Flexible Segments#8715
A great mathematician Vladimir Germanovich has noticed an interesting property of some segments of positive integers while exploring them for new patterns.
Vladimir calls the segment of positive integers , l + 1, , flexible if he is able to change every number of this segment by exactly one in such way, that the product of numbers on this segment doesn't change. That is, there exists a sequence a_l, a_{l+1}, , 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 if he is able to build flexible segment of any length. Given positive integer find any flexible segment that consists of n consecutive positive integers or tell that there is no such segment.
One integer (1 \le n \le 10\,000) - the length of required segment.
The first line must contain **"YES"** if there exists a flexible segment of positive integers. Otherwise it must contain **"NO"**.
If such segment exists the second and the third lines must contain the description of this segment.
The second line should contain the only integer (1 \le l \le 1\,000\,000) - the first element of this segment. It is guaranteed that if a flexible segment of length exists then there exists a flexible segment [l, r] of length such that 1 \le l \le 1\,000\,000.
The third line should contain a string of length 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.
Example 1
Example 2
In the second example n = 4, l = 2, r = l + n - 1 = 5. The answer is the following: a_2 = 2 - 1 = 1, a_3 = 3 + 1 = 4, a_4 = 4 + 1 = 5, a_5 = 5 + 1 = 6. The product of integers from to is 2 \cdot 3 \cdot 4 \cdot 5 = 120. The product of 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 is flexible.