⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⡃⢇⢇⢕⢕⢔⢤⣄⡐⣄⡀⠌⠪⡢⠱⡀⡠⡰⡰⡨⢂⠢⠁⠀⠀⢀⢀⢀⢀⢀⠀⠀⠀⡀⠠⠀⠄⢀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⢑⣄⡐⠀⠀⠈⠎⠌⢷⣵⣱⡱⡱⡙⣯⢷⢍⠪⣂⠊⡎⡎⡎⡪⠢⡈⢢⠁⠠⠐⢌⠢⡑⢌⠢⠑⠌⢄⠂⢀⠐⠀⠂⡀⠄⠈⠀⠀⠀⠨⠘⡈⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⡀⠀⠠⠀⡜⠨⢰⣯⣿⣻⣷⡶⣷⣦⢦⣙⢷⢽⢕⢧⡣⡫⢳⢱⢨⠣⡊⡎⡎⡊⠢⡈⡆⠐⢀⢣⢑⠕⠈⠂⠀⠂⠁⠀⠑⠠⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠂⢰⢕⠡⢸⣷⣿⣿⣷⣿⣿⣮⡳⡽⡵⡭⣫⡳⣝⢝⣆⠕⡜⡜⡔⢕⢕⠌⢌⢂⠂⠠⢑⠌⡂⠄⡁⠄⡁⠐⠈⠀⠂⠀⠁⡀⠂⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠂⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠂⡐⠀⠂⢄⢈⢸⢢⠨⡐⣿⣿⣿⣿⣟⣯⢮⣯⡺⡪⡫⡚⡞⡎⣗⣕⢧⢱⢱⡱⣝⡕⢌⢆⢂⠂⠨⠀⠅⢄⢑⠌⡌⡂⡪⢀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠠⠀⠄⢀⠁⢀⠐⠀⠌⠺⣌⡂⠎⢟⢿⢟⢏⡯⡟⡎⡎⣎⢎⢎⣎⢮⡲⣱⡹⡜⡜⡜⡜⡜⡌⡒⢔⠨⢘⠄⢅⠢⡡⡑⠔⠁⢈⠀⠁⠀⢀⠀⢀⠀⠀⢀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈⠀⠀⠂⢀⠈⢂⠀⢂⠀⠀⠨⡂⡐⡀⡉⡙⣐⣴⡕⣝⡳⡹⢮⢯⢾⣺⣳⢯⡳⣝⢮⣪⣪⡮⡪⡸⡐⡕⡱⣐⠑⠄⢕⠠⡱⠈⢀⠠⡐⠀⠀⠐⠈⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢀⠀⠀⡀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠂⠈⠠⠀⠀⠀⠀⠠⠐⠀⠁⠀⡀⢐⠀⠀⠢⡀⡀⡊⢷⣽⢼⣕⢯⡚⢞⠮⠯⠿⣿⣿⣿⣯⢳⡯⣞⡾⣣⣿⣯⡣⣣⣣⡱⡜⢌⠆⡝⠌⠄⢕⠐⡈⠢⠡⠀⡀⠁⡀⠄⠀⡀⠀⠀⠀⠀⠂⠀⠂⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠄⠀⢀⠀⡀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠠⠀⠠⠀⠀⢐⠀⡈⠄⠁⠀⠠⠀⠀⢂⠌⠢⠱⢐⢝⢿⣺⣽⣝⣗⣷⣷⣷⣿⣿⣿⢿⣎⡻⣿⣽⣿⣿⣾⡯⡷⡫⡱⡑⡅⢇⢪⠪⡪⡀⠅⡐⠠⠀⠑⢄⢑⠀⠄⠀⠀⠀⠄⠈⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⡀⠄⠂⠈⠀⢀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠂⠀⠠⠀⡀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠠⠐⠀⠀⠂⢁⢂⠐⠀⠐⠈⠄⠡⠐⡀⠄⠀⡀⢀⠈⡠⣺⠾⠻⠛⡛⢛⠛⡛⣛⣻⣿⣿⣿⣿⣿⣿⣷⣎⡎⡲⢮⢮⢝⢜⢜⢔⢵⢸⡨⡪⣪⢊⢆⠪⡂⡂⡂⠌⠠⠈⢀⢀⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⡀⠠⠀⠠⠀⠀⡀⠁⠀⠀⠀⠀⠂⠈⠀⠠⠀⠠⠁⠀
⠀⠀⠀⠀⠀⠐⠈⠐⠠⠀⠁⠀⠂⠄⠐⠀⠐⠀⠄⠐⠀⠂⠂⠄⠊⡀⠡⢁⠨⠐⠡⠐⠐⠀⠐⠀⠔⠀⠄⢂⢁⠂⣢⢲⢩⣹⣾⣾⣿⣿⢿⢻⣛⢯⢯⣯⢯⢮⢮⡪⣕⣝⢮⣫⡺⢎⢢⢯⢪⢸⢪⠪⡈⡢⠐⡈⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠐⠐⠀⠄⠀⠄⠁⠐⢁⠀⠀⠀⠄⠠⠀⠐⠀⠂⠌⠀⠐⠈⠀⠈⠀⠀⠄⠐⠀
⠀⠀⠀⠀⠀⠈⡀⠡⠐⠀⢀⠁⢂⠐⠈⠈⠀⠁⠠⢁⠈⠀⠌⠠⠁⠄⠡⢀⠐⢀⠁⠨⢀⠁⡈⠄⠀⠀⠌⡀⢢⡞⡕⣜⣾⣿⣿⣿⣫⣵⣿⠟⢟⢛⠳⡹⢹⢳⢵⣝⢮⢮⢳⢃⠇⡵⣫⢯⢸⢸⢸⡐⠅⠢⠁⠄⢁⠠⠀⠂⠁⠀⠀⠀⠂⠁⠀⠀⠀⠀⠂⡀⠁⠅⢐⠈⢀⠁⠈⡀⠄⠂⠀⡂⠐⠈⡀⠁⠐⠀⠄⠀⠀⠀⠀⡀⠁⠀⠀⠀
⠀⡀⠀⠀⠀⢀⠀⡂⠄⠁⡀⠐⡀⠂⠂⠈⠀⠁⢈⠀⠄⠠⠁⡐⢈⠐⡀⢂⠈⡀⢂⠁⠠⠀⡀⠀⠀⠌⡐⢰⡫⡺⡼⣟⣿⣻⣻⢽⢯⣟⣴⣿⣿⣿⣷⣾⣶⣴⣅⣎⢮⡪⡪⠢⣱⣝⢾⢝⠰⡈⢮⠪⠨⠈⠌⡐⢀⠀⠂⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢁⠠⢈⠐⢀⠈⡀⠄⠠⠀⠄⠂⠄⠂⠈⠠⠀⠄⠨⠀⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀
⠀⡂⠀⠀⠀⠀⠠⠀⠐⠀⠄⠂⠀⠁⠐⠈⠀⠂⠀⠐⠀⠄⠂⠀⠐⠄⠂⠐⠀⠐⠀⠐⠈⠀⠀⠀⠀⠡⢠⡳⢝⢝⣼⣳⡳⣗⡯⣯⢿⢞⣟⣟⣯⡹⣿⣿⣻⡿⣯⡟⡏⣎⢜⢊⡔⢮⣫⡳⢑⠘⡄⠹⡈⠌⢐⠀⢀⠀⡁⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠠⠠⠐⠀⠀⠀⠄⠐⠈⠀⠁⠄⠂⠁⠀⠂⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⢄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠁⢀⠐⠈⠀⢀⠀⠀⡀⣀⢖⠕⡕⣵⢫⣞⢾⡽⠷⠽⣞⢯⣫⣺⣺⢽⣷⡵⣝⣗⢯⠷⡗⡏⣡⡲⣮⢫⢪⢮⢇⠰⠁⢝⠄⠐⡈⠄⠐⠀⠀⡀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠐⠘⠒⡡⠊⠊⡱⡽⠊⠡⠐⡐⡜⣜⢵⡱⣳⣝⢛⢚⢛⠃⡛⠯⣿⢽⢯⣗⣯⠯⢪⡺⣝⠆⡘⢈⠸⡅⠀⡂⠨⠐⠀⠠⠀⠀⠐⠀⠀⡀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⠀⠐⠀⠀⠀⠀⠌⠀⡈⢄⠏⢐⠈⣨⢂⢧⠫⠚⠚⠫⠓⢛⠝⣲⢢⠲⢘⠨⢈⠉⡉⢌⣢⢮⡳⣽⡳⠁⡐⡐⢌⠇⢀⢂⠁⠀⠁⠀⠠⠐⠀⠠⠀⠀⠨⠀⠀⠀⠀⡀⠄⠂⠁⠈⠀⠐⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡁⢀⠄⠂⡁⢄⠅⠀⠌⠐⠀⡢⠇⡊⡐⠠⠈⠀⠂⠜⠔⡸⡰⢡⢱⢘⢜⢬⠴⡺⣺⣪⡳⣯⢛⢐⠌⠄⠌⠨⠐⢠⠂⡀⠁⡀⠁⠀⠀⢀⠀⠡⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠂⡁⠐⠀⠄⢀⠀⢀⠅⠈⡔⡡⡃⡐⡀⠂⡀⠡⠈⠌⡠⠣⢉⠒⠅⠕⡑⡀⡖⣝⡞⠎⡴⠡⢊⠠⠈⠄⠅⠅⠢⡀⠠⠀⠄⢀⠀⠂⠁⠀⢀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠠⠀⠌⠀⠀⢁⠊⠄⠂⠁⠠⠐⠀⠁⢀⢀⠂⡰⠀⠂⡁⠄⡪⡨⠐⢀⠡⠐⢠⡝⠊⠅⡐⠡⢂⠣⡁⡂⠁⠂⠅⠈⠄⡌⢐⠀⠀⠀⠀⢀⠈⠄⠂⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠂⠁⠠⠀⠀⡀⠂⠨⠈⡊⡀⠁⢀⠈⡐⠁⢀⠂⢌⢌⠂⠠⣐⢌⢉⡕⢂⠀⠨⠊⠀⠅⠢⢐⢑⠄⢇⠀⠂⠅⡁⠄⢀⠨⠐⢀⠀⠀⠈⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⡂⠀⢂⡤⢶⡀⡐⠐⠠⠁⠀⠂⠄⠂⢀⠄⢑⠔⡑⡐⡈⡗⢟⢻⢓⠂⠅⡁⡎⠨⠨⠢⡑⡀⠁⢄⠌⡐⠀⡂⠔⠀⡊⠀⠀⠠⠐⠀⠀⡀⠀⢁⠂⠀⠀⠀⢀⣀⢀⢀⡤⣄⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⡀⡀⡀⣀⢀⢄⠠⣀⣀⡀⣀⢄⡀⡄⡠⣀⢄⢂⣀⢄⣀⣄⣠⣰⣠⣢⡪⣗⣶⡺⣕⢜⣤⣻⡴⣅⣇⣗⢼⣄⠡⠀⠄⠂⡐⠅⡊⠔⠅⡇⢏⠎⡎⡊⢆⢣⠣⠈⠄⠅⠊⡢⠠⢐⡐⠔⠁⠠⠀⠂⠀⡈⠀⢀⢰⡦⡖⣄⣳⣵⢾⠾⢾⢺⢝⡬⡍⢕⠠⡂⡙⡤⡤⢔⠔⠢⡠⡀⡀⡀⠀⡀⡀⡀⡀⡀⡀⡀⡀⡠⢀⢀⢀⢀⠀⡀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢀⠀⠈⠀⠀⢀⠀⠌⠀⠉⠙⠩⠡⠡⠈⠠⡀⠐⡡⠊⠌⢌⢌⠢⡑⢌⠪⡪⢪⡃⢈⠀⡑⠡⡀⠣⠠⠀⠀⠈⠀⠌⠀⠀⢀⠀⢀⠚⠛⠛⠙⠈⠊⠂⢑⠔⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠕⠒⠀⠀⠀⠁⣀⠀⠀⡊⠌⢌⢂⠢⢑⠌⡢⡑⢜⢔⢑⠆⠄⢀⠁⠂⠡⠁⠁⠁⢀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠁⢀⠀⠕⠐⢠⠁⠀⠈⠀⠀⠈⠁⠨⡈⡂⠢⠑⢄⢑⢐⠌⡂⡢⢑⢝⢔⢄⠀⡁⠀⠁⠈⠠⠀⠀⠠⠀⠂⠀⠀⠕⠂⠀⠀⠀⠀⠁⠀⠀⠀⠈⠐⠠⠁⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠀⠠⠃⠔⠠⠁⠁⠀⠀⠀⠀⠀⠀⠢⠨⠨⡈⡂⡂⡢⢑⢐⠨⢂⢇⠣⡣⡀⠠⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠠⠁⠀⠀⠠⠁⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⡀⠠⠀⠀⠠⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠡⡑⡐⡐⡐⢌⢐⢐⠅⡂⢆⠪⡘⢔⠤⡠⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠊⡀⢈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⡂⠢⠨⢐⠐⢄⠑⢌⠢⡑⢌⠢⠁⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠐⠀⢐⠁⠐⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⠨⠨⠨⠐⠈⠂⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⡀⠄⡸⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡐⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢐⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠅⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀