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:
//package com.example.programming;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Scanner;


public class CodeforcesProblems {


    static class Pair {
        public Pair(int key, int val) {
            this.key = key;
            this.val = val;
        }
        int key;
        int val;
    }


    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        //String[] strings = br.readLine().split(" ");
        int n = Integer.parseInt(br.readLine());

        String[] strings = br.readLine().split(" ");
        int[] arr = new int[n];
        for(int i = 0; i<n; i++) {
            arr[i] = Integer.parseInt(strings[i]);
        }


        HashMap<Integer, ArrayList<Pair>> segments = new HashMap<>();
        for(int r = 0; r<arr.length; r++) {
            int sum = 0;
            for(int l = r; l>=0; l--) {
                sum += arr[l];
                ArrayList<Pair> pairs = segments.get(sum);
                if(pairs == null) {
                    pairs = new ArrayList<>();
                    segments.put(sum, pairs);
                }
                pairs.add(new Pair(l, r));
            }
        }

        int res = 0;
        ArrayList<Pair> result = new ArrayList<>();
        for(ArrayList<Pair> pairs: segments.values()) {
            ArrayList<Pair> temp = new ArrayList<>();
            int count = 0;
            int r = -1;
            for(Pair p : pairs) {
                if(p.key>r) {
                    count++;
                    temp.add(p);
                    r = p.val;
                }
            }
            if(count>res) {
                res = count;
                result = temp;
            }
        }
        System.out.println(res);
        StringBuilder sb = new StringBuilder();
        for(Pair p : result){
            sb.append(p.key+1).append(' ').append(p.val+1).append('\n');
        }
        System.out.print(sb);
    }
}