Delivery driver Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣀⡬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⡠⠴⢒⣩⠥⢚⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠤⡖⠏⢹⠉⠉⢠⢀⡤⠜⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠚⣜⣾⡀⢀⡴⠋⠀⠀⢀⡝
⠀⠀⠀⠀⡔⠀⢲⣶⠒⠒⠒⠒⠂⣶⡶⠒⢠⠈⠒⠾⣮⡫⣻⣀⣀⣠⡔⠋
⠀⠀⠀⢰⡇⢀⣸⣿⣀⣀⣀⣀⣀⣿⣇⡀⢸⠀⠀⢰⡏⠙⠾⡭⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⢸⢹⠉⢹⣿⠉⠉⠉⠉⠉⣿⡏⠉⡏⠀⢠⠃⡇⠀⠀⠘⢦⣿⡳⠤⠤⠤⣤⣴⠤⡤⣿⡧⠄⣀⡀
⠀⠀⠀⢸⣸⠀⢸⣿⢀⠤⠤⠤⠤⣿⡷⠄⡇⠀⢸⠀⠘⢄⠀⠀⠀⠟⠋⠉⠉⠉⢈⡷⠯⢏⡁⠛⠀⠀⢸⡇
⠀⠀⠀⢸⣿⠀⢸⣿⢸⠀⠀⠀⠀⣿⡇⢸⡇⠀⢸⠀⠀⠀⠉⠒⠤⢤⣤⠤⠒⠊⠁⠀⠀⠀⠈⡆⠀⠀⢸⠇
⠀⠀⠀⠀⢻⠀⢸⣿⠸⡀⠀⠀⠀⣿⡇⡘⡇⠀⢸⠀⠀⠀⠀⢀⣀⠤⠗⠓⠀⠒⠢⡀⠀⠀⠀⢹⠋⠉⢇
⠀⠀⠀⢴⣚⣒⣚⣛⣒⣚⣛⣛⣛⣻⣟⣒⣓⣒⡦⠿⡉⠉⠉⠁⠀⠀⠀⠀⠀⡠⠀⡇⠀⠀⠀⢸⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⢈⢷⣄⢀⡀⣀⣈⡑⠦⠤⢤⠤⠤⢒⡏⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢹⣷⡀⠤⠽⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⡼⡇⠀⠀⡏⡄⠀⠀⡾⠀⠀⣒⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⢀⠃⡇⠀⢰⠀⢣⠀⠀⡇⠀⠀⣠⠖⠉⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⣇⠀⣼⢐⡮⣀⡰⠁⢀⠎⣀⡠⠤⢤⡤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠶⠶⠶⠶⠶⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⣿⣬⣭⣷⣶⡿⠁⢀⡧⢊⡥⠶⠦⣄⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠩⠭⠭⠭⠭⠭⠤⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⣈⣉⣉⣉⣀⣀⣀⣸⠁⡎⠀⣶⡆⠈⡆⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢏⠙⠯⣉⣩⠝⠉⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠘⠦⣀⡠⠜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠴⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⣀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠎⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢳⣶⣶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢆⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢽⡞⠀⣀⠤⠒⠊⠁⠀⢀⡠⠔⠁⠀⢸⡏⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢈⠟⣈⣇⠀⣀⡠⠔⠊⢹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢦⣤⡷⠛⠉⣉⣀⣀⣀⣀⣸⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠄⡸⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⠌⢠⠃⠀⢸⠀⠀⠀⣤⠤⠤⠤⢤⠤⠤⠴⠿⠧⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠀⡎⠀⠀⢸⠀⠀⠀⣇⣀⣀⡔⠉⠉⠉⠉⠉⠉⠉⠉⡟⡏⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⡄⢱⠀⠀⢸⠀⠀⠀⠙⢄⡸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⡉⢉⡿⣄⠀⠈⡄⢣⢠⠜⠒⠒⢲⠀⠾⣃⣀⣠⣀⣀⣀⡀⣀⣀⣀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡔⣩⠭⣏⢴⠉⢦⠒⡈⠌⠷⠶⠶⠶⠾⠾⠶⠋⠀⠀⠀⣸⢁⡔⣩⠭⣍⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⢇⣛⡼⢠⠂⢸⠱⢌⡒⠂⠀⠀⠀⠀⠐⠂⢢⠀⢀⡴⡥⠤⡤⢧⣛⡸⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠙⠢⠤⠔⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⠢⠤⠔⠋⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋

⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⣀⣀⡀
⠀⠀⢠⣾⣼⣴⣶⡀⡀⠀⢴⠄⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣷⡆⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⣿⡇⠀⠀⢀⢤⢴
⠀⠀⣿⢻⣿⣿⣿⡇⣤⣤⣶⣤⣤⣼⣦⣤⣤⣄⠀⠀⠀⢿⣿⣿⣿⡟⣿⢘⡦⠀⠀⠠⢆⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣧⣤⠀⠀⠈⢷⣄⡀
⠀⠀⠻⢸⣿⣿⡟⣇⠛⠛⠛⠛⠛⠛⠛⣟⡟⠛⠀⠀⠀⠸⢫⣿⣿⣇⠛⠸⢵⠤⠞⢱⠙⠈⠣⠀⠀⠀⠛⣿⣿⡿⠋⣾⣛⡿⠦⠤⠤⢼⣛⡧
⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠑⠒⠃⠀⠀⠀⠓⠚⠁⠀⠀⠀⠀⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⣿⠏⢁⣤⣄⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⠗
⠀⠀⢠⣾⣆⣰⣷⡔⠒⡖⠒⠲⠒⠒⢲⠒⣶⠀⠀⠈⠛⠛⣷⣶⣾⣮⢿⣿⣿⣿⣿⣷⠀⠀⢂⠀⠀⠀⣴⡆⠛⢰⣦⢸⣿⣿⣷⠒⢢
⠀⠀⢸⣿⣿⣿⡏⣷⣿⣿⣿⣿⣿⣿⣿⠀⣻⠀⠀⠀⠀⠀⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⡿⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⡿⡿⣿⡀
⠀⠀⠸⢻⣿⣿⡇⠟⠲⠉⠉⠉⠉⠑⠊⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠸⠓⠊⠀⠀⠀⠀⠘⠖⠀⠀⠀⠀⠗⣿⣿⣿⠸⠋⠀⠉⠉⠉⠁⠈⠒
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⢀⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⢻⣅⡻⠟⣁⠀⢠⠤⠤⢤⠤⠤⣄⠀⠀⠀⠀⠀⠀⢈⠻⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⣀⣤⣄⡀
⠀⠀⠀⢸⣧⣮⣿⣧⣥⣤⣤⣤⣤⣤⣬⣴⠆⠀⠀⠀⣼⣿⣵⣼⣿⡖⣶⣶⡆⠀⠀⠒⣜⠃⠀⠀⠀⢰⡟⠈⠁⢿⡆⣥⣅⢀⣁
⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⡟⠛⠛⣿⣿⣿⡇⠀⠀⣴⣿⣼⣿⣿⣿⣇⣿⣿⣿⡆⠀⠀⢹⣷⣄⠀⠀⣾⣁⣀⣀⣸⣗⣻⣿⣿⣿⣿⣷⣦⣤⣷⠶
⠀⠀⠀⢸⣿⣿⡇⢩⣿⠛⠛⠛⠛⠛⢻⣿⠁⠀⠈⠻⢿⣿⣯⣿⡏⠁⠻⣥⠟⠛⠛⠛⠸⣧⡟⠀⠀⠘⢸⣿⣿⡯⣧⠟⠙⠹⣤⡟⠙
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠘⠿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠠⠀⠀⠀⠀⠀⠠⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⢻⣧⡀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠷⠲⣾⣿⣇⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡏⠀⠀⠀⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣠⣴⣦⣀⡀⠀⢀⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠟⠛⠉⢁⠉⣽⠉⠙⠻⢿⣦⡀⠀⢰⠀⠀⠀⠀⠀⣻⣦⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⡖⠀⠀⠀⠉⠛⣛⣫⣤⣶⣾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣁⣤⣴⣶⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠟⢻⣿⣿⠇
⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⣠⣤⣶⡿⠟⠛⠉⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⢸⣿⠿⠶⠦⠴⣶⠄⡰⠃⠀⠈⠻⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢑⡾⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⢀⡀⢀⣖⣀⣰⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⢸⣧⣼⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⡈⠀⠉⠁
⠀⠀⢀⣠⣴⣶⣾⣿⣿⣇⡀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⢀⣾⡿⠿⢿⣿⣿⣿⣿⡈⠳⣶⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⣿⣧⡀
⢰⡿⠁⢀⣀⡀⠈⢻⣿⣿⣷⣎⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⢸⣿⣭⣭⣽⣭⣽⣽⣭⣭⣿⣿⡇
⣿⡇⠀⢾⣿⣿⠀⠀⣿⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠾⠿⢿⣿⠛⠻⣿⣿⡟⠙⢻⡏⠁
⠘⣷⣄⠀⠉⠀⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⠁⢀⣠⡿⠁
⠀⠀⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣟⣋⣀⣀⣀⣀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠠⠄⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠜⠀⠀⠀⠆⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡟⠛⠟⠛⢻⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠛⠛⠛⠛⢻⠛⣛⡛⠛⣇⡄
⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠸⢿⡀⠀⠀⠀⣸⢀⣬⣥⠀⡿⠇⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⣀
⠀⠀⠀⣶⣶⣴⣿⣶⣒⡄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⡞⠉⠉⠹⠟⣆⠀⠀⠀⢠⣾⡀⠘⠿⠿⠷⠂
⠀⠀⠀⢹⣿⣼⡿⣿⠘⣦⣀⠀⠀⠀⣿⡁⣹⣿⣛⣛⣛⣿⣏⠈⣿⠀⠀⠀⣾⣳⣿⣿⣿⣿⣻⡆⠀⠀⢘⣯⡉⠠⣴⣾⣆
⠀⠀⠀⠘⠯⠽⠛⢻⠖⠯⠿⠀⠀⠀⠩⣿⠉⠉⠉⠉⠉⠉⠉⣽⠍⠀⠀⠀⢻⡟⠛⠛⠛⠛⣿⠂⠀⠀⡼⠃⢿⠀⠙⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⢴⡾⢿⡷⣈⣋⣁⡀⠀⠀⠀⢀⣤⣀⣀⣀⡈⡍⡀⠀⠀⠀⠠⣄⣠⡌⣁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠧⠀⠀⠙⠛⠛⠛⠛⢻⣇⣆⣿⠋⠀⠀⠀⠛⠛⣒⣂⡷⠶⠾⠖⠂⠀⠀⠀⢰⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣦⣤⣴⣦⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠛⠋⠙⠛⠘⠙⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋

⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⠀⠀⣴⣦⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠆⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣇⠀⢰⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡏⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢃⣀⣀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢉⣉⣁⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⠿⠿⠿⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢆⠀⠀⢠⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⢐⢹⣷⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡀⠀⠹⣆⢀
⠀⠀⠠⠘⠻⢷⣿⣾⡟⠃⠀⠀⠀⠀⠀⠀⢀⠄⠢⢀⠈⠁⠉⠁
⡀⠀⣀⠀⢀⣀⣿⣀⣀⡀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡆
⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠸⠿⣿⠿⠿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠄⠀⢐⡄⠀⠠⠄⠀⣲⣠⣴⠈⣿⠁
⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠄⠂⠁⠸⣿⡿⠀⣿
⡇⣶⣶⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢄⠀⣿⢀
⡇⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠇⢤⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠤⠀⢁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⡀⠀⠀⠀⢠⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠉⢐⠄⠀⠀⠀⠀⠀⠡⠀⠠⢤⠄⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠆⠀⢀⣴⣶⣶⡶⠄⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠉⠉⠍⡉⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⠐⠃⠉⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⣿⣶⣄⠑⠄⠀⠀⠐⡀⠀⠰⢀⠰⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢁⣴⣶⣄⣹⣿⣦⣨⡄⠀⠀⠈⠀⠈⠉⠈⠉⠉⠉⠁⠉⠀⠀⠀⠁⣼⣦⡄⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠸⣿⣿⡿⠛⣿⡿⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢼⣿⣿⡟⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⣁⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣌⣡⣴⣿⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣯⣥⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡤⢄⡀⢠⠤⠄⣀⠀⢀⢠⡀⠀⡀⣠⠤⠀⡤⢄⡠⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⡹⢸⠒⠂⣿⠀⢸⠀⢧⣰⠃⡷⠒⠀⡗⢾⡁⢹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠄⠹⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠉⠉⠉⠀⠈⠁⠀⠉⠉⠀⠁⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠒⠂
⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⣀⡀⣀⣀⣴⣿⡿⠟⠻⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣰⣿⡿⠿⠿⢿⣿⣦⡤⣤⠤
⠀⠻⠿⠯⠽⣿⡏⢰⣾⡦⢺⣿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣿⠁⣾⣷⠒⣿⡿⣏⠍⠭⠬
⠀⠀⠀⠀⠀⠹⣿⣦⣉⣡⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣼⣩⣴⡿⠃
⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣷⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣦⣦⣶⣽⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠂⠒⠢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠄⠠⠀⠈⠁⠀⠀⠀⣀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡔⠀⠀⠁⠀⠠⠈⠄⠀⠀⠀⠀⠀⠀⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⡀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠠⠈⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠙⠛⠉⠉⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⡄⡎⠉⠉⠁⢠⢠⣷⣶⢠⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢛⡻⠟⡋⠀⢰⣶
⠀⠀⠀⠀⠀⠣⠷⠶⠶⠶⠶⠏⡼⠛⠨⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡄⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣟⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣤⣤⣤⣤⣿⡧⡀
⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⡿⠙⠋⢉⡉⢩⣙⣿⣶⣶⣶⣶⣲⣲⣶⣶⣶⣖⠀⠀⠀⠀⣸⣿⣿⠿⠿⠿⠿⠏⠄⠐
⠀⠀⠀⠀⠀⠀⠐⢿⣛⡟⠻⠒⢠⣏⡹⣼⣿⠇⠯⠀⢇⣿⣏⠟⠛⠛⣿⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠀⠐⠀⠂⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣦⣄⢀⣤⣤⠆⠰⠀⠛⠛⠛⠛⠃⠚⠀⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⡴⢶⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⢤⣀
⢠⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣸⣷⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⢓⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣾⠷⠶⠶⠶⠶⠶⣾⡗⠀⣼⠃⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠉⠉⠉⠉⠉⠁⣈⠀⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉
⢿⡶⠶⠶⠶⠶⠶⢾⡇⢀⣿⠀⠈⣷⣤⠙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⢀⣴⠟⠛⠛⢶⡄⠀⠀⠀⠀⢸⡇
⣾⠷⠶⠶⠶⠶⠶⢾⡇⢸⡟⠛⠛⠿⣬⡿⢿⣼⢿⡇⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⣼⣧⣤⣤⣤⣬⣿⡄⠀⠀⠀⢸⡇⣴
⢿⡟⠛⠛⠛⠛⠛⢿⡟⠛⠻⣶⢦⣤⠀⢹⣦⡿⢾⡇⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⢦⡄⢸⡇⠻
⠈⠛⣿⠟⠛⠛⠛⠛⠛⢻⡟⠋⣰⡏⣠⣿⡟⠁⣾⣁⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢿⣭⣭⣽⠂⠀⠀⢿⣭⣭⣿⢸⡇⢸⡇
⠀⠀⣻⡿⠛⠛⢷⣄⠀⢸⣧⣴⣿⣴⣿⠏⠀⣸⠏⠉⠻⣆⠀⠀⠀⠀⣿⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣿⢸⡷⣾⣇⣀⣀
⠀⠀⣿⣤⣤⣤⣤⣿⣤⣼⣯⣤⣤⣤⣤⣤⣴⡟⠛⠛⢻⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⡯⢸⡇⢸⡏⣻⠟
⠀⠀⠈⠻⢦⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠩⣿⠀⠁⠈⠀⠉
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠋
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⣶⠶⠶⣶⠶⠶⠶⠶⠶⣶⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣤⣤⣤⢴⣿⡤⠤⣿⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⡀⠺
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠘⠶⠴⠟⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⡇⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇⣿⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠈⢁⡄⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⠀⠀⠀⠀⠀⠀⠸⣯⣽⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⣾⠁⣿⠀⣿⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢿⠀⠀⠀⠀⣤⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⣿⠀⣿⠀⣿⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠠⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢰⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣀⣀⣿⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⢠⣤⠤⠄⣤⠤⣤⡀⣠⡤⣤⡀⣤⡤⣤⡀⠀⢠⣤⢤⣄⢠⡤⠤⠄⣤⠀⢠⡄⣤⡀⢠⡄⣤⡤⠤⢠⡤⣤⡠⣤⢀⡤
⠀⠀⠀⢸⡟⠒⠸⣇⣀⣸⠗⣿⣀⣸⡇⣿⣀⣸⡇⠀⢸⣇⣀⣿⢸⣗⣒⠨⣗⣀⢸⡇⠸⣧⣾⠁⣿⣓⡂⢸⡷⣾⠃⠘⣿⠁
⣶⣶⣶⢾⣷⣶⣶⣾⣿⣿⣶⣾⣿⣿⣶⣿⣿⣷⣶⣶⣾⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⣷⣶⣿⣷⣶⣿⣿⣿⣾⣷⣾⣷⣶⣷⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⣄⣰⣿⣀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠞⠋⠉⠀⠀⠉⠙⠳⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠃⠀⠀⠀⣿⣿⠀⠀⠀⠘⣧⣴⠄⠀⠀⠀⢀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡇⠀⠀⢀⣤⣼⣧⣤⡀⠀⠀⢸⣇⡀⢀⣤⣀⣿⠷⠶⠿⠶⣾⣟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣸⠋⣡⣀⡽⠋⠀⠀⣠⣤⡀⠀⠈⠻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢹⣆⠀⠸⠿⠿⠿⠿⠇⠀⣰⠟⠿⠉⡿⠁⠀⠀⠀⠻⡿⠃⠀⠀⠀⢹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢻⣦⣤⣤⣠⣤⣴⠛⠿⠆⠘⠻⡇⠀⠀⢠⣾⣿⣿⣿⡆⠀⠀⢈⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠙⢳⣦⠿⣣⡈⠛⠀⠀⠀⠀⣶⣿⡀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡴⠟⠛⠛⠛⠛⠿⣇⣠⣄⠀⠀⠀⠀⣠⣿⣤⡈⠋⠛⠛⠛⠃⣠⣾⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⠋⠀⠀⢠⣶⣦⠀⠀⠈⢻⣅⣀⠀⠀⠀⠈⠀⢸⡿⠛⣶⡶⠺⣿⡁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⣈⣛⣋⡀⠀⠀⠀⢻⡋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⣸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢷⡀⠀⢸⣿⣿⣿⣿⡇⠀⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢦⣈⡈⠉⠉⣈⣠⠾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠙⣿⠋⠹⠷⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠿⠿⠿⠷⠖⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⣑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢶⣸⢹⣏⡷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢔⡋⠉⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢒⣒⣒⣲⣿⡭⢽⣲⣦⣄⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢤⠶⠒⠚⠛⠉⠉⠉⠉⠁⠀⠈⣷⠀⠀⠈⠉⣿⠙⠲⢤⡀⠀⡴⢋⡉⠙⢦⠀⠀⢰⢋⣶⢤⠈
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢸⠶⣦⠀⠀⣏⡀⠀⠀⢸⠃⣇⠈⢻⠆⣸⠀⠀⠸⡀⠓⣟⠝
⠀⠀⠀⠀⠀⢹⠀⠀⠘⢋⣩⣭⣍⡀⠀⠀⢸⣄⠉⠀⣸⠛⠓⠀⢠⠏⠀⠈⠓⠒⠒⠁⠀⠀⠀⠈⠒⠒⠋
⠀⠀⠀⠀⠀⠸⡆⠀⠐⢿⣤⣤⠼⠃⠀⠀⣸⠾⠃⢀⣿⡆⠀⣠⠏⠀⣀⣀⠀⠀⠀⠀⡤⠒⢒⠲⣄
⠀⠀⠀⠀⠀⢀⡇⠀⠀⣠⠶⠒⢲⣄⠀⣀⣿⡀⠀⡜⠀⠀⡰⠃⢠⠋⡴⣀⡙⡄⠀⢸⠁⢧⢏⡳⢸
⠀⠀⠀⠀⢠⣯⣿⠤⠤⠿⠷⠶⢾⣁⣏⠉⡿⠁⣰⠃⢀⡼⠁⠀⠸⡘⠻⠴⢃⠇⠀⠀⠳⢬⣀⠤⠋
⠀⠀⠀⢀⡿⣫⠖⠚⠉⠉⠉⠙⠒⠲⢬⣙⠳⣤⡇⢠⡞⠀⠀⠀⠀⠈⠑⠊⠁
⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢮⠳⣯⢳⠀⢀⡤⠒⠢⣄
⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢹⡿⠀⢸⡀⠸⠀⢸
⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠑⠒⠒⠁
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⣀⣀⡀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠓⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⠠⠴⠤⠤⢀⣀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣶⣾⣿⡿⠿⠿⠿⠶⣮⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠿⠃⠀⠀⠀⠙⠂⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡄⠰⠶⠀⡤⠀⠛⠂⠀⠉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢧⠀⠐⣖⣒⣒⡽⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⢬⣍⣭⣤⣾⣁⣀
⠀⠀⠀⠀⠀⡴⠶⠶⠖⠒⢲⠖⠶⢤⡀⠀⠀⣠⠖⠙⠮⠓⠚⠰⠀⡀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠘⡇⢀⡜⠁⢠⢂⠤⠤⡤⠤⢤⡏⠙⠢⡀⠈⢦
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡌⠃⢀⣀⣇⣾⠀⢠⡇⢸⠒⠀⠑⠂⢩⢹⠀⢀⣸⡀⢸⡀
⠀⠀⠀⠀⠀⡼⠤⠤⠤⠤⠧⢼⡿⠿⡿⠿⠧⣿⡇⠘⢄⣀⠀⢀⠼⣸⣶⣿⢦⡼⡾⣤⡀
⠀⠀⠀⠀⠀⢳⠒⠒⠒⠒⠒⠚⠶⠶⡷⠒⢲⠻⢧⠤⠤⠤⠤⠤⠕⠺⣌⠉⣻⣾⡇⢡⢱
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠘⣄⠀⠀⠐⣶⡀⠀⠈⢳⡇⠉⣷⢬⠟
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣼⠴⠤⠬⠷⣄⠀⠘⣏⡷⠀⣸⢿⡈⢹⡀⣇
⠀⠀⠀⠀⠀⣀⣝⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢺⡏⠀⢰⣿⣄⣰⡟⢠⡇⢀⠏⠉⠉⠓⠦⡀
⠀⠀⠀⠀⢺⣸⣁⣀⡇⡠⠀⠀⠀⠀⠀⠤⡀⠐⠂⠐⢸⣥⣤⣾⣿⣿⣴⠁⡼⠀⢈⡸⡤⠤⠤⡤⠕
⠀⠀⠀⠀⢰⠋⠤⠤⣜⡞⠉⣽⣿⣍⠉⣷⢸⠠⠤⠀⠸⠿⠿⠿⠿⠜⠃⢠⡇⣠⠏⣧⢻⣶⠀⢹
⠀⠀⠀⠀⠀⠉⠉⠉⠉⢇⠀⠻⠿⠟⢀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢣⡀⠻⠿⠟⠀⡸
⠀⠀⠀⠀⠀⠀⠠⠤⣤⣬⣷⣤⣤⠴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⢦⣤⣤⢾⠥⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣺⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠋⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣿⠿⣿⢿⣷⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠀⠀⠀⢀⣤⣤⣶⣿⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⣿⠟⠁⣠⣧⡀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣭⠶⠷⢮⣷⣄⡀⢨⣿⣿⠟⠉⢉⡟⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣷⣶⣶⠸⢿⣿⡟⠛⣿⣿⡟⠛⣻⣿⠿⠁⣤⣀⣤⡄⠀⠘⣏⣟⠙⢦⣴⠋⢹⣼⢡⣾⣿⡏⠙⢲⣿⣄⣀⣿⣿⡿⠇
⠀⠀⠀⠀⠀⢀⣰⣿⠯⣤⣞⠹⣿⣦⢀⣿⣷⣦⣀⣇⣠⣶⣿⣇⢠⣾⡿⡛⣻⣿⣶⢄⣦⢷⣴⠋⠉⢢⣼⣹⡏⠹⣿⣿⣄⣼⠁⢀⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠙⣿⣦⣜⣉⣽⣿⠃⠈⣿⠋⠛⣿⣿⡟⠋⢻⡏⢸⣿⣤⠛⢣⣼⣿⠀⣤⠙⣭⡛⠟⣭⡟⣡⡄⠀⢾⡿⣿⣿⣿⣿⡿⠟⠟
⠀⠀⠀⠀⠀⠀⢶⡟⠛⢿⡿⠛⢹⡷⠀⠸⣇⠀⣨⣭⡀⢀⡾⠀⢶⡉⢿⠿⠿⠟⢀⡖⠹⣇⠈⣤⣤⡀⢀⡿⠀⠀⠐⣆⠀⠈⠛⠋⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠈⢧⢰⣿⣿⡄⡼⠁⠀⠀⠹⣆⠿⠿⢇⡾⠁⠀⠈⣧⢰⣿⣿⠄⡾⠁⠀⢹⡌⠿⠿⢃⡾⠁⠀⠀⠀⠹⣆⢼⣿⣷⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣭⣭⣼⠃⠀⠀⠀⠀⢻⣷⣶⣿⠃⠀⠀⠀⠘⣧⣭⣭⣼⠃⠀⠀⠀⢻⣷⣶⣿⠁⠀⠀⠀⠀⠀⢹⣬⣭⣥⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⠀⠸⣿⢿⡏⠀⠀⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⠸⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢁⡴⠖⠲⣄⠀⠖⠒⢦⡀⠐⣶⠒⢶⡖⠲⣆⠰⣖⠀⢲⡖⠀⣲⠆⣠⠖⠲⢦⡀⢲⡶⠖⠀⡇⣰⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣟⠚⠒⠛⢰⡏⠉⣻⡇⠀⡇⠀⢸⠇⠀⡿⠀⠹⣤⡟⢹⣰⠏⠀⣧⠀⠀⣸⠇⢸⡇⠀⠀⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠉⠛⠛⠁⠈⠙⠛⠛⠃⠘⠛⠀⠛⠃⠘⠛⠀⠀⠙⠀⠀⠋⠀⠀⠈⠛⠛⠉⠀⠛⠃⠀⠘⠛⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢿⡿⣿⣿⣶⣶⣦⣤⣤⡄⢠⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣘⣿⣯⣲⣦⠀⠀⠀⠀⢀⠄⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠈⣧⠀⠀⢠⣿⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⢿⣿⣿⣆⣿⡇⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣽⣿⣿⣿⣿⣿⠷⠚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⣩⣿⣿⣿⣾⣶⡶⢲⣾⡑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⣾⣿⣿⣿⣿⠟⣸⠃⠈⠻⡿⣄⠁⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⡀⠋⢠⡄⣤⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⢀⣴⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣽⣯⠀⠀⣿⣿⡟⡇⣿⠿⠛⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⠀⢿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠛⢹⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠀⢠⣤⣿⢸⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢈⣹⣻⣿⣿⣷⡶⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⢀⠠⠀⠀⠀⢀⣿⣿⣼⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣤⣮⣿⣿⣿⣿⣿⣿⣷⣂⣀⡤⠖⣾⣿⣏⢻⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⢷
⠀⠀⠀⠀⢶⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣽⣿⠿⢛⣁⣀⣀⣿⣿⣷⡬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠛⠛⣿⣯⣍⣉⣉⣉⡙⠛⠛⠻⠿⡯⠔⠚⠋⠉⠉⣙⡻⣿⣿⣧⢀⡀⢰⣁⠀⠀⠀⡆⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠐⠿⠿⠿⣿⣿⣿⣻⣻⣶⣶⣦⣤⣄⣀⡀⠐⠉⠁⣀⣿⣿⣿⣧⡬⠙⠿⠿⡿⠀⣂⣠⡤⠞⠋⠁
⠀⠀⠀⠀⢸⣶⣦⣤⣀⣀⡀⠊⠉⠉⠛⠛⠻⠿⣿⣯⡤⠴⣚⣉⣽⡿⠿⣿⣿⣿⣿⣿⣻⣟⠁⡿⠟
⠀⠀⠀⠀⠙⠿⠷⠾⣯⣿⣿⣿⣶⣶⣦⣤⣀⣤⠼⠗⠊⢉⣉⡠⠼⠁⠀⠀⣌⠁⠀⠀⢠⡿⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣧⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⡼⢽⡧⠀⠼⣏⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣻⡗⢀⡚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠷⢦⣯⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⡤⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣒⣒⣢⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠄⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣶⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣿⣿⣿⣯⡀⠀⠀⠀⢻⡗⠀⠀⠀⡀⠈⣻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣟⠀⠀⢾⡷⢾⣿⣶⣿⠚⠿⠚⢿⣿⣿⠟⠀⠀⠀⠀⣤⣶⣶⣄
⠀⠀⠀⣁⠀⠀⠀⣠⣴⣶⣤⣿⣿⡿⣿⠟⠻⠿⠃⠀⠀⠀⢴⣿⠿⣿⠆⠀⠐⢾⡟⠡⣿⣦⡀⠀⢸⠏⠉⠛⠻⠄
⠀⠀⠀⠙⣷⡀⢸⡿⠋⠉⠉⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠈⢷⣦⡻⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣴⣦⣀
⠀⠀⠀⠀⠀⠀⢻⣿⣧⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠻⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⡄
⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⣤⡉⠁
⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣥⣤⣤⣤⣤⣼⣿⣧⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣯⣬⣿⣿⣧
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢉⣉⣉⣉⣉⣉⣉⡉⠉⠉⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣠⠞⠛⠛⠛⠛⠻⠿⠛⣿⠀⣿⣇⡇⠀⠀⠀⣴⣄⠀⣴⠦⠀⡆⠀⢠⠀⡄⢀⡄⡶⠦⢰⣦⡠⡄⢠⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣰⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⠀⠀⠀⣿⢘⡇⣿⡄⠀⡇⠀⢸⠀⣿⢸⠇⣧⠄⢸⡾⠃⢻⣾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⡇⠀⠀⠀⣿⡼⠃⣿⣀⠈⣇⡀⢸⠀⢸⡿⠀⣇⣀⣾⠻⡄⢨⡇⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢷⣿⣤⣤⣤⣤⣤⣤⣤⣤⣽⠀⣿⡇⡇⠀⠀⠀⠈⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠭⠭⠿⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠉⣿⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣒⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⢀⣿⠀⠀⢀⣴⣿⠟⠛⠉⠉⠙⠻⢿⣗⢄⠀⣿⣧⡧⠤⠤⠤⢤⣤⣤⣤⣤⡴⣿⠟⠋⠉⣉⡉⠛⠻⣮⡳⣀⣀⣀⣀⣀⣀⣸⡇
⠀⡀⠀⠀⣿⣸⣿⣀⣀⣞⣿⠃⠀⣔⣭⠿⣷⣆⠀⢹⣿⣆⣻⣇⣇⠀⠀⠀⠀⠀⠀⠀⣘⣼⡏⠀⡔⣩⠶⢯⡷⡄⠘⣿⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢻⣟⣛⣛⣛⣻⣿⠀⠸⣿⣇⠀⣸⢿⠀⢸⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⡄⠀⣇⣧⣀⣠⠇⡇⠀⣿⣟⣛⣛⣛⣛⣿⣿⣿
⠀⡀⠀⠀⠸⣷⣶⣶⣶⣶⣿⣆⠀⠙⠛⠿⠗⠁⠀⣼⣯⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣷⡀⠈⠛⠿⠷⠊⠀⣰⣿⣭⣭⣭⣥⣤⣤⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣴⡾⠟⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⠖⠛⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣤⣀⠀⠀⢸⣧⣅⣀⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡱⠃⠀⠀⠀⢈⡷⠀⣼⡳⢤⣭⣩⣥⣼⣿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢿⣍⡛⠒⠒⢛⣿⠇⠀⢻⣙⠓⠒⠒⠚⣿⡟⠀⠀⢀⣠⡴⢖⣫⣍⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠾⢬⣭⣭⡭⣿⡇⠀⠀⠀⠈⠉⢛⣛⣭⣥⣴⠖⠋⠉⠀⠀⠉⠀⠀⠙⠂⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⣶⣛⣡⣤⠤⠶⠒⠛⠉⢙⢿⣿⣿⣷⣄⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣧⡀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⣿⣿⣷⣤⡘⡇⠀⠀⠀⠀⢀⣠⠶⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⡀⠙⢦⡀⠀⠀⠀⠀⠈⠻⢶⣄⣈⠻⣿⣿⣿⣦⣀⣠⡴⣞⣩⢴⣚⣽⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⣝⢦⣀⠙⠳⣌⠲⣄⣀⣀⡀⠈⠉⣁⣈⣿⣿⣿⣿⣷⡿⢟⣛⡭⢷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡙⢮⡳⣍⠳⣄⠈⠳⠬⠥⢶⣒⣿⢿⣿⣿⢿⣿⣿⡿⢖⣻⡭⠗⠚⣩⢵⡖⠚⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡳⣌⠳⠖⢚⣋⡭⠷⣚⣩⠵⣖⣻⣿⠿⠟⠉⠀⠀⠀⠀⣷⣍⣀⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡓⣛⣭⠴⣒⣯⠵⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣞⠷⢦⣬⣉⣭⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡭⠵⠚⠋⠁⠀⠀⠀⠀⢀⡤⣶⠖⠒⠲⢦⡀⠀⣯⡛⠒⠶⠒⢚⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣁⣀⣀⣀⣠⣿⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣬⣉⣉⣥⠼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠿⣯⠉⢉⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⣨⢷⡋⠁⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣷⣦⡴⢿⣿⣁⣀⣻⣾⣿⢡⣤⣼⣷⣴⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⣡⡜⢻⣿⡎⠉⠛⠻⠋⠋⢠⣶⡿⣫⣽⣭⡹⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⡄⣾⣿⣿⡠⢻⠃⣴⣿⠇⠀⠀⠀⠀⠀⢠⣿⡇⢿⣯⣽⡿⣹⣿⡁⣠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⣱⡿⢋⣿⣿⣿⡿⡟⣯⣴⣦⣴⣀⡀⠀⠀⢹⣿⣦⣭⣯⣷⣿⣿⣇⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡿⠋⠀⠀⣀⣿⢻⣧⡶⣾⣿⣷⡆⠀⠀⠀⠛⠉⠻⠻⣿⣬⣿⣷⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢼⡇⢾⣏⠶⣩⣷⣻⣟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢿⣆⠀⠀⠀⠀⠀⠐⢿⣾⡛⠻⣛⣷⣿⠉⢀⡀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠈⣿⠃⠀⣀⣀⣶⣤⣼⡍⠛⠻⠏⣛⣸⣷⣾⠿⢿⣿⣶⡆⠀⠀⢰⡿⠋⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⢰⡿⢠⣤⣿⣿⣿⣿⣿⣿⡟⠀⣀⣿⡿⠻⣷⡀⠀⣨⣿⣿⣿⠀⢸⣿⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⣶⣿⣶⣿⣤⡄⢠⣿⣿⣿⠁⠀⣿⣿⣿⠟⣹⣿⠁⠀⣈⣷⡾⠋⠁⢹⣿⠗⠈⠛⣠⣀⣌⢛
⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⠋⠀⠀⠀⠈⢻⣷⡆⣹⣿⣿⣷⣾⣿⣿⠿⠃⢙⣿⣶⡿⠋⠁⢻⣦⣀⣾⡿⠦⣤⡿⠛⠛⠛⢿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇⡀⠀⠀⠀⠀⠀⣿⡷⠀⠈⠿⠛⣿⠛⠛⠀⠀⠈⠙⣿⣷⣦⣤⣤⣿⣿⠟⠇⢺⣿⠀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⣴⣿⣿⣦⢿⣿⣇⠀⠀⠀⣀⣼⡿⠇⢻⣧⢀⣴⣶⣄⠀⣿⠇⠀⠀⠁⠈⠛⠙⣿⡏⢩⣴⣦⣝⣿⣄⢀⣄⠀⣠⣿⡋
⠀⠀⠀⠀⠻⢿⡿⢋⣼⣿⢻⣿⣿⡿⣿⠛⠋⠀⢸⣿⠸⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣿⣿⡿⠈⢿⣿⠿⡿⠛⠃
⠀⠀⠀⠀⢠⣶⣶⣾⣿⣥⣾⡿⠋⠀⠀⠀⠀⠀⠈⠻⣷⣬⣭⣵⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣭⣭⣤⣶⡿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⢀⣿⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⣿
⠀⠀⠀⣼⡿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠙⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢛⣋⣭⣭⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⣠⣴⠾⠛⠉⠁⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠟⠋⠀⠀⣀⣠⣤⣤⣶⣶⣶⣤⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⠴⠟⣉⣠⣤⡶⠾⠛⠋⠉⠁⠀⠀⠀⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣤⣤⣤⣤⣤⣤⣴⡶⠾⠛⠋⢉⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⣠⣴⣿⡟⠿⢿⣿⣿⣆⠀⠀⠀⠀⣤⣤⡀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣰⣿⣿⢡⡆⣷⣾⣿⣿⣿⠀⠀⠀⠘⢿⣿⡿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣄⡀⠀⠀⠀⢀⣿⣿⣿⣤⡅⣤⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣿⡷⠀⠀⠀⠘⣿⣿⣿⡙⠇⢋⣼⣿⠟⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⡀⠉⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⠿⠛⠁⠀⢀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠉⠉⠉⠀⠀⠈⠉⠉⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣠⣤⣤⣤⣶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⢂⠔⣈⡔⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⣪⢚⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡤⠔⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠰⠑⠁⢼⠀⠀⠀⠀⠀⠀⠂⢀⣶⠶⠞⠺⢿⡖⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⠄⢀⠃⠀⠀⢸⠀⠀⣤⡤⠴⢖⠛⠙⡇⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠈⠰⠠⠆⠼⠶⢯⡇⠀⠀⢸⢸⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⠤⠖⢈⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠉⠀⠀⡘⠀⠀⠐⠗⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠸⠀⢸⡇⠀⠀⢸⠀⢠⣷⠦⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠠⠀⠠⠀⠀⠀⢠⠰⠀⠀⠃⠀⠀⠀⠀⠐⠀⣹⡇⠀⠀⣸⣿⣻⡿⢶⣾⣯⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠂⠐⠨⠀⠀⠠⢰⡈⠋⠉⠙⢹⠀⢹⡗⠀⢨⣿⣿⠿⣧⣾⣯⣽⣿⡇
⠀⠀⠀⠀⠀⠸⡇⠄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⣖⣊⡇⣁⣾⣷⣸⢶⣷⡿⢛⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⡇⠀⠈⠉⠛⡟⡟⠛⠊⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠐⠀⠄⡀⡗⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠀⠉⠀⠤⠁⠀⠀⠀⠠⡄⠂⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠈⠠⠀⠀⠀⠀⠄⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠀⠳⣀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠡
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠠⠖⠂⠠⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⣶⣶⠟⠁⠀⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠠⠈⠀⠒
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠁⢦⡀⠀⠀⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⣠⡾⠋⠀⠀⠀⠠⠀⠀⠰⡀
⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠰⠀⠀⠀⣠⡾⠍⠁⠀⠀⠀⠀⠀⠀⠊⠂⠉⢦⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠐⠻⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⡴⡾⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣠⣥⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠡⠴⠛⠒⠴⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠿⣿⣶⣷⠄⠀⣠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠛⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⣡⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠆⠀⠀⠊
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢻⣿⣿⣧⠀⢀⠘⢋⣿⣿⣿⣿⣿⠃⠀⢻⣧⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠈⡃
⠀⠀⠀⠀⠀⣸⣿⠿⣿⣿⣿⢸⣿⣿⣿⣾⡿⡷⠟⠛⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠸⠄⠀⢠⡃⠀⠠
⠀⠀⠀⠀⠀⣿⣿⣤⣿⣯⣤⠈⣿⣿⠙⠋⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠙⣋⣿⣿⣿⠀⡿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠀⡗⠿⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠸⡷⠾⠿⠿⢿⡇⠙⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠛⠛⣿⣷⣦⣤⣀⣈⠄⠇⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣤⣴⣶⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⢿⣿⡿⠁⠈⠈⣗⣀⣤⣴⣾⣧⣤⣤⠤⠤⠀⠐⢲⠒⠂⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣿⠟⠁⣼⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡥⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⣿⠙⠿⣿⣻⡿⠟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡃⠀⠀⣿⡉⠀⠀⠀⠀⠿⠿⠿⠿⢿⡟⠋⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⡆⠀⡸⣿⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣿⣴⣧⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠇⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠛⠛⠛⠉⠉⠙⢯⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣀⣀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡦⠀⠀⠀⢰⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠀⠀⠀⠋⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠀⠀⠀⠀⠀⢀⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠛⠋⠁⠀⡘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠈⠣⡀⠀⠀⠀⠀⠀⠀⠉⠠⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣧⠀⠀⠈⠂⠄⠀⠀⠀⢀⠀⠀⣈⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠑⣄⠀⠀⠀⢂⠀⠔⠋⢀⠰⣸⣿⣿⣿⣿⡿⣳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠀⠀⠀⠈⠃⠀⠀⠘⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠄⢸⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⠃⡀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠓⠓⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠶⠶⠷⠶⠶⠶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣥⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣰⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⡄
⠀⠀⠀⠀⠀⢰⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢻
⠀⠀⠀⠀⢀⠇⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻
⠀⠀⠀⢠⡗⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇
⠀⠀⢠⡍⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄
⠀⠀⢸⠇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⠛⠀⠀⠀⠰⡗
⠀⠀⡇⠀⢠⡴⠁⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠂⠀⠀⠁⣤⠇
⠀⠀⡀⢰⡁⠀⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠀⠈⢁⠀⢹
⠀⠀⠙⢾⡇⠀⠀⠉⠃⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠁⠀⠀⡿⢂⡜
⠀⠀⠀⠈⢣⠀⠀⠛⠖⠦⠤⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠁⢀⡼⠛⠋
⠀⠀⠀⠀⠀⠙⡀⠒⠶⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠒⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣛⠛⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⣿⣿⣷⣶⣶⣤⣤⣤⣤⣽⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣥⣥⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣫⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⣾⡏⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣆⡀
⠀⠀⠀⠀⣿⡇⢠⣿⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⢻⣧
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣠⠟⠉⠉⠉⠉⠉⠉⠁⢀⣿⣀⠀⠀⠉⠉⠉⠉⠉⠉⠙⣆⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⢸⣿⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⢸⣿
⠀⠀⠀⠀⣿⡇⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠀⠀⣿⡇⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠀⠀⢻⣧⣼⣿⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠈⠻⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠁⢸⣿
⠀⠀⠀⠀⠀⠈⠹⣿⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣃⣀⣙⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣁⣀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠎⠀⠀⡃⠀⠀⠀⡆⠀⠀⢨⠀⠀⠀⢐⠀⠀⠱⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣠⣮⣤⣤⣤⣮⣤⣤⣤⣧⣤⣤⣤⣥⣤⣤⣬⣤⣤⣤⣼⣤⣤⣤⣵⣤⣤⣤⣵⣄
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡸⢇⠀⠀⡨⢇⠀⠀⢨⢇⠀⠀⡸⢅⠀⠀⡸⢇⠀⠀⠨⢇⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠀⣠⣱⣪⣥⣤⣵⣪⣥⣤⣭⣨⣤⣬⣅⣬⣤⣤⣵⣊⣅⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣧⣠⣤⣤⣼⣧⣤⣤⣄⣼⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⠿⢿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⢀⡀⣰⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣆⢀⡀
⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⢀⣠⠤⠤⣤⠤⠤⣤⡤⠤⣄⣀⡀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⠛⠋⢉⡽⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣆⣀⣠⣀⣴⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠦⠤⠴⠶⣦⠀⠀⠀⠀⠀⠀⣀⡤⠾⠿⡿⠿⠿⠿⢿⠿⠧⣄⠀⠀⠀⠀⠀⠀⢯⡉⠉⠓⠋⠉⠉⢳⡖⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢳⣤⣤⣤⣄⡼⠁⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⣳⣄⣤⣠⣤⣤⡏⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⢿⠿⢿⡿⠷⣄⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣠⠿⠿⡿⠿⠿⠟⢿⡀
⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠤⠾⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⣠⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⡼⠁⠀⠀⠀⠀⢰⠋⠉⠉⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡞⠉⠉⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠓⠦⢤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠙⠶⠤⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⣠⠇⠀⠘⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡀⣀⡼⠀⠀⠀⠀⠀⢠⡇
⠀⠂⠀⢹⡀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠹⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠘⠥⠟⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣅⣀⠤⠀⠀⠀⠀⠀⠀⣀⣤⠞⡁⣀⣀
⠀⠀⠀⠀⠈⠁⡤⠛⢉⡽⠋⣩⠟⣋⠿⢋⡵⠋⣠⠞⢩⠗⢲⠶⣶⠶⠶⡶⠶⢲⡶⠖⡶⠖⣲⠗⣲⠟⣱⠋⣠⢏⡽⠓⠖⢲⠖⣶⠋⢡⠋⠞⠟⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠁⠘⠁⠀⠉⠀⠘⠁⠀⠉⠴⢣⠞⠁⠠⠞⠀⠰⠋⠀⠞⠁⠞⠁⠰⠃⠀⠀⠀⠀⠈⠀⠀⠐⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠂
⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⡀⠂⠀⠁⠖⠒⠛⠛⠛⠟⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠐⠻⢦⠀⠀⠀⠀⠀⠀⠑⠂⠄
⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡤⠐⢤⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣼⡻⠀⢀⡞⠀⡠⣶⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢾⡄⡔⠀⢻⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡿⠃⠀⠀⠈⣧⢁⠀⠀⢻⡞⡆⠀⠀⣠⣤⣶⣦⣤⡤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢦⠀⠀⢀⡤⡞⠋⠀⠀⠀⠀⠀⠀⢸⡆⡆⠀⠀⣷⣷⣶⣾⠏⠙⢩⣿⠟⠟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠸⣶⡺⠟⠉⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣶⡶⣿⣿⡟⠿⠻⣷⠀⠈⠳⣌⢂⠀⠉⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⢸⣁⣀⢀⣀⠀⠀⠀⠀⣰⡿⠿⠊⠋⢻⣿⣿⢸⣿⢂⢀⢡⡀⠀⠀⠈⠈⢢⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠺⠛⠛⠉⠁⠀⢀⣤⣼⣯⡀⠀⠐⠀⡀⢻⣟⣾⠻⣧⠠⠀⠡⠡⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⠀⣆⠀⠀⠀⠀⢀⣼⣿⡿⣿⣷⣄⠀⠀⠀⠈⠉⢉⠣⡘⣧⠠⠠⠡
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⠤⢤⣌⢳⠀⠀⠀⣾⣿⠉⠀⠉⢿⣝⣆⠀⠀⠀⠀⠀⠀⠁⠘⢧
⠀⠀⠀⠀⠀⠀⠀⢠⢟⡆⠀⢰⣏⡏⠀⢀⣴⣿⡉⢆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⢀⡟⣸⠀⢠⡟⣸⢀⣶⡿⡟⡩⢷⡱
⠀⠀⠀⠀⠀⠀⣸⢣⠃⠀⠈⣹⣷⣾⣿⡄⠘⡓⡀⠧
⠀⠀⠀⠀⢀⣤⣿⣶⣶⣶⣿⣿⡿⠛⣿⠙⡄
⠀⠀⠀⢀⡾⣿⣿⣿⢂⠙⢝⣿⠣⠨⡿⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⡀⠀⡠⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⣶⣤⡀⢀⠋⠉⠀⠀⢀⣴⡎⠁⠀⠀⠀⢀⡠⢖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⠿⣿⣇⠀⠀⢹⣾⣷⣶⣶⣶⣶⣐⠨⢬⣭⣼⣷⠁
⠀⠀⠀⠀⢀⡠⠤⠤⠒⠒⠈⠉⠉⢱⣦⣄⡈⠉⠒⠚⢿⣿⣿⠿⠿⠿⣮⠭⣐⣻⣿⣻⡄
⠀⠀⠀⠀⢸⣍⡒⠢⢄⡀⠀⠀⣀⣀⣈⣥⣤⣥⢺⠏⠁⠀⠤⢅⣲⣾⣋⣑⠒⢾⣿⣿⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠈⢆⡀⠀⠀⠈⢙⣻⣿⣿⣿⣿⣿⣿⣸⡤⣤⡴⡮⣐⣚⣿⣖⠢⠭⣿⣿⣿⡎⢭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣓⠢⠄⣀⠻⣿⡿⠿⢋⣉⣤⣿⣿⢁⣠⣒⠠⢭⣿⡧⠬⣙⣻⣿⣻⡧⣐⣺⣷⣾⠇
⠀⠀⠀⠀⠠⡦⣉⣑⠢⠤⠀⠀⠀⠈⢠⣿⡿⣿⣿⡏⣉⠍⠧⢭⣙⣿⣟⡁⠠⢬⣿⣿⡃⠲⢿⣿⠿⠃
⠀⠀⠀⠀⠀⣧⠀⠈⠉⠓⠒⠤⢄⣀⠭⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠉⠑⠢⠭⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠄⣀⣀⣒⣫⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉





⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠿⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠶⠶⠿⣼⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣽⣷⣤⣄⢀⢄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠁⠀⠀⣷⠢⠎⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢷⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢬⡆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡇⠀⢠⠂⠀⠀⠀⠀⠀⠀⡏⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢐⠄⡸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⠀⡔⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢜⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠊⡀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢎⠎⣽
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⣸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⡐⢈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣧⠀⠀⠀⠀⠀⠀⢀⡾⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠊⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⠦⣄⣀⣀⣠⡴⡟⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⢥⣾⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢪⢺⡆
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠆⢀⠔⠀⠀⢀⠔⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡱⢣⢾⡇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠐⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⡰⢣⠞⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⡡⠃⣧
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡱⠃⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠱⢁⢺⡇
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠳⠦⢼⠇
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠻⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠠⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⢫⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⠻⡁⠈⠀⠀⠀⠀⢀⢠⠄⢒⡒⠒⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠊⠃⠀⠤⠼⡀⠜⠊⣥⠀⠀⢹⣧⠈⠐⢄⠀⠀⠀⠠⡂⢀⣄⣀⠐⢬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢐⡦⠀⠉⠐⢳⠄⠘⣿⠤⠄⠀⠂⡀⢰⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⠁⢀⡈⡶⢤⣀⣥⠄⠊⠙⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠩⠀⠅⠀⠀⠀⠀⠈⠏⠂⠴⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⠂⠀⠰⠀⠀⠀⠀⠐⠂⠀⠀⢀⣈
⠀⠀⠀⠀⢠⣴⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢠⡆⠀⣮⠲⠦⠖⠀⠂⠀⠀⠀⠉⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠁⢂⡀⠀⠀⠀⡠⠃⠄⡉⠃⢀⠒
⠀⠀⠀⠀⢿⣿⣿⠛⠟⠀⠀⡠⡅⠀⠀⠔⠀⠀⠠⠀⢠⠂
⠀⠀⠀⠀⠀⠙⠻⢶⠀⠀⠀⣄⡃⠠⠈⠀⠀⡠⢁⠄⠁
⠀⠀⠀⠀⠀⠀⡀⠜⠂⠀⠀⠀⠀⠀⠀⠀⢌⠕⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠂⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢡

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢀⣀⣀⠀⠀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⣀⡻⣿⣿⠟⣁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣤⣬⣛⣛⣥⣤⠀⠀⠀⣠⣬⣛⣟⣫⣤⠰⣿⣿⣿⡆⣠⣬⣻⣟⣫⣄
⠀⠀⠀⠀⣾⣿⣿⣶⣶⣿⣿⣷⠀⠀⠀⣰⣶⣭⣿⣵⣶⡽⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⢿⣵⣽⣛⣯⣶⣝⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⠿⠛⠁⠀⠀⠻⠿⣿⣿⠿⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀⠙⠛⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⠀⠀⠀⣴⣿⣶⠀⠀⠀⢰⣾⣷
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣽⣿⣵⡄⠀⢠⣮⣿⣯⣦⠀⢠⣬⣿⣯⣦⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⣼⣿⡄⢠⣼⣿⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣺⣿⡛⠛⣻⣿⡛⠛⣻⣿⡀⠀⠀⠀⠀⠉⠉⣵⣾⣽⣷⣮⠉⢹⣾⣽⣷⣾⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡗⠸⣿⣿⡿⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠀⠸⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠍⠀⠉⠁⠀⠀⠈⠀⠀⠀⣀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠔⡄⢀⡀⠀⠀⠐⣂⠀⠊⠁⠁⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠐⠀⠀⢀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠶⠦⠖⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠉⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⠒⠒⠉⠉⠉⠁⢸⠀⠀⠀⠀⠀⠘⠰⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠤⠤⠬⠽⡄⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠐⠁⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠒⠂⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢀⠀⡀⠀⠀⠈⠀⠀⠠⠄⣀⠀⠀⠀⠀⠘⣄⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⣀⡀⠄⡀⠀⠀⠀⠉⠐⠒⠠⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣤⣀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢄⡀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠒⠤⠄⢄⠀⠠⠉⢁⠠⠭⠑⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢣
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣄⣤⣤⣤
⣿⣽⣭⣭⣭⣬⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣯⣿⣿⣿⣿⣯⣿⣿

⠀⠀⠀⠈⢶⣄⡀
⠀⠀⠀⠀⠸⣿⡿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⢿⣷⠀⠙⠻⢿⣶⣦⣤⣤⣤⣤⣤⣶⣾⠿⠟⠛⠋⠉⠁⠉⣹⣿⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠘⣿⣇⠀⠠⡀⠀⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣶⣿⣿⣿
⢰⣦⣤⣤⣀⡀⢹⣿⡄⠀⢺⣕⣦⣤⣀⣀⣀⣀⣠⣤⣲⠶⢿⣲⢶⡆⠀⣿⡿⠋⠁⣿⡇
⠀⠹⣿⣿⡛⠿⢿⣿⣿⡀⠘⣾⣷⡄⠈⠉⠙⠛⠉⠁⠀⠀⢸⣿⢼⠄⠀⣿⡁⠀⢸⣿⠁
⠀⠀⠈⢿⣷⡄⠀⠈⢻⣷⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⠀⠀⣿⡟⠀⣼⡏
⠀⠀⠀⠈⢻⣿⣄⠐⡜⣿⣇⠀⢻⣿⣧⠀⠀⠀⠐⠂⠀⠀⠘⣿⣿⠀⠀⣿⡇⠀⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠹⣿⣆⠈⠽⣿⡄⠀⠟⠋⠀⠀⠀⠀⡟⡄⠀⠀⠉⢹⠀⠀⣿⠃⢸⣿⠀⠉⠉⣿⡟
⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⢿⣿⡀⢠⠀⠀⠀⠀⠀⠱⡇⠀⠀⠀⢸⠀⢀⣿⣀⣾⡏⡟⢀⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡈⢻⣧⠀⢇⠀⠀⠀⠀⠀⠤⠂⠀⢀⣴⣿⠿⠛⠛⠿⢿⣦⣾⣣⣭⣿⡿⠶
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣄⢻⣇⠈⡄⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣯⡀
⠀⠀⠀⣀⣴⣾⠿⠛⠋⠉⠙⢿⣆⢻⡄⢑⣀⣤⣶⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⣼⡿⢋⠁⠀⠀⠀⠀⠉⠲⣿⣷⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⢸⣿⠃⢸⠁⠀⠀⠀⠀⠀⢰⣿⠥⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠈⣿⡆⠸⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢰⣠⣾⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀
⠀⠀⣠⣼⣿⣿⣦⣄⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣦⣤
⢀⣾⡿⢋⠉⠈⠉⠙⠛⠿⣷⣾⡇⢀⡤⠶⠶⠶⣄⠀⠀⢀⣿⠿⢷⣦⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠉⠙
⢸⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⣿⠀⠀⣼⡟⠙⢷⡈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⣿⡆⠸⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢀⡿⠀⣸⡟⠀⠀⣸⠇⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣇⠓⠤⠤⠔⠛⢀⣼⣟⠙⡛⢛⣉⣠⣿⠏⢻⣆
⠀⠀⣨⣿⠿⠛⠟⠛⠟⠿⠿⠿⠻⢿⣶⣶⣶⠾⠛⠉⠉⠉⡽⠯⠭⣝⢿⣧⠈⢿⣤⣀⣀⣀⣤⣤⡴⠖⠋⠁
⠀⢰⣿⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⢸⢈⣿⡆⠈⢿⡏⠉⠉⠉
⠀⢸⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠑⠒⠒⢋⣾⡿⣿⡄⠘⢿⡄
⠀⠈⢿⣧⡀⠓⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⡶⠶⠶⠶⣶⣶⡾⣿⡋⢱⡘⣿⡄⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠻⢷⣶⣶⠶⠾⠟⠛⠛⠋⠉⠉⠀⡄⠀⠀⠀⠀⠁⠈⢙⢹⣧⠀⢡⠹⣷⡀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠢⠐⣫⣾⠇⠀⠈⣆⢻⣷⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠟⠛⢩⠆⠀⠀⢸⡆⢻⣧⠀⠈⢻⣦⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⢀⣀⣤⣴⡾⠟⣿⡇⢸⠀⠀⠀⠤⠔⠀⠀⠀⢻⡈⢿⣧⠀⠀⢻⣷⡀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⣾⡏⠨⣿⠇⢀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠹⡾⢷⠈⣿⣧⠀⠀⠹⣿⣾⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⠀⢠⣿⠀⢸⣷⡆⠀⠀⠀⠀⠀⣀⣘⣘⣇⠘⣿⡀⠀⠀⠘⢿⣦⠈⠙⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣸⡏⠀⠸⣿⠀⢸⣿⡇⠀⢀⡤⠚⠉⠀⠀⠉⠙⠆⠸⣿⣿⣿⠿⠿⢿⣧⠀⠀⠀⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠃⠀⢠⣿⠀⢸⠷⠥⠖⠉⢀⣤⣶⣾⣿⣿⣿⣶⣤⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣾⣿⡟⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠁⣾⣧⣤⣶⡾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⠛⠛⠋⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣄⡀⠀⢠⣾⣯⣤⣤⣤⣿⣧⣤⣤⣬⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⢸⣿⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣧⡀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠙⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⡏⠀⠀⠀⠀⠈⠙⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃

⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⠤⠀⠀⣴⣥⡀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠞⠁⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⢠⡄⠀⠀⡄⠀⠀⠀⠁⢶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠂
⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠰⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⢠⣴⠢⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠘⠠⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠈⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠄⡀⠀⠀⠀⡠⠢⠤⠁⠀⠀⠀⠒⠰⠀⠀⠀⠀⠄⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠊⠂⠀⡀⢈⠔⠀⠈⠢⡑⠢⠐⠍⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠑⠁⠁⠀⠀⠀⠀⠈⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠏⡅⡊⠉
⠀⠀⠑⠂⠠⠤⠄⠀⠀⠀⢀⡀⠀⠀⠀⣀⣼⣠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠇⣇⡇⣀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠳⠿⠆⠆⠢⠄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡎⠀⠀⠀⠀⠀⢀⡄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⡶⣶⡶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠒⠂⡴⣒⠀⠠⠔⠂⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠒⠓⠀⠒⠬⠀⠼⠟⠒⠀⠁
⠀⠀⢀⠤⣄⠒⠶⢲⢀⠒⣤⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠠⡤⣀
⠀⠘⠈⠉⠉⠁⠐⠌⢋⡍⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠠⠂⠀⠐⢀⡇⢀⠀⠀⠀⠀⠀⠀⣋⠐⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠥⡙⠉⢀⠀⠀⠈⠁⠀⠠⠄⠀⣈⡲⡄⢠⡞⠀⠀⠀⢿⠛⠂⠒⠚⠹⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⢂⠕⠀⠀⠀⠀⠠⠀⠀⠈⠁⠉⠀⠀⠈⠀⠀⠀⠈⢉⠰⠻⢛⢶⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠃⠀⠀⠀⢀⠀⠈⠂
⠀⠀⠀⠀⠀⠘⠲⢤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠩⡽⠉⠈⠓⣠⡄⣀⠀⢀⢀⣐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠧⠒⠊⠀⠙⢶⣝⠅
⠀⠀⠀⠀⡀⣀⡠⡤⠤⢠⠀⠃⠐⠦⠄⢹⡐⠿⠐⠢⠤⢤⡁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⣀⠀⡉
⠀⠀⠀⠏⡀⢈⣀⡀⢴⠶⠕⠀⠀⠀⠀⠀⠈⠀⠒⣲⢒⡒⠈
⠀⠀⠈⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠠⣤⣴⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠛⠀⢄
⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠴⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡦⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣛⣋⣭⣍⣙⣛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠶⠛⠉⠁⣀⡀⠉⠉⠛⢦⣙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡾⠁⠀⠀⣠⠶⢟⠻⢦⡀⠀⠀⠙⣦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠁⠀⠀⢰⡏⠀⣿⣧⣤⡷⠀⠀⠀⠘⣇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠻⣦⣀⠙⠳⣄⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⢰⡟⠛⣿⡇⠀⣿⠀⠀⠀⢀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⣆⠀⠀⠀⠻⣤⣝⣡⡴⠏⠀⠀⢀⡾⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠳⣄⡀⠀⠀⠛⠋⠀⠀⣀⣴⢟⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠘⠷⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣝⣓⡶⠶⠶⢖⣛⣭⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇
⠀⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠙⠻⣿⣦
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣴⣿⠿⠛⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣾⡿⠟⠛⠿⣿⣦⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣤⣤⣼⣿⠏⠀⠀⠀⠀⢹⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣴⣿⡟⠀⠀⠀⠀⠘⣿⣧⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⣿⣇⠀⠀⠀⠀⣼⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣧⡀⠀⠀⠀⣰⣿⡟⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁





⡿⢿⠿⡿⡿⣻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠈⢳⠀⠀⡠⠄⢿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠸⡆⠉⣹⠀⡜⠀⠀⠈⡦⠊⠈⠱⡀⠀⢠⠊⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠻⠖⠁⠀⠈⢢⠀⢰⠀⠀⡀⠀⡇⠀⣊⠑⣠⣎
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢢⠀⡀⠀⠀⠀⣄⠀⠳⡏⢀⠀⡇⢠⠃⡔⠞⠉⠀⣁⠀⢀⠐⠂⠲⡄
⠀⠀⠀⠀⡠⠤⢤⣸⠤⡴⠁⠇⠁⢄⠀⠀⡏⡧⡀⠱⡟⢠⠇⡼⠀⡧⠂⢀⠀⡏⠀⢘⢄⣀⡀⡇
⠀⠀⠀⢸⠀⠀⢠⢻⢢⢨⠏⠀⣠⣀⠑⠲⢇⡇⠱⣀⡅⡘⢀⡧⠊⣣⢔⣋⣰⠥⠆⠀⣉⠈⣨⠁
⠀⠀⡔⠉⢂⣤⠎⣤⣀⡉⠀⠠⣇⠀⠑⠢⠴⣑⣤⣶⡿⠟⢍⠉⠭⠤⠳⠤⢤⠤⠄⣼⡀⠀⠈⡆
⠀⢸⠁⠀⠀⠀⠀⢀⡨⠐⠒⠛⠊⠀⠀⠈⢉⠽⠫⡀⠕⢶⡰⣉⠒⠧⢀⣀⡎⠦⣀⣡⡭⠦⢼⠃⠈⢆
⠀⠈⢇⠀⠀⠀⢀⡎⠀⠀⣼⡤⠤⣔⡲⠚⣣⠊⢠⢃⠘⡆⠉⠊⠑⢦⡀⠈⠉⠉⣵⠋⠐⢄⠀⠀⠀⡸
⠀⠀⠈⢆⠀⢰⢡⢣⠖⢉⠭⠔⠈⠁⣠⡞⡡⢤⠃⠈⡄⠘⡄⠀⠘⣄⣙⣯⣐⠒⣿⡄⢀⣸⡄⡀⣰⠁
⠀⠀⠀⠘⡗⢶⢸⡇⠀⠀⠀⠀⣠⢊⠎⡜⠀⠀⡇⠀⢱⠀⠘⢄⢰⠋⠀⠈⡆⠀⠀⠀⠀⣇⡇⣧⠇
⠀⠀⠀⠀⡇⠈⠄⢷⣄⠀⠀⠀⣧⡇⠀⢧⣀⣠⠇⠀⠈⡆⠀⠈⠛⣦⣀⡴⡃⠀⠀⠀⠀⠉⢀⡏
⠀⠀⠀⠀⡇⠀⠰⡆⢹⠓⠂⠉⢸⡇⠀⠀⠉⠒⠈⠐⢄⢸⡀⠀⠀⠈⠉⠀⠑⢦⠀⠀⠀⢹⠋⠇
⠀⠀⠀⠀⠃⠀⠀⠀⡼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠸


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⢶⣶⣾⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣩⣿⣿⣥⣶⠶⠶⠾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡶⢧⡀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⡾⣷⣦⣞⣱⠃⠈⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣟⡿⣿⣟⣿⣿⣶⣇⣀⡟
⠀⠀⠀⠀⠀⠀⢠⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⢻⣿⣿⣿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡛⣾⣿⣳⢿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⡪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡟⢃⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣻⢡⣿⣗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠉⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣛⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⠻⣿⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁


⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠣⠤⠔⢑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠒⠁⠀⢀⡀⠀⠈⠢⠤⣄⣀⠖⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡔⠁⠀⠱⠀⠀⡴⢪⡇⢸⡱⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⡀⠀⠘⠤⠤⠊⠀⠀⠳⣄⣘⠖⢤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⢈⡆⠀⣀⡀⠀⡴⢊⡶⠝⠀⠁⠉⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠕⠈⠉⠁⠘⠵⢮⠀⠈⠆⠂⢀⠅⠀⡎⢉⠆⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⡐⠉⠑⠀⠀⡎⠀⠀⠀⠀⠈⠑⡄⣈⡁⡠⠬⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠤⠀⢠⠃⠀⠐⠤⠔⠁⢀⢉⠆⠀⠀⠀⢀⡀⣍⠀⠑⠁⠀⠀⠀⢠⠤⠋⠑⠊⡆
⠀⠀⠀⠀⠀⡌⠜⡠⡾⡍⢑⠀⡤⠤⣀⡅⢔⢄⠀⠀⠀⠘⣃⡬⠀⠀⠀⠀⠀⠀⡴⠀⢎⢉⠆⢨⠃
⠀⠀⠀⠀⠀⢣⠑⢴⠁⠟⠀⠉⠀⠀⠀⠀⠈⠪⡒⠀⠐⠂⢸⡆⠒⠤⣀⣀⢔⡲⠀⢇⠤⣀⡔⠚⢠⢖⣄
⠀⠀⠀⠀⠀⠀⠱⡀⢸⢈⡑⠠⢐⡩⠃⠀⠀⠀⠀⠀⠘⠀⢸⠁⠘⠐⠒⠒⠁⠀⠀⠀⢔⠤⡀⠀⠳⣰⡃
⠀⠀⠀⠀⠀⠀⠀⢃⡼⢠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠆⡄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠨⠭⠥⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡳⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢐⠠⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⣉⡡⠂
⠀⠀⠀⠀⠀⠀⠀⡠⢃⠄⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⡄⢈⢹⠰⡄
⠀⠀⠀⠀⠀⠀⣎⠔⠁⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡈⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠃⠀⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠤⠘⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⡀⠀⠀⢀⡤⢀⣤⡅⠀⠈⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠂⠙⡀⠒⠁⠐⠊⠉⠈⠁⢀⣀⣀⠍⠉⠓⠲⠆
⠀⠀⠀⠀⢀⣀⠀⠀⠀⢨⠀⠀⠀⠒⢈⡇⠀⠀⠀⠀⢀⣀⢌⡉⢉⠀⠀⠀⠋⠉⢒⡒⡀⠀⠀⣀⢲
⠀⠀⠀⠨⠁⠀⠀⡅⠅⢀⠀⠀⠀⠉⠉⡔⠲⠄⢙⡦⡗⠒⠳⠬⠙⠛⠗⠡⠒⠤⠀⡤⠶⠖⠁⠀⠀⡀
⠀⠀⠀⠐⠠⢀⡴⠒⠱⠲⠈⠉⠉⠉⠁⡭⡀⠈⡨⡧⢄⠤⣀⣀⣤⣀⣌⣁⠀⠀⡀⠤⠔⣊⡊⠤⠒⠃⠉
⠀⠀⠀⠀⠀⠀⠂⠤⠤⠴⠦⠀⠀⠤⠴⠋⠁⠊⣼⠒⠐⢂⡀⢀⠀⠈⠉⠙⠃⠀⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠞

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠤⢤⣤⣤⣤⣤⣤⣤⣄⡀⡀
⠀⠀⣀⣴⣥⣼⣿⣿⣿⣿⣏⡀⠀⠀⢀⡠⣊⣹⣿⣿⣿⣿⣷⠶⠆⠦⠀⢀⣠⣮⣬⣿⣤⣀⠀⡀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣶⠂
⠀⠘⢻⡻⠻⠿⠿⣟⡿⠛⠛⠉⠀⠺⢿⢻⣿⣿⣿⢻⣿⠿⠟⠉⠈⠁⠀⠛⣟⠟⠻⠿⠷⠷⠈⠀⠀⢻⣛⡿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠤⠁⢸⠛⢲⡀⠀⠀⠀⢀⣤⣠⣤⣤⣤⣤⡄⣀⣀⡀⠀⠀⠀⠀⠀⢐⣾⣂⠀⠐⣶⠀⠀⠀⠀⠀⠀⢰⣿⣿⣴⣿⠤⡄
⠀⠀⢰⣾⣶⣿⣿⣿⣿⣷⡄⠀⢠⣶⣾⣿⣿⣿⣿⣿⡇⣿⠟⠀⠠⠄⠴⣶⣿⣿⣿⣿⡟⠀⣼⣧⡄⠀⠐⢒⡶⣾⣿⣿⣿⣹⢃⣿⣤
⠀⠀⠘⠯⠟⠛⠛⠛⠯⠟⠃⠀⠈⠯⠟⠛⠛⠛⠛⠭⠃⠃⠀⠀⠀⠀⠀⠀⠿⠭⠟⠛⠛⠛⠉⢯⠽⠀⠀⠀⠁⠙⠶⠛⠛⠛⠋⠘⠶

⠀⠀⢀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣶⣶⣶⣦⣤⣤⡀
⠀⢀⣬⣅⣷⣾⣍⣿⠓⢶⡦⢠⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀⠘⣇⠀⠐⠲⠶⣶⣾⣿⣿⣿⠉⢉⣿⣷
⠀⢸⣿⢿⣇⢿⣏⣹⠷⢶⣷⡊⠉⠀⠐⠶⣶⣿⣿⣿⣿⣿⣷⠀⠤⠈⠼⢿⣿⣿⣿⣿⣁⣠⣿⣷⡄⠈⠉⠉⠙⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠑⠞⠁⠀⠁⠀⠀⠘⠖⠃⠀⠀⠉⠙⠛⠳⠟⠉⠉⠧⠃⠀⠀⠀⠀⠐⠿⠼⠛⠉⠉⠉⠘⠧⠇⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣴⠷⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⣤⠀⠀⢀⣰⣿⣿⣿⣿⣷⣴⣿⣶⠄⠀⣼⣤⣤⣥
⠠⠨⢽⣿⣿⡇⠀⠆⠈⣷⣶⣦⠀⠀⠀⣀⣤⣴⣿⣏⣽⣏⡹⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣼⣋⣳⣄
⠀⠉⠀⠘⢋⣷⣄⣀⣴⣿⡿⠃⣀⡠⢽⣾⣿⣿⣿⣯⡴⠋⠀⠀⠐⠒⠛⠿⢿⣿⣿⠿⢿⣿⣿⣿⠀⠀⡸⢿⣿⢿⡿⡿⣿⣿⡿⢿⡿
⠀⠀⠀⠀⠘⠔⠀⠉⠘⠔⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠖⠛⠛⠉⠁⠀⠀⠙⠊⠙⠚⠀⠀⠀⠀⠙⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡸⠀⢀⣀⣀⣀⣀⠜⠀⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠔⠉⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠈⠑⠄⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠸⡀⠀⠀⠀⢨⠂⠂⠀⠀⠀⠀⠀⠀⠀⠂⢺⠀⠀⠀⠀⠸⠂⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣿⣿⠿⠿⠿⠿⢿⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣫⣷⣶⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣶⣾⣝⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠳⣿⣿⣿⣿⡷⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢺⣿⣿⣿⣿⠏⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢂⠀⠈⣹⢻⣍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⣬⣝⣛⣁⣀⣠⣤⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠨⣭⣉⣭⣭⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⣤⣤⣤⣤⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣭⣽⠟⠋⢑⣦⠠⣀⣀⣀⣤⡄⢸⡟
⠀⠀⠀⠀⠀⠀⢠⠉⠒⠶⠶⠶⠶⠾⢿⣿⡦⣤⣄⣤⣤⠄⢼⡷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣑⣛⣛⡉⢨⣿⠀⠤⠤⠤⠴⠆⢸⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠤⠤⠤⠆⢸⣿⠀⠲⠶⠶⠶⠖⢼⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠒⠚⡃⢸⣿⠀⠒⠶⠶⠶⠆⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣉⣉⣉⣅⣘⣿⣤⠤⣴⡖⠒⠛⠉⠉⣁⠄⠀⣉⡓⠶⣤⣄⣀
⠀⠀⠀⠀⢀⣀⣈⡤⠤⠶⣲⣿⣉⠉⠁⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⠉⠛⠋⠀⠀⣄⠬⡍⠛⠳⠶⣤⣄
⢀⠀⡀⠉⠉⡀⣄⣒⣤⠅⠒⠚⠉⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣄⠤⢚⣛⣺⡥⠤⢒⣂⣴⡆
⢸⡀⠈⠲⢄⠈⠒⠿⢿⣑⡦⠤⣄⡀⢀⣀⠩⠓⠤⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⡏⠉⠁⢒⡊⠭⠑⠂⣾⡇
⠸⡟⠢⣄⠀⠉⠲⢄⡀⠈⢍⣳⣦⣹⣇⠴⠊⣉⣠⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⡇⢀⣠⠤⠖⠚⢉⣉⣿⠁
⠀⡇⠢⣌⠙⢦⣀⠀⠉⠓⠤⠉⣉⣥⠶⣞⡛⠉⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣯⡤⠤⠶⠚⣋⣩⣭⣿⡀
⠀⠋⠳⢄⡑⠦⡈⠓⢤⡀⠀⢸⣟⣚⡭⠤⢖⣚⡭⠤⢸⠀⠀⠀⠀⠀⠀⠀⢀⣿⠴⣖⡚⢯⣙⣥⣴⣿⠿
⠀⠈⠳⣤⡉⠀⠀⠀⠀⠈⠓⢼⣯⠴⠖⠋⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣬⣿⣷⣾⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⢸⡇⢀⣀⣤⡴⠶⠛⠁⣹⣠⣤⣶⡾⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⢸⡏⣉⣨⢥⣒⣴⡶⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣾⣋⠽⠖⠛⠉
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⠀⠀⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠢⡄⠕⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⠀⠃⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠀⠉⢺⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⢦⢀⣀⡤⡠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠇⡤⠤⠤⠀⠀⠠⢈⠬⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠨⠀⣂⡀⠀⣀⣠⠄⠀⠀⠈
⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⠒⢀⡀⠀⠠⢄⡀⠉⠀⠀⠀⠀⠈⠰⠀⠬⡧⠤⠠⠌
⠀⠀⠃⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⡀⠀⠀⠀⠀⠈⠐⠀⠂
⠀⢀⠔⣡⠊⣀⣀⡀⠀⠀⠀⢐⠀⠂⠤⠄⠀⠀⠀⠠⠤⡠⠀⠀⠁⢀⠂⡀⠀⠀⠀⢠⠀⠁
⠤⠶⠞⠒⠒⠂⠀⠀⠀⠀⠁⡈⠁⠉⠀⠀⠀⠀⠀⠀⠂⠚⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠄⠀⠁⠺⠉⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠍⠀⠈⠁⠡⠀⠀⠀⠀⠀⢀⠀⠚⢅⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠤⠤⠤⠄⢠⠤⠤⠤⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⠈⢀⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠊
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉⠦⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠡⠀⠈⠢⡀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⣀⠀⡆⠀⠀⠀⠀⠀⣀⢀⣀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠄⢤⠒⠈⠇⠋⠀⠃⠋⠑⠢⠄⠠⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⣴⣦⠀⠀⠀⣾⡆⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠁⠀⣇⠀⠙⠁⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠠⠈
⠀⠀⠀⡈⠧⠀⠀⠀⠌⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀⡀⠑⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠁⠀⠈⢓⡀⢈⠀⡀⢁⡘⢄
⠀⠏⠓⣇⡄⠐⠀⠘⠑⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣠⣨⠀⠒⠒⠂⢸⠅⠀⠀⠀⠀⠀⠀⠀⡔⠒⠂⠤⠀⠐⠀⠀⠙⡌⠠⠉⢺⣅
⠀⡄⠙⣯⡄⠀⠀⠄⠙⢿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠉⠀⠀⢄⠀⠀⢀⠌⠀⠀⠀⠠⡀⠀⠀⠀⠳⢢⡰⠁⠚⠕⠒⠠⠈⠀⠀⠈⠻⣥⠄⢰
⠐⡀⠛⡷⠆⡘⠀⠀⠙⢺⠖⡈⠀⣶⣀⣀⣈⣀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⣰⡆⠀⠉⠂⠀⠋⠀⠀⠀⠀⢀⠈⢛⠶⢀
⠀⠀⠀⠇⠁⠀⠀⠀⠀⢸⠁⠀⢀⣿⣶⣦⣦⣶⡶⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⠀⠠⢹⡧⠀⠀⢠⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠌⠀⠈⠂⡔⠃⠈⠓⢤⠀⠀⠀⢈⠠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠌⠀⡅⠶⠀⠀⠠⠄⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⠂⠁⠙⠃⠒⠂⠐⠒⠐⠂⠀⠈
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠘⠀⠀⠠⢦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠈⠖⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⡀⠀⠀⠀⠈⣄⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⡰⠐⠀⠂⠀⠀⠀⠀⠀⠀⣀⡤⠤⠀⠀⠀⡀⠀⠈⠈⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠍⠀⠘⠀⠒⠀⠀⣀⠀⡀⠀⠀⡀⠏
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⣬⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠩⠀⠀⠂⠰⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⢐⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠠⠐⠈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠠⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠁⠀⠐⠊⠀⠈⠀⠈⠁⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠩⠍⠠⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡠⠊
⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣽⣽⣽⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣷⣾⣿⣷⣶⣶⣶⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⡤⢤⣤⣤⣤⣤⣤⣤⡄⠠⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⡼⠋⠉⠉⠉⠉⠉⠉⠉⢹⡇⢨⣿⢸⡇⠀⠀⠀⣿⢷⡄⣾⠛⠀⣾⠀⠀⣷⢸⡆⢰⡆⡟⠋⢸⣿⡆⢷⢀⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⢸⡇⠀⠀⠀⣿⠀⡇⣽⠖⠀⣿⠀⠀⣿⠀⣧⣾⠀⡷⠂⢸⣿⠃⠘⣿⠃⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⢸⡇⠀⠀⠀⣿⡼⠃⢿⣤⡀⢿⣤⠀⡿⠀⢹⡏⠀⣧⣤⢸⠙⣧⠀⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠘⠿⢯⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣭⣭⣽⠇⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣼⡏⢹⡇⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣶⣶⣶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⢀⣴⣿⡿⠟⠛⠛⠛⠿⣿⣷⢦⠀⢸⣿⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⢞⣷⠿⠛⠛⠛⠛⠻⢷⣽⣦⡀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⣾⣿⠋⠀⡠⣒⣶⣦⣄⠀⠹⣿⣷⠈⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⢏⣿⠃⢀⡴⣪⣭⣗⢦⡀⠙⣷⣿⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⢹⣿⠿⠷⠾⠿⢿⡏⠀⢸⣱⡏⠀⢹⡟⡇⠀⣿⡿⠾⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠾⣾⡏⠀⢸⢸⡏⠀⢸⡇⡇⠀⣿⣿⣶⣶⣶⣶⣶⣶⣿⣦
⠀⠀⠀⠀⠈⣿⣉⣉⣉⣉⣹⣷⠀⠈⠻⣷⣶⣾⠽⠁⢀⣿⡓⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⣿⡀⠈⠫⣿⣶⣛⡵⠁⢀⣿⠓⠒⠒⠒⠒⠒⢒⣺⡿
⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠛⠻⣷⣄⡀⠀⠀⠀⢀⣠⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⣄⣀⠀⠀⠀⢀⣠⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠙⠓⠦⣄
⠀⠀⠀⢀⠖⠉⢀⡤⠖⠛⠉⢙⡓⠦⣄⠀⠙⣄
⠀⠀⢠⠏⠀⡴⠁⠀⠀⢰⠚⠛⢦⠀⠈⢧⠀⠘⡆
⠀⠀⡟⠀⢸⠁⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠤⠤⢤⣀⡀
⠀⠀⢷⠀⠸⡆⠀⠠⣄⣀⣠⠇⠀⠀⢀⡞⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣡⠴⢒⡚⠛⢛⣻⣿⣖⣲⡤⡉⠓
⠀⠀⠘⣧⠀⠘⠦⣄⡘⠁⠀⣀⣠⠴⠋⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠳⣜⣛⣶⠖⠋⠀⢀⣘⣉⡤⠟⢀
⠀⠀⠀⠘⢷⣦⣄⡀⠉⠉⠉⠁⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣶⣤⣤⣉⣉⣉⣉⣉⣁⣤⣤⣶⣿
⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⣼⣟⣷⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⡤⢒⣋⡍⠉⢉⡭⠿⢯⣙⡶⢤⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠙⠮⢭⣟⣛⣉⣀⣀⣨⡥⠴⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⠟⠋⠉⠉⠉⠉⠛⠻⣿⡿⣿⣯
⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⡴⠚⠋⠉⠓⠲⣄⠀⠙⣿⣿
⢠⠔⢋⣩⠤⠴⠖⠒⢒⣶⣶⠤⣍⡙⠻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢷
⣇⠀⠯⣐⡚⠧⠤⠞⠉⠀⠹⠋⣁⡽⠀⢸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⠀⢸⠠⢴⡇⠀⢀⡴⠛⢦⡀⢹⡀⠸
⣿⣷⣤⣄⣉⡉⠛⠛⠛⠛⠉⣉⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣆⠀⠙⠦⠞⠀⠀⡼⠉⢸⠇
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⡀⠘⢦⡀⠀⠀⠀⠀⠀⣠⠞⠀⣸
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⢿⣿⣦⡀⠉⠓⠲⠶⠖⠚⠁⢀⡴⠃
⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣤⣤⣤⣤⠖⠋

⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠲⡄
⠀⠀⠀⢸⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡗⠀⠤⠤⠄⣀⣀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡏⠛⠛⢶⡀⢸⢣
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⠈⢷⠈⡆⢣
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡇⠀⠀⠀⠘⣇⠸⡀⢣
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠓⠒⠒⠒⠚⠋⠀⠓⠒⠣⣀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡗⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄
⠀⠀⠀⣾⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣆⠘⢧
⠀⠀⠀⣿⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁⡇⠀⠀⠀⠀⠀⢸⡟⢉⣤⣤⣉⠻⣿⣏⣉
⠀⠀⠀⠈⠒⠒⠒⠒⠒⠛⡇⣿⠁⠀⢘⡇⢹⠛⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⢾⠀⡏⠀⠀⢹⡆⠻⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⠳⠶⠞⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⠶⠶⠛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡈⠉⠃
⠀⠀⠀⠀⠀⢀⢀⠁⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠸⠿⠿⣿⣼⠛⠿⠃⢸⣿⠟⠦⠾⠿⠃⠀⠀⢀⣿⣿⣧⠀⠀⠀⢸⣿⣿⡀⠀⣸⣿⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣤⣤⣤⣤⠀⠀⠀⣾⡿⠘⣿⣆⠀⠀⢸⣿⢻⣧⢀⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢀⡆⠀⣡⣿⠀⠀⠀⢸⣿⠉⠉⠉⠉⠀⠀⣼⣿⣷⣤⣿⣿⡄⠀⢸⣿⠘⣿⣼⡿⢸⣿⣿⣏⠘⠃
⠀⠀⠀⠀⠸⡿⠀⣿⣿⢀⡤⠂⢸⣿⣶⣶⡶⣶⡆⣰⣿⢏⢱⣤⠬⢻⣿⡀⢹⣿⠀⢿⣭⡇⢸⣿⡿⠇
⠀⠀⡀⠀⠀⠀⠀⠀⢠⠞⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⢠⣦⠀⠀⢠⣤⠄⠀⠀⣠⣤⠀⠀⣠⣴⣶⣦⣤⡀⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⣠⠈⣇⡀⢀⣤⣤
⠀⠀⠀⠸⣿⡇⠀⡾⠁⢀⡀⢀⣿⡏⢀⣾⡿⠉⠁⠉⠋⠹⡄⢀⣿⡏⣩⣭⠙⣿⡇⠀⣿⣶⢉⣴⣿⠟⠁
⠀⠀⠀⠀⢿⣷⢸⣶⠀⢿⣧⢸⣿⠁⢸⣿⡇⠀⠀⠑⢄⣾⡇⠀⣿⣷⣾⣿⣿⠟⠃⠀⣿⣿⣿⢿⣷⡀
⠀⠀⠀⠀⠸⣿⣿⡏⠀⠸⣿⣿⡏⠀⠈⢿⣷⣀⣀⣀⣼⣿⠃⠀⣿⡇⠀⠙⢿⣷⡀⠀⣿⣿⠁⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠛⠛⡡⠄⠀⠛⠛⠁⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠛⠃⠀⠀⠈⠛⠛⠀⠛⠛⠀⠀⠀⠛⠛⠂
⠀⠀⠀⠀⠀⠐⠉⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣰⠶⠶⠛⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⠉⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠈⠉⠉⠉⠉⣉⣁⡀⠀⣀⢀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⢽⣿⡇⠀⠀⠀⠀⢰⣹⣿⣸⠀⠻⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⣽⣿⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠸⡄⡞⠉⣭⣭⣭⣄⢸⠀⡏⠀⠐⠀⠐⢸⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⣸⣿⣿⣿⣿⠘⡀⡇⠢⠀⢴⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠻⠿⢿⣿⠿⠆⡇⢇⠀⠀⠀⠀⠄⠿⡿⢻⡟⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⢈⣒⣒⣲⠶⠎⢍⣁⣨⠭⠭⠽⠿⠟⠛⢇⠸⡇⠀⠀⠈⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⢠⣀⠤⡀⢸⡇⠀⠐⣄⠐⠆⠀⢸⠀⣷⠀⠀⠰⣶⣿⣿⣿⣿⣤⣤⠄⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⡠⠂⠈⠐⠀⢸⣷⠀⠀⠀⠗⠦⠄⠸⠄⠛⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢻⡇⠀⠶⠇⠀⠈⣿⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⡿⢃⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠘⠦⣤⣤⣤⣶⣖⣚⢉⣉⣉⣩⣭⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣿⣿⠟⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⢸⢀⡤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠐⠂⠀⠐⠂⢸⢸⠈⠁⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠻⠃⠀⢸⠈⡠⠦⠆⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣅⡘⣒⣒⣒⣒⣊⣉⣀⣓⣀⣭⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⠿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣻⡟⠉⠛⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠀⠀⠀⠐⠚⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣀⣡⣤⣶⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⣀⣤⣴⣶⠿⠛⠋⠉⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣴⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢘⣿⠆⠘⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣡⣤⣶⡾⢛⠋⠉⠉⠙⡛⢷⡦⠀⠀⠀⠀⢀⣀⣡⣤⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⣀⣤⣴⡾⠿⠛⢫⣿⡫⠬⠀⠛⠀⣀⣀⣠⣤⣴⣶⡶⠿⠿⠛⠛⠋⠉⠁⠀⣿⣇
⠀⠀⠀⠀⠀⠀⢠⣴⣶⡿⠟⠛⠉⠀⢀⣀⣀⣠⣤⣴⣶⣶⡿⠟⠛⠉⠉⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⣴⣶⣾⠿⠟⠛⠛⠉⠉⣠⣿⣋⠊⢀⣸⣦⣄⡀⠀⠀⡙⣷⡀⠀⣀⢊⣤⣄⢀⡈⣿⣇⢈⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⠿⡋⠉⢁⡈⠉⠙⠻⣯⡍⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠡⠀⠀⣠⢾⡷⣤⠀⠈⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣿⡇⠀⢀⣤⣄⠐⠀⠀⣿⠃⠀⠀⠀⣷⣼⣇⠛⠁⠀⠀⠀⣿⡄⠀⠀⣡⣤⡈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⡇⠀⠘⠿⠟⢀⠀⠀⣿⡀⠀⠀⠀⣈⢹⡟⢷⡄⠀⠀⠀⣿⠇⠀⠀⠻⠿⠇⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠁⠀⠀⠹⣧⠀⠀⠈⠿⣼⣧⡼⠃⠀⡀⣱⡟⠀⠀⠀⠀⠀⠈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠘⠃⠀⢀⣨⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣆⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⠁⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⣟⣲⡲⣄⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⠒⠒⠒⠒⠒⠒⢲⢎⡷⠿⠧⠤⢬⣽⣷⣄⣀⢈⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣋⣀⣀⣀⣀⣀⣠⣿⢟⣄⣄⠀⡄⠀⠀⢘⣿⠉⠉⠉⠉⠉⠛⠓⠒⣒⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⡿⣿⡏⠩⠉⢹⠿⣿⣿⠟⠻⠿⠻⠷⠻⠿⠾⢿⡦⣿⣷⣧⣧⣤⣶⣸⣏⠩⡪⢂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠚⠋⢠⡶⣤⠀⠉⡸⠇⠂⠀⠀⡞⣋⡟⠀⠀⢸⣷⢿⡆⢀⠀⢸⣏⢙⣿⡆⢘⢕⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡠⣤⠀⠀⠒⣫⣤⢄⣈⠁⠀⢀⡂⠑⠔⠊⠀⠀⠓⠃⠀⠀⠀⠠⠈⠓⠃⣾⣇⠀⡩⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠧⡾⠀⢀⣾⢋⣥⡈⡙⢷⡰⣷⡄⡆⠀⠀⢀⣀⠀⠀⠠⢊⠀⡐⠄⠀⠁⣿⣿⡀⠪⢀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠓⣲⣾⣷⣾⡷⠾⠷⠾⠿⠶⠾⠥⣤⣤⣯⣴⣆⠀⢀⠠⡑⣣⠃⠀⠺⣿⣘⣇⠀⢕⡹⣇
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⡋⠀⠀⠀⣀⣾⠋⢴⡄⠈⢻⣆⠀⣤⠀⠀⠀⠀⠀⢀⣠⠔⠻⡇⠀⠑⠒⠉⠀⠀⣀⣸⠀⢿⡀⠩⢆⢿⡄
⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠺⠶⢿⣯⣤⣤⣤⣧⣧⣿⣤⣀⣦⣄⣤⣴⣸⣏⠁⠠⡈⣧⠀⠀⠀⠈⠀⢸⢿⣿⠄⠸⣇⠐⠕⠸⣧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢹⠀⠈⡀⢹⣀⣤⠄⢤⡀⠌⠒⢻⠅⠀⢿⡀⠠⠂⢿⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣔⢍⣿⠻⠲⢻⠇⠀⠀⢸⠇⡀⠸⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⡷⠒⢲⣤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠔⡡⣷⠨⠉⠡⠀⠀⠀⢸⡇⠂⠀⣷⠀⢠⠶⠸⣇
⠀⠀⠀⠀⠀⣾⡇⠗⡅⠀⣰⡖⠀⠑⣤⠊⠙⢄⡠⠋⠡⣈⡩⠋⠫⣉⡝⠛⣍⣹⣷⠀⠪⠀⢸⣠⣄⡀⠀⡔⠒⢌⣇⠁⠀⢸⡀⠐⠩⣂⢹⡄
⠀⠀⠀⠀⠀⣿⣅⠀⢈⠾⡁⠈⡢⡊⠀⠑⣴⠋⠑⢄⡠⠊⠢⣀⠴⠋⢄⡠⠚⢻⣿⡆⢀⠀⢸⡟⠙⠁⠀⠷⣷⠞⣿⠀⠀⣼⢟⠻⣻⣿⠿⠃
⠀⠀⠀⠀⠀⣿⢈⠶⡁⠀⡸⢎⠀⠈⣦⠋⠈⠣⣠⠊⠣⣀⡰⠋⢢⡠⠊⠑⢄⢼⣿⣷⠀⠄⡨⣇⣀⠀⠀⠀⠀⠀⣿⠀⣼⣏⣵⡾⠛⠁
⠀⠀⠀⠀⢠⡟⢄⠀⡸⢎⠀⠀⡱⡎⠀⠑⣤⠊⠈⢢⡔⠉⢢⡠⠊⠑⢤⠔⠉⢺⣿⢿⡄⠘⠄⣿⣧⡷⠀⠀⣰⣏⣻⣼⡿⠟⠁
⠀⠀⠀⠀⢸⣇⡠⠛⣄⠀⡱⢎⠀⠈⡦⡊⠀⢱⡔⠁⠑⣤⠊⠑⢤⠔⠁⠑⣤⢺⡿⣽⣧⣴⣇⣼⠛⠙⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⢸⡋⠢⣀⡠⠫⡀⠈⡷⡊⠀⢙⢶⠁⠈⡲⡊⠀⢳⡔⠁⠑⣤⠎⠀⢹⣿⣿⠣⢈⣽⠟
⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠶⠾⠶⢧⣤⣵⣎⣀⡈⣤⠃⠈⢢⡔⠉⠣⡤⢺⣿⢯⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠳⠷⠤⣮⣌⣾⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⣡⠚⣨⠏⠀⠀⠈⠑⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⣥⣶⣿⡷⠚⠁⠀⠀⠀⠀⠀⠀⡠⠦⣍⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠓⠶⣾⠻⠿⢯⣅⠀⠀⠀⠀⠀⠀⣀⣤⣊⣧⠜⢀⡴⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⣻⣧⣄⡀⠀⠀⠀⠀⠀⠉⠓⠦⣌⡙⣆⠀⣠⣴⣾⣿⠟⣋⡥⢚⣥⠾⢛⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣈⣥⣶⣾⣿⡿⠟⢿⡙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣛⣭⣶⣯⣷⣻⣽⣶⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠀⠀⣠⣤⣲⢹⣁⡯⠟⠛⠉⠀⠀⠀⠀⠛⢦⣀⠉⠛⢶⣤⣀⠀⠀⠀⣀⣠⣤⢹⠿⣟⡿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠈⠒⠤⣉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠿⢟⣫⣿⣿⡆⣿⣿⣿⣿⢸⡽⣖⣿⡽⣟⣿⣽⡇
⠀⠀⠀⠀⡀⠀⠀⠀⡒⠭⣓⠦⣄⡀⢠⣴⣚⢹⣠⠬⢟⣋⣭⣶⣿⠿⣟⡯⢽⡇⣿⣿⣿⣿⣾⣻⣽⣶⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠈⠑⠶⣴⣮⣕⡲⠍⡒⠉⠓⠮⣍⣩⣴⣾⣿⣿⣿⣟⣺⡭⢖⣻⠽⣷⣿⣿⣿⣿⡿⣟⣯⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢄⠀⠈⠛⠿⣿⢷⣄⡁⠀⠀⠈⣿⣿⣿⣿⣿⣿⠽⢖⣫⣽⣶⣿⣿⠿⣛⣭⣷⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠑⣦⡀⡢⠎⠙⠾⣝⡳⢦⣄⣿⠿⢟⣫⣽⣶⣿⣿⡿⢟⣛⣭⣶⣿⡿⢟⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣔⡀⠀⠀⢹⣷⣷⣶⣿⣿⣿⠿⢟⣫⣵⣾⣿⣿⠿⡻⣝⡮⣗⣯⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠈⠻⢦⣄⢸⣿⣿⠿⢛⣩⣴⠾⣛⣽⡿⣟⢭⣢⢵⣫⡵⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣕⠆⠙⠻⣯⣶⠾⣛⣭⣶⣿⣿⣿⣿⣺⣽⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠈⠛⣿⣿⣿⣿⣿⣿⡷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠾⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⠅⣸⡀⣷⢼⠅⣿
⠀⠀⠀⠀⠀⠀⡏⠀⠙⠁⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⢉⡁⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠙⣆⡀⢾⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠟⠋
⠀⠀⠀⠀⢀⡠⣀⠀⠙⣀⡁⢀⡠
⠀⠀⠀⠀⢸⠀⡿⡁⣧⠏⣇⢸⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣄⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⠆⠙⠚⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⢹⠛⣽⡏⣿⢿⡟⣟⡿⢿⢟⢿⠉⣿⡿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣜⣛⣴⣜⣮⣤⣧⣤⣼⣮⣾⣰⣽⣦⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡰⠿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠙⠛⠛⠛⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠀⣿⡈⠉⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢟⣳⠶⣞⣻⣿⣿⡿⠂
⠀⠀⠀⡄⣠⢀⣀⢩⡅⡄⣀⢩⡁⣀⡄⢠⠔⠖⢀⣄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣿⣼⣿⣿⣿⣷⣿⠟
⠀⠀⠀⠃⠉⠈⠛⠂⠙⠃⠋⠐⠙⠉⠃⠊⠃⠃⠋⠈⠁⠙⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢉⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⡴⢰⡀⡆⢠⡶⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣏⣹⡉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠁⠈⠁⠁⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⡀⢄⠠⢄⣀⢠⡄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⠁⠏⠘⠉⠚⠸⠣⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠋⠉⠉⢉⣉⣙⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⢀⡴⠛⠋⠉⠙⢿⣿⣶⡄⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⣿⣯⣿⡄⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠛⠓⠶⣶⣶⣿⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣤⣤⠾⠋⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⣼⣿⣿⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠛⣿⠛⢻⣿⣟⣿⡿⠁⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡾⠃⠀⠀⠀⢸⣧⣼⠿⠛⠁⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠉⠉⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⠛⠷⢶⣿⣽⣷⠀⠀⠀⠀⣾⣾⠇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣴⣾⣉⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⢸⡏⠉⠛⠳⢦⣤⣤⡞⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣷⡿⠀⣀⣀⣞⣿⠃⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢰⡟⠇⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣀⡀⢀⣴⣿⣿⣿⣿⣿⡄⠛⠻⢿⡿⠏⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠘⣿⣳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣷⠟⠁⠀⠀⢀⣴⣿⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣿⡿⠛⠁⠀⢀⣠⣶⣿⠛⠁⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣤⣀⠀⠀⠀⠀⢸⣿⣿⠓⠀⠀⣠⣶⣿⣿⣿⡿⣿⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣈⢷⣤⣀⣠⡾⠿⠿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠯⣷⡄⠀⠀⠀⠀⠀⠀⠀⡞⡾⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠘⡇⠀⠀⢀⣶⣶⣶⣖⠛⡗⣒⣛⣿⣫⡽⠿⣤⠀⣀⣤⡀
⠀⠀⢸⣿⣏⣉⡉⡏⠉⠉⠉⠉⡏⠉⣹⣟⣿⡿⠛⠻⣿⠋⠉⠁⠉⠀⣰⠦⣿⣺⣧⠀⢹
⠀⠀⢸⠉⠉⠉⠉⠋⠉⠉⠉⢩⣯⣭⣭⣽⣿⣤⣤⡤⢼⠤⠤⠤⢿⣯⣽⣰⡇⠈⢹⡗⠾⣄⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⡇⠀⠀⠀⣸⣀⣀⣀⣸⣾⡀⠙⠷⢤⣸⠁⠀⢀⣩⣷⣦
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠏⠉⠉⠉⠛⠉⠉⠉⠉⠉⡇⠀⠀⠀⠙⠓⢤⡼⡇⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠢⣄⠀⠀⠀⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠙⠦⣄⣿⠗⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⢀⣴⣿⡿⠿⣿⣦⡀⣾⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣻⣻⣟⣿⢸⣿⣿⡶⢃⣿⣿⡇⣿⣻⣟⣿⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣽⣿⡿⠃⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⠋⠉⠙⠛⠉⠁⠀⠀⠉⢻⡟⠉⠀⠀⠈⠙⠛⠋⠉⠙⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⣿⣿⣿⣿⡟⠻⣿⣷⣄⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⣠⣾⣿⠟⢹⣿⣿⣿⣿⣿⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⣿⣿⣿⣿⣿⡇⠀⠈⠻⠿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⣿⡿⠋⢹⣿⣿⣿⣿⡏⠙⢿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢹⣿⡇⠀⠀⠀⠙⠋⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠙⠋⠀⠀⠀⢸⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠸⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠘⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠦⠤⢤⡤⠤⠖⠒⢲⠖⠒⠒⠒⠒⡶⠒⠒⠒⠒⡶⠶⠶⢴⡦⠦⠴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡼⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢳⠀⠀⠀⢧⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡰⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⠀⠀⠀⠸⡄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⢣⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⡆⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠤⠤⠤⠤⠾⠤⠤⠤⠤⠤⠶⠺⠒⠒⠒⠒⠒⠒⠺⠒⠲⠶⠶⠶⢿⠶⠶⠒⢠⠛⠒⠒⡒⠶⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣼⡇⠀⢀⣶⠀⠀⣸⡀⠀⠀⣸⡀⠀⠀⣸⡀⠀⠀⣸⣀⠀⠀⡸⢇⣀⣀⡼⣄⣀⣀⣷⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠋⣿⠋⠉⠀⠉⠉⣹⣉⣉⣉⣀⣉⣉⣉⣀⣈⣒⣚⣁⣈⣉⣉⣀⣸⡁⠀⠀⠀⠈⣷⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣠⡿⠤⣀⠀⠀⢸⠉⠏⠉⠈⠀⠀⠀⠀⠀⠀⡀⣀⡀⣠⢤⠉⣉⠙⠉⠉⡇⠀⠀⡏⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠉⣉⣄⢀⣄⣸⡄⠀⢸⠐⡮⠀⣇⣀⣎⡳⢳⠞⠦⠃⢿⡦⠸⠻⠌⢓⣦⠀⢠⠇⣰⠚⠋⠛⢿⢤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣵⢰⣾⠁⠈⠉⢈⠿⠼⠀⢸⣄⡥⣤⡭⠤⠤⠴⠶⠲⠶⠶⠖⠒⠒⠒⠒⠚⠒⠒⠾⢘⣏⢠⣤⡴⣄⣤⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡶⠸⣄⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢰⠛⡄⠀⠀⣸⡇⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⢁⣀⠀⢠⢦⡀⠀⠀⠀⢀⣠⣤⣀⡤⢤⣄⠀⠀⠀⠀⠀⠀⢀⢶⡀⠸⣼⠀⢻⢲⡖⠋⢇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠛⢊⣙⠒⠓⣤⠿⡴⢲⣀⡀⡧⠴⣏⢀⡤⣀⠹⣄⣀⣀⡴⠶⢋⣦⢷⠴⣄⣴⢺⠜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠑⡦⢣⡠⠇⠐⢇⡤⢤⠈⢁⣽⣅⢖⡌⣻⢶⡚⢀⡏⢀⡟⢥⠀⣬⣹⣄⠀⠁⠸⡄⠀⠡⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠙⠣⠤⣶⠦⠴⠋⣛⠉⣆⢈⣿⠮⣉⡴⣇⣠⠟⡟⣉⠙⠧⣏⠛⠁⠀⣉⢧⣤⡖⠳⠼⠶⣏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⡸⠽⢀⠈⢳⠀⠸⠭⢇⠈⣻⠣⢴⠡⡏⣝⠹⣆⠙⠋⢀⡶⣏⣰⣀⣶⡼⠀⠀⡳⢀⠀⡘⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠚⣇⠀⣸⡟⢛⣶⠞⣆⡸⠉⢳⡠⠾⣆⡑⢚⣡⠋⡵⢚⡛⣿⠀⠀⢠⠿⢶⠀⡀⣱⠊⠒⠉⠑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⡁⣽⠋⠁⠻⢤⠃⢸⡃⢠⣙⣇⢯⡀⣤⠉⢻⣆⠑⠔⠋⡸⠛⣤⣾⣋⡈⠋⠉⣯⣤⠀⡀⢀⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⣸⢯⠿⣤⠜⠳⠔⠓⠶⠋⠈⠒⠬⠤⠠⠜⠀⠉⠉⠉⠀⠀⠀⠀⠙⠦⠚⠓⠁⠘⠖⢹⠇⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⢀⢠⡤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⢤⡤⠤⠤⠤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⠀⠀⠸⡆⠀⠀⢡⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢠⡇⠀⠀⡄⢀
⠀⠀⠀⠒⠒⠉⠁⠉⠙⠁⠓⠒⠚⠓⠦⠤⠼⠆⠒⠒⠚⠓⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠛⠒⠒⠒⠚⠓⠂⠉⠙⠹⠦⠤⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⢋⣉⡛⠛⣋⣤⡌⠛⣉⣴⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣰⣿⣿⣿⣿⠟⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⣡⣾⣿⣿⠿⢋⣤⣾⣿⣿⠿⢋⣥⡙⠻⠿⠟⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢋⣴⣿⠿⢋⣡⣾⣿⣿⡿⢛⣡⣶⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⢛⣡⣶⣿⣿⣿⠛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠟⣩⣴⣿⣿⣿⣿⣿⣅⠹⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⣉⣴⣾⣿⣿⠟⢋⣴⣿⣿⡟⠀⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢋⣴⣾⣿⣿⠟⢋⣤⣾⣿⣿⣿⣿⣇⠀⠻⠿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣤⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⣴⣿⢋⣤⣾⣿⣿⣿⠋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣶⣶⡄⠈⣿⣿⣿⣿⣿⠿⢋⣥⣾⣿⣿⠿⠋
⠀⠀⠀⠀⣠⣾⣿⡇⣾⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⡿⠇⢀⣿⣿⣿⢋⣡⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣿⣿⣿⣧⡘⢿⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣠⣄⠸⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣷⡌⢻⣿⣿⣦⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⠹⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣴⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⡈⢿⣿⣿⣄⠻⠿⠿⠿⢿⣿⣿⠟⢋⣴⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣄⠻⣿⣿⣷⣶⣿⣷⣦⣉⣤⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠻⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⣉⠉⠁⠀⠀⢀⡏⢝⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢒⣩⠘⡯⢫⢟⠱⡲⢶⢤⡤⣀⡀⠀⠀⠀⡇⠉⠁⠀⠀⠀⠀⢸⡮⢓⠭⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠘⠂⡯⢔⠥⡪⢖⢕⡠⠪⡪⢙⢝⢗⢲⡇⠀⠀⠀⠀⠀⠀⢸⡪⢐⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢗⠕⣪⣆⠵⠵⠒⠚⠚⠉⢹⢟⡿⢦⣀⠀⠀⠀⠀⠀⣿⡪⠕⣺⠁⠀⠀⣀⠤⠤⠀⠀⠒⣲⡤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣀⡇⠀⠀⠀⠀⡖⡉⠉⠄⠀⠐⠀⠀⠀⠀⠀⣾⠕⡊⢔⠮⣷⢄⠀⠀⠀⡭⣒⠅⡞⠀⠀⡜⢁⣠⡤⢴⣴⣼⣧⠾⠏
⠀⠀⠀⠀⠀⢠⠔⠱⠌⣗⢔⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢍⡪⢔⢺⣇⢕⠀⠀⠀⡯⢒⢭⠇⠀⡔⢁⡞
⠀⠀⠀⠀⠀⠀⢣⠀⠀⢻⣂⣺⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣀⡀⠀⠠⠤⠿⠥⠮⠷⠽⠷⠵⠤⠤⠼⠯⠶⠼⠤⠔⢁⡎
⠀⠀⠀⠀⢠⠊⣉⣍⢭⣍⣩⡉⢉⡥⠤⠤⡤⠤⡄⢀⡴⠖⠒⠲⠀⡖⠒⡶⢖⣶⠀⣶⠚⢛⢛⠀⣰⠞⡺⣶⡲⢀⡞
⠀⠀⠀⠀⠈⠆⠳⣡⠀⠀⢻⢻⡈⣇⠁⠀⡇⠁⠁⢸⣥⠄⠀⢸⠀⡇⢰⡯⣐⡏⢸⣿⢌⠢⡸⠀⣿⠅⣪⡿⢀⡜
⠀⠀⠀⠀⠀⠘⡄⢹⣆⢠⡘⣟⣷⠸⡆⠀⡇⠀⢸⠘⡾⠀⠀⢸⠀⡏⢸⣏⣾⠀⣼⣿⣵⣭⠇⠰⣇⣅⡾⠁⡜
⠀⠀⠀⠀⠀⠀⠘⡄⠙⠛⠓⠛⠛⠁⠙⠒⠓⣒⡁⠀⢉⣉⣉⡁⠀⣉⣭⣭⣁⢀⣤⡤⢤⢦⢀⣤⡶⢦⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⣯⣟⣿⢣⢸⡍⡏⠀⢸⠀⡏⠀⠀⢸⢸⡇⢸⡳⡟⢸⢕⡏⡢⡝⢸⢻⢢⡏⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⡄⢙⢘⡆⣷⠇⠀⠌⠀⡇⠀⠄⡈⢈⠆⣿⣲⠇⣸⣹⣗⣼⠁⣏⣾⡞⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⠒⠂⠃⠘⠓⠒⠚⠀⢈⣀⣉⣁⣈⣙⣉⣉⣄⠬⠭⠥⠤⠤⢤⣤⠠⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣂⣀⣀⢀⣀⣀⣀⣀⣉⣉⣉⡉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⡉⠉⢉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡞⣛⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠹⠛⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣥⣕⡼⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⡽⣦⡆
⠀⠀⠀⠀⠀⢤⡠⢀⠱⣿⣿⣋⢴⠠⢄⠠⣀⠠⢀⠠⢄⠠⢄⠠⠀⣀⠀⣀⠀⡀⢄⡠⢄⠠⡀⠄⡀⢄⡠⣏⡻⠿⢗⡵⡠⣀⠤⣄⣤⡠⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠐⠀⠁⠊⠁⠂⠁⠊⠁⠊⠑⠉⠐⠁⠊⠁⠈⠀⠉⠉⠉⠁⠉⠀⠉⠈⠁⠉⠑⠉⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⢀⣀⣀⣀⣀⢀⡀⢀⡀⣀⣀⣀⣀⣀⡀⠤⣤⢔⠲⡏⢥⣹⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣴⣶⢀⣖⠠⢁⣿⡀⢆⣰⣿⣿⡿⢿⡻⡇⣼⠟⡡⢾⡷⠶⠾⠿⠿⠿⠿⠿⠿⠀⠷⠘⢚⡉⠉⢻⢸⣿⢻⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣣⠞⠉⠉⠀⠀⠀⠄⠀⠀⠀⢀⠔⢊⣴⡏⢰⢰⡡⣎⠀⠀⡄⠐⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⡸⡸⢿⡟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⠞⠁⠀⠀⠀⡔⣤⠂⡄⠀⠀⢀⣎⣴⣿⡟⡰⡇⣸⢣⡟⠀⠀⡏⠀⠀⠀⣴⣴⣶⣴⢲⠀⠀⠀⠀⠀⢀⢇⢇⣿⢰⡿⡇
⠀⠀⠀⠀⠀⠀⢀⠜⡴⠁⠀⠒⠀⠀⠀⠛⠄⠚⠀⠀⠀⢸⣾⣿⣯⠞⣰⡇⡟⣻⣿⠀⣠⠃⠀⠀⠐⠋⠛⠛⠙⠋⠀⠀⠀⡀⠀⡞⡜⣸⣿⣿⣷⠃
⠀⠀⠀⠀⠀⢠⢊⣾⡀⣀⣀⡀⣀⠀⠀⢠⢄⠬⠄⠀⠀⠀⣼⣿⠏⡴⣻⠁⣿⠛⣣⠘⠁⠀⠐⠵⠀⠀⠊⠖⠀⠸⠶⠗⣛⣋⡜⡴⣱⢃⣿⣿⠃
⠀⠀⠀⠀⡰⠁⠾⣟⣛⣛⣛⣀⣛⣘⣓⠛⠐⠃⠿⠿⠿⠿⢿⠏⡼⠐⢻⠀⡿⠿⠿⠭⠿⠯⠶⠦⠶⠶⠦⠬⠭⠟⣙⣋⣁⣈⣴⢗⣷⣾⣿⠃
⠀⠀⠀⠀⢹⡽⣭⣿⣟⣛⣛⣛⣻⣿⣯⣯⣽⣿⣷⣶⣶⣶⣾⣾⣷⣾⣿⣶⣿⣿⣿⡛⠛⠛⢿⣿⣷⠶⠞⠛⣛⣋⣉⣉⣒⢚⣋⣾⣿⣿⠇
⠀⠀⠀⠀⢸⡩⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⡿⣿⣿⣿⣭⣭⣿⣛⣛⣳⣦⣤⣤⣤⣤⣭⣭⣭⣽⣿⣿⣯⡟
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠯⠽⣾⣯⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣦⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡁⠄⠀⠨⣙⠳⣁⠀⠀⠈⠉⠙⢫⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡌⠀⠀⠀⣼⢸⠑⠄⠑⡀⠀⠀⠀⠀⢳⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠀⢒⡀⠛⢧⠀⠈⠂⢑⠀⠀⠀⠀⠈⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⠀⠀⠢⡤⡀⠄⠀⣰⣄⢀⠘⠀⠂⠠⠄⠠⠀⣘⡘
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⡀⢿⣧⢠⠿⢤⡉⢅⢀⡀⢰⡄⠀⠀⠀⢰⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢐⡄⠁⠿⣟⣲⡾⠦⣗⣠⠄⣴⣴⣀⣀⢀⣯⡟⠉⠉⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡟⠠⣆⡏⢠⠀⠀⠀⣨⠀⠓⣾⠃⠀⠐⠢⡈⢳⣤⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⡏⠒⠤⢉⢀⠲⡦⣤⡘⢀⣣⣘⣦⠀⡤⠤⠴⠂⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠷⣀⡏⠀⠠⠠⠤⠀⣀⠀⠊⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠊⠀⠀⠠⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢐⠀⠀⠄⡠⠀⠁⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠐⠀⠄⠀⡀⠠⠀⠀⠐⠡⠀⠀⠀⠐⠀⡀⠀⠄⠂⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⡂⠈⠄⠂⠀⠀⠀⠁⠀⠀⠈⠀⣀⣈⠀⠐⠒⠊⠉⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠒⠒⠒⠐⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠀⠂⠂⠀⠀⠉⠉⠁⠁⠈⠁⠁⠁⠉⠀⠈⠈⠉⠈⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠀⠠⠤⠠⠀⠠⠀⠠⠠⠀⠀⠂⠀⠀⠂⠀⠀⠈⠉⠈⠁⠁⠁⠈⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⠐⠀⠀⡀⠈⠁⡄⢀⠀⠀⠀⠀⠉⠨⣆⠀⠀⠀⠀⠀⡃⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠤⠠⠀⠀⠂⠀⡀⠀⠀⢀⣤⣿⡏⢇⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠰⠒⠂⠐⠀⠉⠄⠀⠐⠀⢀⠠⡤⠈⠁⠂⠀⣀⣰⠂⡘⡦⠍⠘⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣤⣤⣀⣀⢈⠁⠀⠀⠚⠁⠀⠂⠀⠐⢀⠴⢰⢢⠀⠃⡏⠀⠂⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠛⠛⠀⠁⠁⠉⠀⠈⠉⣖⠀⢤⣀⠀⠀⠋⠘⠉⠉⠀⣦⠀⠀⠀⠀⣠⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡌⡇⡀⢀⠀⠢⢅⠆⠀⠽⠃⠀⠀⣸⢭⣀⠄⠸⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢽⣇⣧⠀⠐⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠋⠃⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠠⠀⠀⠀⠠⠤⠤⠤⠄⠤⠤⠤⠀⠀⠒⡄⢀⠀⡔⢀⠀⠒⠐⠢⡄⠀⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡡⢀⣄⣠⠘⣁⣄⢄⡤⡅⢀⣆⣤⡤⡤⢤⠄
⠀⠀⠀⠀⠀⠤⠀⠒⠖⠒⠂⠰⢾⠱⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠈⠉⠉⠀⠨⣇⣭⣴⣱⢀⡀⠀⡅⢶⡥
⠀⠀⠀⠀⠀⠀⢰⠆⣀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘