Little Mishka is a great traveller and she visited many countries. After thinking about where to travel this time, she chose XXX− beautiful, but little-known northern country.

Here are some interesting facts about XXX:

1. XXX consists of n cities, k of whose (just imagine!) are capital cities.
2. All of cities in the country are beautiful, but each is beautiful in its own way. Beauty value of i-th city equals to c_i.
3. All the cities are consecutively connected by the roads, including 1-st and n-th city, forming a cyclic route 1−2−...−n−1. Formally, for every 1≤i<n there is a road between i-th and i+1-th city, and another one between 1-st and n-th city.
4. Each capital city is connected with each other city directly by the roads. Formally, if city x is a capital city, then for every 1≤i≤n,i≠x, there is a road between cities x and i.
5. There is at most one road between any two cities.
6. Price of passing a road directly depends on beauty values of cities it connects. Thus if there is a road between cities i and j, price of passing it equals c_i·c_j.

Mishka started to gather her things for a trip, but didn't still decide which route to follow and thus she asked you to help her determine summary price of passing each of the roads in XXX. Formally, for every pair of cities a and b (a<b), such that there is a road between a and b you are to find sum of products c_a·c_b. Will you help her?