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 double EPS = (double)1e-9;
const double PI = (double)acos(-1.0);
int irand(int lo, int hi) {
  return (((double)rand()) / (RAND_MAX + 1.0)) * (hi - lo + 1) + lo;
}
string toString(long long x) {
  stringstream ss;
  ss << x;
  return ss.str();
}
long long toNumber(string S) {
  long long ret;
  sscanf(S.c_str(), "%lld", &ret);
  return ret;
}
const int INF = (int)2e9;
const long long MOD = (long long)1e9 + 7;
pair<int, int> temp[1500 * 1500 + 5];
pair<int, int> maxx[1500 * 1500 + 5];
int solve(vector<pair<int, int> >& dat, vector<pair<int, int> >& res) {
  int sz = (int)dat.size();
  dat.push_back(make_pair(INF, INF));
  temp[sz] = make_pair(0, INF);
  maxx[sz] = make_pair(0, sz);
  for (int i = sz - 1; i >= 0; i--) {
    int idx =
        lower_bound(dat.begin(), dat.end(), make_pair(dat[i].second + 1, 0)) -
        dat.begin();
    temp[i] = make_pair(maxx[idx].first + 1, maxx[idx].second);
    maxx[i] = maxx[i + 1];
    if (temp[i] > maxx[i] || (temp[i] == maxx[i]))
      maxx[i] = make_pair(temp[i].first, i);
  }
  if ((int)res.size() >= maxx[0].first) return 0;
  res.clear();
  for (int idx = maxx[0].second; idx < sz; idx = temp[idx].second)
    res.push_back(dat[idx]);
  return maxx[0].first;
}
map<int, int> hashh;
vector<vector<pair<int, int> > > slot;
int dat[1505];
int main() {
  int n;
  scanf("%d", &n);
  dat[0] = 0;
  for (int i = 1; i <= n; i += 1) scanf("%d", dat + i), dat[i] += dat[i - 1];
  for (int i = 1; i <= n; i += 1)
    for (int j = i; j <= n; j += 1) {
      if (hashh.find(dat[j] - dat[i - 1]) == hashh.end()) {
        hashh[dat[j] - dat[i - 1]] = (int)slot.size();
        slot.push_back(vector<pair<int, int> >());
      }
      slot[hashh[dat[j] - dat[i - 1]]].push_back(make_pair(i, j));
    }
  vector<pair<int, int> > res;
  res.clear();
  for (pair<int, int> x : hashh) solve(slot[x.second], res);
  printf("%d\n", (int)res.size());
  for (pair<int, int> x : res) printf("%d %d\n", x.first, x.second);
  return 0;
}