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:
class solution(object):
    def __init__(self, a):
        self.a = a

    def sol(self):
        n = len(self.a)
        acc = [0]
        interval = []

        for i in xrange(1, n + 1):
            acc.append(acc[i - 1] + self.a[i - 1])
        
        st = set()
        for i in xrange(1, n + 1):
            for j in xrange(i, n + 1):
                interval.append((i, j, acc[j] - acc[i - 1]))
                st.add(acc[j] - acc[i - 1])
        
        interval.sort(cmp=self.cmp) 
        rs = None 
        nm = 0
        fq = {}

        for x in interval:
            if not x[2] in fq:
                fq[x[2]] = [(-1, -1, x[2])]
            l = len(fq[x[2]]) - 1
            if fq[x[2]][l][1] < x[0]:
                fq[x[2]].append(x)
            if nm < len(fq[x[2]]):
                nm = len(fq[x[2]])
                rs = x[2]
        
        return fq[rs]

    
    def cmp(self, x, y):
        if x[1] == y[1]:
            return x[0] - y[0]
        
        return x[1] - y[1]    


def main():
    n = int(raw_input())
    a = [int(e) for e in raw_input().split()]
    sol = solution(a)
    l = sol.sol()
    print(len(l) - 1)
    st = ''
    for i in xrange(1, len(l)):
        st += str(l[i][0]) + ' ' + str(l[i][1]) + '\n'
    print(st)    
    return 0

if __name__ == '__main__':
    main()