1141_F2. Same Sum Blocks (Hard)
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
```python
n=int(input())
a=list(map(int,input().split()))
dic={}
for i in range(n):
    sm=0
    for j in range(i,n):
        sm+=a[j]
        if sm in dic:
            dic[sm].append((i,j))
        else:
            dic[sm]=[(i,j)]
ans=0
anskey=-1
for key in dic:
    cnt=0
    last=-1
    for a,b in sorted(dic[key]):
        if a>last:
            cnt+=1
            last=b
        elif b<last:
            last=b
    if cnt>ans:
        ans=cnt
        anskey=key
last=-1
tmp=[]
for a,b in sorted(dic[anskey]):
    if a>last:
        last=b
        tmp.append(str(a+1)+" "+str(b+1))
    elif b<last:
        last=b
        tmp.pop()
        tmp.append(str(a+1)+" "+str(b+1))
print(ans,'\n'.join(tmp),sep='\n')
```