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