Distinct Values Subsequences

Given an array of n integers, count the number of subsequences where each element is distinct. A subsequence is a sequence of array elements from left to right that may have gaps.

Input

The first line has an integer n: the array size. The second line has n integers x_1,x_2,\dots,x_n: the array contents.

Output

Print the number of subsequences with distinct elements. The answer can be large, so print it modulo 10^9+7.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le x_i \le 10^9$

Example

Input

4
1 2 1 3

Output

11

Explanation: The subsequences are [1] (two times), [2], [3], [1,2], [1,3] (two times), [2,1], [2,3], [1,2,3] and [2,1,3].