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 PYTHON3):

Solution:
from collections import defaultdict as ddict

def main():
    n = int(input())
    a = list(map(int, input().split()))

    dp = ddict(int)
    last_idx = ddict(lambda :-1)

    for i in range(len(a)):
        s = a[i]
        dp[s] += 1
        last_idx[s] = i

        for j in range(i-1, -1, -1):
            s += a[j]
            if j > last_idx[s]:
                dp[s] += 1
                last_idx[s] = i

    k = max(dp.keys(), key=lambda x: dp[x])
    v = dp[k]

    stack = []
    last_idx = -1
    for i in range(len(a)):
        s = a[i]
        if s == k:
            last_idx = i
            stack.append((i+1, i+1))

        for j in range(i-1, -1, -1):
            s += a[j]
            if j > last_idx:
                if s == k:
                    last_idx = i
                    stack.append((j+1, i+1))

    print(v)

    out_str = []
    for ia, ib in stack:
        out_str.append(str(ia) + ' ' + str(ib))
    print('\n'.join(out_str))




main()