Ones

We define 1-expressions as numeric expressions that contain only ones, addition signs, multiplication signs, and parentheses. In such an expression no two digits may be adjacent: every two ones must be separated by an operator. Expressions follow the usual order of evaluation. For example, multiplication has higher priority than addition.

For example, each of the following 1-expressions evaluates to 6:

(1+1)*(1+1+1), (1+1+1)*(1+1)*1, ((1+1)+1)*(1+1), 1+1+1+1+1+1, 1+(1+(1+(1+(1+1)))).

Formally, the following grammar describes all valid 1-expressions $E$:

E ::= 1 | E+E | E*E | (E+E) | (E*E)

Write a program that, given an integer $k$ ($k \le 10^9$), outputs a 1-expression evaluating to $k$ that contains at most 100 ones.

The first line of the input contains a single integer $t$ ($1 \le t \le 100$), the number of testcases.

Each of the following $t$ lines describes a single testcase. The $i$-th of these lines describes the $i$-th test and contains a single integer $k\_i$ ($1 \le k\_i \le 10^9$).

You must output exactly $t$ lines.

If no 1-expression evaluates to $k\_i$ and contains at most 100 ones, output NO on the $i$-th line. Otherwise, that line must contain a valid expression. Do not print any spaces inside the expression. If there is more than one valid solution, print any of them.