Overflow Possibility in Integer Multiplication

Analyzing the data range is crucial in programming contests. In this problem, you are given two int type variables x and y along with their respective ranges. You need to determine whether the product x \times y could possibly exceed the range representable by a 32-bit int.

The int type has a range of \( [-2147483648,\;2147483647] \) which can also be written as \( [-2^{31},\;2^{31}-1] \). That is, the minimum value is \(-2147483648\) and the maximum value is \(2147483647\).

You are given four integers: the minimum and maximum values for x and the minimum and maximum values for y. Determine if there exists a pair \((x, y)\) from the given ranges such that the product x \times y is strictly less than \(-2147483648\) or strictly greater than \(2147483647\). If so, output YES, otherwise output NO.

inputFormat

The input consists of a single line containing four space-separated integers:

• x_min - the minimum possible value of x
• x_max - the maximum possible value of x
• y_min - the minimum possible value of y
• y_max - the maximum possible value of y

outputFormat

Output a single line containing YES if it is possible for the product x \times y to fall outside the range of a 32-bit int \( [-2^{31},\;2^{31}-1] \). Otherwise, output NO.

sample

1 10 1 10

NO