//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
//#pragma GCC optimize("Ofast,fast-math")
//#pragma GCC target("avx,avx2")
//#pragma GCC optimize(2)
//#pragma GCC optimize(3)
//#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
//#define int long long
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef double db;
#define F(i, a, b) for(int i = a; i <= (b); ++i)
#define F2(i, a, b) for(int i = a; i < (b); ++i)
#define dF(i, a, b) for(int i = a; i >= (b); --i)
template<typename T> void debug(string s, T x) {
	cerr << "[" << s << "] = [" << x << "]\n";
}
template<typename T, typename... Args> void debug(string s, T x, Args... args) {
	for (int i = 0, b = 0; i < (int)s.size(); i++) if (s[i] == '(' || s[i] == '{') b++;
	else if (s[i] == ')' || s[i] == '}') b--;
	else if (s[i] == ',' && b == 0) {
		cerr << "[" << s.substr(0, i) << "] = [" << x << "] | ";
		debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);
		break;
	}
}
#ifdef ONLINE_JUDGE
#define Debug(...)
#else
#define Debug(...) debug(#__VA_ARGS__, __VA_ARGS__)
#endif
#define pb push_back
#define fi first
#define se second
#define Mry fprintf(stderr, "%.3lf MB\n", (&Med - &Mbe) / 1048576.0)
#define Try cerr << 1e3 * clock() / CLOCKS_PER_SEC << " ms\n";
typedef long long ll;
// namespace Fread {const int SIZE = 1 << 17; char buf[SIZE], *S, *T; inline char getchar() {if (S == T) {T = (S = buf) + fread(buf, 1, SIZE, stdin); if (S == T) return '\n';} return *S++;}}
// namespace Fwrite {const int SIZE = 1 << 17; char buf[SIZE], *S = buf, *T = buf + SIZE; inline void flush() {fwrite(buf, 1, S - buf, stdout), S = buf;} inline void putchar(char c) {*S++ = c;if (S == T) flush();} struct NTR {~NTR() {flush();}} ztr;}
// #ifdef ONLINE_JUDGE
// #define getchar Fread::getchar
// #define putchar Fwrite::putchar
// #endif
inline int ri() {
	int x = 0;
	bool t = 0;
	char c = getchar();
	while (c < '0' || c > '9') t |= c == '-', c = getchar();
	while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
	return t ? -x : x;
}
inline void wi(int x) {
	if (x < 0) {
		putchar('-'), x = -x;
	}
	if (x > 9) wi(x / 10);
	putchar(x % 10 + 48);
}
inline void wi(int x, char s) {
	wi(x), putchar(s);
}
bool Mbe;
// mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
const ll infll = 0x3f3f3f3f3f3f3f3f;
const int _ = 2e5 + 5;

int n, b[1005][1005], a[_];

int fa[_];

vi g[_];

int find(int x) {
	return fa[x] ==x ? x : fa[x] = find(fa[x]);
}

void merge(int x, int y) {
	x = find(x), y = find(y);
	if(x == y) return;
	if(g[x].size() > g[y].size()) swap(x, y);
	for(int v : g[x]) g[y].pb(v);
	fa[x] = y;
	g[x].clear();
	g[x].shrink_to_fit();
}

void solve() {
	n = ri();
	F(i, 1, n) a[i] = ri();
	F(i, 1, n) F(j, 1, n) b[i][j] = ri();
	ll ans = 0;
	F(i, 1, n) g[i].clear();
	F(i, 1, n) fa[i] = i, g[i].pb(i);
	F(i, 1, n) {
		pii mn = {inf, 0};
		F(j, 1, n) mn = min(mn, make_pair(b[i][j], j));
		Debug(i, a[i], mn.fi, mn.se);
		assert(mn.se);
		if(find(i) != find(mn.se)) ans += 1ll * (a[i]) * mn.fi;
		else ans += 1ll * (a[i] - 1) * mn.fi;
		merge(i, mn.se);
		
	}
	vi A;
	F(z, 1, 10) {
	F(i, 1, n) if(find(i) == i) {
		Debug(i, find(2));
		pii mn = make_pair(inf, 0);
		for(int v1 : g[i]) {
			Debug(v1);
			F(j, 1, n) if(find(v1) != find(j)) mn = min(mn, make_pair(b[v1][j], j));
		}
		if(mn.fi != inf) {
			ans += mn.fi;
			merge(i, mn.se);
		}
	}
	}
	cout << ans << '\n';
}
bool Med;
signed main() {
	// Mry;
	int T = ri();
	while(T--) {
		solve();
	}
	// Try;
	return 0;
}