2 3

15

The $3 ^ 2 = 9$ sequences and the value of $f$ for those are as follows: - For $A = (1, 1)$, we can make $X$ equal it with one operation with $(l = 1, r = 2, v = 1)$, so $f(A) = 1$. - For $A = (1, 2)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 2, r = 2, v = 2)$, so $f(A) = 2$. - For $A = (1, 3)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 2, r = 2, v = 3)$, so $f(A) = 2$. - For $A = (2, 1)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 1, r = 1, v = 2)$, so $f(A) = 2$. - For $A = (2, 2)$, we can make $X$ equal it with one operation with $(l = 1, r = 2, v = 2)$, so $f(A) = 1$. - For $A = (2, 3)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 2)$ , $(l = 2, r = 2, v = 3)$, so $f(A) = 2$. - For $A = (3, 1)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 1, r = 1, v = 3)$ so $f(A) = 2$. - For $A = (3, 2)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 2)$ and $(l = 1, r = 1, v = 3)$, so $f(A) = 2$. - For $A = (3, 3)$, we can make $X$ equal it with one operation with $(l = 1, r = 2, v = 3)$, so $f(A) = 1$. The sum of these values is $3 \times 1 + 6 \times 2 = 15$.