{

vector<int> sums(nums.size() + 1);

vector<int> valley; //the valleys of sums

//To traverse sums, nums ans poles

vector<int>::const_iterator n_it;

vector<int>::iterator s_it;

vector<int>::iterator valley_it;

//discrete integration, count non-positive and obtain nums maximum

int num_max = *nums.begin();

sums[0] = 0;

for(n_it = nums.cbegin(), s_it = sums.begin() + 1;

s_it != sums.end();

n_it++, s_it++)

{

if(*n_it > num_max)

num_max = *n_it;

*s_it = *(s_it - 1) + *n_it;

}

#ifdef _DEBUG

cout << "nums_max = " << num_max << endl;

cout << "Sums = ";

for(const auto ele : sums)

cout << ele << " ";

cout << endl;

#endif

//If all elements of nums are non-positive

if(num_max <= 0)

return num_max;

//The difference between a peak and a valley is called a fall

int fall;

int fall_max = 0;

int current_sum;

//Generate valleys

if(*sums.begin() <= *(sums.begin() + 1))

valley.push_back(*(sums.begin()));

for(s_it = sums.begin() + 1; s_it != sums.end() - 1; s_it++)

{

current_sum = *s_it;

//A valley

if(current_sum <= *(s_it + 1) &&

current_sum < *(s_it - 1))

valley.push_back(current_sum);

//A peak

else if(current_sum >= *(s_it + 1) &&

current_sum > *(s_it - 1))

{

for(valley_it = valley.begin(); valley_it != valley.end();

valley_it++)

{

fall = current_sum - *valley_it;

fall_max = fall > fall_max ? fall : fall_max;

}

}

}

#ifdef _DEBUG

cout << "valley:" << endl;

if(valley.empty())

cout<<"<empty>"<<endl;

else

{

for(auto ele : valley)

cout << ele << " ";

cout<< endl;

}

#endif

if(*(sums.end() - 1) > *(sums.end() - 2))

{

current_sum = *(sums.end() - 1);

for(valley_it = valley.begin(); valley_it != valley.end();

valley_it++)

{

fall = current_sum - *valley_it;

fall_max = fall > fall_max ? fall : fall_max;

}

}

return fall_max;