Wave Sorting

Have the function WaveSorting(arr) take the array of positive integers stored in arr and return the string true if the numbers can be arranged in a wave pattern: a1 > a2 < a3 > a4 < a5 > ..., otherwise return the string false. For example, if arr is: [0, 1, 2, 4, 1, 4], then a possible wave ordering of the numbers is: [2, 0, 4, 1, 4, 1]. So for this input your program should return the string true. The input array will always contain at least 2 elements. More examples are given below as sample test cases.

Examples

Input: [0, 1, 2, 4, 1, 1, 1]
Output: false

Input: [0, 4, 22, 4, 14, 4, 2]
Output: true