Beauty salon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢾⣻⣿⣿⣟⣻⡶⣦⢯⣙⠳⡄⠘⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⢉⡵⠞⣛⡛⠚⠥⣭⡺⣝⣿⣿⣿⡇⢸⣾⢿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⣢⢞⣵⣷⣿⣿⣿⣛⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢰⣰⣯⣾⣟⣯⣥⣶⣶⣿⣟⡓⠈⡛⠋⠉⠀⠀⠙⠉⠙⢿⣿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⣤⣼⡿⢟⣩⣾⡿⢓⣉⣤⣬⣿⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠘⠙⣋⣴⠿⣫⠵⠾⠛⣛⣻⣿⡗⠀⠠⠔⠒⠶⢦⣤⠀⠀⢀⡤⢿⣧⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⢛⣩⡶⠛⠁⣀⣠⣶⣿⢿⣿⠁⠀⢀⣤⣴⣶⣦⠀⠀⢠⣏⣶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⡴⠁⡄⠀⠀⢀⡟⢩⣾⣿⣿⠿⠯⣭⣭⡽⠛⢿⣟⣣⡀⠀⠀⠉⠛⠛⠀⠀⠀⠸⡟⢿⠛⠁⢹
⠀⠀⠀⠀⠀⢰⠃⠀⠱⢤⡤⠎⠁⢈⣯⣵⣶⣶⣶⣿⡿⣿⡀⢵⡙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⢘⡇
⠀⠀⠀⠀⠀⠘⠀⢀⣠⣤⠶⠤⣅⠟⣽⢛⣿⡿⠯⠵⠊⣽⣿⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⡅⣸⠁
⠀⠀⠀⠀⢀⡴⣳⢛⡥⠖⢛⣫⢟⡔⠡⢋⣡⣴⣶⣶⣾⣋⣾⠸⣅⡟⠢⣀⠀⠀⠀⠀⠀⠉⢉⡹⣱⠃
⠀⠀⠀⠀⡾⠀⣿⠏⣠⣾⠟⢱⡋⣿⢰⢯⠿⣛⣛⣻⣭⣾⣿⡄⠈⠀⠀⠈⢳⣦⣄⣀⡀⠀⠀⢠⠏
⠀⠀⠀⠀⠹⢤⣟⣴⣱⢯⢸⠘⣧⣹⡏⡴⠟⠋⠉⠉⣠⣟⣿⡇⠀⠀⢰⡀⠀⢻⣿⠋⠉⠉⠉⠁
⠀⠀⠀⡇⠀⢸⣿⡿⣿⢸⡜⢧⣲⣶⣿⣿⣿⣿⣿⣿⣿⢟⣽⠇⠀⠀⠀⢧⡀⢸⡇
⠀⠀⠀⣇⠀⠨⣯⣷⣹⣯⡛⠾⠿⠿⠿⠿⠿⠿⣿⡿⠖⠋⠈⠀⠀⠀⠀⠈⠳⣼⡇
⠀⠀⠀⠘⢦⡀⠠⢉⣉⣉⣛⠿⠬⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠉⠙⠛⠓⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠻⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⠶⣤⣌⠻⡆⠀⣀⣀⣀⠀⠀⢀⣤⠶⢚⣋⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠤⢈⣥⣾⢿⡿⢋⣵⣾⣶⣿⣵⣾⣿⣿⣿⣿⣿⣦⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⣀⣤⣤⣤⡄⢿⣿⡇⣿⠀⣾⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⣼⣿⣿⣿⣿⣿⣌⠻⣿⣹⡄⢻⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⣼⣿⣿⣿⣷⣝⢿⣿⣷⣌⡻⢿⣶⣍⣻⣿⣿⣿⣷⣽⣿⣻⣽⣿⣿⢏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡃⢠⣿⣿⣿⣿⡿⣿⣷⣝⡿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣟⣛⣩⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢇⡇⠘⣿⣿⣿⡻⣿⣮⣻⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣇⠀⢿⣿⣿⣿⣮⣻⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠸⣿⡄⠈⣿⣿⣎⠀⠄⠹⠋⠀⠀⡀⠈⠉⠉⠙⠻⣶⣄⡀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⡄⣿⣷⠀⠘⣿⣿⡄⠀⠀⠀⠀⢲⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠠⠚⢓⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣧⢹⣿⡇⠠⡘⣿⣷⣀⠀⠀⠀⠀⠈⢻⢦⣭⣝⠛⠀⠀⢠⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⢰⣧⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡾⣿⣿⡇⣼⣿⢸⡿⣿⡏⢳⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣟⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣌⢻⣿⠟⠛⠛⢿⣿⣾⡇⣿⡇⠀⠙⢷⣄⠀⠀⠀⡙⠟⠒⢀⣤⣟⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣾⡏⣾⣿⣾⢀⡏⣰⣿⣿⡄⣿⣿⢳⣿⣿⠀⠀⠀⠙⢷⣤⡀⢈⣡⣶⣿⣿⣿⡿⢛⣉⣁⡀
⠀⠀⠀⠀⠀⢸⣿⣧⡙⠿⢋⡼⢠⣿⣿⣿⢁⣿⣟⣾⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣶⣿⣿⡿⣃⣾⣿⣿⣿⠋⠀⠻⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣮⣿⣽⠟⣼⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠝⠛⠋⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⢠⣴⡤⣤⡦⣠⣤⢠⣤⣤⣤⣤⣦⡤⠀⢠⣤⢠⣤⡦⣴⣤⠀⣤⣴⢄⣴⡀⡦⣴⣦⠀⢠⣦⠄⣤⡄⣤⠀⣴⣦⣤⣤⡄
⠀⠀⠸⠿⠗⠿⠷⠿⠿⠸⠿⠃⠿⠀⠸⠇⠀⠿⠿⠼⠻⠇⠿⠟⠀⠿⠿⠾⠿⠷⠷⠿⠿⠀⠸⠿⠻⠿⠷⠿⠟⠿⠿⠻⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡄⠀⠀⢴⣦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡄⠀⢀⣿⣿⣷⠀⣀⠈⣿⣇⠀⢹⡇⠀⣰⣿⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡹⣿⣿⡄⠸⣿⣿⣿⣆⣿⠀⠘⣿⣆⠈⡇⠀⠙⢿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠷⠿⠏⠉⠀⢻⣿⣿⣿⡿⠀⠀⠉⠻⡄⠀⣸⠃⠀⠉⠻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠋⠁⢀⣶⣦⠀⣰⠒⠒⠄⡀⠈⠻⣿⣿⡇⠐⠄⠀⠀⠹⡀⠋⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣿⡿⠃⠀⠈⢁⣁⡬⠅⠀⠀⠛⡋⠁⠀⢀⡈⠀⠀⠱⠀⢰⠀⠀⢤⣿⣿⡿⠉⠉⣁⣴⡾⠟
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣼⣿⠟⢀⣤⣶⠞⠋⠁⢀⣠⠀⣰⣟⣻⣧⠀⠀⠹⣦⠀⠀⠁⣸⠀⢰⣿⣿⡿⠁⠀⣈⣥⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣾⡿⠋⠀⠀⠙⠁⣀⣤⡶⠟⠉⠁⠘⢿⣭⢽⣷⡀⠀⠹⠷⠀⠀⣿⠀⣿⣿⠟⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⡟⠀⢀⡾⠁⠀⠀⠀⢠⣴⣾⡿⠁⠀⠀⠀⠀⠀⠈⣿⣷⣿⣇⠀⠀⠀⠀⠀⣿⠐⠟⠁⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢠⠋⠁⣠⠟⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣠⣿⣧⡀⠀⠀⠛⠿⣇⠀⠀⠀⢀⢺⣿⠀⠀⠀⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏
⠀⠀⢀⠂⢃⡰⢇⠀⠀⣴⡗⠀⢀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⢻⣆⠀⠀⠀⣾⣿⡄⠀⠀⣷⠀⠶⠦⠤⠉⠛⠻⠟⠛⠉⣀
⠀⠀⠈⠀⠉⢦⠄⠀⣼⡟⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⣩⡉⠁⠀⣶⣿⣧⠀⠹⣦⠀⠴⣿⣿⣿⡖⠀⠿⠀⠀⠀⣠⠀⣠⡀⠀⢠⣾⠟⣠⣶⠄
⠀⠀⠀⠀⠀⠈⠀⣼⡿⠀⠸⣿⣿⣿⣿⣿⠿⠋⠀⠀⣰⠟⠁⠀⠀⠻⣿⡾⠀⠀⢉⠠⠄⡀⠈⠋⠀⠀⢀⣠⠶⠋⠁⢠⣿⣇⣰⣿⣿⣾⣿⣣⣶
⠀⠀⠀⠀⢠⠚⣿⣿⠃⠀⠀⠘⠛⠻⣿⣿⡆⠀⠀⢠⠋⠀⠀⣀⡀⠀⠈⣷⠀⠀⠀⢀⠂⠊⣀⣤⣴⠾⠋⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄
⠀⠀⠀⠀⠉⢘⣿⠏⠀⠀⡠⠀⠂⠀⢻⣿⣿⣇⠀⠀⠀⠀⣲⣿⡟⠓⠀⠸⡆⠀⢜⠁⡙⠋⣠⠞⠁⠀⢤⢺⣧⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⣼⣿⠏⠀⢠⠞⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⣴⣿⠟⠀⢠⣀⠀⢣⠀⠀⢠⠋⢈⠇⠀⣠⡀⠈⢻⣿⡄⠻⣿⣿⣿⣿⣿⠿⢋
⠀⠀⠀⢴⣿⠏⢀⣴⠏⠀⢀⣠⡶⠀⠀⠂⠹⣿⠀⠀⢸⣿⠯⠀⣰⣿⡟⠀⠀⠀⠀⠊⠁⢠⣀⠀⠹⣿⡀⠀⢹⣇⠀⠀⠙⢿⠟⠁⣴⣿⢟⠲
⠀⠀⠀⠀⠁⢠⣾⡟⠀⣴⣿⣿⣷⣄⠀⠀⠀⣈⠀⢠⡟⠁⠀⢠⣿⠋⢠⣦⡀⠀⠀⢿⣦⡈⠚⢦⡀⢻⣷⠀⠀⣿⠀⠀⣤⡀⠀⣼⣿⣯⠊
⠀⠀⠀⠀⠠⠿⢫⠃⠈⢻⣾⣏⠀⠉⠓⢀⣾⠟⢡⠏⢀⣀⠀⠛⠁⠀⢈⠰⠈⡀⠀⠀⠙⣿⣦⠀⠀⠈⣿⣇⠀⠸⠀⠨⠀⠇⣼⣿⣿⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣦⣤⡀⠋⠀⠰⠋⠀⠈⠉⠙⠒⠄⠀⠈⠄⠠⠰⡀⠀⠀⠈⠻⣷⣄⠀⠘⣿⡄⠀⠀⠰⠌⢠⣿⢿⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀⣤⡀⢿⣦⡀⠀⢠⣄⠀⠀⠘⡄⢀⡑⠀⠀⠀⠀⡘⢿⣧⡀⠹⣷⡀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃⣤⣙⢿⣦⣿⣷⣄⣿⣿⠀⠀⠀⠸⣿⣿⡆⠀⠠⡀⠀⠀⠙⣷⡄⠹⣧⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⡀⠀⠈⠳⣤⡀⠈⠻⣦⣻⡆⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢠⡆⢻⣿⣷⠀⠀⠀⠘⣿⣦⡀⠘⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠋⢠⣿⡇⠈⣿⣿⣧⠀⠀⠂⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠺⠿⠀⠀⠘⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⢰⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣷⣿⣿⣿⣟⣿⡿⣶⣆⢀⡀⣄⠀⣠
⠸⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⣿⣿⠉⠻⣿⣿⣿⠟⠉⠻⣿⣿⠟⢹⣿⣿⠀⠀⠈⠻⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⣿⣿⣧⡀⠘⠿⠁⠀⠀⠉⣻⠏⣠⣿⣿⣿⠀⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⡟⠛⠛⠛⢦⡀⠠⣼⣠⣠⢟⣴⠟⠛⢿⣿⠀⣷⣦⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⠆⢈⡁⣫⣾⣿⡂⣶⣿⣿⠀⡿⣿⣿⣷⣦⣄⡀⠀⠀⠉⠛⢿⣿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣴⣎⣽⣿⠿⣿⡇⠿⠛⢿⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣙⡯⣷⣾⡟⠀⣤⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⣼⣞⣿⣿⣿⣿⣾⢯⣿⣷⣿⢸⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣶⣤
⢀⠀⢀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢸⣿⣿⣿⠿⢛⣥⡄⠀⣸⣿⣿⣿⣿⣿
⣽⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⢰⣿⠀⠀⠀⣿⣿⣶⣀⢰⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⡿⢁⣠⣾⡿⠇⣰⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣀⣤⠀⠿⠿⠿⠿⠿⠷⠾⠿⠿⠟⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡶⢦⡀
⠀⠀⠀⠀⢠⠞⡿⣷⡿⢫⣶⢰⡏⡾⠁⠀⠀⠀⠀⠉⠙⠛⢷⣝⣆
⠀⢠⠞⢠⠏⡜⣱⡿⢁⣿⠇⣿⠀⡇⡆⠀⠀⠀⠀⢀⣠⣤⠀⠈⢺⡆
⠀⠃⠀⡞⠀⠀⣿⠁⢸⡟⢹⡇⠀⣇⢱⡀⠀⢀⠞⠋⠁⠀⠀⠀⠀⠙
⠀⠀⢰⠇⡀⢸⡇⠀⣿⡇⢸⡇⠀⢿⡄⢳⡀⠊⠀⠀⠀⣀⣤⣿⡾⠄
⠀⠀⣾⠀⠀⢸⠇⠀⣿⡇⠀⡇⠀⢸⡷⡄⠹⣄⠀⠈⠛⠛⠉⠉⠀⠀⠀⠀⠀⠁
⠀⠀⣿⠀⠀⢸⠀⠀⢻⣧⡀⢱⠀⠀⢷⡹⣆⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡀
⠀⠀⣿⠀⠀⢸⠀⠀⢸⣿⣇⠀⠄⠀⠈⢧⠘⣧⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠹⠋
⠀⠀⣿⠀⠀⠘⡇⠆⠈⣿⣿⡄⠈⢆⠀⠈⢧⡘⣧⠈⢇
⠀⢠⣿⢰⢀⠀⣇⠰⠀⢻⡿⣿⣄⠈⢂⠀⠈⠳⡜⣆⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠿⠃⣼⢸⡀⢻⠀⡆⠘⣷⢣⠻⣦⣄⠑⢄⠀⠙⢿⡄⢠⣀⡀⠀⢀⣠⡴⠚⠁
⣶⠶⠿⠃⢸⡇⠈⡀⠸⡀⢹⣧⡳⡈⠻⣷⣦⣑⣤⡀⠙⢾⣿⣿⡿⠛⠁
⠈⠲⣤⣴⡿⠃⠀⢳⡀⢱⠈⣿⡷⣜⢦⡈⠻⢿⣿⣿⣶⣄⢻⡏
⢤⡀⠀⠀⠀⠀⢠⣿⢳⡀⢇⠸⣿⣌⠳⣌⠳⢤⣙⠾⣝⠿⣷⣇
⣶⣝⠳⠶⠶⢞⣻⣿⡎⢧⠈⡄⢻⢿⣧⡈⠻⢦⣉⠓⢮⡳⡌⢿⡄
⠻⢿⣿⣷⣾⣿⣿⢿⠇⠀⠀⠰⠸⣯⢻⣿⣦⡀⠉⠳⣄⠱⡙⡌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠈⠉⠉⠉⣁⡞⡼⠀⡀⠀⢠⣿⢦⠹⣿⣿⣦⡀⠘⡆⠠⠁⢸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠋⣉⣉⣩⣉⣙⡛⢷⣦⡀
⣿⣶⣶⣶⣶⣞⣯⠞⠁⣠⡇⠀⢸⣿⡈⢧⡘⢿⣿⣿⡆⠀⠀⠀⠈⢂⠱⢄⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋⠁⣀⣤⣶⠿⢛⣛⣿⣿⣿⣿⣷⣌⢷⡀
⠈⠻⢮⣭⣉⣉⣠⣤⣾⡟⠀⡌⣾⣿⣇⠀⠻⣄⠙⣿⣿⠀⠀⠀⠀⠀⢧⡀⠉⠒⠒⠒⠛⠋⠉⠀⣠⣴⠾⢛⣩⠴⠛⣋⣉⣁⣀⡀⠉⠙⢿⡆⢣
⠳⣦⣀⠉⠛⠛⠛⠛⠉⣠⢞⣼⣿⣿⣿⣆⠀⠘⢆⠘⣿⠀⠄⠀⢸⡇⠈⠻⢦⣤⣄⣠⣤⡴⠶⠛⠉⣠⠴⠋⣡⡶⣛⣩⣭⣭⣭⣙⠳⣄⠀⣿
⠀⠀⠉⠛⠶⠶⠶⣶⣿⣵⡿⠿⠛⠛⠛⠿⣦⡀⠈⠆⢹⠀⠁⠀⢸⣹⡀⠈⠲⢤⣀⣀⣀⣀⣤⠴⠊⢁⣴⣾⠗⢋⣁⣀⠀⠀⠀⠈⠑⢌⡆⣿
⠙⠛⠓⠶⠖⢛⣛⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⡎⠀⠀⠀⢸⣇⠳⣄⠀⠀⠀⠈⠁⠀⣀⣤⡾⢟⡫⠖⠊⠉⠉⠀⠉⠐⢄⠀⠀⠈⢧⢸
⣾⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠘⣿⣆⠈⠛⠲⠶⠶⠾⠛⢋⣩⠖⢋⡠⢖⡢⠬⠤⢀⠀⠀⠀⢣⠀⠀⠘⢸⣇⠀⡴⣶⣶⣄
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡾⠀⠀⢠⠀⠀⠹⣿⣷⣤⣀⣀⣠⣤⣾⠟⣡⠴⡫⠚⠁⠀⠀⠀⠀⢳⡀⠀⠀⢦⠀⠀⠀⣿⣄⡀⣨⣿⣿
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡼⡅⠀⢀⠈⢧⠀⠀⠈⠛⠻⠿⠿⠛⠉⣠⠾⣫⠞⠀⣠⣶⣿⣟⠀⠀⣸⡇⠀⠀⠘⣷⡀⢳⣌⠛⠿⠿⢛⡽
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢀⣇⠀⠈⢧⠈⠳⣦⣄⣀⣀⣀⣠⡴⠞⣡⠞⠁⢀⡾⢹⢻⠻⣿⣿⣿⡿⠃⣰⠀⣸⣿⠟⢦⣭⣻⣶⣾⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠡⠀⢸⣿⡄⠀⠈⠳⣤⣀⡉⠉⢉⣉⣡⡴⠟⠁⠀⣠⣿⡇⠸⡌⠳⣤⣉⣉⣤⠞⠁⣴⡿⠋⣠⣾⣿⣿⣥⣤⣶⣿

⠀⠀⠀⠀⠰⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡀⠠⠀⠀⢀⠆⠀⠀⠀⠀⠄⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠐⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⢠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠁⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣸⡅⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⣯⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⠉⠛⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡏⠙⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⣷⣷⠄⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠋⠀⠀⠀⠀⣴⣿⣿⣻⣿⣿⡿⠁⠀⠀⠀⠀⢀⣼⢿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠠⠂⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠣⠒⠤
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⡠⢂⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⠄⠐⣦⡀
⠀⠀⠀⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠁⠀⠀⢀⡜⡡⠃⠀⠀⠀⠀⠀⠀⠀⠖⠑⠀⠀⡀⠂⢀
⠀⠀⠀⠀⠁⠒⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠏⠀⠀⢀⠎⡐⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢸⣶⣶⣾⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⠁⠀⡰⢃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉⣇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡌⢀⡜⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣽⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡠⠂⠀⢀⡤⢖⣿⢁⣴⣾⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⠋⡠⣪⠞⠉⣰⣿⢇⡿⣫⣽⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣫⡟⣡⢾⠞⢁⣠⣾⣿⠏⣼⣿⡏⠈⠉⣿⣷⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⡟⣴⡷⢃⡴⣻⣿⢿⣷⣾⣿⣟⣀⣀⠀⢘⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⣰⠟⣱⣯⣾⣿⣷⣿⣿⠿⠟⠉⠉⠙⠃⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇⢃⣾⢋⣼⣿⣿⠿⣫⠗⠁⠀⠛⠛⠃⠀⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣾⢁⣾⣿⡟⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⠃⣾⣿⣿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢿⡀⣿⣿⡝⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡇⣿⣿⣷⠹⣿⡆⠈⢶⣤⣄⣀⡀⠀⠀⣸⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡏⣿⣿⠀⣿⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢸⠟⢰⡿⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣟⡽⣫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢁⠏⣰⠟⠁⣠⣾⣿⠿⠟⠛⠛⣻⠽⣺⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢃⣏⡾⠁⠀⠀⠋⠁⠀⠀⢀⣰⠽⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⣭⣿⣽⣿⣿⣷⣠⣾⣿⣿⣿⣿⣭⣙⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠛⣿⣻⣿⣿⣶⣤⣌⠉⠻⣿⣧⡘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⣿⣿⠋⣠⣴⠶⡟⠋⠀⠈⠹⣿⣿⣇⢠⠹⣿⡇⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡾⠋⠀⠀⠁⠀⠀⠀⣠⣿⣼⡟⢸⢠⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠤⡀⠀⠲⠾⡿⠿⢛⡱⢃⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢀⣀⠀⠈⠀⠀⠈⠀⣩⣵⡾⠿⠟⠋⠁⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⣏⣤⢤⣀⠀⢭⢻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⣿⣿⢧⣼⠇⣿⣧⢸⣧⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣾⣿⢏⣾⠇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠉⠉⢙⣡⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠻⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡹⣧⡸⣷⢰⣄⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⣣⣿⠇⢀⣾⣿⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⢯⣥⣴⢿⣿⡟⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⠒⠚⢛⣡⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⠻⠿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠄⠠
⠀⠢⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠁⠀⢉⠩⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠙⢦⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⠀⠢⢄⠀⢠⠤⠀⠈⣧⢀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠘⠷⠂⠀⠀⠲⠗⡀⣿⢸⡜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣀⡀⠀⢠⢇⣿⣼⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡔⣄⣉⡁⣠⠏⣼⣿⣿⠇⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⣷⢿⡿⣵⢋⣾⣿⣿⡿⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣰⡟⢸⡾⣡⣿⣿⣿⡿⠁⣼⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⣋⣴⠟⣡⠟⣰⣿⣿⣿⣿⠁⢠⡏⢸⣷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⠾⠋⠁⣴⠏⢰⣿⣿⣿⣿⠇⡄⣼⢰⠀⣿⡸⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⢋⠀⠀⠀⣼⡏⠀⣿⣿⣿⣿⣿⢀⣧⡇⢸⣇⠸⣧⠹⣄⠀⠀⠀⠀⢠⢸
⠀⠀⠀⠀⠀⠀⢸⣧⠋⠀⠀⣸⣿⠁⢰⣿⣿⣿⣿⣿⠸⣿⣇⠈⣿⣦⡘⢷⣬⣙⠒⠒⣒⣡⠏
⠀⠀⠀⠀⠀⠀⠀⢏⠀⡆⠀⢻⣿⡄⠀⣿⣿⣿⣿⣿⡄⢻⣿⡄⠈⠿⣿⣶⣮⣍⣉⣭⣭⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣄⠘⢿⣷⡀⠘⣿⣝⠿⣿⣿⣄⠙⠿⣦⣀⠈⠉⠉⠉⢉⣉⣠⣤⣄⡀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣿⣿⣦⡈⠻⣷⣄⡉⠛⠓⠢⠀⠀⣀⣠⣴⡾⠟⠋⠉⠉⠉⠙⢷⡄⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⡌⠛⠿⠿⢶⣶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡜⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⣼⠃⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⡸⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡅⠀⠀⣾⣿⠃⠐⠂⢀⡤⢤⡦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣧⠀⢰⣿⡟⢿⣦⣄⠿⢾⠿⠃⠀⠀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠣⡀⢿⣷⡘⣿⣿⣿⣦⡀⠀⡠⠞⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣷⡜⣿⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣿⡼⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠇⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣾⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢹⣻⣧⣉⣭⠍⠀⠀⠀⠀⠀⣤⢄⣶⣶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⣿⣾⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣦⣀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣭⣿⣿⣬⣿
⣯⣭⣭⣝⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣡⠶⢚⣓⠒⠬⣙⠢⣀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⢿⣟⡯⠶⠿⢿⣿⣿⣿⣾⣷⣌⡳⢄⡀⠀⠠⠤⠖⠋⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣈⣉⠁⠁⠈⠉⠻⣶⣌⠻⣿⣿⣿⣿⣿⣶⣭⣙⣒⣒⣒⣩⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣫⡅⠀⣀⠀⠀⠀⣈⢿⣷⡌⢿⣿⣿⣿⣿⣝⠻⠿⠿⠟⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⣶⡾⠁⠀⠨⣷⣶⠝⢿⣦⡙⢿⣿⣿⣿⣿⣷⣾⡿⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⣛⠂⠈⣉⣛⣛⣩⣵⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣤⣀⠀⢀⣾⣿⣦⣌⡛⠻⠿⠿⣿⣿⣿⢟⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣄⠈⠛⢁⡠⠋⠠⢬⣉⣛⠻⠿⠿⠿⣛⣫⡷⠋⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠈⠁⠉⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⢋⣁⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠀⣸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣶⣿⣿⣿⠟⢀⣴⡿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⠿⠟⢋⣠⣴⢟⣽⣿⡟⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⣛⣉⣩⣤⣶⠾⠛⣉⣴⣿⣿⠏⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠶⠛⠛⠛⠉⠉⠀⣀⣴⣾⣿⣿⣿⣵⣿⠟⢁⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠘⣿⢁⣀⡠⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⠋⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⢟⡥⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢶⢶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⠗⣡⣾⣿⣿⣿⡿⢋⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠸⡟⣸⣿⣿⣿⢿⡟⠀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⢸⡇⠀⣿⣿⣿⡿⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⠘⣷⡀⠙⣿⣿⣧⡞⠀⠢⡀⠈⠉⠉⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⠈⠻⣦⡈⠻⣿⣷⠀⠀⠈⠂⠀⠀⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠓⠄⠈⠻⣦⣄⠙⠷⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠐⢄⡀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣍⡒⠤⣄⡀⠠⣌⣙⠷⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣭⣷⣤⡙⣿⣦⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⣌⣙⢿⣿⣿⣷⠘⣿⣿⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⡿⢋⣼⣿⡿⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣵⣾⣿⣿⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣤⣶⣶⠶⠶⣦⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⣤⣽⣿⣷⣄⡰⣿⣡⣤⣶⠾⡿⢏⡁⠈⠒⣶⣽⣿⣬⣼⢿⣖⣦⡀
⠀⠀⣠⡾⠃⣀⠀⠀⠙⣯⣷⣶⣔⣿⡶⠿⣿⣿⣿⡿⢟⣿⣧⡤⠖⢋⣷⣶⣭⣷⣾⣿⠟⠛⢿⣿⣿⣧⡀
⠀⠀⢿⡐⣦⠀⠚⢯⠐⣄⢀⣀⢽⣯⡾⣿⣶⣾⣿⣿⣿⣿⣹⣶⣶⣿⣿⣿⣿⡟⠉⠀⠀⡀⠀⣿⣿⣿⠃
⠀⠀⠈⠉⠁⢤⣲⣦⣷⣽⣄⣹⣦⣿⣧⣯⣽⣿⣭⣤⣾⣿⣿⣿⣿⡏⣹⢻⡏⠀⠀⠲⢾⠟⢀⡜⣯⠛⠳⣄
⠀⠀⠀⠁⠀⠀⣩⣿⣿⣿⣯⣯⣙⡲⠿⣿⣝⣛⣛⡿⠟⣻⣿⣿⣿⣿⣅⡈⠛⠀⠀⠀⠀⠀⠘⠃⠹⣦⠀⠈⠁
⠀⠀⢀⣴⣤⠘⠍⠊⠁⠋⢸⣷⣯⣝⣿⣿⡿⢟⣫⣴⣿⡿⣋⣭⣿⡿⡿⣇⠀⠀⠀⠀⠀⢤⡏⠀⠐⣾⡀⠀⡠
⠀⠀⠀⢄⣸⡇⠀⠠⣯⠤⣤⣽⡿⢿⣿⠷⠿⢟⣿⡿⢋⣼⣿⣿⡾⠁⡇⠙⣷⣦⣄⣀⠀⠛⠀⠀⠈⠀⠉
⠀⠀⠀⢮⣩⢶⣿⠃⣲⣷⣾⣤⣴⣶⣶⣾⣿⠟⣡⣾⣿⣿⣿⡿⠁⠀⡇⠀⢸⣿⠉⠉⠉⠁⠀⠒⢤⡀⠤⠄⢀
⠀⠀⠀⠠⣿⣿⣿⣟⡛⠿⣿⣯⣾⣿⡟⣽⣧⣾⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠈⣿⣀⠈⠛⠶⡰⣴⣌⣿⢠
⠀⠀⠀⠀⠿⠟⠉⠛⣙⣿⣿⣿⣿⣋⣴⣿⣿⡿⠛⠉⠉⠁⣤⠀⠀⠶⠀⢀⣼⠻⣿⣷⣄⠀⠁⠘⣿⠏⣼
⠀⠀⠠⣶⢤⡄⣤⠀⠨⢽⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠉⠛⣖⡤⢚⣡⡾⣣⠂⢀⠄
⠀⠀⠀⠁⠀⠀⠻⣤⡴⢀⡴⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⡠⠔⣊⣥⡶⣛⣥⣚⡥⠞⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡎⠀⡻⣧⣏⢹⣿⣿⣧⣤⣤⣤⣤⢾⣻⠀⠀⠀⠠⢐⣨⣵⠶⣛⣫⡵⡾⣛⠯⠅⠂⠈
⠀⠀⠀⠀⠀⠀⠈⠳⢦⠀⠛⠛⠛⠛⠛⠛⠛⠋⠉⠐⠋⣁⣀⣤⠴⠶⣛⣯⠵⠖⣛⡭⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠤⠤⠀⢒⣚⡛⠯⠭⠭⠗⠒⠋⠉⠁⠄⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡤⠴⠶⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣀⣠⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢦⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠝⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠄⢢⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⢀⠼⡋⠉⠳⢹⢰⠀⠀⠀⠀⠀⡠⠚⢉⠄⠀⡀⢀⠢⡀
⠀⢰⡉⠉⠁⡔⠀⠀⠀⠀⠀⣀⠀⠀⢠⢯⠏⠀⠀⠀⠀⠯⠀⠀⠀⠀⣸⠁⡴⠁⠔⠚⡁⠀⢧⢱
⠀⢸⡁⠰⣂⡼⠀⠃⠀⠂⠀⡡⠃⠀⠸⡀⠐⠈⠁⠀⠠⠐⠆⠀⠀⠀⡇⢰⠁⠄⠀⠀⠀⠈⢸⠈⡇
⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠁⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢊⠜

⠀⠀⢀⠤⣤⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠠⠠⠦
⠀⠀⡟⠚⠋⠤⣴⠖⠊⠀⠀⠀⠀⢀⡠⠤⠖⠋⢁⡔⡡⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠐
⠀⠀⠈⠂⠉⠋⠁⠀⠤⠠⠀⠀⠐⠁⠀⣀⣤⠴⠋⣰⠃⠄⠀⠆⢠⡀⠀⠀⠀⠀⣀⠀⠐⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠰⠉⠀⢀⣀⠴⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⡄⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠁⠀⠡⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠰⢀⠀⡀⠀⢀⣰⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡀⢆
⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠈⠂⠠⠄⠠⠌⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⡇⢨⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢠⡾⠁⠀⠀⠀⠀⣠⡶⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐⠶⠾⠋⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠃⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡤⠀⠀⠀⠀⣦⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣾⣿⣿⠟⠓⠒⠦⣤⣤⣴⡿⠁⢀⣼⠋⠀⣀⠀⠀⢠⡁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠀⠀⠘⣿⣿⠃⠀⠀⠀⡄⠀⠉⢉⣴⡤⠟⠁⠚⠋⠁⠀⠀⠈⠉⠀⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⢀⣾⠃⠀⢠⡾⢻⡇⠀⠀⠰⠶⠶⠖⠀⠈⠳⣴⡶⣯⣟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢀⠌⢀⣠⣴⣿⢏⣠⣶⡿⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⢟⣾⡿⠟⣫⡾⣻⣿⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⢨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⡏⢸⠉⠀⠀⣿⠰⣿⡇⠀⣰⠃⠀⣾⣿⣿⡦⠀⠀⠀⠈⠀⠠⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠹⣷⡘⢷⣦⣄⡘⠀⠙⣷⣼⡏⠀⠄⠈⠉⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠈⢷⡈⢻⣿⣿⣦⢂⢸⣿⡇⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠻⣷⡌⡇⠀⣿⡿⣿⣟⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡟⢀⡴⢋⣴⣿⡿⠋⢸⡿⡌⠑⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡞⠋⢠⣯⡴⢻⣿⠏⠀⠀⠈⣷⡙⢦⡀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠃⠀⣾⣿⠀⠘⣿⡀⠀⠀⣰⣿⡇⢠⣿⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠙⣿⡿⣦⡀⠈⢳⣴⠞⠋⠉⢀⣾⣿⠇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣠⣾⣿⣷⠈⠙⢦⡙⢿⣦⡀⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠃⠀⠀⠀⢹⠀⣼⡧⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢰⡄⠀⠀⢸⡟⠋⠀⡟⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡠⠞⠁⠀⣰⣿⠁⠀⣰⣇⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢻⣷⡀⠰⠃⡏⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠙⠢⠀⠸⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠒⠚⠁⠀⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣴⣷⣭⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⣾⣿⣿⣟⡷⣽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⣿⡳⢯⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⣿⣿⣿⢿⣝⡳⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⣿⣿⡿⣯⣛⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⢷⡀⠀⠀⠀⠀⠀⢠⠋⣰⣿⣿⣿⣟⡷⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠻⣄⠀⠀⠀⡰⠃⣼⣿⣿⣿⡳⢮⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⣆⠀⡰⠁⣼⣿⣿⣿⠿⣝⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡖⣮⢿⡁⠘⣿⣿⡷⣯⣛⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠁⠀⠳⣄⣉⣻⣽⡶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣄⣀⠀⠙⢆⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠻⡈⢹⠲⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡴⠁⠀⢳⢸⡄⠀⠑⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠜⠀⠀⠀⠈⢇⢇⠀⠀⠀⠳⡌⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠊⠀⠀⠀⠀⠀⢸⡌⡆⠀⠀⠀⠘⡄⠈⣩⠭⣽⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡡⠃⠀⠀⠀⠀⠀⠀⠀⡇⠘⢆⠀⠀⠀⡘⣼⠁⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⣬⣕⡢⡀⢰⣹⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡼⠁⠀⠀⠙⣾⣧⠷⣝⢦⣀⣀⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢳⠀⠀⠀⠀⢸⣿⠀⠈⠙⠒⠓⠛⢬⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡳⣄⣀⣀⡼⡿⠀⠀⠀⠀⠀⠀⠀⠳⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠺⠗⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠟⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣤⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠙⠲⠄
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠉⠉⠁⠠⠄⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠋⠃⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠙⠛⠿⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣟⣹⣿⣼⣿⣙⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠀⠀⠀⠀⠀⣰⣿⣤⠟⠋⠉⠉⠉⠛⢧⡼⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣶⣆⠀⠀⠀⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⢷⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⠁⠁⠀⠀⠀⣷⣾⡇⠀⠀⠀⠀⠀⡀⠀⢸⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠋⠉⠀⠀⠀⠀⠀⣷⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣸⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⣀⣀⣀⠀⣯⣽⣯⣼⣿⣬⣿⣭⣿⣭⣿⣥⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⠄⢠⣤⣤⡖⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠙⠻⣿⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠿⠿⣶⢠⣴⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡛⢛⣻⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣽⡿⠿⠇⣿⡿⠟⠻⠿⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⣀⣀⠀⣠⠲⣤⣦⣤⡀⠀⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠘⠋⠴⢋⡤⣛⣷⣿⣿⣿⣦⡄⠀⠀⠀⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠋⣴⡟⢙⣫⣿⣿⣿⣿⡄⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣀⠐⣷⠾⣋⣼⡿⣿⡿⠛⣽⣿⡷⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣡⠶⢁⣤⣻⣯⣼⠏⣰⠞⢹⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠉⠴⢟⡵⠋⠁⠀⠀⠀⠰⣟⣿⣿⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠊⢁⣤⣤⣶⣶⣤⣤⣄⠈⠉⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠉⠛⢩⣿⣷⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⣰⣿⣷⠓⠶⠀⠀⠀⠐⠉⢉⣿⣿⡄⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣴⢏⣿⡟⠀⢴⠆⠀⠀⠀⠶⠘⣿⣿⣇⢀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠊⠙⣧⡀⠀⠀⠀⠀⠀⠀⣤⡾⢿⣭⣯⡽⠋⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠤⣀⠀⠀⠀⠈⢛⡀⠀⢴⣶⠆⢀⡟⠀⠀⠀⣀⡤⠚⢻⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠻⠂⠈⡻⣦⡀⠀⢸⡇⠐⢀⣤⣤⣿⠀⠀⣠⠞⢋⣤⠀⠀⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣻⣀⣈⣋⠀⠙⣦⡈⣣⡀⠀⠀⢀⡙⠀⣿⡇⢀⣈⣁⣀⣈⣛⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⠉⠛⢻⣷⣿⠟⣹⡟⠉⠲⠶⠛⢁⣴⡏⠀⠈⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠛⠁⠉⠛⠛⠙⠿⠇⣸⠋⢹⣶⡿⠆⠚⣛⠋⢀⣾⠀⣤⡌⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⢰⣦⠀⠀⠘⠛⠀⠀⠀⠀⢻⡄⢀⠙⠿⣷⡆⠉⣠⣾⡿⠀⠈⠁⠀⣀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠿⠂⠈⢿⡄⠰⣶⠤⠴⠟⠛⠋⠠⡶⠀⠀⠘⠛⠀⠀⠈⠁⠘⠋⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⡀⠀⠘⠟⠀⢀⣀⠀⠀⢀⠈⣿⡄⠀⠀⠀⣶⠄⠀⠀⠀⣀⣠⣤⣤⣀⡀⠐⠷⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⠛⠀⠀⠀⠀⠘⠋⠀⠀⠉⠀⠼⠿⣿⣦⡄⢀⣠⣴⠾⠟⠋⠉⠉⠀⠨⡇⢀⣀⠀⠰⣶⠀⢿⡄
⠀⠀⠀⠀⠀⢸⣿⡀⠘⠃⠀⠀⠀⠀⠿⠂⠠⡄⠀⠀⣀⠀⠀⠀⠀⠈⢁⠈⣁⠀⠀⠀⠀⠀⠀⠀⠐⡇⠘⠋⠀⠀⠀⢀⣼⣿⡀
⠀⠀⠀⠀⣠⣿⡿⠀⣀⠀⠀⢶⡦⠀⣀⡀⣀⢠⣜⠷⣉⠀⠁⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠛⢂⠤⠠⣷⣄⠠⣶⠀⣴⠟⠁⠈⠛⢦⣀
⠀⠀⠀⠀⠘⠿⢧⣄⠉⠀⠀⠀⠀⢀⡙⠃⠀⠀⢹⣶⣫⡴⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⠿⣿⠀⠀⠈⠉⠳⣤⠀⠙⣦⡀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢀⡴⠀⠀⠀⠙⠧⢀⣀⣰⡶⠂⠀⠀⣀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠉⠰⢶⣤⣤⣀⡀⠙⠓⠴⠿⡶⠦⠤⠄⠀⠙⢷⣄⠀⠀⠀⠀⠈⠁
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣤⠶⠟⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠸⠃
⣸⠇⠀⠀⠀⠀⠀⢀⣀⡠⠶⢾⣿⣷⣴⣆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⢀⣠⠖⠻⠇⠀⢀⣬⠛⢿⣦⣄⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡄
⣿⣦⣤⣤⣴⣶⣶⠟⠉⠑⠶⣤⡈⢻⣿⠁⢀⠘⠳⠆⠀⢀⣀⡀⠀⠀⠀⠁⠀⠃⠀⠀⣠⣄⠒⠉⠁⠀⠀⠀⠀⠀⣉⠑⢀⡈⠉⠙⣿⠶⣶⣶⠿⠋
⠈⠛⠛⠛⠋⠁⢸⣄⣈⣁⣤⡉⠀⠈⣿⣧⠈⠁⢀⡀⠀⠀⣀⠈⠛⢛⣶⣶⣶⣶⣶⣄⠀⠙⠛⠿⣶⣤⡀⢀⠀⡀⠀⠀⠈⢉⡉⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⣿⠀⢀⣿⡿⠀⠀⠘⠛⠀⠀⢈⣤⣾⣿⣿⣿⡿⠛⠉⠉⠳⣄⠀⢀⠈⠙⠇⠈⣾⠃⠀⣴⠿⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢸⣿⠀⢀⣤⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⡆⠸⠷⠀⠀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢸⠏⣾⣿⠁⠰⣾⣿⣿⣿⣿⡿⠛⠻⣇⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢴⣿⣷⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣤⠀⣄⣼⣿⠃⠀⣰⣿⣿⣿⣿⣿⠁⠀⠀⠈⢷⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠙⢷⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣠⢿⣦⢻⣿⡿⠷⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⣿⡄⢸⣆⠀⠀⠀⠙⠦⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⢿⣼⢿⣿⣿⡇⠀⠰⣿⣿⣿⣿⣿⡇⠸⣧⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⣷⠀⠉⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠛⡇⢸⡿⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠹⠷⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢿⡆⢠⣿⠃⢠⣿⣿⣷⣶⠄⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⡇⠀⠻⣿⣿⣧⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⡀⢰⣶⠀⠀⠀⢰⣶⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢿⣿⣿⣀⡀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡧⠀⠀⡀⠘⣿⣿⣿⠟⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⡇⠀⠀⣠⣄⠀⠀⠀⠀⣤⣄⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠸⣿⠀⠈⠛⠛⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠙⠋⠀⠀⢹⣿⡇⠀⠀⢠⡄
⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣧⠀⣤⡄⠀⠀⢰⡆⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⢴⡆⠀⠀⠀⠈⠁⢀⣰⠿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹⣿⣿⡀⠈⠀⠀⠀⠈⠁⠀⠀⣠⣀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⡀⠀⠀⣠⠟⠁⠀⠻⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⠟⠻⣷⣶⠖⠒⠲⡦⠠⣄⠀⠙⠛⠀⠀⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠘⢿⣧⠀⢶⠆⠀⠀⢛⣴⠞⡏⠀⠀⠀⠀⠀⠉⣿⠀⠀⠸⠉⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⠀⠈⣿⠀⠀⢰⡇⠀⠀⠻⣦⡀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣴⣾⡁⠀⠃⠀⠀⠀⠀⠀⠀⣿⠀⢠⡄⠀⠀⠙⠻⠿⠿⠟⠁⠀⣿⠀⠈⢀⠀⣿⠀⠀⣤⠁⠀⠀⠀⢸⣿⡄⢰⡿⠃⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⢹⣧⠀⣄⠀⠀⠀⠀⠀⠀⣿⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢾⣿⠀⣴⠁⠀⠀⠀⠀⠈⠿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠘⢇⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣷⠇⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡿⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⣸⣷⠀⠀⠀⠀⠀⠀⠀⣼⡏⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢉⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣧⢀⣴⠟⠁⣸
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢨⣿⠇⠀⠀⠀⠀⠀⠀⠘⠿⣥⡤⠔⠁
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢹⣿⠄⢉⡆⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠶⠿⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠦⠄


⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣿⣷⡄⠀⠀⠀⠀⢸⠁⠙⢿⣝⢮⡹⣧⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡟⠛⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⡄⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠈⢀⣀⢨⣿⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⡇⣿⠆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣾⣫⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠘⠉⠉⠉⠁⠙⠖⠃⠀⠀⠀⠀⠀⠀⠿⠶⠶⠇⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠿⢿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠺⠋⣀⠀⠀⣀⠛⠗⠀⠀⠀⠀⠀⠀⠀⢪⢔⡵⡃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⣫⢞⡅
⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣕⣡⡆
⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣍⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⡈⢿⣷⡀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢲⣅⠀⠀⠀⠈⢉⣭⣤⣤⣀⡀⠀⢸⣿⣷⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠘⠁⠻⠟⠹⠛⠋⢀⣿⣿⠀⠀⠀⢘⣿⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣸⡿⢸⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⢀⣴⠟⢡⠏⢠⣿⡟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⣠⠞⢋⠔⢁⣴⣿⠟⠁⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⡀⠀⠀⠀⠀⢰⣿⠏⠀⢠⡞⢁⠔⢁⣴⡿⠋⠁⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠷⠂⠀⠀⣿⡏⠀⣰⠏⡰⢁⣴⠟⠁⢀⣠⣴⡾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡟⡜⣠⡿⠁⣠⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣷⢠⡿⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠘⣿⣾⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠀⠀⢀⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣠⠟⣡⣿⣿⣿⣿⣿⣿⡿⠙⢿⣷⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢍⣉⣉⣡⣾⣿⣿⣿⢟⣫⣾⠟⠁⠀⠈⢿⣎⢷⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⣤⣾⣟⣯⣽⠾⠿⠏⠁⠀⠠⠀⠀⢸⣿⠈⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⡿⣿⣿⠙⠲⠖⠀⠀⠀⠐⠶⠖⣿⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣫⣾⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⠟⣿⢳⣿⣷⡄⠀⠤⠶⠦⠀⠀⣿⢹⢱⡏⢙⣧⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⡸⣿⣿⣿⣦⣀⠉⢁⠤⠊⢿⣿⣧⣙⠛⠁⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠸⣇⢿⣿⡿⣿⣿⠉⠁⠀⠀⠈⠻⣿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣄⡈⠻⣿⣿⣮⡛⠷⣤⡀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠻⣿⣶⣬⣙⡿⣿⣦⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠉⠛⠿⣿⡺⣿⣿⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠚⠁⠀⠈⢳⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⢀⣼⣯⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠭⠽⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⣶⣶⣶⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⡴⣫⣷⣿⣿⣿⣿⡿⠶⠾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢖⣵⢞⣽⣾⣻⣿⣿⡿⠋⠁⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣫⣷⣿⣿⣿⣿⣿⠋⠀⠐⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣫⣾⡿⠁⠀⠀⠀⠾⢿⣿⡄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣳⣿⣿⣿⡿⢋⣴⣿⢏⠔⠀⠀⠀⠀⠀⠀⠁⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣼⣿⣿⡿⠋⣠⣿⣿⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣸⣿⣿⠏⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⠃⣰⢟⣿⠏⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠙⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⢠⣏⣾⠇⠀⡴⠀⢀⡄⠀⢸⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢸⢸⣿⠀⣸⡇⢠⣿⠃⠀⢸⡿⠋⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢸⣧⠀⣿⡇⣿⣿⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣿⡀⢿⣧⣿⣿⡀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣜⢷⡈⠻⢿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡻⣆⠘⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⠣⢻⡇⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢶⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⡀⠀⠀⠀⢠⣶⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣠⠂
⠀⠀⠀⠘⣿⣿⣿⣿⣧⢠⣿⠀⡀⠀⣼⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡞⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣼⣿⢠⣿⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⡴⢋⠏⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠇⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⢹
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⡟⠀⠀⡰⠊⡛⢀⣼⠀⠀⠀⠀⠀⠀⡔⠘⠋⣀⡎⠀⠀⠀⠀⠀⢀⡃⢈⠁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠇⠀⢸⣿⣿⣿⠟⠀⠀⠀⠑⠒⢹⠁⢸⠂⠀⠀⠀⠀⠀⠓⠂⢛⠁⡹⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⡟⠀⠀⠀⠀⠀⠀⢀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⡈⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⡫⠊⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢏⠂⠀⠀⠀⠀⠀⠀⠀⠠⣿⣾⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣿⠿⠿⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏
⠀⠀⠀⢠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣝⢽⠋
⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠟⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣄⠀⠀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣰⣾⠀⠀⠀⣼⣵⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠙⢿⡄⠀⠀⠙⠿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⣼⡿⠀⠀⢀⣾⡟⠁⠀⠀⣴⠟⠁⠀⢼⣿⡷⡄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣰⣿⠋⠀⠀⠀⠈⠀⠀⠀⢀⣿⣾⣷⣇
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣵⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢴⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⡀⠀⠀⠀⢠⣶⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣠⠂
⠀⠀⠀⠘⣿⣿⣿⣿⣧⢠⣿⠀⡀⠀⣸⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡞⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣼⣿⢀⣷⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⡴⠋⡏⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⠃⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢹
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⡟⠀⠀⠠⠚⠻⢀⣼⠀⠀⠀⠀⠀⠀⡔⠛⡏⢀⡎⠀⠀⠀⠀⠀⠀⠊⢩⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠇⠀⢸⣿⣿⣿⠟⠀⠀⠀⠐⠄⢻⠃⢨⠀⠀⠀⠀⠀⠀⠃⠐⢻⠁⡹⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢯⠀⠁⠀⠀⠀⠀⠀⠀⣴⣿⡟⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢟⠔⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠗⠅⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣺⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟
⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢝⢝⠏
⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠂⠀⠀⣴⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠀⠀⠀⠺⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣠⣶⠀⠀⠀⣼⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡌⠁⠙⢷⡀⠀⠀⠻⢿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⣼⣿⠁⠀⢀⣼⡿⠃⠀⠀⣰⠟⠁⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣻⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⢠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣠⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⣾⣷⣷⡇
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠛
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⣿⠛⡿⢿⡿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⢀⣤⣾⣿⠟⢛⣋⠙⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⢀⣴⣿⣿⠋⣤⡾⢋⣡⣴⣶⣶⣤⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⣠⣾⣿⡟⢡⣾⠋⣰⣿⣿⠟⠉⠉⠉⠉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣴⣿⣿⠟⢠⣿⠃⢰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣼⣿⣿⠏⢠⣿⠃⠀⣾⣿⡇⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⣼⣿⣿⠏⢀⣾⠇⠀⠀⣿⣿⡇⠀⠀⠀⠔⠛⠛⠛⠛⠻⠿⠦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⣾⣿⣿⠏⠀⣼⡏⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠋⠀⣠⣿⣿⣿⠏⠀⣼⡟⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠲⠟⠛⠃⠀⠈⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⣠⣾⣿⣿⣿⠏⠀⣰⡟⠀⠀⡀⠀⠀⡀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⠀⠐⠦⣄⣀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡟⠁⠀⣴⡟⠀⠀⢰⡇⠀⢰⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚
⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠉⢀⣠⠾⠋⠀⠀⢠⣿⠃⠀⣸⡇⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠐⠚⠋⠁⠀⠀⢀⣴⣿⠏⠀⢀⣿⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⠿⠃⡀⠀⣾⡟⠀⠀⠈⣿⣿⣿⣿⣿⠀⣇⠀⠀⠀⠀⠀⠀⠙⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⠿⠟⠋⠁⣠⡔⠁⣼⡿⠁⢠⠆⠀⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⢀⣠⣶⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⢀⣠⣴⡾⠋⢀⣾⡿⠁⣰⡏⠀⠀⣿⣿⣿⣿⡿⠀⣿⡇
⠀⠀⣠⣾⡿⠋⣡⡴⠚⠉⠀⣀⣤⣴⣶⣿⠿⠛⠉⢀⣴⡿⠋⣠⣾⠏⠀⠀⢀⣿⣿⣿⣿⠃⣸⣿⠃
⠀⢠⣿⠋⣰⡿⠋⠀⣀⣴⡾⠿⠛⠉⠁⠀⠀⠀⠐⠋⣁⣤⣾⡿⠋⠀⣠⠆⣼⣿⣿⡿⠃⣴⣿⡿
⠀⢸⠇⣸⡟⠁⢠⡾⠛⠁⠀⠀⣀⣀⣤⣤⣴⣶⣾⣿⣿⡿⠋⠀⢀⡴⠃⣼⡿⠟⢋⣠⣾⣿⡟⠁
⠀⠘⢀⡿⠁⠐⠋⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢀⣠⣶⠟⠀⠈⣁⣤⣾⣿⣿⡿⠋
⠀⠀⢸⡇⠀⢀⣴⣿⣿⣿⣿⡿⠟⠋⠉⣁⣀⣤⣤⣶⣾⠿⠋⣀⣤⣶⣿⣿⣿⡿⠟⠉⠀⡼
⠀⠀⠘⠁⠀⣾⣿⣿⡿⠛⠁⢀⣤⣶⡿⠿⠟⠛⠋⠉⣠⣴⣾⣿⣿⡿⠿⠛⠉⠀⠀⣠⡾⠁
⠀⠀⠀⠀⢸⣿⣿⡟⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠁⠀⠀⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠸⣿⣿⠀⠀⠞⠁⠀⢀⡴⠂⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣴⠋⠀⠀⣰⣿⡿⠋⠀⠀⠀⢀⣤⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⣾⠇⠀⠀⠀⣿⡿⠁⠀⠀⠀⣠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⡟⠀⠀⠀⠐⣿⠇⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡧⠀⠀⠀⠀⠀⠀⠸⡿⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⣿⠟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠦
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣾⡿⠃⠀⡠⠖⠉⠀⢀⠀⣤⣶⣷⡄⠀⢳⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠟⠀⠀⠀⠀⢀⣴⠾⠛⠁⠘⣿⣿⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡄⠀⠈⠁⠀⠀⠀⠀⠘⠟⠉⠁⠀⠀⠀⡀⠄
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠂⠋⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⠀⠀⠀⠠⠇⢀⣶⠄⠰⠁⠒⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡄⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣰⡿⠁⠀⠇⠀⠠⠴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⡄⠀⠀⠀⠀⠀⠘⠋⣼⡟⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠤⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠁⣀⡄⠀⠀⠀⡜⠁⠀⢀⣀⠀⠈⠀⠰⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄⠀⢷⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣰⡲⣦⣍⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠾⣭⣛⢶⡿⢯⣖⠵⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⢷⡀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣰⣏⡻⣶⣽⣯⣛⠷⣭⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠻⣄⠀⠀⠀⠀⢀⠞⠀⠀⣜⡳⣮⣟⣷⣻⢶⣝⡳⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⣦⠀⠀⢀⠎⠀⢀⡾⣭⣛⢶⡽⣫⣟⠷⣮⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢧⣠⠋⠀⢀⣞⡻⢶⣽⣫⣚⠷⣭⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⣳⡄⢀⡾⣮⣙⡷⣫⢶⣝⡻⢦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠾⠙⣾⣛⢷⣽⣻⣟⡷⣮⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⡄⠀⠈⢻⣻⣚⠷⣭⡛⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠹⡐⢢⣄⡙⢽⡻⢦⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⡠⢳⢸⠦⢭⣮⡻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⠎⠀⠀⢇⢇⠀⠀⠙⢌⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢀⠇⠀⠀⠀⠸⡘⡄⠀⠀⠈⢇⢀⡭⠿⢵⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡇⠘⢄⠀⠀⢸⢸⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢰⣣⠖⠒⢾⣦⡼⢾⢆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢩⣇⠀⠀⠀⠹⣾⠉⠪⢝⣶⡾⣝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠘⣜⢄⠀⠀⢠⣿⠀⠀⠀⠀⠀⠈⢫⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠽⠿⠝⠋⠀⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⠿⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⢞⡽⢐⣯⣷⣮⣍⡻⣆
⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⣿⠼⣩⣶⢿⣛⣲⣉⠳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⡄⠘⠷⣿⢸⣇⠾⢋⣤⣤⣌⠛⢾⡆
⠀⠀⠀⠀⠀⣼⠟⠉⠀⠉⠉⠀⠉⠀⠉⠉⢭⣿⢷⡀⠀⠀⠀⠀⠀⠀⢠⢞⣛⣛⡛⠳⠦⠙⠳⠙⠂⠀⠀⠉⢻⣧⢠⠁
⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⣴⠟⡛⣩⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣸⢠
⠀⠀⠀⠀⠈⣥⠤⠴⠦⠤⣤⠤⣤⠤⠶⠤⢦⡤⠉⠁⠀⠀⠀⠀⠀⢀⣴⢏⠾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⡟⣸
⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⡏⠀⢻⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⡿⢋⡴⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣿⣻⣄
⠀⠀⠀⠀⠀⣧⠉⠉⠉⠉⠀⠀⠈⠉⠉⠋⠁⡾⠀⠀⠀⠀⢀⡴⢛⣱⡿⢣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⠙⢷⣉⠁
⠀⠀⠀⠀⠀⠸⣇⡀⣠⣤⡶⠐⣶⣤⣄⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⢠⡖⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠹⣧⣐⢮⣥⣤⡤
⠀⠀⠀⠀⠀⢠⣧⣉⡉⠉⢀⡀⠀⠉⢉⡭⣼⡄⠀⠀⠀⠀⠀⠀⢀⣨⣾⠟⣴⢸⡆⠀⠀⠐⣿⣛⣿⡆⠀⠀⠀⢙⠿⠦⠭⠤
⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡘⣿⣇⣀⣾⣇⡿⠃⠀⠀⠀⠀⠀⠉⢉⣭⡴⠟⣡⢸⣷⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡼⣿⣌⢷
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⣘⣿⣮⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⢹⣎⢻⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢻⡇⠀⠀⠀⠀⠀⠀⢀⡟⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠘⠅⠃
⠀⠀⠀⠀⠀⠀⠠⣦⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⢁⣴⠃⠀⡀⠀⣀⢄⢰⡄⢠⠀⣿⠃⣸⠇⣠⠀⣰⡿⠋⠉⠳⠀⠀⢠⡎⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣿⢀⢹⡇⣾⡉⣸⣧⡞⢸⡇⣼⢀⣿⢀⣿⢠⡇⠀⢹⣷⠀⠀⣀⡤⡀⣿⠀⢜⣤⣀⢀⣤⣄⢀⣶⠴⣄
⠀⠀⠀⠀⠀⠀⠘⠻⣧⣾⠃⠈⠉⠈⠉⠓⠉⠋⠻⠚⠿⠊⠈⣽⠃⠀⢀⣿⣿⣸⣋⣼⠃⣿⡀⢸⡏⢸⢸⡏⢸⣇⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡿⠀⠀⣾⣀⣿⠋⠉⠻⠂⠙⠧⡼⠷⠚⠀⠻⠛⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣛⣿⣛⡳⢦⣤⣠⣤⣶⣿⣿⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡾⢱⠿⠿⣿⣿⣆⠀⠉⠉⠀⠐⠚⠲⣶⡝⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠈⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠘⠿⢄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⢿⣷⣤⣤⣤⠶⠶⠿⣿⣿⡆⠈⠙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⢠⣦⡉⠀⠀⡄⠀⠀⠘⣿⡇⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠒⠀⠀⢸⡏⣷⣄⠀⢿⣆⠀⠀⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠻⣷⣮⣿⣿⣦⣄⣢⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⣴⣶⣤⠘⣆⠀⢹⣿⡝⣷⠈⠛⢷⢹⣆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠙⠛⠋⢀⠸⣷⣸⡟⠁⠃⣀⣤⡞⣸⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠒⠀⠀⣿⡟⢠⣠⣾⣿⠏⣰⠏⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣷⣸⣟⢿⣏⠀⢇⣼⠟⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢼⣿⠈⠻⣿⣷⣝⢦⡘⢿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠂⠀⠀⠀⣴⠁⣾⣇⠀⠀⠈⣿⡏⢳⣷⠀⢙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⡄⠙⠿⣦⡀⡰⠋⠀⣸⣿⡧⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⢀⣿⠗⡠⠞⢫⣿⣧⡀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣿⠁⡞⠀⠀⠈⠻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡇⠈⢳⡇⠀⠀⣰⠐⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢻⡄⠀⢿⣆⠀⠘⠢⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠁⣠⡾⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠘⠛⠶⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢹⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠾⠷⠦⢤⣤⣄⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⡶⠿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣦⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢹⡆⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣸⡇⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⣀⣀⣠⣴⠞⠁⣠⣿⡄⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⠛⠉⣉⣀⣀⣉⡉⣉⣉⣉⣁⣀⣤⠾⠋⠀⢻⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⡞⠁⠀⠀⠀⠐⠶⠶⠶⢤⡄⠀⠀⠀⠀⠀⠀⣤⡶⠶⠶⠖⠀⠀⠀⠙⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣗⠀⠀⠀⠀⠰⠟⢻⣏⡿⠳⣄⠀⠀⠀⠀⠀⢠⡞⢿⣿⡟⠛⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠳⣤⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣤⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⢙⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⢻⡄⣸⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠃⠀⠀⠀⠀⠈⠉⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⡾⠻⠶⠛⣰⠶⣬⣿⣏
⠀⠀⠀⠀⠀⠀⣾⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠟⢷⡆⠀⠀⠀⠀⣤⣀⠀⠀⠀⣀⣤⠀⢿⡀⠀⡶⢿⡆⠹⣇⠹⣆
⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠰⠶⠶⢾⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠈⢳⣬⣷⠀⣿⠀⢿⡀⢿⡀
⠀⠀⠀⠀⠀⠀⣿⠀⢠⣤⣤⣤⡄⠠⣤⡤⠀⣤⣄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⡆⢸⡇⠸⡇⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⡏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣷⠸⣇⠈⣷⠀⣿⠀⢿⡟⣷
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⢸⡇⠀⣿⠙⠳⢦⣄⣀⣀⣠⣤⡶⠛⠉⠀⣿⠀⣿⠀⢻⠀⠻⠀⠸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠘⠛⠛⠛⠒⠛⠛⠛⠛⠛⠋⠀⢸⡇⢠⡟⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⠀⠉⠀⠘⠁⠀⠀⢠⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠟⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙


⡏⠉⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡏
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⡖⠐⢢⢰⠀⢲⠂⢀⠶⠀⢰⢒⡆⣶⠀⢰⡆⠂⠀⢰⡂⠀⢰⡆⢐⡆⣲⢠⠂⠒⡄⢰⡰⠂⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⣇⣀⡜⢸⡀⢸⠀⡼⠒⢇⢸⣉⡗⣻⣀⣸⣇⣀⠀⢀⣈⠆⢸⡇⢈⡏⢳⠘⣄⣠⠆⣘⠑⣄⣏⣁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠈⢁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⢄⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⣤⣸⡅⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠤⣄⣯⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⠉⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡏⠑⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⡄⠀⠀⠀⠀⢠⣿⣿⣯⣿⣤⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡋⠀⠀⠀⠀⣰⣿⣿⣯⣿⣿⡿⠃⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠋⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠛⠷⣿⣿⡿⠁⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣴⣀⡄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁
⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟

⠀⠀⠀⠠⠆⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠂⠖⢠
⠀⠀⠀⠖⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡌⡟⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠈⠀⠀⠐⣦
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠁⠀⠀⠀⡴⠡⠊⠀⠀⠀⠀⠀⠀⠀⠶⠱⠀⠰⠀⠀⢈⠁
⠀⠀⠀⠀⠁⠴⡀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡞⠀⠀⢀⠞⡐⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⣠⢋⠜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⠙⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡏⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢘⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⢈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣉⣙⣏⣩⣏⣩⣍⣩⣽⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠉⠙⠛⠛⠿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣈⠙⢦⡀⠀⠀⢀⣤⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⡙⢄⠀⠀⠑⡺⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢹⣿⣿⣯⡻⣿⣷⣄⠀⠀⠨⡺⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣌⢻⣿⣷⣄⠀⠈⢙⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢀⣤⡶⠖⠛⠒⢸⣿⣿⣿⣿⣧⡙⣿⣿⣆⠀⠈⢑⣽⡿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⠛⠁⠠⠴⠶⣶⠞⣿⣿⣿⣿⣿⣷⡈⢿⣿⡆⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠠⣤⣤⣴⣯⠀⣿⣿⣿⣿⣿⣿⣧⠘⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⡿⠛⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠘⣿⠏⠀⣴⣿⣿⣿⣿⠟⣩⣾⣿⣿⣿⣿⠿⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⠃
⠀⠀⠀⠀⠀⠘⠀⢰⣿⣿⣿⠟⢡⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠲⣿⣿⣿⡷⠂⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⠁⠀⢳⣄⠀⠀⠈⠉⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⠀⠈⢿⣷⣦⣄⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠸⣿⡏⣿⣿⣿⣿⠀⠀⠀⠈⢿⡟⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢻⣿⣿⣿⣧⠀⠀⠀⠘⠇⠀⣰⣿⣿⣿⠋⢸⣿⣿⡇⠰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠻⣿⣿⣿⣷⡀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠙⠻⠷⠄⠈⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⢿⣿⣿⣷⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⢶⣶⣤⣀⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣤⡉⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⡔⠉⡿⠋⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⣄⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡉⢿⣴⣶⣤⢀⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⣿⠋⠁⠀⠀⢀⣴⣿⣦⣄⡀⠀⠀⠀⠀⠘⠁⣠⣸⣯⡛⠻⠟
⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⡀⠀⠀⠠⣤⣿⣿⣿⣿⣷⣶⣶⠏⠀⣀⡀⢉⣹⣃
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣿⣦⠞⠁⠀⣦⣾⢻⣯⡻⢿⣿⣿⣿⣿⠀⠘⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⠀⢹
⣿⣶⣦⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⠃⠀⠀⠀⠈⠻⣿⢿⡻⡄⢻⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣤⡀⣶⣾⡆⣾
⣿⣿⣿⣧⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣆⠓⣿⡈⣿⣿⣿⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽
⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠾⡇⠀⣠⣤⣤⣈⣿⣶⢸⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠈⠿⠞⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠨⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⣻⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⢿⣷⣶⣶⣾⣿⣷⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⣛⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣾⠖⠐⠼⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠎⡀⢀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠆⠸⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⣾⣤⣤⠀⠀⠈⢃⣠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠟⠟⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠄⠐⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠌⣰⠛⣿⡏⢰⣤⣤⣤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣈⡂⠁⠀⠘⢴⣷⠟⡩⠀⠋⠉⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⡴⠃⡀⠀⠈⠁⠀⠀⠀⡠⣴⢿⠻⠁⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣤⣘⠀⡿⠀⠀⠭⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⢹⣹⡗⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣺⡅⠀⠀⢰⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠈⠑⢂⣴⠟⡡⣪⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣟⣥⣀⣴⠃⠟⣿⡜⡱⡿⠫⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣡⣻⠝⢁⠈⠀⠀⠀⠐⠉⢠⡄⠈⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠋⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠀⠀⠐⢀⠀⠀⠖⢀⠀⠠⠠

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣛⣷⠀⣿⣛⣛⠀⣰⢿⣆⠀⣿⠀⢸⡇⠙⢻⡟⠋⢻⣆⣾⠃⠀⠀⣾⣛⡛⠀⢠⡿⣇⠀⣾⡇⠀⢠⡾⠛⢳⡄⢸⣷⡄
⣿⣍⣽⠇⣿⣭⣭⢠⡿⠶⢿⡄⢿⣄⣼⠇⠀⢸⡇⠀⠀⢹⡇⠀⠀⠀⣬⣉⣿⢂⣿⠷⢿⡆⢻⣧⣤⠘⣧⣀⣼⠇⢸⡇⠻


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠚⠋⠉⣉⣀⣤⣤⣬⣍⣉⣛⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠴⠞⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⡀⠀⠀⣠⠖⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣽⣦⣀⣀⢀⣀⣤⡞⠁⡴⠛⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡾⠁⠀⢩⠞⡽⢻⢻⣿⡿⣏⠳⣄⠀⠀⠀⠀⠀⠀⣼⠐⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⣧⠀⠀⠀⠘⠡⠏⢼⠀⠇⠘⠆⠈⣠⣴⣄⣀⣀⣰⠏⠀⠀⠀⠙⠳⢤⣀
⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⠋⠛⢯⡍⢻⡄⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠹⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢹⡄⠹⣆⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⢀⢀⣀⣈⡳⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠰⠏
⠀⡟⢻⠉⢉⣉⣉⠉⠉⢉⣉⡉⠉⢳⠀⣴⠶⣦⠀⣀⡀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣠⠶⠚⢛⡉⢉⠛⠓⠦⣄⠀⢠⣼⢷⣄
⠀⡇⢸⢠⡏⠁⠉⣧⢰⡏⠀⠙⡆⢸⠀⢿⣠⡇⠰⣏⣿⠀⠀⠀⠀⠰⢿⡁⣹⠿⠀⠀⡦⢸⡇⢸⠀⣶⠀⠈⠳⣄⠙⠏
⠀⡇⢸⠀⠳⠦⠴⠋⠈⠳⠤⠾⠃⢸⠀⢸⢹⡇⢰⡏⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠀⡇⢸⡇⢸⠀⣿⠀⡇⠀⠘⣆
⠀⡇⢸⢀⡴⠚⠲⣄⢀⡴⠒⢶⡄⢼⠀⢸⣼⡇⠸⣇⣿⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠀⣇⢸⡇⢸⠀⣿⠀⡇⢸⡇⢹⡄
⠀⡇⢸⠘⣧⣀⣠⡟⠸⣇⣀⣠⠇⢸⠀⢸⢸⡇⢸⡇⣿⠀⠀⠀⠀⠀⢸⠟⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⢻⡇
⠀⡇⢸⠀⣀⣭⣅⡀⠀⣈⣭⣅⠀⣸⠀⢸⢸⡇⢸⡇⣿⠀⠀⠀⠀⠀⣾⢾⡇⠐⠛⢋⠛⠂⠀⠀⠘⢛⡙⠛⠀⢸⠿⣧
⠀⡇⢸⢰⡏⠀⠈⣷⢸⡃⠀⢈⡇⢸⠀⢸⢸⡇⢸⡇⣿⠀⠀⠀⠀⢰⣇⢸⡇⠀⠀⠘⠀⠀⣼⠀⠀⠈⠃⠀⠀⢸⠁⣿⡄
⠀⡇⢸⠀⠙⠲⠞⠁⠀⠛⠶⠚⠁⢸⠀⢸⢸⡇⢸⡇⣿⠀⠀⠀⠀⣾⠙⠶⣧⠀⠀⠀⠀⠀⠻⠤⠀⠀⠀⠀⠀⣾⠞⠉⣇
⠀⡇⢸⢀⡞⠋⠛⣦⢠⡞⠉⠳⡄⢹⠀⢸⢸⡇⢸⡇⣿⠘⢦⡾⢱⡇⣶⠀⠹⣆⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣸⠃⠰⡆⢹
⠀⡇⢸⠈⢧⣄⣤⠏⠘⢧⣄⣴⠇⢼⠀⢸⢸⡇⠸⡇⣿⠀⠀⠀⣾⡀⣿⢸⡇⠙⢦⡀⠀⠀⠉⠁⠀⠀⢀⡼⠃⢸⠀⣧⢈
⣀⣧⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣞⣀⣈⣋⣁⣀⣙⣁⣀⣀⣀⣉⣉⣉⣛⣛⣛⣛⣛⡲⣦⣤⣤⣴⢞⣛⣛⣛⣛⣋⣉⣉
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⡃⠀⠀⠀⠒⢛⣋⣉⠉⠁⠀⢻⣿⡄⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠐⠋⠹⠿⠻⠷⠒⢸⣿⡇⠀⠀⠈⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⢰⣿⢸⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⣠⡿⢡⠎⢸⣿⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⢠⡾⠋⠔⢁⣴⡿⠏⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⣸⡿⠃⢀⡴⢋⠔⢁⣴⠟⠋⠀⣀⣠⣴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠀⢀⣿⠇⠀⡾⡡⢋⣴⠟⠁⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡧⢣⡾⢁⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⡇⣿⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣯⣴⣭⣯⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⡿⣿⣋⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏⢿⡇⠻⢷⣿⣟⣻⣿⣶⣯⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣷⣦⣀⣤⣤⣬⣙⣿⣿⣿⣿⣿⣿⠅⢀⣴⣄
⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⡉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⠟⣻⡇⠀⡀
⠀⠀⠀⠀⢀⡄⠻⣿⣦⣉⣻⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⣿⣿⣿⣶⣶⣾⣿⣶⣿⣧
⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣋⣍⣀⣤⣀⣀⠐⠒⠈⠉⠙⠿⠿⠿⠟⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠈⠉⢁⣽⡿⣿⠟⠙⠉⣀⣽⣿⣭⣤⣄⣀⣄⣩⣭⣽⣿⣿⣿⣿⣾⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢠⣾⡏⢀⣡⣴⣶⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠿⣭⣽⣻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣾⣿⢻⡟⠋⣈⣴⣾⣿⣿⣿⡛⠛⠻⠿⡉⠛⣿⣶⣶⣶⣦⣿⣿⣿⠛⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠈⠁⣿⣿⠿⠃⠉⣤⣾⣿⣿⡟⠛⠋⠉⢉⣉⠳⣶⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠇⠀⢸⣿⠀⣤⣾⣿⣿⣿⣍⠋⢉⣵⣶⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡉⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⠿⠿⠿⠛⠛⢶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢰⢠⣿⣿⣿⣿⣿⣿⡶⠦⢀⣠⣾⢋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⣭⣥⣤⣾⣿⣿⣷⠃⠀⠀⠀⠀⠠⠶⠶⠶⢶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠿⠿⠿⣿⣿⡟⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣿⣿⣶⣿⣿⠿⢿⡀⢻⡇⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⢷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⢃⠀⢿⣿⣿⣿⣿⠁⢴⡄⠹⣎⣷⡀⠀⠀⠀⠀⠉⠛⠧⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠡⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⣿⣿⣿⣿⠀⠀⠁⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣆⠀⠀⢿⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠸⠷⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢸⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣷⡄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⢻⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣿⣿⡟⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠁⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠟⠉⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⠿⠿⢷⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄


⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣵⠗⠺⣯⣥⣈⣉⣭⣍⣡⣄⣉⣤⣉⣥⣬⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⣶⡄⠀⠘⣷⠀⢠⡄⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣧⠀⣿⣿⣷⣸⠀⠸⣧⠀⡇⠐⢿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠳⠿⠛⠁⢹⣿⣿⣿⠀⠀⠛⢇⠀⡸⠀⠈⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣠⣾⡆⠰⠀⢀⠢⠀⠹⣿⣧⠀⠀⠀⠈⠆⠁⠀⠀⠀⣬⣿⣿⣿⠟⠁⣀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⣴⡿⠋⣀⣠⠴⠒⠀⠀⢠⣴⣤⠀⠐⣄⠀⠈⠀⡆⢀⣼⣿⡟⠁⠀⣒⣋⣁⣀
⠀⠀⠀⠀⠀⡾⠀⠀⣾⠟⠁⠈⠛⢁⣠⡴⠞⠃⠸⣯⠿⣧⠀⠈⠷⠀⢀⡇⣸⣿⠟⠀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣸⠇⢠⡞⠁⠀⠀⢠⣶⠿⠁⠀⠀⠀⠀⠘⣿⣽⡇⠀⠀⠀⢸⡇⠛⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⡔⢠⠰⠋⢀⡀⠀⠀⠀⠁⢀⣀⣤⣾⣿⣄⠀⠈⠙⣧⠀⠀⠀⣿⡇⠀⠀⡄⢀⡀⠘⢿⣿⣿⣿⠏
⠀⠀⠂⠐⣈⠀⢠⡿⢡⣴⣾⣿⣿⣿⣿⡿⠟⠛⠋⢠⣤⡄⠘⣧⠀⠀⣿⣿⣄⠀⡧⠈⠉⢉⠀⠀⠀⢠⣶⢂⣠
⠀⠀⠀⠀⠀⢠⡿⠁⢻⣿⣿⣿⡿⠟⠁⠀⡼⠃⠀⠀⢯⡽⠀⠈⠁⠀⠉⠙⠁⠀⣀⡤⠚⠁⢸⣷⣠⣿⣷⣿⣫⡦
⠀⠀⠀⣠⢹⣿⠃⠀⠀⠉⠙⣿⣷⡀⠀⠘⠁⠀⣤⣄⠀⢻⠀⠀⡀⢀⡀⠤⡶⠟⠁⣀⠀⠀⣿⣿⣿⣿⣿⣿⣯⡦
⠀⠀⠀⢠⣼⠏⠀⡠⠂⠀⠀⠘⣿⣷⠀⠀⢀⣼⡿⠃⠀⠈⠆⠀⠀⡮⢤⠊⠀⠀⠢⣿⡄⣼⣿⣿⣿⣿⡿⠟⠉
⠀⠀⢠⣿⠏⢀⡾⠁⠀⣠⡄⠀⠘⣿⡆⠀⣾⣿⠁⣰⣿⠂⠀⠀⠀⠂⣈⠀⠸⣷⠀⠹⣇⠈⠙⢿⡿⠋⣴⣶⢄
⠀⠀⠀⠁⣰⣿⠀⣴⣿⣿⣄⡀⠀⢈⡀⣰⠋⠀⢰⡟⠁⡦⠀⠀⠸⣦⡈⠳⠄⢻⣇⠀⢻⠀⠀⠄⢀⣾⡿⡋
⠀⠀⠀⠐⠛⠃⠀⢹⣿⡆⠀⢁⡴⠋⡰⠁⠴⣤⣈⠀⠐⠀⠀⠄⠀⠈⢿⣦⠀⠈⢿⡄⠘⠀⡆⡀⣼⡿⠅
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⢀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⣷⡀⠀⠈⣴⠟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⢠⣝⣷⣾⣿⣄⣾⣇⠀⠀⢱⣿⣦⠀⢄⡀⠈⠻⣦⠘⣧⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⣽⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⡄⠀⠙⢦⣄⠈⢳⣽⡂⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⠀⣼⠁⢿⣿⡀⠀⠀⢛⠷⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⢸⡟⠀⠘⠿⠗
⠀⣀⡀⠀⡀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⣀⠤⠔⠛⠛⢻⣿⣿⣿⣿⣿⡻⣿⣿⣿⣷⣤⡀
⠀⠀⠀⣞⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⢬⡿⢿⣝⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠘⠶⣄⡀⠀⠀⠀⠙⠿⣿⣿⡄⠀⠀⠈⠓⠯⢟⡿⣿⣿⣿⣶⣦⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠃⠀⢄⡀⠀⠛⠀⠀⠀⠈⠉⠽⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⢀⣤⣆⡀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠁⢀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⢧⠀⠀⣠⠾⠥⠤⠤⠐⠀⣰⠋⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⢣⠀⠈⠻⣿⣿⣧⠰⠇⠀⠀⠀⠀⣄⡰⢁⡞⢠⠆⡞⠀⣴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⡀⠈⠀⠀⠀⢈⣿⡿⠀⠀⡠⠀⠀⠜⠁⠁⠈⢀⠎⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⣼⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠀⠀⠒⠛⠀⠀⠀⠀⠐⢦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡠⠇⠀⢀⣴⣤⠀⠀⢀⣠⣰⠆⠀⠀⠀⡀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢈⠀⠀⠀⠈⠛⠉⠀⠘⢜⠛⠻⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⡞⠁⠀⠀⠀⠀⡄⢀⡉⠉⢀⠂⠀⠀⠀⣤⠭⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠀⠈⠀⠀⠑⣄⠀⠀⠀⠈⢁⡠⠂⠀⠀⠀⠀⢖⡫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⢀⠀⠃⠀⠁⣀⢀⠍⠈⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⢈⢰⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣜⠊⠀⠀⢱⠀⡤⠀⠲⠔⠊⡗⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢻⡇
⠀⠀⠀⠀⠀⠀⠀⡘⠆⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⠇⠀⠀⠑⢄⠀⣀⡀⠀⣀⠠⠇⠸⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡜⠁⢆⡐⢤⡱⠖⣢⣄⣁⢚⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠑⠀⡀⣀⠼⠁⠀⡠⣶⡞⢀⠌⡔⢻⣿⠘⣇⠌⠙⢷⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⡀⠀⢘⠀⠀⠀⢀⡤⠔⠋⠀⠀⡠⠲⠉⣝⣔⡥⢊⠀⢸⣮⠀⠈⣳⢬⡘
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠈⡠⠀⠈⠑⠖⠊⠁⠀⠀⢀⡠⠊⠀⠀⠀⡛⡏⠀⣥⡤⠘⠩⢀⣤⡬⠀⠀⣄⣄
⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠠⠞⢦⡀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠐⢘⣿⠀⠛⠃⢀⠄⠈⠙⠁⠀⢸⢯⠸
⠀⠀⠀⠀⠀⢺⣇⠀⠀⠐⠁⠀⠀⠉⠒⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣄⠀⠀⠈⠀⠀⠀⠀⢀⠌⢧⣂
⠀⠀⠀⠀⠀⠘⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣆⠡⣦⣤⠀⠠⡤⠀⣣⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠋⣀⡁⠈⠐⡾⠇⠀⠈⠁⢪⠸
⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠃⣠⣤⠀⠀⠘⠿⠀⢀⣉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣣⡀⠀⠀⢀⠈⣐⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠻⠏⠀⠀⠈⠉⠀⣴⡄⠀⠀⠹⠛⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠠⣀⠔⠁⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡴⢄⡀⠀⢀⠜⠁⠀⠀⠀⠈⡄⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠠⠙⠋⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠚⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⣚⣓⣒⣒⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⢀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⠉⠉⠉⠉⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠎
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠉⠲⢄⢀⠔⠉⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⣀⡀⠤⠒⠊⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡀⣀⣀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠒⠒⠒⠀⠐⠚⠃⢢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣁⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⣒⣒⣂⣀⣀⣀⣀⣀⣀⣀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠀⠒⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⢰⣷⡆⠀⠙⣧⠀⢶⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡹⣿⡄⢻⣿⣷⣾⠀⢹⣆⠸⠀⡛⢿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⣉⠉⢙⢋⠀⠈⢿⣿⡟⠀⠀⠉⠄⠰⠁⠀⠙⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣼⡟⠁⠁⣀⠈⠀⠈⠟⠓⠀⡀⠀⠈⠀⠀⠀⢠⣾⡿⠛⢋⣡⠶
⠀⠀⠀⠀⢠⠇⠀⣠⣿⠋⠠⡶⠋⢁⣠⡄⢸⣟⣷⡀⠈⢦⡀⠀⡇⢠⣿⡿⠁⣠⣴⣶⣶⣶⣦⣄
⠀⠀⠀⠀⣼⠀⣠⠏⠁⠀⢀⣤⡾⠋⠁⠀⠀⠻⣞⣷⠀⠈⠁⠀⡇⢾⠟⠀⠰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡈⡁⡴⠁⠀⠀⠀⠘⠉⠀⢀⣠⣶⡄⠀⠙⢻⡅⠀⠀⢰⣇⠀⠀⡀⠀⠈⢿⣿⣿⣿⡟⠁
⠀⠀⠈⠖⠁⠀⣼⢃⣤⣶⣶⣾⣿⣿⠿⠿⠗⢀⣠⡄⢻⡄⠀⣸⣿⣄⠀⡇⠙⠛⠂⠉⠉⢉⣴⠀⣀
⠀⠀⠀⠀⠀⣼⠇⢸⣿⣿⣿⡿⠋⠁⣰⠇⠀⠀⢯⡟⠀⠙⠀⠉⠙⠃⠀⣀⠴⠊⢁⣿⣀⣾⣯⣾⣧⡄
⠀⠀⠀⠄⣿⡏⠀⠀⠉⠙⣿⣧⠀⠀⠁⠀⣤⣄⠀⢧⠀⠀⠀⡠⠀⡶⠋⢁⡀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⣴⡟⠀⡠⠂⠀⠀⠹⣿⡇⠀⠀⣼⡿⠁⣀⠘⠀⠀⠰⠐⠎⢀⡀⠫⣿⠠⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠸⠟⢀⡾⠁⣀⣴⠂⠀⠙⠿⠀⣸⠿⠁⣼⡟⠀⠀⠀⡈⠠⣄⠘⣷⠀⠸⡇⠀⠙⠟⢁⣾⡟⠂
⠀⠀⠀⢠⣿⠃⢼⣿⠟⠳⠄⢀⡶⣰⠃⠀⠸⠋⠐⠓⠀⠀⠻⣦⡈⠂⠹⣇⠀⠇⠀⠒⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⡐⠉⠰⢁⠈⠛⠂⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢻⡆⠀⠘⠄⣼⠿⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⢦⣜⣷⡀⢠⡄⠀⠀⢠⣤⠀⠀⠀⠙⢷⡈⢻⡀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁⢙⣿⣿⣿⣿⣾⣷⠀⠀⠘⣿⣇⠀⠲⣄⠈⠻⣌⣧⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣧⠀⣴⢹⣿⡄⠀⠈⢿⣦⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠁⢸⡇⠀⢿⡿

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠦⠀⢀⣾⣶⣦⠀⠀⠀⡀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠘⠉⠒⠀⠀⠀⠀⠀⠘⠀⠀⢠⣠⡤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠃⠠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⠗⣄⠀⠀⠀⠀⣠⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠀⠀⠙⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⡀⠊
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡖⣳⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠐⠘⠃⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠠⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠄⠀⢀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠸⡆⡇⡏⡆⢸⠉⠂⣧⢸⠀⡎⣿⣆⡇⠀⠀⠀⠐⢏⠠⠀⠀⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡟⢣⡖⢧⢃⡷⡁⢀⠑⣴⠺⣸⡀⢇⠙⠹⡇⢀⡔⠀⠀⡀⠋⠀⠀⣴⣿⠏
⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢁⠈⡁⢀⠁⠈⠉⠀⠀⢀⠉⡈⠀⢀⠀⠈⠃⠠⠀⠀⠄⠒⡄⠘⠃⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⡄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠲⠚⠛⠁⠀⠀⠀⠀⠀⠂⢠⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠞⢡⠄⠀⢢⡀⣧⠀⠀⠀⠀⢀⣴⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⢀⡰⠃⠀⠠⠀⠀⠀⢳⣿⠀⠀⢀⠀⠙⠿⠀⠀⠀⠀⠁
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢰⣎⠁⠀⠀⠀⢀⡏⠙⠶⢤⡈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⣐⠦
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢇⠅⠀⠐⠂⠓⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⠀⠁⣴⠊⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠋⠶⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠆⠀⠀⢉⡈⠀⢸⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠰⠿⡿⠇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠀⠈⡁⠀⣄⣤⠀⠀⡆⠀⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠁⠁⠛⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⣋⣩⣭⣬⣭⣉⡙⠛⠿⣷⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡾⠃⣠⣶⡿⠟⠋⠉⠉⠉⠉⠙⠓⠄⠈⠻⣷⣽⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⣴⡿⢁⣴⣶⣿⣿⣿⣷⣶⣄⠙⢦⣄⠀⠈⢿⣧⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣿⣿⣿⢰⡿⢀⣾⣿⡿⠿⠿⣿⣿⣿⣿⣷⡈⢿⣷⡰⡌⣿⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡻⣿⣿⣿⠈⣇⠸⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⣿⣷⣷⠈⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣉⠻⠿⣧⡈⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡿⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⣙⠛⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢀⣿⣿⡿⠁⣼⡿⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⢀⣠⣤⣀⣀⠀⠀⠀⠀⢠⣿⣿⡿⢡⣿⡿⠋⢠⡾⠋⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠉⠛⠿⣦⡄⢀⣿⣿⠟⢰⣿⢏⠀⢀⡡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡇⠀⢿⡟⠛⠓⠆⠀⠈⠀⢸⣿⡟⠀⣿⠃⡆⣠⡾⠁⠀⠸⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠃⠀⢼⣿⣦⣤⣤⠄⠀⠀⠸⣿⡇⣆⢻⡀⢷⣿⣇⢠⣀⠑⠒⢛⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠻⣇⢻⣦⡑⠈⢻⣿⣦⡈⠙⠛⢛⠋⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣶⣄⡙⢿⡿⢷⣦⣬⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⢉⠻⢿⣷⣝⣦⡈⢉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⣄⡀⠀⠀⠀⢻⣷⣌⠻⣿⣷⠈⣿⣶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⣿⣿⣿⣿⠏⢀⣀⣠⣾⢿⣿⡇⣹⡟⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣫⡵⠿⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠾⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⢀⣤⣴⣶⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄
⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⢀⡿⢿⣆
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⣀⢀⣾⠇⠘⣿⡀
⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢹⣿⣿⣿⣿⣾⠃⠀⠈⢻⣿⠄
⠀⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣧⡞⠀⠀⣾⣿⡄
⠀⠀⠀⠈⠙⠻⠿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⢿⣶⣡⠾⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠮⡱⣿⠍⠉⠳⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠈⠊⣝⣚⠛⠛⠆⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⣀⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠻⣷⠆⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠻⢧⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠖⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣿⡟⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⢀⣾⡟⠀⠀⠀⢀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⢀⣾⠏⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⣰⡿⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⣴⡿⠃⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠢⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠈⢿⣝⠛⠉⠉⠻⣾⣹⠆⠀⣿⣿⣿⣿⡀⠀⠀⣾⠁⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⣄⣤⣞⣽⠀⠀⢹⣿⣿⣿⣷⣄⠀⠙⠳⠄⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⡇⢹⢇⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠉⡐⠦⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⠧⣀⣽⠀⠀⠀⠀⠀⠀⠀⢠⠐⢦⡷⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠼⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⠦⡴⠃⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⠀⠀⠀⠀⣠⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⣰⣿⣷⡗⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⣰⣿⣿⣟⣿⡿⠃⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠀⠀⢼⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⡜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⢯⠙⠁⠂⠀⢀
⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢣⠃⠀⠀⢀⠎⠝⠀⠀⠀⠀⠀⠀⣠⣈⠃⡀⠀⠈⠋
⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡌⠞⠀⠀⡠⢋⠌⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣦⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠃⠀⡔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢢⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣴⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠂⢀⣤⣾⣿⣥⡿⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣠⣴⣿⣿⣿⡿⠋⠀⢈⠢⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣤⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠡⠐⠄⠀⠀⠀⠀⣤⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣄⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⡰⠀⠈⢆⠀⣠⣾⡿⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣶⣿⣿⣆⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣾⣿⣿⠟⢄⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢲⣤⣄⣀⠀⠀⢾⣿⣿⡿⠻⡀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣌⡻⠟⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠃⠀⠀⠀⠈⠳⣄
⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⢾⣿⣀⣸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠻⣤⣿⣿⣶⣄⠀⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠛⠂⠈⠻⠿⠿⠿⠿⣶⣄⡀⠀⠀⠈⠑⠲⠦⠤⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⡴⠟⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠙⠷⣄⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣴⠋⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣴⣶⣤⣤⡀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠘⣧⠀⠀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⡗⠀⠀⢀⣴⣿⠃⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠙⠿⣦⣄⣀⣀⣿⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡶⡿⠿⠛⠁⠀⢸⠉⡏⢹⠙⡟⢻⠉⡇⢸⠈⡏⢹⠙⡏⢻⠹⡏⢿⠀⠀⠈⠙⠛⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠹⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠀⠁⠘⠀⠁⠘⠀⠁⠘⠀⠁⠈⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣠⣴⣿⣿⠿⠿⠛⠛⠪⡉⠉⠛⠛⢿⣿⣿⣷⣶⣤⣄
⠀⠀⠸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⡿⣾⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣶⣶⣧⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⠿⠿⠟⠋⠁⠀⠉⠙⠄
⠀⠀⠀⠀⠀⢤⣤⣾⣿⣿⣿⡿⣿⡿⠿⠿⠿⢿⡿⢶⣽⠔⠢⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⣍⠁⠀⢿⡄⠰⠾⠃⣸⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⣒⣶⣶⣶⣆⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡈⠻⠓⠶⠞⠋⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⣽⠙⣿⠈⠙⠻⢿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⢧⣍⣡⡼⠃⠀⡀⠄⢠⡝⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠤⠤⢴⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡀⠔⡰⠃⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠀⡴⠁⠈⠉⠳⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠖⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⠒⠀⠐⠣⡰⠀⢀⡔⡀⠁⣰⢃⡔⢠⠂⢀⡔⣠⠊⠀⠀⠲⣄⡔⣀⠃⣼⠀⣠⢆⠁⢠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠉⠀⠁⠈⠁⠈⠁⠀⡥⠧⠀⠀⠈⠀⠀⠁⠉⠀⠉⠁⠈⠁⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⠀⠀⢤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠠⠆⠁⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⣡⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⢟⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠒⢦⡀⠀⠀⠀⢀⣀⠀⠡⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘⠻⣦⣀⡈⠃⠀⠀⠀⠐⠠⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⣴⣿⠿⠓⠴⠄⠀⠀⠀⠀⠉⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠐⠲⠂⠒⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠐⠙⡄
⠀⠀⠀⠀⠀⠀⠁⢠⠐⠒⠀⢷⣶⡀⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⢠⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡃
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠐⡔⠂⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡴⠋⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠠⠀⠐⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡧⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡎⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⠤⠀⠀⠀⢀⣀⠀⠠⠄⠀⠀⠁⠀⠀⠠⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐
⠁⠀⠀⠀⠀⠀⠀⠀⠐⠈⠅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⢀⣠⢆⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠰⠂⠂⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠄⠚⠀⠀⠀⡐⠚⠖⠁⠀⠊⠟⡔⠒⡆⠀⢠⡀⠀⢀⡀⡀⢀⢀⠀⢠⠀⠈⠀⠀⢀
⣀⣀⣀⣀⣒⣒⣒⣒⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣒⣒⣛⣒⣃⣀⣀⣀⣀⣈⣐⣁⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣁⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⢠⡞⠉⠉⣷⣄⢰⡀⢳⠀⠢
⠀⠀⠀⠀⠀⢸⣿⣿⣗⣹⣿⠨⣃⢸⡇⣱⣠⡆
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠓⠉⠉⠱⡄
⠀⠀⠀⠀⠀⠀⢀⣿⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢠⡟⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⢸⣿⠇⢀⢿⡇⠀⠀⠀⠀⠀⠀⡄⠀⡄⢰⣤⠄⠀⠀⣗
⠀⠀⠀⠀⣿⣽⠈⢯⣿⣆⠀⠀⠀⠑⢤⠛⠶⣓⡦⣙⡳⢤⠔⠉⠆
⠀⠀⠀⠀⢻⣾⣶⡜⡾⣿⡆⠀⠀⠀⠄⠈⢃⡈⢁⡈⣁⡀⠀⠀⠈⣄⣠⣤⠤⠶⠒⠒⣛⣉⣹⣭⣉⡅
⠀⠀⠀⠀⠘⣟⣟⣁⠷⠼⠷⠒⠒⠚⠋⠉⠉⢉⣍⠋⠉⠙⡄⡆⠀⢻⣶⣶⣶⠾⠛⠋⠉⠉⠉
⠀⠀⠀⢰⣿⣩⣤⣴⡄⢀⣀⣀⣤⣦⣾⣾⡿⠛⠛⠛⡃⢹⠀⡆⠀⣸⣿⠋
⠀⠀⠀⠘⣿⣯⣶⣿⣿⣿⣿⣿⡟⠁⠀⠀⡇⠀⣠⢠⡇⣾⣸⣷⣤⠿⠇⠠⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣀
⠀⠀⠀⠀⠈⠉⣿⢻⡿⠀⢋⣿⣷⠀⠀⢠⣷⣰⣿⣾⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢱
⠀⠀⠀⠀⠀⠀⢸⡄⠀⢰⢸⣿⣾⣷⣾⣟⣯⣭⣍⣠⣤⡤⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣧⣾⣦⠣⡻⣿⣿⠛⡟⠉⠉⢉⣉⣉⣩⣭⣭⣉⠉⠳⣴⠀⠀⠀⡀⢀⠀⠀⠀⣶⣸⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣖⠻⣿⣎⣐⣻⣿⢻⡍⠭⠭⢁⣒⣒⡒⠲⢬⣱⡄⣿⡇⠀⠀⠀⢸⡂⣶⢰⣿⣿⡿⠿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⢾⢯⣉⣉⣿⢿⡉⡋⠉⠁⣹⣡⣄⡮⠟⣿⣿⡇⠀⣸⣆⣾⣿⠿⠟⠋⠉⢀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠪⠬⠽⣮⣯⣉⣀⣻⣛⣋⣉⣥⡞⣿⣿⣷⡾⠟⠛⠉⢀⠀⠀⠱⢄⠘⠁⠀⢈⡇⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠖⠂⢾⣏⣂⣾⣽⣿⣿⣿⣍⠀⠘⢛⢿⣓⣆⠀⠀⢸⡁⠀⠦⣤⠈⠐⠁⢸⡇⠀⢀⡤⢒⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠦⠤⢤⣤⣥⣬⣼⡏⢿⣿⣇⣈⡈⠺⣿⣿⡝⣆⠀⠉⠙⢦⠀⠀⣦⣴⡟⣋⡵⠊⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣖⠻⠝⢙⠛⣽⠃⣨⣿⡞⣿⣿⣿⣿⣿⢿⣿⡄⠀⢀⣼⣶⠞⢫⡉⣻⣇⠀⠀⣶⢸⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⠋⠈⠁⠀⠀⠀⠀⠒⣊⣹⣿⣿⣿⣿⣿⣿⣿⠈⢹⣷⠶⠛⠁⢠⠈⢼⣇⣸⡏⢰⣼⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠁⠒⢀⡄⢀⣠⣿⠿⢿⣿⣿⠿⠿⣿⣽⢿⣿⡾⠛⠋⢉⡙⠛⣹⣿⣿⢿⣷⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠾⣿⣿⣛⣉⣛⣛⣋⣉⣠⣤⣾⣿⣷⠿⠛⡋⠁⠤⢉⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢀⣼⣿⣿⠋⠉⠙⠛⠛⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⠿⠟⠛⢿⣿⣧
⠀⠀⣻⣿⡟⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠐⣹⣿⣿⠇⣿⣿⡿⢸⠏⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠟⠉⠀⠏⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠰⠿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠘⢿⡅⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣹⣇⠀⠀⠀⠀⠀⠀⢀⣿⢷⡈⠁⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠈⠛⠄⠀⠀⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠃⠀⠀⠀⠀⠈⣽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⣰⢧⣄
⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣴⣶⣶⣣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣧
⠀⠀⠀⢠⣿⡿⠋⠉⠉⠀⠉⠉⠛⣿⣆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⡼⠛⠋
⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⢠⢾⣿⣿⣿⡯⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣾⡿⠿⠟⠻⠿⠿⠿⠿⣿⡄
⠀⠀⠸⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⢀⣾⣿⣿⡟⢷⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢻⡷⠀⠀⠀⠀⠀⠀⠀⠊⣿⠇⠀⢸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠆⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⢸⣿⣿⠻⠄⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠘⠋⢛⣧⠀⠀⠀⠀⠀⠀⣠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠉⠉⢹⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠘⣿⣿⡿⣿⣿⣿⣿⣷
⠀⠀⠈⣿⣿⣿⡏⠀⢻⣿⣿⡇⣿⠁⢹⣿⣿⠃⠀⠀⠀⣿⣿⡿⣿⠟⣿⣿⠃⠀⠀⠈⣿⣿⡇⠀⠀⠰⢻⣿⣿⣿⢹⠀⠀⢹⠏⠀⠹⣿⣿⣿⡟
⠀⠁⠀⢹⣿⣿⡇⠀⠀⠙⠟⠀⠀⠀⣼⣿⠹⠀⠀⠀⠀⢻⣿⡇⠘⠆⠘⣿⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠈⠇⠣⠀⠀⠀⠀⠀⠀⠀⠠⢟⠟⠀⠀⠀⠀⠈⠘⣿⣟⠄⠀⠀⠀⠀⠀⠀⢘⣿⠛⠁
⠀⠀⠀⠀⠀⠿⣇⠀⠀⠀⠀⠀⠀⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠰⡯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣶⡀⠀⠺⣷⠀⢠⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⡄⠰⣿⣿⣇⢰⠀⢹⣧⠈⣷⠀⢿⣿⣿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⢮⡿⠟⠀⢿⣿⣿⣿⠀⠀⠻⢇⠈⢰⠆⠙⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠉⣠⣦⠀⡄⠒⠠⡀⠈⢻⣿⣏⠀⠄⠀⠈⠆⠊⠀⠀⠀⢈⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣼⡿⠋⠀⣀⣩⠤⠀⠀⢈⣉⡁⠀⠢⡀⠀⠈⠀⡀⠀⢰⣾⣿⠏⠉⣡⠶⠟⠃
⠀⠀⠀⠀⠀⢰⠃⠀⢠⣿⡟⠁⠲⡿⠋⢀⣠⡴⠄⢿⣯⢿⡄⠀⠹⣦⡀⠀⡇⢀⣿⣿⠏⠀⣤⣶⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⢀⡟⠀⢠⠞⠉⠀⠀⣀⣤⣾⠛⠁⠀⠀⠈⢿⣮⣿⡆⠀⠈⠀⠀⡇⢸⡿⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠞⡇⡴⠋⠀⠀⠀⠀⠛⠋⠀⠀⢀⣴⣦⠀⠈⠹⢿⡇⠀⠀⠀⢴⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠐⢻⡰⠇⠀⣰⡖⢀⣀⣤⣤⣤⣶⣾⣿⣿⣿⡦⠀⠀⡀⢻⣆⠀⢠⣾⣿⡀⠀⣸⠀⠶⠦⠌⠛⠛⠛⠋⣠
⠀⠀⠈⠀⢰⠀⣰⡟⢠⣿⣿⣿⣿⣿⡿⠟⠉⣠⠄⠀⢸⡿⢷⠀⠹⡆⠐⠿⢿⡿⠀⠛⠀⢀⡤⠂⣴⡄⢀⣾⢏⣴⡗⡀
⠀⠀⠀⠀⣠⣴⣿⠁⠈⠿⣿⣿⣿⡋⠀⠀⣰⠋⠀⠀⠀⠙⣿⠀⠀⠀⠀⠠⠀⢀⣀⡴⠞⠉⠀⢀⣿⣧⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠘⢱⣿⠃⠀⠀⠀⠀⠸⣿⣷⡂⠀⠁⠀⣠⣿⡦⠀⢸⡀⠀⠔⢰⠖⢈⠝⠉⢀⢴⡆⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⣰⣾⠇⢀⡴⠁⠀⠀⠀⠹⣿⣧⠀⠀⣰⣿⠟⢀⣀⠀⠃⠀⠀⡝⢘⠃⢀⣄⠈⢺⣷⠐⢿⣿⣿⣿⡿⢛⡁
⠀⠀⠰⠿⠏⢠⡾⠁⢀⣴⡖⠀⠀⠙⢿⠀⢈⡿⠏⢀⣾⡟⠁⠀⠀⢀⡁⢠⠄⠀⢿⡆⠀⢿⡆⠀⠙⠿⠋⣠⣿⣿⡶
⠀⠀⠀⠀⣰⣿⠀⣴⣿⡿⠷⢤⡀⢀⣤⢠⡞⠀⠀⣼⠋⠀⠷⢀⠀⠘⢿⣦⡀⠲⠐⣷⡀⠘⡇⠀⠒⡄⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠉⠈⠀⠀⣿⣷⣀⠀⠴⠛⢡⠏⠀⠳⠦⢄⠀⠈⡌⠀⢂⠀⠀⠙⣷⣄⠀⠹⣧⠀⠁⠸⡠⢡⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⣀⠰⣦⡀⠀⢀⠀⠀⠘⡀⠈⠄⠀⠀⠈⠻⣧⡀⢻⣇⠀⠀⣠⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⣤⣽⣷⣽⣿⣄⣿⡇⠀⠀⢸⣿⣷⠀⠠⣀⠀⠘⢷⡄⢻⡄⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⣿⣆⠀⠈⠳⣤⡀⠹⣮⣗⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⠀⣼⠇⢿⣿⡄⠀⠀⠙⡿⠆⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠀⢸⡿⠀⠘⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠀⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠄⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠙⠿⠟⠉⠿⠇⠀⠀⠀⠀⠀⠀⢠⠞⠃⡞⠻⣿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⣘⠋⠉⠉⢀⠀⡀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠁⣰⡿⢛⠁⢶⠀⠀⠀⠀⠀⠀⠻⣿⣶⣾⣿⠇⡀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⣶⡜⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣷⠀⠀⠀⠀⠀⠀⢸⣇⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢳⡀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡹⣿⣻⣿⠏⠀⠀⠀⠀⠀⠀⠈⢹⡏⣴⡔⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠉⠃⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⢻⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡔⣠⡾⣫⡖⣩⡶⠋⠀⠀⠀⠀⢸⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣾⠏⣴⡿⢰⣿⢊⠔⠂⠀⠀⠀⠀⠀⠀⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣧⠀⣿⡏⢰⣿⠁⣿⡇⡎⠀⠀⠀⠀⠀⠀⠀⠠⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡅⠀⠀⢸⡆⠘⠇⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⢀⣀⡤⠀⠀⢪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣠⡾⠃⠀⢰⣿⡇⢸⣿⣿⣇⠀⠀⣴⠾⠋⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⠗⠊⣡⣶⠞⢹⣧⣸⡏⣿⣿⣆⠀⠀⣀⣀⣤⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠉⠁⠁⢀⡄⣿⡿⠁⢹⣿⣿⣆⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡤⠂⠀⣀⣀⣤⣴⠟⢠⢿⡇⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣰⣶⣿⡿⠛⠉⠀⢀⣴⢸⡇⠀⠀⢸⣿⡿⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣿⣿⣿⣷⣶⣶⣿⠿⠃⡼⠁⢠⠀⢰⣿⠇⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠉⠉⠀⣀⣀⣄⣀⣀⣀⣀⠅⣠⣾⠏⠀⠀⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢠⠂⢀⣴⡿⠛⠉⠉⠉⠉⠐⠖⢚⣩⡿⠀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣾⡿⠅⠀⠀⠀⢀⣠⣤⣶⡿⠟⠀⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⣴⣴⣾⡿⠟⠋⠁⣰⠈⣧⠀⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⣿⣿⡿⠉⢀⣀⣴⣾⠟⣼⣿⡆⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣠⣶⡿⠿⠛⣡⣾⣿⡿⣱⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⢀⡆⣴⣿⣿⣟⣿⡿⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣾⢸⣿⣿⣿⡿⠋⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⢫⡄⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠻⡇⢾⣧⣫⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷

⠀⢀⡀⠀⠀⣀⡀⠤⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣀⡀⠀⠀⢀⡀⠀⡠⠤⡀
⠀⢸⡇⠀⠸⠁⠀⠀⠀⢸⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠄⠀⢸⠀⠀⡇⠀⠸⣧⠀⠀⢸⡇⢰⠃⠀⢳
⠀⢸⡇⠀⠀⡆⠀⠀⠀⡘⠀⠀⠉⢹⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡇⠀⠈⣿⠀⠀⢸⡇⠸⡆⠀⡾
⠀⢸⡇⠀⠀⠙⠲⣴⠒⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠃⠀⠲⣿⠀⠀⢾⡇⠀⠙⡞⠁
⠀⢸⡷⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢠⣧
⠀⣾⣷⠈⠆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠀⠈⠀⠀⠀⠀⠀⠿⠀⠀⠺⠇⠀⠘⠟
⠀⢸⡏⠀⠀⠀⠀⢀⣀⠀⠀⠢⡀⢣⠀⠀⢀⠴⠊⠉⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⣠⣤⣤⡀
⠀⢸⡇⠀⠀⡔⠉⠀⠀⠉⠢⡀⠘⢾⣧⠀⠀⠀⢀⣾⣿⣿⣶⣤⣀⠀⠀⠀⠈⢙⣿⡋⠁⠀⠰⣿⠀⢈⣿
⠀⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠙⣦⡀⠀⠀⠈⠉⢻⣿⣿⣿⣷⣆⣀⠀⠈⠉⠁⠀⠀⠀⠙⠛⠛⠁
⠀⠈⡇⠀⠸⣦⡀⠀⠀⠀⣰⠏⠀⠀⠀⡇⠈⠢⠄⠀⠀⠀⢻⣿⣿⣿⣿⣯⠓⠂⠀⢠⠀⠀⢠⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠈⠊⢡⡬⠙⠀⠀⠀⠀⠊⢡⡀⠀⠂⠘⢄⠀⠀⠛⠻⢿⣿⣿⣷⡀⠀⣼⣤⣤⣼⠀⠀⣿⠁
⠀⠀⣾⡀⠀⠀⠈⠉⠉⠁⠀⣀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠉⠙⠁⠀⣿⣿⣿⣿⠀⠀⣿⡆
⠀⢸⣿⣷⠀⢤⣤⣤⡄⠀⠀⣶⠀⠀⠀⣾⣾⡷⠀⠀⠀⠀⣽⣿⣿⣶⢄⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠉
⠀⢸⣿⣿⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⢀⣿⡿⠁⠀⡀⠀⠼⠋⠀⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀⠀⡇
⠀⢸⣿⣿⠀⢸⣿⣿⠁⠀⣿⣿⣿⠀⠀⢸⡇⠀⠀⣧⠀⠀⢀⣤⣿⣿⣤⡀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⡇
⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⣿⠀⠀⢸⠀⠀⢀⣿⠀⠀⣾⣿⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⢸⣿⡿⠀⠀⣟⣿⠀⠀⣿⣿⣿⠀⠀⢸⠀⠀⢸⣿⡇⠀⠘⢿⣿⣿⡿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⣹⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣤⠎⠀⠀⢀⡜⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⢀⡴⠋⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⡏⠁⠀⠀⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠀⠨⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠂⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣤⡾⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⠀⠀⠀⢠⢆⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠌⠀⣠⣴⠏⡁⠂⠈⠃
⠀⠀⠀⠀⠀⠀⢠⠆⠛⠋⢑⠄⠀⠀⠀⠀⠀⠀⠘⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⢀⣴⠟⠁⠀⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⠄⠂⠀⠀⠀⠀⠀⡴⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⣄⠀⢼⠇⢀⣠⣶⠾⣼⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠰⡖⠴⢀⡀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⡠⢫⣿⠃⠀⠈⠙⢿⡿⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣶⣿⠃⢀⡀⢀⡀⠀⣻⣦⡘⡻⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣒⣡⣟⡯⠛⠁⠘⠛⠃⠘⠛⠛⠻⡟⠻⣶⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠉⠙⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠸⣷⡼
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⣀⠀⣠⠖⠁⡠⣤⡀⣤⣺⣿⢧⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠁⢀⣼⠀⠀⠀⠉⢿⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠋⠀⠁⠀⠈⠀⠀⠾⢀⡗⠙⠉⠀⠀⣄⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣀⢉⣽⡀⠀⠀⠀⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠂⠀⡀⠁⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⢀⢄⣾⢟⣋⣛⣀⠠⢇⡇⢠⡇⠀⠁⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡿⣷⠿⠋⠁⠛⣿⣗⣻⣿⡌⣼⡃⠰⠀⠘⢟⡉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡛⢁⠠⠄⠒⠊⢹⡍⣿⡿⢛⣾⣿⡀⠀⠀⠸⣇⣤⣤⠂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠁⠀⠈⠛⢻⠛⠂⠀⠂⠉⠠⡈⢛⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠃⡐⠀⠔⢠⡐⠐⢰⠂⡀⡐⠴⠂