A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Constraints

* $2 \leq |V| \leq 100$
* $1 \leq |E| \leq 1000$
* $0 \leq c_i \leq 10000$

Input

A flow network is given in the following format.

$|V|\;|E|$
$u_0\;v_0\;c_0$
$u_1\;v_1\;c_1$
:
$u_{|E|-1}\;v_{|E|-1}\;c_{|E|-1}$



$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., $|V|-1$. The source is 0 and the sink is $|V|-1$.

$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Example

Input

4 5
0 1 2
0 2 1
1 2 1
1 3 1
2 3 2


Output

3
import java.io.*;
import java.util.*;

public class Main {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int v = sc.nextInt();
		int e = sc.nextInt();

		FordFulkerson ff = new FordFulkerson(v);

		for (int i = 0; i < e; i++) {
			int uu = sc.nextInt();
			int vv = sc.nextInt();
			int cc = sc.nextInt();

			ff.addEdge(uu, vv, cc);
		}

		pr.println(ff.getMaxflow(0, v - 1));
	}

	private static class FordFulkerson {
		private static final int INF = Integer.MAX_VALUE;
		List<List<Edge>> edges;
		boolean[] used;
		int n;

		FordFulkerson(int n) {
			this.n = n;
			edges = new ArrayList<>(n);
			for (int ii = 0; ii < n; ii++) {
				edges.add(new ArrayList<>());
			}
			used = new boolean[this.n];
		}

		// i, j:0-indexed
		public void addEdge(int i, int j, int c) {
			edges.get(i).add(new Edge(j, c, edges.get(j).size(), false));
			// add reverse edge
			edges.get(j).add(new Edge(i, c, edges.get(i).size() - 1, true));
		}

		public int getMaxflow(int s, int t) {
			// initialize flow
			for (int i = 0; i < n; i++) {
				for (Edge e : edges.get(i)) {
					if (!e.revFlag) {
						e.f = 0;
					} else {
						e.f = e.w;
					}
				}
			}

			int ret = 0;
			while (true) {
				Arrays.fill(used, false);
				int augmentation = dfs(s, t, INF);
				if (augmentation == 0) {
					break;
				}

				ret += augmentation;
			}

			return ret;
		}

		// find max flow (less than f), on u -> v path
		private int dfs(int u, int v, int f) {
			if (u == v) {
				return f;
			}
			used[u] = true;
			for (Edge e : edges.get(u)) {
				if (!used[e.v] && e.w - e.f > 0) {
					int a = dfs(e.v, v, Math.min(f, e.w - e.f));
					if (a != 0) {
						e.f += a;
						edges.get(e.v).get(e.revIndex).f -= a;

						return a;
					}
				}
			}

			return 0;
		}

		private static class Edge {
//			int u; // from
			int v; // to
			int w; // cost
			int f; // flow
			int revIndex; // index of reverse edge
			boolean revFlag; // flag of reverse edge

			Edge(int v, int w, int re, boolean f) {
//				this.u = u;
				this.v = v;
				this.w = w;
				this.f = 0;
				this.revIndex = re;
				this.revFlag = f;
			}
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(INPUT == null ? System.in : new ByteArrayInputStream(INPUT.getBytes()));
		pr = new Printer(System.out);

		solve();

//		pr.close();
		pr.flush();
//		sc.close();
	}

	static String INPUT = null;

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(OutputStream out) {
			super(out);
		}
	}
}

