Uolevi and Maija are going sledding. They are traveling along a road, seeking the tallest hill to descend. The road is $n$ meters long and the height at $i$ meters from the start of the road is $a_i$. Help Uolevi and Maija find the tallest hill, i.e. a monotonically increasing or decreasing segment where the height difference between the endpoints is maximized. Find the endpoints $L$ and $R$ of such a segment.

Input

The first line contains a single integer $n$. The second line contains $n$ integers $a_1,\,a_2,\ldots,\,a_n$.

Output

Print the endpoints of the segment, $L$ and $R$. If there are multiple answers, print any.

Constraints

• $2 \leq n \leq 10^5$
• $1 \leq a_i \leq 10^9$
• $a_i \neq a_j$ if $i \neq j$
• $1 \leq L < R \leq n$

Example 1

Input:

5
1 11 9 19 4

Output:

4 5

Example 2

Input:

10
3 5 17 18 19 20 8 2 1 7

Output:

6 9

Example 3

Input:

3
1 1000000000 2

Output:

1 2