#include <bits/stdc++.h>
#define ll long long
#define int ll
#define pii pair<ll, ll> 
#define ff first
#define ss second
#define mp make_pair
#define pb push_back

using namespace std;

ll MOD = 998244353;

ll pwr(ll x, ll y, ll mod = MOD) {
	ll res = 1;
	x = x%mod;
	while (y > 0) {
		if (y&1) res = (res*x)%mod;

		y = y>>1;
		x = (x*x)%mod;
	}
	return res;
}

inline ll addmod(ll a, ll b){
	return ((a+b)%MOD);
}

inline ll mulmod(ll a, ll b){
	return ((a*b)%MOD);
}

bool check_composite(int n, int a, int d, int s) {
	int x = pwr(a, d, n);
	if (x == 1 || x == n - 1)
		return false;
	for (int r = 1; r < s; r++) {
		x = x * x % n;
		if (x == n - 1)
			return false;
	}
	return true;
};

const int first12prime[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};

bool isPrime(int n) {			// O(log n) time complexity
	if (n < 2)
		return false;

	int r = 0;
	int d = n - 1;
	while ((d & 1) == 0) {
		d >>= 1;
		r++;
	}

	for (int i = 0; i < 12; i++) {
		int a = first12prime[i];
		if (n == a)
			return true;

		if (check_composite(n, a, d, r))
			return false;
	}
	return true;
}

const int PM = 2e5+5;

vector<int> primes;
vector<bool> is_comp;

void sieve () {
	is_comp.resize(PM, false);
	for (int i = 2; i < PM; i++) {
		if (!is_comp[i]) primes.pb(i);
		for (int j = 0; j < primes.size() && primes[j]*i < PM; j++) {
			is_comp[primes[j]*i] = true;
			if (i % primes[j] == 0) break;
		}
	}
}

inline int sfunc(int a, int b) {
	return a+b;
}

int n;									// array size
int *stree;								// stree = new int[2 * n]

void build() {							// build the tree
	for (int i = n - 1; i > 0; --i) stree[i] = sfunc(stree[i<<1], stree[i<<1|1]);
}

void modify(int p, int value) {			// set value at position p
	for (stree[p += n] = value; p > 1; p >>= 1) stree[p>>1] = sfunc(stree[p], stree[p^1]);
}

int query(int l, int r) {				// query on interval [l, r)
	int res = 0;						// DEFAULT
	for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
		if (l&1) res = sfunc(res, stree[l++]);
		if (r&1) res = sfunc(res, stree[--r]);
	}
	return res;
}

signed main () {
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

	int t; cin >> t;
	
	while (t--) {
		int n; cin >> n;
		string s[3];
		cin >> s[0] >> s[1] >> s[2];
		int p[3] = {0};

		string ans(3*n, '0');
		for (int i = 0; i < 3*n; i++) {
			// cout << p[0] << ' ' << p[1] << ' ' << p[2] << '\n';
			if (p[0]+p[1] == 4*n || p[2]+p[1] == 4*n || p[0]+p[2] == 4*n) break;
			if (p[0] < 2*n) {
				if (p[1] < 2*n) {
					if (p[2] < 2*n) {
						if (s[0][p[0]] == s[1][p[1]]) {
							ans[i] = s[0][p[0]];
							if (s[2][p[2]] == s[0][p[0]]) p[2]++;
							p[0]++; p[1]++;
						}
						else {
							// cout << "I am here\n";
							ans[i] = s[2][p[2]];
							if (s[0][p[0]] == s[2][p[2]]) p[0]++;
							else p[1]++;
							p[2]++;
						}
					}
					else {
						if (p[0] >= p[1]) ans[i] = s[0][p[0]++];
						else ans[i] = s[1][p[1]++];
					}
				}
				else {
					if (p[0] >= p[2]) ans[i] = s[0][p[0]++];
					else ans[i] = s[2][p[2]++];
				}
			}
			else {
				if (p[1] >= p[2]) ans[i] = s[1][p[1]++];
				else ans[i] = s[2][p[2]++];
			}
		}
		cout << ans << '\n';
	}
}


### Prompt

Please formulate a cpp solution to the following problem:

A bitstring is a string that contains only the characters 0 and 1.

Koyomi Kanou is working hard towards her dream of becoming a writer. To practice, she decided to participate in the Binary Novel Writing Contest. The writing prompt for the contest consists of three bitstrings of length 2n. A valid novel for the contest is a bitstring of length at most 3n that contains at least two of the three given strings as subsequences.

Koyomi has just received the three prompt strings from the contest organizers. Help her write a valid novel for the contest.

A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero) characters.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

Each of the following three lines contains a bitstring of length 2n. It is guaranteed that these three strings are pairwise distinct.

It is guaranteed that the sum of n across all test cases does not exceed 10^5.

Output

For each test case, print a single line containing a bitstring of length at most 3n that has at least two of the given bitstrings as subsequences.

It can be proven that under the constraints of the problem, such a bitstring always exists.

If there are multiple possible answers, you may output any of them.

Example

Input


2
1
00
11
01
3
011001
111010
010001


Output


010
011001010

Note

In the first test case, the bitstrings 00 and 01 are subsequences of the output string: 010 and 010. Note that 11 is not a subsequence of the output string, but this is not required.

In the second test case all three input strings are subsequences of the output string: 011001010, 011001010 and 011001010.

### Response

```cpp
#include <bits/stdc++.h>
#define ll long long
#define int ll
#define pii pair<ll, ll> 
#define ff first
#define ss second
#define mp make_pair
#define pb push_back

using namespace std;

ll MOD = 998244353;

ll pwr(ll x, ll y, ll mod = MOD) {
	ll res = 1;
	x = x%mod;
	while (y > 0) {
		if (y&1) res = (res*x)%mod;

		y = y>>1;
		x = (x*x)%mod;
	}
	return res;
}

inline ll addmod(ll a, ll b){
	return ((a+b)%MOD);
}

inline ll mulmod(ll a, ll b){
	return ((a*b)%MOD);
}

bool check_composite(int n, int a, int d, int s) {
	int x = pwr(a, d, n);
	if (x == 1 || x == n - 1)
		return false;
	for (int r = 1; r < s; r++) {
		x = x * x % n;
		if (x == n - 1)
			return false;
	}
	return true;
};

const int first12prime[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};

bool isPrime(int n) {			// O(log n) time complexity
	if (n < 2)
		return false;

	int r = 0;
	int d = n - 1;
	while ((d & 1) == 0) {
		d >>= 1;
		r++;
	}

	for (int i = 0; i < 12; i++) {
		int a = first12prime[i];
		if (n == a)
			return true;

		if (check_composite(n, a, d, r))
			return false;
	}
	return true;
}

const int PM = 2e5+5;

vector<int> primes;
vector<bool> is_comp;

void sieve () {
	is_comp.resize(PM, false);
	for (int i = 2; i < PM; i++) {
		if (!is_comp[i]) primes.pb(i);
		for (int j = 0; j < primes.size() && primes[j]*i < PM; j++) {
			is_comp[primes[j]*i] = true;
			if (i % primes[j] == 0) break;
		}
	}
}

inline int sfunc(int a, int b) {
	return a+b;
}

int n;									// array size
int *stree;								// stree = new int[2 * n]

void build() {							// build the tree
	for (int i = n - 1; i > 0; --i) stree[i] = sfunc(stree[i<<1], stree[i<<1|1]);
}

void modify(int p, int value) {			// set value at position p
	for (stree[p += n] = value; p > 1; p >>= 1) stree[p>>1] = sfunc(stree[p], stree[p^1]);
}

int query(int l, int r) {				// query on interval [l, r)
	int res = 0;						// DEFAULT
	for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
		if (l&1) res = sfunc(res, stree[l++]);
		if (r&1) res = sfunc(res, stree[--r]);
	}
	return res;
}

signed main () {
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

	int t; cin >> t;
	
	while (t--) {
		int n; cin >> n;
		string s[3];
		cin >> s[0] >> s[1] >> s[2];
		int p[3] = {0};

		string ans(3*n, '0');
		for (int i = 0; i < 3*n; i++) {
			// cout << p[0] << ' ' << p[1] << ' ' << p[2] << '\n';
			if (p[0]+p[1] == 4*n || p[2]+p[1] == 4*n || p[0]+p[2] == 4*n) break;
			if (p[0] < 2*n) {
				if (p[1] < 2*n) {
					if (p[2] < 2*n) {
						if (s[0][p[0]] == s[1][p[1]]) {
							ans[i] = s[0][p[0]];
							if (s[2][p[2]] == s[0][p[0]]) p[2]++;
							p[0]++; p[1]++;
						}
						else {
							// cout << "I am here\n";
							ans[i] = s[2][p[2]];
							if (s[0][p[0]] == s[2][p[2]]) p[0]++;
							else p[1]++;
							p[2]++;
						}
					}
					else {
						if (p[0] >= p[1]) ans[i] = s[0][p[0]++];
						else ans[i] = s[1][p[1]++];
					}
				}
				else {
					if (p[0] >= p[2]) ans[i] = s[0][p[0]++];
					else ans[i] = s[2][p[2]++];
				}
			}
			else {
				if (p[1] >= p[2]) ans[i] = s[1][p[1]++];
				else ans[i] = s[2][p[2]++];
			}
		}
		cout << ans << '\n';
	}
}


```