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;
const int N = 150005;
int n, len, h, a[N], b[N];
struct TNode {
  int l, r, v;
} t[N << 2];
int lazy[N << 2];
inline int lc(int pos) { return pos << 1; }
inline int rc(int pos) { return pos << 1 | 1; }
void build(int pos, int l, int r) {
  t[pos].l = l;
  t[pos].r = r;
  if (l == r) return;
  int mid = (l + r) >> 1;
  build(lc(pos), l, mid);
  build(rc(pos), mid + 1, r);
}
void pushdown(int pos) {
  t[lc(pos)].v += lazy[pos];
  t[rc(pos)].v += lazy[pos];
  lazy[lc(pos)] += lazy[pos];
  lazy[rc(pos)] += lazy[pos];
  lazy[pos] = 0;
}
void modify(int pos, int l, int r, int v) {
  if (l > r) return;
  if (t[pos].l == l && t[pos].r == r) {
    t[pos].v += v;
    lazy[pos] += v;
    return;
  }
  pushdown(pos);
  int mid = (t[pos].l + t[pos].r) >> 1;
  if (r <= mid)
    modify(lc(pos), l, r, v);
  else if (l > mid)
    modify(rc(pos), l, r, v);
  else
    modify(lc(pos), l, mid, v), modify(rc(pos), mid + 1, r, v);
  t[pos].v = min(t[lc(pos)].v, t[rc(pos)].v);
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> len >> h;
  for (int i = 1; i <= len; i++) cin >> b[i];
  sort(b + 1, b + len + 1);
  build(1, 1, len);
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    a[i] = lower_bound(b + 1, b + len + 1, h - a[i]) - b;
  }
  for (int i = 1; i <= len; i++) modify(1, i, i, -i);
  for (int i = 1; i < len; i++) modify(1, a[i], len, 1);
  int ans = 0;
  for (int i = len; i <= n; i++) {
    modify(1, a[i], len, 1);
    if (t[1].v >= 0) ++ans;
    modify(1, a[i - len + 1], len, -1);
  }
  cout << ans << endl;
  return 0;
}
