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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class SolutionArch2 {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = Integer.valueOf(scanner.nextLine());
        String s = scanner.nextLine();
        int[] arr = Arrays.stream(s.split(" "))
                .mapToInt(Integer::valueOf)
                .toArray();
        int[] prefixSum = new int[n + 1];
        for (int i = 0; i < n; i++) {
            prefixSum[i + 1] = prefixSum[i] + arr[i];
        }
        Map<Integer, List<int[]>> map = new HashMap<>();
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                int subarraySum = prefixSum[j + 1] - prefixSum[i];
                map.putIfAbsent(subarraySum, new ArrayList<>());
                int l = i + 1, r = j + 1;
                map.get(subarraySum).add(new int[]{l, r});
            }
        }
        List<int[]> resultPairs = new ArrayList<>();
        for (Map.Entry<Integer, List<int[]>> e : map.entrySet()) {
            List<int[]> result = new ArrayList<>();
            int[] curr = new int[2];
            List<int[]> pairs = e.getValue();
            Collections.sort(pairs, Comparator.<int[]>comparingInt(a -> a[1]));
            for (int[] next : pairs) {
                if (next[0] > curr[1]) {
                    result.add(next);
                    curr = next;
                }
            }
            if (resultPairs.size() < result.size()) {
                resultPairs = result;
            }
        }
        printResult(resultPairs);
    }

    private static void printResult(List<int[]> list) {
        StringBuilder sb = new StringBuilder();
        sb.append(list.size()).append("\n");
        for (int[] pair : list) {
            sb.append(pair[0]).append(" ").append(pair[1]).append("\n");
        }
        System.out.print(sb);
    }
}