data <-
structure(list(x1 = c(3, 3, 2, 3, 3, 4, 3, 5, 2, 3, 4, 3, 3, 
3, 3, 2, 3, 3, 3, 4, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 
2, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 3, 4, 3, 3, 3, 2, 2, 3, 2, 3, 
2, 3, 4, 2, 2, 3, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 
4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 1, 3, 4, 2, 2, 
3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 4, 3, 3, 2, 2, 3, 4, 4, 4, 4, 3, 
3, 3, 2, 3, 3, 2, 4, 4, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 2, 3, 2, 
3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 
2, 3, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 4, 4, 4, 2, 4, 4, 3, 3, 3, 3, 3, 2, 3, 4, 3, 4, 3, 2, 3, 3, 
3, 4, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 4, 3, 4, 3, 
2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 
3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 4, 4, 4, 3, 3, 3, 
3, 2, 3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 
3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 
3, 2, 4, 1, 3, 3, 3, 2, 3, 3, 3, 1, 3, 3, 3, 4, 3, 3, 3, 4, 3, 
3, 3, 3, 4, 3, 3, 3, 2, 3, 2, 3, 3, 4, 3, 3, 3, 3, 4, 2, 3, 2, 
3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 3, 2, 3, 2, 3, 
2, 3, 3, 3, 2, 4, 3, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 2, 2, 3, 3, 
3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 5, 
4, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 1, 3, 3, 3, 
3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 
3, 4, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 4, 4, 3, 4, 2, 3, 3, 
4, 4, 3, 3, 4, 3, 3, 4, 2, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 4, 
3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 
3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 
3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 2, 3, 3, 3, 
3, 3, 3, 2, 3, 2, 2, 5, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 4, 3, 4, 
3, 2, 5, 3, 2, 2, 3, 3, 3, 3, 3, 1, 2, 4, 3, 3, 3, 2, 3, 4, 2, 
3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 
3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 2, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 
3, 4, 3, 3, 2, 3, 3, 3, 4, 4, 3, 2, 4, 4, 3, 3, 3, 4, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 2, 3, 4, 2, 3, 2, 3, 3, 2, 3, 2, 4, 3, 3, 
3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 3, 
3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 4, 3, 2, 4, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 
4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 
3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 
3, 4, 3, 3, 2, 3, 3, 3, 4, 2, 3, 2, 3, 3, 3, 3, 3, 2, 2, 3, 2, 
3, 3, 3, 3, 3, 3, 2, 3, 4, 4, 3, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 
2, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 2, 4, 2, 
3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 2, 3, 2, 3, 4, 3, 3, 4, 3, 3, 3, 
4, 3, 3, 3, 4, 3, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 
3, 3, 3, 2, 3, 4, 4, 3, 2, 2, 2, 3, 4, 2, 3, 3, 3, 2, 4, 3, 3, 
4, 3, 4, 2, 1, 4, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 2, 2, 3, 
3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 2, 3, 2, 3, 
3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 2, 3, 4, 3, 3, 4, 3, 3, 3, 
3, 2, 4, 3, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 
3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 4, 4, 2, 2, 3, 3, 3, 3, 2, 3, 
4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 
2, 3, 3, 2, 4, 4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 4, 3, 3, 
3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 2, 4, 3, 2, 3, 3, 
4, 3, 3, 3, 3, 4, 3, 5, 3, 2, 3, 4, 3, 3, 3, 2, 3, 2, 3, 4, 4, 
3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 2, 4, 4, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 
3, 2, 2, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 
3, 3, 3, 3, 4, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 
3, 3, 2, 3, 3, 3, 2, 4, 4, 4, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 
3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 4, 4, 3, 3, 3, 4, 2, 3, 3, 3, 3, 
3, 4, 3, 4, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 
3, 2, 3, 4, 2, 3, 3, 3, 3, 3, 4, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 
2, 3, 3, 4, 3, 3, 4, 2, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 
2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 
2, 3, 3, 3, 4, 2, 3, 4, 3, 3, 2, 2, 4, 3, 3, 3, 3, 1, 3, 3, 3, 
3, 4, 3, 3, 1, 3, 3, 3, 4, 3, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 
3, 3, 4, 3, 3, 3, 3, 3, 3, 2, 4, 3, 2, 4, 3, 3, 2, 3, 2, 3, 3, 
3, 3, 3, 4, 2, 3, 3, 3, 3, 1, 4, 4, 3, 2, 3, 3, 4, 3, 4, 2, 3, 
3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3), x2 = c(3, 
3, 2, 3, 3, 4, 3, 5, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 
2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 4, 3, 4, 3, 3, 4, 4, 
4, 4, 3, 4, 3, 3, 3, 2, 2, 3, 2, 3, 2, 3, 4, 2, 2, 3, 3, 2, 4, 
2, 3, 4, 2, 3, 3, 3, 2, 2, 3, 3, 3, 4, 2, 3, 3, 3, 2, 3, 2, 4, 
3, 2, 2, 3, 2, 2, 2, 1, 3, 4, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 
3, 4, 3, 3, 2, 2, 3, 4, 4, 4, 4, 4, 3, 2, 2, 3, 3, 2, 5, 4, 3, 
2, 4, 3, 4, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 4, 
3, 3, 3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 3, 4, 3, 3, 
2, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 2, 4, 4, 4, 2, 4, 4, 3, 3, 
3, 3, 3, 2, 3, 4, 3, 4, 3, 2, 2, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 
3, 5, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 
3, 3, 3, 2, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 2, 4, 3, 2, 3, 3, 3, 
3, 3, 2, 3, 3, 2, 4, 4, 4, 3, 3, 3, 3, 1, 3, 3, 3, 2, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 3, 2, 2, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 2, 4, 1, 3, 3, 3, 2, 3, 
3, 3, 1, 3, 3, 3, 4, 3, 3, 3, 5, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 
2, 3, 3, 4, 3, 3, 3, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 3, 2, 
3, 3, 3, 4, 3, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 4, 4, 4, 4, 
2, 4, 3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 
3, 3, 3, 4, 2, 3, 3, 4, 3, 4, 3, 5, 4, 3, 3, 3, 2, 3, 3, 2, 3, 
3, 3, 3, 3, 4, 3, 3, 3, 1, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 
2, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 3, 2, 2, 2, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 
2, 3, 2, 3, 3, 4, 4, 3, 4, 2, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 2, 
4, 3, 4, 3, 3, 3, 3, 2, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 2, 3, 3, 
3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 4, 3, 3, 3, 4, 4, 3, 4, 3, 3, 
3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 
3, 4, 4, 3, 3, 3, 4, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 5, 3, 
3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 2, 4, 3, 3, 3, 
3, 3, 4, 3, 3, 3, 1, 3, 3, 4, 4, 4, 3, 2, 5, 3, 2, 2, 3, 3, 4, 
3, 4, 1, 2, 4, 3, 3, 3, 2, 3, 4, 2, 3, 4, 3, 3, 3, 3, 2, 4, 3, 
3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 3, 3, 3, 1, 4, 2, 3, 3, 2, 3, 3, 
3, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 2, 3, 3, 3, 4, 
4, 3, 2, 4, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 
4, 2, 3, 2, 3, 3, 2, 3, 2, 4, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 
3, 3, 4, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 4, 3, 3, 3, 3, 3, 
3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 
3, 3, 3, 2, 3, 3, 3, 4, 3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 2, 3, 3, 
3, 4, 2, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 
3, 3, 4, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 
3, 4, 2, 3, 2, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 
2, 3, 2, 3, 3, 3, 4, 3, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 
4, 3, 3, 4, 5, 2, 4, 3, 4, 3, 3, 3, 2, 2, 3, 2, 4, 3, 3, 3, 3, 
2, 3, 3, 4, 2, 4, 3, 4, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 3, 2, 4, 
4, 2, 3, 2, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 2, 3, 
3, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 4, 3, 2, 
2, 2, 3, 4, 2, 3, 4, 3, 2, 4, 3, 3, 4, 3, 4, 2, 1, 4, 3, 3, 3, 
3, 2, 2, 2, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 
3, 3, 3, 4, 4, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 
3, 2, 3, 2, 3, 4, 3, 4, 4, 3, 3, 4, 3, 2, 4, 4, 4, 3, 2, 3, 3, 
4, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 4, 3, 3, 2, 
2, 3, 3, 4, 2, 2, 2, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 4, 
3, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 2, 4, 5, 3, 3, 3, 
2, 3, 2, 4, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 4, 3, 
3, 3, 3, 3, 3, 4, 3, 2, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 
3, 2, 3, 3, 3, 3, 2, 4, 3, 2, 3, 3, 4, 3, 3, 3, 3, 4, 2, 5, 3, 
2, 3, 4, 3, 3, 3, 2, 3, 2, 3, 5, 4, 3, 1, 3, 3, 3, 3, 3, 2, 2, 
3, 4, 3, 3, 3, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 
3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 4, 3, 
3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 4, 3, 3, 2, 3, 
2, 3, 2, 4, 3, 3, 4, 3, 2, 4, 2, 3, 3, 3, 2, 3, 3, 3, 2, 4, 4, 
4, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 
3, 4, 4, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 2, 4, 3, 
3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 3, 
3, 3, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 4, 2, 3, 
3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 
3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 2, 3, 4, 3, 
3, 2, 2, 4, 3, 4, 3, 3, 1, 3, 3, 3, 3, 4, 3, 3, 1, 3, 3, 3, 4, 
3, 2, 2, 3, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 4, 3, 3, 3, 3, 3, 3, 
2, 4, 3, 2, 4, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 
1, 4, 4, 3, 2, 3, 3, 4, 3, 4, 2, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 
3, 3, 5, 3, 3, 4, 3, 3), x3 = c(3, 3, 2, 3, 3, 3, 3, 4, 2, 3, 
4, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 3, 4, 3, 3, 3, 2, 2, 
3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 3, 2, 
3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 
4, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 4, 3, 3, 2, 2, 3, 4, 4, 
4, 4, 3, 3, 3, 2, 3, 3, 2, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 
2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 2, 4, 3, 3, 
3, 3, 3, 2, 3, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 4, 4, 4, 2, 4, 4, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 
2, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 
3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 
3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 4, 4, 
3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 
3, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 4, 3, 4, 3, 3, 
3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 2, 3, 3, 4, 3, 3, 3, 3, 4, 
3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 
3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 4, 2, 
2, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 
3, 3, 4, 4, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 
3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 
3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 4, 4, 3, 4, 
2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 4, 
3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 
3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 
3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 2, 
3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 
4, 3, 4, 3, 2, 4, 3, 2, 3, 3, 3, 4, 3, 3, 2, 2, 4, 3, 3, 3, 2, 
3, 4, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 3, 
3, 3, 3, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 2, 3, 4, 2, 3, 3, 4, 3, 
3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 4, 3, 2, 4, 4, 3, 3, 3, 4, 
3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 4, 2, 3, 2, 3, 3, 2, 3, 2, 
4, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 
3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 
2, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 2, 
3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 3, 3, 
3, 4, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 4, 3, 2, 
2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 4, 3, 3, 4, 4, 2, 4, 3, 3, 
3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 
2, 4, 2, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 2, 3, 2, 3, 4, 3, 3, 4, 
3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 
3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 2, 2, 3, 4, 2, 3, 4, 3, 2, 
3, 3, 3, 4, 3, 4, 2, 2, 4, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 
2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 2, 
3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 
3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 2, 2, 2, 3, 
3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 4, 3, 2, 2, 3, 3, 3, 
3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 4, 3, 
3, 3, 3, 2, 3, 3, 2, 4, 4, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 
2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 4, 3, 
2, 3, 3, 4, 3, 3, 3, 3, 4, 3, 4, 3, 2, 3, 4, 3, 3, 3, 2, 3, 2, 
3, 4, 4, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 2, 4, 4, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 
3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 
3, 4, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 
3, 2, 3, 3, 4, 2, 3, 3, 3, 2, 3, 4, 4, 3, 2, 3, 3, 3, 3, 3, 2, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 2, 3, 
3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 
2, 2, 3, 3, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 4, 4, 3, 
3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 
3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 2, 3, 3, 3, 4, 2, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 1, 
3, 3, 3, 3, 4, 3, 3, 1, 3, 3, 3, 4, 3, 2, 2, 3, 2, 3, 3, 2, 2, 
3, 2, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 2, 3, 
2, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 3, 2, 4, 4, 3, 2, 3, 3, 4, 3, 
4, 2, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3), 
    y1 = c(3, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 
    3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 
    3, 3, 4, 2, 2, 3, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 
    3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 
    3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 4, 3, 3, 2, 3, 
    3, 4, 4, 4, 3, 3, 3, 3, 2, 3, 3, 2, 4, 3, 3, 2, 3, 3, 4, 
    3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 4, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 
    3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 
    3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 4, 3, 3, 3, 
    3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 3, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 
    3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 
    4, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 4, 3, 3, 3, 3, 
    2, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 
    2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 
    3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 
    3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 3, 
    4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 4, 3, 4, 3, 3, 3, 
    3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 
    3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 
    3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 
    3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 
    4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 2, 4, 
    3, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 4, 2, 3, 
    4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 
    3, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 2, 3, 4, 3, 3, 3, 4, 3, 
    3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 
    3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 3, 
    3, 2, 3, 2, 4, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 
    2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 2, 
    3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 4, 4, 2, 4, 3, 
    3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 4, 
    3, 4, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 
    3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 2, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 
    2, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 2, 4, 3, 
    3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 
    3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 2, 2, 2, 3, 3, 4, 3, 
    4, 4, 2, 3, 3, 3, 3, 2, 3, 2, 3, 5, 3, 4, 3, 3, 2, 3, 3, 
    2, 4, 4, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 
    2, 3, 3, 3, 2, 3, 4, 3, 2, 2, 2, 3, 4, 4, 2, 2, 2, 3, 3, 
    3, 2, 3, 5, 3, 3, 3, 3, 2, 3, 3, 4, 3, 2, 3, 4, 2, 3, 3, 
    4, 3, 3, 3, 3, 2, 3, 3, 2, 4, 5, 3, 3, 3, 2, 3, 2, 4, 3, 
    3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 4, 3, 2, 3, 3, 
    3, 3, 4, 3, 2, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 
    2, 3, 3, 3, 3, 1, 4, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 2, 5, 
    2, 2, 3, 4, 3, 3, 3, 2, 3, 1, 3, 5, 4, 3, 1, 3, 3, 3, 3, 
    3, 2, 2, 3, 4, 3, 3, 3, 2, 4, 4, 3, 3, 3, 4, 3, 3, 3, 3, 
    3, 2, 4, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 2, 
    2, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 
    3, 3, 3, 3, 4, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 4, 3, 2, 4, 
    2, 3, 4, 4, 2, 3, 3, 3, 2, 4, 4, 4, 3, 2, 3, 3, 4, 3, 3, 
    2, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 3, 4, 3, 4, 4, 3, 3, 3, 
    4, 2, 3, 3, 3, 3, 3, 5, 4, 4, 3, 3, 2, 4, 3, 3, 3, 3, 3, 
    3, 3, 3, 2, 2, 2, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 3, 3, 3, 
    2, 3, 4, 2, 5, 4, 3, 3, 3, 3, 2, 3, 3, 5, 3, 3, 4, 2, 3, 
    3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 
    3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 4, 
    2, 4, 4, 3, 3, 2, 2, 4, 2, 3, 3, 3, 1, 3, 3, 3, 3, 4, 3, 
    3, 1, 3, 3, 3, 4, 3, 2, 2, 3, 2, 4, 2, 2, 2, 3, 2, 2, 3, 
    3, 4, 3, 2, 3, 3, 3, 3, 2, 4, 3, 2, 4, 3, 3, 2, 3, 2, 3, 
    2, 2, 3, 3, 4, 2, 2, 3, 3, 3, 1, 4, 4, 3, 2, 3, 3, 4, 3, 
    4, 2, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 4, 3, 
    3), y2 = c(3, 3, 2, 3, 3, 3, 3, 4, 2, 3, 4, 3, 3, 3, 3, 3, 
    3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 
    3, 3, 3, 4, 3, 3, 4, 4, 4, 3, 3, 4, 3, 3, 3, 2, 2, 3, 2, 
    3, 3, 3, 4, 2, 2, 3, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 2, 2, 
    3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 
    2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 4, 3, 3, 2, 
    3, 3, 4, 4, 4, 4, 3, 3, 3, 2, 3, 3, 2, 4, 3, 3, 2, 3, 3, 
    4, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 4, 3, 
    3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 
    4, 3, 3, 3, 3, 3, 2, 3, 4, 3, 4, 3, 2, 3, 3, 3, 4, 4, 3, 
    3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 4, 4, 3, 
    3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 2, 3, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 
    4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 2, 3, 
    3, 4, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 
    3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 4, 3, 3, 3, 
    3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 
    3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 
    2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 
    3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 
    3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 
    3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 
    3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 
    4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 
    3, 3, 4, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 
    2, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 
    3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 2, 
    4, 3, 2, 3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 3, 3, 3, 4, 2, 
    3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 
    3, 3, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 2, 3, 4, 3, 3, 3, 4, 
    3, 3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 4, 3, 2, 4, 4, 3, 
    3, 3, 4, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 4, 2, 3, 2, 
    3, 3, 2, 3, 2, 4, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 2, 3, 3, 3, 3, 3, 4, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 2, 4, 3, 3, 3, 3, 3, 
    3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 
    2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 4, 4, 2, 4, 
    3, 3, 3, 3, 3, 2, 2, 3, 2, 4, 3, 3, 3, 2, 2, 3, 3, 4, 3, 
    3, 3, 4, 3, 2, 3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 
    3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 2, 3, 3, 
    3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 
    2, 2, 2, 3, 4, 2, 3, 3, 3, 3, 4, 4, 3, 4, 3, 4, 3, 2, 4, 
    3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 2, 3, 4, 3, 3, 3, 
    3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 2, 3, 2, 4, 3, 4, 
    2, 4, 4, 2, 3, 3, 3, 3, 2, 3, 2, 3, 5, 3, 4, 4, 3, 3, 4, 
    3, 2, 4, 4, 4, 3, 2, 3, 4, 4, 3, 2, 3, 3, 2, 2, 2, 3, 3, 
    3, 2, 3, 3, 3, 2, 3, 4, 3, 2, 2, 2, 3, 4, 4, 1, 2, 3, 3, 
    3, 3, 2, 3, 5, 2, 3, 3, 3, 2, 3, 3, 4, 3, 2, 3, 4, 2, 3, 
    3, 4, 3, 3, 3, 3, 2, 3, 3, 2, 5, 5, 3, 3, 3, 2, 3, 2, 4, 
    3, 3, 3, 2, 3, 2, 3, 4, 3, 4, 2, 3, 3, 3, 5, 4, 3, 2, 3, 
    3, 3, 3, 4, 3, 2, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 4, 
    3, 2, 3, 3, 3, 3, 1, 4, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 2, 
    5, 2, 2, 3, 4, 3, 3, 3, 2, 3, 1, 3, 5, 4, 3, 1, 3, 2, 2, 
    3, 3, 2, 2, 3, 4, 3, 3, 3, 2, 4, 4, 3, 3, 3, 4, 3, 3, 4, 
    3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 
    2, 2, 3, 3, 2, 3, 4, 4, 3, 4, 3, 2, 3, 3, 3, 3, 3, 4, 4, 
    2, 3, 3, 3, 3, 4, 4, 3, 2, 3, 1, 2, 2, 4, 3, 3, 4, 3, 2, 
    4, 2, 3, 4, 4, 2, 3, 3, 3, 2, 4, 4, 4, 3, 2, 3, 3, 4, 3, 
    3, 2, 3, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 3, 4, 4, 3, 3, 
    3, 4, 2, 3, 3, 3, 3, 3, 5, 4, 4, 2, 3, 2, 4, 3, 3, 3, 3, 
    4, 3, 4, 3, 2, 2, 2, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 3, 3, 
    4, 2, 3, 4, 2, 5, 4, 3, 3, 4, 4, 2, 3, 3, 5, 3, 3, 4, 2, 
    3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 
    2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 
    5, 2, 3, 4, 3, 3, 2, 2, 4, 2, 3, 3, 3, 1, 3, 3, 3, 3, 4, 
    3, 2, 1, 3, 4, 3, 4, 3, 2, 1, 3, 1, 4, 2, 2, 2, 3, 2, 2, 
    2, 3, 4, 2, 2, 3, 3, 3, 3, 2, 4, 4, 2, 4, 3, 3, 2, 3, 2, 
    3, 2, 2, 3, 3, 4, 2, 2, 3, 3, 4, 1, 4, 4, 3, 2, 3, 3, 4, 
    3, 4, 2, 3, 2, 4, 2, 3, 3, 3, 3, 3, 4, 4, 3, 5, 3, 3, 4, 
    3, 3), y3 = c(3, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 2, 3, 
    3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 4, 2, 3, 3, 3, 3, 3, 3, 3, 
    3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
    2, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 
    2, 3, 3, 4, 4, 4, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 2, 3, 
    3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
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    3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 4, 3, 2, 3, 3, 2, 2, 3, 3, 
    3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 2, 3, 3, 
    3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 4, 2, 
    3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 2, 4, 4, 3, 3, 3, 3, 3, 2, 
    3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 
    3, 3, 3, 3, 4, 3, 2, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 
    3, 3, 2, 3, 3, 3, 3, 2, 4, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 
    3, 5, 3, 2, 3, 4, 3, 3, 3, 2, 3, 2, 3, 4, 4, 3, 2, 3, 3, 
    3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 2, 4, 4, 3, 3, 3, 3, 3, 3, 
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    3, 2, 2, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 
    4, 2, 3, 3, 3, 3, 4, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 
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    4, 3, 4, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 
    4, 3, 3), group = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
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    2, 2, 2, 2, 2)), .Names = c("x1", "x2", "x3", "y1", "y2", 
"y3", "group"), row.names = c(NA, -1500L), class = "data.frame")
