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 of f(n). For example, digital root of 987 is 6. Your task is to find digital root for expression A₁*A₂*…*A_N + A₁*A₂*…*A_N-1 + … + A₁*A₂ + A_1.

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 number N is written on the first place of test case (N<=1000). After it there are N positive integer numbers (sequence A). Each of this numbers is non-negative and not more than 10^9.

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