write a go solution for C. Twin Polynomialstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA polynomial f(x)=a_0+a_1x+a_2x^2+ldots+a_nx^n is called a valid polynomial of degree n if and only if a_i is a non-negative integer for all 0<=i<=n and a_n is not 0.For a valid polynomial f(x)=a_0+a_1x+a_2x^2+ldots+a_nx^n of degree n, its twin polynomial g(x) is defined as:  g(x) = \sum_{i=0}^n i \cdot x^{a_i}  For example, for f(x)=1+2x+2x^3, its twin polynomial is: g(x) = 0 \cdot x^{1} + 1 \cdot x^{2} + 2 \cdot x^{0} + 3 \cdot x^{2} = 0+x^2+2+3x^2= 2 + 4x^2 A valid polynomial f(x) of degree n is called cool if and only if f(x)=g(x). In other words, a valid polynomial of degree n is cool if and only if its twin polynomial equals itself.You are given an incomplete valid polynomial f(x)=a_0+a_1x+a_2x^2+ldots+a_nx^n of degree n. Some of a_i have been determined, while others have not been determined. Additionally, it is guaranteed that a_0 and a_n are not determined.Please count the number of cool valid polynomials of degree n that can be found by determining all undetermined a_i's. Since the answer may be large, you need to output it modulo 1,000,000,007.InputEach test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of the test cases follows. For each test case, the first line contains an integer n (1<=n<=4*10^5).The second line contains n+1 integers a_0,a_1,ldots,a_n (-1<=a_i<=10^9). Here, a_i=-1 means a_i has not been determined, while a_ineq-1 means a_i has been determined as its value.It is guaranteed that a_0 and a_n are always -1 in the input.It is guaranteed that the sum of n over all test cases does not exceed 4*10^5.OutputFor each test case, output the number of cool valid polynomials of degree n found by determining the undetermined a_i's, modulo 1,000,000,007.ExampleInput61-1 -12-1 2 -12-1 -1 -13-1 -1 3 -13-1 2 3 -15-1 -1 -1 1 0 -1Output113203NoteIn the first test case, only f(x)=x satisfies the condition above.In the second test case, only f(x)=x^2+2x satisfies the condition above.In the third test case, f(x)=2x^2+x, f(x)=x^2+2x, and f(x)=2x^2+1 satisfy the condition above.. Output only the code with no comments, explanation, or additional text.