Educational Codeforces Round 44 (Rated for Div. 2) B. Switches and Lamps

B. Switches and Lamps

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given n switches and m lamps. The i-th switch turns on some subset of the lamps. This information is given as the matrix aconsisting of n rows and m columns where ai, j = 1 if the i-th switch turns on the j-th lamp and ai, j = 0 if the i-th switch is not connected to the j-th lamp.

Initially all m lamps are turned off.

Switches change state only from "off" to "on". It means that if you press two or more switches connected to the same lamp then the lamp will be turned on after any of this switches is pressed and will remain its state even if any switch connected to this lamp is pressed afterwards.

It is guaranteed that if you push all n switches then all m lamps will be turned on.

Your think that you have too many switches and you would like to ignore one of them.

Your task is to say if there exists such a switch that if you will ignore (not use) it but press all the other n - 1 switches then all the mlamps will be turned on.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2000) — the number of the switches and the number of the lamps.

The following n lines contain m characters each. The character ai, j is equal to '1' if the i-th switch turns on the j-th lamp and '0' otherwise.

It is guaranteed that if you press all n switches all m lamps will be turned on.

Output

Print "YES" if there is a switch that if you will ignore it and press all the other n - 1 switches then all m lamps will be turned on. Print "NO" if there is no such switch.

Examples

input

Copy

4 5
10101
01000
00111
10000

output

Copy

YES

input

Copy

4 5
10100
01000
00110
00101

output

Copy

NO

题意：给你n行m列的0 1序列，每行代表一种开关，每列代表一个位置的灯泡，0代表关闭，1代表开启，只要该位置有一个开关开启该灯泡就会亮，求如果去掉某一个开关（即去掉某一行）所有位置的灯泡是否仍然都亮。

思路：大暴力，遍历去掉每一个开关，判断是否存在都亮的情况。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
using namespace std;
#define ll long long
const int maxn = 2005;
char s[maxn][maxn];
int a[maxn];

int main()
{
        int n, m;
        memset(a, 0, sizeof(a));
        scanf("%d%d", &n, &m);
        for (int i = 0; i < n; i ++) {
                scanf("%s", s[i]);
        }
        for (int i = 0; i < n; i ++) {
                for (int j = 0; j < m; j ++) {
                        a[j] += s[i][j]-'0';
                }
        }
        int flag;
        for (int i = 0; i < n; i ++) {
                flag = 1;
                for (int j = 0; j < m; j ++) {
                        if (a[j] - (s[i][j]-'0') == 0) {
                                flag = 0;
                                break;
                        }
                }
                if (flag) {
                        break;
                }
        }
        if (flag) printf("YES\n");
        else printf("NO\n");
}