#include <bits/stdc++.h>

using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a) - 1; i >= (b); i--)
#define SZ(a) int(a.size())
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
#define F first
#define S second 

typedef long long LL;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef double db;

const int N = 100'447;
const int INF = 1e9 + 47;
int n;
PII a[N];
int recov[N];

int find(int l, int r, int bit)
{
	FOR (i, l, r)
		if (a[i].F & (1 << bit))
			return i;
	return r;
}

int brute(int l, int r)
{
	VI nums;
	FOR (i, l, r)
		nums.PB(a[i].F);
	int ans = 0;
	FOR (i, 0, 1 << SZ(nums))
	{
		VI f[2];
		FOR (j, 0, SZ(nums))
		{
			f[(i >> j) & 1].PB(nums[j]);
		}
		VI res(2, INF);
		FOR (t, 0, 2)
		{
			FOR (j, 0, SZ(f[t]))
			{
				FOR (k, j + 1, SZ(f[t]))
					res[t] = min(res[t], f[t][j] ^ f[t][k]);
			}
		}
		int nres = min(res[0], res[1]);
		if (ans < nres)
		{
			ans = nres;
			FOR (j, 0, SZ(nums))
				recov[a[j + l].S] = (i >> j) & 1;
		}
	}
	return ans;
}

int solve(int l, int r, int bit)
{
	if (l == r)	
		return INF;
	if (bit == -1)
	{	
		if (r - l > 2)
			return 0;
		return brute(l, r);
	}
	int m = find(l, r, bit);
	if (m - l > 2 || r - m > 2)
		return min(solve(l, m, bit - 1), solve(m, r, bit - 1));
	else
		return brute(l, r);
}

void solve()
{
	cin >> n;
	FOR (i, 0, n) 
	{
		cin >> a[i].F;
		a[i].S = i;
	}
	sort(a, a + n);
	cout << solve(0, n, 30) << '\n';
	FOR (i, 0, n)
	{
		cout << recov[i] + 1;
	}
	cout << '\n';
}

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	int t;
	cin >> t;
	while (t--)
	{
		solve();
	}
	
	return 0;
}