⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⣔⢖⣖⢮⣖⢗⡵⡫⣞⢮⣖⢶⣲⡲⣔⡤⣠⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡲⣝⠵⠳⡙⡊⠣⢑⢈⢂⠂⠅⡂⠅⡂⠢⠠⡁⡂⢅⠑⠍⡓⠕⠯⣺⣲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣲⡳⡳⢙⠩⠠⠡⡁⠢⠨⠨⢐⠐⠄⠅⠅⡂⠅⡂⠅⠅⡂⡂⡂⠅⠅⡂⠅⠅⡂⠌⠕⠳⢝⢷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⡳⡓⡑⡐⡐⡐⠨⡈⠢⠨⠨⠨⠨⢐⠨⠨⡈⡂⡂⠅⡂⠅⠅⡂⡂⡂⠅⠅⡂⠅⡊⠄⡑⠨⠨⠠⠩⢙⠮⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣞⡕⡃⡂⡂⡂⡂⠢⡈⠢⠨⠨⠨⠨⠨⠨⢐⠨⢐⢐⠐⠄⠅⡂⠅⡊⠄⡂⡂⠅⠅⡂⠅⡂⠅⠌⠌⠌⠌⢌⢐⠨⠨⠳⡻⡦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⢞⠮⢃⢐⢐⢐⢐⢐⠨⢐⠨⠨⠨⠨⠨⠨⠨⠨⢐⠨⢐⠠⠡⠡⡁⡂⠅⡂⠅⡂⠔⢁⠅⠂⠅⡂⠅⡡⠡⠡⢑⠐⡐⠨⠨⢐⠨⠹⣝⡦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢼⣪⠫⠨⢐⢐⢐⢐⢐⢐⠨⢐⠨⠨⠨⠨⠨⠨⠨⠨⢐⠨⢐⠨⢈⢂⢂⠂⠅⡂⠅⡂⠌⠔⠨⡈⡂⡂⠅⡂⠅⡊⡐⠨⠠⠡⠑⢄⢑⢐⠨⢺⢵⡄⠀⠀⠀
⠀⠀⠀⢀⢮⠯⢂⠌⠌⡐⡐⡐⡐⡐⡐⠨⢐⠨⠨⢈⠌⠌⡐⠡⡁⠢⠨⢐⠨⢐⢐⠠⠡⡁⡂⠅⡂⠅⠅⠅⡂⡂⡂⠅⡂⠅⡂⠌⠌⠌⠌⢌⢐⢐⢐⠨⡀⢳⣫⢆⠀⠀
⠀⠀⠀⡮⡯⢑⢐⠨⢐⢐⢐⢐⢐⠠⢂⢑⢐⠨⠨⢐⠨⢐⢈⠢⠨⠨⠨⢐⠨⢐⢐⢈⢂⢂⠂⠅⡂⠅⠅⠅⡂⠔⠠⡁⡂⠅⡂⠅⠅⠅⡑⡐⡐⡐⡐⡐⠨⡀⢳⣫⢆⠀
⠀⠀⡸⣝⠕⡐⡐⠨⢐⢐⢐⢐⢐⠨⢐⢐⢐⠨⠨⢐⠨⢐⢐⠨⠨⠨⠨⢐⠨⢐⢐⢐⠐⠄⠅⠅⡂⠅⠅⠅⡂⠅⠅⡂⡂⠅⡂⠅⡊⡐⡐⡐⡐⡐⡐⠨⢐⠨⠠⣳⣳⠀
⠀⠀⡽⣎⢂⢂⠂⠅⠅⡂⢂⢂⠂⢌⢐⢐⢐⠨⠨⢐⠨⢐⠐⡨⠨⠨⠨⢐⠨⢐⢐⢐⠨⠨⡈⡂⡂⠅⠅⡡⢂⠡⢁⢂⠂⠅⡂⠅⡂⡂⡂⡂⡂⠢⠨⠨⢐⠨⢐⢘⢮⠇
⠀⠠⣻⡪⢐⢐⠨⡈⠢⠨⢐⠠⢑⢐⢐⢐⢐⠨⠨⢐⠨⢐⠨⢐⠨⢐⢁⠢⠨⢐⢐⢐⠨⢐⢐⠐⠄⠅⠅⡂⡂⠌⡂⡂⠅⠅⡂⠅⡂⢂⢂⠢⠨⠨⠨⠨⢐⠨⢐⠈⡯⡧
⠀⠈⢞⣵⣐⢐⢐⠨⠨⠨⢐⠨⢐⢐⢐⢐⢐⠨⠨⢐⠨⢐⠨⢐⠨⢐⢐⠨⠨⢐⢐⢐⠨⢐⢐⠨⠨⡈⡂⡂⡂⠅⡂⡂⠅⡡⢂⠡⢂⢁⠢⠨⠨⠨⠨⠨⢐⠨⠠⡱⡽⡍
⠀⠀⠀⠓⠽⣕⢧⢮⢬⢌⣔⢨⢐⢐⢐⢐⢐⠨⠨⢐⠨⢐⠨⠠⠨⢐⠠⢊⠨⢐⢐⢐⠨⢐⠐⡨⢐⢐⢐⠐⠄⠅⡂⡂⠅⡂⡂⢌⢐⢐⠨⠨⣐⢡⡡⣪⢔⡮⡯⡫⠋⠀
⢔⢴⡸⡜⣎⢎⢏⢝⢙⠕⠫⠯⡫⠯⡞⣞⢮⢞⣞⣖⣗⢶⡺⣜⣮⣲⡪⣖⡼⣲⡲⣲⢜⣖⡼⡴⣲⣲⡲⡮⣺⡲⣖⢾⣜⣖⣗⢵⣳⡳⡫⡟⡞⠵⡫⡳⡝⣎⢦⢢⢤⢠
⠁⠁⣱⣽⡼⡵⣹⢜⢮⣪⡫⣲⢲⡱⡔⣔⢤⡡⣂⣐⠨⡨⠨⢁⠅⠅⡩⠁⠍⠌⡊⠡⠩⡈⡊⡉⠅⠅⡩⠉⠌⠌⡊⠌⡐⠠⢂⢡⢠⢢⠬⡔⣆⢧⡣⣳⡹⣜⢮⣧⣗⠁
⠀⢐⣿⣳⣫⣻⡺⣝⣗⣗⢽⢮⣳⡳⣝⡮⣮⡺⣜⣜⣕⢧⡫⣲⢪⡲⡔⡥⢥⡡⣂⢅⢅⠂⠔⠠⡁⡅⣄⢥⡡⡕⡴⣱⢪⡫⣣⢏⡮⡧⣯⣺⣺⡺⡮⣳⢽⣺⡳⣽⣻⡆
⠀⢸⣽⣗⢗⣗⡽⡵⣳⡳⣝⣗⢷⢝⣗⡽⡮⡯⣞⣞⢮⣗⢯⣞⢵⣳⣝⢮⢧⡳⣕⢧⡳⡹⡭⡳⣕⣝⢼⢼⣜⡮⣗⢷⣝⢾⣕⣟⢮⣻⣪⢞⡮⣞⡽⣵⡫⣞⡮⡷⣟⡇
⠀⠐⣿⢾⣝⣞⢮⢯⣳⣝⣗⢗⡯⣯⣺⡺⣝⢾⣕⢷⣝⡮⡷⣝⣗⢗⣗⢯⢯⣫⢞⡽⣺⢽⢝⡾⡵⡽⡽⣕⢷⣝⢾⢵⣳⢽⣪⢞⡽⣺⡪⣟⢮⢷⢝⣞⡮⡷⡽⣽⢿⠅
⠀⠀⠘⣿⢾⣮⢯⢯⡺⣮⡺⣝⣞⣞⢮⢯⣺⣳⡳⡽⣺⡪⣟⢞⡮⣯⡺⡽⣕⡯⣳⢯⡳⡯⣳⢏⡯⣞⡽⣺⡳⣳⣝⣗⢷⢝⣞⡽⣺⢵⣫⢗⡯⡯⣫⢞⣞⣽⣾⣻⠏⠀
⠀⠀⠀⢀⣹⢽⢿⣻⣟⣷⢿⡷⣷⢷⣟⣷⢷⣗⣯⣯⣷⢯⣷⣻⡾⣮⣯⢿⣮⣟⣮⣷⢯⣟⣾⣽⣞⣷⣽⢷⣽⣗⣷⣳⣯⢿⣺⣾⣳⡿⣞⣿⢾⣻⣟⣿⡽⣷⣫⠀⠀⠀
⠀⠀⣔⢷⠝⠩⡁⡂⡂⠔⡁⢅⢑⠩⠨⢉⠍⠩⡉⠕⠩⢙⠩⢉⠫⢙⠩⢋⠓⡙⡙⢚⠙⠝⡙⢊⢋⢃⢋⢋⢃⠫⡉⡋⡊⠫⠩⢑⠩⢉⠍⠌⠅⠅⡂⠔⡈⡊⢞⡽⣂⠀
⠀⢐⣗⢇⠡⡁⡂⡂⡂⠅⡂⡂⠢⠨⠨⢐⢈⢂⠂⢅⢑⢐⠨⢐⠨⢐⠨⢐⠨⢐⠨⠠⠡⡁⡂⠅⡂⢂⢂⢂⢂⢂⢂⠢⠨⠨⠨⢐⠨⢐⠠⠡⠡⡁⡂⠅⡂⡂⠅⣝⣞⠄
⠀⢸⣺⡐⡐⡐⡐⡐⠄⠅⡂⡂⠅⠅⡑⡐⡐⠄⡑⡐⡐⡐⠨⢐⠨⢐⠨⢐⠨⢐⠨⠨⢐⠐⠄⠅⡂⠅⡂⡂⡂⡂⠢⠨⠨⠨⠨⢐⠨⢐⠨⡈⡂⡂⡂⠅⡂⡂⠅⣸⣺⡂
⠀⢘⢮⡂⡂⡂⡂⡂⠅⠅⡂⡂⠅⠅⡂⡂⡂⠅⡂⡂⠢⠨⠨⢐⠨⢐⠨⢐⠨⢐⠈⢌⢐⠨⡈⡂⡂⠅⡂⡂⡂⠌⠌⠌⠌⠌⢌⢐⠨⢐⢐⢐⢐⠐⠄⠅⡂⡂⠅⣜⣞⠄
⠀⠀⢯⣳⣐⢐⠐⠄⠅⠅⡂⢂⠅⠅⡂⡂⡂⠅⡂⡂⠅⢅⢑⢐⠨⢐⠨⢐⠨⢐⠨⢐⢐⢐⢐⠐⠄⠅⡂⡂⡂⠅⠅⠅⠅⠅⡂⠢⠨⢐⢐⠐⠄⠅⠅⠅⡂⡂⣥⣳⡓⠀
⠀⠀⠀⠓⢽⣪⢮⣪⢬⣰⢨⣐⡠⣁⡂⡂⡂⢅⢂⠂⠅⡂⡂⠢⠨⢐⠨⢐⠨⢐⠨⢐⠐⡐⠄⠅⠅⠅⡂⡂⡂⠅⠅⡡⠡⠡⡨⠨⡨⣐⣐⡨⣨⡨⡬⣔⢶⣕⠷⠑⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠊⠓⠙⠕⠳⠝⠞⠞⠽⠝⢗⠽⡝⡯⡳⡽⡽⡽⣕⡯⣳⢽⡺⡮⣳⢽⡺⡽⣝⡽⣝⣞⢞⣞⢽⢽⢺⢝⢟⢞⠽⠳⠳⠵⠫⠳⠹⠙⠊⠁⠀⠀⠀⠀⠀