C.Alyona and Spreadsheet

During the lesson small girl Alyona works with one famous spreadsheet computer program and learns how to edit tables.

Now she has a table filled with integers. The table consists of n rows and mcolumns. By a_i, j we will denote the integer located at the i-th row and the j-th column. We say that the table is sorted in non-decreasing order in the column j ifa_i, j ≤ a_{i + 1, j} for all i from 1 to n - 1.

Teacher gave Alyona k tasks. For each of the tasks two integers l and r are given and Alyona has to answer the following question: if one keeps the rows from l to rinclusive and deletes all others, will the table be sorted in non-decreasing order in at least one column? Formally, does there exist such j that a_i, j ≤ a_{i + 1, j} for alli from l to r - 1 inclusive.

Alyona is too small to deal with this task and asks you to help!

Input

Output

Example

5 4
1 2 3 5
3 1 3 2
4 5 2 3
5 5 3 2
4 4 3 4
6
1 1
2 5
4 5
3 5
1 3
1 5

Yes
No
Yes
Yes
Yes
No

Note

#include <iostream>
using namespace std;
int n,m,a[100005],b[100005],pre[100005],x,l,r,i,j,k;
int main(){
    cin>>n>>m;
    for(i=1;i<=n;i++){
        pre[i]=i;
        for(j=1;j<=m;j++){
            cin>>x;
            if(x<a[j])
            b[j]=i;
            a[j]=x;
            if(b[j]<pre[i])
            pre[i]=b[j];
        }
    }
    cin>>k;
    while(k--){
        cin>>l>>r;
        if(pre[r]<=l)
        cout<<"Yes"<<endl;
        else
        cout<<"No"<<endl;
    }
}