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 N = 1500 * 1500 + 5;
map<int, vector<pair<int, int>>> maping;
int Next[N];
int dp[N];
int arr[1505];
int range[1505];
int size;
void solve() {
  for (int i = size - 1; i >= 0; i--) {
    dp[i] = 0;
    if (i + 1 < size) dp[i] = max(dp[i], dp[i + 1]);
    if (Next[i] < size)
      dp[i] = max(dp[i], dp[Next[i]] + 1);
    else
      dp[i] = max(dp[i], 1);
  }
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> arr[i];
  for (int i = 1; i <= n; i++) {
    int cur = 0;
    for (int j = i; j <= n; j++) {
      cur += arr[j];
      maping[cur].push_back({i, j});
    }
  }
  int Max = -1, idx = -1;
  for (auto &cur : maping) {
    vector<pair<int, int>> &vec = cur.second;
    size = vec.size();
    if (size <= Max) continue;
    memset(range, -1, sizeof range);
    for (int i = size - 1; i >= 0; i--) {
      int st = vec[i].first;
      if (range[st - 1] == -1)
        range[st - 1] = i;
      else
        range[st - 1] = min(range[st - 1], i);
    }
    for (int i = 1500; i >= 1; i--) {
      if (range[i] == -1) range[i] = size + 5;
      if (i < 1500) range[i] = min(range[i], range[i + 1]);
    }
    for (int i = 0; i < size; i++) Next[i] = range[vec[i].second];
    solve();
    if (dp[0] > Max) {
      Max = dp[0];
      idx = cur.first;
    }
  }
  cout << Max << '\n';
  vector<pair<int, int>> &vec = maping[idx];
  size = vec.size();
  memset(range, -1, sizeof range);
  for (int i = size - 1; i >= 0; i--) {
    int st = vec[i].first;
    if (range[st - 1] == -1)
      range[st - 1] = i;
    else
      range[st - 1] = min(range[st - 1], i);
  }
  for (int i = 1500; i >= 1; i--) {
    if (range[i] == -1) range[i] = size + 5;
    if (i < 1500) range[i] = min(range[i], range[i + 1]);
  }
  for (int i = 0; i < size; i++) Next[i] = range[vec[i].second];
  solve();
  int cur = 0;
  while (cur < size) {
    int c1 = 0, c2 = 0;
    if (cur + 1 < size) c1 = dp[cur + 1];
    if (Next[cur] < size)
      c2 = dp[Next[cur]] + 1;
    else
      c2 = 1;
    if (c1 >= c2)
      cur = cur + 1;
    else {
      cout << vec[cur].first << ' ' << vec[cur].second << '\n';
      cur = Next[cur];
    }
  }
  return 0;
}