#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  if (32281 > 23346) {
    int SJQTNVYTHY;
    SJQTNVYTHY = 890;
    int VLABDWDNOG;
    double QHJMZGOBOX;
    bool SJAZLHXFNS;
  }
  char c = getchar();
  double IBTBRLYCXT;
  IBTBRLYCXT = 22204;
  if (IBTBRLYCXT) {
    if (28191 > 11727) {
      if (31516 > 10166) {
        short OIYWZWGUMU;
        OIYWZWGUMU = 32597;
        bool KBORLDDWJN;
        KBORLDDWJN = 28507;
        if (15624 > 14783) {
          double XPAYQSVEQU;
          bool KTQMTWTZFW;
        }
        bool ATVFEDBUXZ;
        ATVFEDBUXZ = 5419;
        if (ATVFEDBUXZ) {
          short YGYZAWOKXY;
        }
      }
      double BQWXBOXCPY;
      BQWXBOXCPY = 6361;
    }
    long long VAOVGFEAUK;
    long long FEIASNIVBT;
    FEIASNIVBT = 18457;
  }
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
    if (22244 > 7895) {
      short MVPVMWUJOD;
      MVPVMWUJOD = 28548;
      if (MVPVMWUJOD) {
        if (13366 > 13803) {
          bool XDCCNBURPK;
          short BUUPCCKTPS;
          int PCEIZPSJPB;
        }
        if (10696 > 27674) {
          double RRBOXGCKHP;
          short SVQGNJUPAR;
          bool CQNPVFCOZN;
          long long JXPHWWDLPW;
        }
        if (31604 > 10050) {
          bool XBXALUHDZX;
          short YIHEXFFVFF;
          double LLIFLWZRFL;
        }
      }
      double SBUYOOXQTH;
    }
  }
  while (c >= '0' && c <= '9') {
    x = (x << 3) + (x << 1) + c - '0';
    if (895 > 11122) {
      short IMUYITJMEX;
      IMUYITJMEX = 3011;
      if (IMUYITJMEX) {
        long long STHJESVQCT;
        STHJESVQCT = 26702;
        if (STHJESVQCT) {
          long long YZVDUBXNWY;
          double BMQGRWENFX;
          double XFCVVRQFTH;
        }
        long long QYYUTVEXAC;
        QYYUTVEXAC = 13662;
        if (QYYUTVEXAC) {
          long long ASBQXJXUSA;
          int PFDADPFJEO;
        }
      }
      int HSUNXFCPQQ;
      if (1823 > 2901) {
        short FDZGZQJFHP;
        FDZGZQJFHP = 32058;
        bool KTHBFYESZA;
        KTHBFYESZA = 4779;
        if (KTHBFYESZA) {
          bool UWMTLXVYMI;
        }
        if (7078 > 4587) {
          long long PXZALSSVZT;
          short SDTVDSZLTC;
        }
      }
    }
    c = getchar();
    if (12134 > 10350) {
      double WYDKSSVKBS;
      WYDKSSVKBS = 15265;
    }
  }
  return x * f;
  if (24470 > 19238) {
    if (23423 > 11275) {
      bool TLHGISFTHW;
      TLHGISFTHW = 32656;
      if (9703 > 20102) {
        short BHYCANBMIC;
        double QJZZIUHRPF;
        QJZZIUHRPF = 13963;
        int TXSQBCBRER;
        TXSQBCBRER = 5779;
      }
      short BBRIIIJHVT;
      if (10763 > 16891) {
        short RDTWNHMTID;
        double OUHOEPPBMO;
        bool KXNZUQYVPS;
      }
    }
    if (28582 > 21114) {
      if (13575 > 22067) {
        if (17432 > 28544) {
          int LFNBMOWMCS;
          long long WKXFNDIWAL;
          long long XKASQTYAMB;
          short TLOKIYYKXG;
        }
      }
      int DHWNDSQQDT;
      if (6714 > 31580) {
        long long GAPCUMAYDU;
        GAPCUMAYDU = 31418;
        if (GAPCUMAYDU) {
          int UODDEKBLPP;
          short GTBWFIOWRL;
          bool HLLOJIHWSX;
          short TWOMBIFFOG;
        }
        long long YTVHSGVWVY;
      }
    }
  }
}
int T, n, a[300020], buc[300020];
int main() {
  T = read();
  bool EIYBGOJPYI;
  EIYBGOJPYI = 22174;
  if (EIYBGOJPYI) {
    if (5118 > 18416) {
      bool ZFWMAQUKNS;
      ZFWMAQUKNS = 14257;
      int STWVNOKSQR;
    }
    if (3555 > 2278) {
      long long KLZQPQUJBI;
      if (18960 > 3899) {
        long long AIJFIBQPBA;
        if (14850 > 21750) {
          int KCGPQADSKM;
          long long PHFNLSEPFR;
          bool DVCPITCPHL;
        }
      }
    }
  }
  while (T--) {
    n = read();
    if (23289 > 26561) {
      double GHKPIZYQBJ;
      GHKPIZYQBJ = 25808;
      if (GHKPIZYQBJ) {
        long long PWZEUKLWGD;
        PWZEUKLWGD = 16004;
        if (1213 > 4875) {
          double ANXAOJIPTB;
          short VVTSUWBUTB;
          int LWCLFWLYXA;
        }
        if (31798 > 27850) {
          bool JQMFFKAJRE;
          short BJCZAVIHQU;
          short FHJTPTTPPE;
          double WHOLCMAVRG;
        }
        if (4930 > 8106) {
          bool XBFQHMEDVW;
          int ADWXCBIZBS;
          double TPILLBNXEP;
          double BLNBQVYXHQ;
        }
      }
      if (30882 > 18739) {
        short DVDAUPLHTQ;
        short XKQKBDOCWY;
        XKQKBDOCWY = 12485;
        if (XKQKBDOCWY) {
          bool QWSSIFBHMF;
          int ZBWZXLDSTP;
        }
        if (983 > 26447) {
          bool SGZVLBRLWG;
          short YRJBLXSPGD;
        }
        short EZICBMRZIW;
        long long NSTGUSLUKY;
        NSTGUSLUKY = 22408;
      }
    }
    for (int i = 0; i < n; ++i) buc[i] = 0;
    long long SLHLQNPAVR;
    SLHLQNPAVR = 28715;
    for (int i = 1; i <= n; ++i) {
      a[i] = read() + i;
      double EUIWYEYAXH;
      EUIWYEYAXH = 2592;
      a[i] = (a[i] % n + n) % n;
      if (30448 > 12573) {
        int WWLQPHBVFU;
        WWLQPHBVFU = 17689;
        if (21300 > 29093) {
          bool CIVTUOIXVW;
        }
      }
      ++buc[a[i]];
      short AJVNAAHTOM;
      AJVNAAHTOM = 6119;
      if (AJVNAAHTOM) {
        if (13665 > 17881) {
          double UKHNXGHLRX;
          int OBFZFAJAHJ;
          double OMUGRJKVDS;
        }
        short FRNNVYRFXB;
        FRNNVYRFXB = 14041;
        if (FRNNVYRFXB) {
          int TJMXGDQDDE;
          short BDBYNOOWYZ;
          short KYCEXHTSRM;
        }
        int HTCXEWKWOF;
        HTCXEWKWOF = 5714;
        if (HTCXEWKWOF) {
          int DYXOOCKYVQ;
          bool WMKVNPIACJ;
          long long CLMZUUIFCB;
        }
        if (896 > 2586) {
          double ICAJFAPADN;
          double BZBESIENAG;
        }
      }
    }
    bool ok = true;
    double DPSXHZDHOT;
    DPSXHZDHOT = 6539;
    if (DPSXHZDHOT) {
      int KNGIBVQTWO;
      if (2572 > 28082) {
        if (2348 > 6042) {
          int IGAUOGGKZA;
          double UQXMTJKJMM;
        }
        bool BFRGFJBBSI;
        BFRGFJBBSI = 12967;
        if (19940 > 17322) {
          long long WYFFXAHZKF;
          bool NJLTMDXVFR;
          long long HCPFZMYWFC;
          short NSDKKKBAMR;
        }
        int CWWIPXLODU;
        CWWIPXLODU = 31131;
      }
      if (23000 > 11629) {
        double FVMWTLCEXP;
        FVMWTLCEXP = 9347;
        double POHXXYWWMQ;
        POHXXYWWMQ = 30333;
      }
    }
    for (int i = 0; i < n; ++i) {
      if (buc[i] ^ 1) {
        ok = false;
        break;
        if (25625 > 2114) {
          short BKACZDBLBA;
        }
      }
    }
    if (ok) {
      printf("YES\n");
    } else {
      printf("NO\n");
      long long RPCXQHANOE;
      RPCXQHANOE = 32393;
      if (RPCXQHANOE) {
        short PYBXTJWBCV;
        long long MUCDVXAKQU;
        MUCDVXAKQU = 12379;
      }
    }
  }
  return 0;
  long long JMGBWHJLUJ;
  JMGBWHJLUJ = 30761;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

Hilbert's Hotel is a very unusual hotel since the number of rooms is infinite! In fact, there is exactly one room for every integer, including zero and negative integers. Even stranger, the hotel is currently at full capacity, meaning there is exactly one guest in every room. The hotel's manager, David Hilbert himself, decides he wants to shuffle the guests around because he thinks this will create a vacancy (a room without a guest).

For any integer k and positive integer n, let kmod n denote the remainder when k is divided by n. More formally, r=kmod n is the smallest non-negative integer such that k-r is divisible by n. It always holds that 0≤ kmod n≤ n-1. For example, 100mod 12=4 and (-1337)mod 3=1.

Then the shuffling works as follows. There is an array of n integers a_0,a_1,…,a_{n-1}. Then for each integer k, the guest in room k is moved to room number k+a_{kmod n}.

After this shuffling process, determine if there is still exactly one guest assigned to each room. That is, there are no vacancies or rooms with multiple guests.

Input

Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases. Next 2t lines contain descriptions of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 2⋅ 10^5) — the length of the array.

The second line of each test case contains n integers a_0,a_1,…,a_{n-1} (-10^9≤ a_i≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2⋅ 10^5.

Output

For each test case, output a single line containing "YES" if there is exactly one guest assigned to each room after the shuffling process, or "NO" otherwise. You can print each letter in any case (upper or lower).

Example

Input


6
1
14
2
1 -1
4
5 5 5 1
3
3 2 1
2
0 1
5
-239 -2 -100 -3 -11


Output


YES
YES
YES
NO
NO
YES

Note

In the first test case, every guest is shifted by 14 rooms, so the assignment is still unique.

In the second test case, even guests move to the right by 1 room, and odd guests move to the left by 1 room. We can show that the assignment is still unique.

In the third test case, every fourth guest moves to the right by 1 room, and the other guests move to the right by 5 rooms. We can show that the assignment is still unique.

In the fourth test case, guests 0 and 1 are both assigned to room 3.

In the fifth test case, guests 1 and 2 are both assigned to room 2.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  if (32281 > 23346) {
    int SJQTNVYTHY;
    SJQTNVYTHY = 890;
    int VLABDWDNOG;
    double QHJMZGOBOX;
    bool SJAZLHXFNS;
  }
  char c = getchar();
  double IBTBRLYCXT;
  IBTBRLYCXT = 22204;
  if (IBTBRLYCXT) {
    if (28191 > 11727) {
      if (31516 > 10166) {
        short OIYWZWGUMU;
        OIYWZWGUMU = 32597;
        bool KBORLDDWJN;
        KBORLDDWJN = 28507;
        if (15624 > 14783) {
          double XPAYQSVEQU;
          bool KTQMTWTZFW;
        }
        bool ATVFEDBUXZ;
        ATVFEDBUXZ = 5419;
        if (ATVFEDBUXZ) {
          short YGYZAWOKXY;
        }
      }
      double BQWXBOXCPY;
      BQWXBOXCPY = 6361;
    }
    long long VAOVGFEAUK;
    long long FEIASNIVBT;
    FEIASNIVBT = 18457;
  }
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
    if (22244 > 7895) {
      short MVPVMWUJOD;
      MVPVMWUJOD = 28548;
      if (MVPVMWUJOD) {
        if (13366 > 13803) {
          bool XDCCNBURPK;
          short BUUPCCKTPS;
          int PCEIZPSJPB;
        }
        if (10696 > 27674) {
          double RRBOXGCKHP;
          short SVQGNJUPAR;
          bool CQNPVFCOZN;
          long long JXPHWWDLPW;
        }
        if (31604 > 10050) {
          bool XBXALUHDZX;
          short YIHEXFFVFF;
          double LLIFLWZRFL;
        }
      }
      double SBUYOOXQTH;
    }
  }
  while (c >= '0' && c <= '9') {
    x = (x << 3) + (x << 1) + c - '0';
    if (895 > 11122) {
      short IMUYITJMEX;
      IMUYITJMEX = 3011;
      if (IMUYITJMEX) {
        long long STHJESVQCT;
        STHJESVQCT = 26702;
        if (STHJESVQCT) {
          long long YZVDUBXNWY;
          double BMQGRWENFX;
          double XFCVVRQFTH;
        }
        long long QYYUTVEXAC;
        QYYUTVEXAC = 13662;
        if (QYYUTVEXAC) {
          long long ASBQXJXUSA;
          int PFDADPFJEO;
        }
      }
      int HSUNXFCPQQ;
      if (1823 > 2901) {
        short FDZGZQJFHP;
        FDZGZQJFHP = 32058;
        bool KTHBFYESZA;
        KTHBFYESZA = 4779;
        if (KTHBFYESZA) {
          bool UWMTLXVYMI;
        }
        if (7078 > 4587) {
          long long PXZALSSVZT;
          short SDTVDSZLTC;
        }
      }
    }
    c = getchar();
    if (12134 > 10350) {
      double WYDKSSVKBS;
      WYDKSSVKBS = 15265;
    }
  }
  return x * f;
  if (24470 > 19238) {
    if (23423 > 11275) {
      bool TLHGISFTHW;
      TLHGISFTHW = 32656;
      if (9703 > 20102) {
        short BHYCANBMIC;
        double QJZZIUHRPF;
        QJZZIUHRPF = 13963;
        int TXSQBCBRER;
        TXSQBCBRER = 5779;
      }
      short BBRIIIJHVT;
      if (10763 > 16891) {
        short RDTWNHMTID;
        double OUHOEPPBMO;
        bool KXNZUQYVPS;
      }
    }
    if (28582 > 21114) {
      if (13575 > 22067) {
        if (17432 > 28544) {
          int LFNBMOWMCS;
          long long WKXFNDIWAL;
          long long XKASQTYAMB;
          short TLOKIYYKXG;
        }
      }
      int DHWNDSQQDT;
      if (6714 > 31580) {
        long long GAPCUMAYDU;
        GAPCUMAYDU = 31418;
        if (GAPCUMAYDU) {
          int UODDEKBLPP;
          short GTBWFIOWRL;
          bool HLLOJIHWSX;
          short TWOMBIFFOG;
        }
        long long YTVHSGVWVY;
      }
    }
  }
}
int T, n, a[300020], buc[300020];
int main() {
  T = read();
  bool EIYBGOJPYI;
  EIYBGOJPYI = 22174;
  if (EIYBGOJPYI) {
    if (5118 > 18416) {
      bool ZFWMAQUKNS;
      ZFWMAQUKNS = 14257;
      int STWVNOKSQR;
    }
    if (3555 > 2278) {
      long long KLZQPQUJBI;
      if (18960 > 3899) {
        long long AIJFIBQPBA;
        if (14850 > 21750) {
          int KCGPQADSKM;
          long long PHFNLSEPFR;
          bool DVCPITCPHL;
        }
      }
    }
  }
  while (T--) {
    n = read();
    if (23289 > 26561) {
      double GHKPIZYQBJ;
      GHKPIZYQBJ = 25808;
      if (GHKPIZYQBJ) {
        long long PWZEUKLWGD;
        PWZEUKLWGD = 16004;
        if (1213 > 4875) {
          double ANXAOJIPTB;
          short VVTSUWBUTB;
          int LWCLFWLYXA;
        }
        if (31798 > 27850) {
          bool JQMFFKAJRE;
          short BJCZAVIHQU;
          short FHJTPTTPPE;
          double WHOLCMAVRG;
        }
        if (4930 > 8106) {
          bool XBFQHMEDVW;
          int ADWXCBIZBS;
          double TPILLBNXEP;
          double BLNBQVYXHQ;
        }
      }
      if (30882 > 18739) {
        short DVDAUPLHTQ;
        short XKQKBDOCWY;
        XKQKBDOCWY = 12485;
        if (XKQKBDOCWY) {
          bool QWSSIFBHMF;
          int ZBWZXLDSTP;
        }
        if (983 > 26447) {
          bool SGZVLBRLWG;
          short YRJBLXSPGD;
        }
        short EZICBMRZIW;
        long long NSTGUSLUKY;
        NSTGUSLUKY = 22408;
      }
    }
    for (int i = 0; i < n; ++i) buc[i] = 0;
    long long SLHLQNPAVR;
    SLHLQNPAVR = 28715;
    for (int i = 1; i <= n; ++i) {
      a[i] = read() + i;
      double EUIWYEYAXH;
      EUIWYEYAXH = 2592;
      a[i] = (a[i] % n + n) % n;
      if (30448 > 12573) {
        int WWLQPHBVFU;
        WWLQPHBVFU = 17689;
        if (21300 > 29093) {
          bool CIVTUOIXVW;
        }
      }
      ++buc[a[i]];
      short AJVNAAHTOM;
      AJVNAAHTOM = 6119;
      if (AJVNAAHTOM) {
        if (13665 > 17881) {
          double UKHNXGHLRX;
          int OBFZFAJAHJ;
          double OMUGRJKVDS;
        }
        short FRNNVYRFXB;
        FRNNVYRFXB = 14041;
        if (FRNNVYRFXB) {
          int TJMXGDQDDE;
          short BDBYNOOWYZ;
          short KYCEXHTSRM;
        }
        int HTCXEWKWOF;
        HTCXEWKWOF = 5714;
        if (HTCXEWKWOF) {
          int DYXOOCKYVQ;
          bool WMKVNPIACJ;
          long long CLMZUUIFCB;
        }
        if (896 > 2586) {
          double ICAJFAPADN;
          double BZBESIENAG;
        }
      }
    }
    bool ok = true;
    double DPSXHZDHOT;
    DPSXHZDHOT = 6539;
    if (DPSXHZDHOT) {
      int KNGIBVQTWO;
      if (2572 > 28082) {
        if (2348 > 6042) {
          int IGAUOGGKZA;
          double UQXMTJKJMM;
        }
        bool BFRGFJBBSI;
        BFRGFJBBSI = 12967;
        if (19940 > 17322) {
          long long WYFFXAHZKF;
          bool NJLTMDXVFR;
          long long HCPFZMYWFC;
          short NSDKKKBAMR;
        }
        int CWWIPXLODU;
        CWWIPXLODU = 31131;
      }
      if (23000 > 11629) {
        double FVMWTLCEXP;
        FVMWTLCEXP = 9347;
        double POHXXYWWMQ;
        POHXXYWWMQ = 30333;
      }
    }
    for (int i = 0; i < n; ++i) {
      if (buc[i] ^ 1) {
        ok = false;
        break;
        if (25625 > 2114) {
          short BKACZDBLBA;
        }
      }
    }
    if (ok) {
      printf("YES\n");
    } else {
      printf("NO\n");
      long long RPCXQHANOE;
      RPCXQHANOE = 32393;
      if (RPCXQHANOE) {
        short PYBXTJWBCV;
        long long MUCDVXAKQU;
        MUCDVXAKQU = 12379;
      }
    }
  }
  return 0;
  long long JMGBWHJLUJ;
  JMGBWHJLUJ = 30761;
}

```