Alexandra has a paper strip with n numbers on it. Let's call them ai from left to right.

Now Alexandra wants to split it into some pieces (possibly 1). For each piece of strip, it must satisfy:

  * Each piece should contain at least l numbers.
  * The difference between the maximal and the minimal number on the piece should be at most s.



Please help Alexandra to find the minimal number of pieces meeting the condition above.

Input

The first line contains three space-separated integers n, s, l (1 ≤ n ≤ 105, 0 ≤ s ≤ 109, 1 ≤ l ≤ 105).

The second line contains n integers ai separated by spaces ( - 109 ≤ ai ≤ 109).

Output

Output the minimal number of strip pieces.

If there are no ways to split the strip, output -1.

Examples

Input

7 2 2
1 3 1 2 4 1 2


Output

3


Input

7 2 2
1 100 1 100 1 100 1


Output

-1

Note

For the first sample, we can split the strip into 3 pieces: [1, 3, 1], [2, 4], [1, 2].

For the second sample, we can't let 1 and 100 be on the same piece, so no solution exists.
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 100, lg = 20, inf = 1e5 + 200;
int maxim[maxn][lg + 1], minim[maxn][lg + 1], dp[maxn][lg + 1];
vector<int> tst;
int par[maxn][lg + 1];
int n, s, l;
void set_rdp(int i, int ans) {
  dp[i][0] = ans;
  for (int f = 1; f < lg; f++) {
    dp[i][f] = min(dp[i][f - 1], dp[max(0, i - (1 << (f - 1)))][f - 1]);
  }
}
int min_dp(int st, int en) {
  if (st == en) return dp[st][0];
  for (int f = lg - 1; f > -1; f--) {
    if (en - (1 << f) >= st) return min(dp[en][f], min_dp(st, en - (1 << f)));
  }
}
int maxi(int st, int en) {
  if (st == en) return maxim[st][0];
  for (int f = lg - 1; f > -1; f--) {
    if (st + (1 << f) <= en) return max(maxim[st][f], maxi(st + (1 << f), en));
  }
}
int mini(int st, int en) {
  if (st == en) return minim[st][0];
  for (int f = lg - 1; f > -1; f--) {
    if (st + (1 << f) <= en) return min(minim[st][f], mini(st + (1 << f), en));
  }
}
bool check_s(int st, int fn) {
  int mx = maxi(st, fn);
  int mn = mini(st, fn);
  if (mx - mn <= s) return 1;
  return 0;
}
bool check_st(int st, int fn) { return tst[st]; }
int bns(int l, int r, int last) {
  if (r - l <= 1) return r;
  int mid = (l + r) / 2;
  if (check_s(mid, last)) return bns(l, mid, last);
  return (bns(mid, r, last));
}
void set_par() {
  for (int i = 0; i < n - 1; i++) {
    par[i][0] = i + 1;
  }
  par[n - 1][0] = n - 1;
  for (int f = 1; f < lg; f++) {
    for (int i = 0; i < n; i++) {
      par[i][f] = par[par[i][f - 1]][f - 1];
      maxim[i][f] = max(maxim[i][f - 1], maxim[par[i][f - 1]][f - 1]);
      minim[i][f] = min(minim[i][f - 1], minim[par[i][f - 1]][f - 1]);
    }
  }
}
void input() {
  cin >> n >> s >> l;
  for (int i = 0; i < n; i++) {
    int t;
    cin >> t;
    maxim[i][0] = t;
    minim[i][0] = t;
  }
}
int find_ans() {
  for (int i = 0; i < n; i++) {
    int z = bns(-1, i, i);
    int ans = inf;
    if (i - z + 1 >= l) {
      if (z == 0)
        ans = 1;
      else {
        ans = min_dp(z - 1, i - l) + 1;
      }
    }
    set_rdp(i, ans);
  }
  return dp[n - 1][0];
}
void test() {
  while (1) {
    int l, r;
    cin >> l >> r;
    cout << min_dp(l, r) << endl;
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  input();
  set_par();
  int ans = find_ans();
  if (ans < inf)
    cout << ans;
  else
    cout << -1;
}
