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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;

public class P1141F {

	static BufferedReader br;
	static BufferedWriter bw;
	static StringTokenizer st;

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

		int n = Integer.parseInt(br.readLine());
		int[] a = new int[n];
		int[][] b = new int[n][n];
		HashMap<Integer, ArrayList<Integer>> map = new HashMap<Integer, ArrayList<Integer>>();
		
		st = new StringTokenizer(br.readLine());
		for(int i = 0; i < n; ++i) {
			a[i] = Integer.parseInt(st.nextToken());
			
			int r = i;
			b[r][r] = a[r];
			if (!map.containsKey(b[r][r]))
				map.put(b[r][r], new ArrayList<Integer>());
			for(int l = 0; l < r; ++l) {
				b[l][r] = b[l][r-1] + a[r];
				if (!map.containsKey(b[l][r]))
					map.put(b[l][r], new ArrayList<Integer>());
			}
		}

		
		for(int r = 0; r < n; ++r) {
			for(int l = 0; l <= r; ++l) {
				int sum = b[l][r];
				ArrayList<Integer> intervals = map.get(sum);
				int last_r = -1;
				if(!intervals.isEmpty())
					last_r = intervals.get(intervals.size()-1);
				
				if(l > last_r) {
					intervals.add(l);
					intervals.add(r);
				}
				
			}
		}
		
		//int best_sum = -1;
		ArrayList<Integer> best_intervals = new ArrayList<Integer>();
		
		for(Map.Entry<Integer, ArrayList<Integer>> entry : map.entrySet()) {
			//int sum = entry.getKey();
			ArrayList<Integer> intervals = entry.getValue();
			
			if(intervals.size() > best_intervals.size()) {
				best_intervals = intervals;
			}
		}
		
		bw.write(best_intervals.size()/2 + "\n");
		for(int i = 0; i < best_intervals.size(); i += 2) {
			bw.write((best_intervals.get(i)+1) + " " + (best_intervals.get(i+1)+1) + "\n");
		}


		br.close();
		bw.close();
	}
}