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;
using namespace std::chrono;
bool cmp(pair<long long, long long> x, pair<long long, long long> y) {
  if (x.second < y.second) {
    return true;
  } else if (x.second == y.second) {
    if (x.first < x.second) {
      return true;
    }
  }
  return false;
}
void snow() {
  long long n;
  cin >> n;
  vector<long long> arr(n);
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
  }
  vector<pair<long long, long long>> v;
  long long pre[n];
  pre[0] = arr[0];
  for (long long i = 1; i < n; i++) {
    pre[i] = pre[i - 1] + arr[i];
  }
  long long ans = 0;
  map<long long, vector<pair<long long, long long>>> p;
  for (long long i = n - 1; i >= 0; i--) {
    for (long long j = i; j < n; j++) {
      long long q = pre[j];
      if (i != 0) {
        q -= pre[i - 1];
      }
      p[q].push_back(make_pair(i, j));
    }
  }
  for (auto x : p) {
    long long right = 1e18;
    vector<pair<long long, long long>> in;
    for (auto y : x.second) {
      if (y.second < right) {
        in.push_back({y.first, y.second});
        right = y.first;
      }
    }
    if ((long long)in.size() > ans) {
      ans = in.size();
      v = in;
    }
  }
  cout << ans << '\n';
  for (auto x : v) {
    cout << x.first + 1 << " " << x.second + 1 << '\n';
  }
}
int32_t main() {
  auto start = high_resolution_clock::now();
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  long long _;
  _ = 1;
  while (_--) snow();
  auto stop = high_resolution_clock::now();
  auto duration = duration_cast<microseconds>(stop - start);
  return 0;
}