You have 2n integers 1, 2, ..., 2n. You have to redistribute these 2n elements into n pairs. After that, you choose x pairs and take minimum elements from them, and from the other n - x pairs, you take maximum elements.

Your goal is to obtain the set of numbers \\{b_1, b_2, ..., b_n\} as the result of taking elements from the pairs.

What is the number of different x-s (0 ≤ x ≤ n) such that it's possible to obtain the set b if for each x you can choose how to distribute numbers into pairs and from which x pairs choose minimum elements?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

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

The second line of each test case contains n integers b_1, b_2, ..., b_n (1 ≤ b_1 < b_2 < ... < b_n ≤ 2n) — the set you'd like to get.

It's guaranteed that the sum of n over test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case, print one number — the number of different x-s such that it's possible to obtain the set b.

Example

Input


3
1
1
5
1 4 5 9 10
2
3 4


Output


1
3
1

Note

In the first test case, x = 1 is the only option: you have one pair (1, 2) and choose the minimum from this pair.

In the second test case, there are three possible x-s. If x = 1, then you can form the following pairs: (1, 6), (2, 4), (3, 5), (7, 9), (8, 10). You can take minimum from (1, 6) (equal to 1) and the maximum elements from all other pairs to get set b.

If x = 2, you can form pairs (1, 2), (3, 4), (5, 6), (7, 9), (8, 10) and take the minimum elements from (1, 2), (5, 6) and the maximum elements from the other pairs.

If x = 3, you can form pairs (1, 3), (4, 6), (5, 7), (2, 9), (8, 10) and take the minimum elements from (1, 3), (4, 6), (5, 7).

In the third test case, x = 0 is the only option: you can form pairs (1, 3), (2, 4) and take the maximum elements from both of them.
#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
void*wmem;
char memarr[96000000];
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
template<class T> inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){
  walloc1d(arr, x2-x1, mem);
  (*arr) -= x1;
}
inline int my_getchar(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline int rd_int(void){
  int x;
  rd(x);
  return x;
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar(a);
}
inline void wt_L(int x){
  int s=0;
  int m=0;
  char f[10];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar('-');
  }
  while(s--){
    my_putchar(f[s]+'0');
  }
}
template<class T> struct Arr1d{
  int n;
  int mem;
  T*d;
  T& operator[](int a){
    return d[a];
  }
  void sort(){
    reset();
    std::sort(d, d+n);
  }
  int set_cumulative_sum;
  int cumulative_sum_mem;
  T*cumulative_sum;
  void setSum(void){
    int i;
    set_cumulative_sum = 1;
    if(cumulative_sum_mem < n+1){
      delete[] cumulative_sum;
      cumulative_sum = new T[n+1];
      cumulative_sum_mem = n+1;
    }
    cumulative_sum[0] = 0;
    for(i=(0);i<(n);i++){
      cumulative_sum[i+1] = cumulative_sum[i] + d[i];
    }
  }
  T getSum(int i, int j){
    if(set_cumulative_sum==0){
      setSum();
    }
    return cumulative_sum[j+1] - cumulative_sum[i];
  }
  int set_const_len_left;
  int const_len_left_mem;
  int*const_len_left;
  void setConstLenLeft(void){
    int i;
    set_const_len_left = 1;
    if(const_len_left_mem < n){
      delete[] const_len_left;
      const_len_left = new int[n];
      const_len_left_mem = n;
    }
    for(i=(0);i<(n);i++){
      const_len_left[i] = 1;
    }
    for(i=(1);i<(n);i++){
      if(d[i]==d[i-1]){
        const_len_left[i] = const_len_left[i-1] + 1;
      }
    }
  }
  int ConstLenLeft(int st, T val){
    if(!set_const_len_left){
      setConstLenLeft();
    }
    if(val != d[st]){
      return 0;
    }
    return const_len_left[st];
  }
  int ConstLenLeft(int st){
    if(!set_const_len_left){
      setConstLenLeft();
    }
    return const_len_left[st];
  }
  int ConstLenLeftCyclic(int st, T val){
    if(!set_const_len_left){
      setConstLenLeft();
    }
    st %= n;
    if(st < 0){
      st += n;
    }
    if(val != d[st]){
      return 0;
    }
    if(const_len_left[st] != st+1 || d[st] != d[n-1]){
      return const_len_left[st];
    }
    if(const_len_left[n-1] == n){
      return 1073709056;
    }
    return const_len_left[st] + const_len_left[n-1];
  }
  int ConstLenLeftCyclic(int st){
    if(!set_const_len_left){
      setConstLenLeft();
    }
    st %= n;
    if(st < 0){
      st += n;
    }
    if(const_len_left[st] != st+1 || d[st] != d[n-1]){
      return const_len_left[st];
    }
    if(const_len_left[n-1] == n){
      return 1073709056;
    }
    return const_len_left[st] + const_len_left[n-1];
  }
  int set_const_len_right;
  int const_len_right_mem;
  int*const_len_right;
  void setConstLenRight(void){
    int i;
    set_const_len_right = 1;
    if(const_len_right_mem < n){
      delete[] const_len_right;
      const_len_right = new int[n];
      const_len_right_mem = n;
    }
    for(i=(0);i<(n);i++){
      const_len_right[i] = 1;
    }
    for(i=(n-1)-1;i>=(0);i--){
      if(d[i]==d[i+1]){
        const_len_right[i] = const_len_right[i+1] + 1;
      }
    }
  }
  int ConstLenRight(int st, T val){
    if(!set_const_len_right){
      setConstLenRight();
    }
    if(val != d[st]){
      return 0;
    }
    return const_len_right[st];
  }
  int ConstLenRight(int st){
    if(!set_const_len_right){
      setConstLenRight();
    }
    return const_len_right[st];
  }
  int ConstLenRightCyclic(int st, T val){
    if(!set_const_len_right){
      setConstLenRight();
    }
    if(val != d[st]){
      return 0;
    }
    st %= n;
    if(st < 0){
      st += n;
    }
    if(const_len_right[st] != n-st || d[st] != d[0]){
      return const_len_right[st];
    }
    if(const_len_right[0] == n){
      return 1073709056;
    }
    return const_len_right[st] + const_len_right[0];
  }
  int ConstLenRightCyclic(int st){
    if(!set_const_len_right){
      setConstLenRight();
    }
    st %= n;
    if(st < 0){
      st += n;
    }
    if(const_len_right[st] != n-st || d[st] != d[0]){
      return const_len_right[st];
    }
    if(const_len_right[0] == n){
      return 1073709056;
    }
    return const_len_right[st] + const_len_right[0];
  }
  int set_dhist;
  int dhist_mem;
  int*dhist;
  T dhist_mn;
  T dhist_mx;
  void setDHist(void){
    int i;
    int len;
    set_dhist = 1;
    if(n==0){
      return;
    }
    dhist_mn = dhist_mx = d[0];
    for(i=(1);i<(n);i++){
      if(dhist_mn > d[i]){
        dhist_mn = d[i];
      }
      if(dhist_mx < d[i]){
        dhist_mx = d[i];
      }
    }
    len = dhist_mx - dhist_mn + 1;
    if(dhist_mem < len){
      delete[] dhist;
      dhist = new int[len];
      dhist_mem = len;
    }
    for(i=(0);i<(len);i++){
      dhist[i] = 0;
    }
    for(i=(0);i<(n);i++){
      dhist[d[i] - dhist_mn]++;
    }
  }
  int dHist(T x){
    if(set_dhist==0){
      setDHist();
    }
    if(n == 0 || x < dhist_mn || x > dhist_mx){
      return 0;
    }
    return dhist[x - dhist_mn];
  }
  int set_prevLE;
  int prevLE_mem;
  int*prevLE;
  int setPrevLE(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_prevLE = 1;
    if(prevLE_mem < n){
      delete[] prevLE;
      prevLE = new int[n];
      prevLE_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(0);i<(n);i++){
      while(s && d[st[s-1]] > d[i]){
        s--;
      }
      if(s==0){
        prevLE[i] = -1;
      }
      else{
        prevLE[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int PrevLE(int i){
    if(set_prevLE==0){
      setPrevLE();
    }
    return prevLE[i];
  }
  int set_prevLT;
  int prevLT_mem;
  int*prevLT;
  int setPrevLT(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_prevLT = 1;
    if(prevLT_mem < n){
      delete[] prevLT;
      prevLT = new int[n];
      prevLT_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(0);i<(n);i++){
      while(s && d[st[s-1]] >= d[i]){
        s--;
      }
      if(s==0){
        prevLT[i] = -1;
      }
      else{
        prevLT[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int PrevLT(int i){
    if(set_prevLT==0){
      setPrevLT();
    }
    return prevLT[i];
  }
  int set_prevGE;
  int prevGE_mem;
  int*prevGE;
  int setPrevGE(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_prevGE = 1;
    if(prevGE_mem < n){
      delete[] prevGE;
      prevGE = new int[n];
      prevGE_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(0);i<(n);i++){
      while(s && d[st[s-1]] < d[i]){
        s--;
      }
      if(s==0){
        prevGE[i] = -1;
      }
      else{
        prevGE[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int PrevGE(int i){
    if(set_prevGE==0){
      setPrevGE();
    }
    return prevGE[i];
  }
  int set_prevGT;
  int prevGT_mem;
  int*prevGT;
  int setPrevGT(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_prevGT = 1;
    if(prevGT_mem < n){
      delete[] prevGT;
      prevGT = new int[n];
      prevGT_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(0);i<(n);i++){
      while(s && d[st[s-1]] <= d[i]){
        s--;
      }
      if(s==0){
        prevGT[i] = -1;
      }
      else{
        prevGT[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int PrevGT(int i){
    if(set_prevGT==0){
      setPrevGT();
    }
    return prevGT[i];
  }
  int set_nextLE;
  int nextLE_mem;
  int*nextLE;
  int setNextLE(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_nextLE = 1;
    if(nextLE_mem < n){
      delete[] nextLE;
      nextLE = new int[n];
      nextLE_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(n)-1;i>=(0);i--){
      while(s && d[st[s-1]] > d[i]){
        s--;
      }
      if(s==0){
        nextLE[i] = n;
      }
      else{
        nextLE[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int NextLE(int i){
    if(set_nextLE==0){
      setNextLE();
    }
    return nextLE[i];
  }
  int set_nextLT;
  int nextLT_mem;
  int*nextLT;
  int setNextLT(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_nextLT = 1;
    if(nextLT_mem < n){
      delete[] nextLT;
      nextLT = new int[n];
      nextLT_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(n)-1;i>=(0);i--){
      while(s && d[st[s-1]] >= d[i]){
        s--;
      }
      if(s==0){
        nextLT[i] = n;
      }
      else{
        nextLT[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int NextLT(int i){
    if(set_nextLT==0){
      setNextLT();
    }
    return nextLT[i];
  }
  int set_nextGE;
  int nextGE_mem;
  int*nextGE;
  int setNextGE(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_nextGE = 1;
    if(nextGE_mem < n){
      delete[] nextGE;
      nextGE = new int[n];
      nextGE_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(n)-1;i>=(0);i--){
      while(s && d[st[s-1]] < d[i]){
        s--;
      }
      if(s==0){
        nextGE[i] = n;
      }
      else{
        nextGE[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int NextGE(int i){
    if(set_nextGE==0){
      setNextGE();
    }
    return nextGE[i];
  }
  int set_nextGT;
  int nextGT_mem;
  int*nextGT;
  int setNextGT(void *mem = wmem){
    int i;
    int s = 0;
    int*st;
    set_nextGT = 1;
    if(nextGT_mem < n){
      delete[] nextGT;
      nextGT = new int[n];
      nextGT_mem = n;
    }
    walloc1d(&st, n, &mem);
    for(i=(n)-1;i>=(0);i--){
      while(s && d[st[s-1]] <= d[i]){
        s--;
      }
      if(s==0){
        nextGT[i] = n;
      }
      else{
        nextGT[i] = st[s-1];
      }
      st[s++] = i;
    }
  }
  int NextGT(int i){
    if(set_nextGT==0){
      setNextGT();
    }
    return nextGT[i];
  }
  void reset(){
    set_cumulative_sum = 0;
    set_const_len_left = 0;
    set_const_len_right = 0;
    set_dhist = 0;
    set_prevLE = set_prevLT = set_prevGE = set_prevGT = 0;
    set_nextLE = set_nextLT = set_nextGE = set_nextGT = 0;
  }
  void memory_expand(int nn){
    if(mem < nn){
      delete[] d;
      d = new T[nn];
      mem = nn;
    }
  }
  void malloc(int nn){
    reset();
    memory_expand(nn);
    n = nn;
  }
  void setN(int nn){
    reset();
    memory_expand(nn);
    n = nn;
  }
  void set(vector<T> &a){
    int i;
    int nn = a.size();
    setN(nn);
    for(i=(0);i<(nn);i++){
      d[i] = a[i];
    }
  }
  void set(int nn, T a[]){
    int i;
    setN(nn);
    for(i=(0);i<(nn);i++){
      d[i] = a[i];
    }
  }
  void free(){
    destructor();
  }
  void constructor(){
    n = mem = 0;
    d = NULL;
    set_cumulative_sum = 0;
    cumulative_sum_mem = 0;
    cumulative_sum = NULL;
    set_const_len_left = 0;
    const_len_left_mem = 0;
    const_len_left = NULL;
    set_const_len_right = 0;
    const_len_right_mem = 0;
    const_len_right = NULL;
    set_dhist = 0;
    dhist_mem = 0;
    dhist = NULL;
    set_prevLE = set_prevLT = set_prevGE = set_prevGT = 0;
    prevLE_mem = prevLT_mem = prevGE_mem = prevGT_mem = 0;
    prevLE = prevLT = prevGE = prevGT = NULL;
    set_nextLE = set_nextLT = set_nextGE = set_nextGT = 0;
    nextLE_mem = nextLT_mem = nextGE_mem = nextGT_mem = 0;
    nextLE = nextLT = nextGE = nextGT = NULL;
  }
  void constructor(int nn){
    constructor();
    malloc(nn);
  }
  void destructor(){
    delete[] d;
    d = NULL;
    mem = n = 0;
    set_cumulative_sum = 0;
    cumulative_sum_mem = 0;
    delete[] cumulative_sum;
    cumulative_sum = NULL;
    set_const_len_left = 0;
    const_len_left_mem = 0;
    delete[] const_len_left;
    const_len_left = NULL;
    set_const_len_right = 0;
    const_len_right_mem = 0;
    delete[] const_len_right;
    const_len_right = NULL;
    set_dhist = 0;
    dhist_mem = 0;
    delete[] dhist;
    dhist = NULL;
  }
  Arr1d(){
    constructor();
  }
  Arr1d(int nn){
    constructor(nn);
  }
  ~Arr1d(){
    destructor();
  }
}
;
int N;
Arr1d<int> A;
int main(){
  int Lj4PdHRW;
  wmem = memarr;
  int KL2GvlyY = rd_int();
  for(Lj4PdHRW=(0);Lj4PdHRW<(KL2GvlyY);Lj4PdHRW++){
    int i;
    int mn = 0;
    int mx = 0;
    int k = 0;
    rd(N);
    A.malloc(N);
    {
      int cTE1_r3A;
      for(cTE1_r3A=(0);cTE1_r3A<(N);cTE1_r3A++){
        rd(A[cTE1_r3A]);A[cTE1_r3A] += (-1);
      }
    }
    for(i=(0);i<(N);i++){
      while(k < A[i] || A.dHist(k)){
        k++;
      }
      if(k >= 2*N){
        break;
      }
      mn++;
      k++;
    }
    k = 2*N - 1;
    for(i=(N)-1;i>=(0);i--){
      while(k > A[i] || A.dHist(k)){
        k--;
      }
      if(k < 0){
        break;
      }
      mx++;
      k--;
    }
    wt_L(mx + mn - N + 1);
    wt_L('\n');
  }
  return 0;
}
// cLay version 20201206-1

// --- original code ---
// //no-unlocked
// int N; Arr1d<int> A;
// {
//   REP(rd_int()){
//     int mn = 0, mx = 0, k = 0;
//     rd(N,(A--)(N));
//     rep(i,N){
//       while(k < A[i] || A.dHist(k)) k++;
//       if(k >= 2N) break;
//       mn++; k++;
//     }
//     k = 2N - 1;
//     rrep(i,N){
//       while(k > A[i] || A.dHist(k)) k--;
//       if(k < 0) break;
//       mx++; k--;
//     }
//     wt(mx + mn - N + 1);
//   }
// }
