Permuted Arithmetic Sequence Solution:

#include <bits/stdc++.h>
using namespace std;

bool isarithmetic(vector<int> v){
    int sumdiff = v[1] - v[0];
    for(int i = 1; i < v.size(); i++){
        if(v[i] - v[i - 1] == sumdiff){
            continue;
        }
        return false;
    }
    return true;
}

int main(){
    // #ifndef TESTING
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    // #endif

    int cases;
    cin >> cases;
    while(cases--){
        int vals;
        cin >> vals;
        vector<int> v(vals);
        for(int &i: v){
            cin >> i;
        }
        
        if(isarithmetic(v)) {
            cout << "arithmetic" << endl;
            continue;
        }
        sort(v.begin(), v.end());
        bool permutedarithmetic = isarithmetic(v);
        if(!permutedarithmetic){
            cout << "non-arithmetic" << endl;
        } else {
            cout << "permuted arithmetic" << endl;
        }
    }

    return 0;   
}