#include<bits/stdc++.h>
using namespace std ;
typedef long long ll ;
typedef unsigned long long ull ;
typedef pair < int , int > pii ;
typedef vector < int > vi ;
#define fi first
#define se second
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()

const int MAXN = 1e6 + 7 ;
int n ;
int ori[ MAXN ] ;
int x[ MAXN ] , y[ MAXN ] , sws[ MAXN ] , srank[ MAXN ] ;
int sa[ MAXN ] , lcp[ MAXN ] ;

void SuffixArray(int lim=256) { // or basic_string<int>
    int k = 0, a, b;
    int len = n + 1 ;
    for ( int i = 0 ; i < len ; ++ i ) {
        sa[ i ] = i ; lcp[ i ] = 0 ;
    }
    x[ len - 1 ] = 0 ;
    // vi x(all(s)+1), y(n), ws(max(n, lim)), rank(n);
    // sa = lcp = y, iota(all(sa), 0);
    for (int j = 0, p = 0; p < len; j = max(1, j * 2), lim = p) {
        p = j;
        for ( int i = 0 ; i < len ; ++ i ) { y[ i ] = len - j + i ; } 
        rep(i,0,len) if (sa[i] >= j) y[p++] = sa[i] - j;
        // fill(all(ws), 0);
        for ( int i = 0 ; i < max ( len , lim ) ; ++ i ) {
            sws[ i ] = 0 ;
        }
        rep(i,0,len) sws[x[i]]++;
        rep(i,1,lim) sws[i] += sws[i - 1];
        for (int i = len; i--;) sa[--sws[x[y[i]]]] = y[i];
        swap(x, y), p = 1, x[sa[0]] = 0;
        rep(i,1,len) a = sa[i - 1], b = sa[i], x[b] =
            (y[a] == y[b] && y[a + j] == y[b + j]) ? p - 1 : p++;
    }
    rep(i,1,len) srank[sa[i]] = i;
    for (int i = 0, j; i < len - 1; lcp[srank[i++]] = k)
        for (k && k--, j = sa[srank[i] - 1];
             ori[i + k] == ori[j + k]; k++);
}


ll freq[ MAXN ] ;
int prv[ MAXN ] , rnk[ MAXN ] , sz[ MAXN ] , lstmod[ MAXN ] ;
vector < int > at_val[ MAXN ] ;

inline int get ( int x ) {
    while ( prv[ x ] != x ) {
        x = prv[ x ] = prv[ prv[ x ] ] ;
    }
    return x ;
}

int ens[ MAXN ] ;

void solve ( ) {
    cin >> n ;
    // n = MAXN - 7 ;
    for ( int i = 0 ; i <= n ; ++ i ) {
        freq[ i ] = 0 ;
        prv[ i ] = i , rnk[ i ] = 0 , sz[ i ] = 1 ;
        at_val[ i ].clear ( ) ;
    }
    for ( int i = 0 ; i < n ; ++ i ) {
        cin >> x[ i ] ;
        ++ x[ i ] ;
        ori[ i ] = x[ i ] ;
        // x = rand ( ) % 100 + 1 ;
    }
    SuffixArray ( 102 ) ;
    for ( int i = 1 ; i <= n ; ++ i ) {
        at_val[ lcp[ i ] ].push_back ( i ) ;
        lstmod[ i ] = n - sa[ i ] ;
    }
    for ( int ctr = n ; ctr >= 0 ; -- ctr ) {
        for ( auto x : at_val[ ctr ] ) { 
            int rt1 = get ( x ) ;
            freq[ sz[ rt1 ] ] += lstmod[ rt1 ] - ctr ;
            lstmod[ rt1 ] = ctr ;
            if ( x > 0 ) {
                int rt2 = get ( x - 1 ) ;
                freq[ sz[ rt2 ] ] += lstmod[ rt2 ] - ctr ;
                lstmod[ rt2 ] = ctr ;
                if ( rnk[ rt1 ] < rnk[ rt2 ] ) { swap ( rt1 , rt2 ) ; }
                rnk[ rt1 ] += ( rnk[ rt1 ] == rnk[ rt2 ] ) ;
                prv[ rt2 ] = rt1 ;
                sz[ rt1 ] += sz[ rt2 ] ;
            }
        }
    }
    /**
    for ( int i = 1 ; i <= n ; ++ i ) {
        printf ( "%d " , freq[ i ] ) ;
    }
    printf ( "\n" ) ;
    **/
    ll up = 0 , down = 1LL * n * ( n + 1 ) / 2 ;
    int rem = -1 ;
    int stpos = 1 , tot = 0 ;
    auto proc = [ & ] ( int x , int y , ll cnt ) {
        up += cnt * ( x + y ) ;
        freq[ x ] -= cnt , freq[ y ] -= cnt ;
        if ( x + y <= n ) {
            freq[ x + y ] += cnt ;
        }
        else {
            while ( cnt > 0 ) {
                -- cnt ;
                ens[ ++ tot ] = x + y ;
            }
        }
    };
    for ( int i = 1 ; i <= n ; ++ i ) {
        if ( freq[ i ] == 0 ) { continue ; }
        if ( rem != -1 ) {
            up += rem + i ;
            -- freq[ rem ] , -- freq[ i ] ;
            if ( rem + i <= n ) { ++ freq[ rem + i ] ; }
            else { ens[ ++ tot ] = rem + i ; }
            rem = -1 ;
        }
        ll cnt = freq[ i ] / 2 ;
        up += cnt * 2 * i ;
        freq[ i ] -= 2 * cnt ;
        if ( 2 * i <= n ) { freq[ 2 * i ] += cnt ; }
        else {
            while ( cnt > 0 ) {
                -- cnt ;
                ens[ ++ tot ] = 2 * i ;
            }
        }
        if ( freq[ i ] > 0 ) { rem = i ; }
    }
    if ( rem != -1 ) {
        ens[ 0 ] = rem ;
        -- stpos ;
    }
    while ( stpos + 1 <= tot ) {
        ll x = ens[ stpos ] , y = ens[ stpos + 1 ] ;
        stpos += 2 ;
        up += x + y ;
        ens[ ++ tot ] = x + y ;
    }
    ll hh = __gcd ( up , down ) ;
    up /= hh , down /= hh ;
    if ( down == 1 ) { cout << up << "\n" ; }
    else { cout << up << "/" << down << "\n" ; }
}

int main ( ) {
    ios_base :: sync_with_stdio ( false ) ;
    cin.tie ( NULL ) ;
    int t = 1 ; cin >> t ;
    while ( t -- ) { solve ( ) ; }
    return 0 ;
}