TrusTa
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁⠀⠈⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣟⡋⠍⠻⠞⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠁⢿⣿⣿⣷⣾⣟⡷⠀⠀⠀⡀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠿⠿⠟⠛⠃⠀⠀⣴⣿⣿⣿⣟⡳⣦⣾⣿⣿⣿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢸⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠢⠀⠀⢠⡄⠂⠀⠀⡼⡇⠀⠈⠙⠃⠌⣾⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠄⠀⠀⡶⠋⠓⠞⢢⣤⣷⣿⡀⢠⢠⢄⣫⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠄⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠋⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡛⡛⠋⠸⠇⣆⠫⣜⣾⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⢀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⣿⣿⠛⠛⣋⣙⣆⠀⡰⢌⣳⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠀⠠⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣿⡋⣵⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠣⡈⠛⠿⠿⣿⠟⢀⠒⣤⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠠⠐⠈⠀⠐⠀⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢀⡞⠁⠹⣯⣿⣿⣿⣿⣿⣿⣿⣟⣷⠃⠐⣄⠀⠀⠀⠨⠿⠿⢾⠋⢄⢢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡀⠐⠈⡀⠈⢀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠳⣄⢀⡀⡀⠡⡀⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠐⠀⠀⠁⠠⠐⢀⠀⠌⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣴⣴⠤⢤⠀⠀⠸⣷⡦⠥⢶⡿⠋⢠⣿⣿⣿⣏⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡐⠀⡈⠀⠠⠁⠐⠠⠐⠠⢈⠠⠐⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠲⠤⠤⠿⠿⠛⠛⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⢻⡇⠀⢉⡀⠀⠀⠹⢿⣿⣿⣿⣿⠿⣿⢿⣁⣠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡀⠄⢈⠠⢈⠀⠂⠌⡐⠠⠐⡈⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡐⠀⢁⠀⡐⠠⢀⠂⠄⣁⠒⢠⠁⠆⠡⡘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠈⠐⢀⠠⠈⠄⡐⢀⠂⠤⢈⠰⠠⡘⠄⡌⠢⡑⠄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⠀⢀⣀⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠄⢁⠂⢁⠀⢂⠁⢂⠐⡠⠌⡐⠤⢁⠆⠡⢌⡐⢡⢂⠱⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠠⢀⠀⠂⠄⡐⠂⡉⠄⣈⠢⠄⡁⠆⠰⣈⠂⡌⢡⠂⡌⠰⡈⢆⠡
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⠀⠁⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠦⣄⠀⠀⠀⠀⠀⠀⠄⠂⠀⠄⠐⠠⠈⠐⠠⢀⠡⠐⢂⠄⡒⡈⠔⡨⢡⠐⢢⠘⡠⢒⠨⡑⠰⡈⢆
⠀⠀⠀⠀⠀⠀⠈⣀⠤⠔⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⢦⣄⠀⠀⠄⠂⡀⠁⢂⠁⠄⡁⢊⠐⠄⢂⠩⡐⠨⢄⠱⡈⠔⡡⢊⠄⢣⠐⡡⢆⠡⣃⠜⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢮⣹⣆⠀⡐⠀⡁⠄⡈⢐⠀⠆⢌⠨⠄⡑⡈⢅⠂⢆⠱⡈⠔⡡⢊⠄⠣⠔⡊⢔⠰⡈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢦⡘⣿⡄⠠⠐⢀⠂⡐⠄⣉⠐⢢⠘⠤⠑⡌⢢⠉⢆⠱⡈⢆⠱⡈⢌⠱⢊⠜⡠⢃⠌⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢰⠁⠀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣼⠟⠀⠰⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡾⣷⠀⠌⡀⢂⠰⠈⡄⡘⢄⠊⡔⢡⠘⠤⡉⢆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠑⠈⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣈⣣⣾⡟⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⠎⡱⣿⠀⢂⠐⠄⡂⡑⢠⠘⡠⠡⢘⠠⡉⠢⢑⣈⣤⡥⠦⠖⠛⣊⣉⡥⣤⠤⢖⡚⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠘⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⡙⡖⣱⡏⠐⡀⠊⠐⠠⢐⣁⣆⣤⠥⠶⠒⠛⣉⣉⣥⠤⢖⡚⡛⠭⣉⡑⢒⠤⣍⠚⣰⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⠚⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠀⠤⢤⡐⢢⡔⣩⠞⣜⣟⣀⡤⠴⠖⠛⢋⣉⣁⡤⠤⢖⡒⢫⠙⣉⠒⡄⠚⠤⡡⢑⠲⡠⢍⠪⢜⣤⠟⠉⠀
⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡜⣉⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣯⣷⣢⣝⣣⢞⣥⠿⢋⣠⠤⠴⠒⠚⠩⣉⠐⢢⢈⡑⢢⠘⡄⢃⠆⠣⢌⢃⡒⠥⣉⠖⡱⣪⠽⠋⠀⠀⠀⠀
⣷⣶⡿⠿⠟⠛⠋⠉⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⢿⡍⠉⠉⢁⠠⢁⠀⠆⡐⠉⠄⢃⠄⡊⠔⢢⠘⡄⢣⠘⡌⡌⡓⢌⠒⣌⠳⢤⡹⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⡠⢄⡀⠀⠀⠀⠀⠀⡀⠀⠄⠀⣄⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠫⣿⠈⠄⠠⢀⠂⠌⡐⢠⠉⡌⢢⠘⠤⡉⢆⠱⡘⠤⢋⡔⢢⠍⢦⠩⣤⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠉⢶⢤⣤⣐⣲⣢⣥⠶⣿⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣇⡿⡆⠌⡐⠠⠌⡰⠐⣂⠱⣀⠣⡘⠤⢱⣈⢒⣩⠜⣡⢜⣡⢞⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠛⢯⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠹⣷⡈⢄⢃⠢⣁⠒⡄⠒⡄⢣⣘⣬⡵⡖⢯⠳⣙⢦⡽⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠅⠨⢷⡈⢆⣱⡤⢷⠼⣛⠏⢯⡙⢦⢣⡙⢦⡽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠂⠀⠀⠀⠀⡀⠤⠀⠐⠒⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⢿⣏⡱⢊⠧⡙⡤⢛⠦⣙⢬⡳⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠩⢧⡣⢎⡱⢅⠏⣶⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⢞⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⢁⣘⡻⣎⣳⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⠀⠀⠀⢻⢮⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠈⢦⠀⠀⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⢳⡀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤⠤⠴⠴⠖⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹
⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠲⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣌⡳⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⡀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⠳⡼⣝⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⢸⠇⣸⣇⠀⣻⠀⠀⢊⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢎⠴⣩⢟⡵⡿⣍⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⢷⣀⠀⠀⠀⠀⣿⢀⣿⢹⡄⢸⣷⡠⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⠹⣌⢷⡹⢮⡙⢌⠳⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⡆⢡⠈⢛⣄⠀⠀⣼⡇⢾⣿⠈⣧⢺⣿⣧⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢢⢍⣼⡟⣼⢣⢟⣥⣞⡜⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡆⢿⣦⡑⡌⢿⡄⢨⣿⣍⣿⢺⢌⣿⢻⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣈⡜⣣⢎⡿⣙⢶⣫⢞⡭⡿⣿⣿⣟
⠀⢀⠀⠀⢀⠠⢀⠡⡀⠎⢰⠀⠌⡀⠄⢂⠈⢀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠡⡘⠤⢿⣶⢍⢾⣷⣨⣿⠰⣿⣹⣸⡿⣹⣾⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢢⡑⣣⠳⣜⣣⢏⢶⡹⣎⠾⣭⢞⡵⣧⢿⡇
⢦⣬⣐⣂⠡⢌⢢⡑⢬⡘⢆⡍⡒⢠⠐⡀⠒⠠⢈⠄⠠⠁⡀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⡐⢠⠑⡊⢖⡹⣎⠾⣿⣟⢆⡳⣿⣺⣿⡧⣹⣧⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡸⢈⢆⣣⠝⣎⢳⠳⣜⢮⣷⣛⣮⡻⢷⡞⡽⣋⣾⠇
⠀⠀⠈⠉⠙⠛⠶⣽⣦⣙⠶⣘⠌⠦⡑⠤⡙⢄⠃⡌⡐⠡⠀⢂⢀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⡀⠂⠄⡃⠬⡑⢎⡱⣋⢞⣿⡼⣏⣵⣿⣿⣿⣧⣼⢿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⣀⠂⡔⣈⠲⣡⢏⡞⡴⣛⡜⢯⣽⡾⡿⣟⣻⢼⡹⢧⣻⢵⡻⣼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣮⣝⢢⡑⠦⣑⠊⡔⡠⢑⠂⠅⢠⠂⠄⢂⠀⠀⡀⠀⢀⠀⠀⠀⢀⠂⢀⠠⢀⠐⡈⠤⡉⢖⡩⢎⡵⣩⢞⣿⡟⣦⣛⢾⣻⣿⣿⣺⠉⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢠⡁⠆⣄⠳⣘⠴⣫⠕⣮⡜⡳⣭⣾⡿⣯⢷⡽⣞⡵⢯⣟⢯⣞⣣⠟⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢻⢾⣷⡤⣋⠴⢡⢊⠜⡠⢂⡐⠌⡀⠄⠂⠀⠀⠂⠀⠠⠐⢀⠀⢀⠂⠀⡐⢠⠑⣌⠲⢥⣋⢖⡳⢎⣿⣽⢪⢵⣫⣾⣿⣿⣁⠎⡀⠡⠀⠂⠈⠀⠀⠀⠠⠄⣉⠒⡄⢢⡙⣤⠳⣍⢾⣡⢟⣦⣿⣿⣿⣻⢽⣯⡟⣾⡽⣞⢯⡞⣳⢎⡳⢻⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣾⣱⡣⢎⡜⡰⣁⠆⡒⢠⠈⠔⡈⢁⠌⡐⢠⠐⡠⢈⠤⢈⠢⢌⠢⡍⢦⡙⢦⣙⢮⡝⣻⡗⣮⢳⣣⢿⣿⣿⣿⣎⠖⠤⣁⠡⠄⠁⢈⢀⠒⡐⢊⡤⢋⡼⢵⡚⣖⢻⣜⣧⣿⣿⣿⣿⣟⣾⣽⡻⣶⣛⢧⡻⣜⢣⠞⡱⣎⣵⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢻⢯⣾⡱⡜⣜⡰⢃⡍⢢⡑⣊⠴⣈⢆⡱⢠⢃⡜⣠⠓⣌⢳⡘⢦⡹⢎⡵⣫⣾⠷⣹⡜⣧⢯⣿⣿⣿⣿⣿⣮⣕⠤⢂⠔⡚⢤⢺⣥⢟⡻⣜⣯⣜⣧⣿⣾⣿⣿⣿⣿⣿⡿⣟⡻⡝⣞⡹⡑⢎⠵⠑⣊⣮⣼⠛⢟⣾⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢷⣟⡶⣭⣳⣜⣣⢳⡜⡲⢥⢎⡴⣓⢬⠲⣥⢛⣬⢣⡝⣎⢷⡻⣜⣿⣣⢟⡵⣹⢮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣼⣿⣿⣿⣿⡿⡿⠿⡛⢯⠫⠟⠪⠅⡓⢌⠱⠘⠠⢄⣁⣨⡴⢛⠛⣤⣦⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢻⣷⣟⡾⣵⢯⢾⣝⢧⣛⠶⣭⢞⣽⢲⣏⡞⣧⣿⡾⣯⣿⣻⣷⣯⣿⣾⣿⣿⣿⣿⢿⣟⣿⡯⢟⠳⡬⣑⡮⠗⢉⡉⠁⠎⡀⠡⠀⠔⣀⠃⠔⡀⠊⢄⡑⢈⠐⠀⢂⣁⡶⠶⢋⣡⡴⣞⣿⣾⡟⣻⡟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⢿⣽⢯⣟⡾⣯⣻⢿⡽⣾⣽⣻⣾⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣻⢯⡷⣟⣻⠮⠵⢊⡙⠠⡑⠀⠂⠀⠂⠀⠐⠂⠐⢂⢁⠂⠐⢈⠐⡀⠁⠄⠀⣀⣬⠶⠫⠉⣄⣼⣺⣿⢿⠋⣉⣄⡖⣿⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠝⢿⣾⣿⣷⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⢷⣟⣻⢯⢟⡛⠥⢃⠎⠁⠃⠈⠐⠀⠀⠀⠉⢀⠐⡈⠄⠁⡀⠠⠀⠁⠀⠀⣀⣰⠶⣿⣉⠤⠒⣿⣽⣽⠿⠋⠅⠒⠺⢾⡿⣇⣿⣀⣤⣶⠿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣿⣳⢯⡷⢫⣓⠮⣑⠎⠜⡈⠡⠁⠄⠁⠈⠀⠀⠂⠈⠀⠂⠐⠀⠠⠐⠀⠀⠁⠀⣠⠶⠚⠉⣁⣐⣾⣽⡇⣴⡿⠋⢀⠂⠑⢈⢠⠆⣽⣻⢟⣷⠿⠋⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⡿⣿⣯⣷⢿⣻⡽⣖⢯⣓⠺⡑⡊⠅⢂⠜⠀⢀⠀⠠⢀⢀⠀⢈⠀⠈⠀⠂⠀⠀⠐⠀⠀⣠⡴⠞⢋⡵⠂⣼⢾⣿⣥⣿⡿⠟⠉⠄⠦⠕⣊⣑⢮⡳⣯⢷⢻⣿⠟⣿⣇⣼⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠿⣷⣟⡾⣯⢗⡻⣜⠢⡕⢪⠑⡨⠌⠁⠠⡀⡀⠆⠂⠂⠄⠀⠀⠈⠀⠄⠀⠀⣀⡤⠖⠋⠁⢀⡴⠋⠀⢸⣏⢾⠟⢻⢋⡀⢆⡡⡜⣼⡩⣧⣯⠗⡫⠓⡉⠘⣿⣯⣟⣿⡯⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠻⣟⣮⢏⡵⢪⡕⢮⢃⠭⡐⢌⡡⠃⠔⡠⠀⠁⡄⠀⠐⠀⠀⣀⣤⠖⠛⠁⢀⣠⡤⣶⠟⠁⠀⠀⠈⣿⢺⣄⠼⠷⠶⠮⣵⣿⡶⠟⡏⢰⢢⢵⢚⡡⢟⣯⣿⣧⢻⡿⠀⠀
⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢾⡱⡫⢜⡆⢫⡔⢣⢅⠒⡉⡔⠠⢁⠐⠀⢀⣠⠴⠛⠉⢀⣠⢵⡚⣯⣷⠟⠉⠀⠀⠀⠀⡀⠸⣷⣹⣀⣠⣶⡶⠟⢋⣐⢡⡼⢝⡻⣧⠿⣙⣯⣿⣿⢡⣺⡇⠀⠀
⠘⠠⠈⠐⣠⡀⢀⠀⠂⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠻⢷⡚⡵⢪⢕⡪⢍⡒⣠⢁⣦⠴⠚⢋⣀⣠⣼⣚⣯⣽⡾⢻⣿⣿⠛⠓⠒⠶⢦⣄⣈⡀⣿⣳⡿⢛⣡⣜⠴⡋⣾⢷⣛⣼⣳⣯⣳⣥⣿⣿⣧⣿⣳⡇⣀⣀