#include <bits/stdc++.h>

using namespace std;
    
typedef long long ll;
const int  N = 1e6 + 12, MOD = 998244353;

int n,a[N],mn[N],c[N];
int t[N * 4],dp[N];
void upd(int pos,int val,int v = 1,int tl = 1,int tr = n) {
    if(tl == tr) {
        t[v] = val;
    } else {
        int tm = (tl + tr) >> 1;
        if(pos <= tm) upd(pos,val,v+v,tl,tm);
        else upd(pos,val,v+v+1,tm+1,tr);
        t[v] = max(t[v + v],t[v + v + 1]);
    }
}
int get(int l,int r,int v = 1,int tl = 1,int tr = n) {
    if(l > r || tl > r || l > tr) return 0;
    if(tl >= l && tr <= r) return t[v];
    int tm = (tl + tr) >> 1;
    return max(get(l,r,v+v,tl,tm),get(l,r,v+v+1,tm+1,tr));
}
int calc(vector<int> &x,int prev) {
    int res = 0;
    sort(x.begin(),x.end());
    for(int j:x) {
        int i = a[j];
        if(i > prev) continue;
        dp[i] = get(i + 1,n) + 1;
        upd(i,dp[i]);
        res = max(res,dp[i]);
    }
    for(int i:x) {
        upd(a[i],0);
    }
    return res;
}
int solve() {
    vector<int> DP(n + 1,1),P(n + 1,0);
    mn[0] = n + 1;
    for(int i = 1;i <= n;i++) {
        c[i] = c[i - 1];
        if(mn[i - 1] > a[i]) {
            mn[i] = a[i];
            c[i]++;
        } else {
            mn[i] = mn[i - 1];
        }
    }
    int res = 2;
    for(int i = n;i >= 1;i--) {
        P[i] = n + 1;
        vector<bool> bad(n+1,false);
        vector<int> vars;
        for(int j = i + 1;j <= n;j++) {
            if(a[j] > a[i] && DP[j] + 1 > DP[i]) {
                DP[i] = DP[j] + 1;
                P[i] = j;
                vars.clear();
                vars.push_back(j);
            } else if(a[j] > a[i] && DP[j] + 1 == DP[i]) {
                vars.push_back(j);
            }
        }
        int mx = -1,opt = n +1;
        // cout << (int)vars.size() << "x\n";
        for(int k:vars) {
            vector<int> lef;
            P[i] = k;
            for(int f = 1;f <= n;f++) {
                bad[f] = 0;
            }
            int it = i;
            while(it <= n) {
                bad[it] = 1;
                // cout << it << ' ';
                it = P[it];
            }
            // cout << '\n';
            for(int j = i + 1;j <= n;j++) {
                if(!bad[j]) {
                    lef.push_back(j);
                }
            }
            int val = calc(lef,n + 1);
            if(val > mx) {
                mx = val;
                opt = k;
                res = max(res,c[i - 1] + DP[i] + calc(lef,mn[i - 1]));
            }
        }
        P[i] = opt;
    }
    return res;
}
void test() {
    cin >> n;
    for(int i = 1;i <= n;i++) {
        cin >> a[i];
    }
    int res = solve();
    for(int i = 1;i <= n;i++) {
        a[i] = n - a[i] + 1;
    }
    res = max(res,solve());
    cout << res << '\n';
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int t = 1; 
    cin >> t;
    while(t--) {
        test();
    }
}