## DCEPCA03 - Totient Extreme

Given the value of N, you will have to find the value of H. The meaning of H is given in the following code:

H=0;
For (i=1; i<=n; i++) {
For (j=1; j<=n; j++) {
H = H + totient(i) * totient(j);
}
}

Totient or phi function, φ(n) is an arithmetic function that counts the number of positive integers less than or equal to n that are relatively prime to n. That is, if n is a positive integer, then φ(n) is the number of integers k in the range 1 ≤ k ≤ n for which gcd(n, k) = 1

0 < T <= 50
0 < N <= 10^4

### Input

The first line contains T, the number of test cases. It is followed by T lines each containing a number N .

### Output

For each line of input produce one line of output. This line contains the value of H for the corresponding N.

### Example

```Input:
2
3
10

Output:
16
1024```

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <bits/stdc++.h>
#include <limits.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef vector<int> vi;

#define MOD (ll)1000000007
#define pb   push_back
#define EPS 1e-9
#define FOR(i,n)  for(int i = 0;i < n; i++)
#define FORE(i,a,b) for(int i = a;i <= b; i++)
#define pi(a)   printf("%d\n", a)
#define all(c)  c.begin(), c.end()
#define tr(container, it)   for(typeof(container.begin()) it = container.begin(); it != container.end(); it++)
#define gc getchar_unlocked
#define sdi(a, b)   si(a);si(b)
#define io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define endl '\n'

template <typename T> T gcd(T a, T b){return (b==0)?a:gcd(b,a%b);}
template <typename T> T lcm(T a, T b){return a*(b/gcd(a,b));}
template <typename T> T mod_exp(T b, T p, T m){T x = 1;while(p){if(p&1)x=(x*b)%m;b=(b*b)%m;p=p>>1;}return x;}
template <typename T> T invFermat(T a, T p){return mod_exp(a, p-2, p);}
template <typename T> T exp(T b, T p){T x = 1;while(p){if(p&1)x=(x*b);b=(b*b);p=p>>1;}return x;}

void si(int &x){
register int c = gc();
x = 0;
int neg = 0;
for(;((c<48 || c>57) && c != '-');c = gc());
if(c=='-') {neg=1;c=gc();}
for(;c>47 && c<58;c = gc()) {x = (x<<1) + (x<<3) + c - 48;}
if(neg) x=-x;
}

const int MAXN = (int)1e4+5;
ll phi[MAXN+1];

ll prefixSum[MAXN+1];
void precal(){
for(int i = 1;i <= MAXN; i++){
phi[i] = i;
}
for(int i = 2; i <= MAXN; i++){
if(phi[i] == i){
for(int j = i; j <= MAXN; j+=i){
phi[j] /= i;
phi[j] *= (i-1);
}
}
}
prefixSum[0] = 0;
prefixSum[1] = phi[1];
for(int i = 2;i <= MAXN; i++){
prefixSum[i] = phi[i]+prefixSum[i-1];
}
}

int main(){
io;
precal();
int t;
cin>>t;
while(t--){
int n;
cin>>n;
ll ans = 0;
for(int i = 1;i <= n; i++){
// cout<<(prefixSum[n]-prefixSum[i-1])<<' '<<phi[i]<<endl;
ans+=(prefixSum[n])*phi[i];
}
cout<<ans<<endl;
}
return 0;
}``````
Copy The Code &

Input

cmd
2
3
10

Output

cmd
16
1024