⡀⡀⡀⢨⡐⢂⡐⡂⢄⢐⡂⡘⣿⣿⣿⣿⣽⣿⣿⣗⡂⢒⢂⠆⡑⡈⡘⡆⠰⡣⢌⢌⢜⡊⡐⡂⡘⢂⡢⠔⢐⢔⡐⠣⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣿⢻⣿⣿⣿⣿
⡀⡀⡀⢸⣅⣅⣠⣄⣑⡐⡨⣌⣺⢿⣿⣽⠁⡀⡀⠉⠙⠮⣌⣈⣡⣀⣀⣀⢈⢁⣈⡑⠁⢈⡁⢂⡂⢈⢕⣢⠦⠼⠶⠬⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⢿⣟⣽⡽⡿⣟
⡀⡀⡀⢘⠫⠓⠓⠋⠝⠙⠛⢛⣿⣿⣿⣿⣆⡀⡀⡀⡀⡀⡀⡀⡀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⡀⡀⡀⡀⡀⢠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⣟⢾⣿⣿⣿⣾
⡀⡀⡀⢸⡾⣗⣺⣷⡷⣻⣷⣼⣿⣿⣿⣾⣟⣓⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣔⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣫⡾⣮⣿⣟⣟
⡀⡀⡀⢸⡷⣟⡷⢵⣾⢿⣷⣽⣿⣻⣿⣿⡿⣷⣶⠤⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⠤⣙⣿⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢈⣯⣞⣯⣿⡿⢽
⡀⡀⡀⠸⣛⣟⡳⣛⣯⢟⣿⣻⣿⣿⣿⣾⣿⣿⠋⡀⡀⡀⡀⡀⢈⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⣿⣿⣿⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⣻⣗⣞⣟⣿⣻
⡀⡀⡀⡀⡴⡔⠤⢤⡤⢤⡠⢄⣜⣻⣯⢿⣻⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡿⡿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⣿⣼⣯⡿⡯⣽
⡀⡀⡀⠨⣷⢮⢮⣺⡺⢽⣿⣿⣿⣺⣿⣺⣷⣿⡀⡀⡀⡀⡀⢾⡀⢮⡆⡀⡀⡀⡀⡀⡀⣶⠰⢻⡀⡀⡀⡀⡀⡀⣶⣧⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣟⣷⡯⡽⣯⢿
⡀⡀⡀⡀⣿⢵⣍⣝⢮⡮⢾⣻⣿⣿⣿⣽⣿⡇⡀⡀⡀⡀⡀⡀⠉⠉⡀⡀⡀⡀⡀⡀⠈⠈⠉⠁⡀⡀⡀⡀⡀⡀⣿⣿⠅⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣽⢽⡾⡷⣻⣺
⡀⡀⡀⡀⣟⢳⢗⡽⢮⡮⢾⣯⣿⣿⣿⣿⣽⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⣟⡅⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣯⡽⣿⣾⢯⢽
⡀⡀⡀⡀⣷⢮⣱⢾⢵⢽⣟⣿⣿⣿⣿⣷⡖⠤⡤⠴⠴⠒⢒⣖⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢐⣂⠤⠤⣀⡀⡀⡀⡀⣿⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢺⣽⣟⣻⡯⣻
⡀⡀⡀⡀⣿⠽⢧⢾⣹⣮⣽⣺⣯⣿⡿⠛⡀⠒⣀⣦⣼⣿⣿⣿⣯⣤⣠⣤⣤⣶⣤⣤⣄⣤⣴⣿⣿⣿⣦⡄⡀⡀⡀⠘⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣟⢗⣝⣻⢷⣻
⡀⡀⣀⡀⣿⣿⢸⣿⢛⡛⣿⣿⣿⣿⣿⠒⢈⠤⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡛⣿⣿⣿⣿⣿⣿⢀⠈⠂⠠⡀⠂⡀⣀⡀⡀⢀⡀⡀⡀⡀⡀⡀⣯⡮⣕⣜⣱⣗
⡀⡀⣿⣀⡙⣿⣨⣍⢨⡅⣉⣭⡙⣿⡟⣠⣤⡀⢋⣭⣍⢉⣍⣭⡋⣭⣭⡙⢋⣭⣙⢸⣅⣉⣿⣿⢋⣭⣉⠓⣨⣤⡀⣤⣭⡀⣿⣀⡄⢨⡄⣤⣤⡀⣄⠙⣉⢛⣭⣉⢿⣻
⡀⡀⣿⠐⠾⣿⡀⣿⢸⡇⠻⣦⡀⣿⡀⣿⡤⠄⣰⠶⣿⡀⡇⢸⡇⣿⡀⣿⣿⡀⣿⢸⡆⠶⢿⣿⣿⢰⡄⡀⡧⢸⡇⣿⡀⣿⣿⡀⡀⢸⡇⣿⡀⣿⣿⡀⣿⢸⣤⣿⢘⣽
⡀⡀⠻⠶⠟⠿⡀⠿⠸⠇⠻⠶⠟⣿⡀⠿⠶⠋⠻⠶⠿⠠⠧⠸⠇⠿⡀⠿⠙⠶⠟⡘⠷⠿⣰⣿⠙⠶⠿⡀⠿⠾⠃⠿⡀⠿⠻⠶⠿⠸⠇⠿⡀⠿⠻⠶⠿⠘⠶⠿⣸⣯
⡀⡀⡀⡀⣿⣿⣿⣿⣿⢿⣿⣿⣿⠃⡀⡀⡀⡀⡀⢃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⡀⡀⡀⡀⡀⡀⡀⠠⠤⠄⡀⡀⡀⡀⡀⡀⢉⢿⣟⡻⡻⢷⣵
⡀⡀⡀⡀⣿⣾⡳⣞⡾⣵⣽⣮⣿⡀⡀⡀⡀⡀⡀⠒⠅⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡋⣗⢻⣜⡪⢕⢭⡹
⡀⡀⡀⡀⣿⢯⡯⢷⡮⢜⡮⡯⣇⡀⡀⡀⡀⡀⡀⠈⡀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⢀⠬⡪⡼⡫⢕⢾⡺⢯
⡀⡀⡀⡀⣿⡽⢯⡽⢯⡽⣺⡯⣞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣤⣞⡣⡎⢹⢇⣜⢪⢮⣝⢞⡵⢫
⡀⡀⡀⡀⢿⣗⢟⣳⣗⣽⣗⣞⡯⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⢿⣿⣿⣿⣿⠿⣿⣿⣏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⡭⢕⢪⡝⡹⡇⢜⡳⢪⢏⣾⣻⡯⣗⡿⣯
⡀⡀⡀⡀⢼⠿⠟⠛⠉⠉⢀⡠⢄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢿⣄⡀⣽⠏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡩⢸⣝⡳⢮⢵⡮⢕⢪⢕⣯⣟⣗⢽⢯⡽
⡀⡀⡀⡀⠤⢄⣔⣖⣊⣉⣄⣤⠆⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⣿⢀⠃⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠑⠮⡵⢮⡕⢣⣍⡪⢜⢷⢟⢟⣺⡾⣷
⣤⣤⡶⠟⢛⠍⠡⢍⡹⠻⠓⠎⡌⢠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠠⢈⡕⡪⢕⢣⡼⢺⣝⡮⢾⣻⣻
⢀⠃⢂⠒⢒⡢⢄⣨⣱⡑⢊⢊⡨⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣠⣤⣀⡀⡀⡀⡀⡀⡀⢀⡀⡀⠄⡀⢀⠐⡁⠌⡏⡕⡎⣫⡵⣗⣳⣻⡿
⢐⠐⠐⠂⢰⡑⢔⡊⡑⢂⡐⠪⡅⢈⠉⠑⠒⠂⠠⠄⡀⡀⣿⣿⣿⣿⣿⣶⣄⡀⡀⢰⣿⣿⣿⣿⣿⣿⡄⡀⡀⡀⡀⡀⢀⡐⠐⠂⡈⠈⢐⢁⡑⡑⠢⢜⣽⣻⡯⢿⣼⣺
⡚⠲⠶⡬⡥⣪⣂⣈⢅⠌⠡⢥⡢⢌⡀⠌⠨⠡⢄⢡⢠⡈⠿⢿⢿⣿⣿⠿⠿⠂⢀⣛⠟⠻⠿⠿⠿⠛⡀⢀⠄⡀⢄⡀⢈⡠⢎⠤⢪⢅⢌⢘⢪⢽⢪⡵⢟⣽⣯⣽⣯⡿
⠙⠃⠒⠊⠚⠛⠑⠒⠓⠉⠉⠙⠛⠒⠒⠒⠒⠂⠘⠊⠂⠘⠛⠛⠛⠛⠋⠛⠛⠐⠑⠚⠚⠓⠚⠛⠙⠚⠂⠐⠑⠊⠋⠘⠋⠑⠒⠊⠊⠑⠃⠂⠊⠑⠐⠚⠛⠛⠛⠛⠛⠓