Duff is one if the heads of Mafia in her country, Andarz Gu. Andarz Gu has n cities (numbered from 1 to n) connected by m bidirectional roads (numbered by 1 to m).
Each road has a destructing time, and a color. i-th road connects cities vi and ui and its color is ci and its destructing time is ti.
Mafia wants to destruct a matching in Andarz Gu. A matching is a subset of roads such that no two roads in this subset has common endpoint. They can destruct these roads in parallel, i. e. the total destruction time is a maximum over destruction times of all selected roads.
They want two conditions to be satisfied:
- The remaining roads form a proper coloring.
- Destructing time of this matching is minimized.
The remaining roads after destructing this matching form a proper coloring if and only if no two roads of the same color have same endpoint, or, in the other words, edges of each color should form a matching.
There is no programmer in Mafia. That's why Duff asked for your help. Please help her and determine which matching to destruct in order to satisfied those conditions (or state that this is not possible).
The first line of input contains two integers n and m (2 ≤ n ≤ 5 × 104 and 1 ≤ m ≤ 5 × 104), number of cities and number of roads in the country.
The next m lines contain the the roads. i - th of them contains four integers vi, ui, ci and ti (1 ≤ vi, ui ≤ n, vi ≠ ui and 1 ≤ ci, ti ≤ 109 for each 1 ≤ i ≤ m).
In the first line of input, print "Yes" (without quotes) if satisfying the first condition is possible and "No" (without quotes) otherwise.
If it is possible, then you have to print two integers t and k in the second line, the minimum destructing time and the number of roads in the matching (
).
In the third line print k distinct integers separated by spaces, indices of the roads in the matching in any order. Roads are numbered starting from one in order of their appearance in the input.
If there's more than one solution, print any of them.
5 7 2 1 3 7 3 1 1 6 5 4 1 8 4 5 1 1 3 2 2 3 4 5 2 5 2 3 2 4
Yes 3 2 4 5
3 5 3 2 1 3 1 3 1 1 3 2 1 4 1 3 2 2 1 3 2 10
No
Graph of Andarz Gu in the first sample case is as follows:
A solution would be to destruct the roads with crosses.
Graph of Andarz Gu in the second sample case is as follows:
题目大意：给出一张无向图，给出图上的边的颜色和破坏它所需的时间。现在要破坏若干条边，要求任意两条被破坏的边不能有公共点，且任意两条没有被破坏且颜色相同的边不能有公共点，求一个被破坏的边的最大破坏时间最小的方案。
首先二分答案，然后把边是否破坏当成布尔变量，用2-SAT验证并构造解。对于被破坏的边没有公共点的限制，可以给每条边建立两个辅助点，具体可以看代码。
代码在此。
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