Stone Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⢠⡶⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⡿⠋⠘⡿⢋⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣙⣩⠽⢦⣼⠉⢯⣫⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣎⢮⣱⠀⠀⠈⢳⡄⠀⠀⣀⢄⡀
⠀⠀⠀⠀⠀⠀⠈⢯⡴⠃⠀⠀⠀⢠⡧⠔⠺⣷⣻⣹⠀⠀⢀⣤⠶⠚⠙⡟⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⡆⢀⣾⠁⠀⠀⠀⠀⠀⢀⡾⠛⠤⣄⡀⠀⢳⠀⠀⠀⠉⡳⣆
⠀⠀⠀⠀⠀⣠⣤⡴⠢⢿⡉⢠⣿⠃⠀⠀⠀⠀⠀⢠⠏⠀⢀⣀⣀⠈⠑⠺⡄⠀⠀⡰⠁⠈⠳⣄
⠀⠀⠀⠀⠰⣿⣋⠟⠀⠀⠈⢺⡇⠀⠀⠀⢀⣠⠴⠿⠚⠛⠉⠉⡏⠙⠲⣄⠙⣄⡼⠁⠀⠀⠀⠘⣟⠓⡲⢦⣀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣷⡀⠀⢰⠟⠵⢄⡀⠀⠀⠀⢰⠃⠀⠀⠘⡇⢸⡄⠀⠀⠀⠀⠀⢸⡎⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢸⡄⠀⠀⠉⢢⡤⠚⠉⠓⠤⣄⣀⣿⡜⠘⡄⠀⠀⢀⣠⠼⠷⢶⣒⠒⠂⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠞⢿⣿⣇⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢈⣽⡧⠴⠾⠖⢛⠟⠳⣄⠀⠀⠉⠳⣔⠀⡷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⣼⡀⠀⣀⣸⣿⡿⠶⣤⣀⡀⠀⠑⣄⣀⣠⡤⠞⠳⢤⣀⡴⠊⠉⠉⠉⠉⢷⡀⠀⠀⠙⣦⡇⠙⣆
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣷⣚⣉⣩⢻⠃⠀⠀⠉⠻⢍⣋⣉⢉⣀⣀⣀⡤⢤⡞⢷⠀⠀⠀⠀⢀⡼⠧⣄⡀⠀⠈⡿⡖⢻⡄
⠀⠀⠀⠀⣠⣤⣏⣀⠀⠀⢀⣧⡴⠶⠾⠿⢦⣄⠀⠀⠀⠈⢣⢸⠁⠀⠀⠀⠀⠀⠱⣘⡇⠀⢀⡴⠋⠀⠀⠀⢉⠖⢻⠓⣿⣼⣇
⠀⠀⢀⡾⠥⢼⡻⢼⡷⠞⠋⠀⠈⠑⣤⣀⣀⣈⣳⡄⠀⠀⣠⠿⠛⠛⢦⡀⠀⠀⣠⡞⠛⠋⠉⠙⠲⠶⢤⣅⣸⠀⣯⡼⠯⣤⠬⠽⣆
⠀⠀⠈⠳⠖⢻⣿⣭⣀⣀⣀⣀⣠⠞⠉⢦⠀⠀⠈⢹⡀⡞⠑⢦⣀⣀⣀⠹⣆⣰⢫⠗⠤⣄⣀⣀⣀⣀⣀⣈⣻⢻⡿⠒⣶⠥⠤⠤⠟
⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⢱⠀⠀⠈⢧⢀⣠⢾⣳⣇⢀⠎⠀⠀⠀⠉⢹⡿⣇⡀⢰⠁⠠⠀⢀⣀⡤⠞⠉⠘⠻⠷⠋⠀⠒
⠀⠀⠀⣴⣾⣶⠙⠲⠶⠶⠤⠤⢤⡧⢶⣞⣛⠉⠉⠛⠒⠚⠛⠦⠤⠤⠶⠞⠋⠀⠈⠉⠛⠛⠋⠉⠉⢱⣾⣳⡆
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠛⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡠⡀⢀⠀⠀⠀⢠⠀⠀⠈⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡕⢄⡀⠀⠀⠀⠑⢄⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣜⢻⡎⠁⣷⡀⠀⠀⠀⠀⡀⠄⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⢳⢿⣿⣿⡄⢸⡝⡄⠀⠀⠀⢁⠀⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⣄⣿⣿⣿⠀⠱⡝⠀⠀⠀⠠⡆⠀⢀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠘⣭⣻⣾⣇⠀⠙⠄⠀⠀⢠⢻⠀⠀⡀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠈⢻⣿⣿⡆⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠰⠿⠗⢿⣿⣿⣿⣦⣀⡀⠀⠛⠻⠇⠀⠀⠄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠘⣿⣿⣿⣷⣝⣿⣷⣦⣤⡀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⡻⣽⢿⢿⣿⣷⣄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢼⣾⣿⣿⣿⣻⣮⡳⣕⣝⢿⣿⣆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣷⣴⣮⣿⣿⣿⣿⣿⣿⣅⠈⠻⣷⢝⣿⣆⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠽⠁⠁⠀⡊⠑⢍⣻⣀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣄⣀⠀⣀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠈⢦⠀⠀⠈⠙⠿⣏⢁⠈⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣀⠀⠉⠣⠀⠀⠀⠀⠈⠳⣄⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠳⣄⠀⠀⡅⠀⠀⡴⠊⠉⠒⣤⣖⠋⠉⠙⣦
⠀⠀⠀⠀⠀⠀⣠⠤⢶⣶⣤⡼⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠃⣀⣇⣠⠞⠀⠀⠀⢰⣿⠇⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣠⡄⣿⣿⣿⠀⠀⠀⠀⢾⣵⣀⠀⢀⡽⠉⢧⡀
⠀⠀⠀⠀⠀⢸⠛⡄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⣠⣼⡏⠀⠀⠁⠀⢸⣿⣿⣶⠏⠀⠰⠟⣳
⠀⠀⠀⠀⠀⣮⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠰⣿⣿⡆⣼⣿⣿⡃⠀⠀⠀⠀⣿⣿⠃⣹⠀⣀⣚⣭⠏
⠀⠀⠀⠀⠀⠙⠛⠛⣧⠀⠀⠀⢀⣀⣠⣴⠾⣅⣀⣤⠗⢦⣖⠲⣤⣿⡿⠟⠉⠁⠸⢭⣂⣀⣀⡀⣻⣿⡦⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠓⠦⣼⠟⠁⠀⢸⡟⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠦⢤⣿⠤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠚⠋⠉⢠⠃⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠉⠁⠀⠉⠙⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠙⣆
⠀⠀⠀⠀⠀⡼⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⡇⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣀⠀⠀⠀⠀⠀⢀⣴⠂⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡀⠀⠘⣦⡀⠀⠀⣠⣾⠃⠀⠈⢷⣄⠀⠀⡰⡻⢃⣼⡟⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢸⠀⣤⣀⠀⢠⣀⡝⣷⣄⠈⢿⣄⡐⡻⢹⠀⠀⠀⠀⢣⠳⡼⢱⢃⠎⡸⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⠀⠈⠛⢿⢦⡉⣷⣌⡄⢳⣀⣬⣤⣥⡼⢤⣤⣤⣄⠀⢳⠁⡟⡎⢀⡟⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢸⡇⠘⠳⣦⡱⣌⢾⣯⡽⠋⠁⠀⠀⠀⢀⡜⠀⠙⣿⡕⡎⢠⣷⠁⡜⢰⣿⠟⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣧⣀⣠⡬⠽⢬⣆⢺⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⡇⢸⣯⢸⣁⣬⣯⣄⣇⡤⢄⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢹⠁⠢⠄⠀⣻⠿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⠴⢯⣇⣸⢽⣏⠀⠀⠀⢀⡟⠀⢀⣇⣀⣀⡇⠀⣀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠋⠁⠀⠈⠙⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠙⠒⠒⠒⠋⠁⠈⠉⠉⠉⠉⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⣠⡀⠀⡀⠀⢀⣠⣾⡿⣿⣿⣿⣿⣿⣽⠆⡀⠀⠀⠀⠠⡀⡀⣞⠒⠠⠐⠒⠂⠀⠀⠀⠠⣤⡈⠹⣿⠟⢀⠔⠀⡆
⠀⠀⠀⣼⡗⢀⡇⠀⠾⠛⠁⠀⠀⠙⢁⠀⠀⠀⠘⣷⠀⠀⠀⠐⠚⢳⣿⠿⠆⠀⠐⠒⠶⠖⠂⠀⠉⠁⠀⠀⠀⠈⠀⣴⣧
⠀⠀⠀⠛⠻⠿⡄⠀⠀⢀⣀⣄⣀⣤⣾⣷⣤⡀⡠⠈⠓⠀⠀⠀⠀⠀⠛⠶⢶⣤⡄⡀⠀⠀⠀⠀⠀⠀⠉⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠟⠛⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠈⢦
⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⠠⡀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠁⠀⣤⣤⠀⠠⣤⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠇⢻⣧⠀⠀⣇⠀⠃⠀⠀⠀⠀⠀⠀⡄⢹⣿⡇⠘⠛⠃
⠀⠀⠈⠐⠰⠤⣤⡠⠀⠀⢤⣤⠀⢰⣶⣶⡿⠁⠀⠀⠀⠀⣜⠈⠙⣿⣷⣦⣉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠚⠳⠀⠀⠾⠃⠠⠘⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣐⣿⣿⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡄⠀⠀⠀⠀⣹⣎⢻⡯⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠇⠀⠘⠺⢻⠂⠀⠀⠀⡀⢻⡏⢣⡻⡆⠀⠀⠀⠀⠀⢚⢼⣿⣷⠈⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⣷⣌⢳⡀⢹⠀⠀⠀⠀⠀⠀⠈⠘⡫⢮⡇⠰⠋⠀⠀⠀⠀⢸⣟⣶⣦⣤⡀⠀⠘⣧⣼⣠
⠀⠀⠀⠀⠦⠤⠄⠴⠞⠁⠀⠀⠀⠀⠻⠿⡖⠠⣼⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⣠⡀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⣂⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠑⠂⠠⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⢠⣐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡠⠀⠀⠀⠀⠀⠀⠰⣇⡀⠀⠀⠀⠀⠀⠸⠇⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⡘⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢐⠇⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠈
⠀⠀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠂⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢠⡉⢂⣀⠀⠀⡀⠀⠈⠁⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢲⠆⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠛⣩⠋⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠼⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣰⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠘⣦
⠀⠀⠀⠀⠀⢰⠟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣀⠀⠀⠰⣄⠀⠀⠀⠀⣠⡿⠀⠈⠻⣦⡀⠀⠀⢀⢾⡟⢠⣾⠏⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡇⢀⠀⠀⠀⠀⠉⣳⣤⡀⠘⢷⡄⢀⣼⡟⡇⠀⠀⠀⠘⣏⢦⣠⢋⡎⣰⢃⣏⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⢸⡇⠘⠻⣷⢤⡙⠺⣇⠱⡙⢦⠈⢟⠎⡜⠀⡇⠀⢀⡀⠀⠘⣨⠇⣼⢰⠃⣼⢟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠈⡇⠀⣤⣌⡳⣝⢦⣿⣟⢧⡴⠓⠛⠛⠉⠉⢉⡟⠛⣿⣷⢄⡜⠀⣏⠇⢠⠏⣼⣿⡞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⠻⣎⢳⡙⣟⡟⠀⠀⠀⠀⠀⡠⠞⠀⠀⠈⢻⣮⡇⢰⣿⠀⡞⢰⢻⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠘⠷⣴⠞⠛⠛⠻⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡇⢸⢻⣠⠗⠚⠛⠛⢾⡖⠛⢲⡀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣑⣀⣠⠿⠛⠧⣄⣀⣀⣀⣤⣤⣤⠤⠤⠖⠛⠛⠧⠾⠺⣧⣀⠀⢀⣀⡼⣁⣀⡼⢧⣤⣤⣧⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣠⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⢦⡴⠒⠒⠒⢄
⠀⠀⠀⠀⠀⣸⠀⣔⠀⣙⣲⠶⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⡼⣅⠙⠿⡴⠿⢷⣤⡀⠀⠈⠣⢄⡀
⠀⠀⠀⠀⢠⠟⠓⣚⣛⢶⣭⣁⣠⣈⣟⣦⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡼⠒⠁⢂⠀⣇⠀⠀⠈⠙⠒⢤⣴⠞⣧
⠀⠀⠀⢀⣾⣨⣭⣭⣟⣻⣭⣷⣯⣓⡀⢠⠃⠀⠀⠀⠀⢸⣅⠄⡀⠀⠀⠘⣷⢿⣻⣿⣿⠿⣿⠋⠀⠀⠐⣗⠁⢊⠀⡠⢸⡆⠀⠀⠀⠀⠘⡿⣼⠇
⠀⠀⠀⢸⢿⣿⣿⡛⣋⣉⣿⠋⣈⣠⣴⠎⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢽⣴⣿⠾⣿⣿⠁⠀⠀⠀⠀⠈⢳⡶⣯⣬⣸⠁⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠈⢮⠻⠿⢭⡭⠿⠿⠛⠋⡡⠂⠀⠀⠀⠀⠀⠀⠀⠸⡏⢆⠑⣴⣰⠯⣶⣶⣶⡿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣦⣄⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠙⢤⣤⣀⠠⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠥⣽⣏⡾⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⣤⣤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣠⣦⡀
⠀⠀⠀⠀⢀⣤⣤⣶⣶⣿⣷⡶⠶⢤⣤⣄⠀⠀⠀⢣⠀⠀⠛⠿⣬⣜⡿⣿⡿⣶⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣮⣽⣻⣿⣿⣿⣷⣀
⠀⠀⠀⢀⣷⡾⣾⣿⣿⣿⣿⣇⠐⣀⣤⠾⡇⠀⠀⠀⣧⠀⠀⠀⠀⢉⠛⣯⡃⢸⣿⣷⣾⣽⣷⣤⣄⠀⠀⠀⠀⣾⣿⣟⣽⣿⣿⡿⠿⣿⣻⡇
⠀⠀⢠⡿⣋⡀⠈⢻⣿⣿⣿⣿⠩⠁⠀⠀⢹⠄⠀⢰⣷⣧⡀⠀⠀⠀⠀⠈⠓⢾⣹⢿⡿⣿⣿⣿⠄⢳⠀⠀⢠⡟⠛⠋⠁⠉⠉⠀⠁⡀⠀⡗
⠀⠀⠘⡷⣬⡛⢦⡘⣿⣿⣿⣿⢉⠂⡴⢃⡎⠀⠀⠸⣿⣟⣿⣆⡀⠀⠀⠀⠀⠀⠙⠳⢶⣿⣝⡻⠁⡜⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠁⡜⠁
⠀⠀⠀⠹⡌⠿⣷⣦⢹⣿⣟⣿⢀⡞⣰⠏⠀⠀⠀⠀⠀⠈⠹⣷⡿⡄⠀⠀⠈⠀⠄⠑⠁⠀⠉⠙⣶⠃⠀⠀⠀⠈⢢⠠⠀⠀⠂⠀⠀⢘
⠀⠀⠀⠀⠙⢦⡀⠉⢁⣙⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢽⡀⠀⠀⠀⠀⢠⡟⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠙⣄⣀⣠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡤⠤⠔⠚⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠤⣖⣯⣷⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠰⠻⠗⠊⠉⢀⣴⢶⣦
⠀⠀⠀⠀⠀⣠⠏⠀⢸⠀⠈⠳⣄⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠸⣦⠀⠀⡀⠼⣿⣿⣻⣿⡆
⠀⠀⠀⠀⢠⢃⠀⡄⠸⠀⠀⠀⠸⣆⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢶⣶⡿⣭⣵⡞⠁⠀⠀⡇⠓⠦⡤⣄⣀⣁⣿⣿⣧
⠀⠀⠀⠀⡇⠀⡇⢇⢰⡄⠀⠀⠀⣸⣦⠸⡇⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠁⣶⡋⡎⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠀⠹⣇⢾⡆
⠀⠀⠀⣠⠃⠀⠘⡸⢨⠁⢁⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠙⡿⣶⣄⣴⣿⣧⠇⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠘⣆⢳
⠀⠀⠀⠙⣆⠀⢠⢧⠈⡌⡘⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡿⢿⣷⣟⠶⢦⣈⣽⢯⣷⠏⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠘⣦⣳⡀
⠀⠀⠀⠀⠘⣆⠸⣼⠀⢓⡿⣩⣿⣿⢯⡏⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⢃⣞⠀⠙⡿⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠄⣠⡀⠀⠀⠸⡎⣻⡄
⠀⠀⠀⠀⠀⠘⣆⢻⣄⡞⣒⣶⣶⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣵⣋⠷⢀⡤⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⣈⡌⠢⡟⢷⣔⠛⢦
⠀⠀⠀⠀⠀⠀⠘⣯⡿⢙⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡿⣿⣿⣿⣿⣿⣷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠥⣭⡵⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠒⠺⢿⣭⡯⠿⢿⢯⣅⣀⣀⠀⣰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠁⢴⠁⠀⣵⣤⣄⠘⠉⣉⠁⠈⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠤⠀⠀⢠⣸⠟⠚⠉⠀⠀⠀⢀⡤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠟⠡⢠⢠⣀⡔⠀⠃⠚⠑⣢
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣄⠆⠀⠀⠈⠛⣋⠁⠀⢈⠐⠀⠁⠀⢀⣤⠔⠂⠈⠁
⠀⠀⠀⣀⠠⠇⠀⠀⠀⠀⠐⢶⠛⠠⠆⠀⠉⠁⠀⠀⠀⠀⢀⡈⠁⠐⠀⠰⠆⠔⠡⠄⠈⠉
⠀⠀⠀⠎⠀⠀⢀⣀⡠⠆⠦⠀⠇⡀⠀⠀⠠⠤⠆⠀⢠⣤⡞⠉⠀⢀⣦⠀⢴⡂⠆⠀⢀⠀⠸⠾⠟⠂
⠀⠀⣤⣴⠖⠀⡼⠅⠀⢠⣴⠶⠆⠓⢀⠀⠐⠲⢶⠆⢠⡄⠠⠄⠀⢉⡀⠀⠀⠀⠀⢀⣼⠷⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠼⠃⠂⠈⠀⠛⠀⠐⠂⠁⠈⠀⠁⠀⠀⠈⢁⠀⠀⠀⠻⡷⠀⠀⢶⠟⠿⠁⢀⢠⣴⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣠⠿⠁⠰⣶⣆⠀⡱⣶⣷⣭⠏⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠑⠒⠚⢻⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⣤⡼⣃⠔⠀⣠⠿⠛⠁⠀⠀⢀⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢛⡇⠀⢀⣠⠚⠁⠀⠀⣠⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠃⠀⠀⠀⠒⠶⢿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠿⠁⢀⣀⡀⣀⣀⣀⣴⣾⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠆⠀⡄⠀⠀⠐⠀⠂⠀⠈⠃⠀⠀⡄⠀⣀⠄⠀⠠⡾⠘⠀⠀⠐⠂⠀⠀⠀⡅⡆⠀⣇⢂⠀⠀⠀⢨⠉⠢⠀⠀⠘⢻
⠀⠀⢀⠀⣤⠜⠁⠀⡀⠀⠀⠙⡇⢀⡀⠀⢁⠠⡆⠀⠝⠀⠀⠀⠜⠂⠀⠀⠁⠀⠒⠀⠾⠋⠁⠀⠋⠀⠀⠀⠀⠴⠓⠒⠈⠀⠀⠙⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠙⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠄⡄⢀⠀⠀⠀⠀⠀⠰⠃⠀⠀⡠⡀⠀⢥⣁⣀⠐⢶⣶⣿⣛⡛⠀⢰⠃⠀⠀⠀⠀⠀⠚⣻⠄
⠀⠀⢠⠘⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠃⠀⠀⠀⠀⠐⠀⠞⠀⠈⠀⠀⢸⠭⠛⠈⠁⢸⡝⠃⠀⠉⠂⠁⠂⢀⣀⣠⡿⠁⠀⠀⠈
⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⢋⢿⡉⣴⣀⣄⣀⣠⢀⣠⠀⣀⣠⣄⣠⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠐⠐⠦⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠚⠑⠃⠓⠋⠋⠿⠝⠃⠀⠃⠙⠑⠓⠋⠂⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠁⠘⠣⠤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⣄⡟⡒⠀⠀⠀⡀⠀⣄⣀⣀⡄⣤⠀⠀⡀⠀⠀⠀⠀⠠⠠⠰⣤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⢀⠤⠄⠂⠀⠀⠀⠀⠀⠀⠋⢩⠗⣦⣄⡂
⠀⠀⠉⠉⠛⠂⠀⠚⠛⠀⠈⠉⠁⠒⠀⠀⠀⠉⠉⠀⠀⠈⠀⠂⠀⠀⠀⠀⠉⠐⠒⠚⠁⠀⠀⠈⠂⠀⠀⠒⠒⠋⠁⠀⠀⠀⠀⠀⠒⠐⠃⠈⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠙⢻⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠈⠈⣷⣀⠀⠀⠀⠱⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣩⣁⢒⠖⠋⠉⠉⡩⢷⣀⣀⣘⣀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠁⠈⢳⡚⢲⠶⢯⠖⠉⠀⠀⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⣠⣤⠷⠼⠤⠼⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣀⡀⡼⣞⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠀⣀⡀⠀⣹⠖⠒⠛⠉⠉⠉⠳⡏⢢⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠈⢳⠖⠶⠾⣄⠀⠀⢠⠞⠉⠉⠉⠉⢳⡥⢄⢀⣠⣄⣀⣀⠀⢹⠀⠙⢦⣤⣼⡆
⠀⠀⠀⠀⠀⠀⢠⡋⠐⠲⠤⢬⣄⣀⠀⠈⢲⠦⢼⣤⠴⠖⠛⠛⠛⢦⡼⠉⠀⠀⠀⠉⠓⢾⡤⠒⢬⠦⣼⠁⠉⢳
⠀⠀⠀⠀⠀⠀⣸⣅⠀⣠⠞⠉⠉⠉⠙⠓⣇⠀⡯⣄⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢹⡖⠛⠲⣯⡀⢠⣌⣳
⠀⠀⠀⣀⠀⠀⠁⣀⣹⠇⠀⠀⠀⠀⠀⠀⢸⢤⡇⠀⠉⡲⢶⡖⠛⠓⠛⠶⣦⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢳⡎⣀⣈⡇
⠀⢠⠞⠙⢭⡉⠉⠓⡞⠀⢠⡒⢒⣄⣀⣀⣈⣈⣳⣤⣤⢧⣼⡀⠀⠀⠀⠀⠈⣧⣠⣤⣤⡴⢯⣀⠀⠀⠀⢸⠇⠀⠀⠙⣆
⠀⡟⠀⠀⠀⠙⠶⢄⠳⣞⠉⠉⠉⠉⠰⠛⠉⠉⠉⠓⠦⣤⣄⣉⠷⣄⣀⡤⠞⠁⠀⠀⠀⠀⠀⣸⠦⠤⣴⠋⠀⠀⠁⠀⢹
⢸⠃⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠛⠛⠛⢦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡏⢣⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢀⡤⠟⣒⣦
⢸⡀⠀⠀⠀⣰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠤⢤⣤⣤⡇⠀⠀⠀⢰⠇⠀⣧⠀⠀⡀⣀⠀⢐⡟⡶⠚⠉⠉⠙⠻⣯⠒⠉⠁⢈
⠀⠓⠦⢤⣄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠀⠙⡆⠀⣠⠾⣤⣴⣍⣑⡶⠶⠚⠲⣎⡼⠀⠀⠀⠀⠀⠀⣻⠤⠤⠖⠛
⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⢀⡟⠉⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⡿⠹⣄⣀⣀⣀⣤⢾⠟⠛⠍⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⢑⣲⡤⠤⠤⠶⠖⠋⣀⣀⠈⠣⣠⣖⠛⠛⠋⠉⠙⠛⢦⡀⣔⣙⡇⠁⠀⠀⠦⢤⠤⠞⠁
⢀⠴⠶⠶⠶⠦⢤⡀⠀⠀⠀⠠⣖⠋⠉⠉⠉⠙⢳⠀⣾⠉⠁⢈⡷⠀⡞⠈⠑⠒⠲⠶⠦⠤⠶⠝⣦⠉
⡏⠀⠀⠄⠤⠄⠀⣿⠀⠀⠀⠀⠑⣍⣉⣈⣀⡤⠞⠀⠈⠉⠉⠉⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⣠⠇
⠈⠓⠶⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠻⣏⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢴⠖⠋⠁⠀⡠⠀⠀⠀⠈⠓⢤⡙⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡾⢃⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⠼⠷⢦
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⣱⠎⠀⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⣰⠁⠀⠹⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣠⢴⠧⠤⠴⣧⣄⣀⠘⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣷⠀⠀⠀⠈⢳⡤⠚⠉⢹
⠀⠀⠀⡴⠋⠀⠈⠳⡀⠀⠀⠀⠉⠳⣌⡇⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣧⡏⠀⠀⠀⠀⠀⢳⠀⠀⡞
⣠⠖⢹⡇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢸⣤⠶⠶⠿⠷⠯⣍⣉⡁⠀⠀⠉⠉⠳⠤⣄⣀⡀⠀⡟⠀⠀⠀⣠⡴⠒⠚⠶⠦⣷
⣇⠀⠀⢳⡀⠀⠀⢀⠔⠚⠛⠳⣄⠔⣻⠁⠑⠤⠀⠀⠀⠀⠀⠉⣳⣆⠀⢀⡤⠖⠚⠋⠉⠉⠉⠛⢦⣸⠁⠙⡄⠀⠀⠀⢘
⠈⠉⠉⠉⠙⠓⠒⠚⠳⢤⣤⠴⠓⠖⠫⠤⣀⣀⣀⣀⡀⠀⠒⠚⣁⡼⡲⠾⢧⣀⠀⠀⣀⣀⣀⣀⣀⡿⠓⠒⠚⠶⠤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢺⣀⠀⣀⡏⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⣺⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠋⠉⠉⠓⢦⡀
⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡼⠋⠒⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠹⡄
⡼⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦
⣧⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣿⠀⠰⣤⡀⠀⠀⢀⣴⠋⣄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢸⠀⠀⠀⠀⠈⠳⣄⡀⠹⣦⠀⣠⡿⡇⠀⠀⠘⢟⢆⣠⢻⢃⠞⣏⣠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⢸⠈⠛⢶⣤⡙⢾⡘⡝⢆⠘⣳⣱⠁⣇⣀⣀⡀⠈⢪⠃⡞⡞⢰⢟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠰⣤⡑⢝⢾⣿⣳⠞⠋⠉⠉⠉⢁⠋⠙⣿⡦⡜⢰⡟⢀⡞⣼⡿⡏⠀⠀⠀⠀⢀
⠈⣇⠀⣀⣹⣮⣧⢳⡏⠀⠀⠀⠀⠐⠁⠀⠀⠈⣿⡇⢸⡇⢘⣀⣳⣇⣠⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠
⠀⠈⣟⠑⠀⠀⢹⠾⣆⠀⠀⠀⠀⢀⣀⣀⣀⡤⠯⣇⣸⢵⡋⠀⠀⠀⡽⠀⢀⣇⣀⣸⡀⣀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠛⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⢻⡄
⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢻⡄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢹⡆
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣀⣸⣇⣤⣤⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠉⠀⠀⠀⠀⠉⠳⣦⣄⣀⡀
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷
⠀⢿⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠈⠒⢤⣀⣀⡀⠀⠀⢸
⠀⢈⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⣠⠤⠴⠖⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠘⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠤⠄⠀⠀⠀⠀⠀⠀⢸⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡄⢸⡄⠈⠉⠙⠛⠛⠓⠛⠛⠛⠒⣶⠟⠛⠳⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⡛⠋⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠻⢮⣇⠀⠀⠀⠀⠀⢀⣀⣤⡴⠛⠁⠀⢀⡤⠶⠖⠛⠛⠛⠛⠉⠉⠉⡹⠙⢶⡀⠈⠻⣆⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠉⠛⠓⠒⠒⠛⠉⠉⠀⠀⠀⠀⣸⠋⠑⠦⣤⣀⣀⣀⣀⣀⣀⣰⠃⠀⢸⡇⠀⠀⠈⠉⠙⠛⠛⠶⠦⠤⠶⠶⠞⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⣗⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⣀⣀⣷⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠂⢂⡤⠒⠂⠉⠁⠀⣉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⣸⡿⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⣏⣇⡤⢄⡀⣇
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢐⣀⡼⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣰⢷⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⢹⡄
⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⠤⢴⣿⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠿⠈⠀⠀⠀⢧⣤⠢⢤⡀
⠀⠀⠀⠀⢀⡾⢠⠊⠉⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣤⠈⣷⣄⠙⣄
⠀⠀⠀⠀⡞⠁⣏⠀⠀⠀⠀⠀⠀⠀⢠⠜⣆⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢉⡟⠉⠉⠛⢿⣀⠀⠙⣆
⠀⠀⠀⡸⡷⠊⢁⣈⠐⡄⠀⠀⠀⠀⠿⠁⠹⣆⠀⠀⠀⠀⠀⠀⢻⠗⠢⢤⣼⠟⠀⠀⠀⠀⣠⠚⢳⣆⣸
⠀⠀⠀⢸⠃⠀⢸⣟⠃⢿⡀⠀⠀⡰⠁⠀⠀⣿⣇⠀⠀⠀⠀⠀⣤⣶⣒⢸⡇⠀⠀⠀⠀⠘⠋⠀⠘⣿⠗
⠀⠀⠀⢟⠀⠀⠈⣅⡀⢸⠷⠀⠀⢀⡀⠀⠀⣿⣿⠆⠀⠀⠀⢠⣿⣿⣿⣹⢧⣀⡀⠀⠀⠀⣇⠀⣠⠃
⠀⠀⠀⠈⠑⠐⠒⠛⠓⠋⠐⢤⣴⣟⠃⠀⠀⠝⠙⠛⠈⠉⠙⠛⠛⠛⠋⠁⠀⠀⠈⠑⠢⠶⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⢿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸
⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣄⣀⣀⣀⣼
⠀⠀⠀⡟⠉⠉⠙⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣷⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠙⣆
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⣆
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣤⠴⠷⠒⠒⠒⢦⣀
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦
⠘⣧⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⠎⠀⠀⠀⠀⠢⣄⣀
⠀⣸⠟⠉⠉⠉⠉⠉⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠤⠴⠒⣿
⡾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢻⡀
⢧⠈⡗⠀⠤⠤⠤⠤⢤⣤⣤⣀⣼⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⢾⡆⠉⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠘⢦⣻⠀⠀⠀⠀⠀⢀⣀⣠⠞⠁⠀⣀⣬⠭⠭⠿⠿⠟⠛⢛⠷⣄⠀⠻⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠉⠓⠲⠶⠖⠚⠉⠉⠀⠀⢠⡞⠓⠤⣀⣀⣀⣀⣀⣀⡞⠀⢸⠀⠀⠈⠙⠛⠒⠲⠤⡤⠤⠶⠶⠒⠛⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠈⠉⠉⠉⢹⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣤⠴⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⣍⣩⣶⢰⣂⠐⣢⣀
⠀⠀⠀⠀⠀⠀⢀⠴⡇⣁⣻⡉⡕⠒⢻⡛⠛⣽⡇
⠀⠀⠀⠀⠀⡠⠿⣈⣻⡛⣩⠓⠻⠿⠟⢃⡞⠹⠁
⠀⠀⠀⠀⣴⠃⠙⢻⣛⠅⠻⢴⣶⡿⣠⡟⠀⢻⣇⣀
⠀⠀⠀⣎⡈⠛⠻⠟⠙⣗⣤⣴⣇⣰⣟⢁⢀⡟⡷⣭⣿⣍⠐⠶⡂⠠⣤⣄⣀⡀
⠀⠀⠀⡆⠂⠈⠉⠁⠒⠒⠂⠤⡾⣻⠣⣀⡿⣿⣟⣻⣋⡹⢽⡶⠏⢾⣤⣨⣦⡜⠛⣗⠒⣄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⣇⣧⣿⢮⡷⠿⣛⠚⠵⣶⣿⢴⢍⣉⣯⣩⠿⢿⠿⣾⡇⠀⠀⠀⠀⠀⠀⣤⢰⢈⣰⣶⣧⣬⣿⣿⣤⣿⢿⣾⣷⢄
⠀⠀⠀⠗⠠⠄⣀⠀⠀⠀⠀⠀⢷⡿⡇⡿⢑⠀⠀⠀⠈⠁⠐⠀⠂⠽⠟⣛⡙⠷⠾⣿⡇⣷⣀⣀⠀⠀⠀⠀⡏⢆⢹⢥⣭⣾⣧⣬⣷⢷⣬⣷⣿⣤⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⣯⠧⢃⣿⡢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢉⢹⡟⣼⡿⣶⣶⡷⣴⡀⣀⣃⠀⣳⢟⠟⠛⢟⢍⢝⢝⠙⡡⠉⠊⠈⢩⣗⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⡾⣿⠫⡫⠑⠒⠦⠤⢄⣀⡀⠀⠀⠀⠀⠈⠸⣥⡟⣀⣿⣵⠶⠿⢿⣤⣌⣷⢷⠔⠕⠅⠑⠑⡡⡠⢊⢀⢔⢀⣴⣿⣏⣠⠉
⠀⠀⢀⢾⠂⠒⣄⣀⡀⠀⠀⠀⣏⡿⠀⢹⢕⢌⠂⠀⠀⠀⠀⠆⠈⠉⠉⠐⠒⠤⠼⣯⡔⢟⣿⣽⡦⣖⣈⢛⣏⢹⣿⡛⠋⠛⠛⠚⠋⠉⠉⠉⠉⠉⠉⠁
⠀⡠⠡⠼⢿⠿⠟⢹⣦⣤⣾⣶⠛⡄⡜⣿⣤⣕⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠧⠵⣿⣿⣳⣿⢹⡅⠁
⣔⠀⢿⣦⣴⡇⢰⣄⣉⣻⣴⠃⡼⠐⣱⠟⠡⠭⢭⠉⠉⠓⠒⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣟⣀⣀⣀⡒
⡏⠉⠐⠒⠂⠠⠬⢿⢟⡿⠃⢰⢡⡷⠉⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠢⠤⣄⣀⣀⠀⠀⠀⢀⡆⣹⣼⣓⣀⣀⣀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⣱⠯⠉⢁⣀⡐⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠿⠿⠿⠿⠿⠭⠭⠧⠀⢀⡀
⠙⠢⠄⣀⣀⠀⠀⠀⠀⣎⡾⠃⠒⠒⠆⠀⠀⡠⠤⣁⣐⣾⣣⣤⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⢤⣶⣖⣲⣾⣯⣭⣿⣆
⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠂⠈⠉⠉⠉⠀⠀⠉⠻⡛⣯⣉⣱⣿⣶⡾⠷⣄⣀⠀⠀⠀⠀⠀⠀⣾⣸⣠⣠⣬⡤⣤⣤⣤⣈⡅⠀⢠⣤⣉⣻⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠫⡉⣏⠁⠐⣗⣦⣼⣿⣍⡁⠂⠀⠀⠈⠋⢣⠡⣯⣉⣽⠿⣲⣶⡿⣿⣿⣿⢿⠿⠿⢻⡟⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠘⢏⠻⢿⡟⠉⢽⣄⣀⣹⣆⠀⠀⠀⢇⠀⢧⡬⠿⢷⠖⢞⢟⢟⢍⠕⡁⠀⢀⠁⣽⣒⣒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⣜⠷⣶⠾⠛⣛⢭⢞⡧⠀⠠⠌⢆⣸⢊⠔⠁⣐⠉⠕⡁⢁⣪⣬⠦⠶⠛⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠣⠤⢖⢛⡭⢢⣾⡏⠥⠄⠄⠈⠷⣥⡦⠶⠷⠾⠯⢙⣉⣁⠀⠐⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⡇⢇⢑⣔⣯⠿⠋⠁⠅⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣷⣗⠛⠁⠀⠐⠂⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙



⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣶⣿⣿⡶⠦⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⣇⣠⡤⠤⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣐⣸⣉⣀⣀⣀⣀⣀⣀⣀⣀⠤⢄⣀⠀⠀⠀⠀⣀⣀⣀⣀⣐⣀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⣼⣧⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣿⣿⣿⣯⣭⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣨⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣯⣶⣶⣶⣶⡖⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠄⠀⠀⢸⣿⣿⣿⡀
⣤⣤⣤⣤⣤⣤⣤⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣀⣀⣠⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⠶⠦⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣗⣶⣶⣶⣶⣦⣤⣴⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠄⣀⡴⠖⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠚⠛⠲⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⡟⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠲⣶⣦⣤⠁⢸⡀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⣇⠘⡇⠰⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠻⣧⣿⣶⣤⣤⣄⣀⢀⠠⠔⠊⡀⢻⣿⡄⢳⣼⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠘⣿⣿⣾⣿⡷⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⡛⢿⡇⠀⠀⢠⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣞⡝⣷⠈⣿⢀⣴⣿⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠂⠉⠉⠉⠐⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠯⣉⡀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢲⠖⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠖⠺⢄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠊⠉⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠑⠢⣼⣤⡤⠴⠒⢺⡏⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⣠⡴⠶⠖⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⢦⡀
⠀⣠⠞⠁⠀⢀⣀⣈⣛⣛⣋⣉⣉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣭⣭⣽⣿⣿⣯⣥⣀⣀⣀⣠⣹
⡞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⣶⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠚
⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀
⠀⠀⢀⡼⠋⠀⠀⠉⠉⠉⠉⠉⠉⠙⠓⠒⠲⠶⣦⢸⠀⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡬⢻⡆
⠀⢰⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⣾⡄⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⡴⠞⠋⠁⠀⠀⡇
⠀⢻⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠒⠶⠶⣞⠀⣸⠃⢉⣳⠶⠖⠶⢤⣄⣀⠀⠀⢸⡇⠀⠀⢀⡠⠖⠁
⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠴⠟⠛⠉⠀⠀⠀⠀⠀⠀⠉⡉⢷⠬⣧⠴⠚⠁
⠀⠈⠉⠉⠉⠙⠓⠒⠒⠶⠶⣤⠤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠑⠤⣀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⢀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⠦⣤⠒⠉⠀⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢄⡀⠀⠀⣿⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢼⡤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⢀⣀⠠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠂⡿⠴⠶⠚⣿⠛⠥⣠⠤⠴⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⢀⠀⣿⡇⠀⢐⠀⠀⢐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠤⣾⡷⠲⠻⠛⣛⣠⣴⠖⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠈⢱⠉⠁⠀⢵⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⣀⠀⠐⠀⠂⠠⣀⠀⠀⠀⠀⠈⠀⠦⠀⢐⢸⣀⣤⡤⣽⠚⠋⠉⣷⣦⣤⠴⠒⢒⣳⡄⠀⣄⡼⠇⠠⢄⡀
⠀⠈⠁⣶⢚⠝⢹⠀⠀⠠⠀⠀⠀⠀⠀⠀⢘⡠⠂⡀⣻⠀⠀⢀⣏⣿⠀⠈⡉⠁⠀⡿⠒⠚⠉⡖⠒⠒⠛⡆
⠄⢠⠄⣷⠀⣠⣼⡆⠄⠀⠀⠀⠀⠂⠄⠒⠈⣇⣀⣤⡾⠓⠛⡫⠔⠿⠤⣀⣧⣤⣴⡟⠀⠐⢦⡇⠀⠀⢘⣦
⠀⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠈⠉⠉⠁⠂⠀⠀⠀⠁⡄⠀⠀⠒⠄⡀⠉⠛⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠁⡏⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠈⠀⠀⢣⣇⣀⣄⣀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣦⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⢿⣿⣿⣿⣿⠟⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠉⠉⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⠉⠉⠉⠙⠊⠁⠀⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡥⠿⠂⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⣀⣤⠀⠐⡾⠟⣯⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⢀⠀⢀⣠⠤⠤⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣠⡴⠃⠠⠐⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠋⢁⣽⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⣤⣉⣄⣀⡀⢴⣿⣿⣿⣿⡟⡝⣼⢯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠓⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⣠⣾⠿⣿⢿⡟⢱⣿⣿⡿⣿⠑⣰⣼⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠠⣴⣿⡿⠷⣄⠀⠁⠈⠋⠉⠀⠈⢉⣼⡿⣫⣾⣣⡾⣫⣹⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣤⣼⣧⣠⣤⣤⣤⢄⠤⠤⠤⢤⣼⠁⠀⠀⠀⠠⠀⠀⠁⠈⠀⠀⠀⠈⢳⣆⢠⡇⡄⣌⠛⡹⢻⣿⡟⡿⣫⣾⠟⣩⡿⣿⣿⣿⣇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣤⣼⣿⣾⡇⠠⡿⡄⣷⠟⣫⡮⣼⠟⣡⢞⢟⡵⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣸⣾⡄⠐⢀⣀⢠⣤⣼⣻⣟⢿⣿⡿⣿⣿⣿⠁⠘⡇⣀⣸⣞⣅⠻⠁⠘⠃⠉⠉⠉⣩⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠠⠀⢠⣥⣾⣿⣿⣿⣠⡿⢃⣞⡿⠡⠙⢋⡞⡑⣙⣿⣿⣿⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⣠⡾⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⠀⠀⠈⣀⣤⡼⢹⣿⣿⡟⠀⠀⠻⠁⠁⠀⠀⠐⠛⢿⣿⣭⣿⣿⣿⣿⠃⠀⠀⠀⡀⠀⢀⢠⣛⢉⡵⠫⠪⣾⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⢻⡿⣆⣸⣶⣿⣟⣯⣴⣾⣿⣿⣷⡴⠿⢶⠂⠶⣶⣷⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣧⡄⠘⣸⡷⣿⣿⣾⣏⠀⠠⢁⣛⡙⠁
⠀⠀⠀⠀⠉⡉⠀⠠⠠⣶⢾⡿⠧⠀⠈⠘⠛⠋⠉⢀⡀⠀⣲⠶⢶⣤⣬⣭⣍⣉⣉⢠⣄⣤⠄⢀⡿⠿⠿⠷⠶⢛⣋⠁⠄⢀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⠈⠀⠠⠄⠀⠈⠉⠁⠀⠈⠉⠉⠉⠉⢋⠀⠀⠠⠄⠀⠻⠶⠶⠶⠀⢀⣀⣤⡤⠖⠉⠛⠛⠒⠳⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠓⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠠⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡘⡷⡀⢠⡄⢠⡟⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣏⣷⣽⣿⣤⡟⠀⠀⠀⠀⠀⠀⠃⠹⡀⠑⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡏⠉⠀⠈⠀⠀⢸⠧⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢿⣠⡾⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢣⠀⠀⠀⠀⣰⡟⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⡇⠀⠀⡀⣀⠀⠀⠸⡿⣡⠔⡪⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡑⢶⢤⣏⣀⠀⠀⠀⠘⢦⡒⠀⣴⠋⠀⠀⠀⠀⣣⡤⠶⠶⣤⡀⠀⡼⢧⡀⠀⢀⣴⠟⢻⣉⠉⠉⠉⠙⠛⠿⣅⡾⡶⣃
⠀⠀⠀⠀⠙⢶⣄⣻⢮⣿⠀⠈⠉⠒⠲⠒⣶⢿⠾⠷⢤⣄⣀⡴⠛⢅⣀⠤⣾⡥⠿⣾⣀⡤⡷⢶⡞⠁⠀⠀⠑⢄⠈⠀⠀⠀⠀⠈⠛⣶⡏
⠀⠀⠀⠀⢀⣀⣙⣽⠿⡿⢤⣄⣀⡀⠀⢸⡏⠙⢳⠀⢠⠻⣇⠀⠀⠀⠣⣰⡯⠤⠤⠬⣿⣀⡇⡿⡆⠀⠀⠀⠀⠈⣳⢄⡀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠈⣹⠞⠁⠀⠱⡄⠀⠈⢹⣷⠚⢷⣤⣤⣧⠃⠀⣹⡦⠤⠶⠖⠛⠷⣤⣠⠶⠛⠙⢻⡇⠘⣄⠀⢀⣀⡰⢁⣀⣉⠒⠤⣉⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢷⡒⠒⠒⠋⠉⢓⠒⣿⠀⢣⠀⠀⠀⣿⢀⡾⠉⠓⠒⠤⡤⡶⠒⠊⢿⢳⡀⠀⠈⣷⣠⣨⡞⠋⡟⣿⣉⡏⢉⠟⣦⠈⡏⠉⣹⠇
⠀⠀⠀⢀⡀⠈⡛⠲⠶⢶⡶⠛⠛⠛⠲⣧⣤⣤⣤⠟⣿⠁⠀⠀⠈⢰⠁⢸⠀⢠⣿⣛⠛⢲⣾⡍⣹⠋⠀⠀⢱⠖⠋⣷⣫⡶⣻⠛⢷⠞⠋
⠀⡀⠀⠀⣤⠶⠶⣤⠀⠾⣄⣀⠉⠀⢂⣼⠃⠒⠂⠀⠈⠟⠫⠛⣛⠺⠶⠾⠟⠋⠻⢮⣭⣥⣤⡿⠻⢧⣀⣠⣧⣤⡴⠏⠙⢷⣡⣤⠞⠀⠉⠛
⠀⠀⠀⠈⠳⠿⠶⠞⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⠞⠛⢳⡦⢤⡀⠂⠀⠀⠀⠈⠭⠄⠀⢀⣭⠤⡄⠑⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣷⣾⣭⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠐⣌⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢩⣽⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣠⡁⠀⠀⠀⠀⠀⢸⣿⣇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠙⠉⠁⠀⠀⠀⠀⠀⠰⠿⠿⠖⠋⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣥⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⣻⠶⠀⠀⠀⠀⠀⠀⢾⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢳⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⡿⡉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⡖⠹⣷⠋⠉⠪⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣳⡀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣿⡿⠀⠀⠀⠀⠀⠠⠀⠀⠀⣻⣶⣦⣠⡇⠀⠀⠀⢳⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⢹⠀⠀⠀⠀⠀⠀⠀⢠⢻⣻⡿⠀⠀⠀⠀⠀⠀⣶⡅⠀⢠⣾⡿⠿⠿⣅⡄⠀⠀⠸⣏⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⣿⠲⠃⠀⠀⠀⠀⢀⠀⡷⣠⣤⣿⠋⠀⠀⡀⠙⢷⡀⠀⠀⢸⡄⢰
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⢀⢠⡶⣶⡿⠋⠁⠈⠉⠄⠀⠀⡆⠀⠘⡇⠀⠀⢸⡠⣿
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⣿⠇⠀⠀⠀⠅⠲⣾⠃⠀⠀⠀⠀⠀⢀⣼⠅⠀⢀⡷⠀⠀⠀⡄⣽
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣸⣯⠀⢠⣤⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⣾⣟⠀⠀⢸⡿⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⢳⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⡀⡒⢵⢷⡿⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠘⣧⠀⢸⠓⡇
⠀⠀⠀⠀⠀⠀⠱⢦⣿⣿⡗⢄⡀⠀⠀⢀⣀⠀⣿⣿⢿⣥⣤⣭⠿⠁⠀⠀⠀⠀⢀⣠⣴⣯⠶⠂⠀⢀⢀⡴⣿⡧⡸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢄⣀⣈⣙⣀⣹⡿⠛⠉⠁⠙⢦⣠⡀⣤⣠⣾⣿⣿⣿⣆⣤⣒⣰⠻⡏⠰⠟⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠚⠿⠿⠿⠯⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡤⡲⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠒⠒⠒⡲⣤⣤⣤⣄⠀⠀⠤⠄⡏⠉⠉⠁⠀⠐⠑⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⠀⠀⠐⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠃⠀⠀⣷⠀⠀⠠⠅⠀⠀⠀⠀⠀⢀⡀⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⠀⢹⡀⠀⢸⠆⢀⠀⠀⠀⣠⠛⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠦⠤⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀⠐⠁⢈⣡⣾⠇
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⠦⣤⣤⡏⠀⠀⢀⠀⠀⢹⡀⢘⠀⠀⠀⢠⣦⣴⣿⠿⠛⠁⠀⠀⠀⣀
⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠤⡌⠉⣉⣘⡛⠛⠺⠇⢘⣀⣤⣾⠿⠓⠁⠀⠀⠀⢀⡠⠖⠋⢩
⠀⠀⡖⠒⣶⠶⠶⠶⠶⠶⢖⣒⠒⠂⡇⠀⠈⢩⣀⣉⡉⠙⠙⠋⠉⠉⠀⠀⠀⣀⡠⠴⠊⡟⠀⠐⠀⢰
⠀⠀⡅⠀⡇⠀⠀⣀⣀⣀⠀⠈⢳⠀⠇⠀⠀⢸⡇⠀⠀⠈⠛⠛⠓⢆⡒⠒⠆⢻⠀⠁⠘⠁⠐⠀⠀⠻
⠀⠀⡇⠀⡄⠀⠀⠧⠤⠬⠂⠀⣰⠀⠀⠀⠀⢸⡇⡰⠀⠀⠀⠀⠀⠀⠹⣦⠤⢼⣶⣶⣶⣶⣦⣶⣶⣾
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠺⢅⠀⠀⠀⠀⢸⣷⠃⠀⣠⡔⠀⢤⣤⡔⠁⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡃⠀⠀⠀⠀⡎⠁⡦⠀⠀⠀⠇⠀⠀⠀⢸⣿⠀⠀⣭⡀⠀⠀⠀⠀⠀⢠⢨⣍⣥⣤⣿⣿⣟⣿⣿
⠀⠀⡇⠀⡇⠀⠀⠉⠉⠀⠀⠀⣠⠇⠀⢠⢀⢸⡇⠀⠀⠈⠓⠂⠐⠢⡀⠀⠀⢘⡄⠀⠀⡤⠈⣼⢋⣿⠂
⠀⡀⠦⠤⠕⠒⠒⠒⠒⠒⠒⠉⠀⠀⠾⢸⣸⢸⣇⡈⢄⡀⠀⠀⠀⢀⣸⠆⠀⢸⠀⠀⡐⢁⣠⠷⠛
⠀⠉⠉⠛⠛⠓⠶⠋⠉⠟⠉⠉⠠⠏⠙⠛⠚⠓⠦⢤⣍⣉⣛⡒⠮⠭⠀⣀⣀⢰⠃⣠⡴⠋⠁⠤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠭⣁⣒⣒⡂⠜⠛⠛⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⠴⠚⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⡦⠀⠀⠀⠀⠀⠀⢠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⣠⡄⠀⠾⢻⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⡀⠀⠀⠠⠒⠐⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⡴⠞⠁⠈⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠿⠋⢡⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢤⡀⠀⠀⠀⠀⢀⣤⣡⣤⡤⣰⣿⣿⡿⠿⣻⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⢈⣿⣦⠀⠀⠐⠿⠯⠛⠿⢸⣿⣿⡽⣢⡶⣿⣿⣿⡇
⠀⠀⢀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠄⠂⠙⠉⠁⠘⢦⡀⣤⡀⡐⢶⢿⣷⢿⣿⣻⣟⣿⣿⣿⣷
⠀⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣼⣷⡏⢠⠧⠼⠟⡻⣮⠟⡫⣺⣫⣺⣿⡇
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢀⣼⣿⡄⣠⡤⣴⡾⢽⡟⡿⠟⣻⣿⣃⣈⣤⣴⡯⠖⠃⠀⠁⠀⢀⣴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢙⣻⢿⣿⣿⠋⠸⡿⠡⠀⠘⠴⣾⣿⣻⣿⣿⣿⠉⠀⠀⠀⠀⢀⠶⢻⠽⢛⣿⣿
⠀⠀⠀⢀⡀⠀⢸⡷⣁⣶⣾⣿⣯⣾⣿⣿⡤⠷⠶⠰⣶⣶⣶⣾⡿⠿⢿⣿⣿⣶⡤⠘⣵⣶⣿⣷⡉⠀⠀⣟⠋
⠀⠀⠀⠉⠄⠀⠀⠷⠿⠷⠀⠀⠙⠉⠁⠠⠀⣹⠒⠶⣶⣤⣤⣤⡠⠤⠖⠠⣟⠛⣛⠛⠉⠁⠀⠠⣤⣀⡠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⡼⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠄⠀⢀⠄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⣟⣤⣇⡼⠁⠀⠀⠀⠠⢱⠀⠀⠀⠀⠀⠀⡞⠓⠒⠚⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⠉⠉⠉⠉⢹⢧⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⣇⣠⠆⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⡴⠋⠀⠈⡄⠀⠀⢀⠟⠉⠙⢆⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⣀⣀⣀⣀⣀⣸⣇⢔⡽⠋
⠀⠀⠀⢄⡀⢦⡹⣾⠓⠤⣀⣀⣙⣮⣰⣋⠀⠀⣀⡼⠚⢉⡹⣦⡠⠋⣢⣀⡴⠋⠙⢖⠀⠄⠀⠉⠓⢾⣯⡄
⠀⠀⠀⠀⡙⣗⣿⣿⣀⣀⠀⠀⡾⠻⢎⠉⡽⡞⠁⠈⢫⢹⣋⣉⣙⣞⠙⣽⡁⠀⠀⠀⠑⣄⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠈⡽⠋⠀⢣⡈⠉⢻⢶⠳⠤⢼⡜⠀⣹⠤⠴⠖⠻⢦⣠⡖⠛⠻⡇⠱⡀⢀⣀⣜⣀⣑⡢⢤⡀⠀⣷
⠀⠀⠀⠈⢯⣉⡉⠁⣈⣭⣿⣈⠂⠀⢸⣇⡞⠁⠉⠒⡖⠏⠉⢹⣱⣄⣀⡿⢦⡞⠉⡟⢯⣝⡨⢛⣆⣉⣉⡟
⠀⠀⠀⢂⣀⣈⠉⣽⠉⠀⠀⠝⡟⢳⡋⠘⣧⠶⠤⢤⣇⣸⡴⢿⣓⣚⠛⣳⢿⡀⠀⣜⣀⣼⠻⣯⢃⣹⠁⠠⠄
⠀⠀⠀⠿⠶⠼⠃⠈⠙⠓⠒⠋⠁⠀⠀⠀⠀⠀⠈⠁⢀⣤⠖⠲⣬⣍⠩⠁⠀⠉⠹⠍⠉⣁⣤⡉⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠶⠯⠶⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠌⢣⡀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠛⠛⠛⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡆⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢊⡠⠠⣓⠵⠟⢷⣆⡀⠀⠀⠀⢰⠋⠄⠊⠀⢰⡿⣿⣿⣿⣿⣿⢢⡀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣇⢸⡆⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠠⡀⢔⠬⠀⠀⠄⣾⣿⠃⠀⠀⢰⠋⠀⠀⠀⠀⡾⠀⠉⠛⠙⢿⡇⠱⣽⣷⡄⠀⠀⠀⠸⣿⣿⠃⣙⣿⠡⢁⠀⠞⢲⡀
⠀⠀⠀⠀⢀⢞⡠⢖⠠⠀⢀⠤⠐⢉⡠⡐⢋⣿⣟⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠄⠂⠠⢼⣿⣞⡚⢏⣿⠀⠀⠀⠀⣽⣿⡎⠀⠘⣧⠄⣼⡆⠀⠁⢂
⠀⠀⠀⡴⠟⣍⠤⠢⠑⠈⡐⢔⠪⠑⣁⣾⣿⣿⣍⠄⠀⠀⠙⣦⠀⠀⢀⣸⠇⠀⠄⠀⢀⡴⠏⠏⣉⣛⣯⠄⠀⠀⠀⠙⠿⣧⡀⠈⠉⣷⠸⣯⣆⠀⠀⢣
⠀⠀⢰⠗⠎⠠⠀⠜⠪⠑⡬⣒⡶⣾⠩⠯⠙⣉⠎⠀⠀⠀⠀⠈⢳⣤⣽⣧⣤⣕⣈⡵⢾⣷⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠠⣄⢀⠁⢈⣓⣴⡾⠁
⠀⠀⡜⠀⣠⠒⣼⣾⣷⣾⣯⠿⠷⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠯⠒⠋
⠀⠀⠑⠠⢁⠂⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠛⣷⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣼⣯⡟⠁⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⠉⠙⢿⣿⣶⣶⠤⣀⡀⠀⠀⠀⠀⠘⣿⣿⡿⣾⣽⣟⡁⠽⠟⠒⢦⡀
⠀⠀⠀⠀⢴⣯⣟⡋⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⢷⣦⡄⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣽⣶⣿⣿⣆
⠀⠀⠀⠀⠈⢿⡍⠙⢶⣄⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⣰⠁⠀⢀⢀⡀⠰⡄⡀⠀⠀⠀⠀⠀⣀⡶⠀⠀⢰⡿⠟⠿⢬⣩⣛⡙⡻⠿⢿⣿⣿⣨⣷
⠀⠀⠀⠀⠀⠀⠘⠦⣴⢿⡀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠙⡄⣶⣦⣈⢻⣶⣄⠙⠷⢤⣀⣀⡰⠏⠀⠀⠀⠀⠳⣀⠐⠀⠈⠩⠉⠙⠳⠾⣵⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣁⣠⣾⡽⣿⡿⠋⠀⠀⠀⠀⠀⠘⢮⣿⣿⣷⣌⡬⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⣹⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠠⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣯⣙⡓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⢘⢿⣧⡀⠀⠀⠀⠀⠀⢸⣇⠙⢦⠈⠙⠛⠭⢷⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣬⣐⡩⣟⣲⣄⡀
⠀⠀⠀⠀⠀⣠⠔⠒⠃⠠⠐⠁⢘⣦⣡⡀⠀⠀⠀⠀⠈⣿⣿⣯⡑⣄⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠸⡌⣧⢾⡭⢿⣳⣯⣝⣛⡲⢦⣄⡀
⠀⠀⠀⠀⠐⣝⠲⣤⡀⠀⢴⠾⠾⢚⡿⣇⠀⠀⠀⠀⠀⣿⣾⣾⡶⠎⢳⠀⢀⣰⡾⠃⠀⠀⠀⠀⠀⠀⠱⡈⠓⢭⡤⣉⡻⠶⣭⣟⢷⣦⣯⣓⡶⣤⢤⡀
⠀⠀⠀⠀⠀⠈⢦⡀⢉⠛⣦⡀⠐⠋⠀⠈⡀⠀⠀⠀⠀⣿⣿⣿⣿⢋⡏⣠⣾⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⠑⢮⣙⣷⣮⣝⣷⠶⠟⠛⠛⠛⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠺⡇⡇⢹⣀⣀⡴⠦⠖⠀⠀⠀⠀⠘⣷⠿⠖⣿⣴⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⠀⠀⠙⠫⠟⠋⠁⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠻⠭⠇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠯⡿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠠⠀⠀⢀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢞⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠚⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠀⠀⣠⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢃⡴⠷⠊⢀⣤⣞⣴⠏⠀⠈⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠛⠉⢀⡠⠖⠉⠚⣡⠎⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⡠⠖⠉⠀⠀⢀⠜⠁⠀⢀⢜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡅⢀⠴⡇⣠⡆⠈⠀⠀⠀⠀⣰⣫⡄⠀⣴⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⡽⠖⠁⠐⠛⡹⠀⠀⠀⠀⠀⠼⠋⡼⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠀⠀⠀⢀⡼⠁⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡤⡿⠀⠀⣠⠎⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⠔⢋⡼⡁⠀⢀⡿⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠊⠀⠀⠚⢫⢇⡤⡾⢁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠟⢋⣞⣥⠋
⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠟⠁
⠀⠀⠀⠀⡠⣴⡿⠚⠛⢋⡉⠙⠛⠉⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⡞⢾⡉⣀⠀⠀⠙⠁⠀⠞⢦⡀⠀⡷⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠘⡇⣨⠇⢧⠀⠀⠀⠀⢀⡀⠀⡷⢰⡇⠀⠀⠀⢀⠔⠋
⠀⠀⡴⠁⢿⠀⠈⢳⠂⠀⠀⢉⠙⢦⠀⠀⣽⠀⣠⠖⠁
⠀⠈⢻⠀⢸⠀⠀⠘⠶⠦⠀⠈⡀⣈⠇⢀⡇⣼⠁
⠀⠀⠈⢻⠈⠛⠒⢦⡀⢀⣀⡀⠉⣡⠴⢫⠖⠋
⠀⠀⢀⣮⠔⣆⡠⡄⠙⣉⠉⣛⠛⡡⠒⠃
⠀⠀⠀⠀⠀⠉⠀⠛⠊⠈⠖⠉⠋

⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠤⣀⣀⡀
⠀⠀⠀⠀⠈⠀⠀⢲⠀⡀⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠰⢄⠀⢀⠀⠀⠠⢘⣪⣿
⠀⠀⠀⠀⣼⠀⠀⣾⢠⡇⠀⠘⠑⣢⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠉⣄⣀⣀⡄⣘⣧⡁⠐⣤⣾⣿⡷⡏
⠀⠀⠴⠷⠴⠷⠴⠾⢾⡀⠀⠠⠾⠷⠴⠇⠀⠠⠷⠤⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠿⠿⠯⠓⠒⠓


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣦⣠⡤⠀⢐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣀⣰⣤⣾⣗⣺⡏⠹⠟⢋⣇⣽⣿
⠀⠀⠀⠷⢤⣀⣴⡞⣫⣿⣶⠒⢁⣉⡈⠲⣶⢟⣉⠉⣀⣙⣿⣿⣿⣿⠿⣷⣴⣾⣿⣽⣿⣿⣶⣄⡀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠛⠛⠓⠒⠉⠉⠋⠚⠛⠙⠉⠙⠛⠓⠛⠊⠉⠛⠋⠉⠙⠉⠙⠁⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢧⠈⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢈⣧⠀⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠠⠁⠈⠈⣇⠀⠀⡤⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⡅⠀⠀⠉⠈⠓⣘⠀⠀⠀⠍⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠢⢔⠇⠐⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠜⠀⠀⠀⠁⢨⠄⠀⠈⢰⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠙⡤⢸⠄⠀⡀⠸⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠛⡌⠀⠀⠘⠉⠆⢸⠀⠫⠀⠀⠀⠀⠄⢂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡅⠀⠀⠀⠀⠀⢣⠀⠨⡀⠐⠠⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡃⠀⠀⠀⠁⠠⢸⠀⠒⢆⠁⡠⢀⠄⠀⡧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢭⠅⠂⠀⠈⠀⣤⠉⠀⡲⢐⠀⠂⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⢄⠀⠁⠀⢰⠁⠀⠀⠠⠒⠒⢚⠒⠂⠰⣶⢵⠈⡆
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠊⣀⠀⠀⢸⡀⠀⡀⠀⣸⠀⠀⠀⠀⠀⠉⠭⠤⢤⠬⡠⢍⠀⢷⡤⠄
⠀⠀⠀⠀⡄⢧⡀⠀⠐⠀⠀⢀⠞⠁⠀⠀⢈⠂⠀⠀⠄⠳⠀⢀⡼⠁⠀⠂⠀⠀⢸⠀⠂⠀⠀⠺⡇
⠀⠀⠀⠀⠈⠲⡄⠄⠀⠀⠆⢸⠁⠀⠀⢠⠆⠈⠀⡀⠀⠐⡴⠁⠀⠀⠀⠀⠡⠲⠈⡆⠀⠁⠀⣠⠇⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠢⠤⣐⣁⠘⠀⠀⠠⠁⠀⠀⠀⠉⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡂⡴⠊⠠⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠤⠤⠄⠤⠍⣂⣓⡀⢀⣠⣌⣠⣤⡤⢠⡄⠊⠁⠠⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠠⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⡅⠀⢰⠒⠒⠒⡆⠀⠠⡤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠑⠂⠘⡖⠖⠶⣧⣄⢸⣄⣀⣀⣷⠴⠤⠷⠶⠶⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠺⡇⠀⠀⠀⠀⢸⠉⢹⡆⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣧⡀⠀⡇⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠉⢀⠀⣤⡴⣧⡴⣷⣀⠀⢀⣀⣘⣠⣼⣧⣶⣶⠖⠒⠃⢀⣀
⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⢸⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠐⣿⢹⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠤⠔⠠⠬⢷⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡿⠛⠶⠶⡄⠀⣸
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠋⠈⡇⠀⠀⠀⠀⠀⢀⠂⠀⢀⠌⡗⠀⠀⢨⡇⠀⣸⣤⡈⠟⠂⠂⠐⠒⢒
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣧⡀⠀⠀⠀⠀⠠⢀⣀⣂⣠⡷⠶⠒⠾⠟⡉⠩⠀⠧⠧⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠛⠋⠐⠂⠀⠀⢀⡈⠉⠉⢉⡀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⡤⢺⣇⣀⣸⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣇⠀⡀⠀⠀⠀⠀⠀⠀⢈⠀⠁⢸⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠓⠛⠛⠂⠀⠀⠠⠀⠀⠀⠀⢸⢀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠛⠓⠀⠉

⠀⠐⢿⡒⠶⠦⠤⣤⣀⣀⠀⠀⠰⢶⡶⠤⢤⣄⣀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⠉⠓⠒⠾⠷⠶⣤⣈⠉⠙⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠙⢦⡀⠈⢯⡙⠓⠲⠶⠤⢤⣄⣀⡻⣿⣒⠶⠤⢤⣀⣀⠉⠙⠒⠶⠤⣄⣘⣷⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠦⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠆⠀⠈⠉⠛⠲⠦⢤⣄⣀⠉⠙⣳⣌⡙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⡀⠀⠘⢯⡓⠒⠶⠤⠤⣔⣿⣗⡲⠦⠤⣄⣀⡀⠈⠉⠓⠺⠿⢯⣓⠦⣍⡓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⡄⠀⠙⢦⡀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠀⠉⠙⠒⠶⠤⣄⣰⣦⣄⣀⠙⠲⣬⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⡀⠈⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠞⠛⠛⠻⠷⢾⣹⣍⡳⢭⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡙⢦⡀⢾⣷⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡉⣱⠞⠁⠀⠀⠀⡀⠀⠀⠀⠈⠉⠟⢛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠂⠳⣍⠳⣄⠐⣿⢦⡀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⢀⠴⠋⠙⢦⠀⠀⠀⠀⠀⠀⠙⢟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠈⠳⡈⠁⠈⠳⣝⠢⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣧⡀⠠⣾⣦⡀⠀⢈⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠙⢦⡘⢮⡻⣄⠈⠳⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⠂⠱⣌⠑⢄⠈⣇⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠈⠳⡄⠀⢹⠐⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⠄⠀⠈⠁⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⢢⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⢰⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠸⡄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣏⠉⠹⣄⠀⠀⣸⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠙⢲⠮⢤⣀⡀⠀⠀⠀⠀⡔⣀⡴⢶⠋⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⣠⠞⠙⠻⠿⣿⡀⣰⣛⣁⣹⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⠬⡷⠯⠵⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡶⠀⠊⠉⠈⠉⠁⠀⠠⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣤⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⠛⠡⠄⠂⠀⠀⠲⠤⠶⠤⣤⣤⣤⣠⡀⡀⠰⠶⡤⠀⠀⠀⠀⠀⠀⢰⡇⠀⡄
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣒⠒⢴⣾⣶⣴⣢⣦⣴⣤⣄⢈⠉⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⡁⠀⢆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢟⡿⠿⠷⠺⠟⠿⠶⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⡆⡀⠀⡀
⠀⠀⠀⠀⡠⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡷⠶⣶⣯⠃⠉⠀⠤⣤⠀⣀⠀⠀⢀⡀⠤⠀⠀⠐⣢⣢⡀⣏⣰⣿⣧⡗⡇⢀
⠀⠀⠀⠀⠀⡱⣷⣈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣘⣿⣀⣀⠀⠀⠀⠀⢀⣄⡜⠿⣿⣿⣿⣿⣿⣽⣷⣿⣷⠥
⠀⠀⢠⣤⣬⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠀⠐⠊⠠⠚⠙⣶⣿⠿⢿⣿⣿⠛⠉⡭⠁
⠀⠠⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣸⣤⣶⣴⣿⠛⠀⣀⣼⣏⣁⡀⢹⡃
⠀⠀⠒⠡⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⡛⠛⠛⠛⠿⠭⢿⠿⠿⠉⣿⠟⠻⣿⠿⣿⠿⠿⠿⠿⠿⢿⣿⣷⣾⣿⣿⣿⣿⣿⠺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⠚⠛⠎⠙⠒⠄⠀⠀⠀⠀⡀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠁⠈⠉⠁⠉⠁⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠓⠲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠀⢀⣀⣀⡀⠈⠉⠛⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠈⠉⠛⠲⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠁⠀⠀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣁⣠⣼⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣿⠙⠓⠲⠦⣤⣀⡀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⠛⠋⠉⢀⣈⣽⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⣿
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⢤⣄⣀⡀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢦⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠈⠉⠳⣄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠁⠀⠀⢀⡀⠀⠀⢸⣿⠃⣶⠆⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⡿⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣿⣿⣷⣤⣄⣹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣶⡄⠀⠀⠀⠀⢀⣼⠟⠀⠀⢠⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠈⠿⣶⣤⣴⡾⠟⠁⠀⠀⠀⡼⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣶⣿⣿⣿⡇⠈⠉⠙⠻⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠿⣿⣿⣿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠦⣤⣀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣤⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣠⡴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⢼⡧⠶⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉⠉⠀⠀⠈⠲⣌⠳⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡍⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣴⠃⡀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣆⣠⠴⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢀⠟⠁⠀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢰⠀⠀⠙⣄⠀⢀⣠⣄
⠀⠀⠀⠀⠀⣀⠴⠚⢏⠉⠛⠒⠲⢤⡑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⠀⠀⠀⠈⢳⡁⠀⡼
⠀⠀⢀⡠⢴⠁⠀⠀⠈⢣⡀⠀⠀⠀⢹⣇⣀⣤⣶⣶⠖⠒⠒⠒⠒⠲⢤⣀⠀⠀⠀⢸⠇⠀⠀⢀⣀⣬⣇⣀⡇
⠀⠀⣼⠀⠘⣆⠀⠀⠀⡠⠔⠲⢄⣠⢼⠏⠢⠀⠀⠈⠉⠙⠓⢦⡀⠀⣀⠬⠽⠛⠒⠚⠲⣄⣰⠋⢆⠀⠀⠈⢳⡀
⠀⠀⠈⠓⠒⠘⠓⠒⠘⠣⢤⣤⠼⠤⠺⠄⣀⣀⣀⣀⠀⠒⠒⣁⢗⠶⢧⣀⠀⠀⣀⣀⣀⣀⠟⠒⠚⠶⠤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢧⣀⣠⠏⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢣
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠄⠀⠀⠀⠀⠸⡁⠔⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠔⠁⠀⠀⠰⠀⢠⠀⠀⠂⠀⠀⡀⠀⠀⠀⢸⠁⡀⠀⠀⢀⠀⠂⢉⡁⠈⠤⠀⠀⠃⠀⠀⠈⡐⠀⢠⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠈⠃
⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⠀⠀⢠⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠎⡉⠉⠐⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠁⠀⠀⠘⠀⠀⠀⠀⠤⠄⠀⠀⠀⠊⠀⠀⠀⠘⠓⠀⠒⠂⠂⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⢲⠀⠀⠀⠀⠐⠈⠐⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢠⡀⠀⡄⠀⠀⠀⠀⠤⠆⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠚⠀⠐⠉⠀⡀⠀⠀⡄⠀⠐⠠⠐⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠅⠀⠀⠀⠄⡀⠀⠀⢸⠁⠀⠀⠀⢠⠂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠐⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⠶⠒⠲⠶⠖⠒⠋⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠬⣳⣄⠀⠐⠒⠖⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠉⠦⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠙⢦⣤⣤⣴⣶⣶⣾⣿⡟⠧⢄⣀⡀⣀⣠⣤⣄⣤⣬⣵⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⠀⠀⠀⠀⠈⣿⣿⣿⡿⣫⣵⢟⣧⠀⠀⠈⠙⣿⠉⢉⣿⢻⣿⣇⣧
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⠀⠈⠀⢿⢟⢥⣾⣿⡷⢋⣿⡆⠀⠀⠀⢇⢳⡸⣿⡏⢻⣿⡘⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⢸⡿⣿⠟⡫⣲⣿⡿⣷⠀⠀⠀⢸⣸⣇⣿⠇⣿⣿⢷⢱⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣿⡇⠀⠀⠈⡏⣵⣽⣾⣽⣿⣿⣫⡇⠀⠀⠀⢹⢸⠹⠀⣿⢻⠈⡆⢳⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⢿⣩⣿⣿⡿⣿⡿⠗⠻⡄⠀⠀⡎⠈⠂⠀⢸⠈⠀⢱⠀⠱⡄
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣾⣧⠀⠀⠀⢸⠨⠟⠵⠊⣁⡠⠴⡄⠀⠀⠀⢸⡀⠀⠀⢸⣶⡄⠈⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣰⣿⣿⣆⠀⠀⠈⡇⠀⠀⠀⢁⠄⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⣧⠀⢀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣄⠀⠀⢧⠀⠀⠐⠁⠈⠀⠼⠁⠀⠀⠀⡁⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⢀⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢾⣄⣀⣀⣠⣤⠤⠤⠤⠤⠶⠶⠧⠬⣦⣄⣀⣀⣀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠉⠙⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠉⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠁⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠙⠿⣷⣤⣀⠀⢀⣠⣴⡿⠟⠉⠀⠀⠀⠀⢀⣿⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠈⠛⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢻⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠁⠀⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⣾⡟⠋⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⡀⠀⠀⣿⡇⠀⠀⣀⣤⣶⠿⠛⠉⠛⠿⣶⣤⣀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣶⣤⣿⣧⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠿⣶⣤⡀⠀⣀⣴⣾⠟⠋⠁⠀⠙⠻⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠙⠻⢷⣦⣄⠀⠀⣿⡇⠀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⣷⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣀⠀⠀⢸⣿⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣼⣿⣴⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉




⠀⠀⠀⠀⠐⠐⠀⠀⡖⠀⡰⡀⡐⢰⢰⠀⢰⣆⠀⠠⢖⡂⢲⡖⢴⣲⢤⡖⢦⢰⣴⠂⣶⡂⠀⢆⢰⢰⡖⢠⡖⠂⠐⡖⢠⠒⠆⣖⣰⠀⢠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠁⠁⠀⠈⠈⠀⠈⠁⠀⠀⠁⠁⠈⠁⠉⠈⠁⠙⠉⠈⠈⠁⠉⠂⠀⠈⠁⠈⠁⠀⠑⠁⠀⠁⠈⠀⠁⠁⠀⠀⠈⠈⠀⠀⠁⠀⠀⠀⠁

⠀⢠⣤⣤⢤⣤⠄⠀⠀⢠⣤⡀⠀⠀⢠⠤⣤⠄⠀⢠⠀⠀⠀⠀⢀⣤⠤⣤⣤⠀⠀⠀⠀⣤⡀⣀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠠⢤⣤⣤⣀⣤⣤⣄
⠀⠘⣿⠁⠀⠉⠀⠀⠀⠀⢿⣿⣷⡶⠁⠀⠀⠀⠀⠈⢷⣠⡤⠀⠀⠘⠀⠀⠀⠈⢷⣞⠉⠉⠉⠉⣩⠃⠙⡇⠀⠀⠀⡀⠀⠉⠀⢻⣟⠀⠁⠙⠃
⣠⣴⣿⡆⠀⠁⠀⠀⠀⣀⣿⣿⣿⢷⣤⣀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⠄⠀⠀⠰⠒⣤⣴⣧⠀⠀⠀⠉⠀⠀⠀⢸⣿⡀
⠁⠈⠉⢻⣦⣤⣶⣾⠿⠏⠉⠁⠀⠀⠉⢻⣿⠶⠶⠶⠶⢷⣤⣄⣠⣼⣷⣤⣶⡤⣴⣿⣶⣴⣦⣶⡟⢻⣿⣿⣧⡀⠀⣀⡀⣀⣠⣾⣿⣅⣀⣀⣀
⠀⠀⡀⠈⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠉⣿⡿⠛⠉⠉⠛⠿⣿⡿⣋⠀⠀⠉⠀⠀⠉⠛⣿⣿⠛⠉⠉⠉⢿⣿⡿⠛⠉⠉⠉
⣿⣾⣶⣦⡴⠟⠛⣿⣿⣶⣾⠇⠴⠶⢾⣟⠀⢄⡀⠀⠀⠀⣰⣿⡁⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢁⠀⠀⠀⠘⣿⠁⠀⠀⠀⠓⢸⣿⣇⣤⣤⣄
⡟⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠘⣿⣶⡤⠌⢁⣴⣿⠋⠁⠁⠐⠦⢤⣶⣿⡿⠓⠖⢠⣴⣿⣿⣶⣶⣶⣿⣿⣿⣶⣦⣤⡾⠋⠉⠉
⣶⠶⢤⣤⣤⠤⠫⢿⣿⣀⣀⣀⣀⣀⣠⡿⠋⠀⠀⠀⠉⣁⣀⣀⠀⠀⢀⣈⠛⠉⠀⠀⠀⠀⠀⢹⡿⠀⠉⠉⠀⠈⠉⠉⠻⣯⣀⡀
⣿⣤⠎⠁⠀⠀⠀⠸⣿⣿⡿⠛⠋⠁⠀⠁⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠻⠿⣧⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⠳⣆⢀⣶
⡋⠇⠀⠀⠀⠀⣀⣠⣿⣿⡀⠀⠀⠀⢠⣧⣤⣀⣴⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⠖⠀⠚⠛⠿⢷⣶⣷⡾⠒⠳⡿⠁⠀⠀⠀⠀⣀⡿⠋
⣷⢶⣶⣶⣿⣿⡿⠛⠁⠀⠉⢳⣄⣀⡼⠟⠋⠉⠀⢰⣿⠟⠛⠛⠒⠄⢠⣄⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⢀⢀⣀⣀⣴⣿⣿⠁
⠃⠀⠄⠀⠐⠹⣧⡀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢘⡇⠀⠙⣀⣀⣀⡀⠀⠀⠀⠀⣽⣤⠀⠀⢀⣿⠟⠋⠉⠀⠘⢶⡶⠓
⣄⣩⢤⠀⠠⣄⣼⣿⣷⣶⣶⣶⣾⣦⣀⣀⣀⣀⣀⣸⣆⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡿⠉⠙⠛⠛⠿⠿⣿⡟⠀⠀⠈⢛⠻⣧⠀⠀⠀⠀⠈⢀⣀
⠈⢻⣿⣯⣷⡿⠟⠋⠁⠀⠀⠈⠹⣿⣿⣿⡿⠟⠻⢿⣅⣷⣀⠀⠀⠀⠀⣾⣷⡶⢤⣖⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⣙⣷⡴⠶⠶⢶⣾⡟
⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠀⠈⠈⠙⠷⣤⣤⠞⠋⠉⠀⠀⠉⢄⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠈⠻
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⣷⡶⠶⠛⠛⠉⠉⠓⠒⠈⠉⣿⡀
⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀
⣴⡦⣄⠀⠀⠀⠀⠀⠉⠉⠉⠃⠀⠉⢛⠀⠀⠴⠂⠰⠶⠒⠂⠹⠻⠿⠿⠿⢻⣶⠶⠖⠶⣿⣧⠀⠀⠀⣀⣀⣠⣴⣶⣿⠛⢿⣀⣀⣀⣠⣄
⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣉⣈⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣙⣋⣉⣁⣉⣀⣀⣀⣉⣉⣙⣀⣘⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠰⣤⡀
⠀⠀⢌⠻⠳⠆
⠀⠀⠘⡆⠒⠄⡇⠄⡀⠀⠀⠀⠀⠒⠊⠝⠢⠀⣒⠤⣀
⠀⠀⠀⠐⠁⠰⠛⡄⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⢤⠑⠔⢄
⠀⠀⠀⠀⠘⠐⠡⠀⠁⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠂⢂⡰⡑⠣⠀⠀⠀⠀⡀⡀⠀⢄⢀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠂⠘⡁⢡⡀⠀⠀⠀⠀⠀⠀⡘⠆⢀⠁⡈⠢⡣⢆⠀⠀⠀⠓⣎⠁⢘⠩⡂
⠀⠀⠀⢀⡀⠀⢈⠆⢂⠀⠈⢄⠀⡙⢷⡆⠲⠴⠦⠞⢋⠀⠀⠀⠀⠁⢄⠢⠑⣀⠀⠠⡬⠀⢀⠢⡀⠁⢀
⠀⠀⠀⠀⢷⡐⠀⣶⡂⠀⠀⠀⠢⣑⠄⠈⠀⠐⠀⠣⠈⠀⠀⠠⡀⢢⠒⠳⢤⣤⣀⢔⡨⢀⠐⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠐⢍⠩⡃⢄⣀⠠⡀⡠⠠⣀⠀⠠⣀⠔⠂⠀⠠⠘⡀⠀⠀⢁⠌⣷⠈⡀⡀⠑⠢⠄⣼⡦⡀⢄⡢⠀⠐⡉⠒⣠⢄⡀
⠀⠀⠀⠀⠀⢀⠹⣊⡐⠂⠥⠀⠘⠚⠒⠄⠂⢄⣠⠀⣇⡀⠂⠙⠅⠊⡀⡛⡀⠀⡨⠈⠸⠦⣔⠌⠉⢊⡐⡤⠄⠀⢀⠀⠤⡬⣇⢡⡂⠄
⠀⠀⠀⠀⠀⠀⠱⣈⠒⢵⣶⠐⠁⠀⠁⠀⠐⠀⠐⠶⡂⠑⠀⣄⠀⢀⠨⠈⢀⢠⣿⣀⠢⣀⣌⢀⣈⣉⣡⠭⠤⠒⡓⠚⠒⠶⠤⡀⠋⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠈⠤⠬⣤⡀⠑⠦⠀⠂⢄⠅⣦⡑⢆⠷⠥⣘⠟⢉⠀⣀⡈⢚⡩⠟⠫⣠⠰⠵⣌⡀⠀⠉⠀⠀⠀⠈⠒⠄⡊⢆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠩⡒⢍⠂⠈⠊⠹⢦⡄⠠⣹⡆⢈⠃⠀⣢⠞⠁⣀⠞⢁⢀⠀⠟⠀⠰⠀⠀⠀⢀⣥⣦⠔⡈⠂⠘⣕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡅⠈⠞⢄⠂⠁⡐⡍⠠⠈⠂⣼⠉⠀⠁⠇⠀⠉⠉⠀⠀⠀⢀⠀⠀⠀⢸⡄⠈⠁⠘⣄⠑⡈⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢅⠀⢲⡠⡈⠂⠁⡌⡼⠁⠀⡁⠠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠁⠐⢿⡆⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⡈⡂⣻⣬⣤⡻⢰⢂⣰⡆⢁⠐⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠖⢊⠄⠀⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡀⠀⢝⣌⠘⢏⢻⡎⢻⠁⠌⢀⢰⣆⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠊⠀⢸⣇⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠈⠻⡕⢝⠶⡇⠊⠀⠓⠀⡌⠀⠁⠀⠀⠀⠀⠀⠀⠲⠁⠃⠀⢈⡑⠔⠀⠀⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢕⠋⣐⠅⠁⠢⠀⠜⠑⠈⠘⠄⠂⠀⠀⠀⡀⠀⠀⢹⠂⠐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⡀⠆⢡⠈⠎⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠳⠆⠁⡊⠀⠀⣰⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⢝⡓⠾⡤⠐⠄⢸⡾⠟⠝⠒⠦⢀⡀⠀⠀⠀⠀⠈⠀⠀⡸⢁⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣅⠘⠄⠘⠢⢄⣔⠙⢶⡄⠀⠀⠠⠞⠀⠀⠠⢈⢀⠤⡪⠜⡡⠊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢖⠢⠄⡐⠙⠳⠶⠬⠤⣀⣉⠀⠫⠔⢊⣩⠕⠀⠔⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢢⣄⢄⠉⠤⠤⠄⠀⠀⠠⠄⢚⠁⠠⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠙⣻⣿⣮⡻⢷⠶⢤⣄⣀⡀⠀⠀⢀⣾⣿⣟⣷⣆⣴⡶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⢋⡩⠿⣧⣄⡈⢹⡿⠿⡓⠒⠒⠈⣉⢲⣤⣀⠌⠙⠛⠛⠋⠉⣹⣷⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣍⠀⠀⠉⠀⠀⠈⠻⢷⣀⣘⡒⠖⠶⠬⠥⠤⣬⠿⢤⣀⠀⠀⠀⠀⠀⠈⣿⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣷⣶⣤⡀⠀⠀⠈⠉⠁⠀⠚⠗⠀⣘⣷⣦⣾⣿⣯⣶⣤⣤⣴⣶⣄⣠⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡉⣹⣷⣷⣦⣤⣤⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡧
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠑⠓⠒⠚⠿⠛⠛⠛⠛⠛⠻⠟⣻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⠛⠛⠛⠛⢿⣿⣶⣶⣶⣷⣤⣤⣤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠺⠂⠀⠈⠀⠀⣠⠂⠀⠀⠀⠖⠀⠀⠀⠀⠈⠉⠉⠉⠁⠃⠂⠐⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⣀⣤⡀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠿⠏⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠠⡈⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢘⣳⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠂⠀⠀⠀⠀⠀⢸⣷⣆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠻⠛⠃⠀⠀⠀⠀⠀⢈⣿⣿⣦⡾⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠔⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠠⢠⡀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣾⡥⠀⠀⠀⠀⠀⠀⠘⢳⠄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠓⠀⠀⠀⠀⠀⠀⠀⣧⣂⣀⡤⣧⣠⠶⢶⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣙⠀⣹⠃⠀⠀⠱⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢷⣶⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡋⠀⠀⠀⠀⠀⣀⡅⠀⠀⣸⡷⣿⡶⡿⠀⠀⠀⠀⣷⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠌⣿⣚⡏⠀⠀⠀⠀⠀⠀⣿⠃⠀⣰⣿⠟⠉⠋⠻⣮⠄⠀⠀⠘⢦⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⢀⡏⠊⠀⠀⠀⠀⢀⣄⣤⣯⠴⠾⣿⠁⠀⠀⢰⠀⠈⣷⠀⠀⠀⣸⢀⡅
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠠⡜⢏⣻⡟⠀⠀⠀⠀⠁⠀⠀⡰⠀⠀⢸⠀⠀⠀⢳⠊⡏
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡿⠀⠀⠀⣄⡂⣙⡿⠁⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⣼⡃⠀⠀⢠⢂⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣷⠀⢰⣶⡾⣿⠋⠀⠀⠀⠀⠄⠀⠀⢸⣿⠄⠀⠀⠿⣇⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠘⣆⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠅⣾⣴⡟⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⢸⣧⠀⡾⠹⡇
⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⡍⠀⠤⠀⠀⠀⣠⡄⠠⣿⡿⣻⣴⣤⣦⠟⠁⠀⠀⠀⠀⣀⣤⣶⠿⠾⠊⠀⠀⢤⡴⢺⣿⣇⣗⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠳⠤⣄⣉⣋⣤⣿⠟⠉⠁⠀⠈⢳⣰⡀⣶⡠⢶⣿⣿⣯⣵⣤⣄⣠⣎⣛⠀⠾⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠛⠛⠒⠚⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠾⢟⡿⠋⢁⣀⣤⣤⣤⣤⣴⡶⣶⣶⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠁⣠⣶⣫⣴⡾⠟⠋⠉⢉⣉⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⡀⠀⣠⡾⠟⠋⡉⠀⠀⣀⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⣠⠞⠀⢀⣡⣤⣶⠏⢀⣠⣾⣫⣤⣤⣤⣤⣤⣴⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⠟⣋⣴⡿⠋⣠⠞⢋⡵⠋⣠⠴⠟⠛⠛⣉⣭⣭⠿⠟⠋
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣡⠞⢋⣼⡡⠚⢁⡴⠋⠀⠀⠀⠀⣠⡶⠟⠋⠁
⠀⠀⠀⠀⠀⢀⣾⣧⣾⠟⠁⢠⠟⠋⢀⣴⣫⣴⣶⠶⢃⣴⠟⠋
⠀⠀⠀⠀⠀⣾⢋⣠⠥⠤⠤⣅⠀⠰⠛⣩⠽⣋⣥⡶⠟⠁
⠀⠀⠀⠀⢸⡿⣩⠘⠁⠀⠀⠈⣧⢠⣞⣵⠟⠉⠁
⠀⠀⠀⠀⠈⣷⠉⣙⠀⠀⢀⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠷⣭⣀⣀⣭⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⣿⣿⣿⣿⡆⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⢺⣿⣿⣿⡗⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉

⣶⣶⣶⣶⡄⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⢰⣶⣶⣶⣶⠀⠀⠀⢠⣶⣶⣶⣶⠀⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⢴⣶⣶⣶⡆⠀⠀⠀⢰⣶⣶⣶⣶
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⠛⠛⠛⠛⠁⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠈⠛⠛⠛⠋

⣶⣶⣶⣶⡄⠀⠀⠀⣴⣶⣶⣶⡄⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⣴⣶⣶⣶⡄⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⢠⣶⣶⣶⣦
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⠛⠛⠛⠛⠁⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠘⠛⠛⠛⠛

⣤⣤⣤⣤⡀⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⢠⣤⣤⣤⣄⠀⠀⠀⢀⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⢀⣤⣤⣤⣤
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣺⣿⣿⣿⡗⠀⠀⠀⢸⣿⣿⣿⣿
⠿⠿⠿⠿⠃⠀⠀⠀⠻⠿⠿⠿⠇⠀⠀⠀⠸⠿⠿⠿⠟⠀⠀⠀⠘⠿⠿⠿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠃⠀⠀⠀⠺⠿⠿⠿⠇⠀⠀⠀⠘⠿⠿⠿⠿

⣀⣀⣀⣠⡀⠀⠀⠀⣠⣀⣀⣠⡀⠀⠀⠀⢀⣀⣄⣀⣄⠀⠀⠀⢀⣀⣀⣀⣄⠀⠀⠀⠀⣠⣠⣀⣠⡀⠀⠀⠀⢀⣄⣀⣀⡀⠀⠀⠀⢀⣄⣄⣀⣄
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⡧⠀⠀⠀⢸⣿⣿⣿⣿
⠿⠿⠿⡿⠇⠀⠀⠀⢿⠿⠿⠿⠇⠀⠀⠀⠸⠿⠿⠿⠿⠀⠀⠀⠸⠿⠿⠿⡿⠀⠀⠀⠀⢿⢿⠿⠿⠇⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠸⡿⠿⠿⠿

⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀
⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠄⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢽⣿⣿⣿⡯⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠉⠉⠉⠉⠉⠉⠀⠉⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⢀⢀⠀⠀⠀⠀⠀⠀⠀⡪⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⠒⠒⠒⠒⠖⠒⠲⠒⠫⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⡠⠠⡀⡀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠤⠤⢤⢬⢬⠤⠥⠮⡤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠄⠄⠄⢀⢄⣀⣀⣀⡀⣀⡀⠀⢀⣀⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠒⠒⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣐⡑⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠉⠀⠀⠈⠀⠉⠉⠽⢻⡒⡶⡲⡢⡍⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠐⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠈⠀⢁⢳
⠀⠀⠀⡀⠤⠀⢐⠀⠄⢀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠄⠀⠀⠀⠐⠀⠀⣢
⡀⡰⢡⠀⠐⠐⠁⠰⠁⠀⠢⢀⠀⠹⠶⠤⣀⣀⠀⠔⠄⠄⠔⠤⠀⠀⠀⠄⢄⣀⣂⣂⣠⡥⢥⢤⣖⡇⠚⢥⠐⠪⠐⢄⠀⡁⢀
⠁⠡⠰⡀⢌⠢⡁⠢⠄⡀⠐⠠⠀⡀⠈⠀⠀⠈⠉⠘⠛⢛⠿⠴⠸⠭⠉⠩⠍⠉⠍⠀⠀⠀⠉⠀⠂⢂⠈⠡⠄⡊⠔⠃⣀⠆⡠
⠈⠢⡐⠌⡀⠑⠠⢀⠀⠀⠄⠀⠒⠤⠄⢁⡀⠀⠀⠀⠀⠒⠀⠠⠠⠡⠁⠄⡀⠀⠐⠀⠁⣀⡁⠈⠁⠀⠀⠈⠄⢐⡀⠥⠂⠀⢀⠠⠊
⠀⠀⠈⠐⠈⠐⠠⠄⠀⠁⠒⠀⠀⠀⠂⠀⠄⠈⠀⠉⣀⣀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠄⠀⠂⣉⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠒⠠⠄⠀⣀⡀⠀⠈⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠤⠀⠐⠀⢀⡀⠀⠠⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠉⠛⠳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⢸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣧⠀⠀⠀⠀⠀⢰⣞⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠸⣿⡀⠀⠀⠀⠀⢸⠟⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣱⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣟⢣⠀⠀⠀⢠⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠶⣕⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣯⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠀⡆⠀⠀⡏⡼⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⡘⢹⡟⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⢤⣿⡀⢰⣧⡟⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠇⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⠀⣿⣷⢸⣹⡟⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢄⠀⠀⠀⠀⠀⢰⠀⣾⡅⢸⡇
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠙⠀⣸⡿⢿⡹⣷⣷⠀⠘⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠄⠀⠀⢀⠇⢠⣿⡇⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠸⣷⢹⣿⣀⡴⠊⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡆⠀⠀⡾⠲⣿⡁⣏⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢠⡇⠀⠀⠀⢫⣼⡿⠃⢠⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣇⠀⣸⠁⠀⣿⡇⠁⠀⣧
⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠟⠀⠀⠀⠚⠈⣿⠀⠀⡸⠀⠀⠀⠀⠸⣾⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡟⢩⣻⣿⣦⣀⡿⣿⡄⣤⣿
⠀⠀⠀⠀⠀⠀⠘⠷⣄⣸⠀⠀⠀⠀⠀⠀⢹⣄⠈⠀⠀⠀⠀⠀⠀⠸⡄⢿⣦⠀⠀⠀⠀⢀⠀⠀⣴⠋⠀⠀⠽⢩⣿⣿⣿⣿⣿⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⣿⡇⠀⠀⠀⠰⠀⠀⣯⠀⠀⠀⠀⡸⠚⣟⠳⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⠀⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠘⣆⡽⠓⠒⠒⠒⠚⠒⠛⠙⠒⠒⠲⠴⠷⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣶⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣞⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⠁⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣦
⠀⠀⠀⠀⠀⢀⣠⠴⣦⡴⠶⠿⢿⣿⣿⣫⣵⣿⡟⠀⠀⠀⠀⠀⠀⡠⢀⣴⣿⣿⠋⠁⠀⠀⠀⠀⠀⣠⠄⣷⣻⣿⣿⣿⣷
⠀⠀⠀⠀⣴⡿⠀⢶⣾⣻⣿⡆⠛⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⣠⣼⣷⡿⣫⣿⠋⠀⠀⠀⠀⠀⠀⡴⠀⠐⠀⢻⣿⣿⣿⣿⡆
⠀⠀⠀⢾⠁⠶⣶⠈⣿⣿⣿⣿⡞⢛⡵⠋⠀⠀⠀⠀⠀⢰⣿⣧⠉⠛⣰⣿⠕⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣤⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⣆⣷⣤⣾⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠷⠠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⣿⣿⣿⣿⣿⣿⣾⠿⠁
⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⢄⠀⠀⠀⠀⠙⢸⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢀⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⠀⠀⢰⣮⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡟⠀⠘⠋⠀⠀⠀⠀⠀⠀⣴⠒⠀⠀⢀⡛⢿⣦⡀
⠀⠀⠀⠀⠀⢀⡤⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣤⢾⡿⢿⡄
⠀⠀⢠⠞⠁⠋⠀⣬⣿⣿⣿⣿⣿⠀⠀⠀⠙⢛⣆⢢⠀⢀⠠⠄⠀⣽⣿⡄⠒⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠰⠟⣠⣿⣾⣿⡟⠁
⠀⠀⠠⣦⠀⢸⠀⣹⣿⣻⣿⠛⠁⠀⠀⠀⠀⠀⡨⢿⠿⠧⠤⢀⣴⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣧⣿⣿⠃
⠀⠀⠀⠸⡇⢸⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢸⣷⣾⣿⡻⣿⣶⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑⠯⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠊⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠙⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠹⣄
⠀⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠈⢧⡀
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢧
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡇
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⣿⣀⣀⣀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠉⠉⠁⠀⠈⠙⠦⣤⣀
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣠⠂⠀⠀⠀⢀⠀⠀⠀⠈
⠀⡹⠚⠛⠉⠉⠉⠉⠛⢢⡀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⣠⠋⠀⠠⠤⢴⡇⠀⠀⠀⠀⠀⠉⠉
⡾⣅⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣇
⢧⠸⡆⠒⠲⠤⠤⠤⠤⠤⣴⠷⠦⣤⣤⣤⣤⣤⣤⣤⡴⠖⢻⡀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠳⣧⣀⠀⢀⣀⣤⠤⠞⠁⢀⡤⠖⠒⠚⠛⠉⠉⢩⠛⣦⠈⠳⣄⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡏⠈⠑⠒⠶⠤⠤⠴⡇⢀⡟⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠀⠀⣀⣠⡷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⡉⠉⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣀⡀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠄⢀⡀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣴⣤⣤⡀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⠀⠀⠀⢈⣿⣿⣿⣷⠀⠀⠀⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⣼⣿⣯⣿⣿⣧⠀⠀⢸⠀⣿⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣸⣿⣿⠉⠉⣿⣿⣇⠀⠀⠀⢻⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⠀⢸⠀⣸⣿⣿⣿⠆⠰⣿⣿⣿⡗⠀⡄⢸⢸⡇
⠀⠀⢸⠳⣄⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇⠸⣤⣤⣤⣤⣥⣤⣤⣤⣤⡤⢤⠠⠇⢸⣸⠙⠒⠒⠒⠂⠤⠤⠤⣤⣄⡀
⠀⠀⢸⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⣤⣤⣤⣤⡤⡤⠤⢤⣤⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣧
⠀⠀⢸⡔⠀⠀⠀⢀⠔⢀⣉⡉⠉⠉⠩⠥⠤⠤⠄⠒⠲⠀⣷⢰⠉⢀⠀⣈⣉⠉⠁⠀⠐⠒⠂⠤⠀⣀⠐⠕⠀⣿
⠀⠀⢸⠄⠀⠀⠀⢸⠀⠀⢠⣶⣶⣶⣶⣿⣿⣶⡀⠀⢸⠀⡇⢸⠀⡀⠀⠀⣀⣤⣌⡉⠉⢉⣐⠒⠢⠀⡇⢈⠄⡿
⠀⠀⢸⠂⠀⠀⠀⢸⠀⡀⠈⠙⣿⣿⠁⣈⣿⣿⠇⠀⢸⠀⡇⢸⠀⡇⠀⣼⣿⣿⣿⡿⣷⣿⣿⠁⢰⠀⠃⠀⡚⡇
⠀⠀⢸⠀⡐⠀⠀⠸⠀⡇⠀⠀⣿⣿⣿⣿⣿⣯⡀⠀⢸⠀⡇⣸⠀⡇⢸⣿⣿⣿⡇⠀⠘⠛⠋⠀⢸⠀⡆⠀⢔⡇
⠀⠀⢸⠔⢀⠀⠀⠆⠀⡇⠀⠀⣿⣿⡏⠉⣹⣿⣿⠄⢸⠀⣷⣿⠀⡇⠸⣿⣿⣿⣇⠀⣠⣤⡄⠀⢸⠀⡇⠀⠐⡇
⠀⠀⠘⢤⠂⠀⠀⠀⠀⡇⠀⣀⣿⣿⣷⣾⣿⡿⠋⠀⢸⠀⣿⣿⠀⡇⠀⠉⠻⢿⣿⣿⣿⠟⠁⠀⢸⠀⡇⠀⢸⡧⠂
⠀⠀⠀⠐⠙⢦⡀⣵⠀⡇⢈⣛⣛⠩⠭⠥⠄⠰⠒⠒⠊⢀⣯⢿⡀⠁⠐⠒⠒⠒⠒⠶⠦⠤⠤⢄⣸⠀⢃⡰⢏⢀⡔⠡⠂
⠀⠀⠀⠀⠀⠀⣻⣾⣄⣀⣀⣀⣠⡤⡤⠤⢖⡶⢒⢟⢋⠵⡢⣀⢝⠍⡡⡒⠒⡲⠲⢤⣤⢤⣄⣀⣀⣠⠟⠔⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚⠊⠊⠑⠙⠋⠒⠉⠁⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠉⠛⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⣀⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠋⠉⠀⠀⠀⠀⠈⠙⠶⣤⣄⡀
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⡠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠈⢷⡴⠶⠶⠶⠶⠶⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣀⣼⠃⠀⠀⠀⠀⠀⠙⠒⠒⠂⠀⠀⡷
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠈⢧⠘⡏⠉⠙⠛⠒⠒⠒⠒⠒⢲⡾⠛⠳⠶⠶⠦⠤⠤⢤⣤⣴⣶⡚⠋⠹⣆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠳⣷⣀⠀⠀⠀⣀⣠⣤⠶⠋⠀⢀⣤⠶⠚⠛⠋⠙⠉⠉⠉⡼⠙⣦⠀⠙⢶⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⡏⠈⠓⠢⠤⣤⣤⣤⣤⣼⠃⠀⣿⠀⠀⠀⠈⠉⠉⠙⠓⠒⠚⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠀⠀⢸⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⠶⠖⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠁⠁⠀⠀⠐⠀⠀⠈⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⢹⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠙⠒⠤⣀⠈⡆⠀⠀⠀⢠⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣀⣠⣤⣤⣄⡀⠉⢣⠀⠀⣰⠃⠀⠀⠙⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠋⠉⠉⠀⠀⡇⠀⠙⠲⡄⠳⡰⠁⠀⠀⠀⠀⠘⣏⢉⠟⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⠛⠦⣀⠀⠀⠀⣠⡃⠀⠀⠀⢻⠀⣷⡀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢳⡔⠋⠀⠉⠢⠤⢤⣸⣶⠀⢳⡀⠀⢀⣠⠴⠟⠒⠾⣍⠉⠉⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠚⠛⠻⡆⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣸⠿⠶⠶⠛⠋⣹⠉⠳⣄⠀⠀⠈⠳⣄⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠦⣇⠀⢀⣀⣀⣀⡟⠲⣤⣀⡀⠀⠙⣄⣀⣠⡤⠞⠛⠶⣤⣠⠒⠉⠉⠉⠉⠉⢷⠀⠀⠀⠘⢧⡇⠈⢷
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⣶⣋⣉⡽⣿⠀⠀⠀⠉⠻⢍⣉⡉⠉⣀⣀⣀⡤⠤⡔⠻⡆⠀⠀⠀⠀⢀⡼⠧⣀⠀⠀⠈⡹⣶⠺⡇
⠀⠀⠀⠀⣀⣤⣿⣀⡀⠀⠀⣸⣤⠤⠶⠿⠿⣤⡀⠀⠀⠀⠈⢣⢨⠋⠀⠀⠀⠀⠀⠈⢆⢻⠀⠄⢀⡴⠋⠀⠀⠀⠉⡖⢺⠓⣿⣠⣇
⠀⠀⠀⣾⣋⣼⣿⠭⣿⡶⠚⠉⠀⠙⠢⣀⣀⣀⡙⢧⡀⠀⠀⢀⡿⠞⠓⢦⡀⠀⠀⢀⣼⠟⠛⠛⠛⠓⠶⠤⣄⣁⣸⠀⣾⡴⠯⣄⣈⣙⣦
⠀⠀⠘⠷⠴⢾⡿⣏⣁⠀⠀⠀⠀⡠⠊⠹⡄⠀⠀⠉⢳⠀⡼⠛⢄⣀⣀⠀⠙⣦⢀⡞⡹⠦⣄⣀⣀⣀⠀⠀⠀⠉⢻⢒⡿⠶⣴⣧⣤⣤⡼⠃
⠀⠀⠀⠀⠀⢸⡏⠁⠀⠉⠉⠉⠙⡄⠀⠀⠘⡄⠀⣠⣼⢶⡇⠀⡼⠁⠈⠉⠉⠙⣿⣷⠁⠀⡼⠁⠉⠉⠉⢉⣩⠿⢋⠸⠯⠭⠿⠁⠠
⠀⠀⠀⣠⡶⣦⠓⢦⣤⣤⣤⣀⣀⣸⣤⣤⠶⠾⠛⠛⠶⠭⠽⠿⣤⣀⣤⣤⡤⠞⠁⠈⠙⠺⠷⠶⠒⠒⠛⢩⣵⢶⡄
⠀⡀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠰⣾⣭⠿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠃
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⡠⠴⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣓⣶⣦⣄⠀⠀⠀⠀⠀⠀⢠⣤⣤⡴⣲⡖⠉⠉⠓⣄
⠀⠀⠀⠀⢠⣇⢾⣅⡬⠽⡛⠲⣄⡀⠀⠀⠀⠀⠀⠀⡾⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣰⢳⢆⠛⡟⠉⠛⠶⣄⠀⠈⢒⣄
⠀⠀⠀⢀⡯⣭⢭⣿⣭⢷⣶⣷⡞⠛⡆⠀⠀⠀⠀⣴⠃⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣋⢄⠤⠂⠳⡄⠀⠀⠀⠉⢿⡿⣽
⠀⠀⠀⣼⣷⣿⣿⡷⠿⣿⡟⠓⠒⣰⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣿⣹⣿⣿⣿⡟⠁⠀⠀⠈⢧⣄⣢⡾⢰⡇⠀⠀⠀⠀⢸⢻⠇
⠀⠀⠀⢣⡻⣿⣶⣿⣻⣾⠿⠟⠻⠋⠀⠀⠀⠀⠀⠀⣹⠠⠰⢀⢀⣟⣩⣭⣽⣿⠇⠀⠀⠀⠀⠀⢹⣽⣿⣿⣅⡀⠀⠀⠀⢸⡜
⠀⠀⠀⠀⠑⢄⣈⣉⢀⡀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⠤⣥⣹⣟⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⡀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢴⣤⡤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣤⣄
⠀⠀⠀⢀⡤⣤⣶⣿⣿⣷⡖⠒⠶⢦⡀⠀⠀⠳⡀⠈⠛⠷⣬⣿⣿⡿⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣧⡀
⠀⠀⢀⣼⡾⠷⣿⣿⣿⣿⣥⣤⠴⠚⢣⠀⠀⠀⣧⠀⠀⠀⡠⠉⠻⣅⣸⣿⣿⣿⣿⣷⠦⡄⠀⠀⢸⣿⣿⡿⢿⢿⠟⠻⠿⢿⡀
⠀⠀⢾⡋⢧⡁⠸⣿⣿⣿⣿⢀⡄⡰⢠⠃⠀⢸⣿⣣⡄⠀⠀⠀⠀⠉⠻⣾⣻⢻⡿⣿⡇⢹⠀⠀⢸⠉⠉⠀⠀⠀⠀⠀⠂⡸⠁
⠀⠀⠘⣟⢶⣭⡂⢻⣿⣿⣏⢈⡼⣡⠋⠀⠀⠈⠛⠻⣿⣶⡀⠀⠀⠀⠀⠀⠭⠛⠳⢾⣅⡏⠀⠀⠈⢆⠀⠀⠀⡀⠀⠀⠜⠁
⠀⠀⠀⠘⣦⡙⠛⠺⢿⣿⣿⣾⠾⠁⠀⠀⠀⠀⠀⠀⠈⣿⣹⡀⠀⠀⠂⠁⢠⠦⠤⠤⠞⠀⠀⠀⠀⠀⠳⡄⠀⢀⣠⠤⠃
⠀⠀⠀⠀⠈⠙⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢄⣀⣀⠠⠏⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⡠⡴⣖⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠹⢿⠝⠛⠂⣠⢤⣄
⠀⠀⠀⠀⢀⡾⠀⢸⠈⠉⠦⣼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⢸⣆⠀⢀⡴⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠌⠄⢀⢸⠀⠀⠀⢹⡌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠶⢶⣿⢯⣵⡞⠁⠀⠘⡎⠒⠦⠤⣤⣤⣿⡿⣇
⠀⠀⠀⢸⠀⢁⢸⠰⡆⠀⠀⢀⣷⣄⡷⠀⠀⠀⠀⠀⠀⡔⠉⠀⣀⣀⡀⠀⢰⣿⣼⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠘⢷⢻⡀
⠀⠀⠀⣎⠀⠈⢸⠠⢠⢠⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣧⣄⣀⡘⢟⡿⣦⢿⢿⠟⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠈⢧⢣⡀
⠀⠀⠀⠘⣆⠸⣼⠀⡇⣦⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣩⣿⡿⢩⠛⢯⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠈⣷⢷⡄
⠀⠀⠀⠀⠘⣆⢻⡇⣸⢃⣛⣻⣯⠏⠀⠀⠀⠀⠀⠀⠘⣿⣟⡴⣷⠄⣘⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠘⠲⠠⣤⣼⣔⡽⣄
⠀⠀⠀⠀⠀⠘⣞⣷⢷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠮⠾⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣿⣷⣾⣶⣿⣦⣬⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣾⡭⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠿⠻⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠶⠶⠶⠶⠦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠾⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠤⣝⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣿⠀⠀⠀⠉⠳⢦⡀⠀⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠢⠤⠀⣸⠆⠀⠀⠉⠙⠛⠛⠺⠶⢶⠞⠋⠉⠉⢳⡤⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠒⠊⠁⠀⠀⣀⣤⣤⣤⣄⣀⠀⡏⠀⠑⠆⠀⠀⣷⠻⣦⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⣀⠀⠀⠨⠻⣮⡲⢤⣀⣠⡴⠏⠀⠈⠛⠦⣤⣄⣠⣃⣀⣀⣀⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠳⣄⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠈⠃⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⢤⣄⣀⣠⡴⠞⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣔⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡻⢷⡕⢜⠦⣄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢽⣮⡓⢌⢦⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠠⡝⣿⣧⠳⣮⣊⡳⣔⣄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢻⡌⣿⡇⢤⠳⡙⠚⠞⢦⡈⢆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢳⡘⠻⣮⣈⣉⠢⣝⢶⡝⢌⡑⢿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣓⡂⠹⣿⡳⣌⢡⣌⢢⡙⠧⢻⣄⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠹⣿⣆⢪⡉⡻⢄⢉⠳⠙⢿⡈⢿⣦⡝⣦⡀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣿⣯⡳⡌⡄⠀⠠⠈⡀⠓⢆⠉⡳⠌⢿⣶⣦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⢷⣤⣝⢦⣄⠧⠠⠀⢂⠀⢁⠀⠐⠉⠂⠲⠫⢿⣏⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣙⢿⣷⣮⢱⡌⠀⠌⠘⠂⣄⠁⡀⠈⠁⠉⠄⢐⡘⢧⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⣿⣿⡿⢷⣦⢀⡂⠀⠠⣀⠀⠆⠐⠀⠐⢈⡌⠀⢀⠁⢸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣌⣙⣻⣑⡲⢀⠈⠀⡄⡀⠀⠠⠄⢠⢈⠀⡀⠈⠈⡀⠈⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣝⢢⠀⢀⢀⠐⠀⠀⠀⢀⠈⠀⠀⠉⠐⢠⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣃⣝⠑⢀⠀⠀⡀⠀⠀⠀⠀⡀⠆⣀⠠⠤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⣷⠶⠀⡀⠁⢀⠀⠀⠆⠀⠤⠀⢦⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣠⣤⣈⣎⡼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠐⢲⠂⠉⠁⣀⡀⠀⠀⠀⠀⠀⠀⡤⠾⠤⠸⠤⣤⣤⣦⡀⠀⠀⡖⠐⠂
⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠸⠉⠀⠀⠀⠁⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⣇⣀⣀⡀
⠀⠀⠀⠀⡃⣀⠠⠾⠒⠤⡤⣤⡄⠀⠀⠀⢸⣆⠤⠔⠦⠄⢀⢀⢀⡀⠀⠀⢂⣀⣀⣥⡄⠈⢀⠀⠈⡏⠁
⠀⠀⠀⢀⣏⠉⠀⠀⠆⠀⢙⠉⠙⠉⠉⡝⠛⢹⠀⠀⠀⢸⡁⠰⠀⠈⠉⠉⡏⠉⠉⡎⠀⠉⠩⠀⠀⡇⣆
⠀⠀⠀⠀⠈⠀⠀⢠⡀⠀⠰⠀⠀⠀⠀⡇⠀⢸⠀⣀⣀⣺⣟⢠⠀⠀⠀⠀⡇⠀⠀⠅⠀⠀⢠⡃⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠥⠤⠶⠀⠀⠀⠀⣢⡤⣞⣉⡉⠊⠀⠙⠒⠖⠂⠴⠾⠓⠲⠼⠤⠴⠶⠞⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⡶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠚⢉⡴⠉⠁⠀⠀⠈⠙⠒⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣷⣿⢿⡇⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⢸⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠋⠁⠉⣿⣿⣿⣄⣸⡇⠀⠀⠀⠀⠀⣺⢿⡖⠛⠈⠉⠈⠉⠛⢦⡀
⠀⠀⠀⠀⠀⣠⠇⢀⡴⠞⢉⣼⣿⣿⣿⣿⡶⠶⢶⡴⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⣴⣧⣶⠋⠀⢰⣾⣿⠏⠈⠓⠁⠀⢢⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⣿⣿⣿⡄⢀⣻⡿⠁⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣿⢹⣿⡇⢺⣿⣤⣤⣶⣲⣖⡒⢿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠶⢤⣀
⠀⠀⠀⠀⠸⣿⣿⡗⢷⣿⣦⣼⡿⢿⣿⣷⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣷⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠈⠙⠷⣤⣿⣿⣿⣷⣦⣈⠘⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⡉⢺⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠓⢤⣯⣥⣿⣿⣿⣷⣤⣄⣀⣀⣠⠤⠚⠉⠙⠿⢿⡿⠽⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠴⠒⠚⠛⠛⠓⠒⣒⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⠉⠀⠚⠉⡀⣀⣤⠤⠤⠴⠒⠋⢁⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⡡⠊⠁⠀⠀⠀⠀⠀⢀⡴⠒⠉⠀⠀⠀⠀⣠⠖⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠞⠁⠐⠉⠀⠀⣀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣀⡤⠞⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠚⠁⠀⠀⠀⠀⡠⠊⢀⣠⣔⣩⠤⠤⠔⠒⠚⠉⠛⠉⠀⠀⢂⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⢀⠞⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣐⣁⡠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⡴⠊⠁⠒⠲⠀⠐⠢⣕⢢⡀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠋⠉
⣼⠁⠁⢴⣦⢾⠆⢺⠅⠈⠆⠃⠀⠀⠀⠀⣀⣠⠤⣤⠶⠒⠛⠉⠉
⡇⠀⢀⠐⠃⢀⣠⣈⣼⠀⡜⠀⢀⣀⣤⠤⠤⠖⠋⠁
⠹⡄⠀⡲⠤⡀⠀⠑⠮⠔⣁⡴⠋⠁
⠀⠈⠢⣌⣑⡒⢂⣀⡤⠞⠁
⣶⡶⠲⠖⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶