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.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class b {

	public static void main(String[] rgs)
	{
		Scanner s=new Scanner(System.in);

		int n=s.nextInt();
		long[] arr=new long[n];
		
		for(int i=0;i<n;i++) {
			arr[i]=s.nextLong();
		}
		HashMap<Long,ArrayList<pair>> map=new HashMap<>();
	
		ArrayList<pair> list=new ArrayList<>();
		for(int i=0;i<n;i++) {
			long sum=0;
			for(int j=i;j<n;j++) {
				sum=sum+arr[j];
				pair ob=new pair(i,j);
				if(map.containsKey(sum))
				{
					ArrayList p=map.get(sum);
					p.add(ob);
					map.put(sum, p);
					
				}else {
					ArrayList<pair> listt=new ArrayList<>();
					listt.add(ob);
					map.put(sum,listt);
				}
			}
		}
	
		
		
		
		
		long in=-1;
		int max=0;
		
		for(Map.Entry<Long, ArrayList<pair>> entry:map.entrySet()) {
			int l=1;
			ArrayList<pair> p=entry.getValue();
			Collections.sort(p,new comp());
			int now=p.get(0).end;
			for(int j=0;j<p.size();j++) {
				
			
			
				if(p.get(j).st>now) {
					l++;
					now=p.get(j).end;
					
				}
			
				
			}
			
			if(l>max) {
				max=l;
				in=entry.getKey();
			}
		}
		
		System.out.println(max);
		
		
		ArrayList<pair> d=map.get(in);
		int now=-1;
		for(int j=0;j<d.size();j++) {
		
			if(d.get(j).st>now) {
				System.out.println((d.get(j).st+1)+" "+(d.get(j).end+1));
				now=d.get(j).end;
				}
		
			
		}
		
		
		
		
	}
}
class pair{
	//long val;
	int st;
	int end;
	public pair(int st,int end) {
		//this.val=val;
		this.st=st;
		this.end=end;
	}
}
class comp implements Comparator<pair>{
	
	public int compare(pair h,pair j) {
		
		if(h.end<j.end) {
			return -1;
		}else if(h.end==j.end) {
			if(h.st<j.st) {
				return 1;
			}else if(h.st==j.st) {
				return 0;
			}else {
				return -1;
			}
		}else {
			return 1;
		}
	}
}