F2. Same Sum Blocks (Hard)
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

This problem is given in two editions, which differ exclusively in the constraints on the number $$$n$$$.

You are given an array of integers $$$a[1], a[2], \dots, a[n].$$$ A block is a sequence of contiguous (consecutive) elements $$$a[l], a[l+1], \dots, a[r]$$$ ($$$1 \le l \le r \le n$$$). Thus, a block is defined by a pair of indices $$$(l, r)$$$.

Find a set of blocks $$$(l_1, r_1), (l_2, r_2), \dots, (l_k, r_k)$$$ 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 $$$i \neq j$$$ either $$$r_i < l_j$$$ or $$$r_j < l_i$$$.
  • For each block the sum of its elements is the same. Formally, $$$$$$a[l_1]+a[l_1+1]+\dots+a[r_1]=a[l_2]+a[l_2+1]+\dots+a[r_2]=$$$$$$ $$$$$$\dots =$$$$$$ $$$$$$a[l_k]+a[l_k+1]+\dots+a[r_k].$$$$$$
  • The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks $$$(l_1', r_1'), (l_2', r_2'), \dots, (l_{k'}', r_{k'}')$$$ satisfying the above two requirements with $$$k' > k$$$.
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 $$$n$$$ ($$$1 \le n \le 1500$$$) — the length of the given array. The second line contains the sequence of elements $$$a[1], a[2], \dots, a[n]$$$ ($$$-10^5 \le a_i \le 10^5$$$).

Output

In the first line print the integer $$$k$$$ ($$$1 \le k \le n$$$). The following $$$k$$$ lines should contain blocks, one per line. In each line print a pair of indices $$$l_i, r_i$$$ ($$$1 \le l_i \le r_i \le n$$$) — 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