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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class F1141 {
	
	private static class Interval {
		public int l;
		public int r;
		
		public Interval(int l,int r) {
			this.l = l;
			this.r = r;
		}
	}

	public static void main(String[] args) throws IOException {
//		BufferedReader br = new BufferedReader(new FileReader("F:/books/input.txt"));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String s = br.readLine();
		int n = Integer.parseInt(s);
		long[] a = new long[n];
		String[] as = br.readLine().split(" ");
		for(int i=0;i<n;i++) {
			a[i] = Long.parseLong(as[i]);
		}
		StringBuffer sb = solve(a,n);
		System.out.println(sb.toString());
	}

	private static StringBuffer solve(long[] a, int n) {
		StringBuffer ret = new StringBuffer("");
		Map<Long,List<Interval>> mp = new HashMap<Long,List<Interval>>();
		long max = 0,maxId = -1;
		for(int i=n-1;i>=0;i--) {
			long s=0;
			long prev = 1;
			for(int j=i;j<n;j++) {
				s+=a[j];
//				System.out.println(i+","+j);
				Interval inter = new Interval(i,j);
//				if(prev==1 || prev==-1) {
					List<Interval> ints = mp.get(s);
					if(ints==null) ints = new ArrayList<Interval>();
					if(ints.size()==0 || ints.get(0).l>j) {
						ints.add(0,inter);
					}
					if(ints.size()>max) {
						max = ints.size();
						maxId = s;
					}
					mp.put(s, ints);
//				}
				if(j<n-1) prev =  a[j+1]-a[j];
			}
		}
		List<Interval> l = mp.get(maxId);
		ret.append(l.size()+ "\n");
		for(Interval inter : l) {
			ret.append((inter.l+1) + " " + (inter.r+1) + "\n");
		}
		return ret;
	}

}