Shortest Path

在Ancient Berland有$n$ 座城市和$m$ 条长度相同的双向道路。城市从$1$ 到$n$ 编号。根据一个古老的迷信说法，如果一个旅行者连续访问了$a_i$ 、$b_i$ 、$c_i$ 三座城市而不去拜访其他城市，来自东方的神秘力量将使他遭受巨大的灾害。传说中一共有$k$ 组这样的城市，每个三元组都是有序的，这意味着你可以按照$a_i$ 、$c_i$ 、$b_i$ 这样的方式来访问一组城市而不遭受灾害。Vasya想要从城市$1$ 走到城市$n$ 并且不受到诅咒。请告诉他最短路的长度，并输出一条路线。 ### 输入格式 第1行$3$ 个整数$n$ ，$m$ ，$k$ ，表示城市数、路径数以及三元组数量。 接下来$m$ 行，每行$2$ 个整数$x_i$ ，$y_i$ ，表示存在一条连接xi与yi的路。 接下来k行，每行3个整数$a_i$ 、$b_i$ 、$c_i$ ，表示一个诅咒三元组。 可能从$1$ 号城市出发并不能到达$n$ 号城市。 ###输出格式 无解输出$-1$ 。 否则第1行输出最短路长度$d$ ，第2行输出$d+1$ 个数，表示一条可行最短路径。 翻译贡献者UID：35718

In Ancient Berland there were $ n $ cities and $ m $ two-way roads of equal length. The cities are numbered with integers from $ 1 $ to $ n $ inclusively. According to an ancient superstition, if a traveller visits three cities $ a_{i} $ , $ b_{i} $ , $ c_{i} $ in row, without visiting other cities between them, a great disaster awaits him. Overall there are $ k $ such city triplets. Each triplet is ordered, which means that, for example, you are allowed to visit the cities in the following order: $ a_{i} $ , $ c_{i} $ , $ b_{i} $ . Vasya wants to get from the city $ 1 $ to the city $ n $ and not fulfil the superstition. Find out which minimal number of roads he should take. Also you are required to find one of his possible path routes.

The first line contains three integers $ n $ , $ m $ , $ k $ ( $ 2<=n<=3000,1<=m<=20000,0<=k<=10^{5} $ ) which are the number of cities, the number of roads and the number of the forbidden triplets correspondingly. Then follow $ m $ lines each containing two integers $ x_{i} $ , $ y_{i} $ ( $ 1<=x_{i},y_{i}<=n $ ) which are the road descriptions. The road is described by the numbers of the cities it joins. No road joins a city with itself, there cannot be more than one road between a pair of cities. Then follow $ k $ lines each containing three integers $ a_{i} $ , $ b_{i} $ , $ c_{i} $ ( $ 1<=a_{i},b_{i},c_{i}<=n $ ) which are the forbidden triplets. Each ordered triplet is listed mo more than one time. All three cities in each triplet are distinct. City $ n $ can be unreachable from city $ 1 $ by roads.

If there are no path from $ 1 $ to $ n $ print -1. Otherwise on the first line print the number of roads $ d $ along the shortest path from the city $ 1 $ to the city $ n $ . On the second line print $ d+1 $ numbers — any of the possible shortest paths for Vasya. The path should start in the city $ 1 $ and end in the city $ n $ .

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

2
1 3 4

3 1 0
1 2

-1

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

4
1 3 2 3 4