Problem: This problem is given in two editions, which differ exclusively in the constraints on the number n.

You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).

Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:

  * They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i. 
  * For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$ 
  * The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k. 

<image> The picture corresponds to the first example. Blue boxes illustrate blocks.

Write a program to find such a set of blocks.

Input

The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).

Output

In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.

Examples

Input


7
4 1 2 2 1 5 3


Output


3
7 7
2 3
4 5


Input


11
-5 -4 -3 -2 -1 0 1 2 3 4 5


Output


2
3 4
1 1


Input


4
1 1 1 1


Output


4
4 4
1 1
2 2
3 3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int solve(vector<long long> v, int n, int sum) {
  if (n == 0) return 0;
  if (n == 0 && sum)
    return max(solve(v, n - 1, sum), solve(v, n - 1, sum + v[n - 1]));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << fixed << setprecision(6);
  long long t = 1;
  while (t--) {
    int n;
    cin >> n;
    vector<long long> v(n + 5);
    for (long long i = 0; i <= n - 1; i++) cin >> v[i];
    unordered_map<int, vector<pair<long long, long long> > > h;
    int sum = 0;
    int ans = 0;
    int index;
    for (int i = 0; i < n; i++) {
      sum = 0;
      for (int j = i; j >= 0; j--) {
        sum += v[j];
        if (h.find(sum) == h.end() || h[sum].back().second < j + 1) {
          h[sum].emplace_back(j + 1, i + 1);
        }
        if ((int)h[sum].size() > ans) {
          index = sum;
          ans = h[sum].size();
        }
      }
    }
    cout << ans << "\n";
    for (auto i : h[index]) {
      cout << i.first << " " << i.second << "\n";
    }
  }
}