⠠⠀⣀⠂⢀⡀⢄⠀⢰⠂⠠⢀⠒⠒⠂⡴⢀⠒⣐⢠⠒⡐⣰⢰⡆⢖⢰⢲⡴⡶⢶⢖⡒⠖⠲⠖⡒⢔⠖⣴⢲⠒⡂⠦⠢⠔⠤⠔⠲⡠⠐⠤⠒⠆⠆⠲⢀⠠⠂⢢⡐⢀⠒⡰⢀
⢀⠃⢀⠀⠀⠀⡀⢠⠐⠂⠀⠄⠂⢀⠨⡐⡠⡄⠠⡀⠠⡄⠤⡀⠤⢁⣤⢠⡁⠦⢤⠤⣴⣬⠠⢋⣤⡀⠴⠂⠀⣠⠄⡀⢤⣌⡤⣀⠉⠄⡀⡄⢄⡄⣄⠡⣄⠀⢠⡀⠠⡀⠀⠐⠆
⢀⡌⠀⠣⡍⠵⠩⠇⠏⠯⠏⠻⠭⠯⠿⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠈⠈⢗
⢈⢂⡐⡣⡍⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠃⠈⠁⠁⠁⠈⠁⠉⠈⠈⠁⠉⠈⠁⠉⠘⠘⠁⠁⠘⠃⠁⠁⠀⠁⠈⢀⠀⡁⠀⠀⠈⢿⣿⠀⠐⡂
⢠⠆⢠⡇⣆⠇⠀⠀⠀⠀⠄⠠⢀⠀⠄⡀⠠⠀⠄⠠⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⢀⠀⠠⠀⢀⠂⠐⠠⢈⠐⡈⡐⢁⠊⠄⣁⠊⠄⢃⡘⠠⡁⢢⠁⠀⢈⢿⣟⠂⡐⣡
⢈⡝⢁⡇⡎⡂⠀⠀⠀⠀⠀⠀⠀⠈⠐⣀⠁⡂⢌⡐⠠⠐⠀⠈⠀⠌⢀⠐⠠⢀⠠⠁⢂⠀⠄⢀⠂⠈⢀⠠⠈⠐⢀⠂⡐⠠⢈⠐⡈⠄⠌⡘⢠⠠⠑⢠⠂⠥⠀⠈⢾⡿⠀⠄⠰
⠠⡂⠔⡆⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⢄⢀⠐⡀⢀⡀⠀⠂⢀⠂⠄⡈⠄⠂⡀⠡⠀⡀⠐⠈⠀⠠⢀⠁⢂⠐⠠⢈⠐⡈⠄⢂⡉⠄⠌⣂⠀⢸⢹⣿⠆⠚⡉
⠰⠁⢨⣖⠣⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⡿⡟⠘⠦⠙⠾⣵⣦⠀⠀⠂⠐⠠⠐⠠⠐⠠⢁⠀⠂⠌⠀⠁⠀⡀⠂⢈⠐⡀⢂⠐⡈⠄⡐⠈⠔⠠⠀⢸⢸⣿⠄⠡⢁
⠀⡁⢂⡧⣛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢁⠣⡁⡘⢄⠂⠌⡐⠀⠌⡐⢀⠀⠄⠂⠀⡀⠄⠂⠐⠠⢀⠉⠄⡁⠂⢸⢼⣿⡯⡘⢠
⠰⠉⢈⢱⣋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⠃⠙⠀⠀⠀⠀⠀⠀⠀⠱⣡⠒⣤⠉⡔⠠⡉⡔⡀⠢⢈⡐⡀⠁⢀⠀⠠⠁⠐⠀⡈⠄⠐⡀⢸⣹⣿⡤⡖⢼
⢘⠒⠈⢧⣋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡞⢿⣷⣴⣾⡆⠀⠀⠀⠀⠀⠀⠐⠫⠖⡩⢒⡱⡘⢴⡡⢓⡌⣲⠱⡈⠄⢂⠐⠠⢈⠀⠄⠐⡀⠀⢸⣸⣿⡇⠐⡐
⠠⠂⢘⣰⢣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠤⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡙⢦⡙⢎⡖⡡⠓⡌⠄⢃⠈⡐⠠⢈⠐⠠⠐⠀⢸⢸⣿⡇⠁⣭
⠈⡁⠠⢝⡆⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣶⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡝⠲⣌⡱⢡⡘⠌⣀⠂⠄⡁⢂⠈⠄⠡⠀⢸⢸⣿⡅⠀⠧
⠸⡀⠔⣻⠸⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠓⡤⢃⠧⡘⠰⡀⠌⡐⢀⠂⠌⠠⢁⠀⢸⢸⣿⡟⠘⣛
⢐⡃⠸⢻⠜⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣦⣦⠄⡀⢀⣉⣠⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢮⠑⣎⠱⢣⠜⡰⠐⠂⠌⠠⢁⠂⠀⢰⢺⣿⡇⢁⠮
⢨⣔⠡⢺⢞⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⢾⣿⣿⣿⣿⣿⣿⣆⢹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡙⢦⡙⠤⡉⠜⠠⡁⠂⠌⠀⢸⢸⣿⡏⠉⣿
⢈⠆⣐⣻⢺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⢙⢻⡿⠇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⠱⣀⢃⠒⠠⢁⠊⠀⢸⢼⣿⡏⠿⣷
⢸⠉⣡⢺⣟⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠃⡁⠂⠌⠀⢸⣼⣿⣧⠡⣖
⢈⡘⡘⢾⣾⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⠀⢸⣿⣿⣿⠐⢬
⢨⡕⢈⢼⡽⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⡇⡱⢋
⠸⣮⠺⣼⣽⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠳⢛
⢘⠆⠄⣻⣽⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡏⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡗⡉⡷
⢘⡂⠘⣸⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⣭⡁⢻⣿⣿⣿⣯⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣻⡌⢨⣽
⠸⡃⠖⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⠿⠇⠀⠉⠋⠛⠫⠉⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⣿⠆⠨⠝
⢘⡏⡐⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡉⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⢸⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠴⠈⢫
⢐⠧⠰⢿⣿⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣤⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⣿⣿⠙⠛⠓⠦⡄⠀⠀⠀⠸⢸⣿⡌⢁⠷
⢸⠚⡬⣿⣿⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡖⣧⠘⡧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⢘⢸⣽⠭⢊⣿
⢠⠊⡤⣿⣻⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⣾⢐⠐⣍
⠈⠄⠸⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠥⠓⡤⣀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣻⢼⠰⢌
⠘⡡⡈⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⡠⠔⣈⠢⠑⡌⠡⠐⠠⠈⠂⠑⢄⠀⠀⠀⠀⠀⠀⢀⢸⣽⡈⠖⣘
⠸⠵⠁⣿⣯⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠁⠂⠄⠀⠀⠈⠁⠀⠤⢀⠁⠐⠀⠄⠀⠤⠀⠀⠀⠀⠀⠰⢸⢼⠂⡐⣲
⠘⢆⠄⣿⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⠈⠐⠠⠀⠁⠂⠀⡈⠑⢢⡀⠀⡀⠈⠀⠀⠀⠀⢘⢘⢺⠈⠄⠥
⢈⡂⠠⢟⡷⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠁⠐⠀⡀⠁⠄⠈⡑⠰⣀⠠⠀⠀⠀⢘⢸⢸⡇⠐⠎
⠠⠄⠨⢹⡗⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⠨⢼⠁⠀⠎
⢀⠂⠀⣹⣛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠨⡘⢮⠁⠀⠔
⢈⡁⠠⢗⡧⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡧⠈⢀⡊
⢀⠀⡀⣏⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⡆⠅⠒⠒
⢨⠐⠁⡆⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠏⡄⠠⠌
⠀⠀⠀⠧⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⡅⠀⠄
⠀⠀⠈⠡⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⡃⠀⠎
⠀⠐⠀⠡⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀