Asthma Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠚⠛⠉⠉⠙⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢹⡄⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⢸⠛⠲⠦⣄⣀⣄⣴⠾⣤⠄⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠸⡿⡄⠈⢢⡀⠈⣳
⠀⠀⠀⠸⡆⠀⠀⠀⠉⠳⡍⠀⢹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⠀⠀⠀⠀⠀⢀⡇⢹⣄⣀⣻⡍
⠀⠀⠀⠀⢻⡀⠀⢀⡩⢽⣿⣀⣼⠁⠀⠀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠞⠁⠈⠛⠛⠛⢿⣛⠋
⠀⠀⠀⠀⠈⣧⠀⣠⠞⠋⠩⠿⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠄⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⢣⠖⠛⠛⠶⣄⠀⠀⣠⠖⠛⠛⠒⢦⡈⠳⣄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣿⠀⠀⠀⠀⠈⠳⣼⠁⣀⠀⠀⠀⠀⡧⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⣤⠖⠒⠒⢦⡀
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣯⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣎⠉⠀⠀⠀⢠⡇⠀⠀⠀⠈⠳⣄⠀⣤⣴⡃⠚⣿⣛⣧⣨⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⠀⠹⡆⠀⠀⠀⠀⢤⡆⢻⡀⠀⢀⣠⠟⠀⣠⠤⣄⠀⠀⠘⢧⣿⠈⢉⡽⣽⣯⠭⠭⣿⡄
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣴⠃⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣸⠛⠛⠉⠁⠀⠐⠁⣠⠎⠀⠀⠀⠈⣿⠀⢸⠀⢻⣤⡤⠄⣸⠇
⠀⠀⢀⡏⠀⠀⠀⠀⠀⣼⠉⢠⣤⠶⣤⡉⠃⠀⠀⠀⠀⠀⠉⠳⣤⣤⣤⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣀⣿⠀⣼⠀⣾⣠⠴⠚⠁
⠀⠀⢸⡇⢀⠀⠀⠀⠀⢷⡀⠀⠀⠁⢀⣡⠔⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⠀⠀⡟⠀⡇⣿
⠀⠀⢸⡇⠘⡄⠀⠠⠀⠈⠙⠒⠒⠛⠉⠀⠀⠀⣀⣽⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣟⡿⠲⠶⠓⡞⠃⡏
⠀⠀⠈⠛⠉⢳⠀⠀⣷⡀⠀⠀⠀⣀⣠⡤⠖⠋⠉⢸⠃⠀⠈⡉⠓⠶⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠞⠉⠀⠀⢀⡼⠃⣸⠃
⠀⠀⠀⠀⠀⠈⢧⣀⣹⡙⠶⠞⠋⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⣯⠉⠉⠉⠁⣸⣧⣯⣤⣤⡤⠶⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⣷⢄⡀⠀⣿⣤⠤⠤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡶⢶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠲⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡏⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡚⠛⠓⠶⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣁⣂⠀⠀⢸⡗⠲⠶⢶⡶⢶⠶⠖⠒⠚⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⡤⠴⠚⠁⠀⠀⢸⡇⢸⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⣸⣀⣀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢧⣀⠀⠀⠒⠒⢛⣟⣉⣉⣠⣤⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠛⠮⣽⠛⢙⣋⣿⣉⠙⠷⠶⠚⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠶⠖⠚⠋⠁⠀⠈⠙⠳⠦⠤⡤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⢰⣟⡛⠃⠛⣿⡟⠃⣿⣀⣀⣿⢰⣿⣧⢰⣿⡇⢀⣾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢾⣷⣠⣍⣻⡷⠀⣿⡇⠀⣿⠋⠙⣿⢸⣿⢻⡿⢹⡇⣼⡷⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠉⠀⠀⠈⠀⠀⠉⠀⠀⠉⠀⠁⠀⠁⠈⠁⠉⠀⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣀⣀⡀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠟⠉⠉⠻⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢹⣿⡏⢠⡿⢻⡆⢹⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡿⠛⠁⠹⣧⡈⢻⡟⢁⣼⡟⠀⠛⢿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣀⣰⣦⣶⠟⠋⠀⠀⣀⣠⡿⠛⢿⡿⠛⢻⣆⣀⡀⠀⠉⠻⢷⣤⣶⣄⣀⣤
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠷⠟⠛⠋⠉⢀⣤⡴⠾⠟⠛⠋⠙⠻⠶⢾⣷⠶⠟⠛⠙⠛⠃⠰⠆⢀⡀⠉⠉⠛⠻⠷⢾⣧⣀⣀
⠀⠀⠀⠀⢠⣶⡾⠋⠁⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⣤⣤⣤⣾⣷⣤⣤⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⣽⣷⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡘⠋
⠀⠀⠀⢀⡀⢈⣿⣶⣄⠀⢸⣧⣼⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠋⠙⠛⠉⢻⣧
⢠⣄⠀⠘⣷⡀⠀⠀⡹⠛⢸⣏⣹⣿⠀⠀⠀⠀⠀⣼⠏⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⢛⣿
⠈⠙⠷⣦⠈⠀⠀⣀⣠⣤⣼⣏⣹⣿⣤⣄⣀⡀⠀⠀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠛⠛⠛⠻⣿
⢶⣶⣤⠀⢀⡄⠘⠋⠉⠀⢹⣏⣹⣿⠁⠉⠙⠛⢷⣄⠀⢠⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠶⠶⠶⠶⣶⠀⠀⠀⣿
⠀⠀⠀⣠⡄⠀⠀⠀⣦⠀⢸⣟⣹⣿⠀⣰⡄⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣶⣶⠀⣿⠀⠀⠀⣿
⠀⠀⣰⡟⠠⣶⢶⣶⡟⠀⢸⡟⢻⣿⠀⢘⣷⣶⢶⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣦⠀⣿⠀⠀⠀⣿
⠀⢠⡿⠀⠀⠀⢀⣬⣿⣶⢿⡇⢸⣿⢷⣾⣯⡀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣿⠀⠀⠀⣿
⠀⣼⡇⢀⣴⠶⢿⡏⠀⠀⢸⡇⢸⣿⠀⠀⢈⣿⠶⢶⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣀⡀⠀⠀⠀⠀⠀⠀⠟
⠀⣿⠀⠀⠀⣤⡾⢻⣆⠀⢸⡇⢸⣿⠀⢠⡿⠻⣦⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠁⠈⠉⠻⣦⠀⠀⠀⠀⠀⠶
⠀⣿⠀⠀⠀⠁⠀⢸⠏⠀⢸⡇⢸⣿⠀⠘⡷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⠀⣴⡶⠟⠛⣷⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⣰⡆
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢴⣤⣤⣶⠶⢿⠇⠀⠹⣧⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠀⢿⡄⠀⠀⣀⣠⣤⣶⠟⠋⠀⠀⠈⠻⢶⣦⣤⣀⡀⠀⢀⣿⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⢻⣇⣀⣠⣿⣆⣀⣠⣴⡶⠟⠛⠉
⣤⣬⣽⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣯⣭⣭⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⢁⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢳⢀⡲⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡠⠖⠃⠀⠑⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⠴⠋⠙⣄⡇⣇⡜⠉⠳⢄⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠏⠀⡄⠀⢻⣀⣸⠃⢠⡀⠈⢧⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡏⠰⠊⠀⠀⣼⠀⢸⡄⠀⠑⠆⠈⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢰⠃⢀⡴⠃⠀⡇⠀⠀⡇⠘⢦⡀⠀⢳⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⡄⢀⡤⠖⠊⠀⠀⠀⠈⠒⠦⣄⠀⡼⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠚⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠂⠀⠀⠀⠛



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⣤⣀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠳⣄⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠘⣧⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⠇⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠟⠉⠀⠀⠀⠀⠈⠛⠶⠾⠂⠀⣿⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⣴⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇⣠⡿⠻⠶⣶⡌⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⢀⣴⠏⠀⢀⡾⢋⡿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⠷⣾⡳⣦⣴⠏⠀⣸⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⢸⣯⠙⠷⣤⡈⣻⡾⠁⠀⣰⡟⠉⠀⠙⣿⣷
⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠹⣞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠛⠶⠶⠶⠶⠛⠙⠳⣤⣈⠛⠛⠛⠛⢻⡟⣠⡴⠶⠶⠘⣿
⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⢸⣵⠏⣠⣤⡄⠀⣿
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣙⠶⣦⣄⣀⣀⣀⣤⡴⢟⣽⠷⢦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣿⣴⠏⠀⠀⣸⣿
⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣭⣭⣭⠴⠾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢠⣿⡟
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠈⣷⠀⠀⠀⠀⠀⢸⣿⡁
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡆⠀⠀⠀⠀⢸⣿⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣶⣶⣾⣿⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣠⣴⣶⣿⣷⡆
⠀⠀⣾⣿⣿⣿⣿⡿⣟⣵⣿⡄
⠀⠀⠹⣿⣿⢟⣽⣾⣿⣿⣿⣿⡄
⠀⠀⢀⣩⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠐⠶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠐⢶⣄⠀⠈⢿⣶⡄⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⢀⡼⠟⠀⢀⣼⡿⠃⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠘⠛⠋⠠⣴⣾⠟⠉

⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠄⣀
⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠤⣄⣀⣀⡀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉⠢⣀
⠀⠀⠀⢀⠞⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣶⡆⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⢄
⠀⠀⡠⠋⠀⢀⠀⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠢⡀
⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠘⢿⠙⣿⣿⠀⠀⠀⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢰⠺⣿⣿⣧⣶⣿⡿⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠄⠿⠛⠋⠉⠁⠈⠐⠒⠂⠠⠤⠄⠐⠂⠤⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠔⠒⠒⠒⠒⠒⠉
⣶⣶⠶⠶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠐⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠦⠤⡄⣀⣀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⠀⡇⠀⠈⠢⡀⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⢀⡞⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⡰⠋⠀⠀⡀⠀⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⠀⠀⠀⠸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⣀⡻⠁⠿⣿⡇⢀⣀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠘⢿⣿⣷⣾⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠣⠞⠋⠁⠈⠀⠀⠉⠉⠐⠒⠒⠒⠂⠑⠒⠂⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠟⠛⠛⠛⠛⠻⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣶⣿⠟⠋⠉⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⣸⣿⠀⠀⣀⣤⣴⣶⣾⡿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣿⡇⠀⢾⣶⣴⣾⠆⠀⠀⠰⣷⣦⣶⡷⠀⢸⣿⠛⣿⣿⠀⢸⣿⢻⣿⡃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⡇⠀⠀⠈⠉⠀⣠⣤⣤⣄⠀⠉⠁⠀⠀⢸⣿⣶⡿⠃⠀⠘⠿⣿⣿⣦⣤⣤⣤⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⣾⡿⠋⠙⢿⣷⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢿⣷⣶⣶⣾⡿⠀⠀⢀⣼⡿⠁⠀⠀⢀⡀⠿⣷⣦⣄⣀⣀⣤⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠈⠉⠉⠁⢀⣠⣴⡿⠟⠀⠀⠀⠀⠹⣿⣦⡈⠉⠛⣿⣿⠋⠉⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠿⣿⣿⠿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠻⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣄⣀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⢠⣶⡄⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣿⣿⡉⠙⠿⣷⣶⣤⣤⣤⣤⣶⣾⠿⠋⢉⣿⣿⢿⣶⣤⡀⠀⢻⣷⣄⣀⣠⣾⡿⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠈⠻⢿⣶⣤⣀⡈⢉⣩⣽⣿⣿⣶⣦⣶⣿⠟⠁⠀⠈⠛⢿⣷⣄⠉⠛⠛⠛⠻⢿⣶⣾⠿⠋
⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⣀⣈⣽⣿⣿⠿⠛⠉⠀⠀⠀⠉⠛⣿⡆⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⣼⣿⣁⣠⣤⣤⣶⣶⣾⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧
⠀⠀⣼⡿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⠀⠸⣿⡄
⠀⠘⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣤⣤⣤⣤⣴⣿⠃
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⢤⣌⣻⣙⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⣄⣀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠯⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⠶⠤⣄⣀⠀⠀⡄⠀⠀⠀⠈⠱⣄⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⢩⠥⠄⠀⠀⠀⠈⠙⠢⣜⡂⠀⠀⠀⠀⠈⠓⠈⠳⡄
⠀⠀⠀⠀⠀⢀⠤⠤⣄⠀⣠⠴⠚⣹⠖⠒⠛⣧⠀⢀⣠⠴⠒⠛⠉⢹⡇⠀⠙⢦⣀⠀⠀⠀⠀⠐⠾⣅⡀
⠀⠀⠀⠀⠀⣻⣰⠶⠻⣿⡄⠀⡜⠁⠀⣤⣠⢃⡴⠋⣴⠄⠀⠀⠀⠸⡇⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣀⠙⣦
⠀⠀⠀⠀⣮⣉⡉⢳⠉⢹⠀⠀⣳⣶⡶⠛⢡⠏⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣠⣚⠁⠀⠀⠀⠀⠸⡗⢾
⠀⠀⠀⢸⠠⣄⣹⢻⠀⢺⣶⡒⠳⠀⠹⠀⢿⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣩⠋⣠⣀⡀⠸⡦⣄⢹
⠀⠀⠀⠘⢦⡀⠸⣼⣀⣸⣧⣃⠀⠀⠀⠀⠘⢷⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⢰⣃⣸⣥⣄⡉⠓⠷⠈⠛
⠀⠀⠀⠀⠀⣽⠰⡶⠻⠤⠼⠙⠲⢄⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣤⣤⡀⢹
⠀⠀⠀⠀⠀⢹⡀⠣⣀⡀⢀⣶⠒⠒⠚⠉⡙⠓⠒⠒⠲⠶⠶⠖⠒⣲⡂⠉⠳⢤⣀⣉⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠓⢤⣀⣀⣿⣿⡆⠀⢀⣠⡇⠀⠀⠀⠀⠠⣀⠀⠀⢧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡧⠞⠉⢸⠁⠀⠀⠀⠀⠀⡟⠀⠀⠸⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠷⠶⣶⣞⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⠀⢸⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⠀⠀⣀⣀⣿⠈⠓⠋⣠⠾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⡿⢹⠉⠉⠙⣆⠀⠀⠠⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠦⢤⣧⣸⣄⣀⡀⠈⠉⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⣟⣳⡶⡤⢼⣧⣄⣀⣀⡀⢀⣀⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡤⠤⠼⠯⠤⣿⣟⣷⡾⢶⣋⡉⠹⢿⡟⠁⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠒⠊⠭⠭⠭⠭⠭⠝⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠚⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣤⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⡿⢣⣿⣿⣽⣿⣿⡿⢿⠁⠈⠑⠦⣄⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠂⠀⠀⣠⣄⣿⣷⣮⣛⡿⢿⡏
⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣧⡎⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢧⠀⠠⠄⠀⠀⠛⢹⣿⣿⣿⣿⣿⣿⠂
⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣾⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠈⠐⠠⢄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢳⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢸⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡞⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣿⡿⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡠⢄⠀⠒⠒⠁⢄⣠⠃⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣯⢿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠒⠒⠀⠉⠉⠉⠉⠑⢆⠈
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠄⠀⠐⠂⠐⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣘⣯⢹⡏⡷⢾⢼⣶⣇⣼⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⡏⣶⡜⡾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⢞⣁⣤⣟⣺⣺⣤⡈⠓⠦⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠉⠀⠀⡞⠉⠀⠀⠀⢹⠀⠀⠀⠀⠱⡄⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡇⢰⠀⠀⠀⠘⢄⣀⣀⣦⣀⣇⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠋⠈⠃⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠛⠦⣿⣿⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⢠⠯⠭⠭⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⢀⠰⠒⣿⣿⠒⠦⣄⢫⡅⠀⠀⠀⠀⠀⠀⢸⡤⠤⣍⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠢⣤⡇⣿⣿⢸⣤⠜⣆⠀⠀⠀⠀⠀⠀⠀⢸⠈⠇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠤⣶⠋⣿⣿⠙⣶⠤⢸⡄⠀⠀⠀⠀⠀⢀⣸⣟⡛⠋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠇⣿⣿⠸⠍⠃⢸⡇⠀⢀⣠⢠⡴⢯⠀⠀⠳⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡤⠔⠃⠘⠲⢤⣄⣸⠇⠉⠋⠁⠀⢧⡨⣧⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣴⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⢿⣿⣿⠏⠀⠀⠈⠃⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠛⠁⠀⠀⠀⠀⣾⠇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⢻⣿⣿⣿⣿⣷⣦⣀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣷⣄
⠀⢨⣿⠃⢠⣤⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣮⣝⠻⢿⣿⣿⣿⣦
⠀⢸⡏⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠛⢿⣦⡙⣿⣿⣿⡄
⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣷⠸⣿⣿⣇
⠀⢸⠁⠐⠐⠛⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢹⣿⡇⢻⣿⣿⡀
⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢿⣿⠸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⣤⣤⡤⠶⠖⠛⢻⣄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣼⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⢠⣤⡤⠶⠆⠀⠀⠰⠶⢤⣤⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⣠⠀⠀⣀⣀⣠⠄⠀⠀⢠⣄⣀⣀⠀⢠⡍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⡀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠠⢦⠶⠀⠀⠀⠀⢀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠹⣦⡀⠀⢀⣀⣀⣀⡀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣧⠀⢸⡟⢦⣈⠉⠙⠻⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⣸⠃⠀⠙⠳⠶⠶⠛⠙⣯⡉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠉⠳⣆⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠉⠉⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠳⠶⠋⠉⠙⠛⠓⢶⣄
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠃

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⣿⣿⣿⣿⡿⣳⣿⣿⣿⡿⡟⠛⠢⢀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠎⠀⠀⠀⣀⣰⣶⣿⣿⣿⠃
⣿⣿⣿⣿⣷⡽⣿⣿⣿⣷⣅⣀⣀⣀⣨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢆⠀⠀⠀⠉⠿⠿⠿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄⠀⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣠⣿⡟⠀⠀⢸⡧⠉⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠁⡞⠁⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠠⠀⠐⠒⡄⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡿⠃⠀⢄⡀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣂⡔⠁⠐⠤⠸⠁⠀⠀⠀⠈⠈⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡤⠀⠀⠀⢠⠖⡉⠂⠠⠀⠀⢀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠄⡽⠀⡀⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠉⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠀⠀⠀⠙⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢀⠒⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢄⡀⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠚⠣⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢀
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣄⠐⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠃
⠀⠀⠀⠀⡄⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠄⢀⡀
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠋⠩⠉⠉⠙⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⡀⢸⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⢸⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣙⠛⠶⠶⠶⠶⠶⠛⣩⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⢸⠀⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⢸⠀⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣸⡇⢸⣿⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⡾⠉⣠⣼⣿⣧⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⠀⣼⣿⣿⣿⣿⣿⣇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⠀⢻⣿⣿⣿⣿⣿⡏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢷⣀⠙⠛⠿⠛⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠉⠓⠲⠶⠖⠛⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣛⣛⣿⣻⣽⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣭⣭⣭⣿⣯⣭⣯⣽⣍⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡆⠀⠀⠒⠀⠈⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠂⠤⠐⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠚⢀⠀⠁⠀⠈⡃⠒⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢀⠓⠄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⢒⣄⠀⠀⠀⠀⠀⠐⠒⠢⠤⠔⠀⠀⠑⠰⠄⠄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢨⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡌⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡟⠀⠀⠀⠀⠀⠀⢀⢀⡠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠰⠁⠈⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂
⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠔⠀⠀⠀⠀⠀⢉⡀⠂⠠⠤⠤⠤⠀⠲⠂⠉⠀⠀⠀⠒⠒⠲⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠠⠄⠤⠄⠀⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⠤⠤⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠁⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣟⣛⣻⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣯⣭⣿⣿⣽⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢀⠇⡇⠀⡠⠴⡄⢀⢠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⠀⡇⠘⠾⠀⠘⠊⠀⠀⠙⠛⢤⠀⠙⢆⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢇⠓⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣙⠚⠁⠀⠀⠀⢀⡠⠔⠒⠉⠑⠒⡶⠀⠀⠀⠀⢨⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡗⡒⠉⠁⢀⣠⣢⠀⠀⡸⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠜⢢⠀⠀⣞⠀⠈⡇⢀⢧⡆⠀⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⡜⠀⠀⢿⢀⡴⠃⣸⠁⠹⠏⣅⢸⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠙⠊⠐⠉⠀⠀⠉⢀⣴⣿⡄⠀⢀⠡⢞⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⠢⣤⣀⣠⣤⣾⡟⠋⢹⠇⠀⢀⣤⠞⢛⣣⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⢿⡿⠛⡟⣀⡴⠋⠀⡴⠋⣟⠉⢹⠈⢩⠃⠁⠀⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢯⠟⠒⡄⠈⠓⠤⣍⣛⣉⣁⣠⠤⠞⠁⢀⣸⠤⠞⠀⢇⣠⠆⢠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⢇⡔⠰⡇⠀⠀⠀⢀⣀⡴⠋⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠑⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠍⠊⠳⣌⡑⠒⣒⣳⠎⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣏⣀⣀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢫⡉⠉⠉⠁⠀⠀⠀⠀⠈⣹⠃⠀⠀⠀⣠⠦⠤⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢨⢗⢳⠀⣀⡤⡀⠀⢀⠀⠀⠉⠒⣦⠀⡠⢷⡒⢦⢀⠀⡝⢝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣾⠀⠙⠊⠁⠀⠈⠉⠻⣄⠀⢀⡴⣃⡰⢋⡵⠟⠳⢮⣎⡠⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠾⢛⣛⡿⢝⡢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠲⣬⠖⠁
⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠈⠑⠪⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣥⢿⣆⠸⠿⠋⠀⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠻⠿⠆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠿⢿⣷⣄⣠⣴⠃
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣄⣀⣀
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⢦⡀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⠀⡀⠀⠀⠀⢀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣶⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠠⢀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠹⣿⣿⣿⠟⠉
⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⣤⣄⣀⠀⠀⠀⠀⢀
⠀⠀⠙⠿⣷⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⡿⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠈⠉⠛⠻⠷⠶⠶⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⢈⡷⣄⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡀⠀⠀⠀⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⡤⠒⠁⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣠⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠛⠢⡺⣯⡆⠀⠀⠀⢰⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⠀⢠⠉⠈⣀⠙⣷⡀⠀⠀⢸⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠐⢹⠀⣿⠀⢸⣿⡑⢾⡇⠀⠀⠀⣿⠃⠀⠐⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡟⠉⠛⠃
⠀⠀⠀⠀⠀⠀⢸⠀⢿⣀⣠⠄⠐⢸⣧⣄⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠨⠀⠀⢸⡟⠉⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⡿⠛⠛⠒⠚⠀⠀⠘⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠰⠁⠀⠀⢠⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡶⣛⠶⠥⠾⠶⢦⡴⡟⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣥⣼⣿⣿⡿⣿⣿⣷
⠀⢸⢹⢳⡒⣿⣥⣄⡴⠛⣁⠀⠀⠄⠤⠊⠀⡇⠀⡇⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⣸⣿⡇
⠀⢸⣏⠀⠀⢸⡟⣡⠂⢩⠃⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⠀⣿⡟⠁⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠘⠋⠀⠀⢸⢸⡇⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠰⠀⠀⠀⠀⠀⠛⠀⠀⠸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠿⢯⣑⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸⡧⠓⢒⡲⠀⠀⠀⠀⠀⠀⣽⣿⣿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠒⠀⠀⠔⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠰⠁⠀⠀⠀⠀⠀⠀⠈⠰⠒⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⠤⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠆⠀⠀⠀⣠⣾⠇⢰⣴⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡤⡀⠀⠸⠀⠀⠀⠚⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡌⠆⢀⠁⠀⠀⠀⢀⣠⠀⢰⠴
⠀⠀⠀⣀⡤⠤⠤⠤⢀⡀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠝⠋⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀⠤⠐⣠⡙⠆
⡞⠙⠛⠁⠀⠀⠀⠀⠀⠈⢩⠒⠂⠀⠀⠀⠀⠀⠀⠸⣇⡴⢷⡴⠃⠀⢠⢐⣠⠥⠔⠂⠈⠭⠐⠁⠀⠀⠈
⠘⠦⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢼⣶⠾⠏⠃⠁⠈⠁
⠺⡄⠀⠀⠀⠀⠀⠀⢐⣺⣿⡇⠀⢀⣀⣀⠀⠀⠀⠋⠁⠰⠆⢠⠊
⠼⠁⠀⠀⠀⠀⠀⠀⠶⠟⠏⠀⠀⠀⠀⠈⠑⢦⡀⠀⢀⣀⡤⠾⡀
⢠⠀⠀⠄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢆⢀⡤⠼⠖⠒⠶⠤⠤⣀⡀
⢸⠆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢢⡀⠀⠀⠀⠀⠳⣴⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⡴⠚⠂⠀⢀⡀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀
⠳⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⢤⣄⣀
⠠⡄⠙⠀⠀⠀⠀⠀⠀⠴⢺⣇⠀⠀⢀⡼⠃⠈⠓⠢⠤⢤⣤⡤⠶⠛⠉⠒⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⡀
⠀⢳⠈⠆⠀⠀⠀⠀⢀⣴⣿⣿⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦
⠀⠀⠒⠒⠒⠂⠈⠉⠀⠀⡀⠝⠋⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠶⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣶⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣀⣀⣀⣐⣒⣒⣒⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣒⣚⣉⣁⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠀⢺⣿⡷⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⢠⡟⢰⣶
⠀⠀⠀⠀⣤⣤⢶⣿⡇⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠠⣿⣯⡳⡄⠀⠀⠀⠀⠀⠀⣧⣸⡿
⠀⠀⠀⠀⠀⣟⠛⡛⠀⠀⠀⠀⠀⠀⠀⣯⠟⠀⠀⠀⠀⠀⡐⠹⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠧⠓
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⣩⣯⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⢰⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢻⣿⣭⡟⠂⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⢀⣾⣿⡧⢄⣀
⠀⠀⠀⠐⠚⠋⣷⠀⠀⠀⠀⠀⠀⢀⢄⢐⡇⠀⠀⠀⠀⠀⣤⣄⢘⡇⠀⠀⠀⠀⢀⣘⣿⣿⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢸⣟⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣠⣆⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣆
⠀⠀⠀⠘⣿⣿⣾⣄⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠙⡟⡟⢻⡿⣧⠀⠀⠀⠈⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠛⠻⡀⠀⠀⠀⠀⢀⡜⢹⠀⠀⠀⠀⠀⠀⠀⣷⠏⠀⠘⢧⠀⠀⠀⡇⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢠⣄⢀⣿⡀⣀⡄⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠠⠤⢿⡿⠤⠄⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠘⠛⣿⡟⠃⠀⠀⠀⠀⠀⢀⣹⣷⡄
⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀⠈⠋⢁⣾⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠲⠶⣆⡟⢸⡆⠀⠀⠀⠀⠀⢸⠀⢷⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠳⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠚⠻⣦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡾⠃⢀⣤⣤⠶⠆⠀⠀⠰⠶⢤⣤⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢡⡀⠀⣀⣀⣠⡄⠀⠀⠠⣄⣀⣀⠀⠀⣌⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⢰⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⢦⡴⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢧⡀⠀⠀⣀⣀⣀⡀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣷⠀⢸⡟⢦⣄⠉⠉⠻⣿⣷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⢸⡇⠀⠉⠳⠦⠴⠞⠙⢷⡉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⠛⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠋⠉⠁⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠶⠟⠉⠙⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠟

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠛⠿⠿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣦⡀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⡤⠀⠀⠀⠀⠀⠀⠛⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢻⣿⣿⣿⣿⣿⣿⣤⣶⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⠇⠀⠀⠀⢀⣶⣄⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⣾⣿⣿⣿⡿⠙⢿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡄⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣧⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣤⣀⡀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⠛⠿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⣸⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣼⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⢀⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣴⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⠀⠀⠀⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⡐⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢨⢠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣧⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢨⠁⠩⡤⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⡼⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢚⡰⠾
⠀⠀⠀⠀⠀⠀⠀⠰⢻⠋⠹⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⢡⠋⣉⣉⢉⡉⠁⡀
⣦⡖⠊⠂⠀⠀⢠⠂⠐⠀⠐⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⠀⠀⠀⠈⡏⠁⡏⠀⡇
⢿⢷⡇⡞⠁⠒⠁⠀⣇⠀⠀⠀⠀⢠⣇⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣯⠔⡖⠒⠊⠈⣮⡄⠀⠀⠘⣯⠉⠙⠃
⠈⠉⠉⠓⢤⣀⣀⠾⡏⡄⠀⠀⡼⣁⠀⡹⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠒⠓⠤⣀⠔⠁⣿⠀⠀⠀⠻⢷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣆⠀⠈⠛⠙⠁⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡄⠄⠐⠊⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠘⠓⠒⠀⠒⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡞⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⠔⠈⠀⠑⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣠⠞⠫⡀⠀⠀⠀⠉⠉⠉⠑⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡴⠋⠈⠢⣀⠀⠀⠀⠀⠀⠈⠑⣤⣠⣀⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡾⠁⠀⠀⠈⠲⢄⣀⡠⠤⠶⣄⣏⠠⢛⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡜⠀⠀⠀⠀⠈⠉⠒⠒⠲⠦⠤⠴⣧⡇⢠⢿
⠀⠀⠀⠀⢀⡼⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠇⠀⠀⢀⠀⠀⠀⠀⡼⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣮⠏
⠀⣀⣀⣾⣉⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠝⠀⠀⠀⠸⣏⠳⠆⢰⣙⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠏
⠑⠪⢿⣍⣉⠙⡷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡢⢄⣨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣝⢿⣿⣿⣿⡟⠈⠻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣛⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣯⣿⣿⣿⣿⣷⡄⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣄⣠⣴⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⣤⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢀
⠀⠀⠀⢰⣋⡽⣀⡤⠖⠚⠉⠓⠢⢄⣀⣏⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡤⢖⡛⢩⣭⠛⠲⢄⣰⠿⠃
⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡀⠻⠃⣨⡍⠐⠿⢂⣹⡄
⠀⢀⣄⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⣤⡀⠀⠀⢀⡀⠀⢀⣠⠴⠿⠧⣄⣀⠀⢀⣀⠀⠀⠀⣀⣀⣀⡇⠻⠟⢴⡶⢙⡋⠰⣶⠞⡚⢹⡀⣀⡀
⠀⠸⣤⠿⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠻⣤⠇⠀⠀⠙⣯⠟⠉⢺⢧⡀⠀⠀⢈⡛⢯⠋⠀⠀⠀⠙⠋⠙⡧⣖⠆⡴⡄⠙⣋⢔⡦⠸⠽⢸⠉⠑⠋
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡼⠁⣠⣄⣈⠀⠀⠀⠐⢻⠋⠈⢧⠀⠀⠀⠀⠀⠀⠱⡄⣤⣯⠀⣘⠞⢀⡸⠿⢠⠏
⠀⠀⠀⢀⡤⣾⠤⣄⡀⠀⠀⠀⢀⣠⢄⣧⢤⡀⠀⢀⣤⣴⡇⠀⢙⠳⠅⠀⣠⢄⠀⠀⠀⠀⢸⡦⣤⡀⠀⠀⢀⢤⠞⠲⢅⣘⡟⣀⣻⡿⠖⢳⡤⡀
⠀⠀⠀⠈⠳⠞⠀⠀⠉⢙⣴⡋⠉⠀⠀⠧⠞⠁⠀⠀⠉⠙⣧⣶⣫⠀⠀⠀⠳⠞⠀⣈⢲⣤⣸⠏⠉⠀⠀⠀⠈⠉⠀⠀⠀⠈⣹⡏⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠀⠀⠀⡦⢠⠄⠈⠈⠙⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠙⠋⠰⣍⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠲⢄⣐⣟⡿⠀⣀⣠⠴⢿⣦⠀⠀⠀⠀⠀⠀⠀⠸⢥⡾⣄⡠⢤⣴⠋⠧⣀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠐⠻⣄⠀⢀⣀⣼⣀⣀⠀⢀⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠰⣭⣼⠃⠀⠈⠙⠶⣻⠤⠇
⠀⠀⠀⠀⠀⠀⢀⡼⢋⣭⡀⢴⡦⢈⣝⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣄⣰⠃⠀⠀⠀⠸⠀⠓⠀⠀⠀⠀⢣
⠀⠀⠠⠷⠤⣠⣞⣤⡈⢉⠡⣖⡄⠈⡋⣠⣿⣄⡤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⠀⠀⠀⠀⠀⠀⠸⠖⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⣠⣸⣄⣠⣄
⠀⠀⠀⠀⠀⢸⠀⠛⠁⠿⢃⡬⡄⠘⠽⣈⡁⢹⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⠤⠞⠸⠤⢤⣀⠀⠀⣀⡀⠀⠀⢸⡀⠀⣀⣼⣠⠆⠀⠈⠉⢿⡠⡷⠚⢧⡼
⠀⠀⢀⠀⣀⣸⡞⠽⠰⣷⠀⣩⣔⠯⢃⣙⠋⣾⣀⡀⡀⠀⠀⠀⠘⢧⡑⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⠖⣡⠋⢀⡤⣴⣣⣄⠳⣬⡷⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠋⠁⠀⠱⣄⢾⠆⣠⣍⢉⡤⡙⢊⡼⠁⠈⠙⠃⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠳⠼⠀⠈⠓⠦⡄⣠⡤⠤⠒⢮⡧⢤
⠀⠀⠀⠀⠀⠀⠀⡼⠓⠦⢭⣋⡤⠽⠗⢻⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣴⠛⣇⠀⠀⠀⠘⠖⠋
⠀⠀⠀⠀⠀⠐⠺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠽⠂⠀⠀⠀⠀⣯⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⣿⠆⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠂⠀⠀⡖⠒⡄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠹⡆⢀⣀⣀⠜⢾⡁⠀⠀⠀⣀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡀⠠⣶⠀⢲⠂⠰⡦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠈⠉⣔⣋⡶⠀⠉⠓⢤⡼⣁⣱⠀⢠⣞⡥⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡳⣄⠀⠀⡀⠚⣣⠴⠛⠋⣩⣍⠛⠳⢤⡛⠂⡀
⠀⠀⠀⠀⠀⠀⣠⣀⢀⡜⠁⠀⠀⠈⡏⠳⠄⠀⠀⠀⢸⠁⠀⠀⠀⠉⠀⠀⠈⠙⠒⢦⢰⠒⠊⠉⠀⠀⠉⠁⠀⡘⢙⡞⠁⠸⠽⠂⣑⠊⠰⣿⠆⢙⣞⠙⡀
⠀⠀⠀⠀⠀⠸⣅⠬⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠞⠀⠀⠀⠀⠀⠀⠀⠘⠛⡟⢴⣳⢀⡤⡌⠷⠃⢀⠤⡔⠯⠟⡖⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠆⣀⠀⠀⠒⢾⢋⣽⡭⣏⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠲⡇⣠⡄⢈⡉⠁⣯⠆⣠⣍⢡⣶⡄⡷⠾
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡗⠀⠸⣉⣻⠀⠀⠀⠀⠀⢉⠞⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⢧⠑⠃⣸⠝⠀⣔⣢⠑⢋⡤⡉⢰⠧⣴
⠀⠀⠀⠀⠀⠀⠀⢻⣀⡏⠙⠲⢬⡁⠀⣀⣀⡠⢄⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠳⡘⠽⠃⣴⢮⠁⡴⣌⢛⡵⢧⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⣎⠁⠀⠀⠘⢧⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡟⠓⣦⢬⣥⣤⢽⠗⠛⣤⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠾⠄⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣶⣶⣤⣄⠀⠀⠀⢹⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣿⣾⣿⣿⣿⣿⣿⣆⠀⠀⢳⡀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡇⠀⠀⠀⠀⢠⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⣵⣭⣛⡇⣩⣭⣭⣭⡹⡇⠀⡞⠁⠀⠀⠀⠀⢸⡇⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠘⠇⠀⠤⠤⠤⠤⣼⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣸⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣭⣝⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢺⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⢸⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⢀⣴⣿⠇⣟⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⡧⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠘⢿⣷⣬⣭⣵⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠸⠇⠹⠇⠿⠸⠻

⠀⠀⠀⠀⢀⠤⠤⡀
⠀⠀⠀⠀⢇⡘⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣐⠞⣗⠀⠀⠀⠀⢠⣀⢀⣦⡀⣠⠄⠀⠀⠀⢀⣤⣀⠯⠼⢄⣴⢄⠀⠀⠀⣩⠒⠛⠐⠻⢤⠄⠀⢀⣔⠒⣠⣷⠴⠧⢤⠂⡀
⠀⠀⢈⡲⣧⠀⠈⡄⠀⠀⠀⢰⢯⠀⠀⢠⠻⠓⢚⠀⢠⢀⡝⡠⠢⣤⠂⡜⣏⡄⠘⢶⡓⢩⡈⠰⡀⣸⠖⠀⠘⡋⡰⠛⢒⣗⡂⠀⢫⣁
⠀⠀⠸⠁⠌⠃⠤⡄⢲⠀⠀⠹⣾⣠⡄⣤⠴⠬⢮⡀⠘⠊⡇⠑⠄⠤⠐⢀⡿⠂⠠⠾⣓⠬⢤⣚⠀⢸⠆⠀⢩⣷⠸⠟⡟⠛⠁⠀⣼⡄
⠀⠀⢙⣅⠀⠀⠀⠀⠞⠂⠀⠈⡮⢭⣁⣀⣀⣴⠁⠀⠀⠐⠯⠒⢲⢦⠐⠻⠋⠀⠀⠀⠟⠑⠲⠐⠷⠛⠃⠀⠀⠚⠳⠦⡴⠴⣶⠛⠇
⠀⠀⠀⠈⠑⠓⠀⠉⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⢅⣀⠀⠀⠀⠀⠀⠀⢠⣠⠤⠦⣄⣀⠀⠀⠀⠀⠀⢁⣀⡅
⠀⠀⡀⢰⡦⠀⠢⠆⣤⡀⠀⠀⢷⣤⠜⣓⡰⢇⠀⡀⠀⠀⠠⠃⠠⠆⢄⡭⣦⡀⠀⠀⠰⢞⠁⠼⠿⢟⡷⠀⠀⠀⢶⠛⡭⠤⣟⣶⠂
⢠⣼⠣⢋⡐⡬⣰⣸⢈⣀⠀⢀⣤⠁⠂⠛⠸⠀⢹⣁⠀⣠⡃⡖⣶⣿⣼⣷⡞⡵⡄⠀⠀⣿⡆⠸⣏⣍⣁⠄⠀⠀⢾⡜⡰⠆⣸⣷⡀
⠈⢙⣸⠦⠖⢛⡹⠟⠛⠿⠂⠀⢀⢱⠌⠂⠂⣡⡊⠉⠀⠿⣄⠀⠹⠾⡿⠏⠁⠼⠃⠀⠀⣸⡅⠀⠀⠀⢹⣆⠀⠀⠀⢷⢺⣿⣿⠇
⠈⠿⢏⠉⠉⠁⠀⠀⢀⠿⠂⠀⠙⠉⠔⠁⠍⠙⠀⠀⠀⠀⠈⠙⠲⠤⢶⠛⠁⠀⠀⠀⠀⠉⢓⡶⢤⡤⠾⠁⠀⠀⠀⠀⢻⡛⠋
⠀⠀⠸⠗⠄⠚⠂⠁⠃⠀⠀⠀⠀⣀⣠⣀⣀⡀⠀⠀⠀⠀⠐⢭⠂⢀⡥⠅⠀⠀⠀⣀⡠⣄⡦⢴⣴⡖⡄⠀⠀⠀⠀⠀⢈⣷⣰⣾⠁
⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⣸⣊⡽⣅⣤⣟⣟⡢⠀⠀⠠⡨⣾⡱⣋⣣⡖⠀⠀⢀⣙⠟⣖⠶⣈⠙⠓⣯⡀⢀⡀⢈⠷⣾⣻⡿⣿⣳⡆⣠
⠀⠀⢀⠞⠍⢀⠀⡈⠱⡄⠀⣯⠘⢶⣄⣈⣉⣩⣄⠀⣀⡹⢡⣿⠿⠿⢿⢩⣀⠀⢴⠁⠂⢀⠁⠐⢠⠅⣼⠂⣈⡙⠁⠈⠁⠈⠁⠀⠁⠀⢩⠤
⠀⠀⢸⠆⠀⡲⣻⠞⠀⣏⠀⢳⡠⠂⠨⠙⠩⢡⡚⠀⠀⢼⡀⠀⠀⠀⠰⣾⠄⠀⠾⡀⠈⠉⠀⠀⠀⢠⡏⠀⠀⢉⣆⠀⠀⠀⠀⠀⡠⣠⠻⠆
⠀⠀⠈⢥⡂⠙⠉⣁⡤⠎⠀⠀⠉⠒⠶⠰⠖⠃⠀⠀⠀⠉⠘⢓⠒⠐⠎⠀⠁⠀⠀⠋⠗⠲⠦⡤⠶⠉⠀⠀⠀⠉⢀⡗⠠⡄⠰⡏⠓⠘⠃
⠀⠀⠀⠀⠈⠉⢉⠁⠀⠀⠀⠀⠀⢀⡴⡂⠦⣄⠀⠀⠀⠀⢀⡦⣜⣃⡄⣀⠀⠀⠀⠀⠀⢠⡴⡀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⡀
⠀⠀⠒⢤⠆⡿⣾⣃⣏⡸⣄⠄⠀⣸⣀⠷⣂⢸⡄⠀⢀⠜⠉⠫⠋⡅⠁⠈⠐⣀⠀⠠⡤⠭⢀⣈⠒⢋⠸⡄⠀⢀⣼⣓⡖⠠⣼⣱⡦
⠀⠀⠀⣾⠰⠶⢤⡜⢋⣠⠿⠀⡴⠃⠁⠐⡀⡆⢡⠀⢘⠀⠀⢀⠄⠊⠐⠂⠀⡅⠀⠀⠳⣄⠐⣛⠦⢆⠸⣀⠀⠀⢸⠢⡑⣶⠃⣝⡓
⠀⠀⠀⠊⠻⡿⢿⠕⢻⡄⠁⠀⣾⢋⡯⠩⠊⢉⡏⠀⠘⠤⣀⠀⠀⠀⠀⢀⡠⠋⠀⠀⢠⡅⠈⢁⠤⡀⠄⣭⠀⢀⣨⠋⣯⣭⢵⠈⢳
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠐⠚⣉⠀⠀⠀⠀⠀⠈⠉⠁⣌⢉⡍⠀⠀⠀⠀⠀⠘⠘⠉⠀⠈⠋⠀⠀⠀⠷⣀⠀⠈⠀⠀⡞⠁
⠀⠀⠀⠀⡗⡶⣱⢛⠱⣶⠀⠀⠀⠰⢆⡀⣧⠀⣼⢁⡤⠀⠀⣦⢾⠋⢉⠱⢇⡀⠀⢀⡤⢀⡴⢢⣀⣀⡀⠀⠀⠀⠀⠋⢹⡃⠒⠈⠉
⠀⠀⠀⠶⣬⠓⠉⠈⠀⢳⡴⠂⠐⠒⣞⡓⣒⡢⢎⢣⠀⠀⠶⢳⡦⠥⠭⠴⢎⠇⠀⢘⣦⠴⣝⣛⡷⢄⣎⠀⠀⠀⣆⡻⢾⢊⣉⡓⢶
⠀⠀⠠⣄⡄⠀⣀⢄⣀⡀⣼⡀⢠⡴⢆⠛⠅⡴⢃⡜⠁⠉⢹⡀⠶⠄⢤⠶⠂⣄⠰⡃⠸⡐⠢⠴⠔⣸⢈⠀⠰⡶⠘⠂⣹⣌⡓⠉⠈⢶⠆
⠀⠀⠀⢀⡢⠤⣅⢀⠬⡘⠣⠁⠀⠀⠾⠉⠐⣖⠀⠈⠉⠀⠐⠳⡀⠀⠀⠀⢠⡅⠀⠉⢻⠉⢓⣒⠚⢹⠉⠀⢀⡶⣀⢀⡿⡟⣪⡤⣁⣆
⠀⠀⠀⠈⠁⠘⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡖⠈⠰⠎⠀⠀⠀⠀⠉⠁⠀⠙⠁⠀⠀⠈⠀⠀⠟⠁⠉⠳⠋⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠉⠉⠉⠁⠒⢤⡤⠒⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣠⣤⣶⠶⠶⠶⠶⣶⣤⡈⢿⡆⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⡁⠤⠤⢀⡀⠀⠀⠈⢻⣌⠻⠦⡀⠀⠀⠑⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⣁⡀⠀⠀⠤⣄⠀⠈⢆⠂⠀⡆⠆⠈⠉⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⣦⠀⠀⠶⠀⠀⠀⠘⢤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡠⡤⠄⠊⠅⠀⠀⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡀⠉⠀⠀⣀⠔⠋⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣩⠀⠀⠀⣒⠖⠂⠁⠀⠸⠉⠉⠀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠀⠀⠊⢠⠀⠀⠀⠀⡧⠀⠀⠠⢄⠀⠈⠢⡀
⡔⠀⠚⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠁⠂⠀⡞⠀⠀⠀⠀⠀⠑⢄⠀⠑⡀
⠁⠀⢠⣿⠉⠐⠀⠠⢀⡀⠀⠀⢀⠄⠈⠑⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⡀
⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⠈⠉⠀⠀⡠⠔⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠐⠂⠁⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⡰⠉⠆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠒⢄⠀⠀⣀⠤⠊⠀⠀⠈⢆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢏⠁⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠎⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣿⠃⠀⣱⠆⠀⠀⠀⠀⠀⠀⢂⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠁⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢏⡴⡚⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢖⠻⠊
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠈⠉⠉⠙⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⠟⠀⠀⣤⣶⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣃⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⣰⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠻⠿⣿⣿⣷⡄⠀⠀⢸⣿⡿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⠀⣿⣿⠀⠀⠈⠛⠁⣴⣶⣶⣶⡄⠀⣠⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⣼⣿⡟⠀⠀⠀⠀⠀⠈⣽⣿⡟⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⠃
⣿⣿⡀⠀⠀⠀⠀⠀⢀⣈⠉⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠙⣿⣷⣦⣤⣄⠀⠀⢸⣿⡇⠀⠀⠀⢹⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠈⠙⠛⢿⣿⣶⣶⣿⡿⠃⠀⠀⠀⠀⠙⠛⠿⠛⠛⠛⠛⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣰⡀⠀⠀⢸⡏⢠⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢘⢱⡀⠤⠩⠧⢈⣦⡞⠁⠀⠔⢑⡆⠔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣁⢱⠀⠀⣰⠖⠋⠁⠂⠓⠄⠀⠀⠀⠙⠁⠉⠒⠷⣋⢴⠟⡝⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠉⠳⠑⠊⡔⠂⣱⠀⠀⠉⠐⢀⡀⠈⠰⢧⠄⠀⠀⠈⢙⢴⡷⠛⠗
⠀⠀⠀⠀⠀⢀⠄⠠⡀⠓⠶⡶⠂⠀⠀⠈⠉⢻⣆⠀⠀⢰⠁⣀⣈⡆⠀⠀⠀⠀⠊⡵⡉⠙⣷⣀⣀⠖⣲
⠀⠀⠀⠀⠀⠘⠀⠒⠮⣖⠴⣀⠀⠀⠀⠀⠀⠀⠄⠡⡀⠀⠑⣴⣊⡀⠀⠀⠰⠉⠐⠄⠑⡠⢁⢀⠊⠉⣉
⠀⠀⠀⠀⠀⠀⢠⠒⢤⡠⠉⠒⠀⠀⠀⠀⠀⠀⠀⡞⢁⡀⡙⡎⠑⠂⠀⢠⣢⣜⣷⠂⠀⠔⡵⢤⣷⢮⣤⠇
⠀⠀⠀⠀⠀⠀⠈⠙⢉⢽⠀⠀⠀⠃⣑⣠⣤⣀⠀⠙⠒⢦⡾⠀⡠⠤⡀⠀⠀⠈⠤⢤⣤⣾⣄⣀⣧⣤⣐⣶⣍⣈
⠀⠀⠀⠀⠀⣀⡀⠀⠈⢣⣀⠀⠀⠓⠘⠁⢰⠀⠀⠀⠀⠈⠄⠺⡀⠖⣨⠄⠀⡠⣂⠝⢅⣱⡥⠔⠛⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠸⣀⡨⠍⠛⢵⠒⠒⠀⠀⠀⢀⣄⣠⡤⠀⠀⠀⠀⣠⠈⠉⠕⢁⣬⠞⠒⣤⠊⡩⢋⡹⠶⠃
⠀⠀⠀⠀⠀⠉⠀⢠⠠⢠⡂⠀⡠⠤⠴⡫⠋⢝⠄⠀⢠⢂⡁⢻⠀⠢⢀⠈⢍⣧⣂⠬⢊⢴⢏⢌⠷⢶⡉⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⢙⡄⢦⣒⠘⠀⠀⣉⡴⠂⡨⠦⡽⠊⡠⣐⠽⡳⢕⡨⠠⢔⠁⡑⠅⣼⠄⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠔⢐⡟⠉⠢⢀⠀⡒⠈⢾⣊⠥⡒⠅⡢⠕⢪⠬⡪⢘⠶⣬⢦⠠⣶⢯⣾⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⢔⠕⠛⢄⠝⠀⡅⠂⠥⡂⢁⠐⣴⡇⠩⣂⢼⡣⠒⠀⣖⡿⠋⠙⠻⡖⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡟⠁⠀⠀⣼⠟⠂⡍⣰⡊⠍⡐⢄⣯⠳⡌⢴⣜⢫⣵⠛⡽⡄⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣬⠟⠀⠰⡱⠁⠉⢰⣶⠘⠣⠕⠋⢻⣄⠀⠀⠀⠘⠵⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠁⠀⠀⣜⣝⡂⠀⠀⠀⣮⢦⡅⠀⠀⠀⢦⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠘⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡠⠀⣀⠤⢀⡠⢄⡠⠄⡀⠔⡀⠄⣂⠤⢂⠠⢂⠠⣊⠄⣂⠔⡠⡢⢔⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠊⠡⠒⠈⠔⢊⠅⠊⠥⠒⠡⠒⡡⠔⢈⠔⠊⠅⠊⠅⠊⠔⠊⠔⠉⠊⠀⠁

⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣫⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠙⠁⠻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠇⠉⠉⠀⠀⠀⠀⠀⢰⣦⠘⠿⠿⢿⡃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⣠⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢛⣁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠓⠒⠛⣻⠆⠀⠉⠉⠉⠉⠙⠚⠓⠢⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠛⠲⢤⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢠⠏⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡼⠁⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡰⠋⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⠖⠋⠀⣀⡴⠞⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣀⢦⢠⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⣀⠀⢀⣀⠤⠔⠚⠉⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠛⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡛⠛⠛⠲⢦⡀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⢠⣶⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠇⠀⠀⣠⡾⠛⢦⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⠟⠻⡄⠀⠀⣤⠞⠀⢀⣴⠞⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠴⠛⠁⢀⡴⠛⠁⠀⠀⠘⡆⠀⠀⠀⠀⢸⡇⠀⠀⣯⠀⠀⡇⠀⠀⢳⣀⣠⠾⢀⣆⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⣀⠀⣀⣀⡤⢾⠃⠀⠀⠀⠀⢸⠃⠀⠀⡇⠀⠀⠱⡀⠀⠀⠀⠀⢀⡠⢦⢾⣄⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠉⠉⣉⣥⣤⠞⠀⠀⠀⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⠙⠓⠶⠖⠛⠉⠀⠀⠀⠉⠓⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣴⣟⠥⠖⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⢠⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠉⠉⠁⠀⢀⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠛⠟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢳⡄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⠀⢸⠂⠀⠀⠀⠀⠀⢰⡆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⢿⡀⡴⠖⢶⠀⣖⠲⢸⣧⡶⠂⣴⣖⣦⠘⢿⠋⢸⡶⠲⣄⣴⠖⢶⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠾⠃⠳⠤⠾⠐⠮⠽⠚⠇⠹⠆⠻⠭⠧⠀⠸⠀⠸⠷⠴⠋⠻⠦⠾⠻⠇⠿

⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣼⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠉⠉⣿⣿⣿⣿⡏
⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠃
⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣄⡉⠀⠈⠛⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠲⢤⡀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠉⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢸⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢠⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⣀⣀⡀⠀⠀⠀⠀⣀⣴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢋⠁⣤⣴⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣉⣤⣴⣾⣿⡆⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⢉⣡⣴⣶⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⡿⢋⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡿⢟⣴⣿⠃⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣀⣤⣦⣴⣏⣠⣿⣿⣿⣯⣟⣿⣤⣀⣛⣛⡛⢺⣿⣿⣯⣿⣭⣽⣟⣛⣛⣿⣿⣿⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣿⡿⠿⠿⠛⢿⣿⠛⠿⠿⠿⠿⠿⣿⠻⠿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⡦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣛⣛⣛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠛⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢰⠹⡀⠀⣀⢤⡄⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠣⡟⠀⠳⠞⠀⠀⠳⠞⣄⡇⠙⢦⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠣⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡟⠓⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠤⠼⠆⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⢀⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⢤⣀⠤⠔⠚⠁⠀⡀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣄⠀⠀⠀⡴⠛⢲⡀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠈⡇⠀⢰⣧⠀⢀⡇⢀⡸⢏⣀⠤⠶⡄⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠟⡰⢁⡄⠘⢧⡤⠞⠀⣼⠀⠀⠋⢴⠄⡿⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⠉⠀⠁⠀⠀⠀⢀⣠⣾⣿⡆⠀⠀⠐⠚⣅⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠑⠲⣤⣤⣴⣶⣿⠟⠁⢨⠇⠀⢀⣤⠖⣉⣓⣒⡢⢄⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠹⣿⠟⠫⡇⣠⡴⠋⠀⣴⠋⢸⠉⠉⡇⠀⡸⠃⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣯⠝⠓⡆⠀⠙⠲⢬⣉⣉⣉⣁⣀⡤⠞⠁⠀⣀⡧⠴⠃⠘⣅⣰⠆⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⢎⡠⠀⠇⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠣⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣐⠪⠔⠲⣄⠑⠦⠤⠼⣯⠏⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⢹⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢖⠒⠒⠶⠖⠋⠉⠉⠉⠉⠑⢶⡇⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⣒⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⢸⡩⣉⠉⠉⠓⣯⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠙⢬⣧⠴⠊⠙⠤⠤⣖⠀⠀⠀⢀⡽⠀⣰⢭⣳⣤⣇⠄⡠⠃⣱⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣴⡓⢺⡀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⠴⣋⠳⢞⡡⠚⠉⠀⠉⠛⠒⠊⠁
⠀⠀⠀⠀⠀⠀⢾⠛⠒⠒⠭⢵⣒⠭⣚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠈⠙⠪⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣒⣒⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⠷⠶⠀⠀⠀⠀⠙⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠛⠻⠟⠋⡡⠤⠀⠉⠀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢄⠀⠈⣧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠁⠀⠠⠀⣼⣿⣶⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠸⡆
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣄⠀⡠⠊⠀⠀⠀⠐⠀⠀⠀⢷
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣇⠀⠀⠀⣀⣀⡀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣷⣄⠈⠉⠉⠁⣀⣴⣿⡿⢿⣿⣿⠓⣇⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠉⠋⢉⡀⠄⠁⠀⠀⠹⣆⢀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠆⠀⠀⠀⠀⠁⠉⡽⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⢉⢡⠐⠀⠀⠀⠀⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡁⠈⠙⠛⠁⠀⠀⠀⠁⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⢠⠤⠤⢠⡀⢀⡄⣤⠤⠄⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢸⠓⠒⠈⢧⡼⠀⣿⠒⠂⣾⠲⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠈⠁⠀⠉⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣯⣟⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠤⢀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣸⣿⣿⣿⣷⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⠁⠂⠤⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢧⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡇⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢧⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡇⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸⠁⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢳⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡎⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣻⣿⣿⣿⣿⣿⣋⣛⣻⣿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠙⢍⠈⠀⠀⠈⡒⣤⣇⣀⣀⣀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣵⡟⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠇⣀⣀⣀⣀⠀⠀⠠⠤⠐⠊⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠄⠀⠒⠒⠂⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⡤⠶⠛⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠏⢀⣀⣀⣀⡼⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠘⠋⠩⠔⣚⣿⣿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣧⠀⠐⠋⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠡⢖⣻⠿⠛⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⣰⠁⠀⠀⠴⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠤⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢨⣿⡆⠀⠀⢠⠤⠀⠀⡆⠀⠉⠁⠀⡀⡠⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣾⣿⣧⠀⢀⢀⠀⠀⠈⠃⠀⠀⠀⠈⠐⠁⣹⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠘⢿⣿⣿⡗⠁⠂⠀⠀⢔⣉⠭⠵⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠉⠻⣿⢿⣿⢷⡀⠀⠀⢸⠛⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⢶⠲⠔⠃⠀⠀⠀⠙⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⡶⠖⠋⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠐⠀⠀⠠⠆
⠀⠀⠀⠀⠀⡀⠀⠀⡆⢀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠋⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⣴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢀⣤⠄⠀⠀⠀⠀⠀⢀⣾⡷⠿⣷⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣂⠸⠛⣤⣾⣀⣀⠀⣸⣿⠁⠀⠰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣀⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠙⠿⠹⣿⡝⠿⠿⠖⠀⠉⢀⠀⣰⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⠢⣤⣐⠏⠀⠀⠀⢀⣤⡴⠦⡀⠀⠀⠀⠀⠀⠀⢿⡤⠉⡅⠁⠙⠧⢀⠀⠠⠀⢠⠞⢀⣁⣾
⠀⠀⠀⠀⠀⢰⠷⣠⣴⡶⢦⡴⠞⠀⠈⠉⠀⠀⠀⢀⡿⠑⢆⠀⣷⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣤⢴⠂⠀⠀⠀⠀⠀⠀⢘⣯⠁
⠀⠀⠀⠀⠀⣰⣾⢧⣏⠀⠀⠴⠄⠀⢠⣠⣠⣤⠀⣾⣿⣤⣉⣵⣇⠀⠀⠀⠀⠀⠀⡇⠀⢰⡆⠐⠀⠀⠘⠓⠀⠀⠀⢁⣀⠁
⠀⠀⠀⠀⣼⡿⢏⠀⠹⢗⠀⠀⠈⢻⠀⢀⣿⣷⣾⣿⣾⣷⣭⡿⣿⣿⣦⠀⠀⠀⠀⠃⠀⠀⠱⠇⠀⡀⢰⣦⠀⠀⠀⠈⢻⠀⠄
⠀⠀⢰⣧⡈⢷⡄⠙⠛⠋⠁⠀⠀⠘⠀⣤⣿⣿⣿⣿⣶⡇⢹⣿⣿⣿⣿⠃⠀⠀⠀⠰⣄⢀⡄⠀⠀⠀⢸⠃
⠀⠀⢸⡟⠁⢀⣿⣄⠀⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⡛⠉⣧⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢈⣤⡄
⠀⠀⠀⣷⣿⠏⠉⠉⠀⠀⠀⣘⣃⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠁⠀⠻⠟⠛⣿⣿⣿⣿⢿⣿⣿⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⡄
⠀⠀⠀⣼⣿⣿⣿⣿⠏⠛⣿⣿⡇⠀⠀⠀⠀⠀⡿⡿⠋⠉⠀⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⠟⢻⢃⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⣷⠶⣶⠶⠶⢿⠷⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡿⢋⣿⣿⡏
⠀⠀⢸⣿⣏⢀⣴⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⡟
⠀⠀⠘⠿⢿⡿⠿⣿⣿⡿⠋⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⣹⠿⠂
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣐⣈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠙⡏⢻⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⣽⡿⠗
⠀⠀⠀⠀⠀⠀⢠⠇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠁⠀⠸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⠉⢷⡄⠀⢾⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠹⢾⣿⣯⣿⣿⣠⣤⡀⣰⡟⠀⠈⢿⣄⠈⠷⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⢶⣛⣽⣟⣀⠀⠀⠈⠻⢧⡴⠋
⠀⠀⠀⠀⠰⣾⠊⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠁⠲⠀⠀⣾⣟⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⠀⢢⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⠿⢿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠄⡀⢀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⣀⠀⡀⣀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢽⣌⣟⡦⢸⠅⣿⠺⡇⡟⡾⣿⣼⢽⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣠⠖⢦⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢻⡇⣿⡇⣹⠧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠞⣋⣀⣠⣟⣺⣞⣧⣀⡈⠛⠦⢤⣄⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠛⠉⠁⢀⡴⠋⠉⠀⠀⠉⢹⠉⠁⠀⠁⠉⠰⣄⠀⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⡇⢀⡀⠀⠀⠀⢸⡄⠀⠀⠀⣀⠀⢹⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠙⠲⠶⠶⣿⠶⢾⠆⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⢀⠀⡈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⣀⣀⣀⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⡄⠛⢦⢸⣷⡇⠀⠀⢀⡖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⠭⠭⠭⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠦⠁⣠⠤⢼⣯⡷⠦⣤⡈⠰⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠁⠀⣤⢸⣟⡇⢠⠀⠙⢦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠩⠭⢹⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⢛⣧⣼⡏⣷⣼⡛⠛⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣃⣸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⢚⣿⡀⢸⡇⡇⢀⣽⡓⠆⢹⠀⠀⠀⠀⠀⠀⠀⣀⡤⠿⢤⡀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠇⢸⡇⡇⠘⠇⠉⠀⢸⠀⠀⠀⣀⡤⢰⠖⠻⡄⠀⠀⠹⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣀⣀⡤⠞⠀⠹⢤⣀⣀⠀⣸⠈⠛⠛⠉⠁⠈⣧⣀⣷⣀⣀⡤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣶⣶⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠉⢻⡇⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠂⠸⠃⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⡀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⡀⠈⠁⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠀⠂⠐⠢⡑⠄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠄⠠⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⠠⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠂⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠴⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠀⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⠀⠂⠄⢀⠀⠀⠀⢀⠀⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⠀⢀⠀⠈⠁⠈⠁⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢈⠦⢀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⡀⠀⣀⣠⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⣿⣿⣿⣿⠛⠻⠋⠐⢄⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠃⠀⠀⠙⣿⣿⠏⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈
⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⢀⣀⠄⢆⠁⠀⣀⠠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠘⡀
⢻⡀⢲⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢡
⠀⢳⡈⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠆
⠀⠀⠻⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢼⣄⣀⡤⠒
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠛⣋⣤⠖⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣯⣭⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⠀⠀⠀⠀⠀⠀⢙⡆⣶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⢿⣀⢀⣀⡤⠤⠶⠞⠁⢿⣀⡀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠉⠉⢁⡴⠚⠛⢳⠀⠀⠈⠙⠳⣄⡀⣀⡷⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠳⢶⠶⣏⠀⠀⠀⠀⠀⠈⠉⢡⡞⠛⠚⠁
⠀⠀⠀⠀⠀⠀⢀⡴⢤⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢸⠀⠘⠂⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⣾⠀⢘⣛⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠘⠒⠋⠈⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⣤⠸⣇⡀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠆⢀⡀⠀⠀⠀⠉⠛⢲⡏⠀⣸⣣⣬⣭⡅⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣤⠶⠿⣴⠋⠁⠀⠀⠀⠀⠀⠈⠳⠞⣱⠇⠀⠀⠛⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡼⢃⣀⡀⠙⢦⣄⣨⠇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢾⠉⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠈⠉⣷⢀⡴⠶⠒⠛⠉⠁⠉⣷⠙⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠸⣅⠀⠀⠀⠀⠀⠀⠳⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⣄⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢠⣿⣿⣿⣿⡿⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠄⢂⠙⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⢸⣿⡏⠟⠋⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠈⠁⠀⠀⢑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠟⠀⠀⠀⠀⠛⠁⠀⠀⠀⢤⠌⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃⠀⠀⣀⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⣄⡄⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⡀⠔⠂⠁⠀⡏⠶⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⢸⡿⡁⠂⢤⣀⠀⠀⠀⠔⠈⠀⠀⠀⠠⠀⡠⠃⠈⢄⠀⡉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠤⠀⣠⡕⠐⢥⠀⢈⡏⠌⠂⠀⢃⠀⢪⠙⡀⠀⠉⠀⠀⠀⠀⠉⠀⠈⠄⡄⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⡋⠀⠀⠀⠑⠊⠀⠈⠈⡄⠈⠄⠀⡄⡨⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢰⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡅⠠⠀⠈⠄⠁⣃⣀⡠⠀⠀⠀⠀⠀⠀⠖⠁⠀⠄⢀⠄⢁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡄⠀⠀⣷⡃⠀⠀⠀⠀⠀⠠⡊⠀⠀⠀⠀⡼⠋⣠⠋⠒⠀⠀⠀⠀⡠⠂⠈⠂⠀⠈⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⠄⠘⠳⠀⠀⣀⡀⠀⡠⠀⠐⡀⠀⠓⠉⢀⠄⣹⣀⡀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢒⠂⠀⠀⠀⠀⠀⠌⠀⠀⠀⠐⢄⡀⠔⠁⠜⠁⠀⠈⠁⠲⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠒⠀⢤⠤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⢨⠀⠀⠀⠀⠀⠘⠀⢄⡀⠀⠀⠀⠀⠀⡐⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣄⠑⠬⣐⠀⠄⢀⠀⢀⠀⠁⠀⠂⠄⣀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠈⠈⠐⠦⠤⠀⠀⣀⣺⡄⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣨⠂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠂
⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⡄
⠀⠀⠀⠀⢀⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣅⡔⢀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠈⢂
⠀⠀⠀⠠⠂⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⡀⠀⢆⣼⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣑⡢
⠀⢀⠴⣁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢦⡘⠈⠁⠑⠄
⡴⡀⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢀⡠⣈⠂⢀
⠈⠂⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃
⣀⣀⣀⣙⣲⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⠙⡇⢸⡟⠉⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠁⠘⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠄⠄⢰⡦⠀⠠⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠠⠃⠀⢸⡟⠀⠀⠄⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠄⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⣀⣞⢻⣄⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠃⠀⣿⣿⣦⣤⣶⣶⣿⣿⣿⠇⠛⢿⣷⣶⣦⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⢩⡁⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⠻⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠰⢿⣇⢸⡇⣸⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢐⣷⣤⣽⣿⣿⣧⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⡀⠻⣿⣿⣿⣿⡿⠃⣀⠀⠀⢡⣤⡞⢻⡟⢷⣤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣰⣿⣿⣦⣌⣉⣉⣉⣤⣾⣿⣿⣦⠀⠙⠁⠾⠷⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⣿⣿⣿⠻⣿⣿⣿⣿⣿⡋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⣿⣿⠀⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⣿⣿⣶⣿⣿⢠⣄⡉⠛⠿⠿⠟⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠿⠿⠿⠿⠿⢸⣿⣿⣷⣦⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠰⣶⠆⣠⡀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠛⠻⣦⣿⣤⡿⠛⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⣿⡁
⠀⠀⠀⠀⠀⠀⢸⠿⠟⣿⣿⣿⡿⠻⡯⠀⠀⣼⣿⣿⣿⠿⣿⣿⣿⡆⠀⠐⣿⡅
⠀⠀⠀⠀⠀⠀⠀⢶⣾⠋⣿⠉⣿⡶⠀⠀⢀⣿⣿⣿⣿⠀⢿⣿⣿⣷⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠃⠈⠀⠀⠀⢸⣿⣿⣿⡇⠀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠀⠀⠒⠻⣷⡂⠐⠄⠀⠀⢀⠀⠠⠀⣀⠀⠀⠀⠠⠂⣲⣄⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣜⠀⢀⡈⠑⠳⣶⣧⣄⣨⠟⠒⠃⠀⠀⢸⣶⣶⣦⣤⣬⠔⠁⣴⣶⠟⣁⣠⣌⣢⡀⢄
⠀⠀⠀⠀⡠⠊⣠⡀⠉⠙⣿⣷⣄⡀⣙⡿⢻⠁⠀⠀⠀⠀⠀⠈⠋⣿⠙⡉⡛⠀⣸⡟⠁⢰⣿⡟⠁⣠⣤⣦⠁
⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⠉⡜⢹⠀⠀⠀⠀⠀⠀⢺⣛⠛⢛⡧⣀⣴⠛⠃⢀⣿⡟⢀⣴⣿⣿⣿⡆⢃
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡏⠋⠉⢉⡆⠀⠀⠀⠃⠀⠀⠐⠇⠈⠀⠐⠶⢿⣿⣿⣿⣿⣿⣿⣷⣶⠈⡀
⠀⠀⠀⠅⠸⢿⠿⣿⣿⣿⣿⣿⣿⣥⣾⣀⣠⡾⠋⠀⠀⠀⠀⣦⣤⣤⣤⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢡
⠀⠀⠀⡁⣀⣤⣾⣿⣿⣿⡿⣽⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⢼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠈⡆
⠀⠀⠀⠀⢹⣿⣿⣿⡟⣿⢰⣿⣿⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢧
⠀⠀⠀⢸⣬⣽⣿⣿⣇⢻⡈⠻⠛⣁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣙⣿⣿⣿⣿⣿⣿⣧⣤⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠉⢿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠸⣿⠿⠿⣆⣤⣴⡆⣤⣤⣤⣤⣤⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠛⠘⠿⠿⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⢷⠞⠚⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠇⠀⠂⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠⣦⠀⢠⣆⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣘⠋⠀⣘⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⣀⣀⠀⢀⡀⠀⢀⡀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠁⠀⠈⠉⠁⠉⠉⠀⠉⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠒⠀⠠⠀⠤⠤⠤⠤⠶⣅⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠢⣀⠀⠀⠤⠀⠀⢰⠊⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣊⢢⠠⡈⠠⠈⢂⣀⡠⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⠅⢠⠈⠋⠐⠠⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⣨⠉⠉⠀⠀⠈⠉⢳⢠⠄⢤⡀⠈⢦⡀⠀⠀⠀⠀⢀⠗⠊
⠀⡀⢀⡀⠀⣦⠀⠂⣠⣚⡥⠤⠐⠒⢻⣉⢳⡀⠀⠀⠀⠀⠀⢸⡀⣀⠗⠢⢤⣙⣆⠀⡀⠀⣸⠶⠒⡆⣀
⠀⡯⢩⠁⣄⣉⣁⡈⡄⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠸⠑⠉⠀⠀⠀⠀⠀⠉⠃⠀⠀⢈⡀⣀⠃
⠀⣏⣹⠀⣟⣁⣀⠊⠇⠀⠀⠀⠀⠀⢀⠸⣀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠉⠒⠒⢀⣠⣤⠴⠖⠀⡉⢁⠀⠀⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣦⣬⣥⣥⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣦⣤⣀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣷⣶⡆
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀
⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠛⠛⠛⠛⠉⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣷⡆
⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠰⠁⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠈⣿⣿⣿⣿⣿⣅⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠹⣿⣿⣿⣿⣿⣷⣤⣈⠀⠘⠛⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⢿⣿⡿⠿⠛⠁
⠀⠀⠈⠉⠛⠻⣿⣿⠛⠛⠉⠀⠲⢶⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠈⢿⣿⠟⠋⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣦⣴⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣤⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⡿⠋

⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡀
⠀⠀⠀⠙⠿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⣢⣁⠓⠠⠗⠢⠀⠀⠀⠀⢀⠺⣷⣮⡢⠀⠀⠀⠀⠀⠀⢠⣾⣷⣴⣶⡀
⠀⠀⠀⠀⠀⠙⠿⣷⢄⠀⠀⠀⠀⠠⢠⡴⠀⠄⠁⠂⠁⠀⠀⠀⠀⠀⠁⠊⢳⣷⠀⠀⠀⠀⠀⠀⣴⣿⣩⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⠁⠚⠈⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠀⠀⠀⠀⠀⠀⠈⠛⠙⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠠⠐⡈⢐⠠⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⣠⠀⠀⠀⠀⠀⠠⣦⠀⠢⣀⠈⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀
⠀⠀⠀⠈⠡⠁⠐⢀⢐⢉⠀⠀⠀⠛⠶⠄⠻⠀⠋⣁⠀⠀⠀⠀⢀⡈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠐⢂⠁⠌⠀⢀⠒⠀⠀⠀⠀⣤⠾⠀⣿⠀⠈⠳⠀⠀⠀⠀⡹⠅⠀⡄⡐⠉⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣄
⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷

⠀⠀⠀⠀⣖⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⡿⣿⠛⢲⡄⠀⠀⠀⠀⠀⡄⠀⠸⠁⠼⠁⠀⠀⠀⠀⢀⣴⡾⠟⠀⣾⠀⣠⠀⠀⠀⠀⡜⢉⡰⡁⠸⠤
⠀⠀⠀⠀⠹⣿⣶⣾⠷⡄⠀⠀⢀⡠⠄⠁⠀⠀⠀⣀⣨⠄⠀⢰⠟⠁⠛⠀⡨⣿⣶⠏⠀⠀⠀⢈⣅⣂⢯⡷⡄⣾
⠀⠀⠀⠀⠀⠀⠸⡿⡧⠀⠀⠀⠀⠈⠉⠑⠀⢄⠀⠈⠐⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠘⠳⠲⠳⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠘⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣄⣸⣶⣾⡀⠀⠀⠀⢀⣸⣯⢿⣻⣿⣧⡀⠀⠀⠀⠀⢁⠀⠑⢄⠀⠀⠀⠀⠀⠀⢐⣢⡒⠠⠀⠀⠠⠂
⠀⠀⠀⠠⣿⣿⠉⢹⣿⠀⠀⠀⠀⢻⣾⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀⠁⢄⠀⢁⠀⠀⠀⠀⠀⠀⠒⠍⠅⢥⠷⣀⢀
⠀⠀⠀⠀⠀⠿⠿⡏⠉⠀⠀⠀⠀⠐⠋⠛⡞⠋⠛⠲⠀⠀⠀⠀⠀⠀⠀⠉⠙⢇⠠⠀⠀⠀⠀⠀⠠⡠⠀⠈⡙⢾⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠩⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠉⠹⡉⠩⡅⢩⠉⠛⠉⠉⠋⢹⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣤⣤⣤⣧⣼⣦⣷⣤⣴⣦⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻

⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡄⣈⢈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠰⣀⠍⠸⢄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢀⠲


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢀⠔⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠉⠉⠉⠉⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠶⠉⠙⡟⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢣⣀⠴⠚⠁⠀⢤⡄⠃⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠀⠀⣤⠘⠋⠀⠀⠀⠀⠈⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢻⡿⠉⠙⠀⠀⠀⠀⠀⣤⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣁⠤⠤⠀⢴⣤⡎⠀⠀⠀⠀⠀⡞⠛⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠟⠙⠀⠀⠀⠀⠀⠃⠘⢆⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡛⠢⠤⠼⢷⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⢀⡞⠀⠀⠀⠹⡄⠀⠀⠀⡆⠉⡄⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡤⠤⠖⠛⠀⠀⢸⡧⠔⠋⠀⠀⠀⠀⠀⠈⠢⠤⠄⠀⠀⢡⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢃⠀⠘⢆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠸⡆⠀⠈⠓⠤⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢻⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⠀⠀⢸⠀⠀⠀⠀⠀⣠⠞⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⡄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⡆⠀⠀⠀⠈⣄⠀⣀⠤⠊⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⢄⠀⠀⡿⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠘⣄⠀⠀⠀⠹⠞⠁⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⡇⢰⠀⠀⠀⠈⠁⠀⠚⠓⠂⠀⢤⡞⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠣⣄⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠘⣲⡿⠃⠤⠤⠤⠤⠄⢀⣀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠈⡝⠒⠒⠀⠤⣤⠤⠤⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡝⠂⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠂⠒⠒⠒⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠱⣄⠀⠀⣀⡔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠈⣷⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⠇
⠀⠀⠀⠀⠀⢠⠋⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠗⠿⠾⢻⡆
⠀⠀⢀⡠⠺⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⠀⠀⠀⠘⢆
⠀⣠⠚⠃⠒⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡑⢆⣤⠀⠀⠀⠈⠳⣄
⢎⠳⣄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠊⣩⠶⢆⣀⡈⠑⢆
⠀⠑⢌⡑⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋
⠀⠀⠀⠉⠾⣵⣄⠀⠳⡄
⠀⠀⠀⠀⠀⠈⠙⢷⣦⣸
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣄⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡿⣉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⡆⠈⠿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣟⣿⡟⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⣧⣀⣠⠆⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣃⣈⡙⠒⠒⢒⠒⠒⠂
⠀⠀⠀⠀⠀⢰⣶⡆⠀⣾⡟⠋⠙⢻⣷⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠸⢬⠿⠿⢹⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣱⠀⠹⣷⠀⠀⣾⠏⢰⣺⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠃⠨⡯⠄⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⣾⣯⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠋⠀⠀⠀⠙⢿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⡇⢴⣮⠉⠀⠀⢸⣿⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⣶⣄
⠀⠀⠀⠀⠀⠀⣣⣝⣯⣀⠀⠀⠈⣿⣷⡟⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣿⣿⣿⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠿⠿⠾⠟⠾⠿⠿⠶⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⣰⣿⠟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣰⣿⠃⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡇⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣿
⣤⣄⠀⠀⠠⣤⡄⠀⠀⢠⣤⡀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣤⣾⡿
⢘⣿⡆⠀⠀⢹⣿⠀⠀⠈⣿⣷⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⠉⠉⠁
⣾⡟⠁⠀⢠⣿⡏⠀⠀⢰⣿⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣀⣀⡀
⢻⣿⡄⠀⠀⢿⣷⠀⠀⠘⣿⣆⠀⣿⡇⠀⠀⠀⠀⠀⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄
⣼⣿⠃⠀⢀⣾⡿⠀⠀⢠⣿⠏⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⠗⠀⠀⠀⠐⠿⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠉⠁⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⣿⡇⠀⠀⠀⠀⠐⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠿⢿⣷⣶⣶⣶⣶⣾⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠹⠂⠀⠠⠖⠉⠀⠀⠀⠐⠂⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔⠊⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡰⠁⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠣⡄⠠⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⠒⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⡀⠤⠈⠁⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡠⠀⠀⠀⠑⠢⣤⣀⡀⠀⠀⠀⢀⣀⠠⠔⠊⠉⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⢳⠀⢀⡀⢀⠔⠹⢸⠀⠀⠀⠩⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢤⡈⠃⠀⠈⠉⡜⠀⠘⡀⠀⠐⠁⠀⢀⠀⠀⠀⣠⠚⠓⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⡀⠀⠀⡠⠃⠀⠈⠉⠁⠀⠀⠀⠉⠄⣀⠈⢘⠀⠈⠢⠦⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠁⡀⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⡀⠈⠢⢀⢀⠀⢀⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⢱⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣠⡂⠀⠀⠈⠢⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠑⠢⡾⠁⠈⠆⠀⠀⠀⢠⢾⡼⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠑⢄⠈⠢⢤⠀⠁⠁⠄⠀⠀⠀⠀⠔⡶⡥⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠂⣠⠄⠀⠀⠀⢣⠀⢀⡠⠴⠊⠀⠂⠈⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠙⠣⢄⠀⡀⠂⢀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⣧⠤⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡂⠈

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

⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣄⡀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠘⡏⠉⠋⠉⠘⣿⣿⣿⠀⠀⠀⠀⠂⢸⣿⠛⠳⠛⢋⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠙⠛⠋⢹⣿⣿⡗⠀⠀⠀⠀⠀⠀⢿⡏⠉⠘⠛⠉⢹⡿
⠀⠀⠀⠀⠀⠳⠀⠃⠀⢁⡿⠃⠀⠀⠀⠀⠀⠠⠋⡑⠃⠠⠘⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠂⠀⢃⡿⠃⠀⠀⠀⠀⠀⠀⠘⡇⠙⢀⠈⠃⠸⠁
⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⡀⠠⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁
⠀⠀⠂⡀⠤⣤⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠐⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢾⣿⡿⢿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠙⠛⠉⢻⡟⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠛⠋⠉⣿⠇⠀⠀⠀⠀⠀⠀⣿⡟⠉⠙⠛⡋⢹⡿
⠀⠀⠀⠘⡇⠰⠄⠀⠤⢸⠏⠀⠀⠀⠀⠀⠀⠀⠸⡇⠛⠀⠘⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⠃⠀⠚⢠⠏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⠀⠀⠃⡸⠁
⠀⠀⠀⠀⠈⠄⠀⠁⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣂⠐
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠊⠁
⠀⠀⠀⠈⠈⡡⠐⡔⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠡⣄⡀⣩⣈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈
⠀⠀⠀⠀⠀⣈⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣬⣤⣁⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⠛⠿⠟⠛⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⡿⠟⠻⠿⠟⢻⡿⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠛⠛⠉⣿⠇⠀⠀⠀⠀⠀⠀⣿⡏⠉⠙⠛⠋⢹⡿
⠀⠀⠀⠸⠶⠀⠰⠀⠙⢹⡿⠀⠀⠀⠀⠀⠀⠀⠘⡇⠰⠀⠀⠂⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠃⠀⠛⢀⠏⠀⠀⠀⠀⠀⠀⠀⠘⡧⠼⠀⠘⢇⠾⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠋⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⢀⠘
⠀⠀⠀⠀⠀⠉⡉⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠚⢴⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠂⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⡄⠀⠀⢸⠀⡀⠀⡠⠂⠐⢀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠄⣀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠀⡇⠈⠒
⠀⠃⠄⢠⠀⢸⠀⡅⠈⢦⠄⠠⠆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⡡⠒⡄⠠⠋⠀⠇⠀⠀⡧
⠀⠀⠀⢈⡀⣸⠀⠀⠀⠈⠆⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⡄⠀⠀⠀⠁⠀⠁⡏⠈⠀⠀⢀⠀⡓
⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⡞⠄⠠⠀⠀⠐⠀⢀⢁⠀⠀⠀⠀⠀⠀⠇⠀⡆⢸⠜⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠐⠀⠀⠈⠁⠀⠀⠠⠀⠀⡈⠀⢀⠀⠀⢀⠀⠀⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠁⠂⠀⠤⠀⡬⡂⠠⠄⢠⠊⢀⣀⠀⡀⠄⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⣀⡐⠀⠇⠀⠀⠀⠁⢙⠘⡅⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠐⠄⡀⢀⠰⠀⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡆⠀⡀⢀⠀⢀⢰⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠲⣶⣿⣿⣾⡀⠀⠇⠀⠅⠄⠆⠈⣄⣤⣾⣶⠶⠦⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⣀⡈⢿⣿⣿⣿⣦⣄⡀⠀⢀⣠⣴⣿⣿⣿⠁⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢘⠀⠣⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠁⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠈⠒⠋⠉⠁⠀⠀⠀⠀⠉⠉⠉⠋⠉⠀⠀⠀⣄⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⡼
⠀⠀⠀⠀⠀⡠⠒⠘⠙⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠒⠠⢄
⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠁⠐⠀⠠⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠒⠉⠉⠉⠲⠚⠉⠉⠉⠓⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠉⠙⠲⠤⣄⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠋⢀⡀⠀⠀⣀⣀⠀⠈⠑⢦⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠠⠦⢄⠀⠀⣠⠋⠲⠃⠞⠁⠈⠀⠀⠁⠀⠤⣀⠀⠀⠳⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧⠸⠀⠙⠶⠁⡗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⡀⠀⣠⠜⣗⠒⠀⠀⠀⣇⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⡴⠁⠀⠸⣄⠀⠀⠀⠘⢆⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠙⠒⠒⠚⠁⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⡤⢄⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⢤⣀⣠⣠⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⡘⠀⢈⣄⠈⠄⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⢤⠶⢦⠐⠀⠀⠗⠦⣤⣄⣠⣀⠀⠀⠀⠀⠀⢸⠀⢠⣀⣠⠀⢰⢸⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠆⠐⠂⡏⠀⠀⠀⠀⠀⠀⠙⢌⠣⡀⠀⠀⢀⠃⠀⠀⠀⠉⠢⢄⠀⠀⠈⠣⣀⠱⢤⠦⠊⠁
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⣀⣠⠂⠀⢀⣀⣀⠀⠀⠀⠀⠳⡌⢤⢀⠎⠀⠀⠀⠀⢱⠀⢀⣁⡦⠀⠀⡄⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡎⠀⠼⠖⠋⠁⠀⡇⠀⠀⠀⠀⠀⠈⠦⠂⠀⠀⠀⠀⠀⠀⢷⠉⠙⠦⣠⠎⠀⡸
⠀⠀⠀⠀⠀⠀⢸⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠁⠀⢠⠃
⠀⠀⠀⢀⡀⠄⠐⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠦⢤⠞
⠀⠀⢰⡁⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠴⠖⠀⠀⠀⠀⣤⡀
⠀⠀⠈⠣⡄⢀⠀⠆⣠⠊⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡠⠊⡀⠈
⠀⠀⠀⠀⠈⠙⠚⠳⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⢀⡜⠀⠀⢳⠀⢀
⠀⠀⠀⡠⢊⠔⡉⠐⡄⠀⠀⠀⠀⠀⠀⠀⢺⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠚⠉⠑⠦⣄⡀⠀⠀⠀⢀⡞⢢⠆⠀⠀⢀⠆
⠀⠀⡔⡱⠁⠘⠤⢀⣼⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠈⠉⠉⠉⠉⠉⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠎⠀⡼⠀⠀⠀⡌
⠀⠌⡘⠀⠀⠀⠀⡎⠀⡈⠑⠲⢄⡀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⢀⣠⠤⠀⠦⢄⡀
⡘⡰⡇⠀⠀⠀⣰⠉⠚⢅⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠒⢒⡧⠊⠁⠐⡂⠀⠀⠂⠙
⣷⠁⠘⢄⣀⡱⠁⠀⠀⠀⠑⢦⡀⠀⠈⢆⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⢊⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠻⣄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⣦⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⢀⠔⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠁⠀⣀⠠⠤⠒⠊⠁
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣧⣷⣤⣶⣵⣾⣽⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⢆⣄⢂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⢶⠀⣸⠟⠀⠀⠀⠈⢼⣿⣿⣷⠍⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡐⣿⡏⣻⡿⢠⣿⣿⣿⣿⡎⠀⠀⠈⣷⣿⣿⣿
⠀⠀⠀⢀⡀⠀⠷⣄⣹⣶⣾⣴⣿⣀⠾⠂⢀⣈⠐⡝⠟⡑⠉⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣏⡹⡇⠈⠃⠛⠁⠿⢏⣽⣿⠿⣾⣦⣤⣾⣷⣿⣿⣿
⠀⠀⠀⠙⠛⠳⢶⣾⣿⣿⣿⣿⣿⣿⣶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣬⡙⠁⠀⠀⠀⠀⠀⠀⠙⣩⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠲⠖⢾⣿⣿⣿⣿⣿⣿⣿⡷⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣤⠶⠛⢿⣿⣿⣿⣿⣿⣿⠛⠲⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⣋⣥⣄⢀⠀⡀⠀⠀⡀⣤⣌⡙⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⠶⠁⣹⠟⢻⠛⣯⠈⠳⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣉⣤⡇⣠⣄⣠⡄⣿⣎⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠻⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢐⣿⣧⣽⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⡞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢀⡾⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⢠⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢾⡉⠻⣦⡀⠀⠀⠀⠀⠀⢀⣠⣼⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⠟⢉⡷
⠀⠀⠀⠀⠀⠙⢦⡈⠻⣦⡀⢀⣴⣾⣿⣿⣿⣀⣈⣉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⣉⣁⣀⣿⣿⣿⣷⣦⡀⢀⣴⠟⣁⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⠟⢹⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⡏⠻⣿⣿⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠛⢁⡄⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⢠⡈⠛⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣴⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣦⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⡄
⢀⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠉⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⠉⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤
⢿⣅⣤⣠⣤⣄⣤⣄⠙⣿⠇⣰⡄⢻⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⡟⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣆⠸⣿⠋⣠⣤⣤⣤⣤⣤⣨
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⣤⣀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⢿⠛⠉⠉⠀⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠂⠀⠀⢨⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⣺⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⢸⡧⠀⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⣼⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⠗⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠉⠹⡞⠁⢈⡇⠀⠀⠀⠀⠀⢓⣶⣞⠋⠙⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠛⢦
⠀⢀⠴⢶⡏⠉⠉⠉⠉⠉⡛⡖⠲⡄⠀⠀⣠⢛⠴⠊⠁⠀⡏⠀⠀⠀⠀⠀⢠⠚⠒⠛⢦⠀⣁⡁⠄⠀⠀⠀⠀⢀⡴⢿⢋⡠⣧⠞
⠀⠘⢄⣸⡧⠀⠀⠀⠀⠀⡇⣧⠴⠃⠀⢸⡵⣫⣠⠖⠒⠶⣇⠀⠀⠀⠀⠀⡏⠉⠉⠉⢹⠀⠠⠠⠐⠀⠀⠀⣰⠁⠀⢈⡩⠚⠁
⠀⠀⠀⠉⠓⠦⢤⣀⡤⠔⠋⠁⠀⠀⠀⢸⣞⣵⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⣞⡵⠲⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠳⢤⡠⠤⠊⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⢀⣴⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏⠲⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⣒⠒⠲⣄⡀
⠀⢀⣾⣿⣿⣿⣿⡟⢀⡍⢹⡀⠶⠀⣠⡀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠖⢀⣧⡘⢃⠰⡦⠀⠀⠀⠀⠀⣾⣟⣀⣀⣛⣛⣁⣀⡘⣿⡄
⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⢮⣱⠠⡦⠉⠀⠀⠀⢀⣼⣿⣿⣿⣟⠀⠀⠈⠦⡇⠛⠃⠀⠀⠀⠀⠀⡜⠸⣄⣉⣉⣁⣉⣉⣉⣠⠇⢳
⠀⠀⠘⢿⣿⣿⣿⣶⠂⠀⢀⡽⠀⣀⣀⣀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⢀⡔⠃⣠⠶⠶⣦⠀⠀⠀⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠉⠛⠉⣹⣤⣤⣿⠀⢾⡇⠀⠸⡇⠀⠀⠈⠙⣿⡇⠰⣿⣿⣿⡇⠘⢿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠓⠂⠚⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠩⠭⠭⢍⣹
⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⣆⠀⠀⠀⢀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⣴⠋⠉⠀⠀⠀⠀⠀⢸⡀⠀⢻⠉⡄⢀⠈⣇⠀⣴⣾⣶⣦⠀⢰⠒⠒⠒⠒⠒⢲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡟
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠾⣄⠀⠀⣠⡇⠐⢿⣿⣿⡿⠁⢸⠀⠀⠀⠀⠀⢸⠛⣿⡄⠀⢰⠋⠉⠉⠉⠉⠉⢲⠈⡇⠀⠀⠀⡇
⠀⠀⢻⢳⠀⢠⣤⡄⠀⠀⠀⠈⣆⠀⠀⠙⠉⣀⠤⣤⡈⠉⠉⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⣷⡇⠀⣼⠛⠛⠛⠛⠛⠛⢻⠀⣇⠀⠀⢠⡇
⠀⠀⠈⣎⣇⠘⢋⣁⣀⣠⣤⣶⠟⠀⠀⠀⢰⡇⠂⠂⣱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡯⠏⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸⠀⣸⣿⢻⣻
⠀⠀⠀⠘⠺⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⠒⠞⠁⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠚⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⢋⡉⠀⠀⠀⠀⠀⠀⠘⣉⠇⠀⠀⠀⢀⠏⢻⠀⠀⠀⡏⢣⠀⠀⠀⡴⠒⠒⠒⠒⡖⠒⠒⣲⠖⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣦⡀
⠀⠰⠁⠀⡃⣠⣀⣀⣠⣄⠎⠀⢀⠀⠀⢠⠏⠀⠘⠶⠶⠞⠁⠈⣇⠀⠀⣟⠀⠀⠀⠀⡇⠀⠐⠁⡜⣷⠀⠀⡤⠤⣤⣴⡾⠛⠁⣀⢕⡽⠂
⠀⢀⣤⣠⡇⠉⠀⠀⠈⠁⣠⣄⣼⠀⠀⢸⠀⠘⠀⠳⠐⠂⠯⠀⢻⠀⠀⣿⢀⡠⠴⡊⡇⠀⠀⠀⠀⣿⠀⣰⢡⠞⢧⡧⣀⣴⡞⢷⠙⡆
⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⢸⠀⠀⠶⠀⠄⠂⠀⠀⢸⠀⠚⣏⠱⢒⡩⠚⡇⠀⠀⠀⠀⣿⢰⡧⠬⠤⠤⠽⠯⠤⠿⠭⠤⡷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⣤⣤⣤⣤⣤⣤⣤⣤⠞⠀⠀⣨⠟⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣶⠖⠢⣀⣀⣶⠲⠼⢷⡾⠥⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⣤⡾⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⣒⡄⠀⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢀⡴⢩⠏⠀⠀⢰⢀⡼⢇⡄⠀⠀⠀⠀⠀⠈⢾⠁⠘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠼⢀⡴⠴⠻⠊⠀⡟⢡⡷⣠⡄⠀⠀⠀⢾⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⢳⡀⠀⢀⣤⡖⠀⠀⢀⠀⠈⠑⢤⡄⠀⡾⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣟⣲⣾⣾⡇⠀⠀⠀⣔⡀⠀⠺⠣⠄⠀⠀⠘⠦⠧⡄⠀⠀⠉⠳⡆⠀⠀⢀⣤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠷⣄⣈⠉⠙⡿⢷⡶⠶⠾⣥⠀⠀⠀⠘⠷⠀⣠⠀⣰⠃⢀⡴⠋⢱⠇⠀⠀⣶⠘⠛⠛⢹⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢉⡟⣋⠉⠛⠶⣄⠀⠉⠙⠒⠷⡀⠀⠀⠀⠀⠓⠀⠀⢀⣠⠞⠛⠋⠁⡴⠋⠀⣰⠋⠀⠀⠀⢻⠀⠀⠀⢸⠀⠀⡟⠛⢻
⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠘⢧⣏⣧⣄⡶⠼⣶⣶⣒⠦⣤⠞⠲⢤⣤⣀⣤⠴⢾⡋⠀⠀⠀⠀⡼⠁⢀⠞⠁⠀⠀⠀⠀⢸⡀⠀⠀⡟⠀⣈⡗⠒⢾
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠠⢯⡀⠀⠀⠉⠓⠦⣤⣘⡡⠖⠉⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⢰⠃
⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠴⣿⠋⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⢦⡀⠸⣄⠀⠀⣀
⠞⠁⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⡴⢀⡟⠒⠒⠒⠲⠦⣄⠀⠀⠀⢀⡘⢟⣦⣖⠽⠃⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⣠⠀⠘⣦⠀⠀⠾⠱⠆⠹⠷
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⣇
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢸⠉⡙⣷⠀⠀⠀⠀⣠⢞⣍⣍⣝⢢⡀⠀⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⡇⣿⣿⣿⣿⡇⡇⠀⠀⠀⠈⢡⠀⣀⢩⣄⠀⠀⠀⢀⣤⣴⣶⣿⡿⠆
⠀⠀⠀⠀⠈⢙⡛⠩⠀⠀⠀⠀⠱⣌⡛⠛⣋⡴⠃⠀⠀⠀⠀⢲⣿⣷⣿⠿⡆⠀⠰⡿⡻⠋⢿⢧
⠀⠀⠀⠀⠀⠐⠃⠀⠘⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠁⠁⠀⠀⠁
⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⡷⡀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠘⣛⡛⠀⢀⣴⠟⠁⠀⠀⡰⠋⠀⣀⠈⠳⡄
⠀⠀⠀⠠⢀⠀⠁⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣠⡍⢁⣴⠟⠁⠀⠀⠀⠀⡇⠀⠺⣾⠇⠀⡗
⠀⠀⠀⠀⠘⢄⣀⣀⣠⠎⠀⠀⠀⣤⣿⢷⣶⡇⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣠⠜⠁

⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⢀⡴⠶⣦⠀⠀⠀⠀⠀⣠⣤⠀⠀⣤⣄⠀⠀⠀⠀⠀⠠⢀⠀⢀⡴
⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠘⡀⠀⡸⠀⠀⠀⠀⣼⣿⣿⡇⢸⣿⣿⣇⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⢷⣶⠇⠀⠀⠀⠀⣿⣿⣿⠇⢸⣿⢿⣿⠀⠀⢠⣶⣿⡇
⠀⠀⠀⠀⠰⠾⠟⠛⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠄⠀⠀⠿⠟⠋⠀⠀⠙⠻⠿⠀⠀⠀⠈⠛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⢠⢰⡆⠈⢿⡏⠀⠀⠀⠀⠀⠀⡈⠅⣀⡀⠀⠀⠀⠸⣿⣏⣹⣿⠃⠀⠀⠀⠸⣿⠋⠐⣤⡀
⠀⠀⠀⠀⠀⢁⡠⣠⣦⡀⠀⠀⢠⡴⢾⡇⢽⣿⡇⠀⠀⠀⠀⢈⣿⣿⡁⠀⠀⠀⠀⠀⠣⢤⣈⠁⣿
⠀⠀⠀⡀⢹⣿⣿⣿⡿⠇⠀⠀⣿⣿⣿⣿⢽⣓⡇⠀⠀⠀⠰⡿⠃⠙⢿⠆⠀⠀⠀⠤⡄⢨⢤⠣⢔⠇
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⢀⡀⡄
⠀⠠⠤⢤⣯⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣡⠗⠀⠀⠀⠀⠀⡇⠈⢳⣷⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡑⠛⠗⠀⠀⠀⠀⢈⡇⠀⢸⣿⠀⠀⡇⠀⠀⠀⠀⠀⣶⢲⣿⣅⡤
⠀⠀⠀⣸⠙⣇⠀⠀⠀⠀⠀⠚⠲⠶⠛⠿⠷⠳⠄⠀⠀⠀⠀⠀⣸⠏⢹⠆⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⡇⠀⠀⠀⠀⢤⣀⡿⠿⣤
⠀⠀⠀⠛⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠘⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⣟⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠿⠗⢦⡠⣦⣠⠖⠿⠇⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⣸⣿⢷⡀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢠⣴⡿⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠠⠤⢴⣿⠥⠤⠄
⠀⠀⢠⡿⡏⠉⠀⠀⠀⠀⠀⠀⢸⡏⠙⣿⠹⡿⠀⠀⠀⠀⠀⡻⢝⣷⠤⢍⠉⡇⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡀
⠀⠀⢸⠇⢿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏⠀⠀⠀⠀⠀⠀⠸⡀⠸⠿⠇⢰⠿⠗⠀⠀⠀⠀⠀⠀⡟⠘⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⣽


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣿⣅⣠⠀⠀⠀⠀⠀⡴⣆⣨⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⣖⠿⠂⠀⠀⠀⠀⠈⠉⣿⡏⠉⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⠴⠂⢀
⠀⠈⢽⣷⣶⠶⣀⣀⠀⠀⠀⠀⠀⣼⠛⣯⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⡏⣻⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡀⠀⠀⠀⠀⠀⠀⠀⣈⡞⢧⠀⠀⡼
⠀⠀⠀⠙⠿⠟⠉⠉⠛⠀⠀⠀⠸⠃⠀⠘⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠘⠇⠀⠀⠀⠀⠀⠤⠤⠤⠤⠼⠤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢹⡟⠀⠀⠀⢀⣀⣤⣤⢤⡄⠀⠈⠛⢿⣶⠖⠋⠁⠀⠀⠀⢠⡖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣰⣟⠀⠀⠀⢸⣿⠿⠋⣀⣤⢏⣀⣀⣀⡞⡎⠀⠀⠀⠀⠀⠀⠈⣿⣷⣞⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠚⠧⣌⢦⡀⢀⣀⣽⠿⠟⠛⣻⠟⠉⠉⠙⢣⡇⠻⠶⢤⣴⠶⢤⣴⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡍⠋⠙⠷⣦⡤⠞⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⡀⠀⠹⣧⠀⠀⢀⣾⠳⣄
⠀⠀⠀⠀⠀⣠⡾⡆⠀⠀⠀⣠⣿⣥⡄⠀⠀⠀⠀⢳⡇⠀⢀⣤⠶⠶⠶⣶⡄⠀⠀⡼⣷⠦⠶⠟⠳⣤⣸⣿⡄⠸⣇
⠀⠀⠀⠀⢰⡟⢰⣧⣀⣀⣼⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⢰⣻⣅⣀⣀⣴⠟⠁⠀⠘⠱⠁⠀⠀⠀⡠⢊⠄⠻⢷⣤⠏
⠀⠀⠀⠀⢻⣧⠟⠓⠀⣿⡇⠀⣠⠿⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡽⠇⠀⠀⣠⠶⢤⡀⠀⠀⠀⠰⠃⡀⠻⣆⠀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠋⠉⠳⠬⠁⠀⢀⣴⠾⢿⠄⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢻⣦⠀⠀⠀⣼⠛⢷⠈⠤⠴⠚⢻⣷⣼⡿
⠀⠀⠀⠀⠀⢀⡶⢆⠠⡇⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠶⠾⠛⠀⠀⣠⣿⡀⢸⡇⠸⣿⠁⠈⠛⠛⠁
⠀⠀⠀⠀⠀⣾⠀⢸⣗⣒⠒⠒⠂⠀⠀⠀⠸⢿⡶⠛⠛⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠿⠁⠀⣿⠀⢀⣀
⠀⠀⠀⠀⠀⣿⣀⡞⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠈⢻⡦⠀⠀⠀⢀⡴⠒⣦⠀⠀⠀⢀⠀⢀⣿⣠⡿⠏⣷
⠀⠀⠀⠀⠀⠈⠉⠀⢾⡇⢰⡟⢿⣦⠤⠖⠋⠀⠀⠀⠀⠀⠀⢸⡻⣦⣤⡾⠁⠀⠀⣸⣿⠁⠀⣸⠀⠀⠀⠨⠭⠭⣭⣿⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⡿⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠀⠀⠀⠀⠈⢿⣀⣰⠃⠀⣀⣄⡀⠀⢀⡏⠘⢷⠟⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠘⣇⠸⣦⣼⠃⠀⠀⣠⢲⡶⢶⣿⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⢿⡿⠁⢨⠇⠀⣼⠇
⠀⠀⠀⠀⠀⣿⡉⢳⣤⡿⢂⠀⠀⠀⠀⠀⢻⣌⢳⡀⢹⣿⠀⠀⠀⠀⣠⡿⠛⠛⢻⣷⠀⠀⠀⢸⣃⣠⠏⠀⣴⡟
⠀⠀⠀⠀⠀⣿⡀⠀⣿⠟⢯⡀⠀⠀⠀⠀⠀⠙⠓⠛⠛⠋⠀⠀⠀⢰⣇⣀⣠⡴⠟⠁⣬⢷⡀⠀⠉⠠⣄⡘⠋⣠⠴⣦
⠀⠀⠀⠀⠀⠘⢷⣴⠏⠀⠀⢙⣦⡀⣠⢏⡀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠈⠁⠀⠀⠀⢀⣽⠞⢛⡿⢈⡷⢦⣙⣿⠃⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠛⢷⣎⠀⠀⠀⠀⣴⠏⠉⠉⠙⢲⣤⠀⡀⡀⠀⢾⣧⣤⣮⠴⠋⠀⠀⢹⡇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⢻⡛⠳⢦⣄⡙⠶⢤⣤⣶⠾⠛⠀⣿⣷⠶⠶⠚⠉⠀⠀⠀⠀⠀⠸⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠃⠀⢀⣨⣿⣿⠛⠛⠛⠉⠉⢉⡿⠿⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣈⣱⡄⠀⠀⢰⣇⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣄⡀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠉⠳⣤⡇⡠⠀⣤⠄⠐⠈⣣⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡠⡴⠚⠙⠦⣀⠀⠀⠘⣧⠁⠀⠄⠀⠀⠀⠄⠳⣌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡅⠀⡏⠀⠀⠀⠀⠀⠈⠳⡄⡔⠃⠀⠀⠀⠀⠠⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄⠀⡇⢀⠀⠄⠀⠀⠀⠀⡇⠙⢦⠀⢲⣀⣀⣀⣛⣭⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠫⣤⠀⢳⢤⣤⣭⣭⣸⠃⣠⠃⠀⠈⢧⡀⠛⠥⠤⠜⢁⡼⠁⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠋⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢥⣄⣀⣮⡒⠀⠊⢡⣾⣁⣀⡀⣤⣠⡬⣷⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠤⣄⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣤⡤⣽⠁⠀⢸⠁⠉⠁⠙⠇⠈⣁⣸⡆⠀⢀⡷⠖⠒⠒⠲⣄⠀⠀⠀⠓⡿⠖⢉⣩⣭⡰⣄
⢀⡔⠛⠖⢤⠀⠀⠀⠀⠀⠀⢠⠏⣠⠃⠸⠄⣤⠞⠛⢻⠓⣦⠞⠋⠉⠀⠀⠀⠀⢀⡀⠤⡀⠀⠈⢦⠀⠀⢰⠁⡴⠉⠀⠀⠀⠙⡆
⢸⠁⠀⢈⡾⡄⠀⠀⠀⠀⢀⡏⢰⠃⡆⠀⠒⠂⠄⢀⢨⡜⠁⠀⢀⠔⠉⠴⢆⠈⠠⠄⠐⢢⢀⠀⣈⣧⠀⠘⡶⠀⠀⠂⠀⠐
⠈⠲⣄⠀⣞⠀⠀⠀⢀⡀⣸⠁⡇⠸⢠⠀⠒⠫⠁⢲⡟⢒⠶⠔⠃⠀⠀⠂⠶⡐⠐⠀⠉⠀⠈⡞⠁⠈⢆⠀⠣⠄⢠⣤⣬⣴⠀⡆
⠀⠀⠘⣆⠘⣆⡴⠋⠩⢙⡟⠀⣸⡆⠈⢀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣠⡤⢤⠴⠀⠀⠀⠀⠀⠀⢱⣄⠀⠘⡀⠀⠈⢎⠁⠄⣩⠞
⠀⠀⠀⢹⣤⠜⡇⠀⢹⡏⠀⣰⢻⠓⠠⠌⢉⣁⡀⠷⢤⡤⠐⠈⠹⠀⠀⠈⠀⠐⠂⠀⠀⠀⠠⢘⠈⣦⠀⢡⠀⣀⣸⠀⠀⢿⡀
⠀⠀⠀⡞⠁⠀⠘⠪⠵⠶⠚⠁⢻⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣄⢼⡆⠀⣡⠎⠘⢤⡴⠟⠈⢳⠀⠀⢀⣠⠴⣄
⠀⠀⠈⡿⠛⡴⢦⣤⡄⡀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡔⠃⠀⡅⠰⠀⠀⠡⠀⠬⠿⢤⠤⠞⠀⠧⡈⣷
⠀⠀⢰⠀⠀⠀⠀⠜⠻⢷⡂⣰⣧⣻⠶⠦⠤⠴⠶⠒⠉⢂⠀⣰⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⡇⠀⢰⠉⠀⠀⠆⢸⡀⣀⣤⠴⠀⠀⠁
⠀⠀⢸⢰⣄⣀⣠⠀⢀⡤⠟⠀⠀⢹⠀⠀⠀⠀⡠⠂⠀⠈⡾⠁⠀⠉⠓⠲⠦⠤⠤⠤⠤⠶⠚⢻⠹⡌⢀⣰⠃⠰⠬⠍⠠⠈⠀⣀⡇⠁
⠀⠀⠈⠫⡑⠊⢁⣴⠋⣀⠀⠀⠀⢈⣆⣀⣰⠊⠀⠀⠀⡼⠁⢀⣀⠀⠀⠀⠀⠀⢀⡰⠂⠀⠀⠀⣇⠈⠁⢟⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠀⢱⡎⠀⠘⠆⠁⠈⠑⠀⡰⠁⠀⠀⠈⠙⠲⣄⡔⢳⠉⠀⠀⠀⠀⠀⠸⡆⠀⢸⡄⠠⠤⠦⠤⠀⠠⢾
⠀⠀⠀⠀⠀⠀⣠⠀⠂⠟⠚⠁⠀⢀⠌⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⡜⠁⠸⡄⠀⠀⠀⠀⠀⢀⣹⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⣀⡤⠒⠋⢹⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡠⡞⡇⠀⠀⢧⣀⡤⠤⠒⢺⠃⠀⠀⢸⡇⠀⠀⠀⣾⡀⠀⡠⠒⠉⠢
⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠹⡄⠀⢘⣆⠀⠀⠀⠴⡅⠱⡤⠤⠴⠊⡰⣰⠁⠀⠀⠀⡆⠀⠀⠀⢸⡃⢀⡀⢸⠓⠂⠠⡤⠁⠙⢮⣀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⡷⢶⠋⠘⢦⠀⠀⠀⠘⣴⠀⠀⢀⠔⣱⠃⠀⠀⠀⠀⢸⡆⠀⠠⠀⣟⠋⠉⠛⠀⠀⢠⠃⠀⠀⠀⡌⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡇⠈⢦⣀⣀⠷⡀⠀⠀⢹⣄⢀⣡⠞⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢹⠲⣄⠀⠀⢀⠂⠀⢀⡠⡞⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣇⠀⠀⠀⠀⠀⡸⠒⠊⠉⢏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢈⣠⠟⠒⠒⠁⠀⠀⢸⡇⠉⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⡀⡸⣆⠀⠀⢀⡜⠁⠀⠀⡀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠉⣠⠟⠀⠀⣼⠀⠀⢄⡨⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠒⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠘
⠀⠀⠀⠀⠀⠀⠈⠥⠤⠒⠉⠀⠀⠀⠀⠙⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠩⠤⠚
⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⡿⢿⣿⣿⠿⢿⣿⠿⣿