Extra Element

A sequence a_1, a_2, ..., a_k is called an arithmetic progression if for each i from 1 to k elements satisfy the condition a_i = a_1 + c ⋅ (i - 1) for some fixed c.

For example, these five sequences are arithmetic progressions: [5, 7, 9, 11], [101], [101, 100, 99], [13, 97] and [5, 5, 5, 5, 5]. And these four sequences aren't arithmetic progressions: [3, 1, 2], [1, 2, 4, 8], [1, -1, 1, -1] and [1, 2, 3, 3, 3].

You are given a sequence of integers b_1, b_2, ..., b_n. Find any index j (1 ≤ j ≤ n), such that if you delete b_j from the sequence, you can reorder the remaining n-1 elements, so that you will get an arithmetic progression. If there is no such index, output the number -1.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2⋅10^5) — length of the sequence b. The second line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9) — elements of the sequence b.

Output

Print such index j (1 ≤ j ≤ n), so that if you delete the j-th element from the sequence, you can reorder the remaining elements, so that you will get an arithmetic progression. If there are multiple solutions, you are allowed to print any of them. If there is no such index, print -1.

Examples

Input

5 2 6 8 7 4

Output

4

Input

8 1 2 3 4 5 6 7 8

Output

1

Input

4 1 2 4 8

Output

-1

Note

Note to the first example. If you delete the 4-th element, you can get the arithmetic progression [2, 4, 6, 8].

Note to the second example. The original sequence is already arithmetic progression, so you can delete 1-st or last element and you will get an arithmetical progression again.

inputFormat

outputFormat

output the number -1.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2⋅10^5) — length of the sequence b. The second line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9) — elements of the sequence b.

Output

Print such index j (1 ≤ j ≤ n), so that if you delete the j-th element from the sequence, you can reorder the remaining elements, so that you will get an arithmetic progression. If there are multiple solutions, you are allowed to print any of them. If there is no such index, print -1.

Examples

Input

5 2 6 8 7 4

Output

4

Input

8 1 2 3 4 5 6 7 8

Output

1

Input

4 1 2 4 8

Output

-1

Note

Note to the first example. If you delete the 4-th element, you can get the arithmetic progression [2, 4, 6, 8].

Note to the second example. The original sequence is already arithmetic progression, so you can delete 1-st or last element and you will get an arithmetical progression again.

样例

8
1 2 3 4 5 6 7 8

1

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