Flexible Segments

The great mathematician Vladimir Germanovich noticed an interesting property of some segments of positive integers while searching for new patterns.

Vladimir calls the segment of positive integers $l, l + 1, \ldots, r$ flexible if he can change every number of this segment by exactly one in such a way that the product of the numbers in the segment does not change. That is, there exists a sequence $a_l, a_{l+1}, \ldots, a_r$ with the following properties:

• $a_k = k \pm 1$
• $l \cdot (l+1)\cdot \ldots \cdot r = a_l \cdot a_{l+1} \cdot \ldots \cdot a_r$

Now Vladimir Germanovich wants to know whether he can build a flexible segment of any length. Given a positive integer $n$, find any flexible segment consisting of $n$ consecutive positive integers, or report that no such segment exists.

The only line contains an integer $n$ ($1 \le n \le 10\,000$), the length of the required segment.

The first line of output must contain "YES" if a flexible segment of $n$ positive integers exists. Otherwise it must contain "NO".

If such a segment exists, the second and third lines must contain the description of this segment.

The second line should contain the only integer $l$ ($1 \le l \le 1\,000\,000$), the first element of this segment. It is guaranteed that if a flexible segment of length $n$ exists, then there exists a flexible segment $[l; r]$ of length $n$ such that $1 \le l \le 1\,000\,000$.

The third line should contain a string of length $n$ without spaces. It must consist of "+" and "-" characters. The $(k-l+1)$-th character of this string should be "-" if $a_k = k - 1$, or "+" if $a_k = k + 1$.

In the second example, $n = 4$, $l = 2$, $r = l + n - 1 = 5$. The answer is as follows: $a_2 = 2 - 1 = 1$, $a_3 = 3 + 1 = 4$, $a_4 = 4 + 1 = 5$, $a_5 = 5 + 1 = 6$. The product of the integers from $l$ to $r$ is $2 \cdot 3 \cdot 4 \cdot 5 = 120$. The product of the $a_k$ is $a_2 \cdot a_3 \cdot a_4 \cdot a_5 = 1 \cdot 4 \cdot 5 \cdot 6 = 120$. Thus, the segment $[2; 5]$ is flexible.