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 PYTHON):

Solution:
import sys
import math
import bisect
from collections import defaultdict
MOD = int(1e9+7)



# n = map(int, raw_input().split())
# input = map(int, raw_input().split())

n = map(int, raw_input().split())[0]
da = map(int, raw_input().split())

sm = [0]
for i in da:
    sm.append(sm[-1] + i)
ta = defaultdict(list)
for i in range(n):
    for j in range(i+1, n+1):
        ta[sm[j] - sm[i]].append((j, i+1))
mx, ans = -1, []
# print sm
# print ta
for k, v in ta.iteritems():
    v.sort()
    tmp_ans = []
    flag = -1
    for pj, pi in v:
        if pi > flag:
            flag = pj
            tmp_ans.append((pi,pj))
    # print k,len(tmp_ans),tmp_ans
    if len(tmp_ans) > mx:
        mx, ans = len(tmp_ans), tmp_ans
print mx;
for i, j in ans:
    print i, j