⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢔⢵⠁⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠆⠀⢀⢔⢵⢹⢊⡠⡺⣪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡮⡀⣔⢵⢹⢪⡫⡣⣏⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣎⢮⢻⢜⢮⡪⡳⣕⢝⢮⢳⢕⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⢝⢮⡪⡮⡳⡹⡜⣎⢧⢳⡹⡪⡳⣕⢝⢖⢝⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢗⢧⢫⡪⡳⡕⣇⢗⡝⣎⢧⢳⢕⢧⢫⢎⡗⡵⡹⣪⡣⢧⢳⢭⣓⢦⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⢻⢪⡣⣏⢞⢎⢗⡝⣜⢵⡱⣣⢳⡣⣏⢮⢳⢕⡳⡹⣪⢺⡪⣫⢳⢕⢮⡪⣇⢯⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣞⢵⢕⡝⡮⣺⡸⣪⢳⢕⢽⡸⣪⢺⢜⢵⡱⡕⡧⡳⣕⡽⡺⡜⡵⡹⣜⠵⣝⢮⡪⡮⣪⢳⡹⣔⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣝⢮⡪⡇⣗⢝⡇⣗⢵⢳⢝⢎⡞⡼⡱⡹⣸⢪⡳⡹⡜⡎⡮⣪⢵⢝⢮⢪⡫⣪⡾⡜⡮⡪⣇⢗⢵⡹⡕⡄⡀⠀⠀⠀⠀⠀
⠀⢀⡼⡱⡕⣇⢗⡝⣼⡝⡮⡺⡸⣕⢝⣕⢝⡺⣜⢽⢸⢱⢱⠱⡱⡱⡹⣸⢪⡺⡪⡣⣏⠮⣇⡛⢮⡳⣕⢝⡎⣞⢼⡱⡣⡆⡄⡀⠀⠀
⢰⡫⣎⢗⣝⢼⢱⡽⡰⡯⣪⢳⡹⡜⡵⣱⢣⢏⢮⡪⡣⡣⡱⡑⢕⠜⡜⡎⣇⢗⣝⡕⠷⢛⢷⢪⠢⡃⡇⢗⢝⠼⡪⢎⢯⢺⡌⢞⢜⠼
⢧⢳⡱⡣⣧⠗⡝⢌⢆⢿⣜⣵⡵⣝⢮⡪⣳⡹⣜⢎⡧⡱⡸⡘⡜⡜⣜⢽⣾⣟⠟⡀⡅⣮⡻⣎⢎⢎⡪⣪⡢⡛⡪⢪⢊⢆⢎⠪⠂⠀
⢕⢧⢛⢍⢆⢇⢇⢇⢇⣇⢯⢳⢤⣐⡉⢙⠻⢻⣟⢟⢽⢸⢸⢸⢸⢸⢰⢝⢼⣱⣪⡳⣝⢮⡺⣹⢳⣕⢜⢔⠜⡌⢎⠪⠘⠈⠀⠀⠀⠀
⢕⠕⡕⢕⢜⠢⡣⣑⢕⢵⣹⢕⣗⢗⡽⣕⢯⡳⣕⠯⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⢯⣪⢳⠽⡮⣣⢳⢬⡈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢱⠸⡨⡢⢣⡳⡱⣝⢵⡱⣏⡮⡳⢹⢨⢣⢪⢒⢍⢎⢎⢎⢎⢎⢎⢎⢎⢎⠎⣎⢲⡸⢜⡝⡮⡪⣇⡗⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠁⠁⠈⠱⣕⢽⡜⣎⢮⡪⢪⢺⠼⢌⡆⡇⢕⢅⡇⢎⢢⠣⡪⠲⢷⣯⣯⢞⢔⠋⠨⡢⡣⡯⡮⡃⠈⠪⡄⠀⠀⠀⠀⠀⠀⠀⢀⡮
⠀⠀⠀⠀⠀⢸⠎⠁⢧⢳⢕⠪⡪⢁⠠⠦⡢⣻⣾⣔⡜⢜⢔⡕⡱⢍⢎⢍⢎⣪⢸⢮⢖⢕⠼⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢜
⠀⠀⠀⠀⠀⠀⢀⣀⣳⣁⣣⣑⠃⠐⡕⡕⣕⠱⡙⡟⠿⠮⡦⡍⢎⢌⢆⢣⢊⢢⢱⢱⢱⡘⡀⡀⣀⣀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠽
⠀⠀⠀⢀⣤⢶⡺⣝⢽⡱⣣⡻⣺⢫⢪⢘⢆⢏⢮⢸⢸⢨⢪⠨⣊⠲⡱⡑⡕⢵⢱⢝⢜⢴⡹⢭⢳⢕⡝⡮⡺⡝⡷⣦⡀⠀⠀⠀⠀⠀
⠀⢀⣴⢫⢎⢧⡣⡧⡳⣱⢣⡳⣕⢝⡎⣎⢜⢜⢜⢜⢎⢞⢜⢱⢐⠕⢔⢕⢕⢇⢇⢧⢳⢕⡝⣕⢧⢳⡹⡜⣞⢜⡎⣏⢟⣷⢶⣠⣀⠀
⡺⡻⣜⢵⡹⣪⢺⢜⢞⣜⢵⡱⡕⡧⡫⣎⢧⣱⡡⢣⠣⡣⣡⠱⡰⢑⢱⢱⢱⡱⢕⣳⣹⣪⡺⡜⣎⢧⢳⡹⣸⡱⡝⣜⢮⢺⢗⣕⢯⢳
⢎⢗⢵⡱⡕⡧⡳⣹⢪⡪⡮⣪⢳⡹⡪⡎⡇⡆⡍⡇⢵⠨⡂⢇⢪⠸⡸⡸⡸⡚⡍⢆⢇⢧⢳⡹⡜⣎⢧⢫⡲⣕⢽⡸⣪⢳⢕⣕⢧⢳
⢷⡹⡪⣎⢗⢝⢪⢪⡳⡕⡧⡳⡕⡧⡫⡸⡐⡕⢜⢌⢆⢇⢣⠱⡐⢕⢊⢆⢇⢕⠜⡌⡆⡕⢕⢳⠽⣜⣮⡕⢜⢔⠱⡙⡜⡎⡗⣎⢮⡣
⣗⢝⢪⠪⡪⡸⡨⡺⢵⡽⢞⢺⢩⠫⡢⡱⡘⡌⡆⢇⢪⢂⢇⢝⢌⢎⢢⠣⡊⡆⡣⡱⡸⡨⡪⡊⡎⡪⢪⢫⣊⢆⢇⢣⠱⡑⡍⢮⡪⣎
⡔⢅⢇⢕⠜⡔⣱⢞⢕⠜⡜⡌⡆⡇⡇⡕⡕⢕⢜⠜⡔⢕⠜⢔⢍⢆⢕⢕⢅⢇⢕⢕⢜⢌⢆⢇⢕⢕⡑⡆⡣⡳⡸⡨⡪⢪⠸⡐⡎⢎