣀⣤⣄⣀⠀⢸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠈⠙⢿
⠧⠀⠘⣿⣿⣿⣿⣿⣿⣷⠸⣇⢻⣿⣿⣿⣿⣿⣿⠀⣴⣾⣿⣿⣿⣿⣇⣴⣦⡀⠀⠉⠉⢿⣾⣧⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷
⣶⣦⠀⠹⣿⣿⣿⣿⣿⣿⡄⢏⠆⠙⢿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠹⣿⣷⣤⡐⢤⣈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⡈⣇⠀⡈⠻⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⠀⠘⢿⣿⣿⣷⣮⣁⠹⣿⣿⣿⣿⣿
⣍⠻⠿⠆⠀⢻⣿⣿⣿⣿⣿⣷⡘⢷⡹⠀⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠂⠀⠻⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿
⣿⣷⣤⣴⡄⠀⠻⣿⣿⣿⣿⣿⣷⡀⢳⡄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠙⠒⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣷⣿⣄⠀⠀⠉⠛⣿⣿⣿⣧⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣎⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⠸⣿⣿⡿⢡⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⡘⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣥⣿⣿⣿⡌⣆⢹⡟⠁⠟⣱⣿⣿⡛⢿⡛⢿⠛⠛⠛⣿⡟⠛⡟⠛⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⡆⠀⢀⡼⣻⣿⣯⡃⢿⣇⠀⠀⠀⠀⣿⠇⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⡒⠒⠂⠀⠀⠈⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣠⣶⡿⣿⣿⡅⢧⣥⣴⣤⣤⣤⣭⣤⣦⣤⣴⣬⣿⣿⣿⣿⣿⣿⣿⣷⡀⠠⠤⣀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⠏⠀⠀⢘⣋⣡⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⠑⠢⠉⠋⢻
⣿⣿⣿⣿⣾⣿⣿⣿⠏⠀⡠⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠁⠀⣀⣤⣼
⣷⣿⣿⣿⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⣿⣇⣤⣄⠀⠀⢠⣦⣰⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢠⣤⡀⠀⣿⣿⡇⣿⣿⣿⣿⣧⠀⣿⣿⡇⣾⣿⣷⣷⡄⠀⠀⣀⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢻⣿⣆⠸⣿⣷⡀⢻⣿⣧⢹⣿⡇⣿⣿⢸⣿⣿⢰⣿⡟⣼⣿⡇⢠⣾⣿⠟⢡⣿⡇
⠀⠀⠀⠀⠀⢠⣾⡟⠻⣷⣄⠈⢿⣿⣄⢿⣿⣿⡎⠿⠿⠈⠛⠃⠙⢋⠈⠛⠃⠘⠿⠁⣿⡿⢠⣿⣿⣏⣴⣿⠟⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠈⢿⣷⣤⣈⣛⠀⠀⠙⢿⣿⠃⠉⠁⠀⣠⡀⠀⠠⣴⣿⣦⡄⠀⢀⣀⠀⠀⠀⠘⣿⣇⣉⠛⠉⣠⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠾⠛⠇⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⢠⣾⣿⠟⠉⠀⢾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠛⠀⠀⣠⢖⣿⣿⣿⣿⣿⣶⣦⣤⠀⣤⣴⣶⣿⣿⣿⣿⣿⡲⣄⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣼⣿⣿⣿⣿⣿⣿⣿⠏⣀⡹⣿⣿⣿⣿⣿⣿⣿⣧⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⢡⡾⠉⡇⠈⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠶⠆⠀⠀⠉⠛⠋⠉⠀⠀⣾⠃⢰⠁⠀⠀⠀⠉⠙⠛⠉⠁⠀⠰⠾⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠀⠀⠀⠀⢀⡀⠀⠤⢸⣿⢠⢃⣀⡀⠀⠀⣀⠀⣠⣄⠀⠀⠀⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠉⢀⠀⠀⣼⠀⢿⣆⣴⠆⢸⣿⣡⠋⢸⡇⣠⡾⠍⠀⣿⡘⢀⠀⠀⣀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⢻⡀⡜⠀⣿⠀⡜⣿⠷⢒⣿⠋⢸⡇⣠⠆⣨⢿⡁⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠻⡴⢡⡏⣀⣾⠏⠀⠀⠉⠁⠀⠣⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠘⢦⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢡⠀⢀⠞⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠂⢄⡀⡼⠁⠀⠀⣀⣀⣀⣀⣀⠓⠁⠀⠀⠀⠰⡤⠤⠤⠤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡬⠗⠒⠉⠉⠉⠀⠀⠀⠈⠉⠉⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠶⢤⡉⠀⠀⠀⠉⠐⠢⢄⣸⢀⡴⠚⠁⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⠝⠁⠀⠀⠀⠀⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠛⠿⣦⠀⠀⠀⠀⠈⠑⣄⠀⢀⠌
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠒⠉⠈⠑⢢⡀⠀⡠⠄⠒⠒⠤⡀⠀⠀⠀⠀⠀⠈⠣⡈⠉⠒⠦⣄⣀⡠⠆
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠱⡜⠁⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⡀⠤⠘⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⣄⠀⠀⡇⢀⢤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⡔⠁
⠀⠀⡠⠊⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠻⠟⠀⠀⡇⠘⠿⠃⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⠲⢅⡀
⠀⠀⠉⠉⠓⢄⠀⠀⣸⠀⠀⠀⠀⡤⠖⠋⠀⠀⠀⠱⣄⠀⠀⠀⢀⡼⠉⠢⣀⠀⣀⠔⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠈⠲⢄⣿⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⣤⣀⣀⡤
⠀⠀⠀⠀⠀⣠⠔⠊⢹⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⣠⠊⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⡏⠓⠦⠤⢀⣀⠀⠀⠀⠀⢀⠀⣀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡠⠔⠁
⠀⠀⡰⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⡈⠉⠉⠁
⠀⢠⣃⠤⠤⠤⣀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢱⡀
⠀⠈⠁⠀⠀⠀⠀⠁⠒⢲⠄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡔⠈⠉⠉⠛⢀⣀⠕⢻⣇⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠙⠦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⠠⠄⠀⠠⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⠒⠀⢙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡘⠀⠀⠉⠓⠶⢤⣄⣀⣀⡀⠀⠀⣀⣀⣀⣤⠴⠖⠋⠁⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡬⠻⡉⠉⠉⠉⠉⡠⠋⢦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡤⠖⠊⠉⠀⠀⠀⠙⣄⠀⠀⡾⠀⠀⠀⠈⠲⠤⣀⣀⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⣤⠀⠀⠀⠀⠀⣀⣄⠀⢀⣀⠀⢀⡀⠀⣀
⠀⠀⠀⠠⣦⠀⠀⣀⣄⡀⠀⠀⠀⣿⠀⣃⢤⡟⢀⣴⠂⢀⣾⡣⣻⡟⢡⡟⢠⣿⡐⣿⠖⢹⡇⣰⡿⠃⠀⣸⡧⠊⠙⠀⠀⣤⢤⣄⠀⠀⡤⢄⡀
⠀⠀⠀⠀⢻⣧⣼⣯⣹⡏⠀⠀⠀⣿⠊⠁⠸⡷⠋⣿⡴⠁⠿⠁⠛⠀⣼⢣⢿⠟⠰⠏⠀⣿⣠⠿⡤⠴⠊⡿⠁⠀⠀⠀⠘⡿⠛⠛⢠⡾⢁⠀⠁
⠀⠀⠀⢰⠛⠛⢛⡻⠻⡁⠀⠀⣮⡾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣄⠘⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣠⠛⠒⠘
⠀⠀⠀⠈⠃⠈⠹⣧⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⢠⡄⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢀⠀⠐⠃⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠹⣇⠀⢃⠀⠀⠀⠀⠀⣿⡆⠀⢠⣿⠃⣴⠄⢸⣿⣴⣶⣦⡄⢠⡿⠋⢹⣿⢸⣿⣉⡙⠃⠀⠀⠀⠀⠀⠢⢀⠀⠀⡠⠂
⠀⠀⠀⠀⠐⡀⠀⠀⠹⠆⠈⠀⠀⠀⠀⠀⢸⣧⠀⣾⠇⠀⣿⠀⢸⣿⠁⢀⣼⡏⢸⣟⠛⠛⠁⠀⠉⠛⠻⣷⡀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠐⠄⠀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠻⡿⠋⠀⠀⣿⠀⢸⣿⠟⠛⠉⠀⠈⠻⣶⣶⠗⠈⠻⣶⣶⠟⠀⠀⠀⠀⠀⠔⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣸⡟⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋
⠀⠀⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⢀⣿⠃⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⢿⣄⠀⢀⣀⣤⣤⣶⣶⠶⠾⠿⠿⣿⡿⠂⠀⠀⠀⠀⣀⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠈⢿⠿⠟⠋⠉⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⢠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠈⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣴⡦⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⣶⠿⠛⠿⣷⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠄⠁⠀⠀⠀⠠⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠡⠄⢉⣀⣐⣀⣀⣀⡘⣆⠀⠌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠃⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣌⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⢚⣟⣯⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢅⠛⠂⠀⠈⠉⠉⠉⠉⠉⠉⣉⡀⠠⢽⡾⣿⣍⢧
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⡾⠁⢦⠀⠀⣀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠀⡈⢱⡵⡿⣎⢷⣶⣶⣶⣶⣤⣤⣤⣤⣀⣠⣀⣀⣀
⠀⢀⡤⢶⣿⢛⣿⣻⣿⣏⠉⠹⢺⣿⣿⣟⣽⣿⡟⣑⣰⠷⡤⠀⠀⠀⢈⣁⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠾⣾⣦⢿⣿⣿⣟⣲⠂⠀⣿⡏⠉⢩⣏⣻⣿⣿⣶⢤⡀
⢠⢏⣠⡾⢿⡶⢼⣿⣿⣿⡿⠉⠉⠉⠛⠉⣿⠛⣴⣽⣻⣿⠒⠂⠤⠤⠤⠀⠀⣀⣠⣤⣤⣤⣤⣤⡴⠦⢘⡟⣻⣣⠟⣿⣷⣿⣶⣴⣿⡛⠓⣾⣯⡿⢟⡿⠃⣵⣽
⣿⣾⢷⢽⠸⣉⠟⢒⣿⡿⢿⠿⢟⣓⣲⣺⣧⣿⣷⣾⣿⣿⡷⢶⣶⣶⣦⡤⠤⢤⣤⣤⣤⣤⣤⣤⣼⣯⣽⣿⣤⣶⣶⣿⣟⣛⣛⡿⣿⢿⠿⣟⠚⢛⡩⣸⡷⣄⣿
⢻⣧⣘⡟⢆⢁⠴⣿⡍⣁⠘⣤⠋⣠⠞⢧⡀⠹⡌⡩⠋⢉⠝⢍⠉⢫⡉⢉⠏⠉⡩⢯⡉⠉⠫⡉⣩⠉⢉⠵⢄⠈⢣⣀⠞⣠⠖⢦⡈⠾⢠⠉⣙⢆⣱⣿⠿⣼⣿
⠀⠳⣬⣿⣾⣧⣴⣁⣣⠙⢆⣠⠾⢁⠤⣀⠙⢆⠉⢀⡴⢁⣀⠀⠳⣄⠙⠁⡠⠚⠀⡀⠙⢦⡀⠈⢁⠴⠋⢀⣄⠳⣄⢁⠞⢁⠔⠢⡙⢦⡞⣰⣀⣮⣷⣿⣿⣷⠟
⠀⠀⠈⠙⠯⣝⣿⢿⣯⣽⣟⡛⠲⡷⣦⣬⣷⣤⣑⣋⣴⣋⣀⣳⣀⣈⣲⡚⢀⢀⡜⠉⢢⣀⠑⠔⠁⣀⣠⣃⣈⣳⣬⣯⣤⡾⠶⠶⢿⣿⣿⣟⣛⣽⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠺⢿⣿⣿⣟⣯⡽⠛⠛⠓⠐⠀⠠⠤⠤⠤⠭⠭⠭⠭⠍⠉⠩⠉⠩⠉⠉⠩⠭⠭⠥⠭⣭⢤⣀⣒⣢⣀⣭⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠚⠿⠶⢦⣬⣬⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠟⠛⠛⠛⠉⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⡄⠀⢀⣀⠀⠀⣀⡀⠀⢀⡀⢪⣃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⢠⢶⣶⣇⢀⣿⣿⣤⢠⡏⠿⣶⡼⠗⠁⢸⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠁⠘⠋⠈⠉⠛⠀⠙⠁⠃⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰⠃⣀⢀⡤⠀⠀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣀⠀⡀⡁⢠⡗⠁⣸⢋⢼⣤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⣿⡘⠹⡷⢺⡇⢻⠉⢁⠜⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠹⡇⠀⠀⢸⣇⠇⠀⠎⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⢆⠈⡄⢠⢠⡄⡌⢀⠆⡰⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠈⢆⠘⡄⢣⠸⡄⣧⢸⢸⡇⡇⣼⢠⠇⡜⢠⠃⡰⠁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢄⠑⣄⢳⣘⣮⠷⠛⠋⠋⠉⠉⠙⠙⠛⠾⣵⣃⡞⣠⠊⡠⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡑⢦⡑⣮⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣵⢎⡤⢊⡠⠔
⠀⠀⠀⠀⠀⠀⠀⣈⠒⠤⣙⣲⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣖⣋⠤⠒⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡒⢮⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡵⢒⡉
⠀⠀⠀⠀⠀⠐⠒⠢⠤⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⠤⠔⠒⠂
⠀⠀⠀⠀⠀⠉⠉⣐⣒⣒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣒⣒⣊⠉⠉
⠀⠀⠀⠀⠀⣀⠀⠬⠭⠭⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠭⠭⠥⠀⣀
⠀⠀⠀⠀⠀⠤⠀⠒⢒⣛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣛⡒⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠒⢈⣉⠥⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡳⠬⣉⡁⠂
⠀⠀⠀⠀⠀⠀⠈⢁⠤⠒⣩⠼⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠧⣍⠓⠤⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⡠⠊⡱⢛⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡓⢌⠑⢄⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠊⡰⢋⡼⢹⢟⡶⣦⣄⣄⣀⣀⣠⣠⣴⢶⡻⡏⢧⡙⢄⠑⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢀⠎⢠⠃⡜⢰⠃⡟⢸⢸⡇⡇⢻⠘⡆⢣⠘⡄⠱⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠎⠀⠁⡈⠈⠃⢁⠈⠆⠱⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠘⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣭⣤⣤⣅⠀⣦⢱⢂⢞⣵⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⡾⠛⠉⠀⠀⣹⢆⡿⡞⢠⡾⠉⢀⢀⣀⣠⠴⣖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⠁⠀⠠⠖⠋⣼⣡⡄⣨⠀⣶⢈⣽⢏⣴⡿⢋⣽⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠶⣤⣤⣤⣄⠀⠋⣸⡇⡿⠂⣿⢫⡏⣾⡟⠛⠉⠁⣰⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢋⡴⢖⣒⣒⠂⠈⢻⡀⠹⠇⠂⠀⠀⠀⠰⢿⣧⣄⣮⣾⠟⠁⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢋⣾⠟⠉⠉⠁⢀⡾⢀⣶⡶⣷⣬⣕⣒⠦⠤⠉⠉⠉⣀⣤⣾⡏⢜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⢹⡈⢿⣤⣠⣤⡴⠟⣡⣾⡟⣶⡿⣩⡿⡿⣛⣿⣷⣞⡻⢟⣿⣋⣀⣈⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠚⠯⢭⣛⡻⢧⣿⣼⣷⡟⡞⡞⢛⠓⣿⢟⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣝⣻⠾⣿⣿⣭⣧⣽⣿⡿⠏⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣭⣭⣁⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢸⣿⡀⢸⣦⡀⣿⡏⠀⣾⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠹⣶⣦⣿⣷⣤⣿⣿⣿⣷⣼⣿⣧⣾⡟⠀⣤⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣼⣿⡿⠟⠛⠋⠉⠉⠙⠛⠿⣿⣿⣧⣾⣷⣀⣴⣾⠟⠁
⠀⠀⠀⠒⠶⢶⣤⣤⣀⠀⠙⠾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⡿⠀⢀⣀⣀⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣩⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⠤
⠀⠀⠒⠛⠛⠛⠛⠛⠛⢛⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡛⠛⠛⠻⠿⠷⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠓⠂
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⢸⣿⠟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠻⢿⣦⣄
⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠋⢁⣴⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⢦⠀⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢻⡟⠀⣿⡿⣿⣿⠻⣿⡿⣿⣧⠈⢻⣷⡀⠀⠀⠀⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠈⠀⣸⣿⠁⠉⡏⠀⣿⣇⠀⠘⠂⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢠⡀⠀⠀⠀⢸⡇⠀⠀⣰⠄⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢷⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠲⣄⠀⠘⢦⠀⢀⠈⢧⠀⡆⢸⡇⡇⣸⢃⠆⢀⡼⠁⠀⢀⣠⠞⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠈⠳⢄⠀⠳⡀⠣⠈⢇⢇⢸⠠⢁⠇⠎⣠⠎⡠⢂⡴⠛⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡐⠦⡑⢄⠈⢂⠁⡀⡀⢸⣄⡀⠈⡴⢁⠞⠴⠋⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢦⣄⣀⠀⢌⡒⠌⡂⠀⡠⠀⡡⠤⠤⠤⢄⡈⠢⡀⢀⠤⠚⣁⠤⠂⣀⣠⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⣤⣤⣀⣀⡀⠀⠉⠙⠒⠬⠀⢨⠋⡠⠋⠀⠀⠀⠀⠀⠈⢢⠈⡁⠀⠩⠄⠒⠉⠁⢀⣀⣠⢀⣀⣀⣠⡴⠒⠤⠤⠤⠴⠦⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠈⠉⠉⠉⠒⠒⠒⠄⠬⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠒⠒⠊⠉⣩⠞⠛⠋⠁
⠠⡴⠶⠒⠒⠒⠚⠉⠉⠀⠀⠀⠉⠙⠲⢄⣀⡈⠈⠀⠀⠐⠀⣆⠀⠀⠀⠀⠀⠀⢀⣠⠧⠬⠦⠦⠤⢄⡴⠚⠁⡀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⣄⣠⠤⠜⠒⠚⠛⠓⠒⠛⠉⠀⠀⠀⠀⢀⡤⠞⢀⣠⠊⠁⠀⠀⠉⠀⣀⡤⠤⠄⠀⠀⠃⠈⠁
⠀⠀⠀⠀⠀⠐⠂⠁⠁⠐⢦⢀⣀⡀⡀⠀⠐⢦⠠⠀⡀⢌⢷⣖⡒⠒⠲⠦⠤⠴⠶⢖⡶⠋⠉⢉⠀⠂⠅⠀⠐⢶⣢⢠⢎⣉⡀⠀⡀
⠀⠀⣠⣤⠀⠤⠄⠠⠀⠀⠤⠀⠤⠤⠬⠭⠶⠶⠦⠦⠤⠦⠶⠾⠿⠓⠀⠀⠀⢀⡤⠾⣀⠀⣀⢠⠄⢠⡀⠠⠀⠤⠒⢈⠷⠀⠉⢭⣍⡣⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠴⠞⣡⠴⠿⠧⠾⠚⠓⠮⣄⣤⣀⣀⣁⡤⢬⣤⣆⣀⣁⣡⣄⣸⣰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⢖⡒⠒⠲⠶⠞⠛⢋⡋⣁⣠⠤⠤⠴⠦⠤⠤⠴⠂⠲⠤⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⣠⣴⠖⠚⠛⠛⠛⠛⠉⠛⠓⣯⣁⡀⠀⠀⠀⠈⣤⡤⢴⣓⣒⣒⡈⢁⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠆⠀⠰⠶⠶⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣄⠀⠀⠀⢰⡄⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠀⡟⣧⠀⢀⢖⢍⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⢫⡪⡓⢤⣀⠇⡘⡄⢸⢈⢪⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⡒⢄⡙⡌⣣⣽⣴⢧⣷⣞⡜⣸⡤⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠐⠻⣽⣆⣀⣀⣘⣌⢢⠜⠫⠉⠁⠈⠉⠈⠉⠙⢧⡞⡝⢁⡤⡒⣒⣒⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣎⣒⣒⢬⠋⠴⣒⣶⣶⡄⢰⣤⣶⣖⢤⡹⣗⡫⢊⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠚⡏⠘⠞⠿⠿⠛⡁⢸⠻⠿⠿⠒⠃⢷⠲⠥⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠤⢤⣉⣿⠄⠀⠀⠀⣾⣅⣸⣷⠀⠀⠀⡀⣾⡭⠥⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡱⢒⣻⡜⠂⠀⡤⢤⣶⣶⣦⠦⠀⠛⣡⠧⣑⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣞⣭⣍⣪⠞⢡⠏⡼⢳⣄⡄⠀⠑⠒⠃⢠⣾⠶⣉⢶⠤⠐⠒⢦⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣧⡪⠔⡏⡜⣩⢿⢳⠒⡟⢏⢙⠑⠮⣃⢳⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠀⠀⣹⠁⡇⠘⣾⢠⠛⠬⣀⡵⡄⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣥⠔⠁⠀⢿⡿⠀⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⢸⠇⠀⠀⠈⠻⠷⠄

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⣿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿
⠀⠀⠀⢠⣠⣿⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣄⠀⠀⠀⠀⠀⢺⡅
⠀⠀⢀⠀⣹⢿⡮⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣂⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠸⠶⠤
⠀⢀⠈⡙⠛⣿⣧⣃⡈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣽⣯⠙⠃⣠⠀⢀⣠⠋⠀⠀⠀⠀⠀⣾⡀⠈⠛⠿⠿⡇
⠀⠈⠻⣇⣶⣾⡝⣍⢁⡠⠀⠀⠀⢾⣷⡀⠀⠀⠀⠀⢀⣴⡿⣯⠜⠦⣤⠀⠿⢿⣿⠶⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⠀⡀
⠀⠀⢾⡉⣀⣿⠷⡀⠀⠀⠀⠀⠀⠛⣿⡏⠀⠀⠀⠀⠨⠹⣷⠑⠄⠢⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⠀⠀⠀⠀⠀⠀⠈⠹⣧
⠰⡠⠂⠁⠙⢿⡆⠘⠒⠀⠀⠀⢠⣾⠋⢰⢀⡄⣠⡀⠈⠙⠻⢶⣴⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⠆⣠⠀⠀⠠⠀⠀⠀⠛⠳⣦
⡆⢛⣧⣶⣷⠂⢠⡔⠠⠀⠂⠀⠈⢁⠀⣿⣾⣿⡿⠀⠀⠀⠀⢠⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠑⠚⠙⢿⡧⣄⣾⡇⠱⡆⠐⠂⠀⢿⣾⣿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⠃
⠀⠀⠀⠀⠛⠻⣏⡼⠟⠀⠀⠀⠀⠀⢉⡛⠀⠀⠀⠀⠀⠀⣤⣀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠑⠆⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⣦⡌⢁⡀
⠀⡄⢀⣀⣀⣀⣀⣀⡰⢾⣄⠀⠀⠁⣠⣀⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠋⠉⠀⠀⠐⠒⠲⠀⠐⠀⠀⡀⠀⠀⣽⣿⣦
⣿⣿⣿⣿⠿⣿⡭⠿⠟⠷⠷⠖⢛⡉⠉⠀⠀⠉⠈⣹⣿⠖⠒⠒⢲⡶⠖⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⢀⡀⠀⣀⠈⢻⣿⣶
⠀⠏⠥⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡉⠀⡀⢀⠀⠉⠀⠀⠀⠀⠙⠳⠶⠤⠤⠶⠆⠀⠀⠀⠀⠐⠀⠀⠀⠐⠚⠁⠘⠋⠀⠀⠉⠛
⠀⠄⠉⠀⠂⠀⠀⠀⠀⣀⡀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⠁⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠘⢃⣀⣉⠀⠰⠇⠀⠀⠀⠀⠀⠀⣄⠹⣇⠹⠀⠀⡜⢀⡀
⠀⠀⠀⠀⠀⡀⣄⣴⠟⢯⡓⣄⠀⠀⠀⠀⠀⠀⠙⠁⡄⠀⡀⠀⡀⠀⠀⠶⠂⠀⠀⠀⠲⠀⠁⢈⣤⣤⣄⠐⣡⡴⡆
⠀⠀⠀⠀⠀⢀⠸⡧⣸⣅⣼⣇⠀⠀⠀⠀⠀⠛⠃⠰⠀⠢⣀⣀⡡⠄⠁⠠⡤⠀⠀⠨⠭⠄⠀⣿⣿⣿⣿⡇⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠛⠏⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠶⠒⣡⠌⠛⠛⠋⠀⢌⡙⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤⠀⠲⠄⠀⠀⠀⠀⠀⠀⠺⠃⠀⡆⢰⠀⠘⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠲⠄⠸⡄⠀⢠⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢃⣀⠃⢠⠆
⠀⠀⠀⠐⠶⣄⠢⠄⠐⠈⡔⢀⣤⡄⠀⠀⠀⠀⠀⢠⠿⣟⣛⡛⠿⣷⡀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣦⡀⠤
⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠠⠄⠀⢤⠄⠀⠀⠀⠀⢿⣜⢾⣜⣟⡶⣿⠁⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡇⠤⠄
⠀⠀⠀⠙⠋⠁⠔⡀⠄⣀⠢⠘⠲⠄⠀⠀⠀⠀⠀⠈⠮⣯⣿⣿⡵⠃⠀⠀⠀⠁⠀⠀⠐⠂⡘⠿⣿⣿⣯⠟⠡⢄
⠀⠀⠀⠀⠚⠁⡸⠁⠀⠘⡄⠐⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⢀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠀⣠⠆
⠀⠀⠀⠀⢠⣀⢻⠢⡸⠣⠞⣏⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣤⣀⣹⠟⠀⠀⠀⠀⠑⠧⢤⣤⣤⠀⠀⠀⠀⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠍⠫⣝⢦
⠀⠀⠀⠀⠈⣲⠄⠀⠀⠀⠀⠀⠺⣍⣀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢆⢞⣻⣾⣿
⠀⠀⠀⠒⠛⣡⣟⣀⠀⠀⠀⠀⣏⠈⠁⠀⠀⠀⠀⠀⠈⠢⣈⣋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠧⣂⠥⣕⣵⠏
⠀⠀⠀⠀⠘⠉⠀⡶⠉⣦⠲⡏⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⢠⣄⠀⢀⣴⣶⣶⣶⣶⣤⣤⣀⣀⣠⠤⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣼⣿⡆⢸⣿⠀⠛⠉⠁⠀⣠⡉⠉⠉⠉⠉⢀⣤⡀⠀⠋⠉⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⠛⢡⣿⣯⣶⣷⠀⢀⣤⣯⠁⢀⣤⣄⡴⢋⣿⠇⣠⣤⢤⡄⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⢀⣾⡿⢁⣿⠏⣠⢯⣿⢏⡴⣻⣿⡟⣡⣿⠏⣼⣿⣥⠾⠏⢀⣾⠇
⠀⠀⠀⠀⠀⣠⣤⡄⢹⣿⣇⠸⣿⠃⣾⡟⡴⠃⣿⣿⠟⢠⣿⡟⣰⣿⠋⡴⣿⣧⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⣿⣿⠁⢈⣿⡿⠀⠉⢸⣿⡟⠁⠀⠛⠁⠀⠘⠋⢰⣿⣧⠞⠀⠈⠛⠓⠛⠁
⠀⠀⠀⠀⠀⠙⠿⣤⣾⠟⠁⠀⠀⠈⢉⡤⠶⠶⠶⣶⣦⣤⣤⣈⣛⣥⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢦⡀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⢰⠂
⠀⠀⠀⠈⠳⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢄⠀⢀⡎⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠐⠉⢠⠃
⠀⠀⠀⠀⠀⠈⢢⡈⠑⠒⠤⣄⡀⠀⠀⠀⢸⠀⠀⠀⢀⣀⡵⠮⠤⠤⠤⠤⣤⣀⠣⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡀⠤⢄⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⠉⠒⠒⢚⡠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⢀⠇⠀⠀⡀⠤⠒⠈⠁⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠓⠉⠁⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⠖⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢴⣁
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠒⠒⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⡠⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠢⣀
⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠑⠤⡀
⠀⠀⢀⠤⠚⠁⠀⠀⣀⣀⣀⠀⠤⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣀⡀⠀⠀⠀⠀⠀⠑⠢⣀
⠤⠮⠅⠒⠒⠉⠉⠁⠀⠀⠀⠀⡰⠃⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠈⢇⠀⠈⠉⠁⠒⠂⠤⠤⣄⣑⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡀⠤⠬⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⢡⢄⡀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠕⠒⠉⠀⠀⠀⢠⠃⠀⠈⠉⠓⣒⠢⠤⠤⠔⠒⣊⠉⠀⠀⠀⢸⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡠⠊⠁⢱⠀⠀⢀⠎⠀⠱⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣠⠊⠀⠀⠀⠈⡆⢀⠎⠀⠀⠀⠘⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠞⠁⠀⠀⠀⠀⠀⢣⠎⠀⠀⠀⠀⠀⠈⢣⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀⠀⢀⣠⣴⣶⣶⣤⣤⣀⡀⠀⠀⣀⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⣿⣷⡀⣸⣿⠀⠾⠛⠋⠉⢉⡙⠛⠛⠛⠛⠋⠁⡀⠀⠠⠞⠛⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⢿⡿⢣⣿⣟⣤⣤⠀⠀⢀⣘⠋⠀⢀⣀⠀⡴⢋⣿⠄⢀⣀⣀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⢀⣾⣿⠋⣿⡟⢀⡴⣿⡿⢁⡴⣿⣿⡞⣡⣿⠏⣴⣿⢋⣽⡗⠀⣸⡟
⠀⠀⠀⠀⠀⠀⣀⡀⠸⣿⣷⠀⢸⣿⠃⣼⡿⢡⡞⣸⣿⣵⠏⣸⣿⠏⣴⣿⠏⣰⣿⡏⠉⠉⠀⣰⡟⠁
⠀⠀⠀⠀⠀⣼⣿⡿⠀⢻⣿⡇⠘⠏⢸⣿⣵⠏⠀⢿⠟⠁⠀⣿⠏⣸⣿⢃⡼⠉⠻⣷⣤⡤⠞⠉
⠀⠀⠀⠀⠀⠹⣿⡁⢀⣾⣿⠃⠀⠀⠻⠿⠃⣀⣀⣀⣀⡀⠀⠀⠀⢿⡿⠋⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠐⠋⠉⠉⠙⠛⠿⢿⣿⣶⣶⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⡀⠀⠀⡇⢸⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣀⠀⠀⠀⢸⠁⢇⠀⢰⠁⠈⡆⢠⢔⠏⡼⠀⠀⠀⣀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⢕⠢⣀⢸⠐⣌⣢⡜⠀⠀⢳⣃⡌⢸⠀⣀⠔⡪⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠑⢄⠙⢳⡭⠖⠓⠋⠙⠚⠲⢭⡞⠊⡠⠊⡔⠁
⠀⠀⠀⠀⠀⠈⠙⠻⣍⡓⠤⠤⢵⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⡾⠒⡒⠒⠶⣲⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣁⢲⢣⠏⠀⠒⣚⡒⢦⡀⠀⡴⢒⣓⠒⠀⠹⡜⣏⠔⠊⠉⠁
⠀⠀⠀⢀⣀⣀⠤⠤⠔⠒⠚⠉⡽⠀⠀⠾⣽⡿⠂⡇⢸⠰⢯⣿⠷⠀⠀⢯⠉⠒⠒⠢⠤⠤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⠒⠒⠢⠤⠤⣀⣳⠀⠀⠀⠀⠀⢠⠃⠘⡄⠀⠀⠀⠀⠀⣞⣀⡤⠤⠔⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⣹⡜⣆⠀⠀⠀⠀⣈⡑⢊⣁⠀⠀⠀⠀⣰⢣⠯⢉⠲⡀
⠀⠀⠀⠀⠀⢀⣴⠯⠦⠤⠬⠤⡾⠉⣦⡀⠀⠀⠀⠒⠒⠀⠀⠀⢀⣴⠉⢗⠒⠒⢬⣙⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡠⠊⡠⡼⣓⠦⡤⣄⣠⢤⠔⣚⢧⣄⠑⢄⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡪⠔⠉⠀⡇⡘⢹⢧⠀⠀⡜⠫⡙⠄⡇⠉⠢⢕⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠉⠀⠀⠀⡞⣰⠔⠃⠸⡀⢀⠇⠀⢱⢀⡇⠀⠀⠀⠉⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⡇⢸⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⡀⠀⠀⢠⣤⡀⠀⠀⣀⠀⠀⣶⠶⠆⠀⢰⣶⣶⣦⡀
⠀⠀⠀⢾⣇⠀⠹⠃⠀⠀⠀⠀⣾⡿⣧⣰⣿⣿⠀⠀⢸⡿⣷⣀⣾⣿⡄⠀⣿⡦⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠈⣉⠻⣧⠀⢠⣶⣶⠀⣿⠃⠹⠏⠀⣿⡇⠀⢸⡇⠘⠟⠁⢹⣇⠀⣿⡀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠛⠛⠃⠀⠈⠻⠃⠀⠉⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠈⠛⠀⠉⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣄⠀⢀⣤⣀⠀⢀⣀⣠⡀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⢸⡏⠀⣿⠀⢸⣿⡟⠀⢸⣏⡉⠀⣿⣁⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⠃⠀⣿⠀⢸⣿⣿⡄⢸⡏⠁⠀⢈⡙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠐⠿⠀⠸⠿⠟⠁⠸⠷⠶⠀⠈⠛⠟⠁