Nurses Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠓⠒⠒⣲⡤⠤⠶⠒⠒⠒⠚⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⠎⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣦⣤⣌⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡴⠁⠀⠀⠀⠀⢀⡴⠚⣟⠛⠛⠿⣦⣾⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⣠⢿⣶⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⣴⣧⢸⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠤⠖⣒⠛⠷⡄⠀⠀⣀⡴⠶⣿⠃
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣰⠿⣿⡋⠁⠀⠀⠼⢶⣶⠦⠀⠀⢰⡿⣶⣾⣿⣆
⠀⠀⠀⠀⠐⠫⠶⠶⠶⢶⣤⡀⠀⣰⣿⣦⣿⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⣇⠉⢹⣿⣽⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⠿⣷⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⣸⣿⠋⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣷⠜⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⡛⠟⢰⠋⠁
⠀⠀⠀⠀⣠⣿⣿⣿⣷⣀⠀⠀⠛⠿⢿⠂⠀⢧⠀⠀⠀⠀⠈⠙⠻⣿⣿⡟⢡⠏
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⣾⠀⠀⠀⠳⢦⣄⡀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠋⠠⣾⠇⠀⠀⠀⠀⠀⠙⢿⣿⣶⡤⠤⠴⠟
⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠠⢿⠿⠟⢫⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠙⣦⡀⠀⢀⠀⣼⣿⡏⢸⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠈⢿⣦⠘⠂⠻⢿⠁⠈⠛⢻⣿⣿⡟⠛⠛⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⡟⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢙⡚⠁⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣠⣾⣿⠇⠈⠙⢷⣄⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡿⠋⠀⢤⡠⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⣴⣿⣿⣿⣿⣿⣿⡤⠤⠴⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠚⠛⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠏⠉⠀⢀⣉⡘⠂⠀⣠⣖⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡍⠀⠀⠀⠀⠈⠛⠁⠀⠀⠛⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣼⣿⣿⡇⠻⢷⣤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣭⣴⡆⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⡐⢰⡟⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⡉⠻⡋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠚⠉⠀⠀⠈⠲⠌⠓⠄⠀⠀⠀⠀⠱⠀⢀⠀⠀⠀⠀⠀⠈⠀⢰⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⢸⠀⠀⠰⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢣⡀⣼⠀⠀⠀⠇
⠀⠀⠀⠀⡰⠋⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⣸⣧⡖⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢷⡏⠀⠀⠀⢰
⠀⠀⢀⡞⠁⠀⠀⠀⠀⢙⣦⡀⠀⠀⣀⢴⣿⣟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡞⠀⠀⠀⠀⢸
⠀⢀⠏⠀⠀⠀⠀⢀⠔⢯⣻⣷⣰⠞⠁⠈⠻⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡸⠀⡇⠀⠀⠀⢸
⠀⠊⠀⠀⠀⠀⠀⠑⠦⡀⠉⠻⠏⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠤⠤⠆⠈⠀⠀⠀⣸⠀⣠⣇⠀⢻⡀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡏⠻⢧⠀⠁⠀⠀⠇
⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⣀⠀⠀⠀⠉⠒⢄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠈⠒⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⣄⣒⣐⣂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣯⣭⣽⣛⡳⢮⣔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠓⢮⡙⢿⣶⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣫⣔⣚⣫⣭⣉⣙⣛⠲⠦⣄⡀⠀⠙⢦⠹⣿⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣂⣍⡓⢦⣀⠁⠹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⣿⣿⣿⡿⠿⢟⣛⣭⠞⠋⠻⣿⣶⡝⢷⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠐⣝⢿⣆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢼⣿⡿⠐⠛⠛⠶⠀⠀⠀⠀⠚⠋⣉⡁⠀⢹⡞⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⠺⢟⣻⡷⠀⠀⠀⠀⠐⠻⣿⠟⠃⠀⢷⣹⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣾⣿⡿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣿⣿⡄⠀⢀⣠⠤⣤⠤⣤⠄⠀⠀⠀⣼⣿⣿⣿⣿⢟⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣿⣿⣄⠀⠙⠶⠤⠼⠋⠀⠀⢀⢴⣿⣿⠿⠿⢷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠔⠁⣸⣿⣷⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣿⠐⠀⠀⠂⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠗⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡇⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠈⠲⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⠿⢛⣤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢈⠩⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⣿⠇⠀⠀⠢⢀⠀⠀⠀⠀⡐⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠈⣉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠦⡅⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠐⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣔⡒⠀⠀⠀⠀⠀⢸⡏⠛⠁⠀⠉⠉⡷⠀⠀⠀⠈⢐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣤⠀⠀⠀⠀⠀⠸⣧⣤⡄⢀⣤⡤⠃⠀⠀⠀⠈⣒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⢸⣇⣹⡄⠀⠀⠀⠀⠀⣀⡱⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠐⡛⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣤⡴⠒⣒⠞⢛⡹⢋⡽⢋⠟⠛⢿⡚⢖⠒⠶⣦⠬⣤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡴⢋⡤⢚⡥⠖⣁⠴⢋⠔⠁⠀⠀⠀⠉⠳⢭⣶⣤⣑⠦⣌⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣴⡿⠞⣩⠴⢛⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣮⡳⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⠴⢋⡡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣡⣖⡁⢄⠐⠒⠒⠒⠠⠤⠀⠤⠀⠤⠄⠠⠤⠤⠤⠤⢄⣀⠹⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⡴⠛⠛⢷⠀⠆⠀⠀⠀⠈⢧⣰⣴⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⣿⡀⠜⡀⠀⠀⠀⠀⡀⣜⡇⠀⠀⠸⣧⡃⠀⠀⠀⢀⠾⣿⣿⠃⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣻⡅⠈⠛⠧⠤⠭⠭⠵⠚⠀⠀⠀⠀⠘⠓⠤⠤⠬⠄⠊⢹⣿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠦⣄⣀⡀⠀⣀⣠⠶⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⡴⠂⣿⠁⠀⠀⠉⠉⠉⠉⠀⠀⠘⣿⣷⠦⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⠖⠛⠿⢹⠃⠈⠃⢪⠞⠁⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⡏⠳⡄⠉⠙⠉⠉⠙⠙⠹⡟⣷⢶⣤⣀
⠀⠀⠀⠀⣠⠚⡏⠨⠃⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⡏⠳⢦⣤⣀⣀⣀⣀⣠⣤⠴⠛⡇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠁⠊⠜⢩⠻⣦⡀
⠀⠀⢀⡾⡁⢼⡇⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢇⠁⢠⡁⢍⠩⠉⠉⢀⠄⠄⢸⠃⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠞⣻⣆
⠀⢀⣮⡀⠌⠂⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⢹⠀⠂⣍⢦⠃⡀⢦⡟⡐⠀⡾⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣧
⠀⣜⠣⢍⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡶⢦⣄⠀⢸⡀⠐⢄⠃⠠⣜⠾⠡⠀⢰⠃⠀⠀⣀⣴⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣚⢽⣇
⢰⠏⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡾⠁⠀⠈⡇⠀⠀⠀⠰⡟⢠⠡⣸⡏⠀⣠⠾⠋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣋⣿⡀
⢸⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢳⠀⠀⢠⡟⢀⢢⡟⣼⠁⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡥⢾⡇
⡎⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠘⡆⠀⠜⠀⢀⡾⢱⡏⠀⠀⠀⠀⠀⠉⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢖⣻⡇
⡇⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣦⡀⠀⠀⠀⢱⠀⠀⠀⣼⣷⡿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⢹⣇
⣇⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣦⡀⠀⠈⣦⠁⣘⡎⣹⠃⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⣿
⣯⢉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠷⣄⠀⢸⡀⣿⢱⡏⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠾⣿
⡗⠢⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣷⡀⣷⣰⡿⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿
⠏⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠭⢼⡿⠥⠤⢤⠼⠥⢤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣀⣀⣹
⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠈⠁⠁⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠠⠀⠁⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠄⠃⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠔⠈⠁⠀⠀⠀⠀⠈⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⢁⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠱⡀⠀⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠈⠙⠓⠀⠀⠀⠀⠉⠀⠀⠀⠤⡀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠰⠖⠗⠒⡴⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠡⠌⠄⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠑⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⣀⢀⣦⣄⠀⠀⠀⠀⢒⡲⠚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⡉⣤⠛⠍⠐⢁⠀⠤⠐⡲⠋⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠐⠉⠀⡏⠀⠘⣀⠈⠄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢣⠀⠉⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⠀⠐⠀⠈⢂⠈⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠐⠀⠁⠈⠀⠀⠀⠀⠀⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⢀⠠⠀⠒⠂⠀⠀⠀⠀⠀⣠⡞⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠰⠀⠀⠀⠀⢀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠇⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠉⠉⠉⠉⠑⠒⢦⣀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠐⠒⠀⠐⠒⠂⠤⢄⡀⠀⠀⠃
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡐⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡌
⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⡘⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⢃⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠈⢄⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠳⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⢀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣤⣤⣤⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⡀⠀⠀⠀⠀⠀⠀⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢾⠈⠁⠀⠈⠉⣹⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⠈⡇⠀⢸⠉⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣀⣤⠤⠶⠿⠿⠷⢤⣀⡤⠤⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠉⣠⠴⠂⠀⠀⠀⠀⣀⢿⢀⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⣠⣮⠤⠒⣲⠴⢃⠀⡰⢣⢿⡀⢳⡜⢧⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⢁⡤⠖⣋⡥⢖⡟⣨⠔⠁⠀⢳⡄⠻⠀⠳⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⡴⠚⣡⠤⠾⠋⠁⠀⠀⣀⠤⣽⣦⡸⣄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡞⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⣶⠌⠀⠙⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢷⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⢰⡇⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣻⡆⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⣾⣃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢶⣄⣀⣀⡴⠊⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠁⠀⠀⢀⣴⠃⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣶⠤⣤⡤⠤⣶⡏⡸⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡇⠀⠀⠀⢀⣿⠳⣦⠀⢷⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠀⠀⣷⠀⠀⠀⠀⡟⠀⠈⢻⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠋⠁⠾⢤⣄⡠⢻⣆⡀⠀⣰⠷⢦⣀⣠⠇⠈⠙⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠁⠀⡞⠁⠀⢷⣽⣪⣾⠀⠀⣹⠆⠀⠀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠙⠳⣄⠈⢷⣠⠃⣠⠞⣁⣀⡀⠀⣏⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀⠈⠳⣜⣧⠞⣵⢞⠓⣶⣿⣶⢿⡄⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⣿⠿⠇⠻⠍⢹⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣧⠀⠀⠀⠀⠀⠀⠀⠟⣿⠀⠙⠒⠛⠛⠋⠉⣸⠋⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠳⣦⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⢀⡴⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⣟⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⡿⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠿⠛⠛⠿⠿⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣠⡴⣶⣶⣶⣶⣶⣤⣄⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣠⣾⣿⣶⣌⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣀⣤⣤⣸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⠛⠿⣿⣿⣏⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⣿⣿⡿⠋⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢈⣿⠁⠀⠀⠈⠉⠙⠳⠆⠀⠀⠀⠀⠀⡀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⢳⠀⠀⠀⠘⠻⣶⣤⣦⠀⠀⠀⠘⠋⠉⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠛⠶⢦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢾⡿⠀⢻⡄⠀⠀⠀⢀⣤⣀⣀⠀⠘⠁⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢰⣿⠃⠀⢸⣿⣦⡀⠀⠀⢀⣉⡉⠛⢁⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠈⢿⡄⠀⠀⢻⣿⣿⣦⣀⠀⠉⢁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡴⠶⠶⠶⠟⠛⠋⠁⣿⠀⠀⠀⠈⢿⡄⠀⠀⠻⣿⣿⣿⣷⠂⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⠙⣿⠃⠀⢸⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢰⠃⠀⠀⠈⣿⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡀⢀⣠⣤⣼⣷⣤⣠⣇⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣙⣧⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣼⠃⣾⠇⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿
⠀⠀⠀⠀⠀⣼⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⣸⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧
⠀⠀⠀⢰⡏⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣄⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢹⣇
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢀⣼⡟
⠀⠀⠀⢹⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢠⣿⣷⡿⢿⣦
⠀⠀⢠⣿⣁⡤⠖⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣧⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡴⢋⡿⠀⠀⠀⠀⢠⠏⣿⠀⣰⣿⠂⣾⠿⠃⠀⣠⢿⣄
⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠉⠀⠀⣼⠇⠀⠀⠀⠀⠀⣰⠏⠀⣼⠃⠀⠀⠀⣰⠏⢰⣧⠞⢁⡿⢿⠏⣠⠖⠋⠁⣀⡈⠻⣦
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣄⣸⡏⠀⠀⠀⠀⠀⣸⠋⠀⠀⢿⣤⡤⠶⠚⠉⢠⠟⢁⡴⠋⣠⣿⣿⣶⡶⠟⠛⠉⠁⠀⠘⢷⣄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⡴⠋⢀⣴⠏⠀⠘⢿⡟⠛⠛⢷⣆⠘⠦⠀⢻⣦
⣼⠋⠀⠀⠀⠀⠀⣴⣾⡵⠶⠞⠀⠀⠈⠛⢿⣿⣿⣿⣄⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠰⢚⣿⡿⠀⠀⠀⣿⠃⠀⠀⠀⠉⠻⢶⣄⠀⢻⣧
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠉⠉⠉⢻⠿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠛⣿⠏⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢻
⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠁⠀⠀⠀⣼⣏⡀⠀⢀⣴⠏
⠀⠙⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢰⣿⣤⡤⠶⠶⠿⠿⠿⢤⣦⣶⣴⣤⣤⣤⣴⠟⠉⢻⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠉⠛⠿⠿⢷⣶⣦⣤⣀⡀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠟⣡⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣾⣧⣄⣀⠀⠀⠀⠋⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠈⠻⣦⣤⠶⠶⠶⣦⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⠛⠷⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣠⠞⠁⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⠶⠶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⡾⠋⠀⣠⠾⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠠⣴⣶⣤⣍⡙⠛⠂⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠉⠀⠀⠉⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠛⠛⠋⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢰⣄⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⣠⣴⣦⣄⣀⠀⠉⠉⠉⠉⠙⠛⠻⠷⣶⣤⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡀⠀⠀⢀⣴⣾⣿⠋⠉⠒⠦⢭⣝⣳⣶⣤⣤⣄⣀⡀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⢠⣾⣿⣿⣯⡇⠀⠀⠀⠤⠤⣤⣍⠉⠛⠉⠉⠉⠻⣿⣿⣿⣷⣶⣶⣬⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⣿⣿⣿⣿⠀⠀⣄⣠⣤⣬⡙⠃⠀⠀⠀⢠⠶⠛⢻⣿⣿⠏⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠿⣿⢉⠙⠀⠀⠀⣰⣿⡿⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠁⠘⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢢⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⢿⣿⣿⡆⠀⠀⠀⠀⢠⡀⠀⢀⡈⠀⠉⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣴⣿⣿⣿⡘⢄⠀⠀⠀⠀⠙⢿⣟⣛⣛⡿⠂⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⣿⣿⣿⣿⡇⠀⠳⣤⡀⠀⠀⠀⠙⠛⠛⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠀⠀⠈⠻⢷⣶⣤⣄⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠙⢷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢶⣿⠋⠀⢺⣦⡀⠀⠠⡀⠀⠀⠀⡀⢀⣾⠇⠀⠙⣿⡛⠛⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠀⣾⣇⣤⣤⠀⠙⢷⣄⠀⣳⠀⠀⠘⢷⡟⠁⠀⣶⠶⠾⢿⠀⠀⠀⠀⠈⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⢠⣿⣄⡀⠀⠙⢦⠀⠀⠀⣰⠏⠀⢀⣤⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠄⠈⠣⡀⠰⠃⠠⠞⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠛⠛⠛⠋⣉⣉⠉⠁⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣀⣀⣿⣿⣀⡀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠿⠿⣿⣿⠻⠟⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠓⠦⠤⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⡇⠈⢳⣄⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡾⠀⠀⠀⠹⣦⡀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⡞⠁⠀⣀⣀⠀⢹⣷⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣴⠏⠀⠐⠉⠁⠀⠀⡆⢿⣇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠞⠁⠀⠀⣀⡴⠟⠁⠀⠀⠚⠋⠐⠒⠂⡇⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠤⣤⠷⠀⠀⠀⠀⢠⠀⠀⣿⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⢀⠤⠄⠄⠀⠀⠀⢀⡞⠀⢠⡇⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢢⡀⠐⠷⣷⠾⠽⠗⠻⠒⠀⡼⠀⠀⡼⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠈⠁⠀⠈⠀⢀⠜⠀⠀⠈⡰⠋⠀⠀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡤⠞⠃⠀⠀⠀⡼⠁⠀⣀⣀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⢢⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠀⠀⢸⠃⠀⠞⠉⠀⢀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⢀⡀⠈⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠈⢀⡀⢀⣠⡴⠋⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡏⠉⠀⣿⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠉⢁⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡈⠐⠚⠉⠀⢀⣠⡴⠋⠀⠀⢠⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠋⠉⠁⠀⠀⠀⠀⠀⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⣂⣀⣩⣭⣭⣭⣥⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢈⣥⣴⡾⠿⠛⠛⠉⠉⠉⠉⠉⠉⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⡷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⣿⠋⠀⠀⠀⠀⠀⠀⣠⣶⡋⠙⡟⠻⢻⣿⣿⣿⣿⣿⣿⣯⢻⣆⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣿⠃⠀⠀⠀⠀⠀⢀⠞⠻⣿⣿⣶⣦⣄⠘⣏⢿⣿⣿⣿⣿⣿⣸⠏⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠰⠀⣾⡏⠀⠀⠀⠀⠀⢠⣣⣄⣠⣠⣿⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⡄⢸⡿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠈⠉⠉⠙⠉⠁⠙
⠀⠀⠀⠀⠀⠀⢠⠀⣾⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢘⠀⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢵⡇⠀⠀⢀⡴⠶⢦⣤⣄⡀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠄⠄⢀⡀⠀⢰⣿⣿⢿⣿⣵⡟⠀⠀⠀⠁⠀⣠⣄⡀⠈⠀⠀⠀⣰⡫⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠉⠐⠙⠉⠀⠀⠀⠀⠀⠚⠙⠿⠀⠀⠀⠀⠀⡛⠃⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⡇⣀⣀⣼⣿⣮⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣤⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⣸⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠑⢄⡀⠀⠀⠀⠀⠈⠻⠯⠭⠿⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡙⡟⠟⠛⠟⠻⠻⣿⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⣧⣴⣀⣦⣶⣷⣾⣿⠀⠀⠄⠀⠀⠀⠀⠀⢸⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠄⠘⠋⠉⠉⡉⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠢⡤⠀⣀
⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⡀⠀⠈⠁⠂⢄⡀
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡀⠀⠀⠀⠀⠑⢄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠤⠒⠈⠁⠈⠢⠀⠀⠀⠀⠀⠆⠆⠀⠒⠠⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⡄⠙⢿⡟⠁⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠇⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠠⠶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠿⠶⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⠛⠾⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠋⠱⣋⠀⢸⡃⢈⣻⠋⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠁⢸⠀⠘⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⠀⠀⢸⠀⠀⢀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣦⣼⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⢻⠛⠻⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣷⣾⣶⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣸⣤⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡛⢻⠛⣻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣼⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠔⣠⡐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⠐⠉⠀⠈⡘⢠⠀⠀⠔⠈⠉⣦⠀⠀⡄⢃⠁⠀⠉⠂⠂⢤⣀⡀
⠀⠀⠸⢄⣉⠉⠛⠓⠒⠚⠋⠉⢉⠋⠁⠀⠀⠀⠀⢀⠜⠠⠃⠀⠈⣄⣀⣴⡿⠁⠀⠘⠄⠱⡀⠀⠀⠀⠀⠈⠉⡉⠉⠉⠛⠓⠒⠚⠉⢉⡠⠃
⠀⠀⠐⢍⡉⠉⠉⠀⠀⠀⠈⠉⠈⣁⣀⠀⠀⠀⠀⢬⠀⠂⡀⠀⡀⣸⢿⣿⡇⢀⡀⢀⡀⠀⡅⠀⠀⠀⠀⢀⣈⠈⠉⠀⠀⠀⠀⠉⠉⣉⡩⠆
⠀⠀⠀⠀⠠⡛⠉⠁⠀⠀⠉⠉⠁⠈⣠⣤⠀⠀⠀⠈⢳⣂⣬⣁⢤⢼⠀⣿⡧⣤⣈⡭⣐⡞⠁⠀⠀⠀⣤⣄⠁⠈⠉⠁⠀⠀⠈⠙⢛⠄
⠀⠀⠀⠀⠀⠀⠉⠐⠒⣖⠐⠂⠈⢁⣀⠠⠖⠂⣠⠀⣈⠀⢈⠁⢀⣻⠀⣷⣗⡀⠈⠁⠀⣁⠀⣄⠐⠒⠄⣀⡈⠁⠐⠂⡰⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠛⠐⠚⠋⠉⣁⣉⡉⢹⠀⣿⡏⢉⣉⣈⠉⠙⠓⠂⠛⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢉⣹⠶⡃⠀⠀⣿⠅⢘⠶⢯⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠨⣿⠟⣋⡷⠀⣿⢶⣙⠻⣿⠅⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡈⠙⠫⠤⣀⣿⡤⠝⠋⢁⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⡀⠉⠓⢤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢈⡛⣦⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⢧⣿⠃⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⡀⠉⠲⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣨⡟⣷⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⡅⣿⠟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠻⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⡷⣄⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⣿⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢣⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣽⣆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡏⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠄⠠⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠈⡦⢤⠄⡀⠠⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠠⠠⠀⠀⠄⡺⠃⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⡀⠠⡀⠉⠒⢢⠖⢚⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠂⠴⠂⠁⠀⠃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠂⠊⠡⠈⠒⠂⠄
⠀⠀⠀⠀⡰⠄⠀⠑⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠠⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠈⢄⠀⠀⠈⢀⠈⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⢀⠸⣄⠠⠁⠀⢱⠀⠑⢄⠀⠀⠀⠀⠁⠀⠁⠀⠀⡠⠈⠓⠀⠠⠴⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡻⡀⠸⠠⠀⠰⠓⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠈⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣀
⠀⠀⠀⠛⠛⡛⠿⠷⠤⢤⠐⠒⠀⣀⠀⠐⠈⠱⠀⡝⠀⢂⢭⠑⠀⠀⠞⣡⠐⠚⢄⠅⠐⠂⠌⠂⠀⠡⡊⠑⡈⡆
⠀⠀⠆⠀⠀⣷⠂⠀⠀⣾⠈⣃⠰⡀⠀⠀⠀⠀⡗⠀⠈⡒⠑⢊⠀⡠⡀⢠⠑⢄⠆⠀⠀⠐⠀⠀⠀⠑⠨⠄⠚
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠸⡢⡀⠀⣀⢇⠀⠈⡉⠀⢰⠀⠢⣈⡢⠒⠁⠀⣀⠀⢠⠀⠂⣀⠔⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠘⢵⣀⣤⠟⢀⡀⡀⠀⠈⠒⠛⠠⠬⢀⠠⠛⠒⠁⠀⠤⠠⣀⡀⢕⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⢀⡀⠫⠔⠀⠠⠉⢠⠒⠊⠉⣩⡍⠉⠑⢢⠀⡇⠀⠈⡇⢀⡔⠂⠙⠂⢀
⠀⠀⡄⠀⡘⠃⠀⠑⠠⡀⢉⠁⠜⠂⠨⣂⠅⢸⣄⢀⠠⠬⠄⣀⣀⢆⠀⠙⠒⠐⠁⠊⠀⢠⠊⠀⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡆⡟⠂⠀⠐⠒⠁⠈⠂⠀⠀⠀⡀⢠⠃⠀⡠⠢⣄⠀⠀⠀⠀⢣⢠⡆⠀⠐⠤⠄⠁⠀⠀⠐⠈⠀⠀⢀⣀
⠀⠀⠀⠅⠃⠀⠀⢄⡲⣀⠐⡀⠄⠀⠈⠁⣸⠠⠊⠀⠀⠀⠉⠒⠠⢄⣘⠀⢀⠄⠄⠁⠀⠀⠀⠀⠈⠰⠀⡔⠅⣨
⠀⠀⠀⠆⠀⠀⠙⠆⠃⠀⠧⠘⠰⢒⠀⠀⢲⡄⠀⠋⠀⠀⠀⠘⠃⢀⢖⠀⢠⠀⠏⠉⠉⠉⠐⠢⡔⢉⠰⠀⢊⠇
⠀⠀⠀⠁⠰⡀⠞⡂⠀⠊⠀⠀⠀⢈⠀⠀⠘⠨⠖⠤⢀⢉⣀⣤⠐⠓⠊⠀⡀⠑⠦⣀⣀⡀⠀⠀⡤⠊⢘⠠⠊
⠀⠀⠀⡇⠈⡮⣀⠀⠢⠤⠴⣀⡠⠼⢠⣿⠤⢁⠄⠐⠮⠄⠊⠀⠱⣄⠀⠀⡁⠂⠀⠀⠡⠉⣉⡉⠀⠀⠰⠂⠀⢰
⠀⠀⢄⠆⠀⠀⠀⠀⢀⡒⢀⡀⢀⠠⠀⠈⠠⠉⡄⠀⠀⠀⠀⠀⠀⠆⢂⠰⠈⠀⠔⠒⢠⢎⢔⢨⡒⠢⡀⠀⠾⠞
⠀⠀⠀⡠⠒⡄⠀⠣⣀⡔⢸⠀⠀⠇⡆⠀⠣⠤⢥⠀⠀⠰⠠⡄⠀⠘⠐⠀⠀⡘⢀⡔⡱⠱⣁⠑⠉⠒⢯⢢⠀⢀
⠀⢠⣇⢡⠔⠁⢇⠀⠈⠀⠘⠂⠐⣃⠆⠀⡇⠀⠘⠁⣀⠀⠘⠁⠀⢈⡠⠀⢀⢣⠊⡎⠀⠀⠀⠀⠀⡠⣪⣪⠊⣼
⠀⠸⡨⠀⠂⠄⡀⢉⡙⠫⡉⢙⠉⠁⠀⠀⠈⠒⠂⠙⠤⠤⠬⠙⡋⠭⠀⢄⠘⠈⠢⣑⢄⡀⠀⢀⢜⠕⡕⢁⠏⠉
⠀⠀⠉⠀⢠⣖⣶⣅⢢⣁⣀⠀⢠⠄⠀⡀⡀⠀⠸⡉⠭⡍⠡⣥⠀⠰⢀⠎⠈⠢⠤⠄⣑⢮⣈⠵⠃⠀⠃⠁⢠⠆
⠀⠀⡔⠉⠁⠀⡠⢄⠀⠀⠈⢣⠈⠢⠼⣤⠂⢙⠀⠈⣓⠢⠤⠤⠴⠚⡁⠀⠐⣢⡤⣤⣄⠈⠀⢰⣀⡠⠄⠈⢀⡄⡀
⠀⠀⡇⠀⠀⡖⠃⠈⢐⡀⠀⢸⠀⠙⢀⠤⣉⠉⠀⡮⠋⢠⠀⠀⠒⠄⠈⠢⡀⠉⠁⠓⣀⡁⠠⠜⡧⡀⠁⠀⠩⣒⠄
⠀⠀⡇⠀⠀⠉⢧⡠⠏⠀⠀⠸⠀⠀⠇⠞⠈⢁⣿⠋⠈⢡⣴⡦⠊⠀⠀⡰⠀⡊⠈⢹⢰⠱⡐⡀⣇⠰⠄⠀⠁
⠀⠀⠱⢤⣀⣀⣀⡤⠤⠤⠄⠊⠀⢄⡔⠖⢠⢋⢎⠀⠀⠈⢃⠀⠀⠀⡴⢡⡄⠠⣀⡸⠌⠦⠙⠉⠁⢄⣒⣒⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠑⠂⠉
⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⡀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⢸⡿⠀⠀⠀⢠⡇⠀⠀⠀⢸⣦⣤⣤⣀⡀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠿⣿⣿⡇⠀⠠⣤⣼⣿⠋⢹⣿⣿⡂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠾⣿⣿⣿⣿⠿⠿⠿⠿⠟⠓⠲⠿⠿⢿⣶⣿⣿⣿⣧⣤⣶⣶⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠋⠉⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠧⢾⠋⠿⣆⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⢸⣿⣧⣴⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡟⠀⣀⠐⡄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠈⣿⡠⣻⣾⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠐⠀⣼⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡀⣠⣿⡇⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣦⣶⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⣾⣿⣇⣿⣿⡄⠀⣾⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⢘⣿⣿⣴⣿⣿⢁⠽⡻⢿⢿⣿⡿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡍⡈⠛⠛⠉⠀⠀⠀⠱⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⣧⠐⠁⠀⠀⠀⠐⠄⣗⡘⠉⠓⠒⠉⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣆⢿⡻⣤⣐⣤⠤⠀⠀⣽⣶⣦⣥⣀⣀⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣯⠙⠌⠳⢬⣟⣁⠀⠀⢠⣿⣤⣦⡈⠉⠉⣉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡀⠀⠀⢐⣽⣶⣤⣬⣵⣶⢟⢅⡠⣰⡴⣞⣻⢮⣿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⣿⣯⠺⣿⣶⢟⡽⠛⢉⡛⣿⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠳⣤⡄⢰⣆⣭⣩⢦⡿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠧⠉⠘⠛⠁⠈⠓⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢾⡿⣿⡛⣷⣶⣶⣄⠀⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡏⡡⢞⣭⣭⡦⢽⣷⠈⢍⣯⢹⣷⡄⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡔⠁⣈⣴⣯⠵⠂⡼⢂⢝⢿⣝⢻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⣸⣿⠿⠟⠀⠀⠟⢍⠈⣿⢻⣿⣿⣿⣿⣿⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣸⢻⣷⡿⢁⣲⡆⠀⢸⣴⡋⢤⣿⣗⣘⣟⣺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡠⢤⣐⠿⠷⢝⡤⠤⡚⠁⠈⠛⠓⢠⣟⡕⢐⢸⡟⠁⠀⠙⠯⣽⣿⣿⣿⠛⢿⡇
⠀⠀⠀⠀⠀⠑⠄⢀⣀⡴⠊⢫⡱⡈⠑⢦⠃⠀⢸⡟⠇⣽⡎⠀⠀⠢⢀⡔⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⡼⢋⠠⠚⠀⠑⢄⠀⠀⠑⢄⠈⠇⢺⠉⠱⢂⠡⠐⠉⠀⠘⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡸⡑⠁⠀⠀⢂⡀⠙⡇⠀⠀⠈⢢⠀⣀⡠⠤⠜⠀⠀⠀⠀⠈⠘⡿⠏
⠀⠀⠀⠀⠀⡐⡕⡁⠀⠁⠀⠀⠁⠤⡈⡀⠀⠀⠀⠹⡌⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡇⠁⠹⠀⠃⠀⠀⠀⠀⡈⠳⡄⠀⠀⠀⠱⢈⡤⢒⠿⠋⠙⢹⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⡇⠀⠀⢧⠰⠀⠀⠀⠀⠐⠄⢰⡀⠀⠀⢀⣰⠀⠀⠀⠁⢊⡜⠀⠀⠀⠀⠀⠠⣪⠎
⠀⠀⠀⠀⡘⠀⠇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡱⠂⠁⠣⡈⠢⡀⠀⡠⠊⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⣆⢀⡇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠱⡀⠗⠉⠀⠐⠒⠒⠒⠒⢒⠋⠀⠀⠰⠀⡦
⠀⠀⠀⢰⡀⡼⠀⠀⠀⢡⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢄⠀⠈⡦⠤⠠⠀⠀⠄⠀⠠⠀⠰⠃
⠀⠀⠀⢸⠄⡇⠀⠀⠀⠈⢂⠘⢄⠀⠀⠀⠀⠐⠀⢀⡔⠂⠀⠀⠀⡥⠤⠑⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣠
⢠⠤⣤⣿⢀⣇⣀⣀⡠⠄⠀⠳⡀⠈⠐⠀⠂⠉⠙⠳⣦⡀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⣧⠰⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠈⠛⠢⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠚

⠀⠀⠀⠀⠐⣖⠀⠀⢀⣠⣄⢀⣤⣶⣿⡗⢀⣀⡉⠀⢀⡋⣛⣀⠀⠀⠘⠃⠈⠻⢿⣿⣄⣤⣤⣾⣦⠀⡖⠶
⠀⠀⠀⠀⡀⡀⠀⠀⠻⡿⢯⣼⣿⠟⡟⠀⢻⣿⠁⠀⠀⠉⠀⠈⠀⠀⠀⠶⠆⢀⣸⣿⣿⣿⣿⣿⣛⠂⠇⣤
⠀⠀⠀⠀⢥⡒⢄⡀⣀⡡⠼⣟⠛⣿⣿⣛⢡⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣿⣿⣿⣏⣿⡥⢛⣼
⠀⠀⠀⠀⣼⣆⠀⠓⣼⠃⠀⡀⠀⢿⣿⣿⣿⠿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⡾⢿⡏⠈⠙⢫⣿⣷⣿⣷
⠀⠀⠀⠀⣽⡉⠐⣤⡤⠀⠀⠉⠀⣠⣿⣿⣿⠁⠘⣦⣀⣀⠀⣀⣀⡆⠀⠈⢰⢾⣀⡀⠻⠇⣠⠊⠳⣿⣿⣿
⠀⠀⠀⠀⠟⡅⠀⠀⢁⠀⠀⠀⠠⣿⣯⣿⣿⣧⡀⢏⣻⣋⣾⢛⣛⠁⠀⠀⠀⣦⡸⢧⣤⡾⣿⣷⠄⣐⣿⣿
⠀⠀⠀⠀⣷⡴⣦⢀⠀⢠⣿⠀⢐⢽⣿⣿⣷⣤⣤⠀⠙⠄⠄⠐⠃⠀⠒⣤⣀⣿⠟⣴⣿⣿⣿⣿⠶⣯⣿⣿
⠀⠀⠀⠀⣟⠉⠉⠂⣠⣌⠁⢀⡢⢿⣿⣿⣿⠉⣁⣀⣀⣴⣿⣧⣀⡀⠀⡀⢁⠉⠀⠿⣿⣿⣿⡿⠟⢛⣟⠋
⠀⠀⠀⠀⠱⢶⣁⠡⠽⠟⢿⣇⣽⡿⠛⡸⣿⣶⣿⡿⢿⣟⠛⡏⠯⣻⣿⣶⠞⠃⢀⣿⣿⠛⢺⡁⠀⣇⠘⠃
⠀⠀⠀⠀⠸⠏⠀⠀⠀⠂⠈⢹⣟⡋⠀⠃⣰⢿⣿⡛⢻⣽⠁⠬⡭⠽⢷⡿⠁⠀⠀⣩⣽⣀⡀⠀⢠⣾⣴⡇
⠀⠀⠀⠀⢿⢠⠐⠀⠀⠀⠀⢴⣿⣷⡆⠀⠃⢈⣧⣉⣛⡻⠄⣸⢿⣟⣿⡃⠀⠀⣀⣷⣿⣿⣿⣶⣿⣿⠏⣥
⠀⠀⠀⠀⠉⢁⠀⢠⠀⢀⡀⠟⠛⠛⢛⠇⠃⢸⣿⣯⠽⣺⡄⣩⣓⢶⣿⠂⠀⢂⠘⠋⠠⠻⣃⠉⢋⡉⢺⣿
⠀⠀⠀⠀⢎⣱⣦⡄⣰⠟⣿⡀⠀⠀⠜⡌⠀⠀⢿⣖⡿⢻⡯⡏⠻⣷⠏⠀⠀⢸⠀⠀⢠⠰⣿⡇⠀⠉⣤⡟
⠀⠀⠀⠀⠉⠉⢩⣽⠉⢭⡝⠛⠀⣘⣸⡇⠀⠀⠀⢉⠀⣸⠭⡇⠀⡀⠀⠀⠀⠘⢂⡀⢈⣴⣖⠿⠄⢿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡟⠁⢠⣽⡭⣅⠀⢠⡋⠙⠒⢾⡭⡇⠘⠉⠃⠀⠠⣸⠿⣻⣿⣿⣿⣿⣟⣷⣿⠟
⠀⠀⠀⠀⢀⠐⠟⢈⣷⢴⡟⠀⠀⢻⢷⣿⡆⠈⣣⠀⠹⡿⢗⣿⡆⢀⡄⠀⠈⢛⣦⡟⠁⣨⡟⠙⣿⣿⣤
⠀⠀⠀⠀⢋⠀⠶⢴⡆⢀⣬⡜⠁⡌⢸⣿⠁⠀⣻⣷⣌⣛⣷⣟⠡⣿⣧⠀⠈⣹⣿⣙⢀⣈⣡⣤⣿⣿⣟⡷
⠀⠀⠀⠀⠘⢠⠖⠚⠀⠙⠂⠰⢷⣿⢸⣡⡦⠀⣯⢡⠘⢭⡓⠩⠆⠠⠰⠀⠀⠷⢿⣿⡿⠿⠿⢿⣏⣀⡙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⠀⢠⣤⣄⠀⣀⣀⡀⠀⠀⣴⣤⡄⣤⣤⡀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢰⣶⡆⠀⢀⣿⣿⠀⣾⣿⣿⠘⣿⣿⣿⡀⠀⣿⣿⠇⣿⣿⢀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡇⠀⢸⣿⣿⠀⣿⣿⣿⡇⣿⣿⣿⣷⡀⣿⣿⢠⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⣿⣿⣤⣼⣿⣿⢰⣿⣿⣿⣷⢸⣿⣿⣿⣷⣿⣿⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⠿⢿⣿⣿⢸⣿⡿⣿⣿⡜⣿⣿⢿⣿⣿⣿⢸⣿⣿⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⠀⢸⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⡎⣿⣿⣿⢸⣿⡏⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠛⠀⠘⠛⣛⠛⠛⠉⠙⠛⠛⠛⠛⠁⠈⠉⠉⠘⢛⡃⠀⠀⠘⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣆⠀⠀⢠⣿⣿⢂⣴⣿⣿⣷⣄⠀⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⣾⣿⠇⣾⣿⡟⠉⢿⣿⡆⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡟⠀⣿⣿⠇⠀⢸⣿⡇⢿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⣿⣿⡀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢿⣿⣇⠀⣾⣿⡇⢸⣿⣧⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠘⣿⣿⣾⣿⡿⠁⠘⣿⣿⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠈⠙⠛⠛⠁



⣤⣄⣄⣤⣤⣄⣀⣀⣀⣄⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣠⣠⣀⣤⣠⣤⣄⣠⣤
⣿⣯⣭⣿⣯⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣯⣽⣭⣭⣿

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



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣴⠟⠀⠀⠀⠀⠠⠄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢠⡄⠀⠀⢀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦⣤⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⡃⢀⠀⢩⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢤⠛⣶⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢽⡛⢐⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠛⣡⡾⠿⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢾⡟⠀⣶⣶⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢻⣶⣿⡟⣻⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣇⣽⣿⣿⣿⣧⣽⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠻⠿⠾⢯⡛⠛⠛⣻⣧⠀⠀⣰⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠙⢦⡍⢹⣿⡆⡀⠉⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⢳⣿⣿⣿⠓⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⡟⢽⣩⣷⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠏⠰⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠆⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡷⠄⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⠚⢧⣀⣸⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⡀⠀⣀⠀⠀⠀⢀⠀⣾⣉⡷⠈⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠿⠿⣿⣷⣶⣶⣤⢷⣦⣤⣤⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⠀⢁⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠸⣇⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢿⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⣈⣿⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣟⠹⡿⠈⣟⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠹⣿⣶⣧⣤⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡼⠤⠐⠂⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢀⠴⡃⣠⠔⢦⠈⡇⠲⡄⠀⣴⣢⠔⡆⡰⡀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠟⠁⠀⡎⡸⠁⡰⢀⠜⢇⠜⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⠁⠀⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⢤⡀⡆⠀⠐⠲⡀⠀⡄⢰⠀⢰⣃⠀⠠⣟⠀⠰⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠣⠀⠀⠀⠇⠙⠆⠀⠸⠴⠁⠀⠈⠷⠀⠸⠤⠀⠰⠬⠃⠰⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⣩⠃⠠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠤⠊⡅⠀⡠⠃⠀⢈⠇⠀⣠⢄⣀⠤⡀⢠⠄⢠⡄⡰⠉⡆⢀⡏⢸⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡠⢋⡤⠊⡏⣸⠁⠸⡠⠺⠴⠃⠘⠇⠀⢧⠋⠁⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠤⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢰⠪⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠰⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⣸⠴⠊⠹⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⣄⠀⣀⡀⠀⠀⠀⠀⠀⢰⡵⠁⠀⢀⡐⠦⢤⡧⠔⠊⣼⠀⠀⢰⡀⠀⡸⠁
⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⡤⢚⡏⡻⠉⠀⢱⡴⠋⡷⠀⣠⣯⣄⣠⢴⠧⠃⠀⡸⢇⠀⣰⠙⢆⣠⠏⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠛⠁⠀⠀⠘⠀⠀⠧⠔⢹⠃⢈⡇⠈⠧⡠⠔⠁⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⢰⣯⠀⠀⡘⢆⠀⠀⠀⠀⠀⣠⠀⠀⡀⡀⠀⠐⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⣿⣟⣡⢸⡵⡇⡠⢸⡏⠀⠀⠀⠀⠀⠘⣿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣩⠓⣿⡿⠿⢞⣿⣴⢇⣨⣭⡤⢤⠂⠆⠀⠀⢈⣿⣳⣾⣿⣿⣆⡀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⣿⣇⣿⣱⣿⣷⡶⢞⣯⣄⣦⣤⡄⣉⠀⢀⣀⣴⣿⣿⣿⣟⢿⣿⡄⠀⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⣙⣿⣿⣿⡉⠙⣻⣯⠿⠿⢶⠶⡤⢼⣤⣀⣠⠛⣉⣽⠃⣸⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠁⣠⣿⣨⠿⣷⡿⢿⣷⣾⡟⠀⠀⢀⣨⣅⣀⠀⠐⠉⠄⠈⠃⣠⡞⠉⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⢩⢄⠉⠽⣪⣤⡾⢿⡟⣄⠠⠔⠻⢿⣿⢿⣿⣿⠚⠛⠉⠉⠙⣿⣤⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⠘⣿⠦⣶⠶⠚⣯⡀⠀⣾⠟⠁⢠⡄⠀⠀⢹⡌⢹⠟⠀⡀⣀⣠⠞⠛⢿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⢹⣶⠟⠚⠛⠁⠋⢰⣿⡆⢤⣌⣧⠀⠀⠈⣿⡾⠷⠟⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠙⢿⡼⠟⢭⠓⠂⠐⠶⠋⢹⡿⢨⣿⣿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢣⠄⣧⡏⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡾⢟⠼⡃⠀⢶⠶⢀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠟⢀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡻⣦⣀⠀⢰⡆
⠀⠀⣿⠀⣰⡿⢃⣴⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⣿⣿⣮⣿⣧⣼⣧
⠀⢰⣿⣾⣿⣷⣿⣿⣿⣿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡿⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⠟⣹⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣼⢇⣾⡆⣠⡄⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⣠⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⣿
⣿⡿⠃⣰⣿⣿⣿⣿⠏⠀⠀⠰⣦⠀⣼⣟⣾⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⢾⡆⣿⣷⣿⣿⡆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿
⠉⢀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⢻⣼⣷⣿⣿⣿⣘⣿⡀⣠⡄⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠙⢿
⣠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣿⠇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⡿⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⣁⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣄⣻⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣘⣿
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡀⣀⣀⣀⣄⣀⣤⣄⣠⣄⣠⣄⣠⣄⣠⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠚⣉⣋⣉⣉⣉⣭⣭⣥⣬⣥⣤⣥⣤⣤⣤⣤⣤⣬⣤⣬⣤⣌⣀⣉⣉⠛⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠻⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡀⠀⠀⠀⠀⣀⠀⠘⡋⠀⢀⡀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⣠⡾⠁⠀⢸⡇⠀⣿⢿⣄⣿⣁⠈⠹⣧⣠⡾⠃⣿⠙⠛⠷⣦⣄⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢸⣇⣤⠞⠁⠀⠀⠀⢸⡇⠀⣿⠀⢻⣮⠙⠛⠛⢻⡏⠀⠀⣿⠀⠀⠀⠈⠻⣷⡀⠀⢸⡇⠀⠛⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣥⡀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢻⣧⠀⠀⢈⡇⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠶⠀⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠈⠻⣦⣄⠀⠀⢸⡇⠀⣿⠀⠀⠀⢻⣧⠀⢸⡇⠀⠀⣿⠀⠀⠀⣠⣾⠟⠀⠀⢸⡇⢀⡀⢤⠄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠙⠷⠄⠸⠇⠀⠛⠀⠀⠀⠀⠻⢷⠟⠀⠀⠀⣿⣴⠶⠟⠋⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠁⠀⠀⠀⣤⡀⠀⢀⣶⡾⠷⣦⡀⢀⣴⣶⣶⣦⣄⠀⠀⣠⣶⡿⠿⠻⠿⣷⣄⠀⢸⡇⠈⠋
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣷⣄⠀⠀⠀⣿⡇⠀⢾⡏⠀⠀⣼⠃⣿⠁⠀⠀⢈⣿⠀⣾⠟⠁⠀⣤⡀⠀⣨⣿⠂⢸⡇
⠀⠀⠀⣬⠁⠀⣿⡇⠀⠈⣿⢻⣦⠀⠀⣿⡇⠀⠈⣻⣦⡄⠀⠀⠻⣷⣄⠈⠛⠁⠈⢿⣦⡀⠀⠙⠿⠿⠟⠋⠀⢸⡇
⠀⠀⠀⠁⠀⠀⢹⡇⠀⠘⣿⠀⢻⣧⠀⢹⡇⢀⣾⡟⠁⠀⢀⡄⠀⠈⠻⣧⠀⠀⠀⠀⠙⠿⣶⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠁⠀⠀⢸⣧⠀⠀⣿⠀⠀⢻⣇⢸⡇⢸⣿⠀⠀⠀⣼⠇⢸⡇⠀⣿⡆⠀⣼⡃⠀⠀⢈⣿⠆⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠐⠀⠈⣿⡀⠀⣿⠀⠀⠀⠻⣿⡇⠘⢿⣄⣀⣴⠏⠀⠈⠻⠶⠟⠀⠀⠘⠿⠶⠶⠟⠋⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠈⠀⠒⠀⠹⣧⠀⠘⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⡉⣉⠉⣉⣉⣉⣁⣀⣀⣀⣀⣠⣠⣄⠤⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠉⠙⠙⠚⠙⠋⠉⠉⠋⠉⠉⠉⠉⠉⠈⠀⠁⠉

⠀⠀⠀⣀⡤⠤⠀⠤⢤⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠶⣄
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠊⠀⠉⠈⢦⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣠⠵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠁⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡡⠤⠠⠤⠒⠒⠁⠀⠀⢀⡤⠦⢤⡀⠾⢤⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠰⠆⢈⡤⠤⢤⡀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣳⠀⠀⠑⠶⠤⠤⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡤⠞⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⣇⠀⠀⠀⠀⠀⣘⡲⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠋⠙⣦⣄⠀⠀⠀⠀⠀⣼⠙⠲⠴⠚⢹⣆⣀⣠⠴⢻⠋⠉⢉⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠓⠾⣄⠙⠒⠒⠛⣋⣧⡤⠀⠀⠀⢸⣿⠉⠀⢀⡏⠀⢠⠏⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢿⠉⠓⠋⠉⢹⡇⠀⠀⠀⠀⡼⠸⡆⢀⣸⣡⠴⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⢿⡀⠀⠀⢰⠛⠛⣏⠉⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠹⡦⠀⠏⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⣀⣀⣼⡇⠀⠀⠘⢦⣀⣀⣀⣀⣤⠤⠟⠀⢙⡏⠉⠉⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠉⠁⣹⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢸⣇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣿⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⣼⠇⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠓⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣤⠀⢠⣴⣦⢀⣀⣀⡀⠀⠀⣴⣦⡄⣤⣤⡄⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢰⣶⡆⠀⠀⣿⣿⠀⣼⣿⣿⠘⣿⣿⣿⡄⠀⣿⣿⠇⣿⣿⢀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣧⠀⢀⣿⣿⠀⣿⣿⣿⡇⣿⣿⣿⣷⡀⣿⣿⢰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢸⣿⣿⣤⣼⣿⣿⢰⣿⣿⣿⣷⢸⣿⣿⣿⣷⣿⣿⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⠿⢿⣿⣿⢸⣿⡟⣿⣿⡜⣿⣿⢿⣿⣿⣿⢸⣿⣿⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡎⣿⣿⣿⢸⣿⡟⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠛⠀⠘⠋⣛⡛⠛⠉⠙⠛⠛⠙⠋⠁⠈⠉⠉⠘⣛⡃⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣆⠀⠀⢠⣿⣿⢃⣴⣿⣿⣿⣦⠀⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⢀⣿⣿⠇⣾⣿⡟⠉⢿⣿⡇⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡟⠀⣿⣿⠁⠀⢸⣿⡇⢻⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠁⠀⣿⣿⡀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢿⣿⣇⠀⣿⣿⡇⢸⣿⣧⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠘⣿⣿⣶⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠛⠿⣶⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣠⣴⠶⠟⠛⠛⠻⢷⣆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣿⠀⠀⡀⠀⠀⢀⣿⠀⣠⣤⡀⣰⡇⠀⠀⣰⣷⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢀⣤⣾⡏⣼⠏⠈⣷⢻⡏⠀⣰⠇⣿⡀⠀⣸⡏⠰
⠀⠀⠀⠀⠀⠂⢀⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⡇⠀⢸⣧⣤⠶⠾⠛⠉⣽⠇⣿⣀⣴⡇⢸⡇⢠⡏⠀⣿⡇⠀⣿⠁⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡇⠀⣸⡿⣦⣄⠀⠀⠀⢿⡄⠈⢩⡟⠀⢸⣧⡞⠀⠀⢹⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣿⡧⠞⢹⡇⠈⠙⢷⣤⡀⠈⠳⠞⠋⠀⠀⠸⣿⠁⠀⠀⢸⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⣠⡾⠁⡴⣿⡇⠀⢸⡇⠀⠀⠀⠉⠻⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣤⣤⣴⠾⠋⠀⢸⢁⣿⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣀⣈⣛⣁⣠⣤⣤⣤⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣴⡶⢾⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢛⣉⣉⣉⡛⠻⠿⠰⠿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣷⣿⣿⣁
⠀⠀⠀⠀⠀⣘⣿⣿⡿⠟⣋⡛⢿⣿⣿⡁⣿⣿⡿⣿⣿⣿⡆⣰⣿⣿⢛⣿⣶⡆⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⡿⠿⢿⣿⣿⡇
⠀⠀⠀⢠⣾⣻⣿⡟⢡⣾⣿⡿⢸⡟⣍⣳⣬⣩⣴⣿⢿⣿⠀⣿⣿⡿⢻⣿⡿⢠⣿⣿⢻⣿⡿⢹⣿⣿⢋⡉⢰⣿⠏⢠⡾⣸⣿⣿⡀
⠀⠀⠀⠈⢙⣿⣿⢠⣿⣿⣿⡃⢸⡧⠱⢿⡿⢋⡛⣿⣿⡟⢰⣿⣿⡇⣼⣿⠃⣼⣿⡏⢸⡿⠁⣾⣿⢃⣾⠇⣾⡟⢀⣩⣴⣿⣿⣿⠇
⠀⠀⠀⢰⣿⣿⡇⢸⣿⠟⣽⡇⢚⣵⠏⡼⢰⡿⢁⣿⡿⠃⣼⣿⣿⠁⣿⣯⠀⣿⣿⠃⡿⡃⢰⣿⡏⢸⢏⢠⣿⠇⢸⣿⠟⣼⣿⣇
⠀⠀⠀⠈⢻⣿⣿⣬⣥⣾⢟⠁⣿⡟⣸⠇⠟⣵⠸⠟⣡⢀⣿⣿⡟⠸⢏⣿⢸⣿⡟⡀⣱⡇⣼⡟⣤⣩⣾⡘⢋⣾⣦⣥⣾⢿⣿⡿
⠀⠀⠀⠀⢾⣿⣿⣿⣿⢣⡿⢰⣿⣷⣤⣿⣿⣿⣿⣿⣿⢸⣿⡟⣼⣷⣿⣿⣌⣋⣾⣿⣿⣷⣉⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⢀⣼⣿⣿⣟⢾⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣋⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠙⠓⠛⠋⠙⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠶⠲⠦⣤⠴⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣤⣤⠴⠖⠋⠀⠈⠙⠶⢤⣤⣄⠀⠀⠈⢻⠶⣤⠖⠋⠁
⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⡇⠀⠀⠦⠀⠀⠀⠠⠆⠀⠀⡿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠹⡄⠀⠀⣀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⢦⡀⠘⠓⠂⠀⣠⠼⠛⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠙⠓⠛⠛⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡋⠀⠉⠓⣦⡶⠋⠁⠈⣳⣀⡀
⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠈⠙⢦⡀⣴⠁⠱⡀⣠⠞⠉⠈⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡴⠋⠀⠀⣀⡀⠀⠈⠳⡄⠀⠀⠀⠀⠀⣿
⠀⠀⣀⠴⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠃⠀⢰⠋⠉⠙⢷⠀⠀⢻⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⢤⡀
⠴⠋⠁⠀⣠⠖⠒⠶⣤⠼⠒⠲⢦⡀⠀⢸⡀⠀⠹⣄⠀⢀⡼⠁⠀⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠳
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢷⡀⠀⠉⠉⠉⠀⠀⣰⠋⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣽⠳⢦⡤⣤⠶⢻⡅
⠀⠀⠀⠀⠀⠙⠳⢦⣀⡤⠖⠋⠁⠀⠀⠀⢰⠇⠀⡾⠀⠸⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣟⡀⣸⠃⠀⠀⢻⡀⣘⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣉⣹⣏⣀⣀⣀⣈⣿⣉⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢀⣰⣟⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡖⢲
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⣲⡿⠋⠈⠉⠉⣽⠏⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⣾⠏⠀⣀⣤⡀⠀⠀⠀⢀⣀⣀⠀⠈⣻⡁⠀⠀⠀⣠⡴⠖⢲⠀⠀⠀⠀⢀⣴⠀⠀⢠⡾⢋⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣠⣿⠏⣠⠞⠁⣼⠏⠀⢠⡾⠋⢁⡼⠀⡼⢁⣿⠀⢠⡾⢋⣠⠴⠋⣀⠤⠀⢀⣾⠃⠀⠀⢸⣷⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢀⡴⢻⣯⠞⠁⠀⣼⠏⠀⢠⡿⠒⠚⠁⢠⠞⢁⡾⠃⢀⣿⠋⠉⠀⡠⠚⠁⠀⠀⣼⡇⠀⢀⡴⠋⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⣠⠞⠁⠸⠋⠀⠀⢸⡏⠀⣠⠛⢧⣀⠤⠖⠁⠀⣾⡃⣠⠋⠙⠦⠖⠋⠀⠀⠀⠀⠀⠹⠷⠖⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠘⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣠⠤⣄⠀⢀⡤⠶⢶⣄⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⢀⡞⢁⠏⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⣼⣯⠞⠉⠀⠀⣼⠀⣏⡤⠀⠀⢻⡇⢀⣾⡝⠀⠀⠀⣾⢸⡇⠀⣠⡶⠛⡩⠃⠘⣧⠏⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⢀⡾⢃⡤⠞⣻⡆
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⣼⡧⠞⣿⠁⠀⠀⣸⣇⣾⠋⠀⢠⡞⠀⠘⢾⡅⣼⡿⠔⠊⠀⢀⡴⠋⣷⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⡾⡱⠋⠀⢠⡿⠁
⠀⠀⠀⠀⣴⡿⢰⣒⣒⡼⠟⠀⠀⠀⡏⠙⠒⢲⡟⠉⣿⠀⣠⣾⠀⠀⠀⡟⠀⣿⠀⠀⢀⡠⠋⠀⣼⠏⠀⠀⠀⠀⠀⣼⠃⠀⡰⢻⡟⠀⠀⢠⣿⠁⠀⡀
⠀⠀⢀⡞⣿⠇⠀⠉⠁⠀⠀⠀⠀⠀⢧⣀⡴⠟⠀⠀⠈⠋⠁⢿⠀⢀⡜⠁⠀⠘⠓⠚⠉⠀⠀⠀⠻⠤⠔⠋⠀⠀⠀⠹⠦⠊⠀⠀⠀⠀⠀⢿⡇⢀⡜⠁
⠀⠀⢸⢠⡿⠀⢀⡴⢚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣴⠟⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢣⡼⢃⡼⢋⡴⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⡼⠁
⠀⠀⠀⣰⡿⠛⣁⡤⠤⣤⠀⠀⠀⠀⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⠞⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡴⢲⡄⢀⡤⠤
⠤⠖⣿⣟⡴⠋⠁⠀⡠⠏⠀⢀⣼⠏⠀⢀⣴⢋⡴⠚⢙⣷⠀⠀⠀⣠⡾⠛⠉⣿⡿⠁⠀⠀⣼⠋⣠⠖⠋⣹⡇⠀⢀⣴⠞⢉⡤⠃⠀⢰⣏⡴⠋⣴⠋⠀⣠
⠀⣸⣿⣥⣤⡤⠖⠋⠀⠀⢠⡾⠃⠀⢀⣾⣣⠋⠀⢀⣾⠃⠀⢀⣾⠏⠀⠀⢠⣿⠀⠀⢀⣾⣣⠞⠁⠀⣰⠟⠀⢠⣿⠥⠖⠋⠀⠀⣠⠾⣯⠀⠀⠹⣦⡈
⢠⣿⠃⠀⠸⣷⠀⠀⠀⡰⣿⠃⠀⡠⣿⡟⠁⠀⠀⣾⠃⠀⣠⣿⠃⠀⢀⡴⢻⡇⠀⣠⣿⡿⠁⠀⠀⣼⠏⠀⡴⣿⠁⠀⠀⢀⡴⠊⡁⠀⣿⠂⣠⠀⢸⡧
⠸⠏⠀⠀⠀⢿⣀⣠⠞⠁⠙⠒⠊⠀⠛⠀⠀⠀⠀⠿⠤⠖⠁⠙⠦⠒⠉⠀⠘⠷⠚⠁⠟⠀⠀⠀⠀⠻⠤⠊⠀⠙⠤⠤⠚⠁⠀⠸⠥⠴⠋⠐⠧⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡄⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢁⡠⠄⠀⠤⣀⠁⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡔⠁⠀⠀⠀⠀⠀⢣⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡁⢸⠁⠀⢄⡀⠀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠣⣀⠀⠈⠉⢁⡠⠎⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡴⠈⠉⡉⠉⢉⠀⢢⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣇⣀⣈⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣨⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⣿⣿⣶⣤⡄⠀⠀⣀⠀⣤⣤⣴⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⢿⣿⣿⡿⠋⠀⢀⣼⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⣤⣴⣦⣤⣤⡙⣄⣮⢦⠤⠚⢉⡱⢄⡈⠑⢏⣤⡶⠋
⠀⠤⠀⠀⠀⠀⢀⣀⣤⢤⣤⣤⣶⣶⣶⡾⠿⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠻⠙⠈⠀⠛⠲⣤⣤⣘⡉⠽⠛⠉
⣠⣤⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠿⠟⠛⠉⠁




⣀⣀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡾⠍⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣼⣿⣷⠀⢸⠡⢀⠀⠐⢈⡇⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣷⡁⣿⣿⢀⣄⢺⡔⣇⢀⠄⠉⡓⠀⠀⠀⠀⠀⠀⠀⠸⠟⠿⢿⣶⣽⣿⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠂⠋⠉⣙⢣⣿⣿⣸⡿⠘⣿⣆⡼⠠⣀⣉⡀⡀⢀⠀⠀⠀⠀⠀⠈⣲⡇⣶⡼⣿⣿⣧⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⣿⢇⣴⣶⣬⣅⣬⡴⠏⠉⡄⠈⢀⡑⠒⠆⠀⠀⠀⢨⣿⡾⠿⠿⢶⣿⣿⡎⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠻⢿⡖⣿⢸⡿⠿⢿⣭⣡⢦⣿⣿⣛⠋⠉⠑⢠⠀⢀⠙⠚⣿⠿⢿⣟⡛⢷⡽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣤⣶⡷⣟⡘⢧⡀⠌⣠⡿⠟⠛⠉⢻⡉⠹⠓⠲⠶⢦⡤⠴⢁⡤⠴⠀⢀⡾⣧⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠈⢀⣠⣾⡈⠞⠷⠂⠥⢣⣎⣷⡿⡏⠁⠀⠀⣀⣀⣧⣀⠀⠀⠀⠀⠠⠀⠀⠃⣀⣶⠋⠐⠇⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⣴⡟⠉⡀⠈⢙⡫⢊⣄⣴⡿⢿⡦⠀⢀⡠⠼⠿⣿⣿⠿⣯⣷⣿⠶⠚⠚⠊⠉⠉⢻⣧⣤⣄⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠉⣽⣐⣁⣈⢉⣠⣴⡟⠃⠁⢀⣸⠶⠖⠁⠀⠀⠀⠈⠻⣆⠻⢟⡽⠄⠀⠀⠀⠀⣀⡴⢿⡾⠾⠏⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⢹⣏⢨⣜⣈⣤⣼⠗⠢⠀⢸⣟⠈⠀⠀⢿⠀⠀⠀⠀⢿⡄⠺⢁⣀⣤⣤⣤⣞⠁⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⢿⡋⠉⠉⠀⠀⠀⢰⡿⣿⡅⢲⣦⣼⡇⠀⠀⠀⢸⡷⠖⠛⠉⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠉⠿⣠⡾⠛⢆⠉⠒⠀⠐⠒⠉⠀⣿⡟⠠⣽⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢃⡀⡻⢸⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡟⣸⠆⠈⢋⣀⣀⡀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⢩⣴⠉⣰⠀⠈⠛⠉⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡿⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⣈⣉⡉⠛⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠩⠄⠀⠒⠀⠬⣙⠲⣄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠙⠂⠱⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⡲⠋⠉⢻⡉⠙⠓⡲⢤⡀⠀⠹⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠋⠀⠀⣀⣀⣉⠑⠀⢠⢡⡈⠳⢄⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⣭⠀⠀⣠⢤⣌⠁⠀⠈⠙⠁⢲⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠙⠀⠀⠀⠈⠁⣐⢢⡴⡁⠤⠎⣰⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⡇⠓⠈⠀⠀⠀⠀⠑⠤⠔⠻⢣⠋⠁⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠸⣟⣿⠞⠀⠀⠀⠀⠀⠓⣹⢠⠂⠺⢒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣼⠦⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⢤⡀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡴⠚⠁⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⣦⠖⠁⠀⠀⣠⠔⠋⠘⠲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⢁⡜⢷⠀⢀⡤⠊⡡⠔⢁⠴⠋⠀⠈⠉⢛⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠉⠉⠉⠉⢩⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⡽⠁⡑⠋⡄⠘⡇⠉⡠⠊⣠⠞⠁⠀⠀⠀⣠⠖⠉⢀⠀⠈⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⣀⡀⢸⠀⠀⠀⠀⠀⠀⡼⠀⢀⡞⠀⡰⠃⡼⠁⠀⠀⠜⢁⡜⠁⠀⠀⠀⣠⠞⠁⢀⠀⠈⢷⡀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠉⠁⢸⠀⠀⠀⠀⠀⡼⠁⢀⡞⠀⣰⠃⠐⠁⠀⠀⠀⣠⠏⠀⠀⠀⢠⠞⠁⡀⠀⢸⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡰⠁⢀⡞⠀⠀⠛⠉⠉⠉⠉⠙⠓⠃⠀⠀⠀⣰⠃⠀⠠⡇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠘⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡇⠀⠀⠙
⣤⠄⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⣓⠒⠒⠊⣉⠉⠉⠉⠳⡄⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠯⠭⢍⣈⡛⠛⠉⢉⣉⣉⠁⠀⠀⠀⠀⣻⢤⣀⠀⠀⠛⠀⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣏⣉⣉⡁⠄⠀⠀⠀⠀⠉⢸⡏⠙⢶⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⣶⣠⣤⣆⠀⢸⠇⠀⢸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢻⡆⠀⠀⢀⡴⠛⣉⡉⠙⢷⣄⣠⡾⠋⠉⠉⠛⢶⡀⠀⠀⢰⡟⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⠁⣼⠋⠁⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⠀⠀⣿⡀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⠀⠀⠘⢷⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣼⡛⢷⣄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡾⢛⣧⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⣷⡀⠙⢷⣄⠀⠈⠻⢦⣄⣠⡴⠟⠁⠀⣠⡾⠋⢀⣾⠃⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠈⢷⡄⠀⠙⢷⡄⠀⠀⠉⠉⠀⠀⢠⡾⠋⠀⢠⡾⠁⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠻⣦⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⡀⢀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣤⣤⡀⠀⣀⣀⡀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⣦⣴⠟⠙⠋⠀⡀⠀⠹⠟⠉⠉⠹⡾⠋⠀⠀⠙⡷⠿⠛⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢀⣤⡶⢦⣅⣠⣇⠀⣼⡏⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⣿⣁⣤⠄⠀⣽⠃⣸⣿⢁⣤⢀⣄⢳⣧⡀⣠⢶⠀⠀⡄⢾⡭⠁⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⠉⠀⠀⢰⡟⡰⢹⣧⢾⣃⡿⢊⠞⣟⣰⡟⣡⡄⢸⣃⠼⣷⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠘⠟⠁⠘⠃⠈⠉⠛⠋⠀⠉⠈⠛⠋⠀⡈⠁⣴⠟⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣶⡦⠀⠀⠀⠀⢀⣤⡀⠀⣠⣦⢀⡀⣀⠀⡄⢠⣶⢼⣿⢀⡀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢰⡇⢠⠋⢰⡇⣼⢧⡿⣾⣡⡟⣸⢧⡟⠋⡰⠋⣿⢁⣼⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⣾⢇⠷⣤⡾⠁⣿⡼⠁⠿⠻⠷⠃⠀⠓⠋⠀⠀⠻⠟⠋⠀⠀⢀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠂⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣴⡀⠘⠃⠀⠀⠀⠀⠀⢰⣇⢾⡷⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣿⠇⠀⢠⡆⢀⠀⠀⠀⠈⠁⠈⠁⣋⠀⠀⠀⠀⠀⠀⣿⡇⢸⡏⣽⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢰⣿⣀⣴⠟⠀⠛⠀⠀⠀⣀⠀⣠⣤⠇⣤⢀⡄⢰⢿⠆⣿⡁⣸⣿⠁⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡛⠁⠀⣾⠃⣰⣟⣸⡏⣸⢃⣾⣰⣷⢺⡧⣿⣋⣼⣽⡏⠁⣿⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⡟⢷⣤⠾⣿⠞⠸⠏⠸⠟⠻⠋⠛⠉⠁⠀⠀⠈⠁⠻⠞⢀⣼⡿⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⣀⠀⠐⠛⠋⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⢀⣠⣾⣦⣀⣴⠞⠻⣷⣤⣀⣤⡶⠟⠙⠿⠶⠟⢿⣆⣀⣀⣀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉





⠠⠀⠄⠄

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣄⣀⡀
⠀⢸⣭⣙⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣷⣦⡁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⠛⣿⣿⣷⣤⣘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⡇
⠀⠀⠹⣿⡿⠀⠸⣿⣿⡿⢿⣷⣌⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠋⠉⠘⣏⣡⣴⣾⣿⣿⣿⣿⣃⣀⣀⣉⠉⠉⠉⠁
⠀⢠⡀⠹⠇⠀⠀⢹⣿⠃⠘⣿⣿⣷⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢟⣡⣶⣿⣷⣿⠟⣫⣿⣿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⢸⣦⠀⣠⣾⡄⠀⡟⢀⠀⣿⣿⣿⣿⣧⡙⢆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⣁⣤⣯⣭⣶⣶⣾⡿⢻⡾⢟⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣾⣿⣿⣧⠀⢀⣾⡀⣻⡏⢸⣿⣿⣧⠈⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣠⣾⣿⡇⢛⣀⢸⣿⣿⣿⣧⢰⠀⠀⠀⠘⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣿⣸⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠙⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⡿⠟⣻⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⣼⣷⣶⣶⡶⠶⠦⣤⣀⡀⠀⠀⠉⠋⢸⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣶⡷⡿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡟⠀⠀⠀⠀⠀⣽⣿⣿⣷⣿⣿⣿⣶⣮⣽⣓⠄⠀⠀⠀⠙⠿⡿⢡⣿⣿⣿⣶⣿⣿⣿⣧⣼⡆
⠀⢸⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡟⢠⣿⠁⠀⠀⠀⢀⣾⣿⣿⣟⠉⠹⣯⣽⣿⠟⢿⣿⣷⣦⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣯⣽⣽⣿⣁⡸⢿⣿⣿⣿⣿⡗⢀⡿⠃⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣶⣼⣦⣤⣤⣤⣿⣿⣯⠃⠀⠀⢀⣸⣿⣿⣿⣿⣭⣭⣭⣭⣽⣛⡁
⠀⠀⠀⠀⠈⠉⠙⡛⣻⣷⣦⣏⠐⢹⠧⠟⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠉⠹⠟⠛⢛⠠⠤⠅⣈⠉⠉⠛⠻⠇
⠀⠀⣀⠤⢐⡒⣚⣓⡛⠟⠉⠉⠳⠎⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠙⡇⠀⠀⠞⠁⠸⣯⣽⣶⠖⠈⡀
⠀⠐⡥⠀⠘⣧⣿⣿⠏⠀⠠⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣲⠁⠀⠀⠀⢄⡐⠛⠛⠀⠀⠀⠐
⠀⠀⠒⠠⠀⠀⠉⣢⠤⠌⠒⠀⠘⣆⠀⠐⠀⠀⠈⠙⠻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢢⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠐⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⢈⡿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⠤⠔⠊⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢣⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠙⡆⠀⠀⠀⠀⠀⢠⡄⠄⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣤⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠠⠴⠤⠥⠆⠠⠤⠀⣒⡂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⢉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣯⣽⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣭⡍⠉⠛⠛⠿⢿⣿⣿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⠟⠀⠀⣠⣤⣶⣟⣷⣦⡀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⡀⠀⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡷⠀⠈⠙⢻⣾⠛⠋⠀⠀⢀⣤⣾⣿⣿⠏
⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⠿⠛⢁⣤⣶⣾⠏⣻⣶⣄⠀⣴⣿⣿⡿⠛⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⢸⣿⣿⡿⢀⣿⣿⠟⠀⣿⣿⡟
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⣒⣉⣩⣭⣭⣭⣍⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣉⣥⣶⡾⠿⠛⠛⠉⠉⠉⠉⠉⠙⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⡿⠃⠀⠀⠀⠀⠀⠀⣤⣾⡉⠛⡛⠿⣿⣿⣿⣿⣿⣿⣿⣟⢷⡍⠙⠇
⠀⠀⠀⠀⠀⠀⢀⠎⣰⡿⠁⠀⠀⠀⠀⠀⣠⠛⢿⣿⣿⣶⣧⣀⢹⣾⣿⣿⣿⣿⣿⣟⡼⠃⠀⡖
⠀⠀⠀⠀⠀⠀⡼⢠⣿⠃⠀⠀⠀⠀⠀⣴⣡⣄⣤⣬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟
⠀⠀⠀⠀⠀⢀⠇⣼⡏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠉⠉⠉⠛⠉⠁⢣
⠀⠀⠀⠀⠀⠸⢀⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⣈⣇
⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠀⠀⠠⠞⠋⣙⣛⠛⠛⠁⠀⠀⡼⢛⣹
⠀⠀⠀⠀⠀⠈⠙⠛⠤⢄⣀⡀⠀⢸⣿⣿⣿⣿⣽⠏⠀⠀⠀⢤⡾⣿⡿⠓⠀⠈⠀⢰⣷⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠉⠟⠛⠁⠀⠀⠀⠀⠀⢈⠉⠁⠀⠀⠀⠀⠀⢇⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⡀⠀⡀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⡅⣈⣠⡽⣿⡯⣄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⠟⢁⣠⠼⠓⠒⢦⠀⠀⠀⠀⠀⢀⣴⣿⣭⣭⣭⡿⢀⠏⠛⡆⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⢻⠀⢿⠁⠀⣴⢲⣠⠷⠶⣄⠀⠀⠸⣿⢭⣛⣋⠿⡀⣾⠀⠀⡇⠀⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡸⠀⠸⠀⠀⢻⣿⠃⢠⣦⣈⣦⠀⠀⠙⠶⠖⠒⠚⡸⠏⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢋⢻⠿⢧⠀⠀⠀⠀⠀⠁⠀⢸⠉⠑⠢⠄⣀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣾⣤⣦⣸⣷⡄⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡏⠉⡽⠉⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⢦⡀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣇⡞⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢀⡠⠤⠤⠔⠚⠉⠉⠉⡇⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢳⠀⢹⠀⠀⠀⠀⠀⢠⡏
⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⣣⠀⠀⠀⠀⠀⢸⢀⠸⡄⠀⠀⠀⠀⠸⡍⠑⠢⢄
⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡾⠀⠀⣷⠀⠀⠀⠀⠀⢳⡀⠀⠀⠱⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⡇⠀⠀⡟⣇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⠄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡠⢴⡏⠀⠀⠀⠀⠀⢸⠀⠀⢰⢡⢻⡀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠉⠀⡾⠀⠀⠀⠀⠀⠀⡞⠀⠀⠎⠁⠀⢧⠀⠀⠀⠀⠀⠀⠱⡄

⠀⠀⠀⠀⠀⠀⠀⢐⡿⠟⡒⠀⡀⡄⡐⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢴⠀⣖⣩⡖⣦⠁⠡⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⣨⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀⠀⠀⠀⠀⠀⠠⠔⠉⠀⠀⠀⠀⠠⠀⡄
⢼⡀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠁⠀⠀⠠⡆⢀⠔⠀⠀⠀⠀⠀⠋⠛⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⡖⠠⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣘⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠉⠀⣠⡤⠀⢼⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠾⠛⠿⠄
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠐⠦⠀⠀⠈⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠰⡉⠑⢦⣀⡤⠁⠢⠂⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡄⠋⠀⠹⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣨⣟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢖⣲⡞⠒⣶⠖⢶⣟⢒⡖⣖⢒⡖⣶⢲⠒⢶⠖⣒⠀⠀⠀⣠⢀
⡀⠀⠀⠀⣀⢀⠀⠀⢂⠀⠀⠠⣌⣩⣇⣐⣟⣤⣸⣿⣸⣇⣿⣸⣧⣉⣼⣀⣼⣄⣚⠀⠠⠵⣞⣿⠃
⠀⠀⠀⠀⣿⡿⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠
⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡌⡀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠧⠀⠄⠁
⠠⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠁⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠈⣶⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⣐⠋⣀⠦⡄⣇⠃⣖⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠠⣈⠀⠈⠹⢡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⠀⠀⠀⠀⠀⠀⣀⠤
⣰⠄⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠿⠿⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠅
⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠕⠀⠀⠀⢈⣺⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣷⣦⡀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠋⠉⣉⠭⡭⢍⡉⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⢀⠎⡡⠼⠹⢤⡙⡆⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⡀⠓⢲⢰⠒⠃⡸⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠳⣄⡸⢼⣀⠴⠁⠀⠀⢠⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠛⠶⠶⣦⣤⣤⣬⣭⣤⣤⠴⠶⠶⠛⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣴⠞⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⡟⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢸⣿⣦⣄⡀⢀⣠⡴⣿⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣴⡇⠀⠈⠙⠋⠁⠀⣿⣤⣤⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠞⢛⣿⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⢹⡟⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⣠⡾⠋⠉⠙⢷⡜⢷⡄⠀⠀⠀⠀⣠⡞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⣆⠙⣦⡀⢀⡼⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠻⠟⠁⠀⠀⠀⠀⠀⠘⣇⣠⡴⢦⣄⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡸⠇⣽⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣈⣛⢲⣆⣀⣰⡖⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣋⣁⣀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⢲⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢀⠹⡆⢀⠀⠸⣆⠱⣾⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠈⠀⠀⠀⢡⣾⣇⡀⠻⠑⠈⠋⠿⠇⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢀⣠⣄⣤⣴⣶⣿⠗⠒⠀⢤⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠙⣿⡿⠛⠁⠀⢠⠀⠜⣻⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣠⡴⠆⠰⢀⣿⡇⡇⠀⠘⡄⢧
⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠂⠘⣡⡎⢀⢼⣿⣷⣿⠀⡇⣧⢸
⠀⠀⠀⠐⢆⡴⠲⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⠀⠐⠘⢿⡀⢉⣾⣿⣿⣿⡇⠙⠳⢸
⠀⠀⠀⢐⡬⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⡄⠀⠄⣼⠇⣼⣿⣿⠇⢿⠇⠀⠀⠈
⠀⠀⠀⠘⡇⠀⠀⣸⣿⣿⣿⡷⣤⣄⠰⠄⠐⠒⠀⠀⡀⠀⠀⠀⠑⠄⠀⠠⢠⣿⣿⢿⣿⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠿⢻⣏⣩⠀⠀⣟⠀⠀⠀⠀⠀⠸⢋⠄⠀⠄⠀⠀⠀⠀⣀⢵⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠘⠀⣶⣶⣶⠶⡶⣄⣈⣈⣴⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢳⡀⠃⢉⠙⣡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠁⠂⢘⣛⣫⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⡇⠀⠀⠀⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⠀⠀⠀⠀⣹⣿⠟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠒⠚⠀⣻⣿⣋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣿⣿⣥⣇⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⢰⡄⢀⣠⣼⣿⣿⣿⣭⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢢⠀⠀⠙⣷⡵⣦⣀⡀⣸⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡆⠀⢧⣠⡖⣿⣿⡏⢿⡇⢻⣿⢃⣿⣷⢿⣿⣷⡆⢀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⣿⠇⢸⡀⣿⣾⡷⠞⠛⣾⣿⠿⣦⡈⢿⡇⢼⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⢨⠆⢿⣿⠁⠀⢰⠟⠁⠀⠀⠛⢿⡇⢀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠰⡄⠸⠀⣰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠀⠁⠀⠀⠀⠀⠀⠐⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⠀⢈⡿⣇⠀⢸⣷⡄⢹⡏⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣼⠧⢿⡄⢸⡇⠹⣾⡇⠀⠘⠋⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠈⣿⡆⠀⠀⣴⡆⠀⣰⣦⠀⠀⠀⠀⢠⣶⠄⠈⠉⠀⠉⠉⠉⠉⠀⠈⠁⠀⣴⡿⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⣿⠀⢾⣿⠷⠶⣿⡷⠆⢾⡆⠰⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠴⢾⣿⠒⢶⣿⡧⠀⢸⣿⠀⢸⣿⠇⢀⣾⡆⠀⣿⡇⠀⣰⣿⠀⠀⣾⡆⠀⣴⡿⠶⣾⣿⠋⢁⣶⡾⢲⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⠀⣿⣟⠀⢸⣿⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣰⣿⡇⢸⣿⡇⠀⣿⣿⠀⢸⣿⣀⡼⠀⡼
⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⢿⣧⡴⢻⣿⣀⡾⣿⣀⣸⢿⣇⡴⢿⣇⣠⠿⠿⠶⠋⣿⣇⣸⢿⣧⡼⢻⣿⠀⡼⢿⣥⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠈⠉⠃⠀⠀⠀⣠⠖⠲⣦⠐⣶⠒⠶⠀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⡇⠀⠀⠈⠉⠉⣉⠀⠀⠀⣿⠀⠀⣿⠀⣿⠚⠂⠀⠀⠀⢈⠉⠉⠁⠀⢰⣷⢀⡀
⠀⠀⠀⢀⣤⣴⣶⣤⡀⠀⠈⠉⠁⠀⠀⠀⠐⠋⡡⠂⠀⠀⠈⠓⠚⠋⠐⠛⠂⠀⠀⠀⠀⢦⡉⠃⠀⠀⠸⣿⠟⠃⠀⣀⣀⣀
⠀⠀⣰⣿⡟⠉⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢀⡀⠀⢠⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⢸⠄
⠀⢀⣿⣿⠀⠐⠚⢡⣤⣴⣷⣄⣀⡀⠀⠀⣀⣀⠀⣀⠀⠘⣿⡟⠃⢺⠟⠀⢻⣿⠛⠀⣀⠀⠀⢀⡀⠀⠀⢀⠀⢸⣿⣃⡠⠊
⠀⠸⣿⣿⠀⠀⠀⢸⣿⠈⢹⠋⣿⡇⠀⣼⡿⠉⢹⣿⡇⢀⣿⡇⠀⣿⡇⠀⣿⡟⠀⢸⣿⠁⠀⣿⡇⠀⣾⡿⠛⢻⣿⠁⢀⣾⡟⢹⡆⢠⡄
⠀⠀⢿⣿⣄⠀⢀⣾⣿⠀⣸⠀⣿⡇⠀⣿⡇⠀⣾⣿⡄⢘⣿⡃⠀⣿⡇⠀⣿⡇⠀⢺⣿⠀⣰⣿⡇⠀⣿⡇⠀⣾⣿⠀⢸⣿⣤⠞⠁⡼
⠀⠀⠀⠙⠛⠛⣋⣽⣿⠔⠁⠀⠘⠿⠶⠛⠻⠛⠀⠿⠧⠞⢿⣧⡴⠻⠷⠴⠻⣷⣤⠟⠛⠛⠁⢻⣷⡤⠿⠷⠞⠹⣿⣄⡼⠻⠷⠤⠞⠁
⠀⠀⠀⠀⣰⠋⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢧⣀⣼⡿⠁⠀⠀⢠⣤⡀⣷⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣴⠆⣀⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⣭⡿⠢⣿⡦⢽⣧⣹⣷⡄⠄⠀⠀⠀⠀⢀⣀⣴⣟⣰⣟⣠⣿⠧⢿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠱⠟⠱⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡎⠿⡆⠻⠷⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠛⠃⠒⠒⠊⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⣀⣠⢠⠤⠄⠀⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠶⠛⠉⣀⡠⣤⣶⣶⢊⣤⠀⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠾⠋⠈⠒⠔⠿⠗⠛⠛⠁⠛⠉⠀⠘⣆⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢿⡀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡸⡇⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⢀⢄⡀⢿⠇⠈⡉⣙⢷⡄⠀⠀⠐⠚⣛⠉⠀⣈⣃⢑⣀⠀⠀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣾⣷⣿⠀⠋⠽⠋⠠⣿⠀⠀⠀⠙⠿⠙⠂⠸⣿⣿⡟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣻⣇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠸⠧⠀⠂⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⣶⣶⣶⠄⠀⠀⠀⡘⠛⠋⠀⠀⠀⠀⠀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠘⣆⠀⠀⠉⠉⠁⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⠁⠀⠀⠀⠀⠈⣷⣤⣀⣀⡀⠀⠀⠀⠀⢣⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠁⠀⠀⠀⠀⠀⣠⣿⠛⠛⠉⠀⠀⠀⠀⠀⠈⠋⠸⣆⠘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⢀⣀⣤⡴⢶⣾⣿⡿⢹⡇⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠘⠶⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣴⣾⣿⡿⠀⠚⠉⣁⢈⠺⣿⡿⢡⣿⣿⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⡠⠉⠙⠛⠻⠿⠉
⠀⠀⠀⠀⠀⣿⣿⡟⢃⠀⠀⣉⠤⠄⠀⠃⠀⡾⠁⡿⡴⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠉⠁⠀⢸⡀⠁⠀⣤⣶⠄⠂⠸⠁⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⡇⠀⠉⢀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⠀⠸⡆⢠⡟⠁⠀⠀⠀⣀⣠⠤⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⣼⠇⠀⠀⠀⢿⡞⠀⠀⠀⠂⣹⡿⠛
⠀⠀⠀⠀⠀⣠⣾⠆⠇⠀⠈⢹⠃⠸⣧⡀⠀⠈⠁⠀⠀⠀⠸⠟⠁
⠀⠀⠀⢠⣾⡿⠁⠀⠈⢆⢀⣿⠀⠀⠹⣷⡀⠀⡄
⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠈⠑⠀⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠂⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡋⠀⠈⣻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣶⣶⡶⠶⠶⠶⢶⣶⣶⣶⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⣆⠀⠀⠀⠀⠀⢀⡾⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠁⠀⠈⠙⠶⠤⠴⠞⠋⠀⠀⠉⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠶⢿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣀⣴⣶⣦⣴⣶⣶⡄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣼⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠉⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧⣤⣬⣽⡿⠋⠀⠀⢄⣀⠀⠀⠀⡀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⠟⠁⠀⠀⢠⣴⡤⠀⠀⢠⡾⢧⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣌⣀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⣿⣿⣿⡇⠻⢿⣦⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣭⣥⠇⠀⠀⠀⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⣿⢷⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⠙⣿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠔⠛⣀⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠋⠁⠈⠑⢄⠑⠦⡀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠀⠀⢠⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠻⠀⠀⠀⡀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡀⠀⢰⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢱⡄⡾⠀⠀⠀⠘
⠀⠀⠀⠀⡴⠋⠀⠈⠙⠢⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⣠⠾⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⠏⡇⠀⠀⠀⠀⡇
⠀⢀⠞⠀⠀⠀⠀⢀⡠⠚⢯⣻⣷⣰⠟⠁⠀⠘⢿⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡜⠀⡇⠀⠀⠀⢀⡇
⠀⠊⠀⠀⠀⠀⠀⠀⠑⢄⡀⠉⠻⠏⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠤⠶⠈⠁⠀⠀⠀⡿⠀⣼⣇⠀⠹
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠉⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡏⠻⣧⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⡀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⡀⠀⠀⠈⠢⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣁⢈⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣠⡾⠋⢳⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡴⠋⠀⠀⠀⠈⠀⠈⠛⠁⠀⠀⢠⡿⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡞⣸⠁⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣿⢁⠞⢀⣤⢦⡄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⠃⠀⠀⢀⡴⠒⣆⢠⡟⠀⣿⠀⣿⠃⢠⡾⠁⣰⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡟⠁⣠⣄⠀⢸⠃⠀⡿⢈⣷⣠⡷⠊⣿⣀⣾⡧⠞⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⡴⣹⠇⢠⡟⠦⣤⠗⣿⢁⡾⠀⢀⣿⠁⢿⡄⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣏⡜⠀⡿⢀⣾⡇⣠⠏⠀⢿⠞⠁⣰⠋⣿⠀⠈⠛⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠛⠀⠀⠷⠞⠀⠉⠁⠀⠀⠀⠀⠀⢯⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⣀⡀⠀⢀⣀⠸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⠀⣠⠞⠀⡆⠀⣶⡄⠀⣿⠀⣴⠖⣿⠀⣿⣦⠀⢸⢣⡟⣉⡿⠰⣏⠉⠁⢻⣆⠀⠀⣚⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠁⢻⣞⠁⠀⠐⡇⢠⡇⠻⣆⣿⢸⡇⣰⢿⡆⣿⠘⣧⣼⠸⣏⡉⣠⠄⡙⣷⠀⠀⢻⡆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢿⠙⠷⣤⠀⡇⠘⡇⠀⠙⠟⠘⠓⠁⠘⠁⠋⠀⠈⠋⠀⠈⠉⠁⠀⠉⠋⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠁⢡⡿⣗⢠⣥⣎⢹⡙⢮⣲⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣾⡷⠟⠃⠛⠁⠠⣕⡾⢀⢈⡘⠿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠒⢃⠀⠀⠀⠀⠀⠀⠙⢮⣬⠑⡝⢦⡻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣷⣌⠳⣝⢦⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠾⢋⡤⡀⠙⠻⣾⣿⢦⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢘⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢁⣀⣠⣃⣠⡀⢱⡔⠇⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢸⡀⠀⣀⣼⣧⣶⠲⠄⠀⠀⠈⠻⢯⣽⣟⡿⣾⣷⡋⠻⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⣧⣿⣿⠿⡿⡿⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠠⡏⡄⠀⡟⠉⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣠⠁⢠⠔⣿⠉⢻⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢗⣼⡇⢠⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠏⢸⣯⢳⣀⠀⠁⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⣼⡴⡿⣏⠑⢸⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣿⠒⠿⠀⠀⠀⠀⠐⠛⠛⠋⠉⠀⠀⠀⣴⣿⢀⡆⢿⠠⢰⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠠⠀⢠⠇⠀⢀⠀⠀⠈⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣟⢈⡷⠈⠳⣼⠁⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠁⠀⣊⠠⠀⠘⠀⠀⠀⠀⠀⠸⠀⠈⠓⠒⠠⠤⠤⠴⠖⠋⠁⠀⣿⣿⣜⡎⢷⡇⠀⠀⠀⢌⠑⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⢀⢂⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⠀⢺⣿⠆⠘⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⢠⡀⣠⣾⣿⣿⣿⡟⠀⢸⣿⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⡀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠴⣿⣿⣿⣦⣶⣿⣟⠙⣿⣿⡟⠀⠀⠸⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡀⣠⠴⠂⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣶⠿⠋⠀⠀⠀⠀⠻⠽⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠁⠀⢆⠀⣠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⢲⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢆⠠⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠆⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⢈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠾⠿⠿⠿⠿⠷⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⢀⠌⠡⠄⠀⠀⠀⠀⠀⠈⠉⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠡⠨⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣀⡤⠤⢒⡒⠚⠉⡉⢉⣟⣙⡒⠦⣄⡴⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠣⣒⣉⣠⠏⡓⠋⠉⠉⠉⠉⠉⠀⠍⠉⢲⠆⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢹⠈⡠⢀⡀⠄⠀⠀⠀⠀⠀⠀⣥⡢⠘⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⣳⠀⠛⠆⡰⢀⠀⠀⠀⠠⠀⠛⠁⠀⣷⠀⠰⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡍⠀⣀⣀⡳⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⢳⡤⠀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⢀⡇⠀⠁⠂⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀⣼⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⣽⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢈⠗⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠁⠀⠀⠸⡀⠀⠉⠳⡦⠤⠤⠤⠤⠖⡺⠋⠀⠀⡜⠀⠀⠀⠀⡝⠢⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠙⡄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⡓⠒⠒⠲⡏⠀⠀⠀⡜⠀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠓⢤⡀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠘⠦⣀⠬⣀⡀⣀⣀⠨⢆⡠⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠄⠀⠀⣠⣼⠀⠀⢰⡋⣉⡷⠀⠀⡴⠒⠀⠐⡆⠀⠀⠀⠀⢸⠀⠀⡴
⢰⠁⠀⠀⠀⠀⠀⠀⠈⢦⠀⡎⢩⡀⡀⣀⡽⣸⠀⢠⡔⠁⠀⠑⢄⠀⢸⠉⠉⠩⡇⠀⠀⠀⠀⠘⢆⡼
⡆⠀⠀⠀⣀⠤⠤⠒⠒⢺⢿⡀⠸⠀⠀⡙⠀⡆⠀⡇⠰⠐⠀⠀⢸⠀⢨⠐⠢⠀⡇⠀⠀⠀⠀⠀⠀⣧⠴⠒⠒⠉⠋⠓⠢⡀
⢇⠀⡠⠋⠀⠀⠀⢀⡤⠤⠴⠋⠸⣆⡔⠀⢠⠇⠀⢧⠀⠀⠁⠀⠼⠀⠸⣆⣀⡠⠇⠀⠀⠀⠀⠀⠘⠧⣤⢤⡆⠀⠀⠀⠀⠘⣶
⠘⢦⠃⠀⠀⠀⣞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⡇
⠀⠘⢇⠀⠀⠀⠈⠉⣉⣩⠥⣛⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⠭⣍⣉⡭⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠙⠢⢤⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠶⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠦⠀⣿⡇⠠⣶⡄⠀⣾⡛⠆⢀⣾⡛⠆⠰⣯⠀⠁⢀⣴⢟⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡜⢻⣧⠁⣿⡇⢸⣿⠗⡘⠸⣿⠗⠘⠀⠙⢷⣄⢺⣿⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠙⠧⠤⠞⠀⠀⠁⠀⢿⡇⡌⠻⠷⠁⠀⠻⠷⠁⠀⠀⡄⣿⡇⠛⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠲⠄⠀⣸⣆⢠⡴⠂⠀⠀⣿⠀⣀⡞⡀⠀⠴⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠭⠁⠀⠘⣇⢸⣇⡀⠀⠀⣿⡠⢹⡗⠁⠀⠭⠥⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⠀⠀⠀⠛⠐⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡠⢲⡆⠀⣠⡄⠀⣀⡀⠐⢹⡆⠀⣠⡤⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⡞⠁⠀⣿⠃⠀⣿⣧⠀⢸⡟⢰⣿⢀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⡀⠀⢿⣀⠄⠙⠃⠀⢸⡇⠌⠻⠋⠈⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠃⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀⠀⣀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠇⠿⠀⠧⠇⠽⠸⡅⠼⠷⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⡤⠄⣄⣤⣠⢤⣠⠤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠑⠂⠃⠉⠙⠚⠘⠚⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢻⠭⢭⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠴⠋⣹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢉⠤⢧⢗⡺⡴⠤⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠈⡄⠈⠲⠗⠁⢠⢸⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠁⢡⠀⠀⠁⢀⣈⣈⢀⣀⢀⣀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢷⠀⣤⣤⣤⣤⣴⣦⠀⠈⠓⠬⣽⠫⡿⠙⡭⠥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠶⢿⣓⣛⣤⣟⣓⣺⠄⠀⠀⠸⡵⣛⣇⣹⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣹⣟⣤⣤⣤⣤⣤⣼⠄⠀⠀⠀⣽⠽⡿⢟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡐⠭⢄⠀⠉⠐⡏⠉⠀⡠⠃⢱⣽⣗⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⢍⣉⣀⣀⠤⠇⠀⠊⠀⠀⠈⠺⡯⠛



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠿⢿⡃⢯⠽⢸⠸⣇⠠⠿⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣠⠤⣤⣠⢠⠤⣀⡤⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠒⠛⠘⠘⠒⠉⠓⠃⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣏⣉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣎⡠⠊⢹⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⡡⢧⢷⣲⢧⠧⣈⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⢸⢠⠈⠳⡧⠋⠀⠸⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣀⣀⣀⣀⣈⣀⡀⠀⠁⠀⣀⣁⠀⣀⡀⣀⣐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⠤⣤⣤⣤⣤⣤⣧⡄⠀⠛⠬⠩⠇⣿⡙⢯⡭⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣬⣿⣿⣿⣧⣿⣿⣿⡇⠀⠀⠀⣯⡗⣖⣒⣔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⣿⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⢸⡫⣿⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠁⠎⣒⡒⠒⠒⡞⠁⠀⢀⠞⠙⣕⣿⡾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⣁⣈⡁⢀⣀⣇⣀⠐⠁⠀⠀⠪⢿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡥⠄⠀⠀⠓⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⠀⠂⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⠔⠂⠙⠁⠀⠉⠢⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢀⡔⠁⠢⢄⣠⠴⠊⠉⠘⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡜⠀⠀⡇⠀⣀⠀⠀⣀⣴⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢌⠟⠀⠀⢸⣀⠘⠛⠀⠈⠋⠹⠑⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣤⠌⠀⠀⢄⠀⢀⠔⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠄⣤⠴⠒⢄⣀⠲⠤⡆⡥⠤⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⣀⣀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⢰⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠘⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡘⠀⠀⡹⠀⢱⡄⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉⡨⠄⠀⠀⠀⠙⠲⣐⠠⠀⡼⣓⢒⠢⡇⠐⢼⠈⠒⠛⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠎⠀⡨⠓⠦⠤⢀⡀⠀⠉⠲⣇⠀⢀⡠⠉⠒⠈⠀⠀⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠃⢀⠞⠀⡜⠀⠀⠀⠀⠡⣀⡀⣪⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠁⠠⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠈⠶⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡂⠤⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⢶⣤⡀⠀⣠⣴⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠈⢻⡾⠋⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⢸⡏⠈⢻⡆⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢰⡟⠀⢹⡇
⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠈⣿⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣦⣀⣴⠿⢶⣄⠀⠀⠀⠀⠙⠷⠾⠛⠁⠀⠀⠀⣠⡶⠿⣦⣀⣴⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠈⠛⢿⣦⡀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣴⡿⠋⠁⠀⢀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠉⠻⣦⡀⠈⠛⣷⠀⠀⠀⠀⣾⠛⠁⢀⣴⠟⠉⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠿⠷⠷⠶⣶⣾⡾⠿⣷⠀⠀⣾⠿⢷⣶⣶⠶⠶⠾⠿⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠿⢿⡇⠀⣿⠀⠀⣿⠀⢸⡿⠿⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠀⠀⠿⠶⠾⠷⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣤⡶⠾⠛⠛⠛⠉⠉⠛⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⠋⠀⠀⠀⠀⠀⡠⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⡰⢿⣿⣦⣄⡀⢿⣿⣿⣿⣿⣿⣸⠃⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣌⣄⣤⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡶⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⢰⡿⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣻⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠅⡀⠀⠀⢰⣿⣿⣿⣯⠟⠀⠀⠁⢀⠈⠉⠛⠀⠀⣰⢯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠁⠛⠏⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⡛⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠿⠿⢷⣄⠀⠈⠢⡀⡠⠀⠀⠀⠀⠈⠁⠀⠀⡀⠘⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣶⣶⣾⣿⣶⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠻⠉⠉⣉⣉⣿⠀⠀⠀⠁⠐⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣷⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⡟⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣽⡆⠀⢸⣿⠀⠀⡀⠀⠀⢼⡟⠀⢀⡀⠀⠀⣿⠆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⣿⡆⠀⢰⡿⠀⢠⡄⠀⢰⣆⠀⠀⣿⠁⠀⢸⣿⢀⣠⡟⠀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇⢠⣿⠀⠀⢸⡇⠀⣿⡇⠀⢸⣿⠀⢸⣿⠀⠀⢼⣿⢸⡏⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠘⢷⡠⠀⠈⠁⠸⣿⠀⠀⠀⠙⠀⠸⣇⠀⠀⠉⠀⢸⡇⠀⠀⠀⠉⠈⢿⡀⠀⠀⢿⡇⠀⠀⠙⠀⠈⢿⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃




⣶⣶⡾⠶⠾⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⢸⣷⣶⣶⣶⡀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⠀⠀⠀⢠⣴⡶⠷⠿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⡇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⣿⡎⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢿⣿⢀⣀⣤⣤⣶⣦⣶⣾⣿⣿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣷⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠘⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠰⢶⣤⣤⣄⣠⣤⣤⣶⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣀⣀⣀⣀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣼⡿⣧⡀⠀⠀⣠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣯⠉⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⣀⠀⠀⠀⠀⠀⠁⣀⠈⠹⣷
⠀⠀⠀⠀⠀⢸⣿⠀⠐⠲⡤⠁⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠻⠛⠃⠀⠀⠀⠀⠎⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢶⣴⠞⠛⢿⣆⢀⣤⠀⠀⠀⠀⠀⠀⣸⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣴⣏⣀⣀⣀⣀⣠⣤⡿⠟⠁⠀⠀⠀⠀⠀⣼⡟⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣏⣉⣩⡿⠋⠀⠀⠀⠀⠀⠀⢠⣾⠋⢱⣆⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⡀⠀⢠⠉⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠹⣦⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⠀⠀⡐⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠀⠀⢿⡀⠀⠘⢷⡄⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠘⠀⢸⠇⠀⡸⠀⠘⢻⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⡇⠰⠀⢱⡄⠀⢻⡄⠀⠀⢻⡀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⠀⠀⡇⠀⡆⠀⠀⡇⠀⡇⢸⡇⠉⠛⠛⠿⠿⠾⠿⠛⠛⠁⠀⠘⣷⡀⠀⠈⠃⠀⠘⠃⠀⠀⠀⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠁⠀⠇⠀⠀⠇⠀⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⡀⠆⠀⠀⠀⠀⠀⠀⡅⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⢠⠀⠰⠀⠘⣦⣤⣾⣿⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠙⢿⣦⡀⠠⠆⠀⠀⠰⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣈⣠⣤⣾⡿⠟⣹⡿⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠙⢿⣦⣄⣀⠐⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠉⠁⠀⠀⣿⠃⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢻⣟⠿⣷⣶⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⢿⡆⠀⠙⠻⣷⣦⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠿⣷⣄
⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⣠⣼⣏⡀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣤⣴⠟⠛⠿⠿⠟⠋⠈⠙⠻⠷⢶⣶⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠛⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡤⠈⠀⠀⠀⠐⢂⣤⣀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⠔⢁⡠⣤⣤⣤⣤⣿⣿⠿⣿⢻⡹⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⡎⠰⢁⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠃⠠⣀⠀⠀⠀⠴⠊⠁⠀⠙⣧⢀⡬⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣀⡀⠀⠀⠀⠀⠀⠠⠄⢢⠄⠈⠌⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠂⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢾⠋⠀⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⠁⢀⠀⠀⠉⣀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣄⣀⠸⠤⠤⠔⠀⠀⢀⡴⠋⣿⠀⠀⢑⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⢀⠀⠀⢡⡈⠳⣄⡀⢀⣀⠔⠉⠀⠀⣿⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠐⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢶⡴⠆⠀⠀⢉⡛⢋⡏⠉⠁⠀⠀⠀⠀⣿⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣀
⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠄⠀⠠⣦⢀⡠⣠⠾⢻⠇⢦⠐⠂⠉⠉⠀⡼⠁⠀⠀⠀⠀⠀⢀⠌⠀⠀⠁⠂⠄⢀⠀⠀⠀⠀⠀⠈⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⡶⠂⢤⠀⢤⡀⡀⠈⣹⠐⠀⠀⠀⢀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠈⠀⠀⠀⠈⠐⠢⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢡⠊⣟⠀⢴⡏⠀⠀⠀⠀⠀⠉⠉⠳⠶⠉⠀⠀⠀⠀⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠻⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⢒⡗⠈⠁⢸⡁⠀⠀⠀⠀⠀⣠⠂⠀⡐⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠂⠠⠀⡴⠀⡀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⠤⠤⡐⠀⠀⢸⠇⠠⠀⣀⠠⠒⠁⠀⠀⠁⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠋⠀⣠⣀⢃⣚⠧⠤⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⢔⡶⣷⠄⢰⡏⠀⠀⠀⠇⠀⠀⠀⠀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠐⠒⠂⠠⢠⢀⡤⢨⠛⢋⠙⢀⣀⠌⠈⠃⠤⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣎⣳⠎⠙⠁⢀⡞⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠸⠈⠧⢿⡐⢟⣳⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣤⣤⡶⠂⠸⠀⠀⠀⡠⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠘⠀⠹⣦⣄⠀⠚⠁⣁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠁⠀⠀⢠⠃⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠈⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣡⠀⢀⡜⠁⠀⠀⠀⢸⠀⠀⠀⠳⠤⠤⣄⣤⣄⣤⣀⣀⣀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠰⣾⡁⢀⣒⠠⣄⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⢀⡼⢥⡢⣴⡄⠹⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢀⡄⠀⠅⠀⢠⠹⠏⢹⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢄⠈⠁⢸⣿⡄⠀⠰⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⠀⠠⠂⡁⢘⢻⣶⡇⢠⠀⡆⢀⠉⠐⢤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⢘⣧⣼⠰⠿⠇⢴⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡸⠀⠳⠽⠿⠻⠟⣡⣟⣴⠋⠀⢀⣠⡴⠟⠛⠛⠛⠳⠶⢶⣤⣀⡀⠀⣠⡞⠉⠻⠿⠛⣡⠀⠘⠂⠠⠦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⠀⠙⠦⠵⠖⢂⣤⣚⣩⠏⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠾⣿⣃⣠⡾⢋⡴⢂⠀⠢⠤⠄⣀
⠀⠀⣀⠤⠒⠊⠉⠀⠀⠈⠛⠒⢒⡚⠛⣉⣉⣭⠅⠀⣤⡀⠀⢦⡀⣰⠖⠀⠀⠀⠐⡆⠀⣶⠀⢠⠄⡤⠤⡤⠀⡀⠈⠉⠙⠦⠤⡀⠐⠀⠀⠉⠁⠒⠤⣀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣬⣉⠀⠸⡇⠀⢰⠇⠹⣄⠀⢹⡃⠀⠀⠀⠀⠀⢹⡜⠈⣡⡏⢸⠗⠶⠆⢠⠇⠀⠀⡿⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠞⠀⠀⠃⠀⠉⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠃⠒⠂⠘⠲⠦⠰⢇⣤⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣀⢰⡇⠀⠀⠁⠀⢀⣀⣀⣤⡤⠤⡶⠖⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠶⣶⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⢸⡇⣀
⠇⠐⡧⠴⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠙⠒⠶⢼⠇⡼
⠀⠀⠓⠠⡄⠀⠀⠀⠀⠀⠀⢀⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠚
⠀⡰⠀⠐⠀⠀⠉⠉⠁⠘⠓⠢⡜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⠖⠚⠃⠈⠉⠁⠀⠀⠀⠀⢦
⠜⠂⠀⠉⠉⠉⠉⠀⠐⠠⢀⣀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣀⡀⠤⠒⠈⠉⠉⠉⠉⠀⠒⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⠉⡇⣿⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠱⢌⠀⠀⡇⢠⡇⡿⠠⣧⢠⡤⠠⠶⠛⠛⠛⠓⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡾⢷⡀⠀⠢⢀⣇⠈⣷⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⣿⣿⣷⠆⠙⣆⠀⠻⠇⠀⠈⠁⠀⠀⠀⠀⠀⣄⣴⣠⠴⣶⢦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡸⠂⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣽⢦⣶⡶⡒⠊⠁⢠⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⣿⣿⠓⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣿⡿⠛⠁⠀⣀⣀⣵⣾⡟⡂⠠⠒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢹⣿⡿⠃⣿⣏⡁⢀⣀⠀⠂⣌⢰⡜⢿⣿⣿⡟⠟⠃⠀⢠⣴⣿⣿⣿⣿⠟⠉⠀⠛⠓⢁
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⢗⣾⢿⡱⣆⠘⢿⣟⡼⣻⣇⣸⣿⣿⣣⣾⣿⠇⠃⠀⠀⢠⣿⣿⡿⠟⢻⣿⣿⣧⣶⣦⣻⣟⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡋⠈⠳⢈⢀⠘⡿⡆⢸⣟⣛⣿⣾⣿⣿⣿⣿⣏⠀⠀⠀⢁⣸⣿⠟⠀⠀⠀⠈⣿⣿⠋⠛⢉⠻⠟⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⣄⣖⣠⣐⠞⠀⣼⣿⣿⣿⠾⠄⠀⢻⣿⣿⣦⣀⣴⣿⣾⣃⡀⢤⡄⠀⠀⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣿⣿⣹⣿⣿⡓⣤⣷⣮⣿⠗⣰⣿⡟⢻⢽⡂⠦⠠⣎⠿⣿⣯⣿⣿⣿⣿⠟⠃⠀⠉⢦⡸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣍⠺⠿⠿⠛⡩⠴⠞⠉⠀⠀⠀⠀⠈⠠⠿⠈⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠀⠹⣿⠇
⠀⠀⠀⠀⠀⣿⣿⡏⣻⣿⠿⡏⢞⡧⠀⠀⠀⠐⠀⠀⠀⢸⡆⢟⢡⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⣙⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⠈⢭⠁⣿⡀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠛⠑⠁⢸⣿⣿⡄⠀⠐⢸⠷⣶⣼⣿⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣗⣿⣿⣄⢮⣔⡎⢹⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠈⢠⣼⢻⣿⣷⡄⠀⣦⡈⠁⠏⢉⡝
⠀⠀⠀⠀⠀⢻⣿⣟⣿⣿⣇⠈⢁⠀⡸⣄⠀⠉⠀⠀⠀⣁⡩⠴⠖⠚⠉⢀⣿⣿⣿⣿⣦⣼⣿⣶⣾⣿⣇
⠀⠀⠀⠀⠀⢸⣿⣯⣿⣻⡿⡂⠀⠁⠀⠁⠀⠁⠀⣠⢚⠁⠀⠀⠀⢠⠒⣼⣿⣿⣿⠿⣿⠹⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⣿⣿⣺⣧⢿⡙⠆⠂⠀⠀⠀⠀⢚⠵⠋⠀⠐⢀⠀⠈⣦⣿⣿⣿⢻⣇⠘⠳⢞⡋⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⡻⣿⣿⣿⣿⠆⠀⠀⢀⡔⠃⠀⠀⠀⠀⡠⠐⣸⣿⡿⣿⣗⠈⣿⢦⣌⣉⠁⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⢀⠔⠋⠂⠂⡀⠀⠀⠀⣰⣾⣿⠿⣼⣿⡅⠀⣿⠎⡿⢯⡙⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡶⣉⡀⠜⠣⡁⠿⡩⠡⠚⣿⣿⢻⡶⣿⡄⠙⢷⡿⣷⠄⡀⣻⣶⣿⡿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣝⣧⢫⡂⠀⢸⡀⢠⠰⠃⣾⠇⡸⢲⡿⢿⣦⣉⠛⠛⣏⣛⣿⣿⣿⠋⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⣿⣿⣾⠲⣤⡀⡀⠀⣇⡎⠀⣰⣿⣤⣇⢨⣿⣦⣿⣿⠷⣶⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣢⡌⢠⡄⢙⣧⣀⣿⣳⣿⣘⠛⣷⣯⡛⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⢢⡇⢸⠻⣿⣧⣿⣻⣿⠃⠀⢈⣲⡈⢹⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⢻⣾⣿⣿⣿⣶⣟⣧⣲⣿⣿⣷⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣿⢃⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠢⠄⣀⣀⣀⡠⠜⠱⠻⢄⣀⣀⣀⠤⠔⠒⠈⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢠⡄⠀⠀⣤⢀⣤⣶⣤⡄⠀⣠⣴⣦⣤⠀⢀⣤⣦⣤⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠻⢾⣇⠀⢀⣿⣾⠃⠀⠈⢿⣴⡟⠀⠀⠹⣧⠸⣧⣀⡙⢹⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣠⣸⡟⠛⢻⣿⢻⣆⠀⢀⣾⠛⣷⡀⠀⣰⡟⣀⠈⠉⣻⣾⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠸⠇⠀⠘⠟⠀⠙⠛⠛⠁⠀⠈⠛⠛⠋⠀⠙⠷⠾⠛⠘⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⢦⠰⣆⠐⣄⢲⡀⠀⠀⠀⠀⠀⠀⣤⣄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣱⢾⡷⢼⡶⢿⠦⠤⠤⠤⠤⠼⣿⣿⣿⣿⠷⠤⠤⠤⠤⠤⠤⠤⢾⣿⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⠔⢡⠞⢡⠎⡴⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢰⣦⢀⣤⢰⣶⢰⣦⡄⣴⡄⣶⣤⣶⣄⢴⣦⣀⣶⢰⣶⡶⠆⣠⡶⣦⢀⣴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⢸⣿⠘⣿⣿⣿⠀⣿⡏⢸⣿⢸⣿⣿⣿⠈⣿⣤⠆⢿⣷⣌⠸⣿⣦⡁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣦⢸⣿⠠⣿⠘⣿⡄⣿⣧⡾⠃⢸⡇⠹⣿⠠⣿⣤⡄⢿⣬⡿⢺⣧⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣄⡀⢀⣤⣤⢤⣄⡀⢀⣠⣤⣤⣤⡀⢀⣀⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣀⠀⠀⣹⣿⡋⠀⠀⠈⢻⡞⠁⠀⠀⢙⣿⣯⠀⠀⣀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⣿⡇⢹⡀⠀⠀⢸⡇⠀⠀⠀⡏⢸⣿⠀⠘⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠁⠀⠀⢸⡇⠀⠀⠀⠷⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠍⠁⠀⠀⠀⣈⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⠿⠉⠀⠀⠆⠀⠀⠀⠀⠀⢱⡀⠈⠛⢻⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠿⠋⠁⠀⠉⠀⠘⠳⢄⡀⠀⢀⠊⠀⠈⢹⣯⣍⣙⣿⣿⣆
⠀⠀⠀⠀⣠⢾⡁⡠⠶⠤⠴⠒⡳⢶⡀⠀⠈⠉⢙⡆⠀⠀⣿⣥⠾⢿⢿⣿⣿⡄
⠀⠀⠀⢠⡣⢣⡍⠀⠀⢀⠜⠐⠒⢸⡄⠀⢀⡴⠊⠀⠀⢸⣿⣿⣦⣶⣾⣿⣿⣆⠈⠐
⠀⠀⠀⣾⢡⠎⠀⣀⠀⠀⠀⣠⡤⢄⢻⡆⢸⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⣀⣾⣷⠋
⠀⠀⢰⣷⢸⠀⠀⠀⣤⠀⠀⢁⡤⠚⠀⢻⣼⡇⢰⣶⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡿⢾⣳⣄
⠀⠀⢸⣿⡙⡧⠁⠀⠘⠓⢤⡀⠀⠀⠈⠁⠙⣿⣿⣿⣀⣤⣄⠀⢀⣿⣿⣿⣿⣿⣴⣿⣿⣿⠄
⠀⠀⠀⢿⣇⣇⠀⢀⠅⠀⢀⠻⠽⠶⣞⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠈⢿⣿⡷⢧⣔⠐⡀⠀⢀⡴⣟⡙⡋⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⢿⡿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⢻⣿⣷⣿⣿⡿⡞⠋⣔⣿⣷⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⠋⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠹⣧⣿⡇⡆⣿⣿⣿⣿⣿⣿⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠁⣿⣿⣿⣿⣿⣿⡿⢷⡐⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠤⢲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡗⣿⣿⣿⣿⣿⣿⣿⣿⣌⡻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣫⣿⣿⣿⣿⣿⣥⣿⣿⣿⣎⢻⣿⣷⡀
⠀⠀⠀⠀⢠⣾⠞⠉⠻⠏⠩⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣷⡙⣿⣧
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⣰⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⡿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣷⡿⣯⢷⡌⢻⡄
⠀⠀⢠⡆⠐⠀⠀⠀⡀⣴⣿⣿⣿⡀⢰⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣯⣿⣿⣿⣷⣦⣄⡀⠙⢿⣿⣿⣧⠸⣿⣿⡴⡅
⠀⠀⠘⢂⠀⢸⣧⣾⣿⣿⣿⡟⠉⠁⢸⣿⣿⣿⣿⣳⣿⣿⣴⡏⠀⣿⣿⡿⠻⣿⠛⢯⣙⢳⣤⡙⣿⣿⣷⣼⣿⢷⡜
⠀⢀⠂⠈⠈⠉⢻⡿⣿⣿⣿⣧⠀⢀⣿⣿⣟⣿⣾⠙⣿⡟⠻⣿⡄⠛⠋⠀⠀⡿⠀⠀⠉⢷⣽⣷⣌⠙⣿⡅⢻⣏⠇⢶
⠀⢸⠀⢀⠀⢀⣿⣇⣿⣿⣿⣿⢧⡘⣿⣿⣿⣿⣿⣀⣯⣴⣶⣾⠇⠀⠀⠀⠈⣇⠀⠀⠀⠀⢻⣿⣿⡄⠛⣿⠆⣿⣆⠘⡃
⠀⢸⡀⠹⣖⣿⣿⣧⣾⣿⣿⣿⠈⢃⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣷⠀⠀⠀⠀⡾⠀⠀⠀⠀⠠⢑⣿⣿⠆⢺⣷⠸⠿⠁
⠀⠀⠉⠉⠛⠿⠍⢰⣟⣿⣿⡿⢦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⢰⣿⣄⣤⣴⣿⣷⣢⣥⣴⣾⣿⣿⣿⡿⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠯⠸⢿⣿⣿⠟⠋⠙⠛⠿⠿⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⡀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⢠⡟⠁⠀⠀⠀⠈⣿⠙⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣄⠀⣠⡶⠀⠀⢿⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⣤⣄⠀⣇⢀⡾⠃⣼⠋⠙⠃⠀⠀⣿
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢸⡇⢸⣇⣴⠞⢶⡀⢠⡟⠛⠻⣷⢸⡿⠁⠀⢻⡀⣿⡿⣧⠀⠘⠷⠶⢦⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠃⠀⢸⡇⣿⠀⠀⠀⣿⠀⣷⠀⠀⢸⡇⣿⠀⠘⣧⠸⣇⣀⣼⠇⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⠀⠀⠀⣧⠸⣦⣀⣠⣿⡆⢿⠀⠀⠸⠇⠻⠂⠀⠙⠁⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠉⠀⠀⠉⣁⣈⣁⣤⣤⡤⠶⠶⠶⠒⣒⣛⣛⣛⡛⣛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣤⡴⠶⠚⠛⠋⠉⣉⡁⠀⠀⠀⠀⣠⡴⠛⣉⠉⠉⠉⠙⢦⣛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠚⠋⠁⠀⠀⢀⣤⣾⣗⠾⠋⡇⠀⢠⡏⣻⠋⠀⠀⣉⡀⠋⠀⠀⠈⣧⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠀⠀⠙⠦⣄⠉⡏⠠⡄⠀⠉⠁⠀⠀⠀⠀⣿⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠚⠛⠲⢤⣀⡀⠀⢳⡄⠻⢦⣤⣠⡴⠋⠀⢠⣿⣽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⠀⠀⠈⠂⣀⠀⠀⠀⣀⠀⠀⠀⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⣀⠃⠀⠀⠀⠁⠀⠹⡆⠀⠀⠀⠀⠀⢠⠈⠀⢀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⢀⠴⠄⢀⡀⠀⠀⠀⠀⡀⠂⠀⠠⠌
⠀⡔⠋⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠀⠀⠀⣤⣴⣶⣿⠀⠀⠀⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠙⠃⠀⠁⡄⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠁⠄⠀⠉⠠⢄⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠉⠙⠂⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⠠⡄⠛⡀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠛⠆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⠀⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⢀⠘⡆⠀⠀⠀⠘⠀⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠄⠀⠀⠀⣠⠄⠀⠀⢀⡔⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡀⠀⢀⣀⣀⠠⢀⡙⠉⠃⠈⠁⠀⠀⠀⠉⠉⠁⢄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠘⣥⠤⠤⠈⠉⠴⠆⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⣀⣀⣀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⠤⡈⢷⡀⠀⠀⠀⠀⠀⠁⢂⣀⠀⠔⠋⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⢤⠄⡀⠀⠈⠀⠠⠤⠀⠠⠐⠁⠀⠇⣸⢁⡀⠀⠀⠀⠀⠀⢠⣋⡤⠔⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠉⠁⢠⡖⢺⠀⠀⠀⠀⠠⠁⠀⢁⠀⠀⢀⡀⠂⠀⠋⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⢠⠀⢀⣄⢰⣎⠈⠁⠀⠃⠐⠀⠀⠀⠀⠰⠀⢦⡀⠁⠀⠀⠛⠀⠉⠀⠀⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠊⣠⠆⠛⠤⠙⢶⡆⠠⢤⠀⠰⠃⠀⠐⡇⠐⢺⡇⠀⠀⠀⠀⠀⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠓⠀⠲⠄⠀⠀⠀⠈⢀⣏⡀⠄⠀⣀⠶⠀⠀⢠⠄⠀⠀⠘⠀⢣⡀⠚⠧⠀⢤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠐⠀⢂⡀⠀⠀⠘⢈⠁⢀⡄⠁⠀⠐⠀⠀⢀⠀⡀⢀⢀⠌⠁⠀⠀⢀⡀⠀⠈⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⣾⠃⠀⡰⠂⡉⠑⢹⣿⣧⣤⣤⣨⣴⠟⠈⠋⢿⡇⠀⠉⠋⠀⠀⢁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⢀⣤⣀⣶⠴⠿⣿⠀⠀⡄⠀⠀⠀⠛⠙⠋⠋⠤⠘⡛⠀⠀⢴⡿⣠⡶⠀⠐⠆⠀⠌⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⢛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠠⠄⠀⡈⠀⠀⡇⠀⡀⢀⡰⠟⣶⠀⢰⠂⠧⠀⡀⢶⡦⣿⣿⣦⣔⣀⣄⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠆⠁⠀⡤⠀⠠⠛⠈⠀⠀⠻⣤⡼⠃⠀⠉⡇⢀⠀⠜⠉⠉⢉⡿⠏⠀⠀⠔⠈⠀⠀⠀⠀⡠⠈⠀⢠⠒⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠴⠈⢀⠛⠀⠰⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠣⠀⢳⠄⠀⠀⣀⠰⠊⠀⠀⠀⢀⡴⠂⠀⣀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢄⠀⠀⠀⡠⠂⠀⠀⠀⠈⠀⠅⠠⠄⠀⠀⠀⠀⠀⠘⠉⠀⠀⠠⠆⠀⠀⠘⠁⠀⠲⠠⣄⡠⠋⢁⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⡞⠀⠸⠇⠀⠀⠀⠤⠀⠀⠒⠚⠀⠀⣤⠁⠐⠀⠀⠉⠂⠀⠀⠚⢃⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢀⡄⢀⣠⣤⣤⣀⠀⠐⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠇⠀⠀⠀⠀⢠⡆⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡈⢡⡄⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠉⠁⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⢠⡄⠀⠤⠀⡄⠀⠂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠂⢀⠞⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⠦⠀⠀⠇⠀⠀⠀⢼⡃⠀⠀⠀⣀⣤⠤⢼⡇⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⠉⠀⣀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠀⠈⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠤⠀⢄⡀⠀⣠⣴⣾⣿⣿⣿⡗⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠧⠴⠶⠶⠿⠿⢿⣾⣿⣿⠟⢿⣿⣿⡯⠀⠀⢀⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⠀⠐⣒⣲⣶⣶⣽⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⢁⠀⣀⠭⠭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣟⢄⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠿⡿⣿⠿⠛⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠈⠑⠈⠂⠹⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⢁⣤⠞⠁⣀⣴⣿⡿⠿⠿⣛⣛⠛⢿⣿⣿⣿⣿⡿⠶⢤⣀⡀⢙⣦⠀⠹⡄
⠀⠀⠀⠀⠀⠀⡙⢷⣆⣨⡿⠋⠛⢁⣶⠟⠁⣠⣾⠟⢋⣥⣶⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿⡷⠦⡀⠙⢿⣿⣿⣷⠀⠹⣶⣢
⠀⠀⠀⠀⠀⠀⠷⢶⣿⣿⣴⣾⠟⠀⡀⠀⠘⢻⡏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⣦⡀⠈⣿⠀⠙⣆⠀⣿⣯⡀
⠀⠀⠀⠀⠀⣴⠳⢶⣿⣿⣿⡇⢀⡞⠀⠀⠀⣾⢠⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠈⠙⢿⡛⢇⠱⣼⣷⡄⠘⣧⡄⠈⢿⣿⣿⡁
⠀⠀⠀⠀⠀⣏⣉⣿⣿⢻⢻⣿⣾⠁⠀⢀⣼⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢻⣿⠙⠀⠹⣿⣤⣼⣿⣿⣳⡆
⠀⠀⠀⠀⠀⠈⢹⣿⣿⠀⣸⣿⣧⣦⣧⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⠀⢰⠀⢿⣿⣿⣻⣿⡛⣧⠀⠀⠀⢀⡀
⠀⠀⢠⣤⣴⣿⠟⣹⠟⢀⣿⣿⣿⣿⣿⣿⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⣇⣼⠏⠹⣷⡻⣿⣿⣆⣠⣴⣤⣿
⢠⣾⠉⠻⣿⣷⣖⣥⣦⢾⣿⣿⣿⣿⣿⣣⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣿⣿⠀⠀⠸⣿⡆⠀⠘⣿⣻⣿⣿⣿⣿⣿⣹⠃
⢙⠻⣿⣿⣯⣿⣿⣏⣥⣾⣿⣿⣿⢿⣿⣿⣿⠶⢶⣦⣤⣤⡀⠀⠀⠀⣠⡶⠿⠛⠋⠉⠁⠀⠀⢻⡇⠀⢿⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠈⢧⣈⣻⣿⣿⣿⣿⣛⣻⡭⢉⡴⢻⣿⣿⣿⣀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣶⠀⠀⢸⠿⡀⠈⠙⠿⣿⣿⣿⣿⣿⢿⢟⣿⣿⣿⡁⣻
⠀⠈⠙⣿⣿⣿⡿⠛⠛⠯⡶⠋⣵⢻⢿⣿⡿⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⠴⢋⣧⣀⠀⠘⢦⣤⣉⣉⠁⢀⣤⣾⣿⣿⡿⠟⠁
⠀⠀⢠⣾⣿⣷⣶⣾⣛⣉⠠⢾⢁⠁⢜⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⣶⣾⣶⣶⣾⣿⣿⣿⠋⠁
⠀⠀⠀⢻⡿⣿⣿⣿⣿⣧⠴⠿⠉⠀⣪⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣼⣿⠿⣇⣹⣿⣌⣀⣽⣿⣼⣫⣿⡄
⠀⠀⠀⠀⠙⠻⣿⣻⣟⣻⣶⣤⡶⢋⠿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢄⡼⢿⣿⠀⠸⣿⣿⠟⠉⠉⣻⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠀⠀⠘⣹⣿⡄⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⣿⣿⣦⠘⣮⣻⣶⠶⣶⣿⣿⣿⠟
⠀⠀⠀⣤⣶⣦⠬⠽⠟⡹⣿⣿⣷⣖⣨⣿⣿⣷⡀⣄⡀⠀⠤⠤⠤⠤⠤⠒⠂⠁⣀⠄⠸⠃⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠉⠓⢦⡀⠀⠐⠛⢿⣷⠛⠻⣿⣯⣿⣿⣿⡟⠲⢄⣀⡤⠤⣤⣰⠶⠋⠁⠀⠀⠀⠀⠘⣷⠶⠓⠒⠚⠋⠭⠵⠾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢸⣿⠷⢿⣿⠉⠛⠿⠿⢿⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠦⡄⠀⠀⠀⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡉⢓⣾⡄⠀⠀⢀⠞⠀⠀⡜⠀⣀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠘⠆⠀⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠀⠀⠀⢠⡄⠀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣶⣾⣿⣶⠆⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣷⡄⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⢿⠿⠿⠟⠛⠁⠀⠈⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢼⣬⣵⠾⢿⣿⡷⣦⣀⣀⣰⢾⣿⡿⠷⣦⣽⡧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⠘⡇⠚⠉⠿⠉⢺⠟⢻⡕⠉⠿⠉⠓⢸⠃⡞⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠀⠳⣄⡀⢀⡠⠞⠀⠀⠳⢄⡀⢀⡠⠞⠀⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⠐⠲⠖⠂⠀⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠳⣟⡓⢚⣳⠞⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠉⠉⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠉⠒⠶⠶⠒⠉⢸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠋⣰⢧⠀⠀⠀⠀⠀⠀⡼⣆⠙⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠁⡼⠁⢠⡇⠈⠀⠀⠀⠀⠀⠀⠁⢸⡄⠈⢧⠈⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠸⠤⣤⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⠤⠇⠀⠀⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠈⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠙⠒⠤⣵⣄⠀⣄⣰⠋⣠⣮⠤⠒⠋⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢠⠟⠢⢤⣀⡀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣧⠞⠁⠀⠀⠀⠀⠘⡖⠀⠀⢻⠀⠀⢀⣀⡤⠔⠻⡄
⠀⠀⠀⠀⠈⢳⠦⢄⣀⡉⠉⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡞⠙⡆⠀⢘⡏⠉⢉⣀⡠⠴⡞⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⡼⠉⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢠⠀⢀⠒⠀⠀⠀⠀⢠⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⡂⠫⡀⣁⡶⠆⢃⢰⡪⠂⠀⠘⠄⣔⡕⠁⢪⠁⡖⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠢⠀⡳⣲⢁⣸⠝⠤⠰⠁⠒⠀⠑⠁⠀⠀⠐⠋⠀⠪⠤⠔⡡⠀⠊⠒⣀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⣖⢄⠀⢨⣄⠐⠅⠈⠉⡀⠐⠈⠉⠉⠂⡐⠈⣳⠀⠀⠈⠀⠂⢄⠀⠉⠀⠬⠃⠉⡎⣑⢀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠂⡸⡅⡡⠑⠁⠀⡠⠐⢁⠤⢶⡀⠀⠀⡴⢘⠒⢿⠰⡄⠀⠀⢀⣤⡈⠢⠀⠀⠀⠐⠈⡀⣕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠂⠥⣴⣚⡡⠖⡩⢛⣶⡀⠁⠘⠀⠘⠂⠁⣰⡖⢟⠳⣍⠲⢄⣁⢀⡤⠀⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠒⠻⣀⠙⠒⢺⠀⣿⠒⠚⠁⣹⠦⠗⠒⠛⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡶⢚⠀⡟⠢⡆⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⠙⠒⠇⣀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⢦⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢧⣀⡏⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠈⠃⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣽⢳⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠙⠾⣁⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⠾⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⣶⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡖⢰⢲⢰⢳⢰⢛⡢⣀⢲⡆⡰⡳⢴⠖⢲⣆⣰⡳⢀⣞⣢⡀⢸⢓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢢⢸⢸⢸⢸⢸⢘⡫⡞⠈⡼⢯⠃⢸⣣⠈⡿⢧⠃⢞⣏⣱⡹⢸⢘⣣⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠸⡬⠗⠊⠘⠾⠙⠿⠀⠱⠞⠀⠸⠏⠀⠳⠞⠀⠈⠫⠵⠁⠸⡼⠹⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⠛⠋⢻⣿⣷⠀⠀⠀⠀⠁⠀⢤⠄⠀⠉⠀⠀⠀⠀⠀⡿⠛⠉⠙⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⣠⣶⣶⣶⣶⣶⣾⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⣰⣿⡿⠛⠋⠁⠹⣿⣿⡆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣷⡄⢠⡿⠋⠀⠀⠀⠀⠀⠈⠛⣿⠀⠀⠀⠸⣿⡏⠉⠉⣹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡕⠀⠐⡌⣻⣿⡇⢸⣿⣶⡀⠀⠀⠀⠀⢠⣶⣿⠀⠀⠀⠀⢙⡿⠶⠾⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠀⢸⣦⣼⠁⠸⣿⡃⠀⠻⣿⣷⣄⠀⢀⣠⣿⣿⠟⠀⠀⠈⢾⠉⠑⠀⠀⠊⠙⢧⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠃⢀⡠⠈⠛⢹⠄⢰⠏⠻⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⠀⠄⠌⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⡆⠀⠀⣁⡀⢘⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠐⠀⠀⠀⠸⠗⠀⠀⠐⠐⡇⠀⠀⢻⠃⢸⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣶⣶⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠒⠤⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⡦⠤⠤⠤⠤⠤⠤⠼⠀⢘⡰⠂⠀⠀⠀⡀⣀⠀⠀⠀⠸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠰⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠘⠀⠀⠈⠁⠉⠁⠀⠀⠃⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⢱⠀⠀⠘⠀⠀⠀⠀⠂⠀⡇⠰⠀⠘⠀⠀⠀⠀⠈⠀⠀⠐⠀⠐⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠛⠒⠒⠒⠒⠁⠘⠒⠒⠒⠒⠃⠙⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠃


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