#include <iostream>
#include <algorithm>
#include <string>
#include <assert.h>
#include <set>
using namespace std;
 
 
 
long long readInt(long long l,long long r,char endd){
	long long x=0;
	int cnt=0;
	int fi=-1;
	bool is_neg=false;
	while(true){
		char g=getchar();
		if(g=='-'){
			assert(fi==-1);
			is_neg=true;
			continue;
		}
		if('0'<=g && g<='9'){
			x*=10;
			x+=g-'0';
			if(cnt==0){
				fi=g-'0';
			}
			cnt++;
			assert(fi!=0 || cnt==1);
			assert(fi!=0 || is_neg==false);
			
			assert(!(cnt>19 || ( cnt==19 && fi>1) ));
		} else if(g==endd){
			assert(cnt>0);
			if(is_neg){
				x= -x;
			}
			assert(l<=x && x<=r);
			return x;
		} else {
			assert(false);
		}
	}
}
string readString(int l,int r,char endd){
	string ret="";
	int cnt=0;
	while(true){
		char g=getchar();
		assert(g!=-1);
		if(g==endd){
			break;
		}
		cnt++;
		ret+=g;
	}
	assert(l<=cnt && cnt<=r);
	return ret;
}
long long readIntSp(long long l,long long r){
	return readInt(l,r,' ');
}
long long readIntLn(long long l,long long r){
	return readInt(l,r,'\n');
}
string readStringLn(int l,int r){
	return readString(l,r,'\n');
}
string readStringSp(int l,int r){
	return readString(l,r,' ');
}

int gcd(int a,int b){
	if(b==0)return a;
	return gcd(b,a%b);
}

int T;
int arr[100100];
int sm_n=0;
int n;
set<int> ind;
set<int>::iterator ii;
int main(){
	//freopen("00.txt","r",stdin);
	//freopen("00o.txt","w",stdout);
	T=readIntLn(1,100);
	while(T--){
		n=readIntLn(2,100000);
		sm_n += n;
		ind.clear();
		assert(sm_n<=1000000);
		for(int i=1;i<=n;i++){
			if(i==n){
				arr[i]=readIntLn(-1,1000000);
			} else {
				arr[i]=readIntSp(-1,1000000);
			}
			assert(arr[i]!=0);
		}
		bool ok=true;
		int prev=-1;
		int atleast = 0;
		for(int i=1;i<=n;i++){
			if(arr[i]==-1)continue;
			ind.insert(i-arr[i]+1);
			atleast=max(atleast,arr[i]);
			if(prev == -1){
				prev=i;
				continue;
			}
			if(i - prev != arr[i] - arr[prev] && arr[i] > i-prev){
				ok=false;
			}
			prev=i;
		}
		if(!ok){
			cout<<"impossible"<<endl;
			continue;
		}
		if(ind.size() <= 1){
			cout<<"inf"<<endl;
			continue;
		}
		int gccd=0;
		prev=-1<<30; 
		for(ii=ind.begin();ii!=ind.end();ii++){
			if(prev == -1<<30){

				prev= *ii;
				continue;
			}
			gccd=gcd(gccd,*ii-prev);
			prev= *ii;
		}
		if(gccd<atleast){
			cout<<"impossible"<<endl;
			continue;
		}
		cout<<gccd<<endl;
	}
	assert(getchar()==-1);
}