There is a trampoline park with n trampolines in a line. The i-th of which has strength S_i.

Pekora can jump on trampolines in multiple passes. She starts the pass by jumping on any trampoline of her choice. 

If at the moment Pekora jumps on trampoline i, the trampoline will launch her to position i + S_i, and S_i will become equal to max(S_i-1,1). In other words, S_i will decrease by 1, except of the case S_i=1, when S_i will remain equal to 1. 

If there is no trampoline in position i + S_i, then this pass is over. Otherwise, Pekora will continue the pass by jumping from the trampoline at position i + S_i by the same rule as above.

Pekora can't stop jumping during the pass until she lands at the position larger than n (in which there is no trampoline). Poor Pekora!

Pekora is a naughty rabbit and wants to ruin the trampoline park by reducing all S_i to 1. What is the minimum number of passes she needs to reduce all S_i to 1?

Input

The first line contains a single integer t (1 ≤ t ≤ 500) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 5000) — the number of trampolines.

The second line of each test case contains n integers S_1, S_2, ..., S_n (1 ≤ S_i ≤ 10^9), where S_i is the strength of the i-th trampoline.

It's guaranteed that the sum of n over all test cases doesn't exceed 5000.

Output

For each test case, output a single integer — the minimum number of passes Pekora needs to do to reduce all S_i to 1.

Example

Input


3
7
1 4 2 2 2 2 2
2
2 3
5
1 1 1 1 1


Output


4
3
0

Note

For the first test case, here is an optimal series of passes Pekora can take. (The bolded numbers are the positions that Pekora jumps into during these passes.)

  * [1,4,2,2,2,2,2] 
  * [1,4,1,2,1,2,1] 
  * [1,3,1,2,1,1,1] 
  * [1,2,1,2,1,1,1] 



For the second test case, the optimal series of passes is show below.

  * [2,3] 
  * [1,3] 
  * [1,2] 



For the third test case, all S_i are already equal to 1.
///****In the name of ALLAH, most Gracious, most Compassionate****//
#include<bits/stdc++.h>

#define Input                   freopen("in.txt","r",stdin)
#define Output                  freopen("out.txt","w",stdout)
#define ll                      long long int
#define ull                     unsigned long long int
#define pii                     pair<int,int>
#define pll                     pair<ll,ll>
#define sc                      scanf
#define scin(x)                 sc("%d",&(x))
#define scin2(x,y)              sc("%d %d",&(x),&(y))
#define scln(x)                 sc("%lld",&(x))
#define scln2(x,y)              sc("%lld %lld",&(x),&(y))
#define pf                      printf
#define all(a)                  (a.begin()),(a.end())
#define UNIQUE(X)               (X).erase(unique(all(X)),(X).end())
#define SORT_UNIQUE(c)          (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define ms(a,b)                 memset(a,b,sizeof(a))
#define pb(a)                   push_back(a)
#define mp                      make_pair
#define db                      double
#define EPS                     10E-10
#define ff                      first
#define ss                      second
#define sqr(x)                  (x)*(x)
#define vi                      vector<int>
#define vl                      vector<ll>
#define vii                     vector<vector<int> >
#define vll                     vector<vector<ll> >
#define DBG                     pf("HI\n")
#define MOD                     1000000007
#define CIN                     ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define RUN_CASE(t,T)           for(__typeof(t) t=1;t<=T;t++)
#define CASE(t)                 printf("Case %d: ",t)
#define CASEl(t)                printf("Case %d:\n",t)
#define intlimit                2147483690
#define longlimit               9223372036854775800
#define infinity                (1<<28)
#define gcd(a,b)                __gcd(a,b)
#define lcm(a,b)                (a)*(b)/gcd(a,b)
#define mxx                     123456789
#define PI                      2*acos(0.0)
#define rep(i,a,b)              for(__typeof(i) i=a;i<=b;i++)
#define rev(i,a,b)              for(__typeof(i) i=a;i>=b;i--)
#define coutv(v)                for(auto it:v)cout<<it<<' ';cout<<'\n';
#define cinv(v)                 for(auto &it:v)cin>>it;
#define srt(v)                  sort(v.begin(),v.end());
#define rsrt(v)                 sort(v.rbegin(),v.rend());
#define rvs(v)                  reverse(v.begin(),v.end());

using namespace std;
/**     toint, tostring, BigMod, Power , sieve, Primefactorize ,frequency in n!     **/
//ll toint(string s){ll n=0,k=1;for(int i=s.size()-1; i>=0; i--){n += ((s[i]-'0')*k);k*=10;}return n;}
//string tostring(ll x){string s="";while(x){s += (x%10)+'0';x/=10;}reverse(s.begin(),s.end());return s;}
//ll BigMod(ll a,ll b){if(b == 0)return 1%MOD;else if(b%2 == 0){ll temp=BigMod(a,b/2);return ((temp%MOD)*(temp%MOD))%MOD;}else{return ((a%MOD)*BigMod(a,b-1)%MOD)%MOD;}}
//ll Power(ll a,ll n){ll ret=1;for(ll i=1 ; i<=n ; i++)ret = ((ret%MOD)*(a%MOD))%MOD;return ret;}
//bool isPrime(ll n){for(ll i=2 ; i*i<=n ; i++){if(n%i == 0)return 0;}return 1;}
//vector<ll>Prime;
//bool mark[10000003];
//void sieve(ll n){ll i,j;mark[1]=1;for(i=4; i<=n; i+=2)mark[i]=1;Prime.push_back(2);for(i=3; i<=n; i+=2){if(!mark[i]){Prime.push_back(i);if(i*i<=n){for(j=i*i; j<=n; j+=(i*2))mark[j]=1;}}}}
//map<ll,ll>Factor;
//void Primefactorize(ll n){for(ll i=0; i<Prime.size() && Prime[i]*Prime[i]<=n; i++){if(n%Prime[i] == 0){while(n%Prime[i] == 0){Factor[Prime[i]]++;n/=Prime[i];}}}if(n>1){Factor[n]++;}}
//ll frequency(ll n,ll factor)/** Frequency of a factor in n! **/{ll cnt=0;while(n){cnt += (n/factor);n /= factor;}return cnt;}
/**     Order Set       **/
//#include <ext/pb_ds/assoc_container.hpp>
//using namespace __gnu_pbds;
//template<typename T> using orderset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
//orderset<int> s ; //orderset<int>::iterator it ;
//orderset<int> X; //X.insert(1); //X.insert(2); //X.insert(4); //X.insert(8); //X.insert(16);
//cout<<*X.find_by_order(0)<<endl; // 2 //cout<<*X.find_by_order(2)<<endl; // 4 //cout<<*X.find_by_order(4)<<endl; // 16 //cout<<(end(X)==X.find_by_order(6))<<endl; // true
//cout<<X.order_of_key(-5)<<endl;  // 0 //cout<<X.order_of_key(1)<<endl;   // 0 //cout<<X.order_of_key(3)<<endl;   // 2 //cout<<X.order_of_key(4)<<endl;   // 2 //cout<<X.order_of_key(400)<<endl; // 5

struct custom_hash {    ///For unordered map or set
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

/** Debugging Tool **/
#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }
void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args)
{
    cerr << *it << " = " << a << endl;
    err(++it, args...);
}
///

inline int add(int a, int b) {a += b; return a >= MOD ? a - MOD : a;}
inline int sub(int a, int b) {a -= b; return a < 0 ? a + MOD : a;}
inline int mul(int a, int b) {return (ll) a * b % MOD;}
int Set(int N, int pos) {return  N = N | (1<<pos);}
int Reset(int N, int pos) {return  N = N & ~(1<<pos);}
bool Cheek(int N, int pos) {return  (bool)(N & (1<<pos));}

//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//int my_rand(int l,int r)
//{
//    return uniform_int_distribution<int>(l , r) (rng);
//}

//string small = "abcdefghijklmnopqrstuvwxyz";
//string capital = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

///------------------Graph Moves-------------------
///const int fx[] = {+1,-1,+0,+0};
///const int fy[] = {+0,+0,+1,-1};
///const int fx[] = {+0,+0,+1,-1,-1,+1,-1,+1}; ///King's move
///const int fy[] = {-1,+1,+0,+0,+1,+1,-1,-1}; ///King's move
///const int fx[] = {-2,-2,-1,-1,+1,+1,+2,+2}; ///Knight's move
///const int fy[] = {-1,+1,-2,+2,-2,+2,-1,+1}; ///Knight's move

ll s[5009],added[5009];

void Solve(int t)
{
    ll i,j,k,n,ans=0;
    scln(n);
    for(i=1 ; i<=n ; i++)
        scln(s[i]);

    for(i=1 ; i<=n ; i++){
        if(s[i] - added[i] <= 1){
            for(j=i+2 ; j<=min(n , i+s[i]) ; j++)
                added[j]++;
            if(added[i] >= s[i]){
                ll xtra = added[i] - (s[i] - 1);
                added[i+1] += xtra;
            }
            continue;
        }

        ll temp = (s[i] - 1) - added[i];
        added[i] += temp;
        ans += temp;

//        error(i , temp);
        for(j=i+2 ; j<=min(n , i+s[i]) ; j++){
            added[j]++;
        }

        if(added[i] >= s[i]){
            ll xtra = added[i] - (s[i] - 1);
            added[i+1] += xtra;
        }
    }
    pf("%lld\n",ans);

    for(i=1 ; i<=n+2 ; i++)
        s[i] = added[i] = 0;
}

int main()
{
    int t,T;
    T = 1;
    cin>>T;
    RUN_CASE(t,T)
    {
        Solve(t);
    }
    return 0;
}

/** Stuff u should look for
    * Avoid overflow
    * Corner(Small) case
    * Don't get stuck on one approach
    * Don't forget to clean used memory in each case
**/
