Problem Statement

AtCoder Ski Area has $N$ open spaces called Space $1$, Space $2$, $\\ldots$, Space $N$. The altitude of Space $i$ is $H_i$. There are $M$ slopes that connect two spaces bidirectionally. The $i$-th slope $(1 \\leq i \\leq M)$ connects Space $U_i$ and Space $V_i$. It is possible to travel between any two spaces using some slopes.

Takahashi can only travel between spaces by using slopes. Each time he goes through a slope, his happiness changes. Specifically, when he goes from Space $X$ to Space $Y$ by using the slope that directly connects them, his happiness changes as follows.

• If the altitude of Space $X$ is strictly higher than that of Space $Y$, the happiness increases by their difference: $H_X-H_Y$.
• If the altitude of Space $X$ is strictly lower than that of Space $Y$, the happiness decreases by their difference multiplied by $2$: $2(H_Y-H_X)$.
• If the altitude of Space $X$ is equal to that of Space $Y$, the happiness does not change.

The happiness may be a negative value.

Initially, Takahashi is in Space $1$, and his happiness is $0$. Find his maximum possible happiness after going through any number of slopes (possibly zero), ending in any space.

Constraints

• $2 \\leq N \\leq 2\\times 10^5$
• $N-1 \\leq M \\leq \\min( 2\\times 10^5,\\frac{N(N-1)}{2})$
• $0 \\leq H_i\\leq 10^8$ $(1 \\leq i \\leq N)$
• $1 \\leq U_i < V_i \\leq N$ $(1 \\leq i \\leq M)$
• $(U_i,V_i) \\neq (U_j, V_j)$ if $i \\neq j$.
• All values in input are integers.
• It is possible to travel between any two spaces using some slopes.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $H_1$ $H_2$ $\\ldots$ $H_N$ $U_1$ $V_1$ $U_2$ $V_2$ $\\vdots$ $U_M$ $V_M$

Output

Print the answer.

Sample Input 1

4 4
10 8 12 5
1 2
1 3
2 3
3 4

Sample Output 1

3

If Takahashi takes the route Space $1$ $\\to$ Space $3$ $\\to$ Space $4$, his happiness changes as follows.

• When going from Space $1$ (altitude $10$) to Space $3$ (altitude $12$), it decreases by $2\\times (12-10)=4$ and becomes $0-4=-4$.
• When going from Space $3$ (altitude $12$) to Space $4$ (altitude $5$), it increases by $12-5=7$ and becomes $\-4+7=3$.

If he ends the travel here, the final happiness will be $3$, which is the maximum possible value.

Sample Input 2

2 1
0 10
1 2

Sample Output 2

0

His happiness is maximized by not moving at all.