## PCPC12I - peaks

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You are given a sequence of numbers s, you are required to find 3 indices i, j, k, where i < j < k and (s[i] <= s[j] >= s[k] or s[i] >= s[j] <= s[k]) if there are many solutions you should find the one where |s[i]-s[j]| + |s[j]-s[k]| is maximized, if there are still many solutions you should find the one which comes earlier in order (i.e. i1, j1, k1, comes before i2, j2, k2, if i1<i2, or if i1=i2, and j1<j2, or if i1=i2, j1=j2, and k1<k2 ).
Input Specification
The problem will be tested on multiple test cases, the first line of the input contains an integer n representing the size of the sequence (3<=n<=10^6) (^ means power), then followed by n integers, All numbers in this sequence do not exceed 10^6 in absolute value. The input is terminated by end of file.
Output Specification
For each test case, output a line containing the 3 indices of the pattern i, j, k space separated. If there is no such pattern output -1 instead.
Sample Input
7
2 3 1 7 2 4 8
5
2 3 5 7 1
Sample Output
3 4 5
1 4 5

You are given a sequence of numbers s, you are required to find 3 indices i, j, k, where i < j < k and (s[i] <= s[j] >= s[k] or s[i] >= s[j] <= s[k]) if there are many solutions you should find the one where |s[i]-s[j]| + |s[j]-s[k]| is maximized, if there are still many solutions you should find the one which comes earlier in order (i.e. i1, j1, k1, comes before i2, j2, k2, if i1<i2, or if i1=i2, and j1<j2, or if i1=i2, j1=j2, and k1<k2 ).

Input Specification

The problem will be tested on multiple test cases, the first line of the input contains an integer n representing the size of the sequence (3<=n<=10^6) (^ means power), then followed by n integers, All numbers in this sequence do not exceed 10^6 in absolute value. The input is terminated by end of file.

Output Specification

For each test case, output a line containing the 3 indices of the pattern i, j, k space separated. If there is no such pattern output -1 instead.

Sample Input

7

2 3 1 7 2 4 8

5

2 3 5 7 1

Sample Output

3 4 5

1 4 5