⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢮⢪⣺⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠮⣷⣧⣠⣄⣤⣄⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⡯⡫⣎⢮⢪⡲⡕⣕⢕⢝⢝⢖⢦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣎⢧⢳⡹⡜⡮⡪⣪⢣⢳⡹⡜⣕⢝⢎⢧⢳⢕⡳⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⡵⡱⣕⢵⡱⡕⣝⢜⢮⡪⡳⡱⣕⢝⢞⣮⡳⡱⣕⢕⡝⡼⡸⡪⡻⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⡳⡹⡜⡮⣪⢪⢎⢮⡪⣳⣗⢝⢜⢮⡪⣪⢣⢳⢻⡓⠷⣵⡝⣎⢮⣓⢷⣵⢹⢳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣞⢮⢺⢜⢮⡪⣪⢣⡳⢵⢕⣏⢿⡕⡧⡣⡳⡕⡝⣎⢧⢻⡪⠤⡽⣾⣪⡪⡪⡺⣻⣺⠞⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡠⠾⣪⣪⢣⡳⣕⢵⡱⣕⣝⡵⠿⠤⠍⢿⡜⣮⣺⣼⣱⢕⣵⢏⢗⢲⣄⠈⠹⢮⡳⣽⣞⡁⠀⠀⠀⠈⠑⣆⠀⠀⠀⠀⠀⠀⠀
⢀⠎⠁⠀⠀⠀⠉⠳⣕⢽⡧⣳⠟⠍⣕⢞⢎⢟⢺⢻⡎⠀⠀⠉⢩⡇⡇⡇⡗⡜⣧⠀⣬⢷⡫⣿⡀⡖⠀⡔⠀⢀⡷⡀⠀⠀⠀⠀⠀⠀
⣏⠀⠀⠀⠀⡄⠀⣄⢻⣕⡿⠁⢀⡞⡕⡕⡕⡕⡕⡕⣽⠄⠀⠀⠀⢷⣕⢕⢕⣕⡯⠀⢹⣳⢕⣵⢿⢙⠚⡑⢀⠊⠄⣳⠀⠀⠀⠀⠀⠀
⢞⢄⢀⢀⢀⡇⢀⣾⢷⡫⣻⠀⢸⣕⢕⢕⢕⢕⢕⢕⣽⢁⣀⣄⣄⣀⠉⠙⠙⠩⡐⡁⡂⠚⣷⣝⢽⡧⢀⢂⢐⠠⠑⡉⢦⠀⠀⠀⠀⠀
⠠⠈⡈⠉⠍⠍⣹⢎⢮⡪⣎⢧⣀⢙⠳⠳⠷⠷⠳⠋⢡⢎⢊⠒⢔⠪⠋⠀⠀⠀⠀⠀⠀⣠⣗⡿⣗⣿⠀⡐⠠⠐⡀⢂⠨⢧⠀⠀⠀⠀
⢀⠡⢀⠁⡂⠈⣟⣸⢱⢕⢵⡱⡝⣖⢧⡷⠁⠀⠀⠀⠸⡂⡂⠅⠢⡈⠂⠀⠀⠀⢀⣠⠶⣫⢻⢮⢯⣘⣇⢀⠂⢂⠐⠠⢀⢹⡄⠀⠀⠀
⠠⠐⢀⠂⠄⡁⣿⢸⢕⢭⡫⣟⠞⠺⠫⢤⣄⣄⣀⢀⠀⠁⠀⠁⠁⠀⠀⠠⠰⠊⡛⠲⣖⠏⡋⠋⠍⠡⠙⠦⡈⠠⠀⠅⠠⣸⠂⠀⠀⠀
⠐⢈⠠⠐⠠⡸⡓⠏⠫⠋⡉⠹⡄⠡⢈⠠⠀⡉⠙⠛⠽⢅⣀⠀⠀⠀⢛⡌⠠⠁⡐⠠⢨⡇⠠⠁⠌⠐⡀⠡⠈⠄⠡⢈⣴⠁⠀⠀⠀⠀
⠈⠄⠐⡈⠠⠁⠄⠂⡁⢐⠀⡁⠙⣧⣆⡔⡀⠂⡁⢁⠂⡐⠈⠓⢦⡀⠀⡇⠂⡁⣤⣞⣎⠂⠨⠐⠈⠄⠂⡁⠨⣠⣵⠚⠀⠀⠀⠀⠀⠀
⠈⠄⠡⠐⢈⠠⠁⢂⠐⡀⠂⠄⡁⠘⣮⢏⢿⡓⡚⠖⠶⢴⠥⣅⡄⠘⠪⠡⠚⠚⢷⣕⣝⣎⢄⣨⣐⣬⢴⢞⢯⣳⠯⠀⠀⠀⠀⠀⠀⠀
⣅⣌⡐⡈⠠⠐⢈⠠⠐⢀⢁⠢⡄⠁⢯⠳⠱⢇⣐⡀⡂⢸⡈⢆⠄⠡⣈⣤⢥⢮⡒⠬⡕⣍⠝⠹⠱⠵⠳⠷⠓⠋⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠈⠉⠉⠙⠙⠑⠓⠙⠙⠉⠉⢯⠂⣹⣌⡩⡰⣕⢽⡹⣝⡇⠀⢫⢏⢯⡪⡳⣕⢝⢦⢲⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⡳⣕⢗⢽⢜⢵⡹⣜⢾⡲⣞⣗⢗⢿⢝⡝⣷⡹⣕⢝⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡼⣕⢝⢮⡳⣕⢝⢮⣟⢼⡱⣝⢮⡪⡳⣕⢧⡫⣺⡳⣕⢧⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀
⠀⠄⠀⢀⠄⠀⡘⠀⠀⠀⠀⣼⢝⢮⡳⣕⢝⢮⡳⣽⢮⡳⡹⣜⢮⡪⡳⣕⢧⡫⣮⡳⣕⢧⡳⣳⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀
⠀⠀⢀⠃⠀⠐⠀⠀⠀⠀⢰⡗⣝⢮⡪⡸⣕⢧⡳⡝⡷⣝⢮⢮⢷⢽⢞⢾⢝⡝⡮⡺⣜⢵⡹⡪⣇⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢮⡪⣣⢹⡪⣎⢗⢵⡹⡪⣎⢗⣝⢕⢗⡝⡮⡳⣝⢮⡳⣕⢧⡫⡺⣪⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡳⡵⣝⣜⢵⡹⣪⢳⢕⡝⡮⣪⢳⢕⣝⢵⣹⢮⢗⣏⢧⡫⣎⢗⣝⣮⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀