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:
from sys import stdin
from collections import defaultdict


class segmenttree:
    def __init__(self, n):
        self.tree, self.n = [0] * (2 * n), n

    # get interval[l,r)
    def query(self, l, r):
        res = -float('inf')
        l += self.n
        r += self.n
        while l < r:
            if l & 1:
                res = max(res, self.tree[l])
                l += 1
            if r & 1:
                r -= 1
                res = max(self.tree[r], res)
            l >>= 1
            r >>= 1

        return res

    def update(self, ix, val):
        ix += self.n

        # set new value
        self.tree[ix] = max(val, self.tree[ix])

        # move up
        while ix > 1:
            self.tree[ix >> 1] = max(self.tree[ix], self.tree[ix ^ 1])
            ix >>= 1

    def delete(self, ix, val):
        ix += self.n

        # set new value
        self.tree[ix] = val

        # move up
        while ix > 1:
            self.tree[ix >> 1] = max(self.tree[ix], self.tree[ix ^ 1])
            ix >>= 1


n, a, ans = int(input()), [int(x) for x in stdin.readline().split()], []
mem, tree = defaultdict(list), segmenttree(n + 2)

for i in range(n):
    tem = sum(a[:i + 1])

    for j in range(i, n):
        mem[tem].append([j - i + 2, j + 2])
        tem -= a[j - i]
        if j < n - 1:
            tem += a[j + 1]

for i, j in mem.items():
    j.sort()
    dis = set()
    for l, r in j:
        tree.update(r, tree.query(1, l) + 1)
        dis.add(r)

    if tree.tree[1] > len(ans):
        cur, lim, ans = tree.tree[1], float('inf'), []

        for l, r in j[::-1]:
            if tree.tree[r + n + 2] == cur and r < lim:
                cur -= 1
                ans.append('%d %d' % (l - 1, r - 1))
                lim = l

    while dis:
        tree.delete(dis.pop(), 0)

print('%d\n%s' % (len(ans), '\n'.join(ans)))