Rain cloud Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠶⠶⠦⣄⠀⡼⠁⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣟⣥⣤⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠳⢤⡀
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠁⣠⠞
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠳⢦⠀⢀⢀⠀⠀⠐⠀⡷
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⢀⡴⠲⠶⠚⠁
⠀⠀⠀⢹⡀⠀⠄⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠆⡄⠀⠀⠀⠔⠐⠀⣠⣄⠀⠀⢸⡏⠉
⠀⠀⠀⠈⠳⣄⣀⣀⣀⣠⠴⠋⠓⢦⣀⣉⣈⣀⣠⡴⠚⠁⠈⠳⠦⣤⣄⣀⣀⣤⡤⠴⠚⠁⠈⠉⠉⠉⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣷⠀⠀⠀⠃⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⡀⠀⠘⠇⠀⠀⢾⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⡆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡄⠀⠀⠀⢰⡆⠀⠘⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⡆⠀⠀⠀⠀⣀⠀⠀⠀⠋⠀⠀⠿⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠃⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣤⠀⠘⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣤⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⢀⣤⣶⣿⠿⠿⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠛⠋⠉⠛⢻⣿⡿⠫⠚⠛⠛⠦⠈⢻⣿⣧⠀⠀⠀⠀⣠⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢰⣿⡟⢡⠞⠋⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣴⣿⡿⣛⣛⣛⢿⣿⣿⣆
⠀⠀⠀⣀⣤⣼⣿⣧⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠹⣿⠏⠚⠁⠀⠉⠓⠙⣿⣿⡆
⠀⣰⣾⡿⠟⠋⠉⠉⠙⠳⣆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠶⠛⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣼⣿⡟⡴⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣇⢀⣼⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⣿⣿⡀⠧⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠉⠋⠁⠀⠀⠀⠀⢸⡇⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣿⣯⡀
⠙⣿⣿⣶⣶⠶⠶⠶⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿
⠀⠀⢹⡟⣤⠊⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⣀⣀⣀⣀⣤⡴⠖⠋⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⡞⣼⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣴⣾⣿⠟
⠀⠀⢸⣷⡙⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠁
⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣤⣶⣾⠿⣿⣆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠛⢿⣿⣷⣶⣶⣶⣿⣿⠟⠃⠀⠉⠉⠁⠀⠙⣿⣮⣓⢦⣄⣀⡀⠀⣀⣠⣶⣿⡟⠀⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⢠⡆⠀⠀⠀⢀⡀⠈⠻⣿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠀⢰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢠⠞⠙⡄⠀⠀⣼⡀⠀⠀⠀⠉⠙⢛⠉⠉⠁⠀⠀⠀⠀⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠉⣧⠀⠀⠀⠘⠒⠚⠁⠀⡞⠁⢹⡄⠀⠀⠀⢀⡾⡄⠀⠀⢀⣿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠀⠀⣀⠀⠀⠀⠀⠀⠙⠒⠋⠀⡀⠀⠀⡞⠀⢻⠀⠀⡜⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡀⠀⠀⢀⠀⠀⠀⠀⢀⣿⠀⠀⠙⠒⠋⠀⠀⠓⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⣱⠀⠀⢸⡄⠀⠀⠀⡜⠈⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡴⠃⢳⠀⠀⠀⠓⠚⠁⠀⠀⠀⡞⢧⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣒⣋⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧⣤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠻⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣠⣤⡶⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⡀⢠⡾⠋⠀⠀⠀⠀⠈⠻⣧⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠉⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠛⠻⢶⣄⢀⣤⣴⠶⣦⣤⣀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠁⠀⠀⠀⠈⠙⣷⡀⠀⣀⡀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠻⢶⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠳⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣠⣼⠏⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣧⠀⠀⠀⢀⣴⠾⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣄⠀⠸⣿⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⣿⠀⠀⢰⡟⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⡇⠀⠙⠻⠿⠟⠁⠀⠀⠀⠀⣰⣷⡀⠀⣿⠃⠀⠀⢠⡿⠀⠀⠸⣷⣄⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⢹⡇⠀⠹⣷⣤⣴⠿⠁⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣠⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠤⠀⠠⢄⡠⠒⠒⡂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⠒⠒⠁
⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢠⠃⡀⠀⠂⠲
⠀⠀⠀⢀⠀⠀⠀⠈⠢⠄⢂⠤⢀⠄⢀⠄⢀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⡔⣠⠂⡰⠁⡔⠁⠈⠠⠡⠂⠆⡸
⠀⠀⠀⠈⠲⠖⠂⠑⠦⠄⠁⠀⣁⡀⢁⢀⡁⠐⠡⠒⠡⠖⠠⠂⡠⠂⡠⠊⡠⠊⠔⠡⠖⠠⠊⢀⠶⠄⠀⠄⠀⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠠⠀⠠⠄⠉⠓⠲⠶⠶⠀⠒⢤⣄⠀⠀⣠⡁⠔⠒⠐⠴⠶⠀⢁⠀⠰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠐⠀⢀⠀⠀⠀⢀⠔⠒⠄⠠⢉⡐⠒⠄⡀⠃⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⢀⡅⠀⠀⡀⡀⠀⠀⠀⢀⡈⠢⡀⠄⠠⠀⡄⠀⠄⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠈⢁⡜⠀⠉⢲⡀⠀⠁⠈⢣⠈⠣⡀⠀⡀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣇⠀⠀⠀⢣⡖⢢⠀⠞⠀⠀⠀⠀⠤⡀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠉⠀⠀⠀⢽⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡃⠀⠀⠀⠀⢸⢀⡤⠀⠄⠀⠀⠀⠀⠀⢡⠈⠑⢦⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⣛⠀⠀⠀⠀⢈⠙⡈⡐⢠⠘⠀⠀⠀⠀⠀⡄⢀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠄⠀⠈⢶⠠⢀⠂⠃⠀⠀⠀⠀⢸⠄⢁⠄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⣅⠂⠄⠀⠈⢧⠂⢾⠀⠀⠀⠠⢀⠧⢊⡠⠔⡁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡄⠠⠄⠀⠀⠱⠆⠀⠀⠐⢀⠜⢂⡡⠔⣊⠄⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠛⡄⠉⣀⠀⠀⠀⠀⠀⢀⣊⡉⠤⠒⣉⠄⡊⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠂⠘⡄⢀⡰⠓⢢⠜⢦⠐⢀⠀⠀⢀⡴⢋⠉⠐⠒⠃⠤⢩⡔⠢⠄⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢂⠡⢂⠹⢋⠥⢀⡌⠀⠠⢃⠴⢲⠖⠋⠔⠡⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠡⠒⡡⠖⡡⠊⢸⡇⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣊⠔⢉⠀⠰⢨⡇⠀⠀⠐⡡⢂⠀⠐⠊⡥⠂⣡⠖⣡⠔⡠⠊⠐⢀⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠡⠚⡡⠀⢰⠀⠁⠀⠀⡡⠔⣉⠀⣟⠳⠶⠶⢤⡬⣥⣬⣡⢤⡴⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢊⠤⠂⠀⡀⢸⠀⠀⠰⢊⡡⠄⠸⢊⠔⡃⢀⠖⡡⠊⡰⢊⠔⠡⢊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠠⠒⣡⠀⠁⠀⡀⠀⠐⡡⠄⠂⡀⢣⠜⣥⠀⠜⠁⠈⡰⠃⠔⠡⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠀⠐⠩⠄⠀⢸⠀⢃⠀⠀⠐⢂⠡⠀⠈⡯⢺⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠁⠀⠀⠀⠀⠀⠀⣈⢃⣹⠀⠀⠀⠄⣂⠁⠀⢰⠭⡀⠀⠀⠀⡠⢊⠔⡡⢀⠀⢰⡄⠄⢀⠠⠤
⠀⠀⠀⠀⠀⠀⠉⠀⠂⠉⠄⠋⠉⠱⠚⡃⠉⣉⠍⠋⠁⠀⠀⠀⠀⠀⢀⡤⠢⢦⣅⣀⡤⠤⢤⠤⠤⡤⠄⠠⠞⢈⠀⢂⠡⠀⡈⠔⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠲⠤⢤⡤⠤⢤⠶⠞⠋⠄⠂⠡⠐⠈⠐⠈⠁⠀⠁⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣚⣛⣉⣛⣛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣚⣛⣩⣙⣛⡲⢦⡴⣫⠴⠟⠛⠛⠛⠛⠿⣿⣦⣍⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠟⠛⠋⠉⠛⠻⠿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡙⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡾⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠛⠛⠛⠻⢷⣶⣄⠻⠿⢿⣷⣦⣌⠳⢦⣀⣀
⠀⠀⠀⠀⣀⣤⠼⠃⣠⣴⠾⠿⠿⠿⠿⢶⣦⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠙⢿⣷⣶⣯⣭⣝⡓⢦⣀
⠀⠀⡴⢞⡵⠞⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⡙⢧⡀
⢀⡞⠑⠉⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢳
⣼⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠸
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠞⠉
⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣤⣤⡤⠶⠚⠁⠀⠉⠛⠒⠒⠒⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣼⣿⠀⠀⣰⢿⡆⠀⠀⠀⠀⣏⠀⣠⣿⡇⠀⣠⠾⣧⠀⠀⠀⠀⢾⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛⠿⠞⠃⢠⡞⠁⢈⣷⠀⠀⠀⣀⠙⠻⠷⠋⠀⣴⠋⠀⣿⡄⠀⠀⢀⡈⠓⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⡀⠀⠀⠀⠸⣄⠠⢾⡿⠀⢀⡾⠹⣇⠀⠀⠀⠀⢧⡠⠴⣿⠇⠀⣴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡇⠀⠀⣠⣦⠈⠉⠉⠀⢰⠏⠀⢠⣿⠀⠀⢀⣴⡌⠉⠋⠁⠀⡾⠁⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣚⡿⠃⢀⡴⠋⢸⡄⠀⠀⠀⠘⢦⣐⣻⠟⠀⣠⠟⠈⣧⠀⠀⠀⠀⠳⣔⣚⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡾⣇⠀⠀⠀⠀⣾⠀⢀⣼⡇⠀⢀⡴⢷⠀⠀⠀⠀⢸⡃⠀⣠⣿⠀⠀⣠⢾⡆
⠀⠀⠀⠀⠀⣴⠋⠀⣿⠀⠀⠀⠀⠘⠶⠭⠟⠁⢠⠞⠁⢸⡇⠀⠀⠀⠈⠳⠮⠽⠋⢀⡼⠃⠀⣷
⠀⠀⠀⠀⠸⣇⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢀⡴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠉⠙⠓⠦⣄⠀⢀⣠⠤⠶⠒⠒⠒⠲⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠉⠙⠛⠲⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠒⠶⢤⣄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢀⣠⠴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠦⣄
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠁⣀⣀⣀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠽⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡇⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠈⠳⢤⣄⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠈⠓⠦⣤⣄⣀⣀⣀⣀⣤⠤⠞⠁⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣧⠀⠀⠀⠀⠀⠀⠀⡟⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣧⠀⢀⣤⡀
⠀⠀⠀⠀⠀⢀⡞⢧⠀⠀⠀⠹⣤⡿⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⢧⣀⡿⠀⠀⠀⠀⢠⡀⠀⠀⠻⣄⡿⠀⣼⠉⣇
⠀⠀⠀⠀⠀⢸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡆⠀⠀⠙⠶⠏⠀⠀⠀⢀⣤⠀⠀⠈⠉⠁⠀⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀⠀⢹⡀⣿
⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡄⠀⠀⠀⠀⣾⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡞⠸⡆⠀⠀⠀⠀⢀⣄⠀⠀⡇⢸⡇⠀⠀⣀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡄⠀⠀⠀⠻⢤⠿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⡾⠙⡆⠀⠙⠞⠁⠀⢰⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⢳⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠠⡇⠀⣿⠀⠀⠀⠀⠀⠸⣆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃⠀⠀⠀⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣴⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠋⠓⠲⣄⢀⡤⠔⠒⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⣠⠖⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣠⠔⠚⠃⠀⠀⠀⠀⠀⢀⡠⢤⣀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⢣⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡀
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁
⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠈⠓⠒⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⡴⠋⠲⢤⣀⣀⣀⣀⣀⡤⠚⠈⠉⠒⠒⠶⠶⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠀⠀⠀⠀⠀⠀⡰⣆⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠀⠀⢠⠛⡄⠀⡀
⠀⠀⠀⠀⠀⢰⢳⠀⠀⠹⠼⠀⠀⠀⣀⠀⠀⡇⢸⠀⠀⠀⠀⠘⣆⡷⠀⠀⢀⣄⠀⠘⢤⠇⢸⠹
⠀⠀⠀⠀⠀⠸⣤⠇⠀⠀⠀⠀⠀⢰⠙⡄⠀⠉⠁⠀⠀⡴⡆⠀⠀⠀⢀⠀⢸⠙⡄⠀⠀⠀⠘⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠸⠤⠇⠀⢀⠀⠀⠀⡇⣸⠀⠀⠀⠞⣆⠘⠶⠁⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠀⠀⠀⠀⠀⢠⠛⡆⠀⠀⠈⠁⠀⠀⠘⣄⡼⠀⠀⠀⠀⠧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⢀⣠⠖⠛⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣖⠋⠉⠉⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠑⣆⣀⠴⠛⠉⠉⠉⠙⠲⣄⠀⠀⢀⠖⠋⠀⠀⠀⠀⠙⢢⣀⡤⠚⠋⠉⠉⠛⠧⣀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣀
⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠞⠁
⠀⠀⠉⠓⠦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠘⢦⣀⠀⠀⠀⠀⢀⡴⠛⠦⣄⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⣠⠞⠙⠲⢤⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠉⠙⠒⠒⠋⠉⠀⠀⢀⣀⠀⠉⠀⠀⠀⠀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣄⠀⠀⠀⠀⢠⡞⠙⣆⠀⠀⠀⠀⡾⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢳⡀⠀⠀⠀⠀⠀⠀⣰⢶⡀⠀⢠⡏⠀⠈⣧⠀⠀⠀⣾⠀⠀⢸⠄⠀⠀⢸⠃⠀⠀⠸⡇
⠀⠀⠀⠀⣰⠛⢦⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢷⠀⠀⠀⠀⠀⠀⢧⣸⠇⠀⣼⠀⠀⠀⢸⠀⠀⠀⠘⠦⠠⠞⠀⠀⠀⠘⢆⡀⢀⣸⠃
⠀⠀⠀⢠⡇⠀⠘⡇⠀⠀⣤⡀⠀⠀⢿⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉⠉
⠀⠀⠀⠘⢧⣀⣠⠇⠀⢸⠁⣷⠀⠀⠈⠳⠤⠴⠋⢠⠟⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣄⠀⠀⠀⢼⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡞⠉⢳⡀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣰⠛⣆⠀⠀⠀⠘⠦⠤⠞⠀⠀⣤⡀⠀⠀⢰⠇⠘⡆⠀⠀⣼⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢀⡞⠈⢳⡀⠀⠀⠀⣇⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢳⡄⠀⠘⠦⡴⠃⠀⠀⠹⣄⣀⣠⠇
⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⠳⡄
⠀⠀⠀⠀⠀⠸⣤⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢀
⢹⠄⡄⠀⠛⠀⠀⢻⡄⠀⢸⡇⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠸⡇⠀⠙⠁⠀⠀⢸⠀⠀⠀⠀⠰⠇⠀⢀⠀⢿⠀⠀⠀⣯
⠀⠰⡽⠀⠀⢰⠀⠈⠀⠀⠀⠁⠀⠀⠀⡷⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢘⡄⠈⠀⠀⢰⡄⠀⠀⠀⢮⡆⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢲⠇⠀⠀⠀⠀⠀⢀⡀⠀⠸⡂⠀⠀⣵
⢸⡀⠀⢰⡄⠀⠀⠀⠀⠘⠁⠀⠀⠸⡄⠀⢸⡆⠀⠀⠀⠀⢴⠀⠨⡇⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⡔⡄⠘⠆⠀⠘⠃⠀⠀⣀
⠈⠀⠀⠘⠃⠀⢠⣆⠀⠀⢰⡀⠀⠘⠃⠀⠀⠀⠀⣀⣀⣀⣿⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠐⣆⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⣠⠀⢀⡄⠀⠋⠀⠀⢈⣀⠤⣠⢶⡶⢒⠩⣀⠦⠅⠒⠈⢋⢩⠅⡒⠒⠶⠦⣤⣄⣀⣀⡋⠀⠀⠀⠀⠀⠀⢸⢣⠀⠸⠆
⠀⠀⢷⡇⠘⠃⠀⣀⡤⠾⢁⣰⡪⢃⠡⡲⢐⡩⠔⠊⠀⠀⠀⠋⣂⢥⡐⠠⠄⠀⠀⠈⠑⠾⣬⡉⠒⠢⠤⣀⠀⠈⠛⠀⠘⠃
⢰⡀⠀⠀⢀⠔⣪⠅⠁⢠⢊⠕⡪⢂⠥⣊⠅⣊⠁⠀⠀⠀⠀⠀⢨⡈⡡⠐⠂⠭⡄⠀⠀⠈⠈⠙⣔⠡⠂⠤⠉⠲⢄⡀⠀⢸⡄
⠘⠃⢠⠜⠥⢂⠂⠀⢠⢃⢔⡡⣊⠕⡪⢐⠩⠀⠀⠀⠀⠀⠀⠀⠀⡆⠅⢂⠡⠄⠐⣀⠀⠀⠀⠀⠈⢫⢔⡨⢐⡀⠀⠙⢆⠈⠁
⠀⡴⡳⣄⠬⠀⠀⠀⣎⢔⠡⠪⡰⢝⠨⢐⠬⢐⠀⠀⠀⠀⠀⠀⠀⠳⠞⡀⠌⢑⣀⡀⠀⠀⠀⠀⠈⠄⢳⡪⠐⡠⠄⣀⠢⡳⡀
⣼⠚⠃⠉⠚⠒⠤⣀⠇⡡⣠⠮⠴⠆⠚⠓⠚⠐⠖⠴⢤⣄⡀⠀⠀⢈⢵⡀⢡⣐⣒⣮⣍⣙⣀⣂⣀⠤⠎⢗⣡⡴⠷⠒⠓⠓⠷
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠳⢤⣸⡵⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⡖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⢠⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⣉⣁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠠⠄⢂⠔⡠⢂⠄⣊⠔⡠⠐⡠⢒⠄⡠⢂⠄⡠⢂⠔⡠⢂⢔⠠⡠⢀⠄⡀⢄⠄⡠⢀⠄⡀⡀⢀⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠁⠈⠐⠁⠋⠐⠁⠊⠖⠑⠋⠊⠐⠁⠊⠐⠁⠊⠒⠕⠡⠪⠂⠕⠡⠊⠔⠡⠊⠞⡕⠰⢢⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠓⢦⡤⠶⢤⣀⡀⠀⠀⠀⣠⠴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠀⡴⠋⠉⠉⠛⣦⣰⣏⠐⠀⠀⠀⠻⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠀⠀⠀⣠⠤⢼⠁⠀⠀⠀⠘⠁⠀⠈⠉⠀⠂⠀⠀⠀⣼⠶⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⡞⠁⠀⠀⣀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣠⠞⠉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⠋⠁⠹⣆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣂⣁⠀⠀⠀⠀⠠⠀⠀⢀⡼⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠐⠲⠤⠴⠒⠀⠀⠀⠲⠀⠀⠀⣠⠋⠉⠓⠤⠄⠀⠀⠀⠐⠒⣉⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⠀⠈⠑⠶⠖⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠖⠋⠡⡀⠀⠀⠀⠀⢠⠀⠀⢀⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠲⣦⡀⠀⣀⡼⠻⣤⣙⠢⣌⣀⡥⠆⠀⠤⣁⢀⣀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⣉⢠⢂⠀⠉⠉⠉⠙⠦⣤⡤⠞⠉⠉⠹⣄⠀⠀⠀⠀⠀⣀⣀⣠⠏⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⡟⢰⠇⡎⡞⠀⠀⣶⡇⠀⢀⡄⢠⠄⣾⡇⠀⠉⠳⠦⠤⠴⠚⠁⠈⢁⠀⠂⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⢁⡟⡘⠸⢀⠃⢰⡟⠀⠀⣼⢁⡟⣸⡾⠀⠁⣠⡄⠀⢀⡤⢰⡇⡜⡞⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠇⣼⢡⢁⠃⠌⠀⣽⠁⠀⢰⠇⣼⢡⢷⠃⠄⠠⣿⠁⠀⣼⠃⡞⢰⢱⠁⠄⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡟⢰⠃⡎⡎⡘⠀⣰⡟⠀⢀⡟⢰⡇⣾⡟⠀⠀⢰⡇⠀⢰⡏⣸⠃⡇⡆⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡾⢁⡏⡰⢸⢡⠃⢠⣿⠁⠀⣼⠁⡞⣸⣽⢁⠃⢰⣿⠁⠀⡾⢀⡏⡸⡸⢀⠁⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠇⡼⢠⢃⠇⠆⠀⣾⡇⠀⢰⡇⣸⢁⣿⡏⠄⠀⣼⠇⠀⣸⠇⣼⢠⢇⠇⠌⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⡏⢰⠃⡄⡘⠀⠀⡸⡟⠀⢀⡿⢀⠏⣸⡿⠰⠀⢰⡿⠀⢀⡟⢠⠇⡎⡼⠠⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⢁⡏⠸⢠⠁⠀⢠⣻⠁⠀⣼⠃⡜⢠⣻⠃⠀⢀⢿⠃⠀⣼⠁⡜⠐⢱⠃⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠇⡼⢠⢃⠇⡀⠀⢾⠇⠀⢰⡏⢰⠃⣞⡟⠀⠀⡜⡎⠀⢰⡏⢠⠁⠄⡎⠀⠀⡘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡎⢐⠃⠎⡌⠀⠀⢈⡾⠀⠀⣾⢀⡇⡸⣼⠁⠀⠰⡽⠀⠀⡾⠀⠇⠰⢰⠁⠀⢀⠱⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⠀⡎⠸⠠⠀⠀⠀⠾⠃⠀⢸⠃⡼⢠⢣⠇⠀⠀⢣⠇⠀⢸⠇⠸⠀⠀⠇⠀⠀⠀⠃



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

⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢀⡄⠀⠀⠀⠀⠀⠲⠁⢸⠀⠀⠀⢸⠈⢃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠀⡀⠀⠀⠀⢁⡀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠓⠤⠈⠉⠈⠁⠂⣀⠠⠄⠀⡀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢰⠀⠀⠀⠀⠠⠅⠉⠈⠉⠉⢈⠝⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⠀⢈⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡐⢩⠀⠀⠀⠀⠈⡁⠀⠄⠀⠀⠐⠈⠁⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠺⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢠⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠁⠐⠒⠈⠀⠄⠀⠉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠠⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠀⠩⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠁⡖⢁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠒⠆⠚⠉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠚⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⡄⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠘⠀⠤⠀⠒⢀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⡎⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂
⣡⣤⣀⣀⣀⣠⣀⣀⣀⣀⣀⣠⣤⣄⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠋⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⡶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⠟⠉⠁⠀⠈⠙⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⢀⣤⠾⠛⠛⠻⠾⠏⠀⠀⠀⠀⠀⠀⠀⠹⠷⠛⠛⠻⢶⣄⡀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠉⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠈⢿⡄
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠻⢶⣌⣷
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣧⡀
⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠈⠛⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⡶⠶⡶⠶⣶⠶⢶⠶⢶⠶⣶⠶⢶⠶⠶⡶⠶⠶⢶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣴⡾⠟⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠛⠻⠟⠀⠀⠀⠸⣿⠶⣶⣄⣀⣀⣀⢠⣶⠟⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠛⠿⠃⠀⠀⠀⠹⠷⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⡟⣿⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣠⣾⠛⠉⠀⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣤⣿⡇⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⣴⣿⡂
⠀⠀⠀⠀⢰⡿⠋⣿⡇⠀⠀⠘⠿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⠃⠀⠀⠀⠀⢰⡿⠉⣿⡇
⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⣤⣾⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⢀⣴⣾⣟
⣿⡋⢸⡿⠀⠀⠀⠀⠀⣿⡋⢸⡿⠀⠀⠀⠀⠀⣿⡋⢸⣿⠀⠀⠀⠀⠀⣿⡋⢸⣿⠀⠀⠀⠀⠀⣿⡋⢸⡿
⠈⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⣴⡾⣿⡇⠀⠀⠀⠀⢀⣴⡾⣿⡇⠀⠀⠀⠀⢀⣴⡾⣿⡅⠀⠀⠀⠀⢀⣴⡾⣿⡅
⠀⠀⠀⠀⢸⣯⣀⣿⠇⠀⠀⠀⠀⢸⣯⣀⣿⠇⠀⠀⠀⠀⢸⣯⣀⣿⠇⠀⠀⠀⠀⢸⣯⣀⣿⠇
⣶⣶⡶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⣤⣤⡤⣀⣤⣤⣠⣶⣶⣶⣶⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣣⣶⣾⣻⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠐⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣏⢩⣤⣤⣤⣤⣤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⣿⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡿⡿⠀⠙⢿⣿⣿⣿⣿⣿⣶⡟⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⠋⠉⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢆⣄⣠⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣧⡼⣿⡽⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⣿⡿⠙⠙⣹⣿⣿⣿⣿⡿⢿⣿⣿⠀⣸⡿⣿⠿⠛⣷⡻⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠀⠀⠀⢠⣶⣿⣿⣿⣿⣧⡀⠹⠿⠀⡛⠡⠄⣴⣿⣞⡛⢿⣿⡆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⣿⣿⣿⣿⣧⣴⣖⣁⣀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣯⣦⣀⡀⢀⣀⣀⣤⣤⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠀⠀⠀⣠⠤⣴⠚⠛⢦⣀⡀⠀⢀⡴⠒⠉⢦⡀⠀⠀⢀⣀⣠⡶⠛⠛⠓⢦⡀
⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠈⠁⠹⢤⠈⠓⠒⠒⠚⠁⠀⡴⠋⠉⠉⠀⠀⠀⠀⠀⠋⠉⠳⡄
⠀⠀⠀⠀⠻⣄⣀⠀⢀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠓⠒⠋⠛⠁⣀⣤⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠹⣄⠈⠧⣄⣀⣰⣄⠀⠀⢳⡀⠀⠀⠀⠀⣠⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⣠⣤⣈⠙⠓⠚⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⠦⠤⠴⠚⠁
⠀⠀⠀⠀⢀⣠⠏⠀⠀⠘⠁⠀⠈⡧⣀⠀⠀⢠⠖⠋⠉⢙⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠋⠑⢦
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠸⢴⣄⣄⣤⠴⠃⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠘⠓⡄
⠀⠀⠀⠀⠈⠙⠛⢦⣀⣀⠷⢤⠴⠓⠋⢀⣀⠀⠀⠀⠀⠀⢀⡴⠚⠳⠦⣄⠀⠀⠉⠛⠛⠓⠒⠒⠊
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡴⠏⠉⠉⠙⢦⠀⠀⠀⢯⡀⠀⡀⢠⣼⠆⠀⠀⣠⠤⣄⣤⣄
⠀⠀⠀⠀⣴⠋⠉⠉⢣⠀⠀⠀⠘⠦⠤⠤⠤⠤⠴⠃⢀⡀⠀⠈⠉⠉⠉⠀⠀⢰⠋⠁⠀⠈⠀⠈⢳⡄
⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠉⠉⢲⠤⣄⠀⠀⠀⠀⠈⠛⢦⣀⣤⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠒⠒⢤⣀⣀⠀⠸⡇⡀⠀⠀⠀⠈⠀⠉⣦⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⡞⠁⠈⠃⠀⠀⠈⠁⠈⢳⡀⠉⠳⣄⣸⣦⣀⣠⠎⣁⣠⠎⠁⠀⠀⠹⣦⠤⣤⡀
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⠀⠀⠀⠀⠈⠁⠀⠀⣹⡀
⠀⠀⠀⠀⠙⢦⣤⣴⠁⠀⠀⠀⠀⠀⣠⣠⠾⠀⠀⠀⠀⠀⡴⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠶⠲⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠚

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

⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠃⢀⣀⣴⣾⣿⡿⠚⠋
⠀⠒⠛⠛⣿⣿⡿⢿⣿⣆
⠀⠀⠀⠀⢹⣿⣿⢠⣽⣿⣦⡀
⠀⠀⢠⡄⠀⣿⣿⣯⣼⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣶⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣙⣦
⠀⠀⢀⠀⠀⠈⠛⠉⡀⠙⢷⣀⡄⠀⠀⠀⠀⠰⣎⠁⠀⠀⠀⠐⢿⡿⡴⠀⠀⠀⠀⠠⢾⡇⠀⠀⠀⠘⢿⡏⠁
⠀⠀⠰⡆⠀⠀⠀⠀⠃⠀⠘⣿⠀⠀⠀⠀⠀⢰⠻⡀⠀⠀⠀⠀⠈⡏⢣⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⠸⣿⡇
⠀⠀⠼⠿⠆⠀⠀⠀⢸⠀⠀⢏⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠺⠄⠘⠶⠀⠀⠀⠀⠈⠈⠀⠀⠀⠴⠦⠷
⣤⣤⣤⡄⢠⣴⡖⠹⣾⡄⠹⣿⡄
⣿⣿⣿⣿⠿⠏⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣠⣟⣭⡶⢿⠿⣶⣌⠻⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣟⣛⠻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣶⡝⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⢿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⡶⣶⣦⣀
⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣟⣭⣵⣶⣶⣮⣭⣻⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡝⢿⣧
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣸⣿⠇
⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡛⢿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢿⣌⢿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠈⠻⣦⣙⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠉⠀⠈⠙⠛⠿⠿⠿⠛⠋⠉⠉⠉⠙⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠁⠀⠀⠱⢀⠀⠀⠀⠀⠘⠆⠀⠀⢀⠀⠀⠀⠀⠀⢄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠱⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠀⠀⠀⠀⠀⠁⠙⠀⠀⠁⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⣦⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣽⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣤⣀⠀⣀⣄⣀⣀⣰⣶⣶⣶⣾⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠉⠙⣷⡀⠀⣀⣀⣀⣀⡀⢘⣭⣿⣿⣯
⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣷⣤⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀
⠀⠀⢀⠄⠘⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⠊⠈⠁⠁⠑⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠉⢂
⠀⢐⠉⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠶⠦⡈⡅⠀⠀⠀⠀⠀⣀⠑⠐⠢
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⡀⠄⠠⡀
⠀⢀⠁⠀⠈⠒⠰⠈⠑⣆⠀⠠⠂⠊⠀⠀⠱⠀⠀⡠⠒⠀⠐⠁⠀⠑⠂⢄⠀⠀⠀⠀⠀⡠⠜⠉⠀⠀⠀⠘⠒⢄
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠀⠀⢈⠀⠀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣲⠀⠀⢎⡀⠀⠀⠀⠀⠀⢀⢀⡀⠅
⠀⠀⠀⢀⣀⠤⠒⠠⠀⠀⠀⠀⠈⠒⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡑⠂⠒⠁
⠀⢀⠴⠀⠀⠀⠀⠀⠓⠠⡀⠀⠀⡐⠁⠀⠑⠒⠂⢄⠀⠀⠄⠐⠁⠀⠈⠒⢄⠀⠀⢀⠄⠠⠊⠀⠀⢡⣀⣠⠤⠤
⠀⠠⡀⠀⠀⠀⠀⠀⠀⡠⠃⠐⠊⠀⠀⠀⠀⠀⠀⢀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠆⢂⠀⠀⠀⠀⠀⠸⡀⠀⠒⠂⡅
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠑⠀⠂⠀⠀⠁⠀⠀⠈⠒⠢⡀⡠⠄⣀⠠⠃⠀⠡⠀⠀⣀⠀⢀⠇⠀⠀⡔⠁
⠀⠀⡔⠈⠲⢄⠎⡠⠘⠓⢄⠀⠀⠀⠀⠀⠔⠈⠁⠢⠄⣤⢀⡀⠀⣀⠀⠀⠀⠀⢀⠀⡀⢈⠁⡀⠈⠁⠈⠑⠊
⠀⠨⣀⣀⠤⠃⠀⠀⠀⠀⠘⠒⢄⠀⡤⠊⠀⠀⠠⠤⠊⠀⠀⠀⠀⠀⢡⠀⢀⣠⣁⡠⠀⠢⡀⠈⠄⢄⡠⠄
⠀⠀⠀⠈⠄⣀⣀⣀⣀⣀⣀⣀⠜⠀⠉⠁⠐⡎⠁⠀⠀⠀⠀⠀⠀⢀⠌⠠⠉⠀⠀⠀⠀⠀⠀⠈⠆⢀⣀⣀⣁⣐⡄
⠀⠀⠀⠀⠀⡠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠉⡉⠁⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀
⠀⠀⡀⠔⠉⠀⠀⣀⡩⠓⠒⢄⠀⠀⠀⠀⠀⠀⠔⠐⠁⢀⠨⢄⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⣀⠔⠒⠊⠀⠈⢂
⠀⢰⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⢢⠀⠤⠁⠀⠀⠉⠙⡀⠉⠐⠀⠀⢐⠁⠀⠀⠑⠀⠄⠊⠁⠢⠈⡃
⠀⠀⠑⠀⠪⢄⢀⡀⡀⠀⠀⢀⠀⠤⠂⠀⠤⠴⢎⣉⠀⠀⠀⠀⠀⠀⣘⣒⡚⠄⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠟⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠉⠉⠉⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⠶⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⢀⣠⣿⠶⠶⣶⣼⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡶⠶⢶⣤⣄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⢷⣤⡾⠛⠛⠛⠛⠿⣦⡀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠈⢻⣦⣤⣤⣤⣤⣀⠘⣿
⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠉⠙⢷⣿⡆
⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣄
⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠈⠻⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠾⠋
⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⣠⣴⠾⠋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠾⠋
⠀⣾⠟⠁⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⡉⠉
⠘⣿⡀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⣀⣤⡾⢻⣷
⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⢻⣷⠀⠀⢠⣾⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡄⠀⠻⣧⣤⣤⡾⠋⠀⠀⠀⠀⠀⣀⠀⠀⢠⡿⠋⠀⠀⢸⡟⠀⠀⢸⣇⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⢸⡇⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣠⡾⢿⡇⠀⢻⣇⠀⠀⣠⣿⠃⠀⠀⠈⠻⠷⠶⠿⠋
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠉⠀⢸⡇⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠻⣧⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣴⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡤⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⠀⣀⠠⠤⠄⢀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡤⠂⠉⠉⠒⢄⠀⣀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠑⢆⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⡜⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⢀⣀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠑⠤⠠⣀⡀⠀⠀⠀⠀⠀⡀
⠀⡀⠤⡰⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠇⠈⠠⢀⡀⠀⠀⠀⠀⠀⠉⠑⡤⢄⡀⠀⠈⠉
⠸⣄⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠆
⠀⠀⠁⠀⠉⠉⠉⢏⣠⡉⠀⠉⢀⣀⣉⡁⠘⠊⠡⠂⠀⠀⠒⠀⠁⠉⠃⠉⠚⠋⠭⠠⠐⠊⠑⠒⠒⠂⠻⠵⡄⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠫⠤⢤⣀⡠⢄⣀⣀⣀⣠⣀⡠⠀⠤⠈⠀⠀⠀⠤⠀⠀⣀⣀⠠⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄
⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⠔⠀⠀⠐⠀⠀⠀⠈⠒⠠⠔⠒⠂⠀⠐⠂⠂⠠⠤⠀⠒⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⣀⡀⠀⠀⣀⢄⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠐⠀⠊⠁⠂⠐⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠑⠒⠊⠒⠒⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢤⣀⡤⣤⡀
⣿⣿⠛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠈⠀⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠱⡀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠦⠤⡀⡀⠄⠠⣀⢂⠀⢀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢀⣄⡀⠐⠃⢢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠄⠈⠂⠀⠀⠈⠀⢀⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠐⣄⡀⠀⠀⠀⠐⣀⠈⢀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠓⠠⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠐⠁⠀⠑⡄⡀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠺⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠁⠀⠀⠂⠒⠂⢋⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠈⠀⠀⠀⠀⠘⠄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠆⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠐⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠐⠈⠀⠀⣄⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⠀⠀⠈⠓⠀⠀⠀⠈⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠈⠀⠀⠀⠀⠘⠄⠀⠀⠈⠣⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠂⠀⠀⠀⢰⡀⠀⠀⠀⢈⠠⠀⠀⠀⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠘⠦⠃⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠇⠀⠀⠀⢤⠀⠀⠀⠀⠘⢀⠀⠀⠀⠈⠛⠈⠃⠓⠀⡀⠲⠀⠀⠀⠈⠀⠘⠀⣤⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠘⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠄⠀⠐⠄⠷⠴⠀⠀⠀⠟⠦⠀⠀⢸⣧⡀⡀⣄⣿⢷⠈⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠺⠖⠐⠂⠸⣧⡇⠉⠀⠙⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠈⠀⠃⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠲⠀⠀⠀⠘⠦⠀⠀⠀⠘⢆⠀⠀⠀⠸⠄⠀⠀⡀⠈⠃⠀⠀⠀⠘⠆⠀⠀⠀⢇⡁⠀⠀⠳⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃⠀⠀⠀⠀⠙⠀⠀⠀⢨⠀⠀⠀⠀⢠⠀⠀⠀⠈⠃⠀⠀⠀⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢑⠀⠀⠀⠀⠸⡈⠀⠀⠀⢇⠀⠀⠀⠀⠸⡈⠀⠀⠈⠇⠂⠀⠀⠈⠓⠀⠀⠀⢧⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢾⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⣾⣿⣿⠏⠙⣛⣿⣷⣄⠱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠑⣼⣿⣿⣿⣿⡿⠑⢂⡺⠭⢿⣿⣿⣧⡀⠈⠡⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠴⣿⠿⣿⣿⣿⣷⠀⠀⠀⢙⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠂⠠⠄⠲⠶⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣻⣿⣿⣿⣏⣀⣠⣤⣴⣶⣦⣤⣼⣿⣽⣿⣿⣿⠀⢀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠈⡏⠙⠉⠉⠛⠂⠛⠁⠿⠿⣿⣿⠙⢹⣿⡿⡟⣛⣿⠃⡿⣿⣿⢿⡇⣿⣿⣿⣿⢿⣿⣧⣿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⡀⠀⠀⠸⡇⠀⠀⣿⠀⠀⠁⠉⠘⠁⡟⡏⠉⢀⠈⠉⠃⠃⡄⠸⡇⢰
⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⡎⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⣸⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠒⣦⣀⠀⠸⠇⠀⠀⠀⢉⡛⣉⣁⣄⠒⣮⠐⢉⣽⠛⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠉⢴⣄⠀⠀⠈⢶⠤⢠⠀⣿⢁⠙⣶⠒⠬⣻⣞⣷⢀⣴⠶⠀⠂⠀⠀⠀⢨⡄⠀⠀⣃⠀⠠
⣠⠀⠀⠀⠀⠀⠢⢴⡿⠆⡙⣿⠛⣽⡛⢩⣾⡶⢛⣉⣵⣶⣤⡃⠀⣨⠡⢶⠄⣾⠧⢀⡈⣯⡀⠀⠀⠀⢠
⠛⠻⠤⠀⠀⠀⠀⠘⠙⠓⢛⢉⡃⠸⣿⣿⡜⢿⣿⣿⣋⣿⣿⣿⣧⣈⣵⣶⡂⠀⢀⡼⢀⠙⠷⡶
⠀⠀⠀⠀⠀⠛⠻⣶⠞⣿⡹⠟⠷⣤⠛⠛⠋⣾⣤⣽⣿⣿⣿⣿⣿⣷⡏⢈⣅⣶⡄⠀⡈⢀⣀⡅⠀⠐⠛
⠀⠀⠠⠀⠀⠀⠘⠻⠟⠿⡇⢁⠚⢿⠧⣾⣋⣿⣎⣹⣧⡿⢿⣧⣤⡿⠱⣾⠏⢭⣅⡤⠔⠛⠋
⠀⠷⡦⠀⠀⡆⠈⠁⠓⢺⣷⢼⣤⡠⡄⢸⣏⠩⣿⣾⠟⡻⣿⣿⡛⡇⠈⢉⢸⣿⠃⠀⡀⠀⠀⠿⠛⠓
⠀⠰⠀⢀⣤⠀⠀⠀⣀⠘⠈⢆⣶⡅⢈⡅⢭⣤⡟⢇⡼⡷⠏⢉⣽⡦⠄⣾⢇⡀⢸⡆⠀⢀⡶⠇
⠛⠀⠈⠀⢀⡴⠿⠘⢯⡤⠄⠈⠚⠁⠀⢿⣷⣉⡈⢬⣉⣤⡾⠿⣦⣴⣸⣟⠉⢷⠀⠀⠀⢀⣤⠀⠀⠠⠔
⠀⠀⠀⠀⠌⠀⠀⠀⣼⣥⣄⣀⠰⠔⡶⣶⠿⠿⠷⢿⣯⣱⡆⠀⣰⣩⢀⣬⠳⡜⠃⠀⠘⠈⠁⠀⣾⡟
⠀⠀⠀⢀⡀⣀⠤⠀⠈⠉⠈⠉⠺⠆⢠⡀⠀⠀⠀⢈⠻⢓⣤⣾⠙⠁⠀⠈⠀⠀⢸⣦⡀⣤⣤⣤⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⠀⠈⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠙⠛⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⣤⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣰⠟⠁⠀⠀⠀⠀⠙⣦⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠳⣤⠶⠛⠛⠛⠶⣄⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⣷⠶⠶⠶⣤⣸⡇
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠉⢻⡟⠛⠛⠛⠛⠛⠛⠛⢻⡛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⣠⡴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠈⣻⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠋
⠀⠀⠀⠀⠀⣾⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⣴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⢁⣼⡄
⠀⠀⠀⠀⠀⠻⣦⣤⠾⠁⠀⠀⠀⠀⢠⡟⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡆⠀⠀⣠⡶⠟⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠸⣧⣀⣠⡟⠀⠀⠀⠀⡀⠀⢀⣴⠛⠁⢀⡇⠀⢰⡏⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢹⡇⠀⠈⠉⠁⠀⠀⢀⣠⡼⢿⡀⠸⣧⣀⣀⣼⠃⠀⠀⠛⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⣼⠁⠀⠀⠀⠀⠀⣰⠟⠉⠀⣸⠁⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠞⠁⠀⠀⠀⠀⠀⠀⠹⣆⣀⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⢉⣽⣿⡏⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡾⡿⠉⠋⠀⠀⠀⠀⠀⠙⢶⣄⡀⢄⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⣠⡶⢛⡽⡻⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣧⣢⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢀⣴⠞⠉⣰⠟⠀⠀⠸⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠀⠀⢣
⠀⠠⠊⠀⢀⣠⣤⣤⣤⣤⠠⠀⢀⣠⣿⣿⣿⠃⠀⢰⡟⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠈⡀
⠀⠅⣰⡟⠉⠀⠀⠀⣀⣠⣤⣭⣿⠿⠟⠛⠁⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠇
⠀⠀⢿⠀⠀⠀⠀⠘⠻⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⢧⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠊
⠀⠀⠀⣸⠾⠖⠛⠛⠁⠀⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⢶⡀⠀⠀⠀⠀⣦⡿⢁⣄⣴⣾⣦⣤⣤⠴⠞⠋⠁
⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣦⡀⠀⠠⠀⡤⠞⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⡷⠛⠉⠉⠉
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣙⣮⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡟
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠼⠛⠛⠛⠛⠛⠛⠻⠷⣶⣄⣀⣀⣤⡄⠔⠀⠀⠀⠀⡸
⠀⠸⡀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠿⢶⣤⣴⣄⣤⣤⣾⡀
⠀⠀⢳⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⠏⣇
⠀⠀⡸⠃⠀⠀⠀⠀⠀⢀⣀⠄⢠⡤⣤⣤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠸
⠀⢰⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⢿⣿⣿⣿⣿⢿⠁⠀⣠⡇
⠀⡏⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠖⠲⠖⠚⢚⣽⠟⠉⠀⠀⠀⡰⠟
⠀⡇⢀⠀⠀⠀⠀⠀⠀⢀⣠⢼⠟⠋⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⡴⠋
⠀⣷⡃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⢀⠞
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠒⠊⠁
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣡⣴⡤⠔⠚⠉⠁⠁
⠀⠀⠀⢣⢠⡇⠀⠀⠀⠀⣰⠟⠉⢸⣇⡀⢀⠀⠀⠠
⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⠃⠀⠀⠀⣿⡴⠗⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⡟⠁
⠀⠀⡀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢰⠁
⠀⢠⣇⡀⢀⣠⡴⠖⠁⡠⠀⠀⠀⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣷⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣶⣿⣿⣿⡿⠋⣈⣿⣿⣷⣌⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⣾⣿⣿⣿⣿⠟⠈⠉⢽⣿⣿⣿⣿⣧⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠰⣴⣿⣿⣿⣿⣿⠇⠀⠀⠒⠺⢿⣿⣿⣿⣿⣇⠀⠀⠀⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⣿⠏⠈⠈⠉⠉⠉⠉⢿⡿⣿⣿⣿⠀⠀⠀⠀⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣯⣵⣿⣿⣿⣿⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣄⣑⡀
⠀⠀⠀⠀⠀⠰⠻⠛⠻⣿⡟⢻⠿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠀⠀⢻⡟⠉⠙⣿⠀⠙⠻⠇⡿⢼⡿⠿⠛⠛⠿⡏⡟⠙⠻⡟⢀
⠀⠀⠀⠀⠀⢸⠀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠸⠀⠀⠈⡇⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠺
⠀⠀⠀⠀⠀⠈⠀⠃⠀⠐⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣄⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣾⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⠋⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠚⠓⢦⣀⣼⠁⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⠤⠤⠦⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⠶⠶⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠙⠲⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⡽
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠠⢾⡁
⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡋⠀⠀⠀⠀⠀⡀⠹⡆
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠐⠐⢀⣀⣀⡴⠃
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠳⡤⠖⠁
⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡱⢦⣄⠈⠦⠂⠂⠀⣀⡴⠋⠳⣄⣈⠘⠁⠀⠀⠈⣀⣤⠞⠙⠶⠶⠞⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠈⠙⡛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠃⠀⠀⢰⡄⠀⠀⢸⠀⠀⠀⠀⠀⢲⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡆⠀⠀⠀⠀⠘⠃⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⡆⠀⠀⠀⢠⡄⠀⠸⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣦⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠢⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠡⠀⠄⠀⢄⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠠
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣈⢀⣀⠔⠒⢢⠖⠒⠴
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠘⠈⡩⠐⠩⢅⠁⠉⠈⠭⣐⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠈⠑⢄⠀⠀⠁⠂⢄⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠬⠦⡀⠀⠀⠀⠐⠂
⠀⠀⠄⠀⠀⠀⠀⣀⠀⠠⠀⠠⠀⠀⠂⡄⠀⠤⠀⠀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⠀⠀⡔⢀⠆⢀⠃⠀⢀⠂⠀⠄⠀⡐⠀⡐⢀⢀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠋⣐⠀⠈⠀⠠⠄⠈⢀⠄⡔⠀⠉⠀⠘⠄⢀⠄⠀⡅⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢠⠀⠀⢸⠀⠊⠀⠀⠚⠀⠀⠀⠇⡀⠘⠀⢈⠄⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠐⠀⠃⢀⡔⠠⠂⠰⠀⡰⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⢛⡛⠛⠓⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⠶⣤⣄⣠⡶⢋⣥⣶⠿⠿⠿⠿⣿⣿⣶⣤⡉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣩⣴⣶⣿⢿⣿⣿⣶⣦⡌⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡈⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠈⢻⣿⣤⣍⣉⡛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠛⠻⢿⣷⣄⡙⠛⠻⠿⣿⣷⣦⡈⠳⣦⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣠⡴⠟⢀⣠⣴⣾⠿⠿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠈⠙⢿⣿⣶⣶⣮⣭⣍⡛⠶⣤⡀
⠀⠀⢀⣤⠞⣫⣵⠾⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣶⣌⠻⣦
⠀⢠⡞⡡⠚⠉⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡈⢷
⢠⡟⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸
⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠶⠶⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢦⣄⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡴⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣿⡇⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⢰⠏⠀⠀⣸⣷⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⢀⡟⠁⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠴⢞⣿⠇⠀⣠⡞⠁⣿⡀⠀⠀⠀⠀⠸⣇⡠⠾⣻⡟⠀⢀⡼⠋⢸⡇⠀⠀⠀⠀⠈⢷⣀⠴⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠉⠙⠉⠁⠀⣼⠋⠀⠀⣿⡇⠀⠀⠀⣠⣦⠈⠙⠋⠉⠀⢠⡟⠀⠀⢸⣿⠀⠀⠀⢀⣴⡀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣷⠀⠀⠀⠀⠀⢻⣄⠤⠾⣻⠇⠀⢀⡾⠋⢿⡄⠀⠀⠀⠀⠸⣇⠠⠴⢿⡿⠀⠀⣴⠏⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⡆⠀⠀⠀⣠⡄⠉⠛⠛⠉⠀⣰⠟⠀⠀⣸⣇⠀⠀⠀⢀⣤⠈⠛⠛⠋⠀⢀⡾⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣤⡾⣿⠇⠀⣠⡾⠋⣿⠀⠀⠀⠀⠀⢻⡄⢠⡴⢿⡟⠀⢀⣴⠏⢻⡆⠀⠀⠀⠀⠸⣇⠀⣤⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠛⠓⠛⠁⠀⣰⠏⠀⠀⣿⡇⠀⠀⠀⢀⡄⠙⠓⠚⠋⠀⢠⡞⠁⠀⢸⣧⠀⠀⠀⢀⣤⠈⠛⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠹⣇⠀⠀⠀⠀⠀⢿⡀⣀⡴⣿⡇⠀⢀⡴⠋⣿⠀⠀⠀⠀⠀⢸⡇⢀⣤⢿⡿⠀⠀⣠⠟⢻⡆
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣿⡀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⣠⠟⠁⠀⣹⡇⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⢀⡾⠃⠀⢸⣷
⠀⠀⠀⠀⠀⠸⣇⠀⣀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢦⡀⠀⠀⠀⠀⠀⣼⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⢦⡀⠀⠀⣼⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠶⠶⠛⠛⠛⠛⠛⠛⠶⠶⣧⣀⠀⠀⣀⣀⣤⣤⣤
⠀⠀⠀⣤⣤⣄⣀⡀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡉⠉⠀⣰⠏
⠀⠀⠀⠙⢷⣌⠉⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣴⣿⠴⠶⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⢀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⣠⡶⠞⠛⠉⠀⢻⡄⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠉⠛⠛⠳⣶⣶⠾⠿⠛⠛⠛⠳⠶⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢶⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠙⠛⠶⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⢛⣛⣛⡛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣚⣛⣛⡒⠶⢤⣀⡴⢋⣵⡾⠿⠿⠿⠿⠿⣿⣶⣤⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⡾⠿⠿⠿⠿⢿⣷⡦⠈⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡹⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠈⢿⣷⣶⣤⣍⡙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠰⠛⠉⠁⠀⠀⠀⠀⠉⠙⠻⢿⣦⡉⠉⠙⠻⢿⣷⣄⣙⡶⠶⠦⣤⣀
⠀⠀⠀⢀⣠⠶⣛⣯⣠⣶⠿⠛⠋⠉⠉⠉⠉⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠙⠛⠿⠿⢿⣷⣦⣍⡛⢦⡀
⠀⢀⡴⢋⡴⠛⢋⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠹⣆
⢀⡾⠁⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠸
⣼⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠉⠳⢦⣄⣀⡀⠀⠀⣀⣠⡤⠞⠛⠒⠶⠶⠚⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠳⠦⣤⣀⣀⣀⣀⣠⡤⠶⠶⠶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠒⠚⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⣿⠀⠀⢀⡼⢿⡄⠀⠀⠀⠀⢾⡀⢀⣠⣿⡇⠀⢀⡴⢻⡆⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠳⠯⠷⠋⠀⣴⠏⠀⢸⣇⠀⠀⠀⢀⡈⠳⠯⠷⠋⠀⣠⠟⠁⢸⣿⠀⠀⠀⠀⣀⠛⠾⠽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣧⠀⠀⠀⠀⠸⣇⢀⣠⣾⣿⠀⠀⣠⠞⣷⠀⠀⠀⠀⠀⣯⠀⣀⣼⣿⠀⠀⣠⡞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⡀⠀⠀⠀⣀⠙⠳⠷⠞⠁⢀⡾⠃⠀⣿⡆⠀⠀⠀⢀⡈⠳⠷⠞⠋⠀⣴⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⣴⣿⠇⠀⢠⡾⢻⡆⠀⠀⠀⠀⢸⡅⢀⣤⢿⡇⠀⢀⡴⠛⣇⠀⠀⠀⠀⠸⣇⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⠲⠞⠋⠀⣴⠋⠀⢸⣷⠀⠀⠀⢀⣀⠙⠲⠖⠋⠀⣠⠟⠀⠀⣿⡀⠀⠀⠀⣀⠙⠳⠖⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣷⠀⠀⠀⠀⠀⣧⠀⣠⣾⣿⠀⠀⣰⠟⢻⡀⠀⠀⠀⠀⢿⡀⣠⡼⣿⠇⠀⣠⠞⢻⡆
⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⡇⠀⠀⠀⠀⠈⠛⠒⠛⠁⢀⡾⠁⠀⢸⣇⠀⠀⠀⠀⠈⠙⠓⠛⠁⠀⣴⠋⠀⢸⣷
⠀⠀⠀⠀⠀⢸⣄⢠⡴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣴⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣤⢾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠎⠛⠅⠈⠑⠔⠒⢄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠄⢠⠄⠀⠀⠀⠀⠀⣄⠈⡵⠤⠴⠒⠊⠀⠀⠖⠐⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣀⡴⠚⠄⠀⠀⠈⠀⠀⠀⠀⢀⡔⡲⠚⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⠚⠁⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⢳⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣩⠤⣀⠤⡤⠤⢄⠀⠀⠀⠀⠀⢰⡟⢡⣄⡀⠐⠁⠀⢀⡀⠀⠀⠀⠺⠀⠀⢈⠁⠀⠀⠀⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠟⠚⠁⠀⠀⠀⠀⠀⠐⢳⡠⣋⠑⡖⠀⠀⠁⠈⠙⠔⠢⡤⡢⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⡂⡄
⠀⠀⠀⠀⠀⠀⡠⠤⢖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠭⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄
⠀⠀⠀⢀⣠⣼⡅⠀⠘⠀⠀⠀⠀⡠⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⠿⢗⠂⣀⡀⢀⣀⢀⣀⣀⣀⣘⣳⣶⣶⣦⣠⣄⣀⣀⣀⣀⣀⡀⠂⢱
⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣅⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣉⢁⣉⣀⣈⣉⢀⣙⣛⡯⠛⠛⠛⠛⠛⠋⠉⠉⠉⠈⠉⠉⠉⠋⠉⠁
⠀⠀⠀⠈⠒⠢⠤⠶⠘⠳⠶⠖⠒⠛⠛⠛⠛⠛⠛⠉⠉⠛⠙⠛⠋⠉⠛⠋⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠈⠀⠀⢀⡏⠀⠀⡼
⠀⠀⠀⠀⠀⠠⡆⠀⠀⣼⠀⠀⡏⠀⢀⡇⠀⠀⠰⠀⠀⠀⠀⡾⠀⠀⠀⢠⠆⠀⠀⠀⠺⠂⠀⢠⡇⠀⠀⣼⠀⠀⡀⠀⠀⣸⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠇⠀⢸⠁⠀⢀⡇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠚⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢰⠃⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⡞⠀⢀⡏⠀⠀⠘⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠀⠀⢸⠁⠀⠀⠀⣀⠀⠀⢰⠃⠀⠀⠀⡞⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣸⠁⠀⣸⠀⠀⢀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠀⠀⡟⠀⢀⠀⠀⠉⠀⠀⡟⠀⡀⠀⢸⠁⠀⠀⠀⢸⠃⢰⡄⠀⠀⠀⠋⠀⢠⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠁⢰⠇⠀⠏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠐⢂⠠⠄⠀⠈⠳⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠂⠀⠀⠀⠀⠄⠀⠉⠀⢙⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡄⢀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠈⣤⠒⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⠠⣀⠀⠀⠙⣆⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠅⠀⢀⡠⠊⠉⠉⠀⠑⢄⣀⡀⠀⠈⠀⠙⠂⠀⠈⠉⠂⣈⠀⢀⣁⠉⠀⠈⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠔⠁⠀⠀⡸⠋⠃⠀⠀⠀⠀⣀⡀⢉⣳⣄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠙⠀⢄⢀⣀⠀⠸⢆
⠀⠀⠀⠀⠀⣀⠠⠄⠞⠁⠀⠐⠈⡃⠀⠠⠼⠆⠀⠀⠀⠀⠉⡀⠀⠀⠈⠻⠦⣀⣠⣷⢇⡠⠶⠔⠖⠦⠤⠴⠶⠦⢾⣓⣤⣈⣀⡤
⠀⠀⠀⠉⠉⠉⠒⠒⠙⠓⠒⠒⠛⠛⠓⠒⠒⠒⠦⢦⣀⣤⠤⣡⠤⠤⠤⠤⠤⠴⠤⠬⠩⣅⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠲⠛⠛⠛⢛⠳⠞⢛⣠⣀⣀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣶⣦⡀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣴⣤⣉⠉⠻⢶⣶⣦⣤⣄⡀⠀⢁⠙⣿⣿⡿⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⢹⣷⣿⣿⣿⣷⣾⣄⠉⣿⡇⠀⢻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⣾⠀⠀⠀⠁⠀⠀⣹⠛⠛⣿⣶⡿⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡝⠀⠐⠋⠀⠀⠀⠀⠀⡴⠁⠀⠀⠈⠻⣿⣿⣿⣶⣄⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⡀⠀⡀⠂⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣷⣽⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⡀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣯⣶⡱⡀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠂⣀⠀⠉⠀⠉⠀⠀⠀⠀⠀⣸⣿⣦⣬⢻⣿⡅⢁⡀⣌⣾⠇
⠀⠀⠀⡀⢇⠀⡀⣿⠊⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⣿⣿⣾⣯⣷⡼⢧⡼⠄
⠀⠀⣻⣿⣄⣿⡁⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠘⠛⢇⣤⡟⡀
⠀⣸⣿⣿⣧⣿⣿⣿⣿⣷⠶⢤⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣷⣲⣾⡗⠁
⠐⢈⣿⣿⣿⣿⣿⡏⣿⣋⣀⠺⡏⣽⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄
⠀⣿⣿⣿⣿⣿⠏⠳⣿⣿⠁⢸⠇⢳⡹⠍⠀⣼⠃⢹⡿⣿⣯⠺⠁⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠠⣀⣀⠀⠀⠑
⠘⠃⢹⣿⣿⣿⣿⡄⣻⣿⡆⠈⠀⠿⣷⣄⣾⣿⣶⣾⡷⡟⢎⠄⠂⣏⢹⡇⠀⠀⠀⠈⢳⡆⠀⠀⠀⠺⢻⡿⣿⣇⠤⠠⢀⡀
⠀⠠⠴⡿⠿⠻⠟⠋⠉⣿⡇⠀⠀⠰⠺⣿⣿⡳⣬⢿⡱⠀⠀⡀⠀⣻⢻⡇⠀⢲⣤⣴⣾⡧⡶⠀⠀⠀⠘⢃⢿⣾⡇⡤⠊⢰⡀⠁
⠀⠀⢄⣀⣀⣀⣤⣤⣴⣿⣇⠀⠀⢀⣴⣿⣿⣧⠈⠁⠡⠀⠀⠀⠀⡟⢸⣏⠀⠛⠛⣿⣿⣷⠃⢀⡀⣀⢠⡤⣶⣿⣿⣞⡖⡷
⠐⢞⠻⢻⣿⣿⣿⡿⣿⢿⣿⢰⡆⠸⣿⣿⣿⣿⣧⣦⣤⣤⢴⣦⢾⡟⡀⣿⠀⢀⣷⣽⣿⣻⡸⣻⣿⣷⣿⣷⠾⣿⣯⠻⠤⠄
⠀⠈⠂⡀⣿⣿⣯⡱⠿⣿⣿⢸⡇⢀⣾⣿⣿⣿⣿⣿⡟⠋⢉⢉⠛⠛⠁⣸⣄⣾⡍⢣⣼⣿⣿⣿⣿⣿⣿⣿⢿⣛⣍⣷⠄⣲⣂
⠀⠀⠀⡑⣾⡿⢿⣟⣦⣾⡿⠘⢇⣼⣿⣿⣿⠻⡝⢿⠢⠀⣸⠸⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣒⠀⠈⢁⠀⠈⠁
⠀⠀⠀⠀⠟⠘⠈⠀⠈⠉⢱⢀⣿⣫⣿⢻⡿⠀⠱⠀⠁⢰⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠣⠀⡳⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠁⢸⡟⠼⢇⠀⠀⠂⠱⠂⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡩⢻⣤⡟⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠀⠀⡅⠞⠀⠀⠀⠠⠄⠀⢺⡝⠿⢿⠿⠿⠟⠻⠁⠊⠃⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⠷⣦⣄⡀⠀⣰⡿⠋⠀⠀⠀⠀⠈⠙⢷⣄⠀⣀⣤⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠉⠛⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠁⠀⠀⠀⠙⢿⣦⡶⠶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⣴⡿⠋⠁⠀⣀⣉⣀⣀⠀⠀⠀⢀⣴⠿⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣄⡀
⠀⠀⢸⡟⠀⠀⢠⡾⠛⠉⠉⠙⠛⢦⣴⠟⠁⠀⣀⣀⣀⠈⠳⣤⠶⠛⠛⠛⢷⣆⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷
⠀⠀⣿⡇⠀⢠⡟⠁⣠⡶⠖⠒⠶⠀⠉⠀⠀⠀⠀⠀⠈⠓⢄⡠⠔⠚⠛⠒⠀⠛⠁⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⡇⠀⣼⠇⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⡿⠿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡎⠀⢠⡂⠉⠐⠠⠀⠀⠀⠀⠉⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠒⠀⡘⠃⠀⠙⠏⡁⡀⠀⠀⠀⠀⠀⠘⠿⠛⢡⡦⠴⡤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠈⠉⠁⠀⠈⣿⡄⠀⠀⠀⠁⠓⠃⠀⠀⠀⠀⠀⠰⣀⠀⠠⠄⠸⢤⠀⡤
⠀⠀⠀⠀⠀⠠⢀⠄⠀⠈⠓⠀⠀⡀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠛⣷⣾⣦
⠀⠀⠀⠀⢀⣴⠛⡄⢰⣤⣿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡄⠉⠙⣿
⠀⠀⠀⠀⠄⠀⠠⢆⡀⠉⠿⡇⠀⠀⠛⠂⠂⠀⠀⠀⠠⢷⠀⠁⠦⣀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⣣⠛⠛⢹⣦
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⣥⡀⢹⣄⡀⠀⠀⡀⠀⠀⢾⣷⢀⣀⣀⣀⡀⠀⠀⢀⠹⣾⣦⣴⠞⠁⠀⠐⠀⣹⠃
⠀⠀⠀⠐⢴⣶⠆⠀⠰⠐⠈⢸⣿⣄⡐⠚⣃⠀⠀⠀⢀⣈⠛⠻⢿⢟⣉⡄⠀⠀⠀⠓⠎⠉⠘⠆
⠀⠀⠀⠀⠀⠁⣦⡲⣦⠀⡀⢾⣿⡽⣷⣼⡿⢯⣝⡛⠿⡉⠀⠠⠄⣄⢤⠀⠀⢀⠀⠠⠀⢤⣀⠀⡣⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠛⠂⢻⡀⢛⣆⡾⠂⢧⡀⠿⢿⠟⠁⡄⢨⡜⠈⠈⠇⠀⠈⡄⠀⠇⠈⠃⠀⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⢧⠀⠀⠘⡄⠀⠸⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠀⠀⠀⠈⠀⠀⠁⠀⠑⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠛⠛⠻⠷⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⢤⣼⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠉⠙⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿
⠀⠀⠀⠀⢻⡏⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣽⡟
⠀⠀⠀⠀⠈⢿⣄⢅⡂⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⡠⢐⠠⢐⣼⠟
⠀⠀⠀⠀⠀⠈⠻⣷⣬⣄⡂⠀⠀⠄⣀⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢤⣄⣅⣂⣌⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉⠑⢦⣥⣅⣐⡐⡀⠀⢂⠄⢅⣐⣐⡽⢿⣦⣄⠄⡀⡀⡀⠀⠀⠄⣄⡶⠟⠁⠀⠈⠉⠉⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⠛⠷⠾⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢤
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣰⡟⠁⢰⡄⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⣾⠋⠀⢱⡀⠀⠀⠀⢿⡄⠀⣸⠇⠀⠀⠀⠀⠀⢰⡟⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠋⠀⠀⢀
⠀⠀⠀⢿⣄⣀⡼⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢀⠀⠀⠘⢧⣀⣠⠟⠀⠀⢀⣴⠞⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡞⠋
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠉⠁⠀⢀⣼⠟⠁⠀⠀⠀⠙⠷⠴⠟⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠋⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣄⠀⠀⠀⠀⣿⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⡾⠁⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠙⢦⡴⠟
⠀⠀⠀⠀⠀⢠⡾⠋⡀⠀⠀⠀⠀⠀⠹⢦⡴⠟⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠙⠶⠾⠋
⠀⠀⠀⠀⠀⣿⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠻⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠐⣄⠀⠀⠀⠀⠀⠀⢼⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠷⠤⠾⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⠔⠂⠀⢀
⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⡇⠀⠈⠢⠤⢄⠀⠀⡀⠀⠔⠡⢐⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠃⡀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠂⠬⡁⠀⠂⠀⠀⠈⠁⠀⠀⡠⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠘⠂⠀⠈⠁⠈⠉⠀⠐⠠⠤⣀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠉⠁⠈⠁⠀⠀⠀⠂⠀⠀⠐⠄⠀⠀⢄⣀⣀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⠤⠤⠔⠉⠁⢀⠄⠁⠀⠀⠀⠈⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠆⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⡤⠔⠨⠆⠀⠖⢤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡛⠀⢠⣄⠀⠀⠤⡀⣶⡈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠄⠀⠀⠀⢀⣀⡄⠀⠹⠗⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡱⠋⡀⣀⠀⠀⠈⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣸⠏⠷⠦⠄⣠⢴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠐⠟⠛⠋⠈⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⢤⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⠀⠀⠐⠹⠏⠀⠀⠠⠀⠀⠰⢶⠦⠀⠀⠀⠀⠀⢀⢀⢀⢀
⠀⠀⠀⠈⢱⡖⠆⠢⣤⣀⢀⠀⠀⠀⣀⣄⡄⠀⠀⠀⠀⠀⠉⠄⠀⠋⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠄⠈⠀⠺⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠀⠀⣶⠀⢰⡖⢲⣶⢀⡶⣶⠀⠀⣶⠒⣂⠀⠀⢠⣶⣶⣶⠒⣶⡖⠒⣶⣤⡖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⢿⣿⣿⢷⣿⣿⠿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⡿⣫⣿⣿⣽⣿⣿⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣫⣷⣷⣟⠽⢿⢿⣿⣿⢷⣿⣿⢿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣽⣿⡞⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠰⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⡄⠀⠠⡄⠀⠠⡄⠀⠀⡄⠀⠠⡄⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⣀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠉⠀⠀⠉⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐⠃⠀⠐⠃⠀⠐⠃⠀⠀⠃⠀⠐⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡄⠀⢀⡄⠀⢀⡄⠀⢀⡄⠀⢀⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣠⡶⠛⠉⠉⠙⠟⠁⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⣠⡴⠚⠛⠉⠙⠛⠓⠶⣄⣀⣀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠛⠯⡀⠀⠀⠀⠀⠚⠂⠀⠀⢀⠀⣿⣀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⣸⠃⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠹⣄⠀⠀⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠈⠹⣇⠁⠁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠙⠳⠦⣤⠴⠶⠦⢤⣤⡔⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠠⠃⠀⢀⠃⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⢶⣅⣀⣀⣀⣀⣤⣎⣀⣀⣀⣀⣀⣠⣴⣁⣀⣠⣤⢶⣤⣤⠴⠟⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠰⡀⢤⣶⣾⣿⣿⣿⣿⣿⣶⣴⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠀⠂⠀⠀⠀⢀⡽⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⣿⣿⣿⣿⠃⠀⠀⠀⠠⣶⠋⠀⠀⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢕⢄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠛⠁⠀⡄⠀⠀⠀⠀⠀⡟⢻⠶⣄⡀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⣠⣾⣦⠀⡀⣻⡇⠀⠀⠀⢸⡇⣾⠀⠈⠻⠃
⠀⠀⠀⠀⣠⠀⠀⠀⣴⣿⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⣿⡇⠀⠉⠛⠛⠋⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⢀⣠
⠀⠀⠀⣼⣿⡆⠀⢀⣿⣿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠐⠻⢧
⠀⠀⢰⣿⣿⣷⠀⣸⣿⣿⡇⣠⡄⣿⣿⣿⠀⢠⣾⡅⠀⠀⠀⠀⣿⠋⠁⠉⠀⢀⠀⠤⠤⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⢀⣿⢽⣧⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣇⣼⣿⡃⠀⠀⠀⠀⠉
⠀⠀⡗⡐⠻⣿⠟⠉⠉⢉⣿⣿⣟⠁⠉⠉⣿⡿⣿⡇⢀⣤⣤⠠⠀⠰⡄⢶⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢠⣀⡀
⠀⠈⠀⠀⠀⠀⠀⠄⠀⢼⡡⣿⣿⠀⠀⠀⠈⠀⠁⠀⠙⠚⢻⣿⣿⣿⣿⣿⣿⡟⠋⠋⠁⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠿⠻⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣽⡿⠁⠀⠀⠀⠠⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣮⣵⣦⣤⣮⣴⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⡀⠀⠀⠀⠀⠀⠀⢙⡏⠛⠉⠉⠉⠉⠉⡉⢙⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠋⠉⠉⠳⣤⠤⣄⠀⠀⠘⠛⢳⡀⠀⠀⠀⠀⣰⠏⠉⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠇⠀⠀⠀⠀⠀⠀⢨⡧⢤⣠⣤⣤⠟⠀⠀⠀⠀⠳⠤⣤⣤⣤⡼⠣⣄⣠⠤⠼⠳⡄
⠀⠀⠀⠀⠀⠀⢠⣠⠖⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠛⢦⣠⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⠀⠀⠈⠀⠀⣷⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠙⠒⠋⢧⣀⡼⠳⣀⣀⣀⡴⠺⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⣦⠤⢤⡀⣀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤⣀⡏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠳⣄⣠⠿⣄⠀⠀⢀⡴⠻⣄⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⣄⠀⠀⣆⠀⠀⠀⠈⢠⠀⢀⠆⠘⠁⠀⠀⠀⠋⠑⠄⢀⡀
⠀⠀⠀⠀⠢⠤⠴⠶⣤⣤⠴⠶⠤⠔⠋⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠑⠒⠒⠒⠒⠒⠂⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠀⠐⠁⠀⠀⠀⠃⠠⢄⠀⠀⠀⠀⠀⠀⢀⠤⠐⠁⠀⠈⠁⠂⣀⡄
⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠓⠂⠠⠒⠠⠄⠊⠉⠁
⠀⠀⠀⠀⠈⠀⠐⠒⠲⠦⠤⠤⠤⠖⠒⠒⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⠤⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⠉⠉⠉⠀⠀⠀⠀⠛⠢⡀
⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠳⠤⡤⢤⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱
⠀⠀⠀⠈⠁⠐⢄⣀⠀⣀⡠⢀⠴⠂⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠢⢄⣠⠔⠒⠲⠤⣤⠜⠉⠋⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠊⠉⢉⡩⠟⠒⠲⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠙⡄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠱⣄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠓⠒⣤⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡰⠋⠀⠈⠳⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣠⠏⠉⠉⡗⠒⠤⢄⡀⠀⡇⢀⣀⣀⣀⣀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡠⠞⢹⠀⠀⢠⠃⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⢀⠆
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⡘⠓⢂⢾⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠎
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠭⢍⠥⡊⠀⡠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢇⠀⠀⠙⠓⠊⠑⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠣⣄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡠⡄⠉⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⢲⢄⣀⠀⠀⠺⠊⠀⠰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡠⠔⠊⠉⢻⣿⠟⠉⢳⣶⣖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡤⠴⠃⠀⠀⢠⠿⠟⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣸⠀⠀⠀⠀⠀⠈⡆⠀⠀⠣⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣠⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⣿⠟⢟⠉⠉⠹⠌⢿⣿⣦
⠀⠀⠀⠀⢀⣾⣿⣷⡦⠊⣿⡆⠀⡆⣀⣴⠀⡼⣿⣿⡇
⠀⠀⠀⠀⣸⣿⡿⣿⢧⠀⠛⠃⠀⠘⠋⠋⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣿⠈⠻⢮⡲⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠎⣭⣟⢻⣤
⠀⠀⠀⢸⣿⡆⠐⠤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⡷⢣⣴⡲⢸⣽⣸⡿
⠀⠀⠀⠀⣿⣿⣄⣠⣶⡆⠀⠀⡠⠚⠉⣅⠀⣄⠸⡋⠁⠀⣄⠀⠀⠀⠀⠀⠀⢠⣟⠂⠀⠂⣼⣎⣿⡇⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠸⣿⣦⣭⡭⠥⠀⠀⠀⠰⠛⠇⠀⠀⠀⠀⢠⠀⢸⡆⠀⠀⠀⠀⡤⠒⡩⡠⠈⡁⣿⣿⣿⡥⠖⠊⠛⣉⢱⡇
⠀⠀⠀⠀⠀⢹⣿⣿⠿⡿⠷⠀⠀⠀⠀⠀⠀⢠⠀⠈⣠⣤⠸⡇⠀⠀⢀⡜⢁⡞⢈⠤⡤⠒⢊⠁⠀⠤⢀⠉⠀⣳⠜⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣧⣹⠓⠀⠀⠀⠀⠀⠐⠣⣖⣩⣤⣯⢐⠇⠀⠀⡎⠀⢰⡿⠀⠈⢰⣂⠁⢆⣾⠨⠈⠀⢂⣡⣜⡤
⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣶⠊⢢⡀⠀⠀⠀⠀⠀⠉⠉⠁⢸⡆⠀⠀⡇⠀⣼⠿⠓⡧⠐⠛⠄⣸⠀⡄⠔⠻⡉⠁
⠀⠀⠀⣀⣴⣶⣿⡋⢿⡍⠙⢷⣦⠙⠒⠤⠤⣤⣄⣤⠤⠤⠚⠀⠀⠸⡇⠐⢯⠷⠿⣏⠂⠬⢑⣿⠀⢢⠇⢰⡇
⠀⠀⣼⡿⣿⣿⡿⠟⢠⣾⢿⣷⣿⠇⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢰⠃⠀⠠⣠⠔⠁⠀⠐⢫⠏⠀⠎⠀⣾⡇
⠀⠀⠹⣇⣿⣿⡞⢶⣾⣷⣾⡟⠃⢀⣀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡾⢦⣀⣀⠇⠀⠀⠀⠀⣸⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠈⣿⣿⣿⣩⣿⣽⠿⠵⢤⣄⠈⠉⠲⢼⡇⠀⠀⠀⠀⠀⣼⠁⠀⠈⢸⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠘⠻⢿⣿⢿⠁⠀⠀⢀⡴⠋⢙⣶⣦⣥⣄⡀⠀⠀⠐⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡇⠀⠀⢜
⠀⠀⠀⠀⠀⣰⣿⡷⡠⠂⢀⣼⡏⠐⢾⢛⣿⣆⠌⢹⣿⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢿⡟⣁⠈⢀⣾⠏⣼⣦⣬⣀⢿⣿⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡏⠙⢻⠏⢼⠀⣊⣻⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠛⡫⠽⠛⠙⠋