Consider the list of pairs of integers used in the previous questions. In Prolog, such lists are denoted by using the following syntax:

$[[2,3],[4,-2],[3,3]][[2,3]]$

$[]$

Write a Prolog predicate intPairList$/1$ which takes only $1$ parameter and evaluates to YES only if this parameter is a list of pairs of integers. You can assume that the constants in the parameters will always be integers $($you don$$t need to check that$).$

Some example queries are given below:

$?-$ intPairList$([[2,3],[4,-2],[3,3]]).$

YES

$?-$ intPairList$([[2,3]]).$

YES

$?-$ intPairList$([]).$

YES

$?-$ intPairList$([1,2])$

NO

$?-$ intPairList$([[1,2,3]]).$

NO

$?-$ intPairList$([[2,3],[4,-2,1],[3,3]]).$

NO

RULES:

$$ You can use only one fact and only one rule.

$$ You must use anonymous variables whenever possible.