De Prezer loves rectangles.He has a n × m rectangle which there is a number in each of its cells. We show the number in the j - th column of the i - th row by ai, j.
De Prezer also loves query. So he gives you q queries. In each query, he gives you number k and asks you to print the number of subrectangles of this rectangle that the difference between the maximum element and the minimum element in them is at most k .
The first line of input contains 3 integers, n, m and q .
In the next n lines, there are informations of the rectangle. i - th line among them, contains m space separated integers, ai, 1, ai, 2, ..., ai, m .
The next q lines, each line contains a single integer k (for that query).
1 ≤ n, m ≤ 400
1 ≤ q ≤ 10
1 ≤ ai, j ≤ 109 (for each 1 ≤ i ≤ n and 1 ≤ j ≤ m)
0 ≤ k ≤ 109 (for each query)
For each query, print the answer in a single line.
## Input
The first line of input contains 3 integers, n, m and q .In the next n lines, there are informations of the rectangle. i - th line among them, contains m space separated integers, ai, 1, ai, 2, ..., ai, m .The next q lines, each line contains a single integer k (for that query).1 ≤ n, m ≤ 4001 ≤ q ≤ 101 ≤ ai, j ≤ 109 (for each 1 ≤ i ≤ n and 1 ≤ j ≤ m)0 ≤ k ≤ 109 (for each query)
## Output
For each query, print the answer in a single line.
[samples]
Let $ n \in \mathbb{Z} $ with $ 1 \leq n \leq 10^5 $.
Let $ n = p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} $ be the prime factorization of $ n $, where $ p_1 < p_2 < \cdots < p_k $ are distinct primes and $ e_i \geq 1 $.
**Objective**:
Compute $ \sum_{i=1}^k p_i $, the sum of the distinct prime factors of $ n $, and store it in the first storage.