Box

Time limit3sMemory limit512 MB

Summary

Given a box with edges a, b, c and a w by h cardboard, decide whether some edge-aligned net of the box fits on the cardboard.

Level: Hard8 of 10
Topics: Geometry, Brute force, Implementation, Math
Solved: No attempts yet

Problem

Bella works in a factory that makes boxes. Every box is a rectangular parallelepiped. To make one box, a net is cut out of a flat rectangular piece of cardboard of size $w \times h$ . The net is a polygon whose sides are all parallel to the sides of the cardboard. The net is bent along several lines and joined along the edges of the resulting parallelepiped to form the box. The net is bent only along the edges of the resulting box.



The first example	The third example

Bella is a software developer, and her task is to check whether a box of size $a \times b \times c$ can be made out of a single piece of cardboard of size $w \times h$ . Bella wrote that program and the factory is already producing boxes. Write the same program.

Input

The first line contains three integers $a$ , $b$ , and $c$ , the edge lengths of the box.

The second line contains two integers $w$ and $h$ , the width and the height of the cardboard.

All integers are positive and do not exceed $10^8$ .

Output

Print Yes if a net of the $a \times b \times c$ box can be cut out of the $w \times h$ cardboard. Print No otherwise.

Hint

A cube has 11 different nets, counting rotations and mirror images as the same.

Examples3

Example 1
Input
```
1 2 3
6 5
```
Expected output
```
Yes
```
Example 2
Input
```
1 2 3
5 5
```
Expected output
```
No
```
Example 3
Input
```
1 1 1
10 2
```
Expected output
```
Yes
```