⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⡂⡂⢆⠲⡨⠢⡑⡌⡢⠢⡒⡐⢔⠠⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢆⢆⢇⢣⠱⡨⠪⡘⢌⠪⡢⡑⢌⢂⢪⢘⠔⡅⢕⠨⢂⠅⢅⠢⡂⡢⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢘⢜⢜⢜⢜⢜⢜⢸⠨⠪⡨⢌⢊⠢⡊⡢⡑⢌⢢⠱⡨⢢⢑⠡⢊⢢⢑⢌⢜⠸⡰⢰⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣜⢜⠜⡜⡜⡜⡜⡜⡔⡕⡅⡇⡇⢎⢢⠡⡃⣊⠢⡑⢅⢕⠑⢌⠢⠢⠡⡑⡌⢆⢕⠰⡑⢌⠢⡑⢔⠰⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡮⡺⡸⡸⡸⡘⡔⡕⢕⢕⢕⠜⡜⡘⡜⡌⡆⢕⢌⠢⡱⡘⢔⠔⡩⠢⡑⢅⠑⠌⢌⠢⡡⡑⢌⠢⠣⡡⠣⡑⡌⡢⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢤⢺⢪⡳⡱⣱⢱⢱⢱⢨⡪⡪⡢⡑⢕⠱⡡⡃⢎⢜⢐⠅⡕⡌⡪⡂⢕⢐⢅⢊⠢⡡⡑⠡⡈⡢⢊⠔⡡⡑⢌⠪⡨⡂⡪⡘⢌⠢⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣜⢵⢝⢎⢮⢺⢜⢎⢎⢎⢇⢇⢇⢪⠨⡢⡃⢎⢌⠢⡑⢔⢱⢨⣊⢢⢪⢨⢢⢣⢱⢑⢌⢦⣱⣐⢌⠢⡑⡰⡨⡂⢇⢢⢑⢌⠪⢪⠨⠢⡀⠀⠀⠀⠀
⠀⠀⠀⠀⡨⣞⣜⢎⢯⡫⢧⢣⢣⢳⢱⢱⢱⡱⣑⢬⠮⠮⠮⠷⠹⠽⠹⠽⠽⢟⢾⢵⣹⠽⠯⠯⢯⠯⠟⠽⠗⠯⠷⠽⠼⡼⣔⢕⢕⢔⢑⢜⠸⡐⡑⢕⢌⢂⠀⠀
⠀⠀⠀⡬⣞⢵⣳⢱⡣⡯⣪⡳⣝⣼⡼⣵⣯⡟⡊⣃⣤⣬⣴⣬⣦⣵⣥⣽⣬⣯⢿⣝⡾⣭⣽⣼⣵⣽⣽⡽⣽⣽⣽⢼⣤⣠⠘⢏⢧⡣⡕⡢⡑⢅⢕⢱⠨⡢⡨⠀
⠀⠀⡸⣝⣗⣝⢮⡳⣕⢯⣺⡺⡼⣷⣻⡯⠨⣰⣻⣻⡿⣻⠏⢏⠍⠯⢿⣽⣗⢯⢟⢼⢺⢝⣾⣺⡷⡿⡪⠪⠐⡨⠽⢟⣷⣻⣯⢠⠹⣳⡣⡣⡊⡢⠢⡑⢕⢌⢊⡂
⠀⢀⡯⣗⣗⢵⢳⢕⣯⣳⡳⡽⣽⣻⢿⣑⣷⣻⣻⣗⠁⠄⠌⠀⡈⢊⢿⣽⣾⡳⡝⡕⡝⡵⣳⣯⡫⠷⠀⠕⠄⠂⡨⠩⢷⣻⣞⢿⣪⣗⣗⠕⡌⠢⡑⢌⢆⢅⠣⡊
⢀⢪⣞⣗⣗⢵⢝⣕⢷⢵⢝⢽⣳⣻⣻⣻⢿⣻⡳⢕⢌⢐⢀⡁⢄⣖⣟⣻⢧⢣⠣⡃⡇⢯⢞⡾⣟⣗⣁⢅⠨⡐⡀⢠⢻⣳⢽⡹⡺⣞⣎⢇⢎⠌⡂⡂⠆⡆⠕⢌
⢸⣺⣺⣺⡪⣎⢗⡽⣝⡕⡯⣳⢯⣗⣻⣺⣟⣻⣷⡗⣦⣷⣷⣾⣟⣻⣻⢽⡪⡪⡪⢌⢎⢎⢗⣻⢽⢯⡿⣽⢾⢾⣞⡾⣝⢎⢇⢏⢎⢎⢎⢎⠢⡑⡐⢌⢌⠢⡑⢅
⣺⣺⡺⡮⡯⣮⡳⣝⣞⢮⡫⣞⢵⣳⣻⣺⣗⣯⣟⣻⣻⣻⡽⣗⡿⡽⡽⣱⢝⢮⣺⣽⢷⣏⢧⢳⡹⡕⣏⢏⡏⡯⣚⢎⢎⢇⢇⢣⢑⢕⠕⡅⢇⠢⡊⡢⢢⠱⡨⠢
⣞⢞⡾⡽⣝⣞⢽⢵⡳⣝⢮⡳⡝⣞⢮⣺⣪⣗⣗⣗⡯⣗⡯⣗⢯⢫⢯⢚⢮⣾⡽⠛⠫⣾⣯⢇⢗⢕⢕⢕⢝⢜⢪⢪⢪⠪⡪⢐⢑⠔⢅⠣⡑⢕⠬⡨⠢⡑⢌⠪
⣗⣟⢾⢝⣗⢽⣝⣗⢽⡪⡧⡳⣝⣾⢳⢟⡾⣚⣕⣻⣽⡺⡺⡜⡝⡎⣎⣗⣽⢗⢣⠐⠌⣻⣯⣷⡱⡕⡇⡇⡣⠪⡢⠡⡑⢅⠅⢕⢐⢅⢅⠥⡑⡅⢕⠸⡘⢌⠢⡱
⢗⣗⢯⣳⣝⣗⢷⢽⣕⢯⣻⡺⣮⡿⢪⣳⣻⣾⣾⣟⣷⣝⢮⢮⡪⣪⣺⣟⣻⠅⠈⠆⢁⠈⠯⣷⣻⢕⢕⢕⢌⢎⢆⡣⡪⣐⢅⢕⢌⠆⢕⠱⡘⢌⠢⡑⡌⢆⠣⣊
⢝⢾⢝⡮⣞⢮⢯⣳⢽⣕⢗⣽⣳⣟⡬⣻⣻⡿⣻⢿⣻⣻⣻⣻⣽⡷⣻⣚⠢⠁⢙⠄⠈⠎⢀⠻⡿⣯⣯⣧⣯⣷⣽⣮⣻⣞⣯⣯⣯⢇⢇⠕⡌⡢⡑⢅⠪⡘⡌⡆
⠸⡽⡽⣺⢽⢝⡽⣺⢵⣫⢗⣗⣟⣻⣻⣻⣻⣇⠆⢳⢰⡐⢜⡚⡣⣊⢢⠢⠡⠈⠄⠠⠠⢣⢂⢂⠐⢐⠑⡛⠗⠓⠃⠓⢑⠐⣸⣻⣳⢣⢣⢱⢨⠢⡑⠥⡑⢜⢌⠪
⠈⡪⣟⢮⢯⣻⡺⣝⣗⣗⡯⣻⣻⣻⣻⣷⡨⡐⢄⢐⢐⡘⣊⠂⡃⠄⡅⢌⠄⠂⠄⠃⡂⡔⢌⢐⠌⠄⡐⢁⠄⠄⠞⡀⣻⣻⡮⡣⡣⠣⡢⡣⡱⡱⡱⢡⢃⢇⢃⠁
⠀⠈⡾⡽⣕⣗⣟⢮⣗⣗⢗⣗⡯⣷⣻⣽⡿⣻⣇⡏⣆⣊⡐⡌⢔⢐⢸⣨⢈⢐⢨⠨⡢⠡⡢⣐⣐⠄⠄⡁⡐⡀⡀⡡⢐⣻⣻⢯⢇⢇⢇⢇⢊⢆⢪⢢⢑⠕⢌⠢
⠀⠀⢩⢟⣞⣞⣞⣗⣗⢵⡫⣞⡽⣳⣳⡳⣟⣻⣻⣻⣲⣜⢝⠾⢸⢰⡀⠇⣍⢢⠲⡐⣐⢨⢂⠆⣐⢌⢌⢂⣂⢢⠨⣘⣾⣻⢯⢏⢧⢣⠣⡊⡆⢕⢔⢕⢅⠣⡃⠇
⠀⠀⠀⡋⣾⣺⣺⡺⡮⣯⡻⣮⣻⡺⡮⣯⣻⢞⣻⣻⣻⣻⣻⣷⣮⠨⠘⡲⡨⠐⡁⡑⠌⡊⠂⢕⠰⣱⢶⠑⢴⣴⣻⣻⣟⡽⣝⢝⢜⢜⢜⢎⢎⢎⢖⢕⢕⢕⠡⠁
⠀⠀⠀⠀⢑⢗⣗⡽⣽⣺⢽⣺⡪⣯⣺⣺⡺⣽⣺⢽⣻⣻⣻⣻⣻⣻⣷⡥⡅⡗⡖⡆⡇⡆⠇⡗⠕⡵⣴⣾⣻⣻⣻⢿⢵⢹⢸⢸⢸⢸⢸⢸⢸⢸⢸⠸⡰⡁⠀⠀
⠀⠀⠀⠀⠀⠁⢳⢽⡺⡮⣳⣳⢽⣺⡪⣮⣻⣺⣺⢽⣞⣻⣻⣻⣻⣻⣻⣻⣻⣾⣶⣡⣪⣪⣮⣾⣻⣻⣻⣻⣟⡯⡯⣻⢸⢜⢼⢸⢪⢢⢣⢣⢣⢣⢣⠣⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠃⢯⢯⣳⡳⣝⣞⢞⣞⢮⣞⢾⢽⣺⣺⣽⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⢽⡺⡝⣕⢕⢕⢇⢗⢝⢜⢎⢮⢣⢣⠣⠣⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠫⢮⣻⡺⣪⢯⣺⢵⡳⡯⣻⢮⣗⣟⢾⢽⣯⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⢾⢝⢎⢮⢪⢪⢣⡫⣪⢣⡫⡺⡜⡜⠎⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠪⢻⡪⡷⣝⣗⢽⢽⣺⣳⡳⡽⡽⣽⡺⣽⣻⢿⣻⣻⣻⣻⣻⣻⢿⡽⡯⡯⡳⣝⣜⢮⡪⣣⢫⡪⣣⢳⠕⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⢞⡮⣯⣻⡺⡮⡯⣯⣻⡺⣮⡳⡯⣻⢽⣻⢿⣻⢿⢽⣫⢾⡹⣺⢝⣞⢮⡳⣝⢮⡳⡝⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠓⠳⠽⣝⢽⣺⡪⣟⢮⢯⣻⡪⣯⡺⣽⣺⢽⢽⣺⡳⣽⡺⣕⡗⣗⢝⠎⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠙⠼⠽⢕⠷⣝⢾⢽⡺⡮⡯⡳⡳⠝⠎⠎⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀