Problem:
Score : 800 points

Problem Statement

There are N positive integers A_1, A_2, ..., A_N.
Takahashi can perform the following operation on these integers any number of times:

Choose 1 \leq i \leq N and multiply the value of A_i by -2.

Notice that he multiplies it by minus two.

He would like to make A_1 \leq A_2 \leq ... \leq A_N holds.
Find the minimum number of operations required. If it is impossible, print -1.

Constraints

1 \leq N \leq 200000

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the answer.

Sample Input 1

4
3 1 4 1

Sample Output 1

3

One possible solution is:

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now 3, 1, 4, -2.

Choose i=1 and multiply the value of A_1 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, -2.

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, 4.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

0

A_1 \leq A_2 \leq ... \leq A_N holds before any operation is performed.

Sample Input 3

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Sample Output 3

7

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

/*
 * じょえチャンネル
 * 高評価・チャンネル登録よろしくおねがいします！
 * https://www.youtube.com/channel/UCRXsI3FL_kvaVL9zoolBfbQ
 */

#include <bits/stdc++.h>

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

#define f(i,n) for(int i=0;i<(n);i++)




//here!!!
// define int long long !!!!!

#define int long long

// define int long long !!!!!


#define mod (int)((1e9)+7)
//constexpr int mod = 998244353ll;


#ifdef int
#define inf (int)(3e18)
#else
#define inf (int)(5e8)
#endif

#define intt long long
#define itn long long
#define P pair<long long,long long>

#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)

#define ALL(v) v.begin(),v.end()

using namespace std;

//Library
//モッドパウ
inline int modpow(int x, int y, int m = mod) {
    int res = 1;
    while (y) {
        if (y & 1) {
            res *= x;
            res %= m;
        }
        x = x * x % m;
        y /= 2;
    }
    return res;
}

int mypow(int x, int y) {
    int res = 1;
    while (y) {
        if (y % 2) {
            res *= x;
        }
        x = x * x;
        y /= 2;
    }
    return res;
}
//is the number (x) a prime number?
bool prime(int x) {
    if (!x || x == 1) {
        return false;
    }
    for (int i = 2; i * i <= x; i++) {
        if (!(x % i)) {
            return false;
        }
    }
    return true;
}


//saidai-kouyakusuu
inline int gcd(int x, int y) {
    if (!y) {
        return x;
    }
    return gcd(y, x % y);
}


//number of keta
int keta(int x) {
    int ans = 0;
    while (x) {
        x /= 10;
        ans++;
    }
    return ans;
}

//sum of keta
int ketasum(int x) {
    int ans = 0;
    while (x) {
        ans += x % 10;
        x /= 10;
    }
    return ans;
}

inline int lcm(int x, int y) {
    int ans = x / gcd(x, y) * y;
    return ans;
}
int twobeki(int x) {
    int ans = 0;
    while (1) {
        if (!(x & 1)) {
            ans++;
            x /= 2;
        }
        else {
            break;
        }
    }
    return ans;
}


template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
    if (lhs < rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
    if (lhs > rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
void Yes(){
    cout<<"Yes"<<endl;
}
void No(){
    cout<<"No"<<endl;
}
void YES(){
    cout<<"YES"<<endl;
}
void NO(){
    cout<<"NO"<<endl;
}


#define fin(i) scanf("%lld",&i)
#define fout(i) printf("%lld",i)
#define fendl printf("\n")

int kai(int x, int y) {
    int res = 1;
    for (int i = x - y + 1; i <= x; i++) {
        res *= i; res %= mod;
    }
    return res;
}

int comb(int x, int y) {
    if (y > x)return 0;
    //    cout<<kai(x, y)<<' '<<modpow(kai(y, y), mod - 2)<<endl;
    return kai(x, y) * modpow(kai(y, y), mod - 2) % mod;
}
//Library-End


#define vecin(v) for(int i=0;i<v.size();i++)scanf("%lld",&v[i]);
#define vecout(v) {for(int i=0;i<(int)v.size();i++)printf("%lld ",v[i]);printf("\n");}


template<typename T, typename U>
class SegTree {
protected:
    unsigned int n = 1, rank = 0;
    std::vector<T> node;
    T nodee;
    virtual T nodef(const T&, const T&)const = 0;
public:
    SegTree(unsigned int m, T init, T nodee):nodee(nodee) {
        while (n < m) {
            n *= 2;
            rank++;
        }
        node.resize(2 * n);
        for (unsigned int i = n; i < 2 * n; i++)node[i] = init;
    }
    SegTree(const std::vector<T>& initvec, T nodee):nodee(nodee) {
        unsigned int m = initvec.size();
        while (n < m) {
            n *= 2;
            rank++;
        }
        node.resize(2 * n);
        for (unsigned int i = n; i < 2 * n; i++) {
            if (i - n < m)node[i] = initvec[i - n];
        }
    }
    virtual void update(int i, U x) {
        i += n;
        node[i] = x;
        while (i != 1) {
            i >>= 1;
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
        }
    }
    virtual T query(int l, int r) {
        l += n; r += n;
        int ls = nodee, rs = nodee;
        while (l < r) {
            if (l & 1) {
                ls = nodef(ls, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rs = nodef(node[r], rs);
            }
            l >>= 1; r >>= 1;
        }
        return nodef(ls, rs);
    }
    virtual T operator[](const int& x) {
        return node[n + x];
    }
    void fill(T x) {
        std::fill(all(node), x);
    }
    void print() {
        rep(i, n)std::cout << operator[](i) << " ";
        std::cout << std::endl;
    }
};
class RSQ :public SegTree<int, int> {
    int nodef(const int& lhs,const int& rhs){return lhs+rhs;}
public:
    RSQ(int size, const int& def = 0) :SegTree<int, int>(size, def, 0) {}
    RSQ(const std::vector<int>& initvec) :SegTree<int, int>(initvec, 0) {}
};
class RMiQ :public SegTree<int, int> {
    int nodef(const int& lhs,const int& rhs){return std::min(lhs,rhs);}
public:
    RMiQ(int size, const int& def = 0) :SegTree<int, int>(size, def, 0) {}
    RMiQ(const std::vector<int>& initvec) :SegTree<int, int>(initvec, 0) {}
};
class RMaQ :public SegTree<int, int> {
    int nodef(const int& lhs,const int& rhs){return std::max(lhs,rhs);}
public:
    RMaQ(int size, const int& def = 0) :SegTree<int, int>(size, def, 0) {}
    RMaQ(const std::vector<int>& initvec) :SegTree<int, int>(initvec, 0) {}
};
template<typename T, typename U>
class IntervalSegTree :public SegTree<T, U> {
protected:
    using SegTree<T, U>::n;
    using SegTree<T, U>::rank;
    using SegTree<T, U>::node;
    using SegTree<T, U>::nodef;
    using SegTree<T, U>::nodee;
    std::vector<U> lazy;
    std::vector<bool> lazyflag;
    std::vector<int> width;
    virtual void lazyf(U&, const U&) = 0;
    virtual void updf(T&, const U&, const unsigned int&) = 0;
    void eval(int k) {
        for (int i = rank; i > 0; i--) {
            int nk = k >> i;
            if (lazyflag[nk]) {
                updf(node[2 * nk], lazy[nk], width[2 * nk]);
                updf(node[2 * nk + 1], lazy[nk], width[2 * nk + 1]);
                if (lazyflag[2 * nk])lazyf(lazy[2 * nk], lazy[nk]);
                else lazy[2 * nk] = lazy[nk];
                if (lazyflag[2 * nk + 1])lazyf(lazy[2 * nk + 1], lazy[nk]);
                else lazy[2 * nk + 1] = lazy[nk];
                lazyflag[2 * nk] = lazyflag[2 * nk + 1] = true;
                lazyflag[nk] = false;
            }
        }
    }
public:
    IntervalSegTree(unsigned int m, T init, T nodee) :SegTree<T, U>(m, init, nodee) {
        lazy.resize(2 * n); lazyflag.resize(2 * n); width.resize(2 * n);
        width[1] = n;
        for (unsigned int i = 2; i < 2 * n; i++) {
            width[i] = width[i >> 1] >> 1;
        }
    }
    IntervalSegTree(T nodee, const std::vector<T>& initvec) :SegTree<T, U>(initvec, nodee) {
        lazy.resize(2 * n); lazyflag.resize(2 * n); width.resize(2 * n);
        width[1] = n;
        for (unsigned int i = 2; i < 2 * n; i++) {
            width[i] = width[i >> 1] >> 1;
        }
    }
    void update(int i, U x) {
        i += n;
        eval(i);
        updf(node[i], x, width[i]);
        if (lazyflag[i])lazyf(lazy[i], x);
        else {
            lazyflag[i] = true;
            lazy[i] = x;
        }
        while (i /= 2)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    void update(int l, int r, U x) {
        l += n; r += n;
        int nl = l, nr = r;
        while (!(nl & 1))nl >>= 1;
        while (!(nr & 1))nr >>= 1;
        nr--;
        eval(nl); eval(nr);
        while (l < r) {
            if (l & 1) {
                updf(node[l], x, width[l]);
                if (lazyflag[l])lazyf(lazy[l], x);
                else {
                    lazyflag[l] = true;
                    lazy[l] = x;
                }
                l++;
            }
            if (r & 1) {
                r--;
                updf(node[r], x, width[r]);
                if (lazyflag[r])lazyf(lazy[r], x);
                else {
                    lazyflag[r] = true;
                    lazy[r] = x;
                }
            }
            l >>= 1; r >>= 1;
        }
        while (nl >>= 1)node[nl] = nodef(node[2 * nl], node[2 * nl + 1]);
        while (nr >>= 1)node[nr] = nodef(node[2 * nr], node[2 * nr + 1]);
    }
    T query(int l, int r) {
        l += n; r += n;
        eval(l); eval(r - 1);
        int ls = nodee, rs = nodee;
        while (l < r) {
            if (l & 1) {
                ls = nodef(ls, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rs = nodef(node[r], rs);
            }
            l >>= 1; r >>= 1;
        }
        return nodef(ls, rs);
    }
    T operator[](const int& x) {
        eval(n + x);
        return node[n + x];
    }
    T queryForAll() {
        return node[1];
    }
};
class RAQRSQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return a + b; }
    void lazyf(int& a, const int& b) { a += b; }
    void updf(int& a, const int& b, const unsigned int& width) { a += width * b; }
public:
    RAQRSQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, 0) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRSQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>((int)0, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RAQRMiQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::min(a, b); }
    void lazyf(int& a, const int& b) { a += b; }
    void updf(int& a, const int& b, const unsigned int& width) { a += b; }
public:
    RAQRMiQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRMiQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RAQRMaQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::max(a, b); }
    void lazyf(int& a, const int& b) { a += b; }
    void updf(int& a, const int& b, const unsigned int& width) { a += b; }
public:
    RAQRMaQ(unsigned int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, -inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRMaQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(-inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRSQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return a + b; }
    void lazyf(int& a, const int& b) { a = b; }
    void updf(int& a, const int& b, const unsigned int& width) { a = width * b; }
public:
    RUQRSQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, 0) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRSQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>((int)0, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRMiQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::min(a, b); }
    void lazyf(int& a, const int& b) { a = b; }
    void updf(int& a, const int& b, const unsigned int& width) { a = b; }
public:
    RUQRMiQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRMiQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRMaQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::max(a, b); }
    void lazyf(int& a, const int& b) { a = b; }
    void updf(int& a, const int& b, const unsigned int& width) { a = b; }
public:
    RUQRMaQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, -inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRMaQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(-inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};

#define R_MIN ([](long long a, long long b) { return min(a, b); })
#define R_MAX ([](long long a, long long b) { return max(a, b); })
#define R_SUM ([](long long a, long long b) { return a + b; })

#define NORMAL_UPDATE ([](long long a, long long b) { return b; })
#define ADD_UPDATE ([](long long a, long long b) { return a + b; })
#define MINUS_UPDATE ([](long long a, long long b) { return a - b; }

class Union_Find {
    vector<int> par;
    vector<int> rankmy;
    vector<int> ookisa;
    
public:
    Union_Find(int size) {
        par = vector<int>(size);
        rankmy = vector<int>(size);
        ookisa=vector<int>(size);
        for (int i = 0; i < size; i++) {
            par[i] = i;
            ookisa[i]=1;
        }
    }
    
    int find(int x) {
        if (par[x] == x) {
            return x;
        }
        return par[x] = find(par[x]);
    }
    
    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) {
            return;
        }
        if (rankmy[x] < rankmy[y]) {
            par[x] = y;
            ookisa[y]+=ookisa[x];
            ookisa[x]=0;
        }
        else {
            par[y] = x;
            ookisa[x]+=ookisa[y];
            ookisa[y]=0;
            if (rankmy[x] == rankmy[y]) {
                rankmy[x]++;
            }
        }
    }
    int size(int i){
        i=find(i);
        return ookisa[i];
    }
    bool same(int x, int y){
        return find(x) == find(y);
    }
    
};

class BIT {
    vector<int> data;
    int size=0;
public:
    BIT(int _size){
        data=vector<int>(_size+1);
        size=_size;
    }
    void add(int i,int x){
        while (i<=size) {
            data[i]+=x;
            i += i & -i;
        }
    }
    int sum(int i){
        int s=0;
        while(i>0){
            s+=data[i];
            i -= i & -i;
        }
        return s;
    }
    int lower_bound(int x){
        if(x<=0){
            return 0;
        }else{
            int i=0;int r=1;
            while(r<size) r=r<<1;
            for(int len=r;len>0;len=len>>1) {
                if(i+len<size && data[i+len]<x){
                    x-=data[i+len];
                    i+=len;
                }
            }
            return i+1;
        }
    }
};

//Union-Find-End

int perm[1000005];
void init_perm() {
    perm[0] = 1;
    REP(i, 1000000) {
        perm[i] = perm[i - 1] * i % mod;
    }
}

int nCk(int x, int y) {
    return perm[x] * modpow(perm[x - y], mod - 2) % mod * modpow(perm[y], mod - 2) % mod;
}

double kyori(pair<int, int> f, pair<int, int> s) {
    double ans = 0;
    double t = fabs(f.first - s.first);
    double y = fabs(f.second - s.second);
    ans = sqrt(t * t + y * y);
    return ans;
}

inline string stringmax(string& x,string& y){
    if (x.size()>y.size()) {
        return x;
    }
    if (x.size()<y.size()) {
        return y;
    }
    rep(i,x.size()){
        if (x[i]>y[i]) {
            return x;
        }
        if (x[i]<y[i]) {
            return y;
        }
    }
    return x;
}

#define endl "\n" //interactive の時に注意！！！
#define printd cout<<fixed<<setprecision(10)
#define smallpriority_queue(x) priority_queue<x,vector<x>,greater<x>>



int n,a[200004],ans,l,r;
signed main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cin>>n;
    REP(i,n)cin>>a[i];
    r=n+1;
    ans=inf;
    rep(angraobk,5) {
        int m=(r-l)/3+l;
        int m2=(r-l)/3*2+l;
        int ka=m,ka2=m2;
        {
            vector<int> v,v2;
            REP(i,m){
                v.emplace_back(a[i]);
            }
            for (int i=m+1; i<=n; i++) {
                v2.emplace_back(a[i]);
            }
            if(m)v[m-1]*=-2;
            
            for (int i=m-2; i>=0; i--) {
                v[i]*=-2;
                while (v[i+1]<v[i]) {
                    v[i]*=4;
                    ka+=2;
                }
            }
            for (int i=m+2; i<=n; i++) {
                while (v2[i-2-m]>v2[i-m-1]) {
                    v2[i-m-1]*=4;
                    ka+=2;
                }
            }
        }
        swap(m,m2);
        {
            vector<int> v,v2;
            REP(i,m){
                v.emplace_back(a[i]);
            }
            for (int i=m+1; i<=n; i++) {
                v2.emplace_back(a[i]);
            }
            if(m)v[m-1]*=-2;
            
            for (int i=m-2; i>=0; i--) {
                v[i]*=-2;
                while (v[i+1]<v[i]) {
                    v[i]*=4;
                    ka2+=2;
                }
            }
            for (int i=m+2; i<=n; i++) {
                while (v2[i-2-m]>v2[i-m-1]) {
                    v2[i-m-1]*=4;
                    ka2+=2;
                }
            }
        }
        swap(m,m2);
        chmin(ans, min(ka,ka2));
        if (ka2<ka) {
            l=m;
        }else{
            r=m2;
        }
    }
    cout<<ans<<endl;
}