Gandalf is travelling from

**Rohan**to**Rivendell**to meet Frodo but there is no direct route from**Rohan**(T1) to**Rivendell**(Tn).
But there are towns T2,T3,T4...Tn-1 such that there are N1 routes from Town T1 to T2, and in general, Ni routes from Tito Ti+1 for i=1 to n-1 and 0 routes for any other Ti to Tj for j ≠ i+1

Find the total number of routes Gandalf can take to reach Rivendell from Rohan.

**Note**

Gandalf has to pass all the towns Ti for i=1 to n-1 in numerical order to reach Tn.

For each Ti , Ti+1 there are only Ni distinct routes Gandalf can take.

**Input Format**

The first line contains an integer T, T test-cases follow.

Each test-case has 2 lines. The first line contains an integer N (the number of towns).

The second line contains N - 1 space separated integers where the ith integer denotes the number of routes, Ni, from the town Ti to Ti+1

**Output Format**

Total number of routes from T1 to Tn modulo 1234567

http://en.wikipedia.org/wiki/Modular_arithmetic

**Constraints**

1 <= T<=1000

2< N <=100

1 <= Ni <=1000

**Sample Input**

```
2
3
1 3
4
2 2 2
```

**Sample Output**

```
3
8
```

**Explanation**

Case 1: 1 route from T1 to T2, 3 routes from T2 to T3, hence only 3 routes.

Case 2: There are 2 routes from each city to the next, at each city, Gandalf has 2 choices to make, hence 2 * 2 * 2 = 8.

Note: Write your code in comments section below.