学步园

118. Digital Root

time limit per test: 0.25 sec.
memory limit per test: 4096 KB

Let f(n) be a sum of digits for positive integer
n. If f(n) is one-digit number then it is a digital root for n and otherwise digital root of n is equal to digital root off(n). For example, digital root of987 is
6. Your task is to find digital root for expressionA₁*A₂*…*A_N + A₁*A₂*…*A_N-1 + … + A₁*A₂+ A₁.

Input

Input file consists of few test cases. There is K (1<=K<=5) in the first line of input. Each test case is a line. Positive integer numberN is written on the first place of test case (N<=1000). After it there areN positive
integer numbers (sequence A). Each of this numbers is non-negative and not more than10⁹.

Output

Write one line for every test case. On each line write digital root for given expression.

Sample Input

1
3 2 3 4

Sample Output

5

将一个数的各位相加得到f(n)，如果f(n)为1位，则f(n)为n的digital root，否则n的digital root为f(n)的digital root

给出一个数组A，求A₁*A₂*…*A_N + A₁*A₂*…*A_N-1 + … + A₁*A₂+ A_{1 
的digital root}

_{样例理解： A1 = 2， A2 = 3， A3 = 4             2*3*4 + 2*3 + 2 = 32    f(32) = f(5) = 5}

_{把题目转化成: A1 + A1*A2 + A1*A2*A3 + A1*A2*A3的形式非常好看}