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;
const int maxn = 2E3 + 50;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
long long a[maxn];
map<int, vector<pair<int, int> > > lis;
bool cmp(pair<int, int> a, pair<int, int> b) { return a.second < b.second; }
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    lis[a[i]].emplace_back(make_pair(i, i));
  }
  for (int i = 1; i <= n; i++) {
    int t = a[i];
    for (int j = i + 1; j <= n; j++) {
      t += a[j];
      lis[t].emplace_back(make_pair(i, j));
    }
  }
  int maxn = -1, tn;
  vector<pair<int, int> > ans, tv;
  for (map<int, vector<pair<int, int> > >::iterator it = lis.begin();
       it != lis.end(); it++) {
    tn = 0;
    tv.clear();
    vector<pair<int, int> > t = it->second;
    sort(t.begin(), t.end(), cmp);
    int mark = 0, len = t.size();
    for (int i = 0; i < len; i++) {
      if (mark < t[i].first) {
        tn++;
        tv.emplace_back(t[i]);
        mark = t[i].second;
      }
    }
    if (maxn < tn) {
      maxn = tn;
      ans = tv;
    }
  }
  cout << maxn << endl;
  for (vector<pair<int, int> >::iterator it = ans.begin(); it != ans.end();
       it++) {
    cout << it->first << " " << it->second << endl;
  }
  return 0;
}