Two Teams Composing CodeForces 1335C

You have nn students under your control and you have to compose exactly two teams consisting of some subset of your students. Each student had his own skill, the ii-th student skill is denoted by an integer aiai (different students can have the same skills).

So, about the teams. Firstly, these two teams should have the same size. Two more constraints:

• The first team should consist of students with distinct skills (i.e. all skills in the first team are unique).
• The second team should consist of students with the same skills (i.e. all skills in the second team are equal).

Note that it is permissible that some student of the first team has the same skill as a student of the second team.

Consider some examples (skills are given):

• [1,2,3][1,2,3], [4,4][4,4] is not a good pair of teams because sizes should be the same;
• [1,1,2][1,1,2], [3,3,3][3,3,3] is not a good pair of teams because the first team should not contain students with the same skills;
• [1,2,3][1,2,3], [3,4,4][3,4,4] is not a good pair of teams because the second team should contain students with the same skills;
• [1,2,3][1,2,3], [3,3,3][3,3,3] is a good pair of teams;
• [5][5], [6][6] is a good pair of teams.

Your task is to find the maximum possible size xx for which it is possible to compose a valid pair of teams, where each team size is xx (skills in the first team needed to be unique, skills in the second team should be the same between them). A student cannot be part of more than one team.

You have to answer tt independent test cases.

Input

The first line of the input contains one integer tt (1≤t≤1041≤t≤104) — the number of test cases. Then tt test cases follow.

The first line of the test case contains one integer nn (1≤n≤2⋅1051≤n≤2⋅105) — the number of students. The second line of the test case contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤n1≤ai≤n), where aiai is the skill of the ii-th student. Different students can have the same skills.

It is guaranteed that the sum of nn over all test cases does not exceed 2⋅1052⋅105 (∑n≤2⋅105∑n≤2⋅105).

Output

For each test case, print the answer — the maximum possible size xx for which it is possible to compose a valid pair of teams, where each team size is xx.

Example

Input

4
7
4 2 4 1 4 3 4
5
2 1 5 4 3
1
1
4
1 1 1 3

Output

3
1
0
2

Note

In the first test case of the example, it is possible to construct two teams of size 33: the first team is [1,2,4][1,2,4] and the second team is [4,4,4][4,4,4]. Note, that there are some other ways to construct two valid teams of size 33.

#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
const ll inf = 1e18;
const int mod = 1000000007;
const int mx = 100; //check the limits, dummy
typedef pair<int, int> pa;
const double PI = acos(-1);
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
#define swa(a,b) a^=b^=a^=b
#define re(i,a,b) for(int i=(a),_=(b);i<_;i++)
#define rb(i,a,b) for(int i=(b),_=(a);i>=_;i--)
#define clr(a) memset(a, 0, sizeof(a))
#define lowbit(x) ((x)&(x-1))
#define mkp make_pair
void sc(int& x) { scanf("%d", &x); }void sc(int64_t& x) { scanf("%lld", &x); }void sc(double& x) { scanf("%lf", &x); }void sc(char& x) { scanf(" %c", &x); }void sc(char* x) { scanf("%s", x); }
ll  m, n,t,x,k,ans=0,sum=0;
ll a[mx], b;

int main()
{
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    cin >> t;
    while (t--) {
        cin >> n;
        vector<int>cnt(n);
        re(i, 0, n) {
            cin >> m;
            --m;
            ++cnt[m];
        }
        int maxx = *max_element(cnt.begin(), cnt.end());
        int cc=0;
        re(i, 0, n) {
            cc += !!cnt[i];
        }
        cout << min(maxx, cc) - (maxx == cc) << endl;
    }
}