Headache Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⢷⣦⣤⣤⣤⣶
⠀⠀⠀⢿⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠷
⠀⠀⠀⠀⠉⠉⠀⣼⡏⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⠿⣶⣄
⢀⣾⢷⣦⣴⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢤⣼⡏⠀⠀⠙
⠚⠋⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⣿⣿⣿⣷⣄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠛⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⡉⠛⠿⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣴⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⣶⡄⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣿⣿⣷⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣿⣿⠇⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⡈⠻⣿⣿⣿⣿⣏⣉⣙⣿⣿⣿⣿⡿⠃⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣈⠙⢿⣿⣿⣿⣿⣿⡿⠟⢁⣠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⡈⠛⠛⠛⢋⣠⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠙⠙⠛⠙⠛⠋⠙⠉⠛⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠙⢿⣿⣿⣿⣿⠟⢁⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣄⠙⢿⣿⣷⣄⠙⠛⠛⢁⣴⣿⣿⠋⢠⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠙⣿⡿⠃⢀⠐⢿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣶⣿⣷⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠈⠲⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠿⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠤⡀⢀⣀⣠⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠦⣄⠀⠀⢀⣀⡔⠉⠉⠹⠋⠀⣠⢾⡿⠋⠉⢳⠀⣀⠀⣀⣠⠴⠚⡿⠖⠋⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⣄⡁⠀⠀⣀⣠⣏⣄⣀⣀⣠⠴⠚⠙⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠀⠀⠙⣳⣤⡷⠶⠶⠦⠀⠉⠙⠳⣄⠀⠙⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠀⠀⠀⢠⣬⡷⣒⣛⣛⣻⡁⠀⠀⠀⠀⠈⠳⣄⠰⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡰⠋⠹⠯⢥⡤⠆⣀⣀⣀⠀⠀⠀⠀⠈⠳⣤⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⠀⢀⡀⣸⠀⠀⣠⡤⢬⡉⠉⠁⢀⣉⣉⠻⢦⡀⠀⠀⠀⠙⢯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⢀⡽⠈⢧⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⡤⣧⠀⠀⠀⠀⣀⡤⠴⠶⠦⢤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠞⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡟⠳⢤⠴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⣠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⢑⠆⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢷⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡶⣤⣤⣤⣀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⠀⠀⠀⠀⣀⣴⣶⣿⡟⢻⡹⠟⠛⠿⣟⣳⡬⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠆⠀⣤⣾⡿⢿⡏⣷⣮⡕⡕⣲⣧⡄⡾⢂⠂⣾⣿⢿⣿⣿⣿⣿⣶⣄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠀⠀⠀⠀⣠⣾⠿⡿⢧⣮⢾⣟⣴⣯⣷⣿⣿⣿⡿⣯⣟⣩⣽⣯⣽⡿⣯⣿⣿⣿⣷⠀⠀⢀⡤⡴⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⣼⡿⠋⢀⠀⣴⣿⠿⠛⠉⢁⣀⣠⣤⡠⠶⠤⠏⢴⣾⣵⣾⣿⠿⣧⠀⠙⢏⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⡇⠀⢾⣿⠟⠀⢀⠔⠛⠉⠁⣀⣀⣀⣠⣤⣤⣦⣜⣿⣮⣿⡄⠈⠢⡀⠀⠳⣄⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⣼⣶⡿⠃⠀⠻⠏⠀⠐⠁⢀⠴⠊⠉⢀⣀⣠⣤⣤⣤⣰⣿⣷⣿⣽⣿⡄⠀⠙⢢⡀⠈⢣⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⣴⢁⣽⠇⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⠉⠁⣀⣠⣤⢠⣝⣻⠈⠹⢉⡻⣿⡈⠢⣄⠀⠙⠆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠻⢿⣿⣽⠿⠛⠉⢉⣤⣼⠏⢹⡍⣿⣦⡈⠒⠄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣄⣀⠀⠀⠁⠠⣴⡃⠐⢘⠑⠋⠀⠁⠀⠛⡻⣷⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡀⠀⠈⠉⠲⡄⠀⠈⠛⠿⠟⣠⠚⠆⣹⢷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⣀⣠⠠⠖⠉⠀⠈⠻⢤⣀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠓⠶⣾⣿⠏⢹⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠀⠀⣠⠋⡴⠓⠒⠒⠢⢄⠀⢀⡟⢡⡀⠀⠀⠀⠀⢠⠁
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣄⡀⠀⠀⢈⣵⣿⠁⠀⢳⠀⠀⠀⠀⢸
⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠛⠻⠷⠾⣿⣿⠀⠀⠘⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠋⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⢰⢻⣿⠀⠀⡞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⠀⠀⢀⡇⠀⠀⠀⠀⣠⢿⠿⢿⣿⡇⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠇⠀⠀⠈⢆⠀⠀⠀⠐⢶⣶⠤⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠻⣄⡁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠦⣙⠤⣌⡳⣀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⠣⣄⠀⠀⠀⠈⠁⠙⠙⠉⣁⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠑⠲⠦⠤⠶⠒⠉⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢡
⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⡄
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠸⠶⠖⠚⠋⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣰⣶⣶⣴⣾⣿⣿⣿⣿⣿⣽⣿⣶⣤⣤⡀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣷⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠀⠀⣾⣿⣿⣏⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡃⠘⠓⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⢀⣼⣿⣌⣿⣧⠛⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⡿⣿⣾⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⣽⣿⣷⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣭⣿⣿⣷⠻⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣠⣾⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣵⣿⣿⡟⠀⠙⠻⠿⠿⠟⠋⢿⣿⣿⣿⠿⣵⡿⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣀⣠⣤⣤⣠⣾⣿⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⠿⠿⠛⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠈⠙⠻⠿⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣠⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢰⡿⠁⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⣀⠀⢙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣆⣀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢹⣷⠀⠀⣻⡆⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⣾⡏⠀⠰⣿⠁⢸⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⠿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⢸⣿⠀⠀⣿⡇⢸⡇⠀⠀⠀⠈⠙⠿⣶⣤⡀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠛⠃⠀⠀⠛⠀⢸⡇⠀⠀⠀⠠⣶⠟⠋⠉⠀⠀⠀⠀⠉⠛⠿⣶⠀⠀⠀⠀⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠛⠛⠛⠛⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣷⣄⡀⠀⠀⠀⠀⢀⣠⣿⣷⣶⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠛⠲⢦⣄⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠳⣤⠞⠉⠙⠶⣤⣀⠀⠀⢀⡼⠋⠀⠀⢀⣠⣤⣀⠀⠀⠈⠛⠞⠋⠉⠉⠉⠻⣦⠀⠀⠀⣀⣤⠶⠛⠉⠳⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢀⡞⠀⠀⠀⠾⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠰⢦⣄⣸⡏⠛⠛⠛⠀⣠⡴⣿⣁⣴⠿⣆⠀⠀⠀⠀⠀⣀⠀⠀⣸⢷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠚⠛⠛⢹⣇⣠⠴⠚
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣴⠋⢠⡌⢿⣁⣴⠛⣳⠀⢀⣠⢾⡏⣠⡼⠋⢘⡇⠀⠀⢀⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡼⢧⡀⠈⢷⣄⣡⣽⣾⣯⠶⠋⠁⠟⠛⠁⠀⠀⠈⡛⠛⠋⠉⢹⡇⠀⣿⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠶⣞⠛⠉⢩⡞⠁⠈⠹⣄⠀⠉⠁⢀⣈⣷⠛⠉⠛⠀⠀⠀⠀⠐⠋⠉⠓⠀⠀⠈⠻⣴⠏⠀⠀⠀⠀⠀⠈⠉⠛⣳⡦
⠀⠀⠀⠀⠀⣀⡼⠟⣰⠏⠀⠀⠀⠀⢸⡟⢿⡋⠉⠉⠁⢠⣤⣤⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⡾⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⠶⠖⠒⠶⠀⠀⠀⢠⡟
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⠦⣤⣤⡤⠴⢾⡏
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣟⣀⣠⣤⡤⠴⠶⢤⣤⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⣀⣀⣀⡀
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⠟⠉⠉⠉⠛⠶⣄
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠚⠋⢀⡀⠀⠀⠀⠀⠀⠈⢧⡀
⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣴⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣶⣿⣀⣀⣀
⣿⣿⠋⣛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⡶⠀⠀⠀⠀⠀⠀⠳⣶⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣦⣴⣧⡲⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠔⠺⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠻⣿⣿⣬⣧⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠀⠀⠉⠁⠀⠀⠀⠀⠙⠒⠀⠀⠴⢿⣿⣿⣅⢨⡟⣿⣿⣷⣤⣤⣴⣾⡛⠲⠄⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠊⣉⣉⠉⣐⠾⠿⣿⣿⣿⣷⣿⣿⣿⡿⢟⢿⡗⠈⡤⠀⠠⠀⠀⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣔⠉⠀⠐⠋⠝⠋⠉⠛⠛⠷⣾⠛⡀⠐⢆⠀⢈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠠⠀⠀⠀⠀⢠⠀⠀⠸⠁⠀⢸⣄⠀⠀⠀⠀⢀⣠⣤⣤⠀⢟⠁⢿⠀⠀⠃⠀⠃⠈⡀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡀⠀⣰⠀⠄⠈⠙⣧⠘⠲⠿⠟⢍⡀⠉⠣⢸⣧⠀⠓⠀⠘⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠈⠈⠉⠃⢸⠇⠀⠠⠔⠊⠁⠀⠀⠉⠁⠒⠓⠀⠀⢠⠿⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⠀⢣⣀⠓⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠀⡌⡇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢀⡀⠤⠄⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⡽⠀⠀⠀⠀⠉⠉⠀⠤⠤⡀⡀⠀⠀⠀⡎⢿⠷⣄⠀⠀⠀⡎
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢘⡈⠄⠊⠹⠀⠀⠀⠀⢀⠀⣁⢀⣀⣀⣱⠁⠀⠀⠀⠀⠉⠒⡼⠃⢄⠀⠘⠖⢀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⡀⠀⠀⠈⠉⠠⣀⡁⢈⡸⠀⠀⠀⢀⠟⠀⠋⠀⢀⡩⠖⠁⠀⠀⠗
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠉⠃⠀⠀⢀⣀⠆⣀⠴⠋⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠒⠤⡀
⠄⠀⠀⠀⠀⠀⠂⠈⠁⠤⡔⠋⠐⠒⠚⠲⠖⠈⠉⠑⠢⣤⠤⠘⢳⠂⠤⠤⠀⠠⠖⢲⠍⠠⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡄⠀⠀⠀⠀⠐⡀
⠠⣀⠀⠀⠀⠀⠛⠉⠀⠀⠐⡀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡀⠘⠁⠀⠘⡆⢤⢀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠱⡄
⠀⠈⠁⠒⠒⠤⠄⣀⡀⣀⠀⠈⠀⠀⠀⠀⠀⠆⠈⢰⢦⡀⠀⡞⠁⠈⠀⠀⠀⠀⠓⠆⠀⠀⢀⠅⠀⠀⠈⠉⠒⠤⣀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢄⡀⠀⠠⠀⠠⠀⠀⠌⠃⠉⠀⡇⠀⠂⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣐⣤⣀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣸⡆⠀⠀⢀⠰⠋⠀⡇⠀⠀⠀⢀⠄⠁⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠈⢦⣀⠀⠀⠀⢀⠔⠁⢀⡀⠜⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⠀⠀⠀⠀⠐⠀⠀⠰⠇⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣁⣤⣐⣂⡀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠋⠁⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠃⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⠂⠁⠀⠀⠀⠠⠤⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢹⡀⠀⠀⠀⠀⠀⣞⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣌⡙⢤⠃⠀⠀⠀⠀⠀⠡⢋⡰⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣶⣶⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣘⣿⣿⣿⣿⣟⣠⣬⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠈⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⣀⡴
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣄⣀⠙⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⠖⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣾⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠣⣶⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⢀⣼⡇⢀⡴⣿⠁⣠⠞⠁⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠰⠷⠚⠋⣹⠁⠀⣀⡀⠀⠀⠀⠀⠀⠘⠛⣶⡄⠠⣶⣟⡁⠀⠀⠀⠀⠀⠀⡴⠃⢻⣠⠞⠈⣷⠏⠀⢿⠞⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠋⣽⠃⣀⡀⠀⠀⠀⠀⠘⠿⣄⠀⠰⠚⠁⠀⠀⠀⠀⢀⡞⣡⣶⡘⠋⣠⣶⠀⣠⣤⠀⢀⣴⡇⠀⣠⠞⠁
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠰⡷⠊⡿⠀⠀⠀⠀⠀⠠⢖⡿⢛⡷⠚⠹⠷⠶⡄⠀⠈⠐⠃⠘⣧⠞⠁⢻⡶⠋⢿⣴⠋⠘⣷⠞⠁
⠀⠀⠀⠷⠶⢻⡇⠀⣀⠀⠀⠀⠸⡷⣻⠃⠀⠀⣶⢤⡏⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠉⠛⠳⢯⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⠷⠚⢻⣀⣤⡄⠀⠀⠋⠀⣠⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⣯⠴⣦⠀⠀⠀⠀⠀⠙⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠰⡧⠶⠂⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⢾⠀⡴⠋⠙⢦⣀⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣲⠇⠀⠀⠀⠀⣤⣰⠛⣇⠰⣄⡀⣀⠈⠳⠇⠀⠀⠀⠹⡏⠓⢄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣴⠁⠀⠀⠀⢀⣠⠏⠁⠀⠈⠓⠛⠉⠉⠙⠒⠤⠦⡀⠀⣲⠟⠀⠈⢳⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠘⡆⠀⡶⠂⠈⠡⠤⠤⢤⣄⣀⣀⠤⠤⠴⠦⠀⠀⠓⠶⠛⢳⠀⠀⠀⢳⡀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢀⣤⣀⣰⡇⠀⡇⢠⡄⠀⢀⡠⠖⢊⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢳⡀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣠⠎⠀⠀⠀⣠⠞⠀⠈⠀⠙⠒⠻⣤⣷⠀⠈⠀⠠⣏⣠⠄⠀⠀⠀⠈⠁⠀⢠⣤⠜⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⣇
⠀⠀⠀⡴⠃⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⠴⣾⢻⠒⣦⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣠⠞⠇⠀⠀⠀⡿
⠀⠀⡼⠀⠀⠴⢯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠰⠃⠀⠘⠦⠔⠁⠀⣠⠞⠀⠀⠀⠀⣠⠴⠒⠉⠀⠀⠀⠀⠀⡼⠁
⠀⠀⣧⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⣀⡴⡞⠁⠀⢀⡤⠖⠉⠀⢻⢸⡀⠀⠀⠀⢠⠞
⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⡇⡏⠉⠉⠓⠲⠤⢄⣀⢸⡛⡛⠛⠛⠉⠀⢻⣴⠖⠉⠀⠀⠀⠀⠀⢧⢳⡀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠴⠧⠧⣤⠀⠀⠀⠀⠀⠈⠙⠃⢎⠢⠄⠀⢤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠣⣱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⠀⠀⢀⡠⠄⠀⠀⠀⢀⡀⠠⠄⠀⠘⠁
⠀⠀⠂⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠈⠢⡀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⡀⠀⠁⠀⢀⠠⠂⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠘⢆⠀⢸⡆⠀⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠊⠁⠀⠀⡀⠐⠀⠉⠁
⠀⠀⣤⠂⠉⠳⠄⠀⣤⣾⡟⣃⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠈⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⣖⠁⠈⢳⡄⢠⡴⢛⠉⠀⣉⡁⢤⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢤⡀
⠈⢷⡄⠀⠙⢦⡀⢀⢳⡜⠈⠁⠎⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠓⠤⠤⣀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⢹
⠀⠀⠙⣦⠀⠈⠷⠋⠘⢷⣄⣀⣀⡴⠋⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠍⢻⠆⠀⠀⠀⠘⣷⡿⠿⠀⠀⡸
⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣤⣤⣀⠀⠲⢦⣄⠀⠀⡀⠁⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠈⠑⠶⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠈⠳⣦⣀⡈⢳⣰⣁⠀⠀⠀⡜⢀⠙⠻⣷⣶⣦⣄⣀⣀⠀⣸⡇⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠛⣀⣀⠤⠤⠖⠈⠉⠉⠉⠉⠛⠻⠿⣶⡶⠠⠂⠀⠀⠀⠙⠛⠛⠉⠀⢲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠋⢁⡤⠒⠀⠀⠀⠀⠀⠐⠢⡄⠀⠈⠙⢷⣄⠀⠀⠀⢀⡀⠤⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⣤⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢳⣦⡴⠋⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⡎⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠀⠀⠀⠀⢤⡀⠻⠋⠀⠀⠀⡘⠿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡠⠤⡤⠤⠤⣤⢤⣄⣀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⢸⡇⠀⠀⠀⣠⣞⣛⣉⠑⠒⠃⠠⢶⣀⠀⢈⠙⢷⡀⠀⠀⠀⠀⣇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣰⠆⠀⠙⣾⡀⠀⡇⠀⠀⠀⠀⠘⡶⠚⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠁⢀⡴⠁⠀⠀⠀⢀⡼⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠛⠚⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⠤⢤⣀⣀⣿⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠖⠒⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡏⠉⠉⠉⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⣶⣶⣷⣿⣷⣾⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣷⣶⣾⣶⣷⣶⣶⣾⣷⣶⣶⣶
⣿⣿⣿⡇⠀⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣦⣤⣤⣤⣴⣶⣶⣤⣄⡀
⠐⢶⣶⣦⣤⣀⠀⠀⠀⠀⡏⠀⠀⢀⡤⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⢦⡄⠈⠹⣦
⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⢧⠀⡐⢁⡠⠤⢤⣈⠙⣿⣦⣄⣀⣀⣀⣀⡀⠀⠀⠈⣿⡆⠀⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠀⠀⠀⠀⠙⢷⣌⡙⠿⢿⣿⣿⣿⣿⣷⡄⢠⣿⣿⠀⣿⣷⣌⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⡼
⠀⠤⠤⠶⠶⠄⠀⠀⠀⣾⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣵⠐⢻⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⡇⠀⡆⠈⡿⠛⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⡀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠙⢣⠀⠀⡇⠀⢸⠀⢠⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠛⠛⢢⠇⠀⠀⠈⠙⠛⠻⢶⣦⡀⠀⠸⡆⠀⠆⠀⡇⠀⢸⠀⠸⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⠞⠁⠀⠀⠀⠠⣄⠀⠀⠀⠀⠙⢦⠀⢧⠀⠘⣶⣗⡒⢺⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠛⠷⠶⡶⠆⠀⠀⠀⢸⡆⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⠀⢤⡀⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠈⡟⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢠⡇⠸⢛⡳⣤⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠻⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠦⢶⡶⠶⠖⠚⠛⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⢀⣨⣷⣄⠀⠀⠀⢀⣀⡤⠞⠋⠁⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⢸⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣲⣶⣶⣶⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⣀⣀⣀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⠿⠿⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⡄⣾⣿⣿⣿⣧⢠⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⢿⠁⠀⠀⠀⠘⡟⠛⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣾⣿⡿⠃⠻⣿⣿⣿⠟⠘⢿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⢀⣼⣄⠀⠀⠀⣰⣧⡀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣤⣤⣤⣬⣭⣥⣤⣤⣤⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠛⠛⠛⠛⠒⠛⠛⠛⠛⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣦⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡷⣿⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⠇⠛⠿⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⢤⣬⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠙⠙⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠔⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢤⡀⠀⠀⠀⢀⠀⣠⣾⠀⠆⢀⡶⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠉⠂⣀⡀⢹⠦⣀⠸⠄⢩⠉⠃⢦⣔⡄⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠟⠁⠈⠙⢱⣦⣈⠑⢦⡔⠀⢠⣁⠘⠀⢀⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⣦⣀⣀⡀⢀⠈⠻⠃⠸⠃⠀⠸⠻⡄⠘⠈⣠⡁⢠⠇⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠴⠚⠉⢙⠋⢁⠘⣶⡃⠀⠀⠀⠀⠀⠰⠁⠀⠀⢿⢰⡜⠀⠀⠀⡀⣼⣸⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣨⡀⠀⠀⠘⠇⠀⡄⡼⣷⠀⠀⠀⠀⡀⢀⡆⠀⠀⠀⠀⠀⢃⢀⣼⡇⢱⣭⠀⡆
⠀⠀⠀⠀⠀⠘⢦⡀⢿⣝⠢⣄⠦⢄⠐⠛⢧⣌⠀⠀⠀⠀⠀⠀⠀⡴⣷⠆⠀⢀⠛⢯⡋⣇⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡙⠷⡄⠁⠀⠀⠀⠀⠈⠃⠐⠀⠀⠀⠀⣈⠻⠱⠆⠀⡾⢷⣄⡉⠋⠁⢠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⠓⣂⡀⢀⠀⠀⠀⠀⠁⠄⠼⠛⢿⡀⠀⠀⠀⡓⠦⣈⠻⠆⠠⠋⢹⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢌⠳⢝⡷⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣧⣦⠉⠀⠀⠀⡀⣠⣬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⣑⣮⠉⠀⣄⠀⠀⠀⠀⠁⠰⢏⠙⠺⢙⠿⣀⠀⠀⣹⡉⢻⡍⠸⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠉⠑⢢⡀⠀⠀⠀⠢⣄⠀⠀⠈⠈⠑⠾⣿⣃⢀⡁⠀⢀⡆⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠌⢢⠀⠄⠀⠈⠓⢤⡀⠀⢂⠄⡂⣹⡯⣷⡀⠉⣤⠤⢄⠀⠠⠐⠙⢒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠙⢦⡑⠄⣀⠀⠙⢶⣧⡈⠀⠈⠀⠈⡷⠈⠙⢆⡉⠉⠉⠉⠒⠭⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢵⠂⣠⣈⠲⢾⣶⣤⠁⠀⠀⠀⠀⠀⡐⠀⠀⠀⠈⡾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠹⡄⠙⠂⠀⠀⠙⢦⣃⠌⠀⢀⠔⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠈⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠈⠐⠠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢇⡀⠀⠀⠀⠀⠘⠃⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢑⢢⠀⠀⠀⠀⠀⡀⠀⠛⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣷⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠉⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠸⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⢠⣄⠈⠀⡈⠀⠀⡀⠀⠀⠈⠓⠖⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⠈⠳⠀⠄⡀⢀⣍⢠⡾⢃⡘⠻⠃⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡀⠘⠀⠀⠸⠀⠀⠈⠛⠀⠙⠁⢠⠀⢠⡀⢀⠇⡚⠂⢻⠀⠘⢂⠈⠀⢀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠈⠀⠀⡄⠳⠀⠆⢠⣄⡄⠈⢆⢈⠀⣤⠀⠈⡀⠋⣠⠀⠶⠉⠉⠠⠀⢯⠀⡠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⡀⠀⡀⠁⠢⠀⠈⠀⠰⠮⣀⠀⠈⠀⠀⠸⣤⠊⠀⠀⠋⣠⠂⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⢠⡙⠀⣠⠈⠀⢧⠀⠀⠘⡀⠀⢳⡀⢸⡇⠀⢠⡴⠈⠀⠀⢸⠆⢀⣿⡤⠀⠠⣾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣶⣀⠀⠛⠠⣀⠀⡃⠀⠀⡃⠀⠀⠙⣿⠀⠀⡟⠀⣠⠤⠔⠃⠈⠁⠀⠀⠘⢩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⣠⠀⠀⠀⠀⠠⢄⠉⠙⢦⢀⠇⠀⢦⣸⣏⢀⡴⠃⣾⣠⡤⠄⠀⠐⠀⠀⡀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠉⠀⠰⠖⢀⠀⠀⠈⠉⠉⠙⢻⣄⡄⠀⣿⡿⠋⠀⠀⡞⠁⠀⡀⠤⠤⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠚⠋⠀⠀⣀⡀⠐⠢⠀⢿⣷⣀⣿⠀⠀⢀⡼⠁⠀⠠⠀⣀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⡄⣨⠆⠀⠀⠀⠙⣯⣿⣧⡞⠋⢀⠒⠂⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠢⢤⣤⣤⣄⣀⣿⣿⡏⠤⣠⠼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣴⣶⣯⣾⣿⣿⣯⣽⣶⣶⣿⣿⣷⣿⡶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣏⣽⣶⣿⣷⣍⡻⣿⣿⣿⣿⣿⣴⣷⣌⣭⣿⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣔⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⡿⣿⠿⠿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣵⣾⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣷⣌⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠋⠉⠉⠟⠛⠛⠛⠉⠋⠉⠉⠉⠁⠀⠈⠉⠉⠙⠛⠉⠈⠉⠉⠀⠈⠛⠛⠛⠿⠟⠿⣿⢿⠿⠛⠷⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢿⠛⡿⢻⡿⢛⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠹⣿⣦
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣿⠇⠀⠀⢻⣿⣇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄⠀⠀⠀⢿⣿⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈⠛⠁⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠈⠙⠻⢿⣷⣄⠀⠙⢿⣷⡄
⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⣿⠀⠀⠿⠿⣿⣷⣦⣄⠀⠙⣿⣷⡀⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠘⣿⣷⠀⠘⣿⣷
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢹⣿⡆⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⠛⠃⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣤⡄⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⠂
⠀⠀⠀⠀⠸⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠸⠿⠇⠀⠸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⢆⠀⠀⠀⠀⠀⣠⠋⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⠀⠀⠀⢀⡴⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⢀⡷⠊⠉⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⡀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠙⢆⠀⢸⡇⠀⠀⠀⠀⠀⡴⠁⠀⢠⡆⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠑⣾⡇⠀⠀⠀⠀⡼⠀⠀⢀⣾⠀⠀⠇⠀⠀⠀⢀⣀⣀⣀⢀⣀⠤⠚⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⢇⠀⠀⠀⠠⡇⠀⡰⠋⡏⠀⢸⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠸⡆⠀⠀⠀⠳⡼⠁⢸⠁⠀⢸⠟⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠉⠒⢦⡀⠀⠈⣧⠀⠀⢀⠀⢷⠀⠀⠀⠀⡇⠀⠸⡄⢠⠃⠀⠠⡀⡀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⢆⠀⢸⡆⠀⢸⡄⢸⠀⠀⠀⠀⡇⠀⠀⢳⣜⠠⡀⢠⡀⢇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⡆⢠⠇⠀⢨⡟⣎⠀⠀⠀⠀⢣⠀⠀⠀⠙⣄⢱⠐⡇⢾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡏⠀⠀⢈⡇⠀⠙⠢⡀⠀⣸⠀⠀⠀⠀⠘⡄⡆⣷⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠈⢡⡄⠀⣸⠁⠀⣀⠀⢸⡆⠁⠀⡜⡅⠀⠀⡇⡇⣾⣸⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣇⠀⣿⠀⠀⠘⡇⡰⢻⠀⣰⠃⠀⢸⠇⠀⠀⡇⢸⠀⢀⠇⡏⢁⡤⠒⣉⠟⣂⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠹⡄⣯⡜⠀⢠⡷⠁⢸⠀⢟⠀⠀⡟⠀⣀⠀⢃⢸⠃⢸⠀⢡⠋⠀⡞⠁⠈⠀⠀⢀⡠⠟⠓⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠹⡄⠙⢷⣱⡀⢸⣇⢰⠈⣇⢸⢰⡀⢿⠀⠈⢷⡘⣼⢾⣿⡀⡏⠀⠀⡆⢀⣸⡀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢦⣀⠙⠳⣄⢿⡘⠂⢸⡎⢸⣹⠘⠂⠀⢸⢳⠀⣾⣿⣷⡇⠀⠀⡇⠘⣿⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢧⡈⠉⡳⢌⠙⢿⠀⠀⠁⢸⠀⢀⡠⠴⠋⡸⣤⠛⣣⣿⠀⠀⠀⢸⢰⠿⠇⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠈⠻⣤⡙⣄⢳⠀⠓⢀⣾⣿⢀⡞⠀⠀⠀⡇⡿⡄⠈⠁⠀⣴⡄⢸⢀⣶⣾⣿⣤⣿⣒⢩⠟⣦⣶⡀
⠀⠀⣀⣤⣴⡰⢶⣶⣶⡟⣈⢩⣍⢩⣭⣈⣓⣄⣈⠙⠊⢷⠃⠀⠸⡇⣿⡀⡇⠀⠀⠀⣟⡱⢃⣾⣾⣾⠟⣠⣾⣿⣿⣿⣟⣻⡧⠤⠼⢾⣽⣿⡝
⠀⢼⠁⢸⣿⣻⣦⠿⠿⠓⠐⠋⠉⠁⠀⣩⠝⠋⠉⣒⡒⡾⠀⠀⠀⠳⠘⠏⠓⠂⠀⢘⣭⢶⣾⣷⣤⣶⠿⣯⣤⡤⢤⣠⣍⠁⠀⠀⠀⠀⠈⢻⡏
⠀⠀⠉⠛⠤⠴⠶⠶⢦⣤⣶⣶⡶⠖⠋⢀⣤⣴⣾⡿⠻⠅⢀⣴⠋⠙⠦⣐⠉⠉⠛⠦⠭⠽⣭⣭⢿⣟⣛⣛⡺⠔⣫⠀⣼⣶⡶⣶⣾⡋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣭⣄⣠⣴⣿⣾⣋⣭⣴⣯⣿⠶⣦⣟⡲⢄⡈⠙⠒⢤⣀⣀⠀⠀⠀⠀⠈⠁⠈⠙⠋⠙⣄⡟⠓⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⣯⠶⣿⣿⣿⡾⠟⣯⣴⣾⣿⣿⣊⢿⣿⣿⣛⡿⣦⡀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠍⠉⠉⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠻⣿⠰⠿⠋⠉⠀⠀⠀⠀⠈⠁⠀⠙⠄⠙⢿⣿⣿⣿⣿⣦⣄⣀⠀⠉⢻⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⢻⣮⣳⣄⣰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣯⣄⣠⡼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠯⣉⠛⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡇⠀⠈⢳⡤⠚⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡤⠔⠚⠁⠀⣀⠴⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⣀⣀⠤⢒⣋⠁⠀⣶⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢻⡋⠉⠀⠀⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠻⣿⡿⢠⣌⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢠⣴⣦⣤⣴⣋⡻⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣢⣴⡷⣦⣽⣟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠛⢀⣼⣷⢿⣿⣧⣿⠿⣟⢫⣿⣤⣡⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡻⠋⠉⣰⣶⣿⣿⢿⣿⣾⠷⣿⣿⣙⣿⠿⣿⠻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⠇⡀⠀⣟⠛⠿⢿⠛⢫⣎⡀⠸⣿⠟⠀⠀⠀⢸⡉⠉⡟⠻⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢦⡑⠀⠿⠻⠿⢿⣏⢸⣿⣷⡴⢃⢐⣦⣶⣾⣶⣂⣶⣳⣮⣨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣝⠢⣽⠆⡾⠿⢛⣻⡇⠐⣯⡟⣠⣴⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡀⣀⣿⣑⢾⣆⢸⣭⡭⣟⣷⣿⢋⣼⢫⣿⣦⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⢼⠦⣙⣿⠈⢗⣛⣿⣿⢣⡾⣳⣿⣧⣿⡇⠁⣿⠀⠂⠉⡻⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠏⠀⠀⠈⠋⠀⠼⣿⣽⠁⢺⣿⣏⡰⠝⢻⠃⠀⡋⠀⠀⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠘⠀⠀⠀⠈⠉⠀⢺⡿⠃⣰⡟⠛⠧⣴⡆⠀⠁⠀⡀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠂⠀⠀⠀⠀⢠⣇⣰⠉⡠⠀⠁⢌⢄⠀⠀⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⡄⠀⠀⠐⠀⡀⣁⣾⡏⢐⣄⣀⠀⢠⣅⡀⡀⣀⡀⠀⠀⢠⣾⣅⣨⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣶⣤⣤⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⠛⡛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡝⠿⣿⣿⣿⣿⣿⣿⠟⣫⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢟⣱⣿⣶⣭⣭⣍⡱⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⣫⣭⣭⣿⠿⠿⣿⣭⣭⣝⠸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢇⡶⣼⢧⡝⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⡿⣸⢧⡟⣼⢣⡝⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢇⣿⣼⣣⡟⣼⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡼⣿⣿⣿⣿⣿⣿⢸⢟⣵⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡷⣹⣿⣿⣿⡿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠇⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⡄⠀⠀⠀⠀⠀⣴⠀⠘⠃⠀⠜⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠸⡆⠀⠀⠀⠀⣟⢧⡀⠙⠤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⣌⠇⠀⠀⠀⠀⢳⡨⢘⠦⣄⠀⠑⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⠀⠀⠀⠀⠀⠀⠈⢖⡡⢂⠠⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡡⠹⡄⠀⣠⠀⠀⠀⠀⠀⠳⣅⠪⢀⠤⠛⢆⠀⠀⠀⠀⠀⠀⣠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠑⠪⢒⠩⡇⢰⢳⠀⠀⠀⠀⠀⠀⠈⢲⠁⡊⢔⠨⢣⠀⠀⠀⢀⠔⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡐⠅⣊⠑⣺⠃⠘⢌⠳⣄⢲⣤⣀⠀⠀⠀⢹⡔⠅⣢⡜⡇⠀⠀⡎⡰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠐⡩⠐⠥⣻⠀⠀⠀⠑⠺⠄⢳⠍⢣⡄⠀⠀⠇⢊⡀⢀⢽⠀⠀⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢕⠀⠷⡀⠐⢧⡀⠀⠀⠀⠀⣜⠠⠲⣷⠀⣜⠁⠸⡁⢀⡸⠀⠀⡴⣷
⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⠀⠀⠀⢹⡡⠀⢇⠈⠢⡀⠙⢆⠀⠀⡼⠑⠀⠀⣷⠞⠁⡠⠁⡆⢀⡇⠀⠀⡏⢸⡆
⠀⠀⠀⠀⠀⠀⠹⡀⠹⠲⣄⠀⠀⠀⢫⠄⠘⣄⠀⠙⢢⡈⢳⣞⠉⡰⢣⠀⠋⢀⠜⠁⠰⠁⡼⠀⠀⣸⡡⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⡘⢆⠀⠀⠀⠳⣄⠈⢆⠀⠀⠱⠀⠁⡜⠀⠈⠄⡴⠃⠀⢠⠃⣼⠁⢀⡴⠏⠀⠡⢸⠀⠀⠀⠀⢀⣻
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣌⡙⠀⠀⠀⠀⠘⣧⠀⢂⠀⠀⢣⡘⠀⠀⢰⠋⠀⠀⢠⠃⣴⣧⠶⠛⠀⣀⠀⠨⣼⠀⠀⠀⡰⠋⣲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡉⠒⢤⡀⠀⠀⢸⡄⠈⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠇⡘⠋⢀⡠⠔⢊⠃⠀⣠⠇⠀⠀⢎⡠⠖⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠕⠈⠹⡄⠀⢸⡃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠀⡠⠊⠁⠀⡰⠁⢀⡰⠃⠀⠀⠘⢁⡤⠞⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠗⡄⢹⣄⣾⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡜⠀⠠⡞⠁⣠⠤⢀⡴⣃⢢⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⡆⠘⡄⠿⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡟⢠⠾⣟⢀⣞⠁⠒⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢠⠁⠀⠶⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⢀⣷⠝⠂⢟⣼⢃⡾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⢸⠀⠀⠘⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇⠈⡇⡼⡇⢻⠟⡎⢠⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠣⣠⠀⠱⡈⢰⠁⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠒⠀⡘⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠌⢲⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⢚⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⣀⠀⢀⡀⠀⠀⠀⠉⠐⠂⠤⠤⠀⠀⢀⣀⣀⣀⣀⠀⠠⠌⠑⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠒⠈⠄⠂⠡⠐⡈⠔⢊⠡⠐⡀⠄⣀⠤⢐⠀⢀⡠⠄⡂⠄⣂⠀⢂⠠⢀⡀⢤⡒⢄⠂⠐⡂⠤⡰⢄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠈⠀⠈⠁⠈⠀⠈⠀⠀⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡴⠖⠛⣋⣽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠯⢭⡉⠙⠳⠤⠞⠁⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⢀⡞⣁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠧⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⠞⢀⠀⠀⠐⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⢷⠀⠀⣷⠈⠛⠦⣽⣟⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢀⣀⠌⠉⠛⠲⠦⣤⣀⡀⠹⣏⠙⠛⠲⣶⠤⣤⣈⣛⣦⣄⠉⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣩⠖⠚⠓⠶⣤⡀⠀⠀⠈⠉⠉⠁⣀⠀⠹⡄⠀⠀⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠙⣦⠀⢀⣤⠖⠒⠛⢧⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⡾⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠞⠁⠀⠀⠀⠘⡇⠀⣹⠦⠤⡄
⠀⠀⠀⠀⢠⡟⢁⣀⣀⣀⠙⠻⣵⠋⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢉⠟⠒⠳⡄
⠀⠀⠀⠀⠈⣇⠀⠀⠙⠮⠿⡄⠙⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⡀⢠⡇⢠⣤⣄⠀⠀⢸⡇⠀⠈⢷⣉⠛⣧
⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣯⣿⡿⠣⣷⣾⡿⢀⣠⠟⢀⣠⠤⣄⠸⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⢙⣓⣶⠞⠁⠀⠀⠉⠉⠉⠀⠠⠋⠀⠀⣸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⢀⡄⢀⡴⠒⠛⣚⣧⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⠀⣼⠀⠀⠀⠀⢠⡏⠉⠙⢲⣒⣒⣾⣤⣬⠵⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣇⣠⡇⠀⠀⠀⠀⢸⡗⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠚⢧⡞⠀⢸⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⡑⠀⠁⠀⡞⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠤⠤⠤⠞⠁⠀⠀⠀⠀⢀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣦⠤⠶⠶⠶⠒⣾⢻⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣿⣸⡤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⠀⠉⣹⣉⣁⣼⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠢⠤⠤⢴⢶⢖⠟⣻⢀⣈⣷⡤⣾⠇⠀⠀⠀⠀⠀⠀⠲⠶⠶⠤⢤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢝⣒⣒⣒⣛⣛⣚⣉⡩⠥⠖⠋⠉⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡶⠒⠒⠀⠠⠤⠬⠭⠉⠉⠻⠿⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠯⠭⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣆⠀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠛⠉⠁⢀⣤⣤⣤⣉⡻⢿⣿⣿⣷⣌⠻⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⡄⠀⠁⠀⠀⠉⣙⣿⣾⣿⣿⣿⡏⠁⠘⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⣸⠀⠀⠀⢠⣾⡟⠛⣿⣿⣿⣇⣾⡇⢰⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡀⠀⠸⣄⠛⠁⢸⣿⣿⡿⢙⣿⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢦⣤⡙⠿⡲⣿⣿⣿⣷⠞⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣠⡄⣤⢒⢀⠀⠠⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣉⡟⣷⣧⡞⣫⠤⣰⣼⡟⣾⣛⣿⣷⡢
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣾⣿⣿⠻⣴⡶⠀⡸⠟⣯⢽⢩⣟⢿⣿⣏⠈⣀⠢⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏⢀⣿⣿⡀⣸⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠇⣸⠛⠀⡟⠸⣧⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡎⠁⠀⡔⠁⠀⠀⠀⠀⡿⠘⠃⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⡧⢤⡆⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⢻⣯⢹⣴⠀⠀⠀⠀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠋⢣⠛⣿⡆⢿⠀⠀⡀⠀⠀⠸⣿⣇⡠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣶⡌⢈⡝⢋⡄⢀⠀⢀⡌⢳⠻⣆⠀⡇⠀⠀⢀⣍⠣⠙⢶⣿⡀⣠⣏⠷⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣔⣁⣀⡀⠀⠀⢿⡿⠊⣰⣿⣿⠂⠀⣾⠃⡾⠀⢸⡷⣧⡀⣠⣾⡯⣀⠀⠀⡙⢷⡿⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠻⠶⣽⣤⣶⡟⣡⡾⣿⢣⠇⠀⣼⣿⠀⡇⠀⢾⣧⣧⢹⠙⢿⣿⠸⣦⡀⠈⢮⣥⠤⡀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠉⢟⣻⡿⠼⢧⣿⣀⣸⣿⣾⣼⣥⠀⢸⣿⣿⣎⣆⣀⣾⣧⡽⠟⠋⠉⠙⠲⣤⠀⠀⠌
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠎⢸⡟⠀⠁⠁⠀⠀⠀⠀⠀⣾⢸⡗⠁⠀⠉⠉⠁⠀⠀⠹⡇⠀⠖⠊⠁⠀⢿⣦⡔
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢰⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣭⢺⡇⠼⠉⠁⠀⠀⠀⠀⠀⣻⣀⣀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⣗⡤⢾⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢽⠇⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⠞⠉⡦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠐⠒⠂⠒⠒⠚⠒⠈⠓⠦⠶⠶⠖⢒⣒⠇⡀⢠⠞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⣤⡷⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡻⢁⡴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣷⠋⣼⣡⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣾⠁⡼⢫⠟
⠀⠀⠀⢀⠀⠀⠀⠀⣸⠃⠀⠁⢈⡴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⠋⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢋⡤⠖⠒⠦⣄⠀⠀⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠘⠤⢄⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡾⠁⠀⠀⠀⠙⣶⠻⠅⠀⠈⢦
⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠐⠳⠤⣀⠀⠀⠀⠙⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣄⣀⣀⡠⠋
⠀⠀⠀⠀⠀⢸⡇⠀⣠⢾⠁⣴⠀⠀⣠⣤⣟⣦⡀⠀⠀⠉⠳⢾⡇⠀⠀⠀⠀⠀⢰⡏⠉
⠀⠀⠀⠀⠀⠈⢷⣼⠃⣾⠀⡟⣆⡼⠁⠀⠉⠻⣿⣦⠀⠀⠀⠀⠻⣄⠀⠀⠶⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠈⠀⠀⡴⠒⠛⠛⠿⢧⠀⠀⠀⠀⠈⠙⢛⡿⠋⠛⠶⢤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠴⠖⢲⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⣄⠀⠉⠙⠓⠶⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⢤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠉⠓⠦⣌⣀⡉⠂⠀⢂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⣦⣄⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠄⠐⣯⠙⣧⠈⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡰⠀⠀⠀⠀⠀⠀⠈⣇⠈⠙⠾⣦⡀⠹⣮⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⠀⠀⣹⣦⣙⠀⠀⠀⠈⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠛⠦⣄⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢺⣁⣀⡽⠟⠢⠤⣄⣀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣲⠶⢤⣀⣈⡏⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⠳⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⠀⠀⠈⠉⠉⠒⠒⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⣷⢤⡿⠆⠀⢀⣀⣘⣦⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣄⡀⠈⠀⠂⠀⠀⠀⠀⠈⠉⢛⠶⣄⢠⠇⠀⠙⠚⠛⠉⠉⣿⣿⠱⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠁⠀⢉⡙⠢⣤⣀⠀⠀⠀⠀⣰⠏⠀⠘⠻⢦⡀⠀⠈⢦⡀⠀⣿⣿⣿⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡉⠀⠀⠀⢀⡴⠋⠁⠀⠀⠉⠛⠲⢦⣴⠏⠀⠀⠠⢴⣾⣷⠀⠀⠀⠙⢶⣿⡛⠛⠒⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣦⣿⡄⠀⢠⠞⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠷⠛⡄⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣳⠞⠉⢳⡄⠀⣠⣿⣿⢿⣠⠏⠰⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣸⠁⢀⡖⠈⡇⣰⢻⡟⠉⠻⠏⠀⣠⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠖⠒⡙⠶⠞⠀⠀⣿⠃⡾⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⢶⠚⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠻⣄⣐⣦⠀⠀⠐⢇⡀⠀⠀⠀⠉⢻⠖⠲⠲⠶⠶⠶⠒⠒⠒⠛⠛⠉⠉⠁⠀⢸⠁⡼⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠈⠉⢈⡷⠒⠲⡬⠻⡄⠀⠀⢀⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣀⡴⠇⠀⠀⠀⢙⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣼⣀⣤⡤⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠃⠄⠀⠀⠀⠀⠀⠀⠐⠚⠛⣛⠾⢻⠿⠍⡁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣑⣀⢤⡐⠄⠀⠀⠀⠐⠂⠉⠀⠀⢀⡏⠀⠀⠀⠀⠀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⣻⣿⠿⠛⠛⠲⠤⠴⠦⠤⠶⠶⠒⠚⠛⠓⠒⠒⠶⠞⣽⣩⠏⠉⠙⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⢯⣷⠞⠛⡛⢯⣀⠿⠙⠛⠛⠯⡬⢿⣙⣛⠒⠒⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡼⢭⣽⠟⠳⣤⣌⣀⣠⣤⣤⣀⣀⣀⣀⣉⣉⡟⠋⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⣀⣼⣤⣤⣿⣿⣿⣿⣿⣇⢀⣻⣿⣿⣤⣤⣭⣾⠥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⢅⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⣼⣿⣿⣿⠿⠛⠛⠛⠛⠿⠿⡏⠙⣿⣆⠈⢂⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⢠⣿⣿⠿⠓⢋⡅⠀⠀⠀⢀⣀⠹⡄⠘⢿⡄⠈⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠁⠤⠴⠞⠥⢄⠀⠀⠀⠘⡀⠠⣙⡄⠈⢷⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⠴⠶⠶⠿⢃⠀⠀⠺⠿⣆⠈⠻⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠲⣶⠂⠀⠀⠀⠀⠐⢺⡆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢒⣿⡄⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢀⡷⣄⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢀⡞⠀⢳⡄⠀⠀⠘⠛⠛⠛⠛⠀⠀⢀⡾⠁⠘⡄⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⡞⠀⠀⢀⡟⠢⣄⠀⠀⠀⠀⠀⢀⡴⢻⣇⠀⠀⢹⡀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣾⣵⣶⣿⣿⣇⠀⠈⠙⠒⠒⠒⠚⠉⠀⠘⣿⣿⣶⣶⣷⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠸⢧⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠙⠲⣤⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⢸⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠙⠁⠀⢇⠀⠀⠀⠘⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢆⠀⠀⠀⠘⣧⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢦⠂⠀⠀⣆⣹⡄⠀⠀⠀⣰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡇⠀⠀⢿⣿⠇⠀⠀⢰⣿⡇⠈⠀⡄⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢸⣿⡇⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡠⠒⢄⡤⣂⢀⡀⠀⠈⠉⠀⣠⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢹⠆⠀⠀⣀⣀⠔⠁⠀⣀⡀⡁⢘⡄⠀⠀⠀⠐⠋⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢼⣿⡏⠀⣾⣿⠟⡿⣽⠟⠁⠴⢦⡀⠀⠀⢃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢀⡧⠛⠂⠈⢉⣷⣤⣿⣿⣿⣿⣿⣿⡅⠀⠀⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡔⠀⠀⡀⣀⢠⣼⣿⣿⣿⣿⣿⡇⠉⢿⣿⠀⠈⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡅⣀⣆⣣⣽⠾⢻⣿⣿⣿⣿⣿⣧⣬⣿⣟⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⢸⣿⣿⣿⣟⠉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢸⣿⣿⣿⣿⠁⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣃⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡻⡟⠢⠚⢿⣿⣿⣿⣿⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣗⣷⠀⣈⣹⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠹⣄⠀⠀⠀⡤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢶⠒⠤⠤⣀⠀⠀⠈⣇⠀⠀⢰⠋⠀⠀⢀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠽⢳⡄
⢸⠀⠀⠀⠸⣀⠀⠀⢸⠀⠀⠈⡇⣠⠖⠉⠀⢀⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣶⡚⠛⠛⠒⠒⠃
⠸⣆⢤⣀⠀⠀⠑⠢⣼⠀⠀⠀⠙⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠉⠒⠤⡀
⠀⠁⠀⠈⠑⠦⣄⠀⠀⡖⢦⡄⣖⢴⡆⣰⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠆⠀⢠⠎⠀⠈⠲⡀⠀⢑⠦
⠀⡠⠛⠦⠤⠤⠬⠿⠦⢦⣤⢰⣇⢲⠂⠑⠒⠒⠦⠤⠞⠳⣄⠀⢠⠖⠒⠲⠤⣄⡀⠀⠀⠀⠀⣠⠖⠒⠒⠲⣤⡠⠴⠒⠛⠓⣆⡴⠋⠀⢀⣀⠤⠼⠀⣌⢳⠆
⠾⣅⡀⢀⣀⣀⣄⠤⠤⢤⡄⠀⠀⡨⠤⠤⣄⣀⣀⡀⠀⠀⠈⢢⡘⢦⣂⡀⠀⠀⠈⠉⠓⠲⠤⣽⣄⡀⠈⡷⣯⠄⠀⠀⢀⡼⠃⠀⠀⣠⣿⡶⠚⠓⠦⠉⠃
⠀⠀⠉⠚⠀⠀⠀⣀⣀⡞⠀⠀⡰⠁⠀⠀⠀⠀⠀⢹⣀⠴⠚⠁⠀⠀⠈⠙⠓⠲⡦⠤⠤⠤⠤⠷⠂⠉⠉⢳⣄⣀⣠⠶⠋⠀⠀⣠⠾⠿⣏
⠀⠀⠀⠀⠀⠀⠀⢳⠉⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠄⠀⠀⢀⡞⡵⠶⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣴⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠚⣻⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣰⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡰⠥⠾⣇⠀⠲⢄⡀⠀⠀⠀⣠⠴⠋⢀⡴⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢒⣼⣆⠀⠀⠀⢀⡤⠚⠁⢀⡴⠋⠀⠀⢀⠀⠀⠙⠖⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⢯⣮⣬⣧⣠⢖⡉⠀⠀⡰⠋⠀⠀⣄⠀⠀⠣⡀⠀⠀⠀⠈⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⡏⠉⠁⣎⣿⣧⠀⠙⠢⠞⠁⠀⠀⠀⠈⣆⠀⣠⠟⠀⢀⡤⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢚⣿⣿⢀⣴⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⡿⣧⠴⠋⢀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠿⢫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡜⢆⢠⢫⠷⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠤⢤⣤⣤⣤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠘⢦⡛⠉⣈⣉⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠳⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡘⣌⣢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠉⠙⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠋⠽⣛⣙⣿⣿⣛⣷⠶⠶⠖⠒⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠲⣿⣿⣿⡗⢲⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠛⢛⣛⣛⠛⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣼⣿⣏⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⣿⣿⣿⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⣿⣿⣿⣭⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣾⣿⣛⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣻⡿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠟⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠀⠀⠈⠻⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟





⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣞⡽⠃⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣹⠀⠀⢠⠀⢀⣭⠶⠛⢉⡵⠟⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡿⠀⢠⣾⢠⡞⠁⠀⢠⡟⣠⠶⢲⡿⠃⢀⡤⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠛⢁⡴⢋⡏⣾⠀⠀⠀⢸⡞⠁⢠⡟⠀⠰⠾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⣏⠄⢸⣇⣿⡕⠀⠀⠈⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣇⢸⣿⣶⠀⠻⠏⠀⠀⠀⠀⣠⠞⢡⣶⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠘⢦⣏⠀⠀⠀⢀⡴⡖⠀⢰⠏⣠⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⢠⡄⡾⠰⢁⡀⢸⡟⠁⣸⠁⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⢰⠃⢷⠇⠀⠛⡆⢀⠀⣠⡿⠞⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⢸⠀⠈⠀⠀⠀⠷⡿⠀⡀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⢣⡀⠀⠀⣀⣴⣃⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⣿⡆⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿⠀⠀⠀⠀⠀⢀⡏⡇⠰⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠀⠀⠀⠀⠀⡼⢠⡇⠀⡇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠁⢹⡄⠀⠀⢀⡼⠁⡄⡀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⡀⠛⠶⠶⠋⢠⠞⢠⠃⠀⠟⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠸⣿⠀⡇⠀⢇⠀⢰⠃⢠⠏⠀⠀⡇⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⢦⡀⠀⠀⡏⠇⢡⡀⢸⠀⠂⢠⢃⣴⡖⠀⡇⣸⠁⠀⠀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⠀⡀⢻⡀⢀⡇⢸⠀⠃⠘⢀⠀⣧⡞⢹⠁⠀⡇⣿⠀⠀⠀⡟⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠃⡇⠀⡃⠈⠷⠼⠃⡘⢀⡴⢻⡟⠙⣿⠁⠸⡆⠀⡇⢻⡄⣀⣼⠃⡇⠀⢹
⠀⠀⠀⠀⠀⠀⢠⠏⢰⠁⠀⢁⠀⠀⠀⢠⢣⡟⢠⡏⠀⠀⢹⠀⠀⢻⡄⠰⠀⠉⠉⣁⠀⣃⠀⢸
⠀⠀⠀⠀⠀⠀⡞⠀⡦⠀⡆⠀⠱⣄⠀⠈⠘⡇⢸⡄⠀⠀⣾⠀⠀⠀⢻⠀⡆⡰⣱⣿⠀⢸⠀⣸
⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⡇⠀⣀⠈⢣⠀⠀⢻⡀⠙⠶⠞⠁⠀⠀⠀⡾⢀⠔⣱⠏⡿⠀⡛⣰⠃
⠀⠀⠀⠀⠀⠀⢹⡀⢳⠀⢰⠀⣿⡆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢼⣁⣤⠞⠁⢰⡇⢠⠃⢿⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠈⢷⡈⢆⠈⢧⣿⠹⣤⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡾⢁⠆⠀⠈⢛⠋⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⢢⡈⠻⡆⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⣤⡄⢀⡠⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠦⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⡴⠛⠐⣩⠞⠁
⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠉⠳⢦⣌⡳⣦⣄⣀⣀⣀⣀⣀⣠⣤⠴⠖⠚⣋⣡⡤⠖⠋⣁⣀⣤⡤⠶⢶⡄
⠀⠀⠀⠀⣿⠀⢄⣀⠉⠛⠲⢦⣄⣀⠀⠉⠛⠲⠿⠿⠭⠭⠴⠶⠶⠖⢚⣋⣭⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣿⠀⢀⠀⠉⠒⠀⠀⠤⣈⡙⠲⠦⣤⣀⣀⢀⣀⣤⠶⠚⠋⠉⠀⡀⠀⠀⠐⢀⣀⠤⠒⠂⠀⣀⣼⠁
⠀⠀⠀⠀⠻⢦⣀⠀⠉⠐⠂⠤⠀⠀⠀⢉⣠⡤⠞⠛⣉⠡⠄⠐⠂⠀⠀⠀⠀⠀⠀⠈⠁⣀⣠⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣤⡤⠶⠛⠉⠀⠀⠀⠉⠀⠀⣀⡠⠤⠖⠀⠀⣀⣤⣴⣖⡋⠉
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⢁⡠⠄⠂⢀⡠⠔⠀⠤⠂⠉⣀⣠⡤⠶⠚⠋⠁⠠⢀⡉⠉⠛⠲⠦⣄⣀⡀
⠀⠀⢠⡶⠛⠻⣍⡀⠀⢀⡈⠄⠒⠂⠉⠀⠀⣀⣠⠴⠶⢯⣉⣀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠂⠀⠀⠉⣹⠿⠶⠦⣄
⠀⢠⡟⡼⢬⡑⡌⣷⠀⢀⡀⠤⣒⣮⠽⠖⠋⠁⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣤⣀⡀⠀⠀⢀⠀⠀⠀⣼⠡⢊⣑⡀⠈⣧
⠀⡸⢧⣳⣬⢔⣱⣧⡤⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⣄⣀⠰⡇⠠⣘⢀⡱⣠⠏
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠉⠉⠉⠉⠛⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣀⡀⠀⡀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢠⣶⣤⣀⣠⣤⣶⡿⠟⠈⠙⠻⠿⠿⣿⡆⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢸⣿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⣿⡆⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⢰⣿⠇⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢻⣷⣾⠿⠿⠿⢿⣿⠿⠿⠿⣷⣾⡟⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⡟⠁⠀⠀⠀⢸⣿⠃⠀⠀⠈⢻⣷⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣠⣼⣿⡁⠀⠀⠀⢀⣾⣿⡀⠀⠀⠀⢈⣿⣧⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⣿⠋⢿⣿⣷⣦⣴⣿⠟⠻⣿⣦⣴⣾⣿⡿⠙⣿⣦⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠉⣻⣿⢿⣷⣄⣠⣾⡿⣿⣟⠉⠀⠀⠈⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣾⡿⠋⠀⠈⠛⠛⠁⠀⠘⢿⣷⡀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣄⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⣠⣼⡿⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⢿⣧⣄⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣾⣶⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠉⢀⡿⠛⠋⡿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣤⣬⣤⣤⣄⣀⡈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠉⢿⣿⣿⡟⢹⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠈⣀⣀⣀⠙⠛⠛⣿⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠛⠛⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢿⣷⣶⣿⠋⠉⠙⣿⣦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⡿⠻⣿⣶⢿
⠀⠀⠀⠀⠀⠀⢾⣿⠁⠀⠀⣀⣀⣀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⢀⢠⡀⠀⠺
⠀⠀⠀⠀⠀⠀⠘⣿⣴⣾⣿⣿⣿⣿⡏⠙⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢁⡽⠏⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣴⡶⠂⠀⠀⢰⣿⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⣠⣴⣿⣟⠁⠀⠀⠀⣿⣿⣿⡿⢿⠉⢿⣏⣙⢋⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡇⠻⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⡿⣛⢳⣴⠞⠛⠉⠉⠉⠛⠶⣼⣋⠻⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠙⠛⠛⠉⠀⠛⠛⠛⠂⠀⣷⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣿⠀⠀⠀⠀⠀⠀⣼⡿⠛⠻⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢰⣿⠇⣀⡀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣶⣾⣿⡿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢈⣹⣯⣤⣼⣧⣤⣄⣀⢀⣾⣿⠀⠀⠀⠀⠀⠛⠛⢿⣏⣻⣛⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣀⣅⣻⣠⣿⣠⣧⣩⣰⣆⣘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⢠⣤⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⣤⡄⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⠀⠹⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠏⠀⠀⠀⣠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠐⠻⢿⣯⡀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⢀⣽⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠶⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠠⠤⠤⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣤⣀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣀⣤⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡴⠋⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⠃⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠖⠚⠉⠙⣆⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢿⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⢿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠰⠞⠉⠀⠀⠀⠀⠉⠳⠆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠞⠉⠉⠉⠉⠳⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⡀⠀⠀⠀⠀⠀⣀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰
⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⠀⣤⠀⠀⠀⢀⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⢀⣿⠀⠇⣀⣼⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⣿⣿⡏⠀⡴⢾⣀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⣄⣀⠀⠀⢠⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣿⣿⣿⡽⢧⠈⡇⣸⣿⣠⣦⡄⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠄⢀⣀⠀⠀⠀⣀⡤⠈⠸⠃⠀⠀⠀⠒
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠑⠘⠛⠀⠀⠀⠚⠿⠟⠛⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⠊⢡⣶⠀⢀⢋⣤⣴⡆⠀⢀⡄
⠀⠀⠀⠀⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡈⠀⣧⣰⣦⣞⣽⠆⠉⠇⣿⣿⡇⠀⣿⠁⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡶⣾⡟⣛⣁⣀⠙⣄⣠⡐⠀⢙⡁⠀⢏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⣭⣤⣿⠛⠁⣾⣿⣶⠃⠒⡛⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣁⣼⠟⢿⡇⠀⠸⣿⡟⠁⣼⠟⠀⠀⢀⣤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠁⠀⢸⠀⠁⠀⠁⠒⠈⢁⠠⣶⠊⢠⡈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⠀⠀⠀⠀⢀⡀⢸⠆⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⠁⠉⠛⢱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠀⠀⠀⠀⠀⠈⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠀⠀⠀⢾⢗⣫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣽⣿⠋⠈⣿⣿⣴⣿⣿⡿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠉⠀⠀⠀⠉⠛⠛⠉⠁⠀⠻⠟⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⢸⣷⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣇⡸⠙⠛⠻⠟⠛⠋⢹⣿⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣀⣤⣄⠀⣿⡁⠀⠀⠀⠀⠀⡄⠀⠀⢀⠙⣿⣷⣤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⡻⢷⣾⣆⣀⣀⣀⣤⣤⣧⣄⣤⣿⣦⣽⣧⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⣭⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣉⣥⣤⣴⣶⣶⣶⣾⣿⢿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡿⠋⣠⣶⡿⣿⣿⣿⣿⣿⣿⣏⠀⠘⣿⣿⢳⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠀⣾⣿⡏⠀⢹⣿⡾⣿⣿⣿⣿⣠⣤⣸⣿⣼⣿⣿⣷⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣬⣽⣻⣿⣧⣿⠈⣿⣿⣷⣿⣶⣿⡇⣾⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⣿⣿⣷⣬⣿⣿⣻⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⠟⣾⣿⡼⣿⠛⣿⡿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡿⢿⣿⣿⣿⣿⣿⢿⣼⣿⣟⣷⣯⣥⣤⣴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣄⣠⣬⣶⣶⣿⣿⢛⣯⣿⠙⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣏⣭⣍⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⣿⣿⣯⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⡿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣄⣈⠻⣿⡿⢿⣿⣿⣿⣿⠈⣿⣿⡿⣿⣿⣿⣿⠿⠃⢀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣿⣟⡗⠀⠉⠀⢌⠙⠛⠓⠒⠋⠙⠻⢿⡿⠀⠁⠀⠐⣿⣿⣿⣟⣻⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠋⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⣶⣆⣀⠀⠀⠀⠀⠀⡀⣀⣤⡿⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⣷⣿⠶⢛⣭⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠟⣁⣴⣾⡿⢟⣹⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣁⣴⣾⠿⠿⠋⠀⠈⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠛⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠶⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣀⣀⡠⠤⠄⠀⢀⣀⡀⠀⠀⠀⠉⠁⠶⠆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢾⠏⠉⠉⠉⠳⣄⠀⠀⠈⠉⠉⠶⢦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠶⠶⠀⣀⣴
⢀⣠⣤⣀⣀⠀⡀⠐⠒⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⣦⠀⠀⠀⠀⠘⠻⣶⠶⠶⠄⣀⡀⠀⠀⠀⠀⣀⠴⠋⠉⠰⠆⣀
⠈⠻⠃⠈⠁⣀⡀⠐⠲⠶⠖⠀⣼⣆⡀⠀⠀⠀⠈⠀⠀⠈⠶⡀⠀⠀⠀⠀⠘⠧⠀⠀⠈⢩⣶⣄⠰⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠿⢧⣀⠀⠀⠀⠀⠀⢹⣤⣀⣠⣀⠀⠸⡿⠒⠂⠀⠈⢹⡆
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠈⠀⠀⠉⢳⣤⡀⠚⠓⠀⠉⠻⣄⠀⠀⠀⢰⡆⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⣦⡀⠀⢀⡄⠀⢻⡇⠀⡄⣼⠗⠚⠀⠺⠋⠙⣿⠟⠢⣤⡀⠀⠈⢳⣄⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠂⢀⡌⠀⠀⢸⠀⠀⠀⠈⣶⡄⠘⠿⠃⠛⠋⠙⠻⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⣷⠀⠀⠀⠀⢸⡄⠀⠀⠘⠋⠀⠀⠀⠆⠀⠀⠀⠁⠀⠘⠛⣦⣤⠤⠄⠀⠀⡀⠀⠤⠤⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠈⠻⡆⠀⠀⠀⠀⠙⣷⣄⣀⠀⣴⡄⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⢤⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢋⡄⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠉⠙⢿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⢶
⠀⣴⣇⡀⠉⠀⠀⠀⠈⢣⡀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠁⠁⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠈⠁⠀⠀⠀⠶⠶⢾⣉⠉⢉⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣀⣀⣀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⢀⠀⠀⠂⠈⠉⠁⠈⠉⠉⠁⠲⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⢾⡷⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⢀⣀⡀⠀⠀⠀⣀⡀⠀⠶⠦⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡆⠀⠉⠉⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠒⢀⣀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢂⣀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠘⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣭⣤⣤⣦⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⣦⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠘⣿⡹⣧⠹⣿⡻⣿⣷⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣾⣷⠹⣧⠘⢷⡙⢷⡝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢹⡆⠈⣷⡈⢿⡄⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡀⠸⣧⠈⢿⡄⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⠀⣿⠀⠸⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠀⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠂⠀⠀⠀⠀⠀⠀⠀⡜⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠇⠀⠀⠀⢸⠀⠀⢠⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡧⠸⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠛⠀⠀⡴⠀⠀⠀⠰⠋⠀⠀⠀⠠⠀⢀⡞⠀⠀⠀⠀⠐⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠀⢡⢧⠂⡆⠀⠀⠀⣴⣄⠀⠀⠀⢁⠀⣀⡆⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠃⠐⠀⣴⠀⠙⡀⠀⡀⠈⣶⡈⠙⠀⢸⠅⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⡅⠸⠁⠀⠉⠃⠀⠀⠈⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠐⡈⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠁⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡆⠳⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡸⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣙⢾⡿⠀⠀⠀⠀⣴⠞⣻⢧⡀⠀⠀⡀⠀⣿⠀⠀⠀⢀⡂⢀⡾⠀⠀⠀⠀⢸⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠁⠀⠀⢀⡴⠃⢀⣾⡿⠁⠠⠜⢻⡎⢹⣿⢄⠀⣸⠿⠽⠟⠶⣴⣦⣀⣀⣀⣂⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣧⣇⢀⡾⠋⠁⠀⡾⠉⠀⠌⠀⡠⣾⠂⢠⣷⠈⠛⢟⡀⠀⠀⠀⠀⠀⠀⠀⠩⠋⢿⠌⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠋⠀⠀⠀⣼⠃⠀⠀⠀⠀⡱⣿⠀⢸⣿⡆⠀⠹⣣⡀⠀⢠⡤⠀⠠⢰⠡⠚⢈⣵⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⡟⠁⠀⠀⣰⠇⠀⠀⠀⠀⢠⡇⣿⠀⠀⣏⣷⡀⠀⢻⢿⣿⠶⢶⣾⣤⣽⣥⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠁⠬⡀⠀⢠⣾⡏⠀⠀⠀⠀⠠⠋⢠⢛⠀⠀⡏⢹⣧⠀⠈⡀⠸⣄⣈⡛⠚⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣆⠀⣈⢷⣾⡿⠀⠀⠀⠀⢠⠃⠁⠈⢸⠀⠀⡧⠋⠐⡄⠀⢱⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢻⠿⢳⠶⠖⠂⣰⣄⡀⠀⠀⢸⠀⣰⡇⠀⠀⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠋⠀⠓⠀⠀⠘⠋⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣉⠹⡤⠴⠂⠀⠀⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠋⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⣦⠀⢸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢘⡃⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡠⠀⣦⠀⢈⡅⠀⠀⠀⠀⠈⠳⣄⠒⠀⠀⠀⠁⠉⠁⠈⠉⠀⠀⠀⡤⠁
⠀⠀⠀⠄⠄⠁⠀⠀⠀⢹⣦⡀⢈⡟⠁⠙⣄⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⣀⣀⣀⣀⡤⢶⡉
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠰⠆⠉⠛⢦⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠳⡀
⠀⠀⠀⢰⠀⣠⣤⣶⡶⠁⠀⠀⠀⠀⢻⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⣤⣧
⠀⠀⠀⠈⣿⣿⠋⠉⠀⠀⠀⠀⠀⣠⠎⠈⠀⠀⠀⠀⠙⠒⠒⠂⠐⠛⠀⠈⠈⠉⠉⠀⢀⠔⠁⠈⡆
⠀⠀⠀⠀⡉⠀⠀⠈⠉⠒⠦⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠐⠁⠉⠉⠙⠚⣇⣀⠀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠤⠄⠐⠒⠈⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⠸⠀⠀⠀⠀⢠⠁⣜⠁⠀⠀⡹⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⢰⠀⠀⠀⠀⠻⠘⠉⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠣⠘⠓⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠒⣄⠀⠀⠀⠀⠀⠀⢀⠄⠓⠒
⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣶⣶⣶
⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡠⠏⣀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡤⢄⣀⣀⣀⣀⣤⠤⠖⠒⠳⠬⠙⠃⠉⠀⠛⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠓⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠿⢝⡂
⠀⠀⠀⠀⠀⠀⠻⣖⣒⣒⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡴⠃⣀⣤⠴⠶⠶⠦⣄⡀⠙⢆⡀
⠀⠀⠀⣀⡴⠚⠉⢉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠤⣄⣹⣞⡴⠚⠉⠀⠀⠀⠀⠀⠈⠹⣄⠀⠙⢦⡀
⠀⠀⠀⠈⠉⢉⠟⠁⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠹⠏⠀⠠⠶⢤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⣳
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢬⣙⠳⡄⠀⠀⠘⡇⠀⠀⣧
⠀⠀⠀⣼⠖⢹⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠁⠀⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⠶⠒⢸
⠀⠀⠀⠀⠀⢸⠠⠤⢼⡄⠀⣀⣀⣀⣀⣤⣤⣴⠾⠛⠋⣴⡄⠀⢠⣆⠀⠀⠀⠀⠀⢀⣿⠀⢠⡏⠑⠂⢸
⠀⠀⠀⠀⠀⢸⠀⠈⠉⡇⠀⠈⢻⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣼⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢧⠀⠀⢳⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣀⣤⡿⠁⠀⢠⡇⠀⠀⣰⣧⣄⡀
⠀⠀⠀⣠⠶⠒⠚⠢⠤⠼⠂⠀⠀⠀⠈⠉⠛⠛⣟⡿⠋⠀⠀⠠⠖⣦⠀⠀⠉⠉⠉⠀⠀⠀⠳⠶⠊⣡⡴⠒⠙⣆
⠀⠀⠀⡏⢀⡴⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⣿⠀⠀⢹
⠀⠀⠀⢷⡀⠀⠼⠈⡧⢸⡀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠒⠂⠁⠐⠒⠒⠤⣄⡀⠀⠀⠀⠀⢠⣆⠙⠀⠋⠀⢀⡿
⠀⠀⠀⠀⠛⢦⣄⣀⣠⠼⢧⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣠⣤⣾⣿⣿⡆⠀⠀⠀⣼⠉⠛⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⡀⠀⠘⢿⢿⣿⢿⣟⣋⣛⣛⣛⣿⣿⠿⠿⣿⣿⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠉⠲⠤⢄⣀⣀⣉⣁⣀⣀⣠⠴⠞⠉⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠚⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡜⠀⠀⠀⠘⠀⡰⠇⠀⠀⠃⠀⡠⠀⠀⠀⠀⢓⠘⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠈⣄⠀⠀⠁⠀⣠⡀⠀⠀⠃⠀⢀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠈⠀⠂⣦⠉⠃⠀⠀⠠⣤⠉⢀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢰⠋⠀⢠⠀⠇⠀⠉⠀⢀⠈⠀⠠⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡤⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠦⠀⠀⠀⢁⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣔⡫⢿⠇⠀⠀⢀⠖⢻⣧⠀⠀⣀⠀⡇⠀⠀⠀⣀⣠⡆⠀⠀⠀⠛⠆
⠀⠀⠀⠀⠀⠀⠀⣐⣀⣀⣀⠀⢀⣠⠞⠀⣼⠞⢀⠐⢻⡇⢹⡿⣄⣼⠓⠛⠙⠲⠷⠤⠤⣴⣴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⡤⠞⠀⠀⡼⠁⠀⠀⠠⣼⡇⢸⣧⠀⢩⡄⠀⠀⠀⠀⠀⢰⢳⠸⣥⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠅⠀⠀⣰⠃⠀⠀⠀⣸⢽⠃⠸⢻⡄⠀⢿⣶⣧⣯⣤⣄⣧⡠⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠥⢁⠀⢀⣼⡏⠀⠀⠀⠀⠃⡼⠁⠀⠏⣷⠀⠘⡈⢇⣀⡛⠻⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣹⣾⡟⠀⠀⠀⠰⠁⠈⠀⠀⢀⡞⠀⠆⠀⣁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠙⠙⢃⣴⠢⣀⠀⠀⣄⣼⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡞⡁⠀⠠⣀⢀⣴⣾⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡟⢁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠆⢀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣶⡻⣿⣿⣯⣛⡛⣿⣿⣿⣿⣿⢀⣁⣀⣀⣀⠀⠀⣘⣠
⠀⠀⠀⠀⢸⣿⣿⣿⡿⣷⡙⢻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⢿⣿⠋⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⢟⢷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣥⠿⢋⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢯⡁⣿⣏⡀⣾⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⡿⠋⠀⠀⢹⣿⣷⡰⢋⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡟⣛⡬⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣿⣿⣿⡇⠘⠃⢸⣿⣿⣿⣿⣿⣿⡇⠘⠃⢸⣿⠛⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠹⣿⣿⣿⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠋⠉
⠀⠀⠀⠀⢨⣧⣀⠀⠀⠁⠀⣿⡿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁
⠀⠀⠀⢠⣴⣿⣿⣿⣷⣤⡀⢿⣧⣿⠻⣿⢿⣿⣿⡿⣿⠿⣾⡿⣿⠏⢛⣿⣿⣿⡏⠄⠀⠀⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⢳⡘⣄⠀⣀⣰⣾⣴⣶⣶⡆⣀⣠⣴⣾⠿⠉⠁⠉⠀⢀⣰⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⠳⡙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣟⣁⣤⣴⣾⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠙⢿⣯⣾⡿⢿⢿⣷⣽⡄⠀⠙⠿⣿⣿⣿⣿⣿⠋⠛⣝⡿⣌⣿⣿⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠿⣏⠢⡙⢿⡇⠀⠀⠀⠀⢀⡀⠀⠀⡀⢀⢙⣃⣙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠐⢦⡼⢧⡀⠀⠈⠛⠻⠿⠟⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⢧⡴⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡀⠈⠓⢺⡗⣳⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⡴⢾⣋⡉⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠂⠀⠸⣇⠈⠉⢡⣨⡿⠀⣸⠇⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣿⣿⠶⠞⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣄⡸⣰⡿⠭⢗⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⣇⣿⣵⠿⠁⠀⢀⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣼⣡⠾⠿⠒⠛⠁⠀⠀⠀⢸⡞⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣁⡈⢻⠏⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣶⡶⠶⠾⢯⣾⣿⣿⣿⠿⣟⡳⠦⣍⡁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠀⢀⣤⠖⠛⠉⠁⠀⠀⠘⠁⣈⣻⡇⠀⠀⠴⠖⢺⣭⠙⠛⠿⣷⣦⣈⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⣠⡾⠋⠀⠀⠀⠀⠀⢾⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠉⠻⢿⣦⡀
⠀⢠⣾⣿⣿⣿⣿⣿⠃⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠈⠛⠛⢿⣿⡿⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠛⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⣀⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣴⣶⣶⣴⣷⣦⣄⣀⠀⠉⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠁⠀⢾⡿⢿⡹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠒⢢⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⢰⣿⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠉⠙⡋⣁⣽⣿⡟⠋⠛⠋⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠉⠙⠛⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠋⢀⣿⣿⣿⣎⢿⣿⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢃⣴⣿⣿⢻⣿⣿⣼⣿⡇⢀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣻⣿⣾⣿⣿⣣⣿⣿⣿⣿⣿⠃⣼⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⣿⠇⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⡟⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢸⣿⣼⣿⣿⣿⣿⡏⠋⢰⠸⣿⣿⣿⣿⣿⠇⣾⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣼⣿⣿⣿⡿⢿⣿⡇⣄⠸⣷⡙⢿⠟⣿⣿⣿⠟⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣿⣿⣿⣿⣧⠈⡛⠳⠙⠀⠘⡇⠀⢰⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⠳⣄⠈⠀⠀⠁⠰⠟⡛⢉⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇⠀⡀⠀⠀⠀⢀⠀⠀⢀⠈⠁⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣾⣇⢀⣾⣆⣸⣷⣼⣷⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⢫⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⣷⣽⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠻⣿⣷⣿⣿⣴⣿⣿⣟⣿⣏⣿⣿⣭⣿⣿⣿⣿⣿⣿⣷⣟⣽⣿⣿⣷⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⠛⠛⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠛⠉

⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠀⢀⣶⣶⡀⠀⣶⣶⡀⣶⣶⠀⣴⣶⣷⣶⠀⣴⣶⣶⣦⣰⣶⡆⠀⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⣿⣿⣀⣽⣿⠀⣸⣿⣿⣇⠀⣿⣿⣧⣸⣿⣸⣿⠋⠀⠀⢸⣿⠃⠈⣿⣿⣿⣷⢸⣿⡇⣿⣿⣀⣀⣸⣿⣇⣨⣿⠇
⠀⠀⠀⠀⠀⣿⣿⠛⣿⣿⢀⣿⣧⣼⣿⡀⣿⡟⢿⣿⣿⢻⣿⡀⢿⣿⢿⣿⡀⠀⣿⣿⢸⣿⣾⡿⠀⣿⣿⠛⠛⢻⣿⡟⢻⣷⡀
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣼⣿⠋⠙⣿⣧⣿⡇⠘⣿⣿⠘⢿⣷⣾⣿⠈⢿⣷⣾⡿⠋⠀⣿⣿⠇⠀⣿⣿⣶⣶⣾⣿⡇⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢤⡀⢤⡄⣠⢼⢨⢠⡤⡄⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠸⠼⠳⠿⠧⠳⠼⠸⠸⠇⠇⡿⢯⠀⠤⠀⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣤⣴⣶⣦⣤⡤⣴⠂⢶⣤⣤⣤⣶⣿⣶⣶⣤⣤⣠⣼⠁⠀⠀⠡⢀⡶⠖⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢴⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⢺⣿⣇⡐⢒⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣸⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢀⣼⣿⣿⣆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠉⠥⣽⣿⠟⢻⡟⠀⠘⣿⣟⠻⠿⠿⠿⠿⠟⠛⣋⣿⢢⡄⠄⢸⣯⡷⠻⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠟⠚⢿⣶⣶⡟⠀⠀⠀⡙⠛⡷⠶⠶⠶⠶⠿⠿⠻⠿⠛⠃⠀⣾⣿⡷⢾⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⡦⠺⣿⣦⣤⣾⣷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⡟⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢀⣤⣼⣻⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀⠀⠀⠀⢀⣠⡾⣯⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣴⣿⣷⣿⣿⡟⠛⠙⠛⠋⢽⣿⣿⣿⣿⣄⣾⣿⣿⣯⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⡶⣷⣶⣶⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢰⠃⢠⠂⠖⢀⠞⡥⠒⢍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸⠘⣸⣿⠀⠘⢦⡀⠈⠀⣼⢷⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⡘⣄⢧⢣⢿⣦⢳⡀⠙⣦⢣⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠀⢂⡄⢢⡻⣦⣷⣆⢻⣧⢧⣦⣿⠆⡇⡀⠈⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡺⢽⡛⢽⣿⣿⣶⡟⣸⣿⣏⠞⢁⠁⣠⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠓⠀⣽⠈⢿⣿⣿⣷⣿⣿⢡⡾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠤⣤⣀⣱⣀⣿⣜⣌⣿⣿⣿⣿⡿⠿⠿⠇⢄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⢀⡇⠁⠊⠈⢛⡿⠛⠛⠁⡀⠀⠀⢀⠀⠀⠀⢠⠟⢝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⣤⣞⡁⣀⡴⣂⡁⠀⠀⠀⢀⣴⠀⢀⣤⣄⣬⣦⣻⡸⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣤⠄⠀⢸⠁⠉⣝⡇⠀⣰⠾⠿⣇⡌⠠⠀⢠⣿⡏⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠈⠻⢀⣠⣼⡧⣬⣽⡷⣿⡄⠐⠀⣽⠿⠲⡒⠛⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠽⠋⢩⡀⠀⠝⠋⠉⠻⠟⠟⠉⠈⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⣆⠀⢠⡀⠀⢀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⢠⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣸⣿⣿⣷⣼⣿⣸⣺⣾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢀⣼⣧⠀⣸⠀⠀⣾⣿⣿⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡺⣿⡇⠀⡏⠀⢰⣿⣿⣿⡟⣇⣇⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠼⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢆⣿⠅⢀⠀⠀⣸⣿⣷⣿⡇⣿⣿⠇
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣼⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⢠⡿⠲⡄⣀⣀⠀⢀⣤⣀⣀⡀⠀⣀⠤⠓⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⣽⣧⣤⡇⣧⣀⣾⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⡀⣀⠀⠁⠀⠠⠄⣀⠀⠀⢘⣿⣿⣿⡇⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇
⢀⣀⣤⡶⢿⣿⣿⣷⣿⣿⣿⡿⠛⠿⠿⣿⣧⣷⣤⡀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠉⠒⢸⣿⣿⣿⠇⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠈⢱⡤⢤⣥⣭⣭⣽⡿⠉⢻⣷⣟⣦⣴⣹⣿⣿⣮⣳⣶⣶⡀⢁⠈⠙⢿⡧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣾⠛⠋⠉⠁⠈⠈⢀⠈⠛⠛⢿⣿⡇
⠀⣼⡇⠀⡖⠒⢺⣿⣧⣯⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⡋⠛⣛⣛⣙⣷⣾⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣟⠀⣠⣦⠼⠂⠙⢶⡷⢶⣒⣞⣉⣇
⢀⣿⡇⠀⣇⣀⣀⣉⣛⣉⣀⣀⣀⡀⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣾⠟⠁⠀⠀⢠⣿⣿⣿⡿⡿⠿⣿
⢘⣿⡇⠀⠆⠀⠀⠐⠆⠀⠰⠀⠀⠰⣷⠖⠲⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⡄⣾⣿⣿⣳⣿⣿⣿⣦
⠀⣿⡇⠀⠀⠀⠰⣆⠂⠀⠀⠀⠀⠀⣯⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⢿⠂⠀⡇⠀⣿⣿⣷⣿⣿⣿⣿⡿
⣠⣿⡇⠀⡀⣀⢀⣀⣀⠀⠀⠀⠀⣘⣟⡀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡄⠀⠀⢸⣿⣿⣿⣟⣸⡷⣾⡅⠃⣿⡟⣿⣿⣿⣿⣿⡇
⠟⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡇⠀⠀⢀⣿⣿⣿⣿⣹⡷⣏⣷⣴⣿⣽⣿⣿⣿⣿⣿⡇
⠈⣿⠃⠀⠃⠀⢀⡤⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡇⡷⠀⠀⠘⣿⣿⢻⣿⣿⣃⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅
⠰⣿⡆⠀⡄⠀⠀⠉⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣦⣭⣽⢛⣛⣉⣽⣿⣷⡇
⠘⣿⡇⠀⠓⠐⠒⠒⠒⠒⠒⠂⠐⢲⣿⠒⠒⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢉⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡁
⢠⣿⡇⠀⣴⣶⣶⣦⣴⣤⣶⣶⣷⣿⣽⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣼⣿⣿⡄
⠈⢿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣇⣿⣾⣿⡿⣿⣿
⠀⠀⠈⠛⠉⠫⠿⢟⠻⠿⠿⡿⠿⠦⣤⣤⣾⣿⣿⣿⣿⣿⣟⣋⣱⣦⣴⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⢿⠿⢿⣶⣷⡀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣉⣈⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣉⣉⣛⣛⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⡀⢀⣲⣦⣴⣤⣶⣶⡄⠄⠈⠀⠀⠀⢀⣤⣀⡀⠀⢀⣰⣦⣴⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠐⡁⢮⣟⡿⠿⣿⡿⢟⣻⣆⢀⠀⠀⠀⢀⣈⣙⠓⠄⢬⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⣶⡟⠑⠛⠳⠶⠾⢿⡆⠀⠀⠀⠀⠈⠉⠉⠉⠀⢺⡟⠛⠛⠻⠿⠿⢿⡿⠐⠡⣴⣤⡆
⠀⠀⠀⠀⠀⠀⠀⢻⠃⣀⣀⠀⣀⡀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣀⠀⣀⣀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠁⠀⠈⠁⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⠁⣀⠈⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠄⠀⠄⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⠠⠀⠠⠒⣀
⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠄⠀⠂⠀⠈⠐⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠐⠠⠠⠀⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠂⠀⠤⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠶⣤⣄⣀⣀⣀⣠⣤⠴⠞⠉⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠈⠉⠉⠳⣤⣀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠉⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠋⠙⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣸⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⠄⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣄⣼⠖⠋⠉⠉⢉⣀⢀⡤⣄⠀⠈⠉⠉⠉⠓⢾⣄⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⡟⠉⡿⠀⣼⠶⣄⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠃⢸⠇⢠⡏⠀⣟⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⣦⠀⢀⡟⠀⡿⠀⣼⠁⢸⠏⣹⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡆⣸⠁⢸⠇⢠⡇⠀⡞⠀⣿⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣧⡏⠀⠀⠀⠈⠁⠸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⠟⠉⠉⠛⠓⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⠀⠀⠀⠀⠀⣀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧



⣇⢸⠆⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠐⠒⠒⠒⠒⠒⠒⠐⠂⢾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⡇⠈⡆⡇⠈⠁⢠⢻⡀⡧⢼⢸⠀⠀⡇⠀⠀⠪⣄⠀⡇⠀⣅⡕⣸⠀⢱⢈⣖⠁⠬
⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣷⣶⣥⣧⣤⣤⣦⣤⣥⣷⣮⣼⣶⣤⣷⣦⣤⣴⣮⣤⣥⣤⣤⣼⣬⣶⣮⣤⣤⣥⣴⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣻⡿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠁⠉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣘⠋
⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⣷⣦
⠀⠀⠀⠀⣼⡏⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠹⠷⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡗⠦⣀⠀⠀⠀⠙⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⢋⣤⡄⠀⠀⠀⣀⡀⠀⢀⣹⠀⠀⠙⠲⠤⣤⠼⠀⠈⠳⣄⠀⡷⢦⡀⠀⠀⠸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠈⠻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠃⠀⠀⠀⠀⠀⠀⣈⡃⠀⠀⠀⠀⠄⠠⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡴⠋⠉⠉⠓⣆⠀⠀⣠⣤⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠀⠘⡆⢸⠱⠀⠈⣧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠦⣀⡞⠀⠀⠀⠸⡄⠀⠀⠀⠀⢿⡇⠘⣆⠀⢀⡟⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠛⠓⣌⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡼⠀⠀⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⢆⠀⠀⠀⠀⠀⠈⠦⠒⠚⠁⠀⠀⣈⠀⣸⠂⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⠦⣄⡀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡔⠀⠀⠀⠉⡷⠒⠶⠴⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢲⠞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣍⡛⠃⠀⡞⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⣂⣀⡴⠧⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠉⠁⠀⠠⢤⠬⢍⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⠉⢻⣙⣒⣶⣶⢟⡒⣻⠋⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠭⠟⠚⠉⠈⠑⠛⠽⠿⠯⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⢻⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠻⣿⣿⡄⠀⠀⠀⠀⠈⢻⣿⡟⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣄⡀⠀⠀⢀⣿⡀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⡿⠃⠈⣿⣿⣿⣿⡿⠋⣀⡴⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣦⣤⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡿⠋⣠⡾⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⡄⠀⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⣰⠟⠉⠐⠚⣁⡤⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⡆⠀⠀⠉⠀⣴⣄⠸⣿⣿⣆⠀⡀⠀⣠⣾⣷⡶⣶⣶⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣷⠈⠉⠉⠀⣰⣿⣿⣿⠏⢠⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣧⠀⠀⢻⣦⣿⣿⣿⣿⣿⠟⢁⠀⠀⣠⣾⣿⡿⠟⢁⣴⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣶⣄⡙⠻⣷⣄⡘⢿⣿⣿⣿⣿⣿⡿⢏⣤⣾⡿⠟⢉⣠⣴⣟⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣶⣄⡉⠛⠚⠻⠿⠿⠿⠟⠛⢛⣉⣥⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣄⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⣋⣤⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢁⣶⣶⣦⣡⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⢃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡙⠻⢿⣿⣿⣿⣿⣿⣿⡿⢡⣶⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠈⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢋⣩⣤⣤⣤⣍⣁⠀⠀⠀⠀⠀⠀⠈⢿⣟⠻⣿⣿⣦⡈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢿⣧⣙⣿⡿⢿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⣿⣿⣿⡿⢋⣥⣤⣌⠻⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣾⣿⣿⣿⠆⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣼⣿⣿⣿⡟⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣸⣿⣿⣿⡟⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢰⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⠃⠀⠀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⣿⣿⣿⣿⣿⣿⣶⣤⣉⡛⢿⠀⠀⠘⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣌⡛⠻⢿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣉⡛⠿⠿⠋⡀⠀⢀⡉⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢌⠀⠀⢠⣼⠂⠀⠤⢐⠺⣵⠤⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⢀⣀⡴⠀⢸⣧⣶⡿⢩⠷⠆⠐⠒⢙⠛⣟⠩⣿⣿⣦⡀⠐⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠶⡯⠐⣚⠛⢻⡷⣔⠉⠐⠋⠛⠳⠄⢲⣍⠁⠾⡖⢋⡕⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠢⢼⡇⠁⠈⡌⠉⠁⠀⠀⢈⣀⣀⡀⠀⠈⠀⠉⠲⣷⣀⣓⣧⡴⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢾⠣⠐⠦⠘⠄⠀⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠂⠾⠫⡥⠀⠀⠘⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⢀⣰⣇⢠⠎⠀⠀⠀⣾⣿⣿⣿⠋⠉⢻⣿⣿⡇⠀⢠⠀⠈⠠⣄⠐⠻⠖⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣉⡾⣝⡋⠛⠂⠀⠀⠀⠉⠉⠉⢁⠀⠀⣸⣿⣿⡏⠀⢈⡿⣅⡀⡽⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠻⢬⠩⠤⠀⠀⢹⢀⡄⢔⣢⡤⠂⢀⣴⣿⣿⣿⠃⠀⠈⠁⠡⡆⣱⡶⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠐⣧⠄⡸⠃⣀⣚⠁⠂⢠⣿⣿⣿⡿⠁⠀⠀⡀⢀⡞⠀⠀⣄⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠉⣀⣡⠠⣶⣹⡀⢿⡁⠀⠀⣿⣿⣿⡏⠀⠀⠄⠒⠋⢻⡟⠢⢁⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣽⣇⠂⠀⠻⣤⡏⣁⡀⠈⠛⠛⠉⡡⢀⣴⠒⠐⢂⡉⠸⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⢯⠠⠔⢃⣿⣿⡟⠃⠀⣿⣿⣿⡄⠀⢛⢡⣀⣼⠀⠀⠉⠋⠓⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⣇⢠⣿⢿⣹⣿⡄⠀⠿⠿⠿⠃⢀⣞⠚⡉⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢋⣼⣇⣹⣿⡥⠃⠀⠤⠠⠖⠞⠉⠛⠉⡙⠉⠙⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢈⣁⣀⣁⣤⣤⣄⣠⣄⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠉⠉⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠤⡄⠀⣠⠤⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⣷⠀⠀⠀⣾⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣤⠴⣾⣯⣗⠤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠚⠛⠛⠻⣿⣷⡄⠀⣉⣷⣠⡖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠠⠄⠒⠒⠊⢹⣷⡊⣆⠉⢻⣕⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠒⣚⣃⠤⠊⠀⠀⠀⠀⠀⠀⠀⠠⣿⡃⡕⠀⠠⣙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠙⠒⠚⠈⠁⠀⠀⠀⡀⠀⠀⠀⡀⠀⣀⣀⣶⣿⡽⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣶⣤⡀⠀⣠⣴⣶⣄⠀⠀⣠⠶⣤⣄⠀⣀⣤⣦⢤⣼⡟⠀⠀⠀⠉⠛⠷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣿⣿⠳⣶⠛⣟⡛⣿⠂⣾⣧⣰⠟⠛⣿⡯⠝⣿⠿⣿⡷⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢻⣵⣾⣿⣿⠿⣿⣧⣤⣽⣟⣠⣿⣈⣇⣀⣰⣿⣤⣤⣏⠀⢽⣧⡤⠤⠔⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⣿⡟⣠⣾⠏⣋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠻⠃⠀⠘⠋⠉⢹⡟⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣿⣛⢀⣽⠇⢀⣏⡐⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠙⠀⠀⠀⠐⠄⠀⠀⠀⠈⠆
⠀⡀⠄⡀⠀⠀⠀⠀⠰⢡⣿⣿⣿⢸⡿⠀⣾⣿⡀⠀⠤⣹⡀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠈⢆
⣼⠀⠀⠇⠀⠀⠀⣠⢷⣿⣟⣿⣯⣿⠀⣰⠋⠁⠀⡀⢲⡟⠩⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠈⢂
⠸⢄⠀⠀⠀⠀⢀⣷⣾⣿⣜⣯⡾⠁⢰⣿⠀⣀⠈⢀⠟⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠆
⠀⠈⠛⠷⠶⠾⠋⡍⠟⣿⠛⠉⡀⠀⠀⠀⠀⠈⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⠓⠀⠀⠈⣟⢩⡈⠊⠀⠀⠀⠀⠈⡄⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠸⠀⣼⡧⠀⣀⠀⠈⠀⠠⠀⢠⣿⡷⠦⣀⠀⠀⠀⠀⠀⠈⠂⠈⠻⢷⣇⠀⢀⣿⡄⠈⠁⣨⠀⠀⠀⢶⣿⠒⠀⠐⠀⠰
⠀⠀⠀⠀⠀⠀⣇⠐⡏⠀⠀⠸⣆⠀⠀⠔⠀⣼⣏⣸⡿⠛⠳⡀⣛⣦⠀⠀⠀⠀⠀⠠⢿⣀⡰⠇⠀⠀⠀⢠⡀⠀⠀⢸⢍⣄
⠀⠀⠀⠀⠀⠀⣏⡴⡇⠀⠂⠀⣹⠀⠀⢠⢰⣿⡇⣿⡀⠒⠆⣼⣏⣿⠷⠀⣀⠀⢀⡠⡽⠟⠛⠛⠋⠀⠲⠶⠧⠀⠀⡼⣈⡹⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⣠⣿⠀⠀⢉⡸⣿⣷⣾⡙⠿⠿⠋⠈⡄⢠⣁⣼⡟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣟⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠠⢻⠀⠈⢻⡄⢿⣿⣿⡂⣠⣤⣶⡌⣻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠐⠧⣴⡸⠀⠀⢼⣯⠈⢿⣿⣿⣿⣿⣿⣷⡟⣟⡁⠀⠀⠀⠀⢀⣀⣾⣷⣶⣾⣦⡴⠀⠀⠀⢀⠀⡀⠀⣰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠋⢤⠣⡀⠀⠀⢱⠨⢿⣿⣿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠁⡾⠛⢿⠻⠛⠻⢁⠗⠀⠀⠀⠰⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢲⡉⡒⠶⠷⠶⠛⠛⠛⠉⠙⢤⣄⠀⠀⠆⠀⠀⢀⡶⠚⢢⡠⠐⠲⠛⠀⠰⠀⢭⣞⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣑⣦⣤⠄⢠⣄⣀⣠⡿⠛⠉⠀⠀⠠⠀⠒⠀⠀⢀⠀⠀⣀⠀⢀⡤⣢⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣸⡿⠿⡇⠀⠀⠄⠀⠀⢀⣴⣷⣶⠿⠶⣚⡻⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠲⠒⢶⡖⠒⠛⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠶⠶⠖⠒⠀⢸⡓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⢀⡀⢾⣣⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣞⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣛⣋⣛⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣿⣿⣭⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡖⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⢳⡈⠳⢤⣤⠴⠚⠡⢄⡀⠀⠀⠀⠀⡇⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⢧⠀⠈⢧⠀⠀⠀⠀⢳⡀⢦⠙⣄⠀⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⡆⠀⠘⣆⠀⠀⠀⠀⠃⠘⠂⠘⡆⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡠⠋⠹⡄⠀⠉⠉⠉⠉⠉⠉⠉⢳⡄⠛⠀⠀⡇⠀⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠐⢦⡰⠊⠀⠀⠀⠙⠶⠤⠤⢤⡤⠤⠤⠤⠾⠤⠤⠤⠤⠇⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠓⠲⠶⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣘⣆⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠒⠒⠒⠒⠀⠀⠀⠒⠒⢺
⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠆⠈⠁⠧⠘⠀⠀⠈⠀⠐⠀⠉⠸⠀⠀⠀⠦⠸

⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠠⠤⠤⠤⢤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢲⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⢢⢸⡂⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⣴⣾⣿⣿⣿⣧⠀⠀⠀⢸
⠀⠀⢀⢸⡌⡠⢰⠂⠀⠒⠒⠐⠂⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⡄⠀⢀⡇⠇⠀⠀⣿⠛⡉⡠⠈⠉⠆⠀⠀⢸
⠀⠀⠈⣦⠁⠀⠃⠀⠀⢀⢀⡀⠀⡀⠀⠄⡟⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢠⠈⡇⠀⠀⠹⡄⠀⠀⠀⢀⠀⠀⢘⢸
⠀⠀⠀⣿⣿⣿⠂⠀⢄⢈⠚⠽⠀⠁⠀⠁⡇⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⡇⠀⠤⢀⠀⠀⠀⠂⠁⠀⢀⣨⢹
⠀⠀⠀⣸⣿⣿⣶⣤⣦⣴⣵⣶⣤⣶⣶⠶⢧⡤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢻⡿⠁⠁⠀⠛⠀⠀⠀⠀⠄⢀⡀⠐⠀⠀⠈⢸
⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⣤⡀⠻⡇⠀⠀⣿⠀⢀⠄⠀⠠⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠻⠷⠄⠁⠀⠀⢻⠈⠉⠁⠀⠀⠀⠄⠂⠀⠐⠛⢺⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⣸⠘⠂⢴⠦⠄⠤⠤⠀⠀⠢⠤⠸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⣄⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢐⡲⠇⠑⢒⠂⠀⠀⠀⠀⠀⠌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⢓⡀⠋⠋⢭⣵⠎⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢂⠀⠀⠠⠀⠀⠠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⡀⠀⠁⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠡⠀⠀⠐⡀⠐⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠡⠀⠐⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠅⢌⠀⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠒⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠔⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⡈⢡⢢⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣶⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⢹⠟⣡⡆⢻⣿⣿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢿⠿⠟⣛⣭⣶⣧⣶⣾⣿⣷⣶⣶⣶⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠀⠀⠀⢾⣿⣿⢫⣝⣿⡿⢿⣿⣋⡍⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⢻⣿⣦⣿⣿⣿⡌⢿⣿⣵⣾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⣛⠻⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢦⠀⠀⠀⠈⢿⣿⢋⢸⢿⠘⡘⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡜⣎⢧⣅⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡐⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣦⠻⣿⣌⡻⣿⡿⢟⣠⣴⣆⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⠟⣤⣶⣿⣿⣿⣿⣌⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡁⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⣾⣇⣿⢸⠗⢯⣸⡯⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠈⠈⠉⠈⠉⠈⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠻⠏⠙⠃⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠄⠂⠀⠈⠉⠉⠀⠒⠢⢄⠀⢀⡼⠇⠀⠀⠀⠀⠀⠤⢱⣄⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠦⣄⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠛⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⡄⠀⠀⠀⢳⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠒⠚⢛⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠚⠉⢀⣀⡉⠓⣄⠀⠀⠀⠀⢀⠔⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⣽⠀⠀⠀⠀⠀⢠⡇⠀⢠⣿⣿⣧⣤⢸⡄⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⣣⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠈⢧⣀⠈⠿⡿⠿⠋⣸⠃⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡼⠀⠀⠀⠀⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡆⠀⠀⠀⠀⠀⠀⠈⠉⠑⠐⠀⠒⠁⠀⠀⠀⠀⠈⠂⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⣸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣴⠲⢦⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⠴⠲⡄
⠀⠀⠀⠀⠀⠙⢦⣄⠉⠳⢤⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⢀⣴⣫⠴⠛⢁⣤⠞⠁
⢀⣴⢒⡛⡏⠉⠉⠉⣤⣤⡀⠹⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠞⣽⠁⢀⢤⡌⠉⠉⠉⣿⣿⡲⣤
⣿⠥⠤⠒⠒⠀⠀⠀⠀⠀⢹⢸⡅⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠂⠀⠀⣽⢠⡁⠀⠀⠀⠀⠀⠒⠲⠦⢬
⢳⣀⣤⠤⠤⠤⠤⠴⢶⡖⠋⠀⢧⠀⠀⠀⠀⣠⠏⠉⣟⠲⠶⠦⣤⣤⡤⠶⠶⣾⠛⢯⡀⠀⠀⠀⢠⡏⠀⠓⣶⠶⠦⠤⠤⠤⠤⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢧⣄⣤⠞⠁⠀⢠⡏⠢⠤⠚⢿⣿⠟⠢⠄⢹⡀⠀⠙⠦⣤⣠⠞⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⢰⣼⡄⠀⠀⠈⡷⣄⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠖⠒⠒⠚⠉⠀⠀⡇⠀⠀⠀⠈⢙⣧⠀⠀⠀⢣⠈⠉⠒⠒⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⡄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⢿⣿⡯⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣶⠒⠲⡆⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢰⠀⢸⠇⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣠⠞⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣟⠁⠀⠀⠀⠀⢹⡄⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣬⣧⡀⠀⠀⣴⣏⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⣄⢀⠄⠒⠒⢤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⢲⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⠒⠆⠀⠀⠱⡄⠀⠀⠀⠀⣬⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠠⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠲⣭⠿
⠀⠀⣠⠴⢶⣶⣶⠀⠰⣀⡀⠀⠀⠀⡰⠠⠒⠒⠒⠒⠦⠀⠀⠀⠀⠀⡶⠊⢙⢏⣷⠒⠀⠀⠀⠉⠉
⠀⠀⢶⣿⣿⣿⡟⠀⠀⢸⠀⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⠢⠄⠴⠃⠉⠀⠀⠀⠀⢸⡆⠀⣀⣀⡀
⠀⠀⠀⠈⠐⢿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣁⣀⠈⠙⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢧⠀⢧
⠀⢠⣾⣿⡅⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠠⠄⡐⣷⠀⠀⢸⡀⢸⡀
⠀⠛⠻⢿⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠃⠂⣿⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠋⠸⢓⠆⠀⠀⢸⡇⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⢹⠁⠀⠀⠀⠀⠀⠀⠁⠰⣿⠀⠀⢸⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⢰⠀⠀⠄⠀⣿⠀⠀⡟⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⣟⠉⠉⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡟⠛⠛⠉⠁
⠀⠀⢀⣠⣄⣰⢄⡀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠁⡇
⠀⠀⠘⠯⣙⢁⣀⣀⡀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠑⢎⣷⣆⡀⢀⡧⣀⣀⢀⠀⢤
⠀⠀⣔⢰⠉⠀⠀⠀⠉⠁⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⡙⣗⡋⣀⠀⠤⠤⢀⡀⢿⣻⡇
⠀⠸⡟⢀⠀⠑⢄⠀⠀⠀⡠⠊⠉⠉⠙⣛⡿⠛⠛⠛⠛⢿⡛⠉⠉⠇⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠰⡀⠀⠀⠀⠈⠉⠃⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠈⠳⣤⠄⠀⠀⠀⡐
⠀⠀⠀⠈⠐⠠⡀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠁

⠀⠀⠀⢠⡄⡀⠀⡀⡀⣀⠀⢠⡄⢠⣀⢀⡀⢀⢀⠀⡀⠀⠀⠀⡀⡀⢀⢀⡀⠀⡄⠀⣄⠀⢀⣀⢠⡀⠀⡄⣠⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠟⡆⡇⠀⣿⠀⠀⢸⠸⢸⣾⡇⣟⢸⢧⡇⠀⠄⠀⠶⠆⣟⠘⣧⠀⠀⠈⢘⢸⡄⡦⢸⠃⠀⡇⡾⠀⠀⠀⠀⠀⣉⠻⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠰⠆⠀⠓⠐⠆⠋⠂⠘⠎⠲⠘⠉⠒⠙⠛⠘⠂⠀⠀⠀⠐⠒⠉⠃⠘⠁⠦⠂⠾⠀⠃⠓⠘⠂⠀⠇⠃

⠀⠀⠀⠸⠉⠉⠩⠙⠉⠉⠉⡉⠉⠈⣩⠉⠉⠉⠍⠉⠉⠉⠹⠉⠉⠁⠁⠀⠈⠉⠙⠉⠩⠉⠉⡈⠉⠉⠙⠻⠏⠉⠉⠉⠉⠀⠀⠀⠁⡆
⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠠⠀⢠⣀⡀⠀⠀⠒⣦⣄⢀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⡉⠉⠀⠀⠈⠉⠅⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⡂⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⢸⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⣶⣶⠖⠂⠀⠂⠀⠀⠀⠀⠰⠦⢀⡀⡀⢤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁
⠀⠀⠀⢸⠀⠠⠄⠀⠡⡄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢁⡄⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢤
⠀⠀⠀⢰⠈⠀⠀⠤⠀⠱⠀⠂⠀⠀⢀⠤⠀⠁⠀⣀⠏⠀⠴⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠐⠐⠂⠉⠁⠀⠀⠠⠀⠀⠄⠀⠀⠀⠚⠁
⠀⠀⠀⠈⠀⠀⠑⠂⠀⠀⠐⠂⠀⢀⠈⠀⠀⠰⠀⠏⠀⠀⠀⠀⠂⠒⠀⠈⠉⠬⠉⠉⢤⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠄⠀⠀⢀⡀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠁⢀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠐⠂⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣄⡀
⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠜⠀⠀⠐⠁⠀⢤⡖⠀⠉⠁⠑⠛⠢⢄⡀⠅⠀⢀⠀⠁⡀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠆⡀⠀⡀⠀⠃⠀⡃⠀⠀⢀⡒⡂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⣈⣀⠀⠀⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢀⡀⠀⠀⠀⠀⢉⡁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⣀⠀⠠⢤⣏⠀⠀⡄⢀⡈⠀⠐⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢁⡄⠀⠀⠀⠀⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣻⣿⣷⡤⠒⠋⠀⠄⠄⢀⠁⠀⠀⠀⠀⠀⠂⠀⠐⠧⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠙⢿⠋⣹⡏⡉⠀⠂⢠⠄⢠⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣷⠀⠀⠀⢤⡁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⠉⠀⠀⢸⠈⠂⡓⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⠀⠀⠈⠋⠀⠀⢀⣛⠃
⠀⠀⠀⢸⠀⠀⠀⢀⡴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠈⠀⠀⠀⠀⢘⡁⠈⢃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢸⠀⠠⠀⠘⢦⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠠⠢⠀⠀⠈⠘⡀⢙⠀⠀⠀⢐⠂⠀⠤⠁⠀⢄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡄
⠀⠀⠀⢸⠀⠀⠀⢀⣻⡄⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠆⢀⢐⢠⡠⢸⠀⠀⠀⢈⣥⣄⠠⠔⠦⠲⠆⠀⠀⠀⠀⠠⡄⠀⠀⠀⠂⠅
⠀⠀⠀⢰⠀⠀⢈⣉⠉⡇⠀⠽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠀⠻⠄⣁⠐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠂⠒⡇⠀⠀⠀⣤⠄
⠀⠀⠀⢾⠀⢀⠀⡙⠈⠒⠶⠒⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠊⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢘⠀⠸⠃⠇⠂⣠⠂⡀⡠⠀⠀⠒⢀⠀⠄⠀⣀⠄⠄⠐⠓⠀⠀⠀⡰⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢸⣤⠀⠀⠂⠤⡀⠀⠐⠀⠹⠀⠀⠀⠀⣀⡁⣀⣀⣀⣀⣀⣀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⡅⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⠟⠃⡀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡟⢉⡝⠀⠀⠀⢩⡟⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠉⠀⢰⠀⠀⠀⠀⠀⢠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⠀⢀⣽⣒⡠⢖⣢⣀⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⡏⠀⠈⠑⠋⢹⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠓⠦⣀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⢀⣼⣿⣶⣄⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⢻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠬⠭⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣁⣈⣉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡋⠉⠉⠉⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠃⠀⠀⣠⠆⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁⠈⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⡇⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠀⠀⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⠶⠄⠀⠀⠀⠀⠀⡞⠉⠙⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣤⡉⠒⠊⡇⠀⠀⠀⢀⠀⠀⣠⢒⡩⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠋⠀⠙⣦⠀⠀⠀⠀⢸⣄⣀⣀⡏⠀⣸⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣟⠓⠈⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢤⠀⡜⠉⠑⠂⠓⢶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⣻⠟⠀⠀⠀⠀⠀⠀⠈⣪⣉⢼⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡘⠒⠀⠀⠀⠀⠀⠀⠈⢁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠣⡀⠀⠀⠀⣀⠴⠊⠙⣿⠃⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡝⠀⠀⠀⠀⠀⣀⣤⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⣈⡩⠤⠖⡋⢸⣻⡄⠀⠀⣤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣀⣤⣄⠐⢯⣀⣨⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡯⣒⡇⠀⠀⡏⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠽⢷⢶⡏⣀⡸⠀⠀⠀⣾⡕⠉⢱⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠖⠁⠀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⡼⠀⠀⠈⠙⠒⠶⢤⡟⠳⢤⡻⠔⠊⠈⢆⠀⠀⡔⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⣀⣀⣀⢀⡁⠀⡆
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠼⠀⠒⠒⠀⠀⢻⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠓⢨⡥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠓⠚⡄⡳⡇
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⣧⣷⠇
⠀⠀⠀⠀⢀⣀⡀⢡⠀⠀⠀⠀⠀⢸⠁⢀⣤⠀⠀⢣⡞⠉⢙⡂⢠⡴⢦⠀⠀⣈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⠀⡏
⠀⠀⠀⢰⠁⠀⢉⣈⡀⠀⠀⣠⣤⢤⣍⠀⠈⡆⠀⠀⠰⡖⠋⠀⠹⣀⠠⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⡀⠀⡇
⠀⠀⠀⠈⢦⣤⠼⠁⢩⠀⠀⢯⡀⠀⣹⣀⣤⡥⠀⠀⠀⢣⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⠷⣾⡤⣇⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠉⠉⠉⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣶⣶⣒⣒⣒⣒⣒⡲⠤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠛⠒⠒⠒⠒⠒⠒⠒⠲⠯⣵⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠂⢀⡤⠆⠀⠀⠰⢤⡀⠐⣇⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠇⠀⢈⣀⡀⠀⠀⢀⣀⡁⠀⢸⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣿⠀⢰⡋⠄⢹⡆⢠⡏⠠⠙⡆⠀⣿⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡟⠀⠀⠓⠶⠊⠀⠀⠑⠲⠚⠀⠀⢻⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇⠀⠀⠀⠀⢤⠀⠀⡤⠀⠀⠀⠀⢸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢈⡷⢾⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠜⠁⠀⠳⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣀⣠⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠉⠉⠉⠉⠙⠒⠒⠰⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣀⠤⠤⠤⠤⠤⠀⣀⣀⡀⢀⢀⣀⡴⠊⠀⠰⡄⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢹⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢤⣤⣤⡄⠀⠀⠀⡤⣴⣦⣦⢀⠀⠀⢸⠓⠠⠀⣿⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠈⠉⠉⠁⠘⠄⠀⠉⠉⠉⠉⠉⠀⠀⠸⡡⠀⣠⣧⡀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⠂⠺⠶⠀⠀⠀⠀⠂⠲⡶⠤⠀⠀⠀⠙⣄⢋⠀⠇⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢀⡇⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡼⠁⠀⠻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣰⠯⠤⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠙⠂⢈⡉⠈⠀⠌⠈⠀⠀⠀⣠⠞
⠀⠀⢀⣀⣀⣸⣌⠢⡀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⢠⠞⡱
⠀⢰⠟⠒⠃⠀⠐⠦⢈⡄⠀⠀⠀⠀⠀⠈⠉⠙⣳⠞⡛⠛⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⠌⠁⠙⠟⠟⣆
⠀⠈⠓⠒⠒⠒⠠⡔⠋⢳⡀⠀⠀⠀⠀⣤⠒⠚⣧⣾⣆⣀⠜⠓⠦⣄⠀⠀⠀⠀⠀⡠⠓⠧⡀⠤⠤⠤⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠁⠙⢦⡀⢠⠞⢸⠀⠀⣴⣿⠠⠀⠀⠀⠸⠋⠳⡀⠀⠀⠴⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⡁⠀⣰⠆⠀⣿⡟⠀⠀⠀⣰⠢⡀⠀⠙⡖⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⡤⠞⠁⡇⠀⠛⠀⠀⠀⢠⡇⠀⠈⠢⣄⠃⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠛⣄⣀⡠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⢹⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⢉⠓⡾⠉⠙⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⢐⢌⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠰⡃⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠸⠀⡁⠂⢄⠀⠀⠀⠈⢠⠀⢇⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠐⠌⠂⠀⠀⠀⠀⡀⠐⠀⠀⠑⠄⠀⠀⠸⠀⡊⠄⠀⠀⠀⠀⡄⠀⠀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠠⠀⠀⠀⠠⠀⠢⡄⢈⠄⠈⠈⠘⢆⠢⡐⠄⠀⠀⡄⠀⢈⠂⠀⢀⠀⠀⢀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠐⠁⣀⠄⠀⣄⠄⠀⠀⠀⠀⠢⡈⠀⠀⠀⠈⢄⠫⠀⠀⠀⠀⠀⠂⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⢠⡀⠀⠀⠀⠀⠀⠀⡂⠘⠀⠈⠀⡠⠀⠰⡔⠀⠀⠀⠀⠐⠈⠢⠀⠠⠀⠀⠑⢄⠀⠀⣀⢨⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠌⠠⠡⠑⢄⠀⠀⡐⠀⢠⡀⠀⢀⡼⠁⠀⠀⢿⠀⠀⡐⢀⢤⡀⠄⢡⠀⡆⡰⠑⢀⠑⡀⠉⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⣀⠑⣀⢁⠇⠇⠑⣆⢠⠃⠀⠀⠀⢸⠀⠸⠀⣐⡎⢳⠀⠈⠀⠀⡼⠈⠀⠀⢡⠐⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⠀⢈⠄⠘⠀⠀⠈⢻⡀⠀⠀⠀⢸⠀⠀⠠⡞⠀⠘⡇⠘⢡⡴⠁⠰⣄⠀⠸⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠁⡶⣄⠀⢨⠀⠀⠀⠀⠃⠀⠀⠀⠘⡆⠀⠴⠀⠀⢀⣃⠄⡀⠁⠀⢀⠇⠀⠀⡈⠄⠂⠸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠈⠀⠉⡇⠀⠙⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠁⠀⠀⠸⡇⠐⠀⠀⢀⡜⠀⡠⠊⠔⣂⢉⠂⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠂⠀⢳⠀⠀⠀⡞⢰⠯⠔⡬⢻⠀⣤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢄⠢⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⡠⠖⠁⢀⠟⢀⠨⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠁⠑⠀⠐⠄⠀⠀⠀⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠆⢠⠀⠀⠈⠿⠁⠀⠠⠏⢀⡟⠀⣠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⢁⡂⠠⠀⠂⠀⠀⠀⢂⠀⠞⣈⠂⢄⡶⡀⠀⠀⠀⠚⢀⡀⠴⠀⠀⠀⠀⣀⣴⡉⠓⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡦⠦⠤⠭⠙⠛⢛⣊⡀⠤⠤⠀⠀⠀⡀⠀⠐⠂⠀⣡⢒⣈⠒⡀⢀⠀⠈⠀⢀⡀⢀⣠⣶⣴⣬⣤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠺⡐⠻⣖⠒⣀⣰⠋⡏⠉⢰⢄⣀⣦⣶⠞⢯⠉⠓⢾⡅⣏⡪⡂⠏⢳⡄⠈⠙⣏⢲⡄⢀⠈⠉⢉⣟⣛⣶⠐⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠋⠉⠁⠈⢯⣅⣸⣿⡿⠯⠬⢝⣶⢾⡇⣲⠞⠀⢧⠁⠧⠀⣨⣿⣄⣀⠁⣼⣷⡦⣤⣸⣹⣋⣷⠺⠚⠻⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠘⠹⠟⠛⠃⠒⠈⠙⠓⠓⠒⠂⠈⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿
⣿⣿⣿⣿⣶⡄⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⡿⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡄⠁⡀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣷⢀⡗⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿
⢈⣉⡉⠉⢁⣈⡉⠉⠉⣉⣉⣉⣉⡉⠈⣉⣉⠉⠉⣉⣉⠈⢉⣉⣉⣉⣉⣉⠉⢉⣉⣀⣉⣉⣉⡉⠉⣈⣉⠉⢉⣉⣉⠈⣉⣉⣉⣉⣉⠉⠉⣉⣉⣉⣉
⢸⣿⡇⠀⢸⣿⡇⢠⣾⣿⠿⢿⣿⣿⢸⣿⣿⡆⠀⣿⣿⠀⣿⣿⡿⠿⠿⠿⠀⢸⣿⣿⠿⢿⣿⡇⠈⣿⣿⠀⢸⣿⡿⠀⣿⣿⠿⠿⠿⢀⣾⣿⠿⢿⣿
⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⣿⣿⡀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⣀⡀⢰⣿⣿⠀⢸⣿
⢸⣿⣿⣿⣿⣿⡇⢸⣿⣷⣶⣾⣿⣿⢸⣿⣿⢿⣷⣿⣿⠀⣿⣿⡇⢰⣶⣶⡆⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⣿⣿⠃⠀⣿⣿⠿⠿⠿⢸⣿⣿⣶⣾⣿
⢸⣿⡇⠀⢸⣿⡇⢸⣿⡟⠉⢹⣿⣿⢸⣿⣿⠘⣿⣿⣿⠀⣿⣿⡇⠈⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠙⣿⣿
⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⣿⠀⠸⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⠸⣿⣿⠀⢹⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⣦⡄⠀⠀⠀⠀⠀⠘⢡⣿⠆⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⢀⣻⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⣿⣿⣀⣠⠤⠆⠀⣀⡤⠶⠚⠋⠉⣀⣤⠤⠶⠒⠛⠉⠉⠉⠙⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢁⣀⠤⠒⠉⣀⣀⣤⣶⣚⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣩⣭⡠⠖⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡟⣰⣾⣶⣦⡀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⢀⡠⠟⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣀⠀⠹⣏⡙⢿⣿⣿⡄⢋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢸⣿⡿⠟⣿⣿⡟⠁⠀⣀⣉⡙⠛⣩⡤⠂⠀⠉⠁⠀⣿⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡠⠚⣁⣀⠀⠘⣿⡅⢠⣿⠏⠀⠀⠉⢁⣈⠉⠛⠁⢀⣴⣶⡄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠀⠘⢛⣿⡷⠀⢻⡇⠘⠿⠀⠀⣴⣾⠿⠻⣿⠀⢰⠟⠋⠹⠇⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⠀⠀⢨⣥⠀⠀⠘⣷⠀⠀⠀⠸⠋⠁⠀⠀⠁⢠⡀⠀⢀⡀⠀⠀⢸⣿⣭⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠀⠀⠀⣠⠶⠦⣿⡄⠀⠀⠀⠀⢠⣶⡆⠀⠀⢷⠀⠻⡿⠀⠀⣾⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀⠀⢰⣿⠀⠛⢻⣷⠀⠀⠀⠀⠀⠙⢡⠆⠀⠸⣇⠐⢦⡀⠀⣿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣇⠀⠀⠀⠀⠴⠋⠀⣀⠀⢻⡀⠀⠁⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣹⡟⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠺⢿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠠⠿⠶⣦⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣀⣴⡧⠾⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣦⣤⣍⣩⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠻⠿⠟⠛⠻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉