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:
import time


def index(key, item, index):
    if key in index:
        index[key].append(item)
    else:
        index[key] = [item]

def schedule2(times):
    # print(times)
    result = []
    a_min = 0
    for s, e in times:
        if s >= a_min:
            result.append((s, e))
            a_min = e
    # print(len(result), ':', times)
    return result

def schedule(times):
    index_by_b = {}
    for time in times:
        index(time[1], time, index_by_b)
    b_keys = sorted(list(index_by_b.keys()))
    result = []
    a_min = 0
    # Get interval with minimun end time whose start time >= a_min.
    for end_time in b_keys:
        start = index_by_b[end_time].pop()[0]
        if start >= a_min:
            result.append((start, end_time)) 
            a_min = end_time
    return result
                
def solve(n, a_l):
    index_by_sum = {}
    for j in range(1, n + 1):
        sum_ = 0
        for i in range(j - 1, -1, -1):
            sum_ += a_l[i]
            # print('sum_:', sum_)

    # for i in range(n):
        # sum_ = 0
        # for j in range(i + 1, n + 1):
            if sum_ in index_by_sum:
                index_by_sum[sum_].append((i, j))
            else:
                index_by_sum[sum_] = [(i, j)]
    # for k, v in index_by_sum.items():
        # print(k ,v)
    result = []
    for sum_, times in index_by_sum.items():
        sub_result = schedule2(times)
        if len(sub_result) > len(result):
            result = sub_result
    return result

def test():
    # n = 7
    # a_l = [4, 1, 2, 2, 1, 5, 3]
    n = 1500
    a_l = list(range(1, n + 1))
    tick = time.time()
    result = solve(n, a_l)
    tock = time.time()
    print(len(result))
    for a, b in result:
        print(a + 1, b)
    print("T:", round(tock - tick, 5))


def main():
    n = int(input())
    a_l = list(map(int, input().split()))
    result = solve(n, a_l)
    print(len(result))
    for a, b in result:
        print(a + 1, b)

if __name__ == "__main__":
    main()