Let's define the matching number for two arrays X and Y, each with size n, as the number of pairs of indices $(i,j)$ such that $X_i = Y_j$ ($1 \le i,j \le n$).

You are given an integer K and two arrays A and B with sizes N and M respectively. Find the number of ways to pick two subarrays with equal size, one from array A and the other from array B, such that the matching number for these two subarrays is $\ge K$.

Note: a subarray consists of one or more consecutive elements of an array.

Constraints

• $1 \le N , M \le 2,000$

• $1 \le A_i \le 1,000,000,000$ for each valid i

• $1 \le B_i \le 1,000,000,000$ for each valid i

• $1 \le K \le NM$

Input format

The first line of the input contains three space-separated integers N, M and K.

The second line contains N space-separated integers $A_1, \dots, A_N$.

The third line contains M space-separated integers $B_1, \dots, B_M$.

Output Format

Print a single line containing one number denoting the number of ways to choose the pair of subarrays.