Crumple Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⡀⣀⠠⣄⡀⠀⠤⠤⠤⠤⠤⠀⢀⡤⢀⣀⡀
⠀⠀⠀⠀⢐⠨⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡱⣈⠆
⠀⠀⠀⠀⡏⠁⠐⠉⠒⠀⠤⠤⠤⠤⠤⠤⠤⠀⠂⠈⠓⠈⠉⠀⡆
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡀⢈
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡀⠤⠄⠀⠠⠄⣀⡠⠁⠐⠀⠀⠉⠒⠠⠀⠀⠀⠤⠤⠤⠀⣀
⠀⠀⠀⠀⢠⠂⠀⠄⠂⠉⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡆
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠈⠈⠉⠉⡑⠠⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠆
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠀⠀⠈⠐⠐⠃⠀⠀⠤⠤⠤⠤⠤⢤⣶⠇⠀⠸
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣠⣶⡇
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠁⠈⣰
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢀⣴⣾⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⠿⠛⠋⠑⡀
⠀⠀⠀⠀⠠⣁⠂⠠⠄⢀⣀⡀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠄⣀⣤⣶⡿
⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠤⠤⠤⢅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠒⠒⠒⠒⠂⠀⠛⠋

⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢨⣀⡄⠀⠀⠈⠉⠀⢰⡏⠉⠉⠉⡍⠉⠋⠉⠛⠋⠤⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣿⣦⡀⠀⡁⠀⠀⠀⠀⠈⠇⠀⠀⣄⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⢴⣄⡀⠠⣤⣀⣀⣀⠀⠈⠳⣄⠀⢼⠄⠁⠟⠛⠘⡇
⠋⠉⠉⠁⠀⢰⠄⠲⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠚⠀⠀⠉⠀⠀⠀⢉⠙⠿⣿⠇⠀⠙⠖⠠⠶⠀⠄⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠇⠀⠠⡰⠀⠐⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢨⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣆
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡧⠀⡄⠀⠀⠀⠂⣠⠖⠀⠀⠀⠉⠉⠛⠀⠀⠲⠆⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢂⣰⣧⣤⣤⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠑⣊⣹⡏⠀⠉⠉⠢⠀⠀⠠⣄⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⢤⣤⠄⠃⣼⠟⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⡀⠀⠀⣀⠀⢸⠇⠀⠀⠻
⡀⠀⠀⠀⢀⣀⠀⠀⢄⡄⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢻⣦⣶⣇⡀⢸⠃
⢰⡆⣠⠀⠀⠀⠉⠀⣄⡀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣀⠀⠀⠀⠀⠀⢀⣠⣭⣤⢰⣮⠙⠓⢘⠃⢀⡀
⣺⡛⠙⠇⠀⠠⠆⠀⠀⢫⡘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⡌⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠤⠴⢿⣿⡿⢯⣿⣿⡶⠀⣿
⣿⡇⣦⡄⠀⢰⡶⠀⠀⠈⢻⣽⡧⢄⠀⠀⠀⠀⠀⠀⠀⣉⡄⠀⠄⠀⠀⠀⠀⠀⠁⠀⢀⣀⣤⡤⢀⡂⠀⡀⠀⠀⠀⠀⣼⣇⣀⣚⢿⣿⣄⠀⣿⠀⠀⠀⠲
⣿⡿⢿⡖⠂⠀⠀⠀⠀⠀⠀⢹⣟⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠤⡄⠀⠲⣤⣴⣿⣽⣿⣷⡿⢛⣵⠁⠀⠀⠀⠀⣿⣿⣾⡦⠈⣏⠙⠄⣿⣄⡀
⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠃⠀⢀⠀⠀⠀⠸⣿⣀⣀⡀⠀⠀⠠⠶⠊⣋⣉⣀⢁⠀⠈⣇⠘⠃⠀⠀⢠⣄⡀⠿⠿⠁⠀⠀⠋⠀⠀⣿⠀⠁⢀
⢹⣿⠁⠂⠐⠲⠖⠀⠀⠀⠀⢛⠇⠸⠶⠀⠀⠐⠒⠆⠚⣉⠉⠉⠁⠀⢠⠖⣾⣟⢋⣭⣹⡿⠛⠳⠄⢿⠲⠂⠒⠄⠀⠀⢺⠒⠀⠀⠀⣆⠉⠀⠙⠉⡟⠻⡤
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠠⠀⠁⠀⠀⠀⣄⢰⣾⠀⠀⠀⠀⣼⣷⣿⠏⢾⣿⣟⠀⡀⠀⠀⢘⡀⠀⠀⠀⠀⠀⢨⡧⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠃
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⣧⢠⣶⠀⠀⠀⣶⣿⣿⣧⣴⣿⣽⡿⠏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡳⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⣦
⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠰⠇⠀⣿⠁⣄⠀⣤⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠀⠀⠀⢤⠀⠀⠘⠆⠘⠀⣿
⠈⡇⠘⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⠀⢻⡿⣿⣥⣿⠋⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠰⡆⠀⠈⠄⠁⠀⡂⠀⠀⠉
⠀⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⡀⢀⡄⠚⠉⠐⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⣤⡤⠀⠀⠀⠂⠙⠓⠶⣔⢂⠰⠀⠀⣿
⠰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠃⣄⠀⠀⠉⠀⠈⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠈⣿⣀
⠀⠇⠀⢀⣠⣤⣤⠤⠴⠶⢤⣬⣀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠙⣅⠀⠀⠀⠀⠀⠀⠹⣦⡄⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆
⠀⡄⠀⠀⠛⠀⣶⠀⡀⠀⠀⢸⣿⢹⣦⣀⡀⠀⢀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⡖⠛⠳⠂⠀⢀⡀⠀⠀⠀⠀⠀⣤⣄
⢠⡶⠶⠀⠀⠀⣸⣦⣄⣄⠀⣸⣿⣿⠤⣌⢁⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⣶⣤⣰⡀⠀⠀⠀⠀⣀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⡭⣷
⢸⡇⠀⠀⠀⠠⠯⣮⡽⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠎⠙⠛⠛⠿⢿⣿⣛⠿⣿⣾⣅⣶⣴⣿⣿⣯⣿⣆⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠛⠛⠂
⢸⡇⠀⠀⢀⣠⣿⠃⠀⠀⣻⣰⡷⠈⡽⠿⠛⠙⠋⠉⠉⠉⠂⠀⠀⠐⠀⢸⣿⢯⣷⣿⣿⡻⠿⠿⠿⠿⢿⣿⣿⣧⣿⣿⡀⣴⣀⠀⠀⣀⠴⢃
⠘⣇⣼⣟⠋⠀⠈⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⠁⠀⠀⣆⠘⡿⠿⣬⣙⡻⠿⠿⢿⣿⣍⣿⣿⠀⠀⡶
⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⡇⠠⠏⠀⠘⠋⠀⠀⠀⢸⣧⡬⢿⣉⡛⡄⠿⠄⢐
⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠤

⢸⡇⠀⠘⠃⠀⠀⣁⠀⢲⡁⠀⠺⣤⢀⣿⣸⠃⠀⠀⠃⣤⡾⡅⠀⠀⠈⠓⢀⣟⣼⡇⢸⣷⣯⢰⣿⣿⡇⡈⣿⡿⢑
⣿⣴⡆⠀⠀⠀⠰⣿⠀⠈⣧⡰⠀⣿⢾⡹⠏⠀⠀⢸⡾⣿⡆⠀⠀⠀⠀⣠⠄⡹⠧⢽⣀⢻⣼⣿⣿⣿⠼⣿⠣⠀⠏
⡧⢸⢟⣼⠀⠀⢸⠏⡇⠀⢾⡇⠻⣧⠟⣴⡄⠈⣆⠸⣱⣿⡄⠀⠁⠀⠘⠏⣠⠃⠀⠸⣿⡝⢿⡇⢻⣾⡇⣸⡷⠀⢀
⢁⣾⠸⠿⣾⣦⠸⣾⡷⢸⣾⡇⢰⡇⢾⣿⠃⠀⠉⠀⠘⣿⣿⡖⠀⠒⢰⡆⣿⣇⠀⠀⠸⣿⢛⠳⣿⡏⣸⠟⡀⢀⢼
⣼⣿⠀⠀⠈⠈⢳⡟⠑⠿⣌⠃⡘⣿⣰⡏⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⣼⠁⣿⣿⡏⠘⣶⠻⠈⠰⣿⢸⠟⣷⡄⣼⡦
⡨⠏⠁⢀⣦⡀⣾⡇⠃⣄⢻⣄⢻⣜⢩⣃⣰⡆⠀⠀⠀⠀⠈⢻⡀⣰⢿⣦⣼⣏⠀⢰⣿⣠⠀⠸⣇⣾⠀⣿⠦⣹⣿
⢹⣦⠀⢀⠈⠇⡟⢵⡘⣏⢸⣿⠀⣽⠀⡿⢻⡇⠀⠀⠀⠀⠀⢀⣸⠇⢾⣷⣿⠸⠠⠀⣿⢻⡤⠀⡿⣿⠰⡟⠀⣽⣿
⠀⠻⠼⢿⡆⠘⠀⢼⡇⠈⢸⣿⣜⠛⠀⠡⢿⡇⠀⠀⠀⠀⠀⢾⡔⣶⢘⣿⣿⡇⠀⣼⠉⠈⣧⣾⢃⠿⠦⣿⠀⢸⣿
⣀⠀⢂⠀⠙⠦⡂⠈⢳⡆⢼⢿⡽⡆⢀⠀⢼⠁⠀⠀⠀⡄⠡⣾⡿⠀⠘⣿⡟⢀⣤⠋⢀⣀⡘⠻⣿⡐⠦⣽⣇⢸⣿
⠙⢷⣌⠛⢶⣦⡁⢡⡜⠀⢲⠸⠃⠁⠈⢰⡄⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠙⠃⣸⠟⢧⠀⠉⡀⠀⠀⠈⠣⣽⣿⣏⣻
⠀⠀⠀⠀⠀⠀⠁⢸⡿⠂⠰⣄⠀⠀⠀⠸⣇⠀⠀⠲⡄⢸⣿⠋⢠⣀⠖⠀⠀⢿⣧⡀⠀⠀⠇⣹⠃⠀⠀⡉⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡆⠈⣧⠀⠀⡀⢹⡆⠀⠀⠀⣾⠃⣴⣿⠋⠀⠀⠰⡆⠙⣄⠀⠀⣰⣿⣧⠀⢠⠏⢻⣿⣷
⠀⠠⡄⠀⡄⠀⠐⠀⢰⠀⣷⡀⢹⣅⢈⠳⡆⠀⢙⡀⠀⢉⠁⣿⣇⠀⠀⢰⠄⢱⠀⠀⠀⠀⠘⣿⠙⢿⡄⢰⠀⣙⡎
⠰⠦⡤⣄⣿⠀⣄⠀⣝⢲⡄⠛⣦⠏⠛⢀⠙⠀⠈⣧⠀⠀⠀⢸⠟⠳⠀⠦⣤⣌⠃⠀⠷⣆⠀⠸⣷⣈⣿⢠⣿⠏⣹
⣠⠀⠀⢠⡏⠀⡷⠀⠛⠈⠁⠈⠀⠀⠀⢸⡇⠀⠀⡈⠀⠀⢄⣹⢰⡆⠀⠀⠙⠻⢧⡀⠀⠛⢶⡀⠟⢬⢉⡿⠋⠀⠻
⠅⠃⢸⠈⢟⡆⢰⡆⢀⠘⠂⠠⠀⠀⠀⠀⣄⠀⠀⢹⠆⠀⢰⡅⢾⡱⣦⡀⠀⠀⠀⢽⢀⠀⠊⠃⠀⠀⢾⢁⠀⣿⠃
⡿⠀⢿⡇⠀⠀⡄⠱⣟⢀⡀⠀⠀⢀⠀⠀⢹⠄⠀⣿⡀⠀⡬⣳⣤⡙⠚⢷⣄⠀⢀⠨⣜⠇⢠⡾⢀⡄⠀⠘⠷⣹⠇
⠃⢠⣄⠁⠀⠀⠀⠀⠟⠈⠇⠀⠀⠀⠀⠀⠀⠀⠘⠿⣇⢸⡃⠀⠸⣟⠃⢰⡏⠠⠉⠐⠘⠀⠀⠙⠋⠳⢸⣇⣀⠀⢀
⠀⠈⠻⣧⣦⡀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⢸⡄⠙⠃⠀⠀⢰⣾⡆⠙⠆⠀⠈⠤⣶⡄⠀⠙⢹⣸⡿⢭⣶⣮
⠀⠀⠀⠈⢿⣿⡆⠀⢰⣇⠀⠀⠀⠑⠀⠀⠀⠐⠂⠀⣤⠀⠀⠀⠀⣾⣹⣿⠁⠀⠀⠀⠀⢻⣿⠀⢀⣄⣿⡁⣼⣷⠎
⠀⠀⠀⠀⠀⠻⡏⠀⡀⠛⠀⠠⡀⠀⣴⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⣿⠸⡟⠀⠀⠀⠀⠀⠀⠻⣧⠀⠏⢸⣿⢻⣿⡇
⠀⠀⣠⠀⠀⠀⠐⣬⣍⠀⠀⠀⠀⠀⢶⡀⠀⠀⢀⣿⡇⠀⠀⠀⢻⢿⡟⠀⠀⠀⠀⢠⡀⠀⠀⡟⠀⣶⣌⠁⢸⣿
⠀⢀⡟⠀⠀⠀⡁⠈⠙⠂⠈⠀⠀⠀⡘⠀⠀⠀⠈⢻⠀⠀⠀⠳⣼⡇⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⣰⣿⠏⠀⢈⣿
⠀⠾⠄⠀⠂⠀⠀⠀⢠⣄⡀⠀⠀⠀⡉⠀⠀⢠⡄⠀⠀⢀⠄⠀⢹⡇⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⢿⡇⠀⢀⣿⡞⢿
⠀⡀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⢠⠄⠀⠀⠀⢺⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⣀⠸⣯⠀⠀⠀⣶⡟⢀⠀⠸⣿⡇⢻
⠀⢉⠀⠀⠀⠙⡄⠀⠀⠁⠀⠀⠸⠀⠀⠀⡆⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀⢀⠀⠉⠲⡛⠀⢠⡀⠈⢳⡎⠀⠀⠂⠀⢠
⠀⠈⠂⠀⠀⢀⡆⠀⠀⠀⠰⠀⠀⠀⢀⠠⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢳⡀⠐⡇⡀⢰⡇⢇⠈⣧⢀⠀⠀⠣
⠀⠀⠀⠀⠀⠈⠧⢑⠀⠀⠂⠀⠀⠀⣬⣠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠁⠠⠰⣶⡀⢙⡏⢸⢻⣮⢀⡄⠂⠠
⠀⠀⠀⠀⠀⠐⠆⢸⡄⠀⠀⠀⠀⠀⠀⠉⠀⠑⠀⠀⠘⠓⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⠀⠸⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⢀⠀⠐⠆⠀⠰⠀⠀⠀⢀⣓⠀⠀⠰⠀⠘⠀⣤⠀⠀⣠⠂⠀⢹⣷⠰⢤
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠃⠀⠀⠠⠀⠙⠃⠀⠘⠀⣿⢦⣿⢦⡴⠁⠀⠀⠈⡹⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⡅⠀⠀⠀⠀⠘⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠂⠀⠠⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠁
⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣥⣤⣧⣤⣦⣤⣶⣥⣾⣯⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⡦⢀⣤⣤⡄⠀⠀⠀⡼⠁⠀⠠⢀⠀⠀⣠⣾⡆⣰⠌⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠤⠤⢄⣤⡗⢹⠷⠛⢡⣠⣤⡄⠀⣈⠀⢀⣰⣶⡸⡻⠀⢘⠻⡇⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠂⢴⡈⠙⠉⠀⠀⠀⢩⣪⢇⡀⠁⠀⠘⠿⠋⠀⡄⠀⠠⠌⠁⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⣐⣂⠚⠂⠱⢌⡁⠀⠀⢀⣤⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠛⠀⠠⠄⠀⠄⠛⠡⠴⣶⣄⠀⢿⣷⡄⠘⠷⠶⠀⠲⣦⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠒⠶⠦⡐⠞⠉⠛⠁⠄⠀⠀⠀⠐⠒⠋⠉⢯⡵⠃⠀⠀⠀⠁⠐⢂
⠀⠀⠀⣴⠂⠈⠁⠀⣀⣠⠄⠀⠀⠈⠀⠀⠻⢦⣄⠑⣄⢁⡠⣄⠀⠒⠐⣤⡀⠀⠀⠀⢠⠊⣸⠃
⠀⠀⠀⠉⠀⠐⠒⠈⢿⠀⠀⠀⣴⣾⡷⡖⠀⢈⠛⠁⠈⠉⠙⠦⡍⠫⠀⠙⠅⠀⡤⢀⠀⠠⣾⡄
⠀⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⠈⠾⣿⣏⡄⠀⠀⢠⠔⠻⠗⡄⠀⠀⠀⠀⠐⠀⠀⠂⡀⠀⠀⢹⠁
⠀⠀⠀⠀⠤⢀⣈⡀⠒⠀⠁⠀⠀⠀⠀⠀⠀⣀⣾⣻⠂⢠⣤⠀⠀⠀⠀⠀⠐⠀⠀⠙⢙⣛
⠀⠀⠀⠀⠀⠀⠁⠈⠙⠳⠶⠂⠀⠀⠀⠋⠉⠁⠈⢁⡴⠟⠁⣀⠶⢂⠰⡀⠀⠀⠈⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠖⠈⠀⠀⠀⠙⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠴⠂⠈⢀⡀⠈⣓⣄⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣧⣤⡾⠿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠟⠻⠛⠉⠉⠉⠉⢿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⣛⣛⣭⣭⡷⡶⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣭⣵⡶⠞⠛⠋⠉⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⢀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⠃⠀⢠⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢆⠀⠀⠀⣀⡀⠀⠀⠀⡇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⠂⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⢋⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⡙⠻⠷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⡶⠾⠟⣛⣉⣥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣭⣭⣉⣉⣉⣙⣋⣩⣭⣭⣥⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣀⡀⣠⡿⠁⠀⠀⠀⠈⠛⠷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠈⠙⠛⠻⢤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠷⠶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⣀⣀⣠⣤⢤⣄⣀⠀⠀⠀⠉⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣉⠁⠀⠀⠀⠀⠉⠛⠲⠦⣤⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣬⡿⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⣀⣀⣤⠤⠶⠚⠛⠉⠉⠁⢀⣤⠴⠶⠚⠛⢻⡇
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⣁⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣠⡤⠖⠻⣧
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⢠⡞⠛⠉⠉⠁⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⣿⣷⠚⠉⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠘⠓⢶⡒⠒⠓⣠⡴⠋⠀⢠⡏⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠀⠀⠙⢦⠞⠉⠀⠀⠀⡾⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠳⣄⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠀⠀⠘⠃⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⢛⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⣀⣤⠴⠟⠀⣀⣠⡤⠾⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠈⠃⠀⢴⠖⠛⠉⢁⣤⣶⣾⣯⣭⣤⣤⣴⣶⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢸⡆⠀⢠⡿⠃⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⣧⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⢤⣰⣦⠀⣴⠃⢈⣱⣆⣠⣶⣆
⠀⠀⠀⠀⠉⠙⠊⠅⡀⣤⢧⣴⣬⡥⠋⢸⣘⣟⡤⢰⢖⠶⡀⠀⣠⠠⠀⣄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣫⡷⣿⢖⣰⡨⡼⣿⠀⣀⠿⣄⢸⡦⣿⢞⠿⢌⠲⣄⢈⠐⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⡝⠀⠻⣿⠏⡩⡇⠈⠛⢻⣿⣗⢹⣷⠛⢐⣷⣖⠅⡨⢹⣷⣤⡆⣳⣦⡱⡀
⠀⠀⠀⠀⠀⢀⢔⣟⡟⣻⣧⠀⠀⣿⡁⢣⠇⠀⢗⣿⣿⣅⠡⠽⠷⠚⡏⣾⡷⡊⡽⠁⣨⢸⡝⣉⣤⣽⠀⡀
⠀⠀⠀⠀⠀⢪⣿⠞⠀⡟⢸⡆⡀⠹⢢⡟⠀⠀⠐⣿⡖⠒⠲⣤⢾⣏⠄⣵⠹⡆⡷⠀⢿⢽⣿⣇⠀⠲⣀⠼⠦⡀
⠀⠀⠀⠀⠘⢏⠡⠐⣼⠁⡘⠾⢻⢃⡾⠃⠀⠀⠈⠠⡇⠀⠄⣄⣿⡟⣤⣿⠀⠻⡟⣦⣌⣧⢿⡻⣧⣰⠯⡞⢠⠺⢆
⠀⠀⠀⠀⠀⠀⠀⠄⢺⣦⣤⡀⠸⣈⠡⠤⠤⠀⣠⠰⢼⣶⡨⣵⢹⡇⠘⣿⡊⢂⣓⣬⡉⠛⠒⠯⢵⡿⣳⣦⣠⣴⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠷⣽⡿⠿⠿⡦⢠⠄⠁⠀⣜⠷⠷⣹⠀⠇⠀⣿⣗⡉⣱⣫⡷⢄⣤⣶⢶⣭⡻⣯⣻⢏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⣟⣿⣅⡬⠴⠾⣞⡿⠛⠛⠻⠨⠹⣄⢠⡗⢸⣊⣿⢛⠲⠟⡫⢫⣵⡾⠟⠟⢻⡎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡘⡏⣿⡧⠙⢄⡐⠋⢀⠀⠀⠀⠈⠈⡹⣌⠺⡾⣻⣿⡧⠀⢸⠏⠉⠃⠀⠀⠂⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣞⢰⣯⢧⢻⣷⣶⣵⣍⠁⠀⠀⠀⠀⠀⠄⠀⡟⢰⣯⠋⢅⡠⠬⠃⠠⠚⠁⠀⢀⣠⡧⣼
⠀⠀⠀⠀⠀⠀⠀⢸⢳⡟⠁⡄⠀⢻⠻⢿⡹⣷⣤⡄⠀⠀⠀⠠⢖⣅⡖⢱⡬⠟⠁⠀⠰⠅⠀⣠⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⡈⢸⡟⢳⣟⣿⣩⣿⣎⣿⣿⡙⣷⣕⢔⡀⢀⡠⠿⠿⢺⡖⠒⢒⣻⢃⠐⡿⠛⠛⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠉⣼⣾⡌⢽⣿⣿⣿⢷⣿⣮⡰⠮⠤⠀⠀⠝⠉⢛⡿⢛⡽⣷⠇⢀⣧⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣌⡛⠷⣌⠹⣿⡯⢞⠅⠉⣹⣗⢺⣟⡩⢻⡿⣰⠾⠫⢸⠏⢠⣊⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣈⡒⢌⡳⢮⡹⠦⡑⠻⡿⠫⢻⣿⡤⣼⣿⣋⢥⣾⠻⠖⠻⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠛⠛⠓⠘⠚⠒⠀⠚⠁⠀⠈⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠄⡀⠄⡠⠀⠀⡠⡠⢀⠄⠀⠄⠠⡀⠔⡠⢀⠄⡠⢀⠔⡠⢂⠔⡠⢂⠀⠠⡠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠁⠀⠁⠀⠊⠀⠀⠊⠐⠁⠊⠐⠀⠀⠁⠈⠐⠁⠀⠈⠀⠈⠐⠁⠊⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠹⣆⡠⠤⠶⠒⠒⢆⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⣛⢋⠋⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠓⠲⠦⣤⣤⡼⠃⠀⠀⠀⠀⠀⢸⠷⣤⣀⣀⣤⣏⡆⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⠏⠀⠀⠉⠛⠲⢮⡷⣄⠀⠈⠳⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⣇⠀⠀⠀⠀⠀⠀⠠⣾⠄⢉⣩⡿⣹⠀⠀⠀⠀⠀⠀⣸⠃⠈⠓⠦⠤⠤⣌⢹⡂
⠀⠀⠀⠀⠀⠀⢀⡤⡖⠻⡖⠹⡆⠀⠀⠀⠑⠀⠀⡟⢠⢿⣿⢣⡿⠃⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢹⠀⠉⠓⠶⣤
⠀⠀⠀⠀⠀⠀⣿⢐⢇⠀⣿⡣⢸⡀⠀⠀⠀⠀⠀⠙⠯⠬⠞⠉⠀⠀⠀⠀⠀⠀⠀⢳⠶⢤⣄⠀⠀⠀⠸⡆⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠙⠷⣤⠝⢿⣣⢃⡳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⣠⠞⡙⠀⢀⣼⠀⠀⠀⠀⠙⢦⣄⣸⠃
⠀⠀⠀⠀⠀⠀⢀⡾⡇⠀⢸⣃⡿⢱⡯⣩⣒⣒⣶⠶⠶⠚⠉⣰⠃⠀⠀⢀⡔⣁⣲⡧⡞⠉⠈⠳⣄⠀⠀⠀⠀⠻⣿⣟⣶⣄
⠀⠀⠀⠀⠀⠀⢿⡟⢳⡀⠀⠛⢛⡿⢟⡟⠛⢦⡀⠀⠀⠀⣸⣻⡓⡄⠒⣹⠶⠛⠁⠀⠁⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⣹⡷⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⡓⡘⡙⡘⡼⠁⠀⣸⠇⠀⠀⠀⣿⠋⠃⣧⠟⠁⠀⠀⠀⠀⠀⣀⣤⠤⠶⠛⠉⠀⢠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠐⡟⡇⠀⢠⠏⠀⠀⠀⠀⢹⠸⢼⠃⠀⠀⠀⠀⠀⠰⣏⡁⣇⠀⠀⠀⠀⠀⡼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠯⠀⠀⠿⣤⡤⠶⣻⠛⢿⡄⠀⠀⠀⠀⣀⣀⣀⣀⣙⡷⢩⠢⢄⠀⣴⣪⣥⣤⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣄⠀⠀⡀⣠⡤⣾⡇⢸⢀⢷⡀⠀⣠⠞⠁⠉⠙⡏⠩⢡⢣⢃⠂⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍⠋⡿⠃⡏⡇⡸⠘⢸⣹⠞⠁⠀⠀⠀⢀⣼⣡⣦⣇⣂⣎⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣰⠇⣧⣁⡇⣠⠞⠓⠲⠶⠤⣄⡴⠋⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡷⠶⠶⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⡀⠴⠟⠿⠶⣤⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣬⠉⠁⠀⠀⠀⠀⡰⠛⠗⠊⠁⢠⠖⠲⣴⢧⠀⢆⠀⠑⢤⡀⠀⠀⠋⠾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠔⠁⠀⠀⠠⡾⠀⠀⠀⢀⢰⠼⡀⠀⠈⠂⠑⠀⠀⠀⠀⠈⣱⠀⠀⠁⠈⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢠⡌⡼⠃⠀⠀⠀⣾⠁⢸⠁⠀⠀⠀⠀⠘⢦⠙⢄⠀⠀⢠⣤⣴⣟⣂⠘⢷
⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠀⠀⢤⠀⡯⠗⠁⠀⠀⢠⠴⠯⡴⢯⡀⠀⠀⠀⠀⠀⠊⠳⡀⠐⡀⠀⠙⠛⠛⠁⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣀⡤⡀⠀⠤⠾⣊⠎
⠀⠀⠀⠀⠀⠀⠀⠸⡘⢄⠘⠢⠀⠀⠀⠀⠀⠀⠉⠀⣸⣦⡄⠀⠀⡄⠀⠀⠀⢀⣠⠤⣔⣾⣧⢉⣿⣗⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⣷⣦⣀⠀⠠⣄⠀⠀⠢⡀⠹⢛⡇⠀⠀⣡⡆⠀⠠⡿⡀⠉⠁⢀⠈⢻⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⠿⣟⣷⣄⡈⠐⣶⣄⠀⠀⠀⠀⠀⠀⠘⠶⠒⠀⣧⡈⣢⣴⣒⠃⣼⡟
⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⡨⠗⠤⢥⡽⠛⠛⠉⠉⠳⣤⣄⣀⡀⠀⠀⠀⠀⣔⣹⣶⣻⠿⠛⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠙⠙⠺⣦⣿⠿⠛⠋⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢚⣚⠋⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡱⣒⣉⡉⠒⠻⡟⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠫⣄⠉⠙⠓⣆⡃⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢤⠐⠁⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠓⠲⢤⣀⠀⠀⣰⠋⠀⠘⠂⠔⠉⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣠⡴⢇⠀⠀⠀⠀⠀⠈⠙⠛⡑⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠄⠒⠻⠟⠧⣀⡗⠒⠒⠒⠂⠀⣴⢃⠅⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠣⡀
⠀⠀⠀⣀⡤⠞⠋⡁⠀⣄⠘⢃⡢⡀⠐⠲⠣⠈⠙⠂⠤⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠈⠢⡀⠀⠀⠘⣄
⠀⠀⠻⣧⡀⠀⠀⢦⣀⠸⠇⡔⠑⢌⠀⠈⠀⢀⡤⢞⠀⠀⣁⡶⢿⠇⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠈⠢⡀⠀⠈⠑⡄
⠀⠀⠀⣿⠙⢦⣀⠀⠀⡄⠀⠈⢆⠈⠢⠓⡲⠥⠒⣁⣴⣞⠭⠴⢏⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠈⠢⡀⠀⢈⡆
⠀⠀⠀⣿⠀⠀⠈⠳⣄⠁⢣⠀⠀⠓⠊⢁⣠⠴⠛⠁⠀⠀⢀⠔⠈⠑⠦⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠖⣁⠈⠢⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠑⢦⡀⣀⣤⡞⠋⠁⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠉⣀⠟⠳⡄⠀⠀⠀⠀⠀⠀⠀⠐⠽⠱⣄⠴
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠛⠉⠀⡇⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⡐⠁⡖⠢⡄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠴⡖⠈⣿⠁⠉⠉⠉⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣈⣀⠟
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⢀⣿⡀⠀⠀⠀⢱⠀⣿⠀⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀⠀⢀⣤⢤⡶⢶⠶⣶⠶⡦⣄
⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⢨⠁⢳⡀⠀⠀⠀⢇⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⢻⣿⣶⣧⠾⣤⠷⣴⣷⡾
⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢸⡇⠀⢀⣧⣀⣀⣸⠀⠀⢳⡀⠀⠀⠘⡇⠀⠀⠀⠀⡿⠀⠸⡇⠀⠀⠀⠀⠈⣿⠷⢼⣤⣷⠴⠷⠺⡇
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⡷⠚⠋⠁⠀⢸⡇⠀⠀⠀⠹⡄⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠸⡷⠶⠒⠛⠛⠋⠀⠀⠀⠀⠀⠹⣄⣀⣀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠀⢈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⢀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠁⠉⠉⠉⠙⠛⠓⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠈⠉⠉⠛⣷⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠯⠤⠤⠤⠤⠤⠀⢰⣇⣀⣀⣀⠀⠀⠀⠀⢿⣠⠞⣷⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⢷⡀⠀⠀⠈⠁⠀⢻⠀⠀⠀⠀⠀⠀⠑⢀⢀⢀⠄
⠀⠀⠀⠀⣠⠖⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⡤⠴⠶⠒⠚⣿⠉⠁⠀⠀⠀⢀⣠⠴⠚⠛⣆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣆⠀⠀⣴⠋⠀⠀⠀⠀⠀⢹⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠈⢳⠟⠙⡏⠁
⠀⠀⠀⠀⢰⡿⣆⣞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣆⠀⠀⠀⢺⡄⠀⢀⣿⡀⠀⢻
⠀⠀⠀⠀⣼⠀⠉⠈⠙⠲⣄⡀⠀⠀⠀⠀⣇⠀⠀⠘⣦⠀⠀⠀⢻⣄⡾⠀⢳⡀⠘⡇⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⢠⡇⠀⢀⡼⠁⠀⠀⢹⣆⡤⠶⠚⠋⠀⠀⠀⠈⢧⣠⠴⠚⠉⠀⠀⣠⠗⠀⢻⠀⠀⠀⠀⠀⠈⠠⠀⠀⠆
⠀⠀⠀⠀⠙⢦⡏⠀⢠⡞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢀⣴⠞⠁⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠙⢶⡏⠀⠀⠈⡉⠛⠛⠒⠒⠶⠶⣴⠏⠀⠀⢀⣴⡋⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣞⡁⢀⡴⠀⠀⣠⣞⣁⣀⣠⠶⠋⠈⠙⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢤⡼⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⢀⠖⠉⠉⠳⠀⡔⠉⠉⠑⡆⠀⡷⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⢀⠀⣇⠀⠀⠀⡌⠀⡇⠈⠢⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣈⣁⡀⠁⢀⣈⣁⣀⠉⣀⣀⣁⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⡠⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢅⣀⠈⠃⢸⣀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⡁⠀⠁⢂⠀⡨⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⣈⠇⢸⣀⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠈⡇⠁⡠⠂⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠐⠓⠀⠈

⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉
⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠒⠖⠆⠂⠦⠐⠆
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠟⠻⠿⠿⠗
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠛⠛⠛⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠑⠚⠉⣹⣙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠑⠚⢉⣙⡙⠇
⡠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡆⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⡠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢱⡄⠀⠀⠀⠀⡞⣹⠚⠿⢛⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⠱⡄⠀⠀⠀⠀⡞⣩⠚⠿⢋⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉
⡿⠇⣸⠃⠀⠀⠀⠘⠒⠃⠀⠴⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⣲⡿⠇⣸⠋⠀⠀⠀⠘⠒⠃⠀⠴⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀
⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠒⠒⠒⠈⠁⠀⠀⠀⠀⠘⢆⠀⠀⣀⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠒⠒⠂⠈⠁⠀⠀⠀⠀⠘⢆
⠁⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠻⢆⠉⠁⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠻⢎
⠚⢋⣙⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⠑⠚⢉⣙⣑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈
⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⠠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡆⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⠠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡖
⢋⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⢱⡄⠀⠀⠀⠀⡞⣩⠚⠿⢛⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⠱⡄⠀⠀⠀⠀⡞⣹⠚
⠁⠀⠰⠃⠀⠀⠀⠀⠀⠀⢀⣢⡿⠇⣸⠋⠀⠀⠀⠘⠒⠃⠀⠴⠁⠀⠰⠃⠀⠀⠀⠀⠀⠀⢀⣺⡿⠇⣸⠋⠀⠀⠀⠘⠒⠃
⠒⠈⠁⠀⠀⠀⠀⠘⢆⠀⠀⣀⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠂⠀⠒⠈⠁⠀⠀⠀⠀⠘⢆⠀⠀⣀⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠻⢎⠉⠁⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠻⢏⠉⠁⠀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠑⠚⢋⣹⣙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠑⠚⢉⣙⡙⠇
⡠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡖⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⡠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡖⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢱⡄⠀⠀⠀⠀⡞⣻⠚⠿⢛⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⠱⡄⠀⠀⠀⠀⡞⣩⠚⠿⢛⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉
⠿⠇⣸⠃⠀⠀⠀⠘⠒⠃⠀⠴⠁⠀⠰⠃⠀⠀⠀⠀⠀⠀⢀⣺⡿⠇⣸⠋⠀⠀⠀⠘⠒⠃⠀⠴⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀
⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠁⠀⠀⠀⠀⠘⢆⠀⠀⢀⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠀⠀⠐⠈⠁⠀⠀⠀⠀⠘⢆
⠁⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠛⢎⠉⠉⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠻⢎
⠚⢋⣹⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠑⠚⢉⣹⣙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈
⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⡠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡖⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⡠⣄⡀⠀⠀⠀⠀⠀⢸⣿⡖
⢛⠝⠛⡿⠀⠀⠀⠀⢰⠟⠉⠀⢀⠀⢱⡄⠀⠀⠀⠀⡞⣹⠚⠿⢛⠝⠛⠿⠀⠀⠀⠀⢰⠟⠉⠀⢀⠀⢹⡄⠀⠀⠀⠀⡏⣩⠚
⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⣺⡿⠇⣸⠋⠀⠀⠀⠘⠐⠃⠀⠴⠁⠀⠰⠃⠀⠀⠀⠀⠀⠀⢀⣲⡿⠇⣸⠃⠀⠀⠀⠘⠒⠃
⠀⠈⠁⠀⠀⠀⠀⠘⢆⠀⠀⣀⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠒⠒⠀⠈⠁⠀⠀⠀⠀⠘⢆⠀⠀⣀⣠⣄⣾⡆⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠛⢦⠉⠉⠁⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠛⢦⠉⠉⠀⢘⡇

⠛⢠⠾⠀⠀⠀⠀⣠⠞⢻⣷⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⣿⠟⢧⡸⣿⣿⠁⠀⠀⠀⠀⠀⡃⠀⠀⠚⠋⠉
⠒⠀⠀⠈⠠⠖⢾⡏⣠⠄⠻⣶⡷⠀⠀⠀⠀⠀⢀⣾⡿⠿⠀⠀⢳⣿⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡀⠀⢰⣾⠇⠋⣿⣿⣿⣿⠦⡎⠤⠀⠀⠈⠀⠀⢀⣶⣰⣾⣿⡇⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠈⢷⡄⣨⣷⣶⣇⣿⣿⣿⠃⠠⡅⠀⠀⠀⠀⠀⢀⣼⡿⠟⠛⠛⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⣧⣿⣟⣅⠙⣿⡿⠟⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⠀⡀⣠⣴⣿⠐⠁⠀⠀⠀⡀⠀⠀⠀⣀⣰
⠀⠀⠀⠀⠿⠋⠈⠁⠀⠁⠠⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⣀⣀⣤⣼⣿⣿⣿⠀⠀⠀⠘⠁⠁⠀⠒⠸⠏⡨
⠀⠀⠀⠀⣿⡿⠿⣷⣿⣿⡆⠻⢃⣐⠏⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣃⣿⡿⠃⠀⠀⢀⣤⠅⠀⠀⠀⢰⣿⣾
⠀⠀⠀⠀⠸⣶⣾⣿⡟⠉⠀⠀⠛⠁⣠⣌⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣟⣷⣿⠃⠀⢀⣴⠞⠇⠀⢠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⠁⠤⠀⠀⠀⠛⢻⢛⠁⣤⠀⠀⠀⠀⣠⣿⣿⠏⠘⣿⣶⢟⡆⠀⠛⣁⣴⣴⡴⠟⣿⣿⣿⡟⠁
⠀⢀⠄⠀⠀⠈⣵⣿⠀⠀⠀⠱⣄⠀⢰⣿⠘⠇⠀⠀⠀⢼⣿⡿⠃⠀⠀⠿⣱⣿⠁⢈⡀⠈⠁⠀⠀⡄⠿⠋⣠⠖
⠀⢸⡆⠀⠀⠀⠘⣿⠀⠀⣠⣾⣿⠄⠘⢡⣠⠀⠀⠀⠀⣼⠟⣁⣀⣤⡾⠙⣿⠁⠟⠀⠀⠀⠈⠁⠀⠀⣠⣌⣩⢳⣤
⠀⠀⠁⠀⠀⠀⠰⡷⠖⠚⠙⢿⣿⠀⠀⣠⣿⠀⠀⠀⢀⣿⣿⣿⣿⠿⠵⠔⠋⠀⠀⠀⠀⠸⣦⠀⠀⢠⣿⡟⢡⣿⠙
⠀⠀⠀⠀⢠⠀⢀⣀⣠⠤⠖⢊⣽⡆⠰⣿⣿⠀⠀⠀⣸⣿⣛⣩⣥⠔⠀⣄⣀⠀⠀⡆⠀⠀⢸⠿⡆⠈⢉⣿⣿⡟⣾
⠀⠀⠀⠀⠀⠀⢚⣭⡇⠀⠀⠹⡏⠳⠐⠛⠁⠰⠀⠾⢻⡿⢛⠋⠁⠀⠀⠹⣿⣇⢀⣥⣀⣠⡴⠀⠀⣶⣿⣿⣿⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⢀⠆⠀⣾⣶⡤⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠃⠀⠈⠁⠀⠀⢸⣧⣦⡀⠀⡴⠛⢢⡀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠻⣿⡟⠀⢿⣿⠞⠁⢀⣿⢀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠨⠤⠌⠰⢀⢻⠑⠐⠀⠋⣣⠀⣉⠁⠨⠉⢠⠀⠀⣼⡿⠷⣴⣿⣿⡆⢀⠞⡏
⣶⡟⣿⠁⠀⡀⣈⣨⡇⢀⠖⠉⢩⠛⢄⠀⠀⣠⢊⠜⢯⠀⠉⠢⡀⠀⠀⠈⠏⠀⠀⠹⠿⣶⡟⠁⠠⠁
⣿⡇⣿⠠⠀⠄⠠⠛⠀⢨⠀⠰⠿⠖⣺⠶⡾⠁⠸⡀⠈⠓⠀⢀⠇⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀
⢙⠃⠉⠀⠀⠀⠀⠀⠀⠀⢱⡤⠤⠴⠁⠀⠀⠀⠀⠵⠦⠤⠴⠎⠀⠀⠀⠁⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⣤⡀⠉⢉⢩⠉
⠉⠀⢠⠁⠀⠀⢀⠀⠀⠈⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣟⣺⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⡀⠐⠆⠀⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡟⣽⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠐⠻
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠐⠁⠘⠀⠀⠀⠁
⠀⠀⠁⢠⣄
⠀⠀⠀⣚⣻⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⡶⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠯⡿⢫⡜⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢹⠆⠀⠀⠀⠀⠀⠀⠈⠉⠈⠒⠚
⠀⠀⠨⣿⣷⠠⢮⣿⣟⣣⡄⢠⣄⠀⠀⠀⠀⠀⠈⢦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⠀⠀⣺⣿⣆⠘
⠀⠀⠀⠀⢮⠟⠀⠀⠈⠀⠀⠸⠁⠀⠀⢀⠀⠀⠚⠘⠓⠈⣀⣀⣀⣴⣶⣶⣦⡀⠀⠀⠈⣻⣿⣿⣿⡄⠀⠉⠻⣿⡆
⠀⠀⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠐⠀⠀⠀⠀⠀⣿⡥⠽⢛⣫⣭⣥⣶⣦⠀⠘⠛⠛⠋⢻⡧⠀⠀⠀⠈⠙⠛⠋
⢀⣶⣿⣽⣭⡙⠰⣠⠄⠀⠐⠀⢚⠋⠀⡀⠀⠀⠀⢀⣐⠀⠘⣷⠁⠀⢈⣉⡁⠁⠀⠀⠀⠀⠀⠀⠾⠙
⠀⠉⠉⠛⠻⠷⠾⣿⣿⠆⠀⠀⠉⠁⠉⠁⠀⠀⠀⠈⠙⢀⠀⠿⡇⠀⣷⣛⠎⠆
⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⢰⡄⠶⠒⠀⠐⠀⠸⠘⠓⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣾⡟⣷⣶
⡀⢤⡼⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁
⢉⣷⢬⣿⣶⠶⠶⠿⠿⠿⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠘⠳⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⣴⠀⣾⣉⣛⣆⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣀⣠⣤⡀⠶⣶⣎⠙⢯⣧⣄⠸⣆⠈⢙⡓⠛⣫⡧⠀⠀⠀⠀⣀⠀⠀⠄
⠀⠀⣔⠀⠀⠀⠀⢠⣤⢤⡀⠚⢿⡈⠉⢮⡳⣶⢤⠀⠈⠻⢿⣢⣯⠓⠯⣿⠄⠈⠙⠉⣉⣀⡤⠶⠚⠋⠉⣀⡀⠰
⠀⢸⣉⠂⠀⠀⠀⠀⠘⢿⣿⠵⣤⣽⣶⣀⠑⣿⣦⣤⠿⠆⠀⠈⠁⢀⣀⣤⠤⠶⠚⠋⣉⣁⠀⠤⠐⠒⠉⡥⠄⡂
⢀⢮⣻⣦⠀⠀⠀⠀⠀⠀⠉⢳⣤⡭⠉⠉⠁⢉⣀⣀⣤⠴⠶⠚⠋⢉⣁⣠⣤⡒⠺⡩⠗⣌⡙⣲⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠳⣤⠙⢻⣦⡀⠆⠀⠀⣀⣨⡤⠶⠖⠚⠋⢉⡉⠀⠠⢔⡒⠊⠉⣽⠙⡶⣅⢼⣀⢙⠂⣚⢲⣱⣦⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠈⠻⡠⡙⢿⣷⣔⠢⣌⠀⠀⠆⣒⡃⠥⠌⠀⠀⠀⢀⠙⠢⡀⢸⠆⣉⢛⢀⣉⣝⣾⢳⣫⠽⠟⣛⡁⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⣒⠀⣰
⠀⠀⠀⠀⠈⢢⡀⡈⢹⢷⣄⢑⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠄⠙⣾⡎⣽⡯⠭⠓⣊⡉⡤⠔⠖⠊⢁⠀⠀⠀⡤⣄⠶⠸⢗⣂⣭⣽⣦⣴⢋⢠
⠀⠀⠀⠀⠀⠀⠈⠪⡀⡁⠙⢗⠦⡀⠄⡂⠄⠠⠀⠀⠀⠀⠀⠀⠀⠈⢤⠤⠖⢛⠁⠁⣀⣄⣤⡤⣧⣴⣦⠀⣬⣯⣶⣾⠿⡟⠻⠋⠋⠉⢁⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢮⠀⠠⠳⡈⠓⣬⣐⢄⠠⡀⢠⠤⠖⠓⡃⣀⢠⣤⣆⣶⢸⣿⣗⣿⣿⣿⣿⠿⠻⠒⠋⠉⠁⠀⠀⠀⠄⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠙⣄⠀⠈⢳⡔⠰⠀⣷⣶⣮⣧⠇⢹⣿⣷⣿⠿⠟⠛⠉⠉⠂⠀⠀⡀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡊⡊⠓⠒⠚⠁⠀⣸⣿⡿⠷⠛⠒⠉⠉⠀⢀⠐⠠⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠤⠂⣀⠤⠚⡫⠄⢀⡀⠠⠔⠊⠐⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠒⠠⠄⣀⡔⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠬⢙⡢⣄⡀
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢠⢶⡀⢀⠀⠀⠈⠉⠛⠦⢄⣀
⠀⠀⠀⠀⠀⢰⠃⠐⠤⣄⡀⠀⠀⠀⠏⠀⢷⠏⡼⢅⠀⠀⡆⢀⡀⠀⠉⠐⠂⠤⢄⣀
⠀⠀⠀⠀⢠⢏⡾⣋⡥⠂⠉⡛⠲⠦⠤⢄⣀⣀⠃⠀⠀⠀⣧⠞⣷⣠⠏⣠⠠⠄⠀⠀⠀⠉⠐⠒⠤⣄
⠀⠀⠀⢠⢏⡾⠚⠁⣠⠴⠊⡡⠔⠀⢈⡆⢀⣀⡉⠑⠒⠤⢄⣀⠛⠁⣀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀⠞⣱⡆
⠀⠀⢀⢏⣎⡤⠖⠋⣡⠔⢋⠠⠔⢂⠞⠀⠀⣁⠈⠒⠢⢤⣄⣀⠉⠑⠒⠬⢄⣀⠀⠀⠀⠀⠀⢠⢎⣴⠥⣬⠂
⠀⢀⡞⡞⠁⣠⢔⠫⠒⠉⣀⡤⢴⠏⠀⠀⠒⠤⢈⡑⠂⠤⠀⠈⠉⠑⠒⠲⠤⠤⣉⡑⠢⠀⢠⣿⣫⠔⠊⠅
⠀⡞⡼⠁⠑⠊⣁⡤⠖⠋⠁⢀⡞⠀⠀⠈⡑⠲⠤⣀⡉⠐⠀⠀⠄⣀⠒⠠⠄⡀⠀⠉⠓⢠⣿⡿⠃⠀⠀⠀⢨
⣸⣱⠃⠀⠚⠉⢁⡤⠖⣚⣩⡞⠀⠀⠬⣑⠒⠬⢔⡂⠌⠁⠀⠒⠦⢄⣉⠐⠂⠤⠁⠀⣠⣿⣟⠑⠠⠤⠄⣴⡿
⡇⠈⠀⠀⠐⠠⢀⡖⣫⠥⣾⠀⢀⠑⠲⢤⣈⠐⠠⢌⡁⠀⡐⠢⠅⣒⠠⢉⠒⠂⠀⣰⣿⡃⠀⠉⠀⢠⣾⠿⠚
⠱⡀⠉⠑⠒⠂⠤⠬⣁⡀⠁⠐⠠⣉⡑⠢⠤⣉⡒⠢⠀⠢⢄⡉⠒⠤⢉⠑⠂⠀⣸⡿⠡⢉⠓⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣌⣁⠒⠢⠄⠠⣀⠒⠤⢌⡙⠒⠤⣈⠁⠀⡿⣍⡑⠂⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⡀⠀⠀⠈⠉⠓⠒⠤⠤⣉⣒⠢⠬⣉⠐⠀⠀⣼⡉⠒⢁⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠀⠀⡼⢥⡈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⡼⠉⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠚⠙⠉⠙⠙⠒⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠶⠾⠁⠀⠀⠀⢤⡠⠤⠤⡠⠄⠀⠀⠀⠹⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡄
⠀⠀⠀⠀⢠⣶⠟⠇⠀⠐⠊⠑⠒⠢⠀⠀⠀⠀⠀⠔⠒⠒⠉⠒⠀⠘⠟⢷⣄⠀⠀⠀⠀⠀⢰⢻⢸⣷
⠀⠀⢀⡤⣾⠷⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣦⡀⠀⠀⠀⢸⣾⢸⣿⡀
⠀⠀⠸⣿⣿⣄⣀⣀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢀⣾⣀⣀⣠⣾⣷⡟⠀⠀⠀⢸⢿⢸⣿⡇
⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⠋⠀⢀⣠⣶⣿⢸⣿⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠙⠻⣯⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣯⡿⠋⠛⠉⠁⠀⠀⠸⠟⠛⢻⠈⣿⠀⡟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠖⠛⠛⠛⠛⠛⠉⠉⠉⠹⠛⠛⠛⠛⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠤⠶⣷⣤⣴⣤⣤⣤⣴⡷⠦⠤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡇⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢿⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢸⡇⢀⣿⡇⢸⣇⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡏⡟⠏⠉⠉
⠀⠀⠀⠀⠀⢀⡤⠔⠉⡩⡤⠖⠂⢸⡇⢸⣿⣧⢸⣿⠀⠒⢤⢌⡉⠳⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣀⣤⣤⣿⣇⡾⣿⠿⣌⣿⣤⣤⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⢸⠀⢸⢸
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠉⠀⠈⠛⠀⠀⠀⠘⠁⠀⠉⢻⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢿⠘⣦⠏⣸
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢶⡤⢷⣤⣴⢦⡴⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣀⣀⢀⣀⣀
⠀⠠⠀⠋⠋⠛⠚⠛⠛⠓⠠⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠒⠉⠓⠀⠉⠀⠉⠒⠘⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⣙⠇⠀⢀⠢⡤⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⢀⡀⣀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠡⠀⠀⠈⠉⠀⠁⠁⣤⠈
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⡄⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠠⠌⠀⠠⡀⠀⠀⠀⠀⠦
⠀⠀⠀⣤⣀⣤⡀⣀⣀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡹⠟⠚⠛⠛⡦⠆⠀⠀⠠⠉⠀⠀⠀⠀⣴⣼⣳⣿⡶⣤⡄⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⠂
⠀⠀⠀⠀⠘⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⡞⠀⠈⠀⠀⠀⣀⠁⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢁⠻⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⡀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠀⠀⠀⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠢⢄⠀⠀⠀⠠⣀⢀⡀⡀⠀⢂⠤⣀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠻⠟⠶⠓
⠀⠀⠀⠑⠒⠂⠀⠀⠀⠈⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠒⠂⠀⠀⠉⠉⠉⠉⠓⠒⣄⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠐⠂⠀⠀⠈⠘⡤⠶⠶⠬⠥⠀⠀⢀⣐⡂⠉⠩⠛⡇⠀⠀⠀⠀⠢⠘
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢛⣉⣉⣈⡉⠉⣉⠁⠨⠕⢲⠊⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠒⠲⠄⠤⠒⠒⠒⠒⠮⡁
⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢐⣀⣈⣉⣭⠉⠰⢒⠎⠀⠀⠀⠀⠴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣀⣙⣛⣭⣍⣭⡕⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣐⣒⣒⠲⠤⡜⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠠⠄⣀⡀⠀⠀⠀⠈⠖⠒⠲⠰⠟⣍⣀⠤⠤⠒⠉⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⣛⠛⠛⠛⢡⠀⠀⠀⠀⠀⡒⠀⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠐⠒⠠⠠⠤⠤⠤⠀⠀⡻⠶⠶⢶⣷⠊⠁⠀⠀⠀⠀⠀⠤⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡭⠭⠖⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⡀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣿⠁⢠⠊⠙⣦⣏⡷⠀⣟⠹⡆⢰⠉⠙⡆⡴⠋⢻⡆⡞⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡼⠦⠴⠃⠟⠳⠖⠿⠘⠷⠜⠦⠞⠅⠳⡤⠞⠇⠳⣤⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠐⠒⠒⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠔⠒⠊⠉⠉⢉⣀⣀⠀⠠⠄⠀⠀⢂⠀⢇
⠀⠀⠀⠀⠀⡤⠄⠒⠈⠉⢁⣀⠠⠤⠄⣒⡒⢈⠭⣄⢰⢒⣤⠉⠀⠀⠀⠀⡀⠸⡄
⠀⠀⠀⠀⠀⢡⡀⠰⡊⠅⠀⢐⠌⡵⢅⢠⡝⠋⢋⠁⠙⣾⣹⠀⠀⠀⠀⡀⣅⠀⢧
⠀⠀⠀⠀⠀⠈⡧⠀⢀⠀⠀⠀⣰⠯⠌⠈⠙⠀⢋⣉⠠⠤⢐⣒⣤⢄⠀⠀⠫⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢱⠀⠀⣀⠀⠀⠄⠀⣒⡂⠭⠅⡲⡒⠟⠋⠉⠁⠀⡀⠀⠀⠀⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠘⡆⠀⢐⢶⣤⡘⡖⠁⠞⠃⠃⠀⢇⠀⠀⠀⠂⠊⠀⠐⠂⡀⡸⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠄⠃⠀⠀⠀⠀⡀⠀⠉⠀⠀⠄⣀⡤⠖⠒⠛⣉⡠⠀⢄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⠀⠂⠈⠄⠀⢀⣂⠤⠤⡇⢠⠑⣒⠂⠍⠀⠠⠦⠐⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢦⠔⠒⡉⢋⣁⡒⡟⢿⣷⠈⡄⠀⠀⠀⠀⠀⠀⠈⠀⢡⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⠀⠂⠂⠈⠛⠓⠛⠉⠀⡆⢠⠈⠡⠀⠀⠀⠀⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡆⠒⠒⡈⠤⠀⢀⠢⠌⢤⠈⠀⠀⠀⠀⠀⠀⡐⣀⣠⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠩⠐⠀⠀⠡⠁⠀⠀⠀⠀⢃⠵⠶⣶⠚⡻⠋⠉⢁⠄⢡⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠄⠰⠠⠀⠀⢀⡀⠸⡀⠀⢹⠎⠠⠖⣀⠀⠀⠨⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠆⠀⠀⢀⡄⢧⢴⣓⠂⠬⠽⠿⡗⢶⡾⢟⣦⣄⡠⠠⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠚⠛⠉⠉⠉⣰⣴⡀⠤⠤⠐⣑⣂⣉⣭⣥⣴⣴⠶⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠒⠂⣉⣉⣭⣤⣴⡶⠾⠟⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠶⠟⠛⠛⠉⠉

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

⠬⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠈⠀⠀⠹⡀⠹⠋⣳⡍⣿⡴⢿⣟⠉⡝⠀⠜⡩⠊⠰⢁⠞⠙⠁⡠⠞⠁
⢤⣄⠀⠀⠀⠀⠀⠁⠈⢢⣴⠦⠤⣤⣄⡀⠀⠀⠀⠀⢠⢖⠛⣧⣄⢸⢱⠟⠋⠀⠀⣻⡜⣁⣤⣀⣁⣀⣀⢄⣀⣤⡈⠀⠀⠀⠀⣠⣔
⣒⠠⠀⠒⠄⠀⠀⠀⠀⣟⡀⠠⢀⠤⣼⠋⠗⠓⢀⢴⢟⡀⠀⠈⠀⠚⠓⡶⠀⠀⠈⠋⠉⠉⠀⠁⠠⠏⠀⢀⠃⠀⢻⡆⡠⠐⠉
⡒⠀⠠⠤⣀⠀⠀⠀⠀⣽⠂⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⠀⢠
⠉⠛⠂⠀⠀⠀⠀⠀⠀⠈⢲⡆⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠠⢿⠉⠉⡧⠀⠀⠀⢘⡆⠀⠀⠀⠀⠑⠉
⠤⠄⠀⠀⠀⠀⠀⢀⡠⠤⣴⢳⡤⠀⠀⠀⠀⠀⠁⠰⠐⠀⣀⠀⠀⢢⠈⡄⠊⠁⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠚⣫⠄
⠴⠒⠦⠤⠀⢀⡜⠉⠛⠁⠘⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠛⠉⠉⠷⣶⢦⡄⢀
⡒⠖⠂⠀⠀⣸⡏⠁⣀⠔⠚⠀⠈⠒⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⠟⣙
⢛⢉⡴⠎⠉⠃⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⡀⠶
⠈⣿⣀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠒⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤
⡒⡚⠻⠷⢶⣟⠀⠈⠳⢴⣎⡠⠀⠀⠀⠀⠀⠈⠀⢠⠀⠄⠆⠀⠀⠀⢀⠀⠠⠄⠈⠈⠀⠀⠀⠀⠀⠁⠀⠄⢰⡄⠀⠀⣀⣀
⢀⣀⡀⠀⠀⠘⠳⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠄⠀⠀⠀⠀⠀⢴⢼⠁⢤⠚⠋⠉⠂⢉⣉
⠿⠁⠀⠀⠀⠀⢀⠀⠍⠁⣻⠀⠀⠀⠀⠈⠙⠉⡉⠀⡀⠀⢀⣀⡁⠀⢆⠀⠀⠈⠁⠀⠈⠉⠀⡠⠶⣤⡤⠞⠋⢀⡖⠀⠈⠐⠒⠄⠠
⠈⠀⠀⠀⡠⠂⠁⠀⢀⣴⠿⣄⣄⣡⠴⡄⠀⣠⡷⢚⠂⠀⠀⣹⡍⠂⢢⣄⣀⣤⠟⠦⠴⢧⣀⣀⣶⠏⠓⠲⠞⠋⠁⠀⠈⠀⢄⠐⠠
⣖⠔⠊⠀⠀⡠⠔⠋⠙⠁⠀⠀⠀⠀⠀⠉⠋⣱⠃⠸⣏⣠⣴⠋⢷⡄⠀⠀⢡⠇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠁⠀⢀⡴⢋⡤⠊⢁⣀⣠⢂⡖⢠⢈⡠⠀⢰⢃⣴⣤⡌⢷⡱⢳⣧⣙⡃⢟⢉⠀⠀⠀⠁⠀⢰⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣄⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠢⣄⢠⠃⠈⠓⢄⣀⠎⠈⠻⢄⡀⠈⠑⠒⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡙⢦⣀⠀⠀⠉⢲⡄⠀⠀⢉⡆⠀⢠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠌⡒⢌⠙⡆⠀⣾⠀⠀⠀⡎⠀⢠⠧⣀⣀⣀⡠⠤⠒⢄
⠀⠀⠀⠀⢰⣭⣉⠉⠑⢄⡐⠬⡒⢸⡟⠀⠘⣆⠀⠸⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡄
⠀⠀⠀⠀⠘⠿⣿⣿⣶⣄⡉⠒⠬⣀⠹⣆⠀⠈⠳⣄⠳⣄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣛⣶⣆
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣻⣿⣷⣤⡈⠙⠒⠻⠷⣦⣬⣵⣮⣷⣦⣵⣶⣤⣦⣤⣶⣶⣿⣯⡭⠿⣾⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢟⢿⣿⢶⣞⣻⠿⠿⢿⣿⣿⣿⣿⣟⣛⣛⡿⠿⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⠷⠶⠛⠛⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣽⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⢛⡛⠛⠻⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣤⢴⣀⣀⣠⣤⠤⢤⣄⠀⠈⠉⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⢉⣠⣀⠀⠀⠀⠳⣌⠉⠀⢠⡠⠤⣫⠴⢋⡠⠤⣄⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠡⣤⣄⣀⡀⠉⠉⢿⡒⠲⠾⣦⠀⣀⡴⠋⡡⠖⠁⠀⠠⣦⣝⢦⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⢀⠤⠚⠉⢀⣄⠀⠈⠉⠙⠓⠲⠷⠀⣀⡴⠞⠁⠴⣋⢠⣤⡰⢶⣝⢷⣝⣷⡙⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠉⢀⡀⠀⠙⠻⢶⣴⡊⠁⠀⠀⠀⢀⣤⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠉⠺⣟⢷⡝⣧⡻⢎⡵⠋⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠉⠙⠢⣄⠀⠀⠉⠻⢶⣤⡤⠔⢉⣠⠾⠋⡀⠔⠀⠂⠀⠀⠀⠀⠀⠀⠈⠳⡻⣮⠕⡫⢀⠄⡠⢸⡇
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠒⠿⣟⠻⠿⠶⠶⠶⠶⣿⣦⣄⡀⠈⠉⣠⡶⠛⢁⠔⡨⢀⠅⡂⢔⠠⢀⠀⡀⢀⠀⡀⠀⠘⡡⢊⠔⡡⠊⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠁⣠⡴⠟⢉⡠⡊⢔⠡⡂⠔⡨⢐⠥⡊⢔⠨⢂⠄⡠⢀⠄⠀⠀⠕⠀⢀⠴⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⠿⠿⣦⣄⡀⠀⠀⠀⠙⡷⠂⠀⣀⣴⠟⠋⡠⢐⠅⡪⢒⠅⡪⢔⡥⣊⢕⡪⢖⠥⣊⠕⣊⠔⡡⢊⠄⠀⢀⡴⠋⣰⠟⠁
⠀⠀⠀⠀⠀⢤⣤⣿⢿⣉⠓⢦⣀⡉⠻⢷⣦⣄⡀⠀⠀⠚⠋⠁⠔⡪⡂⢕⠥⡊⢔⡩⣒⠕⡪⢔⡩⢒⡥⢊⡥⢊⠴⢋⠔⣡⠂⡀⠈⣠⡾⠃
⠀⠀⠀⠴⣿⣟⠳⠮⣅⡈⠙⢒⠮⣝⡓⠶⢤⣭⣛⡳⠶⢤⣄⣀⡀⠀⠀⠑⠪⢖⠵⣪⢕⡩⢖⡩⢞⡡⠖⣡⠞⣡⠞⣡⢞⡥⠊⣠⡾⠋
⠀⢀⣴⣾⣟⣛⣛⣓⠢⢬⣑⠢⢄⡐⠨⣝⡒⠦⣭⣉⣛⠻⠶⢾⣭⣿⣲⣦⣤⣀⠈⠒⣩⠖⣩⠖⣫⠴⢋⡴⢊⡵⠚⡡⠊⣠⣾⠋
⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣶⣯⣶⣬⣑⠦⣍⡒⢤⣉⠛⠻⢷⣶⣤⣉⠙⠻⢿⣿⡻⣦⣄⠋⡴⢚⣡⠞⣩⡴⢋⡴⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡾⣝⡷⣬⣛⢦⣄⠉⠛⠿⣿⣶⣄⠙⢿⣎⢻⣦⠀⢋⣥⠞⢉⡴⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⡛⢾⣝⣷⣍⡻⣦⣄⠈⠙⢿⣷⣄⢹⡆⢻⡇⠈⣡⡶⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⠿⣮⣛⢮⣙⠷⢦⣤⡿⠟⢠⠇⣼⡇⠀⠉⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⣷⣝⠳⢦⣤⡤⠴⢋⣴⡿⢁⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⡙⠿⢶⣶⣶⣾⣿⣿⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢖⣚⣫⣭⠿⠶⠟⣛⣛⣋⡩⠭⠭⠭⠶⠶⠖⠒⠒⠒⠒⠲⠶⠶⠶⢾⣭⣽⣿⣿⣿
⠀⠀⠀⢀⣠⣴⠶⠛⠉⠥⠖⠚⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠭⠭⠭⠭⠽⣿⣿⣿⣿⡿
⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣬⣤⣭⣥⣤⣴⡿⠟⠋
⣾⡏⠀⠀⠀⠀⢀⣠⣤⣶⠾⠛⠉⠁⣀⣀⡤⠴⢒⣂⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠿⠛⠋⠁
⠙⢷⣦⣤⣴⣾⡿⠛⢉⣠⣤⠶⣚⣫⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉
⠀⠀⢮⣭⣙⣛⣛⣛⣻⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣟⣻⠿⠯⠭⠭⠤⠤⠴⠶⠶⠒⠒⠂
⠀⠀⠀⠀⠀⠈⢻⣿⣶⣦⣭⣭⣭⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣛⣛⡿⠷⠶⠶⠶⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⢮⣭⣭⣭⣛⣛⣓⣒⣒⣒⣂⣀⣀⣠⣤⣤⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣶⠶⠭⠭⢭⣭⣭⣭⠭⠥⠤⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣩⣭⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠭⠍⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡭⠭⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠟⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣻⡴
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣏⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣿⣯⣽⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠉⠉⣉⡉⠉⣉⠉⣉⣉⣉⣉⠉⢉⣁⠉⢉⡉⣉⣉⡉⠉⠉⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣷⡀⣿⠀⣿⣉⡉⢹⡇⣸⣿⠀⣿⢸⣏⡉⠁⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⠈⢿⣿⠀⣿⠉⠁⠈⣷⡟⢸⣿⠇⢀⡈⢹⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠉⠀⠀⠉⠀⠉⠉⠉⠀⠉⠁⠀⠉⠀⠈⠙⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠢⣄⡈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⠤⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠙⠳⡂⢌⡛⢶⠤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠳⡃⠀⡤⠚⠉⠉⠲⣄⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠲⢌⠉⠓⠊⠙⠳⡴⠚⠓⠶⠉⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡇⠀⣀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡽⠄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠗⢋⣵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢿⠄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠦⡼⠘⢤⠃⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⡆⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⠀⠀⠉⢹⣃⣀⣤⣤⠶⠚⠉⠀⠀⠀⠀⠰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢈⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣁⣀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠅⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠆⠀⠀⠐⠒⠛⠻⠶⡄⠀⠀⠀⠀⠀⠀⠀⡤⢝⣷⣌⡉⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠉⠓⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠔⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⣴⣴⡀⣶⣾⡁⠚⠆⠀⠀⠀⠀⠀⠀⠀⢺⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠘⠇⢷⡏⠃⠙⠀⠀⠀⠀⡔⠢⠤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⣞⠉⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠙⠢⢤⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠰⣕⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣖⠚⠁⠀⠀⠀⠀⠀⠀⠁⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡏⠹⡄⠀⠀⠀⢀⡄⠀⠀⠀⡇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡘⠀⠀⠉⠓⠒⠚⠁⠘⠦⠤⠞⠁⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣾⠿⠂⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⡄⠂⠀⠀⠀⠀⣠⣼⡆⠀⠀⠀⠀⠀⢀⣴⣿⠿⠝⠿⣳⣴⡆
⠀⠀⠀⠀⠀⢀⣤⣷⣾⣷⣦⣤⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⠁⠀⠀⣌⣀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⡀⠉⠁⠀⠐⠿⠿⠟
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⣿⣿⣿⠟⣶⣧⡼⢿⣿⣿⡿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠻⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣄⣛⣟⢁⣼⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣷⠉⠓⠀⠀⠀⠀⡄⠀⣿⣟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⠿⣿⣶⡆⠀⢠⣾⣷⣶⣿⠏
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠀⠀⠘⣿⣿⣿⣟⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠻⡟⠉⠁
⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠂⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣀⣤
⠀⠀⠀⣠⢴⣞⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⢻⣛⣛⣛⣛⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠛⣙⣿⣿⣿⠇
⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⢹⣿⡿⣿⣿⣟⢹⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⡀⠀⠀⠉⠉⠙⠋⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣈⡀⠀⢀⣴⣿⣴⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠝⠋⠛⢛⠟⠋⡇⣀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⡷⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⠀⠺⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⣿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⠋⠁⠀⠀⠀⠀⠀⣼⠂⠀⠉⠉⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿


⠀⠀⠀⣤⣶⣾⣿⣿⣶⣶⣄⠀⠀⠀⠀⢀⣠⣤⣤⣦⣵⣤⣤⣀⠀⠀⠀⠀⠀⣴⠶⠶⠚⠛⠛⠛⠛⠷⠶⢦⡄
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢈⢛⣟⣛⣛⣛⣛⣛⢛⡁⠀⠀⠀⠀⠸⠶⢶⣶⣤⣤⣴⣤⡶⠶⠾
⠀⠀⠀⢸⣿⣿⢛⠛⣿⣿⠀⠀⠀⠀⢏⣻⠐⡇⢸⡇⢸⠀⣿⢰⣏⡇⠀⠀⠀⠠⣴⣄⣄⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠠⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⢸⣿⠉⣿⠿⢙⣿⠀⠀⠀⠀⠀⢹⠈⡇⢸⡇⢸⠀⣿⢸⡇⠀⠀⠀⠀⠀⣀⡀⠈⠉⠉⠉⠨⠀⣀⠀⠀⠀⠀⠀⢹⣶⣾⢻⣶⣾⣻⣷⣾⡟⣷⣶⡏
⠀⠀⠀⢸⣿⣷⣾⣶⣿⣿⠀⠀⠀⠀⠀⢸⡀⣷⢸⡇⢸⠀⣿⢸⠇⠀⠀⠀⠀⠀⢉⡋⠛⠛⠓⠛⠛⠉⣉⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⢹⣿⣿⡇⣿⣿⡇
⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⢸⣇⣿⢸⡇⣸⠀⣿⣸⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣶⣶⣾⣿⡏⠀⠀⠀⠀⠀⠶⠿⠿⠾⠿⠿⠾⠿⠿⠷⠿⠿⠶
⠀⠀⠸⠟⠿⠿⠿⠿⠿⠟⠿⠀⠀⠀⠀⠀⠺⠭⠽⡧⡿⠭⠽⠒⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠋⠉⠀⠀⠠⠀⠀⠉⠉⠉⠉⠙⠛⠛⣻⣶⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠋⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⣉⣨⡵⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⢿⣍⡉⠀⠀⠀⠀⠀⠒⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣋⡤⠶⠛⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣟⣛⣛⣛⠷⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⢛⣛⣛⣛⣛⣻⣟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠿⠿⠿⠿⠿⣿⣿⣿⠟⠻⠟⠛⠛⠿⠶⣦⣤⡴⠿⠿⠿⠿⠿⣿⣿⡿⢟⢻⢿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣁⣀⣤⣤⣤⣤⣤⣭⣿⣿⣷⣦⣄⡂⠄⡁⠂⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⢫⡱⢼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣉⣁⠀⠬⠕⠒⠒⠒⠒⠈⡛⠿⣽⣲⣄⡀⠀⠀⣀⣴⢿⠛⠉⣁⡴⠚⠑⠂⠼⣗⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠛⠛⠓⠒⠒⠒⠠⠀⠈⠁⠈⠙⠚⠛⢦⡾⠛⢉⣠⣤⠂⠀⢀⣀⣤⠴⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⢶⣖⡛⠛⠮⠤⣴⣤⣄⣀⣐⠒⠛⢛⡛⣻⡿⠞⠛⣉⣠⡴⠟⠋⠙⢶⣄⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣳⡄⠙⠉⠛⠶⢦⣄⣀⠈⠉⠛⠛⠿⣷⣶⣾⣶⣿⣿⣿⡝⠂⢀⣠⣴⡶⠿⣟⣛⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⡉⢷⡀⠈⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀⠀⠉⠉⠛⠝⢋⣡⣴⣾⣟⣩⣴⣾⣛⡋⠉⢥⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⢳⡈⠷⣤⡤⠶⠶⠶⠶⠶⣶⣆⣉⡙⠲⢤⣀⣤⢾⣿⡿⠛⠛⣉⡩⠍⠋⢉⣻⡗⠶⠆
⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠤⢈⣳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣉⣙⣻⣿⣶⣿⡥⠶⠾⠛⠋⣁⣤⢾⡏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠛⠓⠲⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⣻⢉⠉⠁⣀⣤⡴⠾⠛⠉⠀⠈⣿⠶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⠋⠓⠒⠲⢦⣭⣝⣛⠶⢤⣄⣀⣠⣾⣇⣠⣤⣿⣠⡵⠒⠉⠥⠤⠤⠄⠀⠀⠀⣧⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠿⠛⠶⠶⢦⣤⣌⣉⣛⠳⠶⢿⣭⣿⠫⣉⣯⣜⣒⡶⠶⢶⠶⠖⠶⠶⣶⣤⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣶⣤⣀⠀⠀⠈⠙⣿⠛⠻⠶⣶⡟⠛⠻⠷⣿⣭⡴⢚⡡⠐⣀⠠⠀⠀⣈⡿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢾⣿⣿⡯⠛⢶⣤⣀⠘⠓⠒⠚⠉⠙⠻⢶⣤⣀⡀⠀⠀⠐⢉⣀⣤⣶⣿⣛⣁⠬⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢁⡼⠉⠛⢷⣦⣾⣿⣿⣶⣄⡀⠀⣀⣴⠾⠧⠽⣿⣶⣶⣾⣿⠿⢛⣉⠭⡁⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣤⣤⣀⣀⡈⠙⠻⠾⠷⢾⠿⢾⣭⣀⣀⣤⣴⠧⠘⢋⡩⠶⣛⣩⣶⣛⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠉⢹⢿⡿⢗⣲⢶⣦⣤⠾⠋⠉⢛⣿⣢⠦⠒⢚⣩⠿⢋⣥⡾⢽⠛⢖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡇⠀⢳⣄⠉⠛⠳⣶⣤⣔⣪⡝⣿⡈⢙⣛⢩⣷⣶⣯⣥⠴⠞⠃⠈⣆⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠙⠲⢤⣹⣦⠶⠛⠉⠀⢈⡝⠛⢿⣿⡷⠾⠛⠋⣉⠤⠄⠂⠀⠀⢀⣸⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠈⠑⠢⣄⡉⠛⠶⣤⡀⠀⣾⠟⠓⣦⡀⠀⠀⠀⠉⢀⣀⣤⣴⣞⣛⣯⣭⣴⠶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢶⣤⣀⠀⠉⠀⠀⠀⠙⣿⣇⡀⢸⠇⢻⣄⣠⣴⠾⠛⠋⠉⠉⠀⠀⢀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢮⡙⠻⢦⣄⡀⠀⢸⣏⣨⡏⠹⣇⠀⠙⠋⣀⡀⠰⠖⢀⠀⣄⣀⡌⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠈⠑⠀⠉⠙⠳⠿⠿⠟⠀⢠⡟⠀⢀⣀⣤⠤⠶⠚⢉⣥⠞⠁⢀⠈⣿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣚⠁⢼⣧⣀⡀⠀⠀⠀⠒⠤⣤⣄⣀⡁⠘⣿⠉⠑⠦⣤⣀⣠⡶⠋⠠⡬⠓⠚⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣷⣦⣭⣙⠻⠶⣄⣀⠀⠀⠨⠭⣛⣿⡟⠒⣀⡀⠀⠉⠁⣀⡀⠀⣀⣤⡾⠿⠿⣄
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⣉⠉⠛⠛⠛⠚⠛⢷⣦⣤⣀⠀⢻⡇⠒⠀⠐⢒⣉⣩⠴⠒⣫⠍⠂⢀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣶⣤⣀⠀⠀⠀⠈⠛⠛⢿⣿⣷⣿⣷⢿⡉⠁⠀⠂⠉⠠⠖⠈⠁⢀⣠⠴⠞⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣦⣄⡄⠀⠒⠸⣇⠀⠘⢳⡝⢦⡀⠀⠀⢀⣠⠔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣖⣾⠾⠟⠍⠻⠞⠳⠤⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠰⣄⣀⠀⠀⢀⣠⣶⠾⠼⢶⣤⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢄⣽⣷⣶⣾⣿⣟⣥⣄⠀⠀⠈⠛⠻⢷⣄⡀⢤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣷⣽⠏⠁⡦⠊⠀⠀⠀⠀⠀⠀⠈⢲⣾⣿⣏⣴⡙⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡄⠀⠀⠀⡠⠔⠚⠓⠒⠄⠀⠈⠙⠍⠙⢿⣧⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠁⠉⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⡀⢠⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣧⡑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣾⣷⣄⢀⡀⢤⣠⢤⡀⠀⠀⠀⡠⠀⠀⠐⢺⣿⠁⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠈⢦⣙⠿⠿⣿⡛⣆⣈⣉⣙⣳⣶⣍⣂⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⢈⠛⠻⠿⠛⡋⠉⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡾⠛⠾⠻⠞⠻⠞⠳⠟⠳⠟⠷⠛⠶⠛⠾⠻⣾⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢈⣤⣉⣤⣉⣤⣩⣤⣡⣌⣡⣌⣡⣌⣤⣍⣤⡉⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠀⢠⣄⣤⢠⡤⢠⣤⣄⣤⣤⠦⠀⠀⠀⢸⣦⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⠛⡟⡟⢛⣟⠻⠛⠟⡛⢛⣿⣿⣿⡇⠘⠛⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠸⠟⠿⠸⠯⠌⠿⠻⠇⠬⠿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣰⣄⣇⣐⣻⣄⣤⣠⣟⣂⣽⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠖⠀⣴⣶⣶⡶⠶⣶⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣉⣉⣉⣉⣉⣿⡏⠉⠉⢉⣉⡉⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠖⠀⠿⠋⠙⢁⣤⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣉⣉⣉⣉⣉⣿⣇⣴⣶⣴⠟⠃⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠖⠀⠰⠾⠿⠿⠿⠿⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣉⣉⣉⣉⣉⣿⣿⣁⣀⣁⣀⣀⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠸⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣤⣤⣴⣶⣶⡄⠀⠀⠀⢹⠿⠁⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠿⡟⠂⢠⣶⣤⣤⣄
⠀⠀⠀⠀⠺⡿⠇⠀⣾⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠛⠙⠛⠛⠻⠿⣶⣤⣀⠀⠀⠀⠀⠈⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⣴⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⣼⡟⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⣇⠀⠠⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⢛⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠀⠀⢸⣿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⣿⡅⠀⠀⣴⡿⠛⠉⠙⠻⢿⣶⣤⣀⡀⣀⣤⣴⡾⠿⠛⣁⣀⡀⠀⠀⠀⢸⣿⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⡇⠀⢰⣿⠁⠀⠀⢀⣀⣠⣤⣿⡿⠿⢿⣿⣧⣶⣶⣿⠟⠛⣿⣄⠀⠀⢸⡿⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣶⣾⣿⡶⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⣿⣶⣶⣿⣷⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⡿⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⣿⣿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠂⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⣠⣾⠟⠛⠛⠛⠻⢿⣦⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠐⠒⠈⠒⠃⠀⠑⠰⠐⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⢀⠀⡀⡀⢀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⣉⣈⣉⣁⣈⣉⡝⠀⠀⠀⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠛⠸⠠⢆⢆⡆⢰⢀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠻⠈⣿⡿⠀⣌⢉⡀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠀⠀⢹⡄⡄⠄⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢋⣸⠀⠀⣻⠇⠘⠽⠜⠞⡾⠄⣰⡀⣄⡀⡀⠀⠀⠀⠀⠀⢀⠁⠀⠃⠃⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠀⠄⡟⠀⠀⠀⠀⠀⠈⠈⠉⠓⠙⠰⠹⢳⢷⢒⡂⢠⡄⣀⣀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠹⠼⠂⣧⢦⠖⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢐⣶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢁⡆⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⣦⣤⣤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠶⠦⢤⣄⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠓⠛⠿⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⣒⣶⣖⣒⣶⣖⣖⣲⣄⠀⠀⣤⣤⣤⣤⣤⣴⣖⣒⣒⣒⣒⣒⣒⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⠇⠀⠘⣯⣯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠈⢿⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠀⠀⠀⠉⠀⢰⡇⠀⠀⠀⠀⠈⣇⠀⠀⠁⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⣶⢲⣦⠀⠀⢸⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣿⠀⠀⠰⣷⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠸⠛⠁⠀⣸⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣄⡇⠀⠀⠀⠀⠀⠀⠀⣏⣤⡀⠀⠀⠀⠀⢸⣧⣄⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⣧⡀⢀⠀⡀⢀⠀⣀⣿⠀⡇⠀⠀⠀⠀⡏⡔⢲⡽⡆⢀⠀⢀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢧⡼⠻⣧⣼⣤⣷⣬⣦⡽⠻⣤⠇⠀⠀⠀⠀⠳⣽⣯⣼⣧⣬⣦⣼⣦⡽⠃





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡀
⠀⠀⠀⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⢉⣁⡰⣦⠱⡄
⠀⠀⠀⣇⠀⠉⠒⠒⠀⠀⠒⠐⠒⠈⣉⣉⣀⠀⣀⣰⡖⢿⣬⣥⣤⡀⠘⣄
⠀⠀⠀⠸⡄⠐⡒⠂⠰⣶⣄⢷⣜⢯⣁⣉⠉⢦⣸⣿⢿⣆⣶⠤⠼⢏⠀⠈⢦⡀
⠀⠀⢰⡒⢳⡀⠁⡀⢤⡹⣿⡻⢿⣮⡻⣦⣤⠴⠍⡛⠀⠨⠵⠖⢑⣀⠥⢔⣦⠙⢦⡀
⠀⠀⢾⣷⡀⢳⡄⠈⠭⠅⣈⡿⢂⡩⠭⠭⠖⢚⣉⡤⣄⠰⣖⠯⢕⣒⣫⣭⠄⠀⡀⠈⠒⠤⢄⣀⣀⡀
⠀⠀⠀⢻⣿⡄⠹⣆⠀⢋⣉⣭⢥⣤⠀⢺⡉⠉⠅⠀⠈⠁⣀⠘⢻⣟⣭⡴⢞⣛⣽⠟⠋⠐⠒⠐⠢⢌⠑⡄
⠀⠀⠀⠀⠙⣿⣆⠈⢣⡀⠉⠙⠋⢍⣤⣄⡙⢦⡀⠀⠀⠀⠉⠳⢤⣌⠒⢟⠉⠉⠀⢀⠀⠀⠀⠀⠀⣨⣄⡇
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠹⣆⠀⠀⠞⡛⢛⣩⣄⣙⢦⣀⡠⠔⠒⢉⣡⡴⠀⠑⡆⠀⢀⣀⣄⣶⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠈⠳⣄⠀⠙⢿⣿⢯⣝⠪⣤⠴⠶⣛⣯⣵⣦⡅⢠⣿⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠊⠙⡶⣄⠐⠛⠂⣭⢖⣺⣽⣿⣻⠷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠑⠎⣧⠀⢼⣾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣤⠼⠖⠋


⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣮⢳⡐⡄⠀⠀⠀⠀⠀⠀⡄⣾⠈⢁⡀
⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⣧⢳⡀⢀⣤⣤⣤⣀⣷⡸⢀⣾⡇⠀⠀⢀⣶⣮
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣸⣿⣟⣷⣿⣿⢟⣛⣿⣿⣷⣼⣿⣷⣶⣷⣿⣿⣃⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢹⣶⣾⣿⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣭⣿⡿⣹⣿⡟⠁⠀⢀⠍⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⣤⣄⠀⠄⢘⢓⣏⠀⣠⣿⣎⣻⣿⣿⣿⣿⣯⣭⣻⡿⣿⣿⣿⡿⠉⢰⣿⣏⣤⠀⠀⠈⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢿⣷⣷⡦⣈⠁⠀⣾⡟⣛⢛⣿⡿⡿⣿⣟⣭⣽⣷⣶⣾⣿⣡⠀⠈⢿⡿⣿⣾⣶⣶⣀⣀⠈⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠺⡦⠀⠀⠀⠀⠀⠀⠉⠳⢶⣦⣝⣲⣿⣿⣁⣿⣿⣿⣿⣯⣹⣿⣿⣽⠛⠛⢿⣧⣎⣴⣿⣷⣹⣿⣟⣿⣿⣿⣿⣾⣵⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣽⣿⣿⣭⣿⠏⠀⢿⡛⠩⠀⠀⠘⠃⣸⣷⣍⢻⣟⣮⢻⣼⣿⠿⠛⢋⣉⣤⣴⠂
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣿⣿⣿⣿⣿⣿⠎⠋⢐⡂⠈⠐⢶⣶⠄⠘⣧⣽⣭⠛⢻⡟⢛⣉⠭⠔⢒⡈⠉⣉⠡⠤⠴⠶⡂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⣉⣿⣿⡿⡿⠆⣐⣿⠀⠀⠀⠀⠁⠀⢀⡿⢿⣿⠀⣠⢫⣧⣶⣾⣿⣯⣭⣶⣶⠖⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣤⣾⢠⣿⢧⢸⣿⣿⣟⢷⣿⠀⠙⠁⠀⠀⢠⣾⣧⡤⠉⣠⣾⣷⣦⣭⡾⢿⡿⣿⣟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠁⢼⣿⣿⣎⣻⣿⣿⣾⣿⣦⡀⣀⠴⠆⣼⣿⣿⡠⠐⠋⠻⠻⢿⣟⣱⡏⣶⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣽⣿⡿⠻⠛⠛⢉⣨⣿⢇⠈⠉⠁⣩⣿⣿⠿⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣦⣤⣠⣶⡿⣿⣿⣟⡷⣶⣿⣿⣏⡀⠀⠀⠓⠘⢿⣿⡿⠁⣸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠟⠉⡈⣩⣴⢿⣿⣧⣽⢷⣼⡿⣿⣿⣤⣬⣽⣻⣿⣎⡓⡄⠀⢈⡻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠹⠿⢷⣽⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡿⣆⠢⡹⣿⣧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠟⠀⠀⠀⠀⡈⠀⠀⠀⠙⣧⢻⣎⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⣆⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢸⣏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀
⢀⡴⠖⠛⢉⢉⣀⡀⠀⠀⠀⠀⠉⠙⠻⢶⣄⠀⠀⠀⢻⣼⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁⠀⣀⣄⣠⡤⢤⡽
⠙⠋⢄⡉⠉⠉⠉⠙⠛⠓⠲⠦⣴⣀⠀⠀⡙⢧⡀⠀⠀⢻⣿⡀⠀⠀⠀⢀⣴⠞⠋⠀⣀⣠⣴⣖⠛⠉⠉⢀⡴⠋
⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⣉⣳⣦⣄⠈⢻⡄⠀⠀⣿⡇⠀⠀⣰⠟⠁⠀⣠⡾⠛⠉⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣌⣷⠀⠀⢸⡇⠀⣼⠋⢀⣠⣾⣫⡤⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣀⣀⣀⣈⣿⣆⠀⢸⡇⣸⠇⣠⡾⠋⠉⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠹⣦⢸⡇⢿⣴⢏⣀⣤⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠶⠶⠶⠞⠛⠛⠛⠛⠛⠋⠉⢻⣿⡏⠉⠉⠉⠉⠉⠉⠙⠛⠛⠶⠶⢦⣤⣄⣀
⠀⠀⣀⣴⠶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢶⡄
⠀⠀⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣧
⠀⠀⣿⠈⠉⠛⠳⠷⠶⢶⣤⣶⣶⣿⣭⣭⣉⣉⣉⣉⣉⣉⣹⣽⣏⣉⣉⣉⣩⣭⣭⣽⣷⣶⡶⠶⠶⠞⠛⠉⠀⠀⣿
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠉⠙⠛⡶⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠖⣻⠉
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠁⠈⠀⠀⠀⠒⢠⠀⡄⡀⠀⠈⠁⠀⠒⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⡀⠂⠀⢀⠂⠢⠆⠄⠠⠀⡀⠀⠀⠀⠉⠀⠂⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠄⠢⡄⠀⢀⠀⠠⢘⠁⡆⡩⠀⠔⠀⠪⠃⠀⢀⠀⡁⣬⠀⠀⣸⠐⠠⠤⢄⡀⠀⠀⠀⠈⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠊⠠⠤⠤⢈⣀⠀⠀⠀⠄⠁⠐⠂⠨⡀⠚⠀⠅⠠⠃⠀⡆⠐⠏⡀⣠⡴⠁⠨⡈⠢⡀⠁⠀⠀⠠⠀⠂⢀⣶⣝⡀
⠀⠀⠀⠀⠀⡐⠁⠀⠈⠍⡒⠲⠤⠈⠁⠀⠀⠀⠀⠈⠀⠁⠊⠠⠃⠐⣂⠠⠅⠁⠀⠃⠈⠠⠬⡠⠨⢀⠄⠀⠀⠀⠀⠀⢠⣾⡏⣔⠇⡀
⠀⠀⠀⠀⡐⠀⠀⠁⠀⠀⠀⠀⠡⠀⠀⠐⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠉⣐⠂⠀⠄⠈⠁⠒⠀⠉⢠⠄⣀⡀⠀⠀⣰⢯⣞⡾⣫⢾⡆
⠀⠀⠀⢠⠀⠀⡁⠈⠀⣀⠀⠀⠀⠀⠄⠀⠀⢀⠄⠂⠀⠀⠀⣒⠀⠀⠀⠀⡡⠋⠰⢤⢄⣄⣀⠈⠁⠀⠐⠓⠈⢠⡞⠕⢠⣾⢯⠡⣾⣳
⠀⠀⠀⠈⡄⠀⠈⠁⡒⠀⠀⠀⠀⠘⠠⠄⡀⠀⢀⠀⠀⠀⠀⢠⠀⢀⡀⡐⢀⡈⠒⠂⠰⠤⠌⡀⠉⠀⠀⠀⡴⡡⠪⣮⣿⢏⣞⣾⡿⠃
⠀⠀⠀⠀⠈⠂⢀⣀⣀⠈⠀⠀⠀⠉⠒⠰⢤⠁⡀⠂⠠⠀⠄⠀⠀⠀⡘⠀⠀⠀⠠⠄⠒⠠⠤⠀⠀⢀⢔⢝⣥⡠⣺⡻⢣⢏⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠴⠀⠀⠠⣀⠀⠀⠀⠩⠉⠁⠒⠄⠀⠀⠀⠀⠈⠤⠀⢀⠀⠀⠐⠀⠀⣠⠽⣱⣵⣪⠞⡝⠕⢡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⠀⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠉⠀⠀⠈⠁⠀⢰⣣⡞⣟⡟⠣⠊⠀⣪⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠄⠀⠆⠀⠀⠀⠄⠈⠁⠐⠀⠀⠀⡏⡋⢀⠙⠶⣢⣮⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠓⠦⢶⣤⣁⡀⠀⣧⠀⠀⠀⠀⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⡀⠀⠀⢀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠅⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡲⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⢎⣴⣾⠟⠿⢦⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠙⠋⠀⠢⠀⣈⠚⠁⠈⡙⠘⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠒⡂⠖⠲⠁⠀⢿⠀⠀⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡄⠀⠠⠀⠠⢀⠀⠂⠀⣼⠃⠹⠁⢲⡏⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡰⠒⠒⠀⠄⡃⠀⢢⠐⣅⠀⣧⡸⣅⡀⣠⢴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠍⢀⠄⠀⠀⡴⢹⠋⠀⢈⠉⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡕⠀⠀⠀⠱⠂⠁⠈⠀⠄⠤⢠⠋⠶⡌⠀⢀⢴⠆⠒⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡈⡀⠰⠀⠀⠀⠨⠀⡐⠆⠰⢀⠀⡺⠀⠀⠀⠄⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠜⠀⠀⢀⠀⠀⠀⠀⠀⣷⣤⣽⡀⠀⠀⢀⠀⠀⢨⣤⡤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⡃⢦⡸⠄⠀⣂⣀⠀⢉⠈⡻⡇⠀⠀⠀⠀⠀⠐⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢁⠀⠀⠁⢧⠀⠀⠀⠀⢸⡴⣿⢵⡖⣒⡲⠒⢪⣇⠼⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⠂⠀⠔⣆⠀⠀⢀⠈⠳⠀⠀⠀⠈⠀⠀⠀⢈⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⣂⠀⠀⠈⣄⠀⠀⠀⠀⠐⡆⠀⠀⣄⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⣍⠂⣈⢆⠈⢀⠀⠀⢂⠀⢀⡉⠆⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠠⠁⠑⠀⠐⢤⡎⠀⠸⡇⡘⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⢱⠇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⠆⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡥⠀⠹⠇⠨⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡤⠴⠆⠰⠤⢤⡤⠆

⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⡀
⢀⢀⡈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡿⡄
⡆⢀⣤⡄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢤⣤⡀
⣇⠙⠛⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣆⠘⢛⡋
⠘⢌⡠⠟⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠸⠌⡠
⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⣴⡶⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢔⢢⠀⠀⡇
⠀⠈⡄⢀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⢠⠁
⣀⣀⣈⣢⣤⣦⣤⣄⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣒⣂⣠⣤⣴⣤⣴⣁⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣈⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⠉⠉⠙⠳⣄⠀⠀⠀⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠋⠉⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⢀⣀⡀⠀⠀⠄⠀⠙⠀⠀⠀⠀⠀⠠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⣠⡴⠚⠉⠀⠀⠀⠀⣠⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⡀⢹⡆⠀⠀⠀⡾⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⠁⠀⠀⠀⢀⣠⠖⠋⠁⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⡼⠁⠐⢁⡜⠀⠀⠀⢀⡤⠊⢀⠂
⠀⠀⠀⠀⠀⠀⠜⠁⢀⡴⠋⠀⠀⠀⠀⠀⣴⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⢀⡴⠋⠀⢀⠤⠖⠉⣀⠴⠁⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⢀⡠⠞⠋⠀⠀⠈⠀⣀⠤⠚⠁⠀⢀⠀⠐⢠⡞
⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠖⠚⠁⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠶⠊⢀⣤⠖⠋⠄
⠀⠀⢀⠞⠁⠀⠀⠀⠳⡄⠀⠀⠐⠶⠲⠶⠖⠒⠶⠒⠊⠉⠁⢀⣀⣤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣤⠶⠊⠉⠀⢀⡜
⠀⠀⢸⡀⠀⠀⠀⠀⠄⠀⠉⣀⣒⣀⣀⣀⣀⣀⡤⡤⠤⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠂⠉⠁⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠻⢆⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢀⣀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⠁⠀⠛⠲⢄⡰
⠀⠀⠀⠀⠀⠉⠛⠛⠒⠶⠶⠶⠶⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⠴⠋⢷
⠀⠀⠀⠀⠀⠉⠑⠖⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠈⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠖⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢉⣁⣠⠤⠒⢂⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⠶⠚⢛⣉⠩⠤⠒⠂⢁⣀⠴⠛⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠊⠉⠀⠀⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠄⠐⠒⠉⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠤⠤⠀⠐⠒⠒⠈⠉⠉⠀⠀⠀⢀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡒⠂⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠉⠉⠉⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡴⠛⠁⠈⠉⠓⠶⠤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠤⢤⣤⣤⣤⠴⠶⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠒⠙⢢⣄⡀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣠
⠀⠀⠀⠀⠀⢠⠊⢀⡾⠃⠈⠓⠤⢄⡈⠉⠒⠒⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⣀⣀⡴⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠳⣼⡁⠀⠀⠀⠀⠀⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢹⡋⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⣤⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠠⠤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠲⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣶⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣙⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡀⢒⣠⣤⡶⠏⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⢀⣀⡀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⣀⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠛⠉⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⢦⣄
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠐⠒⠂⠀⠀⠀⠀⠠⠴⢞⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠂⠀⠀⠀⠀⢀⣠⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⠈⡀⠀⠀⣙⠇
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣴⠋
⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢶⡒⠒⠶⣶⡶⠞⠋⠉⠉⠉⠙⠓⠶⠦⣤⣤⠶⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⠀⠈⠷⠀⠀⠋⠀⠀⠰⡄⠀⠀⠀⠀⠀⠘⠋⠀⢀⡀⠀⠀⣿⣷⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣟⠳⢤⡈⠛⢦⣀⣴⢦⣤⡦⠶⣶⠿⣤⣄⡀⠀⠀⠠⠀⣠⠞⠀⢀⢠⡿⠉⢷⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠉⢳⡦⠤⣤⣀⣿⠠⣞⠁⢤⡀⠸⣄⠀⢨⡟⠻⣟⠛⢾⡗⠶⢦⣾⠈⠁⠀⣠⡟⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⣴⠋⢤⠀⢀⡴⠋⠀⠀⠈⠉⢻⣤⡼⠷⢦⣍⣀⣈⣀⣼⣃⣀⢌⣉⣈⣉⣷⣀⣹⣟⣄⣠⣯⠀⠀⠄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢈⣤⠀⠀⠀⠀⣴⠟⠙⢧⢀⡀⠀⠉⠉⠉⠉⡿⠙⠻⠿⠿⢯⡍⠉⠉⠉⠀⠀⠻⡄⠀⠀⠀⠀⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠋⠀⠀⠀⠀⠚⠁⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠘⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠻⣆⠀⠀⠄⣤⠀⠀⡀⠀⣷⠀⠀⠣⠂⣤⠀⠀⠀⠀⠠⠀⠈⢧⠀⠀⣄⠀⠀⠀⠀⡆⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢤⡄⡇⠀⣈⣤⡤⣼⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⠞⣧⠀⣀⣤⠴⠦⣄⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⠟⠋⠉⠀⠀⠈⠛⠛⠛⠛⠓⠒⠒⠖⠖⠒⠋⠀⠀⠈⠉⠉⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠰⡂⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢿⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣼⢃⠀⠘⠉⠓⠶⡄⠀⠀⠀⢸⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⣟⠂⠀⠀⠀⠁⠀⢹⡄⠀⠀⠀⠻⣟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡇⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠙⠲⢦⡈⠂⠀⣠⡟⠀⠀⠀⠀⠀⠈⠳⢮⣟⡲⠦⢤⣤⣤⣤⣀⣀⣀⣠⣤⠴⠖⣛⣭⠞⠋⠀⣠⢶⠛⢻⠉⠉⠙⣇
⠀⠀⠀⠀⠀⠀⠙⠒⠚⠋⠀⣠⡴⠞⢦⡀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠤⠤⠤⠤⠶⠶⠚⠋⠉⠀⠀⠀⠀⣏⠈⠆⡀⠀⣈⣥⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⡈⢿⠛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣤⣷⣋⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡳⣤⣙⠀⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣍⣛⣻⡶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⡿⠿⣿⣿⣿⣿⠿⣻⣿⣯⣵⣾⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣯⣝⣻⠿⠏⠀⠀⠀⠉⠀⠈⠐⣦⠀⠹⣯⣶⠿⢟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢲⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢲⣀⣀⣀⣀⣰⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⡼⠿⢷⣶⣶⣿⣿⠛⢻⣟⣋⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⠿⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠃⠀⡀⢸⣾⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣶⣿⣿⣾⣿⣿⣷⣀⣀⣀⡀
⠤⠤⠤⢤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠛⠁⠽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⢛⣒⣒⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣥⣤⣴⣶⣾⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⢋⣤⣿⡟⢉⠀⠀⠙⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡿⣿⡿⠛⡻⠟⠉⠀⠀⠁⣹⣯⣿⡿⠿⢦⣤⠀⣠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡶⠾⠷⠈⠀⠀⠀⠀⠠⢞⡋⠉⠁⠀⠀⠀⠀⠛⢛⣋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣴⡶⠚⢻⣆⠈⠀⠀⠀⢀⡼⢤⣒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⠿⣿⡶⠖⠶⠖⠒⠒⢿⣦⠀⢀⣾⡿⠛⠬⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣟⣻⢻⣿⣿⣿⡷⠀⠀⠀⢀⠀⠈⣿⣷⣼⣇⠀⣤⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⢿⣷⠛⢷⡄⠻⣧⠘⠹⣷⠋⣿⡆⣽⡟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣽⣿⣿⣿⣿⡟⣿⡀⢸⡇⠀⣿⠀⠀⣿⠀⣿⠃⣽⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⣿⠀⠀⣿⠀⣿⠂⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⣿⠀⢀⡏⠀⣿⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⢸⡇⠀⣿⠀⢸⡇⢰⣿⢸⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢈⣿⠀⣿⡀⢸⡇⢸⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⢷⣼⣿⣿⣿⣿⣿⣯⣿⡍⣿⠀⢸⡇⢸⣧⢸⣿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⡇⢀⣿⢸⣯⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⢫⡿⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡆⠈⡇⠈⣿⢸⡗⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠊⣴⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⠀⠁⠀⠟⢸⡧⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣿⣿⣿⣿⣿⣿⣛⣻⡿⠿⠸⠃⢠⡄⣀⣙⣨⡥⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣽⣿⣿⣿⡟⣿⣿⣿⣿⠿⠀⠀⠀⢰⣧⠈⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣟⣿⣿⣿⣿⣿⣆⡀⠀⠀⣸⣿⣤⣼⡷⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⢀⢔⠆⡻⠁⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠠⠊⠄⠂⠀⠐⡌⢂⠀⠀⠀⠀⠀⠳⢣⢝⡤⣒⡤⡩⣪⣂⠀⠀⠀⠀⠀⠀⡂⠄⠀⠈⢠⠠
⠀⠀⠀⠀⠈⢀⠀⠀⠀⠸⢈⠀⠀⠀⠀⠀⢏⠇⣨⡫⠪⣎⣶⠡⢹⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⢌⠢⠄⠠⠔⠁⠎⠀⠀⠀⠀⢪⣪⣦⢉⣚⡡⢡⣆⡾⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠈⠂⠓⠶⢊⡲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⣠⣴⠾⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⣠⠖⢋⣉⣉⡙⠲⣄
⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠠⠀⠀⠀⢰⠋⣴⡾⠟⠻⢦⡙⣿⡄⠀⠀⠀⢀⣾⡿⠉⠀⠀⠈⠻⣿⣆⠀⠀⠀⣼⢁⡾⣫⠖⠲⢍⢷⡘⣇
⠀⠀⠀⠀⠀⠸⡏⠀⢈⣇⡀⠀⠀⠀⠀⠀⢸⡟⢰⠃⠀⢨⠇⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⡇⢸⡱⡇⠀⠀⢸⢸⠇⡿
⠀⠀⠀⠀⠀⠈⠛⠳⠻⠑⠀⢀⠀⠀⠀⠀⠸⣿⡘⢷⣤⣤⡾⠟⣠⠇⠀⠀⠘⣿⣧⡀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠱⡈⢧⡙⠮⠬⠷⣋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣴⠾⠋⠀⠀⠀⠀⠈⠻⢿⣿⡿⡿⠛⠁⠀⠀⠀⠀⠀⠑⠄⠉⠛⠛⠛⠉

⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠛⠻⢷⣦⡀⠀⠀⠀⠀⣠⡲⣝⣛⣛⣦⣢⢄
⠀⠀⠀⢠⣿⣿⡽⠛⠻⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⡖⣫⠭⢍⠲⡘⣷⡀⠀⠀⢰⢯⡿⡯⣒⣒⣟⣟⣝⢆
⠀⠀⠀⣿⣿⢿⠀⠀⠈⣮⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⢸⠀⠀⠀⡃⡗⢸⡇⠀⠀⢬⢺⣸⣸⡥⣼⣹⢹⢸⣺
⠀⠀⠀⢘⣿⣿⣗⣶⣖⣵⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⣌⠢⢔⡮⠞⣡⡿⠀⠀⠀⠸⣷⣻⣿⠯⠝⣿⣿⣟⡎
⠀⠀⠀⠀⠙⠻⡿⠿⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⠈⠛⠶⠶⠛⠉⠀⠀⠀⠀⠀⠈⠓⠯⠟⡯⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⡱⠊⠉⠐⢝⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣶⣾⣷⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⡀⠀⠀⠈⡆⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣾⡏⠀⠈⢹⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣝⡢⠤⢚⣔⣿⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⢿⣷⣾⠟⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠁⠀⠈⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣺⣿⡻⢓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⠿⠕⠒⠉⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣠⣾⣛⣹⣿⣶⣶⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣉⣭⣽⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⢀⣀⣀⠠⠠⠄⠒⠈⠁⠀⠀⠀⠀⠘⡆
⢀⣀⣠⣤⣤⣴⣶⣶⣾⣿⡿⠿⠟⠛⠛⠉⠉⠀⠀⠘⢿⣷⡀⠀⠉⠉⠁
⠈⣻⡛⢭⡉⠉⠉⠁⠀⠀⣀⣀⡀⠀⠀⠐⠊⠉⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⣾⣿⣿⣮⣿⣆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⠤⠚
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣀⣀⠤⠤⠔⠒⠊⠉⠉
⠹⣿⣏⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠷⠒⠊⠉⠉
⠀⠹⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠉
⠀⠀⠈⢿⣿⣿⣿⡟⠀⣀⡠⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠢⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠄⢀⣀⠀⠄⠀⠢⠤⠄⠤⠄⠐⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠈⠉⠈⠉⠲⢄⠀⠐⠈
⠀⠀⠀⠀⠀⠀⡀⠀⡁⠂⠀⠑⡄
⢀⡂⠀⠀⠀⠘⠟⠀⠏⠀⠀⠀⢱
⢠⠑⡄⠢⠄⣀⠀⠀⠀⡀⠀⠀⠘
⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⡌⠑⠢⢄⣀⢀⠀⡄⠊
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⢄
⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠁
⣶⣶⡶⡶⠶⢶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠈⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⣀⣤⠀⠀⠣⠀⠀⢀⠔⠀⠀⠀⠀⠄⣉⡀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠳⡥⣴⠠⢀⡰⠎⠀⠀⠀⠀⠀⠀⠠⠤⡀⢠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠁⠁⠘⢆⠀⠀⢀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⢀⠀⢀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠓⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⢀⠀⠄⢂⠈⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⠷⡀⠀⠠⠀⠀⠀⠀⢀⡠⠲⢠⠀⠀⢀⠄⠀⠀⢠⡀⠈⠉⢡⢌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⡆⠀⠀⠀⠀⢾⠀⠠⠞⢁⠤⠊⠄⠀⠀⠀⠑⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡋⠒⠂⠤⠤⠤⡄⠒⣮⣤⢤⣄⢠⠀⠀⠈⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⠀⠀⣤⡴⠁⠁⠀⢀⡘⠀⢻⡛⢄⠀⠈⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠄⢻⠁⠀⢦⠀⣀⡘⠁⠀⠈⣅⠀⠱⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⡠⠜⢄⠀⠀⠈⠀⠀⠀⠀⠀⢿⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠉⠁⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠈⠈⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⠀⠀⠀⠀⠀⠈⠓⡔⠂⠐⠀⠒⢀⡉⠄⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠸⡀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡠⠁⠀⠀⠀⠈⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡰⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⠀⠀⡸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣉⣉⣉⣉⡉⠤⠔⠀⠀⠀⠀⠀⢇⠀⠉⠀⠒⠀⠉⢀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠙⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢆⠀⠀⢐⢒⣂⠀⠀⢿⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠈⡄⡧⠌⣴⣓⣀⠒⠂⣨⣷⣘⡇⠀⢀⡈⠀⠀⠀⠀⠀⣀⣀⡀⠠⣤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠐⡓⠷⢴⡏⠀⢙⡟⢻⡁⠀⢉⣷⣄⡤⢰⠶⠖⠚⢉⣉⠡⠄⠀⠒⠈⠙⠉⠌⡗
⠀⠀⠀⠀⠀⢋⢭⡉⠙⠛⠒⠲⠶⠤⢤⣀⣐⠠⠤⡀⢀⢀⡀⠀⠀⠀⠐⢏⢠⠀⠙⢒⣋⣠⣤⢿⢖⡋⠡⠄⠒⠀⠁⢈⢁⢀⡀⣤⠢⢺⠆⣯⢍⠀⢠
⠀⠀⠀⠀⠀⠈⡄⠅⠀⠈⠡⠀⠀⠀⠀⠀⠀⠉⣉⠒⠈⠑⠪⢽⡒⠴⡖⣤⣹⡠⠴⢚⠩⠑⠈⣀⠀⣤⣠⢤⠒⢥⡀⠤⠈⢋⡙⠙⢀⣨⣤⣀⠖⠂⢰
⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠀⣡⠀⠀⠀⠈⠕⠊⠂⠀⠚⠉⠀⢶⣄⠁⢹⡂⠈⢃⠩⢘⡩⠏⠈⠙⣐⠘⠤⠄⠰⠒⡢⢖⠂⢠
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠆⠈⠌⡠⡂⣛⠼⢙⠂⢸⠀⠀⠀⠀⠄⠘⠀⠀⠀⢀⡈⠄⠒⠬⣈⠠⠄⠒⡀⠈⡉⠀⠰⢲⠰⣫⣑⠀⠃⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠥⠄⠀⠀⠁⠒⠀⠀⡂⠀⢁⠁⢸⠀⠀⠀⢀⠀⠀⠀⠀⠊⣈⠄⠐⢊⡡⠤⢄⢠⠏⡁⡆⡴⠮⢀⢨⠢⠑⢠⠀⣛⡛⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢁⡠⢤⠈⠑⠀⠀⠬⢉⣃⠐⠦⠭⠄⠈⠁⠀⢐⠀⠀⠀⠀⠀⠀⡡⠔⢀⠄⠀⢘⡳⢁⠂⠀⡆⠑⢌⠐⣆⠐⠔⠤⢿⠀⣳⣉⠐⠳⡄
⠀⠀⠀⠀⠀⠀⠔⢈⠤⢾⡀⠀⠀⠀⠂⡤⢀⡙⠀⠠⠀⠈⠅⠀⠀⡀⠠⠀⢠⠀⠎⢠⠋⠑⠃⠀⠈⡁⢆⠀⡄⡃⣎⠓⢠⠻⠴⠈⢉⣡⡄⢸⣁⣁⠈⡇
⠀⠀⠀⠀⠀⠀⢣⠰⠶⡞⠀⣀⠀⠀⠒⠠⠡⠐⡀⠨⠥⠒⡀⠀⢀⠭⠄⠀⢸⢸⠀⢠⠀⠀⡀⢸⠈⠑⡈⡂⠣⠀⠈⣉⡤⠴⠂⠉⡁⠠⡔⢸⣉⡉⡸
⠀⠀⠀⠀⠀⠀⠨⡀⢶⠁⠀⢉⡙⠀⠒⠆⢰⣠⣀⠈⠁⠒⠀⠀⢐⡛⠰⠀⠸⠀⠣⣀⠉⡁⣈⠀⠚⡁⠈⠤⢖⡊⠄⠀⠒⠀⠇⡀⠄⠑⠀⠸⢧⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠟⠃⡠⠀⠄⡐⠂⠀⠐⠂⠠⠀⢁⠘⠖⠲⢠⣄⣈⠉⠀⢸⠀⠀⠈⣉⠉⠡⢞⡛⠇⠰⠈⠵⠲⠄⠀⣾⠱⠗⠿⣿⣻⡆⠰⡿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠨⠁⠀⣀⠐⠀⠌⠀⢂⠀⠁⠀⠄⠉⡒⠀⢸⠀⠀⡉⠭⡐⠈⢝⣃⠀⣤⢀⣂⣤⣶⠦⣤⣠⣤⡼⠿⠛⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠈⠠⠄⣀⠠⠄⠁⠀⠀⣁⠀⠀⢸⠀⠄⢂⠨⠐⡨⢵⡆⠀⣤⣠⡬⠤⢦⣤⡤⠤⠴⣦⣤⠤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠤⠍⠉⠁⠓⠲⠤⠄⠀⡀⡀⠀⠀⠠⢀⠈⠀⠘⠀⠩⢐⠀⠐⠀⠍⠀⠀⠭⠐⠀⠠⠀⠔⠠⠀⠈⠃⠀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠁⠀⢀⣀⠀⠀⠤⠀⠭⡐⠂⠀⠉⠑⢲⠀⠀⠀⠀⡆⠀⠨⠐⠊⠤⠖⠂⠀⠀⢈⠀⠈⠀⠀⠒⠀⠀⠈⠑⣂⣀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠈⠀⠄⠀⠠⠈⠀⠀⢀⠁⠠⢒⡩⢀⠀⡁⠀⠀⢀⡠⠄⠒⠒⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠤⠤⣀⣁⠀⠁⠀⠀⠁⠄⠀⠀⢸⠀⢐⡩⠐⠈⢁⡠⠔⠈⠁
⠀⠀⠀⠀⠀⠀⡠⢠⠠⣐⠠⢐⠀⢀⠀⠀⡀⠄⡀⠉⢐⠢⠤⣀⠀⠀⠀⢸⠀⢀⡠⠐⢈⠀⡀⢀⡠⢀⠀⢀⠠⣀⠄⡀⢐⠠⢐⠠⡀⠄⡠⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠐⠁⠒⠨⠀⠄⢂⠄⡉⢕⡲⠰⠊⠁⠔⡫⠀⠅⠂⠅⠊⠔⠈⠔⠈⠐⠡⠂⠁⠂⠔⠈⠐⠁⠈⠀⠐⠁⠉

⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡷⣶⣷⡄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠄⠀⠀⢠⣿
⠀⠀⠀⠀⢸⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣧⣶⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣧⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡧⣶⣶⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣥⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣥⣶⣶⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣧⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡆⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣥⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡿
⠀⠀⠀⠀⣿⡇⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠐⠀⠀⣿⣧⣶⣶⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⢤⢤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠄⠀⠀⣸⡇
⠀⢀⠀⠀⣿⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿⡇
⠀⠈⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠇
⠀⠸
⠀⠐

⡟⠁⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀⠀⠀⣎⡑⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠰⢃⣷⣆⣡⣤⡀⠀⠀⠀⠀⠀⢀⣤⢠⣶⡆
⠀⠀⢀⠀⡀⠀⠀⠻⠇⠀⠀⠀⠚⠛⠛⠉⠀⢤⣌⣀⠀⠀⠀⠀⠸⢿⡏⢸⡿⠃⠀⠀⠀⠀⣴⣿⣿⡏⠿⠛⠀⠀⢠⣤⡦⠐⠿⠛⠀⠙⢿⣿⡆
⠀⣠⡺⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⣀⣀⠈⠛⠁⠀⢢⡤⣄⣰⠀⠀⠀⠀⣼⠀⠀⢰⡈⠉⠉⠀⠐⠿⠂⠀⠘⠟⡡⣶⠀⠀⠀⢀⣀⡀
⠀⠙⣿⣿⠀⣤⠀⠀⠀⠀⠀⠾⠆⠛⠀⠀⠛⠋⠰⠎⠁⠀⠀⠴⣜⣿⠀⡀⢰⡾⠇⠀⠀⠸⣧⡀⠀⢠⣶⠂⠀⠀⠠⣧⡄⠉⠀⠀⠀⠿⡋
⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠈⠁⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⣰⣿⡏⣁⡄⠀⣤⣀⠀⠀⡀⠛⠁⠤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡰⣶⡶⢀⠀⠀⢀⠀⠉⢰⡆⠀⢀⠀⠀⠀⢤⠄
⠀⣿⣿⡁⣿⡄⠅⢉⠉⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⡀⠀⡀⢂⣸⠃⠀⠀⠀⢠⣴⡶⠈⠛⠛⠃⠀⠻⣿⣷⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⢈⣴⢾⡿
⠀⠹⣿⣷⣮⣀⣀⣀⡤⠀⠀⠀⠀⠐⠀⠰⣿⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⢸⠟⢁⣾⠌⠀⠀⠀⣀⡂⠀⠀⠀⠘⠻⠟⠹⠿⣶⠇⠀⠈⠉⠉
⠀⠀⠙⠳⠾⠿⠟⠋⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⠷⠼⠃⠀⠀⠀⠰⣶⡄⠉⠀⠰⠀⠺⠟⠁⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⠏
⠀⠀⠀⡠⠶⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⣡⣿⣷⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⡷⠀⠀⢀⣾⡟⢁⣤⠀⣠⣀⠀⠀⢀⠀⣤⣶⡜⢿⣧⣄⠀⠀⠀⠀⢀
⠀⠀⠸⣿⣿⠇⢙⣅⡀⠀⠠⢀⡄⠈⠀⠀⠀⠐⠀⠀⠀⢀⣶⣭⠀⠀⠀⢸⣿⡇⢻⡅⠀⠈⠉⠀⣾⡿⢁⡌⠉⠀⠀⠙⠛⠃⠀⠀⠀⣄⡝⠁
⠀⢸⡆⠀⠀⠀⢀⠉⠀⠀⠄⢘⡗⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⠀⠀⠀⠈⢿⣿⢶⣤⣤⣤⡤⠀⢨⡀⠺⠃⠀⠀⣴⡖⠀⠀⠀⠀⢀⡾⣿⡀
⠀⠈⠻⠂⠀⠰⠟⠁⠀⠀⠂⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠈⠋⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⢀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠀⠀⠀⢀⠀⠉⣰⡄⠀⢀⠀⠀⠀⣄⡀
⠀⣰⣿⡇⣠⡶⠀⣴⣤⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⡄⠀⠀⠃⢀⣀⣄⠰⣾⠿⠆⠛⣷⣶⣄⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⢀⣠⣶⣷
⠀⢿⣿⣇⢷⠆⠂⠀⠀⠀⠀⠉⠀⠀⠀⢰⡷⠀⠀⠀⠐⠀⢹⣶⡀⠀⠀⠀⢸⣿⠇⣤⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⠿⠇⠿⢿⣴⠃⠀⠙⠛⠚
⠀⠘⢿⣿⢳⣤⣤⣤⠖⠀⠀⠀⢂⠀⠀⠐⠁⠀⠀⠀⠀⢠⣟⣻⡇⠀⠀⠀⢰⣄⠈⠿⠀⢠⠀⣴⡶⠂⠀⠀⠀⠀⠀⠀⣰⣟⠋
⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠻⠏
⠀⠀⠀⠀⠠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠂⠀⠀⣰⡆⠀⠀⠄⠀⡞⠑⣀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠰⢢⣶⣎⣠⣤⡀⠀⠀⠀⠀⠀⣀⣌⢴⣶⠆
⠀⠀⠀⣀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠺⠛⠛⠋⠀⢤⣘⠆⠀⠀⠀⠀⠸⣿⡇⢹⡿⠃⠀⠀⠀⠀⣴⣿⣿⠏⠿⠋⠀⠀⢠⣴⡆⠘⠟⠛⠀⠙⢿⣿
⠀⠀⣦⣝⢃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣁⡀⠙⠛⠁⠀⢦⡤⣀⠸⠀⠀⠀⢀⣼⠀⠀⣴⠈⠋⠉⠀⠜⠿⠀⠀⠘⠟⢡⡷⠀⠀⠀⠀⣀
⠀⠀⠘⠿⣿⠀⡶⠀⠀⠀⠀⠀⠶⠄⠗⠀⠀⠛⠃⠰⠏⠀⠀⠀⠷⣝⡿⢀⡀⣰⡾⠃⠀⠀⠸⣦⠀⠀⢠⡶⠂⠀⠀⠰⣶⠀⠃⠀⠀⠀⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⡠⠠⢄⡀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠘⣸⣿⣧⣴⣦⠀⠀⠀⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⢠⣾⡏⢁⡀⢀⣀⡀⠀⠀⠀⢀⣤⣦⠺⣿⣀⡀
⠀⠀⣾⣿⣿⠈⢛⣁⠀⠀⠄⢀⡀⠀⠀⢀⠀⠆⠀⠀⠀⢠⣬⣍⠀⠀⠀⣾⣿⡁⣯⡁⠈⠙⠉⠀⣾⡿⣀⠉⠉⠀⠈⠿⠟⠀⠀⠀⠠⣀⡒
⠀⣾⠀⠁⠀⠀⠈⠋⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⠀⠀⠀⢙⠉⠛⠀⠀⠀⠹⣿⣷⣯⣀⣀⣀⡄⠀⣉⠐⢿⠁⠀⢀⣤⠄⠀⠀⠀⠀⢠⣿⣷
⣄⠘⢷⠒⠀⢾⠟⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠓⠿⠿⠛⠉⠀⠀⠙⠃⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣯⣭⣭⣭⣭⠙⣿⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⠉⠉⠠⠾⠛⠀⠀⠀⠀⠀⠀⠛⠧⠀⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣶⣤⣤⣤⣀⣐⣒⣒⣒⣒⣀⣀⣤⣤⣤⣶⣾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠟⣒⣲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣙⣛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠾⠿⠛⢛⣉⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠉⢻⣿⠛⠻⢷⣶⠶⠶⢶⣾⠟⠛⣿⡟⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡏⠀⠀⣿⡇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⠇⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⠀⠀⢸⣿⠀⠀⣼⡇⠀⠀⣿⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⡄⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡟⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⣤⣼⣿⣀⣀⣿⣧⣤⣼⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣿⡒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠛⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⣤⣴⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⡟⣠⠴⠚⠉⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠲⠤⣬⣍⣉⣉⣉⣩⣭⡭⠤⣿⠗⣸⣿⣷⣶⣶⡄⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢰⣶⣶⣶⡶⠒⠶⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⠟⠋⣁⠤⠀⠀⠈⠉⠉⠉⠻⢬⡉⠛⠻⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⢠⡴⠦⡀⠀⠀⠀⡤⢶⣤⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣤⣅⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠛⠓⠒⠛⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣬⣙⣛⣛⣛⣩⣴⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠀⠐⠂⠀⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠁⣤⠀⠀⡀⠔⠀⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⠀⡄⠄⠐⠑⠀⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⡘⠀⢈⡄⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠄⠊⠀⠀⠠⠈⡀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠂⠐⠒⠠⠂⠀⠈
⠀⠀⠀⠳⠀⠀⠀⠀⢀⠎⠈⠀⠀⠉⠘⡄⠀⠠⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⠎⠑⠂⠀⠀⡀⠀⠀⠀⠀⠀⣀⠄⠄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡀⠤⣠⠊⠁⠀⠉⠦⠠⠤⡀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢠⠊⠁⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢄⠀⡀⠀⠰⠉⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠒⠢⡀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⢲⢀⡔⢦⢠⡖⡄⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⢄⣀⡀⡀⡀⢀⠝
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⡇⠀⠀⠀⠀⠘⠁⠈⠣⠞⠘⠋⠐⠆⠀⠀⠀⠘⠀⠀⢀⠀⠄⠀⠀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⣀⣀⢀⡀⡸⠀⠀⠀⠀⠀⠀⢠⠛⠀⠠⡆⠰⠗⠰⢒⠀⣂⠀⣖⠀⠠⠀⠆⠀⡜⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠤⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠠⡀⠀⠀⠀⠀⠀⠔⠀⠀⠘⠀⠁
⠀⠀⠀⠀⢠⣀⡀⠀⠈⠀⠀⠀⠀⠀⠈⣄⠀⠑⠂⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠒⠘⠁⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠈⠒⠀⠒⢄⣀⣀⠔⠓⠂⠂⠀⠀⠀⠀⡰⠤⠤⡀⠀⠀⠈⠂⠀⠉⠀⠉⠀⠩
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠐⡁
⠀⠀⢀⠂⠈⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠄⡀⠀⠀⢠⠋⠀⠀⠀⠀⠉⠠⠀⠀⠀⠐⠂⠁⠀⠠⠄⠄⡀⠀⠀⠀⣰⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠞⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⠀⠱⡀⠀⠀⠀⠀⢀⡪⠀⢀⠄⠐⠐⠀⠂⠠⡀⠀⠀⠀⠉
⠀⠀⠂⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠉⠓⠒⠢⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠑⠂⠅⠉⠀⠀⠀⣴⠀⠀⠀⠀⠈⠢⠀⠀⣀⠄⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡀⠈⠀⢀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⣒⠄⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢻⣛⣟⣙⣛⣟⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣂⣐⠒⠒⣢⢱⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡂⠁⠀⡠⠀⠀⡠⠂⠀⠀⠐⢄⠀⠠⢀⠀⠀⢂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢛⠁⠒⠂⠀⠀⠀⠤⠤⠬⠤⠤⠤⠤⠤⠤⠥⠤⠤⠀⠀⠐⠒⠒⠈⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠠⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠄⡀⠀⠀⣀⡀⠀⠀⠐⠀⠐⠂⠀⠀⣀⣀⠀⠀⢀⠤⢤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠂⢤⠀⠀⠀⡇⠀⠈⠀⠀⠇⠀⢸⠀⠀⠆⠀⠀⠀⠀⠃⠀⠀⠀⢠⠀⡤⠐⢂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢃⠈⠲⠀⡀⠀⡇⠀⠀⠀⠀⠄⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠖⠁⡘⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⢤⡀⡇⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠁⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡇⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⡇⠀⡁⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠤⠇⠀⠀⡇⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠠⠄⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣁⠒⠤⠀⠁⠒⠁⠀⠀⠄⠸⠀⠀⠈⠒⠁⡀⠤⠒⣈⠤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢈⡑⠂⠀⠠⠌⠉⠉⠁⠈⠉⠉⠥⠄⠀⠐⢈⠡⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢭⠉⠉⠉⠉⠉⠉⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡴⠛⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡡⠋⠀⠀⠀⠱⣌⢣⡤⠤⠤⠤⠤⠤⠤⠤⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⠞⠁⠀⠀⠀⠀⠀⠈⠣⡙⢆⣀⣀⣀⣀⣀⣀⣀⣈⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠮⡴⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠽⡦⠷⠤⠤⠤⠤⠤⠤⠤⢤⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡤⠤⠤⠤⠤⡄⠀⠀⡇⠀⢀⣤⢤⡤⡤⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠐⠀⠀⠀⠂⡇⠀⠀⡇⠀⢸⠀⠀⡀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠁⠈⠁⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠚⠀⡇⠀⠀⡇⠀⠘⠒⠚⠓⠒⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠒⠒⠒⠒⠒⠓⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⢀⣤⡀⣠⡀⣠⣄⢀⣤⡀⣤⡀⣠⣄⢀⣄⢀⣤⡀⣠⣄⢀⣄⢀⣤⡀⣠⡀
⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⢀⣀⡀⣀⡀⢀⣀⣀⡀⣀⡀⢀⣀⡀⣀⣀⢀⣀⣄⣀⠀⠀⢸⣿⢰⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣧⣿⡇⢸⣿⡟⠃⣿⣇⣾⣿⡇⣿⣿⢾⣿⡹⠿⠆⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⡆
⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⡇⢸⣿⡿⠇⣿⣿⣿⣿⣷⣿⡇⠘⠻⣿⣶⡀⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⠹⣿⡇⢸⣿⣧⡄⢸⣿⣿⠸⣿⣿⡇⢸⣿⣸⣿⠇⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⠈⠉⠀⠉⠁⠈⠉⠉⠁⠈⠉⠉⠀⠉⠉⠀⠀⠉⠉⠉⠀⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⢹⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⢀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠘⣿⣆⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠙⠛⠛⠛⠛⠛⠛⠃⠀⠘⣿⣇⠀⢸⣿⠃⢸⣿⡇
⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⠟⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠁

⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⣤⣾⣤⣤⣶⣆⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⢸⣿
⠀⠀⠛⢿⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣀⣽⣀⣀⣤⡄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿
⠀⠀⠯⣿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢾⠀⠀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿
⠀⠀⣛⣿⣟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣽⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠶⣾⡶⣶⣶⣦⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿
⠀⠀⠛⢻⠋⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣄⣼⣅⣤⣤⣄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿
⠀⠀⠶⢿⠷⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⣸⡀⢀⣀⡀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⢸⣿⡇
⠀⠀⣭⣿⣯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢼⠀⠀⠉⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢸⣿⡇
⠀⠀⣒⣿⣗⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠉⣽⠉⠙⠛⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢸⣿⡇
⠀⠀⣤⣿⣤⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠛⢿⠛⠻⠿⠟⠀⠀⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣸⣿
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠀⠀⣿⣿
⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣣⠏
⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠭⠭⠭⠯⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⡿⠟⠛⠩⠛⣿⡘⡋⡈⠛⢻⣏⣉⡘⢹⠘⡿⠬⠛⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠄⣤⣄⣠⠤⠄⠘⡟⠋⠋⠛⠛⡏⠉⠉⠛⢻⣃⡀⢀⡿⠤⡞⣻⣿⡟⠢⠉⠛⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠙⠀⡄⣈⣧⠀⠀⠀⠀⣀⠤⠄⠄⠐⠇⠀⠀⠀⠀⠀⡉⠛⠁⠀⠀⢻⣤⣀⠀⠀⠁⢀⣼⠟⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⡁⠀⠀⠀⠀⠈⠁⡀⠔⠒⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⡆⠀⠀⠈⠉⠒⣵⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣠⠞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠒⠀⠀⠀⠀⢠⠎⠀⠀⠀⠠⠊⠀⠀⠀⠀⠤⠒⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⡿⠌⠊⠙⡧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠖⠓⢤⣉⠉⠀⠲⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣟⣿⢻⡅⣿⡿⠀⠀⢸⠁⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠉⠙⠛⠂⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠻⠋⠁
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣿⣧⣀⡀⣸⠀⠀⠀⠠⢀⡀⠸⠓⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡯⠉⡉⠉⢙⠛⠒⠢⠤⠄⢀⡉⠁⠐⠠⠄⣀⠉⠓⠀⢀⠀⡠⠒⠊⠀⠀⠐⠁⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠄⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠢⠍⠀⠀⠀⠀⢀⠄⠐⠉⠀⠐⠒⠂⠀⠒⠒⠒⠂⠀⠂⠈⠈⠉⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⣉⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠒⠒⠦⠤⣄⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠛⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⣁⠒⠒⠚⠉⢀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍
⣿⣿⣿⣿⣿⣯⣿⣿⢬⣦⣀⣠⣩⣦⠀⠀⠀⣀⣀⡤⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠃⠀⠒⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣏⢋⠉⠈⠘⣷⠛⠉⠀⠀⠀⠀⠀⠀⠂⠁⠀⠈⠁⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠀⢀
⣿⣿⣿⣿⣿⣿⣽⣟⣹⣿⣽⢷⣀⣶⡿⠟⠀⢀⡠⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠘⠲⠶⠲⠶
⣿⣿⣷⣴⣿⣿⣿⣿⡧⡿⢿⣧⠉⠁⢀⣴⠚⠉⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⢠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐
⢿⣿⣿⣿⣿⣿⣿⣿⣳⡿⣛⠟⢰⣿⠟⠋⠁⠢⠀⣠⡶⠉⠀⠀⠀⠀⡘⠀⢣⠧⠄⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠐⡀
⣬⣿⣿⣿⣿⣿⣿⣿⣯⡿⣅⣶⢟⠛⠷⣢⡀⠀⠀⠉⠠⣀⠀⠀⢀⣼⣀⣀⡆⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⡤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢫⠖⠀⣠⡿⠇⢄⠀⠀⠀⡙⠲⣾⠟⠀⠀⠀⠉⠈⠃⠀⠀⠀⠀⡏⠉⠉⠀⠀⠀⠀⠀⠤⠒⣏⠀⠀⠈⣆⣀⣠⡴⠞
⣿⣿⣿⣿⣿⣿⣿⣿⢛⣔⣿⣵⡳⣬⣾⠟⠁⠀⠀⠉⠲⠞⠀⣰⡏⠀⠀⠀⠀⠀⠀⢤⢄⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⢧⣤⡾⢿⣿⠡⠄⡠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠐⠉⠐⣿⣤⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⢉⡶⠒⠒⠒⠈⠉⣄⣀⣶⡴⠶⡋⣼⠀⠀⣠⣷⣎⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣸⣿⣿⣖⣛⠿⡶⢰⡤⣾⣤⣤⣄⣠⡷⠀⠀⠀⠀⠀⢿⣄⣀⢤⣍⣷⣼⣦⡶⢟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣮⣶⣷⣠⣦⣬⣭⠀⠀⠀⠀⢀⠀⢼⣿⣽⣾⣿⣿⣿⣿⣿⣈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣾⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠋⠁⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⢟⣣⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠛⠁⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣫⣭⣶⣿⣿⣿⣿⠿⣫⣵⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣄⣀⠴⠾⠿⠿⠿⠿⠿⣟⣛⣛⣛⣭⣭⣵⣶⣾⣿⣿⣿⣿⣿⠿⣛⣭⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣛⣭⣵⣾⣿⣿⣿⣿⡿⠟⠋⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣫⣭⣵⣶⣶⣿⣿⣿⣿⡿⠿⢛⣛⣭⠴⣒⣥⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣒⠒⠲⠶⠿⠿⢿⠿⢿⠿⠿⠿⠿⠿⣛⣛⣫⣭⣭⣶⡶⠿⣛⣭⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⢛⣫⣵⣶⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⢛⣛⣛⣩⣭⣶⣾⣿⣿⡿⠿⠿⢛⣋⠉⣡⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣬⣭⣭⣭⣭⣥⣤⣶⣶⣶⣶⡿⣟⣯⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⣛⣿⣭⣿⣾⣿⡿⠿⣟⢋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣷⣶⣾⣿⣿⣭⣭⣽⣿⠶⠶⣚⣯⣷⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢿⣿⣿⣯⣿⣶⣶⣿⣿⣿⢿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣶⣶⣿⣿⣿⠿⢶⣖⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣚⣛⣿⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣛⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠉⠩⠙⢋⡀⡈⠉⠉⠩⠰⡒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢄⣠⠀⣠⠖⠋⠉⠀⠀⠀⠀⠉⠙⠲⢌⠀⠣⡀⠉⢙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡤⠊⢀⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠱⡀⠈⡗⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⠃⢁⠎⠀⠀⠀⣠⣴⠒⡶⣋⠶⢆⠀⠀⠀⠀⢱⠀⢣⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠖⠂⢸⠀⠀⠀⠘⡄⠓⠀⠓⠉⢁⠎⠀⢀⠀⠂⢈⠀⢀⠕⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣔⠁⡀⢸⠀⠀⠀⡀⢸⡀⠀⠀⠀⡎⠀⠀⠀⠀⠁⡸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⡄⠈⢆⠀⠀⠠⢀⡇⠀⠀⢸⠀⠀⠀⢠⠐⢠⠃⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠴⠎⣀⠀⠈⢦⡀⠀⠀⠛⠀⠀⡃⡀⡄⡆⠀⡰⠃⠀⠀⡔⠋⠁⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠤⠤⢄⠀⠸⠀⠀⠀⠀⠀⠀⠀⢱⣠⡄⡉⠢⢄⣸⡀⢑⣇⣠⠤⠔⠋⠀⠂⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠑⠀⢇⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠰⣎⡀⢘⡽⢟⡆⠈⠑⢦⡜⠁⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠀⠠⠔⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣉⣉⣤⡴⢞⡧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡘
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⢠⣀⣴⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡌⠀⡜
⠀⠀⠀⠀⠀⠰⡁⠀⢀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠠⠀⠀⠀⠀⠀⠈⠻⣙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠘⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠊⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⣀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠰⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡔⠉⠉⠲⡀⠀⠀⠀⢻⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢥⣌⣊⠔⠰⠀⠆⡔⡠⢠⢀⠎⡞⠠⠃⢋⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠑⠂⠄⠊⠀⠀⠀⠀⢸⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠢⠤⠤⠤⠤⠤⠔⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣱⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢣⡸⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⢈⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡴⠆⣨⢔⠵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⣷⠆⢐⠵⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠕⡪⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣩⣂⠅⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣩⣿⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⣻⢹⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢕⡏⢸⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⡠⢀⠴⣂⢔⡢⢊⠤⣂⠔⡪⠔⡡⢐⡠⢂⠴⣂⠔⣢⢔⡠⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠥⢻⡰⣛⢕⡾⢳⣄⣿⢔⡠⢂⠄⡢⡤⠔⠔⠠⠀⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠉⠠⡀⣀⢀⣤⡦⠛⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣦⠀⠸⠟⠀⢀⡀⠒⠙⣛⢻⠟⠁⢀⡀⢻⠾⠛⢱⣤⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⣶⣯⠛⠉⠃⠀⠔⠁⠱⣤⣶⣿⣿⣶⡴⠈⠉⢲⣧⡀⠘⠪⣽⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠓⠒⠒⠚⠛⠓⠒⠒⠛⠛⠛⠛⠛⢥⡀
⠀⠀⠀⠀⠀⠀⡸⠁⣤⣭⣭⣭⡍⢩⣽⣻⢛⠉⠉⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠛⠛⠛⠛⣻⣭⣭⣭⣌⢇
⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡌⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣎⢂
⠀⠀⠀⠀⠀⢠⠄⠤⠭⠭⠭⠭⠥⠬⠍⠓⠒⠒⠐⠂⣿⣿⣿⣿⣿⣿⣿⣾⣿⡗⠒⠒⠒⠂⠋⠟⠛⠛⠛⠋⠀⠡
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣶⣶⣶⣿⠈⠃⠀⠀⠀⣟⠛⠛⠻⠛⠛⠛⠛⢛⡇⠀⠀⠀⠋⢰⣿⣿⣿⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣯⢥⠉⢲⡄⠀⠀⠐⢍⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⡿⡿⠿⠿⣿⣀⠀⠀⠀⠀⣇⠄⠚⠁⠀⠀⠀⠀⣸⡇⠀⠀⠀⣀⣸⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠢⠤⠈⠛⢻⣸⠀⠀⢀⣇⡿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⣏⡍⠀⠀⣸⢸⠇⠠⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣶⣭⠞⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⢮⣵⣮⡵⠋

⠀⠀⠀⣀⠀⠀⣠⡦⢰⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶
⠰⠐⠇⠙⢙⣿⣻⢏⠈⡄⠀⢠⠀⡀⣀⠈⠈⠀⠀⠀⠀⠀⢀⣀⠀⠐⠆⠀⡀⠀⣠⠀⢀⠀⠃⠀⠀⠹⠿
⢠⣴⣿⣶⣿⡏⠀⢧⠶⣧⠀⢘⡟⢱⣯⠅⣿⡳⠀⠀⠀⠀⠈⠙⠁⢀⡦⠞⠛⠉⠉⠙⠻⢤⣴⣚⣶⡄
⠘⠉⣉⠙⠻⠷⠒⠆⠀⠸⠀⠈⠁⠘⢳⡘⠮⠇⠀⢀⠀⠀⠀⠀⠐⡞⢀⠀⠀⠀⢀⠃⡀⢀⢈⡿⢁⠙⠆
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠴⣇⠀⠤⣦⣷⣨⣤⣷⣧⣾⡵⡏
⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠘⢦⣐⣚⣭⠭⡙⠛⣫⠭⠕⠃
⠀⠀⠈⠕⠂⠶⠠⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠤⡀⠀⠀⠀⠸⠀⠁⠀⠡⠀⠀⠀⢰
⠐⠽⠆⠀⢂⠁⠀⠀⠀⠈⠨⢉⠀⠻⠀⠀⠠⠁⠈⠀⣀⣤⡤⠀⣄⡠⠇
⠀⠀⠁⣰⠜⡿⢬⡀⠀⠀⠀⣁⠈⠃⠀⠀⠁⢰⠾⠛⠋⠉⢀⡶⠳⠶⠾⠶⠄
⠀⠰⣀⠻⣗⡀⠀⠀⠑⠀⣠⣄⢀⠀⠀⠀⠁⠀⡀⠠⢰⠺⠁⠉⠂⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⣤⣤⣄⢆
⠀⠀⠁⠠⠄⠑⠀⠤⠒⢚⠙⢋⢐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⡿⣿⡆⡿⣿⣿⣯
⢠⣶⣶⣶⣶⡖⠊⠁⠛⠃⢓⠃⠈⠐⠆⠀⠀⠀⢀⡤⣤⡂⠀⠀⠀⠀⠀⣶⠀⠀⠈⣉⠛⣍⠳⠷⣯⡽⢻
⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣶⣴⠤⡶⠀⣿⢾⣦⠡⣿⢰⡧⡄⠀⠈⣶⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⡆⠀⠀⠀⠀⡠⡈⣄⣙⣋⠤⡛⢛⣀⠒⠂⣒⠘⠛⢐⣻⣝⣳⠇⢀⣴⣿⣿
⠸⠒⠀⠀⢀⣠⠝⠻⣿⣿⣿⠕⢾⣶⣶⣶⣷⣎⡺⠊⠙⠲⠮⢭⣤⣉⠉⠉⣉⣉⣁⣭⣭⡵⢾⣿⢿⣿⡿
⠀⠀⠀⠐⠐⠀⢲⡀⠀⠀⢀⡖⠀⠀⠀⠀⠈⠈⠈⠈⠀⠀⠈⠉⣩⣉⣧⣮⣭⣿⡅⡉⢩⠉⠉⠉⠉⠈⠘
⠀⢠⢿⣤⣏⣠⡀⢁⣄⢀⣀⡀⡀⣀⡴⣦⣸⢳⡟⠟⠦⣤⢠⣠⠄⢻⣿⣿⣿⣿⣧⣿⣇⣤⡖⢀⡀
⢠⠟⠈⠿⠻⠼⠃⠿⠿⠿⠼⠛⠯⢋⣛⡏⡟⠚⠀⠀⠀⠀⠀⢀⣠⣿⣿⢿⡛⣛⢿⣋⣯⣹⣙⣫⡀
⢀⠢⠤⠂⣀⣄⣀⣄⣀⢤⣴⣶⣽⡿⠔⠓⠀⠀⠀⠀⠐⠀⠀⠚⠛⠛⣿⣶⣿⣿⢿⡿⢿⡿⢯⠙⠃
⠾⠿⠧⠀⠠⡥⠿⠇⠀⠀⠉⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠴⠽⠿⠿⠿⠿⠼⠇⠸⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠀⠈⠉⠉⠛⠒⠲⠤⠤⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠉⠲⠤⣄⣀⠀⠀⠀⣠⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢌⡃⠀⡀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⠀⢧⡉⠒⢍⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⠒⢬⡲⢤⣭⠢⡍⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡐⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡛⡆⡈⠑⠯⣛⠾⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡈⠂⠄⡀⠀⠀⠀⠀⢉⢁⢢⢃⢠⣆⢨⠙⠢⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣁⠃⡀⠀⠀⠀⠸⡄⢸⡈⡀⡈⡄⡔⡈⡓⢤⡀⢤⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⠭⠳⢤⣙⠢⠀⠆⡇⠀⠇⠁⠁⢃⢠⢡⢱⢂⢍⠲⣌⠧⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠤⠬⠭⠭⠓⢦⣀⠃⠀⠸⠀⣸⠸⡘⠈⡈⡘⠘⡼⢨⠑⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣀⡀⠀⠨⠭⠄⣰⠟⠢⣅⠃⠅⡆⠇⠃⢡⠃⢃⠣⠇⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠐⠒⠒⣂⡀⣽⠋⠀⠀⠀⠙⠾⣵⢰⠸⠸⠐⠸⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠠⠤⠤⠤⢠⡖⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣇⣆⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠤⠉⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠄⠉⠉⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢒⡒⢪⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⠀⠀⠀⣀⣒⡒⠒⢒⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠒⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠁⠀⠀⠀⠤⠀⠀⠩⣭⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠂⠀⠀⠀⣀⡁⢐⡀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⠈⠀⠀⠀⢀⠀⠲⠂⠐⢂⡾⠁
⠀⠀⠀⠀⠀⠀⡰⠁⠔⠀⠀⠀⠀⠠⠤⠤⠤⠤⢤⡟⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢈⣀⣒⣒⡂⣀⡞
⠀⠀⠀⠀⠀⠈⢦⡀⠀⢀⡐⠒⠒⠀⠀⠐⣐⠞
⠀⠀⠀⠀⠀⠀⠀⠑⢶⡀⠠⠤⠍⠥⠀⣒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢭⣭⣭⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⡠⢐⡡⢉⡤⣊⠕⡣⠔⡠⢒⡠⠊⡡⠒⡡⠐⡠⠔⡡⢖⡠⢖⡠⢂⡠⢂⡠⠄⡠⢀⡠⢀⡄⠀⠀⢀
⠀⠀⠀⠀⠈⠐⠀⠈⠔⢩⠔⣡⢔⡡⢊⠕⢋⠔⡩⠔⣁⠔⢉⠔⢋⠔⢊⠔⣋⠔⣩⠔⣉⠔⢉⠔⢉⠔⢊⠔⣉⢔⡡⣪⢞⡵⢋⠔⡡⢊⠔⡡⢀⢔⡠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⠈⠀⠘⠁⠈⠁⠈⠁⠀⠁⠈⠁⠈⠁⠘⠁⠈⠁⠘⠁⠘⠁⠚⠁⠉⠘⠁⠉⠀⠁⠈⠀⠁⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢒⠒⢩⣝⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠘⢉⣔⡂⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠩⠴⠦⣭⡝⣣⠔⢺⢋⡠⠤⣀⠀⠀⠀⢀⡠⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⠒⢒⡖⢪⠞⠁⠀⡷⠁⠀⠀⠀⠈⠁⠉⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡀⢠⠊⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⡸⠀⢠⠔⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⢠⠃⠀⡆⠀⣰⠁⡸⠢⠤⠀⠀⠠⠤⠤⠔⠒⠂⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡎⠀⢀⡇⠀⢲⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠸⠁⠀⢸⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡴⠒⢾⠁
⠀⠀⠀⢀⠀⠀⠀⣾⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠌⠀⠀⠈⡂
⠀⠀⢀⠎⠀⠀⠀⡆⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⡰
⠀⠀⡜⠀⠀⠀⠀⠇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠚⠁
⠀⣰⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢀⠇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇
⡘⠀⠀⠀⠀⠀⠓⠤⣀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡇
⢇⠀⠀⠀⠀⠀⠀⠀⠀⡩⠒⠒⠢⠤⠤⣈⣦⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⡇⠀⣀⡠⠤⠤⠤⢄⡀
⠈⠲⢤⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠒⠚⠙⡋⠀⠀⠀⠀⢠⠋⠉⠀⠀⠀⠀⠀⣸⠉⠳⡄
⠀⠀⠀⠈⠑⠦⣀⡏⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡆⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⠘⣆⣀⡀⠀⠀⠀⢀
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠱⠄⠈⢁⣀⣵⡙⠳⡿⠄⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⢀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢕⣤⠀⠀⣠⠊
⢀⣴⣕⠄⠛⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠉⠀⠛⠀⢀⡀⠀⠀⠀⡔⢠⠀⠀⠀⠘⠁⠀⠜⠁⠸⣆
⣝⠂⠙⢀⣴⠄⠓⠀⠀⠀⣠⠰⠲⠲⠆⠁⠀⠀⠴⠀⠒⠠⠀⠀⠈⠀⠀⠀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠠⠀⠀⠈
⡙⠂⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡚⠶⠄⠀⠀⢀⠥⠒⢄⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠘⠉⠁⢢⠀⠀⠀⠈⠀⠀⢸⠒⠒⢀⡀⠀⠀⠀⠁⠀⠔⠀⠀⠀⡠⠚⠁
⠀⠀⢠⠀⠤⠰⠇⠀⠀⠀⢰⠃⠚⠁⠠⡄⠀⠀⢁⠇⠰⠀⠀⠀⢰⠤⠐⣀⠸⠂⠒⢀⠰⡄⠀⢀⡀⠀⠀⠀⠠
⡰⠈⠙⠂⠀⠈⡱⠔⠶⠤⠌⢠⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠜⠀⠸⡀⠀⠉⣠
⠳⠦⠀⠀⠀⠀⣁⠀⡤⠬⠗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⠄⠀⠠⠅⠀⠠⠒
⣦⠀⠀⠀⢰⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢈⠂⠀⠀⠉⠉
⠀⠈⡁⠀⠘⠠⠂⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣤⡤⠤⠄
⣤⡦⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣴⡶⠖⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣼⡷⠖⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⢴⡶⠟⣋⠄⠀⠀⣠⠔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠢⣌⠙⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠛⠫⢟⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡘⠀⠀⠀⠙⠫⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⠶⠶⠶⢶⣿⣛⣛⣛⣛⣛⣛⣻⣿⣷⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠒⠒⡄⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠁⠀⢸⠀⠀⠀⡇⠹⠀⠀⡏⠀⠉⠑⢻⠽⣻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠇⠀⠀⠘⠢⡀⠀⡎⠉⠉⢹⠓⠒⠊⠉⠉⠉⠀⠀⡎⠀⡇⡠⢲⢄⣀⣀⣀⠜⠀⠀⢈⠟⠻⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠒⠢⢄⠀⠈⠒⠃⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⠔⠁⡜⠀⠀⠀⣀⠀⠀⠀⠣⣄⣘⠤⠞⣹⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⡏⠙⠲⣄⡸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣠⠔⢃⠔⢙⠆⢀⠇⠀⣠⠋⠈⠑⠆⠀⠀⠈⠀⠱⢤⣿
⠀⠀⠀⠀⠀⠀⠀⣼⢷⢦⠀⠀⠀⠀⠀⡸⠉⢲⠀⣸⠀⠀⠀⠀⠀⠀⠑⢄⡙⠒⠋⠀⣸⠀⢰⠁⠀⠀⠈⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢧⠀⠀⠀⡠⠁⣤⠀⠑⡗⡄⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡏⠀⣇⠤⣒⡒⠒⠚⠀⢠⠠⢄⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣯⣳⢄⡀⠓⠤⠴⠁⢶⠆⠀⢀⠃⢇⡀⠀⣠⠤⢄⠀⠀⠀⡇⠀⢀⠃⠀⠀⠈⣛⣁⠀⠀⠀⠀⠑⡀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣯⣢⣄⠀⠀⠀⠀⠀⢸⠖⢲⠑⠚⠁⠀⢀⠇⠀⢠⠇⠀⢸⠀⠀⢰⠋⠀⢸⠀⢀⡴⠊⠚⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡢⢄⠀⠀⡞⠓⠁⠀⠀⠀⠀⢸⡀⢠⠃⠀⠀⡎⠀⠀⠀⠣⡀⠈⠓⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣕⣤⣇⠠⠤⠤⠤⠤⠤⠤⠷⣧⣤⣤⣤⡧⣀⡀⢀⠴⠁⠀⣏⣉⠗⠀⢀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠷⢾⣽⣶⣢⣄⣀⣰⠒⠒⠃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠷⢿⣷⣖⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⡶⠟⠋⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠐⠈⠉⠉⠑⠢⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠙⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⠀⠀⠤⠄⠀⠀⡄⠀⠀⠀⠑⠖⠖⢀⣀⠄⠀⠀⢀⣄⣀⠄⠀⠀⠈⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠒⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⢀⡉⢣⠀⠀⠀⠀⠐⠦⠤⠄⢀⣀⡀⠀⠢⠤⠔⠊⠒⠃⠀⣠⢀⠄⠀⠀⢠⠀⠀⠀⠈⢢
⠀⠀⠀⠰⠊⠁⠀⢀⠀⠀⣈⣧⣀⠉⡉⠀⠙⠓⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡜⣠⠀⠀⠀⠀⠁⢳
⠀⢀⡤⠂⠀⠐⠊⠹⣄⡀⢀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡀⠀⢀⡜⠀⠀⡀⠈⠹⠄⠀⠀⠀⠀⠀⠒⠉⠈⠀⠀⠀⡴⠀⠀⠈⠀⢤
⠀⠊⠀⠀⠒⣆⠀⠀⣀⡍⠀⠀⠀⠑⢪⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠠⣄⡀⠐⠆⠀⠒⠁⠒⠒⠋⠀⢀⠦⠔⠄⠈⠇
⡀⠀⠀⠀⢤⡈⠁⠀⠰⡁⠀⠸⣄⠀⡀⠑⠂⢄⠀⠰⣄⡀⠄⠀⠀⣀⠀⠀⠣⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⣰⠤⠂⠈⠋⠁⢀⠄⠀⠀⡀
⢇⠱⠄⠀⠀⣉⠁⣠⠀⠉⠀⠀⢀⠉⡀⠀⠀⠀⠉⠁⠀⢀⠀⣉⡉⢀⣀⡠⢄⣈⠉⣉⣁⡀⠠⣄⣠⡄⠀⠀⢤⡀⠀⠀⠈⠉⠁⠠⠖⢊⡁
⠈⠢⠀⡄⣄⠈⠀⠻⠀⠀⠙⠤⠈⠉⣁⡜⠐⠋⠈⡐⠊⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⣀⣜⠃⠀⠀⠀⠠⠴⠒⠊⠀⠄⠈⡄⠊
⠀⠀⠀⠈⠢⡁⠀⠤⡀⠄⠐⠂⠀⠀⠀⠈⠋⠉⠉⠀⣿⠀⠀⠀⢰⠀⡇⠰⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠀⠉⠒⠂⠐⠤⡍⠉⢀⣐⡊⡐⠒⠀⠀⠖⡿⠀⠀⠀⢸⠀⢇⡇⠀⡈⠠⢸⠃⠒⠓⠒⠂⠀⠀⠉⡈⣁⣀⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠑⠄⠀⢺⡀⢈⠸⠈⡇⠸⠀⢃⠇⡆⡿⠖⠤⠒⠐⠊⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡆⡀⡇⡄⠠⣸⢰⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⡇⠁⠀⡇⡏⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡼⢇⡠⠴⢧⣇⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠌⠉⠁⠀⠀⠀⠀⠀⠁⠘⠋⠳⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢠⣴⠦⣴⠠⢤⣤⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠲⠄⠠⣿⡇⣿⠀⢸⠀⢸⢣⠔⠢⠤⠆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⡿⠀⡇⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⡇⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢳⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠴⢦⠀⠀⢈⠤⢤⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠣⠀⠀⠀⠀⠋⠑⡀⠀⠀⠉⠀⠀⠁⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠀⠀⠔⢢⡤⡈⠂⢀⡀⢩⠤⠒⢤⢤⡀⠙⠀⠐⠳⡄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠀⠠⠄⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠑⠲⠀⠈⠓⠀⠈⠈⠋⠂
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣤⡤⠖⠚⠛⠛⠽⠿⠛⠈⠉⠉⠻⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠻⢦⣶⣶⣶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣸⠟⠉⠀⣄⣤⣶⣶⣶⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⡈⠉⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠋⠀⠀⢀⡄⢿⣿⣿⠿⠿⣫⡾⡇⠀⠈⢀⣤⡾⣿⣾⣿⣿⣷⡄⠀⠀⠈⠣⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⠀⠀⠀⠀⠈⠟⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠿⢾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠻⠟⣳⢶⣦
⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣛⣭⡾⠇⠀⠀⠀⠀⠀⠐⣾⢹⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣇⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢰⢻⣧⠀⠀⠠⠀⠀⣴⡀⠀⠁⠀⠀⠀⠞⣿⣿⣿⣶⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⡘⣿⡷
⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡾⣿⠂⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⣾⣿⠾⠃
⠀⠀⠀⠀⠀⠘⢿⡦⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠐⣻⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠀⠀⠀⢿⣿⣿⣿⣄⡀⠈⠛⠋⣭⣙⡫⣿⠋⠀⠀⠀⠀⢐⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠰⠀⠙⠻⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⢠⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣴⣂⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣤⣈⠻⣦⠀⠁⠀⠀⠀⠀⠀⠸⠿⠯⠍⠀⠁⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⢶⣶⣤⣤⣟⣻⣧⣠⣼⣏⣡⣀⣀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠿⣯⡽⠿⠁⠀⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠀⠶⠀⠠⠄⠠⣤⠀⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠴⠀⠠⡄⠀⣤⠀⢠⡄⠀⣈⠀⠀⠁⠀⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠶⠀⠰⠆⠀⣤⠀⣠⡄⢀⣀⠀⣈⠁⠀⠛⠀⠘⠃⠀⠖⠀⠰⠄⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠠⡄⠀⣤⠀⢠⣄⣀⣈⣁⣈⡋⠀⠛⠃⠘⠟⠀⠶⠆⢰⡦⠀⣤⠀⢀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠰⠆⠀⣤⠀⣠⡄⢀⣤⠖⠉⠀⠀⠀⠀⠀⠉⠛⢿⡀⢾⡦⢠⣦⠀⣤⡄⢀⣀⠀⢈⠁⠀⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⣤⠀⢀⡄⠀⣈⠀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⠖⠁⠀⠀⠀⠀⠘⣏⠀⠛⠁⠘⠇⠀⠶⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠤⠀⢠⡀⢀⣀⠀⢈⡁⠀⣻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⡶⠿⠀⢶⠆⢠⡄⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡩⠊⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠀⠀⠄⣠⡀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠘
⠀⠀⠀⠀⠀⠈⠁⠀⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠖⠀⠠
⠀⠀⠀⠀⠀⠛⠀⠰⠆⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠄⢠⡄⠀⣀
⠀⠀⠀⠀⠰⠦⠀⣤⠄⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢠⡄⠀⣀⠀⣈⡉⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⢀⡁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠁⠀⠙⠁⠘⠟⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢉⣉⠀⢈⠁⠀⠛⠀⠘⠂
⠀⠀⠀⠀⠉⠀⠘⠃⣴⠟⠋⠙⠣⢰⣶⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠛⠀⠛⠃⠐⠗⠀⠰
⠀⠀⠀⠀⠀⠀⠺⢸⣏⠀⠀⠀⠀⣤⣤⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠇⠐⠷⠀⢰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⣦⠀⢻⣦⣤⣤⠖⣉⡁⢈⡛⠻⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⠆⢰⡆⠀⣤
⠀⠀⠀⠀⠀⣾⠁⢀⣄⠀⢀⡁⠀⠙⠁⠘⠛⠐⠿⠛⢿⡿⢿⣿⡿⣿⣿⢩⣭⡁⣙⡻⣿⣶⣤⣤⣤⣤⣴⣶⣿⡟⢠⣦⠀⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠘⠃⠘⠛⠀⠾⠇⢰⣶⠀⣴⡄⣠⣭⢀⣭⡁⢈⣛⠀⠛⠃⠸⠿⠛⢿⠟⢻⣿⠁⣤⠀⢠⡄⠀⣈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠀⠰⠆⠀⣶⠀⣠⡄⢀⣭⠀⣈⡉⠈⡛⠁⠻⠟⠘⠿⠃⢾⡷⢠⣶⠀⣤⡄⢀⣌⠀⢈⠁⠀⠉⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣄⠀⣈⠁⢈⡋⠀⠛⠃⠘⠿⠀⠿⠇⢰⡶⠀⣴⡄⢠⣄⠀⣉⠁⠈⠉⠀⠛⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠘⠋⠐⠿⠂⠲⠖⠠⣶⠀⣤⡄⢀⣌⠀⢈⡁⠀⠉⠀⠘⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠰⡶⠀⣤⡄⢠⣄⠀⣈⠀⠀⠉⠀⠙⠁⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⠒⠒⠒⠓⠒⠒⠒⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⡗⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠄⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⠀⠀⣻⣿⣷⣶⣿⣿⣿⡿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⣿⣿⣷⡿⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠏⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠓



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠎⡁⠊⠀⠀⠀⠤⢀⠀⡀⠀⠉⠀⠒⠀⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠈⠀⠑⠁⠂⠠⢀⡢⠀⠀⡀⠀⠀⠀⠈⠐⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⠀⣀⠀⠀⠀⠀⠀⠰⠁⡆⢚⠎⢠⢂⢔⡒⠀⠀⠄⠘⢀⠊⢁⠀⣖⠤⢀⡀⠀⠀⠀⠈⠁⠀⠐⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⡈⠐⠂⠈⠠⢈⣁⠒⠨⠡⢀⡑⠂⠴⢁⠂⠀⠄⠀⢰⠀⢷⠘⠃⡀⡼⠁⠈⠠⣀⠹⠃⠀⠀⠠⠄⠀⠀⣠⡳⡄
⠀⠀⠀⠀⠀⠀⠔⠀⠐⠢⠬⢁⣉⡒⠠⠀⠀⠀⠀⠀⠂⠤⠃⠰⠀⡄⠄⡀⠀⠘⠤⠀⢰⣀⠟⢀⣂⠀⠠⠈⡇⠀⠀⠀⠀⠀⠀⣼⣾⣃⢥
⠀⠀⠀⠀⢀⠊⠀⠠⠀⠀⠁⠀⠀⠡⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠉⢀⠁⠒⠤⢉⠐⠂⠂⠠⠅⢈⡂⠁⠊⠀⠀⠀⠀⠀⢀⡾⡻⢻⡶⢫⡇
⠀⠀⠀⠀⡈⠀⠀⡠⠀⢂⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠠⠄⠀⠀⠀⡔⠰⠀⡀⠁⠀⠒⠀⠄⠀⠛⢰⣄⠢⠀⣠⢎⠨⣡⣿⡾⢃⣷⡀
⠀⠀⠀⠀⡀⠀⠢⠄⣁⡀⠀⠁⠂⠀⢀⠀⠀⠠⠐⢊⡁⠀⠀⡀⠋⠁⠀⠀⠀⡔⢀⣄⣉⠋⡚⠓⠖⠠⠤⠀⠀⠀⢠⠞⡱⣡⣾⣟⢵⢃⣟⣞⠇
⠀⠀⠀⠀⠡⡀⠀⠁⠀⠀⠀⠀⠀⠀⢄⡀⠒⠨⠉⡀⠀⠀⢄⠤⠐⠂⢐⠂⠈⠀⠂⠀⠀⡈⠉⠑⠒⠂⠀⠀⢀⣪⢋⠈⣈⣾⡿⡡⣱⣿⠝⠁
⠀⠀⠀⠀⠀⠀⠐⠲⢶⣀⡄⠀⠀⠀⠂⠀⠉⠓⠠⠤⣌⠉⡐⠂⠍⠁⣂⠌⠀⠀⢀⡀⠄⠀⣂⠈⠐⠀⢀⢔⠕⢅⢤⣨⢞⠞⠝⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠠⠄⠐⠦⠄⠀⠨⢐⡀⠀⠉⡁⠀⠀⠀⠀⠈⠀⢂⡐⠪⠤⢀⠀⠀⢀⡆⣡⣾⢟⠝⣡⠪⡪⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠤⡀⠀⠀⠐⠀⠅⠀⠀⠀⠄⠒⢀⠄⠀⠀⠀⠀⣞⡴⠩⣿⠋⠔⢁⢄⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⠀⠀⢀⡐⠀⠢⠀⠁⠀⠀⢸⣾⠀⠀⠘⠫⠴⣿⠛
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠮⠤⣤⠀⠘⣎⡈⠂⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡨⠐⠨⠀⠀⠀⠄⠈⠀⡈⠀⠈⠀⢀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠄⠀⠀⠀⠀⢀⠄⡀⠔⡀⠐⡀⠀⠀⠂⠀⡀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠐⠁⠊⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⡛⠿⠛⠻⠻⡻⢛⣿⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⠤⠤⠤⠄⠒⠀⠀⡈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠒⠂⠉⢉⡀⡀⡀⠀⠠⠄⠠⠒⠒⡂⠀⣠⡇⣀
⠀⠰⠂⠀⠚⠉⠉⠉⠀⠠⠤⠀⢦⠀⠀⠀⢠⡠⠠⠐⠐⠒⣉⣉⡉⣄⠀⠠⡀⠀⠈⠁⢯⣀⡀⠀⠀⠀⠂
⠀⠀⠀⠐⢄⠈⠀⢳⡄⠤⠄⠖⠐⠁⠀⠀⠐⣦⡀⠈⡀⠀⢧⢀⠀⠘⢦⡀⢙⣄⡸⠀⢀⠉⢹⠆⠀⢀⣀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠑⢄⠀⢄⠀⠀⠀⠀⠀⠠⡀⠀⢹⡙⢦⣱⠀⠸⡏⠀⡀⠀⠳⠎⠈⠃⢀⡙⠂⠩⠄⠐⠂⠉⠀⠀⣄⠀⠀⠐
⠀⠀⠀⠀⠠⠀⠈⠣⠈⠣⠀⠀⠀⠀⠀⠐⠀⠀⠓⠀⠉⠀⡀⠁⠀⠁⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠁⠐⠀⠀⢀⡀⢚
⠀⠀⠀⢠⠀⢁⠀⠀⠈⢄⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⡈⠇⠸
⠀⠀⠰⠈⢣⠀⠡⠀⠀⠀⢠⠀⢄⣠⣤⡶⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⠀⠀⢄⡶⠄
⠀⠀⠀⠑⡄⠁⠀⠁⠀⠀⠀⠐⠀⠁⢀⠀⠀⢀⠐⠀⠀⠈⡀⠀⠀⠀⠈⠉⠁⠐⠂⠀⠀⠐⠂⠀⠀⠈⡄⠀⠀⠂⠑⡈⠀⡀⠀⠁
⠀⠀⠀⠀⠈⢆⠀⡀⠱⡀⠀⠀⠰⡀⠎⠐⠀⠈⢀⠀⠀⠀⠀⠀⠀⢰⣀⣀⠈⢀⣠⠳⠐⡂⠀⠀⠀⠀⠐⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⡀⢄⠘⣄⠀⠀⠐⡀⢀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠈⠉⠹⠟⠛⠉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⡈⢢⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠱⡀⠀⢠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢣⠈⢆⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠐⣀⣀⡠⠄⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠤⠀⠐⠂⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢈⣀⣀⡀⡀⠀⠤⠠⠀⠀⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠒⡾⢤⡀⠀⠀⠀⣀⣀⡤⡄⠀⠃⣸⠃⠞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⢺⠀⠉⢁⠀⢀⡔⢺⡈⠁⢸⠘⠀⣿⠌⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⣆⠀⠀⣀⡠⢼⡴⠻⡙⠄⠙⣶⢾⠉⠹⣯⣬⣙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠉⠂⠈⠓⠾⡟⠓⠉⠇⠀⠀⢀⡔⠁⠈⢤⠬⢄⣀⡔⢳⢀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠋⠓⢶⠀⠠⠗⠒⠀⣺⣶⠶⠤⠧⠤⠤⠤⢤⣐⣚⠯⠧⣄⢙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢰⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⡀⣤⡤⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠣⣀⡀⢉⡑⠃⠀⠀⠶⣶⠖⣺⢚⡯⡱⢰⣯⣼⠹⣻⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠤⣈⣉⡿⠯⠀⠀⠀⠿⠀⠙⠋⠉⠚⠉⠀⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠉⠒⠀⠀⠒⠒⡆⠀⠀⠀⠒⠒⠂⠄⠀⠐⠒⠈⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠉⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡁⡘⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠂⠙⡭⡝⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠋
⠀⠀⠀⠀⠀⢀⣀⣀⣬⠤⣀⠀⡀⠁⠈⠙⢤⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠄⣀
⠀⠀⠀⢰⠉⠉⣁⣀⠉⠉⠉⠂⠀⢸⣤⣀⣀⠬⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠸⠉⠉⠉⠉⡸⠛⢎⠉⠁
⠀⠀⠀⠘⡲⢞⠛⠀⠉⠋⠉⠈⠑⢬⣾⢨⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡙⠛⠛⠫⢭⣉⡩⢦⣄⣈⡢
⠀⢀⠤⠴⢡⢄⡰⡀⠀⠘⢆⠀⠐⠀⠟⢻⠀⢄⣀⠇⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⠔⢈⡧⠬⣁⡒⠒⠋⠀⠛⠚⠤⢀⡉⠑
⢏⣁⣴⣋⣁⣀⠿⠚⢄⢀⣀⠧⣀⡀⠀⠾⠗⠲⣤⣤⣤⣀⣈⣉⣉⣀⣤⣤⡤⠶⠖⠋⠁⠀⠀⠈⠉⠓⠊⠉⠉⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠒⠀⠁⠈⠈⣁⢀⣀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠂⠤⣀
⠀⠀⢀⠤⠒⠉⠀⠀⠠⠀⠒⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠄⣀⠀⠀⠀⠑⢦
⠀⠰⠁⠀⠀⠀⠀⢀⠠⠄⡒⠠⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠁
⠀⠰⡀⠀⢀⠔⢈⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠂⠤⢀⡀⠀⠀⠀⠀⡠⠃
⠀⠀⠉⠢⣌⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣢⡴⠕⠊
⠀⠀⠀⠀⠘⠬⡙⠳⢦⣤⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠄⠒⠉⢃⠄
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢍⣙⣢⠮⠭⠭⠀⣀⣀⣀⣀⣈⣉⡉⠀⠁⠀⠂⠀⣀⣠⠤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⡀⠁⠡⣍⠙⡓⠛⠚⠲⠶⠴⠦⠀⠉⡛⠒⡒⠪⠭⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠐⠶⠤⠉⣉⢁⣀⠀⠀⠀⠀⠀⠉⠉⠉⣁⣤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⡖⠭⠭⠭⠛⠛⠛⠛⠋⠭⠉⠁⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢶⣚⡀⣀⣀⣀⣀⣠⠶⠷⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠤⠄⠀⠈⠀⠈⣉⡶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⠄⠠⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⠁⢌⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⢀⠀⠀⠀⠄⢧⠀⡄⠀⠀⡀⠀⠀⠀⠀⢰⠰⠀⠀⠀⠀⠀⢆⠀⡄⠀⠀⠀⣀⢀⡀⠀⠄⢠⠀⢀⠄⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⢘⡆⢑⠀⠀⠀⠀⠀⠀⠀⠸⠸⡆⡆⠀⡄⡄⠐⠀⠃⠀⠀⢰⢃⡞⠀⠂⠀⠈⡠⠀⣠⠊⠁⢀⡴
⠀⠀⠰⡀⠀⠀⠀⠁⠀⢣⡈⡆⠀⠀⣰⠀⠐⠀⠀⡇⡇⣷⢸⡇⠃⠀⠀⣠⠀⢀⠏⡼⠀⠀⠀⢀⡜⢡⠞⠁⢀⡴⠀⠀⠄
⠀⠀⠀⠙⢄⢀⠡⡀⠰⡜⣧⠸⠀⡀⢿⡀⠀⡆⠀⢇⣷⠈⢸⡇⢰⠀⢰⡏⠀⡜⣰⠁⠀⠀⠀⠊⠐⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠳⡙⠄⠈⠘⣧⢁⢡⢸⡇⢀⠃⢸⢸⢸⣀⣼⡇⣸⠀⣾⠁⣸⢱⡇⠀⣠⠈⠀⠀⠀⠀⠀⣀⣠⠊⠀⠀⡠
⢀⠀⠀⠀⠀⠰⡄⠙⢔⣄⠀⠘⢧⠀⡜⣷⠀⠸⢸⡎⣘⡇⢹⣷⡇⣇⡇⢆⢃⣿⠁⣤⠏⡰⠁⢀⠄⢀⠼⠋⠁⠀⠀⠊⡄
⠀⠃⠀⢠⠀⠀⠙⣆⠸⣾⡣⣜⠘⢄⠃⣿⣧⠀⣿⡇⣏⡇⢸⣿⡇⢹⡸⠈⡾⢃⣾⢃⡼⠁⣠⠞⠐⣡⡾⠃⠀⠀⠀⠀⡀
⠸⠆⠀⠀⠣⠀⠀⠘⢆⠀⢦⠸⡷⣌⠀⢻⣿⡆⠸⡇⣿⠃⠘⡇⠁⣿⣷⡼⢡⠟⣡⡿⢁⣴⣿⣶⣿⠋⠀⠀⣠⠆⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣎⠎⡆⢽⣮⡀⠘⣿⣷⠀⠣⢿⡄⠘⡟⠀⣿⣿⡅⡫⣺⡿⡡⣿⡿⢻⡿⡡⢊⡴⢞⠑⢉⡥⡪⠞
⠀⠀⠀⠠⡀⢠⡄⠀⠀⠸⣿⡌⠈⣿⡇⠀⠘⣿⢀⠀⠸⡇⠀⠃⠀⣿⡟⠁⡼⠛⢃⣾⠟⣴⣿⢋⣀⣬⢞⠏⠐⠋⠀⢀⡀
⠀⠀⠀⠀⠈⢷⣌⠀⡄⠀⢻⣿⡄⠘⣷⠀⢀⠸⢸⡀⠀⠃⠀⠀⠀⠋⠀⠘⠁⡠⢈⠁⣺⡟⣱⣿⠟⣡⠞⢉⣤⠴⠚⣋⠄
⢈⡓⠂⠀⠀⠀⠙⠷⣌⡀⠀⢻⣷⡀⠘⠄⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⢃⡼⢋⣼⡿⣫⣾⣫⠔⣋⣀⠴⠊⣁⠤
⠀⠉⠉⠓⠂⠄⢀⣳⣬⡻⣆⠀⠙⣗⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⢋⡼⢛⣩⣶⡟⠉⠀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠉⠉⠛⠛⣛⣂⠈⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣾⣟⣋⣀
⢰⡶⠶⠶⠶⠶⠶⠤⠤⠜⠛⢁⣀⣠⠶⢋⣡⣶⠆⢀⡀⢀⡿⢂⠀⣤⡄⣀⠒⢦⡘⠚⢛⣋⣉⣉⣿⣿⣿⠿⣿⣿⣿⣿⣿
⣾⣷⡶⠶⠿⠿⢀⡀⣐⣛⣛⣓⣠⣴⣾⣿⡽⢂⣴⡟⣰⣞⣥⣣⣿⡹⢥⡌⠷⣔⢌⡻⣷⣍⠻⣯⣙⠊⠉⠉⠉⠛⣛⣻⣿
⣿⠧⣤⣄⣠⣤⣤⣤⡈⠉⠉⢉⣉⡀⡛⢉⣴⣿⡋⣼⣭⠉⠉⠛⣿⣿⣌⢻⣦⠀⠁⠉⠊⠉⠀⠈⠉⠁⠐⠻⠶⣦⣄⣙⣿
⣿⣶⣦⣬⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣭⣴⣶⣤⣤⣤⣬⣭⣭⣬⣭⣥⣶⣾⣿⣦⣾⠿⠿⠷⠶⠶⠶⠶⠶⠾⠿⠟
⣿⣿⢟⠿⢛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢶⣶⠒⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⣻⣿⣿⣿⣯⡥⣽⣿⣿⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠛⠛⠛⠛⢻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⣿⣿⣿⣧⡀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡽⢿⣿⣿⡿⣻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢺⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⡖⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠋⠉⠀⠀⠀⠀⡇⠀⠀⠀⠉⠑⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀
⠀⠀⠀⠀⠀⣸⠁⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠙⡆
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⢹
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠤⠚⠓⠤⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠈⠑⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹
⠀⠀⠀⠀⠀⠀⠈⡇⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣧⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢹⠈⢧⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⡸⠀⠀⢸⠀⠈⢆⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡴⠃⠀⠀⢸⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠶⠶⢶⠶⠶⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢍⠉⠃⠀⠀⠀⢀⠄⠒⠒⠂⢀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣺⣯⣶⠄⢀⠤⠄⠂⠀⣀⠀⠀⠔⠃⠀⠐⠤⡀⠐⠄⠀⢀⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡝⠟⠉⡀⠎⠉⣶⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⢀⡈⢹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣫⡞⠀⢼⠀⢀⡀⣷⡀⠀⢄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⡇⠊⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⣿⣾⣦⣼⣶⣤⣽⣿⣿⣶⣾⣷⣤⣿⣿⣦⣄⣀⣀⣤⣄⡀⢀⣀⣁⡀⠀⠀⠁⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣝⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⡿⠿⠶⣶⣦⣴⢀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠳⣭⣿⣥⣝⣿⣷⣶⣿⣿⣿⣿⣁⡀⠀⣀⡀⢠⣿⣿⣿⣾⣿⡿⠿⣿⣫⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠉⠀⠀⢸⠿⢿⣿⣷⣿⣏⠉⢻⡟⣿⣇⠉⠋⠀⠀⡟⠃⣼⠟⠉⣹⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣤⣤⣤⣤⣬⡉⢿⡙⢿⣆⠀⠁⣿⣿⠀⠀⠀⢠⡇⢰⠏⢀⣾⣿⠟⣡⣾⣿⠁⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠲⣝⠆⠙⢧⠀⣿⣿⠀⠀⠀⠈⡇⠀⣠⡿⢋⡴⡚⠱⠂⠀⠀⠀⠀⠘⠻⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣭⣙⡛⠂⠁⠀⠀⢰⣿⣿⠀⠀⠀⠀⢱⡐⠋⠀⠑⠊⠁⠔⢛⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣭⣽⣛⣛⠟⠃⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠴⠒⢛⣛⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣾⣿⣿⣿⡄⠔⠒⢂⣀⠜⠆⡀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠁⡀⠀⠀⠈⠺⣿⠟⠛⠻⣿⣦⣴⣈⡀⠀⢀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣖⣁⣀⣀⣀⣈⣙⢿⠶⣶⣀⣀⣠⡤⠈⠛⠉⠙⠛⢿⣿⣁⣙⣒⣲⣷⣶⣶⣀⣾⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣛⣟⣹⢛⣟⣻⡿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠐⡆⠻⣶⡤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⢖⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⡀⠉⠉⠙⠛⠒⠲⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠄⠐⠂⣉⠉⠉⠀⠂⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⠀⡇⣄⠀⢠⢰⡀⠄⠀⠀⠀⠀⠈⠉⠛⠓⢶⡖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⡛⠋⠠⠤⢔⣂⡀⢉⢰⠃
⠀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠀⢃⠀⠲⠸⠀⢡⡜⣤⠀⠫⡀⠈⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠈⠡⠈⠔⠋⠀⠀⠀⠂⣨⠀⠀⠘⣼
⠀⠀⠀⠀⠀⠀⢰⢣⠀⠄⢀⡄⠈⠀⠀⠀⡆⠀⠀⠤⠉⠡⠎⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢠⡆⣏
⠀⠀⠀⠀⠀⠀⠰⠎⠄⢀⠞⠁⠀⠁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡁⢀⡄⣋⢳⡄
⠀⠀⠀⠀⠀⠀⡇⠘⠠⠊⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢩⠉⠉⠑⣄⡘⣇
⠀⠀⠀⠀⠀⠀⠡⡒⠠⠾⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠁⡀⠀⠀⣦⢄⡐⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠰⠄⠒⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠱⠀⠀⠀⠀⠁⠒⠐⠀⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⢌⣁⣠⠀⢶⣶⣶⣶⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠤⣤⣀⠀⠀⠇⠀⠀⣀⣠⣤⠤⠤⠄⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠓⠚⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡻⡿⠛⠿⢿⣿⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿