Coral Reef Emojis & Symbols

⠀⠀⠀⠀⠠⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠻⣿⡆⠀⢿⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⢀⢘
⣰⣿⣶⡄⠰⢯⡽⣿⣿⣷⣤⠀⡇⢀⡶⠂⠀⠀⠀⢀⣤⣤⣄⡄⣤⡐⠶⣷⣦⠘⡿⢀⠀⠀⠀⠀⡀⠀⠀⠐⣄⠀⡟⢠⠰⠾⣣
⢹⣧⣿⣴⣦⡀⠻⠛⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⡄⠀⠉⢙⢷⡇⡈⢿⣾⣷⠽⡿⣷⡾⢀⣾⣶⣦⣷⣤⡎⠙⢌⡆⢇⡏⢸⣷⡿
⣿⣿⡿⠋⣙⣟⢀⣺⣿⣿⣿⡿⣿⣷⣆⢲⣀⣽⠇⢀⠀⢈⣷⣷⣥⢺⣿⣿⣷⣰⢿⣅⣸⣿⣿⣿⣿⣿⢷⡇⣸⣽⣸⢤⣦⡿⣿
⣿⠟⢀⡘⣦⣽⡦⡿⢿⣿⣟⣾⣽⣿⣿⣿⣿⡗⡀⠀⠁⠙⣿⣿⣿⣮⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣧⣿⡿⣵⣽⣿⣿⣶⣿⣷⣿
⣿⣾⣿⢁⣄⣺⣿⣷⣦⣿⣿⡏⠛⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣽⢟⣡⢿⣿⣿⣿⣿⣿⣟⣿⣷⣽⣿⣿⣿⣞⣿⣿⣿
⠻⠓⠖⠩⠋⠽⣿⣿⣿⣿⣿⡅⠀⣾⣿⣿⣿⣿⠶⠛⠸⠿⡿⣿⣿⣿⣿⣿⣿⡅⢾⣿⣿⣿⢿⣿⣿⣿⡿⠿⠿⠿⠙⡿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠈⠛⠿⠛⠋⠃⠀⠀⠀⠀⠈⠛⠛⠛⠹⠃⠀⠸⠿⠿⠋⠀⠈⠉⠉

⣶⣶⣶⢶⠶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⢠⡄⢠⠀⠀⠀⠀⠀⠠⠰⠁⠦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠞⢀⠶⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠬⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠈⣨⠂⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠈⠅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣀⠀⠀⠀⠘⡄⣵⠚⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣈⡅⠀⠋
⠀⠴⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡫⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⢀⡀⠀⢫⢹⣆⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢀⠰⠏⠀⠀⠀⣬⡃⠀⠀⠀⠀⠴⠀⡐⠆⠡⠀⢀⢯⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢄⡀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠠⣤⡄
⠀⠀⠠⠀⠀⠀⠙⠑⠀⠀⠔⣆⡢⠠⣇⣄⣠⡇⢐⣷⣿⢗⠀⠀⠀⠀⠀⣀⡀⠂⣀⠀⠀⠂⢀⢀⡀⢢⣷⡟⠀⠀⢸⡃⠀⠀⠀⠠⡶
⠀⠀⠀⠄⠀⠀⠀⣠⠀⠹⣠⠐⢿⡆⢿⣿⣿⣇⢸⣏⢃⠟⠀⠐⠂⡄⡾⣿⠇⠀⢺⠶⠦⠆⣾⠚⣁⠘⡿⠁⠄⠀⣺⠖
⢀⣠⣄⠀⠀⠀⠐⣿⠀⠀⣿⡇⢸⡇⢸⡛⠋⢻⣹⣿⣿⢸⣧⡀⠸⣯⣶⣿⠀⣶⣼⣿⣷⡀⢽⢠⠏⠀⠀⣄⢀⣶⣇⣤⣶⣦⣤⡀
⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢠⣤⣦⡀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠶⠀⢩⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⡛⠃⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠐⢶⠄⢀⡄⠈⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⠀⢀⣤⠀⢀⣷⠂⡄⣻⣧⠏⢰⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠛⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⣸⠇⣀⠀⠀⠀⠀⢰⣠⡈⣤⣜⠐⢄⣀⢠⡟⠀⣸⣿⡘⣿⡿⣻⠀⣾⠀⠌⣡⢁⡎⢤⣖⡐⠀⠀⠁⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢰⡆⠀⣾⠁⢀⡿⢤⢢⡀⠨⠆⣿⣷⡟⢹⣸⡇⡄⢘⣷⠠⣿⠋⠀⠀⠀⢈⠁⠛⢮⡶⣷⠎⣡⠘⣡⣿⡕⢄⠀⠀⠀⠠⣠⠀⠀⢧
⠀⠀⢸⣷⡠⣿⡅⢸⡇⠘⣬⡇⣤⠄⢻⣼⠛⣾⣿⠇⠁⠌⠙⣦⣧⠀⠀⠀⢀⠈⠀⠀⠘⡿⠛⠛⠋⠀⠹⣧⣟⣻⣄⠀⠀⠀⠀⠀⣧⢈⡆⢰
⠀⠀⢀⣜⣷⣬⣷⣾⣷⣄⡀⢣⢈⣾⡎⡽⢗⣿⡿⠀⠀⢿⣿⣿⣿⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣬⣿⣥⣤⣄⠈⠀⢀⣯⣸⢣⡟⠰⣄⢀⡅⠁
⣠⣾⡿⣿⣿⡟⢿⣿⣿⣿⡄⠈⡄⠻⠕⣱⣿⣿⡇⠀⠀⠹⠛⢹⣿⠟⠋⠁⠀⠀⠀⢀⠀⠀⠠⣤⣄⠀⠀⠀⣹⠟⠿⢿⣿⣿⣶⣾⣿⣿⣿⣿⠻⣿⣿⣿⣤
⣿⣿⣿⣿⣟⠁⢈⣿⠿⣿⡛⠀⠹⠀⢰⣧⢡⣿⣿⡦⠀⠀⠀⢸⠁⠀⣠⣶⡾⠀⠀⠈⠀⠀⣀⠉⡉⠀⠀⠐⣣⡤⡾⡀⢘⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿
⠟⠗⠈⠻⠋⠀⣼⡏⠀⠢⡁⠀⠀⠀⠀⢃⣥⣾⣿⣟⠀⠀⠀⢠⣆⡀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⣾⠰⣆⠁⢸⠿⠋⠉⠛⣿⣿⠻⠿⠟⠀⢨⣿⡏⠘
⡞⠛⠀⠀⠀⠠⡏⠁⠀⡼⠤⡄⠀⠀⠴⣹⠟⣩⣿⣿⣄⡀⠀⣼⣿⣿⣯⠀⠀⡀⠰⡇⢀⣥⡀⠘⠃⠀⠈⢿⣿⡇⠀⢐⠊⢐⠂⢸⣦⡺⠺⠃⠀⢀⡎⠁
⠿⠚⠀⠀⠀⠐⠁⠠⡔⠁⠦⠁⠀⠀⠚⠡⠾⣿⠟⠋⠘⢁⣤⣿⣟⣿⣿⣦⡀⢳⠀⢀⠘⠿⢿⠷⠀⠀⠀⠼⠿⣷⠀⠀⢰⡿⠼⣜⢻⣧⠘⣧⠀⢠⠆⢠⣿
⠀⣿⣇⠀⠀⠀⠀⢼⣿⡄⠰⣦⠀⠀⣿⣄⠀⠀⠀⠀⠀⠘⠻⢿⣯⡛⠛⠋⢀⡜⢠⣿⣶⣶⣿⡄⠀⠀⠀⠀⠐⣿⠀⠀⣼⣿⠿⣶⣶⣌⡀⠉⠀⠘⠀⢼⡟
⠀⠉⠉⠁⠀⠙⠂⠘⠛⠃⠀⠋⠀⠀⣹⡿⠀⠀⠀⠀⠀⠀⣈⣓⣿⣿⣿⡿⣿⣷⣜⣿⡿⠿⠷⠄⠀⠀⠀⠀⠞⠛⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠻⠆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠴⠆⠈⠀⠀⣄⠈⠋⠉⠉⠛⠋⠀⠙⢊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠁⠈⠉⠁⠀⠁⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⠶⡶⣶⣶⠶⢶⣶⠶⣶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣽⡖

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐
⢀⣠⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⣀⣤⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈
⠘⠃⢴⡏⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣀⣀⣄⢄⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣾⣛⣷⣖⣠⣿⠉⣠
⠀⢨⣥⡀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠘⣿⣻⣶⣿⣶⣾⣿⣾⣃⣦⠦⢀⢤⣴⡆⢰⡀⠀⠀⠀⢀⠀⢤⣶⣾⣿⣿⣿⣿⣿⠭⢚⡋⠀⢀⡯
⣴⣼⣺⣏⣀⣾⣦⣾⣥⣿⣶⣷⡶⢄⠀⠀⠀⠐⠶⡉⣩⣿⣿⣯⣿⣶⣿⣷⣇⢰⠉⠀⠈⠙⠈⠀⠀⠀⣾⣿⡟⢚⢻⣿⣿⣿⡿⣿⣟⣿⣿⣷⣤⣬⠟
⣿⣾⣤⣿⣿⣿⣿⣿⣻⣾⣟⣼⣷⣶⣼⣲⣶⣾⣿⡟⣿⣿⣿⣿⣿⣿⣤⣍⣃⡉⣓⣼⡗⠒⢢⡄⡄⠻⣿⣶⣷⢾⣾⣿⡿⣿⣯⣿⣽⣵⣿⣩⣿⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣷⣿⣿⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣬⣵⣿⣿⣯⣤⣴⣿⡿⠀⠔⠛⣿⡟⡝⣴⠟⡷⣤⣦⣿⡿⣿⣿⣿⣟⣿⣿
⡿⠿⠛⠛⠻⠿⠿⢿⡿⠿⠿⠿⣿⡿⠋⠳⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⡿⠿⢿⠟⢿⠻⣿⣿⣿⠷⢀⣠⠿⠷⢾⣿⣶⠷⣿⣿⡹⠟⠻⢿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⡀
⠀⠀⠀⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠐⠀⠣⠀⠐⠀⠈⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⢀⠀⠀⠀⠱⣄⠀⠀⠈⠀⢁⠘⠁⢀⡄⠀⢀⠀⠰⣦⠀⢀⠵⠢
⠀⠀⠠⣈⡀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠈⠁⠸⠐⠊⡁
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⢠⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠊⢀⠄⢀⠀⢀⠀⠊⠁⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⢀⡀⠄⠠⠀⠁⡄⠀⠀⠛⠈⠁⠀⢀⡀⠀⠁⠀⣼⡀⢾⠋⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠠⡁⠀⠄⠰⠃⠀⠁⠀⠀⠀⠀⠉⠁⠀⠰⠛⡄⠥⢬⣄
⠀⠀⠠⠄⠠⠀⠀⠈⠂⡱⠂⡁⠀⡀⢁⠰⠋⠈⢡⠀⠓⠁
⠀⠀⠀⠀⢠⡤⡈⠲⠐⠙⠂⠁⠀⠁⠤⠂⠀⠈⠜⠛⡓⢄⠀⠀⠀⠀⠐
⠒⠂⢤⣴⣁⣀⠀⠀⢀⠈⣥⡀⡉⠁⠂⠀⠀⢀⠆⣹⠓⠖⠛⠁⠘
⠀⠀⠀⠀⠠⠀⠀⠸⠟⢄⠸⢀⡀⢁⠄⠀⠄⢢⡈⢻⠐⠂⢀⡁⢠⠤⢀⠀⠀⠀⠀⠂⠰⢄⣄⣠⡤⠤⠆
⠐⠀⠀⠀⠀⠀⠀⠃⢢⠀⠦⠄⠁⡀⠀⡈⠰⣥⣸⠂⠰⠐⠀⠀⠄⠀⢀⡀⠀⠐⠀⠁⠲⢤⠚⠉⠄
⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠃⠐⡀⠐⣡⠈⠀⠠⠛⣈⡁⠐⠒⡹⢛⣀⣄⠀⠁⠁⠀⠀⠀⠂
⠣⠴⢴⣀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠤⣰⠀⠒⢁⡀⣁⠽⢀⡾⠛⠇⢠⡄⠀⠒
⠀⠀⠀⠠⢊⠟⠁⠀⢀⡀⠀⠀⢠⠀⢀⡈⠀⠀⠀⠈⠙⠀⠥⡌⠀⠀⠀⠀⡐⠋⠘⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠘⠀⣄⠀⠀⢀⣰⡖⠃⢳⠦⢥⣶⢤⣴⠎⠈⡀⢉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠂⢀⣠⢀⠺⡂⢈⠄⣠⠴⣎⣠⡴⠚⣤⣼⢇⣠⠩⣏⡳⠯⣀⡀⡠⠄⠐⠀⡀⠄⢀⠀⠀⠀⢰⠀⠃
⠀⠀⠀⠀⠀⠀⣨⠠⠌⠌⠉⠱⣶⡥⢀⡈⢚⡀⠀⣸⡄⣦⣿⠃⠀⣵⠀⠸⠃⢀⣤⡤⠀⠀⠄⠚⠀⠆⢀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⡔⠂⠀⠈⠁⢜⠉⢹⡏⠙⡶⠈⠹⡆⠘⢶⣈⠁⠀⠤⠄⣤⡤⠀⠂⠸⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠤⣤⠀⠀⠀⠀⠀⡀⠙⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠒⠠⢁⠄⠁
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⡄⠀⠄⠀⠀⡆⢳⡀⡄⠀⠀⢀⡿⠀⣇⠀⠀⢀⡄⠀⠀⠈⠅⠈⢀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠀⢀⡏⡀⠀⡀⢀⢰⣄⢃⣐⡜⡔⠡⣸⠘⠀⠑⡇⠀⣿⠀⢨⣏⠥⢂⣤⣁⡴⠀⠀⠀⢀⢸⡄
⠀⠠⠌⠡⢉⣱⠆⢰⠎⢰⡇⠀⢲⣸⠆⣿⣜⢱⣀⠀⠀⠉⠀⠀⠀⠑⠀⠾⡅⣸⣇⣳⡼⢻⣿⡇⠇⢀⠠⢺⡀⢹⡆⢰⡄
⠀⠁⠀⠀⣸⢻⡇⢾⡁⣿⢶⣤⣾⣽⢪⠁⠉⠈⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣿⣸⣷⣿⣿⢛⣿⠁⣴⣿⡴⢸⡇⣼⢇⡾⢃
⠀⠀⣶⠐⡇⣸⣹⣌⣵⣧⣾⣿⠟⠻⢷⣦⣤⣤⣾⣧⣀⣴⣄⣀⣱⣾⢿⢿⣿⣿⣿⣿⣿⠏⠙⠿⠟⢿⣦⣾⣿⣿⣾⣅⣄
⣶⣿⣿⣾⣿⡿⣿⣿⣿⡟⠓⡀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⠀⠃⡿⡽⢻⣯⣀⠀⠀⠀⢀⡈⠉⣻⣿⢻⣿⣿⣿
⣿⠟⡍⣯⡳⠾⣰⠻⣻⣿⣾⣿⣿⡏⡾⣫⢷⢿⡏⠿⣿⠋⠀⠈⣿⠏⠀⠇⢡⠞⢻⠿⠛⡃⣶⣇⣾⣿⣶⣿⠗⣿⣿⣿⣿
⡙⣶⣦⠙⡿⠀⠟⢋⣛⠟⣻⢉⡈⠉⠙⡋⣶⡟⠀⠀⡄⠀⠀⠀⠉⢀⠀⠀⠀⠠⣜⠎⢷⢻⠈⣿⣏⣾⣿⠟⣾⠉⡉⢻⣿
⡉⢿⠟⠑⠀⢰⠟⠁⢩⣼⠀⢠⢆⣬⠀⠀⠀⠐⡖⢠⠖⠀⠀⠀⠀⠈⠀⠀⢒⢁⠀⠁⠀⠤⣧⠜⣇⣛⢾⡰⣿⡏⢓⣪⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⢰⠀⠀⠀⠘
⠀⠀⠃⡀⠀⠀⡱⠇⠀⠀⠀⠢⢴⠀⠀⠀⢀⠀⠁⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⢰⣅⢠⠃⠀⠀⡎⡄⠀⠀⢠⡅⠀⠀⠀⢰⣀
⠀⠸⡀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢈⠀⠀⢀⠀⠸⡆⠀⠀⠀⠀⠀⡈⠀⢀⠐⠀⠀⢸⠟⡾⠀⢀⢸⠠⠂⠀⡘⡾⠀⠀⠀⠀⡀⣿
⠀⠠⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢈⡆⠀⣠⠐⠁⠀⠀⠀⠦⠁⠀⠘⠀⠀⠀⠀⣄⠃⠀⠘⢾⣾⠀⠀⠇⠁⠀⠀⠀⠀⣿⡿
⠀⠀⢹⠇⠀⠀⠀⠀⡀⠀⣠⣀⠄⠀⠀⠰⠀⠀⠀⠂⡏⠙⠃⠀⠀⢠⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠂⢃⠂⠀⠀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⡀⢀⠀⠑⠆⠀⠈⠀⠀⠀⠁
⠀⢈⠀⡀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢐⠀⠈⠀⠀⠀⠀⠀⠈⠀⠂⠐
⠀⣠⠈⡁⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠐
⠀⡌⠘⠀⢁⠐⠀⠀⠀⠈⠀⢀⣀⠀⠀⠀⢗⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠐⠀⠀⠄⠀⠀⠰⠀⡀
⠀⠁⡀⠀⠈⠀⠡⠀⠀⠀⠀⠘⠛⠁⠀⠀⡸⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠁⠀⠀⠀⠐⠀⠀⠢⠀⠀⠀⠀⠄⠘⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠐⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠰⢤
⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠂⠀⠀⠐⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣶⣧⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡄⠀⡔⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠉⠛⠉⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠂
⠀⠀⠀⣁⣀⣀⡀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠅⠈⠀⠱⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⡠⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠀⠀⠀⠀⠀⠺⢿⣿⠀⠀⠀⠐⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠤⠄⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣧⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣤⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠻⠿⠷⠛⠋
⠀⠀⠀⠀⢰⡰⡜⣧⣧⢔⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠠⠦⠵⠦⢠⢀
⠀⠀⠀⢐⣢⠷⣜⣏⢳⣿⣦⢴⠂⠀⠄⡀⣂⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠘⠓⠒⠶⠶⠶⠷⠛⠋
⠀⠀⢀⠀⠋⠛⠒⢻⠿⣿⣻⡵⢤⡑⢴⡤⠠⣞⠑⠀⠴⣂⣠⣤⡠⠤⡄
⠀⢠⡌⢀⠀⠀⢰⣿⣙⣿⢿⣧⣴⣯⣿⣧⣶⢶⣴⡔⠶⣦⣔⣛⠯⠖⣂⠾⠰⠄
⠀⢨⢻⡀⣆⢰⠛⠿⢾⡚⢉⣽⣯⣐⢶⢯⡏⢿⣻⠃⢯⠉⢹⣿⠿⢥⣌⠉⡇⡖⢲⠀⡤⣀
⠀⢸⡌⣷⢸⡞⣄⠀⣠⣏⢺⣿⣿⣿⣿⢷⣿⣦⣧⣴⣾⡆⢰⣿⡀⢾⣿⣇⣿⢀⣿⣼⠁⡨⠂
⠀⢈⣧⣼⣿⣷⣿⠏⠉⠓⣶⣿⣿⣿⣟⣿⣾⣿⣿⠏⣾⡻⠾⢿⣧⡿⠁⠀⣿⡞⢉⣽⣮⣶⠃
⠰⠿⠿⠿⠿⠿⠿⠤⠤⠼⠯⠯⠿⠻⠛⠻⠿⠿⠿⠿⠭⠥⠤⠤⠿⠷⠤⠾⠛⠚⠛⠛⠛⠛⠓⠂

⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⠆⠀⠀⠐⢠⢤⡀⠘⣿⡿⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠦⢧⡈⠣⡈⠲⠈⠳⡀⠀⢾⠀⠘⢁⡞⠁
⠀⠀⠀⠀⠀⣴⢀⡤⣠⠀⠀⠀⠠⡀⣁⠈⠈⠀⠀⠙⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⢤⡹⣆⢻⡕⢀⠀⠈⢂⡜⢠⣀⠜⣤⣴⣠
⣺⡷⢲⠀⢀⡽⢎⡽⠁⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⢣⠳⡀⢹⣸⡇⢄⠑⢄⡌⢴⠋⠀⣠⠉⣸⣇
⡏⠀⢘⡶⠊⣴⠊⣀⢀⡴⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡛⠧⣇⠀⢻⡗⣨⡃⠈⣧⠃⠀⣰⣮⠴⢻⡏
⠀⣠⡟⣿⡄⡬⠰⢣⠞⢟⣁⣄⠀⠀⠀⠀⢀⣠⠆⠀⠐⣍⢣⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡴⢫⡇⣄⢱⠘⡇⠈⠣⠘⣇⠀⣠⠟⢡⣶⣨⡷
⠀⠙⠀⢹⣼⣣⠤⣼⢖⡿⠚⠉⠀⡀⠀⠐⠌⢁⣀⠀⠆⠌⠙⢧⠀⡎⠀⠀⡄⢠⠀⠀⡔⠀⢲⢸⠄⡇⢸⡀⠘⣼⠀⡰⠘⡀⢿⠈⢾⣧⠀⢸⡇⢿
⢸⠁⣇⡴⢻⠁⣠⠸⡏⠀⠀⠢⠁⠀⣤⠀⡅⠀⠙⢷⡄⠠⡄⢈⣧⠀⣄⠉⠳⡐⠁⣌⣀⡄⠀⢻⡀⢿⡀⠙⠢⡀⣿⠰⠊⠁⢹⣠⡆⠻⣤⡾⠃⢈⡆
⠁⣠⠿⠒⣺⠏⠀⣸⠁⠀⠀⠀⢠⠀⠈⠳⢶⡀⠀⢄⠙⡦⣼⢸⡇⠀⠀⠱⣤⠀⠀⠀⠀⠀⠀⠈⡗⠀⣿⢶⡀⠸⣿⡄⠀⠀⢸⠃⣟⠁⣹⢄⡀⡄⣧
⠊⠁⠀⢀⡧⠔⠋⠀⠀⣠⣤⣐⣏⢢⠀⠀⠀⠛⣆⠛⡀⠘⢶⡖⣧⡶⠂⠠⣏⡤⠊⠉⢹⡆⠀⠐⣇⠀⢻⢠⠌⢶⡁⠙⣦⡀⣼⠀⡆⡜⣾⠀⠉⠱⣯
⠀⢀⣴⠋⠀⣠⠂⣠⠞⠀⠀⠉⠉⣱⠦⠀⠀⠀⠘⣦⣙⠠⠸⠇⡏⠀⣱⡦⠏⠁⠀⣀⡀⣘⣆⡀⠈⠑⢾⣠⠀⠸⠃⢸⣡⠎⢻⣜⢁⡏⣿⠀⠀⠀⡿
⣉⠉⣌⣡⠆⠠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢌⡉⠙⢳⡆⠀⢧⣷⣸⠆⠀⠀⠀⠀⡉⠀⠉⠀⠑⠲⢤⠈⢷⠃⠀⢰⠇⢠⡀⢻⡏⠀⣸⣦⠴⠾⠛
⣛⣭⠁⡀⠔⠃⢀⣀⣀⡀⠀⣀⣤⠀⠀⠀⠀⢠⡄⠈⠓⠦⢽⡟⢿⡟⢃⣠⠗⠛⠿⠟⠑⠒⠒⢶⣄⡀⠀⠙⠻⡄⠀⢾⠀⠀⠓⢤⣇⣠⣿⠁⠀⢀⣴
⠁⠀⢠⣃⡤⠴⠋⠀⠀⠉⠉⢉⠍⠀⠀⠀⠀⢐⠞⠉⠙⠺⢶⡇⢸⠟⣛⠀⠀⠀⠀⠀⠀⠲⠒⠦⠬⠿⢶⡒⢲⡛⠓⢼⣦⡀⠀⢠⣿⠏⠁⠀⡴⠛⠁
⠁⡼⠋⢀⡀⠔⣢⠤⠤⠔⠂⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠾⠲⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡄⠈⠛⠛⠲⢦⣿⡄⠀⣴⠃⢀⠔
⣾⣋⣒⣉⢀⡐⣁⡀⢀⣀⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠠⡄⠐⠒⢒⠆⣤⣀⠀⠀⠀⠀⠀⠀⠀⢙⣓⡆⠒⠋⠀⢙⣷⣰⠇⢀⣞⣀
⠧⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠋⠸⠌⠰⠁⠀⢀⡾⠀⡀⢉⠑⠢⢄⡀⢤⣀⠀⠀⠻⢇⡀⠀⢀⣼⣿⠟⢾⡭⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⡀⠠⢂⡔⠀⣰⠏⠀⢠⢁⠋⠄⠀⣞⠞⠂⡸⣵⡀⠀⠈⢳⣴⣿⡿⠤⠊⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠻⡅⠰⣆⡦⢼⣷⣳⠞⠂⢵⣯⠀⠀⠆⡌⡔⠀⣴⡏⠀⣰⢰⠁⡃⠀⠀⢾⣿⠷⠐⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⡑⢦⠀⣹⣭⡿⢽⢡⡀⣴⠋⡇⠀⡰⢐⡏⠀⣶⢹⣀⢜⡡⠃⠀⡓⠄⠀⠀⠁
⣄⠀⠀⢀⣸⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⢷⡈⢧⠟⠅⣇⠈⡚⠱⠃⠀⡇⣰⠇⢸⣧⡞⢁⣞⡥⡏⠀⠀⢠⠖⠁⡈⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣇⠐⠿⣿⣿⣿⠀⣿⣶⡄⠀⠀⠀⢰⠙⠿⠶⣬⡷⣼⡢⣔⢸⡏⢂⢸⢰⡀⡼⠃⢠⡾⠋⢰⣷⠏⠀⣇⡤⠔⣣⠔⠚⠛⠈⡅⠀⠀⠀⠀⠀⠀⢀⣈
⡙⢿⣆⠀⠀⠹⣿⠀⣼⣿⣃⣴⡦⠀⠀⣦⡐⠊⢲⠀⢈⢟⡺⣿⣟⣹⣿⠛⠠⣧⡞⠉⠀⢈⣿⠋⠀⣰⠋⢀⠊⠁⠀⠁⣠⠞⠀⠀⠀⠀⠀⢻⣷⡙⠻
⣻⣌⠻⣷⡀⠀⣿⣷⣿⣿⣿⠟⠁⠀⠀⢜⢘⣓⣺⠋⢀⠠⢹⡏⢿⣏⡸⣆⣰⠃⠀⢀⡴⠛⠀⣠⠞⠁⣠⠎⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣀⠙⠻⠦
⣿⣿⣆⠉⢻⣿⣿⣿⡿⠋⠀⣀⠋⠀⠀⠁⢈⡀⠉⢷⡀⠀⢸⣇⣠⡿⠁⢹⡏⠀⣰⡏⠀⠀⣸⠃⣠⡾⠫⡰⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣙⠻⢶⣄
⣿⣿⣿⣇⠀⣿⣿⡟⠀⠀⡜⠁⠀⠈⠠⣄⠀⢔⡀⠀⠙⣤⣼⡏⠀⠀⢀⡿⢁⣴⡟⣀⣠⣴⣷⡟⣋⣠⣀⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢺⣿
⣿⡝⢿⣿⣷⣸⣿⠁⠀⠀⠱⠀⡨⢄⠀⠈⢢⠀⢘⢂⠁⠀⢹⡇⣤⡾⣋⣶⡿⠟⠛⠻⢭⣄⠀⠐⠀⠀⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠟⠋
⠻⣿⣄⣿⣿⣿⣿⡇⠀⠀⢠⠒⠐⠊⠛⢒⣾⣦⡀⢸⠑⠈⢸⣿⣷⡾⠟⠁⠀⠀⠀⢄⠀⢀⠈⣡⠴⠐⠋⠀⠀⠀⡄⡄⢲⠄⠀⠀⣆⠀⢠⣀⢀⡀
⠀⠀⠉⠻⣿⣿⣿⣷⡀⠀⠀⠁⠠⠂⠴⠋⡂⠀⠈⠻⣆⢠⣿⣟⠅⢈⢀⢸⠉⠒⠢⢤⣤⠶⠞⠁⠀⠀⢠⠀⢠⠅⢘⣇⣀⠆⠀⠀⣢⡔⠉⡄⢘⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠠⣃⠐⠉⡀⠀⠀⠁⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⠀⠀⣄⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠁⠀⠹⢤⣤⠀⣤⡐⣠⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢏⡼⢿⡿⢷⣶⠆⡀
⠀⠀⠀⠀⠀⠈⡘⣁⣄⣻⣏⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣴⠦⠦⡌⠋⠀⠠⠄
⠀⠀⠀⡀⢀⡤⠿⠉⠉⠉⡽⠋⠁⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⠂⠂⠃⠀⠂⠀⠁
⠀⠀⠀⠀⠈⠘⡄⡀⠈⣿⠗⠉⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠸⢤⣾⣷⠘⠳⠲⢣⡄⠀⠄⠀⠀⠀⠄⢀⣤⡀⠀⢗⣀⠆⠈⠀⠀⠀⡀⠀⠀⠀⠠⠂⡄
⠀⠀⠀⠠⠀⠒⠀⠘⠻⠟⠲⡦⠼⠛⠀⠀⠀⠀⠀⠀⠀⢾⣿⡧⢠⠀⠨⠀⠀⠀⠀⠀⠀⠀⣾⡞⠁⣀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⣼⣀⠀⣤⣄⠀⠀⠀⠰⠯⠛⢿⡗⢫⡠
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢠⣦⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⡸⣿⠟⢀⣀⠀⠘⢦⠆⣐⠙⠋⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣍⣌⣻⣿⣿⡿⠒⡜⠀⠀⠀⠈⡀⠀⣀⣬⡀⠰⠖⡛⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡤⡖⢰⡿⠃⠀⠀⠀⠙⢲⠾⢇⡀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢐⠛⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⢄⠳⠤⣍⡱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣛⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⢄⠈⠲⡀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠊⡔⠉⠀⡅⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⠎⠀⠀⠈⠢⠜⠁⠀⠀⠀⠎⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠘⠓⠒⠋⠀⠀⢸⠀⠀⠀⠀⢰⢲⠖⢫⠲⠀⠀⠈⠓⠤⠤⠤⢄⡀⠀⠀⠀⠀⡜⠀⠀⡘⠙⣝⢏⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢰⠀⠀⠀⠀⠀⢆⠀⠀⠀⢸⠀⠉⠋⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢣⣀⠔⠀⠀⠈⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣕⢄⠀⠀⠀⠈⢢⡀⠀⠈⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠁⡠⢔⡱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢕⡢⣄⠀⠈⠒⠚⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠔⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⢀⡠⠃⠀⠀⠀⢪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢰⠁⠀⠀⢀⠔⡿⢖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠰⢢⠀⠁⠉⠁⢀⠔⢒⡀⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⠎⠀⠱⢌⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠰⠴⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠐⠓⠶⠶⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠋⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠸⠤⠒⠁⠀⢀⠠⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠟⢦⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢀⠀⠀⠳⢄⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢶⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣃⡠⠚⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠁⠈⠁⠒⠂⢤⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣍⠑⠤⠄⢤⠴⠊⠉⠙⠒⠠⠤⠤⠇⡀⠀⠀⠀⢸⡤⠒⠈⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠁⠒⣾⡀⠀⠀⠀⠀⣀⣀⣀⡀⣬⣦⠀⠀⢸⣤⣄⡀⠀⠀⢀⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠭⠉⣉⡉⠒⠦⠐⠈⢨⡉⠁⠒⠂⠁⢀⠤⠀⠀⠰⣟⣆⣈⠡⠔⢚⣟⣒⣂⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠒⠊⠁⠉⠀⠀⠐⠈⠁⠀⠀⠀⠀⠈⠑⠒⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠃⠀⠃⣰⡇⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⢲⠤⠖⠚⢋⠀⠎⠇⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠕⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠡⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⣴⣇⠘⠁⠜⢀⠖⠒⠒⠉⠀⠀⠀⠄⢀⠀⠀⢀⠃⠀⠰⠆⠨
⠀⠀⠀⠀⠀⠀⠀⠂⠴⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠢⢄⠀⠀⡘⠂⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⠔⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢴⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣠⠴⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡘⠃⣡⠆⣰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣀⠼⠅⠀⠰⠋⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠈⡀⠡⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⢫⢄⠀⣰⠒⢂⡀⠀⠀⠀⠀⠘⡄⡄⢀⠄
⠀⠀⠀⠀⠀⡆⠀⡠⠊⠀⠀⠀⠀⠀⠂⠌⠀⠠⠀⠀⠀⠀⠀⠀⠘⠉⠀⢅⠀⢛⢉⡀⢼⠀⠀⠀⠀⢌⡸⡀⡀⢀⡆
⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⢀⠀⠀⡏⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠠⠀⠓⠈⠈⠀⢠⠀⠀⠀⠀⢠⠢⢁⡅⡎⢀⢀⡂⠀⠀⠀⠀⠘⡠⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠣⣀⡀⠁⠀⣀⡀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠒⠈⠁⠀⠁⠀⠀⠀⠀⠀⠣⢀⣂⣓⠜⠀⠀⠀⠀⠀⠰⠀⠀⣿⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⡇⣼⣧⢂⠰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⢰⠇⢀⠎⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠃⣧⠸⣇⠃⡎⢈
⠀⠀⠀⠀⠀⠀⢀⠄⠄⠄⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢺⠁⡸⠀⡜⠀⡴⠁⠀⠀⠀⠠⠀⠒⠸⠄⠀⠡⢊⠀⠀⠀⠀⠀⠈⠳⠀⡆⠉⣅⡸⠎
⠀⠀⢀⢠⠂⠠⡹⠂⠈⠀⢨⠐⠀⡀⠈⢀⠰⠀⠀⠀⠀⡗⠄⣀⠀⣸⠊⠀⠀⠀⠀⠘⠀⠑⠀⠄⠀⡠⠀⠘⠁⡀⠀⠀⠀⠀⠀⠐⢃⡰⠀⠡
⠀⠀⠈⠈⠋⢁⠀⡧⠔⣀⠀⠒⠹⠀⠉⢠⠀⠀⠀⠀⠀⢣⡀⡟⢀⣿⠀⠀⠀⠀⠀⠈⢀⡄⠁⠸⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢄⣀⢃⢠⣠⣠⢊⡄⠤⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⡾⠃⠀⠀⠀⠀⠀⠀⠐⠀⠰⠃⡀⠀⠐⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠀⠀⡆⠀⠀⠀⠁
⠀⠀⢠⠀⠀⣸⠁⠀⠀⠈⠐⠊⠀⠀⠀⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠀⠀⡔⠀⠀⢀⣰⠊⠀⠀⠀⢧⠄
⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢄⠀⠀⠛⡀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠘⠡⠇⠀⣆⣇⡇⠀⡜⠏⠀⠀⠀⢠⣹⠂
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠴⠃⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣿⡁⠀⡀⠀⠀⠀⠀⣼⠟
⠀⠀⠉⠀⠀⠀⠀⠐⠐⠛⠊⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠳⡄⠀⠲⠀⠀⠐⠁
⠀⢐⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠃⠀⠀⠀⠀⠐⠤
⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠂
⠀⣁⠈⠈⡀⠂⠀⠀⠀⠀⢀⣤⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆
⠀⠉⡀⠀⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠁⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣾⡄⢠⠇
⠀⠀⠠⠀⢤⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠋⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂
⠀⠀⠠⠤⢤⠀⠀⠀⠀⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠀⠀⢂⠀⠀⠀⠈⠁⠐⠀⠀⣼⣿⡖⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⢟⣿⣶⣃⣠⠀⠀⠀⠀⠀⠀⣰⣯⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣼⢡⡞⣱⢟⣿⢷⣾⣁⡠⠀⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡞⣼⢣⣟⣼⢣⡞⣱⢏⡽⣻⢷⣾⣿⣿⡿⣫⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢯⣿⣽⣷⣿⣾⣷⣿⣾⣵⣯⣾⣵⣯⣿⣿⣿⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢁⡯⠞⠛⠛⠛⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣭⣶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣻⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⢒⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⣫⣿⣿⣿⣿⣗⡩⠙⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⢟⣿⣿⣿⣿⣟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⡝⣧⠀⠀⠀⠀⠀⣀⠴⣺⣿⠃⠀⠀⢊⢿⣿⣿⣿⣯⣭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣰⣯⠖⠛⢿⣮⣷⣄⠀⢀⠀⠀⢀⡿⢸⣧⠰⣤⡶⣛⡵⣿⣿⡏⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣟⣿⡧
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠠⣿⣿⢿⣿⢇⣿⣿⣿⠀⠈⠀⠀⠈⣳⣤⣿⡆⢟⡾⣫⣾⣴⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣀⣾⡃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡾⡷⠋⠀⠀⠀⠀⠀⠈⣿⣿⡟⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⢾⣭⣍⣉⠙⠒⠶⢤⣄⡀⠈⠉⢉⠉⠀⢀⠀⠀⠀⠀⠀⠀⢰⣽⣿⠃⣿⣿⣻⣿⣿⣿⣿⣶⣤⡀⠀⣸⣿⣿⣿⣿⣾⠏
⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣄⠈⡛⢦⡑⣤⣠⣀⠀⠀⠀⠈⠀⠀⢀⠞⣿⡟⣸⣿⣿⡿⣵⣿⣿⠿⠛⠉⢀⣰⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠸⢭⣛⣛⣉⣉⣛⣛⣛⣦⣈⣿⣎⣿⣿⣆⡀⠐⣈⣀⢁⣡⣾⡟⣡⣿⣿⣿⣾⡿⠿⠿⠒⠀⠀⣼⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠙⠻⠿⢯⣭⣍⣉⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⡿⠿⢻⠍⠄⠀⠀⢀⣠⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣾⣯⣭⣭⣵⣶⣿⠿⠋⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⠿⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣿⡟⠻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⡄⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡦⠀⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⡠⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡁⠀⠀⠀⠀⣰⠥⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠂⣀⠔⠀⠀⠀⣠⠎⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡸⠁⠀⠀⠀⠀⠀⡰⢡⠎⠀⠀⠀⠀⡰⢻⠀⢀⠤⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⢠⡰⠁⠀⠀⠀⠀⠰⠁⠀⡔⢁⡴⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢃⡰⢾⠒⢩⢔⠜⠉⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⠜⠀⠆⢰⠁⠆⠀⠀⠀⠀⠀⡠⢊⠔
⠀⠀⠀⠀⠀⠹⡦⡄⠀⠀⢃⢰⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠸⢀⡌⠀⢠⠀⡜⠀⠀⠀⡠⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠘⡌⡆⠀⠈⢻⣀⠀⠀⠀⠀⠀⢄⣣⡀⠀⠀⢀⡇⡏⠠⠀⢠⠋⠀⠀⠀⠊⡰⠃
⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠈⠦⡁⠄⠀⠀⠀⠀⠈⠑⡦⡄⠀⠃⢃⡰⢀⠆⡀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⠈⠢⣱⠀⠀⠀⠀⢀⠖⣼⠎⠀⢨⠓⣼⠀⡇⠔⠉⠇⠀⣠⡴⠂⠀⠀⠀⢀⠜⡜
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⢠⣟⠀⠀⠠⡄⡿⡸⡌⢀⠜⢔⠟⠉⠀⠀⢀⣤⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⢠⡸⡌⢃⠀⣠⢃⡧⢰⡴⢃⡞⠁⠀⠀⠀⡴⡱⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢎⠲⢄⠀⠀⠀⠀⠑⢴⡀⠀⠀⠀⢹⠸⣀⠟⢡⣎⠔⡏⢠⠻⠀⠀⠀⠀⠀⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠠⣤⣀⣀⠈⠣⣄⡀⠀⠸⢀⡧⣦⡋⠤⠊⠀⢸⡘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⢦⢜⣌⢣⣦⢈⠜⠇⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⣠⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡎⣇⠎⡘⢀⡠⢤⠶⠚⢛⠟⠲⠖⠾⠭⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠺⠋⡜⠰⡡⠊⢀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠀⡄⢷⡡⢊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢴⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠄⣀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⣴⣿⣿⡦⠀⠀⠀⠀⠐⣌⣉⠆⢠⠁⣬⠂⠀⡥⠈⡠
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⡜⠁⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⢀⠲⡀⠀⠃⢶⠴⢃⠀⡰⠒⠉⡂⠠
⠀⠀⠀⣆⠀⠐⢄⠀⠠⠀⡀⠀⢀⠀⠀⠀⠀⠀⢠⠀⢁⠰⠀⠁⡃⠞⠀⠄⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠈⠘⠉⠉⠀⠻⣦⠀⣶⡵⠲⠤⠐
⠀⠀⠀⠨⠀⠀⠀⢷⡄⢡⢣⣦⠆⠀⠀⠀⠀⠀⠘⡤⠘⠐⢀⠀⡁⠀⢠⠆⠀⠀⢂⡠⠂⢠⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣹⣞⡁
⠀⠀⠀⠀⠀⠀⠂⠀⢙⣾⠞⠋⠁⠀⠀⠀⠀⠀⠀⠘⢦⣻⡀⣀⡰⠊⠀⠀⠀⠰⡆⠀⠘⠠⠀⠀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡸⢞⠃⠀⡂⡧⢌⠁
⠀⠀⣸⠇⢲⢠⢸⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢀⡆⢰⠖
⠀⠀⢹⡀⠾⠘⡈⢸⠃⠀⠀⠀⠀⠐⠀⡀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢽⡄⠇⡿⢂⣛
⠀⠀⠈⢇⠀⢸⢣⡎⠀⠀⠀⠀⠀⠀⠀⢈⢦⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠬⢧⡟⣼⠇⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠘⣦⣾⠏⠀⠀⠀⠈⠐⠂⢄⠐⠁⠸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠈⠆
⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠇⠀⠀⠀⡀⠀⠀⡄⢀⠀⠀⠀⠠⠀⢠⡀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠼⠴⡙⡘⣐⡄⠔⠰⢸⡆⠀⠀⢠⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢂⠀⠀⠀⠸⡀⠀⡆⠀⠀⠀⠀⠘⢿⡸⡼⡱⠎⡙⣱⢋⣿⠟⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠉⠉⠠⡐⡍⡎⠐⢁⠀⠀⠀⠀⠀⠉⠙⢿⣴⠷⠑⠚⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⣤⣀⡶⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⡇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣼⣯⣷⣷⠀⠀⠀⠀⠀⠂⠈⠀⠈⠀⠀⠀⢰⡗⢾⣤⡟⠛⣇⣹
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠨⡟⣻⣤⡟⠛⣧⣼⠂
⠀⠀⠀⠀⠀⠀⠀⢳⣱⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠀⠀⠀⠀⠀⢀⣀⢢⠔⠁⣾⠈⣷⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⣀⢤⡰⡆⣴⢢⡷⡶⣰⠄⠄⣀⠀⠀⠀⠀⠀⢺⠀⢀⠃⠂⠀⠀⠀⠰⣄⣌⣿⣌⠀⠀⢽⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠛⠷⣷⣷⣸⡼⢰⠓⣯⣯⠾⠚⠀⠀⠀⠀⠀⠸⣀⢂⠀⠀⠀⠀⠀⠀⠈⠨⡀⣸⠟⠶⣾⣧⣀⡼⢑⠀⠀⠀⠀⠀⠐⠀⡡⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠉⠻⣧⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠹⠐⠋⠀⠀⠻⣿⡄⠀⠁⠀⠀⠀⠂⠀⢀⢀⠀⣀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠙⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣯⣿⣬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣷⣾⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣬⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣽⣃⠽⣧⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢘⠇⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⡁⢻⡄⠀⠀⠀⣾⡁⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⢀⠀⣸⠠⠄⠩⡅⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡆⢸⡇⠀⠀⣸⠏⠀⣽⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠀⢠⠀⡟⠀⠀⠑⡇⠀⠀⠀⠀⠀⣿⠝⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣹⡇⠀⣸⣟⠈⢸⡶⠀⠀⣴⠁⡄⢀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠃⠀⠰⠆⣻⠈⠀⠐⡇⢠⣦⠀⠀⠈⣿⡌⢭⣇⠀⠀⠀⣠⣄⠀⠀⠀⢹⣿⡷⡞⣇⣰⡿⠀⢰⣿⠁⠀⠀⢛⠀⠙⠻⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⣀⠀⠅⢹⠀⠒⠡⣧⣼⣿⡇⠀⠀⢻⣷⠂⢿⠀⠀⣼⢏⡹⣧⠀⠀⠸⣿⡷⠈⠸⠟⠂⢠⡾⠁⠀⠀⠀⣸⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⣆⠀⠐⠠⠚⢼⠁⠀⣠⠘⡿⠆⠔⡆⠰⢿⢎⢤⡏⠀⠀⠀⢿⣿⠍⠑⠀⢚⣿⠃⠀⠀⠀⢀⣇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⡀⠰⢼⣧⡄⠈⠐⢺⣆⠀⣿⡀⠙⠀⠠⠼⠃⠀⢠⠟⠀⠀⠀⠀⠸⣿⣤⠈⠄⠺⣿⠀⠀⠀⠀⡾⠁⢀⠀⠰⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢄⠈⠛⢂⠀⠀⠀⢹⣧⡈⢷⡀⠀⠀⢂⠀⢜⡏⠀⠀⠀⠀⠀⠀⣿⣿⣆⢠⣄⣿⠀⠀⠀⢰⣏⡀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠛⠷⣵⣬⠅⡀⠀⣨⡹⣿⣾⡏⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⢸⣿⣉⠂⠹⢟⡇⠀⢠⣿⠯⠁⡀⣌⡟
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢰⡅⠐⡎⠛⢷⣏⡀⠁⢀⣻⣷⣷⠀⠀⠀⠀⠲⠇⠀⠀⣯⠻⣆⠀⢸⣿⣝⠁⠐⣊⣧⣴⠏⠄⠒⠄⢁⡟
⠀⠀⢀⣀⣀⠀⣶⡀⠀⠱⠀⠀⠸⣷⠀⠙⡀⠀⠹⣾⡏⠈⠹⣻⠻⡁⠀⠂⠠⠠⢽⡄⠀⣿⡀⠽⠀⣸⣿⣯⠃⠀⠀⠙⠋⠁⠡⢌⣰⠟
⠀⠀⠈⢷⡟⡻⠿⡷⠀⠀⠘⠦⡀⠻⣟⠀⠑⣄⠀⠘⢶⣦⠀⠈⠆⠉⠀⠠⠐⣚⢿⣿⣆⢹⣇⠨⣷⣿⣿⠎⠐⡀⠀⠀⠠⠠⣌⡟⠉
⠀⠀⠀⠈⠛⠻⠿⢾⣷⣨⡀⠤⠛⢷⠾⠻⠀⠀⠙⠲⠌⠛⠳⠀⠀⠀⠐⠀⢄⠀⠘⢿⣿⣧⢿⢀⠸⢟⡈⢁⠀⠀⠀⠠⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣧⣴⣄⡀⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠡⠀⡠⠀⠐⣿⣿⣘⠇⠀⠄⡁⢠⠀⡄⢾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣷⣿⣾⣿⣿⣶⣤⡄⡈⠀⠀⠐⡠⣹⣟⣷⠘⠀⠀⠃⡁⢄⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣷⣴⣃⣀⣥⣹⣿⣟⢡⡄⢐⣴⠁⣭⢂⣿⠀⠀⣴⡛⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⠹⣿⣟⡐⡤⠠⡝⣳⠂⠄⢹⣶⡾⠛⠖⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣎⢘⢫⣿⣿⣿⣿⣿⣿⣿⡻⣿⡿⢇⢓⣳⣾⣧⡾⢅⣤⠉⠍⣠⣹⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠣⢛⣿⣿⣿⣿⣿⣿⣞⣩⣿⣿⡶⣟⡭⣿⡿⣆⡘⢫⠠⣀⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣶⣟⣿⣷⡿⣷⡦⠹⣈⢄⡄⣁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣷⢌⣟⣴⢤⢀⣈⣔⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠛⠛⠛⠋⠉⠉⠈⠉⠉⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠿⠛⠁⠀⠈⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⣠⣀⣤⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠉⠉⠀⢀⣤⣴⡿⢿⣟⣿⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⠈⣨⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⡿⣬⢹⢿⣿⡿⠋⢋⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⠿⠛⡟⠉⠀⠀⠑⢭⣦⠴⠟⡼⢡⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⡿⠟⠛⠛⠛⠛⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⠖⠊⣩⠉⠂⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠸⡿⣆⠀⠀⠀⡀⠈⠢⠄⠀⠀⠐⠊⠀⠀⠊⢁⡠⠜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣷⣌⠲⣄⣠⡈⠲⠤⠤⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⡿⠃⠀⠀⢠⣴⣾⠿⣛⠛⠊⢉⣿⣿⠛⠳⠦⢬⣍⣙⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣭⡾⠃⠀⠀⢀⣠⣴⣾⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣀⣤⠶⠚⢿⣿⡿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠈⢷⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣄⣈⢹⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⣀⣀⣠⣤⣤⣬⠻⣾⣶⣿⣷⢀⣀⡀⠀⡀
⠀⠀⢠⠊⠀⢀⢠⠻⣍⣀⠄⠈⠉⠒⠛⢿⣿⣦⡀⠀⠀⠀⢿⣀⣠⣼⣿⡿⠿⢛⣻⣿⠏⠀⢈⣹⣛⣧⡤⠥⠚⠇⠀⣢⠀⣢⡄
⠀⠀⠸⣇⢸⣬⣿⣷⣌⣻⣶⣤⣐⣲⠶⠦⠽⠿⣷⣦⣤⣀⢀⣿⣿⣿⣿⣋⣭⣽⣿⣿⡶⣛⣫⣭⡭⠁⢀⣀⡔⡼⢠⢇⡖⠉
⠀⠀⠀⠙⢌⢮⣝⣷⣽⣿⣿⣷⣌⡋⠙⠲⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⢧⣾⠿⢛⣉⣁⣈⣃⣩⣴⢟⣵⡋⠉
⠀⠀⠀⠀⠀⠉⠚⢿⢿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣶⣿⣵⣿⣿⣿⣿⣟⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠉⠋⠙⢿⣿⣷⣶⣦⣭⣽⣿⣿⣿⣭⡿⠿⠾⠟⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢁⠐⢧⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣆⠀⠈⣿⣦⡎⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠉⠉⠳⠉⠙⣿⠀⠀⢸⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠥⡀⠀⠀⠘⠀⣴⡿⢀⣤⣾⣿⣄⣠⡇⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠹⣶⡷⠀⢀⡇⠀⢸⡅⠀⣿⣿⠋⠀⢀⣿⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⠘⢻⣇⠀⠀⢹⠆⠀⣿⠀⠀⣀⣿⡇⠀⠈⠀⢀⣾⡿⠛⠁⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⢘⡇⠀⠈⢿⣦⡀⠀⠀⠀⢠⡀⡀⣤⣼⠇⠀⢶⣿⣿⠋⠀⠀⣀⣾⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠻⠀⠀⠈⠻⡿⠾⣄⣀⣰⡟⠉⠁⠀⣀⣰⡾⠛⢧⡄⠀⣰⣿⣿⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠋⠁⡀⠀⠀⠆⠀⣿⡏⠉⠁⠀⠀⠀⠉⣹⠃⠀⠃⢀⠐⢻⣍⢉⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠴⢷⠀⠀⠰⢷⣿⠋⠀⠀⠀⢀⠤⠂⢙⣆⠔⠀⡴⠓⣿⠟⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⠂⠄⠴⣿⣿⠃⣠⣄⠀⠀⣀⠞⢻⣿⣤⣶⢿⡞⢿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣤⡆⠀⣌⠉⠉⢳⠞⠉⢰⡛⠀⣽⣇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠖⢿⣿⡦⠶⠿⠷⠾⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⣀⣴⣞⣡⡄
⠀⠀⠀⠀⠀⠀⡔⣿⣿⣮⢞⡵⣫⠝⠁
⠀⠀⠀⠀⢠⢖⡣⣞⡿⠁⢀⣜⣡
⠀⠀⠀⠀⣎⣿⣿⣿⣷⣠⠜⠻⡀⠀⠀⢀⡀⠀⠀⠀⠈⠁⢀⣀⡀
⠀⠀⠀⠀⠙⠿⣿⣿⠿⣇⠀⠀⠱⣄⠀⢉⡤⢤⣀⠀⢀⠞⠁⠀⢸⠂
⠀⠀⠀⠀⠙⠓⣼⣅⠀⠀⠑⢢⡄⠀⠙⠺⣆⠀⠈⠳⣼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⡎⢻⣷⣄⠀⢀⣭⡓⢤⡀⠈⢣⡀⠀⠈⢳⡭⠥⠤⠤⠤⠤⠔⠒⠚⠉⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠳⢿⡈⢮⣑⢮⡀⠈⠙⢿⣦⡀⠙⠲⢤⠤⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⡤⢔⡛⠿⠆⠀⠀⠀⠃⠀⠀⢹⡉⠁⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠋⣉⠴⠚⢇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⠻⡖⠚⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠓⠿⣶⡄⢀⣤⣶⠿⠛⣁⣸⠾⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⡭⠞⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⣄⠀⠀⣾⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠷⢖⠤⣈⣋⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⡼⠂⠀⠙⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠔⣊⡥⠄⠒⠂⠀⠀⢲⡀⢱⠀⠁⠀⠱⢬⡑⢤⡀⠀⠀⠀⠀⠀⣈⡦⡇⠀⠀⠈⠳⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⠳⢄⡠⢊⡵⠊⠁⠀⠀⠀⠀⠀⢰⡣⠷⠞⠀⠀⠀⠀⠈⢯⠓⢬⡒⠒⣒⡩⠥⠒⠊⠹⣤⣀⡀⠠⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠑⣒⣻⡀⠀⣀⠉⣉⣉⡹⠂⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠕⠊⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣀⣀⣀⣀⣀⣀⢤⠤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠧⡔⠈⢋⠫⠏⠉⢖⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⠋⢀⢿⣾⣿⡛⠺⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⠷⠞⠿⢳⣾⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⡴⢩⠃⠀⠀⣠⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡀⠈⣛⣦⣀⡀⣀⣨⠇⣴⡉⠀⠀⢉⣑⣾⣖⠒⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣏⡫⢟⣽⡩⠊⠀⠀⠉⠒⠭⣓⠿⣏⡩⣟⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⠷⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⢰⠁⠀⠀⠀⣠⡚⣟⠿⣶⠀⠀⠀⢬⠐⡲⣄⠊⡄
⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢠⠐⡆⠇⢸⠀⣆⠆⠀⠻⢯⣭⣿⡝⠀⠀⢄⠦⠅⣅⠛⢤⡁
⠀⠀⠀⠀⠀⢤⣟⣇⠄⠀⠀⠀⠀⠀⠀⠀⢣⠸⡸⠎⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠘⣯⠵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠠⠀⢀⢸⢉⢠⡤⡄⠀⠃⡀⡀⠀⠀⠀⠑⠦⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠢⠽⡈⢇⠀⢣⠁⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⡄⡤⠂⡀
⠀⠀⠀⠀⠀⠐⠬⣣⣼⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⢀⢁⣠⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡀⠀⠀⠀⠀⠰⣌⠀⠀⠀⠀⠀⠼⡀⠀⠀⠀⠀⣤⢹⠈⡷⠃
⠀⠀⠢⠀⠀⣰⠌⢁⠀⢴⠀⢀⡴⠥⠂⠀⠀⠀⡀⠀⠀⢐⡆⠀⡀⡺⣝⣄⠀⠤⠠⠀⠙⠄⢀⠀⠀⡀⡀⢁⠀⠀⠦⢬⣇⡌⢹⡋⠉
⠀⠀⠀⠀⠛⠀⠀⠈⢣⠃⣟⡼⠂⠀⣆⠄⠀⠠⠢⡈⠄⠀⠡⡠⠃⢐⣯⠁⢠⡄⠆⠀⠂⢠⠈⡆⠀⣅⢣⢘⡰⠀⠀⢒⢾⡀⣯⣤⠃
⠀⠀⠀⠀⠀⠀⡄⡴⡘⣱⣫⡠⠄⠤⠋⠀⠀⠀⢀⠙⣬⠀⠀⠉⣿⢻⣤⡔⢭⡤⠔⠀⠀⢀⢢⢣⢰⢫⢻⢸⠀⠀⠈⠺⢿⡟⠁⠈⠁
⠀⠀⠚⡀⠀⠀⣏⣼⠟⠉⠁⠈⠳⠤⠀⢀⡀⠀⠀⠀⠈⣀⣰⣀⣿⣿⣻⠄⠀⠀⠀⠀⠀⠀⣄⠙⡎⢾⢸⡇⢀⠄⠀⠀⠀⠁
⠀⢐⣿⡏⠀⠀⣸⣣⡞⣉⠈⠁⠀⠀⢠⡈⣇⢠⣄⡿⠀⠀⠙⠿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢠⠈⠄⣇⣨⠎⡀⠄
⠀⠈⠛⠃⠀⢸⡟⠁⠀⠀⠀⠀⠀⣿⡄⢧⣻⣾⣿⠟⠀⠀⢀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢆⣈⡟⢃⠰⠂
⠀⠀⠠⠄⠀⠸⠀⠀⠀⠰⠀⠀⠐⣾⣿⡜⣿⣿⠃⢀⡀⠀⠀⠑⢃⢤⠳⣸⠀⠊⠎⠀⠀⣰⠾⠁⠂⠁
⠀⠈⡁⡀⣀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣇⣿⣿⣿⣼⣃⠀⠽⣜⡈⠀⠆⣳⠈⠈⠃⠈⠀⠃⠀⢠⡄⣗⠖
⠀⠈⠃⠣⠈⠀⠀⢀⠆⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠁⠀⡤⠁⠴⠀⠁⠀⠀⠀⠀⠰⡴⢫⠦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠐⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣀⣛⣛⡛⠻⠿⢯⣛⠿⢦⠀⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢁⣀⠀⠀⠚⠋⣉⣩⣭⣟⠛⠶⠀⠈⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣿⣡⠴⠀⠀⠸⠟⣦⣀⣀⣠⣴⣶⡄⠀⠀⠀⠀⣠⡶⠶⣤⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡟⣡⠾⠋⠀⠀⠀⠀⢉⣩⢴⣿⡽⠂⠀⠀⠠⡾⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢸⠃⣠⠆⠀⠀⣀⣾⣯⣶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣴⠶⣠⣾⠃⠀⠀⠀⣉⡵⢞⣽⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⡶⠿⠦⠀⠙⢷⣄⠀⠀⣠⣄
⠀⠀⠀⣀⡴⠿⠀⠀⣠⢴⡟⠀⢸⠇⡿⠀⠀⠀⠀⠉⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⡟⠉⠻⢶⣤⡶⢶⣄⣀
⠀⠀⣾⠋⣰⠟⢡⣾⡟⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠙⠷⢾⣧⣽⡿⣦⠀⠀⣠⠶⡆
⠀⠸⣏⠀⠿⠀⡿⠘⠇⠀⠀⠰⣄⡀⠀⠀⠀⠲⣦⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣞⣡⠞
⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣤⣴⢿⣯⣩⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣙⠶⢤⣤⣤⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢧⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡖⢀⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠻⠶⠖⠂⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠿⣤⡌⠻⠓⢶⣦⣤⣀⡀⠀⠀⠀⢠⡏⢀⡾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠈⢻⡄⠀⠀⠓⠀⠈⣹⠟⠲⠦⣼⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⣶⣶⠶⠛⠁⠀⣀⣼⣄⣠⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⣿⠆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠛⠉⠈⠙⢷⣶⣶⣤⣴⣟⠉⠙⠛⠓⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠶⢦⣤⣄⣀⠀⠀⠙⠿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⠛⠂⠀⠀⣀⠀⠀⠈⠙⢦⠀⣤⣿⣧⡀⠀⣀⡠⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠴⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢶⣶⡉⣿⠟⢋⣡⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠗⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⢻⣽⡏⠀⡈⢻⡿⠳⠶⢦⣤⣤⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠛⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠛⣅⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣼⠂⠀⠀⠀⠀⢿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣗⠀⠈⠙⠷⣦⡀⠀⠀⢀⣴⣿⠋⠀⠚⠁⠀⠀⠀⠀⠀⠈⢿⡉⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⣷⠀⠈⠙⠆⣴⡟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢶⡶⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠿⡅⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⣀⡞⠁⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⣶⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠠⢞⣰⡇⣘⠶⣤⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠂⢀⡀⠠
⣠⡠⠀⢘⣛⠛⢰⣿⢠⢇⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠐⠀⠀⠄⢀⠀⡀⠢⠀⠀⠀⢀
⠈⢡⣾⡿⣍⣛⣂⣹⣆⠻⣿⡵⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢡⠀⡀⠀⠀⠀⠎⠄⠀⠀⠀⠀⠀⠙⢀⡆⢂⣓⣍⠘⢢⠄⢀⠀⠔
⠀⠀⠘⠋⢳⣭⠭⣠⣇⣷⡬⠁⠀⠀⠀⠀⢀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢂⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣱⣿⣟⣏⣳⣤⡶⠟
⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢄⢇⠀⠸⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠟⠟⠛⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⠀⢺⡇⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠐⡄⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠀⠄⠇⠀⠀⠀⠀⠀⡆⢧⠘⠆⠀⡜
⠀⠀⠀⠁⠘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡀⠀⠸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠀⠀⣿⠀⠀⠀⠀⠀⠀⢡⣸⣦⣦⡄⢠⡴
⠀⠀⠀⠀⠄⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠃⠘⠁⣠
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠃⡜⡯⣰⠁⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠈⡆
⠀⠀⠀⢀⠜⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣧⣃⠀⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⡮
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠠⠀⠀⡄⠐⠂⠀⠀⠀⠒⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠢⠀⠀⠀⠠⠂⢀⠀⠴
⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠈⣁⡄⢀⡴⠀⠠⠞⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠁⣠⠂⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠂⡼⠃⢠⠟⠁⣳⠈⣇⡀⠀⣤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢯⠉⠉⠂⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠊⠁⠀⠀⠈⣉⣊⣁⣚⣹⣷⡦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡤⣤⣤⣀⣀⣀⠀⣀⣤⣶⣾⣵⣰⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⢾⣯⡻⣿⢿⣤⡶⠈⠻⣿⣭⣙⠻⠿⣿⣿⣿⣿⣇⠈⠀⠁⠐⢢⠙⠒⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣍⠓⠄⠀⣠⡄⣼⣹⣿⣿⣶⣤⣙⠻⣿⣧⠀⠞⠓⠀⠘⠀⠒⢢⠳⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠀⠀⠀⠉⢜⣵⡿⡿⠿⢿⣿⣿⣿⣬⣛⢶⣄⣰⠋⠙⠢⢤⠤⠖⠛⠳⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣮⡿⣿⣷⣦⠈⢲⠰⢀⠍⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣶⣦⣭⣁⡀⠀⠀⠉⠛⢿⣿⣷⣞⣿⣿⠀⣦⣤⣀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠙⠻⣿⣿⣿⡆⠲⡄⢹⡇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠀⠀⠀⠻⠿⠟⠛⠀⠘⢿⣿⣿⣿⣿⡢⠘⢿⣿⣷⠀⣁⣬⣔⣊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣴⠚⠲⣏⠙⡆⠀⠀⡇⠀⣈⠃⡀⠘⠊⢳⡀⠘⣿⡟⢈⡡⠴⠒⠆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⣝⠢⣄⢈⣧⡘⢄⠐⠒⠊⣉⢹⠔⣉⡀⢈⡇⣼⡿⠡⠋⠠⣒⣚⡛⠋
⠀⠀⠀⠀⠀⠀⢀⠤⡘⢁⢤⡤⣙⢮⡣⠀⠉⠲⣅⣒⣠⠞⢀⣈⣁⣨⣼⣿⠟⠁⣀⠴⠋⣉⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠥⣙⡲⠬⠁⠂⣀⣴⣾⣿⣿⣿⣿⣿⡁⠀⠤⠤⠤⣄⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡴⠛⠉⠹⢻⣿⣿⣿⣿⡇⠀⠁⢀⡠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⢠⡁⠔⠁⡔⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⢻⠳⠾⠔⠅⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡌⠙⡣⠖⠌⠀⢑⣳
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠰⣧⢀⡤⠂⢠⠄
⠀⠀⠀⠀⠀⢀⠈⢦⣠⢀⠴⢛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠑⠀⢠⣴⡀⣀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⡄⢈⢳⠆⣐⣥⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠦⣀⣬⣩⡉⣠⢔⣨⠅
⠀⠀⠀⠀⠀⠀⠫⣀⡉⢅⡤⡰⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣀⣀⡈⣭⡌⢈⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠑⣭⡙⣆⢀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢈⢣⣠⡇⠈⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠘⢣⣷⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡌⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⢩⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠁⣼⠄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢉⠋⠀⠗⠉⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⠋⠉⠘⠀⠀⠀⠀⠀⣀⠀⠑⢄⠉⡺⠠⢈⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠚⢠⡾⠀⠈⡠⠀⠀⠀⠀⠀⡄⠈⢊⠀⣺⠗⠆⡀
⠀⠀⠀⠀⠀⠀⠁⢤⡀⢰⠆⠠⠮⡄⠀⠀⠀⠀⠄⠈⠀⢠⠝⡀⠀⣊
⠀⠀⠀⠀⠀⠀⢈⡀⠀⣸⠂⠙⠛⠠⠂⠀⠀⢀⠁⠢⢴⡇⠤⠤⢂⠁
⠀⠀⠀⠀⠀⠄⡀⠁⠌⠸⡖⠊⠤⡱⠀⠀⠀⢬⢢⡀⣾⠆⠥⠴⢠
⠀⠀⠀⠀⠀⠀⠈⠐⠨⠘⠿⠆⠀⠀⠀⠈⠣⠀⠪⢎⡇⣀⡤⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⢰⣯⡁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⢠⠀⠀⠁⠀⠀⠀⠀⠎⠄⡂⠘⡠⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠘⠺⡀⠀⠀⠐⡢⠀⠀⠀⠀⠷⡀⡅⠃⠈⠀⠀⠤⠀⠀⠀⢠⣒⠂⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡴⠀⡠⠂⢀⠀⠀⠀⠀⠌⠵⠄⡴
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠠⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡴⣀⠀⠀⠀⠀⠀⠐⠳⠀⠀⠁
⠀⠀⠀⠀⢠⠈⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠙⠋⠁⠀⠀⠀⠀⠀⠐⠂⠀⠃⡀⠀⢀⡀
⠀⠀⠀⠐⡀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡘⣰⠃⠀⠀⠆
⠀⠀⠀⠀⠠⡠⣄⡇⠀⠁⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢂⠠⠃⡇
⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠐⠐⠀⠢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠒⡂⠑⢫⠈⡤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠂⠀⡀⠀⠀⠀⠀⢀⠀⡅⢀⢁⡏⠈⣧⠀⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠉⠈⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠟⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡯⠀⠀⣀⣤⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣿⢿⣿⣋⣠⣶⣿⣿⣿⣿⢿⣏⠻⣿⡻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣶⣿⣿⣿⠁⣾⢿⣿⣯⣙⣶⣿⣓⣠⡴⣳⡁⠈⢹⡇
⠀⠀⠀⠀⠀⠀⢸⠟⡿⡿⠛⣻⣿⣥⣶⣶⣟⣷⣾⣿⣿⣿⡿⣿⣽⣿⣿⣿⣷⣒⣀⠀⡁
⠀⠀⠀⠀⠀⠀⠁⢀⣤⣾⣿⡿⣿⣿⣿⣟⣿⣞⣿⣟⣿⢿⣿⣾⣚⣿⢿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣽⣿⣿⡟⢷⣿⣿⡽⣿⡛⠟⣿⢿⣿⣿⢸⠏⠿⢿⣿
⠀⠀⠀⠀⠀⣰⣿⣿⢏⢟⢱⣿⣿⣿⣟⢾⣿⣿⣿⠻⣏⠀⠈⢸⣿⣿⡗⠄⠀⠈⠁
⠀⠀⠀⠀⠀⡿⠙⠈⠂⠀⣾⣿⣿⡌⠚⠁⣿⣟⠦⠄⣿⡂⠀⠊⠙⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡝⠌⠀⠀⢻⣿⠦⠀⣸⡧⣾⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⣩⠴⣿⢿⡷⠉⠛⢿⡙⢿⣟⠉⠉⠲⢤⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣾⣿⣛⣟⣑⡉⠉⢺⣇⣤⣤⣤⡃⣘⣉⢡⣄⡒⢢⣝⣓⣾⣷⣦⣤⣶⣦⣤⣄
⠀⠀⠀⠀⠤⠤⢤⣀⣈⡠⠤⠀⠀⠘⠛⠛⠛⠲⢛⣿⢺⣗⠤⠄⢦⡄⠐⠛⠏⠬⠽⠾⡟⠛⣉⣉⣉⣁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠾⠛⠉⠉⠉⠀⠀⠀⠀⣾⡇⢰⡆⣿⡇⣸⣠⠎⠀⠒⣒⣲⣿⣭⣤⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠿⠀⣺⢼⠙⢑⠿⣵⣹⡔⠀⠀⢉⣻⣿⣿⡿⠷⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠚⢿⡿⠿⠃⢠⣇⢾⡗⢯⠓⠬⢿⣿⣷⣶⣶⣿⣯⣥⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡟⠀⢠⣾⣿
⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣵⣿⣿⣿
⠀⠀⠙⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿
⣾⣿⣄⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⣿⣿
⠛⠛⠋⠉⠀⠄⠀⠀⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣛⣲⣿⣿⣷
⠀⠉⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠙⠻⠛
⣶⣴⣶⣴⣦⣶⣤⣤⣼⣿⣿⡿⠿⠟⠻⠷⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠉⣋⠋⠛⠿⠛⣛⣉⣉⣉⡉⠁⠀⠀⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⢀⣠⣴⣿⣿⣴⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠆⢀⣠⣦⣾⣿⣿⣿⣿⣿⡇⣻⣿⣿⠿⠛⠛⠛⠛⠿⠿⠿⠿
⣛⣿⣿⣿⣿⣿⣿⣿⣿⡵⠀⣠⠐⠃⣠⣶⣾⣷⣿⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀
⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠃⢀⢤⣤⣤⣀
⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣹⣿⣿⣿⣿⣿⣿⣟⡛⠋⠙⠓⠀⠀⠛⠉⠉⠉⠁
⠺⠛⠟⠻⣿⢿⣿⠿⠿⣭⣏⢉⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⠟⠉⠹⣿⠟⣿⣿⣷⣦⡄⠁⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠹⢾⣇⣿⣤⣼⣿⣿⣉⠋⠉⠉⠀⠀⣈⣿⠁⠀⠙⠂⠉⠙⠒⠀⠀⠀⠀⢀⡐⢀⣇⠀⡀⠐⠚⠋⠁⠀⠀⠀⢸⠀⠈⠁⠀⠙⠷⣄⡀⣀⡀⠀⠀⣀⣨
⣤⣤⣄⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣺⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠹⣿⣎⡠⠤⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⣀⣀⣀⣈⣸⣯⣄⣀⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⡟⠀⠀⠀⠀⠀⠀⠒⠒⢿⡄⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣤⣬⣥⣽⣿⣿⣿⣽⣿⣿⣿⣿⣥⣤⣤⣤⣽⣿⣿⣿⣯⣀⠀⠀⠴⠦⠤⠤⠀⠤⠤⣤⣴⣶⣾⡧⠤⢤⣤⠤⠤⠤⠤⠴⠾⠿⠀⠀⠀⠀⠀⠀⠟⠛⣷⠾⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣛⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣾⣿
⢿⣿⣿⠿⢿⣿⡿⠿⠁⠐⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠚⣃⣐⣒⠀⣀⣤⣤⣶⠶⠶⠖⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡠⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢘⢆⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⣀⡄⠀⠀⠀⠀⢘⡆⠀⠀⠀⢠⠙⠀⠀⠀⡀⠀⠀⠀⠐⡝⠀⠀⠈⠠⢠⠉⠀⣀⣴⠀⠀⠀⠀⠀⣒⡀⠀⠀⠀⢠⠋⠀⠀⠀⢄⠀⠀⠀⠐⡙⠀⠀⠀⠀⣬
⠀⠉⠉⠑⣀⠀⠀⠀⠈⣑⡏⠠⡀⠓⡀⠀⠀⢀⠙⣀⠀⠀⠐⢒⣸⡋⠤⡈⢓⠀⠀⠁⠈⠁⡙⢀⡀⠈⢉⣸⡋⢀⡈⢒⠀⠀⠀⠀⠀⡁⠆⠀⠐⢂⣺⠉⢄⠘⢂
⡶⣔⡭⠊⠉⣳⠀⠀⠀⠹⠀⠀⠇⠀⠙⡦⣞⡕⠈⠉⡲⠀⠀⠀⠛⠀⠐⠏⠈⠹⠦⣞⠕⠈⠉⡶⠀⠀⠀⠟⠀⠰⠇⠈⢱⠴⣊⠕⠉⠉⡶⠀⠀⠈⠗⠀⠸⡇⠈
⠀⣣⠄⠀⢤⡷⠶⠂⠙⢀⠀⠴⠤⠀⠀⠘⡡⠈⠀⢵⡷⠖⠂⠙⣀⠀⠴⠤⠐⠀⢘⡤⠈⠀⣼⠶⠖⠀⠛⣀⠀⠶⠤⠀⠀⢘⡤⠁⠀⣼⠴⠖⠈⠓⣀⠀⠦⠄
⠀⠀⢴⣀⣼⡆⠀⠦⠀⣼⠄⠀⢠⣀⣀⠀⠀⣖⣀⣾⡄⠐⠄⠀⡽⠄⠀⢠⣀⡀⠀⠀⣞⣀⣶⡄⠐⠄⢀⡽⠀⠀⢠⣀⡀⠀⠀⣆⣀⣾⡀⠐⠄⢀⡧⠀⠀⢤⣀
⠀⠀⠛⠍⠀⠠⡤⠀⣬⣁⡄⠀⢄⣫⠀⠀⠀⢫⠙⠀⠡⡤⢀⣬⣠⡄⠀⢀⣣⠀⠀⠀⢫⠉⠀⢡⠄⢀⣬⣠⠄⠠⣈⣣⠀⠀⠀⠫⠃⠀⢠⠄⢀⣌⣠⠄⠠⣘⣇
⠠⡀⠓⠀⠀⠀⠀⠑⢉⠸⠁⣀⠄⢹⡃⠀⡈⠓⠀⠀⠀⠀⠀⢉⠺⠁⣠⠀⣙⠃⢠⡈⠓⠀⠀⠀⠈⠐⣍⠮⢁⣠⠈⣹⠁⢠⡈⠃⠀⠀⠀⠈⠀⡁⠎⢀⣠⠈⣹

⠀⠀⠀⠀⢀⣀⣀⣀⣠⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⡦
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⣖⢒⡇
⠀⠀⠀⠀⢸⠀⣴⡜⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠿⠯⢼
⠀⠀⠀⠀⠘⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂


⠀⠀⠀⠀⠀⣀⣀⣀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢠
⠀⠀⠀⠀⢰⠁⠀⠨⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠸⠘⠄
⠀⠀⠀⠀⢇⠀⠀⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⠓⡆
⠀⠀⠀⠀⠀⠁⠒⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⣰⣁⣰⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠄
⠀⠀⠀⠀⢸⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠱⠋⠉⠉⠉⠉⠙⡗⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠘⡀⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⣇⡇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻





⠀⠀⠀⠀⡀
⣷⣶⣶⣶⣧⣶⣦⣤⣤⣾⣤⣀⢀⣦⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣤⣾⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⠒⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠁⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠻⠉⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠫⠃⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⢻⡍⠉⠀⣈⠀⠀⢀⠀⠀⢀⠁⠤⠀⠐⠠⠀⠀⠠⠀⠀⠀⠀⠈⠀⠈⣁⢤⣴⣿⣿⣿⣿⣿⣿⣿⢿
⠛⠁⠀⠀⠀⡤⠆⠀⠩⡗⢂⣀⠀⠀⠐⡀⠀⣀⠃⢀⡀⠀⠀⡀⠀⠀⠀⠀⠙⠀⠛⠉⣻⣿⣿⣿⣿⣿⣿
⢈⡃⠀⠀⠈⡀⠒⠋⠀⠐⠞⠉⣀⡠⠀⠁⠀⠀⢠⡄⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄⢠⣾⣶⡄⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠾⣟⡛⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠡⠀⠠⢴⡾⢶⣿⣿⣿⠛⠡⠤⢤⣙⢿⣿⣿⣿⡆⣿⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠠⠦⡌⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠒⠉⢀⡚⠒⠛⠳⢝⢿⣿⠰⠻⣡⡀⣘⡇
⠀⠀⠀⠀⠀⣰⠀⠘⣇⠹⣿⢿⢷⣶⣄⡀⢀⠀⠀⣰⡇⠰⠂⠈⠙⢦⣄⣀⣐⣄⣄⠀⢣⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢷⣤⣌⣳⣶⣤⠦⣉⠻⣿⣮⡟⠛⠟⠀⠀⠀⠀⢶⣄⣬⠉⠉⣿⣿⡄⠞⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠢⠌⠳⣦⣴⠾⢃⡀⠀⠀⠀⠀⠛⠯⠀⡀⢀⣿⣿⣧⠈⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣀⠀⠀⠀⠀⠁⠀⢤⡶⠟⠛⠶⠀⠀⠀⠤⠶⠾⠋⡼⢻⣿⣿⠀⣿⣿⡀⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡞⠁⣼⢿⡏⢠⡘⠿⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⢳⡄⠀⠀⠀⠀⢠⠞⣷⣦⡀⠀⠀⠀⠀⠀⢡⡌⢻⣁⣾⠧⣄⣙⠳⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠿⣧⠀⠀⠀⠀⠀⢤⠿⠛⠁⠀⠀⠀⠀⠀⢲⡄⢸⣿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠙⠂⠉⠀⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢫⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠠⣴⠶⠶⠦⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⠛⠛⠁⠀⠀⠀⣴⣊⠉⠁⠀⠀⠀⣀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣽⠀⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠾⣅⢘⠀⠀⠀⠀⠀⢀⡀⣀⠜⠚⢻⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠈⢿⡅⣀⣙⠀⠏⢉⡽⢁⠄⣠⠞⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡆⢀⣒⠚⠇⢹⣿⡗⠀⠉⢚⣿⠋⣠⠔⣡⠾⡄⠀⢀⡴⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⡟⠀⠀⠈⠙⣿⣾⣿⣿⣧⠰⢻⣷⡞⣡⠞⢁⣴⡷⠖⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⢠⡟⢰⡟⠀⠀⠀⠀⠀⢈⣿⣿⣋⠁⢀⠈⠹⣿⢧⠾⠋⣡⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⡟⠠⣾⣃⠀⠀⠀⠀⠀⠘⡿⠿⠟⠃⠘⠳⠟⠛⠃⢰⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠏⠀⠀⣈⣛⡛⣦⠀⠀⠀⠐⣿⣿⣽⣧⣿⣴⣷⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠈⣍⡉⠙⢧⠀⠀⠀⢻⣿⣄⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⣄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠟⠛⠿⢃⣠⠟
⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⣰⡟⠀⠀⠚⠋⠁
⠀⠀⢀⣀⣿⠃⠀⠀⣀⣤⡾⠋
⠀⠀⠛⣩⣿⣄⠀⠀⠈⣿
⠀⠀⠈⢧⠼⢿⣷⣤⣀⠁⣼⢿
⠀⠀⠀⠀⢶⣼⡟⢳⡇⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠃
⣤⣀⠐⠛⠽⠿⢦⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇
⠛⠒⠀⠀⠀⠀⠀⠙⠷⠦⣈⣹⡯⣤⣶⣞⠓⠄⠀⠀⠄⢤⣄⠀⠀⠒⠛⠶⣄⠀⠀⠀⣴⣾⣿⣿⡟
⠀⢉⠉⡁⠀⠉⠁⠀⣉⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⣀⠀⠀⣨⠉⠂⠀⠀⠀⠌⠙⠛⣝⡻⠿⢿⣿⠿⢿⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⡠⠀⠒⠂⠀⠶⠶⠚⢷⣶⡭⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠘⠂⠀⠶⠀⠀⠀⠄⠀⠢⠀⢉⠒⠀⡦⢤⡶⢤⡐⠛⠛⠳⢦⡴⠤
⠀⠀⠀⠤⢤⣬⣁⣀⣠⣄⣈⠁⠈⠩⠷⠶⠶⣶⠤⠤⠐⠀⠀⠀⠀⢠⣴⣤⣀⡀⠀⠢⠤⠚⠋⢁⣀⣀⠀⠀⠀⠠⠶⠀⠀⠐⠄⠀⠀⠀⠐⠖⠀⠤
⡴⠦⢄⣀⡤⠌⠙⠛⠻⠦⠉⠓⠦⠄⠠⢦⣄⡁⠀⠶⢾⣿⣒⣒⡛⠋⠉⠁⠀⢀⣀⠀⠁⠒⠲⠟⠛⠛⠓⣶⣤⡤⠀⠀⠀⠀⠀⠀⠤⠶⠛⠓⠦⠠⣄
⣠⣀⣤⣴⣿⣷⣤⣤⣄⡛⠃⢀⣠⣤⣤⡀⠉⠛⠒⠀⠀⠈⠉⠉⠉⠉⠙⠿⠿⠿⠷⠶⠶⢦⣤⡄⠤⠄⠀⠀⠀⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄
⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠟⠛⠿⠿⣟⠛⢛⣛⠳⠶⠄⠀⠀⠀⠀⠀⠀⣀⣠⣬⣁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⣀⣠⡤⠶⠈⠀⢀⡀
⠀⣀⣤⣤⣤⣄⣀⣉⣁⣀⣀⠀⠀⢀⣀⠀⠈⠉⠀⣀⣀⣀⠠⠠⠖⠒⠀⠈⢉⣴⠤⢶⣦⡄⠀⠀⠀⣀⣀⣀⣠⣴⣶⠿⣟⣉⣭⣡⣤⠀⠀⠀⠉⠀⣠
⠀⣉⣽⣿⣿⡿⠛⠛⠛⠛⠛⠷⣄⣀⣀⠀⠀⠀⠉⠁⠈⠛⠗⠂⠀⠒⠒⠆⠀⠀⠀⠈⠀⠀⢀⣉⣉⣀⣀⡀⠀⠀⣀⣠⣼⣿⠁⠀⢀⣤⢤⣤⠴⠞⠋
⠀⠛⠿⠿⠿⠿⠿⠶⠶⣤⣤⣤⣈⣙⠛⠶⠤⠄⠉⠙⠛⠀⠀⠤⠤⠤⠖⠂⠀⠹⣦⣶⠶⠿⠯⠭⠀⠀⠠⠤⠭⠭⠍⠉⠁⢀⠀⠈⠀⠀⢀⣀⣀
⠀⣐⣒⠀⠦⣤⣄⣀⣀⣠⣼⠿⠛⠛⠛⠒⠒⠒⠒⠚⠛⣛⣳⣶⣤⣤⣴⣶⣶⡶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⣤⣤⣶⣶⣶⢾
⣿⣿⣿⠿⠶⣄⡀⠉⠉⣉⣁⡀⢀⣠⣤⣄⣉⠉⠀⠀⠈⠉⠉⠉⢉⣥⡶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠄⠀⠀⢘⣛⠛⠋⢉⣉⣥⣌
⣤⣴⣶⣶⣶⣿⣿⡛⠛⠛⠛⠿⠛⠉⠉⠉⠉⢉⠛⠋⠉⠁⣀⣠⠀⠀⠴⢶⠶⠖⠛⠀⠀⢀⣀⡠⠼⠁⠀⠀⠀⠀⣠⠴⠶⠀⠀⠈⠙⠻⠿⠿⠿⠃⠈
⣿⣿⡿⠿⠿⠿⠟⠛⠻⠶⠶⠶⠒⠂⣠⠴⠚⠻⠿⠛⠒⠉⠉⠀⠈⠙⠂⠠⠖⠚⠋⠉⢋⣩⣥⢤⡤⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⢀⡄⠀⣠⣄⣠⣴⣾⣿⣿⣿⠗⢀⣀⣀⡀⠀⠀⣀⣀⡴⠋⠀⠠⠴⠂⠴⣾⣶⣦⠀⠀⠀⣹⣿⣿⣶⣦⣄
⠀⠀⢠⣤⣄⣀⣠⠔⠂⠀⣀⡀⠀⠉⠁⠀⠀⣈⡽⠟⠛⠛⠛⢉⣠⡾⠋⠀⢀⣠⠴⠛⠉⢙⣿⠟⠀⠀⠦⣄⠀⠈⠛⠋⠀⠀⠙⠛⠋⠉⠉⢉⣡⣄⣀
⠀⠰⠛⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠁⠠⠖⠂⠀⠈⠋⠉⠀⠀⠈⠉⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠂⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⣤⣤⣤⣤⡶⠶⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣠⠞⠋⠉⠁⣐⣒⡒⠾⠿⣟⡶⢦⠠⣤⡇
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣁⡄⠀⠚⢉⣩⣭⠭⠛⠒⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⡞⠁⠀⠀⣴⡋⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠘⣇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢺⢗⣩⠄⠀⠁⠙⠲⢒⣯⣟⠇⠀⠀⣠⠞⠉⠙⠃⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⡞⢁⠄⠀⢀⣴⣾⣽⣫⠅⠀⠀⠀⠁⠀⠀⢶⠀⢻⡄
⠀⠀⠀⠀⣧⠀⠀⠀⣠⡶⢦⢶⠃⠀⠀⢈⡵⢫⡟⠁⠀⠀⠀⠀⠀⠳⠶⠾⠓⠀⠛⢦⡀⠀⣤⣄
⠀⠀⣠⠖⣻⢀⣠⢶⠏⠀⡏⠻⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠈⠛⢶⣛⣷⢶⣄⡀⠀⠀⢀⡀
⠀⢸⠇⢾⠁⡞⣿⠘⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠃⠀⠀⠀⠀⠉⠙⠻⣯⣷⣀⠔⡩⠃
⠀⠘⢧⡀⠈⠁⠀⠀⠀⠈⠛⠶⣤⣤⣬⣽⣟⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣤⡀
⠀⠀⠀⢻⠀⠀⠀⠀⣝⠶⠤⡤⠶⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣤⣤⣤⠤⠤⠤⠤⠤⢀⣠⣀⣀⡴⢀⡟
⠀⠀⠀⠘⣇⠀⠀⠀⠈⠙⠛⠁⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠶⡎⠋⠛⣶⠶⢤⣄⣀⠀⢼⢁⡞
⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣤⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢹⣦⠀⠀⢀⡴⠋⠉⠙⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⠙⠻⠛⠙⠳⣤⣤⣄⣰⡞⠒⠶⠦⢤⣤⣤⡶⠏⠀⠀⠀⠘⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠰⠶⣤⣄⣀⠀⠙⠿⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡀⠀⠀⠉⠛⠶⣄⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡴⠛⠉⠀⠀⠐⢦⡀⠀⠈⠁⢐⣛⢿⣤⡴⠆⡶⠀⠀⠀⠀⣼⠄⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⡄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⢿⣷⠇⠀⠶⡶⢤⣤⣤⣠⡷⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡟⠃⠀⠀⠀⠘⠃⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢠⣖⣒⡛⠡⣤⣀⠀⠀⠀⠀⢀⣠⠆⢀⠞⠀⠀⠀⠈⢿⣯⣤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⣤⣤⠙⠳⣄⢀⣴⠿⣧⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⢦⣤⣤⠘⢧⡀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⢿⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢰⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠸⠶⠃⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠿⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢸⡠⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡄⠀⠀⠲⠶⠦⠤⠄⠀⢸⡇⠀⢿⠻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⢀⣴⠞⡀⠀⢸⡇⣠⡌⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠞⠱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣴⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⡀⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⢿⣿⠁⣾⡟⠀⠀⠀⠘⠠⠀⢄⢸⠙⠀⡀⠀⠀⠙⠤⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⣿⣿⣷⡆⠉⠁⠙⠃⠀⠀⠠⡄⠀⢀⠉⡄⠘⠥⠛⠃⡀⡀⠂⠈⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠁⢄⠁⠐⠈⠀⠀⠰⢇⠀⠀⠑⠁⠄⠀⠀⠀⠀⠀⠠⠌⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠁⠀⠔⠀⠂⢀⠀⠄⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡠⢊⣓⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠹⣀⡖⠠⠐⢀⠀⠀⠀⠠⠀⠀⠀⠂⠠⢤⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⢀⡀⠀⠀⠐⠀⠈⠈⠀⠀⠀⠀⠐⠄⡄⠀⢫⠐⡍⠀⠂⠊⢡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠌⠀⠈⠈⢀⡃⠄⢤⣔⠀⠀⠀⠠⡄⠀⠀⠀⠀⡠⢄⠌⢀⣈⠐
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣦⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠠⠚⠀⢈⠘⠊⠀⠨⠀⠄⠀⠁⠩⠀⠄⢛⠃⢀⠄⠁⡀⢂⠀⠀⠘⠁⢃⠚⢀
⠀⠀⠀⠀⠀⠰⡇⠛⢩⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠠⠀⡀⠀⠬⠒⠀⠆⠈⠆⠀⠐⠀⠌⠐⠊⠑⠄⠹⠈⣆⣀⣀⡂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠈⡀⢁⠀⠐⡀⠀⠈⢄⠀⢀⡠⠆⠀⠀⠀⠠⠂⠰⠀⢀⣠⡴⠟⢛⣉⣩⣄⣭⣬⣹⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡄⣄⡅⠚⠴⠀⠃⠠⠓⠂⠀⠀⠈⠈⠑⠠⠊⠛⢳⠶⣦⡋⠩⠟⢁⣀⣺⣿⣿⣿⣿⡙⢿⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠻⠙⠛⣧⣶⠀⠀⠄⠠⠄⠀⠐⠂⢠⠀⠀⠀⠀⠀⡀⢁⣤⣿⠷⣄⠲⢶⣭⣉⡙⠛⠛⠛⠛⠊⠉⠀⠀⠀⠁
⠀⠀⠀⠂⠈⢀⡀⠀⠀⢸⡗⠆⠀⠀⠀⣼⡏⠀⡀⠀⠂⠂⠀⠀⠐⠣⢤⠢⠒⠂⠄⠈⠉⠁⠀⠄⠀⠈⣞⠡⢸⡽⠟⠋⠙⠈⠢⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠻⣦⣀⡀⢠⠌⡇⠀⢀⠀⠁⠁⠀⠀⠀⠊⢦⠶⢤⡀⠀⠃⠀⠀⠀⠀⠠⠁⡈⠤⣨⠤⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠒⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⢤⡤⢲⠋⠉⠁⠀⠸⠁⢙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠀⠀⠀⠀⢠⣍⠀⠨⠀⢀⠀⠀⠐⠇⠘⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢠⠈⣏⠙⠛⠛⠚⠲⢆⠘⠁⠀⠀⢀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢻⡟⠛⠛⠛⣿⠌⡀⣿⠀⣀⣀⣠⡤⠎⠸⠀⠀⠊⠀⠀⣤⢴⠶⠶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⠂⠂⠋⠛⠛⠛⠋⡹⠏⠂⡀⣿⠀⣯⣟⣀⡀⠀⠀⡆⣇⠀⠀⠀⡇⡸⣇⣀⣿⡭⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢢⡛⠛⠒⠳⠤⣀⣉⠉⣳⡆⢸⡗⢄⡀⣳⣧⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠑⢦⡀⠀⢀⣠⠧⠶⠶⠾⠧⣀⠀⠀⠀⠀⠀⢩⠃⢠⠘⣷⠀⠀⠈⠉⠙⠛⠒⠒⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠹⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠆⠤⣯⣇⣀⣀⣿⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡙⠓⠶⢦⣀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⣠⠴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠛⠛⠛⢹⡇⠀⡟⠣⠄⡠⠤⠐⠖⠋⠉⠉⠉⠉⣛⠀⠀⠛⡙⠓⠒⠲⠒⠒⠋⢸⠀⢠⠿⣠⡾⢛⣻⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢄⣀⠀⢀⠈⠉⠙⠓⢤⠈⠀⠀⠀⣠⡔⠂⠛⠋⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣾⡀⡞⠀⠹⠖⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠹⡄⠀⠀⢀⡤⠃⠀⠀⠰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⣼⡧⢝⢧⣀⠀⡰⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣀⣡⡌⠢⣄⢘⣨⠀⠀⠀⡀⣽⠓⠂⠤⠤⠤⠤⠤⠤⠀⠂⠣⠤⢦⡴⠒⠛⠛⠺⠶⣾⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠣⠁⠈⣻⠻⣤⡀⠀⡆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⣆⠂⠹⡄⠀⠉⢳⡇⢀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠹⡔⣀⢻⡀⢂⣀⡅⠀⠀⡜⣧⠀⠀⠀⠀⢸⠖⠒⠲⠖⠒⣸⠃⠀⠀⠀⢀⡴⠋⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡙⠛⠛⠛⣿⢡⠛⠉⠀⡇⠀⡀⠀⠈⢷⡀⠀⠀⢸⠀⠀⠀⢀⠞⠁⠀⢠⠄⣠⠞⡡⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢹⡷⣤⣀⣀⡷⠤⠦⠶⠤⡈⢧⠀⠀⣹⠀⢀⡴⠋⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⢻⣿⣆⠀⠀⢀⠠⠲⠟⠀⠸⡇⢀⡏⣴⠏⠀⠀⢀⣠⡶⠋⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠝⣿⣄⠀⠠⣄⣀⣀⡤⠤⠚⣾⣞⣡⠤⠖⠚⠙⠋⠁⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠌⢦⣄⣠⣀⢶⣿⡿⠷⠖⠒⠒⠒⠚⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠁⢀⠂⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠄⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠤⠤⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⠈⡁⠞⢻⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣨⣄⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠂⡂⢄⣐⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠓⠐⡀⠁⠄⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⡈⢃⡈⠤⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠤⠐⢂⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉