import java.util.*;
import java.io.*; 
import java.text.*;
//Solution Credits: Taranpreet Singh
public class Main{
    //SOLUTION BEGIN
    void solve(int TC) throws Exception{
        int n = ni();
        boolean flag = false;
        int[] a = new int[n];int cnt = 0, mx = 0;
        for(int i = 0; i< n; i++){
            int x = ni();
            if(x>0)flag = true;
            if(flag)a[cnt++] = x;
            mx = Math.max(mx, x);
        }
        if(cnt==0){
            pn("inf");return;
        }
        while(cnt>0 && a[cnt-1]==-1)cnt--;
        HashSet<Long> set = new HashSet<>();
        boolean imp = false, finite = false;
        int prev = 0;
        for(int i = 1; i< cnt && !imp; i++){
            if(a[i]!=-1){
                if(i-prev != a[i]-a[prev]){
                    int c = i-prev-1;
                    if(c<a[i]-1)imp = true;
                    else if(!finite){
                        finite = true;
                        long d = c-(a[i]-1)+a[prev];
                        for(long f = 1; f*f<=d; f++){
                            if(d%f!=0)continue;
                            if(f>=mx)set.add(f);
                            if(d/f>=mx)set.add(d/f);
                        }
                    }
                }
                prev = i;
            }
        }
        if(imp)pn("impossible");
        else if(!finite)pn("inf");
        else{
            long ans = -1;
            v:for(long x:set){
                for(int i = 0; i< cnt; i++)
                    if(a[i]!=-1 && (a[i]-a[0]+x)%x!=i%x)continue v;
                ans = Math.max(ans, x);
            }
            if(ans==-1)pn("impossible");
            else pn(ans);
        }
    }
    //SOLUTION ENDS
    long mod = (long)1e9+7, IINF = (long)1e17;
    final int MAX = (int)1e6+1, INF = (int)2e9, root = 3;
    DecimalFormat df = new DecimalFormat("0.000000000000");
    double PI = 3.1415926535897932384626433832792884197169399375105820974944, eps = 1e-8;
    static boolean multipleTC = true, memory = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        in = new FastReader();
        out = new PrintWriter(System.out);
        int T = (multipleTC)?ni():1;
        //Solution Credits: Taranpreet Singh
        for(int i = 1; i<= T; i++)solve(i);
        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n(){return in.next();}
    String nln(){return in.nextLine();}
    int ni(){return Integer.parseInt(in.next());}
    long nl(){return Long.parseLong(in.next());}
    double nd(){return Double.parseDouble(in.next());}

    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }

        String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine(){
            String str = "";
            try{    
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }   
            return str;
        }
    }
}