Given an array $$A$$ , a subsequence of A is said to be good subsequence, if it has at least one pair of consecutive elements such that their absolute difference is less than equal to 1.

Formally, if the subsequence $$B$$ has $$m$$ elements, then it is a good subsequence if there exists at least one index $$i$$ ($$2 \le i \le m$$) such that $$abs(B_i - B_{i-1}) \le 1$$.

You have to find the total number of good subsequences of array A modulo $$10^9+7$$.

Obviously, a good subsequence has to have at least 2 elements in it.

For example if sequence has 3 elements [3, 4, 5], subsequence [3, 4], [4, 5] and [3, 4, 5] are good subsequnces. So our answer will be 3 in this case.

Input Format

The first line contains a single integer $$N$$ ($$2 \le n \le 10^5$$), denoting the number of elements in A

The second line contains $$N$$ integers $$A_1, A_2, \ldots, A_n$$ ($$1 \le A_i \le 10^5$$).

Output Format

Output the total number of good subsequences of the array $$A$$ modulo $$10^9$$+7