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:
#!/usr/bin/env python2
"""
This file is part of https://github.com/cheran-senthil/PyRival
Cheran Senthilkumar <hello@cheran.io>
"""
from __future__ import division, print_function

import os
import sys
from atexit import register
from cStringIO import StringIO
from collections import defaultdict
from itertools import ifilter, imap, izip

range = xrange
filter, map, zip = ifilter, imap, izip

sys.stdout = StringIO()
register(lambda: os.write(1, sys.stdout.getvalue()))
input = StringIO(os.read(0, os.fstat(0).st_size)).readline


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

    p = [0] * (n + 1)
    for i, j in enumerate(a):
        p[i + 1] = p[i] + j

    s = defaultdict(list)
    for i in range(n + 1):
        for j in range(i):
            s[p[i] - p[j]].append((j, i))

    sol = []
    for i in s:
        s[i] = sorted(s[i], key=lambda x: x[1])
        psol = [s[i].pop(0)]

        for p in s[i]:
            if p[0] >= psol[-1][1]:
                psol.append(p)

        sol = max(sol, psol, key=len)


    print(len(sol))
    for i in sol:
        print(i[0] + 1, i[1])



if __name__ == '__main__':
    main()