House cleaning Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⠓⠒⠖⠶⠠⠔⠋⢉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡙⢠⡀⠀⠀⠉⠃⠀⠀⠘⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣷⣆⠉⠰⢶⠖⣀⠀⠟⠀⠀⠹⣧⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠋⢀⡠⢤⡍⠛⣿⣶⣄⣤⣤⣀⣴⣆⠀⠀⢱⠊⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢉⣠⡤⠶⠛⠁⠀⡌⠁⠈⠟⢿⣿⢻⣿⣿⣷⡟⠀⠀⠀⢶⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣶⣿⣿⠿⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠟⠛⠛⠁⠀⠀⠀⠈⢧⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣶⣶⣤⣄⠀⢀⠀⣀⣀⠈⢆⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠷⠀⠀⠀⠀⣠⣴⠖⣺⣶⣄⠈⢻⣧⠜⣟⣾⣿⣿⣿⠀⢻⣿⣿⡿⢷⣾⣆⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢣⠀⣠⠦⡌⠁⠰⠟⢸⣿⣶⡀⠙⣷⠸⡜⢿⣿⣿⠀⢸⣷⡞⣿⣾⣿⣻⡷⡆⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢀⢲⡟⣦⡄⠙⡖⢢⠙⣾⣿⣷⠀⠸⣁⣧⣨⣿⣿⠀⢾⣿⣷⣽⡷⣻⡿⢀⡏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠈⢿⣿⢇⠀⣋⡤⣰⣿⣿⣿⣧⠀⠻⣇⠸⣸⣿⠀⢸⣿⣿⣿⣷⣏⣤⣤⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⡽⣷⠀⢸⣿⡿⣋⢿⣿⣿⣇⠈⢷⣄⢧⡟⢠⣻⣿⣿⣿⣶⡿⠿⠿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⠜⣿⡉⠀⠉⠉⠀⠹⢮⡹⣾⣿⣆⠸⣇⣾⠁⣼⣿⠋⠛⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠰⠈⢳⣀⠀⠀⠴⣷⣎⢿⣿⡟⣿⡆⢸⡏⢰⣿⡧⠀⠘⠂⠙⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢡⠀⠀⢀⣠⠞⠛⠉⠀⠹⣿⣾⣿⡶⣇⣻⠥⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⢀⠟⢀⠀⢠⣾⣿⠳⣄⠀⠃⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠐⠁⣠⡾⢿⣿⣇⠙⣦⣠⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⣰⠟⠀⢸⣿⣿⠀⠈⠻⢿⣎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣰⡏⠀⠀⢸⡟⣿⡀⠀⠀⠀⠹⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⢀⡿⠀⠀⠀⢸⡇⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⢷⠄⣼⠇⠀⠀⠀⠘⠁⡄⣿⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⡯⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⢸⣿⡀⠀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡠⠈⣿⣷⡄⠀⢳⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠤⣤⣀⠀⢠⡇⠀⢸⡇⠀⣿⡏⣧⠀⠀⠙⠦⣤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠃⠀⢸⡇⠀⢻⣷⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣾⣿⡀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠶⣤⢶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⡄⣿⡏⣻⣿⢶⣾⣿⢟⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⢀⣿⠏⣼⢿⡷⠀⢠⣤⣴⡖⢲⣶⣤⣀⣘⣧⡾⢀⣿⣷⡹⢿⠏⡻⣿⣨⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣼⣿⠐⣙⣿⠃⠀⣀⣿⣇⢇⠘⢦⣿⠉⠏⡼⠀⡚⠸⣿⠐⣿⣧⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⢿⡀⠀⠹⣦⠻⡂⠀⢸⣿⠂⣼⠇⡘⢁⣶⠙⠧⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠿⠽⣦⣁⡔⠊⢹⣷⡞⠘⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢧⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⣿⡟⠛⠁⠿⠇⠠⠤⠄

⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⣠⡾⢋⣽⢿⣿⡯⣉⠉⠉⠉⠉⠙⠛⠿⣿⣮⡓⢦⡀
⠀⢰⡏⣰⢟⠌⢰⡟⠻⢦⡀⠀⠉⠀⠒⠀⠤⢀⡙⢿⣄⢹⡄
⠀⢹⣷⣿⣊⣴⠟⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⢘⣿⣾⡃
⣴⠟⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠚⠛⠋⢩⡿⢹⡆
⣿⡀⢸⣇⠀⠀⠀⠀⡀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡇
⠈⢛⣾⣿⣆⠀⠀⠉⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠶⠋
⢠⡟⠱⣈⠻⢷⣄⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⣠⣴⣯⡀
⠀⢻⣶⣤⡭⣦⣍⡛⢶⣦⢤⣤⣤⣤⢶⣶⠋⠁⢈⣿⠙⢦⣄
⢰⡏⣤⣈⣷⠀⢹⢺⢘⣧⡀⠈⣻⣶⡿⠳⣤⣤⢾⣧⠀⠀⠙⣧⡀
⠈⠷⣬⣭⣥⣴⠏⣪⣾⠏⠛⠟⠉⠉⣇⠀⠀⠀⠀⠹⣆⠀⣴⠟⢧⣀
⠀⠀⠀⠉⣻⣿⣟⢉⡿⠀⠀⠀⠀⡤⠟⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠙⢷⣄⡀
⠀⠀⠀⣰⣿⠃⠉⣻⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣧⣄⠀⠀⠀⠙⢿⣦⡀
⠀⠀⣴⡿⠁⠀⢠⡿⣮⣠⣀⣀⣀⠚⣹⣆⣀⣀⣦⠤⠞⢉⣿⣟⠷⣄⠀⠀⠀⢹⡇
⠀⢸⣿⠃⠀⣠⣿⣧⣄⣀⣉⣉⣉⣉⣉⣉⣩⣤⣤⠶⠞⠋⠁⠙⢷⣽⡗⠀⠀⣿⡇
⠀⣿⠃⢀⣼⠏⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⣉⣀⣀⣀⣀⣤⣾⠀⠀⢻⣇⠀⢠⣿
⢸⡏⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⠻⣟⠙⡇⢻⡇⠀⠀⢿⣷⣾⣿⡀
⢸⡇⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⡄⢻⠀⢡⢸⡇⠀⠀⢸⣿⠀⠙⣿⡀
⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢇⠘⡄⢸⣾⠃⠀⠀⣸⣿⡶⣾⣏⡻⣦⣠⣴⠶⢦⣤⣄⣀⡀
⠀⠀⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣆⣷⡾⠃⠀⠀⣠⢿⠛⣷⡄⠈⠙⣿⣿⣿⢿⣦⣑⠒⣩⡿
⠀⠀⢠⣿⣻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣀⣤⣞⠟⠁⣰⠟⠀⠀⣸⡏⢿⡟⠻⣿⣝⣿⣅
⠀⠀⠘⠛⠷⢿⣽⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣛⣻⣥⡵⠖⠋⠁⠀⠀⠀⣿⠙⠈⣿⠢⢈⣷⣥⣽⠷
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠙⠛⠛⠛⠛⠻⣿⠿⠛⠛⠛⠻⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡔⠂⣿⣄⠢⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠶⠯⠉⠛⠶⡷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡿⢸⣤⡦⡀⠀⡀⠀⢀⠠⠁⡾⣢⠄⠀⡀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢸⠀⠀⠀⠀⣸⠃⠸⠀⡇⢭⠻⠛⠣⢾⠁⠠⡇⠃⠠⡼⠇⢾⢤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠷⢶⣤⣼⠀⣀⡤⠶⠿⠶⣄⠀⠀⠀⢀⡀⡀⣀⣀⣀⢀⠀⣄⣀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠈⣿⣿⢋⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠴⠦⠤⠤⠴⢿⣿⠾⠶⠶⠖⠒⢶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⠄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣧⠀⠀⠀⢸⣿⣿⣿⠟⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢸⣿⣿⣧⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⣠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠤⠶⠿⠿⠿⠿⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢖⣫⣭⣝⡶⣄⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⣽⣾⣿⣿⣿⣿⣿⣷⣭⡓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣤⣤⣤⣤⣤⠀⠄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⢻⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣲⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⠟⠓⠒⠚⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣤⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢷
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⢿⣇⣸
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⠀⠸⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠂⢢⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡄⢰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢨⠀⠸⡀⣀⣠⣤⣤⠀⠀⢾⣿⣿⣿⣿⢸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣀⡀⠀⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⠀⠀⠈⠻⠿⠟⠃⣼⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⢸⠀⠀⢸⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⡄⠿⠿⠿⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢸⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡀⠉⠉⠉⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⣠⣤⡈⢳⡀⢸⡿⠛⠛⠁⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠛⠓⠲⠶⠶⠶⠶⠶⠖⠒⠒
⠀⠀⠀⠀⢰⣹⣿⡟⠈⡇⢸⠇⢀⣀⣀⡀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⢤⣴⣮⣥⡠⣄
⠀⠀⠀⠀⠘⣽⣿⡷⢀⡇⢸⡾⣿⣿⣿⣂⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡹⣧⡀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡆
⠀⠀⠀⠀⠀⠈⠉⣠⠞⠀⢸⣇⣿⣞⣿⣿⣿⣿⠀⠀⠀⢀⡆⠀⠀⠀⠀⣿⣿⣿⣿⣷⡹⣷⡀⠀⠀⠀⠀⠀⠘⡇⢸⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⢸⣿⢹⣿⣿⣿⣿⡏⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡹⣷⠀⠀⠀⠀⠀⠀⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡹⣇⠀⠀⠀⠀⠀⣏⣿
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡹⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⢉⣉⣛⣻⣿⣻⣇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢟⡇⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⠸⠃⠀⠀⠇⠀⠐⠃
⠀⠀⠀⣀⣀⣤⣤⣤⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠨⠿⠈⠀⠀⠀⠈⠂
⠀⠀⠻⠿⠿⢻⣿⡿⠿⠿⠟⠇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣶⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠆⠀⠀⢀⣀⣿⠀⠀⠀⠀⠛⠛⢿⠿⠿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠇
⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠄⠈⠀⠀⠀⠀⠀⠀⠈⣧⣤⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣤⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠙⢛⣛⣻⣿⣿⣦⣄⣀⣀⣀⣀⣄⣀⣴⣟⠛⠛⠀⠀⠀⠀⢐⣺⣿⣿⣿⣓⠀⢹⡄⠀⢻⣀⡀⠀⠀⢿⣇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⡿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢐⣚⣿⣿⣿⣒⢦⣤⡿⢄⠀⠈⠀⠀⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠿⠷⠒⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠈⠟⠀⠀⠀⠀⢠⣖⠁⠈⠢⡀⠀⠀⢀⠣⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠈⠓⢄
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⡛⠀⠀⢰⠃⠀⠀⠈⢄⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠒⠒⠁⠀⠀⠀⠀⠀⠑⠂⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠒⠀⠀⠈⠢⡀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⡠⠃
⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠢⡀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠈⠑⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢠⡄⠀⡴⠄⠀⣴⡄⢠⡄⠀⢠⠐⣶⠆⣠⡀⠀⣤⢀⡴⠀⠀⠀⠀⠀⠀⡠⠟⠚⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⣧⡀⠀⠸⡇⢸⠹⡀⢸⠀⣿⠀⣟⢳⠀⡏⢸⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢰⣒⣒⡆⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⡇⠀⢰⡇⡇⢸⠀⢣⣸⠀⣿⠀⣿⠈⢇⡇⢸⠐⢲⠀⠀⠀⠀⠀⣷⡒⠒⣒⡇
⠀⠀⠀⠀⡮⠉⠀⢀⠮⣢⡀⠀⠀⠀⠳⣤⠸⣤⡄⢧⡄⠼⠀⠿⠸⠀⠈⠟⠀⠿⠄⠻⠀⠸⠇⠘⢦⠼⠀⠀⠀⠀⢐⠁⠀⠀⠀⠈⠆
⠀⠀⠀⠠⠁⠀⠀⠈⠢⠨⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⡄⢀⣄⢀⣄⠀⡀⠀⢠⢠⣤⠀⢀⣤⢀⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⢸⣼⠇⢳⠀⡏⠀⡇⠀⡏⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠐⠄⣀⣀⠀⢀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠘⡆⢸⠉⢈⣟⠀⠸⣀⠃⠀⡇⠀⡇⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢸⣀⢰⡜⡄⠀⣿⠀⢀⣧⠀⣧⣀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢀⠆⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢬⣍⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⢀⠈⡄⢠⠁⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣾⠰⠇⡌⠀⠀⠀⠀⠀⠏⢆⠋⠄⠉⡀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠇⢻⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠃⠁⠀⠐⢀⠔⠆⠀⠀⠀⠸⡈⣾⠸⡀⢠⠸⠀⠀⠀⠀⠀⢸⡧⠉⠉⢭⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠶⢁⠌⠀⠀⠀⢀⠀⢡⠈⠀⠇⢸⢀⠀⠀⠀⠀⠀⡌⠉⠉⠈⠉⢁
⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠊⠀⠀⠀⠀⠢⡑⢌⡆⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⡴⠋⠀⠠⠀⢀⡠⠤⠄⠈⠳⡄⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⡈⠁⠀⠀⢐⠇⠀⠀⠀⠀⠀⠘⠒⠀⠀⠒⠉
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠠⣾⠒⢚⡆⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠐⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠰⠆⠀⢤⠀⢀⡀⢀⣀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢰⣿⣶⣿⣿⣌⠧⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠅⠄⢸⣿⠀⢀⣰⣾⣷⣤
⠀⠀⠀⠂⢀⣴⣶⣴⣿⣿⣿⣿⣧⣍⣄⣠⣤⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⠀⠈⠈⣿⣿⡟⠙⠶⠄⠀⢀⠀⠀⠁⠀⢸⣿⠀⠚⠻⣿⠟⠛
⠀⠀⠀⢠⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢐⣿⡇⠀⢰⣿⣿⣿⠀⠀⠀⠀⣾⣷⣾⣦⡀⢸⣿⠀⠄⠀⣿⠀⢠
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠃⠀⠀⠀⠇⠀⣿⣟⣿⣿⣿⣿⣿⡏⠀⢰⣿⠁⠀⣾⣿⣿⣿⣷⣤⠀⠘⢿⡿⠻⡟⠁⢸⡇⠀⠀⠀⣿⠀⢨
⠀⠀⠊⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠸⠿⠀⢠⡟⣿⣿⣿⢸⣿⡅⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠄⠀⣾⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢰⣦⠀⢸⣿⣿⣿⣿⣼⣿⠀⢀⡀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠛
⠀⠀⠀⠀⠁⠀⠀⠙⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⠀⣿⠀⠀⢠⠀⢿⣿⣿⡿⠿⠏⠀⠀⠈⠁⠀⠘⠛⠛⠛⠛⠛⠋⠀⣿⣽⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠆⡀⢀⣾⣶⣀⢰⣿⣿⣆⣀⠀⠀⠀⠀⣿⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⢐⠀⠀⠀⣿⣿⠀⠀⠂⠒⠀⠀⡀⢀
⠀⠀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⣄⢠⠀⣿⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⠏⢠⣾⣿⣿⢶⣄⡀⠀⠐⠄⠀⢹⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣠⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⠀⠀⣠⣶⣿⣿⣿⣧⠀⠀⢈⠀⢸⣿⣿⣿⣀⣹⣷⠀⢀⣠⡄⢸⡇⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠆⠀⣿⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⣿⡇⢸⣟⣿⣿⣿⣿⣿⠈⠻⣿⡇⢸⡇⠐⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢏⠁⠀⢠⣿⠀⠀⢉⠛⠿⣿⣿⠟⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣧⠀⠌⠀⠈⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠠⣿⣾⢿⡿⣿⣿⣿⣿⣿⡿⠿⠟⠠⡎⠀⠀⢸⣿⠀⠀⠀⢈⠐⠀⠉⠀⠀⠀⠛⠋⠀⠉⠉⠉⠉⠉⠁⠀⠀⠄⠀⣿⣿⠀⠀⠀⠀⢿⣿⡿⣿⢿⣿⠀⠢⠆
⠀⠀⠀⠈⠁⠀⠄⠘⠻⢿⣿⡏⠀⠀⠀⠀⣀⣀⣀⣸⣇⣀⣀⣀⠀⠀⠀⠂⣠⢾⣿⣿⣿⣷⣦⠀⠀⣘⣿⠀⠀⠀⠀⠀⢹⡟⠀⠠⠀⠀⠸⠿⠿⢿⣿⠇
⠀⠀⢀⠀⣀⣀⠀⠀⠀⢸⣿⡇⠀⠈⠁⢠⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⡀⣼⣿⣟⣿⣾⣿⣿⣿⣇⠀⣿⣿⡇⠀⠈⠀⠀⢸⡇⠀⠈⠠⠀⠀⠀⢤⠀⡄
⠀⠀⠉⢀⣿⠿⣿⡖⠀⠘⠿⠗⠀⠀⠀⠈⠉⠈⠈⠉⠁⠉⠁⠁⢁⠘⡀⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⡆⠀⣀⠀⢸⣇⠀⠀⠀⡀⢠⡹⣎⣇⣷⠀⡄
⠀⠀⡀⠀⠀⢾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢁⠀⠁⠹⣿⣿⣿⣿⣿⣿⠟⠀⠹⠿⠿⠿⠃⠀⠀⢰⣿⣿⡆⠐⢃⡀⠈⢻⣾⣿⣿⣧⣷
⠀⠐⠀⢀⣤⣼⣿⡇⠀⠄⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⡟⠀⠀⠀⠂⠳⠀⠀⣀⠉⠛⠛⠉⠀⣤⣤⣤⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⢿⣿⣿⣿⣾⣧
⠀⠀⢰⣿⣿⣿⣿⡇⠀⠁⣠⣾⣿⣼⣟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠘⠀⠀⠆⢠⣶⠶⣦⣄⠀⠙⠿⠏⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⢤⢶⣾⣿⣿⣿⣿⡏
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣾⣿⣿⣿⣿⣏⡿⠟⠙⠛⠛⠷⠶⠀⠤⠈⣿⣿⣿⣿⣧⠀⠀⣀⣤⣴⣶⣶⡄⢰⢿⣿⣿⣿⣿⣿⡆⣠⢶⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠈⠉⠉⠉⠉⠀⣄⠀⠀⠙⢿⣿⣿⠿⠿⠟⢻⡇⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⡿⠏⠀⠀⣿⣿⡿⠟⠋⠁⠸⠟⣿⣿⣿⣿⣿⠇⠰⠟⡿⡿⠋⠈⠁
⠀⢀⠉⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠁⠀⢀⡄⠀⠀⢀⣶⣶⠂⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⢀⠀⠉⠁⠄⠀⢁⡀⠀⠀⣉⠉⠁⠀⠠
⠀⠀⢀⣴⣶⣶⣿⣿⣾⣷⣶⣦⣄⠀⠠⠈⠂⠀⢰⣿⣿⡧⠉⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⣴⣿⠗⠀⣀⣰⣿⣿⡿⠀⠤⠋⠀⠤⠀⠈⠋⠀⠀⠀⢀⣠⣴⣷
⠀⠐⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠛⠛⠁⠀⠀⢀⣼⣭⣭⣴⣶⣶⠆⠀⠈⠁⣶⢿⣻⣿⠏⠁⠀⠀⢀⣤⣤⣤⣤⣤⣤⣄⠀⠀⢸⣿⣿⣦
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠶⣶⣶⣦⣄⠀⠀⠀⠻⠿⠿⠟⠛⠛⠀⠀⡀⠘⢿⣿⠿⠋⠀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠘⠟⠿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⢀⣸⣿⠆⠀⠀⠔⢈⣤⣄⠀⢸⣯⣭⣽⣷⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⣠⡀⠀⠄⠀⣠⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⡄⠀⣀⣸⣿⣿⠀⢸⣿⣿⣿⣿⠀⢰⣿⣿⣿⠀⠀⠀⠘⠿⠿⠿⠟⠛⠛⠁⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⣧⣤⣤⣤⣤⣶⠶⠶⠶⠶⠟⠛⠛⠛⠛⠛⢻⣿⣿⠀⢸⣿⣿⣿⣿⠀⠘⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣦⠀⠘⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠐⠔⠈⠛⠋⠀⠈⠛⠛⠛⠋⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒









⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠦⠬⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⡀⢀⢄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⡀⢀⠀⢠⠏⠠⠆⡢⣙⣉⡀
⠀⠀⠀⠀⠀⢀⡀⢀⠀⠐⡏⠀⠀⠀⠀⠀⡁⠀⡠⠀⠀⠠⢠⣲⣛⣛⠉⠉⠉⠉⠉⢉⠩⠅⠀⢀⣀⣺⣽⢽
⠀⠀⠀⠀⠀⠈⢶⠁⡰⠢⢀⡃⠚⡃⠙⠂⠀⠀⣢⣤⣤⣤⣘⠀⠉⣽⢻⡟⠛⠛⠛⠛⠃⠀⠀⠀⢹⠀⠉⠋
⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⢃⠈⠈⠁⠁⢤⠁⠀⣀⣀⡀⠈⠂⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣠⠈⠀⢀⣄⣈⣀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⢁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢩⡀
⠀⠀⠀⢤⣀⡍⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣀⣀⣀⣀⣀⣀⣡⣈⣀⡔⠀⠀⠀⠀⠀⠀⠐⠤⠀⠰⠂⢘⣇⣀⣸⡃
⠀⠀⠀⢰⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠘⡇⠘⠀⡇⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠘⠀⠠⠄
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡇⠀⠀⡇⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠉⠁⡗⠘⡟⢸⡇⠒⠊⡇⠀⡇⠀⡇⢠⣤⡷⢴⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⠀⠐⠂⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠄⠐⠀⠛⠀⠃⠘⠃⠐⠀⠃⠀⠳⠒⠓⠚⠟⠉⠈⢉⠟⣛⣲⣆⣒⣐⣒⠂⠂⠈⠁
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⢚⡀⣄⣠⣀⣀⡀⣼⠉⠛⠿⠉⠛⠛⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠠⠄⠤⠤⠤⠒⠒⠉

⣶⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⠋⠀⠀⠈⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡖⠁⠀⢠⢤⠀⠀⠀⠀⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢚⠀⠀⡜⢀⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣭⠃⠀⠙⠋⢁⠀⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠸⣦⣀⡼⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⡀⠀⡉⠑⠒⡄⢀⠀⠀⠀⡰⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢒⠏⠻⠤⠕⠀⢾⣿⣿⣿⢖⠝⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣴⣶⣤⣴⣿⣿⣿⡷⡍⣴⡁⠀⠀⠀⣀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣯⢟⠞⠱⡄⠈⠓⣖⠉⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⢿⣿⣿⣿⡿⡣⢯⠶⠚⠙⠦⣤⡼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣹⠊⠀⢀⢞⠞⡔⠛⠿⣬⡉⠁⠀⡶⠒⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠰⣇⢀⡰⡻⠃⠀⢸⠀⢀⣨⣿⡆⣸⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠙⢦⠌⡐⣟⠀⠀⢠⠃⠀⢻⣿⡿⠙⠋
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣢⠾⠁⠀⡰⠁⠠⣾⣿⡟
⠀⠀⠀⠀⢠⡏⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠜⠁⠀⢀⠜⠀⠀⣤⣾⣿
⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡡⠋⠀⠀⢠⣾⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⢀⠤⠒⠤⣾⠝⠀⠀⠀⠐⠛⠛⢻⠉⠙⣯⠉⠙⣇
⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⢀⠔⠡⢄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⢇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⠄⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢣⢀⡇⠘⡄⢸
⠀⠀⠀⠀⠀⠠⠴⠚⣉⠄⢀⠅⠀⡠⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⢣⢸
⠀⠀⠀⠀⠀⠀⠠⠭⠒⠭⡀⢄⣪⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠈⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠛⣿⣿⡀
⠀⢠⣾⣿⣿⡟⢻⠷⠆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠈⠛⣿⣷⡄
⠀⠈⠻⣿⣿⡇⠨⠀⠠⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠇⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣇
⠀⠀⠀⠀⠀⠀⣰⣦⣥⠀⠀⠀⠀⠀⠀⣰⣿⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢠⡿⡗⠰⣿⡁⠀⠀⠀⢀⡴⠚⠓⢦⡀⠀⠀⠀⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠀⠀⠀⠸⠰⠧⣤⡇⠕⠀⠀⠀⢸⡀⠀⠀⢀⡇⠀⠀⠀⣿⡟⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⢠⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⢿⠇⠸⡿
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⢀⣴⣿⡟⢻⠶⠄⠀⠀⠀⠀⠀⠀⣴⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⡟⣿⣿⣦⡀
⠀⠀⠀⢿⣿⣿⣷⠬⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠛⠃⠀⣿⡿⠀⠀⠀⠀⠐⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣘⠻⠗⠀⠀⠀⠀⠀⠀⢨⣷⡆⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠀⣬⣵⡆
⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⡆⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣧⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢹⣝
⠀⠀⠀⣀⠀⠀⢰⣿⠀⢸⣿⠀⠀⠀⠀⠀⣼⢿⣿⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⡇⠈⣿⡀⢀⣀
⠀⠀⠀⠛⢧⠄⠘⠛⠀⠘⠛⠂⠀⠴⠄⠐⠟⠘⠟⠀⠀⠀⠀⠸⣿⣿⡿⠀⠸⠿⠁⠀⠿⠃⠸⢿⡿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠒⠒⢂⠀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠈⠑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⠒⠒⢲⡔⠊⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⢀⢀⡤⠖⠂⠀⢈⣉⠩⠅⠀⠀⠰⡄⠀⠀⢀⠤⠒⠀⠀⠀⢖⠉⠓⢤⡎⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢜⡄
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠹⡀⡴⠁⣀⡠⠀⠀⠀⠀⠉⠛⣿⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⢀⠆⠀⠀⠀⢠⡎⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣠⡾⠟⠁⠀⠀⠀⠀⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠑⢦⡀⠀⣿⡟⡠⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠖⠒⠂⠤⢄⣀⣀⣀⡀⠀⠠⠤⣀⡀⠀⣠⠔⠂⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠈⠳⡶⠲⢾⣶⠦⢄⡀⠀⠉⢉⣩⣥⣤⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣈⠱⠦⣤⣀⣈⣩⡤⠤⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⠷⣄⣈⠀⢉⠼⣇⠀⠀⢹⠁⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⠀⠀⢀⣹⣯⠄⠀⠀⣸⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠉⣹⠇⡀⠈⠁⠀⠀⣷⣶⣴⣿⣷⣦⣄⣀⡈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠛⠋⠉⠀⠀⠀⣰⡇⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠙⠓⠀⡷⢄⠀⠀⠀⠀⢠⠃⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠓⠲⢤⣄⡀⠀⠀⠀⠀⢸⠀⢀⣀⣠⡤⠶⣻⣿⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡔⢺⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⢸⠋⠉⡡⠤⡄⠀⢻⣇⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢃⠐⡄⠐⠒⠶⠀⠀⢸⠓⢦⠀⠀⠀⠀⠀⠤⠶⢄⠀⠀⠀⠀⠀⠼⡆⠀⠀⠀⣸⠀⢰⠁⠀⠆⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠀⢫⠁⠂⠀⠀⠀⠈⣇⠘⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠀⡆⠀⠸⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡆⠘⣏⠑⠒⠒⠀⠀⡿⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠀⢠⠃⢰⠁⠀⡇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠄⢘⡦⡀⠀⣀⢴⠁⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡦⠔⠁⠀⣈⠀⠜⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁⠀⠀⠀⠸⣀⡀⣠⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⣆⢀⡠⠅⠀⠀⠀⠁⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢺⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠇⠀⠀⠀⡖⠒⠢⠀⠀⠀⢠⠤⠤⢤⠀⠀⠀⠀⠖⠂⢲⠀⠀⢠⠁⠀⡆⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠇⠀⢸⠀⠀⠀⠃⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠈⠀⢰⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⠀⠀⡆⠀⠀⢠⠀⠀⡅⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠀⢀⠃⠀⡌⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠑⠐⠁⠀⠀⠸⡀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢆⠀⢠⠃⠀⠀⠑⠊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠉⠊⠁⠀⠀⠈⠦⠤⠴⠀⠀⠀⠈⠉⠁⠀⢀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠔⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⢀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⠦⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠖⠦⣄⡤⠴⠖⠁⠀⠀⠀⠂⡨⠏⠙⠟⠢⢤⣀
⠀⠀⠀⠀⠀⢠⡤⣤⡀⠀⠀⢀⣠⠴⠒⠛⠁⠐⠀⠸⠁⠀⠂⢁⡀⠀⠀⠰⡉⠀⡠⠴⠲⠒⠊⠨⢦⡀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⢿⢱⣎⢳⡄⡴⠋⠀⠀⠈⠉⢀⠟⠉⠀⠠⠀⠙⠉⠋⠀⠀⠀⠈⠁⠀⠘⡀⠀⠀⠀⠀⢳⣠⡟⣇⢹⠂
⠀⠀⠀⠀⠀⢸⡞⣯⣧⣿⢰⣦⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠇⠐⡀⢰⣦⡄⠉⢿⣽⢸⡇
⠀⠀⠀⠀⠀⢸⡟⢮⣿⣇⠀⠉⠀⠀⠀⠀⠠⠄⢀⠂⠀⢀⠄⠀⠀⠀⠤⠀⠀⠀⢀⠀⡄⢀⠀⠈⠀⠀⠂⣸⠼⣾⡇
⠀⠀⠀⠀⠀⠀⢷⣤⣽⣍⡙⣮⠥⠄⣀⣰⣀⣀⣁⠄⠖⠺⠐⠄⠀⠀⠀⢤⡂⠀⢸⠀⣠⣘⣋⣠⣦⠶⠾⣡⣬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣟⠛⣿⡟⠛⢻⣶⣾⣮⣀⣀⡩⠀⠀⠀⠐⠀⠀⠀⣸⡛⣳⣂⣉⣙⣫⣭⣭⠷⠿⠖⣛⣉⡼
⠀⠀⠀⠀⠀⠀⠀⢻⡍⢫⡙⠻⠿⠯⢏⡉⠛⠛⡇⠀⠀⠀⢀⠀⢴⣿⣿⠉⠭⠭⠭⠽⠿⠷⣴⣶⡶⠟⡿⠋⡗
⠀⠀⠀⠀⠀⠀⠀⢸⡗⢾⡛⠷⢶⣆⡚⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠉⡗⣒⣲⣂⣴⣶⣶⣬⡥⣤⣶⢿⣶⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⣶⢶⡖⠿⢤⣤⣶⡇⠀⠀⠀⠀⠃⠀⠀⣯⠤⢭⣭⣤⣤⣴⣚⣉⣠⣥⢾⡗⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡳⣽⣦⣌⣹⡷⣦⣤⣽⠆⠀⠀⠀⠀⠀⠀⢠⣗⣒⣚⣛⣙⣩⣤⣟⠉⣭⣐⣿⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢯⣦⣉⣙⡲⢀⣉⡟⢀⣴⣦⡄⠀⠀⠀⢸⡷⠈⠛⠛⣏⢋⣩⣷⣛⣉⣽⠿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⢧⣙⡛⠯⡬⢛⡃⠘⠻⡿⠀⠀⠂⠀⢸⡕⡬⠵⠾⠟⠋⠡⠕⣛⣫⢾⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⢦⣍⡙⢻⡍⢛⡇⠀⠀⠀⠀⠀⡀⠀⣏⣩⠷⠿⠾⠝⢛⡫⠗⢋⣴⠷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⢮⣙⡻⠿⣻⠇⠀⠈⠀⠀⢀⣿⣦⢋⡴⠖⠲⠾⢛⣫⡷⢛⣩⣶⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡷⣮⣛⠭⣝⠢⠦⠤⢥⣤⣖⡦⠍⣛⣛⠾⠴⠛⣛⣫⣛⣩⣵⡿⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⡦⣍⣛⣍⡛⠻⣶⣳⢄⣛⣛⣛⣻⡯⡽⠛⢛⣻⣽⣯⡥⢾⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⡙⠨⣛⣦⣉⣛⡿⢿⣍⣩⣉⣩⣍⣭⡔⣛⣉⣭⣾⡯⠖⣉⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⠳⢿⠿⢮⣙⣛⣛⣂⣤⣭⣥⣤⣍⣉⣹⡭⠶⣗⡴⠊⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣁⠢⠬⢭⢉⢵⣦⡤⣥⡴⡽⠍⠤⠒⠉⣁⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⣤⣤⣤⣤⣤⣤⠤⠶⠒⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣪⢍⠕⢼⡁⠀⠀⠐⢮⡓⢄⠀⠀⣀⠤⠔⢒⣦⢤⣤⣤⡀
⠀⠀⠀⠀⠀⣀⣀⠀⣠⠎⢸⡁⡀⠼⠤⠤⡻⢶⡛⣷⣒⠬⣻⢔⠋⠀⠀⣴⣿⣿⣿⠿⠛⣇⡀
⠀⠀⠀⡎⠉⠀⠀⣈⣭⣟⡛⠛⠛⠓⠒⠒⠯⣉⠁⠀⣀⣙⣎⠁⢳⣠⣾⣿⣿⡯⣒⠒⠒⠁⠈⠉⠩⡇
⠀⠀⠀⡟⠀⣠⢮⣽⣒⣂⡀⠭⠭⢝⣲⠀⠀⣀⣻⣖⡤⡀⠉⢈⡿⡿⢛⡻⣿⣵⣛⢮⠷⣮⣤⠛⡷⣮⣦⡤⣀
⠀⢠⣾⣇⣰⢈⠟⢹⣟⣓⠻⠦⣴⡿⣣⣼⣿⣿⣿⣧⣦⣬⣽⣧⣄⢃⠀⠤⢈⡽⠛⠋⠁⢀⠶⠧⣟⣱⠿⠃⡸
⢰⠋⡇⣨⢣⠊⠀⢸⠀⠀⠉⠑⠒⠬⠭⣙⣛⠻⠿⠿⢿⣿⣿⣿⣿⣬⣶⣿⣀⠠⠷⣦⠔⠁⠀⢀⡼⠖⠒⡏
⠀⠑⠷⠤⡅⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⢆⢀⠴⠋⠀⠀⢀⡇
⠀⢀⠀⠀⠈⢑⠖⣃⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⡀⡤⣀⣤⣀⢤⠀⠀⢠⢤⢠⣤⢠⢲⢠⣷⢰⣷⠀⠀⢸
⠀⢸⠀⠀⡠⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⡇⡟⣤⣿⢸⡄⠀⢸⣾⢸⢻⢸⢸⢸⢹⢸⢻⠀⠀⣸
⠀⢸⣠⠊⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡃⢻⡃⣳⡃⣳⠋⣲⠁⠀⢘⣟⢘⣎⢨⣏⢨⢏⡰⢧⠀⠀⡇
⠀⣿⠃⠀⠀⢿⡃⠈⡆⠀⠀⠀⠀⠀⠀⡿⡇⡇⡇⡇⡇⡇⡇⣧⡇⠀⢸⣸⢸⢸⣸⢿⣷⡞⣿⡇⠀⠀⡇
⠀⠸⡄⠀⠀⣸⣧⡤⣻⡄⠀⠀⠀⠀⠀⢧⠇⢧⠇⠷⠇⠧⠇⠧⠇⠀⠸⠼⠸⠜⠙⠊⠙⠃⠙⠁⠀⢸
⠀⠀⠈⢶⡫⠗⠚⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣠⡾⠳⡀⠀⠀⠀⢀⡠⣚⢦⡤⡀
⠀⠀⠀⠀⠀⣾⣧⠏⢑⢾⣄⣠⠔⠉⠀⣸⠄⢠⣿⢳⡶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⠟⡠⢚⢁⠂⠙⠧⣀⣀⡀⠁⠀⢧⡏⣸⠅⣿⣃⠄⣩⠖⠉⢙⡦⠴⣒⠉⠳⣤⣄⣀⡀
⠀⠀⠀⠸⡗⠒⠚⠋⣉⡭⣷⣺⡥⢠⣿⠢⣠⣠⠇⡯⢾⠉⡠⠊⣠⠴⢚⡩⠔⠚⣩⣄⠀⠙⢶⡉⠍⠻⡄
⢀⣀⠀⠀⡌⠙⠒⣊⣁⣨⠄⢀⢀⡞⢂⢢⢹⡿⠖⠉⡠⠊⡠⠚⠶⠚⠁⠀⡔⠉⠀⠈⠙⠓⠲⠥⢬⡀⡇⡰⠲
⣾⢉⠱⠀⡄⢠⢠⢃⢠⡄⠆⠋⢰⠡⣸⠜⠋⣀⡀⣎⣴⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠁⠳⡅⣽⢡
⠸⡜⣇⠀⢳⠃⢃⡎⢁⠀⢠⡄⠛⡙⠁⠘⢉⢠⡖⠉⢀⡇⢰⠻⣦⣀⣀⣀⡀⢃⣠⠵⠒⠒⠒⠓⠢⡄⠈⢋⣮
⠀⢡⠙⢦⡈⠁⠘⠀⠁⢴⣾⡇⠰⢁⣤⡶⣿⣾⡘⠀⠀⣠⠊⢠⠄⠀⣀⣠⡜⢋⣠⠒⠁⣀⠀⠀⣸⢒⣀⡼⠛
⠀⠀⢹⢤⡀⠀⠀⢀⡠⠿⠷⠧⠶⠥⠞⣛⡛⠃⣾⣆⠀⠁⠀⠉⠀⡟⣏⣧⢁⡻⣮⢣⠀⠉⠀⠀⡏⢉⢀⠆
⠀⠀⠘⣧⠙⠄⠐⠐⣟⠉⢩⣭⠉⠉⢙⣛⡀⠀⣿⢸⡆⠀⡔⠀⡰⠋⢹⣬⠏⠱⣜⢮⣝⣓⣓⡀⠠⡂⡜
⠀⠀⠀⠘⣦⠁⠀⠀⠤⠆⠀⠴⠆⠀⠐⠒⠂⠀⢿⢸⡇⠀⢀⡼⠁⠀⢨⣭⠁⠀⠀⣛⡒⠫⣭⠇⢝⡲
⠀⠀⠀⠀⠹⣆⢐⠀⠩⠥⠀⠩⠭⠄⠀⠭⠄⠀⠬⢿⣇⡴⠯⠭⠀⠀⢘⣒⠀⠀⢀⣒⠀⢠⠄⢠⣱⠁
⠀⠀⠀⠀⠀⢹⡄⠂⠀⠩⠄⠀⠭⠥⠀⠩⠭⠀⠨⠭⠛⠀⠭⠭⠀⠀⢀⣀⠀⠀⠒⠃⠀⠝⢐⣪⡇
⠀⠀⠀⠀⠀⠀⢻⡌⠀⠀⠯⠀⠈⠭⠄⠈⠭⠀⠨⠭⠁⠀⠭⠭⠀⠀⠭⠀⠀⢀⣚⠀⣸⠃⢪⡿
⠀⠀⠀⠀⠀⠀⠈⢿⡔⡂⠈⣧⡀⠩⡭⠀⠭⠥⠈⠭⠅⠀⠭⠭⠀⠀⢭⠂⠀⠸⠁⢀⡞⢨⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⠄⠈⢥⠀⢈⡂⠐⣒⠀⢐⠀⠀⣉⣉⠀⢘⣛⠀⠀⡿⠀⣜⢁⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠈⠥⠀⣒⡀⢒⡂⢒⣂⠀⢐⣒⠀⠐⠃⠀⠨⠅⠠⠃⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠴⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢆⠀⠀⠀⠀⣠⢖⣦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⠋⣳⣧⣀⡴⠊⠁⢸⡅⢠⣿⢲⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢴⣫⣐⡈⠻⢤⣀⣀⠉⠀⠷⡏⣼⢠⣿⡤⣀⠽⠊⢉⡷⠶⣚⠉⠳⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⡒⠋⢁⡴⡺⠿⠵⢦⡾⠷⣤⣴⠁⡗⠯⣡⠞⣡⠴⣊⡥⠖⢋⠩⢤⣀⠙⢮⠄⡉⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠆⠍⢋⡥⠤⠶⢀⡄⡾⢙⠆⣻⠟⠋⢁⠞⣡⠞⠑⠋⠁⠀⠼⠁⠀⠀⠩⠉⠓⠒⢦⣸⢰⡋⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡡⡌⠀⣆⡐⡜⣤⠶⠚⠉⢠⣇⡴⢋⣡⠤⢀⡷⢾⡄⢀⡀⠀⠀⠀⠀⡀⠀⡀⢐⣀⣀⡀⠀⠻⣼⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠧⢿⡀⠹⠐⢸⠁⠆⢀⣶⠀⡐⠀⢀⣤⣲⢯⠀⠸⢁⡿⠙⠲⠶⠶⠤⣤⠖⢋⠍⠉⠉⠉⣵⢀⠨⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⠂⠀⠀⠀⢈⣿⣿⢀⣤⣺⣯⣿⡿⣦⡀⠠⠊⠀⠎⢠⣴⢶⠫⣤⡺⡅⠀⠆⠀⠀⡯⠖⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⢦⡀⡠⢾⡦⠤⢼⡥⠴⢶⣶⡂⠀⣿⢷⠀⠀⡀⠀⣼⠼⡼⣦⢦⣻⣜⠤⠤⠤⠘⢀⢂⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢀⠀⠘⣣⠀⢸⣧⠀⠐⡶⠆⠀⣿⢸⡆⠈⢀⡼⠁⠀⢻⡇⠀⠙⣿⣿⣛⣓⡦⡴⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠤⠀⢒⡀⠐⣛⡀⠀⠘⡀⠀⣹⣾⡇⣰⣿⡄⠀⠀⠿⠆⠀⠀⠭⠀⢈⠁⢐⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠄⠀⠦⠀⠘⢓⠀⢐⣒⠀⠐⠛⠟⢐⣒⠁⠀⠨⠭⠁⠀⢰⠃⠀⠿⠠⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡈⠀⠨⠤⠀⠶⠄⠀⠒⠀⠀⠤⠀⠀⠭⠅⠀⠭⠭⠀⠀⣒⠀⣼⠃⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡠⠀⢹⡄⠘⣟⡀⠸⠧⠀⡭⠀⠈⠩⠅⠀⢨⡃⠀⢸⠁⢀⡖⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡡⠀⠭⠄⠘⠇⠀⣓⠀⣿⠀⠈⣛⡁⠀⣻⡃⠀⡿⠀⣼⢡⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠩⠄⠩⠄⠐⠀⠠⠄⠀⠤⠤⠀⠉⠀⠀⠇⠐⠂⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⠶⠶⠤⠤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠒⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣗⣈⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⢫
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⡜⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢱⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣎
⠀⠀⠀⠀⠀⣇⡀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⢤⣀⡀⠀⢀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢰⡉⠀⠈⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢉⡆
⠀⠀⠀⠹⣏⣉⣉⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⠏
⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣦⠀⠀⡴⠢⡀⠀⡠⠲⡄⠀⢠⠖⢄⠀⢠⠔⢦⠀⠀⡴⢢⡀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⡟⠚⡇⠀⡟⠒⡇⠀⢸⠒⣻⠀⢸⠓⢻⠀⠀⠓⠚⡀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠠⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⢹⠀⠀⡧⢤⡇⠀⣧⠤⡇⠀⢸⠤⣾⠀⢸⡤⢼⠀⠀⡧⢴⠁⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⡇⠀⡇⠀⡇⠀⡇⠀⢸⠀⢺⠀⢸⠀⢸⠀⠀⠆⠀⡇⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣸⠀⠀⡟⠚⡇⠀⡟⠛⡇⠀⢸⠛⢻⠀⢸⠋⢻⠀⠀⡟⠛⡄⠀⢸
⠀⠀⠀⠀⠀⣇⠀⢠⠁⠨⠉⠉⡗⠒⡖⠊⡟⠉⡟⠑⢲⠒⢶⠒⢶⠶⢲⠒⠁⡇⢸⠀⠀⣇⣠⡇⠀⣧⣀⡇⠀⢸⣀⣼⠀⢸⣀⣸⠀⠀⣅⣠⠆⠀⣼
⠀⠀⠀⠀⠀⣸⠀⢰⠓⢚⠀⠀⡟⠚⡇⠀⣟⠒⡇⠀⢸⠒⢻⠀⢸⠓⢻⠀⠀⡗⢺⠀⠀⡇⠀⡇⠀⡇⠀⡇⠀⢸⠀⢸⠀⢸⠀⢸⠀⠀⡇⠈⠀⠀⡇
⠀⠀⠀⠀⠀⢹⠀⢀⡦⢼⠀⠀⡧⠤⡇⠀⣿⠤⡇⠀⢸⠤⣾⠀⢸⠤⢼⠀⠀⡧⢼⠀⠀⡗⠒⡇⠀⡷⠒⡇⠀⢸⠒⢿⠀⢸⠒⢺⠀⠀⠗⠺⡁⠀⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠳⠞⠀⠀⠓⠔⠁⠀⠙⠶⠃⠀⠘⠢⠋⠀⠈⠢⠚⠀⠀⠳⠞⠀⠀⠓⠖⠁⠀⠙⠖⠃⠀⠘⠶⠋⠀⠈⠢⠚⠀⠀⠳⠞⠀⢠⠇
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉

⠀⠀⠀⣾⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡶
⠀⠰⠿⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⡶⠲⠶⠶⠶⠶⠶⠶⠶⢾⢿⡿⠿⠂
⠀⠀⠀⠿⠆⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠠⣿⣿⡟⠛⠛⠛⠛⣻⣯⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠐⣿⠃⢿⠀⠀⣠⡿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣀⣨⣀⣀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡍⠻⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉
⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⣀⢸⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⢩⢨⡇⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣶⡘⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠈⣻⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⢈⡃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣶⣆⣶⣤⣤⣦⣹⣿⣿⣷⡿⠁⠀⠀⠀⣾⣷⣾⣾⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢘⢉⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⠟⣻⠛⠁
⠀⠁⠀⠀⠀⠘⣿⣿⣿⠃⠙⠀⡁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⢠⠛⡄⠄
⠀⠄⠀⠀⠀⠀⠛⠛⠛⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⣴⣾⣿⣙⡋⠀⠀⠉⠀⠀⢈⣋⣹⣷⣶⣾⣾⣍⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠘⠮⠄⣀⡙⢋⣽⣶⣦⣶⣿⣍⣛⢁⡠⠬⠥⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠛⠛⠛⠛⠿⠶⠶⠶⣦⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⣉⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣉⣉⡉⠛⠛⠛⠷⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣤⡶⠟⠛⣩⣴⠟⠿⣿⡟⠛⠩⣉⠉⠉⠛⠛⠻⠟⠛⢻⣧⣭⣭⣿⡿⣿⣿⡿⣷⣶⣶⣤⣤⣄⣩⣭⣟⢿⡄
⠀⠀⠀⠀⣼⠏⠀⢴⣿⣏⣀⣙⣂⡈⠻⣶⣶⣧⡶⠶⠾⠛⠛⠷⢶⣌⣿⡄⢰⠈⢢⣀⠹⡻⣿⣍⣽⣿⡛⠋⠉⢤⡙⢿⣇
⠀⠀⠀⠀⠹⣧⣀⣀⡀⠉⠉⠉⠛⠛⠻⠶⠿⣿⣶⣶⣔⣀⣒⣒⣈⣉⣻⣿⣼⠶⣦⣄⣤⡶⠿⠿⢭⡉⠙⢦⡀⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠈⠹⣿⠛⠛⠻⠶⠶⢶⣤⣤⣤⣀⣀⣀⠈⠉⠙⠛⠛⠿⠿⢿⣶⣦⣤⣽⡿⢿⡷⣦⡀⠉⠀⠀⠀⢀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⠶⠶⣦⣤⣤⣄⣀⣀⣀⣠⣼⣷⠘⣷⠀⠹⠄⠀⢸⡇⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⢻⡆⠀⢰⠦⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⣿⠀⢿⡄⠀⠀⡆⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣧⣨⡇⠀⢸⡀⡇⠀⢸⠉⣿⠀⢸⠛⡶⠀⣠⣤⡄⠀⠀⠀⢰⣿⡇⢸⡇⠀⠀⠃⠀⠀⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢰⡶⣦⠀⢨⣭⡁⠀⠘⠶⠿⠀⢸⣤⣇⠀⣿⠀⡇⠀⠀⠀⠸⢾⡇⣿⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣇⣹⠀⢸⡇⣿⠀⢸⡏⢻⠀⢰⠶⣤⠀⢙⡛⠃⠀⠀⠀⢀⣸⣧⢻⣿⠀⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣬⢭⡄⠈⣛⡛⠀⠸⠧⣾⠀⢸⡀⣿⠀⣿⠉⡇⠀⠀⠀⢸⣯⣿⢸⡏⠀⣧⠀⠀⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡀⡇⠀⡏⢹⠀⢰⡶⣦⠀⢀⣉⣉⠀⠻⠶⠇⠀⠀⠀⠘⢻⡇⣸⡇⠀⢸⡆⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⠓⠇⠀⢿⣼⠀⢸⣇⣻⠀⢸⡇⢹⠀⢰⠶⣦⠀⠀⠀⢰⡟⣿⣿⣄⣤⣬⣇⣠⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠷⠼⠂⢸⣀⡏⠀⠀⠀⠸⠷⢋⣼⠟⠋⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⢶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠶⣦⣤⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠬⠧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠏⠁⠀⠀⠉⠦⠒⠒⠢⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⠂⠋⠀⠀⠀⠀⢀⠔⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣥⣤⣤⣤⣤⣮⣭⣭⣤⣤⣤⣀⡀⣤⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣀⣀⣠⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣷⣾⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠬⠇





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠁⠀⠀⡇⠀⠈⠙⠳⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠀⠀⣀⣠⣤⠴⠞⠛⡟⠓⠦⣤⣀⠀⠈⠉⠛⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⣀⣠⣤⠶⠞⠛⠉⠉⠀⠀⠀⢰⡇⠀⠀⠀⠉⠛⠲⢤⣄⡀⠀⠈⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠛⠛⠉⠉⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣠⣴⠦⣤⣤⣄⣀⠈⠉⠛⠶⢤⣀⡀⠀⠉⠛⠶⣤⣀⡀
⠀⢀⣀⣤⠴⠚⠉⠁⠀⠀⣀⣀⣤⡴⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⣦⣿⡾⠋⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠈⠉⢛⡳⢦
⠀⢿⠓⢤⣀⣀⡤⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠤⢤⣄⣀⣬⠿⠶⠚⠉⢁⣼
⠀⢸⣆⡀⠈⠙⠲⢦⣄⡀⡠⠴⠖⢶⣤⡶⠟⠋⠙⢢⡀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⢶⣤⠒⠋⠁⠀⠀⣀⡤⠞⠋⣿
⠀⠀⣿⠉⠓⠲⢦⣄⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⣀⣀⣀⣤⣀⣀⣀⡀⠀⠀⠙⠶⣤⣄⣀⣠⠴⠖⠛⢿⡁⠀⠀⠀⢻⣀⣤⠴⠖⠋⠁⠀⠀⢠⡇
⠀⠀⢸⡆⠀⠀⠀⠈⢙⠶⣤⣀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠙⠯⣍⣉⣉⣉⠉⠉⠉⠙⠛⢷⣤⠤⠖⠋⠉⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣷⠀⠀⠀⠀⢸⣠⡇⠈⠛⠦⣄⡈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣦⠸⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢹⡆⠀⠀⠀⠈⣟⣇⠀⠀⠀⠀⠙⠲⣄⣀⠈⠉⠛⠷⣦⣄⡀⣀⡤⠖⠋⠉⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿⠀⣿⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⢮⣗⣦⣄⡀⠀⠀⠀⠉⣻⠶⢦⣄⡀⠉⣿⠁⣀⡤⠖⠚⠉⢉⡇⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⣿⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣤⡴⠋⠀⠀⠀⠉⠓⣿⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⠀⡄⠀⠀⠀⣿⠀⠀⠁⠀⢸⡇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⠃⣸⠁⠀⠀⠀⣿⠀⢀⣀⣀⣼⡇⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⣿⠾⠛⠋⠉⠉⠀⠀⠀⣀⣴⡟
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠃⠀⠁⠀⠀⢀⣀⡛⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉
⠀⠀⠀⠀⠀⠈⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣤⣤⡶⠶⠟⠛⠉⠀⢀⣠⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇⣠⡴⠞⠉⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⣿⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⠶⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⢣⡱⡞⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡙⠄⠀⡠⠔⠉⢉⣀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⢀⡀⠀⠀⠀⢀⡠⠊⠁⠀⣈⣆⣯⠀⣠⣶⠗⠉⠱⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠁⢠⢃⢾⠱⣀⠠⣚⢣⠀⢀⠴⠊⠀⠑⠤⡙⠓⠤⠤⠀⠠⠬⠆⠒⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡌⠰⢁⠎⠀⠳⡈⠢⣀⠡⠻⡁⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠒⠂⠉⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⢠⠁⠎⠀⠀⠀⠈⠲⢄⡐⠤⡘⣄⠀⠀⣀⠀⠀⠠⠠⢄⠀⠀⡠⠒⠢⢄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⠊⠀⣂⡸⠄⠒⠉⢃⠀⣀⡀⠬⠷⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈⠢⣀⠷⡀
⠀⠀⠀⣠⠄⠠⠤⢒⡡⢊⠥⠔⠊⠁⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠢⡀
⠀⠀⠀⠏⠀⠀⠈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⣘⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠃⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡘⠒⠄⣀⠂⣀⠠⠤⠐⠀⠲⠀⢂⠀⠀⠀⢀⡠⠤⠦⡄⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠤⢤⡀⡀⠀⢸⠀⡠⠤⠀⠀⠒⠂⠀⠀⠠⠄⣀
⠐⡤⠄⠤⠦⢼⠀⠀⠀⠀⠀⠆⠀⢨⡄⠄⠤⠼⠵⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡴⠡⠤⠠⠤⢯⠀⠒⢄⠀⠀⠀⠀⠀⠀⠈⠱⢲⣄⡀
⡠⠇⠀⠀⠠⡌⠀⠀⠀⠀⠀⠰⡀⡰⠀⠀⠀⠀⠀⠈⢆⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠎⠀⠀⠀⠀⠀⠀⢂⠀⠀⢣⠀⠀⠀⠀⠀⡰⣱⣗⣝⢝⢓
⠓⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠨⠀⠆⠀⠀⠀⠀⠀⠀⠀⠓⠢⣸⠀⠀⠀⠀⡔⢰⢏⢾⣢⢃⠊
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡌⢀⣀⠀⣀⣀⠀⣀⡀⢀⣈⣄⠀⠈⢢⠀⠀⠀⠀⠀⠀⣀⣤⣧⣀⢀⣀⡀⢀⣀⠀⣀⣀⠀⠉⠢⢄⡌⣰⢣⡿⣱⢃⠂
⠀⠀⠀⡶⠒⠀⠒⠀⢀⠀⠀⡐⠁⠀⠀⡇⡇⠅⢸⠀⣀⠸⠀⠈⢦⡀⠀⠱⣄⣠⠔⡖⣋⢠⠀⡳⢾⢸⡰⡇⡇⠀⡅⡇⠘⠀⠀⠀⠀⠉⢳⢿⣼⢣⠂
⠀⠀⠀⠐⣄⠀⠀⠀⠀⠑⣴⠁⠀⠀⠀⡅⡇⢹⢸⠀⣧⢰⠀⠀⠂⠐⠤⠆⣉⢘⡩⡇⠖⠸⠀⠽⢸⢸⠀⡇⡅⠀⡃⡇⢘⠀⠀⠀⠀⠀⠘⠀⠈⠁
⠀⠀⠀⠀⠈⡗⠂⠀⠒⠉⠀⣒⡁⢈⢒⠁⢑⣋⠀⣓⡋⢈⢒⠁⢙⣊⠀⣑⡋⢈⣓⡁⢘⣊⠀⣑⡋⠈⣒⡁⢉⣚⠀⣑⡊⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠈⠀⡇⡇⠈⢸⠁⢉⢸⠐⠆⡥⢬⠀⣇⡿⠀⠀⡇⠀⠈⠀⠃⢸⢸⠀⡇⠁⠀⠁⠃⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⢸⠀⠈⢸⠀⠀⠆⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⠀⡇⡄⠀⡀⡆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠂⡁⢈⠂⠁⠑⡊⠈⠁⡃⢈⠐⠁⢙⢘⠀⡃⡃⠈⡀⡁⢘⢈⠀⠑⠈⠈⡂⡁⢉⢈⠁⡑⡊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠁⠈⠀⠇⡇⠈⢸⠁⢐⠸⠀⠀⠁⠈⠀⠁⠈⠈⠀⡇⠀⢨⠀⡇⢸⢸⠀⡇⡇⠀⠁⡇⢈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⢸⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⢾⢸⠀⠇⡇⠀⠁⡇⢰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⣀⡃⢈⣐⠁⢑⣊⠈⣃⡀⢈⣐⠁⢙⣈⠀⣃⡋⢈⡂⡁⢘⣈⠀⣃⡈⠈⣐⠁⢙⣈⠁⣁⡊⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠁⠈⠀⠇⡇⠈⢸⠁⠀⢸⠀⠀⠅⠈⠀⠁⠀⠈⠀⡇⠂⠨⠀⠁⢸⠸⢆⡃⠏⠀⠀⡇⠸⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⡆⡇⠀⢸⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⢸⢸⠈⡇⠃⠀⡆⡇⢠⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠂⠃⠈⠒⠁⠑⠊⠈⠓⠂⠘⠒⠁⠑⠘⠀⠃⠊⠈⠂⠁⠑⠘⠀⠑⠊⠈⠒⠃⠑⠒⠁⠓⠊⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠁
⣿⣿⡿⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡴⠛⠉⠳⣄⠳⠟⠀⡤⢤⢰⡇⠀⠀⠘⡶⠦⡄⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠰⣇⣈⡇⣇⠀⠀⠀⡽⣠⠴⠚⢧⡼⠋⠳⣤⣤⠾⣅⣠⠏⠀⢿⣀⣸⢂⣀
⠀⠀⠀⠀⣰⠶⢶⣶⣶⡧⠤⣬⣥⣤⡾⣗⣒⣋⣁⣏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠋⣳⣀⣩⣥⣽⠼⢷⣶⣶⡶⠶⣆
⠀⠀⠀⠀⠙⠲⢦⣄⠉⠉⠛⠓⠶⠶⠿⣭⣭⣍⣉⣙⣶⣤⣞⣛⣛⣛⣛⣛⣉⣉⣩⣽⣭⠥⠶⠶⠚⠛⠉⠉⣠⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠞⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠳⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⢀⣽⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⣯⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡤⠤⣄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⡆⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠃⠀⠀⠈⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡤⠞⠀⠀⠀⡏⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡖⢲⡀⡇⠀⡇⠀⣀⡀⠸⣥⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠒⢦⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣀⣸⣇⣠⣇⣇⣀⣇⢸⠁⢸⠀⠀⢰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢳⠀⢀⡖⠛⢲⣤⠤⣄⠀⠀⢠⠏⠉⢹⡄
⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠶⠤⠬⣯⣅⣀⣀⣀⣀⣀⣀⣀⣀⣧⣠⣤⣤⠤⠤⠾⠶⠾⢦⣀⡼⠁⠀⠈⡿⠉⠉⠳⠤⠾⡄
⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠴⠃⣀⡀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠉⢳⠲⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⢼⣉⣹⢲⠏⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣇⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⡼⠙⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠁⢹⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣉⣉⣁⡀⠀⠉⠉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣷⣛⣋⣉⣉⣉⣿⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠉⢉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠤⣄⠀⠀⣠⠤⣄⠀⠀⣠⠤⣄⠀⠀⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡇⠀⣿⠀⠀⡇⠀⢹⠀⠀⡏⠀⢹⠀⠀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣇⠀⣿⠀⠀⣇⠀⣼⠀⠀⣇⠀⣸⠀⠀⣇⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢛⣁⠀⠀⠙⢛⣃⠀⠀⠙⣛⡋⠀⠀⢙⣛⠛⢧⠞⣛⡓⢦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣾⠉⣷⠀⢰⡏⠹⡇⠀⣼⠉⢹⠀⠀⡏⠉⣧⠀⢰⠋⢹⡆⢻⡀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⢸⠀⠀⡇⠀⣿⠀⢸⡀⢸⡇⠘⡇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠶⠋⠀⠈⠳⠞⠁⠀⠘⠲⠛⠀⠀⠛⠾⠃⠀⠈⠳⠞⠁⠀⡇⠀⠀⢰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡴⠲⣆⠀⣰⠚⣦⠀⢠⡖⢶⡀⢀⡶⢳⡄⠀⣴⠒⣆⠀⣰⣿⠀⠀⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⠘⢶⠴⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠴⠃⠀⠹⠦⠟⠀⠘⠧⠞⠁⠈⠳⠼⠃⠀⠻⠴⠏⠀⠘⠦⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠷⠼⠃⠈⠧⠼⠃⠈⠧⠼⠁⠈⠧⠼⠁⠘⠧⠾⠁⠘⠧⠾⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣤⡄⠀⣠⣤⡀⠀⣠⣤⠀⢀⣤⣄⠀⢀⣤⣄⠀⢠⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⣿⠀⣿⠀⡇⠀⡇⢸⡇⢸⡇⢸⠀⢸⠀⣿⠀⣿⠀⡷⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠹⣤⠟⠀⠻⡴⠇⠀⠷⡼⠃⠘⢧⡾⠀⠸⢦⠟⠀⠻⣤⠏⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



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

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⢩⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⠋⢉⣀⡤⠴⠖⠋⣻⠙⠲⢤⣀⠉⠛⠲⢤⣄⡀
⠀⠀⠀⠀⢀⣠⠤⠴⠒⠚⠉⢁⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⢀⡇⣠⣤⣄⣈⡉⠓⠢⢤⣀⠉⠓⠦⣄⡀
⠀⣤⠒⠊⢁⣀⡤⠤⠖⠚⠉⠉⠀⠀⠀⠀⢀⣠⠴⠒⠚⠓⢺⠟⠁⠀⠀⠀⠙⢦⣀⣀⡈⠙⠢⣄⣈⡩⠗
⠀⣇⡉⠚⠯⣄⣀⠤⠴⣤⡴⠖⠲⣄⣠⠖⠋⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣀⣠⢬⡭⠟⠋⠉⣀⠤⢺
⠀⢹⡈⠉⠲⢤⡙⠲⢤⣄⡀⠀⠀⠈⠣⣤⠤⠤⠤⠤⠤⣤⣈⠑⣲⠤⠖⠊⠙⡇⠀⠀⢷⠔⠚⠉⠀⠀⢸
⠀⠈⣇⠀⠀⢰⣿⠑⠢⢌⡙⠶⣤⣀⡀⠈⠉⠉⠁⠀⣀⢴⡛⠉⠀⠀⠀⠀⠀⢱⠀⢠⢸⠀⠀⠀⠀⠀⡟
⠀⠀⢹⠀⠀⠀⢿⣄⡀⠀⠉⠲⢤⣈⡙⠳⢦⡤⠒⢉⣠⠴⡇⠀⠀⠀⡀⠀⠀⢸⠀⣸⢸⡆⠀⠀⠀⢠⡇
⠀⠀⠸⡆⠀⠀⠀⠙⠛⠷⣤⣀⡴⠁⠉⠓⠲⡗⠋⠁⠀⢰⡇⠀⠀⡸⢀⠀⠀⢸⠀⠋⠀⡇⠀⠀⠀⡼
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⠇⡌⠀⠀⢸⣀⡤⠴⠇⠀⠀⢠⠇
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣾⠀⠀⠘⠀⠀⠀⢀⡼⠁⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⣠⠴⠒⠒⠋⢉⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠋⠁⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⡇⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠧⠖⠚⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⢠⠄⠀⢤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠄⢀⠄⠁⠀⠀⠀⠀⢀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠄⠃⠀⠠⠀⢀⠀⠀⠀⠀⠀⠐⡰⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡎⠀⠀⠀⠀⠀⠀⠀⡄⣄⠘⠀⠀⠉⠁⠠⠀⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣸⠀⠀⢰⠳⡈⠢⣤⠀⠒⠊⠁⢗⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⢁⡉⠠⠉⠁⡙⠀⠇⠀⠀⠀⠀⠀⠀⠀⢿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠏⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⢸⡄⡸⠀⠀⡠⠂⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⡰⡇⠀⠀⠊⠀⠀⠀⢀⡤⠆⠀⡄⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⣀⠀⠀⠀⠀⠁⡀⢀⠄⠀⠀⠀⢀⠔⠁⠃⠀⠂⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⠀⠊⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠈⠀⣀⡀⠄⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠰
⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠙⠉⠁⠙⡖⠲⢇⣠⠀⠀⠀⠀⠀⠄⠀⠀⣇⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡎⠸⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠳⠶⠀⠤⣔⠉⠀⠀⠀⠀⠀⢀⡷⠀⠈⠳⣀⣀⣠⣤⣀⣤⣄⣼⣦⠴⠶⠃⠿⢸⢒⡤⢄⡀
⠀⠀⠀⡁⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⡠⠀⣀⠠⣀⣸⠁⠀⠀⠰⠃⠤⠾⢸⡒⢦⡀⠘⠉⠝⢀⢁⠀⡀⢀⡏⠐⠴⠒⢞⢦⠄⣀⠑⢪⡑⡄
⠀⠀⠀⢱⢄⡀⠀⠀⠈⠁⠒⠶⠤⣈⣤⡀⠁⠀⠄⠈⢆⠈⠐⠒⢈⡠⡔⠒⠃⠀⢱⠘⢢⢀⠅⢉⡩⠋⠨⠂⢀⣘⡱⠦⠄⠒⠈⠉⠁⠀⡇
⠀⠀⠀⠈⡄⠈⠑⠂⠤⢀⡀⠀⠀⠀⠀⠉⠉⠑⠒⠂⠈⠇⠰⠾⠯⠤⠄⠤⠤⠤⠷⠶⠾⠗⠐⠚⠒⠈⠉⠁⠀⠀⠀⠀⠀⣀⡠⠤⠒⡋
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠐⠒⠒⠉⠁⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠑⣆⢇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠄⣲⠎⠛⢢⠀⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠄⠤⠘⠀⡸⠀⣔⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠋⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠤⠤⠄⠚

⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠀⠀⢀⢄
⢠⣄⡰⠂⣈⡥⠂⠀⠶⣟⣀⢄⡾⠛⣁⣀⣤⡀
⡀⠀⠀⡩⠟⠿⠿⠷⠶⠾⠷⠾⠟⠋⠉⠙⣋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠏
⠈⠉⠐⠠⠤⢄⢀⣀⡀⠀⠀⠀⣀⡀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠠⠤⠀⠠⣠⠤⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢿⡏⠀⠀⠀⡠⠔⠶⠁⠐⠐⠈⠀⠀⠒⠻⣷⣬⡁⢀⣀⡉⢈⣺⡷⢂⢤⡀
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢿⢢⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠘⠂⠌⠉⠄⠄⠀⠀⠀⠈⠙⡎⠡⠆
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡋⠀⠀⠀⠀⠀⠲⠆⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣐⡀⣬⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣽⡆⠀⠀⠀⠀⠀⢙⡂⠲⠤⠀⠀⠀⠀⢈⣉⣉⢨⣭⠍⠬⠤⠄⣒⣚
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⡇⠀⠀⠀⠀⠀⠀⠭⢘⡒⠀⠀⠀⠀⠠⠥⠤⠐⢒⡂⣒⣛⢉⣭⠥
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣯⡅⠀⠀⠀⠀⠀⠀⢑⡠⢭⠀⠀⠀⠀⢘⣛⣃⢨⠭⠄⠤⠶⠐⣒⡂
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠰⠶⠆⠐⠒⠀⠛⠁⠈⠉
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣭⣿⣯
⠀⠀⠈⠀⠠⠀⠒⠀⢤⠴⠶⢾⣟⠹⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠠⠜⠉⢆⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠚⠒⠈⡐⡆⢄⡀⠀⡐⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⡤⠔⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡠⠔⢀⡀⠀⠀⠛⢶⢇⠀⠀⠀⠀⠈⠄⠀⠈⠂⠔⠉⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣀⡠⠤⠤⠤⠇⠚⠁⠀⢠⡞⠉⠉⠁⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⣄⡐⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠩⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⡰⢨⠀⠀⠀⠀⠀⠀⢠⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠚⠋⠴⠒⠲⠦⠤⣄⣀⣀⣐⣹⠄⣀⠀⠀⠀⡀⠎⠂⠉⡄⠀⠀⠀⠀⠀⣬⣹⣀⣀⡀⠤⠤⠤⠀⠒⠂⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈⠉⠙⠛⠋⠋⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⢑⠒⠢⠤⠤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠒⠈⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠬⠀⠀⡃⠀⠆⠀⢸⠈⠉⠉⠉⠷⢒⡒⠀⠀⣀⠐⠪⡏⠀⢘⠁⠈⠇⠀⢰⠊⠀⠀⠀⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠈⠉⠁⠀⠘⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⠑⠤⠆⠀⠘⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⠀⠀⣏⣰⡆⠀⢠⠤⠤⠀⠀⣀⣀⣀⠀⠀⣀⣀⢀⡀⠀⢠⠤⠀⡄⠀⢰⣉⠽⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠸⠀⠀⠇⠈⠗⠀⢨⠀⠀⠀⠀⡀⠀⠘⠀⠀⡁⠀⠀⠀⠀⢀⠀⠀⠁⠀⢰⠀⠘⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢⠀⠀⠃⠀⠈⠀⠀⠁⠁⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢠⠤⢤⠀⠀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⢠⠤⠤⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⡁⠀⢸⠀⠘⠀⠀⠗⠀⢠⠀⠀⡅⠤⠤⡄⠀⠸⠒⠒⠃⠀⢠⠤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠉⠃⠀⠈⠀⠀⠀⠀⠃⠀⠠⠀⠀⠇⠀⠠⠆⠀⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠂⠀⢠⠤⣄⠀⠀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⢠⠤⠤⠄⠀⢰⠈⢹⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⡇⠀⢨⠀⠈⠀⠀⡁⠀⠈⠀⠀⠗⠀⠠⡄⠀⠘⠀⠀⠀⠀⢸⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠐⠃⠀⠈⠀⠀⠀⠀⠓⠠⠨⠀⠀⢤⡤⡤⠄⠀⠘⠀⠀⠁⠀⠈⠉⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢰⡒⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡝⠆⠀⠸⠀⠘⠀⠀⠆⠀⢴⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠃⠀⢨⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠴⠀⠀⢤⣀⣰⠀⠀⡍⠀⠰⠇⠀⠰⠤⠤⠃⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠠⣄⠀⠀⠀⢀⡀⢀⠀⠀⣀⣀⣀⡀⠀⠀⠤⠤⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠈⠉⠀⠀⠈⠀⣻⠀⠀⡏⠀⠈⡁⠀⠠⠄⠀⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡆⣾⣿⣴⣿⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⣿⣦⣿⣷⢸⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡹⠟⣼⣫⠟⠁⠀⠀⠈⠻⣿⣯⣽⣿⠟⠀⠀⠀⠈⢿⣝⣧⠻⢏⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢀⣠⣤⣤⣤⣭⣭⣤⣤⣤⣄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣄⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣾⣿⣿⠗⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠸⣿⣿⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣦⣌⣛⠿⢿⣿⣿⡿⠿⣛⣡⣴⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣚⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠒⠉⠙⠛⠿⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠰⡀⠀⠀⠁⠈⠁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣄⣠⣶⣶⣷⣶⣶⣦⡀⠀⠀⠙⠒⠀⠂⠁⠤⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⡿⠃⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠋⠀⠀⢿⠆⣤⢸⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣰⣿⣤⡄⠀⠀⠀⠀⠘⣿⣿⣷⣶⡀
⢠⡶⠂⠀⠀⠀⠀⠀⠻⠃⡠⠀⢀⢀⣤⣤⣀⠀⢠⣿⣿⣵⣶⣾⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣣⠀⠀⠀⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠉⠉⢰⣶⣶⣴⣶⣤⠀⣉⠋⠀⠀⠀⠀⠀⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⢿⣿⣿⣿⡦⡤⢤⣀⡀⠀⠀⠀⢀⣸⣿⣶⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠒⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠏⠉⠉⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠻⣿⣿⣇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣸⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁

⠀⠀⢀⣠⣄⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⠻⢿⣿⣿⠿⠛⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡋⠙⣿⡏⠀⠀⠹⡏⠀⠀⠈⢿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠃⠀⠀⠈⣿⠁⠀⠈⣿⠋⠉⣿⣿⣿⣿⣿
⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣤⣤⣤⣾⣧⣤⣤⣤⣿⣧⣤⣤⣤⣿⣦⣤⣤⣴⣿⣶⣶⣶⣿⣿⣿⣿⡿⡟⠋⠁
⠀⠀⠀⠀⠈⠉⢿⠁⠈⠹⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⡟⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠘⣆⠀⣰⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣇⠀⣠⠇
⠀⠀⠀⠀⠀⠀⣤⣿⡿⠻⣿⡿⠉⠉⢻⡏⣿⡇⢹⣿⠀⠀⠘⣿⡇⠀⠀⢸⡟⢹⣿⠉⣿⠋⠉⢻⣿⠿⢿⣿⣤⠆
⠀⠀⠀⠀⠀⠀⠋⢹⡇⠀⠸⣿⠀⠀⢸⡇⢸⡇⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⡇⢸⣿⢠⡿⠀⠀⣼⡇⠀⢸⣏⡹
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣶⣿⣧⣀⢈⣿⣾⣷⣤⣿⣀⠀⣸⣿⣇⠀⢀⣸⣧⣼⣿⣼⡇⣀⣴⣿⣷⣴⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⣿⣿⡛⢻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠛⣿⣿⠁⠀⡝
⠀⠀⠀⠀⠀⠀⠀⢠⣈⣷⡾⣿⣿⠛⠻⣿⠻⣿⠏⣿⠁⠀⠈⣿⠃⠀⠀⣿⠟⣿⡟⢻⡿⠛⢻⣿⠷⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⠀⢻⠀⠀⢿⠀⣿⡄⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀⣿⠀⢸⠇⠀⠸⠁⠀⢹⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠀⠀⢸⠀⠀⢸⡄⣿⡇⣸⡇⠀⠀⣿⡀⠀⠀⣿⠀⣿⠀⣼⠀⠀⡄⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠖⣾⣧⣀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣄⣴⡿⠒⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣒⣒⣦⣤⣀⣠⡤⢄⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠑⠒⠮⠥⣌⢻⡗⢦⢡⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⠀⠀⠀⢰⣖⡒⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠡⠇⡸⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⡢⢄⡀⠀⠀⡀⢴⡩⢉⢹⢎⠢⡀⠀⠀⠈⠢⣀⠀⠀⠀⢀⡰⠂⠈⣩⡶⠾⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡙⠒⠤⣄⡧⠞⠋⠀⠑⢌⡑⠸⠤⠤⠜⠁⢸⡉⢁⣀⣴⠞⡡⢊⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠈⠑⠒⠤⣈⠑⠢⣠⠀⠀⠈⢑⡶⠀⠐⠀⢠⣌⣙⠛⣓⣫⠴⢃⡀
⠀⠀⠀⠀⠀⠐⠤⣀⣤⣤⢴⣴⡒⣢⣀⣠⣄⣎⣩⣉⣳⣄⣈⣒⣂⡰⢙⣱⣋⣣⣳⣿⣏⣀⣉⣄⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠭⠵⣆⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠽⠈⠉⠀⠀⣠⠐⠀⠀⠀⢀⢴⣙⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣠⡺⠋⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠙⢴⡀⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⡠⠖⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠈⠃⠀⠀⠀⠃⢀⣙⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠁⠀⡨⠇⡠⠠⠔⠐⠲⠤⣄⠘⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣀⡀⠉⠋⠁⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣤⣀⣀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠼⠋⠀⠀⠀⠈⠷⢀⡀⠀⠀⠀⠀⠀⠈⠉⠓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢠⠞⡕⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⡆⠀⠉⠉⣱⠟⠂⠀⠀⠀⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢢⠑⠀⠀⠀⠀⢰⠏⠀⠣⣀⠀⠀⠻⠲⣀⠀⠀⠀⠀⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢠⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠜⠀⡀⢀⠀⠀⡏⠀⢠⠄⠬⡙⠒⠒⠈⠋⠁⢀⣀⣜⠀⠀⠀⠀⣯⠀⣀⡀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⡩⠭⣉⠙⡦⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡠⠖⠢⣀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⣈⠉⢈⣉⡼⠁
⠀⢀⠠⠤⠀⠀⠠⠠⠀⠀⠀⡀⣠⣲⠉⠙⣏⠉⠑⠔⠒⠒⠉⠙⠒⠀⠤⠤⠀⠀⠠⠤⠤⠴⠒⢾⠭⡀⢏⣉⢉⠉⠁⢸⠂⠁⠈⠒⠀⠀⠀⠀⠀⠀⣀⡀
⠰⡁⢰⣖⠆⠐⠀⠀⠑⠢⠠⡙⢁⡠⢤⣠⠬⡄⠢⣠⠔⠲⠄⠀⡄⠀⠒⠀⠀⠰⠖⠆⠀⢂⠙⡋⠙⢆⣠⠷⠈⠙⠒⠙⠲⠀⠀⠀⠀⠀⠀⠠⠄⢤⣲⠝
⠀⠙⢦⣍⣙⡒⠀⠤⠀⣀⣀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠉⣠
⠀⠀⠀⢻⡈⠉⠙⠒⠒⠀⠤⠄⢈⣉⡀⠐⠒⠂⠀⠤⠤⠤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠠⠤⠄⠐⠒⠀⢁⣀⡤⠤⠖⠒⣽⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠀⠤⠤⢤⣬⣉⣉⣉⣉⣉⠛⣉⣉⣉⣉⣉⠀⠠⠄⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⣤⠘⠙⠁⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⠋⠷⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣇⡔⠂⢀⢀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⢦⣘⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⠈⠉⠛⠀⠲⠶⠀⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⠴⠶⠒⠚⡇⠀⣨
⠀⠀⠀⠀⠀⠀⢠⠖⠊⠁⠀⠛⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠃⠀⠙⠒⢦⡀
⠀⠀⠀⠀⠴⢶⣿⣶⣧⣀⣀⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣀⣠⣷⣶⣷⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣠⠖⠉⠉⠀⠉⠙⠲⡄
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠻⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠼⠆
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢤⣀⣠⣀⠀⠀⠀⠀⢀⣠⡤⣄⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠀⠀⠀⣀⡀⠀⢀⡈⠛⠋⠛⠶⠋⠀⠀⠀⠉⢦⣤⣄⡀⣀⣀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠖⠒⠲⠤⠖⣒⠃⠀⠀⣴⡄⢀⡀⠙⠁⠀⠘⠋⠀⠀⠰⣶⠀⠀⠠⣶⠄⠀⠀⠀⠛⠁⠀⠈⠙⢦
⠀⠀⠀⢸⠀⠀⣀⡤⠞⠀⢰⡦⠀⠀⢈⡛⠀⠀⠀⠈⠀⠘⠋⠀⠀⣠⣄⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠘⠟⠀⠀⢀⣀⠀⠀⠚⠓⠒⢦⡀
⠀⠀⠀⢸⠀⡼⠁⠀⠀⠀⠀⠀⣀⠀⠙⠋⢀⠀⠐⠿⠀⡀⠐⠿⠂⠈⠁⣠⡀⠈⠛⢀⣀⠈⠛⠁⣀⡀⠀⢶⠆⠈⠉⢀⣄⠐⠿⠂⠀⢽⣤⣀⡀
⠀⠀⠀⣸⣀⣇⣀⣀⣀⣀⣀⣀⣛⣁⣀⣀⣛⣃⣀⣀⣘⣟⣀⣀⣀⣀⣀⣉⣁⣀⣀⣈⣋⣀⣀⣀⣙⣃⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣙⣆⣀
⠀⢰⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡆
⠀⠈⠳⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠞⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠛⠙⢻⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠋⡿⠛⠛⢏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⣶⠒⠒⣶⠶⡶⠶⡶⠶⡶⠶⡶⠶⠶⡶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⢶⡶⣶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣆⡀
⠀⠀⠀⢀⡶⣄⡀⠀⣀⣴⣾⣿⡿⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠿⣿⣿⣦⣄⠀⠀⣀⡴⡆
⠀⠀⢙⣺⣷⣿⢿⣿⣿⣟⣉⣁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣉⣙⣿⣿⣿⢿⣷⣷⡊
⠀⠀⠀⠀⠈⠁⢾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠆⠉
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⣿⣿⣿⣿⣟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⠀⠀⠀⠀⠻⠿⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠚⠛⠛⢀⠀⠘⠛⠛⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠲⠶⠖⠈⡇⠀⠳⠶⠃⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠓⠒⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣥⣀⣀⣀⣬⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⢷⡀⠀⠀⠈⠓⠦⣖⣒⠒⠶⣤⠶⠋⠀⠀⢀⡴⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⣀⠀⠙⠳⢤⣀⣠⡶⠤⠭⠇⠀⠀⠀⢀⣠⡴⠋⠀⠀⢀⣀⡈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣈⡉⠓⠲⠶⠶⠶⠒⢛⣉⣥⠴⠖⠚⠋⠉⠉⠉⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠓⠶⠶⠒⠒⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⠀⠀⢀⢀⣀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠂⠒⠠⠤⣄⠒⠂⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠉⠀⠀⠀⠀⡠⠒⠒⠒⠠⠁⠂⢤⣀⠤⠀⠌⠉⠗⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠠⠠⠤⠤⠀⠤⠶⡩⢍⡉⠉⠁⠀⠐⠒⡩⠐⠒⠒⠲⠤⠦⠤⠬⣇
⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⢠⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠒⠒⠀⠀⠀⠀⠂⠚⠃⠀⠀⠐⠺⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡧⠤⣤⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠁⠉⠁⠉⠙⠉⠉⠉⠋⠈⠉⠉⠛⠉⠉⠉⠉⠈⠓⢄⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⢤⡤⠤⠤⡤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠊⠉⠙⠉⠉⠙⠉⠙⠁⠁⠛⠈⠉⠉⠙⠋⠉⠛⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⣄⠄⠠⠀⠤⠤⠠⣠⠤⠤⠤⠀⠤⠤⠠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠉⠉⠛⠉⠉⠉⠋⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⡤⠤⢤⡤⠤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠥⠤⠤⠼⠫⠤⠤⠤⠤⠤⠤⠤⠯⠯⠤⠤⠼⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠀⠠⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠛⠉⠁⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣤⣴⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠠⠤⠀⠀⠂⠀⠀⠀⠀⠤⠤⠤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⡀⠀⠀⠀⢸⢕⡇⠀⢯⡽⠀⢮⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠈⠀⠁⠀⠀⠀⠐⠂⠒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⠳⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠁⠀⠈⠛⠆⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⣰⠁⠀⠀⠀⠀⠀⡑⡈⢇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⡤⠠⠄⢘⣃⠀⢀⡴⣟⠩⠥⡀⢁⣐⠚⢠⡀⠀⡠⠤⠊⠀⣣⠀⠀⣾
⠀⠀⠀⠀⠂⣈⣉⠑⠲⢿⣯⣋⠩⠽⣩⡃⠐⡂⢬⣰⣊⠸⣥⢉⣘⣷⠷⠶⡶⠧⣇⣴⣾⢶⢰⢰⡄
⠀⠀⠀⠀⢊⣀⣀⣀⣀⡀⠀⠀⠄⣸⠿⠷⠀⠶⠶⠀⢿⡇⠈⠃⣤⣷⠴⠖⠴⠻⠆⠶⠶⠿⠘⠚⡇
⠀⠀⠀⠀⠀⣸⠌⢛⠛⢛⠙⠛⣚⠛⢘⣛⠃⢛⠚⠀⢛⣳⡄⢸⣅⣩⡛⣧⡽⠟⠋⠉⠉⠉⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠉⡛⡈⣓⣃⢙⢛⢈⡁⣁⢈⣉⡁⣉⣉⠁⡞⠀⢈⣉⣁⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠭⠥⠭⠭⠬⣭⠭⠭⠭⠬⠭⠤⠭⠥⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⠛⠃⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠊⠁⠀⠑⠤⠒⠢⣄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠒⠋⠀⠀⣀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⠚⠒⠒⠒⠚⠒⠒⠒⠒⠒⠤⠴⢄⠀⢀⠤⠤⠴⢄⣀⡠⠤⠔⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢀⠞⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠙⢆⠘⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿