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