Are They All Integers?

Interview

Time limit2sMemory limit1024 MB

Summary

Decide whether (A[i]-A[j])/A[k] is an integer for every choice of three distinct indices in a sorted list.

Level: Easy3 of 10
Topics: Brute force, Math, Number theory, Implementation
Solved: No attempts yet

Problem

Computing with integers alone is a dream for every programmer. There is no need to deal with floating point numbers, estimated errors, and the like. We do not even need floating point units in our computers for divisions!

Your company claims it has a brand new computational model that solves integer problems efficiently. As a software engineer at the Integer Computing Processors Company (ICPC), you are going to write a validator that checks the following.

Given a list of positive integers A[0], ..., A[n − 1]. Suppose you pick three different elements of this list arbitrarily, A[i], A[j], A[k], with i, j, k being mutually different. Is it true that (A[i]−A[j])/A[k] is always an integer?

Input

The first line of the input contains one integer n indicating the number of positive integers in the list. The second line of the input contains n positive integers A[0], ..., A[n − 1] separated by blanks.

Output

If (A[i]−A[j])/A[k] is always an integer, output yes. Otherwise output no.

Constraints

3 ≤ n ≤ 50
1 ≤ A[0] ≤ A[1] ≤ ... ≤ A[n − 1] ≤ 100

Examples2

Example 1
Input
```
5
1 1 1 1 4
```
Expected output
```
yes
```
Example 2
Input
```
5
1 2 4 8 16
```
Expected output
```
no
```