Root vegetable Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢺⣟⢿⡋⣻⣤⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠷⠛⠀⠀⢫⡭⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣇⠀⠀⠈⡧⣆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠈⠐⡄⠀⠘⡀⠀⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⡰⠿⠶⣶⣈⡀⣷⡁⠀⢠⡀⠀⠠⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠄⠙⠶⢁⠀⠃⠈⠂⠃⡰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⢰⠀⠆⠡⣠⠤⢟⠛⠩⢄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠖⠂⠂⢄⣀⣁⡀⠐⣄⠀⠀⢣⣀⡜⠃⠤⢀⣤⠀⠀⢱⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡼⠛⢛⡧⠙⢛⣱⢤⣬⢩⠀⠀⠀⠈⠂⠆⠐⠚⠈⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠒⠉⡄⠄⠏⠀⠀⠹⠀⠀⠀⠀⠕⡀⢁⣀⣠⣼⠊⠁⠀⡀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠄⠀⢠⡀⠀⣠⠦⣞⣉⠙⢟⠋⠙⠫⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠠⣈⣄⡐⠀⢀⡌⡁⡴⠅⠀⣱⡀⠈⠪⣷⣄⡀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠄⡉⠉⢻⢶⣼⠇⠏⠑⠀⠀⠈⡄⠉⠉⠁⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⠋⠈⢘⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠁⠀⢀⣤⣀⠡⣁⣀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⠉⠈⠉⠉⢻⡷⣿⡆⡲⣦⣶⣦⠹⢿⣿⡟⠉⠉⠙⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⢀⣠⣾⣟⣫⣼⢇⣽⣻⣿⣜⢷⣿⡅⠀⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠛⠉⠻⣿⣿⡿⣫⣾⣙⣿⣿⣿⣿⣿⣄⣀⣀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⣰⣿⣿⣷⣿⡿⠿⡟⠉⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣤⣤⣴⣿⠏⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣆⠀⢀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢄⢘⡿⣤⣰⡟⡀
⠀⠀⠀⠀⠀⢲⣟⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠙⠛⠲⣄⠀⠀⠀⢸⣿⡏⢁⠸⣏⢠⡇
⠀⠀⠀⠀⢀⣬⣛⣻⣛⣛⣛⣛⣠⣁⡀⠀⠀⠀⠀⠘⠤⠜⢳⣦⡀⠀⠙⣵⣦⠀⠀⡀⠀⠀⠀⠘⣿⣷⢀⠀⠀⠄⢛⡆⠀⠀⢻⡇⠸⡛⠉⡟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⡿⣯⣿⣿⡟⡿⡇⠀⠀⠀⠠⠒⠶⢮⣗⢾⣿⣎⣴⡏⣀⣤⡾⠁⠀⠀⠀⠀⠙⣿⣿⣧⣂⡀⠀⢹⡄⠀⠀⠛⢚⣿⡾⠂
⠀⠀⠀⠀⠀⠉⠉⠛⠓⠛⠛⠛⠛⠃⠁⠀⣀⠀⠀⠀⠀⠈⠙⠳⠾⣿⣿⡸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⠀⢸⠅⠀⠀⠀⡸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⢶⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠞⠀⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢠⠀⠀⠀⣸⡇⠀⢸⣶⣆⡀⣾⣿⣭⣠⡴⠂⠀⢀⡀⠀⠀⠹⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢢⣤⣀⣶⡄⣰⢆⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠘⢦⣴⣶⡿⠃⠀⠈⠿⣿⡛⢿⡿⣿⣻⣴⣧⣿⡟⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢐⡘⢳⠹⡞⣏⢻⣦⣩⡾⣄⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣶⣿⣽⡟⣿⡇⣸⡿⠓⠛⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⣋⣁⣽⣿⣶⣇⡉⣽⣿⡥⠘⠂⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠂⠂⢀⠀⠀⠀⠀⠈⠀⠘⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⢿⢹⣿⣿⣿⣿⣿⡶⣀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢷⡀⠀⠀⠘⣷⠀⠀⠀⠀⢠⡶⠟⠲⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⢼⡟⢻⣻⢾⡏⣋⣟⡍⠃
⠀⠀⠀⠈⢿⣶⣶⣾⡿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢠⢀⣏⡗⠀⠀⣤⣸⡄⠀⠀⠀⠀⠀⠃⣞⡇⡞⣱⠇⠋⠃⠀⠀⢠⣧⣶⣼⡄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⢸⠊⡯⠀⢀⠈⡀⢀⣁⠀⠀⠀⠀⠀⠀⠸⣳⠇⡟⠀⠀⠀⠀⠀⠀⣻⣿⡿⠂
⠀⠀⠀⢠⣶⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣻⡇⢠⠊⣽⣶⠟⠈⡁⠀⠀⠀⢠⠾⠋⠻⠾⢿⣄⠀⠀⠀⠀⠀⣨⣿⣇⡀
⠀⠀⠀⢸⣿⣆⠀⠀⠀⠄⠀⠀⠀⢸⣇⠐⠀⠀⠀⠀⠀⠀⠼⣟⣵⣥⣭⣍⢁⡀⠈⠀⠀⠀⠸⠃⠀⠀⠀⢀⢩⣿⣧⠀⠀⠀⡎⠉⠉⠉⢻⡄
⠀⠀⠀⠀⢿⣿⣄⠀⠀⣤⠀⠀⠀⠀⣇⡄⠀⠀⠀⣠⣤⣴⠿⠟⠛⠓⠂⠉⠁⠀⠀⠀⠀⠀⢰⡤⠀⠀⠀⠐⣨⣿⡿⠀⠀⠀⠳⣤⣠⣴⠟
⠀⠀⠀⠀⠈⠻⢿⣷⠾⠋⠀⠀⠀⠀⠘⠀⠀⠀⢸⢧⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⡀⠤⢤⣾⡿⠃⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠰⠂⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠐⠶⡄⢀⡀⠀⠀⣀⠈⠇⠀⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣶⠾⢀⠔⠀⠈⠀⠀⠀⡆⠀⠀⠀⠀⢀⣄⡴
⠀⠀⠀⠀⠸⢷⠃⢀⠴⠅⢀⡇⠀⢡⠐⡁⠀⢀⢀⡄⡉⠀⠄⠀⠐⣷⢿⢇⡟⠀⠀⡀⠀⡘⢐⡞⠀⡀⢠⡀⣠⡼⠃⠀⠀⠀⡀⣬⣧⠄
⠀⠀⠀⠀⠀⠸⣦⣜⣹⡀⣼⣋⠀⢘⣾⠠⠒⣱⠏⠀⢀⠈⠀⠀⠀⢸⣽⣈⡁⠀⠀⠘⢶⣤⠶⢍⠁⢰⣇⢼⡋⠀⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠺⢿⣿⡈⠤⢽⣏⠀⢿⣇⣠⣠⠿⠒⢴⠊⠀⢀⣴⣿⣿⣿⠿⣿⣷⣦⡀⠀⠊⠀⠺⣇⠈⠙⠂⠈⠀⠀⣧⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠠⠆⠿⢿⣿⠸⡗⣶⠞⢋⣾⡫⠀⠀⢹⠀⠀⣾⠿⠉⠀⠉⠘⠈⠙⠻⡇⠀⠀⢀⣤⣿⣦⡀⠀⠀⢀⡴⡿⠆⡀⠐⠀⢀
⠀⠀⠀⠀⠀⢄⠀⡀⠀⠉⠳⡷⣿⢰⠟⠁⠀⠈⠁⠈⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢸⣧⣀⣹⡇⠀⠀⠈⠆⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣠⠋⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⣿⠛⢛⣿⣦⡄⠀⠀⢄⣠⣤⡠⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣧⡏⠀⡈⠀⠀⣭⣽⣿⡄⠀⠈⢷⣻⡾⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣕⣤⣨⠧⣤⣴⣾⣿⣿⠀⠀⠠⠞⠛⠓⡄⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣶⣿⣿⡿⠟⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⣥⠘⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⢀⣥⣀⠒⠸⠉⡰⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢟⡛⢤⠀⢀⢆⠗⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠟⡷⢿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⢹⢸⣇
⠀⠀⠀⢀⢰⡄⢸⢀⣷⡠⣰⠈⡗⠀⢠⠀⠀⠀⠨⡆⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⡀⠀⠀⠀⢀⡤⠚⣻⠃⣿⣾⡞⠿⠂⢀⡀
⠀⠀⠀⠃⢣⠉⡏⢁⡂⠂⢸⣶⠀⠀⠀⠑⠳⠴⠚⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢾⡏⠀⣽⠀⠀⣴⠣⢤⠠⠀⠀⠈⠈⠁⢀⡄⠃⠙⣦
⠀⠀⠀⠀⠴⡷⠇⢠⠿⠟⠁⠹⡀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡥⠀⡇⠀⢸⣷⣳⡓⢀⠂⡁⡄⠰⣆⡋⠁⠔⠀⣴⡆
⠀⠀⠀⢰⠆⠀⡀⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡀⠔⠀⠁⠈⢆⠀⠀⠀⠀⢸⢀⠀⡇⠀⣾⣿⣾⣍⠆⢒⡀⡀⢐⣛⠻⠉⠀⠞⠈⡇
⠀⠀⠀⢿⠀⣰⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⡇⠑⡇⠀⢸⣿⣿⣿⣟⣷⡶⢶⣄⣄⣠⣷⣦⣴⠲⠇
⠀⠀⠀⠸⣷⣏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠒⠠⣄⠤⠒⠁⠀⠀⠀⠀⢄⠘⣯⢠⡇⠀⠀⣿⣿⣿⣿⣿⣻⣟⣿⣭⡛⠛⢹⣧⡵⠁
⠀⠀⠀⠀⠙⠻⢦⣴⡄⢰⣠⣷⠟⠋⠀⠀⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢀⠇⠀⢿⣰⠇⠀⠀⠙⢿⣿⣿⣿⣿⣿⡷⢿⣿⢦⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⢄⠀⢀⡠⠂⠀⠀⠀⠄⠠⠠⠐⠁⠀⠀⠘⡟⠀⠀⠀⠀⠀⠉⠌⢿⣯⣽⣣⠿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡐⢀⠀⠀⠀⠀⠀⠘⠀⠄⠀⠙⢯⠀⠀⠀⠀⠀⠀⠀⢀⠸⣨⢐⡀
⠀⠀⠀⡠⡷⠂⣀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⠈⠀⠉⠆⠀⠀⠀⠀⠠⠁⠀⡦⠈⣼⡀⠀⢀⣠⡄⠀⡐⡞⠔⠀⠜⠃
⠀⠀⠀⠁⠙⡄⠉⠈⠀⠀⢀⡤⠞⢜⡂⠒⢦⠀⠀⠐⠀⢀⠀⠀⡄⠙⣡⣶⣄⠉⠀⠀⠀⠀⠀⢀⢠⡏⠱⡌⡎⢗⠆⡻⠿⠂⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⡇⠀⠀⠀⡠⠀⠀⠀⠀⡙⣆⠀⢳⠀⠀⠀⠀⠓⣠⠦⠴⡿⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⡥⠁⠈⡀⣿⡇⠀⠀⠀⠀⢠⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠰⡃⢄⠈⠀⠀⠀⠈⠈⢨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡀⠠⠀⠀⠉⠁⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⠇⠀⠇⠀⠁⠠⠶⠿⠂⠐⠀⠘⠄⡇
⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠲⢦⡤⠴⠀⠀⠈⠰⣐⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁
⠀⠀⠀⠀⠄⠀⠥⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢜⠀⡇⠈⢠⠀⢀⢠⠜⢀⠀⠀⠠⠖⠠⢄⠀⠐⠰⠋⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠠⣸⣆⠚⢰⡇⢠⡞⠀⣸⡁⠤⠆⠀⢰⠁⠀⢰⠋⣦⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⢠⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⣂⠐⠒⢁⡑⠓⢁⡀⠀⠀⠀⠙⢶⡞⡗⡶⢑⣿⡇⠀⠂⠀⠀⠀⠣⠄⠘⢉⣽⠪⡁⠰⢄⠀⠀⠀⠀⠀⣀⣀⡁⢨⡀⢀⠄⠈
⠀⠀⠀⠀⢀⠉⠴⠶⣅⣠⠂⢋⡀⠀⠀⠀⠀⠀⠈⢻⣧⠋⠀⠀⠀⠀⠀⠀⠀⢀⣐⣣⠈⠽⡟⠟⠢⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⢸⡌⠁⠘⠻⡆
⠀⠀⠀⠀⠀⠉⠟⠁⠊⡄⢉⡇⠀⠀⠀⠀⠀⠀⠐⠈⠭⠑⠂⢄⠀⠀⠀⠀⠀⢀⣲⣿⡺⠂⠆⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠰⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠐⠒⠁⠂⠀⠐⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡊⠉⢹⡄⠀⠜⠉⠀⠀⠁⠀⠀⠀⡾⣧⠊⢀⠀⡄⠀⠀⠁⠀⡀
⠀⠀⢀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢐⡄⠀⠀⠐⢄⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠃⠁⠀⠈⠦⡐⢄⡀⢀⣴
⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⣀⣄⠀⣀⢀⠀⠀⠀⠀⢹⣿⠊⠁⠀⠀⣠⣖⣶⣀⠀⠀⠀⠀⠀⠀⡰⣪⡿⠀⣀⡀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠁⠀⡠⠖⠛⠁⠀⠀⠀⠀⢹⣿⡿⠂⠁⠀⠀⠘⠓⠒⠚⣁⣠⣾⠵⠋⠀⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⣞⠀⢀⡠⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⢤⡀⠀⠀⠀⠅⠀⡀⢽⠀⠀⠀⡀⠀⣰⡌⢒⡔
⠀⠀⠊⠳⠘⠈⠀⠀⣀⠴⣆⠠⢄⠀⠐⠀⠀⠀⡀⠟⣤⣄⠂⠀⠀⠀⠀⢀⡞⢅⡛⣦⢴⣾⠇⠀⠉
⠀⠀⠀⠠⠄⠀⢀⠄⠀⠀⠈⣧⠈⡧⠀⠀⠈⠲⠆⠺⠏⠩⠀⠀⠀⠀⠀⠀⡟⢸⠈⠠⢐⡇⠀⠀⠀⢰⠧
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⢸⢘
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠃⠐⠀⢤⡶⠄⠀⠨⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠲⠴⠂⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠸⡀⡀⣼⠀⡦⠀⡔⠁⠀⢀⠄⠁⡰⠀⠈⠁⠀⠀⠀⠀⠀⢢⠀⠐⠀⠀⠀⡠
⠀⠀⠀⠀⢐⠤⠂⠰⠆⡀⠀⠈⠻⣤⢿⣬⢡⡾⠁⠊⠀⠈⢆⠀⢗⣻⠂⢠⡀⠀⠀⠀⢀⠀⠂⠅⠀⡀⠊
⠀⠀⠀⢈⡁⠒⢅⢐⠘⡄⠀⠀⠀⠀⢙⣧⡋⠀⠀⠀⠀⠀⢠⢶⣌⠿⠛⠁⠀⠀⠀⠀⠀⢉⠀⠉⡶⠁⠙⡧
⠀⠀⠀⠀⢈⡁⡁⠂⡇⠀⠀⠀⠀⠀⠁⠈⠉⠀⡀⠀⠀⠀⠸⢿⡟⠙⡆⠘⠀⠀⠀⠀⡤⢀⠄⠀⠃
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠰⠛⠁⠱⡀⢄⠀⢀⡆
⠀⠀⠁⠋⠀⠀⠀⢀⣠⡀⣀⣀⠀⠀⢀⡶⠈⠁⠀⣠⣶⣤⡀⠀⠀⠀⠠⣶⠆⢀⣀⠐⡀⠀⠀⠈⠂⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠉⠉⠁⠒⠓⠉⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠶⢤⣄⠀⠀⠀⠀⣀⢶⣦⣟⣻⢛⣄⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⢀⣴⠀⠀⠻⣷⣤⠀⠀⠹⣄⠀⠀⣿⣆⣻⢹⡗⠈⣿⣿⣴⠀⠀⣖⢾⠾⠀⠜⠙⡟⠀⠀⢠⣄⡀⢀⣿⣿⠂
⠀⠀⠀⠰⠁⢸⣇⠀⠀⠙⢿⣷⣶⡄⢸⠀⠀⠈⢽⣿⣾⡏⣠⣟⣾⠟⠀⠀⣾⣜⢀⢜⣲⣼⢛⠂⠀⠀⢿⡷⢾⣿⣷⡶⢏⢀⣀⡀
⠀⠀⠀⠆⠀⠹⣿⠀⣤⣀⣀⠉⠙⢷⡞⠀⠀⠀⠀⢸⣿⣼⡿⠋⠁⠀⠀⠀⣾⣻⣮⣽⣟⠁⠁⠀⠀⢰⢾⣿⡾⣿⠉⣿⣿⣿⠋
⠀⠀⠀⡄⠀⠀⣿⠀⢻⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣀⣴⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢁⡅⠋⠉
⠀⠀⠀⡄⠈⣼⣿⠀⠈⠿⣦⠀⠀⠀⠀⠀⠰⣿⡿⢄⣸⡗⢀⠀⠀⣿⣴⡿⠀⠀⠀⢠⠄⠀⣤⡄⠀⠀⠀⣾⠛⠓⠀⠀⠀⠙⣦
⠀⠀⠀⢻⣶⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⣿⡿⠏⠉⠀⠀⠀⠉⠀⠀⠀⢀⡌⢷⡷⠿⣇⣔⡆⢸⣏⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠻⡿⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠁⠀⠘⣧⡸⣇⡆⠸⣷⠁⢸⡇⠠⠀⠀⣠⠞
⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣤⣧⣼⠇⠀⢸⡁⠂⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣶⣶⣿⣷⠀⠀⠀⠀⠀⠉⢿⡖⠀⠀⠀⢸⡌⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡿⣿⡿⡀⠠⠀⠀⠀⠀⡏⠉⠄⠀⠀⡈
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠧⢂⣶⡄⠀⢠⡇⠀⠀⣿⣿⣶⣷⣾⣶⣶⣶⣶⣶⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⣀⣀⣶⡀⣤⡀
⠀⠀⠀⠀⡄⠘⣻⠶⣶⣄⣀⣀⢈⣿⠀⣰⡿⠁⠀⠀⠘⠻⠿⠿⠼⠿⠿⢿⠿⠝⠀⠀⠀⡇⠀⠀⠀⠀⢐⡘⣂⡿⢯⣻⣦⣵⢧
⠀⠀⠀⠀⠈⠙⡉⣒⡴⠾⡿⣿⣾⣇⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣭⣤⣿⣷⣯⣤⣿⣿⠀⠁
⠀⠀⠀⠀⠜⠉⠉⠉⠝⠲⠶⠛⠻⢿⣷⣤⣤⣤⡀⠀⠀⠀⣤⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠾⠏⣿⣿⣯⣿⡿⢿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⣹⣿⡄⠀⣼⣻⣿⣞⠫⠓⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣸⣾⢻⢳⡾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠸⣿⣾⣭⡬⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠸⣧⣏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠢⠀⠀⠈⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠾⠀⠀⡴⠓⠾⠾⣷⣄
⠀⠀⠀⠀⠀⡀⢀⣴⣅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢈⣧⠀⠀⡠⢤⣼⡿⠉⠀⠀⠸⠀⠀⠀⠀⢩⣿⡄
⠀⠀⠀⠀⣟⠀⣠⡿⠿⠷⣶⣶⣏⠀⠀⠀⠀⢀⠀⠀⣹⡇⠀⠀⠙⠻⠿⠿⠟⠃⠀⢸⠀⠀⠉⣷⠀⠀⠀⠸⣆⡀⠀⠀⣶⣿⠃
⠀⠀⠀⠀⠻⢿⣿⠄⠀⠀⠀⢹⣿⣷⣦⠞⠀⠈⠳⠾⠿⠁⠀⠀⠐⢲⣄⠀⠀⠀⠀⢈⡷⠶⠟⠃⠀⠀⠀⠀⠙⠶⠬⠽⠟⠉
⠀⠀⠀⠀⠀⠘⠿⠿⠷⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣴⣾⠏⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣀⠀⣴⣦⠔⢤⣴⣄⣠⣤
⠀⠀⠀⢠⣘⠉⡿⣿⣨⠐⣿⠋⡹⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⢀
⠀⠀⠀⠸⣀⢿⡀⠟⢨⡆⢹⠹⠀⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠙⠚⢿⣯⣴⠓⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⠤⣼⠛⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗
⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⡀⠈⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠑⠦⣄⣴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆⠀⠀⡀⠀⢙⠇⠀⡄⠂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⢀⠈⠀⢈⢀⡀⢠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢆⣫⠾⠄⠜⣍⠆⠀⠐⠙⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⡀⢀⠃⡤⣧⡀⠁⠀⠂⠀⠀⣠⠀⠒⠃⠀⠀⠀⠈⠑⢠⡂⠁⢸⠀⠀⡄⠙⠂⠀⠀⠀⠀⢃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠠⣗⡍⡁⠈⠀⠀⠀⠀⠁⠀⢒⠀⢀⠀⠀⠀⣀⠘⠃⣸⠃⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢟⣳⠁⠀⠀⠀⠀⠀⠀⠀⠊⠡⠄⠀⣤⠒⠉⣰⣞⠁⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣁⠀⢀⣼⠀⣀⠀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠃⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡒⣸⠿⣴⢯⠎⠚⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⡸⣜⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢛⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣀⠀⠀⢹⡤⠀⣺⠃⠀⣼⠃⢀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢹⣄⡀⠨⡷⠀⢼⠃⢠⡯⢀⣸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⡫⢃⡖
⠀⠀⠀⠀⠀⢠⡌⠳⣄⠇⠀⠙⡃⡎⣠⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣞⡴⡻
⠀⠀⠰⣐⡄⠘⣧⠀⠈⢆⠀⠀⢹⠞⠉⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠞⡱⡇⢋⡴⠁
⠀⠀⠀⠈⠉⠲⣅⠀⠀⢘⡇⠀⡮⠀⡀⣸⠋⠁⠀⠀⠀⠀⠀⢠⠋⡴⣼⠱⠏
⠀⠀⠀⠀⠒⢦⡈⢇⠀⠈⢣⢸⠀⢀⡟⠃⠀⠀⠀⠀⠀⠀⢀⡇⠰⡱⡙⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢄⠀⠀⠀⠀⠀⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢸⠘⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣷⢣⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢈⠂⡀⢀⠄⠊⡄⠘⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣘⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠃⠇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢆⢀⡜⢀⠘⠇⠈⢀⢁⢃⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⡇⡟⡘⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢛⠀⡌⡸⠘⠀⡸⠉⠀⠀⣆⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡇⣷⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢌⠘⡖⠠⢳⠀⠶⠄⠲⠅⢀⡥⡀⠄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠃⡿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⠙⠢⢑⢰⣆⠼⣤⠤⢐⡞⠩⠟⠨⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⠀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠂⠀⠀⠀⠀⠀⠙⠓⠚⢽⡰⡱⠚⠂⠡⠨⠅⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢸⠀⠀⠀⠀⠀⢸⢀⣣⠁⠀⠀⠀⠀⠀⠘⡿⠱⠂⠼⠷⡛⠀⠀⠀⠀⢠⠂⠀⠙⠛⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⠀⠀⠀⠀⠀⡘⢻⠿⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⢡⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⡅⠀⠀⠀⠀⢸⠀⠀⠈⡄⠀⠀⠀⠀⢰⡀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢱⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⠀⡸⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠃⠀⠀⠀⢸⠀⠀⠀⠈⡆⠀⠀⠀⡇⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣆⠀⠀⢀⠇⠀⠀⢰⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢻⠿⡧⠀⠀⠀⠧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠡⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⠆⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⠀⡄⠒⠍⡰⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⠀⠀⠁⠰⠦⠀⠀⠀⠀⠀⠐⡄⠀⢠⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠋⡙⠰⠀⠀⠂⠚⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢻⠟⣲⣤⣄⠌⠂⠀⠀⠀⠀⠀⠀⠠⠄⢘⣃⡀⠀⠀⠠⣀⡴⠁
⠀⠀⠀⠀⠀⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⣀⡀⠈⡄⠀⣾⡿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠘⢁⡀⢐⣦⠘⢏
⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠈⠆⠀⠉⢻⠃⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠈⠈⠅⠈
⠀⠀⠀⠀⠀⠀⢀⡷⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠟
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡃⠀⢂⠀⠀⠀⠀⠀⠀⠒⢤⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⡄⠂⠀⣴⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢠⢀⡇⢠⣏⠀⢀⡾⠀⠀⢡⠋⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢿⡂⡠⢨⣏⠀⠻⠁⢠⣠⠟⠀⢐⠈⠀⠀⠀⣀⡤⠀⣴⣀⠢⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⢿⡀⢻⢸⠇⢀⡾⠯⠀⡀⠈⠀⠀⠰⠂⢈⠶⠲⠊⠀⠉⡼⠓⢬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢿⡠⠋⠀⠀⠀⠀⠀⠀⠀⣠⢶⡏⠀⠀⢰⠴⠺⡀⠀⢀⣹⠿
⠀⠀⠀⠀⠀⠀⠀⠒⣒⣜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠜⠞⠳⠢⢀⠀⠀⠀⠀⠀⠀⠁⠀⡰⠶⠾⢇⡐⠀⡜⠃⠈⠡⡠
⠀⠀⠀⠀⠀⡀⠀⠂⢀⢩⠇⠉⠁⠰⠦⡀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠈⠀⠀⢆⠀⠀⠀⠙⠓⠶⢅⣴⠢⣄⡹⠛⠸⠒⣄⡔⠃⠊
⠀⠀⠀⠀⠀⠠⠶⡀⠜⢙⣶⢶⠶⢄⠀⠀⠆⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠚⢀⡂⠀⠈⢳⣀⣀⣼⠔
⠀⠀⠀⠀⠀⠁⢺⡏⣌⡉⠘⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠲⠴⠶⠢⣼⠋⡀⢀⠠⠶⠃
⠀⠀⠀⠀⢄⣽⣟⡿⠝⠉⠲⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠈⠁⠐⢠⣤⣀⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁
⠀⠀⠀⢸⠁⠀⠈⣷⠀⠀⡠⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⡀
⠀⠀⠀⠈⠂⠀⠴⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁

⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⣆⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣠⣀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠞⠛⠛⠿⢿⣧⠀⠀⠦⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⠃⠀⠠⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠐⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣺⡇
⠀⠀⠀⠀⠲⢷⡶⠀⡎⠀⢀⡄⠀⠀⠀⣀⣡⣾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢄⣅⠀⠀⠀⠘⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⣿⠁⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡤⠄⡀⢸⣯⢭⣿⣿⣿⣿⣿⡿⠀⠠⠀⠀⠀⠠⢿⠀⠀⠄⢀⡇⠀⠘⣇⠘⠂⠀⠤⠊
⠀⠀⠀⠀⠀⠈⠁⡰⡀⠀⠨⠃⠀⠘⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠀⠀⠀⣾⠁⠀⠀⢹⠂⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠁⠀⠀⠀⢀⠀⠀⣰⡏⠀⢐⠀⡎⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢀⡀⠀⢀⣀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠱⣿⠋⠀⠀⠀⠜⠀⠀⡾⣱⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢳⠀⠀⢿⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣼⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠸⣇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠁⠀⠀⠀⠁⢧⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⣀⣶⡎⠁⠀⠐
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠸⢫⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣏⡉⠀⠈⠛⠛⠻⠾⣮⣋⢝⡻⢛⡷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠇⡰⢠⠙⣧⠀⠀⠀⠀⠀⠀⠈⠻⢧⣶⡭⠶⠛⠋⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢰⠀⡘⢠⢁⠇⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⡏⢠⠃⠆⡰⢡⢃⠎⡐⢰⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡽⣷⡄
⠀⠀⠀⠀⠀⠀⣼⡿⠡⢁⠇⡌⡰⢁⢂⠞⣄⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⣸⣯⣴⡾⢿⣆
⠀⠀⠀⠀⠀⣼⣿⢡⠃⠎⡌⡰⠁⢂⠎⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢟⠝⡩⣻⣯⢒⢝⣿⡆
⠀⠀⠀⠀⢰⡿⢸⠆⡜⡜⢰⠃⢀⠎⡰⢡⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣕⡡⣊⡼⠋⠙⠓⠛⠛⣿
⠀⠀⠀⠀⢸⡷⠿⣤⣵⢠⠃⢄⠎⡰⢡⣿⣵⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣀⣴⢿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠹⣇⣸⡎⡰⢱⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⢏⠕⡡⢻⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠉⠙⠓⠦⣭⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢕⣕⠡⠊⡠⣺⡇
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡽⢷⠶⢲⠖⡶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣣⡿⠃⡠⣮⠎⣽⠇
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠎⢡⠃⠠⢁⠇⡈⢸⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠟⡠⢊⠔⢡⢾⡿
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠹⣶⣰⠆⡰⠃⡌⢠⢃⠇⢌⡼⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⢊⠔⡡⠚⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠈⢻⡔⠁⡜⢀⢆⠎⢜⣞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢊⢔⣩⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠹⡎⢀⢂⢏⢎⢎⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢹⣣⠏⢎⢎⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⣟⡘⠎⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⣿⡌⡜⡿⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠾⠷⠶⠶⠶⠾⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣤⣤⣶⠶⠶⢶⡖⢶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⠋⠩⢡⣢⡤⠄⠒⠛⢶⣤⣶⣾⣿⣿⣯⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⣠⠹⣿⠀⠀⠀⢠⣿⣯⣼⣿⡿⣷⡝⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⢠⣴⡾⢻⡁⣰⡿⠀⢀⣠⠾⣣⠞⠟⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⣀⠀⠈⠿⠁⠘⢻⣿⣿⠞⢿⣿⡟⠿⢴⣶⡁⡀⢠⣆⠀⠀⠀⠀⠀⠀⠸⣤
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠼⠁⠀⠀⠀⠀⠻⡆⠀⠀⠀⣤⠴⢿⣏⣤⡄⢀⣀⣀⡎⡙⣿⠇⠛⠃⠀⡄⠀⡀⠀⠻⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠈⠙⣁⣴⣤⣥⠶⠟⠗⠀⠁⠈⢻⣿⣶⣗⠂⠀⠀⠀⢈⢀⠸⡿⠗⠀⠘⠂
⠀⠀⠀⠀⠀⡄⠀⢰⣿⠀⠈⠀⠀⠀⠀⢀⣼⣿⣿⠉⠀⠀⠀⠀⠀⢤⠀⠀⢹⣿⠿⠇⣠⣶⣾⡆⣄⢠⣄⣤⡀⠀⠠⣤⣾⡄
⠀⠀⠀⠀⠀⠀⢠⡿⣿⡇⢠⣿⣟⢳⡀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣤⡤⠝⠛⠋⢻⣿⡿⠟⠛⢣⡀⠀⠈⢸⣧
⠀⠀⠀⠀⠀⠀⢸⣗⣿⣆⠸⠋⣽⣭⡻⠿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠛⠁⣾⡿⠏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠘⠛⢿⢿⣿⡄⢹⡟⣿⣤⣌⣻⣶⣧⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢻⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠈⠈⢿⣷⣌⠛⠛⠛⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣸⠃⠰
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠛⢠⣹⣿⠃⠀⡤⣄⢨⠙⠻⣧⡀⠀⠀⠀⢀⡿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⡿⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠸⣦⠦⡀⠀⢻⡁⠞⠉⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠈⠿⢇⣀⣀⣠⣤⣶⣤⡆⣿⠿⠏⠀⠖⢀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⢄⠢⠈⠢⢀⣵⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠑⠢⣿⡷⠀⠀⠈⠉⠉⠿⢿⣿⣿⣇⢀⡖⠀⠀⡀⣠⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢷⣄⠀⣆⣄⡀⠀⠁⠀⠀⠀⠀⣠⣿⡾⠆⠀⣀⠀⠀⠔⠙⣿⣿⠘⢶⡀⢀⣼⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠱⣬⡀⠀⠀⠹⡇⡿⠉⠿⣠⡄⠀⠀⠀⢾⣿⡟⠀⠀⠈⠁⠀⠀⠀⣧⣾⡇⠀⠀⢠⡞⠝⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠳⣧⢃⠀⠀⠉⠀⣰⣿⣿⠋⠋⠀⠀⠀⠀⣀⡀⠴⠾⠿⣿⡇⢀⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣞⠻⣯⡀⠀⣠⣾⣿⣿⣋⣠⠤⠂⠀⢚⠁⠄⠀⢀⣀⣼⠿⢿⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠙⠻⠿⣦⣿⣿⣿⣿⣿⠿⠟⠛⠟⠛⠛⠛⠶⢿⠿⠟⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠐⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣠⡄⠀⠀⠀⠀⠘⠿⣿⡆⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠐⢠⡄⠀⢸⠆⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠘⠒⠀⠀⠀⢀⣠⡄⠀⠐⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⣀⠠⠄⠀⠀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠘⠆⣀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⢈⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⡀⠀⠀⠀⢀⣴⠞⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀⢐⡀⡤⠄⠓⠚⠒⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⠀⠀⠀⠈⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⣼⠋⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠒⢀⡀
⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢡⠉⠀⠀⠀⠀⠀⠤⠤⠦⠀⠉⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⡀⢀⡿⠀⠀⠠⠄⠋⠀⠀⠀⠀⠓⢄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠄
⠁⠸⠁⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢠⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠿⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⡐⠉⠙⠛⠀⠀⠀⠀⠀⠀⠁
⠉⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⠻⢿⡷⠀⠸⣿⣦⠀⢀⣤⠀⠀⠀⠀⠀⡀⠀⢰⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠛⠀⠸⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⢀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠋⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡞⠁⢀⣴⣾⠆⠈⣴⣦⡀
⠀⠘⠳⣄⡀⠂⣄⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⠋⠁⣶⣦⠈⠛⠿
⠀⠀⠀⠈⠑⠂⠤⠅⠐⠒⠀⠀⠀⠀⠀⠒⠒⠀⠀⡠⠂⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢿⠏
⠀⠀⠀⠀⠀⠀⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡀⠈⢀⣤⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠛⠛⠛⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢠⡀⠀⠰⣀⠀⠰⢶⣶⣦⡀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡄⢀⣰⠎
⠀⠀⠀⠀⠀⠘⠛⠿⠟⠃⠀⣠⣶⠀⠀⠀⠀⠀⡆⠰⡀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡌⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠘⠂⠈⠢⠄⠀⠀⠠⠄⠁⠀⠀⡀⠀⠤⠤⠤⠤⠐⢀⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⣤⣬⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠙⠿⠇⠲⠦⠀⠀⠀⠀⠙⠛⠛⢶⡀⠀⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠗⠀⠀⢼⣷⡄⠀⠀⠀⠀⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠠⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠎⠁⢠⣶⣾⠿⠀⠀⠋⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠉⠀⠀⠀⠛⠛⠋⢁⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢀⣀⠀⠀⠐⠀⢸⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡠⠔⠃⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠘⠿⣷⣀⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠀⠀⠀⠀⠀⠈⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠒⠂⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣅⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠛⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⣙⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⡤⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⣌⠳⠶⠚⠛⢫⡄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⢀⣀⣀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠓⠊⠁⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠠⠤⠤⠤⠤⠤⠤⠤⠄⠠⠀⠀⠀⣀⠤⠀⠠⠤⠂⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⡿⠿⠿⠿⡿⠿⠿⠿⡉⠿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣟⣛⠛⢛⣛⡛⣻⣿⣟⡛⠛⣛⠛⣿
⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢀⣤⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠛⠛⠛⠳⠶⣦⣄
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣸⠃
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣤⣤⣤⣾⡄
⠀⢹⡄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠉⠀⠀⠈⠙⢟⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠁
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣀⣵⣄⣈⡉⠙⠒⠒⠒⠛⠛⠉
⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣰⠊⠉⠀⠀⠀⠀⠀⠈⠉⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠠⣄⠀⢻⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣄⣀⣀⣀⣀⣤⣿⡿⠳⣮⣳⣤⡙⣷⡄⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠻⢿⣿⣿⣿⣦⣀⠀⠠⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠳⠾⠿⢿⣝⡒⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣤⣤⣤⣤⣭⣭⡴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣴⣧⣴⡄⠀⢀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⡿⢿⣿⣧⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣍⠛⠛⠻⢿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠹⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣴⣿⣷⣤⣄⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠻⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠉⠁⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣶⣿⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠻⠻⡿⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⠉⠛⠀⠉⠙⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⣻⣿⠟⣿⣿⢟⣭⣿⣿⣿⡛⣿⡛⠓⠾⣭⣍⣱⠶⠶⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⣊⠿⠛⠓⡻⢛⣹⣤⡾⣿⢺⣍⣠⡿⢣⢻⣿⣻⡿⣶⢶⡶⠦⣍⣍⠙⢛⠒⠶⣈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡰⠊⠀⠀⠀⠀⠀⣩⢾⡟⣿⢻⣼⠛⣿⠃⠸⢸⡆⠙⣷⡺⠲⣧⠐⣹⣆⠁⠀⠁⠄⠀⠑⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⡎⠀⠾⠛⡿⠐⠸⡆⠀⠀⡏⠂⠸⠳⠤⢿⠄⠈⠈⡉⠓⠠⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘⠀⠀⠀⠞⢡⡀⠀⠘⠀⠀⠇⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠑⠲⣄⠀⡤⠖⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠏⠀⠀⠀⠀⠀⠈⢻⠀⢀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⣿⠀⠀⠰⠆⠀⠀⠀⢸⠀⠈⠀⠀⢠⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢀⡾⠓⠶⠴⠞⠁⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣰⠂⠀⠀⠀⠀⠙⢷⣤⣤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠸⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠀⠀⢹⣧
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⡿⠋⠉⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠸⣀⡸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠙⢿⡿⠟⠻⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⡀⠀⠀⠀⢀⣀⣈⣿⡗⠀⠀⠀⠀⠀⠰⠒⢆⠀⠀⠀⢻⣇
⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠣⢀⠜⠀⠀⠀⠈⢿⡆
⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢀⣿⠁⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠹⣷
⢸⣿⠀⠀⠀⠀⡎⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠋⠀⠀⠀⠀⠀⢻
⠸⣿⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠙⠦⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⢆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣙⠄⠀⠀⠀⠀⣼⡟
⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⢣⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣶⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠉⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⢾⣭⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠉⠁⠀⠀⢀⣤⣤⣘⣿⣧
⠀⠀⠀⠀⠀⢀⣿⡿⠶⠶⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⣤⣄⢸⡇⠀⠉⢻⣿⡆
⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⡾⠇⠙⡆⠀⠀⣿⣷
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠚⢶⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣤⣤⣤⠾⠃⠀⠀⢹⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣠⠟⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⣀⣠⡼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀⠈⠷⠴⠶⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⣠⠞⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣄⠀⢸⣿
⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⢻⡄⣀⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⠛⠶⣤⡀⢠⡴⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣼⡿
⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠈⠛⠋⠀⣼⠃⠀⠀⠀⠀⠀⣯⡈⠙⠛⠻⣆⠀⠀⠀⢻⣾⡄⠀⢀⡴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠈⠷⣤⣤⣤⠟⠀⠀⠀⣾⠀⠙⠓⠋⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⣠⣿⠀⣠⡴⠶⣄⠀⠀⠀⠀⠀⣰⠟⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠹⢦⡀⣹⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⡙⠋⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣤⣄⣀⣀⣼⣇⣀⣀⣈⣀⣀⣀⣤⣤⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠈⣳⣄⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠲⢤⣼⠃⠀⣠⠖⠋⠉⠀⢀⡟⠉⠀⠙⠲⡔⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⣚⣫⣽⣁⠀⠀⢀⣀⣤⣤⣿⣤⣄⣿⡀⠀⢀⣀⣼⣄⡀⠀⠀⠀⣹⣤⣬⣧⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⠟⠁⠀⠀⠈⢳⡞⠉⠀⠀⠀⠀⠀⠀⠈⣿⢿⠋⠀⢀⣀⣙⣦⣠⠋⠁⠀⠀⠀⠉⠓⢦⡀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠸⣄⠀⠀⠀⠀⠀⢹⡄⠀⣠⠶⠚⠉⠙⢳⡏⠘⡤⠚⠉⠀⠈⠙⣿⠀⢀⣀⣀⡀⠀⠀⠀⢹⡆⠀⠸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⣏⣹⠃⠀⠀⠀⠀⠀⢳⡜⠁⠀⠀⠀⣠⠔⠋⠉⠁⠀⠀⠉⣦⡤⠖⠋⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠦⣤⣄⡀⠀⠀⠈⠉⠉⠛⠛⠒⠦⢤⣀⣀⣀⣸⣇⣀⣀⣀⣞⣡⡤⠤⠤⠖⠒⠊⠉⠁⠀⠀⣀⡤⣀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢝⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠛⠛⠋⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠉⠓⠊⠉⠙⠓⠲⢤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠔⠃⠊⢣
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢧⡄
⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠓⠦⣀⣀⣀⣀⠀⠠⣤⣤⣀⣀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣴⣠⡤⠶⠾⠴⠒⠋⠉⡤⠞⠛⠛⠛⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠓⠲⠶⠶⠶⠶⠖⠒⠋⠉⠁⠀⣀⡤⠖⠚⠋⠉⠛⠓⠲⢤⣀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠚⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠙⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠙⠲⣍⣓⠶⠦⠤⠤⠶⠚⠉⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠛⠲⢤⡀⠀⠀⣀⣀⣤⡤⠤⠴⠦⣤⣤
⠀⠀⢀⣀⣀⣀⣩⠿⠗⣂⣤⣶⠾⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣄⠀⠀⠙⠛⠋⣉⣡⠤⠖⠚⠋⠉⠉⠉
⢶⠿⠿⠿⠿⢶⣖⣚⡿⢟⣫⠴⠒⣿⠀⢀⡴⣶⠃⠀⣠⠶⣄⠀⠀⠀⡔⢳⠀⠀⠀⠀⠀⠐⣏⠁⠀⠀⠈⢣⡀⢶⡚⠋⠉
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠀⠀⣠⡟⠀⣸⡵⠏⠀⢰⠇⠀⠈⢧⡀⠀⢻⡟⠀⢀⠀⠀⢀⠀⠈⠳⣤⡀⠀⠀⠙⢦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢉⣠⡼⣋⣤⡆⠀⣾⠀⠀⢀⣼⠃⠀⢸⡇⠀⣿⡀⠀⢸⡳⣦⠀⠀⠉⠓⢦⣤⣤⣭⣓⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⡴⢊⣥⠶⠛⢩⣯⠞⠉⢸⠃⢠⡇⠀⢠⡞⢁⡀⠀⣿⡇⠀⣿⠁⡀⠀⠙⢾⡆⢻⠓⢦⣄⠀⠲⡶⠮⣭⡻⣄
⠀⠀⠀⠀⠀⢠⣿⠞⠉⠀⠀⠀⠙⠋⠀⢀⡾⠀⡘⣇⠀⡾⢠⠏⢷⠀⣿⡇⢸⣿⢰⡏⠳⢦⡀⢹⣜⣧⠀⠈⠳⣄⠹⡄⠀⠙⠾⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⡞⣷⢸⣸⢇⡏⠀⣸⢀⡿⢀⠈⣿⡘⡇⠀⠈⡇⢸⡟⢿⡧⠀⠀⠸⡆⣿⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣋⡥⠞⠋⠀⣾⣸⣿⡾⠀⠀⢿⡿⣡⢾⡇⡟⣇⣷⠀⠀⢿⠈⡇⠀⠀⠀⠀⠀⣧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠷⠛⠉⠁⠀⠀⠀⢰⢧⠏⠈⠀⣠⣴⣫⠞⠃⢸⢳⣧⣿⠇⠀⠀⠘⣇⢷⠀⠀⠀⠀⠀⢻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠻⠛⠋⠁⠀⠀⣾⡾⠉⠁⠀⠀⠀⠀⠙⣾⣧⡀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢹⣶⡴⣗⢲⣾⣶⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠾⣃⡀⣅⣠⠎⡀⠫⢰⣅⠉⣹⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣦⠀⢨⡵⡎⠷⡈⠳⡏⢉⢠⡼⠙⡴⢩⣴⠌⠦⠤⠰⣴⣇⠰⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠈⠉⡘⠆⣤⠀⣤⣯⠀⡟⣋⠀⣷⠼⡏⠗⠀⡄⡴⠾⠇⠈⠁⢀⠉⢤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠒⠃⢀⢜⠈⠛⠁⠈⣃⠀⢰⡧⢫⠤⠀⣄⢧⠤⠶⣇⡰⠀⠸⢗⠱⡜⠀⡀⠤⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠳⡄⠉⠲⣼⠈⠳⢪⡇⠰⠬⠢⣿⡀⠀⡾⡈⠳⠙⣇⡼⣁⠀⢧⣖⠘⠂⡷⢋⠐⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠡⠖⢀⣈⣻⡄⠐⠶⠘⡀⠀⡨⠽⢿⣧⡌⣧⡾⠯⠘⡁⡆⢒⡈⢀⡾⡁⣀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠉⠀⣠⠹⣄⡈⠒⢧⡀⡟⠢⡴⣿⣿⠏⡙⠖⠀⢠⠇⠊⣦⡼⢿⡯⠇⠀⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠢⢍⣀⣊⣭⠿⠛⢛⡻⠿⣷⣼⣿⣎⣴⣤⣾⠷⠶⣟⣭⣐⣀⠤⠊⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠊⠁⢅⠀⠀⡸⠔⠋⠉⠛⢻⣿⡿⠏⠐⠈⠀⠤⠀⠈⠉⠈⠐⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⡴⢻⣟⣹⣿⢿⡿⣌⢛⢧⡀⠇⠈⠐⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠖⠁⢒⡿⢰⣿⠟⣽⣿⠘⣿⣿⠻⡦⣕⠒⠤⠤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⣐⣀⣀⣠⣥⢶⣿⣱⢚⣿⣏⣧⣿⣾⣷⠀⡌⠉⠱⠒⠤⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⣚⣡⡼⣯⣼⡏⣡⣟⣵⣻⡷⣝⡀⢭⠐⠀⠈⠂⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠹⡄⠉⣠⠜⢣⠟⡗⠁⡽⡖⠦⠤⣐⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱⠞⠁⠈⠟⠔⠁⠀⠈⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠉⠉⠈⠉⠉⠉⠉⠉⠉⠛⠒⠶⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⡡⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠾⠉⠻⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣅⢌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠲⠄⠀⠐⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣥⣙⡋⢘⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⠿⢏⠵⡹⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣤⡰⣌⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣿⠓⢣⣶⠹⢷⣀⠀⠐⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⢀⢀⡚⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⢛⣿⣻⡏⡛⢹⣆⣤⡈⠀⠀⠂⠀⠀⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀⢹⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡻⢿⣿⣯⢿⣦⣠⠑⠀⣷⡻⣷⠃⡃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢯⣾⡷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡿⣿⣿⣻⣿⣿⣶⣼⢧⡮⣿⢻⣉⣥⠀⠀⠂⠀⠀⠐⣠⡀⠀⠐⠂⠀⠲⣰⣔⣾⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢽⣿⣿⣿⣯⣛⣪⣴⣤⣎⣉⡱⢎⣴⣴⡆⠐⣀⠉⠀⢠⢤⣮⣵⣾⣶⣿⣿⣯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣟⣿⣿⣿⣿⣿⣿⣟⣿⣎⢛⠟⢀⣠⣾⣶⣹⣾⢿⣿⣾⣿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡟⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣯⣵⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣽⡻⣿⣻⣿⣿⡿⣿⣿⣿⣿⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠾⠿⠿⠿⠿⠛⠋⠁






⣀⣀⣀⣄⣀⣤⣀⣄⣤⣤⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣟⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣽⣽⣿⣯⣭⣭⣿⣭⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢤⣰⠤⠒⡲⢩⣉⠙⣯⡸⢇⣵⣶⣦⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠋⠓⠶⠾⠞⠛⠷⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡞⠁⠠⡀⠀⠭⠛⠦⡤⠒⠶⠦⢚⣩⠉⣩⠅⡠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣇⠀⠀⡀⠄⠀⠀⠀⠁⠀⠘⣟⠰⣦⣙⠋⣄⣀⡡⣬⡶⡀
⠀⠀⠀⠀⠀⢀⣴⠿⣬⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠁⠀⠀⠀⡀⠀⣄⢀⡉⠀⠉⠉⡤⣄⣬⠨⠏⢀⢠⣦
⠀⠀⠀⠀⣀⠘⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠇⠀⢄⡄⠀⠀⠑⢀⠛⠆⠀⠢⠸⣀⠀⠉⡀⠁⠘⠀⠠⠄⠈
⠀⠀⠀⢠⣤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠪⠚⣶⣁⠀⠁⠀⠀⠂⠈⠀⠉⠀⠀⠀⢀⠀⡄⠁⠀⠀⠀⠀⠠⠀⢨⢶⣸⠇
⠀⠀⢠⢄⣠⠀⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢀⣴⢏⠟⠇⢄⠀⠩⠀⠖⠁⠈⡁⠰⠆⢀⡀⠀⠀⠀⠀⠄⠀⠈⠐⠀⠀⢁⠀⠰⣬⠿⡴⠆
⠀⠀⣀⣴⢶⠀⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣟⣸⠏⢂⠀⠲⣬⣀⠈⡀⢀⠑⠂⠀⠊⠀⠀⠅⡀⠀⠀⡀⠢⠠⠌⠀⠈⠀⠁⠄⠁⠉⠺⠳⠃
⠀⣰⠿⠶⠦⠊⠠⣢⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢣⡤⠀⠒⢊⠴⡖⣟⠐⠉⠢⠶⠀⠐⢒⢶⠌⢠⠀⣤⠀⣠⠀⠀⠈⠐⢠⠐⠀⢂⠀⠇⠀⠘
⠰⠃⣠⣤⢲⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡯⢉⡭⠴⢴⡊⢉⣂⡐⢀⠓⠢⠴⠊⠀⠐⠎⠀⢧⠈⠁⡈⢀⡦⢀⠀⠈⠀⠀⠠⠀⡀
⠰⢃⠶⠢⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣃⠀⢰⡋⢀⣀⣤⡹⣞⠉⠳⢤⣀⠘⡲⠘⠆⡀⠰⡼⣠⠄⢘⡃⠀⡰⠁⠀⠛⠈⠉⢅⡐⡄⠀⢀
⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠿⠿⠟⠋⠝⢫⡋⠙⢿⣶⣶⣬⡓⢠⢄⠘⠀⡀⢿⡙⠶⠼⣧⠀⠏⠀⠀⠀⠰⡖⠄⣫⢍
⠂⢹⡆⣀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠅⠀⠀⠁⠀⠀⠌⠀⣀⡄⠀⡘⠀⢻⡙⣆⠀⠱⡶⠠⠹⣀⠀⠙⢾⡆⢀⣠⡇⢀⠴⢓⡯⢱⣤⢂
⠳⣏⣟⣩⣧⣠⣴⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡟⣇⡀⠀⢀⠗⣀⢀⠐⠐⠀⠠⠆⠈⢠⡀⠱⠜⣏⠳⣴⣷⡤⠖⠉⠀⠀⠀⠉⠻⣼⣽⠏⠀⢸⡔⣿⠁
⠀⠀⣼⢩⡧⡴⠎⡷⢶⠾⣇⠀⡀⠀⠀⠐⠀⢸⡇⠋⠀⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⢀⠀⠋⠁⠢⠉⠓⠶⠲⢟⡳⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠹⣿⡇
⠀⠀⠳⣽⢄⡘⠀⠏⡼⢼⣭⡟⡛⣦⠀⠀⠀⠀⠱⣦⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠉⠛
⠀⠀⠀⢸⡂⡨⠘⢃⡇⢖⣢⣞⣙⣼⠃⠀⠀⠀⠐⠀⠉⠛⠛⠛⠲⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⣳⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⡓⠂⠐⡋
⠀⠀⠀⣾⢃⡀⣴⠢⡔⡆⠫⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠐⠐⠦⣂⡼⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣨⠿⠀⠂
⠀⠀⠀⠹⣆⣤⣿⢠⢀⣏⢲⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠐⠲⢤⡂⠜⢻⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢥⡀⠂
⠀⠀⠀⠀⠹⡄⠙⠿⠾⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⡀⠑⠬⠯⠺⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⢻⠀⠐⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⣏⠡⢉⡂⡂⢌⡿⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠐⢾⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⢤⣰⠟⠁⢾⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⠶⠲⢶⣿⠯⣿⣖⣲⣤⣠⣤⣤⡁⣀⠴⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡾⢿⡿⠛⠁⠀⠀⠀⠀⠒⠈⣉⣙⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠿⠟⠛⠋⢉⣥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣦
⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢿⣧
⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⢑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⢸⡧⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠸⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠘⠣⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠄⠐⠀⠁⠐⢿⡇
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⢺⣿⡀
⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣿⣇
⠀⣯⣈⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣿⡇
⣿⠀⡠⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣹⣷
⣿⠌⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿
⢹⡆⠀⡰⠁⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠸⣷⣰⠁⠀⠀⠀⠀⠀⠀⠺⣄⣀⣀⣀⣀⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿
⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣿
⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣼⣿
⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢀⣴⠟⣹⡿
⠀⠀⠀⠈⢻⣿⡳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢠⣿⠇
⠀⠀⠀⠀⠀⠙⢿⣦⡉⠛⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⣄⡐⠒⠂⠤⠤⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣶⣤⣬⣷⣄⣀⣠⣋⣈⣹⣦⣤⣤⣤⣶⣾⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⢀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⢀⣴⣿⡿⠟⠁⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢢⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⡄⠀⠀⠈⣿⣡⠴⠒⠻⣿⣯⣭⡙⠓⠿⣿⣿⣿⡿⠿⠛⠀⠀⡀⠀⠀⠀⠀⠀⠈⡑⢛⡂⠀⠀⠁⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡴⠻⣷⣶⣦⡀⠙⠻⢿⣿⣦⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠅⠀⠀⠠⢧
⠀⠀⠀⠀⠀⠙⠿⣦⡼⠁⠀⠈⠻⠿⣷⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡣⠄⠀⠀⠀⠃⡀
⠀⠀⠀⢻⣶⣦⠀⠈⡇⠀⣠⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⡀
⠀⠀⠀⠀⠻⢿⣦⣄⣧⡾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠥⠀⠀⠀⢀⡠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢀⣴⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢶⣶⣦⣌⢦⣀⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠛⠳⠤⣄⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⡀⢤⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢲⡀⠀⠀⠀⠀⠀⢈⡂⠴⣼⣆⢔⠡⡀⠀⠀⠀⠀⠀⣄⡀⠘⣿⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⢀⡞⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠑⣘⡇⠁⢐⡀⠀⠀⠀⠀⠀⠙⢿⡆⢿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⢧⠀⢸⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠂⠁⠠⣈⡅⠊⣠⠃⠀⠀⠀⠀⠀⠀⠈⠻⣼⡄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠀⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠄⢹⣇⠔⢀⠝⠀⠀⠀⠀⠀⢶⣄⠀⠹⡿⠁⠀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠘⣆⣿⠞⡡⠖⠛⠋⣹⠟⠀⠀⠀⠀⠘⠉⠁⢀⢙⡃⠠⠐⠀⠆⠀⠀⠀⠀⠈⠻⣆⠀⡇⠀⣾⡟
⠀⠀⠀⠀⠀⢸⠀⠙⣆⠀⢸⠿⠿⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠐⠀⠀⠌⣹⣏⠡⠀⠐⢢⠀⠀⠀⠀⠀⠀⠈⢦⡇⢰⠏
⠀⠀⠀⠀⠀⠘⣆⠀⢸⣦⠃⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠀⢁⢹⡇⡀⠀⠀⢁⠀⠀⠀⠀⢸⣦⡀⠈⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢦⣸⣧⠚⠉⠀⢈⡩⠛⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⠀⡇⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠈⢺⡖⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢧⣇⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢺⡗⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠶⠦⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⢾⣁⣀⡠⠤⠖⠒⠲⠦⠤⠴⠒⠛⠛⠓⠲⠤⠤⠤⠴⠒⠲⠼⠷⣄
⠀⠀⠀⠀⠀⣠⠿⠤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄
⠀⠀⠀⢀⡼⠁⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⠒⠦⠤⠤⠔⠚⠓⠒⠒⠋⠁⠈⢧⡀
⠀⠀⢀⡾⠁⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⡾⠁⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣸⠇⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣇
⠀⣿⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⡇⠀⠀⡞⠹⡄⢻
⢰⡏⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⢠⠞⠀⠀⠳⣀⡏⠀⠀⡇⢸
⢸⡇⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠖⠁⠀⠈⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠁⠀⢠⠇⢸
⠀⣷⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣼
⠀⢹⡄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⡏
⠀⠀⢷⠀⠀⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⡼⠀⡾
⠀⠀⠈⢧⡀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⢀⡰⠃⡼⠁
⠀⠀⠀⠈⢳⡄⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠤⠖⠋⠓⠶⠖⠒⢲⡄⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣴⣒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⠋⠭⠭⠝⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠈⠒⠒⠀⠀⠀⠀⠀⢀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢶⣛⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠑⠀⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠈⠉⠙⠳⠶⣼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⣀⣀⡀⠀⠀⠀⣀⠀⠀⢀⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠾⠭⠴⠶⠖⠚⠛⠉⠉⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠉



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣤⣍⣥⣮⣭⣿⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⡀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠈⠈⠁⠐⠒
⠀⠀⠀⠀⢀⠀⠀⠐⠘⢰⣄⡴⠁⠀⠀⠂⡔⠉⠀⠀⡀⠀⠀⠀⠀⠐⡄⠀⠀⢀⠀⠀⠒⠀⠆⣛⠀⢀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠆⠀⠀⠀⠙⠲⠀⠀⠄⠀⠉⠒⠢⠜⠄⠐⢠⠀⠠⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠂⠄⡁⠀⠀⠀⡠⠂⠐⠂⠀⢢⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠖⠲⢄⡀⡄⠀⠀⡀⠘⠁
⠀⠀⢀⠀⡀⠀⠈⠀⠀⠶⠈⠀⠀⡈⠀⡎⠀⡀⠀⠄⠰⠁⠉⠀⠀⢀⡀⠈⠠⣄⠠⠦⠒⠉⠀⠀⠠⠦⠤⠈⡀⢠⠀⠀⠉⢻⡠⠂⠀⠀⡄
⠀⠀⠐⠀⠀⠀⠀⠁⡘⠀⠄⠀⠀⢁⠐⠀⠀⠀⠈⠀⠇⢀⢄⡅⠀⠈⡄⣀⠀⠀⠁⠀⠀⠀⠀⠠⠀⢀⡀⠖⠁⣀⠀⠀⢤⣬
⠀⠜⠁⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⡘⠀⠀⠀⠀⠤⢠⢰⠃⠀⠀⠀⠀⠈⠒⢣⠘⢁⠀⠀⠀⠀⠀⢀⡀⢈⠐⠂⠀⠀⠀⠀⠈⣇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠤⠠⠀⠤⠠⠀⠀⠘⢰⠐⠈⠀⡀⡠⡨⠦⣠⠄⠀⠈⠀⠈⠁⡄⠀⠀⠤⢀⠄⠂⠈⠁⠠⣀⠈⠀⡊⢂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⡘⠈⠀⠃⠰⠀⠀⠀⢀⠀⠰⣄⠈⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠰⡦⡀⠀⠀⡨⠀⢀⠀⠀⠀⠀⢀⠠⢄⠄⠀⠀⠀⠀⠰⠄⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠉⠈⢀⡀⠀⠀⠁⠸⡄⣸⣃⡀⠉⠀⠀⡀⠀⠁⢠⠯⠰⠀⠀⠐⠦⡀⠀⣨⣘⣆⣣⣀⢐⠒⠀⠀⠢
⠀⠀⠀⡀⠐⢢⡀⠀⠀⠁⡌⡰⠂⢀⠀⠀⠋⠙⠢⠀⠙⠃⠈⠁⠀⢩⡄⠄⠀⠀⠀⡈⠁⠀⠂⠀⡀⢐⠀⡛⠛⣕⢋⠅⠀⠘⠳⠦⣄⠀⠂
⠀⠀⠀⠀⣰⠆⠚⠐⣲⡈⡉⠡⠔⠊⠀⠀⢀⡀⠘⠛⠠⠱⠰⠔⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⠄⠈⠀⠀⡌⠜⢨⠃⠀⠀⠉⠁⠀⠁⠌⡾
⠀⠐⢸⠖⠀⠉⠉⠰⠒⠀⠀⠀⠀⠀⣀⠀⠈⠀⠠⢿⡄⣠⠀⠈⠋⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠈⠀⠀⡠⠔⠐⠁⠂⠂⢄⠀⠡⣳
⠀⠁⡗⠭⠀⠀⠀⠀⡂⣀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⣤⣄⠀⢗⡋⠰⠤⠄⠑⠊⠑⠠⣆⠀⢹
⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠠⠀⠀⠂⠀⠀⠺⠖⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠳⠄⠈⠐⠐⠒⠂⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠒⠛⠛⠒⠒⠒⠶⠶⠦⢤⣤⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠋⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠮⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠘⢧
⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣇
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⢸
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠁⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠤⠦⣀⡀⠀⠀⣀⣴⠏
⢸⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠁
⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⢺⠱⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠸⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⢶⡾⠟⠁
⠀⠀⠈⠳⣄⡀⠀⠀⠀⢐⢒⢒⡄⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⠛⣳⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⠋⠉⠳⣦⡀
⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠘⠀⠀⠀⠊⢳⡀
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠀⠠⢄⡀
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣴⣴⣦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠷⣾⣛⢉⡵⠾⠳⢶⠦⣄
⠀⠀⠀⠙⠦⢤⣤⣤⠴⠿⠾⠛⠛⢁⣠⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⠀⣾⠋⠁⠀⠀⠀⢸⣿⣿⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠘⠉⠀⠈⢉⣱⣦⠀⠀⣼⠰⣠⠀⠀⣰⢳⣶⣀⠀⠀⣀⢈⣧⠟⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢽⡇⠀⢇⠀⢹⡷⢴⣿⠞⠉⠉⠉⠻⣿⣾⢏⡴⢠⠏
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⠳⠦⣤⡄⠀⠀⢀⡀⠀⣠⡼⠃⠀⣾⡀⢀⢳⣤⣿⣤⣤⡤⠴⠶⠟⡣⠞⢡⡇
⠀⠀⠀⠀⢀⣴⣿⠀⠈⠁⢛⠻⢷⡄⠈⠛⠒⠲⠚⠓⠚⠋⠁⠀⢸⠀⠱⡈⠓⠦⠄⠀⠀⠀⠀⠈⠀⣀⡴⣿
⠀⠀⠀⡼⠋⠁⠉⠁⠀⠀⠈⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠓⠶⠶⢶⣤⣤⣶⣚⣩⣅⣤⡿
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠠⣤⣤⣤⠴⠞⠛⠉⠉⠙⢿⠶⣦
⠀⠀⢹⣄⠀⠀⢀⣰⣇⣀⣠⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣄⡀⠀⠈⠀⠀⠀⠀⠀⢀⡤⠖⠒⠉
⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠛⠛⠛⠛⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣖⠀⣀⣀⣴⠛⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢸⣭⠀⣿⢰⡟⣾⠓⣋⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠟⠃⠉⠀⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡆⠀⣼⣿⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣿⣧⣿⣿⡇⢃⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠎⢹⡇⣿⣿⠀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣸⣇⠙⢿⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢹⣿⠀⢸⣌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡸⣻⢀⣸⡇⠱⡹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢐⠈⠈⣿⠂⢹⡇⠀⠰⢡⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠂⢿⠀⠘⠀⢀⢫⡆⢈⡓⢤⡀⠂⡤⠚⡁⣀
⠀⠀⠀⠀⠀⠀⢀⠄⠒⠉⠠⠁⠂⠀⣸⠀⢃⠀⠂⢾⡇⢸⣏⠁⠪⠅⠒⢭⠤⠒
⠀⠀⠀⠀⠀⡚⠁⠀⠀⠀⡀⠀⠀⢀⠁⠀⠀⠀⠀⢸⠇⢸⡿⠀⠀⠐⠉⠢⡑⢦⡀
⠀⠀⠀⠁⠰⠀⠀⠀⠀⠐⡞⠀⢀⠆⠀⠰⠂⠐⠠⢠⡆⠸⠗⢈⠀⡀⠂⠀⠈⠳⠕⢦⡀
⠀⡀⠀⠠⠁⠀⠀⠀⠀⠈⠀⠀⠊⡄⠀⠀⠀⡔⡄⠀⡇⢀⣿⠀⠁⢌⠢⡄⠒⠀⠀⠗⠩⡒⠤⡀
⠈⠀⠀⠀⠀⠀⠀⠠⠇⠐⠀⠊⢀⡃⠀⢀⣣⠀⠀⢰⠁⠗⣿⠄⡀⠃⠐⡜⠆⠒⢄⢰⠀⣡⠁⠲⢕⣦⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⠃⠀⡸⠁⠀⢀⠆⡀⢀⣿⠀⠈⡀⠀⠐⠘⡄⠀⠀⠀⠇⡦⠀⠀⠉⢻⠲⣄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡾⠀⡤⡇⠀⢠⠎⠀⢡⠸⣿⡄⠀⡇⢀⠀⡁⢰⠀⠀⠀⠀⢳⠀⠀⠀⠀⠳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠱⠀⠀⠀⠐⠀⡜⠀⣼⡇⠀⢇⠀⠀⢡⢀⠃⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⠢⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⠂⠀⠀⠐⢀⠀⢀⡟⠐⠀⢸⠀⠀⢈⠘⠐⠀⠀⠀⠀⠹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠃⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⡌⠀⠀⠂⡆⠠⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⢀⠄⢘⠀⠀⢠⡇⠀⠈⡐⢱⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠁⠀⠀⠀⣔⡛⠂⢹⡄⠀⠀⡇⠀⢠⠁⠈⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⡔⠇⠀⢀⢸⠻⡄⠀⠃⠀⠀⠀⣰⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡄⠃⠀⢾⠀⠹⡄⠰⠀⠀⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⣰⠣⠀⠀⢸⢁⠀⢝⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⣰⠇⠀⡇⠀⢸⢸⠀⠘⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠔⢉⠇⠈⠀⠀⠀⢸⡎⠀⠀⣇⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢸⠀⠀⠀⠀⠀⢸⡁⠀⠀⠉⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠎⠃⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠲⢶⣚⢽⠛⠀⠀⠒⠒⢦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⣛⡾⣿⣸⡣⢝⡙⡆⠀⠀⠀⣸⠀⣠⢝⡓⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⣾⡅⡪⠒⢫⣔⡭⢚⣿⢀⣴⡫⢔⡫⢖⡩⢚⡥⠂⣱⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠗⠁⢀⡤⠷⣺⢕⡫⢟⡭⢚⡡⢔⡡⠞⢉⠔⠛⣴⢊⠵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⢓⡩⢒⡥⢚⡥⢒⡭⠒⣉⣤⡚⣏⠀⠀⠓⠊⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡀⠀⠀⠀⠀⠀⠀⢀⡾⢔⡥⣚⠥⢚⡥⠚⣡⠔⣪⣿⣷⣹⠈⢖⣹⠃⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡩⢇⠀⠀⠀⡀⢠⣤⡘⢶⡥⢊⡥⠚⣡⠔⣫⠔⣫⡴⠟⣫⢔⡏⠁⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⣹⣄⡀⠸⣿⣝⡩⢘⡩⠞⣡⠔⣉⢔⡫⣰⠟⣋⢔⣪⠏⠉⡔⣰⢦⢫⢹⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣊⠔⣋⠝⣆⠀⠫⡖⣉⠔⢋⢔⡪⣶⠕⣊⠴⣪⠗⣡⢜⠶⣼⢟⡵⢋⡵⠝⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢊⡥⠚⣩⣷⠀⠀⠀⠉⠙⢍⣋⡴⢊⠵⣋⠴⡪⠖⡡⢺⠉⠁⠉⠉⠀⠀⣀⠀⡰⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠔⢋⡤⢿⡀⠀⠀⠀⠀⠀⠈⢘⡕⢊⡴⢊⠔⣩⢔⡇⠀⠀⠀⠀⠀⠀⠘⣷⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢊⡡⠒⡩⠟⣦⢤⡀⠀⠀⠀⣼⠔⡡⢚⡥⣪⢕⡽⢛⠶⠲⣄⠀⠀⠀⠀⣇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡴⢋⠴⢊⠤⢊⡽⡄⢀⣴⠗⣋⢔⡫⢚⠕⣡⠖⢁⠀⢋⠙⠃⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣖⣡⠖⣡⠔⣇⢸⡡⢚⡵⣋⠔⡡⠚⢁⠔⢫⡜⣉⢈⣹⣻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠤⣚⣹⢺⡶⣫⢞⡵⠋⣠⠞⢁⠔⢁⠜⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠓⠫⠤⠾⠥⠴⠇⠒⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡠⢀⡠⢀⡀⣀⢀⡀⢀⠀⣀⠀⡀⠀⡀⠀⡠⠀⣠⢀⡀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉⠀⠉⠈⠁⠉⠈⠁⠈⠁⠉⠀⠈⠀⠈⠀⠈⠁⠈⠀⠀⠀⠉

⠀⠀⠀⠀⣤⠀⢀⠀⡀⠀⠀⣀⣀⡄
⠀⠠⢲⢖⡁⠲⢿⠟⠃⣀⠈⡙⠋
⠠⠖⠟⠀⠀⠒⡀⠀⢠⣥⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠐⠟⠀⠀⠀⠦⡾⣿⣟⡛
⠀⠀⠀⠐⢒⠚⢢⢻⠙⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⡿⠋⣿
⠀⠀⠀⠀⠀⡄⠀⢻
⠀⠀⠀⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠸
⠀⠀⠀⠀⠀⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡏⠀⢰⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢘⡃⢠⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⣸⠀⠀⡏⢀⣀⠀⢸⡄⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠆⠀⠀⠘⠌⡄⢸⠏⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⠰⠀⠀⠰⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⢣⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠘⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⢀⡟⢀⡅⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠰⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡄⠠⠀⣹⣮⠇⢸⡇⠀⡄⠀⠀⠸⠙⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢸⣇⡈⠀⢻⠃⠇⢸⣧⠀⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⣿⠀⠑⣾⢸⠀⠀⣿⡇⠁⠰⠁⠀⠟⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠁⠀⠀⡇⢸⠀⢀⢣⠁⠀⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢠⠃⢸⢀⡌⢸⠀⠀⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⠀⠠⡀⢸⣾⠃⢸⡇⢰⡇⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣃⣀⣀⣃⣸⣿⣀⣈⣇⣸⣀⣀⣀⣀⣘⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣤
⠀⠀⠀⢠⡄⠀⠀⢀⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣼⢀⡄⠀⠀⠀⢠⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢀⣿⡟
⠀⠀⠀⢸⡇⠀⣠⡿⠃⠀⠀⠀⠘⣿⣧⠀⣠⣴⣶⠆⠀⢠⡌⢧⢏⡼⢁⠀⠀⠀⠀⠉⣿⡿⠃⠀⠀⠀⠀⣠⣼⣇⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⡼⠃
⠀⠀⣄⠘⣇⠸⠉⣠⠄⠀⢠⣄⠀⠘⠛⠿⠿⠛⠉⠀⠀⣤⠙⢦⣃⡴⠏⣰⠀⠀⣠⣶⡌⢁⠀⠀⠀⠀⣼⣿⣿⣿⠿⣶⠀⠀⠀⠀⠀⠀⢀⣸⢀⣴⣿
⠀⠀⢻⣆⠈⠀⣾⠟⠀⡄⠘⣿⣷⣄⠀⣀⣤⣶⡶⠀⢠⡜⢷⡄⢁⡴⠾⢃⡄⠀⠻⠿⣿⣿⡇⠀⢰⣿⣌⣿⣇⣿⣾⣣⣿⣷⡀⠀⠀⢀⣈⢃⣾⠟⠁
⠀⠀⠀⡙⠳⠌⠀⣠⣾⠇⠀⠈⣛⠋⠄⠿⠟⠛⠁⠀⠈⢿⡄⢱⠁⣠⣴⠿⠁⠀⠀⢀⠀⠉⠀⠀⣸⠿⣿⣿⡿⣿⣿⣿⡿⢿⣁⠀⠀⢸⣿⢾⠃
⠀⠀⠀⣷⡀⠀⢰⠟⠁⠀⠀⠘⢿⣷⡾⣀⣴⣶⡆⠀⢿⣄⠱⡼⢋⣁⣤⠎⠀⢠⣴⣾⣴⣶⡀⢸⣿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣜⠶⠂⢀
⠀⠀⠀⠈⢿⣄⠃⠀⠀⠀⠀⢀⣈⠛⢣⠿⠟⠋⠀⠀⢰⡝⣆⠷⠛⠋⠁⠀⠀⠈⠛⠛⠻⠷⠃⢠⣭⣝⣿⣿⣿⣿⣿⣿⣏⣻⠿⠃⣴⣆⠀⢹⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠙⢃⣶⠀⠀⠀⠘⢿⣷⣎⣴⣾⡗⠀⠀⠈⢣⣃⣴⠞⠀⠀⠀⠀⠀⣤⣄⡀⣠⠀⠈⢿⣅⣹⡿⠃⢻⣿⣤⣿⣿⣷⠀⠙⠿⠀⣼⠋⣉⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠙⡿⠟⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢿⠗⠀⠀⠉⠉⠀⠀⠀⠻⣿⣿⠿⠃⠀⠀⠀⢰⢣⣾⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘
⠀⠀⠀⢸⣿⣷⡄⢠⡀⠀⠀⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⣶⣿⣷⠀⠀⠀⠀⢀⠀⠀⢸⡏⣠⡆⠀⠀⢸⣿⡄⠀⣠⡀
⠀⠀⠀⠀⢻⣿⡗⠸⠀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡛⠛⠁⠀⠀⠀⠀⠻⣷⡄⠀⢸⡿⠃⠀⠀⠀⠙⠇⢰⣿⠃
⠀⠀⠀⠀⠈⠛⢑⣰⣿⣿⡿⠀⠀⠀⠀⠈⠻⣿⡏⠀⣠⣶⣶⠀⣀⣀⠀⢸⡿⢿⣶⡦⠀⠀⣀⣀⣀⣈⣉⣀⠈⠀⢀⣀⡘⢷⣶⣤⣨⠁⠀⢠⣾⡷
⠀⠀⠀⠀⠀⠀⠙⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠸⠁⣾⣿⣿⠏⠀⠻⠟⠃⠀⠓⡈⣩⣤⡀⠀⠻⠿⠋⠀⠀⠙⡔⠉⠛⠿⠟⠀⠉⠉⠈⢦⠀⢻⠿⠁
⠀⠀⢰⣾⣿⣷⣆⣦⡀⣠⣴⣶⣦⠀⢰⣿⣦⡀⠃⣿⠛⠁⠀⠀⠀⢿⣿⡇⠀⢀⣿⣿⠇⠀⠀⣴⣾⣆⠀⠀⡇⢀⣤⣶⠀⠀⠀⠀⠈⠑⢦⠃⡴⠂
⠀⠀⠀⠻⠿⠿⠋⠻⣄⣿⣿⣿⠟⠀⠀⢿⣿⣧⠘⡇⠀⣠⣿⣷⠀⠈⠋⠉⠲⡄⠀⢀⠄⠀⠀⠘⢿⣿⠀⠸⣰⣿⠿⠋⠀⠀⠀⣶⣦⡄⢸
⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠉⠁⠀⠀⠀⠀⠉⠻⡄⣷⣿⣿⣿⡟⠀⠀⠀⠐⣄⢀⢰⠋⠀⠀⠀⠀⠀⠈⢂⡞⠉⠀⠀⠀⠀⠀⠀⠈⠛⡏⠜
⠀⠀⠀⠀⢠⣴⣿⣿⣯⠀⣠⣤⡀⢸⣿⣶⣦⠀⢹⠿⠟⠋⠁⠀⠀⠀⠀⠀⠈⢺⠇⠀⠀⠀⠀⢀⠀⠀⠘⠁⣀⠄⠀⠀⠀⠀⠀⡀⢠⡏
⠀⠀⠀⠀⠈⠛⠛⠛⠁⣾⣿⡿⠃⠈⢿⣿⣿⣃⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⡀⣸⠞⠁⠀⠀⠀⠀⠀⠀⣇⣨⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣤⠲⠶⢶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣯⠿⣿⣿⣿⣿⣶⣴⣶⣤⣶⣍⠻⣿⣿⣻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣾⣿⣶⣿⣿⣟⠉⠁⠈⠁⢠⣾⣿⡇⠻⣿⣤⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠶⢻⣬⣿⣿⣿⣿⣿⣷⡄⣰⣿⣷⣍⣉⠀⠀⠀⠙⠿⠋⠀⠀⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡿⠉⠈⠁⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⣿⢿⣿⣯⡀⣠⡀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠻⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡟⠁⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣤⣀⣀⢀⡀⠀⠀⠈⣡⣤⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠾⠷⠿⠶⠶⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡟⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⢿⣿⡿⠟⣽⡿⠋⠻⣷⡄⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⡟⠋⠁⣰⡿⢫⠀⣾⠿⡀⠀⠀⣸⠻⣦⡃⠙⣿⡓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⡏⠀⡇⠀⠀⣿⠀⢸⠀⣿⠀⠈⡄⢰⠁⠀⠙⣧⠀⢈⠙⠶⣌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠆⢸⠇⠰⢀⡤⠔⣿⠀⠠⠀⢻⣆⠀⡃⢳⠀⠀⠀⢻⠀⠆⠀⠀⢸⠳⣍⠲⠤⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠌⢀⡿⠀⠁⠁⠀⢰⡟⢦⠀⠀⡰⢻⣆⠐⢘⡆⠀⠀⣼⠓⣄⠀⠀⡼⠀⠹⡇
⠀⠀⠀⠀⠀⠊⠀⠀⢡⡞⢳⠀⠰⠀⠀⣾⠁⠸⢀⡞⠀⠀⢹⡆⢸⠇⠀⠀⣿⠀⠈⠀⠀⠱⢄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠀⠀⠀⣸⡇⠀⠀⢹⡄⠀⠀⢸⡗⢄⠀⠀⢸⢻⡄⠀⢆⠀⠀⠀⠂⠀⠙⢄
⠀⠀⠀⠀⠀⠀⢊⠟⠀⠀⠀⠠⠔⢨⡟⠱⡀⠀⢸⠃⠀⢠⡟⠀⠈⡄⠀⣸⠘⣿⠂⠈⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡔⠀⠀⡾⠀⠀⠇⠀⠘⠀⠔⡿⠙⢢⠀⠈⢀⠋⠀⢸⢧⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⡄⣇⠀⠀⡃⠀⢠⠀⢠⠏⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢢⠀⠑⠀⠀⠀⠃⠹⣆⠀⡇⠀⠀⠀⢰⡀⠀⠈⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠸⡄⠈⠄⠀⠀⠀⢡⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣰⣶⡾⠿⠀⠀⠀⠀⠀⢀⣤⣴⣾⣶⠿⣶⣾⣶⣶⣴⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢠⠘⠋⠉⠋⠉⠀⠀⠈⠀⠀⠀⠤⠿⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡟⠀⠀⠀⠣⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣴⠷⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⣧⣄⠀⡰⠀⣠⣾⣧⣀⡀⢠⡇
⠀⠀⠀⠀⠀⠿⠯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣂⠀⢀⣾⣿⣿⣿⣿⣷⣿⣿⡿⠿⠛⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣧⣤⣿⣖⣠⣠⣦⡴⠶⠿⠿⣿⣿⢻⣿⡿⣿⣿⣿⣬⡿⠿⣿⣶⣶⣬⣼⣛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⢿⣿⠿⠟⠲⣽⣿⣷⣯⣄⡀⠹⠋⠻⠿⣷⣦⣴⣿⣥⣨⣏⢙⣛⣻⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣿⣿⣿⣿⣿⣦⣤⣤⣀⣈⣁⣉⣻⣋⠛⣃⠙⠷⠋⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⡻⢿⣿⣿⣮⣹⣿⣿⣯⣽⣽⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣹⡿⣿⣷⣾⣍⣛⠻⠿⣷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⢿⣿⣿⣿⣿⣿⣭⣛⠻⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⠛⠟⠛⠃⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠋⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢠⡾⠛⠛⠳⢦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠛⢳
⣯⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⡷⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣠⠶⠛⠛⠳⣶⠞⠁
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢸⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢰
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⣧⠀⠀⢸⠀⠀⠀⠀⢳⠀⡇⠀⠀⠀⠀⣿⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠘⣦⠀⠆⠀⠀⠀⠀⠹⡆⠀⡿⠀⠀⠀⠀⠈⢱⡇⠀⠀⡄⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⠳⣀⡆⠀⠀⡇⠀⢳⠀⡇⠀⠀⠀⠀⠀⠈⡇⢀⡼⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⢱⠀⢰⠇⠀⠸⣷⡇⠀⠀⠀⠀⠀⢰⡇⡼⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢿⡀⠀⠀⠙⢦⣀⠙⡄⠀⠘⣇⠀⠀⠀⠀⠀⠈⡆⢸⠀⠀⠀⢿⡇⠀⠀⢰⡄⠀⢰⠟⠀⢀⡟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⠳⡼⣄⠀⣿⠶⢦⣄⠀⠀⠀⢻⡌⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⣾⠀⠀⡼⠀⠀⠀⠀⢷⠀⡘⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⢻⣦⠀⠸⣇⠀⠀⠀⠈⣧⠀⠀⠀⠻⡀⣿⠀⣸⠇⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⢀⡞⢀⣤⠞⠁⡼⠃
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠙⣧⡀⢻⠀⠀⠀⠀⢹⡆⠀⠀⠀⢳⡟⢀⡟⠀⠀⠀⠀⠀⠀⡷⠀⣠⡖⠁⣸⡷⠋⠁⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠠⣀⢺⠀⠀⠀⠀⠀⠀⠙⣷⢨⡇⠀⠀⠀⠸⣷⡄⠀⠀⢸⡇⣸⠁⠀⠀⠀⠀⠀⢸⢁⡴⠋⠀⢀⡟⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠘⣦⢿⠀⠀⣴⠁⣿⢡⠀⠀⢸⣡⡇⠀⠀⠀⣇⠀⢠⡇⠈⠀⠀⠀⣼⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⡀⠀⠳⣌⣄⠀⣆⠘⣿⡇⡸⠃⠀⣿⠘⣄⠀⡞⣿⠁⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⣴⠃⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠘⣧⠀⠀⠀⠙⢆⡿⠀⢹⣿⠁⠀⠀⠈⠀⠁⠀⠇⠋⢠⠀⠀⠀⢹⣼⠃⠀⠀⠀⢰⡏⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⢢⣘⣆⠀⠀⡀⠸⡇⠀⠀⢿⡀⠀⠀⢸⡆⠀⣶⢰⡄⢸⠀⠀⠀⣸⠃⠀⠀⠀⢠⣿⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠉⠻⣆⠀⠙⢦⣽⡄⠀⠈⡇⠀⠀⢸⡇⠀⢻⣼⠀⢸⡆⠀⢠⡏⣠⡴⠖⢡⡟⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠹⣆⠀⠀⠈⢷⢀⡞⢸⡆⢀⣾⡇⢠⠈⡇⠀⠀⡇⠀⡞⠉⠁⠀⢠⡟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⣧⠳⣄⠈⣟⠀⠘⣧⡼⢸⡇⠘⢶⡇⠀⠀⢣⡼⠀⠀⠀⣠⢏⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠼⠷⠼⠷⠬⠷⠾⠦⠤⠿⠤⠼⠧⠶⢴⠧⠤⠤⠾⠧⠤⠤⢴⠿⠾⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⡶⠲⠶⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⢶⣤⣤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣍⣭⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠛⠻⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣄⣠⣤⣄⣤⣶⣶⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣀⠶⢼⠙⣿⣽⣦⣯⡙⡋⠿⣾⠾⣟⢻⣿⣧⣴⢂⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣶⣿⣴⣤⠃⢠⣿⡆⢳⡿⣥⣴⣍⡴⣾⡐⣿⡿⢺⣏⡝⢛⣡⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⢷⣬⣿⠟⣻⣶⣯⣿⠾⠯⣙⠷⠾⣿⣾⣯⣿⣳⣿⠿⠋⢴⣿⣛⣿⢾⣏⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣿⠃⣙⢣⣼⣧⠁⣛⠻⢿⣿⡷⢿⣶⣷⡿⣿⠙⣛⣿⣤⢺⣾⣆⣼⢾⣇⣴⡍⢻⡟⣣⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣾⣿⣴⣶⠳⣼⣿⣶⠿⣶⢾⣿⣦⣛⣹⣿⣦⣼⠇⢻⣿⡿⢯⡥⢶⣻⡎⣬⣤⣱⣯⢿⣍⡛⢷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣻⣿⠂⣾⢟⣿⣙⣋⡼⢉⣯⣬⠻⣿⣽⣿⠁⢉⣾⣿⣽⣟⡟⠁⣉⣼⣷⠿⠻⢍⣶⠛⢛⡱⠶⣿⣶
⠀⠀⠀⠀⠀⠀⠒⣖⣛⠙⣧⣄⣆⣶⣏⡟⣥⣼⣷⣺⣟⢽⣾⡭⠙⣿⡇⣾⣿⣤⣿⣟⣷⣾⠛⣿⣩⣴⣾⣿⡿⣭⠿⡷⣿⣧⠾⣤
⠀⠀⠀⠀⠀⣼⡎⣿⠛⣾⣹⣯⣹⣿⣽⣷⣾⠻⣛⣿⣻⣿⠷⣷⣄⣿⣿⣿⣿⣷⣿⣿⣋⣹⣋⣹⣾⡵⣨⢁⣅⣸⣇⣿⢋⢿⣰⡿⠆
⠀⠀⠀⠀⠀⣀⣦⣻⣿⣬⣿⣟⣻⢧⣎⣫⣭⣤⣽⠟⠗⠋⠒⠸⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⡟⡛⣛⡿⠟⢻⡟⠿⣿⣷⡿⣾⠟⠋
⠀⠀⠀⠀⠀⠸⠋⠉⠈⠋⠀⠀⠙⠀⠙⠋⠀⠛⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⠀⠉⠁⠀⠐⠛⠇⠲⠀⠈⠁⠀⠀⠙⠻⠙⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠄⠀⠤⠤⠴⠞⠛⢛⣿⡿⠟⣿⣿⣿⣿⡿⠟⠛⠛⠿⢿⣦⡤⠤⠶⠶⣄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠦⢤⣀⠀⣀⣤⠾⠟⠁⢠⠞⢻⣿⠻⣿⣷⣤⣄⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠚⠋⠉⠀⠀⠀⠀⢃⣴⣿⡿⠿⢿⣿⠉⠻⣿⡁⠀⠀⠀⠉⠛⠓⠺⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡠⠤⠤⠤⣤⣄⣠⡴⠟⠁⣿⠇⠀⢸⣿⢀⠀⠹⣧⣀⠀⠀⠀⢀⣀⣤⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠖⠋⠉⠉⠉⠀⢀⣴⠟⠀⢠⣿⣷⣄⠀⠀⠈⣿⠛⠒⠾⠯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣿⠀⠈⣿⡄⠀⠀⠙⢦⡀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⡼⢻⡀⠀⠘⠷⣦⣤⣄⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃


⠐⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⠤⠤⠤⢤⣤⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣀⣀⣠⣴⣟⣁
⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⢷⣄
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⢸⠁
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠿⠓⠲⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠸⣦⡀⠀⠘⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠀⠀⠀⠀⠀⠀⠑⢌⠙⠲⠦⣄⣀⣀⣀⣠⣤⠶⠛⠁
⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠖⠛⠓⠰⠤⢤⣀
⠀⠀⠀⠀⠈⠙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠋⠒⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⠀⠈⢧⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⣸⣿⢦⣙⢦⡈⢳⣄⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠾⠟⠛⠉⠀⠙⢷⣿⣷⣿⣧⣄⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠶⢬⣽⣿⣗⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣀⣖⣚⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⣶⣢⣤⢏⢤⣂⠀⡀⠂⠁⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⣳⡶⣷⣞⡳⣞⣯⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠢⡙⡆⡆⠀⠀⠀⠁⠁⠀⠈⢑⠁⠀⠀⠰⠆⠠⣭⡖⠢⠏⠠
⠀⠀⠀⠀⠀⢹⣛⣙⣉⣙⣛⡋⠀⠀⣶⠶⡶⣶⢶⡆⠀⠀⠎⠑⠐⡕⠀⠢⠀⠀⢠⣦⣐⢀⠀⡚⠀⠀⠁⡖⡪⡡⠤⠲⠒⢎⠃
⠀⠀⠀⠀⠀⠸⠥⠬⠨⠅⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢹⢹⣹⢹⠁⠀⠐⢘⣛⢰⣶⡟⠃⠀⠀⠈⠐⠓⠀⠓⠉⠃
⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⡄⠀⠀⠀⢐⣶⣶⣶⣶⠀⠀⠀⢹⣘⣸⢸⣷⡟⠀⠀⠀⠠⠿⢠⡤⠆⠀⠀⠀⠀⢲⡶⠶⠶⣶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⢀⡔⠀⠄⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂
⠀⠀⠀⠀⢀⠀⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠉⠁⢀⣀⠄
⠀⠀⠀⠀⠂⠈⠀⠁⠀⠈⠐⠀⠀⠀⠀⠀⢔⣦⠀⠀⠀⠀⢀⠀⠑⠀⠀⠀⠅⠰⠀⠀⢀⠀⠐⠁⡀⠀⠀⠘⠉⠠⠀⢀⣤⠁⠈
⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠘⢓⠆⠊⠍⠆⠀⣄⡈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣈⡨⢀⠀⠀⢀⣀⣄⣟⣀⡃
⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠈⠐⠀⡅⢘⢩⠏⠁⠀⠀⣾⠐⣶⡆⣿⠂⠀⠘⠿⠤⣋⢱⡄⡄⠀⠀⠸⠃⠄⢛
⠀⠀⠀⠀⠀⠀⡇⣾⢸⢰⡆⡇⠀⠀⠀⢳⣶⣶⠶⡾⠀⠀⠀⠀⢹⡀⣿⡇⡿⠀⠀⠀⠄⢤⡄⢠⣾⠃⠀⠀⠀⠘⢡⣌⠠⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⡶⢒⢲⠆⠀⠀⠀⠀⢸⣇⣿⣧⡇⠀⠀⠀⢀⠶⠠⡤⡆⠀⠀⠀⠀⠁⠤⢁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⣶⡶⢿⠙⢿⡟⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠉⢙⠃⢩⣦⠀⣤⣀⠸⣯⢛⡚⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣦⣻⣦⠴⠦⠲⣜⣉⠑⡼⠷⡀⣯⣈⣗⣰⣾⣝⡲⢂⠷⢿⠰⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡛⠂⠉⡴⣿⡀⠻⠇⣌⡸⣿⢨⡧⠻⠟⣟⠳⠆⠉⠱⠛⡴⠀⠀⠚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⠉⠈⡁⢠⣎⡀⠉⣀⠀⢸⠀⢰⡏⣤⢰⡞⠓⢻⡄⣶⢄⣠⡄⣉⠈⢆⢀⠋⠀⣺⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠏⠃⠈⠻⣏⢁⡛⠟⠀⢄⡓⢼⡓⠪⠆⢀⣠⡼⠟⠁⠀⠁⠊⣽⢀⡾⠭⠀⠑⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠂⣘⣆⢥⠄⠀⡎⠁⣦⣽⢷⣴⣾⢯⡷⡖⠀⣰⠺⠲⢶⣟⡆⠀⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡦⣉⢃⡀⠙⠟⠳⣄⣀⣳⣄⡿⠙⠋⢻⣿⣀⣤⣥⠾⠥⣴⢖⠋⠙⢸⠇⢋⡐⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣉⠀⠈⠰⠦⠴⠖⢋⡉⠉⠛⠻⢷⣾⣿⠋⠁⠀⣦⣲⠀⠉⠛⠛⠁⠰⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣍⠉⠉⠉⠉⠉⣉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⢶⣶⣶⣿⣿⣿⣿⣏⣟⣻⣷⡶⠾⣽⡩⠉⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠁⠔⠀⡟⠉⣹⠟⣡⣿⣿⣌⠙⢷⡜⢟⢦⡀⠹⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⢀⡜⠁⢀⣴⡶⢿⡇⠁⠙⣷⣄⠀⠈⠀⠟⠢⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠄⠀⠀⠈⠰⡼⠉⣿⣄⠛⡝⠀⡤⣿⠈⢧⠀⠀⠀⠀⠀⣹⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠹⡆⡄⠃⠀⣸⠗⠄⠘⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠓⢀⠀⠀⠁⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣰⠃⠀⣀⡤⠷⠒⢢⡤⠴⢤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⡴⠋⠁⠀⠀⠈⠹⣇⠀⢸⠁⠀⠀⠀⡎⠀⠀⠀⠙⣇⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⡴⠊⠉⠉⠲⣤⠖⠋⠉⠉⠉⠉⠙⣷⣶⠚⠉⠉⠑⢄⢠⠖⠋⠉⠉⠛⠯⣍⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠘⢇⠀⠀⠀⠀⠙⡆⠀⣠⠴⠒⠛⠲⡟⢘⡤⠚⠉⠉⠻⣯⠀⢀⣀⡀⠀⠀⠈⢷⡀⠸⠛⡆
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠙⠲⢤⣀⣀⣻⣹⠁⠀⠀⠀⠀⢳⡞⠀⠀⠀⢀⠔⠉⠉⠉⠀⢉⣳⠤⠒⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠦⢦⣄⠀⠀⠀⠉⠉⠉⠛⠒⠦⠤⢤⣸⣇⣠⣠⣴⠥⠴⠒⠒⠚⠉⠉⠀⢀⣀⣤⣢⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠪⢝⡒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣀⣠⡤⠴⠒⠚⠉⠁⠈⠀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠗⠒⠒⠲⠖⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠚⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠴⠢⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠷⡄
⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣤⣤⣤⣤⣤⡽
⠀⠀⠀⠀⠀⠉⠓⠤⠤⠤⣤⡀⠶⠶⠤⠤⠤⠶⠦⠤⣤⣀⣀⡀⠀⠀⠀⢀⣀⣤⠾⠴⠒⠛⢓⣋⣁⣠⣖⠉⠉⠉⠉⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢠⠔⠋⠉⠀⠀⠀⠈⠉⠳⣄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠴⠶⠒⠉

⠀⠀⠀⠀⣀⡤⠶⠖⠛⠛⠛⠻⠶⢦⣤⡀
⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⢹⡷⠶⠶⣄⣀
⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠙⢳⡄
⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⣿⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗
⣸⠇⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⣿⠀⠀⠈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡟
⣿⠀⢰⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⣀⣠⣤⣇⣤⣤⣤⣤⣀⣀
⠸⣧⣌⣿⣢⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⡀⣄⣀⣄⣠⣿⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢷⣯⡿⣿⣿⣿⣷⣶⣾⣵⢠⣤⣖⣴⣤⣿⠗⣤⣀⣤⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠛⢧⣿⣿⣿⢯⣿⣿⣾⣿⢿⣿⣿⣟⣾⣿⣿⣿⣷⣿⠿⠾⠿⠿⠿⠻⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡋⣤⢤⣤⣠⠖⠚⠛⠛⠓⢦⡀⠀⠀⠀⣀⣤⡶⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣿⣥⣬⣛⣃⣛⠲⡄⠀⠀⠀⠘⢧⠀⠀⠐⢿⣤⣤⣤⡀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⠉⡇⠀⠀⣀⡾⠀⠀⣀⣀⣀⣠⡼⠃⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢧⣀⡾⠁⠀⠀⢺⡏⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠀⠀⠀⣀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⢸⡷⣄⠀⢠⡞⠋⠉⠛⠓⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠳⢦⣿⠷⢦⡄⠀⠀⠀⣠⣀⠀⠀⠀⠸⡇
⠀⣾⠀⢸⡇⢸⡇⠸⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠀⠀⠀⢀⣼⣇⣈⢻⣆⠀⢸⡇⠘⠳⣄⠀⠀⣿
⠀⣿⠀⠀⣻⠞⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣿⣿⣿⣥⠀⠐⣇⢠⡴⡿
⠀⣿⠀⢸⡏⠀⠀⠀⠀⠉⠙⢷⡀⠀⠀⠀⠀⠀⠈⠿⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⠋⢀⡇
⠀⢹⣄⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⣀⣀⣸⠇
⠀⠘⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡏⠀⠀⣠⡞⠉⠁⣽
⠀⠀⠸⣆⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠘⣷⣶⡄⢿⠀⠀⣼⠏
⠀⠀⠀⠹⣆⠀⠀⠙⢷⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣰⣿⣿⠀⣿⣄⣼⠏
⠀⠀⠀⠀⠘⢧⡀⠀⢸⡇⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⢀⡾⠁⠿⠃⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⣈⠳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡴⠟⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⣳⣟⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠚⠛⠛⠛⠓⠒⠶⠤⣄⣀⡀
⠀⠀⠀⣤⡴⠖⠛⠉⠉⠉⠉⠉⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⣀⣤⡤⠴⠖⠒⠂⢀⣤⠞⠋
⠀⠀⠀⠀⠉⠳⣄⠀⠉⠉⠟⠒⠶⣦⣀⠀⠀⠙⢦⡀⠀⠀⠀⢠⠏⠀⢠⣴⠟⠋⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠉⠻⣶⠀⠀⢷⠀⠀⠀⣾⠀⢠⠟⠁⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⣧⡀⢸⠀⠀⠀⢿⣰⠋⣀⣀⣠⡤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠦⢤⣀⣳⣼⠀⠀⢀⡾⡽⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣳⡀⡾⡾⠁⠀⠀⠀⢀⣀⣠⣤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠶⠒⠲⠶⠦⢤⣀⠀⠀⠀⢳⣻⣿⠇⠀⢀⡤⠞⠉⠁⠀⠀⢀⣀⣀⣄⠀⠈⢉⣷⠟
⠀⠀⠀⠈⠛⠧⣄⠀⠀⠦⠤⣤⣄⣀⡀⠀⠈⠙⢦⡀⠈⣯⢸⠀⢠⠟⠀⠀⣠⣴⠞⠛⠉⠙⠀⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠉⠻⢶⣤⡄⠀⢹⡄⢻⢸⠀⡟⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢷⡀⠀⣷⢸⣼⠀⡇⢠⠟⠀⠀⠀⠀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣀⣀⡀⠀⠻⡄⡿⢸⣿⡆⡷⣯⠴⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢿⣳⣼⣿⡿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⡟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣇⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣀⣀⣄⡀⠀⠈⢤⣠⣌⠹⢷⠖⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠁⠉⠉⠛⣉⣱⡦⢀⡀⠉⠉⠛⣶⣶⣤⣦⡈⢯⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠶⣤⢧⠀⠀⠀⠹⣿⣷⣤⠀⠀⠀⠐⣶⢿⣟⣉⣷⣿⣿⣟⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⡠⠀⠀⢂⣴⣹⣆⠀⢀⣴⣿⣿⣿⣇⠀⠉⣹⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣀⠐⠁⠀⢀⣀⣥⣾⣿⣿⣶⣶⣿⣿⣿⣽⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠉⣿⣷⡄
⠀⠀⠀⣾⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⣟⣡⣼⣿⠁⢠⣴⣿⣿⣿⣿⣿⣿⡟⣛⣫⡿⠛⠟⠛⣋⠛⢿⣿⣿⣷
⠀⢠⣿⣿⣿⣿⣿⣼⣿⣿⣀⠀⠞⠉⠛⢻⣿⠀⢩⣱⢿⠟⢛⡛⢻⣿⣀⣳⣖⣩⣄⡈⢁⣿⣷⠀⠸⣿⣿⡆
⠀⠈⣾⣽⣾⢿⢿⣬⣿⡫⠒⠠⠮⢂⣅⣺⡟⢡⣤⣏⣹⣿⣿⣿⢷⡄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⢀⣯⡿⣿⣷⣿⣿⣿⣿⣶⠠⣤⣾⡿⡟⢃⣹⣿⣿⣿⣿⣻⣿⣾⣿⣿⣿⣿⣾⣿⡭⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡿⡿⣩⣏⢸⣿⣷⣾⠛⠋⠀⠩⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣜⢋⣿⣿⣿⣿⣿⡇
⠀⠀⢹⣿⣿⣿⣿⣋⣻⣿⢉⡙⢣⢸⡯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣻⣿⠻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠘⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣝⠉⠳⠴⠚⣿⠯⠟⠾⠿⠟⣿⣿⣿⣿⣿⣿⣙⣿⠇⠹⢿⣿⣿⣿⡏
⠀⠀⠀⠈⣏⠦⠁⠸⣿⣿⣋⠀⠉⠈⠡⢿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡯⢴⣿⣿⣧⠀⠸⢹⣿⡟
⠀⠀⠀⠀⠈⠁⢤⠀⠸⣿⣿⣿⣭⣬⡓⢿⡿⣿⠟⣿⣶⡆⠀⠀⠀⠀⠀⠈⣰⡿⣃⠋⠋⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠛⠷⠀⠙⢯⡝⡿⣿⣷⠄⠁⣿⡐⠛⠛⠁⣤⠀⠀⣄⠀⠀⠸⠟⠉⠀⠤⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢵⣵⠶⠌⠓⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠋⠉⠉⠉⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⠞⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⡜⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⢰⠁⠀⠀⠀⠀⠈⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠞⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣣⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⢄⣀⣀⡤⠤⠖⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⢀⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠈⠙⠿⣦⣄
⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠈⠻⣷⣄
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⣰⡟⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⢰⡟⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣾⡇⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⡿
⣿⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⡟⠁
⢿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠟⠋
⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠈⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠈⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⣤⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣶⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠶⠶⣤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⣀⣀⠀⠀⠀⠘⣋⣴⡟⠛⢋⣭⣵⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⣠⣶⡀⢋⠉⡀⡀⠙⠦⠙⠁⠀⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⣤⣤⣤⣀⣀⣤⣀⠰⣿⠿⠟⠈⡁⠠⢾⣿⣤⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣼⣷⣤⠀⠀⢹⣿⡀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠆⠀⠰⢿⡿⠋⠀⠀⣾⣿⣿⡿⠟⠓⠁⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢑⡿⠟⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣶⠀⣀⠀⠀⠀⠙⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⡛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢧⡀⠉⣽⡄
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠋⠉⢻
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣶⣾⡅
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠶⠮⠿⠶⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠀⠀⠀⠉⠀⠈⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⡌⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⡀⠀⠌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠄⠈⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠱⣀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠋⠉⠓⠲⢤⡀⠙⢧⡀⠀⡀⠀⠀⡉⠑⠴⠆⡄⢀⠂⢠⠒⠂⡐⠴⠥⡠⠀⠀⠤⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠉⠳⣾⣁⠄⠀⢦⡀⠀⠈⣈⠠⡄⢰⣈⡢⣄⣤⣀⠠⢀⠉⠀⡼
⠀⠀⠀⠀⠀⢰⠏⠀⠀⢠⠃⠀⠀⠀⠐⠀⣀⡀⠒⢀⣀⢹⠀⠀⠀⠀⠉⠳⢽⣒⠐⠂⠔⣨⡉⠒⠒⠄⢀⡒⠠⣳⡴⠄⣠⠞⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⠀⢀⡴⠚⠉⠀⠀⠀⠠⠀⠉⠳⣄⠀⠀⠀⠀⠀⠈⠛⠾⢿⣿⣶⣾⣮⡷⠖⢒⣉⣂⡤⠞⠁
⠀⠀⠀⠀⠀⣿⠀⠀⢄⡇⠀⠰⠋⠀⠀⠀⠀⠀⣀⡥⠴⠒⠀⠙⠛⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⢔⠟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠇⢠⠀⠀⠀⢠⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠹⣌⠍⡸⡄⠰⠀⠀⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⡿⡍⠀⠀⢠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠸⡌⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡂⢱⡔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣆⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣑⠢⣀⠀⢀⠀⣀⡠⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠖⠚⠉

⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠘⠻⣷⡀⠘⠀⠀⠘⠈⡽⠃⠀⠉⠁⠂⠀⠀⠀⠀⠜⠀⠠⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠈⠆
⡀⠁⠉⠐⠰⠦⡀⠀⠀⠀⠀⢠⣎⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⡤⠀⠘
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣼⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠛⠒⠀⠠⠀⠀⠉⠁⠀⠀⠂⠐⠂⠀⠀⠀⠀⠤⠀⢷⡀⠄
⠠⠀⠀⢀⣠⠟⠑⠑⠞⠚⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠃⡸⣇
⣴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣀⡀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⣌⡀⡖⣢⠄⠀⠀⠀⠈⠳
⡀⠀⡀⠀⠀⠄⠀⠀⠀⠠⠜⠁⠀⠀⠀⠉⣿⣄⣀⡀⠀⠀⠀⠜⠳⣥⡄⠀⢀⡰⢃⡄⠀⠀⠀⠀⠛⠐⠬⡗⠻⣖⣺⣇
⡴⣒⠟⠳⠶⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⠀⠀⠀⠀⠐⠶⠝⠳⠏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⣿⡧
⡾⡃⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠙⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣤⠀⠀⢀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⣦⣠⣤⠶⠂⠁⠀⠠⣰⣤⣟⠒⡀⠒⠋⠀⠀⠀⠀⠡⢠⡟⠈⠁⠀⠀⢠⡀⠑⢤⠀⠀⠀⠀⠀⢃⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠠⠃⠀⢈⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⢻⡆⠀⡤
⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠃⠀⠸⠂⠀⠀⠀⠀⠀⠈⠲⢦⣤⠤⠶⠖⠛⠡⣈⠀⠀⠀⣱⣶⠊⠧⠄⠀⢸⠀⢀⣀⠁⠐⠂
⠈⠀⠀⠀⠀⠀⠛⠥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢾⡿⠉⠃⠀⠀⠀⢸⡆⠀⠈⠉⠀⠐
⣀⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⠐
⠟⢠⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠀⠀⠠⠠⠒⠦⣄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⣀⣀⡤
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⠀⢰⣡⢌⣠⣿⣷⡖⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⣤⡀
⠀⠀⠄⠠⣤⠇⢤⡰⠂⠀⠀⠈⢿⣂⠀⢡⡴⡷⣶⠋⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡖⠊⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠽⡃⢀⡀⠀⠀⠀⠀⠹⠿⣿⡶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦⠴⠋⠋⠀⠀⠀⠀⠀⠉⠁⣼⢆⡀
⣀⢀⡀⡤⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠃⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡝⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⠈⠁⠲⠉⠀⠀⠀⠀⠘⠃⣰⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⣀⣀⣐⣀⣀⣀⣀⣀⣀⣠⣄⣠⣀⣒⣀⣉⣛⣷⣠⣬⣃⣀⣁⣀⣀⣀⣀⣀⣀⣸⣋⣀⣃⣀⣂⣐⣃⣀⣀⣀⣀⣂⣸⣋⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⠄⣴⣀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡘⡆⡬⢰⣣⣍⣰⡍⣑⣆⣰⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠄⠷⢼⠱⣷⣞⠵⢾⣔⣶⣷⠲⠐⣁⢋⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠸⣧⣸⣇⣝⣸⢷⣟⣗⣿⡰⣌⣧⣿⣆⣟⣜⡑⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⣃⢹⣫⠟⡼⢮⣭⣿⣋⣨⡿⣿⣱⢿⡿⠿⢿⣧⢁⡋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⢩⡿⡑⣿⣻⣯⠗⣻⣎⣵⡽⡿⠷⣾⡬⢳⣆⡋⢼⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢧⣸⣦⣓⣻⣍⣷⣍⣿⣿⣟⣻⣿⡽⣓⢼⣿⡍⣊⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⠺⠇⣠⣦⡟⠲⣛⣿⣿⣿⡟⠛⣹⣫⡱⢶⣅⣾⢻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡳⠂⠀⣾⣹⠉⠈⣿⣿⠀⠾⠻⠥⣡⠶⢟⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠸⠟⠀⠀⣿⣿⠀⠀⠀⠀⠉⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢈⡉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠶⣋⣠⡴⠟⣡⠆⡀⠀⠳⣄⡉⠛⠻⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⡾⠛⣁⣠⣶⠟⢀⣷⡘⢄⠈⠻⣿⢷⣦⠲⣦⣭⣭⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣾⣿⡷⠟⣡⣾⡿⣟⠋⠀⣎⣿⣎⢶⡈⢢⠘⢿⣿⣧⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣷⣟⢟⣻⣱⣖⣾⠟⣹⣾⡟⠀⢸⣿⣟⣛⢊⣴⡀⢷⣌⣛⠻⠿⠿⠿⠿⠿⢛⣫⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣡⣾⣿⣿⣿⣭⣶⡼⣿⠃⣄⠸⠻⢯⣿⣞⢧⣽⣬⣓⢿⣷⣻⣿⡖⣮⡙⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣯⣾⣿⣿⣿⡿⣿⣛⣯⣥⣿⣁⡹⢇⣌⠳⣌⣙⡄⣙⣛⠿⣷⣮⠛⣿⣫⢷⣿⡬⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢷⡟⣿⣿⣿⣿⢣⢿⡌⣿⡄⢿⣞⡇⣿⣿⣧⣮⣿⡇⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⡿⣾⣡⡏⣶⠸⣿⣿⣿⣻⣿⣷⠿⢳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣷⣿⣿⣞⣿⣿⣿⣿⣿⣷⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠒⠁⠀⠀⠀⠐⢤⠡⠀⠀⠉⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⠁⠈⠁⠀⢀⡀⠀⠀⣧⢶⣗⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠘⠀⢀⡀⢚⡄⣴⠓⠁⠀⠀⠁⠀⠀⠀⠀⠀⢈⠆⠀⠀⠈⢓
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⣀⡔⢰⣯⢚⢬⠚⠁⠠⠀⢰⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⢀⠈⢆⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⡾⠐⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠈⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢜⣤⣦⣀⡀⠀⢀⠴⡮⣖⠀⢐⠠⡁⠐⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠗⠁⠀⠘⣷⢵⡶⡴⠒⠐⠐⠁⠀⢇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢁
⠀⠀⠀⠀⠀⡄⠀⠀⡔⠉⠉⠀⠽⡀⠀⠈⠁⠙⠛⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠢⠘
⠀⠀⠀⠀⠀⠁⢠⡈⠁⠀⠀⠀⠀⠉⠒⠉⠓⠀⢂⣣⠀⠀⠀⠰⠓⠦⠤⡠⠴⠒⢄⡀⡀⠀⠀⠀⠀⠈⢱⠰⠈⠂
⠀⠀⠀⠀⠀⡄⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠱⣤⠀⠀⠐⠑⠊⢀⠆⠀⠀⠉⠳⣤⠐⠀⠀⠀⠀⠢⢰⡄
⠀⠀⠀⠀⠀⠁⢺⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠙⢦⣀⠀⠀⡠⠌⠀⠀⠀⠀⠀⠈⠂⢠⠀⠀⠀⠶⣤⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠱⠌⣿⠶⢚⠁⠀⠀⠀⢐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠁⠀⠳⠗⢾⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠀⠀⠂⣀⠄⠀⠠⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠴⠁⠀⠐⠀⢈⡠⠄⢀⠤⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠳⡀⠈⢿⣠⠂⠀⠀⠀⡐⠟⠀⢰⠂⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡂⠀⣻⣟⠀⠀⠀⠙⠀⣄⠙⡄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠘⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣌⡻⣔⣀⠀⠀⠀⢈⡴⠉⢐⣄⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣶⣼⣁⣈⣀⣁⣀⠠⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠂⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣴⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠁⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣿⣻⣧⣤⣤⣤⣄⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⡠⠤⠚⠛⠛⠛⠻⣿⣿
⠀⠀⢰⣿⣽⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡟⠀⠂⠀⠈⡡⠊⠀⠰⠀⠀⠀⠈⠀⠀⣹⣿
⠀⠀⠈⢿⣿⣿⡏⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣄⠀⠀⢰⠁⠀⡀⠀⠀⢀⠀⠀⠠⢀⣿⣿
⠀⠀⠀⠀⠈⠉⠁⠻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⣄⡀⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿




⠀⠀⢀
⠀⢀⡇
⠀⠸⣷⡀
⠀⠀⠈⠛⠓⠢⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠲⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠐⠀⢠⠀⠀⠀⠀⠀⠀⣠⠚⠀⢸⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠳⡀⠀⢱⡄⠀⠀⢠⡾⠁⠀⢀⣾⠀⠃⠀⠀⠀⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢠⢳⣄⢀⠨⠷⠿⠶⣬⣿⢄⠀⣻⢧⣀⣴⣿⡿⠶⠆⠀⠀⣼⠃⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⣀⣆⠙⡶⠀⠀⠀⠀⢀⡟⠀⢣⠏⠘⣿⡍⠁⠀⠀⠀⢀⣞⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⠀⠀⠀⣀⢀⣞⠀⠀⣿⢀⡠⠿⢦⣠⣄⣤⣠⠎⠉⠁⢰⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⣻⠁⠀⠀⡱⠊⢻⡇⠀⠠⣀⣁⣀⡨⠉⠀⢀⡤⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠙⡖⠲⠖⠀⠀⠘⠉⠈⢀⠏⠉⠁⠀⣡⠞⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠁⠀⠁⠀⠀⠀⠀⠀⡞⢠⠃⣸⠟⠁⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢢⡄⡀⠀⠀⠀⠂⠀⠀⠀⢰⠁⡎⢸⠏⠀⠀⠀⠐⠀⠀⣸⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⡇⢛⢦⡀⢠⠀⠀⠀⠀⣾⠰⣇⣿⣤⡤⠤⠦⠀⠀⢀⣟⣀⡴⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢢⡙⢦⣧⢨⣦⣻⣮⡆⠀⠀⠈⡇⡔⢸⠁⠀⠀⠀⠀⢀⣠⣾⡿⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠑⠂⠀⠀⠙⢣⠹⣧⠀⠀⠀⣿⣃⣼⢤⢀⡀⠀⠀⣸⠩⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠳⢦⡀⠀⢸⡄⢹⠀⠀⠀⣿⠁⠀⢘⠛⠛⠋⠉⣀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⡙⢛⠀⠺⡇⠀⠀⣿⡴⢻⣯⡴⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡖⠿⠠⠀⠊⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⢀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠺


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⡠⠀⢉⡁⠉⠀⠈⢀⠉⠐⣢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡂⠁⡠⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠘⣄⠀⡀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠴⢣⡮⠄⠔⡠⢌⠀⠀⢀⡤⠂⠓⠐⣆⡔⠢⠇⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⢠⠎⡠⠠⠎⠀⠀⠀⠀⠀⠉⠁⠀⠀⢎⠀⣞⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠰⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢭⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠣⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠲⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⣠⠔⠒⠈⠢⡀⠀⣠⡩⠴⠀⠀⠘⢄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢠⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠫⠤⠀⠤⠀⠀⠹⠒⠁⠣⠤⢰⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣁
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠑⠂⢀⠖⠂⠠⠤⠘⢄⠀⠀⠀⢷⠦⢀⡤⠰⣄⡀⠀⠂⢹
⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⢄⠀⠀⠀⠓⠁⢡⠀⠀⠱⡀⠃⠘
⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠢⡀⠀⠀⡠⠊⠀⠀⠀⠡⣌⢀
⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠨⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢜⠒⣉⢀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠰⠀⠈⢀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠎⠘⠀⠀⠀⠀⠰
⠀⠀⠀⢆⠀⢈⠂⠀⠀⠀⠀⠑⠊⠁⠀⠀⠁⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠈⢆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠘⢡⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠑⢀⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⣠⠊⠀⠨⠆⠁⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢠⠤⠂⠁⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠤⠀⣀⣀⣀⣀⣀⣀⡀⠤⠴⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠘⠆⠁⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠸⣧⠀⠀⡸⠁⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⢠⡄⠀⡇⢀⣜⠅⠀⠀⠋⠀⣠⠈⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠉⠘⢦⡀⣸⡟⠋⠀⢠⢀⠔⠀⡼⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠐⠀⠀⠐⢄⠀⠀⠘⣷⡟⠀⢀⡤⠖⠁⠀⢠⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠘⢀⠙⢦⡆⣿⣇⡼⠋⠀⡠⠂⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⢤⣷⡀⢻⣼⣿⡅⢀⣾⡶⠛⠉⢀⡀⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣿⣷⣿⠷⠖⠒⠛⠻⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡝⠛⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⠀⠀⢀⠀⢉⣛⣛⣛⠛⣛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣉⣥⢤⣾⠋⡎⠀⢾⣷⣄⣉⠛⠿⣿⣬⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣾⣿⡟⣷⢟⣡⣺⠀⢰⣌⠻⣿⣮⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⡟⢀⠸⣿⣷⣬⣛⢿⣿⣧⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⡟⣡⢾⡆⠉⠻⣿⣿⣿⣝⣿⣌⢷⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣾⣏⣼⣿⢸⣷⡔⣽⣿⣿⡻⣿⣾⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⡏⣨⣿⣿⡎⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⡠⠄⠀⢀⣀⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢙⡥⠖⣢⡝⠋⠀⠀⢀⣼⣿⡏⠉⠙⣻⣷⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⡴⠚⣡⣾⣿⣿⡟⠀⠀⠀⠚⠉⠦⣜⣿⢷⣍⠰⣼⣯⣍⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠞⢁⠎⠁⣀⠙⠿⠉⠀⠀⠀⠀⠀⠀⠒⠈⠉⢳⣼⣿⠄⠈⢹⣇⠀⠈⠑⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⠞⠁⡶⠋⠀⣘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⡤⡶⠈⠈⠙⠛⠊⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣠⠋⠀⢦⡀⣠⢾⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠋⠁⠀⠀⢀⠰⡟⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⠟⠋⠀⠀⠻⠁⣼⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⣠⡴⠖⠀⠀⠢⢀⣨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⣯⣀⣤⣤⠀⣸⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⣵⠶⠻⡁⠀⡀⠲⣄⣦⠻⠋⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣾⡟⡏⢨⠘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠹⢠⠔⣹⣦⡿⡯⢻⡦⣆⢁⡴⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢰⣿⣇⣀⣰⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠻⢭⡦⠞⠋⡀⠘⠻⡵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⡏⠋⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣹⣿⡀⢠⡄⠓⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⢰⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⡀⠻⢷⣿⣄⡀⠀⠀⣀⣀⣀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢣⠀⠀⠀⠝⠷⣤⡴⠁⠀⠀⠀⠀⠉⠉⠁⢀⣲⣤⠤⣖⡩⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢻⣷⠀⠄⠀⠀⠀⠀⠀⠀⣇⡀⣀⣠⣤⡴⠶⠛⠋⠁⠀⠀⠀⣀⣦⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡇⢿⣧⠘⠆⠒⠒⠓⠀⠺⠛⠏⠉⠀⠀⠀⠀⢀⣤⡴⠶⠀⠈⠁⠙⣼⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢻⠈⢿⣦⡈⢄⡀⠀⢀⠀⠑⢶⣦⠸⠒⠋⠉⠀⢆⠀⣀⣀⣀⡴⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⣿⡓⣄⠡⣀⠀⠀⠀⠀⠉⠒⠢⢶⡴⠶⠚⢻⠋⠉⢅⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠘⣷⡀⠀⠌⠳⢄⠀⠀⠀⠀⠀⠀⠻⣦⣠⣄⢷⠿⢛⡟⠁⠀⠀⠀⠀⠐⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠹⣷⡀⠀⠁⠄⡉⠲⢔⡂⠀⠀⠈⠉⣻⣏⣦⣠⠎⠀⠀⠁⠀⠀⠀⢀⡠⠔⢊⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⣧⠀⠀⠀⠈⠑⠦⢌⢉⠛⠲⠤⠌⢻⣿⣷⣶⣶⠀⠤⠄⠒⣚⣯⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠀⠀⠤⠄⠐⠒⠊⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢻⣧⡠⠄⠔⠲⠒⠂⠀⣶⣷⣺⣿⣿⠛⠖⠶⣶⣶⣦⢤⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⠀⠀⢈⣿⣷⡀⠀⠐⠒⠲⣶⢛⣛⡛⠛⠛⠚⠛⠛⠛⠿⠧⠦⣄⠀⠀⣩⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡙⢷⡎⠘⠛⣿⣇⣀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠢⢤⠀⠀⠀⠀⠀⠀⣀⣈⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⠄⣠⢈⣟⣿⠟⣶⣶⠖⢲⠶⠶⠖⠶⠒⠒⠒⠒⢻⡟⡻⢋⣹⣄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠐⠛⠚⠲⠬⠠⠤⠤⠄⠀⠠⠤⠀⠘⠓⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢰⣦⣄⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣤⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣤⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣿⣿⣟⢿⣿⣿⡏⠉⠁⠋⠉⣿⣿⣿⢟⣿⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⠻⡿⠁⠀⠀⠀⠀⠹⡿⢣⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠿⣿⣿⣿⠿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣶⣶⣶⡖⠀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠃⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢄⡀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠻⡀⠀⠀⠘⠀⠁⣄⠀⠀⠀⢠⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠹⣆⠀⠀⠀⠀⢻⠀⠀⠀⢁⡀⠀⢰⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠤⢄⡀⠀⠀⢸⠀⠀⠘⣦⠀⣀⡀⠀⣤⠌⣠⠛⠁⠀⡆⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⠅⠀⠀⠈⣿⠏⠹⢦⠍⢰⠇⠀⠀⢰⠁⢀⡾⢁⠀⠀⠀⠀⣀⠤⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠈⠳⣶⠀⠀⢀⡌⠀⠆⠈⢻⡇⠀⡆⠀⣎⣰⠏⠀⠌⠀⢠⠄⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠉⠳⢤⣽⠀⠀⣼⠁⠀⠀⠀⠀⢱⡀⠇⢠⡿⠁⠀⣾⡄⠈⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠰⢶⣶⣦⣄⢀⡀⠈⠳⣄⠀⠈⠳⢦⡟⠀⠀⢀⡀⠀⠈⣷⣶⠎⠀⢀⡾⠋⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢌⡋⢤⡉⠠⠙⣦⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⠃⠀⣰⣏⣀⣀⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⢦⣀⠙⢷⡀⠀⠀⠀⠻⣤⡁⠀⣰⡦⠚⠃⠉⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⡀⠀⠙⢀⠹⣶⠘⠛⠂⣤⣄⡀⠘⣧⠞⠁⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠙⠦⡀⠳⣄⠀⠀⠈⠉⠲⣦⡀⠀⠀⠀⢀⠀⣤⣼⠀⠒⠒⠀⠀⠉⡡⠿⠟⠁
⠀⠀⠀⠀⠀⠈⠓⢂⡀⠶⠄⠘⠂⠀⠛⠶⢶⠀⠹⠆⠀⠀⠀⠀⠀⠻⡄⣀⡴⠞⠋⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⡖⠒⢀⠤⢄⣀⠳⠀⠸⠦⢄⠀⣀⠀⠤⠾⣁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠖⡄⠐⠀⠉⠛⠻⣦⣀⠀⠛⠁⠀⠀⠀⠈⠳⡆⠁⠀⢀⡄⢀⣀⣀⠠⠐⠒⠚
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⠦⡄⢠⣄⠢⡔⢄⠀⠀⠙⠲⣤⡀⢀⣤⠄⠒⠚⠒⠂⠰⢿⣦⠈⠉⠉⠐⠒⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠼⣿⣦⣤⣄⠀⠀⠈⠃⣀⡀⠆⠀⠀⠀⢀⣹⣧⠀⠀⠀⠀⡀⣤⣥⡴⠶⠖⠈⢉⠉⠉⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠛⠷⢶⣋⡉⠿⠶⣉⣀⠀⠀⠀⢀⣀⠴⠟⣤⠤⠞⠋⠀⣀⡀⠀⠠⢤⡤⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡒⠂⢠⠈⠳⠖⠠⢀⠈⠛⠷⡁⠀⠀⣀⣀⡈⠁⣤⠶⠋⢉⡄⠐⠀⠉⠁⠀⢠⡄⠀⠙
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣶⣶⠞⠿⠓⠚⠓⠨⢷⣄⠀⠹⠒⠀⠀⠈⠙⠛⢠⣤⢀⡈⠀⠈⠁⢴⣀⠤⠌⠃
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢈⣧⣤⣤⢠⡶⠒⠂⢠⡈⠣⣄⠘⣀⠀⠀⠀⢠⡴⠒⠻⡷⠖⠂⢠⣄⡉⠀⠀⠱⠃⡀
⠀⠀⠀⣀⠀⠀⡌⠁⠲⡀⠸⡇⠀⡤⠁⠤⠀⠀⠀⠘⠆⠙⣄⢉⡷⠉⠹⢦⣤⠈⠀⠈⠀⠁⠄⠘⡉⠀⠂⢲⠀⠑
⠀⠀⠀⠈⠓⢰⡿⠀⠀⣾⣶⠷⠦⣤⠄⣰⡆⠀⢰⡷⡤⠚⢻⡶⢀⣤⣀⠁⠀⠈⢠⡌⢱⣣⣄⠘⠗⠀⠈⠀⠶⡈
⠀⠀⠀⠀⣠⡋⠀⠀⡰⠋⠃⡀⠀⠀⠀⠙⡛⠃⠀⠛⠆⠀⠀⢳⣀⡄⢩⣐⡦⠈⠛⠀⢀⠍⠛⢳⡆⠀⠀⠀⣀⠙⠀⠀⠰⡆
⠀⠀⠀⡐⠿⠃⠀⠰⠁⠀⠀⠑⠀⠀⣀⠊⠀⣀⡤⢴⣤⣴⣞⠉⠁⡧⠈⠁⠐⣦⠄⠛⢫⡤⠀⡀⠘⣂⡀⠀⠁⠀⠀⢠⠄⠃
⠀⢰⡤⠃⢀⢀⡼⢤⡀⠀⢀⣤⠲⡖⠙⠓⢾⡋⠀⣸⡆⠀⠙⢇⠁⠀⠀⠀⡌⠁⠀⠀⢸⠀⠀⢹⡞⠉⠉⠖⠂⠀⢠⡦⠀⣤⠰
⠀⢸⠇⢀⡼⠁⠄⠀⢹⡟⠉⢀⡴⠃⠀⠀⢀⠉⠈⠉⠳⠀⠀⠺⣷⠶⠶⢤⡿⠀⠀⠀⠊⠀⠁⠰⡇⠀⠀⠋⣀⣼⡏
⡀⠘⢀⡌⠳⠖⠀⠀⠀⠛⠰⠂⢡⠀⠀⠀⠸⠂⠀⠀⠀⠀⣠⠞⠁⠀⡀⠀⠘⢣⡀⠀⠀⠀⠀⠀⢧⡀⠀⡀⠀⢸⡇⠀⠀⠰⡆
⠈⣄⡿⠁⠀⠀⠣⠄⢀⣀⠀⠀⠀⠀⢀⡼⠟⠛⡟⠓⠦⣠⡏⠀⠀⠀⠁⠀⠀⠀⣿⣠⠤⠴⣶⠴⢎⡁⠀⠀⠀⠸⣇⠠⠎⠠⡇
⠀⠉⠰⣧⠈⠳⣄⢀⡜⠋⠘⠓⣄⣠⡟⠀⠀⠀⠁⠀⠀⠹⠇⠀⠐⠀⠀⠀⠒⠂⣼⠃⠀⠀⠀⠀⠀⠙⢦⡤⡖⠢⡀⠀⠀⣠
⠀⢠⣾⣹⠆⠀⠘⣿⡀⢀⠀⠀⠈⠿⠀⣤⡴⠀⣆⠀⠀⠀⡃⠀⣀⣤⣤⣤⣄⢀⣿⠀⠀⠀⡀⢠⡤⣴⠟⠀⢀⡄⠀⣦⠐⢠⡦
⠀⢮⡄⠉⠀⢄⠀⠛⠑⠞⠀⠄⠀⠘⣇⠀⠀⠀⠈⠁⠀⠈⣡⠞⠁⠀⢄⠀⠈⠛⣏⠉⠀⠉⠁⠀⢠⡏⠀⠀⡞⠐⡿⠁⠘
⠀⠾⢫⣴⠶⢄⡀⠰⣄⣤⣄⣀⠀⠀⢙⠶⠉⠙⠋⠁⠶⣤⡏⠀⠀⠀⠈⠀⠀⠀⠈⣣⠶⠆⠀⢶⡜⠃⠀⢉⡀⠼⠇⣀⠀⡟
⠀⢠⠸⡇⠐⠀⠙⣶⠋⠀⠉⠈⠛⢶⡎⠀⠀⠀⠃⠀⠀⠈⢷⠀⠙⠛⠁⠀⠙⢠⠟⠁⠀⠀⢰⠆⢱⣆⣰⠋⢥⡀⣀⣥⣴⠇
⠀⢸⣧⠀⠛⡀⠀⠘⣷⠴⢀⡀⠀⠀⢻⡀⠢⣤⠀⠠⠄⠀⠠⣧⣠⣤⣤⣄⣰⠇⠀⠀⠀⡰⠃⠤⠋⢨⠋⠠⠜⢁⠙⠁⢼⠆
⠀⠸⠙⣧⡀⠑⢤⡀⢡⠀⠈⠑⠂⠀⢀⣧⠀⠀⠀⠀⠀⣠⡴⠋⠁⢠⠇⠈⠳⣆⠈⠁⢈⣤⠒⠶⢦⡀⠀⠀⠀⡮⠠⠂⣠
⠀⠀⣠⠀⠑⣄⠀⣨⡽⠶⣤⡀⣠⠖⠉⠉⠉⠉⠱⢦⠾⠁⠀⠀⣠⠘⡀⠀⠀⢸⣤⠖⠉⠀⠀⣷⠀⣴⣶⠶⢢⡀⢀⠾⠋
⠀⠀⠙⣶⡆⠀⢻⡁⢰⡄⠀⠹⣧⢀⣀⢀⡀⠀⠀⠈⣦⠀⠈⠉⠀⠀⢉⠁⠀⢀⣏⣀⣀⣀⡴⠛⠻⠃⠈⡇⢀⡼⣾⠃
⠀⠀⠀⠘⢷⠄⠈⠁⠙⢠⠀⠀⠙⡄⠀⠀⠑⠠⠄⠠⠛⢀⡠⠤⠛⠋⠁⠀⠙⠧⡀⠀⠀⠀⠀⠀⠇⢀⡀⠁⢨⠟⡀
⠀⠀⠀⠀⠀⠂⣰⣧⣀⡀⢑⡀⠠⣧⡤⠒⠒⠲⠒⠢⣴⠏⠀⡀⠀⠀⠀⣠⠀⣀⡿⠒⠒⠛⢶⣞⠓⠀⢀⡘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠙⣯⠙⣇⠉⠁⠺⠏⠀⠀⠀⠀⠀⠀⠈⢣⠈⠉⠐⠀⠁⠉⠸⠋⠀⠀⠀⠀⠀⠛⠓⠫⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠂⠀⠀⠐⠄⠁⠂⠀⠶⠐⠂⠐⢷⣀⠀⠀⠀⢀⣇⠀⢀⠀⠒⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢌⣀⣸⣆⠀⠀⠀⠀⣠⠆⠉⠉⠛⠀⠈⢙⡟⠉⣀⠤⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣾⣿⣶⣶⣦⣤⣤⣤⣯⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⢰⡔⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⣗⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣿⠾⠛
⠈⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣷⠉⣷⠀⢠
⠀⠢⡀⠀⠄⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⡰⢻⢁⣦
⠀⠀⠐⡞⠀⠀⠀⠑⢦⡀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⢀⣿⢷
⠀⠀⠀⠑⠀⠀⠀⠀⠈⣇⠀⣀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣬⣿⡾⣫⣾
⠣⠀⠀⠀⠈⠀⣇⠀⠀⠀⠀⠀⢀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⣷⣿
⠀⠁⠀⠀⠀⠱⣝⠆⠈⠀⠀⠐⠁⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢠⠾⠁⣜⠅⠀⠂⠉⠳
⠀⡖⠀⠀⠀⠀⠘⠋⠘⠓⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠁⠀⣸⠐⠀⠀⠀⠀⠦
⠀⡄⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣟⠀⠀⠀⠀⠀⢠
⠀⠃⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⣾
⠀⢽⢸⠀⠀⠠⠀⠀⠀⢀⠄⠀⠘⡆⠀⠰⠀⠃⠆⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⠌⠠⡆
⠀⠸⠀⠆⠀⠘⠄⠀⠂⠀⡃⠐⢆⡀⠀⠣⠄⠠⠊⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠁
⠀⠈⠇⢠⠀⠀⠀⠀⣀⠒⠂⣶⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣏⠀⠀⠀⠀⡏
⢦⡀⠐⠈⡇⠀⠈⠀⠘⠗⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠴⠻⠀⠀⠀⡸⠇
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠘⠿⣷⠀⠀⠀⠀⠀⢣⡘⠃⣤⠸⠆⢸⠆⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠶⣾⣿⣶⣦⠀⠀⠉⠀⠀⠀⠉⠁⠀⠉⢶⠐⠗⠀⠀⠀⠀⠀⣹⣿⡄
⠀⠀⠀⠀⠀⠈⠉⠀⢰⣷⡄⠀⠀⠲⠆⠀⠶⠀⠀⠀⢀⢀⡶⠁⠀⠀⣿⣿⠇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠺⠂⠲⠂⠀⣠⠀⡈⠀⠑⠃⠀⠀⠈⠳⣾⣿⣿⣿⠆⢀⣤⡤⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⣀⣀⠀⠀⣠⣤⡄⠉⠁⣄⡀⠀⠀⣰⣿⡆⠈⢉⣁⠀⢰⣿⣿⠀⠀⠀⠀⠀⢙⡀⠛⢂⠀⢶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠃⠰⠿⠛⠀⠀⠀⠙⠃⠀⠾⠿⠟⠑⢿⣿⣿⣷⣜⡿⠋⠀⠀⢠⡄⠀⠉⠁⠶⠉⠁⠀⠾⠅⠀⠀⠀⠀⣠⣶⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢉⡀⠀⠀⠐⠎⠡⠄⠀⠀⠀⢤⡄⢀⣀⠀⠀⠀⠀⠀⠛⢉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⣀⠀⠘⢃⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⡠⠰⣤⡆⠀⢰⡄⢠⡉⠀⠀⢠⣴⠆⠙⢿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠉⠀⣀⠘⠃⠀⢤⣾⡀⣴⠆⠀⠀⠀⠀⠀⠈⠛⠿⠀⠰⠟⠀⠀⢠⣤⣄⠀⠀⠈⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠢⣄⠙⠃⠀⠠⠀⠀⠀⠀⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⣤⣶⣦⡀⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⡀⠀⠀⠀⠀⡦⠰⢶⣦⠝⠁⠀⠀⠀⣠⠀⠀⠀⣠⣤⡈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡰⠇⠠⠶⠠⠦⠀⠀⠘⣷⠀⠠⠦⠈⠀⣀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠰⣦⠀⠉⠀⠹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡙⢿⣿⡏⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⣦⠙⠛⠿⠿⠋⡁⠀⠀⢀⣴⠂⠀⢰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡉⠀⠀⠀⢀⠀⢘⡃⠀⠀⣾⣿⠀⢀⣤⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⢀⡈⠋⠀⠀⠀⠉⠁⢈⣁⠀⢀⣘⠃⠀⠾⢿⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⢴⣶⣬⡁⢰⡇⠀⠄⢠⣾⣿⡏⢠⣿⣿⠀⢀⠀⢀⡰⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠃⠀⠀⣠⠌⠀⠂⠀⠀⠈⠿⠟⠀⠈⢿⡟⠀⠂⠀⢸⣿⢹⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⣾⡇⠀⠀⣿⣶⣶⠶⢄⣰⡆⢰⣷⣦⡀⣀⠟⠀⣠⡀⠘⠟⠀⠈⠙⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣡⣤⡀⠛⠛⠁⠀⢸⡿⢀⠻⣿⣿⣿⠀⢀⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢩⣶⡀⠈⠉⠀⠉⠀⠙⠃⠈⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠘⣿⣿⠀⠀⠛⠀⠘⢃⣤⣾⣿⣆⣰⡶⠆⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⠛⠃⢈⡉⢉⡁⣼⠇⠀⠀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⣤⣤⣤⣤⡀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠻⠿⠟⠉⢀⣤⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣠⡄⠀⣇⠀⠀⣼⣿⠗⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠐⣿⠃⠀⣋⠀⠀⡿⠋⣘⠡⠖⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠛⠀⠀⠝⡀⠀⠀⠀⠙⠆⠙⠿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡿⠋⠀⠀⣠⠀⠁⠀⠀⠀⢠⡀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠋⠀⠀⠀⠟⠀⠀⠀⠚⠂⠀⠸⣷⢀⣿⡏⠀⠀⣴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠷⠀⠠⡦⠀⠀⠀⠀⠰⠆⠀⣤⠌⠋⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠀⠀⠀⠁⠀⠀⠢⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢀⣄⠀⠀⠀⣀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠛⠾⣿⡇⢀⣾⣿⡿⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⣮⡙⠃⠀⠈⠱⠾⠛⠉⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠙⢿⠠⡞⠀⠀⠰⣿⣿⣆⠀⠀⢠⣾⡿⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣦⠀⢄⠀⠀⠀⠀⠀⠙⠛⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠛⠉⠉⠉⠉⠉⠉⠛⣲⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣛⣡⣾⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠻⡅⢠⣄⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢦⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⢀⣿⣏⠀⢠⣿⣿⡇⠀⢀⣴⡾⢿⣿⡛⣛⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣳⣄
⠀⠀⠀⢀⡜⠁⠀⠀⠀⣾⣿⣿⡇⠀⠻⠻⣿⣿⣿⣦⣾⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⢃⠘⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠤⠐⠛⠛⢻⣷⣷⣼⣄⣀⠀⠀⠀⠀⠈
⣾⣿⡄⠀⠀⠀⣠⣴⣶⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⠋⠙⠛⠛
⣿⣿⣿⣷⠀⠀⢿⡿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣄⡀⠛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⢿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠛⠁⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡿⣿⠁
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣴⡏⡼⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠃⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣆⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠒⠒⠒⠒⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⠍⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠴⠶⠒⠒⠚⠛⠲⠶⠶⠶⠤⠤⠾⠿⢵⣀⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⡰⠋⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡇
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⡀⠀⠀⢀⡠⢀⡀⣊⡾⠃
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⣿⣭⠭⢐⣂⣵⠞⠋
⠀⠀⠘⢦⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣰⠟⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠈⠳⣬⡓⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⢀⠠⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠭⣭⣭⣭⣴⣯⣭⣼⣟⣒⣒⣒⣒⣒⣠⣤⣬⠴⠿⠶⠛⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣜⠂⠀⣇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡴⡊⠜⠂⢐⢫⡉⠀⢦⡰⡅⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠔⣿⡿⣄⠲⣏⠠⠧⣇⣤⡀⢀⣀⢇⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢼⠀⠀⠂⢒⡇⠏⠒⣶⠄⣈⢀⣉⣀⢰⡉⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡁⣿⠸⡆⢈⢟⣹⣷⡿⣿⠴⡿⣪⣿⣎⠻⠱⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡱⣮⣧⣬⣛⣷⣍⡲⢷⣿⢿⣾⣄⠀⢠⡀⢀⢞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠻⣤⣰⢴⣄⠻⠿⣟⣿⣿⣿⣾⣛⣿⢏⠲⡞⢠⡵⠜⠠⣯⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠶⠿⠛⡖⢿⣿⣦⣿⢻⣿⣿⡿⣽⣟⢺⣗⣞⠷⣶⠲⠀⠁⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⢀⣀⢈⠛⢙⡈⢿⣻⣿⣽⣿⣤⣿⢿⢳⣛⣧⢲⡍⡄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢹⡟⢗⣚⣿⣫⣤⣏⣹⣟⣿⣟⣶⣾⡏⠻⢥⡖⡋⢄⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⣹⠛⢻⠛⠻⠟⢻⣿⡟⠝⠂⣄⠀⠀⠁⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣿⡇⠀⠀⠀⠁
⢀⢀⣠⣄⣤⣤⣀⣀⣀⣠⣤⣤⣀⣀⣤⣀⣤⣤⣶⣄⣀⣀⣤⣤⣄⣤⣀⣼⣿⣇⡀⣤⣠⣤⣄⣀⢀⣠⣤⣤⣀⣀⣤⢀⣠⣤⣶⣄⣀⣀⣤⣤⣄⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠁⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡛⠻⠿⠟⠋⠀⠀⢀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠈⠉⠉⢉⣙⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡞⠉⣉⡡⠄⠂⢀⠀⢀⡀⠀⠀⠠⠄⠀⣀⠀⠀⠠⠀⠀⠀⢀⠈⠃⣍⣉⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⣀⣛⠉⡀⠀⠴⠀⠀⠉⠀⡄⡄⠐⠀⠀⠈⠐⢷⠀⠆⣸⠃⣀⣈⠀⠈⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡃⢘⣃⢠⡄⢀⣠⣆⠀⠖⣀⠸⠁⣤⠀⠻⠆⠘⣼⠀⠦⠈⣀⠉⣉⠛⠀⠡⠜⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⠈⠁⠜⠡⡙⠟⠉⠄⠀⠛⠀⡘⢃⡄⠀⠀⢬⣸⢐⡆⠀⢠⢀⠈⡿⡈⣿⣰⠆⠹⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡦⠻⣸⡗⢠⣶⠗⡀⠀⣾⠀⢃⢸⡇⢾⢷⡄⠛⡼⠳⠇⢀⠈⡁⠈⡅⢠⢴⡌⠃⢠⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣘⠟⠡⢺⡿⢡⣿⡶⢀⠠⡆⣹⡤⢀⡈⢰⣿⣿⠃⠠⣤⣶⠰⡎⠿⢿⡀⠀⣦⣬⣥⣞⣿⣽⣎⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣇⢸⣟⡃⣺⡷⣠⣍⢠⣞⢱⣌⠻⠃⣼⡆⣙⣮⡀⢡⣆⠛⣷⣤⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠛⣱⣿⣿⣮⣽⠞⢋⣾⣿⣷⡄⢩⢈⡛⢿⣿⡎⣿⣷⣝⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣶⣷⡹⣿⣿⣿⣷⣾⣷⣿⣿⣿⠇⣸⣧⣿⡈⢿⣿⣮⣟⣻⣿⣎⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⣿⣿⣿⣦⣬⡟⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣏⠿⣿⣿⣿⣿⣿⣿⣷⡘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⣶⣿⣿⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣿⡌⢿⣿⣿⣿⣷⣮⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿