bool lft(ld x, ld R){
    ll l, r, m;
    l = 1; r = n;
    while(r - l > 1){
        m = (r + l) / 2;
        if(arr[m] >= x){
            r = m;
        }else{
            l = m;
        }
    }

    ld u = x - R;


    if(u > arr[l]){
        return false;
    }
    for(int i = l; i >= 2; i--){
        if(arr[i - 1] < u){
            R = R - 1.0;
            u = arr[i] - R;
            if(arr[i - 1] < u){
                return false;
            }
        }
    }
    return true;
}

bool right(ld x, ld R){
    ll l, r, m;
    l = 1; r = n;
    while(r - l > 1){
        m = (r + l) / 2;
        if(arr[m] >= x){
            r = m;
        }else{
            l = m;
        }
    }


    ld u = x + R;
    if(u < arr[l]){
        return false;
    }
    for(int i = l; i <= n - 1; i++){
        if(arr[i + 1] > u){
            R = R - 1.0;
            u = arr[i] + R;
            if(arr[i + 1] > u){
                return false;
            }
        }
    }
    return true;
}


bool check(ld R){
    ld l = 0, r = arr[n], m;
    m = (l + r) / 2;
    if(!lft(m, R) && !right(m, R)){
        return false;
    }

    for(int i = 1; i <= 50; i++){

        m = (l + r) / 2;
        if(right(m, R)){
            r = m;
        }else{
            l = m;
        }
    }

    if(lft(l, R) && right(r, R)){
        return true;
    }else{
        return false;
    }

}