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.*;

public class Main {
	
	public static class node implements Comparable<node>{
		int l,r;
		node(){}
		node(int l,int r) {
			this.l=l;
			this.r=r;
		}
		@Override
		public int compareTo(node rhs) {
			return r-rhs.r;
		}
	}
	
	public static void main(String args[]){
		Scanner in = new Scanner(System.in);
		int a = in.nextInt();
		int x[] = new int[a];
		for(int n=0;n<a;n++){
			x[n] = in.nextInt();
		}
		int max = 1;
		int t = 0;
		HashMap<Integer, ArrayList<node>> map = new HashMap<Integer, ArrayList<node>>();
		for(int n=0;n<a;n++){
			int num = 0;
			for(int m=n;m<a;m++){
				num += x[m];
				node node = new node(n, m);
				if(!map.containsKey(num)){
					ArrayList<node> list = new ArrayList<node>();
					list.add(node);
					map.put(num, list);
					if(max == 1)t = num;
				}
				else{
					ArrayList<node> list = map.get(num);
					int left = 0;
					int right = list.size()-1;				
					int res = list.size();
					while(left <= right){
						int mid = (left + right) >> 1;
						//System.out.println(mid +" "+ left +" " +right);
						if(list.get(mid).r >= n){
							res = mid;
							right = mid - 1;
						}
						else{
							left = mid + 1;
						}
					}
					if(res == list.size()){
						list.add(node);
						if(max < res+1){
							max = res+1;
							t = num;
						}
					}
					else if(list.get(res).r>m){
						list.set(res, node);
						if(max < res){
							max = list.size();
							t = num;
						}
					}
					
				}
			}
		}
		System.out.println(max);
		for(int n=0;n<max;n++){
			System.out.println((map.get(t).get(n).l+1)+" "+(map.get(t).get(n).r+1));
		}
		
	}
}