Bandaid Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠶⠒⠒⢒⣒⣶⡶⠶⠶⠶⠦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠀⣤⠶⠒⠛⣋⠉⠉⠉⠉⠉⠳⡄⠀⠀⠀⠠⠀⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣏⡛⢉⡇⠀⠀⠀⣧⠀⠄⠀⠀⠄⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠁⠈⢧⡀⠀⠀⠀⠙⠋⠀⠀⠀⢀⡿⠀⡄⠀⠀⠄⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠂⠀⠀⠀⠀⠙⠒⠒⠒⠒⢒⣒⣒⣛⣉⣥⣤⠤⠤⠶⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠒⠒⠚⠛⠓⠒⣒⣒⣒⣒⣒⣒⣒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠄⠀⡞⠉⠀⣠⢴⢤⡀⠉⢱⡄⠐⠀⠀⠁⠀⠈⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠠⠀⠀⣇⠀⠈⢷⣞⣲⠇⠀⢸⡇⠐⠀⠀⠀⠀⠐⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠂⠀⠤⠀⠀⠙⠦⢤⣤⣍⣁⣀⣠⡼⠁⠀⠆⠀⠂⠀⣐⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠒⠶⠶⠶⠤⠶⠶⠶⠒⠒⠒⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠒⠒⠒⠒⢦⡀⠀⠀⠀⠀⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠁⠀⡟⠀⢀⡤⠴⠛⢢⡀⠀⠀⣷⠀⠁⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠐⠀⢸⡇⠀⠙⠒⠒⠒⠒⠚⠀⠀⣿⠀⠉⠀⠀⠁⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡐⠀⠐⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⡴⠏⠀⠒⠀⠀⠁⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠲⠶⠦⠤⠤⠤⠤⠶⠶⠶⠒⠒⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣶⣦⣄⡀
⠀⠀⠀⣠⣾⡿⠟⠛⠉⠉⠀⠀⠀⠈⠙⠻⢿⣷⣦⣀
⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄
⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⣤⣀
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠉⠙⠻⢿⣦⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⣴⣶⣦⠀⠀⠙⠿⣷⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠈⠛⢿⣦⡀
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⣤⣦⣄⠀⠀⠙⢿⣦⡀
⠘⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠻⣿⣦
⠀⠛⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣴⣶⣦⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⣠⣤⣤⠀⠀⠘⣿⣧
⠀⠀⠀⠈⠙⠻⣿⣷⣄⡀⠀⠀⢸⣿⠁⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣄⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⠻⠟⠁⠀⠀⠀⠀⣰⣿⠟⠁⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⣠⣤⣴⣶⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⠀⠐⠗⠀⢀⠀⠀⠾⠀⢀⡴⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠓⢦⡀⠀⠷⠀⠀⡀⠀⠺⠂⠀⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠛⠀⢀⣄⠀⠘⠃⠀⣤⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠀⠘⠃⠀⣠⡀⠀⠛⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⣴⠀⠀⠁⠀⢰⡆⠀⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⢠⡆⠀⠈⠀⠀⣦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣀⠀⠐⠗⠀⢀⡀⠀⠿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠟⠀⢀⡀⠀⠺⠂⠀⣀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⠀⢀⣄⠀⠘⠁⠀⣤⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠃⠀⣤⠀⠈⠃⠀⣠⡀⠀⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣥⣤⣤⣤⣤⣬⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠻⣿⣿⣿⣿⠛⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⠛⣿⣿⣿⣿⠟⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣉⣿⣿⣿⣿⣏⣹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⣹⣿⣿⣿⣿⣉⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣤⣿⡿⢿⣿⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⡿⢿⣿⣥⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣟⢛⣿⣷⣾⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣷⣾⣿⠛⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣉⣿⣿⣿⣿⣏⣹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣹⣿⣿⣿⣿⣉⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣴⣿⣿⣿⣿⣤⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣤⣿⣿⣿⣿⣦⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠉⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⡛⠛⠛⠛⠛⢛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⡛⠛⠛⠛⠛⢛⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠀⠈⠋⠀⢠⡀⠀⠛⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠛⠀⢀⡄⠀⠙⠁⠀⣄⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠉⠀⠠⡦⠀⠈⠁⠀⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠀⠈⠁⠀⢴⠄⠀⠉⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠀⠀⡀⠀⠸⠇⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠘⠇⠀⢀⠀⠀⠟⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣤⠀⠈⠋⠀⢠⡄⠀⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠀⢠⡄⠀⠙⠁⢀⣤⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠀⠠⡶⠀⠈⠀⠀⠶⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠟⠀⠀⠶⠀⠀⠁⠀⢶⠄⠀⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣾⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣾⣿⣿⣿⣷⣿⣯⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣽⣿⣾⣿⣽⣿⣿⣿⣯⣿⣷⣿⣯⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣾⣿⣽⣿⣾⣿⣯⣿⣷⣿⣯⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣿⣿⣽⣿⣿⣿⣾⣿⣽⣿⣿⣿⣯⣿⣷⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣯⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣻⣿⣽⣿⣻⣿⣽⣿⣿⣿⣽⣿⣻⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣿⣿⣿⣟⣻⣿⣽⣿⣻⣿⣽⣿⣿⣻⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣟⣿⣯⣿⣟⣿⣿⣽⣿⣿⣿⣽⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣯⣿⣟⣿⣯⣿⣟⣿⣯⣿⣟⣿⣿⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣟⣿⣫⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣻⣿⣿⣿⣟⣿⡿⣿⣿⣿⣟⣿⣟⣻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣻⣿⢿⣿⣿⣿⡿⣿⣟⣿⡿⣿⣯⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣻⣿⢿⣿⣻⣿⣿⣿⣟⣿⡿⣿⣟⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣟⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣿⢿⣿⢿⣿⣿⣿⡿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣾⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠰⡦⠐⠗⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣤⠀⢶⠄⠺⠂⡙⠃⣀⠀⠀⠙⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⡀⢠⣌⢠⡦⠐⠷⠈⠋⢀⡉⠀⢀⣴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢘⠃⣨⡁⣤⡄⠲⠆⠘⠃⠈⢁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⠀⠀⠛⢀⣉⢠⣤⠀⠶⠀⠛⢀⣴⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠈⠉⣠⡄⠴⠆⢀⣴⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⡿⠿⠋





⣿⣶⣶⣾⣶⡷⣾⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⢷⡶⠶⠶⠶⠿⣿⣿⢶⠿⠷⠾⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢀⡤⠖⢒⢲⡶⠶⠶⢮⡒⠓⠒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠩⢹⠓⠒⠒⠲⡄⠀⠉⠉⣦
⠀⢸⡇⡀⠀⢸⣄⣀⡀⣠⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠸⠤⠤⣄⡴⠃⠀⠀⢀⡇
⠀⠀⠙⠒⠒⠒⠒⠿⠿⠭⠤⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⠒⠒⠒⠉
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢠⡏⠁⠐⢰⠛⠛⠛⠓⡆⠀⠀⠈⣷⠀⠀⣸⠉⠀⠀⢰⠒⠒⠒⢲⡀⠀⠀⢹
⠀⠸⢧⣀⣀⣘⡲⠤⠤⠴⠃⠁⠀⣠⠇⠀⠀⣇⠀⠀⠀⠸⠤⠤⠤⣼⣃⣀⣤⠼
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⢛⠿⠛⠻⢿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠚⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣋⠁⡈⠁⠐⠂⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠚⣫⡅⠀⠀⡄⠀⠁⠀⠐⠀⢀⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢛⣫⡵⠞⡋⢡⠘⣦⠀⠀⠀⠛⠀⠰⠀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⣩⡴⠞⠋⢡⡆⢤⢹⣾⠀⠈⢷⡀⠘⠃⠠⠄⠀⠉⠀⣠⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⣉⡤⠞⢋⣡⡀⢹⣄⠈⢧⠈⣧⠻⡝⠒⣀⣿⡆⠀⢀⣠⡤⠖⠋⠋
⠀⠀⠀⢠⣀⣤⠶⠛⠩⡄⢀⡈⢧⠀⠘⣌⠀⢻⡻⠎⢧⡈⠛⣋⣤⠶⠛⢁⣠⡴⠞⠋⠁
⠀⠀⠐⡟⠉⠀⠦⠀⣀⠀⠀⠀⠘⣧⠀⠙⣆⠈⠇⣀⣤⠶⠛⢉⣠⡴⠞⠋⠁
⠀⠀⠀⣧⠀⠦⠀⡤⠀⠀⠉⠀⠴⠘⣆⣀⣬⠶⠛⢉⣠⡴⠞⠋⠁
⠀⠀⠀⢹⡄⠀⢤⠀⠀⠉⠀⠖⠀⠀⠛⢉⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠹⣦⡀⠀⠈⠁⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠳⣦⣴⡞⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣾⣶⡄⡀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠙⢿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡹⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣋⣠⣼⣄⣠⣤⠶⠶⠴⢿⣶⣤⣤⣤⡤⠿⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠛⠛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠿⣷⡾⣷⣶⣶⣶⡶⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⡙⠁⢠⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠰⣴⡟⠀⣀⣤⣄⣠⣤⣤⣠⣤⣾⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⣶⣤⣤⣴⣠⣼⣤⣴⣦⣬⡷⡾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⡄⠀⠈⠑⠦⣀⠀⠀⠀⠀⣠⠞⠀⢠⡄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠓⢦⣀⡴⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠳⢄⡶⠀⠀⠀⠀⠈⠀⠀⢠⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠃⠀⠀⠀⠙⠦⣄⠲⠀⠀⠀⠀⠈⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⣤⠀⠀⠀⣠⠖⠦⣄⠀⠈⠑⢦⣀⠶⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠑⠦⣀⠀⠈⠓⢤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠈⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠈⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠷⢄⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⣄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣀⠙⠲⣄⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⣀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠁⠀⠀⠀⠙⢦⣀⠀⠙⠢⣄⠀⣀⠞⠁⠀⠓⠀⠀⠀⠀⠉⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⠀⠀⠀⠀⠀⠛⠀⠀⠈⠳⢤⡀⠀⠉⠁⠀⡄⠀⠀⠀⠀⠖⠀⠀⠀⠀⠚⠂⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⣠⠟⠳⢤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡴⠃⠀⠀⠀⠈⠳⢤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠈⠁⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⠆⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⡀⠑⢄⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡀⠈⠀⠀⠈⠀⠀⡱⢊⠀⠀⠁⠀⠀⠁⢀⠀⠀⢀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠠⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠙⢦⡀⠀⠀⠀⠀⠀⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠁⠀⠀⡠⠊⣠⠞⠀⠀⠀⠀⠙⢦⡀⠀⠈⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡤⠊⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⠟⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⡞⠁⠀⠀⠀⠀⠀⠀⢀⡴⢃⠔⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠄⠀⠙⢦⡀⠀⠀⠀⢀⡴⢋⡴⠁⠀⠀⠠⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠀⠂⠀⠐⠀⠀⠙⢦⣀⡴⢋⡴⠋⠀⠀⠀⠂⠀⠀⠀⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠄⠀⠀⠄⠀⠀⠀⢉⠔⠻⣄⠀⠀⠈⠠⠀⠀⠠⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠐⠀⡀⠐⣠⠞⠁⠀⠀⠈⠳⣄⠂⢀⠀⠂⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠀⠈⠉⠉⠁⠀⠒⠤⣀
⠀⣀⠄⠊⠡⠀⠀⢀⠀⠐⠀⠭⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⢀⡀⠀⢨⡀⠀⢀⠀⠀⡄⠑⣄
⡌⠀⢈⠀⠀⠄⠠⠄⠀⢉⠀⠈⣁⠀⠐⢉⠰⠄⠄⡀⠀⢀⠠⢖⡁⠒⠀⡉⠀⠀⡄⠀⠠⠄⠀⠠⠄⠀⢠⣀⡜
⠑⢤⡈⠀⠈⢁⠀⠒⠀⠠⠄⠀⡀⠀⠀⢀⡠⠐⠈⠉⠍⠁⠀⠀⠈⠓⠦⣄⠀⠀⡄⠀⠠⠄⠀⠀⢄⠀⣠⠞
⠀⠀⠈⠑⠪⣀⢄⠈⢁⡤⢖⡉⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠉⠀⠀⠀⠠⠀⠀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠑⢦⣀⠙⡒⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠤⣒⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡼⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⢁⡥⠶⠛⠻⢃⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠒⢡⠀⠘⠢⠦⡀⠀⠀⢀⠈⠱⠉⣠⠔⠉⢀⡡⠞⠉⠀⠀⠀⠀⠊⠀⠌⠒⠠⣀
⠀⠀⠀⠀⡠⠔⠤⠀⠀⠤⠀⠠⠄⠈⠘⢓⠄⠀⠀⠰⠘⢀⣤⠖⠉⠀⠀⠀⢀⣀⣔⡋⠁⣀⡀⠈⢁⠀⠁⢢⣄⡀
⠀⡠⠔⡌⠀⠤⠀⠀⠰⠀⠀⠐⠂⠀⠒⠀⠀⠒⠂⠔⣰⣋⠩⠗⠬⠑⠀⠀⡿⠉⣉⡀⠀⣉⡀⠀⢉⡁⠀⠛⠃⠉⠓⠦⣄⡀
⠎⠀⠠⠀⠀⠦⠀⠀⠆⠀⠀⠃⠀⢀⠃⠀⠈⣄⡤⠚⠁⠈⠙⠢⢌⡀⠀⠀⢤⠀⢨⡀⠀⠈⣁⠀⠈⠉⠀⠀⠛⠃⠀⠛⠂⠙⢦
⠠⡀⠤⠀⠀⠤⢀⠒⠂⢀⡘⠀⠀⡉⢀⡨⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠄⠀⠀⣀⠀⠉⠀⠀⠈⠃⠀⠀⠋⠀⡀⠓⠀⢼
⠀⠉⠢⢄⡐⠀⠀⢻⡊⠀⠙⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⡀⠀⠉⠁⡀⢀⣆⣀⣐⣾⣃⠠⣠⠊
⠀⠀⠀⠀⠈⠉⠒⠒⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣀⠨⡛⠡⠀⠲⠶⠌⢀⡤⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣻⣿⣽⣿⣟⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣽⣿⣻⣿⣯⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣟⣿⣿⢿⣿⣛⣿⡿⣿⣟⣻⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣟⣿⡿⣿⣿⣻⣿⠿⣿⣟⣿⡿⢿⣿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⢾⣿⣿⣿⡷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⣿⣾⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣽⣿⣾⣿⣯⣿⣷⣿⣿⣽⣿⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣽⣿⣯⣿⣿⣿⣿⣾⣿⣽⣿⣷⣿⣯⣿⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣿⣿⣯⣿⣟⣿⣯⣽⣿⣻⣿⣽⣿⣯⢟⣥⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⢟⣽⣿⣿⣟⣿⣯⣿⣟⣻⣿⣽⣿⣻⢿⣿⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⣻⣿⢿⣿⣟⣿⡿⣿⣟⣿⣿⣻⣿⣙⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣟⣿⣿⣿⣿⣻⣿⠿⣿⣟⣿⡿⣿⣟⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⡿⣿⣟⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢾⣿⣿⣿⡷⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣷⣿⣿⣽⣿⣾⣿⣯⣿⣷⣿⣿⣽⣿⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣻⣿⣽⣿⣟⣿⣯⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣽⣿⣿⣿⣏⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠛⣷⣾⠛⣦⡀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣦⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣹⣿⣏⣹⣿⣟⢻⣦⡀⠀⠀⢀⣴⠛⣷⣾⠛⣿⣿⡛⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣿⣿⣍⣿⣿⠿⠿⢆⣴⠟⢿⣿⣏⣹⣿⣏⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⠟⠁⢀⣴⠟⠁⠀⠀⠙⢿⣿⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢂⣴⠟⠁⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣴⠟⢱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣿⣦⡀⠀⠀⢀⣴⠟⠁⣠⣾⣿⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣿⣿⣋⣿⣿⣦⣶⠟⠱⣦⣾⣿⣏⣹⣿⣏⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣹⣿⣏⣹⣿⣯⣼⠟⠁⠀⠀⠈⢻⣤⡿⢿⣤⡿⢿⣍⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣤⡿⢿⣤⠟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣾⠟⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁


⣾⡾⠛⠛⢶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣀⠀⠀⠙⠳⣦⡀⠀⠀⣠⣴⠟⠁⠀⠀⡄⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⣦⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⡀⠀⠀⡄⠀⠀⠰⠄⣠⡾⠋⠀⠀⠀⠰⠀⠀⠀⠶⠀⠀⠠⠄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠈⠀⠀⠀⠀⠀⠀⣠⡾⠋⣀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠰⠆⣠⡾⠋⣠⡾⠋⠁⠀⠀⠉⠻⣦⡀⠀⠘⠁⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢀⡴⠋⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠏⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣴⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣰⠟⠁⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠦⠀⠘⢷⣄⠀⠀⠀⠀⣠⡾⠋⣠⠞⠁⠐⠃⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⡶⠞⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⣀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⠃⠀⠀⠘⠀⠀⠀⠆⠀⠀⠀⣠⠾⠋⠀⠚⠀⠀⠈⠁⠀⠀⠉⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠞⠙⢷⣄⠀⠀⠀⠀⢀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠈⠁⠀⣀⡴⠛⠁⠀⠀⠀⠙⢷⣄⣀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠉⠻⣦⡀⠀⠀⢀⡞⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠂⠀⠀⠈⠻⣦⠀⠘⣆⠀⠀⠘⣄⣠⠴⠲⣆⠀⠀⢀⣤⠞⠋⠉⠈⠙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⠀⠀⠀⠀⠀⠤⠀⠙⢷⡄⠘⣆⠀⠀⠀⠀⠀⠀⣿⣤⡶⠋⠁⠀⢀⡀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠋⠀⠀⠀⣀⠈⢻⣦⡿⠀⠀⠀⣀⣤⡾⠛⠁⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠈⠀⠀⠀⠆⠀⠀⡀⠀⠹⣷⣠⣴⠾⠋⠁⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣦⠀⠃⠀⠀⡄⠀⠁⣠⡴⠟⠋⠀⣀⡀⠀⠀⢀⠀⠀⠄⠀⠀⠠⠀⠀⠀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⡞⠻⡇⠀⠀⠀⣇⠀⠀⠙⢷⡀⠈⠀⣀⡴⠞⠉⠀⠀⣰⠞⠉⠙⠢⡀⠀⠂⠀⠐⠂⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⢀⡼⠂⠀⠀⢈⣿⡶⠛⠁⠀⠀⣠⠴⠋⠁⠀⠀⡀⠀⢹⠀⠀⠂⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⣴⡾⠟⠁⠀⠀⠀⠀⡞⠁⢆⡀⠀⠀⠀⠉⢀⡼⠀⠀⢀⣠⡾⠋⢷⣀⡠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠁⠀⠀⠳⡄⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⣿⡁⠀⠀⠀⠀⠀⣀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⢀⠀⠈⠀⠀⠁⣀⠀⠘⠳⣤⡤⠞⠁⠀⣠⣶⠿⠛⠉⢿⣄⠀⠀⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢠⠀⠀⠀⠀⢀⣤⠞⠋⡀⠀⠂⠀⠀⠹⣧⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⠀⠀⠀⠈⡀⠀⠈⠀⠀⠀⠀⠀⣠⣴⡟⠁⠒⠀⠀⠀⡀⠀⠉⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠁⠄⠀⢁⠀⠀⠁⠀⢀⣴⡟⠉⠈⠻⣦⠀⠀⠂⠀⠀⠀⢠⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⡗⠀⠀⣀⣈⣷⣤⡀⠀⠘⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣤⣴⡶⠟⠋⠀⠀⠰⣇⢀⡴⠋⠉⠁⠈⠻⢶⣤⣤⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⡀⠀⠀⠀⠀⢰⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠹⡆⠀⠀⠀⠈⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠀⠐⠀⢈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⡁⠀⠂⠀⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡀⠐⠀⠈⠀⠠⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠄⠀⠁⠀⠂⢀⡀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠂⢀⡀⠐⠀⠈⠀⠠⠀⠈⠀⠀⣈⣑⠢⣄⣠⠔⣊⣁⠀⠀⠉⠀⠄⠀⠁⠀⠂⢀⡀⠐⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠂⠀⡀⠀⠂⠈⠀⠠⠀⠈⠀⡴⣁⡤⢛⡭⠖⠉⠀⠈⢦⠀⠁⠀⠄⠀⠁⠐⠀⢀⠀⠐⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠆⠈⠁⠠⢄⣠⠜⣫⠵⠊⠁⠀⠀⠀⠀⠀⠈⢣⡀⠠⠄⠈⠁⠰⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡥⠖⠉⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢜⡠⠔⢋⠉⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⡀⠀⠂⢀⡀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣀⠤⣚⢭⠖⠉⠀⠀⢀⡀⠐⠀⢀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠄⠀⠁⠐⠂⢀⠀⠘⠀⠠⠀⠱⣄⢀⡠⢔⣫⢵⡋⣡⠎⠀⠄⠀⠃⠀⡀⠐⠂⠈⠀⠠⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠄⢀⠀⠐⠀⢀⠀⠐⠀⠠⠀⠀⣈⡭⠒⠉⠉⠒⢭⣁⠀⠀⠄⠀⠂⠀⡀⠀⠂⠀⡀⠠⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢈⠀⠐⠀⢀⠀⠐⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠂⠀⡀⠀⠂⠀⡁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠈⠀⠐⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠂⠀⠁⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠁





⠀⠀⡀⠀⢀⠀⡀
⣿⣏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⡍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠰⠂⠀⠉⠳⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠠⡀⠀⣀⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⠴⠋⠄⠀⠀⠆⠀⠘⠀⠈⢳
⠀⠀⠀⠀⣸⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠙⠦⣀⠀⢀⠔⢋⠀⢀⡄⠀⢠⠄⠀⢠⠀⢀⠈⡇
⠀⠀⠀⠀⣿⠈⡀⠰⠀⠀⠉⠀⠀⠉⠀⠀⡠⠤⣈⠙⠧⣀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⠁
⠀⠀⠀⠀⠙⢦⣀⠀⠤⠀⠠⠄⠀⠂⠀⠔⠁⠀⠀⠑⠠⡈⠙⢦⡈⠁⠀⠀⠁⠀⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⣀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠑⢄⠉⠢⣀⠰⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠧⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠉⢂⠈⠳⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡶⢄⡑⠤⡀⠀⡀⠀⠀⠀⠀⡠⠂⠀⠲⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠚⠀⠈⠂⢍⠲⣌⠲⢄⠀⢀⠀⡐⠁⢀⡀⠀⠤⠀⠰⠌⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⢡⡄⠀⠰⠀⠀⡤⠀⠑⢌⢙⠦⡑⠢⠜⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢤⠹⡆
⠀⠀⠀⠀⠀⣾⢡⠀⢀⠀⠀⣀⠀⠀⣀⠀⢀⠀⢁⡴⠛⠳⣄⠒⠀⠐⠂⠀⠈⠁⠀⠈⠀⠀⢰⠇
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠁⠀⠀⠁⠀⢀⡴⠋⠀⠀⠀⠈⠓⢦⡀⠠⠄⠀⠰⠀⠀⠓⢀⡞
⠀⠀⠀⠀⠀⠀⠳⣔⠘⠁⠀⠚⠀⠈⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠰⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⢀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⠀⠈⠀⡀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⢀⠀⠉⠀⡀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢠⠀⠀⠀⡄⠀⠀⠠⠀⠈⠳⣄⣠⠞⠁⠀⠄⠀⠀⢠⠀⠀⠀⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⣠⠞⢁⣄⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠂⠀⠀⠐⠂⠀⠀⠀⣠⠞⢁⡴⠋⠈⠳⣄⠀⠀⠀⠀⠂⠀⠀⠐⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠁⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠐⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠄⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠠⠀⠈⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠐⠀⠀⠀⠂⠀⠀⠙⢦⡀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠐⠀⠀⠀⠂⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠁⠀⡀⠘⠀⠀⠀⠃⠀⠀⠙⠋⣠⣾⡁⠀⠀⠀⠘⠀⠀⠀⠃⢀⠀⠈⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠁⢀⡀⠈⠀⢀⠀⢁⣠⠞⠁⠈⠙⢦⡈⠀⡀⠀⠁⢀⡀⠈⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠠⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢰⣶⡆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠸⢿⠇⠈⠳⣄
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⡀⠈⢉⡁⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣤⡀⣴⣦⠀⣴⣶⡌⠳⣄
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠘⠿⠟⠀⢿⡿⠀⣿⡿⠀⠈⠻⣦⡀⠀⣠⠞⠁⠀⠀⠙⠛⠁⢙⡋⠀⢈⡉⠀⣠⣍⠳⣄
⠀⠀⠀⠘⣧⡀⠀⣿⣷⠀⣴⣦⠀⣴⣦⡀⢠⣤⡀⢀⣤⡈⠻⣾⡁⢠⣶⣦⢰⣿⡇⠀⢿⡿⠀⢿⡿⠀⠻⠟⠁⣹⠆
⠀⠀⠀⠀⠈⠻⣦⡈⠀⠀⢙⣋⠀⠙⠋⠀⠘⠛⠃⠙⠿⠃⢀⣈⡻⣦⡉⠁⢀⣬⡀⢀⣤⡄⢠⣶⣦⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠻⠿⠃⢸⣿⡆⢰⣿⡇⠀⢀⡴⠋⠉⠙⢾⡻⣦⡘⠿⠃⠘⠛⠃⠀⠙⠉⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⣤⣄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢮⡻⣦⡀⢼⣿⡆⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠛⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣻⣦⡀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠻⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣬⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠛⠛⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣿⣿⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⣶⣦⠀⣿⣷⠀⢿⡿⠈⠻⣿⣷⣄⠀⠀⢀⣴⠟⠁⣴⢦⡀⣠⣶⡄⢀⣤⡈⠻⣦⡀
⠀⠀⠀⠀⣠⠞⠁⡀⠀⢀⣉⡁⢀⣤⡀⠀⣤⣄⢠⡶⣮⠻⣿⡷⠶⠟⢁⣀⠀⠙⣛⠀⠘⠛⠁⠸⠿⠃⠀⠈⠻⣦⡀
⠀⠀⠀⣾⠁⠀⢾⣿⠇⠘⠿⠇⠘⠿⠃⠀⠛⠛⠈⠙⠉⣠⡾⠻⣦⡀⠺⠿⠇⢺⣿⠇⢰⣿⡇⢰⣿⡷⢀⡶⣦⠈⣷
⠀⠀⠀⠙⢷⣄⠀⠀⠀⣴⣶⡀⢰⣶⡆⢼⣿⡆⠀⣠⡾⠋⠀⠀⠈⠻⣦⡀⠀⢀⣤⣄⢀⣭⣄⠀⣈⣀⠀⠙⣩⠞⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⠋⠀⣀⣉⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠛⠋⠘⠻⠋⠀⠿⠿⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠿⠿⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣶⣷⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠀⡀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠑⢦⠁⣀⠀⠀⠀⠃⠠⠀⠐⠸⡄
⠀⠀⠀⠀⠀⡀⠀⠄⠀⠈⠁⠀⠀⠀⠀⢀⠀⠤⠀⠐⢀⡀⠀⠀⠘⣆⡀⠀⠀⠈⠀⠀⠀⠂⠀⢣
⠀⠀⠀⡤⠈⠀⠀⠀⠀⢀⡀⠠⠀⠀⠁⡀⠀⠄⠈⠀⡀⠀⠂⠀⠁⠸⡀⠀⠀⠁⠀⠀⠐⠀⢀⣼
⠀⠀⢘⠀⠀⠠⠀⠈⠀⡀⠀⠄⠀⠠⠠⠀⠐⠀⡈⠀⠄⠐⠀⠀⠀⠀⢁⠀⠀⠁⠀⠀⠀⢀⡼⠏
⠀⠀⠘⡆⠀⠄⠀⠃⢀⠀⠀⠂⠈⠁⠀⠀⠂⠀⠀⢀⠀⠐⠀⢈⣀⠴⠃⠀⢀⣀⠤⠔⠚⠉
⠀⠀⠀⢃⠠⠀⠐⠀⡀⠀⠐⠀⠈⠀⣀⠀⠀⢈⣀⠤⠴⠚⢉⣀⠤⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠤⠔⠚⠉⠁
⠀⠀⠀⠀⠐⢄⠀⠈⠀⠀⢀⡀⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠊⠉




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢈⠃⡍⠠⠄⠀⠙⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡁⢀⡋⣬⠰⠆⠒⣘⠃⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢠⡍⠤⠰⠆⡛⣈⠁⢈⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠆⣘⢠⡁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⡠⠒⠒⠒⢄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⢄⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠑⢄⠀⠀⣠⠞⠁⠀⠀⠀⠈⡆
⠀⠀⠀⢸⠀⣀⣀⣀⡀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢦⡀⠀⠀⠀⠀⠀⡑⢞⠁⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⢸⢸⠀⠀⠀⡇⡇⠀⡔⠉⠀⠈⠑⢄⠀⡠⠊⠀⠈⠑⢄⠙⢦⡀⠀⡠⠊⠈⠳⢕⢄⠀⠀⡠⠊
⠀⠀⠀⢸⢨⠪⣉⠕⡇⡇⠘⡀⠀⠀⠀⠀⠀⡙⢄⠀⠀⠀⠀⢸⠀⠀⣹⢮⡢⡐⢍⣪⠎⠱⡕⢎
⠀⠀⠀⢸⢸⠀⠀⠀⡇⡇⠀⠙⢆⡀⠀⡠⣊⣈⡳⡕⢄⢀⠔⠁⣠⠞⠁⠀⠙⢮⡢⡀⢀⠔⠁⠀⠑⢄
⠀⠀⠀⢸⠀⠉⠉⠉⠁⡇⠀⠀⠀⠙⢌⡢⡑⠤⢃⢜⠜⠁⢀⠞⠁⠀⠀⠀⠀⠀⡹⢮⡁⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢮⣒⠕⠁⠀⠀⠘⡀⠀⠀⠀⠀⡠⠊⠀⠀⠙⢦⡀⠀⠀⠀⢀⠇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⠤⠔⠊⠀⠀⠀⠀⠀⠀⠉⠢⠤⠔⠋
⠀⠀⠀⠀⠑⠤⠤⠤⠊

⠀⠀⠀⠀⡠⠒⠒⠒⢄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⢄⠀⠀⠀⠀⠀⠀⣠⠔⠒⠢⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠑⢄⠀⠀⣠⠞⠁⠀⠀⠀⠈⡆
⠀⠀⠀⢸⢀⣀⣀⣀⡀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢦⡀⠀⠀⠀⠀⠀⡑⢞⠁⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⢸⢸⠀⠀⠀⡇⡇⠀⡔⠉⠀⠈⠑⢄⠀⡠⠊⠀⠈⠑⢄⠙⢦⡀⠀⡠⠊⠈⠳⢕⢄⠀⠀⡠⠊
⠀⠀⠀⢸⢸⠪⣉⠕⡇⡇⠸⡀⠀⠀⠀⠀⠀⡙⢄⠀⠀⠀⠀⢸⠀⠀⣹⢮⡢⡐⢍⣪⠆⠱⡕⢎
⠀⠀⠀⢸⢸⠀⠀⠀⡇⡇⠀⠙⢦⡀⠀⡠⣊⣈⡣⡕⢄⢀⠔⠁⣠⠞⠁⠀⠙⢮⡢⡀⢀⠔⠁⠀⠑⢄
⠀⠀⠀⢸⠀⠉⠉⠉⠁⡇⠀⠀⠀⠙⢎⡢⡑⠤⢃⢜⠜⠁⢀⠞⠁⠀⠀⠀⠀⠀⡹⢮⡁⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢮⣒⠕⠁⠀⠀⠘⡄⠀⠀⠀⠀⡠⠊⠀⠀⠙⢦⡀⠀⠀⠀⢀⠇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⠤⠔⠊⠀⠀⠀⠀⠀⠀⠙⠢⠤⠔⠋
⠀⠀⠀⠀⠑⠤⠤⠤⠊

⠀⠀⠀⠀⢀⠔⠂⠐⠒⢄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⠢⡴⠋⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⡇⠊⠉⠉⠉⡆⡇⠀⢀⠔⠒⠒⠢⡀⠀⠀⢀⠔⠒⠒⠢⡀⠑⢄⠀⠀⠀⢀⠔⠑⢌⠢⡀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⡇⢢⠤⠤⡄⡇⡇⢠⠃⠀⠀⠀⠀⠈⠢⡔⠁⠀⠀⠀⠀⠘⡄⠀⠑⢄⢰⡁⢀⠤⡤⡕⢌⠢⣠⠞⠁
⠀⠀⠀⠀⡇⠀⠑⠊⠀⡇⡇⠈⢧⡀⠀⠀⠀⢀⠴⠪⡢⡀⠀⠀⢀⡴⠀⢀⡴⠊⠑⢝⢦⡑⠞⠁⢀⡕⠈⠢⡀
⠀⠀⠀⠀⡇⢄⣀⣀⡠⠇⡇⠀⠀⠙⢦⡀⡴⢣⠢⠔⡌⢪⢢⡴⠋⢀⡴⠊⠀⠀⠀⠀⠑⢝⠦⠔⠋⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢮⡢⡑⢊⢔⡵⠋⠀⠀⡎⠀⠀⠀⠀⠀⠀⣠⠞⠑⢄⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢮⡵⠊⠀⠀⠀⠀⢇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊
⠀⠀⠀⠀⠈⠢⠤⠤⠔⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⠀⠐⠗⠀⢀⠀⠀⠾⠀⢀⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢦⡀⠀⠶⠀⠀⠀⠀⠾⠂⠀⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠛⠀⢀⣄⠀⠘⠃⠀⣤⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠀⠘⠋⠀⣠⡀⠀⠛⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⣴⠀⠀⠁⠀⢰⡆⠀⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⢠⡆⠀⠈⠀⠀⡦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣀⠀⠐⠗⠀⢀⡀⠀⠿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠟⠀⢀⡀⠀⠺⠂⠀⣀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⠀⢀⣄⠀⠘⠁⠀⣤⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠃⠀⣤⠀⠈⠃⠀⣠⡀⠀⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣥⣤⣤⣤⣤⣬⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠻⣿⣿⣿⣿⠛⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⠛⣿⣿⣿⣿⠟⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣉⣿⣿⣿⣿⣏⣹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⣹⣿⣿⣿⣿⣉⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣤⣿⡿⢿⣿⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⡿⢿⣿⣤⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⠛⣿⣷⣾⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣷⣾⣿⠛⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣉⣿⣿⣿⣿⣏⣹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣹⣿⣿⣿⣿⣉⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣴⣿⣿⣿⣿⣤⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣤⣿⣿⣿⣿⣦⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⡛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠀⠈⠛⠀⢠⡀⠀⠛⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠛⠀⢀⡄⠀⠙⠁⠀⣄⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠀⠠⡦⠀⠈⠁⠀⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⠀⠈⠁⠀⢴⠄⠀⠉⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠀⠀⡀⠀⠸⠇⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠸⠇⠀⢀⠀⠀⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣤⠀⠈⠋⠀⣠⡄⠀⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠀⢠⡄⠀⠙⠁⢀⣤⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡈⠀⠠⡦⠀⠈⠀⠀⠶⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⡶⠀⠀⠁⠀⢶⠄⠀⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋


⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⣅⠈⠉⢫⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡭⡿⣦⠟⠂⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢴⡚⠳⣦⠀⠠⡈⠳⣄⡀⣀⡠⠞⠻⠋⠀⣴⣡⣽⣄⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⣀⠀⠈⢳⡄⠈⢳⣦⠘⢦⣄⣉⣉⡷⠀⠀⢠⣾⣿⣿⣫⣞⣟⣿⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣟⠳⣄⠀⠹⣆⠀⠙⣧⠈⢳⡀⠉⠉⠛⢦⠈⠹⠟⣛⣻⣭⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⡘⢧⣌⣳⣄⠈⠷⠴⠚⠃⡀⠙⠛⠓⢲⡤⣷⠶⠶⢮⣹⠋⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣄⣈⡉⢉⣀⡀⠐⢿⠉⠹⣆⠘⢿⠲⣍⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠻⠟⠛⠿⠋⠁⢙⢦⡈⠳⣄⠘⢷⡌⢣⡈⢳⡈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠳⣶⣤⡶⡻⠋⠀⠹⣕⠈⢧⡈⢻⣆⠙⢮⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⢹⢤⢧⡀⠀⠀⠈⢳⡀⠙⢦⡹⣇⠈⠁⢰⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⢀⣠⠼⠒⠛⠛⠛⣲⡶⠤⠽⠆⠈⠳⠛⠀⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⢽⡗⢐⣔⡕⠋⠉⢷⠲⣆⠀⠀⢿⡻⣄⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠲⣿⠃⠉⠁⠀⠀⣼⠀⢹⡀⠀⠬⣷⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠠⢄⣀⣀⣀⣠⣖⣥⠞⠁⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⢷⣄⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣹⠁⠀⠀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠀⠀⠻⣿⣿⠇⢷⡄⠀⠺⢷⣦⣄⡈⠡⠋⢀⠔⡥⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⠗⠁⠀⠈⢙⠀⢀⢀⣀⣼⣔⣠⣶⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠠⢀⠂⠀⣿⠞⠉⠉⠉⠁⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠠⠃⠀⠀⡼⠉⠀⠀⠀⢀⡠⠐⠒⠢⢄⣸⠇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠈⠢⣤⣶⠏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣔⠀⠀⠀⣶⣤⣄⡀⠀⠀⠁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡶⠃⠀⠀⣰⣿⠃⠀⠀⠀⢾⡄⠀⠀⠹⣿⡿⠿⣿⣷⣴⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⣰⣾⠋⠉⠞⠀⠀⢀⠀⠈⢙⠀⠀⠀⣿⡿⠟⠾⣧⡉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡀⢸⣀⠂⣄⠀⠀⠀⠀⢠⠁⠀⠀⠀⣿⢿⣆⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⡼⠁⣼⡇⠨⡍⠀⠀⠀⠀⢀⠄⠀⠀⠀⣿⠈⢳⣄⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡾⠛⣱⡾⠻⢇⣨⠅⠀⠀⠀⠀⢸⠀⠀⠀⠀⢙⣦⠀⠹⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣴⣏⠀⢰⠀⡺⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⡿⠨⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠑⠘⡀⠐⠅⠀⠀⠀⠁⠀⠃⠀⠀⢀⣼⠃⣽⠂⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡅⠀⠂⠀⠀⠀⠀⢸⠀⠑⠀⡜⡄⠨⣃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠁⠀⠉⠀⠐⣸⠃⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⠀⠁⠸⠁⠀⢠⣿⠀⠀⡌⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠂⠀⢀⣼⡇⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠒⠿⠿⡤⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠒⠚⠛⠒⠒⠒⠒⠒⢒⡒⠒⠒⠒⠒⡆⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠎⠉⠙⠞⠉⠙⡆⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠳⢄⡀⠀⣠⠞⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣈⣋⣀⣀⣀⣀⣀⣀⡼⠀⠀⠰⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⢤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠾⠋







⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠉⠉⠉⠉⢉⡭⠭⠭⣭⣭⠭⠭⠭⠭⢭⡉⠉⠉⠉⠉⠉⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠠⠀⠀⠄⠈⠀⢸⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⡇⠀⠁⠠⠀⠀⠄⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠈⠁⠤⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠁⠠⠈⠁⠄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠁⠀⠈⠀⠘⠲⠶⠶⠶⠶⠶⠶⠶⠶⠖⠃⠀⠁⠀⠈⠁⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⡤⠤⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⢀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⡀⠂⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠄⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠉⠉⠀⠀⠀⠀⠈⠉⠉⠛⠛⢶⣄⡀
⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢻⣄
⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣀⠀⠀⣼⠁⠀⢻⡆
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⣠⡶⠀⠘⣿⠏⢹⡇⠀⠻⠀⠀⢸⡇
⢸⡇⠀⢀⣴⢶⣄⢰⡆⠀⢸⡇⠻⣶⡶⠄⠛⠀⠈⠉⠰⠆⠀⠀⢸⣇⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⢸⡇⠀⢸⣇⢀⣹⡇⠻⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣁⣸⡿⢶⡆⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠟⠛⠛⠛⠛⠛⠶⢦⣤⣀
⠀⢷⡀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠈⠙⠙⠷⢿⡟⢳⣤⡴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠏⠀⣀⣠⣤⡶⠾⠛⠙⢿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠈⣿
⠀⠀⠀⠈⠳⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠟⠉⠀⢀⡿⢫⣅⠀⠀⠀⠀⠀⠀⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠉⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠾⠛⠋⠉⠀⠀⣀⣤⣴⠾⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣀⠀⠈⠙⠷⢦⣤⣤⣤⣤⣤⣴⠶⠶⠛⠛⠉⠉⠀⣀⣀⣤⣴⠾⠛⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣍⡁⠀⠈⠙⠶⢦⣤⡴⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢷⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣈⠁⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠟⠁⠀⠀⠀⢻⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣙⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢉⠻⣇⠀⠀⠀⠀⠀⣾⠇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠙⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡾⠋⢁⠀⠂⠈⣀⢻⡄⠀⠀⢀⡾⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢦⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡆⠆⠈⢀⠰⠆⠈⠀⢻⣄⣴⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣄⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠾⠉⢿⡀⠶⠈⢀⠀⠆⠉⢀⣿⠁⠀⠀⠀⠀⠀⣿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡉⠀⠀⠀⠀⠀⣿⠀⢠⡾⠁⠀⠀⠘⣷⡀⠶⠈⠁⣠⡶⠟⠋⠀⠀⠀⠀⠀⢸⡟⠐⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⡙⠃⠀⠀⠀⠀⣿⠀⣾⡁⠀⠀⠀⠀⣨⣷⣤⣴⠾⠋⠀⠀⠀⠀⣠⠄⣴⠛⢸⡇⠰⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⡙⠃⠀⠀⠀⠀⢹⡄⠘⣧⠀⠀⣠⡾⠋⠀⠉⠀⠀⣤⡀⣼⠻⠄⣿⠖⢈⣹⢜⡇⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣙⠷⠀⠀⠀⠀⢸⡇⠀⠈⠻⠛⠋⣠⠠⣔⣿⢲⣤⣿⣷⢻⢘⡧⠿⠚⠂⠉⣸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣝⠛⠀⠀⠀⠀⢸⡇⣶⢻⡆⣿⣧⢹⣷⣿⣿⡼⠿⠃⠘⠉⠋⢁⣠⣤⣶⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡋⠻⣯⡛⠀⠀⠀⠀⢸⡇⢻⢻⡇⡟⠹⠞⠊⠋⠈⢀⣠⣤⡴⢶⣾⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣙⣶⣌⠻⣦⡀⠀⠀⠈⠁⠘⠛⠀⢀⣀⣤⡴⠶⢛⣋⣭⡴⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⣛⣻⣮⡙⢶⣤⣤⣤⡴⠶⢛⣛⣭⡴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢩⣭⠴⠟⢷⣤⣤⠶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠰⡷⠀⠀⠸⠷⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠸⠟⠀⠀⠸⠗⠀⠀⠺⠗⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⠷⠀⠀⠺⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⠟⠀⠀⠺⠗⠀⠀⠺⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠰⠷⠀⠀⠺⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⠗⠀⠀⠺⠗⠀⠀⠺⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢶⠆⠀⠀⢶⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢶⡆⠀⠀⢶⡆⠀⠀⣶⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢾⠆⠀⠀⢾⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⡆⠀⠀⣴⡆⠀⠀⣶⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢶⡆⠀⠀⣶⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢴⡦⠀⠀⢴⡆⠀⠀⢶⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠺⠗⠀⠀⠾⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⡦⠀⠀⢴⡆⠀⠀⢶⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠾⠇⠀⠀⢾⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢴⡆⠀⠀⢶⡆⠀⠀⢶⡆⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠾⠇⠀⠀⠾⠇⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣶⣶⣶⠾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⢤⠄⠀⠀⠈⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⠀⠀⠛⣀⠘⠃⣀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠈⠳⣄⠀⠉⢠⡄⠉⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣤⡀⠀⠀⠈⠳⣄⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⢠⡀⠀⠀⠈⠳⣤⡀⠀⠀⠉⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠙⢦⡀⠀⠀⠈⠁⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⢠⣄⠛⣠⡀⠀⠙⢦⡀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠶⢀⠰⠆⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠙⠁⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠉⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⣀⠀⠛⠃⠀⠀⣠⣄⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠘⠿⠃⠀⠀⣀⠀⠙⠋⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠈⠻⠃⠀⠀⣠⡀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣠⣶⣷⣦⡀⠀⠀⠀⠀⠀⠸⠿⠀⠀⢀⣀⠈⠛⠁⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣀⣾⣿⠟⠙⢿⣿⣦⡀⠀⠸⠿⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣠⣾⣿⠟⠁⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠻⠗⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⠁⣠⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠟⠁⢀⣴⣿⡿⠋
⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⣶⡆⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⣿⡿⠋
⠀⠀⢠⣿⡿⠃⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⣶⡆⠀⠈⠻⣿⣷⣤⣴⣿⠟⠁⢀⣴⣿⡿⠋
⠀⠀⣾⣿⠃⠀⠀⢠⣤⠀⠉⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁⢀⣴⣿⡿⠋
⠀⠀⣿⣿⠀⠀⠀⠈⠉⠀⠀⢠⣤⡀⠈⠀⠀⠀⣿⠆⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⣿⣿⠀⠀⠀⠀⠀⣠⣄⠈⠉⠀⠀⢰⣶⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⢹⣿⣧⠀⠀⠀⠀⠙⠋⠀⠀⣠⣦⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠉⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣤⠶⠶⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡏
⠀⢠⡿⠁⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣼⠃
⠀⣾⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠉⠻⠶⣤⣤⣴⡟⠀⠀⠀⠰⣿⣼⠇⠀⠀⣤⣶⡄⠀⠀⠀⢠⡿
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⣼⢣⡾⢷⣤⣀⠉⠁⠀⠀⠸⣧⡾⠃⠀⠀⠀⣼⠇
⠀⠘⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣷⣄⡈⠙⠻⠶⣤⣤⣀⣀⣀⣀⡀⠀⢀⣿⡀
⠀⠀⠈⠳⣦⣉⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣸⠇⠈⢷⣌⠛⢶⣤⣄⣀⡈⠉⠉⠉⣉⣻⠆⣼⠏⠻⣦⣄⡀
⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢷⣤⣀⡉⠉⠛⠛⠛⣛⣿⠏⢠⡿⠀⠀⠀⠉⠙⠛⠛⠳⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⢦⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠛⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣸⡟⢷⣤⡀⠀⠀⠛⠁⠀⠀⠀⣤⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⠙⠻⠶⢦⣤⣄⣀⣀⡀⢀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⠀⠀⠀⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠶⢖⠒⢲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡬⡩⢉⢕⡲⣤⡀
⠀⠀⠀⠀⠀⢀⣠⠲⠡⠐⣉⠈⢀⡀⠀⣀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠁⠁⢈⠀⠁⣀⠈⠐⡩⠲⣄
⠀⠀⠀⠀⣰⠎⠒⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⠂⠀⠈⠁⠀⠈⠀⠀⠀⠱⡪⢣⡀
⠀⠀⢀⡼⡢⠁⠀⠈⠁⠀⠛⠀⠘⠃⠀⠛⠀⠘⠃⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⠊⠀⠛⠀⠘⠃⠀⠛⠀⠀⠗⠀⠐⠁⡘⡄
⠀⠀⣜⣫⠐⠦⠀⠰⠂⠀⠶⠀⠰⠆⠀⠶⠀⠀⠆⠀⠰⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⠁⠋⠰⠆⠀⠶⠀⠰⠆⠀⠰⠀⠀⠶⠀⠐⢊⠔⠸
⠀⠀⡇⡂⠀⣤⠀⢠⠀⠀⣤⠀⢠⡄⠀⣤⡀⠀⣄⠀⢠⡀⠀⣤⠙⢦⡀⠀⠀⠀⠀⡠⠊⢠⡀⠀⣄⠀⢠⡄⠀⣤⠀⢠⣄⠀⣤⡀⠀⡄⠀⢘⠕⡪
⠀⠀⠣⡉⠀⡀⠀⢀⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⡀⠀⢀⠀⢀⣀⠀⠀⢉⣦⡀⡠⠊⡀⠀⠈⠁⠀⠀⠀⠈⡀⠀⣀⠀⢀⡁⠀⢀⠀⢀⡀⠀⠰⢊⠔⡰
⠀⠀⠀⠈⠢⡉⠀⠈⠁⠀⠋⠀⠈⠋⠀⠙⠁⠈⠉⠀⠈⠁⠀⠉⡐⠚⢿⡴⠋⠀⠈⠁⠀⠙⠁⠀⠛⠀⠈⠃⠀⠛⠀⠈⠉⠀⠛⠃⠈⠉⠀⡺⡫⠞
⠀⠀⠀⠀⠀⠈⠢⡘⠃⠀⠿⠀⠐⠃⠀⠳⠀⠐⠇⠀⠸⠂⠠⠌⣭⡽⢋⡀⣘⡠⣀⠛⠀⠿⠀⠀⠆⠀⠸⠇⠀⠿⠀⠘⠃⠀⠺⠀⠐⠓⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠶⠀⠠⣤⠀⢤⠄⠰⡆⠀⠠⠄⢡⡴⢊⠔⡡⠀⣤⠙⢮⣡⠆⡀⠀⠠⣦⠀⢠⡄⠀⢦⠀⢠⡄⠀⣤⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢀⡄⠀⣀⠀⠀⠠⠌⢑⡴⢋⠔⠡⢂⡀⠀⢀⠀⢀⠙⢮⠪⡦⡀⠀⠀⢠⡀⠀⣀⠀⢠⡄⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠁⠀⠈⢀⡐⢤⡽⢋⠴⡡⠊⠀⠌⠁⠀⠙⠁⠐⠕⡠⠙⢌⠻⣂⣀⠈⠁⣀⠁⠀⠈⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣒⣶⣷⠏⠔⠁⣀⠈⠛⠀⠐⠗⠀⠺⠂⠀⠷⠀⠑⠀⠕⢎⡸⠂⡨⢔⠗⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⢁⡄⠑⢌⠉⠆⠶⠀⠠⡄⠀⠶⠆⠰⡢⠀⠰⠆⢀⡢⢱⠀⠔⡡⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢡⡀⢀⡁⢀⣌⠳⣌⠲⠷⣀⣤⠀⣀⠀⢀⣄⠀⣠⠢⠑⢠⠞⣠⠪⢴⠂⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⣀⠀⢈⡁⠀⠉⠀⢈⡑⢌⠑⡡⡀⣈⠀⠈⠡⡐⠈⣠⠞⢁⠾⠃⡆⠀⢀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠈⠋⠀⠉⠀⠈⠃⠀⠛⠀⠈⠛⠀⠱⣌⠀⠟⡀⠀⠝⡠⠚⢁⣜⣋⡛⠙⠀⠀⠙⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠶⠀⠰⠆⠀⠶⠀⠘⠇⠀⠻⠂⠰⠶⠀⠶⠈⠳⣄⠀⣠⠎⢀⣼⠛⠋⠁⠀⠸⠇⠀⢶⠆⠘⠿⠀⠾⠎⠳⣄
⠀⠀⠀⠀⠀⡠⠊⢠⡄⠀⣤⠀⢰⡆⠀⣤⡀⢠⣄⠀⣤⠀⠠⣤⠀⢰⡆⠀⠀⠉⢁⡴⡷⣮⠉⢁⣀⡀⢀⣄⢀⣠⡀⢠⣄⠀⣴⡄⠀⣨⣷⣄
⠀⠀⠀⡠⠊⡀⠀⢀⠀⢀⣀⠀⢀⡀⠀⣈⠀⢀⡀⠀⢀⠀⠀⣀⠀⠀⡠⠶⢀⡔⣉⡒⠁⢀⡀⠀⣈⠀⢀⡀⠀⣀⠀⢀⡁⠀⢀⠀⠀⣈⠈⠛⠑⣄
⠀⠀⡎⡠⣪⠆⠀⠈⠁⠀⠉⠀⠀⠁⠀⠉⠀⠈⠁⠀⠙⠀⠀⠉⡠⣪⢖⠕⠁⠈⢢⠈⠀⠘⠁⠀⠉⠀⠈⠁⠀⠉⠀⠈⠋⠀⠙⠁⠀⡉⠀⠀⠈⠠⢳
⠀⠀⣋⢜⡕⡠⠀⠚⠂⠐⠗⠀⠘⠃⠀⠖⠀⠘⠃⠀⠺⠀⠀⠀⣪⠞⠁⠀⠀⠀⠀⠑⢄⠘⠃⠀⠛⠀⠘⠆⠀⠛⠀⠐⠖⠀⠺⠂⠀⠛⠀⠘⠃⠀⠽
⠀⠀⢱⠪⢊⠔⡀⠶⠆⢠⣤⠀⢰⠄⠀⣤⠀⢠⡦⠀⢀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢴⠀⠰⠆⠀⢴⠄⠀⣤⠀⠰⡦⠀⢶⠄⢠⡦⡀⡘
⠀⠀⠀⢳⡡⡾⠋⣀⡀⠀⣁⠀⢀⡄⠀⣤⡀⢀⢔⠴⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣀⠀⣤⡀⢀⣀⠀⣠⡄⠀⣀⠀⠀⠐⡜⠁
⠀⠀⠀⠀⠑⢄⠀⢈⠄⡠⢉⠄⠈⠉⠀⢉⢜⡵⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠀⢈⡀⠀⠁⠀⠀⠀⠀⠉⡐⡤⠋
⠀⠀⠀⠀⠀⠀⠑⠤⡊⠔⠡⢪⢎⠔⡄⠰⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠁⠀⠛⠀⠙⡁⢌⡦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠬⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠦⠵⠝⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠒⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢰⣶⠀⢠⣄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠉⠉⠈⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣴⡆⠀⣀⡀⠈⠋⠀⢰⡷⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⠀⠛⠁⠀⣶⡆⠀⠀⠀⣀⡄⠀⠙⢦⣀⣤⠶⠛⠉⠀⡀⠀⠀⠺⠿⠀⠐⠿⠇⠀⢾⡷⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠘⠛⠀⢠⣶⠀⠀⠀⠀⣠⠞⠁⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣤⣄⠀⢠⣤⡀⠀⣠⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣴⡦⠀⠀⠀⢀⣠⠞⣁⣤⠞⠋⠁⠀⢀⣠⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⠁⠀⠈⠋⠀⠈⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⢀⣴⣯⠴⠛⠉⠀⠀⣀⡴⠚⠉⠀⠘⣆⠀⠀⠀⠀⠀⠘⣆⠀⠀⠰⣿⠆⠀⢾⡷⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⡴⠟⠋⠁⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⠰⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⢧⠀⠀⠘⠛⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⢠⡄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠃⠀⠀⣀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⣠⡀⠀⠀⠹⡄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠹⣆⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⢀⣠⣴⠞⠉⠙⢦⡀
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢾⡷⠀⠰⣿⠆⠀⠀⠘⣆⠀⠀⠀⠀⠈⢧⠀⠀⢀⡠⠖⠋⠁⠀⣀⣤⠖⣻⠟⠁⠀⢀⡀⠈⠻⣄
⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣤⡀⠀⣠⡀⠀⢀⣄⠀⠀⠘⣦⠀⠀⠀⠀⠈⠳⠚⠉⠀⢀⣠⡴⠛⢉⡴⠊⠁⠀⠀⠀⠻⠋⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⠋⠀⠈⠛⠁⠀⠙⠛⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⢀⡴⠋⠀⠀⠀⠘⠿⠃⠀⣤⡄⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢾⡷⠀⢰⣷⠄⠀⣾⡦⠀⠀⠈⠀⢀⣤⠶⠛⠉⠳⣄⠀⠘⠉⠀⠀⠀⠺⠟⠀⢠⣤⠀⠉⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠿⠇⠀⣤⡄⠈⠉⠀⠺⠟⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠉⠁⠀⠿⠇⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠈⠉⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠡⠄⢒⡀⠀⠀⠀⠀⠀⠈⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡉⣀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⡅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠛⠃⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠁⠀⠀⠀⠀⣀⣠⡴⠞⠛⢿⣿⡿⢟⣫⣥⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠙⠃⠀⣠⡄⠘⢛⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢰⣏⡁⣀⣤⡶⣞⣯⠷⠚⠽⠿⠿⣷⣄⠀⠀⠀⠀⠀⣀⢠⡄⠘⠛⣠⡀⠶⠈⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣬⠿⣛⣭⠷⠋⠉⠀⠀⠀⠀⠀⠀⠀⢈⣁⡀⠀⠀⠀⠉⠁⠴⠟⠃⠀⢁⣤⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⠛⢉⡴⢚⣩⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡆⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠁⠀⠀⣯⣴⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣭⠟⠛⠁⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⢀⣤⡶⣾⡏⠁
⠀⠀⢀⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠃⠀⠀⣀⣤⠖⠋⠁⢀⣠⡴⢾⣿⣿⠆⠙⢻⣆
⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⠉⠀⣠⣴⣾⣿⣥⣤⠖⠋⠁⢠⣤⢀⣹⣦
⠀⡼⠀⠀⠀⠀⠀⠀⢠⠄⢀⡉⢀⡘⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡯⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⢈⡉⠙⣷⡀
⠀⢿⠀⠀⠀⣠⠀⣀⠀⣀⡈⢀⡈⠁⠘⠃⠀⢀⣠⡴⠞⠋⠁⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠛⢷⡀
⠀⠘⢧⡀⠀⢠⡄⠉⣀⡈⠀⠈⠁⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠾⢿⣄
⠀⠀⠀⠙⢦⣄⠀⠀⠉⢁⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠘⠃⢠⠿⣆
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠠⣶⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⠴⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣴⣦⠀⢴⣷⠄⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢈⠉⠀⣀⡁⠀⣤⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠠⣿⡆⠐⢿⠗⠀⠻⠟⠀⠙⠋⠀⣀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡀⠀⢀⣄⠀⢠⣤⡀⢰⣶⡄⠰⣿⠆⠘⠿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠳⣄⠺⠿⠂⠘⠛⠁⠈⠛⠁⢀⡉⠀⣠⣄⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠳⣄⠀⣶⣦⠀⢿⡿⠀⠻⠟⠀⠙⠛⠀⠈⠉⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⢀⣤⡀⢠⣶⡄⠰⣿⡆⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠛⠁⢀⡉⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⠿⠂⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⣠⡾⠋⠀⢰⣶⡄⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡉⠀⣠⣄⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⢠⡾⠋⠀⠀⢿⡿⠀⠻⠟⠀⠙⠛⠀⢀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣠⡏⢀⣀⡀⢀⣤⡀⢠⣶⡄⠠⣿⡆⠐⢿⠗⠀⠙⢷⡄⠀⠀⠀⣠⠞⠁
⣿⠀⠘⠿⠃⠈⠛⠁⢀⡉⠁⢀⣌⠀⢠⣤⡀⢰⣶⡄⠙⢷⣤⠞⠁
⢿⡀⣴⣶⠀⢾⣿⠀⠻⠿⠀⠙⠟⠁⠈⠛⠁⠀⠉⠀⣠⠞⠁
⠈⢷⣌⠁⢀⣤⡄⢀⣴⣄⠀⣾⣦⠀⢿⡷⠀⠀⣠⠞⠁
⠀⠀⠙⢷⣌⠛⠋⠀⡉⠁⢀⣈⡁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⢷⣄⠸⡿⠇⠘⠿⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⠶⠟⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⠉⠉⠉⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠁⠀⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⢿⣷⣄
⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄
⣾⣿⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠰⠿⠂⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠸⠗⠀⠀⠀⢹⣿
⢿⣿⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣀⣴⣾⣿⡿⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣠⣾⠟⠁⠀⣠⣾⡿⠟⠉⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⣴⣿⠏
⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠉⠀⣠⣾⠟⠁⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⣾⠟⠁⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣴⡿⠃⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠏⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⢀⣴⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⣰⣿⠟⠁⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣾⡿⠋⠀⣤⡄⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⣠⣾⡿⠋⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣤⣤⣤⣴⣿⠿⠋⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠁⠀⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠾⠗⠀⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠰⣷⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠁⠀⠀⣰⣿
⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏
⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠈⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣄⡀⠀⠀⠀⣀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣦⣤⣤⣴⣾⡿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣿⣿⣿⣿⣟⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣀⠀⠠⡄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠀⠀⠀⢀⡀⠀⠤⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⣄⠈⠁⡈⠀⠀⠀⣀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣠⠞⠁⠈⢷⡈⠋⠀⠉⠀⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢀⡴⠛⢁⡴⣆⠀⠈⣧⠀⠛⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⢸⡉⠀⠰⣟⡃⣹⠀⡴⠋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠤⠀⠈⢳⡀⠀⠈⠉⣡⢞⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡄⠀⠀⠄⠀⠳⣄⡴⣋⡵⠋
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠁⢀⠀⠀⡄⠀⠰⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠁⠀⡀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠁⠀⣉⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣰⠞⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠒⠲⣄
⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⢄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣾⠀⠀⠠⠄⠀⠐⠤⠂⠀⠀⠠⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠤⠀⠀⠘⠤⠂⠀⠀⠀⠀⠀⣇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠄⠀⠀⠤⣀⡈⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⡂⠀⠀⢀⢒⠀⠀⢀⢀⠀⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⠀⠐⡂⠀⠀⡀⠀⠀⢐⠒⠀⠀⢸
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠤⠀⢸⡆⠀⠀⠀⠈⠐⠠⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡟⠀⠀⠄⠀⠀⢀⠤⡀⠀⠠⠀⠀⠀⡿
⢹⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠈⢷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⣚⣻⣭⣭⣽⣶⣶⣶⠯⢽⡳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣩⠴⣚⣭⠿⣛⣋⣭⡥⠤⠤⣬⠉⣢⠘⡎⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⠖⣫⠶⢛⣭⣖⣫⠽⢖⣲⣶⣷⣫⡵⢞⡡⠞⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡏⢸⠁⢾⣍⣼⣿⣿⣿⣿⣿⣿⠽⠖⢛⣁⣤⠴⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⢮⣛⡒⠚⠛⣛⣛⣉⣩⣥⣴⣖⡚⠋⠉⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠙⢦⡀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⡴⠒⢦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢂⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⢸⣇⣀⢽⡀⠘⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡉⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⡖⠚⠋⢿⣀⣀⣇⠀⣿⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⠖⠒⢻⡏⠀⠘⠛⠉⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠸⣔⣀⣹⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡆⠀⣴⠛⢧⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⠀⠀⠀⠀⢀⡤⠶⢤⠀⠀⢈⣧⡤⢼⡀⠈⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣌⡇⡀⠀⠀⠈⣇⠀⠈⡗⠋⠉⣿⣀⡤⣧⢀⣻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⣾⢳⠁⠀⠀⠀⢻⠀⠀⠰⠒⠋⢻⠁⠀⠈⠉⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠋⠇⠀⠀⠀⠀⠘⣖⣠⡵⠀⠀⢸⡇⠀⠀⢀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣛⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⣻⣷⠄
⠰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠰⠛⠋⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠶⠶⠆⠀⠀⠀⠀⣶⠶⢶⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⢶⡆⠀⠀⠀⠀⢹⣦⣼⢧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣴⠟⠀⠀⠀⠀⠰⢶⣤⣤⣀⡀
⠀⠀⠀⡶⢦⠀⣴⡄⢰⡄⢠⢠⠶⣄⢀⣦⠀⡤⠲⠄⣴⠶⢀⡴⠦⠀⠀⠀⠀⠀⠀⠀⢶⣭⣍⣁⡀⠀⠀⠀⠀⢀⣸⣧⡶⠟⠃
⠀⠀⠀⣏⡽⢴⠷⢷⢸⠙⢾⢸⣤⠾⠼⠾⠇⢧⣬⡗⢿⣭⠤⢭⡽⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡽⠟⠀⠀⠀⠀⢈⣭⣤⣤⣤⡄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⢴⡄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⣠⠀⣹⡇⠀⠀⠀⠀⠛⠛⢛⣛⣋
⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⢹⠞⠚⠁⠀⠀⠀⠀⠸⣥⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠋⠀⠀⠀⠀⠀⣿⠛⠋⠉⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠴⠴⠆⠠⠆⠀⠀⠀⢈⣿⡽⠆⠀⠀⠀⠀⠈⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡟⢻⡇⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠈
⠀⠀⠐⠖⠒⠂⠂⠠⠰⠀⠀⠀⠨⠶⣶⠆⠀⠀⠀⠀⢬⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠛⠘⠇⠀⠀⠀⠀⠙⢿⡶⠶⣤⡄
⠀⠀⠀⠢⠀⠶⠰⠐⠤⠀⠀⠀⠐⠿⢓⣒⠀⠀⠀⠀⠴⣾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠐⠂⠀⠀⠀⠀⢠⣼⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⡽⠀⠀⠀⠀⡖⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠊⠀⠀⠀⢀⡴⠛⠛⢳⡄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢲⡯⣤⡀⠀⠀⠠⣽⣚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣫⣅⠀⠀⠀⠠⢷⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣥⣤⣤
⠀⠀⠀⣠⣶⠟⣷⣦⡄⠀⠀⠀⠀⢺⣠⢨⠇⠀⠀⣞⣉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠀⣿
⠀⠀⢰⣿⣛⣙⣿⣹⣿⡄⠀⠀⠀⢰⠶⡖⡦⠀⠀⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢈⣀⣉
⠀⠀⠈⢯⣭⣭⣽⣭⡿⠀⠀⠀⠀⠘⠀⠁⠁⠀⠀⠃⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠉⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⣁⠀⠀⠛⢀⣀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠈⠉⠀⠀⠀⠈⠉⢀⡀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠘⠃⣀⠀⠀⠛⢃⡀⠀⠀⠘⢣⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣁⣤⠶⠶⣤⡀⠀⠀⠙⠀⣀⠀⠘⠃⠀⠀⠀⠀⠰⠗⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣁⡴⠞⠉⠀⠀⠀⠈⠛⢷⣄⠀⠀⠛⢀⡀⠀⠘⠃⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⢡⡄⠀⣀⣴⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣤⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⣀⣴⠾⠋⢁⣤⣾⣿⣿⣿⣿⣿⡏⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡀⠀⠀⢴⠆⠀⠀⠈⠛⠿⢶⣶⣶⠿⠛⠁⣀⣴⣿⣿⣿⣿⠇⢸⣿⣿⠀⠘⣿⣿⡇⠀⣾⣄
⠀⠀⠀⠀⠀⠀⢰⡏⣀⠀⠀⠉⢠⡀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠀⠈⠻⠋⠀⢐⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⡇⠉⣀⠀⠀⠈⠁⣤⠀⠀⠀⠀⡶⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⠁⠀⠀⠀⠉⣠⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⢠⣆⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠘⠃⣤⠀⠀⠀⠀⢀⣴⠟⢹⣿⣿⣿⢿⣿⣿⣷⠸⣿⣿⢿⣿⣿⡇⠀⢸⣿⡆⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣉⣀⣀⣤⡾⠛⠁⠀⠈⣿⣿⣿⢸⣿⣿⣿⠀⠛⠋⠈⣿⣿⣿⠀⢸⣿⣧⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⢻⣿⡟⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠈⠛⠋⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠉⠉⠉⠉⠐⠂⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠁⠒⠢⠤⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢮⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⢈⣦⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢴⣿⣿⡟⠻⢧⡀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢧⣀⠀⠀⢳⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⠠⣄⣈⡌⢌⠒⠐⠁⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⢠⣿⣿⡏⠋⠒⢠⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢜⢏⡙⠻⠤⣠⠀⣠⠃⠈
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⠢⡄⠀⠈
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣧⡧⠄⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠁⠀⣿⣿⣷⢀⣀⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠐⠚⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠀⢀⠤⠂⠁
⣶⣶⡶⢶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⣛⣛⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣰⣟⡔⣩⢽⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⢠⡿⢸⡷⢍⡒⠭⣞⣓⠶⢿⣯⡭⠿⢯⣥⣶⣶⣂⡰⠮⠭⢛⣹⢭⢟⣻⡷⣾⣿⣿⣿⣿⢦⣄
⠀⠀⠀⠀⠀⣾⠃⠈⢧⡀⠉⠙⠲⢬⣍⣓⠲⠭⣝⣒⣒⠮⢿⣶⣶⠯⠍⣁⢒⣂⣬⣔⣻⣭⠚⢿⣯⠻⡷⡌⢳⡄
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠳⣾⡴⣲⠀⠈⠉⠛⠓⠶⠦⣭⣭⣙⣚⣛⣫⠿⠿⣷⣾⣿⣿⣿⣿⣶⣞⣙⣁⠇⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠻⢧⣀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠶⠶⠶⢦⣭⣭⣙⣛⣂⣈⣤⣾⡏
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣼⣶⠷⢺⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣖⡿⣯⣟⢝⠵⠋⢸⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠚⠵⠭⠋⠙⠁⠀⠀⡾
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⢹⡆⠀⠀⢦⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠓⡓⠽⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢶⡾⠟⠁⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⡈⠻⣦⡀⠙⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡇⠀⠈⢻⣗⠲⠶⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠶⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠰⠀⠀⠠⠀⠀⡏⣭⣭⣭⠭⠭⠉⠉⠉⠉⠉⢹⠀⠀⠄⠀⠀⠆⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠁⢠⠀⠁⢠⠀⠀⡇⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠈⠀⡄⠈⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠂⢀⠀⠂⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠐⠀⡀⠐⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠁⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣿⣿⡿⣿⣿⡟⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⢻⣿⣿⢿⣿⣿⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⡇⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣷⣿⣻⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣟⣿⣾⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣿⣿⣷⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⡄⠈⠀⠀⡁⠁⡀⠄⠐⠉⠉⠉⠁⠀⠀⢸⠀⠀⠁⢠⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⡀⠐⠂⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠐⠂⢀⠀⠒⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠁⠠⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠄⠈⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁



⡟⠉⢻⡟⠿⠿⠿⠻⢿⠛⠟⠿⢿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡀⠠⠄⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠠⠄⢀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣀⠀⠆⠈⠀⠠⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠄⠀⠁⠰⠀⣀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢀⠀⠂⠀⡀⠠⠀⠁⠀⢀⣭⣒⣄⡤⣒⠭⡀⠀⠈⠀⠄⢀⠀⠐⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠈⠣⣀⠁⠠⠀⠂⠀⡀⠐⠀⠀⣰⣣⢴⡪⠕⠋⠁⠀⠘⣄⠈⠀⠂⢀⠀⠐⠀⠄⠈⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠈⠀⠄⢀⡠⢖⠭⠒⠉⠀⠀⠀⠀⠀⠀⠈⢆⠀⠂⠠⠀⠁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠶⠚⠁⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢀⡤⠶⣉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢀⠀⠂⠠⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠤⣺⠵⠊⠅⠐⠀⡀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠐⠀⠄⠀⠁⠠⠀⡀⠙⡄⠀⢀⡠⢔⡫⠗⢩⠋⢀⠀⠄⠈⠀⠠⠀⠂⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⡸⠀⠠⠀⠈⠀⠄⢀⠁⠐⠀⡀⠀⠈⣛⠽⠚⠙⠮⣛⠁⠀⢀⠀⠂⠈⡀⠠⠀⠁⠀⠄⠀⢇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡉⠀⠂⢀⠀⠐⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠂⠀⡀⠐⠀⢉⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠐⠂⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠐⠂⠈⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣡⣾⠏⠉⢉⠍⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⢉⠉⠁⠀⣠⣤⣤⣤⣶⣶⣟⡻⠿⢿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⡡⠞⠉⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡠⠀⠀⣠⣶⣾⡿⣛⣋⣭⣉⣉⣛⣛⠻⣦⣭⡉⠻⣿⣷⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠟⣡⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠊⠀⣠⣾⣿⠟⣫⠞⠋⣉⣉⣉⣉⣉⡙⠳⣤⣍⠻⣦⣈⡙⠿⣿⣄⠘⢦
⠀⠀⠀⠀⠀⣰⣿⡧⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠂⠀⠆⠀⠘⠁⠀⢀⣾⣿⡟⣡⠞⢡⢖⡛⠋⣉⡭⠉⠉⠿⣷⣦⠙⣷⣍⠻⣿⣦⠸⣿⣦
⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣿⠟⣰⡇⠂⠀⢉⠔⠚⢉⡤⠒⠲⣦⣄⡙⢷⡘⢿⣷⡈⢿⡆⠙⢿⣧
⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⣰⣿⢀⡿⢃⡆⢀⢸⡆⢸⡿⢀⣼⡿⢷⣍⢳⡄⣿⣀⢻⣿⡌⢿⡄⠸⣿
⠀⠀⠀⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠠⠀⠁⠠⣿⡇⢸⡇⢸⡃⣿⠀⣷⠀⢠⡌⠉⠀⠶⠙⢆⠻⠘⣿⠘⣿⡷⢸⣧⠀⣿
⠀⠀⠀⣿⣿⡆⠘⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠘⠁⠀⠀⢀⠀⠀⣈⠀⠃⢸⣿⡇⢸⡇⠸⠇⢸⡄⠹⢃⠈⣡⢞⡃⠀⣴⣾⠁⢸⡿⢁⣿⡗⣸⣿⠀⣿
⠀⠀⠀⣽⣿⡇⡇⠘⠂⠀⠚⢀⠀⣼⠀⠈⠀⣶⠀⢸⡄⠙⠀⠀⢿⠀⠀⠘⣿⡇⢸⣯⠀⢃⠸⣷⡄⠻⣦⡙⠚⠋⢺⣿⠋⣠⣿⣿⡌⣿⣇⢹⡇⢀⣿
⠀⠀⠀⢹⣿⡇⡄⢠⠀⠀⣤⠙⠀⠈⠀⣾⡆⠙⠀⡄⠀⠲⠀⠀⠈⠀⠁⠀⢻⣧⠈⣿⣇⠸⣷⡙⢷⡤⣄⣀⣠⡿⠟⠁⣰⣿⠟⠛⣷⣿⡏⣸⠇⣼⣿
⠀⠀⠀⠘⣿⣿⡇⢤⡀⠄⠙⠃⠀⢶⡄⠘⠁⣶⠀⢼⠃⣿⠀⠀⡞⢦⢠⠀⠘⣿⡄⢸⣿⡄⢈⡻⣦⣷⣶⣾⣤⣥⣤⣶⡿⠃⣠⣾⣿⢋⣴⠇⣰⣿⡟
⠀⠀⠀⠀⢹⣿⣯⣼⡇⠀⣤⡂⠰⠎⠁⡄⠀⢰⢰⡦⠁⢤⠸⣇⠀⠘⠷⡀⠀⢹⣿⣄⠙⣿⣦⠙⢶⣬⣬⣍⣙⠻⠿⢋⣵⣾⣿⢟⣵⣿⠇⣠⣿⡟
⠀⠀⠀⠀⠀⣿⡟⣿⠧⡄⠙⠛⡀⠸⠗⡀⢸⠄⠉⣴⡜⢆⡀⢸⠐⢃⠘⢿⠀⠈⢻⣿⣷⡈⠻⣷⣄⠈⠙⠛⠛⠿⠾⡿⠟⠛⠁⣹⣿⠁⣼⣿⠏
⠀⠀⠀⠀⠀⢸⣷⠹⠇⠁⠰⠆⠁⢠⡜⠛⢀⡀⠰⠉⢡⡘⣿⠀⡀⢿⡆⢠⡓⠀⠈⣿⣿⣿⣦⣌⡙⠻⢿⣷⣬⣷⣶⣤⣴⣿⣿⠟⢁⣤⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣧⠘⢰⣄⠸⣿⠀⢡⣦⡀⠛⡀⠸⢧⠀⢡⡄⣇⠈⡱⠈⣿⡆⠀⢻⣿⣿⣿⣿⣿⣦⣤⣈⣭⣍⣛⠛⠉⣩⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⡆⠻⠆⠀⠆⠶⠙⣡⢀⡳⠀⢀⠲⢈⡁⢡⠸⠇⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢻⣿⢀⡀⢃⡀⠻⠀⠠⢷⣌⠁⢃⡄⠈⡷⠀⠆⠈⠀⠃⠀⡄⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠸⡇⠈⠃⢠⡙⠀⠘⠋⣄⠘⠇⠀⡄⠀⣀⠀⠃⠀⠀⣥⠀⠀⠀⣿⣿⠀⠹
⠀⠀⠀⠀⢠⠀⠈⣿⠀⠁⡀⢠⠀⠃⠀⠴⠀⠛⢀⠀⠀⠋⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠄
⠀⠀⠀⠀⠈⠀⢰⣿⠂⠃⠁⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⢀⣾⣟⠀⠀⠀⠀⠐⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠐⠃
⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⣸⣿⣿⠁⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⣰⡿⠁⡴
⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠘⠃⠀⠀⢀⡠⠆⢀⣾⡿⠁⡼⠃
⠀⠀⣰⣿⡿⠉⠀⠀⠀⣀⠀⠀⠀⣠⡄⢈⣀⠰⠟⡀⠐⢃⣤⠄⣀⣀⣠⣾⡿⢁⡜⠁
⢀⣾⣿⣿⣡⣤⣤⣤⣾⣥⣴⣦⣾⣿⣴⣿⣷⣴⣾⣷⣾⣿⣷⣿⣿⣿⣿⠟⠁⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣽⣤⣏⣹⣏⣼⣏⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡴⠒⡢⣄⡀⣀⠤⠒⢦⡀
⠀⠀⠀⠸⣅⠐⣨⣶⡿⠳⡅⠀⢡⡿
⠀⠀⠀⢀⠼⠋⢾⡁⢀⡴⣫⠖⠫⣄
⠀⠀⠀⣇⠀⠀⠂⢙⡭⣞⠁⠢⠀⢈⡇
⠀⠀⠀⠈⠓⠶⠚⠉⠀⠈⠑⠲⠖⠁

⠀⠀⠀⢀⡴⠒⠦⣄⠀⣀⠤⠒⢦⡀⠀⠀⠀⢠⠖⢒⢤⣀⢀⣠⠔⠒⣄⠀⠀⠀⢀⡴⠋⠒⢤⣀⣠⠴⠚⠲⡄
⠀⠀⠀⠸⡄⠀⡨⢞⠿⢳⡀⠀⢀⡗⠀⠀⠀⢯⡀⢂⡥⣾⠟⢦⠀⠀⣸⠇⠀⠀⠸⣄⠀⡠⣖⠽⠳⡄⠀⢀⠝
⠀⠀⠀⢀⠜⠋⢞⠁⢀⡴⣣⠔⠫⣀⠀⠀⠀⡠⠟⠱⡏⠀⣀⢜⡥⠚⢥⡀⠀⠀⢀⠔⠁⢺⡁⢀⡴⣫⠞⠓⢄
⠀⠀⠰⡅⠀⠀⠈⢙⣭⡊⠁⠀⠀⢈⠆⠀⢸⡀⠀⠐⠈⣋⣵⡋⠐⠀⠀⣹⠀⠀⣇⠀⠀⠀⢉⡵⣎⠀⠀⠀⢀⠇
⠀⠀⠀⠈⠲⠴⠒⠁⠀⠈⠓⠦⠖⠁⠀⠀⠀⠙⠦⠖⠊⠁⠀⠉⠒⠶⠊⠁⠀⠀⠀⠑⠒⠊⠁⠀⠀⠉⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣀⣀⡀
⠀⢠⠖⠋⠍⡿⠛⠛⠻⡍⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡏⠉⠉⠙⡆⠀⠀⠈⡇
⠀⠸⣄⣀⣀⠳⠤⠤⠴⠃⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⣝⣒⣒⣚⣁⣀⣀⡼
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⢠⠔⠒⡒⣶⠶⠶⢶⡒⠒⠒⠢⡀⠀⢀⡴⠒⠒⢒⡒⣒⣒⡒⠒⠒⢲
⠀⢸⡀⠀⠀⢧⣀⣀⣠⠇⠀⠀⢰⠃⠀⢸⠀⠀⠀⢼⣀⣀⣀⡿⠀⠀⣸⠃
⠀⠀⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠋⠀⠀⠈⠒⠒⠒⠂⠒⠒⠚⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⢀⠃⠄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⠔⠒⢌⠄⠐⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢰⠁⠀⠀⠠⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⠐⢂⠑⠂⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠌⠠⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠁


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

⠀⢀⠔⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠒⠄
⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠈⠢⡀⠀⠀⠀⠐⠁⠈⠢
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠢⡔⠀⠀⠀⠀⡠
⠀⠀⠁⠀⠀⡟⠀⡐⠁⠀⠑⢄⡠⠊⠀⠈⢂⠀⠑⠄⠠⠊⠈⠻⡢⡀⡠⠊⠀⠆⠉⠉⠉⠉⢩⠐⠀⠐⡌⠉⠉⠉⠉⠑⡄
⠀⠀⡀⠀⠀⣇⠀⠡⡀⠀⠀⡠⠑⣄⠀⠀⠔⠀⠀⠈⠁⢦⡀⠀⡨⠊⠢⡀⠀⢄⠀⠀⠀⠀⠸⢀⠀⢀⠇⠀⠀⠀⠀⢀⠆
⠀⠀⠁⠀⠀⢱⠀⠀⠈⠢⣎⠀⠀⣐⠕⠁⢀⠀⠀⠀⠀⠀⡹⢌⠀⠀⠀⠈⠢⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠣⠜⠁⠀⠀⠘⣄⠀⠀⡠⠊⠀⠀⠁⢄⠀⠀⡠
⠀⠘⢄⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠐⢄⠀⣀⠄

⢀⠔⠋⠉⠉⠙⠢⡀
⡏⠀⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⡀
⡇⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠀⠀⠈⢣
⡇⠀⠄⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⠞⠁
⡇⠀⣀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠁⠀⠈⠀⠀⠁⠀⠈⠳⣞⠁⠀⠈⠀⠀⠁⠀⠈⢀⡼
⡇⡎⠉⠉⠉⠉⢳⢸⠀⠀⢀⡴⠚⢉⠉⠓⢄⠀⠀⠀⢀⡴⠚⠉⠉⠓⢤⡀⠑⢄⠀⠐⠀⠀⢀⠔⠉⠑⢌⠳⣄⠀⠀⠀⠂⢀⡴⠋
⡇⡇⣠⢄⡠⣄⢸⢸⠀⢀⡏⠀⠀⠀⠀⠀⠀⠑⢤⡴⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠑⢄⠀⣴⠁⠀⣀⣀⣀⡑⢬⠳⣄⢀⡴⠋
⡇⡇⠙⢤⡴⠋⢸⢸⠀⠈⣇⠀⠀⠀⠀⠀⠁⠀⣀⡑⢄⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣠⠗⢌⠳⣄⠳⣌⡠⠋⠀⠑⡌⠻⣄
⡇⡇⠀⠀⠀⠀⢸⢸⠀⠀⠈⠢⡀⠀⠀⠀⣠⠞⠁⠈⠢⡑⢤⠐⠀⣠⠞⠁⠀⣠⠞⠁⠀⠀⠑⢌⠳⣌⠀⠀⣠⠞⠁⠀⠈⠳⣄
⡇⠑⠦⠶⠦⠴⠊⢸⠀⠀⠀⠀⠈⠢⡀⢼⠁⢮⡙⢋⡗⢈⡆⣱⠞⠁⠀⣠⠎⠁⠀⠈⠀⠀⠀⠀⠙⢎⡓⠚⠁⠀⠀⠀⠁⠀⠈⠳⣄
⡇⠀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠙⢋⡴⣫⠞⠁⠀⠀⣸⠁⠀⠂⠀⠐⠀⠀⠂⢀⡴⠋⠙⢦⡀⠐⠀⠀⠂⠀⠐⠀⠘
⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⣫⠞⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠠⠀⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⠀⠄⠀⠀⠀⢠
⡇⠀⠄⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣠⠴⠋
⠳⡀⠀⠀⠀⠀⢀⠞
⣤⣬⣷⣶⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠲⡀
⠀⠀⠀⠀⢸⠀⢀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡠⠊⠀⠀⠁⠀⠀⠀⢹
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠂⠀⠙⢦⡊⠀⠀⠀⠀⠂⠀⠀⢀⠞
⠀⠀⠀⠀⢸⢰⠉⠉⠉⠉⡇⡇⠀⠀⣠⠖⠋⠙⠲⣄⠀⠀⠀⣠⠖⠋⠙⠲⢄⠈⠲⡀⠀⠀⠀⢀⠔⠋⠳⣝⢦⡀⠀⠀⠂⢀⡴⠁
⠀⠀⠀⠀⢸⢸⢠⢤⡤⣄⡇⡇⠀⣸⠁⠀⠀⠀⠀⠈⠳⣤⠞⠁⠀⠀⠀⠀⠈⢧⠀⠈⠢⡀⢰⠁⠀⡠⣀⣬⠳⣝⢤⣀⡔⠋
⠀⠀⠀⠀⢸⢸⠈⠳⠔⠁⡇⡇⠀⠹⡀⠀⠀⠀⠀⠀⢀⡤⡓⣄⠀⠀⠀⠀⢀⡏⠀⠀⡠⠚⠢⡑⢄⠳⢤⠞⠁⠈⡧⠙⢆⡀
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡇⡇⠀⠀⠙⢦⡀⠀⢀⡔⣃⣀⣈⠢⡳⣄⢀⡴⠋⠀⡠⠎⠀⠀⠀⠈⠢⡑⢄⠀⣠⠞⠁⠀⡀⠑⢦
⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠁⡇⠀⠀⠀⠀⠙⢦⡹⣄⠳⣌⠜⣡⢟⡼⠋⠀⢠⠞⢀⠀⢀⠀⠀⡀⠀⢈⡦⡉⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⢸⠀⠐⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠙⢮⡳⢤⢞⡵⠋⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠢⣀⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠙⠲⠤⠤⠖⠋