Manao is solving a problem with the following statement:

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He came up with a solution that produces the correct answers but is too slow. You are given the pseudocode of his solution, where the function getAnswer calculates the answer to the problem:
    
    
      
    getAnswer(a[1..n], b[1..len], h)  
      answer = 0  
      for i = 1 to n-len+1  
        answer = answer + f(a[i..i+len-1], b, h, 1)  
      return answer  
      
    f(s[1..len], b[1..len], h, index)  
      if index = len+1 then  
        return 1  
      for i = 1 to len  
        if s[index] + b[i] >= h  
          mem = b[i]  
          b[i] = 0  
          res = f(s, b, h, index + 1)  
          b[i] = mem  
          if res > 0  
            return 1  
      return 0  
    

Your task is to help Manao optimize his algorithm.

Input

The first line contains space-separated integers n, len and h (1 ≤ len ≤ n ≤ 150000; 1 ≤ h ≤ 109). The second line contains len space-separated integers b1, b2, ..., blen (1 ≤ bi ≤ 109). The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print a single number — the answer to Manao's problem.

Examples

Input

5 2 10
5 3
1 8 5 5 7


Output

2
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:36777216")
using namespace std;
struct seg_tree {
  int l, r, s, mark, mn;
  int mid() { return l + r >> 1; }
} tree[150055 << 2];
void init_tree(int l, int r, int x) {
  tree[x].l = l, tree[x].r = r;
  if (l == r) return;
  int mid = tree[x].mid();
  init_tree(l, mid, (x << 1));
  init_tree(mid + 1, r, ((x << 1) + 1));
}
void push_down(int x) {
  if (tree[x].mark) {
    tree[(x << 1)].mark += tree[x].mark,
        tree[((x << 1) + 1)].mark += tree[x].mark;
    tree[(x << 1)].mn += tree[x].mark, tree[((x << 1) + 1)].mn += tree[x].mark;
    tree[x].mark = 0;
  }
}
void insert(int l, int r, int x, int num) {
  if (l <= tree[x].l && tree[x].r <= r) {
    tree[x].mark += num, tree[x].mn += num;
    return;
  }
  push_down(x);
  int mid = tree[x].mid();
  if (l <= mid) insert(l, r, (x << 1), num);
  if (r > mid) insert(l, r, ((x << 1) + 1), num);
  tree[x].mn = min(tree[(x << 1)].mn, tree[((x << 1) + 1)].mn);
}
int n, m, K, a[150055], b[150055], ans;
int main() {
  scanf("%d%d%d", &n, &m, &K);
  for (int i = 1; i <= m; i++) scanf("%d", &b[i]);
  sort(b + 1, b + 1 + m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    a[i] = lower_bound(b + 1, b + 1 + m, K - a[i]) - b;
  }
  init_tree(1, m + 1, 1);
  for (int i = 1; i <= m + 1; i++) insert(i, i, 1, m + 1 - i);
  for (int i = 1; i <= m; i++) insert(1, a[i], 1, -1);
  for (int i = m + 1; i <= n; i++) {
    ans += (tree[1].mn >= 0);
    insert(1, a[i], 1, -1);
    insert(1, a[i - m], 1, 1);
  }
  ans += (tree[1].mn >= 0);
  printf("%d\n", ans);
}
