You are given strings s and t, both of length N. s and t consist of `0` and `1`. Additionally, in these strings, the same character never occurs three or more times in a row.

You can modify s by repeatedly performing the following operation:

* Choose an index i (1 \leq i \leq N) freely and invert the i-th character in s (that is, replace `0` with `1`, and `1` with `0`), under the condition that the same character would not occur three or more times in a row in s after the operation.



Your objective is to make s equal to t. Find the minimum number of operations required.

Constraints

* 1 \leq N \leq 5000
* The lengths of s and t are both N.
* s and t consists of `0` and `1`.
* In s and t, the same character never occurs three or more times in a row.

Input

Input is given from Standard Input in the following format:


N
s
t


Output

Find the minimum number of operations required to make s equal to t. It can be proved that the objective is always achievable in a finite number of operations.

Examples

Input

4
0011
0101


Output

4


Input

1
0
0


Output

0


Input

8
00110011
10101010


Output

10
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % mod;
		x = x * x % mod; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}


vector<int> trans(string s) {
	vector<int> res;
	rep(i, s.size()) {
		if (i + 1 < s.size() && s[i] == s[i + 1]) {
			res.push_back(2); i++;
		}
		else res.push_back(1);
	}
	return res;
}

int calc2(string s, string t) {
	vector<int> a = trans(s);
	vector<int> b = trans(t);
	int c2 = 0;
	rep(i, a.size())if (a[i] == 2)c2++;

	int res = mod;
	for (int i = 0; i <= c2; i++) {
		int cx = (s[0] == '1');
		int cy = (t[0] == '1');
		if (i % 2)cx ^= 1;
		if (cx != cy)continue;

		int sum = 0;
		int rest = i;
		int x = 0;
		vector<int> v;
		rep(j, a.size()) {
			if (a[j] == 1) {
				v.push_back(1);
				x++;
			}
			else {
				if (rest > 0) {
					sum += x;
					rest--;
				}
				else {
					v.push_back(2);
				}
			}
		}
		for (int j = 0; j < i; j++) {
			sum += 1 + 2 * j;
		}
		vector<int> w(2 * i, 1);
		for (int ad : v)w.push_back(ad);

		if (w.size() < b.size()) {
			int dif = b.size() - w.size();
			vector<int> nw;

			int x = 0;
			per(i, (int)w.size()) {
				if (w[i] == 1) {
					x++;
					nw.push_back(1);
				}
				else {
					if (dif > 0) {
						dif--;
						sum += x;
					}
					else {
						nw.push_back(2);
					}
				}
			}
			reverse(all(nw));
			dif = b.size() - w.size();
			rep(j, dif) {
				nw.push_back(1);
				nw.push_back(1);
				sum += 1 + 2 * (dif - j - 1);
			}
			swap(nw, w);
		}
		if (w.size() > b.size()) {
			int dif = w.size() - b.size();
			vector<int> nw;
			int x = 0;

			int rest = 2 * dif;
			per(j, (int)w.size()) {
				if (w[j] == 1) {
					if (rest > 0) {
						sum += x; rest--;
					}
					else {
						nw.push_back(1);
					}
				}
				else {
					nw.push_back(2);
					x++;
				}
			}
			reverse(all(nw));
			rep(j, dif) {
				nw.push_back(2);
				sum += 1 + 2 * (dif - 1 - j);
			}
			swap(nw, w);
		}
		vector<int> a1, b1;
		rep(i, w.size())if (w[i] == 2)a1.push_back(i);
		rep(i, b.size())if (b[i] == 2)b1.push_back(i);
		rep(i, a1.size()) {
			sum += abs(a1[i] - b1[i]);
		}
		//cout << s << " " <<t<<" "<< i << " " << sum << "\n";
		res = min(res, sum);
	}
	return res;
}
int calc(string s, string t) {
	vector<int> a = trans(s);
	vector<int> b = trans(t);
	int c1 = 0;
	rep(i, a.size())if (a[i] == 1)c1++;

	int res = mod;
	for (int i = 0; 2 * i <= c1; i++) {
		int cx = (s[0] == '1');
		int cy = (t[0] == '1');
		if (i % 2)cx ^= 1;
		if (cx != cy)continue;

		int sum = 0;
		int tmp = 0;
		vector<int> v;
		rep(j, a.size()) {
			if (a[j] == 1) {
				if (tmp < 2 * i) {
					sum += j - tmp;
					tmp++;
				}
				else {
					v.push_back(1);
				}
			}
			else {
				v.push_back(2);
			}
		}
		for (int j = i-1; j >= 0; j--) {
			sum += 1 + 2 * j;
		}
		
		vector<int>w(i, 2);
		for (int ad : v)w.push_back(ad);

		if (w.size() < b.size()) {
			int dif = b.size() - w.size();
			vector<int> nw;

			int x = 0;
			per(i, (int)w.size()) {
				if (w[i] == 1) {
					x++;
					nw.push_back(1);
				}
				else {
					if (dif > 0) {
						dif--;
						sum += x;
					}
					else {
						nw.push_back(2);
					}
				}
			}
			reverse(all(nw));
			dif = b.size() - w.size();
			rep(j, dif) {
				nw.push_back(1);
				nw.push_back(1);
				sum += 1 + 2 * (dif - j - 1);
			}
			swap(nw, w);
		}
		if (w.size() > b.size()) {
			int dif = w.size() - b.size();
			vector<int> nw;
			int x = 0;

			int rest = 2 * dif;
			per(j, (int)w.size()) {
				if (w[j] == 1) {
					if (rest > 0) {
						sum += x; rest--;
					}
					else {
						nw.push_back(1);
					}
				}
				else {
					nw.push_back(2);
					x++;
				}
			}
			reverse(all(nw));
			rep(j, dif) {
				nw.push_back(2);
				sum += 1 + 2 * (dif - 1 - j);
			}
			swap(nw, w);
		}
		vector<int> a1, b1;
		rep(i, w.size())if (w[i] == 2)a1.push_back(i);
		rep(i, b.size())if (b[i] == 2)b1.push_back(i);
		rep(i, a1.size()) {
			sum += abs(a1[i] - b1[i]);
		}
		//cout << s << " " <<t<<" "<< i << " " << sum << "\n";
		res = min(res, sum);
	}
	return res;

}
void solve() {
	int n; cin >> n;
	string s, t; cin >> s >> t;
	if (n <= 2) {
		int ans = 0;
		rep(i, n)if(s[i] != t[i])ans++;
		cout << ans << "\n"; return;
	}
	if (n <= 2) {
		int ans = 0;
		if (s == t) {
			cout << ans << "\n"; return;
		}
		map<string, bool> used;
		vector<string> cur; cur.push_back(s);
		used[s] = true;

		auto valid = [&](string s)->bool {
			rep1(i, n - 1)if (s[i - 1] == s[i] && s[i] == s[i + 1])return false;
			return true;
		};
		while (true) {
			ans++;
			vector<string> nex;
			for (string a : cur) {
				rep(i, n) {
					string cop = a;
					cop[i] = '0' + '1' - cop[i];
					if (valid(cop) && !used[cop]) {
						nex.push_back(cop);
						used[cop] = true;
					}
				}
			}
			swap(cur, nex);
			for (string a : cur)if (a == t) {
				cout << ans << "\n"; return;
			}
		}
	}

	

	if (trans(s).size() < trans(t).size()) {
		swap(s, t);
	}
	int ans = calc(s, t);
	ans = min(ans, calc2(s, t));
	reverse(all(s)); reverse(all(t));
	ans = min(ans, calc(s, t));
	ans = min(ans, calc2(s, t));

	cout << ans << "\n";
}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
