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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;


public class F{
	
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
	static class Pair
	{
		int l;
		int r;
		Pair(int l,int r)
		{
			this.l = l;
			this.r = r;
		}
	}
	public static void main(String[] args) 
	{
		OutputStream outputStream = System.out;
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
        int n = sc.nextInt();
        int a[] = new int[n];
        Pair pr;
        HashMap<Long,ArrayList> hm = new HashMap<>();
        ArrayList<Pair> ar;
        for(int i = 0; i < n; i++)
        {
        	a[i] = sc.nextInt();
        }
        long sum = 0;
        for(int r = 0; r < n; r++)
        {	
        	sum = 0;
        	for(int l = r; l >= 0; l--)
        	{
        		sum += a[l];
        		if(!hm.containsKey(sum))
        		{
        			ar = new ArrayList<>();
        			ar.add(new Pair(l,r));
        			hm.put(sum,ar);
        		}
        		else
        		{
        			ar = hm.get(sum);
        			ar.add(new Pair(l,r));
        			hm.put(sum,ar);
        		}
        	}
        }
        
        int count = 0;
        int maxCount = 0;
        long maxSum = 0;
        for(Map.Entry<Long,ArrayList> entry:hm.entrySet())
        {
        	sum = entry.getKey();
        	ar = entry.getValue();
        	count = 0;
        	int r = -1;
        	for(int i = 0; i < ar.size(); i++)
        	{
        		if(ar.get(i).l > r)
        		{
        			count++;
        			r = ar.get(i).r;
        		}
        	}
        	if(count > maxCount)
        	{
        		maxCount = count;
        		maxSum = sum;
        	}
        	
        }
        ar = hm.get(maxSum);
        out.println(maxCount);
        //out.println((ar.get(0).l+1)+" "+(ar.get(0).r+1));
        
        int r = -1;
        for(int i = 0; i < ar.size(); i++)
    	{
    		if(ar.get(i).l > r)
    		{
    			out.println((ar.get(i).l+1) +" "+(ar.get(i).r+1));
    			r = ar.get(i).r;
    		}
    	}
        out.close();
	}

}