Be Geeks!

The musical band Be Geeks! did not get its name by accident, since every member is a genuine math geek. Among other things, they love examining various properties of number sequences. Here is one example of a subject that interests them.

• Let $A$ be a nonempty sequence of positive integers, $A = (a_1, a_2, \ldots, a_N)$.
• Let $G(i, j) = \gcd(a_i, a_{i+1}, \ldots, a_j)$, where $1 \le i \le j \le N$.
• Let $M(i, j) = \max(a_i, a_{i+1}, \ldots, a_j)$, where $1 \le i \le j \le N$.
• Let $P(i, j) = G(i, j) \cdot M(i, j)$, where $1 \le i \le j \le N$.
• Let $F(A) = \sum P(i, j)$, where the sum runs over all integer pairs $1 \le i \le j \le N$.

The function $\gcd$ stands for the greatest common divisor of the given values. The greatest common divisor of a nonempty sequence of integers is the largest integer that divides every integer in the sequence evenly.

The first line contains one integer $N$ ($1 \le N \le 2 \cdot 10^5$). The next line contains $N$ integers $a_1, a_2, \ldots, a_N$ ($1 \le a_i \le 10^9$).

Print the value of $F(A)$ modulo $1\,000\,000\,007$.