⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⢦⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡍⡎⡯⢾⢷⣻⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢞⠮⣎⢮⣫⢯⣻⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣗⢽⡪⣯⣺⢵⣫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⢸⢸⢪⢳⠹⡜⡎⣗⢭⡫⣎⢧⡣⡲⡤⡠⠠⠠⡀⠄⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢮⠪⡕⢕⠕⢕⢑⠕⡍⢎⢎⢎⢮⢺⢜⢮⡺⣵⣳⡽⣕⣕⢌⢆⠪⡈⢐⠠⢺⡪⡯⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢳⢫⡙⡪⡪⡢⡹⡘⡜⡜⡜⣜⢼⢸⣪⢳⢝⢵⠁⠉⡽⣻⢿⣽⣓⢧⢣⣊⢢⢨⢞⢎⣯⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢎⢗⢕⢜⢌⠆⡕⢜⢸⢨⢪⡪⢮⡪⡳⣕⢽⢕⠏⠀⡸⣪⢗⢯⡻⣪⡳⣣⡳⡝⡮⡪⣳⡳⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡨⠠⠑⢕⡇⡇⡆⡇⢎⢪⢪⡪⣚⣚⠽⣮⢫⢮⡳⠍⠀⣰⡫⡷⣯⡳⡽⣕⢯⣺⢪⡫⡎⡋⡐⠨⡲⡲⡀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡵⠱⡌⡎⡌⠔⡈⠣⡳⣜⢜⢼⢜⡼⣪⡮⣻⢸⡕⣗⠝⠀⣰⡫⣟⡯⡷⡝⣝⢎⢷⢝⣵⣳⡪⡈⡘⡌⠪⢚⢨⢈⠢⣐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢁⢂⣧⡾⣻⣼⡸⡐⡅⠌⠜⢵⡹⣺⣜⠷⣽⠝⡼⡵⡝⡀⣰⢷⣟⣗⢯⢣⠣⡣⠫⡣⡳⣕⢵⢝⡪⡪⡔⡔⡨⠢⠃⠃⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣰⣬⠨⡀⡂⡻⡳⡽⣵⡳⣫⢷⡱⡡⡑⢔⠩⠨⡨⡐⡔⡌⡔⡰⡐⡅⣏⣿⡺⣪⡪⡪⡪⠪⡪⡒⢬⢢⢳⢱⢝⡎⣗⢽⢜⡵⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡴⣏⢧⡳⣳⢆⠢⡈⠹⡺⣼⣺⡵⠿⢊⢪⢨⢢⢣⢣⢣⡣⡧⣣⡗⠵⣣⡳⢹⢮⠫⣞⣞⢼⡸⡸⡰⡘⡌⢜⢸⢸⢱⢝⢼⢕⡏⣏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⡌⢾⠿⠮⢚⢘⢨⢰⢨⢢⠡⡩⢓⠩⡠⡱⡰⣱⡪⣞⢼⡸⡪⣞⣽⡳⠀⡌⢠⡿⠫⠫⢀⠀⠙⠵⣫⣞⢮⡺⣜⢜⡔⣅⢇⢗⢕⢧⡫⣎⢗⡤⣄⠀⠀⠀⠀⠀
⠨⡢⡪⣢⢢⢕⣜⣼⣼⣾⠿⡢⢣⢪⢰⢱⣕⣷⢿⣪⢯⢯⢳⡹⣪⣫⡴⢀⠼⢋⠡⠐⠈⠈⠀⠨⠀⠂⠈⠘⠳⢝⣮⡳⣝⢮⢮⡳⣹⢕⢽⡸⡵⣽⢾⣻⣦⡀⠀⠀
⠈⠪⣫⡢⣌⢉⢉⠍⡍⡢⡱⣸⡸⣸⢜⢵⠉⡉⠉⡁⡡⢔⡝⣞⢼⠚⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⡁⠄⠀⠄⠙⠱⠯⣳⢝⡮⡯⣳⢝⣾⣟⣿⣻⣽⡿⣆⠀
⠀⠀⠀⠫⡪⣪⡪⠮⠎⡓⠩⡀⠢⡈⢗⡵⣅⡴⠦⠳⠳⣵⡫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⡀⠂⡀⠄⠈⠉⠙⠚⠿⠯⢿⣽⡿⣽⡿⡻⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠁⠈⠄⠐⠀⠄⠀⠀⠀⠀⠀⠀ 
