⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠤⢄⢆⢒⢒⠕⡒⡒⡲⠤⠤⢤⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠤⡒⡪⡑⡐⢅⠕⡐⢌⠢⡑⢌⢂⠪⠨⡊⢔⠡⡂⡪⠩⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠝⢳⡵⣲⢭⣢⢑⠌⠔⢌⢌⠢⡊⢌⠢⡑⢌⢂⠪⡨⢊⠔⡡⢊⠔⢌⠪⡐⢅⢢⣉⡧⣤⣲⡺⠊⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡁⠄⠙⢮⡳⣹⢹⡺⣜⡔⡐⢅⠪⡐⣑⢌⡢⡡⡑⢌⢢⢑⠌⡂⡪⣐⡥⣞⢮⢳⢕⣽⠞⠡⢀⠡⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⢅⠐⡈⠐⠠⠙⣮⡳⣹⢪⣫⡳⡧⣧⡑⡅⡲⢌⢎⠪⡩⢊⢥⡧⣗⢯⢳⢝⢮⢎⡷⡛⢐⠠⢁⠐⡀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣜⢂⠰⡰⢕⠕⠢⢆⢿⢼⡱⣕⢵⢝⡺⣪⢎⡪⡂⠆⢕⢌⡮⡯⡺⡪⡮⡳⡝⡮⡳⠙⠈⣒⢢⡐⠠⠐⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢌⢎⠂⢔⠎⢍⡁⠂⠀⢀⠈⠳⣕⢗⢵⢝⢎⣗⢽⢦⢯⢞⡝⡮⣎⠯⣎⢗⣝⢮⢇⠄⠀⠄⠈⡉⢇⢂⠁⣗⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡗⢁⠐⡤⠃⠁⢀⠈⠀⡀⡔⣖⢟⢵⡹⣕⢕⡗⣝⢎⢧⡫⣞⢮⡫⣎⢗⢵⡹⣕⢗⣴⡠⡀⠀⡦⡃⡎⡞⡆⢝⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡓⡀⡪⡢⣄⣅⢔⡴⣳⢹⣚⢎⡯⡳⡕⡧⡳⣝⢼⡱⣳⢹⢜⢭⣻⣜⢭⡣⣏⢾⣕⢧⡫⣺⢲⡬⡄⢊⣖⡪⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⡎⡫⡘⣮⢖⣝⡝⠎⡮⣣⢯⢮⢳⢕⢗⡯⢮⢳⡹⣚⠎⠇⠯⢎⣗⡝⡵⣕⢷⡣⣏⢞⣜⢾⣕⢝⡮⠁⠉⢟⣞⡆⡊⡓⢦⡠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡔⢞⠨⡂⢆⡳⣝⢵⡣⡧⣠⡰⡯⣻⡪⣳⡹⣽⣝⢕⣗⡝⣞⠔⠀⢀⡠⡴⡝⡮⣪⡻⡮⣎⢧⢳⣹⠳⢗⡗⣎⢗⢽⢜⢞⣮⠨⡂⣪⠽⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠓⠵⠌⣖⢽⢜⣕⢗⣝⢜⡮⢁⠘⣮⣺⢜⢾⡮⡳⡵⣝⢼⡹⣝⢜⢮⢳⡹⣪⡺⣚⣯⡪⣞⢵⣽⣴⣤⣽⣮⡳⡝⣎⢧⡫⣷⡊⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡝⣞⢵⢕⢧⢳⣝⣢⣾⣿⣿⣿⣿⣿⣽⣎⢟⡮⣣⡳⣕⢏⡗⡵⣝⡜⡮⡮⣗⣵⣿⣿⣿⣿⣿⣿⣎⢟⡞⣎⢧⡳⣕⡿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡾⣽⡪⣟⢎⡗⣝⢞⢾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣏⢿⣜⢜⣎⢧⡫⡺⡜⣎⢗⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⠄⣫⢞⣜⢮⢺⣺⢝⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡻⡪⣞⡮⡯⣇⢯⣪⡏⢼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⡷⡷⣝⣜⢮⢺⡹⣪⢗⢷⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⡃⢼⣣⢳⡹⣪⣞⢵⣫⠄⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢯⡺⡹⣜⢵⣏⣷⡣⡷⠱⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡘⡌⠑⠳⠵⠛⠺⠙⠉⡀⠣⣹⣿⣿⣿⣿⣿⣿⣿⡿⡸⣝⢎⢧⣟⡷⡳⣹⢮⡃⠀⠀⠀⠀
⠀⠀⠀⠀⣞⢵⡹⡪⡮⣳⢯⡺⣳⣽⡀⠙⢿⣿⣿⣿⣿⣿⣿⡿⡁⡢⠐⢀⠁⠄⢁⠈⠠⠈⠠⠀⠂⡀⢉⠻⢻⢿⢿⢿⠛⡉⡴⡳⡽⣝⡜⣎⢯⣺⡳⡣⠀⠀⠀⠀
⠀⠀⠀⣸⡣⣗⢝⢵⡹⣺⣇⢯⡪⡿⣱⢈⠀⠌⠋⡛⠻⠛⠫⠉⡐⠀⢂⠀⢂⠐⢀⠈⠄⠈⠄⢈⠠⠀⠄⡀⠂⡀⠂⠠⠐⠀⡈⠄⢺⢕⢽⡸⣕⣽⡪⡇⠀⠀⠀⠀
⠀⠀⠀⣞⢮⣪⢳⢳⣹⢵⢗⢷⡧⣯⣺⡲⡄⠂⠁⡀⠂⡈⢀⠂⠠⠈⡀⠐⡀⠐⡀⠐⠈⠠⠈⠀⠄⠂⠠⠀⠂⠠⠈⡀⠂⢁⠠⠐⣸⢝⢵⢕⢷⡳⡽⠀⠀⠀⠀⠀
⠀⠀⠀⢗⢧⢳⡹⡕⣗⢵⢻⢝⣷⡤⢀⠀⠄⢈⠠⠀⠂⠠⠀⢂⠠⠁⢀⠂⢀⠂⠠⠈⡀⠁⠄⢁⠐⠈⡀⠌⠐⠀⢂⠀⢂⠠⠀⣢⢟⢎⡗⣽⠻⠺⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠗⠳⠵⠏⢟⢮⡳⡹⣼⡺⣣⡠⠈⡀⠄⢈⠀⡁⢈⠀⡀⠂⡆⡄⡂⡄⡢⠡⠢⡌⡤⡄⡦⠕⠄⠐⠈⡀⠂⠐⢀⢰⢼⢝⢮⡳⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡸⣻⢮⡻⣦⣄⠐⢀⠐⠀⠄⠂⢀⠂⠠⠈⠐⠀⠂⠐⡀⠐⢀⠂⠠⠈⡀⢁⠐⢀⢈⡰⣼⣝⣞⠽⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⢷⣙⠹⢮⢑⠦⣄⡡⠐⠈⡀⠐⡀⠁⠌⢀⠁⡁⠠⠈⡀⠐⢀⠁⠠⣀⡢⡒⢅⠝⠚⠣⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠀⢀⠣⡂⡐⠨⠙⢒⠢⢕⠴⣬⡰⡠⡢⠔⠴⢴⣴⡼⡔⢞⢉⠂⡂⡐⢹⡀⠂⠀⠄⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠀⠁⠈⢀⠀⡀⢣⢂⠡⢁⠂⠌⢄⢕⢊⢗⡆⡦⢕⢵⢳⣳⣅⠍⡊⠲⠰⡐⠠⢱⡂⠐⠀⠠⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⡀⠁⢀⠀⢀⢸⢐⠨⠠⢨⠸⢈⢂⢮⢏⢎⢎⢎⢎⢎⢎⣞⢦⢂⠡⢁⢂⠡⢘⡆⠀⡈⠀⠠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠀⠀⠄⢸⢐⠠⢁⠂⢌⢰⢙⢜⢎⢎⢎⢎⢎⢎⠦⡹⢭⢳⡔⡐⠠⠨⢐⡅⠠⠀⠀⢢⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢄⠁⢀⠁⢀⢸⠂⢌⢐⠨⡴⢃⢜⡕⡕⡕⡕⡕⡕⡕⡕⡭⡪⢧⠚⢮⡈⠌⠰⡅⠠⠀⢁⠢⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡀⠁⠀⠂⡀⠠⠀⢸⡌⡐⡤⡋⢎⠠⣪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢇⢂⢻⢘⢌⠆⠀⠄⠄⠠⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠠⠀⠁⡀⠄⠠⢐⡝⡞⡞⠅⢌⢐⠠⡳⡱⡱⡱⡱⡱⡱⡱⡑⡕⡕⡕⡝⡆⢂⠅⠌⡣⢀⠁⢈⠀⠀⠂⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀