## Is it a Tree?

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Points: 7 (partial)
Time limit: 2.0s
Memory limit: 256M

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Mine is playing a game with Tatsumi, where one person sketches some branches and knots and the other determines whether the sketch is of a tree or not. After playing this for a few hours, they've gotten bored and have decided to make the game more abstract. Now, instead of drawing pictures of trees, the couple fill in a adjacency matrix with either 0 or 1.

Their adjacency matrix stores the relationship between any two knots and . Specifically, if , then there is a branch connecting . Since branches are undirected, a branch from implies a branch from . In this way, the adjacency matrix is symmetrical in that .

An adjacency matrix representing a tree has exactly one path between any pair of and , and hence has 1 less branches than it has knots. Any less and the tree would be disconnected (a forest), and any more and a cycle would exist.

You've decided to join in the fun. Given a adjacency matrix, can you determine whether it represents a tree or not?

#### Input Specification

An adjacency matrix, represented by 4 lines, each containing 4 space-separated integers, either 0 or 1.

#### Output Specification

Yes if the given adjacency matrix represents a tree, or No otherwise.

#### Tips

If you are unfamiliar with the definition of a tree, this Wikipedia article might help.

#### Sample Input 1

0 0 0 1
0 0 0 1
0 0 0 1
1 1 1 0

#### Sample Output 1

Yes

#### Sample Input 2

0 1 0 1
1 0 0 1
0 0 0 1
1 1 1 0

#### Sample Output 2

No

#### Explanation of Output for Sample Input 2

Between Sample 1 and Sample 2 there is a difference of one branch: . This branch creates a cycle, and therefore the number of knots is the same as the number of branches. Hence, it is not a tree.