1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cmath>
#include<queue>
#include<queue>
#include<stack>
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <chrono>

using namespace std;
using namespace __gnu_pbds;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef long long LL;
typedef unsigned long long ULL;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<LL> VLL;
typedef vector<LD> VLD;
typedef vector<VLL > VVLL;
typedef vector<VLD > VVLD;
typedef vector<PII > VPII;
typedef vector<PLL > VPLL;
typedef __int128 int128;
template<class TIn>
using indexed_set = tree<
        TIn, null_type, less<TIn>,
        rb_tree_tag, tree_order_statistics_node_update>;
template<class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;

#define FOR(x, b, e) for(int x=b; x<=(e); ++x)
#define FORD(x, b, e) for(int x=b; x>=(e); --x)
#define REP(x, n) for(int x=0; x<(n); ++x)
#define VAR(v, n) __typeof(n) v = (n)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(x) ((int)(x).size())
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define PB push_back
#define ST first
#define ND second
#define THIS (*this)
#define LSB(x) (x & -x)
#define SQR(x) ((x)*(x))

int calcMaxP(int x) {
    int i = 1;
    while ((i - 1)*(i - 2)*i / 6 < x) i++;
    return i;
}
int maxP;

vector<unordered_map<LL, int> > memo;

bool check(VI &a, int b, LL x, LL sp) {
    //printf("check %d %lld %lld\n", b, x, sp);
    if (b == a.size()) return x >= 0;
    if (memo[b].count(x)) return memo[b][x];
    //printf("memo[%d] size: %d\n", b + 1, memo[b + 1].size());
    FOR(i, a[b] == 0 ? 0 : 1, a[b] == 0 ? 7 : maxP) {
        LL sn = x - i;
        if (sn < 0) break;
        //printf("x: %lld\n", sp * i * sn + i * (i - 1) * (sp + sn) / 2 + i * (i - 1) * (i - 2) / 6);
        if (sp * i * sn + i * (i - 1) * (sp + sn) / 2 + i * (i - 1) * (i - 2) / 6 >= a[b]) {
            bool ans = check(a, b + 1, sn, sp + i);
            if (ans) return memo[b][x] = true;
            else if (b > 0) return memo[b][x] = false;
        }
    }
    return memo[b][x] = false;
}

bool possible(VI &a, LL p) {
    //printf("check if possible %lld\n", p);
    memo.assign(a.size(), unordered_map<LL, int>());
    return check(a, 0, p, 0);
}

int main() {
	ios_base::sync_with_stdio(0);
    cin.tie(NULL); cout.tie(NULL);
    int t; cin >> t;
    while (t--) {
        int n; cin >> n;
        VI a;
        int maxA = 0;
        REP(i, n) {
            int x; cin >> x;
            maxA = max(maxA, x);
            if (x == 0) {
                if (i == 0 || i == n - 1) a.PB(x);
            } else a.PB(x);
        }
        maxP = calcMaxP(maxA);
        LL lo = 0, hi = 1e9;
        while (lo + 1 < hi) {
            LL mid = (lo + hi) / 2;
            if (possible(a, mid)) hi = mid;
            else lo = mid;
        }
        cout << hi << '\n';
    }

    return 0;
}