Bricks

Time limit1sMemory limit128 MB

Summary

Given a rectangular brick and a rectangular hole, decide whether the brick can pass through the hole in any orientation.

Level: Medium6 of 10
Topics: Geometry, Math, Implementation
Solved: No attempts yet

Problem

A prisoner of the "IF" castle plans to escape by taking his cell's brick wall apart, one brick at a time. To keep the guards from noticing, he must secretly get rid of every brick he removes. Each brick is a rectangular box measuring $A \times B \times C$ inches and is far too strong to break. In the cell floor there is a small rectangular drain of size $D \times E$ inches that continues straight down as a well of the same cross-section; it is so deep that its depth can be ignored. The prisoner has measured $A$ , $B$ , $C$ , $D$ , $E$ exactly (to a tenth of an inch). Determine whether the bricks can be dropped through the hole.

Input

A single line with five numbers $A$ , $B$ , $C$ , $D$ , $E$ separated by spaces. $A$ , $B$ , $C$ are the lengths of the brick's sides and $D$ , $E$ are the lengths of the hole's sides. Every length is between $1$ and $10$ inches inclusive and has at most one digit after the decimal point.

Output

Print YES on a single line if the bricks can be disposed of through the hole, and NO otherwise.

Examples2

Example 1
Input
```
1.0 2.0 1.5 1.4 1.0
```
Expected output
```
NO
```
Example 2
Input
```
1.0 2.0 1.5 1.5 1.0
```
Expected output
```
YES
```