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.Scanner;
import java.util.Vector;
import java.util.HashMap;
import java.util.Comparator;


public class F2{
	static class Pair{
		int l;
		int r;
		Pair(int l, int r){
			this.l = l;
			this.r = r;
		}
		public String toString(){
			return "(" + l + ", " + r + ")";
		}
	}
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] a = new int[n+1];
		for(int i = 1;i<=n;++i){
			a[i] = in.nextInt();
		}
		HashMap<Integer, Vector<Pair>> map = new HashMap<>();
		for(int i = 1;i<=n;++i){
			int sum = 0;
			for(int j = i;j<=n;++j){
				sum+=a[j];
				if(!map.containsKey(sum))
					map.put(sum,new Vector<>());
				map.get(sum).add(new Pair(i,j));
			}
		}
		Vector<Pair> an = null;
		for(Integer key : map.keySet()){
			Vector<Pair> vec = map.get(key);
			Vector<Pair> ans = new Vector<>();
			ans.add(vec.get(0));
			int size = 1;
			for(int i = 1;i<vec.size();++i){
				if(ans.get(size-1).r > vec.get(i).r)
					ans.set(size-1,vec.get(i));
				else if(ans.get(size-1).r < vec.get(i).l){
					ans.add(vec.get(i));
					size++;
				}
			}
			if(an == null || an.size() < size) an = ans;
		}
		StringBuilder res = new StringBuilder().append(an.size() + "\n");
		for(int i = 0;i<an.size();++i)
			res.append(an.get(i).l + " " + an.get(i).r + "\n");
		System.out.println(res);
	}
}