C: Short-circuit evaluation

problem

Naodai-kun and Hokkaido University-kun are playing games. Hokkaido University first generates the following logical formula represented by BNF.


<formula> :: = <or-expr>
<or-expr> :: = <and-expr>
| <or-expr> "|" <and-expr>
<and-expr> :: = <term>
| <and-expr> "&" <term>
<term> :: = "(" <or-expr> ")" | "?"


`&` represents the logical product, `|` represents the logical sum, and `&` is evaluated before `|`.

Naodai reads this formula from the left (as a string), and when he finds a `?`, He does the following:

* If it is certain that the evaluation result of the formula does not change regardless of whether the `?` Is `0` or` 1`, read it without doing anything.
* If not, pay 1 yen to Hokkaido University and replace the `?` With `0` or` 1`.



The logical expression is evaluated as follows. It is a so-called ordinary formula.


(0 &?) == 0
(1 & 0) == 0
(1 & 1) == 1
(0 | 0) == 0
(0 | 1) == 1
(1 |?) == 1


What is the minimum amount Naodai has to pay to finalize the evaluation result of a well-formed formula? Obtain the evaluation result depending on whether it is set to `0` or` 1`.

Input format

A formula that follows the BNF above is given in one line.

Constraint

The length of the formula does not exceed 2 \ times 10 ^ 5.

Output format

Output the minimum amount required to make the evaluation result `0`,` 1`, separated by blanks.

Input example 1


? &? |? &? |? &?

Output example 1


3 2

If you want to make it `0`, rewrite it with` 0 0 0` to make it `0 &? | 0 &? | 0 &?`, If you want to make it `1`, rewrite it with` 1 1` and make it `1 & 1 |? &? |? & It is best to use? `.

Input example 2


? &? &? |? &? &?

Output example 2


twenty three

They are `0 &? &? | 0 &? &?` And `1 & 1 & 1 |? &? &?`, Respectively.

Input example 3


(? |? |?) &? &? &? &? |? &? |? &?

Output example 3


4 4





Example

Input

?&?|?&?|?&?


Output

3 2
#pragma GCC optimize("O2")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdarg>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <deque>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

#define whlie while
#define retunr return
#define reutrn return
#define reutnr return
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define inf 1001001001
#define infLL (1LL << 61)
#define MOD 1000000007
#define FOR(i,a,b) for(int (i)=(int)(a); (i)<(int)(b); (i)++) // [a,b)
#define rep(i,N) FOR((i), 0, (int)(N)) // [0,N)
#define FORR(i,a,b) for(int (i)=(int)(b) - 1; (i)>=(int)(a); (i)--)
#define repr(i,N) FORR((i), 0, (int)(N))
#define each(x,v) for(auto &x : v)
#define all(v) (v).begin(),(v).end()
#define sz(v) ((int)(v).size())
#define vrep(v,it) for(auto it=v.begin();it!=v.end();it++)
#define vrepr(v,it) for(auto it=v.rbegin();it!=v.rend();it++)
#define ini(...) int __VA_ARGS__; in(__VA_ARGS__)
#define inl(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define inc(...) char __VA_ARGS__; in(__VA_ARGS__)
#define ins(...) string __VA_ARGS__; in(__VA_ARGS__)
#define ind(...) double __VA_ARGS__; in(__VA_ARGS__)
#define inpii(...) pii __VA_ARGS__; in(__VA_ARGS__)
#define rand mtrand
#define randinit random_device seed_gen; mt19937 mtrand(seed_gen()+2)

#ifdef LOCAL  
  #define trc(...) do { cout << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0)
  #define stopif(val) assert( !(val) )
  #define trcv(v,...) do { cout << #v << " = "; vector_debug(v , ##__VA_ARGS__);cout << endl;} while(0)
#else
  #define trc(...)
  #define stopif(...)
  #define trcv(...)
#endif

using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vs = vector<string>;
using vpii = vector<pii>;
using vvi = vector< vector<int> >;

struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(15);} } iosetupnya;
/* 
int gcd(int a, int b){if(a>b) swap(a,b); return a==0 ? b : gcd(b%a,a);} ll gcd(ll a, ll b){if(a>b) swap(a,b); return a==0 ? b : gcd(b%a,a);}
ll lcm(int a, int b){return (1LL * a / gcd(a,b)) * b;} ll lcm(ll a, ll b){return (a / gcd(a,b)) * b;}
*/
inline ll pow(int a, int b){ll ans = 1; rep(i,b) ans *= a; return ans;} inline ll pow(ll a, ll b){ll ans = 1; rep(i,b) ans*= a; return ans;}
inline ll pow(int a, ll b){ll ans = 1; rep(i,b) ans *= a; return ans;} inline ll pow(ll a, int b){ll ans = 1; rep(i,b) ans*= a; return ans;}
template<typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template<typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename C> inline void _cin(C &c){cin >> c;}
template<typename T,typename U> inline void _cin(pair<T,U> &p){cin >> p.fi; cin >> p.se;}
template<typename C> inline void _cout(const C &c){cout << c;}
template<typename T,typename U> inline void _cout(const pair<T,U> &p){cout << p.fi << ' ' << p.se;}
void in(){} template <typename T,class... U> void in(T &t,U &...u){ _cin(t); in(u...);}
void out(){cout << "\n";} template <typename T,class... U> void out(const T &t,U ...u){ _cout(t); if(sizeof...(u)) cout << ' '; out(u...);}
template<typename C> inline void in(vector<C> &v,int N=-1){if(sz(v) != 0){int M=(N == -1) ? sz(v) : N; rep(i,M) _cin(v[i]);}else{C c;rep(i,N) v.pb((_cin(c),c));}}
template<typename C> inline void in(C v[],int N){rep(i,N) _cin(v[i]);}
template<typename C> inline void out(const vector<C> &v,int N=-1){int M=(N == -1) ? sz(v) : N; rep(i,M) {cout<<( (i)?" ":"" ); _cout(v[i]);} cout<<"\n";}
template<typename C> inline void out(C v[],int N){rep(i,N) {cout<<( (i)?" ":"" ); _cout(v[i]);} cout<<"\n";}
template<typename C> inline void vector_debug(const vector<C> &v,int N=-1){cout << "{"; int M=(N == -1) ? sz(v) : N; rep(i,M) {cout<<( (i)?", ":"" ); _cout(v[i]);} cout<<"}";}
template<typename C> inline void vector_debug(C v[], int N){cout << "{"; rep(i,N) {cout<<((i)?", ":""); _cout(*(v+i));} cout<<"}";}
void dbg_out(){cout << endl;} template <typename T,class... U> void dbg_out(const T &t,U ...u){ _cout(t); if(sizeof...(u)) cout << ", "; dbg_out(u...);}
template<typename C,class... U> void dbg_out(const vector<C> &v,U ...u){vector_debug(v); if(sizeof...(u)) cout << ", "; dbg_out(u...);}
template<typename C,class... U> void dbg_out(const vector<vector<C>> &v,U ...u){cout << "{ "; rep(i,sz(v)) {if(i)cout<<", "; vector_debug(v[i]);} cout << " }"; if(sizeof...(u)) cout << ", "; dbg_out(u...);}
template<typename C> inline C vmax(const vector<C> &v){C n=v[0]; rep(i,sz(v)) amax(n,v[i]); return n;} template<typename C> inline C vmax(C v[], int N){C n=v[0]; rep( i , N ) amax(n,v[i]); return n;}
template<typename C> inline C vmin(const vector<C> &v){C n=v[0]; rep(i,sz(v)) amin(n,v[i]); return n;} template<typename C> inline C vmin(C v[], int N){C n=v[0]; rep( i , N ) amin(n,v[i]); return n;}
void die(string s){out(s); exit(0);}

////////////
/// main ///
////////////

string S;
using P = pair<int , int>;
// 0のとき　1のとき
int idx = 0;
P eval_and();
P eval_or();
P eval_kakko();
P eval_q();

P eval_or(){
// 最初　あたま　おわり　おわりの次(すなわち文末)
  trc("or",idx);
  P ret = P(0 , inf);
  while(1){
    P cur;
    if(S[idx] == '('){
      cur = eval_and();
    }
    else { // アンドに投げる
      cur = eval_and();
    }
    //trc("or totyu" , cur , ret);
    ret.se = min(ret.se , ( min(ret.fi , ret.se) + cur.se));
    ret.fi = ret.fi + cur.fi;
    //trc("or totyu" , ret , idx);
    if(idx + 1 == sz(S) || S[idx + 1] == ')'){
      trc("or", idx , ret);
      return ret;
    }
    idx += 2; // '|'のぶん
  }
}

P eval_and(){
  // 最初　あたま　終わり　終わりの次( すなわち | )
  trc("and",idx);
  P ret = P(inf , 0);
  while(1){
    P cur;
    if(S[idx] == '('){
      cur = eval_kakko();
    }
    else { // はてなしかない
      assert(S[idx] == '?');
      cur = P(1,1);
    }
    ret.fi = min( ret.fi , min(ret.fi ,ret.se) + cur.fi);
    ret.se = ret.se + cur.se;
    //trc("and totyu",ret , idx);
    if(idx + 1 == sz(S) || S[idx + 1] == '|' || S[idx + 1] == ')'){
      trc("and",idx , ret);
      return ret;
    }
    idx += 2;// '&'のぶん
  }
}

P eval_kakko(){
// 最初　左かっこ　終わり　右かっこの次
// orと同じ処理をして最後にかっこの分だけイテレータを進める
  idx++;
  P ret = eval_or();
  idx++;
  trc("kakko",idx , ret);
  return ret;
}



int main(){
  in(S);
  P ans = eval_or();
  out(ans);


}
