Jim is planning to visit one of his best friends in a town in the mountain area. First, he leaves his hometown and goes to the destination town. This is called the go phase. Then, he comes back to his hometown. This is called the return phase. You are expected to write a program to find the minimum total cost of this trip, which is the sum of the costs of the go phase and the return phase.

There is a network of towns including these two towns. Every road in this network is one-way, i.e., can only be used towards the specified direction. Each road requires a certain cost to travel.

In addition to the cost of roads, it is necessary to pay a specified fee to go through each town on the way. However, since this is the visa fee for the town, it is not necessary to pay the fee on the second or later visit to the same town.

The altitude (height) of each town is given. On the go phase, the use of descending roads is inhibited. That is, when going from town *a* to *b*, the altitude of *a* should not be greater than that of *b*. On the return phase, the use of ascending roads is inhibited in a similar manner. If the altitudes of *a* and *b* are equal, the road from *a* to *b* can be used on both phases.

The input consists of multiple datasets, each in the following format.

*n m
d _{2} e_{2}
d_{3} e_{3}
.
.
.
d_{n-1} e_{n-1}
a_{1} b_{1} c_{1}
a_{2} b_{2} c_{2}
.
.
.
a_{m} b_{m} c_{m}
*

Every input item in a dataset is a non-negative integer. Input items in a line are separated by a space.

*n* is the number of towns in the network. *m* is the number of (one-way) roads. You can assume the inequalities 2 ≤ *n* ≤ 50 and 0 ≤ *m* ≤ *n*(*n*−1) hold. Towns are numbered from 1 to *n*, inclusive. The town 1 is Jim's hometown, and the town *n* is the destination town.

*d _{i}* is the visa fee of the town

The *j*-th road is from the town *a _{j}* to

The last dataset is followed by a line containing two zeros (separated by a space).

For each dataset in the input, a line containing the minimum total cost, including the visa fees, of the trip should be output. If such a trip is not possible, output “-1”.

3 6 3 1 1 2 1 2 3 1 3 2 1 2 1 1 1 3 4 3 1 4 3 6 5 1 1 2 1 2 3 1 3 2 1 2 1 1 1 3 4 3 1 4 4 5 3 1 3 1 1 2 5 2 3 5 3 4 5 4 2 5 3 1 5 2 1 2 1 1 0 0

7 8 36 -1

Source: ACM International Collegiate Programming Contest
, Asia Regional Fukuoka, Fukuoka, Japan, 2011-11-13

http://icpc2011.ait.kyushu-u.ac.jp/

http://icpc2011.ait.kyushu-u.ac.jp/