Ecosystem Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠸⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⡆⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢼⣿⣿⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠻⡎⢃⠀⡇⠀⣰⢿⡇⠀⠀⠠⠖⢴⡇⣷⠔⠦⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡃⢀⡅⠛⠁⠀⢰⣿⢳⡿⡇⣾⡧⢻⣷⠀⠀⣤⣄⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠀⠀⠀⠀⢰⣶⢰⣶⡆⣶⡦⣰⣶⠀⠀⢹⢏⣴⣾⣿⣷⣮⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣅⢭⡅⣭⢅⡭⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣛⣿⣿⡆⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢭⣟⣛⠿⠿⠿⣛⣫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣄⡀⠀⠀⠀⠉⠛⠃⠉⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⢰⣄⠀⠀⠀⠂⢸⣿⡿⣃⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢶⢂⡀⠀⠀⠸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣾⣿⡆
⢰⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟
⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⢴⢤⣶⣶⣁⡅⡠⠤⠀⠉⠛⠙⢿⠋
⣿⣿⣿⣿⣏⣀⣀⣰⣶⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⢿⠇⠛⠛⠉⠁⠀⠉⠀⣀⣉⣁⣀⣀⠀⠀⠀⠀⠀⢸⡆
⠿⣿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣆⣠⣠⣄⣀⡀⠀⠀⠀⠤⠤⠄⠀⠀⠉⠉⠀⣀⣀⣀⣀⡀⠀⣠⣤⣤⣿⣷⣶
⠀⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠛⠛⠛
⢸⡟⡴⢁⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⣰⣖⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣾⣟⡔⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠿⠿⠿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠋⠉⠀⡁
⣿⣿⠟⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡶⠖⢒⡠⡖⠁⠀⠀⠀⠀⠀⠀⠄⠦⠤⠴⠄
⣿⣿⠃⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠛⠋⠀⠀⠿⠿⢿⣿⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠖⣚⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿
⠶⠒⠒⠒⠶⠶⠶⠿⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣃⣶⣤⣤⣤⣾⣦⣤⣶⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡞⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠙⠀⠀⠀⠘⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⣠⠶⣄⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠐⠀⠐⠀⠀⠀⠀⣴⠃⠀⠙⣆⣈⣁⡀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠹⣆⠀⠀⠀⠉⢀⠘⢀⠘⠀⠈⠀⠀⠀⠀⠐⣇⠀⣴⠆⣸⠁⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡄⢸⠀⠀⠁⢀⠈⢠⠈⢠⠈⠀⠀⠀⠀⠀⠀⠙⠲⠶⢾⡃⠀⠀⢀⡟⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⣄⡀⠙⢾⡷⠋⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠉⠓⠚⠋⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣄⢻⡄⢸⡇⠀⣴⠞⠋⣷⠀⠀⢀⡤⢶⡿⢻⡟⢿⡶⣤⡀⠀⠁⠀⠀⢸⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠼⢿⡁⢸⡇⢸⣃⡶⢀⡿⠀⣠⠟⠶⡾⠤⢼⡧⠬⣷⠾⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠇⢠⠟⠓⠋⠀⢀⡏⠀⢸⡇⠀⢸⠃⠀⢸⡄⠀⣻⠀⢸⠋⠓⢦⣀⣀⣀⣀⣤⠖⠋⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⣹⣷⣋⣀⣀⣀⠀⠐⡏⠉⢹⡏⠉⢹⡏⠉⢹⠏⠉⣹⠀⠸⡇⣠⠞⠉⠀⠀⠈⠙⢦⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡤⣷⠴⢾⡷⠦⣾⢤⣤⠏⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠲⠶⠖⠶⣄⠀⠀⠙⠳⣼⣦⣸⣇⣼⣥⠞⠁⠀⠠⣾⣁⡀⠀⠄⠀⠀⠀⠄⠀⢀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠛⠉⠀⠈⣉⣀⣉⣠⡟⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⢯⡉⠛⠲⡶⠶⡶⠚⠋⣉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡴⠒⠲⢦⡀⠀⠀⠀⠙⠓⠒⠛⠛⠓⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡚⢻⡟⠶⡄⠀⠀⠀⠤⡟⠀⠁⢀⣨⡧⠤⠴⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣠⡿⠛⢷⠖⢻⡀⠀⠀⠀⣷⠀⠀⠈⠁⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢧⡞⠉⣻⠀⠀⠘⠃⠀⠀⠀⠀⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠓⡶⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣠⡬⣤⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⣡⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡄⢀⡤⠤⠞⠁⠀⠀⠀⠀⠘⣆⡒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⡠⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡌⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰⠃⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢤
⠀⠀⠀⠀⠀⠀⠼⠀⠀⣀⣀⠀⢀⣀⠀⠀⠐⠦⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⣄
⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠈⠛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣸⠁⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢠⢀⡠⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢳⡀⣿⠀⡀⣴⠀⠀⢿
⠀⠀⠀⢀⡤⠖⠋⢀⣠⡭⠃⠀⠀⠋⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠸⣥⠇⠀⠙⣿⠀⠀⠸⡄
⠀⠀⢀⡏⠀⠂⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣏⢀⡏⠀⠀⠀⣿⠀⠀⠀⠹⡀
⠀⠀⠘⠦⠤⡄⠀⠀⠈⠉⠉⠉⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⣿⢸⡇⠀⠀⠀⣿⠀⡰⠂⢀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⣠⠖⠓⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⣿⠀⢳⡀⠀⠀⣿⠞⠀⢀⡼
⠀⠀⠀⠀⠀⢻⠀⡀⢧⠀⠀⠀⠀⢀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣿⠉⠉⠙⠦⠄⣿⢠⠴⠋
⠀⠀⠀⠀⣤⠞⣠⠇⢨⡿⠶⠀⣴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠵⠶⠖⠒⠲⠆⣿⠠⣄⡀
⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠉⠒⠀⢤⠀⣀⡀⠀⠀⢀⡀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⠁⠀⠉⠛⠒⠒⠶⠶⠶⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠆⠀⠀⢠⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⣤⣶⣶⣾⣿⡗⠒⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⢀⠀⠁⠀⣀⣠⣶⣿⣿⣿⣷⢴⠟⢋⣻⣷⣄⠀⠀⠈⠹⣦⣀⢀⠀⠀⠂⠀⢿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠜⠛⠛⠻⡝⠋⠀⠞⠛⠿⠟⠁⠐⠀⠀⡈⣿⣿⣿⡖⠀⠀⠂⠈⠉⠁
⠀⠀⠀⠁⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣴⣶⣄⣼⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣇⣟⣋⣽⣿⣿⣿⣿⣿⣿⣿⡀
⠀⢀⠀⠠⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣤⡄⠕⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠂
⠀⣠⡆⢀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣤⣬⣿⣿⢿⣿⣿⣿⡟⠉⠀⠀⠁
⠈⠉⠀⠀⠀⠒⠀⢻⣿⡟⠁⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠎⠹⣟⠇⠀⠀⠈⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣘⡋⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⠈⠀⣀
⠀⠀⠀⠀⠰⠄⠐⠀⠀⠘⠷⢄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁⠀⠀⢀⢴⠧⠀⠀⢀⠀⢠⣶⠄
⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⠁⠢⢄⡀⠀⠘⠿⠿⠿⠛⠉⠀⠈⠀⠀⠁⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠃⢀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⢠
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⡠⠐⠊
⠀⠀⠀⠀⠀⠠⠂⠀⠀⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠒⠄⠀⠀⠀⠀⢀⠄⠀⠂⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠂⠀⣀⣀⣠⠴⣊⠴⢤⠍⠀⠂⠀⠀⠀⠀⠀⠀⠈⠡⢄⠀⣠⠄⢀⠀⢈⠱⠄⠈⡠⠱⠈
⢀⠴⠤⣞⢄⣀⣠⣴⣿⣋⢈⠩⠀⢰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔
⡘⢐⠈⠡⣉⠁⠀⣀⠈⠿⡀⠤⠤⠘⠀⠀⠀⠀⣠⡴⠷⠶⠚⠁⠀⠁⠀⠀⠀⠀⠀⠊⠠⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠠⠀⠠
⠀⠃⠀⠀⠀⠁⠀⠀⠐⡄⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠰⣤⣤⣤⣤⣤⣤⣤⣼⣷⣦⡀⢰
⠀⣀⡀⢀⢀⠀⠠⡀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠩⠍⠉⠉⠉⠙⠉⠛⡛⢿⣇
⠒⣏⣋⠘⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠃⠀⠀⠀⠰⠀⠀⠀⢰⡂⢨
⣠⢈⠃⠀⢰⠀⣠⣤⣶⣾⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⢀⠀⠀⢀⠀⠘⢡⢸
⠈⠸⠆⢠⠾⠿⠿⠿⡿⣿⣿⣿⣿⣷⣷⣮⣤⠤⠂⠄⠈⢀⡀⠀⠀⢈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢎⠀⠀⠀⠀⠑⠄⠀⣠⡀⠃⡾
⠀⠘⣠⣤⡌⠀⡀⠀⠀⠀⠀⠁⢤⡀⠥⠀⠐⡰⠂⠀⠉⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠸⢧⢙⠐
⡀⠀⣣⣬⠇⣤⠀⢠⠂⡠⠄⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⡀⠄⠀⠀⠀⠀⠀⠸⠼⠀⠠⠀⠀⡠⠀⠀⠃⠇⠘⡏
⣧⠆⡼⣄⣄⠘⢣⢠⠴⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠈⠀⠁⠀⠀⠰⠈⠀⠢⠠⣴⠠⠆⢸
⣿⢸⡱⠉⡸⢀⡟⡴⢀⠆⠀⠀⠀⠽⡾⢦⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡖⢘⡇
⣿⡌⠀⡀⠐⣸⣇⣘⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠄⣀
⠟⡟⠘⠀⡀⠁⠀⢀⣰⠠⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣀⠻⢦⠀⣀⡤⠤⠼⠀⠄⢼⣉
⠀⣱⡞⣀⠅⠀⡀⠀⢁⣀⣈⡄⠀⠀⠀⣀⡘⢤⣤⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠉⠨⢙⣃⠤⡀⠀⠀⠀⠀⠋⠞
⠀⠈⡄⢟⠒⠉⣘⣶⠂⠉⠴⡦⠧⠀⠈⠁⠀⠑⠠⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠐⣽⣒⡆⡀⠨⠥⠙⠣⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠽⡧⢀⠣⣶⡖⠂⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠛⠃⠛⠉⠃⠃⠀⠃⠘⠘⠟⠙⠰⠋⠃⠃⠛⠙⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠂⠑⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆
⠀⠒⠀⠀⠂⠀⠀⠐⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄
⠀⠃⠀⢀⡤⢃⠀⠤⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⢤⡄⡀
⠀⢀⣎⣌⡁⠋⣃⡈⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⣀⣄⢩⣄⠀⠠⡄⠀⢒⣑⡿
⠀⡀⠈⣧⢘⢷⣟⣶⢤⡤⠶⠤⠤⠀⠀⠰⣫⣍⣟⢲⡄⠀⠐⠒⠂⠐⠀⠀⠀⠀⣈⣉⣉⣁⠀⠀⠀⠀⠚⠻⢿⣻⣻⣻⣋⡄⠈⠁⠂⢶⡆
⠀⡇⠐⠒⣿⡆⠓⠈⠃⠀⠀⠀⠀⠀⠀⠀⡟⡏⢹⡖⢷⡄⠀⢀⠀⠀⢀⠀⢰⠫⣑⣠⣶⣮⠆⠀⠀⠀⠀⣀⡞⣙⡇⣀⣹⢻⠰⠂⠀⣸⡇
⠀⠓⠂⢀⣿⣇⡀⠀⠀⣀⣀⡀⢉⣀⣢⣈⣁⣉⣈⣁⡈⠩⠤⠬⠴⠤⢌⠀⣿⣿⡏⠀⠈⢿⢂⠀⣀⠘⠛⠉⠀⠉⢀⠀⠉⠁⠀⠀⠔⠚⠁
⠀⠀⠛⠀⠀⠀⠀⠀⠄⠁⠁⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⢘⡿⠧⠄⠀⠿⠉⣀⠀⠀⠀⠊⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢠⡀⣀⡀⡀⠐⣿⣷⡆⡆⠀⠁⠀⠤⠔⠀⠀⠀⢠⣄⣸⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣟⣶⡿⢟⠗⠄⠀⠀⠀⠀⠀⢠⣀⡠⠎⠉⠉⠀⠀⠀⠀⢀⠄⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠢⡙⠂⢀⣠⣤⣄⢀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⢠⣿⣋⡟⢻⡘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠿⠅⠒⠈⡁⠌⠀⠀⠀⠀⠀⠀⠀⠄⡂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠈⠀⠀⠀⠀⠀⠐⣾⠀⠀⠁⠆⡀⠀⠀⠀⠀⠀⠀⠢⠄⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠈⠑⠒⠈⠀⡇⠀⡀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠀⠀⠀⠈⠀⠀⠀⠃⠀⠂⠄⠀⠀⠇⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠀⣠⠀⠀⡂⠀⠀⠀⠀⠀⠈⠠⠀⢠⣼⣭⠀⠀⠀⠉⠀⠈⠀⠀⠐⠂⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠊⢠⣀⡀⢘⠀⡄⡄⡔⢄⣌⡀⠀⡿⠓⠎⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢡⠦⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠊⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠠⠠⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠙⠀⢒⡉⠁⠀⠀⠀⠀⣀⠈⣠⣠⣰⣶⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠠⠌⠀⢂⣈⣤⣤⣶⡾⣬⣈⣄⡛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠀⠀⠀⠐⠊⠉⠓⠒⠲⠤⠤⠿⠿⠟⠛⠓⠛⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠑⠄⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣤⣤⡄⣀⣂⣤⣶⣵⠿⠯⣭⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⡿⠻⢿⢯⠕⢶⠶⠆⢠⡘⠷⢶⣤⣤⡉⠈⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣶⢿⣻⣿⣿⣶⣦
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⢿⣿⣿⡲⠤⠤⡀⠑⠒⠛⠉⠀⠀⠀⠀⢹⣄⠀⣀⣔⢙⣷⣤⣀⣤⣤⣀⣤⣤⣝⡿⣟⡙⣿⣿⣟⠉⡀⡀
⠀⠀⠀⠀⠐⣿⣿⣿⣽⣿⣿⣷⡿⠟⠙⠛⠒⠉⠙⣛⣋⣁⠂⢂⣠⣰⣶⣾⣿⣿⡿⠿⠿⠟⣛⣋⣹⠏⣩⡍⠛⠾⣿⣿⣿⣿⣿⣷⠾⠅
⠀⠀⠀⠀⠀⠳⠾⢝⣿⣯⣯⣶⣝⣻⣤⡤⠖⣚⣯⣭⠤⠒⠀⠐⠒⠂⠀⠀⣀⣤⣤⣤⡴⠟⠙⠁⠀⢀⣤⣤⣤⢿⣿⣷⣿⣿⣿⣟⠂
⠀⠀⠀⠀⢠⣐⠒⠾⠿⠟⠉⠉⠞⠭⠓⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⢀⡚⠛⠭⠤⠁⢈⠻⣟⣻⡿⢿⡶⠆
⠀⠀⠀⢀⣈⣉⣹⣩⣤⣴⣾⣴⣤⣤⣼⡿⠭⠷⠦⠴⠲⠺⣿⣯⠓⠐⢘⢦⠤⠤⡀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⢀⣹⣺⠛⠁⡸
⠀⠀⠀⠈⠋⠻⠟⣿⣉⣿⡿⢭⠹⣏⣩⡄⠀⠀⠈⠉⠀⠈⠉⡏⠿⢻⠩⠁⡈⠁⠠⠀⠀⠀⠠⠄⠠⡥⠀⠀⠀⢂⣤⠉⢲⡾⠄⢀⠠
⠀⠀⠀⠀⠠⠤⠿⣇⠀⠹⣭⣼⡿⣿⣿⡇⣼⠄⠀⠀⡀⠀⠀⠐⣤⠏⠀⠀⡀⠀⠀⠀⠀⣄⡴⣬⣷⣦⣤⠀⠙⠂⠀⢺⣐⣿⠂
⠀⠀⠀⠀⠠⠤⣄⣀⠀⢩⡹⣿⣟⣻⣿⡅⠇⠈⡇⡠⢷⣶⣧⢸⣏⣀⠀⠀⢀⣀⡀⢠⣮⢛⣩⣡⣤⣯⣼⡷⣴⠁⢀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠁⠩⢦⣀⠊⣿⡟⡿⢿⢋⣯⠀⣥⡙⢮⣁⡩⡻⠹⣿⣶⣿⠺⠤⡔⣿⣼⣿⡿⣿⣿⣿⣿⣳⣬⣿⣧⢈⣉⣩⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠻⠀⠃⠊⠙⠘⠻⠯⢫⡿⠠⠿⠂⠟⠰⠀⠐⠛⠦⠀⠀⢸⣟⣻⣈⣿⣯⣭⣹⣟⣿⣿⣗⣫⣟⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⢀⣠⣴⠾⠧⢀⡀⡀⢀⠀⠀⠀⠈⠐⠂⠀⣀⡆⠀⡀⠀⣀⢸⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠏⠙⠇⢠⣴⠃
⠘⠛⠁⠀⠀⠈⠙⡷⠤⢂⠄⢀⣆⣶⣅⠀⠉⠱⠴⠶⠒⢡⣾⣶⣮⡌⠀⠀⠀⠀⠀⣒⡦⢀⠀⠘⠶⠒⣒⡤⠀⢀⠴⠃⠀⠀⠀⠀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠙⠁⠈⠲⠀⢀⣠⢀⡶⠃⠀⠀⠉⠁⣲⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⢤⡀⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠉⠚⠋⠉⢀⣠⣤⠆⠀⠈⠀⠀⠐⠋⠁⠐⠀⠒⠒⠰⠞⠉⠀⠀⠀⠀⠈⠘⠛⠚⡅⠘⠧⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⣀⡀⠂⠀⠀⠿⠏⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⠀⠈⠀⠀⠠⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣤⡉⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠉⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠠⣤⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠩⣀⠀⠐⠒⠀⡀⡀⠖⠢⠀⡩⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠂⠁⠀⠀⣘⠁⣉⢡⠀⡄⠈⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠁⠀⠀⠀⠀⠈⠂⠐⡈⠉⣤⡀⠁⠀⠀⠀⠧⠠⠄⠀⠂⠉⠠⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣬⠀⣀⡀⠀⠀⠀⠀⠐⡁⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠎⢘⠏⠐⠀⠈⠉⠢⠄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⢠⣥⣼⠀⠀⢀⣀⡀⠤⡄
⠀⠀⠀⠀⠀⠈⠉⠑⠂⠠⢄⣽⡀⠘⠿⢦⡢⠀⠤⠊⠀⢀⠀⠀⠄⡀⠀⠀⡀⠀⢀⠀⡠⠁⢐⡤⠔⠓⠋⠉⠉⠁⠀⢀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠁⠒⠤⣙⢦⠀⢲⡦⠨⠊⢔⠠⢂⠅⠪⡂⢀⠔⣨⣄⠔⠉⢠⠀⠀⠀⠀⠀⠀⡠⠁⠄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠉⠲⣆⠔⠨⢂⠄⠈⡂⢐⣀⠀⡴⢺⠔⠁⠀⢀⠂⠢⡀⠀⠀⢀⠄⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠑⠑⢄⠀⠀⠀⠀⠀⠀⠀⠑⢮⠂⢑⠠⠂⠁⠗⠨⡴⠁⠀⠀⠀⡇⠀⢰⠈⠀⡰⠁⠈⠀⠀⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⢀⠀⠂⠑⠄⠀⠀⠀⠀⠀⠀⠀⠑⣄⠊⠊⡐⢵⠊⠐⠀⢱⠀⠀⠀⢤⢠⡾⠊⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠂⠤⠬⠁⠀⠢⡀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡸⠁⠀⠐⢤⠏⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠠⠤⠀⠀⠚⠢⢄⠀⠀⠀⠀⠀⢸⡷⠁⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⢀⠀⢀⣠⠖⠋⠀⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡉⢀⣢⠤⠤⠭⣷⣦⡀⠐⡀⠀⡃⠀⠄⢀⣠⣐⣥⣄⡀⠀⡀⢀⣨⡼⠋⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠚⠋⠁⠠⡀⠐⠛⠶⠒⠛⠁⠀⠀⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡤⠀⠀⢀⣠⠔⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⠤⠤⠤⠤⠤⠤⠚⠉⠀⠄⠜⢋⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠉⠁⠀⠀⠐⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠐⠀⠀⠈⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠤⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⡈⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠋⠁⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠔⠁⠈⠈⠓⡄⠀⢸⠀⠀⠀⠰⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⢀⡤⠖⠊⢉⠉⠉⠉⠑⠲⢄⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠐⠈⠁⠉⢲⠀⢸⠀⢰⠀⠀⠀⠀⠀⡇⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠱⡀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠂⡜⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠈⠉⠛⠒⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢡⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⢀⠈⠀⠀⠀⠓⠀⠒⠊⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠐⠂⣀⢀⠀⠁⠐⠀⠈⠀⠀⠊
⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡎⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠀⠘⠃⡈⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠈⠉⠉⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡈⡸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠈⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠄⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠸⠁⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣄⣀⣀⣀⣀⣠⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠞⠛⠋⠉⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠤⣀⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢉⠉⠉⠉⢉⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠄⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠌⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠐⠆⡠⠄⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠄⠀⠀⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⠋⡀⠀⠁⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠁⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠠⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠠⠀⠀⢠⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠰⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠙⠳⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠐⠁⠀⡐⠂⠐⠂⠀⠑⠒⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠤⠀⠀⠀⠼⢤⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠂⢤⣀⣀⡁⠀⠀⢧⠀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠂⠠⡂⠀⠀⠀⣠⠄⠀⠀⠠⠀⠀⠀⠀⠐⢄⠀⠀⠀⠁⡦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⡎⠀⢀⡀⠀⠀⠐⠀⠀⢀⡀⠀⢐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⡈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⣖⠒⠒⣲⠶⠦⢄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⡽⠻⣅⠀⠀⠀⠈⠓⢤⡀
⣿⣿⣿⣿⡿⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⢤⡀⠀⣠⠞⠁⠀⠀⠈⠳⣄⠀⢀⡠⠖⠛⣄
⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢈⠿⢅⠀⠀⠀⠀⠀⠀⣨⠷⣏⠀⠀⠀⠈⢆
⣿⣿⣿⣿⣅⣉⣉⣉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡰⠋⠀⠀⠙⢦⡀⠀⣠⠞⠁⠀⠈⢦⡀⠀⠀⢘⡆
⣿⣿⣿⣿⠟⣩⣭⡙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠢⣄⡞⠁⠀⠀⠀⠀⠀⣹⣞⠁⠀⠀⠀⠀⠀⠳⣄⡴⠋⡇
⣿⣿⣿⣿⠸⣿⣿⡇⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡞⠳⣄⠀⠀⠀⠀⡴⠁⠈⢳⡀⠀⠀⠀⢀⠔⠻⡄⠀⡇
⣿⣿⣿⣿⣷⣤⣥⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡞⠀⠀⠈⢣⡀⢀⠞⠀⠀⠀⠀⠹⡄⢀⡴⠋⠀⠀⠹⣴⠇
⣿⣿⣿⣿⢡⣾⣿⣎⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢹⣏⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⢠⠏
⣿⣿⣿⣿⣌⠻⠟⣃⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡞⠈⢧⠀⠀⠀⠀⣰⠃⠹⡄⠀⠀⡠⠋
⣿⣿⡟⢿⠟⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠽⠦⠼⠤⠤⠬⠧⠤⠤⠴⠧⠤⠤⠷⠴⠮⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠰⠶⡀⠀⠀⠓⡶⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠢⠀⠈⠀⠀⠀⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡇⠀⠀⠀⠀⠐⠒⠓⠒⠀⠐⠀⠀⠀⠀⠀⠀⣠⠀⠀⠔⠒⢒⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⢠⠀⠀⢀⠀⠀⠀⠀⣠⣄⣴⢰⣄⢤⡀⠀⠀⠘⢵⢟⣴⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⡀⢸⠀⡼⣿⠇⠀⠀⣴⣶⣠⣭⢨⣭⡤⣶⡄⠀⠀⢰⣿⡻⠿⠿⠿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⢠⠂⠁⠀⠀⠀⣭⣍⣭⣭⢨⣭⡅⣭⡅⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠐⠛⠓⠒⠒⠂⠀⠀⠻⢟⢙⣛⢘⣛⢓⡿⠃⠀⠀⢸⣿⣣⣭⣭⣥⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠈⠃⠛⠘⠃⠋⠁⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢿⡟⣼⠋⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⣠⣰⣿⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠁⠀⠀⠀⣰⣿⣿⣷⢀⣾⣄⠀⠀⢻⣿⡏⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠉⠀⠈⠁

⠀⠀⠀⠠⠀⠈⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣸⡄⠀⠈
⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠸⢷⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄
⠀⠀⠐⠃⠁⠀⠀⠘⣀⠀⠀⠀⠠⣦⠉⠀⠃⠀⠀⣤⠀⠀⠈⠀⠀⢀⣀⠈⠑⠠⠔⠠⠄
⠀⠀⠀⠄⠉⣠⡀⠠⠀⠀⠀⠀⠃⣦⠀⠀⡐⠀⠀⡈⠀⠉⠀⠀⠀⠀⠁⠀⢤⠄⠠⠘⣤⣶⠠⡀
⠀⠀⠀⠀⠘⣉⣤⢀⣠⣤⢠⣶⡄⣻⣿⣼⢠⣴⣀⣦⣀⣄⣠⣬⣶⢀⣿⣶⣤⣦⣤⠀⣉⣿⣆⣤⡄
⠀⠀⠈⠉⠙⠋⠈⠙⠛⠋⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠋⠘⠋⠛⠉⠉⠙⠙⠋⠙⠙⠚⠉⠙⠙⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡠⠀⣀⠀⢤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣂⣠⣾⣤⡶⠀⠀⠀⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠸⠟⠃⠘⣿⠘⠋⠁⠀⠈⣷⢦⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠰⡋⢰⠆⠈⡇⠸⣷⠛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⣾⣀⣾⣦⠀⣀⡀⢈⣘⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢶⣾⣿⣒⣶⣶⣾⣟⣿⠛⣿⣿⡦⠋⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣻⣿⡛⠁⢃⣼⣶⣿⣿⠿⣿⢻⣿⣿⣿⣶⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠹⣿⣿⣷⣿⡏⣽⣼⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⣥⣽⣟⣀⣉⣰⣿⡿⣯⣿⣶⣟⣹⣿⣿⣿⣟⣿⢾⣟⢸⣿⠋⣉⢻⣿⣿⣾⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⣛⣿⣿⣿⣈⢿⣽⣿⣡⡹⠟⣤⣴⢿⣝⣿⡿⠟⣹⣿⣿⣿⣧⡭⢀⣩⣸⣿⡿⠻⢿⣿⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣃⣿⣽⣭⢿⡿⣿⡟⣿⣯⠇⣴⣟⣡⣿⣿⡏⢵⣼⣿⣿⣻⣿⢿⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡈⠱⠏⣿⣿⣿⢿⣿⠀⠛⢻⣿⣽⢿⣿⣤⣿⠌⣼⢿⡉⢠⠘⣿⣽⣿⣿⣿⣿⣯⣽⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣿⣧⡩⢶⣾⡿⢿⣿⣿⣧⣀⣴⡷⣿⣿⣼⡿⢿⣿⣶⣿⣿⣧⣤⣒⠿⣏⣼⣿⣿⡿⣿⣯⠋⢹⡟⣢
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣯⣿⣿⠽⣿⢾⣿⡝⢻⣿⣷⣼⣟⣿⣷⣿⣿⢻⣷⣾⠟⣯⣿⣿⢻⣿⣿⠖⠂⠂⣿⣿⣿⣿⣿⣉⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢋⡷⠙⢿⣤⣝⣾⣯⣿⡏⠿⠋⠹⣾⣻⣿⢻⡿⠿⣥⡿⢿⣿⣿⣿⣿⣿⣿⡿⠠⠺⣷⣿⠟⠻⣟⢟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣶⣷⢳⡖⢲⣽⣿⣿⣿⣹⣦⣬⣴⣬⣿⣿⣿⣷⣾⠿⠟⣿⣿⡿⠿⢿⣿⠿⣣⣤⣼⣿⣿⣦⡶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣏⣼⣿⣿⣤⣽⣻⣷⣿⣻⣿⣿⣶⣿⣅⣶⣿⣟⢻⣠⣿⡀⢊⣹⣿⣷⣧⣾⢟⣶⣿⣿⣿⣿⣿⣿⡗⢙⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⣧⣷⣾⣿⣿⣿⣿⠁⡌⣿⣿⡿⣿⡿⣬⣿⣿⣾⣿⣿⣻⣿⣿⢿⣇⣿⣿⣿⣯⣽⣿⣷⣿⣦⣀⣽⣿⣿⣿
⠀⠀⠀⠀⢠⡴⠿⠃⠀⢀⣴⣏⢻⣿⣁⣿⣿⣿⣦⣴⣾⣿⣿⣿⢶⣮⣻⣿⣿⣿⣬⣿⣹⣯⣾⣿⣿⣿⢛⣹⣿⡿⠛⢿⣿⣿⣿⣿⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡼⠛⢀⣼⣟⢳⣿⣿⣿⣯⣿⣿⣯⣿⣿⣩⡌⣿⣫⣱⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⡄⡀⣸⣿⠙⢿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⣰⡏⠶⣦⣤⣾⠻⣠⠏⢰⡿⠈⢻⡟⢠⡿⠷⠏⢙⣿⣿⣷⣿⣿⣿⡹⢿⣿⠿⣽⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⠏
⠀⠀⠀⠀⣀⡀⠀⠈⠱⢆⣠⣤⡿⠖⠛⠀⣾⠇⢸⣿⠃⢸⡗⠶⠀⣻⠇⢸⡟⢦⣿⣿⡷⢾⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣻⡿⠁
⠀⠀⠀⠈⠉⠡⢦⣠⡀⣦⢀⣄⠀⣄⠀⠀⣽⡗⠋⡽⠻⡟⠻⠀⣿⠇⠀⢸⡏⠈⣁⡉⠈⡿⠉⢳⣬⣷⡾⡏⠸⠋⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣉⠿⠻⡿⠟⠉⠹⠶⠀⠘⢋⣄⡁⠀⣟⣰⡟⠁⢀⡀⢸⡟⠀⡹⣇⣠⣿⠛⣶⠃⢹⡄⢉⣼⠇⠀⠙⠛⢄
⠀⠀⠀⠀⠀⢀⠆⠀⣤⠊⠀⠀⠀⠀⠸⢇⠙⡈⠛⠛⠛⠛⠁⣀⣶⣶⣄⡀⢿⣇⡀⠋⣹⣡⡷⠉⠀⠈⢷⣬⡘
⠀⠀⠀⠀⠰⠆⢀⡜⠀⠀⠀⠀⠀⠀⠀⠙⠃⣠⣴⣧⡄⠿⠆⠙⣡⠜⠻⣏⠀⠉⠻⠷⠟⠋⣀⡰⠶⠀⢀⠙⠃
⠀⠀⠀⠀⡿⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡈⣁⣀⠦⠄⢩⠀⠀⢿⣍⡡⠀⣀⣰⣶⠿⡇⠀⠙⣴⢆⡀
⠀⠀⠀⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠈⠅⠀⠀⡾⠀⠀⢨⠿⣀⠿⠋⢻⠀⢀⡷⠀⠈⠷⣏⠘⠂
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⠲⡾⠋⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⠀⢀⠀⠚⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⣀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠠⠀⠰⠄⠀⠀⢈⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⢀⠔⠚⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠳⡄⢹⣄⢀⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠣⠈⠁⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢀

⠀⢠⣴⠶⢶⣶⡿⠿⣶⣤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⠁⣼⡤⣏⠰⠶⣿⠰⠶⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⢔⢐⣴⡆⡄⣀⠴⢄⢤⠢⣖⠂⠀⢈⠄⠀⠀⠀⠀⠀⡄⠃⢀
⠀⠙⠷⠤⠴⠻⢷⣾⡿⠿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⣀⣀⣀⡀⢀⡀⢀⣠⠜⠀⠀⡠⠊⡀⢸⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠗⠁⠀⠀⠀⠐⠁⠀⠡⠞⢩⠙⠂⠤⣈⠂
⠀⠀⢀⡶⠀⠀⠀⠀⠀⠲⡔⢒⡊⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠛⠖⠚⠀⠀⠀⠥
⠀⡰⠁⡇⠑⡀⠀⠀⠎⡔⠉⠀⠀⠀⢢⡀⠄⠀⠀⠀⠀⠳⣴⣫⠗⣠⠞⠆⢠⠎⠙⣧⢀⣡⢀⡞⠀⠀⠀⢘⡿⡅⠈⠀⠀⠐⢄⠀⢰⠀⠀⠀⡠⠂
⠀⣇⠀⡇⠀⡱⠈⢰⠰⡀⠁⠀⠀⠈⠀⠇⡀⠒⠀⠀⠀⠀⠻⠤⠴⠻⣤⡤⠛⣦⡤⠎⠀⠈⠉⠀⠐⠀⢀
⠀⠈⠒⡇⠀⠀⠀⠄⢀⠱⣀⠠⠤⠊⠠⠁⢋⡀⠀⠀⡀⠀⠠⢄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠘⢘⠀⢢⢤⣀⠖⠃⠀⠀⠀⢸⠀⠒⠒⠃⢠⠁⣠⣈⡧⢀⠄⢀⡉⢢⡀⠀⢠⠁⠀⠒⠤⢠⡤⠴⠊⠁⠀⠀⠇⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⣀⣠⡀⢸⡀⠔⠂⠀⠀⠘⠀⠀⠀⢸⠀⠁⢹⠀⣇⠀⠈⠂⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠉⠁
⡰⠨⢤⠉⠄⠀⢀⢰⠂⠐⠊⠐⢀⠀⠀⠰⠁⠀⠉⠿⢤⣀⣀⠀⠸⣄⣀⣀⡀⠸⣀⡀⠈⣠⠇⠀⠀⠀⣀⠤⠒⠁⠀⠈⠱⠄⠀⠀⡀⠀⠀⠐⠄
⠑⠊⠩⠔⠂⠀⠀⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠉⠀⠀⠙⠛⠛⠁⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠐⠃⢠⠀⠀⠀⠀⣾⡆⠀⠈
⠀⠀⢀⣤⡖⠒⠂⠒⠒⣲⣤⡀⠀⠀⠀⠀⠀⠀⣰⣊⡉⠉⠉⢱⢦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠄⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⣠⡙⢻⡷⠀⠄⠐⣋⣭⣿⣿⣦⠀⠀⠀⠀⢠⠀⠇⢮⡁⢠⣷⠣⢹⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠱⣀⠀⠀⠂⠁⢈⠕⠀⠀⡐⠀⠀⠀⠀⠂
⢰⠹⠟⣃⡀⠀⠀⠼⠛⠟⠿⢿⣿⡇⠀⠀⠀⠎⠀⠈⠉⠑⠆⠘⡇⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⡇⢸⠒⠊
⢸⣷⣿⣿⠁⠀⠀⢠⣾⣿⣧⣙⠿⡇⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀
⠀⣿⠉⢁⡀⠀⠀⠙⠿⠿⣿⡿⢡⠇⠀⠀⠀⢸⠈⢀⡀⠀⠀⡰⠁⠀⠀⡎⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠰⠿⠿⠿⠇
⠀⠘⢿⣿⣿⣶⠀⠀⠀⠀⢿⡧⠊⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠇⠀⠀⠀⠣⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⣀⠀⠀⠀⠀⢀⣀⣀⣈⣥⣤⣄⠀⠀⠀⠀⢰⣁⠯⠆⡈
⠀⢠⠊⠁⢀⠀⠀⢀⠀⠀⠀⠄⠸⠀⠘⠇⠒⠒⠒⠀⠀⠀⠀⠏⠀⠀⢀⡤⠚⠙⠀⠀⠀⠘⡇⠀⠀⢠⣿⢩⡍⢹⠁⠌⣿⡇⠀⠀⠀⠀⠀⠐⠁
⠀⠸⣀⡡⠃⠉⠡⠏⠌⢹⠐⠂⠂⠀⠀⠀⠀⢠⠀⠀⠠⡄⠀⠀⠀⢰⠏⠠⠀⠀⠀⡀⢀⣀⠇⠀⠀⠈⠻⢶⣶⡿⢗⣶⡿⢶⣦⡀⠀⠂⠀⢶⡄
⠀⠀⠀⠐⠒⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⡀⠠⠀⠀⠀⠀⣄⠀⠀⢀⠴⠭⠤⢤⡟⠐⠀⠀⠀⠀⢀⣿⣇⡛⣉⣇⣄⣻⡷⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⠈⠀⣀⣠⠭⠶⠆⠀⠀⠀⠀⠠⠀⣀⣀⣀⠠⠆⠀⠀⠉⠀⠠⠋⠀⣀⡴⠋⠀⡘⠀⠀⠀⣼⡏⠛⢹⡏⣿⢩⣹⣿⠁⠀⠀⠀⢀
⠀⢀⡀⠀⠞⠋⠋⠁⣀⠔⠁⠀⠀⠀⠀⠖⠰⢠⠂⠖⡔⠂⠀⡇⠀⠀⠀⣜⣴⣞⡉⠤⠀⠀⠀⠀⠀⠀⠻⣧⣷⣾⡷⢿⣮⣿⡿⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡰⠽⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⢐⠀⡄
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠁⠲⠏⢴⠛⠄⠀⠀⠀⠀⠀⠉⠁⠀⠐⢀⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠹⠇⠙⠐⠁⠀⠀⠀⠀⣀
⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⠄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢠⠔⠲⠋⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢⡀⠀⠀⠀⢰⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠱⡀⠀⡠⠦⠖⠓⠋⠁
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⢥⡀⠀⠀⠀⠀⠠⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠠⡀⠤
⠀⠀⠀⠀⠀⠀⣤⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠒⠀⠀⠀⡀⡀⠁
⠀⠀⠀⢠⡖⠁⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠙⠓⠊⠁⠒⠐⠒⠐⠂⠒⠂⠀⢀⡤⠤⢔⣂⡤⠤⢄⣴⣁⣤⣰⠐
⠀⠀⠀⡎⠈⠂⠀⠀⠑⣆⠀⠐⠃⠐⠀⠀⠀⠀⠀⣨⡀⠀⠀⠀⠀⠀⠀⢐⣁⣐⢀⠀⠙⢯⣋⠄⣰⠆⡄⣈⡽⠉
⠀⠀⢈⡀⢀⠀⢄⡀⢈⡀⣣⠀⠀⠀⣰⠀⠀⠀⢀⣾⡋⠙⠁⠀⠀⠸⠊⡀⠃⠈⢻⡇⠀⠀⠉⠚⠓⠛⢉⣽⡖⠱⠲⢤⡀
⠀⠀⠈⠀⠀⠂⠠⠠⠀⢀⡯⠀⠀⠈⡠⠀⠀⠀⠁⠻⠏⠉⠀⠀⠀⠀⠈⠛⠔⠿⠟⠃⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠐⠠⠀⠀⠂⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠛⠶⠋⠉⠀⠀⢹⠉⢳⡄⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⢦⣀⠀⠀⠀⢸⣈⡴⠃⠀⠀⢀⡴⣞⢻⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠸⠤⠟⠉⢷⠋⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠥⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⡟⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠳⣤⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡴⠃⠀⣰⠃⠀⠶⣿⣿⠀⣠⠖⣿⠋⡟⠻⡗⢦⡀⠈⢳⡄⢈⣿⠋⠆⠈⢻⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣤⡤⠞⠁⠀⠀⢸⠃⠋⣼⠋⢻⠟⠒⡟⠚⢿⠋⢻⡄⠀⢻⠀⢹⠀⠀⠚⠉⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡷⠤⢾⠦⠴⡷⠤⢾⠦⠴⡇⠀⢸⡇⠈⠃⡀⠀⠀⠸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣧⣤⣞⠁⣀⢸⡄⠀⢳⣀⣸⣄⣠⣧⣄⣼⣀⣰⠇⡀⣸⠁⠀⠀⢉⣻⡟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣾⣭⣤⣭⣷⡟⠀⢳⡀⠀⠻⢯⣷⣀⣇⣰⣯⠽⠃⢸⣷⣧⠄⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠐⠂⡇⠐⢸⣧⡄⠀⠙⢦⣀⠀⠈⠉⠉⠉⠀⠀⠀⠘⠋⠀⠀⠀⢦⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢈⣧⣄⣇⣠⣞⠀⠃⠀⠀⠀⠈⠉⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⣠⠶⢾⠥⣿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⠉⠀⠸⠀⠀⠀⡾⠋⢛⣦⠤⠤⠴⠤⢤⣞⠋⠻⡆⠸⣧⣠⣞⠓⢻⣆⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠋⠆⣠⠴⠶⢤⡀⠎⢳⣼⠃⠀⠀⠀⠙⠲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣼⠱⡟⠉⡷⢹⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢿⣀⠙⡟⢁⣸⠇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⡇



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

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⡀⠀⢀⢀⣀⢀⡀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠘⠐⠂⡤⠀⡸⠀⢸⠀⡠⠠⠄⠀⡇⠐⠀⠒⢄⠑⡆⠀⠈⢠⠤⡄⠱
⠀⠀⠀⠀⠀⠀⡜⠁⡔⠁⠀⢸⠀⣀⣀⡀⠀⡇⠠⡠⠠⠊⢀⠂⠀⠀⠆⠀⢠⠀⡀
⠀⠀⠀⠀⢀⠎⢀⠌⠀⠀⠀⢸⠀⡤⠤⠃⠀⠇⠀⢄⠀⠂⠁⠀⢰⠀⠀⠀⠘⠀⡃
⠀⠀⠀⢀⠎⠠⠏⠀⠠⡀⠀⠸⠀⠇⢀⡀⠀⠀⢦⠈⢢⠀⠀⠀⠀⡀⠣⠠⠂
⠀⠀⠀⠘⠤⠤⠤⠤⠤⠂⠀⠰⠤⠤⠤⠃⠀⠦⠂⠁⠤⠃⠀⠀⠀⠐⠠⠠⠐⠁

⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠒⢲⠀⠀⠔⠐⠄⠀⠀⢀⠖⠉⠉⠲⡀⢰⠀⠀⠀⠀⠈⠀⠀⡀⠀⠖⠂⠀⠐
⠀⠀⠀⠈⡄⢰⠀⠀⡠⠤⡀⠀⠀⠃⡀⠀⠐⠀⠀⠘⠀⠀⡂⢰⠁⠀⠉⠀⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⡇⠈⠉⠉
⠀⠀⠀⠀⢡⠀⡆⠰⢡⡄⢱⠀⠰⢀⠁⠀⡀⢈⠁⠀⠀⠀⠑⠄⢉⣁⠐⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠰⠤⠤
⠀⠀⠀⠀⠘⡄⠰⠇⠎⢸⠘⡀⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⡖⠀⠈
⠀⠀⠀⠀⠀⢃⠀⡜⠀⠈⡄⠓⠁⠇⠀⢈⠀⠔⡄⠀⠀⢐⠁⣀⣀⠠⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠣⠤⢤
⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠒⠊⠀⠀⠐⠐⠀⠑⠒⠀⠀⠑⠂⠀⠒⠁⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠘⠂⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠤⣤⣤⣄⣀⠀⠀⢠⠞⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⡟⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⡞⠉⣽⣯⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣀⣠⣤⢤⣄⠀⠀⠀⠀⠀⠀⣴⠶⠖⠛⠋⠉⠁⠀⠘⠧⠀⠀⠀⠻⠶⠶⠋⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⣧⠀⠀⢶⡖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⠛⣻⠂⢰⡏⣀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠙⢦⡀⠘⠳⢦⣤⣤⣤⣤⡤⠴⠶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣠⡤⠤⣤⣉⠀⣸⠃⠉⠙⠛⠛⠒⠒⠚⠛⠁⠙⠳⠄⠙⢦⣀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⣰⠟⢡⡴⢦⣄⠙⢧⢉⡀⠀⣀⡀⣀⣤⣀⠀⢠⠀⠀⣀⢠⣤⣀⠁⠀⠀⢀⣤⣤⡄⣠⣤⣤⠀⣄⠀⢀⡀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⡀⢿⡄⠀⣸⠇⢸⡇⠹⣶⠋⣼⠋⠀⠙⣧⢸⠀⠀⣿⢸⣀⣹⠇⠀⠀⠀⢸⡇⠀⣿⣤⣄⠀⠙⣶⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⠳⢦⡴⠞⠋⢀⡼⠁⠀⣿⠀⠘⢦⣤⡴⠋⠸⣦⣴⠏⢼⠉⢻⡄⠀⠀⠀⢸⡇⠀⣿⣤⣤⠀⡾⠋⢷⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣤⡤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⠄⠀⠄⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡤⢿⠆
⠀⠀⠀⠁⠈⠃⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⢠⡿⣾⠋⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡀⠀⡀⠀⡀⢀⡀⠀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠠⠠⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠈⠁⠂⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡤⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠃⠐⠈⠈⠀⠂⠈⠀⠂⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠐⠁⠀⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⢘⣀⠘⢆⠀⠋⠁⠀⠈⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠚⠃
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⠋⣀⠀⠀⠀⠀⠀⢰⣦⠌⠀⡀⠊⢈⠀⠈⢰⣦⡀⠀⠀⠀⠠⠄⠀⠀⡰⢂⠄⠀⠘⠂⠦⠞⠠⠴⠂
⠀⠀⠀⠀⢀⠀⠲⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢰⠢⣀⠁⠠⠀⡄⢰⠈⠀⠀⠘⠁⠔⠗⠀⠀⠀⠀⠀⠨⠋⠀⠀⡀⢀⠀⠀⠐⠛⠀⢤⡄⣀
⠀⠀⠀⠀⠐⠂⢤⡼⣿⠀⠀⠂⠀⠀⠀⠀⢀⠀⠠⣼⣦⣤⢀⡕⠰⠀⠀⢀⢆⠀⠀⠀⠀⠀⢠⡀⠀⢠⢰⡀⠀⠹⠃⠀⠉⠀⢼⣿⣞⣆⠈⠇
⠀⠀⠀⠀⠀⢀⠈⢃⣀⣤⡀⣁⢰⣠⠄⣠⣿⣆⡄⣩⣇⣽⣾⡇⣤⣾⠂⢈⣥⣠⣄⣆⣰⣦⣦⡖⠂⢨⣻⣷⣡⣤⡴⢦⣤⠀⠀⣅⣿⣿⣨⣆⢠
⠀⠀⠀⠀⠚⠘⠓⠿⠷⠟⠳⠿⠻⠿⠒⠟⠟⠟⠓⠻⠿⠻⠿⠷⠿⠿⠿⠿⠟⠻⠃⠽⠏⠿⠻⠛⠛⠻⠛⠟⠿⠛⠃⠟⠿⠴⠾⠛⠻⠟⠛⠛⠺

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡴⢳⢣⣤⡄⠀⠀⠀⢀⠔⡊⠡⠌⡒⢢⠀⠀⠀⠨⠵⠒⡀⣠⠀⠰⠴⠀⠀⠀⠀⠀⡀⣯⡓⠃⠀⠀⠀⢀⠓⠐⣋⠀⣙⠀⡋⡆
⠀⠀⢼⠃⠠⡀⠀⡔⠀⠄⠀⠀⠜⠘⢀⣔⢒⠈⡌⠢⠀⠀⣰⡂⢺⠕⢊⠤⣄⡢⠀⠀⠀⠠⠺⠇⠃⠟⠢⠀⠀⠀⠘⢂⢈⠨⠀⠅⠃⡘⡇
⠀⠀⢸⡅⠀⠀⠀⡗⠒⡇⠀⠀⢱⠐⢄⠁⠚⡠⠠⠋⠀⠀⠁⠁⡇⠙⠥⢴⢲⠀⠀⠀⠀⠗⠸⠂⠀⠺⠐⠇⠀⠀⠰⡒⠀⠘⠶⠁⡄⢂⠇
⠀⠀⠈⠚⠦⠴⠤⠃⠀⠁⠀⠀⠀⠑⠒⠄⠤⠒⠊⠀⠀⠀⠀⠘⠝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠠⠿⠊⠀⠀⠀⠀⠀⠘⠈⠉⠠⠃

⠀⠀⠀⠖⠀⠄⠍⠑⢤⠀⠀⠀⠀⠀⠠⠤⠤⠀⣈⡢⠀⠀⠠⢀⡀⢀⠀⠉⠉⠁⠀⠀⠀⣀⣀⡄⢠⠤⠢⢄⠀⠀⠀⠀⡔⠰⠭⠐⢆
⠀⠀⠃⢀⠄⠷⠧⠄⠀⠁⠀⠀⢎⡉⠠⠤⠄⠀⢈⠀⠀⠀⠀⠀⠀⣠⠢⠐⡂⡠⠀⠀⢀⢤⣠⢤⣯⢯⣽⢯⠀⠀⠀⠀⡀⢀⠤⡀⢈
⠀⠀⡄⠸⣀⠀⢀⡀⠀⠄⠀⠀⢀⡀⠀⠨⠭⠭⢭⠕⠀⠀⠀⠘⠃⠓⠒⠃⠀⡆⠀⠀⢨⢾⣨⢯⠏⡑⠂⡁⠀⠀⠀⠀⢁⠬⡪⠤⡀
⠀⠀⠈⠢⠄⢀⠀⠐⠎⠀⠀⠀⠣⡤⠬⠭⠀⠀⠀⠀⠀⠀⠈⠀⢶⡀⣠⠦⠈⠁⠀⠀⠀⠙⠚⠉⠈⠁⠀⠀⠀⠀⠀⠀⠸⣤⠀⡤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠤⠤⣢⠀⠀⠀⠀⠀⠀⠀⡚⢲⠀⠀⠀⠀⠀⠀⢀⡀⠠⡦⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⢠⠁⠈⢆⠀⢀⠊⠈⠂⠀⠀⣌⠀⠀⡀⡀⠀⠀⡁⠀⠀⠀⠀⠖⠊⠑⠒⠀⠀⠀⠀⠀⡈⠃⠄⡃⠄⠋⡀⠀⠀⢀⠧⠧⠠⠶⠀⠥⠤⡀
⠀⢀⡃⡠⢪⠷⣯⠠⡀⣀⠀⠀⠀⠁⠒⢿⡗⠐⠁⠀⠀⠀⢠⠂⠳⢄⡠⠞⠐⠄⠀⠀⢈⡉⠁⠚⠜⠀⠉⡋⠀⠀⠘⠆⠴⣎⠉⡱⠦⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠂⠄⠀⠀⠈⠒⠄⢠⠄⠠⠀⠁⠀⠀⠈⠉⠀⠢⠡⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠠⢒⡀⣐⢢⠀⠀⠀⠀⠀⠀⣎⡰⢎⡰⠀⠀⠀⠀⠀⣠⢒⠂⣘⣖⣤⠀⠀⠀⠀⠀⠀⠀⣆⡾⠆⠀⠀⠀⢠⣴⡤⠔⠒⠆⢠⣤⡆
⠀⠀⠀⠀⢆⠀⢈⠀⠀⠀⠀⠀⠀⡞⠀⢠⠀⠀⠇⠀⠀⠀⠈⠀⠘⠙⡇⠯⠀⢑⠀⠀⠀⠀⠀⠠⠣⠀⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠈⠃⠁
⠀⠀⠠⠘⢄⠉⢁⠎⠤⠀⠀⠀⠀⢻⠀⢸⠀⠠⠆⠀⠀⠀⠉⠉⢉⠁⠊⠑⠈⢹⠀⠀⠀⠀⡐⠁⡂⠳⡀⠀⠀⠀⠀⢡⠀⠀⣀⠀⢀⠄
⠀⠀⠀⠈⠄⠲⠃⠈⠀⠀⠀⠀⠀⠀⡀⢐⢸⢐⠀⠀⠀⠀⠈⠲⢙⡁⢈⣋⠖⠁⠀⠀⠀⡔⠀⠁⠃⠁⠐⡀⠀⠀⠀⠀⠁⡞⠞⡢⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢀⡰⠴⢢⠀⠀⠀⠀⠀⡠⠐⠂⠀⠰⣀⠀⠀⠀⣦⢶⢀⣀⣀⡀⣴⢦⠀⠀⠀⠠⠔⢒⡀⠐⢄⡀⠀⠀⠐⢒⢂⠐⡖⠀⣶⠐⡄
⠀⠀⢪⠀⠈⠀⠒⢘⠈⠂⠀⠀⡌⢀⠴⠊⡒⠦⡈⠂⠀⠀⢉⡍⢀⠤⠤⡀⠉⠉⠀⠀⠰⠃⢆⠵⠲⢕⢤⠵⠀⠀⠰⠆⣀⠔⡄⠆⣀⠐⡇
⠀⠀⢸⠀⣃⣉⣁⡁⡀⠀⠀⠀⡀⢅⡉⣠⠀⡈⠝⡀⠀⠀⠀⠀⠨⡢⢔⠄⢠⡄⠀⠀⢀⠀⡸⣂⣄⡸⡐⢰⠀⠀⠘⢉⢤⠉⢟⠈⣬⠘⡄
⠀⠀⡆⠑⣄⣤⣤⠄⠑⡆⠀⠀⠘⢢⡀⠀⠈⣀⠔⠁⠀⠀⢾⣳⠠⠤⠤⠄⣷⣾⠀⠀⠈⠢⣋⠐⠱⣊⡠⠊⠀⠀⢰⠎⠉⠆⣘⠦⠉⠴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠁⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠛⠻⣭⠁⠀⠀⠉⠈⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⣠⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠄⠀⠄⠀⠀⡰⠃⠱⡀⢠⠇⢩⠀⠀⠈⢣⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠄⢠⠄⠘⠄⠀⠀⠱⡴⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⠙⠻⠧⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠶⡒⠒⠂⠀⠉⠹⡀⠂⠰⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⢀⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊
⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⢀⠎⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⡀⠀⠀⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡦⠀⠀⡀⠀⠱⡀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠱⡀⠀⠀⡔⡥⠦⠤⠠⠤⠄⡄⠁⠀⠀⠀⡠⠃⠪⠤⠤⠤⠤⠤⠬⠴⠖⠗⢠⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠑⡄⢸⡎⠀⠀⠀⠀⠀⠀⡏⠀⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠑⢦⡀⠀⠠⠀⠀⠃⢀⠀⠀⠘⢦⠀⢰⡂⠀⠀⣀⣀⡤⢞⡙⢫⣄⠀⠀⢀⠀⠴⡉⢋⠒⢄
⠐⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠈⠠⡀⠀⠀⠑⢾⠉⠉⠁⢍⠀⢴⣿⣦⣥⡍⠀⠄⠠⠾⠾⣿⣿⣣⢨
⠛⠄⠀⠛⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠈⠢⢅⣇⠠⠉⠁⠈⠄⠀⠘⠦⣉⣋⣡⠎
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠳⣤⣠⠶⠚⠃⠀⢻⡗⢦⡀⠐⢧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⢈⡁⠀⠀⠀⠀⢸⡇⠆⣿⠀⠀⠀⠀⢀⣤⢴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠴⠋⠙⠲⢦⣤⣤⣼⠷⠞⠁⠀⠀⠀⣾⠋⣷⠼⣇⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠸⣦⡾⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡀⠀⠀⣼⠀⠀⢀⣠⣤⠀⠀⠀⣀⣀⣤⣀⣀⠀⠈⠙⢦⡀⠀⢀⡀⣠⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠞⠁⠀⣰⠇⠀⠘⢻⠟⡏⢀⣴⣋⡿⠁⣿⠘⣯⣛⣦⡀⠀⢻⡄⠠⣿⠁⠚⠀⣈⣧⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠳⠦⠶⠞⠁⠀⠀⠀⡟⠈⢁⡞⠉⢹⠋⠙⣿⠋⠹⡏⠉⢷⠀⠀⢿⠀⢸⡀⠀⠈⠁⠀⢠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⢸⡷⠶⣾⠶⠶⣿⠶⠶⡷⠶⢾⡇⠀⢸⡆⠀⠃⣀⠀⠀⠀⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣧⣤⣼⠃⢀⡈⣧⠀⠈⣧⣀⣹⣤⣀⣿⣠⣠⣏⣀⡼⢃⠀⣿⠀⠀⠀⠉⢙⣿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣞⣙⣀⣉⣷⣼⠃⠙⣆⠀⠈⠻⣍⣿⡀⣿⢀⣟⣩⠟⠁⣼⣴⣣⡄⠀⠀⠈⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠠⠄⣿⠠⠈⣧⣀⠀⠈⠳⣄⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠟⠋⠁⠀⠀⣄⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠹⣆⠀⣿⢀⣰⠃⠹⠀⠀⠀⠈⠙⠒⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣋⣹⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠙⠛⠋⢹⡇⠀⠀⢀⡴⠶⢦⣄⣀⣀⣀⣀⣀⣠⠴⠶⢦⠀⢰⡏⠀⣸⣧⣼⣆⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⣇⣠⠞⡉⠉⣁⣀⣈⠉⢙⠳⣄⣸⠃⠀⠙⠛⠻⣄⣠⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⢠⢞⡭⠤⣭⡳⡄⠀⢹⡏⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⠈⠷⣤⠾⠁⣿⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠙⠦⣤⣿⣤⠴⠋⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⣀⣤⣤⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣻⡇⠸⢏⣿⡟⣾⡋⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠿⠶⠶⢦⣭⣴⣭⡉⢷⣀⠀⠀⠀⠀⢻⡆⠀⠀⠘⠻⠾⠿⠿⣦⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣹⠃⠀⠀⣠⡼⠃⠀⢀⣀⣀⣀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⢻⣄⢀⡾⠁⠀⠀⠀⣿⡋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠈⠉⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣭⣉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢰⡟⠳⣦⠀⢰⡟⠁⣀⣀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠁⠈⠙⠛⢾⣝⠛⣿⣆⠀⠀⠀⣠⠶⣦⡀⠀⠀⠀⢹⡆
⠀⢸⡇⠀⢿⡇⢸⡇⠀⠻⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠋⠀⠀⠀⠀⢀⣾⣯⣤⣈⢻⣆⠀⠀⣿⠀⠈⠻⣦⠀⠀⢸⣇
⠀⣸⡇⠀⠈⣿⠚⠷⠚⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⢿⣿⣛⣿⣯⡄⠀⠐⣿⠀⣤⢴⡏
⠀⢻⡇⠀⣾⠏⠀⠀⠀⠀⠈⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⡇⠀⠀⠙⠛⠃⢸⡇
⠀⢸⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢠⡶⠟⠀⠀⠀⣠⠶⠶⠶⣿
⠀⠀⢹⣏⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣼⠏⠀⠀⣸⡏
⠀⠀⠀⢻⡄⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⡷⠘⣷⠀⠀⣰⡟
⠀⠀⠀⠀⢻⡄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⢰⣏⣀⣴⡟
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣿⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣾⠉⣿⠞⠁⠈⣩⡿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠹⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⡾⠃⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣙⠷⣄⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⣿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁
⡶⠶⠶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⣶⢶⣶⠶⠶⠶⢶⡶⠶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠿⠿⠿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣄⠀⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⣿⣧⣄⡀⢀⣤⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠈⠻⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠋⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠿⠿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⢨⣿⠃⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢻⣯
⠀⠀⢀⣀⣀⣿⠇⠀⢀⣾⠏⠀⢀⣤⣤⣤⣤⣤⣤⣤⣿⠿⣿⣤⣤⣤⣄⠀⠘⢿⣆⠀⠀⢿⣇⣀⣀
⠀⠀⣿⡟⠛⠋⠀⠀⣸⡟⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⢿⣶⠿⠋⠉⠉⠉⠀⠀⠘⣿⡀⠀⠈⠛⠛⣿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣠⣴⡿⢿⣦⣠⣀⣄⣀⣀⣀⣀⣄⡀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⠉⠻⣷⣾⠟⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⢿⣧⣤⣄⠀⠀⢹⣷⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣴⡿⢿⣦⣀⣀⠀⠀⢰⣿⠁⠀⢀⣤⣤⣿⡇
⠀⠀⠀⠉⠉⣿⡆⠀⠀⢿⣧⠀⠈⠙⠉⠙⠛⠛⠛⠉⠉⠻⣷⣶⡿⠛⠉⠀⢠⣿⠇⠀⠀⣾⡏⠉⠁
⠀⠀⠀⠀⠀⢘⣿⡄⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⣼⣟
⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣶⣶⡾⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⣴⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣄⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⣿⡟⠉⠁⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⡿⠁

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣦⣠⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⢀⣀⣤⣾⣿⣷⡚⠓⠂⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⡤⠊⠁⢈⠂⠀⠀⠙⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⡧
⠀⠀⠀⢀⠀⠉⠘⠒⠤⠀⡤⠀⡀⠴⠦⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠈⠳⡄⠀⣀⡴⠋⠀⠀⠀⢀⠀⠀⠘⢛⣟⠃⠟⠙⠛⠛⢻⣿⣦⣄⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠷⠶⠶⠶⠓⠚⠉⠀⠀⠀⠀⠚⠰⣦⠀⠀⢹⡶⣤⣀⣀⢢⣄⣮⣵⣿⣷⠶⠶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣀⣀⣠⣀⣾⣿⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣯⡉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣇⢁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⢻⢠⣏⠂⡴⢐⢸⡇⣴⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠋⠀⠙⠊⠋⠉⠉⣇⠘⢺⡗⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡾⠋⠡⠊⡀⠀⢸⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠘⢷⣶⣆⡘⠁⠀⠸⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣤⣴⣿⣾⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣰⡄⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠶⠚⠙
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⢻⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣀
⠑⠃⠀⡰⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⡞⠋⠁⡢
⠀⠀⣸⡇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⢰⡞⠂
⠀⠀⢿⡇⠀⡞⠀⢀⡔⠀⠀⢠⡄⠀⢡⠀⣧⠀⢠⠰⡟⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠁⠀⣻⡇⢠⡇⢀⡿⠁⠀⠀⠀⠀⠘⡉⣇⣻⠀⡆⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠄⠀⣿⣇⡼⠁⣼⠇⠀⠀⠀⠀⠀⠀⢹⣿⡟⣸⣏⣴⣿⢃⡀⠀⠀⣀⣀⡤⠘⢿⣼⣸⠟⠶⣶⣶⣦⣤⣀⠐
⠀⢠⣿⡟⢁⣼⠇⠀⠄⠀⠀⠒⠀⠀⠀⠙⠷⠟⠿⠿⠛⠚⣠⣴⣾⣷⣶⣶⣆⣀⣿⡗⠇⢤⣼⡾⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣤⣀
⠀⣸⠟⡴⠟⢁⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡏⢀⣹⣧⡷⣀⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣰⠟⣭⣷⣦⣽⣧
⢰⣿⣫⠔⠚⠋⠉⠀⠈⠉⠙⢶⡀⠀⡀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠒⣶⣿⣶⣿⡿⠙⢿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⡖⠔⡄⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⣾⣿⣿⠟⠫⠁⠈⠲⡟⢿⣿⣷⡄⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠋⠈⠉⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠀⠀⢀⣀⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣛⣋⣭⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠙⠻⣭⠭⠿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⡶⣶⣰⠤⢦⢴⢠⣦⣤⡤⡆⣴⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠉⠈⠋⠘⠉⠀⠁⠉⠁⠁⠉⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠄
⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠹⠤⢍⡉⠋⠛⠛⠋⠉⠉⠥⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠲⢖⣲⠶⠖⠒⠒⠒⠒⢶⢒⡶⠶⠶⠶⣶⠊⠁
⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⠝⠉⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠉
⠀⠀⣠⢸⡿⠗⢏⡗⣫⠼⠓⠶⢾⠀⠿⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠡⢄⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢺⡤⠀⠀⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠤⠄
⠀⢀⡴⠋⠀⠐⢢⣧⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡤⠴⠒⠒⠒⠒⠲⠊
⠀⡸⠂⠀⠀⠀⢀⣀⢹⡥⠤⢒⠲⢖⡀⠀⠀⠀⣀⠴⠋⠁
⠀⢇⠀⢀⣠⢞⣉⡝⠈⠀⢸⠁⠉⠒⠮⠤⡶⠊⠁
⠀⠀⠉⢉⡉⠀⠀⢣⠀⠀⣏⠀⠀⠀⢀⢬⣅⡉⠉⠉⠉⠁⠀⡀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠖⠒⠒⠒⢀⠒⣀⣀⣀⣀⣐⣶⣖⣒⣒⣒⣖⡂
⠀⣠⠊⡡⢧⡄⢠⠃⠀⠀⢸⡄⠀⢰⣃⠖⠂⡈⠉⢢⣄⡀⡜⡧⢆⡄⠆
⠀⠳⣼⠟⡊⠀⠀⢇⠀⠀⠘⠦⣀⡀⠓⠔⢻⠳⠤⢾⣊⣧⡇⡿⢸⡟⠐⢠⣄⡏⠀⡰⠀⠀⠀⢸⣠⡆⡀
⠀⠀⣿⠯⢉⣉⣩⡞⠀⠀⡀⢀⡻⡛⢞⠛⠾⠞⠓⡶⢧⠀⠿⠧⢨⣿⠀⣿⣿⢸⣰⡇⢰⣴⢠⢰⡹⢠⠇⣶⠳⡎⣞⣶⣷⣞⡗⢫⣸⠗⡶⣶⡇⣾⣶⡇
⠀⠠⠤⡴⠋⠁⡜⡡⡎⡰⠛⢌⣇⠙⢆⠁⠁⠢⡄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠣⠤⣼⣁⢹⣿⡇⣼⡇⢸⠀⣤⠀⡆⠉⠀⠀⠈⠀⠁⠀⠀⠀⠀⠡⠀⠀⠁
⠀⠀⠠⢤⣤⠟⠉⠀⣷⠃⠀⠀⠙⣷⣄⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣟⢻⢿⣏⠠⣯⢛⠉⡏⢹⠏⢹⢻⠉⠉⠉⠁⢀⡋⠀⠈
⠀⠀⣴⠋⠀⠀⠀⣠⢿⣄⠁⠀⠐⠁⡏⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣬⡏⢀⠃⡘⠀⠀⠸⡀⠜⠰⢠⠀⠀⠀⠛
⠀⠠⢂⡇⠀⡶⣫⠔⣼⡆⡡⠄⠄⢰⡡⠤⢝⢖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠃⠆⡅⠈⠀⡄⠀⡠
⠀⢰⣏⢊⠇⠹⣄⣪⠞⠙⢞⠠⠘⠐⡧⠀⠜⠈⡜⠉⠑⠂⡄⢠⠒⠒⠒⠒⠒⠒⠠⡄⢀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠦⢀⡛⠰⠀⡧⡶
⠀⠀⡏⠃⠀⠐⠁⣩⠀⠀⠈⢣⠀⠀⢓⠂⠠⢄⠁⠒⠂⠚⢁⠆⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⣀⠀⠨⠆⠀⣰⠒⠀⠀⠀⠠⡄⠀⠀⠀⠀⠉⠙⠀⠓⠃
⠀⠀⡖⠀⠀⠀⠜⠙⠂⠀⠀⠘⡗⠀⠈⠆⠀⠀⠙⠭⡀⠀⠨⣀⡀⠀⠀⠀⠀⠀⠀⢸⠰⡖⠒⣀⠰⠀⢠⠇⠀⠀⠀⠀⢀⠆⠀⠀⠀⡀⠔⠒⠒⠢⠤
⠀⠀⠀⠀⠀⠀⡆⡖⢒⢲⣶⡖⡖⣖⣶⢶⣴⣰⠀⣶⢰⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠅⠉⠀⠀⠀⠈⠉⠉⠉⠁⠀⠁⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠁⠁⠈⠈⠉⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠤⠠⢄⠀⠀⠀⠀⢀⠐⠀⠒⠀⠂⠀⠈⢢⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣌⢻⣷⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⣿⠶⠶⠶⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⣰⠋⠙⢻⠛⠉⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡶⠒⣿⠖⢲⡖⠃⢠⣶⣶⣞⠁⠀⠀⢸⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⢸⡇⠀⠹⣿⣿⠟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣆⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠁⠀⣿⠀⠈⠛⠶⣄⡀⠀⠀⠀⠘⣿⣿⣿⡟⠀⣴⠒⢺⡗⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠉⠁⠀⠀⢿⣀⣨⣇⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣴⣶⣦⣄⣙⣠⣴⣶⣦⣀⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⡇⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣙⢿⣿⡿⠟⣛⣛⡛⠻⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⠴⠒⠃⢸⡇⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⢹⣷⢰⣾⣿⣿⣿⢸⣷⠈⣿⣿⣿⠃⠀⢀⡴⠋⠁⣀⣄⡀⠨⡇⢀⣠⣄⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⢛⣵⣶⣬⣍⣛⣛⣈⣩⣾⣿⣿⠏⠀⢀⡞⠓⠖⠋⠁⠀⠙⠓⠖⠋⠀⠀⠙⠲⠚⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠞⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠶⠶⠒⠂⢲⠒⠦⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⡡⠀⠈⠀⠀⠔⠁⠀⠀⠀⢸⠀⠀⠈⠠⡀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠔⠁⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠁⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢀⣀⡠⠤⣀⠀⠀⣤⠤⠔⠢⢤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠈⠀⠀⠀⠠⢀⠏⠀⠀⠀⠈⢱⡾⠧⣄⠀⢀⠤⠼⠢⢤⣸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⡀
⠀⠀⠀⠠⠁⠀⠀⠀⢠⢁⡷⠀⠀⠀⠀⠀⠈⣇⠀⠈⣧⠞⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠄⢎⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡁⠀⠀⠀⠀⢸⢧⠀⢀⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠢⠤⣀⠀⠀⢀⡠⠋⠀⠀⣰⠃⠀⠀⠀⠀⢰⠞⠀⡾⠀⠀⠀⢳⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡏⢹⠙⠳⠖⡖⠚⡇⢹⠑⢶⢲⠒⢻⠀⠸⣀⠀⠀⠀⣠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⠤⠒⡇⢸⠚⢺⠀⣇⠀⡇⢸⡤⡾⢸⠒⢚⠒⠲⢌⣙⣾⡊⠁⣀⠴⠒⠒⠒⠒⠒⠤⢄⡀
⢀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡇⢸⠀⢸⠀⡏⠉⡇⢸⠀⡇⢸⠀⢰⠀⠀⠀⠉⡇⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄
⠐⠆⠀⠀⠀⠀⠐⠂⠀⠓⠂⠀⠐⠃⠚⠒⠘⠂⠓⠀⠃⠚⠀⠓⠘⠂⠐⠀⠀⠀⠐⠓⠃⠓⠀⠀⠐⠀⠀⠀⠀⠀⠒⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣴⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⣀⣀⡀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⡀⠀⠀⣀⣀⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣶⣶⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀
⢀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠉⠉⠛⢻⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⣠⣶⣶⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠘⠛⠻⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠟⠋⠁⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠉⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣻⣟⣀⣀⣀⣀⣀⣀⣀⣘⣿⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣻⣩⣛⣿⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠐⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⡂⣄⠀⠀⣸⠀⡈⠁⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠀⠀⣀⠀⠀⠀⢀⡶⠀⠀⡄
⣀⡄⠈⣿⠀⠀⠀⠀⠀⠀⠤⠀⡰⣄⠀⠸⠇⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠈⠐⢶⠗⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠰
⠶⠦⠛⠉⠹⣋⢛⣴⣦⣤⡆⠄⣐⠀⢣⠰⠛⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⠔⠊⢁⠀⠀⡀⠀⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠙⠂⠘⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠮⠡⡀⠀⠀⠈⠉⠉⠻⠂⠀⢠⣄
⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⠄⣀⣀⡄⠔⠂⠈⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣀⢀⣀⡀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠉⠑⠖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠰⠿⡓⠡⠆⠂⠤⣥⣖⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⠦⡖⠀⠀⠀⠀⠀⠀⠀⠃⠐⢠⡼⠉⢝⠲⠀⢀⣶⠠⠔⠀⠁⠀⠀⠆⠈⠁
⠀⠀⢠⢤⡤⣶⢏⡌⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠙⢤⠤⣶⢺⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⢄⠚⣶⡄⠀⠀⠀⣆⡁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠙⢤⡆⡀
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⠌⠠⠋⠀⠉⠀⠀⣰⢃⡃⠀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠠⠀⠀⠀⠘
⣤⣤⣦⣜⣀⡛⠀⠈⠈⠀⠐⢀⠊⠀⠀⠀⢰⡾⠞⠁⠎⠀⠀⠐⠀⠀⠀⡆⠐⠀⠈⠐⠁⠒⠀⠉⠀⢀⣠⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤
⠈⠁⡉⠀⠐⠃⡤⠀⠤⠠⠞⠁⠀⠀⠀⠀⠛⠁⠈⠂⠀⠀⠀⠀⠀⠀⠍⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣀
⠠⠐⢀⠄⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⣠⡀⢄⠀⠠⠁⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢰⡆⡀⠀⠘⠿⠃⠂⠀⢈
⠟⠀⢁⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠈⠀⠀⠀⠀⠈⡴⠀⢀⡀⠀⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⢀⡀⠢⠠⠈⠓⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡄⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⢄⠀⠀⠀⠀⠀⠀⡂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠆⠀⠀⠀⠀⠀⠘⡂⠀⠀⠠⢾⡿⠈
⠀⠀⠀⠀⡨⠣⠄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢣⠹⠌⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠁⠈⠀⠀⣠
⠀⠀⠀⠘⠀⠀⠂⠀⠄⠀⠀⠀⢀⣰⠆⠀⠀⠀⣀⠀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠄⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⣀⡔⠁
⠈⠀⠀⠀⠀⠄⠤⠊⠈⠀⢣⡀⠠⠁⡆⣀⠖⠉⠀⠁⠀⠈⢋⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠔⠈⠀⢀
⠀⠈⠐⣄⠀⠀⠀⠀⠀⢈⠄⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢰⡵⠂⠉
⠺⠃⠀⠁⠐⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠠⠀⠉⠊⠉⢳⠂⠀⢄⡰⢾⠀⠀⠚
⢂⠒⠀⠀⠀⠀⠀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈⠺⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠚⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡂⠀⠼⡇
⠀⠀⠀⠀⠒⢦⣤⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡴⠿⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠙⠛⠉⠉
⠠⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀
⠀⠙⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⣒⣰⣖⢄⠀⠀⢠⠤⡶⣦⣤⣄⠈⠂
⠀⠀⠀⠉⠑⡀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⢰⢀⢚⣻⡟⢿⠇⠀⠀⠠⠀⠀⡀⠁⠀⠁
⠀⠀⠀⠉⠀⠀⠀⠛⠃⠋⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⠁⠀⢀⡆⠀⠀⡄⠀⠁⠀⠀⠀⠠⠈
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠀⠀⠀⠀⠀⠉⠀⠛⠠⠴⠊⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣶⣾⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠀⠁⠀⡀⠙⠛⠓⠆⠀⠀⠃⠀⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠂⠀⠀⠂⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⢀⢒⠒
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢤⣴⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣖⡓⠛⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠑⠀⠀⠀⠀⠀⠂⠀⠀⠉⠋⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠒⡦⢺⡪⢗⡷⢶⣦⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⢁⡠⠭⠭⣀⠀⢸⣿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣏⠀⡴⠁⢀⡤⣄⠀⠱⡄⢈⣙⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢞⡎⡇⡇⠀⣇⠀⢀⡇⠀⡇⢸⢞⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠯⣄⠱⣄⠈⠉⠉⢀⡴⠁⠈⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⡁⠀⠉⣐⣋⠁⢀⣴⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠶⢸⢝⡯⡇⠸⠬⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢠⢴⠠⣄⣤⣠⠀⡄⡄⣀⡤⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠋⠈⠈⠁⠁⠁⠉⠈⠈



⣏⣈⣯⣭⣿⣯⣿⣹⣽⣽⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠰⢦⣄⣀⣛⣙⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣭⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣟⡽⠚⠋⠉⠀⠈⠁⠀⠀⠀⠠⣄⠀⠰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣶⣦⣤⣤⣤⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⢿⣿⣟⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣄⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣷⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣳⣿⣿⣝⢿⣿⣿⣿⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣯⣟⢷⣽⡻⣿⣿⣿⣿⣿⡍⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣽⣿⡿⠛⣿⣿⣿⣿⡄⠈⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⢷⣝⣯⣻⣿⣾⣿⣿⣿⣿⣿⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠛⠉⠀⠀⠘⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⡃⠙⢿⣿⣿⣿⣿⣿⣎⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⠏⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠙⠓⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡄⣠⣾⣿⣿⣿⣿⢟⣯⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠸⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣳⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⣿⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⣿⠟⠫⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣾⣿⣿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⡫⠁⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣾⡋⠁⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠱⡄⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⡇⣰⡏⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⢴⠶⡖⢶⢤⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡄⣄⢠⡀
⠀⠀⠀⠀⠀⠀⣸⢁⡇⠀⢀⡞⢳⡿⠶⡷⠾⡗⠛⣆⠀⠀⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⣬⠁⣬⡁⣩⡈⣥⣄⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⢠⣇⣼⡃⠀⢸⠦⢼⡧⠴⡧⠤⣿⠤⢾⠀⠀⣳⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢘⣛⠀⣛⡁⣛⡃⣙⣛⠀⠀⠀⡻⣇
⠀⠀⠀⠀⠀⢸⠈⣇⠳⡄⠘⣆⣨⣧⢤⡧⢤⣧⣀⡟⢀⡴⢣⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⡀⠀⠸⠿⠂⢛⡃⣛⠃⠿⠟⠀⠀⣴⢯⣿
⠀⠀⠀⠀⠀⠘⣇⠈⢧⠙⢦⡈⠳⢽⣦⣧⡾⠶⠋⣠⠞⣠⠏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣦⡀⠈⠛⠘⠃⠋⠘⠋⠀⣠⣾⣯⣿⡏
⠀⠀⠀⠀⠀⠀⠈⢢⡈⠃⠀⢳⡀⠀⠀⠀⠀⠀⣼⠁⠀⠃⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣸⠁⠀⠀⠀⠀⠀⢻⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣽⠀⠀⠀⠀⠀⠀⢸⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠤⠄
⠀⢠⠖⠁⠀⠀⠀⠀⠀⠑⢦⡀⢠⠞⠁⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡠⠊⠉⢀⠐⠃⠀⠀⢀⣤⡿⠶⢄
⢠⠃⠀⢀⡦⠀⠀⠄⠀⢄⠈⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠑⡀⠀⠀⢠⠊⠀⠀⠈⠀⠓⢲⣴⡛⠛⠁⠀⠀⠀⡳⡀
⢈⠀⠀⠀⠉⢀⠠⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⢀⠇⠀⠀⠀⠀⠀⣰⣴⠿⠀⠀⠀⠀⠀⠀⠁⠱
⠘⡀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⢰⠀⡄⠀⠀⢀⣷⠙⢲⡀⠀⠀⠀⠀⠂⠒
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠀⠘⠸⠀⠘⠇⢠⣼⠁⠀⠀⠁⠀⠀⠀⠀⠠
⠀⠀⠙⢄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⢄⠀⠀⠀⢺⡅⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⡰
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⣔⡴⠁
⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⡀⠀⠀⠀⢈⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠈⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢣
⠀⠀⠀⠀⠈⡟⠻⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢇
⠀⠀⠀⠀⠀⡇⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⢁⠁⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⢁⠠⠆⠦⠀⠁⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇
⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⢀⣧⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠻⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠟⠁⠀⠀⠀⠀⠀⠙⢷⣶⠶⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣠⡴⠆⠀⢸⠁⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⣧⣀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣄⣀⣉⣹⠀⡇
⠀⠀⠀⠀⢠⣏⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡏⠉⠉⠁⠀⡇⠀⠀⠀⣠⠶⢦⡀
⠀⠀⠀⠀⠀⠉⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⡧⠀⠀⠀⠀⡇⠀⠀⠀⡏⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣶⠚⠛⠁⠀⠀⢀⡤⠶⠶⣄⠀⢷⣀⣀⣠⠇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣀⣀⠀⢰⡿⠷⠶⠶⠶⠶⠚⠛⢹⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠁⠀⠀⣸⣧⠀⠉⠉⠁⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠉⠈⢻⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⣶⠋⠛⣿⠀⠀⢰⡏⠈⡧⢀⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡟⠀⣀⣀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣾⢹⡆⠀⣿⠀⠀⠀⠳⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⢸⠋⠉⣷⠀⠹⣆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠙⠾⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⣿⠀⠀⠘⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⡀⠀⣿⠀⠀⠀⠈⢷⡦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣬⣷⢤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢰⠟⠙⣦⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠈⠳⠞⠃⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁



⡖⠲⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠖
⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⡔⠢⡄⢠⠐⡴⠂⢠⡄⢀⡖⢤⢠⠀⠀⡔⠂⠀⢠⠐⠀⠲⡔⢠⠔⢤⢀⠔⢢⡀⡄⡠⠀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⡇⠀⡜⢸⠀⡇⢀⠇⠾⠰⡇⠳⢸⠀⠀⡟⠀⠀⠀⠑⡆⠀⠇⢸⠒⢃⠸⡀⢀⠇⡟⢣⠀⡇
⣶⣶⡶⠶⡶⠶⣶⣶⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾⣿⣷⣾⣷⣾⣷⣿⣶⣿⣿⣶⣿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣦⣤⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣤⣤⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⣿⣍⣽⣿⣾⣿⣿⡿⣿⢟⣿⣽⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢤⣽⣿⣿⣿⡟⠻⣿⣟⣯⣯⣯⣽⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣫⣿⣾⣿⣿⣿⣷⣿⣿⣫⣿⣍⣿⣽⣿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⢹⣟⠋⣹⣿⡿⣿⣫⣿⣷⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢈⣿⣿⡿⠏⠉⠁⠀⠀⠀⠉⠉⠧⠀⠼⠟⠀⣀⣽⡗⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⣰⣶⡗⣨⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⡌⣿⣿⡾⣏⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⡯⡗⣍⣧⡍⢭⣁⡀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⢠⡏⢱⡛⣻⣤⡛⣁⠃
⠀⠀⠀⠀⠀⠀⠀⠲⣏⢷⣍⢿⣟⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠼⣿⣿⣷⣇⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏⡯⠞⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣆⠀⠀⢠⣿⣏⡛⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⢩⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣬⣛⣿⣿⠋⠘⢿⣿⣇⠡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠠⠱⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⡶⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠋⠃⠀⠠
⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧
⠀⠀⠀⠀⠀⢣⣥⡆⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠀⠈⠀⠲⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠘⡃⡔⠀⠀⢸⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠄⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠢⢞⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠘⠁⢐⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢁⡀⢀⠀⠀⠀⡀⠀⠐⠋⠘⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠈⠃⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠖⢰⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⠀⢀⡂⠀⠀⠀⣀⣀⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣅⠉⠀⢀⠛⡔⠀⠁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣶⣌⣠⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠘⠃⢋⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠂⠀⠀⢠⢷⡾⠋⠁⠄⠸⡷⠆⠀⠐⠃⠀⠰⠆⠈⠁⠀⣄⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠒⠦⣄⠀⠀⠀⠀⣠⠴⠒⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣘⣦⣶⣈⡇⠀⠀⢸⣁⣶⣴⣃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠟⢑⣦⣴⡊⠻⠤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠱⡄⠀⠀⠀⣠⠖⢫⠟⢹⡏⠻⡝⠲⣌⠳⣄⠀⢠⠎⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⣸⠁⠀⢠⠞⠀⢹⡿⠤⢼⡧⠤⢿⡏⠀⠳⡌⢧⠈⣇⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠇⠀⠀⡏⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⢹⠘⠂⠸⡄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⣾⢤⡀⠀⡗⠒⠒⢿⠒⠒⢺⡗⠒⠒⡿⠒⠒⢺⠀⢀⡤⣷⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠁⠀⢹⠀⢧⠀⠀⢸⡀⠀⢸⡇⠀⢀⡇⠀⠀⡼⠀⡏⠀⠀⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⢸⠀⣈⠳⣀⠼⢿⠉⢹⡏⠉⡿⠧⣀⠞⠁⠀⡇⠀⠀⡇⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠘⣆⠈⠳⣌⡓⠮⢷⣼⣧⣾⠵⠚⠁⠀⠀⣰⠃⠀⠀⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⣀⠀⡀⠀⡀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⣠⡇⠀⠀⠣⠈⠣⠘⠇⠘⠇⠘⠇⠀⢸⣄⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢹⡇⠸⠆⠸⠂⠹⠂⠹⠂⡽⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠐⠄⡀⡆⠔⠂⢠⠀⠐⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣾⢀⣤⡰⣧⢄⣴⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣿⢿⣿⣯⣼⣿⡗⠛⣼⢛⣵⣿⡇⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡙⢿⣿⡿⠠⣬⣥⣬⡛⣼⣇⣀⢺⣿⢟⡰⢩⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣷⣬⢠⣆⢰⣦⡙⢿⣿⣿⣿⡟⣿⠂⣴⣿⢧⣾⣿⠟⢴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣟⢫⣼⣯⡽⠟⢘⣿⡇⣿⠈⣩⡌⣿⠉⠁⣿⣏⣠⠉⢀⣵⣶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣷⣬⠂⣙⠛⠛⣾⠻⠿⣿⡻⣼⠿⠃⣻⣧⡾⠧⢾⣯⢀⣸⣿⡿⠁⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⢟⣬⣝⠷⢦⣼⣧⣬⣙⡿⢻⡆⢷⣿⣏⣤⡶⠿⢾⣟⢣⣾⣏⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠿⠿⠋⠰⠛⠀⠀⠈⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠀⠛⠿⠇⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡶⢞⣉⣭⣽⡿⠿⠶⠦⣄⣤⣶⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢋⣹⣿⣿⣿⣿⣿⡽⠖⠛⠀⠀⠀⠙⢿⣿⣿⡿⠂⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣾⣿⣿⣿⣿⣿⣿⣏⡡⠾⢿⣦⣤⣠⡀⠀⠙⢿⡁⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠁⠀⠠⡀⠀⢨⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣾⣿⣿⣿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⡿⣿⣿⡏⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣿⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⠀⠀⠽⠻⣿⣧⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠁⠈⠙⣷⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣤⣤⣌⣡⣬⣭⡴⠟⠋⠙⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⡿⢿⡿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⡿⠁⣿⡇⢸⣷⠈⢿⡟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣿⠇⠀⣿⠃⠘⣿⠀⠘⣿⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⢸⡿⢿⣿⠿⠿⣿⠿⠿⣿⠿⠿⣿⡿⢿⡇⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢹⣷⠸⣷⠀⣿⡄⠀⣿⡀⢀⣿⠀⢠⣿⠀⣾⡇⣾⡏⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢸⣿⠀⠻⣷⣹⣷⡀⣿⡇⢸⣿⢀⣾⣏⣼⠟⠀⣿⡇⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣼⣏⡀⠀⠘⠻⣿⣷⣾⣧⣼⣷⣾⣿⠟⠋⠀⢀⣹⣧⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠰⣿⠛⢿⣦⡀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠀⢀⣴⡿⠋⣿⠆⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢻⣧⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣼⡟⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠹⠷⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠾⠏⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⣀⣀⣀⣼⣧⠀⠀⠀⠀⠀⠀⣼⣧⣀⣀⣀⣀⣸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⣩⡉⣿⡇⠀⠀⠀⠀⢸⣿⢉⣍⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣬⣤⣿⡇⠀⠀⠀⠀⢸⣿⣤⣥⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣠⡀⢠⡀⡀⣀⣄⠤⣤⣠⢠⢄⣄⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠘⡄⣀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠠⠶⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠛⠀⠀⠛⠃⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠃⢰⠞⠛⠛⠳⡄⠀⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠘⢦⣀⣄⡴⠇⠀⠰⠆⠷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠗⢀⣤⡀⠀⣠⣄⠘⠖⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠘⠛⠛⠀⠀⠀⠀⠠⣆⡀⠀⠰⠋⠀⠀⠀⠀⡾⠃⠀⠀⠀⢀⡏⠐⠂⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⠀⠀⢀⡾⠁⠀⠈⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠋⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⡴⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣻⣄⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠈⠉⠉⠉⠓⠢⢄⡀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⡀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠶⠷⠶⠒⠒⠒⠒⠲⣤⣀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢠⣖⠋⠉⠁⠀⠰⠒⠲⠶⠖⠶⠲⠖⠤⢤⣤⠤⠄⠀⠀⠀⠄⣀⠀⣀⣀⠀⠀⠀⠀⠻⣷⣦⠀⠀⠀⠤⠔⠊
⠀⠀⠈⠛⠶⠶⣦⣤⣤⡀⠀⠀⢀⣀⣀⠀⡄⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⢡⠀⠀⠀⠉⠉⠉⠙⠁⠀⠀⠀⠀⠈⢿⠇

⠀⠀⠀⠀⠀⠀⠸⢼⠇⠀⠀⠀⠀⢠⣶⣦⡀⠀⢰⠀⠀⠁⠀⠀⠀⢘⣈⠁⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠧⠀⠀⠀⢸⡇⠈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹
⠀⠀⢠⠀⠀⠀⠀⠀⠚⡀⠁⠀⢠⡥⢿⣄⠀⢻⣶⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⢸⡀⠀⠀⠀⠀⠠⠁⡄⠀⠈⠀⠈⠙⣧⢸⡆⠀⠤⣀⢒⣾⣿⣀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⢀⣀⣀
⡿⠋⠉⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⢀⣿⡥⣾⡿
⠃⠀⠀⣸⠏⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣧⠀⢀⡀⠀⠀⠰⣶⣦⣼⡄⠀⠀⠀⠀⠈⢧⠀⠈⢿⡇⠀⠃
⠀⠀⠀⢫⠾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡏⠁⠐⠂⠀⠀⠀⠀⠈⠐⠀⠀⠀⡀⠈⢇⠀⠀⠈⢀
⠀⡠⠀⠀⠀⠀⠉⠀⣀⣀⣤⣶⠛⠛⡐⠂⠀⠀⢤⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡼⠶⣶⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⠏⠉⢛⡷⣾⣛⠉⠉⠀⠀⠀⠈⠈
⠀⠀⢤⡀⢀⠠⠖⠉⠀⢀⠈⠉⠀⠀⡠⠀⢤⡀⠀⠀⠀⠁⠀⠀⠱⡍⠢⢭⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠐⠓⠀⠀⠐⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⡶⣧⡇⠀⠀⠀⠉⠉⠛⠛⢷⡴⠞⠁⠀⠀⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⡀⠀⠀⠸⠇⠀⠀⠀⣀⡘
⢙⣀⢀⠀⠀⠀⢀⡦⠀⠀⠀⢀⣀⣀⡦⠀⠀⢀⠀⠀⠀⠀⢀⠎⠲⣀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠐⣾⠐⠉⠳⠒
⠋⡏⣸⠧⠤⠖⠋⢀⣶⢟⡺⢯⣍⣭⡄⠀⠀⠠⠀⠀⠀⢠⡟⣗⠀⠈⠑⠂⠀⠀⠀⢻⠀⡔⠻⠆⡠⠚⠐⠟
⢀⡁⠀⠀⠀⠀⠀⢸⡟⢸⣋⣐⡤⠄⠀⠀⠀⠀⠳⡀⠀⠈⡤⠚⣀⠀⠀⠀⠀⠀⠀⢈⣾⣱⡁⢀⡷⠤⣴⠋⢰
⠘⠀⠀⠀⠀⠀⠀⣠⡿⢛⠿⡿⣿⢯⣧⣠⡀⣰⠀⡗⠀⠀⣹⡉⠱⠆⠀⠀⠀⠀⠀⢸⣬⡉⠙⣿⡀⠠⣟⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠏⠐⣾⠚⠇⠈⣷⡦⣤⣴⡇⠘⠀⠀⠀⢹⡖⠆⢛⠀⠀⠀⢀⡜⡀⠠⠿⣤⣯⣤⣟⣁⣠⣀
⢶⡄⠀⠀⠀⢀⡀⠀⠀⢩⠀⠀⠀⣿⣼⠛⢿⡸⡆⠀⠀⠀⠘⣷⠬⠋⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠉⠈⠉⠉⠉
⠉⠀⢀⡴⡞⢯⠉⠳⠄⠈⠀⠀⢀⣿⡇⠀⠰⣇⠁⠀⠀⠀⠀⠿⡂⠴⣢
⠀⠀⢸⠀⠀⠀⠀⣄⡗⠀⠀⠠⠞⡿⠁⠠⠴⠋⠀⠀⠀⠀⠀⠈⠣⠿⠟⠀⠀⠀⠀⠀⢀⡔⠛⠛⠐⠒⢠⡀
⣀⣀⣰⣛⣆⣀⣂⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣐⣒⣄⣀⣀⣀⣀⣄⣀⣀⣀⣀⣸⣀⣘⣛⣀⣀⣀⣘⣄
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⡀⠀⠠⣄⠀⢀⡀⠀⣠⢤⣀⠀⠀⠀⠀⠀⢠⡀⠀⣠⡀⠀⣀⠀⢀⣠⡀⠀⠀⠀⡀⠀⠀⣀⣀⣤⣄⣀⠀⣀⣀
⠀⢠⢣⣷⠀⢀⢤⠀⡎⠀⠈⢙⡛⠉⣰⣿⣦⡀⢡⣯⣇⢸⣿⡟⢸⣿⣆⢸⣿⣿⠀⠉⠀⠘⠀⢋⣴⣿⣿⣿⣿⠗⣿⠃⡇
⠀⠈⣿⣿⠃⠘⠊⠀⢷⡴⠁⣿⣿⡇⢸⣿⣿⠁⠸⣟⠟⠈⣾⠇⠻⣿⡿⠈⠛⡿⠈⠢⠤⠖⢀⢀⣉⡉⠛⠋⢡⡀⢻⠘⠁
⠀⣠⠘⠏⢰⣾⣿⣦⠀⡀⠀⠙⠛⠁⠈⠿⠟⢰⢁⡀⢀⡆⠀⢠⠶⠀⠀⢠⠀⠁⠀⠀⠀⠀⠟⠀⠙⠋⢨⣴⣾⣿⠀⣠
⠀⢇⡄⠀⢈⣻⣛⣉⠀⠉⣠⣤⣶⡖⠂⡠⠤⢦⡍⠁⠀⠀⠀⠈⠉⠀⠀⠀⣀⣀⠀⠐⣆⣶⢀⣔⣱⣦⡌⢻⣿⣿⠀⡹⡄
⠀⠀⠁⠀⠻⡿⣿⡿⢇⣤⣤⠘⣿⡁⢸⠀⠰⣾⡟⠁⠀⣨⠄⠀⠀⠀⠀⣠⡜⣿⣷⠀⣯⡟⠘⠧⣴⣿⠟⠀⠏⠉⠀⠛⠁
⠀⢠⠄⣆⠀⢀⣄⣀⠘⠿⠟⠃⢻⣧⠈⠳⣶⣼⣴⣴⡾⠋⠀⠀⠀⠀⠀⠛⠛⠛⠁⣸⠟⢠⢴⣶⣶⡤⠂⠁⠀⠀⣴⣷⠄
⠀⠘⠻⠛⠰⣿⣿⣿⠷⠀⣾⣾⡄⠉⠳⠀⠀⠉⣉⣥⣶⣾⣿⣷⣦⣄⣀⠀⠀⢀⣤⣤⣤⣬⣍⡉⢡⠆⢰⡄⢠⣶⠈⠳
⠀⡆⠰⠞⣆⠀⣉⣤⣤⣤⣈⠉⡁⠤⣤⣄⡀⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⠀⠀⣀⠀⢸⣇⠀⠀⠆
⠀⠻⣶⣾⠏⠘⠛⠀⠀⠛⠛⠀⣇⣀⣾⣿⠟⠈⢿⡓⣿⣿⣇⢿⣿⣾⠝⠋⢤⣤⡀⠀⢤⣤⣤⣄⠐⣷⣼⡧⠀⠁⢸
⠀⠀⢠⢄⠀⠀⠀⠀⠛⠒⠒⠶⠤⠉⡀⢢⠀⠀⢤⣄⠈⠙⠋⣉⠉⠉⠀⠰⠺⠿⠟⠀⠾⠛⠋⠁⠤⢤⡀⢤⣦⡤⠈⠹⡁
⠀⠀⠈⠉⠀⠀⠀⢂⡰⠀⠀⢰⣾⡆⢣⡾⠀⢧⠘⣿⡄⠀⠀⠈⡇⠀⠰⠂⡀⣰⣶⣶⠄⠀⠘⠂⠠⡘⠃⠀⢠⠀⢤
⠀⠃⢀⣀⣀⡀⠀⠈⠃⠀⠀⠈⠻⢃⠀⠀⠀⠈⢧⣿⡇⠀⠘⠰⠁⠰⣼⡿⢡⣨⡉⠁⠀⠀⠀⣠⣄⠀⢠⣀⣄⠀⡀
⠀⠀⡿⣿⣿⠏⠆⠀⢼⣶⡁⠲⣤⣾⡁⠰⠿⠀⠀⠉⣥⣀⣀⣠⣤⠀⠀⠀⠈⠉⠀⣀⣤⡂⠀⢠⣇⠀⠘⣿⡏⠀⡇⠈
⠀⠀⣀⣀⡁⠈⡀⢰⠈⠁⠀⣤⠿⣿⠛⠁⠠⣶⣷⡄⠉⠉⠉⠉⠉⠀⠀⠘⠀⠀⠸⠀⣽⠉⠀⣾⣿⠀⣾⣿⣿⠈⠀⣿⡀
⠀⢸⣿⣿⣿⡆⢉⠯⣖⠂⠀⠀⠀⠈⠀⠀⠀⠛⠛⠀⠀⢀⣢⣀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠂⠀⠸⠏⠀⠹⣿⠟⠀⢸⣇⡇
⠀⠈⣉⡉⠉⢠⣤⣶⣬⠀⣰⣿⣷⠀⠀⠀⣤⡤⠠⠀⠀⠃⢏⠇⠀⠀⠐⢘⣤⡂⠀⠀⠀⣤⣤⠀⠈⡛⠀⠀⠀⣠⣤⠉
⠀⠻⠿⠿⠆⠹⣿⣿⡿⠀⠈⠉⠁⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠛⠋⠀⠀⠁⠀⠀⠈⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣴⠏⠀⠀⠈⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠋⠹⡿⠋⣀⣤⠖⠀⠀⠈⣻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣦⡤⣼⣿⣷⣀⣴⠟⡤⡞⣻⣿⣿⣿⣿⣞⡀⠠⣤⣤⣤⣀⠀⡤⢤⣀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠈⢸⣿⣿⠟⢿⣧⣀⣀⣀⣥⡾⠐⣿⣿⣿⣿⣧⣵⣄⣷⣧⣬⣠⣐⣿⣧⣍⣀⡀⢀⣀⣄⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⣾⣿⠋⢀⣸⣿⣿⣟⢛⡍⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣧⡠⢰⣿⣷⣄
⠀⠀⠀⠀⣀⣽⣶⣶⢿⣄⠸⣿⣯⣴⣿⣿⣿⡿⣳⡏⠉⠀⠀⠙⠧⠿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⡏⠀⠈⠀⠙⠛⠿⣿⣿⡧⠃⠉⠂
⠀⠀⠀⠠⢜⡛⢛⣄⣤⣽⡷⣿⣶⣍⣿⣿⣿⢶⣿⡅⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠘⣿⡀⠀⠀⠀⠀⣀⣀⡈⡿⠀⣤⣿⣧
⠀⠀⠀⠀⢀⡿⣿⣏⣵⣬⣤⣴⣶⣿⣿⣿⡇⢸⣿⣷⡀⠀⢂⠀⠀⡀⠸⢖⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠹⣧⡀⠀⠀⢀⣨⣿⣿⢦⡶⢿⡛⢿⣆
⠀⠀⠀⠀⠀⢬⡿⠿⠛⠉⠻⣿⣿⣿⣿⣿⣿⡀⢿⣿⡿⢄⢘⡇⠀⠀⢀⣾⡿⣾⣿⣥⣿⠟⢿⣿⣿⡄⠀⠘⠻⠷⣸⣟⡚⡉⢛⣿⣿⣦⡀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠂⡐⠃⠸⡿⢿⣿⣿⣿⣿⣿⣗⣿⣿⣿⡝⡗⠀⠰⢘⣧⣾⡟⠛⠙⠛⠁⡀⣮⠛⠁⠀⢘⣷⣦⣿⣽⣿⣿⣿⡛⣿⣿⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠑⢦⡀⠀⠻⠽⣿⣿⣿⣿⣿⣄⣽⡿⠁⣠⠶⠋⠈⠁⠀⠀⠀⠀⢶⡧⢧⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⡟⠛⠛⢻⣿⢃⡜
⠀⠀⠀⠀⠀⢀⡀⠀⣉⢶⣄⠙⢆⠀⠀⠐⠌⠀⠠⠑⠙⠋⣡⠾⠋⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⣻⣿⡇⠀⢤⡾⠟⠊
⠀⠀⠀⠀⠀⠲⢹⣦⣄⢾⣿⣧⣄⡱⢄⠀⠀⠀⠀⠀⢀⣴⣿⣀⣠⠾⡩⢀⣡⣾⣖⠀⠀⠀⠀⠀⠀⠀⠦⣤⣚⣿⣿⢻⣿⡟⠁⠃⠁⠀⢠⠁⡀
⠀⠀⠀⠀⠀⠀⠀⢉⣙⠙⣿⣿⣿⣟⣿⠷⣰⠀⠀⣴⢻⣿⣿⣿⢡⣾⡿⣿⣿⣿⣽⣶⣦⠄⢀⡤⠄⢀⣠⠘⣥⣿⣷⣿⠏⠀⠀⠀⠀⠀⢊⡀⠐
⠀⠀⠀⠀⠀⠠⡄⢈⠈⠝⣻⣻⡿⠻⠞⠷⠟⢁⣾⣥⡶⠋⠁⢉⣥⣶⢚⣯⡿⢟⣭⠟⣋⣴⣻⣾⣾⣿⣿⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⡃⠀⠀⠀⢀⣴⣿⣾⡏⣀⣤⣶⣿⣿⣿⣯⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣯⣦⣰⣶⣀⣡⡤⢾⣒⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣾⡿⠋⣻⡿⠿⣟⣻⣽⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣼⣿⣻⣿⣿⣿⣿⡟⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⣠⡞⣫⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣽⡟⡿⣶⣾⣿⣿⣿⡿⠟⠛⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠏⠞⠁⢀⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣶⣡⣿⣿⣿⣫⣔⡰⠻⡗⢟⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⡼⠖⠛⠛⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⠄⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢖⠎⠉⠿⠶⠛⠉⡉⢉⣈⡉⠻⠉⢉⣿⡿⠋⠀⠀⠀⠀⠀⡀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⣴⠋⡀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⢦⡄⠄⠀⠀⠀⠀⠀⠁⠀⠙⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡀⠒⠚⠁⠀⠀⠐
⠀⠀⠀⠀⠀⣸⢃⣠⣴⣿⡿⣿⢿⡿⠃⠉⠉⠉⠀⠀⠀⠰⢤⣴⡟⢹⣿⣘⣦⣲⣤⣴⣄⣀⣤⣤⡀⠀⡤⠖⠛⠀⠁⡼⠛⠁
⣀⣀⣀⣀⣀⣉⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣘⣛⣻⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣉⣉⣀⣀⣐⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢠⠄⠐⠶⠀⠈⢈⡠⠊⠁⠀⠐⠃⠸⠃⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢟⠏⠉⠀⠈
⠀⠀⢰⢁⡾⠀⠀⠀⣀⡼⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠂⡔
⠀⠀⠈⠠⢤⣀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢠⠄⠁⠀⠶⠘⢲⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⡤⠀⠀⠀⠶⠁⢀⡴⡁⠈⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢶⣶⢶⢲⠒⡆
⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠐⡷⣮⡏⠿⠘⢰⠃⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢤⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣤⣴⡖⡖⡆⠀⠀⠀⠚⠳⠧⠆⠎
⠀⠀⠀⠾⠀⢠⠆⠀⠀⠰⣄⠀⢸⣴⡇⠀⠀⠀⠀⠤⠔⠀⠀⠀⢲⣾⡏⡇⠀⡇
⠀⠀⡀⠀⠰⠈⠀⠀⠀⠐⢂⢼⣿⣷⠯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⣰⡾⣠⠀⠀⠀⠀⡤⣡⠻⡟⠻⡕⠀⠀⠀⠀⢠⢿⣷⠀⣠⡤⣶⣶⡶⠀⠀⠀⣄⠒⣄⠀⢠⠀⠀⡆⠂
⢠⠀⠀⢐⣿⠁⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠩⠬⠱⡰⠉⠁⠀⠀⠀⠀⠈⠁⠘⢀
⢸⡄⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡽⣆⠁⠀⠀⠀⠑⣃⠀⠀⠀⠀⠀⠀⣀⡝⠀⠄⠀⣤
⠀⢳⡄⢰⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢸⣿⠁⠝⠀⠠⠄⠀⠄⡑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠃
⠇⣺⡄⣾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⡄⠚⠃⠀⠈⠠⠢⠁⡀⠒⠬⣆⠀⠄⠀⠀⠀⠶⠄⠀⠁⠈
⣇⣟⣼⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠸⠾⠛⠋⠈⠙⠀⣆⠀⠀⠀⠀⠀⡀
⠘⠋⠁⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⡇⠀⠀⠈⠢
⣤⠶⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠈⣆⠘⡇⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⡀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠨⡇⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡯⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢆⣰⡂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⢀⠀⢀⠄⠀⠀⢸⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣏⢀⣤⢤⣤⣤⣠⡾⠛⠛⠛⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⢀⣤⣴⡿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣾⠏⠀⠙⠦⠿⠱⢿⣤⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢰⣿⣋⣁⣀⣀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠈⠛⠛⠛⠛⠷⠶⠿⢷⣆⠹⣦⣄⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠉⠛⠛⠛⠻⣷⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢠⡟⠀⠀⢀⣤⡾⠃⠀⠀⣀⣀⣀⣠⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠘⣧⡀⢀⡿⠁⠀⠀⠀⠸⣿⡋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠶⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣼⣧⣀⠀⠀⠀⣴⠿⠛⠛⠛⠷⠶⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠾⠶⣦⣤⣹⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⢀⣿⠈⢻⣷⠀⢸⣿⠀⣠⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡟⠀⠀⠀⠀⠈⠹⣷⡀⠈⣿⣦⠀⠀⠀⢰⡟⠛⣷⣀⠀⠀⠀⠀⣿⡄
⠀⢸⡿⠀⠀⣿⣄⢸⡟⠀⠈⠛⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠉⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣄⢻⣧⡀⠀⣸⡇⠀⠈⠙⣷⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢈⣿⠜⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣛⣿⣯⣤⡀⠀⠀⣿⠀⣠⡶⣾⠇
⠀⢸⡇⠀⢀⣾⠏⠀⠀⠀⠀⠀⠈⠻⠶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⠃⠀⠀⠙⠷⠟⠀⣿
⠀⠸⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⢀⣀⣠⣀⣸⡏
⠀⠀⢸⣇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⣰⡟⠉⠉⠀⣽⠇
⠀⠀⠀⢿⡆⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣤⠀⣼⡟⠁⠀⠀⣰⡿
⠀⠀⠀⠈⢿⡄⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢘⣷⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣿⠀⣾⣧⣄⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⠉⣿⡿⠃⠀⠈⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠈⣿⡄⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⢀⣴⡿⠃⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡈⠻⣦⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⡻⣾⣟⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠉⠉⠛⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣸⣷⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⢀⡴⠞⠋⠉⠹⠟⠉⠀⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣤⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣤⣤⣤⣤⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣟⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⡃⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⣿⣶⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠸⠋⠻⣄⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⣠⠄⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠈⠙⠶⢤⣠⣾⣿⣿⣿⣄⣤⠴⠚⠁⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣠⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣤⣤⣀⣀⣤⣤⣤⠶⠞⠛⠉

⠀⢀⠀⣀⠀⠀⠀⣠⣤⠀⠀⣠⡄⢀⣠⡀⠀⠀⡤⠠⠄⠀⠠⠀⢀⣠⣄⣀⡀⠀⠀⣀⣀⣀⡀
⠀⠸⠀⠉⡜⠀⠀⠙⠿⠃⠐⠿⠀⠐⠛⢋⣤⣤⣤⣶⣶⣤⣤⣄⣈⠙⠉⠉⠁⠀⠻⢿⣿⣿⡿⠂
⠀⢠⠠⠊⠀⠴⢶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠁⣀⣀⠀⠀⠀⠀⡀⠄⠀⢸⢰⢺⡇
⠀⡄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠘⠿⣿⣿⣿⣿⣿⡿⡛⠛⠛⠛⠛⢻⣿⠛⠁⠀⢤⢠⣿⠇⠀⠀⠈⠈⠈⠁
⠀⠈⠑⠀⠀⣾⣖⠀⠀⢠⣤⠀⠀⠉⠉⠀⠀⠀⢡⠄⠀⣀⠀⠀⢠⣶⣆⠀⠈⠻⠀⠀⠀⠈⠛⠀⠀⠀⠀⣶⢠⡄⡆
⠀⢰⣿⣷⡄⠙⠇⠀⠀⠘⠋⢠⠀⠀⢠⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠉⠁⢠⣴⡶⠿⡇⠀⠀⠀⠀⣍⡀⠀⠛⠘⠃⠃
⠀⠘⣿⠀⠀⠀⠀⠘⠃⠀⡀⢸⡇⠀⠈⠉⠡⢠⢀⣤⢠⠉⠉⠀⡤⠀⢀⠘⠻⢷⣦⡇⠀⠀⠀⢸⣿⠄⠀⢠⢀⣀⡄
⠀⠀⣿⠀⠀⠀⠀⢸⣦⠀⣿⢸⣷⠀⠑⠀⠀⠀⠄⠀⠀⠀⢀⠠⠈⠀⠈⣀⣀⠀⠀⠀⠀⠀⢠⠀⠋⠀⠀⢸⠸⠯⡇
⠀⠂⠻⠤⢝⣤⡄⠀⣿⣆⣿⣿⡿⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⢿⡇⠀⠐⠄⠀⠀⢰⡀
⠀⠘⢷⣲⣼⡽⠀⠀⠈⠿⣿⠟⢁⣀⡈⠉⠀⠀⡆⢰⢶⡶⠂⠀⠀⡄⠈⠀⠀⠀⣰⣿⣿⣿⣦⠀⣳⠀⠀⢸⣶⣴⡇
⠀⠀⠀⠉⣿⣇⠀⠐⠀⢀⣴⣾⣿⡟⠓⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠰⣿⡄⠀⠈⠈⠉⠁
⠀⠠⡀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⠃⠀⠀⢰⣿⣷⡄⠐⠐⠄⠀⠄⠀⠀⠀⠀⣀⣸⣿⣿⣿⣥⣄⢼⠃⠀⢀⢤⣤⡆
⠀⠀⠀⠀⠘⣿⠿⡿⢛⡉⠿⠛⠁⠀⠄⠀⠀⠉⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⢿⠿⣿⢻⡆⢀⠀⠰⠛⠹⠇
⠀⠀⠀⣶⣤⠈⠓⠁⠋⡀⠀⠀⣴⠀⠘⡶⠀⠸⠏⢹⡏⠀⠀⣿⠘⣿⡄⠙⢛⣱⢇⡇⣿⢸⣇⡀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⢿⠟⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⢸⣿⠙⠓⠁⠀⠀⠀⠀⣰⣆⣺⣷⢰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⡀⠀⠀⢶⣆⣿⡏⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⢀⠀⠀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⢀⣀⡀⡂⣀⣀⡀⢀⣀⢰⠀⢀⣤⣤⣄⠀⠀⠀⢠⣹⡞⠷⠁
⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠹⠻⠩⠇⠇⠇⠇⠟⠯⠿⠸⠀⣿⣿⣿⣿⡇⠐⠀⠀⠈⠁
⠀⠀⠀⠼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠋
⠀⠀⠀⠘⠣⣄⠀⠀⠀⢀⣿⣧⣠⢾⡇⡴⡆⣴⢦⢸⡇⡴⡆⢾⠂⡇⡴⣦⣶⢦⢴⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠈⠛⠁⠛⠋⡿⠋⠈⠁⠛⠃⠘⠀⠃⠛⠁⠉⠘⠙⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠐⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠂⠐⠀⠀⠠⠀⠀⠀⢂⡀⣀⣦⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠈⠻⠻⢷⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⢛⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠸⠿⠛⠿⠂⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⣻⣶⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠀⠀⠀⠀⠀⠀⠑⠓⠀⠀⠀⠀⢸
⠛⡻⠀⠀⠀⠀⣀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣵⣠⣶⣶⡶⢶⣖⠒⠀⠀⠀⠀⠀⠐⠛⠀⠺⠿⠿⠀⠀⠀⠀⠀⡏⡀⠀⠠⣧⣷⣾⣷⣾⢿⠇
⠀⠀⠰⠶⡀⠳⣿⣜⢿⣛⠛⢛⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⣼⣿⠿⣟⡆
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣳⠫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣤⣄⡀⠀⠀⠀⠀⠘⣯⣾⡿⠁
⡀⠀⠀⠀⠀⠀⠣⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣠⡴⠾⠟⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⣀⣸⣾⠆⠀⠀⠀⢰⣶⣶
⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⣠⠀⣄⠄⠄⠀⠀⠀⡟⠉⠀⠀⠘⠃⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠠⢤⣀⣄⣠⠎⣽⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠑⢤⣀⢹⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⣀⣀⣀⣺⠩⠁⣀⣬⣤⣤⣒⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠛⢷⣿⡟⠢⠀⠀⠀⡀⢀⣿⣿⣶⡎⣀⠀⢈⣀⣠⣤⣴⡿⣽⣿⢾⡷⣷⡷⠟⢿⣿⣿⣿⣿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⡀⠀⠀⢀⣤⣾⣿⣿⣷⣿⣶⣿⣿⣛⣿⢿⣟⠿⣯⡭⠾⠃⠀⠀⠈⠙⢻⡿⠟⠉
⣤⣄⣤⣴⣆⠀⠀⠀⠀⠀⠰⠝⠿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠐⠀⣠⠬⠟⠚⡻⠟⠀⠀⠀⢀⡠⠔⠋⠁⠀⢀⣀
⠉⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⣽⣿⣀⡀⡠⠄⠒⠀⠠⠽⠖⣚⣋⣉⠠⠄⠀⠶⠿⡿⠿⠂⠀⠀⠀⠛⠛⠃
⠀⠹⣿⠏⠀⠀⠰⠶⠶⠀⠀⠀⠀⣠⠒⠛⣿⣿⠋⠐⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠬⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠟⠛⡉⠉⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⡿⠂⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣶⣶⣭⣵⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠄
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠟⠯⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⢀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠃⢈⣿⡷⠂
⠿⠟⠛⠒⠤⠀⠀⢸⡁⡠⠄⠀⠀⢠⣶⣴⣤⣷⠄⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢺⠟⠛⠁⠀⢺⠟⠁⠀⠀⢰⠤⠤⠴
⠀⠐⠂⠀⠀⠀⠀⠀⠑⠚⠃⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⡀⢠⣶⣾⣿⣯⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⢀⣠⢄⣀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠁⠀⠿⣷⣷⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⡴⠆⢴⡇⠀⠀⠀⠀⣺⡏⢹⣗⠀⠀⠀⠀⢹⣷⣦⣀⣀⡀⠀⠀⠀⠰⠰⣡⣿⡇⠀⠀⠀⠀⣤⣼⣷⡀
⠀⠀⡟⣅⡀⠶⡇⠀⠀⠀⠀⠈⠛⡛⠁⠀⠀⠀⠀⠀⠙⢹⡟⠋⠀⠀⠀⠐⠿⣿⣾⠻⠿⠀⠀⠀⠀⣽⣿⣿⣿
⠀⠀⠈⠚⠓⠊⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⢠⣤⢠⡖⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠠⣂⣂⡂⠄⠀⠀⠀⢠⣶⣲⣖⣶⡆
⠀⠀⣄⠠⣿⠀⠀⠀⠀⠀⢀⢲⣸⣆⡴⠀⠀⠀⡔⢀⢊⣀⢸⠆⠐⡄⠀⠠⢱⡁⠀⢸⠬⠀⠀⠀⢸⠾⠰⠷⠿⣿
⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠇⠀⠀⠑⠀⠊⠉⠈⠂⠐⠁⠀⠀⠑⠙⡒⠍⠊⠀⠀⠀⠈⠉⠭⠯⠍⠁

⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⣠⡓⠒⢢⡄⠀⠀⠀⠀⢰⡿⢿⡇⠀⠀⠀⠀⡐⡞⣡⡙⣖⡀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⢠⣿⣿⢠⣤⡄
⠀⠀⠁⡷⠶⣪⡀⠀⠀⠀⠀⠀⣶⣾⠄⠀⠀⠀⠀⠐⠛⣍⡝⠂⠀⠀⠀⠀⠰⣿⡿⢻⠀⠀⠀⠀⠀⢹⠉⠈⡿⠁
⠀⠀⠀⠇⠀⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡏⠭⢽⡉⢷⠀⠀⠀⠀⢎⣇⣸⡡⠀⠀⠀⠀⢠⠴⠯⠷⢄⠀⠀⠀⠀⢐⣾⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⡷
⠀⠀⣿⠶⣾⡇⢨⠀⠀⠀⠀⠄⡱⢎⠱⠀⠀⠀⠀⢸⠀⣠⡄⢸⠀⠀⠀⠀⢸⡏⠶⢻⠀⠀⠀⠀⢸⡿⠆⣠⣤⣠
⠀⠰⠿⠶⠿⠏⠁⠀⠀⠀⠀⠊⠒⠒⠑⠀⠀⠀⠀⠘⠤⠬⠤⠜⠀⠀⠀⠀⠈⠿⠿⠿⠀⠀⠀⠀⠈⠁⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠲⢿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣾⡿⢈⣭⣵⣾⣿⣾⡿⠷⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⣫⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⣣⣶⣶⣿⣿⡿⢛⣭⣔⣒⠾⣿⣿⣿⣿⡿⣰⣦⡍⠻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠋⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⡍⣩⣭⣤⣝⢿⡇⣷⡘⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣭⣙⡛⠿⠿⠿⠿⠇⢿⣿⣿⣿⣷⡄⣿⡇⣀⣠⣤⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣝⠻⣿⣿⣿⢹⡇⢿⣿⣟⡰⣿⠿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣜⢿⡟⣼⣧⢸⣿⣿⣿⡆⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣝⠛⣫⣥⣶⣮⣙⠻⣿⣿⣿⣿⣿⣷⡅⣿⣿⠈⠙⠻⣿⣿⢌⣭⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⡿⢱⣿⡟⠀⠀⠀⢻⣿⡜⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⣿⢸⣿⣿⣿⢟⣃⡻⣿⣿⣿⣿⣿⣿⣿⣮⠻⣛⣵⣿⡟⠁⠀⠀⠀⢸⣿⢰⣷⡆
⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⠟⢈⢿⢏⣵⣿⣿⣿⣮⣻⣿⣿⣿⡿⠟⣫⣾⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣮⡛
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⢸⣷⣮⣭⣭⣭⣭⣭⣴⣶⣶⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣩⣭⣭⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⣻⣿⢟⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠁



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