D. Equal Halves
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Monocarp has an array consisting of $$$n$$$ integers, where $$$n$$$ is an even number.

Monocarp has to perform exactly one swap in his array according to the following rules: choose a position $$$x$$$ in the left half of the array ($$$1 \le x \le \frac{n}{2}$$$), choose a position $$$y$$$ in the right half of the array ($$$\frac{n}{2} + 1 \le y \le n$$$), and swap the elements at positions $$$x$$$ and $$$y$$$.

Your task is to determine whether Monocarp can perform exactly one described swap so that the sum of all elements in the left half of the array becomes equal to the sum of all elements in the right half of the array.

Input

The first line contains an even integer $$$n$$$ ($$$2 \le n \le 200\,000$$$) — the number of elements in the array.

The next line contains a sequence of integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10\,000$$$), where $$$a_i$$$ is the $$$i$$$-th element of the array.

Output

If it is impossible to perform exactly one described swap, output "NO" (without quotes).

Otherwise, in the first line, output "YES" (without quotes). In the second line, output two integers — the position for the swap from the left half of the array and the position for the swap from the right half of the array. If there are multiple answers, print any of them.

Examples
Input
6
4 1 2 6 7 6
Output
YES
2 5
Input
4
5 4 3 5
Output
NO
Note

In the first example, Monocarp has to swap the second and fifth elements. Then the array will become $$$[4, 7, 2, 6, 1, 6]$$$. The sum of the left half will be $$$4 + 7 + 2 = 13$$$, and the sum of the right half will be $$$6 + 1 + 6 = 13$$$. Thus, the sums of the left and right halves of the array will become equal.

In the second example, it is impossible to perform a swap so that the sums of the left and right halves of the array become equal.