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:
n = int(input())
a = list(map(int, input().split()))
if n == 1:
    print(1)
    print('1 1')
else:
    d = [[]]*(n-1)
    d[0] = a
    for i in range(1,n-1):
        d[i] = [d[i-1][j]+a[j+i] for j in range(0,n-i)]
    d2 = {}
    for i,d_ in enumerate(d):
        for j,x in enumerate(d_):
            if x in d2:
                d2[x].append([j+1,j+i+1])
            else:
                d2[x]=[[j+1,j+i+1]]
    list_keys = list(d2.keys())
    #res = 0
    ma = 0
    for key in list_keys:
        d2[key].sort(key=lambda x:x[1]) 
        after = -1 
        cnt = 0
        tmp = []
            
        for y,z in d2[key]:
            if y > after:
                cnt += 1
                after = z
                tmp.append([y,z])
        if cnt > ma:
            ma = cnt
            res = tmp
#         for j in range(len(d2[key])):
#             after = -1 
#             cnt = 0
#             tmp = []
            
#             for y,z in d2[key][j:]:
#                 if y > after:
#                     cnt += 1
#                     after = z
#                     tmp.append([y,z])
#             if cnt > ma:
#                 ma = cnt
#                 res = tmp
    print(len(res))
    for x in res:
        print(*x)