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.*;
import java.util.*;

public class CF1141F {
	static class V {
		int l, r, a;
		V(int l, int r, int a) {
			this.l = l; this.r = r; this.a = a;
		}
	}
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int[] aa = new int[n + 1];
		for (int i = 1; i <= n; i++)
			aa[i] = Integer.parseInt(st.nextToken());
		for (int i = 1; i <= n; i++)
			aa[i] += aa[i - 1];
		int m = n * (n + 1) / 2;
		V[] vv = new V[m];
		m = 0;
		for (int i = 1; i <= n; i++)
			for (int j = i; j <= n; j++)
				vv[m++] = new V(i, j, aa[j] - aa[i - 1]);
		Arrays.sort(vv, (u, v) -> u.a != v.a ? u.a - v.a : u.r - v.r);
		int[] ii_ = new int[m];
		int[] ii = new int[m];
		int k_ = 0;
		for (int i = 0, j; i < m; i = j) {
			j = i + 1;
			while (j < m && vv[j].a == vv[i].a)
				j++;
			int k = 0, r = 0;
			for (int h = i; h < j; h++)
				if (vv[h].l > r) {
					ii[k++] = h;
					r = vv[h].r;
				}
			if (k_ < k) {
				k_ = k;
				int[] tmp = ii_; ii_ = ii; ii = tmp;
			}
		}
		pw.println(k_);
		for (int h = 0; h < k_; h++) {
			int i = ii_[h];
			pw.println(vv[i].l + " " + vv[i].r);
		}
		pw.close();
	}
}