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F2. Same Sum Blocks (Hard)

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThis 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$$$.

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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