Problem Statement

You are given a sequence $C$ of $N$ integers. Find the number of sequences $A$ of $N$ integers satisfying all of the following conditions.

• $1 \\leq A_i \\leq C_i\\, (1 \\leq i \\leq N)$
• $A_i \\neq A_j\\, (1 \\leq i < j \\leq N)$

Since the count may be enormous, print it modulo $(10^9+7)$.

Constraints

• $1 \\leq N \\leq 2 \\times 10^5$
• $1 \\leq C_i \\leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $C_1$ $C_2$ $\\ldots$ $C_N$

Output

Print the number of sequences $A$ of $N$ integers satisfying all of the following conditions, modulo $(10^9+7)$.

Sample Input 1

2
1 3

Sample Output 1

2

We have two sequences $A$ satisfying all of the conditions: $(1,2)$ and $(1,3)$.
On the other hand, $A=(1,1)$, for example, does not satisfy the second condition.

Sample Input 2

4
3 3 4 4

Sample Output 2

12

Sample Input 3

2
1 1

Sample Output 3

0

We have no sequences $A$ satisfying all of the conditions, so we should print $0$.

Sample Input 4

10
999999917 999999914 999999923 999999985 999999907 999999965 999999914 999999908 999999951 999999979

Sample Output 4

405924645

Be sure to print the count modulo $(10^9+7)$.