A computer program evaluates expressions without parentheses in the following way:

1) First, it performs the multiplications and divisions from left to right one by one.
2) Then, it performs the additions and subtractions again from left to right.

For example, the value of the expression $1-2 / 3-4$ is $-3 \frac{2}{3}$. How many different results can we get if in the following expression we write one of the signs $+- /, \times$ independently in each $*$ position?

$1 * 1 * 1 * 1 * 1 * 1 * 1 * 1$
Let's assume that we have already placed the operational symbols in the expression in some way. First, let's examine the parts of the expression where only × or / operations lie between the 1s! The computer first calculates the value of these parts. The result can only be 1, since the initial value of 1 can only be multiplied or divided by 1. Thus, the effect of multiplication and division is the same: they "collapse" multiple 1s. Therefore, the value of the expression does not change if we replace every "× 1" and "/1" with "+0".

The resulting expression is an eight-term sum, where the first term is always 1, and the others can be +1, 0, or -1. It is clear that the value of the expression will be an integer. It reaches its maximum when all terms are maximal, i.e., +1, and in this case the sum is 8, while it reaches its minimum when the other terms are all -1; in this case the sum is -6.

If the value of the expression is not maximal, it can be increased by one. Indeed, in this case, at least one zero or -1 term appears, which, when increased by 1 (replacing +0 with +1, i.e., × 1 or /1 with +1; while replacing -1 with +0, i.e., × 1 or /1) will increase the sum by 1. The consequence of this is that the expression takes on every integer value between 8 and -6. Therefore, the answer to the question of the problem is the number of integers between 8 and -6, which is 15.