⡄⡎⠎⡜⡠⣑⣐⢐⢄⢅⢁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡣⡑⡜⣜⢮⣳⡣⣯⡳⣝⣞⡼⡔⡄⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡢⡆⡇⡇⢎⢮⡳⣝⣞⢮⣗⢽⣣⡗⡽⡽⣕⡇⡜⢔⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢕⢵⢹⣪⢪⢊⠎⡞⡼⣕⡗⣽⢪⡟⡼⡽⣽⢪⡗⣽⢸⠘⡜⡕⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡣⢣⢣⢇⢇⢅⢣⢹⢪⠧⡯⣳⢹⣪⣻⢼⣳⡹⣪⠳⣕⠱⡘⢜⢜⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠢⢣⠱⢀⠃⡜⡸⡱⡝⣼⣳⢽⣺⢪⣗⢧⣟⢼⣣⢳⠨⢐⠅⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠨⠐⡐⡜⡜⣜⢕⣗⢽⢽⡺⣽⡪⣗⣗⢽⣪⢪⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢣⢫⢪⡎⡆⡣⢪⢸⢸⢸⢱⡙⠩⡻⣼⡣⣟⢾⢼⢑⠑⡇⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠰⡱⢱⠱⠩⢃⢣⢫⢪⠢⡱⡱⡹⡜⡦⡴⣜⢷⣝⢧⢯⣳⢢⡪⡪⢢⢳⡀⠀⠀⠀⠀⠀⢀⢠⣪⢫⢝⢧⢳⡀
⠀⠀⠀⠀⠀⠀⢄⡃⡂⠢⡈⠪⢈⠔⡕⡎⡎⡌⡎⡎⢯⢽⣝⠧⢟⢮⢯⣳⠳⡝⡎⡎⠬⡪⡎⡄⠀⠀⢀⢀⠆⡇⢷⢱⠁⢇⠃
⠀⠀⠀⠀⠀⠘⢔⠨⢂⢑⢠⢵⣻⣎⢪⢝⢖⠌⡎⡎⣗⢽⣺⣢⢡⣈⣈⡠⡼⣜⢕⠅⢝⢜⡕⣷⣰⢰⢱⢑⢈⠀⡁⠐⠀⠂⠀
⠀⠀⠀⠀⠀⠍⢜⠘⡌⠢⣝⣗⣗⣟⡆⡝⣺⠨⡪⡪⣎⡗⡷⣝⣗⣗⢧⣟⢼⣣⢳⠁⡇⣗⢕⢷⡕⢕⠨⡂⠅⠃⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠠⡑⠠⣝⡞⡾⣼⣳⣇⢣⢳⡑⢜⢜⡜⡽⣽⢺⣺⣪⡗⣽⢣⢗⡕⢱⢸⢸⢪⣟⡎⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢔⡜⣞⡼⡺⣝⣞⣞⡗⡌⢮⢪⠸⡸⣜⢽⡺⡣⡣⣳⡫⣗⢯⡳⡱⠡⡪⡣⡻⣮⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⢜⡞⡼⣝⡞⣼⣳⡫⡂⢏⢎⠪⡪⡎⡗⡕⡇⣽⢺⢮⣳⣽⡟⡎⠜⡜⡌⣟⣮⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⢳⢝⡞⡼⣝⣞⡮⣗⠡⡫⡪⡊⢮⢝⢜⢜⢜⢷⢽⢽⣺⣟⢽⡘⠌⣞⠸⡵⣳⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢽⢸⡣⣏⡟⣼⣪⢿⢜⠄⡇⡗⡸⣨⢳⢕⢕⢭⢳⢽⢝⣞⣗⡗⡕⢡⢇⢝⢽⣺⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢧⡫⣞⢼⣹⢺⢮⢯⣓⠌⢎⢎⠜⡜⣮⢻⣔⢕⢕⢽⣣⢗⡗⣯⡊⡜⡜⣜⢽⣺⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢼⢜⢮⢳⡳⡽⡽⣧⣓⠨⢣⢣⠣⡣⡗⣽⢺⡪⡪⡺⣜⣗⢽⡗⡆⡪⡪⡪⣗⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡎⣗⡝⡧⣏⡯⣟⣞⢖⢑⢕⢕⢱⢩⡝⣷⢹⢜⢜⡼⣕⣗⣿⣛⢆⢪⠪⡮⣗⣗⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⡹⡜⣎⡟⣼⢺⢷⣝⣇⠢⡣⡣⡱⡱⡝⡎⡮⡪⣞⢮⣳⣿⢳⡣⡣⢸⠪⡮⣗⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢇⢯⢧⢯⣳⣫⣟⡞⣖⠡⡣⡣⡪⡪⣇⢇⢧⢻⢼⡝⣾⣻⡳⣝⠔⢕⢕⢽⣺⣺⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⢻⢼⡕⣗⣗⣯⢿⣜⠘⡜⡎⡜⡜⣦⢃⢏⢽⢪⣟⢼⢧⣟⢼⠨⢕⢕⢽⣺⡺⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢕⢕⡗⡽⣺⢺⡮⡿⣜⡘⢼⢸⢸⢸⡪⣗⡕⡕⢽⢜⣗⢽⣳⣝⠌⡇⡇⣟⢮⣟⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡕⣝⢽⢺⢽⢯⣟⣎⠆⡝⣜⢸⢸⡪⣗⡗⡇⡧⣹⢪⡗⣷⣳⠡⡣⡣⡫⡿⣼⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢕⢧⡫⣏⢯⣟⡾⣜⢌⢎⢎⢜⢜⢮⣳⢫⡣⡣⡣⣟⣾⣿⢕⢅⢣⢣⢫⡟⣾⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⢣⢻⢼⢽⣪⣟⡖⡄⡫⡪⢢⢳⡱⡱⢱⠱⣵⢹⢧⡳⣕⢗⠄⢣⠣⢧⢯⣳⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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