Turn the Rectangles (水题)

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本文介绍了一个有趣的问题：如何通过旋转矩形使其高度按非升序排列。提供了算法思路及实现代码，通过比较每个矩形的高度和宽度来决定是否旋转。

Turn the Rectangles

There are n rectangles in a row. You can either turn each rectangle by 90

degrees or leave it as it is. If you turn a rectangle, its width will be height, and its height will be width. Notice that you can turn any number of rectangles, you also can turn all or none of them. You can not change the order of the rectangles.

Find out if there is a way to make the rectangles go in order of non-ascending height. In other words, after all the turns, a height of every rectangle has to be not greater than the height of the previous rectangle (if it is such).

Input

The first line contains a single integer n

(1≤n≤105

) — the number of rectangles.

Each of the next n
lines contains two integers wi and hi (1≤wi,hi≤109) — the width and the height of the i

-th rectangle.

Output

Print "YES" (without quotes) if there is a way to make the rectangles go in order of non-ascending height, otherwise print "NO".

You can print each letter in any case (upper or lower).

Examples
Input

3
3 4
4 6
3 5

Output

YES

Input

2
3 4
5 5

Output

NO

Note

In the first test, you can rotate the second and the third rectangles so that the heights will be [4, 4, 3].

In the second test, there is no way the second rectangle will be not higher than the first one.

每次选择小于等于前一个的较大值，如果找不到就是no，如果完成循环，就是yes

code：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int maxn = 1e5+10;
int n;
int re[maxn][2];
int s[maxn];
int top = -1;
int main(){
    cin >> n;
    for(int i = 0; i < n; i++){
        scanf("%d%d",&re[i][0],&re[i][1]);
    }
    s[++top] = max(re[0][0],re[0][1]);
    int flag = 1;
    for(int i = 1; i < n; i++){
        int tmp = -1;
        if(re[i][0] <= s[top]) tmp = re[i][0];
        if(re[i][1] <= s[top]) tmp = re[i][1];
        if(re[i][0] <= s[top] && re[i][1] <= s[top]) tmp = max(re[i][0],re[i][1]);
        if(tmp == -1){
            flag = 0;
            break;
        }
        s[++top] = tmp;
    }
    if(flag) printf("YES\n");
    else printf("NO\n");
    return 0;
}