Square Deal

Time limit2sMemory limit512 MB

Summary

Given three rectangles, decide whether they can be glued edge to edge into a square, with rotations allowed.

Level: Medium4 of 10
Topics: Geometry, Implementation, Brute force
Solved: No attempts yet

Problem

You are given the height and width of three rectangles. Decide whether the three rectangles can be glued together along their edges to form a single square. The three rectangles must cover the square with no gaps, and they must not overlap. A rectangle may be rotated by 90 degrees.

Input

The input consists of three lines. Line $j$ contains the height $H_j$ and the width $W_j$ of the $j$ -th rectangle, separated by a space.

$100 \ge H_j \ge W_j \ge 1$ and $H_1 \ge H_2 \ge H_3$ .

Output

Print YES on one line if the three rectangles can form a square, and NO otherwise.

Examples3

Example 1
Input
```
7 3
7 1
7 3
```
Expected output
```
YES
```
Example 2
Input
```
9 2
7 4
7 5
```
Expected output
```
YES
```
Example 3
Input
```
3 1
3 2
3 3
```
Expected output
```
NO
```