Problem Statement

You are given an undirected tree with $N$ vertices. Let us call the vertices Vertex $1$, Vertex $2$, $\ldots$, Vertex $N$. For each $1\leq i\leq N-1$, the $i$-th edge connects Vertex $U_i$ and Vertex $V_i$. Additionally, each vertex is assigned a positive integer: Vertex $i$ is assigned $A_i$.

The cost between two distinct vertices $s$ and $t$, $C(s,t)$, is defined as follows.

Let $p_1(=s)$, $p_2$, $\ldots$, $p_k(=t)$ be the vertices of the simple path connecting Vertex $s$ and Vertex $t$, where $k$ is the number of vertices in the path (including the endpoints). Then, let $C(s,t)=k\times \gcd (A_{p_1},A_{p_2},\ldots,A_{p_k})$, where $\gcd (X_1,X_2,\ldots, X_k)$ denotes the greatest common divisor of $X_1,X_2,\ldots, X_k$.

Find $\displaystyle\sum_{i=1}^{N-1}\sum_{j=i+1}^N C(i,j)$, modulo $998244353$.

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq A_i\leq 10^5$
• $1\leq U_i<V_i\leq N$
• All values in input are integers.
• The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N
U_1 V_1
U_2 V_2
\vdots
U_{N-1} V_{N-1}

Output

Print $\displaystyle\sum_{i=1}^{N-1}\sum_{j=i+1}^N C(i,j)$, modulo $998244353$.