⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠺⣺⢮⣻⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣞⡾⣦⡤⣖⢯⣫⢯⣞⡯⣷⣫⣗⣗⣾⣳⢷⡯⣿⣷⡾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡽⣽⣻⡽⣾⣞⣯⣟⢞⢮⡳⡯⣿⡺⣝⣗⡷⣳⣟⣷⣻⡽⣯⢷⢷⣻⣽⣻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢯⣯⢿⡽⣾⣻⡷⣿⢝⡷⣝⢵⢝⡞⡮⡮⡳⣵⡻⣟⣾⣳⡯⣿⢽⣻⡽⣗⣿⣺⣟⣾⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣻⡽⡯⣿⡯⣷⢻⢝⡕⣟⢮⢯⣳⢝⡵⣯⢿⠵⣝⢮⡳⣯⢿⣽⢯⡗⡟⣽⣾⣷⣻⣞⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣳⣿⣪⡳⣝⢮⡳⡳⣝⢎⣗⢽⢜⣽⡹⣜⢮⡫⡮⡳⣝⢮⡳⡽⣝⣗⢷⢽⣺⢽⣟⣾⣫⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣞⢿⡺⣕⢯⡺⣕⡯⡯⡮⣳⢕⢯⣳⢽⣺⣪⡳⣝⢭⢯⢮⡳⣝⢞⢮⢮⡫⡯⡺⣝⢮⡳⣯⡯⡇⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣳⡽⡳⣝⢮⡳⣝⣮⡯⢯⢚⣞⢙⢉⠊⡠⠡⠉⠍⡋⡓⢓⠳⢽⢽⢽⣕⢗⣝⢮⣻⣺⢽⣪⡳⣝⢽⡕⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠉⠸⡽⣽⣪⡳⣝⢮⠎⠌⡐⡈⠏⡃⠄⡂⠂⠌⠌⢾⠻⢐⠐⡈⠄⡑⡑⣯⡳⣕⢯⡺⣞⢵⡳⣝⣯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡺⣝⡽⡮⣲⢝⢮⡳⡅⣅⣦⣬⣨⠐⡐⠠⠡⢁⠊⣄⣬⡴⡴⣴⣅⡐⡀⢺⡺⣪⡳⣝⢞⡵⣝⢮⡺⣮⡫⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢵⢝⢮⣫⡳⣝⣝⢿⠅⠂⣮⡗⠄⠅⢊⢀⠂⠞⠁⣾⣳⡌⢟⠋⡀⣺⢝⢮⣺⡪⣗⣝⢮⢳⢝⢷⡹⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⡵⣝⢷⢽⣔⢀⠂⢽⣻⠈⠌⠠⠂⠌⡀⠠⣟⢾⢃⠠⠨⢠⢗⣽⢵⡳⣝⢮⢮⡳⣝⣽⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⡴⣲⢽⢕⡯⣮⡫⡆⡅⠕⡰⢐⠈⠌⣌⠨⠠⢁⠂⢄⠨⠨⠢⡑⠅⡋⢍⡼⡯⣫⢮⣳⣳⢿⣺⢺⡪⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣪⣗⢽⢽⢽⣻⢾⣌⠄⠅⠌⡐⡀⡊⠄⠡⡈⠄⡂⠅⠅⠂⢅⣢⡽⣝⣞⣮⢷⣻⡺⣝⢮⡳⣝⢮⢯⡻⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢧⣗⣯⢯⣻⣺⣳⢽⣳⢮⣔⣀⠢⠰⡈⡐⠠⢁⣐⢨⣴⣳⣻⣺⣻⣼⣺⣳⢯⣞⡽⣮⡳⣝⡮⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢽⡳⠷⢻⡽⣺⢽⣺⢽⢽⣳⢖⡮⡪⣧⢮⡻⡪⣞⢾⣺⣞⡾⣽⣺⣳⣳⣻⢵⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡯⣯⠳⢯⣻⣺⣽⣿⣲⣼⣟⣯⣟⣾⣻⡽⣞⣯⣷⡳⡗⠷⠽⠽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣸⢌⢏⣛⡅⢾⡫⣿⡽⣞⣯⢿⢾⣺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⣪⣑⡕⡤⣝⡷⣟⣯⢿⡽⣞⣟⣯⢷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⢿⡽⣾⣺⡯⣟⣯⢿⣽⢯⡿⣽⢯⣟⡾⣯⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⢿⡽⣗⣯⢿⡽⣞⣯⡿⣯⢿⣽⣻⣞⣯⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡽⣯⢿⡽⣞⣯⢿⡽⣞⣿⣽⣻⣞⣷⣻⡾⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠝⡫⡻⠽⡻⡞⠏⢿⢹⢷⣗⣿⣺⣷⣻⡽⣗⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⣱⡦⣮⢮⣬⣮⣵⡵⣞⣯⢷⡯⣿⣺⣗⣿⢽⡯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣯⣿⣽⣯⡷⣿⣞⣿⢿⢺⠻⢝⢗⢛⢞⢿⠻⠟⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣻⣾⣳⣯⡿⣷⣻⣽⢏⢆⠣⢃⠪⢘⠸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣞⣯⣷⢿⣯⢿⣞⠁⠔⢈⠄⠌⠄⠌⡰⠁⠀⠀⠀⠀⠀⠀⠀⣸⢝⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣯⡷⣟⣯⣿⣻⠐⡁⠌⠄⢂⠡⠨⢐⠜⠀⠀⠀⠀⠀⠀⢀⡴⣫⡳⣝⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣦⢤⡀⠀⠀⢀⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣽⣞⣿⣻⣶⡴⣽⡯⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡲⣳⡫⡯⡳⣟⡾⡯⣿⣻⢽⡻⣝⣖⢦⣀⡀⠀⠀⢀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⣀⡠⡮⣳⡳⣝⢮⢮⡫⣝⢮⡺⣝⢗⡽⣳⢻⢮⢮⡳⡵⣝⢖⡞⡮⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢯⢏⣗⡽⣞⣯⢿⣻⣻⡽⡿⣮⢳⢝⣎⢗⣝⢮⡳⣝⢵⡻⣗⣷⣳⡽⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡮⣫⣳⡯⣿⢽⣞⣯⣟⣷⣻⣟⡗⡽⣱⢳⡳⣕⢗⣝⢮⡳⣝⣿⣺⢷⡿⣮⢻⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡯⡳⣝⢮⡺⣫⢿⣽⢷⣻⣾⣳⢿⢵⡹⣚⢎⢧⡫⡮⡳⡕⡷⣝⢽⢿⣞⣟⣿⢽⡳⣕⢯⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢝⢮⡫⡮⡳⣝⢮⡳⣝⢽⡻⣞⢯⢳⡱⡕⣕⣝⡜⣜⢜⣜⢎⢮⢪⣪⣻⣯⢟⢾⢟⣝⢎⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⡳⣝⢮⡫⡮⡳⡝⣎⢷⢝⡮⡮⡣⡧⣻⡽⣞⢼⢜⡜⡮⣳⢹⣪⢎⢮⢯⢧⡳⣝⢮⡳⡵⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⣎⣗⢝⢮⣫⡺⣪⢿⢝⠜⡜⡸⡘⢆⠣⠪⠸⠨⡊⠪⠪⡙⣟⡯⡻⣪⡳⣹⢼⡱⣳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡦⣺⡪⡮⡫⡧⡣⣏⢾⠕⡁⢧⢕⢾⣽⡙⢎⢧⠡⢁⠂⢅⠱⣼⡍⢝⢾⢕⣝⢮⡺⡺⣪⡳⣢⡲⡪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣝⢞⢮⢮⡫⡮⣫⡺⣪⢳⡣⠂⡂⠕⣿⣳⡯⠂⠨⠠⠡⠨⢐⢸⣽⡆⠐⡼⣕⢕⡗⣝⣝⢮⢮⡳⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣕⢗⣽⣳⢳⢝⢞⢮⡺⣪⡳⢽⡰⡐⢅⢓⠳⢋⠄⠅⡊⠨⡈⡐⡸⢳⢡⢨⡳⣕⢗⣝⢮⣪⡳⡵⡝⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠳⢳⢽⣕⢏⢯⡺⣺⣪⡺⡳⠝⠞⡐⡐⠨⢐⠠⡁⡂⠅⡂⡂⠝⡐⠕⡳⡽⣺⡳⣕⢗⢵⢝⢮⡫⡞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡠⣖⢗⣕⢯⡳⣝⢵⣫⢯⣟⡧⣥⣂⠌⠌⡐⡐⡐⠄⡱⢘⢐⢐⠠⣡⡲⣯⣳⣝⢮⡫⡳⣝⢵⢝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠱⣕⢗⣝⢮⡳⣝⣗⣗⣟⣞⣞⢽⣳⢆⢦⢢⢅⣆⢦⣲⣲⣝⢷⣝⣞⣞⢼⣚⢮⡫⡎⠫⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢮⢗⢽⣪⣺⢼⣞⣞⢾⢽⣟⣿⡾⣾⢾⣾⣻⡺⣮⣺⣳⡳⣽⣺⣽⡪⣗⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠄⠑⠝⣟⣞⣾⢽⢯⢫⢳⢟⢿⢻⠷⡹⣹⣺⢺⢞⠙⠑⠑⠑⠉⠁⠀⢠⠢⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⠊⢅⠱⢹⣇⠇⡎⡪⡪⡪⢪⢢⢫⡧⡧⡧⣄⣀⢤⢔⡄⠀⣗⠨⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡠⢁⠢⠨⠨⣷⡁⡊⠌⠌⡊⠌⡂⡂⢿⢽⡺⡜⡼⡱⣣⢻⡪⡪⡪⡡⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡁⡂⡂⢌⢐⢁⢚⡧⠠⠡⢁⠂⠅⡂⡐⣹⡽⣽⡪⡳⡹⡜⣕⢷⡑⡕⡆⡹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡯⡀⠢⢐⠐⡐⢔⣴⣿⣿⣷⣤⡡⢑⢐⣰⣷⣿⣷⡫⣇⢯⢺⢜⠮⡪⠢⣣⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⣟⣿⣻⣗⡷⣾⢽⣯⢿⡾⣟⣯⣿⣖⣾⣿⣻⣷⡅⠈⠊⠁⠁⢁⡀⡀⣼⣻⣞⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣟⣾⣳⡯⣿⣽⣻⣞⣯⢿⡽⣞⡷⣯⢿⡾⣽⡞⡣⡢⠪⣗⡪⡪⡩⢹⣺⡷⣯⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢾⣳⣯⢷⢿⡽⣞⡷⣯⢿⡽⣯⣿⡽⣾⣟⣿⣽⡗⠡⠠⡁⡚⣧⣂⠪⠑⣕⡿⣽⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣗⣯⣟⣯⢿⡽⣯⣿⣽⣟⡿⣞⣿⣟⣾⣻⡾⢈⠌⢂⠂⡂⠸⣶⣟⣯⢿⡽⣯⢿⣺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣀⠀⠀⠀⠀⠉⣾⢷⣟⣿⣻⡿⡾⣷⢿⣻⣟⣯⢿⣽⣻⣽⢦⠨⢐⠈⣄⡷⣟⣯⡿⣯⢿⡽⣯⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢞⢶⡠⡀⠀⠐⢿⡽⣯⢿⡽⣽⣻⣽⣻⡽⣾⢽⣻⢾⡽⣯⡿⣷⣢⡷⣟⣿⢯⡿⣯⣿⣻⣽⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣝⢽⢕⢯⡳⡵⡴⣌⣿⢽⡯⣿⢽⣳⣟⡾⣯⢿⡽⣯⢿⡽⣯⣿⢿⣽⡂⠙⢽⣟⣿⣽⢾⣻⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⡳⣝⢵⢝⣞⡺⡪⣞⢯⣿⢽⡯⣷⢯⡿⣽⢯⡿⣽⣯⢿⣻⣾⢿⣽⢷⠀⠀⠁⠙⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀