PCPC12I - peaks

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

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

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

Output:
3 4 5
1 4 5

Added by:abdelkarim
Date:2012-12-28
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:The First Palestinian Collegiate Programming Contest

hide comments
2015-06-10 23:22:11 .:frUstrAteD:.
why pair of integer array works faster than two separate integer arrays -_- ??
2013-01-05 20:40:22 (Tjandra Satria Gunawan)(曾毅昆)
0.25s is my best speed ;-)
Note: It's Impossible to become faster than 0.15s because huge input data...

Last edit: 2013-01-05 21:19:20
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