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;
map<int, vector<pair<int, int> > > M;
int a[2000], dp[1550][1550] = {0}, Y[1550];
pair<int, int> Ans[1550];
set<int> v;
bool cmp(pair<int, int> a, pair<int, int> b) {
  return (a.first == b.first ? a.second < b.second : a.first < b.first);
}
int find_ans(int index) {
  int ans = 0, xx, yy;
  sort(M[index].begin(), M[index].end(), cmp);
  xx = M[index][0].first;
  yy = 0;
  for (int i = 0; i < M[index].size(); i++) {
    int x = M[index][i].first;
    int y = M[index][i].second;
    if (x > yy) {
      ans++;
      xx = x;
      yy = y;
    } else if (y < yy) {
      yy = y;
      xx = x;
    }
  }
  return ans;
}
void print(int index) {
  int ans = 0, xx, yy;
  sort(M[index].begin(), M[index].end(), cmp);
  xx = M[index][0].first;
  yy = 0;
  for (int i = 0; i < M[index].size(); i++) {
    int x = M[index][i].first;
    int y = M[index][i].second;
    if (x > yy) {
      ans++;
      xx = x;
      yy = y;
      Y[x] = y;
      Ans[ans] = make_pair(x, y);
    } else if (y < yy) {
      yy = y;
      xx = x;
      Ans[ans] = make_pair(x, y);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  ;
  int n, in;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    for (int j = i; j >= 1; j--) {
      dp[j][i] = dp[j + 1][i] + a[j];
      int k = dp[j][i];
      M[k].push_back(make_pair(j, i));
      v.insert(k);
    }
  }
  int ans = 0;
  set<int>::iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    int val = find_ans(*it);
    if (val > ans) in = *it, ans = val;
  }
  cout << ans << endl;
  print(in);
  for (int i = 1; i <= ans; i++)
    cout << Ans[i].first << " " << Ans[i].second << endl;
}