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>
using namespace std;
struct Node {
  int l, r;
  int maxv, lazy;
  void add(int x) { maxv += x, lazy += x; }
} nde[200007 << 2];
int a[200007], b[200007];
void up(int p) { nde[p].maxv = max(nde[p << 1].maxv, nde[p << 1 | 1].maxv); }
void build(int l, int r, int p) {
  nde[p].l = l, nde[p].r = r;
  nde[p].lazy = 0;
  if (l >= r) {
    nde[p].maxv = a[l];
    return;
  }
  int m = (l + r) >> 1;
  build(l, m, p << 1);
  build(m + 1, r, p << 1 | 1);
  up(p);
}
void down(int p) {
  if (nde[p].lazy) {
    nde[p << 1].add(nde[p].lazy);
    nde[p << 1 | 1].add(nde[p].lazy);
    nde[p].lazy = 0;
  }
}
void update(int l, int r, int p, int x) {
  if (l > r) return;
  if (l <= nde[p].l && r >= nde[p].r) {
    nde[p].add(x);
    return;
  }
  if (l > nde[p].r || r < nde[p].l) return;
  down(p);
  update(l, r, p << 1, x);
  update(l, r, p << 1 | 1, x);
  up(p);
}
int main() {
  int n, m, h;
  cin >> n >> m >> h;
  for (int i = 1; i <= m; ++i) a[i] = i;
  build(1, m, 1);
  for (int i = 0; i < m; ++i) scanf("%d", b + i);
  sort(b, b + m);
  int id;
  for (int i = 1; i <= m; ++i) {
    scanf("%d", a + i);
    id = lower_bound(b, b + m, h - a[i]) - b + 1;
    update(id, m, 1, -1);
  }
  int ans = 0;
  if (nde[1].maxv == 0) ++ans;
  for (int i = m + 1; i <= n; ++i) {
    scanf("%d", a + i);
    id = lower_bound(b, b + m, h - a[i]) - b + 1;
    update(id, m, 1, -1);
    id = lower_bound(b, b + m, h - a[i - m]) - b + 1;
    update(id, m, 1, 1);
    if (nde[1].maxv == 0) ++ans;
  }
  cout << ans << endl;
}
