#include <bits/stdc++.h>

using namespace std;

// c++ short types
#define vt vector
typedef long long ll;
typedef long double ld;

void whattime() { cout << "finished in " << clock() * 1.0 / CLOCKS_PER_SEC << " sec" << endl; }
const int inf = 1e9;
const int mod = 998244353;
bool debug = false;

void solve() {
	int n; cin >> n;
	string s; cin >> s;
	vt<vt<int>> g(n);
	vt<int> a(n);
	for(int i = 0; i < n; ++i) {
		a[i] = s[i] == '(' ? +1 : -1;
	}
	for(int i = 1; i < n; ++i) {
		int u, v; cin >> u >> v;
		g[--u].push_back(--v);
		g[v].push_back(u);
	}
	vt<int> count(2 * n, 0);
	vt<int> used(n, false), sizes(n, 0);
	auto solve = [&](int mid) -> long long {
		auto cnt = [&](vt<int> &start, vt<pair<int, int>> &end) -> long long {
			vt<int> ids;
			for(auto &x: end) {
				int sum = x.first, min_value = x.second;
				assert(sum <= 0);
				if(-sum + min_value >= 0) {
					count[sum + n] ++;
				}
			}
			ll res = 0;
			for(auto &x: start) {
				res += count[-x + n];
			}
			for(auto &x: end) {
				int sum = x.first, min_value = x.second;
				assert(sum <= 0);
				count[sum + n] = 0;
			}
			return res;
		};
		auto stuff = [&](int e, int p) -> long long {
			vt<int> start, stack = {0, a[mid]};
			vt<pair<int, int>> end;
			auto dfs1 = [&](auto self, int e, int p, int sum, int min_sum) -> void {
				if(used[e]) {
					return ;
				}
				sum += a[e];
				min_sum = min(min_sum, sum);
				if(sum <= 0) {
					end.push_back({sum, min_sum});
				}
				for(int to: g[e]) if(to ^ p) {
						self(self, to, e, sum, min_sum);
					}
			};
			auto dfs2 = [&](auto self, int e, int p, int value) -> void {
				if(used[e]) {
					return ;
				}
				value += a[e];
				assert(not stack.empty());
				stack.push_back(max(stack.back(), value));
				if(value >= 0 && value - stack.back() >= 0) {
					start.push_back(value);
				}
				for(auto to: g[e]) if(to ^ p){
						self(self, to, e, value);
					}
				stack.pop_back();
			};
			dfs1(dfs1, e, p, 0, 0);
			dfs2(dfs2, e, p, a[mid]);
			return cnt(start, end);
		};
		vt<int> start, stack = {0};
		vt<pair<int, int>> end;
		auto dfs1 = [&](auto self, int e, int p, int sum, int min_sum) -> void {
			if(used[e]) {
				return ;
			}
			sum += a[e];
			min_sum = min(min_sum, sum);
			if(sum <= 0) {
				end.push_back({sum, min_sum});
			}
			for(int to: g[e]) if(to ^ p) {
				self(self, to, e, sum, min_sum);
			}
		};
		auto dfs2 = [&](auto self, int e, int p, int value) -> void {
			if(used[e]) {
				return ;
			}
			value += a[e];
			assert(not stack.empty());
			stack.push_back(max(stack.back(), value));
			if(value >= 0 && value - stack.back() >= 0) {
				start.push_back(value);
			}
			for(auto to: g[e]) if(to ^ p){
				self(self, to, e, value);
			}
			stack.pop_back();
		};
		dfs1(dfs1, mid, mid, -a[mid], 0);
		dfs2(dfs2, mid, mid, 0);
//		cout << "mid=" << mid << "\n";
//		for(auto &x: start) {
//			cout << x << " ";
//		}
//		cout << "\n";
//		for(auto &x: end) {
//			cout << x.first << " " << x.second << "\n";
//		}
//		cout << "\n";
		long long res = cnt(start, end);
		for(int to: g[mid]) if(!used[to]) {
			res -= stuff(to, mid);
		}
//		cout << "\n";
//		cout << "\n";
		return res;
	};
	auto centroid = [&](auto selfc, int start) -> long long {
		auto dfs = [&](auto self, int e, int p) -> int {
			if(used[e]) {
				return 0;
			}
			sizes[e] = 1;
			for(int to: g[e]) if(to ^ p) {
					sizes[e] += self(self, to, e);
				}
			return sizes[e];
		};
		int sz = dfs(dfs, start, start);
		auto fnd = [&](auto self, int e, int p) -> int {
			for(int to: g[e]) if(to != p && !used[to] && 2 * sizes[to] >= sz) {
					return self(self, to, e);
				}
			return e;
		};
		int mid = fnd(fnd, start, start);
		long long res = solve(mid);
		used[mid] = 1;
		for(int to: g[mid]) if(!used[to]) {
			res += selfc(selfc, to);
		}
		return res;
	};
	cout << centroid(centroid, 0) << '\n';
}

int main()
{
	ios::sync_with_stdio(false); cin.tie(nullptr);
	int tt = 1;
	if(debug) {
		tt = 1e3;
	} else {
//		cin >> tt;
	}
	for(int t = 0; t < tt; ++t) {
		solve();
	}
	return 0;
}