///////////////////////Loading Payloads.......////////////////////////////
#include<bits/stdc++.h>
#define f(i,a,b) for(int i = a; i < b; i++)
#define fd(i,a,b) for(int i = a; i > b;i--)
#define fld(i,a,b) for(ll i = a ; i > b;i--)
#define ll long long
#define fl(i,a,b) for(ll i = a; i < b; i++)
#define VI vector<int>
#define VP vector<pair<int,int>>
#define VPL vector<pair<ll,ll>>
#define VS vector<string>
#define VL vector<long long>
#define VC vector<char>
#define VF vector<float>
#define VD vector<double>
#define VB vector<bool>
#define PB push_back
#define F first
#define S second
#define fa(i,skill) for(auto i : skill)
#define fr(i,skill) for(VI :: reverse_iterator i = skill.rbegin(); i != skill.rend(); i++)
#define PI pair<int,int>
#define mi map<int,int>
#define ml map<ll,ll>
#define mci map<char,int>
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define MAX 1000000000.00
#define INF 1000000000
#define debug(x) cout<<"This side    ----> "<<#x<<" -> "<<x<<endl
using namespace std;

///////////////////////Engine Check.......////////////////////////////
void edit(VI &skill,int n)
{
    f(i,0,n)
        {
            int x;
            cin >> x;
            skill.PB(x);
        }
}
void editl(VL &skill,ll n)
{
    fl(i,0,n)
        {
            ll x;
            cin >> x;
            skill.PB(x);
        }
}
void editpl(VPL &skill,ll n)
{
    fl(i,0,n)
        {
            ll x,y;
            cin >> x >> y;
            skill.PB({x,y});
        }
}

ll mod(ll a, ll b) {
  ll c = a % b;
  return (c < 0) ? c + b : c;
}


bool isGoogles = 0;
bool testcase = 1;
void achilles() 
{
    ll n,m,d;cin >> n >>m >> d;
    ll x = m-1 + (n-1)*m;

    if(d==x)cout << "YES\n";
    else cout << "NO\n";

}


///////////////////////3....2....1...Ignition////////////////////////////

int main()
{
    ios :: sync_with_stdio(0);
    cin.tie(0);
    //freopen("out.txt","r",stdin);
    ll t=1,w=1;
    if(testcase)
    cin >>t;
 
    while(t--)
    {   if (isGoogles) {cout << "Case #" << w << ": ";}
        
        achilles();
        w++;

        

    }
    return 0;  
}
### Prompt

Generate a Cpp solution to the following problem:

There is a n × m grid. You are standing at cell (1, 1) and your goal is to finish at cell (n, m).

You can move to the neighboring cells to the right or down. In other words, suppose you are standing at cell (x, y). You can: 

  * move right to the cell (x, y + 1) — it costs x burles; 
  * move down to the cell (x + 1, y) — it costs y burles. 



Can you reach cell (n, m) spending exactly k burles?

Input

The first line contains the single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first and only line of each test case contains three integers n, m, and k (1 ≤ n, m ≤ 100; 0 ≤ k ≤ 10^4) — the sizes of grid and the exact amount of money you need to spend.

Output

For each test case, if you can reach cell (n, m) spending exactly k burles, print YES. Otherwise, print NO.

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).

Example

Input


6
1 1 0
2 2 2
2 2 3
2 2 4
1 4 3
100 100 10000


Output


YES
NO
YES
NO
YES
NO

Note

In the first test case, you are already in the final cell, so you spend 0 burles.

In the second, third and fourth test cases, there are two paths from (1, 1) to (2, 2): (1, 1) → (1, 2) → (2, 2) or (1, 1) → (2, 1) → (2, 2). Both costs 1 + 2 = 3 burles, so it's the only amount of money you can spend.

In the fifth test case, there is the only way from (1, 1) to (1, 4) and it costs 1 + 1 + 1 = 3 burles.

### Response

```cpp
///////////////////////Loading Payloads.......////////////////////////////
#include<bits/stdc++.h>
#define f(i,a,b) for(int i = a; i < b; i++)
#define fd(i,a,b) for(int i = a; i > b;i--)
#define fld(i,a,b) for(ll i = a ; i > b;i--)
#define ll long long
#define fl(i,a,b) for(ll i = a; i < b; i++)
#define VI vector<int>
#define VP vector<pair<int,int>>
#define VPL vector<pair<ll,ll>>
#define VS vector<string>
#define VL vector<long long>
#define VC vector<char>
#define VF vector<float>
#define VD vector<double>
#define VB vector<bool>
#define PB push_back
#define F first
#define S second
#define fa(i,skill) for(auto i : skill)
#define fr(i,skill) for(VI :: reverse_iterator i = skill.rbegin(); i != skill.rend(); i++)
#define PI pair<int,int>
#define mi map<int,int>
#define ml map<ll,ll>
#define mci map<char,int>
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define MAX 1000000000.00
#define INF 1000000000
#define debug(x) cout<<"This side    ----> "<<#x<<" -> "<<x<<endl
using namespace std;

///////////////////////Engine Check.......////////////////////////////
void edit(VI &skill,int n)
{
    f(i,0,n)
        {
            int x;
            cin >> x;
            skill.PB(x);
        }
}
void editl(VL &skill,ll n)
{
    fl(i,0,n)
        {
            ll x;
            cin >> x;
            skill.PB(x);
        }
}
void editpl(VPL &skill,ll n)
{
    fl(i,0,n)
        {
            ll x,y;
            cin >> x >> y;
            skill.PB({x,y});
        }
}

ll mod(ll a, ll b) {
  ll c = a % b;
  return (c < 0) ? c + b : c;
}


bool isGoogles = 0;
bool testcase = 1;
void achilles() 
{
    ll n,m,d;cin >> n >>m >> d;
    ll x = m-1 + (n-1)*m;

    if(d==x)cout << "YES\n";
    else cout << "NO\n";

}


///////////////////////3....2....1...Ignition////////////////////////////

int main()
{
    ios :: sync_with_stdio(0);
    cin.tie(0);
    //freopen("out.txt","r",stdin);
    ll t=1,w=1;
    if(testcase)
    cin >>t;
 
    while(t--)
    {   if (isGoogles) {cout << "Case #" << w << ": ";}
        
        achilles();
        w++;

        

    }
    return 0;  
}
```