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Codeforces

Easy

Arrays

Math

Young Physicist

Check whether a set of 3D force vectors adds up to the zero vector.

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Problem Statement

You are given $n$ force vectors in 3D space. Each vector is described by its $x$ , $y$ , and $z$ components.

Your task is to determine whether the physicist can keep the body in equilibrium, which happens exactly when the sum of all vectors is the zero vector.

In other words, after adding all $x$ components together, all $y$ components together, and all $z$ components together, each total must be $0$.

Print YES if the body is in equilibrium, otherwise print NO.

Input Format

The first line contains an integer $n$ .
Each of the next $n$ lines contains three integers $x$ , $y$ , and $z$ describing one vector.

Output Format

Print YES if the sum of all vectors is $(0, 0, 0)$ .
Otherwise print NO.

Constraints

$1 \le n$
Each coordinate is an integer.
The exact bounds are not required for solving this task; use integer arithmetic.

Examples

Sample cases returned by the problem API.

Example 1

Input

3
4 1 7
-2 4 -1
-2 -5 -6

Output

YES

Explanation

The component-wise sums are $4-2-2=0$ , $1+4-5=0$ , and $7-1-6=0$ .

Example 2

Input

3
3 -1 7
-5 2 -4
2 -1 -2

Output

NO

Explanation

The sums are $3-5+2=0$ , $-1+2-1=0$ , and $7-4-2=1$ , so the result is not the zero vector.

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